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diff --git a/math/README b/math/README
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--- /dev/null
+++ b/math/README
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+
+The IRAF math library provides a collection of general purpose numerical
+routines for use in scientific applications programs.  This library is
+continually growing as we collect numerical packages from around the country.
+
+At present the library is just a collection of untested routines from various
+sources.  As time goes on, these routines will be edited to conform to a
+standard which has not yet been developed.  The standard is expected to provide
+for different classes of routines, according to how well the routines have
+been integrated into the system and tested.  The standard for the math library
+will affect programming style, naming conventions, documentation, and the
+subset of Fortran which portable library routines are expected to comply with.
+
+A fundamental part of the standard is that math library routines should not do
+i/o.  Some of the otherwise numerical routines in these directories print
+error messages when an error occurs, using Fortran i/o.  This is bad because
+Fortran i/o is not used elsewhere in the IRAF system, and because it is
+preferable for a numerical routine to return an error code in the event of an
+error.  Before these codes are used in IRAF applications programs, this will
+have to be fixed.
diff --git a/math/Revisions b/math/Revisions
new file mode 100644
index 00000000..44110034
--- /dev/null
+++ b/math/Revisions
@@ -0,0 +1,406 @@
+.help revisions Jun88 math
+.nf
+
+gsurfit/gs_deval.gx
+iminterp/mrider.x
+iminterp/mrieval.x
+	Fixed some procedure calls being closed with a ']' insted of
+	a ')'  (2/17/08, MJF)
+
+gsurfit/gs_chomat.gx
+	The test for singularity would fail with certain kinds of problems
+	because the test used EPSILON (should have been EPSILOND for the
+	double precision) but this is for distinguishing numbers small
+	numbers from 1 and not from each other.  The test is now done
+	with a comparison against the smallest real or double difference.
+	The place where this was found to be a problem was with CCSETWCS.
+	(8/31/04, Valdes)
+
+========
+V2.12.2a
+========
+
+curfit/cvinit.gx
+	If one of the error checks caused an error return the cv pointer
+	would have been allocated (cv != NULL) but some of the pointer
+	fields could have garbage values since a malloc was used instead
+	of a calloc.  A later call to cvfree could result in a segmentation
+	error.  This was changed so that 1) a null cv pointer is returned
+	in the initial error checks cause an error return and 2) the
+	cv pointer is initially allocated with calloc so that no pointer
+	fields will be non-NULL until explicitly set.
+	(11/18/02, Valdes)
+
+=======
+V2.12.1
+=======
+
+gsurfit/gsder.gx
+gsurfit/gsderr.x
+gsurfit/gsderd.x
+gsurfit/gs_fder.gx
+gsurfit/gs_fderr.x
+gsurfit/gs_fderd.x
+gsurfit/gs_deval.gx
+gsurfit/gs_devalr.x
+gsurfit/gs_devald.x
+	Rewrote the routines which compute the derivatives of the polynomial
+	surfaces. There were some renormalization problems in this code
+	for non-linear chebyshev and legendre polynomial surfaces.  The new
+	code uses recursion relations for computation the derivatives which
+	could cause small errors if they are used to do flux conservation.
+	(27/10/99 LED)
+
+curfit/mkpkg
+deboor/mkpkg
+iminterp/mkpkg
+	Added some missing file dependencies to the above mkpkg files.
+	(20/9/99 LED)
+
+slalib
+	Upgraded slalib from Version 1.6.3 to Version 2.3.0. Seventeen
+	new routines were added including 4 dealing with FK5 to ICRS
+	coordinate conversions (17/6/99 LED).
+
+arbpix.x
+arider.x
+arieval.x
+asider.x
+asieval.x
+asifit.x
+asifree.x
+asigeti.x
+asigetr.x
+asigrl.x
+asiinit.x
+asirestore.x
+asisave.x
+asisinit.x
+asitype.x
+asivector.x
+ii_1dinteg.x
+ii_bieval.x
+ii_cubspl.f
+ii_eval.x
+ii_greval.x
+ii_pc1deval.x
+ii_pc2deval.x
+ii_polterp.x
+ii_sinctable.x
+ii_spline.x
+ii_spline2d.x
+im1interpdef.h
+im2interpdef.h
+mkpkg
+mrider.x
+mrieval.x
+msider.x
+msieval.x
+msifit.x
+msifree.x
+msigeti.x
+msigetr.x
+msigrid.x
+msigrl.x
+msiinit.x
+msirestore.x
+msisave.x
+msisinit.x
+msisqgrl.x
+msitype.x
+msivector.x
+	The 1D interpolation routines were replaced with new versions which
+	support look-up table since and drizzle interpolation. Minor
+	modifications were also made to the existing 1D sinc routines. The 2D
+	image interpolation routines were replaced with new versions modified
+	which support sinc, look-up table sinc and drizzle interpolation.
+	(12/28/98 Davis)
+
+iminterp.hd
+iminterp.men
+iminterp.spc
+arbpix.hlp
+arider.hlp
+arieval.hlp
+asider.hlp
+asieval.hlp
+asifit.hlp
+asifree.hlp
+asigeti.hlp
+asigetr.hlp
+asigrl.hlp
+asiinit.hlp
+asirestore.hlp
+asisave.hlp
+asisinit.hlp
+asitype.hlp
+asivector.hlp
+iminterp.hlp
+mrider.hlp
+mrieval.hlp
+msider.hlp
+msieval.hlp
+msifit.hlp
+msifree.hlp
+msigeti.hlp
+msigetr.hlp
+msigrid.hlp
+msigrl.hlp
+msiinit.hlp
+msirestore.hlp
+msisave.hlp
+msisinit.hlp
+msisqgrl.hlp
+msitype.hlp
+msivector.hlp
+	The 1D and 2D image interpolation routines help pages were updated
+	to reflect the changes in both packages. (12/28/98 Davis)
+
+math$nlfit/nlchomat.gx
+math$nlfit/nlchomatr.x
+math$nlfit/nlchomatd.x
+	Modified the singular matrix test to make a comparison against
+	EPSILON instead of 0.0 to avoid floating point problems.
+
+	(8/1/98 Davis)
+
+math$gsurfit/
+	Installed a completely new version of gsurfit which support "half"
+	or "diagonal" cross terms. All the .gx and .x files were replaced.
+
+	(4/30/97 Davis)
+
+math$gsurfit/gsrestore.gx
+math$gsurfit/gsrestorer.x
+math$gsurfit/gsrestored.x
+	Changed the type declaration of the xmin, xmax, ymin, ymax variables
+	from real to PIXEL to avoid machine precision problems.
+
+	(3/21/96 Davis)
+
+math$nlfit/nlfit.gx
+math$nlfit/nlfitr.x
+math$nlfit/nlfitd.x
+	Fixed a divide by zero error in the nlscatter routine which occurs
+	if the fit has no degrees of freedom and the weighting type is
+	WTS_SCATTER.
+
+	(6/13/94 Davis)
+
+math/gsurfit/gssub.gx
+math/gsurfit/gssubd.x
+	The gsurfit double precision routine gssubd was incorrectly calling
+	the real precision routine gsgeti instead of the double precision
+	routine dgsgeti due to an error in the gssub.gx file. This bug
+	results in the wrong value of the parameter GSNSAVE being returned to
+	the calling routine gssubd in the double precision case.
+
+	(1/17/94 Davis)
+
+math/iminterp/arbpix.x
+math/interp/arbpix.x
+        Changed all if (x == INDEF) constructs to IS_INDEF(x) constructs.
+
+	(1/15/93 Davis)
+
+math/surfit/iseval.x
+	Two indices were not being initialized before being used in a pointer
+	offset computation in the spline1 and spline3 single input point code
+	producing incorrect results.
+
+	(12/17/92 Davis)
+
+math/nlfit/nlfit.gx
+math/nlfit/nlfitr.x
+math/nlfit/nlfitd.x
+math/nlfit/nliter.gx
+math/nlfit/nliterr.x
+math/nlfit/nliterd.x
+	Added a test for lambda<=0.0 in the nlfit loop and in the iteration
+	loop. Precision problems could cause the code to go into an infinite
+	loop in some circumstances. The code returns a NOT_DONE status
+	message if the convergence criteria have not been met in this
+	circumstance. Made some other minor changes to the convergence
+	criteria.
+
+	(7/20/92 Davis)
+
+math/nlfit/nlacpts.gx
+math/nlfit/nlerrors.gx
+	Fixed a bug in the routine nlacpts where the variable sum was
+	not being initialized properly for each iteration. This could
+	cause a slow drift in repeated fits. Also fixed a related problem
+	in the error computation. Note this was not a problem
+	with the version of nlfit in apphot in versions 2.9 or in 
+	testphot.
+
+	(1/9/92 Davis)
+
+math/nlfit/nlfit.gx
+math/nlfit/nlfitr.x
+math/nlfit/nlfitd.x
+	Added some code to force the nlfit package to do at least MINITER
+	iterations whether or not the solution actually converged; MINITER
+	+ 1 if the weighting type is WTS_SCATTER.
+	(1/3/91 Davis)
+
+math/nlfit/nliter.gx
+math/nlfit/nliterr.x
+math/nlfit/nliterd.x
+	Simplied the test for determining whether the lambda factor needs
+	to be increased or decreased.
+	(1/3/91 Davis)
+
+math/nlfit/nlzero.gx
+math/nlfit/nlfitdefr.h
+math/nlfit/nlfitdefd.h
+	Removed an extra argument from two aclr$t routines. Also these routines
+	were being called with the pointer instead of the array as the 
+	argument. (10/3/91 Davis)
+
+lib/math/iminterp.h
+math/iminterp/arbpix.x
+math/iminterp/arider.x
+math/iminterp/arieval.x
+math/iminterp/asider.x
+math/iminterp/asieval.x
+math/iminterp/asifit.x
+math/iminterp/asiffree.x
+math/iminterp/asigrl.x
+math/iminterp/asiinit.x
+math/iminterp/asirestore.x
+math/iminterp/asisave.x
+math/iminterp/asivector.x
+math/iminterp/ii_1dinteg.x
+math/iminterp/ii_eval.x
+math/iminterp/ii_pc1deval.x
+math/iminterp/im1interpdef.h
+math/iminterp/doc/arbpix.hlp
+math/iminterp/doc/arider.hlp
+math/iminterp/doc/arieval.hlp
+math/iminterp/doc/asider.hlp
+math/iminterp/doc/asieval.hlp
+math/iminterp/doc/asifit.hlp
+math/iminterp/doc/asigrl.hlp
+math/iminterp/doc/asiinit.hlp
+math/iminterp/doc/asivector.hlp
+	The 1D image interpolation routines were replaced with new versions
+	modified by Frank Valdes to support sinc interpolation. (7/26/91 Davis)
+
+lib/math/curfit.h
+lib/math/gsurfit.h
+lib/math/iminterp.h
+lib/math/interp.h
+lib/math/surfit.h
+	Added dictionary string definitions for the interpolator types and
+	weights.  Use of these strings insures that strdic/clgwrd will
+	return the correct type code.  Currently one has to assume the code
+	definitions will not change or put a lookup table with a data
+	statement containing the macro definitions.  The code would also
+	have to be modified to add new types.  The dates were restored to
+	their original values to avoid recompilation.  (5/9, Valdes)
+
+math$curfit/cverrors.gx: Davis, May 6, 1991
+math$curfit/cvpower.gx
+math$curfit/cvrefit.gx
+math$curfit/cvrestore.gx
+    Finished cleanup of curfit package .gx files.
+
+math$gsurfit/gs_f1deval.gx: Davis, May 6, 1991
+    Changed the line "call amulk$t (,,,2.,,,)" to "call amulk$t (,,,2$f,,,)
+    to remove a type dependence problem found by ftoc on the Mac.
+
+math$curfit/cvpower.gx: Davis, May 6, 1991
+    Changed the constant from INDEFR to INDEF in the amov$t call in cvpower.gx.
+    This was causing a problem for the Mac compiler.
+
+math$curfit/cv_b1eval.gx: Davis, April 23, 1991
+math$curfit/cv_beval.gx
+math$curfit/cv_feval.gx
+math$curfit/cvaccum.gx
+math$curfit/cvacpts.gx
+math$curfit/cvchomat.gx
+math$curfit/cvfree.gx
+math$curfit/cvinit.gx
+    Did some cleaning up in the following .gx files to make the code easier
+    to read.
+
+math$nlfit/: Davis, Jan 31, 1991
+    Added the nlfit package to the math package. 
+
+math$surfit/isreplace.x: Davis, September 18, 1990
+    1. Changed the int calls in isreplace.x to nint calls. This is a totally
+    safe way to do the conversion from floating point to integer
+    quantities in the surfit package and removes any potential precision
+    problems for task which must read the surfit structure back from a
+    text database file.
+
+math$gsurfit/gsrestore.gx,gsrestorer.x,gsrestored.x: Davis, September 18, 1990
+    1. Changed the int calls in gsrestore.gx to nint calls. This is a totally
+    safe way to do the conversion from floating point to integer
+    quantities in the gsurfit package and removes any potential precision
+    problems for task which must read the gsurfit structure back from a
+    text database file.
+
+math$curfit/cvrestore.gx,cvrestorer.x,cvrestored.x: Davis, September 18, 1990
+    1. Changed the int calls in cvrestore.gx to nint calls. This is a totally
+    safe way to do the conversion from floating point to integer
+    quantities in the curfit package and removes any potential precision
+    problems for task which must read the curfit structure back from a
+    text database file.
+
+math$gsurfit/gsder.gx,gsderd.x: Davis, August 1, 1990
+    1. Fixed a typo in the routine which computes the double precision
+    derivatives of a surface. Due to this type the salloc routine was being
+    passed a pointer instead of size. When the value of this pointer
+    got very large this could cause an out of memory allocation error.
+
+math$iminterp/msigrl.x: Davis, Feb 8, 1989
+    1. There was a bug in the shift and wrap routines in the 2D routine
+    which integrates in polygonal apertures. If the vertices of the
+    polygon  were listed in certain orders the routine would produce
+    wrong results. The routine has been totally rewritten to use
+    the polygon clipping code in polyphot.
+
+math$interp/asigrl.x: Davis, Jan 27, 1988
+    1. The routine ii_getpcoeff was duplicated in the files asigrl.x and
+    ii_1dinteg.x. I removed the copy in asigrl.x and rebuilt the library.
+
+math$interp/arider.x: Davis, February 10, 1988
+    1. The routines iidr_poly3, iidr_poly5 and iidr_spine3 were declared
+    as functions but called everywhere as subroutines. I removed the
+    function declarations.
+
+math$gsurfit/gsder.gx: Davis, October 16, 1987
+    1. changed a real type conversion call to double in the gsder routine.
+    This error was causing the derivative evaluations to fail on the sun.
+
+math$gsurfit/gsder.gx: Davis, August 11, 1987
+    1. A call in gsder to gscoeff was not being set to double precision.
+
+math$gsurfit: Davis, January 22, 1986
+    1. A new version of the gsurfit package was installed. A double precision
+    gsurfit has  been added. The double precision calls are the same as
+    the single precision calls but prefixed by a d. Some of the evaluation
+    routines were vectorized and run significantly faster than the old version.
+    A power series polynomial function was added to the package for convenience
+    in evaluating the simple rotation transformation functions.
+
+math$iminterp/arider.x: Davis, September 7, 1986
+    1. The routines ii_pcpoly3, ii_pcpoly5 and ii_pcspline3 were declared
+    as functions but called everywhere as subroutines. Removed the function
+    declaration. I also moved these routines into a file of their own
+    ii_pc1deval.x and changed the prefix to ia_ from ii_ to avoid conflict
+    with the 2D equivalents.
+
+math$interp/arider.x: Davis, September 7, 1986
+    1. The routines ii_pcpoly3, ii_pcpoly5 and ii_pcspline3 were declared
+    as functions but called everywhere as subroutines. Removed the function
+    declaration.
+
+From Davis Jan 8, 1986
+
+1. Added documentation for surfit package.
+
+----------------------------------------------------------------------------
+.endhelp
diff --git a/math/_math.hd b/math/_math.hd
new file mode 100644
index 00000000..1d4c8877
--- /dev/null
+++ b/math/_math.hd
@@ -0,0 +1,5 @@
+# Root help directory for the MATH branch of the help database.
+
+math		sys = math$README, 
+		hlp = math$math.men,
+		pkg = math$math.hd
diff --git a/math/bevington/README b/math/bevington/README
new file mode 100644
index 00000000..d0b3f778
--- /dev/null
+++ b/math/bevington/README
@@ -0,0 +1,13 @@
+This directory cotnains the original Fortran source for the Bevington
+routines, as copied from his book.
+
+Jun85	Removed the nonstandard & in col 1 UNIX style continuation and
+	replaced it with standard Fortran (col 6) continuation.
+
+Oct85   Added an extran continuation statement to chifit.f to avoid ambiguous
+	transfer of control to statement 70
+
+Nov85   It was possible to get a floating point divide by zero in regres.f
+	when rmul=1 in the calculation in statement 135 of ftest.  The value
+	of rmul (the correlation) is now tested before the division and a 
+	value of ftest = -99999.  is returned when rmul=1.
diff --git a/math/bevington/agauss.f b/math/bevington/agauss.f
new file mode 100644
index 00000000..6aefc503
--- /dev/null
+++ b/math/bevington/agauss.f
@@ -0,0 +1,40 @@
+c function agauss.f
+c
+c source
+c   Bevington, page 48.
+c
+c purpose
+c   evaluate integral of gaussian probability function
+c
+c usage
+c   result = agauss (x, averag, sigma)
+c
+c description of parameters
+c   x      - limit for integral
+c   averag - mean of distribution
+c   sigma  - standard deviation of distribution
+c   integration range is averag +/- z*sigma
+c      where z = abs(x-averag)/sigma
+c
+c subroutines and function subprograms required
+c   none
+c
+	function agauss (x,averag,sigma)
+	double precision z,y2,term,sum,denom
+11	z=abs(x-averag)/sigma
+	agauss=0.
+	if (z) 42,42,21
+21	term=0.7071067812*z
+22	sum=term
+	y2=(z**2)/2.
+	denom=1.
+c
+c accumulate sums of terms
+c
+31	denom=denom+2.
+32	term=term*(y2*2./denom)
+33	sum=sum+term
+	if (term/sum-1.e-10) 41,41,31
+41	agauss=1.128379167*sum*dexp(-y2)
+42	return
+	end
diff --git a/math/bevington/area.f b/math/bevington/area.f
new file mode 100644
index 00000000..ae89d35a
--- /dev/null
+++ b/math/bevington/area.f
@@ -0,0 +1,79 @@
+c function area.f
+c
+c source
+c   Bevington, pages 272-273.
+c
+c purpose
+c   integrate the area beneath a set of data points
+c
+c usage
+c   result = area (x, y, npts, nterms)
+c
+c description of parameters
+c   x	   - array of data points for independent variable
+c   y	   - array of data points for dependent variable
+c   npts   - number of pairs of data points
+c   nterms - number of terms in fitting polynomial
+c
+c subroutines and function subprograms required
+c   integ (x, y, nterms, i1, x1, x2 sum)
+c      fits a polynomial with nterms starting at i1
+c      and integrates area from x1 to x2
+c
+	function area (x,y,npts,nterms)
+	double precision sum
+	dimension x(1),y(1)
+11	sum=0.
+	if (npts-nterms) 21,21,13
+13	neven=2*(nterms/2)
+	idelta=nterms/2-1
+	if (nterms-neven) 31,31,51
+c
+c fit all points with one curve
+c
+21	x1=x(1)
+	x2=x(npts)
+23	call integ (x,y,npts,1,x1,x2,sum)
+	goto 71
+c
+c even number of terms
+c
+31	x1=x(1)
+	j=nterms-idelta
+	x2=x(j)
+	call integ (x,y,nterms,1,x1,x2,sum)
+	i1=npts-nterms+1
+	j=i1+idelta
+	x1=x(j)
+	x2=x(npts)
+39	call integ (x,y,nterms,i1,x1,x2,sum)
+	if (i1-2) 71,71,41
+41	imax=i1-1
+	do 46 i=2,imax
+	j=i+idelta
+	x1=x(j)
+	x2=x(j+1)
+46	call integ (x,y,nterms,i,x1,x2,sum)
+	goto 71
+c
+c odd number of terms
+c
+51	x1=x(1)
+	j=nterms-idelta
+	x2=(x(j)+x(j-1))/2.
+	call integ (x,y,nterms,1,x1,x2,sum)
+	i1=npts-nterms+1
+	j=i1+idelta
+	x1=(x(j)+x(j+1))/2.
+	x2=x(npts)
+59	call integ (x,y,nterms,i1,x1,x2,sum)
+	if (i1-2) 71,71,61
+61	imax=i1-1
+	do 66 i=2,imax
+	j=i+idelta
+	x1=(x(j+1)+x(j))/2.
+	x2=(x(j+2)+x(j+1))/2.
+66	call integ (x,y,nterms,i,x1,x2,sum)
+71	area=sum
+	return
+	end
diff --git a/math/bevington/chifit.f b/math/bevington/chifit.f
new file mode 100644
index 00000000..ff4b0669
--- /dev/null
+++ b/math/bevington/chifit.f
@@ -0,0 +1,169 @@
+C SUBROUTINE CHIFIT.F 
+C
+C SOURCE
+C   BEVINGTON, PAGES 228-231.
+C
+C PURPOSE
+C   MAKE A LEAST-SQUARES FIT TO A NON-LINEAR FUNCTION
+C      WITH A PARABOLIC EXPANSION OF CHI SQUARE 
+C
+C USAGE 
+C   CALL CHIFIT (X, Y, SIGMAY, NPTS, NTERMS, MODE, A, DELTAA,
+C      SIGMAA, YFIT, CHISQR)
+C
+C DESCRIPTION OF PARAMETERS
+C   X      - ARRAY OF DATA POINTS FOR INDEPENDENT VARIABLE
+C   Y      - ARRAY OF DATA POINTS FOR DEPENDENT VARIABLE
+C   SIGMAY - ARRAY OF STANDARD DEVIATIONS FOR Y DATA POINTS
+C   NPTS   - NUMBER OF PAIRS OF DATA POINTS
+C   NTERMS - NUMBER OF PARAMETERS
+C   MODE   - DETERMINES METHOD OF WEIGHTING LEAST-SQUARES FIT
+C            +1 (INSTRUMENTAL) WEIGHT(I) = 1./SIGMAY(I)**2
+C             0 (NO WEIGHTING) WEIGHT(I) = 1.
+C            -1 (STATISTICAL)  WEIGHT(I) = 1./Y(I)
+C   A      - ARRAY OF PARAMETERS
+C   DELTAA - ARRAY OF INCREMENTS FOR PARAMETERS A
+C   SIGMAA - ARRAY OF STANDARD DEVIATIONS FOR PARAMETERS A
+C   YFIT   - ARRAY OF CALCULATED VALUES OF Y
+C   CHISQR - REDUCED CHI SQUARE FOR FIT 
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED 
+C   FUNCTN (X, I, A)
+C      EVALUATES THE FITTING FUNCTION FOR THE ITH TERM
+C   FCHISQ (Y, SIGMAY, NPTS, NFREE, MODE, YFIT) 
+C      EVALUATES REDUCED CHI SQUARED FOR FIT TO DATA
+C   MATINV (ARRAY, NTERMS, DET) 
+C      INVERTS A SYMMETRIC TWO-DIMENSIONAL MATRIX OF DEGREE NTERMS
+C      AND CALCULATES ITS DETERMINANT
+C
+C COMMENTS
+C   DIMENSION STATEMENT VALID FOR NTERMS UP TO 10
+C
+      SUBROUTINE CHIFIT (X,Y,SIGMAY,NPTS,NTERMS,MODE,A,DELTAA,
+     *SIGMAA,YFIT,CHISQR)
+      DOUBLE PRECISION ALPHA
+      DIMENSION X(1),Y(1),SIGMAY(1),A(1),DELTAA(1),SIGMAA(1), 
+     *YFIT(1)
+      DIMENSION ALPHA(10,10),BETA(10),DA(10)
+      REAL FUNCTN
+      EXTERNAL FUNCTN
+C 
+11    NFREE=NPTS-NTERMS
+      FREE=NFREE
+      IF (NFREE) 14,14,16
+14    CHISQR=0.
+      GOTO 120
+16    DO 17 I=1,NPTS
+17    YFIT(I)=FUNCTN (X,I,A)
+      CHISQ1=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+C 
+C EVALUATE ALPHA AND BETA MATRICES
+C 
+20    DO 60 J=1,NTERMS
+C 
+C A(J) + DELTAA(J)
+C 
+21    AJ=A(J) 
+      A(J)=AJ+DELTAA(J)
+      DO 24 I=1,NPTS
+24    YFIT(I)=FUNCTN (X,I,A)
+      CHISQ2=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+      ALPHA(J,J)=CHISQ2-2.*CHISQ1
+      BETA(J)=-CHISQ2 
+31    DO 50 K=1,NTERMS
+      IF (K-J) 33,50,36
+33    ALPHA(K,J)=(ALPHA(K,J)-CHISQ2)/2.
+      ALPHA(J,K)=ALPHA(K,J)
+      GOTO 50 
+36    ALPHA(J,K)=CHISQ1-CHISQ2
+C 
+C A(J) + DELTAA(J) AND A(K) + DELTAA(K) 
+C 
+41    AK=A(K) 
+      A(K)=AK+DELTAA(K)
+      DO 44 I=1,NPTS
+44    YFIT(I)=FUNCTN (X,I,A)
+      CHISQ3=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+      ALPHA(J,K)=ALPHA(J,K)+CHISQ3
+      A(K)=AK 
+50    CONTINUE
+C 
+C A(J) - DELTAA(J)
+C 
+51    A(J)=AJ-DELTAA(J)
+      DO 53 I=1,NPTS
+53    YFIT(I)=FUNCTN (X,I,A)
+      CHISQ3=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+      A(J)=AJ 
+      ALPHA(J,J)=(ALPHA(J,J)+CHISQ3)/2.
+      BETA(J)=(BETA(J)+CHISQ3)/4.
+60    CONTINUE
+C 
+C ELIMINATE NEGATIVE CURVATURE
+C 
+61    DO 70 J=1,NTERMS
+      IF (ALPHA(J,J)) 63,65,70
+63    ALPHA(J,J)=-ALPHA(J,J)
+      GOTO 66 
+65    ALPHA(J,J)=0.01 
+C Changed from DO 70
+66    DO 700 K=1,NTERMS		
+C Changed from 68, 70, 68
+      IF (K-J) 68,700,68
+68    ALPHA(J,K)=0.
+      ALPHA(K,J)=0.
+C New continuation statement
+700   CONTINUE
+70    CONTINUE
+C 
+C INVERT MATRIX AND EVALUATE PARAMETER INCREMENTS
+C 
+71    CALL MATINV (ALPHA,NTERMS,DET)
+      DO 76 J=1,NTERMS
+      DA(J)=0.
+74    DO 75 K=1,NTERMS
+75    DA(J)=DA(J)+BETA(K)*ALPHA(J,K)
+76    DA(J)=0.2*DA(J)*DELTAA(J)
+C 
+C MAKE SURE CHI SQUARE DECREASES
+C 
+81    DO 82 J=1,NTERMS
+82    A(J)=A(J)+DA(J) 
+83    DO 84 I=1,NPTS
+84    YFIT(I)=FUNCTN (X,I,A)
+      CHISQ2=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+      IF (CHISQ1-CHISQ2) 87,91,91
+87    DO 89 J=1,NTERMS
+      DA(J)=DA(J)/2.
+89    A(J)=A(J)-DA(J) 
+      GOTO 83 
+C 
+C INCREMENT PARAMETERS UNTIL CHI SQUARE STARTS TO INCREASE
+C 
+91    DO 92 J=1,NTERMS
+92    A(J)=A(J)+DA(J) 
+      DO 94 I=1,NPTS
+94    YFIT(I)=FUNCTN (X,I,A)
+      CHISQ3=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+      IF (CHISQ3-CHISQ2) 97,101,101
+97    CHISQ1=CHISQ2
+      CHISQ2=CHISQ3
+99    GOTO 91 
+C 
+C FIND MINIMUM OF PARABOLA DEFINED BY LAST THREE POINTS 
+C 
+101   DELTA=1./(1.+(CHISQ1-CHISQ2)/(CHISQ3-CHISQ2))+0.5
+      DO 104 J=1,NTERMS
+      A(J)=A(J)-DELTA*DA(J)
+104   SIGMAA(J)=DELTAA(J)*SQRT(FREE*ALPHA(J,J))
+      DO 106 I=1,NPTS 
+106   YFIT(I)=FUNCTN (X,I,A)
+      CHISQR=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+111   IF (CHISQ2-CHISQR) 112,120,120
+112   DO 113 J=1,NTERMS
+113   A(J)=A(J)+(DELTA-1.)*DA(J)
+      DO 115 I=1,NPTS 
+115   YFIT(I)=FUNCTN (X,I,A)
+      CHISQR=CHISQ2
+120   RETURN
+      END
diff --git a/math/bevington/curfit.f b/math/bevington/curfit.f
new file mode 100644
index 00000000..523a4c17
--- /dev/null
+++ b/math/bevington/curfit.f
@@ -0,0 +1,128 @@
+C SUBROUTINE CURFIT.F 
+C
+C SOURCE
+C   BEVINGTON, PAGES 237-239.
+C
+C PURPOSE
+C   MAKE A LEAST-SQUARES FIT TO A NON-LINEAR FUNCTION
+C      WITH A LINEARIZATION OF THE FITTING FUNCTION
+C
+C USAGE 
+C   CALL CURFIT (X, Y, SIGMAY, NPTS, NTERMS, MODE, A, DELTAA,
+C      SIGMAA, FLAMDA, YFIT, CHISQR)
+C
+C DESCRIPTION OF PARAMETERS
+C   X	   - ARRAY OF DATA POINTS FOR INDEPENDENT VARIABLE
+C   Y	   - ARRAY OF DATA POINTS FOR DEPENDENT VARIABLE
+C   SIGMAY - ARRAY OF STANDARD DEVIATIONS FOR Y DATA POINTS
+C   NPTS   - NUMBER OF PAIRS OF DATA POINTS
+C   NTERMS - NUMBER OF PARAMETERS
+C   MODE   - DETERMINES METHOD OF WEIGHTING LEAST-SQUARES FIT
+C	     +1 (INSTRUMENTAL) WEIGHT(I) = 1./SIGMAY(I)**2
+C	      0 (NO WEIGHTING) WEIGHT(I) = 1.
+C	     -1 (STATISTICAL)  WEIGHT(I) = 1./Y(I)
+C   A	   - ARRAY OF PARAMETERS
+C   DELTAA - ARRAY OF INCREMENTS FOR PARAMETERS A
+C   SIGMAA - ARRAY OF STANDARD DEVIATIONS FOR PARAMETERS A
+C   FLAMDA - PROPORTION OF GRADIENT SEARCH INCLUDED
+C   YFIT   - ARRAY OF CALCULATED VALUES OF Y
+C   CHISQR - REDUCED CHI SQUARE FOR FIT 
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED 
+C   FUNCTN (X, I, A)
+C      EVALUATES THE FITTING FUNCTION FOR THE ITH TERM
+C   FCHISQ (Y, SIGMAY, NPTS, NFREE, MODE, YFIT) 
+C      EVALUATES REDUCED CHI SQUARED FOR FIT TO DATA
+C   FDERIV (X, I, A, DELTAA, NTERMS, DERIV)
+C      EVALUATES THE DERIVATIVES OF THE FITTING FUNCTION
+C      FOR THE ITH TERM WITH RESPECT TO EACH PARAMETER
+C   MATINV (ARRAY, NTERMS, DET) 
+C      INVERTS A SYMMETRIC TWO-DIMENSIONAL MATRIX OF DEGREE NTERMS
+C      AND CALCULATES ITS DETERMINANT
+C
+C COMMENTS
+C   DIMENSION STATEMENT VALID FOR NTERMS UP TO 10
+C   SET FLAMDA = 0.001 AT BEGINNING OF SEARCH
+C
+      SUBROUTINE CURFIT (X,Y,SIGMAY,NPTS,NTERMS,MODE,A,DELTAA,
+     *SIGMAA,FLAMDA,YFIT,CHISQR)
+      DOUBLE PRECISION ARRAY
+      DIMENSION X(1),Y(1),SIGMAY(1),A(1),DELTAA(1),SIGMAA(1), 
+     *YFIT(1)
+      DIMENSION WEIGHT(100),ALPHA(10,10),BETA(10),DERIV(10),
+     *ARRAY(10,10),B(10)
+      REAL FUNCTN
+      EXTERNAL FUNCTN
+
+C
+11     NFREE=NPTS-NTERMS
+       IF (NFREE) 13,13,20
+13     CHISQR=0.
+       GOTO 110
+C
+C EVALUATE WEIGHTS
+C
+20     DO 30 I=1,NPTS
+21     IF (MODE) 22,27,29
+22     IF (Y(I)) 25,27,23
+23     WEIGHT(I)=1./Y(I)
+       GOTO 30 
+25     WEIGHT(I)=1./(-Y(I))
+       GOTO 30 
+27     WEIGHT(I)=1.
+       GOTO 30 
+29     WEIGHT(I)=1./SIGMAY(I)**2
+30     CONTINUE
+C
+C EVALUATE ALPHA AND BETA MATRICES
+C
+31     DO 34 J=1,NTERMS
+       BETA(J)=0.
+       DO 34 K=1,J
+34     ALPHA(J,K)=0.
+41     DO 50 I=1,NPTS
+       CALL FDERIV (X,I,A,DELTAA,NTERMS,DERIV) 
+       DO 46 J=1,NTERMS
+       BETA(J)=BETA(J)+WEIGHT(I)*(Y(I)-FUNCTN(X,I,A))*DERIV(J) 
+       DO 46 K=1,J
+46     ALPHA(J,K)=ALPHA(J,K)+WEIGHT(I)*DERIV(J)*DERIV(K)
+50     CONTINUE
+51     DO 53 J=1,NTERMS
+       DO 53 K=1,J
+53     ALPHA(K,J)=ALPHA(J,K)
+C
+C EVALUATE CHI SQUARE AT STARTING POINT 
+C
+61     DO 62 I=1,NPTS
+62     YFIT(I)=FUNCTN (X,I,A)
+63     CHISQ1=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+C
+C INVERT MODIFIED CURVATURE MATRIX TO FIND NEW PARAMETERS
+C
+71     DO 74 J=1,NTERMS
+       DO 73 K=1,NTERMS
+73     ARRAY(J,K)=ALPHA(J,K)/SQRT(ALPHA(J,J)*ALPHA(K,K))
+74     ARRAY(J,J)=1.+FLAMDA
+80     CALL MATINV (ARRAY,NTERMS,DET)
+81     DO 84 J=1,NTERMS
+       B(J)=A(J)
+       DO 84 K=1,NTERMS
+84     B(J)=B(J)+BETA(K)*ARRAY(J,K)/SQRT(ALPHA(J,J)*ALPHA(K,K))
+C
+C IF CHI SQUARE INCREASED, INCREASE FLAMDA AND TRY AGAIN
+C
+91     DO 92 I=1,NPTS
+92     YFIT(I)=FUNCTN (X,I,B)
+93     CHISQR=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+       IF (CHISQ1-CHISQR) 95,101,101
+95     FLAMDA=10.*FLAMDA
+       GOTO 71 
+C
+C EVALUATE PARAMETERS AND UNCERTAINTIES 
+C
+101    DO 103 J=1,NTERMS
+       A(J)=B(J)
+103    SIGMAA(J)=SQRT(ARRAY(J,J)/ALPHA(J,J))
+       FLAMDA=FLAMDA/10.
+110    RETURN
+       END
diff --git a/math/bevington/determ.f b/math/bevington/determ.f
new file mode 100644
index 00000000..4bdc2778
--- /dev/null
+++ b/math/bevington/determ.f
@@ -0,0 +1,54 @@
+C FUNCTION DETERM.F
+C
+C SOURCE
+C   BEVINGTON, PAGE 294.
+C
+C PURPOSE
+C   CALCULATE THE DETERMINANT OF A SQUARE MATRIX
+C
+C USAGE 
+C   DET = DETERM (ARRAY, NORDER)
+C
+C DESCRIPTION OF PARAMETERS
+C   ARRAY  - MATRIX
+C   NORDER - ORDER OF DETERMINANT (DEGREE OF MATRIX)
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED 
+C   NONE
+C
+C COMMENTS
+C   THIS SUBPROGRAM DESTROYS THE INPUT MATRIX ARRAY
+C   DIMENSION STATEMENT VALID FOR NORDER UP TO 10
+C
+	FUNCTION DETERM (ARRAY,NORDER)
+	DOUBLE PRECISION ARRAY,SAVE
+	DIMENSION ARRAY(10,10)
+C
+10	DETERM=1.
+11	DO 50 K=1,NORDER
+C
+C INTERCHANGE COLUMNS IF DIAGONAL ELEMENT IS ZERO
+C
+	IF (ARRAY(K,K)) 41,21,41
+21	DO 23 J=K,NORDER
+	IF (ARRAY(K,J)) 31,23,31
+23	CONTINUE
+	DETERM=0.
+	GOTO 60 
+31	DO 34 I=K,NORDER
+	SAVE=ARRAY(I,J) 
+	ARRAY(I,J)=ARRAY(I,K)
+34	ARRAY(I,K)=SAVE 
+	DETERM=-DETERM
+C
+C SUBTRACT ROW K FROM LOWER ROWS TO GET DIAGONAL MATRIX 
+C
+41	DETERM=DETERM*ARRAY(K,K)
+	IF (K-NORDER) 43,50,50
+43	K1=K+1
+	DO 46 I=K1,NORDER
+	DO 46 J=K1,NORDER
+46	ARRAY(I,J)=ARRAY(I,J)-ARRAY(I,K)*ARRAY(K,J)/ARRAY(K,K)
+50	CONTINUE
+60	RETURN
+	END
diff --git a/math/bevington/factor.f b/math/bevington/factor.f
new file mode 100644
index 00000000..23b23307
--- /dev/null
+++ b/math/bevington/factor.f
@@ -0,0 +1,39 @@
+c function factor.f
+c
+c source
+c   Bevington, page 32.
+c
+c purpose
+c   calculates factorial function for integers
+c
+c usage
+c   result = factor (n)
+c
+c description of parameters
+c   n      - integer argument
+c
+c subroutines and function subprograms required
+c   none
+c
+	function factor (n)
+	double precision fi,sum
+11	factor=1.
+	if (n-1) 40,40,13
+13	if (n-10) 21,21,31
+c
+c n less than 11
+c
+21	do 23 i=2,n
+	fi=i
+23	factor=factor*fi
+	goto 40
+c
+c n greater than 10
+c
+31	sum=0.
+	do 34 i=11,n
+	fi=i
+34	sum=sum+dlog(fi)
+35	factor=3628800.*dexp(sum)
+40	return
+	end
diff --git a/math/bevington/fchisq.f b/math/bevington/fchisq.f
new file mode 100644
index 00000000..1f9a8dc2
--- /dev/null
+++ b/math/bevington/fchisq.f
@@ -0,0 +1,54 @@
+C FUNCTION FCHISQ.F
+C
+C SOURCE
+C   BEVINGTON, PAGE 194.
+C
+C PURPOSE
+C   EVALUATE REDUCED CHI SQUARE FOR FIT OF DATA 
+C     FCHISQ = SUM ((Y-YFIT)**2 / SIGMA**2) / NFREE
+C
+C USAGE 
+C   RESULT = FCHISQ (Y, SIGMAY, NPTS, NFREE, MODE, YFIT)
+C
+C DESCRIPTION OF PARAMETERS
+C   Y	   - ARRAY OF DATA POINTS
+C   SIGMAY - ARRAY OF STANDARD DEVIATIONS FOR DATA POINTS
+C   NPTS   - NUMBER OF DATA POINTS
+C   NFREE  - NUMBER OF DEGREES OF FREEDOM
+C   MODE   - DETERMINES METHOD OF WEIGHTING LEAST-SQUARES FIT
+C	     +1 (INSTRUMENTAL) WEIGHT(I) = 1./SIGMAY(I)**2
+C	      0 (NO WEIGHTING) WEIGHT(I) = 1.
+C	     -1 (STATISTICAL)  WEIGHT(I) = 1./Y(I)
+C   YFIT   - ARRAY OF CALCULATED VALUES OF Y
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED 
+C   NONE
+C
+	FUNCTION FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT) 
+	DOUBLE PRECISION CHISQ,WEIGHT
+	DIMENSION Y(1),SIGMAY(1),YFIT(1)
+11	CHISQ=0.
+12	IF (NFREE) 13,13,20
+13	FCHISQ=0.
+	GOTO 40 
+C
+C ACCUMULATE CHI SQUARE 
+C
+20	DO 30 I=1,NPTS
+21	IF (MODE) 22,27,29
+22	IF (Y(I)) 25,27,23
+23	WEIGHT=1./Y(I)
+	GOTO 30 
+25	WEIGHT=1./(-Y(I))
+	GOTO 30 
+27	WEIGHT=1.
+	GOTO 30 
+29	WEIGHT=1./SIGMAY(I)**2
+30	CHISQ=CHISQ+WEIGHT*(Y(I)-YFIT(I))**2
+C
+C	DIVIDE BY NUMBER OF DEGREES OF FREEDOM
+C
+31	FREE=NFREE
+32	FCHISQ=CHISQ/FREE
+40	RETURN
+	END
diff --git a/math/bevington/fderiv.f b/math/bevington/fderiv.f
new file mode 100644
index 00000000..720953cb
--- /dev/null
+++ b/math/bevington/fderiv.f
@@ -0,0 +1,39 @@
+c subroutine fderiv.f (non-analytical)
+c
+c source
+c   Bevington, page 242.
+c
+c purpose
+c   evaluate derivatives of function for least-squares search
+c      for arbitrary function given by functn
+c
+c usage
+c   call fderiv (x, i, a, deltaa, nterms, deriv)
+c
+c description of parameters
+c   x	   - array of data points for independent variable
+c   i	   - index of data points
+c   a	   - array of parameters
+c   deltaa - array of parameter increments
+c   nterms - number of parameters
+c   deriv  - derivatives of function
+c
+c subroutines and function subprograms required
+c   functn (x, i, a)
+c      evaluates the fitting function for the ith term
+c
+	subroutine fderiv (x,i,a,deltaa,nterms,deriv)
+	dimension x(1),a(1),deltaa(1),deriv(1)
+        real FUNCTN
+        external FUNCTN
+
+11	do 18 j=1,nterms
+	aj=a(j)
+	delta=deltaa(j)
+	a(j)=aj+delta
+	yfit=functn(x,i,a)
+	a(j)=aj-delta
+	deriv(j)=(yfit-functn(x,i,a))/(2.*delta)
+18	a(j)=aj
+	return
+	end
diff --git a/math/bevington/gamma.f b/math/bevington/gamma.f
new file mode 100644
index 00000000..9c393649
--- /dev/null
+++ b/math/bevington/gamma.f
@@ -0,0 +1,49 @@
+c function gamma.f
+c
+c source
+c   Bevington, page 126.
+c
+c purpose
+c   calculate the gamma function for integers and half-integers
+c
+c usage
+c   result = gamma (x)
+c
+c description of parameters
+c   x      - integer or half-integer
+c
+c subroutines or function subprograms required
+c   factor (n)
+c      calculates n factorial for integers
+c
+	function gamma (x)
+	double precision prod,sum,fi
+c
+c integerize argument
+c
+11	n=x-0.25
+	xn=n
+13	if (x-xn-0.75) 31,31,21
+c
+c argument is integer
+c
+21	gamma=factor(n)
+	goto 60
+c
+c argument is half-integer
+c
+31	prod=1.77245385
+	if (n) 44,44,33
+33	if (n-10) 41,41,51
+41	do 43 i=1,n
+	fi=i
+43	prod=prod*(fi-0.5)
+44	gamma=prod
+	goto 60
+51	sum=0.
+	do 54 i=11,n
+	fi=i
+54	sum=sum+dlog(fi-0.5)
+55	gamma=prod*639383.8623*dexp(sum)
+60	return
+	end
diff --git a/math/bevington/gradls.f b/math/bevington/gradls.f
new file mode 100644
index 00000000..f6b88d68
--- /dev/null
+++ b/math/bevington/gradls.f
@@ -0,0 +1,113 @@
+C SUBROUTINE GRADLS.F 
+C
+C SOURCE
+C   BEVINGTON, PAGES 220-222.
+C
+C PURPOSE
+C   MAKE A GRADIENT-SEARCH LEAST-SQUARES FIT TO DATA WITH A
+C      SPECIFIED FUNCTION WHICH IS NOT LINEAR IN COEFFICIENTS
+C
+C USAGE 
+C   CALL GRADLS (X, Y, SIGMAY, NPTS, NTERMS, MODE, A, DELTAA,
+C      YFIT, CHISQR)
+C
+C DESCRIPTION OF PARAMETERS
+C   X	   - ARRAY OF DATA POINTS FOR INDEPENDENT VARIABLE
+C   Y	   - ARRAY OF DATA POINTS FOR DEPENDENT VARIABLE
+C   SIGMAY - ARRAY OF STANDARD DEVIATIONS FOR Y DATA POINTS
+C   NPTS   - NUMBER OF PAIRS OF DATA POINTS
+C   NTERMS - NUMBER OF PARAMETERS
+C   MODE   - DETERMINES METHOD OF WEIGHTING LEAST-SQUARES FIT
+C	     +1 (INSTRUMENTAL) WEIGHT(I) = 1./SIGMAY(I)**2
+C	      0 (NO WEIGHTING) WEIGHT(I) = 1.
+C	     -1 (STATISTICAL)  WEIGHT(I) = 1./Y(I)
+C   A	   - ARRAY OF PARAMETERS
+C   DELTAA - ARRAY OF INCREMENTS FOR PARAMETERS A
+C   YFIT   - ARRAY OF CALCULATED VALUES OF Y
+C   CHISQR - REDUCED CHI SQUARE FOR FIT 
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED 
+C   FUNCTN (X, I, A)
+C      EVALUATES THE FITTING FUNCTION FOR THE ITH TERM
+C   FCHISQ (Y, SIGMAY, NPTS, NFREE, MODE, YFIT) 
+C      EVALUATES REDUCED CHI SQUARED FOR FIT TO DATA
+C
+C COMMENTS
+C   DIMENSION STATEMENT VALID FOR NTERMS UP TO 10
+C
+      SUBROUTINE GRADLS (X,Y,SIGMAY,NPTS,NTERMS,MODE,A,DELTAA,
+     *YFIT,CHISQR)
+      DIMENSION X(1),Y(1),SIGMAY(1),A(1),DELTAA(1),YFIT(1)
+      DIMENSION GRAD(10)
+      REAL FUNCTN
+      EXTERNAL FUNCTN
+
+C
+C EVALUATE CHI SQUARE AT BEGINNING
+C
+11    NFREE=NPTS-NTERMS
+      IF (NFREE) 13,13,21
+13    CHISQR=0.
+      GOTO 110
+21    DO 22 I=1,NPTS
+22    YFIT(I)=FUNCTN (X,I,A)
+      CHISQ1=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+C
+C EVALUATE GRADIENT OF CHI SQUARE
+C
+31    SUM=0.
+32    DO 39 J=1,NTERMS
+      DELTA=0.1*DELTAA(J)
+      A(J)=A(J)+DELTA 
+      DO 36 I=1,NPTS
+36    YFIT(I)=FUNCTN (X,I,A)
+      A(J)=A(J)-DELTA 
+      GRAD(J)=CHISQ1-FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+39    SUM=SUM+GRAD(J)**2
+41    DO 42 J=1,NTERMS
+42    GRAD(J)=DELTAA(J)*GRAD(J)/SQRT(SUM)
+C
+C EVALUATE CHI SQUARE AT NEW POINT
+C
+51    DO 52 J=1,NTERMS
+52    A(J)=A(J)+GRAD(J)
+53    DO 54 I=1,NPTS
+54    YFIT(I)=FUNCTN (X,I,A)
+      CHISQ2=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+C
+C MAKE SURE CHI SQUARE DECREASES
+C
+61    IF (CHISQ1-CHISQ2) 62,62,71
+62    DO 64 J=1,NTERMS
+      A(J)=A(J)-GRAD(J)
+64    GRAD(J)=GRAD(J)/2.
+      GOTO 51 
+C
+C INCREMENT PARAMETERS UNTIL CHI SQUARE STARTS TO INCREASE
+C
+71    DO 72 J=1,NTERMS
+72    A(J)=A(J)+GRAD(J)
+      DO 74 I=1,NPTS
+74    YFIT(I)=FUNCTN (X,I,A)
+75    CHISQ3=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+76    IF (CHISQ3-CHISQ2) 81,91,91
+81    CHISQ1=CHISQ2
+82    CHISQ2=CHISQ3
+      GOTO 71 
+C
+C FIND MINIMUM OF PARABOLA DEFINED BY LAST THREE POINTS 
+C
+91    DELTA=1./(1.+(CHISQ1-CHISQ2)/(CHISQ3-CHISQ2))+0.5
+      DO 93 J=1,NTERMS
+93    A(J)=A(J)-DELTA*GRAD(J) 
+      DO 95 I=1,NPTS
+95    YFIT(I)=FUNCTN (X,I,A)
+      CHISQR=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+101   IF (CHISQ2-CHISQR) 102,110,110
+102   DO 103 J=1,NTERMS
+103   A(J)=A(J)+(DELTA-1.)*GRAD(J)
+104   DO 105 I=1,NPTS 
+105   YFIT(I)=FUNCTN (X,I,A)
+106   CHISQR=CHISQ2
+110   RETURN
+      END
diff --git a/math/bevington/gridls.f b/math/bevington/gridls.f
new file mode 100644
index 00000000..e62d3219
--- /dev/null
+++ b/math/bevington/gridls.f
@@ -0,0 +1,102 @@
+C SUBROUTINE GRIDLS.F 
+C
+C SOURCE
+C   BEVINGTON, PAGES 212-213.
+C
+C PURPOSE
+C   MAKE A GRID-SEARCH LEAST-SQUARES FIT TO DATA WITH A SPECIFIED
+C   FUNCTION WHICH IS NOT LINEAR IN COEFFICIENTS
+C
+C USAGE 
+C   CALL GRIDLS (X, Y, SIGMAY, NPTS, NTERMS, MODE, A, DELTAA,
+C      SIGMAA, YFIT, CHISQR)
+C
+C DESCRIPTION OF PARAMETERS
+C   X	   - ARRAY OF DATA POINTS FOR INDEPENDENT VARIABLE
+C   Y	   - ARRAY OF DATA POINTS FOR DEPENDENT VARIABLE
+C   SIGMAY - ARRAY OF STANDARD DEVIATIONS FOR Y DATA POINTS
+C   NPTS   - NUMBER OF PAIRS OF DATA POINTS
+C   NTERMS - NUMBER OF PARAMETERS
+C   MODE   - DETERMINES METHOD OF WEIGHTING LEAST-SQUARES FIT
+C	     +1 (INSTRUMENTAL) WEIGHT(I) = 1./SIGMAY(I)**2
+C	      0 (NO WEIGHTING) WEIGHT(I) = 1.
+C	     -1 (STATISTICAL)  WEIGHT(I) = 1./Y(I)
+C   A	   - ARRAY OF PARAMETERS
+C   DELTAA - ARRAY OF INCREMENTS FOR PARAMETERS A
+C   SIGMAA - ARRAY OF STANDARD DEVIATIONS FOR PARAMETERS A
+C   YFIT   - ARRAY OF CALCULATED VALUES OF Y
+C   CHISQR - REDUCED CHI SQUARE FOR FIT 
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED 
+C   FUNCTN (X, I, A)
+C      EVALUATES THE FITTING FUNCTION FOR THE ITH TERM
+C   FCHISQ (Y, SIGMAY, NPTS, NFREE, MODE, YFIT) 
+C      EVALUATES REDUCED CHI SQUARED FOR FIT TO DATA
+C
+C COMMENTS
+C   DELTAA VALUES ARE MODIFIED BY THE PROGRAM
+C
+      SUBROUTINE GRIDLS (X,Y,SIGMAY,NPTS,NTERMS,MODE,A,DELTAA,
+     *SIGMAA,YFIT,CHISQR)
+      DIMENSION X(1),Y(1),SIGMAY(1),A(1),DELTAA(1),SIGMAA(1), 
+     *YFIT(1)
+      REAL FUNCTN
+      EXTERNAL FUNCTN
+
+C
+11    NFREE=NPTS-NTERMS
+      FREE=NFREE
+      CHISQR=0.
+      IF (NFREE) 100,100,20
+20    DO 90 J=1,NTERMS
+C
+C EVALUATE CHI SQUARE AT FIRST TWO SEARCH POINTS
+C
+21    DO 22 I=1,NPTS
+22    YFIT(I)=FUNCTN (X,I,A)
+23    CHISQ1=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+      FN=0.
+      DELTA=DELTAA(J) 
+41    A(J)=A(J)+DELTA 
+      DO 43 I=1,NPTS
+43    YFIT(I)=FUNCTN (X,I,A)
+44    CHISQ2=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+45    IF (CHISQ1-CHISQ2) 51,41,61
+C
+C REVERSE DIRECTION OF SEARCH IF CHI SQUARE IS INCREASING
+C
+51    DELTA=-DELTA
+      A(J)=A(J)+DELTA 
+      DO 54 I=1,NPTS
+54    YFIT(I)=FUNCTN (X,I,A)
+      SAVE=CHISQ1
+      CHISQ1=CHISQ2
+57    CHISQ2=SAVE
+C
+C INCREMENT A(J) UNTIL CHI SQUARE INCREASES
+C
+61    FN=FN+1.
+      A(J)=A(J)+DELTA 
+      DO 64 I=1,NPTS
+64    YFIT(I)=FUNCTN (X,I,A)
+      CHISQ3=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+66    IF (CHISQ3-CHISQ2) 71,81,81
+71    CHISQ1=CHISQ2
+      CHISQ2=CHISQ3
+      GOTO 61 
+C
+C FIND MINIMUM OF PARABOLA DEFINED BY LAST THREE POINTS 
+C
+81    DELTA=DELTA*(1./(1.+(CHISQ1-CHISQ2)/(CHISQ3-CHISQ2))+0.5)
+82    A(J)=A(J)-DELTA 
+83    SIGMAA(J)=DELTAA(J)*SQRT(2./(FREE*(CHISQ3-2.*CHISQ2+CHISQ1)))
+84    DELTAA(J)=DELTAA(J)*FN/3.
+90    CONTINUE
+C
+C EVALUATE FIT AND CHI SQUARE FOR FINAL PARAMETERS
+C
+91    DO 92 I=1,NPTS
+92    YFIT(I)=FUNCTN (X,I,A)
+93    CHISQR=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
+100   RETURN
+      END
diff --git a/math/bevington/integ.f b/math/bevington/integ.f
new file mode 100644
index 00000000..153bafe1
--- /dev/null
+++ b/math/bevington/integ.f
@@ -0,0 +1,58 @@
+c subroutine integ.f
+c
+c source
+c   Bevington, page 274.
+c
+c purpose
+c   integrate the area beneath two data points
+c
+c usage
+c   call integ (x, y, nterms, i1, x1, x2, sum)
+c
+c description of parameters
+c   x	   - array of data points for independent variable
+c   y	   - array of data points for dependent variable
+c   nterms - number of terms in fitting polymonial
+c   i1	   - first data point for fitting polynomial
+c   x1	   - first value of x for integration
+c   x2	   - final value of x for integration
+c
+c subroutines and function subprograms required
+c   none
+c
+c comments
+c   dimension statement valid for nterms up to 10
+c
+	subroutine integ (x,y,nterms,i1,x1,x2,sum)
+	double precision xjk,array,a,denom,deltax,sum
+	dimension x(1),y(1)
+	dimension array(10,10)
+c
+c construct square matrix and invert
+c
+11	do 17 j=1,nterms
+	i=j+i1-1
+	deltax=x(i)-x(i1)
+	xjk=1.
+	do 17 k=1,nterms
+	array(j,k)=xjk
+17	xjk=xjk*deltax
+21	call matinv (array,nterms,det)
+	if (det) 31,23,31
+23	imid=i1+nterms/2
+	sum=sum+y(imid)*(x2-x1)
+	goto 40
+c
+c evaluate coefficients and integrate
+c
+31	dx1=x1-x(i1)
+	dx2=x2-x(i1)
+33	do 39 j=1,nterms
+	i=j+i1-1
+	a=0.
+	do 37 k=1,nterms
+37	a=a+y(i)*array(j,k)
+	denom=j
+39	sum=sum+(a/denom)*(dx2**j-dx1**j)
+40	return
+	end
diff --git a/math/bevington/interp.f b/math/bevington/interp.f
new file mode 100644
index 00000000..75ca1b23
--- /dev/null
+++ b/math/bevington/interp.f
@@ -0,0 +1,85 @@
+C SUBROUTINE INTERP.F 
+C
+C SOURCE
+C   BEVINGTON, PAGES 266-267.
+C
+C PURPOSE
+C   INTERPOLATE BETWEEN DATA POINTS TO EVALUATE A FUNCTION
+C
+C USAGE 
+C   CALL INTERP (X, Y, NPTS, NTERMS, XIN, YOUT) 
+C
+C DESCRIPTION OF PARAMETERS
+C   X	   - ARRAY OF DATA POINTS FOR INDEPENDENT VARIABLE
+C   Y	   - ARRAY OF DATA POINTS FOR DEPENDENT VARIABLE
+C   NPTS   - NUMBER OF PAIRS OF DATA POINTS
+C   NTERMS - NUMBER OF TERMS IN FITTING POLYNOMIAL
+C   XIN    - INPUT VALUE OF X
+C   YOUT   - INTERPOLATED VALUE OF Y
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED 
+C   NONE
+C
+C COMMENTS
+C   DIMENSION STATEMENT VALID FOR NTERMS UP TO 10
+C   VALUE OF NTERMS MAY BE MODIFIED BY THE PROGRAM
+C
+	SUBROUTINE INTERP (X,Y,NPTS,NTERMS,XIN,YOUT)
+	DOUBLE PRECISION DELTAX,DELTA,A,PROD,SUM
+	DIMENSION X(1),Y(1)
+	DIMENSION DELTA(10),A(10)
+C
+C SEARCH FOR APPROPRIATE VALUE OF X(1)
+C
+11	DO 19 I=1,NPTS
+	IF (XIN-X(I)) 13,17,19
+13	I1=I-NTERMS/2
+	IF (I1) 15,15,21
+15	I1=1
+	GOTO 21 
+17	YOUT=Y(I)
+18	GOTO 61 
+19	CONTINUE
+	I1=NPTS-NTERMS+1
+21	I2=I1+NTERMS-1
+	IF (NPTS-I2) 23,31,31
+23	I2=NPTS 
+	I1=I2-NTERMS+1
+25	IF (I1) 26,26,31
+26	I1=1
+27	NTERMS=I2-I1+1
+C
+C EVALUATE DEVIATIONS DELTA
+C
+31	DENOM=X(I1+1)-X(I1)
+	DELTAX=(XIN-X(I1))/DENOM
+	DO 35 I=1,NTERMS
+	IX=I1+I-1
+35	DELTA(I)=(X(IX)-X(I1))/DENOM
+C
+C ACCUMULATE COEFFICIENTS A
+C
+40	A(1)=Y(I1)
+41	DO 50 K=2,NTERMS
+	PROD=1. 
+	SUM=0.
+	IMAX=K-1
+	IXMAX=I1+IMAX
+	DO 49 I=1,IMAX
+	J=K-I
+	PROD=PROD*(DELTA(K)-DELTA(J))
+49	SUM=SUM-A(J)/PROD
+50	A(K)=SUM+Y(IXMAX)/PROD
+C
+C ACCUMULATE SUM OF EXPANSION
+C
+51	SUM=A(1)
+	DO 57 J=2,NTERMS
+	PROD=1. 
+	IMAX=J-1
+	DO 56 I=1,IMAX
+56	PROD=PROD*(DELTAX-DELTA(I))
+57	SUM=SUM+A(J)*PROD
+60	YOUT=SUM
+61	RETURN
+	END
diff --git a/math/bevington/legfit.f b/math/bevington/legfit.f
new file mode 100644
index 00000000..eb00b824
--- /dev/null
+++ b/math/bevington/legfit.f
@@ -0,0 +1,173 @@
+c subroutine legfit.f
+c
+c source
+c   Bevington, pages 155-157.
+c
+c purpose
+c   make a least-squares fit to data with a legendre polynomial
+c      y = a(1) + a(2)*x + a(3)*(3x**2-1)/2 + ...
+c        = a(1) * (1. + b(2)*x + b(3)*(3x**2-1)/2 + ... )
+c      where x = cos(theta)
+c
+c usage
+c   call legfit (theta, y, sigmay, npts, norder, neven, mode, ftest,
+c      yfit, a, sigmaa, b, sigmab, chisqr)
+c
+c description of parameters
+c   theta  - array of angles (in degrees) of the data points
+c   y      - array of data points for dependent variable
+c   sigmay - array of standard deivations for y data points
+c   npts   - number of pairs of data points
+c   norder - highest order of polynomial (number of terms - 1)
+c   neven  - determines odd or even character of polynomial
+c            +1 fits only to even terms
+c             0 fits to all terms
+c            -1 fits only to odd terms (plus constant term)
+c   mode   - determines mode of weighting least-squares fit
+c            +1 (instrumental) weight(i) = 1./sigmay(i)**2
+c             0 (no weighting) weight(i) = 1.
+c            -1 (statistical)  weight(i) = 1./y(i)
+c   ftest  - array of values of f(l) for an f test
+c   yfit   - array of calculated values of y
+c   a      - array of coefficients of polynomial
+c   sigmaa - array of standard deviations for coefficients
+c   b      - array of normalized relative coefficients
+c   sigmab - array of standard deviations for relative coefficients
+c   chisqr - reduced chi square for fit
+c
+c subroutines and function subprograms required
+c   matinv (array, nterms, det)
+c      inverts a symmetric two-dimensional matrix of degree nterms
+c      and calculates its determinant
+c
+c comments
+c   dimension statement valid for npts up to 100 and order up to 9
+c   dcos changed to cos in statement 31
+c
+      subroutine legfit (theta,y,sigmay,npts,norder,neven,mode,
+     *ftest,yfit,a,sigmaa,b,sigmab,chisqr)
+      double precision cosine,p,beta,alpha,chisq
+      dimension theta(1),y(1),sigmay(1),ftest(1),yfit(1),
+     *a(1),sigmaa(1),b(1),sigmab(1)
+      dimension weight(100),p(100,10),beta(10),alpha(10,10)
+c
+c accumulate weights and legendre polynomials
+c
+11    nterms=1
+      ncoeff=1
+      jmax=norder+1
+20    do 40 i=1,npts
+21    if (mode) 22,27,29
+22    if (y(i)) 25,27,23
+23    weight(i)=1./y(i)
+      goto 31
+25    weight(i)=1./(-y(i))
+      goto 31
+27    weight(i)=1.
+      goto 31
+29    weight(i)=1./sigmay(i)**2
+31    cosine=cos(0.01745329252*theta(i))
+      p(i,1)=1.
+      p(i,2)=cosine
+      do 36 l=2,norder
+      fl=l
+36    p(i,l+1)=((2.*fl-1.)*cosine*p(i,l)-(fl-1.)*p(i,l-1))/fl
+40    continue
+c
+c accumulate matrices alpha and beta
+c
+51    do 54 j=1,nterms
+      beta(j)=0.
+      do 54 k=1,nterms
+54    alpha(j,k)=0.
+61    do 66 i=1,npts
+      do 66 j=1,nterms
+      beta(j)=beta(j)+p(i,j)*y(i)*weight(i)
+      do 66 k=j,nterms
+      alpha(j,k)=alpha(j,k)+p(i,j)*p(i,k)*weight(i)
+66    alpha(k,j)=alpha(j,k)
+c
+c delete fixed coefficients
+c
+70    if (neven) 71,91,81
+71    do 76 j=3,nterms,2
+      beta(j)=0.
+      do 75 k=1,nterms
+      alpha(j,k)=0.
+75    alpha(k,j)=0.
+76    alpha(j,j)=1.
+      goto 91
+81    do 86 j=2,nterms,2
+      beta(j)=0.
+      do 85 k=1,nterms
+      alpha(j,k)=0.
+85    alpha(k,j)=0.
+86    alpha(j,j)=1.
+c
+c invert curvature matrix alpha
+c
+91    do 95 j=1,jmax
+      a(j)=0.
+      sigmaa(j)=0.
+      b(j)=0.
+95    sigmab(j)=0.
+      do 97 i=1,npts
+97    yfit(i)=0.
+101   call matinv (alpha,nterms,det)
+      if (det) 111,103,111
+103   chisqr=0.
+      goto 170
+c
+c calculate coefficients, fit, and chi square
+c
+111   do 115 j=1,nterms
+      do 113 k=1,nterms
+113   a(j)=a(j)+beta(k)*alpha(j,k)
+      do 115 i=1,npts
+115   yfit(i)=yfit(i)+a(j)*p(i,j)
+121   chisq=0.
+      do 123 i=1,npts
+123   chisq=chisq+(y(i)-yfit(i))**2*weight(i)
+      free=npts-ncoeff
+      chisqr=chisq/free
+c
+c test for end of fit
+c
+131   if (nterms-jmax) 132,151,151
+132   if (ncoeff-2) 133,134,141
+133   if (neven) 137,137,135
+134   if (neven) 135,137,135
+135   nterms=nterms+2
+      goto 138
+137   nterms=nterms+1
+138   ncoeff=ncoeff+1
+      chisq1=chisq
+      goto 51
+141   fvalue=(chisq1-chisq)/chisqr
+      if (ftest(nterms)-fvalue) 134,143,143
+143   if (neven) 144,146,144
+144   nterms=nterms-2
+      goto 147
+146   nterms=nterms-1
+147   ncoeff=ncoeff-1
+      jmax=nterms
+149   goto 51
+c
+c calculate remainder of output
+c
+151   if (mode) 152,154,152
+152   varnce=1.
+      goto 155
+154   varnce=chisqr
+155   do 156 j=1,nterms
+156   sigmaa(j)=dsqrt(varnce*alpha(j,j))
+161   if (a(1)) 162,170,162
+162   do 166 j=2,nterms
+      if (a(j)) 164,166,164
+164   b(j)=a(j)/a(1)
+165   sigmab(j)=b(j)*dsqrt((sigmaa(j)/a(j))**2+(sigmaa(1)/a(1))**2
+     *-2.*varnce*alpha(j,1)/(a(j)*a(1)))
+166   continue
+      b(1)=1.
+170   return
+      end
diff --git a/math/bevington/linfit.f b/math/bevington/linfit.f
new file mode 100644
index 00000000..132c62b0
--- /dev/null
+++ b/math/bevington/linfit.f
@@ -0,0 +1,79 @@
+c subroutine linfit.f
+c
+c source
+c   Bevington, pages 104-105.
+c
+c purpose
+c   make a least-squares fit to a data set with a straight line
+c
+c usage
+c   call linfit (x, y, sigmay, npts, mode, a, sigmaa, b, sigmab, r)
+c
+c description of parameters
+c   x      - array of data points for independent variable
+c   y      - array of data points for dependent variable
+c   sigmay - array of standard deviations for y data points
+c   npts   - number of pairs of data points
+c   mode   - determines method of weighting least-squares fit
+c            +1 (instrumental) weight(i) = 1./sigmay(i)**2
+c             0 (no weighting) weight(i) = 1.
+c            -1 (statistical)  weight(i) = 1./y(i)
+c   a      - y intercept of fitted straight line
+c   sigmaa - standard deviation of a
+c   b      - slope of fitted straight line
+c   sigmab - standard deviation of b
+c   r      - linear correlation coefficient
+c
+c subroutines and function subprograms required
+c   none
+c
+      subroutine linfit (x,y,sigmay,npts,mode,a,sigmaa,b,sigmab,r)
+      double precision sum,sumx,sumy,sumx2,sumxy,sumy2
+      double precision xi,yi,weight,delta,varnce
+      dimension x(1),y(1),sigmay(1)
+c
+c accumulate weighted sums
+c
+11    sum=0.
+      sumx=0.
+      sumy=0.
+      sumx2=0.
+      sumxy=0.
+      sumy2=0.
+21    do 50 i=1,npts
+      xi=x(i)
+      yi=y(i)
+      if (mode) 31,36,38
+31    if (yi) 34,36,32
+32    weight=1./yi
+      goto 41
+34    weight=1./(-yi)
+      goto 41
+36    weight=1.
+      goto 41
+38    weight=1./sigmay(i)**2
+41    sum=sum+weight
+      sumx=sumx+weight*xi
+      sumy=sumy+weight*yi
+      sumx2=sumx2+weight*xi*xi
+      sumxy=sumxy+weight*xi*yi
+      sumy2=sumy2+weight*yi*yi
+50    continue
+c
+c calculate coefficients and standard deviations
+c
+51    delta=sum*sumx2-sumx*sumx
+      a=(sumx2*sumy-sumx*sumxy)/delta
+53    b=(sumxy*sum-sumx*sumy)/delta
+61    if (mode) 62,64,62
+62    varnce=1.
+      goto 67
+64    c=npts-2
+      varnce=(sumy2+a*a*sum+b*b*sumx2
+     *-2.*(a*sumy+b*sumxy-a*b*sumx))/c
+67    sigmaa=dsqrt(varnce*sumx2/delta)
+68    sigmab=dsqrt(varnce*sum/delta)
+71    r=(sum*sumxy-sumx*sumy)/
+     *dsqrt(delta*(sum*sumy2-sumy*sumy))
+      return
+      end
diff --git a/math/bevington/man/agauss.3m b/math/bevington/man/agauss.3m
new file mode 100644
index 00000000..4f66e826
--- /dev/null
+++ b/math/bevington/man/agauss.3m
@@ -0,0 +1,24 @@
+.TH AGAUSS 3M
+.SH NAME
+agauss 
+.SH DESCRIPTION
+function agauss.f
+
+source
+  Bevington, page 48.
+
+purpose
+  evaluate integral of Gaussian probability function
+
+usage
+  result = agauss (x, averag, sigma)
+
+description of parameters
+  x      - limit for integral
+  averag - mean of distribution
+  sigma  - standard deviation of distribution
+    integration range is averag +/- z*sigma
+      where z = abs(x-averag)/sigma
+
+subroutines and function subprograms required
+  none
diff --git a/math/bevington/man/area.3m b/math/bevington/man/area.3m
new file mode 100644
index 00000000..1505ef4d
--- /dev/null
+++ b/math/bevington/man/area.3m
@@ -0,0 +1,25 @@
+.TH AREA 3M
+.SH NAME
+area
+.SH DESCRIPTION
+function area.f
+
+source
+  Bevington, pages 272-273.
+
+purpose
+  integrate the area beneath a set of data points
+
+usage
+  result = area (x, y, npts, nterms)
+
+description of parameters
+  x      - array of data points for independent variable
+  y      - array of data points for dependent variable
+  npts   - number of pairs of data points
+  nterms - number of terms in fitting polynomial
+
+subroutines and function subprograms required
+  integ (x, y, nterms, i1, x1, x2 sum)
+    fits a polynomial with nterms starting at i1
+      and integrates area from x1 to x2
diff --git a/math/bevington/man/chifit.3m b/math/bevington/man/chifit.3m
new file mode 100644
index 00000000..ec8f7f2c
--- /dev/null
+++ b/math/bevington/man/chifit.3m
@@ -0,0 +1,44 @@
+.TH CHIFIT 3M
+.SH NAME
+chifit
+.SH DESCRIPTION
+subroutine chifit.f 
+
+source
+  Bevington, pages 228-231.
+
+purpose
+  make least-squares fit to a non-linear function
+    with a parabolic expansion of chi square 
+
+usage 
+  call chifit (x, y, sigmay, npts, nterms, mode, a, deltaa,
+    sigmaa, yfit, chisqr)
+
+description of parameters
+  x      - array of data points for independent variable
+  y      - array of data points for dependent variable
+  sigmay - array of standard deviations for y data points
+  npts   - number of pairs of data points
+  nterms - number of parameters
+  mode   - determines method of weighting least-squares fit
+           +1 (instrumental) weight(i) = 1./sigmay(i)**2
+            0 (no weighting) weight(i) = 1.
+           -1 (statistical)  weight(i) = 1./y(i)
+  a      - array of parameters
+  deltaa - array of increments for parameters a
+  sigmaa - array of standard deviations for parameters a
+  yfit   - array of calculated values of y
+  chisqr - reduced chi square for fit 
+
+subroutines and function subprograms required 
+  functn (x, i, a)
+    evaluates the fitting function for the ith term
+  fchisq (y, sigmay, npts, nfree, mode, yfit) 
+    evaluates reduced chi squared for fit to data
+  matinv (array, nterms, det) 
+    inverts symmetric two-dimension matrix of degree nterms
+      and calculates its determinant
+
+comments
+  valid for nterms up to 10
diff --git a/math/bevington/man/curfit.3m b/math/bevington/man/curfit.3m
new file mode 100644
index 00000000..799f0545
--- /dev/null
+++ b/math/bevington/man/curfit.3m
@@ -0,0 +1,49 @@
+.TH CURFIT 3M
+.SH NAME
+curfit
+.SH DESCRIPTION
+subroutine curfit.f 
+
+source
+  Bevington, pages 237-239.
+
+purpose
+  make least-squares fit to a non-linear function
+    with a linearization of the fitting function
+
+usage 
+  call curfit (x, y, sigmay, npts, nterms, mode, a, deltaa,
+    sigmaa, flamda, yfit, chisqr)
+
+description of parameters
+  x      - array of data points for independent variable
+  y      - array of data points for dependent variable
+  sigmay - array of standard deviations for y data points
+  npts   - number of pairs of data points
+  nterms - number of parameters
+  mode   - determines method of weighting least-squares fit
+           +1 (instrumental) weight(i) = 1./sigmay(i)**2
+            0 (no weighting) weight(i) = 1.
+           -1 (statistical)  weight(i) = 1./y(i)
+  a      - array of parameters
+  deltaa - array of increments for parameters a
+  sigmaa - array of standard deviations for parameters a
+  flamda - proportion of gradient search included
+  yfit   - array of calculated values of y
+  chisqr - reduced chi square for fit 
+
+subroutines and function subprograms required 
+  functn (x, i, a)
+    evaluates the fitting function for the ith term
+  fchisq (y, sigmay, npts, nfree, mode, yfit) 
+    evaluates reduced chi squared for fit to data
+  fderiv (x, i, a, deltaa, nterms, deriv)
+    evaluates the derivatives of the fitting function
+      for the ith term with respect to each parameter
+  matinv (array, nterms, det) 
+    inverts symmetric two-dimension matrix of degree nterms
+      and calculates its determinant
+
+comments
+  valid for nterms up to 10
+  set flamda = 0.001 at beginning of search
diff --git a/math/bevington/man/determ.3m b/math/bevington/man/determ.3m
new file mode 100644
index 00000000..5ec86d06
--- /dev/null
+++ b/math/bevington/man/determ.3m
@@ -0,0 +1,25 @@
+.TH DETERM 3M
+.SH NAME
+determ
+.SH DESCRIPTION
+function determ.f
+
+source
+  Bevington, page 294.
+
+purpose
+  calculate the determinant of a square matrix
+
+usage 
+  result = determ (array, norder)
+
+description of parameters
+  array  - matrix
+  norder - order of determinant (degree of matrix)
+
+subroutines and function subprograms required 
+  none
+
+comments
+  this subprogram destroys the input matrix array
+  valid for norder up to 10
diff --git a/math/bevington/man/factor.3m b/math/bevington/man/factor.3m
new file mode 100644
index 00000000..1127c5d0
--- /dev/null
+++ b/math/bevington/man/factor.3m
@@ -0,0 +1,20 @@
+.TH FACTOR 3M
+.SH NAME
+factor
+.SH DESCRIPTION
+function factor.f
+
+source
+  Bevington, page 32.
+
+purpose
+  calculates factorial function for integers
+
+usage
+  result = factor (n)
+
+description of parameters
+  n      - integer argument
+
+subroutines and function subprograms required
+  none
diff --git a/math/bevington/man/fchisq.3m b/math/bevington/man/fchisq.3m
new file mode 100644
index 00000000..0511409b
--- /dev/null
+++ b/math/bevington/man/fchisq.3m
@@ -0,0 +1,29 @@
+.TH FCHISQ 3M
+.SH NAME
+fchisq
+.SH DESCRIPTION
+function fchisq.f
+
+source
+  Bevington, page 194.
+
+purpose
+  evaluate reduced chi square for fit of data 
+    fchisq = sum ((y-yfit)**2 / sigma**2) / nfree
+
+usage 
+  result = fchisq (y, sigmay, npts, nfree, mode, yfit)
+
+description of parameters
+  y      - array of data points
+  sigmay - array of standard deviations for data points
+  npts   - number of data points
+  nfree  - number of degrees of freedom
+  mode   - determines method of weighting least-squares fit
+           +1 (instrumental) weight(i) = 1./sigmay(i)**2
+            0 (no weighting) weight(i) = 1.
+           -1 (statistical)  weight(i) = 1./y(i)
+  yfit   - array of calculated values of y
+
+subroutines and function subprograms required 
+  none
diff --git a/math/bevington/man/fderiv.3m b/math/bevington/man/fderiv.3m
new file mode 100644
index 00000000..d9c88aeb
--- /dev/null
+++ b/math/bevington/man/fderiv.3m
@@ -0,0 +1,27 @@
+.TH FDERIV 3M
+.SH NAME
+fderiv
+.SH DESCRIPTION
+subroutine fderiv.f (non-analytical)
+
+source
+  Bevington, page 242.
+
+purpose
+  evaluate derivatives of function for least-squares search
+    for arbitrary function given by functn
+
+usage
+  call fderiv (x, i, a, deltaa, nterms, deriv)
+
+description of parameters
+  x      - array of data points for independent variable
+  i      - index of data points
+  a      - array of parameters
+  deltaa - array of parameter increments
+  nterms - number of parameters
+  deriv  - derivatives of function
+
+subroutines and function subprograms required
+  functn (x, i, a)
+    evaluates the fitting function for the ith term
diff --git a/math/bevington/man/gamma.3m b/math/bevington/man/gamma.3m
new file mode 100644
index 00000000..31939ef3
--- /dev/null
+++ b/math/bevington/man/gamma.3m
@@ -0,0 +1,21 @@
+.TH GAMMA 3M
+.SH NAME
+gamma
+.SH DESCRIPTION
+function gamma.f
+
+source
+  Bevington, page 126.
+
+purpose
+  calculate gamma function for integers and 1/2-integers
+
+usage
+  result = gamma (x)
+
+description of parameters
+  x      - integer or half-integer
+
+subroutines or function subprograms required
+  factor (n)
+    calculates n factorial for integers
diff --git a/math/bevington/man/gradls.3m b/math/bevington/man/gradls.3m
new file mode 100644
index 00000000..681c93f4
--- /dev/null
+++ b/math/bevington/man/gradls.3m
@@ -0,0 +1,40 @@
+.TH GRADLS 3M
+.SH NAME
+gradls
+.SH DESCRIPTION
+subroutine gradls.f 
+
+source
+  Bevington, pages 220-222.
+
+purpose
+  make gradient-search least-squares fit to data with a
+    specified function which is not linear in coefficients
+
+usage 
+  call gradls (x, y, sigmay, npts, nterms, mode, a, deltaa,
+    yfit, chisqr)
+
+description of parameters
+  x      - array of data points for independent variable
+  y      - array of data points for dependent variable
+  sigmay - array of standard deviations for y data points
+  npts   - number of pairs of data points
+  nterms - number of parameters
+  mode   - determines method of weighting least-squares fit
+           +1 (instrumental) weight(i) = 1./sigmay(i)**2
+            0 (no weighting) weight(i) = 1.
+           -1 (statistical)  weight(i) = 1./y(i)
+  a      - array of parameters
+  deltaa - array of increments for parameters a
+  yfit   - array of calculated values of y
+  chisqr - reduced chi square for fit 
+
+subroutines and function subprograms required 
+  functn (x, i, a)
+    evaluates the fitting function for the ith term
+  fchisq (y, sigmay, npts, nfree, mode, yfit) 
+    evaluates reduced chi squared for fit to data
+
+comments
+  valid for nterms up to 10
diff --git a/math/bevington/man/gridls.3m b/math/bevington/man/gridls.3m
new file mode 100644
index 00000000..331a566c
--- /dev/null
+++ b/math/bevington/man/gridls.3m
@@ -0,0 +1,41 @@
+.TH GRIDLS 3M
+.SH NAME
+gridls
+.SH DESCRIPTION
+subroutine gridls.f 
+
+source
+  Bevington, pages 212-213.
+
+purpose
+  make grid-search least-squares fit to data with specified
+    function which is not linear in coefficients
+
+usage 
+  call gridls (x, y, sigmay, npts, nterms, mode, a, deltaa,
+    sigmaa, yfit, chisqr)
+
+description of parameters
+  x      - array of data points for independent variable
+  y      - array of data points for dependent variable
+  sigmay - array of standard deviations for y data points
+  npts   - number of pairs of data points
+  nterms - number of parameters
+  mode   - determines method of weighting least-squares fit
+           +1 (instrumental) weight(i) = 1./sigmay(i)**2
+            0 (no weighting) weight(i) = 1.
+           -1 (statistical)  weight(i) = 1./y(i)
+  a      - array of parameters
+  deltaa - array of increments for parameters a
+  sigmaa - array of standard deviations for parameters a
+  yfit   - array of calculated values of y
+  chisqr - reduced chi square for fit 
+
+subroutines and function subprograms required 
+  functn (x, i, a)
+    evaluates the fitting function for the ith term
+  fchisq (y, sigmay, npts, nfree, mode, yfit) 
+    evaluates reduced chi squared for fit to data
+
+comments
+  deltaa values are modified by the program
diff --git a/math/bevington/man/integ.3m b/math/bevington/man/integ.3m
new file mode 100644
index 00000000..e6200645
--- /dev/null
+++ b/math/bevington/man/integ.3m
@@ -0,0 +1,28 @@
+.TH INTEG 3M
+.SH NAME
+integ
+.SH DESCRIPTION
+subroutine integ.f
+
+source
+  Bevington, page 274.
+
+purpose
+  integrate the area beneath two data points
+
+usage
+  call integ (x, y, nterms, i1, x1, x2, sum)
+
+description of parameters
+  x      - array of data points for independent variable
+  y      - array of data points for dependent variable
+  nterms - number of terms in fitting polymonial
+  i1     - first data point for fitting polynomial
+  x1     - first value of x for integration
+  x2     - final value of x for integration
+
+subroutines and function subprograms required
+  none
+
+comments
+  valid for nterms up to 10
diff --git a/math/bevington/man/interp.3m b/math/bevington/man/interp.3m
new file mode 100644
index 00000000..0a25b2b0
--- /dev/null
+++ b/math/bevington/man/interp.3m
@@ -0,0 +1,29 @@
+.TH INTERP 3M
+.SH NAME
+interp
+.SH DESCRIPTION
+subroutine interp.f 
+
+source
+  Bevington, pages 266-267.
+
+purpose
+  interpolate between data points to evaluate a function
+
+usage 
+  call interp (x, y, npts, nterms, xin, yout) 
+
+description of parameters
+  x      - array of data points for independent variable
+  y      - array of data points for dependent variable
+  npts   - number of pairs of data points
+  nterms - number of terms in fitting polynomial
+  xin    - input value of x
+  yout   - interpolated value of y
+
+subroutines and function subprograms required 
+  none
+
+comments
+  valid for nterms up to 10
+  value of nterms may be modified by the program
diff --git a/math/bevington/man/legfit.3m b/math/bevington/man/legfit.3m
new file mode 100644
index 00000000..efe61c07
--- /dev/null
+++ b/math/bevington/man/legfit.3m
@@ -0,0 +1,49 @@
+.TH LEGFIT 3M
+.SH NAME
+legfit
+.SH DESCRIPTION
+subroutine legfit.f
+
+source
+  Bevington, pages 155-157.
+
+purpose
+  make least-squares fit to data with a Legendre polynomial
+    y = a(1) + a(2)*x + a(3)*(3x**2-1)/2 + ...
+      = a(1) * (1. + b(2)*x + b(3)*(3x**2-1)/2 + ... )
+      where x = cos(theta)
+
+usage
+  call legfit (theta, y, sigmay, npts, norder, neven, mode,
+    ftest, yfit, a, sigmaa, b, sigmab, chisqr)
+
+description of parameters
+  theta  - array of angles (in degrees) of the data points
+  y      - array of data points for dependent variable
+  sigmay - array of standard deivations for y data points
+  npts   - number of pairs of data points
+  norder - highest order of polynomial (number of terms - 1)
+  neven  - determines odd or even character of polynomial
+           +1 fits only to even terms
+            0 fits to all terms
+           -1 fits only to odd terms (plus constant term)
+  mode   - determines mode of weighting least-squares fit
+           +1 (instrumental) weight(i) = 1./sigmay(i)**2
+            0 (no weighting) weight(i) = 1.
+           -1 (statistical)  weight(i) = 1./y(i)
+  ftest  - array of values of f(l) for an f test
+  yfit   - array of calculated values of y
+  a      - array of coefficients of polynomial
+  sigmaa - array of standard deviations for coefficients
+  b      - array of normalized relative coefficients
+  sigmab - array of std. deviations of relative coefficients
+  chisqr - reduced chi square for fit
+
+subroutines and function subprograms required
+  matinv (array, nterms, det)
+    inverts symmetric two-dimension matrix of degree nterms
+      and calculates its determinant
+
+comments
+  valid for npts up to 100 and order up to 9
+  one source line modified - cos substituted for dcos
diff --git a/math/bevington/man/linfit.3m b/math/bevington/man/linfit.3m
new file mode 100644
index 00000000..e6e63f75
--- /dev/null
+++ b/math/bevington/man/linfit.3m
@@ -0,0 +1,33 @@
+.TH LINFIT 3M
+.SH NAME
+linfit
+.SH DESCRIPTION
+subroutine linfit.f
+
+source
+  Bevington, pages 104-105.
+
+purpose
+  make least-squares fit to a data set with a straight line
+
+usage
+  call linfit (x, y, sigmay, npts, mode, a, sigmaa,
+    b, sigmab, r)
+
+description of parameters
+  x      - array of data points for independent variable
+  y      - array of data points for dependent variable
+  sigmay - array of standard deviations for y data points
+  npts   - number of pairs of data points
+  mode   - determines method of weighting least-squares fit
+           +1 (instrumental) weight(i) = 1./sigmay(i)**2
+            0 (no weighting) weight(i) = 1.
+           -1 (statistical)  weight(i) = 1./y(i)
+  a      - y intercept of fitted straight line
+  sigmaa - standard deviation of a
+  b      - slope of fitted straight line
+  sigmab - standard deviation of b
+  r      - linear correlation coefficient
+
+subroutines and function subprograms required
+  none
diff --git a/math/bevington/man/matinv.3m b/math/bevington/man/matinv.3m
new file mode 100644
index 00000000..6b2d1c44
--- /dev/null
+++ b/math/bevington/man/matinv.3m
@@ -0,0 +1,25 @@
+.TH MATINV 3M
+.SH NAME
+matinv
+.SH DESCRIPTION
+subroutine matinv.f 
+
+source
+  Bevington, pages 302-303.
+
+purpose
+  invert a symmetric matrix and calculate its determinant
+
+usage 
+  call matinv (array, norder, det)
+
+description of parameters
+  array  - input matrix which is replaced by its inverse
+  norder - degree of matrix (order of determinant)
+  det    - determinant of input matrix
+
+subroutines and function subprograms required 
+  none
+
+comments
+  valid for norder up to 10
diff --git a/math/bevington/man/pbinom.3m b/math/bevington/man/pbinom.3m
new file mode 100644
index 00000000..344a62b3
--- /dev/null
+++ b/math/bevington/man/pbinom.3m
@@ -0,0 +1,23 @@
+.TH PBINOM 3M
+.SH NAME
+pbinom
+.SH DESCRIPTION
+function pbinom.f
+
+source
+  Bevington, page 31.
+
+purpose
+  evaluate binomial probability coefficient
+
+usage
+  result = pbinom (nobs, ntotal, prob)
+
+description of parameters
+  nobs   - number of items observed
+  ntotal - total number of items
+  prob   - probability of observing each item
+
+subroutines and function subprograms required
+  factor (n)
+    calculates n factorial for integers
diff --git a/math/bevington/man/pchisq.3m b/math/bevington/man/pchisq.3m
new file mode 100644
index 00000000..1f4c6742
--- /dev/null
+++ b/math/bevington/man/pchisq.3m
@@ -0,0 +1,26 @@
+.TH PCHISQ 3M
+.SH NAME
+pchisq
+.SH DESCRIPTION
+function pchisq.f
+
+source
+  Bevington, pages 192-193.
+
+purpose
+  evaluate probability for exceeding chi square
+
+usage
+  result = pchisq (chisqr, nfree)
+
+description of parameters
+  chisqr - comparison value of reduced chi square
+  nfree  - number of degrees of freedom
+
+subroutines and function subprograms required
+  gamma (x)
+    calculates gamma function for integers and 1/2-integers
+
+comments
+  calculation is approximate for nfree odd and
+    chi square greater than 50
diff --git a/math/bevington/man/pcorre.3m b/math/bevington/man/pcorre.3m
new file mode 100644
index 00000000..832c6640
--- /dev/null
+++ b/math/bevington/man/pcorre.3m
@@ -0,0 +1,22 @@
+.TH PCORRE 3M
+.SH NAME
+pcorre
+.SH DESCRIPTION
+function pcorre.f
+
+source
+  Bevington, pages 124-125.
+
+purpose
+  evaluate probability of no correlation between 2 variables
+
+usage
+  result = pcorre (r, npts)
+
+description of parameters
+  r      - linear correlation coefficient
+  npts   - number of data points
+
+subroutines and function subprograms required
+  gamma (x)
+    calculates gamma function for integers and 1/2-integers
diff --git a/math/bevington/man/pgauss.3m b/math/bevington/man/pgauss.3m
new file mode 100644
index 00000000..4f0c7c7d
--- /dev/null
+++ b/math/bevington/man/pgauss.3m
@@ -0,0 +1,22 @@
+.TH PGAUSS 3M
+.SH NAME
+pgauss
+.SH DESCRIPTION
+function pgauss.f
+
+source
+  Bevington, page 45.
+
+purpose
+  evaluate Gaussian probability function
+
+usage
+  result = pgauss (x, averag, sigma)
+
+description of parameters
+  x      - value for which probability is to be evaluated
+  averag - mean of distribution
+  sigma  - standard deviation of distribution
+
+subroutines and function subprograms required
+  none
diff --git a/math/bevington/man/ploren.3m b/math/bevington/man/ploren.3m
new file mode 100644
index 00000000..dfd485f5
--- /dev/null
+++ b/math/bevington/man/ploren.3m
@@ -0,0 +1,22 @@
+.TH PLOREN 3M
+.SH NAME
+ploren
+.SH DESCRIPTION
+function ploren.f
+
+source
+  Bevington, page 51.
+
+purpose
+  evaluate Lorentzian probability function
+
+usage
+  result = ploren (x, averag, width)
+
+description of parameters
+  x      - value for which probability is to be evaluated
+  averag - mean of distribution
+  width  - full width at half maximum of distribution
+
+subroutines and function subprograms required
+  none
diff --git a/math/bevington/man/polfit.3m b/math/bevington/man/polfit.3m
new file mode 100644
index 00000000..9553e619
--- /dev/null
+++ b/math/bevington/man/polfit.3m
@@ -0,0 +1,36 @@
+.TH POLFIT 3M
+.SH NAME
+polfit
+.SH DESCRIPTION
+subroutine polfit.f 
+
+source
+  Bevington, pages 140-142.
+
+purpose
+  make least-squares fit to data with a polynomial curve
+    y = a(1) + a(2)*x + a(3)*x**2 + a(3)*x**3 + . . .
+
+usage 
+  call polfit (x, y, sigmay, npts, nterms, mode, a, chisqr)
+
+description of parameters
+  x      - array of data points for independent variable
+  y      - array of data points for dependent variable
+  sigmay - array of standard deviations for y data points
+  npts   - number of pairs of data points
+  nterms - number of coefficients (degree of polynomial + 1)
+  mode   - determines method of weighting least-squares fit
+           +1 (instrumental) weight(i) = 1./sigmay(i)**2
+            0 (no weighting) weight(i) = 1.
+           -1 (statistical)  weight(i) = 1./y(i)
+  a      - array of coefficients of polynomial
+  chisqr - reduced chi square for fit 
+
+subroutines and function subprograms required 
+  determ (array, norder)
+    evaluates the determinant of a symetrical
+      two-dimension matrix of order norder
+
+comments
+  valid for nterms up to 10
diff --git a/math/bevington/man/ppoiss.3m b/math/bevington/man/ppoiss.3m
new file mode 100644
index 00000000..0197768f
--- /dev/null
+++ b/math/bevington/man/ppoiss.3m
@@ -0,0 +1,22 @@
+.TH PPOISS 3M
+.SH NAME
+ppoiss
+.SH DESCRIPTION
+function ppoiss.f
+
+source
+  Bevington, page 39.
+
+purpose
+  evaluate Poisson probability function
+
+usage
+  result = ppoiss (nobs, averag)
+
+description of parameters
+  nobs   - number of items observed
+  averag - mean of distribution
+
+subroutines and function subprograms required
+  factor (n)
+    calculates n factorial for integers
diff --git a/math/bevington/man/regres.3m b/math/bevington/man/regres.3m
new file mode 100644
index 00000000..e8cf076d
--- /dev/null
+++ b/math/bevington/man/regres.3m
@@ -0,0 +1,49 @@
+.TH REGRES 3M
+.SH NAME
+regres
+.SH DESCRIPTION
+subroutine regres.f
+
+source
+  Bevington, pages 172-175.
+
+purpose
+  make mulitple linear regression fit to data with specified
+    function which is linear in coefficients
+
+usage
+  call regres (x, y, sigmay, npts, nterms, m, mode, yfit,
+    a0, a, sigma0, sigmaa, r, rmul, chisqr, ftest)
+
+description of parameters
+  x      - array of points for independent variable
+  y      - array of points for dependent variable
+  sigmay - array of standard deviations for y data points
+  npts   - number of pairs of data points
+  nterms - number of coefficients
+  m      - array of inclusion/rejection criteria for fctn
+  mode   - determines method of weighting least-squares fit
+           +1 (instrumental) weight(i) = 1./sigmay(i)**2
+            0 (no weighting) weight(i) = 1.
+           -1 (statistical)  weight(i) = 1./y(i)
+  yfit   - array of calculated values of y
+  a0     - constant term
+  a      - array of coefficients
+  sigma0 - standard deviation of a0
+  sigmaa - array of standard deviations for coefficients
+  r      - array of linear correlation coefficients
+  rmul   - multiple linear correlation coefficient
+  chisqr - reduced chi square for fit
+  ftest  - value of f for test of fit
+
+subroutines and function subprograms required
+  fctn (x, i, j, m)
+    evaluates function for the jth term and the ith data
+      point using array m to specify terms in function
+  matinv (array, nterms, det)
+    inverts symmetric two-dimension matrix of degree nterms
+      and calculates its determinant
+
+comments
+  valid for npts up to 100 and nterms up to 10
+  one source line modified - sigmaa substituted for sigmaag
diff --git a/math/bevington/man/smooth.3m b/math/bevington/man/smooth.3m
new file mode 100644
index 00000000..6db69d22
--- /dev/null
+++ b/math/bevington/man/smooth.3m
@@ -0,0 +1,21 @@
+.TH SMOOTH 3M
+.SH NAME
+smooth
+.SH DESCRIPTION
+subroutine smooth.f
+
+source
+  Bevington, page 260.
+
+purpose
+  smooth a set of data points by averaging adjacent channels
+
+usage
+  call smooth (y, npts)
+
+description of parameters
+  y      - array of data points
+  npts   - number of data points
+
+subroutines and function subprograms required
+  none
diff --git a/math/bevington/man/xfit.3m b/math/bevington/man/xfit.3m
new file mode 100644
index 00000000..53ed8ae8
--- /dev/null
+++ b/math/bevington/man/xfit.3m
@@ -0,0 +1,29 @@
+.TH XFIT 3M
+.SH NAME
+xfit
+.SH DESCRIPTION
+subroutine xfit.f
+
+source
+  Bevington, page 76.
+
+purpose
+  calculate mean and estimated errors for set of data points
+
+usage
+  call xfit (x, sigmax, npts, mode, xmean, sigmam, sigma)
+
+description of parameters
+  x      - array of data points
+  sigmax - array of standard deviations for data points
+  npts   - number of data points
+  mode   - determines method of weighting
+           +1 (instrumental) weight(i) = 1./sigmax(i)**2
+            0 (no weighting) weight(i) = 1.
+           -1 (statistical)  weight(i) = 1.
+  xmean  - weighted mean
+  sigmam - standard deviation of mean
+  sigma  - standard deviation of data
+
+subroutines and function subprograms required
+  none
diff --git a/math/bevington/matinv.f b/math/bevington/matinv.f
new file mode 100644
index 00000000..5b1815c2
--- /dev/null
+++ b/math/bevington/matinv.f
@@ -0,0 +1,96 @@
+C SUBROUTINE MATINV.F 
+C
+C SOURCE								       
+C   BEVINGTON, PAGES 302-303.
+C
+C PURPOSE
+C   INVERT A SYMMETRIC MATRIX AND CALCULATE ITS DETERMINANT
+C
+C USAGE 
+C   CALL MATINV (ARRAY, NORDER, DET)
+C
+C DESCRIPTION OF PARAMETERS
+C   ARRAY  - INPUT MATRIX WHICH IS REPLACED BY ITS INVERSE
+C   NORDER - DEGREE OF MATRIX (ORDER OF DETERMINANT)
+C   DET    - DETERMINANT OF INPUT MATRIX
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED 
+C   NONE
+C
+C COMMENT
+C   DIMENSION STATEMENT VALID FOR NORDER UP TO 10
+C
+	SUBROUTINE MATINV (ARRAY,NORDER,DET)
+	DOUBLE PRECISION ARRAY,AMAX,SAVE
+	DIMENSION ARRAY(10,10),IK(10),JK(10)
+C
+10	DET=1.
+11	DO 100 K=1,NORDER
+C
+C FIND LARGEST ELEMENT ARRAY(I,J) IN REST OF MATRIX
+C
+	AMAX=0. 
+21	DO 30 I=K,NORDER
+	DO 30 J=K,NORDER
+23	IF (DABS(AMAX)-DABS(ARRAY(I,J))) 24,24,30
+24	AMAX=ARRAY(I,J) 
+	IK(K)=I 
+	JK(K)=J 
+30	CONTINUE
+C
+C INTERCHANGE ROWS AND COLUMNS TO PUT AMAX IN ARRAY(K,K)
+C
+31	IF (AMAX) 41,32,41
+32	DET=0.
+	GOTO 140
+41	I=IK(K) 
+	IF (I-K) 21,51,43
+43	DO 50 J=1,NORDER
+	SAVE=ARRAY(K,J) 
+	ARRAY(K,J)=ARRAY(I,J)
+50	ARRAY(I,J)=-SAVE
+51	J=JK(K) 
+	IF (J-K) 21,61,53
+53	DO 60 I=1,NORDER
+	SAVE=ARRAY(I,K) 
+	ARRAY(I,K)=ARRAY(I,J)
+60	ARRAY(I,J)=-SAVE
+C
+C ACCUMULATE ELEMENTS OF INVERSE MATRIX 
+C
+61	DO 70 I=1,NORDER
+	IF (I-K) 63,70,63
+63	ARRAY(I,K)=-ARRAY(I,K)/AMAX
+70	CONTINUE
+71	DO 80 I=1,NORDER
+	DO 80 J=1,NORDER
+	IF (I-K) 74,80,74
+74	IF (J-K) 75,80,75
+75	ARRAY(I,J)=ARRAY(I,J)+ARRAY(I,K)*ARRAY(K,J)
+80	CONTINUE
+81	DO 90 J=1,NORDER
+	IF (J-K) 83,90,83
+83	ARRAY(K,J)=ARRAY(K,J)/AMAX
+90	CONTINUE
+	ARRAY(K,K)=1./AMAX
+100	DET=DET*AMAX
+C
+C RESTORE ORDERING OF MATRIX
+C
+101	DO 130 L=1,NORDER
+	K=NORDER-L+1
+	J=IK(K) 
+	IF (J-K) 111,111,105
+105	DO 110 I=1,NORDER
+	SAVE=ARRAY(I,K) 
+	ARRAY(I,K)=-ARRAY(I,J)
+110	ARRAY(I,J)=SAVE 
+111	I=JK(K) 
+	IF (I-K) 130,130,113
+113	DO 120 J=1,NORDER
+	SAVE=ARRAY(K,J) 
+	ARRAY(K,J)=-ARRAY(I,J)
+120	ARRAY(I,J)=SAVE 
+130	CONTINUE
+140	RETURN
+	END
diff --git a/math/bevington/mkpkg b/math/bevington/mkpkg
new file mode 100644
index 00000000..5d9bef3f
--- /dev/null
+++ b/math/bevington/mkpkg
@@ -0,0 +1,35 @@
+# Make the Bevington library.
+
+$checkout libbev.a lib$
+$update   libbev.a
+$checkin  libbev.a lib$
+$exit
+
+libbev.a:
+	agauss.f
+	area.f
+	chifit.f
+	curfit.f
+	determ.f
+	factor.f
+	fchisq.f
+	fderiv.f
+	gamma.f
+	gradls.f
+	gridls.f
+	integ.f
+	interp.f
+	legfit.f
+	linfit.f
+	matinv.f
+	pbinom.f
+	pchisq.f
+	pcorre.f
+	pgauss.f
+	ploren.f
+	polfit.f
+	ppoiss.f
+	regres.f
+	smooth.f
+	xfit.f
+	;
diff --git a/math/bevington/pbinom.f b/math/bevington/pbinom.f
new file mode 100644
index 00000000..325f6f70
--- /dev/null
+++ b/math/bevington/pbinom.f
@@ -0,0 +1,26 @@
+c function pbinom.f
+c
+c source
+c   Bevington, page 31.
+c
+c purpose
+c   evaluate binomial probability coefficient
+c
+c usage
+c   result = pbinom (nobs, ntotal, prob)
+c
+c description of parameters
+c   nobs   - number of items observed
+c   ntotal - total number of items
+c   prob   - probability of observing each item
+c
+c subroutines and function subprograms required
+c   factor (n)
+c      calculates n factorial for integers
+c
+      function pbinom (nobs,ntotal,prob)
+1     notobs=ntotal-nobs
+2     pbinom=factor(ntotal)/(factor(nobs)*factor(notobs))*
+     *       (prob**nobs)*(1.-prob)**notobs
+      return
+      end
diff --git a/math/bevington/pchisq.f b/math/bevington/pchisq.f
new file mode 100644
index 00000000..0dbe6d9b
--- /dev/null
+++ b/math/bevington/pchisq.f
@@ -0,0 +1,62 @@
+c function pchisq.f
+c
+c source
+c   Bevington, pages 192-193.
+c
+c purpose
+c   evaluate probability for exceeding chi square
+c
+c usage
+c   result = pchisq (chisqr, nfree)
+c
+c description of parameters
+c   chisqr - comparison value of reduced chi square
+c   nfree  - number of degrees of freedom
+c
+c subroutines and function subprograms required
+c   gamma (x)
+c      calculates gamma function for integers and half-integers
+c
+c comments
+c   calculation is approximate for nfree odd and
+c      chi square greater than 50
+c
+	function pchisq (chisqr,nfree)
+	double precision z,term,sum
+11	if (nfree) 12,12,14
+12	pchisq=0.
+	goto 60
+14	free=nfree
+	z=chisqr*free/2.
+	neven=2*(nfree/2)
+	if (nfree-neven) 21,21,41
+c
+c number of degrees of freedom is even
+c
+21	imax=nfree/2
+	term=1.
+	sum=0.
+31	do 34 i=1,imax
+	fi=i
+	sum=sum+term
+34	term=term*z/fi
+35	pchisq=sum*dexp(z)
+	goto 60
+c
+c number of degrees of freedom is odd
+c
+41	if (z-25) 44,44,42
+42	z=chisqr*(free-1.)/2.
+	goto 21
+44	pwr=free/2.
+	term=1.
+	sum=term/pwr
+51	do 56 i=1,1000
+	fi=i
+	term=-term*z/fi
+	sum=sum+term/(pwr+fi)
+55	if (dabs(term/sum)-0.00001) 57,57,56
+56	continue
+57	pchisq=1.-(z**pwr)*sum/gamma(pwr)
+60	return
+	end
diff --git a/math/bevington/pcorre.f b/math/bevington/pcorre.f
new file mode 100644
index 00000000..9c0b0ae3
--- /dev/null
+++ b/math/bevington/pcorre.f
@@ -0,0 +1,69 @@
+c function pcorre.f
+c
+c source
+c   Bevington, pages 124-125.
+c
+c purpose
+c   evaluate probability for no correlation between two variables
+c
+c usage
+c   result = pcorre (r, npts)
+c
+c description of parameters
+c   r      - linear correlation coefficient
+c   npts   - number of data points
+c
+c subroutines and function subprograms required
+c   gamma (x)
+c      calculates gamma function for integers and half-integers
+c
+	function pcorre (r,npts)
+	double precision r2,term,sum,fi,fnum,denom
+c
+c evaluate number of degrees of freedom
+c
+11	nfree=npts-2
+	if (nfree) 13,13,15
+13	pcorre=0.
+	goto 60
+15	r2=r**2
+	if (1.-r2) 13,13,17
+17	neven=2*(nfree/2)
+	if (nfree-neven) 21,21,41
+c
+c number of degrees of freedom is even
+c
+21	imax=(nfree-2)/2
+	free=nfree
+23	term=abs(r)
+	sum=term
+	if (imax) 60,26,31
+26	pcorre=1.-term
+	goto 60
+31	do 36 i=1,imax
+	fi=i
+	fnum=imax-i+1
+	denom=2*i+1
+	term=-term*r2*fnum/fi
+36	sum=sum+term/denom
+	pcorre=1.128379167*(gamma((free+1.)/2.)/gamma(free/2.))
+	pcorre=1.-pcorre*sum
+	goto 60
+c
+c number of degrees of freedom is odd
+c
+41	imax=(nfree-3)/2
+42	term=abs(r)*dsqrt(1.-r2)
+43	sum=datan(r2/term)
+	if (imax) 57,45,51
+45	sum=sum+term
+	goto 57
+51	sum=sum+term
+52	do 56 i=1,imax
+	fnum=2*i
+	denom=2*i+1
+	term=term*(1.-r2)*fnum/denom
+56	sum=sum+term
+57	pcorre=1.-0.6366197724*sum
+60	return
+	end
diff --git a/math/bevington/pgauss.f b/math/bevington/pgauss.f
new file mode 100644
index 00000000..56cf5d4e
--- /dev/null
+++ b/math/bevington/pgauss.f
@@ -0,0 +1,25 @@
+c function pgauss.f
+c
+c source
+c   Bevington, page 45.
+c
+c purpose
+c   evaluate gaussian probability function
+c
+c usage
+c   result = pgauss (x, averag, sigma)
+c
+c description of parameters
+c   x      - value for which probability is to be evaluated
+c   averag - mean of distribution
+c   sigma  - standard deviation of distribution
+c
+c subroutines and function subprograms required
+c   none
+c
+	function pgauss (x,averag,sigma)
+	double precision z
+1	z=(x-averag)/sigma
+2	pgauss=0.3989422804/sigma*dexp(-(z**2)/2.)
+	return
+	end
diff --git a/math/bevington/ploren.f b/math/bevington/ploren.f
new file mode 100644
index 00000000..20fcb7c3
--- /dev/null
+++ b/math/bevington/ploren.f
@@ -0,0 +1,23 @@
+c function ploren.f
+c
+c source
+c   Bevington, page 51.
+c
+c purpose
+c   evaluate lorentzian probability function
+c
+c usage
+c   result = ploren (x, averag, width)
+c
+c description of parameters
+c   x      - value for which probability is to be evaluated
+c   averag - mean of distribution
+c   width  - full width at half maximum of distribution
+c
+c subroutines and function subprograms required
+c   none
+c
+	function ploren (x,averag,width)
+1	ploren=0.1591549431*width/((x-averag)**2+(width/2.)**2)
+	return
+	end
diff --git a/math/bevington/polfit.f b/math/bevington/polfit.f
new file mode 100644
index 00000000..cfbdb178
--- /dev/null
+++ b/math/bevington/polfit.f
@@ -0,0 +1,100 @@
+C SUBROUTINE POLFIT.F 
+C
+C SOURCE
+C   BEVINGTON, PAGES 140-142.
+C
+C PURPOSE
+C   MAKE A LEAST-SQUARES FIT TO DATA WITH A POLYNOMIAL CURVE
+C      Y = A(1) + A(2)*X + A(3)*X**2 + A(3)*X**3 + . . .
+C
+C USAGE 
+C   CALL POLFIT (X, Y, SIGMAY, NPTS, NTERMS, MODE, A, CHISQR)
+C
+C DESCRIPTION OF PARAMETERS
+C   X	   - ARRAY OF DATA POINTS FOR INDEPENDENT VARIABLE
+C   Y	   - ARRAY OF DATA POINTS FOR DEPENDENT VARIABLE
+C   SIGMAY - ARRAY OF STANDARD DEVIATIONS FOR Y DATA POINTS
+C   NPTS   - NUMBER OF PAIRS OF DATA POINTS
+C   NTERMS - NUMBER OF COEFFICIENTS (DEGREE OF POLYNOMIAL + 1)
+C   MODE   - DETERMINES METHOD OF WEIGHTING LEAST-SQUARES FIT
+C	     +1 (INSTRUMENTAL) WEIGHT(I) = 1./SIGMAY(I)**2
+C	      0 (NO WEIGHTING) WEIGHT(I) = 1.
+C	     -1 (STATISTICAL)  WEIGHT(I) = 1./Y(I)
+C   A	   - ARRAY OF COEFFICIENTS OF POLYNOMIAL
+C   CHISQR - REDUCED CHI SQUARE FOR FIT 
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED 
+C   DETERM (ARRAY, NORDER)
+C      EVALUATES THE DETERMINANT OF A SYMETRICAL
+C      TWO-DIMENSIONAL MATRIX OF ORDER NORDER
+C
+C COMMENTS
+C   DIMENSION STATEMENT VALID FOR NTERMS UP TO 10
+C
+	SUBROUTINE POLFIT (X,Y,SIGMAY,NPTS,NTERMS,MODE,A,CHISQR)
+	DOUBLE PRECISION SUMX,SUMY,XTERM,YTERM,ARRAY,CHISQ
+	DIMENSION X(1),Y(1),SIGMAY(1),A(1)
+	DIMENSION SUMX(19),SUMY(10),ARRAY(10,10)
+C
+C ACCUMULATE WEIGHTED SUMS
+C
+11	NMAX=2*NTERMS-1 
+	DO 13 N=1,NMAX
+13	SUMX(N)=0.
+	DO 15 J=1,NTERMS
+15	SUMY(J)=0.
+	CHISQ=0.
+21	DO 50 I=1,NPTS
+	XI=X(I) 
+	YI=Y(I) 
+31	IF (MODE) 32,37,39
+32	IF (YI) 35,37,33
+33	WEIGHT=1./YI
+	GOTO 41 
+35	WEIGHT=1./(-YI) 
+	GOTO 41 
+37	WEIGHT=1.
+	GOTO 41 
+39	WEIGHT=1./SIGMAY(I)**2
+41	XTERM=WEIGHT
+	DO 44 N=1,NMAX
+	SUMX(N)=SUMX(N)+XTERM
+44	XTERM=XTERM*XI
+45	YTERM=WEIGHT*YI 
+	DO 48 N=1,NTERMS
+	SUMY(N)=SUMY(N)+YTERM
+48	YTERM=YTERM*XI
+49	CHISQ=CHISQ+WEIGHT*YI**2
+50	CONTINUE
+C
+C CONSTRUCT MATRICES AND CALCULATE COEFFICIENTS 
+C
+51	DO 54 J=1,NTERMS
+	DO 54 K=1,NTERMS
+	N=J+K-1 
+54	ARRAY(J,K)=SUMX(N)
+	DELTA=DETERM (ARRAY,NTERMS)
+	IF (DELTA) 61,57,61
+57	CHISQR=0.
+	DO 59 J=1,NTERMS
+59	A(J)=0. 
+	GOTO 80 
+61	DO 70 L=1,NTERMS
+62	DO 66 J=1,NTERMS
+	DO 65 K=1,NTERMS
+	N=J+K-1 
+65	ARRAY(J,K)=SUMX(N)
+66	ARRAY(J,L)=SUMY(J)
+70	A(L)=DETERM (ARRAY,NTERMS) /DELTA
+C
+C CALCULATE CHI SQUARE
+C
+71	DO 75 J=1,NTERMS
+	CHISQ=CHISQ-2.*A(J)*SUMY(J)
+	DO 75 K=1,NTERMS
+	N=J+K-1 
+75	CHISQ=CHISQ+A(J)*A(K)*SUMX(N)
+76	FREE=NPTS-NTERMS
+77	CHISQR=CHISQ/FREE
+80	RETURN
+	END
diff --git a/math/bevington/ppoiss.f b/math/bevington/ppoiss.f
new file mode 100644
index 00000000..4782fde8
--- /dev/null
+++ b/math/bevington/ppoiss.f
@@ -0,0 +1,23 @@
+c function ppoiss.f
+c
+c source
+c   Bevington, page 39.
+c
+c purpose
+c   evaluate poisson probability function
+c
+c usage
+c   result = ppoiss (nobs, averag)
+c
+c description of parameters
+c   nobs   - number of items observed
+c   averag - mean of distribution
+c
+c subroutines and function subprograms required
+c   factor (n)
+c      calculates n factorial for integers
+c
+	function ppoiss (nobs,averag)
+1	ppoiss=((averag**nobs)/factor(nobs))*exp(-averag)
+	return
+	end
diff --git a/math/bevington/regres.f b/math/bevington/regres.f
new file mode 100644
index 00000000..ef23a574
--- /dev/null
+++ b/math/bevington/regres.f
@@ -0,0 +1,173 @@
+c subroutine regres.f
+c
+c source
+c   Bevington, pages 172-175.
+c
+c purpose
+c   make a mulitple linear regression fit to data with a specified
+c      function which is linear in coefficients
+c
+c usage
+c   call regres (x, y, sigmay, npts, nterms, m, mode, yfit,
+c      a0, a, sigma0, sigmaa, r, rmul, chisqr, ftest)
+c
+c description of parameters
+c   x	   - array of points for independent variable
+c   y	   - array of points for dependent variable
+c   sigmay - array of standard deviations for y data points
+c   npts   - number of pairs of data points
+c   nterms - number of coefficients
+c   m	   - array of inclusion/rejection criteria for fctn
+c   mode   - determines method of weighting least-squares fit
+c	     +1 (instrumental) weight(i) = 1./sigmay(i)**2
+c	      0 (no weighting) weight(i) = 1.
+c	     -1 (statistical)  weight(i) = 1./y(i)
+c   yfit   - array of calculated values of y
+c   a0	   - constant term
+c   a	   - array of coefficients
+c   sigma0 - standard deviation of a0
+c   sigmaa - array of standard deviations for coefficients
+c   r	   - array of linear correlation coefficients
+c   rmul   - multiple linear correlation coefficient
+c   chisqr - reduced chi square for fit
+c   ftest  - value of f for test of fit
+c
+c subroutines and function subprograms required
+c   fctn (x, i, j, m)
+c      evaluates the function for the jth term and the ith data point
+c      using the array m to specify terms in the function
+c   matinv (array, nterms, det)
+c      inverts a symmetric two-dimensional matrix of degree nterms
+c      and calculates its determinant
+c
+c comments
+c (dim npts changed 100->1000 21-may-84 dct)
+c   dimension statement valid for npts up to 100 and nterms up to 10
+c   sigmaag changed to sigmaa in statement following statement 132
+c
+      subroutine regres (x,y,sigmay,npts,nterms,m,mode,yfit,
+     *a0,a,sigma0,sigmaa,r,rmul,chisqr,ftest)
+      double precision array,sum,ymean,sigma,chisq,xmean,sigmax
+      dimension x(1),y(1),sigmay(1),m(1),yfit(1),a(1),sigmaa(1),
+     *r(1)
+      dimension weight(1000),xmean(10),sigmax(10),array(10,10)
+      REAL FCTN
+      EXTERNAL FCTN
+
+c
+c initialize sums and arrays
+c
+11    sum=0.
+      ymean=0.
+      sigma=0.
+      chisq=0.
+      rmul=0.
+      do 17 i=1,npts
+17    yfit(i)=0.
+21    do 28 j=1,nterms
+      xmean(j)=0.
+      sigmax(j)=0.
+      r(j)=0.
+      a(j)=0.
+      sigmaa(j)=0.
+      do 28 k=1,nterms
+28    array(j,k)=0.
+c
+c accumulate weighted sums
+c
+30    do 50 i=1,npts
+31    if (mode) 32,37,39
+32    if (y(i)) 35,37,33
+33    weight(i)=1./y(i)
+      goto 41
+35    weight(i)=1./(-y(i))
+      goto 41
+37    weight(i)=1.
+      goto 41
+39    weight(i)=1./sigmay(i)**2
+41    sum=sum+weight(i)
+      ymean=ymean+weight(i)*y(i)
+      do 44 j=1,nterms
+44    xmean(j)=xmean(j)+weight(i)*fctn(x,i,j,m)
+50    continue
+51    ymean=ymean/sum
+      do 53 j=1,nterms
+53    xmean(j)=xmean(j)/sum
+      fnpts=npts
+      wmean=sum/fnpts
+      do 57 i=1,npts
+57    weight(i)=weight(i)/wmean
+c
+c accumulate matrices r and array
+c
+61    do 67 i=1,npts
+      sigma=sigma+weight(i)*(y(i)-ymean)**2
+      do 67 j=1,nterms
+      sigmax(j)=sigmax(j)+weight(i)*(fctn(x,i,j,m)-xmean(j))**2
+      r(j)=r(j)+weight(i)*(fctn(x,i,j,m)-xmean(j))*(y(i)-ymean)
+      do 67 k=1,j
+67    array(j,k)=array(j,k)+weight(i)*(fctn(x,i,j,m)-xmean(j))*
+     *(fctn(x,i,k,m)-xmean(k))
+71    free1=npts-1
+72    sigma=dsqrt(sigma/free1)
+      do 78 j=1,nterms
+74    sigmax(j)=dsqrt(sigmax(j)/free1)
+      r(j)=r(j)/(free1*sigmax(j)*sigma)
+      do 78 k=1,j
+      array(j,k)=array(j,k)/(free1*sigmax(j)*sigmax(k))
+78    array(k,j)=array(j,k)
+c
+c invert symmetric matrix
+c
+81    call matinv (array,nterms,det)
+      if (det) 101,91,101
+91    a0=0.
+      sigma0=0.
+      rmul=0.
+      chisqr=0.
+      ftest=0.
+      goto 150
+c
+c calculate coefficients, fit, and chi square
+c
+101   a0=ymean
+102   do 108 j=1,nterms
+      do 104 k=1,nterms
+104   a(j)=a(j)+r(k)*array(j,k)
+105   a(j)=a(j)*sigma/sigmax(j)
+106   a0=a0-a(j)*xmean(j)
+107   do 108 i=1,npts
+108   yfit(i)=yfit(i)+a(j)*fctn(x,i,j,m)
+111   do 113 i=1,npts
+      yfit(i)=yfit(i)+a0
+113   chisq=chisq+weight(i)*(y(i)-yfit(i))**2
+      freen=npts-nterms-1
+115   chisqr=chisq*wmean/freen
+c
+c calculate uncertainties
+c
+121   if (mode) 122,124,122
+122   varnce=1./wmean
+      goto 131
+124   varnce=chisqr
+131   do 133 j=1,nterms
+132   sigmaa(j)=array(j,j)*varnce/(free1*sigmax(j)**2)
+      sigmaa(j)=sqrt(sigmaa(j))
+133   rmul=rmul+a(j)*r(j)*sigmax(j)/sigma
+      freej=nterms
+c +noao: When rmul = 1, the following division (stmt 135) would blow up.
+c        It has been changed so ftest is set to -99999. in this case.
+      if (1. - rmul) 135, 935, 135
+135   ftest=(rmul/freej)/((1.-rmul)/freen)
+      goto 136
+935   ftest = -99999.
+c -noao
+136   rmul=sqrt(rmul)
+141   sigma0=varnce/fnpts
+      do 145 j=1,nterms
+      do 145 k=1,nterms
+145   sigma0=sigma0+varnce*xmean(j)*xmean(k)*array(j,k)/
+     *(free1*sigmax(j)*sigmax(k))
+146   sigma0=sqrt(sigma0)
+150   return
+      end
diff --git a/math/bevington/smooth.f b/math/bevington/smooth.f
new file mode 100644
index 00000000..19c2c457
--- /dev/null
+++ b/math/bevington/smooth.f
@@ -0,0 +1,29 @@
+c subroutine smooth.f
+c
+c source
+c   Bevington, page 260.
+c
+c purpose
+c   smooth a set of data points by averaging adjacent channels
+c
+c usage
+c   call smooth (y, npts)
+c
+c description of parameters
+c   y	   - array of data points
+c   npts   - number of data points
+c
+c subroutines and function subprograms required
+c   none
+c
+	subroutine smooth (y,npts)
+	dimension y(1)
+11	imax=npts-1
+	yi=y(1)
+21	do 24 i=1,imax
+	ynew=(yi+2.*y(i)+y(i+1))/4.
+	yi=y(i)
+24	y(i)=ynew
+25	y(npts)=(yi+3.*y(npts))/4.
+	return
+	end
diff --git a/math/bevington/xfit.f b/math/bevington/xfit.f
new file mode 100644
index 00000000..a097d4af
--- /dev/null
+++ b/math/bevington/xfit.f
@@ -0,0 +1,59 @@
+c subroutine xfit.f
+c
+c source
+c   Bevington, page 76.
+c
+c purpose
+c   calculate the mean and estimated errors for a set of data points
+c
+c usage
+c   call xfit (x, sigmax, npts, mode, xmean, sigmam, sigma)
+c
+c description of parameters
+c   x      - array of data points
+c   sigmax - array of standard deviations for data points
+c   npts   - number of data points
+c   mode   - determines method of weighting
+c            +1 (instrumental) weight(i) = 1./sigmax(i)**2
+c             0 (no weighting) weight(i) = 1.
+c            -1 (statistical)  weight(i) = 1.
+c   xmean  - weighted mean
+c   sigmam - standard deviation of mean
+c   sigma  - standard deviation of data
+c
+c subroutines and function subprograms required
+c   none
+c
+	subroutine xfit (x,sigmax,npts,mode,xmean,sigmam,sigma)
+	double precision sum,sumx,weight,free
+	dimension x(1),sigmax(1)
+c
+c accumulate weighted sums
+c
+11	sum=0.
+	sumx=0.
+	sigma=0.
+	sigmam=0.
+20	do 32 i=1,npts
+21	if (mode) 22,22,24
+22	weight=1.
+	goto 31
+24	weight=1./sigmax(i)**2
+31	sum=sum+weight
+32	sumx=sumx+weight*x(i)
+c
+c evaluate mean and standard deviations
+c
+41	xmean=sumx/sum
+51	do 52 i=1,npts
+52	sigma=sigma+(x(i)-xmean)**2
+	free=npts-1
+54	sigma=dsqrt(sigma/free)
+61	if (mode) 62,64,66
+62	sigmam=dsqrt(xmean/sum)
+	goto 70
+64	sigmam=sigma/dsqrt(sum)
+	goto 70
+66	sigmam=dsqrt(1./sum)
+70	return
+	end
diff --git a/math/curfit/README b/math/curfit/README
new file mode 100644
index 00000000..b622c824
--- /dev/null
+++ b/math/curfit/README
@@ -0,0 +1,6 @@
+Linear Least squares curve fitting package.
+Contains routines to fit Legendre and Chebyshev polynomials and linear
+cubic splines in the least squares sense to 1-dimensional data.
+The normal equations are accumulated and solved using Cholesky factorization.
+The package contains separate entry points for accumulating points,
+solving the matrix equations, rejecting points and evaluating the curve.
diff --git a/math/curfit/Revisions b/math/curfit/Revisions
new file mode 100644
index 00000000..ea59404b
--- /dev/null
+++ b/math/curfit/Revisions
@@ -0,0 +1,118 @@
+.help revisions Jun89 math.curfit
+.nf
+From Davis, September 20, 1999
+
+Added some missing file dependices to the mkpkg file.
+pkg/math/curfit/mkpkg
+
+From Davis, March 20, 1997
+
+The weights computed by the WTS_CHISQ option in the routines cvacpts[rd]
+were not being forced to be positive as intended.
+math/curfit/cvacpts.gx
+math/curfit/cvacptsr.x
+math/curfit/cvacptsd.x
+
+There was an inconsistency in the way the ncoeff argument to the cvpower[rd]
+routines was being used. Ncoeff was intended to be an output argument.
+pkg/math/curfit/doc/cvpower.hlp
+pkg/math/curfit/cvpower.gx
+pkg/math/curfit/cvpowerr.x
+pkg/math/curfit/cvpowerd.x
+
+From Davis, June 13, 1995
+
+Added a new routine cvepower to the curfit math package. Cvepower computes
+errors of the equivalent power series coefficients for the fitted Legendre
+and Chebyshev polynomials and has the same calling sequence as the 
+cverrors routine.
+math/curfit/cvpower.gx
+math/curfit/cvpowerr.x
+math/curfit/cvpowerd.x
+math/curfit/doc/curfit.hd
+math/curfit/doc/curfit.men
+math/curfit/doc/cvepower.hlp
+
+From Davis, May, 6, 1990
+
+Finished cleaning up the .gx files in curfit.
+math/curfit/cverrors.gx
+math/curfit/cvpower.gx
+math/curfit/cvrefit.gx
+math/curfit/cvpower.gx
+
+From Davis, May 6, 1990
+
+Changed the constant from INDEFR to INDEF in the amov$t call in cvpower.gx.
+This was causing a problem for the Mac compiler.
+
+From Davis, April 23, 1991
+
+Did some cleaning up in the following .gx files to make the code easier to read.
+math/curfit/cv_b1eval.gx
+math/curfit/cv_beval.gx
+math/curfit/cv_feval.gx
+math/curfit/cvaccum.gx
+math/curfit/cvacpts.gx
+math/curfit/cvchomat.gx
+math/curfit/cvfree.gx
+math/curfit/cvinit.gx
+
+From Davis, September 18, 1990
+
+Changed the int calls in cvrestore.gx to nint calls. This is a totally
+safe way to do the conversion from double precision to integer
+quantities in the curfit package and removes any potential precision
+problems for task which must read the curfit structure back from a
+text database file.
+
+From Davis, July 14, 1988:
+
+The calling sequence for the cverrors routine as been changed to include
+an npts argument. This edition removesd the possibility for error when
+points have been rejected by setting w[i] = 0.
+
+-----------------------------------------------------------------------------
+
+From Davis, April 30, 1986:
+
+1. Several bugs involving double precision constants in the double precision
+version of curfit detected on the SUN have been fixed.
+
+-----------------------------------------------------------------------------
+
+From Davis, March 13, 1986:
+
+1. A double precision version of CURFIT has been installed in IRAF. The entry
+points for the double precision version are identical to those of the real
+version with the addition of a preceeding d (e.g. cveval and dcveval). All
+internal arithmetic is done in double and the data is entered in double.
+
+2. A user function facility has been added to CURFIT. The user may enter
+any linear function in the following manner.
+
+	extern func
+
+	...
+
+	call cvinit (cv, USERFNC, nterms, xmin, xmax)
+	call cvuser (cv, func)
+	call cvfit (cv, x, y, w, npts, WTS_USER, ier)
+	call cvvector (cv, x, yfit, npts)
+	call cvfree (cv)
+
+	...
+
+The user function must have the following form.
+
+	procedure func (x, nterms, k1, k2, basis)
+
+where
+
+	real	x		x value
+	int	nterms		number of basis functions
+	real	k1, k2		optional normalization parameters
+	real	basis[ARB]	computed basis functions
+
+-------------------------------------------------------------------------------
+.endhelp
diff --git a/math/curfit/curfit.sem b/math/curfit/curfit.sem
new file mode 100644
index 00000000..28058626
--- /dev/null
+++ b/math/curfit/curfit.sem
@@ -0,0 +1,708 @@
+# Semi-code for curfit.h
+
+# define the permitted types of curves
+
+define	CHEBYSHEV	1
+define	LEGENDRE	2
+define	L2SPLINE4	3
+
+# define the weighting flags
+
+define	NORMAL		1	# user enters weights
+define	UNIFORM		2	# equal weights, weight 1.0
+define	SPACING		3	# weigth proportional to spacing of data points
+
+define	SPLINE_ORDER	4
+
+# set up the curve fitting structure
+
+define	LEN_CVSTRUCT
+
+struct curfit {
+
+define	CV_TYPE		Memi[]		# Type of curve to be fitted
+define	CV_ORDER	Memi[]		# Order of the fit
+define	CV_NPIECES	Memi[]		# Number of polynomial pieces, spline
+define	CV_NCOEFF	Memi[]		# Number of coefficients
+define	CV_XMAX		Memr[]		# Maximum x value
+define	CV_XMIN		Memr[]		# Minimum x value
+define	CV_RANGE	Memr[]		# Xmax minus xmin
+define	CV_MAXMIN	Memr[]		# Xmax plus xmin
+define	CV_SPACING	Memr[]		# Knot spacing for splines
+define	CV_YNORM	Memr[]		# Norm of the Y vector
+define	CV_NPTS		Memi[]		# Number of data points
+
+define	CV_MATRIX	Memi[]		# Pointer to original matrix
+define	CV_CHOFAC	Memi[]		# Pointer to Cholesky factorization
+define	CV_BASIS	Memi[]		# Pointer to basis functions
+define	CV_VECTOR	Memi[]		# Pointer to  vector
+define	CV_COEFF	Memi[]		# Pointer to coefficient vector
+define	CV_LEFT		Memi[]		#
+
+}
+
+# matrix and vector element definitions
+
+define	MATRIX		Memr[$1+($2-1)*NCOEFF(cv)]	# Matrix element
+define	CHOFAC		Memr[$1+($2-1)*NCOEFF(cv)]	# Triangular matrix
+define	VECTOR		Memr[$1+$2]			# Right side
+define	COEFF		Memr[$1+$2]			# Coefficient vector
+define	LEFT		Memi[$1+$2]
+
+# matrix and vector definitions
+
+define	MAT		Memr[$1]
+define	CHO		Memr[$1]
+define	VECT		Memr[$1]
+define	COF		Memr[$1]
+
+# semi-code for the initialization procedure
+
+include "curfit.h"
+
+# CVINIT --  Procedure to set up the curve  descriptor.
+
+procedure cvinit (cv, curve_type, order, xmin, xmax)
+
+pointer	cv		# pointer to curve descriptor structure
+int	curve_type	# type of curve to be fitted
+int	order		# order of curve to be fitted, or in the case of the
+			# spline the number of polynomial pieces to be fit
+real	xmin		# minimum value of x
+real	xmax		# maximum value of x
+
+begin
+	# allocate space for the curve descriptor
+	call smark (sp)
+	call salloc (cv, LEN_CVSTRUCT, TY_STRUCT)
+
+	if (order < 1)
+	    call error (0, "CVINIT: Illegal order.")
+
+	if (xmax <= xmin)
+	    call error (0, "CVINIT: xmax <= xmin.")
+
+	switch (curve_type) {
+	case CHEBYSHEV, LEGENDRE:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(CV) = order
+	    CV_RANGE(cv) = xmax - xmin
+	    CV_MAXMIN(cv) = xmax + xmin
+	case L2SPLINE4:
+	    CV_ORDER(cv) = SPLINE_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE_ORDER - 1
+	    CV_NPIECES(cv) = order
+	    CV_SPACING(cv) = (xmax - xmin) / order
+	default:
+	    call error (0, "CVINIT: Unknown curve type.")
+	}
+
+	CV_TYPE(cv) = curve_type
+	CV_XMIN(cv) = xmin
+	CV_XMAX(cv) = xmax
+
+	# allocate space for the matrix and vectors
+	call calloc (CV_MATRIX(cv), CV_ORDER(cv)*CV_NCOEFF(cv), TY_REAL)
+	call calloc (CV_CHOFAC(cv), CV_ORDER(cv)*CV_NCOEFF(cv), TY_REAL)
+	call calloc (CV_VECTOR(cv), CV_NCOEFF(cv), TY_REAL)
+	call calloc (CV_COEFF(cv), CV_NCOEFF(cv), TY_REAL)
+
+	# initialize pointer to basis functions to null
+	CV_BASIS(cv) = NULL
+
+	CV_NPTS(cv) = 0
+	CV_YNORM(cv) = 0.
+end
+
+# semi-code for cvaccum
+
+include "curfit.h"
+
+# CVACCUM -- Procedure to add a single point to the data set.
+
+procedure cvaccum (cv, x, y, w, wtflag)
+
+pointer	cv		# curve descriptor
+real	x		# x value
+real	y		# y value
+real	w		# weight of the data point
+int	wtflag		# type of weighting desired
+
+begin
+	# calculate the weights
+	switch (wtflag) {
+	case UNIFORM:
+	    w = 1.0
+	case NORMAL, SPACING: 		# problem spacing
+	default:
+	    w = 1.0
+	}
+
+	# caculate all non-zero basis functions for a given data point
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 1
+	    call chebyshev (cv, x, basis)
+	case LEGENDRE:
+	    left = 1
+	    call legendre (cv, x, basis)
+	case L2SPLINE4:
+	    call l2spline4 (cv, x, left, basis)
+	}
+
+	# accumulate into the matrix
+	leftm1 = left - 1
+	vptr = CV_VECTOR(cv) - 1
+	do i = 1, CV_ORDER(cv) {
+	    bw = basis[i] * w
+	    jj = leftm1 + i
+	    mptr = CV_MATRIX(cv) + jj - 1
+	    VECTOR(vptr, jj) = VECTOR(vptr, jj) + bw * y
+	    ii = 1
+	    do j = i, CV_ORDER(cv) {
+		MATRIX(mptr, ii) = MATRIX(mptr, ii) + basis[j] * bw
+		ii = ii + 1
+	    }
+	}
+
+	CV_NPTS(cv) = CV_NPTS(cv) + 1
+	CV_YNORM(cv) = CV_YNORM(cv) + w * y * y
+end
+
+# semi-code for cvreject
+
+include "curfit.h"
+
+# CVREJECT -- Procedure to subtract a single datapoint from the data set
+# to be fitted.
+
+procedure cvreject (cv, x, y, w)
+
+pointer	cv		# curve fitting image descriptor
+real	x		# x value
+real	y		# y value
+real	w		# weight of the data point
+
+begin
+	# caculate all type non-zero basis functions for a given data point
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 1
+	    call chebyshev (cv, x, basis)
+	case LEGENDRE:
+	    left = 1
+	    call legendre (cv, x, basis)
+	case L2SPLINE4:
+	    call l2spline4 (cv, x, left, basis)
+	}
+
+	# subtract the data point from the matrix
+	leftm1 = left - 1
+	vptr = CV_VECTOR(cv) - 1
+	do i = 1, CV_ORDER(cv) {
+	    bw = basis[i] * w
+	    jj = leftm1 + i
+	    mptr = CV_MATRIX(cv) + jj - 1
+	    VECTOR(vptr, jj) = VECTOR(vptr, jj) - bw * y
+	    ii = 1
+	    do j = i, CV_ORDER(cv) {
+		MATRIX(mptr, ii) = MATRIX(mptr, ii) - basis[j] * bw
+		ii = ii + 1
+	    }
+	}
+
+	CV_NPTS(cv) = CV_NPTS(cv) - 1
+	CV_NORM(cv) = CV_NORM(cv) - w * y * y
+end
+
+# semi-code for cvsolve
+
+include "curfit.h"
+
+# CVSOLVE -- Procedure to  solve a matrix equation of the form Ax = B.
+# The Cholesky factorization of matrix A is calculated in the first
+# step, followed by forward and back substitution to solve for the vector
+# x.
+
+procedure cvsolve (cv, ier)
+
+pointer	cv 		# pointer to the image descriptor structure
+int	ier		# ier = 0, everything OK
+			# ier = 1, matrix is singular
+
+begin
+	# solve matrix by adapting Deboor's bchfac.f and bchslv.f routines
+	# so that the original matrix and vector are not destroyed
+
+	call chofac (MAT(CV_MATRIX(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		     CHO(CV_CHOFAC(cv)), ier)
+	call choslv (CHO(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		     VECT(CV_VECTOR(cv)), COF(CV_COEFF(cv)))
+end
+
+# semi-code for cvfit
+
+include "curfit.h"
+
+# CVFIT -- Procedure to fit a curve to an array of data points x and y with
+# weights w.
+
+procedure cvfit (x, y, w, npts, wtflag, ier)
+
+real	x[npts]		# array of abcissa
+real	y[npts]		# array of ordinates
+real	w[npts]		# array of weights
+int	wtflag		# type of weighting
+int	ier
+
+begin
+	# calculate weights
+	switch (wtflag) {
+	case UNIFORM:
+	    call amovkr (1., w, npts)
+	case SPACING:
+	    w[1] = x[2] - x[1]			# check for npts > 1
+	    do i = 2, npts - 1
+		w[i] = x[i+1] - x[i-1]
+	    w[npts] = x[npts] - x[npts-1]
+	case NORMAL:
+	default:
+	    call amovkr (1., w, npts)
+	}
+
+	# accumulate data points
+	do i = 1, npts {
+
+	    CV_NPTS(cv) = CV_NPTS(cv) + 1
+
+	    # calculate the norm of the Y vector
+	    CV_YNORM(cv) = CV_YNORM(cv) + w[i] * y[i] * y[i]
+
+	    # calculate non zero basis functions
+	    switch (CV_TYPE(cv)) {
+	    case CHEBYSHEV:
+		left = 1
+		call chebyshev (cv, x, basis)
+	    case LEGENDRE:
+		left = 1
+		call legendre (cv, x, basis)
+	    case L2SPLINE4:
+		call l2spline4 (cv, x, left, basis)
+	    }
+
+	    # accumulate the matrix
+	    leftm1 = left - 1
+	    vptr = CV_VECTOR(cv) - 1
+	    do i = 1, CV_ORDER(cv) {
+	        bw = basis[i] * w
+	        jj = leftm1 + i
+		mptr = CV_MATRIX(cv) + jj - 1
+	        VECTOR(vptr, jj) = VECTOR(vptr, jj) + bw * y
+	        ii = 1
+	        do j = i, CV_ORDER(cv) {
+		    MATRIX(mptr, ii) = MATRIX(mptr, ii) + basis[j] * bw
+		    ii = ii + 1
+	        }
+	    }
+	}
+
+	# solve the matrix
+	ier = 0
+	call chofac (MAT(CV_MATRIX(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		     CHO(CV_CHOFAC(cv)), ier)
+	call choslv (CHO(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		     VECT(CV_VECTOR(cv)), COF(CV_COEFF(cv)))
+end
+
+# semi-code for cvrefit
+
+include "curfit.com"
+
+# CV_REFIT -- Procedure to refit the data assuming that the x and w values do
+# not change.
+
+procedure cvrefit (cv, x, y, w, ier)
+
+pointer	cv
+real	x[ARB]
+real	y[ARB]
+real	w[ARB]
+int	ier
+
+begin
+	# if first call to refit then calculate and store the basis
+	# functions
+
+	vcptr = CV_VECTOR(cv) - 1
+	do i = 1, NCOEFF(cv)
+	    VECTOR(vcptr+i) = 0.
+
+	CV_YNORM(cv) = 0.
+	lptr = CV_LEFT(cv) - 1
+	bcptr = CV_BASIS(cv) - CV_NPTS(cv)
+
+	if (CV_BASIS(cv) == NULL) {
+
+	    call calloc (CV_BASIS(cv), CV_NPTS(cv)*CV_ORDER(cv), TY_REAL)
+	    call calloc (CV_LEFT(cv), CV_NPTS(cv), TY_INT)
+
+	    do l = 1, CV_NPTS(cv) {
+		bptr = bcptr + l * CV_NPTS(cv)
+		switch (CV_TYPE(cv)) {
+		case LEGENDRE:
+		    LEFT(lptr+l) = 1
+		    call legendre (cv, x, BASIS(bptr))
+		case CHEBYSHEV:
+		    LEFT(lptr+l) = 1
+		    call chebyshev (cv, x, BASIS(bptr))
+		case L2SPLINE4:
+		    call l2spline4 (cv, x, LEFT(lptr+l), BASIS(bptr))
+		}
+	    }
+	}
+
+	# reset vector to zero
+
+	# accumulate right side of the matrix equation
+	do l = 1, CV_NPTS(cv) {
+
+	    CV_YNORM(cv) = CV_YNORM(cv) + w[l] * y[l] * y[l]
+	    leftm1 = LEFT(lptr+l) - 1
+	    bptr = bcptr + l * CV_NPTS(cv) 
+
+	    do i = 1, CV_ORDER(cv) {
+		vptr = vcptr + leftm1 + i
+		VECTOR(vptr) = VECTOR(vptr) + BASIS(bptr) * w[l] * y[l]
+	    }
+	}
+
+	# solve the matrix
+	call choslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(CV),
+		    VECTOR(CV_VECTOR(cv)), COEFF(CV_COEFF(cv)))
+end
+
+# semi-code for cvcoeff
+
+# CVCOEFF -- Procedure to fetch the number and magnitude of the coefficients.
+
+procedure cvcoeff (cv, coeff, ncoeff)
+
+pointer	cv		# pointer to the curve fitting descriptor
+real	coeff[ncoeff]	# the coefficients of the fit
+int	ncoeff		# the number of coefficients
+
+begin
+	ncoeff = CV_NCOEFF(cv)
+	cptr = CV_COEFF(cv) - 1
+	do i = 1, ncoeff
+	    coeff[i] = COEFF(cptr, i)
+end
+
+# semi-code for cvvector
+
+include "curfit.h"
+
+# CVVECTOR -- Procedure to evaluate the fitted curve
+
+procedure cvvector (cv, x, npts, yfit)
+
+pointer	cv		# pointer to the curve descriptor structure
+real	x[npts]		# data x values
+int	npts		# number of data points
+real	yfit[npts]	# the fitted y values
+
+begin
+	do l = 1, npts {
+
+	    # calculate the non-zero basis functions
+	    switch (CV_TYPE(cv) {
+	    case LEGENDRE:
+		left = 1
+		call legendre (cv, x[l], XBASIS(CV_XBASIS(cv)))
+	    case CHEBYSHEV:
+		left = 1
+		call chebyshev (cv, x[l], XBASIS(CV_XBASIS(cv)))
+	    case L2SPLINE4:
+		call l2spline4 (cv, x[l], left, XBASIS(CV_XBASIS(cv)))
+	    }
+
+	    sum = 0.0
+	    leftm1 = left - 1
+	    cptr = CV_COEFF(cv) - 1
+	    xptr = CV_XBASIS(cv) - 1
+
+	    do i = 1, CV_NCOEFF(cv) {
+		jj = leftm1 + i
+		sum = sum + XBASIS(xptr + i) * COEFF(cptr + jj)
+	    }
+	}
+end
+
+# semi-code for cveval
+
+include "curfit.h"
+
+# CVEVAL -- Procedure to evaluate curve at a given x
+
+real procedure cveval (cv, x)
+
+pointer	cv		# pointer to image descriptor structure
+real	x		# x value
+
+int	left, leftm1, i
+pointer	cptr, xptr
+real	sum
+
+begin
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 1
+	    call chebyshev (cv, x, XBASIS(CV_XBASIS(cv)))
+	case LEGENDRE:
+	    left = 1
+	    call legendre (cv, x, XBASIS(CV_XBASIS(cv)))
+	case L2SPLINE4:
+	    call l2spline4 (cv, x, left, XBASIS(CV_XBASIS(cv)))
+	}
+
+	sum = 0.
+	leftm1 = left - 1
+	cptr = CV_COEFF(cv) - 1
+	xptr = CV_XBASIS(cv) - 1
+	do i = 1, CV_NCOEFF(cv) {
+	    jj = leftm1 + i
+	    sum = sum + XBASIS(xptr + i) * COEFF(cptr + jj)
+	}
+
+	return (sum)
+end
+
+# semi-code for cverrors
+
+include "curfit.h"
+
+# CVERRORS -- Procedure to calculate the standard deviation of the fit and the
+# standard deviations of the coefficients
+
+procedure cverrors (cv, rms, errors)
+
+pointer	cv		# curve descriptor
+real	rms		# standard deviation of data with respect to fit
+real	errors[ARB]	# errors in coefficients
+
+begin
+	# calculate the variance
+	rms = CV_YNORM(cv)
+	cptr = CV_COEFF(cv) - 1
+	vptr = CV_VECTOR(cv) - 1
+	do i = 1, CV_NCOEFF(cv)
+	    rms = rms - COEFF(cptr, i) * VECTOR(vptr, i)
+	rms = rms / (CV_NPTS(cv) - CV_NCOEFF(cv))
+
+	# calculate the standard deviations
+	do i = 1, CV_NCOEFF(cv) {
+	    do j = 1, CV_NCOEFF(cv)
+		cov[j] = 0.
+	    cov[i] = 1.
+	    call choslv (CHO(CV_CHOFAC(cv)), CV_ORDER(cv),
+	    		CV_NCOEFF(cv), cov, cov)
+	    errors[i] = sqrt (cov[i] * rms)
+	}
+
+	rms = sqrt (rms)
+end
+
+# semi-code for CVFREE
+
+# CVFREE -- Procedure to free the curve descriptor
+
+procedure cvfree (cv)
+
+pointer	cv
+
+begin
+	call sfree (cv)
+end
+
+include "curfit.h"
+
+# LEGENDRE -- Procedure to calculate the Legendre functions.
+
+procedure legendre (cv, x, basis)
+
+pointer	cv
+real	x
+real	basis[ARB]
+
+begin
+	# normalize to the range x = -1. to 1.
+	xnorm = (2. * x - CV_MAXMIN(cv)) / CV_RANGE(cv)
+
+	b[1] = 1.0
+	if (CV_ORDER(cv) == 1)
+	    return
+
+	b[2] = xnorm
+	if (CV_ORDER(cv) == 2)
+	    return
+
+	do i = 3, CV_ORDER(cv) {
+	    ri = i
+	    b[i] = ((2.*ri-3.)*xnorm*b[i-1] - (ri-2.)*b[i-2]) / (ri-1.)
+	}
+end
+
+# CHEBYSHEV -- Procedure to calculate Chebyshev polynomials.
+
+procedure chebyshev (cv, x, basis)
+
+real	x
+int	order
+real	basis[ARB]
+
+begin
+	# normalize to the range -1. to 1.
+	xnorm = (2. * x - CV_MAXMIN(cv)) / CV_RANGE(cv)
+
+	b[1] = 1.
+	if (CV_ORDER(cv) == 1)
+	    return
+
+	b[2] = xnorm
+	if (CV_ORDER(cv) == 2)
+	    return
+
+	do i = 3, CV_ORDER(cv) {
+	    ri = i
+	    b[i] = 2.*xnorm*b[i-1] - b[i-2]
+	}
+end
+
+define	NPTS_SPLINE	401	# Number of points in the spline lookup table 
+define	INTERVALS	100	# Number of intervals per spline knot
+
+# L2SPLINE4 -- Procedure to calculate the cubic spline functions
+
+procedure (cv, x, left, basis)
+
+pointer	cv
+real	x
+int	left
+real	basis[ARB]
+
+real	table[NPTS_SPLINE]
+
+# data table containing the spline
+include "table.dat"
+
+begin
+	xnorm = (x - CV_XMIN(cv)) / CV_SPACING(cv)
+	temp = min (int (xnorm), npieces - 1)
+	left = temp +  1
+	xnorm = xnorm - temp
+
+	near = int ((1. - xnorm + 0.5) * INTERVALS) + 1
+	basis[1] = table[near]
+	near = table[near] + INTERVALS
+	basis[2] = table[near]
+	near = table[near] + INTERVALS
+	basis[3] = table[near]
+	near = table[near] + INTERVALS
+	basis[4] = table[near]
+end
+
+# CHOFAC -- Routine to calculate the Cholesky factorization of a banded
+# matrix.
+
+procedure chofac (matrix, nbands, nrows, matfac, ier)
+
+real	matrix[nbands, nrows]
+int	nbands
+int	nrows
+real	matfac[nbands, nrows]
+int	ier
+
+begin
+	ier = 0
+
+	if (nrows == 1) {
+	    if (matrix[1,1] .gt. 0.)
+	        matfac[1,1] = 1./matrix[1,1]
+	    return
+	}
+
+		
+	# copy matrix into matfac
+	do n = 1, nrows {
+	    do j = 1, nbands
+		matfac[j,n] = matrix[j,n]
+	}
+
+	do n = 1, nrows {
+
+	    # test to see if matrix is singular
+	    if (matfac[1,n] + matrix[1,n] <= matrix[1,n]) {
+		do j = 1, nbands
+		    w[j,n] = 0.
+		ier = 1
+		next
+	    }
+
+	    matfac[1,n] = 1./matfac[1,n]
+	    imax = min (nbands - 1, nrows - n)
+	    if (imax < 1)
+		next
+
+	    jmax = imax
+	    do i = 1, imax {
+		ratio = matfac[i+1,n] * matfac[1,n]
+		do j = 1, jmax
+		    matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
+		jmax = jmax - 1
+		matfac[i+1,n] = ratio
+	    }
+	}
+end
+
+# CHOSLV -- Solve the matrix whose Cholesky factorization was calculated in
+# CHOFAC.
+
+procedure choslv (matfac, nbands, nrows, vector, coeff)
+
+real	matfac[nbands,nrows]
+int	nbands
+int	nrows
+real	vector[nrows]
+real	coeff[nrows]
+
+begin
+	if (nrows == 1) {
+	    coeff[1] = vector[1] * matfac[1,1]
+	    return
+	}
+
+	# copy vector to coefficients
+	do i = 1, nrows
+	    coeff[i] = vector[i]
+
+	# forward substitution
+	nbndm1 = nbands - 1
+	do n = 1, nrows {
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax < 1)
+		next
+	    do j = 1, jmax
+		coeff[j+n] = coeff[j+n] - matfac[j+1,n] * b[n]
+	}
+
+	# back substitution
+	for (n = nrows; n > 0; n = n - 1) {
+	    coeff[n] = coeff[n] * matfac[1,n]
+	    jmax = min (nbndm1, nrows - 1)
+	    if (jmax >= 1) {
+		do j = 1, jmax
+		    coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
+	    }
+	}
+
+end
diff --git a/math/curfit/curfitdef.h b/math/curfit/curfitdef.h
new file mode 100644
index 00000000..b72349ac
--- /dev/null
+++ b/math/curfit/curfitdef.h
@@ -0,0 +1,55 @@
+# Header file for the curve fitting package
+
+# set up the curve descriptor structure
+
+define	LEN_CVSTRUCT	20
+
+define	CV_TYPE		Memi[$1]	# Type of curve to be fitted
+define	CV_ORDER	Memi[$1+1]	# Order of the fit
+define	CV_NPIECES	Memi[$1+2]	# Number of polynomial pieces - 1
+define	CV_NCOEFF	Memi[$1+3]	# Number of coefficients
+define	CV_XMAX		Memr[P2R($1+4)]	# Maximum x value
+define	CV_XMIN		Memr[P2R($1+5)]	# Minimum x value
+define	CV_RANGE	Memr[P2R($1+6)]	# 2. / (xmax - xmin), polynomials
+define	CV_MAXMIN	Memr[P2R($1+7)]	# - (xmax + xmin) / 2., polynomials
+define	CV_SPACING	Memr[P2R($1+8)]	# order / (xmax - xmin), splines
+define	CV_NPTS		Memi[$1+9]	# Number of data points
+
+define	CV_XBASIS	Memi[$1+10]	# Pointer to non zero basis for single x
+define	CV_MATRIX	Memi[$1+11]	# Pointer to original matrix
+define	CV_CHOFAC	Memi[$1+12]	# Pointer to Cholesky factorization
+define	CV_VECTOR	Memi[$1+13]	# Pointer to  vector
+define	CV_COEFF	Memi[$1+14]	# Pointer to coefficient vector
+define	CV_BASIS	Memi[$1+15]	# Pointer to basis functions (all x)
+define	CV_LEFT		Memi[$1+16]	# Pointer to first non-zero basis
+define	CV_WY		Memi[$1+17]	# Pointer to y * w (cvrefit)
+define	CV_USERFNC	Memi[$1+18]	# Pointer to external user subroutine
+define	CV_USERFNCR	Memr[P2R($1+18)]# Real version of above for cvrestore.
+					# one free slot left
+
+# matrix and vector element definitions
+
+define	XBASIS		Memr[P2P($1)]	# Non zero basis for single x
+define	MATRIX		Memr[P2P($1)]	# Element of MATRIX
+define	CHOFAC		Memr[P2P($1)]	# Element of CHOFAC
+define	VECTOR		Memr[P2P($1)]	# Element of VECTOR
+define	COEFF		Memr[P2P($1)]	# Element of COEFF
+define	BASIS		Memr[P2P($1)]	# Element of BASIS
+define	LEFT		Memi[P2P($1)]	# Element of LEFT
+
+# structure definitions for restore
+
+define	CV_SAVETYPE	$1[1]
+define	CV_SAVEORDER	$1[2]
+define	CV_SAVEXMIN	$1[3]
+define	CV_SAVEXMAX	$1[4]
+define	CV_SAVEFNC	$1[5]
+
+define	CV_SAVECOEFF	5
+
+
+# miscellaneous
+
+define	SPLINE3_ORDER	4
+define	SPLINE1_ORDER	2
+define	DELTA		EPSILON
diff --git a/math/curfit/cv_b1eval.gx b/math/curfit/cv_b1eval.gx
new file mode 100644
index 00000000..bd77f0ed
--- /dev/null
+++ b/math/curfit/cv_b1eval.gx
@@ -0,0 +1,110 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# CV_B1LEG -- Procedure to evaluate all the non-zero Legendrefunctions for
+# a single point and given order.
+
+procedure $tcv_b1leg (x, order, k1, k2, basis)
+
+PIXEL	x		# array of data points
+int	order		# order of polynomial, order = 1, constant
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# basis functions
+
+int	i
+PIXEL	ri, xnorm
+
+begin
+	basis[1] = PIXEL(1.0)
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2 
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order {
+	    ri = i
+	    basis[i] = ((PIXEL(2.0) * ri - PIXEL(3.0)) * xnorm * basis[i-1] -
+		(ri - PIXEL(2.0)) * basis[i-2]) / (ri - PIXEL(1.0))	
+	}
+end
+
+
+# CV_B1CHEB -- Procedure to evaluate all the non zero Chebyshev function
+# for a given x and order.
+
+procedure $tcv_b1cheb (x, order, k1, k2, basis)
+
+PIXEL	x		# number of data points
+int	order		# order of polynomial, 1 is a constant
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# array of basis functions
+
+int	i
+PIXEL	xnorm
+
+begin
+	basis[1] = PIXEL(1.0)
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order
+	    basis[i] = PIXEL(2.0) * xnorm * basis[i-1] - basis[i-2]
+end
+
+
+# CV_B1SPLINE1 -- Evaluate all the non-zero spline1 functions for a
+# single point.
+
+procedure $tcv_b1spline1 (x, npieces, k1, k2, basis, left)
+
+PIXEL	x		# set of data points
+int	npieces		# number of polynomial pieces minus 1
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# basis functions
+int	left		# index of the appropriate spline functions
+
+PIXEL	xnorm
+
+begin
+	xnorm = (x + k1) * k2
+	left = min (int (xnorm), npieces)
+
+	basis[2] = max (PIXEL(0.0), min (PIXEL(1.0), xnorm - left))
+	basis[1] = max (PIXEL(0.0), min (PIXEL(1.0), PIXEL(1.0) - basis[2]))
+end
+
+
+# CV_B1SPLINE3 --  Procedure to evaluate all the non-zero basis functions
+# for a cubic spline.
+
+procedure $tcv_b1spline3 (x, npieces, k1, k2, basis, left)
+
+PIXEL	x		# array of data points
+int	npieces		# number of polynomial pieces
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# array of basis functions
+int	left		# array of indices for first non-zero spline
+
+PIXEL	sx, tx
+
+begin
+	sx = (x + k1) * k2
+	left = min (int (sx), npieces)
+
+	sx = max (PIXEL(0.0), min (PIXEL(1.0), sx - left))
+	tx = max (PIXEL(0.0), min (PIXEL(1.0), PIXEL(1.0) - sx))
+
+	basis[1] = tx * tx * tx
+	basis[2] = PIXEL(1.0) + tx * (PIXEL(3.0) + tx * (PIXEL(3.0) -
+	    PIXEL(3.0) * tx))
+	basis[3] = PIXEL(1.0) + sx * (PIXEL(3.0) + sx * (PIXEL(3.0) -
+	    PIXEL(3.0) * sx))
+	basis[4] = sx * sx * sx
+end
diff --git a/math/curfit/cv_b1evald.x b/math/curfit/cv_b1evald.x
new file mode 100644
index 00000000..d5254ed8
--- /dev/null
+++ b/math/curfit/cv_b1evald.x
@@ -0,0 +1,110 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# CV_B1LEG -- Procedure to evaluate all the non-zero Legendrefunctions for
+# a single point and given order.
+
+procedure dcv_b1leg (x, order, k1, k2, basis)
+
+double	x		# array of data points
+int	order		# order of polynomial, order = 1, constant
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# basis functions
+
+int	i
+double	ri, xnorm
+
+begin
+	basis[1] = double(1.0)
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2 
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order {
+	    ri = i
+	    basis[i] = ((double(2.0) * ri - double(3.0)) * xnorm * basis[i-1] -
+		(ri - double(2.0)) * basis[i-2]) / (ri - double(1.0))	
+	}
+end
+
+
+# CV_B1CHEB -- Procedure to evaluate all the non zero Chebyshev function
+# for a given x and order.
+
+procedure dcv_b1cheb (x, order, k1, k2, basis)
+
+double	x		# number of data points
+int	order		# order of polynomial, 1 is a constant
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# array of basis functions
+
+int	i
+double	xnorm
+
+begin
+	basis[1] = double(1.0)
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order
+	    basis[i] = double(2.0) * xnorm * basis[i-1] - basis[i-2]
+end
+
+
+# CV_B1SPLINE1 -- Evaluate all the non-zero spline1 functions for a
+# single point.
+
+procedure dcv_b1spline1 (x, npieces, k1, k2, basis, left)
+
+double	x		# set of data points
+int	npieces		# number of polynomial pieces minus 1
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# basis functions
+int	left		# index of the appropriate spline functions
+
+double	xnorm
+
+begin
+	xnorm = (x + k1) * k2
+	left = min (int (xnorm), npieces)
+
+	basis[2] = max (double(0.0), min (double(1.0), xnorm - left))
+	basis[1] = max (double(0.0), min (double(1.0), double(1.0) - basis[2]))
+end
+
+
+# CV_B1SPLINE3 --  Procedure to evaluate all the non-zero basis functions
+# for a cubic spline.
+
+procedure dcv_b1spline3 (x, npieces, k1, k2, basis, left)
+
+double	x		# array of data points
+int	npieces		# number of polynomial pieces
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# array of basis functions
+int	left		# array of indices for first non-zero spline
+
+double	sx, tx
+
+begin
+	sx = (x + k1) * k2
+	left = min (int (sx), npieces)
+
+	sx = max (double(0.0), min (double(1.0), sx - left))
+	tx = max (double(0.0), min (double(1.0), double(1.0) - sx))
+
+	basis[1] = tx * tx * tx
+	basis[2] = double(1.0) + tx * (double(3.0) + tx * (double(3.0) -
+	    double(3.0) * tx))
+	basis[3] = double(1.0) + sx * (double(3.0) + sx * (double(3.0) -
+	    double(3.0) * sx))
+	basis[4] = sx * sx * sx
+end
diff --git a/math/curfit/cv_b1evalr.x b/math/curfit/cv_b1evalr.x
new file mode 100644
index 00000000..fd6fb8e7
--- /dev/null
+++ b/math/curfit/cv_b1evalr.x
@@ -0,0 +1,110 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# CV_B1LEG -- Procedure to evaluate all the non-zero Legendrefunctions for
+# a single point and given order.
+
+procedure rcv_b1leg (x, order, k1, k2, basis)
+
+real	x		# array of data points
+int	order		# order of polynomial, order = 1, constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+
+int	i
+real	ri, xnorm
+
+begin
+	basis[1] = real(1.0)
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2 
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order {
+	    ri = i
+	    basis[i] = ((real(2.0) * ri - real(3.0)) * xnorm * basis[i-1] -
+		(ri - real(2.0)) * basis[i-2]) / (ri - real(1.0))	
+	}
+end
+
+
+# CV_B1CHEB -- Procedure to evaluate all the non zero Chebyshev function
+# for a given x and order.
+
+procedure rcv_b1cheb (x, order, k1, k2, basis)
+
+real	x		# number of data points
+int	order		# order of polynomial, 1 is a constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# array of basis functions
+
+int	i
+real	xnorm
+
+begin
+	basis[1] = real(1.0)
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order
+	    basis[i] = real(2.0) * xnorm * basis[i-1] - basis[i-2]
+end
+
+
+# CV_B1SPLINE1 -- Evaluate all the non-zero spline1 functions for a
+# single point.
+
+procedure rcv_b1spline1 (x, npieces, k1, k2, basis, left)
+
+real	x		# set of data points
+int	npieces		# number of polynomial pieces minus 1
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+int	left		# index of the appropriate spline functions
+
+real	xnorm
+
+begin
+	xnorm = (x + k1) * k2
+	left = min (int (xnorm), npieces)
+
+	basis[2] = max (real(0.0), min (real(1.0), xnorm - left))
+	basis[1] = max (real(0.0), min (real(1.0), real(1.0) - basis[2]))
+end
+
+
+# CV_B1SPLINE3 --  Procedure to evaluate all the non-zero basis functions
+# for a cubic spline.
+
+procedure rcv_b1spline3 (x, npieces, k1, k2, basis, left)
+
+real	x		# array of data points
+int	npieces		# number of polynomial pieces
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# array of basis functions
+int	left		# array of indices for first non-zero spline
+
+real	sx, tx
+
+begin
+	sx = (x + k1) * k2
+	left = min (int (sx), npieces)
+
+	sx = max (real(0.0), min (real(1.0), sx - left))
+	tx = max (real(0.0), min (real(1.0), real(1.0) - sx))
+
+	basis[1] = tx * tx * tx
+	basis[2] = real(1.0) + tx * (real(3.0) + tx * (real(3.0) -
+	    real(3.0) * tx))
+	basis[3] = real(1.0) + sx * (real(3.0) + sx * (real(3.0) -
+	    real(3.0) * sx))
+	basis[4] = sx * sx * sx
+end
diff --git a/math/curfit/cv_beval.gx b/math/curfit/cv_beval.gx
new file mode 100644
index 00000000..3bb2b2e1
--- /dev/null
+++ b/math/curfit/cv_beval.gx
@@ -0,0 +1,147 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# CV_BCHEB -- Procedure to evaluate all the non-zero Chebyshev functions for
+# a set of points and given order.
+
+procedure $tcv_bcheb (x, npts, order, k1, k2, basis)
+
+PIXEL	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# basis functions
+
+int	k, bptr
+
+begin
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1)
+		call amovk$t (PIXEL(1.0), basis, npts)
+	    else if (k == 2)
+		call alta$t (x, basis[bptr], npts, k1, k2)
+	    else {
+		call amul$t (basis[1+npts], basis[bptr-npts], basis[bptr],
+				npts)
+		call amulk$t (basis[bptr], PIXEL(2.0), basis[bptr], npts)
+		call asub$t (basis[bptr], basis[bptr-2*npts], basis[bptr], npts)
+	    }
+	    bptr = bptr + npts
+	}
+end
+
+
+# CV_BLEG -- Procedure to evaluate all the non zero Legendre function
+# for a given order and set of points.
+
+procedure $tcv_bleg (x, npts, order, k1, k2, basis)
+
+PIXEL	x[npts]		# number of data points
+int	npts		# number of points
+int	order		# order of polynomial, 1 is a constant
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# array of basis functions
+
+int	k, bptr
+PIXEL	ri, ri1, ri2
+
+begin
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1)
+		call amovk$t (PIXEL(1.0), basis, npts)
+	    else if (k == 2)
+		call alta$t (x, basis[bptr], npts, k1, k2)
+	    else {
+		ri = k
+		ri1 = (PIXEL(2.0) * ri - PIXEL(3.0)) / (ri - PIXEL(1.0))
+		ri2 = - (ri - PIXEL(2.0)) / (ri - PIXEL(1.0))
+		call amul$t (basis[1+npts], basis[bptr-npts], basis[bptr],
+		    npts)
+		call awsu$t (basis[bptr], basis[bptr-2*npts],
+		    basis[bptr], npts, ri1, ri2)
+	    }
+	    bptr = bptr + npts
+	}
+end
+
+
+# CV_BSPLINE1 -- Evaluate all the non-zero spline1 functions for a set
+# of points.
+
+procedure $tcv_bspline1 (x, npts, npieces, k1, k2, basis, left)
+
+PIXEL	x[npts]		# set of data points
+int	npts		# number of points
+int	npieces		# number of polynomial pieces minus 1
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# basis functions
+int	left[ARB]	# indices of the appropriate spline functions
+
+int	k
+
+begin
+	call alta$t (x, basis[1+npts], npts, k1, k2)
+	call acht$ti (basis[1+npts], left, npts)
+	call aminki (left, npieces, left, npts)
+
+	do k = 1, npts {
+	    basis[npts+k] = max (PIXEL(0.0), min (PIXEL(1.0),
+	        basis[npts+k] - left[k]))
+	    basis[k] = max (PIXEL(0.0), min (PIXEL(1.0), PIXEL(1.0) -
+	        basis[npts+k]))
+	}
+end
+
+
+# CV_BSPLINE3 --  Procedure to evaluate all the non-zero basis functions
+# for a cubic spline.
+
+procedure $tcv_bspline3 (x, npts, npieces, k1, k2, basis, left)
+
+PIXEL	x[npts]		# array of data points
+int	npts		# number of data points
+int	npieces		# number of polynomial pieces minus 1
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# array of basis functions
+int	left[ARB]	# array of indices for first non-zero spline
+
+int	i
+pointer	sp, sx, tx
+PIXEL	dsx, dtx
+
+begin
+	# allocate space
+	call smark (sp)
+	call salloc (sx, npts, TY_PIXEL)
+	call salloc (tx, npts, TY_PIXEL)
+
+	# calculate the index of the first non-zero coeff
+	call alta$t (x, Mem$t[sx], npts, k1, k2)
+	call acht$ti (Mem$t[sx], left, npts)
+	call aminki (left, npieces, left, npts)
+
+	do i = 1, npts {
+	    Mem$t[sx+i-1] = max (PIXEL(0.0), min (PIXEL(1.0),
+	        Mem$t[sx+i-1] - left[i]))
+	    Mem$t[tx+i-1] = max (PIXEL(0.0), min (PIXEL(1.0), PIXEL(1.0) -
+	        Mem$t[sx+i-1]))
+	}
+
+	# calculate the basis function
+	#call apowk$t (Mem$t[tx], 3, basis, npts)
+	do i = 1, npts {
+	    dsx = Mem$t[sx+i-1]
+	    dtx = Mem$t[tx+i-1]
+	    basis[i] = dtx * dtx * dtx
+	    basis[npts+i] = PIXEL(1.0) + dtx * (PIXEL(3.0) + dtx *
+	        (PIXEL(3.0) - PIXEL(3.0) * dtx))
+	    basis[2*npts+i] = PIXEL(1.0) + dsx * (PIXEL(3.0) + dsx *
+	        (PIXEL(3.0) - PIXEL(3.0) * dsx))
+	    basis[3*npts+i] = dsx * dsx * dsx
+	}
+	#call apowk$t (Mem$t[sx], 3, basis[1+3*npts], npts)
+
+	# release space
+	call sfree (sp)
+end
diff --git a/math/curfit/cv_bevald.x b/math/curfit/cv_bevald.x
new file mode 100644
index 00000000..7d7f6e44
--- /dev/null
+++ b/math/curfit/cv_bevald.x
@@ -0,0 +1,147 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# CV_BCHEB -- Procedure to evaluate all the non-zero Chebyshev functions for
+# a set of points and given order.
+
+procedure dcv_bcheb (x, npts, order, k1, k2, basis)
+
+double	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# basis functions
+
+int	k, bptr
+
+begin
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1)
+		call amovkd (double(1.0), basis, npts)
+	    else if (k == 2)
+		call altad (x, basis[bptr], npts, k1, k2)
+	    else {
+		call amuld (basis[1+npts], basis[bptr-npts], basis[bptr],
+				npts)
+		call amulkd (basis[bptr], double(2.0), basis[bptr], npts)
+		call asubd (basis[bptr], basis[bptr-2*npts], basis[bptr], npts)
+	    }
+	    bptr = bptr + npts
+	}
+end
+
+
+# CV_BLEG -- Procedure to evaluate all the non zero Legendre function
+# for a given order and set of points.
+
+procedure dcv_bleg (x, npts, order, k1, k2, basis)
+
+double	x[npts]		# number of data points
+int	npts		# number of points
+int	order		# order of polynomial, 1 is a constant
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# array of basis functions
+
+int	k, bptr
+double	ri, ri1, ri2
+
+begin
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1)
+		call amovkd (double(1.0), basis, npts)
+	    else if (k == 2)
+		call altad (x, basis[bptr], npts, k1, k2)
+	    else {
+		ri = k
+		ri1 = (double(2.0) * ri - double(3.0)) / (ri - double(1.0))
+		ri2 = - (ri - double(2.0)) / (ri - double(1.0))
+		call amuld (basis[1+npts], basis[bptr-npts], basis[bptr],
+		    npts)
+		call awsud (basis[bptr], basis[bptr-2*npts],
+		    basis[bptr], npts, ri1, ri2)
+	    }
+	    bptr = bptr + npts
+	}
+end
+
+
+# CV_BSPLINE1 -- Evaluate all the non-zero spline1 functions for a set
+# of points.
+
+procedure dcv_bspline1 (x, npts, npieces, k1, k2, basis, left)
+
+double	x[npts]		# set of data points
+int	npts		# number of points
+int	npieces		# number of polynomial pieces minus 1
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# basis functions
+int	left[ARB]	# indices of the appropriate spline functions
+
+int	k
+
+begin
+	call altad (x, basis[1+npts], npts, k1, k2)
+	call achtdi (basis[1+npts], left, npts)
+	call aminki (left, npieces, left, npts)
+
+	do k = 1, npts {
+	    basis[npts+k] = max (double(0.0), min (double(1.0),
+	        basis[npts+k] - left[k]))
+	    basis[k] = max (double(0.0), min (double(1.0), double(1.0) -
+	        basis[npts+k]))
+	}
+end
+
+
+# CV_BSPLINE3 --  Procedure to evaluate all the non-zero basis functions
+# for a cubic spline.
+
+procedure dcv_bspline3 (x, npts, npieces, k1, k2, basis, left)
+
+double	x[npts]		# array of data points
+int	npts		# number of data points
+int	npieces		# number of polynomial pieces minus 1
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# array of basis functions
+int	left[ARB]	# array of indices for first non-zero spline
+
+int	i
+pointer	sp, sx, tx
+double	dsx, dtx
+
+begin
+	# allocate space
+	call smark (sp)
+	call salloc (sx, npts, TY_DOUBLE)
+	call salloc (tx, npts, TY_DOUBLE)
+
+	# calculate the index of the first non-zero coeff
+	call altad (x, Memd[sx], npts, k1, k2)
+	call achtdi (Memd[sx], left, npts)
+	call aminki (left, npieces, left, npts)
+
+	do i = 1, npts {
+	    Memd[sx+i-1] = max (double(0.0), min (double(1.0),
+	        Memd[sx+i-1] - left[i]))
+	    Memd[tx+i-1] = max (double(0.0), min (double(1.0), double(1.0) -
+	        Memd[sx+i-1]))
+	}
+
+	# calculate the basis function
+	#call apowk$t (Mem$t[tx], 3, basis, npts)
+	do i = 1, npts {
+	    dsx = Memd[sx+i-1]
+	    dtx = Memd[tx+i-1]
+	    basis[i] = dtx * dtx * dtx
+	    basis[npts+i] = double(1.0) + dtx * (double(3.0) + dtx *
+	        (double(3.0) - double(3.0) * dtx))
+	    basis[2*npts+i] = double(1.0) + dsx * (double(3.0) + dsx *
+	        (double(3.0) - double(3.0) * dsx))
+	    basis[3*npts+i] = dsx * dsx * dsx
+	}
+	#call apowk$t (Mem$t[sx], 3, basis[1+3*npts], npts)
+
+	# release space
+	call sfree (sp)
+end
diff --git a/math/curfit/cv_bevalr.x b/math/curfit/cv_bevalr.x
new file mode 100644
index 00000000..b36aebad
--- /dev/null
+++ b/math/curfit/cv_bevalr.x
@@ -0,0 +1,147 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# CV_BCHEB -- Procedure to evaluate all the non-zero Chebyshev functions for
+# a set of points and given order.
+
+procedure rcv_bcheb (x, npts, order, k1, k2, basis)
+
+real	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+
+int	k, bptr
+
+begin
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1)
+		call amovkr (real(1.0), basis, npts)
+	    else if (k == 2)
+		call altar (x, basis[bptr], npts, k1, k2)
+	    else {
+		call amulr (basis[1+npts], basis[bptr-npts], basis[bptr],
+				npts)
+		call amulkr (basis[bptr], real(2.0), basis[bptr], npts)
+		call asubr (basis[bptr], basis[bptr-2*npts], basis[bptr], npts)
+	    }
+	    bptr = bptr + npts
+	}
+end
+
+
+# CV_BLEG -- Procedure to evaluate all the non zero Legendre function
+# for a given order and set of points.
+
+procedure rcv_bleg (x, npts, order, k1, k2, basis)
+
+real	x[npts]		# number of data points
+int	npts		# number of points
+int	order		# order of polynomial, 1 is a constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# array of basis functions
+
+int	k, bptr
+real	ri, ri1, ri2
+
+begin
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1)
+		call amovkr (real(1.0), basis, npts)
+	    else if (k == 2)
+		call altar (x, basis[bptr], npts, k1, k2)
+	    else {
+		ri = k
+		ri1 = (real(2.0) * ri - real(3.0)) / (ri - real(1.0))
+		ri2 = - (ri - real(2.0)) / (ri - real(1.0))
+		call amulr (basis[1+npts], basis[bptr-npts], basis[bptr],
+		    npts)
+		call awsur (basis[bptr], basis[bptr-2*npts],
+		    basis[bptr], npts, ri1, ri2)
+	    }
+	    bptr = bptr + npts
+	}
+end
+
+
+# CV_BSPLINE1 -- Evaluate all the non-zero spline1 functions for a set
+# of points.
+
+procedure rcv_bspline1 (x, npts, npieces, k1, k2, basis, left)
+
+real	x[npts]		# set of data points
+int	npts		# number of points
+int	npieces		# number of polynomial pieces minus 1
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+int	left[ARB]	# indices of the appropriate spline functions
+
+int	k
+
+begin
+	call altar (x, basis[1+npts], npts, k1, k2)
+	call achtri (basis[1+npts], left, npts)
+	call aminki (left, npieces, left, npts)
+
+	do k = 1, npts {
+	    basis[npts+k] = max (real(0.0), min (real(1.0),
+	        basis[npts+k] - left[k]))
+	    basis[k] = max (real(0.0), min (real(1.0), real(1.0) -
+	        basis[npts+k]))
+	}
+end
+
+
+# CV_BSPLINE3 --  Procedure to evaluate all the non-zero basis functions
+# for a cubic spline.
+
+procedure rcv_bspline3 (x, npts, npieces, k1, k2, basis, left)
+
+real	x[npts]		# array of data points
+int	npts		# number of data points
+int	npieces		# number of polynomial pieces minus 1
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# array of basis functions
+int	left[ARB]	# array of indices for first non-zero spline
+
+int	i
+pointer	sp, sx, tx
+real	dsx, dtx
+
+begin
+	# allocate space
+	call smark (sp)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (tx, npts, TY_REAL)
+
+	# calculate the index of the first non-zero coeff
+	call altar (x, Memr[sx], npts, k1, k2)
+	call achtri (Memr[sx], left, npts)
+	call aminki (left, npieces, left, npts)
+
+	do i = 1, npts {
+	    Memr[sx+i-1] = max (real(0.0), min (real(1.0),
+	        Memr[sx+i-1] - left[i]))
+	    Memr[tx+i-1] = max (real(0.0), min (real(1.0), real(1.0) -
+	        Memr[sx+i-1]))
+	}
+
+	# calculate the basis function
+	#call apowk$t (Mem$t[tx], 3, basis, npts)
+	do i = 1, npts {
+	    dsx = Memr[sx+i-1]
+	    dtx = Memr[tx+i-1]
+	    basis[i] = dtx * dtx * dtx
+	    basis[npts+i] = real(1.0) + dtx * (real(3.0) + dtx *
+	        (real(3.0) - real(3.0) * dtx))
+	    basis[2*npts+i] = real(1.0) + dsx * (real(3.0) + dsx *
+	        (real(3.0) - real(3.0) * dsx))
+	    basis[3*npts+i] = dsx * dsx * dsx
+	}
+	#call apowk$t (Mem$t[sx], 3, basis[1+3*npts], npts)
+
+	# release space
+	call sfree (sp)
+end
diff --git a/math/curfit/cv_feval.gx b/math/curfit/cv_feval.gx
new file mode 100644
index 00000000..759bb193
--- /dev/null
+++ b/math/curfit/cv_feval.gx
@@ -0,0 +1,242 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# CV_EVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure $tcv_evcheb (coeff, x, yfit, npts, order, k1, k2)
+
+PIXEL	coeff[ARB]		# 1D array of coefficients
+PIXEL	x[npts]			# x values of points to be evaluated
+PIXEL	yfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	order			# order of the polynomial, 1 = constant
+PIXEL	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer sp
+PIXEL	c1, c2
+
+begin
+	# fit a constant
+	if (order == 1) {
+	    call amovk$t (coeff[1], yfit, npts)
+	    return
+	}
+
+	# fit a linear function
+	c1 = k2 * coeff[2]
+	c2 = c1 * k1 + coeff[1]
+	call altm$t (x, yfit, npts, c1, c2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_PIXEL)
+	call salloc (pn, npts, TY_PIXEL)
+	call salloc (pnm1, npts, TY_PIXEL)
+	call salloc (pnm2, npts, TY_PIXEL)
+
+	# a higher order polynomial
+	call amovk$t (PIXEL(1.0), Mem$t[pnm2], npts)
+	call alta$t (x, Mem$t[sx], npts, k1, k2)
+	call amov$t (Mem$t[sx], Mem$t[pnm1], npts)
+	call amulk$t (Mem$t[sx], PIXEL(2.0), Mem$t[sx], npts)
+	do i = 3, order {
+	    call amul$t (Mem$t[sx], Mem$t[pnm1], Mem$t[pn], npts)
+	    call asub$t (Mem$t[pn], Mem$t[pnm2], Mem$t[pn], npts)
+	    if (i < order) {
+	        call amov$t (Mem$t[pnm1], Mem$t[pnm2], npts)
+	        call amov$t (Mem$t[pn], Mem$t[pnm1], npts)
+	    }
+	    call amulk$t (Mem$t[pn], coeff[i], Mem$t[pn], npts)
+	    call aadd$t (yfit, Mem$t[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
+
+# CV_EVLEG -- Procedure to evaluate a Legendre polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure $tcv_evleg (coeff, x, yfit, npts, order, k1, k2)
+
+PIXEL	coeff[ARB]		# 1D array of coefficients
+PIXEL	x[npts]			# x values of points to be evaluated
+PIXEL	yfit[npts]		# the fitted points
+int	npts			# number of data points
+int	order			# order of the polynomial, 1 = constant
+PIXEL	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer	sp
+PIXEL	ri, ri1, ri2
+
+begin
+
+	# fit a constant
+	if (order == 1) {
+	    call amovk$t (coeff[1], yfit, npts)
+	    return
+	}
+
+	# fit a linear function
+	ri1 = k2 * coeff[2]
+	ri2 = ri1 * k1 + coeff[1]
+	call altm$t (x, yfit, npts, ri1, ri2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_PIXEL)
+	call salloc (pn, npts, TY_PIXEL)
+	call salloc (pnm1, npts, TY_PIXEL)
+	call salloc (pnm2, npts, TY_PIXEL)
+
+	# a higher order polynomial
+	call amovk$t (PIXEL(1.0), Mem$t[pnm2], npts)
+	call alta$t (x, Mem$t[sx], npts, k1, k2)
+	call amov$t (Mem$t[sx], Mem$t[pnm1], npts)
+	do i = 3, order {
+	    ri = i
+	    ri1 = (PIXEL(2.0) * ri - PIXEL(3.0)) / (ri - PIXEL(1.0))
+	    ri2 = - (ri - PIXEL(2.0)) / (ri - PIXEL(1.0))
+	    call amul$t (Mem$t[sx], Mem$t[pnm1], Mem$t[pn], npts)
+	    call awsu$t (Mem$t[pn], Mem$t[pnm2], Mem$t[pn], npts, ri1, ri2)
+	    if (i < order) {
+	        call amov$t (Mem$t[pnm1], Mem$t[pnm2], npts)
+	        call amov$t (Mem$t[pn], Mem$t[pnm1], npts)
+	    }
+	    call amulk$t (Mem$t[pn], coeff[i], Mem$t[pn], npts)
+	    call aadd$t (yfit, Mem$t[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
+
+# CV_EVSPLINE1 -- Procedure to evaluate a piecewise linear spline function
+# assuming that the coefficients have been calculated.
+
+procedure $tcv_evspline1 (coeff, x, yfit, npts, npieces, k1, k2)
+
+PIXEL	coeff[ARB]		# array of coefficients
+PIXEL	x[npts]			# array of x values
+PIXEL	yfit[npts]		# array of fitted values
+int	npts			# number of data points
+int	npieces			# number of fitted points minus 1
+PIXEL	k1, k2			# normalizing constants
+
+int	j
+pointer sx, tx, azindex, aindex, index
+pointer	sp
+
+begin
+
+	# allocate the required space
+	call smark (sp)
+	call salloc (sx, npts, TY_PIXEL)
+	call salloc (tx, npts, TY_PIXEL)
+	call salloc (index, npts, TY_INT)
+
+	# calculate the index of the first non-zero coefficient
+	# for each point
+	call alta$t (x, Mem$t[sx], npts, k1, k2)
+	call acht$ti (Mem$t[sx], Memi[index], npts)
+	call aminki (Memi[index], npieces, Memi[index], npts)
+
+	# transform sx to range 0 to 1
+	azindex = sx - 1
+	do j = 1, npts {
+	    aindex = azindex + j
+	    Mem$t[aindex] = max (PIXEL(0.0), min (PIXEL(1.0), Mem$t[aindex] -
+	        Memi[index+j-1]))
+	    Mem$t[tx+j-1] = max (PIXEL(0.0), min (PIXEL(1.0), PIXEL(1.0) -
+	        Mem$t[aindex]))
+	}
+
+    	# calculate yfit using the two non-zero basis function
+	do j = 1, npts
+	    yfit[j] = Mem$t[tx+j-1] * coeff[1+Memi[index+j-1]] +
+		      Mem$t[sx+j-1] * coeff[2+Memi[index+j-1]]
+
+        # free space
+	call sfree (sp)
+
+end
+
+# CV_EVSPLINE3 -- Procedure to evaluate the cubic spline assuming that
+# the coefficients of the fit are known.
+
+procedure $tcv_evspline3 (coeff, x, yfit, npts, npieces, k1, k2)
+
+PIXEL	coeff[ARB]	# array of coeffcients
+PIXEL	x[npts]		# array of x values
+PIXEL	yfit[npts]	# array of fitted values
+int	npts		# number of data points
+int	npieces		# number of polynomial pieces
+PIXEL	k1, k2		# normalizing constants
+
+int	i, j
+pointer	sx, tx, temp, index, sp
+
+begin
+
+	# allocate the required space
+	call smark (sp)
+        call salloc (sx, npts, TY_PIXEL)
+	call salloc (tx, npts, TY_PIXEL)
+	call salloc (temp, npts, TY_PIXEL)
+	call salloc (index, npts, TY_INT)
+
+	# calculate to which coefficients the x values contribute to
+        call alta$t (x, Mem$t[sx], npts, k1, k2)
+        call acht$ti (Mem$t[sx], Memi[index], npts)
+        call aminki (Memi[index], npieces, Memi[index], npts)
+
+        # transform sx to range 0 to 1
+	do j = 1, npts {
+	    Mem$t[sx+j-1] = max (PIXEL(0.0), min (PIXEL(1.0), Mem$t[sx+j-1] -
+	        Memi[index+j-1]))
+	    Mem$t[tx+j-1] = max (PIXEL(0.0), min (PIXEL(1.0), PIXEL(1.0) -
+	        Mem$t[sx+j-1]))
+	}
+
+        # calculate yfit using the four non-zero basis function
+	call aclr$t (yfit, npts)
+        do i = 1, 4 {
+
+	    switch (i) {
+	    case 1:
+		call apowk$t (Mem$t[tx], 3, Mem$t[temp], npts)
+	    case 2:
+		do j = 1, npts {
+		    Mem$t[temp+j-1] = PIXEL(1.0) + Mem$t[tx+j-1] *
+		        (PIXEL(3.0) + Mem$t[tx+j-1] * (PIXEL(3.0) -
+			PIXEL(3.0) * Mem$t[tx+j-1]))
+		}
+	    case 3:
+		do j = 1, npts {
+		    Mem$t[temp+j-1] = PIXEL(1.0) + Mem$t[sx+j-1] *
+		        (PIXEL(3.0) + Mem$t[sx+j-1] * (PIXEL(3.0) -
+			PIXEL(3.0) * Mem$t[sx+j-1]))
+		}
+	    case 4:
+		call apowk$t (Mem$t[sx], 3, Mem$t[temp], npts)
+	    }
+
+	    do j = 1, npts
+		Mem$t[temp+j-1] = Mem$t[temp+j-1] * coeff[i+Memi[index+j-1]]
+	    call aadd$t (yfit, Mem$t[temp], yfit, npts)
+	}
+
+	# free space
+	call sfree (sp)
+
+end
diff --git a/math/curfit/cv_fevald.x b/math/curfit/cv_fevald.x
new file mode 100644
index 00000000..9293a821
--- /dev/null
+++ b/math/curfit/cv_fevald.x
@@ -0,0 +1,242 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# CV_EVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure dcv_evcheb (coeff, x, yfit, npts, order, k1, k2)
+
+double	coeff[ARB]		# 1D array of coefficients
+double	x[npts]			# x values of points to be evaluated
+double	yfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	order			# order of the polynomial, 1 = constant
+double	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer sp
+double	c1, c2
+
+begin
+	# fit a constant
+	if (order == 1) {
+	    call amovkd (coeff[1], yfit, npts)
+	    return
+	}
+
+	# fit a linear function
+	c1 = k2 * coeff[2]
+	c2 = c1 * k1 + coeff[1]
+	call altmd (x, yfit, npts, c1, c2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_DOUBLE)
+	call salloc (pn, npts, TY_DOUBLE)
+	call salloc (pnm1, npts, TY_DOUBLE)
+	call salloc (pnm2, npts, TY_DOUBLE)
+
+	# a higher order polynomial
+	call amovkd (double(1.0), Memd[pnm2], npts)
+	call altad (x, Memd[sx], npts, k1, k2)
+	call amovd (Memd[sx], Memd[pnm1], npts)
+	call amulkd (Memd[sx], double(2.0), Memd[sx], npts)
+	do i = 3, order {
+	    call amuld (Memd[sx], Memd[pnm1], Memd[pn], npts)
+	    call asubd (Memd[pn], Memd[pnm2], Memd[pn], npts)
+	    if (i < order) {
+	        call amovd (Memd[pnm1], Memd[pnm2], npts)
+	        call amovd (Memd[pn], Memd[pnm1], npts)
+	    }
+	    call amulkd (Memd[pn], coeff[i], Memd[pn], npts)
+	    call aaddd (yfit, Memd[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
+
+# CV_EVLEG -- Procedure to evaluate a Legendre polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure dcv_evleg (coeff, x, yfit, npts, order, k1, k2)
+
+double	coeff[ARB]		# 1D array of coefficients
+double	x[npts]			# x values of points to be evaluated
+double	yfit[npts]		# the fitted points
+int	npts			# number of data points
+int	order			# order of the polynomial, 1 = constant
+double	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer	sp
+double	ri, ri1, ri2
+
+begin
+
+	# fit a constant
+	if (order == 1) {
+	    call amovkd (coeff[1], yfit, npts)
+	    return
+	}
+
+	# fit a linear function
+	ri1 = k2 * coeff[2]
+	ri2 = ri1 * k1 + coeff[1]
+	call altmd (x, yfit, npts, ri1, ri2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_DOUBLE)
+	call salloc (pn, npts, TY_DOUBLE)
+	call salloc (pnm1, npts, TY_DOUBLE)
+	call salloc (pnm2, npts, TY_DOUBLE)
+
+	# a higher order polynomial
+	call amovkd (double(1.0), Memd[pnm2], npts)
+	call altad (x, Memd[sx], npts, k1, k2)
+	call amovd (Memd[sx], Memd[pnm1], npts)
+	do i = 3, order {
+	    ri = i
+	    ri1 = (double(2.0) * ri - double(3.0)) / (ri - double(1.0))
+	    ri2 = - (ri - double(2.0)) / (ri - double(1.0))
+	    call amuld (Memd[sx], Memd[pnm1], Memd[pn], npts)
+	    call awsud (Memd[pn], Memd[pnm2], Memd[pn], npts, ri1, ri2)
+	    if (i < order) {
+	        call amovd (Memd[pnm1], Memd[pnm2], npts)
+	        call amovd (Memd[pn], Memd[pnm1], npts)
+	    }
+	    call amulkd (Memd[pn], coeff[i], Memd[pn], npts)
+	    call aaddd (yfit, Memd[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
+
+# CV_EVSPLINE1 -- Procedure to evaluate a piecewise linear spline function
+# assuming that the coefficients have been calculated.
+
+procedure dcv_evspline1 (coeff, x, yfit, npts, npieces, k1, k2)
+
+double	coeff[ARB]		# array of coefficients
+double	x[npts]			# array of x values
+double	yfit[npts]		# array of fitted values
+int	npts			# number of data points
+int	npieces			# number of fitted points minus 1
+double	k1, k2			# normalizing constants
+
+int	j
+pointer sx, tx, azindex, aindex, index
+pointer	sp
+
+begin
+
+	# allocate the required space
+	call smark (sp)
+	call salloc (sx, npts, TY_DOUBLE)
+	call salloc (tx, npts, TY_DOUBLE)
+	call salloc (index, npts, TY_INT)
+
+	# calculate the index of the first non-zero coefficient
+	# for each point
+	call altad (x, Memd[sx], npts, k1, k2)
+	call achtdi (Memd[sx], Memi[index], npts)
+	call aminki (Memi[index], npieces, Memi[index], npts)
+
+	# transform sx to range 0 to 1
+	azindex = sx - 1
+	do j = 1, npts {
+	    aindex = azindex + j
+	    Memd[aindex] = max (double(0.0), min (double(1.0), Memd[aindex] -
+	        Memi[index+j-1]))
+	    Memd[tx+j-1] = max (double(0.0), min (double(1.0), double(1.0) -
+	        Memd[aindex]))
+	}
+
+    	# calculate yfit using the two non-zero basis function
+	do j = 1, npts
+	    yfit[j] = Memd[tx+j-1] * coeff[1+Memi[index+j-1]] +
+		      Memd[sx+j-1] * coeff[2+Memi[index+j-1]]
+
+        # free space
+	call sfree (sp)
+
+end
+
+# CV_EVSPLINE3 -- Procedure to evaluate the cubic spline assuming that
+# the coefficients of the fit are known.
+
+procedure dcv_evspline3 (coeff, x, yfit, npts, npieces, k1, k2)
+
+double	coeff[ARB]	# array of coeffcients
+double	x[npts]		# array of x values
+double	yfit[npts]	# array of fitted values
+int	npts		# number of data points
+int	npieces		# number of polynomial pieces
+double	k1, k2		# normalizing constants
+
+int	i, j
+pointer	sx, tx, temp, index, sp
+
+begin
+
+	# allocate the required space
+	call smark (sp)
+        call salloc (sx, npts, TY_DOUBLE)
+	call salloc (tx, npts, TY_DOUBLE)
+	call salloc (temp, npts, TY_DOUBLE)
+	call salloc (index, npts, TY_INT)
+
+	# calculate to which coefficients the x values contribute to
+        call altad (x, Memd[sx], npts, k1, k2)
+        call achtdi (Memd[sx], Memi[index], npts)
+        call aminki (Memi[index], npieces, Memi[index], npts)
+
+        # transform sx to range 0 to 1
+	do j = 1, npts {
+	    Memd[sx+j-1] = max (double(0.0), min (double(1.0), Memd[sx+j-1] -
+	        Memi[index+j-1]))
+	    Memd[tx+j-1] = max (double(0.0), min (double(1.0), double(1.0) -
+	        Memd[sx+j-1]))
+	}
+
+        # calculate yfit using the four non-zero basis function
+	call aclrd (yfit, npts)
+        do i = 1, 4 {
+
+	    switch (i) {
+	    case 1:
+		call apowkd (Memd[tx], 3, Memd[temp], npts)
+	    case 2:
+		do j = 1, npts {
+		    Memd[temp+j-1] = double(1.0) + Memd[tx+j-1] *
+		        (double(3.0) + Memd[tx+j-1] * (double(3.0) -
+			double(3.0) * Memd[tx+j-1]))
+		}
+	    case 3:
+		do j = 1, npts {
+		    Memd[temp+j-1] = double(1.0) + Memd[sx+j-1] *
+		        (double(3.0) + Memd[sx+j-1] * (double(3.0) -
+			double(3.0) * Memd[sx+j-1]))
+		}
+	    case 4:
+		call apowkd (Memd[sx], 3, Memd[temp], npts)
+	    }
+
+	    do j = 1, npts
+		Memd[temp+j-1] = Memd[temp+j-1] * coeff[i+Memi[index+j-1]]
+	    call aaddd (yfit, Memd[temp], yfit, npts)
+	}
+
+	# free space
+	call sfree (sp)
+
+end
diff --git a/math/curfit/cv_fevalr.x b/math/curfit/cv_fevalr.x
new file mode 100644
index 00000000..ac019042
--- /dev/null
+++ b/math/curfit/cv_fevalr.x
@@ -0,0 +1,242 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# CV_EVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure rcv_evcheb (coeff, x, yfit, npts, order, k1, k2)
+
+real	coeff[ARB]		# 1D array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	yfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	order			# order of the polynomial, 1 = constant
+real	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer sp
+real	c1, c2
+
+begin
+	# fit a constant
+	if (order == 1) {
+	    call amovkr (coeff[1], yfit, npts)
+	    return
+	}
+
+	# fit a linear function
+	c1 = k2 * coeff[2]
+	c2 = c1 * k1 + coeff[1]
+	call altmr (x, yfit, npts, c1, c2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (pn, npts, TY_REAL)
+	call salloc (pnm1, npts, TY_REAL)
+	call salloc (pnm2, npts, TY_REAL)
+
+	# a higher order polynomial
+	call amovkr (real(1.0), Memr[pnm2], npts)
+	call altar (x, Memr[sx], npts, k1, k2)
+	call amovr (Memr[sx], Memr[pnm1], npts)
+	call amulkr (Memr[sx], real(2.0), Memr[sx], npts)
+	do i = 3, order {
+	    call amulr (Memr[sx], Memr[pnm1], Memr[pn], npts)
+	    call asubr (Memr[pn], Memr[pnm2], Memr[pn], npts)
+	    if (i < order) {
+	        call amovr (Memr[pnm1], Memr[pnm2], npts)
+	        call amovr (Memr[pn], Memr[pnm1], npts)
+	    }
+	    call amulkr (Memr[pn], coeff[i], Memr[pn], npts)
+	    call aaddr (yfit, Memr[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
+
+# CV_EVLEG -- Procedure to evaluate a Legendre polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure rcv_evleg (coeff, x, yfit, npts, order, k1, k2)
+
+real	coeff[ARB]		# 1D array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	yfit[npts]		# the fitted points
+int	npts			# number of data points
+int	order			# order of the polynomial, 1 = constant
+real	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer	sp
+real	ri, ri1, ri2
+
+begin
+
+	# fit a constant
+	if (order == 1) {
+	    call amovkr (coeff[1], yfit, npts)
+	    return
+	}
+
+	# fit a linear function
+	ri1 = k2 * coeff[2]
+	ri2 = ri1 * k1 + coeff[1]
+	call altmr (x, yfit, npts, ri1, ri2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (pn, npts, TY_REAL)
+	call salloc (pnm1, npts, TY_REAL)
+	call salloc (pnm2, npts, TY_REAL)
+
+	# a higher order polynomial
+	call amovkr (real(1.0), Memr[pnm2], npts)
+	call altar (x, Memr[sx], npts, k1, k2)
+	call amovr (Memr[sx], Memr[pnm1], npts)
+	do i = 3, order {
+	    ri = i
+	    ri1 = (real(2.0) * ri - real(3.0)) / (ri - real(1.0))
+	    ri2 = - (ri - real(2.0)) / (ri - real(1.0))
+	    call amulr (Memr[sx], Memr[pnm1], Memr[pn], npts)
+	    call awsur (Memr[pn], Memr[pnm2], Memr[pn], npts, ri1, ri2)
+	    if (i < order) {
+	        call amovr (Memr[pnm1], Memr[pnm2], npts)
+	        call amovr (Memr[pn], Memr[pnm1], npts)
+	    }
+	    call amulkr (Memr[pn], coeff[i], Memr[pn], npts)
+	    call aaddr (yfit, Memr[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
+
+# CV_EVSPLINE1 -- Procedure to evaluate a piecewise linear spline function
+# assuming that the coefficients have been calculated.
+
+procedure rcv_evspline1 (coeff, x, yfit, npts, npieces, k1, k2)
+
+real	coeff[ARB]		# array of coefficients
+real	x[npts]			# array of x values
+real	yfit[npts]		# array of fitted values
+int	npts			# number of data points
+int	npieces			# number of fitted points minus 1
+real	k1, k2			# normalizing constants
+
+int	j
+pointer sx, tx, azindex, aindex, index
+pointer	sp
+
+begin
+
+	# allocate the required space
+	call smark (sp)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (tx, npts, TY_REAL)
+	call salloc (index, npts, TY_INT)
+
+	# calculate the index of the first non-zero coefficient
+	# for each point
+	call altar (x, Memr[sx], npts, k1, k2)
+	call achtri (Memr[sx], Memi[index], npts)
+	call aminki (Memi[index], npieces, Memi[index], npts)
+
+	# transform sx to range 0 to 1
+	azindex = sx - 1
+	do j = 1, npts {
+	    aindex = azindex + j
+	    Memr[aindex] = max (real(0.0), min (real(1.0), Memr[aindex] -
+	        Memi[index+j-1]))
+	    Memr[tx+j-1] = max (real(0.0), min (real(1.0), real(1.0) -
+	        Memr[aindex]))
+	}
+
+    	# calculate yfit using the two non-zero basis function
+	do j = 1, npts
+	    yfit[j] = Memr[tx+j-1] * coeff[1+Memi[index+j-1]] +
+		      Memr[sx+j-1] * coeff[2+Memi[index+j-1]]
+
+        # free space
+	call sfree (sp)
+
+end
+
+# CV_EVSPLINE3 -- Procedure to evaluate the cubic spline assuming that
+# the coefficients of the fit are known.
+
+procedure rcv_evspline3 (coeff, x, yfit, npts, npieces, k1, k2)
+
+real	coeff[ARB]	# array of coeffcients
+real	x[npts]		# array of x values
+real	yfit[npts]	# array of fitted values
+int	npts		# number of data points
+int	npieces		# number of polynomial pieces
+real	k1, k2		# normalizing constants
+
+int	i, j
+pointer	sx, tx, temp, index, sp
+
+begin
+
+	# allocate the required space
+	call smark (sp)
+        call salloc (sx, npts, TY_REAL)
+	call salloc (tx, npts, TY_REAL)
+	call salloc (temp, npts, TY_REAL)
+	call salloc (index, npts, TY_INT)
+
+	# calculate to which coefficients the x values contribute to
+        call altar (x, Memr[sx], npts, k1, k2)
+        call achtri (Memr[sx], Memi[index], npts)
+        call aminki (Memi[index], npieces, Memi[index], npts)
+
+        # transform sx to range 0 to 1
+	do j = 1, npts {
+	    Memr[sx+j-1] = max (real(0.0), min (real(1.0), Memr[sx+j-1] -
+	        Memi[index+j-1]))
+	    Memr[tx+j-1] = max (real(0.0), min (real(1.0), real(1.0) -
+	        Memr[sx+j-1]))
+	}
+
+        # calculate yfit using the four non-zero basis function
+	call aclrr (yfit, npts)
+        do i = 1, 4 {
+
+	    switch (i) {
+	    case 1:
+		call apowkr (Memr[tx], 3, Memr[temp], npts)
+	    case 2:
+		do j = 1, npts {
+		    Memr[temp+j-1] = real(1.0) + Memr[tx+j-1] *
+		        (real(3.0) + Memr[tx+j-1] * (real(3.0) -
+			real(3.0) * Memr[tx+j-1]))
+		}
+	    case 3:
+		do j = 1, npts {
+		    Memr[temp+j-1] = real(1.0) + Memr[sx+j-1] *
+		        (real(3.0) + Memr[sx+j-1] * (real(3.0) -
+			real(3.0) * Memr[sx+j-1]))
+		}
+	    case 4:
+		call apowkr (Memr[sx], 3, Memr[temp], npts)
+	    }
+
+	    do j = 1, npts
+		Memr[temp+j-1] = Memr[temp+j-1] * coeff[i+Memi[index+j-1]]
+	    call aaddr (yfit, Memr[temp], yfit, npts)
+	}
+
+	# free space
+	call sfree (sp)
+
+end
diff --git a/math/curfit/cv_userfnc.gx b/math/curfit/cv_userfnc.gx
new file mode 100644
index 00000000..7a4e80e8
--- /dev/null
+++ b/math/curfit/cv_userfnc.gx
@@ -0,0 +1,84 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include	<math/curfit.h>
+
+$if (datatype == r)
+include	"curfitdef.h"
+$else
+include	"dcurfitdef.h"
+$endif
+
+# Interface Routine for external user functions
+
+# CV_B1USER - Evaluate basis functions at a single point with
+# external user routine.
+
+procedure $tcv_b1user (cv, x)
+
+pointer	cv
+PIXEL	x
+
+begin
+	if (CV_USERFNC(cv) == NULL)
+	    call error (0, "CV_USERFNC: Pointer not set")
+
+	call zcall5 (CV_USERFNC(cv), x, CV_ORDER(cv), CV_MAXMIN(cv),
+			CV_RANGE(cv), XBASIS(CV_XBASIS(cv)))
+end
+
+# CV_BUSER - Evaluate basis functions at a set of points with
+# external user routine.
+
+procedure $tcv_buser (cv, x, npts)
+
+pointer	cv
+PIXEL   x[ARB]
+int	npts
+
+int	i, j
+
+begin
+	do i = 1, npts {
+	    call $tcv_b1user (cv, x[i])
+	    do j = 1, CV_ORDER(cv)
+		BASIS(CV_BASIS(cv)-1+i + npts*(j-1)) = 
+			XBASIS(CV_XBASIS(cv)-1+j)
+	}
+end
+
+# CV_EVUSER - Evaluate user function at a set of points using present
+# coefficient values
+
+procedure $tcv_evuser (cv, x, yfit, npts)
+
+pointer	cv
+PIXEL	x[ARB],  yfit[ARB]
+int	npts
+
+int	i
+PIXEL	adot$t
+
+begin
+	do i = 1, npts {
+	    call $tcv_b1user (cv, x[i])
+	    yfit[i] = adot$t ( XBASIS(CV_XBASIS(cv)), COEFF(CV_COEFF(cv)),
+				CV_ORDER(cv))
+	}
+end
+
+# CVUSERFNC - Set external user function.
+
+$if (datatype == r)
+procedure cvuserfnc (cv, fnc)
+$else
+procedure dcvuserfnc (cv, fnc)
+$endif
+
+pointer	cv
+extern	fnc()
+
+int	locpr()
+
+begin
+	CV_USERFNC(cv) = locpr (fnc)
+end
diff --git a/math/curfit/cv_userfncd.x b/math/curfit/cv_userfncd.x
new file mode 100644
index 00000000..ae05d372
--- /dev/null
+++ b/math/curfit/cv_userfncd.x
@@ -0,0 +1,76 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include	<math/curfit.h>
+
+include	"dcurfitdef.h"
+
+# Interface Routine for external user functions
+
+# CV_B1USER - Evaluate basis functions at a single point with
+# external user routine.
+
+procedure dcv_b1user (cv, x)
+
+pointer	cv
+double	x
+
+begin
+	if (CV_USERFNC(cv) == NULL)
+	    call error (0, "CV_USERFNC: Pointer not set")
+
+	call zcall5 (CV_USERFNC(cv), x, CV_ORDER(cv), CV_MAXMIN(cv),
+			CV_RANGE(cv), XBASIS(CV_XBASIS(cv)))
+end
+
+# CV_BUSER - Evaluate basis functions at a set of points with
+# external user routine.
+
+procedure dcv_buser (cv, x, npts)
+
+pointer	cv
+double   x[ARB]
+int	npts
+
+int	i, j
+
+begin
+	do i = 1, npts {
+	    call dcv_b1user (cv, x[i])
+	    do j = 1, CV_ORDER(cv)
+		BASIS(CV_BASIS(cv)-1+i + npts*(j-1)) = 
+			XBASIS(CV_XBASIS(cv)-1+j)
+	}
+end
+
+# CV_EVUSER - Evaluate user function at a set of points using present
+# coefficient values
+
+procedure dcv_evuser (cv, x, yfit, npts)
+
+pointer	cv
+double	x[ARB],  yfit[ARB]
+int	npts
+
+int	i
+double	adotd
+
+begin
+	do i = 1, npts {
+	    call dcv_b1user (cv, x[i])
+	    yfit[i] = adotd ( XBASIS(CV_XBASIS(cv)), COEFF(CV_COEFF(cv)),
+				CV_ORDER(cv))
+	}
+end
+
+# CVUSERFNC - Set external user function.
+
+procedure dcvuserfnc (cv, fnc)
+
+pointer	cv
+extern	fnc()
+
+int	locpr()
+
+begin
+	CV_USERFNC(cv) = locpr (fnc)
+end
diff --git a/math/curfit/cv_userfncr.x b/math/curfit/cv_userfncr.x
new file mode 100644
index 00000000..b9f502c3
--- /dev/null
+++ b/math/curfit/cv_userfncr.x
@@ -0,0 +1,76 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include	<math/curfit.h>
+
+include	"curfitdef.h"
+
+# Interface Routine for external user functions
+
+# CV_B1USER - Evaluate basis functions at a single point with
+# external user routine.
+
+procedure rcv_b1user (cv, x)
+
+pointer	cv
+real	x
+
+begin
+	if (CV_USERFNC(cv) == NULL)
+	    call error (0, "CV_USERFNC: Pointer not set")
+
+	call zcall5 (CV_USERFNC(cv), x, CV_ORDER(cv), CV_MAXMIN(cv),
+			CV_RANGE(cv), XBASIS(CV_XBASIS(cv)))
+end
+
+# CV_BUSER - Evaluate basis functions at a set of points with
+# external user routine.
+
+procedure rcv_buser (cv, x, npts)
+
+pointer	cv
+real   x[ARB]
+int	npts
+
+int	i, j
+
+begin
+	do i = 1, npts {
+	    call rcv_b1user (cv, x[i])
+	    do j = 1, CV_ORDER(cv)
+		BASIS(CV_BASIS(cv)-1+i + npts*(j-1)) = 
+			XBASIS(CV_XBASIS(cv)-1+j)
+	}
+end
+
+# CV_EVUSER - Evaluate user function at a set of points using present
+# coefficient values
+
+procedure rcv_evuser (cv, x, yfit, npts)
+
+pointer	cv
+real	x[ARB],  yfit[ARB]
+int	npts
+
+int	i
+real	adotr
+
+begin
+	do i = 1, npts {
+	    call rcv_b1user (cv, x[i])
+	    yfit[i] = adotr ( XBASIS(CV_XBASIS(cv)), COEFF(CV_COEFF(cv)),
+				CV_ORDER(cv))
+	}
+end
+
+# CVUSERFNC - Set external user function.
+
+procedure cvuserfnc (cv, fnc)
+
+pointer	cv
+extern	fnc()
+
+int	locpr()
+
+begin
+	CV_USERFNC(cv) = locpr (fnc)
+end
diff --git a/math/curfit/cvaccum.gx b/math/curfit/cvaccum.gx
new file mode 100644
index 00000000..fb5a957b
--- /dev/null
+++ b/math/curfit/cvaccum.gx
@@ -0,0 +1,108 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVACCUM -- Procedure to add a data point to the set of normal equations.
+# The inner products of the basis functions are added into the CV_ORDER(cv)
+# by CV_NCOEFF(cv) array MATRIX. The first row of MATRIX
+# contains the main diagonal of the matrix followed by
+# the CV_ORDER(cv) lower diagonals. This method of storing MATRIX
+# minimizes the space required by large symmetric, banded matrices.
+# The inner products of the basis functions and the data ordinates are
+# stored in VECTOR which has CV_NCOEFF(cv) elements. The integers left
+# and leftm1 are used to determine which elements of MATRIX and VECTOR
+# are to receive the data.
+
+$if (datatype == r)
+procedure cvaccum (cv, x, y, w, wtflag)
+$else
+procedure dcvaccum (cv, x, y, w, wtflag)
+$endif
+
+pointer	cv		# curve descriptor
+PIXEL	x		# x value
+PIXEL	y		# y value
+PIXEL	w		# weight of the data point
+int	wtflag		# type of weighting desired
+
+int	left, i, ii, j
+PIXEL	bw
+pointer	xzptr
+pointer	mzptr, mzzptr
+pointer	vzptr
+
+begin
+
+	# increment number of points
+	CV_NPTS(cv) = CV_NPTS(cv) + 1
+
+	# calculate the weights
+	switch (wtflag) {
+	case WTS_UNIFORM, WTS_SPACING:
+	    w = 1.0
+	case WTS_USER:
+	    # user defined weights
+	case WTS_CHISQ:
+	    # data assumed to be scaled to photons with Poisson statistics
+	    if (y > 0.0)
+	        w = 1.0 / y
+	    else if (y < 0.0)
+		w = - 1.0 / y
+	    else
+		w = 0.0
+	default:
+	    w = 1.0
+	}
+
+	# calculate all non-zero basis functions for a given data point
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 0
+	    call $tcv_b1cheb (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case LEGENDRE:
+	    left = 0
+	    call $tcv_b1leg (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case SPLINE3:
+	    call $tcv_b1spline3 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	         CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case SPLINE1:
+	    call $tcv_b1spline1 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	         CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case USERFNC:
+	    left = 0
+	    call $tcv_b1user (cv, x)
+	}
+
+	# index the pointers
+	xzptr = CV_XBASIS(cv) - 1
+	vzptr = CV_VECTOR(cv) + left - 1
+	mzptr = CV_MATRIX(cv) + CV_ORDER(CV) * (left - 1)
+
+	# accumulate the data point into the matrix and vector
+	do i = 1, CV_ORDER(cv) {
+
+	    # calculate the non-zero basis functions
+	    bw = XBASIS(xzptr+i) * w
+
+	    # add the inner product of the basis functions and the ordinate
+	    # into the appropriate element of VECTOR
+	    VECTOR(vzptr+i) = VECTOR(vzptr+i) + bw * y
+
+	    # accumulate the inner products of the basis functions into
+	    # the apprpriate element of MATRIX
+	    mzzptr = mzptr + i * CV_ORDER(cv)
+	    ii = 0
+	    do j = i, CV_ORDER(cv) {
+		MATRIX(mzzptr+ii) = MATRIX(mzzptr+ii) + XBASIS(xzptr+j) * bw
+		ii = ii + 1
+	    }
+	}
+end
diff --git a/math/curfit/cvaccumd.x b/math/curfit/cvaccumd.x
new file mode 100644
index 00000000..2a30b584
--- /dev/null
+++ b/math/curfit/cvaccumd.x
@@ -0,0 +1,100 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+# CVACCUM -- Procedure to add a data point to the set of normal equations.
+# The inner products of the basis functions are added into the CV_ORDER(cv)
+# by CV_NCOEFF(cv) array MATRIX. The first row of MATRIX
+# contains the main diagonal of the matrix followed by
+# the CV_ORDER(cv) lower diagonals. This method of storing MATRIX
+# minimizes the space required by large symmetric, banded matrices.
+# The inner products of the basis functions and the data ordinates are
+# stored in VECTOR which has CV_NCOEFF(cv) elements. The integers left
+# and leftm1 are used to determine which elements of MATRIX and VECTOR
+# are to receive the data.
+
+procedure dcvaccum (cv, x, y, w, wtflag)
+
+pointer	cv		# curve descriptor
+double	x		# x value
+double	y		# y value
+double	w		# weight of the data point
+int	wtflag		# type of weighting desired
+
+int	left, i, ii, j
+double	bw
+pointer	xzptr
+pointer	mzptr, mzzptr
+pointer	vzptr
+
+begin
+
+	# increment number of points
+	CV_NPTS(cv) = CV_NPTS(cv) + 1
+
+	# calculate the weights
+	switch (wtflag) {
+	case WTS_UNIFORM, WTS_SPACING:
+	    w = 1.0
+	case WTS_USER:
+	    # user defined weights
+	case WTS_CHISQ:
+	    # data assumed to be scaled to photons with Poisson statistics
+	    if (y > 0.0)
+	        w = 1.0 / y
+	    else if (y < 0.0)
+		w = - 1.0 / y
+	    else
+		w = 0.0
+	default:
+	    w = 1.0
+	}
+
+	# calculate all non-zero basis functions for a given data point
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 0
+	    call dcv_b1cheb (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case LEGENDRE:
+	    left = 0
+	    call dcv_b1leg (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case SPLINE3:
+	    call dcv_b1spline3 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	         CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case SPLINE1:
+	    call dcv_b1spline1 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	         CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case USERFNC:
+	    left = 0
+	    call dcv_b1user (cv, x)
+	}
+
+	# index the pointers
+	xzptr = CV_XBASIS(cv) - 1
+	vzptr = CV_VECTOR(cv) + left - 1
+	mzptr = CV_MATRIX(cv) + CV_ORDER(CV) * (left - 1)
+
+	# accumulate the data point into the matrix and vector
+	do i = 1, CV_ORDER(cv) {
+
+	    # calculate the non-zero basis functions
+	    bw = XBASIS(xzptr+i) * w
+
+	    # add the inner product of the basis functions and the ordinate
+	    # into the appropriate element of VECTOR
+	    VECTOR(vzptr+i) = VECTOR(vzptr+i) + bw * y
+
+	    # accumulate the inner products of the basis functions into
+	    # the apprpriate element of MATRIX
+	    mzzptr = mzptr + i * CV_ORDER(cv)
+	    ii = 0
+	    do j = i, CV_ORDER(cv) {
+		MATRIX(mzzptr+ii) = MATRIX(mzzptr+ii) + XBASIS(xzptr+j) * bw
+		ii = ii + 1
+	    }
+	}
+end
diff --git a/math/curfit/cvaccumr.x b/math/curfit/cvaccumr.x
new file mode 100644
index 00000000..a2184840
--- /dev/null
+++ b/math/curfit/cvaccumr.x
@@ -0,0 +1,100 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+# CVACCUM -- Procedure to add a data point to the set of normal equations.
+# The inner products of the basis functions are added into the CV_ORDER(cv)
+# by CV_NCOEFF(cv) array MATRIX. The first row of MATRIX
+# contains the main diagonal of the matrix followed by
+# the CV_ORDER(cv) lower diagonals. This method of storing MATRIX
+# minimizes the space required by large symmetric, banded matrices.
+# The inner products of the basis functions and the data ordinates are
+# stored in VECTOR which has CV_NCOEFF(cv) elements. The integers left
+# and leftm1 are used to determine which elements of MATRIX and VECTOR
+# are to receive the data.
+
+procedure cvaccum (cv, x, y, w, wtflag)
+
+pointer	cv		# curve descriptor
+real	x		# x value
+real	y		# y value
+real	w		# weight of the data point
+int	wtflag		# type of weighting desired
+
+int	left, i, ii, j
+real	bw
+pointer	xzptr
+pointer	mzptr, mzzptr
+pointer	vzptr
+
+begin
+
+	# increment number of points
+	CV_NPTS(cv) = CV_NPTS(cv) + 1
+
+	# calculate the weights
+	switch (wtflag) {
+	case WTS_UNIFORM, WTS_SPACING:
+	    w = 1.0
+	case WTS_USER:
+	    # user defined weights
+	case WTS_CHISQ:
+	    # data assumed to be scaled to photons with Poisson statistics
+	    if (y > 0.0)
+	        w = 1.0 / y
+	    else if (y < 0.0)
+		w = - 1.0 / y
+	    else
+		w = 0.0
+	default:
+	    w = 1.0
+	}
+
+	# calculate all non-zero basis functions for a given data point
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 0
+	    call rcv_b1cheb (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case LEGENDRE:
+	    left = 0
+	    call rcv_b1leg (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case SPLINE3:
+	    call rcv_b1spline3 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	         CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case SPLINE1:
+	    call rcv_b1spline1 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	         CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case USERFNC:
+	    left = 0
+	    call rcv_b1user (cv, x)
+	}
+
+	# index the pointers
+	xzptr = CV_XBASIS(cv) - 1
+	vzptr = CV_VECTOR(cv) + left - 1
+	mzptr = CV_MATRIX(cv) + CV_ORDER(CV) * (left - 1)
+
+	# accumulate the data point into the matrix and vector
+	do i = 1, CV_ORDER(cv) {
+
+	    # calculate the non-zero basis functions
+	    bw = XBASIS(xzptr+i) * w
+
+	    # add the inner product of the basis functions and the ordinate
+	    # into the appropriate element of VECTOR
+	    VECTOR(vzptr+i) = VECTOR(vzptr+i) + bw * y
+
+	    # accumulate the inner products of the basis functions into
+	    # the apprpriate element of MATRIX
+	    mzzptr = mzptr + i * CV_ORDER(cv)
+	    ii = 0
+	    do j = i, CV_ORDER(cv) {
+		MATRIX(mzzptr+ii) = MATRIX(mzzptr+ii) + XBASIS(xzptr+j) * bw
+		ii = ii + 1
+	    }
+	}
+end
diff --git a/math/curfit/cvacpts.gx b/math/curfit/cvacpts.gx
new file mode 100644
index 00000000..56a36cb2
--- /dev/null
+++ b/math/curfit/cvacpts.gx
@@ -0,0 +1,186 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVACPTS -- Procedure to add a set of points to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the CV_ORDER(cv) by CV_NCOEFF(cv) matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals. This method
+# of storage is particularly efficient for the large symmetric
+# banded matrices produced during spline fits. The inner product
+# of the basis functions and the data ordinates are stored in the
+# CV_NCOEFF(cv)-vector VECTOR. The array LEFT stores the
+# indices which show which elements of MATRIX and VECTOR are
+# to receive the inner products.
+
+$if (datatype == r)
+procedure cvacpts (cv, x, y, w, npts, wtflag)
+$else
+procedure dcvacpts (cv, x, y, w, npts, wtflag)
+$endif
+
+pointer	cv		# curve descriptor
+PIXEL	x[npts]		# array of abcissa
+PIXEL	y[npts]		# array of ordinates
+PIXEL	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+
+int	i, ii, j, k
+pointer	sp
+pointer	vzptr, vindex, mzptr, mindex, bptr, bbptr
+pointer	bw, rows
+
+begin
+
+	# increment the number of points
+	CV_NPTS(cv) = CV_NPTS(cv) + npts
+
+	# remove basis functions calculated by any previous cvrefit call
+	if (CV_BASIS(cv) != NULL) {
+
+	    call mfree (CV_BASIS(cv), TY_PIXEL)
+	    call mfree (CV_WY(cv), TY_PIXEL)
+
+	    CV_BASIS(cv) = NULL
+	    CV_WY(cv) = NULL
+
+	    if (CV_LEFT(cv) != NULL) {
+	        call mfree (CV_LEFT(cv), TY_INT)
+	        CV_LEFT(cv) = NULL
+	    }
+	}
+
+	# calculate weights
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    call amovk$t (PIXEL(1.0), w, npts)
+	case WTS_SPACING:
+	    if (npts == 1)
+		w[1] = 1.
+	    else
+	        w[1] = abs (x[2] - x[1])
+	    do i = 2, npts - 1
+		w[i] = abs (x[i+1] - x[i-1])
+	    if (npts == 1)
+		w[npts] = 1.
+	    else
+	        w[npts] = abs (x[npts] - x[npts-1])
+	case WTS_USER:
+	    # user supplied weights
+	case WTS_CHISQ:
+	    # data assumed to be scaled to photons with Poisson statistics
+	    do i = 1, npts {
+		if (y[i] > PIXEL(0.0))
+		    w[i] = PIXEL(1.0) / y[i]
+		else if (y[i] < PIXEL(0.0))
+		    w[i] = -PIXEL(1.0) / y[i]
+		else
+		    w[i] = PIXEL(0.0)
+	    }
+	default:
+	    call amovk$t (PIXEL(1.0), w, npts)
+	}
+
+
+	# allocate space for the basis functions
+	call smark (sp)
+	call salloc (CV_BASIS(cv), npts * CV_ORDER(cv), TY_PIXEL)
+
+	# calculate the non-zero basis functions
+	switch (CV_TYPE(cv)) {
+	case LEGENDRE:
+	    call $tcv_bleg (x, npts, CV_ORDER(cv), CV_MAXMIN(cv),
+	    		  CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	case CHEBYSHEV:
+	    call $tcv_bcheb (x, npts, CV_ORDER(cv), CV_MAXMIN(cv),
+	    		  CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	case SPLINE3:
+	    call salloc (CV_LEFT(cv), npts, TY_INT)
+	    call $tcv_bspline3 (x, npts, CV_NPIECES(cv), -CV_XMIN(cv),
+			      CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+			      LEFT(CV_LEFT(cv)))
+	case SPLINE1:
+	    call salloc (CV_LEFT(cv), npts, TY_INT)
+	    call $tcv_bspline1 (x, npts, CV_NPIECES(cv), -CV_XMIN(cv),
+			      CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+			      LEFT(CV_LEFT(cv)))
+	case USERFNC:
+	    call $tcv_buser (cv, x, npts)
+	}
+
+
+	# allocate temporary storage space for matrix accumulation
+	call salloc (bw, npts, TY_PIXEL)
+	call salloc (rows, npts, TY_INT)
+
+	# one index the pointers
+	vzptr = CV_VECTOR(cv) - 1
+	mzptr = CV_MATRIX(cv)
+	bptr = CV_BASIS(cv)
+
+	switch (CV_TYPE(cv)) {
+
+	case LEGENDRE, CHEBYSHEV, USERFNC:
+
+	    # accumulate the new right side of the matrix equation
+	    do k = 1, CV_ORDER(cv) {
+	        call amul$t (w, BASIS(bptr), Mem$t[bw], npts) 
+		vindex = vzptr + k
+	        do i = 1, npts
+	            VECTOR(vindex) = VECTOR(vindex) + Mem$t[bw+i-1] * y[i]
+	        bbptr = bptr
+	        ii = 0
+	        do j = k, CV_ORDER(cv) {
+		    mindex = mzptr + ii
+		    do i = 1, npts
+		        MATRIX(mindex) = MATRIX(mindex) + Mem$t[bw+i-1] *
+				            BASIS(bbptr+i-1)	
+		    ii = ii + 1
+		    bbptr = bbptr + npts
+		}
+		bptr = bptr + npts
+		mzptr = mzptr + CV_ORDER(cv)
+	    }
+
+	case SPLINE1,SPLINE3:
+
+	    call amulki (LEFT(CV_LEFT(cv)), CV_ORDER(cv), Memi[rows], npts)
+	    call aaddki (Memi[rows], CV_MATRIX(cv), Memi[rows], npts)
+	    call aaddki (LEFT(CV_LEFT(cv)), vzptr, LEFT(CV_LEFT(cv)), npts) 
+
+	    # accumulate the new right side of the matrix equation
+	    do k = 1, CV_ORDER(cv) {
+	        call amul$t (w, BASIS(bptr), Mem$t[bw], npts) 
+	        do i = 1, npts {
+		    vindex = LEFT(CV_LEFT(cv)+i-1) + k
+	            VECTOR(vindex) = VECTOR(vindex)+ Mem$t[bw+i-1] * y[i]
+		}
+	        bbptr = bptr
+	        ii = 0
+	        do j = k, CV_ORDER(cv) {
+		    do i = 1, npts {
+			mindex = Memi[rows+i-1] + ii
+		        MATRIX(mindex) = MATRIX(mindex) + Mem$t[bw+i-1] *
+			    BASIS(bbptr+i-1)
+		    }
+		    ii = ii + 1
+		    bbptr = bbptr + npts
+		}
+	        bptr = bptr + npts
+	        call aaddki (Memi[rows], CV_ORDER(cv), Memi[rows], npts)
+	    }
+	}
+
+	# release the space
+	call sfree (sp)
+	CV_BASIS(cv) = NULL
+	CV_LEFT(cv) = NULL
+end
diff --git a/math/curfit/cvacptsd.x b/math/curfit/cvacptsd.x
new file mode 100644
index 00000000..aa4665d8
--- /dev/null
+++ b/math/curfit/cvacptsd.x
@@ -0,0 +1,178 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+# CVACPTS -- Procedure to add a set of points to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the CV_ORDER(cv) by CV_NCOEFF(cv) matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals. This method
+# of storage is particularly efficient for the large symmetric
+# banded matrices produced during spline fits. The inner product
+# of the basis functions and the data ordinates are stored in the
+# CV_NCOEFF(cv)-vector VECTOR. The array LEFT stores the
+# indices which show which elements of MATRIX and VECTOR are
+# to receive the inner products.
+
+procedure dcvacpts (cv, x, y, w, npts, wtflag)
+
+pointer	cv		# curve descriptor
+double	x[npts]		# array of abcissa
+double	y[npts]		# array of ordinates
+double	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+
+int	i, ii, j, k
+pointer	sp
+pointer	vzptr, vindex, mzptr, mindex, bptr, bbptr
+pointer	bw, rows
+
+begin
+
+	# increment the number of points
+	CV_NPTS(cv) = CV_NPTS(cv) + npts
+
+	# remove basis functions calculated by any previous cvrefit call
+	if (CV_BASIS(cv) != NULL) {
+
+	    call mfree (CV_BASIS(cv), TY_DOUBLE)
+	    call mfree (CV_WY(cv), TY_DOUBLE)
+
+	    CV_BASIS(cv) = NULL
+	    CV_WY(cv) = NULL
+
+	    if (CV_LEFT(cv) != NULL) {
+	        call mfree (CV_LEFT(cv), TY_INT)
+	        CV_LEFT(cv) = NULL
+	    }
+	}
+
+	# calculate weights
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    call amovkd (double(1.0), w, npts)
+	case WTS_SPACING:
+	    if (npts == 1)
+		w[1] = 1.
+	    else
+	        w[1] = abs (x[2] - x[1])
+	    do i = 2, npts - 1
+		w[i] = abs (x[i+1] - x[i-1])
+	    if (npts == 1)
+		w[npts] = 1.
+	    else
+	        w[npts] = abs (x[npts] - x[npts-1])
+	case WTS_USER:
+	    # user supplied weights
+	case WTS_CHISQ:
+	    # data assumed to be scaled to photons with Poisson statistics
+	    do i = 1, npts {
+		if (y[i] > double(0.0))
+		    w[i] = double(1.0) / y[i]
+		else if (y[i] < double(0.0))
+		    w[i] = -double(1.0) / y[i]
+		else
+		    w[i] = double(0.0)
+	    }
+	default:
+	    call amovkd (double(1.0), w, npts)
+	}
+
+
+	# allocate space for the basis functions
+	call smark (sp)
+	call salloc (CV_BASIS(cv), npts * CV_ORDER(cv), TY_DOUBLE)
+
+	# calculate the non-zero basis functions
+	switch (CV_TYPE(cv)) {
+	case LEGENDRE:
+	    call dcv_bleg (x, npts, CV_ORDER(cv), CV_MAXMIN(cv),
+	    		  CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	case CHEBYSHEV:
+	    call dcv_bcheb (x, npts, CV_ORDER(cv), CV_MAXMIN(cv),
+	    		  CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	case SPLINE3:
+	    call salloc (CV_LEFT(cv), npts, TY_INT)
+	    call dcv_bspline3 (x, npts, CV_NPIECES(cv), -CV_XMIN(cv),
+			      CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+			      LEFT(CV_LEFT(cv)))
+	case SPLINE1:
+	    call salloc (CV_LEFT(cv), npts, TY_INT)
+	    call dcv_bspline1 (x, npts, CV_NPIECES(cv), -CV_XMIN(cv),
+			      CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+			      LEFT(CV_LEFT(cv)))
+	case USERFNC:
+	    call dcv_buser (cv, x, npts)
+	}
+
+
+	# allocate temporary storage space for matrix accumulation
+	call salloc (bw, npts, TY_DOUBLE)
+	call salloc (rows, npts, TY_INT)
+
+	# one index the pointers
+	vzptr = CV_VECTOR(cv) - 1
+	mzptr = CV_MATRIX(cv)
+	bptr = CV_BASIS(cv)
+
+	switch (CV_TYPE(cv)) {
+
+	case LEGENDRE, CHEBYSHEV, USERFNC:
+
+	    # accumulate the new right side of the matrix equation
+	    do k = 1, CV_ORDER(cv) {
+	        call amuld (w, BASIS(bptr), Memd[bw], npts) 
+		vindex = vzptr + k
+	        do i = 1, npts
+	            VECTOR(vindex) = VECTOR(vindex) + Memd[bw+i-1] * y[i]
+	        bbptr = bptr
+	        ii = 0
+	        do j = k, CV_ORDER(cv) {
+		    mindex = mzptr + ii
+		    do i = 1, npts
+		        MATRIX(mindex) = MATRIX(mindex) + Memd[bw+i-1] *
+				            BASIS(bbptr+i-1)	
+		    ii = ii + 1
+		    bbptr = bbptr + npts
+		}
+		bptr = bptr + npts
+		mzptr = mzptr + CV_ORDER(cv)
+	    }
+
+	case SPLINE1,SPLINE3:
+
+	    call amulki (LEFT(CV_LEFT(cv)), CV_ORDER(cv), Memi[rows], npts)
+	    call aaddki (Memi[rows], CV_MATRIX(cv), Memi[rows], npts)
+	    call aaddki (LEFT(CV_LEFT(cv)), vzptr, LEFT(CV_LEFT(cv)), npts) 
+
+	    # accumulate the new right side of the matrix equation
+	    do k = 1, CV_ORDER(cv) {
+	        call amuld (w, BASIS(bptr), Memd[bw], npts) 
+	        do i = 1, npts {
+		    vindex = LEFT(CV_LEFT(cv)+i-1) + k
+	            VECTOR(vindex) = VECTOR(vindex)+ Memd[bw+i-1] * y[i]
+		}
+	        bbptr = bptr
+	        ii = 0
+	        do j = k, CV_ORDER(cv) {
+		    do i = 1, npts {
+			mindex = Memi[rows+i-1] + ii
+		        MATRIX(mindex) = MATRIX(mindex) + Memd[bw+i-1] *
+			    BASIS(bbptr+i-1)
+		    }
+		    ii = ii + 1
+		    bbptr = bbptr + npts
+		}
+	        bptr = bptr + npts
+	        call aaddki (Memi[rows], CV_ORDER(cv), Memi[rows], npts)
+	    }
+	}
+
+	# release the space
+	call sfree (sp)
+	CV_BASIS(cv) = NULL
+	CV_LEFT(cv) = NULL
+end
diff --git a/math/curfit/cvacptsr.x b/math/curfit/cvacptsr.x
new file mode 100644
index 00000000..fde31363
--- /dev/null
+++ b/math/curfit/cvacptsr.x
@@ -0,0 +1,178 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+# CVACPTS -- Procedure to add a set of points to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the CV_ORDER(cv) by CV_NCOEFF(cv) matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals. This method
+# of storage is particularly efficient for the large symmetric
+# banded matrices produced during spline fits. The inner product
+# of the basis functions and the data ordinates are stored in the
+# CV_NCOEFF(cv)-vector VECTOR. The array LEFT stores the
+# indices which show which elements of MATRIX and VECTOR are
+# to receive the inner products.
+
+procedure cvacpts (cv, x, y, w, npts, wtflag)
+
+pointer	cv		# curve descriptor
+real	x[npts]		# array of abcissa
+real	y[npts]		# array of ordinates
+real	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+
+int	i, ii, j, k
+pointer	sp
+pointer	vzptr, vindex, mzptr, mindex, bptr, bbptr
+pointer	bw, rows
+
+begin
+
+	# increment the number of points
+	CV_NPTS(cv) = CV_NPTS(cv) + npts
+
+	# remove basis functions calculated by any previous cvrefit call
+	if (CV_BASIS(cv) != NULL) {
+
+	    call mfree (CV_BASIS(cv), TY_REAL)
+	    call mfree (CV_WY(cv), TY_REAL)
+
+	    CV_BASIS(cv) = NULL
+	    CV_WY(cv) = NULL
+
+	    if (CV_LEFT(cv) != NULL) {
+	        call mfree (CV_LEFT(cv), TY_INT)
+	        CV_LEFT(cv) = NULL
+	    }
+	}
+
+	# calculate weights
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    call amovkr (real(1.0), w, npts)
+	case WTS_SPACING:
+	    if (npts == 1)
+		w[1] = 1.
+	    else
+	        w[1] = abs (x[2] - x[1])
+	    do i = 2, npts - 1
+		w[i] = abs (x[i+1] - x[i-1])
+	    if (npts == 1)
+		w[npts] = 1.
+	    else
+	        w[npts] = abs (x[npts] - x[npts-1])
+	case WTS_USER:
+	    # user supplied weights
+	case WTS_CHISQ:
+	    # data assumed to be scaled to photons with Poisson statistics
+	    do i = 1, npts {
+		if (y[i] > real(0.0))
+		    w[i] = real(1.0) / y[i]
+		else if (y[i] < real(0.0))
+		    w[i] = -real(1.0) / y[i]
+		else
+		    w[i] = real(0.0)
+	    }
+	default:
+	    call amovkr (real(1.0), w, npts)
+	}
+
+
+	# allocate space for the basis functions
+	call smark (sp)
+	call salloc (CV_BASIS(cv), npts * CV_ORDER(cv), TY_REAL)
+
+	# calculate the non-zero basis functions
+	switch (CV_TYPE(cv)) {
+	case LEGENDRE:
+	    call rcv_bleg (x, npts, CV_ORDER(cv), CV_MAXMIN(cv),
+	    		  CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	case CHEBYSHEV:
+	    call rcv_bcheb (x, npts, CV_ORDER(cv), CV_MAXMIN(cv),
+	    		  CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	case SPLINE3:
+	    call salloc (CV_LEFT(cv), npts, TY_INT)
+	    call rcv_bspline3 (x, npts, CV_NPIECES(cv), -CV_XMIN(cv),
+			      CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+			      LEFT(CV_LEFT(cv)))
+	case SPLINE1:
+	    call salloc (CV_LEFT(cv), npts, TY_INT)
+	    call rcv_bspline1 (x, npts, CV_NPIECES(cv), -CV_XMIN(cv),
+			      CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+			      LEFT(CV_LEFT(cv)))
+	case USERFNC:
+	    call rcv_buser (cv, x, npts)
+	}
+
+
+	# allocate temporary storage space for matrix accumulation
+	call salloc (bw, npts, TY_REAL)
+	call salloc (rows, npts, TY_INT)
+
+	# one index the pointers
+	vzptr = CV_VECTOR(cv) - 1
+	mzptr = CV_MATRIX(cv)
+	bptr = CV_BASIS(cv)
+
+	switch (CV_TYPE(cv)) {
+
+	case LEGENDRE, CHEBYSHEV, USERFNC:
+
+	    # accumulate the new right side of the matrix equation
+	    do k = 1, CV_ORDER(cv) {
+	        call amulr (w, BASIS(bptr), Memr[bw], npts) 
+		vindex = vzptr + k
+	        do i = 1, npts
+	            VECTOR(vindex) = VECTOR(vindex) + Memr[bw+i-1] * y[i]
+	        bbptr = bptr
+	        ii = 0
+	        do j = k, CV_ORDER(cv) {
+		    mindex = mzptr + ii
+		    do i = 1, npts
+		        MATRIX(mindex) = MATRIX(mindex) + Memr[bw+i-1] *
+				            BASIS(bbptr+i-1)	
+		    ii = ii + 1
+		    bbptr = bbptr + npts
+		}
+		bptr = bptr + npts
+		mzptr = mzptr + CV_ORDER(cv)
+	    }
+
+	case SPLINE1,SPLINE3:
+
+	    call amulki (LEFT(CV_LEFT(cv)), CV_ORDER(cv), Memi[rows], npts)
+	    call aaddki (Memi[rows], CV_MATRIX(cv), Memi[rows], npts)
+	    call aaddki (LEFT(CV_LEFT(cv)), vzptr, LEFT(CV_LEFT(cv)), npts) 
+
+	    # accumulate the new right side of the matrix equation
+	    do k = 1, CV_ORDER(cv) {
+	        call amulr (w, BASIS(bptr), Memr[bw], npts) 
+	        do i = 1, npts {
+		    vindex = LEFT(CV_LEFT(cv)+i-1) + k
+	            VECTOR(vindex) = VECTOR(vindex)+ Memr[bw+i-1] * y[i]
+		}
+	        bbptr = bptr
+	        ii = 0
+	        do j = k, CV_ORDER(cv) {
+		    do i = 1, npts {
+			mindex = Memi[rows+i-1] + ii
+		        MATRIX(mindex) = MATRIX(mindex) + Memr[bw+i-1] *
+			    BASIS(bbptr+i-1)
+		    }
+		    ii = ii + 1
+		    bbptr = bbptr + npts
+		}
+	        bptr = bptr + npts
+	        call aaddki (Memi[rows], CV_ORDER(cv), Memi[rows], npts)
+	    }
+	}
+
+	# release the space
+	call sfree (sp)
+	CV_BASIS(cv) = NULL
+	CV_LEFT(cv) = NULL
+end
diff --git a/math/curfit/cvchomat.gx b/math/curfit/cvchomat.gx
new file mode 100644
index 00000000..c9324a32
--- /dev/null
+++ b/math/curfit/cvchomat.gx
@@ -0,0 +1,117 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVCHOFAC -- Routine to calculate the Cholesky factorization of a
+# symmetric, positive semi-definite banded matrix. This routines was
+# adapted from the bchfac.f routine described in "A Practical Guide
+# to Splines", Carl de Boor (1978).
+
+procedure $tcvchofac (matrix, nbands, nrows, matfac, ier)
+
+PIXEL   matrix[nbands, nrows]	# data matrix
+int	nbands			# number of bands
+int	nrows			# number of rows
+PIXEL   matfac[nbands, nrows]	# Cholesky factorization
+int	ier			# error code
+
+int	i, n, j, imax, jmax
+PIXEL   ratio
+
+begin
+	if (nrows == 1) {
+	    if (matrix[1,1] > 0.)
+	        matfac[1,1] = 1. / matrix[1,1]
+	    return
+	}
+
+		
+	# copy matrix into matfac
+	do n = 1, nrows {
+	    do j = 1, nbands
+		matfac[j,n] = matrix[j,n]
+	}
+
+	do n = 1, nrows {
+
+	    # test to see if matrix is singular
+	    $if (datatype == r)
+	    if(((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= 10. * EPSILONR) {
+	    $else
+	    if(((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= 10. * EPSILOND) {
+	    $endif
+		do j = 1, nbands
+		    matfac[j,n] = PIXEL (0.0)
+		ier = SINGULAR
+		next
+	    }
+
+	    matfac[1,n] = 1. / matfac[1,n]
+	    imax = min (nbands - 1, nrows - n)
+	    if (imax < 1)
+		next
+
+	    jmax = imax
+	    do i = 1, imax {
+		ratio = matfac[i+1,n] * matfac[1,n]
+		do j = 1, jmax
+		    matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
+		jmax = jmax - 1
+		matfac[i+1,n] = ratio
+	    }
+	}
+end
+
+# CVCHOSLV -- Solve the matrix whose Cholesky factorization was calculated in
+# CVCHOFAC for the coefficients. This routine was adapted from bchslv.f
+# described in "A Practical Guide to Splines", by Carl de Boor (1978).
+
+procedure $tcvchoslv (matfac, nbands, nrows, vector, coeff)
+
+PIXEL   matfac[nbands,nrows] 		# Cholesky factorization
+int	nbands				# number of bands
+int	nrows				# number of rows
+PIXEL   vector[nrows]			# right side of matrix equation
+PIXEL   coeff[nrows]			# coefficients
+
+int	i, n, j, jmax, nbndm1
+
+begin
+	if (nrows == 1) {
+	    coeff[1] = vector[1] * matfac[1,1]
+	    return
+	}
+
+	# copy vector to coefficients
+	do i = 1, nrows
+	    coeff[i] = vector[i]
+
+
+	# forward substitution
+	nbndm1 = nbands - 1
+	do n = 1, nrows {
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+	        do j = 1, jmax
+		    coeff[j+n] = coeff[j+n] - matfac[j+1,n] * coeff[n]
+	    }
+	}
+
+
+	# back substitution
+	for (n = nrows; n >= 1; n = n - 1) {
+	    coeff[n] = coeff[n] * matfac[1,n]
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+		do j = 1, jmax
+		    coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
+	    }
+	}
+end
diff --git a/math/curfit/cvchomatd.x b/math/curfit/cvchomatd.x
new file mode 100644
index 00000000..1afef515
--- /dev/null
+++ b/math/curfit/cvchomatd.x
@@ -0,0 +1,109 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+# CVCHOFAC -- Routine to calculate the Cholesky factorization of a
+# symmetric, positive semi-definite banded matrix. This routines was
+# adapted from the bchfac.f routine described in "A Practical Guide
+# to Splines", Carl de Boor (1978).
+
+procedure dcvchofac (matrix, nbands, nrows, matfac, ier)
+
+double   matrix[nbands, nrows]	# data matrix
+int	nbands			# number of bands
+int	nrows			# number of rows
+double   matfac[nbands, nrows]	# Cholesky factorization
+int	ier			# error code
+
+int	i, n, j, imax, jmax
+double   ratio
+
+begin
+	if (nrows == 1) {
+	    if (matrix[1,1] > 0.)
+	        matfac[1,1] = 1. / matrix[1,1]
+	    return
+	}
+
+		
+	# copy matrix into matfac
+	do n = 1, nrows {
+	    do j = 1, nbands
+		matfac[j,n] = matrix[j,n]
+	}
+
+	do n = 1, nrows {
+
+	    # test to see if matrix is singular
+	    if(((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= 10. * EPSILOND) {
+		do j = 1, nbands
+		    matfac[j,n] = double (0.0)
+		ier = SINGULAR
+		next
+	    }
+
+	    matfac[1,n] = 1. / matfac[1,n]
+	    imax = min (nbands - 1, nrows - n)
+	    if (imax < 1)
+		next
+
+	    jmax = imax
+	    do i = 1, imax {
+		ratio = matfac[i+1,n] * matfac[1,n]
+		do j = 1, jmax
+		    matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
+		jmax = jmax - 1
+		matfac[i+1,n] = ratio
+	    }
+	}
+end
+
+# CVCHOSLV -- Solve the matrix whose Cholesky factorization was calculated in
+# CVCHOFAC for the coefficients. This routine was adapted from bchslv.f
+# described in "A Practical Guide to Splines", by Carl de Boor (1978).
+
+procedure dcvchoslv (matfac, nbands, nrows, vector, coeff)
+
+double   matfac[nbands,nrows] 		# Cholesky factorization
+int	nbands				# number of bands
+int	nrows				# number of rows
+double   vector[nrows]			# right side of matrix equation
+double   coeff[nrows]			# coefficients
+
+int	i, n, j, jmax, nbndm1
+
+begin
+	if (nrows == 1) {
+	    coeff[1] = vector[1] * matfac[1,1]
+	    return
+	}
+
+	# copy vector to coefficients
+	do i = 1, nrows
+	    coeff[i] = vector[i]
+
+
+	# forward substitution
+	nbndm1 = nbands - 1
+	do n = 1, nrows {
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+	        do j = 1, jmax
+		    coeff[j+n] = coeff[j+n] - matfac[j+1,n] * coeff[n]
+	    }
+	}
+
+
+	# back substitution
+	for (n = nrows; n >= 1; n = n - 1) {
+	    coeff[n] = coeff[n] * matfac[1,n]
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+		do j = 1, jmax
+		    coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
+	    }
+	}
+end
diff --git a/math/curfit/cvchomatr.x b/math/curfit/cvchomatr.x
new file mode 100644
index 00000000..cce25ecf
--- /dev/null
+++ b/math/curfit/cvchomatr.x
@@ -0,0 +1,109 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+# CVCHOFAC -- Routine to calculate the Cholesky factorization of a
+# symmetric, positive semi-definite banded matrix. This routines was
+# adapted from the bchfac.f routine described in "A Practical Guide
+# to Splines", Carl de Boor (1978).
+
+procedure rcvchofac (matrix, nbands, nrows, matfac, ier)
+
+real   matrix[nbands, nrows]	# data matrix
+int	nbands			# number of bands
+int	nrows			# number of rows
+real   matfac[nbands, nrows]	# Cholesky factorization
+int	ier			# error code
+
+int	i, n, j, imax, jmax
+real   ratio
+
+begin
+	if (nrows == 1) {
+	    if (matrix[1,1] > 0.)
+	        matfac[1,1] = 1. / matrix[1,1]
+	    return
+	}
+
+		
+	# copy matrix into matfac
+	do n = 1, nrows {
+	    do j = 1, nbands
+		matfac[j,n] = matrix[j,n]
+	}
+
+	do n = 1, nrows {
+
+	    # test to see if matrix is singular
+	    if(((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= 10. * EPSILONR) {
+		do j = 1, nbands
+		    matfac[j,n] = real (0.0)
+		ier = SINGULAR
+		next
+	    }
+
+	    matfac[1,n] = 1. / matfac[1,n]
+	    imax = min (nbands - 1, nrows - n)
+	    if (imax < 1)
+		next
+
+	    jmax = imax
+	    do i = 1, imax {
+		ratio = matfac[i+1,n] * matfac[1,n]
+		do j = 1, jmax
+		    matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
+		jmax = jmax - 1
+		matfac[i+1,n] = ratio
+	    }
+	}
+end
+
+# CVCHOSLV -- Solve the matrix whose Cholesky factorization was calculated in
+# CVCHOFAC for the coefficients. This routine was adapted from bchslv.f
+# described in "A Practical Guide to Splines", by Carl de Boor (1978).
+
+procedure rcvchoslv (matfac, nbands, nrows, vector, coeff)
+
+real   matfac[nbands,nrows] 		# Cholesky factorization
+int	nbands				# number of bands
+int	nrows				# number of rows
+real   vector[nrows]			# right side of matrix equation
+real   coeff[nrows]			# coefficients
+
+int	i, n, j, jmax, nbndm1
+
+begin
+	if (nrows == 1) {
+	    coeff[1] = vector[1] * matfac[1,1]
+	    return
+	}
+
+	# copy vector to coefficients
+	do i = 1, nrows
+	    coeff[i] = vector[i]
+
+
+	# forward substitution
+	nbndm1 = nbands - 1
+	do n = 1, nrows {
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+	        do j = 1, jmax
+		    coeff[j+n] = coeff[j+n] - matfac[j+1,n] * coeff[n]
+	    }
+	}
+
+
+	# back substitution
+	for (n = nrows; n >= 1; n = n - 1) {
+	    coeff[n] = coeff[n] * matfac[1,n]
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+		do j = 1, jmax
+		    coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
+	    }
+	}
+end
diff --git a/math/curfit/cvcoeff.gx b/math/curfit/cvcoeff.gx
new file mode 100644
index 00000000..46c58c0f
--- /dev/null
+++ b/math/curfit/cvcoeff.gx
@@ -0,0 +1,26 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVCOEFF -- Procedure to fetch the number and magnitude of the coefficients.
+
+$if (datatype == r)
+procedure cvcoeff (cv, coeff, ncoeff)
+$else
+procedure dcvcoeff (cv, coeff, ncoeff)
+$endif
+
+pointer	cv		# curve descriptor
+PIXEL	coeff[ARB]	# the coefficients of the fit
+int	ncoeff		# the number of coefficients
+
+begin
+	ncoeff = CV_NCOEFF(cv)
+
+	# fetch coefficients
+	call amov$t (COEFF(CV_COEFF(cv)), coeff, ncoeff)
+end
diff --git a/math/curfit/cvcoeffd.x b/math/curfit/cvcoeffd.x
new file mode 100644
index 00000000..1d63b9cf
--- /dev/null
+++ b/math/curfit/cvcoeffd.x
@@ -0,0 +1,18 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "dcurfitdef.h"
+
+# CVCOEFF -- Procedure to fetch the number and magnitude of the coefficients.
+
+procedure dcvcoeff (cv, coeff, ncoeff)
+
+pointer	cv		# curve descriptor
+double	coeff[ARB]	# the coefficients of the fit
+int	ncoeff		# the number of coefficients
+
+begin
+	ncoeff = CV_NCOEFF(cv)
+
+	# fetch coefficients
+	call amovd (COEFF(CV_COEFF(cv)), coeff, ncoeff)
+end
diff --git a/math/curfit/cvcoeffr.x b/math/curfit/cvcoeffr.x
new file mode 100644
index 00000000..69e73848
--- /dev/null
+++ b/math/curfit/cvcoeffr.x
@@ -0,0 +1,18 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "curfitdef.h"
+
+# CVCOEFF -- Procedure to fetch the number and magnitude of the coefficients.
+
+procedure cvcoeff (cv, coeff, ncoeff)
+
+pointer	cv		# curve descriptor
+real	coeff[ARB]	# the coefficients of the fit
+int	ncoeff		# the number of coefficients
+
+begin
+	ncoeff = CV_NCOEFF(cv)
+
+	# fetch coefficients
+	call amovr (COEFF(CV_COEFF(cv)), coeff, ncoeff)
+end
diff --git a/math/curfit/cverrors.gx b/math/curfit/cverrors.gx
new file mode 100644
index 00000000..07288c7f
--- /dev/null
+++ b/math/curfit/cverrors.gx
@@ -0,0 +1,91 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+define	COV	Mem$t[P2P($1)]	# element of COV
+
+# CVERRORS -- Procedure to calculate the reduced chi-squared of the fit
+# and the standard deviations of the coefficients. First the variance
+# and the reduced chi-squared of the fit are estimated. If these two
+# quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+$if (datatype == r)
+procedure cverrors (cv, y, w, yfit, npts, chisqr, errors)
+$else
+procedure dcverrors (cv, y, w, yfit, npts, chisqr, errors)
+$endif
+
+pointer	cv		# curve descriptor
+PIXEL	y[ARB]		# data points
+PIXEL	yfit[ARB]	# fitted data points
+PIXEL	w[ARB]		# array of weights
+int	npts		# number of points
+PIXEL	chisqr		# reduced chi-squared of fit
+PIXEL	errors[ARB]	# errors in coefficients
+
+int	i, n, nfree
+PIXEL   variance, chisq, hold
+pointer	sp, covptr
+
+begin
+	# allocate space for covariance vector
+	call smark (sp)
+	call salloc (covptr, CV_NCOEFF(cv), TY_PIXEL)
+
+	# estimate the variance and chi-squared of the fit
+	n = 0
+	variance = 0.
+	chisq = 0.
+	do i = 1, npts {
+	    if (w[i] <= 0.0)
+		next
+	    hold = (y[i] - yfit[i]) ** 2
+	    variance = variance + hold
+	    chisq = chisq + hold * w[i]
+	    n = n + 1
+	}
+
+	# calculate the reduced chi-squared
+	nfree = n - CV_NCOEFF(cv)
+	if (nfree  > 0)
+	    chisqr = chisq / nfree
+	else
+	    chisqr = 0.
+
+	# if the variance equals the reduced chi_squared as in the
+	# case of uniform weights then scale the errors in the coefficients
+	# by the variance not the reduced chi-squared
+	if (abs (chisq - variance) <= DELTA)
+	    if (nfree > 0)
+	        variance = chisq / nfree
+	    else
+		variance = 0.
+	else
+	    variance = 1.
+
+	# calculate the  errors in the coefficients
+	# the inverse of MATRIX is calculated column by column
+	# the error of the j-th coefficient is the j-th element of the
+	# j-th column of the inverse matrix
+	do i = 1, CV_NCOEFF(cv) {
+	    call aclr$t (COV(covptr), CV_NCOEFF(cv))
+	    COV(covptr+i-1) = 1.
+	    call $tcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+	    	    COV(covptr), COV(covptr))
+	    if (COV(covptr+i-1) >= 0.)
+	        errors[i] = sqrt (COV(covptr+i-1) * variance)
+	    else
+		errors[i] = 0.
+	}
+
+
+	call sfree (sp)
+end
diff --git a/math/curfit/cverrorsd.x b/math/curfit/cverrorsd.x
new file mode 100644
index 00000000..ed0cf9dc
--- /dev/null
+++ b/math/curfit/cverrorsd.x
@@ -0,0 +1,83 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+
+include "dcurfitdef.h"
+
+define	COV	Memd[P2P($1)]	# element of COV
+
+# CVERRORS -- Procedure to calculate the reduced chi-squared of the fit
+# and the standard deviations of the coefficients. First the variance
+# and the reduced chi-squared of the fit are estimated. If these two
+# quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+procedure dcverrors (cv, y, w, yfit, npts, chisqr, errors)
+
+pointer	cv		# curve descriptor
+double	y[ARB]		# data points
+double	yfit[ARB]	# fitted data points
+double	w[ARB]		# array of weights
+int	npts		# number of points
+double	chisqr		# reduced chi-squared of fit
+double	errors[ARB]	# errors in coefficients
+
+int	i, n, nfree
+double   variance, chisq, hold
+pointer	sp, covptr
+
+begin
+	# allocate space for covariance vector
+	call smark (sp)
+	call salloc (covptr, CV_NCOEFF(cv), TY_DOUBLE)
+
+	# estimate the variance and chi-squared of the fit
+	n = 0
+	variance = 0.
+	chisq = 0.
+	do i = 1, npts {
+	    if (w[i] <= 0.0)
+		next
+	    hold = (y[i] - yfit[i]) ** 2
+	    variance = variance + hold
+	    chisq = chisq + hold * w[i]
+	    n = n + 1
+	}
+
+	# calculate the reduced chi-squared
+	nfree = n - CV_NCOEFF(cv)
+	if (nfree  > 0)
+	    chisqr = chisq / nfree
+	else
+	    chisqr = 0.
+
+	# if the variance equals the reduced chi_squared as in the
+	# case of uniform weights then scale the errors in the coefficients
+	# by the variance not the reduced chi-squared
+	if (abs (chisq - variance) <= DELTA)
+	    if (nfree > 0)
+	        variance = chisq / nfree
+	    else
+		variance = 0.
+	else
+	    variance = 1.
+
+	# calculate the  errors in the coefficients
+	# the inverse of MATRIX is calculated column by column
+	# the error of the j-th coefficient is the j-th element of the
+	# j-th column of the inverse matrix
+	do i = 1, CV_NCOEFF(cv) {
+	    call aclrd (COV(covptr), CV_NCOEFF(cv))
+	    COV(covptr+i-1) = 1.
+	    call dcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+	    	    COV(covptr), COV(covptr))
+	    if (COV(covptr+i-1) >= 0.)
+	        errors[i] = sqrt (COV(covptr+i-1) * variance)
+	    else
+		errors[i] = 0.
+	}
+
+
+	call sfree (sp)
+end
diff --git a/math/curfit/cverrorsr.x b/math/curfit/cverrorsr.x
new file mode 100644
index 00000000..89533b7b
--- /dev/null
+++ b/math/curfit/cverrorsr.x
@@ -0,0 +1,83 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+
+include "curfitdef.h"
+
+define	COV	Memr[P2P($1)]	# element of COV
+
+# CVERRORS -- Procedure to calculate the reduced chi-squared of the fit
+# and the standard deviations of the coefficients. First the variance
+# and the reduced chi-squared of the fit are estimated. If these two
+# quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+procedure cverrors (cv, y, w, yfit, npts, chisqr, errors)
+
+pointer	cv		# curve descriptor
+real	y[ARB]		# data points
+real	yfit[ARB]	# fitted data points
+real	w[ARB]		# array of weights
+int	npts		# number of points
+real	chisqr		# reduced chi-squared of fit
+real	errors[ARB]	# errors in coefficients
+
+int	i, n, nfree
+real   variance, chisq, hold
+pointer	sp, covptr
+
+begin
+	# allocate space for covariance vector
+	call smark (sp)
+	call salloc (covptr, CV_NCOEFF(cv), TY_REAL)
+
+	# estimate the variance and chi-squared of the fit
+	n = 0
+	variance = 0.
+	chisq = 0.
+	do i = 1, npts {
+	    if (w[i] <= 0.0)
+		next
+	    hold = (y[i] - yfit[i]) ** 2
+	    variance = variance + hold
+	    chisq = chisq + hold * w[i]
+	    n = n + 1
+	}
+
+	# calculate the reduced chi-squared
+	nfree = n - CV_NCOEFF(cv)
+	if (nfree  > 0)
+	    chisqr = chisq / nfree
+	else
+	    chisqr = 0.
+
+	# if the variance equals the reduced chi_squared as in the
+	# case of uniform weights then scale the errors in the coefficients
+	# by the variance not the reduced chi-squared
+	if (abs (chisq - variance) <= DELTA)
+	    if (nfree > 0)
+	        variance = chisq / nfree
+	    else
+		variance = 0.
+	else
+	    variance = 1.
+
+	# calculate the  errors in the coefficients
+	# the inverse of MATRIX is calculated column by column
+	# the error of the j-th coefficient is the j-th element of the
+	# j-th column of the inverse matrix
+	do i = 1, CV_NCOEFF(cv) {
+	    call aclrr (COV(covptr), CV_NCOEFF(cv))
+	    COV(covptr+i-1) = 1.
+	    call rcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+	    	    COV(covptr), COV(covptr))
+	    if (COV(covptr+i-1) >= 0.)
+	        errors[i] = sqrt (COV(covptr+i-1) * variance)
+	    else
+		errors[i] = 0.
+	}
+
+
+	call sfree (sp)
+end
diff --git a/math/curfit/cveval.gx b/math/curfit/cveval.gx
new file mode 100644
index 00000000..995b4f74
--- /dev/null
+++ b/math/curfit/cveval.gx
@@ -0,0 +1,59 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVEVAL -- Procedure to evaluate curve at a given x. The CV_NCOEFF(cv)
+# coefficients are assumed to be in COEFF.
+
+$if (datatype == r)
+PIXEL procedure cveval (cv, x)
+$else
+PIXEL procedure dcveval (cv, x)
+$endif
+
+pointer	cv		# curve descriptor
+PIXEL	x		# x value
+
+int	left
+pointer	cptr, xptr
+PIXEL	yfit
+
+PIXEL	adot$t()
+
+begin
+
+	# calculate the non-zero basis functions
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 0
+	    call $tcv_b1cheb (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			   XBASIS(CV_XBASIS(cv)))
+	case LEGENDRE:
+	    left = 0
+	    call $tcv_b1leg (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			   XBASIS(CV_XBASIS(cv)))
+	case SPLINE3:
+	    call $tcv_b1spline3 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	    		      CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case SPLINE1:
+	    call $tcv_b1spline1 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	    		      CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case USERFNC:
+	    left = 0
+	    call $tcv_b1user (cv, x)
+	}
+
+
+	# accumulate the fitted value
+	cptr = CV_COEFF(cv) + left
+	xptr = CV_XBASIS(cv)
+	yfit = adot$t (XBASIS(xptr), COEFF(cptr), CV_ORDER(cv))
+
+	return (yfit)
+end
diff --git a/math/curfit/cvevald.x b/math/curfit/cvevald.x
new file mode 100644
index 00000000..c1c1f052
--- /dev/null
+++ b/math/curfit/cvevald.x
@@ -0,0 +1,51 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+# CVEVAL -- Procedure to evaluate curve at a given x. The CV_NCOEFF(cv)
+# coefficients are assumed to be in COEFF.
+
+double procedure dcveval (cv, x)
+
+pointer	cv		# curve descriptor
+double	x		# x value
+
+int	left
+pointer	cptr, xptr
+double	yfit
+
+double	adotd()
+
+begin
+
+	# calculate the non-zero basis functions
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 0
+	    call dcv_b1cheb (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			   XBASIS(CV_XBASIS(cv)))
+	case LEGENDRE:
+	    left = 0
+	    call dcv_b1leg (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			   XBASIS(CV_XBASIS(cv)))
+	case SPLINE3:
+	    call dcv_b1spline3 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	    		      CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case SPLINE1:
+	    call dcv_b1spline1 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	    		      CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case USERFNC:
+	    left = 0
+	    call dcv_b1user (cv, x)
+	}
+
+
+	# accumulate the fitted value
+	cptr = CV_COEFF(cv) + left
+	xptr = CV_XBASIS(cv)
+	yfit = adotd (XBASIS(xptr), COEFF(cptr), CV_ORDER(cv))
+
+	return (yfit)
+end
diff --git a/math/curfit/cvevalr.x b/math/curfit/cvevalr.x
new file mode 100644
index 00000000..56c4c772
--- /dev/null
+++ b/math/curfit/cvevalr.x
@@ -0,0 +1,51 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+# CVEVAL -- Procedure to evaluate curve at a given x. The CV_NCOEFF(cv)
+# coefficients are assumed to be in COEFF.
+
+real procedure cveval (cv, x)
+
+pointer	cv		# curve descriptor
+real	x		# x value
+
+int	left
+pointer	cptr, xptr
+real	yfit
+
+real	adotr()
+
+begin
+
+	# calculate the non-zero basis functions
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 0
+	    call rcv_b1cheb (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			   XBASIS(CV_XBASIS(cv)))
+	case LEGENDRE:
+	    left = 0
+	    call rcv_b1leg (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			   XBASIS(CV_XBASIS(cv)))
+	case SPLINE3:
+	    call rcv_b1spline3 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	    		      CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case SPLINE1:
+	    call rcv_b1spline1 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+	    		      CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case USERFNC:
+	    left = 0
+	    call rcv_b1user (cv, x)
+	}
+
+
+	# accumulate the fitted value
+	cptr = CV_COEFF(cv) + left
+	xptr = CV_XBASIS(cv)
+	yfit = adotr (XBASIS(xptr), COEFF(cptr), CV_ORDER(cv))
+
+	return (yfit)
+end
diff --git a/math/curfit/cvfit.gx b/math/curfit/cvfit.gx
new file mode 100644
index 00000000..65c3bfb5
--- /dev/null
+++ b/math/curfit/cvfit.gx
@@ -0,0 +1,66 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVFIT -- Procedure to add a set of points to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the CV_ORDER(cv) by CV_NCOEFF(cv) matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals. This method
+# of storage is particularly efficient for the large symmetric
+# banded matrices produced during spline fits. The inner product
+# of the basis functions and the data ordinates are stored in the
+# CV_NCOEFF(cv)-vector VECTOR. The array LEFT is
+# used for the indices describing which elements of MATRIX and VECTOR are
+# to receive the inner products. After accumulation is complete
+# the Cholesky factorization of MATRIX is calculated and stored
+# in the CV_ORDER(cv) by CV_NCOEFF(cv) matrix CHOFAC. Finally
+# the coefficients are calculated by forward and back substitution
+# and placed in COEFF.
+
+$if (datatype == r)
+procedure cvfit (cv, x, y, w, npts, wtflag, ier)
+$else
+procedure dcvfit (cv, x, y, w, npts, wtflag, ier)
+$endif
+
+pointer	cv		# curve descriptor
+PIXEL	x[npts]		# array of abcissa
+PIXEL	y[npts]		# array of ordinates
+PIXEL	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+int	ier		# error code
+
+
+begin
+	$if (datatype == r)
+
+	# zero the appropriate arrays
+	call cvzero (cv)
+
+	# enter data points
+	call cvacpts (cv, x, y, w, npts, wtflag)
+
+	# solve the system
+	call cvsolve (cv, ier)
+
+	$else
+
+	# zero the appropriate arrays
+	call dcvzero (cv)
+
+	# enter data points
+	call dcvacpts (cv, x, y, w, npts, wtflag)
+
+	# solve the system
+	call dcvsolve (cv, ier)
+
+	$endif
+end
diff --git a/math/curfit/cvfitd.x b/math/curfit/cvfitd.x
new file mode 100644
index 00000000..bd4f9e83
--- /dev/null
+++ b/math/curfit/cvfitd.x
@@ -0,0 +1,45 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+# CVFIT -- Procedure to add a set of points to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the CV_ORDER(cv) by CV_NCOEFF(cv) matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals. This method
+# of storage is particularly efficient for the large symmetric
+# banded matrices produced during spline fits. The inner product
+# of the basis functions and the data ordinates are stored in the
+# CV_NCOEFF(cv)-vector VECTOR. The array LEFT is
+# used for the indices describing which elements of MATRIX and VECTOR are
+# to receive the inner products. After accumulation is complete
+# the Cholesky factorization of MATRIX is calculated and stored
+# in the CV_ORDER(cv) by CV_NCOEFF(cv) matrix CHOFAC. Finally
+# the coefficients are calculated by forward and back substitution
+# and placed in COEFF.
+
+procedure dcvfit (cv, x, y, w, npts, wtflag, ier)
+
+pointer	cv		# curve descriptor
+double	x[npts]		# array of abcissa
+double	y[npts]		# array of ordinates
+double	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+int	ier		# error code
+
+
+begin
+
+	# zero the appropriate arrays
+	call dcvzero (cv)
+
+	# enter data points
+	call dcvacpts (cv, x, y, w, npts, wtflag)
+
+	# solve the system
+	call dcvsolve (cv, ier)
+
+end
diff --git a/math/curfit/cvfitr.x b/math/curfit/cvfitr.x
new file mode 100644
index 00000000..53374278
--- /dev/null
+++ b/math/curfit/cvfitr.x
@@ -0,0 +1,45 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+# CVFIT -- Procedure to add a set of points to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the CV_ORDER(cv) by CV_NCOEFF(cv) matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals. This method
+# of storage is particularly efficient for the large symmetric
+# banded matrices produced during spline fits. The inner product
+# of the basis functions and the data ordinates are stored in the
+# CV_NCOEFF(cv)-vector VECTOR. The array LEFT is
+# used for the indices describing which elements of MATRIX and VECTOR are
+# to receive the inner products. After accumulation is complete
+# the Cholesky factorization of MATRIX is calculated and stored
+# in the CV_ORDER(cv) by CV_NCOEFF(cv) matrix CHOFAC. Finally
+# the coefficients are calculated by forward and back substitution
+# and placed in COEFF.
+
+procedure cvfit (cv, x, y, w, npts, wtflag, ier)
+
+pointer	cv		# curve descriptor
+real	x[npts]		# array of abcissa
+real	y[npts]		# array of ordinates
+real	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+int	ier		# error code
+
+
+begin
+
+	# zero the appropriate arrays
+	call cvzero (cv)
+
+	# enter data points
+	call cvacpts (cv, x, y, w, npts, wtflag)
+
+	# solve the system
+	call cvsolve (cv, ier)
+
+end
diff --git a/math/curfit/cvfree.gx b/math/curfit/cvfree.gx
new file mode 100644
index 00000000..1c18d637
--- /dev/null
+++ b/math/curfit/cvfree.gx
@@ -0,0 +1,45 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVFREE -- Procedure to free the curve descriptor
+
+$if (datatype == r)
+procedure cvfree (cv)
+$else
+procedure dcvfree (cv)
+$endif
+
+pointer	cv	# the curve descriptor
+
+errchk	mfree
+
+begin
+	if (cv == NULL)
+	    return
+
+	if (CV_XBASIS(cv) != NULL)
+	    call mfree (CV_XBASIS(cv), TY_PIXEL)
+	if (CV_VECTOR(cv) != NULL)
+	    call mfree (CV_VECTOR(cv), TY_PIXEL)
+	if (CV_COEFF(cv) != NULL)
+	    call mfree (CV_COEFF(cv), TY_PIXEL)
+
+	if (CV_BASIS(cv) != NULL)
+	    call mfree (CV_BASIS(cv), TY_PIXEL)
+	if (CV_LEFT(cv) != NULL)
+	    call mfree (CV_LEFT(cv), TY_INT)
+	if (CV_WY(cv) != NULL)
+	    call mfree (CV_WY(cv), TY_PIXEL)
+
+	if (CV_MATRIX(cv) != NULL)
+	    call mfree (CV_MATRIX(cv), TY_PIXEL)
+	if (CV_CHOFAC(cv) != NULL)
+	    call mfree (CV_CHOFAC(cv), TY_PIXEL)
+
+	call mfree (cv, TY_STRUCT)
+end
diff --git a/math/curfit/cvfreed.x b/math/curfit/cvfreed.x
new file mode 100644
index 00000000..42971c86
--- /dev/null
+++ b/math/curfit/cvfreed.x
@@ -0,0 +1,37 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "dcurfitdef.h"
+
+# CVFREE -- Procedure to free the curve descriptor
+
+procedure dcvfree (cv)
+
+pointer	cv	# the curve descriptor
+
+errchk	mfree
+
+begin
+	if (cv == NULL)
+	    return
+
+	if (CV_XBASIS(cv) != NULL)
+	    call mfree (CV_XBASIS(cv), TY_DOUBLE)
+	if (CV_VECTOR(cv) != NULL)
+	    call mfree (CV_VECTOR(cv), TY_DOUBLE)
+	if (CV_COEFF(cv) != NULL)
+	    call mfree (CV_COEFF(cv), TY_DOUBLE)
+
+	if (CV_BASIS(cv) != NULL)
+	    call mfree (CV_BASIS(cv), TY_DOUBLE)
+	if (CV_LEFT(cv) != NULL)
+	    call mfree (CV_LEFT(cv), TY_INT)
+	if (CV_WY(cv) != NULL)
+	    call mfree (CV_WY(cv), TY_DOUBLE)
+
+	if (CV_MATRIX(cv) != NULL)
+	    call mfree (CV_MATRIX(cv), TY_DOUBLE)
+	if (CV_CHOFAC(cv) != NULL)
+	    call mfree (CV_CHOFAC(cv), TY_DOUBLE)
+
+	call mfree (cv, TY_STRUCT)
+end
diff --git a/math/curfit/cvfreer.x b/math/curfit/cvfreer.x
new file mode 100644
index 00000000..95adffca
--- /dev/null
+++ b/math/curfit/cvfreer.x
@@ -0,0 +1,37 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "curfitdef.h"
+
+# CVFREE -- Procedure to free the curve descriptor
+
+procedure cvfree (cv)
+
+pointer	cv	# the curve descriptor
+
+errchk	mfree
+
+begin
+	if (cv == NULL)
+	    return
+
+	if (CV_XBASIS(cv) != NULL)
+	    call mfree (CV_XBASIS(cv), TY_REAL)
+	if (CV_VECTOR(cv) != NULL)
+	    call mfree (CV_VECTOR(cv), TY_REAL)
+	if (CV_COEFF(cv) != NULL)
+	    call mfree (CV_COEFF(cv), TY_REAL)
+
+	if (CV_BASIS(cv) != NULL)
+	    call mfree (CV_BASIS(cv), TY_REAL)
+	if (CV_LEFT(cv) != NULL)
+	    call mfree (CV_LEFT(cv), TY_INT)
+	if (CV_WY(cv) != NULL)
+	    call mfree (CV_WY(cv), TY_REAL)
+
+	if (CV_MATRIX(cv) != NULL)
+	    call mfree (CV_MATRIX(cv), TY_REAL)
+	if (CV_CHOFAC(cv) != NULL)
+	    call mfree (CV_CHOFAC(cv), TY_REAL)
+
+	call mfree (cv, TY_STRUCT)
+end
diff --git a/math/curfit/cvinit.gx b/math/curfit/cvinit.gx
new file mode 100644
index 00000000..f3518dab
--- /dev/null
+++ b/math/curfit/cvinit.gx
@@ -0,0 +1,95 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+include	<mach.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVINIT --  Procedure to initialize the curve  descriptor.
+
+$if (datatype == r)
+procedure cvinit (cv, curve_type, order, xmin, xmax)
+$else
+procedure dcvinit (cv, curve_type, order, xmin, xmax)
+$endif
+
+pointer	cv		# curve descriptor
+int	curve_type	# type of curve to be fitted
+int	order		# order of curve to be fitted, or in the case of the
+			# spline the number of polynomial pieces to be fit
+PIXEL	xmin		# minimum value of x
+PIXEL	xmax		# maximum value of x
+
+errchk	malloc, calloc
+
+begin
+	# check for bad parameters.
+	cv = NULL
+	if (order < 1)
+	    call error (0, "CVINIT: Illegal order.")
+
+	if (xmax <= xmin)
+	    call error (0, "CVINIT: xmax <= xmin.")
+
+	# allocate space for the curve descriptor
+	call calloc (cv, LEN_CVSTRUCT, TY_STRUCT)
+
+	# specify the curve-type dependent parameters
+	switch (curve_type) {
+	case CHEBYSHEV, LEGENDRE:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    CV_RANGE(cv) = 2. / (xmax - xmin)
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	case SPLINE3:
+	    CV_ORDER(cv) = SPLINE3_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE3_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (xmax - xmin)
+	case SPLINE1:
+	    CV_ORDER(cv) = SPLINE1_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE1_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (xmax - xmin)
+	case USERFNC:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    # Prevent abort for non-linear userfnc, where these values
+	    #  may be arbitrary arguments to pass to external.
+	    if ( abs(xmax-xmin) > EPSILON ) {
+		CV_RANGE(cv) = 2. / (xmax - xmin)
+	    } else {
+		CV_RANGE(cv) = 0.
+	    }
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	default:
+	    call error (0, "CVINIT: Unknown curve type.")
+	}
+
+	# set remaining parameters
+	CV_TYPE(cv) = curve_type
+	CV_XMIN(cv) = xmin
+	CV_XMAX(cv) = xmax
+
+	# allocate space for the matrix and vectors
+	call calloc (CV_XBASIS(cv), CV_ORDER(cv), TY_PIXEL)
+	call calloc (CV_MATRIX(cv), CV_ORDER(cv)*CV_NCOEFF(cv), TY_PIXEL)
+	call calloc (CV_CHOFAC(cv), CV_ORDER(cv)*CV_NCOEFF(cv), TY_PIXEL)
+	call calloc (CV_VECTOR(cv), CV_NCOEFF(cv), TY_PIXEL)
+	call calloc (CV_COEFF(cv), CV_NCOEFF(cv), TY_PIXEL)
+
+	# initialize pointer to basis functions to null
+	CV_BASIS(cv) = NULL
+	CV_WY(cv) = NULL
+	CV_LEFT(cv) = NULL
+
+	# set null user function
+	CV_USERFNC(cv) = NULL
+
+	# set data points counter
+	CV_NPTS(cv) = 0
+end
diff --git a/math/curfit/cvinitd.x b/math/curfit/cvinitd.x
new file mode 100644
index 00000000..6613d88a
--- /dev/null
+++ b/math/curfit/cvinitd.x
@@ -0,0 +1,87 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+include	<mach.h>
+
+include "dcurfitdef.h"
+
+# CVINIT --  Procedure to initialize the curve  descriptor.
+
+procedure dcvinit (cv, curve_type, order, xmin, xmax)
+
+pointer	cv		# curve descriptor
+int	curve_type	# type of curve to be fitted
+int	order		# order of curve to be fitted, or in the case of the
+			# spline the number of polynomial pieces to be fit
+double	xmin		# minimum value of x
+double	xmax		# maximum value of x
+
+errchk	malloc, calloc
+
+begin
+	# check for bad parameters.
+	cv = NULL
+	if (order < 1)
+	    call error (0, "CVINIT: Illegal order.")
+
+	if (xmax <= xmin)
+	    call error (0, "CVINIT: xmax <= xmin.")
+
+	# allocate space for the curve descriptor
+	call calloc (cv, LEN_CVSTRUCT, TY_STRUCT)
+
+	# specify the curve-type dependent parameters
+	switch (curve_type) {
+	case CHEBYSHEV, LEGENDRE:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    CV_RANGE(cv) = 2. / (xmax - xmin)
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	case SPLINE3:
+	    CV_ORDER(cv) = SPLINE3_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE3_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (xmax - xmin)
+	case SPLINE1:
+	    CV_ORDER(cv) = SPLINE1_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE1_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (xmax - xmin)
+	case USERFNC:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    # Prevent abort for non-linear userfnc, where these values
+	    #  may be arbitrary arguments to pass to external.
+	    if ( abs(xmax-xmin) > EPSILON ) {
+		CV_RANGE(cv) = 2. / (xmax - xmin)
+	    } else {
+		CV_RANGE(cv) = 0.
+	    }
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	default:
+	    call error (0, "CVINIT: Unknown curve type.")
+	}
+
+	# set remaining parameters
+	CV_TYPE(cv) = curve_type
+	CV_XMIN(cv) = xmin
+	CV_XMAX(cv) = xmax
+
+	# allocate space for the matrix and vectors
+	call calloc (CV_XBASIS(cv), CV_ORDER(cv), TY_DOUBLE)
+	call calloc (CV_MATRIX(cv), CV_ORDER(cv)*CV_NCOEFF(cv), TY_DOUBLE)
+	call calloc (CV_CHOFAC(cv), CV_ORDER(cv)*CV_NCOEFF(cv), TY_DOUBLE)
+	call calloc (CV_VECTOR(cv), CV_NCOEFF(cv), TY_DOUBLE)
+	call calloc (CV_COEFF(cv), CV_NCOEFF(cv), TY_DOUBLE)
+
+	# initialize pointer to basis functions to null
+	CV_BASIS(cv) = NULL
+	CV_WY(cv) = NULL
+	CV_LEFT(cv) = NULL
+
+	# set null user function
+	CV_USERFNC(cv) = NULL
+
+	# set data points counter
+	CV_NPTS(cv) = 0
+end
diff --git a/math/curfit/cvinitr.x b/math/curfit/cvinitr.x
new file mode 100644
index 00000000..0af12853
--- /dev/null
+++ b/math/curfit/cvinitr.x
@@ -0,0 +1,87 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+include	<mach.h>
+
+include "curfitdef.h"
+
+# CVINIT --  Procedure to initialize the curve  descriptor.
+
+procedure cvinit (cv, curve_type, order, xmin, xmax)
+
+pointer	cv		# curve descriptor
+int	curve_type	# type of curve to be fitted
+int	order		# order of curve to be fitted, or in the case of the
+			# spline the number of polynomial pieces to be fit
+real	xmin		# minimum value of x
+real	xmax		# maximum value of x
+
+errchk	malloc, calloc
+
+begin
+	# check for bad parameters.
+	cv = NULL
+	if (order < 1)
+	    call error (0, "CVINIT: Illegal order.")
+
+	if (xmax <= xmin)
+	    call error (0, "CVINIT: xmax <= xmin.")
+
+	# allocate space for the curve descriptor
+	call calloc (cv, LEN_CVSTRUCT, TY_STRUCT)
+
+	# specify the curve-type dependent parameters
+	switch (curve_type) {
+	case CHEBYSHEV, LEGENDRE:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    CV_RANGE(cv) = 2. / (xmax - xmin)
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	case SPLINE3:
+	    CV_ORDER(cv) = SPLINE3_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE3_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (xmax - xmin)
+	case SPLINE1:
+	    CV_ORDER(cv) = SPLINE1_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE1_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (xmax - xmin)
+	case USERFNC:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    # Prevent abort for non-linear userfnc, where these values
+	    #  may be arbitrary arguments to pass to external.
+	    if ( abs(xmax-xmin) > EPSILON ) {
+		CV_RANGE(cv) = 2. / (xmax - xmin)
+	    } else {
+		CV_RANGE(cv) = 0.
+	    }
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	default:
+	    call error (0, "CVINIT: Unknown curve type.")
+	}
+
+	# set remaining parameters
+	CV_TYPE(cv) = curve_type
+	CV_XMIN(cv) = xmin
+	CV_XMAX(cv) = xmax
+
+	# allocate space for the matrix and vectors
+	call calloc (CV_XBASIS(cv), CV_ORDER(cv), TY_REAL)
+	call calloc (CV_MATRIX(cv), CV_ORDER(cv)*CV_NCOEFF(cv), TY_REAL)
+	call calloc (CV_CHOFAC(cv), CV_ORDER(cv)*CV_NCOEFF(cv), TY_REAL)
+	call calloc (CV_VECTOR(cv), CV_NCOEFF(cv), TY_REAL)
+	call calloc (CV_COEFF(cv), CV_NCOEFF(cv), TY_REAL)
+
+	# initialize pointer to basis functions to null
+	CV_BASIS(cv) = NULL
+	CV_WY(cv) = NULL
+	CV_LEFT(cv) = NULL
+
+	# set null user function
+	CV_USERFNC(cv) = NULL
+
+	# set data points counter
+	CV_NPTS(cv) = 0
+end
diff --git a/math/curfit/cvpower.gx b/math/curfit/cvpower.gx
new file mode 100644
index 00000000..0e3cb62a
--- /dev/null
+++ b/math/curfit/cvpower.gx
@@ -0,0 +1,526 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include	<math/curfit.h>
+
+$if (datatype == r)
+include	"curfitdef.h"
+$else
+include	"dcurfitdef.h"
+$endif
+
+# CVPOWER -- Convert legendre or chebyshev coeffecients to power series.
+
+$if (datatype == r)
+procedure cvpower (cv, ps_coeff, ncoeff)
+$else
+procedure dcvpower (cv, ps_coeff, ncoeff)
+$endif
+
+pointer	cv				# Pointer to curfit structure
+PIXEL	ps_coeff[ncoeff]		# Power series coefficients (output)
+int	ncoeff				# Number of coefficients in fit
+
+pointer	sp, cf_coeff, elm
+int	function
+$if (datatype == r)
+int	cvstati()
+$else
+int	dcvstati()
+$endif
+
+begin
+	$if (datatype == r)
+	function = cvstati (cv, CVTYPE)
+	ncoeff = cvstati (cv, CVNCOEFF)
+	$else
+	function = dcvstati (cv, CVTYPE)
+	ncoeff = dcvstati (cv, CVNCOEFF)
+	$endif
+
+	if (function != LEGENDRE && function != CHEBYSHEV) {
+	    call eprintf ("Cannot convert coefficients - wrong function type\n")
+	    call amovk$t (INDEF, ps_coeff, ncoeff)
+	    return
+	}
+
+	call smark (sp)
+	call salloc (elm, ncoeff ** 2, TY_DOUBLE)
+	call salloc (cf_coeff, ncoeff, TY_PIXEL)
+
+	call amovkd (0.0d0, Memd[elm], ncoeff ** 2)
+
+	# Get existing coefficients
+	$if (datatype == r)
+	call cvcoeff (cv, Memr[cf_coeff], ncoeff)
+	$else
+	call dcvcoeff (cv, Memd[cf_coeff], ncoeff)
+	$endif
+
+	switch (function){
+	case (LEGENDRE):
+	    call $tcv_mlegen (Memd[elm], ncoeff)
+	    call $tcv_legen (Memd[elm], Mem$t[cf_coeff], ps_coeff, ncoeff)
+	case (CHEBYSHEV):
+	    call $tcv_mcheby (Memd[elm], ncoeff)
+	    call $tcv_cheby (Memd[elm], Mem$t[cf_coeff], ps_coeff, ncoeff)
+	}
+
+	# Normalize coefficients
+	call $tcv_normalize (cv, ps_coeff, ncoeff)
+
+	call sfree (sp)
+end
+
+
+# CVEPOWER -- Procedure to calculate the reduced chi-squared of the fit
+# and the standard deviations of the power series coefficients. First the
+# variance and the reduced chi-squared of the fit are estimated. If these
+# two quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+$if (datatype == r)
+procedure cvepower (cv, y, w, yfit, npts, chisqr, perrors)
+$else
+procedure dcvepower (cv, y, w, yfit, npts, chisqr, perrors)
+$endif
+
+pointer	cv		# curve descriptor
+PIXEL	y[ARB]		# data points
+PIXEL	yfit[ARB]	# fitted data points
+PIXEL	w[ARB]		# array of weights
+int	npts		# number of points
+PIXEL	chisqr		# reduced chi-squared of fit
+PIXEL	perrors[ARB]	# errors in coefficients
+
+int	i, j, n, nfree, function, ncoeff
+PIXEL	variance, chisq, hold
+pointer	sp, covar, elm
+$if (datatype == r)
+int	cvstati()
+$else
+int	dcvstati()
+$endif
+
+begin
+	# Determine the function type.
+	$if (datatype == r)
+	function = cvstati (cv, CVTYPE)
+	ncoeff = cvstati (cv, CVNCOEFF)
+	$else
+	function = dcvstati (cv, CVTYPE)
+	ncoeff = dcvstati (cv, CVNCOEFF)
+	$endif
+
+	# Check the function type.
+	if (function != LEGENDRE && function != CHEBYSHEV) {
+	    call eprintf ("Cannot convert errors - wrong function type\n")
+	    call amovk$t (INDEF, perrors, ncoeff)
+	    return
+	}
+
+        # Estimate the variance and chi-squared of the fit.
+        n = 0
+        variance = 0.
+        chisq = 0.
+        do i = 1, npts {
+            if (w[i] <= 0.0)
+                next
+            hold = (y[i] - yfit[i]) ** 2
+            variance = variance + hold
+            chisq = chisq + hold * w[i]
+            n = n + 1
+        }
+
+        # Calculate the reduced chi-squared.
+        nfree = n - CV_NCOEFF(cv)
+        if (nfree  > 0)
+            chisqr = chisq / nfree
+        else
+            chisqr = 0.
+
+        # If the variance equals the reduced chi_squared as in the case of
+	# uniform weights then scale the errors in the coefficients by the
+	# variance not the reduced chi-squared
+        if (abs (chisq - variance) <= DELTA) {
+            if (nfree > 0)
+                variance = chisq / nfree
+            else
+                variance = 0.
+        } else
+            variance = 1.
+
+
+	# Allocate space for the covariance and conversion matrices.
+	call smark (sp)
+	call salloc (covar, ncoeff * ncoeff, TY_DOUBLE)
+	call salloc (elm, ncoeff * ncoeff, TY_DOUBLE)
+
+	# Compute the covariance matrix.
+	do j = 1, ncoeff {
+	    call aclr$t (perrors, ncoeff)
+	    perrors[j] = PIXEL(1.0)
+	    call $tcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv),
+	        CV_NCOEFF(cv), perrors, perrors)
+	    call amulk$t (perrors, PIXEL(variance), perrors, ncoeff)
+	    call acht$td (perrors, Memd[covar+(j-1)*ncoeff], ncoeff)
+	}
+
+	# Compute the conversion matrix.
+	call amovkd (0.0d0, Memd[elm], ncoeff * ncoeff)
+	switch (function) {
+	case LEGENDRE:
+	    call $tcv_mlegen (Memd[elm], ncoeff)
+	case CHEBYSHEV:
+	    call $tcv_mcheby (Memd[elm], ncoeff)
+	}
+
+	# Normalize the errors to the appropriate data range.
+	call $tcv_enormalize (cv, Memd[elm], ncoeff)
+
+	# Compute the new squared errors.
+	call $tcv_etransform (cv, Memd[covar], Memd[elm], perrors, ncoeff)
+
+	# Compute the errors.
+	do j = 1, ncoeff {
+	    if (perrors[j] >= 0.0)
+	        perrors[j] = sqrt(perrors[j])
+	    else
+		perrors[j] = 0.0
+	}
+
+	call sfree (sp)
+end
+
+
+# CV_MLEGEN -- Compute the matrix required to convert from legendre
+# coefficients to power series coefficients. Summation notation for Legendre
+# series taken from Arfken, page 536, equation 12.8.
+
+procedure $tcv_mlegen (matrix, ncoeff)
+
+double	matrix[ncoeff, ncoeff]
+int	ncoeff
+
+int	s, n, r
+double	$tcv_legcoeff()
+
+begin
+	# Calculate matrix elements.
+	do s = 0, ncoeff - 1 {
+	    if (mod (s, 2) == 0) 
+	        r = s / 2
+	    else 
+	        r = (s - 1) / 2
+
+	    do n = 0, r
+		matrix[s+1, (s+1) - (2*n)] = $tcv_legcoeff (n, s)
+	}
+end
+
+
+# CV_ETRANSFORM -- Convert the square of the fitted polynomial errors
+# to the values appropriate for the equivalent power series polynomial.
+
+procedure $tcv_etransform (cv, covar, elm, perrors, ncoeff)
+
+pointer	cv
+double	covar[ncoeff,ncoeff]
+double	elm[ncoeff,ncoeff]
+PIXEL	perrors[ncoeff]
+int	ncoeff
+
+int	i, j, k
+double	sum
+
+begin
+	do i = 1, ncoeff {
+	    sum = 0.0d0
+	    do j = 1, ncoeff {
+		sum = sum + elm[j,i] * covar[j,j] * elm[j,i]
+		do k = j + 1, ncoeff {
+		    sum = sum + 2.0 * elm[j,i] * covar[j,k] * elm[k,i]
+		}
+	    }
+	    perrors[i] = sum
+	}
+end
+
+
+# CV_LEGEN -- Convert legendre coeffecients to power series coefficients.
+# Scaling the coefficients from -1,+1 to the full data range is done in a 
+# seperate procedure (cf_normalize).
+
+procedure $tcv_legen (matrix, cf_coeff, ps_coeff, ncoeff)
+
+double	matrix[ncoeff, ncoeff]
+PIXEL	cf_coeff[ncoeff]
+PIXEL	ps_coeff[ncoeff]
+int	ncoeff
+
+int	n, i
+double	sum
+
+begin
+	# Multiply matrix columns by curfit coefficients and sum.
+	do n = 1, ncoeff {
+	    sum = 0.0d0
+	    do i = 1, ncoeff
+	        sum = sum + (matrix[i,n] * cf_coeff[i])
+	    ps_coeff[n] = sum
+	}
+end
+
+
+# CV_LEGCOEFF -- calculate matrix elements for converting legendre coefficients
+# to powers of x.
+
+double procedure $tcv_legcoeff (k, n)
+
+int	k
+int	n
+
+double	fcn, sum1, divisor
+double	$tcv_factorial()
+
+begin
+	sum1 = ((-1) ** k) * $tcv_factorial (2 * n - 2 * k)
+	divisor = (2**n) * $tcv_factorial (k) * $tcv_factorial (n-k) * 
+	    $tcv_factorial (n - 2*k)
+	fcn = sum1 / divisor
+
+	return (fcn)
+end
+
+
+# CV_MCHEBY -- Compute the matrix required to convert from Chebyshev
+# coefficient to power series coefficients. Summation notation for Chebyshev
+# series from Arfken, page 628, equation 13.83
+
+procedure $tcv_mcheby (matrix, ncoeff)
+
+double	matrix[ncoeff, ncoeff]		# Work array for matrix elements
+int	ncoeff				# Number of coefficients
+
+int	s, n, m
+double	$tcv_chebcoeff()
+
+begin
+	# Set first matrix element.
+	matrix[1,1] = 1.0d0
+
+	# Calculate remaining matrix elements.
+	do s = 1, ncoeff - 1 {
+	    if (mod (s, 2) == 0)
+	        n = s / 2
+	    else 
+	        n = (s - 1) / 2
+
+	    do m = 0, n
+		matrix[(s+1),(s+1)-(2*m)] = (double(s)/2.0) *
+		    $tcv_chebcoeff (m, s)
+	}
+end
+
+
+# CV_CHEBY -- Convert chebyshev coeffecients to power series coefficients.
+# Scaling the coefficients from -1,+1 to the full data range is done in a 
+# seperate procedure (cf_normalize).
+
+procedure $tcv_cheby (matrix, cf_coeff, ps_coeff, ncoeff)
+
+double	matrix[ncoeff, ncoeff]		# Work array for matrix elements
+PIXEL	cf_coeff[ncoeff]		# Input curfit coefficients
+PIXEL	ps_coeff[ncoeff]		# Output power series coefficients
+int	ncoeff				# Number of coefficients
+
+int	n, i
+double	sum
+
+begin
+	# Multiply matrix columns by curfit coefficients and sum.
+	do n = 1, ncoeff {
+	    sum = 0.0d0
+	    do i = 1, ncoeff
+	        sum = sum + (matrix[i,n] * cf_coeff[i])
+	    ps_coeff[n] = sum
+	}
+end
+
+
+# CV_CHEBCOEFF -- calculate matrix elements for converting chebyshev 
+# coefficients to powers of x.
+
+double procedure $tcv_chebcoeff (m, n)
+
+int	m	# Summation notation index
+int	n	# Summation notation index
+
+double	fcn, sum1, divisor
+double	$tcv_factorial()
+
+begin
+	sum1 = ((-1) ** m) * $tcv_factorial (n - m - 1) * (2 ** (n - (2*m)))
+	divisor = $tcv_factorial (n - (2*m)) * $tcv_factorial (m)
+	fcn = sum1 / divisor
+
+	return (fcn)
+end
+
+
+# CV_NORMALIZE -- Return coefficients scaled to full data range.
+
+procedure $tcv_normalize (cv, ps_coeff, ncoeff)
+
+pointer	cv			# Pointer to curfit structure
+int	ncoeff			# Number of coefficients in fit
+PIXEL	ps_coeff[ncoeff]	# Power series coefficients
+
+pointer	sp, elm, index
+int	n, i, k
+double	k1, k2, bc, sum
+
+double	$tcv_bcoeff()
+
+begin
+	# Need space for ncoeff**2 matrix elements
+	call smark (sp)
+	call salloc (elm, ncoeff ** 2, TY_DOUBLE)
+
+	k1 = CV_RANGE(cv)
+	k2 = k1 * CV_MAXMIN(cv)
+
+	# Fill matrix, after zeroing it. 
+	call amovkd (0.0d0, Memd[elm], ncoeff ** 2)
+	do n = 1, ncoeff {
+	    k = n - 1
+	    do i = 0, k {
+		bc = $tcv_bcoeff (k, i)
+		index = elm + k * ncoeff + i
+		Memd[index] =  bc * ps_coeff[n] * (k1 ** i) * (k2 ** (k-i))
+	    }
+	}
+
+	# Now sum along matrix columns to get coefficient of individual 
+	# powers of x.
+	do n = 1, ncoeff {
+	   sum = 0.0d0
+	   do i = 1, ncoeff {
+	       index = elm + (n-1) + (i-1) * ncoeff
+	       sum = sum + Memd[index]
+	    }
+	    ps_coeff[n] = sum
+	}
+
+	call sfree (sp)
+end
+
+
+# CV_ENORMALIZE -- Return the squares of the errors scaled to full data range.
+
+procedure $tcv_enormalize (cv, elm, ncoeff)
+
+pointer	cv			# Pointer to curfit structure
+double	elm[ncoeff,ncoeff]	# Input transformed matrix
+int	ncoeff			# Number of coefficients in fit
+
+pointer	sp, norm, onorm, index
+int	n, i, k
+double	k1, k2, bc
+
+double	$tcv_bcoeff()
+
+begin
+	# Need space for ncoeff**2 matrix elements
+	call smark (sp)
+	call salloc (norm, ncoeff ** 2, TY_DOUBLE)
+	call salloc (onorm, ncoeff ** 2, TY_DOUBLE)
+
+	k1 = CV_RANGE(cv)
+	k2 = k1 * CV_MAXMIN(cv)
+
+	# Fill normalization matrix after zeroing it. 
+	call amovkd (0.0d0, Memd[norm], ncoeff ** 2)
+	do n = 1, ncoeff {
+	    k = n - 1
+	    do i = 0, k {
+		bc = $tcv_bcoeff (k, i)
+		index = norm + i * ncoeff + k
+		Memd[index] =  bc * (k1 ** i) * (k2 ** (k-i))
+	    }
+	}
+
+	# Multiply the input transformation matrix by the normalization
+	# matrix.
+	call cv_mmuld (Memd[norm], elm, Memd[onorm], ncoeff)
+	call amovd (Memd[onorm], elm, ncoeff ** 2)
+
+	call sfree (sp)
+end
+
+
+# CV_BCOEFF -- calculate and return binomial coefficient as function value.
+
+double procedure $tcv_bcoeff (n, i)
+
+int	n
+int	i
+
+double	$tcv_factorial()
+
+begin
+	if (i == 0)
+	    return (1.0d0)
+	else if (n == i)
+	    return (1.0d0)
+	else
+	    return ($tcv_factorial (n) / ($tcv_factorial (n - i) *
+	        $tcv_factorial (i)))
+end
+
+
+# CV_FACTORIAL -- calculate factorial of argument and return as function value.
+
+double procedure $tcv_factorial (n)
+
+int	n
+
+int	i
+double	fact
+
+begin
+	if (n == 0)
+	    return (1.0d0)
+	else {
+	    fact = 1.0d0
+	    do i = n, 1, -1
+	        fact = fact * double (i)
+	    return (fact)
+	}
+end
+
+
+# CV_MMUL -- Matrix multiply.
+
+procedure cv_mmul$t (a, b, c, ndim)
+
+PIXEL   a[ndim,ndim]            #I left input matrix
+PIXEL   b[ndim,ndim]            #I right input matrix
+PIXEL   c[ndim,ndim]            #O output matrix
+int     ndim                    #I dimensionality of system
+
+int     i, j, k
+PIXEL   v
+
+begin
+        do j = 1, ndim
+            do i = 1, ndim {
+                v = PIXEL(0.0)
+                do k = 1, ndim
+                    #v = v + a[k,j] * b[i,k]
+                    v = v + a[k,j] * b[i,k]
+                c[i,j] = v
+            }
+end
+
diff --git a/math/curfit/cvpowerd.x b/math/curfit/cvpowerd.x
new file mode 100644
index 00000000..626aa723
--- /dev/null
+++ b/math/curfit/cvpowerd.x
@@ -0,0 +1,492 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include	<math/curfit.h>
+
+include	"dcurfitdef.h"
+
+# CVPOWER -- Convert legendre or chebyshev coeffecients to power series.
+
+procedure dcvpower (cv, ps_coeff, ncoeff)
+
+pointer	cv				# Pointer to curfit structure
+double	ps_coeff[ncoeff]		# Power series coefficients (output)
+int	ncoeff				# Number of coefficients in fit
+
+pointer	sp, cf_coeff, elm
+int	function
+int	dcvstati()
+
+begin
+	function = dcvstati (cv, CVTYPE)
+	ncoeff = dcvstati (cv, CVNCOEFF)
+
+	if (function != LEGENDRE && function != CHEBYSHEV) {
+	    call eprintf ("Cannot convert coefficients - wrong function type\n")
+	    call amovkd (INDEFD, ps_coeff, ncoeff)
+	    return
+	}
+
+	call smark (sp)
+	call salloc (elm, ncoeff ** 2, TY_DOUBLE)
+	call salloc (cf_coeff, ncoeff, TY_DOUBLE)
+
+	call amovkd (0.0d0, Memd[elm], ncoeff ** 2)
+
+	# Get existing coefficients
+	call dcvcoeff (cv, Memd[cf_coeff], ncoeff)
+
+	switch (function){
+	case (LEGENDRE):
+	    call dcv_mlegen (Memd[elm], ncoeff)
+	    call dcv_legen (Memd[elm], Memd[cf_coeff], ps_coeff, ncoeff)
+	case (CHEBYSHEV):
+	    call dcv_mcheby (Memd[elm], ncoeff)
+	    call dcv_cheby (Memd[elm], Memd[cf_coeff], ps_coeff, ncoeff)
+	}
+
+	# Normalize coefficients
+	call dcv_normalize (cv, ps_coeff, ncoeff)
+
+	call sfree (sp)
+end
+
+
+# CVEPOWER -- Procedure to calculate the reduced chi-squared of the fit
+# and the standard deviations of the power series coefficients. First the
+# variance and the reduced chi-squared of the fit are estimated. If these
+# two quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+procedure dcvepower (cv, y, w, yfit, npts, chisqr, perrors)
+
+pointer	cv		# curve descriptor
+double	y[ARB]		# data points
+double	yfit[ARB]	# fitted data points
+double	w[ARB]		# array of weights
+int	npts		# number of points
+double	chisqr		# reduced chi-squared of fit
+double	perrors[ARB]	# errors in coefficients
+
+int	i, j, n, nfree, function, ncoeff
+double	variance, chisq, hold
+pointer	sp, covar, elm
+int	dcvstati()
+
+begin
+	# Determine the function type.
+	function = dcvstati (cv, CVTYPE)
+	ncoeff = dcvstati (cv, CVNCOEFF)
+
+	# Check the function type.
+	if (function != LEGENDRE && function != CHEBYSHEV) {
+	    call eprintf ("Cannot convert errors - wrong function type\n")
+	    call amovkd (INDEFD, perrors, ncoeff)
+	    return
+	}
+
+        # Estimate the variance and chi-squared of the fit.
+        n = 0
+        variance = 0.
+        chisq = 0.
+        do i = 1, npts {
+            if (w[i] <= 0.0)
+                next
+            hold = (y[i] - yfit[i]) ** 2
+            variance = variance + hold
+            chisq = chisq + hold * w[i]
+            n = n + 1
+        }
+
+        # Calculate the reduced chi-squared.
+        nfree = n - CV_NCOEFF(cv)
+        if (nfree  > 0)
+            chisqr = chisq / nfree
+        else
+            chisqr = 0.
+
+        # If the variance equals the reduced chi_squared as in the case of
+	# uniform weights then scale the errors in the coefficients by the
+	# variance not the reduced chi-squared
+        if (abs (chisq - variance) <= DELTA) {
+            if (nfree > 0)
+                variance = chisq / nfree
+            else
+                variance = 0.
+        } else
+            variance = 1.
+
+
+	# Allocate space for the covariance and conversion matrices.
+	call smark (sp)
+	call salloc (covar, ncoeff * ncoeff, TY_DOUBLE)
+	call salloc (elm, ncoeff * ncoeff, TY_DOUBLE)
+
+	# Compute the covariance matrix.
+	do j = 1, ncoeff {
+	    call aclrd (perrors, ncoeff)
+	    perrors[j] = double(1.0)
+	    call dcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv),
+	        CV_NCOEFF(cv), perrors, perrors)
+	    call amulkd (perrors, double(variance), perrors, ncoeff)
+	    call achtdd (perrors, Memd[covar+(j-1)*ncoeff], ncoeff)
+	}
+
+	# Compute the conversion matrix.
+	call amovkd (0.0d0, Memd[elm], ncoeff * ncoeff)
+	switch (function) {
+	case LEGENDRE:
+	    call dcv_mlegen (Memd[elm], ncoeff)
+	case CHEBYSHEV:
+	    call dcv_mcheby (Memd[elm], ncoeff)
+	}
+
+	# Normalize the errors to the appropriate data range.
+	call dcv_enormalize (cv, Memd[elm], ncoeff)
+
+	# Compute the new squared errors.
+	call dcv_etransform (cv, Memd[covar], Memd[elm], perrors, ncoeff)
+
+	# Compute the errors.
+	do j = 1, ncoeff {
+	    if (perrors[j] >= 0.0)
+	        perrors[j] = sqrt(perrors[j])
+	    else
+		perrors[j] = 0.0
+	}
+
+	call sfree (sp)
+end
+
+
+# CV_MLEGEN -- Compute the matrix required to convert from legendre
+# coefficients to power series coefficients. Summation notation for Legendre
+# series taken from Arfken, page 536, equation 12.8.
+
+procedure dcv_mlegen (matrix, ncoeff)
+
+double	matrix[ncoeff, ncoeff]
+int	ncoeff
+
+int	s, n, r
+double	dcv_legcoeff()
+
+begin
+	# Calculate matrix elements.
+	do s = 0, ncoeff - 1 {
+	    if (mod (s, 2) == 0) 
+	        r = s / 2
+	    else 
+	        r = (s - 1) / 2
+
+	    do n = 0, r
+		matrix[s+1, (s+1) - (2*n)] = dcv_legcoeff (n, s)
+	}
+end
+
+
+# CV_ETRANSFORM -- Convert the square of the fitted polynomial errors
+# to the values appropriate for the equivalent power series polynomial.
+
+procedure dcv_etransform (cv, covar, elm, perrors, ncoeff)
+
+pointer	cv
+double	covar[ncoeff,ncoeff]
+double	elm[ncoeff,ncoeff]
+double	perrors[ncoeff]
+int	ncoeff
+
+int	i, j, k
+double	sum
+
+begin
+	do i = 1, ncoeff {
+	    sum = 0.0d0
+	    do j = 1, ncoeff {
+		sum = sum + elm[j,i] * covar[j,j] * elm[j,i]
+		do k = j + 1, ncoeff {
+		    sum = sum + 2.0 * elm[j,i] * covar[j,k] * elm[k,i]
+		}
+	    }
+	    perrors[i] = sum
+	}
+end
+
+
+# CV_LEGEN -- Convert legendre coeffecients to power series coefficients.
+# Scaling the coefficients from -1,+1 to the full data range is done in a 
+# seperate procedure (cf_normalize).
+
+procedure dcv_legen (matrix, cf_coeff, ps_coeff, ncoeff)
+
+double	matrix[ncoeff, ncoeff]
+double	cf_coeff[ncoeff]
+double	ps_coeff[ncoeff]
+int	ncoeff
+
+int	n, i
+double	sum
+
+begin
+	# Multiply matrix columns by curfit coefficients and sum.
+	do n = 1, ncoeff {
+	    sum = 0.0d0
+	    do i = 1, ncoeff
+	        sum = sum + (matrix[i,n] * cf_coeff[i])
+	    ps_coeff[n] = sum
+	}
+end
+
+
+# CV_LEGCOEFF -- calculate matrix elements for converting legendre coefficients
+# to powers of x.
+
+double procedure dcv_legcoeff (k, n)
+
+int	k
+int	n
+
+double	fcn, sum1, divisor
+double	dcv_factorial()
+
+begin
+	sum1 = ((-1) ** k) * dcv_factorial (2 * n - 2 * k)
+	divisor = (2**n) * dcv_factorial (k) * dcv_factorial (n-k) * 
+	    dcv_factorial (n - 2*k)
+	fcn = sum1 / divisor
+
+	return (fcn)
+end
+
+
+# CV_MCHEBY -- Compute the matrix required to convert from Chebyshev
+# coefficient to power series coefficients. Summation notation for Chebyshev
+# series from Arfken, page 628, equation 13.83
+
+procedure dcv_mcheby (matrix, ncoeff)
+
+double	matrix[ncoeff, ncoeff]		# Work array for matrix elements
+int	ncoeff				# Number of coefficients
+
+int	s, n, m
+double	dcv_chebcoeff()
+
+begin
+	# Set first matrix element.
+	matrix[1,1] = 1.0d0
+
+	# Calculate remaining matrix elements.
+	do s = 1, ncoeff - 1 {
+	    if (mod (s, 2) == 0)
+	        n = s / 2
+	    else 
+	        n = (s - 1) / 2
+
+	    do m = 0, n
+		matrix[(s+1),(s+1)-(2*m)] = (double(s)/2.0) *
+		    dcv_chebcoeff (m, s)
+	}
+end
+
+
+# CV_CHEBY -- Convert chebyshev coeffecients to power series coefficients.
+# Scaling the coefficients from -1,+1 to the full data range is done in a 
+# seperate procedure (cf_normalize).
+
+procedure dcv_cheby (matrix, cf_coeff, ps_coeff, ncoeff)
+
+double	matrix[ncoeff, ncoeff]		# Work array for matrix elements
+double	cf_coeff[ncoeff]		# Input curfit coefficients
+double	ps_coeff[ncoeff]		# Output power series coefficients
+int	ncoeff				# Number of coefficients
+
+int	n, i
+double	sum
+
+begin
+	# Multiply matrix columns by curfit coefficients and sum.
+	do n = 1, ncoeff {
+	    sum = 0.0d0
+	    do i = 1, ncoeff
+	        sum = sum + (matrix[i,n] * cf_coeff[i])
+	    ps_coeff[n] = sum
+	}
+end
+
+
+# CV_CHEBCOEFF -- calculate matrix elements for converting chebyshev 
+# coefficients to powers of x.
+
+double procedure dcv_chebcoeff (m, n)
+
+int	m	# Summation notation index
+int	n	# Summation notation index
+
+double	fcn, sum1, divisor
+double	dcv_factorial()
+
+begin
+	sum1 = ((-1) ** m) * dcv_factorial (n - m - 1) * (2 ** (n - (2*m)))
+	divisor = dcv_factorial (n - (2*m)) * dcv_factorial (m)
+	fcn = sum1 / divisor
+
+	return (fcn)
+end
+
+
+# CV_NORMALIZE -- Return coefficients scaled to full data range.
+
+procedure dcv_normalize (cv, ps_coeff, ncoeff)
+
+pointer	cv			# Pointer to curfit structure
+int	ncoeff			# Number of coefficients in fit
+double	ps_coeff[ncoeff]	# Power series coefficients
+
+pointer	sp, elm, index
+int	n, i, k
+double	k1, k2, bc, sum
+
+double	dcv_bcoeff()
+
+begin
+	# Need space for ncoeff**2 matrix elements
+	call smark (sp)
+	call salloc (elm, ncoeff ** 2, TY_DOUBLE)
+
+	k1 = CV_RANGE(cv)
+	k2 = k1 * CV_MAXMIN(cv)
+
+	# Fill matrix, after zeroing it. 
+	call amovkd (0.0d0, Memd[elm], ncoeff ** 2)
+	do n = 1, ncoeff {
+	    k = n - 1
+	    do i = 0, k {
+		bc = dcv_bcoeff (k, i)
+		index = elm + k * ncoeff + i
+		Memd[index] =  bc * ps_coeff[n] * (k1 ** i) * (k2 ** (k-i))
+	    }
+	}
+
+	# Now sum along matrix columns to get coefficient of individual 
+	# powers of x.
+	do n = 1, ncoeff {
+	   sum = 0.0d0
+	   do i = 1, ncoeff {
+	       index = elm + (n-1) + (i-1) * ncoeff
+	       sum = sum + Memd[index]
+	    }
+	    ps_coeff[n] = sum
+	}
+
+	call sfree (sp)
+end
+
+
+# CV_ENORMALIZE -- Return the squares of the errors scaled to full data range.
+
+procedure dcv_enormalize (cv, elm, ncoeff)
+
+pointer	cv			# Pointer to curfit structure
+double	elm[ncoeff,ncoeff]	# Input transformed matrix
+int	ncoeff			# Number of coefficients in fit
+
+pointer	sp, norm, onorm, index
+int	n, i, k
+double	k1, k2, bc
+
+double	dcv_bcoeff()
+
+begin
+	# Need space for ncoeff**2 matrix elements
+	call smark (sp)
+	call salloc (norm, ncoeff ** 2, TY_DOUBLE)
+	call salloc (onorm, ncoeff ** 2, TY_DOUBLE)
+
+	k1 = CV_RANGE(cv)
+	k2 = k1 * CV_MAXMIN(cv)
+
+	# Fill normalization matrix after zeroing it. 
+	call amovkd (0.0d0, Memd[norm], ncoeff ** 2)
+	do n = 1, ncoeff {
+	    k = n - 1
+	    do i = 0, k {
+		bc = dcv_bcoeff (k, i)
+		index = norm + i * ncoeff + k
+		Memd[index] =  bc * (k1 ** i) * (k2 ** (k-i))
+	    }
+	}
+
+	# Multiply the input transformation matrix by the normalization
+	# matrix.
+	call cv_mmuld (Memd[norm], elm, Memd[onorm], ncoeff)
+	call amovd (Memd[onorm], elm, ncoeff ** 2)
+
+	call sfree (sp)
+end
+
+
+# CV_BCOEFF -- calculate and return binomial coefficient as function value.
+
+double procedure dcv_bcoeff (n, i)
+
+int	n
+int	i
+
+double	dcv_factorial()
+
+begin
+	if (i == 0)
+	    return (1.0d0)
+	else if (n == i)
+	    return (1.0d0)
+	else
+	    return (dcv_factorial (n) / (dcv_factorial (n - i) *
+	        dcv_factorial (i)))
+end
+
+
+# CV_FACTORIAL -- calculate factorial of argument and return as function value.
+
+double procedure dcv_factorial (n)
+
+int	n
+
+int	i
+double	fact
+
+begin
+	if (n == 0)
+	    return (1.0d0)
+	else {
+	    fact = 1.0d0
+	    do i = n, 1, -1
+	        fact = fact * double (i)
+	    return (fact)
+	}
+end
+
+
+# CV_MMUL -- Matrix multiply.
+
+procedure cv_mmuld (a, b, c, ndim)
+
+double   a[ndim,ndim]            #I left input matrix
+double   b[ndim,ndim]            #I right input matrix
+double   c[ndim,ndim]            #O output matrix
+int     ndim                    #I dimensionality of system
+
+int     i, j, k
+double   v
+
+begin
+        do j = 1, ndim
+            do i = 1, ndim {
+                v = double(0.0)
+                do k = 1, ndim
+                    #v = v + a[k,j] * b[i,k]
+                    v = v + a[k,j] * b[i,k]
+                c[i,j] = v
+            }
+end
+
diff --git a/math/curfit/cvpowerr.x b/math/curfit/cvpowerr.x
new file mode 100644
index 00000000..a100d057
--- /dev/null
+++ b/math/curfit/cvpowerr.x
@@ -0,0 +1,492 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include	<math/curfit.h>
+
+include	"curfitdef.h"
+
+# CVPOWER -- Convert legendre or chebyshev coeffecients to power series.
+
+procedure cvpower (cv, ps_coeff, ncoeff)
+
+pointer	cv				# Pointer to curfit structure
+real	ps_coeff[ncoeff]		# Power series coefficients (output)
+int	ncoeff				# Number of coefficients in fit
+
+pointer	sp, cf_coeff, elm
+int	function
+int	cvstati()
+
+begin
+	function = cvstati (cv, CVTYPE)
+	ncoeff = cvstati (cv, CVNCOEFF)
+
+	if (function != LEGENDRE && function != CHEBYSHEV) {
+	    call eprintf ("Cannot convert coefficients - wrong function type\n")
+	    call amovkr (INDEFR, ps_coeff, ncoeff)
+	    return
+	}
+
+	call smark (sp)
+	call salloc (elm, ncoeff ** 2, TY_DOUBLE)
+	call salloc (cf_coeff, ncoeff, TY_REAL)
+
+	call amovkd (0.0d0, Memd[elm], ncoeff ** 2)
+
+	# Get existing coefficients
+	call cvcoeff (cv, Memr[cf_coeff], ncoeff)
+
+	switch (function){
+	case (LEGENDRE):
+	    call rcv_mlegen (Memd[elm], ncoeff)
+	    call rcv_legen (Memd[elm], Memr[cf_coeff], ps_coeff, ncoeff)
+	case (CHEBYSHEV):
+	    call rcv_mcheby (Memd[elm], ncoeff)
+	    call rcv_cheby (Memd[elm], Memr[cf_coeff], ps_coeff, ncoeff)
+	}
+
+	# Normalize coefficients
+	call rcv_normalize (cv, ps_coeff, ncoeff)
+
+	call sfree (sp)
+end
+
+
+# CVEPOWER -- Procedure to calculate the reduced chi-squared of the fit
+# and the standard deviations of the power series coefficients. First the
+# variance and the reduced chi-squared of the fit are estimated. If these
+# two quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+procedure cvepower (cv, y, w, yfit, npts, chisqr, perrors)
+
+pointer	cv		# curve descriptor
+real	y[ARB]		# data points
+real	yfit[ARB]	# fitted data points
+real	w[ARB]		# array of weights
+int	npts		# number of points
+real	chisqr		# reduced chi-squared of fit
+real	perrors[ARB]	# errors in coefficients
+
+int	i, j, n, nfree, function, ncoeff
+real	variance, chisq, hold
+pointer	sp, covar, elm
+int	cvstati()
+
+begin
+	# Determine the function type.
+	function = cvstati (cv, CVTYPE)
+	ncoeff = cvstati (cv, CVNCOEFF)
+
+	# Check the function type.
+	if (function != LEGENDRE && function != CHEBYSHEV) {
+	    call eprintf ("Cannot convert errors - wrong function type\n")
+	    call amovkr (INDEFR, perrors, ncoeff)
+	    return
+	}
+
+        # Estimate the variance and chi-squared of the fit.
+        n = 0
+        variance = 0.
+        chisq = 0.
+        do i = 1, npts {
+            if (w[i] <= 0.0)
+                next
+            hold = (y[i] - yfit[i]) ** 2
+            variance = variance + hold
+            chisq = chisq + hold * w[i]
+            n = n + 1
+        }
+
+        # Calculate the reduced chi-squared.
+        nfree = n - CV_NCOEFF(cv)
+        if (nfree  > 0)
+            chisqr = chisq / nfree
+        else
+            chisqr = 0.
+
+        # If the variance equals the reduced chi_squared as in the case of
+	# uniform weights then scale the errors in the coefficients by the
+	# variance not the reduced chi-squared
+        if (abs (chisq - variance) <= DELTA) {
+            if (nfree > 0)
+                variance = chisq / nfree
+            else
+                variance = 0.
+        } else
+            variance = 1.
+
+
+	# Allocate space for the covariance and conversion matrices.
+	call smark (sp)
+	call salloc (covar, ncoeff * ncoeff, TY_DOUBLE)
+	call salloc (elm, ncoeff * ncoeff, TY_DOUBLE)
+
+	# Compute the covariance matrix.
+	do j = 1, ncoeff {
+	    call aclrr (perrors, ncoeff)
+	    perrors[j] = real(1.0)
+	    call rcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv),
+	        CV_NCOEFF(cv), perrors, perrors)
+	    call amulkr (perrors, real(variance), perrors, ncoeff)
+	    call achtrd (perrors, Memd[covar+(j-1)*ncoeff], ncoeff)
+	}
+
+	# Compute the conversion matrix.
+	call amovkd (0.0d0, Memd[elm], ncoeff * ncoeff)
+	switch (function) {
+	case LEGENDRE:
+	    call rcv_mlegen (Memd[elm], ncoeff)
+	case CHEBYSHEV:
+	    call rcv_mcheby (Memd[elm], ncoeff)
+	}
+
+	# Normalize the errors to the appropriate data range.
+	call rcv_enormalize (cv, Memd[elm], ncoeff)
+
+	# Compute the new squared errors.
+	call rcv_etransform (cv, Memd[covar], Memd[elm], perrors, ncoeff)
+
+	# Compute the errors.
+	do j = 1, ncoeff {
+	    if (perrors[j] >= 0.0)
+	        perrors[j] = sqrt(perrors[j])
+	    else
+		perrors[j] = 0.0
+	}
+
+	call sfree (sp)
+end
+
+
+# CV_MLEGEN -- Compute the matrix required to convert from legendre
+# coefficients to power series coefficients. Summation notation for Legendre
+# series taken from Arfken, page 536, equation 12.8.
+
+procedure rcv_mlegen (matrix, ncoeff)
+
+double	matrix[ncoeff, ncoeff]
+int	ncoeff
+
+int	s, n, r
+double	rcv_legcoeff()
+
+begin
+	# Calculate matrix elements.
+	do s = 0, ncoeff - 1 {
+	    if (mod (s, 2) == 0) 
+	        r = s / 2
+	    else 
+	        r = (s - 1) / 2
+
+	    do n = 0, r
+		matrix[s+1, (s+1) - (2*n)] = rcv_legcoeff (n, s)
+	}
+end
+
+
+# CV_ETRANSFORM -- Convert the square of the fitted polynomial errors
+# to the values appropriate for the equivalent power series polynomial.
+
+procedure rcv_etransform (cv, covar, elm, perrors, ncoeff)
+
+pointer	cv
+double	covar[ncoeff,ncoeff]
+double	elm[ncoeff,ncoeff]
+real	perrors[ncoeff]
+int	ncoeff
+
+int	i, j, k
+double	sum
+
+begin
+	do i = 1, ncoeff {
+	    sum = 0.0d0
+	    do j = 1, ncoeff {
+		sum = sum + elm[j,i] * covar[j,j] * elm[j,i]
+		do k = j + 1, ncoeff {
+		    sum = sum + 2.0 * elm[j,i] * covar[j,k] * elm[k,i]
+		}
+	    }
+	    perrors[i] = sum
+	}
+end
+
+
+# CV_LEGEN -- Convert legendre coeffecients to power series coefficients.
+# Scaling the coefficients from -1,+1 to the full data range is done in a 
+# seperate procedure (cf_normalize).
+
+procedure rcv_legen (matrix, cf_coeff, ps_coeff, ncoeff)
+
+double	matrix[ncoeff, ncoeff]
+real	cf_coeff[ncoeff]
+real	ps_coeff[ncoeff]
+int	ncoeff
+
+int	n, i
+double	sum
+
+begin
+	# Multiply matrix columns by curfit coefficients and sum.
+	do n = 1, ncoeff {
+	    sum = 0.0d0
+	    do i = 1, ncoeff
+	        sum = sum + (matrix[i,n] * cf_coeff[i])
+	    ps_coeff[n] = sum
+	}
+end
+
+
+# CV_LEGCOEFF -- calculate matrix elements for converting legendre coefficients
+# to powers of x.
+
+double procedure rcv_legcoeff (k, n)
+
+int	k
+int	n
+
+double	fcn, sum1, divisor
+double	rcv_factorial()
+
+begin
+	sum1 = ((-1) ** k) * rcv_factorial (2 * n - 2 * k)
+	divisor = (2**n) * rcv_factorial (k) * rcv_factorial (n-k) * 
+	    rcv_factorial (n - 2*k)
+	fcn = sum1 / divisor
+
+	return (fcn)
+end
+
+
+# CV_MCHEBY -- Compute the matrix required to convert from Chebyshev
+# coefficient to power series coefficients. Summation notation for Chebyshev
+# series from Arfken, page 628, equation 13.83
+
+procedure rcv_mcheby (matrix, ncoeff)
+
+double	matrix[ncoeff, ncoeff]		# Work array for matrix elements
+int	ncoeff				# Number of coefficients
+
+int	s, n, m
+double	rcv_chebcoeff()
+
+begin
+	# Set first matrix element.
+	matrix[1,1] = 1.0d0
+
+	# Calculate remaining matrix elements.
+	do s = 1, ncoeff - 1 {
+	    if (mod (s, 2) == 0)
+	        n = s / 2
+	    else 
+	        n = (s - 1) / 2
+
+	    do m = 0, n
+		matrix[(s+1),(s+1)-(2*m)] = (double(s)/2.0) *
+		    rcv_chebcoeff (m, s)
+	}
+end
+
+
+# CV_CHEBY -- Convert chebyshev coeffecients to power series coefficients.
+# Scaling the coefficients from -1,+1 to the full data range is done in a 
+# seperate procedure (cf_normalize).
+
+procedure rcv_cheby (matrix, cf_coeff, ps_coeff, ncoeff)
+
+double	matrix[ncoeff, ncoeff]		# Work array for matrix elements
+real	cf_coeff[ncoeff]		# Input curfit coefficients
+real	ps_coeff[ncoeff]		# Output power series coefficients
+int	ncoeff				# Number of coefficients
+
+int	n, i
+double	sum
+
+begin
+	# Multiply matrix columns by curfit coefficients and sum.
+	do n = 1, ncoeff {
+	    sum = 0.0d0
+	    do i = 1, ncoeff
+	        sum = sum + (matrix[i,n] * cf_coeff[i])
+	    ps_coeff[n] = sum
+	}
+end
+
+
+# CV_CHEBCOEFF -- calculate matrix elements for converting chebyshev 
+# coefficients to powers of x.
+
+double procedure rcv_chebcoeff (m, n)
+
+int	m	# Summation notation index
+int	n	# Summation notation index
+
+double	fcn, sum1, divisor
+double	rcv_factorial()
+
+begin
+	sum1 = ((-1) ** m) * rcv_factorial (n - m - 1) * (2 ** (n - (2*m)))
+	divisor = rcv_factorial (n - (2*m)) * rcv_factorial (m)
+	fcn = sum1 / divisor
+
+	return (fcn)
+end
+
+
+# CV_NORMALIZE -- Return coefficients scaled to full data range.
+
+procedure rcv_normalize (cv, ps_coeff, ncoeff)
+
+pointer	cv			# Pointer to curfit structure
+int	ncoeff			# Number of coefficients in fit
+real	ps_coeff[ncoeff]	# Power series coefficients
+
+pointer	sp, elm, index
+int	n, i, k
+double	k1, k2, bc, sum
+
+double	rcv_bcoeff()
+
+begin
+	# Need space for ncoeff**2 matrix elements
+	call smark (sp)
+	call salloc (elm, ncoeff ** 2, TY_DOUBLE)
+
+	k1 = CV_RANGE(cv)
+	k2 = k1 * CV_MAXMIN(cv)
+
+	# Fill matrix, after zeroing it. 
+	call amovkd (0.0d0, Memd[elm], ncoeff ** 2)
+	do n = 1, ncoeff {
+	    k = n - 1
+	    do i = 0, k {
+		bc = rcv_bcoeff (k, i)
+		index = elm + k * ncoeff + i
+		Memd[index] =  bc * ps_coeff[n] * (k1 ** i) * (k2 ** (k-i))
+	    }
+	}
+
+	# Now sum along matrix columns to get coefficient of individual 
+	# powers of x.
+	do n = 1, ncoeff {
+	   sum = 0.0d0
+	   do i = 1, ncoeff {
+	       index = elm + (n-1) + (i-1) * ncoeff
+	       sum = sum + Memd[index]
+	    }
+	    ps_coeff[n] = sum
+	}
+
+	call sfree (sp)
+end
+
+
+# CV_ENORMALIZE -- Return the squares of the errors scaled to full data range.
+
+procedure rcv_enormalize (cv, elm, ncoeff)
+
+pointer	cv			# Pointer to curfit structure
+double	elm[ncoeff,ncoeff]	# Input transformed matrix
+int	ncoeff			# Number of coefficients in fit
+
+pointer	sp, norm, onorm, index
+int	n, i, k
+double	k1, k2, bc
+
+double	rcv_bcoeff()
+
+begin
+	# Need space for ncoeff**2 matrix elements
+	call smark (sp)
+	call salloc (norm, ncoeff ** 2, TY_DOUBLE)
+	call salloc (onorm, ncoeff ** 2, TY_DOUBLE)
+
+	k1 = CV_RANGE(cv)
+	k2 = k1 * CV_MAXMIN(cv)
+
+	# Fill normalization matrix after zeroing it. 
+	call amovkd (0.0d0, Memd[norm], ncoeff ** 2)
+	do n = 1, ncoeff {
+	    k = n - 1
+	    do i = 0, k {
+		bc = rcv_bcoeff (k, i)
+		index = norm + i * ncoeff + k
+		Memd[index] =  bc * (k1 ** i) * (k2 ** (k-i))
+	    }
+	}
+
+	# Multiply the input transformation matrix by the normalization
+	# matrix.
+	call cv_mmuld (Memd[norm], elm, Memd[onorm], ncoeff)
+	call amovd (Memd[onorm], elm, ncoeff ** 2)
+
+	call sfree (sp)
+end
+
+
+# CV_BCOEFF -- calculate and return binomial coefficient as function value.
+
+double procedure rcv_bcoeff (n, i)
+
+int	n
+int	i
+
+double	rcv_factorial()
+
+begin
+	if (i == 0)
+	    return (1.0d0)
+	else if (n == i)
+	    return (1.0d0)
+	else
+	    return (rcv_factorial (n) / (rcv_factorial (n - i) *
+	        rcv_factorial (i)))
+end
+
+
+# CV_FACTORIAL -- calculate factorial of argument and return as function value.
+
+double procedure rcv_factorial (n)
+
+int	n
+
+int	i
+double	fact
+
+begin
+	if (n == 0)
+	    return (1.0d0)
+	else {
+	    fact = 1.0d0
+	    do i = n, 1, -1
+	        fact = fact * double (i)
+	    return (fact)
+	}
+end
+
+
+# CV_MMUL -- Matrix multiply.
+
+procedure cv_mmulr (a, b, c, ndim)
+
+real   a[ndim,ndim]            #I left input matrix
+real   b[ndim,ndim]            #I right input matrix
+real   c[ndim,ndim]            #O output matrix
+int     ndim                    #I dimensionality of system
+
+int     i, j, k
+real   v
+
+begin
+        do j = 1, ndim
+            do i = 1, ndim {
+                v = real(0.0)
+                do k = 1, ndim
+                    #v = v + a[k,j] * b[i,k]
+                    v = v + a[k,j] * b[i,k]
+                c[i,j] = v
+            }
+end
+
diff --git a/math/curfit/cvrefit.gx b/math/curfit/cvrefit.gx
new file mode 100644
index 00000000..448ac684
--- /dev/null
+++ b/math/curfit/cvrefit.gx
@@ -0,0 +1,111 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVREFIT -- Procedure to refit the data assuming that the x and w values have
+# not changed. MATRIX and CHOFAC are assumed to remain unchanged from the
+# previous fit. It is only necessary to accumulate a new VECTOR and 
+# calculate the coefficients COEFF by forward and back substitution. On
+# the first call to cvrefit the basis functions for all data points are
+# calculated and stored in BASIS. Subsequent calls to cvrefit reference these
+# functions. Intervening calls to cvfit or cvzero zero the basis functions.
+
+$if (datatype == r)
+procedure cvrefit (cv, x, y, w, ier)
+$else
+procedure dcvrefit (cv, x, y, w, ier)
+$endif
+
+pointer	cv		# curve descriptor
+PIXEL	x[ARB]		# x array
+PIXEL	y[ARB]		# y array
+PIXEL	w[ARB]		# weight array
+int	ier		# error code
+
+int	i, k
+pointer	bzptr
+pointer	vzptr, vindex
+
+
+begin
+	# zero the right side of the matrix equation
+	call aclr$t (VECTOR(CV_VECTOR(cv)), CV_NCOEFF(cv))
+	vzptr = CV_VECTOR(cv) - 1
+
+	# if first call to cvrefit then calculate and store the basis
+	# functions
+	if (CV_BASIS(cv) == NULL) {
+
+	    # allocate space for the basis functions and array containing
+	    # the index of the first non-zero basis function
+	    call malloc (CV_BASIS(cv), CV_NPTS(cv)*CV_ORDER(cv), TY_PIXEL)
+	    call malloc (CV_WY(cv), CV_NPTS(cv), TY_PIXEL)
+
+	    # calculate the non-zero basis functions
+	    switch (CV_TYPE(cv)) {
+	    case LEGENDRE:
+		call $tcv_bleg (x, CV_NPTS(cv), CV_ORDER(cv), CV_MAXMIN(cv),
+		    CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	    case CHEBYSHEV:
+		call $tcv_bcheb (x, CV_NPTS(cv), CV_ORDER(cv), CV_MAXMIN(cv),
+			    CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	    case SPLINE3:
+	        call malloc (CV_LEFT(cv), CV_NPTS(cv), TY_INT)
+		call $tcv_bspline3 (x, CV_NPTS(cv), CV_NPIECES(cv),
+		    -CV_XMIN(cv), CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+		    LEFT(CV_LEFT(cv)))
+		call aaddki (LEFT(CV_LEFT(cv)), vzptr, LEFT(CV_LEFT(cv)),
+		    CV_NPTS(cv))
+	    case SPLINE1:
+	        call malloc (CV_LEFT(cv), CV_NPTS(cv), TY_INT)
+		call $tcv_bspline1 (x, CV_NPTS(cv), CV_NPIECES(cv),
+		    -CV_XMIN(cv), CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+		    LEFT(CV_LEFT(cv)))
+		call aaddki (LEFT(CV_LEFT(cv)), vzptr, LEFT(CV_LEFT(cv)),
+		    CV_NPTS(cv))
+	    case USERFNC:
+		call $tcv_buser (cv, x, CV_NPTS(cv))
+	    }
+	}
+
+
+	# accumulate the new right side of the matrix equation
+	call amul$t (w, y, Mem$t[CV_WY(cv)], CV_NPTS(cv))
+	bzptr = CV_BASIS(cv)
+
+	switch (CV_TYPE(cv)) {
+
+	case SPLINE1, SPLINE3:
+
+	    do k = 1, CV_ORDER(cv) {
+	        do i = 1, CV_NPTS(cv) {
+		    vindex = LEFT(CV_LEFT(cv)+i-1) + k
+	            VECTOR(vindex) = VECTOR(vindex) + Mem$t[CV_WY(cv)+i-1] *
+		        BASIS(bzptr+i-1)
+		}
+	        bzptr = bzptr + CV_NPTS(cv)
+	    }
+
+	case LEGENDRE, CHEBYSHEV, USERFNC:
+
+	    do k = 1, CV_ORDER(cv) {
+		vindex = vzptr + k
+	        do i = 1, CV_NPTS(cv)
+	            VECTOR(vindex) = VECTOR(vindex) + Mem$t[CV_WY(cv)+i-1] *
+			BASIS(bzptr+i-1)
+	        bzptr = bzptr + CV_NPTS(cv)
+	    }
+
+	}
+
+	# solve for the new coefficients using forward and back
+	# substitution
+	call $tcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		    VECTOR(CV_VECTOR(cv)), COEFF(CV_COEFF(cv)))
+end
diff --git a/math/curfit/cvrefitd.x b/math/curfit/cvrefitd.x
new file mode 100644
index 00000000..2714beb6
--- /dev/null
+++ b/math/curfit/cvrefitd.x
@@ -0,0 +1,103 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+# CVREFIT -- Procedure to refit the data assuming that the x and w values have
+# not changed. MATRIX and CHOFAC are assumed to remain unchanged from the
+# previous fit. It is only necessary to accumulate a new VECTOR and 
+# calculate the coefficients COEFF by forward and back substitution. On
+# the first call to cvrefit the basis functions for all data points are
+# calculated and stored in BASIS. Subsequent calls to cvrefit reference these
+# functions. Intervening calls to cvfit or cvzero zero the basis functions.
+
+procedure dcvrefit (cv, x, y, w, ier)
+
+pointer	cv		# curve descriptor
+double	x[ARB]		# x array
+double	y[ARB]		# y array
+double	w[ARB]		# weight array
+int	ier		# error code
+
+int	i, k
+pointer	bzptr
+pointer	vzptr, vindex
+
+
+begin
+	# zero the right side of the matrix equation
+	call aclrd (VECTOR(CV_VECTOR(cv)), CV_NCOEFF(cv))
+	vzptr = CV_VECTOR(cv) - 1
+
+	# if first call to cvrefit then calculate and store the basis
+	# functions
+	if (CV_BASIS(cv) == NULL) {
+
+	    # allocate space for the basis functions and array containing
+	    # the index of the first non-zero basis function
+	    call malloc (CV_BASIS(cv), CV_NPTS(cv)*CV_ORDER(cv), TY_DOUBLE)
+	    call malloc (CV_WY(cv), CV_NPTS(cv), TY_DOUBLE)
+
+	    # calculate the non-zero basis functions
+	    switch (CV_TYPE(cv)) {
+	    case LEGENDRE:
+		call dcv_bleg (x, CV_NPTS(cv), CV_ORDER(cv), CV_MAXMIN(cv),
+		    CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	    case CHEBYSHEV:
+		call dcv_bcheb (x, CV_NPTS(cv), CV_ORDER(cv), CV_MAXMIN(cv),
+			    CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	    case SPLINE3:
+	        call malloc (CV_LEFT(cv), CV_NPTS(cv), TY_INT)
+		call dcv_bspline3 (x, CV_NPTS(cv), CV_NPIECES(cv),
+		    -CV_XMIN(cv), CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+		    LEFT(CV_LEFT(cv)))
+		call aaddki (LEFT(CV_LEFT(cv)), vzptr, LEFT(CV_LEFT(cv)),
+		    CV_NPTS(cv))
+	    case SPLINE1:
+	        call malloc (CV_LEFT(cv), CV_NPTS(cv), TY_INT)
+		call dcv_bspline1 (x, CV_NPTS(cv), CV_NPIECES(cv),
+		    -CV_XMIN(cv), CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+		    LEFT(CV_LEFT(cv)))
+		call aaddki (LEFT(CV_LEFT(cv)), vzptr, LEFT(CV_LEFT(cv)),
+		    CV_NPTS(cv))
+	    case USERFNC:
+		call dcv_buser (cv, x, CV_NPTS(cv))
+	    }
+	}
+
+
+	# accumulate the new right side of the matrix equation
+	call amuld (w, y, Memd[CV_WY(cv)], CV_NPTS(cv))
+	bzptr = CV_BASIS(cv)
+
+	switch (CV_TYPE(cv)) {
+
+	case SPLINE1, SPLINE3:
+
+	    do k = 1, CV_ORDER(cv) {
+	        do i = 1, CV_NPTS(cv) {
+		    vindex = LEFT(CV_LEFT(cv)+i-1) + k
+	            VECTOR(vindex) = VECTOR(vindex) + Memd[CV_WY(cv)+i-1] *
+		        BASIS(bzptr+i-1)
+		}
+	        bzptr = bzptr + CV_NPTS(cv)
+	    }
+
+	case LEGENDRE, CHEBYSHEV, USERFNC:
+
+	    do k = 1, CV_ORDER(cv) {
+		vindex = vzptr + k
+	        do i = 1, CV_NPTS(cv)
+	            VECTOR(vindex) = VECTOR(vindex) + Memd[CV_WY(cv)+i-1] *
+			BASIS(bzptr+i-1)
+	        bzptr = bzptr + CV_NPTS(cv)
+	    }
+
+	}
+
+	# solve for the new coefficients using forward and back
+	# substitution
+	call dcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		    VECTOR(CV_VECTOR(cv)), COEFF(CV_COEFF(cv)))
+end
diff --git a/math/curfit/cvrefitr.x b/math/curfit/cvrefitr.x
new file mode 100644
index 00000000..5de9abe2
--- /dev/null
+++ b/math/curfit/cvrefitr.x
@@ -0,0 +1,103 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+# CVREFIT -- Procedure to refit the data assuming that the x and w values have
+# not changed. MATRIX and CHOFAC are assumed to remain unchanged from the
+# previous fit. It is only necessary to accumulate a new VECTOR and 
+# calculate the coefficients COEFF by forward and back substitution. On
+# the first call to cvrefit the basis functions for all data points are
+# calculated and stored in BASIS. Subsequent calls to cvrefit reference these
+# functions. Intervening calls to cvfit or cvzero zero the basis functions.
+
+procedure cvrefit (cv, x, y, w, ier)
+
+pointer	cv		# curve descriptor
+real	x[ARB]		# x array
+real	y[ARB]		# y array
+real	w[ARB]		# weight array
+int	ier		# error code
+
+int	i, k
+pointer	bzptr
+pointer	vzptr, vindex
+
+
+begin
+	# zero the right side of the matrix equation
+	call aclrr (VECTOR(CV_VECTOR(cv)), CV_NCOEFF(cv))
+	vzptr = CV_VECTOR(cv) - 1
+
+	# if first call to cvrefit then calculate and store the basis
+	# functions
+	if (CV_BASIS(cv) == NULL) {
+
+	    # allocate space for the basis functions and array containing
+	    # the index of the first non-zero basis function
+	    call malloc (CV_BASIS(cv), CV_NPTS(cv)*CV_ORDER(cv), TY_REAL)
+	    call malloc (CV_WY(cv), CV_NPTS(cv), TY_REAL)
+
+	    # calculate the non-zero basis functions
+	    switch (CV_TYPE(cv)) {
+	    case LEGENDRE:
+		call rcv_bleg (x, CV_NPTS(cv), CV_ORDER(cv), CV_MAXMIN(cv),
+		    CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	    case CHEBYSHEV:
+		call rcv_bcheb (x, CV_NPTS(cv), CV_ORDER(cv), CV_MAXMIN(cv),
+			    CV_RANGE(cv), BASIS(CV_BASIS(cv)))
+	    case SPLINE3:
+	        call malloc (CV_LEFT(cv), CV_NPTS(cv), TY_INT)
+		call rcv_bspline3 (x, CV_NPTS(cv), CV_NPIECES(cv),
+		    -CV_XMIN(cv), CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+		    LEFT(CV_LEFT(cv)))
+		call aaddki (LEFT(CV_LEFT(cv)), vzptr, LEFT(CV_LEFT(cv)),
+		    CV_NPTS(cv))
+	    case SPLINE1:
+	        call malloc (CV_LEFT(cv), CV_NPTS(cv), TY_INT)
+		call rcv_bspline1 (x, CV_NPTS(cv), CV_NPIECES(cv),
+		    -CV_XMIN(cv), CV_SPACING(cv), BASIS(CV_BASIS(cv)),
+		    LEFT(CV_LEFT(cv)))
+		call aaddki (LEFT(CV_LEFT(cv)), vzptr, LEFT(CV_LEFT(cv)),
+		    CV_NPTS(cv))
+	    case USERFNC:
+		call rcv_buser (cv, x, CV_NPTS(cv))
+	    }
+	}
+
+
+	# accumulate the new right side of the matrix equation
+	call amulr (w, y, Memr[CV_WY(cv)], CV_NPTS(cv))
+	bzptr = CV_BASIS(cv)
+
+	switch (CV_TYPE(cv)) {
+
+	case SPLINE1, SPLINE3:
+
+	    do k = 1, CV_ORDER(cv) {
+	        do i = 1, CV_NPTS(cv) {
+		    vindex = LEFT(CV_LEFT(cv)+i-1) + k
+	            VECTOR(vindex) = VECTOR(vindex) + Memr[CV_WY(cv)+i-1] *
+		        BASIS(bzptr+i-1)
+		}
+	        bzptr = bzptr + CV_NPTS(cv)
+	    }
+
+	case LEGENDRE, CHEBYSHEV, USERFNC:
+
+	    do k = 1, CV_ORDER(cv) {
+		vindex = vzptr + k
+	        do i = 1, CV_NPTS(cv)
+	            VECTOR(vindex) = VECTOR(vindex) + Memr[CV_WY(cv)+i-1] *
+			BASIS(bzptr+i-1)
+	        bzptr = bzptr + CV_NPTS(cv)
+	    }
+
+	}
+
+	# solve for the new coefficients using forward and back
+	# substitution
+	call rcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		    VECTOR(CV_VECTOR(cv)), COEFF(CV_COEFF(cv)))
+end
diff --git a/math/curfit/cvreject.gx b/math/curfit/cvreject.gx
new file mode 100644
index 00000000..bbaffef4
--- /dev/null
+++ b/math/curfit/cvreject.gx
@@ -0,0 +1,82 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVREJECT -- Procedure to subtract a single datapoint from the data set.
+# The normal equations for the data point are calculated
+# and subtracted from MATRIX and VECTOR. After all rejected points
+# have been subtracted from the fit CVSOLVE, must be called to generate
+# a new set of coefficients.
+
+$if (datatype == r)
+procedure cvrject (cv, x, y, w)
+$else
+procedure dcvrject (cv, x, y, w)
+$endif
+
+pointer	cv		# curve fitting image descriptor
+PIXEL	x		# x value
+PIXEL	y		# y value
+PIXEL	w		# weight of the data point
+
+int	left, i, ii, j
+pointer	xzptr
+pointer mzptr, mzzptr
+pointer	vzptr
+PIXEL   bw
+
+begin
+
+	# increment the number of points
+	CV_NPTS(cv) = CV_NPTS(cv) - 1
+
+	# calculate all type non-zero basis functions for a given data point
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 0
+	    call $tcv_b1cheb (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case LEGENDRE:
+	    left = 0
+	    call $tcv_b1leg (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case SPLINE3:
+	    call $tcv_b1spline3 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+			       CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case SPLINE1:
+	    call $tcv_b1spline1 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+			       CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)	
+	case USERFNC:
+	    left = 0
+	    call $tcv_b1user (cv, x)
+	}
+
+	# index the pointers
+	xzptr = CV_XBASIS(cv) - 1
+	mzptr = CV_MATRIX(cv) + CV_ORDER(cv) * (left - 1)
+	vzptr = CV_VECTOR(cv) + left - 1
+
+	# calculate the normal equations for the data point and subtract
+	# them from the fit
+	do i = 1, CV_ORDER(cv) {
+
+	    # subtract inner product of basis functions and data ordinate
+	    # from the fit
+	    bw = XBASIS(xzptr+i) * w
+	    VECTOR(vzptr+i) = VECTOR(vzptr+i) - bw * y
+
+	    # subtract inner product of basis functions from the fit
+	    ii = 0
+	    mzzptr = mzptr + i * CV_ORDER(cv)
+	    do j = i, CV_ORDER(cv) {
+		MATRIX(mzzptr+ii) = MATRIX(mzzptr+ii) - XBASIS(xzptr+j) * bw
+		ii = ii + 1
+	    }
+	}
+end
diff --git a/math/curfit/cvrejectd.x b/math/curfit/cvrejectd.x
new file mode 100644
index 00000000..903ef594
--- /dev/null
+++ b/math/curfit/cvrejectd.x
@@ -0,0 +1,74 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+# CVREJECT -- Procedure to subtract a single datapoint from the data set.
+# The normal equations for the data point are calculated
+# and subtracted from MATRIX and VECTOR. After all rejected points
+# have been subtracted from the fit CVSOLVE, must be called to generate
+# a new set of coefficients.
+
+procedure dcvrject (cv, x, y, w)
+
+pointer	cv		# curve fitting image descriptor
+double	x		# x value
+double	y		# y value
+double	w		# weight of the data point
+
+int	left, i, ii, j
+pointer	xzptr
+pointer mzptr, mzzptr
+pointer	vzptr
+double   bw
+
+begin
+
+	# increment the number of points
+	CV_NPTS(cv) = CV_NPTS(cv) - 1
+
+	# calculate all type non-zero basis functions for a given data point
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 0
+	    call dcv_b1cheb (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case LEGENDRE:
+	    left = 0
+	    call dcv_b1leg (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case SPLINE3:
+	    call dcv_b1spline3 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+			       CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case SPLINE1:
+	    call dcv_b1spline1 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+			       CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)	
+	case USERFNC:
+	    left = 0
+	    call dcv_b1user (cv, x)
+	}
+
+	# index the pointers
+	xzptr = CV_XBASIS(cv) - 1
+	mzptr = CV_MATRIX(cv) + CV_ORDER(cv) * (left - 1)
+	vzptr = CV_VECTOR(cv) + left - 1
+
+	# calculate the normal equations for the data point and subtract
+	# them from the fit
+	do i = 1, CV_ORDER(cv) {
+
+	    # subtract inner product of basis functions and data ordinate
+	    # from the fit
+	    bw = XBASIS(xzptr+i) * w
+	    VECTOR(vzptr+i) = VECTOR(vzptr+i) - bw * y
+
+	    # subtract inner product of basis functions from the fit
+	    ii = 0
+	    mzzptr = mzptr + i * CV_ORDER(cv)
+	    do j = i, CV_ORDER(cv) {
+		MATRIX(mzzptr+ii) = MATRIX(mzzptr+ii) - XBASIS(xzptr+j) * bw
+		ii = ii + 1
+	    }
+	}
+end
diff --git a/math/curfit/cvrejectr.x b/math/curfit/cvrejectr.x
new file mode 100644
index 00000000..3f275cce
--- /dev/null
+++ b/math/curfit/cvrejectr.x
@@ -0,0 +1,74 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+# CVREJECT -- Procedure to subtract a single datapoint from the data set.
+# The normal equations for the data point are calculated
+# and subtracted from MATRIX and VECTOR. After all rejected points
+# have been subtracted from the fit CVSOLVE, must be called to generate
+# a new set of coefficients.
+
+procedure cvrject (cv, x, y, w)
+
+pointer	cv		# curve fitting image descriptor
+real	x		# x value
+real	y		# y value
+real	w		# weight of the data point
+
+int	left, i, ii, j
+pointer	xzptr
+pointer mzptr, mzzptr
+pointer	vzptr
+real   bw
+
+begin
+
+	# increment the number of points
+	CV_NPTS(cv) = CV_NPTS(cv) - 1
+
+	# calculate all type non-zero basis functions for a given data point
+	switch (CV_TYPE(cv)) {
+	case CHEBYSHEV:
+	    left = 0
+	    call rcv_b1cheb (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case LEGENDRE:
+	    left = 0
+	    call rcv_b1leg (x, CV_ORDER(cv), CV_MAXMIN(cv), CV_RANGE(cv),
+			    XBASIS(CV_XBASIS(cv)))
+	case SPLINE3:
+	    call rcv_b1spline3 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+			       CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)
+	case SPLINE1:
+	    call rcv_b1spline1 (x, CV_NPIECES(cv), -CV_XMIN(cv),
+			       CV_SPACING(cv), XBASIS(CV_XBASIS(cv)), left)	
+	case USERFNC:
+	    left = 0
+	    call rcv_b1user (cv, x)
+	}
+
+	# index the pointers
+	xzptr = CV_XBASIS(cv) - 1
+	mzptr = CV_MATRIX(cv) + CV_ORDER(cv) * (left - 1)
+	vzptr = CV_VECTOR(cv) + left - 1
+
+	# calculate the normal equations for the data point and subtract
+	# them from the fit
+	do i = 1, CV_ORDER(cv) {
+
+	    # subtract inner product of basis functions and data ordinate
+	    # from the fit
+	    bw = XBASIS(xzptr+i) * w
+	    VECTOR(vzptr+i) = VECTOR(vzptr+i) - bw * y
+
+	    # subtract inner product of basis functions from the fit
+	    ii = 0
+	    mzzptr = mzptr + i * CV_ORDER(cv)
+	    do j = i, CV_ORDER(cv) {
+		MATRIX(mzzptr+ii) = MATRIX(mzzptr+ii) - XBASIS(xzptr+j) * bw
+		ii = ii + 1
+	    }
+	}
+end
diff --git a/math/curfit/cvrestore.gx b/math/curfit/cvrestore.gx
new file mode 100644
index 00000000..cfec56d7
--- /dev/null
+++ b/math/curfit/cvrestore.gx
@@ -0,0 +1,100 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVRESTORE -- Procedure to restore fit parameters saved by CVSAVE 
+# for use by CVEVAL and CVVECTOR. The parameters are assumed to
+# be stored in fit in the following order, curve_type, order, xmin,
+# xmax, followed by the coefficients.
+
+$if (datatype == r)
+procedure cvrestore (cv, fit)
+$else
+procedure dcvrestore (cv, fit)
+$endif
+
+pointer	cv		# curve descriptor
+PIXEL	fit[ARB]	# array containing fit parameters
+
+int	curve_type, order
+
+errchk malloc
+
+begin
+	# allocate space for curve descriptor
+	call malloc (cv, LEN_CVSTRUCT, TY_STRUCT)
+
+	order = nint (CV_SAVEORDER(fit))
+	if (order < 1)
+	    call error (0, "CVRESTORE: Illegal order.")
+
+	if (CV_SAVEXMAX(fit) <= CV_SAVEXMIN(fit))
+	    call  error (0, "CVRESTORE: xmax <= xmin.")
+
+	# set curve_type dependent curve descriptor parameters
+	curve_type = nint (CV_SAVETYPE(fit))
+	switch (curve_type) {
+	case CHEBYSHEV, LEGENDRE:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    CV_RANGE(cv) = 2. / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_MAXMIN(cv) = - (CV_SAVEXMAX(fit) + CV_SAVEXMIN(fit)) / 2.
+	    CV_USERFNC(cv) = NULL
+	case SPLINE3:
+	    CV_ORDER(cv) = SPLINE3_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE3_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_USERFNC(cv) = NULL
+	case SPLINE1:
+	    CV_ORDER(cv) = SPLINE1_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE1_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_USERFNC(cv) = NULL
+	case USERFNC:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    CV_RANGE(cv) = 2. / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_MAXMIN(cv) = - (CV_SAVEXMAX(fit) + CV_SAVEXMIN(fit)) / 2.
+	    $if (datatype == r)
+	    CV_USERFNCR(cv) = CV_SAVEFNC(fit)	# avoids type conversion
+	    $else
+	    CV_USERFNCD(cv) = CV_SAVEFNC(fit)	# avoids type conversion
+	    $endif
+	default:
+	    call error (0, "CVRESTORE: Unknown curve type.")
+	}
+
+	# set remaining curve parameters
+	CV_TYPE(cv) = curve_type
+	CV_XMIN(cv) = CV_SAVEXMIN(fit)
+	CV_XMAX(cv) = CV_SAVEXMAX(fit)
+
+	# allocate space for xbasis and coefficient arrays, set remaining
+	# pointers to NULL
+
+	call calloc (CV_XBASIS(cv), CV_ORDER(cv), TY_PIXEL)
+	call calloc (CV_COEFF(cv), CV_NCOEFF(cv), TY_PIXEL)
+
+	CV_MATRIX(cv) = NULL
+	CV_CHOFAC(cv) = NULL
+	CV_VECTOR(cv) = NULL
+	CV_BASIS(cv) = NULL
+	CV_LEFT(cv) = NULL
+	CV_WY(cv) = NULL
+
+	# restore coefficients
+	if (CV_TYPE(cv) == USERFNC)
+	    call amov$t (fit[CV_SAVECOEFF+1], COEFF(CV_COEFF(cv)),
+	        CV_NCOEFF(cv))
+	else
+	    call amov$t (fit[CV_SAVECOEFF], COEFF(CV_COEFF(cv)),
+	        CV_NCOEFF(cv))
+end
diff --git a/math/curfit/cvrestored.x b/math/curfit/cvrestored.x
new file mode 100644
index 00000000..e528c1f0
--- /dev/null
+++ b/math/curfit/cvrestored.x
@@ -0,0 +1,88 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+# CVRESTORE -- Procedure to restore fit parameters saved by CVSAVE 
+# for use by CVEVAL and CVVECTOR. The parameters are assumed to
+# be stored in fit in the following order, curve_type, order, xmin,
+# xmax, followed by the coefficients.
+
+procedure dcvrestore (cv, fit)
+
+pointer	cv		# curve descriptor
+double	fit[ARB]	# array containing fit parameters
+
+int	curve_type, order
+
+errchk malloc
+
+begin
+	# allocate space for curve descriptor
+	call malloc (cv, LEN_CVSTRUCT, TY_STRUCT)
+
+	order = nint (CV_SAVEORDER(fit))
+	if (order < 1)
+	    call error (0, "CVRESTORE: Illegal order.")
+
+	if (CV_SAVEXMAX(fit) <= CV_SAVEXMIN(fit))
+	    call  error (0, "CVRESTORE: xmax <= xmin.")
+
+	# set curve_type dependent curve descriptor parameters
+	curve_type = nint (CV_SAVETYPE(fit))
+	switch (curve_type) {
+	case CHEBYSHEV, LEGENDRE:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    CV_RANGE(cv) = 2. / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_MAXMIN(cv) = - (CV_SAVEXMAX(fit) + CV_SAVEXMIN(fit)) / 2.
+	    CV_USERFNC(cv) = NULL
+	case SPLINE3:
+	    CV_ORDER(cv) = SPLINE3_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE3_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_USERFNC(cv) = NULL
+	case SPLINE1:
+	    CV_ORDER(cv) = SPLINE1_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE1_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_USERFNC(cv) = NULL
+	case USERFNC:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    CV_RANGE(cv) = 2. / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_MAXMIN(cv) = - (CV_SAVEXMAX(fit) + CV_SAVEXMIN(fit)) / 2.
+	    CV_USERFNCD(cv) = CV_SAVEFNC(fit)	# avoids type conversion
+	default:
+	    call error (0, "CVRESTORE: Unknown curve type.")
+	}
+
+	# set remaining curve parameters
+	CV_TYPE(cv) = curve_type
+	CV_XMIN(cv) = CV_SAVEXMIN(fit)
+	CV_XMAX(cv) = CV_SAVEXMAX(fit)
+
+	# allocate space for xbasis and coefficient arrays, set remaining
+	# pointers to NULL
+
+	call calloc (CV_XBASIS(cv), CV_ORDER(cv), TY_DOUBLE)
+	call calloc (CV_COEFF(cv), CV_NCOEFF(cv), TY_DOUBLE)
+
+	CV_MATRIX(cv) = NULL
+	CV_CHOFAC(cv) = NULL
+	CV_VECTOR(cv) = NULL
+	CV_BASIS(cv) = NULL
+	CV_LEFT(cv) = NULL
+	CV_WY(cv) = NULL
+
+	# restore coefficients
+	if (CV_TYPE(cv) == USERFNC)
+	    call amovd (fit[CV_SAVECOEFF+1], COEFF(CV_COEFF(cv)),
+	        CV_NCOEFF(cv))
+	else
+	    call amovd (fit[CV_SAVECOEFF], COEFF(CV_COEFF(cv)),
+	        CV_NCOEFF(cv))
+end
diff --git a/math/curfit/cvrestorer.x b/math/curfit/cvrestorer.x
new file mode 100644
index 00000000..859d434f
--- /dev/null
+++ b/math/curfit/cvrestorer.x
@@ -0,0 +1,88 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+# CVRESTORE -- Procedure to restore fit parameters saved by CVSAVE 
+# for use by CVEVAL and CVVECTOR. The parameters are assumed to
+# be stored in fit in the following order, curve_type, order, xmin,
+# xmax, followed by the coefficients.
+
+procedure cvrestore (cv, fit)
+
+pointer	cv		# curve descriptor
+real	fit[ARB]	# array containing fit parameters
+
+int	curve_type, order
+
+errchk malloc
+
+begin
+	# allocate space for curve descriptor
+	call malloc (cv, LEN_CVSTRUCT, TY_STRUCT)
+
+	order = nint (CV_SAVEORDER(fit))
+	if (order < 1)
+	    call error (0, "CVRESTORE: Illegal order.")
+
+	if (CV_SAVEXMAX(fit) <= CV_SAVEXMIN(fit))
+	    call  error (0, "CVRESTORE: xmax <= xmin.")
+
+	# set curve_type dependent curve descriptor parameters
+	curve_type = nint (CV_SAVETYPE(fit))
+	switch (curve_type) {
+	case CHEBYSHEV, LEGENDRE:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    CV_RANGE(cv) = 2. / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_MAXMIN(cv) = - (CV_SAVEXMAX(fit) + CV_SAVEXMIN(fit)) / 2.
+	    CV_USERFNC(cv) = NULL
+	case SPLINE3:
+	    CV_ORDER(cv) = SPLINE3_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE3_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_USERFNC(cv) = NULL
+	case SPLINE1:
+	    CV_ORDER(cv) = SPLINE1_ORDER
+	    CV_NCOEFF(cv) = order + SPLINE1_ORDER - 1
+	    CV_NPIECES(cv) = order - 1
+	    CV_SPACING(cv) = order / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_USERFNC(cv) = NULL
+	case USERFNC:
+	    CV_ORDER(cv) = order
+	    CV_NCOEFF(cv) = order
+	    CV_RANGE(cv) = 2. / (CV_SAVEXMAX(fit) - CV_SAVEXMIN(fit))
+	    CV_MAXMIN(cv) = - (CV_SAVEXMAX(fit) + CV_SAVEXMIN(fit)) / 2.
+	    CV_USERFNCR(cv) = CV_SAVEFNC(fit)	# avoids type conversion
+	default:
+	    call error (0, "CVRESTORE: Unknown curve type.")
+	}
+
+	# set remaining curve parameters
+	CV_TYPE(cv) = curve_type
+	CV_XMIN(cv) = CV_SAVEXMIN(fit)
+	CV_XMAX(cv) = CV_SAVEXMAX(fit)
+
+	# allocate space for xbasis and coefficient arrays, set remaining
+	# pointers to NULL
+
+	call calloc (CV_XBASIS(cv), CV_ORDER(cv), TY_REAL)
+	call calloc (CV_COEFF(cv), CV_NCOEFF(cv), TY_REAL)
+
+	CV_MATRIX(cv) = NULL
+	CV_CHOFAC(cv) = NULL
+	CV_VECTOR(cv) = NULL
+	CV_BASIS(cv) = NULL
+	CV_LEFT(cv) = NULL
+	CV_WY(cv) = NULL
+
+	# restore coefficients
+	if (CV_TYPE(cv) == USERFNC)
+	    call amovr (fit[CV_SAVECOEFF+1], COEFF(CV_COEFF(cv)),
+	        CV_NCOEFF(cv))
+	else
+	    call amovr (fit[CV_SAVECOEFF], COEFF(CV_COEFF(cv)),
+	        CV_NCOEFF(cv))
+end
diff --git a/math/curfit/cvsave.gx b/math/curfit/cvsave.gx
new file mode 100644
index 00000000..95fedd2b
--- /dev/null
+++ b/math/curfit/cvsave.gx
@@ -0,0 +1,56 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVSAVE -- Procedure to save the parameters of the fit for later
+# use by cveval and cvvector. Only curve_type, order, xmin, xmax
+# and the coefficients are saved. The parameters are saved in fit
+# in the order curve_type, order, xmin, xmax, followed by the
+# coefficients.
+
+$if (datatype == r)
+procedure cvsave (cv, fit)
+$else
+procedure dcvsave (cv, fit)
+$endif
+
+pointer	cv		# curve descriptor
+PIXEL	fit[ARB]	# PIXEL array containing curve parameters
+
+begin
+	# set common curve parameters
+	CV_SAVETYPE(fit) = CV_TYPE(cv)
+	CV_SAVEXMIN(fit) = CV_XMIN(cv)
+	CV_SAVEXMAX(fit) = CV_XMAX(cv)
+	if (CV_TYPE(cv) == USERFNC)
+	    $if (datatype == r)
+	    CV_SAVEFNC(fit) = CV_USERFNCR(cv)	# no type conversion
+	    $else
+	    CV_SAVEFNC(fit) = CV_USERFNCD(cv)
+	    $endif
+
+	# set curve-type dependent parmeters
+	switch (CV_TYPE(cv)) {
+	case LEGENDRE, CHEBYSHEV, USERFNC:
+	    CV_SAVEORDER(fit) = CV_ORDER(cv)
+	case SPLINE1, SPLINE3:
+	    CV_SAVEORDER(fit) = CV_NPIECES(cv) + 1
+	default:
+	    call error (0, "CVSAVE: Unknown curve type.")
+	}
+
+
+	# set coefficients
+	if (CV_TYPE(cv) == USERFNC)
+	    call amov$t (COEFF(CV_COEFF(cv)), fit[CV_SAVECOEFF+1],
+	        CV_NCOEFF(cv)) 
+	else
+	    call amov$t (COEFF(CV_COEFF(cv)), fit[CV_SAVECOEFF],
+	        CV_NCOEFF(cv)) 
+end
diff --git a/math/curfit/cvsaved.x b/math/curfit/cvsaved.x
new file mode 100644
index 00000000..04cb7c8b
--- /dev/null
+++ b/math/curfit/cvsaved.x
@@ -0,0 +1,44 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+# CVSAVE -- Procedure to save the parameters of the fit for later
+# use by cveval and cvvector. Only curve_type, order, xmin, xmax
+# and the coefficients are saved. The parameters are saved in fit
+# in the order curve_type, order, xmin, xmax, followed by the
+# coefficients.
+
+procedure dcvsave (cv, fit)
+
+pointer	cv		# curve descriptor
+double	fit[ARB]	# PIXEL array containing curve parameters
+
+begin
+	# set common curve parameters
+	CV_SAVETYPE(fit) = CV_TYPE(cv)
+	CV_SAVEXMIN(fit) = CV_XMIN(cv)
+	CV_SAVEXMAX(fit) = CV_XMAX(cv)
+	if (CV_TYPE(cv) == USERFNC)
+	    CV_SAVEFNC(fit) = CV_USERFNCD(cv)
+
+	# set curve-type dependent parmeters
+	switch (CV_TYPE(cv)) {
+	case LEGENDRE, CHEBYSHEV, USERFNC:
+	    CV_SAVEORDER(fit) = CV_ORDER(cv)
+	case SPLINE1, SPLINE3:
+	    CV_SAVEORDER(fit) = CV_NPIECES(cv) + 1
+	default:
+	    call error (0, "CVSAVE: Unknown curve type.")
+	}
+
+
+	# set coefficients
+	if (CV_TYPE(cv) == USERFNC)
+	    call amovd (COEFF(CV_COEFF(cv)), fit[CV_SAVECOEFF+1],
+	        CV_NCOEFF(cv)) 
+	else
+	    call amovd (COEFF(CV_COEFF(cv)), fit[CV_SAVECOEFF],
+	        CV_NCOEFF(cv)) 
+end
diff --git a/math/curfit/cvsaver.x b/math/curfit/cvsaver.x
new file mode 100644
index 00000000..513083a5
--- /dev/null
+++ b/math/curfit/cvsaver.x
@@ -0,0 +1,44 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+# CVSAVE -- Procedure to save the parameters of the fit for later
+# use by cveval and cvvector. Only curve_type, order, xmin, xmax
+# and the coefficients are saved. The parameters are saved in fit
+# in the order curve_type, order, xmin, xmax, followed by the
+# coefficients.
+
+procedure cvsave (cv, fit)
+
+pointer	cv		# curve descriptor
+real	fit[ARB]	# PIXEL array containing curve parameters
+
+begin
+	# set common curve parameters
+	CV_SAVETYPE(fit) = CV_TYPE(cv)
+	CV_SAVEXMIN(fit) = CV_XMIN(cv)
+	CV_SAVEXMAX(fit) = CV_XMAX(cv)
+	if (CV_TYPE(cv) == USERFNC)
+	    CV_SAVEFNC(fit) = CV_USERFNCR(cv)	# no type conversion
+
+	# set curve-type dependent parmeters
+	switch (CV_TYPE(cv)) {
+	case LEGENDRE, CHEBYSHEV, USERFNC:
+	    CV_SAVEORDER(fit) = CV_ORDER(cv)
+	case SPLINE1, SPLINE3:
+	    CV_SAVEORDER(fit) = CV_NPIECES(cv) + 1
+	default:
+	    call error (0, "CVSAVE: Unknown curve type.")
+	}
+
+
+	# set coefficients
+	if (CV_TYPE(cv) == USERFNC)
+	    call amovr (COEFF(CV_COEFF(cv)), fit[CV_SAVECOEFF+1],
+	        CV_NCOEFF(cv)) 
+	else
+	    call amovr (COEFF(CV_COEFF(cv)), fit[CV_SAVECOEFF],
+	        CV_NCOEFF(cv)) 
+end
diff --git a/math/curfit/cvset.gx b/math/curfit/cvset.gx
new file mode 100644
index 00000000..fed1cf46
--- /dev/null
+++ b/math/curfit/cvset.gx
@@ -0,0 +1,98 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVSET -- Procedure to store the fit parameters derived from outside
+# the CURFIT package inside the curve descriptor structure for use
+# by the CVEVAL and CVVECTOR proocedures. The curve_type is one of
+# LEGENDRE, CHEBYSHEV or SPLINE3. For the polynomials the number of
+# coefficients is equal to one plus the order of the polynomial. In the
+# case of the cubic spline the number of coefficients equals three plus
+# the number of polynomial pieces. The polynomials are normalized over
+# from xmin to xmax.
+
+$if (datatype == r)
+procedure cvset (cv, curve_type, xmin, xmax, coeff, ncoeff)
+$else
+procedure dcvset (cv, curve_type, xmin, xmax, coeff, ncoeff)
+$endif
+
+pointer	cv		# curve descriptor
+int	curve_type	# the functional form of the curve
+PIXEL	xmin		# the minimum x value
+PIXEL	xmax		# the maximum x value
+PIXEL	coeff[ncoeff]	# the coefficient array
+int	ncoeff		# the number of coefficients
+
+errchk	malloc
+
+begin
+	# allocate space for curve descriptor
+	call malloc (cv, LEN_CVSTRUCT, TY_STRUCT)
+
+	if (ncoeff < 1)
+	    call error (0, "CVSET: Illegal number of coefficients.")
+
+	if (xmin >= xmax)
+	    call  error (0, "CVSET: xmax <= xmin.")
+
+	# set curve_type dependent curve descriptor parameters
+	switch (curve_type) {
+	case CHEBYSHEV, LEGENDRE:
+	    CV_ORDER(cv) = ncoeff
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_RANGE(cv) = 2. / (xmax - xmin)
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	case SPLINE3:
+	    CV_ORDER(cv) = SPLINE3_ORDER
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_NPIECES(cv) = ncoeff - SPLINE3_ORDER
+	    CV_SPACING(cv) = (CV_NPIECES(cv) + 1) / (xmax - xmin) 
+	case SPLINE1:
+	    CV_ORDER(cv) = SPLINE1_ORDER
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_NPIECES(cv) = ncoeff - SPLINE1_ORDER
+	    CV_SPACING(cv) = (CV_NPIECES(cv) + 1) / (xmax - xmin) 
+	case USERFNC:
+	    CV_ORDER(cv) = ncoeff
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_RANGE(cv) = 2. / (xmax - xmin)
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	default:
+	    call error (0, "CVSET: Unknown curve type.")
+	}
+
+	# set remaining curve parameters
+	CV_TYPE(cv) = curve_type
+	CV_XMIN(cv) = xmin
+	CV_XMAX(cv) = xmax
+
+	# allocate space for xbasis and coefficient arrays, set remaining
+	# pointers to NULL
+
+	$if (datatype == r)
+	call malloc (CV_XBASIS(cv), CV_ORDER(cv), TY_REAL)
+	call malloc (CV_COEFF(cv), CV_NCOEFF(cv), TY_REAL)
+	$else
+	call malloc (CV_XBASIS(cv), CV_ORDER(cv), TY_DOUBLE)
+	call malloc (CV_COEFF(cv), CV_NCOEFF(cv), TY_DOUBLE)
+	$endif
+
+	CV_MATRIX(cv) = NULL
+	CV_CHOFAC(cv) = NULL
+	CV_VECTOR(cv) = NULL
+	CV_BASIS(cv) = NULL
+	CV_WY(cv) = NULL
+	CV_LEFT(cv) = NULL
+
+	CV_USERFNC(cv) = NULL
+
+	# restore coefficients
+	call amov$t (coeff, COEFF(CV_COEFF(cv)), CV_NCOEFF(cv))
+end
diff --git a/math/curfit/cvsetd.x b/math/curfit/cvsetd.x
new file mode 100644
index 00000000..c0f41f09
--- /dev/null
+++ b/math/curfit/cvsetd.x
@@ -0,0 +1,85 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+# CVSET -- Procedure to store the fit parameters derived from outside
+# the CURFIT package inside the curve descriptor structure for use
+# by the CVEVAL and CVVECTOR proocedures. The curve_type is one of
+# LEGENDRE, CHEBYSHEV or SPLINE3. For the polynomials the number of
+# coefficients is equal to one plus the order of the polynomial. In the
+# case of the cubic spline the number of coefficients equals three plus
+# the number of polynomial pieces. The polynomials are normalized over
+# from xmin to xmax.
+
+procedure dcvset (cv, curve_type, xmin, xmax, coeff, ncoeff)
+
+pointer	cv		# curve descriptor
+int	curve_type	# the functional form of the curve
+double	xmin		# the minimum x value
+double	xmax		# the maximum x value
+double	coeff[ncoeff]	# the coefficient array
+int	ncoeff		# the number of coefficients
+
+errchk	malloc
+
+begin
+	# allocate space for curve descriptor
+	call malloc (cv, LEN_CVSTRUCT, TY_STRUCT)
+
+	if (ncoeff < 1)
+	    call error (0, "CVSET: Illegal number of coefficients.")
+
+	if (xmin >= xmax)
+	    call  error (0, "CVSET: xmax <= xmin.")
+
+	# set curve_type dependent curve descriptor parameters
+	switch (curve_type) {
+	case CHEBYSHEV, LEGENDRE:
+	    CV_ORDER(cv) = ncoeff
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_RANGE(cv) = 2. / (xmax - xmin)
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	case SPLINE3:
+	    CV_ORDER(cv) = SPLINE3_ORDER
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_NPIECES(cv) = ncoeff - SPLINE3_ORDER
+	    CV_SPACING(cv) = (CV_NPIECES(cv) + 1) / (xmax - xmin) 
+	case SPLINE1:
+	    CV_ORDER(cv) = SPLINE1_ORDER
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_NPIECES(cv) = ncoeff - SPLINE1_ORDER
+	    CV_SPACING(cv) = (CV_NPIECES(cv) + 1) / (xmax - xmin) 
+	case USERFNC:
+	    CV_ORDER(cv) = ncoeff
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_RANGE(cv) = 2. / (xmax - xmin)
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	default:
+	    call error (0, "CVSET: Unknown curve type.")
+	}
+
+	# set remaining curve parameters
+	CV_TYPE(cv) = curve_type
+	CV_XMIN(cv) = xmin
+	CV_XMAX(cv) = xmax
+
+	# allocate space for xbasis and coefficient arrays, set remaining
+	# pointers to NULL
+
+	call malloc (CV_XBASIS(cv), CV_ORDER(cv), TY_DOUBLE)
+	call malloc (CV_COEFF(cv), CV_NCOEFF(cv), TY_DOUBLE)
+
+	CV_MATRIX(cv) = NULL
+	CV_CHOFAC(cv) = NULL
+	CV_VECTOR(cv) = NULL
+	CV_BASIS(cv) = NULL
+	CV_WY(cv) = NULL
+	CV_LEFT(cv) = NULL
+
+	CV_USERFNC(cv) = NULL
+
+	# restore coefficients
+	call amovd (coeff, COEFF(CV_COEFF(cv)), CV_NCOEFF(cv))
+end
diff --git a/math/curfit/cvsetr.x b/math/curfit/cvsetr.x
new file mode 100644
index 00000000..9a3ec193
--- /dev/null
+++ b/math/curfit/cvsetr.x
@@ -0,0 +1,85 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+# CVSET -- Procedure to store the fit parameters derived from outside
+# the CURFIT package inside the curve descriptor structure for use
+# by the CVEVAL and CVVECTOR proocedures. The curve_type is one of
+# LEGENDRE, CHEBYSHEV or SPLINE3. For the polynomials the number of
+# coefficients is equal to one plus the order of the polynomial. In the
+# case of the cubic spline the number of coefficients equals three plus
+# the number of polynomial pieces. The polynomials are normalized over
+# from xmin to xmax.
+
+procedure cvset (cv, curve_type, xmin, xmax, coeff, ncoeff)
+
+pointer	cv		# curve descriptor
+int	curve_type	# the functional form of the curve
+real	xmin		# the minimum x value
+real	xmax		# the maximum x value
+real	coeff[ncoeff]	# the coefficient array
+int	ncoeff		# the number of coefficients
+
+errchk	malloc
+
+begin
+	# allocate space for curve descriptor
+	call malloc (cv, LEN_CVSTRUCT, TY_STRUCT)
+
+	if (ncoeff < 1)
+	    call error (0, "CVSET: Illegal number of coefficients.")
+
+	if (xmin >= xmax)
+	    call  error (0, "CVSET: xmax <= xmin.")
+
+	# set curve_type dependent curve descriptor parameters
+	switch (curve_type) {
+	case CHEBYSHEV, LEGENDRE:
+	    CV_ORDER(cv) = ncoeff
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_RANGE(cv) = 2. / (xmax - xmin)
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	case SPLINE3:
+	    CV_ORDER(cv) = SPLINE3_ORDER
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_NPIECES(cv) = ncoeff - SPLINE3_ORDER
+	    CV_SPACING(cv) = (CV_NPIECES(cv) + 1) / (xmax - xmin) 
+	case SPLINE1:
+	    CV_ORDER(cv) = SPLINE1_ORDER
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_NPIECES(cv) = ncoeff - SPLINE1_ORDER
+	    CV_SPACING(cv) = (CV_NPIECES(cv) + 1) / (xmax - xmin) 
+	case USERFNC:
+	    CV_ORDER(cv) = ncoeff
+	    CV_NCOEFF(cv) = ncoeff
+	    CV_RANGE(cv) = 2. / (xmax - xmin)
+	    CV_MAXMIN(cv) = - (xmax + xmin) / 2.
+	default:
+	    call error (0, "CVSET: Unknown curve type.")
+	}
+
+	# set remaining curve parameters
+	CV_TYPE(cv) = curve_type
+	CV_XMIN(cv) = xmin
+	CV_XMAX(cv) = xmax
+
+	# allocate space for xbasis and coefficient arrays, set remaining
+	# pointers to NULL
+
+	call malloc (CV_XBASIS(cv), CV_ORDER(cv), TY_REAL)
+	call malloc (CV_COEFF(cv), CV_NCOEFF(cv), TY_REAL)
+
+	CV_MATRIX(cv) = NULL
+	CV_CHOFAC(cv) = NULL
+	CV_VECTOR(cv) = NULL
+	CV_BASIS(cv) = NULL
+	CV_WY(cv) = NULL
+	CV_LEFT(cv) = NULL
+
+	CV_USERFNC(cv) = NULL
+
+	# restore coefficients
+	call amovr (coeff, COEFF(CV_COEFF(cv)), CV_NCOEFF(cv))
+end
diff --git a/math/curfit/cvsolve.gx b/math/curfit/cvsolve.gx
new file mode 100644
index 00000000..08e0bf92
--- /dev/null
+++ b/math/curfit/cvsolve.gx
@@ -0,0 +1,51 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+
+# CVSOLVE -- Solve the matrix normal equations of the form ca = b for a,
+# where c is a symmetric, positive semi-definite, banded matrix with
+# CV_NCOEFF(cv) rows and a and b are CV_NCOEFF(cv)-vectors.
+# Initially c is stored in the CV_ORDER(cv) by CV_NCOEFF(cv) matrix MATRIX
+# and b is stored in VECTOR.
+# The Cholesky factorization of MATRIX is calculated and stored in CHOFAC.
+# Finally the coefficients are calculated by forward and back substitution
+# and stored in COEFF.
+
+$if (datatype == r)
+procedure cvsolve (cv, ier)
+$else
+procedure dcvsolve (cv, ier)
+$endif
+
+
+pointer	cv 		# curve descriptor
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+int	nfree
+
+begin
+	ier = OK
+	nfree = CV_NPTS(cv) - CV_NCOEFF(cv)
+
+	if (nfree < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# calculate the Cholesky factorization of the data matrix
+	call $tcvchofac (MATRIX(CV_MATRIX(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		    CHOFAC(CV_CHOFAC(cv)), ier)
+
+	# solve for the coefficients by forward and back substitution
+	call $tcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		    VECTOR(CV_VECTOR(cv)), COEFF(CV_COEFF(cv)))
+end
diff --git a/math/curfit/cvsolved.x b/math/curfit/cvsolved.x
new file mode 100644
index 00000000..ba61be19
--- /dev/null
+++ b/math/curfit/cvsolved.x
@@ -0,0 +1,43 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+
+# CVSOLVE -- Solve the matrix normal equations of the form ca = b for a,
+# where c is a symmetric, positive semi-definite, banded matrix with
+# CV_NCOEFF(cv) rows and a and b are CV_NCOEFF(cv)-vectors.
+# Initially c is stored in the CV_ORDER(cv) by CV_NCOEFF(cv) matrix MATRIX
+# and b is stored in VECTOR.
+# The Cholesky factorization of MATRIX is calculated and stored in CHOFAC.
+# Finally the coefficients are calculated by forward and back substitution
+# and stored in COEFF.
+
+procedure dcvsolve (cv, ier)
+
+
+pointer	cv 		# curve descriptor
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+int	nfree
+
+begin
+	ier = OK
+	nfree = CV_NPTS(cv) - CV_NCOEFF(cv)
+
+	if (nfree < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# calculate the Cholesky factorization of the data matrix
+	call dcvchofac (MATRIX(CV_MATRIX(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		    CHOFAC(CV_CHOFAC(cv)), ier)
+
+	# solve for the coefficients by forward and back substitution
+	call dcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		    VECTOR(CV_VECTOR(cv)), COEFF(CV_COEFF(cv)))
+end
diff --git a/math/curfit/cvsolver.x b/math/curfit/cvsolver.x
new file mode 100644
index 00000000..b52f012e
--- /dev/null
+++ b/math/curfit/cvsolver.x
@@ -0,0 +1,43 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+
+# CVSOLVE -- Solve the matrix normal equations of the form ca = b for a,
+# where c is a symmetric, positive semi-definite, banded matrix with
+# CV_NCOEFF(cv) rows and a and b are CV_NCOEFF(cv)-vectors.
+# Initially c is stored in the CV_ORDER(cv) by CV_NCOEFF(cv) matrix MATRIX
+# and b is stored in VECTOR.
+# The Cholesky factorization of MATRIX is calculated and stored in CHOFAC.
+# Finally the coefficients are calculated by forward and back substitution
+# and stored in COEFF.
+
+procedure cvsolve (cv, ier)
+
+
+pointer	cv 		# curve descriptor
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+int	nfree
+
+begin
+	ier = OK
+	nfree = CV_NPTS(cv) - CV_NCOEFF(cv)
+
+	if (nfree < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# calculate the Cholesky factorization of the data matrix
+	call rcvchofac (MATRIX(CV_MATRIX(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		    CHOFAC(CV_CHOFAC(cv)), ier)
+
+	# solve for the coefficients by forward and back substitution
+	call rcvchoslv (CHOFAC(CV_CHOFAC(cv)), CV_ORDER(cv), CV_NCOEFF(cv),
+		    VECTOR(CV_VECTOR(cv)), COEFF(CV_COEFF(cv)))
+end
diff --git a/math/curfit/cvstat.gx b/math/curfit/cvstat.gx
new file mode 100644
index 00000000..e98367b9
--- /dev/null
+++ b/math/curfit/cvstat.gx
@@ -0,0 +1,61 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include	<math/curfit.h>
+
+$if (datatype == r)
+include	"curfitdef.h"
+$else
+include	"dcurfitdef.h"
+$endif
+
+# CVSTATI -- Return integer paramters from the curfit package
+
+$if (datatype == r)
+int procedure cvstati (cv, param)
+$else
+int procedure dcvstati (cv, param)
+$endif
+
+pointer	cv			# Curfit pointer
+int	param			# Parameter
+
+begin
+	switch (param) {
+	case CVTYPE:
+	    return (CV_TYPE(cv))
+	case CVORDER:
+	    switch (CV_TYPE(cv)) {
+	    case LEGENDRE, CHEBYSHEV, USERFNC:
+	        return (CV_ORDER(cv))
+	    case SPLINE1, SPLINE3:
+		return (CV_NPIECES(cv) + 1)
+	    }
+	case CVNSAVE:
+	    if (CV_TYPE(cv) == USERFNC)
+	        return (CV_SAVECOEFF + CV_NCOEFF(cv))
+	    else
+		return (CV_SAVECOEFF + CV_NCOEFF(cv) - 1)
+	case CVNCOEFF:
+	    return (CV_NCOEFF(cv))
+	}
+end
+
+# CVSTATR -- Return real paramters from the curfit package
+
+$if (datatype == r)
+PIXEL procedure cvstatr (cv, param)
+$else
+PIXEL procedure dcvstatd (cv, param)
+$endif
+
+pointer	cv			# Curfit pointer
+int	param			# Parameter
+
+begin
+	switch (param) {
+	case CVXMIN:
+	    return (CV_XMIN(cv))
+	case CVXMAX:
+	    return (CV_XMAX(cv))
+	}
+end
diff --git a/math/curfit/cvstatd.x b/math/curfit/cvstatd.x
new file mode 100644
index 00000000..fae7c87e
--- /dev/null
+++ b/math/curfit/cvstatd.x
@@ -0,0 +1,49 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include	<math/curfit.h>
+
+include	"dcurfitdef.h"
+
+# CVSTATI -- Return integer paramters from the curfit package
+
+int procedure dcvstati (cv, param)
+
+pointer	cv			# Curfit pointer
+int	param			# Parameter
+
+begin
+	switch (param) {
+	case CVTYPE:
+	    return (CV_TYPE(cv))
+	case CVORDER:
+	    switch (CV_TYPE(cv)) {
+	    case LEGENDRE, CHEBYSHEV, USERFNC:
+	        return (CV_ORDER(cv))
+	    case SPLINE1, SPLINE3:
+		return (CV_NPIECES(cv) + 1)
+	    }
+	case CVNSAVE:
+	    if (CV_TYPE(cv) == USERFNC)
+	        return (CV_SAVECOEFF + CV_NCOEFF(cv))
+	    else
+		return (CV_SAVECOEFF + CV_NCOEFF(cv) - 1)
+	case CVNCOEFF:
+	    return (CV_NCOEFF(cv))
+	}
+end
+
+# CVSTATR -- Return real paramters from the curfit package
+
+double procedure dcvstatd (cv, param)
+
+pointer	cv			# Curfit pointer
+int	param			# Parameter
+
+begin
+	switch (param) {
+	case CVXMIN:
+	    return (CV_XMIN(cv))
+	case CVXMAX:
+	    return (CV_XMAX(cv))
+	}
+end
diff --git a/math/curfit/cvstatr.x b/math/curfit/cvstatr.x
new file mode 100644
index 00000000..ee5ef05b
--- /dev/null
+++ b/math/curfit/cvstatr.x
@@ -0,0 +1,49 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include	<math/curfit.h>
+
+include	"curfitdef.h"
+
+# CVSTATI -- Return integer paramters from the curfit package
+
+int procedure cvstati (cv, param)
+
+pointer	cv			# Curfit pointer
+int	param			# Parameter
+
+begin
+	switch (param) {
+	case CVTYPE:
+	    return (CV_TYPE(cv))
+	case CVORDER:
+	    switch (CV_TYPE(cv)) {
+	    case LEGENDRE, CHEBYSHEV, USERFNC:
+	        return (CV_ORDER(cv))
+	    case SPLINE1, SPLINE3:
+		return (CV_NPIECES(cv) + 1)
+	    }
+	case CVNSAVE:
+	    if (CV_TYPE(cv) == USERFNC)
+	        return (CV_SAVECOEFF + CV_NCOEFF(cv))
+	    else
+		return (CV_SAVECOEFF + CV_NCOEFF(cv) - 1)
+	case CVNCOEFF:
+	    return (CV_NCOEFF(cv))
+	}
+end
+
+# CVSTATR -- Return real paramters from the curfit package
+
+real procedure cvstatr (cv, param)
+
+pointer	cv			# Curfit pointer
+int	param			# Parameter
+
+begin
+	switch (param) {
+	case CVXMIN:
+	    return (CV_XMIN(cv))
+	case CVXMAX:
+	    return (CV_XMAX(cv))
+	}
+end
diff --git a/math/curfit/cvvector.gx b/math/curfit/cvvector.gx
new file mode 100644
index 00000000..eb005a1a
--- /dev/null
+++ b/math/curfit/cvvector.gx
@@ -0,0 +1,42 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVVECTOR -- Procedure to evaluate  a curve. The CV_NCOEFF(cv) coefficients
+# are assumed to be in COEFF.
+
+$if (datatype == r)
+procedure cvvector (cv, x, yfit, npts)
+$else
+procedure dcvvector (cv, x, yfit, npts)
+$endif
+
+pointer	cv		# curve descriptor
+PIXEL	x[npts]		# data x values
+PIXEL	yfit[npts]	# the fitted y values
+int	npts		# number of data points
+
+begin
+	switch (CV_TYPE(cv)) {
+	case LEGENDRE:
+	    call $tcv_evleg (COEFF(CV_COEFF(cv)), x, yfit, npts, CV_ORDER(cv), 
+		    CV_MAXMIN(cv), CV_RANGE(cv))
+	case CHEBYSHEV:
+	    call $tcv_evcheb (COEFF(CV_COEFF(cv)), x, yfit, npts, CV_ORDER(cv), 
+		    CV_MAXMIN(cv), CV_RANGE(cv))
+	case SPLINE3:
+	    call $tcv_evspline3 (COEFF(CV_COEFF(cv)), x, yfit, npts,
+	    			CV_NPIECES(cv), -CV_XMIN(cv), CV_SPACING(cv))
+	case SPLINE1:
+	    call $tcv_evspline1 (COEFF(CV_COEFF(cv)), x, yfit, npts,
+	    			CV_NPIECES(cv), -CV_XMIN(cv), CV_SPACING(cv))
+	case USERFNC:
+	    call $tcv_evuser (cv, x, yfit, npts)
+	}
+end
diff --git a/math/curfit/cvvectord.x b/math/curfit/cvvectord.x
new file mode 100644
index 00000000..f23e988e
--- /dev/null
+++ b/math/curfit/cvvectord.x
@@ -0,0 +1,34 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "dcurfitdef.h"
+
+# CVVECTOR -- Procedure to evaluate  a curve. The CV_NCOEFF(cv) coefficients
+# are assumed to be in COEFF.
+
+procedure dcvvector (cv, x, yfit, npts)
+
+pointer	cv		# curve descriptor
+double	x[npts]		# data x values
+double	yfit[npts]	# the fitted y values
+int	npts		# number of data points
+
+begin
+	switch (CV_TYPE(cv)) {
+	case LEGENDRE:
+	    call dcv_evleg (COEFF(CV_COEFF(cv)), x, yfit, npts, CV_ORDER(cv), 
+		    CV_MAXMIN(cv), CV_RANGE(cv))
+	case CHEBYSHEV:
+	    call dcv_evcheb (COEFF(CV_COEFF(cv)), x, yfit, npts, CV_ORDER(cv), 
+		    CV_MAXMIN(cv), CV_RANGE(cv))
+	case SPLINE3:
+	    call dcv_evspline3 (COEFF(CV_COEFF(cv)), x, yfit, npts,
+	    			CV_NPIECES(cv), -CV_XMIN(cv), CV_SPACING(cv))
+	case SPLINE1:
+	    call dcv_evspline1 (COEFF(CV_COEFF(cv)), x, yfit, npts,
+	    			CV_NPIECES(cv), -CV_XMIN(cv), CV_SPACING(cv))
+	case USERFNC:
+	    call dcv_evuser (cv, x, yfit, npts)
+	}
+end
diff --git a/math/curfit/cvvectorr.x b/math/curfit/cvvectorr.x
new file mode 100644
index 00000000..b344ab84
--- /dev/null
+++ b/math/curfit/cvvectorr.x
@@ -0,0 +1,34 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/curfit.h>
+
+include "curfitdef.h"
+
+# CVVECTOR -- Procedure to evaluate  a curve. The CV_NCOEFF(cv) coefficients
+# are assumed to be in COEFF.
+
+procedure cvvector (cv, x, yfit, npts)
+
+pointer	cv		# curve descriptor
+real	x[npts]		# data x values
+real	yfit[npts]	# the fitted y values
+int	npts		# number of data points
+
+begin
+	switch (CV_TYPE(cv)) {
+	case LEGENDRE:
+	    call rcv_evleg (COEFF(CV_COEFF(cv)), x, yfit, npts, CV_ORDER(cv), 
+		    CV_MAXMIN(cv), CV_RANGE(cv))
+	case CHEBYSHEV:
+	    call rcv_evcheb (COEFF(CV_COEFF(cv)), x, yfit, npts, CV_ORDER(cv), 
+		    CV_MAXMIN(cv), CV_RANGE(cv))
+	case SPLINE3:
+	    call rcv_evspline3 (COEFF(CV_COEFF(cv)), x, yfit, npts,
+	    			CV_NPIECES(cv), -CV_XMIN(cv), CV_SPACING(cv))
+	case SPLINE1:
+	    call rcv_evspline1 (COEFF(CV_COEFF(cv)), x, yfit, npts,
+	    			CV_NPIECES(cv), -CV_XMIN(cv), CV_SPACING(cv))
+	case USERFNC:
+	    call rcv_evuser (cv, x, yfit, npts)
+	}
+end
diff --git a/math/curfit/cvzero.gx b/math/curfit/cvzero.gx
new file mode 100644
index 00000000..c6774758
--- /dev/null
+++ b/math/curfit/cvzero.gx
@@ -0,0 +1,47 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+$if (datatype == r)
+include "curfitdef.h"
+$else
+include "dcurfitdef.h"
+$endif
+
+# CVZERO -- Procedure to zero the accumulators before doing
+# a new fit in accumulate mode. The inner products of the basis functions
+# are accumulated in the CV_ORDER(cv) by CV_NCOEFF(cv) array MATRIX, while
+# the inner products of the basis functions and the data ordinates are
+# accumulated in the CV_NCOEFF(cv)-vector VECTOR.
+
+$if (datatype == r)
+procedure cvzero (cv)
+$else
+procedure dcvzero (cv)
+$endif
+
+pointer	cv	# pointer to curve descriptor
+
+errchk	mfree
+
+begin
+	# zero the accumulators
+	CV_NPTS(cv) = 0
+	call aclr$t (MATRIX(CV_MATRIX(cv)), CV_ORDER(cv)*CV_NCOEFF(cv))
+	call aclr$t (VECTOR(CV_VECTOR(cv)), CV_NCOEFF(cv))
+
+	# free the basis functions defined from previous calls to cvrefit
+	if (CV_BASIS(cv) != NULL) {
+	    $if (datatype == r)
+	    call mfree (CV_BASIS(cv), TY_REAL)
+	    call mfree (CV_WY(cv), TY_REAL)
+	    $else
+	    call mfree (CV_BASIS(cv), TY_DOUBLE)
+	    call mfree (CV_WY(cv), TY_DOUBLE)
+	    $endif
+	    CV_BASIS(cv) = NULL
+	    CV_WY(cv) = NULL
+	    if (CV_LEFT(cv) != NULL) {
+		call mfree (CV_LEFT(cv), TY_INT)
+		CV_LEFT(cv) = NULL
+	    }
+	}
+end
diff --git a/math/curfit/cvzerod.x b/math/curfit/cvzerod.x
new file mode 100644
index 00000000..f9395fc1
--- /dev/null
+++ b/math/curfit/cvzerod.x
@@ -0,0 +1,34 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "dcurfitdef.h"
+
+# CVZERO -- Procedure to zero the accumulators before doing
+# a new fit in accumulate mode. The inner products of the basis functions
+# are accumulated in the CV_ORDER(cv) by CV_NCOEFF(cv) array MATRIX, while
+# the inner products of the basis functions and the data ordinates are
+# accumulated in the CV_NCOEFF(cv)-vector VECTOR.
+
+procedure dcvzero (cv)
+
+pointer	cv	# pointer to curve descriptor
+
+errchk	mfree
+
+begin
+	# zero the accumulators
+	CV_NPTS(cv) = 0
+	call aclrd (MATRIX(CV_MATRIX(cv)), CV_ORDER(cv)*CV_NCOEFF(cv))
+	call aclrd (VECTOR(CV_VECTOR(cv)), CV_NCOEFF(cv))
+
+	# free the basis functions defined from previous calls to cvrefit
+	if (CV_BASIS(cv) != NULL) {
+	    call mfree (CV_BASIS(cv), TY_DOUBLE)
+	    call mfree (CV_WY(cv), TY_DOUBLE)
+	    CV_BASIS(cv) = NULL
+	    CV_WY(cv) = NULL
+	    if (CV_LEFT(cv) != NULL) {
+		call mfree (CV_LEFT(cv), TY_INT)
+		CV_LEFT(cv) = NULL
+	    }
+	}
+end
diff --git a/math/curfit/cvzeror.x b/math/curfit/cvzeror.x
new file mode 100644
index 00000000..bd84029f
--- /dev/null
+++ b/math/curfit/cvzeror.x
@@ -0,0 +1,34 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "curfitdef.h"
+
+# CVZERO -- Procedure to zero the accumulators before doing
+# a new fit in accumulate mode. The inner products of the basis functions
+# are accumulated in the CV_ORDER(cv) by CV_NCOEFF(cv) array MATRIX, while
+# the inner products of the basis functions and the data ordinates are
+# accumulated in the CV_NCOEFF(cv)-vector VECTOR.
+
+procedure cvzero (cv)
+
+pointer	cv	# pointer to curve descriptor
+
+errchk	mfree
+
+begin
+	# zero the accumulators
+	CV_NPTS(cv) = 0
+	call aclrr (MATRIX(CV_MATRIX(cv)), CV_ORDER(cv)*CV_NCOEFF(cv))
+	call aclrr (VECTOR(CV_VECTOR(cv)), CV_NCOEFF(cv))
+
+	# free the basis functions defined from previous calls to cvrefit
+	if (CV_BASIS(cv) != NULL) {
+	    call mfree (CV_BASIS(cv), TY_REAL)
+	    call mfree (CV_WY(cv), TY_REAL)
+	    CV_BASIS(cv) = NULL
+	    CV_WY(cv) = NULL
+	    if (CV_LEFT(cv) != NULL) {
+		call mfree (CV_LEFT(cv), TY_INT)
+		CV_LEFT(cv) = NULL
+	    }
+	}
+end
diff --git a/math/curfit/dcurfitdef.h b/math/curfit/dcurfitdef.h
new file mode 100644
index 00000000..ab611450
--- /dev/null
+++ b/math/curfit/dcurfitdef.h
@@ -0,0 +1,54 @@
+# Header file for the curve fitting package
+
+# set up the curve descriptor structure
+
+define	LEN_CVSTRUCT	30
+
+define	CV_XMAX		Memd[P2D($1)]	# Maximum x value
+define	CV_XMIN		Memd[P2D($1+2)]	# Minimum x value
+define	CV_RANGE	Memd[P2D($1+4)]	# 2. / (xmax - xmin), polynomials
+define	CV_MAXMIN	Memd[P2D($1+6)]	# - (xmax + xmin) / 2., polynomials
+define	CV_SPACING	Memd[P2D($1+8)]	# order / (xmax - xmin), splines
+define	CV_USERFNCD	Memd[P2D($1+10)]# Real version of above for cvrestore.
+define	CV_TYPE		Memi[$1+12]	# Type of curve to be fitted
+define	CV_ORDER	Memi[$1+13]	# Order of the fit
+define	CV_NPIECES	Memi[$1+14]	# Number of polynomial pieces - 1
+define	CV_NCOEFF	Memi[$1+15]	# Number of coefficients
+define	CV_NPTS		Memi[$1+16]	# Number of data points
+
+define	CV_XBASIS	Memi[$1+17]	# Pointer to non zero basis for single x
+define	CV_MATRIX	Memi[$1+18]	# Pointer to original matrix
+define	CV_CHOFAC	Memi[$1+19]	# Pointer to Cholesky factorization
+define	CV_VECTOR	Memi[$1+20]	# Pointer to  vector
+define	CV_COEFF	Memi[$1+21]	# Pointer to coefficient vector
+define	CV_BASIS	Memi[$1+22]	# Pointer to basis functions (all x)
+define	CV_LEFT		Memi[$1+23]	# Pointer to first non-zero basis
+define	CV_WY		Memi[$1+24]	# Pointer to y * w (cvrefit)
+define	CV_USERFNC	Memi[$1+25]	# Pointer to external user subroutine
+					# one free slot left
+
+# matrix and vector element definitions
+
+define	XBASIS		Memd[$1]	# Non zero basis for single x
+define	MATRIX		Memd[$1]	# Element of MATRIX
+define	CHOFAC		Memd[$1]	# Element of CHOFAC
+define	VECTOR		Memd[$1]	# Element of VECTOR
+define	COEFF		Memd[$1]	# Element of COEFF
+define	BASIS		Memd[$1]	# Element of BASIS
+define	LEFT		Memi[$1]	# Element of LEFT
+
+# structure definitions for restore
+
+define	CV_SAVETYPE	$1[1]
+define	CV_SAVEORDER	$1[2]
+define	CV_SAVEXMIN	$1[3]
+define	CV_SAVEXMAX	$1[4]
+define	CV_SAVEFNC	$1[5]
+
+define	CV_SAVECOEFF	5
+
+# miscellaneous
+
+define	SPLINE3_ORDER	4
+define	SPLINE1_ORDER	2
+define	DELTA		EPSILON
diff --git a/math/curfit/doc/curfit.hd b/math/curfit/doc/curfit.hd
new file mode 100644
index 00000000..b8a00640
--- /dev/null
+++ b/math/curfit/doc/curfit.hd
@@ -0,0 +1,24 @@
+# Help directory for the CURFIT (curve fitting) package.
+
+$curfit	= "math$curfit/"
+
+cvaccum		hlp = cvaccum.hlp,	src = curfit$cvaccum.gx
+cvacpts		hlp = cvacpts.hlp,	src = curfit$cvacpts.gx
+cvcoeff		hlp = cvcoeff.hlp,	src = curfit$cvcoeff.gx
+cvepower	hlp = cvepower.hlp,	src = curfit$cvepower.gx
+cverrors	hlp = cverrors.hlp,	src = curfit$cverrors.gx
+cveval		hlp = cveval.hlp,	src = curfit$cveval.gx
+cvinit		hlp = cvinit.hlp,	src = curfit$cvinit.gx
+cvfit		hlp = cvfit.hlp,	src = curfit$cvfit.gx
+cvfree		hlp = cvfree.hlp,	src = curfit$cvfree.gx
+cvpower		hlp = cvpower.hlp,	src = curfit$cvpower.gx
+cvrefit		hlp = cvrefit.hlp,	src = curfit$cvrefit.gx
+cvreject	hlp = cvreject.hlp,	src = curfit$cvreject.gx
+cvrestore	hlp = cvrestore.hlp,	src = curfit$cvrestore.gx
+cvsave		hlp = cvsave.hlp,	src = curfit$cvsave.gx
+cvsolve		hlp = cvsolve.hlp,	src = curfit$cvsolve.gx
+cvstati		hlp = cvstati.hlp,	src = curfit$cvstat.gx
+cvstatr		hlp = cvstatr.hlp,	src = curfit$cvstat.gx
+cvvector	hlp = cvvector.hlp,	src = curfit$cvvector.gx
+cvzero		hlp = cvzero.hlp,	src = curfit$cvzero.gx
+cvset		hlp = cvset.hlp,	src = curfit$cvset.gx
diff --git a/math/curfit/doc/curfit.hlp b/math/curfit/doc/curfit.hlp
new file mode 100644
index 00000000..35950c08
--- /dev/null
+++ b/math/curfit/doc/curfit.hlp
@@ -0,0 +1,163 @@
+.help curfit Jul84 "Math Package"
+.ih
+NAME
+curfit -- curve fitting package
+.ih
+SYNOPSIS
+
+.nf
+        cvinit	(cv, curve_type, order, xmin, xmax)
+	cvzero	(cv)
+       cvaccum	(cv, x, y, weight, wtflag)
+      cvreject	(cv, x, y, weight)
+       cvsolve	(cv, ier)
+	 cvfit	(cv, x, y, weight, npts, wtflag, ier)
+       cvrefit	(cv, x, y, weight, ier)
+    y = cveval	(cv, x)
+      cvvector	(cv, x, yfit, npts)
+       cvcoeff	(cv, coeff, ncoeff)
+      cverrors	(cv, y, weight, yfit, rms, errors)
+	cvsave	(cv, fit)
+       cvstati  (cv, parameter, ival)
+       cvstatr  (cv, parameter, ival)
+     cvrestore	(cv, fit)
+         cvset	(cv, curve_type, xmin, xmax, coeff, ncoeff)
+        cvfree	(cv)
+.fi
+.ih
+DESCRIPTION
+The curfit package provides a set of routines for fitting data to functions
+linear in their coefficients using least squares techniques. The numerical
+technique employed is the solution of the normal equations by the
+Cholesky method.
+.ih
+NOTES
+The fitting function curve_type is chosen at run time from the following
+list.
+
+.nf
+    LEGENDRE	# Legendre polynomials
+    CHEBYSHEV	# Chebyshev polynomials
+    SPLINE3	# cubic spline with uniformly spaced break points
+    SPLINE1	# linear spline with uniformly spaced break points
+.fi
+
+
+The CURFIT package performs a weighted fit.
+The weighting options are WTS_USR, WTS_UNIFORM and WTS_SPACING.
+The user must supply a weight array. In WTS_UNIFORM mode the curfit
+routines set the weights to 1. In WTS_USER mode the user must supply an
+array of weight values.
+In WTS_SPACING mode
+the weights are set to the difference between adjacent data points.
+The data must be sorted in x in order to use the WTS_SPACING mode.
+In WTS_UNIFORM mode the reduced chi-squared returned by CVERRORS 
+is the variance of the fit and the errors in the coefficients are scaled
+by the square root of this variance. Otherwise the weights are
+interpreted as one over the variance of the data and the true reduced
+chi-squared is returned.
+
+The routines assume that all the x values  of interest lie in the region
+xmin <= x <= xmax. Checking for out of bounds x values is the responsibility
+of the calling program. The package routines assume that INDEF values
+have been removed from the data set prior to entering the package
+routines.
+
+In order to make the package definitions available to the calling program
+an include <curfit.h> statement must be included in the user program.
+CVINIT must be called before each fit. CVFREE frees space used by the
+CURFIT package.
+.ih
+EXAMPLES
+.nf
+Example 1: Fit curve to data, unifrom weighting
+
+    include <math/curfit.h>
+
+    ...
+
+    call cvinit (cv, CHEBYSHEV, 4, 1., 512.)
+
+    call cvfit (cv, x, y, weight, 512, WTS_UNIFORM, ier)
+    if (ier != OK)
+	call error (...)
+
+    do i = 1, 512 {
+	x = i
+	call printf ("%g %g\n")
+	    call pargr (x)
+	    call pargr (cveval (cv, x))
+    }
+
+    call cvfree (cv)
+
+
+Example 2: Fit curve using accumulate mode, weight based on spacing
+
+    include <math/curfit.h>
+
+    ...
+
+    old_x = x
+    do i = 1, 512 {
+	x = real (i)
+	if (y[i] != INDEF) {
+	    call cvaccum (cv, x, y, weight, x - old_x, WTS_USER)
+	    old_x = x
+	}
+    }
+
+    call cvsolve (cv, ier)
+    if (ier != OK)
+	call error (...)
+
+    ...
+
+    call cvfree (cv)
+
+
+Example 3: Fit and subtract smooth curve from image lines
+
+    include <math/curfit.h>
+
+    ...
+
+    call cvinit (cv, CHEBYSHEV, order, 1., 512.)
+
+    do line = 1, nlines {
+	inpix = imgl2r (im, line)
+	outpix = impl2r (im, line)
+	if (line == 1)
+	    call cvfit (cv, x, Memr[inpix], weight, 512, WTS_UNIFORM, ier)
+	else
+	    call cvrefit (cv, x, Memr[inpix], weight, ier)
+	if (ier != OK)
+	    ...
+	call cvvector (cv, x, y, 512)
+	call asubr (Memr[inpix], y, Memr[outpix], 512)
+    }
+
+    call cvfree (cv)
+
+
+Example 4: Fit curve, save fit for later use by CVEVAL. LEN_FIT must be a least
+	   order + 7 elements long.
+
+    include <math/curfit.h>
+
+    real  fit[LEN_FIT]
+
+    ...
+    call cvinit (cv, CHEBYSHEV, order, xmin, xmax)
+    call cvfit (cv, x, y, w, npts, WTS_UNIFORM, ier)
+    if (ier != OK)
+	...
+    call cvsave (cv, fit)
+    call cvfree (cv)
+    ...
+    call cvrestore (cv, fit)
+    do i = 1, npts
+	yfit[i] = cveval (cv, x[i])
+    call cvfree (cv)
+    ...
+.fi
diff --git a/math/curfit/doc/curfit.men b/math/curfit/doc/curfit.men
new file mode 100644
index 00000000..b061badc
--- /dev/null
+++ b/math/curfit/doc/curfit.men
@@ -0,0 +1,20 @@
+	cvaccum	- Accumulate point into data set
+	cvacpts - Accumulate points into a data set
+	cvcoeff - Get coefficients 
+       cvepower - Convert errors to power series equivalents
+       cverrors	- Calculate chi-squared and errors in coefficients
+	 cveval	- Evaluate curve at x
+	  cvfit	- Fit curve
+	 cvfree - Free space allocated by cvinit
+	 cvinit - Make ready to fit a curve; set up parameters of fit
+	cvpower - Convert coefficients to power series coefficients
+	cvrefit	- Refit curve, same x and weight, different y
+       cvreject	- Reject point from data set
+      cvrestore - Restore curve parameters and coefficients
+	 cvsave - Save curve parameters and coefficients
+	  cvset - Input coefficients derived external to the CURFIT package
+	cvsolve	- Solve matrix for coefficients
+	cvstati - Get integer parameter
+	cvstatr - Get real parameter
+       cvvector - Evaluate curve at an array of x
+	 cvzero - Zero arrays for new fit
diff --git a/math/curfit/doc/curfit.spc b/math/curfit/doc/curfit.spc
new file mode 100644
index 00000000..f5e555a3
--- /dev/null
+++ b/math/curfit/doc/curfit.spc
@@ -0,0 +1,479 @@
+.help curfit May84 "Math Package"
+.ce
+Specifications for the Curfit Package
+.ce
+Lindsey Davis
+.ce
+July 1984
+
+.sh
+1. Introduction
+
+The CURFIT package provides a set of routines for fitting data to
+functions linear in their coefficients using least
+squares techniques. The basic numerical technique employed
+is the solution of the normal equations by the Cholesky method.
+This document presents the formal requirements for the package
+and describes the algorithms used.
+
+.sh
+2. Requirements
+
+.ls 4
+.ls (1)
+The package shall take as input a set of x and y values and their
+corresponding weights. The package routines asssume that data values
+equal to INDEF have been rejected from the data set or replaced with
+appropriate interpolated values prior to entering the package
+routines. The input data may be arbitrarily spaced in x. No assumptions
+are made about the ordering of the x values, but see (3) below. 
+.le
+.ls (2)
+The package shall perform the following operations:
+.ls o
+Determine the coefficients of the fitting function by solving the normal
+equations. The fitting function is selected at run time from the following
+list: (1) LEGENDRE, Legendre polynomials, (2) CHEBYSHEV,
+Chebyshev polynomials, (3) SPLINE3, Cubic spline
+with uniformly spaced break points, SPLINE1, Linear spline with evenly
+spaced break points.  The calling sequence must be
+invariant to the form of the fitting function.
+.le
+.ls o
+Set an error code if the numerical routines are unable to fit the
+specified function.
+.le
+.ls o
+Output the values of the coefficients.
+The coefficients are stored internal to the CURFIT package.
+However in some applications it is the coefficients which are of primary
+interest. A package routine shall exist to extract the
+the coefficients from the curve descriptor structure.
+.le
+.ls o
+Evaluate the fitting function at arbitrary value(s) of x.  The evaluating
+routines shall use the coefficients calculated and
+the user supplied x value(s).
+.le
+.ls o
+Calculate the standard deviation of the coefficients and the standard deviation
+of the fit.
+.le
+.le
+.ls (3)
+The program shall perform a weighted fit using a user supplied weight
+array and weight flag. The weighting options are WTS_USER, WTS_UNIFORM and
+WTS_SPACING. In WTS_USER  mode the package routines apply user supplied
+weights to the individual data points, otherwise the package routines
+calculate the weights. In WTS_SPACING mode the program assumes that the data
+are sorted in x, and sets the individual weights to the difference between
+adjacent x values. In WTS_UNIFORM mode the weights are set to 1.
+.le
+.ls (4)
+The input data set and output coefficent, error, and fitted y arrays are single
+precision real quantities. All package arithmetic shall be done in single
+precision. The package shall however be designed with
+conversion to double precision arithmetic in mind.
+.le
+.le
+
+.sh
+3. Specifications
+
+.sh
+3.1. List of Routines
+
+The package prefix will be cv for curve fit.
+The following procedures shall be part of the package.
+Detailed documentation for each procedure can be found by invoking
+the help facility.
+
+.nf
+        cvinit	(cv, curvetype, order, xmin, xmax)
+	cvzero	(cv)
+       cvaccum	(cv, x, y, w, wtflag)
+      cvreject	(cv, x, y, w)
+       cvsolve	(cv, ier)
+	 cvfit	(cv, x, y, w, npts, wtflag, ier)
+       cvrefit	(cv, x, y, w, ier)
+    y = cveval	(cv, x)
+      cvvector	(cv, x, yfit, npts)
+       cvcoeff	(cv, coeff, ncoeff)
+      cverrors	(cv, y, w, yfit, rms, errors)
+        cvsave	(cv, fit)
+     cvrestore	(cv, fit)
+	 cvset	(cv, curve_type, xmin, xmax, coeff, ncoeff)
+        cvfree	(cv)
+.fi
+
+.sh
+3.2. Algorithms
+
+.sh
+3.2.1. Polynomial Basis Functions
+
+The approximating function is assumed to be of the form
+
+.nf
+    f(x) = a(1)*F(1,x) + a(2)*F(2,x) + ... + a(ncoeff)*F(ncoeff,x)
+.fi
+
+where the F(n,x) are polynomial basis functions containing terms
+of order x**(n-1), and the a(n) are the coefficients.
+In order to avoid a very ill-conditioned linear system for moderate or large n
+the Legendre and Chebyshev polynomials  were chosen for the basis functions.
+The Chebyshev and Legendre polynomials are
+orthogonal over -1. <= x <= 1. The data x values are normalized to
+this regime using minimum and maximum x values supplied by the user.
+For each data point the ncoeff basis functions are calculated using the
+following recursion relations.
+
+.nf
+    Legendre series
+    F(1,x) = 1.
+    F(2,x) = x
+    F(n,x) = [(2*n-3)*x*F(n-1,x)-(n-2)*F(n-2,x)]/(n-1)
+
+    Chebyshev series
+    F(1,x) = 1.
+    F(2,x) = x
+    F(n,x) = 2*x*F(n-1,x)-F(n-2,x)
+.fi
+
+.sh
+3.2.2. Cubic Cardinal B-Spline
+
+The approximating function is assumed to be of the form
+
+.nf
+    f(x) = a(1)*F(1,x) + a(2)*F(2,x) + ... a(ncoeff)*F(ncoeff,x)
+.fi
+
+where the basis functions, F(n, x), are the cubic cardinal B-splines
+(Prenter 1975).
+The user supplies minimum and maximum x values and the number of polynomial
+pieces, npieces, to be fit to the data set. The number of cubic spline
+coefficents, ncoeff, will be
+
+.nf
+    ncoeff = npieces + 3
+.fi
+
+The cardinal B-spline is stored in a lookup table. For each x the appropriate
+break point is selected and the four non-zero B-splines are calculated by
+nearest neighbour interpolation in the lookup table.
+
+.sh
+3.2.3. The Normal Equations
+
+The coefficients, a, are determined by the solution of the normal equations
+
+.nf
+    c * a = b
+.fi
+
+where
+
+.nf
+    c[i,j] = (F(i,x), F(j,x))
+    b[j] = (F(j,x), f(x))
+.fi
+
+F(i,x) is the ith basis function at x, f(x) is the function to be
+approximated and the inner product of two functions G and H, (G,H),
+is given by
+
+.nf
+    (G, H) = sum (G(x[i]) * H(x[i]) * weight[i]) i=1,...npts
+.fi
+
+The resulting matrix is symmetric and positive semi-definite.
+Therefore it is necessary to store the ncoeff bands at or below the
+diagonal. Storage is particularly efficient for the cubic spline
+as only the diagonal and three adjacent lower bands are non-zero
+(deBoor 1978).
+
+.sh
+3.2.4. Method of Solution
+
+Since the matrix is symmetric, positive semi-definite and banded
+it may be solved by the Cholesky method. The data matrix c may be
+written as
+
+.nf
+    c = l * d * l-transpose
+.fi
+
+where l is a unit lower triangular matrix and d is the diagonal of c
+(deBoor 1978). Near zero pivots are handled in the following way.
+At the nth elimination step the current value of the nth diagonal
+element is compared with the original nth diagonal element. If the diagonal
+element has been reduced by one computer word length, the entire nth
+row is declared linearly dependent on the previous n-1 rows and
+a(n) = 0.
+
+The triangular system
+
+.nf
+    l * w = b
+.fi
+
+is solved for w (forward substitution), the vector d ** (-1) * w
+is computed and the triangular system
+
+.nf
+    l-transpose * a = d ** (-1) * w
+.fi
+
+solved for the coefficients, a (backward substitution).
+
+.sh
+3.2.5. Errors
+
+The reduced ch-squared of the fit is defined as the weighted sum of
+the squares of the residuals divided by the number of degrees of
+freedom.
+
+.nf
+    rms = sqrt (sum (weight * (y - yfit) ** 2) / nfree)
+    nfree = npts - ncoeff
+.fi
+
+The error of the j-th coefficient, error[j], is equal to the square root
+of the j-th diagonal element of inverse data matrix times a scale factor.
+
+.nf
+    error[j] = sqrt (c[j,j]-inverse) * scale
+.fi
+
+The scale factor is the square root of the variance of the data when
+all the weights are equal, otherwise scale is one.
+
+.sh
+4. Usage
+
+.sh
+4.1. User Notes
+
+The following series of steps illustrates the use of the package.
+
+.ls 4
+.ls (1)
+Insert an include <curfit.h> statement in the calling program to
+make the CURFIT package definitions available to the user program.
+.le
+.ls (2)
+Call CVINIT to initialize the curve fitting parameters.
+.le
+.ls (3)
+Call CVACCUM to select a weighting function
+and accumulate data points into the appropriate arrays and vectors.
+.le
+.ls (4)
+Call CVSOLVE to solve the normal equations and calculate the coefficients
+of the fitting function. Test for an error condition.
+.le
+.ls (5)
+Call CVEVAL or CVVECTOR to evaluated the fitted function at the
+x value(s) of interest.
+.le
+.ls (6)
+Call CVCOEFF to fetch the number and value of the coefficients of the fitting
+function.
+.le
+.ls (7)
+Call CVERRORS to calculate the standard deviations in the
+coefficients and the standard deviation of the fit.
+.le
+.ls (8)
+Call CVFREE to release the space allocated for the fit.
+.le
+.le
+
+Steps (2) and (3) may be combined in a single step by calling CVFIT
+and inputting an array of x, y and weight values. Individual points may
+be rejected from the fit by calling CVREJECT and CVSOLVE to determine
+a new set of coefficients. If the x and weight values remain the same
+and only the y values change from fit to fit, CVREFIT can be called.
+
+
+.sh
+4.2. Examples
+
+.nf
+Example 1: Fit curve to data, no weighting
+
+	include <curfit.h>
+	...
+	call cvinit (cv, CHEBYSHEV, 4, 1., 512.)
+
+	call cvfit (cv, x, y, w, 512, WTS_UNIFORM, ier)
+	if (ier != OK)
+	    call error (...)
+
+	do i = 1, 512 {
+	    x = i
+	    call printf ("%g %g\n")
+	        call pargr (x)
+	        call pargr (cveval (cv, x))
+	}
+
+	call cvfree (cv)
+
+Example 2: Fit curve using accumulate mode, weight based on spacing
+
+	include <curfit.h>
+	...
+	call cvinit (cv, SPLINE3, npolypieces, 1., 512.)
+
+	old_x = 0.0
+	do i =1, 512 {
+	    x = real (i)
+	    if (y[i] != INDEF) {
+		call cvaccum (cv, x, y, x - old_x, WTS_USER)
+		old_x = x
+	    }
+	}
+
+	call cvsolve (cv, ier)
+	if (ier != OK)
+	    call error (...)
+	...
+	call cvfree (cv)
+
+Example 3: Fit and subtract smooth curve from image lines
+
+	include <curfit.h>
+	...
+	call cvinit (cv, CHEBYSHEV, order, 1., 512.)
+
+	do line = 1, nlines {
+	    inpix = imgl2r (im, line)
+	    outpix = impl2r (im, line)
+	    if (line == 1)
+		call cvfit (cv, x, Memr[inpix], w, 512, WTS_USER, ier)
+	    else
+		call cvrefit (cv, x, Memr[inpix], w, WTS_USER, ier)
+	    if (ier != OK)
+		...
+	    call cvvector (cv, x, y, 512)
+	    call asubr (Memr[inpix], y, Memr[outpix], 512)
+	}
+
+	call cvfree (cv)
+
+Example 4: Fit curve and save parameters for later use by CVEVAL
+	   Fit must be at least order + 7 elements long.
+
+	include <curfit.h>
+
+	real  fit[LEN_FIT)
+	...
+	call cvinit (cv, LEGENDRE, order, xmin, xmax)
+	call cvfit (cv, x, y, w, npts, WTS_UNIFORM, ier)
+	if (ier != OK) 
+	    ...
+	call cvsave (cv, fit)
+	call cvfree (cv)
+	...
+	call cvrestore (cv, fit)
+	do i = 1, npts
+	    yfit[i] = cveval (cv, x[i])
+	call cvfree (cv)
+	...
+
+.fi
+
+.sh
+5. Detailed Design
+
+.sh
+5.1. Curve Descriptor Structure
+
+The CURFIT parameters, and the
+size and location of the arrays and vectors used in the fitting procedure
+are stored in the curve descriptor structure. The structure is referenced
+by the pointer cv returned by the CVINIT routine.  The curve
+descriptor structure is defined in the package
+header file curfit.h. The structure is listed below.
+
+.nf
+define	LEN_CVSTRUCT	17
+
+# CURFIT parameters
+
+define	CV_TYPE		Memi[$1]	# Type of curve to be fitted
+define	CV_ORDER	Memi[$1+1]	# Order of the fit
+define	CV_NPIECES	Memi[$1+2]	# Number of polynomial pieces (spline)
+define	CV_NCOEFF	Memi[$1+3]	# Number of coefficients
+define	CV_XMAX		Memr[$1+4]	# Maximum x value
+define	CV_XMIN		Memr[$1+5]	# Minimum x value
+define	CV_RANGE	Memr[$1+6]	# Xmax minus xmin
+define	CV_MAXMIN	Memr[$1+7]	# Xmax plus xmin
+define	CV_SPACING	Memr[$1+8]	# Break point spacing (spline)
+define	CV_NPTS		Memi[$1+9]	# Number of data points
+
+# Pointers to storage arrays and vectors
+
+define	CV_XBASIS	Memi[$1+10]	# Basis functions single x
+define	CV_MATRIX	Memi[$1+11]	# Pointer to matrix
+define	CV_CHOFAC	Memi[$1+12]	# Pointer to Cholesky factorization
+define	CV_VECTOR	Memi[$1+13]	# Pointer to vector
+define	CV_COEFF	Memi[$1+14]	# Pointer to coefficient vector
+
+# Used only by CVREFIT
+
+define	CV_BASIS	Memi[$1+15]	# Pointer to basis functions all x
+define	CV_LEFT		Memi[$1+16]	# Pointer to index array (spline)
+.fi
+
+.sh
+5.2. Storage Requirements
+
+The storage requirements are listed below.
+
+.ls 4
+.ls real MATRIX[order,ncoeff]
+The real array, matrix, stores the original accumulated data. Storage of this
+array is required by the CURFIT routines CVACCUM and CVREJECT which accumulate
+and reject individual points from the data set respectively. If the fitting
+function is SPLINE3 then order = 4, otherwise order = ncoeff.
+.le
+.ls real CHOFAC[order, ncoeff]
+The real array chofac stores the Cholesky factorization of matrix.
+Storage of CHOFAC is required by the CURFIT routines CVERRORS and
+CVREFIT.
+.le
+.ls real VECTOR[ncoeff]
+Ncoeff real storage units must be allocated for the vector containing
+the right side of the matrix equation. VECTOR is stored for use by the
+CVREJECT and CVACCUM routines. Vector is zeroed before every CVREFIT call.
+.le
+.ls real COEFF[ncoeff]
+The coefficients of the fitted function must be stored for use by
+the CVEVAL, CVVECTOR, and CVCOEFF routines.
+.le
+.ls real BASIS[order,npts]
+Space is allocated for the basis functions only if the routine CVREFIT is
+called.  The first call to CVREFIT generates an array of basis functions and
+subsequent calls reference the array.
+.le
+.ls int	LEFT[npts]
+Space for the array left is allocated only if
+CVREFIT is called. The array indicates to which element of
+the matrix a given spline function should be accumulated.
+.le
+.le
+
+.sh
+6. References
+
+.ls (1)
+Carl de Boor, "A Practical Guide to Splines", 1978, Springer-Verlag New
+York Inc.
+.le
+.ls (2)
+P.M. Prenter, "Splines and Variational Methods", 1975, John Wiley and Sons
+Inc.
+.le
+.endhelp
diff --git a/math/curfit/doc/cvaccum.hlp b/math/curfit/doc/cvaccum.hlp
new file mode 100644
index 00000000..4fc3a37b
--- /dev/null
+++ b/math/curfit/doc/cvaccum.hlp
@@ -0,0 +1,51 @@
+.help cvaccum Jun84 "Curfit Package"
+.ih
+NAME
+cvaccum -- accumulate a single data point into the matrix
+.ih
+SYNOPSIS
+include <math/curfit.h>
+
+cvaccum (cv, x, y, weight, wtflag)
+
+.nf
+pointer	cv		# curve descriptor
+real	x		# x value
+real	y		# y value
+real	weight		# weight
+int	wtflag		# type of weighting
+.fi
+.ih
+ARGUMENTS
+.ls cv    
+Pointer to the curve descriptor structure.
+.le
+.ls x   
+X value. Checking for out of bounds x values is the responsibility of the
+user.
+.le
+.ls y    
+Y value.
+.le
+.ls weight   
+Weight assigned to the data point.
+.le
+.ls wtflag
+Type of weighting. The options are WTS_USER, WTS_UNIFORM or WTS_SPACING.
+If wtflag equals WTS_USER the weight for each point is supplied by the user.
+If wtflag is either WTS_UNIFORM or WTS_SPACING the routine sets weight
+to one.
+.le
+.ih
+DESCRIPTION
+Calculate the non-zero basis functions for the given value of x.
+Compute the contribution of the data point to the normal equations and
+sum into the appropriate arrays and vectors.
+.ih
+NOTES
+The WTS_SPACING option cannot be used with CVACCUM. Weights will be set
+to 1.
+.ih
+SEE ALSO
+cvfit, cvrefit
+.endhelp
diff --git a/math/curfit/doc/cvacpts.hlp b/math/curfit/doc/cvacpts.hlp
new file mode 100644
index 00000000..c5a6cffd
--- /dev/null
+++ b/math/curfit/doc/cvacpts.hlp
@@ -0,0 +1,54 @@
+.help cvacpts Jun84 "Curfit Package"
+.ih
+NAME
+include <math/curfit.h>
+
+cvacpts -- fit a curve to a set of data values
+.ih
+SYNOPSIS
+cvacpts (cv, x, y, weight, npts, wtflag)
+
+.nf
+pointer	cv		# curve descriptor
+real	x[]		# array of x values
+real	y[]		# array of y values
+real	weight[]	# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+.fi
+.ih
+ARGUMENTS
+.ls cv    
+Pointer to the curve descriptor structure.
+.le
+.ls x    
+Array of x values.
+.le
+.ls y
+Array of y values
+.le
+.ls weight
+Array of weights
+.le
+.ls wtflag
+Type of weighting. The options are WTS_USER, WTS_SPACING and
+WTS_UNIFORM. If wtflag = WTS_USER individual weights for each data point
+are supplied by the calling program and points with zero-valued weights are
+not included in the fit. If wtflag = WTS_UNIFORM, all weights are assigned
+values of 1. If wtflag = WTS_SPACING, the weights are set equal to the
+difference between adjacent data points. In order to correctly use the
+WTS_SPACING option the data must be sorted in x.
+.le
+.ih
+DESCRIPTION
+CVACPTS zeroes the matrix and vectors, calculates the non-zero basis functions,
+calculates the contribution
+of each data point to the normal equations and accumulates it into the
+appropriate array and vector elements.
+.ih
+NOTES
+Checking for out of bounds x values is the responsibility of the user.
+.ih
+SEE ALSO
+cvaccum
+.endhelp
diff --git a/math/curfit/doc/cvcoeff.hlp b/math/curfit/doc/cvcoeff.hlp
new file mode 100644
index 00000000..6467cd60
--- /dev/null
+++ b/math/curfit/doc/cvcoeff.hlp
@@ -0,0 +1,36 @@
+.help cvcoeff Jun84 "Curfit Package"
+.ih
+NAME
+cvcoeff -- get the number and values of the coefficients
+.ih
+SYNOPSIS
+cvcoeff (cv, coeff, ncoeff)
+
+.nf
+pointer	cv		# curve descriptor
+real	coeff[]		# the coefficient array
+int	ncoeff		# the number of coefficients
+.fi
+.ih
+ARGUMENTS
+.ls pointer
+Pointer to the curve descriptor.
+.le
+.ls coeff
+Array of coefficients.
+.le
+.ls ncoeff
+The number of coefficients.
+.le
+.ih
+DESCRIPTION
+CVCOEFF fetches the coefficient array and the number of coefficients from the
+curve descriptor structure.
+.ih
+NOTES
+The variable ncoeff is only equal to the order specified in CVINIT if the
+curve_type is LEGENDRE or CHEBYSHEV. If curve_type is SPLINE3 then
+ncoeff = order + 3. If curve_type is SPLINE1 then ncoeff = order + 1.
+.ih
+SEE ALSO
+.endhelp
diff --git a/math/curfit/doc/cvepower.hlp b/math/curfit/doc/cvepower.hlp
new file mode 100644
index 00000000..58e78dae
--- /dev/null
+++ b/math/curfit/doc/cvepower.hlp
@@ -0,0 +1,55 @@
+.help cvepower Jun95 "Curfit Package"
+.ih
+NAME
+cvepower -- compute the errors of the equivalent power series
+.ih
+SYNOPSIS
+cvepower (cv, y, weight, yfit, npts, chisqr, errors)
+
+.nf
+pointer	cv		# curve descriptor
+real	y[]		# array of y data points
+weight	weight[]	# array of weights
+real	yfit[]		# array of fitted data points
+int	npts		# number of points
+real	chisqr		# the standard deviation of the fit
+real	errors[]	# standard deviations of the power series coefficients
+.fi
+.ih
+ARGUMENTS
+.ls cv     
+Pointer to the curve descriptor structure
+.le
+.ls y   
+Array of y data points
+.le
+.ls yfit  
+Array of fitted y values
+.le
+.ls npts
+The number of points
+.le
+.ls chisqr
+Reduced chi-squared of the fit.
+.le
+.ls errors
+Array of standard deviations of the equivalent power series coefficients.
+.le
+.ih
+DESCRIPTION
+Calculate the reduced chi-squared of the fit and the standard deviation
+of the equivalent power series coefficients for fitted Legendre and
+Chebyshev polynomials. The errors are rescaled to the equivalent power 
+series and to the original data range.
+.ih
+NOTES
+The standard deviation of the fit is the square root of the sum of the
+weighted squares of the residuals divided by the number of degrees of freedom.
+If the weights are equal, then the reduced chi-squared is the
+variance of the fit
+The error of the j-th coefficient is the square root of the j-th diagonal
+element of the inverse of the data matrix. If the weights are equal to one,
+then the errors are scaled by the square root of the variance of the data.
+.ih
+SEE ALSO
+.endhelp
diff --git a/math/curfit/doc/cverrors.hlp b/math/curfit/doc/cverrors.hlp
new file mode 100644
index 00000000..a0a0fbb2
--- /dev/null
+++ b/math/curfit/doc/cverrors.hlp
@@ -0,0 +1,53 @@
+.help cverrors Jun84 "Curfit Package"
+.ih
+NAME
+cverrors -- calculate the standard deviation of the fit and errors
+.ih
+SYNOPSIS
+cverrors (cv, y, weight, yfit, npts, chisqr, errors)
+
+.nf
+pointer	cv		# curve descriptor
+real	y[]		# array of y data points
+weight	weight[]	# array of weights
+real	yfit[]		# array of fitted data points
+int	npts		# number of points
+real	chisqr		# the standard deviation of the fit
+real	errors[]	# standard deviations of the coefficients
+.fi
+.ih
+ARGUMENTS
+.ls cv     
+Pointer to the curve descriptor structure
+.le
+.ls y   
+Array of y data points
+.le
+.ls yfit  
+Array of fitted y values
+.le
+.ls npts
+The number of points
+.le
+.ls chisqr
+Reduced chi-squared of the fit.
+.le
+.ls errors
+Array of standard deviations of the coefficients.
+.le
+.ih
+DESCRIPTION
+Calculate the reduced chi-squared of the fit and the standard deviation
+of the coefficients.
+.ih
+NOTES
+The standard deviation of the fit is the square root of the sum of the
+weighted squares of the residuals divided by the number of degrees of freedom.
+If the weights are equal, then the reduced chi-squared is the
+variance of the fit
+The error of the j-th coefficient is the square root of the j-th diagonal
+element of the inverse of the data matrix. If the weights are equal to one,
+then the errors are scaled by the square root of the variance of the data.
+.ih
+SEE ALSO
+.endhelp
diff --git a/math/curfit/doc/cveval.hlp b/math/curfit/doc/cveval.hlp
new file mode 100644
index 00000000..48cd7f10
--- /dev/null
+++ b/math/curfit/doc/cveval.hlp
@@ -0,0 +1,33 @@
+.help cveval Jun84 "Curfit Package"
+.ih
+NAME
+cveval -- evaluate the fitted function at a single x value
+.ih
+SYNOPSIS
+y = cveval (cv, x)
+
+.nf
+pointer	cv	# curve descriptor
+real	x	# x value
+.fi
+.ih
+ARGUMENTS
+.ls cv    
+Pointer to the curve descriptor structure.
+.le
+.ls x   
+X value at which the curve is to be evaluated.
+.le
+.ih
+DESCRIPTION
+Evaluate the curve at the specified value of x. CVEVAL is a real
+function which returns the fitted y value.
+.ih
+NOTES
+It uses the coefficient array stored in the curve descriptor structure.
+The x values are assumed to lie in the region xmin <= x <= xmax. Checking
+for out of bounds x values is the responsibility of the user.
+.ih
+SEE ALSO
+cvvector
+.endhelp
diff --git a/math/curfit/doc/cvfit.hlp b/math/curfit/doc/cvfit.hlp
new file mode 100644
index 00000000..cb6beb24
--- /dev/null
+++ b/math/curfit/doc/cvfit.hlp
@@ -0,0 +1,62 @@
+.help cvfit Jun84 "Curfit Package"
+.ih
+NAME
+cvfit -- fit a curve to a set of data values
+.ih
+SYNOPSIS
+cvfit (cv, x, y, weight, npts, wtflag, ier)
+
+.nf
+pointer	cv		# curve descriptor
+real	x[]		# array of x values
+real	y[]		# array of y values
+real	weight[]	# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+int	ier		# error code
+.fi
+.ih
+ARGUMENTS
+.ls cv    
+Pointer to the curve descriptor structure.
+.le
+.ls x    
+Array of x values.
+.le
+.ls y
+Array of y values
+.le
+.ls weight
+Array of weights
+.le
+.ls wtflag
+Type of weighting. The options are WTS_USER, WTS_SPACING and
+WTS_UNIFORM. If wtflag = WTS_USER individual weights for each data point
+are supplied by the calling program and points with zero-valued weights are
+not included in the fit. If wtflag = WTS_UNIFORM, all weights are assigned
+values of 1. If wtflag = WTS_SPACING, the weights are set equal to the
+difference between adjacent data points. In order to correctly use the
+WTS_SPACING option the data must be sorted in x.
+.le
+.ls ier
+Error code for the fit. The options are OK, SINGULAR and
+NO_DEG_FREEDON. If ier = SINGULAR, the numerical routines will compute a
+solution but one or more of the coefficients will be
+zero. If ier = NO_DEG_FREEDOM, there were too few data points to solve the
+matrix equations and the routine returns without fitting the data.
+.le
+.ih
+DESCRIPTION
+CVFIT zeroes the matrix and vectors, calculates the non-zero basis functions,
+calculates the contribution
+of each data point to the normal equations and accumulates it into the
+appropriate array and vector elements. The Cholesky factorization of the
+data array is computed and the coefficients of the fitting function are
+calculated.
+.ih
+NOTES
+Checking for out of bounds x values is the responsibility of the user.
+.ih
+SEE ALSO
+cvrefit, cvaccum, cvsolve, cvchofac, cvcholsv
+.endhelp
diff --git a/math/curfit/doc/cvfree.hlp b/math/curfit/doc/cvfree.hlp
new file mode 100644
index 00000000..c486b306
--- /dev/null
+++ b/math/curfit/doc/cvfree.hlp
@@ -0,0 +1,26 @@
+.help cvfree Jun84 "Curfit Package"
+.ih
+NAME
+cvfree -- free the curve descriptor structure
+.ih
+SYNOPSIS
+cvfree (cv)
+
+.nf
+pointer	cv	# curve descriptor
+.fi
+.ih
+ARGUMENTS
+.ls cv     
+Pointer to the curve descriptor structure.
+.le
+.ih
+DESCRIPTION
+Frees the curve descriptor structure.
+.ih
+NOTES
+CVFREE should be called after each curve fit.
+.ih
+SEE ALSO
+cvinit
+.endhelp
diff --git a/math/curfit/doc/cvinit.hlp b/math/curfit/doc/cvinit.hlp
new file mode 100644
index 00000000..dc891ed2
--- /dev/null
+++ b/math/curfit/doc/cvinit.hlp
@@ -0,0 +1,55 @@
+.help cvinit Jun84 "Curfit Package"
+.ih
+NAME
+cvinit -- initialise curve descriptor
+.ih
+SYNOPSIS
+include <math/curfit.h>
+
+cvinit (cv, curve_type, order, xmin, xmax)
+
+.nf
+pointer		cv		# curve descriptor
+int		curve_type	# the fitting function
+int		order		# order of the fit
+real		xmin		# minimum x value
+real		xmax		# maximum x value
+.fi
+.ih
+ARGUMENTS
+.ls cv      
+Pointer to the curve descriptor structure.
+.le
+.ls curve_type
+Fitting function.
+Permitted values are LEGENDRE and CHEBYSHEV, for Legendre and
+Chebyshev polynomials and SPLINE3 and SPLINE1 for a cubic spline
+and linear spline with uniformly spaced
+break points.
+.le
+.ls order
+Order of the polynomial to be fit or the number of polynomial pieces
+to be fit by a cubic spline. Order must be greater than or equal to one.
+If curve_type is set to LEGENDRE or CHEBYSHEV and order equals one, a constant
+term is fit to the data.
+.le
+.ls xmax, xmin
+Minimum and maximum x values. All x values of interest
+including the data x values and the x values of any curve to be evaluated
+must fall in the range xmin <= x <= xmax. Checking for out of bounds x
+values is the responsibility of user.
+.le
+.ih
+DESCRIPTION
+Allocate space for the curve descriptor structure and the arrays and
+vectors used by the numerical routines. Initialize all arrays and vectors
+to zero. Return the
+curve descriptor to the calling routine.
+.ih
+NOTES
+CVINIT must be the first CURFIT routine called. CVINIT returns if an
+illegal curve type is requested.
+.ih
+SEE ALSO
+cvfree
+.endhelp
diff --git a/math/curfit/doc/cvpower.hlp b/math/curfit/doc/cvpower.hlp
new file mode 100644
index 00000000..386558ce
--- /dev/null
+++ b/math/curfit/doc/cvpower.hlp
@@ -0,0 +1,40 @@
+.help cvpower Jan86 "Curfit Package"
+.ih
+NAME
+cvpower -- convert coefficients to power series coefficients.
+.ih
+SYNOPSIS
+.nf
+include <math/curfit.h>
+include "curfitdef.h"
+
+cvpower (cv, ps_coeff, ncoeff)
+
+pointer	cv			# Curve descriptor
+real	ps_coeff[ncoeff]	# Power series coefficients
+int	ncoeff			# Number of coefficients in fit
+.fi
+.ih
+ARGUMENTS
+.ls cv      
+Pointer to the curve descriptor structure.
+.le
+.ls ps_coeff
+The output array of power series coefficients.
+.le
+.ls ncoeff
+The output number of coefficients in the fit.
+.le
+.ih
+DESCRIPTION
+This routine routines the equivlalent power series fit coefficients
+and the number of coefficients.
+
+The coefficients of either a legendre or chebyshev solution can be converted
+to power series coefficients of the form y = a0 + a1*x + a2*x**2 + a3*x**3...
+The output coefficients are scaled to the original data range.
+.ih
+NOTES
+Only legendre and chebyshev coefficients are converted. An error is
+reported for other curve types.
+.endhelp
diff --git a/math/curfit/doc/cvrefit.hlp b/math/curfit/doc/cvrefit.hlp
new file mode 100644
index 00000000..4612b4c6
--- /dev/null
+++ b/math/curfit/doc/cvrefit.hlp
@@ -0,0 +1,52 @@
+.help cvrefit Jun84 "Curfit Package"
+.ih
+NAME
+cvrefit -- refit new y vector using old x vector and weights
+.ih
+SYNOPSIS
+cvrefit (cv, x, y, w, ier)
+
+.nf
+pointer	cv		# curve descriptor
+real	x[]		# array of x values
+real	y[]		# array of y values
+real	weight[]	# array of weights
+int	ier		# error code
+.fi
+.ih
+ARGUMENTS
+.ls cv
+Pointer to the curve descriptor
+.le
+.ls x  
+Array of x values.
+.le
+.ls y    
+Array of y values.
+.le
+.ls weight
+Array of weights.
+.le
+.ls ier  
+Error code. The options are OK, SINGULAR and NO_DEG_FREEDOM. If ier equals
+singular a solution is computed but one or more of the coefficients may
+be zero. If ier equals NO_DEG_FREEDOM, there are insufficient data points
+to compute a solution and CVREFIT returns without solving for the coefficients.
+.le
+.ih
+DESCRIPTION
+In some application the x and weight values remain unchanged from fit to fit
+and only the y values vary. In this case it is redundant to reaccumulate
+the matrix and perform the Cholesky factorization. CVREFIT zeros and
+reaccumulates the vector on the right hand side of the matrix equation
+and performs the forward and back substitution phase to fit for a new
+coefficient vector.
+.ih
+NOTES
+In the first call to CVREFIT space is allocated for the non-zero basis
+functions. Subsequent call to CVREFIT reference this array to avoid
+recaculating basis functions at every call.
+.ih
+SEE ALSO
+cvfit, cvaccum, cvsolve, cvchoslv
+.endhelp
diff --git a/math/curfit/doc/cvreject.hlp b/math/curfit/doc/cvreject.hlp
new file mode 100644
index 00000000..52e5ca4f
--- /dev/null
+++ b/math/curfit/doc/cvreject.hlp
@@ -0,0 +1,41 @@
+.help cvreject June84 "Curfit Package"
+.ih
+NAME
+cvreject -- reject a single data point from the data set to be fit
+.ih
+SYNOPSIS
+cvreject (cv, x, y, weight)
+
+.nf
+pointer	cv		# curve descriptor
+real	x		# x value
+real	y		# y value
+real	weight		# weight value
+.fi
+.ih
+ARGUMENTS
+.ls cv    
+Pointer to the curve descriptor structure.
+.le
+.ls x   
+X value.
+.le
+.ls y
+Y value.
+.le
+.ls weight
+The weight value.
+.le
+.ih
+DESCRIPTION
+CVREJECT removes an individul data point from the data set.
+The non-zero basis functions for each x are calculated. The contribution
+of each x to the normal equations is computed and subtracted from the
+appropriate arrays and vectors.
+An array of points can be removed from the fit by repeated calls to CVREJECT
+followed by a single call to CVSOLVE to calculate a new set of coefficients.
+.ih
+NOTES
+.ih
+SEE ALSO
+.endhelp
diff --git a/math/curfit/doc/cvrestore.hlp b/math/curfit/doc/cvrestore.hlp
new file mode 100644
index 00000000..84d352ee
--- /dev/null
+++ b/math/curfit/doc/cvrestore.hlp
@@ -0,0 +1,32 @@
+.help cvrestore Aug84 "Curfit Package"
+.ih
+NAME
+cvrestore -- restore fit parameters
+.ih
+SYNOPSIS
+cvrestore (cv, fit)
+
+.nf
+pointer	cv		# pointer to curve descriptor
+real	fit[]		# array containing curve parameters
+.fi
+.ih
+ARGUMENTS
+.ls cv    
+Pointer to curve descriptor structure. Returned by CVRESTORE.
+.le
+.ls fit  
+Array containing the curve parameters. Must have at least 7 + order
+elements, where order is the parameter set in CVINIT.
+.le
+.ih
+DESCRIPTION
+CVRESTORE returns oldcv the pointer to the curve descriptor and
+stores the curve parameters in fit in the structure ready for
+use by cveval or cvvector.
+.ih
+NOTES
+.ih
+SEE ALSO
+cvsave
+.endhelp
diff --git a/math/curfit/doc/cvsave.hlp b/math/curfit/doc/cvsave.hlp
new file mode 100644
index 00000000..144beaff
--- /dev/null
+++ b/math/curfit/doc/cvsave.hlp
@@ -0,0 +1,35 @@
+.help cvsave Aug84 "Curfit Package"
+.ih
+NAME
+cvsave -- save parameters of fit
+.ih
+SYNOPSIS
+call cvsave (cv, fit)
+
+.nf
+pointer	cv		# curve descriptor
+real	fit[]		# array containing the fit parameters
+.fi
+.ih
+ARGUMENTS
+.ls cv     
+The pointer to the curve descriptor structure.
+.le
+.ls fit  
+Array containing the fit parameters.
+Fit must contain at least 7 + order elements, where order is the order of the
+fit as set in CVINIT.
+.le
+.ih
+DESCRIPTION
+CVSAVE saves the curve parameters in the real array fit.
+The first four elements of fit contain the curve_type, order, xmin and xmax.
+The coefficients are stored in the remaining array elements.
+.ih
+NOTES
+CVSAVE does not preserve the matrices and vectors used by the fitting
+routines.
+.ih
+SEE ALSO
+cvrestore
+.endhelp
diff --git a/math/curfit/doc/cvset.hlp b/math/curfit/doc/cvset.hlp
new file mode 100644
index 00000000..5eb79f30
--- /dev/null
+++ b/math/curfit/doc/cvset.hlp
@@ -0,0 +1,56 @@
+.help cvset Nov84 "Curfit Package"
+.ih
+NAME
+cvset -- input fit parameters derived external to CURFIT
+.ih
+SYNOPSIS
+include <math/curfit.h>
+
+cvset (cv, curve_type, xmin, xmax, coeff, ncoeff)
+
+.nf
+pointer	cv		# pointer to curve descriptor
+int	curve_type	# functional form of the curve to be fitted
+real	xmin, xmax	# minimum and maximum x values
+real	coeff[ncoeff]	# coefficient array
+int	ncoeff		# number of coefficients
+.fi
+.ih
+ARGUMENTS
+.ls cv    
+Pointer to curve descriptor structure. Returned by CVSET.
+.le
+.ls curve_type
+Type of curve to be input. Must be one of LEGENDRE, CHEBYSHEV, SPLINE3
+or SPLINE1.
+.le
+.ls xmin, xmax
+The minimum and maximum data or fitted x values. The Legendre and
+Chebyshev polynomials are assumed to be normalized over this range.
+For the cubic and linear spline functions, the data range (xmax - xmin) is
+divided into (ncoeff - 3) and (ncoeff - 1) evenly spaced polynomial pieces
+respectively.
+.le
+.ls coeff
+Array containing the coefficients. Must have at least 7 + order
+elements, where order has the same meaning as the order parameter set in CVINIT.
+.le
+.ls ncoeff
+The number of coefficients. For polynomial functions, ncoeff
+equals 1 plus the order of the polynomial, e.g. a second order
+polynomial curve will have three coefficients. For the cubic
+and linear spline the number of polynomial pieces fit are
+(ncoeff - 3) and (ncoeff - 1) respectively.
+.le
+.ih
+DESCRIPTION
+CVSET returns cv the pointer to the curve descriptor and
+stores the curve parameters  in the CURFIT structure ready for
+use by CVEVAL or CVVECTOR.
+.ih
+NOTES
+The splines are assumed to have been fit in the least squares sense.
+.ih
+SEE ALSO
+cvsave
+.endhelp
diff --git a/math/curfit/doc/cvsolve.hlp b/math/curfit/doc/cvsolve.hlp
new file mode 100644
index 00000000..16badae2
--- /dev/null
+++ b/math/curfit/doc/cvsolve.hlp
@@ -0,0 +1,39 @@
+.help cvsolve Jun84 "Curfit Package"
+.ih
+NAME
+cvsolve -- solve a linear system of eqns by the Cholesky method
+.ih
+SYNOPSIS
+cvsolve (cv, ier)
+
+.nf
+pointer	cv	# curve descriptor
+int	ier	# error code
+.fi
+.ih
+ARGUMENTS
+.ls cv    
+Pointer to the curve descriptor
+.le
+.ls ier    
+Error code returned by the fitting routines. The options are
+OK, SINGULAR and NO_DEG_FREEDOM. If ier is SINGULAR the matrix is singular,
+CVSOLVE will compute a solution to the normal equationsbut one or more of the
+coefficients will be zero.
+If ier equals NO_DEG_FREEDOM, too few data points exist for a reasonable
+solution to be computed. CVSOLVE returns
+without fitting the data.
+.le
+.ih
+DESCRIPTION
+CVSOLVE call two routines CVCHOFAC and CVCHOSLV. CVCHOFAC computes the
+Cholesky factorization of the data matrix. CVCHOSLV solves for the
+coefficients of the fitting function by forward and back substitution.
+An error code is returned by CVSOLVE if it is unable to solve the normal
+equations as formulated.
+.ih
+NOTES
+.ih
+SEE ALSO
+cvchofac, cvchoslv
+.endhelp
diff --git a/math/curfit/doc/cvstati.hlp b/math/curfit/doc/cvstati.hlp
new file mode 100644
index 00000000..ffd05d0a
--- /dev/null
+++ b/math/curfit/doc/cvstati.hlp
@@ -0,0 +1,47 @@
+.help cvstati May85 "Curfit Package"
+.ih
+NAME
+cvstati -- get integer parameter
+.ih
+SYNOPSIS
+include <math/curfit.h>
+
+ival = cvstati (cv, parameter)
+
+.nf
+pointer	cv		# curve descriptor
+int	parameter	# parameter to be returned
+.fi
+.ih
+ARGUMENTS
+.ls cv     
+The pointer to the curve descriptor structure.
+.le
+.ls parameter
+Parameter to be return.  Definitions in curfit.h are:
+.nf
+	define	CVTYPE		1	# curve type
+	define	CVORDER		2	# order
+	define	CVNCOEFF	3	# number of coefficients
+	define	CVNSAVE		4	# length of save buffer
+.fi
+.le
+.ih
+DESCRIPTION
+The values of integer parameters are returned.  The parameters include
+the curve type, the order, the number of coefficients, and the length
+of the buffer required by CVSAVE (which is of TY_REAL).
+.ih
+EXAMPLES
+.nf
+	include <curfit.h>
+
+	int	cvstati()
+
+	call malloc (buf, cvstati (cv, CVNSAVE), TY_REAL)
+	call cvsave (cv, Memr[buf])
+.fi
+.ih
+SEE ALSO
+cvstatr
+.endhelp
diff --git a/math/curfit/doc/cvstatr.hlp b/math/curfit/doc/cvstatr.hlp
new file mode 100644
index 00000000..f4d959c2
--- /dev/null
+++ b/math/curfit/doc/cvstatr.hlp
@@ -0,0 +1,44 @@
+.help cvstatr May85 "Curfit Package"
+.ih
+NAME
+cvstatr -- get real parameter
+.ih
+SYNOPSIS
+include <math/curfit.h>
+
+rval = cvstatr (cv, parameter)
+
+.nf
+pointer	cv		# curve descriptor
+int	parameter	# parameter to be returned
+.fi
+.ih
+ARGUMENTS
+.ls cv     
+The pointer to the curve descriptor structure.
+.le
+.ls parameter
+Parameter to be return.  Definitions in curfit.h are:
+.nf
+	define	CVXMIN		5	# minimum ordinate
+	define	CVORDER		6	# maximum ordinate
+.fi
+.le
+.ih
+DESCRIPTION
+The values of real parameters are returned.  The parameters include
+the minimum and maximum ordinate values of the curve.
+.ih
+EXAMPLES
+.nf
+	include <curfit.h>
+
+	real	cvstatr()
+
+	xmin = cvstatr (cv, CVXMIN)
+	xmax = cvstatr (cv, CVXMAX)
+.fi
+.ih
+SEE ALSO
+cvstati
+.endhelp
diff --git a/math/curfit/doc/cvvector.hlp b/math/curfit/doc/cvvector.hlp
new file mode 100644
index 00000000..79c0282f
--- /dev/null
+++ b/math/curfit/doc/cvvector.hlp
@@ -0,0 +1,41 @@
+.help cvvector Jun84 "Curfit Package"
+.ih
+NAME
+cvvector -- evaluate the fitted curve at a set of points
+.ih
+SYNOPSIS
+cvvector (cv, x, yfit, npts)
+
+.nf
+pointer	cv		# curve descriptor
+real	x[]		# x array
+real	yfit[]		# array of fitted y values
+int	npts		# number of x values
+.fi
+.ih
+ARGUMENTS
+.ls cv   
+Pointer to the curve descriptor structure.
+.le
+.ls x     
+Array of x values
+.le
+.ls yfit   
+Array of fitted y values
+.le
+.ls npts   
+The number of x values at which the curve is to be evaluated.
+.le
+.ih
+DESCRIPTION
+Fit the curve to an array of data points. CVVECTOR uses the coefficients
+stored in the curve descriptor structure.
+.ih
+NOTES
+The x values are assumed to lie
+in the region xmin <= x <= xmax. Checking for out of bounds x values is the
+responsibility of the user.
+.ih
+SEE ALSO
+cveval
+.endhelp
diff --git a/math/curfit/doc/cvzero.hlp b/math/curfit/doc/cvzero.hlp
new file mode 100644
index 00000000..7f9e07e2
--- /dev/null
+++ b/math/curfit/doc/cvzero.hlp
@@ -0,0 +1,26 @@
+.help cvzero Aug84 "Curfit Package"
+.ih
+NAME
+cvzero -- set up for a new curve fit
+.ih
+SYNOPSIS
+cvzero (cv)
+
+.nf
+pointer	cv	# curve descriptor
+.fi
+.ih
+ARGUMENTS
+.ls cv     
+Pointer to the curve descriptor structure.
+.le
+.ih
+DESCRIPTION
+CVZERO zeros the matrix and right side of the matrix equation.
+.ih
+NOTES
+CVZERO can be used to reinitialize the matrix and right side of the matrix
+equation to begin a new fit in accumulate mode.
+.ih
+SEE ALSO
+cvfit, cvinit
diff --git a/math/curfit/mkpkg b/math/curfit/mkpkg
new file mode 100644
index 00000000..345ec582
--- /dev/null
+++ b/math/curfit/mkpkg
@@ -0,0 +1,87 @@
+# Curve fitting tools library.
+
+$checkout libcurfit.a lib$
+$update libcurfit.a
+$checkin libcurfit.a lib$
+$exit
+
+tfiles:
+	$set	GEN = "$$generic -k -t rd"
+
+	$ifolder (cv_b1evalr.x, cv_b1eval.gx)	$(GEN) cv_b1eval.gx $endif
+	$ifolder (cv_bevalr.x, cv_beval.gx)	$(GEN) cv_beval.gx  $endif
+	$ifolder (cv_fevalr.x, cv_feval.gx)	$(GEN) cv_feval.gx  $endif
+	$ifolder (cv_userfncr.x, cv_userfnc.gx) $(GEN) cv_userfnc.gx $endif
+	$ifolder (cvaccumr.x, cvaccum.gx)	$(GEN) cvaccum.gx  $endif
+	$ifolder (cvacptsr.x, cvacpts.gx)	$(GEN) cvacpts.gx   $endif
+	$ifolder (cvchomatr.x, cvchomat.gx)	$(GEN) cvchomat.gx  $endif
+	$ifolder (cvcoeffr.x, cvcoeff.gx)	$(GEN) cvcoeff.gx   $endif
+	$ifolder (cverrorsr.x, cverrors.gx)	$(GEN) cverrors.gx  $endif
+	$ifolder (cvevalr.x, cveval.gx)		$(GEN) cveval.gx    $endif
+	$ifolder (cvfitr.x, cvfit.gx)		$(GEN) cvfit.gx     $endif
+	$ifolder (cvfreer.x, cvfree.gx)		$(GEN) cvfree.gx    $endif
+	$ifolder (cvinitr.x, cvinit.gx)		$(GEN) cvinit.gx    $endif
+	$ifolder (cvpowerr.x, cvpower.gx)	$(GEN) cvpower.gx   $endif
+	$ifolder (cvrefitr.x, cvrefit.gx)	$(GEN) cvrefit.gx   $endif
+	$ifolder (cvrejectr.x, cvreject.gx)	$(GEN) cvreject.gx  $endif
+	$ifolder (cvrestorer.x, cvrestore.gx)	$(GEN) cvrestore.gx $endif
+	$ifolder (cvsaver.x, cvsave.gx)		$(GEN) cvsave.gx    $endif
+	$ifolder (cvsetr.x, cvset.gx)		$(GEN) cvset.gx     $endif
+	$ifolder (cvsolver.x, cvsolve.gx)	$(GEN) cvsolve.gx   $endif
+	$ifolder (cvstatr.x, cvstat.gx)		$(GEN) cvstat.gx    $endif
+	$ifolder (cvvectorr.x, cvvector.gx)	$(GEN) cvvector.gx  $endif
+	$ifolder (cvzeror.x, cvzero.gx)		$(GEN) cvzero.gx    $endif
+	;
+
+libcurfit.a:
+
+	$ifeq (USE_GENERIC, yes) $call tfiles $endif
+
+	cvaccumr.x	curfitdef.h <math/curfit.h>
+	cvacptsr.x	curfitdef.h <math/curfit.h>
+	cv_bevalr.x	
+	cv_b1evalr.x	
+	cvchomatr.x	curfitdef.h <mach.h> <math/curfit.h>
+	cvcoeffr.x	curfitdef.h
+	cverrorsr.x	curfitdef.h <mach.h>
+	cvevalr.x	curfitdef.h <math/curfit.h>
+	cv_fevalr.x	
+	cvfitr.x	curfitdef.h <math/curfit.h>
+	cvfreer.x	curfitdef.h
+	cvinitr.x	curfitdef.h <math/curfit.h> <mach.h>
+	cvpowerr.x	curfitdef.h <math/curfit.h> <mach.h>
+	cvrefitr.x	curfitdef.h <math/curfit.h>
+	cvrejectr.x	curfitdef.h <math/curfit.h>
+	cvrestorer.x	curfitdef.h <math/curfit.h>
+	cvsaver.x	curfitdef.h <math/curfit.h>
+	cvsetr.x	curfitdef.h <math/curfit.h>
+	cvsolver.x	curfitdef.h <math/curfit.h>
+	cvstatr.x	curfitdef.h <math/curfit.h>
+	cv_userfncr.x	curfitdef.h <math/curfit.h>
+	cvvectorr.x	curfitdef.h <math/curfit.h>
+	cvzeror.x	curfitdef.h
+
+	cvaccumd.x	dcurfitdef.h <math/curfit.h>
+	cvacptsd.x	dcurfitdef.h <math/curfit.h>
+	cv_bevald.x	
+	cv_b1evald.x	
+	cvchomatd.x	dcurfitdef.h <mach.h> <math/curfit.h>
+	cvcoeffd.x	dcurfitdef.h
+	cverrorsd.x	dcurfitdef.h <mach.h>
+	cvevald.x	dcurfitdef.h <math/curfit.h>
+	cv_fevald.x	
+	cvfitd.x	dcurfitdef.h <math/curfit.h>
+	cvfreed.x	dcurfitdef.h
+	cvinitd.x	dcurfitdef.h <math/curfit.h> <mach.h>
+	cvpowerd.x	dcurfitdef.h <math/curfit.h> <mach.h>
+	cvrefitd.x	dcurfitdef.h <math/curfit.h>
+	cvrejectd.x	dcurfitdef.h <math/curfit.h>
+	cvrestored.x	dcurfitdef.h <math/curfit.h>
+	cvsaved.x	dcurfitdef.h <math/curfit.h>
+	cvsetd.x	dcurfitdef.h <math/curfit.h>
+	cvsolved.x	dcurfitdef.h <math/curfit.h>
+	cvstatd.x	dcurfitdef.h <math/curfit.h>
+	cv_userfncd.x	dcurfitdef.h <math/curfit.h>
+	cvvectord.x	dcurfitdef.h <math/curfit.h>
+	cvzerod.x	dcurfitdef.h
+	;
diff --git a/math/deboor/Notes b/math/deboor/Notes
new file mode 100644
index 00000000..e3c51470
--- /dev/null
+++ b/math/deboor/Notes
@@ -0,0 +1,36 @@
+  0  4 20     chapter xii     example 2     run 1
+  3  4 20     chapter xii     example 2     run 2
+  8  4 20     chapter xii     example 3     run 1
+  6  4 20     chapter xii     example 3     run 2
+  4  4 20     chapter xii     example 3     run 3
+  8  4 20     chapter xii     example 4     run 1
+  6  4 20     chapter xii     example 4     run 2
+  7 10	4     chapter xiii    example 1     run 1
+.000001       chapter xiii    example 1     run 1
+2.	      chapter xiii    example 1     run 1
+  7 10	4     chapter xiii    example 1     run 2
+0.	      chapter xiii    example 1     run 2
+2.	      chapter xiii    example 1     run 2
+  0  4 20     chapter xiii    example 2     run 1
+  3  4 20     chapter xiii    example 2     run 2
+  6  4 20     chapter xiii    example 2     run 3
+  0  4 20     chapter xiii    example 2m    run 1
+  1  4 20     chapter xiii    example 2m    run 2
+  2  4 20     chapter xiii    example 2m    run 3
+  2  7	      chapter xiv     example 1
+600000.       chapter xiv     example 1
+60000.	      chapter xiv     example 1
+6000.	      chapter xiv     example 1
+600.	      chapter xiv     example 1
+60.	      chapter xiv     example 1
+6.	      chapter xiv     example 1
+.6	      chapter xiv     example 1
+  1  0.       chapter xiv     example 2
+ononon	      chapter xiv     example 2
+ 20  1.       chapter xiv     example 3   need fake newnot routine which
+ofofof	      chapter xiv     example 3   returns uniform knots .
+  4  2.       chapter xiv     example 4
+ononof	      chapter xiv     example 4
+2.5	      chapter xvi     example 2
+-1.	      chapter xvi     example 2
+      end
diff --git a/math/deboor/README b/math/deboor/README
new file mode 100644
index 00000000..c0ecd1f4
--- /dev/null
+++ b/math/deboor/README
@@ -0,0 +1,20 @@
+These directories contain the codes described in the book "A Practical Guide
+to Splines", by Carl DeBoor, Springer-Verlag, 1978.  The directory math/deboor
+contains the single precision routines.  The same routines, edited to provide
+double precision, are in the directory "dblprec", which may disappear at some
+point in the future if we decide we don't need these.  The directory "progs"
+contains a number of example programs from the book.
+
+A number of the routines herein write error messages using Fortran i/o,
+violating our convention that numerical routines should not perform i/o.
+These routines have been flagged by adding the suffix "_io".  These routines
+have not been compiled and installed in the library "deboor.a".  The most useful
+routines either did not do i/o, or have had the i/o removed (e.g., splint.f).
+
+Note: use the new SPLLSQ for smoothing with splines, instead of L2APPR, if a
+uniform knot sequence is desired.  Use BSPLN to evaluate the coefficient array
+from SPLLSQ.
+
+Oct 85	Rearranged the order of argument declarations in cwidth.f, dtblok.f,
+	factrb.f, fcblok.f, sbblok.f, shiftb.f, slvblk.f, subbak.f, subfor.f
+	to conform with Fortran standard
diff --git a/math/deboor/Revisions b/math/deboor/Revisions
new file mode 100644
index 00000000..bf131052
--- /dev/null
+++ b/math/deboor/Revisions
@@ -0,0 +1,7 @@
+.help revisions Sep99 math.deboor
+.nf
+From Davis, September 20, 1999
+
+Added some missing file dependices to the mkpkg file.
+pkg/math/deboor/mkpkg
+.endhelp
diff --git a/math/deboor/banfac.f b/math/deboor/banfac.f
new file mode 100644
index 00000000..56906927
--- /dev/null
+++ b/math/deboor/banfac.f
@@ -0,0 +1,110 @@
+      subroutine banfac ( w, nroww, nrow, nbandl, nbandu, iflag )
+c  from  * a practical guide to splines *  by c. de boor
+c  returns in  w  the lu-factorization (without pivoting) of the banded
+c  matrix  a  of order	nrow  with  (nbandl + 1 + nbandu) bands or diag-
+c  onals in the work array  w .
+c
+c******  i n p u t  ******
+c  w.....work array of size  (nroww,nrow)  containing the interesting
+c	 part of a banded matrix  a , with the diagonals or bands of  a
+c	 stored in the rows of	w , while columns of  a  correspond to
+c	 columns of  w . this is the storage mode used in  linpack  and
+c	 results in efficient innermost loops.
+c	    explicitly,  a  has  nbandl  bands below the diagonal
+c			     +	   1	 (main) diagonal
+c			     +	 nbandu  bands above the diagonal
+c	 and thus, with    middle = nbandu + 1,
+c	   a(i+j,j)  is in  w(i+middle,j)  for i=-nbandu,...,nbandl
+c					       j=1,...,nrow .
+c	 for example, the interesting entries of a (1,2)-banded matrix
+c	 of order  9  would appear in the first  1+1+2 = 4  rows of  w
+c	 as follows.
+c			   13 24 35 46 57 68 79
+c			12 23 34 45 56 67 78 89
+c		     11 22 33 44 55 66 77 88 99
+c		     21 32 43 54 65 76 87 98
+c
+c	 all other entries of  w  not identified in this way with an en-
+c	 try of  a  are never referenced .
+c  nroww.....row dimension of the work array  w .
+c	 must be  .ge.	nbandl + 1 + nbandu  .
+c  nbandl.....number of bands of  a  below the main diagonal
+c  nbandu.....number of bands of  a  above the main diagonal .
+c
+c******  o u t p u t  ******
+c  iflag.....integer indicating success( = 1) or failure ( = 2) .
+c     if  iflag = 1, then
+c  w.....contains the lu-factorization of  a  into a unit lower triangu-
+c	 lar matrix  l	and an upper triangular matrix	u (both banded)
+c	 and stored in customary fashion over the corresponding entries
+c	 of  a . this makes it possible to solve any particular linear
+c	 system  a*x = b  for  x  by a
+c	       call banslv ( w, nroww, nrow, nbandl, nbandu, b )
+c	 with the solution x  contained in  b  on return .
+c     if  iflag = 2, then
+c	 one of  nrow-1, nbandl,nbandu failed to be nonnegative, or else
+c	 one of the potential pivots was found to be zero indicating
+c	 that  a  does not have an lu-factorization. this implies that
+c	 a  is singular in case it is totally positive .
+c
+c******  m e t h o d  ******
+c     gauss elimination  w i t h o u t	pivoting is used. the routine is
+c  intended for use with matrices  a  which do not require row inter-
+c  changes during factorization, especially for the  t o t a l l y
+c  p o s i t i v e  matrices which occur in spline calculations.
+c     the routine should not be used for an arbitrary banded matrix.
+c
+      integer iflag,nbandl,nbandu,nrow,nroww,	i,ipk,j,jmax,k,kmax
+     *					      ,middle,midmk,nrowm1
+      real w(nroww,nrow),   factor,pivot
+c
+      iflag = 1
+      middle = nbandu + 1
+c			  w(middle,.) contains the main diagonal of  a .
+      nrowm1 = nrow - 1
+      if (nrowm1)			999,900,1
+    1 if (nbandl .gt. 0)		go to 10
+c		 a is upper triangular. check that diagonal is nonzero .
+      do 5 i=1,nrowm1
+	 if (w(middle,i) .eq. 0.)	go to 999
+    5	 continue
+					go to 900
+   10 if (nbandu .gt. 0)		go to 20
+c	       a is lower triangular. check that diagonal is nonzero and
+c		  divide each column by its diagonal .
+      do 15 i=1,nrowm1
+	 pivot = w(middle,i)
+	 if(pivot .eq. 0.)		go to 999
+	 jmax = min0(nbandl, nrow - i)
+	 do 15 j=1,jmax
+   15	    w(middle+j,i) = w(middle+j,i)/pivot
+					return
+c
+c	 a  is not just a triangular matrix. construct lu factorization
+   20 do 50 i=1,nrowm1
+c				   w(middle,i)	is pivot for i-th step .
+	 pivot = w(middle,i)
+	 if (pivot .eq. 0.)		go to 999
+c		  jmax	is the number of (nonzero) entries in column  i
+c		      below the diagonal .
+	 jmax = min0(nbandl,nrow - i)
+c	       divide each entry in column  i  below diagonal by pivot .
+	 do 32 j=1,jmax
+   32	    w(middle+j,i) = w(middle+j,i)/pivot
+c		  kmax	is the number of (nonzero) entries in row  i  to
+c		      the right of the diagonal .
+	 kmax = min0(nbandu,nrow - i)
+c		   subtract  a(i,i+k)*(i-th column) from (i+k)-th column
+c		   (below row  i ) .
+	 do 40 k=1,kmax
+	    ipk = i + k
+	    midmk = middle - k
+	    factor = w(midmk,ipk)
+	    do 40 j=1,jmax
+   40	       w(midmk+j,ipk) = w(midmk+j,ipk) - w(middle+j,i)*factor
+   50	 continue
+c					check the last diagonal entry .
+  900 if (w(middle,nrow) .ne. 0.)	return
+  999 iflag = 2
+					return
+      end
diff --git a/math/deboor/banslv.f b/math/deboor/banslv.f
new file mode 100644
index 00000000..154ae051
--- /dev/null
+++ b/math/deboor/banslv.f
@@ -0,0 +1,53 @@
+      subroutine banslv ( w, nroww, nrow, nbandl, nbandu, b )
+c  from  * a practical guide to splines *  by c. de boor
+c  companion routine to  banfac . it returns the solution  x  of the
+c  linear system  a*x = b  in place of	b , given the lu-factorization
+c  for	a  in the workarray  w .
+c
+c******  i n p u t  ******
+c  w, nroww,nrow,nbandl,nbandu.....describe the lu-factorization of a
+c	 banded matrix	a  of roder  nrow  as constructed in  banfac .
+c	 for details, see  banfac .
+c  b.....right side of the system to be solved .
+c
+c******  o u t p u t  ******
+c  b.....contains the solution	x , of order  nrow .
+c
+c******  m e t h o d  ******
+c     (with  a = l*u, as stored in  w,) the unit lower triangular system
+c  l(u*x) = b  is solved for  y = u*x, and  y  stored in  b . then the
+c  upper triangular system  u*x = y  is solved for  x  . the calcul-
+c  ations are so arranged that the innermost loops stay within columns.
+c
+      integer nbandl,nbandu,nrow,nroww,   i,j,jmax,middle,nrowm1
+      real w(nroww,nrow),b(nrow)
+      middle = nbandu + 1
+      if (nrow .eq. 1)			go to 49
+      nrowm1 = nrow - 1
+      if (nbandl .eq. 0)		go to 30
+c				  forward pass
+c	     for i=1,2,...,nrow-1, subtract  right side(i)*(i-th column
+c	     of  l )  from right side  (below i-th row) .
+      do 21 i=1,nrowm1
+	 jmax = min0(nbandl, nrow-i)
+	 do 21 j=1,jmax
+   21	    b(i+j) = b(i+j) - b(i)*w(middle+j,i)
+c				  backward pass
+c	     for i=nrow,nrow-1,...,1, divide right side(i) by i-th diag-
+c	     onal entry of  u, then subtract  right side(i)*(i-th column
+c	     of  u)  from right side  (above i-th row).
+   30 if (nbandu .gt. 0)		go to 40
+c				 a  is lower triangular .
+      do 31 i=1,nrow
+   31	 b(i) = b(i)/w(1,i)
+					return
+   40 i = nrow
+   41	 b(i) = b(i)/w(middle,i)
+	 jmax = min0(nbandu,i-1)
+	 do 45 j=1,jmax
+   45	    b(i-j) = b(i-j) - b(i)*w(middle-j,i)
+	 i = i - 1
+	 if (i .gt. 1)			go to 41
+   49 b(1) = b(1)/w(middle,1)
+					return
+      end
diff --git a/math/deboor/bchfac.f b/math/deboor/bchfac.f
new file mode 100644
index 00000000..a2a95471
--- /dev/null
+++ b/math/deboor/bchfac.f
@@ -0,0 +1,87 @@
+      subroutine bchfac ( w, nbands, nrow, diag )
+c  from  * a practical guide to splines *  by c. de boor
+constructs cholesky factorization
+c		      c  =  l * d * l-transpose
+c  with l unit lower triangular and d diagonal, for given matrix c of
+c  order  n r o w , in case  c	is (symmetric) positive semidefinite
+c  and	b a n d e d , having  n b a n d s  diagonals at and below the
+c  main diagonal.
+c
+c******  i n p u t  ******
+c  nrow.....is the order of the matrix	c .
+c  nbands.....indicates its bandwidth, i.e.,
+c	   c(i,j) = 0 for abs(i-j) .gt. nbands .
+c  w.....workarray of size (nbands,nrow)  containing the  nbands  diago-
+c	 nals in its rows, with the main diagonal in row  1 . precisely,
+c	 w(i,j)  contains  c(i+j-1,j), i=1,...,nbands, j=1,...,nrow.
+c	   for example, the interesting entries of a seven diagonal sym-
+c	 metric matrix	c  of order  9	would be stored in  w  as
+c
+c			11 22 33 44 55 66 77 88 99
+c			21 32 43 54 65 76 87 98
+c			31 42 53 64 75 86 97
+c			41 52 63 74 85 96
+c
+c	 all other entries of  w  not identified in this way with an en-
+c	 try of  c  are never referenced .
+c  diag.....is a work array of length  nrow .
+c
+c******  o u t p u t  ******
+c  w.....contains the cholesky factorization  c = l*d*l-transp, with
+c	 w(1,i) containing  1/d(i,i)
+c	 and  w(i,j)  containing  l(i-1+j,j), i=2,...,nbands.
+c
+c******  m e t h o d  ******
+c   gauss elimination, adapted to the symmetry and bandedness of  c , is
+c   used .
+c     near zero pivots are handled in a special way. the diagonal ele-
+c  ment c(n,n) = w(1,n) is saved initially in  diag(n), all n. at the n-
+c  th elimination step, the current pivot element, viz.  w(1,n), is com-
+c  pared with its original value, diag(n). if, as the result of prior
+c  elimination steps, this element has been reduced by about a word
+c  length, (i.e., if w(1,n)+diag(n) .le. diag(n)), then the pivot is de-
+c  clared to be zero, and the entire n-th row is declared to be linearly
+c  dependent on the preceding rows. this has the effect of producing
+c   x(n) = 0  when solving  c*x = b  for  x, regardless of  b. justific-
+c  ation for this is as follows. in contemplated applications of this
+c  program, the given equations are the normal equations for some least-
+c  squares approximation problem, diag(n) = c(n,n) gives the norm-square
+c  of the n-th basis function, and, at this point,  w(1,n)  contains the
+c  norm-square of the error in the least-squares approximation to the n-
+c  th basis function by linear combinations of the first n-1 . having
+c  w(1,n)+diag(n) .le. diag(n) signifies that the n-th function is lin-
+c  early dependent to machine accuracy on the first n-1 functions, there
+c  fore can safely be left out from the basis of approximating functions
+c     the solution of a linear system
+c			c*x = b
+c   is effected by the succession of the following  t w o  calls:
+c     call bchfac ( w, nbands, nrow, diag )	  , to get factorization
+c     call bchslv ( w, nbands, nrow, b, x )	       , to solve for x.
+c
+      integer nbands,nrow,   i,imax,j,jmax,n
+      real w(nbands,nrow),diag(nrow),	ratio
+      if (nrow .gt. 1)			go to 9
+      if (w(1,1) .gt. 0.) w(1,1) = 1./w(1,1)
+					return
+c					 store diagonal of  c  in  diag.
+    9 do 10 n=1,nrow
+   10	 diag(n) = w(1,n)
+c							 factorization .
+      do 20 n=1,nrow
+	 if (w(1,n)+diag(n) .gt. diag(n)) go to 15
+	 do 14 j=1,nbands
+   14	    w(j,n) = 0.
+					go to 20
+   15	 w(1,n) = 1./w(1,n)
+	 imax = min0(nbands-1,nrow - n)
+	 if (imax .lt. 1)		go to 20
+	 jmax = imax
+	 do 18 i=1,imax
+	    ratio = w(i+1,n)*w(1,n)
+	    do 17 j=1,jmax
+   17	       w(j,n+i) = w(j,n+i) - w(j+i,n)*ratio
+	    jmax = jmax - 1
+   18	    w(i+1,n) = ratio
+   20	 continue
+					return
+      end
diff --git a/math/deboor/bchslv.f b/math/deboor/bchslv.f
new file mode 100644
index 00000000..ec848b8f
--- /dev/null
+++ b/math/deboor/bchslv.f
@@ -0,0 +1,50 @@
+      subroutine bchslv ( w, nbands, nrow, b )
+c  from  * a practical guide to splines *  by c. de boor
+c  solves the linear system	c*x = b   of order  n r o w  for  x
+c  provided  w	contains the cholesky factorization for the banded (sym-
+c  metric) positive definite matrix  c	as constructed in the subroutine
+c    b c h f a c  (quo vide).
+c
+c******  i n p u t  ******
+c  nrow.....is the order of the matrix	c .
+c  nbands.....indicates the bandwidth of  c .
+c  w.....contains the cholesky factorization for  c , as output from
+c	 subroutine bchfac  (quo vide).
+c  b.....the vector of length  n r o w	containing the right side.
+c
+c******  o u t p u t  ******
+c  b.....the vector of length  n r o w	containing the solution.
+c
+c******  m e t h o d  ******
+c  with the factorization  c = l*d*l-transpose	available, where  l  is
+c  unit lower triangular and  d  is diagonal, the triangular system
+c  l*y = b  is solved for  y (forward substitution), y is stored in  b,
+c  the vector  d**(-1)*y is computed and stored in  b, then the triang-
+c  ular system	l-transpose*x = d**(-1)*y is solved for  x (backsubstit-
+c  ution).
+      integer nbands,nrow,   j,jmax,n,nbndm1
+      real w(nbands,nrow),b(nrow)
+      if (nrow .gt. 1)			go to 21
+      b(1) = b(1)*w(1,1)
+					return
+c
+c		  forward substitution. solve l*y = b for y, store in b.
+   21 nbndm1 = nbands - 1
+      do 30 n=1,nrow
+	 jmax = min0(nbndm1,nrow-n)
+	 if (jmax .lt. 1)		go to 30
+	 do 25 j=1,jmax
+   25	    b(j+n) = b(j+n) - w(j+1,n)*b(n)
+   30	 continue
+c
+c     backsubstitution. solve l-transp.x = d**(-1)*y  for x, store in b.
+      n = nrow
+   31	 b(n) = b(n)*w(1,n)
+	 jmax = min0(nbndm1,nrow-n)
+	 if (jmax .lt. 1)		go to 40
+	 do 35 j=1,jmax
+   35	    b(n) = b(n) - w(j+1,n)*b(j+n)
+   40	 n = n-1
+      if (n.gt.0)			go to 31
+					return
+      end
diff --git a/math/deboor/bsplbv.f b/math/deboor/bsplbv.f
new file mode 100644
index 00000000..2187db14
--- /dev/null
+++ b/math/deboor/bsplbv.f
@@ -0,0 +1,91 @@
+      subroutine bsplvb ( t, jhigh, index, x, left, biatx )
+c  from  * a practical guide to splines *  by c. de boor
+calculates the value of all possibly nonzero b-splines at  x  of order
+c
+c		jout  =  max( jhigh , (j+1)*(index-1) )
+c
+c  with knot sequence  t .
+c
+c******  i n p u t  ******
+c  t.....knot sequence, of length  left + jout	, assumed to be nonde-
+c	 creasing.  a s s u m p t i o n . . . .
+c			t(left)  .lt.  t(left + 1)   .
+c   d i v i s i o n  b y  z e r o  will result if  t(left) = t(left+1)
+c  jhigh,
+c  index.....integers which determine the order  jout = max(jhigh,
+c	 (j+1)*(index-1))  of the b-splines whose values at  x	are to
+c	 be returned.  index  is used to avoid recalculations when seve-
+c	 ral columns of the triangular array of b-spline values are nee-
+c	 ded (e.g., in	bvalue	or in  bsplvd ). precisely,
+c		      if  index = 1 ,
+c	 the calculation starts from scratch and the entire triangular
+c	 array of b-spline values of orders 1,2,...,jhigh  is generated
+c	 order by order , i.e., column by column .
+c		      if  index = 2 ,
+c	 only the b-spline values of order  j+1, j+2, ..., jout  are ge-
+c	 nerated, the assumption being that  biatx , j , deltal , deltar
+c	 are, on entry, as they were on exit at the previous call.
+c	    in particular, if  jhigh = 0, then	jout = j+1, i.e., just
+c	 the next column of b-spline values is generated.
+c
+c  w a r n i n g . . .	the restriction   jout .le. jmax (= 20)  is im-
+c	 posed arbitrarily by the dimension statement for  deltal  and
+c	 deltar  below, but is	n o w h e r e  c h e c k e d  for .
+c
+c  x.....the point at which the b-splines are to be evaluated.
+c  left.....an integer chosen (usually) so that
+c		   t(left) .le. x .le. t(left+1)  .
+c
+c******  o u t p u t  ******
+c  biatx.....array of length  jout , with  biatx(i)  containing the val-
+c	 ue at	x  of the polynomial of order  jout  which agrees with
+c	 the b-spline  b(left-jout+i,jout,t)  on the interval (t(left),
+c	 t(left+1)) .
+c
+c******  m e t h o d  ******
+c  the recurrence relation
+c
+c			x - t(i)	      t(i+j+1) - x
+c     b(i,j+1)(x)  =  -----------b(i,j)(x) + ---------------b(i+1,j)(x)
+c		      t(i+j)-t(i)	     t(i+j+1)-t(i+1)
+c
+c  is used (repeatedly) to generate the (j+1)-vector  b(left-j,j+1)(x),
+c  ...,b(left,j+1)(x)  from the j-vector  b(left-j+1,j)(x),...,
+c  b(left,j)(x), storing the new values in  biatx  over the old. the
+c  facts that
+c	     b(i,1) = 1  if  t(i) .le. x .lt. t(i+1)
+c  and that
+c	     b(i,j)(x) = 0  unless  t(i) .le. x .lt. t(i+j)
+c  are used. the particular organization of the calculations follows al-
+c  gorithm  (8)  in chapter x of the text.
+c
+c     parameter jmax = 20
+      integer index,jhigh,left,   i,j,jp1
+c     real biatx(jhigh),t(1),x,   deltal(jmax),deltar(jmax),saved,term
+      real biatx(jhigh),t(1),x,   deltal(20),deltar(20),saved,term
+c     dimension biatx(jout), t(left+jout)
+current fortran standard makes it impossible to specify the length of
+c  t  and of  biatx  precisely without the introduction of otherwise
+c  superfluous additional arguments.
+      data j/1/
+c     save j,deltal,deltar (valid in fortran 77)
+c
+					go to (10,20), index
+   10 j = 1
+      biatx(1) = 1.
+      if (j .ge. jhigh) 		go to 99
+c
+   20	 jp1 = j + 1
+	 deltar(j) = t(left+j) - x
+	 deltal(j) = x - t(left+1-j)
+	 saved = 0.
+	 do 26 i=1,j
+	    term = biatx(i)/(deltar(i) + deltal(jp1-i))
+	    biatx(i) = saved + deltar(i)*term
+   26	    saved = deltal(jp1-i)*term
+	 biatx(jp1) = saved
+	 j = jp1
+	 if (j .lt. jhigh)		go to 20
+c
+   99					return
+      end
diff --git a/math/deboor/bspln.h b/math/deboor/bspln.h
new file mode 100644
index 00000000..ccee7b64
--- /dev/null
+++ b/math/deboor/bspln.h
@@ -0,0 +1,14 @@
+define	KMAX		20		# maximum order spline permitted
+
+# Spline descriptor structure -- stored at beginning of BSPLN array.
+# All of the information needed to describe the spline is collected
+# in one place.  Space is left in the header for expansion.
+# Space required:  REAL BSPLN [2*N+30]
+
+define	NCOEF		bspln[1]	# number of coeff in the spline
+define	ORDER		bspln[2]	# order of spline (cubic = 4)
+define	XMIN		bspln[3]	# minimum x-value
+define	XMAX		bspln[4]	# maximum x-value
+define	KINDEX		bspln[5]	# position during evaluation (SEVAL)
+define	KNOT1		NCOEF+10	# offset to the first knot
+define	COEF1		10		# offset to the first coefficient
diff --git a/math/deboor/bsplpp.f b/math/deboor/bsplpp.f
new file mode 100644
index 00000000..3af00b3b
--- /dev/null
+++ b/math/deboor/bsplpp.f
@@ -0,0 +1,105 @@
+      subroutine bsplpp ( t, bcoef, n, k, scrtch, break, coef, l )
+c  from  * a practical guide to splines *  by c. de boor
+calls  bsplvb
+c
+converts the b-representation  t, bcoef, n, k  of some spline into its
+c  pp-representation  break, coef, l, k .
+c
+c******  i n p u t  ******
+c  t.....knot sequence, of length  n+k
+c  bcoef.....b-spline coefficient sequence, of length  n
+c  n.....length of  bcoef  and	dimension of spline space  spline(k,t)
+c  k.....order of the spline
+c
+c  w a r n i n g  . . .  the restriction   k .le. kmax (= 20)	is impo-
+c	 sed by the arbitrary dimension statement for  biatx  below, but
+c	 is  n o w h e r e   c h e c k e d   for.
+c
+c******  w o r k   a r e a  ******
+c  scrtch......of size	(k,k) , needed to contain bcoeffs of a piece of
+c	 the spline and its  k-1  derivatives
+c
+c******  o u t p u t  ******
+c  break.....breakpoint sequence, of length  l+1, contains (in increas-
+c	 ing order) the distinct points in the sequence  t(k),...,t(n+1)
+c  coef.....array of size (k,n), with  coef(i,j) = (i-1)st derivative of
+c	 spline at break(j) from the right
+c  l.....number of polynomial pieces which make up the spline in the in-
+c	 terval  (t(k), t(n+1))
+c
+c******  m e t h o d  ******
+c     for each breakpoint interval, the  k  relevant b-coeffs of the
+c  spline are found and then differenced repeatedly to get the b-coeffs
+c  of all the derivatives of the spline on that interval. the spline and
+c  its first  k-1  derivatives are then evaluated at the left end point
+c  of that interval, using  bsplvb  repeatedly to obtain the values of
+c  all b-splines of the appropriate order at that point.
+c
+c     parameter kmax = 20
+      integer k,l,n,   i,j,jp1,kmj,left,lsofar
+      real bcoef(n),break(1),coef(k,1),t(1),   scrtch(k,k)
+     *					      ,biatx(20),diff,fkmj,sum
+c    *					      ,biatx(kmax),diff,fkmj,sum
+c     dimension break(l+1),coef(k,l),t(n+k)
+current fortran standard makes it impossible to specify the length of
+c  break , coef  and  t  precisely without the introduction of otherwise
+c  superfluous additional arguments.
+      lsofar = 0
+      break(1) = t(k)
+      do 50 left=k,n
+c				 find the next nontrivial knot interval.
+	 if (t(left+1) .eq. t(left))	go to 50
+	 lsofar = lsofar + 1
+	 break(lsofar+1) = t(left+1)
+	 if (k .gt. 1)			go to 9
+	 coef(1,lsofar) = bcoef(left)
+					go to 50
+c	 store the k b-spline coeff.s relevant to current knot interval
+c			      in  scrtch(.,1) .
+    9	 do 10 i=1,k
+   10	    scrtch(i,1) = bcoef(left-k+i)
+c
+c	 for j=1,...,k-1, compute the  k-j  b-spline coeff.s relevant to
+c	 current knot interval for the j-th derivative by differencing
+c	 those for the (j-1)st derivative, and store in scrtch(.,j+1) .
+	 do 20 jp1=2,k
+	    j = jp1 - 1
+	    kmj = k - j
+	    fkmj = float(kmj)
+	    do 20 i=1,kmj
+	       diff = t(left+i) - t(left+i - kmj)
+	       if (diff .gt. 0.)  scrtch(i,jp1) =
+     *			     ((scrtch(i+1,j)-scrtch(i,j))/diff)*fkmj
+   20	       continue
+c
+c	 for  j = 0, ..., k-1, find the values at  t(left)  of the  j+1
+c	 b-splines of order  j+1  whose support contains the current
+c	 knot interval from those of order  j  (in  biatx ), then comb-
+c	 ine with the b-spline coeff.s (in scrtch(.,k-j) ) found earlier
+c	 to compute the (k-j-1)st derivative at  t(left)  of the given
+c	 spline.
+c	    note. if the repeated calls to  bsplvb  are thought to gene-
+c	 rate too much overhead, then replace the first call by
+c	    biatx(1) = 1.
+c	 and the subsequent call by the statement
+c	    j = jp1 - 1
+c	 followed by a direct copy of the lines
+c	    deltar(j) = t(left+j) - x
+c		   ......
+c	    biatx(j+1) = saved
+c	 from  bsplvb . deltal(kmax)  and  deltar(kmax)  would have to
+c	 appear in a dimension statement, of course.
+c
+	 call bsplvb ( t, 1, 1, t(left), left, biatx )
+	 coef(k,lsofar) = scrtch(1,k)
+	 do 30 jp1=2,k
+	    call bsplvb ( t, jp1, 2, t(left), left, biatx )
+	    kmj = k+1 - jp1
+	    sum = 0.
+	    do 28 i=1,jp1
+   28	       sum = biatx(i)*scrtch(i,kmj) + sum
+   30	    coef(kmj,lsofar) = sum
+   50	 continue
+      l = lsofar
+					return
+      end
diff --git a/math/deboor/bsplvd.f b/math/deboor/bsplvd.f
new file mode 100644
index 00000000..d48d0adc
--- /dev/null
+++ b/math/deboor/bsplvd.f
@@ -0,0 +1,111 @@
+      subroutine bsplvd ( t, k, x, left, a, dbiatx, nderiv )
+c  from  * a practical guide to splines *  by c. de boor
+calls bsplvb
+calculates value and deriv.s of all b-splines which do not vanish at x
+c
+c******  i n p u t  ******
+c  t	 the knot array, of length left+k (at least)
+c  k	 the order of the b-splines to be evaluated
+c  x	 the point at which these values are sought
+c  left  an integer indicating the left endpoint of the interval of
+c	 interest. the	k  b-splines whose support contains the interval
+c		(t(left), t(left+1))
+c	 are to be considered.
+c  a s s u m p t i o n	- - -  it is assumed that
+c		t(left) .lt. t(left+1)
+c	 division by zero will result otherwise (in  b s p l v b ).
+c	 also, the output is as advertised only if
+c		t(left) .le. x .le. t(left+1) .
+c  nderiv   an integer indicating that values of b-splines and their
+c	 derivatives up to but not including the  nderiv-th  are asked
+c	 for. ( nderiv	is replaced internally by the integer  m h i g h
+c	 in  (1,k)  closest to it.)
+c
+c******  w o r k   a r e a  ******
+c  a	 an array of order (k,k), to contain b-coeff.s of the derivat-
+c	 ives of a certain order of the  k  b-splines of interest.
+c
+c******  o u t p u t  ******
+c  dbiatx   an array of order (k,nderiv). its entry  (i,m)  contains
+c	 value of  (m-1)st  derivative of  (left-k+i)-th  b-spline of
+c	 order	k  for knot sequence  t , i=m,...,k, m=1,...,nderiv.
+c
+c******  m e t h o d  ******
+c  values at  x  of all the relevant b-splines of order k,k-1,...,
+c  k+1-nderiv  are generated via  bsplvb  and stored temporarily in
+c  dbiatx .  then, the b-coeffs of the required derivatives of the b-
+c  splines of interest are generated by differencing, each from the pre-
+c  ceding one of lower order, and combined with the values of b-splines
+c  of corresponding order in  dbiatx  to produce the desired values .
+c
+      integer k,left,nderiv,   i,ideriv,il,j,jlow,jp1mid,kp1,kp1mm
+     *			      ,ldummy,m,mhigh
+      real a(k,k),dbiatx(k,nderiv),t(1),x,   factor,fkp1mm,sum
+      mhigh = max0(min0(nderiv,k),1)
+c     mhigh is usually equal to nderiv.
+      kp1 = k+1
+      call bsplvb(t,kp1-mhigh,1,x,left,dbiatx)
+      if (mhigh .eq. 1) 		go to 99
+c     the first column of  dbiatx  always contains the b-spline values
+c     for the current order. these are stored in column k+1-current
+c     order  before  bsplvb  is called to put values for the next
+c     higher order on top of it.
+      ideriv = mhigh
+      do 15 m=2,mhigh
+	 jp1mid = 1
+	 do 11 j=ideriv,k
+	    dbiatx(j,ideriv) = dbiatx(jp1mid,1)
+   11	    jp1mid = jp1mid + 1
+	 ideriv = ideriv - 1
+	 call bsplvb(t,kp1-ideriv,2,x,left,dbiatx)
+   15	 continue
+c
+c     at this point,  b(left-k+i, k+1-j)(x) is in  dbiatx(i,j) for
+c     i=j,...,k and j=1,...,mhigh ('=' nderiv). in particular, the
+c     first column of  dbiatx  is already in final form. to obtain cor-
+c     responding derivatives of b-splines in subsequent columns, gene-
+c     rate their b-repr. by differencing, then evaluate at  x.
+c
+      jlow = 1
+      do 20 i=1,k
+	 do 19 j=jlow,k
+   19	    a(j,i) = 0.
+	 jlow = i
+   20	 a(i,i) = 1.
+c     at this point, a(.,j) contains the b-coeffs for the j-th of the
+c     k  b-splines of interest here.
+c
+      do 40 m=2,mhigh
+	 kp1mm = kp1 - m
+	 fkp1mm = float(kp1mm)
+	 il = left
+	 i = k
+c
+c	 for j=1,...,k, construct b-coeffs of  (m-1)st	derivative of
+c	 b-splines from those for preceding derivative by differencing
+c	 and store again in  a(.,j) . the fact that  a(i,j) = 0  for
+c	 i .lt. j  is used.
+	 do 25 ldummy=1,kp1mm
+	    factor = fkp1mm/(t(il+kp1mm) - t(il))
+c	    the assumption that t(left).lt.t(left+1) makes denominator
+c	    in	factor	nonzero.
+	    do 24 j=1,i
+   24	       a(i,j) = (a(i,j) - a(i-1,j))*factor
+	    il = il - 1
+   25	    i = i - 1
+c
+c	 for i=1,...,k, combine b-coeffs a(.,i) with b-spline values
+c	 stored in dbiatx(.,m) to get value of	(m-1)st  derivative of
+c	 i-th b-spline (of interest here) at  x , and store in
+c	 dbiatx(i,m). storage of this value over the value of a b-spline
+c	 of order m there is safe since the remaining b-spline derivat-
+c	 ives of the same order do not use this value due to the fact
+c	 that  a(j,i) = 0  for j .lt. i .
+   30	 do 40 i=1,k
+	    sum = 0.
+	    jlow = max0(i,m)
+	    do 35 j=jlow,k
+   35	       sum = a(j,i)*dbiatx(j,m) + sum
+   40	    dbiatx(i,m) = sum
+   99					return
+      end
diff --git a/math/deboor/bspp2d.f b/math/deboor/bspp2d.f
new file mode 100644
index 00000000..87c3433f
--- /dev/null
+++ b/math/deboor/bspp2d.f
@@ -0,0 +1,122 @@
+      subroutine bspp2d ( t, bcoef, n, k, m, scrtch, break, coef, l )
+c  from  * a practical guide to splines *  by c. de boor
+calls  bsplvb
+c  this is an extended version of  bsplpp  for use with tensor products
+c
+converts the b-representation  t, bcoef(.,j), n, k  of some spline into
+c  its pp-representation  break, coef(j,.,.), l, k , j=1, ..., m  .
+c
+c******  i n p u t  ******
+c  t.....knot sequence, of length  n+k
+c  bcoef(.,j) b-spline coefficient sequence, of length	n ,j=1,...,m
+c  n.....length of  bcoef  and	dimension of spline space  spline(k,t)
+c  k.....order of the spline
+c
+c  w a r n i n g  . . .  the restriction   k .le. kmax (= 20)	is impo-
+c	 sed by the arbitrary dimension statement for  biatx  below, but
+c	 is  n o w h e r e   c h e c k e d   for.
+c
+c  m	 number of data sets
+c
+c******  w o r k   a r e a  ******
+c  scrtch   of size  (k,k,m), needed to contain bcoeffs of a piece of
+c	 the spline and its  k-1  derivatives	for each of the m sets
+c
+c******  o u t p u t  ******
+c  break.....breakpoint sequence, of length  l+1, contains (in increas-
+
+c	 ing order) the distinct points in the sequence  t(k),...,t(n+1)
+c  coef(mm,.,.)  array of size (k,n), with  coef(mm,i,j) = (i-1)st der-
+c	 ivative of  mm-th  spline at break(j) from the right, mm=1,.,m
+c  l.....number of polynomial pieces which make up the spline in the in-
+c	 terval  (t(k), t(n+1))
+c
+c******  m e t h o d  ******
+c     for each breakpoint interval, the  k  relevant b-coeffs of the
+c  spline are found and then differenced repeatedly to get the b-coeffs
+
+c  of all the derivatives of the spline on that interval. the spline and
+c  its first  k-1  derivatives are then evaluated at the left end point
+
+c  of that interval, using  bsplvb  repeatedly to obtain the values of
+c  all b-splines of the appropriate order at that point.
+c
+c     parameter kmax = 20
+      integer k,l,m,n,	 i,j,jp1,kmj,left,lsofar,mm
+      real bcoef(n,m),break(1),coef(m,k,1),t(1),   scrtch(k,k,m)
+     *					      ,biatx(20),diff,fkmj,sum
+c
+c    *					      ,biatx(kmax),diff,fkmj,sum
+c     dimension break(l+1),coef(k,l),t(n+k)
+current fortran standard makes it impossible to specify the length of
+c  break , coef  and  t  precisely without the introduction of otherwise
+c  superfluous additional arguments.
+      lsofar = 0
+      break(1) = t(k)
+      do 50 left=k,n
+c				 find the next nontrivial knot interval.
+	 if (t(left+1) .eq. t(left))	go to 50
+	 lsofar = lsofar + 1
+	 break(lsofar+1) = t(left+1)
+	 if (k .gt. 1)			go to 9
+	 do 5 mm=1,m
+    5	    coef(mm,1,lsofar) = bcoef(left,mm)
+					go to 50
+c	 store the k b-spline coeff.s relevant to current knot interval
+
+c			      in  scrtch(.,1) .
+    9	 do 10 i=1,k
+	    do 10 mm=1,m
+   10	       scrtch(i,1,mm) = bcoef(left-k+i,mm)
+c
+c	 for j=1,...,k-1, compute the  k-j  b-spline coeff.s relevant to
+c	 current knot interval for the j-th derivative by differencing
+c	 those for the (j-1)st derivative, and store in scrtch(.,j+1) .
+
+	 do 20 jp1=2,k
+	    j = jp1 - 1
+	    kmj = k - j
+	    fkmj = float(kmj)
+	    do 20 i=1,kmj
+	       diff = (t(left+i) - t(left+i - kmj))/fkmj
+	       if (diff .le. 0.)	 go to 20
+	       do 15 mm=1,m
+   15		  scrtch(i,jp1,mm) =
+     *		  (scrtch(i+1,j,mm) - scrtch(i,j,mm))/diff
+   20	       continue
+c
+c	 for  j = 0, ..., k-1, find the values at  t(left)  of the  j+1
+
+c	 b-splines of order  j+1  whose support contains the current
+c	 knot interval from those of order  j  (in  biatx ), then comb-
+
+c	 ine with the b-spline coeff.s (in scrtch(.,k-j) ) found earlier
+c	 to compute the (k-j-1)st derivative at  t(left)  of the given
+c	 spline.
+c	    note. if the repeated calls to  bsplvb  are thought to gene-
+c	 rate too much overhead, then replace the first call by
+c	    biatx(1) = 1.
+c	 and the subsequent call by the statement
+c	    j = jp1 - 1
+c	 followed by a direct copy of the lines
+c	    deltar(j) = t(left+j) - x
+c		   ......
+c	    biatx(j+1) = saved
+c	 from  bsplvb . deltal(kmax)  and  deltar(kmax)  would have to
+c	 appear in a dimension statement, of course.
+c
+	 call bsplvb ( t, 1, 1, t(left), left, biatx )
+	 do 25 mm=1,m
+   25	    coef(mm,k,lsofar) = scrtch(1,k,mm)
+	 do 30 jp1=2,k
+	    call bsplvb ( t, jp1, 2, t(left), left, biatx )
+	    kmj = k+1 - jp1
+	    do 30 mm=1,m
+	       sum = 0.
+	       do 28 i=1,jp1
+   28		  sum = biatx(i)*scrtch(i,kmj,mm) + sum
+   30	       coef(mm,kmj,lsofar) = sum
+   50	 continue
+      l = lsofar
+					return
+      end
diff --git a/math/deboor/bvalue.f b/math/deboor/bvalue.f
new file mode 100644
index 00000000..6b038939
--- /dev/null
+++ b/math/deboor/bvalue.f
@@ -0,0 +1,138 @@
+      real function bvalue ( t, bcoef, n, k, x, jderiv )
+c  from  * a practical guide to splines *  by c. de boor
+calls  interv
+c
+calculates value at  x	of  jderiv-th derivative of spline from b-repr.
+c  the spline is taken to be continuous from the right.
+c
+c******  i n p u t ******
+c  t, bcoef, n, k......forms the b-representation of the spline  f  to
+c	 be evaluated. specifically,
+c  t.....knot sequence, of length  n+k, assumed nondecreasing.
+c  bcoef.....b-coefficient sequence, of length	n .
+c  n.....length of  bcoef  and dimension of spline(k,t),
+c	 a s s u m e d	positive .
+c  k.....order of the spline .
+c
+c  w a r n i n g . . .	 the restriction  k .le. kmax (=20)  is imposed
+c	 arbitrarily by the dimension statement for  aj, dl, dr  below,
+c	 but is  n o w h e r e	c h e c k e d  for.
+c
+c  x.....the point at which to evaluate .
+c  jderiv.....integer giving the order of the derivative to be evaluated
+c	 a s s u m e d	to be zero or positive.
+c
+c******  o u t p u t  ******
+c  bvalue.....the value of the (jderiv)-th derivative of  f  at  x .
+c
+c******  m e t h o d  ******
+c     the nontrivial knot interval  (t(i),t(i+1))  containing  x  is lo-
+c  cated with the aid of  interv . the	k  b-coeffs of	f  relevant for
+c  this interval are then obtained from  bcoef (or taken to be zero if
+c  not explicitly available) and are then differenced  jderiv  times to
+c  obtain the b-coeffs of  (d**jderiv)f  relevant for that interval.
+c  precisely, with  j = jderiv, we have from x.(12) of the text that
+c
+c     (d**j)f  =  sum ( bcoef(.,j)*b(.,k-j,t) )
+c
+c  where
+c		    / bcoef(.), 		    ,  j .eq. 0
+c		    /
+c    bcoef(.,j)  =  / bcoef(.,j-1) - bcoef(.-1,j-1)
+c		    / ----------------------------- ,  j .gt. 0
+c		    /	 (t(.+k-j) - t(.))/(k-j)
+c
+c     then, we use repeatedly the fact that
+c
+c    sum ( a(.)*b(.,m,t)(x) )  =  sum ( a(.,x)*b(.,m-1,t)(x) )
+c  with
+c		  (x - t(.))*a(.) + (t(.+m-1) - x)*a(.-1)
+c    a(.,x)  =	  ---------------------------------------
+c		  (x - t(.))	  + (t(.+m-1) - x)
+c
+c  to write  (d**j)f(x)  eventually as a linear combination of b-splines
+c  of order  1 , and the coefficient for  b(i,1,t)(x)  must then be the
+c  desired number  (d**j)f(x). (see x.(17)-(19) of text).
+c
+c     parameter kmax = 20
+      integer jderiv,k,n,   i,ilo,imk,j,jc,jcmin,jcmax,jj,kmj,km1,mflag
+     *			   ,nmi,jdrvp1
+      real bcoef(n),t(1),x,   aj(20),dl(20),dr(20),fkmj
+c     real bcoef(n),t(1),x,   aj(kmax),dl(kmax),dr(kmax),fkmj
+c     dimension t(n+k)
+current fortran standard makes it impossible to specify the length of  t
+c  precisely without the introduction of otherwise superfluous addition-
+c  al arguments.
+      bvalue = 0.
+      if (jderiv .ge. k)		go to 99
+c
+c  *** find  i	 s.t.	1 .le. i .lt. n+k   and   t(i) .lt. t(i+1)   and
+c      t(i) .le. x .lt. t(i+1) . if no such i can be found,  x	lies
+c      outside the support of  the spline  f  and  bvalue = 0.
+c      (the asymmetry in this choice of  i  makes  f  rightcontinuous)
+      call interv ( t, n+k, x, i, mflag )
+      if (mflag .ne. 0) 		go to 99
+c  *** if k = 1 (and jderiv = 0), bvalue = bcoef(i).
+      km1 = k - 1
+      if (km1 .gt. 0)			go to 1
+      bvalue = bcoef(i)
+					go to 99
+c
+c  *** store the k b-spline coefficients relevant for the knot interval
+c     (t(i),t(i+1)) in aj(1),...,aj(k) and compute dl(j) = x - t(i+1-j),
+c     dr(j) = t(i+j) - x, j=1,...,k-1 . set any of the aj not obtainable
+c     from input to zero. set any t.s not obtainable equal to t(1) or
+c     to t(n+k) appropriately.
+    1 jcmin = 1
+      imk = i - k
+      if (imk .ge. 0)			go to 8
+      jcmin = 1 - imk
+      do 5 j=1,i
+    5	 dl(j) = x - t(i+1-j)
+      do 6 j=i,km1
+	 aj(k-j) = 0.
+    6	 dl(j) = dl(i)
+					go to 10
+    8 do 9 j=1,km1
+    9	 dl(j) = x - t(i+1-j)
+c
+   10 jcmax = k
+      nmi = n - i
+      if (nmi .ge. 0)			go to 18
+      jcmax = k + nmi
+      do 15 j=1,jcmax
+   15	 dr(j) = t(i+j) - x
+      do 16 j=jcmax,km1
+	 aj(j+1) = 0.
+   16	 dr(j) = dr(jcmax)
+					go to 20
+   18 do 19 j=1,km1
+   19	 dr(j) = t(i+j) - x
+c
+   20 do 21 jc=jcmin,jcmax
+   21	 aj(jc) = bcoef(imk + jc)
+c
+c		*** difference the coefficients  jderiv  times.
+      if (jderiv .eq. 0)		go to 30
+      do 23 j=1,jderiv
+	 kmj = k-j
+	 fkmj = float(kmj)
+	 ilo = kmj
+	 do 23 jj=1,kmj
+	    aj(jj) = ((aj(jj+1) - aj(jj))/(dl(ilo) + dr(jj)))*fkmj
+   23	    ilo = ilo - 1
+c
+c  *** compute value at  x  in (t(i),t(i+1)) of jderiv-th derivative,
+c     given its relevant b-spline coeffs in aj(1),...,aj(k-jderiv).
+   30 if (jderiv .eq. km1)		go to 39
+      jdrvp1 = jderiv + 1
+      do 33 j=jdrvp1,km1
+	 kmj = k-j
+	 ilo = kmj
+	 do 33 jj=1,kmj
+	    aj(jj) = (aj(jj+1)*dl(ilo) + aj(jj)*dr(jj))/(dl(ilo)+dr(jj))
+   33	    ilo = ilo - 1
+   39 bvalue = aj(1)
+c
+   99					return
+      end
diff --git a/math/deboor/chol1d.f b/math/deboor/chol1d.f
new file mode 100644
index 00000000..fa0434ab
--- /dev/null
+++ b/math/deboor/chol1d.f
@@ -0,0 +1,58 @@
+      subroutine chol1d ( p, v, qty, npoint, ncol, u, qu )
+c  from  * a practical guide to splines *  by c. de boor
+c  from  * a practical guide to splines *  by c. de boor
+c to be called in  s m o o t h
+constructs the upper three diags. in v(i,j), i=2,,npoint-1, j=1,3, of
+c  the matrix  6*(1-p)*q-transp.*(d**2)*q + p*r, then computes its
+c  l*l-transp. decomposition and stores it also in v, then applies
+c  forward and backsubstitution to the right side q-transp.*y in  qty
+c  to obtain the solution in  u .
+      integer ncol,npoint,   i,npm1,npm2
+      real p,qty(npoint),qu(npoint),u(npoint),v(npoint,7),   prev,ratio
+     *	  ,six1mp,twop
+      npm1 = npoint - 1
+c     construct 6*(1-p)*q-transp.*(d**2)*q  +  p*r
+      six1mp = 6.*(1.-p)
+      twop = 2.*p
+      do 2 i=2,npm1
+	 v(i,1) = six1mp*v(i,5) + twop*(v(i-1,4)+v(i,4))
+	 v(i,2) = six1mp*v(i,6) + p*v(i,4)
+    2	 v(i,3) = six1mp*v(i,7)
+      npm2 = npoint - 2
+      if (npm2 .ge. 2)			go to 10
+      u(1) = 0.
+      u(2) = qty(2)/v(2,1)
+      u(3) = 0.
+					go to 41
+c  factorization
+   10 do 20 i=2,npm2
+	 ratio = v(i,2)/v(i,1)
+	 v(i+1,1) = v(i+1,1) - ratio*v(i,2)
+	 v(i+1,2) = v(i+1,2) - ratio*v(i,3)
+	 v(i,2) = ratio
+	 ratio = v(i,3)/v(i,1)
+	 v(i+2,1) = v(i+2,1) - ratio*v(i,3)
+   20	 v(i,3) = ratio
+c
+c  forward substitution
+      u(1) = 0.
+      v(1,3) = 0.
+      u(2) = qty(2)
+      do 30 i=2,npm2
+   30	 u(i+1) = qty(i+1) - v(i,2)*u(i) - v(i-1,3)*u(i-1)
+c  back substitution
+      u(npoint) = 0.
+      u(npm1) = u(npm1)/v(npm1,1)
+      i = npm2
+   40	 u(i) = u(i)/v(i,1)-u(i+1)*v(i,2)-u(i+2)*v(i,3)
+	 i = i - 1
+	 if (i .gt. 1)			go to 40
+c  construct q*u
+   41 prev = 0.
+      do 50 i=2,npoint
+	 qu(i) = (u(i) - u(i-1))/v(i-1,4)
+	 qu(i-1) = qu(i) - prev
+   50	 prev = qu(i)
+      qu(npoint) = -qu(npoint)
+					return
+      end
diff --git a/math/deboor/colloc_io.f b/math/deboor/colloc_io.f
new file mode 100644
index 00000000..023612f2
--- /dev/null
+++ b/math/deboor/colloc_io.f
@@ -0,0 +1,139 @@
+      subroutine colloc(aleft,aright,lbegin,iorder,ntimes,addbrk,relerr,ier)
+c  from  * a practical guide to splines *  by c. de boor
+chapter xv, example. solution of an ode by collocation.
+calls colpnt, difequ(ppvalu(interv)), knots, eqblok(putit(difequ*,
+c     bsplvd(bsplvb)))), slvblk(various subprograms), bsplpp(bsplvb*),
+c     newnot
+c
+c******  i n p u t  ******
+c  aleft, aright  endpoints of interval of approximation
+c  lbegin   initial number of polynomial pieces in the approximation.
+c	    a uniform breakpoint sequence is chosen.
+c  iorder   order of polynomial pieces in the approximation
+c  ntimes   number of passes through  n e w n o t  to be made
+c  addbrk   the number (possibly fractional) of breaks to be added per
+c	    pass through newnot. e.g., if addbrk = .33334, then a break-
+c	    point will be added at every third pass through newnot.
+c  relerr   a tolerance. newton iteration is stopped if the difference
+c	    between the b-coeffs of two successive iterates is no more
+c	    than  relerr*(absol.largest b-coefficient).
+c
+c******  p r i n t e d	 o u t p u t  ******
+c     consists of the pp-representation of the approximate solution,
+c     and of the error at selected points.
+c
+c******  m e t h o d  ******
+c  the m-th order ordinary differential equation with  m  side condit-
+c  ions, to be specified in subroutine	d i f e q u , is solved approx-
+c  imately by collocation.
+c  the approximation  f  to the solution  g  is pp of order  k+m  with
+c  l  pieces and  m-1 continuous derivatives.  f  is determined by the
+c  requirement that it satisfy the d.e. at  k  points per interval (to
+c  be specified in  c o l p n t ) and the  m  side conditions.
+c     this usually nonlinear system of equations for  f  is solved by
+c  newton's method. the resulting linear system for the b-coeffs of an
+c  iterate is constructed appropriately in  e q b l o k  and then solved
+c  in  s l v b l k , a program designed to solve  a l m o s t  b l o c k
+c  d i a g o n a l  linear systems efficiently.
+c     there is an opportunity to attempt improvement of the breakpoint
+c  sequence (both in number and location) through use of  n e w n o t .
+c
+c     parameter npiece=100, ndim=200, ncoef=2000, lenblk=2000
+c     integer iorder,lbegin,ntimes,   i,iflag,ii,integs(3,npiece),iside
+c    *			,iter,itermx,k,kpm,l,lnew,m,n,nbloks,nncoef,nt
+      integer iorder,lbegin,ntimes,   i,iflag,ii,integs(3,100),iside
+     *		  ,iter,itermx,k,kpm,l,lnew,m,n,nbloks,ncoef,nncoef,nt
+c     real addbrk,aleft,aright,relerr,	 a(ndim),amax,asave(ndim)
+c    *	   ,b(ndim),bloks(lenblk),break,coef,dx,err,rho,t(ndim)
+c    *	   ,templ(lenblk),temps(ndim),xside
+      real addbrk,aleft,aright,relerr,	 a(200),amax,asave(200)
+     *	   ,b(200),bloks(2000),break,coef,dx,err,rho,t(200)
+     *	   ,templ(2000),temps(200),xside
+      equivalence (bloks,templ)
+c     common /approx/ break(npiece), coef(ncoef), l,kpm
+      common /approx/ break(100), coef(2000), l,kpm
+      common /side/ m, iside, xside(10)
+      common /other/ itermx,k,rho(19)
+      data ncoef,lenblk / 2000,2000 /
+c
+      ier = 0
+      kpm = iorder
+      if (lbegin*kpm .gt. ncoef)	go to 999
+c  *** set the various parameters concerning the particular dif.equ.
+c     including a first approx. in case the de is to be solved by
+c     iteration ( itermx .gt. 0) .
+      call difequ (1, temps(1), temps )
+c  *** obtain the  k  collocation points for the standard interval.
+      k = kpm - m
+      call colpnt ( k, rho )
+c  *** the following five statements could be replaced by a read in or-
+c     der to obtain a specific (nonuniform) spacing of the breakpnts.
+      dx = (aright - aleft)/float(lbegin)
+      temps(1) = aleft
+      do 4 i=2,lbegin
+    4	 temps(i) = temps(i-1) + dx
+      temps(lbegin+1) = aright
+c  *** generate, in knots, the required knots t(1),...,t(n+kpm).
+      call knots ( temps, lbegin, kpm, t, n )
+      nt = 1
+c  *** generate the almost block diagonal coefficient matrix  bloks  and
+c     right side  b  from collocation equations and side conditions.
+c     then solve via  slvblk , obtaining the b-representation of the ap-
+c     proximation in  t , a ,  n  , kpm  .
+   10	 call eqblok(t,n,kpm,temps,a,bloks,lenblk,integs,nbloks,b)
+	 call slvblk(bloks,integs,nbloks,b,temps,a,iflag)
+	 iter = 1
+	 if (itermx .le. 1)		go to 30
+c  *** save b-spline coeff. of current approx. in  asave , then get new
+c     approx. and compare with old. if coeff. are more than  relerr
+c     apart (relatively) or if no. of iterations is less than  itermx ,
+c     continue iterating.
+   20	    call bsplpp(t,a,n,kpm,templ,break,coef,l)
+	    do 25 i=1,n
+   25	       asave(i) = a(i)
+	    call eqblok(t,n,kpm,temps,a,bloks,lenblk,integs,nbloks,b)
+	    call slvblk(bloks,integs,nbloks,b,temps,a,iflag)
+	    err = 0.
+	    amax = 0.
+	    do 26 i=1,n
+	       amax = amax1(amax,abs(a(i)))
+   26	       err = amax1(err,abs(a(i)-asave(i)))
+	    if (err .le. relerr*amax)	go to 30
+	    iter = iter+1
+	    if (iter .lt. itermx)	go to 20
+c  *** iteration (if any) completed. print out approx. based on current
+c     breakpoint sequence, then try to improve the sequence.
+   30	 print 630,kpm,l,n,(break(i),i=2,l)
+  630	 format(47h approximation from a space of splines of order,i3
+     *	       ,4h on ,i3,11h intervals,/13h of dimension,i4
+     *	       ,16h.  breakpoints -/(5e20.10))
+ 	 if (itermx .gt. 0)  print 635,iter,itermx
+  635	 format(6h after,i3,3h of,i3,20h allowed iterations,)
+	 call bsplpp(t,a,n,kpm,templ,break,coef,l)
+ 	 print 637
+  637	 format(46h the pp representation of the approximation is)
+ 	 do 38 i=1,l
+ 	    ii = (i-1)*kpm
+   38	    print 638, break(i),(coef(ii+j),j=1,kpm)
+  638	 format(f9.3,e13.6,10e11.3)
+c  *** the following call is provided here for possible further analysis
+c     of the approximation specific to the problem being solved.
+c     it is, of course, easily omitted.
+ 	 call difequ ( 4, temps(1), temps )
+c
+	 if (nt .gt. ntimes)		return
+c  *** from the pp-rep. of the current approx., obtain in  newnot  a new
+c     (and possibly better) sequence of breakpoints, adding (on the ave-
+c     rage)  a d d b r k  breakpoints per pass through newnot.
+	 lnew = lbegin + int(float(nt)*addbrk)
+	 if (lnew*kpm .gt. ncoef)	go to 999
+	 call newnot(break,coef,l,kpm,temps,lnew,templ)
+	 call knots(temps,lnew,kpm,t,n)
+	 nt = nt + 1
+					go to 10
+  999 nncoef = ncoef
+      print 699,nncoef
+  699 format(11h **********/23h the assigned dimension,i5
+     *	    ,25h for  coef  is too small.)
+ 					return
+      end
diff --git a/math/deboor/colpnt_io.f b/math/deboor/colpnt_io.f
new file mode 100644
index 00000000..715541eb
--- /dev/null
+++ b/math/deboor/colpnt_io.f
@@ -0,0 +1,65 @@
+      subroutine colpnt(k,rho)
+c  from  * a practical guide to splines *  by c. de boor
+c  the	k collocation points for the standard interval (-1,1) are sup-
+c  plied here as the zeros of the legendre polynomial of degree k ,
+c  provided  k .le. 8 . otherwise, uniformly spaced points are given.
+      integer k,  j
+      real rho(k),  fkm1o2
+      if (k .gt. 8)		       go to 99
+				       go to (10,20,30,40,50,60,70,80),k
+   10 rho(1) = 0.
+				       return
+c$    (single/double) dpdata
+   20 rho(2) = .57735 02691 89626 d0
+      rho(1) = - rho(2)
+				       return
+   30 rho(3) = .77459 66692 41483 d0
+      rho(1) = - rho(3)
+      rho(2) = 0.
+				       return
+   40 rho(3) = .33998 10435 84856 d0
+      rho(2) = - rho(3)
+      rho(4) = .86113 63115 94053 d0
+      rho(1) = - rho(4)
+				       return
+   50 rho(4) = .53846 93101 05683 d0
+      rho(2) = - rho(4)
+      rho(5) = .90617 98459 38664 d0
+      rho(1) = - rho(5)
+      rho(3) = 0.
+				       return
+   60 rho(4) = .23861 91860 83197 d0
+      rho(3) = - rho(4)
+      rho(5) = .66120 93864 66265 d0
+      rho(2) = - rho(5)
+      rho(6) = .93246 95142 03152 d0
+      rho(1) = - rho(6)
+				       return
+   70 rho(5) = .40584 51513 77397 d0
+      rho(3) = - rho(5)
+      rho(6) = .74153 11855 99394 d0
+      rho(2) = - rho(6)
+      rho(7) = .94910 79123 42759 d0
+      rho(1) = - rho(7)
+      rho(4) = 0.
+				       return
+   80 rho(5) = .18343 46424 95650 d0
+      rho(4) = - rho(5)
+      rho(6) = .52553 24099 16329 d0
+      rho(3) = - rho(6)
+      rho(7) = .79666 64774 13627 d0
+      rho(2) = - rho(7)
+      rho(8) = .96028 98564 97536 d0
+      rho(1) = - rho(8)
+c$lbl dpdata
+				       return
+c  if k .gt. 8, use equispaced points, but print warning
+   99 print 699,k
+  699 format(11h **********/
+     *	     49h equispaced collocation points are used since k =,i2,
+     *	     19h is greater than 8.)
+      fkm1o2 = float(k-1)/2.
+      do 100 j=1,k
+  100	 rho(j) = float(j-1)/fkm1o2 - 1.
+				       return
+      end
diff --git a/math/deboor/cubspl.f b/math/deboor/cubspl.f
new file mode 100644
index 00000000..4bb54964
--- /dev/null
+++ b/math/deboor/cubspl.f
@@ -0,0 +1,119 @@
+      subroutine cubspl ( tau, c, n, ibcbeg, ibcend )
+c  from  * a practical guide to splines *  by c. de boor
+c     ************************	input  ***************************
+c     n = number of data points. assumed to be .ge. 2.
+c     (tau(i), c(1,i), i=1,...,n) = abscissae and ordinates of the
+c	 data points. tau is assumed to be strictly increasing.
+c     ibcbeg, ibcend = boundary condition indicators, and
+c     c(2,1), c(2,n) = boundary condition information. specifically,
+c	 ibcbeg = 0  means no boundary condition at tau(1) is given.
+c	    in this case, the not-a-knot condition is used, i.e. the
+c	    jump in the third derivative across tau(2) is forced to
+c	    zero, thus the first and the second cubic polynomial pieces
+c	    are made to coincide.)
+c	 ibcbeg = 1  means that the slope at tau(1) is made to equal
+c	    c(2,1), supplied by input.
+c	 ibcbeg = 2  means that the second derivative at tau(1) is
+c	    made to equal c(2,1), supplied by input.
+c	 ibcend = 0, 1, or 2 has analogous meaning concerning the
+c	    boundary condition at tau(n), with the additional infor-
+c	    mation taken from c(2,n).
+c     ***********************  output  **************************
+c     c(j,i), j=1,...,4; i=1,...,l (= n-1) = the polynomial coefficients
+c	 of the cubic interpolating spline with interior knots (or
+c	 joints) tau(2), ..., tau(n-1). precisely, in the interval
+c	 interval (tau(i), tau(i+1)), the spline f is given by
+c	    f(x) = c(1,i)+h*(c(2,i)+h*(c(3,i)+h*c(4,i)/3.)/2.)
+c	 where h = x - tau(i). the function program *ppvalu* may be
+c	 used to evaluate f or its derivatives from tau,c, l = n-1,
+c	 and k=4.
+      integer ibcbeg,ibcend,n,	 i,j,l,m
+      real c(4,n),tau(n),   divdf1,divdf3,dtau,g
+c****** a tridiagonal linear system for the unknown slopes s(i) of
+c  f  at tau(i), i=1,...,n, is generated and then solved by gauss elim-
+c  ination, with s(i) ending up in c(2,i), all i.
+c     c(3,.) and c(4,.) are used initially for temporary storage.
+      l = n-1
+compute first differences of tau sequence and store in c(3,.). also,
+compute first divided difference of data and store in c(4,.).
+      do 10 m=2,n
+	 c(3,m) = tau(m) - tau(m-1)
+   10	 c(4,m) = (c(1,m) - c(1,m-1))/c(3,m)
+construct first equation from the boundary condition, of the form
+c	      c(4,1)*s(1) + c(3,1)*s(2) = c(2,1)
+      if (ibcbeg-1)			11,15,16
+   11 if (n .gt. 2)			go to 12
+c     no condition at left end and n = 2.
+      c(4,1) = 1.
+      c(3,1) = 1.
+      c(2,1) = 2.*c(4,2)
+					go to 25
+c     not-a-knot condition at left end and n .gt. 2.
+   12 c(4,1) = c(3,3)
+      c(3,1) = c(3,2) + c(3,3)
+      c(2,1) =((c(3,2)+2.*c(3,1))*c(4,2)*c(3,3)+c(3,2)**2*c(4,3))/c(3,1)
+					go to 19
+c     slope prescribed at left end.
+   15 c(4,1) = 1.
+      c(3,1) = 0.
+					go to 18
+c     second derivative prescribed at left end.
+   16 c(4,1) = 2.
+      c(3,1) = 1.
+      c(2,1) = 3.*c(4,2) - c(3,2)/2.*c(2,1)
+   18 if(n .eq. 2)			go to 25
+c  if there are interior knots, generate the corresp. equations and car-
+c  ry out the forward pass of gauss elimination, after which the m-th
+c  equation reads    c(4,m)*s(m) + c(3,m)*s(m+1) = c(2,m).
+   19 do 20 m=2,l
+	 g = -c(3,m+1)/c(4,m-1)
+	 c(2,m) = g*c(2,m-1) + 3.*(c(3,m)*c(4,m+1)+c(3,m+1)*c(4,m))
+   20	 c(4,m) = g*c(3,m-1) + 2.*(c(3,m) + c(3,m+1))
+construct last equation from the second boundary condition, of the form
+c	    (-g*c(4,n-1))*s(n-1) + c(4,n)*s(n) = c(2,n)
+c     if slope is prescribed at right end, one can go directly to back-
+c     substitution, since c array happens to be set up just right for it
+c     at this point.
+      if (ibcend-1)			21,30,24
+   21 if (n .eq. 3 .and. ibcbeg .eq. 0) go to 22
+c     not-a-knot and n .ge. 3, and either n.gt.3 or  also not-a-knot at
+c     left end point.
+      g = c(3,n-1) + c(3,n)
+      c(2,n) = ((c(3,n)+2.*g)*c(4,n)*c(3,n-1)
+     *		  + c(3,n)**2*(c(1,n-1)-c(1,n-2))/c(3,n-1))/g
+      g = -g/c(4,n-1)
+      c(4,n) = c(3,n-1)
+					go to 29
+c     either (n=3 and not-a-knot also at left) or (n=2 and not not-a-
+c     knot at left end point).
+   22 c(2,n) = 2.*c(4,n)
+      c(4,n) = 1.
+					go to 28
+c     second derivative prescribed at right endpoint.
+   24 c(2,n) = 3.*c(4,n) + c(3,n)/2.*c(2,n)
+      c(4,n) = 2.
+					go to 28
+   25 if (ibcend-1)			26,30,24
+   26 if (ibcbeg .gt. 0)		go to 22
+c     not-a-knot at right endpoint and at left endpoint and n = 2.
+      c(2,n) = c(4,n)
+					go to 30
+   28 g = -1./c(4,n-1)
+complete forward pass of gauss elimination.
+   29 c(4,n) = g*c(3,n-1) + c(4,n)
+      c(2,n) = (g*c(2,n-1) + c(2,n))/c(4,n)
+carry out back substitution
+   30 j = l
+   40	 c(2,j) = (c(2,j) - c(3,j)*c(2,j+1))/c(4,j)
+	 j = j - 1
+	 if (j .gt. 0)			go to 40
+c****** generate cubic coefficients in each interval, i.e., the deriv.s
+c  at its left endpoint, from value and slope at its endpoints.
+      do 50 i=2,n
+	 dtau = c(3,i)
+	 divdf1 = (c(1,i) - c(1,i-1))/dtau
+	 divdf3 = c(2,i-1) + c(2,i) - 2.*divdf1
+	 c(3,i-1) = 2.*(divdf1 - c(2,i-1) - divdf3)/dtau
+   50	 c(4,i-1) = (divdf3/dtau)*(6./dtau)
+					return
+      end
diff --git a/math/deboor/cwidth.f b/math/deboor/cwidth.f
new file mode 100644
index 00000000..93b976b6
--- /dev/null
+++ b/math/deboor/cwidth.f
@@ -0,0 +1,220 @@
+      subroutine cwidth ( w,b,nequ,ncols,integs,nbloks, d, x,iflag )
+c  this program is a variation of the theme in the algorithm bandet1
+c  by martin and wilkinson (numer.math. 9(1976)279-307). it solves
+c  the linear system
+c			    a*x  =  b
+c  of  nequ  equations in case	a  is almost block diagonal with all
+c  blocks having  ncols  columns using no more storage than it takes to
+
+c  store the interesting part of  a . such systems occur in the determ-
+
+c  ination of the b-spline coefficients of a spline approximation.
+c
+c			    parameters
+c  w	 on input, a two-dimensional array of size (nequ,ncols) contain-
+c	 ing the interesting part of the almost block diagonal coeffici-
+c	 ent matrix  a (see description and example below). the array
+c	 integs  describes the storage scheme.
+c	 on output, w  contains the upper triangular factor  u	of the
+c	 lu factorization of a possibly permuted version of  a . in par-
+c	 ticular, the determinant of  a  could now be found as
+c	     iflag*w(1,1)*w(2,1)* ... * w(nequ,1)  .
+c  b	 on input, the right side of the linear system, of length  nequ.
+c	 the contents of  b  are changed during execution.
+c  nequ  number of equations in system
+c  ncols block width, i.e., number of columns in each block.
+c  integs  integer array, of size (2,nequ), describing the block struct-
+c	 ure of  a .
+c	    integs(1,i) = no. of rows in block i	       =  nrow
+c	    integs(2,i) = no. of elimination steps in block i
+c			= overhang over next block	       =  last
+c  nbloks  number of blocks
+c  d	 work array, to contain row sizes . if storage is scarce, the
+c	 array	x  could be used in the calling sequence for  d .
+c  x	 on output, contains computed solution (if iflag .ne. 0), of
+c	 length  nequ .
+c  iflag  on output, integer
+c	  = (-1)**(no.of interchanges during elimination)
+c		 if  a	is invertible
+c	  =  0	 if  a	is singular
+c
+c	 ------  block structure of  a	------
+c     the interesting part of  a  is taken to consist of  nbloks  con-
+c  secutive blocks, with the i-th block made up of  nrowi = integs(1,i)
+
+c  consecutive rows and  ncols	consecutive columns of	a , and with
+c  the first  lasti = integs(2,i) columns to the left of the next block.
+c  these blocks are stored consecutively in the workarray  w .
+c     for example, here is an 11th order matrix and its arrangement in
+c  the workarray  w . (the interesting entries of  a  are indicated by
+c  their row and column index modulo 10.)
+c
+c		   ---	 a   ---			  ---	w   ---
+
+c
+c		      nrow1=3
+c	   11 12 13 14					   11 12 13 14
+c	   21 22 23 24					   21 22 23 24
+c	   31 32 33 34	    nrow2=2			   31 32 33 34
+c   last1=2	 43 44 45 46				   43 44 45 46
+c		 53 54 55 56	     nrow3=3		   53 54 55 56
+c	  last2=3	  66 67 68 69			   66 67 68 69
+c			  76 77 78 79			   76 77 78 79
+c			  86 87 88 89	nrow4=1 	   86 87 88 89
+c		   last3=1   97 98 99 90   nrow5=2	   97 98 99 90
+c		      last4=1	08 09 00 01		   08 09 00 01
+c				18 19 10 11		   18 19 10 11
+c			 last5=4
+c
+c  for this interpretation of  a  as an almost block diagonal matrix,
+c  we have  nbloks = 5 , and the integs array is
+c
+c			 i=  1	 2   3	 4   5
+c		   k=
+c  integs(k,i) =      1      3	 2   3	 1   2
+c		      2      2	 3   1	 1   4
+c
+c	--------  method  --------
+c     gauss elimination with scaled partial pivoting is used, but mult-
+
+c  ipliers are	n o t  s a v e d  in order to save storage. rather, the
+
+c  right side is operated on during elimination.
+c     the two parameters
+c		   i p v t e q	 and  l a s t e q
+c  are used to keep track of the action.  ipvteq is the index of the
+c  variable to be eliminated next, from equations  ipvteq+1,...,lasteq,
+
+c  using equation  ipvteq (possibly after an interchange) as the pivot
+c  equation. the entries in the pivot column are  a l w a y s  in column
+c  1 of  w . this is accomplished by putting the entries in rows
+c  ipvteq+1,...,lasteq	revised by the elimination of the  ipvteq-th
+c  variable one to the left in	w . in this way, the columns of the
+c  equations in a given block (as stored in  w ) will be aligned with
+c  those of the next block at the moment when these next equations be-
+c  come involved in the elimination process.
+c     thus, for the above example, the first elimination steps proceed
+c  as follows.
+c
+c  *11 12 13 14    11 12 13 14	  11 12 13 14	 11 12 13 14
+c  *21 22 23 24   *22 23 24	  22 23 24	 22 23 24
+c  *31 32 33 34   *32 33 34	 *33 34 	 33 34
+c   43 44 45 46    43 44 45 46	 *43 44 45 46	*44 45 46	 etc.
+c   53 54 55 56    53 54 55 56	 *53 54 55 56	*54 55 56
+c   66 67 68 69    66 67 68 69	  66 67 68 69	 66 67 68 69
+c	 .		.	       .	      .
+c
+c     in all other respects, the procedure is standard, including the
+c  scaled partial pivoting.
+c
+      integer nbloks, ipvtp1, jmax
+      integer iflag,integs(2,nbloks),ncols,nequ,   i,ii,icount,ipvteq
+     *			   ,istar,j,lastcl,lasteq,lasti,nexteq,nrowad
+      real b(nequ),d(nequ),w(nequ,ncols),x(nequ),   awi1od,colmax
+     *	   ,ratio,sum				   ,rowmax,temp
+      iflag = 1
+      ipvteq = 0
+      lasteq = 0
+c				  the i-loop runs over the blocks
+      do 50 i=1,nbloks
+c
+c	 the equations for the current block are added to those current-
+c	 ly involved in the elimination process, by increasing	lasteq
+c	 by  integs(1,i) after the rowsize of these equations has been
+c	 recorded in the array	d .
+c
+	 nrowad = integs(1,i)
+	 do 10 icount=1,nrowad
+	    nexteq = lasteq + icount
+	    rowmax = 0.
+	    do 5 j=1,ncols
+    5	       rowmax = amax1(rowmax,abs(w(nexteq,j)))
+	    if (rowmax .eq. 0.) 	go to 999
+   10	    d(nexteq) = rowmax
+	 lasteq = lasteq + nrowad
+c
+c	 there will be	lasti = integs(2,i)  elimination steps before
+c	 the equations in the next block become involved. further,
+c	 l a s t c l  records the number of columns involved in the cur-
+c	 rent elimination step. it starts equal to  ncols  when a block
+
+c	 first becomes involved and then drops by one after each elim-
+c	 ination step.
+c
+	 lastcl = ncols
+	 lasti = integs(2,i)
+	 do 30 icount=1,lasti
+	    ipvteq = ipvteq + 1
+	    if (ipvteq .lt. lasteq)	go to 11
+	    if ( abs(w(ipvteq,1))+d(ipvteq) .gt. d(ipvteq) )
+     *					go to 50
+					go to 999
+c
+c	 determine the smallest  i s t a r  in	(ipvteq,lasteq)  for
+c	 which	abs(w(istar,1))/d(istar)  is as large as possible, and
+c	 interchange equations	ipvteq	and  istar  in case  ipvteq
+c	 .lt. istar .
+c
+   11	    colmax = abs(w(ipvteq,1))/d(ipvteq)
+	    istar = ipvteq
+	    ipvtp1 = ipvteq + 1
+	    do 13 ii=ipvtp1,lasteq
+	       awi1od = abs(w(ii,1))/d(ii)
+	       if (awi1od .le. colmax)	go to 13
+	       colmax = awi1od
+	       istar = ii
+   13	       continue
+	    if ( abs(w(istar,1))+d(istar) .eq. d(istar) )
+     *					go to 999
+	    if (istar .eq. ipvteq)	go to 16
+	    iflag = -iflag
+	    temp = d(istar)
+	    d(istar) = d(ipvteq)
+	    d(ipvteq) = temp
+	    temp = b(istar)
+	    b(istar) = b(ipvteq)
+	    b(ipvteq) = temp
+	    do 14 j=1,lastcl
+	       temp = w(istar,j)
+	       w(istar,j) = w(ipvteq,j)
+   14	       w(ipvteq,j) = temp
+c
+c	 subtract the appropriate multiple of equation	ipvteq	from
+c	 equations  ipvteq+1,...,lasteq to make the coefficient of the
+c	 ipvteq-th unknown (presently in column 1 of  w ) zero, but
+c	 store the new coefficients in	w  one to the left from the old.
+c
+   16	    do 20 ii=ipvtp1,lasteq
+	       ratio = w(ii,1)/w(ipvteq,1)
+	       do 18 j=2,lastcl
+   18		  w(ii,j-1) = w(ii,j) - ratio*w(ipvteq,j)
+	       w(ii,lastcl) = 0.
+   20	       b(ii) = b(ii) - ratio*b(ipvteq)
+   30	    lastcl = lastcl - 1
+   50	 continue
+c
+c  at this point,  w  and  b  contain an upper triangular linear system
+
+c  equivalent to the original one, with  w(i,j) containing entry
+c  (i, i-1+j ) of the coefficient matrix. solve this system by backsub-
+
+c  stitution, taking into account its block structure.
+c
+c			   i-loop over the blocks, in reverse order
+      i = nbloks
+   59	 lasti = integs(2,i)
+	 jmax = ncols - lasti
+	 do 70 icount=1,lasti
+	    sum = 0.
+	    if (jmax .eq. 0)		go to 61
+	    do 60 j=1,jmax
+   60	       sum = sum + x(ipvteq+j)*w(ipvteq,j+1)
+   61	    x(ipvteq) = (b(ipvteq)-sum)/w(ipvteq,1)
+	    jmax = jmax + 1
+   70	    ipvteq = ipvteq - 1
+	 i = i - 1
+	 if (i .gt. 0)			go to 59
+					return
+  999 iflag = 0
+					return
+      end
diff --git a/math/deboor/difequ_io.f b/math/deboor/difequ_io.f
new file mode 100644
index 00000000..a8bc2709
--- /dev/null
+++ b/math/deboor/difequ_io.f
@@ -0,0 +1,100 @@
+      subroutine difequ ( mode, xx, v )
+c  from  * a practical guide to splines *  by c. de boor
+calls  ppvalu(interv)
+c  to be called by   c o l l o c ,  p u t i t
+c  information about the differential equation is dispensed from here
+c
+c******  i n p u t  ******
+c  mode  an integer indicating the task to be performed.
+c	 = 1   initialization
+c	 = 2   evaluate  de  at  xx
+c	 = 3   specify the next side condition
+c	 = 4   analyze the approximation
+c  xx a point at which information is wanted
+c
+c******  o u t p u t  ******
+c  v  depends on the  mode  . see comments below
+c
+c     parameter npiece=100,ncoef=2000
+      integer mode,   i,iside,itermx,k,kpm,l,m
+      real v(20),xx,   break,coef,eps,ep1,ep2,error,factor,rho,solutn
+     *		      ,s2ovep,un,x,xside
+      real ppvalu
+c     common /approx/ break(npiece),coef(ncoef),l,kpm
+      common /approx/ break(100),coef(2000),l,kpm
+      common /side/ m,iside,xside(10)
+      common /other/ itermx,k,rho(19)
+c
+c  this sample of  difequ  is for the example in chapter xv. it is a
+c  nonlinear second order two point boundary value problem.
+c
+					go to (10,20,30,40),mode
+c  initialize everything
+c  i.e. set the order  m  of the dif.equ., the nondecreasing sequence
+c  xside(i),i=1,...,m, of points at which side cond.s are given and
+c  anything else necessary.
+   10 m = 2
+      xside(1) = 0.
+      xside(2) = 1.
+c  *** print out heading
+      print 499
+  499 format(37h carrier,s nonlinear perturb. problem)
+      eps = .5e-2
+      print 610, eps
+  610 format(5h eps ,e20.10)
+c  *** set constants used in formula for solution below.
+      factor = (sqrt(2.) + sqrt(3.))**2
+      s2ovep = sqrt(2./eps)
+c  *** initial guess for newton iteration. un(x) = x*x - 1.
+      l = 1
+      break(1) = 0.
+      do 16 i=1,kpm
+   16	 coef(i) = 0.
+      coef(1) = -1.
+      coef(3) = 2.
+      itermx = 10
+					return
+c
+c  provide value of left side coeff.s and right side at  xx .
+c  specifically, at  xx  the dif.equ. reads
+c	 v(m+1)d**m + v(m)d**(m-1) + ... + v(1)d**0  =	v(m+2)
+c  in terms of the quantities v(i),i=1,...,m+2, to be computed here.
+   20 continue
+      v(3) = eps
+      v(2) = 0.
+      un = ppvalu(break,coef,l,kpm,xx,0)
+      v(1) = 2.*un
+      v(4) = un**2 + 1.
+					return
+c
+c  provide the	m  side conditions. these conditions are of the form
+c	 v(m+1)d**m + v(m)d**(m-1) + ... + v(1)d**0  =	v(m+2)
+c  in terms of the quantities v(i),i=1,...,m+2, to be specified here.
+c  note that v(m+1) = 0  for customary side conditions.
+   30 v(m+1) = 0.
+					go to (31,32,39),iside
+   31 v(2) = 1.
+      v(1) = 0.
+      v(4) = 0.
+					go to 38
+   32 v(2) = 0.
+      v(1) = 1.
+      v(4) = 0.
+   38 iside = iside + 1
+   39					return
+c
+c  calculate the error near the boundary layer at  1.
+   40 continue
+      print 640
+  640 format(44h x, g(x)  and  g(x)-f(x)  at selected points)
+      x = .75
+      do 41 i=1,9
+	 ep1 = exp(s2ovep*(1.-x))*factor
+	 ep2 = exp(s2ovep*(1.+x))*factor
+	 solutn = 12./(1.+ep1)**2*ep1 + 12./(1.+ep2)**2*ep2 - 1.
+	 error = solutn - ppvalu(break,coef,l,kpm,x,0)
+	 print 641,x,solutn,error
+  641	 format(3e20.10)
+   41	 x = x + .03125
+					return
+      end
diff --git a/math/deboor/dtblok.f b/math/deboor/dtblok.f
new file mode 100644
index 00000000..57e67ae6
--- /dev/null
+++ b/math/deboor/dtblok.f
@@ -0,0 +1,36 @@
+      subroutine dtblok ( bloks, integs, nbloks, ipivot, iflag,
+     *			  detsgn, detlog )
+c  computes the determinant of an almost block diagonal matrix whose
+c  plu factorization has been obtained previously in fcblok.
+c  *** the logarithm of the determinant is computed instead of the
+c  determinant itself to avoid the danger of overflow or underflow
+c  inherent in this calculation.
+c
+c parameters
+c    bloks, integs, nbloks, ipivot, iflag  are as on return from fcblok.
+c	     in particular, iflag = (-1)**(number of interchanges dur-
+c	     ing factorization) if successful, otherwise iflag = 0.
+c    detsgn  on output, contains the sign of the determinant.
+c    detlog  on output, contains the natural logarithm of the determi-
+c	     nant if determinant is not zero. otherwise contains 0.
+c
+      integer nbloks, index, nrow
+      integer integs(3,nbloks),ipivot(1),iflag, i,indexp,ip,k,last
+      real bloks(1),detsgn,detlog
+c
+      detsgn = iflag
+      detlog = 0.
+      if (iflag .eq. 0) 		return
+      index = 0
+      indexp = 0
+      do 2 i=1,nbloks
+	 nrow = integs(1,i)
+	 last = integs(3,i)
+	 do 1 k=1,last
+	    ip = index + nrow*(k-1) + ipivot(indexp+k)
+	    detlog = detlog + alog(abs(bloks(ip)))
+    1	    detsgn = detsgn*sign(1.,bloks(ip))
+	 index = nrow*integs(2,i) + index
+    2	 indexp = indexp + nrow
+					return
+      end
diff --git a/math/deboor/eqblok_io.f b/math/deboor/eqblok_io.f
new file mode 100644
index 00000000..9c8f4f5b
--- /dev/null
+++ b/math/deboor/eqblok_io.f
@@ -0,0 +1,91 @@
+       subroutine eqblok ( t, n, kpm,  work1, work2,
+     *		       bloks, lenblk, integs, nbloks,  b )
+c  from  * a practical guide to splines *  by c. de boor
+calls putit(difequ,bsplvd(bsplvb))
+c  to be called in  c o l l o c
+c
+c******  i n p u t  ******
+c  t   the knot sequence, of length n+kpm
+c  n   the dimension of the approximating spline space, i.e., the order
+c      of the linear system to be constructed.
+c  kpm = k+m, the order of the approximating spline
+c  lenblk   the maximum length of the array  bloks  as allowed by the
+c	    dimension statement in  colloc .
+c
+c******  w o r k   a r e a s  ******
+c  work1    used in  putit, of size (kpm,kpm)
+c  work2    used in  putit, of size (kpm,m+1)
+c
+c******  o u t p u t  ******
+c  bloks    the coefficient matrix of the linear system, stored in al-
+c	    most block diagonal form, of size
+c	       kpm*sum(integs(1,i) , i=1,...,nbloks)
+c  integs   an integer array, of size (3,nbloks), describing the block
+c	    structure.
+c	    integs(1,i)  =  number of rows in block  i
+c	    integs(2,i)  =  number of columns in block	i
+c	    integs(3,i)  =  number of elimination steps which can be
+c			carried out in block  i  before pivoting might
+c			bring in an equation from the next block.
+c  nbloks   number of blocks, equals number of polynomial pieces
+c  b   the right side of the linear system, stored corresponding to the
+c      almost block diagonal form, of size sum(integs(1,i) , i=1,...,
+c      nbloks).
+c
+c******  m e t h o d  ******
+c  each breakpoint interval gives rise to a block in the linear system.
+c  this block is determined by the  k  colloc.equations in the interval
+c  with the side conditions (if any) in the interval interspersed ap-
+c  propriately, and involves the  kpm  b-splines having the interval in
+c  their support. correspondingly, such a block has  nrow = k + isidel
+c  rows, with  isidel = number of side conditions in this and the prev-
+c  ious intervals, and	ncol = kpm  columns.
+c     further, because the interior knots have multiplicity  k, we can
+c  carry out (in slvblk)  k  elimination steps in a block before pivot-
+c  ing might involve an equation from the next block. in the last block,
+c  of course, all kpm elimination steps will be carried out (in slvblk).
+c
+c  see the detailed comments in the solveblok package for further in-
+c  formation about the almost block diagonal form used here.
+      integer integs(3,1),kpm,lenblk,n,nbloks,	 i,index,indexb,iside
+     *					    ,isidel,itermx,k,left,m,nrow
+      real b(1),bloks(1),t(1),work1(1),work2(1),   rho,xside
+      common /side/ m, iside, xside(10)
+      common /other/ itermx,k,rho(19)
+      index = 1
+      indexb = 1
+      i = 0
+      iside = 1
+      do 20 left=kpm,n,k
+	 i = i+1
+c	 determine integs(.,i)
+	 integs(2,i) = kpm
+	 if (left .lt. n)		go to 14
+	 integs(3,i) = kpm
+	 isidel = m
+					go to 16
+   14	 integs(3,i) = k
+c	 at this point,  iside-1  gives the number of side conditions
+c	 incorporated so far. adding to this the side conditions in the
+c	 current interval gives the number  isidel .
+	 isidel = iside-1
+   15	 if (isidel .eq. m)		go to 16
+	 if (xside(isidel+1) .ge. t(left+1))
+     *					go to 16
+	 isidel = isidel+1
+					go to 15
+   16	 nrow = k + isidel
+	 integs(1,i) = nrow
+c	 the detailed equations for this block are generated and put
+c	 together in  p u t i t .
+	 if (lenblk .lt. index+nrow*kpm-1)go to 999
+	 call putit(t,kpm,left,work1,work2,bloks(index),nrow,b(indexb))
+	 index = index + nrow*kpm
+   20	 indexb = indexb + nrow
+      nbloks = i
+					return
+  999 print 699,lenblk
+  699 format(11h **********/23h the assigned dimension,i5
+     *	      ,38h for	bloks  in  colloc  is too small.)
+					stop
+      end
diff --git a/math/deboor/factrb.f b/math/deboor/factrb.f
new file mode 100644
index 00000000..4bb88e13
--- /dev/null
+++ b/math/deboor/factrb.f
@@ -0,0 +1,87 @@
+      subroutine factrb ( w, ipivot, d, nrow, ncol, last, iflag )
+c  adapted from p.132 of 'element.numer.analysis' by conte-de boor
+c
+c  constructs a partial plu factorization, corresponding to steps 1,...,
+c   l a s t   in gauss elimination, for the matrix  w  of order
+c   ( n r o w ,  n c o l ), using pivoting of scaled rows.
+c
+c  parameters
+c    w	     contains the (nrow,ncol) matrix to be partially factored
+c	     on input, and the partial factorization on output.
+c    ipivot  an integer array of length nrow containing a record of the
+c	     pivoting strategy used; row ipivot(i) is used during the
+c	     i-th elimination step, i=1,...,last.
+c    d	     a work array of length nrow used to store row sizes
+c	     temporarily.
+c    nrow    number of rows of w.
+c    ncol    number of columns of w.
+c    last    number of elimination steps to be carried out.
+c    iflag   on output, equals iflag on input times (-1)**(number of
+c	     row interchanges during the factorization process), in
+c	     case no zero pivot was encountered.
+c	     otherwise, iflag = 0 on output.
+c
+      integer nrow
+      integer ipivot(nrow),ncol,last,iflag, i,ipivi,ipivk,j,k,kp1
+      real w(nrow,ncol),d(nrow), awikdi,colmax,ratio,rowmax
+c  initialize ipivot, d
+      do 10 i=1,nrow
+	 ipivot(i) = i
+	 rowmax = 0.
+	 do 9 j=1,ncol
+    9	    rowmax = amax1(rowmax, abs(w(i,j)))
+	 if (rowmax .eq. 0.)		go to 999
+   10	 d(i) = rowmax
+c gauss elimination with pivoting of scaled rows, loop over k=1,.,last
+      k = 1
+c	 as pivot row for k-th step, pick among the rows not yet used,
+c	 i.e., from rows ipivot(k),...,ipivot(nrow), the one whose k-th
+c	 entry (compared to the row size) is largest. then, if this row
+c	 does not turn out to be row ipivot(k), redefine ipivot(k) ap-
+c	 propriately and record this interchange by changing the sign
+c	 of  i f l a g .
+   11	 ipivk = ipivot(k)
+	 if (k .eq. nrow)		go to 21
+	 j = k
+	 kp1 = k+1
+	 colmax = abs(w(ipivk,k))/d(ipivk)
+c	       find the (relatively) largest pivot
+	 do 15 i=kp1,nrow
+	    ipivi = ipivot(i)
+	    awikdi = abs(w(ipivi,k))/d(ipivi)
+	    if (awikdi .le. colmax)	go to 15
+	       colmax = awikdi
+	       j = i
+   15	    continue
+	 if (j .eq. k)			go to 16
+	 ipivk = ipivot(j)
+	 ipivot(j) = ipivot(k)
+	 ipivot(k) = ipivk
+	 iflag = -iflag
+   16	 continue
+c	 if pivot element is too small in absolute value, declare
+c	 matrix to be noninvertible and quit.
+	 if (abs(w(ipivk,k))+d(ipivk) .le. d(ipivk))
+     *					go to 999
+c	 otherwise, subtract the appropriate multiple of the pivot
+c	 row from remaining rows, i.e., the rows ipivot(k+1),...,
+c	 ipivot(nrow), to make k-th entry zero. save the multiplier in
+c	 its place.
+	 do 20 i=kp1,nrow
+	    ipivi = ipivot(i)
+	    w(ipivi,k) = w(ipivi,k)/w(ipivk,k)
+	    ratio = -w(ipivi,k)
+	    do 20 j=kp1,ncol
+   20	       w(ipivi,j) = ratio*w(ipivk,j) + w(ipivi,j)
+	 k = kp1
+c	 check for having reached the next block.
+	 if (k .le. last)		go to 11
+					return
+c     if  last	.eq. nrow , check now that pivot element in last row
+c     is nonzero.
+   21 if( abs(w(ipivk,nrow))+d(ipivk) .gt. d(ipivk) )
+     *					return
+c		    singularity flag set
+  999 iflag = 0
+					return
+      end
diff --git a/math/deboor/fcblok.f b/math/deboor/fcblok.f
new file mode 100644
index 00000000..db7b20ec
--- /dev/null
+++ b/math/deboor/fcblok.f
@@ -0,0 +1,56 @@
+      subroutine fcblok ( bloks, integs, nbloks, ipivot, scrtch, iflag )
+calls subroutines  f a c t r b	and  s h i f t b .
+c
+c   f c b l o k  supervises the plu factorization with pivoting of
+c  scaled rows of the almost block diagonal matrix stored in the arrays
+c   b l o k s  and  i n t e g s .
+c
+c   factrb = subprogram which carries out steps 1,...,last of gauss
+c	     elimination (with pivoting) for an individual block.
+c   shiftb = subprogram which shifts the remaining rows to the top of
+c	     the next block
+c
+c parameters
+c    bloks   an array that initially contains the almost block diagonal
+c	     matrix  a	to be factored, and on return contains the com-
+c	     puted factorization of  a .
+c    integs  an integer array describing the block structure of  a .
+c    nbloks  the number of blocks in  a .
+c    ipivot  an integer array of dimension  sum (integs(1,n) ; n=1,
+c	     ...,nbloks) which, on return, contains the pivoting stra-
+c	     tegy used.
+c    scrtch  work area required, of length  max (integs(1,n) ; n=1,
+c	     ...,nbloks).
+c    iflag   output parameter;
+c	     = 0  in case matrix was found to be singular.
+c	     otherwise,
+c	     = (-1)**(number of row interchanges during factorization)
+c
+      integer nbloks
+      integer integs(3,nbloks),ipivot(1),iflag, i,index,indexb,indexn,
+     *	      last,ncol,nrow
+      real bloks(1),scrtch(1)
+      iflag = 1
+      indexb = 1
+      indexn = 1
+      i = 1
+c			 loop over the blocks.	i  is loop index
+   10	 index = indexn
+	 nrow = integs(1,i)
+	 ncol = integs(2,i)
+	 last = integs(3,i)
+c	 carry out elimination on the i-th block until next block
+c	 enters, i.e., for columns 1,...,last  of i-th block.
+	 call factrb(bloks(index),ipivot(indexb),scrtch,nrow,ncol,last,
+     *		  iflag)
+c	  check for having reached a singular block or the last block
+	 if (iflag .eq. 0 .or. i .eq. nbloks)
+     *					return
+	 i = i+1
+	 indexn = nrow*ncol + index
+c	       put the rest of the i-th block onto the next block
+	 call shiftb(bloks(index),ipivot(indexb),nrow,ncol,last,
+     *		  bloks(indexn),integs(1,i),integs(2,i))
+	 indexb = indexb + nrow
+					go to 10
+      end
diff --git a/math/deboor/fsplin.x b/math/deboor/fsplin.x
new file mode 100644
index 00000000..ba290e05
--- /dev/null
+++ b/math/deboor/fsplin.x
@@ -0,0 +1,63 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+
+include	"bspln.h"
+
+.help fsplin	2	"math library"
+.ih
+NAME
+fsplin -- fast fit of b-spline interpolant.
+.ih
+USAGE
+fsplin (y, q, bspln)
+.ih
+PARAMETERS
+.ls y
+(real[n]).  Array of y-values of new data set.
+.le
+.ls q
+(real[(2*k-1)*n]).  Array containing the triangular factorization of the
+coefficient matrix of the linear system for the b-spline coefficients of
+the spline interpolant of dimension N and order K.  Q is produced by a
+prior call to SPLINE.
+.le
+.ls bspln
+(real[2*n+30]).  The spline descriptor array.  On input to FSPLIN, should
+contain a valid spline header (containing N, K, etc.), and knot array.
+As long as SPLINE is called before FSPLIN, the bspln array will be set up
+properly.  On output, the N b-spline coefficients are stored in BSPLN,
+ready for immediate input to SEVAL to evaluate the spline.
+.le
+.ih
+DESCRIPTION
+Fsplin is used following an initial SPLINE to efficiently fit a Kth order
+b-spline to a data set that differs from the data set input to SPLINE only
+in the y-values of the data points.  SPLINE and FSPLIN are used to
+interpolate an arbitrary array of data points (x,y), by fitting a piecewise
+Kth order curve, continuous in the first K-1 derivatives, through the
+data points.
+.ih
+SOURCE
+See Carl De Boor, "A Practical Guide to Splines", pg. 204-207.
+.ih
+SEE ALSO
+spline(2), seval(2)
+.endhelp ______________________________________________________________
+
+
+procedure fsplin (y, q, bspln)
+
+real	y[ARB], q[ARB]
+real	bspln[ARB]
+int	n, k, offset, i
+
+begin
+	offset = COEF1 - 1			#copy data into COEF array
+	do i = 1, NCOEF
+	    bspln[offset+i] = y[i]
+
+	n = NCOEF
+	k = ORDER
+
+	call banslv (q, 2*k - 1, n, k-1, k-1, bspln[offset+1])
+end
diff --git a/math/deboor/interv.f b/math/deboor/interv.f
new file mode 100644
index 00000000..e2116616
--- /dev/null
+++ b/math/deboor/interv.f
@@ -0,0 +1,95 @@
+      subroutine interv ( xt, lxt, x, left, mflag )
+c  from  * a practical guide to splines *  by c. de boor
+computes  left = max( i , 1 .le. i .le. lxt  .and.  xt(i) .le. x )  .
+c
+c******  i n p u t  ******
+c  xt.....a real sequence, of length  lxt , assumed to be nondecreasing
+c  lxt.....number of terms in the sequence  xt .
+c  x.....the point whose location with respect to the sequence	xt  is
+c	 to be determined.
+c
+c******  o u t p u t  ******
+c  left, mflag.....both integers, whose value is
+c
+c   1	  -1	  if		   x .lt.  xt(1)
+c   i	   0	  if   xt(i)  .le. x .lt. xt(i+1)
+c  lxt	   1	  if  xt(lxt) .le. x
+c
+c	 in particular,  mflag = 0 is the 'usual' case.  mflag .ne. 0
+c	 indicates that  x  lies outside the halfopen interval
+c	 xt(1) .le. y .lt. xt(lxt) . the asymmetric treatment of the
+c	 interval is due to the decision to make all pp functions cont-
+c	 inuous from the right.
+c
+c******  m e t h o d  ******
+c  the program is designed to be efficient in the common situation that
+c  it is called repeatedly, with  x  taken from an increasing or decrea-
+c  sing sequence. this will happen, e.g., when a pp function is to be
+c  graphed. the first guess for  left  is therefore taken to be the val-
+c  ue returned at the previous call and stored in the  l o c a l  varia-
+c  ble	ilo . a first check ascertains that  ilo .lt. lxt (this is nec-
+c  essary since the present call may have nothing to do with the previ-
+c  ous call). then, if	xt(ilo) .le. x .lt. xt(ilo+1), we set  left =
+c  ilo	and are done after just three comparisons.
+c     otherwise, we repeatedly double the difference  istep = ihi - ilo
+c  while also moving  ilo  and	ihi  in the direction of  x , until
+c		       xt(ilo) .le. x .lt. xt(ihi) ,
+c  after which we use bisection to get, in addition, ilo+1 = ihi .
+c  left = ilo  is then returned.
+c
+      integer left,lxt,mflag,	ihi,ilo,istep,middle
+      real x,xt(lxt)
+      data ilo /1/
+c     save ilo	(a valid fortran statement in the new 1977 standard)
+      ihi = ilo + 1
+      if (ihi .lt. lxt) 		go to 20
+	 if (x .ge. xt(lxt))		go to 110
+	 if (lxt .le. 1)		go to 90
+	 ilo = lxt - 1
+	 ihi = lxt
+c
+   20 if (x .ge. xt(ihi))		go to 40
+      if (x .ge. xt(ilo))		go to 100
+c
+c	       **** now x .lt. xt(ilo) . decrease  ilo	to capture  x .
+      istep = 1
+   31	 ihi = ilo
+	 ilo = ihi - istep
+	 if (ilo .le. 1)		go to 35
+	 if (x .ge. xt(ilo))		go to 50
+	 istep = istep*2
+					go to 31
+   35 ilo = 1
+      if (x .lt. xt(1)) 		go to 90
+					go to 50
+c	       **** now x .ge. xt(ihi) . increase  ihi	to capture  x .
+   40 istep = 1
+   41	 ilo = ihi
+	 ihi = ilo + istep
+	 if (ihi .ge. lxt)		go to 45
+	 if (x .lt. xt(ihi))		go to 50
+	 istep = istep*2
+					go to 41
+   45 if (x .ge. xt(lxt))		go to 110
+      ihi = lxt
+c
+c	    **** now xt(ilo) .le. x .lt. xt(ihi) . narrow the interval.
+   50 middle = (ilo + ihi)/2
+      if (middle .eq. ilo)		go to 100
+c     note. it is assumed that middle = ilo in case ihi = ilo+1 .
+      if (x .lt. xt(middle))		go to 53
+	 ilo = middle
+					go to 50
+   53	 ihi = middle
+					go to 50
+c**** set output and return.
+   90 mflag = -1
+      left = 1
+					return
+  100 mflag = 0
+      left = ilo
+					return
+  110 mflag = 1
+      left = lxt
+					return
+      end
diff --git a/math/deboor/knots.f b/math/deboor/knots.f
new file mode 100644
index 00000000..ad73f964
--- /dev/null
+++ b/math/deboor/knots.f
@@ -0,0 +1,38 @@
+      subroutine knots ( break, l, kpm, t, n )
+c  from  * a practical guide to splines *  by c. de boor
+c  to be called in  c o l l o c .
+c  constructs from the given breakpoint sequence  b r e a k  the knot
+c  sequence  t	so that
+c  spline(k+m,t) = pp(k+m,break) with  m-1  continuous derivatives .
+c  this means that
+c  t(1),...,t(n+kpm)  =  break(1) kpm times, then break(2),...,
+c	 break(l) each	k  times, then, finally, break(l+1) kpm times.
+c
+c******  i n p u t  ******
+c  break(1),...,break(l+1)  breakpoint sequence
+c  l  number of intervals or pieces
+c  kpm	 = k + m, order of the pp function or spline
+c
+c******  o u t p u t  ******
+c  t(1),...,t(n+kpm)  the knot sequence.
+c  n	 = l*k + m  =  dimension of  spline(k+m,t).
+c
+      integer l,kpm,n,	 iside,j,jj,jjj,k,ll,m
+      real break(1),t(1),   xside
+      common /side/ m,iside,xside(10)
+      k = kpm - m
+      n = l*k + m
+      jj = n + kpm
+      jjj = l + 1
+      do 11 ll=1,kpm
+	 t(jj) = break(jjj)
+   11	 jj = jj - 1
+      do 12 j=1,l
+      jjj = jjj - 1
+	 do 12 ll=1,k
+	    t(jj) = break(jjj)
+   12	    jj = jj - 1
+      do 13 ll=1,kpm
+   13	 t(ll) = break(1)
+					return
+      end
diff --git a/math/deboor/l2appr.f b/math/deboor/l2appr.f
new file mode 100644
index 00000000..6f61150c
--- /dev/null
+++ b/math/deboor/l2appr.f
@@ -0,0 +1,109 @@
+      subroutine l2appr ( t, n, k, q, diag, bcoef )
+c  from  * a practical guide to splines *  by c. de boor
+c  to be called in main program  l 2 m a i n .
+calls subprograms  bsplvb, bchfac/slv
+c
+constructs the (weighted discrete) l2-approximation by splines of order
+c  k  with knot sequence  t(1), ..., t(n+k)  to given data points
+c  ( tau(i), gtau(i) ), i=1,...,ntau. the b-spline coefficients
+c  b c o e f   of the approximating spline are determined from the
+c  normal equations using cholesky's method.
+c
+c******  i n p u t  ******
+c  t(1), ..., t(n+k)  the knot sequence
+c  n.....the dimension of the space of splines of order k with knots t.
+c  k.....the order
+c
+c  w a r n i n g  . . .  the restriction   k .le. kmax (= 20)	is impo-
+c	 sed by the arbitrary dimension statement for  biatx  below, but
+c	 is  n o w h e r e   c h e c k e d   for.
+c
+c******  w o r k  a r r a y s  ******
+c  q....a work array of size (at least) k*n. its first	k  rows are used
+c	for the  k  lower diagonals of the gramian matrix  c .
+c  diag.....a work array of length  n  used in bchfac .
+c
+c******  i n p u t  via  c o m m o n  /data/  ******
+c  ntau.....number of data points
+c  (tau(i),gtau(i)), i=1,...,ntau     are the  ntau  data points to be
+c	 fitted .
+c  weight(i), i=1,...,ntau    are the corresponding weights .
+c
+c******  o u t p u t  ******
+c  bcoef(1), ..., bcoef(n)  the b-spline coeffs. of the l2-appr.
+c
+c******  m e t h o d  ******
+c  the b-spline coefficients of the l2-appr. are determined as the sol-
+c  ution of the normal equations
+c     sum ( (b(i),b(j))*bcoef(j) : j=1,...,n)  = (b(i),g),
+c						i = 1, ..., n .
+c  here,  b(i)	denotes the i-th b-spline,  g  denotes the function to
+c  be approximated, and the  i n n e r	 p r o d u c t	of two funct-
+c  ions  f  and  g  is given by
+c      (f,g)  :=  sum ( f(tau(i))*g(tau(i))*weight(i) : i=1,...,ntau) .
+c  the arrays  t a u  and  w e i g h t	are given in common block
+c   d a t a , as is the array  g t a u	containing the sequence
+c  g(tau(i)), i=1,...,ntau.
+c  the relevant function values of the b-splines  b(i), i=1,...,n, are
+c  supplied by the subprogram  b s p l v b .
+c     the coeff.matrix	c , with
+c	    c(i,j)  :=	(b(i), b(j)), i,j=1,...,n,
+c  of the normal equations is symmetric and (2*k-1)-banded, therefore
+c  can be specified by giving its k bands at or below the diagonal. for
+c  i=1,...,n,  we store
+c   (b(i),b(j))  =  c(i,j)  in	q(i-j+1,j), j=i,...,min0(i+k-1,n)
+c  and the right side
+c   (b(i), g )	in  bcoef(i) .
+c  since b-spline values are most efficiently generated by finding sim-
+c  ultaneously the value of  e v e r y	nonzero b-spline at one point,
+c  the entries of  c  (i.e., of  q ), are generated by computing, for
+c  each ll, all the terms involving  tau(ll)  simultaneously and adding
+c  them to all relevant entries.
+c     parameter kmax=20,ntmax=200
+      integer k,n,   i,j,jj,left,leftmk,ll,mm,ntau
+c     real bcoef(n),diag(n),q(k,n),t(1),  biatx(kmax),dw,gtau,tau,weight
+      real bcoef(n),diag(n),q(k,n),t(1),  biatx(  20),dw,gtau,tau,weight
+c     dimension t(n+k)
+current fortran standard makes it impossible to specify the exact dimen-
+c  sion of  t  without the introduction of additional otherwise super-
+c  fluous arguments.
+c     common / data / ntau, tau(ntmax),gtau(ntmax),weight(ntmax)
+      common / data / ntau, tau(  200),gtau(  200),weight(  200)
+      do 7 j=1,n
+	 bcoef(j) = 0.
+	 do 7 i=1,k
+    7	    q(i,j) = 0.
+      left = k
+      leftmk = 0
+      do 20 ll=1,ntau
+c		    locate  l e f t  s.t. tau(ll) in (t(left),t(left+1))
+   10	    if (left .eq. n)		go to 15
+	    if (tau(ll) .lt. t(left+1)) go to 15
+	    left = left+1
+	    leftmk = leftmk + 1
+					go to 10
+   15	 call bsplvb ( t, k, 1, tau(ll), left, biatx )
+c	 biatx(mm) contains the value of b(left-k+mm) at tau(ll).
+c	 hence, with  dw := biatx(mm)*weight(ll), the number dw*gtau(ll)
+c	 is a summand in the inner product
+c	    (b(left-k+mm), g)  which goes into	bcoef(left-k+mm)
+c	 and the number biatx(jj)*dw is a summand in the inner product
+c	    (b(left-k+jj), b(left-k+mm)), into	q(jj-mm+1,left-k+mm)
+c	 since	(left-k+jj) - (left-k+mm) + 1  =  jj - mm + 1 .
+	 do 20 mm=1,k
+	    dw = biatx(mm)*weight(ll)
+	    j = leftmk + mm
+	    bcoef(j) = dw*gtau(ll) + bcoef(j)
+	    i = 1
+	    do 20 jj=mm,k
+	       q(i,j) = biatx(jj)*dw + q(i,j)
+   20	       i = i + 1
+c
+c	      construct cholesky factorization for  c  in  q , then use
+c	      it to solve the normal equations
+c		     c*x  =  bcoef
+c	      for  x , and store  x  in  bcoef .
+      call bchfac ( q, k, n, diag )
+      call bchslv ( q, k, n, bcoef )
+					return
+      end
diff --git a/math/deboor/l2err_io.f b/math/deboor/l2err_io.f
new file mode 100644
index 00000000..ac7fcf01
--- /dev/null
+++ b/math/deboor/l2err_io.f
@@ -0,0 +1,69 @@
+      subroutine l2err ( prfun , ftau , error )
+c  from  * a practical guide to splines *  by c. de boor
+c  this routine is to be called in the main program  l 2 m a i n .
+calls subprogram  ppvalu(interv)
+c  this subroutine computes various errors of the current l2-approxi-
+c  mation , whose pp-repr. is contained in common block  approx  ,
+c  to the given data contained in common block	data . it prints out
+c  the average error  e r r l 1 , the l2-error	e r r l 2,  and the
+c  maximum error  e r r m a x .
+c
+c******  i n p u t  ******
+c  prfun  a hollerith string.  if prfun = 2hon, the routine prints out
+c	   the value of the approximation as well as its error at
+c	   every data point.
+c
+c******  o u t p u t  ******
+c  ftau(1), ..., ftau(ntau),  with  ftau(i)  the approximation	f at
+c	   tau(i), all i.
+c  error(1), ..., error(ntau),	with  error(i) = scale*(g - f)
+c	   at tau(i), all i. here,  s c a l e  equals  1. in case
+c	   prfun .ne. 2hon , or the abs.error is greater than 100 some-
+c	   where. otherwise, s c a l e	is such that the maximum of
+c	   abs(error))	over all  i  lies between  10  and  100. this
+c	   makes the printed output more illustrative.
+c
+      integer prfun,   ie,k,l,ll,ntau,on
+      real ftau(1),error(1),  break,coef,err,errmax,errl1,errl2
+     *			     ,gtau,scale,tau,totalw,weight
+c     dimension ftau(ntau),error(ntau)
+      real ppvalu
+c     parameter lpkmax=100,ntmax=200,ltkmax=2000
+c     common / data / ntau, tau(ntmax),gtau(ntmax),weight(ntmax),totalw
+c     common /approx/ break(lpkmax),coef(ltkmax),l,k
+      common / data / ntau, tau(200),gtau(200),weight(200),totalw
+      common /approx/ break(100),coef(2000),l,k
+      data on /2hon /
+      errl1 = 0.
+      errl2 = 0.
+      errmax = 0.
+      do 10 ll=1,ntau
+	 ftau(ll) = ppvalu (break, coef, l, k, tau(ll), 0 )
+	 error(ll) = gtau(ll) - ftau(ll)
+	 err = abs(error(ll))
+	 if (errmax .lt. err)	errmax = err
+	 errl1 = errl1 + err*weight(ll)
+   10	 errl2 = errl2 + err**2*weight(ll)
+      errl1 = errl1/totalw
+      errl2 = sqrt(errl2/totalw)
+      print 615,errl2,errl1,errmax
+  615 format(///21h least square error =,e20.6/
+     1		21h average error      =,e20.6/
+     2		21h maximum error      =,e20.6//)
+      if (prfun .ne. on)		return
+c     **  scale error curve and print  **
+      ie = 0
+      scale = 1.
+      if (errmax .ge. 10.)		go to 18
+      do 17 ie=1,9
+	 scale = scale*10.
+	 if (errmax*scale .ge. 10.)	go to 18
+   17	 continue
+   18 do 19 ll=1,ntau
+   19	 error(ll) = error(ll)*scale
+      print 620,ie,(ll,tau(ll),ftau(ll),error(ll),ll=1,ntau)
+  620 format(///14x,36happroximation and scaled error curve/7x,
+     110hdata point,7x,13happroximation,3x,16hdeviation x 10**,i1/
+     2(i4,f16.8,f16.8,f17.6))
+					return
+      end
diff --git a/math/deboor/l2knts.f b/math/deboor/l2knts.f
new file mode 100644
index 00000000..5f11b1e4
--- /dev/null
+++ b/math/deboor/l2knts.f
@@ -0,0 +1,33 @@
+      subroutine l2knts ( break, l, k, t, n )
+c  from  * a practical guide to splines *  by c. de boor
+c  to be called in main program  l 2 m a i n .
+converts the breakpoint sequence  b r e a k   into a corresponding knot
+c  sequence  t	to allow the repr. of a pp function of order  k  with
+c  k-2 continuous derivatives as a spline of order  k  with knot
+c  sequence  t . this means that
+c  t(1), ..., t(n+k) =	break(1) k times, then break(i), i=2,...,l, each
+c			once, then break(l+1) k times .
+c  therefore,  n = k-1 + l.
+c
+c******  i n p u t  ******
+c  k	 the order
+c  l	 the number of polynomial pieces
+c  break(1), ...,break(l+1)  the breakpoint sequence
+c
+c******  o u t p u t  ******
+c  t(1),...,t(n+k)   the knot sequence
+c  n	 the dimension of the corresp. spline space of order  k .
+c
+      integer k,l,n,   i,km1
+      real break(1),t(1)
+c     dimension break(l+1),t(n+k)
+      km1 = k - 1
+      do 5 i=1,km1
+    5	 t(i) = break(1)
+      do 6 i=1,l
+    6	 t(km1+i) = break(i)
+      n = km1 + l
+      do 7 i=1,k
+    7	 t(n+i) = break(l+1)
+					return
+      end
diff --git a/math/deboor/mkpkg b/math/deboor/mkpkg
new file mode 100644
index 00000000..95e084a8
--- /dev/null
+++ b/math/deboor/mkpkg
@@ -0,0 +1,49 @@
+# Makelib for the single precision Deboor spline package.
+
+$checkout libdeboor.a lib$
+$update   libdeboor.a
+$checkin  libdeboor.a lib$
+$exit
+
+libdeboor.a:
+	banfac.f
+	banslv.f
+	bchfac.f
+	bchslv.f
+	bsplbv.f
+	bsplpp.f
+	bsplvd.f
+	bspp2d.f
+	bvalue.f
+	chol1d.f
+	cubspl.f
+	cwidth.f
+	dtblok.f
+	factrb.f
+	fcblok.f
+	fsplin.x	bspln.h
+	interv.f
+	knots.f
+	l2appr.f
+	l2knts.f
+	newnot_fake.f
+	ppvalu.f
+	round.f
+	sbblok.f
+	setdat.f
+	setdat2.f
+	setdat3.f
+	setupq.f
+	seval.x		bspln.h
+	shiftb.f
+	slvblk.f
+	smooth.f
+	spline.x	bspln.h
+	splint.f
+	spllsq.x	bspln.h
+	splsqv.x	bspln.h
+	subbak.f
+	subfor.f
+	tautsp.f
+	titand.f
+	;
diff --git a/math/deboor/newnot_fake.f b/math/deboor/newnot_fake.f
new file mode 100644
index 00000000..a4d27eb3
--- /dev/null
+++ b/math/deboor/newnot_fake.f
@@ -0,0 +1,30 @@
+      subroutine newnot ( break, coef, l, k, brknew, lnew, coefg )
+c  from  * a practical guide to splines *  by c. de boor
+c  this is a fake version of  n e w n o t  , of use in example 3 of
+c  chapter xiv .
+c  returns  lnew+1  knots in  brknew  which are equidistributed on (a,b)
+c  = (break(1),break(l+1)) .
+c
+      integer k,l,lnew,   i
+      real break(1),brknew(1),coef(k,l),coefg(2,l),   step
+c******  i n p u t ******
+c  break, coef, l, k.....contains the pp-representation of a certain
+c	 function  f  of order	k . specifically,
+c	 d**(k-1)f(x) = coef(k,i)  for	break(i).le. x .lt.break(i+1)
+c  lnew.....number of intervals into which the interval (a,b) is to be
+c	 sectioned by the new breakpoint sequence  brknew .
+c
+c******  o u t p u t  ******
+c  brknew.....array of length  lnew+1  containing the new breakpoint se-
+c	 quence
+c  coefg.....the coefficient part of the pp-repr.  break, coefg, l, 2
+c	 for the monotone p.linear function  g	wrto which  brknew  will
+c	 be equidistributed.
+c
+      brknew(1) = break(1)
+      brknew(lnew+1) = break(l+1)
+      step = (break(l+1) - break(1))/float(lnew)
+      do 93 i=2,lnew
+   93	 brknew(i) = break(1) + float(i-1)*step
+					return
+      end
diff --git a/math/deboor/newnot_io.f b/math/deboor/newnot_io.f
new file mode 100644
index 00000000..8788dd11
--- /dev/null
+++ b/math/deboor/newnot_io.f
@@ -0,0 +1,108 @@
+      subroutine newnot ( break, coef, l, k, brknew, lnew, coefg )
+c  from  * a practical guide to splines *  by c. de boor
+c  returns  lnew+1  knots in  brknew  which are equidistributed on (a,b)
+c  = (break(1),break(l+1)) wrto a certain monotone fctn  g  related to
+c  the k-th root of the k-th derivative of the pp function  f  whose pp-
+c  representation is contained in  break, coef, l, k .
+c
+c******  i n p u t ******
+c  break, coef, l, k.....contains the pp-representation of a certain
+c	 function  f  of order	k . specifically,
+c	 d**(k-1)f(x) = coef(k,i)  for	break(i).le. x .lt.break(i+1)
+c  lnew.....number of intervals into which the interval (a,b) is to be
+c	 sectioned by the new breakpoint sequence  brknew .
+c
+c******  o u t p u t  ******
+c  brknew.....array of length  lnew+1  containing the new breakpoint se-
+c	 quence
+c  coefg.....the coefficient part of the pp-repr.  break, coefg, l, 2
+c	 for the monotone p.linear function  g	wrto which  brknew  will
+c	 be equidistributed.
+c
+c******  optional  p r i n t e d  o u t p u t  ******
+c  coefg.....the pp coeffs of  g  are printed out if  iprint  is set
+c	 .gt. 0  in data statement below.
+c
+c******  m e t h o d  ******
+c     the k-th derivative of the given pp function  f  does not exist
+c  (except perhaps as a linear combination of delta functions). never-
+c  theless, we construct a p.constant function	h  with breakpoint se-
+c  quence  break  which is approximately proportional to abs(d**k(f)).
+c  specifically, on  (break(i), break(i+1)),
+c
+c     abs(jump at break(i) of pc)    abs(jump at break(i+1) of pc)
+c h = --------------------------  +  ----------------------------
+c	break(i+1) - break(i-1) 	break(i+2) - break(i)
+c
+c  with  pc  the p.constant (k-1)st derivative of  f .
+c      then, the p.linear function  g  is constructed as
+c
+c    g(x)  =  integral of  h(y)**(1/k)	for  y	from  a  to  x
+c
+c  and its pp coeffs. stored in  coefg .
+c     then  brknew  is determined by
+c
+c	 brknew(i)  =  a + g**(-1)((i-1)*step) , i=1,...,lnew+1
+c
+c  where  step = g(b)/lnew  and  (a,b) = (break(1),break(l+1)) .
+c     in the event that  pc = d**(k-1)(f) is constant in  (a,b)  and
+c  therefore  h = 0 identically,  brknew  is chosen uniformly spaced.
+c
+      integer k,l,lnew,   i,iprint,j
+      real break(1),brknew(1),coef(k,l),coefg(2,l),   dif,difprv,oneovk
+     *						     ,step,stepi
+c     dimension break(l+1), brknew(lnew+1)
+current fortran standard makes it impossible to specify the dimension
+c  of  break   and  brknew  without the introduction of additional
+c  otherwise superfluous arguments.
+      data iprint /0/
+c
+      brknew(1) = break(1)
+      brknew(lnew+1) = break(l+1)
+c				if  g  is constant,  brknew  is uniform.
+      if (l .le. 1)			go to 90
+c			 construct the continuous p.linear function  g .
+      oneovk = 1./float(k)
+      coefg(1,1) = 0.
+      difprv = abs(coef(k,2) - coef(k,1))/(break(3)-break(1))
+      do 10 i=2,l
+	 dif = abs(coef(k,i) - coef(k,i-1))/(break(i+1) - break(i-1))
+	 coefg(2,i-1) = (dif + difprv)**oneovk
+	 coefg(1,i) = coefg(1,i-1)+coefg(2,i-1)*(break(i)-break(i-1))
+   10	 difprv = dif
+      coefg(2,l) = (2.*difprv)**oneovk
+c						      step  =  g(b)/lnew
+      step = (coefg(1,l)+coefg(2,l)*(break(l+1)-break(l)))/float(lnew)
+c
+      if (iprint .gt. 0) print 600, step,(i,coefg(1,i),coefg(2,i),i=1,l)
+  600 format(7h step =,e16.7/(i5,2e16.5))
+c			       if  g  is constant,  brknew  is uniform .
+      if (step .le. 0.) 		go to 90
+c
+c      for i=2,...,lnew, construct  brknew(i) = a + g**(-1)(stepi),
+c      with  stepi = (i-1)*step .  this requires inversion of the p.lin-
+c      ear function  g .  for this,  j	is found so that
+c	  g(break(j)) .le. stepi .le. g(break(j+1))
+c      and then
+c	  brknew(i)  =	break(j) + (stepi-g(break(j)))/dg(break(j)) .
+c      the midpoint is chosen if  dg(break(j)) = 0 .
+      j = 1
+      do 30 i=2,lnew
+	 stepi = float(i-1)*step
+   21	    if (j .eq. l)		go to 27
+	    if (stepi .le. coefg(1,j+1))go to 27
+	    j = j + 1
+					go to 21
+   27	 if (coefg(2,j) .eq. 0.)	go to 29
+	    brknew(i) = break(j) + (stepi - coefg(1,j))/coefg(2,j)
+					go to 30
+   29	    brknew(i) = (break(j) + break(j+1))/2.
+   30	 continue
+					return
+c
+c			       if  g  is constant,  brknew  is uniform .
+   90 step = (break(l+1) - break(1))/float(lnew)
+      do 93 i=2,lnew
+   93	 brknew(i) = break(1) + float(i-1)*step
+					return
+      end
diff --git a/math/deboor/ppvalu.f b/math/deboor/ppvalu.f
new file mode 100644
index 00000000..edb04002
--- /dev/null
+++ b/math/deboor/ppvalu.f
@@ -0,0 +1,48 @@
+      real function ppvalu (break, coef, l, k, x, jderiv )
+c  from  * a practical guide to splines *  by c. de boor
+calls  interv
+calculates value at  x	of  jderiv-th derivative of pp fct from pp-repr
+c
+c******  i n p u t  ******
+c  break, coef, l, k.....forms the pp-representation of the function  f
+c	 to be evaluated. specifically, the j-th derivative of	f  is
+c	 given by
+c
+c     (d**j)f(x) = coef(j+1,i) + h*(coef(j+2,i) + h*( ... (coef(k-1,i) +
+c			      + h*coef(k,i)/(k-j-1))/(k-j-2) ... )/2)/1
+c
+c	 with  h = x - break(i),  and
+c
+c	i  =  max( 1 , max( j ,  break(j) .le. x , 1 .le. j .le. l ) ).
+c
+c  x.....the point at which to evaluate.
+c  jderiv.....integer giving the order of the derivative to be evaluat-
+c	 ed.  a s s u m e d  to be zero or positive.
+c
+c******  o u t p u t  ******
+c  ppvalu.....the value of the (jderiv)-th derivative of  f  at  x.
+c
+c******  m e t h o d  ******
+c     the interval index  i , appropriate for  x , is found through a
+c  call to  interv . the formula above for the	jderiv-th derivative
+c  of  f  is then evaluated (by nested multiplication).
+c
+      integer jderiv,k,l,   i,m,ndummy
+      real break(l),coef(k,l),x,   fmmjdr,h
+      ppvalu = 0.
+      fmmjdr = k - jderiv
+c	       derivatives of order  k	or higher are identically zero.
+      if (fmmjdr .le. 0.)		go to 99
+c
+c	       find index  i  of largest breakpoint to the left of  x .
+      call interv ( break, l, x, i, ndummy )
+c
+c      evaluate  jderiv-th derivative of  i-th polynomial piece at  x .
+      h = x - break(i)
+      m = k
+    9	 ppvalu = (ppvalu/fmmjdr)*h + coef(m,i)
+	 m = m - 1
+	 fmmjdr = fmmjdr - 1.
+	 if (fmmjdr .gt. 0.)		go to 9
+   99					return
+      end
diff --git a/math/deboor/progs/prog1.f b/math/deboor/progs/prog1.f
new file mode 100644
index 00000000..2a0b869c
--- /dev/null
+++ b/math/deboor/progs/prog1.f
@@ -0,0 +1,45 @@
+chapter ii. runge example
+c  from  * a practical guide to splines *  by c. de boor
+      integer i,istep,j,k,n,nmk,nm1
+      real aloger,algerp,d(20),decay,dx,errmax,g,h,pnatx,step,tau(20),x
+      data step, istep /20., 20/
+      g(x) = 1./(1.+(5.*x)**2)
+      print 600
+  600 format(28h  n   max.error   decay exp.//)
+      decay = 0.
+      do 40 n=2,20,2
+c	 choose interpolation points  tau(1), ..., tau(n) , equally
+c	 spaced in (-1,1), and set  d(i) = g(tau(i)), i=1,...,n.
+	 nm1 = n-1
+	 h = 2./float(nm1)
+	 do 10 i=1,n
+	    tau(i) = float(i-1)*h - 1.
+   10	    d(i) = g(tau(i))
+c	 calculate the divided differences for the newton form.
+c
+	 do 20 k=1,nm1
+	    nmk = n-k
+	    do 20 i=1,nmk
+   20	       d(i) = (d(i+1)-d(i))/(tau(i+k)-tau(i))
+c
+c	 estimate max.interpolation error on (-1,1).
+	 errmax = 0.
+	 do 30 i=2,n
+	    dx = (tau(i)-tau(i-1))/step
+	    do 30 j=1,istep
+	       x = tau(i-1) + float(j)*dx
+c	       evaluate interp.pol. by nested multiplication
+c
+	       pnatx = d(1)
+	       do 29 k=2,n
+   29		  pnatx = d(k) + (x-tau(k))*pnatx
+c
+   30	       errmax = amax1(errmax,abs(g(x)-pnatx))
+	 aloger = alog(errmax)
+	 if (n .gt. 2)	decay =
+     *	     (aloger - algerp)/alog(float(n)/float(n-2))
+	 algerp = aloger
+   40	 print 640,n,errmax,decay
+  640 format(i3,e12.4,f11.2)
+					stop
+      end
diff --git a/math/deboor/progs/prog10.f b/math/deboor/progs/prog10.f
new file mode 100644
index 00000000..dc580c99
--- /dev/null
+++ b/math/deboor/progs/prog10.f
@@ -0,0 +1,76 @@
+chapter xii, example 4. quasi-interpolant with good knots.
+c  from  * a practical guide to splines *  by c. de boor
+calls bsplpp(bsplvb)
+c
+      integer i,irate,istep,j,l,m,mmk,n,nlow,nhigh,nm1
+      real algerp,aloger,bcoef(22),break(20),c(4,20),decay,dg,ddg,x
+     *	  ,dtip1,dtip2,dx,errmax,g,h,pnatx,scrtch(4,4),step,t(26),taui
+c     istep and step = float(istep) specify point density for error det-
+c     ermination.
+      data step, istep /20., 20/
+c	 g  is the function to be approximated,  dg  is its first, and
+c	 ddg  its second derivative .
+      g(x) = sqrt(x+1.)
+      dg(x) = .5/g(x)
+      ddg(x) = -.5*dg(x)/(x+1.)
+      decay = 0.
+c      read in the exponent  irate  for the knot distribution and the
+c      lower and upper limit for the number  n	.
+      read 500,irate,nlow,nhigh
+  500 format(3i3)
+      print 600
+  600 format(28h  n   max.error   decay exp./)
+c			       loop over  n = dim( spline(4,t) ) - 2 .
+c	       n  is chosen as the parameter in order to afford compar-
+c	       ison with examples 2 and 3  in which cubic spline interp-
+c	       olation at  n  data points was used .
+      do 40 n=nlow,nhigh,2
+	 nm1 = n-1
+	 h = 1./float(nm1)
+	 m = n+2
+	 mmk = m-4
+	 do 5 i=1,4
+	    t(i) = -1.
+    5	    t(m+i) = 1.
+c		  interior knots are equidistributed with respect to the
+c		  function  (x + 1)**(1/irate) .
+	 do 6 i=1,mmk
+    6	    t(i+4) = 2.*(float(i)*h)**irate - 1.
+c					    construct quasi-interpolant.
+c						 bcoef(1) = g(-1.) = 0.
+	 bcoef(1) = 0.
+	 dtip2 = t(5) - t(4)
+	 taui = t(5)
+c			    special choice of  tau(2)  to avoid infinite
+c			    derivatives of  g  at left endpoint .
+	 bcoef(2) = g(taui) - 2.*dtip2*dg(taui)/3.
+     *		   + dtip2**2*ddg(taui)/6.
+	 do 15 i=3,m
+	    taui = t(i+2)
+	    dtip1 = dtip2
+	    dtip2 = t(i+3) - t(i+2)
+c				       formula xii(30) of text is used .
+   15	    bcoef(i) = g(taui) + (dtip2-dtip1)*dg(taui)/3.
+     *		     - dtip1*dtip2*ddg(taui)/6.
+c					  convert to pp-representation .
+	 call bsplpp(t,bcoef,m,4,scrtch,break,c,l)
+c			     estimate max.interpolation error on (-1,1).
+	 errmax = 0.
+c					      loop over cubic pieces ...
+	 do 30 i=1,l
+	    dx = (break(i+1)-break(i))/step
+c			error is calculated at	istep  points per piece.
+	    do 30 j=1,istep
+	       h = float(j)*dx
+	       pnatx = c(1,i)+h*(c(2,i)+h*(c(3,i)+h*c(4,i)/3.)/2.)
+   30	       errmax = amax1(errmax,abs(g(break(i)+h)-pnatx))
+c					      calculate decay exponent .
+	 aloger = alog(errmax)
+	 if (n .gt. nlow)  decay =
+     *	     (aloger - algerp)/alog(float(n)/float(n-2))
+	 algerp = aloger
+c
+   40	 print 640,n,errmax,decay
+  640 format(i3,e12.4,f11.2)
+					stop
+      end
diff --git a/math/deboor/progs/prog11.f b/math/deboor/progs/prog11.f
new file mode 100644
index 00000000..2deea951
--- /dev/null
+++ b/math/deboor/progs/prog11.f
@@ -0,0 +1,69 @@
+chapter xiii, example 1. a large norm amplifies noise.
+c  from  * a practical guide to splines *  by c. de boor
+calls splint(banfac/slv,bsplvb),bsplpp(bsplvb*),ppvalu(interv),round
+c     an initially uniform data point distribution of  n  points is
+c  changed  i t e r m x  times by moving the  j c l o s e -th data point
+c  toward its left neighbor, cutting the distance between the two by a
+c  factor of  r a t e  each time . to demonstrate the corresponding
+c  increase in the norm of cubic spline interpolation at these data
+c  points, the data are taken from a cubic polynomial (which would be
+c  interpolated exactly) but with noise of size  s i z e  added. the re-
+c  sulting noise or error in the interpolant (compared to the cubic)
+c  gives the norm or noise amplification factor and is printed out
+c  together with the diminishing distance  h  between the two data
+c  points.
+c     parameter nmax=200,nmaxt4=800,nmaxt7=1400,nmaxp4=204
+      integer i,iflag,istep,iter,itermx,j,jclose,l,n,nm1
+c     real amax,bcoef(nmax),break(nmax),coef(nmaxt4),dx,fltnm1,fx
+c    * ,gtau(nmax),h,rate,scrtch(nmaxt7),size,step,t(nmaxp4),tau(nmax),x
+      real amax,bcoef(200),break(200),coef(800),dx,fltnm1,fx
+     * ,gtau(200),h,rate,scrtch(1400),size,step,t(204),tau(200),x
+      real ppvalu,round,g
+      common /rount/ size
+      data step, istep / 20., 20 /
+c					   function to be interpolated .
+      g(x) = 1.+x*(1.+x*(1.+x))
+      read 500,n,itermx,jclose,size,rate
+  500 format(3i3/e10.3/e10.3)
+      print 600,size
+  600 format(16h size of noise =,e8.2//
+     *	    25h    h	       max.error)
+c					start with uniform data points .
+      nm1 = n - 1
+      fltnm1 = float(nm1)
+      do 10 i=1,n
+   10	 tau(i) = float(i-1)/fltnm1
+c		     set up knot sequence for not-a-knot end condition .
+      do 11 i=1,4
+	 t(i) = tau(1)
+   11	 t(n+i) = tau(n)
+      do 12 i=5,n
+   12	 t(i) = tau(i-2)
+c
+      do 100 iter=1,itermx
+	 do 21 i=1,n
+   21	    gtau(i) = round(g(tau(i)))
+	 call splint ( tau, gtau, t, n, 4, scrtch, bcoef, iflag )
+					go to (24,23),iflag
+   23	 print 623
+  623	 format(27h something wrong in splint.)
+					stop
+   24	 call bsplpp ( t, bcoef, n, 4, scrtch, break, coef, l )
+c				     calculate max.interpolation error .
+	 amax = 0.
+	 do 30 i=4,n
+	    dx = (break(i-2) - break(i-3))/step
+	    do 25 j=2,istep
+	       x = break(i-2) - dx*float(j-1)
+	       fx = ppvalu(break,coef,l,4,x,0)
+   25	       amax = amax1(amax,abs(fx-g(x)))
+   30	    continue
+	 h = tau(jclose) - tau(jclose-1)
+	 print 630,h,amax
+  630	 format(e9.2,e15.3)
+c		  move tau(jclose) toward its left neighbor so as to cut
+c		  their distance by a factor of  rate .
+	 tau(jclose) = (tau(jclose) + (rate-1.)*tau(jclose-1))/rate
+  100	 continue
+					stop
+      end
diff --git a/math/deboor/progs/prog12.f b/math/deboor/progs/prog12.f
new file mode 100644
index 00000000..6efe8614
--- /dev/null
+++ b/math/deboor/progs/prog12.f
@@ -0,0 +1,70 @@
+chapter xiii, example 2. cubic spline interpolant at knot averages
+c			 with good knots.
+c  from  * a practical guide to splines *  by c. de boor
+calls splint(banfac/slv,bsplvb),newnot,bsplpp(bsplvb*)
+c     parameter nmax=20,nmaxp6=26,nmaxp2=22,nmaxt7=140
+      integer i,istep,iter,itermx,n,nhigh,nmk,nlow
+c     real algerp,aloger,bcoef(nmaxp2),break(nmax),decay,dx,errmax,
+c    *	  c(4,nmax),g,gtau(nmax),h,pnatx,scrtch(nmaxt7),step,t(nmaxp6),
+c    *	  tau(nmax),tnew(nmax)
+      real algerp,aloger,bcoef(22),break(20),decay,dx,errmax,
+     *	  c(4,20),g,gtau(20),h,pnatx,scrtch(140),step,t(26),
+     *	  tau(20),tnew(20),x
+c     istep and step = float(istep) specify point density for error det-
+c     ermination.
+      data step, istep /20., 20/
+c				the function  g  is to be interpolated .
+      g(x) = sqrt(x+1.)
+      decay = 0.
+c      read in the number of iterations to be carried out and the lower
+c      and upper limit for the number  n  of data points to be used.
+      read 500,itermx,nlow,nhigh
+  500 format(3i3)
+      print 600, itermx
+  600 format(i4,22h cycles through newnot//
+     *	    28h  n   max.error	 decay exp./)
+c				  loop over  n = number of data points .
+      do 40 n=nlow,nhigh,2
+    4	 nmk = n-4
+	 h = 2./float(nmk+1)
+	 do 5 i=1,4
+	    t(i) = -1.
+    5	    t(n+i) = 1.
+	 if (nmk .lt. 1)		go to 10
+	 do 6 i=1,nmk
+    6	    t(i+4) = float(i)*h - 1.
+   10	 iter = 1
+c		construct cubic spline interpolant. then, itermx  times,
+c		 determine new knots from it and find a new interpolant.
+   11	    do 12 i=1,n
+	       tau(i) = (t(i+1)+t(i+2)+t(i+3))/3.
+   12	       gtau(i) = g(tau(i))
+	    call splint ( tau, gtau, t, n, 4, scrtch, bcoef, iflag )
+	    call bsplpp ( t, bcoef, n, 4, scrtch, break, c, l )
+	    if (iter .gt. itermx)	go to 19
+	    iter = iter + 1
+	    call newnot ( break, c, l, 4, tnew, l, scrtch )
+   15	    do 18 i=2,l
+   18	       t(3+i) = tnew(i)
+					go to 11
+c		       estimate max.interpolation error on  (-1,1) .
+   19	 errmax = 0.
+c			    loop over polynomial pieces of interpolant .
+	 do 30 i=1,l
+	    dx = (break(i+1)-break(i))/step
+c		 interpolation error is calculated at  istep  points per
+c		     polynomial piece .
+	    do 30 j=1,istep
+	       h = float(j)*dx
+	       pnatx = c(1,i)+h*(c(2,i)+h*(c(3,i)+h*c(4,i)/3.)/2.)
+   30	    errmax = amax1(errmax,abs(g(break(i)+h)-pnatx))
+c					      calculate decay exponent .
+	 aloger = alog(errmax)
+	 if (n .gt. nlow)  decay =
+     *	     (aloger - algerp)/alog(float(n)/float(n-2))
+	 algerp = aloger
+c
+   40	 print 640,n,errmax,decay
+  640 format(i3,e12.4,f11.2)
+					stop
+      end
diff --git a/math/deboor/progs/prog13.f b/math/deboor/progs/prog13.f
new file mode 100644
index 00000000..45e6362f
--- /dev/null
+++ b/math/deboor/progs/prog13.f
@@ -0,0 +1,77 @@
+chapter xiii, example 2m. cubic spline interpolant at knot averages
+c			 with good knots. modified around label 4.
+c  from  * a practical guide to splines *  by c. de boor
+calls splint(banfac/slv,bsplvb),newnot,bsplpp(bsplvb*)
+c     parameter nmax=20,nmaxp6=26,nmaxp2=22,nmaxt7=140
+      integer i,istep,iter,itermx,n,nhigh,nmk,nlow
+c     real algerp,aloger,bcoef(nmaxp2),break(nmax),decay,dx,errmax,
+c    *	  c(4,nmax),g,gtau(nmax),h,pnatx,scrtch(nmaxt7),step,t(nmaxp6),
+c    *	  tau(nmax),tnew(nmax)
+      real algerp,aloger,bcoef(22),break(20),decay,dx,errmax,
+     *	  c(4,20),g,gtau(20),h,pnatx,scrtch(140),step,t(26),
+     *	  tau(20),tnew(20),x
+c     istep and step = float(istep) specify point density for error det-
+c     ermination.
+      data step, istep /20., 20/
+c				the function  g  is to be interpolated .
+      g(x) = sqrt(x+1.)
+      decay = 0.
+c      read in the number of iterations to be carried out and the lower
+c      and upper limit for the number  n  of data points to be used.
+      read 500,itermx,nlow,nhigh
+  500 format(3i3)
+      print 600, itermx
+  600 format(i4,22h cycles through newnot//
+     *	    28h  n   max.error	 decay exp./)
+c				  loop over  n = number of data points .
+      do 40 n=nlow,nhigh,2
+	 if (n .eq. nlow)		go to 4
+	 call newnot ( break, c, l, 4, tnew, l+2, scrtch )
+	 l = l + 2
+	 t(5+l) = 1.
+	 t(6+l) = 1.
+	 iter = 1
+					go to 15
+    4	 nmk = n-4
+	 h = 2./float(nmk+1)
+	 do 5 i=1,4
+	    t(i) = -1.
+    5	    t(n+i) = 1.
+	 if (nmk .lt. 1)		go to 10
+	 do 6 i=1,nmk
+    6	    t(i+4) = float(i)*h - 1.
+   10	 iter = 1
+c		construct cubic spline interpolant. then, itermx  times,
+c		 determine new knots from it and find a new interpolant.
+   11	    do 12 i=1,n
+	       tau(i) = (t(i+1)+t(i+2)+t(i+3))/3.
+   12	       gtau(i) = g(tau(i))
+	    call splint ( tau, gtau, t, n, 4, scrtch, bcoef, iflag )
+	    call bsplpp ( t, bcoef, n, 4, scrtch, break, c, l )
+	    if (iter .gt. itermx)	go to 19
+	    iter = iter + 1
+	    call newnot ( break, c, l, 4, tnew, l, scrtch )
+   15	    do 18 i=2,l
+   18	       t(3+i) = tnew(i)
+					go to 11
+c		       estimate max.interpolation error on  (-1,1) .
+   19	 errmax = 0.
+c			    loop over polynomial pieces of interpolant .
+	 do 30 i=1,l
+	    dx = (break(i+1)-break(i))/step
+c		 interpolation error is calculated at  istep  points per
+c		     polynomial piece .
+	    do 30 j=1,istep
+	       h = float(j)*dx
+	       pnatx = c(1,i)+h*(c(2,i)+h*(c(3,i)+h*c(4,i)/3.)/2.)
+   30	    errmax = amax1(errmax,abs(g(break(i)+h)-pnatx))
+c					      calculate decay exponent .
+	 aloger = alog(errmax)
+	 if (n .gt. nlow)  decay =
+     *	     (aloger - algerp)/alog(float(n)/float(n-2))
+	 algerp = aloger
+c
+   40	 print 640,n,errmax,decay
+  640 format(i3,e12.4,f11.2)
+					stop
+      end
diff --git a/math/deboor/progs/prog14.f b/math/deboor/progs/prog14.f
new file mode 100644
index 00000000..03804f47
--- /dev/null
+++ b/math/deboor/progs/prog14.f
@@ -0,0 +1,37 @@
+chapter xiii, example 3 . test of optimal spline interpolation routine
+c			  on titanium heat data .
+c  from  * a practical guide to splines *  by c. de boor
+calls titand,splopt(bsplvb,banfac/slv),splint(*),bvalue(interv)
+c
+c     lenscr = (n-k)(2k+3)+5k+3  is the length of scrtch required in
+c				 splopt .
+c     parameter n=12,ntitan=49,k=5,npk=17,lenscr=119
+c     integer i,iflag,ipick(n),ipicki,lx,nmk
+c     real a(n),gtitan(ntitan),gtau(ntitan),scrtch(lenscr),t(npk),tau(n)
+c    *	  ,x(ntitan)
+      real bvalue
+      integer i,iflag,ipick(12),ipicki,lx,nmk
+      real a(12),gtitan(49),gtau(49),scrtch(119),t(17),tau(12)
+     *	  ,x(49)
+      data n,k /12,5/
+      data ipick /1,5,11,21,27,29,31,33,35,40,45,49/
+      call titand ( x, gtitan, lx )
+      do 10 i=1,n
+	 ipicki = ipick(i)
+	 tau(i) = x(ipicki)
+   10	 gtau(i) = gtitan(ipicki)
+      call splopt ( tau, n, k, scrtch, t, iflag )
+      if (iflag .gt. 1) 		stop
+      call splint ( tau, gtau, t, n, k, scrtch, a, iflag )
+      if (iflag .gt. 1) 		stop
+      do 20 i=1,lx
+	 gtau(i) = bvalue ( t, a, n, k, x(i), 0 )
+   20	 scrtch(i) = gtitan(i) - gtau(i)
+      print 620,(i,x(i),gtitan(i),gtau(i),scrtch(i),i=1,lx)
+  620 format(41h  i, data point, data, interpolant, error//
+     2	       (i3,f8.0,f10.4,f9.4,e11.3))
+      nmk = n-k
+      print 621,(i,t(k+i),i=1,nmk)
+  621 format(///16h optimal knots =/(i5,f15.9))
+					stop
+      end
diff --git a/math/deboor/progs/prog15.f b/math/deboor/progs/prog15.f
new file mode 100644
index 00000000..2158931e
--- /dev/null
+++ b/math/deboor/progs/prog15.f
@@ -0,0 +1,48 @@
+chapter xiv, example 1. cubic smoothing spline
+c  from  * a practical guide to splines *  by c. de boor
+calls  bsplpp(bsplvb), ppvalu(interv), smooth(setupq,chol1d)
+c     values from a cubic b-spline are rounded to  n d i g i t	places
+c  after the decimal point, then smoothed via  s m o o t h  for
+c  various values of the control parameter  s .
+      integer i,is,j,l,lsm,ndigit,npoint,ns
+      real a(61,4),bcoef(7),break(5),coef(4,4),coefsm(4,60),dely,dy(61)
+     *	  ,s(20),scrtch(427),sfp,t(11),tenton,x(61),y(61)
+      real ppvalu,smooth
+      equivalence (scrtch,coefsm)
+      data t /4*0.,1.,3.,4.,4*6./
+      data bcoef /3*0.,1.,3*0./
+      call bsplpp(t,bcoef,7,4,scrtch,break,coef,l)
+      npoint = 61
+      read 500,ndigit,ns,(s(i),i=1,ns)
+  500 format(2i3/(e10.4))
+      print 600,ndigit
+  600 format(24h exact values rounded to,i2,21h digits after decimal
+     *	     ,7h point./)
+      tenton = 10.**ndigit
+      dely = .5/tenton
+      do 10 i=1,npoint
+	 x(i) = .1*float(i-1)
+	 y(i) = ppvalu(break,coef,l,4,x(i),0)
+	 y(i) = float(int(y(i)*tenton + .5))/tenton
+   10	 dy(i) = dely
+      do 15 i=1,npoint,5
+	 do 15 j=1,4
+   15	    a(i,j) = ppvalu(break,coef,l,4,x(i),j-1)
+      print 615,(i,(a(i,j),j=1,4),i=1,npoint,5)
+  615 format(52h value and derivatives of noisefree function at some
+     *	    ,7h points/(i4,4e15.7))
+      do 20 is=1,ns
+	 sfp = smooth ( x, y, dy, npoint, s(is), scrtch, a )
+	 lsm = npoint - 1
+	 do 16 i=1,lsm
+	    do 16 j=1,4
+   16	       coefsm(j,i) = a(i,j)
+	 do 18 i=1,npoint,5
+	    do 18 j=1,4
+   18	       a(i,j) = ppvalu(x,coefsm,lsm,4,x(i),j-1)
+   20	 print 620, s(is), sfp, (i,(a(i,j),j=1,4),i=1,npoint,5)
+  620 format(15h prescribed s =,e10.3,23h, s(smoothing spline) =,e10.3/
+     *	     54h value and derivatives of smoothing spline at corresp.
+     *	    ,7h points/(i4,4e15.7))
+					stop
+      end
diff --git a/math/deboor/progs/prog16.f b/math/deboor/progs/prog16.f
new file mode 100644
index 00000000..4dd39911
--- /dev/null
+++ b/math/deboor/progs/prog16.f
@@ -0,0 +1,115 @@
+c  main program for least-squares approximation by splines
+c  from  * a practical guide to splines *  by c. de boor
+calls setdat,l2knts,l2appr(bsplvb,bchfac,bchslv),bsplpp(bsplvb*)
+c     ,l2err(ppvalu(interv)),ppvalu*,newnot
+c
+c  the program, though ostensibly written for l2-approximation, is typ-
+c  ical for programs constructing a pp approximation to a function gi-
+c  ven in some sense. the subprogram  l 2 a p p r , for instance, could
+c  easily be replaced by one carrying out interpolation or some other
+c  form of approximation.
+c
+c******  i n p u t  ******
+c  is expected in  s e t d a t	(quo vide), specifying both the data to
+c  be approximated and the order and breakpoint sequence of the pp ap-
+c  proximating function to be used. further,  s e t d a t  is expected
+c  to  t e r m i n a t e  the run (for lack of further input or because
+c   i c o u n t  has reached a critical value).
+c     the number  n t i m e s  is read in in the main program. it speci
+c  fies the number of passes through the knot improvement algorithm in
+c  n e w n o t	to be made. also,  a d d b r k	is read in to specify
+c  that, on the average, addbrk knots are to be added per pass through
+c  newnot. for example,  addbrk = .34  would cause a knot to be added
+c  every third pass (as long as  ntimes .lt. 50).
+c
+c******  p r i n t e d	o u t p u t  ******
+c  is governed by the three print control hollerith strings
+c  p r b c o  = 2hon  gives printout of b-spline coeffs. of approxim.
+c  p r p c o  = 2hon  gives printout of pp repr. of approximation.
+c  p r f u n  = 2hon  gives printout of approximation and error at
+c		      every data point.
+c  the order  k , the number of pieces	l, and the interior breakpoints
+c  are always printed out as are (in l2err) the mean, mean square, and
+c  maximum errors in the approximation.
+c
+c     parameter lpkmax=100,ntmax=200,ltkmax=2000
+      integer i,icount,ii,j,k,l,lbegin,lnew,ll,n,nt,ntimes,ntau
+     *	     ,on,prbco,prfun,prpco
+c     real addbrk,bcoef(lpkmax),break,coef,gtau,q(ltkmax),scrtch(ntmax)
+c    *	  ,t(ntmax),tau,totalw,weight
+c     common / data / ntau, tau(ntmax),gtau(ntmax),weight(ntmax),totalw
+      real addbrk,bcoef(100),break,coef,gtau,q(2000),scrtch(200)
+     *	  ,t(200),tau,totalw,weight
+      common / data / ntau, tau(200),gtau(200),weight(200),totalw
+c     common /data/ also occurs in setdat, l2appr and l2err. it is ment-
+c     ioned here only because it might otherwise become undefined be-
+c     tween calls to those subroutines.
+c     common /approx/ break(lpkmax),coef(ltkmax),l,k
+      common /approx/ break(100),coef(2000),l,k
+c     common /approx/ also occurs in setdat and l2err.
+      data on /2hon /
+c
+      icount = 0
+c	 i c o u n t  provides communication with the data-input-and-
+c     termination routine  s e t d a t . it is initialized to  0  to
+c     signal to setdat when it is being called for the first time. after
+c     that, it is up to setdat to use icount for keeping track of the
+c     passes through setdat .
+c
+c     information about the function to be approximated and order and
+c     breakpoint sequence of the approximating pp functions is gathered
+c     by a
+    1 call setdat(icount)
+c
+c     breakpoints are translated into knots, and the number  n	of
+c     b-splines to be used is obtained by a
+      call l2knts ( break, l, k, t, n )
+c
+c     the integer  n t i m e s	and the real  a d d b r k  are requested
+c     as well as the print controls  p r b c o ,  p r p c o  and
+c     p r f u n .  ntimes  passes  are made through the subroutine new-
+c     not, with an increase of	addbrk	knots for every pass .
+      print 600
+  600 format(52h ntimes,addbrk , prbco,prpco,prfun =? (i3,f10.5/3a2))
+      read 500,ntimes,addbrk,prbco,prpco,prfun
+  500 format(i3,f10.5/3a2)
+c
+      lbegin = l
+      nt = 1
+c	 the b-spline coeffs.  b c o e f  of the l2-approx. are obtain-
+c	 ed by a
+   10	 call l2appr ( t, n, k, q, scrtch, bcoef )
+	 if (prbco .eq. on)  print 609, (bcoef(i),i=1,n)
+  609	 format(//22h b-spline coefficients/(5e16.9))
+c
+c	 convert the b-repr. of the approximation to pp repr.
+	 call bsplpp ( t, bcoef, n, k, q, break, coef, l )
+	 print 610, k, l, (break(ll),ll=2,l)
+  610	 format(//34h approximation by splines of order,i3,4h on ,
+     *	       i3,25h intervals. breakpoints -/(5e16.9))
+	 if (prpco .ne. on)		go to 15
+	 print 611
+  611	 format(/36h pp-representation for approximation)
+	 do 12 i=1,l
+	    ii = (i-1)*k
+   12	    print 613,break(i),(coef(ii+j),j=1,k)
+  613	 format(f9.3,5e16.9/(11x,5e16.9))
+c
+c	 compute and print out various error norms by a
+   15	 call l2err ( prfun, scrtch, q )
+c
+c	 if newnot has been applied less than  n t i m e s  times, try
+c	 it again to obtain, from the current approx. a possibly improv-
+c	 ed sequence of breakpoints with  addbrk  more breakpoints (on
+c	 the average) than the current approximation has.
+c	    if only an increase in breakpoints is wanted, without the
+c	 adjustment that newnot provides, a fake newnot routine could be
+c	 used here which merely returns the breakpoints for  l n e w
+c	 equal intervals .
+	 if (nt .ge. ntimes)		go to 1
+	 lnew = lbegin + float(nt)*addbrk
+	 call newnot (break, coef, l, k, scrtch, lnew, t )
+	 call l2knts ( scrtch, lnew, k, t, n )
+	 nt = nt + 1
+					go to 10
+      end
diff --git a/math/deboor/progs/prog17.f b/math/deboor/progs/prog17.f
new file mode 100644
index 00000000..1008c3a1
--- /dev/null
+++ b/math/deboor/progs/prog17.f
@@ -0,0 +1,10 @@
+c  main program for example in chapter xv.
+c  from  * a practical guide to splines *  by c. de boor
+c  solution of a second order nonlinear two point boundary value
+c  problem  on (0., 1.) , by collocation with pp functions having  4
+c  pieces of order  6 .  2  passes through newnot are to be made,
+c  without any knots being added. newton iteration is to be stopped
+c  when two iterates agree to  6  decimal places.
+       call colloc(0.,1.,4,6,2,0.,1.e-6)
+					stop
+       end
diff --git a/math/deboor/progs/prog18.f b/math/deboor/progs/prog18.f
new file mode 100644
index 00000000..fad18c62
--- /dev/null
+++ b/math/deboor/progs/prog18.f
@@ -0,0 +1,35 @@
+chapter xvi, example 2, taut spline interpolation to the
+c  titanium heat data of example xiii.3.
+c  from  * a practical guide to splines *  by c. de boor
+calls titand,tautsp,ppvalu(interv)
+      integer i,iflag,ipick(12),ipicki,k,l,lx,n,npoint
+      real break(122),coef(4,22),gamma,gtau(49),gtitan(49),plotf(201)
+     *	  ,plott(201),plotts(201),scrtch(119),step,tau(12),x(49)
+      real ppvalu
+      data n,ipick /12,1,5,11,21,27,29,31,33,35,40,45,49/
+      data k,npoint /4,201/
+      call titand ( x, gtitan, lx )
+      do 10 i=1,n
+	 ipicki = ipick(i)
+	 tau(i) = x(ipicki)
+   10	 gtau(i) = gtitan(ipicki)
+      call tautsp(tau,gtau,n,0.,scrtch,break,coef,l,k,iflag)
+      if (iflag .gt. 1) 		stop
+      step = (tau(n) - tau(1))/float(npoint-1)
+      do 20 i=1,npoint
+	 plott(i) = tau(1) + step*float(i-1)
+   20	 plotf(i) = ppvalu(break,coef,l,k,plott(i),0)
+    1 print 601
+  601 format(18h gamma = ? (f10.3))
+      read 500,gamma
+  500 format(f10.3)
+      if (gamma .lt. 0.)		stop
+      call tautsp(tau,gtau,n,gamma,scrtch,break,coef,l,k,iflag)
+      if (iflag .gt. 1) 		stop
+      do 30 i=1,npoint
+   30	 plotts(i) = ppvalu(break,coef,l,k,plott(i),0)
+      print 602,gamma,(plott(i),plotf(i),plotts(i),i=1,npoint)
+  602 format(/42h cubic spline vs. taut spline with gamma =,f6.3//
+     *	    (f15.7,2e20.8))
+					go to 1
+      end
diff --git a/math/deboor/progs/prog19.f b/math/deboor/progs/prog19.f
new file mode 100644
index 00000000..6595b76c
--- /dev/null
+++ b/math/deboor/progs/prog19.f
@@ -0,0 +1,58 @@
+chapter xvi, example 3. two parametrizations of some data
+c  from  * a practical guide to splines *  by c. de boor
+calls  splint(bsplvb,banfac/slv),bsplpp(bsplvb*),banslv*,ppvalu(interv)
+c     parameter k=4,kpkm1=7, n=8,npk=12, npiece=6,npoint=21
+c     integer i,icount,iflag,kp1,l
+c     real bcoef(n),break(npiece),ds,q(n,kpkm1),s(n),scrtch(k,k)
+c    *	  ,ss,t(npk),x(n),xcoef(k,npiece),xx(npoint),y(n)
+c    *	  ,ycoef(k,npiece),yy(npoint)
+      integer i,icount,iflag,k,kpkm1,kp1,l,n,npoint
+      real bcoef(8),break(6),ds,q(8,7),s(8),scrtch(4,4)
+     *	  ,ss,t(12),x(8),xcoef(4,6),xx(21),y(8)
+     *	  ,ycoef(4,6),yy(21)
+      real ppvalu
+      data k,kpkm1,n,npoint /4,7,8,21/
+      data x /0.,.1,.2,.3,.301,.4,.5,.6/
+c  *** compute y-component and set 'natural' parametrization
+      do 1 i=1,n
+	 y(i) = (x(i)-.3)**2
+    1	 s(i) = x(i)
+      print 601
+  601 format(26h 'natural' parametrization/6x,1hx,11x,1hy)
+      icount = 1
+c  *** convert data abscissae to knots. note that second and second
+c     last data abscissae are not knots.
+    5 do 6 i=1,k
+	 t(i) = s(1)
+    6	 t(n+i) = s(n)
+      kp1 = k+1
+      do 7 i=kp1,n
+    7	 t(i) = s(i+2-k)
+c  *** interpolate to x-component
+      call splint(s,x,t,n,k,q,bcoef,iflag)
+      call bsplpp(t,bcoef,n,k,scrtch,break,xcoef,l)
+c  *** interpolate to y-component. since data abscissae and knots are
+c     the same for both components, we only need to use backsubstitution
+      do 10 i=1,n
+   10	 bcoef(i) = y(i)
+      call banslv(q,kpkm1,n,k-1,k-1,bcoef)
+      call bsplpp(t,bcoef,n,k,scrtch,break,ycoef,l)
+c  *** evaluate curve at some points near the potential trouble spot,
+c     the fourth and fifth data points.
+      ss = s(3)
+      ds = (s(6)-s(3))/float(npoint-1)
+      do 20 i=1,npoint
+	 xx(i) = ppvalu(break,xcoef,l,k,ss,0)
+	 yy(i) = ppvalu(break,ycoef,l,k,ss,0)
+   20	 ss = ss + ds
+      print 620,(xx(i),yy(i),i=1,npoint)
+  620 format(2f12.7)
+      if (icount .ge. 2)		stop
+c  *** now repeat the whole process with uniform parametrization
+      icount = icount + 1
+      do 30 i=1,n
+   30	 s(i) = float(i)
+      print 630
+  630 format(/26h 'uniform' parametrization/6x,1hx,11x,1hy)
+					go to 5
+      end
diff --git a/math/deboor/progs/prog2.f b/math/deboor/progs/prog2.f
new file mode 100644
index 00000000..1da20d52
--- /dev/null
+++ b/math/deboor/progs/prog2.f
@@ -0,0 +1,48 @@
+chapter iv. runge example, with cubic hermite interpolation
+c  from  * a practical guide to splines *  by c. de boor
+      integer i,istep,j,n,nm1
+      real aloger,algerp,c(4,20),decay,divdf1,divdf3,dtau,dx,errmax,g,h
+     *	  ,pnatx,step,tau(20),x
+      data step, istep /20., 20/
+      g(x) = 1./(1.+(5.*x)**2)
+      print 600
+  600 format(28h  n   max.error   decay exp.//)
+      decay = 0.
+      do 40 n=2,20,2
+c	 choose interpolation points  tau(1), ..., tau(n) , equally
+c	 spaced in (-1,1), and set  c(1,i) = g(tau(i)), c(2,i) =
+c	 gprime(tau(i)) = -50.*tau(i)*g(tau(i))**2, i=1,...,n.
+	 nm1 = n-1
+	 h = 2./float(nm1)
+	 do 10 i=1,n
+	    tau(i) = float(i-1)*h - 1.
+	    c(1,i) = g(tau(i))
+   10	    c(2,i) = -50.*tau(i)*c(1,i)**2
+c	 calculate the coefficients of the polynomial pieces
+c
+	 do 20 i=1,nm1
+	    dtau = tau(i+1) - tau(i)
+	    divdf1 = (c(1,i+1) - c(1,i))/dtau
+	    divdf3 = c(2,i) + c(2,i+1) - 2.*divdf1
+	    c(3,i) = (divdf1 - c(2,i) - divdf3)/dtau
+   20	    c(4,i) = (divdf3/dtau)/dtau
+c
+c	 estimate max.interpolation error on (-1,1).
+	 errmax = 0.
+	 do 30 i=2,n
+	    dx = (tau(i)-tau(i-1))/step
+	    do 30 j=1,istep
+	       h = float(j)*dx
+c	       evaluate (i-1)st cubic piece
+c
+	       pnatx = c(1,i-1)+h*(c(2,i-1)+h*(c(3,i-1)+h*c(4,i-1)))
+c
+   30	       errmax = amax1(errmax,abs(g(tau(i-1)+h)-pnatx))
+	 aloger = alog(errmax)
+	 if (n .gt. 2)	decay =
+     *	     (aloger - algerp)/alog(float(n)/float(n-2))
+	 algerp = aloger
+   40	 print 640,n,errmax,decay
+  640 format(i3,e12.4,f11.2)
+					stop
+      end
diff --git a/math/deboor/progs/prog20.f b/math/deboor/progs/prog20.f
new file mode 100644
index 00000000..78143095
--- /dev/null
+++ b/math/deboor/progs/prog20.f
@@ -0,0 +1,62 @@
+chapter xvii, example 2. bivariate spline interpolation
+c  from  * a practical guide to splines *  by c. de boor
+calls  spli2d(bsplvb,banfac/slv),interv,bvalue(bsplvb*,interv*)
+c     parameter nx=7,kx=3,ny=6,ky=4
+c     integer i,iflag,j,jj,lefty,mflag,
+c     real bcoef(nx,ny),taux(nx),tauy(ny),tx(10),ty(10)
+c    *	       ,work1(nx,ny),work2(nx),work3(42)
+      integer i,iflag,j,jj,kp1,kx,ky,lefty,mflag,nx,ny
+      real bcoef(7,6),taux(7),tauy(6),tx(10),ty(10)
+     *	       ,work1(7,6),work2(7),work3(42)
+      real bvalue,g,x,y
+      data nx,kx,ny,ky /7,3,6,4/
+      g(x,y) = amax1(x-3.5,0.)**2 + amax1(y-3.,0.)**3
+c *** set up data points and knots
+c     in x, interpolate between knots by parabolic splines, using
+c     not-a-knot end condition
+      do 10 i=1,nx
+   10	 taux(i) = float(i)
+      do 11 i=1,kx
+	 tx(i) = taux(1)
+   11	 tx(nx+i) = taux(nx)
+      kp1 = kx+1
+      do 12 i=kp1,nx
+   12	 tx(i) = (taux(i-kx+1) + taux(i-kx+2))/2.
+c     in y, interpolate at knots by cubic splines, using not-a-knot
+c     end condition
+      do 20 i=1,ny
+   20	 tauy(i) = float(i)
+      do 21 i=1,ky
+	 ty(i) = tauy(1)
+   21	 ty(ny+i) = tauy(ny)
+      kp1 = ky+1
+      do 22 i=kp1,ny
+   22	 ty(i) = tauy(i-ky+2)
+c  *** generate and print out function values
+      print 620,(tauy(i),i=1,ny)
+  620 format(11h given data//6f12.1)
+      do 32 i=1,nx
+	 do 31 j=1,ny
+   31	    bcoef(i,j) = g(taux(i),tauy(j))
+   32	 print 632,taux(i),(bcoef(i,j),j=1,ny)
+  632 format(f5.1,6e12.5)
+c
+c  *** construct b-coefficients of interpolant
+c
+      call spli2d(taux,bcoef,tx,nx,kx,ny,work2,work3,work1,iflag)
+      call spli2d(tauy,work1,ty,ny,ky,nx,work2,work3,bcoef,iflag)
+c
+c  *** evaluate interpolation error at mesh points and print out
+      print 640,(tauy(j),j=1,ny)
+  640 format(//20h interpolation error//6f12.1)
+      do 45 j=1,ny
+	 call interv(ty,ny,tauy(j),lefty,mflag)
+	 do 45 i=1,nx
+	    do 41 jj=1,ky
+   41	       work2(jj)=bvalue(tx,bcoef(1,lefty-ky+jj),nx,kx,taux(i),0)
+   45	    work1(i,j) = g(taux(i),tauy(j)) -
+     *			bvalue(ty(lefty-ky+1),work2,ky,ky,tauy(j),0)
+      do 46 i=1,nx
+   46	 print 632,taux(i),(work1(i,j),j=1,ny)
+					stop
+      end
diff --git a/math/deboor/progs/prog21.f b/math/deboor/progs/prog21.f
new file mode 100644
index 00000000..6d8ca62a
--- /dev/null
+++ b/math/deboor/progs/prog21.f
@@ -0,0 +1,74 @@
+chapter xvii, example 3. bivariate spline interpolation
+c  followed by conversion to pp-repr and evaluation
+c  from  * a practical guide to splines *  by c. de boor
+calls  spli2d(bsplvb,banfac/slv),interv,bspp2d(bsplvb*),ppvalu(interv*)
+c     parameter nx=7,kx=3,ny=6,ky=4
+c     integer i,iflag,j,jj,lefty,lx,ly,mflag
+c     real bcoef(nx,ny),breakx(6),breaky(4),coef(kx,5,ky,3),taux(nx)
+c    *	  ,tauy(ny),tx(10),ty(10)
+c    *	       ,work1(nx,ny),work2(nx),work3(42)
+c    *	       ,work4(kx,kx,ny),work5(ny,kx,5),work6(ky,ky,21)
+      integer i,iflag,j,jj,kp1,kx,ky,lefty,lx,ly,mflag,nx,ny
+      real bcoef(7,6),breakx(6),breaky(4),coef(3,5,4,3),taux(7)
+     *	  ,tauy(6),tx(10),ty(10)
+     *	       ,work1(7,6),work2(7),work3(42)
+     *	       ,work4(3,3,6),work5(6,3,5),work6(4,4,21)
+      real ppvalu,g,x,y
+      data nx,kx,ny,ky / 7,3,6,4 /
+c     note that , with the above parameters, lx=5, ly = 3
+      equivalence (work4,work6)
+      g(x,y) = amax1(x-3.5,0.)**2 + amax1(y-3.,0.)**3
+c *** set up data points and knots
+c     in x, interpolate between knots by parabolic splines, using
+c     not-a-knot end condition
+      do 10 i=1,nx
+   10	 taux(i) = float(i)
+      do 11 i=1,kx
+	 tx(i) = taux(1)
+   11	 tx(nx+i) = taux(nx)
+      kp1 = kx+1
+      do 12 i=kp1,nx
+   12	 tx(i) = (taux(i-kx+1) + taux(i-kx+2))/2.
+c     in y, interpolate at knots by cubic splines, using not-a-knot
+c     end condition
+      do 20 i=1,ny
+   20	 tauy(i) = float(i)
+      do 21 i=1,ky
+	 ty(i) = tauy(1)
+   21	 ty(ny+i) = tauy(ny)
+      kp1 = ky+1
+      do 22 i=kp1,ny
+   22	 ty(i) = tauy(i-ky+2)
+c  *** generate and print out function values
+      print 620,(tauy(i),i=1,ny)
+  620 format(11h given data//6f12.1)
+      do 32 i=1,nx
+	 do 31 j=1,ny
+   31	    bcoef(i,j) = g(taux(i),tauy(j))
+   32	 print 632,taux(i),(bcoef(i,j),j=1,ny)
+  632 format(f5.1,6e12.5)
+c
+c  *** construct b-coefficients of interpolant
+c
+      call spli2d(taux,bcoef,tx,nx,kx,ny,work2,work3,work1,iflag)
+      call spli2d(tauy,work1,ty,ny,ky,nx,work2,work3,bcoef,iflag)
+c
+c  *** convert to pp-representation
+c
+      call bspp2d(tx,bcoef,nx,kx,ny,work4,breakx,work5,lx)
+      call bspp2d(ty,work5,ny,ky,lx*kx,work6,breaky,coef,ly)
+c
+c  *** evaluate interpolation error at mesh points and print out
+      print 640,(tauy(j),j=1,ny)
+  640 format(//20h interpolation error//6f12.1)
+      do 45 j=1,ny
+	 call interv(breaky,ly,tauy(j),lefty,mflag)
+	 do 45 i=1,nx
+	    do 41 jj=1,ky
+   41	     work2(jj)=ppvalu(breakx,coef(1,1,jj,lefty),lx,kx,taux(i),0)
+   45	    work1(i,j) = g(taux(i),tauy(j)) -
+     *	    ppvalu(breaky(lefty),work2,1,ky,tauy(j),0)
+      do 46 i=1,nx
+   46	 print 632,taux(i),(work1(i,j),j=1,ny)
+					stop
+      end
diff --git a/math/deboor/progs/prog3.f b/math/deboor/progs/prog3.f
new file mode 100644
index 00000000..337fe7ef
--- /dev/null
+++ b/math/deboor/progs/prog3.f
@@ -0,0 +1,44 @@
+chapter ix. example comparing the b-representation of a cubic  f  with
+c  its values at knot averages.
+c  from  * a practical guide to splines *  by c. de boor
+c
+      integer i,id,j,jj,n,nm4
+      real bcoef(23),d(4),d0(4),dtip1,dtip2,f(23),t(27),tave(23),x
+c	     the taylor coefficients at  0  for the polynomial	f  are
+      data d0 /-162.,99.,-18.,1./
+c
+c		  set up knot sequence in the array  t .
+      n = 13
+      do 5 i=1,4
+	 t(i) = 0.
+    5	 t(n+i) = 10.
+      nm4 = n-4
+      do 6 i=1,nm4
+    6	 t(i+4) = float(i)
+c
+      do 50 i=1,n
+c	 use nested multiplication to get taylor coefficients  d  at
+c		t(i+2)	from those at  0 .
+	 do 20 j=1,4
+   20	    d(j) = d0(j)
+	 do 21 j=1,3
+	    id = 4
+	    do 21 jj=j,3
+	       id = id-1
+   21	       d(id) = d(id) + d(id+1)*t(i+2)
+c
+c		 compute b-spline coefficients by formula (9).
+	 dtip1 = t(i+2) - t(i+1)
+	 dtip2 = t(i+3) - t(i+2)
+	 bcoef(i) = d(1) + (d(2)*(dtip2-dtip1)-d(3)*dtip1*dtip2)/3.
+c
+c		   evaluate  f	at corresp. knot average.
+	 tave(i) = (t(i+1) + t(i+2) + t(i+3))/3.
+	 x = tave(i)
+   50	 f(i) = d0(1) + x*(d0(2) + x*(d0(3) + x*d0(4)))
+c
+      print 650, (i,tave(i), f(i), bcoef(i),i=1,n)
+  650 format(45h  i   tave(i)	   f at tave(i)      bcoef(i)//
+     *	     (i3,f10.5,2f16.5))
+					stop
+      end
diff --git a/math/deboor/progs/prog4.f b/math/deboor/progs/prog4.f
new file mode 100644
index 00000000..8fc73304
--- /dev/null
+++ b/math/deboor/progs/prog4.f
@@ -0,0 +1,35 @@
+chapter x. example 1. plotting some b-splines
+c  from  * a practical guide to splines *  by c. de boor
+calls  bsplvb, interv
+      integer i,j,k,left,leftmk,mflag,n,npoint
+      real dx,t(10),values(7),x,xl
+c  dimension, order and knot sequence for spline space are specified...
+      data n,k /7,3/, t /3*0.,2*1.,3.,4.,3*6./
+c  b-spline values are initialized to 0., number of evaluation points...
+      data values /7*0./, npoint /31/
+c  set leftmost evaluation point  xl , and spacing  dx	to be used...
+      xl = t(k)
+      dx = (t(n+1)-t(k))/float(npoint-1)
+c
+      print 600,(i,i=1,5)
+  600 format(4h1  x,8x,5(1hb,i1,3h(x),7x))
+c
+      do 10 i=1,npoint
+	 x = xl + float(i-1)*dx
+c		      locate  x  with respect to knot array  t .
+	 call interv ( t, n, x, left, mflag )
+	 leftmk = left - k
+c	    get b(i,k)(x)  in  values(i) , i=1,...,n .	k  of these,
+c	 viz.  b(left-k+1,k)(x), ..., b(left,k)(x),  are supplied by
+c	 bsplvb . all others are known to be zero a priori.
+	 call bsplvb ( t, k, 1, x, left, values(leftmk+1) )
+c
+	 print 610, x, (values(j),j=3,7)
+  610	 format(f7.3,5f12.7)
+c
+c	    zero out the values just computed in preparation for next
+c	 evalulation point .
+	 do 10 j=1,k
+   10	    values(leftmk+j) = 0.
+					stop
+      end
diff --git a/math/deboor/progs/prog5.f b/math/deboor/progs/prog5.f
new file mode 100644
index 00000000..b1fbb927
--- /dev/null
+++ b/math/deboor/progs/prog5.f
@@ -0,0 +1,27 @@
+chapter x. example 2. plotting the pol,s which make up a b-spline
+c  from  * a practical guide to splines *  by c. de boor
+calls  bsplvb
+c
+      integer ia,left
+      real biatx(4),t(11),values(4),x
+c		  knot sequence set here....
+      data t / 4*0.,1.,3.,4.,4*6. /
+      do 20 ia=1,40
+	 x = float(ia)*.2 - 1.
+	 do 10 left=4,7
+	    call bsplvb ( t, 4, 1, x, left, biatx )
+c
+c	    according to  bsplvb  listing,  biatx(.) now contains value
+c	    at	x  of polynomial which agrees on the interval  (t(left),
+c	    t(left+1) )  with the b-spline  b(left-4 + . ,4,t) . hence,
+c	    biatx(8-left)  now contains value of that polynomial for
+c	    b(left-4 +(8-left) ,4,t) = b(4,4,t) . since this b-spline
+c	    has support  (t(4),t(8)), it makes sense to run  left = 4,
+c	    ...,7, storing the resulting values in  values(1),...,
+c	    values(4)  for later printing.
+c
+   10	    values(left-3) = biatx(8-left)
+   20	 print 620, x, values
+  620 format(f10.1,4f20.8)
+					stop
+      end
diff --git a/math/deboor/progs/prog6.f b/math/deboor/progs/prog6.f
new file mode 100644
index 00000000..10c55c1f
--- /dev/null
+++ b/math/deboor/progs/prog6.f
@@ -0,0 +1,23 @@
+chapter x. example 3. construction and evaluation of the pp-representat-
+c		      ion of a b-spline.
+c  from  * a practical guide to splines *  by c. de boor
+calls bsplpp(bsplvb),ppvalu(interv)
+c
+      integer ia,l
+      real bcoef(7),break(5),coef(4,4),scrtch(4,4),t(11),value,x
+      real ppvalu
+c		 set knot sequence  t  and b-coeffs for  b(4,4,t)  ....
+      data t / 4*0.,1.,3.,4.,4*6. /, bcoef / 3*0.,1.,3*0. /
+c			   construct pp-representation	....
+      call bsplpp ( t, bcoef, 7, 4, scrtch, break, coef, l )
+c
+c     as a check, evaluate  b(4,4,t)  from its pp-repr. on a fine mesh.
+c	      the values should agree with (some of) those generated in
+c			 example 2 .
+      do 20 ia=1,40
+	 x = float(ia)*.2 - 1.
+	 value = ppvalu ( break, coef, l, 4, x, 0 )
+   20	 print 620, x, value
+  620 format(f10.1,f20.8)
+					stop
+      end
diff --git a/math/deboor/progs/prog7.f b/math/deboor/progs/prog7.f
new file mode 100644
index 00000000..e08ab120
--- /dev/null
+++ b/math/deboor/progs/prog7.f
@@ -0,0 +1,17 @@
+chapter x.  example 4. construction of a b-spline via  bvalue
+c  from  * a practical guide to splines *  by c. de boor
+calls  bvalue(interv)
+      integer ia
+      real bcoef(1),t(5),value,x
+      real bvalue
+c		   set knot sequence  t  and  b-coeffs for  b(1,4,t)
+      data t / 0.,1.,3.,4.,6. / , bcoef / 1. /
+c	evaluate  b(1,4,t)  on a fine mesh.  on (0,6), the values should
+c		coincide with those obtained in example 3 .
+      do 20 ia=1,40
+	 x = float(ia)*.2 - 1.
+	 value = bvalue ( t, bcoef, 1, 4, x, 0 )
+   20	 print 620, x, value
+  620 format(f10.1,f20.8)
+					stop
+      end
diff --git a/math/deboor/progs/prog8.f b/math/deboor/progs/prog8.f
new file mode 100644
index 00000000..197f56f3
--- /dev/null
+++ b/math/deboor/progs/prog8.f
@@ -0,0 +1,63 @@
+chapter xii, example 2. cubic spline interpolation with good knots
+c  from  * a practical guide to splines *  by c. de boor
+calls  cubspl, newnot
+c     parameter nmax=20
+      integer i,istep,iter,itermx,j,n,nhigh,nlow,nm1
+c     real algerp,aloger,decay,dx,errmax,c(4,nmax),g,h,pnatx
+c    *	  ,scrtch(2,nmax),step,tau(nmax),taunew(nmax)
+      real algerp,aloger,decay,dx,errmax,c(4,20),g,h,pnatx
+     *	  ,scrtch(2,20),step,tau(20),taunew(20),x
+c     istep and step = float(istep) specify point density for error det-
+c     ermination.
+      data step, istep /20., 20/
+c				the function  g  is to be interpolated .
+      g(x) = sqrt(x+1.)
+      decay = 0.
+c      read in the number of iterations to be carried out and the lower
+c      and upper limit for the number  n  of data points to be used.
+      read 500,itermx,nlow,nhigh
+  500 format(3i3)
+      print 600, itermx
+  600 format(i4,22h cycles through newnot//
+     *	    28h  n   max.error	 decay exp./)
+c				  loop over  n = number of data points .
+      do 40 n=nlow,nhigh,2
+c					 knots are initially equispaced.
+	 nm1 = n-1
+	 h = 2./float(nm1)
+	 do 10 i=1,n
+   10	    tau(i) = float(i-1)*h - 1.
+	 iter = 1
+c		construct cubic spline interpolant. then, itermx  times,
+c		 determine new knots from it and find a new interpolant.
+   11	    do 15 i=1,n
+   15	       c(1,i) = g(tau(i))
+	    call cubspl ( tau, c, n, 0, 0 )
+	    if (iter .gt. itermx)	go to 19
+	    iter = iter+1
+	    call newnot(tau,c,nm1,4,taunew,nm1,scrtch)
+	    do 18 i=1,n
+   18	       tau(i) = taunew(i)
+					go to 11
+   19	 continue
+c			     estimate max.interpolation error on (-1,1).
+	 errmax = 0.
+c			    loop over polynomial pieces of interpolant .
+	 do 30 i=1,nm1
+	    dx = (tau(i+1)-tau(i))/step
+c		 interpolation error is calculated at  istep  points per
+c		     polynomial piece .
+	    do 30 j=1,istep
+	       h = float(j)*dx
+	       pnatx = c(1,i)+h*(c(2,i)+h*(c(3,i)+h*c(4,i)/3.)/2.)
+   30	    errmax = amax1(errmax,abs(g(tau(i)+h)-pnatx))
+c					      calculate decay exponent .
+	 aloger = alog(errmax)
+	 if (n .gt. nlow)  decay =
+     *	     (aloger - algerp)/alog(float(n)/float(n-2))
+	 algerp = aloger
+c
+   40	 print 640,n,errmax,decay
+  640 format(i3,e12.4,f11.2)
+					stop
+      end
diff --git a/math/deboor/progs/prog9.f b/math/deboor/progs/prog9.f
new file mode 100644
index 00000000..a0dcfd60
--- /dev/null
+++ b/math/deboor/progs/prog9.f
@@ -0,0 +1,38 @@
+chapter xii, example 3. cubic spline interpolation with good knots
+c  from  * a practical guide to splines *  by c. de boor
+calls cubspl
+      integer i,irate,istep,j,n,nhigh,nlow,nm1
+      real algerp,aloger,c(4,20),decay,dx,errmax,g,h,pnatx,step,tau(20)
+     *	  ,x
+      data step, istep /20., 20/
+      g(x) = sqrt(x+1.)
+      decay = 0.
+      read 500,irate,nlow,nhigh
+  500 format(3i3)
+      print 600
+  600 format(28h  n   max.error   decay exp./)
+      do 40 n=nlow,nhigh,2
+	 nm1 = n-1
+	 h = 1./float(nm1)
+	 do 10 i=1,n
+	    tau(i) = 2.*(float(i-1)*h)**irate - 1.
+   10	    c(1,i) = g(tau(i))
+c	 construct cubic spline interpolant.
+	 call cubspl ( tau, c, n, 0, 0 )
+c	 estimate max.interpolation error on (-1,1).
+	 errmax = 0.
+	 do 30 i=1,nm1
+	    dx = (tau(i+1)-tau(i))/step
+	    do 30 j=1,istep
+	       h = float(j)*dx
+	       pnatx = c(1,i)+h*(c(2,i)+h*(c(3,i)+h*c(4,i)/3.)/2.)
+	       x = tau(i) + h
+   30	       errmax = amax1(errmax,abs(g(x)-pnatx))
+	 aloger = alog(errmax)
+	 if (n .gt. nlow)  decay =
+     *	     (aloger - algerp)/alog(float(n)/float(n-2))
+	 algerp = aloger
+   40	 print 640,n,errmax,decay
+  640 format(i3,e12.4,f11.2)
+					stop
+      end
diff --git a/math/deboor/putit_io.f b/math/deboor/putit_io.f
new file mode 100644
index 00000000..c3e97c5a
--- /dev/null
+++ b/math/deboor/putit_io.f
@@ -0,0 +1,82 @@
+      subroutine putit ( t, kpm, left, scrtch, dbiatx, q, nrow, b )
+c  from  * a practical guide to splines *  by c. de boor
+calls  bsplvd(bsplvb),difequ(*)
+c  to be called by  e q b l o k .
+c
+c  puts together one block of the collocation equation system
+c
+c******  i n p u t  ******
+c  t	 knot sequence, of size  left+kpm (at least)
+c  kpm	 order of spline
+c  left  integer indicating interval of interest, viz the interval
+c	    (t(left), t(left+1))
+c  nrow  number of rows in block to be put together
+c
+c******  w o r k  a r e a  ******
+c  scrtch   used in bsplvd, of size (kpm,kpm)
+c  dbiatx   used to contain derivatives of b-splines, of size (kpm,m+1)
+c	    with dbiatx(j,i+1) containing the i-th derivative of the
+c	    j-th b-spline of interest
+c
+c******  o u t p u t  ******
+c  q  the block, of size (nrow,kpm)
+c  b  the corresponding piece of the right side, of size (nrow)
+c
+c******  m e t h o d  ******
+c  the	k  collocation equations for the interval  (t(left),t(left+1))
+c  are constructed with the aid of the subroutine  d i f e q u ( 2, .,
+c  . ) and interspersed (in order) with the side conditions (if any) in
+c  this interval, using  d i f e q u ( 3, ., . )  for the information.
+c     the block  q  has  kpm  columns, corresponding to the  kpm  b-
+c  splines of order  kpm  which have the interval (t(left),t(left+1))
+c  in their support. the block's diagonal is part of the diagonal of the
+c  total system. the first equation in this block not overlapped by the
+c  preceding block is therefore equation  l o w r o w , with lowrow =
+c  number of side conditions in preceding intervals (or blocks).
+c
+      integer kpm,left,nrow,   i,irow,iside,itermx,j,k,ll,lowrow,m,mode
+     *			      ,mp1
+      real b(1),dbiatx(kpm,1),q(nrow,kpm),scrtch(1),t(1),   dx,rho,sum
+     *						      ,v(20),xm,xside,xx
+      common /side/ m, iside, xside(10)
+      common /other/ itermx,k,rho(19)
+      mp1 = m+1
+      do 10 j=1,kpm
+	 do 10 i=1,nrow
+   10	    q(i,j) = 0.
+      xm = (t(left+1)+t(left))/2.
+      dx = (t(left+1)-t(left))/2.
+c
+      ll = 1
+      lowrow = iside
+      do 30 irow=lowrow,nrow
+	 if (ll .gt. k) 		go to 22
+	 mode = 2
+c	 next collocation point is ...
+	 xx = xm + dx*rho(ll)
+	 ll = ll + 1
+c	 the corresp.collocation equation is next unless the next side
+c	 condition occurs at a point at, or to the left of, the next
+c	 collocation point.
+	 if (iside .gt. m)		go to 24
+	 if (xside(iside) .gt. xx)	go to 24
+	 ll = ll - 1
+   22	 mode = 3
+	 xx = xside(iside)
+   24	 call difequ ( mode, xx, v )
+c	 the next equation, a collocation equation (mode = 2) or a side
+c	 condition (mode = 3), reads
+c   (*)   (v(m+1)*d**m + v(m)*d**(m-1) +...+ v(1)*d**0)f(xx) = v(m+2)
+c	 in terms of the info supplied by  difequ . the corresponding
+c	 equation for the b-coeffs of  f  therefore has the left side of
+c	 (*), evaluated at each of the	kpm  b-splines having  xx  in
+c	 their support, as its	kpm  possibly nonzero coefficients.
+	 call bsplvd ( t, kpm, xx, left, scrtch, dbiatx, mp1 )
+	 do 26 j=1,kpm
+	    sum = 0.
+	    do 25 i=1,mp1
+   25	       sum = v(i)*dbiatx(j,i) + sum
+   26	    q(irow,j) = sum
+   30	 b(irow) = v(m+2)
+					return
+      end
diff --git a/math/deboor/round.f b/math/deboor/round.f
new file mode 100644
index 00000000..df02c939
--- /dev/null
+++ b/math/deboor/round.f
@@ -0,0 +1,10 @@
+      real function round ( x )
+c  from  * a practical guide to splines *  by c. de boor
+called in example 1  of chapter xiii
+      real x,	flip,size
+      common /rount/ size
+      data flip /-1./
+      flip = -flip
+      round = x + flip*size
+					return
+      end
diff --git a/math/deboor/sbblok.f b/math/deboor/sbblok.f
new file mode 100644
index 00000000..8c4a77fb
--- /dev/null
+++ b/math/deboor/sbblok.f
@@ -0,0 +1,48 @@
+      subroutine sbblok ( bloks, integs, nbloks, ipivot, b, x )
+calls subroutines  s u b f o r	and  s u b b a k .
+c
+c  supervises the solution (by forward and backward substitution) of
+c  the linear system  a*x = b  for x, with the plu factorization of  a
+c  already generated in  f c b l o k .	individual blocks of equations
+c  are solved via  s u b f o r	and  s u b b a k .
+c
+c parameters
+c    bloks, integs, nbloks, ipivot    are as on return from fcblok.
+c    b	     the right side, stored corresponding to the storage of
+c	     the equations. see comments in  s l v b l k  for details.
+c    x	     solution vector
+c
+      integer nbloks
+      integer integs(3,nbloks),ipivot(1), i,index,indexb,indexx,j,last,
+     *	      nbp1,ncol,nrow
+      real bloks(1),b(1),x(1)
+c
+c      forward substitution pass
+c
+      index = 1
+      indexb = 1
+      indexx = 1
+      do 20 i=1,nbloks
+	 nrow = integs(1,i)
+	 last = integs(3,i)
+	 call subfor(bloks(index),ipivot(indexb),nrow,last,b(indexb),
+     *		     x(indexx))
+	 index = nrow*integs(2,i) + index
+	 indexb = indexb + nrow
+   20	 indexx = indexx + last
+c
+c     back substitution pass
+c
+      nbp1 = nbloks + 1
+      do 30 j=1,nbloks
+	 i = nbp1 - j
+	 nrow = integs(1,i)
+	 ncol = integs(2,i)
+	 last = integs(3,i)
+	 index = index - nrow*ncol
+	 indexb = indexb - nrow
+	 indexx = indexx - last
+   30	 call subbak(bloks(index),ipivot(indexb),nrow,ncol,last,
+     *		     x(indexx))
+					return
+      end
diff --git a/math/deboor/setdat.f b/math/deboor/setdat.f
new file mode 100644
index 00000000..40012a38
--- /dev/null
+++ b/math/deboor/setdat.f
@@ -0,0 +1,41 @@
+      subroutine setdat(icount)
+c  from  * a practical guide to splines *  by c. de boor
+c  to be called in main program  l 2 m a i n .
+c     this routine is set up to provide the specific data for example 2
+c     in chapter xiv. for a general purpose l2-approximation program, it
+c     would have to be replaced by a subroutine reading in
+c	    ntau, tau(i), gtau(i), i=1,...,ntau
+c     and reading in or setting
+c	     k, l, break(i),i=1,...,l+1,  and weight(i),i=1,...,ntau,
+c	    as well as	totalw = sum( weight(i) , i=1,...,ntau).
+c    i c o u n t  is equal to zero when setdat is called in  l 2 m a i n
+c     for the first time. after that, it is up to setdat to use icount
+c     for keeping track of the passes through setdat . this is important
+c     since l2main relies on setdat for  t e r m i n a t i o n .
+      integer icount,  i,k,l,lp1,ntau,ntaum1
+      real break,coef,gtau,step,tau,totalw,weight
+c     parameter lpkmax=100,ntmax=200,ltkmax=2000
+c     common / data / ntau, tau(ntmax),gtau(ntmax),weight(ntmax),totalw
+c     common /approx/ break(lpkmax),coef(ltkmax),l,k
+      common / data / ntau, tau(200),gtau(200),weight(200),totalw
+      common /approx/ break(100),coef(2000),l,k
+      if (icount .gt. 0)		stop
+      icount = icount + 1
+      ntau = 10
+      ntaum1 = ntau-1
+      do 8 i=1,ntaum1
+    8	 tau(i) = 1. - .5**(i-1)
+      tau(ntau) = 1.
+      do 9 i=1,ntau
+    9	 gtau(i) = tau(i)**2  + 1.
+      do 10 i=1,ntau
+   10	 weight(i) = 1.
+      totalw = ntau
+      l = 6
+      lp1 = l+1
+      step = 1./float(l)
+      k = 2
+      do 11 i=1,lp1
+   11	 break(i) = (i-1)*step
+					return
+      end
diff --git a/math/deboor/setdat2.f b/math/deboor/setdat2.f
new file mode 100644
index 00000000..cf767a59
--- /dev/null
+++ b/math/deboor/setdat2.f
@@ -0,0 +1,29 @@
+      subroutine setdt2(icount)
+c  from  * a practical guide to splines *  by c. de boor
+c  to be called in main program  l 2 m a i n .
+c     this routine is set up to provide the specific data for example 3
+c     in chapter xiv.
+c
+      integer icount,  i,k,l,ntau
+      real break,coef,gtau,step,tau,totalw,weight,x,round
+c     parameter lpkmax=100,ntmax=200,ltkmax=2000
+c     common / data / ntau, tau(ntmax),gtau(ntmax),weight(ntmax),totalw
+c     common /approx/ break(lpkmax),coef(ltkmax),l,k
+      common / data / ntau, tau(200),gtau(200),weight(200),totalw
+      common /approx/ break(100),coef(2000),l,k
+      round(x) = float(ifix(x*100.))/100.
+      if (icount .gt. 0)		stop
+      icount = icount + 1
+      ntau = 65
+      step = 3./float(ntau-1)
+      do 10 i=1,ntau
+	 tau(i) = i*step
+	 gtau(i) = round(exp(tau(i)))
+   10	 weight(i) = 1.
+      totalw = ntau
+      l = 1
+      break(1) = tau(1)
+      break(2) = tau(ntau)
+      k = 3
+					return
+      end
diff --git a/math/deboor/setdat3.f b/math/deboor/setdat3.f
new file mode 100644
index 00000000..3524e489
--- /dev/null
+++ b/math/deboor/setdat3.f
@@ -0,0 +1,27 @@
+      subroutine setdt3(icount)
+c  from  * a practical guide to splines *  by c. de boor
+c  to be called in main program  l 2 m a i n .
+c	calls titand
+c     this routine is set up to provide the specific data for example 4
+c     in chapter xiv.
+      integer icount,  i,k,l,n,ntau
+      real break,brkpic(9),coef,gtau,tau,totalw,weight
+c     parameter lpkmax=100,ntmax=200,ltkmax=2000
+c     common / data / ntau, tau(ntmax),gtau(ntmax),weight(ntmax),totalw
+c     common /approx/ break(lpkmax),coef(ltkmax),l,k
+      common / data / ntau, tau(200),gtau(200),weight(200),totalw
+      common /approx/ break(100),coef(2000),l,k
+      data brkpic,n/595.,730.985,794.414,844.476,880.06,907.814,
+     *		    938.001,976.752,1075.,9/
+      if (icount .gt. 0)		stop
+      icount = icount + 1
+      call titand ( tau, gtau, ntau )
+      do 10 i=1,ntau
+   10	 weight(i) = 1.
+      totalw = ntau
+      l = n-1
+      k = 5
+      do 11 i=1,n
+   11	 break(i) = brkpic(i)
+					return
+      end
diff --git a/math/deboor/setupq.f b/math/deboor/setupq.f
new file mode 100644
index 00000000..dea21a3b
--- /dev/null
+++ b/math/deboor/setupq.f
@@ -0,0 +1,40 @@
+      subroutine setupq ( x, dx, y, npoint, v, qty )
+c  from  * a practical guide to splines *  by c. de boor
+c  to be called in  s m o o t h
+c  put	delx = x(.+1) - x(.)  into  v(.,4),
+c  put	the three bands of  q-transp*d	into  v(.,1-3), and
+c  put the three bands of  (d*q)-transp*(d*q)  at and above the diagonal
+c     into  v(.,5-7) .
+c     here,  q is  the tridiagonal matrix of order (npoint-2,npoint)
+c  with general row  1/delx(i) , -1/delx(i) - 1/delx(i+1) , 1/delx(i+1)
+c  and	 d  is the diagonal matrix  with general row  dx(i) .
+      integer npoint,	i,npm1
+      real dx(npoint),qty(npoint),v(npoint,7),x(npoint),y(npoint),
+     *							  diff,   prev
+      npm1 = npoint - 1
+      v(1,4) = x(2) - x(1)
+      do 11 i=2,npm1
+	 v(i,4) = x(i+1) - x(i)
+	 v(i,1) = dx(i-1)/v(i-1,4)
+	 v(i,2) = - dx(i)/v(i,4) - dx(i)/v(i-1,4)
+   11	 v(i,3) = dx(i+1)/v(i,4)
+      v(npoint,1) = 0.
+      do 12 i=2,npm1
+   12	 v(i,5) = v(i,1)**2 + v(i,2)**2 + v(i,3)**2
+      if (npm1 .lt. 3)			go to 14
+      do 13 i=3,npm1
+   13	 v(i-1,6) = v(i-1,2)*v(i,1) + v(i-1,3)*v(i,2)
+   14 v(npm1,6) = 0.
+      if (npm1 .lt. 4)			go to 16
+      do 15 i=4,npm1
+   15	 v(i-2,7) = v(i-2,3)*v(i,1)
+   16 v(npm1-1,7) = 0.
+      v(npm1,7) = 0.
+construct  q-transp. * y  in  qty.
+      prev = (y(2) - y(1))/v(1,4)
+      do 21 i=2,npm1
+	 diff = (y(i+1)-y(i))/v(i,4)
+	 qty(i) = diff - prev
+   21	 prev = diff
+					return
+      end
diff --git a/math/deboor/seval.x b/math/deboor/seval.x
new file mode 100644
index 00000000..ee9cd1e9
--- /dev/null
+++ b/math/deboor/seval.x
@@ -0,0 +1,159 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+
+include <iraf.h>
+include	"bspln.h"
+
+.help seval 2 "math library"
+.ih
+NAME
+seval -- evaluate the Dth derivative of a Kth order b-spline at X.
+.ih
+USAGE
+y = seval (x, deriv, bspln)
+.ih
+PARAMETERS
+The single precision real value returned by SEVAL is the value of the D-th
+derivative of the b-spline at X.  INDEF is returned if X lies outside the
+domain of the spline.
+.ls x
+(real).  Logical x-value at which the spline is to be evaluated.
+.le
+.ls deriv
+The derivative to be evaluated.  The zeroth derivative is the function value.
+.le
+.ls bspln
+(real[2*n+30]).  B-spline descriptor structure, generated by a previous
+call to SPLINE, SPLLSQ, etc.
+.le
+.ih
+DESCRIPTION
+Calculate the Dth derivative of a Kth order B-spline.  Based on BVALUE, from
+"A Practical Guide to Splines", by C. DeBoor.  The main changes incorporated
+in SEVAL involve the use of the BSPLN array to convey all of the information
+needed to describe the spline.  This simplifies the calling sequences, and
+improves the communication between routines.  SEVAL is designed to be easy to
+use, and reasonably efficient in the case where a N point spline is to be
+evaluated N times or less.  If a spline is to be fitted and then evaluated
+many times, conversion to PP representation may be warranted to gain maximum
+efficiency.
+.ih
+METHOD
+See DeBoor, pg. 144, or the listing of BVALUE, for a detailed explanation
+of the mathematics involved.  In short, we find the knot interval containing
+X, choosing the next interval to the left if X happens to fall square on a
+knot.  The distances of X from the K-1 knots to the left and right are then
+calculated, and the K b-spline coefficients contributing to the interval are
+extracted.  Calculation of divided differences follows, if a derivative is
+to be calculated.  Finally the value of the b-spline at X is evaluated and
+returned.
+.ih
+BUGS
+The special case ND == 0 and ORDER == 4 (cubic spline) should be recognized,
+and specially optimized code used to evaluate the spline in that case.
+.ih
+SEE ALSO
+spline(2), fsplin(2), spllsq(2).
+.endhelp _____________________________________________________________
+
+
+real procedure seval (x, deriv, bspln)
+
+real	x			# logical x value
+real	bspln[ARB]		# ARB = [2 * NCOEF + 30]
+int	deriv			# derivative = 0,1,2,...,k-1
+
+int	i, j, k, n, jj, ilo, kmj, km1, offset, knots, coefs
+real	aj[KMAX], dl[KMAX], dr[KMAX], fkmj
+
+begin
+	if (x < XMIN || x > XMAX)	# x out of range?
+	    return (INDEF)
+
+	k = ORDER			# fetch k from bspln header
+	if (deriv >= k)			# Kth deriv K degree polyn is zero
+	    return (0.)
+ 
+# Find i such that X is in the interval T[i] <= X < T[i+1].  First we fetch
+# KINDEX from the bspln header.  This is the index into the knot array from
+# the last call (many, if not most, calls to SEVAL are sequential in nature).
+# Usually, KINDEX will already be the right interval, or will be one off.  If
+# more than one off, DeBoors INTERV is called to find the correct index via a
+# binary search.  INTERV handles the special cases (x == XMAX). 
+
+	i = KINDEX			# previous index for this spline
+	n = NCOEF
+	knots = KNOT1
+
+	if (x >= bspln[i+1]) {			# go right
+	    i = i + 1
+	    if (x >= bspln[i+1]) {
+		call interv (bspln[knots], n, x, i, j)
+		i = i + knots - 1
+	    }
+
+	} else if (x < bspln[i]) {		# go left
+	    i = i - 1
+	    if (x < bspln[i]) {
+		call interv (bspln[knots], n, x, i, j)
+		i = i + knots - 1
+	    }
+	}
+	KINDEX = i
+
+
+	km1 = k - 1
+	coefs = i - knots - k + COEF1
+
+	if (km1 <= 0)		# if order=1 (& deriv=0), bvalue = bspln[i].
+	    return (bspln[coefs+1])
+ 
+
+# Store the ORDER b-spline coefficients relevant for the knot interval
+# (T[i],T[i+1]) in aj[1],...,aj[k] and compute dl[j] = x - t[i+k-j],
+# dr[j] = t[i+k-1+j] - x, j=1,...,k-1.  Note that the K knots at each endpoint
+# all have the same T-value, hence we use the lookup table T, rather than
+# calculate the DL and DR from the knot spacing.
+
+	offset = i + 1
+	do j = 1, km1
+	    dl[j] = x - bspln[offset-j]
+
+	offset = offset - 1
+	do j = 1, km1
+	    dr[j] = bspln[i+j] - x
+
+	do j = 1, k		  		# fetch K coefficients
+	    aj[j] = bspln[coefs+j]
+
+
+# Difference the coefficients deriv times.
+
+	if (deriv != 0) {			# only if taking a derivative
+	    do j = 1, deriv {
+		kmj = k - j
+		fkmj = real (kmj)
+		ilo = kmj
+		do jj = 1, kmj {
+		    aj[jj] = ((aj[jj+1] - aj[jj]) / (dl[ilo] + dr[jj])) * fkmj
+		    ilo = ilo - 1
+		}
+	    }
+	}
+
+
+# Compute value at X in (t[i],t[i+])) of deriv-th derivative, given its
+# relevant b-spline coeffs in aj[1],...,aj[k-deriv].
+
+	if (deriv != km1) {
+	    do j = deriv + 1, km1 {
+		kmj = k - j
+		ilo = kmj
+		do jj = 1, kmj {
+		    aj[jj] = (aj[jj+1] * dl[ilo] + aj[jj] * dr[jj]) / (dl[ilo] + dr[jj])
+		    ilo = ilo - 1
+		}
+	    }
+	}
+	return (aj[1])
+end
diff --git a/math/deboor/shiftb.f b/math/deboor/shiftb.f
new file mode 100644
index 00000000..144c60f8
--- /dev/null
+++ b/math/deboor/shiftb.f
@@ -0,0 +1,50 @@
+      subroutine shiftb ( ai, ipivot, nrowi, ncoli, last,
+     *			  ai1, nrowi1, ncoli1 )
+c  shifts the rows in current block, ai, not used as pivot rows, if
+c  any, i.e., rows ipivot(last+1),...,ipivot(nrowi), onto the first
+c  mmax = nrow-last rows of the next block, ai1, with column last+j of
+c  ai  going to column j , j=1,...,jmax=ncoli-last. the remaining col-
+c  umns of these rows of ai1 are zeroed out.
+c
+c			      picture
+c
+c	original situation after	 results in a new block i+1
+c	last = 2 columns have been	 created and ready to be
+c	done in factrb (assuming no	 factored by next factrb call.
+c	interchanges of rows)
+c		    1
+c	       x  x 1x	x  x	       x  x  x	x  x
+c		    1
+c	       0  x 1x	x  x	       0  x  x	x  x
+c  block i	    1			    ---------------
+c  nrowi = 4   0  0 1x	x  x	       0  0 1x	x  x  0  01
+c  ncoli = 5	    1			    1		  1
+c  last = 2    0  0 1x	x  x	       0  0 1x	x  x  0  01
+c  -------------------------------	    1		  1   new
+c		    1x	x  x  x  x	    1x	x  x  x  x1  block
+c		    1			    1		  1   i+1
+c  block i+1	    1x	x  x  x  x	    1x	x  x  x  x1
+c  nrowi1= 5	    1			    1		  1
+c  ncoli1= 5	    1x	x  x  x  x	    1x	x  x  x  x1
+c  -------------------------------	    1-------------1
+c		    1
+c
+      integer nrowi, ncoli, nrowi1, ncoli1
+      integer ipivot(nrowi),last, ip,j,jmax,jmaxp1,m,mmax
+      real ai(nrowi,ncoli),ai1(nrowi1,ncoli1)
+      mmax = nrowi - last
+      jmax = ncoli - last
+      if (mmax .lt. 1 .or. jmax .lt. 1) return
+c	       put the remainder of block i into ai1
+      do 10 m=1,mmax
+	 ip = ipivot(last+m)
+	 do 10 j=1,jmax
+   10	    ai1(m,j) = ai(ip,last+j)
+      if (jmax .eq. ncoli1)		return
+c	       zero out the upper right corner of ai1
+      jmaxp1 = jmax + 1
+      do 20 j=jmaxp1,ncoli1
+	 do 20 m=1,mmax
+   20	    ai1(m,j) = 0.
+					return
+      end
diff --git a/math/deboor/slvblk.f b/math/deboor/slvblk.f
new file mode 100644
index 00000000..80be1302
--- /dev/null
+++ b/math/deboor/slvblk.f
@@ -0,0 +1,127 @@
+      subroutine slvblk ( bloks, integs, nbloks, b, ipivot, x, iflag )
+c    this program solves  the  linear system  a*x = b  where a is an
+c  almost block diagonal matrix.  such almost block diagonal matrices
+c  arise naturally in piecewise polynomial interpolation or approx-
+c  imation and in finite element methods for two-point boundary value
+c  problems.  the plu factorization method is implemented here to take
+c  advantage of the special structure of such systems for savings in
+c  computing time and storage requirements.
+c
+c		   parameters
+c  bloks   a one-dimenional array, of length
+c		    sum( integs(1,i)*integs(2,i) ; i = 1,nbloks )
+c	   on input, contains the blocks of the almost block diagonal
+c	   matrix  a  .  the array integs (see below and the example)
+c	   describes the block structure.
+c	   on output, contains correspondingly the plu factorization
+c	   of  a  (if iflag .ne. 0).  certain of the entries into bloks
+c	   are arbitrary (where the blocks overlap).
+c  integs  integer array description of the block structure of	a .
+c	     integs(1,i) = no. of rows of block i	 =  nrow
+c	     integs(2,i) = no. of colums of block i	 =  ncol
+c	     integs(3,i) = no. of elim. steps in block i =  last
+c			   i  = 1,2,...,nbloks
+c	   the linear system is of order
+c		 n  =  sum ( integs(3,i) , i=1,...,nbloks ),
+c	   but the total number of rows in the blocks is
+c	       nbrows = sum( integs(1,i) ; i = 1,...,nbloks)
+c  nbloks  number of blocks
+c  b	   right side of the linear system, array of length nbrows.
+c	   certain of the entries are arbitrary, corresponding to
+c	   rows of the blocks which overlap (see block structure and
+c	   the example below).
+c  ipivot  on output, integer array containing the pivoting sequence
+c	   used. length is nbrows
+c  x	   on output, contains the computed solution (if iflag .ne. 0)
+c	   length is n.
+c  iflag   on output, integer
+c	     = (-1)**(no. of interchanges during factorization)
+c		    if	a  is invertible
+c	     = 0    if	a  is singular
+c
+c		    auxiliary programs
+c  fcblok (bloks,integs,nbloks,ipivot,scrtch,iflag)  factors the matrix
+c	    a , and is used for this purpose in slvblk. its arguments
+c	   are as in slvblk, except for
+c	       scrtch = a work array of length max(integs(1,i)).
+c
+c  sbblok (bloks,integs,nbloks,ipivot,b,x)  solves the system a*x = b
+c	   once  a  is factored. this is done automatically by slvblk
+c	   for one right side b, but subsequent solutions may be
+c	   obtained for additional b-vectors. the arguments are all
+c	   as in slvblk.
+c
+c  dtblok (bloks,integs,nbloks,ipivot,iflag,detsgn,detlog) computes the
+c	   determinant of  a  once slvblk or fcblok has done the fact-
+c	   orization.the first five arguments are as in slvblk.
+c	       detsgn  = sign of the determinant
+c	       detlog  = natural log of the determinant
+c
+c	      ------ block structure of  a  ------
+c  the nbloks blocks are stored consecutively in the array  bloks .
+c  the first block has its (1,1)-entry at bloks(1), and, if the i-th
+c  block has its (1,1)-entry at bloks(index(i)), then
+c	  index(i+1) = index(i)  +  nrow(i)*ncol(i) .
+c    the blocks are pieced together to give the interesting part of  a
+c  as follows.	for i = 1,2,...,nbloks-1, the (1,1)-entry of the next
+c  block (the (i+1)st block ) corresponds to the (last+1,last+1)-entry
+c  of the current i-th block.  recall last = integs(3,i) and note that
+c  this means that
+c      a. every block starts on the diagonal of  a .
+c      b. the blocks overlap (usually). the rows of the (i+1)st block
+c	  which are overlapped by the i-th block may be arbitrarily de-
+c	  fined initially. they are overwritten during elimination.
+c    the right side for the equations in the i-th block are stored cor-
+c  respondingly as the last entries of a piece of  b  of length  nrow
+c  (= integs(1,i)) and following immediately in  b  the corresponding
+c  piece for the right side of the preceding block, with the right side
+c  for the first block starting at  b(1) . in this, the right side for
+c  an equation need only be specified once on input, in the first block
+c  in which the equation appears.
+c
+c	      ------ example and test driver ------
+c    the test driver for this package contains an example, a linear
+c  system of order 11, whose nonzero entries are indicated in the fol-
+c  lowing schema by their row and column index modulo 10. next to it
+c  are the contents of the  integs  arrray when the matrix is taken to
+c  be almost block diagonal with  nbloks = 5, and below it are the five
+c  blocks.
+c
+c		       nrow1 = 3, ncol1 = 4
+c	    11 12 13 14
+c	    21 22 23 24   nrow2 = 3, ncol2 = 3
+c	    31 32 33 34
+c  last1 = 2	  43 44 45
+c		  53 54 55	      nrow3 = 3, ncol3 = 4
+c	 last2 = 3	   66 67 68 69	 nrow4 = 3, ncol4 = 4
+c			   76 77 78 79	    nrow5 = 4, ncol5 = 4
+c			   86 87 88 89
+c		  last3 = 1   97 98 99 90
+c		     last4 = 1	 08 09 00 01
+c				 18 19 10 11
+c			last5 = 4
+c
+c	  actual input to bloks shown by rows of blocks of  a .
+c      (the ** items are arbitrary, this storage is used by slvblk)
+c
+c  11 12 13 14	/ ** ** **  / 66 67 68 69  / ** ** ** **  / ** ** ** **
+c  21 22 23 24 /  43 44 45 /  76 77 78 79 /  ** ** ** ** /  ** ** ** **
+c  31 32 33 34/   53 54 55/   86 87 88 89/   97 98 99 90/   08 09 00 01
+c							    18 19 10 11
+c
+c  index = 1	  index = 13  index = 22     index = 34     index = 46
+c
+c	  actual right side values with ** for arbitrary values
+c  b1 b2 b3 ** b4 b5 b6 b7 b8 ** ** b9 ** ** b10 b11
+c
+c  (it would have been more efficient to combine block 3 with block 4)
+c
+      integer nbloks
+      integer integs(3,nbloks),ipivot(1),iflag
+      real bloks(1),b(1),x(1)
+c     in the call to fcblok,  x  is used for temporary storage.
+      call fcblok(bloks,integs,nbloks,ipivot,x,iflag)
+      if (iflag .eq. 0) 		return
+      call sbblok(bloks,integs,nbloks,ipivot,b,x)
+					return
+      end
diff --git a/math/deboor/smooth.f b/math/deboor/smooth.f
new file mode 100644
index 00000000..9ae041a7
--- /dev/null
+++ b/math/deboor/smooth.f
@@ -0,0 +1,112 @@
+      real function smooth ( x, y, dy, npoint, s, v, a )
+c  from  * a practical guide to splines *  by c. de boor
+calls  setupq, chol1d
+c
+c  constructs the cubic smoothing spline  f  to given data  (x(i),y(i)),
+c  i=1,...,npoint, which has as small a second derivative as possible
+c  while
+c  s(f) = sum( ((y(i)-f(x(i)))/dy(i))**2 , i=1,...,npoint ) .le. s .
+c
+c******  i n p u t  ******
+c  x(1),...,x(npoint)	data abscissae,  a s s u m e d	to be strictly
+c	 increasing .
+c  y(1),...,y(npoint)	  corresponding data ordinates .
+c  dy(1),...,dy(npoint)     estimate of uncertainty in data,  a s s u m-
+c	 e d  to be positive .
+c  npoint.....number of data points,  a s s u m e d  .gt. 1
+c  s.....upper bound on the discrete weighted mean square distance of
+c	 the approximation  f  from the data .
+c
+c******  w o r k  a r r a y s  *****
+c  v.....of size (npoint,7)
+c  a.....of size (npoint,4)
+c
+c*****	o u t p u t  *****
+c  a(.,1).....contains the sequence of smoothed ordinates .
+c  a(i,j) = d**(j-1)f(x(i)), j=2,3,4, i=1,...,npoint-1 ,  i.e., the
+c	 first three derivatives of the smoothing spline  f  at the
+c	 left end of each of the data intervals .
+c     w a r n i n g . . .   a  would have to be transposed before it
+c	 could be used in  ppvalu .
+c
+c******  m e t h o d  ******
+c     the matrices  q-transp*d	and  q-transp*d**2*q  are constructed in
+c   s e t u p q  from  x  and  dy , as is the vector  qty = q-transp*y .
+c  then, for given  p , the vector  u  is determined in  c h o l 1 d  as
+c  the solution of the linear system
+c		(6(1-p)q-transp*d**2*q + p*r)u	= qty  .
+c  from  u , the smoothing spline  f  (for this choice of smoothing par-
+c  ameter  p ) is obtained in the sense that
+c			 f(x(.))  =  y - 6(1-p)d**2*q*u        and
+c		   (d**2)f(x(.))  =  6*p*u			.
+c     the smoothing parameter  p  is found (if possible) so that
+c		 sf(p)	=  s ,
+c  with  sf(p) = s(f) , where  f  is the smoothing spline as it depends
+c  on  p .  if	s = 0, then p = 1 . if	sf(0) .le. s , then p = 0 .
+c  otherwise, the secant method is used to locate an appropriate  p  in
+c  the open interval  (0,1) . specifically,
+c		 p(0) = 0,  p(1) = (s - sf(0))/dsf
+c  with  dsf = -24*u-transp*r*u  a good approximation to  d(sf(0)) = dsf
+c  + 60*(d*q*u)-transp*(d*q*u) , and  u  as obtained for  p = 0 .
+c  after that, for n=1,2,...  until sf(p(n)) .le. 1.01*s, do....
+c     determine  p(n+1)  as the point at which the secant to  sf  at the
+c     points  p(n)  and  p(n-1)  takes on the value  s .
+c     if  p(n+1) .ge. 1 , choose instead  p(n+1)  as the point at which
+c     the parabola  sf(p(n))*((1-.)/(1-p(n)))**2  takes on the value  s.
+c     note that, in exact arithmetic, always  p(n+1) .lt. p(n) , hence
+c     sf(p(n+1)) .lt. sf(p(n)) . therefore, also stop the iteration,
+c     with final  p = 1 , in case  sf(p(n+1)) .ge. sf(p(n)) .
+c
+      integer npoint,	i,npm1
+      real a(npoint,4),dy(npoint),s,v(npoint,7),x(npoint),y(npoint)
+     *	   ,change,p,prevsf,prevp,sfp,sixp,six1mp,utru
+      call setupq(x,dy,y,npoint,v,a(1,4))
+      if (s .gt. 0.)			go to 20
+   10 p = 1.
+      call chol1d(p,v,a(1,4),npoint,1,a(1,3),a(1,1))
+      sfp = 0.
+					go to 60
+   20 p = 0.
+      call chol1d(p,v,a(1,4),npoint,1,a(1,3),a(1,1))
+      sfp = 0.
+      do 21 i=1,npoint
+   21	 sfp = sfp + (a(i,1)*dy(i))**2
+      sfp = sfp*36.
+      if (sfp .le. s)			go to 60
+      prevp = 0.
+      prevsf = sfp
+      utru = 0.
+      do 25 i=2,npoint
+   25	 utru = utru + v(i-1,4)*(a(i-1,3)*(a(i-1,3)+a(i,3))+a(i,3)**2)
+      p = (sfp-s)/(24.*utru)
+c  secant iteration for the determination of p starts here.
+   30 call chol1d(p,v,a(1,4),npoint,1,a(1,3),a(1,1))
+      sfp = 0.
+      do 35 i=1,npoint
+   35	 sfp = sfp+ (a(i,1)*dy(i))**2
+      sfp = sfp*36.*(1.-p)**2
+      if (sfp .le. 1.01*s)		go to 60
+      if (sfp .ge. prevsf)		go to 10
+      change = (p-prevp)/(sfp-prevsf)*(sfp-s)
+      prevp = p
+      p = p - change
+      prevsf = sfp
+      if (p .lt. 1.)			go to 30
+      p = 1. - sqrt(s/prevsf)*(1.-prevp)
+					go to 30
+correct value of p has been found.
+compute pol.coefficients from  q*u (in a(.,1)).
+   60 smooth = sfp
+      six1mp = 6.*(1.-p)
+      do 61 i=1,npoint
+   61	 a(i,1) = y(i) - six1mp*dy(i)**2*a(i,1)
+      sixp = 6.*p
+      do 62 i=1,npoint
+   62	 a(i,3) = a(i,3)*sixp
+      npm1 = npoint - 1
+      do 63 i=1,npm1
+	 a(i,4) = (a(i+1,3)-a(i,3))/v(i,4)
+   63	 a(i,2) = (a(i+1,1)-a(i,1))/v(i,4)
+     *			    - (a(i,3)+a(i,4)/3.*v(i,4))/2.*v(i,4)
+					return
+      end
diff --git a/math/deboor/spli2d_io.f b/math/deboor/spli2d_io.f
new file mode 100644
index 00000000..a39f7db5
--- /dev/null
+++ b/math/deboor/spli2d_io.f
@@ -0,0 +1,130 @@
+      subroutine spli2d ( tau, gtau, t, n, k, m, work, q, bcoef, iflag )
+c  from  * a practical guide to splines *  by c. de boor
+calls bsplvb, banfac/slv
+c  this is an extended version of  splint , for the use in tensor prod-
+c  uct interpolation.
+c
+c   spli2d  produces the b-spline coeff.s  bcoef(j,.)  of the spline of
+c   order  k  with knots  t (i), i=1,..., n + k , which takes on the
+c   value  gtau (i,j)  at  tau (i), i=1,..., n , j=1,..., m .
+c
+c******  i n p u t  ******
+c  tau.....array of length  n , containing data point abscissae.
+c    a s s u m p t i o n . . .	tau  is strictly increasing
+c  gtau(.,j)..corresponding array of length  n , containing data point
+c	 ordinates, j=1,...,m
+c  t.....knot sequence, of length  n+k
+c  n.....number of data points and dimension of spline space  s(k,t)
+c  k.....order of spline
+c  m.....number of data sets
+c
+c******  w o r k   a r e a  ******
+c  work  a vector of length  n
+c
+c******  o u t p u t  ******
+c  q.....array of size	(2*k-1)*n , containing the triangular factoriz-
+
+c	 ation of the coefficient matrix of the linear system for the b-
+c	 coefficients of the spline interpolant.
+c	    the b-coeffs for the interpolant of an additional data set
+c	 (tau(i),htau(i)), i=1,...,n  with the same data abscissae can
+c	 be obtained without going through all the calculations in this
+
+c	 routine, simply by loading  htau  into  bcoef	and then execut-
+c	 ing the    call banslv ( q, 2*k-1, n, k-1, k-1, bcoef )
+c  bcoef.....the b-coefficients of the interpolant, of length  n
+c  iflag.....an integer indicating success (= 1)  or failure (= 2)
+c	 the linear system to be solved is (theoretically) invertible if
+c	 and only if
+c	       t(i) .lt. tau(i) .lt. tau(i+k),	  all i.
+c	 violation of this condition is certain to lead to  iflag = 2 .
+
+c
+c******  m e t h o d  ******
+c     the i-th equation of the linear system  a*bcoef = b  for the b-co-
+c  effs of the interpolant enforces interpolation at  tau(i), i=1,...,n.
+c  hence,  b(i) = gtau(i), all i, and  a  is a band matrix with  2k-1
+c   bands (if it is invertible).
+c     the matrix  a  is generated row by row and stored, diagonal by di-
+c  agonal, in the  r o w s  of the array  q , with the main diagonal go-
+c  ing into row  k .  see comments in the program below.
+c     the banded system is then solved by a call to  banfac (which con-
+
+c  structs the triangular factorization for  a	and stores it again in
+c   q ), followed by a call to	banslv (which then obtains the solution
+
+c   bcoef  by substitution).
+c     banfac  does no pivoting, since the total positivity of the matrix
+c  a  makes this unnecessary.
+c
+      integer iflag,k,m,n,   i,ilp1mx,j,jj,km1,kpkm2,left,lenq,np1
+      real bcoef(m,n),gtau(n,m),q(1),t(1),tau(n),work(n),   taui
+c     dimension q(2*k-1,n), t(n+k)
+current fortran standard makes it impossible to specify precisely the
+c  dimension of  q  and  t  without the introduction of otherwise super-
+c  fluous additional arguments.
+      np1 = n + 1
+      km1 = k - 1
+      kpkm2 = 2*km1
+      left = k
+c		 zero out all entries of q
+      lenq = n*(k+km1)
+      do 5 i=1,lenq
+    5	 q(i) = 0.
+c
+c  ***	 loop over i to construct the  n  interpolation equations
+      do 30 i=1,n
+	 taui = tau(i)
+	 ilp1mx = min0(i+k,np1)
+c	 *** find  left  in the closed interval (i,i+k-1) such that
+c		 t(left) .le. tau(i) .lt. t(left+1)
+c	 matrix is singular if this is not possible
+	 left = max0(left,i)
+	 if (taui .lt. t(left)) 	go to 998
+   15	    if (taui .lt. t(left+1))	go to 16
+	    left = left + 1
+	    if (left .lt. ilp1mx)	go to 15
+	 left = left - 1
+	 if (taui .gt. t(left+1))	go to 998
+c	 *** the i-th equation enforces interpolation at taui, hence
+c	 a(i,j) = b(j,k,t)(taui), all j. only the  k  entries with  j =
+
+c	 left-k+1,...,left actually might be nonzero. these  k	numbers
+
+c	 are returned, in  work  (used for temp.storage here), by the
+c	 following
+   16	 call bsplvb ( t, k, 1, taui, left, work )
+c	 we therefore want  work(j) = b(left -k+j)(taui) to go into
+c	 a(i,left-k+j), i.e., into  q(i-(left+j)+2*k,(left+j)-k) since
+c	 a(i+j,j)  is to go into  q(i+k,j), all i,j,  if we consider  q
+
+c	 as a two-dim. array , with  2*k-1  rows (see comments in
+c	 banfac). in the present program, we treat  q  as an equivalent
+
+c	 one-dimensional array (because of fortran restrictions on
+c	 dimension statements) . we therefore want  work(j) to go into
+c	 entry
+c	     i -(left+j) + 2*k + ((left+j) - k-1)*(2*k-1)
+c		    =  i-left+1 + (left -k)*(2*k-1) + (2*k-2)*j
+c	 of  q .
+	 jj = i-left+1 + (left-k)*(k+km1)
+	 do 30 j=1,k
+	    jj = jj+kpkm2
+   30	    q(jj) = work(j)
+c
+c     ***obtain factorization of  a  , stored again in	q.
+      call banfac ( q, k+km1, n, km1, km1, iflag )
+					go to (40,999), iflag
+c     *** solve  a*bcoef = gtau  by backsubstitution
+   40 do 50 j=1,m
+	 do 41 i=1,n
+   41	    work(i) = gtau(i,j)
+	 call banslv ( q, k+km1, n, km1, km1, work )
+	 do 50 i=1,n
+   50	    bcoef(j,i) = work(i)
+					return
+  998 iflag = 2
+  999 print 699
+  699 format(41h linear system in  splint  not invertible)
+					return
+      end
diff --git a/math/deboor/spline.x b/math/deboor/spline.x
new file mode 100644
index 00000000..d77c8122
--- /dev/null
+++ b/math/deboor/spline.x
@@ -0,0 +1,93 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+
+include	"bspln.h"
+
+.help spline 2 "math library"
+.ih
+NAME
+spline -- generalized spline interpolation with b-splines.
+.ih
+USAGE
+spline (x, y, n, bspln, q, k, ier)
+.ih
+PARAMETERS
+.ls x,y
+(real[n]).  Abcissae and ordinates of the N data points.
+.le
+.ls n
+The number of input data points, and the number of spline coefficients
+to be generated.
+.le
+.ls bspln
+(real[2*n+30]).  Output array of N b-spline coefficients, N+K knots,
+and the spline descriptor array.
+.le
+.ls q
+(real[(2*K-1)*N]).  On output, will contain the
+triangular factorization of the coefficient matrix of the linear
+system for the b-coefficients of the spline interpolant.  If a new
+data set differs only in the Y values, Q may be input to FSPLIN to
+efficiently solve for the b-spline coefficients of the new data set.
+.le
+.ls k
+The order of the spline (2-20).  Must be EVEN at present
+(k=4 is the cubic spline).
+.le
+.ls ier
+Zero if ok, nonzero if error (invalid input parameters).
+.le
+.ih
+DESCRIPTION
+General spline interpolation.  SPLINE is a thinly disguised version of SPLINT
+(DeBoor, pg. 204).  SPLINE differs from SPLINT in that the knot spacing T is
+calculated automatically, using the not-a-knot boundary conditions.  Only even
+K are permitted at present (K = 2, 4, 6,...).  The cubic spline interpolant
+corresponds to K = 4.  SPLINE saves a complete description of the spline in the
+BSPLN array, for use later by SEVAL (used to evaluate the fitted spline) and
+FSPLIN (used after a call to SPLINE to more efficiently fit subsequent data
+sets).
+.ih
+SOURCE
+See the listing of SPLINT, or Chapter XIII of DeBoors book.
+.ih
+SEE ALSO
+seval(2), fsplin(2).
+.endhelp ______________________________________________________________
+
+
+procedure spline (x, y, n, bspln, q, k, ier)
+
+real	x[n], y[n]
+int	n, k, ier
+real	q[ARB], bspln[ARB]		#q[(2*k-1)*n], bspln[2*n+30]
+int	m, i, knot
+
+begin
+	if (k < 2 || mod (k, 2) != 0) {
+	    ier = 1
+	    return
+	}
+
+	NCOEF = n			#set up spline descriptor
+	ORDER = k
+	XMIN = x[1]
+	XMAX = x[n]
+
+	knot = int (KNOT1) - 1		#offset to knot array in bspln
+	KINDEX = knot + k		#initial posn for SEVAL
+
+	m = knot + n
+	do i = 1, k {			#not-a-knot knot boundary conditions
+	    bspln[knot+i] = XMIN
+	    bspln[m+i] = XMAX
+	}
+
+	m = k / 2			#use data x-values inside
+	do i = k+1, n
+	    bspln[knot+i] = x[i+m-k]
+
+	call splint (x, y, bspln[knot+1], n, k, q, bspln[COEF1], ier)
+	if (ier == 1)			#1=success, 2==failure
+	    ier = 0
+end
diff --git a/math/deboor/splint.f b/math/deboor/splint.f
new file mode 100644
index 00000000..3354dadf
--- /dev/null
+++ b/math/deboor/splint.f
@@ -0,0 +1,113 @@
+      subroutine splint ( tau, gtau, t, n, k, q, bcoef, iflag )
+c  from  * a practical guide to splines *  by c. de boor
+calls bsplvb, banfac/slv
+c
+c   splint  produces the b-spline coeff.s  bcoef  of the spline of order
+c   k  with knots  t(i), i=1,..., n + k , which takes on the value
+c   gtau(i) at	tau(i), i=1,..., n .
+c
+c******  i n p u t  ******
+c  tau.....array of length  n , containing data point abscissae.
+c    a s s u m p t i o n . . .	tau  is strictly increasing
+c  gtau.....corresponding array of length  n , containing data point or-
+c	 dinates
+c  t.....knot sequence, of length  n+k
+c  n.....number of data points and dimension of spline space  s(k,t)
+c  k.....order of spline
+c
+c******  o u t p u t  ******
+c  q.....array of size	(2*k-1)*n , containing the triangular factoriz-
+c	 ation of the coefficient matrix of the linear system for the b-
+c	 coefficients of the spline interpolant.
+c	    the b-coeffs for the interpolant of an additional data set
+c	 (tau(i),htau(i)), i=1,...,n  with the same data abscissae can
+c	 be obtained without going through all the calculations in this
+c	 routine, simply by loading  htau  into  bcoef	and then execut-
+c	 ing the    call banslv ( q, 2*k-1, n, k-1, k-1, bcoef )
+c  bcoef.....the b-coefficients of the interpolant, of length  n
+c  iflag.....an integer indicating success (= 1)  or failure (= 2)
+c	 the linear system to be solved is (theoretically) invertible if
+c	 and only if
+c	       t(i) .lt. tau(i) .lt. tau(i+k),	  all i.
+c	 violation of this condition is certain to lead to  iflag = 2 .
+c
+c******  m e t h o d  ******
+c     the i-th equation of the linear system  a*bcoef = b  for the b-co-
+c  effs of the interpolant enforces interpolation at  tau(i), i=1,...,n.
+c  hence,  b(i) = gtau(i), all i, and  a  is a band matrix with  2k-1
+c   bands (if it is invertible).
+c     the matrix  a  is generated row by row and stored, diagonal by di-
+c  agonal, in the  r o w s  of the array  q , with the main diagonal go-
+c  ing into row  k .  see comments in the program below.
+c     the banded system is then solved by a call to  banfac (which con-
+c  structs the triangular factorization for  a	and stores it again in
+c   q ), followed by a call to	banslv (which then obtains the solution
+c   bcoef  by substitution).
+c     banfac  does no pivoting, since the total positivity of the matrix
+c  a  makes this unnecessary.
+c
+      integer iflag,k,n,   i,ilp1mx,j,jj,km1,kpkm2,left,lenq,np1
+      real bcoef(n),gtau(n),q(1),t(1),tau(n),	taui
+c     dimension q(2*k-1,n), t(n+k)
+current fortran standard makes it impossible to specify precisely the
+c  dimension of  q  and  t  without the introduction of otherwise super-
+c  fluous additional arguments.
+      np1 = n + 1
+      km1 = k - 1
+      kpkm2 = 2*km1
+      left = k
+c		 zero out all entries of q
+      lenq = n*(k+km1)
+      do 5 i=1,lenq
+    5	 q(i) = 0.
+c
+c  ***	 loop over i to construct the  n  interpolation equations
+      do 30 i=1,n
+	 taui = tau(i)
+	 ilp1mx = min0(i+k,np1)
+c	 *** find  left  in the closed interval (i,i+k-1) such that
+c		 t(left) .le. tau(i) .lt. t(left+1)
+c	 matrix is singular if this is not possible
+	 left = max0(left,i)
+	 if (taui .lt. t(left)) 	go to 998
+   15	    if (taui .lt. t(left+1))	go to 16
+	    left = left + 1
+	    if (left .lt. ilp1mx)	go to 15
+	 left = left - 1
+	 if (taui .gt. t(left+1))	go to 998
+c	 *** the i-th equation enforces interpolation at taui, hence
+c	 a(i,j) = b(j,k,t)(taui), all j. only the  k  entries with  j =
+c	 left-k+1,...,left actually might be nonzero. these  k	numbers
+c	 are returned, in  bcoef (used for temp.storage here), by the
+c	 following
+   16	 call bsplvb ( t, k, 1, taui, left, bcoef )
+c	 we therefore want  bcoef(j) = b(left-k+j)(taui) to go into
+c	 a(i,left-k+j), i.e., into  q(i-(left+j)+2*k,(left+j)-k) since
+c	 a(i+j,j)  is to go into  q(i+k,j), all i,j,  if we consider  q
+c	 as a two-dim. array , with  2*k-1  rows (see comments in
+c	 banfac). in the present program, we treat  q  as an equivalent
+c	 one-dimensional array (because of fortran restrictions on
+c	 dimension statements) . we therefore want  bcoef(j) to go into
+c	 entry
+c	     i -(left+j) + 2*k + ((left+j) - k-1)*(2*k-1)
+c		    =  i-left+1 + (left -k)*(2*k-1) + (2*k-2)*j
+c	 of  q .
+	 jj = i-left+1 + (left-k)*(k+km1)
+	 do 30 j=1,k
+	    jj = jj+kpkm2
+   30	    q(jj) = bcoef(j)
+c
+c     ***obtain factorization of  a  , stored again in	q.
+      call banfac ( q, k+km1, n, km1, km1, iflag )
+					go to (40,999), iflag
+c     *** solve  a*bcoef = gtau  by backsubstitution
+   40 do 41 i=1,n
+   41	 bcoef(i) = gtau(i)
+      call banslv ( q, k+km1, n, km1, km1, bcoef )
+					return
+  998 iflag = 2
+  999 return
+c 999 print 699
+c 699 format(41h linear system in  splint  not invertible)
+c					return
+      end
diff --git a/math/deboor/spllsq.x b/math/deboor/spllsq.x
new file mode 100644
index 00000000..8760c8a0
--- /dev/null
+++ b/math/deboor/spllsq.x
@@ -0,0 +1,160 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include	"bspln.h"
+
+.help spllsq 2 "math library"
+.ih ___________________________________________________________________________
+NAME
+spllsq -- general smoothing b-spline with uniform knots.
+.ih
+USAGE
+spllsq (x, y, w, npts, bspln, q, work, k, n, wflg, ier)
+.ih
+PARAMETERS
+See the listing of SPLSQV if a more detailed discussion of the parameters
+than that given here is desired.
+.ls x,y,w
+(real[npts]).  Abscissae, ordinates, and weights of the data points.
+X[1] and X[NPTS] determine the range of the spline (the interval over which
+it can be evaluated).  Dummy data points with zero weight can be supplied
+to fix the range if desired.
+.le
+.ls npts
+The number of data points.
+.le
+.ls bspln
+(real[2*n+30]).  Output array of N b-spline coefficients, N+K knots,
+and the spline descriptor structure.
+.le
+.ls q
+(real[n,k]).  Work array.
+.le
+.ls work
+(real[n]).  Work array.
+.le
+.ls k
+The order of the desired spline (1-20) (Cubic == 4).
+.le
+.ls n
+N is the number of b-spline coefficients to be output.  The relationship
+between N and the number of polynomial pieces in the spline (NPP)
+is given by NPP = N-K-1.  Note that NPP is the important parameter.
+N is used in the parameter list rather than NPP because it is used in
+dimensioning the arrays.
+.le
+.ls wflg
+Weight generation flag.  Options:
+
+.nf
+    0  pass W on to SPLSQV as is
+    1  calculate default weights
+    2  same as 1, but set W[i] only
+         if W[i] already NONZERO
+.fi
+
+If WFLG==2, data points may be rejected from the fit by setting their
+corresponding weight to zero, before calling SPLLSQ (good points must be
+assigned nonzero ws before calling SPLLSQ).  Use WFLG==1 if no points
+are to be rejected, to avoid having to initialize the W array on every
+call.
+.le
+.ls ier
+Error return.  Zero if no error.  Nonzero indicates invalid combination
+of N, K, and NPTS.
+.le
+.ih
+DESCRIPTION
+A general algorithm for smoothing with uniform B-splines of arbitrary order.
+Calls SPLSQV, which is adapted from L2APPR, as described in "A Practical
+Guide To Splines", by C. DeBoor.
+ 
+SPLLSQ is identical to SPLSQV, except that (1): the array T[n+k], giving
+the x-positions of the knots of the b-spline, is generated internally,
+rather than by the calling program, and (2): the weights associated with
+the data points may be calculated automatically.  The knots are generated
+with a uniform spacing.  Note that the x-values of the data points do not
+have to be uniformly spaced, but they must be monotonically increasing, and
+(1) both must span the same range, and (2) if N spline coefficients are
+desired, there must be at least N+K data points.
+.ih
+BUGS
+A routine FSPLSQ needs to be written to make use of the Cholesky factorization
+returned by SPLSQV in W1, for more efficient fitting of subsequent data sets
+that differ only in the y-values of the data points.
+.ih
+SEE ALSO
+seval(2)
+.endhelp _______________________________________________________________________
+
+
+procedure spllsq (x, y, w, npts, bspln, q, work, k, n, wflg, ier)
+
+real	x[npts], y[npts], w[npts]
+real	q[n,k], work[n]
+real	bspln[ARB]
+int	wflg, npts, n, k, ier
+int	i, npp, km1, knot
+real	dx
+
+begin
+	ier = 0				#successful return value
+	npp = n - k + 1			#number of polynomial pieces
+	if (npp <= 0) {		
+	    ier = 1
+	    return
+	}				
+
+	# Set up spline descriptor in the array BCOEF, for later evaluation
+	# of the spline by BSPLN (see "bcoef.h" for definitions of the fields).
+
+	NCOEF = n				#number of b-spline coeff
+	ORDER = k				#order of the spline
+	XMIN = x[1]				#x at left endpoint
+	XMAX = x[npts]				#x at right endpoint
+	KINDEX = KNOT1 - 1 + k			#for SEVAL
+
+
+	# Set values of knots.  First K knots take on the value of the first
+	# breakpoint, next npp-1 knots have spacing DX, and the last K knots
+	# take on the value of the last breakpoint.
+
+	dx = (XMAX - XMIN ) / npp		#span(x) = span(t)
+
+	km1 = k - 1
+	knot = KNOT1 - 1
+
+	do i = 1, km1
+	    bspln[knot+i] = XMIN
+
+	knot = knot + km1
+	do i = 1, npp
+	    bspln[knot+i] = XMIN + (i-1) * dx
+
+	knot = knot + npp
+	do i = 1, k
+	    bspln[knot+i] = XMAX
+
+
+	# Calculate default weights.  The default weight of a datapoint is
+	# proportional to the spacing.
+
+	if (wflg > 0) {
+	    if (w[1] > 0  ||  wflg == 1)
+		w[1] = x[2] - x[1]
+
+	    do i = 2, npts - 1 {
+		if (w[i] > 0  ||  wflg == 1)
+		    w[i] = (x[i+1] - x[i-1]) / 2.
+	    }
+	    if (w[npts] > 0  ||  wflg == 1)
+		w[npts] = x[npts] - x[npts-1]
+	}
+
+
+	# Call SPLSQV to do the actual spline fit.  The N b-spline coefficients
+	# of order K, N+K knots, and the spline descriptor are returned in
+	# BSPLN, for evaluation of the spline via SEVAL.
+
+	call splsqv (x, y, w, npts, bspln[nint(KNOT1)], n, k, q,
+	    work, bspln[COEF1], ier)
+end
diff --git a/math/deboor/splopt_io.f b/math/deboor/splopt_io.f
new file mode 100644
index 00000000..7ee5e1a1
--- /dev/null
+++ b/math/deboor/splopt_io.f
@@ -0,0 +1,196 @@
+      subroutine splopt ( tau, n, k, scrtch, t, iflag )
+c  from  * a practical guide to splines *  by c. de boor
+calls bsplvb, banfac/slv
+computes the knots  t  for the optimal recovery scheme of order  k
+c  for data at	tau(i), i=1,...,n .
+c
+c******  i n p u t  ******
+c  tau.....array of length  n , containing the interpolation points.
+c     a s s u m e d  to be nondecreasing, with tau(i).lt.tau(i+k),all i.
+c  n.....number of data points .
+c  k.....order of the optimal recovery scheme to be used .
+c
+c******  w o r k  a r r a y  *****
+c  scrtch.....array of length  (n-k)(2k+3) + 5k + 3 . the various
+c	 contents are specified in the text below .
+c
+c******  o u t p u t  ******
+c  iflag.....integer indicating success (=1) or failure (=2) .
+c     if iflag = 1, then
+c  t.....array of length  n+k  containing the optimal knots ready for
+c	 use in optimal recovery. specifically,  t(1) = ... = t(k) =
+c	 tau(1)  and  t(n+1) = ... = t(n+k) = tau(n) , while the  n-k
+c	 interior knots  t(k+1), ..., t(n)  are calculated as described
+c	 below under  *method* .
+c     if iflag = 2, then
+c	 k .lt. 3, or n .lt. k, or a certain linear system was found to
+c	 be singular.
+c
+c******  p r i n t e d	o u t p u t  ******
+c  a comment will be printed in case  ilfag = 2  or newton iterations
+c  failed to converge in  n e w t m x  iterations .
+c
+c******  m e t h o d  ******
+c     the (interior) knots  t(k+1), ..., t(n)  are determined by newtons
+c  method in such a way that the signum function which changes sign at
+c   t(k+1), ..., t(n)  and nowhere else in  (tau(1),tau(n)) is orthogon-
+c  al to the spline space  spline( k , tau )  on that interval .
+c     let  xi(j)  be the current guess for  t(k+j), j=1,...,n-k. then
+c  the next newton iterate is of the form
+c	       xi(j)  +  (-)**(n-k-j)*x(j)  ,  j=1,...,n-k,
+c  with  x  the solution of the linear system
+c			 c*x  =  d  .
+c  here,  c(i,j) = b(i)(xi(j)), all j, with  b(i)  the i-th b-spline of
+c  order  k  for the knot sequence  tau , all i, and  d  is the vector
+c  given by  d(i) = sum( -a(j) , j=i,...,n )*(tau(i+k)-tau(i))/k, all i,
+c  with  a(i) = sum ( (-)**(n-k-j)*b(i,k+1,tau)(xi(j)) , j=1,...,n-k )
+c  for i=1,...,n-1, and  a(n) = -.5 .
+c     (see chapter  xiii  of text and references there for a derivation)
+c     the first guess for  t(k+j)  is  (tau(j+1)+...+tau(j+k-1))/(k-1) .
+c     iteration terminates if  max(abs(x(j))) .lt. t o l  , with
+c		  t o l  =  t o l r t e *(tau(n)-tau(1))/(n-k) ,
+c  or else after  n e w t m x  iterations , currently,
+c		  newtmx, tolrte / 10, .000001
+c
+      integer iflag,k,n,   i,id,index,j,km1,kpk,kpkm1,kpn,kp1,l,left
+     *,leftmk,lenw,ll,llmax,llmin,na,nb,nc,nd,newtmx,newton,nmk,nmkm1,nx
+      real scrtch(1),t(1),tau(n),   del,delmax,floatk,sign,signst,sum
+     *				   ,tol,tolrte,xij
+c     dimension scrtch((n-k)*(2*k+3)+5*k+3), t(n+k)
+current fortran standard makes it impossible to specify the precise dim-
+c  ensions of  scrtch  and  t  without the introduction of otherwise
+c  superfluous additional arguments .
+      data newtmx,tolrte / 10,.000001/
+      nmk = n-k
+      if (nmk)				1,56,2
+    1 print 601,n,k
+  601 format(13h argument n =,i4,29h in  splopt  is less than k =,i3)
+					go to 999
+    2 if (k .gt. 2)			go to 3
+      print 602,k
+  602 format(13h argument k =,i3,27h in  splopt  is less than 3)
+					go to 999
+   3  nmkm1 = nmk - 1
+      floatk = k
+      kpk = k+k
+      kp1 = k+1
+      km1 = k-1
+      kpkm1 = kpk-1
+      kpn = k+n
+      signst = -1.
+      if (nmk .gt. (nmk/2)*2)  signst = 1.
+c  scrtch(i) = tau-extended(i), i=1,...,n+k+k
+      nx = n+kpk+1
+c  scrtch(i+nx) = xi(i),i=0,...,n-k+1
+      na = nx + nmk + 1
+c  scrtch(i+na) = -a(i), i=1,...,n
+      nd = na + n
+c  scrtch(i+nd) = x(i) or d(i), i=1,...,n-k
+      nb = nd + nmk
+c  scrtch(i+nb) = biatx(i),i=1,...,k+1
+      nc = nb + kp1
+c  scrtch(i+(j-1)*(2k-1) + nc) = w(i,j) = c(i-k+j,j), i=j-k,...,j+k,
+c						      j=1,...,n-k.
+      lenw = kpkm1*nmk
+c  extend  tau	to a knot sequence and store in scrtch.
+      do 5 j=1,k
+	 scrtch(j) = tau(1)
+    5	 scrtch(kpn+j) = tau(n)
+      do 6 j=1,n
+    6	 scrtch(k+j) = tau(j)
+c  first guess for  scrtch (.+nx)  =  xi .
+      scrtch(nx) = tau(1)
+      scrtch(nmk+1+nx) = tau(n)
+      do 10 j=1,nmk
+	 sum = 0.
+	 do 9 l=1,km1
+    9	    sum = sum + tau(j+l)
+   10	 scrtch(j+nx) = sum/float(km1)
+c  last entry of  scrtch (.+na)  =  - a  is always ...
+      scrtch(n+na) = .5
+c  start newton iteration.
+      newton = 1
+      tol = tolrte*(tau(n) - tau(1))/float(nmk)
+c  start newton step
+compute the 2k-1 bands of the matrix c and store in scrtch(.+nc),
+c  and compute the vector  scrtch(.+na) = -a.
+   20 do 21 i=1,lenw
+   21	 scrtch(i+nc) = 0.
+      do 22 i=2,n
+   22	 scrtch(i-1+na) = 0.
+      sign = signst
+      left = kp1
+      do 28 j=1,nmk
+	 xij = scrtch(j+nx)
+   23	    if (xij .lt. scrtch(left+1))go to 25
+	    left = left + 1
+	    if (left .lt. kpn)		go to 23
+	    left = left - 1
+   25	 call bsplvb(scrtch,k,1,xij,left,scrtch(1+nb))
+c	 the tau sequence in scrtch is preceded by  k  additional knots
+c	 therefore,  scrtch(ll+nb)  now contains  b(left-2k+ll)(xij)
+c	 which is destined for	c(left-2k+ll,j), and therefore for
+c	     w(left-k-j+ll,j)= scrtch(left-k-j+ll + (j-1)*kpkm1 + nc)
+c	 since we store the 2k-1 bands of  c  in the 2k-1  r o w s  of
+c	 the work array w, and	w  in turn is stored in  s c r t c h ,
+c	 with  w(1,1) = scrtch(1 + nc) .
+c	     also, c  being of order  n-k, we would want  1 .le.
+c	 left-2k+ll .le. n-k  or
+c	    llmin = 2k-left  .le.  ll  .le.  n-left+k = llmax .
+	 leftmk = left-k
+	 index = leftmk-j + (j-1)*kpkm1 + nc
+	 llmin = max0(1,k-leftmk)
+	 llmax = min0(k,n-leftmk)
+	 do 26 ll=llmin,llmax
+   26	    scrtch(ll+index) = scrtch(ll+nb)
+	 call bsplvb(scrtch,kp1,2,xij,left,scrtch(1+nb))
+	 id = max0(0,leftmk-kp1)
+	 llmin = 1 - min0(0,leftmk-kp1)
+	 do 27 ll=llmin,kp1
+	    id = id + 1
+   27	     scrtch(id+na) = scrtch(id+na) - sign*scrtch(ll+nb)
+   28	 sign = -sign
+      call banfac(scrtch(1+nc),kpkm1,nmk,km1,km1,iflag)
+					go to (45,44),iflag
+   44 print 644
+  644 format(32h c in  splopt  is not invertible)
+					return
+compute  scrtch (.+nd) =  d  from  scrtch (.+na) = - a .
+   45 i=n
+   46	 scrtch(i-1+na) = scrtch(i-1+na) + scrtch(i+na)
+	 i = i-1
+	 if (i .gt. 1)			go to 46
+      do 49 i=1,nmk
+   49	 scrtch(i+nd) = scrtch(i+na)*(tau(i+k)-tau(i))/floatk
+compute  scrtch (.+nd) =  x .
+      call banslv(scrtch(1+nc),kpkm1,nmk,km1,km1,scrtch(1+nd))
+compute  scrtch (.+nd) = change in  xi . modify, if necessary, to
+c  prevent new	xi  from moving more than 1/3 of the way to its
+c  neighbors. then add to  xi  to obtain new  xi  in scrtch(.+nx).
+      delmax = 0.
+      sign = signst
+      do 53 i=1,nmk
+	 del = sign*scrtch(i+nd)
+	 delmax = amax1(delmax,abs(del))
+	 if (del .gt. 0.)		go to 51
+	 del = amax1(del,(scrtch(i-1+nx)-scrtch(i+nx))/3.)
+					go to 52
+   51	 del = amin1(del,(scrtch(i+1+nx)-scrtch(i+nx))/3.)
+   52	 sign = -sign
+   53	 scrtch(i+nx) = scrtch(i+nx) + del
+call it a day in case change in  xi  was small enough or too many
+c  steps were taken.
+      if (delmax .lt. tol)		go to 54
+      newton = newton + 1
+      if (newton .le. newtmx)		go to 20
+      print 653,newtmx
+  653 format(33h no convergence in  splopt  after,i3,14h newton steps.)
+   54 do 55 i=1,nmk
+   55	 t(k+i) = scrtch(i+nx)
+   56 do 57 i=1,k
+	 t(i) = tau(1)
+   57	 t(n+i) = tau(n)
+					return
+  999 iflag = 2
+					return
+      end
diff --git a/math/deboor/splsqv.x b/math/deboor/splsqv.x
new file mode 100644
index 00000000..1b4db248
--- /dev/null
+++ b/math/deboor/splsqv.x
@@ -0,0 +1,149 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+
+include	"bspln.h"
+define	ILLEGAL_ORDER	2	#error returns
+define	NO_DEG_FREEDOM	3
+
+
+.help splsqv 2 "IRAF Math Library"
+
+Adapted from L2APPR, * A Practical Guide To Splines *  by C. DeBoor.
+Eliminated data entry via the common /data/ (D.Tody, 4-july-82).  Calls
+subprograms  BSPLVB, BCHFAC, BCHSLV.
+
+SPLSQV constructs the (weighted discrete) l2-approximation by splines of
+order K with knot sequence  T[1], ..., t[nt+k]  to given data points
+(TAU[i], GTAU[i]), i=1,...,ntau.  The b-spline coefficients BCOEF of the
+approximating spline are determined from the normal equations using
+Cholesky'smethod.
+
+SPLSQV (tau, gtau, weight, ntau, t, nt, k, work, diag, bcoef, ier)
+
+
+INPUT -----
+
+ntau		Number of data points
+tau[ntau]	x-value of the data points.
+gtau[ntau]	y-value of the data points.
+weight[ntau]	The corresponding weights.
+t[nt]		The knot sequence
+nt		The dimension of the space of splines of order k with knots t.
+k		The order of the b-spline to be fitted.
+
+
+WORK ARRAYS -----
+
+work[k,nt]	A work array of size (at least) K*NT. its first K rows are used
+		for the K lower diagonals of the gramian matrix C.
+diag[nt]	A work array of length NT used in BCHFAC.
+
+
+OUTPUT -----
+
+bcoef[nt]	The b-spline coefficients of the l2-approximation.
+ier		Error code: zero if ok, else small integer error code.
+
+
+METHOD -----
+
+The b-spline coefficients of the l2-appr. are determined as the solution
+of the normal equations
+
+	sum ((B[i],B[j]) * BCOEF[j] : j=1:nt) = (B[i],G), 	i = 1 to nt.
+
+where, B[i] denotes the i-th b-spline, G denotes the function to be
+approximated, and the INNER PRODUCT of two functions F and G is given by
+
+	(F,G)  :=  sum (F(TAU[i]) * G(TAU[i]) * WEIGHT[i] : i=1:ntau).
+
+The relevant function values of the b-splines  B[i], i=1:nt, are supplied
+by the subprogram BSPLVB.  The coeff. matrix C, with
+
+	C(i,j) :=  (B[i], B[j]), i,j=1:n,
+
+of the normal equations is symmetric and (2*k-1)-banded, therefore can be
+specified by giving its k bands at or below the diagonal. for i=1,...,n,
+we store
+
+	(B[i],B[j])  =  B[i,j]  in  WORK[i-j+1,j], j=i,...,min0(i+k-1,nt)
+
+and the right side
+
+	(B[i], G)  in  BCOEF[i].
+
+since b-spline values are most efficiently generated by finding simultaneously
+the value of EVERY nonzero b-spline at one point, the entries of C (i.e., of
+WORK), are generated by computing, for each ll, all the terms involving
+TAU(ll) simultaneously and adding them to all relevant entries.
+.endhelp _______________________________________________________________
+
+
+procedure splsqv (tau, gtau, weight, ntau, t, nt, k, work, diag, bcoef, ier)
+
+real	tau[ntau], gtau[ntau], weight[ntau]
+real	t[nt], work[k,nt], diag[nt], bcoef[nt]
+int	ntau, nt, k, ier
+int	i, j, jj, left, leftmk, ll, mm
+real	biatx[KMAX], dw
+
+begin
+	ier = 0
+	if (k < 1 || k > KMAX) {
+	    ier = ILLEGAL_ORDER
+	    return
+	}
+	if (nt <= k || nt >= ntau+k) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	do j = 1, nt {
+	    bcoef[j] = 0.
+	    do i = 1, k
+		work[i,j] = 0.
+	}
+
+	left = k
+	leftmk = 0
+
+	do ll = 1, ntau {
+	    while (left != nt) {
+		if (tau[ll] < t[left+1])
+		    break
+		left = left + 1
+		leftmk = leftmk + 1
+	    }
+
+	    call bsplvb (t, k, 1, tau[ll], left, biatx)
+
+#   BIATX[mm] contains the value of B[left-k+mm] at TAU[ll].
+#   hence, with DW := BIATX[mm] * WEIGHT[ll], the number DW * GTAU[ll]
+#   is a summand in the inner product
+#      (B[left-k+mm],G)  which goes into  BCOEF[left-k+mm]
+#   and the number BIATX[jj] * dw is a summand in the inner product
+#      (B[left-k+jj],  B[left-k+mm]),  into  WORK[jj-mm+1,left-k+mm]
+#   since (left-k+jj) - (left-k+mm) + 1 = jj - mm + 1.
+
+	    do mm = 1, k {
+		dw = biatx[mm] * weight[ll]
+		j = leftmk + mm
+		bcoef[j] = dw * gtau[ll] + bcoef[j]
+		i = 1
+
+		do jj = mm, k {
+		    work[i,j] = biatx[jj] * dw + work[i,j]
+		    i = i + 1
+		}
+	    }
+	}
+
+#  construct cholesky factorization for C in WORK,  then use it to solve
+#  the normal equations
+#       c * x = bcoef
+#  for X, and store X in BCOEF.
+
+	call bchfac (work, k, nt, diag)
+	call bchslv (work, k, nt, bcoef)
+	return
+end
diff --git a/math/deboor/subbak.f b/math/deboor/subbak.f
new file mode 100644
index 00000000..7851c216
--- /dev/null
+++ b/math/deboor/subbak.f
@@ -0,0 +1,33 @@
+      subroutine subbak ( w, ipivot, nrow, ncol, last, x )
+c  carries out backsubstitution for current block.
+c
+c parameters
+c    w, ipivot, nrow, ncol, last  are as on return from factrb.
+c    x(1),...,x(ncol)  contains, on input, the right side for the
+c	     equations in this block after backsubstitution has been
+c	     carried up to but not including equation ipivot(last).
+c	     means that x(j) contains the right side of equation ipi-
+c	     vot(j) as modified during elimination, j=1,...,last, while
+c	     for j .gt. last, x(j) is already a component of the solut-
+c	     ion vector.
+c    x(1),...,x(ncol) contains, on output, the components of the solut-
+c	     ion corresponding to the present block.
+c
+      integer nrow, ncol
+      integer ipivot(nrow),last,  ip,j,k,kp1
+      real w(nrow,ncol),x(ncol), sum
+      k = last
+      ip = ipivot(k)
+      sum = 0.
+      if (k .eq. ncol)			go to 4
+      kp1 = k+1
+    2	 do 3 j=kp1,ncol
+    3	    sum = w(ip,j)*x(j) + sum
+    4	 x(k) = (x(k) - sum)/w(ip,k)
+	 if (k .eq. 1)			return
+	 kp1 = k
+	 k = k-1
+	 ip = ipivot(k)
+	 sum = 0.
+					go to 2
+      end
diff --git a/math/deboor/subfor.f b/math/deboor/subfor.f
new file mode 100644
index 00000000..344aff0c
--- /dev/null
+++ b/math/deboor/subfor.f
@@ -0,0 +1,45 @@
+      subroutine subfor ( w, ipivot, nrow, last, b, x )
+c  carries out the forward pass of substitution for the current block,
+c  i.e., the action on the right side corresponding to the elimination
+c  carried out in  f a c t r b	for this block.
+c     at the end, x(j) contains the right side of the transformed
+c  ipivot(j)-th equation in this block, j=1,...,nrow. then, since
+c  for i=1,...,nrow-last, b(nrow+i) is going to be used as the right
+c  side of equation  i	in the next block (shifted over there from
+c  this block during factorization), it is set equal to x(last+i) here.
+c
+c parameters
+c    w, ipivot, nrow, last  are as on return from factrb.
+c    b(j)   is expected to contain, on input, the right side of j-th
+c	    equation for this block, j=1,...,nrow.
+c    b(nrow+j)	 contains, on output, the appropriately modified right
+c	    side for equation j in next block, j=1,...,nrow-last.
+c    x(j)   contains, on output, the appropriately modified right
+c	    side of equation ipivot(j) in this block, j=1,...,last (and
+c	    even for j=last+1,...,nrow).
+c
+      integer nrow
+      integer ipivot(nrow), ip,jmax,k, j
+      integer last, nrowml, lastp1
+c     dimension b(nrow + nrow-last)
+      real w(nrow,last),b(1),x(nrow),sum
+      ip = ipivot(1)
+      x(1) = b(ip)
+      if (nrow .eq. 1)			go to 99
+      do 15 k=2,nrow
+	 ip = ipivot(k)
+	 jmax = amin0(k-1,last)
+	 sum = 0.
+	 do 14 j=1,jmax
+   14	    sum = w(ip,j)*x(j) + sum
+   15	 x(k) = b(ip) - sum
+c
+c     transfer modified right sides of equations ipivot(last+1),...,
+c     ipivot(nrow) to next block.
+      nrowml = nrow - last
+      if (nrowml .eq. 0)		go to 99
+      lastp1 = last+1
+      do 25 k=lastp1,nrow
+   25	 b(nrowml+k) = x(k)
+   99					return
+      end
diff --git a/math/deboor/tautsp.f b/math/deboor/tautsp.f
new file mode 100644
index 00000000..86e8eeb4
--- /dev/null
+++ b/math/deboor/tautsp.f
@@ -0,0 +1,313 @@
+      subroutine tautsp ( tau, gtau, ntau, gamma, s,
+     *			  break, coef, l, k, iflag )
+c  from  * a practical guide to splines *  by c. de boor
+constructs cubic spline interpolant to given data
+c	  tau(i), gtau(i), i=1,...,ntau.
+c  if  gamma .gt. 0., additional knots are introduced where needed to
+c  make the interpolant more flexible locally. this avoids extraneous
+c  inflection points typical of cubic spline interpolation at knots to
+c  rapidly changing data.
+c
+c  parameters
+c	     input
+c  tau	    sequence of data points. must be strictly increasing.
+c  gtau     corresponding sequence of function values.
+c  ntau     number of data points. must be at least  4 .
+c  gamma    indicates whether additional flexibility is desired.
+c	   = 0., no additional knots
+c	   in (0.,3.), under certain conditions on the given data at
+c		 points i-1, i, i+1, and i+2, a knot is added in the
+c		 i-th interval, i=2,...,ntau-2. see description of meth-
+c		 od below. the interpolant gets rounded with increasing
+c		 gamma. a value of  2.5  for gamma is typical.
+c	   in (3.,6.), same , except that knots might also be added in
+c		 intervals in which an inflection point would be permit-
+c		 ted.  a value of  5.5	for gamma is typical.
+c	     output
+c  break, coef, l, k  give the pp-representation of the interpolant.
+c	   specifically, for break(i) .le. x .le. break(i+1), the
+c	 interpolant has the form
+c  f(x) = coef(1,i) +dx(coef(2,i) +(dx/2)(coef(3,i) +(dx/3)coef(4,i)))
+c	 with  dx = x - break(i) and i=1,...,l .
+c  iflag   = 1, ok
+c	   = 2, input was incorrect. a printout specifying the mistake
+c	     was made.
+c	     workspace
+c  s	 is required, of size (ntau,6). the individual columns of this
+c	 array contain the following quantities mentioned in the write-
+c	 up and below.
+c     s(.,1) = dtau = tau(.+1) - tau
+c     s(.,2) = diag = diagonal in linear system
+c     s(.,3) = u = upper diagonal in linear system
+c     s(.,4) = r = right side for linear system (initially)
+c	     = fsecnd = solution of linear system , namely the second
+c			derivatives of interpolant at  tau
+c     s(.,5) = z = indicator of additional knots
+c     s(.,6) = 1/hsecnd(1,x) with x = z or = 1-z. see below.
+c
+c  ------  m e t h o d	------
+c  on the i-th interval, (tau(i), tau(i+1)), the interpolant is of the
+c  form
+c  (*)	f(u(x)) = a + b*u + c*h(u,z) + d*h(1-u,1-z) ,
+c  with  u = u(x) = (x - tau(i))/dtau(i). here,
+c	z = z(i) = addg(i+1)/(addg(i) + addg(i+1))
+c  (= .5, in case the denominator vanishes). with
+c	addg(j) = abs(ddg(j)), ddg(j) = dg(j+1) - dg(j),
+c	dg(j) = divdif(j) = (gtau(j+1) - gtau(j))/dtau(j)
+c  and
+c	h(u,z) = alpha*u**3 + (1 - alpha)*(max(((u-zeta)/(1-zeta)),0)**3
+c  with
+c	alpha(z) = (1-gamma/3)/zeta
+c	zeta(z) = 1 - gamma*min((1 - z), 1/3)
+c  thus, for 1/3 .le. z .le. 2/3,  f  is just a cubic polynomial on
+c  the interval i. otherwise, it has one additional knot, at
+c	  tau(i) + zeta*dtau(i) .
+c  as  z  approaches  1, h(.,z) has an increasingly sharp bend	near 1,
+c  thus allowing  f  to turn rapidly near the additional knot.
+c     in terms of f(j) = gtau(j) and
+c	fsecnd(j) = 2.derivative of  f	at  tau(j),
+c  the coefficients for (*) are given as
+c	a = f(i) - d
+c	b = (f(i+1) - f(i)) - (c - d)
+c	c = fsecnd(i+1)*dtau(i)**2/hsecnd(1,z)
+c	d = fsecnd(i)*dtau(i)**2/hsecnd(1,1-z)
+c  hence can be computed once fsecnd(i),i=1,...,ntau, is fixed.
+c   f  is automatically continuous and has a continuous second derivat-
+c  ive (except when z = 0 or 1 for some i). we determine fscnd(.) from
+c  the requirement that also the first derivative of  f  be contin-
+c  uous. in addition, we require that the third derivative be continuous
+c  across  tau(2) and across  tau(ntau-1) . this leads to a strictly
+c  diagonally dominant tridiagonal linear system for the fsecnd(i)
+c  which we solve by gauss elimination without pivoting.
+c
+      integer iflag,k,l,ntau,	i,method,ntaum1
+      real break(1),coef(4,1),gamma,gtau(ntau),s(ntau,6),tau(ntau)
+     *	  ,alpha,c,d,del,denom,divdif,entry,entry3,factor,factr2,gam
+     *	  ,onemg3,onemzt,ratio,sixth,temp,x,z,zeta,zt2
+      real alph
+      alph(x) = amin1(1.,onemg3/x)
+c
+c  there must be at least  4  interpolation points.
+      if (ntau .ge. 4)			go to 5
+c     print 600,ntau
+c 600 format(8h ntau = ,i4,20h. should be .ge. 4 .)
+					go to 999
+c
+construct delta tau and first and second (divided) differences of data
+c
+    5 ntaum1 = ntau - 1
+      do 6 i=1,ntaum1
+	 s(i,1) = tau(i+1) - tau(i)
+	 if (s(i,1) .gt. 0.)		go to 6
+c	 print 610,i,tau(i),tau(i+1)
+c 610	 format(7h point ,i3,13h and the next,2e15.6,15h are disordered)
+					go to 999
+    6	 s(i+1,4) = (gtau(i+1)-gtau(i))/s(i,1)
+      do 7 i=2,ntaum1
+    7	 s(i,4) = s(i+1,4) - s(i,4)
+c
+construct system of equations for second derivatives at  tau. at each
+c  interior data point, there is one continuity equation, at the first
+c  and the last interior data point there is an additional one for a
+c  total of  ntau  equations in  ntau  unknowns.
+c
+      i = 2
+      s(2,2) = s(1,1)/3.
+      sixth = 1./6.
+      method = 2
+      gam = gamma
+      if (gam .le. 0.)	 method = 1
+      if ( gam .le. 3.) 		go to 9
+      method = 3
+      gam = gam - 3.
+    9 onemg3 = 1. - gam/3.
+c		  ------ loop over i ------
+   10 continue
+c	   construct z(i) and zeta(i)
+      z = .5
+					go to (19,11,12),method
+   11 if (s(i,4)*s(i+1,4) .lt. 0.)	go to 19
+   12 temp = abs(s(i+1,4))
+      denom = abs(s(i,4)) + temp
+      if (denom .eq. 0.)		go to 19
+      z = temp/denom
+      if (abs(z - .5) .le. sixth)  z = .5
+   19 s(i,5) = z
+c   ******set up part of the i-th equation which depends on
+c	  the i-th interval
+      if (z - .5)			21,22,23
+   21 zeta = gam*z
+      onemzt = 1. - zeta
+      zt2 = zeta**2
+      alpha = alph(onemzt)
+      factor = zeta/(alpha*(zt2-1.) + 1.)
+      s(i,6) = zeta*factor/6.
+      s(i,2) = s(i,2) + s(i,1)*((1.-alpha*onemzt)*factor/2. - s(i,6))
+c     if z = 0 and the previous z = 1, then d(i) = 0. since then
+c     also u(i-1) = l(i+1) = 0, its value does not matter. reset
+c     d(i) = 1 to insure nonzero pivot in elimination.
+      if (s(i,2) .le. 0.) s(i,2) = 1.
+      s(i,3) = s(i,1)/6.
+					go to 25
+   22 s(i,2) = s(i,2) + s(i,1)/3.
+      s(i,3) = s(i,1)/6.
+					go to 25
+   23 onemzt = gam*(1. - z)
+      zeta = 1. - onemzt
+      alpha = alph(zeta)
+      factor = onemzt/(1. - alpha*zeta*(1.+onemzt))
+      s(i,6) = onemzt*factor/6.
+      s(i,2) = s(i,2) + s(i,1)/3.
+      s(i,3) = s(i,6)*s(i,1)
+   25 if (i .gt. 2)			go to 30
+      s(1,5) = .5
+c  ******the first two equations enforce continuity of the first and of
+c	 the third derivative across tau(2).
+      s(1,2) = s(1,1)/6.
+      s(1,3) = s(2,2)
+      entry3 = s(2,3)
+      if (z - .5)			26,27,28
+   26 factr2 = zeta*(alpha*(zt2-1.) + 1.)/(alpha*(zeta*zt2-1.)+1.)
+      ratio = factr2*s(2,1)/s(1,2)
+      s(2,2) = factr2*s(2,1) + s(1,1)
+      s(2,3) = -factr2*s(1,1)
+					go to 29
+   27 ratio = s(2,1)/s(1,2)
+      s(2,2) = s(2,1) + s(1,1)
+      s(2,3) = -s(1,1)
+					go to 29
+   28 ratio = s(2,1)/s(1,2)
+      s(2,2) = s(2,1) + s(1,1)
+      s(2,3) = -s(1,1)*6.*alpha*s(2,6)
+c	at this point, the first two equations read
+c	       diag(1)*x1 + u(1)*x2 + entry3*x3 = r(2)
+c	-ratio*diag(1)*x1 + diag(2)*x2 + u(2)*x3 = 0.
+c	eliminate first unknown from second equation
+   29 s(2,2) = ratio*s(1,3) + s(2,2)
+      s(2,3) = ratio*entry3 + s(2,3)
+      s(1,4) = s(2,4)
+      s(2,4) = ratio*s(1,4)
+					go to 35
+   30 continue
+c  ******the i-th equation enforces continuity of the first derivative
+c	 across tau(i). it has been set up in statements 35 up to 40
+c	 and 21 up to 25 and reads now
+c	  -ratio*diag(i-1)*xi-1 + diag(i)*xi + u(i)*xi+1 = r(i) .
+c	 eliminate (i-1)st unknown from this equation
+      s(i,2) = ratio*s(i-1,3) + s(i,2)
+      s(i,4) = ratio*s(i-1,4) + s(i,4)
+c
+c  ******set up the part of the next equation which depends on the
+c	 i-th interval.
+   35 if (z - .5)			36,37,38
+   36 ratio = -s(i,6)*s(i,1)/s(i,2)
+      s(i+1,2) = s(i,1)/3.
+					go to 40
+   37 ratio = -(s(i,1)/6.)/s(i,2)
+      s(i+1,2) = s(i,1)/3.
+					go to 40
+   38 ratio = -(s(i,1)/6.)/s(i,2)
+      s(i+1,2) = s(i,1)*((1.-zeta*alpha)*factor/2. - s(i,6))
+c	  ------  end of i loop ------
+   40 i = i+1
+      if (i .lt. ntaum1)		go to 10
+      s(i,5) = .5
+c
+c	 ------  last two equations  ------
+c  the last two equations enforce continuity of third derivative and
+c  of first derivative across  tau(ntau-1).
+      entry = ratio*s(i-1,3) + s(i,2) + s(i,1)/3.
+      s(i+1,2) = s(i,1)/6.
+      s(i+1,4) = ratio*s(i-1,4) + s(i,4)
+      if (z - .5)			41,42,43
+   41 ratio = s(i,1)*6.*s(i-1,6)*alpha/s(i-1,2)
+      s(i,2) = ratio*s(i-1,3) + s(i,1) + s(i-1,1)
+      s(i,3) = -s(i-1,1)
+					go to 45
+   42 ratio = s(i,1)/s(i-1,2)
+      s(i,2) = ratio*s(i-1,3) + s(i,1) + s(i-1,1)
+      s(i,3) = -s(i-1,1)
+					go to 45
+   43 factr2 = onemzt*(alpha*(onemzt**2-1.)+1.)/
+     *		     (alpha*(onemzt**3-1.)+1.)
+      ratio = factr2*s(i,1)/s(i-1,2)
+      s(i,2) = ratio*s(i-1,3) + factr2*s(i-1,1) + s(i,1)
+      s(i,3) = -factr2*s(i-1,1)
+c     at this point, the last two equations read
+c	      diag(i)*xi + u(i)*xi+1 = r(i)
+c      -ratio*diag(i)*xi + diag(i+1)*xi+1 = r(i+1)
+c     eliminate xi from last equation
+   45 s(i,4) = ratio*s(i-1,4)
+      ratio = -entry/s(i,2)
+      s(i+1,2) = ratio*s(i,3) + s(i+1,2)
+      s(i+1,4) = ratio*s(i,4) + s(i+1,4)
+c
+c	 ------ back substitution ------
+c
+      s(ntau,4) = s(ntau,4)/s(ntau,2)
+   50	 s(i,4) = (s(i,4) - s(i,3)*s(i+1,4))/s(i,2)
+	 i = i - 1
+	 if (i .gt. 1)			go to 50
+      s(1,4) = (s(1,4)-s(1,3)*s(2,4)-entry3*s(3,4))/s(1,2)
+c
+c	 ------ construct polynomial pieces ------
+c
+      break(1) = tau(1)
+      l = 1
+      do 70 i=1,ntaum1
+	 coef(1,l) = gtau(i)
+	 coef(3,l) = s(i,4)
+	 divdif = (gtau(i+1)-gtau(i))/s(i,1)
+	 z = s(i,5)
+	 if (z - .5)			61,62,63
+   61	 if (z .eq. 0.) 		go to 65
+	 zeta = gam*z
+	 onemzt = 1. - zeta
+	 c = s(i+1,4)/6.
+	 d = s(i,4)*s(i,6)
+	 l = l + 1
+	 del = zeta*s(i,1)
+	 break(l) = tau(i) + del
+	 zt2 = zeta**2
+	 alpha = alph(onemzt)
+	 factor = onemzt**2*alpha
+	 coef(1,l) = gtau(i) + divdif*del
+     *		   + s(i,1)**2*(d*onemzt*(factor-1.)+c*zeta*(zt2-1.))
+	 coef(2,l) = divdif + s(i,1)*(d*(1.-3.*factor)+c*(3.*zt2-1.))
+	 coef(3,l) = 6.*(d*alpha*onemzt + c*zeta)
+	 coef(4,l) = 6.*(c - d*alpha)/s(i,1)
+	 coef(4,l-1) = coef(4,l) - 6.*d*(1.-alpha)/(del*zt2)
+	 coef(2,l-1) = coef(2,l) - del*(coef(3,l) -(del/2.)*coef(4,l-1))
+					go to 68
+   62	 coef(2,l) = divdif - s(i,1)*(2.*s(i,4) + s(i+1,4))/6.
+	 coef(4,l) = (s(i+1,4)-s(i,4))/s(i,1)
+					go to 68
+   63	 onemzt = gam*(1. - z)
+	 if (onemzt .eq. 0.)		go to 65
+	 zeta = 1. - onemzt
+	 alpha = alph(zeta)
+	 c = s(i+1,4)*s(i,6)
+	 d = s(i,4)/6.
+	 del = zeta*s(i,1)
+	 break(l+1) = tau(i) + del
+	 coef(2,l) = divdif - s(i,1)*(2.*d + c)
+	 coef(4,l) = 6.*(c*alpha - d)/s(i,1)
+	 l = l + 1
+	 coef(4,l) = coef(4,l-1) + 6.*(1.-alpha)*c/(s(i,1)*onemzt**3)
+	 coef(3,l) = coef(3,l-1) + del*coef(4,l-1)
+	 coef(2,l) = coef(2,l-1)+del*(coef(3,l-1)+(del/2.)*coef(4,l-1))
+	 coef(1,l) = coef(1,l-1)+del*(coef(2,l-1)+(del/2.)*(coef(3,l-1)
+     *			+(del/3.)*coef(4,l-1)))
+					go to 68
+   65	 coef(2,l) = divdif
+	 coef(3,l) = 0.
+	 coef(4,l) = 0.
+   68	 l = l + 1
+   70	 break(l) = tau(i+1)
+      l = l - 1
+      k = 4
+      iflag = 1
+					return
+  999 iflag = 2
+					return
+      end
diff --git a/math/deboor/titand.f b/math/deboor/titand.f
new file mode 100644
index 00000000..3b323923
--- /dev/null
+++ b/math/deboor/titand.f
@@ -0,0 +1,18 @@
+      subroutine titand ( tau, gtau, n )
+c  from  * a practical guide to splines *  by c. de boor
+c  these data represent a property of titanium as a function of
+c  temperature. they have been used extensively as an example in spline
+c  approximation with variable knots.
+      integer n,   i
+      real gtau(49),tau(49),gtitan(49)
+      data gtitan /.644,.622,.638,.649,.652,.639,.646,.657,.652,.655,
+     2		   .644,.663,.663,.668,.676,.676,.686,.679,.678,.683,
+     3		   .694,.699,.710,.730,.763,.812,.907,1.044,1.336,1.881,
+     4		   2.169,2.075,1.598,1.211,.916,.746,.672,.627,.615,.607
+     5		  ,.606,.609,.603,.601,.603,.601,.611,.601,.608/
+      n = 49
+      do 10 i=1,n
+	 tau(i) = 585. + 10.*float(i)
+   10	 gtau(i) = gtitan(i)
+					return
+      end
diff --git a/math/gsurfit/README b/math/gsurfit/README
new file mode 100644
index 00000000..4ab4a0f3
--- /dev/null
+++ b/math/gsurfit/README
@@ -0,0 +1,6 @@
+Linear least squares surface fitting package.
+Contains routines to fit Legendre and Chebyshev polynomials
+in the least squares sense to 2-dimensional data.
+The normal equations are accumulated and solved using Cholesky factorization.
+The package contains separate entry points for accumulating points,
+solving the matrix equations, rejecting points and evaluating the surface.
diff --git a/math/gsurfit/dgsurfitdef.h b/math/gsurfit/dgsurfitdef.h
new file mode 100644
index 00000000..5888cb81
--- /dev/null
+++ b/math/gsurfit/dgsurfitdef.h
@@ -0,0 +1,61 @@
+# Header file for the surface fitting package
+
+# set up the curve descriptor structure
+
+define	LEN_GSSTRUCT	64
+
+define	GS_XREF		Memd[P2D($1)]	# x reference value
+define	GS_YREF		Memd[P2D($1+2)]	# y reference value
+define	GS_ZREF		Memd[P2D($1+4)]	# z reference value
+define	GS_XMAX		Memd[P2D($1+6)]	# Maximum x value
+define	GS_XMIN		Memd[P2D($1+8)]	# Minimum x value
+define	GS_YMAX		Memd[P2D($1+10)]# Maximum y value
+define	GS_YMIN		Memd[P2D($1+12)]# Minimum y value		
+define	GS_XRANGE	Memd[P2D($1+14)]# 2. / (xmax - xmin), polynomials
+define	GS_XMAXMIN	Memd[P2D($1+16)]# - (xmax + xmin) / 2., polynomials
+define	GS_YRANGE	Memd[P2D($1+18)]# 2. / (ymax - ymin), polynomials
+define	GS_YMAXMIN	Memd[P2D($1+20)]# - (ymax + ymin) / 2., polynomials
+define	GS_TYPE		Memi[$1+22]	# Type of curve to be fitted
+define	GS_XORDER	Memi[$1+23]	# Order of the fit in x
+define	GS_YORDER	Memi[$1+24]	# Order of the fit in y
+define	GS_XTERMS	Memi[$1+25]	# Cross terms for polynomials
+define	GS_NXCOEFF	Memi[$1+26]	# Number of x coefficients
+define	GS_NYCOEFF	Memi[$1+27]	# Number of y coefficients
+define	GS_NCOEFF	Memi[$1+28]	# Total number of coefficients
+define	GS_NPTS		Memi[$1+29]	# Number of data points
+
+define	GS_MATRIX	Memi[$1+30]	# Pointer to original matrix
+define	GS_CHOFAC	Memi[$1+31]	# Pointer to Cholesky factorization
+define	GS_VECTOR	Memi[$1+32]	# Pointer to  vector
+define	GS_COEFF	Memi[$1+33]	# Pointer to coefficient vector
+define	GS_XBASIS	Memi[$1+34]	# Pointer to basis functions (all x)
+define	GS_YBASIS	Memi[$1+35]	# Pointer to basis functions (all y)
+define	GS_WZ		Memi[$1+36]	# Pointer to w * z (gsrefit)
+
+# matrix and vector element definitions
+
+define	XBASIS		Memd[$1]	# Non zero basis for all x
+define	YBASIS		Memd[$1]	# Non zero basis for all y
+define	XBS		Memd[$1]	# Non zero basis for single x
+define	YBS		Memd[$1]	# Non zero basis for single y
+define	MATRIX		Memd[$1]	# Element of MATRIX
+define	CHOFAC		Memd[$1]	# Element of CHOFAC
+define	VECTOR		Memd[$1]	# Element of VECTOR
+define	COEFF		Memd[$1]	# Element of COEFF
+
+# structure definitions for restore
+
+define	GS_SAVETYPE	$1[1]
+define	GS_SAVEXORDER	$1[2]
+define	GS_SAVEYORDER	$1[3]
+define	GS_SAVEXTERMS	$1[4]
+define	GS_SAVEXMIN	$1[5]
+define	GS_SAVEXMAX	$1[6]
+define	GS_SAVEYMIN	$1[7]
+define	GS_SAVEYMAX	$1[8]
+
+# data type
+
+define	DELTA		EPSILON
+
+# miscellaneous
diff --git a/math/gsurfit/doc/gsaccum.hlp b/math/gsurfit/doc/gsaccum.hlp
new file mode 100644
index 00000000..afa63f70
--- /dev/null
+++ b/math/gsurfit/doc/gsaccum.hlp
@@ -0,0 +1,51 @@
+.help gsaccum Aug85 "Gsurfit Package"
+.ih
+NAME
+gsaccum -- accumulate a single data point into the fit
+.ih
+SYNOPSIS
+include <math/gsurfit.h>
+
+gsaccum (sf, x, y, weight, wtflag)
+
+.nf
+pointer	sf		# surface descriptor
+real	x		# x value, xmin <= x <= xmax
+real	y		# y value, ymin <= y <= ymax
+real	z		# z value
+real	weight		# weight
+int	wtflag		# type of weighting
+.fi
+.ih
+ARGUMENTS
+.ls sf      
+Pointer to the surface descriptor structure.
+.le
+.ls x, y
+The x and y values.
+.le
+.ls z      
+Data value.
+.le
+.ls weight
+The weight assigned to the data point.
+.le
+.ls wtflag
+Type of weighting. The options are WTS_USER and WTS_UNIFORM. If wtflag
+equals WTS_USER the weight for each data point is supplied by the user.
+If wtflag equals WTS_UNIFORM the routine sets the weight to 1.
+.le
+.ih
+DESCRIPTION
+GSACCUM calculates the non-zero basis functions for the given x and
+y values, computes the contribution of each data point to the normal
+equations and sums that contribution into the appropriate arrays and
+vectors.
+.ih
+NOTES
+Checking for out of bounds x and y values and INDEF valued data points is
+the responsibility of the calling program.
+.ih
+SEE ALSO
+gsacpts, gsfit, gsrefit
+.endhelp
diff --git a/math/gsurfit/doc/gsacpts.hlp b/math/gsurfit/doc/gsacpts.hlp
new file mode 100644
index 00000000..1e253c61
--- /dev/null
+++ b/math/gsurfit/doc/gsacpts.hlp
@@ -0,0 +1,56 @@
+.help gsacpts Aug85 "Gsurfit Package"
+.ih
+NAME
+gsacpts -- accumulate an array of data points into the fit
+.ih
+SYNOPSIS
+include <math/gsurfit.h>
+
+gsacpts (sf, x, y, z, weight, npts, wtflag)
+
+.nf
+pointer	sf		# surface descriptor
+real	x[npts]		# x values, xmin <= x <= xmax
+real	y[npts]		# y values, ymin <= y <= ymax
+real	z[npts]		# z values
+real	weight[npts]	# array of weights
+int	npts		# the number of data points
+int	wtflag		# type of weighting
+.fi
+.ih
+ARGUMENTS
+.ls sf      
+Pointer to the surface descriptor structure.
+.le
+.ls x, y
+Array of x and y values.
+.le
+.ls z      
+Array of data values.
+.le
+.ls weight
+The weights assigned to the data points.
+.le
+.ls npts
+The number of data points.
+.le
+.ls wtflag
+Type of weighting. The options are WTS_USER and WTS_UNIFORM. If wtflag
+equals WTS_USER the weight for each data point is supplied by the user.
+If wtflag equals WTS_UNIFORM the routine sets the weight to 1.
+The weight definitions are contained in the package header file gsurfit.h.
+.le
+.ih
+DESCRIPTION
+GSACCUM calculates the non-zero basis functions for the given x and
+y values, computes the contribution of each data point to the normal
+equations and sums that contribution into the appropriate arrays and
+vectors.
+.ih
+NOTES
+Checking for out of bounds x and y values and INDEF valued data points is
+the responsibility of the calling program.
+.ih
+SEE ALSO
+gsaccum, gsfit, gsrefit
+.endhelp
diff --git a/math/gsurfit/doc/gsadd.hlp b/math/gsurfit/doc/gsadd.hlp
new file mode 100644
index 00000000..84d388fd
--- /dev/null
+++ b/math/gsurfit/doc/gsadd.hlp
@@ -0,0 +1,35 @@
+.help gsadd Aug85 "Gsurfit Package"
+.ih
+NAME
+gsadd -- add two surface fits together
+.ih
+SYNOPSIS
+gsadd (sf1, sf2, sf3)
+
+.nf
+pointer	sf1		# first surface descriptor
+pointer	sf2		# second surface descriptor
+pointer	sf3		# resultant surface descriptor
+.fi
+.ih
+ARGUMENTS
+.ls sf1    
+Pointer to the first surface descriptor.
+.le
+.ls sf2    
+Pointer to the second surface descriptor.
+.le
+.ls sf3    
+Pointer to the resultant surface descriptor.
+.le
+.ih
+DESCRIPTION
+The coefficients of the two surfaces are added together. GSADD checks
+that the curve_types are the same and that the fits are normalized over
+the same range of data.
+.ih
+NOTES
+.ih
+SEE ALSO
+gscopy, gssub
+.endhelp
diff --git a/math/gsurfit/doc/gscoeff.hlp b/math/gsurfit/doc/gscoeff.hlp
new file mode 100644
index 00000000..e4b792db
--- /dev/null
+++ b/math/gsurfit/doc/gscoeff.hlp
@@ -0,0 +1,39 @@
+.help gscoeff Aug85 "Gsurfit Package"
+.ih
+NAME
+gscoeff - get the number and values of the coefficients
+.ih
+SYNOPSIS
+gscoeff (sf, coeff, ncoeff)
+
+.nf
+pointer	sf		# surface descriptor
+real	coeff[ncoeff]	# coefficient array
+int	ncoeff		# number of coefficients
+.fi
+.ih
+ARGUMENTS
+.ls sf   
+Pointer to the surface descriptor.
+.le
+.ls coeff
+Array of coefficients.
+.le
+.ls ncoeff
+The number of coefficients. Ncoeff may be obtained by a call
+to gsstati.
+.le
+
+.nf
+	ncoeff = gsstati (sf, GSNCOEFF)
+.fi
+.ih
+DESCRIPTION
+GSCOEFF fetches the coefficient array and the number of coefficients from
+the surface descriptor structure.
+.ih
+NOTES
+.ih
+SEE ALSO
+gserrors
+.endhelp
diff --git a/math/gsurfit/doc/gscopy.hlp b/math/gsurfit/doc/gscopy.hlp
new file mode 100644
index 00000000..46a0935f
--- /dev/null
+++ b/math/gsurfit/doc/gscopy.hlp
@@ -0,0 +1,32 @@
+.help gscopy Aug85 "Gsurfit Package"
+.ih
+NAME
+gscopy -- copy a surface fit
+.ih
+SYNOPSIS
+gscopy (sf1, sf2)
+
+.nf
+pointer	sf1		# old surface descriptor
+pointer	sf2		# new surface descriptor
+.fi
+.ih
+ARGUMENTS
+.ls sf1    
+Pointer to the old surface descriptor structure.
+.le
+.ls sf2   
+Pointer to the new surface descriptor structure.
+.le
+.ih
+DESCRIPTION
+The surface fit and parameters are copied for later use by
+GSEVAL or GSVECTOR.
+.ih
+NOTES
+The matrices and vectors used by the numerical fitting routines are not
+stored.
+.ih
+SEE ALSO
+gsadd, gssub
+.endhelp
diff --git a/math/gsurfit/doc/gsder.hlp b/math/gsurfit/doc/gsder.hlp
new file mode 100644
index 00000000..e1af66e9
--- /dev/null
+++ b/math/gsurfit/doc/gsder.hlp
@@ -0,0 +1,48 @@
+.help gsder Aug85 "Gsurfit Package"
+.ih
+NAME
+gsder -- evaluate the derivatives of the fitted surface
+.ih
+SYNOPSIS
+gsder (sf, x, y, zfit, npts, nxder, nyder)
+
+.nf
+pointer	sf		# surface descriptor
+real	x[npts]		# x array, xmin <= x[i] <= xmax
+real	y[npts]		# y array, ymin <= x[i] <= ymax
+real	zfit[npts]	# data values
+int	npts		# number of data points
+int	nxder		# order of x derivative, 0 = function
+int	nyder		# order of y derivative, 0 = function
+.fi
+.ih
+ARGUMENTS
+.ls sf    
+Pointer to the surface descriptor structure.
+.le
+.ls x, y
+Array of x and y values.
+.le
+.ls zfit
+Array of fitted values.
+.le
+.ls npts
+The number of points to be fit.
+.le
+.ls nxder, nyder
+The order of derivative to be fit. GSDER is the same as GSVECTOR if nxder = 0
+and nyder = 0. If nxder = 1 and nyder = 0 GSDER calculates the first
+derivatives of the surface with respect to x.
+.le
+.ih
+DESCRIPTION
+Evaluate the derivatives of a surface at a set of data points.
+GSDER uses the coefficients stored in the surface descriptor structure.
+.ih
+NOTES
+Checking for out of bounds x and y values is the responsibility of the
+calling program.
+.ih
+SEE ALSO
+gseval, gsvector
+.endhelp
diff --git a/math/gsurfit/doc/gserrors.hlp b/math/gsurfit/doc/gserrors.hlp
new file mode 100644
index 00000000..fed9a82e
--- /dev/null
+++ b/math/gsurfit/doc/gserrors.hlp
@@ -0,0 +1,61 @@
+.help gserrors Aug85 "Gsurfit Package"
+.ih
+NAME
+.nf
+gserrors -- calculate errors of the coefficients and the chi-square
+	    of the fit
+.fi
+.ih
+SYNOPSIS
+gserrors (sf, y, weight, yfit, chi_square, errors)
+
+.nf
+pointer	sf		# surface descriptor
+real	y[ARB]		# array of data values
+real	weight[ARB]	# array of weights
+real	yfit[ARB]	# array of fitted values
+real	chi_square	# chi_square of fit
+real	errors[ARB]	# array of errors
+.fi
+.ih
+ARGUMENTS
+.ls sf
+Pointer to the surface descriptor structure.
+.le
+.ls y
+Array of data values.
+.le
+.ls weight
+Array of weights.
+.le
+.ls yfit
+Array of fitted values.
+.le
+.ls chi_square
+The reduced chi-square of the fit.
+.le
+.ls errors
+The array of errors of the coefficients. The number of coefficients
+can be obtained by a call to gsstati.
+.le
+
+.nf
+	    nerrors = gsstati (sf, GSNCOEFF)
+.fi
+.ih
+DESCRIPTION
+GSCOEFF calculates the reduced chi-square of the fit and the standard
+deviation of the coefficients.
+The chi-square of the fit is the square root of the sum of the
+weighted squares of the residuals divided by the number of degrees
+of freedom. If the weights are equal, then the reduced chi-square is
+the variance of the fit. The error of the j-th coefficient is the
+square root of the j-th diagonal element of the inverse of the data
+matrix. If the weights are equal to one, then the errors are scaled
+by the square root of the variance of the data.
+.ih
+NOTES
+.ih
+SEE ALSO
+gscoeff
+.endhelp
diff --git a/math/gsurfit/doc/gseval.hlp b/math/gsurfit/doc/gseval.hlp
new file mode 100644
index 00000000..b9cd08bb
--- /dev/null
+++ b/math/gsurfit/doc/gseval.hlp
@@ -0,0 +1,34 @@
+.help gseval Aug85 "Gsurfit Package"
+.ih
+NAME
+gseval -- evaluate the fitted surface at x and y
+.ih
+SYNOPSIS
+y = gseval (sf, x, y)
+
+.nf
+pointer	sf		# surface descriptor
+real	x		# x value, xmin <= x <= xmax
+real	y		# y value, ymin <= y <= ymax
+.fi
+.ih
+ARGUMENTS
+.ls sf      
+Pointer to the surface descriptor structure.
+.le
+.ls x, y
+X and y values at which the surface is to be evaluated.
+.le
+.ih
+DESCRIPTION
+Evaluate the surface at the specified value of x and y. GSEVAL is a real
+valued function which returns the fitted value.
+.ih
+NOTES
+GSEVAL uses the coefficient array stored in the surface descriptor structure.
+Checking for out of bounds x and y values is the responsibility of the calling
+program.
+.ih
+SEE ALSO
+gsvector, gsder
+.endhelp
diff --git a/math/gsurfit/doc/gsfit.hlp b/math/gsurfit/doc/gsfit.hlp
new file mode 100644
index 00000000..4abdc546
--- /dev/null
+++ b/math/gsurfit/doc/gsfit.hlp
@@ -0,0 +1,64 @@
+.help gsfit Aug85 "Gsurfit Package"
+.ih
+NAME
+gsfit -- fit a surface to a set of data values
+.ih
+SYNOPSIS
+include <math/gsurfit.h>
+
+gsfit (sf, x, y, z, weight, npts, wtflag, ier)
+
+.nf
+pointer	sf		# surface descriptor
+real	x[npts]		# x array, xmin <= x[i] <= xmax
+real	y[npts]		# y array, ymin <= y[i] <= ymax
+real	z[npts]		# data values
+real	weight[npts]	# weight array
+int	npts		# number of data points
+int	wtflag		# type of weighting
+int	ier		# error coded
+.fi
+.ih
+ARGUMENTS
+.ls sf    
+Pointer to the surface descriptor structure.
+.le
+.ls x, y
+X and y value arrays.
+.le
+.ls z      
+Array of data values.
+.le
+.ls weight
+Array of weights.
+.le
+.ls npts
+Number of data points
+.le
+.ls wtflag
+Type of weighting. The options are WTS_USER and WTS_UNIFORM. If wtflag =
+WTS_USER individual weights for each data point are supplied by the calling
+program and points with zero-valued weights are not included in the fit.
+If wtflag = WTS_UNIFORM, all weights are assigned values of 1.
+.le
+.ls ier     
+Error code for the fit. The options are OK, SINGULAR and NO_DEG_FREEDOM.
+If ier = SINGULAR, the numerical routines will compute a solution but one
+or more of the coefficients will be zero. If ier = NO_DEG_FREEDOM there
+were too few data points to solve the matrix equations and the routine
+returns without fitting the data.
+.le
+.ih
+DESCRIPTION
+GSFIT zeroes the matrix and vectors, calculates the non-zero basis functions,
+computes the contribution of each data point to the normal equations
+and accumulates it into the appropriate array and vector elements. The
+Cholesky factorization of the coefficient array is computed and the coefficients
+of the fitting function are calculated.
+.ih
+NOTES
+Checking for out of bounds x and y values is the responsibility of the user.
+.ih
+SEE ALSO
+gsrefit, gsaccum, gsacpts, gssolve, gszero
+.endhelp
diff --git a/math/gsurfit/doc/gsfree.hlp b/math/gsurfit/doc/gsfree.hlp
new file mode 100644
index 00000000..a576b2e1
--- /dev/null
+++ b/math/gsurfit/doc/gsfree.hlp
@@ -0,0 +1,26 @@
+.help gsfree Aug85 "Gsurfit Package"
+.ih
+NAME
+gsfree -- free the surface descriptor structure
+.ih
+SYNOPSIS
+gsfree (sf)
+
+.nf
+pointer	sf		# surface descriptor
+.fi
+.ih
+ARGUMENTS
+.ls sf    
+Pointer to the surface descriptor structure.
+.le
+.ih
+DESCRIPTION
+Frees the surface descriptor structure.
+.ih
+NOTES
+GSFREE should be called after each surface fit.
+.ih
+SEE ALSO
+gsinit
+.endhelp
diff --git a/math/gsurfit/doc/gsgcoeff.hlp b/math/gsurfit/doc/gsgcoeff.hlp
new file mode 100644
index 00000000..78fdc707
--- /dev/null
+++ b/math/gsurfit/doc/gsgcoeff.hlp
@@ -0,0 +1,31 @@
+.help gsgcoeff Aug85 "Gsurfit Package"
+.ih
+NAME
+gsgcoeff -- Procedure to fetch a coefficient
+.ih
+SYNOPSIS
+rval = gsgcoeff (sf, xorder, yorder)
+
+.nf
+    pointer	sf	# surface descriptor	
+    int		xorder	# x order of desired coefficient
+    int		yorder	# y order of desired coefficient
+.fi
+.ih
+ARGUMENTS
+.ls sf    
+Pointer to the surface descriptor.
+.le
+.ls xorder, yorder
+The x and y order of the desired coefficient.
+.le
+.ih
+DESCRIPTION
+GSGCOEFF fetches the coefficient of x ** (xorder - 1) * y ** (yorder - 1).
+INDEF is returned if xorder and yorder are out of range.
+.ih
+NOTES
+.ih
+SEE ALSO
+gsscoeff
+.endhelp
diff --git a/math/gsurfit/doc/gsinit.hlp b/math/gsurfit/doc/gsinit.hlp
new file mode 100644
index 00000000..3a647a8c
--- /dev/null
+++ b/math/gsurfit/doc/gsinit.hlp
@@ -0,0 +1,64 @@
+.help gsinit Aug85 "Gsurfit Package"
+.ih
+NAME
+gsinit -- initialize surface descriptor
+.ih
+SYNOPSIS
+include <math/gsurfit.h>
+
+.nf
+gsinit (sf, surface_type, xorder, yorder, xterms, xmin, xmax,
+	ymin, ymax)
+.fi
+
+.nf
+pointer	sf		# surface descriptor
+int	surface_type	# surface function
+int	xorder		# order of function in x
+int	yorder		# order of function in y
+int	xterms		# include cross-terms? (YES/NO)
+real	xmin		# minimum x value
+real	xmax		# maximum x value
+real	ymin		# minimum y value
+real	ymax		# maximum y value
+.fi
+.ih
+ARGUMENTS
+.ls sf    
+Pointer to the surface descriptor structure.
+.le
+.ls surface_type
+Fitting function. Permitted values are GS_LEGENDRE and GS_CHEBYSHEV for
+Legendre and Chebyshev polynomials.
+.le
+.ls xorder, yorder
+Order of the polynomial to be fit. The order must be greater than or
+equal to 1. If xorder == 1 and yorder == 1 a constant is fit to the data.
+.le
+.ls xterms
+Set the cross-terms type? The options are GS_XNONE (the old NO option) for
+no cross terms, GS_XHALF for diagonal cross terms (new option), and GS_XFULL
+for full cross terms (the old YES option).
+.le
+.ls xmin, xmax
+Minimum and maximum x values. All the x values of interest including the
+data x values and the x values of any surface to be evaluated must
+fall in the range xmin <= x <= xmax.
+.le
+.ls ymin, ymax
+Minimum and maximum y values. All the y values of interest including the
+data y values and the y values of any surface to be evaluated must
+fall in the range ymin <= y <= ymax.
+.le
+.ih
+DESCRIPTION
+GSINIT allocates space for the surface descriptor and the arrays and vectors
+used by the numerical routines. It initializes all arrays and vectors to zero
+and returns the surface descriptor to the calling routine.
+.ih
+NOTES
+GSINIT must be the first GSURFIT routine called.
+.ih
+SEE ALSO
+gsfree
+.endhelp
diff --git a/math/gsurfit/doc/gsrefit.hlp b/math/gsurfit/doc/gsrefit.hlp
new file mode 100644
index 00000000..629697e8
--- /dev/null
+++ b/math/gsurfit/doc/gsrefit.hlp
@@ -0,0 +1,55 @@
+.help gsrefit Aug85 "Gsurfit Package"
+.ih
+NAME
+gsrefit -- refit with new z vector using old x, y and weight vector
+.ih
+SYNOPSIS
+include < math/gsurfit.h>
+
+gsrefit (sf, x, y, z, w, ier)
+
+.nf
+pointer	sf		# surface descriptor
+real	x[ARB]		# x array, xmin <= x[i] <= xmax
+real	y[ARB]		# y array, ymin <= y[i] <= ymax
+real	z[ARB]		# array of data values
+real	w[ARB]		# array of weights
+int	ier		# error code
+.fi
+.ih
+ARGUMENTS
+.ls sf          
+Pointer to the surface descriptor structure.
+.le
+.ls x, y
+Array of x and y values.
+.le
+.ls z    
+Array of data values.
+.le
+.ls w    
+Array of weights.
+.le
+.ls ier    
+Error code. The options are OK, SINGULAR and NO_DEG_FREEDOM. If ier =
+SINGULAR a solution is computed but one or more coefficients may be zero.
+If ier equals NO_DEG_FREEDOM, there are insufficient data points to
+compute a solution and GSREFIT returns without solving for the coefficients.
+.le
+.ih
+DESCRIPTION
+In some applications the x, y and weight values remain unchanged from fit
+to fit and only the z values vary. In this case it is redundant to
+reaccumulate the matrix and perform the Cholesky factorization. GSREFIT
+zeros and reaccumulates the vector on the right hand side of the matrix
+equation and performs the forward and back substitution phase to fit for
+a new coefficient vector.
+.ih
+NOTES
+In the first call to GSREFIT space is allocated for the non-zero basis
+functions. Subsequent calls to GSREFIT reference this array to avoid
+recalculating basis functions at every call.
+.ih
+SEE ALSO
+gsfit, gsaccum, gsacpts, gssolve
+.endhelp
diff --git a/math/gsurfit/doc/gsreject.hlp b/math/gsurfit/doc/gsreject.hlp
new file mode 100644
index 00000000..96344ac2
--- /dev/null
+++ b/math/gsurfit/doc/gsreject.hlp
@@ -0,0 +1,44 @@
+.help gsreject Aug85 "Gsurfit Package"
+.ih
+NAME
+gsreject -- reject a data point from the fit
+.ih
+SYNOPSIS
+gsreject (sf, x, y, z, weight)
+
+.nf
+pointer	sf		# surface descriptor
+real	x		# x value, xmin <= x <= xmax
+real	y		# y value, ymin <= y <= ymax
+real	z		# data value
+real	weight		# weight
+.fi
+.ih
+ARGUMENTS
+.ls sf     
+Pointer to the surface descriptor structure.
+.le
+.ls x, y
+X and y values.
+.le
+.ls z      
+Data value.
+.le
+.ls weight
+Weight value.
+.le
+.ih
+DESCRIPTION
+GSREJECT removes a data point from the fit. The non-zero basis functions for
+each x and y are calculated, and the contribution of the point to the normal
+equations is computed and subtracted from the appropriate arrays and vectors.
+An array of points can be removed from the fit by repeated calls to GSREJECT
+followed by a single call to GSSOLVE to calculate a new set of coefficients.
+.ih
+NOTES
+Out of bounds x and y values and INDEF valued data values are the responsibility
+of the calling program.
+.ih
+SEE ALSO
+gsaccum, gsacpts
+.endhelp
diff --git a/math/gsurfit/doc/gsrestore.hlp b/math/gsurfit/doc/gsrestore.hlp
new file mode 100644
index 00000000..f71aab56
--- /dev/null
+++ b/math/gsurfit/doc/gsrestore.hlp
@@ -0,0 +1,36 @@
+.help gsrestore Aug85 "Gsurfit Package"
+.ih
+NAME
+gsrestore -- restore fit parameters
+.ih
+SYNOPSIS
+gsrestore (sf, fit)
+
+.nf
+pointer	sf		# surface descriptor
+real	fit[ARB]	# fit array
+.fi
+.ih
+ARGUMENTS
+.ls sf   
+Pointer to the surface descriptor structure. Returned by GSRESTORE.
+.le
+.ls fit    
+Array containing the surface parameters. The size of the fit array
+can be determined by a call gsstati.
+
+.nf
+	    len_fit = gsstati (gs, GSNSAVE)
+.fi
+.le
+.ih
+DESCRIPTION
+GSRESTORE returns the surface descriptor to the calling program and
+restores the surface parameters and fit ready for use by GSEVAL or
+GSVECTOR.
+.ih
+NOTES
+.ih
+SEE ALSO
+gssave
+.endhelp
diff --git a/math/gsurfit/doc/gssave.hlp b/math/gsurfit/doc/gssave.hlp
new file mode 100644
index 00000000..a6faf568
--- /dev/null
+++ b/math/gsurfit/doc/gssave.hlp
@@ -0,0 +1,39 @@
+.help gssave Aug85 "Gsurfit Package"
+.ih
+NAME
+gssave -- save parameters of the fit
+.ih
+SYNOPSIS
+call gssave (sf, fit)
+
+.nf
+pointer	sf		# surface descriptor
+real	fit[ARB]	# fit array
+.fi
+.ih
+ARGUMENTS
+.ls sf     
+Pointer to the surface descriptor structure.
+.le
+.ls fit    
+Array containing fit parameters. The size of the fit array can be determined
+by a call to gsstati.
+.le
+
+.nf
+	    len_fit = gsstati (sf, GSNSAVE)
+.fi
+.ih
+DESCRIPTION
+GSSAVE saves the surface parameters in the real array fit. The first eight
+elements of fit contain the surface_type, xorder, yorder, xterms, xmin,
+xmax, ymin and ymax. The coefficients are stored in the remaining array
+elements.
+.ih
+NOTES
+GSSAVE does not preserve the matrices and vectors used by the fitting
+routines.
+.ih
+SEE ALSO
+gsrestore
+.endhelp
diff --git a/math/gsurfit/doc/gsscoeff.hlp b/math/gsurfit/doc/gsscoeff.hlp
new file mode 100644
index 00000000..5f5e4a6a
--- /dev/null
+++ b/math/gsurfit/doc/gsscoeff.hlp
@@ -0,0 +1,35 @@
+.help gsscoeff Aug85 "Gsurfit Package"
+.ih
+NAME
+gsscoeff -- Procedure to set a coefficient
+.ih
+SYNOPSIS
+gsscoeff (sf, xorder, yorder, coeff)
+
+.nf
+    pointer	sf	# surface descriptor	
+    int		xorder	# x order of desired coefficient
+    int		yorder	# y order of desired coefficient
+    real	coeff	# coefficient value
+.fi
+.ih
+ARGUMENTS
+.ls sf    
+Pointer to the surface descriptor.
+.le
+.ls xorder, yorder
+The x and y order of the desired coefficient.
+.le
+.ls coeff
+The value of the coefficient to be set.
+.le
+.ih
+DESCRIPTION
+GSSCOEFF sets the coefficient of x ** (xorder - 1) * y ** (yorder - 1).
+GSSCOEFF returns if xorder and yorder are out of range.
+.ih
+NOTES
+.ih
+SEE ALSO
+gsgcoeff
+.endhelp
diff --git a/math/gsurfit/doc/gssolve.hlp b/math/gsurfit/doc/gssolve.hlp
new file mode 100644
index 00000000..8ddf42fc
--- /dev/null
+++ b/math/gsurfit/doc/gssolve.hlp
@@ -0,0 +1,40 @@
+.help gssolve Aug85 "Gsurfit Package"
+.ih
+NAME
+gssolve -- solve a linear system of equations by the Cholesky method
+.ih
+SYNOPSIS
+include <math/gsurfit.h>
+
+gssolve (sf, ier)
+
+.nf
+pointer	sf		# surface descriptor
+int	ier		# error code
+.fi
+.ih
+ARGUMENTS
+.ls sf     
+Pointer to the surface descriptor structure.
+.le
+.ls ier      
+Error code returned by the fitting routines. The options are OK, SINGULAR,
+and NO_DEG_FREEDOM. If ier = SINGULAR the matrix is singular, GSSOLVE
+will compute a solution to the normal equations but one or more of the
+coefficients will be zero. If ier = NO_DEG_FREEDOM, too few data points
+exist for a reasonable solution to be computed. GSSOLVE returns without
+fitting the data.
+.le
+.ih
+DESCRIPTION
+GSSOLVE computes the Cholesky factorization of the data matrix and
+solves for the coefficients
+of the fitting function by forward and back substitution. An error code is
+returned by GSSOLVE if it is unable to solve the normal equations as
+formulated.
+.ih
+NOTES
+.ih
+SEE ALSO
+gsfit, gsrefit, gsaccum, gsacpts
+.endhelp
diff --git a/math/gsurfit/doc/gsstati.hlp b/math/gsurfit/doc/gsstati.hlp
new file mode 100644
index 00000000..7b1b7f2e
--- /dev/null
+++ b/math/gsurfit/doc/gsstati.hlp
@@ -0,0 +1,35 @@
+.help gsstati Aug85 "Gsurfit Package"
+.ih
+NAME
+include <math/gsurfit.h>
+
+gsstati -- get integer parameter
+.ih
+SYNOPSIS
+ival = gsstati (sf, parameter)
+
+.nf
+pointer	sf		# surface descriptor
+int	parameter	# integer parameter to be returned
+.fi
+.ih
+ARGUMENTS
+.ls sf     
+The pointer to the surface descriptor structure.
+.le
+.ls parameter
+Parameter to be returned. The options are GSTYPE, GSXORDER, GSYORDER,
+GSNXCOEFF, GSNYCOEFF, and GSNSAVE. The parameter definitions are
+found in the package header file math/gsurfit.h.
+.le
+.ih
+DESCRIPTION
+The values of the integer parameters are returned. The parameters include
+the surface_type, the x and y orders, the number of x and y coefficients
+and the length of the buffer required by GSSAVE.
+.ih
+NOTES
+.ih
+SEE ALSO
+gsstatr
+.endhelp
diff --git a/math/gsurfit/doc/gsstatr.hlp b/math/gsurfit/doc/gsstatr.hlp
new file mode 100644
index 00000000..5a5578f2
--- /dev/null
+++ b/math/gsurfit/doc/gsstatr.hlp
@@ -0,0 +1,34 @@
+.help gsstatr Aug85 "Gsurfit Package"
+.ih
+NAME
+gsstatr -- get real parameter
+.ih
+SYNOPSIS
+include <math/gsurfit.h>
+
+rval = gsstatr (sf, parameter)
+
+.nf
+pointer	sf		# surface descriptor
+real	parameter	# real parameter to be returned
+.fi
+.ih
+ARGUMENTS
+.ls sf     
+The pointer to the surface descriptor structure.
+.le
+.ls parameter
+Parameter to be returned. The options are GSXMIN, GSXMAX, GSYMIN and
+and GSYMAX. The parameter definitions are
+found in the package header file math/gsurfit.h.
+.le
+.ih
+DESCRIPTION
+The values of the integer parameters are returned. The parameters include
+the minimum and maximum x values and the minimum and maximum y values.
+.ih
+NOTES
+.ih
+SEE ALSO
+gsstati
+.endhelp
diff --git a/math/gsurfit/doc/gssub.hlp b/math/gsurfit/doc/gssub.hlp
new file mode 100644
index 00000000..2c771612
--- /dev/null
+++ b/math/gsurfit/doc/gssub.hlp
@@ -0,0 +1,35 @@
+.help gssub Aug85 "Gsurfit Package"
+.ih
+NAME
+gssub -- subtract surface 1 from surface 2
+.ih
+SYNOPSIS
+gssub (sf1, sf2, sf3)
+
+.nf
+pointer	sf1		# first surface descriptor
+pointer	sf2		# second surface descriptor
+pointer	sf3		# resultant surface descriptor
+.fi
+.ih
+ARGUMENTS
+.ls sf1    
+Pointer to the first surface descriptor.
+.le
+.ls sf2   
+Pointer to the second surface descriptor.
+.le
+.ls sf3    
+Pointer to the resultant surface descriptor.
+.le
+.ih
+DESCRIPTION
+The coefficients of surface 2 are subtracted from surface 1. GSSUB checks
+that the surface_types are the same and that the fits are normalized over
+the same range of data.
+.ih
+NOTES
+.ih
+SEE ALSO
+gscopy, gsadd
+.endhelp
diff --git a/math/gsurfit/doc/gsurfit.hd b/math/gsurfit/doc/gsurfit.hd
new file mode 100644
index 00000000..169961f7
--- /dev/null
+++ b/math/gsurfit/doc/gsurfit.hd
@@ -0,0 +1,25 @@
+# Help directory for the GSURFIT (surface fitting) package.
+
+$gsurfit	= "math$gsurfit/"
+
+gsaccum		hlp = gsaccum.hlp,	src = gsurfit$gsaccum.x
+gsacpts		hlp = gsacpts.hlp,	src = gsurfit$gsacpts.x
+gsadd		hlp = gsadd.hlp,	src = gsurfit$gsadd.x
+gscoeff		hlp = gscoeff.hlp,	src = gsurfit$gscoeff.x
+gscopy		hlp = gscopy.hlp,	src = gsurfit$gscopy.x
+gsder		hlp = gsder.hlp,	src = gsurfit$gsder.x
+gserrors	hlp = gserrors.hlp,	src = gsurfit$gserrors.x
+gseval		hlp = gseval.hlp,	src = gsurfit$gseval.x
+gsinit		hlp = gsinit.hlp,	src = gsurfit$gsinit.x
+gsfit		hlp = gsfit.hlp,	src = gsurfit$gsfit.x
+gsfree		hlp = gsfree.hlp,	src = gsurfit$gsfree.x
+gsrefit		hlp = gsrefit.hlp,	src = gsurfit$gsrefit.x
+gsreject	hlp = gsreject.hlp,	src = gsurfit$gsreject.x
+gsrestore	hlp = gsrestore.hlp,	src = gsurfit$gsrestore.x
+gssave		hlp = gssave.hlp,	src = gsurfit$gssave.x
+gssolve		hlp = gssolve.hlp,	src = gsurfit$gssolve.x
+gsstati		hlp = gsstati.hlp,	src = gsurfit$gsstat.x
+gsstatr		hlp = gsstatr.hlp,	src = gsurfit$gsstat.x
+gssub		hlp = gssub.hlp,	src = gsurfit$gssub.x
+gsvector	hlp = gsvector.hlp,	src = gsurfit$gsvector.x
+gszero		hlp = gszero.hlp,	src = gsurfit$gszero.x
diff --git a/math/gsurfit/doc/gsurfit.hlp b/math/gsurfit/doc/gsurfit.hlp
new file mode 100644
index 00000000..99f42444
--- /dev/null
+++ b/math/gsurfit/doc/gsurfit.hlp
@@ -0,0 +1,169 @@
+.help gsurfit Aug85 "Math Package"
+.ih
+NAME
+gsurfit -- surface fitting package
+.ih
+SYNOPSIS
+
+.nf
+        gsinit (sf, surf_type, xorder, yorder, xterms, xmin, xmax, ymin, ymax)
+       gsaccum (sf, x, y, z, w, wtflag)
+       gsacpts (sf, x, y, z, w, npts, wtflag)
+      gsreject (sf, x, y, z, w)
+       gssolve (sf, ier)
+         gsfit (sf, x, y, z, w, npts, wtflag, ier)
+       gsrefit (sf, x, y, z, w, ier)
+    y = gseval (sf, x, y)
+      gsvector (sf, x, y, zfit, npts)
+         gsder (sf, x, y, zfit, npts, nxder, nyder)
+       gscoeff (sf, coeff, ncoeff)
+      gserrors (sf, z, w, zfit, rms, errors)
+        gssave (sf, fit)
+     gsrestore (sf, fit)
+ival = gsstati (sf, param)
+rval = gsstatr (sf, param)
+         gsadd (sf1, sf2, sf3)
+         gssub (sf1, sf2, sf3)
+        gscopy (sf1, sf2)
+        gsfree (sf)
+.fi
+.ih
+DESCRIPTION
+The gsurfit package provides a set of routines for fitting data to functions
+of two variables, linear in their coefficients, using least squares
+techniques. The numerical technique employed is the solution of the normal
+equations by the Cholesky method.
+.ih
+NOTES
+The fitting function is chosen at run time from the following list.
+
+.nf
+	GS_LEGENDRE		# Lengendre polynomials in x and y
+	GS_CHEBYSHEV		# Chebyshev polynomials in x and y
+.fi
+
+The gsurfit package performs a weighted fit. The weighting options are
+WTS_USER and WTS_UNIFORM. The user must supply a weight array. In the
+WTS_UNIFORM mode the gsurfit routines set the weights to 1. In WTS_USER
+mode the user must supply an array of weight values.
+
+In WTS_UNIFORM mode the reduced chi-square returned by GSERRORS is the
+variance of the fit and the errors in the coefficients are scaled
+by the square root of this variance. Otherwise the weights are
+interpreted as one over the variance of the data and the true reduced
+chi-square is returned.
+
+The routines assume that all the x and y values of interest lie in the
+region xmin <= x <= xmax and ymin <= y <= ymax. Checking for out of
+bounds x and y values is the responsibility of the calling program.
+The package routines assume that INDEF valued data points have been removed
+from the data set prior to entering the package routines.
+
+In order to make the package definitions available to the calling program
+an include <math/gsurfit.h> statement must be inserted in the calling program.
+GSINIT must be called before each fit. GSFREE frees the space used by
+the GSURFIT package.
+.ih
+EXAMPLES
+.nf
+Example 1: Fit surface to data, uniform weighting
+
+include <math/gsurfit.h>
+
+...
+
+call gsinit (sf, GS_CHEBYSHEV, 4, 4, NO, 1., 512., 1., 512.)
+
+call gsfit (sf, x, y, z, w, npts, WTS_UNIFORM, ier)
+if (ier != OK)
+    call error (...)
+
+do i = 1, 512 {
+    call printf ("x = %g y = %g z = %g zfit = %g\n")
+	call pargr (x[i])
+	call pargr (y[i])
+	call pargr (z[i])
+	call pargr (gseval (sf, x[i], y[i]))
+}
+
+call gsfree (sf)
+
+...
+
+Example 2: Fit a surface using accumulate mode, uniform weighting
+
+include <math/gsurfit.h>
+
+...
+
+do i = 1, 512 {
+    if (y[i] != INDEF)
+	call gsaccum (sf, x[i], y[i], z[i], weight[i], WTS_UNIFORM)
+}
+
+call gssolve (sf, ier)
+if (ier != OK)
+    call error (...)
+
+...
+
+call gsfree (sf)
+
+...
+
+Example 3: Fit and subtract a smooth surface from image lines
+
+include <math/gsurfit.h>
+
+...
+
+call gsinit (gs, GS_CHEBYSHEV, xorder, yorder, YES, 1., 512., 1., 512.)
+
+call gsfit (sf, xpts, ypts, zpts, w, WTS_UNIFORM, ier)
+if (ier != OK)
+    call error (...)
+
+do i = 1, 512
+    Memr[x+i-1] = i
+
+do line = 1, 512 {
+
+    inpix = imgl2r (im, line)
+    outpix = imgl2r (im, line)
+
+    yval = line
+    call amovkr (yval, Memr[y], 512)
+    call gsvector (sf, Memr[x], Memr[y], Memr[outpix], 512)
+    call asubr (Memr[inpix], Memr[outpix], Memr[outpix, 512) 
+}
+
+call gsfree (sf)
+
+...
+
+Example 4: Fit curve, save fit for later use for GSEVAL
+
+include <math/gsurfit.h>
+
+call gsinit (sf, GS_LEGENDRE, xorder, yorder, YES, xmin, xmax, ymin, ymax)
+
+call gsfit (sf, x, y, z, w, npts, WTS_UNIFORM, ier)
+if (ier != OK)
+    ...
+
+nsave = gsstati (sf, GSNSAVE)
+call salloc (fit, nsave, TY_REAL)
+call gssave (sf, Memr[fit])
+call gsfree (sf)
+
+...
+
+call gsrestore (sf, Memr[fit])
+do i = 1, npts
+    zfit[i] = gseval (sf, x[i], y[i])
+
+call gsfree (sf)
+
+...
+.fi
+.endhelp
diff --git a/math/gsurfit/doc/gsurfit.men b/math/gsurfit/doc/gsurfit.men
new file mode 100644
index 00000000..0b938ac8
--- /dev/null
+++ b/math/gsurfit/doc/gsurfit.men
@@ -0,0 +1,21 @@
+	gsaccum	- Accumulate point into data set
+	gsacpts - Accumulate points into a data set
+	  gsadd - Add two surfaces
+	gscoeff - Get coefficients 
+	 gscopy - Copy one surface to another
+	  gsder - Evaluate the derivatives of a surface
+       gserrors	- Calculate chi-square and errors in coefficients
+	 gseval	- Evaluate surface at x and y
+	  gsfit	- Fit surface
+	 gsfree - Free space allocated by gsinit
+	 gsinit - Make ready to fit a surface; set up parameters of fit
+	gsrefit	- Refit surface, same x, y and weight, different z
+       gsreject	- Reject point from data set
+      gsrestore - Restore surface parameters and coefficients
+	 gssave - Save surface parameters and coefficients
+	gssolve	- Solve matrix for coefficients
+	gsstati - Get integer parameter
+	gsstatr - Get real parameter
+	  gssub - Subtract one surface from another
+       gsvector - Evaluate surface at an array of x and y
+	 gszero - Zero arrays for new fit
diff --git a/math/gsurfit/doc/gsvector.hlp b/math/gsurfit/doc/gsvector.hlp
new file mode 100644
index 00000000..16003101
--- /dev/null
+++ b/math/gsurfit/doc/gsvector.hlp
@@ -0,0 +1,41 @@
+.help gsvector Aug85 "Gsurfit Package"
+.ih
+NAME
+gsvector -- evaluate the fitted surface at a set of points
+.ih
+SYNOPSIS
+gsvector (sf, x, y, zfit, npts)
+
+.nf
+pointer	sf		# surface descriptor
+real	x[npts]		# x array, xmin <= x <= xmax
+real	y[npts]		# y array, ymin <= y <= ymax
+real	zfit[npts]	# data values
+int	npts		# number of data points
+.fi
+.ih
+ARGUMENTS
+.ls sf    
+Pointer to the surface descriptor structure.
+.le
+.ls x, y
+Array of x and y values.
+.le
+.ls zfit
+Array of fitted values.
+.le
+.ls npts
+The number of points to be fit.
+.le
+.ih
+DESCRIPTION
+Fit the surface to an array of data points. GSVECTOR uses the coefficients
+stored in the surface descriptor structure.
+.ih
+NOTES
+Checking for out of bounds x and y values is the responsibility of the
+calling program.
+.ih
+SEE ALSO
+gseval, gsder
+.endhelp
diff --git a/math/gsurfit/doc/gszero.hlp b/math/gsurfit/doc/gszero.hlp
new file mode 100644
index 00000000..c7d411dd
--- /dev/null
+++ b/math/gsurfit/doc/gszero.hlp
@@ -0,0 +1,27 @@
+.help gszero Aug85 "Gsurfit Package"
+.ih
+NAME
+gszero -- set up for a new surface fit
+.ih
+SYNOPSIS
+gszero (sf)
+
+.nf
+pointer	sf		# surface descriptor
+.fi
+.ih
+ARGUMENTS
+.ls sf     
+Pointer to the surface descriptor structure.
+.le
+.ih
+DESCRIPTION
+GSZERO zeros the matrix and right side of the matrix equation.
+.ih
+NOTES
+GSZERO can be used to reinitialize the matrix and right side of the
+equation to begin a new fit in accumulate mode.
+.ih
+SEE ALSO
+gsinit, gsfit, gsrefit, gsaccum, gsacpts
+.endhelp
diff --git a/math/gsurfit/gs_b1eval.gx b/math/gsurfit/gs_b1eval.gx
new file mode 100644
index 00000000..6f474aa3
--- /dev/null
+++ b/math/gsurfit/gs_b1eval.gx
@@ -0,0 +1,85 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_B1POL -- Procedure to evaluate all the non-zero polynomial functions
+# for a single point and given order.
+
+procedure $tgs_b1pol (x, order, k1, k2, basis)
+
+PIXEL	x		# data point
+int	order		# order of polynomial, order = 1, constant
+PIXEL	k1, k2		# nomalizing constants, dummy in this case
+PIXEL	basis[ARB]	# basis functions
+
+int	i
+
+begin
+	basis[1] = 1.
+	if (order == 1)
+	    return
+
+	basis[2] = x
+	if (order == 2)
+	    return
+
+	do i = 3, order
+	    basis[i] = x * basis[i-1]
+
+end
+
+# GS_B1LEG -- Procedure to evaluate all the non-zero Legendre functions for
+# a single point and given order.
+
+procedure $tgs_b1leg (x, order, k1, k2, basis)
+
+PIXEL	x		# data point
+int	order		# order of polynomial, order = 1, constant
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# basis functions
+
+int	i
+PIXEL	ri, xnorm
+
+begin
+	basis[1] = 1.
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2 
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order {
+	    ri = i
+	    basis[i] = ((2. * ri - 3.) * xnorm * basis[i-1] -
+		       (ri - 2.) * basis[i-2]) / (ri - 1.)	
+	}
+end
+
+
+# GS_B1CHEB -- Procedure to evaluate all the non zero Chebyshev function
+# for a given x and order.
+
+procedure $tgs_b1cheb (x, order, k1, k2, basis)
+
+PIXEL	x		# number of data points
+int	order		# order of polynomial, 1 is a constant
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# array of basis functions
+
+int	i
+PIXEL	xnorm
+
+begin
+	basis[1] = 1.
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order
+	    basis[i] = 2. * xnorm * basis[i-1] - basis[i-2]
+end
diff --git a/math/gsurfit/gs_b1evald.x b/math/gsurfit/gs_b1evald.x
new file mode 100644
index 00000000..50fdf0bd
--- /dev/null
+++ b/math/gsurfit/gs_b1evald.x
@@ -0,0 +1,85 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_B1POL -- Procedure to evaluate all the non-zero polynomial functions
+# for a single point and given order.
+
+procedure dgs_b1pol (x, order, k1, k2, basis)
+
+double	x		# data point
+int	order		# order of polynomial, order = 1, constant
+double	k1, k2		# nomalizing constants, dummy in this case
+double	basis[ARB]	# basis functions
+
+int	i
+
+begin
+	basis[1] = 1.
+	if (order == 1)
+	    return
+
+	basis[2] = x
+	if (order == 2)
+	    return
+
+	do i = 3, order
+	    basis[i] = x * basis[i-1]
+
+end
+
+# GS_B1LEG -- Procedure to evaluate all the non-zero Legendre functions for
+# a single point and given order.
+
+procedure dgs_b1leg (x, order, k1, k2, basis)
+
+double	x		# data point
+int	order		# order of polynomial, order = 1, constant
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# basis functions
+
+int	i
+double	ri, xnorm
+
+begin
+	basis[1] = 1.
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2 
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order {
+	    ri = i
+	    basis[i] = ((2. * ri - 3.) * xnorm * basis[i-1] -
+		       (ri - 2.) * basis[i-2]) / (ri - 1.)	
+	}
+end
+
+
+# GS_B1CHEB -- Procedure to evaluate all the non zero Chebyshev function
+# for a given x and order.
+
+procedure dgs_b1cheb (x, order, k1, k2, basis)
+
+double	x		# number of data points
+int	order		# order of polynomial, 1 is a constant
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# array of basis functions
+
+int	i
+double	xnorm
+
+begin
+	basis[1] = 1.
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order
+	    basis[i] = 2. * xnorm * basis[i-1] - basis[i-2]
+end
diff --git a/math/gsurfit/gs_b1evalr.x b/math/gsurfit/gs_b1evalr.x
new file mode 100644
index 00000000..a313a043
--- /dev/null
+++ b/math/gsurfit/gs_b1evalr.x
@@ -0,0 +1,85 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_B1POL -- Procedure to evaluate all the non-zero polynomial functions
+# for a single point and given order.
+
+procedure rgs_b1pol (x, order, k1, k2, basis)
+
+real	x		# data point
+int	order		# order of polynomial, order = 1, constant
+real	k1, k2		# nomalizing constants, dummy in this case
+real	basis[ARB]	# basis functions
+
+int	i
+
+begin
+	basis[1] = 1.
+	if (order == 1)
+	    return
+
+	basis[2] = x
+	if (order == 2)
+	    return
+
+	do i = 3, order
+	    basis[i] = x * basis[i-1]
+
+end
+
+# GS_B1LEG -- Procedure to evaluate all the non-zero Legendre functions for
+# a single point and given order.
+
+procedure rgs_b1leg (x, order, k1, k2, basis)
+
+real	x		# data point
+int	order		# order of polynomial, order = 1, constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+
+int	i
+real	ri, xnorm
+
+begin
+	basis[1] = 1.
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2 
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order {
+	    ri = i
+	    basis[i] = ((2. * ri - 3.) * xnorm * basis[i-1] -
+		       (ri - 2.) * basis[i-2]) / (ri - 1.)	
+	}
+end
+
+
+# GS_B1CHEB -- Procedure to evaluate all the non zero Chebyshev function
+# for a given x and order.
+
+procedure rgs_b1cheb (x, order, k1, k2, basis)
+
+real	x		# number of data points
+int	order		# order of polynomial, 1 is a constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# array of basis functions
+
+int	i
+real	xnorm
+
+begin
+	basis[1] = 1.
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order
+	    basis[i] = 2. * xnorm * basis[i-1] - basis[i-2]
+end
diff --git a/math/gsurfit/gs_beval.gx b/math/gsurfit/gs_beval.gx
new file mode 100644
index 00000000..da45f122
--- /dev/null
+++ b/math/gsurfit/gs_beval.gx
@@ -0,0 +1,120 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_BPOL -- Procedure to evaluate all the non-zero polynomial functions for
+# a set of points and given order.
+
+procedure $tgs_bpol (x, npts, order, k1, k2, basis)
+
+PIXEL	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# basis functions
+
+int	bptr, k
+
+begin
+	bptr = 1
+	do k = 1, order {
+
+	    if (k == 1)
+		$if (datatype == r)
+	        call amovkr (1.0, basis, npts)
+		$else
+	        call amovkd (1.0d0, basis, npts)
+		$endif
+	    else if (k == 2)
+		call amov$t (x, basis[bptr], npts)
+	    else 
+		call amul$t (basis[bptr-npts], x, basis[bptr], npts)
+		
+	    bptr = bptr + npts
+	}
+end
+
+# GS_BCHEB -- Procedure to evaluate all the non-zero Chebyshev functions for
+# a set of points and given order.
+
+procedure $tgs_bcheb (x, npts, order, k1, k2, basis)
+
+PIXEL	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# basis functions
+
+int	k, bptr
+
+begin
+	bptr = 1
+	do k = 1, order {
+
+	    if (k == 1)
+		$if (datatype == r)
+	        call amovkr (1.0, basis, npts)
+		$else
+		call amovkd (1.0d0, basis, npts)
+		$endif
+	    else if (k == 2)
+		call alta$t (x, basis[bptr], npts, k1, k2)
+	    else {
+		call amul$t (basis[1+npts], basis[bptr-npts], basis[bptr],
+		    npts)
+		$if (datatype == r)
+		call amulkr (basis[bptr], 2.0, basis[bptr], npts)
+		$else
+		call amulkd (basis[bptr], 2.0d0, basis[bptr], npts)
+		$endif
+		call asub$t (basis[bptr], basis[bptr-2*npts], basis[bptr], npts)
+	    }
+		
+	    bptr = bptr + npts
+	}
+end
+
+
+# GS_BLEG -- Procedure to evaluate all the non zero Legendre function
+# for a given order and set of points.
+
+procedure $tgs_bleg (x, npts, order, k1, k2, basis)
+
+PIXEL	x[npts]		# number of data points
+int	npts		# number of points
+int	order		# order of polynomial, 1 is a constant
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# array of basis functions
+
+int	k, bptr
+PIXEL	ri, ri1, ri2
+
+begin
+	bptr = 1
+	do k = 1, order {
+
+	    if (k == 1)
+		$if (datatype == r)
+		call amovkr (1.0, basis, npts)
+		$else
+		call amovkd (1.0d0, basis, npts)
+		$endif
+	    else if (k == 2)
+		call alta$t (x, basis[bptr], npts, k1, k2)
+	    else {
+		$if (datatype == r)
+		ri = k
+		ri1 = (2. * ri - 3.) / (ri - 1.)
+		ri2 = - (ri - 2.) / (ri - 1.)
+		$else
+		ri = k
+		ri1 = (2.0d0 * ri - 3.0d0) / (ri - 1.0d0)
+		ri2 = - (ri - 2.0d0) / (ri - 1.0d0)
+		$endif
+		call amul$t (basis[1+npts], basis[bptr-npts], basis[bptr],
+		    npts)
+		call awsu$t (basis[bptr], basis[bptr-2*npts],
+			basis[bptr], npts, ri1, ri2)
+	    }
+			
+	    bptr = bptr + npts
+	}
+end
diff --git a/math/gsurfit/gs_bevald.x b/math/gsurfit/gs_bevald.x
new file mode 100644
index 00000000..7820fa39
--- /dev/null
+++ b/math/gsurfit/gs_bevald.x
@@ -0,0 +1,98 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_BPOL -- Procedure to evaluate all the non-zero polynomial functions for
+# a set of points and given order.
+
+procedure dgs_bpol (x, npts, order, k1, k2, basis)
+
+double	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# basis functions
+
+int	bptr, k
+
+begin
+	bptr = 1
+	do k = 1, order {
+
+	    if (k == 1)
+	        call amovkd (1.0d0, basis, npts)
+	    else if (k == 2)
+		call amovd (x, basis[bptr], npts)
+	    else 
+		call amuld (basis[bptr-npts], x, basis[bptr], npts)
+		
+	    bptr = bptr + npts
+	}
+end
+
+# GS_BCHEB -- Procedure to evaluate all the non-zero Chebyshev functions for
+# a set of points and given order.
+
+procedure dgs_bcheb (x, npts, order, k1, k2, basis)
+
+double	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# basis functions
+
+int	k, bptr
+
+begin
+	bptr = 1
+	do k = 1, order {
+
+	    if (k == 1)
+		call amovkd (1.0d0, basis, npts)
+	    else if (k == 2)
+		call altad (x, basis[bptr], npts, k1, k2)
+	    else {
+		call amuld (basis[1+npts], basis[bptr-npts], basis[bptr],
+		    npts)
+		call amulkd (basis[bptr], 2.0d0, basis[bptr], npts)
+		call asubd (basis[bptr], basis[bptr-2*npts], basis[bptr], npts)
+	    }
+		
+	    bptr = bptr + npts
+	}
+end
+
+
+# GS_BLEG -- Procedure to evaluate all the non zero Legendre function
+# for a given order and set of points.
+
+procedure dgs_bleg (x, npts, order, k1, k2, basis)
+
+double	x[npts]		# number of data points
+int	npts		# number of points
+int	order		# order of polynomial, 1 is a constant
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# array of basis functions
+
+int	k, bptr
+double	ri, ri1, ri2
+
+begin
+	bptr = 1
+	do k = 1, order {
+
+	    if (k == 1)
+		call amovkd (1.0d0, basis, npts)
+	    else if (k == 2)
+		call altad (x, basis[bptr], npts, k1, k2)
+	    else {
+		ri = k
+		ri1 = (2.0d0 * ri - 3.0d0) / (ri - 1.0d0)
+		ri2 = - (ri - 2.0d0) / (ri - 1.0d0)
+		call amuld (basis[1+npts], basis[bptr-npts], basis[bptr],
+		    npts)
+		call awsud (basis[bptr], basis[bptr-2*npts],
+			basis[bptr], npts, ri1, ri2)
+	    }
+			
+	    bptr = bptr + npts
+	}
+end
diff --git a/math/gsurfit/gs_bevalr.x b/math/gsurfit/gs_bevalr.x
new file mode 100644
index 00000000..9d22e3dc
--- /dev/null
+++ b/math/gsurfit/gs_bevalr.x
@@ -0,0 +1,98 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_BPOL -- Procedure to evaluate all the non-zero polynomial functions for
+# a set of points and given order.
+
+procedure rgs_bpol (x, npts, order, k1, k2, basis)
+
+real	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+
+int	bptr, k
+
+begin
+	bptr = 1
+	do k = 1, order {
+
+	    if (k == 1)
+	        call amovkr (1.0, basis, npts)
+	    else if (k == 2)
+		call amovr (x, basis[bptr], npts)
+	    else 
+		call amulr (basis[bptr-npts], x, basis[bptr], npts)
+		
+	    bptr = bptr + npts
+	}
+end
+
+# GS_BCHEB -- Procedure to evaluate all the non-zero Chebyshev functions for
+# a set of points and given order.
+
+procedure rgs_bcheb (x, npts, order, k1, k2, basis)
+
+real	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+
+int	k, bptr
+
+begin
+	bptr = 1
+	do k = 1, order {
+
+	    if (k == 1)
+	        call amovkr (1.0, basis, npts)
+	    else if (k == 2)
+		call altar (x, basis[bptr], npts, k1, k2)
+	    else {
+		call amulr (basis[1+npts], basis[bptr-npts], basis[bptr],
+		    npts)
+		call amulkr (basis[bptr], 2.0, basis[bptr], npts)
+		call asubr (basis[bptr], basis[bptr-2*npts], basis[bptr], npts)
+	    }
+		
+	    bptr = bptr + npts
+	}
+end
+
+
+# GS_BLEG -- Procedure to evaluate all the non zero Legendre function
+# for a given order and set of points.
+
+procedure rgs_bleg (x, npts, order, k1, k2, basis)
+
+real	x[npts]		# number of data points
+int	npts		# number of points
+int	order		# order of polynomial, 1 is a constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# array of basis functions
+
+int	k, bptr
+real	ri, ri1, ri2
+
+begin
+	bptr = 1
+	do k = 1, order {
+
+	    if (k == 1)
+		call amovkr (1.0, basis, npts)
+	    else if (k == 2)
+		call altar (x, basis[bptr], npts, k1, k2)
+	    else {
+		ri = k
+		ri1 = (2. * ri - 3.) / (ri - 1.)
+		ri2 = - (ri - 2.) / (ri - 1.)
+		call amulr (basis[1+npts], basis[bptr-npts], basis[bptr],
+		    npts)
+		call awsur (basis[bptr], basis[bptr-2*npts],
+			basis[bptr], npts, ri1, ri2)
+	    }
+			
+	    bptr = bptr + npts
+	}
+end
diff --git a/math/gsurfit/gs_chomat.gx b/math/gsurfit/gs_chomat.gx
new file mode 100644
index 00000000..023b3c12
--- /dev/null
+++ b/math/gsurfit/gs_chomat.gx
@@ -0,0 +1,110 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSCHOFAC -- Routine to calculate the Cholesky factorization of a
+# symmetric, positive semi-definite banded matrix. This routines was
+# adapted from the bchfac.f routine described in "A Practical Guide
+# to Splines", Carl de Boor (1978).
+
+procedure $tgschofac (matrix, nbands, nrows, matfac, ier)
+
+PIXEL matrix[nbands, nrows]	# data matrix
+int	nbands			# number of bands
+int	nrows			# number of rows
+PIXEL matfac[nbands, nrows]	# Cholesky factorization
+int	ier			# error code
+
+int	i, n, j, imax, jmax
+PIXEL	ratio
+
+begin
+	if (nrows == 1) {
+	    if (matrix[1,1] > 0.)
+	        matfac[1,1] = 1. / matrix[1,1]
+	    return
+	}
+
+	# copy matrix into matfac
+	do n = 1, nrows {
+	    do j = 1, nbands
+		matfac[j,n] = matrix[j,n]
+	}
+
+	do n = 1, nrows {
+
+	    # test to see if matrix is singular
+	    if (((matfac[1,n]+matrix[1,n])-matrix[1,n]) <= 1000/MAX_PIXEL) {
+		do j = 1, nbands
+		    matfac[j,n] = 0.
+		ier = SINGULAR
+		next
+	    }
+
+	    matfac[1,n] = 1. / matfac[1,n]
+	    imax = min (nbands - 1, nrows - n)
+	    if (imax < 1)
+		next
+
+	    jmax = imax
+	    do i = 1, imax {
+		ratio = matfac[i+1,n] * matfac[1,n]
+		do j = 1, jmax
+		    matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
+		jmax = jmax - 1
+		matfac[i+1,n] = ratio
+	    }
+	}
+end
+
+
+# GSCHOSLV -- Solve the matrix whose Cholesky factorization was calculated in
+# GSCHOFAC for the coefficients. This routine was adapted from bchslv.f
+# described in "A Practical Guide to Splines", by Carl de Boor (1978).
+
+procedure $tgschoslv (matfac, nbands, nrows, vector, coeff)
+
+PIXEL matfac[nbands,nrows] 		# Cholesky factorization
+int	nbands				# number of bands
+int	nrows				# number of rows
+PIXEL vector[nrows]			# right side of matrix equation
+PIXEL coeff[nrows]			# coefficients
+
+int	i, n, j, jmax, nbndm1
+
+begin
+	if (nrows == 1) {
+	    coeff[1] = vector[1] * matfac[1,1]
+	    return
+	}
+
+	# copy vector to coefficients
+	do i = 1, nrows
+	    coeff[i] = vector[i]
+
+	# forward substitution
+	nbndm1 = nbands - 1
+	do n = 1, nrows {
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+	        do j = 1, jmax
+		    coeff[j+n] = coeff[j+n] - matfac[j+1,n] * coeff[n]
+	    }
+	}
+
+	# back substitution
+	for (n = nrows; n >= 1; n = n - 1) {
+	    coeff[n] = coeff[n] * matfac[1,n]
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+		do j = 1, jmax
+		    coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
+	    }
+	}
+end
diff --git a/math/gsurfit/gs_chomatd.x b/math/gsurfit/gs_chomatd.x
new file mode 100644
index 00000000..ce15a087
--- /dev/null
+++ b/math/gsurfit/gs_chomatd.x
@@ -0,0 +1,106 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSCHOFAC -- Routine to calculate the Cholesky factorization of a
+# symmetric, positive semi-definite banded matrix. This routines was
+# adapted from the bchfac.f routine described in "A Practical Guide
+# to Splines", Carl de Boor (1978).
+
+procedure dgschofac (matrix, nbands, nrows, matfac, ier)
+
+double matrix[nbands, nrows]	# data matrix
+int	nbands			# number of bands
+int	nrows			# number of rows
+double matfac[nbands, nrows]	# Cholesky factorization
+int	ier			# error code
+
+int	i, n, j, imax, jmax
+double	ratio
+
+begin
+	if (nrows == 1) {
+	    if (matrix[1,1] > 0.)
+	        matfac[1,1] = 1. / matrix[1,1]
+	    return
+	}
+
+	# copy matrix into matfac
+	do n = 1, nrows {
+	    do j = 1, nbands
+		matfac[j,n] = matrix[j,n]
+	}
+
+	do n = 1, nrows {
+
+	    # test to see if matrix is singular
+	    if (((matfac[1,n]+matrix[1,n])-matrix[1,n]) <= 1000/MAX_DOUBLE) {
+		do j = 1, nbands
+		    matfac[j,n] = 0.
+		ier = SINGULAR
+		next
+	    }
+
+	    matfac[1,n] = 1. / matfac[1,n]
+	    imax = min (nbands - 1, nrows - n)
+	    if (imax < 1)
+		next
+
+	    jmax = imax
+	    do i = 1, imax {
+		ratio = matfac[i+1,n] * matfac[1,n]
+		do j = 1, jmax
+		    matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
+		jmax = jmax - 1
+		matfac[i+1,n] = ratio
+	    }
+	}
+end
+
+
+# GSCHOSLV -- Solve the matrix whose Cholesky factorization was calculated in
+# GSCHOFAC for the coefficients. This routine was adapted from bchslv.f
+# described in "A Practical Guide to Splines", by Carl de Boor (1978).
+
+procedure dgschoslv (matfac, nbands, nrows, vector, coeff)
+
+double matfac[nbands,nrows] 		# Cholesky factorization
+int	nbands				# number of bands
+int	nrows				# number of rows
+double vector[nrows]			# right side of matrix equation
+double coeff[nrows]			# coefficients
+
+int	i, n, j, jmax, nbndm1
+
+begin
+	if (nrows == 1) {
+	    coeff[1] = vector[1] * matfac[1,1]
+	    return
+	}
+
+	# copy vector to coefficients
+	do i = 1, nrows
+	    coeff[i] = vector[i]
+
+	# forward substitution
+	nbndm1 = nbands - 1
+	do n = 1, nrows {
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+	        do j = 1, jmax
+		    coeff[j+n] = coeff[j+n] - matfac[j+1,n] * coeff[n]
+	    }
+	}
+
+	# back substitution
+	for (n = nrows; n >= 1; n = n - 1) {
+	    coeff[n] = coeff[n] * matfac[1,n]
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+		do j = 1, jmax
+		    coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
+	    }
+	}
+end
diff --git a/math/gsurfit/gs_chomatr.x b/math/gsurfit/gs_chomatr.x
new file mode 100644
index 00000000..deb4c198
--- /dev/null
+++ b/math/gsurfit/gs_chomatr.x
@@ -0,0 +1,106 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSCHOFAC -- Routine to calculate the Cholesky factorization of a
+# symmetric, positive semi-definite banded matrix. This routines was
+# adapted from the bchfac.f routine described in "A Practical Guide
+# to Splines", Carl de Boor (1978).
+
+procedure rgschofac (matrix, nbands, nrows, matfac, ier)
+
+real matrix[nbands, nrows]	# data matrix
+int	nbands			# number of bands
+int	nrows			# number of rows
+real matfac[nbands, nrows]	# Cholesky factorization
+int	ier			# error code
+
+int	i, n, j, imax, jmax
+real	ratio
+
+begin
+	if (nrows == 1) {
+	    if (matrix[1,1] > 0.)
+	        matfac[1,1] = 1. / matrix[1,1]
+	    return
+	}
+
+	# copy matrix into matfac
+	do n = 1, nrows {
+	    do j = 1, nbands
+		matfac[j,n] = matrix[j,n]
+	}
+
+	do n = 1, nrows {
+
+	    # test to see if matrix is singular
+	    if (((matfac[1,n]+matrix[1,n])-matrix[1,n]) <= 1000/MAX_REAL) {
+		do j = 1, nbands
+		    matfac[j,n] = 0.
+		ier = SINGULAR
+		next
+	    }
+
+	    matfac[1,n] = 1. / matfac[1,n]
+	    imax = min (nbands - 1, nrows - n)
+	    if (imax < 1)
+		next
+
+	    jmax = imax
+	    do i = 1, imax {
+		ratio = matfac[i+1,n] * matfac[1,n]
+		do j = 1, jmax
+		    matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
+		jmax = jmax - 1
+		matfac[i+1,n] = ratio
+	    }
+	}
+end
+
+
+# GSCHOSLV -- Solve the matrix whose Cholesky factorization was calculated in
+# GSCHOFAC for the coefficients. This routine was adapted from bchslv.f
+# described in "A Practical Guide to Splines", by Carl de Boor (1978).
+
+procedure rgschoslv (matfac, nbands, nrows, vector, coeff)
+
+real matfac[nbands,nrows] 		# Cholesky factorization
+int	nbands				# number of bands
+int	nrows				# number of rows
+real vector[nrows]			# right side of matrix equation
+real coeff[nrows]			# coefficients
+
+int	i, n, j, jmax, nbndm1
+
+begin
+	if (nrows == 1) {
+	    coeff[1] = vector[1] * matfac[1,1]
+	    return
+	}
+
+	# copy vector to coefficients
+	do i = 1, nrows
+	    coeff[i] = vector[i]
+
+	# forward substitution
+	nbndm1 = nbands - 1
+	do n = 1, nrows {
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+	        do j = 1, jmax
+		    coeff[j+n] = coeff[j+n] - matfac[j+1,n] * coeff[n]
+	    }
+	}
+
+	# back substitution
+	for (n = nrows; n >= 1; n = n - 1) {
+	    coeff[n] = coeff[n] * matfac[1,n]
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+		do j = 1, jmax
+		    coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
+	    }
+	}
+end
diff --git a/math/gsurfit/gs_deval.gx b/math/gsurfit/gs_deval.gx
new file mode 100644
index 00000000..38b90dac
--- /dev/null
+++ b/math/gsurfit/gs_deval.gx
@@ -0,0 +1,241 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_DPOL -- Procedure to evaluate the polynomial derivative basis functions.
+
+procedure $tgs_dpol (x, npts, order, nder, k1, k2, basis)
+
+PIXEL	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of new polynomial, order = 1, constant
+int	nder		# order of derivative, order = 0, no derivative
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# basis functions
+
+int	bptr, k, kk
+PIXEL	fac
+
+begin
+	# Optimize for oth and first derivatives.
+	if (nder == 0) {
+	    call $tgs_bpol (x, npts, order, k1, k2, basis)
+	    return
+	} else if (nder == 1) {
+	    call $tgs_bpol (x, npts, order, k1, k2, basis)
+	    do k = 1, order {
+		call amulk$t(basis[1+(k-1)*npts], PIXEL (k),
+		    basis[1+(k-1)*npts], npts)
+	    }
+	    return
+	}
+
+	# Compute the polynomials.
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1)
+		call amovk$t (PIXEL(1.0), basis, npts)
+	    else if (k == 2)
+		call amov$t (x, basis[bptr], npts)
+	    else 
+		call amul$t (basis[bptr-npts], x, basis[bptr], npts)
+	    bptr = bptr + npts
+	}
+
+	# Apply the derivative factor.
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1) {
+	        fac = PIXEL(1.0)
+		do kk = 2, nder
+		    fac = fac * PIXEL (kk)
+	    } else {
+	        fac = PIXEL(1.0)
+		do kk = k +  nder - 1, k, -1 
+	            fac = fac * PIXEL(kk)
+	    }
+	    call amulk$t (basis[bptr], fac, basis[bptr], npts)
+	    bptr = bptr + npts
+	}
+end
+
+
+# GS_DCHEB -- Procedure to evaluate the chebyshev polynomial derivative
+# basis functions using the usual recursion relation.
+
+procedure $tgs_dcheb (x, npts, order, nder, k1, k2, basis)
+
+PIXEL	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+int	nder		# order of derivative, order = 0, no derivative
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# basis functions
+
+int	i, k
+pointer	fn, dfn, xnorm, bptr, fptr
+PIXEL	fac
+
+begin
+	# Optimze the no derivatives case.
+	if (nder == 0) {
+	    call $tgs_bcheb (x, npts, order, k1, k2, basis)
+	    return
+	}
+
+	# Allocate working space for the basis functions and derivatives.
+	call calloc (fn, npts * (order + nder), TY_PIXEL)
+	call calloc (dfn, npts * (order + nder), TY_PIXEL)
+
+	# Compute the normalized x values.
+	call malloc (xnorm, npts, TY_PIXEL)
+        call alta$t (x, Mem$t[xnorm], npts, k1, k2)
+
+	# Compute the current solution.
+        bptr = fn
+        do k = 1, order + nder {
+	    if (k == 1)
+	        call amovk$t (PIXEL(1.0), Mem$t[bptr], npts)
+	    else if (k == 2)
+	        call amov$t (Mem$t[xnorm], Mem$t[bptr], npts)
+	    else {
+	        call amul$t (Mem$t[xnorm], Mem$t[bptr-npts], Mem$t[bptr], npts)
+	        call amulk$t (Mem$t[bptr], PIXEL(2.0), Mem$t[bptr], npts)
+		call asub$t (Mem$t[bptr], Mem$t[bptr-2*npts], Mem$t[bptr], npts)
+	    }
+	    bptr = bptr + npts
+        }
+
+	# Compute the derivative basis functions.
+	do i = 1, nder {
+
+	    # Compute the derivatives.
+	    bptr = fn
+	    fptr = dfn
+	    do k = 1, order + nder {
+		if (k == 1)
+		    call amovk$t (PIXEL(0.0), Mem$t[fptr], npts)
+		else if (k == 2) {
+		    if (i == 1)
+		        call amovk$t (PIXEL(1.0), Mem$t[fptr], npts)
+		    else
+		        call amovk$t (PIXEL(0.0), Mem$t[fptr], npts)
+		} else {
+	            call amul$t (Mem$t[xnorm], Mem$t[fptr-npts], Mem$t[fptr],
+		        npts)
+	            call amulk$t (Mem$t[fptr], PIXEL(2.0), Mem$t[fptr], npts)
+		    call asub$t (Mem$t[fptr], Mem$t[fptr-2*npts], Mem$t[fptr],
+		        npts)
+		    fac = PIXEL (2.0) * PIXEL (i)
+		    call awsu$t (Mem$t[bptr-npts], Mem$t[fptr], Mem$t[fptr],
+			npts, fac, PIXEL(1.0))
+		    
+		}
+	        bptr = bptr + npts
+	        fptr = fptr + npts
+	    }
+
+	    # Make the derivatives the old solution
+	    if (i < nder)
+		call amov$t (Mem$t[dfn], Mem$t[fn], npts * (order + nder))
+	}
+
+	# Copy the solution into the basis functions.
+	call amov$t (Mem$t[dfn+nder*npts], basis[1], order * npts)
+
+	call mfree (xnorm, TY_PIXEL)
+	call mfree (fn, TY_PIXEL)
+	call mfree (dfn, TY_PIXEL)
+end
+
+
+# GS_DLEG -- Procedure to evaluate the Legendre polynomial derivative basis
+# functions using the usual recursion relation.
+
+procedure $tgs_dleg (x, npts, order, nder, k1, k2, basis)
+
+PIXEL	x[npts]		# number of data points
+int	npts		# number of points
+int	order		# order of new polynomial, 1 is a constant
+int	nder		# order of derivate, 0 is no derivative
+PIXEL	k1, k2		# normalizing constants
+PIXEL	basis[ARB]	# array of basis functions
+
+int	i, k
+pointer	fn, dfn, xnorm, bptr, fptr
+PIXEL	ri, ri1, ri2, fac
+
+begin
+	# Optimze the no derivatives case.
+	if (nder == 0) {
+	    call $tgs_bleg (x, npts, order, k1, k2, basis)
+	    return
+	}
+
+	# Allocate working space for the basis functions and derivatives.
+	call calloc (fn, npts * (order + nder), TY_PIXEL)
+	call calloc (dfn, npts * (order + nder), TY_PIXEL)
+
+	# Compute the normalized x values.
+	call malloc (xnorm, npts, TY_PIXEL)
+        call alta$t (x, Mem$t[xnorm], npts, k1, k2)
+
+	# Compute the basis functions.
+	bptr = fn
+	do k = 1, order + nder {
+	    if (k == 1)
+		call amovk$t (PIXEL(1.0), Mem$t[bptr], npts)
+	    else if (k == 2)
+		call amov$t (Mem$t[xnorm], Mem$t[bptr], npts)
+	    else {
+		ri = k
+		ri1 = (PIXEL(2.0) * ri - PIXEL(3.0)) / (ri - PIXEL(1.0))
+		ri2 = - (ri - PIXEL(2.0)) / (ri - PIXEL(1.0))
+		call amul$t (Mem$t[xnorm], Mem$t[bptr-npts], Mem$t[bptr], npts)
+		call awsu$t (Mem$t[bptr], Mem$t[bptr-2*npts], Mem$t[bptr],
+		    npts, ri1, ri2)
+	    }
+	    bptr = bptr + npts
+	}
+
+	# Compute the derivative basis functions.
+	do i = 1, nder {
+
+	    # Compute the derivatives.
+	    bptr = fn
+	    fptr = dfn
+	    do k = 1, order + nder {
+		if (k == 1)
+		    call amovk$t (PIXEL(0.0), Mem$t[fptr], npts)
+		else if (k == 2) {
+		    if (i == 1)
+		        call amovk$t (PIXEL(1.0), Mem$t[fptr], npts)
+		    else
+		        call amovk$t (PIXEL(0.0), Mem$t[fptr], npts)
+		} else {
+		    ri = k
+		    ri1 = (PIXEL(2.0) * ri - PIXEL(3.0)) / (ri - PIXEL(1.0))
+		    ri2 = - (ri - PIXEL(2.0)) / (ri - PIXEL(1.0))
+		    call amul$t (Mem$t[xnorm], Mem$t[fptr-npts], Mem$t[fptr],
+		        npts)
+		    call awsu$t (Mem$t[fptr], Mem$t[fptr-2*npts], Mem$t[fptr],
+		        npts, ri1, ri2)
+		    fac = ri1 * PIXEL (i)
+		    call awsu$t (Mem$t[bptr-npts], Mem$t[fptr], Mem$t[fptr],
+			npts, fac, PIXEL(1.0))
+		    
+		}
+	        bptr = bptr + npts
+	        fptr = fptr + npts
+	    }
+
+	    # Make the derivatives the old solution
+	    if (i < nder)
+		call amov$t (Mem$t[dfn], Mem$t[fn], npts * (order + nder))
+	}
+
+	# Copy the solution into the basis functions.
+	call amov$t (Mem$t[dfn+nder*npts], basis[1], order * npts)
+
+	call mfree (xnorm, TY_PIXEL)
+	call mfree (fn, TY_PIXEL)
+	call mfree (dfn, TY_PIXEL)
+end
diff --git a/math/gsurfit/gs_devald.x b/math/gsurfit/gs_devald.x
new file mode 100644
index 00000000..131b18dc
--- /dev/null
+++ b/math/gsurfit/gs_devald.x
@@ -0,0 +1,241 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_DPOL -- Procedure to evaluate the polynomial derivative basis functions.
+
+procedure dgs_dpol (x, npts, order, nder, k1, k2, basis)
+
+double	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of new polynomial, order = 1, constant
+int	nder		# order of derivative, order = 0, no derivative
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# basis functions
+
+int	bptr, k, kk
+double	fac
+
+begin
+	# Optimize for oth and first derivatives.
+	if (nder == 0) {
+	    call dgs_bpol (x, npts, order, k1, k2, basis)
+	    return
+	} else if (nder == 1) {
+	    call dgs_bpol (x, npts, order, k1, k2, basis)
+	    do k = 1, order {
+		call amulkd(basis[1+(k-1)*npts], double (k),
+		    basis[1+(k-1)*npts], npts)
+	    }
+	    return
+	}
+
+	# Compute the polynomials.
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1)
+		call amovkd (double(1.0), basis, npts)
+	    else if (k == 2)
+		call amovd (x, basis[bptr], npts)
+	    else 
+		call amuld (basis[bptr-npts], x, basis[bptr], npts)
+	    bptr = bptr + npts
+	}
+
+	# Apply the derivative factor.
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1) {
+	        fac = double(1.0)
+		do kk = 2, nder
+		    fac = fac * double (kk)
+	    } else {
+	        fac = double(1.0)
+		do kk = k +  nder - 1, k, -1 
+	            fac = fac * double(kk)
+	    }
+	    call amulkd (basis[bptr], fac, basis[bptr], npts)
+	    bptr = bptr + npts
+	}
+end
+
+
+# GS_DCHEB -- Procedure to evaluate the chebyshev polynomial derivative
+# basis functions using the usual recursion relation.
+
+procedure dgs_dcheb (x, npts, order, nder, k1, k2, basis)
+
+double	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+int	nder		# order of derivative, order = 0, no derivative
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# basis functions
+
+int	i, k
+pointer	fn, dfn, xnorm, bptr, fptr
+double	fac
+
+begin
+	# Optimze the no derivatives case.
+	if (nder == 0) {
+	    call dgs_bcheb (x, npts, order, k1, k2, basis)
+	    return
+	}
+
+	# Allocate working space for the basis functions and derivatives.
+	call calloc (fn, npts * (order + nder), TY_DOUBLE)
+	call calloc (dfn, npts * (order + nder), TY_DOUBLE)
+
+	# Compute the normalized x values.
+	call malloc (xnorm, npts, TY_DOUBLE)
+        call altad (x, Memd[xnorm], npts, k1, k2)
+
+	# Compute the current solution.
+        bptr = fn
+        do k = 1, order + nder {
+	    if (k == 1)
+	        call amovkd (double(1.0), Memd[bptr], npts)
+	    else if (k == 2)
+	        call amovd (Memd[xnorm], Memd[bptr], npts)
+	    else {
+	        call amuld (Memd[xnorm], Memd[bptr-npts], Memd[bptr], npts)
+	        call amulkd (Memd[bptr], double(2.0), Memd[bptr], npts)
+		call asubd (Memd[bptr], Memd[bptr-2*npts], Memd[bptr], npts)
+	    }
+	    bptr = bptr + npts
+        }
+
+	# Compute the derivative basis functions.
+	do i = 1, nder {
+
+	    # Compute the derivatives.
+	    bptr = fn
+	    fptr = dfn
+	    do k = 1, order + nder {
+		if (k == 1)
+		    call amovkd (double(0.0), Memd[fptr], npts)
+		else if (k == 2) {
+		    if (i == 1)
+		        call amovkd (double(1.0), Memd[fptr], npts)
+		    else
+		        call amovkd (double(0.0), Memd[fptr], npts)
+		} else {
+	            call amuld (Memd[xnorm], Memd[fptr-npts], Memd[fptr],
+		        npts)
+	            call amulkd (Memd[fptr], double(2.0), Memd[fptr], npts)
+		    call asubd (Memd[fptr], Memd[fptr-2*npts], Memd[fptr],
+		        npts)
+		    fac = double (2.0) * double (i)
+		    call awsud (Memd[bptr-npts], Memd[fptr], Memd[fptr],
+			npts, fac, double(1.0))
+		    
+		}
+	        bptr = bptr + npts
+	        fptr = fptr + npts
+	    }
+
+	    # Make the derivatives the old solution
+	    if (i < nder)
+		call amovd (Memd[dfn], Memd[fn], npts * (order + nder))
+	}
+
+	# Copy the solution into the basis functions.
+	call amovd (Memd[dfn+nder*npts], basis[1], order * npts)
+
+	call mfree (xnorm, TY_DOUBLE)
+	call mfree (fn, TY_DOUBLE)
+	call mfree (dfn, TY_DOUBLE)
+end
+
+
+# GS_DLEG -- Procedure to evaluate the Legendre polynomial derivative basis
+# functions using the usual recursion relation.
+
+procedure dgs_dleg (x, npts, order, nder, k1, k2, basis)
+
+double	x[npts]		# number of data points
+int	npts		# number of points
+int	order		# order of new polynomial, 1 is a constant
+int	nder		# order of derivate, 0 is no derivative
+double	k1, k2		# normalizing constants
+double	basis[ARB]	# array of basis functions
+
+int	i, k
+pointer	fn, dfn, xnorm, bptr, fptr
+double	ri, ri1, ri2, fac
+
+begin
+	# Optimze the no derivatives case.
+	if (nder == 0) {
+	    call dgs_bleg (x, npts, order, k1, k2, basis)
+	    return
+	}
+
+	# Allocate working space for the basis functions and derivatives.
+	call calloc (fn, npts * (order + nder), TY_DOUBLE)
+	call calloc (dfn, npts * (order + nder), TY_DOUBLE)
+
+	# Compute the normalized x values.
+	call malloc (xnorm, npts, TY_DOUBLE)
+        call altad (x, Memd[xnorm], npts, k1, k2)
+
+	# Compute the basis functions.
+	bptr = fn
+	do k = 1, order + nder {
+	    if (k == 1)
+		call amovkd (double(1.0), Memd[bptr], npts)
+	    else if (k == 2)
+		call amovd (Memd[xnorm], Memd[bptr], npts)
+	    else {
+		ri = k
+		ri1 = (double(2.0) * ri - double(3.0)) / (ri - double(1.0))
+		ri2 = - (ri - double(2.0)) / (ri - double(1.0))
+		call amuld (Memd[xnorm], Memd[bptr-npts], Memd[bptr], npts)
+		call awsud (Memd[bptr], Memd[bptr-2*npts], Memd[bptr],
+		    npts, ri1, ri2)
+	    }
+	    bptr = bptr + npts
+	}
+
+	# Compute the derivative basis functions.
+	do i = 1, nder {
+
+	    # Compute the derivatives.
+	    bptr = fn
+	    fptr = dfn
+	    do k = 1, order + nder {
+		if (k == 1)
+		    call amovkd (double(0.0), Memd[fptr], npts)
+		else if (k == 2) {
+		    if (i == 1)
+		        call amovkd (double(1.0), Memd[fptr], npts)
+		    else
+		        call amovkd (double(0.0), Memd[fptr], npts)
+		} else {
+		    ri = k
+		    ri1 = (double(2.0) * ri - double(3.0)) / (ri - double(1.0))
+		    ri2 = - (ri - double(2.0)) / (ri - double(1.0))
+		    call amuld (Memd[xnorm], Memd[fptr-npts], Memd[fptr],
+		        npts)
+		    call awsud (Memd[fptr], Memd[fptr-2*npts], Memd[fptr],
+		        npts, ri1, ri2)
+		    fac = ri1 * double (i)
+		    call awsud (Memd[bptr-npts], Memd[fptr], Memd[fptr],
+			npts, fac, double(1.0))
+		    
+		}
+	        bptr = bptr + npts
+	        fptr = fptr + npts
+	    }
+
+	    # Make the derivatives the old solution
+	    if (i < nder)
+		call amovd (Memd[dfn], Memd[fn], npts * (order + nder))
+	}
+
+	# Copy the solution into the basis functions.
+	call amovd (Memd[dfn+nder*npts], basis[1], order * npts)
+
+	call mfree (xnorm, TY_DOUBLE)
+	call mfree (fn, TY_DOUBLE)
+	call mfree (dfn, TY_DOUBLE)
+end
diff --git a/math/gsurfit/gs_devalr.x b/math/gsurfit/gs_devalr.x
new file mode 100644
index 00000000..06449e38
--- /dev/null
+++ b/math/gsurfit/gs_devalr.x
@@ -0,0 +1,241 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_DPOL -- Procedure to evaluate the polynomial derivative basis functions.
+
+procedure rgs_dpol (x, npts, order, nder, k1, k2, basis)
+
+real	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of new polynomial, order = 1, constant
+int	nder		# order of derivative, order = 0, no derivative
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+
+int	bptr, k, kk
+real	fac
+
+begin
+	# Optimize for oth and first derivatives.
+	if (nder == 0) {
+	    call rgs_bpol (x, npts, order, k1, k2, basis)
+	    return
+	} else if (nder == 1) {
+	    call rgs_bpol (x, npts, order, k1, k2, basis)
+	    do k = 1, order {
+		call amulkr(basis[1+(k-1)*npts], real (k),
+		    basis[1+(k-1)*npts], npts)
+	    }
+	    return
+	}
+
+	# Compute the polynomials.
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1)
+		call amovkr (real(1.0), basis, npts)
+	    else if (k == 2)
+		call amovr (x, basis[bptr], npts)
+	    else 
+		call amulr (basis[bptr-npts], x, basis[bptr], npts)
+	    bptr = bptr + npts
+	}
+
+	# Apply the derivative factor.
+	bptr = 1
+	do k = 1, order {
+	    if (k == 1) {
+	        fac = real(1.0)
+		do kk = 2, nder
+		    fac = fac * real (kk)
+	    } else {
+	        fac = real(1.0)
+		do kk = k +  nder - 1, k, -1 
+	            fac = fac * real(kk)
+	    }
+	    call amulkr (basis[bptr], fac, basis[bptr], npts)
+	    bptr = bptr + npts
+	}
+end
+
+
+# GS_DCHEB -- Procedure to evaluate the chebyshev polynomial derivative
+# basis functions using the usual recursion relation.
+
+procedure rgs_dcheb (x, npts, order, nder, k1, k2, basis)
+
+real	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+int	nder		# order of derivative, order = 0, no derivative
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+
+int	i, k
+pointer	fn, dfn, xnorm, bptr, fptr
+real	fac
+
+begin
+	# Optimze the no derivatives case.
+	if (nder == 0) {
+	    call rgs_bcheb (x, npts, order, k1, k2, basis)
+	    return
+	}
+
+	# Allocate working space for the basis functions and derivatives.
+	call calloc (fn, npts * (order + nder), TY_REAL)
+	call calloc (dfn, npts * (order + nder), TY_REAL)
+
+	# Compute the normalized x values.
+	call malloc (xnorm, npts, TY_REAL)
+        call altar (x, Memr[xnorm], npts, k1, k2)
+
+	# Compute the current solution.
+        bptr = fn
+        do k = 1, order + nder {
+	    if (k == 1)
+	        call amovkr (real(1.0), Memr[bptr], npts)
+	    else if (k == 2)
+	        call amovr (Memr[xnorm], Memr[bptr], npts)
+	    else {
+	        call amulr (Memr[xnorm], Memr[bptr-npts], Memr[bptr], npts)
+	        call amulkr (Memr[bptr], real(2.0), Memr[bptr], npts)
+		call asubr (Memr[bptr], Memr[bptr-2*npts], Memr[bptr], npts)
+	    }
+	    bptr = bptr + npts
+        }
+
+	# Compute the derivative basis functions.
+	do i = 1, nder {
+
+	    # Compute the derivatives.
+	    bptr = fn
+	    fptr = dfn
+	    do k = 1, order + nder {
+		if (k == 1)
+		    call amovkr (real(0.0), Memr[fptr], npts)
+		else if (k == 2) {
+		    if (i == 1)
+		        call amovkr (real(1.0), Memr[fptr], npts)
+		    else
+		        call amovkr (real(0.0), Memr[fptr], npts)
+		} else {
+	            call amulr (Memr[xnorm], Memr[fptr-npts], Memr[fptr],
+		        npts)
+	            call amulkr (Memr[fptr], real(2.0), Memr[fptr], npts)
+		    call asubr (Memr[fptr], Memr[fptr-2*npts], Memr[fptr],
+		        npts)
+		    fac = real (2.0) * real (i)
+		    call awsur (Memr[bptr-npts], Memr[fptr], Memr[fptr],
+			npts, fac, real(1.0))
+		    
+		}
+	        bptr = bptr + npts
+	        fptr = fptr + npts
+	    }
+
+	    # Make the derivatives the old solution
+	    if (i < nder)
+		call amovr (Memr[dfn], Memr[fn], npts * (order + nder))
+	}
+
+	# Copy the solution into the basis functions.
+	call amovr (Memr[dfn+nder*npts], basis[1], order * npts)
+
+	call mfree (xnorm, TY_REAL)
+	call mfree (fn, TY_REAL)
+	call mfree (dfn, TY_REAL)
+end
+
+
+# GS_DLEG -- Procedure to evaluate the Legendre polynomial derivative basis
+# functions using the usual recursion relation.
+
+procedure rgs_dleg (x, npts, order, nder, k1, k2, basis)
+
+real	x[npts]		# number of data points
+int	npts		# number of points
+int	order		# order of new polynomial, 1 is a constant
+int	nder		# order of derivate, 0 is no derivative
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# array of basis functions
+
+int	i, k
+pointer	fn, dfn, xnorm, bptr, fptr
+real	ri, ri1, ri2, fac
+
+begin
+	# Optimze the no derivatives case.
+	if (nder == 0) {
+	    call rgs_bleg (x, npts, order, k1, k2, basis)
+	    return
+	}
+
+	# Allocate working space for the basis functions and derivatives.
+	call calloc (fn, npts * (order + nder), TY_REAL)
+	call calloc (dfn, npts * (order + nder), TY_REAL)
+
+	# Compute the normalized x values.
+	call malloc (xnorm, npts, TY_REAL)
+        call altar (x, Memr[xnorm], npts, k1, k2)
+
+	# Compute the basis functions.
+	bptr = fn
+	do k = 1, order + nder {
+	    if (k == 1)
+		call amovkr (real(1.0), Memr[bptr], npts)
+	    else if (k == 2)
+		call amovr (Memr[xnorm], Memr[bptr], npts)
+	    else {
+		ri = k
+		ri1 = (real(2.0) * ri - real(3.0)) / (ri - real(1.0))
+		ri2 = - (ri - real(2.0)) / (ri - real(1.0))
+		call amulr (Memr[xnorm], Memr[bptr-npts], Memr[bptr], npts)
+		call awsur (Memr[bptr], Memr[bptr-2*npts], Memr[bptr],
+		    npts, ri1, ri2)
+	    }
+	    bptr = bptr + npts
+	}
+
+	# Compute the derivative basis functions.
+	do i = 1, nder {
+
+	    # Compute the derivatives.
+	    bptr = fn
+	    fptr = dfn
+	    do k = 1, order + nder {
+		if (k == 1)
+		    call amovkr (real(0.0), Memr[fptr], npts)
+		else if (k == 2) {
+		    if (i == 1)
+		        call amovkr (real(1.0), Memr[fptr], npts)
+		    else
+		        call amovkr (real(0.0), Memr[fptr], npts)
+		} else {
+		    ri = k
+		    ri1 = (real(2.0) * ri - real(3.0)) / (ri - real(1.0))
+		    ri2 = - (ri - real(2.0)) / (ri - real(1.0))
+		    call amulr (Memr[xnorm], Memr[fptr-npts], Memr[fptr],
+		        npts)
+		    call awsur (Memr[fptr], Memr[fptr-2*npts], Memr[fptr],
+		        npts, ri1, ri2)
+		    fac = ri1 * real (i)
+		    call awsur (Memr[bptr-npts], Memr[fptr], Memr[fptr],
+			npts, fac, real(1.0))
+		    
+		}
+	        bptr = bptr + npts
+	        fptr = fptr + npts
+	    }
+
+	    # Make the derivatives the old solution
+	    if (i < nder)
+		call amovr (Memr[dfn], Memr[fn], npts * (order + nder))
+	}
+
+	# Copy the solution into the basis functions.
+	call amovr (Memr[dfn+nder*npts], basis[1], order * npts)
+
+	call mfree (xnorm, TY_REAL)
+	call mfree (fn, TY_REAL)
+	call mfree (dfn, TY_REAL)
+end
diff --git a/math/gsurfit/gs_f1deval.gx b/math/gsurfit/gs_f1deval.gx
new file mode 100644
index 00000000..17981daf
--- /dev/null
+++ b/math/gsurfit/gs_f1deval.gx
@@ -0,0 +1,189 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_1DEVPOLY -- Procedure to evaulate a 1D polynomial
+
+procedure $tgs_1devpoly (coeff, x, yfit, npts, order, k1, k2)
+
+PIXEL	coeff[ARB]		# EV array of coefficients
+PIXEL	x[npts]			# x values of points to be evaluated
+PIXEL	yfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	order			# order of the polynomial, 1 = constant
+PIXEL	k1, k2			# normalizing constants
+
+int	i
+pointer	sp, temp
+
+begin
+	# fit a constant
+	call amovk$t (coeff[1], yfit, npts)
+	if (order == 1)
+	    return
+
+	# fit a linear function
+	call altm$t (x, yfit, npts, coeff[2], coeff[1])
+	if (order == 2)
+	    return
+
+	call smark (sp)
+	$if (datatype == r)
+	call salloc (temp, npts, TY_REAL)
+	$else
+	call salloc (temp, npts, TY_DOUBLE)
+	$endif
+
+	# accumulate the output vector
+	call amov$t (x, Mem$t[temp], npts)
+	do i = 3, order {
+	    call amul$t (Mem$t[temp], x, Mem$t[temp], npts)
+	    $if (datatype == r)
+	    call awsur (yfit, Memr[temp], yfit, npts, 1.0, coeff[i])
+	    $else
+	    call awsud (yfit, Memd[temp], yfit, npts, 1.0d0, coeff[i])
+	    $endif
+	}
+
+	call sfree (sp)
+
+end
+
+# GS_1DEVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure $tgs_1devcheb (coeff, x, yfit, npts, order, k1, k2)
+
+PIXEL	coeff[ARB]		# EV array of coefficients
+PIXEL	x[npts]			# x values of points to be evaluated
+PIXEL	yfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	order			# order of the polynomial, 1 = constant
+PIXEL	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer sp
+PIXEL	c1, c2
+
+begin
+	# fit a constant
+	call amovk$t (coeff[1], yfit, npts)
+	if (order == 1)
+	    return
+
+	# fit a linear function
+	c1 = k2 * coeff[2]
+	c2 = c1 * k1 + coeff[1]
+	call altm$t (x, yfit, npts, c1, c2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	$if (datatype == r)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (pn, npts, TY_REAL)
+	call salloc (pnm1, npts, TY_REAL)
+	call salloc (pnm2, npts, TY_REAL)
+	$else
+	call salloc (sx, npts, TY_DOUBLE)
+	call salloc (pn, npts, TY_DOUBLE)
+	call salloc (pnm1, npts, TY_DOUBLE)
+	call salloc (pnm2, npts, TY_DOUBLE)
+	$endif
+
+	# a higher order polynomial
+	$if (datatype == r)
+	call amovkr (1., Memr[pnm2], npts)
+	$else
+	call amovkd (1.0d0, Memd[pnm2], npts)
+	$endif
+	call alta$t (x, Mem$t[sx], npts, k1, k2)
+	call amov$t (Mem$t[sx], Mem$t[pnm1], npts)
+	call amulk$t (Mem$t[sx], 2$f, Mem$t[sx], npts)
+	do i = 3, order {
+	    call amul$t (Mem$t[sx], Mem$t[pnm1], Mem$t[pn], npts)
+	    call asub$t (Mem$t[pn], Mem$t[pnm2], Mem$t[pn], npts)
+	    if (i < order) {
+	        call amov$t (Mem$t[pnm1], Mem$t[pnm2], npts)
+	        call amov$t (Mem$t[pn], Mem$t[pnm1], npts)
+	    }
+	    call amulk$t (Mem$t[pn], coeff[i], Mem$t[pn], npts)
+	    call aadd$t (yfit, Mem$t[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
+
+
+# GS_1DEVLEG -- Procedure to evaluate a Legendre polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure $tgs_1devleg (coeff, x, yfit, npts, order, k1, k2)
+
+PIXEL	coeff[ARB]		# EV array of coefficients
+PIXEL	x[npts]			# x values of points to be evaluated
+PIXEL	yfit[npts]		# the fitted points
+int	npts			# number of data points
+int	order			# order of the polynomial, 1 = constant
+PIXEL	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer	sp
+PIXEL	ri, ri1, ri2
+
+begin
+	# fit a constant
+	call amovk$t (coeff[1], yfit, npts)
+	if (order == 1)
+	    return
+
+	# fit a linear function
+	ri1 = k2 * coeff[2]
+	ri2 = ri1 * k1 + coeff[1]
+	call altm$t (x, yfit, npts, ri1, ri2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	$if (datatype == r)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (pn, npts, TY_REAL)
+	call salloc (pnm1, npts, TY_REAL)
+	call salloc (pnm2, npts, TY_REAL)
+	$else
+	call salloc (sx, npts, TY_DOUBLE)
+	call salloc (pn, npts, TY_DOUBLE)
+	call salloc (pnm1, npts, TY_DOUBLE)
+	call salloc (pnm2, npts, TY_DOUBLE)
+	$endif
+
+	# a higher order polynomial
+	$if (datatype == r)
+	call amovkr (1., Memr[pnm2], npts)
+	$else
+	call amovkd (1.0d0, Memd[pnm2], npts)
+	$endif
+	call alta$t (x, Mem$t[sx], npts, k1, k2)
+	call amov$t (Mem$t[sx], Mem$t[pnm1], npts)
+	do i = 3, order {
+	    ri = i
+	    ri1 = (2. * ri - 3.) / (ri - 1.)
+	    ri2 = - (ri - 2.) / (ri - 1.)
+	    call amul$t (Mem$t[sx], Mem$t[pnm1], Mem$t[pn], npts)
+	    call awsu$t (Mem$t[pn], Mem$t[pnm2], Mem$t[pn], npts, ri1, ri2)
+	    if (i < order) {
+	        call amov$t (Mem$t[pnm1], Mem$t[pnm2], npts)
+	        call amov$t (Mem$t[pn], Mem$t[pnm1], npts)
+	    }
+	    call amulk$t (Mem$t[pn], coeff[i], Mem$t[pn], npts)
+	    call aadd$t (yfit, Mem$t[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
diff --git a/math/gsurfit/gs_f1devald.x b/math/gsurfit/gs_f1devald.x
new file mode 100644
index 00000000..6f20e7e7
--- /dev/null
+++ b/math/gsurfit/gs_f1devald.x
@@ -0,0 +1,159 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_1DEVPOLY -- Procedure to evaulate a 1D polynomial
+
+procedure dgs_1devpoly (coeff, x, yfit, npts, order, k1, k2)
+
+double	coeff[ARB]		# EV array of coefficients
+double	x[npts]			# x values of points to be evaluated
+double	yfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	order			# order of the polynomial, 1 = constant
+double	k1, k2			# normalizing constants
+
+int	i
+pointer	sp, temp
+
+begin
+	# fit a constant
+	call amovkd (coeff[1], yfit, npts)
+	if (order == 1)
+	    return
+
+	# fit a linear function
+	call altmd (x, yfit, npts, coeff[2], coeff[1])
+	if (order == 2)
+	    return
+
+	call smark (sp)
+	call salloc (temp, npts, TY_DOUBLE)
+
+	# accumulate the output vector
+	call amovd (x, Memd[temp], npts)
+	do i = 3, order {
+	    call amuld (Memd[temp], x, Memd[temp], npts)
+	    call awsud (yfit, Memd[temp], yfit, npts, 1.0d0, coeff[i])
+	}
+
+	call sfree (sp)
+
+end
+
+# GS_1DEVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure dgs_1devcheb (coeff, x, yfit, npts, order, k1, k2)
+
+double	coeff[ARB]		# EV array of coefficients
+double	x[npts]			# x values of points to be evaluated
+double	yfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	order			# order of the polynomial, 1 = constant
+double	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer sp
+double	c1, c2
+
+begin
+	# fit a constant
+	call amovkd (coeff[1], yfit, npts)
+	if (order == 1)
+	    return
+
+	# fit a linear function
+	c1 = k2 * coeff[2]
+	c2 = c1 * k1 + coeff[1]
+	call altmd (x, yfit, npts, c1, c2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_DOUBLE)
+	call salloc (pn, npts, TY_DOUBLE)
+	call salloc (pnm1, npts, TY_DOUBLE)
+	call salloc (pnm2, npts, TY_DOUBLE)
+
+	# a higher order polynomial
+	call amovkd (1.0d0, Memd[pnm2], npts)
+	call altad (x, Memd[sx], npts, k1, k2)
+	call amovd (Memd[sx], Memd[pnm1], npts)
+	call amulkd (Memd[sx], 2.0D0, Memd[sx], npts)
+	do i = 3, order {
+	    call amuld (Memd[sx], Memd[pnm1], Memd[pn], npts)
+	    call asubd (Memd[pn], Memd[pnm2], Memd[pn], npts)
+	    if (i < order) {
+	        call amovd (Memd[pnm1], Memd[pnm2], npts)
+	        call amovd (Memd[pn], Memd[pnm1], npts)
+	    }
+	    call amulkd (Memd[pn], coeff[i], Memd[pn], npts)
+	    call aaddd (yfit, Memd[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
+
+
+# GS_1DEVLEG -- Procedure to evaluate a Legendre polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure dgs_1devleg (coeff, x, yfit, npts, order, k1, k2)
+
+double	coeff[ARB]		# EV array of coefficients
+double	x[npts]			# x values of points to be evaluated
+double	yfit[npts]		# the fitted points
+int	npts			# number of data points
+int	order			# order of the polynomial, 1 = constant
+double	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer	sp
+double	ri, ri1, ri2
+
+begin
+	# fit a constant
+	call amovkd (coeff[1], yfit, npts)
+	if (order == 1)
+	    return
+
+	# fit a linear function
+	ri1 = k2 * coeff[2]
+	ri2 = ri1 * k1 + coeff[1]
+	call altmd (x, yfit, npts, ri1, ri2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_DOUBLE)
+	call salloc (pn, npts, TY_DOUBLE)
+	call salloc (pnm1, npts, TY_DOUBLE)
+	call salloc (pnm2, npts, TY_DOUBLE)
+
+	# a higher order polynomial
+	call amovkd (1.0d0, Memd[pnm2], npts)
+	call altad (x, Memd[sx], npts, k1, k2)
+	call amovd (Memd[sx], Memd[pnm1], npts)
+	do i = 3, order {
+	    ri = i
+	    ri1 = (2. * ri - 3.) / (ri - 1.)
+	    ri2 = - (ri - 2.) / (ri - 1.)
+	    call amuld (Memd[sx], Memd[pnm1], Memd[pn], npts)
+	    call awsud (Memd[pn], Memd[pnm2], Memd[pn], npts, ri1, ri2)
+	    if (i < order) {
+	        call amovd (Memd[pnm1], Memd[pnm2], npts)
+	        call amovd (Memd[pn], Memd[pnm1], npts)
+	    }
+	    call amulkd (Memd[pn], coeff[i], Memd[pn], npts)
+	    call aaddd (yfit, Memd[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
diff --git a/math/gsurfit/gs_f1devalr.x b/math/gsurfit/gs_f1devalr.x
new file mode 100644
index 00000000..5fdab143
--- /dev/null
+++ b/math/gsurfit/gs_f1devalr.x
@@ -0,0 +1,159 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# GS_1DEVPOLY -- Procedure to evaulate a 1D polynomial
+
+procedure rgs_1devpoly (coeff, x, yfit, npts, order, k1, k2)
+
+real	coeff[ARB]		# EV array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	yfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	order			# order of the polynomial, 1 = constant
+real	k1, k2			# normalizing constants
+
+int	i
+pointer	sp, temp
+
+begin
+	# fit a constant
+	call amovkr (coeff[1], yfit, npts)
+	if (order == 1)
+	    return
+
+	# fit a linear function
+	call altmr (x, yfit, npts, coeff[2], coeff[1])
+	if (order == 2)
+	    return
+
+	call smark (sp)
+	call salloc (temp, npts, TY_REAL)
+
+	# accumulate the output vector
+	call amovr (x, Memr[temp], npts)
+	do i = 3, order {
+	    call amulr (Memr[temp], x, Memr[temp], npts)
+	    call awsur (yfit, Memr[temp], yfit, npts, 1.0, coeff[i])
+	}
+
+	call sfree (sp)
+
+end
+
+# GS_1DEVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure rgs_1devcheb (coeff, x, yfit, npts, order, k1, k2)
+
+real	coeff[ARB]		# EV array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	yfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	order			# order of the polynomial, 1 = constant
+real	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer sp
+real	c1, c2
+
+begin
+	# fit a constant
+	call amovkr (coeff[1], yfit, npts)
+	if (order == 1)
+	    return
+
+	# fit a linear function
+	c1 = k2 * coeff[2]
+	c2 = c1 * k1 + coeff[1]
+	call altmr (x, yfit, npts, c1, c2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (pn, npts, TY_REAL)
+	call salloc (pnm1, npts, TY_REAL)
+	call salloc (pnm2, npts, TY_REAL)
+
+	# a higher order polynomial
+	call amovkr (1., Memr[pnm2], npts)
+	call altar (x, Memr[sx], npts, k1, k2)
+	call amovr (Memr[sx], Memr[pnm1], npts)
+	call amulkr (Memr[sx], 2.0, Memr[sx], npts)
+	do i = 3, order {
+	    call amulr (Memr[sx], Memr[pnm1], Memr[pn], npts)
+	    call asubr (Memr[pn], Memr[pnm2], Memr[pn], npts)
+	    if (i < order) {
+	        call amovr (Memr[pnm1], Memr[pnm2], npts)
+	        call amovr (Memr[pn], Memr[pnm1], npts)
+	    }
+	    call amulkr (Memr[pn], coeff[i], Memr[pn], npts)
+	    call aaddr (yfit, Memr[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
+
+
+# GS_1DEVLEG -- Procedure to evaluate a Legendre polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure rgs_1devleg (coeff, x, yfit, npts, order, k1, k2)
+
+real	coeff[ARB]		# EV array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	yfit[npts]		# the fitted points
+int	npts			# number of data points
+int	order			# order of the polynomial, 1 = constant
+real	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer	sp
+real	ri, ri1, ri2
+
+begin
+	# fit a constant
+	call amovkr (coeff[1], yfit, npts)
+	if (order == 1)
+	    return
+
+	# fit a linear function
+	ri1 = k2 * coeff[2]
+	ri2 = ri1 * k1 + coeff[1]
+	call altmr (x, yfit, npts, ri1, ri2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (pn, npts, TY_REAL)
+	call salloc (pnm1, npts, TY_REAL)
+	call salloc (pnm2, npts, TY_REAL)
+
+	# a higher order polynomial
+	call amovkr (1., Memr[pnm2], npts)
+	call altar (x, Memr[sx], npts, k1, k2)
+	call amovr (Memr[sx], Memr[pnm1], npts)
+	do i = 3, order {
+	    ri = i
+	    ri1 = (2. * ri - 3.) / (ri - 1.)
+	    ri2 = - (ri - 2.) / (ri - 1.)
+	    call amulr (Memr[sx], Memr[pnm1], Memr[pn], npts)
+	    call awsur (Memr[pn], Memr[pnm2], Memr[pn], npts, ri1, ri2)
+	    if (i < order) {
+	        call amovr (Memr[pnm1], Memr[pnm2], npts)
+	        call amovr (Memr[pn], Memr[pnm1], npts)
+	    }
+	    call amulkr (Memr[pn], coeff[i], Memr[pn], npts)
+	    call aaddr (yfit, Memr[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
diff --git a/math/gsurfit/gs_fder.gx b/math/gsurfit/gs_fder.gx
new file mode 100644
index 00000000..1620e189
--- /dev/null
+++ b/math/gsurfit/gs_fder.gx
@@ -0,0 +1,288 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+
+# GS_DERPOLY -- Evaluate the new polynomial derivative surface.
+
+procedure $tgs_derpoly (coeff, x, y, zfit, npts, xterms, xorder, yorder, nxder,
+	nyder, k1x, k2x, k1y, k2y)
+
+PIXEL	coeff[ARB]		# 1D array of coefficients
+PIXEL	x[npts]			# x values of points to be evaluated
+PIXEL	y[npts]
+PIXEL	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+int	nxder,nyder		# order of the derivatives in x and y
+PIXEL	k1x, k2x		# normalizing constants
+PIXEL	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	$if (datatype == r)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+	$else
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+	$endif
+
+	# calculate basis functions
+	call $tgs_dpol (x, npts, xorder, nxder, k1x, k2x, Mem$t[xb])
+	call $tgs_dpol (y, npts, yorder, nyder, k1y, k2y, Mem$t[yb])
+
+	# accumulate the output vector
+	cptr = 0
+	call aclr$t (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclr$t (Mem$t[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    $if (datatype == r)
+		    call awsu$t (Mem$t[accum], Mem$t[xbptr], Mem$t[accum], npts,
+		        1.0, coeff[cptr+k])
+		    $else
+		    call awsu$t (Mem$t[accum], Mem$t[xbptr], Mem$t[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    $endif
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvp$t (Mem$t[accum], Mem$t[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    call amul$t (Mem$t[xb], Mem$t[yb], zfit, npts)
+	    call amulk$t (zfit, coeff[1], zfit, npts)
+	    xbptr = xb + npts
+	    do k = 1, xorder - 1 {
+		$if (datatype == r)
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k+1])
+		$else
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k+1])
+		$endif
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		$if (datatype == r)
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		$else
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		$endif
+		ybptr = ybptr + npts
+	    }
+	}
+
+
+	call sfree (sp)
+end
+
+# GS_DERCHEB -- Evaluate the new Chebyshev polynomial derivative surface.
+
+procedure $tgs_dercheb (coeff, x, y, zfit, npts, xterms, xorder, yorder,
+	nxder, nyder, k1x, k2x, k1y, k2y)
+
+PIXEL	coeff[ARB]		# 1D array of coefficients
+PIXEL	x[npts]			# x values of points to be evaluated
+PIXEL	y[npts]
+PIXEL	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+int	nxder,nyder		# order of the derivatives in x and y
+PIXEL	k1x, k2x		# normalizing constants
+PIXEL	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	$if (datatype == r)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+	$else
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+	$endif
+
+	# calculate basis functions
+	call $tgs_dcheb (x, npts, xorder, nxder, k1x, k2x, Mem$t[xb])
+	call $tgs_dcheb (y, npts, yorder, nyder, k1y, k2y, Mem$t[yb])
+
+	# accumulate thr output vector
+	cptr = 0
+	call aclr$t (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclr$t (Mem$t[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    $if (datatype == r)
+		    call awsur (Memr[accum], Memr[xbptr], Memr[accum], npts,
+		        1.0, coeff[cptr+k])
+		    $else
+		    call awsud (Memd[accum], Memd[xbptr], Memd[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    $endif
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvp$t (Mem$t[accum], Mem$t[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    call amul$t (Mem$t[xb], Mem$t[yb], zfit, npts)
+	    call amulk$t (zfit, coeff[1], zfit, npts)
+	    xbptr = xb + npts
+	    do k = 1, xorder - 1 {
+		$if (datatype == r)
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k+1])
+		$else
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k+1])
+		$endif
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		$if (datatype == r)
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		$else
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		$endif
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+
+# GS_DERLEG -- Evaluate the new Legendre polynomial derivative surface.
+
+procedure $tgs_derleg (coeff, x, y, zfit, npts, xterms, xorder, yorder,
+	nxder, nyder, k1x, k2x, k1y, k2y)
+
+PIXEL	coeff[ARB]		# 1D array of coefficients
+PIXEL	x[npts]			# x values of points to be evaluated
+PIXEL	y[npts]
+PIXEL	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+int	nxder,nyder		# order of the derivatives in x and y
+PIXEL	k1x, k2x		# normalizing constants
+PIXEL	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, accum, xbptr, ybptr
+
+begin
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	$if (datatype == r)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+	$else
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+	$endif
+
+	# calculate basis functions
+	call $tgs_dleg (x, npts, xorder, nxder, k1x, k2x, Mem$t[xb])
+	call $tgs_dleg (y, npts, yorder, nyder, k1y, k2y, Mem$t[yb])
+
+	cptr = 0
+	call aclr$t (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        xbptr = xb
+	        call aclr$t (Mem$t[accum], npts)
+	        do k = 1, xincr {
+		    $if (datatype == r)
+		    call awsur (Memr[accum], Memr[xbptr], Memr[accum], npts,
+		        1.0, coeff[cptr+k])
+		    $else
+		    call awsud (Memd[accum], Memd[xbptr], Memd[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    $endif
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvp$t (Mem$t[accum], Mem$t[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    call amul$t (Mem$t[xb], Mem$t[yb], zfit, npts)
+	    call amulk$t (zfit, coeff[1], zfit, npts)
+	    xbptr = xb + npts
+	    do k = 1, xorder - 1 {
+		$if (datatype == r)
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k+1])
+		$else
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k+1])
+		$endif
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		$if (datatype == r)
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		$else
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		$endif
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gs_fderd.x b/math/gsurfit/gs_fderd.x
new file mode 100644
index 00000000..8f5cd628
--- /dev/null
+++ b/math/gsurfit/gs_fderd.x
@@ -0,0 +1,231 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+
+# GS_DERPOLY -- Evaluate the new polynomial derivative surface.
+
+procedure dgs_derpoly (coeff, x, y, zfit, npts, xterms, xorder, yorder, nxder,
+	nyder, k1x, k2x, k1y, k2y)
+
+double	coeff[ARB]		# 1D array of coefficients
+double	x[npts]			# x values of points to be evaluated
+double	y[npts]
+double	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+int	nxder,nyder		# order of the derivatives in x and y
+double	k1x, k2x		# normalizing constants
+double	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+
+	# calculate basis functions
+	call dgs_dpol (x, npts, xorder, nxder, k1x, k2x, Memd[xb])
+	call dgs_dpol (y, npts, yorder, nyder, k1y, k2y, Memd[yb])
+
+	# accumulate the output vector
+	cptr = 0
+	call aclrd (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclrd (Memd[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    call awsud (Memd[accum], Memd[xbptr], Memd[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpd (Memd[accum], Memd[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    call amuld (Memd[xb], Memd[yb], zfit, npts)
+	    call amulkd (zfit, coeff[1], zfit, npts)
+	    xbptr = xb + npts
+	    do k = 1, xorder - 1 {
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k+1])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+
+	call sfree (sp)
+end
+
+# GS_DERCHEB -- Evaluate the new Chebyshev polynomial derivative surface.
+
+procedure dgs_dercheb (coeff, x, y, zfit, npts, xterms, xorder, yorder,
+	nxder, nyder, k1x, k2x, k1y, k2y)
+
+double	coeff[ARB]		# 1D array of coefficients
+double	x[npts]			# x values of points to be evaluated
+double	y[npts]
+double	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+int	nxder,nyder		# order of the derivatives in x and y
+double	k1x, k2x		# normalizing constants
+double	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+
+	# calculate basis functions
+	call dgs_dcheb (x, npts, xorder, nxder, k1x, k2x, Memd[xb])
+	call dgs_dcheb (y, npts, yorder, nyder, k1y, k2y, Memd[yb])
+
+	# accumulate thr output vector
+	cptr = 0
+	call aclrd (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclrd (Memd[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    call awsud (Memd[accum], Memd[xbptr], Memd[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpd (Memd[accum], Memd[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    call amuld (Memd[xb], Memd[yb], zfit, npts)
+	    call amulkd (zfit, coeff[1], zfit, npts)
+	    xbptr = xb + npts
+	    do k = 1, xorder - 1 {
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k+1])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+
+# GS_DERLEG -- Evaluate the new Legendre polynomial derivative surface.
+
+procedure dgs_derleg (coeff, x, y, zfit, npts, xterms, xorder, yorder,
+	nxder, nyder, k1x, k2x, k1y, k2y)
+
+double	coeff[ARB]		# 1D array of coefficients
+double	x[npts]			# x values of points to be evaluated
+double	y[npts]
+double	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+int	nxder,nyder		# order of the derivatives in x and y
+double	k1x, k2x		# normalizing constants
+double	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, accum, xbptr, ybptr
+
+begin
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+
+	# calculate basis functions
+	call dgs_dleg (x, npts, xorder, nxder, k1x, k2x, Memd[xb])
+	call dgs_dleg (y, npts, yorder, nyder, k1y, k2y, Memd[yb])
+
+	cptr = 0
+	call aclrd (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        xbptr = xb
+	        call aclrd (Memd[accum], npts)
+	        do k = 1, xincr {
+		    call awsud (Memd[accum], Memd[xbptr], Memd[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpd (Memd[accum], Memd[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    call amuld (Memd[xb], Memd[yb], zfit, npts)
+	    call amulkd (zfit, coeff[1], zfit, npts)
+	    xbptr = xb + npts
+	    do k = 1, xorder - 1 {
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k+1])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gs_fderr.x b/math/gsurfit/gs_fderr.x
new file mode 100644
index 00000000..9d47dcb4
--- /dev/null
+++ b/math/gsurfit/gs_fderr.x
@@ -0,0 +1,228 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+
+# GS_DERPOLY -- Evaluate the new polynomial derivative surface.
+
+procedure rgs_derpoly (coeff, x, y, zfit, npts, xterms, xorder, yorder, nxder,
+	nyder, k1x, k2x, k1y, k2y)
+
+real	coeff[ARB]		# 1D array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	y[npts]
+real	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+int	nxder,nyder		# order of the derivatives in x and y
+real	k1x, k2x		# normalizing constants
+real	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+
+	# calculate basis functions
+	call rgs_dpol (x, npts, xorder, nxder, k1x, k2x, Memr[xb])
+	call rgs_dpol (y, npts, yorder, nyder, k1y, k2y, Memr[yb])
+
+	# accumulate the output vector
+	cptr = 0
+	call aclrr (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclrr (Memr[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    call awsur (Memr[accum], Memr[xbptr], Memr[accum], npts,
+		        1.0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpr (Memr[accum], Memr[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    call amulr (Memr[xb], Memr[yb], zfit, npts)
+	    call amulkr (zfit, coeff[1], zfit, npts)
+	    xbptr = xb + npts
+	    do k = 1, xorder - 1 {
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k+1])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+
+	call sfree (sp)
+end
+
+# GS_DERCHEB -- Evaluate the new Chebyshev polynomial derivative surface.
+
+procedure rgs_dercheb (coeff, x, y, zfit, npts, xterms, xorder, yorder,
+	nxder, nyder, k1x, k2x, k1y, k2y)
+
+real	coeff[ARB]		# 1D array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	y[npts]
+real	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+int	nxder,nyder		# order of the derivatives in x and y
+real	k1x, k2x		# normalizing constants
+real	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+
+	# calculate basis functions
+	call rgs_dcheb (x, npts, xorder, nxder, k1x, k2x, Memr[xb])
+	call rgs_dcheb (y, npts, yorder, nyder, k1y, k2y, Memr[yb])
+
+	# accumulate thr output vector
+	cptr = 0
+	call aclrr (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclrr (Memr[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    call awsur (Memr[accum], Memr[xbptr], Memr[accum], npts,
+		        1.0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpr (Memr[accum], Memr[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    call amulr (Memr[xb], Memr[yb], zfit, npts)
+	    call amulkr (zfit, coeff[1], zfit, npts)
+	    xbptr = xb + npts
+	    do k = 1, xorder - 1 {
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k+1])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+
+# GS_DERLEG -- Evaluate the new Legendre polynomial derivative surface.
+
+procedure rgs_derleg (coeff, x, y, zfit, npts, xterms, xorder, yorder,
+	nxder, nyder, k1x, k2x, k1y, k2y)
+
+real	coeff[ARB]		# 1D array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	y[npts]
+real	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+int	nxder,nyder		# order of the derivatives in x and y
+real	k1x, k2x		# normalizing constants
+real	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, accum, xbptr, ybptr
+
+begin
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+
+	# calculate basis functions
+	call rgs_dleg (x, npts, xorder, nxder, k1x, k2x, Memr[xb])
+	call rgs_dleg (y, npts, yorder, nyder, k1y, k2y, Memr[yb])
+
+	cptr = 0
+	call aclrr (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        xbptr = xb
+	        call aclrr (Memr[accum], npts)
+	        do k = 1, xincr {
+		    call awsur (Memr[accum], Memr[xbptr], Memr[accum], npts,
+		        1.0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpr (Memr[accum], Memr[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    call amulr (Memr[xb], Memr[yb], zfit, npts)
+	    call amulkr (zfit, coeff[1], zfit, npts)
+	    xbptr = xb + npts
+	    do k = 1, xorder - 1 {
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k+1])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gs_feval.gx b/math/gsurfit/gs_feval.gx
new file mode 100644
index 00000000..e28ad46d
--- /dev/null
+++ b/math/gsurfit/gs_feval.gx
@@ -0,0 +1,332 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+
+# GS_EVPOLY -- Procedure to evluate the polynomials
+
+procedure $tgs_evpoly (coeff, x, y, zfit, npts, xterms, xorder, yorder, k1x,
+    k2x, k1y, k2y)
+
+PIXEL	coeff[ARB]		# 1D array of coefficients
+PIXEL	x[npts]			# x values of points to be evaluated
+PIXEL	y[npts]
+PIXEL	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+PIXEL	k1x, k2x		# normalizing constants
+PIXEL	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# fit a constant
+	if (xorder == 1 && yorder == 1) {
+	    call amovk$t (coeff[1], zfit, npts)
+	    return
+	}
+
+	# fit first order in x and y
+	if (xorder == 2 && yorder == 1) {
+	    call altm$t (x, zfit, npts, coeff[2], coeff[1])
+	    return
+	}
+	if (yorder == 2 && xorder == 1) {
+	    call altm$t (x, zfit, npts, coeff[2], coeff[1])
+	    return
+	}
+	if (xorder == 2 && yorder == 2 && xterms == NO) {
+	    do i = 1, npts
+		zfit[i] = coeff[1] + x[i] * coeff[2] + y[i] * coeff[3]
+	    return
+	}
+
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	$if (datatype == r)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+	$else
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+	$endif
+
+	# calculate basis functions
+	call $tgs_bpol (x, npts, xorder, k1x, k2x, Mem$t[xb])
+	call $tgs_bpol (y, npts, yorder, k1y, k2y, Mem$t[yb])
+
+	# accumulate the output vector
+	cptr = 0
+	call aclr$t (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclr$t (Mem$t[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    $if (datatype == r)
+		    call awsu$t (Mem$t[accum], Mem$t[xbptr], Mem$t[accum], npts,
+		        1.0, coeff[cptr+k])
+		    $else
+		    call awsu$t (Mem$t[accum], Mem$t[xbptr], Mem$t[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    $endif
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvp$t (Mem$t[accum], Mem$t[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    xbptr = xb
+	    do k = 1, xorder {
+		$if (datatype == r)
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k])
+		$else
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k])
+		$endif
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		$if (datatype == r)
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		$else
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		$endif
+		ybptr = ybptr + npts
+	    }
+	}
+
+
+	call sfree (sp)
+end
+
+# GS_EVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure $tgs_evcheb (coeff, x, y, zfit, npts, xterms, xorder, yorder, k1x,
+    k2x, k1y, k2y)
+
+PIXEL	coeff[ARB]		# 1D array of coefficients
+PIXEL	x[npts]			# x values of points to be evaluated
+PIXEL	y[npts]
+PIXEL	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+PIXEL	k1x, k2x		# normalizing constants
+PIXEL	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# fit a constant
+	if (xorder == 1 && yorder == 1) {
+	    call amovk$t (coeff[1], zfit, npts)
+	    return
+	}
+
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	$if (datatype == r)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+	$else
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+	$endif
+
+	# calculate basis functions
+	call $tgs_bcheb (x, npts, xorder, k1x, k2x, Mem$t[xb])
+	call $tgs_bcheb (y, npts, yorder, k1y, k2y, Mem$t[yb])
+
+	# accumulate thr output vector
+	cptr = 0
+	call aclr$t (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclr$t (Mem$t[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    $if (datatype == r)
+		    call awsur (Memr[accum], Memr[xbptr], Memr[accum], npts,
+		        1.0, coeff[cptr+k])
+		    $else
+		    call awsud (Memd[accum], Memd[xbptr], Memd[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    $endif
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvp$t (Mem$t[accum], Mem$t[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    xbptr = xb
+	    do k = 1, xorder {
+		$if (datatype == r)
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k])
+		$else
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k])
+		$endif
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		$if (datatype == r)
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		$else
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		$else
+		$endif
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+
+# GS_EVLEG -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure $tgs_evleg (coeff, x, y, zfit, npts, xterms, xorder, yorder, k1x, k2x,
+    k1y, k2y)
+
+PIXEL	coeff[ARB]		# 1D array of coefficients
+PIXEL	x[npts]			# x values of points to be evaluated
+PIXEL	y[npts]
+PIXEL	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+PIXEL	k1x, k2x		# normalizing constants
+PIXEL	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, accum, xbptr, ybptr
+
+begin
+	# fit a constant
+	if (xorder == 1 && yorder == 1) {
+	    call amovk$t (coeff[1], zfit, npts)
+	    return
+	}
+
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	$if (datatype == r)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+	$else
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+	$endif
+
+	# calculate basis functions
+	call $tgs_bleg (x, npts, xorder, k1x, k2x, Mem$t[xb])
+	call $tgs_bleg (y, npts, yorder, k1y, k2y, Mem$t[yb])
+
+	cptr = 0
+	call aclr$t (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        xbptr = xb
+	        call aclr$t (Mem$t[accum], npts)
+	        do k = 1, xincr {
+		    $if (datatype == r)
+		    call awsur (Memr[accum], Memr[xbptr], Memr[accum], npts,
+		        1.0, coeff[cptr+k])
+		    $else
+		    call awsud (Memd[accum], Memd[xbptr], Memd[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    $endif
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvp$t (Mem$t[accum], Mem$t[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    xbptr = xb
+	    do k = 1, xorder {
+		$if (datatype == r)
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k])
+		$else
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k])
+		$endif
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		$if (datatype == r)
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		$else
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		$endif
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+# GS_ASUMVP -- Procedure to add the product of two vectors to another vector
+
+procedure gs_asumvp$t (a, b, c, d, npts)
+
+PIXEL	a[ARB]		# first input vector
+PIXEL	b[ARB]		# second input vector
+PIXEL	c[ARB]		# third vector
+PIXEL	d[ARB]		# output vector
+int	npts		# number of points
+
+int	i
+
+begin
+	do i = 1, npts
+	    d[i] = c[i] + a[i] * b[i]
+end
diff --git a/math/gsurfit/gs_fevald.x b/math/gsurfit/gs_fevald.x
new file mode 100644
index 00000000..68265e9c
--- /dev/null
+++ b/math/gsurfit/gs_fevald.x
@@ -0,0 +1,274 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+
+# GS_EVPOLY -- Procedure to evluate the polynomials
+
+procedure dgs_evpoly (coeff, x, y, zfit, npts, xterms, xorder, yorder, k1x,
+    k2x, k1y, k2y)
+
+double	coeff[ARB]		# 1D array of coefficients
+double	x[npts]			# x values of points to be evaluated
+double	y[npts]
+double	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+double	k1x, k2x		# normalizing constants
+double	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# fit a constant
+	if (xorder == 1 && yorder == 1) {
+	    call amovkd (coeff[1], zfit, npts)
+	    return
+	}
+
+	# fit first order in x and y
+	if (xorder == 2 && yorder == 1) {
+	    call altmd (x, zfit, npts, coeff[2], coeff[1])
+	    return
+	}
+	if (yorder == 2 && xorder == 1) {
+	    call altmd (x, zfit, npts, coeff[2], coeff[1])
+	    return
+	}
+	if (xorder == 2 && yorder == 2 && xterms == NO) {
+	    do i = 1, npts
+		zfit[i] = coeff[1] + x[i] * coeff[2] + y[i] * coeff[3]
+	    return
+	}
+
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+
+	# calculate basis functions
+	call dgs_bpol (x, npts, xorder, k1x, k2x, Memd[xb])
+	call dgs_bpol (y, npts, yorder, k1y, k2y, Memd[yb])
+
+	# accumulate the output vector
+	cptr = 0
+	call aclrd (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclrd (Memd[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    call awsud (Memd[accum], Memd[xbptr], Memd[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpd (Memd[accum], Memd[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    xbptr = xb
+	    do k = 1, xorder {
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+
+	call sfree (sp)
+end
+
+# GS_EVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure dgs_evcheb (coeff, x, y, zfit, npts, xterms, xorder, yorder, k1x,
+    k2x, k1y, k2y)
+
+double	coeff[ARB]		# 1D array of coefficients
+double	x[npts]			# x values of points to be evaluated
+double	y[npts]
+double	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+double	k1x, k2x		# normalizing constants
+double	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# fit a constant
+	if (xorder == 1 && yorder == 1) {
+	    call amovkd (coeff[1], zfit, npts)
+	    return
+	}
+
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+
+	# calculate basis functions
+	call dgs_bcheb (x, npts, xorder, k1x, k2x, Memd[xb])
+	call dgs_bcheb (y, npts, yorder, k1y, k2y, Memd[yb])
+
+	# accumulate thr output vector
+	cptr = 0
+	call aclrd (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclrd (Memd[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    call awsud (Memd[accum], Memd[xbptr], Memd[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpd (Memd[accum], Memd[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    xbptr = xb
+	    do k = 1, xorder {
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+
+# GS_EVLEG -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure dgs_evleg (coeff, x, y, zfit, npts, xterms, xorder, yorder, k1x, k2x,
+    k1y, k2y)
+
+double	coeff[ARB]		# 1D array of coefficients
+double	x[npts]			# x values of points to be evaluated
+double	y[npts]
+double	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+double	k1x, k2x		# normalizing constants
+double	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, accum, xbptr, ybptr
+
+begin
+	# fit a constant
+	if (xorder == 1 && yorder == 1) {
+	    call amovkd (coeff[1], zfit, npts)
+	    return
+	}
+
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_DOUBLE)
+	call salloc (yb, yorder * npts, TY_DOUBLE)
+	call salloc (accum, npts, TY_DOUBLE)
+
+	# calculate basis functions
+	call dgs_bleg (x, npts, xorder, k1x, k2x, Memd[xb])
+	call dgs_bleg (y, npts, yorder, k1y, k2y, Memd[yb])
+
+	cptr = 0
+	call aclrd (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        xbptr = xb
+	        call aclrd (Memd[accum], npts)
+	        do k = 1, xincr {
+		    call awsud (Memd[accum], Memd[xbptr], Memd[accum], npts,
+		        1.0d0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpd (Memd[accum], Memd[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    xbptr = xb
+	    do k = 1, xorder {
+		call awsud (zfit, Memd[xbptr], zfit, npts, 1.0d0, coeff[k])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsud (zfit, Memd[ybptr], zfit, npts, 1.0d0,
+		    coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+# GS_ASUMVP -- Procedure to add the product of two vectors to another vector
+
+procedure gs_asumvpd (a, b, c, d, npts)
+
+double	a[ARB]		# first input vector
+double	b[ARB]		# second input vector
+double	c[ARB]		# third vector
+double	d[ARB]		# output vector
+int	npts		# number of points
+
+int	i
+
+begin
+	do i = 1, npts
+	    d[i] = c[i] + a[i] * b[i]
+end
diff --git a/math/gsurfit/gs_fevalr.x b/math/gsurfit/gs_fevalr.x
new file mode 100644
index 00000000..7988f66a
--- /dev/null
+++ b/math/gsurfit/gs_fevalr.x
@@ -0,0 +1,271 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+
+# GS_EVPOLY -- Procedure to evluate the polynomials
+
+procedure rgs_evpoly (coeff, x, y, zfit, npts, xterms, xorder, yorder, k1x,
+    k2x, k1y, k2y)
+
+real	coeff[ARB]		# 1D array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	y[npts]
+real	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+real	k1x, k2x		# normalizing constants
+real	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# fit a constant
+	if (xorder == 1 && yorder == 1) {
+	    call amovkr (coeff[1], zfit, npts)
+	    return
+	}
+
+	# fit first order in x and y
+	if (xorder == 2 && yorder == 1) {
+	    call altmr (x, zfit, npts, coeff[2], coeff[1])
+	    return
+	}
+	if (yorder == 2 && xorder == 1) {
+	    call altmr (x, zfit, npts, coeff[2], coeff[1])
+	    return
+	}
+	if (xorder == 2 && yorder == 2 && xterms == NO) {
+	    do i = 1, npts
+		zfit[i] = coeff[1] + x[i] * coeff[2] + y[i] * coeff[3]
+	    return
+	}
+
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+
+	# calculate basis functions
+	call rgs_bpol (x, npts, xorder, k1x, k2x, Memr[xb])
+	call rgs_bpol (y, npts, yorder, k1y, k2y, Memr[yb])
+
+	# accumulate the output vector
+	cptr = 0
+	call aclrr (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclrr (Memr[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    call awsur (Memr[accum], Memr[xbptr], Memr[accum], npts,
+		        1.0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpr (Memr[accum], Memr[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    xbptr = xb
+	    do k = 1, xorder {
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+
+	call sfree (sp)
+end
+
+# GS_EVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure rgs_evcheb (coeff, x, y, zfit, npts, xterms, xorder, yorder, k1x,
+    k2x, k1y, k2y)
+
+real	coeff[ARB]		# 1D array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	y[npts]
+real	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+real	k1x, k2x		# normalizing constants
+real	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, xbptr, ybptr, accum
+
+begin
+	# fit a constant
+	if (xorder == 1 && yorder == 1) {
+	    call amovkr (coeff[1], zfit, npts)
+	    return
+	}
+
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+
+	# calculate basis functions
+	call rgs_bcheb (x, npts, xorder, k1x, k2x, Memr[xb])
+	call rgs_bcheb (y, npts, yorder, k1y, k2y, Memr[yb])
+
+	# accumulate thr output vector
+	cptr = 0
+	call aclrr (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        call aclrr (Memr[accum], npts)
+	        xbptr = xb
+	        do k = 1, xincr {
+		    call awsur (Memr[accum], Memr[xbptr], Memr[accum], npts,
+		        1.0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpr (Memr[accum], Memr[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    xbptr = xb
+	    do k = 1, xorder {
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+
+# GS_EVLEG -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure rgs_evleg (coeff, x, y, zfit, npts, xterms, xorder, yorder, k1x, k2x,
+    k1y, k2y)
+
+real	coeff[ARB]		# 1D array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	y[npts]
+real	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+real	k1x, k2x		# normalizing constants
+real	k1y, k2y
+
+int	i, k, cptr, maxorder, xincr
+pointer	sp, xb, yb, accum, xbptr, ybptr
+
+begin
+	# fit a constant
+	if (xorder == 1 && yorder == 1) {
+	    call amovkr (coeff[1], zfit, npts)
+	    return
+	}
+
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+
+	# calculate basis functions
+	call rgs_bleg (x, npts, xorder, k1x, k2x, Memr[xb])
+	call rgs_bleg (y, npts, yorder, k1y, k2y, Memr[yb])
+
+	cptr = 0
+	call aclrr (zfit, npts)
+	if (xterms != GS_XNONE) {
+	    maxorder = max (xorder + 1, yorder + 1)
+	    xincr = xorder
+	    ybptr = yb
+	    do i = 1, yorder {
+	        xbptr = xb
+	        call aclrr (Memr[accum], npts)
+	        do k = 1, xincr {
+		    call awsur (Memr[accum], Memr[xbptr], Memr[accum], npts,
+		        1.0, coeff[cptr+k])
+		    xbptr = xbptr + npts
+	        }
+	        call gs_asumvpr (Memr[accum], Memr[ybptr], zfit, zfit, npts)
+	        cptr = cptr + xincr
+	        ybptr = ybptr + npts
+		switch (xterms) {
+		case GS_XHALF:
+		    if ((i + xorder + 1) > maxorder)
+			xincr = xincr - 1
+		default:
+		    ;
+		}
+	    }
+	} else {
+	    xbptr = xb
+	    do k = 1, xorder {
+		call awsur (zfit, Memr[xbptr], zfit, npts, 1.0, coeff[k])
+		xbptr = xbptr + npts
+	    }
+	    ybptr = yb + npts
+	    do k = 1, yorder - 1 {
+		call awsur (zfit, Memr[ybptr], zfit, npts, 1.0, coeff[xorder+k])
+		ybptr = ybptr + npts
+	    }
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+# GS_ASUMVP -- Procedure to add the product of two vectors to another vector
+
+procedure gs_asumvpr (a, b, c, d, npts)
+
+real	a[ARB]		# first input vector
+real	b[ARB]		# second input vector
+real	c[ARB]		# third vector
+real	d[ARB]		# output vector
+int	npts		# number of points
+
+int	i
+
+begin
+	do i = 1, npts
+	    d[i] = c[i] + a[i] * b[i]
+end
diff --git a/math/gsurfit/gsaccum.gx b/math/gsurfit/gsaccum.gx
new file mode 100644
index 00000000..f9958263
--- /dev/null
+++ b/math/gsurfit/gsaccum.gx
@@ -0,0 +1,193 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSACCUM -- Procedure to add a point to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# NCOEFF(sf)-vector VECTOR.
+
+$if (datatype == r)
+procedure gsaccum (sf, x, y, z, w, wtflag)
+$else
+procedure dgsaccum (sf, x, y, z, w, wtflag)
+$endif
+
+pointer	sf		# surface descriptor
+PIXEL	x		# x value
+PIXEL	y		# y value
+PIXEL	z		# z value
+PIXEL	w		# weight
+int	wtflag		# type of weighting
+
+bool	refsub
+int	ii, j, k, l
+int	maxorder, xorder, xxorder, xindex, yindex, ntimes
+pointer	sp, vzptr, mzptr, xbptr, ybptr
+PIXEL	x1, y1, z1, byw, bw
+
+begin
+	# increment the number of points
+	GS_NPTS(sf) = GS_NPTS(sf) + 1
+
+	# remove basis functions calculated by any previous gsrefit call
+	if (GS_XBASIS(sf) != NULL || GS_YBASIS(sf) != NULL) {
+
+	    $if (datatype == r)
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_REAL)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_REAL)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_REAL)
+	    GS_WZ(sf) = NULL
+	    $else
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_DOUBLE)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_DOUBLE)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_DOUBLE)
+	    GS_WZ(sf) = NULL
+	    $endif
+
+	}
+
+	# calculate weight
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    $if (datatype == r)
+	    w = 1.
+	    $else
+	    w = 1.0d0
+	    $endif
+	case WTS_USER:
+	    # user supplied weights
+	default:
+	    $if (datatype == r)
+	    w = 1.
+	    $else
+	    w = 1.0d0
+	    $endif
+	}
+
+	# allocate space for the basis functions
+	call smark (sp)
+	call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_PIXEL)
+	call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_PIXEL)
+
+	# subtract reference value
+	refsub = !(IS_INDEF(GS_XREF(sf)) || IS_INDEF(GS_YREF(sf)) ||
+	    IS_INDEF(GS_ZREF(sf)))
+	if (refsub) {
+	    x1 = x - GS_XREF(sf)
+	    y1 = y - GS_YREF(sf)
+	    z1 = z - GS_ZREF(sf)
+	} else {
+	    x1 = x
+	    y1 = y
+	    z1 = z
+	}
+
+	# calculate the non-zero basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE:
+	    call $tgs_b1leg (x1, GS_XORDER(sf), GS_XMAXMIN(sf),
+		GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call $tgs_b1leg (y1, GS_YORDER(sf), GS_YMAXMIN(sf),
+		GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_CHEBYSHEV:
+	    call $tgs_b1cheb (x1, GS_XORDER(sf), GS_XMAXMIN(sf),
+		GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call $tgs_b1cheb (y1, GS_YORDER(sf), GS_YMAXMIN(sf),
+		GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_POLYNOMIAL:
+	    call $tgs_b1pol (x1, GS_XORDER(sf), GS_XMAXMIN(sf),
+		GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call $tgs_b1pol (y1, GS_YORDER(sf), GS_YMAXMIN(sf),
+		GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	default:
+	    call error (0, "GSACCUM: Unkown surface type.")
+	}
+
+	# one index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	mzptr = GS_MATRIX(sf) - 1
+	xbptr = GS_XBASIS(sf) - 1
+	ybptr = GS_YBASIS(sf) - 1
+
+
+	switch (GS_TYPE(sf)) {
+
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    xorder = GS_XORDER(sf)
+	    ntimes = 0
+
+	    do l = 1, GS_YORDER(sf) {
+		byw = w * YBASIS(ybptr+l)
+	        do k = 1, xorder {
+	            bw = byw * XBASIS(xbptr+k)
+	            VECTOR(vzptr+k) = VECTOR(vzptr+k) + bw * z
+	            ii = 1
+		    xindex = k
+		    yindex = l
+		    xxorder = xorder
+		    do j = k + ntimes, GS_NCOEFF(sf) {
+		        MATRIX(mzptr+ii) = MATRIX(mzptr+ii) + bw *
+			    XBASIS(xbptr+xindex) * YBASIS(ybptr+yindex)	
+			if (mod (xindex, xxorder) == 0) {
+			    xindex = 1
+			    yindex = yindex + 1
+			    switch (GS_XTERMS(sf)) {
+			    case GS_XNONE:
+				xxorder = 1
+			    case GS_XHALF:
+				if ((yindex + GS_XORDER(sf)) > maxorder)
+				    xxorder = xxorder - 1
+			    default:
+				;
+			    }
+			} else
+			    xindex = xindex + 1
+		        ii = ii + 1
+		    }
+		    mzptr = mzptr + GS_NCOEFF(sf)
+	        }
+
+		vzptr = vzptr + xorder
+		ntimes = ntimes + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown surface type.")
+	}
+
+	# release the space
+	call sfree (sp)
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+end
diff --git a/math/gsurfit/gsaccumd.x b/math/gsurfit/gsaccumd.x
new file mode 100644
index 00000000..71ed9f90
--- /dev/null
+++ b/math/gsurfit/gsaccumd.x
@@ -0,0 +1,165 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSACCUM -- Procedure to add a point to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# NCOEFF(sf)-vector VECTOR.
+
+procedure dgsaccum (sf, x, y, z, w, wtflag)
+
+pointer	sf		# surface descriptor
+double	x		# x value
+double	y		# y value
+double	z		# z value
+double	w		# weight
+int	wtflag		# type of weighting
+
+bool	refsub
+int	ii, j, k, l
+int	maxorder, xorder, xxorder, xindex, yindex, ntimes
+pointer	sp, vzptr, mzptr, xbptr, ybptr
+double	x1, y1, z1, byw, bw
+
+begin
+	# increment the number of points
+	GS_NPTS(sf) = GS_NPTS(sf) + 1
+
+	# remove basis functions calculated by any previous gsrefit call
+	if (GS_XBASIS(sf) != NULL || GS_YBASIS(sf) != NULL) {
+
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_DOUBLE)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_DOUBLE)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_DOUBLE)
+	    GS_WZ(sf) = NULL
+
+	}
+
+	# calculate weight
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    w = 1.0d0
+	case WTS_USER:
+	    # user supplied weights
+	default:
+	    w = 1.0d0
+	}
+
+	# allocate space for the basis functions
+	call smark (sp)
+	call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_DOUBLE)
+	call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_DOUBLE)
+
+	# subtract reference value
+	refsub = !(IS_INDEFD(GS_XREF(sf)) || IS_INDEFD(GS_YREF(sf)) ||
+	    IS_INDEFD(GS_ZREF(sf)))
+	if (refsub) {
+	    x1 = x - GS_XREF(sf)
+	    y1 = y - GS_YREF(sf)
+	    z1 = z - GS_ZREF(sf)
+	} else {
+	    x1 = x
+	    y1 = y
+	    z1 = z
+	}
+
+	# calculate the non-zero basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE:
+	    call dgs_b1leg (x1, GS_XORDER(sf), GS_XMAXMIN(sf),
+		GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call dgs_b1leg (y1, GS_YORDER(sf), GS_YMAXMIN(sf),
+		GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_CHEBYSHEV:
+	    call dgs_b1cheb (x1, GS_XORDER(sf), GS_XMAXMIN(sf),
+		GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call dgs_b1cheb (y1, GS_YORDER(sf), GS_YMAXMIN(sf),
+		GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_POLYNOMIAL:
+	    call dgs_b1pol (x1, GS_XORDER(sf), GS_XMAXMIN(sf),
+		GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call dgs_b1pol (y1, GS_YORDER(sf), GS_YMAXMIN(sf),
+		GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	default:
+	    call error (0, "GSACCUM: Unkown surface type.")
+	}
+
+	# one index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	mzptr = GS_MATRIX(sf) - 1
+	xbptr = GS_XBASIS(sf) - 1
+	ybptr = GS_YBASIS(sf) - 1
+
+
+	switch (GS_TYPE(sf)) {
+
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    xorder = GS_XORDER(sf)
+	    ntimes = 0
+
+	    do l = 1, GS_YORDER(sf) {
+		byw = w * YBASIS(ybptr+l)
+	        do k = 1, xorder {
+	            bw = byw * XBASIS(xbptr+k)
+	            VECTOR(vzptr+k) = VECTOR(vzptr+k) + bw * z
+	            ii = 1
+		    xindex = k
+		    yindex = l
+		    xxorder = xorder
+		    do j = k + ntimes, GS_NCOEFF(sf) {
+		        MATRIX(mzptr+ii) = MATRIX(mzptr+ii) + bw *
+			    XBASIS(xbptr+xindex) * YBASIS(ybptr+yindex)	
+			if (mod (xindex, xxorder) == 0) {
+			    xindex = 1
+			    yindex = yindex + 1
+			    switch (GS_XTERMS(sf)) {
+			    case GS_XNONE:
+				xxorder = 1
+			    case GS_XHALF:
+				if ((yindex + GS_XORDER(sf)) > maxorder)
+				    xxorder = xxorder - 1
+			    default:
+				;
+			    }
+			} else
+			    xindex = xindex + 1
+		        ii = ii + 1
+		    }
+		    mzptr = mzptr + GS_NCOEFF(sf)
+	        }
+
+		vzptr = vzptr + xorder
+		ntimes = ntimes + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown surface type.")
+	}
+
+	# release the space
+	call sfree (sp)
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+end
diff --git a/math/gsurfit/gsaccumr.x b/math/gsurfit/gsaccumr.x
new file mode 100644
index 00000000..4e973cfa
--- /dev/null
+++ b/math/gsurfit/gsaccumr.x
@@ -0,0 +1,165 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSACCUM -- Procedure to add a point to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# NCOEFF(sf)-vector VECTOR.
+
+procedure gsaccum (sf, x, y, z, w, wtflag)
+
+pointer	sf		# surface descriptor
+real	x		# x value
+real	y		# y value
+real	z		# z value
+real	w		# weight
+int	wtflag		# type of weighting
+
+bool	refsub
+int	ii, j, k, l
+int	maxorder, xorder, xxorder, xindex, yindex, ntimes
+pointer	sp, vzptr, mzptr, xbptr, ybptr
+real	x1, y1, z1, byw, bw
+
+begin
+	# increment the number of points
+	GS_NPTS(sf) = GS_NPTS(sf) + 1
+
+	# remove basis functions calculated by any previous gsrefit call
+	if (GS_XBASIS(sf) != NULL || GS_YBASIS(sf) != NULL) {
+
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_REAL)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_REAL)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_REAL)
+	    GS_WZ(sf) = NULL
+
+	}
+
+	# calculate weight
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    w = 1.
+	case WTS_USER:
+	    # user supplied weights
+	default:
+	    w = 1.
+	}
+
+	# allocate space for the basis functions
+	call smark (sp)
+	call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_REAL)
+	call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_REAL)
+
+	# subtract reference value
+	refsub = !(IS_INDEFR(GS_XREF(sf)) || IS_INDEFR(GS_YREF(sf)) ||
+	    IS_INDEFR(GS_ZREF(sf)))
+	if (refsub) {
+	    x1 = x - GS_XREF(sf)
+	    y1 = y - GS_YREF(sf)
+	    z1 = z - GS_ZREF(sf)
+	} else {
+	    x1 = x
+	    y1 = y
+	    z1 = z
+	}
+
+	# calculate the non-zero basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE:
+	    call rgs_b1leg (x1, GS_XORDER(sf), GS_XMAXMIN(sf),
+		GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call rgs_b1leg (y1, GS_YORDER(sf), GS_YMAXMIN(sf),
+		GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_CHEBYSHEV:
+	    call rgs_b1cheb (x1, GS_XORDER(sf), GS_XMAXMIN(sf),
+		GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call rgs_b1cheb (y1, GS_YORDER(sf), GS_YMAXMIN(sf),
+		GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_POLYNOMIAL:
+	    call rgs_b1pol (x1, GS_XORDER(sf), GS_XMAXMIN(sf),
+		GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call rgs_b1pol (y1, GS_YORDER(sf), GS_YMAXMIN(sf),
+		GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	default:
+	    call error (0, "GSACCUM: Unkown surface type.")
+	}
+
+	# one index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	mzptr = GS_MATRIX(sf) - 1
+	xbptr = GS_XBASIS(sf) - 1
+	ybptr = GS_YBASIS(sf) - 1
+
+
+	switch (GS_TYPE(sf)) {
+
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    xorder = GS_XORDER(sf)
+	    ntimes = 0
+
+	    do l = 1, GS_YORDER(sf) {
+		byw = w * YBASIS(ybptr+l)
+	        do k = 1, xorder {
+	            bw = byw * XBASIS(xbptr+k)
+	            VECTOR(vzptr+k) = VECTOR(vzptr+k) + bw * z
+	            ii = 1
+		    xindex = k
+		    yindex = l
+		    xxorder = xorder
+		    do j = k + ntimes, GS_NCOEFF(sf) {
+		        MATRIX(mzptr+ii) = MATRIX(mzptr+ii) + bw *
+			    XBASIS(xbptr+xindex) * YBASIS(ybptr+yindex)	
+			if (mod (xindex, xxorder) == 0) {
+			    xindex = 1
+			    yindex = yindex + 1
+			    switch (GS_XTERMS(sf)) {
+			    case GS_XNONE:
+				xxorder = 1
+			    case GS_XHALF:
+				if ((yindex + GS_XORDER(sf)) > maxorder)
+				    xxorder = xxorder - 1
+			    default:
+				;
+			    }
+			} else
+			    xindex = xindex + 1
+		        ii = ii + 1
+		    }
+		    mzptr = mzptr + GS_NCOEFF(sf)
+	        }
+
+		vzptr = vzptr + xorder
+		ntimes = ntimes + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown surface type.")
+	}
+
+	# release the space
+	call sfree (sp)
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+end
diff --git a/math/gsurfit/gsacpts.gx b/math/gsurfit/gsacpts.gx
new file mode 100644
index 00000000..59a8ae72
--- /dev/null
+++ b/math/gsurfit/gsacpts.gx
@@ -0,0 +1,257 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSACPTS -- Procedure to add a set of points to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# NCOEFF(sf)-vector VECTOR.
+
+$if (datatype == r)
+procedure gsacpts (sf, x, y, z, w, npts, wtflag)
+$else
+procedure dgsacpts (sf, x, y, z, w, npts, wtflag)
+$endif
+
+pointer	sf		# surface descriptor
+PIXEL	x[npts]		# array of x values
+PIXEL	y[npts]		# array of y values
+PIXEL	z[npts]		# data array
+PIXEL	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+
+bool	refsub
+int	i, ii, j, jj, k, l, ll
+int	maxorder, xorder, xxorder, ntimes
+pointer	sp, vzptr, vindex, mzptr, mindex, bxptr, bbxptr, byptr, bbyptr
+pointer	x1, y1, z1, byw, bw
+
+PIXEL	adot$t()
+
+begin
+	# increment the number of points
+	GS_NPTS(sf) = GS_NPTS(sf) + npts
+
+	# remove basis functions calculated by any previous gsrefit call
+	if (GS_XBASIS(sf) != NULL || GS_YBASIS(sf) != NULL) {
+
+	    $if (datatype == r)
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_REAL)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_REAL)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_REAL)
+	    GS_WZ(sf) = NULL
+	    $else
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_DOUBLE)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_DOUBLE)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_DOUBLE)
+	    GS_WZ(sf) = NULL
+	    $endif
+	}
+
+	# calculate weights
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    $if (datatype == r)
+	    call amovkr (1., w, npts)
+	    $else
+	    call amovkd (1.0d0, w, npts)
+	    $endif
+	case WTS_SPACING:
+	    if (npts == 1)
+		$if (datatype == r)
+		w[1] = 1.
+		$else
+		w[1] = 1.0d0
+		$endif
+	    else
+	        w[1] = abs (x[2] - x[1])
+	    do i = 2, npts - 1
+		w[i] = abs (x[i+1] - x[i-1])
+	    if (npts == 1)
+		$if (datatype == r)
+		w[npts] = 1.
+		$else
+		w[npts] = 1.0d0
+		$endif
+	    else
+	        w[npts] = abs (x[npts] - x[npts-1])
+	case WTS_USER:
+	    # user supplied weights
+	default:
+	    $if (datatype == r)
+	    call amovkr (1., w, npts)
+	    $else
+	    call amovkd (1.0d0, w, npts)
+	    $endif
+	}
+
+
+	# allocate space for the basis functions
+	call smark (sp)
+	call salloc (GS_XBASIS(sf), npts * GS_XORDER(sf), TY_PIXEL)
+	call salloc (GS_YBASIS(sf), npts * GS_YORDER(sf), TY_PIXEL)
+
+	# subtract reference value
+	refsub = !(IS_INDEF(GS_XREF(sf)) || IS_INDEF(GS_YREF(sf)) ||
+	    IS_INDEF(GS_ZREF(sf)))
+	if (refsub) {
+	    call salloc (x1, npts, TY_PIXEL)
+	    call salloc (y1, npts, TY_PIXEL)
+	    call salloc (z1, npts, TY_PIXEL)
+	    call asubk$t (x, GS_XREF(sf), Mem$t[x1], npts)
+	    call asubk$t (y, GS_YREF(sf), Mem$t[y1], npts)
+	    call asubk$t (z, GS_ZREF(sf), Mem$t[z1], npts)
+	}
+
+	# calculate the non-zero basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE:
+	    if (refsub) {
+		call $tgs_bleg (Mem$t[x1], npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call $tgs_bleg (Mem$t[y1], npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    } else {
+		call $tgs_bleg (x, npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call $tgs_bleg (y, npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    }
+	case GS_CHEBYSHEV:
+	    if (refsub) {
+		call $tgs_bcheb (Mem$t[x1], npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call $tgs_bcheb (Mem$t[y1], npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    } else {
+		call $tgs_bcheb (x, npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call $tgs_bcheb (y, npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    }
+	case GS_POLYNOMIAL:
+	    if (refsub) {
+		call $tgs_bpol (Mem$t[x1], npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call $tgs_bpol (Mem$t[y1], npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    } else {
+		call $tgs_bpol (x, npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call $tgs_bpol (y, npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    }
+	default:
+	    call error (0, "GSACCUM: Illegal curve type.")
+	}
+
+	# allocate temporary storage space for matrix accumulation
+	$if (datatype == r)
+	call salloc (byw, npts, TY_REAL)
+	call salloc (bw, npts, TY_REAL)
+	$else
+	call salloc (byw, npts, TY_DOUBLE)
+	call salloc (bw, npts, TY_DOUBLE)
+	$endif
+
+	# one index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	mzptr = GS_MATRIX(sf)
+	bxptr = GS_XBASIS(sf)
+	byptr = GS_YBASIS(sf)
+
+	switch (GS_TYPE(sf)) {
+
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    xorder = GS_XORDER(sf)
+	    ntimes = 0
+
+	    do l = 1, GS_YORDER(sf) {
+
+		call amul$t (w, YBASIS(byptr), Mem$t[byw], npts)
+	        bxptr = GS_XBASIS(sf)
+	        do k = 1, xorder {
+	            call amul$t (Mem$t[byw], XBASIS(bxptr), Mem$t[bw], npts) 
+		    vindex = vzptr + k
+	            VECTOR(vindex) = VECTOR(vindex) + adot$t (Mem$t[bw], z,
+		        npts)
+		    bbyptr = byptr
+	            bbxptr = bxptr
+		    xxorder = xorder
+		    jj = k
+		    ll = l
+	            ii = 0
+		    do j = k + ntimes, GS_NCOEFF(sf) {
+		        mindex = mzptr + ii
+		        do i = 1, npts
+		            MATRIX(mindex) = MATRIX(mindex) + Mem$t[bw+i-1] *
+				XBASIS(bbxptr+i-1) * YBASIS(bbyptr+i-1)	
+			if (mod (jj, xxorder) == 0) {
+			    jj = 1
+			    ll = ll + 1
+			    bbxptr = GS_XBASIS(sf)
+			    bbyptr = bbyptr + npts
+			    switch (GS_XTERMS(sf)) {
+			    case GS_XNONE:
+				xxorder = 1
+			    case GS_XHALF:
+				if ((ll + GS_XORDER(sf)) > maxorder)
+		    		    xxorder = xxorder - 1
+			    default:
+				;
+			    }
+			} else {
+			    jj = jj + 1
+			    bbxptr = bbxptr + npts
+			}
+		        ii = ii + 1
+		    }
+		    mzptr = mzptr + GS_NCOEFF(sf)
+		    bxptr = bxptr + npts
+	        }
+
+		vzptr = vzptr + xorder
+		ntimes = ntimes + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+		byptr = byptr + npts
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown curve type.")
+	}
+
+	# release the space
+	call sfree (sp)
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+end
diff --git a/math/gsurfit/gsacptsd.x b/math/gsurfit/gsacptsd.x
new file mode 100644
index 00000000..0b0b1695
--- /dev/null
+++ b/math/gsurfit/gsacptsd.x
@@ -0,0 +1,216 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSACPTS -- Procedure to add a set of points to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# NCOEFF(sf)-vector VECTOR.
+
+procedure dgsacpts (sf, x, y, z, w, npts, wtflag)
+
+pointer	sf		# surface descriptor
+double	x[npts]		# array of x values
+double	y[npts]		# array of y values
+double	z[npts]		# data array
+double	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+
+bool	refsub
+int	i, ii, j, jj, k, l, ll
+int	maxorder, xorder, xxorder, ntimes
+pointer	sp, vzptr, vindex, mzptr, mindex, bxptr, bbxptr, byptr, bbyptr
+pointer	x1, y1, z1, byw, bw
+
+double	adotd()
+
+begin
+	# increment the number of points
+	GS_NPTS(sf) = GS_NPTS(sf) + npts
+
+	# remove basis functions calculated by any previous gsrefit call
+	if (GS_XBASIS(sf) != NULL || GS_YBASIS(sf) != NULL) {
+
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_DOUBLE)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_DOUBLE)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_DOUBLE)
+	    GS_WZ(sf) = NULL
+	}
+
+	# calculate weights
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    call amovkd (1.0d0, w, npts)
+	case WTS_SPACING:
+	    if (npts == 1)
+		w[1] = 1.0d0
+	    else
+	        w[1] = abs (x[2] - x[1])
+	    do i = 2, npts - 1
+		w[i] = abs (x[i+1] - x[i-1])
+	    if (npts == 1)
+		w[npts] = 1.0d0
+	    else
+	        w[npts] = abs (x[npts] - x[npts-1])
+	case WTS_USER:
+	    # user supplied weights
+	default:
+	    call amovkd (1.0d0, w, npts)
+	}
+
+
+	# allocate space for the basis functions
+	call smark (sp)
+	call salloc (GS_XBASIS(sf), npts * GS_XORDER(sf), TY_DOUBLE)
+	call salloc (GS_YBASIS(sf), npts * GS_YORDER(sf), TY_DOUBLE)
+
+	# subtract reference value
+	refsub = !(IS_INDEFD(GS_XREF(sf)) || IS_INDEFD(GS_YREF(sf)) ||
+	    IS_INDEFD(GS_ZREF(sf)))
+	if (refsub) {
+	    call salloc (x1, npts, TY_DOUBLE)
+	    call salloc (y1, npts, TY_DOUBLE)
+	    call salloc (z1, npts, TY_DOUBLE)
+	    call asubkd (x, GS_XREF(sf), Memd[x1], npts)
+	    call asubkd (y, GS_YREF(sf), Memd[y1], npts)
+	    call asubkd (z, GS_ZREF(sf), Memd[z1], npts)
+	}
+
+	# calculate the non-zero basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE:
+	    if (refsub) {
+		call dgs_bleg (Memd[x1], npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call dgs_bleg (Memd[y1], npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    } else {
+		call dgs_bleg (x, npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call dgs_bleg (y, npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    }
+	case GS_CHEBYSHEV:
+	    if (refsub) {
+		call dgs_bcheb (Memd[x1], npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call dgs_bcheb (Memd[y1], npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    } else {
+		call dgs_bcheb (x, npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call dgs_bcheb (y, npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    }
+	case GS_POLYNOMIAL:
+	    if (refsub) {
+		call dgs_bpol (Memd[x1], npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call dgs_bpol (Memd[y1], npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    } else {
+		call dgs_bpol (x, npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call dgs_bpol (y, npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    }
+	default:
+	    call error (0, "GSACCUM: Illegal curve type.")
+	}
+
+	# allocate temporary storage space for matrix accumulation
+	call salloc (byw, npts, TY_DOUBLE)
+	call salloc (bw, npts, TY_DOUBLE)
+
+	# one index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	mzptr = GS_MATRIX(sf)
+	bxptr = GS_XBASIS(sf)
+	byptr = GS_YBASIS(sf)
+
+	switch (GS_TYPE(sf)) {
+
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    xorder = GS_XORDER(sf)
+	    ntimes = 0
+
+	    do l = 1, GS_YORDER(sf) {
+
+		call amuld (w, YBASIS(byptr), Memd[byw], npts)
+	        bxptr = GS_XBASIS(sf)
+	        do k = 1, xorder {
+	            call amuld (Memd[byw], XBASIS(bxptr), Memd[bw], npts) 
+		    vindex = vzptr + k
+	            VECTOR(vindex) = VECTOR(vindex) + adotd (Memd[bw], z,
+		        npts)
+		    bbyptr = byptr
+	            bbxptr = bxptr
+		    xxorder = xorder
+		    jj = k
+		    ll = l
+	            ii = 0
+		    do j = k + ntimes, GS_NCOEFF(sf) {
+		        mindex = mzptr + ii
+		        do i = 1, npts
+		            MATRIX(mindex) = MATRIX(mindex) + Memd[bw+i-1] *
+				XBASIS(bbxptr+i-1) * YBASIS(bbyptr+i-1)	
+			if (mod (jj, xxorder) == 0) {
+			    jj = 1
+			    ll = ll + 1
+			    bbxptr = GS_XBASIS(sf)
+			    bbyptr = bbyptr + npts
+			    switch (GS_XTERMS(sf)) {
+			    case GS_XNONE:
+				xxorder = 1
+			    case GS_XHALF:
+				if ((ll + GS_XORDER(sf)) > maxorder)
+		    		    xxorder = xxorder - 1
+			    default:
+				;
+			    }
+			} else {
+			    jj = jj + 1
+			    bbxptr = bbxptr + npts
+			}
+		        ii = ii + 1
+		    }
+		    mzptr = mzptr + GS_NCOEFF(sf)
+		    bxptr = bxptr + npts
+	        }
+
+		vzptr = vzptr + xorder
+		ntimes = ntimes + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+		byptr = byptr + npts
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown curve type.")
+	}
+
+	# release the space
+	call sfree (sp)
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+end
diff --git a/math/gsurfit/gsacptsr.x b/math/gsurfit/gsacptsr.x
new file mode 100644
index 00000000..705bb8d7
--- /dev/null
+++ b/math/gsurfit/gsacptsr.x
@@ -0,0 +1,216 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSACPTS -- Procedure to add a set of points to the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# NCOEFF(sf)-vector VECTOR.
+
+procedure gsacpts (sf, x, y, z, w, npts, wtflag)
+
+pointer	sf		# surface descriptor
+real	x[npts]		# array of x values
+real	y[npts]		# array of y values
+real	z[npts]		# data array
+real	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+
+bool	refsub
+int	i, ii, j, jj, k, l, ll
+int	maxorder, xorder, xxorder, ntimes
+pointer	sp, vzptr, vindex, mzptr, mindex, bxptr, bbxptr, byptr, bbyptr
+pointer	x1, y1, z1, byw, bw
+
+real	adotr()
+
+begin
+	# increment the number of points
+	GS_NPTS(sf) = GS_NPTS(sf) + npts
+
+	# remove basis functions calculated by any previous gsrefit call
+	if (GS_XBASIS(sf) != NULL || GS_YBASIS(sf) != NULL) {
+
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_REAL)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_REAL)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_REAL)
+	    GS_WZ(sf) = NULL
+	}
+
+	# calculate weights
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    call amovkr (1., w, npts)
+	case WTS_SPACING:
+	    if (npts == 1)
+		w[1] = 1.
+	    else
+	        w[1] = abs (x[2] - x[1])
+	    do i = 2, npts - 1
+		w[i] = abs (x[i+1] - x[i-1])
+	    if (npts == 1)
+		w[npts] = 1.
+	    else
+	        w[npts] = abs (x[npts] - x[npts-1])
+	case WTS_USER:
+	    # user supplied weights
+	default:
+	    call amovkr (1., w, npts)
+	}
+
+
+	# allocate space for the basis functions
+	call smark (sp)
+	call salloc (GS_XBASIS(sf), npts * GS_XORDER(sf), TY_REAL)
+	call salloc (GS_YBASIS(sf), npts * GS_YORDER(sf), TY_REAL)
+
+	# subtract reference value
+	refsub = !(IS_INDEFR(GS_XREF(sf)) || IS_INDEFR(GS_YREF(sf)) ||
+	    IS_INDEFR(GS_ZREF(sf)))
+	if (refsub) {
+	    call salloc (x1, npts, TY_REAL)
+	    call salloc (y1, npts, TY_REAL)
+	    call salloc (z1, npts, TY_REAL)
+	    call asubkr (x, GS_XREF(sf), Memr[x1], npts)
+	    call asubkr (y, GS_YREF(sf), Memr[y1], npts)
+	    call asubkr (z, GS_ZREF(sf), Memr[z1], npts)
+	}
+
+	# calculate the non-zero basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE:
+	    if (refsub) {
+		call rgs_bleg (Memr[x1], npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call rgs_bleg (Memr[y1], npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    } else {
+		call rgs_bleg (x, npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call rgs_bleg (y, npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    }
+	case GS_CHEBYSHEV:
+	    if (refsub) {
+		call rgs_bcheb (Memr[x1], npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call rgs_bcheb (Memr[y1], npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    } else {
+		call rgs_bcheb (x, npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call rgs_bcheb (y, npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    }
+	case GS_POLYNOMIAL:
+	    if (refsub) {
+		call rgs_bpol (Memr[x1], npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call rgs_bpol (Memr[y1], npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    } else {
+		call rgs_bpol (x, npts, GS_XORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+		call rgs_bpol (y, npts, GS_YORDER(sf), GS_YMAXMIN(sf),
+		    GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    }
+	default:
+	    call error (0, "GSACCUM: Illegal curve type.")
+	}
+
+	# allocate temporary storage space for matrix accumulation
+	call salloc (byw, npts, TY_REAL)
+	call salloc (bw, npts, TY_REAL)
+
+	# one index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	mzptr = GS_MATRIX(sf)
+	bxptr = GS_XBASIS(sf)
+	byptr = GS_YBASIS(sf)
+
+	switch (GS_TYPE(sf)) {
+
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    xorder = GS_XORDER(sf)
+	    ntimes = 0
+
+	    do l = 1, GS_YORDER(sf) {
+
+		call amulr (w, YBASIS(byptr), Memr[byw], npts)
+	        bxptr = GS_XBASIS(sf)
+	        do k = 1, xorder {
+	            call amulr (Memr[byw], XBASIS(bxptr), Memr[bw], npts) 
+		    vindex = vzptr + k
+	            VECTOR(vindex) = VECTOR(vindex) + adotr (Memr[bw], z,
+		        npts)
+		    bbyptr = byptr
+	            bbxptr = bxptr
+		    xxorder = xorder
+		    jj = k
+		    ll = l
+	            ii = 0
+		    do j = k + ntimes, GS_NCOEFF(sf) {
+		        mindex = mzptr + ii
+		        do i = 1, npts
+		            MATRIX(mindex) = MATRIX(mindex) + Memr[bw+i-1] *
+				XBASIS(bbxptr+i-1) * YBASIS(bbyptr+i-1)	
+			if (mod (jj, xxorder) == 0) {
+			    jj = 1
+			    ll = ll + 1
+			    bbxptr = GS_XBASIS(sf)
+			    bbyptr = bbyptr + npts
+			    switch (GS_XTERMS(sf)) {
+			    case GS_XNONE:
+				xxorder = 1
+			    case GS_XHALF:
+				if ((ll + GS_XORDER(sf)) > maxorder)
+		    		    xxorder = xxorder - 1
+			    default:
+				;
+			    }
+			} else {
+			    jj = jj + 1
+			    bbxptr = bbxptr + npts
+			}
+		        ii = ii + 1
+		    }
+		    mzptr = mzptr + GS_NCOEFF(sf)
+		    bxptr = bxptr + npts
+	        }
+
+		vzptr = vzptr + xorder
+		ntimes = ntimes + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+		byptr = byptr + npts
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown curve type.")
+	}
+
+	# release the space
+	call sfree (sp)
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+end
diff --git a/math/gsurfit/gsadd.gx b/math/gsurfit/gsadd.gx
new file mode 100644
index 00000000..516f1b1f
--- /dev/null
+++ b/math/gsurfit/gsadd.gx
@@ -0,0 +1,181 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSADD -- Procedure to add the fits from two surfaces together. The surfaces
+# must be the same type and the fit must cover the same range of data in x
+# and y. This is a special function.
+
+$if (datatype == r)
+procedure gsadd (sf1, sf2, sf3)
+$else
+procedure dgsadd (sf1, sf2, sf3)
+$endif
+
+pointer	sf1		# pointer to the first surface
+pointer	sf2		# pointer to the second surface
+pointer	sf3		# pointer to the output surface
+
+int	i, order, nmove1, nmove2, nmove3, maxorder1, maxorder2, maxorder3
+pointer	ptr1, ptr2, ptr3
+bool	fpequal$t()
+
+begin
+	# test for NULL surface
+	if (sf1 == NULL && sf2 == NULL) {
+	    sf3 = NULL
+	    return
+	} else if (sf1 == NULL) {
+	    $if (datatype == r)
+	    call gscopy (sf2, sf3)
+	    $else
+	    call dgscopy (sf2, sf3)
+	    $endif
+	    return
+	} else if (sf2 == NULL) {
+	    $if (datatype == r)
+	    call gscopy (sf1, sf3)
+	    $else
+	    call dgscopy (sf1, sf3)
+	    $endif
+	    return
+	}
+
+	# test that function type is the same
+	if (GS_TYPE(sf1) != GS_TYPE(sf2))
+	    call error (0, "GSADD: Incompatable surface types.")
+
+	# test that mins and maxs are the same
+	if (! fpequal$t (GS_XMIN(sf1), GS_XMIN(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequal$t (GS_XMAX(sf1), GS_XMAX(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequal$t (GS_YMIN(sf1), GS_YMIN(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+	if (! fpequal$t (GS_YMAX(sf1), GS_YMAX(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+
+	# allocate space for the pointer
+	call calloc (sf3, LEN_GSSTRUCT, TY_STRUCT)
+
+	# copy parameters
+	GS_TYPE(sf3) = GS_TYPE(sf1)
+
+	switch (GS_TYPE(sf3)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf3) = max (GS_NXCOEFF(sf1), GS_NXCOEFF(sf2))
+	    GS_XORDER(sf3) = max (GS_XORDER(sf1), GS_XORDER(sf2))
+	    GS_XMIN(sf3) = GS_XMIN(sf1)
+	    GS_XMAX(sf3) = GS_XMAX(sf1)
+	    GS_XRANGE(sf3) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf3) = GS_XMAXMIN(sf1)
+	    GS_NYCOEFF(sf3) = max (GS_NYCOEFF(sf1), GS_NYCOEFF(sf2))
+	    GS_YORDER(sf3) = max (GS_YORDER(sf1), GS_YORDER(sf2))
+	    GS_YMIN(sf3) = GS_YMIN(sf1)
+	    GS_YMAX(sf3) = GS_YMAX(sf1)
+	    GS_YRANGE(sf3) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf3) = GS_YMAXMIN(sf1)
+	    if (GS_XTERMS(sf1) == GS_XTERMS(sf2))
+		GS_XTERMS(sf3) = GS_XTERMS(sf1)
+	    else if (GS_XTERMS(sf1) == GS_XFULL || GS_XTERMS(sf2) == GS_XFULL)
+		GS_XTERMS(sf3) = GS_XFULL
+	    else
+		GS_XTERMS(sf3) = GS_XHALF
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) + GS_NYCOEFF(sf3) - 1
+	    case GS_XHALF:
+		order = min (GS_XORDER(sf3), GS_YORDER(sf3))
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3) - order *
+		    (order - 1) / 2
+	    default:
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3)
+	    }
+	default:
+	    call error (0, "GSADD: Unknown curve type.")
+	}
+
+	# set pointers to NULL
+	GS_XBASIS(sf3) = NULL
+	GS_YBASIS(sf3) = NULL
+	GS_MATRIX(sf3) = NULL
+	GS_CHOFAC(sf3) = NULL
+	GS_VECTOR(sf3) = NULL
+	GS_COEFF(sf3) = NULL
+	GS_WZ(sf3) = NULL
+
+	# calculate the coefficients
+	$if (datatype == r)
+	call calloc (GS_COEFF(sf3), GS_NCOEFF(sf3), TY_REAL)
+	$else
+	call calloc (GS_COEFF(sf3), GS_NCOEFF(sf3), TY_DOUBLE)
+	$endif
+
+	# set up line counters.
+	maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+	maxorder2 = max (GS_XORDER(sf2) + 1, GS_YORDER(sf2) + 1)
+	maxorder3 = max (GS_XORDER(sf3) + 1, GS_YORDER(sf3) + 1)
+
+	# add in the first surface.
+	ptr1 = GS_COEFF(sf1)
+	ptr3 = GS_COEFF(sf3)
+	nmove1 = GS_NXCOEFF(sf1)
+	nmove3 = GS_NXCOEFF(sf3)
+	do i = 1, GS_NYCOEFF(sf1) {
+	    call amov$t (COEFF(ptr1), COEFF(ptr3), nmove1)
+	    ptr1 = ptr1 + nmove1
+	    ptr3 = ptr3 + nmove3
+	    switch (GS_XTERMS(sf1)) {
+	    case GS_XNONE:
+		nmove1 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf1) + 1) > maxorder1)
+		    nmove1 = nmove1 - 1
+	    case GS_XFULL:
+		;
+	    }
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		nmove3 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+		    nmove3 = nmove3 - 1
+	    case GS_XFULL:
+		;
+	    }
+	}
+
+	# add in the second surface.
+	ptr2 = GS_COEFF(sf2)
+	ptr3 = GS_COEFF(sf3)
+	nmove2 = GS_NXCOEFF(sf2)
+	nmove3 = GS_NXCOEFF(sf3)
+	do i = 1, GS_NYCOEFF(sf2) {
+	    call aadd$t (COEFF(ptr3), COEFF(ptr2), COEFF(ptr3), nmove2) 
+	    ptr2 = ptr2 + nmove2
+	    ptr3 = ptr3 + nmove3
+	    switch (GS_XTERMS(sf2)) {
+	    case GS_XNONE:
+		nmove2 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf2) + 1) > maxorder2)
+		    nmove2 = nmove2 - 1
+	    case GS_XFULL:
+		;
+	    }
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		nmove3 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+		    nmove3 = nmove3 - 1
+	    case GS_XFULL:
+		;
+	    }
+	}
+end
diff --git a/math/gsurfit/gsaddd.x b/math/gsurfit/gsaddd.x
new file mode 100644
index 00000000..f637d08a
--- /dev/null
+++ b/math/gsurfit/gsaddd.x
@@ -0,0 +1,161 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSADD -- Procedure to add the fits from two surfaces together. The surfaces
+# must be the same type and the fit must cover the same range of data in x
+# and y. This is a special function.
+
+procedure dgsadd (sf1, sf2, sf3)
+
+pointer	sf1		# pointer to the first surface
+pointer	sf2		# pointer to the second surface
+pointer	sf3		# pointer to the output surface
+
+int	i, order, nmove1, nmove2, nmove3, maxorder1, maxorder2, maxorder3
+pointer	ptr1, ptr2, ptr3
+bool	fpequald()
+
+begin
+	# test for NULL surface
+	if (sf1 == NULL && sf2 == NULL) {
+	    sf3 = NULL
+	    return
+	} else if (sf1 == NULL) {
+	    call dgscopy (sf2, sf3)
+	    return
+	} else if (sf2 == NULL) {
+	    call dgscopy (sf1, sf3)
+	    return
+	}
+
+	# test that function type is the same
+	if (GS_TYPE(sf1) != GS_TYPE(sf2))
+	    call error (0, "GSADD: Incompatable surface types.")
+
+	# test that mins and maxs are the same
+	if (! fpequald (GS_XMIN(sf1), GS_XMIN(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequald (GS_XMAX(sf1), GS_XMAX(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequald (GS_YMIN(sf1), GS_YMIN(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+	if (! fpequald (GS_YMAX(sf1), GS_YMAX(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+
+	# allocate space for the pointer
+	call calloc (sf3, LEN_GSSTRUCT, TY_STRUCT)
+
+	# copy parameters
+	GS_TYPE(sf3) = GS_TYPE(sf1)
+
+	switch (GS_TYPE(sf3)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf3) = max (GS_NXCOEFF(sf1), GS_NXCOEFF(sf2))
+	    GS_XORDER(sf3) = max (GS_XORDER(sf1), GS_XORDER(sf2))
+	    GS_XMIN(sf3) = GS_XMIN(sf1)
+	    GS_XMAX(sf3) = GS_XMAX(sf1)
+	    GS_XRANGE(sf3) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf3) = GS_XMAXMIN(sf1)
+	    GS_NYCOEFF(sf3) = max (GS_NYCOEFF(sf1), GS_NYCOEFF(sf2))
+	    GS_YORDER(sf3) = max (GS_YORDER(sf1), GS_YORDER(sf2))
+	    GS_YMIN(sf3) = GS_YMIN(sf1)
+	    GS_YMAX(sf3) = GS_YMAX(sf1)
+	    GS_YRANGE(sf3) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf3) = GS_YMAXMIN(sf1)
+	    if (GS_XTERMS(sf1) == GS_XTERMS(sf2))
+		GS_XTERMS(sf3) = GS_XTERMS(sf1)
+	    else if (GS_XTERMS(sf1) == GS_XFULL || GS_XTERMS(sf2) == GS_XFULL)
+		GS_XTERMS(sf3) = GS_XFULL
+	    else
+		GS_XTERMS(sf3) = GS_XHALF
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) + GS_NYCOEFF(sf3) - 1
+	    case GS_XHALF:
+		order = min (GS_XORDER(sf3), GS_YORDER(sf3))
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3) - order *
+		    (order - 1) / 2
+	    default:
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3)
+	    }
+	default:
+	    call error (0, "GSADD: Unknown curve type.")
+	}
+
+	# set pointers to NULL
+	GS_XBASIS(sf3) = NULL
+	GS_YBASIS(sf3) = NULL
+	GS_MATRIX(sf3) = NULL
+	GS_CHOFAC(sf3) = NULL
+	GS_VECTOR(sf3) = NULL
+	GS_COEFF(sf3) = NULL
+	GS_WZ(sf3) = NULL
+
+	# calculate the coefficients
+	call calloc (GS_COEFF(sf3), GS_NCOEFF(sf3), TY_DOUBLE)
+
+	# set up line counters.
+	maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+	maxorder2 = max (GS_XORDER(sf2) + 1, GS_YORDER(sf2) + 1)
+	maxorder3 = max (GS_XORDER(sf3) + 1, GS_YORDER(sf3) + 1)
+
+	# add in the first surface.
+	ptr1 = GS_COEFF(sf1)
+	ptr3 = GS_COEFF(sf3)
+	nmove1 = GS_NXCOEFF(sf1)
+	nmove3 = GS_NXCOEFF(sf3)
+	do i = 1, GS_NYCOEFF(sf1) {
+	    call amovd (COEFF(ptr1), COEFF(ptr3), nmove1)
+	    ptr1 = ptr1 + nmove1
+	    ptr3 = ptr3 + nmove3
+	    switch (GS_XTERMS(sf1)) {
+	    case GS_XNONE:
+		nmove1 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf1) + 1) > maxorder1)
+		    nmove1 = nmove1 - 1
+	    case GS_XFULL:
+		;
+	    }
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		nmove3 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+		    nmove3 = nmove3 - 1
+	    case GS_XFULL:
+		;
+	    }
+	}
+
+	# add in the second surface.
+	ptr2 = GS_COEFF(sf2)
+	ptr3 = GS_COEFF(sf3)
+	nmove2 = GS_NXCOEFF(sf2)
+	nmove3 = GS_NXCOEFF(sf3)
+	do i = 1, GS_NYCOEFF(sf2) {
+	    call aaddd (COEFF(ptr3), COEFF(ptr2), COEFF(ptr3), nmove2) 
+	    ptr2 = ptr2 + nmove2
+	    ptr3 = ptr3 + nmove3
+	    switch (GS_XTERMS(sf2)) {
+	    case GS_XNONE:
+		nmove2 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf2) + 1) > maxorder2)
+		    nmove2 = nmove2 - 1
+	    case GS_XFULL:
+		;
+	    }
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		nmove3 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+		    nmove3 = nmove3 - 1
+	    case GS_XFULL:
+		;
+	    }
+	}
+end
diff --git a/math/gsurfit/gsaddr.x b/math/gsurfit/gsaddr.x
new file mode 100644
index 00000000..4df5ee48
--- /dev/null
+++ b/math/gsurfit/gsaddr.x
@@ -0,0 +1,161 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSADD -- Procedure to add the fits from two surfaces together. The surfaces
+# must be the same type and the fit must cover the same range of data in x
+# and y. This is a special function.
+
+procedure gsadd (sf1, sf2, sf3)
+
+pointer	sf1		# pointer to the first surface
+pointer	sf2		# pointer to the second surface
+pointer	sf3		# pointer to the output surface
+
+int	i, order, nmove1, nmove2, nmove3, maxorder1, maxorder2, maxorder3
+pointer	ptr1, ptr2, ptr3
+bool	fpequalr()
+
+begin
+	# test for NULL surface
+	if (sf1 == NULL && sf2 == NULL) {
+	    sf3 = NULL
+	    return
+	} else if (sf1 == NULL) {
+	    call gscopy (sf2, sf3)
+	    return
+	} else if (sf2 == NULL) {
+	    call gscopy (sf1, sf3)
+	    return
+	}
+
+	# test that function type is the same
+	if (GS_TYPE(sf1) != GS_TYPE(sf2))
+	    call error (0, "GSADD: Incompatable surface types.")
+
+	# test that mins and maxs are the same
+	if (! fpequalr (GS_XMIN(sf1), GS_XMIN(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequalr (GS_XMAX(sf1), GS_XMAX(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequalr (GS_YMIN(sf1), GS_YMIN(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+	if (! fpequalr (GS_YMAX(sf1), GS_YMAX(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+
+	# allocate space for the pointer
+	call calloc (sf3, LEN_GSSTRUCT, TY_STRUCT)
+
+	# copy parameters
+	GS_TYPE(sf3) = GS_TYPE(sf1)
+
+	switch (GS_TYPE(sf3)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf3) = max (GS_NXCOEFF(sf1), GS_NXCOEFF(sf2))
+	    GS_XORDER(sf3) = max (GS_XORDER(sf1), GS_XORDER(sf2))
+	    GS_XMIN(sf3) = GS_XMIN(sf1)
+	    GS_XMAX(sf3) = GS_XMAX(sf1)
+	    GS_XRANGE(sf3) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf3) = GS_XMAXMIN(sf1)
+	    GS_NYCOEFF(sf3) = max (GS_NYCOEFF(sf1), GS_NYCOEFF(sf2))
+	    GS_YORDER(sf3) = max (GS_YORDER(sf1), GS_YORDER(sf2))
+	    GS_YMIN(sf3) = GS_YMIN(sf1)
+	    GS_YMAX(sf3) = GS_YMAX(sf1)
+	    GS_YRANGE(sf3) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf3) = GS_YMAXMIN(sf1)
+	    if (GS_XTERMS(sf1) == GS_XTERMS(sf2))
+		GS_XTERMS(sf3) = GS_XTERMS(sf1)
+	    else if (GS_XTERMS(sf1) == GS_XFULL || GS_XTERMS(sf2) == GS_XFULL)
+		GS_XTERMS(sf3) = GS_XFULL
+	    else
+		GS_XTERMS(sf3) = GS_XHALF
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) + GS_NYCOEFF(sf3) - 1
+	    case GS_XHALF:
+		order = min (GS_XORDER(sf3), GS_YORDER(sf3))
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3) - order *
+		    (order - 1) / 2
+	    default:
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3)
+	    }
+	default:
+	    call error (0, "GSADD: Unknown curve type.")
+	}
+
+	# set pointers to NULL
+	GS_XBASIS(sf3) = NULL
+	GS_YBASIS(sf3) = NULL
+	GS_MATRIX(sf3) = NULL
+	GS_CHOFAC(sf3) = NULL
+	GS_VECTOR(sf3) = NULL
+	GS_COEFF(sf3) = NULL
+	GS_WZ(sf3) = NULL
+
+	# calculate the coefficients
+	call calloc (GS_COEFF(sf3), GS_NCOEFF(sf3), TY_REAL)
+
+	# set up line counters.
+	maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+	maxorder2 = max (GS_XORDER(sf2) + 1, GS_YORDER(sf2) + 1)
+	maxorder3 = max (GS_XORDER(sf3) + 1, GS_YORDER(sf3) + 1)
+
+	# add in the first surface.
+	ptr1 = GS_COEFF(sf1)
+	ptr3 = GS_COEFF(sf3)
+	nmove1 = GS_NXCOEFF(sf1)
+	nmove3 = GS_NXCOEFF(sf3)
+	do i = 1, GS_NYCOEFF(sf1) {
+	    call amovr (COEFF(ptr1), COEFF(ptr3), nmove1)
+	    ptr1 = ptr1 + nmove1
+	    ptr3 = ptr3 + nmove3
+	    switch (GS_XTERMS(sf1)) {
+	    case GS_XNONE:
+		nmove1 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf1) + 1) > maxorder1)
+		    nmove1 = nmove1 - 1
+	    case GS_XFULL:
+		;
+	    }
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		nmove3 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+		    nmove3 = nmove3 - 1
+	    case GS_XFULL:
+		;
+	    }
+	}
+
+	# add in the second surface.
+	ptr2 = GS_COEFF(sf2)
+	ptr3 = GS_COEFF(sf3)
+	nmove2 = GS_NXCOEFF(sf2)
+	nmove3 = GS_NXCOEFF(sf3)
+	do i = 1, GS_NYCOEFF(sf2) {
+	    call aaddr (COEFF(ptr3), COEFF(ptr2), COEFF(ptr3), nmove2) 
+	    ptr2 = ptr2 + nmove2
+	    ptr3 = ptr3 + nmove3
+	    switch (GS_XTERMS(sf2)) {
+	    case GS_XNONE:
+		nmove2 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf2) + 1) > maxorder2)
+		    nmove2 = nmove2 - 1
+	    case GS_XFULL:
+		;
+	    }
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		nmove3 = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+		    nmove3 = nmove3 - 1
+	    case GS_XFULL:
+		;
+	    }
+	}
+end
diff --git a/math/gsurfit/gscoeff.gx b/math/gsurfit/gscoeff.gx
new file mode 100644
index 00000000..84c495f7
--- /dev/null
+++ b/math/gsurfit/gscoeff.gx
@@ -0,0 +1,31 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSCOEFF -- Procedure to fetch the number and magnitude of the coefficients.
+# If the GS_XTERMS(sf) = GS_XBI (YES) then the number of coefficients will be
+# (GS_NXCOEFF(sf) * GS_NYCOEFF(sf)); if GS_XTERMS is GS_XTRI then the number
+# of coefficients will be (GS_NXCOEFF(sf) *  GS_NYCOEFF(sf) - order *
+# (order - 1) / 2) where order is the minimum of the x and yorders;  if
+# GS_XTERMS(sf) = GS_XNONE then the number of coefficients will be
+# (GS_NXCOEFF(sf) + GS_NYCOEFF(sf) - 1).
+
+$if (datatype == r)
+procedure gscoeff (sf, coeff, ncoeff)
+$else
+procedure dgscoeff (sf, coeff, ncoeff)
+$endif
+
+pointer	sf		# pointer to the surface fitting descriptor
+PIXEL	coeff[ARB]	# the coefficients of the fit
+int	ncoeff		# the number of coefficients
+
+begin
+	# calculate the number of coefficients
+	ncoeff = GS_NCOEFF(sf)
+	call amov$t (COEFF(GS_COEFF(sf)), coeff, ncoeff)
+end
diff --git a/math/gsurfit/gscoeffd.x b/math/gsurfit/gscoeffd.x
new file mode 100644
index 00000000..2090eec1
--- /dev/null
+++ b/math/gsurfit/gscoeffd.x
@@ -0,0 +1,23 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "dgsurfitdef.h"
+
+# GSCOEFF -- Procedure to fetch the number and magnitude of the coefficients.
+# If the GS_XTERMS(sf) = GS_XBI (YES) then the number of coefficients will be
+# (GS_NXCOEFF(sf) * GS_NYCOEFF(sf)); if GS_XTERMS is GS_XTRI then the number
+# of coefficients will be (GS_NXCOEFF(sf) *  GS_NYCOEFF(sf) - order *
+# (order - 1) / 2) where order is the minimum of the x and yorders;  if
+# GS_XTERMS(sf) = GS_XNONE then the number of coefficients will be
+# (GS_NXCOEFF(sf) + GS_NYCOEFF(sf) - 1).
+
+procedure dgscoeff (sf, coeff, ncoeff)
+
+pointer	sf		# pointer to the surface fitting descriptor
+double	coeff[ARB]	# the coefficients of the fit
+int	ncoeff		# the number of coefficients
+
+begin
+	# calculate the number of coefficients
+	ncoeff = GS_NCOEFF(sf)
+	call amovd (COEFF(GS_COEFF(sf)), coeff, ncoeff)
+end
diff --git a/math/gsurfit/gscoeffr.x b/math/gsurfit/gscoeffr.x
new file mode 100644
index 00000000..96cccce5
--- /dev/null
+++ b/math/gsurfit/gscoeffr.x
@@ -0,0 +1,23 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "gsurfitdef.h"
+
+# GSCOEFF -- Procedure to fetch the number and magnitude of the coefficients.
+# If the GS_XTERMS(sf) = GS_XBI (YES) then the number of coefficients will be
+# (GS_NXCOEFF(sf) * GS_NYCOEFF(sf)); if GS_XTERMS is GS_XTRI then the number
+# of coefficients will be (GS_NXCOEFF(sf) *  GS_NYCOEFF(sf) - order *
+# (order - 1) / 2) where order is the minimum of the x and yorders;  if
+# GS_XTERMS(sf) = GS_XNONE then the number of coefficients will be
+# (GS_NXCOEFF(sf) + GS_NYCOEFF(sf) - 1).
+
+procedure gscoeff (sf, coeff, ncoeff)
+
+pointer	sf		# pointer to the surface fitting descriptor
+real	coeff[ARB]	# the coefficients of the fit
+int	ncoeff		# the number of coefficients
+
+begin
+	# calculate the number of coefficients
+	ncoeff = GS_NCOEFF(sf)
+	call amovr (COEFF(GS_COEFF(sf)), coeff, ncoeff)
+end
diff --git a/math/gsurfit/gscopy.gx b/math/gsurfit/gscopy.gx
new file mode 100644
index 00000000..9f0a6d09
--- /dev/null
+++ b/math/gsurfit/gscopy.gx
@@ -0,0 +1,69 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSCOPY -- Procedure to copy the fit from one surface into another.
+
+$if (datatype == r)
+procedure gscopy (sf1, sf2)
+$else
+procedure dgscopy (sf1, sf2)
+$endif
+
+pointer	sf1		# pointer to original surface
+pointer	sf2		# pointer to the new surface
+
+begin
+	if (sf1 == NULL) {
+	    sf2 = NULL
+	    return
+	}
+
+	# allocate space for new surface descriptor
+	call calloc (sf2, LEN_GSSTRUCT, TY_STRUCT)
+
+	# copy surface independent parameters 
+	GS_TYPE(sf2) = GS_TYPE(sf1)
+
+	switch (GS_TYPE(sf1)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf2) = GS_NXCOEFF(sf1)
+	    GS_XORDER(sf2) = GS_XORDER(sf1)
+	    GS_XMIN(sf2) = GS_XMIN(sf1)
+	    GS_XMAX(sf2) = GS_XMAX(sf1)
+	    GS_XRANGE(sf2) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf2) = GS_XMAXMIN(sf1)
+	    GS_NYCOEFF(sf2) = GS_NYCOEFF(sf1)
+	    GS_YORDER(sf2) = GS_YORDER(sf1)
+	    GS_YMIN(sf2) = GS_YMIN(sf1)
+	    GS_YMAX(sf2) = GS_YMAX(sf1)
+	    GS_YRANGE(sf2) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf2) = GS_YMAXMIN(sf1) 
+	    GS_XTERMS(sf2) = GS_XTERMS(sf1)
+	    GS_NCOEFF(sf2) = GS_NCOEFF(sf1)
+	default:
+	    call error (0, "GSCOPY: Unknown surface type.")
+	}
+
+	# set space pointers to NULL
+	GS_XBASIS(sf2) = NULL
+	GS_YBASIS(sf2) = NULL
+	GS_MATRIX(sf2) = NULL
+	GS_CHOFAC(sf2) = NULL
+	GS_VECTOR(sf2) = NULL
+	GS_COEFF(sf2) = NULL
+	GS_WZ(sf2) = NULL
+
+	# restore coefficient array
+	$if (datatype == r)
+	call calloc (GS_COEFF(sf2), GS_NCOEFF(sf2), TY_REAL)
+	$else
+	call calloc (GS_COEFF(sf2), GS_NCOEFF(sf2), TY_DOUBLE)
+	$endif
+	call amov$t (COEFF(GS_COEFF(sf1)), COEFF(GS_COEFF(sf2)), GS_NCOEFF(sf2))
+end
diff --git a/math/gsurfit/gscopyd.x b/math/gsurfit/gscopyd.x
new file mode 100644
index 00000000..b5b93912
--- /dev/null
+++ b/math/gsurfit/gscopyd.x
@@ -0,0 +1,57 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSCOPY -- Procedure to copy the fit from one surface into another.
+
+procedure dgscopy (sf1, sf2)
+
+pointer	sf1		# pointer to original surface
+pointer	sf2		# pointer to the new surface
+
+begin
+	if (sf1 == NULL) {
+	    sf2 = NULL
+	    return
+	}
+
+	# allocate space for new surface descriptor
+	call calloc (sf2, LEN_GSSTRUCT, TY_STRUCT)
+
+	# copy surface independent parameters 
+	GS_TYPE(sf2) = GS_TYPE(sf1)
+
+	switch (GS_TYPE(sf1)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf2) = GS_NXCOEFF(sf1)
+	    GS_XORDER(sf2) = GS_XORDER(sf1)
+	    GS_XMIN(sf2) = GS_XMIN(sf1)
+	    GS_XMAX(sf2) = GS_XMAX(sf1)
+	    GS_XRANGE(sf2) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf2) = GS_XMAXMIN(sf1)
+	    GS_NYCOEFF(sf2) = GS_NYCOEFF(sf1)
+	    GS_YORDER(sf2) = GS_YORDER(sf1)
+	    GS_YMIN(sf2) = GS_YMIN(sf1)
+	    GS_YMAX(sf2) = GS_YMAX(sf1)
+	    GS_YRANGE(sf2) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf2) = GS_YMAXMIN(sf1) 
+	    GS_XTERMS(sf2) = GS_XTERMS(sf1)
+	    GS_NCOEFF(sf2) = GS_NCOEFF(sf1)
+	default:
+	    call error (0, "GSCOPY: Unknown surface type.")
+	}
+
+	# set space pointers to NULL
+	GS_XBASIS(sf2) = NULL
+	GS_YBASIS(sf2) = NULL
+	GS_MATRIX(sf2) = NULL
+	GS_CHOFAC(sf2) = NULL
+	GS_VECTOR(sf2) = NULL
+	GS_COEFF(sf2) = NULL
+	GS_WZ(sf2) = NULL
+
+	# restore coefficient array
+	call calloc (GS_COEFF(sf2), GS_NCOEFF(sf2), TY_DOUBLE)
+	call amovd (COEFF(GS_COEFF(sf1)), COEFF(GS_COEFF(sf2)), GS_NCOEFF(sf2))
+end
diff --git a/math/gsurfit/gscopyr.x b/math/gsurfit/gscopyr.x
new file mode 100644
index 00000000..251b5327
--- /dev/null
+++ b/math/gsurfit/gscopyr.x
@@ -0,0 +1,57 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSCOPY -- Procedure to copy the fit from one surface into another.
+
+procedure gscopy (sf1, sf2)
+
+pointer	sf1		# pointer to original surface
+pointer	sf2		# pointer to the new surface
+
+begin
+	if (sf1 == NULL) {
+	    sf2 = NULL
+	    return
+	}
+
+	# allocate space for new surface descriptor
+	call calloc (sf2, LEN_GSSTRUCT, TY_STRUCT)
+
+	# copy surface independent parameters 
+	GS_TYPE(sf2) = GS_TYPE(sf1)
+
+	switch (GS_TYPE(sf1)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf2) = GS_NXCOEFF(sf1)
+	    GS_XORDER(sf2) = GS_XORDER(sf1)
+	    GS_XMIN(sf2) = GS_XMIN(sf1)
+	    GS_XMAX(sf2) = GS_XMAX(sf1)
+	    GS_XRANGE(sf2) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf2) = GS_XMAXMIN(sf1)
+	    GS_NYCOEFF(sf2) = GS_NYCOEFF(sf1)
+	    GS_YORDER(sf2) = GS_YORDER(sf1)
+	    GS_YMIN(sf2) = GS_YMIN(sf1)
+	    GS_YMAX(sf2) = GS_YMAX(sf1)
+	    GS_YRANGE(sf2) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf2) = GS_YMAXMIN(sf1) 
+	    GS_XTERMS(sf2) = GS_XTERMS(sf1)
+	    GS_NCOEFF(sf2) = GS_NCOEFF(sf1)
+	default:
+	    call error (0, "GSCOPY: Unknown surface type.")
+	}
+
+	# set space pointers to NULL
+	GS_XBASIS(sf2) = NULL
+	GS_YBASIS(sf2) = NULL
+	GS_MATRIX(sf2) = NULL
+	GS_CHOFAC(sf2) = NULL
+	GS_VECTOR(sf2) = NULL
+	GS_COEFF(sf2) = NULL
+	GS_WZ(sf2) = NULL
+
+	# restore coefficient array
+	call calloc (GS_COEFF(sf2), GS_NCOEFF(sf2), TY_REAL)
+	call amovr (COEFF(GS_COEFF(sf1)), COEFF(GS_COEFF(sf2)), GS_NCOEFF(sf2))
+end
diff --git a/math/gsurfit/gsder.gx b/math/gsurfit/gsder.gx
new file mode 100644
index 00000000..e0ee95bd
--- /dev/null
+++ b/math/gsurfit/gsder.gx
@@ -0,0 +1,264 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSDER -- Procedure to calculate a new surface which is a derivative of
+# the previous surface
+
+$if (datatype == r)
+procedure gsder (sf1, x, y, zfit, npts, nxd, nyd)
+$else
+procedure dgsder (sf1, x, y, zfit, npts, nxd, nyd)
+$endif
+
+pointer	sf1		# pointer to the previous surface
+PIXEL	x[npts]		# x values
+PIXEL	y[npts]		# y values
+PIXEL	zfit[npts]	# fitted values
+int	npts		# number of points
+int	nxd, nyd	# order of the derivatives in x and y
+
+PIXEL	norm
+int	ncoeff, nxder, nyder, i, j
+int	order, maxorder1, maxorder2, nmove1, nmove2
+pointer	sf2, sp, coeff, ptr1, ptr2
+
+begin
+	if (sf1 == NULL)
+	    return
+
+	if (nxd < 0 || nyd < 0)
+	    call error (0, "GSDER: Order of derivatives cannot be < 0")
+
+	if (nxd == 0 && nyd == 0) {
+	    $if (datatype == r)
+	    call gsvector (sf1, x, y, zfit, npts)
+	    $else
+	    call dgsvector (sf1, x, y, zfit, npts)
+	    $endif
+	    return
+	}
+
+	# allocate space for new surface
+	call calloc (sf2, LEN_GSSTRUCT, TY_STRUCT)
+
+	# check the order of the derivatives and return 0 if the order is
+	# high
+	nxder = min (nxd, GS_NXCOEFF(sf1))
+	nyder = min (nyd, GS_NYCOEFF(sf1))
+	if (nxder >= GS_NXCOEFF(sf1) && nyder >= GS_NYCOEFF(sf1))
+	    call amovk$t (PIXEL(0.0), zfit, npts)
+
+	# set up new surface
+	GS_TYPE(sf2) = GS_TYPE(sf1)
+
+	# set the derivative surface parameters
+	switch (GS_TYPE(sf2)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    GS_XTERMS(sf2) = GS_XTERMS(sf1)
+
+	    # find the order of the new surface
+	    switch (GS_XTERMS(sf2)) {
+	    case GS_XNONE: 
+		if (nxder > 0 && nyder > 0) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = 1
+		} else if (nxder > 0) {
+		    GS_NXCOEFF(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
+		    GS_XORDER(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = GS_NXCOEFF(sf2)
+		} else if (nyder > 0) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
+		    GS_YORDER(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
+		    GS_NCOEFF(sf2) = GS_NYCOEFF(sf2)
+		}
+
+	    case GS_XHALF:
+		if ((nxder >= GS_NXCOEFF(sf1)) || (nyder >= GS_NYCOEFF(sf1)) ||
+		    (nxder + nyder) >= max (GS_NXCOEFF(sf1),
+		    GS_NYCOEFF(sf1))) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = 1
+		} else {
+		    maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+		    order = max (1, min (maxorder1 - 1 - nyder - nxder,
+		        GS_NXCOEFF(sf1) - nxder))
+	            GS_NXCOEFF(sf2) = order
+	            GS_XORDER(sf2) = order
+		    order = max (1, min (maxorder1 - 1 - nyder - nxder,
+		        GS_NYCOEFF(sf1) - nyder))
+	            GS_NYCOEFF(sf2) = order
+	            GS_YORDER(sf2) = order
+		    order = min (GS_XORDER(sf2), GS_YORDER(sf2))
+		    GS_NCOEFF(sf2) = GS_NXCOEFF(sf2) * GS_NYCOEFF(sf2)  -
+			order * (order - 1) / 2
+		}
+
+	    default:
+		if (nxder >= GS_NXCOEFF(sf1) || nyder >= GS_NYCOEFF(sf1)) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = 1
+		} else {
+	            GS_NXCOEFF(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
+	            GS_XORDER(sf2) = max (1, GS_XORDER(sf1) - nxder)
+	            GS_NYCOEFF(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
+	            GS_YORDER(sf2) = max (1, GS_YORDER(sf1) - nyder)
+		    GS_NCOEFF(sf2) = GS_NXCOEFF(sf2) * GS_NYCOEFF(sf2) 
+		}
+	    }
+
+	    # define the data limits
+	    GS_XMIN(sf2) = GS_XMIN(sf1)
+	    GS_XMAX(sf2) = GS_XMAX(sf1)
+	    GS_XRANGE(sf2) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf2) = GS_XMAXMIN(sf1)
+	    GS_YMIN(sf2) = GS_YMIN(sf1)
+	    GS_YMAX(sf2) = GS_YMAX(sf1)
+	    GS_YRANGE(sf2) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf2) = GS_YMAXMIN(sf1)
+
+	default:
+	    call error (0, "GSDER: Unknown surface type.")
+	}
+
+	# set remaining surface pointers to NULL
+	GS_XBASIS(sf2) = NULL
+	GS_YBASIS(sf2) = NULL
+	GS_MATRIX(sf2) = NULL
+	GS_CHOFAC(sf2) = NULL
+	GS_VECTOR(sf2) = NULL
+	GS_COEFF(sf2) = NULL
+	GS_WZ(sf2) = NULL
+
+	# allocate space for coefficients
+	call calloc (GS_COEFF(sf2), GS_NCOEFF(sf2), TY_PIXEL)
+
+	# get coefficients
+	call smark (sp)
+	call salloc (coeff, GS_NCOEFF(sf1), TY_PIXEL)
+	$if (datatype == r)
+	call gscoeff (sf1, Mem$t[coeff], ncoeff)
+	$else
+	call dgscoeff (sf1, Mem$t[coeff], ncoeff)
+	$endif
+
+	# compute the new coefficients
+	switch (GS_XTERMS(sf2)) {
+	case GS_XFULL:
+	    if (nxder >= GS_NXCOEFF(sf1) || nyder >= GS_NYCOEFF(sf1))
+		COEFF(GS_COEFF(sf2)) = 0.
+	    else {
+	        ptr2 = GS_COEFF(sf2) + (GS_NYCOEFF(sf2) - 1) * GS_NXCOEFF(sf2)
+	        ptr1 = coeff + (GS_NYCOEFF(sf1) - 1) * GS_NXCOEFF(sf1)
+	        do i = GS_NYCOEFF(sf1), nyder + 1, -1 {
+		    call amov$t (Mem$t[ptr1+nxder], COEFF(ptr2),
+		        GS_NXCOEFF(sf2))
+	            ptr2 = ptr2 - GS_NXCOEFF(sf2)
+	            ptr1 = ptr1 - GS_NXCOEFF(sf1)
+	        }
+	    }
+
+	case GS_XHALF:
+	    if ((nxder >= GS_NXCOEFF(sf1)) || (nyder >= GS_NYCOEFF(sf1)) ||
+	        (nxder + nyder) >= max (GS_NXCOEFF(sf1), GS_NYCOEFF(sf1)))
+		COEFF(GS_COEFF(sf2)) = 0.
+	    else {
+	        maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+	        maxorder2 = max (GS_XORDER(sf2) + 1, GS_YORDER(sf2) + 1)
+	        ptr2 = GS_COEFF(sf2) + GS_NCOEFF(sf2)
+	        ptr1 = coeff + GS_NCOEFF(sf1)
+	        do i = GS_NYCOEFF(sf1), nyder + 1, -1 {
+		    nmove1 = max (0, min (maxorder1 - i, GS_NXCOEFF(sf1)))
+		    nmove2 = max (0, min (maxorder2 - i + nyder,
+		        GS_NXCOEFF(sf2)))
+		    ptr1 = ptr1 - nmove1
+		    ptr2 = ptr2 - nmove2
+		    call amov$t (Mem$t[ptr1+nxder], COEFF(ptr2), nmove2)
+	        }
+	    }
+
+	default:
+	    if (nxder > 0 && nyder > 0)
+		COEFF(GS_COEFF(sf2)) = 0.
+	    else if (nxder > 0) { 
+		if (nxder >= GS_NXCOEFF(sf1))
+		    COEFF(GS_COEFF(sf2)) = 0.
+		else {
+		    ptr1 = coeff
+		    ptr2 = GS_COEFF(sf2) + GS_NCOEFF(sf2) - 1
+		    do j = GS_NXCOEFF(sf1), nxder + 1, -1 {
+		        COEFF(ptr2) = Mem$t[ptr1+j-1]
+		        ptr2 = ptr2 - 1
+		    }
+		}
+	    } else if (nyder > 0) {
+		if (nyder >= GS_NYCOEFF(sf1))
+		    COEFF(GS_COEFF(sf2)) = 0.
+		else {
+		    ptr1 = coeff + GS_NCOEFF(sf1) - 1
+		    ptr2 = GS_COEFF(sf2)
+		    do i = GS_NYCOEFF(sf1), nyder + 1, -1
+		        ptr1 = ptr1 - 1
+		    call amov$t (Mem$t[ptr1+1], COEFF(ptr2), GS_NCOEFF(sf2))
+		}
+	    }
+	}
+
+	# evaluate the derivatives
+	switch (GS_TYPE(sf2)) {
+	case GS_POLYNOMIAL:
+	    call $tgs_derpoly (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
+	        GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
+		nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
+		GS_YRANGE(sf2))
+
+	case GS_CHEBYSHEV:
+	    call $tgs_dercheb (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
+	        GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
+	        nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
+	        GS_YRANGE(sf2))
+
+	case GS_LEGENDRE:
+	    call $tgs_derleg (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
+	        GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
+	        nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
+	        GS_YRANGE(sf2))
+
+	default:
+	    call error (0, "GSVECTOR: Unknown surface type.")
+	}
+
+        # Normalize.
+        if (GS_TYPE(sf2) != GS_POLYNOMIAL) {
+            norm = (2. / (GS_XMAX(sf2) - GS_XMIN(sf2))) ** nxder * (2. /
+                (GS_YMAX(sf2) - GS_YMIN(sf2))) ** nyder
+            call amulk$t (zfit, norm, zfit, npts)
+        }
+
+	# free the space
+	$if (datatype == r)
+	call gsfree (sf2)
+	$else
+	call dgsfree (sf2)
+	$endif
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gsderd.x b/math/gsurfit/gsderd.x
new file mode 100644
index 00000000..851b7b9b
--- /dev/null
+++ b/math/gsurfit/gsderd.x
@@ -0,0 +1,244 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSDER -- Procedure to calculate a new surface which is a derivative of
+# the previous surface
+
+procedure dgsder (sf1, x, y, zfit, npts, nxd, nyd)
+
+pointer	sf1		# pointer to the previous surface
+double	x[npts]		# x values
+double	y[npts]		# y values
+double	zfit[npts]	# fitted values
+int	npts		# number of points
+int	nxd, nyd	# order of the derivatives in x and y
+
+double	norm
+int	ncoeff, nxder, nyder, i, j
+int	order, maxorder1, maxorder2, nmove1, nmove2
+pointer	sf2, sp, coeff, ptr1, ptr2
+
+begin
+	if (sf1 == NULL)
+	    return
+
+	if (nxd < 0 || nyd < 0)
+	    call error (0, "GSDER: Order of derivatives cannot be < 0")
+
+	if (nxd == 0 && nyd == 0) {
+	    call dgsvector (sf1, x, y, zfit, npts)
+	    return
+	}
+
+	# allocate space for new surface
+	call calloc (sf2, LEN_GSSTRUCT, TY_STRUCT)
+
+	# check the order of the derivatives and return 0 if the order is
+	# high
+	nxder = min (nxd, GS_NXCOEFF(sf1))
+	nyder = min (nyd, GS_NYCOEFF(sf1))
+	if (nxder >= GS_NXCOEFF(sf1) && nyder >= GS_NYCOEFF(sf1))
+	    call amovkd (double(0.0), zfit, npts)
+
+	# set up new surface
+	GS_TYPE(sf2) = GS_TYPE(sf1)
+
+	# set the derivative surface parameters
+	switch (GS_TYPE(sf2)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    GS_XTERMS(sf2) = GS_XTERMS(sf1)
+
+	    # find the order of the new surface
+	    switch (GS_XTERMS(sf2)) {
+	    case GS_XNONE: 
+		if (nxder > 0 && nyder > 0) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = 1
+		} else if (nxder > 0) {
+		    GS_NXCOEFF(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
+		    GS_XORDER(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = GS_NXCOEFF(sf2)
+		} else if (nyder > 0) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
+		    GS_YORDER(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
+		    GS_NCOEFF(sf2) = GS_NYCOEFF(sf2)
+		}
+
+	    case GS_XHALF:
+		if ((nxder >= GS_NXCOEFF(sf1)) || (nyder >= GS_NYCOEFF(sf1)) ||
+		    (nxder + nyder) >= max (GS_NXCOEFF(sf1),
+		    GS_NYCOEFF(sf1))) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = 1
+		} else {
+		    maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+		    order = max (1, min (maxorder1 - 1 - nyder - nxder,
+		        GS_NXCOEFF(sf1) - nxder))
+	            GS_NXCOEFF(sf2) = order
+	            GS_XORDER(sf2) = order
+		    order = max (1, min (maxorder1 - 1 - nyder - nxder,
+		        GS_NYCOEFF(sf1) - nyder))
+	            GS_NYCOEFF(sf2) = order
+	            GS_YORDER(sf2) = order
+		    order = min (GS_XORDER(sf2), GS_YORDER(sf2))
+		    GS_NCOEFF(sf2) = GS_NXCOEFF(sf2) * GS_NYCOEFF(sf2)  -
+			order * (order - 1) / 2
+		}
+
+	    default:
+		if (nxder >= GS_NXCOEFF(sf1) || nyder >= GS_NYCOEFF(sf1)) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = 1
+		} else {
+	            GS_NXCOEFF(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
+	            GS_XORDER(sf2) = max (1, GS_XORDER(sf1) - nxder)
+	            GS_NYCOEFF(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
+	            GS_YORDER(sf2) = max (1, GS_YORDER(sf1) - nyder)
+		    GS_NCOEFF(sf2) = GS_NXCOEFF(sf2) * GS_NYCOEFF(sf2) 
+		}
+	    }
+
+	    # define the data limits
+	    GS_XMIN(sf2) = GS_XMIN(sf1)
+	    GS_XMAX(sf2) = GS_XMAX(sf1)
+	    GS_XRANGE(sf2) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf2) = GS_XMAXMIN(sf1)
+	    GS_YMIN(sf2) = GS_YMIN(sf1)
+	    GS_YMAX(sf2) = GS_YMAX(sf1)
+	    GS_YRANGE(sf2) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf2) = GS_YMAXMIN(sf1)
+
+	default:
+	    call error (0, "GSDER: Unknown surface type.")
+	}
+
+	# set remaining surface pointers to NULL
+	GS_XBASIS(sf2) = NULL
+	GS_YBASIS(sf2) = NULL
+	GS_MATRIX(sf2) = NULL
+	GS_CHOFAC(sf2) = NULL
+	GS_VECTOR(sf2) = NULL
+	GS_COEFF(sf2) = NULL
+	GS_WZ(sf2) = NULL
+
+	# allocate space for coefficients
+	call calloc (GS_COEFF(sf2), GS_NCOEFF(sf2), TY_DOUBLE)
+
+	# get coefficients
+	call smark (sp)
+	call salloc (coeff, GS_NCOEFF(sf1), TY_DOUBLE)
+	call dgscoeff (sf1, Memd[coeff], ncoeff)
+
+	# compute the new coefficients
+	switch (GS_XTERMS(sf2)) {
+	case GS_XFULL:
+	    if (nxder >= GS_NXCOEFF(sf1) || nyder >= GS_NYCOEFF(sf1))
+		COEFF(GS_COEFF(sf2)) = 0.
+	    else {
+	        ptr2 = GS_COEFF(sf2) + (GS_NYCOEFF(sf2) - 1) * GS_NXCOEFF(sf2)
+	        ptr1 = coeff + (GS_NYCOEFF(sf1) - 1) * GS_NXCOEFF(sf1)
+	        do i = GS_NYCOEFF(sf1), nyder + 1, -1 {
+		    call amovd (Memd[ptr1+nxder], COEFF(ptr2),
+		        GS_NXCOEFF(sf2))
+	            ptr2 = ptr2 - GS_NXCOEFF(sf2)
+	            ptr1 = ptr1 - GS_NXCOEFF(sf1)
+	        }
+	    }
+
+	case GS_XHALF:
+	    if ((nxder >= GS_NXCOEFF(sf1)) || (nyder >= GS_NYCOEFF(sf1)) ||
+	        (nxder + nyder) >= max (GS_NXCOEFF(sf1), GS_NYCOEFF(sf1)))
+		COEFF(GS_COEFF(sf2)) = 0.
+	    else {
+	        maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+	        maxorder2 = max (GS_XORDER(sf2) + 1, GS_YORDER(sf2) + 1)
+	        ptr2 = GS_COEFF(sf2) + GS_NCOEFF(sf2)
+	        ptr1 = coeff + GS_NCOEFF(sf1)
+	        do i = GS_NYCOEFF(sf1), nyder + 1, -1 {
+		    nmove1 = max (0, min (maxorder1 - i, GS_NXCOEFF(sf1)))
+		    nmove2 = max (0, min (maxorder2 - i + nyder,
+		        GS_NXCOEFF(sf2)))
+		    ptr1 = ptr1 - nmove1
+		    ptr2 = ptr2 - nmove2
+		    call amovd (Memd[ptr1+nxder], COEFF(ptr2), nmove2)
+	        }
+	    }
+
+	default:
+	    if (nxder > 0 && nyder > 0)
+		COEFF(GS_COEFF(sf2)) = 0.
+	    else if (nxder > 0) { 
+		if (nxder >= GS_NXCOEFF(sf1))
+		    COEFF(GS_COEFF(sf2)) = 0.
+		else {
+		    ptr1 = coeff
+		    ptr2 = GS_COEFF(sf2) + GS_NCOEFF(sf2) - 1
+		    do j = GS_NXCOEFF(sf1), nxder + 1, -1 {
+		        COEFF(ptr2) = Memd[ptr1+j-1]
+		        ptr2 = ptr2 - 1
+		    }
+		}
+	    } else if (nyder > 0) {
+		if (nyder >= GS_NYCOEFF(sf1))
+		    COEFF(GS_COEFF(sf2)) = 0.
+		else {
+		    ptr1 = coeff + GS_NCOEFF(sf1) - 1
+		    ptr2 = GS_COEFF(sf2)
+		    do i = GS_NYCOEFF(sf1), nyder + 1, -1
+		        ptr1 = ptr1 - 1
+		    call amovd (Memd[ptr1+1], COEFF(ptr2), GS_NCOEFF(sf2))
+		}
+	    }
+	}
+
+	# evaluate the derivatives
+	switch (GS_TYPE(sf2)) {
+	case GS_POLYNOMIAL:
+	    call dgs_derpoly (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
+	        GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
+		nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
+		GS_YRANGE(sf2))
+
+	case GS_CHEBYSHEV:
+	    call dgs_dercheb (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
+	        GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
+	        nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
+	        GS_YRANGE(sf2))
+
+	case GS_LEGENDRE:
+	    call dgs_derleg (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
+	        GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
+	        nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
+	        GS_YRANGE(sf2))
+
+	default:
+	    call error (0, "GSVECTOR: Unknown surface type.")
+	}
+
+        # Normalize.
+        if (GS_TYPE(sf2) != GS_POLYNOMIAL) {
+            norm = (2. / (GS_XMAX(sf2) - GS_XMIN(sf2))) ** nxder * (2. /
+                (GS_YMAX(sf2) - GS_YMIN(sf2))) ** nyder
+            call amulkd (zfit, norm, zfit, npts)
+        }
+
+	# free the space
+	call dgsfree (sf2)
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gsderr.x b/math/gsurfit/gsderr.x
new file mode 100644
index 00000000..00409c0b
--- /dev/null
+++ b/math/gsurfit/gsderr.x
@@ -0,0 +1,244 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSDER -- Procedure to calculate a new surface which is a derivative of
+# the previous surface
+
+procedure gsder (sf1, x, y, zfit, npts, nxd, nyd)
+
+pointer	sf1		# pointer to the previous surface
+real	x[npts]		# x values
+real	y[npts]		# y values
+real	zfit[npts]	# fitted values
+int	npts		# number of points
+int	nxd, nyd	# order of the derivatives in x and y
+
+real	norm
+int	ncoeff, nxder, nyder, i, j
+int	order, maxorder1, maxorder2, nmove1, nmove2
+pointer	sf2, sp, coeff, ptr1, ptr2
+
+begin
+	if (sf1 == NULL)
+	    return
+
+	if (nxd < 0 || nyd < 0)
+	    call error (0, "GSDER: Order of derivatives cannot be < 0")
+
+	if (nxd == 0 && nyd == 0) {
+	    call gsvector (sf1, x, y, zfit, npts)
+	    return
+	}
+
+	# allocate space for new surface
+	call calloc (sf2, LEN_GSSTRUCT, TY_STRUCT)
+
+	# check the order of the derivatives and return 0 if the order is
+	# high
+	nxder = min (nxd, GS_NXCOEFF(sf1))
+	nyder = min (nyd, GS_NYCOEFF(sf1))
+	if (nxder >= GS_NXCOEFF(sf1) && nyder >= GS_NYCOEFF(sf1))
+	    call amovkr (real(0.0), zfit, npts)
+
+	# set up new surface
+	GS_TYPE(sf2) = GS_TYPE(sf1)
+
+	# set the derivative surface parameters
+	switch (GS_TYPE(sf2)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    GS_XTERMS(sf2) = GS_XTERMS(sf1)
+
+	    # find the order of the new surface
+	    switch (GS_XTERMS(sf2)) {
+	    case GS_XNONE: 
+		if (nxder > 0 && nyder > 0) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = 1
+		} else if (nxder > 0) {
+		    GS_NXCOEFF(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
+		    GS_XORDER(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = GS_NXCOEFF(sf2)
+		} else if (nyder > 0) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
+		    GS_YORDER(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
+		    GS_NCOEFF(sf2) = GS_NYCOEFF(sf2)
+		}
+
+	    case GS_XHALF:
+		if ((nxder >= GS_NXCOEFF(sf1)) || (nyder >= GS_NYCOEFF(sf1)) ||
+		    (nxder + nyder) >= max (GS_NXCOEFF(sf1),
+		    GS_NYCOEFF(sf1))) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = 1
+		} else {
+		    maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+		    order = max (1, min (maxorder1 - 1 - nyder - nxder,
+		        GS_NXCOEFF(sf1) - nxder))
+	            GS_NXCOEFF(sf2) = order
+	            GS_XORDER(sf2) = order
+		    order = max (1, min (maxorder1 - 1 - nyder - nxder,
+		        GS_NYCOEFF(sf1) - nyder))
+	            GS_NYCOEFF(sf2) = order
+	            GS_YORDER(sf2) = order
+		    order = min (GS_XORDER(sf2), GS_YORDER(sf2))
+		    GS_NCOEFF(sf2) = GS_NXCOEFF(sf2) * GS_NYCOEFF(sf2)  -
+			order * (order - 1) / 2
+		}
+
+	    default:
+		if (nxder >= GS_NXCOEFF(sf1) || nyder >= GS_NYCOEFF(sf1)) {
+		    GS_NXCOEFF(sf2) = 1
+		    GS_XORDER(sf2) = 1
+		    GS_NYCOEFF(sf2) = 1
+		    GS_YORDER(sf2) = 1
+		    GS_NCOEFF(sf2) = 1
+		} else {
+	            GS_NXCOEFF(sf2) = max (1, GS_NXCOEFF(sf1) - nxder)
+	            GS_XORDER(sf2) = max (1, GS_XORDER(sf1) - nxder)
+	            GS_NYCOEFF(sf2) = max (1, GS_NYCOEFF(sf1) - nyder)
+	            GS_YORDER(sf2) = max (1, GS_YORDER(sf1) - nyder)
+		    GS_NCOEFF(sf2) = GS_NXCOEFF(sf2) * GS_NYCOEFF(sf2) 
+		}
+	    }
+
+	    # define the data limits
+	    GS_XMIN(sf2) = GS_XMIN(sf1)
+	    GS_XMAX(sf2) = GS_XMAX(sf1)
+	    GS_XRANGE(sf2) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf2) = GS_XMAXMIN(sf1)
+	    GS_YMIN(sf2) = GS_YMIN(sf1)
+	    GS_YMAX(sf2) = GS_YMAX(sf1)
+	    GS_YRANGE(sf2) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf2) = GS_YMAXMIN(sf1)
+
+	default:
+	    call error (0, "GSDER: Unknown surface type.")
+	}
+
+	# set remaining surface pointers to NULL
+	GS_XBASIS(sf2) = NULL
+	GS_YBASIS(sf2) = NULL
+	GS_MATRIX(sf2) = NULL
+	GS_CHOFAC(sf2) = NULL
+	GS_VECTOR(sf2) = NULL
+	GS_COEFF(sf2) = NULL
+	GS_WZ(sf2) = NULL
+
+	# allocate space for coefficients
+	call calloc (GS_COEFF(sf2), GS_NCOEFF(sf2), TY_REAL)
+
+	# get coefficients
+	call smark (sp)
+	call salloc (coeff, GS_NCOEFF(sf1), TY_REAL)
+	call gscoeff (sf1, Memr[coeff], ncoeff)
+
+	# compute the new coefficients
+	switch (GS_XTERMS(sf2)) {
+	case GS_XFULL:
+	    if (nxder >= GS_NXCOEFF(sf1) || nyder >= GS_NYCOEFF(sf1))
+		COEFF(GS_COEFF(sf2)) = 0.
+	    else {
+	        ptr2 = GS_COEFF(sf2) + (GS_NYCOEFF(sf2) - 1) * GS_NXCOEFF(sf2)
+	        ptr1 = coeff + (GS_NYCOEFF(sf1) - 1) * GS_NXCOEFF(sf1)
+	        do i = GS_NYCOEFF(sf1), nyder + 1, -1 {
+		    call amovr (Memr[ptr1+nxder], COEFF(ptr2),
+		        GS_NXCOEFF(sf2))
+	            ptr2 = ptr2 - GS_NXCOEFF(sf2)
+	            ptr1 = ptr1 - GS_NXCOEFF(sf1)
+	        }
+	    }
+
+	case GS_XHALF:
+	    if ((nxder >= GS_NXCOEFF(sf1)) || (nyder >= GS_NYCOEFF(sf1)) ||
+	        (nxder + nyder) >= max (GS_NXCOEFF(sf1), GS_NYCOEFF(sf1)))
+		COEFF(GS_COEFF(sf2)) = 0.
+	    else {
+	        maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+	        maxorder2 = max (GS_XORDER(sf2) + 1, GS_YORDER(sf2) + 1)
+	        ptr2 = GS_COEFF(sf2) + GS_NCOEFF(sf2)
+	        ptr1 = coeff + GS_NCOEFF(sf1)
+	        do i = GS_NYCOEFF(sf1), nyder + 1, -1 {
+		    nmove1 = max (0, min (maxorder1 - i, GS_NXCOEFF(sf1)))
+		    nmove2 = max (0, min (maxorder2 - i + nyder,
+		        GS_NXCOEFF(sf2)))
+		    ptr1 = ptr1 - nmove1
+		    ptr2 = ptr2 - nmove2
+		    call amovr (Memr[ptr1+nxder], COEFF(ptr2), nmove2)
+	        }
+	    }
+
+	default:
+	    if (nxder > 0 && nyder > 0)
+		COEFF(GS_COEFF(sf2)) = 0.
+	    else if (nxder > 0) { 
+		if (nxder >= GS_NXCOEFF(sf1))
+		    COEFF(GS_COEFF(sf2)) = 0.
+		else {
+		    ptr1 = coeff
+		    ptr2 = GS_COEFF(sf2) + GS_NCOEFF(sf2) - 1
+		    do j = GS_NXCOEFF(sf1), nxder + 1, -1 {
+		        COEFF(ptr2) = Memr[ptr1+j-1]
+		        ptr2 = ptr2 - 1
+		    }
+		}
+	    } else if (nyder > 0) {
+		if (nyder >= GS_NYCOEFF(sf1))
+		    COEFF(GS_COEFF(sf2)) = 0.
+		else {
+		    ptr1 = coeff + GS_NCOEFF(sf1) - 1
+		    ptr2 = GS_COEFF(sf2)
+		    do i = GS_NYCOEFF(sf1), nyder + 1, -1
+		        ptr1 = ptr1 - 1
+		    call amovr (Memr[ptr1+1], COEFF(ptr2), GS_NCOEFF(sf2))
+		}
+	    }
+	}
+
+	# evaluate the derivatives
+	switch (GS_TYPE(sf2)) {
+	case GS_POLYNOMIAL:
+	    call rgs_derpoly (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
+	        GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
+		nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
+		GS_YRANGE(sf2))
+
+	case GS_CHEBYSHEV:
+	    call rgs_dercheb (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
+	        GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
+	        nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
+	        GS_YRANGE(sf2))
+
+	case GS_LEGENDRE:
+	    call rgs_derleg (COEFF(GS_COEFF(sf2)), x, y, zfit, npts,
+	        GS_XTERMS(sf2), GS_XORDER(sf2), GS_YORDER(sf2), nxder,
+	        nyder, GS_XMAXMIN(sf2), GS_XRANGE(sf2), GS_YMAXMIN(sf2),
+	        GS_YRANGE(sf2))
+
+	default:
+	    call error (0, "GSVECTOR: Unknown surface type.")
+	}
+
+        # Normalize.
+        if (GS_TYPE(sf2) != GS_POLYNOMIAL) {
+            norm = (2. / (GS_XMAX(sf2) - GS_XMIN(sf2))) ** nxder * (2. /
+                (GS_YMAX(sf2) - GS_YMIN(sf2))) ** nyder
+            call amulkr (zfit, norm, zfit, npts)
+        }
+
+	# free the space
+	call gsfree (sf2)
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gserrors.gx b/math/gsurfit/gserrors.gx
new file mode 100644
index 00000000..5f78cfab
--- /dev/null
+++ b/math/gsurfit/gserrors.gx
@@ -0,0 +1,90 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+define	COV	Mem$t[P2P($1)]	# element of COV
+
+# GSERRORS -- Procedure to calculate the reduced chi-squared of the fit
+# and the standard deviations of the coefficients. First the variance
+# and the reduced chi-squared of the fit are estimated. If these two
+# quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+$if (datatype == r)
+procedure gserrors (sf, z, w, zfit, chisqr, errors)
+$else
+procedure dgserrors (sf, z, w, zfit, chisqr, errors)
+$endif
+
+pointer	sf		# curve descriptor
+PIXEL	z[ARB]		# data points
+PIXEL	w[ARB]		# array of weights
+PIXEL	zfit[ARB]	# fitted data points
+PIXEL	chisqr		# reduced chi-squared of fit
+PIXEL	errors[ARB]	# errors in coefficients
+
+int	i, nfree
+PIXEL	variance, chisq, hold
+pointer	sp, covptr
+
+begin
+	# allocate space for covariance vector
+	call smark (sp)
+	$if (datatype == r)
+	call salloc (covptr, GS_NCOEFF(sf), TY_REAL)
+	$else
+	call salloc (covptr, GS_NCOEFF(sf), TY_DOUBLE)
+	$endif
+
+	# estimate the variance and chi-squared of the fit
+	variance = 0.
+	chisq = 0.
+	do i = 1, GS_NPTS(sf) {
+	    hold = (z[i] - zfit[i]) ** 2
+	    variance = variance + hold
+	    chisq = chisq + hold * w[i]
+	}
+
+	# calculate the reduced chi-squared
+	nfree = GS_NPTS(sf) - GS_NCOEFF(sf)
+	if (nfree  > 0)
+	    chisqr = chisq / nfree
+	else
+	    chisqr = 0.
+
+	# if the variance equals the reduced chi_squared as in the
+	# case of uniform weights then scale the errors in the coefficients
+	# by the variance not the reduced chi-squared
+
+	if (abs (chisq - variance) <= DELTA)
+	    if (nfree > 0)
+	        variance = chisq / nfree
+	    else
+		variance = 0.
+	else
+	    variance = 1.
+
+	# calculate the  errors in the coefficients
+	# the inverse of MATRIX is calculated column by column
+	# the error of the j-th coefficient is the j-th element of the
+	# j-th column of the inverse matrix
+
+	do i = 1, GS_NCOEFF(sf) {
+	    call aclr$t (COV(covptr), GS_NCOEFF(sf))
+	    COV(covptr+i-1) = 1.
+	    call $tgschoslv (CHOFAC(GS_CHOFAC(sf)), GS_NCOEFF(sf),
+	        GS_NCOEFF(sf), COV(covptr), COV(covptr))
+	    if (COV(covptr+i-1) >= 0.)
+	        errors[i] = sqrt (COV(covptr+i-1) * variance)
+	    else
+		errors[i] = 0.
+	}
+
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gserrorsd.x b/math/gsurfit/gserrorsd.x
new file mode 100644
index 00000000..6ebdc87e
--- /dev/null
+++ b/math/gsurfit/gserrorsd.x
@@ -0,0 +1,78 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include "dgsurfitdef.h"
+
+define	COV	Memd[P2P($1)]	# element of COV
+
+# GSERRORS -- Procedure to calculate the reduced chi-squared of the fit
+# and the standard deviations of the coefficients. First the variance
+# and the reduced chi-squared of the fit are estimated. If these two
+# quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+procedure dgserrors (sf, z, w, zfit, chisqr, errors)
+
+pointer	sf		# curve descriptor
+double	z[ARB]		# data points
+double	w[ARB]		# array of weights
+double	zfit[ARB]	# fitted data points
+double	chisqr		# reduced chi-squared of fit
+double	errors[ARB]	# errors in coefficients
+
+int	i, nfree
+double	variance, chisq, hold
+pointer	sp, covptr
+
+begin
+	# allocate space for covariance vector
+	call smark (sp)
+	call salloc (covptr, GS_NCOEFF(sf), TY_DOUBLE)
+
+	# estimate the variance and chi-squared of the fit
+	variance = 0.
+	chisq = 0.
+	do i = 1, GS_NPTS(sf) {
+	    hold = (z[i] - zfit[i]) ** 2
+	    variance = variance + hold
+	    chisq = chisq + hold * w[i]
+	}
+
+	# calculate the reduced chi-squared
+	nfree = GS_NPTS(sf) - GS_NCOEFF(sf)
+	if (nfree  > 0)
+	    chisqr = chisq / nfree
+	else
+	    chisqr = 0.
+
+	# if the variance equals the reduced chi_squared as in the
+	# case of uniform weights then scale the errors in the coefficients
+	# by the variance not the reduced chi-squared
+
+	if (abs (chisq - variance) <= DELTA)
+	    if (nfree > 0)
+	        variance = chisq / nfree
+	    else
+		variance = 0.
+	else
+	    variance = 1.
+
+	# calculate the  errors in the coefficients
+	# the inverse of MATRIX is calculated column by column
+	# the error of the j-th coefficient is the j-th element of the
+	# j-th column of the inverse matrix
+
+	do i = 1, GS_NCOEFF(sf) {
+	    call aclrd (COV(covptr), GS_NCOEFF(sf))
+	    COV(covptr+i-1) = 1.
+	    call dgschoslv (CHOFAC(GS_CHOFAC(sf)), GS_NCOEFF(sf),
+	        GS_NCOEFF(sf), COV(covptr), COV(covptr))
+	    if (COV(covptr+i-1) >= 0.)
+	        errors[i] = sqrt (COV(covptr+i-1) * variance)
+	    else
+		errors[i] = 0.
+	}
+
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gserrorsr.x b/math/gsurfit/gserrorsr.x
new file mode 100644
index 00000000..594dff29
--- /dev/null
+++ b/math/gsurfit/gserrorsr.x
@@ -0,0 +1,78 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include "gsurfitdef.h"
+
+define	COV	Memr[P2P($1)]	# element of COV
+
+# GSERRORS -- Procedure to calculate the reduced chi-squared of the fit
+# and the standard deviations of the coefficients. First the variance
+# and the reduced chi-squared of the fit are estimated. If these two
+# quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+procedure gserrors (sf, z, w, zfit, chisqr, errors)
+
+pointer	sf		# curve descriptor
+real	z[ARB]		# data points
+real	w[ARB]		# array of weights
+real	zfit[ARB]	# fitted data points
+real	chisqr		# reduced chi-squared of fit
+real	errors[ARB]	# errors in coefficients
+
+int	i, nfree
+real	variance, chisq, hold
+pointer	sp, covptr
+
+begin
+	# allocate space for covariance vector
+	call smark (sp)
+	call salloc (covptr, GS_NCOEFF(sf), TY_REAL)
+
+	# estimate the variance and chi-squared of the fit
+	variance = 0.
+	chisq = 0.
+	do i = 1, GS_NPTS(sf) {
+	    hold = (z[i] - zfit[i]) ** 2
+	    variance = variance + hold
+	    chisq = chisq + hold * w[i]
+	}
+
+	# calculate the reduced chi-squared
+	nfree = GS_NPTS(sf) - GS_NCOEFF(sf)
+	if (nfree  > 0)
+	    chisqr = chisq / nfree
+	else
+	    chisqr = 0.
+
+	# if the variance equals the reduced chi_squared as in the
+	# case of uniform weights then scale the errors in the coefficients
+	# by the variance not the reduced chi-squared
+
+	if (abs (chisq - variance) <= DELTA)
+	    if (nfree > 0)
+	        variance = chisq / nfree
+	    else
+		variance = 0.
+	else
+	    variance = 1.
+
+	# calculate the  errors in the coefficients
+	# the inverse of MATRIX is calculated column by column
+	# the error of the j-th coefficient is the j-th element of the
+	# j-th column of the inverse matrix
+
+	do i = 1, GS_NCOEFF(sf) {
+	    call aclrr (COV(covptr), GS_NCOEFF(sf))
+	    COV(covptr+i-1) = 1.
+	    call rgschoslv (CHOFAC(GS_CHOFAC(sf)), GS_NCOEFF(sf),
+	        GS_NCOEFF(sf), COV(covptr), COV(covptr))
+	    if (COV(covptr+i-1) >= 0.)
+	        errors[i] = sqrt (COV(covptr+i-1) * variance)
+	    else
+		errors[i] = 0.
+	}
+
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gseval.gx b/math/gsurfit/gseval.gx
new file mode 100644
index 00000000..d57d21c7
--- /dev/null
+++ b/math/gsurfit/gseval.gx
@@ -0,0 +1,104 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSEVAL -- Procedure to evaluate the fitted surface at a single point.
+# The GS_NCOEFF(sf) coefficients are stored in the vector COEFF.
+
+$if (datatype == r)
+real procedure gseval (sf, x, y)
+$else
+double procedure dgseval (sf, x, y)
+$endif
+
+pointer	sf		# pointer to surface descriptor structure
+PIXEL	x		# x value
+PIXEL	y		# y value
+
+PIXEL	sum, accum
+int	i, ii, k, maxorder, xorder
+pointer	sp, xb, xzb, yb, yzb, czptr
+errchk	smark, salloc, sfree
+
+begin
+	call smark (sp)
+
+	# allocate space for the basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    $if (datatype == r)
+	    call salloc (xb, GS_NXCOEFF(sf), TY_REAL)
+	    call salloc (yb, GS_NYCOEFF(sf), TY_REAL)
+	    $else
+	    call salloc (xb, GS_NXCOEFF(sf), TY_DOUBLE)
+	    call salloc (yb, GS_NYCOEFF(sf), TY_DOUBLE)
+	    $endif
+	    xzb = xb - 1
+	    yzb = yb - 1
+	    czptr = GS_COEFF(sf) - 1
+	default:
+	    call error (0, "GSEVAL: Unknown curve type.")
+	}
+
+	# calculate the basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_CHEBYSHEV:
+	    call $tgs_b1cheb (x, GS_NXCOEFF(sf), GS_XMAXMIN(sf), GS_XRANGE(sf),
+		XBS(xb))
+	    call $tgs_b1cheb (y, GS_NYCOEFF(sf), GS_YMAXMIN(sf), GS_YRANGE(sf),
+		YBS(yb))
+	case GS_LEGENDRE:
+	    call $tgs_b1leg (x, GS_NXCOEFF(sf), GS_XMAXMIN(sf), GS_XRANGE(sf),
+		XBS(xb))
+	    call $tgs_b1leg (y, GS_NYCOEFF(sf), GS_YMAXMIN(sf), GS_YRANGE(sf),
+		YBS(yb))
+	case GS_POLYNOMIAL:
+	    call $tgs_b1pol (x, GS_NXCOEFF(sf), GS_XMAXMIN(sf), GS_XRANGE(sf),
+		XBS(xb))
+	    call $tgs_b1pol (y, GS_NYCOEFF(sf), GS_YMAXMIN(sf), GS_YRANGE(sf),
+		YBS(yb))
+	default:
+	    call error (0, "GSEVAL: Unknown surface type.")
+	}
+
+	# initialize accumulator
+	# basis functions
+	sum = 0.
+
+	# loop over y basis functions
+	maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	xorder = GS_XORDER(sf)
+	ii = 1
+	do i = 1, GS_YORDER(sf) {
+
+	    # loop over the x basis functions
+	    accum = 0.
+	    do k = 1, xorder {
+		accum = accum + COEFF(czptr+ii) * XBS(xzb+k) 
+		ii = ii + 1
+	    }
+	    accum = accum * YBS(yzb+i)
+	    sum = sum + accum
+
+	    # elements of COEFF where neither k = 1 or i = 1
+	    # are not calculated if GS_XTERMS(sf) = NO
+	    switch (GS_XTERMS(sf)) {
+	    case GS_XNONE:
+		xorder = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf) + 1) > maxorder)
+		    xorder = xorder - 1
+	    default:
+		;
+	    }
+	}
+
+	call sfree (sp)
+
+	return (sum)
+end
diff --git a/math/gsurfit/gsevald.x b/math/gsurfit/gsevald.x
new file mode 100644
index 00000000..e7909d91
--- /dev/null
+++ b/math/gsurfit/gsevald.x
@@ -0,0 +1,91 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSEVAL -- Procedure to evaluate the fitted surface at a single point.
+# The GS_NCOEFF(sf) coefficients are stored in the vector COEFF.
+
+double procedure dgseval (sf, x, y)
+
+pointer	sf		# pointer to surface descriptor structure
+double	x		# x value
+double	y		# y value
+
+double	sum, accum
+int	i, ii, k, maxorder, xorder
+pointer	sp, xb, xzb, yb, yzb, czptr
+errchk	smark, salloc, sfree
+
+begin
+	call smark (sp)
+
+	# allocate space for the basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    call salloc (xb, GS_NXCOEFF(sf), TY_DOUBLE)
+	    call salloc (yb, GS_NYCOEFF(sf), TY_DOUBLE)
+	    xzb = xb - 1
+	    yzb = yb - 1
+	    czptr = GS_COEFF(sf) - 1
+	default:
+	    call error (0, "GSEVAL: Unknown curve type.")
+	}
+
+	# calculate the basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_CHEBYSHEV:
+	    call dgs_b1cheb (x, GS_NXCOEFF(sf), GS_XMAXMIN(sf), GS_XRANGE(sf),
+		XBS(xb))
+	    call dgs_b1cheb (y, GS_NYCOEFF(sf), GS_YMAXMIN(sf), GS_YRANGE(sf),
+		YBS(yb))
+	case GS_LEGENDRE:
+	    call dgs_b1leg (x, GS_NXCOEFF(sf), GS_XMAXMIN(sf), GS_XRANGE(sf),
+		XBS(xb))
+	    call dgs_b1leg (y, GS_NYCOEFF(sf), GS_YMAXMIN(sf), GS_YRANGE(sf),
+		YBS(yb))
+	case GS_POLYNOMIAL:
+	    call dgs_b1pol (x, GS_NXCOEFF(sf), GS_XMAXMIN(sf), GS_XRANGE(sf),
+		XBS(xb))
+	    call dgs_b1pol (y, GS_NYCOEFF(sf), GS_YMAXMIN(sf), GS_YRANGE(sf),
+		YBS(yb))
+	default:
+	    call error (0, "GSEVAL: Unknown surface type.")
+	}
+
+	# initialize accumulator
+	# basis functions
+	sum = 0.
+
+	# loop over y basis functions
+	maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	xorder = GS_XORDER(sf)
+	ii = 1
+	do i = 1, GS_YORDER(sf) {
+
+	    # loop over the x basis functions
+	    accum = 0.
+	    do k = 1, xorder {
+		accum = accum + COEFF(czptr+ii) * XBS(xzb+k) 
+		ii = ii + 1
+	    }
+	    accum = accum * YBS(yzb+i)
+	    sum = sum + accum
+
+	    # elements of COEFF where neither k = 1 or i = 1
+	    # are not calculated if GS_XTERMS(sf) = NO
+	    switch (GS_XTERMS(sf)) {
+	    case GS_XNONE:
+		xorder = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf) + 1) > maxorder)
+		    xorder = xorder - 1
+	    default:
+		;
+	    }
+	}
+
+	call sfree (sp)
+
+	return (sum)
+end
diff --git a/math/gsurfit/gsevalr.x b/math/gsurfit/gsevalr.x
new file mode 100644
index 00000000..738e9915
--- /dev/null
+++ b/math/gsurfit/gsevalr.x
@@ -0,0 +1,91 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSEVAL -- Procedure to evaluate the fitted surface at a single point.
+# The GS_NCOEFF(sf) coefficients are stored in the vector COEFF.
+
+real procedure gseval (sf, x, y)
+
+pointer	sf		# pointer to surface descriptor structure
+real	x		# x value
+real	y		# y value
+
+real	sum, accum
+int	i, ii, k, maxorder, xorder
+pointer	sp, xb, xzb, yb, yzb, czptr
+errchk	smark, salloc, sfree
+
+begin
+	call smark (sp)
+
+	# allocate space for the basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    call salloc (xb, GS_NXCOEFF(sf), TY_REAL)
+	    call salloc (yb, GS_NYCOEFF(sf), TY_REAL)
+	    xzb = xb - 1
+	    yzb = yb - 1
+	    czptr = GS_COEFF(sf) - 1
+	default:
+	    call error (0, "GSEVAL: Unknown curve type.")
+	}
+
+	# calculate the basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_CHEBYSHEV:
+	    call rgs_b1cheb (x, GS_NXCOEFF(sf), GS_XMAXMIN(sf), GS_XRANGE(sf),
+		XBS(xb))
+	    call rgs_b1cheb (y, GS_NYCOEFF(sf), GS_YMAXMIN(sf), GS_YRANGE(sf),
+		YBS(yb))
+	case GS_LEGENDRE:
+	    call rgs_b1leg (x, GS_NXCOEFF(sf), GS_XMAXMIN(sf), GS_XRANGE(sf),
+		XBS(xb))
+	    call rgs_b1leg (y, GS_NYCOEFF(sf), GS_YMAXMIN(sf), GS_YRANGE(sf),
+		YBS(yb))
+	case GS_POLYNOMIAL:
+	    call rgs_b1pol (x, GS_NXCOEFF(sf), GS_XMAXMIN(sf), GS_XRANGE(sf),
+		XBS(xb))
+	    call rgs_b1pol (y, GS_NYCOEFF(sf), GS_YMAXMIN(sf), GS_YRANGE(sf),
+		YBS(yb))
+	default:
+	    call error (0, "GSEVAL: Unknown surface type.")
+	}
+
+	# initialize accumulator
+	# basis functions
+	sum = 0.
+
+	# loop over y basis functions
+	maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	xorder = GS_XORDER(sf)
+	ii = 1
+	do i = 1, GS_YORDER(sf) {
+
+	    # loop over the x basis functions
+	    accum = 0.
+	    do k = 1, xorder {
+		accum = accum + COEFF(czptr+ii) * XBS(xzb+k) 
+		ii = ii + 1
+	    }
+	    accum = accum * YBS(yzb+i)
+	    sum = sum + accum
+
+	    # elements of COEFF where neither k = 1 or i = 1
+	    # are not calculated if GS_XTERMS(sf) = NO
+	    switch (GS_XTERMS(sf)) {
+	    case GS_XNONE:
+		xorder = 1
+	    case GS_XHALF:
+		if ((i + GS_XORDER(sf) + 1) > maxorder)
+		    xorder = xorder - 1
+	    default:
+		;
+	    }
+	}
+
+	call sfree (sp)
+
+	return (sum)
+end
diff --git a/math/gsurfit/gsfit.gx b/math/gsurfit/gsfit.gx
new file mode 100644
index 00000000..60251596
--- /dev/null
+++ b/math/gsurfit/gsfit.gx
@@ -0,0 +1,49 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSFIT -- Procedure to solve the normal equations for a surface.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# GS_NCOEFF(sf)-vector VECTOR. The Cholesky factorization of MATRIX
+# is calculated and stored in CHOFAC. Forward and back substitution
+# is used to solve for the GS_NCOEFF(sf)-vector COEFF.
+
+$if (datatype == r)
+procedure gsfit (sf, x, y, z, w, npts, wtflag, ier)
+$else
+procedure dgsfit (sf, x, y, z, w, npts, wtflag, ier)
+$endif
+
+pointer	sf		# surface descriptor
+PIXEL	x[npts]		# array of x values
+PIXEL	y[npts]		# array of y values
+PIXEL	z[npts]		# data array
+PIXEL	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+begin
+	$if (datatype == r)
+	    call gszero (sf)
+	    call gsacpts (sf, x, y, z, w, npts, wtflag)
+	    call gssolve (sf, ier)
+	$else
+	    call dgszero (sf)
+	    call dgsacpts (sf, x, y, z, w, npts, wtflag)
+	    call dgssolve (sf, ier)
+	$endif
+end
diff --git a/math/gsurfit/gsfit1.gx b/math/gsurfit/gsfit1.gx
new file mode 100644
index 00000000..4e7341e4
--- /dev/null
+++ b/math/gsurfit/gsfit1.gx
@@ -0,0 +1,117 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSFIT1 -- Procedure to solve the normal equations for a surface.
+#
+# This version modifies the fitting matrix to remove the first
+# term from the fitting.  For the polynomial functions this means
+# constraining the constant term to be zero.  Note that the first
+# coefficent is still returned but with a value of zero.
+
+$if (datatype == r)
+procedure gsfit1 (sf, x, y, z, w, npts, wtflag, ier)
+$else
+procedure dgsfit1 (sf, x, y, z, w, npts, wtflag, ier)
+$endif
+
+pointer	sf		# surface descriptor
+PIXEL	x[npts]		# array of x values
+PIXEL	y[npts]		# array of y values
+PIXEL	z[npts]		# data array
+PIXEL	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+begin
+	$if (datatype == r)
+	    call gszero (sf)
+	    call gsacpts (sf, x, y, z, w, npts, wtflag)
+	    call gssolve1 (sf, ier)
+	$else
+	    call dgszero (sf)
+	    call dgsacpts (sf, x, y, z, w, npts, wtflag)
+	    call dgssolve1 (sf, ier)
+	$endif
+end
+
+
+# GSSOLVE1 -- Solve the matrix normal equations of the form ca = b for
+# a, where c is a symmetric, positive semi-definite, banded matrix with
+# GS_NXCOEFF(sf) * GS_NYCOEFF(sf) rows and a and b are GS_NXCOEFF(sf) *
+# GS_NYCOEFF(sf)-vectors.  Initially c is stored in the matrix MATRIX and b
+# is stored in VECTOR.  The Cholesky factorization of MATRIX is calculated
+# and stored in CHOFAC.  Finally the coefficients are calculated by forward
+# and back substitution and stored in COEFF.
+#
+# This version modifies the fitting matrix to remove the first
+# term from the fitting.  For the polynomial functions this means
+# constraining the constant term to be zero.  Note that the first
+# coefficent is still returned but with a value of zero.
+
+$if (datatype == r)
+procedure gssolve1 (sf, ier)
+$else
+procedure dgssolve1 (sf, ier)
+$endif
+
+pointer	sf 		# curve descriptor
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+int	i, ncoeff, offset
+pointer	sp, vector, matrix
+
+begin
+
+	# test for number of degrees of freedom
+	offset = 1
+	ncoeff = GS_NCOEFF(sf) - offset
+	ier = OK
+	i = GS_NPTS(sf) - ncoeff
+	if (i < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# allocate working space for the reduced vector and matrix
+	call smark (sp)
+	call salloc (vector, ncoeff, TY_PIXEL)
+	call salloc (matrix, ncoeff*ncoeff, TY_PIXEL)
+
+	# eliminate the first term from the vector and matrix
+	call amov$t (VECTOR(GS_VECTOR(sf)+offset), Mem$t[vector], ncoeff)
+	do i = 0, ncoeff-1
+	    call amov$t (MATRIX(GS_MATRIX(sf)+(i+offset)*GS_NCOEFF(sf)),
+		Mem$t[matrix+i*ncoeff], ncoeff)
+
+	# solve for the coefficients.
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    # calculate the Cholesky factorization of the data matrix
+	    call $tgschofac (Memd[matrix], ncoeff, ncoeff,
+	        CHOFAC(GS_CHOFAC(sf)), ier)
+
+	    # solve for the coefficients by forward and back substitution
+	    COEFF(GS_COEFF(sf)) = 0.
+	    call $tgschoslv (CHOFAC(GS_CHOFAC(sf)), ncoeff, ncoeff,
+	        Memd[vector], COEFF(GS_COEFF(sf)+offset))
+
+	default:
+	    call error (0, "GSSOLVE1: Illegal surface type.")
+	}
+
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gsfit1d.x b/math/gsurfit/gsfit1d.x
new file mode 100644
index 00000000..8937103f
--- /dev/null
+++ b/math/gsurfit/gsfit1d.x
@@ -0,0 +1,99 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSFIT1 -- Procedure to solve the normal equations for a surface.
+#
+# This version modifies the fitting matrix to remove the first
+# term from the fitting.  For the polynomial functions this means
+# constraining the constant term to be zero.  Note that the first
+# coefficent is still returned but with a value of zero.
+
+procedure dgsfit1 (sf, x, y, z, w, npts, wtflag, ier)
+
+pointer	sf		# surface descriptor
+double	x[npts]		# array of x values
+double	y[npts]		# array of y values
+double	z[npts]		# data array
+double	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+begin
+	    call dgszero (sf)
+	    call dgsacpts (sf, x, y, z, w, npts, wtflag)
+	    call dgssolve1 (sf, ier)
+end
+
+
+# GSSOLVE1 -- Solve the matrix normal equations of the form ca = b for
+# a, where c is a symmetric, positive semi-definite, banded matrix with
+# GS_NXCOEFF(sf) * GS_NYCOEFF(sf) rows and a and b are GS_NXCOEFF(sf) *
+# GS_NYCOEFF(sf)-vectors.  Initially c is stored in the matrix MATRIX and b
+# is stored in VECTOR.  The Cholesky factorization of MATRIX is calculated
+# and stored in CHOFAC.  Finally the coefficients are calculated by forward
+# and back substitution and stored in COEFF.
+#
+# This version modifies the fitting matrix to remove the first
+# term from the fitting.  For the polynomial functions this means
+# constraining the constant term to be zero.  Note that the first
+# coefficent is still returned but with a value of zero.
+
+procedure dgssolve1 (sf, ier)
+
+pointer	sf 		# curve descriptor
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+int	i, ncoeff, offset
+pointer	sp, vector, matrix
+
+begin
+
+	# test for number of degrees of freedom
+	offset = 1
+	ncoeff = GS_NCOEFF(sf) - offset
+	ier = OK
+	i = GS_NPTS(sf) - ncoeff
+	if (i < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# allocate working space for the reduced vector and matrix
+	call smark (sp)
+	call salloc (vector, ncoeff, TY_DOUBLE)
+	call salloc (matrix, ncoeff*ncoeff, TY_DOUBLE)
+
+	# eliminate the first term from the vector and matrix
+	call amovd (VECTOR(GS_VECTOR(sf)+offset), Memd[vector], ncoeff)
+	do i = 0, ncoeff-1
+	    call amovd (MATRIX(GS_MATRIX(sf)+(i+offset)*GS_NCOEFF(sf)),
+		Memd[matrix+i*ncoeff], ncoeff)
+
+	# solve for the coefficients.
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    # calculate the Cholesky factorization of the data matrix
+	    call dgschofac (Memd[matrix], ncoeff, ncoeff,
+	        CHOFAC(GS_CHOFAC(sf)), ier)
+
+	    # solve for the coefficients by forward and back substitution
+	    COEFF(GS_COEFF(sf)) = 0.
+	    call dgschoslv (CHOFAC(GS_CHOFAC(sf)), ncoeff, ncoeff,
+	        Memd[vector], COEFF(GS_COEFF(sf)+offset))
+
+	default:
+	    call error (0, "GSSOLVE1: Illegal surface type.")
+	}
+
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gsfit1r.x b/math/gsurfit/gsfit1r.x
new file mode 100644
index 00000000..fe3be3ed
--- /dev/null
+++ b/math/gsurfit/gsfit1r.x
@@ -0,0 +1,99 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSFIT1 -- Procedure to solve the normal equations for a surface.
+#
+# This version modifies the fitting matrix to remove the first
+# term from the fitting.  For the polynomial functions this means
+# constraining the constant term to be zero.  Note that the first
+# coefficent is still returned but with a value of zero.
+
+procedure gsfit1 (sf, x, y, z, w, npts, wtflag, ier)
+
+pointer	sf		# surface descriptor
+real	x[npts]		# array of x values
+real	y[npts]		# array of y values
+real	z[npts]		# data array
+real	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+begin
+	    call gszero (sf)
+	    call gsacpts (sf, x, y, z, w, npts, wtflag)
+	    call gssolve1 (sf, ier)
+end
+
+
+# GSSOLVE1 -- Solve the matrix normal equations of the form ca = b for
+# a, where c is a symmetric, positive semi-definite, banded matrix with
+# GS_NXCOEFF(sf) * GS_NYCOEFF(sf) rows and a and b are GS_NXCOEFF(sf) *
+# GS_NYCOEFF(sf)-vectors.  Initially c is stored in the matrix MATRIX and b
+# is stored in VECTOR.  The Cholesky factorization of MATRIX is calculated
+# and stored in CHOFAC.  Finally the coefficients are calculated by forward
+# and back substitution and stored in COEFF.
+#
+# This version modifies the fitting matrix to remove the first
+# term from the fitting.  For the polynomial functions this means
+# constraining the constant term to be zero.  Note that the first
+# coefficent is still returned but with a value of zero.
+
+procedure gssolve1 (sf, ier)
+
+pointer	sf 		# curve descriptor
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+int	i, ncoeff, offset
+pointer	sp, vector, matrix
+
+begin
+
+	# test for number of degrees of freedom
+	offset = 1
+	ncoeff = GS_NCOEFF(sf) - offset
+	ier = OK
+	i = GS_NPTS(sf) - ncoeff
+	if (i < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# allocate working space for the reduced vector and matrix
+	call smark (sp)
+	call salloc (vector, ncoeff, TY_REAL)
+	call salloc (matrix, ncoeff*ncoeff, TY_REAL)
+
+	# eliminate the first term from the vector and matrix
+	call amovr (VECTOR(GS_VECTOR(sf)+offset), Memr[vector], ncoeff)
+	do i = 0, ncoeff-1
+	    call amovr (MATRIX(GS_MATRIX(sf)+(i+offset)*GS_NCOEFF(sf)),
+		Memr[matrix+i*ncoeff], ncoeff)
+
+	# solve for the coefficients.
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    # calculate the Cholesky factorization of the data matrix
+	    call rgschofac (Memd[matrix], ncoeff, ncoeff,
+	        CHOFAC(GS_CHOFAC(sf)), ier)
+
+	    # solve for the coefficients by forward and back substitution
+	    COEFF(GS_COEFF(sf)) = 0.
+	    call rgschoslv (CHOFAC(GS_CHOFAC(sf)), ncoeff, ncoeff,
+	        Memd[vector], COEFF(GS_COEFF(sf)+offset))
+
+	default:
+	    call error (0, "GSSOLVE1: Illegal surface type.")
+	}
+
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gsfitd.x b/math/gsurfit/gsfitd.x
new file mode 100644
index 00000000..b432cc3f
--- /dev/null
+++ b/math/gsurfit/gsfitd.x
@@ -0,0 +1,35 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSFIT -- Procedure to solve the normal equations for a surface.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# GS_NCOEFF(sf)-vector VECTOR. The Cholesky factorization of MATRIX
+# is calculated and stored in CHOFAC. Forward and back substitution
+# is used to solve for the GS_NCOEFF(sf)-vector COEFF.
+
+procedure dgsfit (sf, x, y, z, w, npts, wtflag, ier)
+
+pointer	sf		# surface descriptor
+double	x[npts]		# array of x values
+double	y[npts]		# array of y values
+double	z[npts]		# data array
+double	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+begin
+	    call dgszero (sf)
+	    call dgsacpts (sf, x, y, z, w, npts, wtflag)
+	    call dgssolve (sf, ier)
+end
diff --git a/math/gsurfit/gsfitr.x b/math/gsurfit/gsfitr.x
new file mode 100644
index 00000000..f5321969
--- /dev/null
+++ b/math/gsurfit/gsfitr.x
@@ -0,0 +1,35 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSFIT -- Procedure to solve the normal equations for a surface.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# GS_NCOEFF(sf)-vector VECTOR. The Cholesky factorization of MATRIX
+# is calculated and stored in CHOFAC. Forward and back substitution
+# is used to solve for the GS_NCOEFF(sf)-vector COEFF.
+
+procedure gsfit (sf, x, y, z, w, npts, wtflag, ier)
+
+pointer	sf		# surface descriptor
+real	x[npts]		# array of x values
+real	y[npts]		# array of y values
+real	z[npts]		# data array
+real	w[npts]		# array of weights
+int	npts		# number of data points
+int	wtflag		# type of weighting
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+begin
+	    call gszero (sf)
+	    call gsacpts (sf, x, y, z, w, npts, wtflag)
+	    call gssolve (sf, ier)
+end
diff --git a/math/gsurfit/gsfree.gx b/math/gsurfit/gsfree.gx
new file mode 100644
index 00000000..b97e960a
--- /dev/null
+++ b/math/gsurfit/gsfree.gx
@@ -0,0 +1,58 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSFREE -- Procedure to free the surface descriptor
+
+$if (datatype == r)
+procedure gsfree (sf)
+$else
+procedure dgsfree (sf)
+$endif
+
+pointer	sf	# the surface descriptor
+errchk	mfree
+
+begin
+	if (sf == NULL)
+	    return
+
+	$if (datatype == r)
+	if (GS_XBASIS(sf) != NULL)
+	    call mfree (GS_XBASIS(sf), TY_REAL)
+	if (GS_YBASIS(sf) != NULL)
+	    call mfree (GS_YBASIS(sf), TY_REAL)
+	if (GS_MATRIX(sf) != NULL)
+	    call mfree (GS_MATRIX(sf), TY_REAL)
+	if (GS_CHOFAC(sf) != NULL)
+	    call mfree (GS_CHOFAC(sf), TY_REAL)
+	if (GS_VECTOR(sf) != NULL)
+	    call mfree (GS_VECTOR(sf), TY_REAL)
+	if (GS_COEFF(sf) != NULL)
+	    call mfree (GS_COEFF(sf), TY_REAL)
+	if (GS_WZ(sf) != NULL)
+	    call mfree (GS_WZ(sf), TY_REAL)
+	$else
+	if (GS_XBASIS(sf) != NULL)
+	    call mfree (GS_XBASIS(sf), TY_DOUBLE)
+	if (GS_YBASIS(sf) != NULL)
+	    call mfree (GS_YBASIS(sf), TY_DOUBLE)
+	if (GS_MATRIX(sf) != NULL)
+	    call mfree (GS_MATRIX(sf), TY_DOUBLE)
+	if (GS_CHOFAC(sf) != NULL)
+	    call mfree (GS_CHOFAC(sf), TY_DOUBLE)
+	if (GS_VECTOR(sf) != NULL)
+	    call mfree (GS_VECTOR(sf), TY_DOUBLE)
+	if (GS_COEFF(sf) != NULL)
+	    call mfree (GS_COEFF(sf), TY_DOUBLE)
+	if (GS_WZ(sf) != NULL)
+	    call mfree (GS_WZ(sf), TY_DOUBLE)
+	$endif
+
+	if (sf != NULL)
+	    call mfree (sf, TY_STRUCT)
+end
diff --git a/math/gsurfit/gsfreed.x b/math/gsurfit/gsfreed.x
new file mode 100644
index 00000000..498bf00c
--- /dev/null
+++ b/math/gsurfit/gsfreed.x
@@ -0,0 +1,33 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "dgsurfitdef.h"
+
+# GSFREE -- Procedure to free the surface descriptor
+
+procedure dgsfree (sf)
+
+pointer	sf	# the surface descriptor
+errchk	mfree
+
+begin
+	if (sf == NULL)
+	    return
+
+	if (GS_XBASIS(sf) != NULL)
+	    call mfree (GS_XBASIS(sf), TY_DOUBLE)
+	if (GS_YBASIS(sf) != NULL)
+	    call mfree (GS_YBASIS(sf), TY_DOUBLE)
+	if (GS_MATRIX(sf) != NULL)
+	    call mfree (GS_MATRIX(sf), TY_DOUBLE)
+	if (GS_CHOFAC(sf) != NULL)
+	    call mfree (GS_CHOFAC(sf), TY_DOUBLE)
+	if (GS_VECTOR(sf) != NULL)
+	    call mfree (GS_VECTOR(sf), TY_DOUBLE)
+	if (GS_COEFF(sf) != NULL)
+	    call mfree (GS_COEFF(sf), TY_DOUBLE)
+	if (GS_WZ(sf) != NULL)
+	    call mfree (GS_WZ(sf), TY_DOUBLE)
+
+	if (sf != NULL)
+	    call mfree (sf, TY_STRUCT)
+end
diff --git a/math/gsurfit/gsfreer.x b/math/gsurfit/gsfreer.x
new file mode 100644
index 00000000..95148363
--- /dev/null
+++ b/math/gsurfit/gsfreer.x
@@ -0,0 +1,33 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "gsurfitdef.h"
+
+# GSFREE -- Procedure to free the surface descriptor
+
+procedure gsfree (sf)
+
+pointer	sf	# the surface descriptor
+errchk	mfree
+
+begin
+	if (sf == NULL)
+	    return
+
+	if (GS_XBASIS(sf) != NULL)
+	    call mfree (GS_XBASIS(sf), TY_REAL)
+	if (GS_YBASIS(sf) != NULL)
+	    call mfree (GS_YBASIS(sf), TY_REAL)
+	if (GS_MATRIX(sf) != NULL)
+	    call mfree (GS_MATRIX(sf), TY_REAL)
+	if (GS_CHOFAC(sf) != NULL)
+	    call mfree (GS_CHOFAC(sf), TY_REAL)
+	if (GS_VECTOR(sf) != NULL)
+	    call mfree (GS_VECTOR(sf), TY_REAL)
+	if (GS_COEFF(sf) != NULL)
+	    call mfree (GS_COEFF(sf), TY_REAL)
+	if (GS_WZ(sf) != NULL)
+	    call mfree (GS_WZ(sf), TY_REAL)
+
+	if (sf != NULL)
+	    call mfree (sf, TY_STRUCT)
+end
diff --git a/math/gsurfit/gsgcoeff.gx b/math/gsurfit/gsgcoeff.gx
new file mode 100644
index 00000000..3d8a294d
--- /dev/null
+++ b/math/gsurfit/gsgcoeff.gx
@@ -0,0 +1,53 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSGCOEFF -- Procedure to fetch a particular coefficient.
+# If the requested coefficient is undefined then INDEF is returned.
+
+$if (datatype == r)
+real procedure gsgcoeff (sf, xorder, yorder)
+$else
+double procedure dgsgcoeff (sf, xorder, yorder)
+$endif
+
+pointer	sf		# pointer to the surface fitting descriptor
+int	xorder		# X order of desired coefficent
+int	yorder		# Y order of desired coefficent
+
+int	i, n, maxorder, xincr
+
+begin
+	if ((xorder > GS_XORDER(sf)) || (yorder > GS_YORDER(sf)))
+	    return (INDEF)
+
+	switch (GS_XTERMS(sf)) {
+	case GS_XNONE:
+	    if (yorder == 1)
+		n = xorder
+	    else if (xorder == 1)
+		n = GS_NXCOEFF(sf) + yorder - 1
+	    else
+		return (INDEF)
+	case GS_XHALF:
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    if ((xorder + yorder) > maxorder)
+		return (INDEF)
+	    n = xorder
+	    xincr = GS_XORDER(sf)
+	    do i = 2, yorder {
+		n = n + xincr
+		if ((i + GS_XORDER(sf) + 1) > maxorder)
+		    xincr = xincr - 1
+	    }
+	case GS_XFULL:
+	    n = xorder + (yorder - 1) * GS_NXCOEFF(sf)
+	}
+
+	return (COEFF(GS_COEFF(sf) + n - 1))
+end
diff --git a/math/gsurfit/gsgcoeffd.x b/math/gsurfit/gsgcoeffd.x
new file mode 100644
index 00000000..32dead75
--- /dev/null
+++ b/math/gsurfit/gsgcoeffd.x
@@ -0,0 +1,45 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSGCOEFF -- Procedure to fetch a particular coefficient.
+# If the requested coefficient is undefined then INDEF is returned.
+
+double procedure dgsgcoeff (sf, xorder, yorder)
+
+pointer	sf		# pointer to the surface fitting descriptor
+int	xorder		# X order of desired coefficent
+int	yorder		# Y order of desired coefficent
+
+int	i, n, maxorder, xincr
+
+begin
+	if ((xorder > GS_XORDER(sf)) || (yorder > GS_YORDER(sf)))
+	    return (INDEFD)
+
+	switch (GS_XTERMS(sf)) {
+	case GS_XNONE:
+	    if (yorder == 1)
+		n = xorder
+	    else if (xorder == 1)
+		n = GS_NXCOEFF(sf) + yorder - 1
+	    else
+		return (INDEFD)
+	case GS_XHALF:
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    if ((xorder + yorder) > maxorder)
+		return (INDEFD)
+	    n = xorder
+	    xincr = GS_XORDER(sf)
+	    do i = 2, yorder {
+		n = n + xincr
+		if ((i + GS_XORDER(sf) + 1) > maxorder)
+		    xincr = xincr - 1
+	    }
+	case GS_XFULL:
+	    n = xorder + (yorder - 1) * GS_NXCOEFF(sf)
+	}
+
+	return (COEFF(GS_COEFF(sf) + n - 1))
+end
diff --git a/math/gsurfit/gsgcoeffr.x b/math/gsurfit/gsgcoeffr.x
new file mode 100644
index 00000000..45ef51e4
--- /dev/null
+++ b/math/gsurfit/gsgcoeffr.x
@@ -0,0 +1,45 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSGCOEFF -- Procedure to fetch a particular coefficient.
+# If the requested coefficient is undefined then INDEF is returned.
+
+real procedure gsgcoeff (sf, xorder, yorder)
+
+pointer	sf		# pointer to the surface fitting descriptor
+int	xorder		# X order of desired coefficent
+int	yorder		# Y order of desired coefficent
+
+int	i, n, maxorder, xincr
+
+begin
+	if ((xorder > GS_XORDER(sf)) || (yorder > GS_YORDER(sf)))
+	    return (INDEFR)
+
+	switch (GS_XTERMS(sf)) {
+	case GS_XNONE:
+	    if (yorder == 1)
+		n = xorder
+	    else if (xorder == 1)
+		n = GS_NXCOEFF(sf) + yorder - 1
+	    else
+		return (INDEFR)
+	case GS_XHALF:
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    if ((xorder + yorder) > maxorder)
+		return (INDEFR)
+	    n = xorder
+	    xincr = GS_XORDER(sf)
+	    do i = 2, yorder {
+		n = n + xincr
+		if ((i + GS_XORDER(sf) + 1) > maxorder)
+		    xincr = xincr - 1
+	    }
+	case GS_XFULL:
+	    n = xorder + (yorder - 1) * GS_NXCOEFF(sf)
+	}
+
+	return (COEFF(GS_COEFF(sf) + n - 1))
+end
diff --git a/math/gsurfit/gsinit.gx b/math/gsurfit/gsinit.gx
new file mode 100644
index 00000000..1d94c027
--- /dev/null
+++ b/math/gsurfit/gsinit.gx
@@ -0,0 +1,124 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSINIT --  Procedure to initialize the surface descriptor.
+
+$if (datatype == r)
+procedure gsinit (sf, surface_type, xorder, yorder, xterms, xmin, xmax,
+    ymin, ymax)
+$else
+procedure dgsinit (sf, surface_type, xorder, yorder, xterms, xmin, xmax,
+    ymin, ymax)
+$endif
+
+pointer	sf		# surface descriptor
+int	surface_type	# type of surface to be fitted
+int	xorder		# x order of surface to be fit
+int	yorder		# y order of surface to be fit
+int	xterms		# presence of cross terms
+PIXEL   xmin		# minimum value of x
+PIXEL	xmax		# maximum value of x
+PIXEL	ymin		# minimum value of y
+PIXEL	ymax		# maximum value of y
+
+int	order
+errchk	malloc, calloc
+
+begin
+	if (xorder < 1 || yorder < 1)
+	    call error (0, "GSINIT: Illegal order.")
+
+	if (xmax <= xmin)
+	    call error (0, "GSINIT: xmax <= xmin.")
+	if (ymax <= ymin)
+	    call error (0, "GSINIT: ymax <= ymin.")
+
+	# allocate space for the gsurve descriptor
+	call calloc (sf, LEN_GSSTRUCT, TY_STRUCT)
+
+	# specify the surface-type dependent parameters
+	switch (surface_type) {
+	case GS_CHEBYSHEV, GS_LEGENDRE:
+	    GS_XORDER(sf) = xorder
+	    GS_YORDER(sf) = yorder
+	    GS_NXCOEFF(sf) = xorder
+	    GS_NYCOEFF(sf) = yorder
+	    GS_XTERMS(sf) = xterms
+	    switch (xterms) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf) = xorder + yorder - 1
+	    case GS_XHALF:
+	        order = min (xorder, yorder)
+		GS_NCOEFF(sf) = xorder * yorder - order * (order - 1) / 2
+	    default:
+		GS_NCOEFF(sf) = xorder * yorder
+	    }
+	    GS_XRANGE(sf) = 2. / (xmax - xmin)
+	    GS_XMAXMIN(sf) = - (xmax + xmin) / 2.
+	    GS_YRANGE(sf) = 2. / (ymax - ymin)
+	    GS_YMAXMIN(sf) = - (ymax + ymin) / 2.
+	case GS_POLYNOMIAL:
+	    GS_XORDER(sf) = xorder
+	    GS_YORDER(sf) = yorder
+	    GS_NXCOEFF(sf) = xorder
+	    GS_NYCOEFF(sf) = yorder
+	    GS_XTERMS(sf) = xterms
+	    switch (xterms) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf) = xorder + yorder - 1
+	    case GS_XHALF:
+	        order = min (xorder, yorder)
+		GS_NCOEFF(sf) = xorder *  yorder - order * (order - 1) / 2
+	    default:
+		GS_NCOEFF(sf) = xorder * yorder
+	    }
+	    GS_XRANGE(sf) = 1.0 
+	    GS_XMAXMIN(sf) = 0.0
+	    GS_YRANGE(sf) = 1.0
+	    GS_YMAXMIN(sf) = 0.0
+	default:
+	    call error (0, "GSINIT: Unknown surface type.")
+	}
+
+	# set remaining parameters
+	GS_TYPE(sf) = surface_type
+	GS_XREF(sf) = INDEF
+	GS_YREF(sf) = INDEF
+	GS_ZREF(sf) = INDEF
+	GS_XMIN(sf) = xmin
+	GS_XMAX(sf) = xmax
+	GS_YMAX(sf) = ymax
+	GS_YMIN(sf) = ymin
+
+	# allocate space for the matrix and vectors
+	switch (surface_type ) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    $if (datatype == r)
+	    call calloc (GS_MATRIX(sf), GS_NCOEFF(sf) ** 2, TY_REAL)
+	    call calloc (GS_CHOFAC(sf), GS_NCOEFF(sf) ** 2, TY_REAL)
+	    call calloc (GS_VECTOR(sf), GS_NCOEFF(sf), TY_REAL)
+	    call calloc (GS_COEFF(sf), GS_NCOEFF(sf), TY_REAL)
+	    $else
+	    call calloc (GS_MATRIX(sf), GS_NCOEFF(sf) ** 2, TY_DOUBLE)
+	    call calloc (GS_CHOFAC(sf), GS_NCOEFF(sf) ** 2, TY_DOUBLE)
+	    call calloc (GS_VECTOR(sf), GS_NCOEFF(sf), TY_DOUBLE)
+	    call calloc (GS_COEFF(sf), GS_NCOEFF(sf), TY_DOUBLE)
+	    $endif
+	default:
+	    call error (0, "GSINIT: Unknown surface type.")
+	}
+
+	# initialize pointer to basis functions to null
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+	GS_WZ(sf) = NULL
+
+	# set data points counter
+	GS_NPTS(sf) = 0
+end
diff --git a/math/gsurfit/gsinitd.x b/math/gsurfit/gsinitd.x
new file mode 100644
index 00000000..ad8e2650
--- /dev/null
+++ b/math/gsurfit/gsinitd.x
@@ -0,0 +1,108 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSINIT --  Procedure to initialize the surface descriptor.
+
+procedure dgsinit (sf, surface_type, xorder, yorder, xterms, xmin, xmax,
+    ymin, ymax)
+
+pointer	sf		# surface descriptor
+int	surface_type	# type of surface to be fitted
+int	xorder		# x order of surface to be fit
+int	yorder		# y order of surface to be fit
+int	xterms		# presence of cross terms
+double   xmin		# minimum value of x
+double	xmax		# maximum value of x
+double	ymin		# minimum value of y
+double	ymax		# maximum value of y
+
+int	order
+errchk	malloc, calloc
+
+begin
+	if (xorder < 1 || yorder < 1)
+	    call error (0, "GSINIT: Illegal order.")
+
+	if (xmax <= xmin)
+	    call error (0, "GSINIT: xmax <= xmin.")
+	if (ymax <= ymin)
+	    call error (0, "GSINIT: ymax <= ymin.")
+
+	# allocate space for the gsurve descriptor
+	call calloc (sf, LEN_GSSTRUCT, TY_STRUCT)
+
+	# specify the surface-type dependent parameters
+	switch (surface_type) {
+	case GS_CHEBYSHEV, GS_LEGENDRE:
+	    GS_XORDER(sf) = xorder
+	    GS_YORDER(sf) = yorder
+	    GS_NXCOEFF(sf) = xorder
+	    GS_NYCOEFF(sf) = yorder
+	    GS_XTERMS(sf) = xterms
+	    switch (xterms) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf) = xorder + yorder - 1
+	    case GS_XHALF:
+	        order = min (xorder, yorder)
+		GS_NCOEFF(sf) = xorder * yorder - order * (order - 1) / 2
+	    default:
+		GS_NCOEFF(sf) = xorder * yorder
+	    }
+	    GS_XRANGE(sf) = 2. / (xmax - xmin)
+	    GS_XMAXMIN(sf) = - (xmax + xmin) / 2.
+	    GS_YRANGE(sf) = 2. / (ymax - ymin)
+	    GS_YMAXMIN(sf) = - (ymax + ymin) / 2.
+	case GS_POLYNOMIAL:
+	    GS_XORDER(sf) = xorder
+	    GS_YORDER(sf) = yorder
+	    GS_NXCOEFF(sf) = xorder
+	    GS_NYCOEFF(sf) = yorder
+	    GS_XTERMS(sf) = xterms
+	    switch (xterms) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf) = xorder + yorder - 1
+	    case GS_XHALF:
+	        order = min (xorder, yorder)
+		GS_NCOEFF(sf) = xorder *  yorder - order * (order - 1) / 2
+	    default:
+		GS_NCOEFF(sf) = xorder * yorder
+	    }
+	    GS_XRANGE(sf) = 1.0 
+	    GS_XMAXMIN(sf) = 0.0
+	    GS_YRANGE(sf) = 1.0
+	    GS_YMAXMIN(sf) = 0.0
+	default:
+	    call error (0, "GSINIT: Unknown surface type.")
+	}
+
+	# set remaining parameters
+	GS_TYPE(sf) = surface_type
+	GS_XREF(sf) = INDEFD
+	GS_YREF(sf) = INDEFD
+	GS_ZREF(sf) = INDEFD
+	GS_XMIN(sf) = xmin
+	GS_XMAX(sf) = xmax
+	GS_YMAX(sf) = ymax
+	GS_YMIN(sf) = ymin
+
+	# allocate space for the matrix and vectors
+	switch (surface_type ) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    call calloc (GS_MATRIX(sf), GS_NCOEFF(sf) ** 2, TY_DOUBLE)
+	    call calloc (GS_CHOFAC(sf), GS_NCOEFF(sf) ** 2, TY_DOUBLE)
+	    call calloc (GS_VECTOR(sf), GS_NCOEFF(sf), TY_DOUBLE)
+	    call calloc (GS_COEFF(sf), GS_NCOEFF(sf), TY_DOUBLE)
+	default:
+	    call error (0, "GSINIT: Unknown surface type.")
+	}
+
+	# initialize pointer to basis functions to null
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+	GS_WZ(sf) = NULL
+
+	# set data points counter
+	GS_NPTS(sf) = 0
+end
diff --git a/math/gsurfit/gsinitr.x b/math/gsurfit/gsinitr.x
new file mode 100644
index 00000000..8c44d6e4
--- /dev/null
+++ b/math/gsurfit/gsinitr.x
@@ -0,0 +1,108 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSINIT --  Procedure to initialize the surface descriptor.
+
+procedure gsinit (sf, surface_type, xorder, yorder, xterms, xmin, xmax,
+    ymin, ymax)
+
+pointer	sf		# surface descriptor
+int	surface_type	# type of surface to be fitted
+int	xorder		# x order of surface to be fit
+int	yorder		# y order of surface to be fit
+int	xterms		# presence of cross terms
+real   xmin		# minimum value of x
+real	xmax		# maximum value of x
+real	ymin		# minimum value of y
+real	ymax		# maximum value of y
+
+int	order
+errchk	malloc, calloc
+
+begin
+	if (xorder < 1 || yorder < 1)
+	    call error (0, "GSINIT: Illegal order.")
+
+	if (xmax <= xmin)
+	    call error (0, "GSINIT: xmax <= xmin.")
+	if (ymax <= ymin)
+	    call error (0, "GSINIT: ymax <= ymin.")
+
+	# allocate space for the gsurve descriptor
+	call calloc (sf, LEN_GSSTRUCT, TY_STRUCT)
+
+	# specify the surface-type dependent parameters
+	switch (surface_type) {
+	case GS_CHEBYSHEV, GS_LEGENDRE:
+	    GS_XORDER(sf) = xorder
+	    GS_YORDER(sf) = yorder
+	    GS_NXCOEFF(sf) = xorder
+	    GS_NYCOEFF(sf) = yorder
+	    GS_XTERMS(sf) = xterms
+	    switch (xterms) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf) = xorder + yorder - 1
+	    case GS_XHALF:
+	        order = min (xorder, yorder)
+		GS_NCOEFF(sf) = xorder * yorder - order * (order - 1) / 2
+	    default:
+		GS_NCOEFF(sf) = xorder * yorder
+	    }
+	    GS_XRANGE(sf) = 2. / (xmax - xmin)
+	    GS_XMAXMIN(sf) = - (xmax + xmin) / 2.
+	    GS_YRANGE(sf) = 2. / (ymax - ymin)
+	    GS_YMAXMIN(sf) = - (ymax + ymin) / 2.
+	case GS_POLYNOMIAL:
+	    GS_XORDER(sf) = xorder
+	    GS_YORDER(sf) = yorder
+	    GS_NXCOEFF(sf) = xorder
+	    GS_NYCOEFF(sf) = yorder
+	    GS_XTERMS(sf) = xterms
+	    switch (xterms) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf) = xorder + yorder - 1
+	    case GS_XHALF:
+	        order = min (xorder, yorder)
+		GS_NCOEFF(sf) = xorder *  yorder - order * (order - 1) / 2
+	    default:
+		GS_NCOEFF(sf) = xorder * yorder
+	    }
+	    GS_XRANGE(sf) = 1.0 
+	    GS_XMAXMIN(sf) = 0.0
+	    GS_YRANGE(sf) = 1.0
+	    GS_YMAXMIN(sf) = 0.0
+	default:
+	    call error (0, "GSINIT: Unknown surface type.")
+	}
+
+	# set remaining parameters
+	GS_TYPE(sf) = surface_type
+	GS_XREF(sf) = INDEFR
+	GS_YREF(sf) = INDEFR
+	GS_ZREF(sf) = INDEFR
+	GS_XMIN(sf) = xmin
+	GS_XMAX(sf) = xmax
+	GS_YMAX(sf) = ymax
+	GS_YMIN(sf) = ymin
+
+	# allocate space for the matrix and vectors
+	switch (surface_type ) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    call calloc (GS_MATRIX(sf), GS_NCOEFF(sf) ** 2, TY_REAL)
+	    call calloc (GS_CHOFAC(sf), GS_NCOEFF(sf) ** 2, TY_REAL)
+	    call calloc (GS_VECTOR(sf), GS_NCOEFF(sf), TY_REAL)
+	    call calloc (GS_COEFF(sf), GS_NCOEFF(sf), TY_REAL)
+	default:
+	    call error (0, "GSINIT: Unknown surface type.")
+	}
+
+	# initialize pointer to basis functions to null
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+	GS_WZ(sf) = NULL
+
+	# set data points counter
+	GS_NPTS(sf) = 0
+end
diff --git a/math/gsurfit/gsrefit.gx b/math/gsurfit/gsrefit.gx
new file mode 100644
index 00000000..00327abb
--- /dev/null
+++ b/math/gsurfit/gsrefit.gx
@@ -0,0 +1,174 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSREFIT -- Procedure to refit the surface assuming that the x, y and w
+# values and the matrices MATRIX and CHOFAC have remained unchanged. It
+# is necessary only to accumulate a new VECTOR. The new coefficients
+# are calculated by forward and back subsitution and stored in COEFF.
+
+$if (datatype == r)
+procedure gsrefit (sf, x, y, z, w, ier)
+$else
+procedure dgsrefit (sf, x, y, z, w, ier)
+$endif
+
+pointer	sf		# surface descriptor
+PIXEL	x[ARB]		# array of x values
+PIXEL	y[ARB]		# array of y values
+PIXEL	z[ARB]		# data array
+PIXEL	w[ARB]		# array of weights
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+int	k, l
+int	xorder, nfree, maxorder
+pointer	sp, vzptr, vindex, bxptr, byptr, bwz
+
+PIXEL	adot$t()
+
+errchk	smark, salloc, sfree
+
+begin
+	# clear accumulator
+	call aclr$t (VECTOR(GS_VECTOR(sf)), GS_NCOEFF(sf))
+
+	# if first call to gsefit calculate basis functions
+	if (GS_XBASIS(sf) == NULL || GS_YBASIS(sf) == NULL) {
+
+	    $if (datatype == r)
+	    call malloc (GS_WZ(sf), GS_NPTS(sf), TY_REAL)
+	    $else
+	    call malloc (GS_WZ(sf), GS_NPTS(sf), TY_DOUBLE)
+	    $endif
+
+	    switch (GS_TYPE(sf)) {
+	    case GS_LEGENDRE:
+		$if (datatype == r)
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_REAL)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_REAL)
+		$else
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_DOUBLE)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_DOUBLE)
+		$endif
+	        call $tgs_bleg (x, GS_NPTS(sf), GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	        call $tgs_bleg (y, GS_NPTS(sf), GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    case GS_CHEBYSHEV:
+		$if (datatype == r)
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_REAL)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_REAL)
+		$else
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_DOUBLE)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_DOUBLE)
+		$endif
+	        call $tgs_bcheb (x, GS_NPTS(sf), GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	        call $tgs_bcheb (y, GS_NPTS(sf), GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    case GS_POLYNOMIAL:
+		$if (datatype == r)
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_REAL)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_REAL)
+		$else
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_DOUBLE)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_DOUBLE)
+		$endif
+	        call $tgs_bpol (x, GS_NPTS(sf), GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	        call $tgs_bpol (y, GS_NPTS(sf), GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    default:
+		call error (0, "GSREFIT: Unknown curve type.")
+	    }
+
+	}
+
+	call smark (sp)
+	$if (datatype == r)
+	call salloc (bwz, GS_NPTS(sf), TY_REAL) 
+	$else
+	call salloc (bwz, GS_NPTS(sf), TY_DOUBLE)
+	$endif
+
+	# index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	byptr = GS_YBASIS(sf)
+
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    call amul$t (w, z, Mem$t[GS_WZ(sf)], GS_NPTS(sf))
+	    xorder = GS_XORDER(sf)
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+
+	    do l = 1, GS_YORDER(sf) {
+		call amul$t (Mem$t[GS_WZ(sf)], YBASIS(byptr), Mem$t[bwz],
+		    GS_NPTS(sf))
+		bxptr = GS_XBASIS(sf)
+	        do k = 1, xorder {
+		    vindex = vzptr + k
+	            VECTOR(vindex) = VECTOR(vindex) + adot$t (Mem$t[bwz],
+		        XBASIS(bxptr), GS_NPTS(sf))
+		    bxptr = bxptr + GS_NPTS(sf)
+	        }
+
+		vzptr = vzptr + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+		byptr = byptr + GS_NPTS(sf)
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown curve type.")
+	}
+
+	# test for number of degrees of freedom
+	ier = OK
+	nfree = GS_NPTS(sf) - GS_NCOEFF(sf)
+	if (nfree < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# calculate the values of the coefficients
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    # solve for the coefficients by forward and back substitution
+	    call $tgschoslv (CHOFAC(GS_CHOFAC(sf)), GS_NCOEFF(sf),
+	        GS_NCOEFF(sf), VECTOR(GS_VECTOR(sf)), COEFF(GS_COEFF(sf)))
+	default:
+	    call error (0, "GSSOLVE: Illegal surface type.")
+	}
+
+	# release the space
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gsrefitd.x b/math/gsurfit/gsrefitd.x
new file mode 100644
index 00000000..a7f7d706
--- /dev/null
+++ b/math/gsurfit/gsrefitd.x
@@ -0,0 +1,137 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSREFIT -- Procedure to refit the surface assuming that the x, y and w
+# values and the matrices MATRIX and CHOFAC have remained unchanged. It
+# is necessary only to accumulate a new VECTOR. The new coefficients
+# are calculated by forward and back subsitution and stored in COEFF.
+
+procedure dgsrefit (sf, x, y, z, w, ier)
+
+pointer	sf		# surface descriptor
+double	x[ARB]		# array of x values
+double	y[ARB]		# array of y values
+double	z[ARB]		# data array
+double	w[ARB]		# array of weights
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+int	k, l
+int	xorder, nfree, maxorder
+pointer	sp, vzptr, vindex, bxptr, byptr, bwz
+
+double	adotd()
+
+errchk	smark, salloc, sfree
+
+begin
+	# clear accumulator
+	call aclrd (VECTOR(GS_VECTOR(sf)), GS_NCOEFF(sf))
+
+	# if first call to gsefit calculate basis functions
+	if (GS_XBASIS(sf) == NULL || GS_YBASIS(sf) == NULL) {
+
+	    call malloc (GS_WZ(sf), GS_NPTS(sf), TY_DOUBLE)
+
+	    switch (GS_TYPE(sf)) {
+	    case GS_LEGENDRE:
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_DOUBLE)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_DOUBLE)
+	        call dgs_bleg (x, GS_NPTS(sf), GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	        call dgs_bleg (y, GS_NPTS(sf), GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    case GS_CHEBYSHEV:
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_DOUBLE)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_DOUBLE)
+	        call dgs_bcheb (x, GS_NPTS(sf), GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	        call dgs_bcheb (y, GS_NPTS(sf), GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    case GS_POLYNOMIAL:
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_DOUBLE)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_DOUBLE)
+	        call dgs_bpol (x, GS_NPTS(sf), GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	        call dgs_bpol (y, GS_NPTS(sf), GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    default:
+		call error (0, "GSREFIT: Unknown curve type.")
+	    }
+
+	}
+
+	call smark (sp)
+	call salloc (bwz, GS_NPTS(sf), TY_DOUBLE)
+
+	# index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	byptr = GS_YBASIS(sf)
+
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    call amuld (w, z, Memd[GS_WZ(sf)], GS_NPTS(sf))
+	    xorder = GS_XORDER(sf)
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+
+	    do l = 1, GS_YORDER(sf) {
+		call amuld (Memd[GS_WZ(sf)], YBASIS(byptr), Memd[bwz],
+		    GS_NPTS(sf))
+		bxptr = GS_XBASIS(sf)
+	        do k = 1, xorder {
+		    vindex = vzptr + k
+	            VECTOR(vindex) = VECTOR(vindex) + adotd (Memd[bwz],
+		        XBASIS(bxptr), GS_NPTS(sf))
+		    bxptr = bxptr + GS_NPTS(sf)
+	        }
+
+		vzptr = vzptr + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+		byptr = byptr + GS_NPTS(sf)
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown curve type.")
+	}
+
+	# test for number of degrees of freedom
+	ier = OK
+	nfree = GS_NPTS(sf) - GS_NCOEFF(sf)
+	if (nfree < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# calculate the values of the coefficients
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    # solve for the coefficients by forward and back substitution
+	    call dgschoslv (CHOFAC(GS_CHOFAC(sf)), GS_NCOEFF(sf),
+	        GS_NCOEFF(sf), VECTOR(GS_VECTOR(sf)), COEFF(GS_COEFF(sf)))
+	default:
+	    call error (0, "GSSOLVE: Illegal surface type.")
+	}
+
+	# release the space
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gsrefitr.x b/math/gsurfit/gsrefitr.x
new file mode 100644
index 00000000..6b550084
--- /dev/null
+++ b/math/gsurfit/gsrefitr.x
@@ -0,0 +1,137 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSREFIT -- Procedure to refit the surface assuming that the x, y and w
+# values and the matrices MATRIX and CHOFAC have remained unchanged. It
+# is necessary only to accumulate a new VECTOR. The new coefficients
+# are calculated by forward and back subsitution and stored in COEFF.
+
+procedure gsrefit (sf, x, y, z, w, ier)
+
+pointer	sf		# surface descriptor
+real	x[ARB]		# array of x values
+real	y[ARB]		# array of y values
+real	z[ARB]		# data array
+real	w[ARB]		# array of weights
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+int	k, l
+int	xorder, nfree, maxorder
+pointer	sp, vzptr, vindex, bxptr, byptr, bwz
+
+real	adotr()
+
+errchk	smark, salloc, sfree
+
+begin
+	# clear accumulator
+	call aclrr (VECTOR(GS_VECTOR(sf)), GS_NCOEFF(sf))
+
+	# if first call to gsefit calculate basis functions
+	if (GS_XBASIS(sf) == NULL || GS_YBASIS(sf) == NULL) {
+
+	    call malloc (GS_WZ(sf), GS_NPTS(sf), TY_REAL)
+
+	    switch (GS_TYPE(sf)) {
+	    case GS_LEGENDRE:
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_REAL)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_REAL)
+	        call rgs_bleg (x, GS_NPTS(sf), GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	        call rgs_bleg (y, GS_NPTS(sf), GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    case GS_CHEBYSHEV:
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_REAL)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_REAL)
+	        call rgs_bcheb (x, GS_NPTS(sf), GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	        call rgs_bcheb (y, GS_NPTS(sf), GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    case GS_POLYNOMIAL:
+	        call malloc (GS_XBASIS(sf), GS_NPTS(sf) * GS_XORDER(sf),
+		    TY_REAL)
+	        call malloc (GS_YBASIS(sf), GS_NPTS(sf) * GS_YORDER(sf),
+		    TY_REAL)
+	        call rgs_bpol (x, GS_NPTS(sf), GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	        call rgs_bpol (y, GS_NPTS(sf), GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	    default:
+		call error (0, "GSREFIT: Unknown curve type.")
+	    }
+
+	}
+
+	call smark (sp)
+	call salloc (bwz, GS_NPTS(sf), TY_REAL) 
+
+	# index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	byptr = GS_YBASIS(sf)
+
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    call amulr (w, z, Memr[GS_WZ(sf)], GS_NPTS(sf))
+	    xorder = GS_XORDER(sf)
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+
+	    do l = 1, GS_YORDER(sf) {
+		call amulr (Memr[GS_WZ(sf)], YBASIS(byptr), Memr[bwz],
+		    GS_NPTS(sf))
+		bxptr = GS_XBASIS(sf)
+	        do k = 1, xorder {
+		    vindex = vzptr + k
+	            VECTOR(vindex) = VECTOR(vindex) + adotr (Memr[bwz],
+		        XBASIS(bxptr), GS_NPTS(sf))
+		    bxptr = bxptr + GS_NPTS(sf)
+	        }
+
+		vzptr = vzptr + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+		byptr = byptr + GS_NPTS(sf)
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown curve type.")
+	}
+
+	# test for number of degrees of freedom
+	ier = OK
+	nfree = GS_NPTS(sf) - GS_NCOEFF(sf)
+	if (nfree < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# calculate the values of the coefficients
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    # solve for the coefficients by forward and back substitution
+	    call rgschoslv (CHOFAC(GS_CHOFAC(sf)), GS_NCOEFF(sf),
+	        GS_NCOEFF(sf), VECTOR(GS_VECTOR(sf)), COEFF(GS_COEFF(sf)))
+	default:
+	    call error (0, "GSSOLVE: Illegal surface type.")
+	}
+
+	# release the space
+	call sfree (sp)
+end
diff --git a/math/gsurfit/gsreject.gx b/math/gsurfit/gsreject.gx
new file mode 100644
index 00000000..b5d8e01e
--- /dev/null
+++ b/math/gsurfit/gsreject.gx
@@ -0,0 +1,188 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSREJ-- Procedure to reject a point from the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# NCOEFF(sf)-vector VECTOR.
+
+$if (datatype == r)
+procedure gsrej (sf, x, y, z, w, wtflag)
+$else
+procedure dgsrej (sf, x, y, z, w, wtflag)
+$endif
+
+pointer	sf		# surface descriptor
+PIXEL	x		# x value
+PIXEL	y		# y value
+PIXEL	z		# z value
+PIXEL	w		# weight
+int	wtflag		# type of weighting
+
+int	ii, j, k, l
+int	maxorder, xorder, xxorder, xindex, yindex, ntimes
+pointer	sp, vzptr, mzptr, xbptr, ybptr
+PIXEL	byw, bw
+
+begin
+	# increment the number of points
+	GS_NPTS(sf) = GS_NPTS(sf) - 1
+
+	# remove basis functions calculated by any previous gsrefit call
+	if (GS_XBASIS(sf) != NULL || GS_YBASIS(sf) != NULL) {
+
+	    $if (datatype == r)
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_REAL)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_REAL)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_REAL)
+	    GS_WZ(sf) = NULL
+	    $else
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_DOUBLE)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_DOUBLE)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_DOUBLE)
+	    GS_WZ(sf) = NULL
+	    $endif
+	}
+
+	# calculate weight
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    w = 1.
+	case WTS_USER:
+	    # user supplied weights
+	default:
+	    w = 1.
+	}
+
+	# allocate space for the basis functions
+	call smark (sp)
+
+	# calculate the non-zero basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE:
+	    $if (datatype == r)
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_REAL)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_REAL)
+	    $else
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_DOUBLE)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_DOUBLE)
+	    $endif
+	    call $tgs_b1leg (x, GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call $tgs_b1leg (y, GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_CHEBYSHEV:
+	    $if (datatype == r)
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_REAL)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_REAL)
+	    $else
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_DOUBLE)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_DOUBLE)
+	    $endif
+	    call $tgs_b1cheb (x, GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call $tgs_b1cheb (y, GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_POLYNOMIAL:
+	    $if (datatype == r)
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_REAL)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_REAL)
+	    $else
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_DOUBLE)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_DOUBLE)
+	    $endif
+	    call $tgs_b1pol (x, GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call $tgs_b1pol (y, GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	default:
+	    call error (0, "GSACCUM: Illegal curve type.")
+	}
+
+	# one index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	mzptr = GS_MATRIX(sf) - 1
+	xbptr = GS_XBASIS(sf) - 1
+	ybptr = GS_YBASIS(sf) - 1
+
+	switch (GS_TYPE(sf)) {
+
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    ntimes = 0
+	    xorder = GS_XORDER(sf)
+	    do l = 1, GS_YORDER(sf) {
+
+		byw = w * YBASIS(ybptr+l)
+	        do k = 1, xorder {
+	            bw = byw * XBASIS(xbptr+k)
+	            VECTOR(vzptr+k) = VECTOR(vzptr+k) - bw * z
+	            ii = 1
+		    xindex = k
+		    yindex = l
+		    xxorder = xorder
+		    do j = k + ntimes, GS_NCOEFF(sf) {
+		        MATRIX(mzptr+ii) = MATRIX(mzptr+ii) - bw *
+			    XBASIS(xbptr+xindex) * YBASIS(ybptr+yindex)	
+			if (mod (xindex, xxorder) == 0) {
+			    xindex = 1
+			    yindex = yindex + 1
+			    switch (GS_XTERMS(sf)) {
+			    case GS_XNONE:
+				xxorder = 1
+			    case GS_XHALF:
+				if ((yindex + GS_XORDER(sf)) > maxorder)
+				    xxorder = xxorder - 1
+			    default:
+		    		;
+			    }
+			} else
+			    xindex = xindex + 1
+		        ii = ii + 1
+		    }
+		    mzptr = mzptr + GS_NCOEFF(sf)
+	        }
+
+		vzptr = vzptr + xorder
+		ntimes = ntimes + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown curve type.")
+	}
+
+	# release the space
+	call sfree (sp)
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+end
diff --git a/math/gsurfit/gsrejectd.x b/math/gsurfit/gsrejectd.x
new file mode 100644
index 00000000..da1d71dd
--- /dev/null
+++ b/math/gsurfit/gsrejectd.x
@@ -0,0 +1,153 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSREJ-- Procedure to reject a point from the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# NCOEFF(sf)-vector VECTOR.
+
+procedure dgsrej (sf, x, y, z, w, wtflag)
+
+pointer	sf		# surface descriptor
+double	x		# x value
+double	y		# y value
+double	z		# z value
+double	w		# weight
+int	wtflag		# type of weighting
+
+int	ii, j, k, l
+int	maxorder, xorder, xxorder, xindex, yindex, ntimes
+pointer	sp, vzptr, mzptr, xbptr, ybptr
+double	byw, bw
+
+begin
+	# increment the number of points
+	GS_NPTS(sf) = GS_NPTS(sf) - 1
+
+	# remove basis functions calculated by any previous gsrefit call
+	if (GS_XBASIS(sf) != NULL || GS_YBASIS(sf) != NULL) {
+
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_DOUBLE)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_DOUBLE)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_DOUBLE)
+	    GS_WZ(sf) = NULL
+	}
+
+	# calculate weight
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    w = 1.
+	case WTS_USER:
+	    # user supplied weights
+	default:
+	    w = 1.
+	}
+
+	# allocate space for the basis functions
+	call smark (sp)
+
+	# calculate the non-zero basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE:
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_DOUBLE)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_DOUBLE)
+	    call dgs_b1leg (x, GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call dgs_b1leg (y, GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_CHEBYSHEV:
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_DOUBLE)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_DOUBLE)
+	    call dgs_b1cheb (x, GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call dgs_b1cheb (y, GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_POLYNOMIAL:
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_DOUBLE)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_DOUBLE)
+	    call dgs_b1pol (x, GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call dgs_b1pol (y, GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	default:
+	    call error (0, "GSACCUM: Illegal curve type.")
+	}
+
+	# one index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	mzptr = GS_MATRIX(sf) - 1
+	xbptr = GS_XBASIS(sf) - 1
+	ybptr = GS_YBASIS(sf) - 1
+
+	switch (GS_TYPE(sf)) {
+
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    ntimes = 0
+	    xorder = GS_XORDER(sf)
+	    do l = 1, GS_YORDER(sf) {
+
+		byw = w * YBASIS(ybptr+l)
+	        do k = 1, xorder {
+	            bw = byw * XBASIS(xbptr+k)
+	            VECTOR(vzptr+k) = VECTOR(vzptr+k) - bw * z
+	            ii = 1
+		    xindex = k
+		    yindex = l
+		    xxorder = xorder
+		    do j = k + ntimes, GS_NCOEFF(sf) {
+		        MATRIX(mzptr+ii) = MATRIX(mzptr+ii) - bw *
+			    XBASIS(xbptr+xindex) * YBASIS(ybptr+yindex)	
+			if (mod (xindex, xxorder) == 0) {
+			    xindex = 1
+			    yindex = yindex + 1
+			    switch (GS_XTERMS(sf)) {
+			    case GS_XNONE:
+				xxorder = 1
+			    case GS_XHALF:
+				if ((yindex + GS_XORDER(sf)) > maxorder)
+				    xxorder = xxorder - 1
+			    default:
+		    		;
+			    }
+			} else
+			    xindex = xindex + 1
+		        ii = ii + 1
+		    }
+		    mzptr = mzptr + GS_NCOEFF(sf)
+	        }
+
+		vzptr = vzptr + xorder
+		ntimes = ntimes + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown curve type.")
+	}
+
+	# release the space
+	call sfree (sp)
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+end
diff --git a/math/gsurfit/gsrejectr.x b/math/gsurfit/gsrejectr.x
new file mode 100644
index 00000000..fea86cef
--- /dev/null
+++ b/math/gsurfit/gsrejectr.x
@@ -0,0 +1,153 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSREJ-- Procedure to reject a point from the normal equations.
+# The inner products of the basis functions are calculated and
+# accumulated into the GS_NCOEFF(sf) ** 2 matrix MATRIX.
+# The main diagonal of the matrix is stored in the first row of
+# MATRIX followed by the remaining non-zero diagonals.
+# The inner product
+# of the basis functions and the data ordinates are stored in the
+# NCOEFF(sf)-vector VECTOR.
+
+procedure gsrej (sf, x, y, z, w, wtflag)
+
+pointer	sf		# surface descriptor
+real	x		# x value
+real	y		# y value
+real	z		# z value
+real	w		# weight
+int	wtflag		# type of weighting
+
+int	ii, j, k, l
+int	maxorder, xorder, xxorder, xindex, yindex, ntimes
+pointer	sp, vzptr, mzptr, xbptr, ybptr
+real	byw, bw
+
+begin
+	# increment the number of points
+	GS_NPTS(sf) = GS_NPTS(sf) - 1
+
+	# remove basis functions calculated by any previous gsrefit call
+	if (GS_XBASIS(sf) != NULL || GS_YBASIS(sf) != NULL) {
+
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_REAL)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_REAL)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_REAL)
+	    GS_WZ(sf) = NULL
+	}
+
+	# calculate weight
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    w = 1.
+	case WTS_USER:
+	    # user supplied weights
+	default:
+	    w = 1.
+	}
+
+	# allocate space for the basis functions
+	call smark (sp)
+
+	# calculate the non-zero basis functions
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE:
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_REAL)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_REAL)
+	    call rgs_b1leg (x, GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call rgs_b1leg (y, GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_CHEBYSHEV:
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_REAL)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_REAL)
+	    call rgs_b1cheb (x, GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call rgs_b1cheb (y, GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	case GS_POLYNOMIAL:
+	    call salloc (GS_XBASIS(sf), GS_XORDER(sf), TY_REAL)
+	    call salloc (GS_YBASIS(sf), GS_YORDER(sf), TY_REAL)
+	    call rgs_b1pol (x, GS_XORDER(sf), GS_XMAXMIN(sf),
+	    		  GS_XRANGE(sf), XBASIS(GS_XBASIS(sf)))
+	    call rgs_b1pol (y, GS_YORDER(sf), GS_YMAXMIN(sf),
+	    		  GS_YRANGE(sf), YBASIS(GS_YBASIS(sf)))
+	default:
+	    call error (0, "GSACCUM: Illegal curve type.")
+	}
+
+	# one index the pointers
+	vzptr = GS_VECTOR(sf) - 1
+	mzptr = GS_MATRIX(sf) - 1
+	xbptr = GS_XBASIS(sf) - 1
+	ybptr = GS_YBASIS(sf) - 1
+
+	switch (GS_TYPE(sf)) {
+
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    ntimes = 0
+	    xorder = GS_XORDER(sf)
+	    do l = 1, GS_YORDER(sf) {
+
+		byw = w * YBASIS(ybptr+l)
+	        do k = 1, xorder {
+	            bw = byw * XBASIS(xbptr+k)
+	            VECTOR(vzptr+k) = VECTOR(vzptr+k) - bw * z
+	            ii = 1
+		    xindex = k
+		    yindex = l
+		    xxorder = xorder
+		    do j = k + ntimes, GS_NCOEFF(sf) {
+		        MATRIX(mzptr+ii) = MATRIX(mzptr+ii) - bw *
+			    XBASIS(xbptr+xindex) * YBASIS(ybptr+yindex)	
+			if (mod (xindex, xxorder) == 0) {
+			    xindex = 1
+			    yindex = yindex + 1
+			    switch (GS_XTERMS(sf)) {
+			    case GS_XNONE:
+				xxorder = 1
+			    case GS_XHALF:
+				if ((yindex + GS_XORDER(sf)) > maxorder)
+				    xxorder = xxorder - 1
+			    default:
+		    		;
+			    }
+			} else
+			    xindex = xindex + 1
+		        ii = ii + 1
+		    }
+		    mzptr = mzptr + GS_NCOEFF(sf)
+	        }
+
+		vzptr = vzptr + xorder
+		ntimes = ntimes + xorder
+		switch (GS_XTERMS(sf)) {
+		case GS_XNONE:
+		    xorder = 1
+		case GS_XHALF:
+		    if ((l + GS_XORDER(sf) + 1) > maxorder)
+		        xorder = xorder - 1
+		default:
+		    ;
+		}
+	    }
+
+	default:
+	    call error (0, "GSACCUM: Unknown curve type.")
+	}
+
+	# release the space
+	call sfree (sp)
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+end
diff --git a/math/gsurfit/gsrestore.gx b/math/gsurfit/gsrestore.gx
new file mode 100644
index 00000000..f8ced0a8
--- /dev/null
+++ b/math/gsurfit/gsrestore.gx
@@ -0,0 +1,102 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSRESTORE -- Procedure to restore the surface fit stored by GSSAVE
+# to the surface descriptor for use by the evaluating routines. The
+# surface parameters, surface type, xorder (or number of polynomial
+# pieces in x), yorder (or number of polynomial pieces in y), xterms,
+# xmin, xmax and ymin and ymax, are stored in the first
+# eight elements of the real array fit, followed by the GS_NCOEFF(sf)
+# surface coefficients.
+
+$if (datatype == r)
+procedure gsrestore (sf, fit)
+$else
+procedure dgsrestore (sf, fit)
+$endif
+
+pointer	sf		# surface descriptor
+PIXEL	fit[ARB]	# array containing the surface parameters and
+			# coefficients
+
+int	surface_type, xorder, yorder, order
+PIXEL	xmin, xmax, ymin, ymax	
+
+begin
+	# allocate space for the surface descriptor
+	call calloc (sf, LEN_GSSTRUCT, TY_STRUCT)
+
+	xorder = nint (GS_SAVEXORDER(fit))
+	if (xorder < 1)
+	    call error (0, "GSRESTORE: Illegal x order.")
+	yorder = nint (GS_SAVEYORDER(fit))
+	if (yorder < 1)
+	    call error (0, "GSRESTORE: Illegal y order.")
+
+	xmin = GS_SAVEXMIN(fit)
+	xmax = GS_SAVEXMAX(fit)
+	if (xmax <= xmin)
+	    call error (0, "GSRESTORE: Illegal x range.")
+	ymin = GS_SAVEYMIN(fit)
+	ymax = GS_SAVEYMAX(fit)
+	if (ymax <= ymin)
+	    call error (0, "GSRESTORE: Illegal y range.")
+
+	# set surface type dependent surface descriptor parameters
+	surface_type = nint (GS_SAVETYPE(fit))
+	switch (surface_type) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf) = xorder
+	    GS_XORDER(sf) = xorder
+	    GS_XMIN(sf) = xmin
+	    GS_XMAX(sf) = xmax
+	    GS_XRANGE(sf) = PIXEL(2.0) / (xmax - xmin)
+	    GS_XMAXMIN(sf) =  - (xmax + xmin) / PIXEL(2.0)
+	    GS_NYCOEFF(sf) = yorder
+	    GS_YORDER(sf) = yorder
+	    GS_YMIN(sf) = ymin
+	    GS_YMAX(sf) = ymax
+	    GS_YRANGE(sf) = PIXEL(2.0) / (ymax - ymin)
+	    GS_YMAXMIN(sf) =  - (ymax + ymin) / PIXEL(2.0)
+	    GS_XTERMS(sf) = GS_SAVEXTERMS(fit)
+	    switch (GS_XTERMS(sf)) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf) = GS_NXCOEFF(sf) + GS_NYCOEFF(sf) - 1
+	    case GS_XHALF:
+		order = min (xorder, yorder)
+		GS_NCOEFF(sf) = GS_NXCOEFF(sf) * GS_NYCOEFF(sf) - order *
+		    (order - 1) / 2
+	    case GS_XFULL:
+		GS_NCOEFF(sf) = GS_NXCOEFF(sf) * GS_NYCOEFF(sf)
+	    }
+	default:
+	    call error (0, "GSRESTORE: Unknown surface type.")
+	}
+
+	# set remaining curve parameters
+	GS_TYPE(sf) = surface_type
+
+	# allocate space for the coefficient array
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+	GS_MATRIX(sf) = NULL
+	GS_CHOFAC(sf) = NULL
+	GS_VECTOR(sf) = NULL
+	GS_COEFF(sf) = NULL
+	GS_WZ(sf) = NULL
+
+	$if (datatype == r)
+	call malloc (GS_COEFF(sf), GS_NCOEFF(sf), TY_REAL)
+	$else
+	call malloc (GS_COEFF(sf), GS_NCOEFF(sf), TY_DOUBLE)
+	$endif
+
+	# restore coefficient array
+	call amov$t (fit[GS_SAVECOEFF+1], COEFF(GS_COEFF(sf)), GS_NCOEFF(sf))
+end
diff --git a/math/gsurfit/gsrestored.x b/math/gsurfit/gsrestored.x
new file mode 100644
index 00000000..11008ec2
--- /dev/null
+++ b/math/gsurfit/gsrestored.x
@@ -0,0 +1,90 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSRESTORE -- Procedure to restore the surface fit stored by GSSAVE
+# to the surface descriptor for use by the evaluating routines. The
+# surface parameters, surface type, xorder (or number of polynomial
+# pieces in x), yorder (or number of polynomial pieces in y), xterms,
+# xmin, xmax and ymin and ymax, are stored in the first
+# eight elements of the real array fit, followed by the GS_NCOEFF(sf)
+# surface coefficients.
+
+procedure dgsrestore (sf, fit)
+
+pointer	sf		# surface descriptor
+double	fit[ARB]	# array containing the surface parameters and
+			# coefficients
+
+int	surface_type, xorder, yorder, order
+double	xmin, xmax, ymin, ymax	
+
+begin
+	# allocate space for the surface descriptor
+	call calloc (sf, LEN_GSSTRUCT, TY_STRUCT)
+
+	xorder = nint (GS_SAVEXORDER(fit))
+	if (xorder < 1)
+	    call error (0, "GSRESTORE: Illegal x order.")
+	yorder = nint (GS_SAVEYORDER(fit))
+	if (yorder < 1)
+	    call error (0, "GSRESTORE: Illegal y order.")
+
+	xmin = GS_SAVEXMIN(fit)
+	xmax = GS_SAVEXMAX(fit)
+	if (xmax <= xmin)
+	    call error (0, "GSRESTORE: Illegal x range.")
+	ymin = GS_SAVEYMIN(fit)
+	ymax = GS_SAVEYMAX(fit)
+	if (ymax <= ymin)
+	    call error (0, "GSRESTORE: Illegal y range.")
+
+	# set surface type dependent surface descriptor parameters
+	surface_type = nint (GS_SAVETYPE(fit))
+	switch (surface_type) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf) = xorder
+	    GS_XORDER(sf) = xorder
+	    GS_XMIN(sf) = xmin
+	    GS_XMAX(sf) = xmax
+	    GS_XRANGE(sf) = double(2.0) / (xmax - xmin)
+	    GS_XMAXMIN(sf) =  - (xmax + xmin) / double(2.0)
+	    GS_NYCOEFF(sf) = yorder
+	    GS_YORDER(sf) = yorder
+	    GS_YMIN(sf) = ymin
+	    GS_YMAX(sf) = ymax
+	    GS_YRANGE(sf) = double(2.0) / (ymax - ymin)
+	    GS_YMAXMIN(sf) =  - (ymax + ymin) / double(2.0)
+	    GS_XTERMS(sf) = GS_SAVEXTERMS(fit)
+	    switch (GS_XTERMS(sf)) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf) = GS_NXCOEFF(sf) + GS_NYCOEFF(sf) - 1
+	    case GS_XHALF:
+		order = min (xorder, yorder)
+		GS_NCOEFF(sf) = GS_NXCOEFF(sf) * GS_NYCOEFF(sf) - order *
+		    (order - 1) / 2
+	    case GS_XFULL:
+		GS_NCOEFF(sf) = GS_NXCOEFF(sf) * GS_NYCOEFF(sf)
+	    }
+	default:
+	    call error (0, "GSRESTORE: Unknown surface type.")
+	}
+
+	# set remaining curve parameters
+	GS_TYPE(sf) = surface_type
+
+	# allocate space for the coefficient array
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+	GS_MATRIX(sf) = NULL
+	GS_CHOFAC(sf) = NULL
+	GS_VECTOR(sf) = NULL
+	GS_COEFF(sf) = NULL
+	GS_WZ(sf) = NULL
+
+	call malloc (GS_COEFF(sf), GS_NCOEFF(sf), TY_DOUBLE)
+
+	# restore coefficient array
+	call amovd (fit[GS_SAVECOEFF+1], COEFF(GS_COEFF(sf)), GS_NCOEFF(sf))
+end
diff --git a/math/gsurfit/gsrestorer.x b/math/gsurfit/gsrestorer.x
new file mode 100644
index 00000000..0b7b0e56
--- /dev/null
+++ b/math/gsurfit/gsrestorer.x
@@ -0,0 +1,90 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSRESTORE -- Procedure to restore the surface fit stored by GSSAVE
+# to the surface descriptor for use by the evaluating routines. The
+# surface parameters, surface type, xorder (or number of polynomial
+# pieces in x), yorder (or number of polynomial pieces in y), xterms,
+# xmin, xmax and ymin and ymax, are stored in the first
+# eight elements of the real array fit, followed by the GS_NCOEFF(sf)
+# surface coefficients.
+
+procedure gsrestore (sf, fit)
+
+pointer	sf		# surface descriptor
+real	fit[ARB]	# array containing the surface parameters and
+			# coefficients
+
+int	surface_type, xorder, yorder, order
+real	xmin, xmax, ymin, ymax	
+
+begin
+	# allocate space for the surface descriptor
+	call calloc (sf, LEN_GSSTRUCT, TY_STRUCT)
+
+	xorder = nint (GS_SAVEXORDER(fit))
+	if (xorder < 1)
+	    call error (0, "GSRESTORE: Illegal x order.")
+	yorder = nint (GS_SAVEYORDER(fit))
+	if (yorder < 1)
+	    call error (0, "GSRESTORE: Illegal y order.")
+
+	xmin = GS_SAVEXMIN(fit)
+	xmax = GS_SAVEXMAX(fit)
+	if (xmax <= xmin)
+	    call error (0, "GSRESTORE: Illegal x range.")
+	ymin = GS_SAVEYMIN(fit)
+	ymax = GS_SAVEYMAX(fit)
+	if (ymax <= ymin)
+	    call error (0, "GSRESTORE: Illegal y range.")
+
+	# set surface type dependent surface descriptor parameters
+	surface_type = nint (GS_SAVETYPE(fit))
+	switch (surface_type) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf) = xorder
+	    GS_XORDER(sf) = xorder
+	    GS_XMIN(sf) = xmin
+	    GS_XMAX(sf) = xmax
+	    GS_XRANGE(sf) = real(2.0) / (xmax - xmin)
+	    GS_XMAXMIN(sf) =  - (xmax + xmin) / real(2.0)
+	    GS_NYCOEFF(sf) = yorder
+	    GS_YORDER(sf) = yorder
+	    GS_YMIN(sf) = ymin
+	    GS_YMAX(sf) = ymax
+	    GS_YRANGE(sf) = real(2.0) / (ymax - ymin)
+	    GS_YMAXMIN(sf) =  - (ymax + ymin) / real(2.0)
+	    GS_XTERMS(sf) = GS_SAVEXTERMS(fit)
+	    switch (GS_XTERMS(sf)) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf) = GS_NXCOEFF(sf) + GS_NYCOEFF(sf) - 1
+	    case GS_XHALF:
+		order = min (xorder, yorder)
+		GS_NCOEFF(sf) = GS_NXCOEFF(sf) * GS_NYCOEFF(sf) - order *
+		    (order - 1) / 2
+	    case GS_XFULL:
+		GS_NCOEFF(sf) = GS_NXCOEFF(sf) * GS_NYCOEFF(sf)
+	    }
+	default:
+	    call error (0, "GSRESTORE: Unknown surface type.")
+	}
+
+	# set remaining curve parameters
+	GS_TYPE(sf) = surface_type
+
+	# allocate space for the coefficient array
+	GS_XBASIS(sf) = NULL
+	GS_YBASIS(sf) = NULL
+	GS_MATRIX(sf) = NULL
+	GS_CHOFAC(sf) = NULL
+	GS_VECTOR(sf) = NULL
+	GS_COEFF(sf) = NULL
+	GS_WZ(sf) = NULL
+
+	call malloc (GS_COEFF(sf), GS_NCOEFF(sf), TY_REAL)
+
+	# restore coefficient array
+	call amovr (fit[GS_SAVECOEFF+1], COEFF(GS_COEFF(sf)), GS_NCOEFF(sf))
+end
diff --git a/math/gsurfit/gssave.gx b/math/gsurfit/gssave.gx
new file mode 100644
index 00000000..a4cbaa82
--- /dev/null
+++ b/math/gsurfit/gssave.gx
@@ -0,0 +1,50 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include	"gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSSAVE -- Procedure to save the surface fit for later use by the
+# evaluate routines. After a call to GSSAVE the first eight elements
+# of fit contain the surface type, xorder (or number of polynomial pieces
+# in x), yorder (or the number of polynomial pieces in y), xterms, xmin,
+# xmax, ymin, and ymax. The remaining spaces are filled by the GS_NCOEFF(sf)
+# coefficients.
+
+$if (datatype == r)
+procedure gssave (sf, fit)
+$else
+procedure dgssave (sf, fit)
+$endif
+
+pointer	sf		# pointer to the surface descriptor
+PIXEL	fit[ARB]	# array for storing fit
+
+begin
+	# get the surface parameters
+	if (sf == NULL)
+	    return
+
+	# order is surface type dependent
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_SAVEXORDER(fit) = GS_XORDER(sf)
+	    GS_SAVEYORDER(fit) = GS_YORDER(sf)
+	default:
+	    call error (0, "GSSAVE: Unknown surface type.")
+	}
+
+	# save remaining parameters
+	GS_SAVETYPE(fit) = GS_TYPE(sf)
+	GS_SAVEXMIN(fit) = GS_XMIN(sf)
+	GS_SAVEXMAX(fit) = GS_XMAX(sf)
+	GS_SAVEYMIN(fit) = GS_YMIN(sf)
+	GS_SAVEYMAX(fit) = GS_YMAX(sf)
+	GS_SAVEXTERMS(fit) = GS_XTERMS(sf)
+
+	# save the coefficients
+	call amov$t (COEFF(GS_COEFF(sf)), fit[GS_SAVECOEFF+1], GS_NCOEFF(sf))
+end
diff --git a/math/gsurfit/gssaved.x b/math/gsurfit/gssaved.x
new file mode 100644
index 00000000..b2bddffd
--- /dev/null
+++ b/math/gsurfit/gssaved.x
@@ -0,0 +1,42 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSSAVE -- Procedure to save the surface fit for later use by the
+# evaluate routines. After a call to GSSAVE the first eight elements
+# of fit contain the surface type, xorder (or number of polynomial pieces
+# in x), yorder (or the number of polynomial pieces in y), xterms, xmin,
+# xmax, ymin, and ymax. The remaining spaces are filled by the GS_NCOEFF(sf)
+# coefficients.
+
+procedure dgssave (sf, fit)
+
+pointer	sf		# pointer to the surface descriptor
+double	fit[ARB]	# array for storing fit
+
+begin
+	# get the surface parameters
+	if (sf == NULL)
+	    return
+
+	# order is surface type dependent
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_SAVEXORDER(fit) = GS_XORDER(sf)
+	    GS_SAVEYORDER(fit) = GS_YORDER(sf)
+	default:
+	    call error (0, "GSSAVE: Unknown surface type.")
+	}
+
+	# save remaining parameters
+	GS_SAVETYPE(fit) = GS_TYPE(sf)
+	GS_SAVEXMIN(fit) = GS_XMIN(sf)
+	GS_SAVEXMAX(fit) = GS_XMAX(sf)
+	GS_SAVEYMIN(fit) = GS_YMIN(sf)
+	GS_SAVEYMAX(fit) = GS_YMAX(sf)
+	GS_SAVEXTERMS(fit) = GS_XTERMS(sf)
+
+	# save the coefficients
+	call amovd (COEFF(GS_COEFF(sf)), fit[GS_SAVECOEFF+1], GS_NCOEFF(sf))
+end
diff --git a/math/gsurfit/gssaver.x b/math/gsurfit/gssaver.x
new file mode 100644
index 00000000..b4f5bf32
--- /dev/null
+++ b/math/gsurfit/gssaver.x
@@ -0,0 +1,42 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include	"gsurfitdef.h"
+
+# GSSAVE -- Procedure to save the surface fit for later use by the
+# evaluate routines. After a call to GSSAVE the first eight elements
+# of fit contain the surface type, xorder (or number of polynomial pieces
+# in x), yorder (or the number of polynomial pieces in y), xterms, xmin,
+# xmax, ymin, and ymax. The remaining spaces are filled by the GS_NCOEFF(sf)
+# coefficients.
+
+procedure gssave (sf, fit)
+
+pointer	sf		# pointer to the surface descriptor
+real	fit[ARB]	# array for storing fit
+
+begin
+	# get the surface parameters
+	if (sf == NULL)
+	    return
+
+	# order is surface type dependent
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_SAVEXORDER(fit) = GS_XORDER(sf)
+	    GS_SAVEYORDER(fit) = GS_YORDER(sf)
+	default:
+	    call error (0, "GSSAVE: Unknown surface type.")
+	}
+
+	# save remaining parameters
+	GS_SAVETYPE(fit) = GS_TYPE(sf)
+	GS_SAVEXMIN(fit) = GS_XMIN(sf)
+	GS_SAVEXMAX(fit) = GS_XMAX(sf)
+	GS_SAVEYMIN(fit) = GS_YMIN(sf)
+	GS_SAVEYMAX(fit) = GS_YMAX(sf)
+	GS_SAVEXTERMS(fit) = GS_XTERMS(sf)
+
+	# save the coefficients
+	call amovr (COEFF(GS_COEFF(sf)), fit[GS_SAVECOEFF+1], GS_NCOEFF(sf))
+end
diff --git a/math/gsurfit/gsscoeff.gx b/math/gsurfit/gsscoeff.gx
new file mode 100644
index 00000000..09b894e3
--- /dev/null
+++ b/math/gsurfit/gsscoeff.gx
@@ -0,0 +1,54 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSSCOEFF -- Procedure to set a particular coefficient.
+# If the requested coefficient is undefined then the coefficient is not set.
+
+$if (datatype == r)
+procedure gsscoeff (sf, xorder, yorder, coeff)
+$else
+procedure dgsscoeff (sf, xorder, yorder, coeff)
+$endif
+
+pointer	sf		# pointer to the surface fitting descriptor
+int	xorder		# X order of desired coefficent
+int	yorder		# Y order of desired coefficent
+PIXEL	coeff		# Coefficient value
+
+int	i, n, maxorder, xincr
+
+begin
+	if ((xorder > GS_XORDER(sf)) || (yorder > GS_YORDER(sf)))
+	    return
+
+	switch (GS_XTERMS(sf)) {
+	case GS_XNONE:
+	    if (yorder == 1)
+		n = xorder
+	    else if (xorder == 1)
+		n = GS_NXCOEFF(sf) + yorder - 1
+	    else
+		return
+	case GS_XHALF:
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    if ((xorder + yorder) > maxorder)
+		return
+	    n = xorder
+	    xincr = GS_XORDER(sf)
+	    do i = 2, yorder {
+		n = n + xincr
+		if ((i + GS_XORDER(sf) + 1) > maxorder)
+		    xincr = xincr - 1
+	    }
+	case GS_XFULL:
+	    n = xorder + (yorder - 1) * GS_NXCOEFF(sf)
+	}
+
+	COEFF(GS_COEFF(sf) + n - 1) = coeff
+end
diff --git a/math/gsurfit/gsscoeffd.x b/math/gsurfit/gsscoeffd.x
new file mode 100644
index 00000000..452eb70b
--- /dev/null
+++ b/math/gsurfit/gsscoeffd.x
@@ -0,0 +1,46 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSSCOEFF -- Procedure to set a particular coefficient.
+# If the requested coefficient is undefined then the coefficient is not set.
+
+procedure dgsscoeff (sf, xorder, yorder, coeff)
+
+pointer	sf		# pointer to the surface fitting descriptor
+int	xorder		# X order of desired coefficent
+int	yorder		# Y order of desired coefficent
+double	coeff		# Coefficient value
+
+int	i, n, maxorder, xincr
+
+begin
+	if ((xorder > GS_XORDER(sf)) || (yorder > GS_YORDER(sf)))
+	    return
+
+	switch (GS_XTERMS(sf)) {
+	case GS_XNONE:
+	    if (yorder == 1)
+		n = xorder
+	    else if (xorder == 1)
+		n = GS_NXCOEFF(sf) + yorder - 1
+	    else
+		return
+	case GS_XHALF:
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    if ((xorder + yorder) > maxorder)
+		return
+	    n = xorder
+	    xincr = GS_XORDER(sf)
+	    do i = 2, yorder {
+		n = n + xincr
+		if ((i + GS_XORDER(sf) + 1) > maxorder)
+		    xincr = xincr - 1
+	    }
+	case GS_XFULL:
+	    n = xorder + (yorder - 1) * GS_NXCOEFF(sf)
+	}
+
+	COEFF(GS_COEFF(sf) + n - 1) = coeff
+end
diff --git a/math/gsurfit/gsscoeffr.x b/math/gsurfit/gsscoeffr.x
new file mode 100644
index 00000000..dacb4bd0
--- /dev/null
+++ b/math/gsurfit/gsscoeffr.x
@@ -0,0 +1,46 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSSCOEFF -- Procedure to set a particular coefficient.
+# If the requested coefficient is undefined then the coefficient is not set.
+
+procedure gsscoeff (sf, xorder, yorder, coeff)
+
+pointer	sf		# pointer to the surface fitting descriptor
+int	xorder		# X order of desired coefficent
+int	yorder		# Y order of desired coefficent
+real	coeff		# Coefficient value
+
+int	i, n, maxorder, xincr
+
+begin
+	if ((xorder > GS_XORDER(sf)) || (yorder > GS_YORDER(sf)))
+	    return
+
+	switch (GS_XTERMS(sf)) {
+	case GS_XNONE:
+	    if (yorder == 1)
+		n = xorder
+	    else if (xorder == 1)
+		n = GS_NXCOEFF(sf) + yorder - 1
+	    else
+		return
+	case GS_XHALF:
+	    maxorder = max (GS_XORDER(sf) + 1, GS_YORDER(sf) + 1)
+	    if ((xorder + yorder) > maxorder)
+		return
+	    n = xorder
+	    xincr = GS_XORDER(sf)
+	    do i = 2, yorder {
+		n = n + xincr
+		if ((i + GS_XORDER(sf) + 1) > maxorder)
+		    xincr = xincr - 1
+	    }
+	case GS_XFULL:
+	    n = xorder + (yorder - 1) * GS_NXCOEFF(sf)
+	}
+
+	COEFF(GS_COEFF(sf) + n - 1) = coeff
+end
diff --git a/math/gsurfit/gssolve.gx b/math/gsurfit/gssolve.gx
new file mode 100644
index 00000000..9008e140
--- /dev/null
+++ b/math/gsurfit/gssolve.gx
@@ -0,0 +1,101 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSSOLVE -- Solve the matrix normal equations of the form ca = b for a,
+# where c is a symmetric, positive semi-definite, banded matrix with
+# GS_NXCOEFF(sf) * GS_NYCOEFF(sf) rows and a and b are GS_NXCOEFF(sf) *
+# GS_NYCOEFF(sf)-vectors.
+# Initially c is stored in the matrix MATRIX
+# and b is stored in VECTOR.
+# The Cholesky factorization of MATRIX is calculated and stored in CHOFAC.
+# Finally the coefficients are calculated by forward and back substitution
+# and stored in COEFF.
+#
+# This version has two options: fit all the coefficients or fix the
+# the zeroth coefficient at a specified reference point.
+
+$if (datatype == r)
+procedure gssolve (sf, ier)
+$else
+procedure dgssolve (sf, ier)
+$endif
+
+pointer	sf 		# curve descriptor
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+int	i, ncoeff
+pointer	sp, vector, matrix
+
+$if (datatype == r)
+PIXEL	gseval()
+$else
+PIXEL	dgseval()
+$endif
+
+begin
+	if (IS_INDEF(GS_XREF(sf)) || IS_INDEF(GS_YREF(sf)) ||
+	    IS_INDEF(GS_ZREF(sf)))
+	    ncoeff = GS_NCOEFF(sf)
+	else
+	    ncoeff = GS_NCOEFF(sf) - 1
+
+	# test for number of degrees of freedom
+	ier = OK
+	i = GS_NPTS(sf) - ncoeff
+	if (i < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	if (ncoeff == GS_NCOEFF(sf)) {
+	    vector = GS_VECTOR(sf)
+	    matrix = GS_MATRIX(sf)
+	} else {
+	    # allocate working space for the reduced vector and matrix
+	    call smark (sp)
+	    call salloc (vector, ncoeff, TY_PIXEL)
+	    call salloc (matrix, ncoeff*ncoeff, TY_PIXEL)
+
+	    # eliminate the terms from the vector and matrix
+	    call amov$t (VECTOR(GS_VECTOR(sf)+1), Mem$t[vector], ncoeff)
+	    do i = 0, ncoeff-1
+		call amov$t (MATRIX(GS_MATRIX(sf)+(i+1)*GS_NCOEFF(sf)),
+		    Mem$t[matrix+i*ncoeff], ncoeff)
+	}
+
+	# solve for the coefficients.
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    # calculate the Cholesky factorization of the data matrix
+	    call $tgschofac (MATRIX(matrix), ncoeff, ncoeff,
+	        CHOFAC(GS_CHOFAC(sf)), ier)
+
+	    # solve for the coefficients by forward and back substitution
+	    call $tgschoslv (CHOFAC(GS_CHOFAC(sf)), ncoeff, ncoeff,
+	        VECTOR(vector), COEFF(GS_COEFF(sf)+GS_NCOEFF(sf)-ncoeff))
+
+	default:
+	    call error (0, "GSSOLVE: Illegal surface type.")
+	}
+
+	if (ncoeff != GS_NCOEFF(sf)) {
+	$if (datatype == r)
+	    COEFF(GS_COEFF(sf)) = GS_ZREF(sf) -
+	        gseval (sf, GS_XREF(sf), GS_YREF(sf))
+	$else
+	    COEFF(GS_COEFF(sf)) = GS_ZREF(sf) -
+	        dgseval (sf, GS_XREF(sf), GS_YREF(sf))
+	$endif
+	    call sfree (sp)
+	}
+end
diff --git a/math/gsurfit/gssolved.x b/math/gsurfit/gssolved.x
new file mode 100644
index 00000000..e3ed43ce
--- /dev/null
+++ b/math/gsurfit/gssolved.x
@@ -0,0 +1,84 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSSOLVE -- Solve the matrix normal equations of the form ca = b for a,
+# where c is a symmetric, positive semi-definite, banded matrix with
+# GS_NXCOEFF(sf) * GS_NYCOEFF(sf) rows and a and b are GS_NXCOEFF(sf) *
+# GS_NYCOEFF(sf)-vectors.
+# Initially c is stored in the matrix MATRIX
+# and b is stored in VECTOR.
+# The Cholesky factorization of MATRIX is calculated and stored in CHOFAC.
+# Finally the coefficients are calculated by forward and back substitution
+# and stored in COEFF.
+#
+# This version has two options: fit all the coefficients or fix the
+# the zeroth coefficient at a specified reference point.
+
+procedure dgssolve (sf, ier)
+
+pointer	sf 		# curve descriptor
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+int	i, ncoeff
+pointer	sp, vector, matrix
+
+double	dgseval()
+
+begin
+	if (IS_INDEFD(GS_XREF(sf)) || IS_INDEFD(GS_YREF(sf)) ||
+	    IS_INDEFD(GS_ZREF(sf)))
+	    ncoeff = GS_NCOEFF(sf)
+	else
+	    ncoeff = GS_NCOEFF(sf) - 1
+
+	# test for number of degrees of freedom
+	ier = OK
+	i = GS_NPTS(sf) - ncoeff
+	if (i < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	if (ncoeff == GS_NCOEFF(sf)) {
+	    vector = GS_VECTOR(sf)
+	    matrix = GS_MATRIX(sf)
+	} else {
+	    # allocate working space for the reduced vector and matrix
+	    call smark (sp)
+	    call salloc (vector, ncoeff, TY_DOUBLE)
+	    call salloc (matrix, ncoeff*ncoeff, TY_DOUBLE)
+
+	    # eliminate the terms from the vector and matrix
+	    call amovd (VECTOR(GS_VECTOR(sf)+1), Memd[vector], ncoeff)
+	    do i = 0, ncoeff-1
+		call amovd (MATRIX(GS_MATRIX(sf)+(i+1)*GS_NCOEFF(sf)),
+		    Memd[matrix+i*ncoeff], ncoeff)
+	}
+
+	# solve for the coefficients.
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    # calculate the Cholesky factorization of the data matrix
+	    call dgschofac (MATRIX(matrix), ncoeff, ncoeff,
+	        CHOFAC(GS_CHOFAC(sf)), ier)
+
+	    # solve for the coefficients by forward and back substitution
+	    call dgschoslv (CHOFAC(GS_CHOFAC(sf)), ncoeff, ncoeff,
+	        VECTOR(vector), COEFF(GS_COEFF(sf)+GS_NCOEFF(sf)-ncoeff))
+
+	default:
+	    call error (0, "GSSOLVE: Illegal surface type.")
+	}
+
+	if (ncoeff != GS_NCOEFF(sf)) {
+	    COEFF(GS_COEFF(sf)) = GS_ZREF(sf) -
+	        dgseval (sf, GS_XREF(sf), GS_YREF(sf))
+	    call sfree (sp)
+	}
+end
diff --git a/math/gsurfit/gssolver.x b/math/gsurfit/gssolver.x
new file mode 100644
index 00000000..5135298a
--- /dev/null
+++ b/math/gsurfit/gssolver.x
@@ -0,0 +1,84 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSSOLVE -- Solve the matrix normal equations of the form ca = b for a,
+# where c is a symmetric, positive semi-definite, banded matrix with
+# GS_NXCOEFF(sf) * GS_NYCOEFF(sf) rows and a and b are GS_NXCOEFF(sf) *
+# GS_NYCOEFF(sf)-vectors.
+# Initially c is stored in the matrix MATRIX
+# and b is stored in VECTOR.
+# The Cholesky factorization of MATRIX is calculated and stored in CHOFAC.
+# Finally the coefficients are calculated by forward and back substitution
+# and stored in COEFF.
+#
+# This version has two options: fit all the coefficients or fix the
+# the zeroth coefficient at a specified reference point.
+
+procedure gssolve (sf, ier)
+
+pointer	sf 		# curve descriptor
+int	ier		# ier = OK, everything OK
+			# ier = SINGULAR, matrix is singular, 1 or more
+			# coefficients are 0.
+			# ier = NO_DEG_FREEDOM, too few points to solve matrix
+
+int	i, ncoeff
+pointer	sp, vector, matrix
+
+real	gseval()
+
+begin
+	if (IS_INDEFR(GS_XREF(sf)) || IS_INDEFR(GS_YREF(sf)) ||
+	    IS_INDEFR(GS_ZREF(sf)))
+	    ncoeff = GS_NCOEFF(sf)
+	else
+	    ncoeff = GS_NCOEFF(sf) - 1
+
+	# test for number of degrees of freedom
+	ier = OK
+	i = GS_NPTS(sf) - ncoeff
+	if (i < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	if (ncoeff == GS_NCOEFF(sf)) {
+	    vector = GS_VECTOR(sf)
+	    matrix = GS_MATRIX(sf)
+	} else {
+	    # allocate working space for the reduced vector and matrix
+	    call smark (sp)
+	    call salloc (vector, ncoeff, TY_REAL)
+	    call salloc (matrix, ncoeff*ncoeff, TY_REAL)
+
+	    # eliminate the terms from the vector and matrix
+	    call amovr (VECTOR(GS_VECTOR(sf)+1), Memr[vector], ncoeff)
+	    do i = 0, ncoeff-1
+		call amovr (MATRIX(GS_MATRIX(sf)+(i+1)*GS_NCOEFF(sf)),
+		    Memr[matrix+i*ncoeff], ncoeff)
+	}
+
+	# solve for the coefficients.
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    # calculate the Cholesky factorization of the data matrix
+	    call rgschofac (MATRIX(matrix), ncoeff, ncoeff,
+	        CHOFAC(GS_CHOFAC(sf)), ier)
+
+	    # solve for the coefficients by forward and back substitution
+	    call rgschoslv (CHOFAC(GS_CHOFAC(sf)), ncoeff, ncoeff,
+	        VECTOR(vector), COEFF(GS_COEFF(sf)+GS_NCOEFF(sf)-ncoeff))
+
+	default:
+	    call error (0, "GSSOLVE: Illegal surface type.")
+	}
+
+	if (ncoeff != GS_NCOEFF(sf)) {
+	    COEFF(GS_COEFF(sf)) = GS_ZREF(sf) -
+	        gseval (sf, GS_XREF(sf), GS_YREF(sf))
+	    call sfree (sp)
+	}
+end
diff --git a/math/gsurfit/gsstat.gx b/math/gsurfit/gsstat.gx
new file mode 100644
index 00000000..d701ea9e
--- /dev/null
+++ b/math/gsurfit/gsstat.gx
@@ -0,0 +1,99 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSGET -- Procedure to fetch a gsurfit parameter
+$if (datatype == r)
+real procedure gsgetr (sf, parameter)
+$else
+double procedure dgsgetd (sf, parameter)
+$endif
+
+pointer	sf		# pointer to the surface fit
+int	parameter	# parameter to be fetched
+
+begin
+	switch (parameter) {
+	case GSXMAX:
+	    return (GS_XMAX(sf))
+	case GSXMIN:
+	    return (GS_XMIN(sf))
+	case GSYMAX:
+	    return (GS_YMAX(sf))
+	case GSYMIN:
+	    return (GS_YMIN(sf))
+	case GSXREF:
+	    return (GS_XREF(sf))
+	case GSYREF:
+	    return (GS_YREF(sf))
+	case GSZREF:
+	    return (GS_ZREF(sf))
+	}
+end
+
+
+# GSSET -- Procedure to set a gsurfit parameter
+$if (datatype == r)
+procedure gsset (sf, parameter, val)
+$else
+procedure dgsset (sf, parameter, val)
+$endif
+
+pointer	sf		# pointer to the surface fit
+int	parameter	# parameter to be fetched
+PIXEL	val		# value to set
+
+begin
+	switch (parameter) {
+	case GSXREF:
+	    GS_XREF(sf) = val
+	case GSYREF:
+	    GS_YREF(sf) = val
+	case GSZREF:
+	    GS_ZREF(sf) = val
+	}
+end
+
+
+# GSGETI -- Procedure to fetch an integer parameter
+
+$if (datatype == r)
+int procedure gsgeti (sf, parameter)
+$else
+int procedure dgsgeti (sf, parameter)
+$endif
+
+pointer sf		# pointer to the surface fit
+int	parameter	# integer parameter
+
+begin
+	switch (parameter) {
+	case GSTYPE:
+	    return (GS_TYPE(sf))
+	case GSXORDER:
+	    switch (GS_TYPE(sf)) {
+	    case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+		return (GS_XORDER(sf))
+	    }
+	case GSYORDER:
+	    switch (GS_TYPE(sf)) {
+	    case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	        return (GS_YORDER(sf))
+	    }
+	case GSXTERMS:
+	    return (GS_XTERMS(sf))
+	case GSNXCOEFF:
+	    return (GS_NXCOEFF(sf))
+	case GSNYCOEFF:
+	    return (GS_NYCOEFF(sf))
+	case GSNCOEFF:
+	    return (GS_NCOEFF(sf))
+	case GSNSAVE:
+	    return (GS_SAVECOEFF+GS_NCOEFF(sf))
+	}
+end
diff --git a/math/gsurfit/gsstatd.x b/math/gsurfit/gsstatd.x
new file mode 100644
index 00000000..b8c551f1
--- /dev/null
+++ b/math/gsurfit/gsstatd.x
@@ -0,0 +1,83 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSGET -- Procedure to fetch a gsurfit parameter
+double procedure dgsgetd (sf, parameter)
+
+pointer	sf		# pointer to the surface fit
+int	parameter	# parameter to be fetched
+
+begin
+	switch (parameter) {
+	case GSXMAX:
+	    return (GS_XMAX(sf))
+	case GSXMIN:
+	    return (GS_XMIN(sf))
+	case GSYMAX:
+	    return (GS_YMAX(sf))
+	case GSYMIN:
+	    return (GS_YMIN(sf))
+	case GSXREF:
+	    return (GS_XREF(sf))
+	case GSYREF:
+	    return (GS_YREF(sf))
+	case GSZREF:
+	    return (GS_ZREF(sf))
+	}
+end
+
+
+# GSSET -- Procedure to set a gsurfit parameter
+procedure dgsset (sf, parameter, val)
+
+pointer	sf		# pointer to the surface fit
+int	parameter	# parameter to be fetched
+double	val		# value to set
+
+begin
+	switch (parameter) {
+	case GSXREF:
+	    GS_XREF(sf) = val
+	case GSYREF:
+	    GS_YREF(sf) = val
+	case GSZREF:
+	    GS_ZREF(sf) = val
+	}
+end
+
+
+# GSGETI -- Procedure to fetch an integer parameter
+
+int procedure dgsgeti (sf, parameter)
+
+pointer sf		# pointer to the surface fit
+int	parameter	# integer parameter
+
+begin
+	switch (parameter) {
+	case GSTYPE:
+	    return (GS_TYPE(sf))
+	case GSXORDER:
+	    switch (GS_TYPE(sf)) {
+	    case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+		return (GS_XORDER(sf))
+	    }
+	case GSYORDER:
+	    switch (GS_TYPE(sf)) {
+	    case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	        return (GS_YORDER(sf))
+	    }
+	case GSXTERMS:
+	    return (GS_XTERMS(sf))
+	case GSNXCOEFF:
+	    return (GS_NXCOEFF(sf))
+	case GSNYCOEFF:
+	    return (GS_NYCOEFF(sf))
+	case GSNCOEFF:
+	    return (GS_NCOEFF(sf))
+	case GSNSAVE:
+	    return (GS_SAVECOEFF+GS_NCOEFF(sf))
+	}
+end
diff --git a/math/gsurfit/gsstatr.x b/math/gsurfit/gsstatr.x
new file mode 100644
index 00000000..826bcafa
--- /dev/null
+++ b/math/gsurfit/gsstatr.x
@@ -0,0 +1,83 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSGET -- Procedure to fetch a gsurfit parameter
+real procedure gsgetr (sf, parameter)
+
+pointer	sf		# pointer to the surface fit
+int	parameter	# parameter to be fetched
+
+begin
+	switch (parameter) {
+	case GSXMAX:
+	    return (GS_XMAX(sf))
+	case GSXMIN:
+	    return (GS_XMIN(sf))
+	case GSYMAX:
+	    return (GS_YMAX(sf))
+	case GSYMIN:
+	    return (GS_YMIN(sf))
+	case GSXREF:
+	    return (GS_XREF(sf))
+	case GSYREF:
+	    return (GS_YREF(sf))
+	case GSZREF:
+	    return (GS_ZREF(sf))
+	}
+end
+
+
+# GSSET -- Procedure to set a gsurfit parameter
+procedure gsset (sf, parameter, val)
+
+pointer	sf		# pointer to the surface fit
+int	parameter	# parameter to be fetched
+real	val		# value to set
+
+begin
+	switch (parameter) {
+	case GSXREF:
+	    GS_XREF(sf) = val
+	case GSYREF:
+	    GS_YREF(sf) = val
+	case GSZREF:
+	    GS_ZREF(sf) = val
+	}
+end
+
+
+# GSGETI -- Procedure to fetch an integer parameter
+
+int procedure gsgeti (sf, parameter)
+
+pointer sf		# pointer to the surface fit
+int	parameter	# integer parameter
+
+begin
+	switch (parameter) {
+	case GSTYPE:
+	    return (GS_TYPE(sf))
+	case GSXORDER:
+	    switch (GS_TYPE(sf)) {
+	    case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+		return (GS_XORDER(sf))
+	    }
+	case GSYORDER:
+	    switch (GS_TYPE(sf)) {
+	    case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	        return (GS_YORDER(sf))
+	    }
+	case GSXTERMS:
+	    return (GS_XTERMS(sf))
+	case GSNXCOEFF:
+	    return (GS_NXCOEFF(sf))
+	case GSNYCOEFF:
+	    return (GS_NYCOEFF(sf))
+	case GSNCOEFF:
+	    return (GS_NCOEFF(sf))
+	case GSNSAVE:
+	    return (GS_SAVECOEFF+GS_NCOEFF(sf))
+	}
+end
diff --git a/math/gsurfit/gssub.gx b/math/gsurfit/gssub.gx
new file mode 100644
index 00000000..533417a7
--- /dev/null
+++ b/math/gsurfit/gssub.gx
@@ -0,0 +1,198 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSSUB -- Procedure to subtract two surfaces. The surfaces
+# must be the same type and the fit must cover the same range of data in x
+# and y. This is a special function.
+
+$if (datatype == r)
+procedure gssub (sf1, sf2, sf3)
+$else
+procedure dgssub (sf1, sf2, sf3)
+$endif
+
+pointer	sf1		# pointer to the first surface
+pointer	sf2		# pointer to the second surface
+pointer	sf3		# pointer to the output surface
+
+int	i, ncoeff, order, maxorder1, maxorder2, maxorder3
+int	nmove1, nmove2, nmove3
+pointer	sp, coeff, ptr1, ptr2, ptr3
+
+bool	fpequal$t()
+$if (datatype == r)
+int	gsgeti()
+$else
+int	dgsgeti()
+$endif
+
+begin
+	# test for NULL surface
+	if (sf1 == NULL && sf2 == NULL) {
+	    sf3 = NULL
+	    return
+	} else if (sf1 == NULL) {
+$if (datatype == r)
+	    ncoeff = gsgeti (sf2, GSNSAVE)
+$else
+	    ncoeff = dgsgeti (sf2, GSNSAVE)
+$endif
+	    call smark (sp)
+	    $if (datatype == r)
+	    call salloc (coeff, ncoeff, TY_REAL)
+	    $else
+	    call salloc (coeff, ncoeff, TY_DOUBLE)
+	    $endif
+	    call gssave (sf2, Mem$t[coeff])
+	    $if (datatype == r)
+	    call amulk$t (Mem$t[coeff], -1.0, Mem$t[coeff], ncoeff)
+	    $else
+	    call amulk$t (Mem$t[coeff], -1.0d0, Mem$t[coeff], ncoeff)
+	    $endif
+	    call gsrestore (sf3, Mem$t[coeff])
+	    call sfree (sp)
+	    return
+	} else if (sf2 == NULL) {
+	    call gscopy (sf1, sf3)
+	    return
+	}
+
+	# test that function type is the same
+	if (GS_TYPE(sf1) != GS_TYPE(sf2))
+	    call error (0, "GSSUB: Incompatable surface types.")
+
+	# test that mins and maxs are the same
+	if (! fpequal$t (GS_XMIN(sf1), GS_XMIN(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequal$t (GS_XMAX(sf1), GS_XMAX(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequal$t (GS_YMIN(sf1), GS_YMIN(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+	if (! fpequal$t (GS_YMAX(sf1), GS_YMAX(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+
+	# allocate space for the pointer
+	call calloc (sf3, LEN_GSSTRUCT, TY_STRUCT)
+
+	# copy parameters
+	GS_TYPE(sf3) = GS_TYPE(sf1)
+
+	switch (GS_TYPE(sf3)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf3) = max (GS_NXCOEFF(sf1), GS_NXCOEFF(sf2))
+	    GS_XORDER(sf3) = max (GS_XORDER(sf1), GS_XORDER(sf2))
+	    GS_XMIN(sf3) = GS_XMIN(sf1)
+	    GS_XMAX(sf3) = GS_XMAX(sf1)
+	    GS_XRANGE(sf3) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf3) = GS_XMAXMIN(sf1)
+	    GS_NYCOEFF(sf3) = max (GS_NYCOEFF(sf1), GS_NYCOEFF(sf2))
+	    GS_YORDER(sf3) = max (GS_YORDER(sf1), GS_YORDER(sf2))
+	    GS_YMIN(sf3) = GS_YMIN(sf1)
+	    GS_YMAX(sf3) = GS_YMAX(sf1)
+	    GS_YRANGE(sf3) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf3) = GS_YMAXMIN(sf1)
+	    if (GS_XTERMS(sf1) == GS_XTERMS(sf2))
+		GS_XTERMS(sf3) = GS_XTERMS(sf1)
+	    else if (GS_XTERMS(sf1) == GS_XFULL || GS_XTERMS(sf2) == GS_XFULL)
+		GS_XTERMS(sf3) = GS_XFULL
+	    else
+		GS_XTERMS(sf3) = GS_XHALF
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) + GS_NYCOEFF(sf3) - 1
+	    case GS_XHALF:
+		order = min (GS_XORDER(sf3), GS_YORDER(sf3))
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3) - order *
+		    (order - 1) / 2
+	    default:
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3)
+	    }
+	default:
+	    call error (0, "GSADD: Unknown curve type.")
+	}
+
+	# set pointers to NULL
+	GS_XBASIS(sf3) = NULL
+	GS_YBASIS(sf3) = NULL
+	GS_MATRIX(sf3) = NULL
+	GS_CHOFAC(sf3) = NULL
+	GS_VECTOR(sf3) = NULL
+	GS_COEFF(sf3) = NULL
+	GS_WZ(sf3) = NULL
+
+	# calculate the coefficients
+	$if (datatype == r)
+	call calloc (GS_COEFF(sf3), GS_NCOEFF(sf3), TY_REAL)
+	$else
+	call calloc (GS_COEFF(sf3), GS_NCOEFF(sf3), TY_DOUBLE)
+	$endif
+
+	# set up the line counters.
+        maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+        maxorder2 = max (GS_XORDER(sf2) + 1, GS_YORDER(sf2) + 1)
+        maxorder3 = max (GS_XORDER(sf3) + 1, GS_YORDER(sf3) + 1)
+
+        # add in the first surface.
+        ptr1 = GS_COEFF(sf1)
+        ptr3 = GS_COEFF(sf3)
+        nmove1 = GS_NXCOEFF(sf1)
+        nmove3 = GS_NXCOEFF(sf3)
+        do i = 1, GS_NYCOEFF(sf1) {
+            call amov$t (COEFF(ptr1), COEFF(ptr3), nmove1)
+            ptr1 = ptr1 + nmove1
+            ptr3 = ptr3 + nmove3
+            switch (GS_XTERMS(sf1)) {
+            case GS_XNONE:
+                nmove1 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf1) + 1) > maxorder1)
+                    nmove1 = nmove1 - 1
+            case GS_XFULL:
+                ;
+            }
+            switch (GS_XTERMS(sf3)) {
+            case GS_XNONE:
+                nmove3 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+                    nmove3 = nmove3 - 1
+            case GS_XFULL:
+                ;
+            }
+        }
+
+        # subtract the second surface.
+        ptr2 = GS_COEFF(sf2)
+        ptr3 = GS_COEFF(sf3)
+        nmove2 = GS_NXCOEFF(sf2)
+        nmove3 = GS_NXCOEFF(sf3)
+        do i = 1, GS_NYCOEFF(sf2) {
+            call asub$t (COEFF(ptr3), COEFF(ptr2), COEFF(ptr3), nmove2)
+            ptr2 = ptr2 + nmove2
+            ptr3 = ptr3 + nmove3
+            switch (GS_XTERMS(sf2)) {
+            case GS_XNONE:
+                nmove2 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf2) + 1) > maxorder2)
+                    nmove2 = nmove2 - 1
+            case GS_XFULL:
+                ;
+            }
+            switch (GS_XTERMS(sf3)) {
+            case GS_XNONE:
+                nmove3 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+                    nmove3 = nmove3 - 1
+            case GS_XFULL:
+                ;
+            }
+        }
+end
diff --git a/math/gsurfit/gssubd.x b/math/gsurfit/gssubd.x
new file mode 100644
index 00000000..7f4dd1ba
--- /dev/null
+++ b/math/gsurfit/gssubd.x
@@ -0,0 +1,170 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSSUB -- Procedure to subtract two surfaces. The surfaces
+# must be the same type and the fit must cover the same range of data in x
+# and y. This is a special function.
+
+procedure dgssub (sf1, sf2, sf3)
+
+pointer	sf1		# pointer to the first surface
+pointer	sf2		# pointer to the second surface
+pointer	sf3		# pointer to the output surface
+
+int	i, ncoeff, order, maxorder1, maxorder2, maxorder3
+int	nmove1, nmove2, nmove3
+pointer	sp, coeff, ptr1, ptr2, ptr3
+
+bool	fpequald()
+int	dgsgeti()
+
+begin
+	# test for NULL surface
+	if (sf1 == NULL && sf2 == NULL) {
+	    sf3 = NULL
+	    return
+	} else if (sf1 == NULL) {
+	    ncoeff = dgsgeti (sf2, GSNSAVE)
+	    call smark (sp)
+	    call salloc (coeff, ncoeff, TY_DOUBLE)
+	    call gssave (sf2, Memd[coeff])
+	    call amulkd (Memd[coeff], -1.0d0, Memd[coeff], ncoeff)
+	    call gsrestore (sf3, Memd[coeff])
+	    call sfree (sp)
+	    return
+	} else if (sf2 == NULL) {
+	    call gscopy (sf1, sf3)
+	    return
+	}
+
+	# test that function type is the same
+	if (GS_TYPE(sf1) != GS_TYPE(sf2))
+	    call error (0, "GSSUB: Incompatable surface types.")
+
+	# test that mins and maxs are the same
+	if (! fpequald (GS_XMIN(sf1), GS_XMIN(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequald (GS_XMAX(sf1), GS_XMAX(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequald (GS_YMIN(sf1), GS_YMIN(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+	if (! fpequald (GS_YMAX(sf1), GS_YMAX(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+
+	# allocate space for the pointer
+	call calloc (sf3, LEN_GSSTRUCT, TY_STRUCT)
+
+	# copy parameters
+	GS_TYPE(sf3) = GS_TYPE(sf1)
+
+	switch (GS_TYPE(sf3)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf3) = max (GS_NXCOEFF(sf1), GS_NXCOEFF(sf2))
+	    GS_XORDER(sf3) = max (GS_XORDER(sf1), GS_XORDER(sf2))
+	    GS_XMIN(sf3) = GS_XMIN(sf1)
+	    GS_XMAX(sf3) = GS_XMAX(sf1)
+	    GS_XRANGE(sf3) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf3) = GS_XMAXMIN(sf1)
+	    GS_NYCOEFF(sf3) = max (GS_NYCOEFF(sf1), GS_NYCOEFF(sf2))
+	    GS_YORDER(sf3) = max (GS_YORDER(sf1), GS_YORDER(sf2))
+	    GS_YMIN(sf3) = GS_YMIN(sf1)
+	    GS_YMAX(sf3) = GS_YMAX(sf1)
+	    GS_YRANGE(sf3) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf3) = GS_YMAXMIN(sf1)
+	    if (GS_XTERMS(sf1) == GS_XTERMS(sf2))
+		GS_XTERMS(sf3) = GS_XTERMS(sf1)
+	    else if (GS_XTERMS(sf1) == GS_XFULL || GS_XTERMS(sf2) == GS_XFULL)
+		GS_XTERMS(sf3) = GS_XFULL
+	    else
+		GS_XTERMS(sf3) = GS_XHALF
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) + GS_NYCOEFF(sf3) - 1
+	    case GS_XHALF:
+		order = min (GS_XORDER(sf3), GS_YORDER(sf3))
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3) - order *
+		    (order - 1) / 2
+	    default:
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3)
+	    }
+	default:
+	    call error (0, "GSADD: Unknown curve type.")
+	}
+
+	# set pointers to NULL
+	GS_XBASIS(sf3) = NULL
+	GS_YBASIS(sf3) = NULL
+	GS_MATRIX(sf3) = NULL
+	GS_CHOFAC(sf3) = NULL
+	GS_VECTOR(sf3) = NULL
+	GS_COEFF(sf3) = NULL
+	GS_WZ(sf3) = NULL
+
+	# calculate the coefficients
+	call calloc (GS_COEFF(sf3), GS_NCOEFF(sf3), TY_DOUBLE)
+
+	# set up the line counters.
+        maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+        maxorder2 = max (GS_XORDER(sf2) + 1, GS_YORDER(sf2) + 1)
+        maxorder3 = max (GS_XORDER(sf3) + 1, GS_YORDER(sf3) + 1)
+
+        # add in the first surface.
+        ptr1 = GS_COEFF(sf1)
+        ptr3 = GS_COEFF(sf3)
+        nmove1 = GS_NXCOEFF(sf1)
+        nmove3 = GS_NXCOEFF(sf3)
+        do i = 1, GS_NYCOEFF(sf1) {
+            call amovd (COEFF(ptr1), COEFF(ptr3), nmove1)
+            ptr1 = ptr1 + nmove1
+            ptr3 = ptr3 + nmove3
+            switch (GS_XTERMS(sf1)) {
+            case GS_XNONE:
+                nmove1 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf1) + 1) > maxorder1)
+                    nmove1 = nmove1 - 1
+            case GS_XFULL:
+                ;
+            }
+            switch (GS_XTERMS(sf3)) {
+            case GS_XNONE:
+                nmove3 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+                    nmove3 = nmove3 - 1
+            case GS_XFULL:
+                ;
+            }
+        }
+
+        # subtract the second surface.
+        ptr2 = GS_COEFF(sf2)
+        ptr3 = GS_COEFF(sf3)
+        nmove2 = GS_NXCOEFF(sf2)
+        nmove3 = GS_NXCOEFF(sf3)
+        do i = 1, GS_NYCOEFF(sf2) {
+            call asubd (COEFF(ptr3), COEFF(ptr2), COEFF(ptr3), nmove2)
+            ptr2 = ptr2 + nmove2
+            ptr3 = ptr3 + nmove3
+            switch (GS_XTERMS(sf2)) {
+            case GS_XNONE:
+                nmove2 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf2) + 1) > maxorder2)
+                    nmove2 = nmove2 - 1
+            case GS_XFULL:
+                ;
+            }
+            switch (GS_XTERMS(sf3)) {
+            case GS_XNONE:
+                nmove3 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+                    nmove3 = nmove3 - 1
+            case GS_XFULL:
+                ;
+            }
+        }
+end
diff --git a/math/gsurfit/gssubr.x b/math/gsurfit/gssubr.x
new file mode 100644
index 00000000..748f7bee
--- /dev/null
+++ b/math/gsurfit/gssubr.x
@@ -0,0 +1,170 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSSUB -- Procedure to subtract two surfaces. The surfaces
+# must be the same type and the fit must cover the same range of data in x
+# and y. This is a special function.
+
+procedure gssub (sf1, sf2, sf3)
+
+pointer	sf1		# pointer to the first surface
+pointer	sf2		# pointer to the second surface
+pointer	sf3		# pointer to the output surface
+
+int	i, ncoeff, order, maxorder1, maxorder2, maxorder3
+int	nmove1, nmove2, nmove3
+pointer	sp, coeff, ptr1, ptr2, ptr3
+
+bool	fpequalr()
+int	gsgeti()
+
+begin
+	# test for NULL surface
+	if (sf1 == NULL && sf2 == NULL) {
+	    sf3 = NULL
+	    return
+	} else if (sf1 == NULL) {
+	    ncoeff = gsgeti (sf2, GSNSAVE)
+	    call smark (sp)
+	    call salloc (coeff, ncoeff, TY_REAL)
+	    call gssave (sf2, Memr[coeff])
+	    call amulkr (Memr[coeff], -1.0, Memr[coeff], ncoeff)
+	    call gsrestore (sf3, Memr[coeff])
+	    call sfree (sp)
+	    return
+	} else if (sf2 == NULL) {
+	    call gscopy (sf1, sf3)
+	    return
+	}
+
+	# test that function type is the same
+	if (GS_TYPE(sf1) != GS_TYPE(sf2))
+	    call error (0, "GSSUB: Incompatable surface types.")
+
+	# test that mins and maxs are the same
+	if (! fpequalr (GS_XMIN(sf1), GS_XMIN(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequalr (GS_XMAX(sf1), GS_XMAX(sf2)))
+	    call error (0, "GSADD: X ranges not identical.")
+	if (! fpequalr (GS_YMIN(sf1), GS_YMIN(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+	if (! fpequalr (GS_YMAX(sf1), GS_YMAX(sf2)))
+	    call error (0, "GSADD: Y ranges not identical.")
+
+	# allocate space for the pointer
+	call calloc (sf3, LEN_GSSTRUCT, TY_STRUCT)
+
+	# copy parameters
+	GS_TYPE(sf3) = GS_TYPE(sf1)
+
+	switch (GS_TYPE(sf3)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+	    GS_NXCOEFF(sf3) = max (GS_NXCOEFF(sf1), GS_NXCOEFF(sf2))
+	    GS_XORDER(sf3) = max (GS_XORDER(sf1), GS_XORDER(sf2))
+	    GS_XMIN(sf3) = GS_XMIN(sf1)
+	    GS_XMAX(sf3) = GS_XMAX(sf1)
+	    GS_XRANGE(sf3) = GS_XRANGE(sf1)
+	    GS_XMAXMIN(sf3) = GS_XMAXMIN(sf1)
+	    GS_NYCOEFF(sf3) = max (GS_NYCOEFF(sf1), GS_NYCOEFF(sf2))
+	    GS_YORDER(sf3) = max (GS_YORDER(sf1), GS_YORDER(sf2))
+	    GS_YMIN(sf3) = GS_YMIN(sf1)
+	    GS_YMAX(sf3) = GS_YMAX(sf1)
+	    GS_YRANGE(sf3) = GS_YRANGE(sf1)
+	    GS_YMAXMIN(sf3) = GS_YMAXMIN(sf1)
+	    if (GS_XTERMS(sf1) == GS_XTERMS(sf2))
+		GS_XTERMS(sf3) = GS_XTERMS(sf1)
+	    else if (GS_XTERMS(sf1) == GS_XFULL || GS_XTERMS(sf2) == GS_XFULL)
+		GS_XTERMS(sf3) = GS_XFULL
+	    else
+		GS_XTERMS(sf3) = GS_XHALF
+	    switch (GS_XTERMS(sf3)) {
+	    case GS_XNONE:
+		GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) + GS_NYCOEFF(sf3) - 1
+	    case GS_XHALF:
+		order = min (GS_XORDER(sf3), GS_YORDER(sf3))
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3) - order *
+		    (order - 1) / 2
+	    default:
+	        GS_NCOEFF(sf3) = GS_NXCOEFF(sf3) * GS_NYCOEFF(sf3)
+	    }
+	default:
+	    call error (0, "GSADD: Unknown curve type.")
+	}
+
+	# set pointers to NULL
+	GS_XBASIS(sf3) = NULL
+	GS_YBASIS(sf3) = NULL
+	GS_MATRIX(sf3) = NULL
+	GS_CHOFAC(sf3) = NULL
+	GS_VECTOR(sf3) = NULL
+	GS_COEFF(sf3) = NULL
+	GS_WZ(sf3) = NULL
+
+	# calculate the coefficients
+	call calloc (GS_COEFF(sf3), GS_NCOEFF(sf3), TY_REAL)
+
+	# set up the line counters.
+        maxorder1 = max (GS_XORDER(sf1) + 1, GS_YORDER(sf1) + 1)
+        maxorder2 = max (GS_XORDER(sf2) + 1, GS_YORDER(sf2) + 1)
+        maxorder3 = max (GS_XORDER(sf3) + 1, GS_YORDER(sf3) + 1)
+
+        # add in the first surface.
+        ptr1 = GS_COEFF(sf1)
+        ptr3 = GS_COEFF(sf3)
+        nmove1 = GS_NXCOEFF(sf1)
+        nmove3 = GS_NXCOEFF(sf3)
+        do i = 1, GS_NYCOEFF(sf1) {
+            call amovr (COEFF(ptr1), COEFF(ptr3), nmove1)
+            ptr1 = ptr1 + nmove1
+            ptr3 = ptr3 + nmove3
+            switch (GS_XTERMS(sf1)) {
+            case GS_XNONE:
+                nmove1 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf1) + 1) > maxorder1)
+                    nmove1 = nmove1 - 1
+            case GS_XFULL:
+                ;
+            }
+            switch (GS_XTERMS(sf3)) {
+            case GS_XNONE:
+                nmove3 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+                    nmove3 = nmove3 - 1
+            case GS_XFULL:
+                ;
+            }
+        }
+
+        # subtract the second surface.
+        ptr2 = GS_COEFF(sf2)
+        ptr3 = GS_COEFF(sf3)
+        nmove2 = GS_NXCOEFF(sf2)
+        nmove3 = GS_NXCOEFF(sf3)
+        do i = 1, GS_NYCOEFF(sf2) {
+            call asubr (COEFF(ptr3), COEFF(ptr2), COEFF(ptr3), nmove2)
+            ptr2 = ptr2 + nmove2
+            ptr3 = ptr3 + nmove3
+            switch (GS_XTERMS(sf2)) {
+            case GS_XNONE:
+                nmove2 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf2) + 1) > maxorder2)
+                    nmove2 = nmove2 - 1
+            case GS_XFULL:
+                ;
+            }
+            switch (GS_XTERMS(sf3)) {
+            case GS_XNONE:
+                nmove3 = 1
+            case GS_XHALF:
+                if ((i + GS_XORDER(sf3) + 1) > maxorder3)
+                    nmove3 = nmove3 - 1
+            case GS_XFULL:
+                ;
+            }
+        }
+end
diff --git a/math/gsurfit/gsurfit.h b/math/gsurfit/gsurfit.h
new file mode 100644
index 00000000..5d46762b
--- /dev/null
+++ b/math/gsurfit/gsurfit.h
@@ -0,0 +1,48 @@
+# definitions for the gsurfit package
+
+# define the permitted types of curves
+
+define	GS_FUNCTIONS	"|chebyshev|legendre|polynomial|"
+define	GS_CHEBYSHEV	1	# chebyshev polynomials
+define	GS_LEGENDRE	2	# legendre polynomials
+define	GS_POLYNOMIAL	3	# power series polynomials
+define	NTYPES		3
+
+# define the xterms flags
+
+define	GS_XTYPES	"|none|full|half|"
+define	GS_XNONE	0	# no x-terms (old NO)
+define	GS_XFULL	1	# full x-terms (new YES)
+define	GS_XHALF	2	# half x-terms (new)
+
+# define the weighting flags
+
+define	GS_WEIGHTS	"|user|uniform|spacing|"
+define	WTS_USER	1	# user enters weights
+define	WTS_UNIFORM	2	# equal weights
+define	WTS_SPACING	3	# weight proportional to spacing of data points
+
+# error conditions
+
+define	SINGULAR	1
+define	NO_DEG_FREEDOM	2
+
+# gsstat/gsset definitions
+
+define	GSTYPE		1
+define	GSXORDER	2
+define	GSYORDER	3
+define	GSXTERMS	4
+define	GSNXCOEFF	5
+define	GSNYCOEFF	6
+define	GSNCOEFF	7
+define	GSNSAVE		8
+define	GSXMIN		9
+define	GSXMAX		10
+define	GSYMIN		11
+define	GSYMAX		12
+define	GSXREF		13
+define	GSYREF		14
+define	GSZREF		15
+
+define	GS_SAVECOEFF	8
diff --git a/math/gsurfit/gsurfitdef.h b/math/gsurfit/gsurfitdef.h
new file mode 100644
index 00000000..7ee6cc1d
--- /dev/null
+++ b/math/gsurfit/gsurfitdef.h
@@ -0,0 +1,61 @@
+# Header file for the surface fitting package
+
+# set up the curve descriptor structure
+
+define	LEN_GSSTRUCT	64
+
+define	GS_TYPE		Memi[$1]	# Type of curve to be fitted
+define	GS_XORDER	Memi[$1+1]	# Order of the fit in x
+define	GS_YORDER	Memi[$1+2]	# Order of the fit in y
+define	GS_XTERMS	Memi[$1+3]	# Cross terms for polynomials
+define	GS_NXCOEFF	Memi[$1+4]	# Number of x coefficients
+define	GS_NYCOEFF	Memi[$1+5]	# Number of y coefficients
+define	GS_NCOEFF	Memi[$1+6]	# Total number of coefficients
+define	GS_XREF		Memr[P2R($1+7)]	# x reference value
+define	GS_YREF		Memr[P2R($1+8)]	# y reference value
+define	GS_ZREF		Memr[P2R($1+9)]	# z reference value
+define	GS_XMAX		Memr[P2R($1+10)]# Maximum x value
+define	GS_XMIN		Memr[P2R($1+11)]# Minimum x value
+define	GS_YMAX		Memr[P2R($1+12)]# Maximum y value
+define	GS_YMIN		Memr[P2R($1+13)]# Minimum y value		
+define	GS_XRANGE	Memr[P2R($1+14)]# 2. / (xmax - xmin), polynomials
+define	GS_XMAXMIN	Memr[P2R($1+15)]# - (xmax + xmin) / 2., polynomials
+define	GS_YRANGE	Memr[P2R($1+16)]# 2. / (ymax - ymin), polynomials
+define	GS_YMAXMIN	Memr[P2R($1+17)]# - (ymax + ymin) / 2., polynomials
+define	GS_NPTS		Memi[$1+18]	# Number of data points
+
+define	GS_MATRIX	Memi[$1+19]	# Pointer to original matrix
+define	GS_CHOFAC	Memi[$1+20]	# Pointer to Cholesky factorization
+define	GS_VECTOR	Memi[$1+21]	# Pointer to  vector
+define	GS_COEFF	Memi[$1+22]	# Pointer to coefficient vector
+define	GS_XBASIS	Memi[$1+23]	# Pointer to basis functions (all x)
+define	GS_YBASIS	Memi[$1+24]	# Pointer to basis functions (all y)
+define	GS_WZ		Memi[$1+25]	# Pointer to w * z (gsrefit)
+
+# matrix and vector element definitions
+
+define	XBASIS		Memr[P2P($1)]	# Non zero basis for all x
+define	YBASIS		Memr[P2P($1)]	# Non zero basis for all y
+define	XBS		Memr[P2P($1)]	# Non zero basis for single x
+define	YBS		Memr[P2P($1)]	# Non zero basis for single y
+define	MATRIX		Memr[P2P($1)]	# Element of MATRIX
+define	CHOFAC		Memr[P2P($1)]	# Element of CHOFAC
+define	VECTOR		Memr[P2P($1)]	# Element of VECTOR
+define	COEFF		Memr[P2P($1)]	# Element of COEFF
+
+# structure definitions for restore
+
+define	GS_SAVETYPE	$1[1]
+define	GS_SAVEXORDER	$1[2]
+define	GS_SAVEYORDER	$1[3]
+define	GS_SAVEXTERMS	$1[4]
+define	GS_SAVEXMIN	$1[5]
+define	GS_SAVEXMAX	$1[6]
+define	GS_SAVEYMIN	$1[7]
+define	GS_SAVEYMAX	$1[8]
+
+# data type
+
+define	DELTA		EPSILON
+
+# miscellaneous
diff --git a/math/gsurfit/gsvector.gx b/math/gsurfit/gsvector.gx
new file mode 100644
index 00000000..60044dd6
--- /dev/null
+++ b/math/gsurfit/gsvector.gx
@@ -0,0 +1,65 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSVECTOR -- Procedure to evaluate the fitted surface at an array of points.
+# The GS_NCOEFF(sf) coefficients are stored in the
+# vector COEFF.
+
+$if (datatype == r)
+procedure gsvector (sf, x, y, zfit, npts)
+$else
+procedure dgsvector (sf, x, y, zfit, npts)
+$endif
+
+pointer	sf		# pointer to surface descriptor structure
+PIXEL	x[ARB]		# x value
+PIXEL	y[ARB]		# y value
+PIXEL	zfit[ARB]	# fits surface values
+int	npts		# number of data points
+
+begin
+	# evaluate the surface along the vector
+	switch (GS_TYPE(sf)) {
+	case GS_POLYNOMIAL:
+	    if (GS_XORDER(sf) == 1) {
+		call $tgs_1devpoly (COEFF(GS_COEFF(sf)), y, zfit, npts,
+		    GS_YORDER(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	    } else if (GS_YORDER(sf) == 1) {
+		call $tgs_1devpoly (COEFF(GS_COEFF(sf)), x, zfit, npts,
+		    GS_XORDER(sf), GS_XMAXMIN(sf), GS_XRANGE(sf))
+	    } else
+	        call $tgs_evpoly (COEFF(GS_COEFF(sf)), x, y, zfit, npts,
+	            GS_XTERMS(sf), GS_XORDER(sf), GS_YORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	case GS_CHEBYSHEV:
+	    if (GS_XORDER(sf) == 1) {
+		call $tgs_1devcheb (COEFF(GS_COEFF(sf)), y, zfit, npts,
+		    GS_YORDER(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	    } else if (GS_YORDER(sf) == 1) {
+		call $tgs_1devcheb (COEFF(GS_COEFF(sf)), x, zfit, npts,
+		    GS_XORDER(sf), GS_XMAXMIN(sf), GS_XRANGE(sf))
+	    } else
+	        call $tgs_evcheb (COEFF(GS_COEFF(sf)), x, y, zfit, npts,
+	            GS_XTERMS(sf), GS_XORDER(sf), GS_YORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	case GS_LEGENDRE:
+	    if (GS_XORDER(sf) == 1) {
+		call $tgs_1devleg (COEFF(GS_COEFF(sf)), y, zfit, npts,
+		    GS_YORDER(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	    } else if (GS_YORDER(sf) == 1) {
+		call $tgs_1devleg (COEFF(GS_COEFF(sf)), x, zfit, npts,
+		    GS_XORDER(sf), GS_XMAXMIN(sf), GS_XRANGE(sf))
+	    } else
+	        call $tgs_evleg (COEFF(GS_COEFF(sf)), x, y, zfit, npts,
+		    GS_XTERMS(sf), GS_XORDER(sf), GS_YORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	default:
+	    call error (0, "GSVECTOR: Unknown surface type.")
+	}
+end
diff --git a/math/gsurfit/gsvectord.x b/math/gsurfit/gsvectord.x
new file mode 100644
index 00000000..8bb980e6
--- /dev/null
+++ b/math/gsurfit/gsvectord.x
@@ -0,0 +1,57 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSVECTOR -- Procedure to evaluate the fitted surface at an array of points.
+# The GS_NCOEFF(sf) coefficients are stored in the
+# vector COEFF.
+
+procedure dgsvector (sf, x, y, zfit, npts)
+
+pointer	sf		# pointer to surface descriptor structure
+double	x[ARB]		# x value
+double	y[ARB]		# y value
+double	zfit[ARB]	# fits surface values
+int	npts		# number of data points
+
+begin
+	# evaluate the surface along the vector
+	switch (GS_TYPE(sf)) {
+	case GS_POLYNOMIAL:
+	    if (GS_XORDER(sf) == 1) {
+		call dgs_1devpoly (COEFF(GS_COEFF(sf)), y, zfit, npts,
+		    GS_YORDER(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	    } else if (GS_YORDER(sf) == 1) {
+		call dgs_1devpoly (COEFF(GS_COEFF(sf)), x, zfit, npts,
+		    GS_XORDER(sf), GS_XMAXMIN(sf), GS_XRANGE(sf))
+	    } else
+	        call dgs_evpoly (COEFF(GS_COEFF(sf)), x, y, zfit, npts,
+	            GS_XTERMS(sf), GS_XORDER(sf), GS_YORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	case GS_CHEBYSHEV:
+	    if (GS_XORDER(sf) == 1) {
+		call dgs_1devcheb (COEFF(GS_COEFF(sf)), y, zfit, npts,
+		    GS_YORDER(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	    } else if (GS_YORDER(sf) == 1) {
+		call dgs_1devcheb (COEFF(GS_COEFF(sf)), x, zfit, npts,
+		    GS_XORDER(sf), GS_XMAXMIN(sf), GS_XRANGE(sf))
+	    } else
+	        call dgs_evcheb (COEFF(GS_COEFF(sf)), x, y, zfit, npts,
+	            GS_XTERMS(sf), GS_XORDER(sf), GS_YORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	case GS_LEGENDRE:
+	    if (GS_XORDER(sf) == 1) {
+		call dgs_1devleg (COEFF(GS_COEFF(sf)), y, zfit, npts,
+		    GS_YORDER(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	    } else if (GS_YORDER(sf) == 1) {
+		call dgs_1devleg (COEFF(GS_COEFF(sf)), x, zfit, npts,
+		    GS_XORDER(sf), GS_XMAXMIN(sf), GS_XRANGE(sf))
+	    } else
+	        call dgs_evleg (COEFF(GS_COEFF(sf)), x, y, zfit, npts,
+		    GS_XTERMS(sf), GS_XORDER(sf), GS_YORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	default:
+	    call error (0, "GSVECTOR: Unknown surface type.")
+	}
+end
diff --git a/math/gsurfit/gsvectorr.x b/math/gsurfit/gsvectorr.x
new file mode 100644
index 00000000..38213ecc
--- /dev/null
+++ b/math/gsurfit/gsvectorr.x
@@ -0,0 +1,57 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSVECTOR -- Procedure to evaluate the fitted surface at an array of points.
+# The GS_NCOEFF(sf) coefficients are stored in the
+# vector COEFF.
+
+procedure gsvector (sf, x, y, zfit, npts)
+
+pointer	sf		# pointer to surface descriptor structure
+real	x[ARB]		# x value
+real	y[ARB]		# y value
+real	zfit[ARB]	# fits surface values
+int	npts		# number of data points
+
+begin
+	# evaluate the surface along the vector
+	switch (GS_TYPE(sf)) {
+	case GS_POLYNOMIAL:
+	    if (GS_XORDER(sf) == 1) {
+		call rgs_1devpoly (COEFF(GS_COEFF(sf)), y, zfit, npts,
+		    GS_YORDER(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	    } else if (GS_YORDER(sf) == 1) {
+		call rgs_1devpoly (COEFF(GS_COEFF(sf)), x, zfit, npts,
+		    GS_XORDER(sf), GS_XMAXMIN(sf), GS_XRANGE(sf))
+	    } else
+	        call rgs_evpoly (COEFF(GS_COEFF(sf)), x, y, zfit, npts,
+	            GS_XTERMS(sf), GS_XORDER(sf), GS_YORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	case GS_CHEBYSHEV:
+	    if (GS_XORDER(sf) == 1) {
+		call rgs_1devcheb (COEFF(GS_COEFF(sf)), y, zfit, npts,
+		    GS_YORDER(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	    } else if (GS_YORDER(sf) == 1) {
+		call rgs_1devcheb (COEFF(GS_COEFF(sf)), x, zfit, npts,
+		    GS_XORDER(sf), GS_XMAXMIN(sf), GS_XRANGE(sf))
+	    } else
+	        call rgs_evcheb (COEFF(GS_COEFF(sf)), x, y, zfit, npts,
+	            GS_XTERMS(sf), GS_XORDER(sf), GS_YORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	case GS_LEGENDRE:
+	    if (GS_XORDER(sf) == 1) {
+		call rgs_1devleg (COEFF(GS_COEFF(sf)), y, zfit, npts,
+		    GS_YORDER(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	    } else if (GS_YORDER(sf) == 1) {
+		call rgs_1devleg (COEFF(GS_COEFF(sf)), x, zfit, npts,
+		    GS_XORDER(sf), GS_XMAXMIN(sf), GS_XRANGE(sf))
+	    } else
+	        call rgs_evleg (COEFF(GS_COEFF(sf)), x, y, zfit, npts,
+		    GS_XTERMS(sf), GS_XORDER(sf), GS_YORDER(sf), GS_XMAXMIN(sf),
+		    GS_XRANGE(sf), GS_YMAXMIN(sf), GS_YRANGE(sf))
+	default:
+	    call error (0, "GSVECTOR: Unknown surface type.")
+	}
+end
diff --git a/math/gsurfit/gszero.gx b/math/gsurfit/gszero.gx
new file mode 100644
index 00000000..e99cbe4d
--- /dev/null
+++ b/math/gsurfit/gszero.gx
@@ -0,0 +1,60 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+$if (datatype == r)
+include "gsurfitdef.h"
+$else
+include "dgsurfitdef.h"
+$endif
+
+# GSZERO -- Procedure to zero the accumulators before doing
+# a new fit in accumulate mode. The inner products of the basis functions
+# are accumulated in the GS_NCOEFF(sf) ** 2
+# array MATRIX, while
+# the inner products of the basis functions and the data ordinates are
+# accumulated in the  NCOEFF(sf)-vector VECTOR.
+
+$if (datatype == r)
+procedure gszero (sf)
+$else
+procedure dgszero (sf)
+$endif
+
+pointer	sf	# pointer to surface descriptor
+errchk	mfree
+
+begin
+	# zero the accumulators
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    GS_NPTS(sf) = 0
+	    call aclr$t (VECTOR(GS_VECTOR(sf)), GS_NCOEFF(sf))
+	    call aclr$t (MATRIX(GS_MATRIX(sf)), GS_NCOEFF(sf) ** 2)
+
+	    # free the basis functions defined from previous calls to sfrefit
+	    $if (datatype == r)
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_REAL)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_REAL)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_REAL)
+	    GS_WZ(sf) = NULL
+	    $else
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_DOUBLE)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_DOUBLE)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_DOUBLE)
+	    GS_WZ(sf) = NULL
+	    $endif
+	default:
+	    call error (0, "GSZERO: Unknown surface type.")
+	}
+end
diff --git a/math/gsurfit/gszerod.x b/math/gsurfit/gszerod.x
new file mode 100644
index 00000000..80c10883
--- /dev/null
+++ b/math/gsurfit/gszerod.x
@@ -0,0 +1,40 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "dgsurfitdef.h"
+
+# GSZERO -- Procedure to zero the accumulators before doing
+# a new fit in accumulate mode. The inner products of the basis functions
+# are accumulated in the GS_NCOEFF(sf) ** 2
+# array MATRIX, while
+# the inner products of the basis functions and the data ordinates are
+# accumulated in the  NCOEFF(sf)-vector VECTOR.
+
+procedure dgszero (sf)
+
+pointer	sf	# pointer to surface descriptor
+errchk	mfree
+
+begin
+	# zero the accumulators
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    GS_NPTS(sf) = 0
+	    call aclrd (VECTOR(GS_VECTOR(sf)), GS_NCOEFF(sf))
+	    call aclrd (MATRIX(GS_MATRIX(sf)), GS_NCOEFF(sf) ** 2)
+
+	    # free the basis functions defined from previous calls to sfrefit
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_DOUBLE)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_DOUBLE)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_DOUBLE)
+	    GS_WZ(sf) = NULL
+	default:
+	    call error (0, "GSZERO: Unknown surface type.")
+	}
+end
diff --git a/math/gsurfit/gszeror.x b/math/gsurfit/gszeror.x
new file mode 100644
index 00000000..f7c4e5ed
--- /dev/null
+++ b/math/gsurfit/gszeror.x
@@ -0,0 +1,40 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/gsurfit.h>
+include "gsurfitdef.h"
+
+# GSZERO -- Procedure to zero the accumulators before doing
+# a new fit in accumulate mode. The inner products of the basis functions
+# are accumulated in the GS_NCOEFF(sf) ** 2
+# array MATRIX, while
+# the inner products of the basis functions and the data ordinates are
+# accumulated in the  NCOEFF(sf)-vector VECTOR.
+
+procedure gszero (sf)
+
+pointer	sf	# pointer to surface descriptor
+errchk	mfree
+
+begin
+	# zero the accumulators
+	switch (GS_TYPE(sf)) {
+	case GS_LEGENDRE, GS_CHEBYSHEV, GS_POLYNOMIAL:
+
+	    GS_NPTS(sf) = 0
+	    call aclrr (VECTOR(GS_VECTOR(sf)), GS_NCOEFF(sf))
+	    call aclrr (MATRIX(GS_MATRIX(sf)), GS_NCOEFF(sf) ** 2)
+
+	    # free the basis functions defined from previous calls to sfrefit
+	    if (GS_XBASIS(sf) != NULL)
+	        call mfree (GS_XBASIS(sf), TY_REAL)
+	    GS_XBASIS(sf) = NULL
+	    if (GS_YBASIS(sf) != NULL)
+	        call mfree (GS_YBASIS(sf), TY_REAL)
+	    GS_YBASIS(sf) = NULL
+	    if (GS_WZ(sf) != NULL)
+	        call mfree (GS_WZ(sf), TY_REAL)
+	    GS_WZ(sf) = NULL
+	default:
+	    call error (0, "GSZERO: Unknown surface type.")
+	}
+end
diff --git a/math/gsurfit/mkpkg b/math/gsurfit/mkpkg
new file mode 100644
index 00000000..f7aaa08f
--- /dev/null
+++ b/math/gsurfit/mkpkg
@@ -0,0 +1,111 @@
+# General surface fitting tools library.
+
+$checkout libgsurfit.a lib$
+$update   libgsurfit.a
+$checkin  libgsurfit.a lib$
+$exit
+
+zzdebug:
+	$update libgsurfit.a
+	$omake zzdebug.x
+	$link	zzdebug.o libgsurfit.a -o zzdebug
+	;
+
+tfiles:
+	$set GEN = "$$generic -k -t rd"
+
+	$ifolder (gs_b1evalr.x, gs_b1eval.gx)	$(GEN)	gs_b1eval.gx	$endif
+	$ifolder (gs_bevalr.x, gs_beval.gx)	$(GEN)	gs_beval.gx	$endif
+	$ifolder (gs_chomatr.x, gs_chomat.gx)	$(GEN)	gs_chomat.gx	$endif
+	$ifolder (gs_f1devalr.x, gs_f1deval.gx)	$(GEN)	gs_f1deval.gx	$endif
+	$ifolder (gs_fevalr.x, gs_feval.gx)	$(GEN)	gs_feval.gx	$endif
+	$ifolder (gs_fderr.x, gs_fder.gx)	$(GEN)	gs_fder.gx	$endif
+	$ifolder (gs_devalr.x, gs_deval.gx)	$(GEN)	gs_deval.gx	$endif
+	$ifolder (gsaccumr.x, gsaccum.gx)	$(GEN)	gsaccum.gx	$endif
+	$ifolder (gsacptsr.x, gsacpts.gx)	$(GEN)	gsacpts.gx	$endif
+	$ifolder (gsaddr.x, gsadd.gx)		$(GEN)	gsadd.gx	$endif
+	$ifolder (gscoeffr.x, gscoeff.gx)	$(GEN)	gscoeff.gx	$endif
+	$ifolder (gscopyr.x, gscopy.gx)		$(GEN)	gscopy.gx	$endif
+	$ifolder (gsderr.x, gsder.gx)		$(GEN)	gsder.gx	$endif
+	$ifolder (gserrorsr.x, gserrors.gx)	$(GEN)	gserrors.gx	$endif
+	$ifolder (gsevalr.x, gseval.gx)		$(GEN)	gseval.gx	$endif
+	$ifolder (gsfitr.x, gsfit.gx)		$(GEN)	gsfit.gx	$endif
+	$ifolder (gsfreer.x, gsfree.gx)		$(GEN)	gsfree.gx	$endif
+	$ifolder (gsgcoeffr.x, gsgcoeff.gx)	$(GEN)	gsgcoeff.gx	$endif
+	$ifolder (gsinitr.x, gsinit.gx)		$(GEN)	gsinit.gx	$endif
+	$ifolder (gsrefitr.x, gsrefit.gx)	$(GEN)	gsrefit.gx	$endif
+	$ifolder (gsrejectr.x, gsreject.gx)	$(GEN)	gsreject.gx	$endif
+	$ifolder (gsrestorer.x, gsrestore.gx)	$(GEN)	gsrestore.gx	$endif
+	$ifolder (gssaver.x, gssave.gx)		$(GEN)	gssave.gx	$endif
+	$ifolder (gsscoeffr.x, gsscoeff.gx)	$(GEN)	gsscoeff.gx	$endif
+	$ifolder (gssolver.x, gssolve.gx)	$(GEN)	gssolve.gx	$endif
+	$ifolder (gsstatr.x, gsstat.gx)		$(GEN)	gsstat.gx	$endif
+	$ifolder (gssubr.x, gssub.gx)		$(GEN)	gssub.gx	$endif
+	$ifolder (gsvectorr.x, gsvector.gx)	$(GEN)	gsvector.gx	$endif
+	$ifolder (gszeror.x, gszero.gx)		$(GEN)	gszero.gx	$endif
+	;
+
+libgsurfit.a:
+
+	$ifeq (USE_GENERIC, yes) $call tfiles $endif
+
+	gs_b1evalr.x	
+	gs_bevalr.x	
+	gs_chomatr.x	gsurfitdef.h <mach.h> <math/gsurfit.h>
+	gs_f1devalr.x	
+	gs_fevalr.x	<math/gsurfit.h>
+	gs_fderr.x	<math/gsurfit.h>
+	gs_devalr.x	
+	gsaccumr.x	gsurfitdef.h <math/gsurfit.h>
+	gsacptsr.x	gsurfitdef.h <math/gsurfit.h>
+	gsaddr.x	gsurfitdef.h <math/gsurfit.h>
+	gscoeffr.x	gsurfitdef.h
+	gscopyr.x	gsurfitdef.h <math/gsurfit.h>
+	gsderr.x	gsurfitdef.h <math/gsurfit.h>
+	gserrorsr.x	gsurfitdef.h <mach.h>
+	gsevalr.x	gsurfitdef.h <math/gsurfit.h>
+	gsfitr.x	gsurfitdef.h <math/gsurfit.h>
+	gsfreer.x	gsurfitdef.h
+	gsgcoeffr.x	gsurfitdef.h <math/gsurfit.h>
+	gsinitr.x	gsurfitdef.h <math/gsurfit.h>
+	gsrefitr.x	gsurfitdef.h <math/gsurfit.h>
+	gsrejectr.x	gsurfitdef.h <math/gsurfit.h>
+	gsrestorer.x	gsurfitdef.h <math/gsurfit.h>
+	gssaver.x	gsurfitdef.h <math/gsurfit.h>
+	gsscoeffr.x	gsurfitdef.h <math/gsurfit.h>
+	gssolver.x	gsurfitdef.h <math/gsurfit.h>
+	gsstatr.x	gsurfitdef.h <math/gsurfit.h>
+	gssubr.x	gsurfitdef.h <math/gsurfit.h>
+	gsvectorr.x	gsurfitdef.h <math/gsurfit.h>
+	gszeror.x	gsurfitdef.h <math/gsurfit.h>
+
+	gs_b1evald.x	
+	gs_bevald.x	
+	gs_chomatd.x	dgsurfitdef.h <mach.h> <math/gsurfit.h>
+	gs_f1devald.x	
+	gs_fevald.x	<math/gsurfit.h>
+	gs_fderd.x	<math/gsurfit.h>
+	gs_devald.x	
+	gsaccumd.x	dgsurfitdef.h <math/gsurfit.h>
+	gsacptsd.x	dgsurfitdef.h <math/gsurfit.h>
+	gsaddd.x	dgsurfitdef.h <math/gsurfit.h>
+	gscoeffd.x	dgsurfitdef.h
+	gscopyd.x	dgsurfitdef.h <math/gsurfit.h>
+	gsderd.x	dgsurfitdef.h <math/gsurfit.h>
+	gserrorsd.x	dgsurfitdef.h <mach.h>
+	gsevald.x	dgsurfitdef.h <math/gsurfit.h>
+	gsfitd.x	dgsurfitdef.h <math/gsurfit.h>
+	gsfreed.x	dgsurfitdef.h
+	gsgcoeffd.x	dgsurfitdef.h <math/gsurfit.h>
+	gsinitd.x	dgsurfitdef.h <math/gsurfit.h>
+	gsrefitd.x	dgsurfitdef.h <math/gsurfit.h>
+	gsrejectd.x	dgsurfitdef.h <math/gsurfit.h>
+	gsrestored.x	dgsurfitdef.h <math/gsurfit.h>
+	gssaved.x	dgsurfitdef.h <math/gsurfit.h>
+	gsscoeffd.x	dgsurfitdef.h <math/gsurfit.h>
+	gssolved.x	dgsurfitdef.h <math/gsurfit.h>
+	gsstatd.x	dgsurfitdef.h <math/gsurfit.h>
+	gssubd.x	dgsurfitdef.h <math/gsurfit.h>
+	gsvectord.x	dgsurfitdef.h <math/gsurfit.h>
+	gszerod.x	dgsurfitdef.h <math/gsurfit.h>
+	;
diff --git a/math/gsurfit/zzdebug.x b/math/gsurfit/zzdebug.x
new file mode 100644
index 00000000..522da747
--- /dev/null
+++ b/math/gsurfit/zzdebug.x
@@ -0,0 +1,348 @@
+task test = t_test
+
+include <math/gsurfit.h>
+
+procedure t_test()
+
+int	i, j, k
+int	xorder, yorder, xterms, stype
+int	ncoeff, maxorder, xincr, npts, stype1, ier
+pointer	gs, ags, sgs
+double	dx, dy, const, accum, sum, rms1, rms2
+double	x[121], y[121], z[121], w[121], zfit[121], coeff[121], save[121]
+int	clgeti()
+double	dgseval(), dgsgcoeff()
+
+begin
+	# Generate x and y grid.
+	dy = -1.0d0
+	npts = 0
+	do i = 1, 9 {
+	    dx = -1.0d0
+	    do j = 1, 9 {
+		x[npts+1] = dx
+		y[npts+1] = dy
+		npts = npts + 1
+		dx = dx + 0.25d0
+	    }
+	    dy = dy + 0.25d0
+	}
+
+	stype = clgeti ("stype")
+	xorder = clgeti ("xorder")
+	yorder = clgeti ("yorder")
+	xterms = clgeti ("xterms")
+	call printf ("\n\nSURFACE: %d XORDER: %d YORDER: %d XTERMS: %d\n")
+	    call pargi (stype)
+	    call pargi (xorder)
+	    call pargi (yorder)
+	    call pargi (xterms)
+
+	# Generate data
+	if (stype > 3) {
+	    switch (xterms) {
+	    case GS_XNONE:
+
+		do i = 1, npts {
+		    sum = 0.0d0
+		    do j = 2, yorder
+			sum = sum + j * y[i] ** (j - 1)
+		    do j = 2, xorder
+			sum = sum + j * x[i] ** (j - 1)
+		    z[i] = sum
+		}
+
+	    case GS_XHALF:
+
+		maxorder = max (xorder + 1, yorder + 1)
+		do i = 1, npts {
+		    sum = 0.0d0
+		    xincr = xorder
+		    do j = 1, yorder {
+			const = j * y[i] ** (j - 1)
+			accum= 0.0d0
+			do k = 1, xincr {
+			    if (j > 1 || k > 1)
+				accum = accum + k * x[i] ** (k - 1)
+			}
+			sum = sum + const * accum
+			if ((j + xorder + 1) > maxorder)
+			    xincr = xincr - 1
+		    }
+		    z[i] = sum
+		}
+
+	    case GS_XFULL:
+
+		do i = 1, npts {
+		    sum = 0.0d0
+		    do j = 1, yorder {
+			const = j * y[i] ** (j - 1)
+			accum = 0.0d0
+			do k = 1, xorder {
+			    if (j > 1 || k > 1)
+				accum = accum + k * x[i] ** (k - 1)
+			}
+			sum = sum + const * accum
+		    }
+		    z[i] = sum
+		}
+	    }
+
+	    stype1 = stype - 3
+	} else {
+	    switch (xterms) {
+	    case GS_XNONE:
+
+		do i = 1, npts {
+		    sum = 0.0d0
+		    do j = 2, yorder
+			sum = sum + j * y[i] ** (j - 1)
+		    do j = 1, xorder
+			sum = sum + j * x[i] ** (j - 1)
+		    z[i] = sum
+		}
+
+	    case GS_XHALF:
+
+		maxorder = max (xorder + 1, yorder + 1)
+		do i = 1, npts {
+		    sum = 0.0d0
+		    xincr = xorder
+		    do j = 1, yorder {
+			const = j * y[i] ** (j - 1)
+			accum= 0.0d0
+			do k = 1, xincr {
+			    accum = accum + k * x[i] ** (k - 1)
+			}
+			sum = sum + const * accum
+			if ((j + xorder + 1) > maxorder)
+			    xincr = xincr - 1
+		    }
+		    z[i] = sum
+		}
+
+	    case GS_XFULL:
+
+		do i = 1, npts {
+		    sum = 0.0d0
+		    do j = 1, yorder {
+			const = j * y[i] ** (j - 1)
+			accum = 0.0d0
+			do k = 1, xorder {
+			    accum = accum + k * x[i] ** (k - 1)
+			}
+			sum = sum + const * accum
+		    }
+		    z[i] = sum
+		}
+	    }
+
+	    stype1 = stype
+	}
+
+	# Print out the data.
+	call printf ("\nXIN:\n")
+	do i = 1, npts {
+	    call printf ("%6.3f ")
+		call pargd (x[i])
+	    if (mod (i, 9) == 0)
+		call printf ("\n")
+	}
+	call printf ("\n")
+
+	call printf ("\nYIN:\n")
+	do i = 1, npts {
+	    call printf ("%6.3f ")
+		call pargd (y[i])
+	    if (mod (i, 9) == 0)
+		call printf ("\n")
+	}
+	call printf ("\n")
+
+	call printf ("\nZIN:\n")
+	do i = 1, npts {
+	    call printf ("%6.3f ")
+		call pargd (z[i])
+	    if (mod (i, 9) == 0)
+		call printf ("\n")
+	}
+	call printf ("\n")
+
+	# Fit surface.
+	call dgsinit (gs, stype1, xorder, yorder, xterms, -1.0d0, 1.0d0,
+	    -1.0d0, 1.0d0)
+	if (stype > 3) {
+	    call dgsset (gs, GSXREF, 0d0)
+	    call dgsset (gs, GSYREF, 0d0)
+	    call dgsset (gs, GSZREF, 0d0)
+	}
+	call dgsfit (gs, x, y, z, w, npts, WTS_UNIFORM, ier) 
+	call printf ("\nFIT ERROR CODE: %d\n")
+	    call pargi (ier)
+
+	# Evaluate the fit and its rms.
+	call dgsvector (gs, x, y, zfit, npts)
+	call printf ("\nZFIT:\n")
+	do i = 1, npts {
+	    call printf ("%6.3f ")
+		call pargd (zfit[i])
+	    if (mod (i, 9) == 0)
+		call printf ("\n")
+	}
+	call printf ("\n")
+	rms1 = 0.0d0
+	do i = 1, npts
+	    rms1 = rms1 + (z[i] - zfit[i]) ** 2 
+	rms1 = sqrt (rms1 / (npts - 1))
+	rms2 = 0.0d0
+	do i = 1, npts
+	    rms2 = rms2 + (z[i] - dgseval (gs, x[i], y[i])) ** 2
+	rms2 = sqrt (rms2 / (npts - 1))
+	#call printf ("\nRMS: vector = %0.14g point = %0.14g\n\n")
+	call printf ("\nRMS: vector = %0.4f point = %0.4f\n\n")
+	    call pargd (rms1)
+	    call pargd (rms2)
+
+	# Print the coefficients.
+	call dgscoeff (gs, coeff, ncoeff)
+	call printf ("GSFIT coeff:\n")
+	call printf ("first %0.14g %0.14g\n")
+	    call pargd (dgsgcoeff (gs, 1, 1))
+	    call pargd (dgsgcoeff (gs, xorder, 1))
+	do i = 1, ncoeff {
+	    call printf ("%d  %0.14g\n")
+		call pargi (i)
+		call pargd (coeff[i])
+	}
+	call printf ("last %0.14g %0.14g\n")
+	    call pargd (dgsgcoeff (gs, 1, yorder))
+	    call pargd (dgsgcoeff (gs, xorder, yorder))
+	call printf ("\n")
+
+	call dgsfree (gs)
+	return
+
+	# Evaluate the first derivatives.
+	call dgsder (gs, x, y, zfit, npts, 1, 0)
+	call printf ("\nZDER: 1 0\n")
+	do i = 1, npts {
+	    call printf ("%0.7g ")
+		call pargd (zfit[i])
+	    if (mod (i, 9) == 0)
+		call printf ("\n")
+	}
+	call printf ("\n")
+
+	call dgsder (gs, x, y, zfit, npts, 0, 1)
+	call printf ("\nZDER: 0 1\n")
+	do i = 1, npts {
+	    call printf ("%0.7g ")
+		call pargd (zfit[i])
+	    if (mod (i, 9) == 0)
+		call printf ("\n")
+	}
+	call printf ("\n")
+
+	call dgsder (gs, x, y, zfit, npts, 1, 1)
+	call printf ("\nZDER: 1 1\n")
+	do i = 1, npts {
+	    call printf ("%0.7g ")
+		call pargd (zfit[i])
+	    if (mod (i, 9) == 0)
+		call printf ("\n")
+	}
+	call printf ("\n")
+
+	# Refit the surface point by point.
+	call dgszero (gs)
+	do i = 1, npts {
+	    call dgsaccum (gs, x[i], y[i], z[i], w[i], WTS_UNIFORM)
+	}
+	if (stype > 3)
+	    call dgssolve1 (gs, ier)
+	else
+	    call dgssolve (gs, ier)
+	call printf ("\nACCUM FIT ERROR CODE: %d\n")
+	    call pargi (ier)
+	call dgsrej (gs, x[1], y[1], z[1], w[1], WTS_UNIFORM)
+	call dgsrej (gs, x[npts], y[npts], z[npts], w[npts], WTS_UNIFORM)
+	call dgsaccum (gs, x[1], y[1], z[1], w[1], WTS_UNIFORM)
+	call dgsaccum (gs, x[npts], y[npts], z[npts], w[npts], WTS_UNIFORM)
+	call dgssolve (gs, ier)
+	call printf ("\nREJ FIT ERROR CODE: %d\n")
+	    call pargi (ier)
+
+	call dgscoeff (gs, coeff, ncoeff)
+	call printf ("GSACCUM coeff:\n")
+	call printf ("first %0.14g %0.14g\n")
+	    call pargd (dgsgcoeff (gs, 1, 1))
+	    call pargd (dgsgcoeff (gs, xorder, 1))
+	do i = 1, ncoeff {
+	    call printf ("%d  %0.14g\n")
+		call pargi (i)
+		call pargd (coeff[i])
+	}
+	call printf ("last %0.14g %0.14g\n")
+	    call pargd (dgsgcoeff (gs, 1, yorder))
+	    call pargd (dgsgcoeff (gs, xorder, yorder))
+	call printf ("\n")
+
+	# Save and restore.
+	call dgssave (gs, save)
+	call dgsfree (gs)
+	call dgsrestore (gs, save)
+
+	call dgscoeff (gs, coeff, ncoeff)
+	call printf ("RESTORE coeff:\n")
+	call printf ("first %0.14g %0.14g\n")
+	    call pargd (dgsgcoeff (gs, 1, 1))
+	    call pargd (dgsgcoeff (gs, xorder, 1))
+	do i = 1, ncoeff {
+	    call printf ("%d  %0.14g\n")
+		call pargi (i)
+		call pargd (coeff[i])
+	}
+	call printf ("last %0.14g %0.14g\n")
+	    call pargd (dgsgcoeff (gs, 1, yorder))
+	    call pargd (dgsgcoeff (gs, xorder, yorder))
+	call printf ("\n")
+
+	# Add two surfaces.
+	call dgsadd (gs, gs, ags)
+	call dgscoeff (ags, coeff, ncoeff)
+	call printf ("GSADD coeff:\n")
+	call printf ("first %0.14g %0.14g\n")
+	    call pargd (dgsgcoeff (ags, 1, 1))
+	    call pargd (dgsgcoeff (ags, xorder, 1))
+	do i = 1, ncoeff {
+	    call printf ("%d  %0.14g\n")
+		call pargi (i)
+		call pargd (coeff[i])
+	}
+	call printf ("last %0.14g %0.14g\n")
+	    call pargd (dgsgcoeff (ags, 1, yorder))
+	    call pargd (dgsgcoeff (ags, xorder, yorder))
+	call printf ("\n")
+
+	# Subtract two surfaces.
+	call dgssub (gs, gs, sgs)
+	call dgscoeff (sgs, coeff, ncoeff)
+	call printf ("GSSUB coeff:\n")
+	call printf ("first %0.14g %0.14g\n")
+	    call pargd (dgsgcoeff (sgs, 1, 1))
+	    call pargd (dgsgcoeff (sgs, xorder, 1))
+	do i = 1, ncoeff {
+	    call printf ("%d  %0.14g\n")
+		call pargi (i)
+		call pargd (coeff[i])
+	}
+	call printf ("last %0.14g %0.14g\n")
+	    call pargd (dgsgcoeff (sgs, 1, yorder))
+	    call pargd (dgsgcoeff (sgs, xorder, yorder))
+	call printf ("\n")
+
+	call dgsfree (gs)
+	call dgsfree (ags)
+	call dgsfree (sgs)
+end
diff --git a/math/ieee/README b/math/ieee/README
new file mode 100644
index 00000000..80b30bfd
--- /dev/null
+++ b/math/ieee/README
@@ -0,0 +1,8 @@
+     This directory contians programs and subroutines from the
+text "Programs for Digital Signal Processing" by the IEEE Press.
+Directories of the name "chap*" correspond to each chapter of
+the text.
+     The files "*mach*" are the machine dependent routines which
+should be edited for the hardware which you are going to run the
+routines on.  The file "uni.c" is a uniform random number generator,
+not the one from the text, but one which uses the UNIX generator.
diff --git a/math/ieee/chap1/README b/math/ieee/chap1/README
new file mode 100644
index 00000000..bf86b45f
--- /dev/null
+++ b/math/ieee/chap1/README
@@ -0,0 +1,14 @@
+     This directory contains the IEEE routines from Chapter 1 -
+Discrete Fourier Transform Programs.  Some of the routines are
+provided here as separete files (fourea.f, wfta.f, ...) but are
+purposely not put into the library, as these routines are not for
+general use (fourea.f is an inefficient, demonstration version;
+wfta.f is the Winograd DFT which is slower than the regular DFT
+and uses far too much memory ona  16-bit machine to be of
+practical use; ...).
+     The directory "test" contains the test routines from the chapter.
+The directory "time" contains some routines to time various of the
+routines.
+     The file "compall" compiles the appropiate routines and then
+"mklib" will make the library, which one will probably want to
+move to "/usr/lib/libieee.a".
diff --git a/math/ieee/chap1/const.f b/math/ieee/chap1/const.f
new file mode 100644
index 00000000..54eb4e41
--- /dev/null
+++ b/math/ieee/chap1/const.f
@@ -0,0 +1,114 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: const
+c   computes the multipliers for the various modules
+c-----------------------------------------------------------------------
+c
+      subroutine const(co3,co8,co16,co9,cdc,cdd)
+      double precision dtheta,dtwopi,dsq32,dsq2
+      double precision dcos1,dcos2,dcos3,dcos4
+      double precision dsin1,dsin2,dsin3,dsin4
+      dimension co3(3),co8(8),co16(18),co9(11),cdc(9),cdd(6)
+      dtwopi=8.0d0*datan(1.0d0)
+      dsq32=dsqrt(0.75d0)
+      dsq2=dsqrt(0.5d0)
+c
+c   multipliers for the three point module
+c
+      co3(1)=1.0
+      co3(2)=-1.5
+      co3(3)=-dsq32
+c
+c   multipliers for the five point module
+c
+      dtheta=dtwopi/5.0d0
+      dcos1=dcos(dtheta)
+      dcos2=dcos(2.0d0*dtheta)
+      dsin1=dsin(dtheta)
+      dsin2=dsin(2.0d0*dtheta)
+      cdd(1)=1.0
+      cdd(2)=-1.25
+      cdd(3)=-dsin1-dsin2
+      cdd(4)=0.5*(dcos1-dcos2)
+      cdd(5)=dsin1-dsin2
+      cdd(6)=dsin2
+c
+c
+c   multipliers for the seven point module
+c
+      dtheta=dtwopi/7.0d0
+      dcos1=dcos(dtheta)
+      dcos2=dcos(2.0d0*dtheta)
+      dcos3=dcos(3.0d0*dtheta)
+      dsin1=dsin(dtheta)
+      dsin2=dsin(2.0d0*dtheta)
+      dsin3=dsin(3.0d0*dtheta)
+      cdc(1)=1.0
+      cdc(2)=-7.0d0/6.0d0
+      cdc(3)=-(dsin1+dsin2-dsin3)/3.0d0
+      cdc(4)=(dcos1+dcos2-2.0d0*dcos3)/3.0d0
+      cdc(5)=(2.0d0*dcos1-dcos2-dcos3)/3.0d0
+      cdc(6)=-(2.0d0*dsin1-dsin2+dsin3)/3.0d0
+      cdc(7)=-(dsin1+dsin2+2.0d0*dsin3)/3.0d0
+      cdc(8)=(dcos1-2.0d0*dcos2+dcos3)/3.0d0
+      cdc(9)=-(dsin1-2.0d0*dsin2-dsin3)/3.0d0
+c
+c   multipliers for the eight point module
+c
+      co8(1)=1.0
+      co8(2)=1.0
+      co8(3)=1.0
+      co8(4)=-1.0
+      co8(5)=1.0
+      co8(6)=-dsq2
+      co8(7)=-1.0
+      co8(8)=dsq2
+c
+c   multipliers for the nine point module
+c
+      dtheta=dtwopi/9.0d0
+      dcos1=dcos(dtheta)
+      dcos2=dcos(2.0d0*dtheta)
+      dcos4=dcos(4.0d0*dtheta)
+      dsin1=dsin(dtheta)
+      dsin2=dsin(2.0d0*dtheta)
+      dsin4=dsin(4.0d0*dtheta)
+      co9(1)=1.0
+      co9(2)=-1.5
+      co9(3)=-dsq32
+      co9(4)=0.5
+      co9(5)=(2.0d0*dcos1-dcos2-dcos4)/3.0d0
+      co9(6)=(dcos1-2.0d0*dcos2+dcos4)/3.0d0
+      co9(7)=(dcos1+dcos2-2.0d0*dcos4)/3.0d0
+      co9(8)=-(2.0d0*dsin1+dsin2-dsin4)/3.0d0
+      co9(9)=-(dsin1+2.0d0*dsin2+dsin4)/3.0d0
+      co9(10)=-(dsin1-dsin2-2.0d0*dsin4)/3.0d0
+      co9(11)=-dsq32
+c
+c   multipliers for the sixteen point module
+c
+      dtheta=dtwopi/16.0d0
+      dcos1=dcos(dtheta)
+      dcos3=dcos(3.0d0*dtheta)
+      dsin1=dsin(dtheta)
+      dsin3=dsin(3.0d0*dtheta)
+      co16(1)=1.0
+      co16(2)=1.0
+      co16(3)=1.0
+      co16(4)=-1.0
+      co16(5)=1.0
+      co16(6)=-dsq2
+      co16(7)=-1.0
+      co16(8)=dsq2
+      co16(9)=1.0
+      co16(10)=-(dsin1-dsin3)
+      co16(11)=-dsq2
+      co16(12)=-co16(10)
+      co16(13)=-1.0
+      co16(14)=-(dsin1+dsin3)
+      co16(15)=dsq2
+      co16(16)=-co16(14)
+      co16(17)=-dsin3
+      co16(18)=dcos3
+      return
+      end
diff --git a/math/ieee/chap1/fast.f b/math/ieee/chap1/fast.f
new file mode 100644
index 00000000..9a0ad713
--- /dev/null
+++ b/math/ieee/chap1/fast.f
@@ -0,0 +1,73 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  fast
+c replaces the real vector b(k), for k=1,2,...,n,
+c with its finite discrete fourier transform
+c-----------------------------------------------------------------------
+c
+      subroutine fast(b, n)
+c
+c the dc term is returned in location b(1) with b(2) set to 0.
+c thereafter the jth harmonic is returned as a complex
+c number stored as  b(2*j+1) + i b(2*j+2).
+c the n/2 harmonic is returned in b(n+1) with b(n+2) set to 0.
+c hence, b must be dimensioned to size n+2.
+c the subroutine is called as  fast(b,n) where n=2**m and
+c b is the real array described above.
+c
+      dimension b(2)
+      common /cons/ pii, p7, p7two, c22, s22, pi2
+c
+c iw is a machine dependent write device number
+c
+      iw = i1mach(2)
+c
+      pii = 4.*atan(1.)
+      pi8 = pii/8.
+      p7 = 1./sqrt(2.)
+      p7two = 2.*p7
+      c22 = cos(pi8)
+      s22 = sin(pi8)
+      pi2 = 2.*pii
+      do 10 i=1,15
+        m = i
+        nt = 2**i
+        if (n.eq.nt) go to 20
+  10  continue
+      write (iw,9999)
+9999  format (33h n is not a power of two for fast)
+      stop
+  20  n4pow = m/2
+c
+c do a radix 2 iteration first if one is required.
+c
+      if (m-n4pow*2) 40, 40, 30
+  30  nn = 2
+      int = n/nn
+      call fr2tr(int, b(1), b(int+1))
+      go to 50
+  40  nn = 1
+c
+c perform radix 4 iterations.
+c
+  50  if (n4pow.eq.0) go to 70
+      do 60 it=1,n4pow
+        nn = nn*4
+        int = n/nn
+        call fr4tr(int, nn, b(1), b(int+1), b(2*int+1), b(3*int+1),
+     *      b(1), b(int+1), b(2*int+1), b(3*int+1))
+  60  continue
+c
+c perform in-place reordering.
+c
+  70  call ford1(m, b)
+      call ford2(m, b)
+      t = b(2)
+      b(2) = 0.
+      b(n+1) = t
+      b(n+2) = 0.
+      do 80 it=4,n,2
+        b(it) = -b(it)
+  80  continue
+      return
+      end
diff --git a/math/ieee/chap1/ffa.f b/math/ieee/chap1/ffa.f
new file mode 100644
index 00000000..dd62ea01
--- /dev/null
+++ b/math/ieee/chap1/ffa.f
@@ -0,0 +1,84 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  ffa
+c fast fourier analysis subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine ffa(b, nfft)
+c
+c this subroutine replaces the real vector b(k),  (k=1,2,...,n),
+c with its finite discrete fourier transform.  the dc term is
+c returned in location b(1) with b(2) set to 0.  thereafter, the
+c jth harmonic is returned as a complex number stored as
+c b(2*j+1) + i b(2*j+2).  note that the n/2 harmonic is returned
+c in b(n+1) with b(n+2) set to 0.  hence, b must be dimensioned
+c to size n+2.
+c subroutine is called as ffa (b,n) where n=2**m and b is an
+c n term real array.  a real-valued, radix 8  algorithm is used
+c with in-place reordering and the trig functions are computed as
+c needed.
+c
+      dimension b(2)
+      common /con/ pii, p7, p7two, c22, s22, pi2
+c
+c iw is a machine dependent write device number
+c
+      iw = i1mach(2)
+c
+      pii = 4.*atan(1.)
+      pi8 = pii/8.
+      p7 = 1./sqrt(2.)
+      p7two = 2.*p7
+      c22 = cos(pi8)
+      s22 = sin(pi8)
+      pi2 = 2.*pii
+      n = 1
+      do 10 i=1,15
+        m = i
+        n = n*2
+        if (n.eq.nfft) go to 20
+  10  continue
+      write (iw,9999)
+9999  format (30h nfft not a power of 2 for ffa)
+      stop
+  20  continue
+      n8pow = m/3
+c
+c do a radix 2 or radix 4 iteration first if one is required
+c
+      if (m-n8pow*3-1) 50, 40, 30
+  30  nn = 4
+      int = n/nn
+      call r4tr(int, b(1), b(int+1), b(2*int+1), b(3*int+1))
+      go to 60
+  40  nn = 2
+      int = n/nn
+      call r2tr(int, b(1), b(int+1))
+      go to 60
+  50  nn = 1
+c
+c perform radix 8 iterations
+c
+  60  if (n8pow) 90, 90, 70
+  70  do 80 it=1,n8pow
+        nn = nn*8
+        int = n/nn
+        call r8tr(int, nn, b(1), b(int+1), b(2*int+1), b(3*int+1),
+     *      b(4*int+1), b(5*int+1), b(6*int+1), b(7*int+1), b(1),
+     *      b(int+1), b(2*int+1), b(3*int+1), b(4*int+1), b(5*int+1),
+     *      b(6*int+1), b(7*int+1))
+  80  continue
+c
+c perform in-place reordering
+c
+  90  call ord1(m, b)
+      call ord2(m, b)
+      t = b(2)
+      b(2) = 0.
+      b(nfft+1) = t
+      b(nfft+2) = 0.
+      do 100 i=4,nfft,2
+        b(i) = -b(i)
+ 100  continue
+      return
+      end
diff --git a/math/ieee/chap1/ffs.f b/math/ieee/chap1/ffs.f
new file mode 100644
index 00000000..2858fdb0
--- /dev/null
+++ b/math/ieee/chap1/ffs.f
@@ -0,0 +1,80 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  ffs
+c fast fourier synthesis subroutine
+c radix 8-4-2
+c-----------------------------------------------------------------------
+c
+      subroutine ffs(b, nfft)
+c
+c this subroutine synthesizes the real vector b(k), where
+c k=1,2,...,n. the initial fourier coefficients are placed in
+c the b array of size n+2.  the dc term is in b(1) with
+c b(2) equal to 0.
+c the jth harmonic is stored as b(2*j+1) + i b(2*j+2).
+c the n/2 harmonic is in b(n+1) with b(n+2) equal to 0.
+c the subroutine is called as ffs(b,n) where n=2**m and
+c b is the n term real array discussed above.
+c
+      dimension b(2)
+      common /con1/ pii, p7, p7two, c22, s22, pi2
+c
+c iw is a machine dependent write device number
+c
+      iw = i1mach(2)
+c
+      pii = 4.*atan(1.)
+      pi8 = pii/8.
+      p7 = 1./sqrt(2.)
+      p7two = 2.*p7
+      c22 = cos(pi8)
+      s22 = sin(pi8)
+      pi2 = 2.*pii
+      n = 1
+      do 10 i=1,15
+        m = i
+        n = n*2
+        if (n.eq.nfft) go to 20
+  10  continue
+      write (iw,9999)
+9999  format (30h nfft not a power of 2 for ffs)
+      stop
+  20  continue
+      b(2) = b(nfft+1)
+      do 30 i=1,nfft
+        b(i) = b(i)/float(nfft)
+  30  continue
+      do 40 i=4,nfft,2
+        b(i) = -b(i)
+  40  continue
+      n8pow = m/3
+c
+c reorder the input fourier coefficients
+c
+      call ord2(m, b)
+      call ord1(m, b)
+c
+      if (n8pow.eq.0) go to 60
+c
+c perform the radix 8 iterations
+c
+      nn = n
+      do 50 it=1,n8pow
+        int = n/nn
+        call r8syn(int, nn, b, b(int+1), b(2*int+1), b(3*int+1),
+     *      b(4*int+1), b(5*int+1), b(6*int+1), b(7*int+1), b(1),
+     *      b(int+1), b(2*int+1), b(3*int+1), b(4*int+1), b(5*int+1),
+     *      b(6*int+1), b(7*int+1))
+        nn = nn/8
+  50  continue
+c
+c do a radix 2 or radix 4 iteration if one is required
+c
+  60  if (m-n8pow*3-1) 90, 80, 70
+  70  int = n/4
+      call r4syn(int, b(1), b(int+1), b(2*int+1), b(3*int+1))
+      go to 90
+  80  int = n/2
+      call r2tr(int, b(1), b(int+1))
+  90  return
+      end
diff --git a/math/ieee/chap1/fft842.f b/math/ieee/chap1/fft842.f
new file mode 100644
index 00000000..37a3a651
--- /dev/null
+++ b/math/ieee/chap1/fft842.f
@@ -0,0 +1,116 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  fft842
+c fast fourier transform for n=2**m
+c complex input
+c-----------------------------------------------------------------------
+c
+      subroutine fft842(in, n, x, y)
+c
+c this program replaces the vector z=x+iy by its  finite
+c discrete, complex fourier transform if in=0.  the inverse transform
+c is calculated for in=1.  it performs as many base
+c 8 iterations as possible and then finishes with a base 4 iteration
+c or a base 2 iteration if needed.
+c
+c the subroutine is called as subroutine fft842 (in,n,x,y).
+c the integer n (a power of 2), the n real location array x, and
+c the n real location array y must be supplied to the subroutine.
+c
+      dimension x(2), y(2), l(15)
+      common /con2/ pi2, p7
+      equivalence (l15,l(1)), (l14,l(2)), (l13,l(3)), (l12,l(4)),
+     *    (l11,l(5)), (l10,l(6)), (l9,l(7)), (l8,l(8)), (l7,l(9)),
+     *    (l6,l(10)), (l5,l(11)), (l4,l(12)), (l3,l(13)), (l2,l(14)),
+     *    (l1,l(15))
+c
+c
+c iw is a machine dependent write device number
+c
+      iw = i1mach(2)
+c
+      pi2 = 8.*atan(1.)
+      p7 = 1./sqrt(2.)
+      do 10 i=1,15
+        m = i
+        nt = 2**i
+        if (n.eq.nt) go to 20
+  10  continue
+      write (iw,9999)
+9999  format (35h n is not a power of two for fft842)
+      stop
+  20  n2pow = m
+      nthpo = n
+      fn = nthpo
+      if (in.eq.1) go to 40
+      do 30 i=1,nthpo
+        y(i) = -y(i)
+  30  continue
+  40  n8pow = n2pow/3
+      if (n8pow.eq.0) go to 60
+c
+c radix 8 passes,if any.
+c
+      do 50 ipass=1,n8pow
+        nxtlt = 2**(n2pow-3*ipass)
+        lengt = 8*nxtlt
+        call r8tx(nxtlt, nthpo, lengt, x(1), x(nxtlt+1), x(2*nxtlt+1),
+     *      x(3*nxtlt+1), x(4*nxtlt+1), x(5*nxtlt+1), x(6*nxtlt+1),
+     *      x(7*nxtlt+1), y(1), y(nxtlt+1), y(2*nxtlt+1), y(3*nxtlt+1),
+     *      y(4*nxtlt+1), y(5*nxtlt+1), y(6*nxtlt+1), y(7*nxtlt+1))
+  50  continue
+c
+c is there a four factor left
+c
+  60  if (n2pow-3*n8pow-1) 90, 70, 80
+c
+c go through the base 2 iteration
+c
+c
+  70  call r2tx(nthpo, x(1), x(2), y(1), y(2))
+      go to 90
+c
+c go through the base 4 iteration
+c
+  80  call r4tx(nthpo, x(1), x(2), x(3), x(4), y(1), y(2), y(3), y(4))
+c
+  90  do 110 j=1,15
+        l(j) = 1
+        if (j-n2pow) 100, 100, 110
+ 100    l(j) = 2**(n2pow+1-j)
+ 110  continue
+      ij = 1
+      do 130 j1=1,l1
+      do 130 j2=j1,l2,l1
+      do 130 j3=j2,l3,l2
+      do 130 j4=j3,l4,l3
+      do 130 j5=j4,l5,l4
+      do 130 j6=j5,l6,l5
+      do 130 j7=j6,l7,l6
+      do 130 j8=j7,l8,l7
+      do 130 j9=j8,l9,l8
+      do 130 j10=j9,l10,l9
+      do 130 j11=j10,l11,l10
+      do 130 j12=j11,l12,l11
+      do 130 j13=j12,l13,l12
+      do 130 j14=j13,l14,l13
+      do 130 ji=j14,l15,l14
+        if (ij-ji) 120, 130, 130
+ 120    r = x(ij)
+        x(ij) = x(ji)
+        x(ji) = r
+        fi = y(ij)
+        y(ij) = y(ji)
+        y(ji) = fi
+ 130    ij = ij + 1
+      if (in.eq.1) go to 150
+      do 140 i=1,nthpo
+        y(i) = -y(i)
+ 140  continue
+      go to 170
+ 150  do 160 i=1,nthpo
+        x(i) = x(i)/fn
+        y(i) = y(i)/fn
+ 160  continue
+ 170  return
+      end
diff --git a/math/ieee/chap1/fftaoh.f b/math/ieee/chap1/fftaoh.f
new file mode 100644
index 00000000..f703c98b
--- /dev/null
+++ b/math/ieee/chap1/fftaoh.f
@@ -0,0 +1,82 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: fftaoh
+c compute dft for real, antisymmetric, odd harmonic, n-point sequence
+c using n/4-point fft
+c antisymmetric sequence means x(m)=-x(n-m), m=1,...,n/2-1
+c odd harmonic means x(2*k)=0, all k, where x(k) is the dft of x(m)
+c x(m) has the property x(m)=x(n/2-m), m=0,1,...,n/4-1,  x(0)=0
+c note: index m is sequence index--not fortran index
+c-----------------------------------------------------------------------
+c
+      subroutine fftaoh(x, n, y)
+      dimension x(1), y(1)
+c
+c  x = real array which on input contains the (n/4+1) points of the
+c      input sequence (antisymmetrical)
+c      on output x contains the n/4 imaginary points of the odd
+c      harmonics of the transform of the input--i.e. the zero
+c      valued real parts are not given nor are the zero-valued
+c      even harmonics
+c  n = true size of input
+c  y = scratch array of size n/4+2
+c
+c
+c handle n = 2 and n = 4 cases separately
+c
+      if (n.gt.4) go to 20
+      if (n.eq.4) go to 10
+c
+c for n=2, assume x(1)=0, x(2)=0, compute dft directly
+c
+      x(1) = 0.
+      return
+c
+c n = 4 case, assume x(1)=x(3)=0, x(2)=-x(4)=x0, compute dft directly
+c
+  10  x(1) = -2.*x(2)
+      return
+  20  twopi = 8.*atan(1.0)
+c
+c form new sequence, y(m)=x(2*m)+(x(2*m+1)-x(2*m-1))
+c
+      no2 = n/2
+      no4 = n/4
+      no8 = n/8
+      if (no8.eq.1) go to 40
+      do 30 i=2,no8
+        ind = 2*i
+        t1 = x(ind) - x(ind-2)
+        y(i) = x(ind-1) + t1
+        ind1 = n/4 + 2 - i
+        y(ind1) = x(ind-1) - t1
+  30  continue
+  40  y(1) = 2.*x(2)
+      y(no8+1) = x(no4+1)
+c
+c the sequence y (n/4 points) has only odd harmonics
+c call subroutine fftohm to exploit odd harmonics
+c
+      call fftohm(y, no2)
+c
+c form original dft from complex odd harmonics of y(k)
+c by unscrambling y(k)
+c
+      tpn = twopi/float(n)
+      cosi = 2.*cos(tpn)
+      sini = 2.*sin(tpn)
+      cosd = cos(tpn*2.)
+      sind = sin(tpn*2.)
+      do 50 i=1,no8
+        ind = 2*i
+        bk = y(ind-1)/sini
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+        ak = y(ind)
+        x(i) = ak - bk
+        ind1 = n/4 + 1 - i
+        x(ind1) = -ak - bk
+  50  continue
+      return
+      end
diff --git a/math/ieee/chap1/fftasm.f b/math/ieee/chap1/fftasm.f
new file mode 100644
index 00000000..30c84b79
--- /dev/null
+++ b/math/ieee/chap1/fftasm.f
@@ -0,0 +1,67 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: fftasm
+c compute dft for real, antisymmetric, n-point sequence x(m) using
+c n/2-point fft
+c antisymmetric sequence means x(m)=-x(n-m), m=1,...,n/2-1
+c note: index m is sequence index--not fortran index
+c-----------------------------------------------------------------------
+c
+      subroutine fftasm(x, n, y)
+      dimension x(1), y(1)
+c
+c x = real array which on input contains the n/2 points of the
+c     input sequence (asymmetrical)
+c     on output x contains the n/2+1 imaginary points of the transform
+c     of the input--i.e. the zero valued real parts are not returned
+c n = true size of input
+c y = scratch array of size n/2+2
+c
+c
+c for n = 2, assume x(1)=0, x(2)=0, compute dft directly
+c
+      if (n.eq.2) go to 30
+      twopi = 8.*atan(1.0)
+c
+c form new sequence, y(m)=x(2*m)+(x(2*m+1)-x(2*m-1))
+c
+      no2 = n/2
+      no4 = n/4
+      do 10 i=2,no4
+        ind = 2*i
+        t1 = x(ind) - x(ind-2)
+        y(i) = x(ind-1) + t1
+        ind1 = no2 + 2 - i
+        y(ind1) = -x(ind-1) + t1
+  10  continue
+      y(1) = 2.*x(2)
+      y(no4+1) = -2.*x(no2)
+c
+c take n/2 point (real) fft of y
+c
+      call fast(y, no2)
+c
+c form original dft by unscrambling y(k)
+c use recursion relation to generate sin(tpn*i) multiplier
+c
+      tpn = twopi/float(n)
+      cosi = 2.*cos(tpn)
+      sini = 2.*sin(tpn)
+      cosd = cosi/2.
+      sind = sini/2.
+      nind = no4 + 1
+      do 20 i=2,nind
+        ind = 2*i
+        bk = y(ind-1)/sini
+        ak = y(ind)
+        x(i) = ak - bk
+        ind1 = no2 + 2 - i
+        x(ind1) = -ak - bk
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+  20  continue
+  30  x(1) = 0.
+      x(no2+1) = 0.
+      return
+      end
diff --git a/math/ieee/chap1/fftohm.f b/math/ieee/chap1/fftohm.f
new file mode 100644
index 00000000..6e3ecc9d
--- /dev/null
+++ b/math/ieee/chap1/fftohm.f
@@ -0,0 +1,101 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: fftohm
+c compute dft for real, n-point, odd harmonic sequences using an
+c n/2 point fft
+c odd harmonic means x(2*k)=0, all k where x(k) is the dft of x(m)
+c note: index m is sequence index--not fortran index
+c-----------------------------------------------------------------------
+c
+      subroutine fftohm(x, n)
+      dimension x(1)
+c
+c x = real array which on input contains the first n/2 points of the
+c     input
+c     on output x contains the n/4 complex values of the odd
+c     harmonics of the input--stored in the sequence re(x(1)),im(x(1)),
+c     re(x(2)),im(x(2)),...
+c ****note: x must be dimensioned to size n/2+2 for fft routine
+c n = true size of x sequence
+c
+c first compute real(x(1)) and real(x(n/2-1)) separately
+c also simultaneously multiply original sequence by sin(twopi*(m-1)/n)
+c sin and cos are computed recursively
+c
+c
+c for n = 2, assume x(1)=x0, x(2)=-x0, compute dft directly
+c
+      if (n.gt.2) go to 10
+      x(1) = 2.*x(1)
+      x(2) = 0.
+      return
+  10  twopi = 8.*atan(1.0)
+      tpn = twopi/float(n)
+c
+c compute x1=real(x(1)) and x2=imaginary(x(n/2-1))
+c x(n) = x(n)*4.*sin(twopi*(i-1)/n)
+c
+      t1 = 0.
+c
+c cosd and sind are multipliers for recursion for sin and cos
+c cosi and sini are initial conditions for recursion for sin and cos
+c
+      cosd = cos(tpn*2.)
+      sind = sin(tpn*2.)
+      cosi = 1.
+      sini = 0.
+      no2 = n/2
+      do 20 i=1,no2,2
+        t = x(i)*cosi
+        x(i) = x(i)*4.*sini
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+        t1 = t1 + t
+  20  continue
+c
+c reset initial conditions (cosi,sini) for new recursion
+c
+      cosi = cos(tpn)
+      sini = sin(tpn)
+      t2 = 0.
+      do 30 i=2,no2,2
+        t = x(i)*cosi
+        x(i) = x(i)*4.*sini
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+        t2 = t2 + t
+  30  continue
+      x1 = 2.*(t1+t2)
+      x2 = 2.*(t1-t2)
+c
+c take n/2 point (real) fft of preprocessed sequence x
+c
+      call fast(x, no2)
+c
+c for n = 4--skip recursion and initial conditions
+c
+      if (n.eq.4) go to 50
+c
+c initial conditions for recursion
+c
+      x(2) = -x(1)/2.
+      x(1) = x1
+c
+c for n = 8, skip recursion
+c
+      if (n.eq.8) go to 50
+c
+c unscramble y(k) using recursion formula
+c
+      nind = no2 - 2
+      do 40 i=3,nind,2
+        t = x(i)
+        x(i) = x(i-2) + x(i+1)
+        x(i+1) = x(i-1) - t
+  40  continue
+  50  x(no2) = x(no2+1)/2.
+      x(no2-1) = x2
+      return
+      end
diff --git a/math/ieee/chap1/fftsoh.f b/math/ieee/chap1/fftsoh.f
new file mode 100644
index 00000000..afc18c17
--- /dev/null
+++ b/math/ieee/chap1/fftsoh.f
@@ -0,0 +1,81 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: fftsoh
+c compute dft for real, symmetric, odd harmonic, n-point sequence
+c using n/4-point fft
+c symmetric sequence means x(m)=x(n-m), m=1,...,n/2-1
+c odd harmonic means x(2*k)=0, all k, where x(k) is the dft of x(m)
+c x(m) has the property x(m)=-x(n/2-m), m=0,1,...,n/4-1,  x(n/4)=0
+c note: index m is sequence index--not fortran index
+c-----------------------------------------------------------------------
+c
+      subroutine fftsoh(x, n, y)
+      dimension x(1), y(1)
+c
+c  x = real array which on input contains the n/4 points of the
+c      input sequence (symmetrical)
+c      on output x contains  the n/4 real points of the odd harmonics
+c      of the transform of the input--i.e. the zero valued imaginary
+c      parts are not given nor are the zero-valued even harmonics
+c  n = true size of input
+c  y = scratch array of size n/4+2
+c
+c
+c handle n = 2 and n = 4 cases separately
+c
+      if (n.gt.4) go to 20
+      if (n.eq.4) go to 10
+c
+c for n=2, assume x(1)=x0, x(2)=-x0, compute dft directly
+c
+      x(1) = 2.*x(1)
+      return
+c
+c n = 4 case, compute dft directly
+c
+  10  x(1) = 2.*x(1)
+      return
+  20  twopi = 8.*atan(1.0)
+c
+c form new sequence, y(m)=x(2*m)+(x(2*m+1)-x(2*m-1))
+c
+      no2 = n/2
+      no4 = n/4
+      no8 = n/8
+      if (no8.eq.1) go to 40
+      do 30 i=2,no8
+        ind = 2*i
+        t1 = x(ind) - x(ind-2)
+        y(i) = x(ind-1) + t1
+        ind1 = n/4 + 2 - i
+        y(ind1) = -x(ind-1) + t1
+  30  continue
+  40  y(1) = x(1)
+      y(no8+1) = -2.*x(no4)
+c
+c the sequence y (n/4 points) has only odd harmonics
+c call subroutine fftohm to exploit odd harmonics
+c
+      call fftohm(y, no2)
+c
+c form original dft from complex odd harmonics of y(k)
+c by unscrambling y(k)
+c
+      tpn = twopi/float(n)
+      cosi = 2.*cos(tpn)
+      sini = 2.*sin(tpn)
+      cosd = cos(tpn*2.)
+      sind = sin(tpn*2.)
+      do 50 i=1,no8
+        ind = 2*i
+        bk = y(ind)/sini
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+        ak = y(ind-1)
+        x(i) = ak + bk
+        ind1 = n/4 + 1 - i
+        x(ind1) = ak - bk
+  50  continue
+      return
+      end
diff --git a/math/ieee/chap1/fftsym.f b/math/ieee/chap1/fftsym.f
new file mode 100644
index 00000000..b1e795bb
--- /dev/null
+++ b/math/ieee/chap1/fftsym.f
@@ -0,0 +1,84 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: fftsym
+c compute dft for real, symmetric, n-point sequence x(m) using
+c n/2-point fft
+c symmetric sequence means x(m)=x(n-m), m=1,...,n/2-1
+c note: index m is sequence index--not fortran index
+c-----------------------------------------------------------------------
+c
+      subroutine fftsym(x, n, y)
+      dimension x(1), y(1)
+c
+c x = real array which on input contains the n/2+1 points of the
+c     input sequence (symmetrical)
+c     on output x contains the n/2+1 real points of the transform of
+c     the input--i.e. the zero valued imaginary parts are not returned
+c n = true size of input
+c y = scratch array of size n/2+2
+c
+c
+c for n = 2, compute dft directly
+c
+      if (n.gt.2) go to 10
+      t = x(1) + x(2)
+      x(2) = x(1) - x(2)
+      x(1) = t
+      return
+  10  twopi = 8.*atan(1.0)
+c
+c first compute b0 term, where b0=sum of odd values of x(m)
+c
+      no2 = n/2
+      no4 = n/4
+      nind = no2 + 1
+      b0 = 0.
+      do 20 i=2,nind,2
+        b0 = b0 + x(i)
+  20  continue
+      b0 = b0*2.
+c
+c for n = 4 skip recursion loop
+c
+      if (n.eq.4) go to 40
+c
+c form new sequence, y(m)=x(2*m)+(x(2*m+1)-x(2*m-1))
+c
+      do 30 i=2,no4
+        ind = 2*i
+        t1 = x(ind) - x(ind-2)
+        y(i) = x(ind-1) + t1
+        ind1 = no2 + 2 - i
+        y(ind1) = x(ind-1) - t1
+  30  continue
+  40  y(1) = x(1)
+      y(no4+1) = x(no2+1)
+c
+c take n/2 point (real) fft of y
+c
+      call fast(y, no2)
+c
+c form original dft by unscrambling y(k)
+c use recursion to give sin(tpn*i) multiplier
+c
+      tpn = twopi/float(n)
+      cosi = 2.*cos(tpn)
+      sini = 2.*sin(tpn)
+      cosd = cosi/2.
+      sind = sini/2.
+      nind = no4 + 1
+      do 50 i=2,nind
+        ind = 2*i
+        bk = y(ind)/sini
+        ak = y(ind-1)
+        x(i) = ak + bk
+        nind1 = n/2 + 2 - i
+        x(nind1) = ak - bk
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+  50  continue
+      x(1) = b0 + y(1)
+      x(no2+1) = y(1) - b0
+      return
+      end
diff --git a/math/ieee/chap1/ford1.f b/math/ieee/chap1/ford1.f
new file mode 100644
index 00000000..4982246f
--- /dev/null
+++ b/math/ieee/chap1/ford1.f
@@ -0,0 +1,24 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  ford1
+c in-place reordering subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine ford1(m, b)
+      dimension b(2)
+c
+      k = 4
+      kl = 2
+      n = 2**m
+      do 40 j=4,n,2
+        if (k-j) 20, 20, 10
+  10    t = b(j)
+        b(j) = b(k)
+        b(k) = t
+  20    k = k - 2
+        if (k-kl) 30, 30, 40
+  30    k = 2*j
+        kl = j
+  40  continue
+      return
+      end
diff --git a/math/ieee/chap1/ford2.f b/math/ieee/chap1/ford2.f
new file mode 100644
index 00000000..8ee26d69
--- /dev/null
+++ b/math/ieee/chap1/ford2.f
@@ -0,0 +1,46 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  ford2
+c in-place reordering subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine ford2(m, b)
+      dimension l(15), b(2)
+      equivalence (l15,l(1)), (l14,l(2)), (l13,l(3)), (l12,l(4)),
+     *    (l11,l(5)), (l10,l(6)), (l9,l(7)), (l8,l(8)), (l7,l(9)),
+     *    (l6,l(10)), (l5,l(11)), (l4,l(12)), (l3,l(13)), (l2,l(14)),
+     *    (l1,l(15))
+      n = 2**m
+      l(1) = n
+      do 10 k=2,m
+        l(k) = l(k-1)/2
+  10  continue
+      do 20 k=m,14
+        l(k+1) = 2
+  20  continue
+      ij = 2
+      do 40 j1=2,l1,2
+      do 40 j2=j1,l2,l1
+      do 40 j3=j2,l3,l2
+      do 40 j4=j3,l4,l3
+      do 40 j5=j4,l5,l4
+      do 40 j6=j5,l6,l5
+      do 40 j7=j6,l7,l6
+      do 40 j8=j7,l8,l7
+      do 40 j9=j8,l9,l8
+      do 40 j10=j9,l10,l9
+      do 40 j11=j10,l11,l10
+      do 40 j12=j11,l12,l11
+      do 40 j13=j12,l13,l12
+      do 40 j14=j13,l14,l13
+      do 40 ji=j14,l15,l14
+        if (ij-ji) 30, 40, 40
+  30    t = b(ij-1)
+        b(ij-1) = b(ji-1)
+        b(ji-1) = t
+        t = b(ij)
+        b(ij) = b(ji)
+        b(ji) = t
+  40    ij = ij + 2
+      return
+      end
diff --git a/math/ieee/chap1/fourea.f b/math/ieee/chap1/fourea.f
new file mode 100644
index 00000000..d412c0e2
--- /dev/null
+++ b/math/ieee/chap1/fourea.f
@@ -0,0 +1,98 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: fourea
+c performs cooley-tukey fast fourier transform
+c-----------------------------------------------------------------------
+c
+      subroutine fourea(data, n, isi)
+c
+c the cooley-tukey fast fourier transform in ansi fortran
+c
+c data is a one-dimensional complex array whose length, n, is a
+c power of two.  isi is +1 for an inverse transform and -1 for a
+c forward transform.  transform values are returned in the input
+c array, replacing the input.
+c transform(j)=sum(data(i)*w**((i-1)*(j-1))), where i and j run
+c from 1 to n and w = exp (isi*2*pi*sqrt(-1)/n).  program also
+c computes inverse transform, for which the defining expression
+c is invtr(j)=(1/n)*sum(data(i)*w**((i-1)*(j-1))).
+c running time is proportional to n*log2(n), rather than to the
+c classical n**2.
+c after program by brenner, june 1967. this is a very short version
+c of the fft and is intended mainly for demonstration. programs
+c are available in this collection which run faster and are not
+c restricted to powers of 2 or to one-dimensional arrays.
+c see -- ieee trans audio (june 1967), special issue on fft.
+c
+      complex data(1)
+      complex temp, w
+      ioutd = i1mach(2)
+c
+c check for power of two up to 15
+c
+      nn = 1
+      do 10 i=1,15
+        m = i
+        nn = nn*2
+        if (nn.eq.n) go to 20
+  10  continue
+      write (ioutd,9999)
+9999  format (30h n not a power of 2 for fourea)
+      stop
+  20  continue
+c
+      pi = 4.*atan(1.)
+      fn = n
+c
+c this section puts data in bit-reversed order
+c
+      j = 1
+      do 80 i=1,n
+c
+c at this point, i and j are a bit reversed pair (except for the
+c displacement of +1)
+c
+        if (i-j) 30, 40, 40
+c
+c exchange data(i) with data(j) if i.lt.j.
+c
+  30    temp = data(j)
+        data(j) = data(i)
+        data(i) = temp
+c
+c implement j=j+1, bit-reversed counter
+c
+  40    m = n/2
+  50    if (j-m) 70, 70, 60
+  60    j = j - m
+        m = (m+1)/2
+        go to 50
+  70    j = j + m
+  80  continue
+c
+c now compute the butterflies
+c
+      mmax = 1
+  90  if (mmax-n) 100, 130, 130
+ 100  istep = 2*mmax
+      do 120 m=1,mmax
+        theta = pi*float(isi*(m-1))/float(mmax)
+        w = cmplx(cos(theta),sin(theta))
+        do 110 i=m,n,istep
+          j = i + mmax
+          temp = w*data(j)
+          data(j) = data(i) - temp
+          data(i) = data(i) + temp
+ 110    continue
+ 120  continue
+      mmax = istep
+      go to 90
+ 130  if (isi) 160, 140, 140
+c
+c for inv trans -- isi=1 -- multiply output by 1/n
+c
+ 140  do 150 i=1,n
+        data(i) = data(i)/fn
+ 150  continue
+ 160  return
+      end
diff --git a/math/ieee/chap1/fr2tr.f b/math/ieee/chap1/fr2tr.f
new file mode 100644
index 00000000..24a103ff
--- /dev/null
+++ b/math/ieee/chap1/fr2tr.f
@@ -0,0 +1,15 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  fr2tr
+c radix 2 iteration subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine fr2tr(int, b0, b1)
+      dimension b0(2), b1(2)
+      do 10 k=1,int
+        t = b0(k) + b1(k)
+        b1(k) = b0(k) - b1(k)
+        b0(k) = t
+  10  continue
+      return
+      end
diff --git a/math/ieee/chap1/fr4syn.f b/math/ieee/chap1/fr4syn.f
new file mode 100644
index 00000000..5ce978f0
--- /dev/null
+++ b/math/ieee/chap1/fr4syn.f
@@ -0,0 +1,109 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  fr4syn
+c radix 4 synthesis
+c-----------------------------------------------------------------------
+c
+c
+      subroutine fr4syn(int, nn, b0, b1, b2, b3, b4, b5, b6, b7)
+      dimension l(15), b0(2), b1(2), b2(2), b3(2), b4(2), b5(2), b6(2),
+     *    b7(2)
+      common /const/ pii, p7, p7two, c22, s22, pi2
+      equivalence (l15,l(1)), (l14,l(2)), (l13,l(3)), (l12,l(4)),
+     *    (l11,l(5)), (l10,l(6)), (l9,l(7)), (l8,l(8)), (l7,l(9)),
+     *    (l6,l(10)), (l5,l(11)), (l4,l(12)), (l3,l(13)), (l2,l(14)),
+     *    (l1,l(15))
+c
+      l(1) = nn/4
+      do 40 k=2,15
+        if (l(k-1)-2) 10, 20, 30
+  10    l(k-1) = 2
+  20    l(k) = 2
+        go to 40
+  30    l(k) = l(k-1)/2
+  40  continue
+c
+      piovn = pii/float(nn)
+      ji = 3
+      jl = 2
+      jr = 2
+c
+      do 120 j1=2,l1,2
+      do 120 j2=j1,l2,l1
+      do 120 j3=j2,l3,l2
+      do 120 j4=j3,l4,l3
+      do 120 j5=j4,l5,l4
+      do 120 j6=j5,l6,l5
+      do 120 j7=j6,l7,l6
+      do 120 j8=j7,l8,l7
+      do 120 j9=j8,l9,l8
+      do 120 j10=j9,l10,l9
+      do 120 j11=j10,l11,l10
+      do 120 j12=j11,l12,l11
+      do 120 j13=j12,l13,l12
+      do 120 j14=j13,l14,l13
+      do 120 jthet=j14,l15,l14
+        th2 = jthet - 2
+        if (th2) 50, 50, 90
+  50    do 60 k=1,int
+          t0 = b0(k) + b1(k)
+          t1 = b0(k) - b1(k)
+          t2 = b2(k)*2.0
+          t3 = b3(k)*2.0
+          b0(k) = t0 + t2
+          b2(k) = t0 - t2
+          b1(k) = t1 + t3
+          b3(k) = t1 - t3
+  60    continue
+c
+        if (nn-4) 120, 120, 70
+  70    k0 = int*4 + 1
+        kl = k0 + int - 1
+        do 80 k=k0,kl
+          t2 = b0(k) - b2(k)
+          t3 = b1(k) + b3(k)
+          b0(k) = (b0(k)+b2(k))*2.0
+          b2(k) = (b3(k)-b1(k))*2.0
+          b1(k) = (t2+t3)*p7two
+          b3(k) = (t3-t2)*p7two
+  80    continue
+        go to 120
+  90    arg = th2*piovn
+        c1 = cos(arg)
+        s1 = -sin(arg)
+        c2 = c1**2 - s1**2
+        s2 = c1*s1 + c1*s1
+        c3 = c1*c2 - s1*s2
+        s3 = c2*s1 + s2*c1
+c
+        int4 = int*4
+        j0 = jr*int4 + 1
+        k0 = ji*int4 + 1
+        jlast = j0 + int - 1
+        do 100 j=j0,jlast
+          k = k0 + j - j0
+          t0 = b0(j) + b6(k)
+          t1 = b7(k) - b1(j)
+          t2 = b0(j) - b6(k)
+          t3 = b7(k) + b1(j)
+          t4 = b2(j) + b4(k)
+          t5 = b5(k) - b3(j)
+          t6 = b5(k) + b3(j)
+          t7 = b4(k) - b2(j)
+          b0(j) = t0 + t4
+          b4(k) = t1 + t5
+          b1(j) = (t2+t6)*c1 - (t3+t7)*s1
+          b5(k) = (t2+t6)*s1 + (t3+t7)*c1
+          b2(j) = (t0-t4)*c2 - (t1-t5)*s2
+          b6(k) = (t0-t4)*s2 + (t1-t5)*c2
+          b3(j) = (t2-t6)*c3 - (t3-t7)*s3
+          b7(k) = (t2-t6)*s3 + (t3-t7)*c3
+ 100    continue
+        jr = jr + 2
+        ji = ji - 2
+        if (ji-jl) 110, 110, 120
+ 110    ji = 2*jr - 1
+        jl = jr
+ 120  continue
+      return
+      end
diff --git a/math/ieee/chap1/fr4tr.f b/math/ieee/chap1/fr4tr.f
new file mode 100644
index 00000000..16ba3fe6
--- /dev/null
+++ b/math/ieee/chap1/fr4tr.f
@@ -0,0 +1,118 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  fr4tr
+c radix 4 iteration subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine fr4tr(int, nn, b0, b1, b2, b3, b4, b5, b6, b7)
+      dimension l(15), b0(2), b1(2), b2(2), b3(2), b4(2), b5(2), b6(2),
+     *    b7(2)
+      common /cons/ pii, p7, p7two, c22, s22, pi2
+      equivalence (l15,l(1)), (l14,l(2)), (l13,l(3)), (l12,l(4)),
+     *    (l11,l(5)), (l10,l(6)), (l9,l(7)), (l8,l(8)), (l7,l(9)),
+     *    (l6,l(10)), (l5,l(11)), (l4,l(12)), (l3,l(13)), (l2,l(14)),
+     *    (l1,l(15))
+c
+c jthet is a reversed binary counter, jr steps two at a time to
+c locate the real parts of intermediate results, and ji locates
+c the imaginary part corresponding to jr.
+c
+      l(1) = nn/4
+      do 40 k=2,15
+        if (l(k-1)-2) 10, 20, 30
+  10    l(k-1) = 2
+  20    l(k) = 2
+        go to 40
+  30    l(k) = l(k-1)/2
+  40  continue
+c
+      piovn = pii/float(nn)
+      ji = 3
+      jl = 2
+      jr = 2
+c
+      do 120 j1=2,l1,2
+      do 120 j2=j1,l2,l1
+      do 120 j3=j2,l3,l2
+      do 120 j4=j3,l4,l3
+      do 120 j5=j4,l5,l4
+      do 120 j6=j5,l6,l5
+      do 120 j7=j6,l7,l6
+      do 120 j8=j7,l8,l7
+      do 120 j9=j8,l9,l8
+      do 120 j10=j9,l10,l9
+      do 120 j11=j10,l11,l10
+      do 120 j12=j11,l12,l11
+      do 120 j13=j12,l13,l12
+      do 120 j14=j13,l14,l13
+      do 120 jthet=j14,l15,l14
+        th2 = jthet - 2
+        if (th2) 50, 50, 90
+  50    do 60 k=1,int
+          t0 = b0(k) + b2(k)
+          t1 = b1(k) + b3(k)
+          b2(k) = b0(k) - b2(k)
+          b3(k) = b1(k) - b3(k)
+          b0(k) = t0 + t1
+          b1(k) = t0 - t1
+  60    continue
+c
+        if (nn-4) 120, 120, 70
+  70    k0 = int*4 + 1
+        kl = k0 + int - 1
+        do 80 k=k0,kl
+          pr = p7*(b1(k)-b3(k))
+          pi = p7*(b1(k)+b3(k))
+          b3(k) = b2(k) + pi
+          b1(k) = pi - b2(k)
+          b2(k) = b0(k) - pr
+          b0(k) = b0(k) + pr
+  80    continue
+        go to 120
+c
+  90    arg = th2*piovn
+        c1 = cos(arg)
+        s1 = sin(arg)
+        c2 = c1**2 - s1**2
+        s2 = c1*s1 + c1*s1
+        c3 = c1*c2 - s1*s2
+        s3 = c2*s1 + s2*c1
+c
+        int4 = int*4
+        j0 = jr*int4 + 1
+        k0 = ji*int4 + 1
+        jlast = j0 + int - 1
+        do 100 j=j0,jlast
+          k = k0 + j - j0
+          r1 = b1(j)*c1 - b5(k)*s1
+          r5 = b1(j)*s1 + b5(k)*c1
+          t2 = b2(j)*c2 - b6(k)*s2
+          t6 = b2(j)*s2 + b6(k)*c2
+          t3 = b3(j)*c3 - b7(k)*s3
+          t7 = b3(j)*s3 + b7(k)*c3
+          t0 = b0(j) + t2
+          t4 = b4(k) + t6
+          t2 = b0(j) - t2
+          t6 = b4(k) - t6
+          t1 = r1 + t3
+          t5 = r5 + t7
+          t3 = r1 - t3
+          t7 = r5 - t7
+          b0(j) = t0 + t1
+          b7(k) = t4 + t5
+          b6(k) = t0 - t1
+          b1(j) = t5 - t4
+          b2(j) = t2 - t7
+          b5(k) = t6 + t3
+          b4(k) = t2 + t7
+          b3(j) = t3 - t6
+ 100    continue
+c
+        jr = jr + 2
+        ji = ji - 2
+        if (ji-jl) 110, 110, 120
+ 110    ji = 2*jr - 1
+        jl = jr
+ 120  continue
+      return
+      end
diff --git a/math/ieee/chap1/fsst.f b/math/ieee/chap1/fsst.f
new file mode 100644
index 00000000..75ce56cb
--- /dev/null
+++ b/math/ieee/chap1/fsst.f
@@ -0,0 +1,71 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  fsst
+c fourier synthesis subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine fsst(b, n)
+c
+c this subroutine synthesizes the real vector b(k), for
+c k=1,2,...,n, from the fourier coefficients stored in the
+c b array of size n+2.  the dc term is in b(1) with b(2) equal
+c to  0.  the jth harmonic is stored as b(2*j+1) + i b(2*j+2).
+c the n/2 harmonic is in b(n+1) with b(n+2) equal to 0.
+c the subroutine is called as fsst(b,n) where n=2**m and
+c b is the real array discussed above.
+c
+      dimension b(2)
+      common /const/ pii, p7, p7two, c22, s22, pi2
+c
+c iw is a machine dependent write device number
+c
+      iw = i1mach(2)
+c
+      pii = 4.*atan(1.)
+      pi8 = pii/8.
+      p7 = 1./sqrt(2.)
+      p7two = 2.*p7
+      c22 = cos(pi8)
+      s22 = sin(pi8)
+      pi2 = 2.*pii
+      do 10 i=1,15
+        m = i
+        nt = 2**i
+        if (n.eq.nt) go to 20
+  10  continue
+      write (iw,9999)
+9999  format (33h n is not a power of two for fsst)
+      stop
+  20  b(2) = b(n+1)
+      do 30 i=4,n,2
+        b(i) = -b(i)
+  30  continue
+c
+c scale the input by n
+c
+      do 40 i=1,n
+        b(i) = b(i)/float(n)
+  40  continue
+      n4pow = m/2
+c
+c scramble the inputs
+c
+      call ford2(m, b)
+      call ford1(m, b)
+c
+      if (n4pow.eq.0) go to 60
+      nn = 4*n
+      do 50 it=1,n4pow
+        nn = nn/4
+        int = n/nn
+        call fr4syn(int, nn, b(1), b(int+1), b(2*int+1), b(3*int+1),
+     *      b(1), b(int+1), b(2*int+1), b(3*int+1))
+  50  continue
+c
+c do a radix 2 iteration if one is required
+c
+  60  if (m-n4pow*2) 80, 80, 70
+  70  int = n/2
+      call fr2tr(int, b(1), b(int+1))
+  80  return
+      end
diff --git a/math/ieee/chap1/iftaoh.f b/math/ieee/chap1/iftaoh.f
new file mode 100644
index 00000000..8cb0a908
--- /dev/null
+++ b/math/ieee/chap1/iftaoh.f
@@ -0,0 +1,87 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: iftaoh
+c compute idft for real, antisymmetric, odd harmonic, n-point sequence
+c using n/4-point fft
+c antisymmetric sequence means x(m)=-x(n-m), m=1,...,n/2-1
+c odd harmonic means x(2*k)=0, all k, where x(k) is the dft of x(m)
+c x(m)has the property x(m)=x(n/2-m), m=0,1,...,n/4-1,  x(0)=0
+c note: index m is sequence index--not fortran index
+c-----------------------------------------------------------------------
+c
+      subroutine iftaoh(x, n, y)
+      dimension x(1), y(1)
+c
+c  x = real array which on input contains the n/4 imaginary points
+c      of the odd harmonics of the transform of the original time
+c      sequence--i.e. the zero valued real parts are not input nor
+c      are the zero-valued even harmonics
+c      on output x contains the first (n/4+1) points of the original
+c      time sequence (antisymmetrical)
+c  n = true size of input
+c  y = scratch array of size n/4+2
+c
+c
+c handle n = 2 and n = 4 cases separately
+c
+      if (n.gt.4) go to 20
+      if (n.eq.4) go to 10
+c
+c for n=2  assume x(1)=0, x(2)=0, compute idft directly
+c
+      x(1) = 0.
+      return
+c
+c for n=4, assume x(1)=x(3)=0, x(2)=-x(4)=x0, compute idft directly
+c
+  10  x(2) = -x(1)/2.
+      x(1) = 0.
+      return
+c
+c code for values of n which are multiples of 8
+c
+  20  twopi = 8.*atan(1.0)
+      no2 = n/2
+      no4 = n/4
+      no8 = n/8
+      tpn = twopi/float(n)
+c
+c scramble original dft (x(k)) to give y(k)
+c use recursion to give sin multipliers
+c
+      cosi = cos(tpn)
+      sini = sin(tpn)
+      cosd = cos(tpn*2.)
+      sind = sin(tpn*2.)
+      do 30 i=1,no8
+        ind = 2*i
+        ind1 = no4 + 1 - i
+        ak = (x(i)-x(ind1))/2.
+        bk = -(x(i)+x(ind1))
+        y(ind) = ak
+        y(ind-1) = bk*sini
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+  30  continue
+c
+c the sequence y(k) is an odd harmonic sequence
+c use subroutine iftohm to give y(m)
+c
+      call iftohm(y, no2)
+c
+c form x sequence from y sequence
+c
+      x(2) = y(1)/2.
+      x(1) = 0.
+      if (n.eq.8) return
+      do 40 i=2,no8
+        ind = 2*i
+        ind1 = no4 + 2 - i
+        x(ind-1) = (y(i)+y(ind1))/2.
+        t1 = (y(i)-y(ind1))/2.
+        x(ind) = t1 + x(ind-2)
+  40  continue
+      x(no4+1) = y(no8+1)
+      return
+      end
diff --git a/math/ieee/chap1/iftasm.f b/math/ieee/chap1/iftasm.f
new file mode 100644
index 00000000..6ec12c7d
--- /dev/null
+++ b/math/ieee/chap1/iftasm.f
@@ -0,0 +1,77 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: iftasm
+c compute idft for real, antisymmetric, n-point sequence x(m) using
+c n/2-point fft
+c antisymmetric sequence means x(m)=-x(n-m), m=1,...,n/2-1
+c note: index m is sequence index--not fortran index
+c-----------------------------------------------------------------------
+c
+      subroutine iftasm(x, n, y)
+      dimension x(1), y(1)
+c
+c x = imaginary array which on input contains the n/2+1 real points of
+c     the transform of the input--i.e. the zero valued real parts
+c     are not given as input
+c     on output x contains the n/2 points of the time sequence
+c     (antisymmetrical)
+c n = true size of input
+c y = scratch array of size n/2+2
+c
+c
+c for n = 2, assume x(1)=0, x(2)=0
+c
+      if (n.gt.2) go to 10
+      x(1) = 0
+      x(2) = 0
+      return
+  10  twopi = 8.*atan(1.0)
+c
+c first compute x1=x(1) term directly
+c use recursion on the sine cosine terms
+c
+      no2 = n/2
+      no4 = n/4
+      tpn = twopi/float(n)
+c
+c scramble original dft (x(k)) to give y(k)
+c use recursion relation to give sin(tpn*i) multiplier
+c
+      cosi = cos(tpn)
+      sini = sin(tpn)
+      cosd = cosi
+      sind = sini
+      nind = no4 + 1
+      do 20 i=2,nind
+        ind = 2*i
+        ind1 = no2 + 2 - i
+        ak = (x(i)-x(ind1))/2.
+        bk = -(x(i)+x(ind1))
+        y(ind) = ak
+        y(ind-1) = bk*sini
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+  20  continue
+      y(1) = 0.
+      y(2) = 0.
+c
+c take n/2 point idft of y
+c
+      call fsst(y, no2)
+c
+c form x sequence from y sequence
+c
+      x(2) = y(1)/2.
+      x(1) = 0.
+      if (n.eq.4) go to 40
+      do 30 i=2,no4
+        ind = 2*i
+        ind1 = no2 + 2 - i
+        x(ind-1) = (y(i)-y(ind1))/2.
+        t1 = (y(i)+y(ind1))/2.
+        x(ind) = t1 + x(ind-2)
+  30  continue
+  40  x(no2) = -y(no4+1)/2.
+      return
+      end
diff --git a/math/ieee/chap1/iftohm.f b/math/ieee/chap1/iftohm.f
new file mode 100644
index 00000000..df084e87
--- /dev/null
+++ b/math/ieee/chap1/iftohm.f
@@ -0,0 +1,83 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: iftohm
+c compute idft for real, n-point, odd harmonic sequences using an
+c n/2 point fft
+c odd harmonic means x(2*k)=0, all k where x(k) is the dft of x(m)
+c note: index m is sequence index--not fortran index
+c-----------------------------------------------------------------------
+c
+      subroutine iftohm(x, n)
+      dimension x(1)
+c
+c x = real array which on input contains the n/4 complex values of the
+c     odd harmonics of the input--stored in the sequence re(x(1)),
+c     im(x(1)),re(x(2)),im(x(2)),...
+c     on output x contains the first n/2 points of the input
+c ****note: x must be dimensioned to size n/2+2 for fft routine
+c n = true size of x sequence
+c
+c first compute real(x(1)) and real(x(n/2-1)) separately
+c also simultaneously multiply original sequence by sin(twopi*(m-1)/n)
+c sin and cos are computed recursively
+c
+c
+c for n = 2, assume x(1)=x0, x(2)=-x0, compute idft directly
+c
+      if (n.gt.2) go to 10
+      x(1) = 0.5*x(1)
+      x(2) = -x(1)
+      return
+  10  twopi = 8.*atan(1.0)
+      tpn = twopi/float(n)
+      no2 = n/2
+      no4 = n/4
+      nind = no2
+c
+c solve for x(0)=x0 directly
+c
+      x0 = 0.
+      do 20 i=1,no2,2
+        x0 = x0 + 2.*x(i)
+  20  continue
+      x0 = x0/float(n)
+c
+c form y(k)=j*(x(2k+1)-x(2k-1))
+c overwrite x array with y sequence
+c
+      xpr = x(1)
+      xpi = x(2)
+      x(1) = -2.*x(2)
+      x(2) = 0.
+      if (no4.eq.1) go to 40
+      do 30 i=3,nind,2
+        ti = x(i) - xpr
+        tr = -x(i+1) + xpi
+        xpr = x(i)
+        xpi = x(i+1)
+        x(i) = tr
+        x(i+1) = ti
+  30  continue
+  40  x(no2+1) = 2.*xpi
+      x(no2+2) = 0.
+c
+c take n/2 point (real) ifft of preprocessed sequence x
+c
+      call fsst(x, no2)
+c
+c solve for x(m) by dividing by 4*sin(twopi*m/n) for m=1,2,...,n/2-1
+c for m=0 substitute precomputed value x0
+c
+      cosi = 4.
+      sini = 0.
+      cosd = cos(tpn)
+      sind = sin(tpn)
+      do 50 i=2,no2
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+        x(i) = x(i)/sini
+  50  continue
+      x(1) = x0
+      return
+      end
diff --git a/math/ieee/chap1/iftsoh.f b/math/ieee/chap1/iftsoh.f
new file mode 100644
index 00000000..6098e6e4
--- /dev/null
+++ b/math/ieee/chap1/iftsoh.f
@@ -0,0 +1,94 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: iftsoh
+c compute idft for real, symmetric, odd harmonic, n-point sequence
+c using n/4-point fft
+c symmetric sequence means x(m)=x(n-m), m=1,...,n/2-1
+c odd harmonic means x(2*k)=0, all k, where x(k) is the dft of x(m)
+c x(m) has the property x(m)=-x(n/2-m), m=0,1,...,n/4-1,  x(n/4)=0
+c note: index m is sequence index--not fortran index
+c-----------------------------------------------------------------------
+c
+      subroutine iftsoh(x, n, y)
+      dimension x(1), y(1)
+c
+c  x = real array which on input contains the n/4 real points of
+c      the odd harmonics of the transform of the original time sequence
+c      i.e. the zero valued imaginary parts are not given nor are the
+c      zero valued even harmonics
+c      on output x contains the first n/4 points of the original input
+c      sequence (symmetrical)
+c  n = true size of input
+c  y = scratch array of size n/4+2
+c
+c
+c handle n = 2 and n = 4 cases separately
+c
+      if (n.gt.4) go to 10
+c
+c for n=2, 4 assume x(1)=x0, x(2)=-x0, compute idft directly
+c
+      x(1) = x(1)/2.
+      return
+c
+c code for values of n which are multiples of 8
+c
+  10  twopi = 8.*atan(1.0)
+      no2 = n/2
+      no4 = n/4
+      no8 = n/8
+      tpn = twopi/float(n)
+c
+c first compute x1=x(1) term directly
+c use recursion on the sine cosine terms
+c
+      cosd = cos(tpn*2.)
+      sind = sin(tpn*2.)
+      cosi = 2.*cos(tpn)
+      sini = 2.*sin(tpn)
+      x1 = 0.
+      do 20 i=1,no4
+        x1 = x1 + x(i)*cosi
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+  20  continue
+      x1 = x1/float(n)
+c
+c scramble original dft (x(k)) to give y(k)
+c use recursion relation to give sin multipliers
+c
+      cosi = cos(tpn)
+      sini = sin(tpn)
+      do 30 i=1,no8
+        ind = 2*i
+        ind1 = no4 + 1 - i
+        ak = (x(i)+x(ind1))/2.
+        bk = (x(i)-x(ind1))
+        y(ind-1) = ak
+        y(ind) = bk*sini
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+  30  continue
+c
+c the sequence y(k) is the odd harmonics dft output
+c use subroutine iftohm to obtain y(m), the inverse transform
+c
+      call iftohm(y, no2)
+c
+c form x(m) sequence from y(m) sequence
+c use x1 initial condition on the recursion
+c
+      x(1) = y(1)
+      x(2) = x1
+      if (no8.eq.1) return
+      do 40 i=2,no8
+        ind = 2*i
+        ind1 = no4 + 2 - i
+        t1 = (y(i)+y(ind1))/2.
+        x(ind-1) = (y(i)-y(ind1))/2.
+        x(ind) = t1 + x(ind-2)
+  40  continue
+      return
+      end
diff --git a/math/ieee/chap1/iftsym.f b/math/ieee/chap1/iftsym.f
new file mode 100644
index 00000000..e45c9a37
--- /dev/null
+++ b/math/ieee/chap1/iftsym.f
@@ -0,0 +1,90 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: iftsym
+c compute idft for real, symmetric, n-point sequence x(m) using
+c n/2-point fft
+c symmetric sequence means x(m)=x(n-m), m=1,...,n/2-1
+c note: index m is sequence index--not fortran index
+c-----------------------------------------------------------------------
+c
+      subroutine iftsym(x, n, y)
+      dimension x(1), y(1)
+c
+c x = real array which on input contains the n/2+1 real points of the
+c     transform of the input--i.e. the zero valued imaginary parts
+c     are not given as input
+c     on output x contains the n/2+1 points of the time sequence
+c     (symmetrical)
+c n = true size of input
+c y = scratch array of size n/2+2
+c
+c
+c for n = 2, compute idft directly
+c
+      if (n.gt.2) go to 10
+      t = (x(1)+x(2))/2.
+      x(2) = (x(1)-x(2))/2.
+      x(1) = t
+      return
+  10  twopi = 8.*atan(1.0)
+c
+c first compute x1=x(1) term directly
+c use recursion on the sine cosine terms
+c
+      no2 = n/2
+      no4 = n/4
+      tpn = twopi/float(n)
+      cosd = cos(tpn)
+      sind = sin(tpn)
+      cosi = 2.
+      sini = 0.
+      x1 = x(1) - x(no2+1)
+      do 20 i=2,no2
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+        x1 = x1 + x(i)*cosi
+  20  continue
+      x1 = x1/float(n)
+c
+c scramble original dft (x(k)) to give y(k)
+c use recursion relation to generate sin(tpn*i) multiplier
+c
+      cosi = cos(tpn)
+      sini = sin(tpn)
+      cosd = cosi
+      sind = sini
+      y(1) = (x(1)+x(no2+1))/2.
+      y(2) = 0.
+      nind = no4 + 1
+      do 30 i=2,nind
+        ind = 2*i
+        nind1 = no2 + 2 - i
+        ak = (x(i)+x(nind1))/2.
+        bk = (x(i)-x(nind1))
+        y(ind-1) = ak
+        y(ind) = bk*sini
+        temp = cosi*cosd - sini*sind
+        sini = cosi*sind + sini*cosd
+        cosi = temp
+  30  continue
+c
+c take n/2 point idft of y
+c
+      call fsst(y, no2)
+c
+c form x sequence from y sequence
+c
+      x(1) = y(1)
+      x(2) = x1
+      if (n.eq.4) go to 50
+      do 40 i=2,no4
+        ind = 2*i
+        ind1 = no2 + 2 - i
+        x(ind-1) = (y(i)+y(ind1))/2.
+        t1 = (y(i)-y(ind1))/2.
+        x(ind) = t1 + x(ind-2)
+  40  continue
+  50  x(no2+1) = y(no4+1)
+      return
+      end
diff --git a/math/ieee/chap1/inishl.f b/math/ieee/chap1/inishl.f
new file mode 100644
index 00000000..925cd657
--- /dev/null
+++ b/math/ieee/chap1/inishl.f
@@ -0,0 +1,179 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: inishl
+c   this subroutine initializes the wfta routine for a given
+c   value of the transform length n.  the factors of n are
+c   determined, the multiplication coefficients are calculated
+c   and stored in the array coef(.), the input and output
+c   permutation vectors are computed and stored in the arrays
+c   indx1(.) and indx2(.)
+c
+c-----------------------------------------------------------------------
+c
+      subroutine inishl(n,coef,xr,xi,indx1,indx2,ierr)
+      dimension coef(1),xr(1),xi(1)
+      integer s1,s2,s3,s4,indx1(1),indx2(1),p1
+      dimension co3(3),co4(4),co8(8),co9(11),co16(18),cda(18),cdb(11),
+     1cdc(9),cdd(6)
+      common na,nb,nc,nd,nd1,nd2,nd3,nd4
+c
+c   data statements assign short dft coefficients.
+c
+      data co4(1),co4(2),co4(3),co4(4)/4*1.0/
+c
+      data cda(1),cda(2),cda(3),cda(4),cda(5),cda(6),cda(7),
+     1 cda(8),cda(9),cda(10),cda(11),cda(12),cda(13),cda(14),
+     2 cda(15),cda(16),cda(17),cda(18)/18*1.0/
+c
+      data cdb(1),cdb(2),cdb(3),cdb(4),cdb(5),cdb(6),cdb(7),cdb(8),
+     1 cdb(9),cdb(10),cdb(11)/11*1.0/
+c
+      data ionce/1/
+c
+c   get multiplier constants
+c
+      if(ionce.ne.1) go to 20
+      call const(co3,co8,co16,co9,cdc,cdd)
+20    ionce=-1
+c
+c   following segment determines factors of n and chooses
+c   the appropriate short dft coefficients.
+c
+      iout=i1mach(2)
+      ierr=0
+      nd1=1
+      na=1
+      nb=1
+      nd2=1
+      nc=1
+      nd3=1
+      nd=1
+      nd4=1
+      if(n.le.0 .or. n.gt.5040) go to 190
+      if(16*(n/16).eq.n) go to 30
+      if(8*(n/8).eq.n) go to 40
+      if(4*(n/4).eq.n) go to 50
+      if(2*(n/2).ne.n) go to 70
+      nd1=2
+      na=2
+      cda(2)=1.0
+      go to 70
+30    nd1=18
+      na=16
+      do 31 j=1,18
+31    cda(j)=co16(j)
+      go to 70
+40    nd1=8
+      na=8
+      do 41 j=1,8
+41    cda(j)=co8(j)
+      go to 70
+50    nd1=4
+      na=4
+      do 51 j=1,4
+51    cda(j)=co4(j)
+70    if(3*(n/3).ne.n) go to 120
+      if(9*(n/9).eq.n) go to 100
+      nd2=3
+      nb=3
+      do 71 j=1,3
+71    cdb(j)=co3(j)
+      go to 120
+100   nd2=11
+      nb=9
+      do 110 j=1,11
+110   cdb(j)=co9(j)
+120   if(7*(n/7).ne.n) go to 160
+      nd3=9
+      nc=7
+160   if(5*(n/5).ne.n) go to 190
+      nd4=6
+      nd=5
+190   m=na*nb*nc*nd
+      if(m.eq.n) go to 250
+      write(iout,210)
+210   format(21h this n does not work)
+      ierr=-1
+      return
+c
+c   next segment generates the dft coefficients by
+c   multiplying together the short dft coefficients
+c
+250   j=1
+      do 300 n4=1,nd4
+      do 300 n3=1,nd3
+      do 300 n2=1,nd2
+      do 300 n1=1,nd1
+      coef(j)=cda(n1)*cdb(n2)*cdc(n3)*cdd(n4)
+      j=j+1
+300   continue
+c
+c   following segment forms the input indexing vector
+c
+      j=1
+      nu=nb*nc*nd
+      nv=na*nc*nd
+      nw=na*nb*nd
+      ny=na*nb*nc
+      k=1
+      do 440 n4=1,nd
+      do 430 n3=1,nc
+      do 420 n2=1,nb
+      do 410 n1=1,na
+405   if(k.le.n) go to 408
+      k=k-n
+      go to 405
+408   indx1(j)=k
+      j=j+1
+410   k=k+nu
+420   k=k+nv
+430   k=k+nw
+440   k=k+ny
+c
+c   following segment forms the output indexing vector
+c
+      m=1
+      s1=0
+      s2=0
+      s3=0
+      s4=0
+      if(na.eq.1) go to 530
+520   p1=m*nu-1
+      if((p1/na)*na.eq.p1) go to 510
+      m=m+1
+      go to 520
+510   s1=p1+1
+530   if(nb.eq.1) go to 540
+      m=1
+550   p1=m*nv-1
+      if((p1/nb)*nb.eq.p1) go to 560
+      m=m+1
+      go to 550
+560   s2=p1+1
+540   if(nc.eq.1) go to 630
+      m=1
+620   p1=m*nw-1
+      if((p1/nc)*nc.eq.p1) go to 610
+      m=m+1
+      go to 620
+610   s3=p1+1
+630   if(nd.eq.1) go to 660
+      m=1
+640   p1=m*ny-1
+      if((p1/nd)*nd.eq.p1) go to 650
+      m=m+1
+      go to 640
+650   s4=p1+1
+660   j=1
+      do 810 n4=1,nd
+      do 810 n3=1,nc
+      do 810 n2=1,nb
+      do 810 n1=1,na
+      indx2(j)=s1*(n1-1)+s2*(n2-1)+s3*(n3-1)+s4*(n4-1)+1
+900   if(indx2(j).le.n) go to 910
+      indx2(j)=indx2(j)-n
+      go to 900
+910   j=j+1
+810   continue
+      return
+      end
diff --git a/math/ieee/chap1/ord1.f b/math/ieee/chap1/ord1.f
new file mode 100644
index 00000000..21e4494e
--- /dev/null
+++ b/math/ieee/chap1/ord1.f
@@ -0,0 +1,24 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  ord1
+c in-place reordering subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine ord1(m, b)
+      dimension b(2)
+c
+      k = 4
+      kl = 2
+      n = 2**m
+      do 40 j=4,n,2
+        if (k-j) 20, 20, 10
+  10    t = b(j)
+        b(j) = b(k)
+        b(k) = t
+  20    k = k - 2
+        if (k-kl) 30, 30, 40
+  30    k = 2*j
+        kl = j
+  40  continue
+      return
+      end
diff --git a/math/ieee/chap1/ord2.f b/math/ieee/chap1/ord2.f
new file mode 100644
index 00000000..10f03ec7
--- /dev/null
+++ b/math/ieee/chap1/ord2.f
@@ -0,0 +1,46 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  ord2
+c in-place reordering subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine ord2(m, b)
+      dimension l(15), b(2)
+      equivalence (l15,l(1)), (l14,l(2)), (l13,l(3)), (l12,l(4)),
+     *    (l11,l(5)), (l10,l(6)), (l9,l(7)), (l8,l(8)), (l7,l(9)),
+     *    (l6,l(10)), (l5,l(11)), (l4,l(12)), (l3,l(13)), (l2,l(14)),
+     *    (l1,l(15))
+      n = 2**m
+      l(1) = n
+      do 10 k=2,m
+        l(k) = l(k-1)/2
+  10  continue
+      do 20 k=m,14
+        l(k+1) = 2
+  20  continue
+      ij = 2
+      do 40 j1=2,l1,2
+      do 40 j2=j1,l2,l1
+      do 40 j3=j2,l3,l2
+      do 40 j4=j3,l4,l3
+      do 40 j5=j4,l5,l4
+      do 40 j6=j5,l6,l5
+      do 40 j7=j6,l7,l6
+      do 40 j8=j7,l8,l7
+      do 40 j9=j8,l9,l8
+      do 40 j10=j9,l10,l9
+      do 40 j11=j10,l11,l10
+      do 40 j12=j11,l12,l11
+      do 40 j13=j12,l13,l12
+      do 40 j14=j13,l14,l13
+      do 40 ji=j14,l15,l14
+        if (ij-ji) 30, 40, 40
+  30    t = b(ij-1)
+        b(ij-1) = b(ji-1)
+        b(ji-1) = t
+        t = b(ij)
+        b(ij) = b(ji)
+        b(ji) = t
+  40    ij = ij + 2
+      return
+      end
diff --git a/math/ieee/chap1/r2tr.f b/math/ieee/chap1/r2tr.f
new file mode 100644
index 00000000..510763fe
--- /dev/null
+++ b/math/ieee/chap1/r2tr.f
@@ -0,0 +1,16 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  r2tr
+c radix 2 iteration subroutine
+c-----------------------------------------------------------------------
+c
+c
+      subroutine r2tr(int, b0, b1)
+      dimension b0(2), b1(2)
+      do 10 k=1,int
+        t = b0(k) + b1(k)
+        b1(k) = b0(k) - b1(k)
+        b0(k) = t
+  10  continue
+      return
+      end
diff --git a/math/ieee/chap1/r2tx.f b/math/ieee/chap1/r2tx.f
new file mode 100644
index 00000000..425c10f8
--- /dev/null
+++ b/math/ieee/chap1/r2tx.f
@@ -0,0 +1,18 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  r2tx
+c radix 2 iteration subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine r2tx(nthpo, cr0, cr1, ci0, ci1)
+      dimension cr0(2), cr1(2), ci0(2), ci1(2)
+      do 10 k=1,nthpo,2
+        r1 = cr0(k) + cr1(k)
+        cr1(k) = cr0(k) - cr1(k)
+        cr0(k) = r1
+        fi1 = ci0(k) + ci1(k)
+        ci1(k) = ci0(k) - ci1(k)
+        ci0(k) = fi1
+  10  continue
+      return
+      end
diff --git a/math/ieee/chap1/r4syn.f b/math/ieee/chap1/r4syn.f
new file mode 100644
index 00000000..77c97bba
--- /dev/null
+++ b/math/ieee/chap1/r4syn.f
@@ -0,0 +1,20 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  r4syn
+c radix 4 synthesis
+c-----------------------------------------------------------------------
+c
+      subroutine r4syn(int, b0, b1, b2, b3)
+      dimension b0(2), b1(2), b2(2), b3(2)
+      do 10 k=1,int
+        t0 = b0(k) + b1(k)
+        t1 = b0(k) - b1(k)
+        t2 = b2(k) + b2(k)
+        t3 = b3(k) + b3(k)
+        b0(k) = t0 + t2
+        b2(k) = t0 - t2
+        b1(k) = t1 + t3
+        b3(k) = t1 - t3
+  10  continue
+      return
+      end
diff --git a/math/ieee/chap1/r4tr.f b/math/ieee/chap1/r4tr.f
new file mode 100644
index 00000000..5fc46eab
--- /dev/null
+++ b/math/ieee/chap1/r4tr.f
@@ -0,0 +1,18 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  r4tr
+c radix 4 iteration subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine r4tr(int, b0, b1, b2, b3)
+      dimension b0(2), b1(2), b2(2), b3(2)
+      do 10 k=1,int
+        r0 = b0(k) + b2(k)
+        r1 = b1(k) + b3(k)
+        b2(k) = b0(k) - b2(k)
+        b3(k) = b1(k) - b3(k)
+        b0(k) = r0 + r1
+        b1(k) = r0 - r1
+  10  continue
+      return
+      end
diff --git a/math/ieee/chap1/r4tx.f b/math/ieee/chap1/r4tx.f
new file mode 100644
index 00000000..4e5649e8
--- /dev/null
+++ b/math/ieee/chap1/r4tx.f
@@ -0,0 +1,29 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  r4tx
+c radix 4 iteration subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine r4tx(nthpo, cr0, cr1, cr2, cr3, ci0, ci1, ci2, ci3)
+      dimension cr0(2), cr1(2), cr2(2), cr3(2), ci0(2), ci1(2), ci2(2),
+     *    ci3(2)
+      do 10 k=1,nthpo,4
+        r1 = cr0(k) + cr2(k)
+        r2 = cr0(k) - cr2(k)
+        r3 = cr1(k) + cr3(k)
+        r4 = cr1(k) - cr3(k)
+        fi1 = ci0(k) + ci2(k)
+        fi2 = ci0(k) - ci2(k)
+        fi3 = ci1(k) + ci3(k)
+        fi4 = ci1(k) - ci3(k)
+        cr0(k) = r1 + r3
+        ci0(k) = fi1 + fi3
+        cr1(k) = r1 - r3
+        ci1(k) = fi1 - fi3
+        cr2(k) = r2 - fi4
+        ci2(k) = fi2 + r4
+        cr3(k) = r2 + fi4
+        ci3(k) = fi2 - r4
+  10  continue
+      return
+      end
diff --git a/math/ieee/chap1/r8syn.f b/math/ieee/chap1/r8syn.f
new file mode 100644
index 00000000..054413d7
--- /dev/null
+++ b/math/ieee/chap1/r8syn.f
@@ -0,0 +1,186 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  r8syn
+c radix 8 synthesis subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine r8syn(int, nn, br0, br1, br2, br3, br4, br5, br6, br7,
+     *    bi0, bi1, bi2, bi3, bi4, bi5, bi6, bi7)
+      dimension l(15), br0(2), br1(2), br2(2), br3(2), br4(2), br5(2),
+     *    br6(2), br7(2), bi0(2), bi1(2), bi2(2), bi3(2), bi4(2),
+     *    bi5(2), bi6(2), bi7(2)
+      common /con1/ pii, p7, p7two, c22, s22, pi2
+      equivalence (l15,l(1)), (l14,l(2)), (l13,l(3)), (l12,l(4)),
+     *    (l11,l(5)), (l10,l(6)), (l9,l(7)), (l8,l(8)), (l7,l(9)),
+     *    (l6,l(10)), (l5,l(11)), (l4,l(12)), (l3,l(13)), (l2,l(14)),
+     *    (l1,l(15))
+      l(1) = nn/8
+      do 40 k=2,15
+        if (l(k-1)-2) 10, 20, 30
+  10    l(k-1) = 2
+  20    l(k) = 2
+        go to 40
+  30    l(k) = l(k-1)/2
+  40  continue
+      piovn = pii/float(nn)
+      ji = 3
+      jl = 2
+      jr = 2
+c
+      do 120 j1=2,l1,2
+      do 120 j2=j1,l2,l1
+      do 120 j3=j2,l3,l2
+      do 120 j4=j3,l4,l3
+      do 120 j5=j4,l5,l4
+      do 120 j6=j5,l6,l5
+      do 120 j7=j6,l7,l6
+      do 120 j8=j7,l8,l7
+      do 120 j9=j8,l9,l8
+      do 120 j10=j9,l10,l9
+      do 120 j11=j10,l11,l10
+      do 120 j12=j11,l12,l11
+      do 120 j13=j12,l13,l12
+      do 120 j14=j13,l14,l13
+      do 120 jthet=j14,l15,l14
+        th2 = jthet - 2
+        if (th2) 50, 50, 90
+  50    do 60 k=1,int
+          t0 = br0(k) + br1(k)
+          t1 = br0(k) - br1(k)
+          t2 = br2(k) + br2(k)
+          t3 = br3(k) + br3(k)
+          t4 = br4(k) + br6(k)
+          t6 = br7(k) - br5(k)
+          t5 = br4(k) - br6(k)
+          t7 = br7(k) + br5(k)
+          pr = p7*(t7+t5)
+          pi = p7*(t7-t5)
+          tt0 = t0 + t2
+          tt1 = t1 + t3
+          t2 = t0 - t2
+          t3 = t1 - t3
+          t4 = t4 + t4
+          t5 = pr + pr
+          t6 = t6 + t6
+          t7 = pi + pi
+          br0(k) = tt0 + t4
+          br1(k) = tt1 + t5
+          br2(k) = t2 + t6
+          br3(k) = t3 + t7
+          br4(k) = tt0 - t4
+          br5(k) = tt1 - t5
+          br6(k) = t2 - t6
+          br7(k) = t3 - t7
+  60    continue
+        if (nn-8) 120, 120, 70
+  70    k0 = int*8 + 1
+        kl = k0 + int - 1
+        do 80 k=k0,kl
+          t1 = bi0(k) + bi6(k)
+          t2 = bi7(k) - bi1(k)
+          t3 = bi0(k) - bi6(k)
+          t4 = bi7(k) + bi1(k)
+          pr = t3*c22 + t4*s22
+          pi = t4*c22 - t3*s22
+          t5 = bi2(k) + bi4(k)
+          t6 = bi5(k) - bi3(k)
+          t7 = bi2(k) - bi4(k)
+          t8 = bi5(k) + bi3(k)
+          rr = t8*c22 - t7*s22
+          ri = -t8*s22 - t7*c22
+          bi0(k) = (t1+t5) + (t1+t5)
+          bi4(k) = (t2+t6) + (t2+t6)
+          bi1(k) = (pr+rr) + (pr+rr)
+          bi5(k) = (pi+ri) + (pi+ri)
+          t5 = t1 - t5
+          t6 = t2 - t6
+          bi2(k) = p7two*(t6+t5)
+          bi6(k) = p7two*(t6-t5)
+          rr = pr - rr
+          ri = pi - ri
+          bi3(k) = p7two*(ri+rr)
+          bi7(k) = p7two*(ri-rr)
+  80    continue
+        go to 120
+  90    arg = th2*piovn
+        c1 = cos(arg)
+        s1 = -sin(arg)
+        c2 = c1**2 - s1**2
+        s2 = c1*s1 + c1*s1
+        c3 = c1*c2 - s1*s2
+        s3 = c2*s1 + s2*c1
+        c4 = c2**2 - s2**2
+        s4 = c2*s2 + c2*s2
+        c5 = c2*c3 - s2*s3
+        s5 = c3*s2 + s3*c2
+        c6 = c3**2 - s3**2
+        s6 = c3*s3 + c3*s3
+        c7 = c3*c4 - s3*s4
+        s7 = c4*s3 + s4*c3
+        int8 = int*8
+        j0 = jr*int8 + 1
+        k0 = ji*int8 + 1
+        jlast = j0 + int - 1
+        do 100 j=j0,jlast
+          k = k0 + j - j0
+          tr0 = br0(j) + bi6(k)
+          ti0 = bi7(k) - br1(j)
+          tr1 = br0(j) - bi6(k)
+          ti1 = bi7(k) + br1(j)
+          tr2 = br2(j) + bi4(k)
+          ti2 = bi5(k) - br3(j)
+          tr3 = bi5(k) + br3(j)
+          ti3 = bi4(k) - br2(j)
+          tr4 = br4(j) + bi2(k)
+          ti4 = bi3(k) - br5(j)
+          t0 = br4(j) - bi2(k)
+          t1 = bi3(k) + br5(j)
+          tr5 = p7*(t0+t1)
+          ti5 = p7*(t1-t0)
+          tr6 = br6(j) + bi0(k)
+          ti6 = bi1(k) - br7(j)
+          t0 = br6(j) - bi0(k)
+          t1 = bi1(k) + br7(j)
+          tr7 = -p7*(t0-t1)
+          ti7 = -p7*(t1+t0)
+          t0 = tr0 + tr2
+          t1 = ti0 + ti2
+          t2 = tr1 + tr3
+          t3 = ti1 + ti3
+          tr2 = tr0 - tr2
+          ti2 = ti0 - ti2
+          tr3 = tr1 - tr3
+          ti3 = ti1 - ti3
+          t4 = tr4 + tr6
+          t5 = ti4 + ti6
+          t6 = tr5 + tr7
+          t7 = ti5 + ti7
+          ttr6 = ti4 - ti6
+          ti6 = tr6 - tr4
+          ttr7 = ti5 - ti7
+          ti7 = tr7 - tr5
+          br0(j) = t0 + t4
+          bi0(k) = t1 + t5
+          br1(j) = c1*(t2+t6) - s1*(t3+t7)
+          bi1(k) = c1*(t3+t7) + s1*(t2+t6)
+          br2(j) = c2*(tr2+ttr6) - s2*(ti2+ti6)
+          bi2(k) = c2*(ti2+ti6) + s2*(tr2+ttr6)
+          br3(j) = c3*(tr3+ttr7) - s3*(ti3+ti7)
+          bi3(k) = c3*(ti3+ti7) + s3*(tr3+ttr7)
+          br4(j) = c4*(t0-t4) - s4*(t1-t5)
+          bi4(k) = c4*(t1-t5) + s4*(t0-t4)
+          br5(j) = c5*(t2-t6) - s5*(t3-t7)
+          bi5(k) = c5*(t3-t7) + s5*(t2-t6)
+          br6(j) = c6*(tr2-ttr6) - s6*(ti2-ti6)
+          bi6(k) = c6*(ti2-ti6) + s6*(tr2-ttr6)
+          br7(j) = c7*(tr3-ttr7) - s7*(ti3-ti7)
+          bi7(k) = c7*(ti3-ti7) + s7*(tr3-ttr7)
+ 100    continue
+        jr = jr + 2
+        ji = ji - 2
+        if (ji-jl) 110, 110, 120
+ 110    ji = 2*jr - 1
+        jl = jr
+ 120  continue
+      return
+      end
diff --git a/math/ieee/chap1/r8tr.f b/math/ieee/chap1/r8tr.f
new file mode 100644
index 00000000..d49ef58c
--- /dev/null
+++ b/math/ieee/chap1/r8tr.f
@@ -0,0 +1,201 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: r8tr
+c radix 8 iteration subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine r8tr(int, nn, br0, br1, br2, br3, br4, br5, br6, br7,
+     *    bi0, bi1, bi2, bi3, bi4, bi5, bi6, bi7)
+      dimension l(15), br0(2), br1(2), br2(2), br3(2), br4(2), br5(2),
+     *    br6(2), br7(2), bi0(2), bi1(2), bi2(2), bi3(2), bi4(2),
+     *    bi5(2), bi6(2), bi7(2)
+      common /con/ pii, p7, p7two, c22, s22, pi2
+      equivalence (l15,l(1)), (l14,l(2)), (l13,l(3)), (l12,l(4)),
+     *    (l11,l(5)), (l10,l(6)), (l9,l(7)), (l8,l(8)), (l7,l(9)),
+     *    (l6,l(10)), (l5,l(11)), (l4,l(12)), (l3,l(13)), (l2,l(14)),
+     *    (l1,l(15))
+c
+c set up counters such that jthet steps through the arguments
+c of w, jr steps through starting locations for the real part of the
+c intermediate results and ji steps through starting locations
+c of the imaginary part of the intermediate results.
+c
+      l(1) = nn/8
+      do 40 k=2,15
+        if (l(k-1)-2) 10, 20, 30
+  10    l(k-1) = 2
+  20    l(k) = 2
+        go to 40
+  30    l(k) = l(k-1)/2
+  40  continue
+      piovn = pii/float(nn)
+      ji = 3
+      jl = 2
+      jr = 2
+      do 120 j1=2,l1,2
+      do 120 j2=j1,l2,l1
+      do 120 j3=j2,l3,l2
+      do 120 j4=j3,l4,l3
+      do 120 j5=j4,l5,l4
+      do 120 j6=j5,l6,l5
+      do 120 j7=j6,l7,l6
+      do 120 j8=j7,l8,l7
+      do 120 j9=j8,l9,l8
+      do 120 j10=j9,l10,l9
+      do 120 j11=j10,l11,l10
+      do 120 j12=j11,l12,l11
+      do 120 j13=j12,l13,l12
+      do 120 j14=j13,l14,l13
+      do 120 jthet=j14,l15,l14
+        th2 = jthet - 2
+        if (th2) 50, 50, 90
+  50    do 60 k=1,int
+          t0 = br0(k) + br4(k)
+          t1 = br1(k) + br5(k)
+          t2 = br2(k) + br6(k)
+          t3 = br3(k) + br7(k)
+          t4 = br0(k) - br4(k)
+          t5 = br1(k) - br5(k)
+          t6 = br2(k) - br6(k)
+          t7 = br3(k) - br7(k)
+          br2(k) = t0 - t2
+          br3(k) = t1 - t3
+          t0 = t0 + t2
+          t1 = t1 + t3
+          br0(k) = t0 + t1
+          br1(k) = t0 - t1
+          pr = p7*(t5-t7)
+          pi = p7*(t5+t7)
+          br4(k) = t4 + pr
+          br7(k) = t6 + pi
+          br6(k) = t4 - pr
+          br5(k) = pi - t6
+  60    continue
+        if (nn-8) 120, 120, 70
+  70    k0 = int*8 + 1
+        kl = k0 + int - 1
+        do 80 k=k0,kl
+          pr = p7*(bi2(k)-bi6(k))
+          pi = p7*(bi2(k)+bi6(k))
+          tr0 = bi0(k) + pr
+          ti0 = bi4(k) + pi
+          tr2 = bi0(k) - pr
+          ti2 = bi4(k) - pi
+          pr = p7*(bi3(k)-bi7(k))
+          pi = p7*(bi3(k)+bi7(k))
+          tr1 = bi1(k) + pr
+          ti1 = bi5(k) + pi
+          tr3 = bi1(k) - pr
+          ti3 = bi5(k) - pi
+          pr = tr1*c22 - ti1*s22
+          pi = ti1*c22 + tr1*s22
+          bi0(k) = tr0 + pr
+          bi6(k) = tr0 - pr
+          bi7(k) = ti0 + pi
+          bi1(k) = pi - ti0
+          pr = -tr3*s22 - ti3*c22
+          pi = tr3*c22 - ti3*s22
+          bi2(k) = tr2 + pr
+          bi4(k) = tr2 - pr
+          bi5(k) = ti2 + pi
+          bi3(k) = pi - ti2
+  80    continue
+        go to 120
+  90    arg = th2*piovn
+        c1 = cos(arg)
+        s1 = sin(arg)
+        c2 = c1**2 - s1**2
+        s2 = c1*s1 + c1*s1
+        c3 = c1*c2 - s1*s2
+        s3 = c2*s1 + s2*c1
+        c4 = c2**2 - s2**2
+        s4 = c2*s2 + c2*s2
+        c5 = c2*c3 - s2*s3
+        s5 = c3*s2 + s3*c2
+        c6 = c3**2 - s3**2
+        s6 = c3*s3 + c3*s3
+        c7 = c3*c4 - s3*s4
+        s7 = c4*s3 + s4*c3
+        int8 = int*8
+        j0 = jr*int8 + 1
+        k0 = ji*int8 + 1
+        jlast = j0 + int - 1
+        do 100 j=j0,jlast
+          k = k0 + j - j0
+          tr1 = br1(j)*c1 - bi1(k)*s1
+          ti1 = br1(j)*s1 + bi1(k)*c1
+          tr2 = br2(j)*c2 - bi2(k)*s2
+          ti2 = br2(j)*s2 + bi2(k)*c2
+          tr3 = br3(j)*c3 - bi3(k)*s3
+          ti3 = br3(j)*s3 + bi3(k)*c3
+          tr4 = br4(j)*c4 - bi4(k)*s4
+          ti4 = br4(j)*s4 + bi4(k)*c4
+          tr5 = br5(j)*c5 - bi5(k)*s5
+          ti5 = br5(j)*s5 + bi5(k)*c5
+          tr6 = br6(j)*c6 - bi6(k)*s6
+          ti6 = br6(j)*s6 + bi6(k)*c6
+          tr7 = br7(j)*c7 - bi7(k)*s7
+          ti7 = br7(j)*s7 + bi7(k)*c7
+c
+          t0 = br0(j) + tr4
+          t1 = bi0(k) + ti4
+          tr4 = br0(j) - tr4
+          ti4 = bi0(k) - ti4
+          t2 = tr1 + tr5
+          t3 = ti1 + ti5
+          tr5 = tr1 - tr5
+          ti5 = ti1 - ti5
+          t4 = tr2 + tr6
+          t5 = ti2 + ti6
+          tr6 = tr2 - tr6
+          ti6 = ti2 - ti6
+          t6 = tr3 + tr7
+          t7 = ti3 + ti7
+          tr7 = tr3 - tr7
+          ti7 = ti3 - ti7
+c
+          tr0 = t0 + t4
+          ti0 = t1 + t5
+          tr2 = t0 - t4
+          ti2 = t1 - t5
+          tr1 = t2 + t6
+          ti1 = t3 + t7
+          tr3 = t2 - t6
+          ti3 = t3 - t7
+          t0 = tr4 - ti6
+          t1 = ti4 + tr6
+          t4 = tr4 + ti6
+          t5 = ti4 - tr6
+          t2 = tr5 - ti7
+          t3 = ti5 + tr7
+          t6 = tr5 + ti7
+          t7 = ti5 - tr7
+          br0(j) = tr0 + tr1
+          bi7(k) = ti0 + ti1
+          bi6(k) = tr0 - tr1
+          br1(j) = ti1 - ti0
+          br2(j) = tr2 - ti3
+          bi5(k) = ti2 + tr3
+          bi4(k) = tr2 + ti3
+          br3(j) = tr3 - ti2
+          pr = p7*(t2-t3)
+          pi = p7*(t2+t3)
+          br4(j) = t0 + pr
+          bi3(k) = t1 + pi
+          bi2(k) = t0 - pr
+          br5(j) = pi - t1
+          pr = -p7*(t6+t7)
+          pi = p7*(t6-t7)
+          br6(j) = t4 + pr
+          bi1(k) = t5 + pi
+          bi0(k) = t4 - pr
+          br7(j) = pi - t5
+ 100    continue
+        jr = jr + 2
+        ji = ji - 2
+        if (ji-jl) 110, 110, 120
+ 110    ji = 2*jr - 1
+        jl = jr
+ 120  continue
+      return
+      end
diff --git a/math/ieee/chap1/r8tx.f b/math/ieee/chap1/r8tx.f
new file mode 100644
index 00000000..9cc4f591
--- /dev/null
+++ b/math/ieee/chap1/r8tx.f
@@ -0,0 +1,107 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  r8tx
+c radix 8 iteration subroutine
+c-----------------------------------------------------------------------
+c
+      subroutine r8tx(nxtlt, nthpo, lengt, cr0, cr1, cr2, cr3, cr4,
+     *    cr5, cr6, cr7, ci0, ci1, ci2, ci3, ci4, ci5, ci6, ci7)
+      dimension cr0(2), cr1(2), cr2(2), cr3(2), cr4(2), cr5(2), cr6(2),
+     *    cr7(2), ci1(2), ci2(2), ci3(2), ci4(2), ci5(2), ci6(2),
+     *    ci7(2), ci0(2)
+      common /con2/ pi2, p7
+c
+      scale = pi2/float(lengt)
+      do 30 j=1,nxtlt
+        arg = float(j-1)*scale
+        c1 = cos(arg)
+        s1 = sin(arg)
+        c2 = c1**2 - s1**2
+        s2 = c1*s1 + c1*s1
+        c3 = c1*c2 - s1*s2
+        s3 = c2*s1 + s2*c1
+        c4 = c2**2 - s2**2
+        s4 = c2*s2 + c2*s2
+        c5 = c2*c3 - s2*s3
+        s5 = c3*s2 + s3*c2
+        c6 = c3**2 - s3**2
+        s6 = c3*s3 + c3*s3
+        c7 = c3*c4 - s3*s4
+        s7 = c4*s3 + s4*c3
+        do 20 k=j,nthpo,lengt
+          ar0 = cr0(k) + cr4(k)
+          ar1 = cr1(k) + cr5(k)
+          ar2 = cr2(k) + cr6(k)
+          ar3 = cr3(k) + cr7(k)
+          ar4 = cr0(k) - cr4(k)
+          ar5 = cr1(k) - cr5(k)
+          ar6 = cr2(k) - cr6(k)
+          ar7 = cr3(k) - cr7(k)
+          ai0 = ci0(k) + ci4(k)
+          ai1 = ci1(k) + ci5(k)
+          ai2 = ci2(k) + ci6(k)
+          ai3 = ci3(k) + ci7(k)
+          ai4 = ci0(k) - ci4(k)
+          ai5 = ci1(k) - ci5(k)
+          ai6 = ci2(k) - ci6(k)
+          ai7 = ci3(k) - ci7(k)
+          br0 = ar0 + ar2
+          br1 = ar1 + ar3
+          br2 = ar0 - ar2
+          br3 = ar1 - ar3
+          br4 = ar4 - ai6
+          br5 = ar5 - ai7
+          br6 = ar4 + ai6
+          br7 = ar5 + ai7
+          bi0 = ai0 + ai2
+          bi1 = ai1 + ai3
+          bi2 = ai0 - ai2
+          bi3 = ai1 - ai3
+          bi4 = ai4 + ar6
+          bi5 = ai5 + ar7
+          bi6 = ai4 - ar6
+          bi7 = ai5 - ar7
+          cr0(k) = br0 + br1
+          ci0(k) = bi0 + bi1
+          if (j.le.1) go to 10
+          cr1(k) = c4*(br0-br1) - s4*(bi0-bi1)
+          ci1(k) = c4*(bi0-bi1) + s4*(br0-br1)
+          cr2(k) = c2*(br2-bi3) - s2*(bi2+br3)
+          ci2(k) = c2*(bi2+br3) + s2*(br2-bi3)
+          cr3(k) = c6*(br2+bi3) - s6*(bi2-br3)
+          ci3(k) = c6*(bi2-br3) + s6*(br2+bi3)
+          tr = p7*(br5-bi5)
+          ti = p7*(br5+bi5)
+          cr4(k) = c1*(br4+tr) - s1*(bi4+ti)
+          ci4(k) = c1*(bi4+ti) + s1*(br4+tr)
+          cr5(k) = c5*(br4-tr) - s5*(bi4-ti)
+          ci5(k) = c5*(bi4-ti) + s5*(br4-tr)
+          tr = -p7*(br7+bi7)
+          ti = p7*(br7-bi7)
+          cr6(k) = c3*(br6+tr) - s3*(bi6+ti)
+          ci6(k) = c3*(bi6+ti) + s3*(br6+tr)
+          cr7(k) = c7*(br6-tr) - s7*(bi6-ti)
+          ci7(k) = c7*(bi6-ti) + s7*(br6-tr)
+          go to 20
+  10      cr1(k) = br0 - br1
+          ci1(k) = bi0 - bi1
+          cr2(k) = br2 - bi3
+          ci2(k) = bi2 + br3
+          cr3(k) = br2 + bi3
+          ci3(k) = bi2 - br3
+          tr = p7*(br5-bi5)
+          ti = p7*(br5+bi5)
+          cr4(k) = br4 + tr
+          ci4(k) = bi4 + ti
+          cr5(k) = br4 - tr
+          ci5(k) = bi4 - ti
+          tr = -p7*(br7+bi7)
+          ti = p7*(br7-bi7)
+          cr6(k) = br6 + tr
+          ci6(k) = bi6 + ti
+          cr7(k) = br6 - tr
+          ci7(k) = bi6 - ti
+  20    continue
+  30  continue
+      return
+      end
diff --git a/math/ieee/chap1/rad4sb.f b/math/ieee/chap1/rad4sb.f
new file mode 100644
index 00000000..dfebf0cc
--- /dev/null
+++ b/math/ieee/chap1/rad4sb.f
@@ -0,0 +1,38 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  rad4sb
+c used by subroutine radix4. never directly accessed by user.
+c-----------------------------------------------------------------------
+c
+       subroutine rad4sb(ntype)
+c
+c      input: ntype = type of butterfly invoked
+c      output: parameters used by subroutine radix4
+c
+       dimension ix(2996)
+       common /xx/ix
+       common ntypl,kkp,index,ixc
+       if(ntype.eq.ntypl) go to 7
+       ix(ixc)=0
+       ix(ixc+1)=ntype
+       ixc=ixc+2
+       if(ntype.ne.4) go to 4
+       indexp=(index-1)*9
+       ix(ixc)=kkp+1
+       ix(ixc+1)=indexp+1
+       ixc=ixc+2
+       go to 6
+4      ix(ixc)=kkp+1
+       ixc=ixc+1
+6      ntypl=ntype
+       return
+7      if(ntype.ne.4) go to 8
+       indexp=(index-1)*9
+       ix(ixc)=kkp+1
+       ix(ixc+1)=indexp+1
+       ixc=ixc+2
+       return
+8      ix(ixc)=kkp+1
+       ixc=ixc+1
+       return
+       end
diff --git a/math/ieee/chap1/radix4.f b/math/ieee/chap1/radix4.f
new file mode 100644
index 00000000..cd703305
--- /dev/null
+++ b/math/ieee/chap1/radix4.f
@@ -0,0 +1,488 @@
+c
+c-----------------------------------------------------------------------
+c subroutine:  radix4
+c computes forward or inverse complex dft via radix-4 fft.
+c uses autogen technique to yield time efficient program.
+c-----------------------------------------------------------------------
+c
+        subroutine radix4(mm,iflag,jflag)
+c
+c       input:
+c             mm = power of 4 (i.e., n = 4**mm complex point transform)
+c             (mm.ge.2 and mm.le.5)
+c
+c          iflag = 1 on first pass for given n
+c                = 0 on subsequent passes for given n
+c
+c          jflag = -1 for forward transform
+c                = +1 for inverse transform
+c
+c       input/output:
+c              a = array of dimensions 2*n with real and imaginary parts
+c                  of dft input/output in odd, even array components.
+c
+c       for optimal time efficiency, common is used to pass arrays.
+c       this means that dimensions of arrays a, ix, and t can be
+c       modified to reflect maximum value of n = 4**mm to be used. note
+c       that array "ix" is also dimensioned in subroutine "rad4sb".
+c
+c    i.e.,    a(    ) ix(  ) t(   )
+c
+c       m =2      32     38     27
+c       m<=3     128    144    135
+c       m<=4     512    658    567
+c       m<=5    2048   2996   2295
+c
+       dimension a(2048),ix(2996),t(2295)
+       dimension nfac(11),np(209)
+       common ntypl,kkp,index,ixc
+       common /aa/a
+       common /xx/ix
+c
+c      check for mm<2 or mm>5
+c
+       if(mm.lt.2.or.mm.gt.5)stop
+c
+c      initialize on first pass """"""""""""""""""""""""""""""""""""""""
+c
+       if(iflag.eq.1) go to 9999
+c
+c      fast fourier transform start ####################################
+c
+8885   kspan=2*4**mm
+       if(jflag.eq.1) go to 8887
+c
+c      conjugate data for forward transform
+c
+       do 8886 j=2,n2,2
+8886   a(j)=-a(j)
+       go to 8889
+c
+c      multiply data by n**(-1) if inverse transform
+c
+8887   do 8888 j=1,n2,2
+       a(j)=a(j)*xp
+8888   a(j+1)=a(j+1)*xp
+8889   i=3
+       it=ix(i-1)
+       go to (1,2,3,4,5,6,7,8),it
+c***********************************************************************
+c
+c                                    8 multiply butterfly
+c
+1      kk=ix(i)
+c
+11     k1=kk+kspan
+       k2=k1+kspan
+       k3=k2+kspan
+c
+       akp=a(kk)+a(k2)
+       akm=a(kk)-a(k2)
+       ajp=a(k1)+a(k3)
+       ajm=a(k1)-a(k3)
+       a(kk)=akp+ajp
+c
+       bkp=a(kk+1)+a(k2+1)
+       bkm=a(kk+1)-a(k2+1)
+       bjp=a(k1+1)+a(k3+1)
+       bjm=a(k1+1)-a(k3+1)
+       a(kk+1)=bkp+bjp
+c
+       bjp=bkp-bjp
+c
+       a(k2+1)=(akp+bjp-ajp)*c707
+       a(k2)=a(k2+1)+bjp*cm141
+c
+       bkp=bkm+ajm
+       akp=akm-bjm
+c
+       ac0=(akp+bkp)*c924
+       a(k1+1)=ac0+akp*cm541
+       a(k1)  =ac0+bkp*cm131
+c
+       bkm=bkm-ajm
+       akm=akm+bjm
+c
+       ac0=(akm+bkm)*c383
+       a(k3+1)=ac0+akm*c541
+       a(k3)  =ac0+bkm*cm131
+c
+       i=i+1
+       kk=ix(i)
+       if (kk) 111,111,11
+111    i=i+2
+       it=ix(i-1)
+       go to (1,2,3,4,5,6,7,8), it
+c***********************************************************************
+c
+c                                    4 multiply butterfly
+c
+2      kk=ix(i)
+c
+22     k1=kk+kspan
+       k2=k1+kspan
+       k3=k2+kspan
+c
+       akp=a(kk)+a(k2)
+       akm=a(kk)-a(k2)
+       ajp=a(k1)+a(k3)
+       ajm=a(k1)-a(k3)
+       a(kk)=akp+ajp
+c
+       bkp=a(kk+1)+a(k2+1)
+       bkm=a(kk+1)-a(k2+1)
+       bjp=a(k1+1)+a(k3+1)
+       bjm=a(k1+1)-a(k3+1)
+       a(kk+1)=bkp+bjp
+       a(k2)=-bkp+bjp
+       a(k2+1)=akp-ajp
+c
+       bkp=bkm+ajm
+c
+       a(k1+1)=(bkp+akm-bjm)*c707
+       a(k1)=a(k1+1)+bkp*cm141
+c
+       akm=akm+bjm
+c
+       a(k3+1)=(akm+ajm-bkm)*c707
+       a(k3)=a(k3+1)+akm*cm141
+c
+       i=i+1
+       kk=ix(i)
+       if (kk) 222,222,22
+222    i=i+2
+       it=ix(i-1)
+       go to (1,2,3,4,5,6,7,8), it
+c***********************************************************************
+c
+c                                    8 multiply butterfly
+c
+3      kk=ix(i)
+c
+33     k1=kk+kspan
+       k2=k1+kspan
+       k3=k2+kspan
+c
+       akp=a(kk)+a(k2)
+       akm=a(kk)-a(k2)
+       ajp=a(k1)+a(k3)
+       ajm=a(k1)-a(k3)
+       a(kk)=akp+ajp
+c
+       bkp=a(kk+1)+a(k2+1)
+       bkm=a(kk+1)-a(k2+1)
+       bjp=a(k1+1)+a(k3+1)
+       bjm=a(k1+1)-a(k3+1)
+       a(kk+1)=bkp+bjp
+c
+       ajp=akp-ajp
+c
+       a(k2+1)=(ajp+bjp-bkp)*c707
+       a(k2)=a(k2+1)+ajp*cm141
+c
+       bkp=bkm+ajm
+       akp=akm-bjm
+c
+       ac0=(akp+bkp)*c383
+       a(k1+1)=ac0+akp*c541
+       a(k1)  =ac0+bkp*cm131
+c
+       bkm=bkm-ajm
+       akm=akm+bjm
+c
+       ac0=(akm+bkm)*cm924
+       a(k3+1)=ac0+akm*c541
+       a(k3)  =ac0+bkm*c131
+c
+       i=i+1
+       kk=ix(i)
+       if (kk) 333,333,33
+333    i=i+2
+       it=ix(i-1)
+       go to (1,2,3,4,5,6,7,8), it
+c***********************************************************************
+c
+c                                    general 9 multiply butterfly
+c
+4      kk=ix(i)
+c
+44     k1=kk+kspan
+       k2=k1+kspan
+       k3=k2+kspan
+c
+       akp=a(kk)+a(k2)
+       akm=a(kk)-a(k2)
+       ajp=a(k1)+a(k3)
+       ajm=a(k1)-a(k3)
+       a(kk)=akp+ajp
+c
+       bkp=a(kk+1)+a(k2+1)
+       bkm=a(kk+1)-a(k2+1)
+       bjp=a(k1+1)+a(k3+1)
+       bjm=a(k1+1)-a(k3+1)
+       a(kk+1)=bkp+bjp
+c
+       ajp=akp-ajp
+       bjp=bkp-bjp
+c
+       j=ix(i+1)
+c
+       ac0=(ajp+bjp)*t(j+8)
+       a(k2+1)=ac0+ajp*t(j+6)
+       a(k2)  =ac0+bjp*t(j+7)
+c
+       bkp=bkm+ajm
+       akp=akm-bjm
+c
+       ac0=(akp+bkp)*t(j+5)
+       a(k1+1)=ac0+akp*t(j+3)
+       a(k1)  =ac0+bkp*t(j+4)
+c
+       bkm=bkm-ajm
+       akm=akm+bjm
+c
+       ac0=(akm+bkm)*t(j+2)
+       a(k3+1)=ac0+akm*t(j)
+       a(k3)  =ac0+bkm*t(j+1)
+c
+       i=i+2
+       kk=ix(i)
+       if (kk) 444,444,44
+444    i=i+2
+       it=ix(i-1)
+       go to (1,2,3,4,5,6,7,8), it
+c***********************************************************************
+c
+c                                    0 multiply butterfly
+c
+5      kk=ix(i)
+c
+55     k1=kk+kspan
+       k2=k1+kspan
+       k3=k2+kspan
+c
+       akp=a(kk)+a(k2)
+       akm=a(kk)-a(k2)
+       ajp=a(k1)+a(k3)
+       ajm=a(k1)-a(k3)
+       a(kk)=akp+ajp
+       a(k2)=akp-ajp
+c
+       bkp=a(kk+1)+a(k2+1)
+       bkm=a(kk+1)-a(k2+1)
+       bjp=a(k1+1)+a(k3+1)
+       bjm=a(k1+1)-a(k3+1)
+       a(kk+1)=bkp+bjp
+       a(k2+1)=bkp-bjp
+c
+       a(k3+1)=bkm-ajm
+       a(k1+1)=bkm+ajm
+       a(k3)=akm+bjm
+       a(k1)=akm-bjm
+c
+       i=i+1
+       kk=ix(i)
+       if (kk) 555,555,55
+555    i=i+2
+       it=ix(i-1)
+       go to (1,2,3,4,5,6,7,8), it
+c***********************************************************************
+c
+c                                       offset reduced
+c
+6      kspan=kspan/4
+       i=i+2
+       it=ix(i-1)
+       go to (1,2,3,4,5,6,7,8), it
+c***********************************************************************
+c
+c                                       bit reversal (shuffling)
+c
+7      ip1=ix(i)
+77     ip2=ix(i+1)
+       t1=a(ip2)
+       a(ip2)=a(ip1)
+       a(ip1)=t1
+       t1=a(ip2+1)
+       a(ip2+1)=a(ip1+1)
+       a(ip1+1)=t1
+       i=i+2
+       ip1=ix(i)
+       if (ip1) 777,777,77
+777    i=i+2
+       it=ix(i-1)
+       go to (1,2,3,4,5,6,7,8), it
+c***********************************************************************
+8      if(jflag.eq.1) go to 888
+c
+c      conjugate output if forward transform
+c
+       do 88 j=2,n2,2
+88     a(j)=-a(j)
+888    return
+c
+c      fast fourier transform ends #####################################
+c
+c      initialization phase starts. done only once
+c
+9999   ixc=1
+       n=4**mm
+       xp=n
+       xp=1./xp
+       ntot=n
+       n2=n*2
+       nspan=n
+       n1test=n/16
+       n2test=n/8
+       n3test=(3*n)/16
+       nspan4=nspan/4
+       ibase=0
+       isn=1
+       inc=isn
+       rad=8.0*atan(1.0)
+       pi=4.*atan(1.0)
+       c707=sin(pi/4.)
+       cm141=-2.*c707
+       c383=sin(pi/8.)
+       c924=cos(pi/8.)
+       cm924=-c924
+       c541=c924-c383
+       cm541=-c541
+       c131=c924+c383
+       cm131=-c131
+10     nt=inc*ntot
+       ks=inc*nspan
+       kspan=ks
+       jc=ks/n
+       radf=rad*float(jc)*.5
+       i=0
+c
+c      determine the factors of n
+c      all factors must be 4 for this version
+c
+       m=0
+       k=n
+15     m=m+1
+       nfac(m)=4
+       k=k/4
+20     if(k-(k/4)*4.eq.0) go to 15
+       kt=1
+       if(n.ge.256) kt=2
+       kspan0=kspan
+       ntypl=0
+c
+100    ndelta=kspan0/kspan
+       index=0
+       sd=radf/float(kspan)
+       cd=2.0*sin(sd)**2
+       sd=sin(sd+sd)
+       kk=1
+       i=i+1
+c
+c      transform for a factor of 4
+c
+       kspan=kspan/4
+       ix(ixc)=0
+       ix(ixc+1)=6
+       ixc=ixc+2
+c
+410    c1=1.0
+       s1=0.0
+420    k1=kk+kspan
+       k2=k1+kspan
+       k3=k2+kspan
+       if(s1.eq.0.0) go to 460
+430    if(kspan.ne.nspan4) go to 431
+       t(ibase+5)=-(s1+c1)
+       t(ibase+6)=c1
+       t(ibase+4)=s1-c1
+       t(ibase+8)=-(s2+c2)
+       t(ibase+9)=c2
+       t(ibase+7)=s2-c2
+       t(ibase+2)=-(s3+c3)
+       t(ibase+3)=c3
+       t(ibase+1)=s3-c3
+       ibase=ibase+9
+c
+431    kkp=(kk-1)*2
+       if(index.ne.n1test) go to 150
+       call rad4sb(1)
+       go to 5035
+150    if(index.ne.n2test) go to 160
+       call rad4sb(2)
+       go to 5035
+160    if(index.ne.n3test) go to 170
+       call rad4sb(3)
+       go to 5035
+170    call rad4sb(4)
+5035   kk=k3+kspan
+       if(kk.le.nt) go to 420
+440    index=index+ndelta
+       c2=c1-(cd*c1+sd*s1)
+       s1=(sd*c1-cd*s1)+s1
+       c1=c2
+       c2=c1*c1-s1*s1
+       s2=c1*s1+c1*s1
+       c3=c2*c1-s2*s1
+       s3=c2*s1+s2*c1
+       kk=kk-nt+jc
+       if(kk.le.kspan) go to 420
+       kk=kk-kspan+inc
+       if(kk.le.jc) go to 410
+       if(kspan.eq.jc) go to 800
+       go to 100
+460    kkp=(kk-1)*2
+       call rad4sb(5)
+5050   kk=k3+kspan
+       if(kk.le.nt) go to 420
+       go to 440
+c
+800    ix(ixc)=0
+       ix(ixc+1)=7
+       ixc=ixc+2
+c
+c      compute parameters to permute the results to normal order
+c      done in two steps
+c      permutation for square factors of n
+c
+       np(1)=ks
+       k=kt+kt+1
+       if(m.lt.k) k=k-1
+       j=1
+       np(k+1)=jc
+810    np(j+1)=np(j)/nfac(j)
+       np(k)=np(k+1)*nfac(j)
+       j=j+1
+       k=k-1
+       if(j.lt.k) go to 810
+       k3=np(k+1)
+       kspan=np(2)
+       kk=jc+1
+       k2=kspan+1
+       j=1
+c
+c      permutation for single variate transform
+c
+820    kkp=(kk-1)*2
+       k2p=(k2-1)*2
+       ix(ixc)=kkp+1
+       ix(ixc+1)=k2p+1
+       ixc=ixc+2
+       kk=kk+inc
+       k2=kspan+k2
+       if(k2.lt.ks) go to 820
+830    k2=k2-np(j)
+       j=j+1
+       k2=np(j+1)+k2
+       if(k2.gt.np(j)) go to 830
+       j=1
+840    if(kk.lt.k2) go to 820
+       kk=kk+inc
+       k2=kspan+k2
+       if(k2.lt.ks) go to 840
+       if(kk.lt.ks) go to 830
+       jc=k3
+       ix(ixc)=0
+       ix(ixc+1)=8
+       go to 8885
+       end
diff --git a/math/ieee/chap1/test/test12.f b/math/ieee/chap1/test/test12.f
new file mode 100644
index 00000000..a830ab2c
--- /dev/null
+++ b/math/ieee/chap1/test/test12.f
@@ -0,0 +1,90 @@
+c
+c-----------------------------------------------------------------------
+c main program: fastmain  -  fast fourier transforms
+c authors:      g. d. bergland and m. t. dolan
+c               bell laboratories, murray hill, new jersey 07974
+c
+c input:        the program calls on a random number
+c               generator for input and checks dft and
+c               idft with a 32-point sequence
+c-----------------------------------------------------------------------
+c
+      dimension x(32), y(32), b(34)
+c
+c generate random numbers and store array in b so
+c the same sequence can be used in all tests.
+c note that b is dimensioned to size n+2.
+c
+c iw is a machine dependent write device number
+c
+      iw = i1mach(2)
+c
+      do 10 i=1,32
+        x(i) = uni(0)
+        b(i) = x(i)
+  10  continue
+      m = 5
+      n = 2**m
+      np1 = n + 1
+      np2 = n + 2
+      knt = 1
+c
+c test fast-fsst then ffa-ffs
+c
+      write (iw,9999)
+  20  write (iw,9998) (b(i),i=1,n)
+      if (knt.eq.1) call fast(b, n)
+      if (knt.eq.2) call ffa(b, n)
+      write (iw,9997) (b(i),i=1,np1,2)
+      write (iw,9996) (b(i),i=2,np2,2)
+      if (knt.eq.1) call fsst(b, n)
+      if (knt.eq.2) call ffs(b, n)
+      write (iw,9995) (b(i),i=1,n)
+      knt = knt + 1
+      if (knt.eq.3) go to 40
+c
+      write (iw,9994)
+      do 30 i=1,n
+        b(i) = x(i)
+  30  continue
+      go to 20
+c
+c test fft842 with real input then complex
+c
+  40  write (iw,9993)
+      do 50 i=1,n
+        b(i) = x(i)
+        y(i) = 0.
+  50  continue
+  60  write (iw,9992) (b(i),i=1,n)
+      write (iw,9991) (y(i),i=1,n)
+      call fft842(0, n, b, y)
+      write (iw,9997) (b(i),i=1,n)
+      write (iw,9996) (y(i),i=1,n)
+      call fft842(1, n, b, y)
+      write (iw,9990) (b(i),i=1,n)
+      write (iw,9989) (y(i),i=1,n)
+      knt = knt + 1
+      if (knt.eq.5) go to 80
+c
+      write (iw,9988)
+      do 70 i=1,n
+        b(i) = x(i)
+        y(i) = uni(0)
+  70  continue
+      go to 60
+c
+9999  format (19h1test fast and fsst)
+9998  format (20h0real input sequence/(4e17.8))
+9997  format (29h0real components of transform/(4e17.8))
+9996  format (29h0imag components of transform/(4e17.8))
+9995  format (23h0real inverse transform/(4e17.8))
+9994  format (17h1test ffa and ffs)
+9993  format (37h1test fft842 with real input sequence/(4e17.8))
+9992  format (34h0real components of input sequence/(4e17.8))
+9991  format (34h0imag components of input sequence/(4e17.8))
+9990  format (37h0real components of inverse transform/(4e17.8))
+9989  format (37h0imag components of inverse transform/(4e17.8))
+9988  format (40h1test fft842 with complex input sequence)
+  80  stop
+      end
diff --git a/math/ieee/chap1/test/test13.f b/math/ieee/chap1/test/test13.f
new file mode 100644
index 00000000..d7157069
--- /dev/null
+++ b/math/ieee/chap1/test/test13.f
@@ -0,0 +1,260 @@
+c
+c-----------------------------------------------------------------------
+c main program: test program for fft subroutines
+c author:      l r rabiner
+c      bell laboratories, murray hill, new jersey, 07974
+c input:       randomly chosen sequences to test fft subroutines
+c      for sequences with special properties
+c      n is the fft length (n must be a power of 2)
+c          2<= n <= 4096
+c-----------------------------------------------------------------------
+c
+      dimension x(4098), y(4098)
+c
+c  define i/0 device codes
+c  input: input to this program is user-interactive
+c        that is - a question is written on the user
+c        terminal (iout1) ad the user types in the answer.
+c
+c output: all output is written on the standard
+c         output unit (iout2).
+c
+      ind = i1mach(1)
+      iout1 = i1mach(4)
+      iout2 = i1mach(2)
+c
+c read in analysis size for fft
+c
+  10  write (iout1,9999)
+9999  format (30h fft size(2.le.n.le.4096)(i4)=)
+      read (ind,9998) n
+9998  format (i4)
+      if (n.eq.0) stop
+      do 20 i=1,12
+        itest = 2**i
+        if (n.eq.itest) go to 30
+  20  continue
+      write (iout1,9997)
+9997  format (45h n is not a power of 2 in the range 2 to 4096)
+      go to 10
+  30  write (iout2,9996) n
+9996  format (11h testing n=, i5, 17h random sequences)
+      write (iout2,9992)
+      np2 = n + 2
+      no2 = n/2
+      no2p1 = no2 + 1
+      no4 = n/4
+      no4p1 = no4 + 1
+c
+c create symmetrical sequence of size n
+c
+      do 40 i=2,no2
+        x(i) = uni(0) - 0.5
+        ind1 = np2 - i
+        x(ind1) = x(i)
+  40  continue
+      x(1) = uni(0) - 0.5
+      x(no2p1) = uni(0) - 0.5
+      do 50 i=1,no2p1
+        y(i) = x(i)
+  50  continue
+      write (iout2,9995)
+9995  format (28h original symmetric sequence)
+      write (iout2,9993) (x(i),i=1,n)
+      write (iout2,9992)
+c
+c compute true fft of n point sequence
+c
+      call fast(x, n)
+      write (iout2,9994) n
+9994  format (1h , i4, 32h point fft of symmetric sequence)
+      write (iout2,9993) (x(i),i=1,np2)
+9993  format (1h , 5e13.5)
+      write (iout2,9992)
+9992  format (1h /1h )
+c
+c use subroutine fftsym to obtain dft from no2 point fft
+c
+      do 60 i=1,no2p1
+        x(i) = y(i)
+  60  continue
+      call fftsym(x, n, y)
+      write (iout2,9991)
+9991  format (17h output of fftsym)
+      write (iout2,9993) (x(i),i=1,no2p1)
+      write (iout2,9992)
+c
+c use subroutine iftsym to obtain original sequence from no2 point dft
+c
+      call iftsym(x, n, y)
+      write (iout2,9990)
+9990  format (17h output of iftsym)
+      write (iout2,9993) (x(i),i=1,no2p1)
+      write (iout2,9992)
+c
+c create antisymmetric n point sequence
+c
+      do 70 i=2,no2
+        x(i) = uni(0) - 0.5
+        ind1 = np2 - i
+        x(ind1) = -x(i)
+  70  continue
+      x(1) = 0.
+      x(no2p1) = 0.
+      do 80 i=1,no2p1
+        y(i) = x(i)
+  80  continue
+      write (iout2,9989)
+9989  format (32h original antisymmetric sequence)
+      write (iout2,9993) (x(i),i=1,n)
+      write (iout2,9992)
+c
+c obtain n point dft of antisymmetric sequence
+c
+      call fast(x, n)
+      write (iout2,9988) n
+9988  format (1h , i4, 36h point fft of antisymmetric sequence)
+      write (iout2,9993) (x(i),i=1,np2)
+      write (iout2,9992)
+c
+c use subroutine fftasm to obtain dft from no2 point fft
+c
+      do 90 i=1,no2
+        x(i) = y(i)
+  90  continue
+      call fftasm(x, n, y)
+      write (iout2,9987)
+9987  format (17h output of fftasm)
+      write (iout2,9993) (x(i),i=1,no2p1)
+      write (iout2,9992)
+c
+c use subroutine iftasm to obtain original sequence from no2 point dft
+c
+      call iftasm(x, n, y)
+      write (iout2,9986)
+9986  format (17h output of iftasm)
+      write (iout2,9993) (x(i),i=1,no2)
+      write (iout2,9992)
+c
+c create sequence with only odd harmonics--begin in frequency domain
+c
+      do 100 i=1,np2,2
+        x(i) = 0.
+        x(i+1) = 0.
+        if (mod(i,4).eq.1) go to 100
+        x(i) = uni(0) - 0.5
+        x(i+1) = uni(0) - 0.5
+        if (n.eq.2) x(i+1) = 0.
+ 100  continue
+      write (iout2,9985) n
+9985  format (1h , i4, 35h point fft of odd harmonic sequence)
+      write (iout2,9993) (x(i),i=1,np2)
+      write (iout2,9992)
+c
+c transform back to time sequence
+c
+      call fsst(x, n)
+      write (iout2,9984)
+9984  format (31h original odd harmonic sequence)
+      write (iout2,9993) (x(i),i=1,n)
+      write (iout2,9992)
+c
+c use subroutine fftohm to obtain dft from no2 point fft
+c
+      call fftohm(x, n)
+      write (iout2,9983)
+9983  format (17h output of fftohm)
+      write (iout2,9993) (x(i),i=1,no2)
+      write (iout2,9992)
+c
+c use subroutine iftohm to obtain original sequence from no2 point dft
+c
+      call iftohm(x, n)
+      write (iout2,9982)
+9982  format (17h output of iftohm)
+      write (iout2,9993) (x(i),i=1,no2)
+      write (iout2,9992)
+c
+c create sequence with only real valued odd harmonics
+c
+      do 110 i=1,np2,2
+        x(i) = 0.
+        x(i+1) = 0.
+        if (mod(i,4).eq.1) go to 110
+        x(i) = uni(0) - 0.5
+ 110  continue
+      write (iout2,9981) n
+9981  format (1h , i4, 45h point fft of odd harmonic, symmetric sequenc,
+     *    1he)
+      write (iout2,9993) (x(i),i=1,np2)
+      write (iout2,9992)
+c
+c transform back to time sequence
+c
+      call fsst(x, n)
+      write (iout2,9980)
+9980  format (42h original odd harmonic, symmetric sequence)
+      write (iout2,9993) (x(i),i=1,n)
+      write (iout2,9992)
+c
+c use subroutine fftsoh to obtain dft from no4 point fft
+c
+      call fftsoh(x, n, y)
+      write (iout2,9979)
+9979  format (17h output of fftsoh)
+      write (iout2,9993) (x(i),i=1,no4)
+      write (iout2,9992)
+c
+c use subroutine iftsoh to obtain original sequence from no4 point dft
+c
+      call iftsoh(x, n, y)
+      write (iout2,9978)
+9978  format (17h output of iftsoh)
+      write (iout2,9993) (x(i),i=1,no4)
+      write (iout2,9992)
+c
+c create sequence with only imaginary valued odd harmonics--begin
+c in frequency domain
+c
+      do 120 i=1,np2,2
+        x(i) = 0.
+        x(i+1) = 0.
+        if (mod(i,4).eq.1) go to 120
+        x(i+1) = uni(0) - 0.5
+ 120  continue
+      write (iout2,9977) n
+9977  format (1h , i4, 41h point fft of odd harmonic, antisymmetric,
+     *    9h sequence)
+      write (iout2,9993) (x(i),i=1,np2)
+      write (iout2,9992)
+c
+c transform back to time sequence
+c
+      call fsst(x, n)
+      write (iout2,9976)
+9976  format (46h original odd harmonic, antisymmetric sequence)
+      write (iout2,9993) (x(i),i=1,n)
+      write (iout2,9992)
+c
+c use subroutine fftaoh to obtain dft from no4 point fft
+c
+      call fftaoh(x, n, y)
+      write (iout2,9975)
+9975  format (17h output of fftaoh)
+      write (iout2,9993) (x(i),i=1,no4)
+      write (iout2,9992)
+c
+c use subroutine iftaoh to obtain original sequence from n/4 point dft
+c
+      call iftaoh(x, n, y)
+      write (iout2,9974)
+9974  format (17h output of iftaoh)
+      write (iout2,9993) (x(i),i=1,no4p1)
+      write (iout2,9992)
+c
+c begin a new page
+c
+      write (iout2,9973)
+9973  format (1h1)
+      go to 10
+      end
diff --git a/math/ieee/chap1/test/test17.f b/math/ieee/chap1/test/test17.f
new file mode 100644
index 00000000..15a34788
--- /dev/null
+++ b/math/ieee/chap1/test/test17.f
@@ -0,0 +1,147 @@
+c
+c-----------------------------------------------------------------------
+c main program: test program to exercise the wfta subroutine
+c   the test waveform is a complex exponential a**i whose
+c   transform is known analytically to be (1 - a**n)/(1 - a*w**k).
+c
+c authors:
+c   james h. mcclellan     and     hamid nawab
+c   department of electrical engineering and computer science
+c   massachusetts of technology
+c   cambridge, mass.  02139
+c
+c inputs:
+c   n-- transform length. it must be formed as the product of
+c       relatively prime integers from the set:
+c           2,3,4,5,7,8,9,16
+c   invrs is the flag for forward or inverse transform.
+c           invrs = 1 yields inverse transform
+c           invrs .ne. 1 gives forward transform
+c   rad and phi are the magnitude and angle (as a fraction of
+c       2*pi/n) of the complex exponential test signal.
+c          suggestion: rad = 0.98, phi = 0.5.
+c-----------------------------------------------------------------------
+c
+      double precision pi2,pin,xn,xj,xt
+      dimension xr(1260),xi(1260)
+      complex cone,ca,can,cnum,cden
+c
+c   output will be punched
+c
+      iout=i1mach(3)
+      input=i1mach(1)
+      cone=cmplx(1.0,0.0)
+      pi2=8.0d0*datan(1.0d0)
+50    continue
+      read(input,130)n
+130   format(i5)
+      write(iout,150) n
+150   format(10h length = ,i5)
+      if(n.le.0 .or. n.gt.1260) stop
+c
+c   enter a 1 to perform the inverse
+c
+c     read(input,130) invrs
+      invrs = 0
+c
+c   enter magnitude and angle (in fraction of 2*pi/n)
+c   avoid multiples of n for the angle if the radius is
+c   close to one.  suggestion: rad = 0.98, phi = 0.5.
+c
+c     read(input,160) rad,phi
+      rad = 0.98
+      phi = 0.5
+160   format(2f15.10)
+      xn=float(n)
+      pin=phi
+      pin=pin*pi2/xn
+c
+c   generate z**j
+c
+      init=0
+      do 200 j=1,n
+      an=rad**(j-1)
+      xj=j-1
+      xj=xj*pin
+      xt=dcos(xj)
+      xr(j)=xt
+      xr(j)=xr(j)*an
+      xt=dsin(xj)
+      xi(j)=xt
+      xi(j)=xi(j)*an
+200   continue
+      can=cmplx(xr(n),xi(n))
+      ca=cmplx(xr(2),xi(2))
+      can=can*ca
+c
+c   print first 50 values of input sequence
+c
+      max=50
+      if(n.lt.50)max=n
+      write(iout,300)(j,xr(j),xi(j),j=1,max)
+c
+c   call the winograd fourier transform algorithm
+c
+      call wfta(xr,xi,n,invrs,init,ierr)
+c
+c   check for error return
+c
+      if(ierr.lt.0) write(iout,250) ierr
+250   format(1x,5herror,i5)
+      if(ierr.lt.0) go to 50
+c
+c   print first 50 values of the transformed sequence
+c
+      write(iout,300)(j,xr(j),xi(j),j=1,max)
+300   format(1x,3hj =,i3,6hreal =,e20.12,6himag =,e20.12)
+c
+c   calculate absolute and relative deviations
+c
+      devabs=0.0
+      devrel=0.0
+      cnum=cone-can
+      pin=pi2/xn
+      do 350 j=1,n
+      xj=j-1
+      xj=-xj*pin
+      if(invrs.eq.1) xj=-xj
+      tr=dcos(xj)
+      ti=dsin(xj)
+      can=cmplx(tr,ti)
+      cden=cone-ca*can
+      cden=cnum/cden
+c
+c   true value of the transform (1. - a**n)/(1. - a*w**k),
+c   where a = rad*exp(j*phi*(2*pi/n)), w = exp(-j*2*pi/n).
+c   for the inverse transform the complex exponential w
+c   is conjugated.
+c
+      tr=real(cden)
+      ti=aimag(cden)
+      if(invrs.ne.1) go to 330
+c
+c   scale inverse transform by 1/n
+c
+      tr=tr/float(n)
+      ti=ti/float(n)
+330   tr=xr(j)-tr
+      ti=xi(j)-ti
+      devabs=sqrt(tr*tr+ti*ti)
+      xmag=sqrt(xr(j)*xr(j)+xi(j)*xi(j))
+      devrel=100.0*devabs/xmag
+      if(devabs.le.devmx1)go to 340
+      devmx1=devabs
+      labs=j-1
+340   if(devrel.le.devmx2)go to 350
+      devmx2=devrel
+      lrel=j-1
+350   continue
+c
+c   print the absolute and relative deviations together
+c   with their locations.
+c
+      write(iout,380) devabs,labs,devrel,lrel
+380   format(1x,21habsolute deviation = ,e20.12,9h at index,i5/
+     1 1x,21hrelative deviation = ,f11.7,8h percent,1x,9h at index,i5)
+      go to 50
+      end
diff --git a/math/ieee/chap1/test/test18.f b/math/ieee/chap1/test/test18.f
new file mode 100644
index 00000000..cf550e01
--- /dev/null
+++ b/math/ieee/chap1/test/test18.f
@@ -0,0 +1,71 @@
+c
+c-----------------------------------------------------------------------
+c main program: time-efficient radix-4 fast fourier transform
+c author:       l. robert morris
+c               department of systems engineering and computing science
+c               carleton university, ottawa, canada k1s 5b6
+c
+c input:        the array "a" contains the data to be transformed
+c-----------------------------------------------------------------------
+c
+c       test program for autogen radix-4 fft
+c
+        dimension a(2048),b(2048)
+        common /aa/a
+c
+        ioutd=i1mach(2)
+c
+c       compute dft and idft for n = 64, 256, and 1024 complex points
+c
+        do 1 mm=3,5
+        n=4**mm
+        do 2 j=1,n
+        a(2*j-1)=uni(0)
+        a(2*j  )=uni(0)
+        b(2*j-1)=a(2*j-1)
+2       b(2*j  )=a(2*j)
+c
+c       forward dft
+c
+        call radix4(mm,1,-1)
+c
+        if(mm.ne.3) go to 5
+c
+c       list dft input, output for n = 64 only
+c
+        write(ioutd,98)
+        write(ioutd,100)
+        do 3 j=1,n
+        write(ioutd,96) b(2*j-1),b(2*j),a(2*j-1),a(2*j)
+3       continue
+c
+c       inverse dft
+c
+5       call radix4(mm,0, 1)
+c
+c       list dft input, idft output for n = 64 only
+c
+        if(mm.ne.3) go to 7
+c
+        write(ioutd,99)
+        write(ioutd,100)
+        do 6 j=1,n
+        write(ioutd,96) b(2*j-1),b(2*j),a(2*j-1),a(2*j)
+6       continue
+c
+c       calculate rms error
+c
+7       err=0.0
+        do 8 j=1,n
+8       err=err+(a(2*j-1)-b(2*j-1))**2+(a(2*j)-b(2*j))**2
+        err=sqrt(err/float(n))
+        write(ioutd,97) mm,err
+1       continue
+c
+96      format(1x,4(f10.6,2x))
+97      format(1x,20h   rms error for m =,i2,4h is ,e14.6/)
+98      format(1x,43h       dft input                dft  output/)
+99      format(1x,43h       dft input                idft output/)
+100     format(1x,44h   real        imag       real          imag/)
+        stop
+        end
diff --git a/math/ieee/chap1/time/time12.f b/math/ieee/chap1/time/time12.f
new file mode 100644
index 00000000..774c2cc9
--- /dev/null
+++ b/math/ieee/chap1/time/time12.f
@@ -0,0 +1,53 @@
+c-----------------------------------------------------------------------
+c
+c-----------------------------------------------------------------------
+c
+      parameter  (SIZE = 1024, ILOOP = 100)
+      complex  a, w
+      real     breal(SIZE), bimag(SIZE), qbreal(SIZE), qbimag(SIZE)
+c
+      ioutd = i1mach(2)
+      nn = SIZE
+      tpi = 8.*atan(1.)
+      tpion = tpi/float(nn)
+      w = cmplx(cos(tpion),-sin(tpion))
+c
+c generate a**k as test function
+c result to b(i) for modification by dft and idft subroutines and
+c a copy to qb(i) to compare final result with for error difference.
+c
+      a = (.9,.3)
+      breal(1) = 1.0
+      bimag(1) = 0.0
+      qbreal(1) = 1.0
+      qbimag(1) = 0.0
+      do 10 k=2,nn
+        w = a**(k-1)
+        breal(k) = real(w)
+        bimag(k) = aimag(w)
+        qbreal(k) = breal(k)
+        qbimag(k) = bimag(k)
+  10  continue
+c
+c now compute dft, idft, dft, idft, ...
+c first dft is computed specially, in case subroutine needs to be started.
+c
+      call fft842(0, SIZE, breal, bimag)
+      do 25 icount = 1, ILOOP
+         call fft842(1, SIZE, breal, bimag)
+         call fft842(0, SIZE, breal, bimag)
+   25 continue
+      call fft842(1, SIZE, breal, bimag)
+c
+c calculate rms error between b(i) and qb(i).
+c
+      err = 0.
+      do 30 i=1,nn
+        err = err + (breal(i)-qbreal(i))**2
+     *            + (bimag(i)-qbimag(i))**2
+  30  continue
+      err = sqrt(err / float(nn))
+      write (ioutd,9994) ILOOP, err
+ 9994 format(' rms error, after ', i5, ' loops = ', e15.8)
+      stop
+      end
diff --git a/math/ieee/chap1/time/time17.f b/math/ieee/chap1/time/time17.f
new file mode 100644
index 00000000..adcce4c2
--- /dev/null
+++ b/math/ieee/chap1/time/time17.f
@@ -0,0 +1,53 @@
+c-----------------------------------------------------------------------
+c
+c-----------------------------------------------------------------------
+c
+      parameter  (SIZE = 1008, ILOOP = 100)
+      complex  a, w
+      real     breal(SIZE), bimag(SIZE), qbreal(SIZE), qbimag(SIZE)
+c
+      ioutd = i1mach(2)
+      nn = SIZE
+      tpi = 8.*atan(1.)
+      tpion = tpi/float(nn)
+      w = cmplx(cos(tpion),-sin(tpion))
+c
+c generate a**k as test function
+c result to b(i) for modification by dft and idft subroutines and
+c a copy to qb(i) to compare final result with for error difference.
+c
+      a = (.9,.3)
+      breal(1) = 1.0
+      bimag(1) = 0.0
+      qbreal(1) = 1.0
+      qbimag(1) = 0.0
+      do 10 k=2,nn
+        w = a**(k-1)
+        breal(k) = real(w)
+        bimag(k) = aimag(w)
+        qbreal(k) = breal(k)
+        qbimag(k) = bimag(k)
+  10  continue
+c
+c now compute dft, idft, dft, idft, ...
+c first dft is computed specially, in case subroutine needs to be started.
+c
+      call wfta(breal, bimag, SIZE, 0, 0, ierr)
+      do 25 icount = 1, ILOOP
+         call wfta(breal, bimag, SIZE, 1, 1, ierr)
+         call wfta(breal, bimag, SIZE, 0, 1, ierr)
+   25 continue
+      call wfta(breal, bimag, SIZE, 1, 1, ierr)
+c
+c calculate rms error between b(i) and qb(i).
+c
+      err = 0.
+      do 30 i=1,nn
+        err = err + (breal(i)-qbreal(i))**2
+     *            + (bimag(i)-qbimag(i))**2
+  30  continue
+      err = sqrt(err / float(nn))
+      write (ioutd,9994) ILOOP, err
+ 9994 format(' rms error, after ', i5, ' loops = ', e15.8)
+      stop
+      end
diff --git a/math/ieee/chap1/time/time18.f b/math/ieee/chap1/time/time18.f
new file mode 100644
index 00000000..87680554
--- /dev/null
+++ b/math/ieee/chap1/time/time18.f
@@ -0,0 +1,48 @@
+c-----------------------------------------------------------------------
+c
+c-----------------------------------------------------------------------
+c
+      parameter  (SIZE = 1024, ILOOP = 100)
+      complex  w, b(SIZE), qb(SIZE), a
+      common   /aa/ b
+c
+      ioutd = i1mach(2)
+      nn = SIZE
+      tpi = 8.*atan(1.)
+      tpion = tpi/float(nn)
+      w = cmplx(cos(tpion),-sin(tpion))
+c
+c generate a**k as test function
+c result to b(i) for modification by dft and idft subroutines and
+c a copy to qb(i) to compare final result with for error difference.
+c
+      a = (.9,.3)
+      b(1) = (1.,0.)
+      qb(1) = b(1)
+      do 10 k=2,nn
+        b(k) = a**(k-1)
+        qb(k) = b(k)
+  10  continue
+c
+c now compute dft, idft, dft, idft, ...
+c first dft is computed specially, in case subroutine needs to be started.
+c
+      call radix4(5, 1, -1)
+      do 25 icount = 1, ILOOP
+         call radix4(5, 0,  1)
+         call radix4(5, 0, -1)
+   25 continue
+      call radix4(5, 0,  1)
+c
+c calculate rms error between b(i) and qb(i).
+c
+      err = 0.
+      do 30 i=1,nn
+        de = cabs(qb(i)-b(i))
+        err = err + de**2
+  30  continue
+      err = sqrt(err / float(nn))
+      write (ioutd,9994) ILOOP, err
+ 9994 format(' rms error, after ', i5, ' loops = ', e15.8)
+      stop
+      end
diff --git a/math/ieee/chap1/weave1.f b/math/ieee/chap1/weave1.f
new file mode 100644
index 00000000..9c83d0ea
--- /dev/null
+++ b/math/ieee/chap1/weave1.f
@@ -0,0 +1,371 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: weave1
+c   this subroutine implements the different pre-weave
+c   modules of the wfta.  the working arrays are sr and si.
+c   the routine checks to see which factors are present
+c   in the transform length n = na*nb*nc*nd and executes
+c   the pre-weave code for these factors.
+c
+c-----------------------------------------------------------------------
+c
+      subroutine weave1(sr,si)
+      common na,nb,nc,nd,nd1,nd2,nd3,nd4
+      dimension q(8),t(16)
+      dimension sr(1),si(1)
+      if(na.eq.1) go to 300
+      if(na.ne.2) go to 800
+c
+c **********************************************************************
+c
+c     the following code implements the 2 point pre-weave module
+c
+c **********************************************************************
+c
+      nlup2=2*(nd2-nb)
+      nlup23=2*nd2*(nd3-nc)
+      nbase=1
+      do 240 n4=1,nd
+      do 230 n3=1,nc
+      do 220 n2=1,nb
+      nr1=nbase+1
+      t0=sr(nbase)+sr(nr1)
+      sr(nr1)=sr(nbase)-sr(nr1)
+      sr(nbase)=t0
+      t0=si(nbase)+si(nr1)
+      si(nr1)=si(nbase)-si(nr1)
+      si(nbase)=t0
+220   nbase=nbase+2
+230   nbase=nbase+nlup2
+240   nbase=nbase+nlup23
+800   if(na.ne.8) go to 1600
+c
+c **********************************************************************
+c
+c     the following code implements the 8 point pre-weave module
+c
+c **********************************************************************
+c
+      nlup2=8*(nd2-nb)
+      nlup23=8*nd2*(nd3-nc)
+      nbase=1
+      do 840 n4=1,nd
+      do 830 n3=1,nc
+      do 820 n2=1,nb
+      nr1=nbase+1
+      nr2=nr1+1
+      nr3=nr2+1
+      nr4=nr3+1
+      nr5=nr4+1
+      nr6=nr5+1
+      nr7=nr6+1
+      t3=sr(nr3)+sr(nr7)
+      t7=sr(nr3)-sr(nr7)
+      t0=sr(nbase)+sr(nr4)
+      sr(nr4)=sr(nbase)-sr(nr4)
+      t1=sr(nr1)+sr(nr5)
+      t5=sr(nr1)-sr(nr5)
+      t2=sr(nr2)+sr(nr6)
+      sr(nr6)=sr(nr2)-sr(nr6)
+      sr(nbase)=t0+t2
+      sr(nr2)=t0-t2
+      sr(nr1)=t1+t3
+      sr(nr3)=t1-t3
+      sr(nr5)=t5+t7
+      sr(nr7)=t5-t7
+      t3=si(nr3)+si(nr7)
+      t7=si(nr3)-si(nr7)
+      t0=si(nbase)+si(nr4)
+      si(nr4)=si(nbase)-si(nr4)
+      t1=si(nr1)+si(nr5)
+      t5=si(nr1)-si(nr5)
+      t2=si(nr2)+si(nr6)
+      si(nr6)=si(nr2)-si(nr6)
+      si(nbase)=t0+t2
+      si(nr2)=t0-t2
+      si(nr1)=t1+t3
+      si(nr3)=t1-t3
+      si(nr5)=t5+t7
+      si(nr7)=t5-t7
+820   nbase=nbase+8
+830   nbase=nbase+nlup2
+840   nbase=nbase+nlup23
+1600  if(na.ne.16) go to 300
+c
+c **********************************************************************
+c
+c     the following code implements the 16 point pre-weave module
+c
+c **********************************************************************
+c
+      nlup2=18*(nd2-nb)
+      nlup23=18*nd2*(nd3-nc)
+      nbase=1
+      do 1640 n4=1,nd
+      do 1630 n3=1,nc
+      do 1620 n2=1,nb
+      nr1=nbase+1
+      nr2=nr1+1
+      nr3=nr2+1
+      nr4=nr3+1
+      nr5=nr4+1
+      nr6=nr5+1
+      nr7=nr6+1
+      nr8=nr7+1
+      nr9=nr8+1
+      nr10=nr9+1
+      nr11=nr10+1
+      nr12=nr11+1
+      nr13=nr12+1
+      nr14=nr13+1
+      nr15=nr14+1
+      nr16=nr15+1
+      nr17=nr16+1
+      jbase=nbase
+      do 1645 j=1,8
+      t(j)=sr(jbase)+sr(jbase+8)
+      t(j+8)=sr(jbase)-sr(jbase+8)
+      jbase=jbase+1
+1645  continue
+      do 1650 j=1,4
+      q(j)=t(j)+t(j+4)
+      q(j+4)=t(j)-t(j+4)
+1650  continue
+      sr(nbase)=q(1)+q(3)
+      sr(nr2)=q(1)-q(3)
+      sr(nr1)=q(2)+q(4)
+      sr(nr3)=q(2)-q(4)
+      sr(nr5)=q(6)+q(8)
+      sr(nr7)=q(6)-q(8)
+      sr(nr4)=q(5)
+      sr(nr6)=q(7)
+      sr(nr8)=t(9)
+      sr(nr9)=t(10)+t(16)
+      sr(nr15)=t(10)-t(16)
+      sr(nr13)=t(14)+t(12)
+      sr(nr11)=t(14)-t(12)
+      sr(nr17)=sr(nr11)+sr(nr15)
+      sr(nr16)=sr(nr9)+sr(nr13)
+      sr(nr10)=t(11)+t(15)
+      sr(nr14)=t(11)-t(15)
+      sr(nr12)=t(13)
+      jbase=nbase
+      do 1745 j=1,8
+      t(j)=si(jbase)+si(jbase+8)
+      t(j+8)=si(jbase)-si(jbase+8)
+      jbase=jbase+1
+1745  continue
+      do 1750 j=1,4
+      q(j)=t(j)+t(j+4)
+      q(j+4)=t(j)-t(j+4)
+1750  continue
+      si(nbase)=q(1)+q(3)
+      si(nr2)=q(1)-q(3)
+      si(nr1)=q(2)+q(4)
+      si(nr3)=q(2)-q(4)
+      si(nr5)=q(6)+q(8)
+      si(nr7)=q(6)-q(8)
+      si(nr4)=q(5)
+      si(nr6)=q(7)
+      si(nr8)=t(9)
+      si(nr9)=t(10)+t(16)
+      si(nr15)=t(10)-t(16)
+      si(nr13)=t(14)+t(12)
+      si(nr11)=t(14)-t(12)
+      si(nr17)=si(nr11)+si(nr15)
+      si(nr16)=si(nr9)+si(nr13)
+      si(nr10)=t(11)+t(15)
+      si(nr14)=t(11)-t(15)
+      si(nr12)=t(13)
+1620  nbase=nbase+18
+1630  nbase=nbase+nlup2
+1640  nbase=nbase+nlup23
+300   if(nb.eq.1) go to 700
+      if(nb.ne.3) go to 900
+c
+c **********************************************************************
+c
+c     the following code implements the 3 point pre-weave module
+c
+c **********************************************************************
+c
+      nlup2=2*nd1
+      nlup23=3*nd1*(nd3-nc)
+      nbase=1
+      noff=nd1
+      do 340 n4=1,nd
+      do 330 n3=1,nc
+      do 310 n2=1,nd1
+      nr1=nbase+noff
+      nr2=nr1+noff
+      t1=sr(nr1)+sr(nr2)
+      sr(nbase)=sr(nbase)+t1
+      sr(nr2)=sr(nr1)-sr(nr2)
+      sr(nr1)=t1
+      t1=si(nr1)+si(nr2)
+      si(nbase)=si(nbase)+t1
+      si(nr2)=si(nr1)-si(nr2)
+      si(nr1)=t1
+310   nbase=nbase+1
+330   nbase=nbase+nlup2
+340   nbase=nbase+nlup23
+900   if(nb.ne.9) go to 700
+c
+c **********************************************************************
+c
+c     the following code implements the 9 point pre-weave module
+c
+c **********************************************************************
+c
+      nlup2=10*nd1
+      nlup23=11*nd1*(nd3-nc)
+      nbase=1
+      noff=nd1
+      do 940 n4=1,nd
+      do 930 n3=1,nc
+      do 910 n2=1,nd1
+      nr1=nbase+noff
+      nr2=nr1+noff
+      nr3=nr2+noff
+      nr4=nr3+noff
+      nr5=nr4+noff
+      nr6=nr5+noff
+      nr7=nr6+noff
+      nr8=nr7+noff
+      nr9=nr8+noff
+      nr10=nr9+noff
+      t3=sr(nr3)+sr(nr6)
+      t6=sr(nr3)-sr(nr6)
+      sr(nbase)=sr(nbase)+t3
+      t7=sr(nr7)+sr(nr2)
+      t2=sr(nr7)-sr(nr2)
+      sr(nr2)=t6
+      t1=sr(nr1)+sr(nr8)
+      t8=sr(nr1)-sr(nr8)
+      sr(nr1)=t3
+      t4=sr(nr4)+sr(nr5)
+      t5=sr(nr4)-sr(nr5)
+      sr(nr3)=t1+t4+t7
+      sr(nr4)=t1-t7
+      sr(nr5)=t4-t1
+      sr(nr6)=t7-t4
+      sr(nr10)=t2+t5+t8
+      sr(nr7)=t8-t2
+      sr(nr8)=t5-t8
+      sr(nr9)=t2-t5
+      t3=si(nr3)+si(nr6)
+      t6=si(nr3)-si(nr6)
+      si(nbase)=si(nbase)+t3
+      t7=si(nr7)+si(nr2)
+      t2=si(nr7)-si(nr2)
+      si(nr2)=t6
+      t1=si(nr1)+si(nr8)
+      t8=si(nr1)-si(nr8)
+      si(nr1)=t3
+      t4=si(nr4)+si(nr5)
+      t5=si(nr4)-si(nr5)
+      si(nr3)=t1+t4+t7
+      si(nr4)=t1-t7
+      si(nr5)=t4-t1
+      si(nr6)=t7-t4
+      si(nr10)=t2+t5+t8
+      si(nr7)=t8-t2
+      si(nr8)=t5-t8
+      si(nr9)=t2-t5
+910   nbase=nbase+1
+930   nbase=nbase+nlup2
+940   nbase=nbase+nlup23
+700   if(nc.ne.7) go to 500
+c
+c **********************************************************************
+c
+c     the following code implements the 7 point pre-weave module
+c
+c **********************************************************************
+c
+      noff=nd1*nd2
+      nbase=1
+      nlup2=8*noff
+      do 740 n4=1,nd
+      do 710 n1=1,noff
+      nr1=nbase+noff
+      nr2=nr1+noff
+      nr3=nr2+noff
+      nr4=nr3+noff
+      nr5=nr4+noff
+      nr6=nr5+noff
+      nr7=nr6+noff
+      nr8=nr7+noff
+      t1=sr(nr1)+sr(nr6)
+      t6=sr(nr1)-sr(nr6)
+      t4=sr(nr4)+sr(nr3)
+      t3=sr(nr4)-sr(nr3)
+      t2=sr(nr2)+sr(nr5)
+      t5=sr(nr2)-sr(nr5)
+      sr(nr5)=t6-t3
+      sr(nr2)=t5+t3+t6
+      sr(nr6)=t5-t6
+      sr(nr8)=t3-t5
+      sr(nr3)=t2-t1
+      sr(nr4)=t1-t4
+      sr(nr7)=t4-t2
+      t1=t1+t4+t2
+      sr(nbase)=sr(nbase)+t1
+      sr(nr1)=t1
+      t1=si(nr1)+si(nr6)
+      t6=si(nr1)-si(nr6)
+      t4=si(nr4)+si(nr3)
+      t3=si(nr4)-si(nr3)
+      t2=si(nr2)+si(nr5)
+      t5=si(nr2)-si(nr5)
+      si(nr5)=t6-t3
+      si(nr2)=t5+t3+t6
+      si(nr6)=t5-t6
+      si(nr8)=t3-t5
+      si(nr3)=t2-t1
+      si(nr4)=t1-t4
+      si(nr7)=t4-t2
+      t1=t1+t4+t2
+      si(nbase)=si(nbase)+t1
+      si(nr1)=t1
+710   nbase=nbase+1
+740   nbase=nbase+nlup2
+500   if(nd.ne.5) return
+c
+c **********************************************************************
+c
+c     the following code implements the 5 point pre-weave module
+c
+c **********************************************************************
+c
+      noff=nd1*nd2*nd3
+      nbase=1
+      do 510 n1=1,noff
+      nr1=nbase+noff
+      nr2=nr1+noff
+      nr3=nr2+noff
+      nr4=nr3+noff
+      nr5=nr4+noff
+      t4=sr(nr1)-sr(nr4)
+      t1=sr(nr1)+sr(nr4)
+      t3=sr(nr3)+sr(nr2)
+      t2=sr(nr3)-sr(nr2)
+      sr(nr3)=t1-t3
+      sr(nr1)=t1+t3
+      sr(nbase)=sr(nbase)+sr(nr1)
+      sr(nr5)=t2+t4
+      sr(nr2)=t4
+      sr(nr4)=t2
+      t4=si(nr1)-si(nr4)
+      t1=si(nr1)+si(nr4)
+      t3=si(nr3)+si(nr2)
+      t2=si(nr3)-si(nr2)
+      si(nr3)=t1-t3
+      si(nr1)=t1+t3
+      si(nbase)=si(nbase)+si(nr1)
+      si(nr5)=t2+t4
+      si(nr2)=t4
+      si(nr4)=t2
+510   nbase=nbase+1
+      return
+      end
diff --git a/math/ieee/chap1/weave2.f b/math/ieee/chap1/weave2.f
new file mode 100644
index 00000000..5c04ff91
--- /dev/null
+++ b/math/ieee/chap1/weave2.f
@@ -0,0 +1,412 @@
+c
+c-----------------------------------------------------------------------
+c
+c subroutine: weave2
+c   this subroutine implements the post-weave modules
+c   of the wfta.  the working arrays are sr and si.
+c   the routine checks to see which factors are present
+c   in the transform length n = na*nb*nc*nd and executes
+c   the post-weave code for these factors.
+c
+c-----------------------------------------------------------------------
+c
+      subroutine weave2(sr,si)
+      common na,nb,nc,nd,nd1,nd2,nd3,nd4
+      dimension sr(1),si(1)
+      dimension q(8),t(16)
+      if(nd.ne.5) go to 700
+c
+c **********************************************************************
+c
+c     the following code implements the 5 point post-weave module
+c
+c **********************************************************************
+c
+      noff=nd1*nd2*nd3
+      nbase=1
+      do 510 n1=1,noff
+      nr1=nbase+noff
+      nr2=nr1+noff
+      nr3=nr2+noff
+      nr4=nr3+noff
+      nr5=nr4+noff
+      t1=sr(nbase)+sr(nr1)
+      t3=t1-sr(nr3)
+      t1=t1+sr(nr3)
+      t4=si(nr2)+si(nr5)
+      t2=si(nr4)+si(nr5)
+      sr(nr1)=t1-t4
+      sr4=t1+t4
+      sr2=t3+t2
+      sr(nr3)=t3-t2
+      t1=si(nbase)+si(nr1)
+      t3=t1-si(nr3)
+      t1=t1+si(nr3)
+      t4=sr(nr2)+sr(nr5)
+      t2=sr(nr4)+sr(nr5)
+      si(nr1)=t1+t4
+      si(nr4)=t1-t4
+      si(nr2)=t3-t2
+      si(nr3)=t3+t2
+      sr(nr2)=sr2
+      sr(nr4)=sr4
+510   nbase=nbase+1
+700   if(nc.ne.7) go to 300
+c
+c **********************************************************************
+c
+c     the following code implements the 7 point post-weave module
+c
+c **********************************************************************
+c
+      noff=nd1*nd2
+      nbase=1
+      nlup2=8*noff
+      do 740 n4=1,nd
+      do 710 n1=1,noff
+      nr1=nbase+noff
+      nr2=nr1+noff
+      nr3=nr2+noff
+      nr4=nr3+noff
+      nr5=nr4+noff
+      nr6=nr5+noff
+      nr7=nr6+noff
+      nr8=nr7+noff
+      t1=sr(nr1)+sr(nbase)
+      t2=t1-sr(nr3)-sr(nr4)
+      t4=t1+sr(nr3)-sr(nr7)
+      t1=t1+sr(nr4)+sr(nr7)
+      t6=si(nr2)+si(nr5)+si(nr8)
+      t5=si(nr2)-si(nr5)-si(nr6)
+      t3=si(nr2)+si(nr6)-si(nr8)
+      sr(nr1)=t1-t6
+      sr6=t1+t6
+      sr2=t2-t5
+      sr5=t2+t5
+      sr(nr4)=t4-t3
+      sr(nr3)=t4+t3
+      t1=si(nr1)+si(nbase)
+      t2=t1-si(nr3)-si(nr4)
+      t4=t1+si(nr3)-si(nr7)
+      t1=t1+si(nr4)+si(nr7)
+      t6=sr(nr2)+sr(nr5)+sr(nr8)
+      t5=sr(nr2)-sr(nr5)-sr(nr6)
+      t3=sr(nr2)+sr(nr6)-sr(nr8)
+      si(nr1)=t1+t6
+      si(nr6)=t1-t6
+      si(nr2)=t2+t5
+      si(nr5)=t2-t5
+      si(nr4)=t4+t3
+      si(nr3)=t4-t3
+      sr(nr2)=sr2
+      sr(nr5)=sr5
+      sr(nr6)=sr6
+710   nbase=nbase+1
+740   nbase=nbase+nlup2
+300   if(nb.eq.1) go to 400
+      if(nb.ne.3) go to 900
+c
+c **********************************************************************
+c
+c     the following code implements the 3 point post-weave module
+c
+c **********************************************************************
+c
+      nlup2=2*nd1
+      nlup23=3*nd1*(nd3-nc)
+      nbase=1
+      noff=nd1
+      do 340 n5=1,nd
+      do 330 n4=1,nc
+      do 310 n2=1,nd1
+      nr1=nbase+noff
+      nr2=nr1+noff
+      t1=sr(nbase)+sr(nr1)
+      sr(nr1)=t1-si(nr2)
+      sr2=t1+si(nr2)
+      t1=si(nbase)+si(nr1)
+      si(nr1)=t1+sr(nr2)
+      si(nr2)=t1-sr(nr2)
+      sr(nr2)=sr2
+310   nbase=nbase+1
+330   nbase=nbase+nlup2
+340   nbase=nbase+nlup23
+900   if(nb.ne.9) go to 400
+c
+c **********************************************************************
+c
+c     the following code implements the 9 point post-weave module
+c
+c **********************************************************************
+c
+      nlup2=10*nd1
+      nlup23=11*nd1*(nd3-nc)
+      nbase=1
+      noff=nd1
+      do 940 n4=1,nd
+      do 930 n3=1,nc
+      do 910 n2=1,nd1
+      nr1=nbase+noff
+      nr2=nr1+noff
+      nr3=nr2+noff
+      nr4=nr3+noff
+      nr5=nr4+noff
+      nr6=nr5+noff
+      nr7=nr6+noff
+      nr8=nr7+noff
+      nr9=nr8+noff
+      nr10=nr9+noff
+      t3=sr(nbase)-sr(nr3)
+      t7=sr(nbase)+sr(nr1)
+      sr(nbase)=sr(nbase)+sr(nr3)+sr(nr3)
+      t6=t3+si(nr10)
+      sr(nr3)=t3-si(nr10)
+      t4=t7+sr(nr5)-sr(nr6)
+      t1=t7-sr(nr4)-sr(nr5)
+      t7=t7+sr(nr4)+sr(nr6)
+      sr(nr6)=t6
+      t8=si(nr2)-si(nr7)-si(nr8)
+      t5=si(nr2)+si(nr8)-si(nr9)
+      t2=si(nr2)+si(nr7)+si(nr9)
+      sr(nr1)=t7-t2
+      sr8=t7+t2
+      sr(nr4)=t1-t8
+      sr(nr5)=t1+t8
+      sr7=t4-t5
+      sr2=t4+t5
+      t3=si(nbase)-si(nr3)
+      t7=si(nbase)+si(nr1)
+      si(nbase)=si(nbase)+si(nr3)+si(nr3)
+      t6=t3-sr(nr10)
+      si(nr3)=t3+sr(nr10)
+      t4=t7+si(nr5)-si(nr6)
+      t1=t7-si(nr4)-si(nr5)
+      t7=t7+si(nr4)+si(nr6)
+      si(nr6)=t6
+      t8=sr(nr2)-sr(nr7)-sr(nr8)
+      t5=sr(nr2)+sr(nr8)-sr(nr9)
+      t2=sr(nr2)+sr(nr7)+sr(nr9)
+      si(nr1)=t7+t2
+      si(nr8)=t7-t2
+      si(nr4)=t1+t8
+      si(nr5)=t1-t8
+      si(nr7)=t4+t5
+      si(nr2)=t4-t5
+      sr(nr2)=sr2
+      sr(nr7)=sr7
+      sr(nr8)=sr8
+910   nbase=nbase+1
+930   nbase=nbase+nlup2
+940   nbase=nbase+nlup23
+400   if(na.eq.1) return
+      if(na.ne.4) go to 800
+c
+c **********************************************************************
+c
+c     the following code implements the 4 point post-weave module
+c
+c **********************************************************************
+c
+      nlup2=4*(nd2-nb)
+      nlup23=4*nd2*(nd3-nc)
+      nbase=1
+      do 440 n4=1,nd
+      do 430 n3=1,nc
+      do 420 n2=1,nb
+      nr1=nbase+1
+      nr2=nr1+1
+      nr3=nr2+1
+      tr0=sr(nbase)+sr(nr2)
+      tr2=sr(nbase)-sr(nr2)
+      tr1=sr(nr1)+sr(nr3)
+      tr3=sr(nr1)-sr(nr3)
+      ti1=si(nr1)+si(nr3)
+      ti3=si(nr1)-si(nr3)
+      sr(nbase)=tr0+tr1
+      sr(nr2)=tr0-tr1
+      sr(nr1)=tr2+ti3
+      sr(nr3)=tr2-ti3
+      ti0=si(nbase)+si(nr2)
+      ti2=si(nbase)-si(nr2)
+      si(nbase)=ti0+ti1
+      si(nr2)=ti0-ti1
+      si(nr1)=ti2-tr3
+      si(nr3)=ti2+tr3
+420   nbase=nbase+4
+430   nbase=nbase+nlup2
+440   nbase=nbase+nlup23
+800   if(na.ne.8) go to 1600
+c
+c **********************************************************************
+c
+c     the following code implements the 8 point post-weave module
+c
+c **********************************************************************
+c
+      nlup2=8*(nd2-nb)
+      nlup23=8*nd2*(nd3-nc)
+      nbase=1
+      do 840 n4=1,nd
+      do 830 n3=1,nc
+      do 820 n2=1,nb
+      nr1=nbase+1
+      nr2=nr1+1
+      nr3=nr2+1
+      nr4=nr3+1
+      nr5=nr4+1
+      nr6=nr5+1
+      nr7=nr6+1
+      t1=sr(nbase)-sr(nr1)
+      sr(nbase)=sr(nbase)+sr(nr1)
+      sr6=sr(nr2)+si(nr3)
+      sr(nr2)=sr(nr2)-si(nr3)
+      t4=sr(nr4)-si(nr5)
+      t5=sr(nr4)+si(nr5)
+      t6=sr(nr7)-si(nr6)
+      t7=sr(nr7)+si(nr6)
+      sr(nr4)=t1
+      sr(nr1)=t4+t6
+      sr3=t4-t6
+      sr5=t5-t7
+      sr(nr7)=t5+t7
+      t1=si(nbase)-si(nr1)
+      si(nbase)=si(nbase)+si(nr1)
+      t3=si(nr2)-sr(nr3)
+      si(nr2)=si(nr2)+sr(nr3)
+      t4=si(nr4)+sr(nr5)
+      t5=si(nr4)-sr(nr5)
+      si(nr6)=t3
+      t6=sr(nr6)+si(nr7)
+      t7=sr(nr6)-si(nr7)
+      si(nr4)=t1
+      si(nr1)=t4+t6
+      si(nr3)=t4-t6
+      si(nr5)=t5+t7
+      si(nr7)=t5-t7
+      sr(nr3)=sr3
+      sr(nr5)=sr5
+      sr(nr6)=sr6
+820   nbase=nbase+8
+830   nbase=nbase+nlup2
+840   nbase=nbase+nlup23
+1600  if(na.ne.16) return
+c
+c **********************************************************************
+c
+c     the following code implements the 16 point post-weave module
+c
+c **********************************************************************
+c
+      nlup2=18*(nd2-nb)
+      nlup23=18*nd2*(nd3-nc)
+      nbase=1
+      do 1640 n4=1,nd
+      do 1630 n3=1,nc
+      do 1620 n2=1,nb
+      nr1=nbase+1
+      nr2=nr1+1
+      nr3=nr2+1
+      nr4=nr3+1
+      nr5=nr4+1
+      nr6=nr5+1
+      nr7=nr6+1
+      nr8=nr7+1
+      nr9=nr8+1
+      nr10=nr9+1
+      nr11=nr10+1
+      nr12=nr11+1
+      nr13=nr12+1
+      nr14=nr13+1
+      nr15=nr14+1
+      nr16=nr15+1
+      nr17=nr16+1
+      t(2)=sr(nbase)-sr(nr1)
+      sr(nbase)=sr(nr1)+sr(nbase)
+      t(4)=sr(nr2)+si(nr3)
+      t(3)=sr(nr2)-si(nr3)
+      t(6)=sr(nr4)+si(nr5)
+      t(5)=sr(nr4)-si(nr5)
+      t(8)=-si(nr6)-sr(nr7)
+      t(7)=-si(nr6)+sr(nr7)
+      t(9)=sr(nr8)+sr(nr14)
+      t(15)=sr(nr8)-sr(nr14)
+      t(13)=-si(nr10)-si(nr12)
+      t(11)=si(nr10)-si(nr12)
+      t(16)=sr(nr15)-sr(nr17)
+      t(12)=sr(nr11)-sr(nr17)
+      t(10)=-si(nr9)-si(nr16)
+      t(14)=-si(nr16)+si(nr13)
+      sr(nr2)=t(5)+t(7)
+      sr6=t(5)-t(7)
+      sr10=t(6)+t(8)
+      sr(nr14)=t(6)-t(8)
+      q(7)=t(9)+t(10)
+      q(8)=t(9)-t(10)
+      q(1)=t(11)+t(12)
+      q(2)=t(11)-t(12)
+      q(4)=t(14)+t(15)
+      q(5)=t(15)-t(14)
+      q(3)=t(13)+t(16)
+      q(6)=t(13)-t(16)
+      sr(nr1)=q(3)+q(7)
+      sr(nr7)=q(7)-q(3)
+      sr9=q(8)+q(6)
+      sr(nr15)=q(8)-q(6)
+      sr5=q(1)+q(4)
+      sr3=q(4)-q(1)
+      sr13=q(2)+q(5)
+      sr11=q(5)-q(2)
+      sr(nr8)=t(2)
+      sr(nr4)=t(3)
+      sr12=t(4)
+      t(2)=si(nbase)-si(nr1)
+      si(nbase)=si(nr1)+si(nbase)
+      t(4)=si(nr2)-sr(nr3)
+      t(3)=si(nr2)+sr(nr3)
+      t(6)=si(nr4)-sr(nr5)
+      t(5)=si(nr4)+sr(nr5)
+      t(8)=sr(nr6)-si(nr7)
+      t(7)=sr(nr6)+si(nr7)
+      t(9)=si(nr8)+si(nr14)
+      t(15)=si(nr8)-si(nr14)
+      t(13)=sr(nr10)+sr(nr12)
+      t(11)=sr(nr12)-sr(nr10)
+      t(16)=si(nr15)-si(nr17)
+      t(12)=si(nr11)-si(nr17)
+      t(10)=sr(nr9)+sr(nr16)
+      si(nr2)=t(5)+t(7)
+      si(nr6)=t(5)-t(7)
+      si(nr10)=t(6)+t(8)
+      si(nr14)=t(6)-t(8)
+      q(7)=t(9)+t(10)
+      q(8)=t(9)-t(10)
+      q(1)=t(11)+t(12)
+      q(2)=t(11)-t(12)
+      q(4)=t(14)+t(15)
+      q(5)=t(15)-t(14)
+      q(3)=t(13)+t(16)
+      q(6)=t(13)-t(16)
+      si(nr1)=q(3)+q(7)
+      si(nr7)=q(7)-q(3)
+      si(nr9)=q(8)+q(6)
+      si(nr15)=q(8)-q(6)
+      si(nr5)=q(1)+q(4)
+      si(nr3)=q(4)-q(1)
+      si(nr13)=q(2)+q(5)
+      si(nr11)=q(5)-q(2)
+      si(nr8)=t(2)
+      si(nr4)=t(3)
+      si(nr12)=t(4)
+      sr(nr3)=sr3
+      sr(nr5)=sr5
+      sr(nr6)=sr6
+      sr(nr9)=sr9
+      sr(nr10)=sr10
+      sr(nr11)=sr11
+      sr(nr12)=sr12
+      sr(nr13)=sr13
+1620  nbase=nbase+18
+1630  nbase=nbase+nlup2
+1640  nbase=nbase+nlup23
+      return
+      end
diff --git a/math/ieee/chap1/wfta.f b/math/ieee/chap1/wfta.f
new file mode 100644
index 00000000..9e819941
--- /dev/null
+++ b/math/ieee/chap1/wfta.f
@@ -0,0 +1,150 @@
+c
+c-----------------------------------------------------------------------
+c subroutine: wfta
+c winograd fourier transform algorithm
+c-----------------------------------------------------------------------
+c
+      subroutine wfta(xr,xi,n,invrs,init,ierr)
+      dimension xr(1),xi(1)
+c
+c inputs:
+c   n-- transform length.  must be formed as the product of
+c       relatively prime integers from the set:
+c           2,3,4,5,7,8,9,16
+c       thus the largest possible value of n is 5040.
+c   xr(.)-- array that holds the real part of the data
+c           to be transformed.
+c   xi(.)-- array that holds the imaginary part of the
+c           data to be transformed.
+c   invrs-- parameter that flags whether or not the inverse
+c           transform is to be calculated.  a division by n
+c           is included in the inverse.
+c           invrs = 1 yields inverse transform
+c           invrs .ne. 1 gives forward transform
+c   init-- parameter that flags whether or not the program
+c          is to be initialized for this value of n.  the
+c          initialization is performed only once in order to
+c          to speed up the computation on succeeding calls
+c          to the wfta routine, when n is held fixed.
+c          init = 0 results in initialization.
+c   ierr-- error code that is negative when the wfta
+c          terminates incorrectly.
+c           0 = successful completion
+c          -1 = this value of n does not factor properly
+c          -2 = an initialization has not been done for
+c               this value of n.
+c
+c
+c   the following two cards may be changed if the maximum
+c   desired transform length is less than 5040
+c
+c  *********************************************************************
+      dimension sr(1782),si(1782),coef(1782)
+      integer indx1(1008),indx2(1008)
+c  *********************************************************************
+c
+      common na,nb,nc,nd,nd1,nd2,nd3,nd4
+c
+c   test for initial run
+c
+      if(init.eq.0) call inishl(n,coef,xr,xi,indx1,indx2,ierr)
+c
+      if(ierr.lt.0) return
+      m=na*nb*nc*nd
+      if(m.eq.n) go to 100
+      ierr=-2
+      return
+c
+c  error(-2)-- program not initialized for this value of n
+c
+100   nmult=nd1*nd2*nd3*nd4
+c
+c   the following code maps the data arrays xr and xi to
+c   the working arrays sr and si via the mapping vector
+c   indx1(.).  the permutation of the data follows the
+c   sino correspondence of the chinese remainder theorem.
+c
+      j=1
+      k=1
+      inc1=nd1-na
+      inc2=nd1*(nd2-nb)
+      inc3=nd1*nd2*(nd3-nc)
+      do 140 n4=1,nd
+      do 130 n3=1,nc
+      do 120 n2=1,nb
+      do 110 n1=1,na
+      ind=indx1(k)
+      sr(j)=xr(ind)
+      si(j)=xi(ind)
+      k=k+1
+110   j=j+1
+120   j=j+inc1
+130   j=j+inc2
+140   j=j+inc3
+c
+c   do the pre-weave modules
+c
+      call weave1(sr,si)
+c
+c   the following loop performs all the multiplications of the
+c   winograd fourier transform algorithm.  the multiplication
+c   coefficients are stored on the initialization pass in the
+c   array coef(.).
+c
+      do 200 j=1,nmult
+      sr(j)=sr(j)*coef(j)
+      si(j)=si(j)*coef(j)
+  200  continue
+c
+c   do the post-weave modules
+c
+      call weave2(sr,si)
+c
+c
+c   the following code maps the working arrays sr and si
+c   to the data arrays xr and xi via the mapping vector
+c   indx2(.).  the permutation of the data follows the
+c   chinese remainder theorem.
+c
+      j=1
+      k=1
+      inc1=nd1-na
+      inc2=nd1*(nd2-nb)
+      inc3=nd1*nd2*(nd3-nc)
+c
+c   check for inverse
+c
+      if(invrs.eq.1) go to 400
+      do 340 n4=1,nd
+      do 330 n3=1,nc
+      do 320 n2=1,nb
+      do 310 n1=1,na
+      kndx=indx2(k)
+      xr(kndx)=sr(j)
+      xi(kndx)=si(j)
+      k=k+1
+310   j=j+1
+320   j=j+inc1
+330   j=j+inc2
+340   j=j+inc3
+      return
+c
+c   different permutation for the inverse
+c
+400   fn=float(n)
+      np2=n+2
+      indx2(1)=n+1
+      do 440 n4=1,nd
+      do 430 n3=1,nc
+      do 420 n2=1,nb
+      do 410 n1=1,na
+      kndx=np2-indx2(k)
+      xr(kndx)=sr(j)/fn
+      xi(kndx)=si(j)/fn
+      k=k+1
+410   j=j+1
+420   j=j+inc1
+430   j=j+inc2
+440   j=j+inc3
+      return
+      end
diff --git a/math/ieee/d1mach.f b/math/ieee/d1mach.f
new file mode 100644
index 00000000..699468ab
--- /dev/null
+++ b/math/ieee/d1mach.f
@@ -0,0 +1,256 @@
+c
+c----------------------------------------------------------------------
+c  function:  d1mach
+c  this routine is from the port mathematical subroutine library
+c  it is described in the bell laboratories computing science
+c  technical report #47 by p.a. fox, a.d. hall and n.l. schryer
+c  a modification to the "i out of bounds" error message
+c  has been made by c. a. mcgonegal - april, 1978
+c----------------------------------------------------------------------
+c
+      double precision function d1mach(i)
+c
+c  double-precision machine constants
+c
+c  d1mach( 1) = b**(emin-1), the smallest positive magnitude.
+c
+c  d1mach( 2) = b**emax*(1 - b**(-t)), the largest magnitude.
+c
+c  d1mach( 3) = b**(-t), the smallest relative spacing.
+c
+c  d1mach( 4) = b**(1-t), the largest relative spacing.
+c
+c  d1mach( 5) = log10(b)
+c
+c  to alter this function for a particular environment,
+c  the desired set of data statements should be activated by
+c  removing the c from column 1.
+c
+c  where possible, octal or hexadecimal constants have been used
+c  to specify the constants exactly which has in some cases
+c  required the use of equivalent integer arrays.
+c
+      integer small(4)
+      integer large(4)
+      integer right(4)
+      integer diver(4)
+      integer log10(4)
+c
+      double precision dmach(5)
+c
+      equivalence (dmach(1),small(1))
+      equivalence (dmach(2),large(1))
+      equivalence (dmach(3),right(1))
+      equivalence (dmach(4),diver(1))
+      equivalence (dmach(5),log10(1))
+c
+c     machine constants for the burroughs 1700 system.
+c
+c     data small(1) / zc00800000 /
+c     data small(2) / z000000000 /
+c
+c     data large(1) / zdffffffff /
+c     data large(2) / zfffffffff /
+c
+c     data right(1) / zcc5800000 /
+c     data right(2) / z000000000 /
+c
+c     data diver(1) / zcc6800000 /
+c     data diver(2) / z000000000 /
+c
+c     data log10(1) / zd00e730e7 /
+c     data log10(2) / zc77800dc0 /
+c
+c     machine constants for the burroughs 5700 system.
+c
+c     data small(1) / o1771000000000000 /
+c     data small(2) / o0000000000000000 /
+c
+c     data large(1) / o0777777777777777 /
+c     data large(2) / o0007777777777777 /
+c
+c     data right(1) / o1461000000000000 /
+c     data right(2) / o0000000000000000 /
+c
+c     data diver(1) / o1451000000000000 /
+c     data diver(2) / o0000000000000000 /
+c
+c     data log10(1) / o1157163034761674 /
+c     data log10(2) / o0006677466732724 /
+c
+c     machine constants for the burroughs 6700/7700 systems.
+c
+c     data small(1) / o1771000000000000 /
+c     data small(2) / o7770000000000000 /
+c
+c     data large(1) / o0777777777777777 /
+c     data large(2) / o7777777777777777 /
+c
+c     data right(1) / o1461000000000000 /
+c     data right(2) / o0000000000000000 /
+c
+c     data diver(1) / o1451000000000000 /
+c     data diver(2) / o0000000000000000 /
+c
+c     data log10(1) / o1157163034761674 /
+c     data log10(2) / o0006677466732724 /
+c
+c     machine constants for the cdc 6000/7000 series.
+c
+c     data small(1) / 00604000000000000000b /
+c     data small(2) / 00000000000000000000b /
+c
+c     data large(1) / 37767777777777777777b /
+c     data large(2) / 37167777777777777777b /
+c
+c     data right(1) / 15604000000000000000b /
+c     data right(2) / 15000000000000000000b /
+c
+c     data diver(1) / 15614000000000000000b /
+c     data diver(2) / 15010000000000000000b /
+c
+c     data log10(1) / 17164642023241175717b /
+c     data log10(2) / 16367571421742254654b /
+c
+c     machine constants for the cray 1
+c
+c     data small(1) / 200004000000000000000b /
+c     data small(2) / 000000000000000000000b /
+c
+c     data large(1) / 577767777777777777777b /
+c     data large(2) / 000007777777777777776b /
+c
+c     data right(1) / 376424000000000000000b /
+c     data right(2) / 000000000000000000000b /
+c
+c     data diver(1) / 376434000000000000000b /
+c     data diver(2) / 000000000000000000000b /
+c
+c     data log10(1) / 377774642023241175717b /
+c     data log10(2) / 000007571421742254654b /
+c
+c     machine constants for the data general eclipse s/200
+c
+c     note - it may be appropriate to include the following card -
+c     static dmach(5)
+c
+c     data small/20k,3*0/,large/77777k,3*177777k/
+c     data right/31420k,3*0/,diver/32020k,3*0/
+c     data log10/40423k,42023k,50237k,74776k/
+c
+c     machine constants for the harris slash 6 and slash 7
+c
+c     data small(1),small(2) / '20000000, '00000201 /
+c     data large(1),large(2) / '37777777, '37777577 /
+c     data right(1),right(2) / '20000000, '00000333 /
+c     data diver(1),diver(2) / '20000000, '00000334 /
+c     data log10(1),log10(2) / '23210115, '10237777 /
+c
+c     machine constants for the honeywell 600/6000 series.
+c
+c     data small(1),small(2) / o402400000000, o000000000000 /
+c     data large(1),large(2) / o376777777777, o777777777777 /
+c     data right(1),right(2) / o604400000000, o000000000000 /
+c     data diver(1),diver(2) / o606400000000, o000000000000 /
+c     data log10(1),log10(2) / o776464202324, o117571775714 /
+c
+c     machine constants for the ibm 360/370 series,
+c     the xerox sigma 5/7/9 and the sel systems 85/86.
+c
+c     data small(1),small(2) / z00100000, z00000000 /
+c     data large(1),large(2) / z7fffffff, zffffffff /
+c     data right(1),right(2) / z33100000, z00000000 /
+c     data diver(1),diver(2) / z34100000, z00000000 /
+c     data log10(1),log10(2) / z41134413, z509f79ff /
+c
+c     machine constants for the pdp-10 (ka processor).
+c
+c     data small(1),small(2) / "033400000000, "000000000000 /
+c     data large(1),large(2) / "377777777777, "344777777777 /
+c     data right(1),right(2) / "113400000000, "000000000000 /
+c     data diver(1),diver(2) / "114400000000, "000000000000 /
+c     data log10(1),log10(2) / "177464202324, "144117571776 /
+c
+c     machine constants for the pdp-10 (ki processor).
+c
+c     data small(1),small(2) / "000400000000, "000000000000 /
+c     data large(1),large(2) / "377777777777, "377777777777 /
+c     data right(1),right(2) / "103400000000, "000000000000 /
+c     data diver(1),diver(2) / "104400000000, "000000000000 /
+c     data log10(1),log10(2) / "177464202324, "476747767461 /
+c
+c     machine constants for pdp-11 fortran's supporting
+c     32-bit integers (expressed in integer and octal).
+c
+      data small(1),small(2) /    8388608,           0 /
+      data large(1),large(2) / 2147483647,          -1 /
+      data right(1),right(2) /  612368384,           0 /
+      data diver(1),diver(2) /  620756992,           0 /
+      data log10(1),log10(2) / 1067065498, -2063872008 /
+c
+c     data small(1),small(2) / o00040000000, o00000000000 /
+c     data large(1),large(2) / o17777777777, o37777777777 /
+c     data right(1),right(2) / o04440000000, o00000000000 /
+c     data diver(1),diver(2) / o04500000000, o00000000000 /
+c     data log10(1),log10(2) / o07746420232, o20476747770 /
+c
+c     machine constants for pdp-11 fortran's supporting
+c     16-bit integers (expressed in integer and octal).
+c
+c     data small(1),small(2) /    128,      0 /
+c     data small(3),small(4) /      0,      0 /
+c
+c     data large(1),large(2) /  32767,     -1 /
+c     data large(3),large(4) /     -1,     -1 /
+c
+c     data right(1),right(2) /   9344,      0 /
+c     data right(3),right(4) /      0,      0 /
+c
+c     data diver(1),diver(2) /   9472,      0 /
+c     data diver(3),diver(4) /      0,      0 /
+c
+c     data log10(1),log10(2) /  16282,   8346 /
+c     data log10(3),log10(4) / -31493, -12296 /
+c
+c     data small(1),small(2) / o000200, o000000 /
+c     data small(3),small(4) / o000000, o000000 /
+c
+c     data large(1),large(2) / o077777, o177777 /
+c     data large(3),large(4) / o177777, o177777 /
+c
+c     data right(1),right(2) / o022200, o000000 /
+c     data right(3),right(4) / o000000, o000000 /
+c
+c     data diver(1),diver(2) / o022400, o000000 /
+c     data diver(3),diver(4) / o000000, o000000 /
+c
+c     data log10(1),log10(2) / o037632, o020232 /
+c     data log10(3),log10(4) / o102373, o147770 /
+c
+c     machine constants for the univac 1100 series.
+c
+c     data small(1),small(2) / o000040000000, o000000000000 /
+c     data large(1),large(2) / o377777777777, o777777777777 /
+c     data right(1),right(2) / o170540000000, o000000000000 /
+c     data diver(1),diver(2) / o170640000000, o000000000000 /
+c     data log10(1),log10(2) / o177746420232, o411757177572 /
+c
+c     machine constants for the vax-11 with
+c     fortran iv-plus compiler
+c
+c     data small(1),small(2) / z00000080, z00000000 /
+c     data large(1),large(2) / zffff7fff, zffffffff /
+c     data right(1),right(2) / z00002480, z00000000 /
+c     data diver(1),diver(2) / z00002500, z00000000 /
+c     data log10(1),log10(2) / z209a3f9a, zcffa84fb /
+c
+      if (i .lt. 1  .or.  i .gt. 5) goto 100
+c
+      d1mach = dmach(i)
+      return
+c
+ 100  iwunit = i1mach(4)
+      write(iwunit, 99)
+  99  format(24hd1mach - i out of bounds)
+      stop
+      end
diff --git a/math/ieee/i1mach.f b/math/ieee/i1mach.f
new file mode 100644
index 00000000..e7b9af2b
--- /dev/null
+++ b/math/ieee/i1mach.f
@@ -0,0 +1,382 @@
+c
+c----------------------------------------------------------------------
+c  function:  i1mach
+c  this routine is from the port mathematical subroutine library
+c  it is described in the bell laboratories computing science
+c  technical report #47 by p.a. fox, a.d. hall and n.l. schryer
+c---------------------------------------------------------------------
+c
+      integer function i1mach(i)
+c
+c  i/o unit numbers.
+c
+c    i1mach( 1) = the standard input unit.
+c
+c    i1mach( 2) = the standard output unit.
+c
+c    i1mach( 3) = the standard punch unit.
+c
+c    i1mach( 4) = the standard error message unit.
+c
+c  words.
+c
+c    i1mach( 5) = the number of bits per integer storage unit.
+c
+c    i1mach( 6) = the number of characters per integer storage unit.
+c
+c  integers.
+c
+c    assume integers are represented in the s-digit, base-a form
+c
+c               sign ( x(s-1)*a**(s-1) + ... + x(1)*a + x(0) )
+c
+c               where 0 .le. x(i) .lt. a for i=0,...,s-1.
+c
+c    i1mach( 7) = a, the base.
+c
+c    i1mach( 8) = s, the number of base-a digits.
+c
+c    i1mach( 9) = a**s - 1, the largest magnitude.
+c
+c  floating-point numbers.
+c
+c    assume floating-point numbers are represented in the t-digit,
+c    base-b form
+c
+c               sign (b**e)*( (x(1)/b) + ... + (x(t)/b**t) )
+c
+c               where 0 .le. x(i) .lt. b for i=1,...,t,
+c               0 .lt. x(1), and emin .le. e .le. emax.
+c
+c    i1mach(10) = b, the base.
+c
+c  single-precision
+c
+c    i1mach(11) = t, the number of base-b digits.
+c
+c    i1mach(12) = emin, the smallest exponent e.
+c
+c    i1mach(13) = emax, the largest exponent e.
+c
+c  double-precision
+c
+c    i1mach(14) = t, the number of base-b digits.
+c
+c    i1mach(15) = emin, the smallest exponent e.
+c
+c    i1mach(16) = emax, the largest exponent e.
+c
+c  to alter this function for a particular environment,
+c  the desired set of data statements should be activated by
+c  removing the c from column 1.  also, the values of
+c  i1mach(1) - i1mach(4) should be checked for consistency
+c  with the local operating system.
+c
+      integer imach(16),output
+c
+      equivalence (imach(4),output)
+c
+c     machine constants for the burroughs 1700 system.
+c
+c     data imach( 1) /    7 /
+c     data imach( 2) /    2 /
+c     data imach( 3) /    2 /
+c     data imach( 4) /    2 /
+c     data imach( 5) /   36 /
+c     data imach( 6) /    4 /
+c     data imach( 7) /    2 /
+c     data imach( 8) /   33 /
+c     data imach( 9) / z1ffffffff /
+c     data imach(10) /    2 /
+c     data imach(11) /   24 /
+c     data imach(12) / -256 /
+c     data imach(13) /  255 /
+c     data imach(14) /   60 /
+c     data imach(15) / -256 /
+c     data imach(16) /  255 /
+c
+c     machine constants for the burroughs 5700 system.
+c
+c     data imach( 1) /   5 /
+c     data imach( 2) /   6 /
+c     data imach( 3) /   7 /
+c     data imach( 4) /   6 /
+c     data imach( 5) /  48 /
+c     data imach( 6) /   6 /
+c     data imach( 7) /   2 /
+c     data imach( 8) /  39 /
+c     data imach( 9) / o0007777777777777 /
+c     data imach(10) /   8 /
+c     data imach(11) /  13 /
+c     data imach(12) / -50 /
+c     data imach(13) /  76 /
+c     data imach(14) /  26 /
+c     data imach(15) / -50 /
+c     data imach(16) /  76 /
+c
+c     machine constants for the burroughs 6700/7700 systems.
+c
+c     data imach( 1) /   5 /
+c     data imach( 2) /   6 /
+c     data imach( 3) /   7 /
+c     data imach( 4) /   6 /
+c     data imach( 5) /  48 /
+c     data imach( 6) /   6 /
+c     data imach( 7) /   2 /
+c     data imach( 8) /  39 /
+c     data imach( 9) / o0007777777777777 /
+c     data imach(10) /   8 /
+c     data imach(11) /  13 /
+c     data imach(12) / -50 /
+c     data imach(13) /  76 /
+c     data imach(14) /  26 /
+c     data imach(15) / -32754 /
+c     data imach(16) /  32780 /
+c
+c     machine constants for the cdc 6000/7000 series.
+c
+c     data imach( 1) /    5 /
+c     data imach( 2) /    6 /
+c     data imach( 3) /    7 /
+c     data imach( 4) /    6 /
+c     data imach( 5) /   60 /
+c     data imach( 6) /   10 /
+c     data imach( 7) /    2 /
+c     data imach( 8) /   48 /
+c     data imach( 9) / 00007777777777777777b /
+c     data imach(10) /    2 /
+c     data imach(11) /   48 /
+c     data imach(12) / -974 /
+c     data imach(13) / 1070 /
+c     data imach(14) /   96 /
+c     data imach(15) / -927 /
+c     data imach(16) / 1070 /
+c
+c     machine constants for the cray 1
+c
+c     data imach( 1) /   100 /
+c     data imach( 2) /   101 /
+c     data imach( 3) /   102 /
+c     data imach( 4) /   101 /
+c     data imach( 5) /    64 /
+c     data imach( 6) /     8 /
+c     data imach( 7) /     2 /
+c     data imach( 8) /    63 /
+c     data imach( 9) /  777777777777777777777b /
+c     data imach(10) /     2 /
+c     data imach(11) /    47 /
+c     data imach(12) / -8192 /
+c     data imach(13) /  8190 /
+c     data imach(14) /    95 /
+c     data imach(15) / -8192 /
+c     data imach(16) /  8190 /
+c
+c     machine constants for the data general eclipse s/200
+c
+c     data imach( 1) /   11 /
+c     data imach( 2) /   12 /
+c     data imach( 3) /    8 /
+c     data imach( 4) /   10 /
+c     data imach( 5) /   16 /
+c     data imach( 6) /    2 /
+c     data imach( 7) /    2 /
+c     data imach( 8) /   15 /
+c     data imach( 9) /32767 /
+c     data imach(10) /   16 /
+c     data imach(11) /    6 /
+c     data imach(12) /  -64 /
+c     data imach(13) /   63 /
+c     data imach(14) /   14 /
+c     data imach(15) /  -64 /
+c     data imach(16) /   63 /
+c
+c     machine constants for the harris slash 6 and slash 7
+c
+c     data imach( 1) /       5 /
+c     data imach( 2) /       6 /
+c     data imach( 3) /       0 /
+c     data imach( 4) /       6 /
+c     data imach( 5) /      24 /
+c     data imach( 6) /       3 /
+c     data imach( 7) /       2 /
+c     data imach( 8) /      23 /
+c     data imach( 9) / 8388607 /
+c     data imach(10) /       2 /
+c     data imach(11) /      23 /
+c     data imach(12) /    -127 /
+c     data imach(13) /     127 /
+c     data imach(14) /      38 /
+c     data imach(15) /    -127 /
+c     data imach(16) /     127 /
+c
+c     machine constants for the honeywell 600/6000 series.
+c
+c     data imach( 1) /    5 /
+c     data imach( 2) /    6 /
+c     data imach( 3) /   43 /
+c     data imach( 4) /    6 /
+c     data imach( 5) /   36 /
+c     data imach( 6) /    6 /
+c     data imach( 7) /    2 /
+c     data imach( 8) /   35 /
+c     data imach( 9) / o377777777777 /
+c     data imach(10) /    2 /
+c     data imach(11) /   27 /
+c     data imach(12) / -127 /
+c     data imach(13) /  127 /
+c     data imach(14) /   63 /
+c     data imach(15) / -127 /
+c     data imach(16) /  127 /
+c
+c     machine constants for the ibm 360/370 series,
+c     the xerox sigma 5/7/9 and the sel systems 85/86.
+c
+c     data imach( 1) /   5 /
+c     data imach( 2) /   6 /
+c     data imach( 3) /   7 /
+c     data imach( 4) /   6 /
+c     data imach( 5) /  32 /
+c     data imach( 6) /   4 /
+c     data imach( 7) /   2 /
+c     data imach( 8) /  31 /
+c     data imach( 9) / z7fffffff /
+c     data imach(10) /  16 /
+c     data imach(11) /   6 /
+c     data imach(12) / -64 /
+c     data imach(13) /  63 /
+c     data imach(14) /  14 /
+c     data imach(15) / -64 /
+c     data imach(16) /  63 /
+c
+c     machine constants for the pdp-10 (ka processor).
+c
+c     data imach( 1) /    5 /
+c     data imach( 2) /    6 /
+c     data imach( 3) /    5 /
+c     data imach( 4) /    6 /
+c     data imach( 5) /   36 /
+c     data imach( 6) /    5 /
+c     data imach( 7) /    2 /
+c     data imach( 8) /   35 /
+c     data imach( 9) / "377777777777 /
+c     data imach(10) /    2 /
+c     data imach(11) /   27 /
+c     data imach(12) / -128 /
+c     data imach(13) /  127 /
+c     data imach(14) /   54 /
+c     data imach(15) / -101 /
+c     data imach(16) /  127 /
+c
+c     machine constants for the pdp-10 (ki processor).
+c
+c     data imach( 1) /    5 /
+c     data imach( 2) /    6 /
+c     data imach( 3) /    5 /
+c     data imach( 4) /    6 /
+c     data imach( 5) /   36 /
+c     data imach( 6) /    5 /
+c     data imach( 7) /    2 /
+c     data imach( 8) /   35 /
+c     data imach( 9) / "377777777777 /
+c     data imach(10) /    2 /
+c     data imach(11) /   27 /
+c     data imach(12) / -128 /
+c     data imach(13) /  127 /
+c     data imach(14) /   62 /
+c     data imach(15) / -128 /
+c     data imach(16) /  127 /
+c
+c     machine constants for pdp-11 fortran supporting
+c     32-bit integer arithmetic.
+c
+      data imach( 1) /    5 /
+      data imach( 2) /    6 /
+      data imach( 3) /    6 /
+      data imach( 4) /    0 /
+      data imach( 5) /   32 /
+      data imach( 6) /    4 /
+      data imach( 7) /    2 /
+      data imach( 8) /   31 /
+      data imach( 9) / 2147483647 /
+      data imach(10) /    2 /
+      data imach(11) /   24 /
+      data imach(12) / -127 /
+      data imach(13) /  127 /
+      data imach(14) /   56 /
+      data imach(15) / -127 /
+      data imach(16) /  127 /
+c
+c     machine constants for pdp-11 fortran supporting
+c     16-bit integer arithmetic.
+c
+c     data imach( 1) /    5 /
+c     data imach( 2) /    6 /
+c     data imach( 3) /    5 /
+c     data imach( 4) /    6 /
+c     data imach( 5) /   16 /
+c     data imach( 6) /    2 /
+c     data imach( 7) /    2 /
+c     data imach( 8) /   15 /
+c     data imach( 9) / 32767 /
+c     data imach(10) /    2 /
+c     data imach(11) /   24 /
+c     data imach(12) / -127 /
+c     data imach(13) /  127 /
+c     data imach(14) /   56 /
+c     data imach(15) / -127 /
+c     data imach(16) /  127 /
+c
+c     machine constants for the univac 1100 series.
+c
+c     note that the punch unit, i1mach(3), has been set to 7
+c     which is appropriate for the univac-for system.
+c     if you have the univac-ftn system, set it to 1.
+c
+c     data imach( 1) /    5 /
+c     data imach( 2) /    6 /
+c     data imach( 3) /    7 /
+c     data imach( 4) /    6 /
+c     data imach( 5) /   36 /
+c     data imach( 6) /    6 /
+c     data imach( 7) /    2 /
+c     data imach( 8) /   35 /
+c     data imach( 9) / o377777777777 /
+c     data imach(10) /    2 /
+c     data imach(11) /   27 /
+c     data imach(12) / -128 /
+c     data imach(13) /  127 /
+c     data imach(14) /   60 /
+c     data imach(15) /-1024 /
+c     data imach(16) / 1023 /
+c
+c     machine constants for the vax-11 with
+c     fortran iv-plus compiler
+c
+c     data imach( 1) /    5 /
+c     data imach( 2) /    6 /
+c     data imach( 3) /    5 /
+c     data imach( 4) /    6 /
+c     data imach( 5) /   32 /
+c     data imach( 6) /    4 /
+c     data imach( 7) /    2 /
+c     data imach( 8) /   31 /
+c     data imach( 9) / 2147483647 /
+c     data imach(10) /    2 /
+c     data imach(11) /   24 /
+c     data imach(12) / -127 /
+c     data imach(13) /  127 /
+c     data imach(14) /   56 /
+c     data imach(15) / -127 /
+c     data imach(16) /  127 /
+c
+      if (i .lt. 1  .or.  i .gt. 16) go to 10
+c
+      i1mach=imach(i)
+      return
+c
+ 10   write(output,9000)
+ 9000 format(39h1error    1 in i1mach - i out of bounds)
+c
+      stop
+c
+      end
diff --git a/math/ieee/r1mach.f b/math/ieee/r1mach.f
new file mode 100644
index 00000000..db71aa68
--- /dev/null
+++ b/math/ieee/r1mach.f
@@ -0,0 +1,177 @@
+c
+c----------------------------------------------------------------------
+c  function:  r1mach
+c  this routine is from the port mathematical subroutine library
+c  it is described in the bell laboratories computing science
+c  technical report #47 by p.a. fox, a.d. hall and n.l. schryer
+c  a modification to the "i out of bounds" error message
+c  has been made by c. a. mcgonegal - april, 1978
+c----------------------------------------------------------------------
+c
+      real function r1mach(i)
+c
+c  single-precision machine constants
+c
+c  r1mach(1) = b**(emin-1), the smallest positive magnitude.
+c
+c  r1mach(2) = b**emax*(1 - b**(-t)), the largest magnitude.
+c
+c  r1mach(3) = b**(-t), the smallest relative spacing.
+c
+c  r1mach(4) = b**(1-t), the largest relative spacing.
+c
+c  r1mach(5) = log10(b)
+c
+c  to alter this function for a particular environment,
+c  the desired set of data statements should be activated by
+c  removing the c from column 1.
+c
+c  where possible, octal or hexadecimal constants have been used
+c  to specify the constants exactly which has in some cases
+c  required the use of equivalent integer arrays.
+c
+      integer small(2)
+      integer large(2)
+      integer right(2)
+      integer diver(2)
+      integer log10(2)
+c
+      real rmach(5)
+c
+      equivalence (rmach(1),small(1))
+      equivalence (rmach(2),large(1))
+      equivalence (rmach(3),right(1))
+      equivalence (rmach(4),diver(1))
+      equivalence (rmach(5),log10(1))
+c
+c     machine constants for the burroughs 1700 system.
+c
+c     data rmach(1) / z400800000 /
+c     data rmach(2) / z5ffffffff /
+c     data rmach(3) / z4e9800000 /
+c     data rmach(4) / z4ea800000 /
+c     data rmach(5) / z500e730e8 /
+c
+c     machine constants for the burroughs 5700/6700/7700 systems.
+c
+c     data rmach(1) / o1771000000000000 /
+c     data rmach(2) / o0777777777777777 /
+c     data rmach(3) / o1311000000000000 /
+c     data rmach(4) / o1301000000000000 /
+c     data rmach(5) / o1157163034761675 /
+c
+c     machine constants for the cdc 6000/7000 series.
+c
+c     data rmach(1) / 00014000000000000000b /
+c     data rmach(2) / 37767777777777777777b /
+c     data rmach(3) / 16404000000000000000b /
+c     data rmach(4) / 16414000000000000000b /
+c     data rmach(5) / 17164642023241175720b /
+c
+c     machine constants for the cray 1
+c
+c     data rmach(1) / 200004000000000000000b /
+c     data rmach(2) / 577767777777777777776b /
+c     data rmach(3) / 377224000000000000000b /
+c     data rmach(4) / 377234000000000000000b /
+c     data rmach(5) / 377774642023241175720b /
+c
+c     machine constants for the data general eclipse s/200
+c
+c     note - it may be appropriate to include the following card -
+c     static rmach(5)
+c
+c     data small/20k,0/,large/77777k,177777k/
+c     data right/35420k,0/,diver/36020k,0/
+c     data log10/40423k,42023k/
+c
+c     machine constants for the harris slash 6 and slash 7
+c
+c     data small(1),small(2) / '20000000, '00000201 /
+c     data large(1),large(2) / '37777777, '00000177 /
+c     data right(1),right(2) / '20000000, '00000352 /
+c     data diver(1),diver(2) / '20000000, '00000353 /
+c     data log10(1),log10(2) / '23210115, '00000377 /
+c
+c     machine constants for the honeywell 600/6000 series.
+c
+c     data rmach(1) / o402400000000 /
+c     data rmach(2) / o376777777777 /
+c     data rmach(3) / o714400000000 /
+c     data rmach(4) / o716400000000 /
+c     data rmach(5) / o776464202324 /
+c
+c     machine constants for the ibm 360/370 series,
+c     the xerox sigma 5/7/9 and the sel systems 85/86.
+c
+c     data rmach(1) / z00100000 /
+c     data rmach(2) / z7fffffff /
+c     data rmach(3) / z3b100000 /
+c     data rmach(4) / z3c100000 /
+c     data rmach(5) / z41134413 /
+c
+c     machine constants for the pdp-10 (ka or ki processor).
+c
+c     data rmach(1) / "000400000000 /
+c     data rmach(2) / "377777777777 /
+c     data rmach(3) / "146400000000 /
+c     data rmach(4) / "147400000000 /
+c     data rmach(5) / "177464202324 /
+c
+c     machine constants for pdp-11 fortran's supporting
+c     32-bit integers (expressed in integer and octal).
+c
+      data small(1) /    8388608 /
+      data large(1) / 2147483647 /
+      data right(1) /  880803840 /
+      data diver(1) /  889192448 /
+      data log10(1) / 1067065499 /
+c
+c     data rmach(1) / o00040000000 /
+c     data rmach(2) / o17777777777 /
+c     data rmach(3) / o06440000000 /
+c     data rmach(4) / o06500000000 /
+c     data rmach(5) / o07746420233 /
+c
+c     machine constants for pdp-11 fortran's supporting
+c     16-bit integers  (expressed in integer and octal).
+c
+c     data small(1),small(2) /   128,     0 /
+c     data large(1),large(2) / 32767,    -1 /
+c     data right(1),right(2) / 13440,     0 /
+c     data diver(1),diver(2) / 13568,     0 /
+c     data log10(1),log10(2) / 16282,  8347 /
+c
+c     data small(1),small(2) / o000200, o000000 /
+c     data large(1),large(2) / o077777, o177777 /
+c     data right(1),right(2) / o032200, o000000 /
+c     data diver(1),diver(2) / o032400, o000000 /
+c     data log10(1),log10(2) / o037632, o020233 /
+c
+c     machine constants for the univac 1100 series.
+c
+c     data rmach(1) / o000400000000 /
+c     data rmach(2) / o377777777777 /
+c     data rmach(3) / o146400000000 /
+c     data rmach(4) / o147400000000 /
+c     data rmach(5) / o177464202324 /
+c
+c     machine constants for the vax-11 with
+c     fortran iv-plus compiler
+c
+c     data rmach(1) / z00000080 /
+c     data rmach(2) / zffff7fff /
+c     data rmach(3) / z00003480 /
+c     data rmach(4) / z00003500 /
+c     data rmach(5) / z209b3f9a /
+c
+      if (i .lt. 1  .or.  i .gt. 5) goto 100
+c
+      r1mach = rmach(i)
+      return
+c
+ 100  iwunit = i1mach(4)
+      write(iwunit, 99)
+  99  format(24hr1mach - i out of bounds)
+      stop
+      end
diff --git a/math/ieee/uni.c b/math/ieee/uni.c
new file mode 100644
index 00000000..8e76c099
--- /dev/null
+++ b/math/ieee/uni.c
@@ -0,0 +1,8 @@
+/* Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+ */
+
+float uni_(dummy)
+float *dummy;
+{
+	return(rand()/ 2147483648.0);	/* return a real [0.0, 1.0) */
+}
diff --git a/math/iminterp/Revisions b/math/iminterp/Revisions
new file mode 100644
index 00000000..b57a092b
--- /dev/null
+++ b/math/iminterp/Revisions
@@ -0,0 +1,7 @@
+.help revisions Sep99 math.deboor
+.nf
+From Davis, September 20, 1999
+
+Added some missing file dependices to the mkpkg file.
+pkg/math/iminterp/mkpkg
+.endhelp
diff --git a/math/iminterp/arbpix.x b/math/iminterp/arbpix.x
new file mode 100644
index 00000000..d22b47c6
--- /dev/null
+++ b/math/iminterp/arbpix.x
@@ -0,0 +1,339 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math.h>
+include <math/iminterp.h>
+include "im1interpdef.h"
+
+define MIN_BDX	0.05	# minimum distance from interpolation point for sinc
+
+# ARBPIX -- Replace INDEF valued pixels with interpolated values. In order to
+# replace bad points the spline interpolator uses a limited data array whose
+# maximum total length is given by SPLPTS.
+
+procedure arbpix (datain, dataout, npts, interp_type, boundary_type)
+
+real	datain[ARB]		# input data array
+real	dataout[ARB]		# output data array - cannot be same as datain
+int	npts			# number of data points
+int	interp_type		# interpolator type
+int	boundary_type		# boundary type, at present must be BOUNDARY_EXT
+
+int	i, badnc, k, ka, kb
+real	ii_badpix()
+
+begin
+	if (interp_type < 1 || interp_type > II_NTYPES)
+	    call error (0, "ARBPIX: Unknown interpolator type.")
+
+	if (boundary_type < 1 || boundary_type > II_NBOUND)
+	    call error (0, "ARBPIX: Unknown boundary type.")
+
+	# Count bad points.
+	badnc = 0
+	do i = 1, npts
+	    if (IS_INDEFR(datain[i]))
+		badnc = badnc + 1
+
+	# Return an array of INDEFS if all points bad.
+	if (badnc == npts) {
+	    call amovkr (INDEFR, dataout, npts)
+	    return
+	}
+
+	# Copy input array to output array if all points good.
+	if (badnc == 0) {
+	    call amovr (datain, dataout, npts)
+	    return
+	}
+
+	# If sinc interpolator use a special routine.
+	if (interp_type == II_SINC || interp_type == II_LSINC) {
+	    call ii_badsinc (datain, dataout, npts, NSINC, MIN_BDX)
+	    return
+	}
+	
+	# Find the first good point.
+	for (ka = 1; IS_INDEFR (datain[ka]); ka = ka + 1)
+	    ;
+
+	# Bad points below first good point are set at first good value.
+	do k = 1, ka - 1
+	    dataout[k] = datain[ka]
+	
+	# Find last good point.
+	for (kb = npts; IS_INDEFR (datain[kb]); kb = kb - 1)
+	    ;
+
+	# Bad points beyond last good point get set at good last value.
+	do k = npts, kb + 1, -1
+	    dataout[k] = datain[kb]
+
+	# Load the other points interpolating the bad points as needed.
+	do k = ka, kb {
+
+	    if (IS_INDEFR(datain[k]))
+		dataout[k] = ii_badpix (datain[ka], kb - ka + 1, k - ka + 1,
+		    interp_type)
+	    else
+		dataout[k] = datain[k]
+
+	}
+end
+
+
+# II_BADPIX -- This procedure fills a temporary array with good points that
+# bracket the bad point and calls the interpolating routine.
+
+real procedure ii_badpix (datain, npix, index, interp_type)
+
+real	datain[ARB]	# datain array, y[1] and y[n] guaranteed to be good
+int	npix		# length of y array
+int	index		# index of bad point to replace
+int	interp_type	# interpolator type
+
+int	j, jj, pdown, pup, npts, ngood
+real	tempdata[SPLPTS], tempx[SPLPTS]
+real	ii_newpix()
+
+begin
+	# This code will work only if subroutines are implemented using
+	# static storage - i.e. the old internal values survive. This avoids
+	# reloading of temporary arrays if there are consequetive bad points.
+
+	# The following test is done to improve speed.
+
+	if (! IS_INDEFR(datain[index-1])) { 
+
+	    # Set number of good points needed on each side of bad point.
+	    switch (interp_type) {
+	    case II_NEAREST:
+		ngood = 1
+	    case II_LINEAR:
+		ngood = 1
+	    case II_POLY3:
+		ngood = 2
+	    case II_POLY5:
+		ngood = 3
+	    case II_SPLINE3:
+		ngood = SPLPTS / 2
+	    case II_DRIZZLE:
+		ngood = 1
+	    }
+
+	    # Search down.
+	    pdown = 0
+	    for (j = index - 1; j >= 1 && pdown < ngood; j = j - 1)
+		if (! IS_INDEFR(datain[j]))
+		    pdown = pdown + 1
+
+	    # Load temporary arrays for values below our INDEF.
+	    npts = 0
+	    for(jj = j + 1; jj < index; jj = jj + 1)
+		if (! IS_INDEFR(datain[jj])) {
+		    npts = npts + 1
+		    tempdata[npts] = datain[jj]
+		    tempx[npts] = jj
+		}
+
+	     # Search and load up from INDEF.
+	     pup = 0
+	     for (j = index + 1; j <= npix && pup < ngood; j = j + 1)
+		if (! IS_INDEFR(datain[j])) {
+		     pup = pup + 1
+		     npts = npts + 1
+		     tempdata[npts] = datain[j]
+		     tempx[npts] = j
+		 }
+	 }
+
+	 # Return value interpolated from these arrays.
+	 return (ii_newpix (real(index), tempx, tempdata,
+	 	npts, pdown, interp_type))
+
+end
+
+
+# II_NEWPIX -- This procedure interpolates the temporary arrays. For the
+# purposes of bad pixel replacement the drizzle replacement algorithm is
+# equated with the linear interpolation replacement algorithm, an equation
+# which is exact if the drizzle integration interval is exactly 1.0 pixels.
+# II_NEWPIX does not represent a general puprpose routine because the
+# previous routine has determined the proper indices.
+
+real procedure ii_newpix (x, xarray, data, npts, index, interp_type)
+
+real	x		# point to interpolate
+real	xarray[ARB]	# x values
+real	data[ARB]	# data values
+int 	npts		# size of data array
+int	index		# index such that xarray[index] < x < xarray[index+1]
+int 	interp_type	# interpolator type
+
+int	i, left, right
+real	cc[SPLINE3_ORDER, SPLPTS], h
+real	ii_polterp()
+
+begin
+	switch (interp_type) {
+
+	case II_NEAREST:
+	    if (x - xarray[1] > xarray[2] - x)
+		return (data[2])
+	     else
+		return (data[1])
+
+	case II_LINEAR, II_DRIZZLE:
+	    return (data[1] + (x - xarray[1]) *
+		    (data[2] - data[1]) / (xarray[2] - xarray[1]))
+
+	case II_SPLINE3:
+	    do i = 1, npts
+		cc[1,i] = data[i]
+
+	    cc[2,1] = 0.
+	    cc[2,npts] = 0.
+
+	     # Use spline routine from C. de Boor's book "A Practical Guide
+	     # to Splines
+
+	     call iicbsp (xarray, cc, npts, 2, 2)
+	     h = x - xarray[index]
+
+	     return (cc[1,index] + h * (cc[2,index] + h *
+			       (cc[3,index] + h * cc[4,index]/3.)/2.))
+
+	# One of the polynomial types.
+	default:
+
+	    # Allow lower order if not enough points on one side.
+	    right = npts
+	    left = 1
+
+	    if (npts - index < index) {
+		right = 2 * (npts - index)
+		left = 2 * index - npts + 1
+	    }
+
+	    if (npts - index > index)
+		right = 2 * index
+
+	    # Finally polynomial interpolate.
+	    return (ii_polterp (xarray[left], data[left], right, x))
+	}
+end
+
+
+# II_BADSINC -- Procedure to evaluate bad pixels with a sinc interpolant
+# This is the average of interpolation to points +-0.05 from the bad pixel.
+# Sinc interpolation exactly at a pixel is undefined. Since this routine
+# is intended to be a bad pixel replacement routine, no attempt has been
+# made to optimize the routine by precomputing the sinc function.
+
+procedure ii_badsinc (datain, dataout, npts, nsinc, min_bdx)
+
+real	datain[ARB]	# input data including bad pixels with INDEF values
+real	dataout[ARB]	# output data 
+int	npts		# number of data values
+int	nsinc		# sinc truncation length
+real	min_bdx		# minimum  distance from interpolation point
+
+int	i, j, k, xc
+real	sconst, a2, a4, dx, dx2, dx4
+real	w, d, z, w1, u1, v1
+
+begin
+	sconst = (HALFPI / nsinc) ** 2
+	a2 = -0.49670
+	a4 = 0.03705
+
+	do i = 1, npts {
+
+	    if (! IS_INDEFR(datain[i])) {
+		dataout[i] = datain[i]
+		next
+	    }
+
+	    # Initialize.
+	    xc = i
+	    w = 1.
+	    u1 = 0.0; v1 = 0.0
+
+	    do j = 1, nsinc {
+
+		# Get the taper.
+		w = -w
+
+		# Sum the low side.
+		k = xc - j
+		if (k >= 1)
+		    d = datain[k]
+		else
+		    d = datain[1]
+		if (! IS_INDEFR(d)) {
+		    dx = min_bdx + j
+		    dx2 = sconst * j * j
+		    dx4 = dx2 * dx2
+		    z = 1. / dx
+		    w1 = w * z * (1.0 + a2 * dx2 + a4 * dx4) ** 2
+		    u1 = u1 + d * w1
+		    v1 = v1 + w1
+		    dx = -min_bdx + j
+		    dx2 = sconst * j * j
+		    dx4 = dx2 * dx2
+		    z = 1. / dx
+		    w1 = -w * z * (1.0 + a2 * dx2 + a4 * dx4) ** 2
+		    u1 = u1 + d * w1
+		    v1 = v1 + w1
+		}
+
+		# Sum the high side.
+		k = xc + j
+		if (k <= npts)
+		    d = datain[k]
+		else
+		    d = datain[npts]
+		if (! IS_INDEFR(d)) {
+		    dx = min_bdx - j
+		    dx2 = sconst * j * j
+		    dx4 = dx2 * dx2
+		    z = 1. / dx
+		    w1 = w * z * (1.0 + a2 * dx2 + a4 * dx4) ** 2
+		    u1 = u1 + d * w1
+		    v1 = v1 + w1
+		    dx = -min_bdx - j
+		    dx2 = sconst * j * j
+		    dx4 = dx2 * dx2
+		    z = 1. / dx
+		    w1 = -w * z * (1.0 + a2 * dx2 + a4 * dx4) ** 2
+		    u1 = u1 + d * w1
+		    v1 = v1 + w1
+		}
+	    }
+
+	    # Compute the result.
+	    if (v1 != 0.) {
+		dataout[i] = u1 / v1
+	    } else {
+		do j = 1, npts {
+		    k = xc - j
+		    if (k >= 1)
+			d = datain[k]
+		    else
+			d = datain[1]
+		    if (!IS_INDEFR(d)) {
+			dataout[i] = d
+			break
+		    }
+		    k = xc + j
+		    if (k <= npts)
+			d = datain[k]
+		    else
+			d = datain[npts]
+		    if (!IS_INDEFR(d)) {
+			dataout[i] = d
+			break
+		    }
+		}
+	    }
+	}
+end
diff --git a/math/iminterp/arider.x b/math/iminterp/arider.x
new file mode 100644
index 00000000..55b3ee32
--- /dev/null
+++ b/math/iminterp/arider.x
@@ -0,0 +1,108 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/iminterp.h>
+include "im1interpdef.h"
+
+# ARIDER -- Return the derivatives of the interpolant. The sinc function
+# width and precision limits are hardwired to the builtin constants NSINC
+# and DX. The look-up table sinc function is aliased to the sinc function.
+# The drizzle function pixel fraction is harwired to the builtin constant
+# PIXFRAC. If PIXFRAC is 1.0 then the drizzle  results are identical to the
+# linear interpolation results.
+
+procedure arider (x, datain, npix, derivs, nder, interp_type)
+
+real	x[ARB]		# need 1 <= x <= n
+real	datain[ARB]	# data values
+int	npix		# number of data values
+real	derivs[ARB]	# derivatives out -- derivs[1] is function value
+int	nder		# total number of values returned in derivs
+int	interp_type	# type of interpolator
+
+int	i, j, k, nterms, nd, nearx
+real	pcoeff[MAX_NDERIVS], accum, deltax, temp, tmpx[2]
+
+begin
+	if (nder <= 0)
+	    return
+
+	# Zero out the derivatives array.
+	do i = 1, nder
+	    derivs[i] = 0.
+
+	switch (interp_type) {
+
+	case II_NEAREST:
+	    derivs[1] = datain[int (x[1] + 0.5)]
+	    return
+
+	case II_LINEAR:
+	    nearx = x[1]
+	    if (nearx >= npix)
+		temp = 2. * datain[nearx] - datain[nearx-1]
+	    else
+		temp = datain[nearx+1]
+	    derivs[1] = (x[1] - nearx) * temp + (nearx + 1 - x[1]) *
+	        datain[nearx]
+	    if (nder >= 2)
+		derivs[2] = temp - datain[nearx]
+	    return
+
+	case II_SINC, II_LSINC:
+	    call ii_sincder (x, derivs, nder, datain, npix, NSINC, DX)
+	    return
+
+	case II_DRIZZLE:
+	    call ii_driz1 (x, derivs[1], 1, datain, BADVAL)
+	    if (nder > 1) {
+		deltax = x[2] - x[1]
+		if (deltax == 0.0)
+		    derivs[2] = 0.0
+		else {
+		    tmpx[1] = x[1]
+		    tmpx[2] = (x[1] + x[2]) / 2.0
+	    	    call ii_driz1 (x, temp, 1, datain, BADVAL)
+		    tmpx[1] = tmpx[2]
+		    tmpx[2] = x[2]
+	    	    call ii_driz1 (x, derivs[2], 1, datain, BADVAL)
+		    derivs[2] = 2.0 * (derivs[2] - temp) / deltax
+		}
+	    }
+	    return
+
+	case II_POLY3:
+	    call ia_pcpoly3 (x, datain, npix, pcoeff)
+	    nterms = 4
+
+	case II_POLY5:
+	    call ia_pcpoly5 (x, datain, npix, pcoeff)
+	    nterms = 6
+
+	case II_SPLINE3:
+	    call ia_pcspline3 (x, datain, npix, pcoeff)
+	    nterms = 4
+
+	}
+
+	# Evaluate the polynomial derivatives.
+
+	nearx = x[1]
+	deltax = x[1] - nearx
+
+	nd = nder
+	if (nder > nterms)
+	    nd = nterms
+
+	do k = 1, nd {	
+
+	    # Evaluate using nested multiplication
+	    accum = pcoeff[nterms - k + 1]
+	    do j = nterms - k, 1, -1
+		accum = pcoeff[j] + deltax * accum
+	    derivs[k] = accum
+
+	    # Differentiate.
+	    do j = 1, nterms - k
+		pcoeff[j] = j * pcoeff[j + 1]
+	}
+end
diff --git a/math/iminterp/arieval.x b/math/iminterp/arieval.x
new file mode 100644
index 00000000..56d2c07a
--- /dev/null
+++ b/math/iminterp/arieval.x
@@ -0,0 +1,147 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/iminterp.h>
+include "im1interpdef.h"
+
+# ARIEVAL -- Evaluate the interpolant at a given value of x. Arieval allows
+# the interpolation of a few isolated points without the storage required for
+# the sequential version. With the exception of the sinc function, the
+# interpolation code is expanded directly in this routine to avoid the
+# overhead of an aditional function call. The precomputed sinc function is
+# not supported and is aliased to the regular sinc function. The default
+# sinc function width and precision limits are hardwired to the builtin
+# constants NSINC and DX. The default drizzle function pixel fraction is
+# hardwired to the builtin constant PIXFRAC. If PIXFRAC is 1.0 then the
+# drizzle results are identical to the linear interpolation results.
+
+real procedure arieval (x, datain, npts, interp_type)
+
+real	x		# x value, 1 <= x <= n
+real	datain[ARB]	# array of data values
+int	npts		# number of data values
+int	interp_type	# interpolant type
+
+int 	i, k, nearx, pindex
+real	a[MAX_NDERIVS], cd20, cd21, cd40, cd41, deltax, deltay, hold
+real	bcoeff[SPLPTS+3], temp[SPLPTS+3], pcoeff[SPLINE3_ORDER]
+
+begin
+	switch (interp_type) {
+
+	case II_NEAREST:
+	    return (datain[int (x + 0.5)])
+
+	case II_LINEAR:
+	    nearx = x
+
+	    # Protect against x = n.
+	    if (nearx >= npts)
+		hold = 2. * datain[nearx] - datain[nearx - 1]
+	    else
+		hold = datain[nearx+1]
+
+	    return ((x - nearx) * hold + (nearx + 1 - x) * datain[nearx])
+
+	case II_POLY3:
+	    nearx = x
+
+	    # Protect against the x = 1 or x = n case.
+	    k = 0
+	    for (i = nearx - 1; i <= nearx + 2; i = i + 1) {
+		k = k + 1
+		if (i < 1)
+		    a[k] = 2. * datain[1] - datain[2-i]
+		else if (i > npts)
+		    a[k] = 2. * datain[npts] - datain[2*npts-i]
+		else
+		    a[k] = datain[i]
+	    }
+
+	    deltax = x - nearx
+	    deltay = 1. - deltax
+
+	    # Second central differences.
+	    cd20 = 1./6. * (a[3] - 2. * a[2] + a[1])
+	    cd21 = 1./6. * (a[4] - 2. * a[3] + a[2])
+
+	    return (deltax * (a[3] + (deltax * deltax - 1.) * cd21) +
+		    deltay * (a[2] + (deltay * deltay - 1.) * cd20))
+
+	case II_POLY5:
+	    nearx = x
+
+	    # Protect against the x = 1 or x = n case.
+	    k = 0
+	    for (i = nearx - 2; i <= nearx + 3; i = i + 1) {
+		k = k + 1
+		if (i < 1)
+		    a[k] = 2. * datain[1] - datain[2-i]
+		else if (i > npts)
+		    a[k] = 2. * datain[npts] - datain[2*npts-i]
+		else
+		    a[k] = datain[i]
+	    }
+
+	    deltax = x - nearx
+	    deltay = 1. - deltax
+
+	    # Second central differences.
+	    cd20 = 1./6. * (a[4] - 2. * a[3] + a[2])
+	    cd21 = 1./6. * (a[5] - 2. * a[4] + a[3])
+
+	    # Fourth central differences.
+	    cd40 = 1./120. * (a[1] - 4. * a[2] + 6. * a[3] - 4. * a[4] + a[5])
+	    cd41 = 1./120. * (a[2] - 4. * a[3] + 6. * a[4] - 4. * a[5] + a[6])
+
+	    return (deltax * (a[4] + (deltax * deltax - 1.) *
+	    	   (cd21 + (deltax * deltax - 4.) * cd41)) +
+	    	   deltay * (a[3] + (deltay * deltay - 1.) *
+		   (cd20 + (deltay * deltay - 4.) * cd40)))
+
+	case II_SPLINE3:
+	    nearx = x
+
+	    deltax = x - nearx
+	    k = 0
+
+	    # Get the data.
+	    for (i = nearx - SPLPTS/2 + 1; i <= nearx + SPLPTS/2; i = i + 1) {
+		if (i < 1 || i > npts)
+		    ;
+		else {
+		    k = k + 1
+		    if (k == 1)
+			pindex = nearx - i + 1
+		    bcoeff[k+1] = datain[i]
+		}
+	    }
+	    bcoeff[1] = 0.
+	    bcoeff[k+2] = 0.
+
+	    # Compute coefficients.
+	    call ii_spline (bcoeff, temp, k)
+
+	    pindex = pindex + 1
+	    bcoeff[k+3] = 0.
+
+	    pcoeff[1] = bcoeff[pindex-1] + 4. * bcoeff[pindex] +
+	    		bcoeff[pindex+1]
+	    pcoeff[2] = 3. * (bcoeff[pindex+1] - bcoeff[pindex-1])
+	    pcoeff[3] = 3. * (bcoeff[pindex-1] - 2. * bcoeff[pindex] +
+	    		bcoeff[pindex+1])
+	    pcoeff[4] = -bcoeff[pindex-1] + 3. * bcoeff[pindex] - 3. *
+	    		bcoeff[pindex+1] + bcoeff[pindex+2]
+		    
+	    return (pcoeff[1] + deltax * (pcoeff[2] + deltax *
+	    	   (pcoeff[3] + deltax * pcoeff[4])))
+
+	case II_SINC, II_LSINC:
+	    call ii_sinc (x, hold, 1, datain, npts, NSINC, DX)
+	    return (hold)
+
+	case II_DRIZZLE:
+	    call ii_driz1 (x, hold, 1, datain, BADVAL)
+	    return (hold)
+
+	}
+end
diff --git a/math/iminterp/asider.x b/math/iminterp/asider.x
new file mode 100644
index 00000000..73e93b4d
--- /dev/null
+++ b/math/iminterp/asider.x
@@ -0,0 +1,154 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/iminterp.h>
+include "im1interpdef.h"
+
+# ASIDER -- Calculate nder derivatives assuming that x lands in the region
+# 1 <= x <= npts.
+
+procedure asider (asi, x, der, nder)
+
+pointer	asi		# interpolant descriptor
+real	x[ARB]		# x value
+real	der[ARB]	# derivatives, der[1] is value der[2] is f prime 
+int	nder		# number items returned = 1 + number of derivatives
+
+int	nearx, i, j, k, nterms, nd
+pointer	c0ptr, n0
+real	deltax, accum, tmpx[2], pcoeff[MAX_NDERIVS], diff[MAX_NDERIVS]
+
+begin
+	# Return zero for derivatives that are zero.
+	do i = 1, nder
+	    der[i] = 0.
+
+	# Nterms is number of terms in case polynomial type.
+	nterms = 0
+
+	# (c0ptr + 1) is the pointer to the first data point in COEFF.
+	c0ptr = ASI_COEFF(asi) - 1 + ASI_OFFSET(asi)
+
+	switch (ASI_TYPE(asi))	{
+
+	case II_NEAREST:
+	    der[1] = COEFF(c0ptr + int(x[1] + 0.5))
+	    return
+
+	case II_LINEAR:
+	    nearx = x[1]
+	    der[1] = (x[1] - nearx) * COEFF(c0ptr + nearx + 1) +
+		     (nearx + 1 - x[1]) * COEFF(c0ptr + nearx)
+	    if (nder > 1)
+		der[2] = COEFF(c0ptr + nearx + 1) - COEFF(c0ptr + nearx)
+	    return
+
+	case II_SINC, II_LSINC:
+	    call ii_sincder (x[1], der, nder,
+		COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)), ASI_NCOEFF(asi),
+		ASI_NSINC(asi), DX)
+	    return
+
+	case II_DRIZZLE:
+	    if (ASI_PIXFRAC(asi) >= 1.0)
+	        call ii_driz1 (x, der[1], 1, COEFF(ASI_COEFF(asi) +
+	            ASI_OFFSET(asi)), ASI_BADVAL(asi))
+	    else
+	        call ii_driz (x, der[1], 1, COEFF(ASI_COEFF(asi) +
+	            ASI_OFFSET(asi)), ASI_PIXFRAC(asi), ASI_BADVAL(asi))
+	    if (nder > 1) {
+		deltax = x[2] - x[1]
+		if (deltax == 0.0)
+		    der[2] = 0.0
+		else {
+		    tmpx[1] = x[1]
+		    tmpx[2] = (x[1] + x[2]) / 2.0
+	    	    if (ASI_PIXFRAC(asi) >= 1.0)
+	                call ii_driz1 (tmpx, accum, 1, COEFF(ASI_COEFF(asi) +
+	                    ASI_OFFSET(asi)), ASI_BADVAL(asi))
+		    else
+	                call ii_driz (tmpx, accum, 1, COEFF(ASI_COEFF(asi) +
+	                    ASI_OFFSET(asi)), ASI_PIXFRAC(asi), ASI_BADVAL(asi))
+		    tmpx[1] = tmpx[2]
+		    tmpx[2] = x[2]
+	    	    if (ASI_PIXFRAC(asi) >= 1.0)
+	                call ii_driz1 (tmpx, der[2], 1, COEFF(ASI_COEFF(asi) +
+	                    ASI_OFFSET(asi)), ASI_BADVAL(asi))
+		    else
+	                call ii_driz (tmpx, der[2], 1, COEFF(ASI_COEFF(asi) +
+	                    ASI_OFFSET(asi)), ASI_PIXFRAC(asi), ASI_BADVAL(asi))
+		    der[2] = 2.0 * (der[2] - accum) / deltax
+		}
+	    }
+	    return
+
+	case II_POLY3:
+	    nterms = 4
+
+	case II_POLY5:
+	    nterms = 6
+
+	case II_SPLINE3:
+	    nterms = 4
+
+	default:
+	    call error (0, "ASIDER: Unknown interpolant type")
+	}
+
+	# Routines falls through to this point if the interpolant is one of
+	# the higher order polynomial types or a third order spline.
+
+	nearx = x[1]
+	n0 = c0ptr + nearx
+	deltax = x[1] - nearx
+
+	# Compute the number of derivatives needed.
+	nd = nder
+	if (nder > nterms)
+	    nd = nterms
+
+	# Generate the polynomial coefficients.
+
+	if (ASI_TYPE(asi) == II_SPLINE3) {
+
+	    pcoeff[1] = COEFF(n0-1) + 4. * COEFF(n0) + COEFF(n0+1)
+	    pcoeff[2] = 3. * (COEFF(n0+1) - COEFF(n0-1))
+	    pcoeff[3] = 3. * (COEFF(n0-1) - 2. * COEFF(n0) + COEFF(n0+1))
+	    pcoeff[4] = -COEFF(n0-1) + 3. * COEFF(n0) - 3. * COEFF(n0+1) +
+				    COEFF(n0+2)
+
+	# Newton's form written in line to get polynomial from data
+	} else {
+
+	    # Load data.
+	    do i = 1, nterms
+		diff[i] = COEFF(n0 - nterms/2 + i)
+
+	    # Generate difference table.
+	    do k = 1, nterms - 1
+		do i = 1, nterms - k
+		    diff[i] = (diff[i+1] - diff[i]) / k
+
+	    # Shift to generate polynomial coefficients.
+	    do k = nterms, 2, -1
+		do i = 2,k
+		    diff[i] = diff[i] + diff[i-1] * (k - i - nterms/2)
+	    do i = 1,nterms
+		pcoeff[i] = diff[nterms + 1 - i]
+	}
+
+	# Compute the derivatives. As the loop progresses pcoeff contains
+	# coefficients of higher and higher derivatives.
+
+	do k = 1, nd {
+
+	    # Evaluate using nested multiplication.
+	    accum = pcoeff[nterms - k + 1]
+	    do j = nterms - k, 1, -1
+		accum = pcoeff[j] + deltax * accum
+	    der[k] = accum
+
+	    # Differentiate polynomial.
+	    do j = 1, nterms - k
+		pcoeff[j] = j * pcoeff[j + 1]
+	}
+end
diff --git a/math/iminterp/asieval.x b/math/iminterp/asieval.x
new file mode 100644
index 00000000..51f9a63b
--- /dev/null
+++ b/math/iminterp/asieval.x
@@ -0,0 +1,67 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/iminterp.h>
+include "im1interpdef.h"
+
+# ASIEVAL -- This procedure finds the interpolated value assuming that
+# x lands in the array, i.e. 1 <= x <= npts.
+
+real procedure asieval (asi, x)
+
+pointer	asi		# interpolator descriptor
+real x[ARB]		# x value
+
+real value
+
+begin
+	switch (ASI_TYPE(asi))	{	# switch on interpolator type
+	
+	case II_NEAREST:
+	    call ii_nearest (x, value, 1,
+	    		    COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)))
+	    return (value)
+
+	case II_LINEAR:
+	    call ii_linear (x, value, 1,
+	    		   COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)))
+	    return (value)
+
+	case II_POLY3:
+	    call ii_poly3 (x, value, 1, COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)))
+	    return (value)
+
+	case II_POLY5:
+	    call ii_poly5 (x, value, 1, COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)))
+	    return (value)
+
+	case II_SPLINE3:
+	    call ii_spline3 (x, value, 1,
+	    		    COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)))
+	    return (value)
+
+	case II_SINC:
+	    call ii_sinc (x, value, 1,
+		COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)), ASI_NCOEFF(asi),
+		ASI_NSINC(asi), DX)
+	    return (value)
+	
+	case II_LSINC:
+	    call ii_lsinc (x, value, 1,
+		COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)), ASI_NCOEFF(asi),
+		LTABLE(ASI_LTABLE(asi)), 2 * ASI_NSINC(asi) + 1,
+		ASI_NINCR(asi), DX)
+	    return (value)
+
+	case II_DRIZZLE:
+	    if (ASI_PIXFRAC(asi) >= 1.0)
+	        call ii_driz1 (x, value, 1, COEFF(ASI_COEFF(asi) +
+		    ASI_OFFSET(asi)), ASI_BADVAL(asi))
+	    else
+	        call ii_driz (x, value, 1, COEFF(ASI_COEFF(asi) +
+		    ASI_OFFSET(asi)), ASI_PIXFRAC(asi), ASI_BADVAL(asi))
+	    return (value)
+
+	default:
+	    call error (0, "ASIEVAL: Unknown interpolator type.")
+	}
+end
diff --git a/math/iminterp/asifit.x b/math/iminterp/asifit.x
new file mode 100644
index 00000000..3ea33041
--- /dev/null
+++ b/math/iminterp/asifit.x
@@ -0,0 +1,146 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/iminterp.h>
+include "im1interpdef.h"
+
+define	TEMP	Memr[P2P($1)]
+
+# ASIFIT -- Fit the interpolant to the data.
+
+procedure asifit (asi, datain, npix)
+
+pointer	asi		# interpolant descriptor
+real	datain[ARB]	# data array
+int	npix		# nunber of data points
+
+int	i
+pointer	c0ptr, cdataptr, cnptr, temp
+
+begin
+	# Check the data array for size and allocate space for the coefficient
+	# array.
+
+	switch (ASI_TYPE(asi)) {
+
+	case II_SPLINE3:
+	    if (npix < 4)
+		call error (0, "ASIFIT: too few points for SPLINE3")
+	    else {
+		ASI_NCOEFF(asi) = npix + 3
+		ASI_OFFSET(asi) = 1
+		if (ASI_COEFF(asi) != NULL)
+		    call mfree (ASI_COEFF(asi), TY_REAL)
+		call malloc (ASI_COEFF(asi), ASI_NCOEFF(asi), TY_REAL)
+		call malloc (temp, ASI_NCOEFF(asi), TY_REAL)
+	    }
+
+	case II_POLY5:
+	    if (npix < 6)
+		call error (0,"ASIFIT: too few points for POLY5")
+	    else {
+		ASI_NCOEFF(asi) = npix + 5
+		ASI_OFFSET(asi) = 2
+		if (ASI_COEFF(asi) != NULL)
+		    call mfree (ASI_COEFF(asi), TY_REAL)
+		call malloc (ASI_COEFF(asi), ASI_NCOEFF(asi), TY_REAL)
+	    }
+
+	case II_POLY3:
+	    if (npix < 4)
+		call error (0, "ASIFIT: too few points for POLY3")
+	    else {
+		ASI_NCOEFF(asi) = npix + 3
+		ASI_OFFSET(asi) = 1
+		if (ASI_COEFF(asi) != NULL)
+		    call mfree (ASI_COEFF(asi), TY_REAL)
+		call malloc (ASI_COEFF(asi), ASI_NCOEFF(asi), TY_REAL)
+	    }
+
+	case II_DRIZZLE, II_LINEAR:
+	    if (npix < 2)
+		call error (0, "ASIFIT: too few points for LINEAR")
+	    else {
+		ASI_NCOEFF(asi) = npix + 1
+		ASI_OFFSET(asi) = 0
+		if (ASI_COEFF(asi) != NULL)
+		    call mfree (ASI_COEFF(asi), TY_REAL)
+	        call malloc (ASI_COEFF(asi), ASI_NCOEFF(asi), TY_REAL)
+	    }
+
+	case II_SINC, II_LSINC:
+	    if (npix < 1)
+		call error (0, "ASIFIT: too few points for SINC")
+	    else {
+		ASI_NCOEFF(asi) = npix
+		ASI_OFFSET(asi) = 0
+		if (ASI_COEFF(asi) != NULL)
+		    call mfree (ASI_COEFF(asi), TY_REAL)
+	        call malloc (ASI_COEFF(asi), ASI_NCOEFF(asi), TY_REAL)
+	    }
+
+	default:
+	    if (npix < 1)
+		call error (0," ASIFIT: too few points for NEAREST")
+	    else {
+		ASI_NCOEFF(asi) = npix
+		ASI_OFFSET(asi) = 0
+		if (ASI_COEFF(asi) != NULL)
+		    call mfree (ASI_COEFF(asi), TY_REAL)
+		call malloc (ASI_COEFF(asi), ASI_NCOEFF(asi), TY_REAL)
+	    }
+
+	}
+
+
+	# Define the pointers.
+	# (c0ptr + 1) points to first element in the coefficient array.
+	# (cdataptr + 1) points to first data element in the coefficient array.
+	# (cnptr + 1) points to the first element after the last data point in
+	# coefficient array.
+
+	c0ptr = ASI_COEFF(asi) - 1
+	cdataptr = ASI_COEFF(asi) - 1 + ASI_OFFSET(asi)
+	cnptr = cdataptr + npix
+
+	# Put data into the interpolant structure.
+	do i = 1, npix 
+	    COEFF(cdataptr + i) = datain[i]
+
+	# Specify the end conditions.
+	switch (ASI_TYPE(asi)) {
+
+	case II_SPLINE3:
+	    # Natural end conditions - second deriv. zero
+	    COEFF(c0ptr + 1) = 0.
+	    COEFF(cnptr + 1) = 0.
+	    COEFF(cnptr + 2) = 0.	# if x = npts
+
+	    # Fit spline - generate b-spline coefficients.
+	    call ii_spline (COEFF(ASI_COEFF(asi)), TEMP(temp), npix)
+	    call mfree (temp, TY_REAL)
+
+	case II_NEAREST, II_SINC, II_LSINC:
+	    # No end conditions required.
+
+	case II_LINEAR, II_DRIZZLE:
+	    COEFF(cnptr + 1) = 2. * COEFF(cdataptr + npix) -	# if x = npts
+	    		       COEFF(cdataptr + npix - 1)
+
+	case II_POLY3:
+	    COEFF(c0ptr + 1) = 2. * COEFF(cdataptr + 1) - COEFF(cdataptr + 2) 
+	    COEFF(cnptr + 1) = 2. * COEFF(cdataptr + npix) -
+	    		       COEFF(cdataptr + npix - 1)
+	    COEFF(cnptr + 2) = 2. * COEFF(cdataptr + npix) -
+	    		       COEFF(cdataptr + npix - 2) 
+
+	case II_POLY5:
+	    COEFF(c0ptr + 1) = 2. * COEFF(cdataptr + 1) - COEFF(cdataptr + 3)
+	    COEFF(c0ptr + 2) = 2. * COEFF(cdataptr + 1) - COEFF(cdataptr + 2)
+	    COEFF(cnptr + 1) = 2. * COEFF(cdataptr + npix) -
+	    		       COEFF(cdataptr + npix - 1)
+	    COEFF(cnptr + 2) = 2. * COEFF(cdataptr + npix) -
+	    		       COEFF(cdataptr + npix - 2)
+	    COEFF(cnptr + 3) = 2. * COEFF(cdataptr + npix) -
+	    		       COEFF(cdataptr + npix - 3)
+	}
+end
diff --git a/math/iminterp/asifree.x b/math/iminterp/asifree.x
new file mode 100644
index 00000000..2feda49b
--- /dev/null
+++ b/math/iminterp/asifree.x
@@ -0,0 +1,17 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im1interpdef.h"
+
+# ASIFREE -- Procedure to deallocate sequential interpolant structure
+
+procedure asifree (asi)
+
+pointer	asi	# interpolant descriptor
+
+begin
+	if (ASI_COEFF(asi) != NULL)
+	    call mfree (ASI_COEFF(asi), TY_REAL)
+	if (ASI_LTABLE(asi) != NULL)
+	    call mfree (ASI_LTABLE(asi), TY_REAL)
+	call mfree (asi, TY_STRUCT)
+end
diff --git a/math/iminterp/asigeti.x b/math/iminterp/asigeti.x
new file mode 100644
index 00000000..fbf1ddc1
--- /dev/null
+++ b/math/iminterp/asigeti.x
@@ -0,0 +1,25 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im1interpdef.h"
+include <math/iminterp.h>
+
+# ASIGETI -- Procedure to fetch an asi integer parameter
+
+int procedure asigeti (asi, param)
+
+pointer	asi		# interpolant descriptor
+int	param		# parameter to be fetched
+
+begin
+	switch (param) {
+	case II_ASITYPE:
+	    return (ASI_TYPE(asi))
+	case II_ASINSAVE:
+	    return (ASI_NSINC(asi) * ASI_NINCR(asi) + ASI_NCOEFF(asi) +
+	        ASI_SAVECOEFF)
+	case II_ASINSINC:
+	    return (ASI_NSINC(asi))
+	default:
+	    call error (0, "ASIGETI: Unknown ASI parameter.")
+	}
+end
diff --git a/math/iminterp/asigetr.x b/math/iminterp/asigetr.x
new file mode 100644
index 00000000..57cdd07f
--- /dev/null
+++ b/math/iminterp/asigetr.x
@@ -0,0 +1,20 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im1interpdef.h"
+include <math/iminterp.h>
+
+# ASIGETR -- Procedure to fetch an msi real parameter
+
+real procedure asigetr (asi, param)
+
+pointer	asi		# interpolant descriptor
+int	param		# parameter to be fetched
+
+begin
+	switch (param) {
+	case II_ASIBADVAL:
+	    return (ASI_BADVAL(asi))
+	default:
+	    call error (0, "ASIGETR: Unknown ASI parameter.")
+	}
+end
diff --git a/math/iminterp/asigrl.x b/math/iminterp/asigrl.x
new file mode 100644
index 00000000..55f2395f
--- /dev/null
+++ b/math/iminterp/asigrl.x
@@ -0,0 +1,194 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/iminterp.h>
+include "im1interpdef.h"
+
+# ASIGRL -- Procedure to find the integral of the interpolant from a to
+# b be assuming that both a and b land in the array.
+
+real procedure asigrl (asi, a, b)
+
+pointer	asi		# interpolant descriptor
+real	a		# lower limit for integral
+real	b		# upper limit for integral
+
+int	neara, nearb, i, j, nterms, index
+real	deltaxa, deltaxb, accum, xa, xb, pcoeff[MAX_NDERIVS]
+pointer	c0ptr, n0ptr
+
+begin
+	# Flip order and sign at end.
+	xa = a
+	xb = b
+	if (a > b) {
+	    xa = b
+	    xb = a
+	}
+
+	# Initialize.
+	c0ptr = ASI_COEFF(asi) - 1 + ASI_OFFSET(asi)
+	neara = xa
+	nearb = xb
+	accum = 0.
+
+	switch (ASI_TYPE(asi)) {
+	case II_NEAREST, II_SINC, II_LSINC, II_DRIZZLE:
+	    nterms = 0
+	case II_LINEAR:
+	    nterms = 1
+	case II_POLY3:
+	    nterms = 4
+	case II_POLY5:
+	    nterms = 6
+	case II_SPLINE3:
+	    nterms = 4
+	}
+
+	# NEAREST_NEIGHBOR, LINEAR, SINC and LSINC are handled differently
+	# because of storage.  Also probably good for speed in the case of
+	# LINEAR and NEAREST_NEIGHBOUR.
+
+	# NEAREST_NEIGHBOR
+	switch (ASI_TYPE(asi)) {
+	case II_NEAREST:
+
+	    # Reset segment to center values.
+	    neara = xa + 0.5
+	    nearb = xb + 0.5
+
+	    # Set up for first segment.
+	    deltaxa = xa - neara
+
+	    # For clarity one segment case is handled separately.
+
+	    # Only one segment involved.
+	    if (nearb == neara) {
+		deltaxb = xb - nearb
+		n0ptr = c0ptr + neara
+		accum = accum + (deltaxb - deltaxa) * COEFF(n0ptr)
+
+	    # More than one segment.
+	    } else {
+
+		# First segment.
+		n0ptr = c0ptr + neara
+		accum = accum + (0.5 - deltaxa) * COEFF(n0ptr)
+
+		# Middle segment.
+		do j = neara + 1, nearb - 1 {
+		    n0ptr = c0ptr + j
+		    accum = accum + COEFF(n0ptr)
+		}
+
+		# Last segment.
+		n0ptr = c0ptr + nearb
+		deltaxb = xb - nearb
+		accum = accum + (deltaxb + 0.5) * COEFF(n0ptr)
+	    }
+
+	# LINEAR
+	case II_LINEAR:
+
+	    # Set up for first segment.
+	    deltaxa = xa - neara
+
+	    # For clarity one segment case is handled separately.
+
+	    # Only one segment is involved.
+	    if (nearb == neara) {
+		deltaxb = xb - nearb
+		n0ptr = c0ptr + neara
+		accum = accum + (deltaxb - deltaxa) * COEFF(n0ptr) +
+		     0.5 * (COEFF(n0ptr+1) - COEFF(n0ptr)) *
+		     (deltaxb * deltaxb - deltaxa * deltaxa)
+
+	    # More than one segment.
+	    } else {
+
+		# First segment.
+		n0ptr = c0ptr + neara
+		accum = accum + (1. - deltaxa) * COEFF(n0ptr) +
+		     0.5 * (COEFF(n0ptr+1) - COEFF(n0ptr)) *
+		     (1. - deltaxa * deltaxa)
+
+		# Middle segment.
+		do j = neara + 1, nearb - 1 {
+		    n0ptr = c0ptr + j
+		    accum = accum + 0.5 * (COEFF(n0ptr+1) + COEFF(n0ptr))
+		}
+
+		# Last segment.
+		n0ptr = c0ptr + nearb
+		deltaxb = xb - nearb
+		accum = accum + COEFF(n0ptr) * deltaxb + 0.5 *
+			(COEFF(n0ptr+1) - COEFF(n0ptr)) * deltaxb * deltaxb
+	    }
+
+	# SINC
+	case II_SINC, II_LSINC:
+	    call ii_sincigrl (xa, xb, accum, COEFF(ASI_COEFF(asi) +
+	        ASI_OFFSET(asi)), ASI_NCOEFF(asi), ASI_NSINC(asi), DX)
+
+	# DRIZZLE
+	case II_DRIZZLE:
+	    if (ASI_PIXFRAC(asi) >= 1.0)
+	        call ii_dzigrl1 (xa, xb, accum, COEFF(ASI_COEFF(asi) +
+	            ASI_OFFSET(asi)))
+	    else
+	        call ii_dzigrl (xa, xb, accum, COEFF(ASI_COEFF(asi) +
+	            ASI_OFFSET(asi)), ASI_PIXFRAC(asi))
+
+	# A higher order interpolant.
+	default:
+
+	    # Set up for first segment.
+	    deltaxa = xa - neara
+
+	    # For clarity one segment case is handled separately.
+
+	    # Only one segment involved.
+	    if (nearb == neara) {
+
+		deltaxb = xb - nearb
+		n0ptr = c0ptr + neara
+		index = ASI_OFFSET(asi) + neara
+		call ii_getpcoeff (COEFF(ASI_COEFF(asi)), index, pcoeff,
+				  ASI_TYPE(asi))
+		do i = 1, nterms
+		    accum = accum + (1./i) * pcoeff[i] *
+		    	    (deltaxb ** i - deltaxa ** i)
+
+	    # More than one segment.
+	    } else {
+
+		# First segment.
+		index = ASI_OFFSET(asi) + neara
+		call ii_getpcoeff (COEFF(ASI_COEFF(asi)), index, pcoeff,
+				  ASI_TYPE(asi))
+		do i = 1, nterms
+		    accum = accum + (1./i) * pcoeff[i] * (1. - deltaxa ** i)
+
+		# Middle segment.
+		do j = neara + 1, nearb - 1 {
+		    index = ASI_OFFSET(asi) + j
+		    call ii_getpcoeff (COEFF(ASI_COEFF(asi)),
+		    		      index, pcoeff, ASI_TYPE(asi))
+		    do i = 1, nterms
+			accum = accum + (1./i) * pcoeff[i]
+		}
+
+		# Last segment.
+		index = ASI_OFFSET(asi) + nearb
+		deltaxb = xb - nearb
+		call ii_getpcoeff (COEFF(ASI_COEFF(asi)), index, pcoeff,
+				   ASI_TYPE(asi))
+		do i = 1, nterms
+		    accum = accum + (1./i) * pcoeff[i] * deltaxb ** i
+	    }
+	}
+
+	if (a < b)
+	    return (accum)
+	else
+	    return (-accum)
+end
diff --git a/math/iminterp/asiinit.x b/math/iminterp/asiinit.x
new file mode 100644
index 00000000..daf99665
--- /dev/null
+++ b/math/iminterp/asiinit.x
@@ -0,0 +1,57 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/iminterp.h>
+include "im1interpdef.h"
+
+# ASIINIT -- initialize the array sequential interpolant structure
+
+procedure asiinit (asi, interp_type)
+
+pointer	asi		# interpolant descriptor
+int	interp_type	# interpolant type
+
+int	nconv
+
+begin
+	if (interp_type < 1 || interp_type > II_NTYPES)
+	    call error (0,"ASIINIT: Illegal interpolant type.")
+	else {
+	    call calloc (asi, LEN_ASISTRUCT, TY_STRUCT)
+	    ASI_TYPE(asi) = interp_type
+	    switch (interp_type) {
+	    case II_LSINC:
+	        ASI_NSINC(asi) = NSINC
+		ASI_NINCR(asi) = NINCR
+		if (ASI_NINCR(asi) > 1)
+		    ASI_NINCR(asi) = ASI_NINCR(asi) + 1
+		ASI_SHIFT(asi) = INDEFR
+		ASI_PIXFRAC(asi) = PIXFRAC
+		nconv = 2 * ASI_NSINC(asi) + 1
+		call calloc (ASI_LTABLE(asi), nconv * ASI_NINCR(asi),
+		    TY_REAL)
+		call ii_sinctable (Memr[ASI_LTABLE(asi)], nconv, ASI_NINCR(asi),
+		    ASI_SHIFT(asi))
+	    case II_SINC:
+	        ASI_NSINC(asi) = NSINC
+		ASI_NINCR(asi) = 0
+		ASI_SHIFT(asi) = INDEFR
+		ASI_PIXFRAC(asi) = PIXFRAC
+	        ASI_LTABLE(asi) = NULL
+	    case II_DRIZZLE:
+	        ASI_NSINC(asi) = 0
+		ASI_NINCR(asi) = 0
+		ASI_SHIFT(asi) = INDEFR
+		ASI_PIXFRAC(asi) = PIXFRAC
+	        ASI_LTABLE(asi) = NULL
+	    default:
+	        ASI_NSINC(asi) = 0
+		ASI_NINCR(asi) = 0
+		ASI_SHIFT(asi) = INDEFR
+		ASI_PIXFRAC(asi) = PIXFRAC
+	        ASI_LTABLE(asi) = NULL
+	    }
+	    ASI_BADVAL(asi) = BADVAL
+	    ASI_COEFF(asi) = NULL
+	}
+
+end
diff --git a/math/iminterp/asirestore.x b/math/iminterp/asirestore.x
new file mode 100644
index 00000000..7c6c81d0
--- /dev/null
+++ b/math/iminterp/asirestore.x
@@ -0,0 +1,50 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im1interpdef.h"
+include	<math/iminterp.h>
+
+# ASIRESTORE -- Procedure to restore the interpolant stored by ASISAVE
+# for use by ASIEVAL, ASIVECTOR, ASIDER and ASIGRL.
+
+procedure asirestore (asi, interpolant)
+
+pointer	asi			# interpolant descriptor
+real	interpolant[ARB]	# array containing the interpolant
+
+int	interp_type, i, nconv
+pointer	cptr
+
+begin
+	interp_type = int (ASI_SAVETYPE(interpolant))
+	if (interp_type < 1 || interp_type > II_NTYPES)
+	    call error (0, "ASIRESTORE: Unknown interpolant type.")
+
+	# Allocate the interpolant descriptor structure and restore
+	# interpolant parameters.
+
+	call malloc (asi, LEN_ASISTRUCT, TY_STRUCT)
+	ASI_TYPE(asi) = interp_type
+	ASI_NSINC(asi) = nint (ASI_SAVENSINC(interpolant))
+	ASI_NINCR(asi) = nint (ASI_SAVENINCR(interpolant))
+	ASI_SHIFT(asi) = ASI_SAVESHIFT(interpolant)
+	ASI_PIXFRAC(asi) = ASI_SAVEPIXFRAC(interpolant)
+	ASI_NCOEFF(asi) = nint (ASI_SAVENCOEFF(interpolant))
+	ASI_OFFSET(asi) = nint (ASI_SAVEOFFSET(interpolant))
+	ASI_BADVAL(asi) = ASI_SAVEBADVAL(interpolant)
+
+	# Allocate space for and restore coefficients.
+	call malloc (ASI_COEFF(asi), ASI_NCOEFF(asi), TY_REAL)
+	cptr = ASI_COEFF(asi) - 1
+	do i = 1, ASI_NCOEFF(asi)
+	    COEFF(cptr+i) = interpolant[ASI_SAVECOEFF+i] 
+
+	# Allocate space for and restore the look-up tables.
+	if (ASI_NINCR(asi) > 0) {
+	    nconv = 2 * ASI_NSINC(asi) + 1
+	    call malloc (ASI_LTABLE(asi), nconv * ASI_NINCR(asi), TY_REAL)
+	    cptr = ASI_LTABLE(asi) - 1
+	    do i = 1, nconv * ASI_NINCR(asi)
+	        LTABLE(cptr+i) = interpolant[ASI_SAVECOEFF+ASI_NCOEFF(asi)+i] 
+	} else
+	    ASI_LTABLE(asi) = NULL
+end
diff --git a/math/iminterp/asisave.x b/math/iminterp/asisave.x
new file mode 100644
index 00000000..6d6d83db
--- /dev/null
+++ b/math/iminterp/asisave.x
@@ -0,0 +1,42 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im1interpdef.h"
+include <math/iminterp.h>
+
+# ASISAVE -- Procedure to save the interpolant for later use by ASIEVAL,
+# ASIVECTOR, ASIDER and ASIGRL.
+
+procedure asisave (asi, interpolant)
+
+pointer	asi			# interpolant descriptor
+real	interpolant[ARB]	# array containing the interpolant
+
+int	i, nconv
+pointer	cptr
+
+begin
+	# Save the interpolant type, number of coefficients, and position of
+	# first data point.
+
+	ASI_SAVETYPE(interpolant) = ASI_TYPE(asi)
+	ASI_SAVENSINC(interpolant) = ASI_NSINC(asi)
+	ASI_SAVENINCR(interpolant) = ASI_NINCR(asi)
+	ASI_SAVESHIFT(interpolant) = ASI_SHIFT(asi)
+	ASI_SAVEPIXFRAC(interpolant) = ASI_PIXFRAC(asi)
+	ASI_SAVENCOEFF(interpolant) = ASI_NCOEFF(asi)
+	ASI_SAVEOFFSET(interpolant) = ASI_OFFSET(asi)
+	ASI_SAVEBADVAL(interpolant) = ASI_BADVAL(asi)
+
+	# Save the coefficients.
+	cptr = ASI_COEFF(asi) - 1
+	do i = 1, ASI_NCOEFF(asi)
+	    interpolant[ASI_SAVECOEFF+i] = COEFF(cptr+i)
+
+	# Save the lookup-tables.
+	if (ASI_NINCR(asi) > 0) {
+	    nconv = 2 * ASI_NSINC(asi) + 1
+	    cptr = ASI_LTABLE(asi) - 1
+	    do i = 1, nconv * ASI_NINCR(asi)
+		interpolant[ASI_SAVECOEFF+ASI_NCOEFF(asi)+i] = LTABLE(cptr+i)
+	}
+end
diff --git a/math/iminterp/asisinit.x b/math/iminterp/asisinit.x
new file mode 100644
index 00000000..dc09ac0e
--- /dev/null
+++ b/math/iminterp/asisinit.x
@@ -0,0 +1,64 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/iminterp.h>
+include "im1interpdef.h"
+
+# ASISINIT -- initialize the interpolant. This is a special entry point
+# for the sinc interpolant although it will initialize the others too.
+
+procedure asisinit (asi, interp_type, nsinc, nincr, shift, badval)
+
+pointer	asi			# interpolant descriptor
+int	interp_type		# interpolant type
+int	nsinc			# sinc interpolant width
+int	nincr			# number of sinc look-up table elements
+real	shift			# sinc interpolant shift
+real	badval			# drizzle bad pixel value
+
+int	nconv
+
+begin
+	if (interp_type < 1 || interp_type > II_NTYPES)
+	    call error (0, "ASISINIT: Illegal interpolant type")
+	else {
+	    call calloc (asi, LEN_ASISTRUCT, TY_STRUCT)
+	    ASI_TYPE(asi) = interp_type
+	    switch (interp_type) {
+	    case II_LSINC:
+		ASI_NSINC(asi) = (nsinc - 1) / 2
+	        ASI_NINCR(asi) = nincr
+		if (ASI_NINCR(asi) > 1)
+		    ASI_NINCR(asi) = ASI_NINCR(asi) + 1
+		if (nincr > 1)
+		    ASI_SHIFT(asi) = INDEFR
+		else
+		    ASI_SHIFT(asi) = shift
+		ASI_PIXFRAC(asi) = PIXFRAC
+		nconv = 2 * ASI_NSINC(asi) + 1
+		call calloc (ASI_LTABLE(asi), nconv * ASI_NINCR(asi),
+		    TY_REAL)
+		call ii_sinctable (Memr[ASI_LTABLE(asi)], nconv, ASI_NINCR(asi),
+		    ASI_SHIFT(asi))
+	    case II_SINC:
+		ASI_NSINC(asi) = (nsinc - 1) / 2
+	        ASI_NINCR(asi) = 0
+		ASI_SHIFT(asi) = INDEFR
+		ASI_PIXFRAC(asi) = PIXFRAC
+		ASI_LTABLE(asi) = NULL
+	    case II_DRIZZLE:
+		ASI_NSINC(asi) = 0
+	        ASI_NINCR(asi) = 0
+		ASI_SHIFT(asi) = INDEFR
+		ASI_PIXFRAC(asi) = max (MIN_PIXFRAC, min (shift, 1.0))
+		ASI_LTABLE(asi) = NULL
+	    default:
+		ASI_NSINC(asi) = 0
+	        ASI_NINCR(asi) = 0
+		ASI_SHIFT(asi) = INDEFR
+		ASI_PIXFRAC(asi) = PIXFRAC
+		ASI_LTABLE(asi) = NULL
+	    }
+	    ASI_COEFF(asi) = NULL
+	    ASI_BADVAL(asi) = badval
+	}
+end
diff --git a/math/iminterp/asitype.x b/math/iminterp/asitype.x
new file mode 100644
index 00000000..708ebf58
--- /dev/null
+++ b/math/iminterp/asitype.x
@@ -0,0 +1,90 @@
+include "im1interpdef.h"
+include <math/iminterp.h>
+
+# ASITYPE -- Decode the interpolation string input by the user.
+
+procedure asitype (interpstr, interp_type, nsinc, nincr, shift)
+
+char	interpstr[ARB]			# the input interpolation string
+int	interp_type			# the interpolation type
+int	nsinc				# the sinc interpolation width
+int	nincr				# the sinc interpolation lut resolution
+real	shift				# the predefined shift or pixfrac
+
+int	ip
+pointer	sp, str
+int	strdic(), strncmp(), ctoi(), ctor()
+
+begin
+	call smark (sp)
+	call salloc (str, SZ_FNAME, TY_CHAR)
+	interp_type = strdic (interpstr, Memc[str], SZ_FNAME, II_FUNCTIONS)
+
+	if (interp_type > 0) {
+	    switch (interp_type) {
+	    case II_LSINC:
+		nsinc = 2 * NSINC + 1
+		nincr = NINCR
+		shift = INDEFR
+	    case II_SINC:
+		nsinc = 2 * NSINC + 1
+		nincr = 0
+		shift = INDEFR
+	    case II_DRIZZLE:
+		nsinc = 0
+		nincr = 0
+		shift = PIXFRAC
+	    default:
+		nsinc = 0
+		nincr = 0
+		shift = INDEFR
+	    }
+	} else if (strncmp (interpstr, "lsinc", 5) == 0) {
+	    interp_type = II_LSINC
+	    ip = 6
+	    if (ctoi (interpstr, ip, nsinc) <= 0) {
+		nsinc = 2 * NSINC + 1
+		nincr = NINCR
+		shift = INDEFR
+	    } else {
+	        if (interpstr[ip] == '[')
+		    ip = ip + 1
+		if (ctor (interpstr, ip, shift) <= 0)
+		    shift = INDEFR
+		if (IS_INDEFR(shift) || interpstr[ip] != ']') {
+		    nincr = NINCR
+		    shift = INDEFR
+		} else if (shift >= -0.5 && shift < 0.5) {
+		    nincr = 1
+		} else {
+		    nincr = nint (shift)
+		    shift = INDEFR
+		}
+	    }
+	} else if (strncmp (interpstr, "sinc", 4) == 0) {
+	    ip = 5
+	    interp_type = II_SINC
+	    if (ctoi (interpstr, ip, nsinc) <= 0)
+		nsinc = 2 * NSINC + 1
+	    nincr = 0
+	    shift = INDEFR
+	} else if (strncmp (interpstr, "drizzle", 7) == 0) {
+	    ip = 8
+	    if (interpstr[ip] == '[')
+	        ip = ip + 1
+	    if (ctor (interpstr, ip, shift) <= 0)
+		shift = PIXFRAC
+	    interp_type = II_DRIZZLE
+	    nsinc = 0
+	    nincr = 0
+	    if (interpstr[ip] != ']')
+		shift = PIXFRAC
+	} else {
+	    interp_type = 0
+	    nsinc = 0
+	    nincr = 0
+	    shift = INDEFR
+	}
+
+	call sfree (sp)
+end
diff --git a/math/iminterp/asivector.x b/math/iminterp/asivector.x
new file mode 100644
index 00000000..153a751a
--- /dev/null
+++ b/math/iminterp/asivector.x
@@ -0,0 +1,56 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/iminterp.h>
+include "im1interpdef.h"
+
+# ASIVECTOR -- Procedure to evaluate the interpolant at an array of ordered
+# points assuming that all points land in 1 <= x <= npts.
+
+procedure asivector (asi, x, y, npix)
+
+pointer	asi		# interpolator descriptor
+real	x[ARB]		# ordered x array
+real	y[ARB]		# interpolated values
+int	npix		# number of points in x
+
+begin
+	switch (ASI_TYPE(asi))	{
+
+	case II_NEAREST:
+	    call ii_nearest (x, y, npix,
+	        COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)))
+
+	case II_LINEAR:
+	    call ii_linear (x, y, npix, COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)))
+
+	case II_POLY3:
+	    call ii_poly3 (x, y, npix, COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)))
+
+	case II_POLY5:
+	    call ii_poly5 (x, y, npix, COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)))
+
+	case II_SPLINE3:
+	    call ii_spline3 (x, y, npix, COEFF(ASI_COEFF(asi) +
+	        ASI_OFFSET(asi)))
+
+	case II_SINC:
+	    call ii_sinc (x, y, npix, COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)),
+	        ASI_NCOEFF(asi), ASI_NSINC(asi), DX)
+
+	case II_LSINC:
+	    call ii_lsinc (x, y, npix, COEFF(ASI_COEFF(asi) + ASI_OFFSET(asi)),
+	        ASI_NCOEFF(asi), LTABLE(ASI_LTABLE(asi)),
+		2 * ASI_NSINC(asi) + 1, ASI_NINCR(asi), DX)
+
+	case II_DRIZZLE:
+	    if (ASI_PIXFRAC(asi) >= 1.0)
+	        call ii_driz1 (x, y, npix, COEFF(ASI_COEFF(asi) +
+		    ASI_OFFSET(asi)), ASI_BADVAL(asi))
+	    else
+	        call ii_driz (x, y, npix, COEFF(ASI_COEFF(asi) +
+		    ASI_OFFSET(asi)), ASI_PIXFRAC(asi), ASI_BADVAL(asi))
+
+	default:
+	    call error (0, "ASIVECTOR: Unknown interpolator type.")
+	}
+end
diff --git a/math/iminterp/doc/arbpix.hlp b/math/iminterp/doc/arbpix.hlp
new file mode 100644
index 00000000..0d7ec9ec
--- /dev/null
+++ b/math/iminterp/doc/arbpix.hlp
@@ -0,0 +1,57 @@
+.help arbpix Dec98 "Image Interpolator Package"
+.ih
+NAME
+arbpix -- replace INDEF valued pixels with interpolated values
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+arbpix (datain, dataout, npix, interp_type, boundary_type)
+
+.nf
+    real	datain[npix]	#I input data
+    real	dataout[npix]	#O output array, dataout != datain
+    int		npix		#I number of data points
+    int		interp_type	#I type of interpolant
+    int		boundary_type	#I type of boundary condition
+.fi
+.ih
+ARGUMENTS
+.ls datain
+Array of input data containing 0 or more INDEF valued pixels.
+.le
+.ls dataout
+Array of output data with INDEFS replaced by interpolated values.
+The dataout array must be different from the datain array.
+.le
+.ls npix   
+Number of data points.
+.le
+.ls interp_type
+Type of interpolant. Options are II_NEAREST, II_LINEAR, II_POLY3, II_POLY5,
+II_SPLINE3, II_SINC / II_LSINC, and II_DRIZZLE. The look-up table sinc
+interpolant is not supported,  and defaults to the sinc interpolant.
+The sinc interpolant width is 31 pixels. The drizzle interpolant is not
+supported and defaults to the linear interpolant. The interpolant type
+definitions are stored in the file math/iminterp.h.
+.le
+.ls boundary_type
+Type of boundary extension. The only supported option is II_BOUNDARYEXT.
+Polynomial interpolants of lower order are used if there are not enough
+good pixels to define the requested interpolant. Nearest neighbor boundary
+extension is used if there are not enough good points to define the sinc
+interpolant. The boundary type definitions are stored in the header file
+math/iminterp.h.
+.le
+.ih
+DESCRIPTION
+If there are no good points in datain, ARBPIX returns INDEFS in dataout.
+Points below and above the first and last good point are replaced by the
+first and last good point values respectively.
+.ih
+NOTES
+The sinc function actually evaluates the interpolant by computing the
+average of two interpolations at +-0.05 pixels about the bad pixel since
+the interpolant is undefined exactly at a pixel.
+.ih
+SEE ALSO
diff --git a/math/iminterp/doc/arider.hlp b/math/iminterp/doc/arider.hlp
new file mode 100644
index 00000000..b8631eaa
--- /dev/null
+++ b/math/iminterp/doc/arider.hlp
@@ -0,0 +1,59 @@
+.help arider Dec98 "Image Interpolator Package"
+.ih
+NAME
+arider -- calculate the interpolant derivatives at x
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+arider (x, datain, npix, der, nder, interp_type)
+
+.nf
+    real	x[2]		#I x value, 1 <= x[1-2] <= npts 
+    real	datain[npix]	#I array of data points
+    int		npix		#I number of data points
+    real	der[nder]	#O derivatives, der[1] = function value
+    int		nder		#I number of derivatives, 1 + max order
+    int		interp_type	#I interpolant type
+.fi
+.ih
+ARGUMENTS
+.ls x     
+Single X value, or pair of X values defining a range in the case of the
+drizzle interpolant.
+.le
+.ls datain
+Array of data values.
+.le
+.ls npix  
+Number of data points.
+.le
+.ls der     
+Array of derivatives. Der[1] contains the function value, der[2] the
+first derivative, and so on.
+.le
+.ls nder
+Number of derivatives. ARIDER checks that the requested number of derivatives
+is sensible.  The sinc interpolant returns the function value and the first
+two derivatives. The drizzle interpolant returns the function and the first
+derivative.
+.le
+.ls interp_type
+Interpolant type. The options are II_NEAREST, II_LINEAR, II_POLY3, II_POLY5,
+II_SPLINE3, II_SINC / II_LSINC, and II_DRIZZLE. The look-up table sinc
+is not supported and defaults to sinc. The sinc interpolant width is 31 pixels.
+The drizzle pixel fraction is 1.0. The interpolant type definitions are found
+in the package header file math/iminterp.h.
+.le
+.ih
+DESCRIPTION
+ARIDER permits the evaluation of the interpolant at a few randomly spaced
+points within datain without the storage requirements of the sequential
+version.
+.ih
+NOTES
+Checking for INDEF valued or out of bounds pixels is the responsibility
+of the user.
+.ih
+SEE ALSO
+asider
diff --git a/math/iminterp/doc/arieval.hlp b/math/iminterp/doc/arieval.hlp
new file mode 100644
index 00000000..52c62148
--- /dev/null
+++ b/math/iminterp/doc/arieval.hlp
@@ -0,0 +1,48 @@
+.help arieval Dec98 "Image Interpolator Package"
+.ih
+NAME
+arieval -- evaluate the interpolant at x
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+y = arieval (x, datain, npix, interp_type)
+
+.nf
+    real	x[2]		#I x value, 1 <= x[1-2] <= npix
+    real	datain[npix]	#I data values
+    int		npix		#I number of data values
+    int		interp_type	#I interpolant type
+.fi
+.ih
+ARGUMENTS
+.ls x      
+Single X value, or a pair of X values specifying a range in the case
+of the drizzle interpolant.
+.le
+.ls datain  
+Array of input data.
+.le
+.ls npix
+Number of data points.
+.le
+.ls interp_type
+Interpolant type. Options are II_NEAREST, II_LINEAR, II_POLY3, II_POLY5,
+II_SPLINE3, II_SINC / II_LSINC, and II_DRIZZLE, for nearest neighbor,
+linear, 3rd and fifth order polynomials, cubic spline, sinc, look-up
+table sinc, and drizzle interpolants respectively. The look-up table sinc
+interpolant is not supported and defaults to the sinc interpolant. The sinc
+width is 31 pixels. The drizzle pixel fraction is 1.0. The interpolant
+type definitions are contained in the package header file math/iminterp.h
+.le
+.ih
+DESCRIPTION
+ARIEVAL allows the evaluation of a few interpolated points without the
+storage required for the sequential interpolant.
+.ih
+NOTES
+Checking for out of bounds and INDEF valued pixels is the responsibility of
+the user.
+.ih
+SEE ALSO
+arider, asieval, asivector
diff --git a/math/iminterp/doc/asider.hlp b/math/iminterp/doc/asider.hlp
new file mode 100644
index 00000000..0c27ffbc
--- /dev/null
+++ b/math/iminterp/doc/asider.hlp
@@ -0,0 +1,52 @@
+.help asider Dec98 "Image Interpolator Package"
+.ih
+NAME
+asider -- evaluate the interpolant derivatives at x
+.ih
+SYNOPSIS
+asider (asi, x, der, nder)
+
+.nf
+    pointer	asi	#I interpolant descriptor
+    real	x[2]	#I x value, 1 <= x[1-2] <= npix
+    real	der[]	#O der[1] = interpolant, der[2] = 1st derivative
+    int		nder	#I number of derivatives 
+.fi
+.ih
+ARGUMENTS
+.ls asi   
+Pointer to the sequential interpolant descriptor.
+.le
+.ls x   
+Single X value, or pair of X values defining a range in the case of
+the drizzle interpolant.
+.le
+.ls der  
+Array containing the derivatives. Der[1] = interpolant at x, der[2] the
+first derivative of the interpolant at x and so on.
+.le
+.ls nder
+Number of derivatives. Nder = 1 + order of the maximum desired derivative.
+ASIDER checks that nder is reasonable.  The sinc interpolant returns the
+interpolant value and first two derivatives. The drizzle interpolant returns
+the interpolant value and the first derivative.
+.le
+.ih
+DESCRIPTION
+The polynomial coefficients are evaluated directly from the data points
+for the polynomial interpolants and from the B-spline coefficients
+for the cubic spline interpolant. The derivatives are evaluated from
+the polynomial coefficients using nested multiplication.  The sinc
+derivatives are analytic but are defined only for the first two derivatives.
+The drizzle derivative is an approximation  defined  for the first derivative
+only.
+.ih
+NOTES
+ASIDER checks that the number of derivatives requested is reasonable.
+Checking for out of bounds and INDEF valued pixels is the responsibility
+of the user. ASIINIT or ASISINIT and ASIFIT must be called before ASIDER
+is called.
+.ih
+SEE ALSO
+asieval, asivector, arieval, arider
+.endhelp
diff --git a/math/iminterp/doc/asieval.hlp b/math/iminterp/doc/asieval.hlp
new file mode 100644
index 00000000..20f70abe
--- /dev/null
+++ b/math/iminterp/doc/asieval.hlp
@@ -0,0 +1,44 @@
+.help asieval Dec98 "Image Interpolator Package"
+.ih
+NAME
+asieval -- procedure to evaluate interpolant at x
+.ih
+SYNOPSIS
+y = asieval (asi, x)
+
+.nf
+    pointer	asi	#I interpolant descriptor
+    real	x[2]	#I x value, 1 <= x[1-2] <= npts
+.fi
+.ih
+ARGUMENTS
+.ls asi   
+Pointer to the sequential interpolant descriptor structure.
+.le
+.ls x    
+Single X value, or pair of X values defining a range in the case of the
+drizzle interpolant.
+.le
+.ih
+DESCRIPTION
+The polynomial coefficients are calculated directly from the data points
+for the polynomial interpolants, and from the B-spline coefficients for
+the cubic spline interpolant. The actual calculation is done by adding and
+multiplying terms according to Everett's central difference interpolation
+formula. The boundary extension algorithm is projection.
+
+The sinc interpolant is computed using a range of data points around
+the desired position. Look-up table sinc interpolation is computed
+using the most appropriate entry in a precomputed look-up table.
+The boundary extension algorithm is nearest neighbor.
+
+The drizzle interpolant is computed by summing the data over the user
+supplied X interval.
+.ih
+NOTES
+Checking for out of bounds and INDEF valued pixels is the responsibility of
+the user. ASIINIT or ASISINIT and ASIFIT must be called before using ASIEVAL.
+.ih
+SEE ALSO
+asivector, arieval
+.endhelp
diff --git a/math/iminterp/doc/asifit.hlp b/math/iminterp/doc/asifit.hlp
new file mode 100644
index 00000000..bcd1fdc8
--- /dev/null
+++ b/math/iminterp/doc/asifit.hlp
@@ -0,0 +1,40 @@
+.help asifit Dec98 "Image Interpolator Package"
+.ih
+NAME
+asifit - fit the interpolant to data
+.ih
+SYNOPSIS
+asifit (asi, datain, npix)
+
+.nf
+    pointer	asi		#I interpolant descriptor
+    real	datain[npix]	#I input data
+    int		npix		#I the number of data points
+.fi
+.ih
+ARGUMENTS
+.ls asi   
+Pointer to sequential interpolant descriptor structure.
+.le
+.ls datain
+Array of input data.
+.le
+.ls npix    
+Number of data points.
+.le
+.ih
+DESCRIPTION
+The datain array is checked for size, memory is allocated for the coefficient
+array, and the end conditions are specified.  The interior polynomial, sinc and
+drizzle interpolants are saved as the data points. The polynomial coefficients
+are calculated directly from the data points in the evaluation stage. The
+B-spline coefficients are calculated in ASIFIT as they depend on the entire
+data array. 
+.ih
+NOTES
+Checking for INDEF valued and out of bounds pixels is the responsibility
+of the user. ASIINIT or ASISINIT and ASIFIT must be called before using
+ASIEVAL, ASIVECTOR, ASIDER or ASIGRL.
+.ih
+SEE ALSO
+.endhelp
diff --git a/math/iminterp/doc/asifree.hlp b/math/iminterp/doc/asifree.hlp
new file mode 100644
index 00000000..c61f2ce0
--- /dev/null
+++ b/math/iminterp/doc/asifree.hlp
@@ -0,0 +1,25 @@
+.help asifree Dec98 "Image Interpolator Package"
+.ih
+NAME
+asifree - free sequential interpolant descriptor
+.ih
+SYNOPSIS
+asifree (asi)
+
+.nf
+pointer	asi	#U interpolant descriptor
+.fi
+.ih
+ARGUMENTS
+.ls asi   
+Pointer to the sequential interpolant descriptor structure.
+.le
+.ih
+DESCRIPTION
+ASIFREE frees the sequential interpolant descriptor structure allocated by
+ASIINIT or ASISINIT. ASIFREE should be called when interpolation is complete.
+.ih
+NOTES
+.ih
+SEE ALSO
+asiinit, asisinit
diff --git a/math/iminterp/doc/asigeti.hlp b/math/iminterp/doc/asigeti.hlp
new file mode 100644
index 00000000..0e9d1964
--- /dev/null
+++ b/math/iminterp/doc/asigeti.hlp
@@ -0,0 +1,36 @@
+.help asigeti Dec98 asigeti.hlp
+.ih
+NAME
+asigeti -- fetch an asi integer parameter
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+value = asigeti (asi, param)
+
+.nf
+    pointer	asi		#I interpolant descriptor
+    int		param		#I parameter
+.fi
+.ih
+ARGUMENTS
+.ls asi      
+Pointer to the sequential interpolant descriptor structure.
+.le
+.ls param
+The parameter to be fetched. The choices are: II_ASITYPE the interpolant
+type, II_ASINSAVE the length of the saved coefficient array, and
+II_ASINSINC the half-width of the sinc interpolant. The parameter
+definitions are contained in the package header file math/iminterp.h.
+.le
+.ih
+DESCRIPTION
+ASIGETI is used to determine the size of the coefficient array that
+must be allocated to save the sequential interpolant description structure,
+and to fetch selected sequential interpolant parameters.
+.ih
+NOTES
+.ih
+SEE ALSO
+asiinit, asisinit, asigetr
+.endhelp
diff --git a/math/iminterp/doc/asigetr.hlp b/math/iminterp/doc/asigetr.hlp
new file mode 100644
index 00000000..8a31deef
--- /dev/null
+++ b/math/iminterp/doc/asigetr.hlp
@@ -0,0 +1,36 @@
+.help asigetr Dec98 asigetr.hlp
+.ih
+NAME
+asigetr -- fetch an asi integer parameter
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+value = asigetr (asi, param)
+
+.nf
+    pointer	asi		#I interpolant descriptor
+    int		param		#I parameter
+.fi
+.ih
+ARGUMENTS
+.ls asi      
+Pointer to the sequential interpolant descriptor structure.
+.le
+.ls param
+The parameter to be fetched. The choices are: II_ASIBADVAL the undefined
+pixel value for the drizzle interpolant. The parameter definitions are
+contained in the package header file math/iminterp.h.
+.le
+.ih
+DESCRIPTION
+ASIGETR is used to set the value of undefined drizzle interpolant pixels.
+Undefined pixels are those for which the interpolation coordinates do not
+overlap the input coordinates, but are still, within the boundaries of the input
+image, a situation which may occur when the pixel fraction is < 1.0.
+.ih
+NOTES
+.ih
+SEE ALSO
+asiinit, asisinit, asigeti
+.endhelp
diff --git a/math/iminterp/doc/asigrl.hlp b/math/iminterp/doc/asigrl.hlp
new file mode 100644
index 00000000..4c3087bb
--- /dev/null
+++ b/math/iminterp/doc/asigrl.hlp
@@ -0,0 +1,40 @@
+.help asigrl Dec98 "Image Interpolator Package"
+.ih
+NAME
+asigrl -- integrate interpolant from a to b
+.ih
+SYNOPSIS
+integral = asigrl (asi, a, b)
+
+.nf
+    pointer	asi	#I interpolant descriptor
+    real	a	#I lower limit for integral, 1 <= a <= npix
+    real	b	#I upper limit for integral, 1 <= b <= npix
+.fi
+.ih
+ARGUMENTS
+.ls asi  
+Pointer to the sequential interpolant descriptor structure.
+.le
+.ls a
+Lower limit to the integral, where 1 <= a <= npix.
+.le
+.ls b
+Upper limit to the integral, where 1 <= b <= npix.
+.le
+.ih
+DESCRIPTION
+The integral is calculated assuming that the interior polynomial, sinc, and
+drizzle interpolants are stored as the data points, and that the spline
+interpolant is stored as an array of B-spline coefficients.
+
+The integral of the sinc interpolant is computed by dividing the integration
+interval into a number of equal size subintervals which are at most one pixel
+wide. The integral of each subinterval is the central value times the interval
+width. The look-up table sinc interpolant is not supported and defaults to
+the sinc interpolant.
+.ih
+NOTES
+ASIINIT or ASISINIT and ASIFIT must be called before using ASIGRL.
+.ih
+SEE ALSO
diff --git a/math/iminterp/doc/asiinit.hlp b/math/iminterp/doc/asiinit.hlp
new file mode 100644
index 00000000..711d7969
--- /dev/null
+++ b/math/iminterp/doc/asiinit.hlp
@@ -0,0 +1,39 @@
+.help asiinit Dec98 "Image Interpolator Package"
+.ih
+NAME
+asiinit -- initialize the sequential interpolant descriptor using default parameters
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+asiinit (asi, interp_type)
+
+.nf
+    pointer	asi		#O interpolant descriptor
+    int		interp_type	#I interpolant type
+.fi
+
+.ih
+ARGUMENTS
+.ls asi   
+Pointer to sequential interpolant descriptor.
+.le
+.ls interp_type
+Interpolant type. The options are II_NEAREST, II_LINEAR, II_POLY3, II_POLY5,
+II_SPLINE3, II_SINC, II_LSINC, and II_DRIZZLE for nearest neighbor, linear,
+3rd order polynomial, 5th order polynomial, cubic spline, sinc, look-up
+table sinc, and drizzle respectively. The interpolant type definitions are
+found in the package header file math/iminterp.h.
+.le
+.ih
+DESCRIPTION
+The interpolant descriptor is allocated and initialized. The pointer asi is
+returned by ASIINIT. The sinc interpolant width defaults to 31 pixels. The
+look-up table sinc interpolant resolution defaults to 20 intervals or
+0.05 pixels. The drizzle pixel fraction defaults to 1.0.
+.ih
+NOTES
+ASIINIT or ASISINIT must be called before using any other ASI routines.
+.ih
+SEE ALSO
+asisinit, asifree
diff --git a/math/iminterp/doc/asirestore.hlp b/math/iminterp/doc/asirestore.hlp
new file mode 100644
index 00000000..6dd70262
--- /dev/null
+++ b/math/iminterp/doc/asirestore.hlp
@@ -0,0 +1,36 @@
+.help asirestore Dec98 "Image Interpolator Package"
+.ih
+NAME
+asirestore -- restore interpolant
+.ih
+SYNOPSIS
+asirestore (asi, interpolant)
+
+.nf
+    pointer	asi		#O interpolant descriptor
+    real	interpolant[]	#I array containing interpolant
+.fi
+.ih
+ARGUMENTS
+.ls asi   
+Pointer to the interpolant descriptor structure.
+.le
+.ls interpolant
+Array containing the interpolant. The length of interpolant can be determined
+by a call to ASIGETI.
+.le
+
+.nf
+		len_interpolant = asigeti (asi, II_ASINSAVE)
+.fi
+.ih
+DESCRIPTION
+ASIRESTORE allocates space for the interpolant descriptor and restores the
+parameters and coefficients stored in the interpolant array to a structure
+for use with ASIEVAL, ASIVECTOR, ASIDER and ASIGRL.
+.ih
+NOTES
+.ih
+SEE ALSO
+asisave
+.endhelp
diff --git a/math/iminterp/doc/asisave.hlp b/math/iminterp/doc/asisave.hlp
new file mode 100644
index 00000000..7c8ff37a
--- /dev/null
+++ b/math/iminterp/doc/asisave.hlp
@@ -0,0 +1,39 @@
+.help asisave Dec98 "Image Interpolator Package"
+.ih
+NAME
+asisave -- save interpolant
+.ih
+SYNOPSIS
+asisave (asi, interpolant)
+
+.nf
+    pointer	asi		#I interpolant descriptor
+    real	interpolant[]	#O array containing the interpolant
+.fi
+.ih
+ARGUMENTS
+.ls asi   
+Pointer to the interpolant descriptor structure.
+.le
+.ls interpolant
+Array where the interpolant is stored. The size of interpolant can be
+determined by a call to asigeti.
+.le
+
+.nf
+		len_interpolant = asigeti (asi, II_ASINSAVE)
+.fi
+.ih
+DESCRIPTION
+The interpolant type, number of coefficients and the position of
+the first data point in the coefficient array, along with various
+parameters such as the sinc interpolant width, sinc look-up table
+resolution, and drizzle pixel fraction, are stored in the first
+7 elements of the interpolant array. The remaining elements contain
+the coefficients calculated by ASIFIT.
+.ih
+NOTES
+.ih
+SEE ALSO
+asirestore
+.endhelp
diff --git a/math/iminterp/doc/asisinit.hlp b/math/iminterp/doc/asisinit.hlp
new file mode 100644
index 00000000..1ec9bc4e
--- /dev/null
+++ b/math/iminterp/doc/asisinit.hlp
@@ -0,0 +1,60 @@
+.help asisinit Dec98 "Image Interpolator Package"
+.ih
+NAME
+asisinit -- initialize the sequential interpolant descriptor using user parameters
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+asisinit (asi, interp_type, nsinc, nincr, rparam, badval)
+
+.nf
+    pointer	asi		#O interpolant descriptor
+    int		interp_type	#I interpolant type
+    int		nsinc		#I sinc interpolant width in pixels
+    int		nincr		#I sinc look-up table resolution
+    real	pixfrac         #I sinc shift or drizzle pixel fraction 
+    real	badval		#I drizzle undefined pixel value
+.fi
+
+.ih
+ARGUMENTS
+.ls asi   
+Pointer to sequential interpolant descriptor.
+.le
+.ls interp_type
+Interpolant type. The options are II_NEAREST, II_LINEAR, II_POLY3, II_POLY5,
+II_SPLINE3, II_SINC, II_LSINC, and II_DRIZZLE for the nearest neighbour, linear,
+3rd order polynomial, 5th order polynomial, cubic spline, sinc, look-up
+table sinc, and drizzle interpolants respectively. The interpolant type
+definitions are found in the package header file math/iminterp.h.
+.le
+.ls nsinc
+The sinc and look-up table sinc interpolant width in pixels. Nsinc is
+rounded up internally to the nearest odd number.
+.le
+.ls nincr
+The look-up table sinc resolution in number of entries. Nincr = 10 implies
+a pixel resolution of 0.1 pixels, nincr = 20 a pixel resolution of 0.05
+pixels, etc.
+.le
+.ls pixfrac
+The look-up table sinc fractional pixel shift if nincr = 1 in which case
+-0.5 <= pixfrac <= 0.5 , or the drizzle pixel fraction in which case
+0.0 <= pixfrac <= 1.0. A minimum value of 0.001 is imposed on pixfrac.
+.le
+.ls badval
+The undefined pixel value for the drizzle interpolant. Pixels within
+the boundaries of the input image which do not overlap the input image
+pixels are assigned a value of badval.
+.le
+.ih
+DESCRIPTION
+The interpolant descriptor is allocated and initialized. The pointer asi is
+returned by ASISINIT.
+.ih
+NOTES
+ASIINIT or ASISINIT must be called before using any other ASI routines.
+.ih
+SEE ALSO
+asisinit, asifree
diff --git a/math/iminterp/doc/asitype.hlp b/math/iminterp/doc/asitype.hlp
new file mode 100644
index 00000000..d8c78b44
--- /dev/null
+++ b/math/iminterp/doc/asitype.hlp
@@ -0,0 +1,95 @@
+.help asitype Dec98 "Image Interpolator Package"
+.ih
+NAME
+asitype -- decode an interpolant string
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+asitype (interpstr, interp_type, nsinc, nincr, rparam)
+
+.nf
+    char	interpstr	#I the input interpolant string
+    int		interp_type	#O interpolant type
+    int		nsinc		#O sinc interpolant width in pixels
+    int		nincr		#O sinc look-up table resolution
+    real	rparam          #O sinc or drizzle pixel fraction 
+.fi
+
+.ih
+ARGUMENTS
+.ls interpstr
+The user supplied interpolant string to be decoded. The options are
+.ls nearest
+Nearest neighbor interpolation.
+.le
+.ls linear
+Linear interpolation
+.le
+.ls poly3
+Cubic polynomial interpolation.
+.le
+.ls poly5
+Quintic polynomial interpolation.
+.le
+.ls spline3
+Cubic spline interpolation.
+.le
+.ls sinc
+Sinc interpolation. Users can specify the sinc interpolant width by
+appending a width value to the interpolant string, e.g. sinc51 specifies
+a 51 pixel wide sinc interpolant. The sinc width will be rounded up to
+the nearest odd number.  The default sinc width is 31.
+.le
+.ls lsinc
+Look-up table sinc interpolation. Users can specify the look-up table sinc
+interpolant width by appending a width value to the interpolant string, e.g.
+lsinc51 specifies a 51 pixel wide look-up table sinc interpolant. The user
+supplied sinc width will be rounded up to the nearest odd number. The default
+sinc width is 31 pixels. Users can specify the resolution of the sinc lookup
+up table by appending the look-up table size in square brackets to the
+interpolant string, e.g. lsinc51[20] specifies a 20 element sinc look-up
+table interpolant with a pixel resolution of 0.05 pixels. The default
+look-up table size and resolution are 20 and 0.05 pixels respectively.
+The fractional pixel shift for a 1 element look-up table sinc may be
+specified by replacing the number of lookup-table elements with the fractional
+shift, e.g. sinc51[0.5] will precompute a lookup table for a 0.5 pixel shift.
+.le
+.ls drizzle
+Drizzle interpolation. Users can specify the drizzle pixel fraction by
+appending the pixel fraction value to the interpolant string in square
+brackets, e.g. drizzle[0.5] specifies a pixel fraction of 0.5.
+The default pixel fraction is 1.0.
+.le
+.le
+.ls interp_type
+The output interpolant type. The options are II_NEAREST, II_LINEAR, II_POLY3,
+II_POLY5, II_SPLINE3, II_SINC, II_LSINC, and II_DRIZZLE for the nearest
+neighbor, linear, 3rd order polynomial, 5th order polynomial, cubic spline,
+sinc, look-up table sinc, and drizzle interpolants respectively. The
+interpolant type definitions are found in the package header file
+math/iminterp.h.
+.le
+.ls nsinc
+The output sinc and look-up table sinc interpolant width in pixels. The
+default value is 31 pixels.
+.le
+.ls nincr
+The output sinc look-up table size. Nincr = 10 implies a pixel resolution
+of 0.1 pixels, nincr = 20 a pixel resolution of 0.05 pixels, etc. The
+default value of nincr is 20.
+.le
+.ls rparam
+The output look-up table sinc fractional pixel shift if nincr = 1 in which case
+-0.5 <= rparam <= 0.5 , or the drizzle pixel fraction in which case
+0.0 <= rparam <= 1.0.
+.le
+.ih
+DESCRIPTION
+The interpolant string is decoded into values suitable for the ASISINIT
+or ASIINIT routines.
+.ih
+NOTES
+.ih
+SEE ALSO
+asinit, asisinit, asifree
diff --git a/math/iminterp/doc/asivector.hlp b/math/iminterp/doc/asivector.hlp
new file mode 100644
index 00000000..95bac138
--- /dev/null
+++ b/math/iminterp/doc/asivector.hlp
@@ -0,0 +1,52 @@
+.help asivector Dec98 "Image Interpolator Package"
+.ih
+NAME
+asivector -- evaluate the interpolant
+.ih
+SYNOPSIS
+asivector (asi, x, y, npix)
+
+.nf
+    pointer	asi		#I interpolator descriptor
+    real	x[npix/2*npix]	#I x array, 1 <= x[i] <= npix
+    real	y[npix]		#O array of interpolated values
+    int		npix		#I number of x values
+.fi
+.ih
+ARGUMENTS
+.ls asi  
+Pointer to the sequential interpolator descriptor structure.
+.le
+.ls x   
+Array of npix x values, or array of npix x ranges if the interpolant is
+drizzle.
+.le
+.ls y
+Array of interpolated values.
+.le
+.ls npix   
+The number of x values.
+.le
+.ih
+DESCRIPTION
+The polynomial coefficients are calculated directly from the data points
+for the polynomial interpolants, and from the B-spline coefficients for
+the cubic spline interpolant. The actual calculation is done by adding and
+multiplying terms according to Everett's central difference interpolation
+formula. The boundary extension algorithm is projection.
+
+The sinc interpolant is computed using a range of data points around
+the desired position. Look-up table sinc interpolation is computed
+using the most appropriate entry in a precomputed look-up table.
+The boundary extension algorithm is nearest neighbor.
+
+The drizzle interpolant is computed by summing the data over the user
+supplied X intervals.
+.ih
+NOTES
+Checking for out of bounds and INDEF valued pixels is the responsibility of the
+user. ASIINIT or ASISINIT and ASIFIT must be called before calling ASIVECTOR.
+.ih
+SEE ALSO
+asieval, asider, arieval, arider
+.endhelp
diff --git a/math/iminterp/doc/im1dinterp.spc b/math/iminterp/doc/im1dinterp.spc
new file mode 100644
index 00000000..ce5b8680
--- /dev/null
+++ b/math/iminterp/doc/im1dinterp.spc
@@ -0,0 +1,525 @@
+.help iminterp Jul84 "Math Package"
+
+.ce
+Specifications for the Image Interpolator Package
+.ce
+Lindsey Davis
+.ce
+Vesa Junkkarinen
+.ce
+August 1984
+
+.sh
+1. Introduction
+
+    One of the most common operations in image processing is
+interpolation in a data array. Due to the large amount of data involved,
+efficiency is highly important. The advantage of having locally written
+interpolators, includes the ability to optimize for uniformly spaced data
+and the possibility of adding features that are useful to the final
+application.
+
+.sh
+2. Requirements
+
+.ls (1)
+The package shall take as input a one-dimensional array containing image
+data. The pixels are assumed to be equally spaced along a line.
+The coordinates of a pixel are assumed to be
+the same as the subscript of the pixel in the data array.
+The coordinate of the first pixel in the array and the spacing between pixels
+is assumed to be 1.0. All pixels are assumed to be good.
+Checking for INDEF valued and out of bounds pixels is the responsibility of the
+user. A routine to remove INDEF valued pixels from a data array shall be
+included in the package.
+.le
+.ls (2)
+The package is divided into array sequential interpolators and array
+random interpolators. The sequential interpolators have been optimized
+for returning many values as is the case when an array is shifted, or
+oversampled at many points in order to produce a
+smooth plot.
+The random interpolators allow the evaluation of a few interpolated
+points without the computing time and storage overhead required for
+setting up the sequential version.
+.le
+.ls (3)
+The quality of the interpolant will be set at run time. The options are:
+
+.nf
+    II_NEAREST		- nearest neighbour
+    II_LINEAR		- linear interpolation
+    II_POLY3		- 3rd order divided differences
+    II_POLY5		- 5th order divided differences
+    II_SPLINE3		- cubic spline
+.fi
+
+The calling sequences shall be invariant to the interpolant selected.
+Routines should be designed so that new interpolants can be added
+with minimal changes to the code and no change to the calling sequences.
+.le
+.ls (4)
+The interpolant parameters and the arrays necessary to store the coefficients
+are stored in a structure referenced by a pointer. The pointer is returned
+to the user program by the initial call to ASIINIT or ASIRESTORE and freed
+by a call to ASIFREE (see section 3.1).
+.le
+.ls (5)
+The package routines shall be able to:
+.ls o
+Calculate the coefficients of the interpolant and store these coefficients in
+the appropriate part of the interpolant descriptor structure.
+.le
+.ls o
+Evaluate the interplant at a given x(s) coordinate(s).
+.le
+.ls o
+Calculate the derivatives of the interpolant at a given value of x.
+.le
+.ls o
+Integrate the interpolant over a specified x interval.
+.le
+.ls o
+Store the interpolant in a user supplied array. Restore the saved interpolant
+to the interpolant descriptor structure for later use by ASIEVAL, ASIVECTOR,
+ASIDER and ASIGRL.
+.le
+
+.sh
+3. Specifications
+
+.sh
+3.1. The Array Sequential Interpolator Routines
+
+    The package prefix is asi and the package routines are:
+
+.nf
+        asiinit	(asi, interp_type)
+         asifit	(asi, datain, npix)
+    y = asieval	(asi, x)
+      asivector	(asi, x, yfit, npix)
+         asider	(asi, x, der, nder)
+     v = asigrl	(asi, a, b)
+        asisave	(asi, interpolant)
+     asirestore	(asi, interpolant)
+        asifree	(asi)
+.fi
+
+.sh
+3.2. The Array Random Interpolator Routines
+
+    The package prefix is ari and the package routines are:
+
+.nf
+    y = arieval	(x, datain, npix, interp_type)
+	 arider	(x, datain, npix, der, nder, interp_type)
+.fi
+
+.sh
+3.3. Miscellaneous
+
+    A routine has been included in the package to remove INDEF valued
+pixels from an array.
+
+.nf
+    arbpix (datain, dataout, npix, interp_type, boundary_type)
+.fi
+
+.sh
+3.4. Algorithms
+
+.sh
+3.4.1. Coefficients
+
+    The coefficient array used by the asi routines is calculated by ASIFIT.
+ASIFIT accepts an array of data, checks that the number
+of data points is appropriate for the interpolant selected, allocates
+space for the interpolant, and calculates the coefficients.
+Boundary coefficient values are calculated
+using boundary projection.  With the exception of the cubic spline interpolant,
+the coefficients are stored as the data points.
+The B-spline coefficients are 
+calculated using natural end conditions (Prenter 1975).
+After a call to ASIFIT the coefficient array contains the following.
+
+.nf
+    case II_NEAREST:
+
+        # no boundary conditions necessary
+	coeff[1] = datain[1]
+	.
+	.
+	.
+	coeff[npts] = datain[npix]
+
+    case II_LINEAR:
+
+        # coeff[npxix+1] required if x = npix
+	coeff[1] = datain[1]
+	.
+	.
+	.
+	coeff[npix] = datain[npix]
+	coeff[npix+1] = 2. * datain[npix] - datain[npix-1]
+
+    case II_POLY3:
+
+        # coeff[0] required if x = 1
+	# coeff[npix+1], coeff[npix+2] required if x = npix
+	coeff[0] = 2. * datain[1] - datain[2]
+	coeff[1] = datain[1]
+	.
+	.
+	.
+	coeff[npix] = datain[npix]
+	coeff[npix+1] = 2. * datain[npix] - datain[npix-1]
+	coeff[npix+2] = 2. * datain[npix] - datain[npix-2]
+
+    case II_POLY5:
+
+        # coeff[1], coeff[0] reqired if x = 1
+	# coeff[npix+1], coeff[npix+2], coeff[npix=3]
+	# required if x = npix
+
+	coeff[-1] = 2. * datain[1] - datain[3]
+	coeff[0] = 2. * datain[1] - datain[2]
+	coeff[1] = datain[1]
+	.
+	.
+	.
+	coeff[npix] = datain[npix]
+	coeff[npix+1] = 2. * datain[npix] - datain[npix-1]
+	coeff[npix+2] = 2. * datain[npix] - datain[npix-2]
+	coeff[npix+3] = 2. * datain[npix] - datain[npix-3]
+
+    case SPLINE3:
+
+        # coeff[0] = 2nd der at x = 1, coeff[0] = 0.
+	# coeff[npix+1] = 2nd der at x = npts, coeff[npix+1] = 0.
+	# coeff[npix+2] = 0., required if x = npix
+	coeff[0] = b[1]
+	coeff[1] = b[2]
+	.
+	.
+	.
+	coeff[npix] = b[npix+1]
+	coeff[npix+1] = b[npix+2]
+	coeff[npix+2] = 0.
+.fi
+
+.sh
+3.4.2. Evaluation
+
+    The ASIEVAL and ASIVECTOR routines have been optimized to be as efficient
+as possible. The values of the II_NEAREST and II_LINEAR interpolants
+are calculated directly. The II_SPLINE3 interpolant is evaluated using
+polynomial coefficients calculated directly from the B-spline coefficients
+(de Boor 1978). Values of the higher order polynomial interpolants
+are calculated using central differences. The equations for each case are
+listed below.
+
+.nf
+case II_NEAREST:
+    
+    y = coeff[int (x + 0.5)]
+
+case II_LINEAR:
+
+    nx = x
+    y = (x - nx) * coeff[nx+1] + (nx + 1 - x) * coeff[nx]
+
+case II_POLY3:
+
+    nx = x
+    s = x - nx
+    t = 1. - s
+
+    # second central differences
+    cd20 = 1./6. * (coeff[nx+1] - 2. * coeff[nx] + coeff[nx-1])
+    cd21 = 1./6. * (coeff[nx+2] - 2. * coeff[nx+1] + coeff[nx])
+
+    y = s * (coeff[nx+1] + (s * s - 1.) * cd21) + t * (coeff[nx] +
+	(t * t - 1.) * cd20)
+
+case II_POLY5:
+
+    nx = x
+    s = x - nx
+    t = 1. - s
+
+    # second central differences
+    cd20 = 1./6. * (coeff[nx+1] - 2. * coeff[nx] + coeff[nx-1])
+    cd21 = 1./6. * (coeff[nx+2] - 2. * coeff[nx+1] + coeff[nx])
+
+    # fourth central diffreences
+    cd40 = 1./120. * (coeff[nx-2] - 4. * coeff[nx-1] + 6. * coeff[nx] - 4. *
+	   coeff[nx+1] + a[nx+2])
+    cd41 = 1./120. * (coeff[nx-1] - 4. * coeff[nx] + 6. * coeff[nx+1] - 4. *
+	   coeff[nx+2] + coeff[nx+3]
+
+    y = s * (coeff[nx+1] + (s * s - 1.) * (cd21 + (s * s - 4.) * cd41)) +
+	t * (coeff[nx] + (t * t - 1.) * (cd20 + (t * t - 4.) * cd40))
+
+case II_SPLINE3:
+
+    nx = x
+    s = x - nx
+
+    pc[1] = coeff[nx-1] + 4. * coeff[nx] + coeff[nx+1]
+    pc[2] = 3. * (coeff[nx+1] - coeff[nx-1])
+    pc[3] = 3. * (coeff[nx-1] - 2. * coeff[nx] + coeff[nx+1])
+    pc[4] = -coeff[nx-1] + 3. * coeff[nx] - 3. * coeff[nx+1] + coeff[nx+2]
+
+    y = pc[1] + s * (pc[2] + s * (pc[3] + s * pc[4]))
+.fi
+
+
+    The ARIEVAL routine uses the expressions above to evaluate the
+interpolant. However unlike ASIEVAL, ARIEVAL does not use a previously
+calculated coefficient array. Instead ARIEVAL selects the appropriate
+portion of the data array, calculates the coefficients and boundary
+coefficients if necessary, and evaluates the interpolant at the time it
+is called. The cubic spline interpolant uses at most SPLTS (currently 16)
+data points to calculate the B-spline coefficients.
+
+.sh
+3.4.3. Derivatives
+
+    Derivatives of the interpolant are calculated by evaluating the
+derivatives of the interpolating polynomial. For all interpolants der[1]
+equals the value of the interpolant at x.
+For the sake of efficiency the derivatives
+of the II_NEAREST and II_LINEAR interpolants are calculated directly.
+
+.nf
+    case II_NEAREST:
+
+	der[1] = coeff[int (x+0.5)]
+
+    case II_LINEAR:
+
+	der[1] = (x - nx) * coeff [nx+1] + (nx + 1 - x) * coeff[nx]
+	der[2] = coeff[nx+1] - coeff[nx]
+.fi
+
+    In order to calculate the derivatives of the cubic spline and
+polynomial interpolants
+the coefficients of the interpolating polynomial must be calculated.
+The polynomial
+coefficients for the cubic spline interpolant are computed directly from the
+B-spline coefficients (see 3.4.2.). The higher order polynomial
+interpolant coefficients are calculated as follows.
+
+First the appropriate portion of the coefficient array is loaded.
+
+.nf
+	do i = 1, nterms
+	    d[i] = coeff[nx - nterms/2 + i]
+.fi
+
+Next the divided differences are calculated (Conte and de Boor 1972).
+
+.nf
+	do k = 1, nterms - 1
+	    do i = 1, nterms - k
+		d[i] = (d[i+1] - d[i]) / k
+.fi
+
+The d[i] are the coefficients of an interpolating polynomial of the
+following form. The x[i] are the nterms data points surrounding the
+point of interest.
+
+.nf
+	p(x) = d[1] * (x-x[1]) * ... * (x-x[nterms-1) +
+	       d[2] * (x-x[2]) * ... * (x-x[nterms-1]) + ... + d[nterms]
+.fi
+
+Next a new set of polynomial coefficients are calculated
+(Conte and de Boor 1972).
+
+.nf
+	do k = nterms, 2, -1
+	    do i = 2, k
+		d[i] = d[i] + d[i-1] * (k - i - nterms/2)
+.fi
+
+The new d[i] are the coefficients of the follwoing polynomial.
+
+.nf
+	nx = x
+	p(x) = d[1] * (x-nx) ** (nterms-1) + d[2] * (x-nx) ** (nterms-2) + ...
+	       d[nterms]
+.fi
+
+The d[i] array is flipped. The value and derivatives
+of the interpolant are then calculated using the d[i] array and
+nested multiplication.
+
+.nf
+	s = x - nx
+
+	do k = 1, nder {
+
+	    accum = d[nterms-k+1]
+
+	    do j = nterms - k, 1, -1
+		accum = d[j] + s * accum
+
+	    der[k] = accum
+
+	    # differnetiate
+	    do j = 1, nterms - k
+		d[j] = j * d[j + 1]
+	}
+.fi
+
+    ARIDER calculates the derivatives of the interpolant using the same
+technique ASIDER. However ARIDER does not use a previously calculated
+coefficient array like ASIDER. Instead ARIDER selects the appropriate portion
+of the data array, calculates the coefficients and boundary coefficients,
+and computes the derivatives at the time it is called.
+
+.sh
+3.4.5. Integration
+
+    ASIGRL calculates the integral of the interpolant between fixed limits
+by integrating the interpolating polynomial. The coefficients of the
+interpolating polynomial are calculated as discussed in section 3.4.4.
+
+.sh 
+4. Usage
+
+.sh
+4.1. User Notes
+
+The following series of steps illustrates the use of the package.
+
+.ls 4
+.ls (1)
+Insert an include <iminterp.h> statement in the calling program to make
+the IINTERP definitions available to the user program.
+.le
+.ls (2)
+Remove INDEF valued pixels from the data using ARBPIX.
+.le
+.ls (3)
+Call ASIINIT to initialize the interpolant parameters.
+.le
+.ls (4)
+Call ASIFIT to calculate the coefficients of the interpolant.
+.le
+.ls (5)
+Evaluate the interpolant at a given value of x(s) using ASIEVAL or
+ASIVECTOR.
+.le
+.ls (6)
+Calculate the derivatives and integral or the interpolant using
+ASIDER and ASIGRL.
+.le
+.ls (7)
+Free the interpolator structure by calling ASIFREE.
+.le
+.le
+
+    The interpolant can be saved and restored using ASISAVE and ASIRESTORE.
+If the values and derivatives of only a few points in an array are desired
+ARIEVAL and ARIDER can be called.
+
+.sh
+4.2. Examples
+
+.nf
+Example 1: Shift a data array by a constant amount
+
+    include <iminterp.h>
+    ...
+    call asiinit (asi, II_POLY5)
+    call asifit (asi, inrow, npix)
+
+    do i = 1, npix
+	outrow[i] = asieval (asi, i + shift)
+
+    call asifree (asi)
+    ...
+
+Example 2: Calculate the integral under the data array
+
+    include <iminterp.h>
+    ...
+    call asiinit (asi, II_POLY5)
+    call asifit (asi, datain, npix)
+
+    integral =  asigrl (asi, 1. real (npix))
+
+    call asifree (asi)
+    ...
+
+Example 2: Store interpolant for later use by ASIEVAL
+	   LEN_INTERP must be at least npix + 8 units long where npix is
+	   is defined in the call to ASIFIT.
+
+    include <iminterp.h>
+
+    real   interpolant[LEN_INTERP]
+    ...
+    call asiinit (asi, II_POLY3)
+    call asifit (asi, datain, npix)
+    call asisave (asi, interpolant)
+    call asifree (asi)
+    ...
+    call asirestore (asi, interpolant)
+    do i = 1, npts
+	yfit[i] = asieval (asi, x[i])
+    call asifree (asi)
+    ...
+.fi
+.sh
+5. Detailed Design
+
+.sh
+5.1. Interpolator Descriptor
+
+    The interpolant parameters and coefficients are stored in a
+structure listed below.
+
+.nf
+    define	LEN_ASISTRUCT	4		# Length in structure units of
+						# interpolant descriptor
+
+    define	ASI_TYPE	Memi[$1]	# Interpolant type
+    define	ASI_NCOEFF	Memi[$1+1]	# No. of coefficients
+    define	ASI_OFFSET	Memi[$1+2]	# First "data" point in
+						# coefficient array
+    define	ASI_COEFF	Memi[$1+3]	# Pointer to coefficient array
+.fi
+
+.sh
+5.2. Storage Requirements
+
+    The interpolant descriptor requires LEN_ASISTRUCT storage units. The
+coefficient array requires ASI_NCOEFF(asi) real storage elements, where
+ASI_NCOEFF(asi) is defined as follows.
+
+.nf
+    ASI_NCOEFF(asi) = npix	# II_NEAREST
+    ASI_NCOEFF(asi) = npix+1	# II_LINEAR
+    ASI_NCOEFF(asi) = npix+3	# II_POLY3
+    ASI_NCOEFF(asi) = npix+5	# II_POLY5
+    ASI_NCOEFF(asi) = npix+3	# II_SPLINE3
+.fi
+
+.sh
+6. References
+
+.ls (1)
+Carl de Boor, "A Practical Guide to Splines", 1978, Springer-Verlag New
+York Inc.
+.le
+.ls (2)
+S.D. Conte and C. de Boor, "Elementary Numerical Analysis", 1972, McGraw-Hill,
+Inc.
+.le
+.ls (3)
+P.M. Prenter, "Splines and Variational Methods", 1975, John Wiley and Sons Inc.
+.le
+.endhelp
diff --git a/math/iminterp/doc/im2dinterp.spc b/math/iminterp/doc/im2dinterp.spc
new file mode 100644
index 00000000..e4d88be3
--- /dev/null
+++ b/math/iminterp/doc/im2dinterp.spc
@@ -0,0 +1,432 @@
+.help iinterp Dec84 "Math Package"
+.ce
+Specifications for the 2D-Image Interpolator Package
+.ce
+Lindsey Davis
+.ce
+December 1984
+
+.sh
+1. Introduction
+
+One of the most common operations required in image processing is
+two-dimensional interpolation in a data array. Any image operator which
+physically moves pixels around requires image interpolation to calculate
+the new gray levels of the pixels. The advantage
+of having a locally written image interpolation package includes the ability to
+optimize for uniformly spaced data and the possibility of adding features
+that are useful to the final application.
+
+.sh
+2. Requirements
+
+.ls (1)
+The package shall take as input a 2-D array containing an image or image
+section. The pixels are assumed to be equally spaced on a rectangular grid.
+The coordinates of the pixels
+are assumed to be the same as the subscripts of the pixel in the data array.
+Therefore the coordinates of the first pixel in the array are assumed
+to be (1,1). For operations on image sections the calling program must
+keep track of any transformations between image and section coordinates.
+All pixels are assumed to be good.
+Checking for INDEF and out of bounds pixels is
+the responsibility of the user. A routine to remove INDEF valued pixels
+ARBPIX is available in the 1-D package.
+.le
+.ls (2)
+The package is divided into array sequential interpolants and array random
+interpolants. The sequential interpolants have been optimized for returning
+many values as when an array is shifted or when an array is oversampled
+at many points in order to produce a smooth surface plot.
+The random interpolants
+allow the evaluation of a few interpolated points without the computing
+time and storage overhead required for setting up the sequential version.
+.le
+.ls (3)
+The quality of the interpolant will be set at run time. The options are:
+
+.nf
+    II_BINEAREST		# nearest neighbour
+    II_BILINEAR			# bilinear
+    II_BIPOLY3			# bicubic interior polynomial
+    II_BIPOLY5			# biquintic interior polynomial
+    II_BISPLINE3		# bicubic spline
+.fi
+
+The calling sequences shall be invariant to the interpolant selected.
+Routines should be designed so that new interpolants can be added with
+minimal changes to the code and no changes to the calling sequences.
+.le
+.ls (4)
+The interpolant parameters and the arrays necessary to store the
+coefficients are stored in a structure referenced by a pointer. The pointer
+is returned to the user program by the initial call to MSIINIT or
+MSIRESTORE and freed by a call to MSIFREE.
+.le
+.ls (5)
+The package routines should be able to:
+.ls o
+Calculate the coefficients of the interpolant and store these coefficients
+in the appropriate part of the interpolant descriptor structure.
+.le
+.ls o
+Evaluate the interpolant at a given x-y(s) coordinate.
+.le
+.ls o
+Evaluate the first nder derivatives at a given value of x-y.
+.le
+.ls o
+Integrate the interpolant over a specified interval in x-y.
+.le
+
+.sh
+3. Specifications
+
+.sh
+3.1. The Matrix Sequential Interpolator Routines
+
+The package prefix is msi and the package routines are:
+
+.nf
+        msiinit	(msi, interp_type)
+         msifit	(msi, datain, nxpix, nypix, len_datain)
+    y = msieval	(msi, x, y)
+      msivector	(msi, x, y, zfit, npix)
+        msigrid	(msi, x, y, zfit, nx, ny, len_zfit)
+         msider	(msi, x, y, der, nxder, nyder, len_der)
+     v = msigrl	(msi, x, y, npts)
+   v = msisqgrl (msi, x1, x2, y1, y2) 
+        msisave	(msi, interpolant)
+     msirestore	(msi, interpolant)
+        msifree	(msi)
+.fi
+
+.sh
+3.2. The Matrix Random Interpolator Routines
+
+The package prefix is mri and the package routines are:
+
+.nf
+    y = mrieval	(x, y, datain, nx, ny, len_datain, interp_type)
+         mrider	(x, y, datain, nx, ny, len_datain, der, nxder, nyder,
+	 	 len_der, interp_type)
+.fi
+
+.sh
+3.3. Miscellaneous
+
+A routine ARBPIX will remove INDEF valued pixels from an
+array and is available in the 1-D package.
+
+.nf
+    arbpix (datain, dataout, npix, interp_type, boundary_type)
+.fi
+
+.sh
+3.4. Algorithms
+
+.sh
+3.4.1. Coefficients
+
+The coefficients for the msi routines are calculated by MSIFIT. MSIFIT
+accepts the input data, checks that the number of data pixels is
+appropriate for the interpolant selected, and allocates space for the
+interpolant. Boundary coefficient values are calculated using boundary
+projection. With the exception of the II_BISPLINE3 option, the interpolant
+is stored as the data points. The B-spline coefficients are calculated
+using the "natural" end conditions in two steps.
+First the B-spline coefficients in x at each value of y are calculated.
+The B-x coefficients are then solved for the B-spline coefficients in x-y.
+After a call to MSIFIT the coefficient
+array contains the following.
+
+.nf
+    CASE II_BINEAREST:
+
+	# no boundary extension required, coeff[1:nx,1:ny]
+
+	coeff[i,j] = data[i,j]				i = 1,...,nx
+							j = 1,...,ny
+
+    case II_BILINEAR:
+
+	# must extend nx by 1 and ny by 1, coeff[1:nx+1,1:ny+1]
+
+	coeff[i,j] = data[i,j]				i = 1,...,nx
+							j = 1,...,ny
+
+	coeff[nx+1,j] = 2 * data[nx] - data[nx-1]	j = 1,...,ny
+	coeff[i,ny+1] = 2 * data[ny] - data[ny-1]	i = 1,...,nx
+
+	coeff[nx+1,ny+1] = 2 * coeff[nx+1,ny] - data[nx,ny]
+
+    case II_BIPOLY3:
+
+	# must extend nx by -1 and 2 and ny by -1 and 2, coeff[0:nx+2,0:ny+2]
+
+	coeff[i,j] = data[i,j]				i = 1,...,nx
+							j = 1,...,ny
+
+	coeff[0,j] = 2 * data[1,j] - data[2,j]		j = 1,...,ny
+	coeff[nx+1,j] = 2 * data[nx,j] - data[nx-1,j]	j = 1,...,ny
+	coeff[nx+2,j] = 2 * data[nx,j] - data[nx-2,j]	j = 1,...,ny
+
+	coeff[i,0] = 2 * data[i,1] - data[i,2]		i = 1,...,ny
+	coeff[i,ny+1] = 2 * data[i,ny] - data[i,ny-1]	i = 1,...,nx
+	coeff[i,ny+2] = 2 * data[i,ny] - data[i,ny-2]	i = 1,...,nx
+
+	# plus remaining points
+
+    case II_BIPOLY5:
+
+	# extend -2 and 3 in nx and -2 and 3 in ny, coeff[-1:nx+3,-1:ny+3]
+
+	coeff[i,j] = data[i,j]				i = 1,...,nx
+							j = 1,...,ny
+
+	coeff[-1,j] = 2 * data[1,j] - data[3,j]		j = 1,...,ny
+	coeff[0,j] = 2 * data[1,j] - data[2,j]		j = 1,...,ny
+	coeff[nx+1,j] = 2 * data[nx,j] - data[nx-1,j]	j = 1,...,ny
+	coeff[nx+2,j] = 2 * data[nx,j] - data[nx-2,j]	j = 1,...,ny
+	coeff[nx+3,j] = 2 * data[nx,j] - data[nx-3,j]	j = 1,...,ny
+
+	coeff[i,-1] = 2 * data[i,1] - data[i,3]		i = 1,...,nx
+	coeff[i,0] = 2 * data[i,1] - data[i,2]		i = 1,...,nx
+	coeff[i,ny+1] = 2 * data[i,ny] - data[i,ny-1]	i = 1,...,nx
+	coeff[i,ny+2] = 2 * data[i,ny] - data[i,ny-2]	i = 1,...,nx
+	coeff[i,ny+3] = 2 * data[i,ny] - data[i,ny-3]	i = 1,...,nx
+
+	# plus remaining conditions
+
+    case II_BISPLINE3:
+
+	# the natural boundary conditions are used, coeff[0:nx+2,0:ny+2]
+
+	coeff[i,j] = data[i,j]				i = 1,...,nx
+							j = 1,...,ny
+
+	coeff[i,0] = 0.					i = 0,...,nx+2
+	coeff[i,ny+1] = 0.				i = 0,...,nx+2
+	coeff[i,ny+2] = 0.				i = 0,...,nx+2
+
+	coeff[0,j] = 0.					j = 1,...,ny
+	coeff[nx+1,j] = 0.				j = 1,...,ny
+	coeff[nx+2,j] = 0.				j = 1,...,ny
+
+	# plus remaining coefficients
+
+.fi
+
+.sh
+3.4.2. Evaluation
+
+The MSIEVAL and MSIVECTOR routines will be optimized to be as efficient
+as possible for evaluating arbitrarily spaced data. A special function
+MSIGRID is included for evaluating closely spaced points on a rectangular grid.
+For the options II_BINEAREST and II_BILINEAR the value of the
+interpolant is calculated directly. The II_BISPLINE3 interpolant is
+evaluated using polynomial coefficients calculated directly from the
+B-spline coefficients. Values of the higher order polynomial interpolants
+are calculated using Everett's central difference formula. The equations
+are listed below.
+
+.nf
+case II_BINEAREST:
+
+    z = coeff[int (x + 0.5), int (y + 0.5))
+
+case II_BILINEAR:
+
+    sx = x - nx		sy = y - ny
+    tx = 1. - sx	ty = 1. - sy
+
+    z = tx * ty * coeff[nx,ny] + sx * ty * coeff[nx+1,ny] +
+	sy * tx * coeff[nx,ny+1] + sx * sy * coeff[nx+1,ny+1]
+
+
+case II_BIPOLY3:
+
+    nx = x
+    sx = x - nx
+    tx = 1. - sx
+
+    # interpolate in x
+
+    i = 1
+
+    do j = ny-1, ny+2 {
+	 
+	cd20[i] = 1./6. * (coeff[nx+1,j] - 2. * coeff[nx,j] + coeff[nx-1,j])
+	cd21[i] = 1./6. * (coeff[nx+2,j] - 2. * coeff[nx+1,j] + coeff[nx,j])
+
+	z[i] = sx * (coeff[nx+1,j] + (sx * sx - 1.) * cd21[i]) +
+	       tx * (coeff[nx,j] + (tx * tx - 1.) * cd20[i])	
+
+	i = i + 1
+    }
+
+    ny = y
+    sy = y - ny
+    ty = 1. - sy
+
+    # interpolate in y
+
+    cd20y = 1./6. * (z[3] - 2. * z[2] + z[1])
+    cd21y = 1./6. * (z[4] - 2. * z[3] + z[2])
+
+    value = sy * (z[3] + (sy * sy - 1.) * cd21y) +
+    	    ty * (z[2] + (ty * ty - 1.) *cd20y) 
+
+
+case II_BIPOLY5:
+
+    nx = x
+    sx = x - nx
+    sx2 = sx * sx
+    tx = 1. - sx
+    tx2 = tx * tx
+
+    # interpolate in x
+
+    i = 1
+
+    do j = ny-2, ny+3 {
+
+	cd20[i] = 1./6. * (coeff[nx+1,j] - 2. * coeff[nx,j] + coeff[nx-1,j])
+	cd21[i] = 1./6. * (coeff[nx+2,j] - 2. * coeff[nx+1,j] + coeff[nx,j])
+	cd40[i] = 1./120. * (coeff[nx-2,j] - 4. * coeff[nx-1,j] +
+		  6. * coeff[nx,j] - 4. * coeff[nx+1,j] + coeff[nx+2,j])
+	cd41[i] = 1./120. * (coeff[nx-1,j] - 4. * coeff[nx,j] +
+		  6. * coeff[nx+1,j] - 4. * coeff[nx+2,j] + coeff[nx+3,j])
+
+	z[i] = sx * (coeff[nx+1,j] + (sx2 - 1.) * (cd21[j] + (sx2 - 4.) *
+	       cd41[j])) + tx * (coeff[nx,j] + (tx2 - 1.) *
+	       (cd20[j] + (tx2 - 4.) * cd40[j]))
+
+	i = i + 1
+    }
+
+    ny = y
+    sy = y - ny
+    sy2 = sy * sy
+    ty = 1. - sy
+    ty2 = ty * ty
+
+    # interpolate in y
+
+    cd20y = 1./6. * (z[3] - 2. * z[2] + z[1])
+    cd21y = 1./6. * (z[4] - 2. * z[3] + z[2])
+    cd40y = 1./120. * (z[1] - 4. * z[2] + 6. * z[3] - 4. * z[4] + z[5])
+    cd41y = 1./120. * (z[2] - 4. * z[3] + 6. * z[4] - 4. * z[5] + z[6])
+
+    value = sy * (z[4] + (sy2 - 1.) * (cd21y + (sy2 - 4.) * cd41y)) +
+	    ty * (z[3] + (ty2 - 1.) * (cd20y + (ty2 - 4.) * cd40y))
+
+case II_BISPLINE3:
+
+    # use the B-spline representation
+
+    value = coeff[i,j] * B[i](x) * B[j](y)
+
+    # the B-splines are the following
+
+    B1(x) = (x - x1) ** 3
+    B2(x) = 1 + 3 * (x - x2) + 3 * (x - x2) ** 2 - 3 * (x - x2) ** 3
+    B3(x) = 1 + 3 * (x3 - x) + 3 * (x3 - x) ** 2 - 3 * (x3 - x) ** 3
+    B4(x) = (x4 - x) ** 3
+
+    # the y B-splines are identical
+
+.fi
+
+.sh
+3.4.3. Derivatives
+
+The derivatives are calculated by evaluating the derivatives of the
+interpolating polynomial. The 0-th derivative is the value of the
+interpolant. The 1-st derivatives are d/dx and d/dy. The second are
+d2/dx2, d2/dy2 and d2/dxdy. The derivatives in the case II_BINEAREST
+and II_BILINEAR are calculated directly.
+
+.nf
+case II_BINEAREST:
+
+    der[1,1] = value				# see previous section
+
+case II_BILINEAR:
+
+    der[1] = value				# see previous section
+
+    # d/dx
+    der[2,1] = -ty * coeff[nx,ny] + ty * coeff[nx+1,ny] -
+    	       sy * coeff[nx,ny+1] + sy * coeff[nx+1,ny+1]
+
+    # d/dy
+    der[1,2] = -tx * coeff[nx,ny] + sx * coeff[nx+1,ny] +
+	       tx * coeff[nx,ny+1] + sx * coeff[nx+1,ny+1]
+
+    # d2/dxdy
+    der[2,2] = coeff[nx,ny] - coeff[nx+1,ny] - coeff[nx,ny+1] + coeff[nx+1,ny+1]
+
+case II_BIPOLY3, II_BIPOLY5, II_BISPLINE3:
+.fi
+
+For the higher order interpolants the coefficients of the interpolating
+polynomial in x and y are calculated. In the case of II_BIPOLY3 and II_BIPOLY5
+this is the Everett polynomial of the 3-rd and 5-th order respectively.
+In the case of II_BISPLINE3 the pp-representation is calculated for
+the B-spline coefficients. The value of the interpolant and its
+derivatives is calculated using nested multiplication.
+
+.sh
+3.4.5. Integration
+
+Integration is most easily accomplished by integrating the interpolant in
+x for each value of y. The resulting function of y can then be integrated
+in y to derive the 2-D integral. The limits of the integral are assumed
+to be the corners of a polygon. At minimum of three points which define
+a triangular region in x-y are required. The integral will be an approximation.
+A special function for integrating over a rectangular region is also
+provided.
+
+.sh
+4. Detailed Design
+
+.sh
+4.1. Interpolant Descriptor
+
+The interpolant parameters and coefficients will be stored in a structure
+as listed below.
+
+.nf
+	define	LEN_MSISTRUCT		10
+
+	struct {
+	    
+	    int msi_type		# interpolant type
+	    int	msi_nxcoeff		# size of coefficient array in x
+	    int	msi_nycoeff		# size of coefficient array in y
+	    int	msi_fstpnt		# first datapoint in coefficient array
+	    int	asi_coeff		# pointer to 1-D coefficient array
+
+	} msistruct
+
+.fi
+
+.sh
+4.2. Storage Requirements
+
+The interpolant descriptor requires LEN_MSISTRUCT storage units.
+The coefficient array storage is dynamically allocated and requires
+msi_nxcoeff * msi_nycoeff real storage elements. The requirements for
+each interpolant type are listed below.
+
+.nf
+	II_BINEAREST		nxpix * nypix
+	II_BILINEAR		(nxpix + 1) * (nypix + 1)
+	II_BIPOLY3		(nxpix + 3) * (nypix + 3)
+	II_BIPOLY5		(nxpix + 5) * (nypix + 5)
+	II_BISPLINE3		(nxpix + 3) * (nypix + 3)
+.fi
+
+.endhelp
diff --git a/math/iminterp/doc/iminterp.hd b/math/iminterp/doc/iminterp.hd
new file mode 100644
index 00000000..de836c3e
--- /dev/null
+++ b/math/iminterp/doc/iminterp.hd
@@ -0,0 +1,37 @@
+# Help directory for the IMINTERP (image interpolator) package.
+
+$iminterp	= "math$iminterp/"
+
+arbpix		hlp = arbpix.hlp,	src = iminterp$arbpix.x
+arider		hlp = arider.hlp,	src = iminterp$arider.x
+arieval		hlp = arieval.hlp,	src = iminterp$arieval.x
+asider		hlp = asider.hlp,	src = iminterp$asider.x
+asieval		hlp = asieval.hlp,	src = iminterp$asieval.x
+asifit		hlp = asifit.hlp,	src = iminterp$asifit.x
+asifree		hlp = asifree.hlp,	src = iminterp$asifree.x
+asigeti		hlp = asigeti.hlp,	src = iminterp$asigeti.x
+asigetr		hlp = asigetr.hlp,	src = iminterp$asigetr.x
+asigrl		hlp = asigrl.hlp,	src = iminterp$asigrl.x
+asiinit		hlp = asiinit.hlp,	src = iminterp$asiinit.x
+asirestore	hlp = asirestore.hlp,	src = iminterp$asirestore.x
+asisave		hlp = asisave.hlp,	src = iminterp$asisave.x
+asisinit	hlp = asisinit.hlp,	src = iminterp$asisinit.x
+asivector	hlp = asivector.hlp,	src = iminterp$asivector.x
+asitype		hlp = asitype.hlp,	src = iminterp$asitype.x
+
+mrider		hlp = mrider.hlp,	src = iminterp$mrider.x
+mrieval		hlp = mrieval.hlp,	src = iminterp$mrieval.x
+msider		hlp = msider.hlp,	src = iminterp$msider.x
+msieval		hlp = msieval.hlp,	src = iminterp$msieval.x
+msifit		hlp = msifit.hlp,	src = iminterp$msifit.x
+msifree		hlp = msifree.hlp,	src = iminterp$msifree.x
+msigeti		hlp = msigeti.hlp,	src = iminterp$msigeti.x
+msigetr		hlp = msigetr.hlp,	src = iminterp$msigetr.x
+msigrid		hlp = msigrid.hlp,	src = iminterp$msigrid.x
+msigrl		hlp = msigrl.hlp,	src = iminterp$msigrl.x
+msiinit		hlp = msiinit.hlp,	src = iminterp$msiinit.x
+msirestore	hlp = msirestore.hlp,	src = iminterp$msirestore.x
+msisave		hlp = msisave.hlp,	src = iminterp$msisave.x
+msisinit	hlp = msisinit.hlp,	src = iminterp$msisinit.x
+msitype		hlp = msitype.hlp,	src = iminterp$msitype.x
+msivector	hlp = msivector.hlp,	src = iminterp$msivector.x
diff --git a/math/iminterp/doc/iminterp.hlp b/math/iminterp/doc/iminterp.hlp
new file mode 100644
index 00000000..c602b43e
--- /dev/null
+++ b/math/iminterp/doc/iminterp.hlp
@@ -0,0 +1,234 @@
+.help iminterp Dec98 "Math Package"
+.ih
+NAME
+iminterp -- image interpolator package
+.ih
+SYNOPSIS
+
+.nf
+	 asitype (interpstr, interp_type, nsinc, nincr, rparam)
+         asiinit (asi, interp_type)
+        asisinit (asi, interp_type, nsinc, nincr, rparam)
+          asifit (asi, datain, npix)
+ivalue = asigeti (asi, param)
+rvalue = asigetr (asi, param)
+     y = asieval (asi, x)
+       asivector (asi, x, yfit, npix)
+          asider (asi, x, der, nder)
+      v = asigrl (asi, a, b)
+         asisave (asi, interpolant)
+      asirestore (asi, interpolant)
+         asifree (asi)
+
+     y = arieval (x, datain, npix, interp_type)
+	  arider (x, datain, npix, der, nder, interp_type)
+
+          arbpix (datain, dataout, npix, interp_type, boundary_type)
+.fi
+
+.nf
+         msitype (interpstr, interp_type, nsinc, nincr, rparam)
+        msisinit (msi, interp_type, nsinc, nxincr, nyincr, rparam1, rparam2)
+         msiinit (msi, interp_type)
+          msifit (msi, datain, nxpix, nypix, len_datain)
+ivalue = msigeti (msi, param)
+rvalue = msigetr (msi, param)
+     y = msieval (msi, x, y)
+       msivector (msi, x, y, zfit, npts)
+          msider (msi, x, y, der, nxder, nyder, len_der)
+      v = msigrl (msi, x, y, npts)
+    v = msisqgrl (msi, x1, x2, y1, y2)
+         msisave (msi, interpolant)
+      msirestore (msi, interpolant)
+         msifree (msi)
+
+      y = mrieval (x, y, datain, nxpix, nypix, len_dataina, interp_type)
+           mrider (x, y, datain, nxpix, nypix, len_datain, der, nxder, nyder,
+	           len_der, interp_type)
+.fi
+
+.ih
+DESCRIPTION
+The iminterp package provides a set of routines for interpolating uniformly
+spaced data assuming that the spacing between data points is 1.0. The
+package is divided into 1D and 2D array sequential interpolants,
+prefixes asi and msi, and 1D and 2D
+array random interpolants, prefixes ari and mri.
+The sequential interpolants have
+been optimized for returning many values as is the case when an array is
+shifted. The random interpolants allow evaluation of a few interpolated
+points without the computing time and storage overhead required for
+setting up the sequential version.
+.ih
+NOTES
+The interpolant is chosen at run time from the following list.
+
+.nf
+    II_NEAREST		# nearest neighbour in x
+    II_LINEAR		# linear interpolation in x
+    II_POLY3		# 3rd order interior polynomial in x
+    II_POLY5		# fifth order interior polynomial in x
+    II_SPLINE3		# cubic spline in x
+    II_SINC		# sinc interpolation in x
+    II_LSINC		# look-up table sinc interpolation in x
+    II_DRIZZLE		# drizzle interpolation in x
+
+    II_BINEAREST	# nearest neighbour in x and y
+    II_BILINEAR		# bilinear interpolation
+    II_BIPOLY3		# 3rd order interior polynomial in x and y
+    II_BIPOLY5		# 5th order interior polynomial in x and y
+    II_BISPLINE3	# bicubic spline
+    II_BISINC		# sinc interpolation in x and y
+    II_BILSINC		# look-up table sinc interpolation in x and y
+    II_BIDRIZZLE	# drizzle interpolation in x and y
+.fi
+
+The routines assume that all x (1D, 2D) and  y (2D) values of interest lie in
+the region 1 <= x <= nxpix, 1 <= y <= nypix.
+Checking for out of bounds x and/or y values is the responsibility
+of the calling program. The asi, ari, msi, and mri routines assume that INDEF
+valued pixels have been removed from the data prior to entering the
+package. The routine ARBPIX has been added to the package to facilitate
+INDEF valued pixel removal.
+
+In order to make the package definitions available to the calling program
+an include <math/iminterp.h> statement must appear in the calling program.
+Either ASIINIT, ASISINIT or ASIRESTORE  must be called before using the
+asi routines. ASIFREE frees the space used by the asi routines. For the
+msi routines the corresponding examples are MSIINIT, MSISINIT, MSIRESTORE
+and MSIFREE.
+.ih
+EXAMPLES
+.nf
+Example 1: Shift a 1D data array by a constant amount using a 5th order
+polynomial interpolant and the drizzle routine respectively. Note that
+in this example the drizzle interpolant is equivalent to the linear
+interpolant since the default drizzle pixel fraction is 1.0 and there
+is no scale change. Out-of-bounds pixels are set to 0.0
+
+    include <math/iminterp.h>
+    ...
+    call asiinit (asi, II_POLY5)
+    call asifit (asi, inrow, npix)
+
+    do i = 1, npix
+	if (i + xshift < 1.0 || i + xshift > npix)
+	    outrow[i] = 0.0
+	else
+	    outrow[i] = asieval (asi, i + xshift)
+
+    call asifree (asi)
+    ...
+
+
+    include <math/iminterp.h>
+
+    real tmpx[2]
+    ...
+    call asiinit (asi, II_DRIZZLE)
+    call asifit (asi, inrow, npix)
+
+    do i = 1, npix
+	tmpx[1] = i + xshift - 0.5
+	tmpx[2] = i + xshift + 0.5
+	if (tmpx[1] < 1 || tmpx[2] > npix)
+	    outrow[i] = 0.0
+	else
+	    outrow[i] = asieval (asi, tmpx)
+
+    call asifree (asi)
+    ...
+
+
+Example 2: Shift a 2D array by a constant amount using a 3rd order polynomial
+interpolant and the drizzle interpolant respectively. Note that
+in this example the drizzle interpolant is equivalent to the linear
+interpolant since the default drizzle pixel fraction is 1.0 and there
+is no scale change. Out-of-bounds pixels are set to 0.0.
+
+    include <math/iminterp.h>
+    ...
+    call msiinit (msi, II_BIPOLY3)
+    call msifit (msi, insection, nxpix, nypix, nxpix)
+
+    do j = 1, nypix
+	if (j + yshift < 1 || j + yshift > nypix)
+	    do i = 1, nxpix
+		outsection[i,j] = 0.0
+	else
+	    do i = 1, nxpix
+		if (i + xshift < 1 || i + xshift > nxpix)
+	            outsection[i,j] = 0.0
+		else
+	            outsection[i,j] = msieval (msi, i + xshift, j + yshift)
+
+    call msifree (msi)
+    ...
+
+
+    include <math/iminterp.h>
+    ...
+    real tmpx[4], tmpy[4]
+    ...
+    call msiinit (msi, II_BIDRIZZLE)
+    call msifit (msi, insection, nxpix, nypix, nxpix)
+
+    do j = 1, nypix {
+	tmpy[1] = j + yshift - 0.5
+	tmpy[2] = j + yshift - 0.5
+	tmpy[3] = j + yshift + 0.5
+	tmpy[4] = j + yshift + 0.5
+	if (tmpy[1] < 1 || tmpy[4] > nypix)
+	    do i = 1, nxpix
+		outsection[i,j] = 0.0
+	else
+	    do i = 1, nxpix
+	        tmpx[1] = i + xshift - 0.5
+	        tmpx[2] = i + xshift + 0.5
+	        tmpx[3] = i + xshift + 0.5
+	        tmpx[4] = i + xshift - 0.5
+		if (tmpx[1] < 1 || tmpx[2] > nxpix)
+		    outsection[i,j] = 0.0
+		else
+	            outsection[i,j] = msieval (msi, tmpx, tmpy)
+    }
+
+    call msifree (msi)
+    ...
+
+
+Example 3: Calculate the integral under a 1D data array
+
+    include <math/iminterp.h>
+    ...
+    call asiinit (asi, II_POLY5)
+    call asifit (asi, datain, npix)
+
+    integral =  asigrl (asi, 1. real (npix))
+
+    call asifree (asi)
+    ...
+
+Example 4: Store a 1D interpolant for later use by ASIEVAL
+
+    include <math/iminterp.h>
+
+    ...
+    call asiinit (asi, II_POLY3)
+    call asifit (asi, datain, npix)
+
+    len_interpolant = asigeti (asi, ASINSAVE)
+    call salloc (interpolant, len_interpolant, TY_REAL)
+    call asisave (asi, Memr[interpolant])
+
+    call asifree (asi)
+    ...
+    call asirestore (asi, Memr[interpolant])
+
+    do i = 1, npts
+	yfit[i] = asieval (asi, x[i])
+
+    call asifree (asi)
+    ...
+.fi
+.endhelp
diff --git a/math/iminterp/doc/iminterp.men b/math/iminterp/doc/iminterp.men
new file mode 100644
index 00000000..9daf5883
--- /dev/null
+++ b/math/iminterp/doc/iminterp.men
@@ -0,0 +1,32 @@
+	 arbpix	- Replace bad pixels in an array
+	 arider	- Calculate derivatives for a few points in a 1-D array
+        arieval	- Evaluate the interpolant at a few points in a 1-D array
+         asider	- Evaluate derivatives at x 
+	asieval	- Evaluate the interpolant at x
+	 asifit	- Fit the 1-D interpolant
+	asifree - Free space allocated by asiinit or asisinit
+	asigeti - Fetch an integer parameter
+	 asigrl	- Calculate the integral under an array
+	asiinit - Initialize 1-D interpolant using default parameters
+     asirestore - Restore interpolant parameters and coefficients
+	asisave - Save interpolant parameters and coefficients
+       asisinit - Initialize 1-D interpolant using user parameters
+	asitype - Decode string into interpolant type and parameters
+      asivector - Evaluate interpolant at an array of x
+
+         mrider	- Calculate derivatives for a few points in a 2-D array
+        mrieval	- Evaluate the interpolant at a few points in a 2-D array
+         msider	- Evaluate derivatives at x and y
+        msieval	- Evaluate the interpolant at x and y
+         msifit	- Fit the 2-D interpolant
+        msifree	- Free space allocated by msiinit or msisinit
+	msigeti - Fetch an integer parameter
+	msigetr - Fetch a real parameter
+         msigrl	- Calculate the integral inside a polygon
+        msiinit	- Initialize the 2-D interpolant using default parameters
+     msirestore	- Restore interpolant parameters and coefficients
+        msisave	- Save 2-D interpolant parameters and coefficients
+       msisinit	- Initialize the 2-D interpolant using user parameters
+       msisqgrl - Calculate the integral inside a rectangle
+	msitype - Decode string into interpolant type and parameters
+      msivector - Evaluate interpolant at an array of x and y
diff --git a/math/iminterp/doc/iminterp.spc b/math/iminterp/doc/iminterp.spc
new file mode 100644
index 00000000..ce5b8680
--- /dev/null
+++ b/math/iminterp/doc/iminterp.spc
@@ -0,0 +1,525 @@
+.help iminterp Jul84 "Math Package"
+
+.ce
+Specifications for the Image Interpolator Package
+.ce
+Lindsey Davis
+.ce
+Vesa Junkkarinen
+.ce
+August 1984
+
+.sh
+1. Introduction
+
+    One of the most common operations in image processing is
+interpolation in a data array. Due to the large amount of data involved,
+efficiency is highly important. The advantage of having locally written
+interpolators, includes the ability to optimize for uniformly spaced data
+and the possibility of adding features that are useful to the final
+application.
+
+.sh
+2. Requirements
+
+.ls (1)
+The package shall take as input a one-dimensional array containing image
+data. The pixels are assumed to be equally spaced along a line.
+The coordinates of a pixel are assumed to be
+the same as the subscript of the pixel in the data array.
+The coordinate of the first pixel in the array and the spacing between pixels
+is assumed to be 1.0. All pixels are assumed to be good.
+Checking for INDEF valued and out of bounds pixels is the responsibility of the
+user. A routine to remove INDEF valued pixels from a data array shall be
+included in the package.
+.le
+.ls (2)
+The package is divided into array sequential interpolators and array
+random interpolators. The sequential interpolators have been optimized
+for returning many values as is the case when an array is shifted, or
+oversampled at many points in order to produce a
+smooth plot.
+The random interpolators allow the evaluation of a few interpolated
+points without the computing time and storage overhead required for
+setting up the sequential version.
+.le
+.ls (3)
+The quality of the interpolant will be set at run time. The options are:
+
+.nf
+    II_NEAREST		- nearest neighbour
+    II_LINEAR		- linear interpolation
+    II_POLY3		- 3rd order divided differences
+    II_POLY5		- 5th order divided differences
+    II_SPLINE3		- cubic spline
+.fi
+
+The calling sequences shall be invariant to the interpolant selected.
+Routines should be designed so that new interpolants can be added
+with minimal changes to the code and no change to the calling sequences.
+.le
+.ls (4)
+The interpolant parameters and the arrays necessary to store the coefficients
+are stored in a structure referenced by a pointer. The pointer is returned
+to the user program by the initial call to ASIINIT or ASIRESTORE and freed
+by a call to ASIFREE (see section 3.1).
+.le
+.ls (5)
+The package routines shall be able to:
+.ls o
+Calculate the coefficients of the interpolant and store these coefficients in
+the appropriate part of the interpolant descriptor structure.
+.le
+.ls o
+Evaluate the interplant at a given x(s) coordinate(s).
+.le
+.ls o
+Calculate the derivatives of the interpolant at a given value of x.
+.le
+.ls o
+Integrate the interpolant over a specified x interval.
+.le
+.ls o
+Store the interpolant in a user supplied array. Restore the saved interpolant
+to the interpolant descriptor structure for later use by ASIEVAL, ASIVECTOR,
+ASIDER and ASIGRL.
+.le
+
+.sh
+3. Specifications
+
+.sh
+3.1. The Array Sequential Interpolator Routines
+
+    The package prefix is asi and the package routines are:
+
+.nf
+        asiinit	(asi, interp_type)
+         asifit	(asi, datain, npix)
+    y = asieval	(asi, x)
+      asivector	(asi, x, yfit, npix)
+         asider	(asi, x, der, nder)
+     v = asigrl	(asi, a, b)
+        asisave	(asi, interpolant)
+     asirestore	(asi, interpolant)
+        asifree	(asi)
+.fi
+
+.sh
+3.2. The Array Random Interpolator Routines
+
+    The package prefix is ari and the package routines are:
+
+.nf
+    y = arieval	(x, datain, npix, interp_type)
+	 arider	(x, datain, npix, der, nder, interp_type)
+.fi
+
+.sh
+3.3. Miscellaneous
+
+    A routine has been included in the package to remove INDEF valued
+pixels from an array.
+
+.nf
+    arbpix (datain, dataout, npix, interp_type, boundary_type)
+.fi
+
+.sh
+3.4. Algorithms
+
+.sh
+3.4.1. Coefficients
+
+    The coefficient array used by the asi routines is calculated by ASIFIT.
+ASIFIT accepts an array of data, checks that the number
+of data points is appropriate for the interpolant selected, allocates
+space for the interpolant, and calculates the coefficients.
+Boundary coefficient values are calculated
+using boundary projection.  With the exception of the cubic spline interpolant,
+the coefficients are stored as the data points.
+The B-spline coefficients are 
+calculated using natural end conditions (Prenter 1975).
+After a call to ASIFIT the coefficient array contains the following.
+
+.nf
+    case II_NEAREST:
+
+        # no boundary conditions necessary
+	coeff[1] = datain[1]
+	.
+	.
+	.
+	coeff[npts] = datain[npix]
+
+    case II_LINEAR:
+
+        # coeff[npxix+1] required if x = npix
+	coeff[1] = datain[1]
+	.
+	.
+	.
+	coeff[npix] = datain[npix]
+	coeff[npix+1] = 2. * datain[npix] - datain[npix-1]
+
+    case II_POLY3:
+
+        # coeff[0] required if x = 1
+	# coeff[npix+1], coeff[npix+2] required if x = npix
+	coeff[0] = 2. * datain[1] - datain[2]
+	coeff[1] = datain[1]
+	.
+	.
+	.
+	coeff[npix] = datain[npix]
+	coeff[npix+1] = 2. * datain[npix] - datain[npix-1]
+	coeff[npix+2] = 2. * datain[npix] - datain[npix-2]
+
+    case II_POLY5:
+
+        # coeff[1], coeff[0] reqired if x = 1
+	# coeff[npix+1], coeff[npix+2], coeff[npix=3]
+	# required if x = npix
+
+	coeff[-1] = 2. * datain[1] - datain[3]
+	coeff[0] = 2. * datain[1] - datain[2]
+	coeff[1] = datain[1]
+	.
+	.
+	.
+	coeff[npix] = datain[npix]
+	coeff[npix+1] = 2. * datain[npix] - datain[npix-1]
+	coeff[npix+2] = 2. * datain[npix] - datain[npix-2]
+	coeff[npix+3] = 2. * datain[npix] - datain[npix-3]
+
+    case SPLINE3:
+
+        # coeff[0] = 2nd der at x = 1, coeff[0] = 0.
+	# coeff[npix+1] = 2nd der at x = npts, coeff[npix+1] = 0.
+	# coeff[npix+2] = 0., required if x = npix
+	coeff[0] = b[1]
+	coeff[1] = b[2]
+	.
+	.
+	.
+	coeff[npix] = b[npix+1]
+	coeff[npix+1] = b[npix+2]
+	coeff[npix+2] = 0.
+.fi
+
+.sh
+3.4.2. Evaluation
+
+    The ASIEVAL and ASIVECTOR routines have been optimized to be as efficient
+as possible. The values of the II_NEAREST and II_LINEAR interpolants
+are calculated directly. The II_SPLINE3 interpolant is evaluated using
+polynomial coefficients calculated directly from the B-spline coefficients
+(de Boor 1978). Values of the higher order polynomial interpolants
+are calculated using central differences. The equations for each case are
+listed below.
+
+.nf
+case II_NEAREST:
+    
+    y = coeff[int (x + 0.5)]
+
+case II_LINEAR:
+
+    nx = x
+    y = (x - nx) * coeff[nx+1] + (nx + 1 - x) * coeff[nx]
+
+case II_POLY3:
+
+    nx = x
+    s = x - nx
+    t = 1. - s
+
+    # second central differences
+    cd20 = 1./6. * (coeff[nx+1] - 2. * coeff[nx] + coeff[nx-1])
+    cd21 = 1./6. * (coeff[nx+2] - 2. * coeff[nx+1] + coeff[nx])
+
+    y = s * (coeff[nx+1] + (s * s - 1.) * cd21) + t * (coeff[nx] +
+	(t * t - 1.) * cd20)
+
+case II_POLY5:
+
+    nx = x
+    s = x - nx
+    t = 1. - s
+
+    # second central differences
+    cd20 = 1./6. * (coeff[nx+1] - 2. * coeff[nx] + coeff[nx-1])
+    cd21 = 1./6. * (coeff[nx+2] - 2. * coeff[nx+1] + coeff[nx])
+
+    # fourth central diffreences
+    cd40 = 1./120. * (coeff[nx-2] - 4. * coeff[nx-1] + 6. * coeff[nx] - 4. *
+	   coeff[nx+1] + a[nx+2])
+    cd41 = 1./120. * (coeff[nx-1] - 4. * coeff[nx] + 6. * coeff[nx+1] - 4. *
+	   coeff[nx+2] + coeff[nx+3]
+
+    y = s * (coeff[nx+1] + (s * s - 1.) * (cd21 + (s * s - 4.) * cd41)) +
+	t * (coeff[nx] + (t * t - 1.) * (cd20 + (t * t - 4.) * cd40))
+
+case II_SPLINE3:
+
+    nx = x
+    s = x - nx
+
+    pc[1] = coeff[nx-1] + 4. * coeff[nx] + coeff[nx+1]
+    pc[2] = 3. * (coeff[nx+1] - coeff[nx-1])
+    pc[3] = 3. * (coeff[nx-1] - 2. * coeff[nx] + coeff[nx+1])
+    pc[4] = -coeff[nx-1] + 3. * coeff[nx] - 3. * coeff[nx+1] + coeff[nx+2]
+
+    y = pc[1] + s * (pc[2] + s * (pc[3] + s * pc[4]))
+.fi
+
+
+    The ARIEVAL routine uses the expressions above to evaluate the
+interpolant. However unlike ASIEVAL, ARIEVAL does not use a previously
+calculated coefficient array. Instead ARIEVAL selects the appropriate
+portion of the data array, calculates the coefficients and boundary
+coefficients if necessary, and evaluates the interpolant at the time it
+is called. The cubic spline interpolant uses at most SPLTS (currently 16)
+data points to calculate the B-spline coefficients.
+
+.sh
+3.4.3. Derivatives
+
+    Derivatives of the interpolant are calculated by evaluating the
+derivatives of the interpolating polynomial. For all interpolants der[1]
+equals the value of the interpolant at x.
+For the sake of efficiency the derivatives
+of the II_NEAREST and II_LINEAR interpolants are calculated directly.
+
+.nf
+    case II_NEAREST:
+
+	der[1] = coeff[int (x+0.5)]
+
+    case II_LINEAR:
+
+	der[1] = (x - nx) * coeff [nx+1] + (nx + 1 - x) * coeff[nx]
+	der[2] = coeff[nx+1] - coeff[nx]
+.fi
+
+    In order to calculate the derivatives of the cubic spline and
+polynomial interpolants
+the coefficients of the interpolating polynomial must be calculated.
+The polynomial
+coefficients for the cubic spline interpolant are computed directly from the
+B-spline coefficients (see 3.4.2.). The higher order polynomial
+interpolant coefficients are calculated as follows.
+
+First the appropriate portion of the coefficient array is loaded.
+
+.nf
+	do i = 1, nterms
+	    d[i] = coeff[nx - nterms/2 + i]
+.fi
+
+Next the divided differences are calculated (Conte and de Boor 1972).
+
+.nf
+	do k = 1, nterms - 1
+	    do i = 1, nterms - k
+		d[i] = (d[i+1] - d[i]) / k
+.fi
+
+The d[i] are the coefficients of an interpolating polynomial of the
+following form. The x[i] are the nterms data points surrounding the
+point of interest.
+
+.nf
+	p(x) = d[1] * (x-x[1]) * ... * (x-x[nterms-1) +
+	       d[2] * (x-x[2]) * ... * (x-x[nterms-1]) + ... + d[nterms]
+.fi
+
+Next a new set of polynomial coefficients are calculated
+(Conte and de Boor 1972).
+
+.nf
+	do k = nterms, 2, -1
+	    do i = 2, k
+		d[i] = d[i] + d[i-1] * (k - i - nterms/2)
+.fi
+
+The new d[i] are the coefficients of the follwoing polynomial.
+
+.nf
+	nx = x
+	p(x) = d[1] * (x-nx) ** (nterms-1) + d[2] * (x-nx) ** (nterms-2) + ...
+	       d[nterms]
+.fi
+
+The d[i] array is flipped. The value and derivatives
+of the interpolant are then calculated using the d[i] array and
+nested multiplication.
+
+.nf
+	s = x - nx
+
+	do k = 1, nder {
+
+	    accum = d[nterms-k+1]
+
+	    do j = nterms - k, 1, -1
+		accum = d[j] + s * accum
+
+	    der[k] = accum
+
+	    # differnetiate
+	    do j = 1, nterms - k
+		d[j] = j * d[j + 1]
+	}
+.fi
+
+    ARIDER calculates the derivatives of the interpolant using the same
+technique ASIDER. However ARIDER does not use a previously calculated
+coefficient array like ASIDER. Instead ARIDER selects the appropriate portion
+of the data array, calculates the coefficients and boundary coefficients,
+and computes the derivatives at the time it is called.
+
+.sh
+3.4.5. Integration
+
+    ASIGRL calculates the integral of the interpolant between fixed limits
+by integrating the interpolating polynomial. The coefficients of the
+interpolating polynomial are calculated as discussed in section 3.4.4.
+
+.sh 
+4. Usage
+
+.sh
+4.1. User Notes
+
+The following series of steps illustrates the use of the package.
+
+.ls 4
+.ls (1)
+Insert an include <iminterp.h> statement in the calling program to make
+the IINTERP definitions available to the user program.
+.le
+.ls (2)
+Remove INDEF valued pixels from the data using ARBPIX.
+.le
+.ls (3)
+Call ASIINIT to initialize the interpolant parameters.
+.le
+.ls (4)
+Call ASIFIT to calculate the coefficients of the interpolant.
+.le
+.ls (5)
+Evaluate the interpolant at a given value of x(s) using ASIEVAL or
+ASIVECTOR.
+.le
+.ls (6)
+Calculate the derivatives and integral or the interpolant using
+ASIDER and ASIGRL.
+.le
+.ls (7)
+Free the interpolator structure by calling ASIFREE.
+.le
+.le
+
+    The interpolant can be saved and restored using ASISAVE and ASIRESTORE.
+If the values and derivatives of only a few points in an array are desired
+ARIEVAL and ARIDER can be called.
+
+.sh
+4.2. Examples
+
+.nf
+Example 1: Shift a data array by a constant amount
+
+    include <iminterp.h>
+    ...
+    call asiinit (asi, II_POLY5)
+    call asifit (asi, inrow, npix)
+
+    do i = 1, npix
+	outrow[i] = asieval (asi, i + shift)
+
+    call asifree (asi)
+    ...
+
+Example 2: Calculate the integral under the data array
+
+    include <iminterp.h>
+    ...
+    call asiinit (asi, II_POLY5)
+    call asifit (asi, datain, npix)
+
+    integral =  asigrl (asi, 1. real (npix))
+
+    call asifree (asi)
+    ...
+
+Example 2: Store interpolant for later use by ASIEVAL
+	   LEN_INTERP must be at least npix + 8 units long where npix is
+	   is defined in the call to ASIFIT.
+
+    include <iminterp.h>
+
+    real   interpolant[LEN_INTERP]
+    ...
+    call asiinit (asi, II_POLY3)
+    call asifit (asi, datain, npix)
+    call asisave (asi, interpolant)
+    call asifree (asi)
+    ...
+    call asirestore (asi, interpolant)
+    do i = 1, npts
+	yfit[i] = asieval (asi, x[i])
+    call asifree (asi)
+    ...
+.fi
+.sh
+5. Detailed Design
+
+.sh
+5.1. Interpolator Descriptor
+
+    The interpolant parameters and coefficients are stored in a
+structure listed below.
+
+.nf
+    define	LEN_ASISTRUCT	4		# Length in structure units of
+						# interpolant descriptor
+
+    define	ASI_TYPE	Memi[$1]	# Interpolant type
+    define	ASI_NCOEFF	Memi[$1+1]	# No. of coefficients
+    define	ASI_OFFSET	Memi[$1+2]	# First "data" point in
+						# coefficient array
+    define	ASI_COEFF	Memi[$1+3]	# Pointer to coefficient array
+.fi
+
+.sh
+5.2. Storage Requirements
+
+    The interpolant descriptor requires LEN_ASISTRUCT storage units. The
+coefficient array requires ASI_NCOEFF(asi) real storage elements, where
+ASI_NCOEFF(asi) is defined as follows.
+
+.nf
+    ASI_NCOEFF(asi) = npix	# II_NEAREST
+    ASI_NCOEFF(asi) = npix+1	# II_LINEAR
+    ASI_NCOEFF(asi) = npix+3	# II_POLY3
+    ASI_NCOEFF(asi) = npix+5	# II_POLY5
+    ASI_NCOEFF(asi) = npix+3	# II_SPLINE3
+.fi
+
+.sh
+6. References
+
+.ls (1)
+Carl de Boor, "A Practical Guide to Splines", 1978, Springer-Verlag New
+York Inc.
+.le
+.ls (2)
+S.D. Conte and C. de Boor, "Elementary Numerical Analysis", 1972, McGraw-Hill,
+Inc.
+.le
+.ls (3)
+P.M. Prenter, "Splines and Variational Methods", 1975, John Wiley and Sons Inc.
+.le
+.endhelp
diff --git a/math/iminterp/doc/mrider.hlp b/math/iminterp/doc/mrider.hlp
new file mode 100644
index 00000000..47515c48
--- /dev/null
+++ b/math/iminterp/doc/mrider.hlp
@@ -0,0 +1,79 @@
+.help mrider Dec98 "Image Interpolation Package"
+.ih
+NAME
+mrider -- calculate the derivatives at x and y
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+.nf
+mrider (x, y, datain, nxpix, nypix, len_datain, der, nxder, nyder, len_der,
+	interp_type)
+.fi
+
+.nf
+real	x[4]			#I x value, 1. <= x[1-4] <= nxpix
+real	y[4]			#I y value, 1. <= y[1-4] <= nypix
+real	datain[len_datain, ARB]	#I data array	
+int	nxpix			#I number of data pixels in x
+int	nypix			#I number of data pixels in y
+int	len_datain		#I length of datain, len_datain >= nxpix
+real	der[len_der, ARB]	#O derivative array
+int	nxder			#I x order of the derivatives
+int	nyder			#I y order of the derivatives
+int	len_der			#I row length of der, len_der >= nxder
+int	interp_type		#I interpolant type
+.fi
+.ih
+ARGUMENTS
+.ls x, y
+The single x and y points or in the case of the drizzle interpolant the
+single quadrilateral at / over which the derivatives are to be evaluated.
+The quadrilateral vertices may be stored in clock-wise or counter-clockwise
+order.
+.le
+.ls datain
+Array of data values.
+.le
+.ls nxpix, nypix
+The number of data values in the x and y directions
+.le
+.ls len_datain
+The row length of the datain array. Len_datain must be >= nxpix.
+.le
+.ls der
+The derivative array. Der[1,1] equals the function value at x and y and
+der[2,1], der[1,2] are the first derivatives with respect to x and y
+respectively.
+.le
+.ls nxder, nyder
+The number of the derivatives in x and y to be returned. MRIDER checks
+that the requested number of derivatives is sensible. The sinc interpolants
+return the interpolant value and all the first and second order derivatives.
+The drizzle interpolant returns the interpolant value and the first
+derivative in x and y.
+.le
+.ls len_der
+The row length of the derivative array. Len_der must be >= nxder.
+.le
+.ls interp_type
+Interpolant type. The options are II_BINEAREST, II_BILINEAR, II_BIPOLY3,
+II_BIPOLY5, II_BISPLINE3, II_SINC / II_LSINC, and II_DRIZZLE. The look-up
+table sinc is not supported and defaults to the sinc interpolant. The
+interpolant width is 31 pixels. The drizzle pixel fraction is 1.0. The
+interpolant type definitions are found in the package header file
+math/iminterp.h.
+.le
+.ih
+DESCRIPTION
+MRIDER is useful for evaluating the function and derivatives at a few
+widely spaced points in a data array without the storage space required
+by the sequential version. 
+.ih
+NOTES
+Checking for out of bounds and INDEF valued pixels is the
+responsibility of the user.
+.ih
+SEE ALSO
+msider
+.endhelp
diff --git a/math/iminterp/doc/mrieval.hlp b/math/iminterp/doc/mrieval.hlp
new file mode 100644
index 00000000..35477614
--- /dev/null
+++ b/math/iminterp/doc/mrieval.hlp
@@ -0,0 +1,57 @@
+.help mrieval Dec98 "Image Interpolation Package"
+.ih
+NAME
+mrieval -- evaluate the interpolant at x and y
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+y = mrieval (x, y, datain, nxpix, nypix, len_datain, interp_type)
+
+.nf
+    real	x[4]			#I x value, 1 <= x[1-4] <= nxpix
+    real	y[4]			#I y value, 1 <= y[1-4] <= nypix
+    real	datain[len_datain, ARB]	#I data array
+    int		nxpix			#I number of x values
+    int		nypix			#I number of y values
+    int		len_datain		#I length datain, len_datain >= nxpix
+    int		interp_type		#I interpolant type
+.fi
+.ih
+ARGUMENTS
+.ls x, y
+The single x and y values or in the case of the drizzle interpolant the
+single quadrilateral at / over which the interpolant is to be evaluated.
+The vertices of the quadilateral must be defined in clock-wise or
+counter-clockwise order.
+.le
+.ls datain
+The array of data values.
+.le
+.ls nxpix, nypix
+The number of data pixels in x and y.
+.le
+.ls len_datain
+The row length of datain. Len_datain must be >= nxpix.
+.le
+.ls interp_type
+Interpolant type. The options are II_BINEAREST, II_BILINEAR, II_BIPOLY3,
+II_BIPOLY5, II_BISPLINE3, II_SINC / II_LSINC, and II_DRIZZLE. The look-up
+table sinc interpolant is not supported and defaults to the sinc interpolant.
+The sinc interpolant width is 31 pixels. The drizzle pixel fraction is 1.0.
+The interpolant type definitions are found in the package header file
+math/iminterp.h.
+.le
+.ih
+DESCRIPTION
+MRIEVAL is useful for evaluating the interpolant at a few selected points
+in the datain array without the storage overhead required for the sequential
+version.
+.ih
+NOTES
+Checking for INDEF valued or out of bounds pixels is the
+responsibility of the user.
+.ih
+SEE ALSO
+msieval, msivector, mrider
+.endhelp
diff --git a/math/iminterp/doc/msider.hlp b/math/iminterp/doc/msider.hlp
new file mode 100644
index 00000000..0139c0a0
--- /dev/null
+++ b/math/iminterp/doc/msider.hlp
@@ -0,0 +1,52 @@
+.help msider Dec98 "Image Interpolation Package"
+.ih
+NAME
+msider -- evaluate the interpolant derivatives at x and y 
+.ih
+SYNOPSIS
+msider (msi, x, y, der, nxder, nyder, len_der)
+
+.nf
+    pointer	msi			#I interpolant descriptor
+    real	x[4]			#I x value, 1 <= x[1-4] <= nxpix
+    real	y[4]			#I y value, 1 <= y[1-4] <= nypix
+    real	der[len_der, ARB]	#O derivative array
+    int		nxder			#I number of x derivatives
+    int		nyder			#I number of y derivatives
+    int		len_der			#I row length of der, len_der >= nxder
+.fi
+.ih
+ARGUMENTS
+.ls msi
+Pointer to the 2D sequential interpolant descriptor.
+.le
+.ls x, y
+The single x and y values or in the case of the drizzle interpolant the
+single quadrilateral at / over which the point is to be evaluated.
+.le
+.ls der
+The array containing the derivatives. Der[1,1] contains the value of
+the interpolant at x and y. Der[2,1] and der[1,2] contain the 1st
+derivatives of x and y respectively.
+.le
+.ls nxder, nyder
+The number derivatives in x and y.
+.le
+.ls len_der
+The row length of der. Len_der must be >= nxder.
+.le
+.ih
+DESCRIPTION
+The polynomial and spline interpolants are evaluated using the polynomial
+coefficients and nested multiplication. The polynomial interpolants are
+stored as the data points. The spline interpolant is stored as a set of
+B-spline coefficients.
+.ih
+NOTES
+MRIDER checks that the number of derivatives requested is reasonable.
+Checking for out of bounds and INDEF valued pixels is the responsibility of the
+user. MSIINIT and MSIFIT must be called before using MSIDER.
+.ih
+SEE ALSO
+mrider
+.endhelp
diff --git a/math/iminterp/doc/msieval.hlp b/math/iminterp/doc/msieval.hlp
new file mode 100644
index 00000000..9a77c006
--- /dev/null
+++ b/math/iminterp/doc/msieval.hlp
@@ -0,0 +1,46 @@
+.help msieval Dec98 "Image Interpolation Package"
+.ih
+NAME
+msieval -- procedure to evaluate the interpolant at x and y
+.ih
+SYNOPSIS
+z = msieval (msi, x, y)
+
+.nf
+pointer		msi		#I interpolant descriptor
+real		x[4]		#I x value, 1 <= x[1-4] <= nxpix
+real		y[4]		#I y value, 1 <= y[1-4] <= nypix
+.fi
+.ih
+ARGUMENTS
+.ls msi    
+The pointer to the sequential interpolant descriptor structure.
+.le
+.ls x, y
+The single x and y values of or in the case of the drizzle interpolant
+the single quadrilateral over which the point is to be evaluated.
+.le
+.ih
+DESCRIPTION
+The polynomial coefficients are calculated from the data points in the
+case of the polynomial interpolants and the B-spline coefficients in
+the case of the spline interpolant. The polynomial interpolants
+are evaluated using Everett's central difference formula. The boundary
+extension algorithm is projection.
+
+The sinc interpolant is evaluated using an array of data points around
+the desired position. The look-up table sinc interpolant is computed
+using an a pre-computed look--up table entry. The boundary extension
+algorithm is nerest neighbor.
+
+The drizzle interpolant is computed by computing the mean value of the
+data within the user supplied quadrilateral.
+.ih
+NOTES
+Checking for out of bounds and INDEF valued pixels is the responsibility of
+the user. MSIINIT or MSISINIT and MSIFIT must be called before calling
+MSIEVAL.
+.ih
+SEE ALSO
+msivector, mrieval, mrider
+.endhelp
diff --git a/math/iminterp/doc/msifit.hlp b/math/iminterp/doc/msifit.hlp
new file mode 100644
index 00000000..9a63ae2d
--- /dev/null
+++ b/math/iminterp/doc/msifit.hlp
@@ -0,0 +1,45 @@
+.help msifit Dec98 "Image Interpolation Package"
+.ih
+NAME
+msifit - fit the interpolant to the data
+.ih
+SYNOPSIS
+msifit (msi, datain, nxpix, nypix, len_datain)
+
+.nf
+    pointer	msi			#I interpolant descriptor
+    real	datain[len_datain,ARB]	#I data array
+    int		nxpix			#I number of x pixels
+    int		nypix			#I number of y pixels
+    int		len_datain		#I length of datain, len_datain >= nxpix
+.fi
+.ih
+ARGUMENTS
+.ls msi     
+Pointer to the sequential interpolant descriptor.
+.le
+.ls datain
+Array containing the data.
+.le
+.ls nxpix, nypix
+The number of pixels in x and y.
+.le
+.ls len_datain
+The row length of the datain array. Len_datain must be >= nxpix.
+.le
+.ih
+DESCRIPTION
+The datain array is checked for size, memory is allocated for the coefficient
+array and the end conditions are specified. The interior polynomial, sinc,
+and drizzle interpolants are saved as the data points. The polynomial
+coefficients are calculated from the data points in the evaluation stage.
+The B-spline coefficients are calculated in MSIFIT as they depend on the
+entire data array.
+.ih
+NOTES
+Checking for INDEF valued pixels is the responsibility of the user.
+MSIINIT or MSISINIT must be called before using MSIFIT.  MSIFIT must be
+called before using MSIEVAL, MSIVECTOR, MSIDER, MSIGRL or MSISQGRL.
+.ih
+SEE ALSO
+.endhelp
diff --git a/math/iminterp/doc/msifree.hlp b/math/iminterp/doc/msifree.hlp
new file mode 100644
index 00000000..79b1966d
--- /dev/null
+++ b/math/iminterp/doc/msifree.hlp
@@ -0,0 +1,26 @@
+.help msifree Dec98 "Image Interpolation Package"
+.ih
+NAME
+msifree -- free sequential interpolant descriptor
+.ih
+SYNOPSIS
+msifree (msi)
+
+.nf
+    pointer	msi		#U interpolant descriptor
+.fi
+.ih
+ARGUMENTS
+.ls msi      
+Pointer to the sequential interpolant descriptor structure.
+.le
+.ih
+DESCRIPTION
+MSIFREE frees the sequential interpolant descriptor structure.
+MSIFREE should be called when interpolation is complete.
+.ih
+NOTES
+.ih
+SEE ALSO
+msiinit, msisinit
+.endhelp
diff --git a/math/iminterp/doc/msigeti.hlp b/math/iminterp/doc/msigeti.hlp
new file mode 100644
index 00000000..5ab46156
--- /dev/null
+++ b/math/iminterp/doc/msigeti.hlp
@@ -0,0 +1,35 @@
+.help msigeti Dec98 msigeti.hlp
+.ih
+NAME
+msigeti -- fetch an msi integer parameter
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+ivalue = msigeti (msi, param)
+
+.nf
+    pointer	msi		#I interpolant descriptor
+    int		param		#I parameter
+.fi
+.ih
+ARGUMENTS
+.ls msi      
+Pointer to the sequential interpolant descriptor structure.
+.le
+.ls param
+The parameter to be fetched. The choices are: II_MSITYPE, the interpolant
+type, II_MSINSAVE, the length of the saved coefficient array, and
+II_MSINSINC, the half-width of the sinc interpolant.
+.le
+.ih
+DESCRIPTION
+MSIGETI is used to determine the size of the coefficient array that
+must be allocated to save the sequential interpolant description structure,
+and to fetch selected sequential interpolant parameters.
+.ih
+NOTES
+.ih
+SEE ALSO
+msiinit, msisinit, msigetr
+.endhelp
diff --git a/math/iminterp/doc/msigetr.hlp b/math/iminterp/doc/msigetr.hlp
new file mode 100644
index 00000000..dadac5c2
--- /dev/null
+++ b/math/iminterp/doc/msigetr.hlp
@@ -0,0 +1,37 @@
+.help msigetr Dec98 msigetr.hlp
+.ih
+NAME
+msigetr -- fetch an msi real parameter
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+rvalue = msigetr (msi, param)
+
+.nf
+    pointer	msi		#I interpolant descriptor
+    int		param		#I parameter
+.fi
+.ih
+ARGUMENTS
+.ls msi      
+Pointer to the sequential interpolant descriptor structure.
+.le
+.ls param
+The parameter to be fetched. The choices are: II_MSIBADVAL, the undefined
+pixel value for the drizzle interpolant. The parameter definitions are
+contained in the package header file math/iminterp.h.
+.le
+.ih
+DESCRIPTION
+MSIGETR is used to set the value of undefined drizzle interpolant pixels.
+Undefined pixels are those for which the interpolation coordinates do not
+overlap the input coordinates, but are still, within the boundaries of the input
+image, a situation which may occur when the pixel fraction is < 1.0.
+.ih
+.ih
+NOTES
+.ih
+SEE ALSO
+msiinit, msisinit, msigeti
+.endhelp
diff --git a/math/iminterp/doc/msigrid.hlp b/math/iminterp/doc/msigrid.hlp
new file mode 100644
index 00000000..6bc110d5
--- /dev/null
+++ b/math/iminterp/doc/msigrid.hlp
@@ -0,0 +1,51 @@
+.help msigrid Dec98 "Image Interpolation Package"
+.ih
+NAME
+msigrid -- evaluate the interpolant on a grid of points
+.ih
+SYNOPSIS
+msigrid (msi, x, y, zfit, nx, ny, len_zfit)
+
+.nf
+    pointer	msi			#I interpolant descriptor
+    real	x[2*nx]			#I x values, 1 <= x[i] <= nx
+    real	y[2*ny]  		#I y values, 1 <= y[i] <= ny
+    real	zfit[len_zfit,ARB]	#O grid of interpolated values
+    int		nx			#I number of x points
+    int		ny			#I number of y points
+    int		len_zfit		#I length zfit, len_zfit >= nx
+.fi
+.ih
+ARGUMENTS
+.ls msi     
+Pointer to the interpolant descriptor structure.
+.le
+.ls x, y
+The x and y arrays of points to be evaluated, or in the case of the drizzle
+interpolant the x and y ranges over which the points are to be evaluated.
+The x and y arrays must be ordered in increasing values of x and y respectively.
+.le
+.ls zfit
+The array of interpolated points.
+.le
+.ls nx, ny
+The number of points in the x and y directions respectively.
+.le
+.ls len_zfit
+The row length of the zfit array. Len_zfit >= nx.
+.le
+.ih
+DESCRIPTION
+MSIGRID evaluates the interpolant at a set of x and y values on a
+rectangular grid or in the case of the drizzle interpolant within
+rectangular regions. It is most efficient for evaluating the interpolant
+at many values which are closely spaced in x and y. For widely spaced
+points MSIVECTOR should be used.
+.ih
+NOTES
+Checking for out of bounds and INDEF valued pixels is the responsibility
+of the user.
+.ih
+SEE ALSO
+msieval, msivector, msider, mrieval, mrider
+.endhelp
diff --git a/math/iminterp/doc/msigrl.hlp b/math/iminterp/doc/msigrl.hlp
new file mode 100644
index 00000000..f6e2326a
--- /dev/null
+++ b/math/iminterp/doc/msigrl.hlp
@@ -0,0 +1,43 @@
+.help msigrl Dec98 "Image Interpolation Package"
+.ih
+NAME
+msigrl -- integrate the interpolant inside a polygon 
+.ih
+SYNOPSIS
+y = msigrl (msi, x, y, npts)
+
+.nf
+    pointer	msi		#I interpolant descriptor
+    real	x[npts]		#I x values, 1 <= x <= npts, x[1] = x[npts]
+    real	y[npts]		#I y values, 1 <= y <= npts, y[1] = y[npts]
+    int		npts		#I number of points
+.fi
+.ih
+ARGUMENTS
+.ls msi    
+Pointer to the sequential interpolant descriptor structure.
+.le
+.ls x, y
+An array of x and y values describing a polygon, where x[1] = x[npts] and
+y[1] = y[npts]. X and y describe a closed curve where any horizontal line
+segment intersects the domain of integration at at most one point.
+.le
+.ls npts
+The number of points describing the polygon. Npts must >= 4 (triangle).
+.le
+.ih
+DESCRIPTION
+MSIGRL integrates the interpolant exactly for rectangular domains
+of integration. For more irregular regions of integration MSIGRL
+returns an approximation whose accuracy depends on the size of the
+integration region and the shape of the polygon.
+.ih
+NOTES
+Checking for out of bound integration regimes is the responsibility of
+the user. Non-rectangular partial pixel domains of integration default
+to rectangular regions.  MSIINIT or MSISINIT and MSIFIT must be called
+before using MSIGRL.
+.ih
+SEE ALSO
+msisqrgl
+.endhelp
diff --git a/math/iminterp/doc/msiinit.hlp b/math/iminterp/doc/msiinit.hlp
new file mode 100644
index 00000000..68dba684
--- /dev/null
+++ b/math/iminterp/doc/msiinit.hlp
@@ -0,0 +1,41 @@
+.help msiinit Dec98 "Image Interpolation Package"
+.ih
+NAME
+msiinit -- initialize the sequential interpolant descriptor
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+msiinit (msi, interp_type)
+
+.nf
+    pointer	msi		#U interpolant descriptor
+    int		interp_type	#I interpolant type
+.fi
+.ih
+ARGUMENTS
+.ls msi     
+Pointer to the sequential interpolant descriptor.
+.le
+.ls interp_type
+Interpolant type. The options are II_BINEAREST, II_BILINEAR, II_BIPOLY3,
+II_BIPOLY5, II_BISPLINE3, II_BISINC, II_BILSINC, and II_BIDRIZZLE, for
+nearest neighbour, bilinear, 3rd and 5th order interior polynomials, bicubic
+spline, sinc, look-up table sinc, and drizzle respectively. The interpolant
+definitions are found in the package header file math/iminterp.h.
+.le
+.ih
+DESCRIPTION
+The interpolant type is allocated and initialized. The pointer msi is
+returned by MSIINIT. The sinc interpolant width defaults to 31 pixels
+in x and y. The look-up table sinc resolution defaults to 20 resolution
+elements or 0.05 pixels in x and y. The drizzle pixel fraction defaults
+to 1.0.
+.ih
+NOTES
+MSIINIT, MSISINIT or MSIRESTORE must be called before using any other
+MSI routines.
+.ih
+SEE ALSO
+msirestore, msifree
+.endhelp
diff --git a/math/iminterp/doc/msirestore.hlp b/math/iminterp/doc/msirestore.hlp
new file mode 100644
index 00000000..664c9b50
--- /dev/null
+++ b/math/iminterp/doc/msirestore.hlp
@@ -0,0 +1,36 @@
+.help msirestore Dec98 "Image Interpolator Package"
+.ih
+NAME
+msirestore -- restore interpolant
+.ih
+SYNOPSIS
+msirestore (msi, interpolant)
+
+.nf
+    pointer	msi		#U interpolant descriptor
+    real	interpolant[]	#I array containing interpolant
+.fi
+.ih
+ARGUMENTS
+.ls msi   
+Pointer to the interpolant descriptor structure.
+.le
+.ls interpolant
+Array containing the interpolant. The amount of space required by interpolant
+can be determined by a call to msigeti.
+.le
+
+.nf
+	    len_interpolant = msigeti (msi, II_MSINSAVE)
+.fi
+.ih
+DESCRIPTION
+MSIRESTORE allocates space for the interpolant descriptor and restores the
+parameters and coefficients stored in the interpolant array to the
+interpolant structure for use by MSIEVAL, MSIVECTOR, MSIDER and MSIGRL.
+.ih
+NOTES
+.ih
+SEE ALSO
+msisave
+.endhelp
diff --git a/math/iminterp/doc/msisave.hlp b/math/iminterp/doc/msisave.hlp
new file mode 100644
index 00000000..7d5f67ef
--- /dev/null
+++ b/math/iminterp/doc/msisave.hlp
@@ -0,0 +1,38 @@
+.help msisave Dec98 "Image Interpolator Package"
+.ih
+NAME
+msisave -- save interpolant
+.ih
+SYNOPSIS
+msisave (msi, interpolant)
+
+.nf
+    pointer	msi		#I interpolant descriptor
+    real	interpolant[]	#O array containing the interpolant
+.fi
+.ih
+ARGUMENTS
+.ls msi   
+Pointer to the interpolant descriptor structure.
+.le
+.ls interpolant
+Array where the interpolant is stored. The required interpolant array length
+required can be determined by a call to msigeti.
+.le
+
+.nf
+	    len_interpolant = msigeti (msi, II_MSINSAVE)
+.fi
+.ih
+DESCRIPTION
+The interpolant type, number of coefficients in x and y, the position of
+the first data point in the coefficient array, and the sinc and drizzle
+interpolant parameters are stored in the first eleven elements of interpolant.
+The remaining elements contain the coefficients and look-up tables
+calculated by MSIFIT.
+.ih
+NOTES
+.ih
+SEE ALSO
+msirestore
+.endhelp
diff --git a/math/iminterp/doc/msisinit.hlp b/math/iminterp/doc/msisinit.hlp
new file mode 100644
index 00000000..0a05e7ab
--- /dev/null
+++ b/math/iminterp/doc/msisinit.hlp
@@ -0,0 +1,61 @@
+.help msisinit Dec98 "Image Interpolator Package"
+.ih
+NAME
+msisinit -- initialize the sequential interpolant descriptor using user parameters
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+msisinit (msi, interp_type, nsinc, nxincr, nyincr, pixfrac1, pixfrac2, badval)
+
+.nf
+    pointer	msi		  #O interpolant descriptor
+    int		interp_type	  #I interpolant type
+    int		nsinc		  #I sinc interpolant width in pixels
+    int		nxincr,nyincr	  #I sinc look-up table resolution
+    real	pixfrac1,pixfrac2 #I sinc or drizzle pixel fractions 
+    real	badval		  #I drizzle undefined pixel value
+.fi
+
+.ih
+ARGUMENTS
+.ls msi   
+Pointer to sequential interpolant descriptor.
+.le
+.ls interp_type
+Interpolant type. The options are II_BINEAREST, II_BILINEAR, II_BIPOLY3,
+II_BIPOLY5, II_BISPLINE3, II_BISINC, II_BILSINC, and II_BIDRIZZLE for the
+nearest neighbour, linear, 3rd order polynomial, 5th order polynomial,
+cubic spline, sinc, look-up table sinc, and drizzle interpolants respectively.
+The interpolant type definitions are found in the package header file
+math/iminterp.h.
+.le
+.ls nsinc
+The sinc and look-up table sinc interpolant width in pixels. Nsinc is
+rounded up internally to the nearest odd number.
+.le
+.ls nxincr, nyincr
+The look-up table sinc resolution in x and y in number of entries. Nxincr = 10
+implies a pixel resolution of 0.1 pixels in x, nxincr = 20 a pixel resolution
+of 0.05 pixels in x, etc. The default value of nxincr and nyincr are 20 and 20
+.le
+.ls pixfrac1, pixfrac2
+The look-up table sinc fractional pixel shifts in x and y if nincr = 1 in
+which case -0.5 <= rparam[1/2] <= 0.5 , or the drizzle pixel fractions in
+which case 0.0 <= rparam[1/2] <= 1.0.
+.le
+.ls badval
+The undefined pixel value for the drizzle interpolant. Pixels within
+the boundaries of the input image which do not overlap the input image
+pixels are assigned a value of badval.
+.le
+.ih
+DESCRIPTION
+The interpolant descriptor is allocated and initialized. The pointer msi is
+returned by MSISINIT.
+.ih
+NOTES
+MSIINIT or MSISINIT must be called before using any other MSI routines.
+.ih
+SEE ALSO
+msisinit, msifree
diff --git a/math/iminterp/doc/msisqgrl.hlp b/math/iminterp/doc/msisqgrl.hlp
new file mode 100644
index 00000000..fc49514d
--- /dev/null
+++ b/math/iminterp/doc/msisqgrl.hlp
@@ -0,0 +1,38 @@
+.help msisqgrl Dec98 "Image Interpolation Package"
+.ih
+NAME
+msisqgrl -- integrate the interpolant over a rectangular region 
+.ih
+SYNOPSIS
+y = msisqgrl (msi, x1, x2, y1, y2)
+
+.nf
+    pointer	msi		#I interpolant descriptor
+    real	x1		#I lower x limit, 1 <= x1 <= nxpix
+    real	x2		#I upper x limit, 1 <= x2 <= nxpix
+    real	y1		#I lower y limit, 1 <= y1 <= nypix
+    real	y2		#I upper y limit, 1 <= y2 <= nypix
+.fi
+.ih
+ARGUMENTS
+.ls msi    
+Pointer to the sequential interpolant descriptor structure.
+.le
+.ls x1, x2
+The x limits of integration
+.le
+.ls y1, y2
+The y limits of integration.
+.le
+.ih
+DESCRIPTION
+MSISQGRL integrates the interpolant exactly for rectangular domains
+of integration, including partial pixel regions.
+.ih
+NOTES
+Checking for out of bound integration regimes is the responsibility of
+the user. MSIFIT must be called before using MSISQGRL.
+.ih
+SEE ALSO
+msigrl
+.endhelp
diff --git a/math/iminterp/doc/msitype.hlp b/math/iminterp/doc/msitype.hlp
new file mode 100644
index 00000000..5da6dc6d
--- /dev/null
+++ b/math/iminterp/doc/msitype.hlp
@@ -0,0 +1,95 @@
+.help msitype Dec98 "Image Interpolator Package"
+.ih
+NAME
+msitype -- decode an interpolant string
+.ih
+SYNOPSIS
+include <math/iminterp.h>
+
+msitype (interpstr, interp_type, nsinc, nincr, pixfrac)
+
+.nf
+    char	interpstr		#I the input interpolant string
+    int		interp_type		#O interpolant type
+    int		nsinc			#O sinc interpolant width in pixels
+    int		nincr			#O sinc look-up table resolution
+    real	pixfrac	                #O sinc or drizzle pixel fraction 
+.fi
+
+.ih
+ARGUMENTS
+.ls interpstr
+The user supplied interpolant string to be decoded. The options are
+.ls nearest
+Nearest neighbor interpolation.
+.le
+.ls linear
+Bilinear interpolation
+.le
+.ls poly3
+Bicubic polynomial interpolation.
+.le
+.ls poly5
+Biquintic polynomial interpolation.
+.le
+.ls spline3
+Bicubic spline interpolation.
+.le
+.ls sinc
+2D sinc interpolation. Users can specify the sinc interpolant width by
+appending a width value to the interpolant string, e.g. sinc51 specifies
+a 51 by 51 pixel wide sinc interpolant. The sinc width will be rounded up to
+the nearest odd number.  The default sinc width is 31 by 31.
+.le
+.ls lsinc
+Look-up table sinc interpolation. Users can specify the look-up table sinc
+interpolant width by appending a width value to the interpolant string, e.g.
+lsinc51 specifies a 51 by 51 pixel wide look-up table sinc interpolant. The user
+supplied sinc width will be rounded up to the nearest odd number. The default
+sinc width is 31 by 31 pixels. Users can specify the resolution of the lookup
+table sinc by appending the look-up table size in square brackets to the
+interpolant string, e.g. lsinc51[20] specifies a 20 by 20 element sinc
+look-up table interpolant with a pixel resolution of 0.05 pixels in x and y.
+The default look-up table size and resolution are 20 by 20 and 0.05 pixels
+in x and y respectively.
+.le
+.ls drizzle
+Drizzle interpolation. Users can specify the drizzle pixel fraction by
+appending the pixel fraction value to the interpolant string in square
+brackets, e.g. drizzle[0.5] specifies a pixel fraction of 0.5 in x and y.
+The default pixel fraction is 1.0. If either of the x or y pixel
+fractions are 0.0, then both are set to 0.0. A minimum value of 0.001
+is imposed on the actual value of pixfrac.
+.le
+.le
+.ls interp_type
+The output interpolant type. The options are II_BINEAREST, II_BILINEAR,
+II_BIPOLY3, II_BIPOLY5, II_BISPLINE3, II_BISINC, II_BILSINC, and II_BIDRIZZLE
+for the nearest neighbor, linear, 3rd order polynomial, 5th order polynomial,
+cubic spline, sinc, look-up table sinc, and drizzle interpolants respectively.
+The interpolant type definitions are found in the package header file
+math/iminterp.h.
+.le
+.ls nsinc
+The output sinc and look-up table sinc interpolant width in pixels. The
+default value is 31 pixels in x and y.
+.le
+.ls nincr
+The output sinc look-up table size. Nincr = 10 implies a pixel resolution
+of 0.1 pixels in x, nincr = 20 a pixel resolution of 0.05 pixels in y, etc. The
+default value of nincr is 20.
+.le
+.ls pixfrac
+The output look-up table sinc fractional pixel shift if nincr = 1 
+in which case -0.5 <= pixfrac <= 0.5 , or the drizzle pixel
+fraction in which case 0.0 <= pixfrac <= 1.0.
+.le
+.ih
+DESCRIPTION
+The interpolant string is decoded into values suitable for the MSISINIT
+or MSIINIT routines.
+.ih
+NOTES
+.ih
+SEE ALSO
+msinit, msisinit, msifree
diff --git a/math/iminterp/doc/msivector.hlp b/math/iminterp/doc/msivector.hlp
new file mode 100644
index 00000000..d6561be7
--- /dev/null
+++ b/math/iminterp/doc/msivector.hlp
@@ -0,0 +1,54 @@
+.help msivector Dec98 "Image Interpolation Package"
+.ih
+NAME
+msivector -- evaluate the interpolant at an array of x and y points
+.ih
+SYNOPSIS
+msivector (msi, x, y, zfit, npts)
+
+.nf
+    pointer	msi		#I interpolant descriptor
+    real	x[npts/4*npts]	#I x values, 1 <= x <= nxpix
+    real	y[npts/4*npts]	#I y values, 1 <= y <= nypix
+    real	zfit[npts]	#O interpolated values
+    int		npts		#I number of points
+.fi
+.ih
+ARGUMENTS
+.ls msi    
+The pointer to the sequential interpolant descriptor
+.le
+.ls x, y
+The array of x and y values at or in the case tof the drizzle interpolant the
+array of quadrilaterals over which to evaluate the interpolant.
+.le
+.ls zfit
+The interpolated values.
+.le
+.ls npts
+The number of points.
+.le
+.ih
+DESCRIPTION
+The polynomial coefficients are calculated directly from the data points,
+The polynomial interpolants are evaluated using Everett's central difference
+formula. The spline interpolant uses the B-spline coefficients
+calculated using the MSIFIT routine. The boundary extension algorithm is
+projection.
+
+The sinc interpolant is evaluated using a array of data points around
+the point in question. The look-up table since is computed by convolving
+the data with a pre-computed look-up table entry. The boundary extension
+algorithm is nearest neighbor.
+
+The drizzle interpolant is evaluated by summing the data over the
+list of user supplied quadrilaterals.
+.ih
+NOTES
+Checking for out of bounds and INDEF valued pixels is the responsibility
+of the user. MSIINIT or MSISINIT and MSIFIT must be called before using
+MSIVECTOR.
+.ih
+SEE ALSO
+msieval, mrieval
+.endhelp
diff --git a/math/iminterp/ii_1dinteg.x b/math/iminterp/ii_1dinteg.x
new file mode 100644
index 00000000..05b80542
--- /dev/null
+++ b/math/iminterp/ii_1dinteg.x
@@ -0,0 +1,372 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im1interpdef.h"
+include <math/iminterp.h>
+
+# II_1DINTEG -- Find the integral of the interpolant from a to b be assuming
+# that both a and b land in the array. This routine is not used directly
+# in the 1D interpolation package but is actually called repeatedly from the
+# 2D interpolation package. Therefore the SINC function interpolator has
+# not been implemented, although it has been blocked in.
+
+real procedure ii_1dinteg (coeff, len_coeff, a, b, interp_type, nsinc, dx,
+	pixfrac)
+
+real	coeff[ARB]	# 1D array of coefficients
+int	len_coeff	# length of coefficient array (used in sinc only)
+real	a		# lower limit for integral
+real	b		# upper limit for integral
+int	interp_type	# type of 1D interpolant
+int	nsinc		# width of sinc function
+real	dx		# sinc precision
+real	pixfrac		# drizzle pixel fraction
+
+int	neara, nearb, i, j, nterms
+real	deltaxa, deltaxb, accum, xa, xb, pcoeff[MAX_NDERIVS]
+
+begin
+	# Flip order and sign at end.
+	xa = a
+	xb = b
+	if (a > b) {
+	    xa = b
+	    xb = a
+	}
+
+	# Initialize.
+	neara = xa
+	nearb = xb
+	accum = 0.
+
+	switch (interp_type) {
+	case II_NEAREST:
+	    nterms = 0
+	case II_LINEAR:
+	    nterms = 1
+	case II_DRIZZLE:
+	    nterms = 0
+	case II_POLY3:
+	    nterms = 4
+	case II_POLY5:
+	    nterms = 6
+	case II_SPLINE3:
+	    nterms = 4
+	case II_SINC, II_LSINC:
+	    nterms = 0
+	}
+
+	switch (interp_type) {
+	# NEAREST
+	case II_NEAREST:
+
+	    # Reset segment to center values.
+	    neara = xa + 0.5
+	    nearb = xb + 0.5
+
+	    # Set up for first segment.
+	    deltaxa = xa - neara
+
+	    # For clarity one segment case is handled separately.
+
+	    # Only one segment involved.
+	    if (nearb == neara) {
+
+		deltaxb = xb - nearb
+		accum = accum + (deltaxb - deltaxa) * coeff[neara]
+
+	    # More than one segment.
+	    } else {
+
+		# First segment.
+		accum = accum + (0.5 - deltaxa) * coeff[neara]
+
+		# Middle segment.
+		do j = neara + 1, nearb - 1 {
+		    accum = accum + coeff[j]
+		}
+
+		# Last segment.
+		deltaxb = xb - nearb
+		accum = accum + (deltaxb + 0.5) * coeff[nearb]
+	    }
+
+	# LINEAR
+	case II_LINEAR:
+
+	    # Set up for first segment.
+	    deltaxa = xa - neara
+
+	    # For clarity one segment case is handled separately.
+
+	    # Only one segment involved.
+	    if (nearb == neara) {
+
+		deltaxb = xb - nearb
+		accum = accum + (deltaxb - deltaxa) * coeff[neara] +
+		     0.5 * (coeff[neara+1] - coeff[neara]) *
+		     (deltaxb * deltaxb - deltaxa * deltaxa)
+
+	    # More than one segment.
+	    } else {
+
+		# First segment.
+		accum = accum + (1. - deltaxa) * coeff[neara] +
+		     0.5 * (coeff[neara+1] - coeff[neara]) *
+		     (1. - deltaxa * deltaxa)
+
+		# Middle segment.
+		do j = neara + 1, nearb - 1 {
+		    accum = accum + 0.5 * (coeff[j+1] + coeff[j])
+		}
+
+		# Last segment.
+		deltaxb = xb - nearb
+		accum = accum + coeff[nearb] * deltaxb + 0.5 *
+			(coeff[nearb+1] - coeff[nearb]) * deltaxb * deltaxb
+	    }
+
+	# DRIZZLE-- Note that to get get pixfrac an interface change was
+	# required.
+	case II_DRIZZLE:
+	    if (pixfrac >= 1.0)
+		call ii_dzigrl1 (a, b, accum, coeff)
+	    else
+		call ii_dzigrl (a, b, accum, coeff, pixfrac)
+
+	# SINC -- Note that to get ncoeff, nsinc, and dx,  an interface change
+	# was required. 
+	case II_SINC, II_LSINC:
+	    call ii_sincigrl (xa, xb, accum, coeff, len_coeff, nsinc, dx)
+
+	# A higher order interpolant.
+	default:
+
+	    # Set up for first segment.
+	    deltaxa = xa - neara
+
+	    # For clarity one segment case is handled separately.
+
+	    # Only one segment involved.
+	    if (nearb == neara) {
+
+		deltaxb = xb - nearb
+		call ii_getpcoeff (coeff, neara, pcoeff, interp_type)
+		do i = 1, nterms
+		    accum = accum + (1./i) * pcoeff[i] *
+		    	    (deltaxb ** i - deltaxa ** i)
+
+	    # More than one segment.
+	    } else {
+
+		# First segment.
+		call ii_getpcoeff (coeff, neara, pcoeff, interp_type)
+		do i = 1, nterms
+		    accum = accum + (1./i) * pcoeff[i] * (1. - deltaxa ** i)
+
+		# Middle segment.
+		do j = neara + 1, nearb - 1 {
+		    call ii_getpcoeff (coeff, j, pcoeff, interp_type)
+
+		    do i = 1, nterms
+			accum = accum + (1./i) * pcoeff[i]
+		}
+
+		# Last segment.
+		deltaxb = xb - nearb
+		call ii_getpcoeff (coeff, nearb, pcoeff, interp_type)
+		do i = 1, nterms
+		    accum = accum + (1./i) * pcoeff[i] * deltaxb ** i
+	    }
+	}
+
+	if (a < b)
+	    return (accum)
+	else
+	    return (-accum)
+end
+
+	
+# II_GETPCOEFF -- Generates polynomial coefficients if the interpolant is
+# SPLINE3, POLY3 or POLY5.
+
+procedure ii_getpcoeff (coeff, index, pcoeff, interp_type)
+
+real	coeff[ARB]	# coefficient array
+int	index		# coefficients wanted for index < x < index + 1
+real	pcoeff[ARB]	# polynomial coefficients
+int	interp_type	# type of interpolant
+
+int	i, k, nterms
+real	diff[MAX_NDERIVS]
+
+begin
+	# generate polynomial coefficients, first for spline
+
+	if (interp_type == II_SPLINE3) {
+
+	    pcoeff[1] = coeff[index-1] + 4. * coeff[index] + coeff[index+1]
+	    pcoeff[2] = 3. * (coeff[index+1] - coeff[index-1])
+	    pcoeff[3] = 3. * (coeff[index-1] - 2. * coeff[index] +
+	    		coeff[index+1])
+	    pcoeff[4] = -coeff[index-1] + 3. * coeff[index] -
+	    		3. * coeff[index+1] + coeff[index+2]
+	} else {
+
+	    if (interp_type == II_POLY5)
+		nterms = 6
+
+	    # must be POLY3
+	    else
+		nterms = 4
+
+	    # Newton's form written in line to get polynomial from data
+
+	    # load data
+	    do i = 1, nterms
+		diff[i] = coeff[index - nterms/2 + i]
+
+	    # generate difference table
+	    do k = 1, nterms - 1
+		do i = 1, nterms - k
+		    diff[i] = (diff[i+1] - diff[i]) / k
+
+	    # shift to generate polynomial coefficients of (x - index)
+	    do k = nterms, 2, -1
+		do i = 2, k
+		    diff[i] = diff[i] + diff[i-1] * (k - i - nterms/2)
+
+	    do i = 1, nterms
+		pcoeff[i] = diff[nterms + 1 - i]
+	}
+end
+
+
+# II_SINCIGRL -- Evaluate integral of sinc interpolator.
+# The integral is computed by dividing interval into a number of equal
+# size subintervals which are at most one pixel wide.  The integral
+# of each subinterval is the central value times the interval width.
+
+procedure ii_sincigrl (a, b, sum, data, npix, nsinc, mindx)
+
+real	a, b			# integral limits
+real	sum			# output integral value
+real	data[npix]		# input data array
+int	npix			# number of pixels
+int	nsinc			# sinc truncation length
+real	mindx			# interpolation minimum
+
+int	n
+real	x, y, dx, x1, x2
+
+begin
+	x1 = min (a, b)
+	x2 = max (a, b)
+	n = max (1, nint (x2 - x1))
+	dx = (x2 - x1) / n
+
+	sum = 0.
+	for (x = x1 + dx / 2; x < x2; x = x + dx) {
+	    call ii_sinc (x, y, 1, data, npix, nsinc, mindx)
+	    sum = sum + y * dx
+	}
+end
+
+
+# II_DZIGRL -- Procedure to integrate the drizzle interpolant.
+
+procedure ii_dzigrl (a, b, sum, data, pixfrac)
+
+real    a, b         	# x start and stop values, must be within [1,npts]
+real    sum		# integgral value returned to the user
+real    data[ARB]       # data to be interpolated
+real    pixfrac         # the drizzle pixel fraction
+
+int     j, neara, nearb
+real    hpixfrac, xa, xb, dx, accum
+
+begin
+        hpixfrac = pixfrac / 2.0
+
+        # Define the interval of integration.
+        xa = min (a, b)
+        xb = max (a, b)
+        neara = xa + 0.5
+        nearb = xb + 0.5
+
+        # Initialize the integration
+        accum = 0.0
+        if (neara == nearb) {
+
+            dx = min (xb, nearb + hpixfrac) - max (xa, neara - hpixfrac)
+            if (dx > 0.0)
+                accum = accum + dx * data[neara]
+
+        } else {
+
+            # first segement
+            dx = neara + hpixfrac - max (xa, neara - hpixfrac)
+            if (dx > 0.0)
+                accum = accum + dx * data[neara]
+
+            # interior segments.
+            do j = neara + 1, nearb - 1
+                accum = accum + pixfrac * data[j]
+
+            # last segment
+            dx = min (xb, nearb + hpixfrac) - (nearb - hpixfrac)
+            if (dx > 0.0)
+                accum = accum + dx * data[nearb]
+        }
+
+        if (a > b)
+            sum = -accum
+        else
+            sum = accum 
+end
+
+
+# II_DZIGRL1 -- Procedure to integrate the drizzle interpolant in the case
+# where pixfrac = 1.0.
+
+procedure ii_dzigrl1 (a, b, sum, data)
+
+real    a, b            # x start and stop values, must be within [1,npts]
+real    sum		# integgral value returned to the user
+real    data[ARB]       # data to be interpolated
+
+int     j, neara, nearb
+real    xa, xb, deltaxa, deltaxb, accum
+
+begin
+        # Define the interval of integration.
+        xa = min (a, b)
+        xb = max (a, b)
+        neara = xa + 0.5
+        nearb = xb + 0.5
+        deltaxa = xa - neara
+        deltaxb = xb - nearb
+
+        # Only one segment involved.
+        accum = 0.0
+        if (neara == nearb) {
+
+            accum = accum + (deltaxb - deltaxa) * data[neara]
+
+        } else {
+
+            # First segment.
+            accum = accum + (0.5 - deltaxa) * data[neara]
+
+            # Middle segment.
+            do j = neara + 1, nearb - 1
+                accum = accum + data[j]
+
+            # Last segment.
+            accum = accum + (deltaxb + 0.5) * data[nearb]
+        }
+
+        if (a > b)
+           sum = -accum 
+        else
+           sum = accum
+end
diff --git a/math/iminterp/ii_bieval.x b/math/iminterp/ii_bieval.x
new file mode 100644
index 00000000..3469128e
--- /dev/null
+++ b/math/iminterp/ii_bieval.x
@@ -0,0 +1,1080 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math.h>
+
+# II_BINEAREST -- Procedure to evaluate the nearest neighbour interpolant.
+# The real array coeff contains the coefficients of the 2D interpolant.
+# The procedure assumes that 1 <= x <= nxpix and 1 <= y <= nypix and that
+# coeff[1+first_point] = datain[1,1].
+ 
+procedure ii_binearest (coeff, first_point, len_coeff, x, y, zfit, npts)
+
+real	coeff[ARB]	# 1D coefficient array
+int	first_point	# offset of first data point
+int	len_coeff	# row length of coeff
+real	x[npts]		# array of x values
+real	y[npts]		# array of y values
+real	zfit[npts]	# array of interpolated values
+int	npts		# number of points to be evaluated
+
+int	nx, ny
+int	index
+int	i
+
+begin
+	do i = 1, npts {
+
+	    nx = x[i] + 0.5
+	    ny = y[i] + 0.5
+
+	    # define pointer to data[nx,ny]
+	    index = first_point + (ny - 1) * len_coeff + nx
+
+	    zfit[i] = coeff[index]
+
+	}
+end
+
+
+# II_BILINEAR -- Procedure to evaluate the bilinear interpolant.
+# The real array coeff contains the coefficients of the 2D interpolant.
+# The procedure assumes that 1 <= x <= nxpix and 1 <= y <= nypix
+# and that coeff[1+first_point] = datain[1,1].
+
+procedure ii_bilinear (coeff, first_point, len_coeff, x, y, zfit, npts)
+
+real	coeff[ARB]	# 1D array of coefficients
+int	first_point	# offset of first data point
+int	len_coeff	# row length of coeff
+real	x[npts]		# array of x values
+real	y[npts]		# array of y values
+real	zfit[npts]	# array of interpolated values
+int	npts		# number of data points
+
+int	nx, ny
+int	index
+int	i
+real	sx, sy, tx, ty
+
+begin
+	do i = 1, npts {
+
+	    nx = x[i]
+	    ny = y[i]
+
+	    sx = x[i] - nx
+	    tx = 1. - sx
+	    sy = y[i] - ny
+	    ty = 1. - sy
+
+	    # define pointer to data[nx,ny]
+	    index = first_point + (ny - 1) * len_coeff + nx
+
+	    zfit[i] = tx * ty * coeff[index] + sx * ty * coeff[index + 1] +
+		      sy * tx * coeff[index+len_coeff] +
+		      sx * sy * coeff[index+len_coeff+1]
+	}
+end
+
+
+# II_BIPOLY3 -- Procedure to evaluate the bicubic polynomial interpolant.
+# The real array coeff contains the coefficients of the 2D interpolant.
+# The procedure assumes that 1 <= x <= nxpix and  1 <= y <= nypix
+# and that coeff[1+first_point] = datain[1,1]. The interpolant is
+# evaluated using Everett's central difference formula.
+
+procedure ii_bipoly3 (coeff, first_point, len_coeff, x, y, zfit, npts)
+
+real	coeff[ARB]	# 1D array of coefficients
+int	first_point	# offset first point
+int	len_coeff	# row length of the coefficient array
+real	x[npts]		# array of x values
+real	y[npts]		# array of y values
+real	zfit[npts]	# array of fitted values
+int	npts		# number of points to be evaluated
+
+int	nxold, nyold, nx, ny
+int	first_row, index
+int	i, j
+real	sx, tx, sx2m1, tx2m1, sy, ty
+real	cd20[4], cd21[4], ztemp[4], cd20y, cd21y
+
+begin
+	nxold = -1
+	nyold = -1
+
+	do i = 1, npts {
+
+	    nx = x[i]
+	    sx = x[i] - nx
+	    tx = 1. - sx
+	    sx2m1 = sx * sx - 1.
+	    tx2m1 = tx * tx - 1.
+
+	    ny = y[i]
+	    sy = y[i] - ny
+	    ty = 1. - sy
+
+	    # define pointer to datain[nx,ny-1]
+	    first_row = first_point + (ny - 2) * len_coeff + nx
+
+	    # loop over the 4 surrounding rows of data
+	    # calculate the  central differences at each value of y
+
+	    # if new data point caculate the central differnences in x
+	    # for each y
+
+	    index = first_row
+	    if (nx != nxold || ny != nyold) {
+	        do j = 1, 4 {
+		   cd20[j] = 1./6. * (coeff[index+1] - 2. * coeff[index] +
+		   	     coeff[index-1])
+		   cd21[j] = 1./6. * (coeff[index+2] - 2. * coeff[index+1] +
+			     coeff[index])
+		    index = index + len_coeff
+	        }
+	    }
+
+	    # interpolate in x at each value of y
+	    index = first_row
+	    do j = 1, 4 {
+		ztemp[j] = sx * (coeff[index+1] + sx2m1 * cd21[j]) +
+			   tx * (coeff[index] + tx2m1 * cd20[j])
+		index = index + len_coeff
+	    }
+
+	    # calculate y central differences
+	    cd20y = 1./6. * (ztemp[3] - 2. * ztemp[2] + ztemp[1])
+	    cd21y = 1./6. * (ztemp[4] - 2. * ztemp[3] + ztemp[2])
+
+	    # interpolate in y
+	    zfit[i] = sy * (ztemp[3] + (sy * sy - 1.) * cd21y) +
+		      ty * (ztemp[2] + (ty * ty - 1.) * cd20y)
+
+	    nxold = nx
+	    nyold = ny
+
+	}
+end
+
+
+# II_BIPOLY5 -- Procedure to evaluate a biquintic polynomial.
+# The real array coeff contains the coefficents of the 2D interpolant.
+# The routine assumes that 1 <= x <= nxpix and 1 <= y <= nypix
+# and that coeff[1+first_point] = datain[1,1]. The interpolant is evaluated
+# using Everett's central difference formula.
+
+procedure ii_bipoly5 (coeff, first_point, len_coeff, x, y, zfit, npts)
+
+real	coeff[ARB]	# 1D array of coefficients
+int	first_point	# offset to first data point
+int	len_coeff	# row length of coeff
+real	x[npts]		# array of x values
+real	y[npts]		# array of y values
+real	zfit[npts]	# array of fitted values
+int	npts		# number of points
+
+int	nxold, nyold, nx, ny
+int	first_row, index
+int	i, j
+real	sx, sx2, sx2m1, sx2m4, tx, tx2, tx2m1, tx2m4, sy, sy2, ty, ty2
+real	cd20[6], cd21[6], cd40[6], cd41[6], ztemp[6]
+real	cd20y, cd21y, cd40y, cd41y
+
+begin
+	nxold = -1
+	nyold = -1
+
+	do i = 1, npts {
+
+	    nx = x[i]
+	    sx = x[i] - nx
+	    sx2 = sx * sx
+	    sx2m1 = sx2 - 1.
+	    sx2m4 = sx2 - 4.
+	    tx = 1. - sx
+	    tx2 = tx * tx
+	    tx2m1 = tx2 - 1.
+	    tx2m4 = tx2 - 4.
+
+	    ny = y[i]
+	    sy = y[i] - ny
+	    sy2 = sy * sy
+	    ty = 1. - sy
+	    ty2 = ty * ty
+
+	    # calculate value of pointer to data[nx,ny-2]
+	    first_row = first_point + (ny - 3) * len_coeff + nx
+
+	    # calculate the central differences in x at each value of y
+	    index = first_row
+	    if (nx != nxold || ny != nyold) {
+		do j = 1, 6 {
+		    cd20[j] = 1./6. * (coeff[index+1] - 2. * coeff[index] +
+		    	      coeff[index-1])
+		    cd21[j] = 1./6. * (coeff[index+2] - 2. * coeff[index+1] +
+			      coeff[index])
+		    cd40[j] = 1./120. * (coeff[index-2] - 4. * coeff[index-1] +
+			      6. * coeff[index] - 4. * coeff[index+1] +
+			      coeff[index+2])
+		    cd41[j] = 1./120. * (coeff[index-1] - 4. * coeff[index] +
+			      6. * coeff[index+1] - 4. * coeff[index+2] +
+			      coeff[index+3])
+		    index = index + len_coeff
+		}
+	    }
+
+	    # interpolate in x at each value of y
+	    index = first_row
+	    do j = 1, 6 {
+		ztemp[j] = sx * (coeff[index+1] + sx2m1 * (cd21[j] + sx2m4 *
+			   cd41[j])) + tx * (coeff[index] + tx2m1 *
+			   (cd20[j] + tx2m4 * cd40[j]))
+		index = index + len_coeff
+	    }
+
+	    # central differences in y
+	    cd20y = 1./6. * (ztemp[4] - 2. * ztemp[3] + ztemp[2])
+	    cd21y = 1./6. * (ztemp[5] - 2. * ztemp[4] + ztemp[3])
+	    cd40y = 1./120. * (ztemp[1] - 4. * ztemp[2] + 6. * ztemp[3] -
+		    4. * ztemp[4] + ztemp[5])
+	    cd41y = 1./120. * (ztemp[2] - 4. * ztemp[3] + 6. * ztemp[4] -
+		    4. * ztemp[5] + ztemp[6])
+
+	    # interpolate in y
+	    zfit[i] = sy * (ztemp[4] + (sy2 - 1.) * (cd21y + (sy2 - 4.) *
+		      cd41y)) + ty * (ztemp[3] + (ty2 - 1.) * (cd20y +
+		      (ty2 - 4.) * cd40y))
+
+	    nxold = nx
+	    nyold = ny
+
+	}
+end
+
+
+# II_BISPLINE3 -- Procedure to evaluate a bicubic spline.
+# The real array coeff contains the B-spline coefficients.
+# The procedure assumes that 1 <= x <= nxpix and 1 <= y <= nypix
+# and that coeff[1+first_point] = B-spline[2].
+
+procedure ii_bispline3 (coeff, first_point, len_coeff, x, y, zfit, npts)
+
+real	coeff[ARB]	# 1D array of coefficients
+int	first_point	# offset to first data point
+int	len_coeff	# row length of coeff
+real	x[npts]		# array of x values
+real	y[npts]		# array of y values
+real	zfit[npts]	# array of interpolated values
+int	npts		# number of points to be evaluated
+
+int	nx, ny
+int	first_row, index
+int	i, j
+real	sx, tx, sy, ty
+real	bx[4], by[4], accum, sum
+
+begin
+	do i = 1, npts {
+
+	    nx = x[i]
+	    sx = x[i] - nx
+	    tx = 1. - sx
+
+	    ny = y[i]
+	    sy = y[i] - ny
+	    ty = 1. - sy
+
+
+	    # calculate the x B-splines
+	    bx[1] = tx ** 3 
+	    bx[2] = 1. + tx * (3. + tx * (3. - 3. * tx))
+	    bx[3] = 1. + sx * (3. + sx * (3. - 3. * sx))
+	    bx[4] = sx ** 3
+
+	    # calculate the y B-splines
+	    by[1] = ty ** 3
+	    by[2] = 1. + ty * (3. + ty * (3. - 3. * ty))
+	    by[3] = 1. + sy * (3. + sy * (3. - 3. * sy))
+	    by[4] = sy ** 3
+
+	    # calculate the pointer to data[nx,ny-1]
+	    first_row = first_point + (ny - 2) * len_coeff + nx
+
+	    # evaluate spline
+	    accum = 0.
+	    index = first_row
+	    do j = 1, 4 {
+		sum = coeff[index-1] * bx[1] + coeff[index] * bx[2] +
+		      coeff[index+1] * bx[3] + coeff[index+2] * bx[4]	
+		accum = accum + sum * by[j]
+		index = index + len_coeff
+	    }
+
+	    zfit[i] = accum
+	}
+end
+
+
+# II_BISINC -- Procedure to evaluate the 2D sinc function.  The real array
+# coeff contains the data. The procedure assumes that 1 <= x <= nxpix and
+# 1 <= y <= nypix and that coeff[1+first_point] = datain[1,1]. The since
+# truncation length is nsinc. The taper is a cosbell function which is
+# valid for 0 <= x <= PI / 2 (Abramowitz and Stegun, 1972, Dover Publications,
+# p 76). If the point to be interpolated is less than mindx and mindy from
+# a data point no interpolation is done and the data point is returned. This
+# routine does not use precomputed arrays.
+
+procedure ii_bisinc (coeff, first_point, len_coeff, len_array, x, y, zfit,
+	npts, nsinc, mindx, mindy)
+
+real	coeff[ARB]	# 1D array of coefficients
+int	first_point	# offset to first data point
+int	len_coeff	# row length of coeff
+int	len_array	# column length of coeff
+real	x[npts]		# array of x values
+real	y[npts]		# array of y values
+real	zfit[npts]	# array of interpolated values
+int	npts		# the number of input points.
+int	nsinc		# sinc truncation length
+real	mindx		# interpolation mininmum in x
+real	mindy		# interpolation mininmum in y
+
+int	i, j, k, nconv, nx, ny, index, mink, maxk, offk, minj, maxj, offj
+int	last_point
+pointer	sp, taper, ac, ar
+real	sconst, a2, a4, sdx, dx, dy, dxn, dyn, ax, ay, px, py, sumx, sumy, sum
+real	dx2
+
+begin
+	# Compute the length of the convolution.
+	nconv = 2 * nsinc + 1
+
+	# Allocate working array space.
+	call smark (sp)
+	call salloc (taper, nconv, TY_REAL)
+	call salloc (ac, nconv, TY_REAL)
+	call salloc (ar, nconv, TY_REAL)
+
+	# Compute the constants for the cosine bell taper.
+        sconst = (HALFPI / nsinc) ** 2
+        a2 = -0.49670
+        a4 = 0.03705
+
+	# Precompute the taper array. Incorporate the sign change portion
+	# of the sinc interpolator into the taper array.
+	if (mod (nsinc, 2) == 0)
+	    sdx = 1.0
+	else
+	    sdx = -1.0
+        do j = -nsinc,  nsinc {
+	    dx2 = sconst * j * j
+            Memr[taper+j+nsinc] = sdx * (1.0 + a2 * dx2 + a4 * dx2 * dx2) ** 2
+            sdx = -sdx
+        }
+
+	do i = 1, npts {
+
+	    # define the fractional pixel interpolation.
+	    nx = nint (x[i])
+	    ny = nint (y[i])
+	    if (nx < 1 || nx > len_coeff || ny < 1 || ny > len_array) {
+		zfit[i] = 0.0
+		next
+	    }
+	    dx = x[i] - nx
+	    dy = y[i] - ny
+
+	    # define pointer to data[nx,ny]
+	    if (abs (dx) < mindx && abs (dy) < mindy) {
+	        index = first_point + (ny - 1) * len_coeff + nx
+		zfit[i] = coeff[index]
+		next
+	    }
+
+	    # initialize.
+	    #dxn = -1-nsinc-dx
+	    #dyn = -1-nsinc-dy
+	    dxn = 1 + nsinc + dx
+	    dyn = 1 + nsinc + dy
+
+	    # Compute the x and y sinc arrays using a cosbell taper.
+	    sumx = 0.0
+	    sumy = 0.0
+	    do j = 1, nconv {
+
+		#ax = j + dxn
+		#ay = j + dyn
+		ax = dxn - j
+		ay = dyn - j
+		if (ax == 0.0)
+		    px = 1.0
+		else if (dx == 0.0)
+		    px = 0.0
+		else
+		    px = Memr[taper+j-1] / ax 
+		if (ay == 0.0)
+		    py = 1.0
+		else if (dy == 0.0)
+		    py = 0.0
+		else
+		    py = Memr[taper+j-1] / ay 
+
+		Memr[ac+j-1] = px
+		Memr[ar+j-1] = py
+		sumx = sumx + px
+		sumy = sumy + py
+	    }
+
+	    # Compute the limits of the convolution.
+	    minj = max (1, ny - nsinc)
+	    maxj = min (len_array, ny + nsinc)
+	    offj = ar - ny + nsinc
+	    mink = max (1, nx - nsinc)
+	    maxk = min (len_coeff, nx + nsinc)
+	    offk = ac - nx + nsinc
+
+	    # Initialize
+	    zfit[i] = 0.0
+
+	    # Do the convolution.
+	    do j = ny - nsinc, minj - 1 {
+		sum = 0.0
+		do k = nx - nsinc, mink - 1
+		    sum = sum + Memr[k+offk] * coeff[first_point+1] 
+	        do k = mink, maxk
+		    sum = sum + Memr[k+offk] * coeff[first_point+k] 
+		do k = maxk + 1, nx + nsinc
+		    sum = sum + Memr[k+offk] * coeff[first_point+len_coeff] 
+
+		zfit[i] = zfit[i] + Memr[j+offj] * sum
+	    }
+
+	    do j = minj, maxj {
+	    	index = first_point + (j - 1) * len_coeff
+		sum = 0.0
+		do k = nx - nsinc, mink - 1
+		    sum = sum + Memr[k+offk] * coeff[index+1] 
+	        do k = mink, maxk
+		    sum = sum + Memr[k+offk] * coeff[index+k] 
+		do k = maxk + 1, nx + nsinc
+		    sum = sum + Memr[k+offk] * coeff[index+len_coeff] 
+
+		zfit[i] = zfit[i] + Memr[j+offj] * sum
+	    }
+
+	    do j = maxj + 1, ny + nsinc {
+	        last_point = first_point + (len_array - 1) * len_coeff
+		sum = 0.0
+		do k = nx - nsinc, mink - 1
+		    sum = sum + Memr[k+offk] * coeff[last_point+1] 
+	        do k = mink, maxk
+		    sum = sum + Memr[k+offk] * coeff[last_point+k] 
+		do k = maxk + 1, nx + nsinc
+		    sum = sum + Memr[k+offk] * coeff[last_point+len_coeff] 
+
+		zfit[i] = zfit[i] + Memr[j+offj] * sum
+	    }
+
+	    # Normalize.
+	    zfit[i] = zfit[i] / sumx / sumy
+	}
+
+	call sfree (sp)
+end
+
+
+# II_BILSINC -- Procedure to evaluate the 2D sinc function.  The real array
+# coeff contains the data. The procedure assumes that 1 <= x <= nxpix and
+# 1 <= y <= nypix and that coeff[1+first_point] = datain[1,1]. The since
+# truncation length is nsinc. The taper is a cosbell function which is
+# valid for 0 <= x <= PI / 2 (Abramowitz and Stegun, 1972, Dover Publications,
+# p 76). If the point to be interpolated is less than mindx and mindy from
+# a data point no interpolation is done and the data point is returned. This
+# routine does use precomputed arrays.
+
+procedure ii_bilsinc (coeff, first_point, len_coeff, len_array, x, y, zfit,
+	npts, ltable, nconv, nxincr, nyincr, mindx, mindy)
+
+real	coeff[ARB]			   # 1D array of coefficients
+int	first_point			   # offset to first data point
+int	len_coeff			   # row length of coeff
+int	len_array			   # column length of coeff
+real	x[npts]				   # array of x values
+real	y[npts]				   # array of y values
+real	zfit[npts]			   # array of interpolated values
+int	npts				   # the number of input points.
+real	ltable[nconv,nconv,nxincr,nyincr]  # the pre-computed look-up table
+int	nconv				   # the sinc truncation full width
+int	nxincr				   # the interpolation resolution in x
+int	nyincr				   # the interpolation resolution in y
+real	mindx				   # interpolation mininmum in x
+real	mindy				   # interpolation mininmum in y
+
+int	i, j, k, nsinc, xc, yc, lutx, luty, minj, maxj, offj, mink, maxk, offk
+int	index, last_point
+real	dx, dy, sum
+
+begin
+	nsinc = (nconv - 1) / 2
+	do i = 1, npts {
+
+	    # Return zero outside of data.
+	    xc = nint (x[i])
+	    yc = nint (y[i])
+	    if (xc < 1 || xc > len_coeff || yc < 1 || yc > len_array) {
+		zfit[i] = 0.0
+		next
+	    }
+
+	    dx = x[i] - xc
+	    dy = y[i] - yc
+	    if (abs(dx) < mindx && abs(dy) < mindy) {
+		index = first_point + (yc - 1) * len_coeff + xc
+		zfit[i] = coeff[index]
+	    }
+
+	    # Find the correct look-up table entry.
+	    if (nxincr == 1)
+		lutx = 1
+	    else 
+		lutx = nint ((-dx + 0.5) * (nxincr - 1)) + 1
+		#lutx = int ((-dx + 0.5) * (nxincr - 1) + 0.5) + 1
+	    if (nyincr == 1)
+		luty = 1
+	    else
+		luty = nint ((-dy + 0.5) * (nyincr - 1)) + 1
+		#luty = int ((-dy + 0.5) * (nyincr - 1) + 0.5) + 1
+
+	    # Compute the convolution limits.
+	    minj = max (1, yc - nsinc)
+	    maxj = min (len_array, yc + nsinc)
+	    offj = 1 - yc + nsinc
+	    mink = max (1, xc - nsinc)
+	    maxk = min (len_coeff, xc + nsinc)
+	    offk = 1 - xc + nsinc
+
+	    # Initialize
+	    zfit[i] = 0.0
+
+	    # Do the convolution.
+	    do j = yc - nsinc, minj - 1 {
+		sum = 0.0
+		do k = xc - nsinc, mink - 1
+		    sum = sum + ltable[k+offk,j+offj,lutx,luty] *
+		        coeff[first_point+1] 
+	        do k = mink, maxk
+		    sum = sum + ltable[k+offk,j+offj,lutx,luty] *
+		        coeff[first_point+k] 
+		do k = maxk + 1, xc + nsinc
+		    sum = sum + ltable[k+offk,j+offj,lutx,luty] *
+		        coeff[first_point+len_coeff] 
+		zfit[i] = zfit[i] +  sum
+	    }
+
+	    do j = minj, maxj {
+	    	index = first_point + (j - 1) * len_coeff
+		sum = 0.0
+		do k = xc - nsinc, mink - 1
+		    sum = sum + ltable[k+offk,j+offj,lutx,luty] * coeff[index+1]
+	        do k = mink, maxk
+		    sum = sum + ltable[k+offk,j+offj,lutx,luty] * coeff[index+k]
+		do k = maxk + 1, xc + nsinc
+		    sum = sum + ltable[k+offk,j+offj,lutx,luty] *
+		        coeff[index+len_coeff] 
+		zfit[i] = zfit[i] + sum
+	    }
+
+	    do j = maxj + 1, yc + nsinc {
+	        last_point = first_point + (len_array - 1) * len_coeff
+		sum = 0.0
+		do k = xc - nsinc, mink - 1
+		    sum = sum + ltable[k+offk,j+offj,lutx,luty] *
+		        coeff[last_point+1] 
+	        do k = mink, maxk
+		    sum = sum + ltable[k+offk,j+offj,lutx,luty] *
+		        coeff[last_point+k] 
+		do k = maxk + 1, xc + nsinc
+		    sum = sum + ltable[k+offk,j+offj,lutx,luty] *
+		        coeff[last_point+len_coeff] 
+		zfit[i] = zfit[i] + sum
+	    }
+
+	}
+end
+
+
+# II_BIDRIZ -- Procedure to evaluate the drizzle interpolant.
+# The real array coeff contains the coefficients of the 2D interpolant.
+# The procedure assumes that 1 <= x <= nxpix and 1 <= y <= nypix and that
+# coeff[1+first_point] = datain[1,1]. Each x and y value is a set of 4
+# values describing the vertices of a quadrilateral in the input data. The
+# integration routine was adapted from the one developed by Bill Sparks at
+# ST and used the DITHER / DRIZZLE software. The 4 points describing the
+# corners of each quadrilateral integration region must be in order, e.g.
+# describe the vertices of a polygon in either CW or CCW order.
+ 
+procedure ii_bidriz (coeff, first_point, len_coeff, x, y, zfit, npts,
+	xfrac, yfrac, badval)
+
+real	coeff[ARB]	# 1D coefficient array
+int	first_point	# offset of first data point
+int	len_coeff	# row length of coeff
+real	x[ARB]		# array of x values
+real	y[ARB]		# array of y values
+real	zfit[npts]	# array of interpolated values
+int	npts		# number of points to be evaluated
+real	xfrac, yfrac	# the x and y drizzle pixel fractions
+real	badval		# undefined pixel value
+
+int	i, ii, jj, kk, index, nearax, nearbx, nearay, nearby
+real	px[5], py[5], dx, xmin, xmax, m, c, ymin, ymax, xtop
+real	ovlap, accum, waccum, dxfrac, dyfrac, hxfrac, hyfrac, dhxfrac, dhyfrac
+bool	negdx
+
+begin
+	dxfrac = max (0.0, min (1.0, 1.0 - xfrac))
+	hxfrac = max (0.0, min (0.5, dxfrac / 2.0))
+	dhxfrac = max (0.5, min (1.0, 1.0 - hxfrac))
+	dyfrac = max (0.0, min (1.0, 1.0 - yfrac))
+	hyfrac = max (0.0, min (0.5, dyfrac / 2.0))
+	dhyfrac = max (0.5, min (1.0, 1.0 - hyfrac))
+
+	do i = 1, npts {
+
+	    # Compute the limits of the integration in x and y.
+	    nearax = nint (min (x[4*i-3], x[4*i-2], x[4*i-1], x[4*i]))
+	    nearbx = nint (max (x[4*i-3], x[4*i-2], x[4*i-1], x[4*i]))
+	    nearay = nint (min (y[4*i-3], y[4*i-2], y[4*i-1], y[4*i]))
+	    nearby = nint (max (y[4*i-3], y[4*i-2], y[4*i-1], y[4*i]))
+
+	    # Initialize.
+	    accum = 0.0
+	    waccum = 0.0
+
+	    # Loop over all pixels which contribute to the integral.
+	    do jj = nearay, nearby {
+		index = first_point + (jj - 1) * len_coeff
+		do kk = 1, 4
+		    py[kk] = y[4*i+kk-4] - jj + 0.5
+		py[5] = py[1]
+		do ii = nearax, nearbx {
+
+		    # Transform the coordinates relative to a unit
+		    # square centered at the origin of the pixel. We
+		    # are going to approximate the new pixel area by
+		    # a quadilateral. Close the quadilateral.
+
+		    do kk = 1, 4
+			px[kk] = x[4*i+kk-4] - ii + 0.5 
+		    px[5] = px[1]
+
+		    # Compute the area overlap of the output pixel with
+		    # the input pixels. 
+		    ovlap = 0.0
+		    do kk = 1, 4 {
+
+			# Check for vertical line segment.
+			dx = px[kk+1] - px[kk]
+			if (dx == 0.0)
+			    next
+
+			# Order the x integration limits.
+			if (px[kk] < px[kk+1]) {
+			    xmin = px[kk]
+			    xmax = px[kk+1]
+			} else {
+			    xmin = px[kk+1]
+			    xmax = px[kk]
+			}
+
+			# Check the x limits ignoring y for now.
+			if ((xmin >= dhxfrac) || (xmax <= hxfrac))
+			    next
+			xmin = max (xmin, hxfrac)
+			xmax = min (xmax, dhxfrac)
+
+			# Get basic info about the line y = mx + c.
+			if (dx < 0.0)
+			    negdx = true
+			else
+			    negdx = false
+			m = (py[kk+1] - py[kk]) / dx
+			c = py[kk] - m * px[kk]
+			ymin = m * xmin + c
+			ymax = m * xmax + c
+
+			# Trap segment entirely below axis.
+			if (ymin <= hyfrac && ymax <= hyfrac)
+			    next
+
+			# Adjust bounds if segment crosses axis in order
+			# to exclude anything below the axis.
+			if (ymin < hyfrac) {
+			    ymin = hyfrac
+			    xmin = (hyfrac - c) / m
+			}
+			if (ymax < hyfrac) {
+			    ymax = hyfrac
+			    xmax = (hyfrac - c) / m
+			}
+
+			# There are four possibilities.
+
+			# Both y above 1.0 - hyfrac. Line segment is entirely
+			# above square.
+			if ((ymin >= dhyfrac) && (ymax >= dhyfrac)) {
+
+			    if (negdx)
+				ovlap = ovlap + (xmin - xmax) * yfrac
+			    else
+				ovlap = ovlap + (xmax - xmin) * yfrac
+
+			# Both y below 1.0 - hyfrac. Segment is entirely
+			# within square.
+			} else if ((ymin <= dhyfrac) && (ymax <= dhyfrac)) {
+
+			    if (negdx)
+				ovlap = ovlap + 0.5 * (xmin - xmax) *
+				    (ymax + ymin - dyfrac)
+			    else
+				ovlap = ovlap + 0.5 * (xmax - xmin) *
+				    (ymax + ymin - dyfrac)
+
+			# One of each. Segment must cross top of square.
+			} else {
+
+			    xtop = (dhyfrac - c) / m
+
+			    # insert precision check ?
+
+			    if (ymin < dhyfrac) {
+				if (negdx)
+				    ovlap = ovlap - (0.5 * (xtop - xmin) *
+				        (ymin + 1.0 - 3.0 * hyfrac) +
+				        (xmax - xtop) * yfrac)
+				else
+				    ovlap = ovlap + (0.5 * (xtop - xmin) *
+				        (ymin + 1.0 - 3.0 * hyfrac) +
+				        (xmax - xtop) * yfrac)
+			     } else {
+				if (negdx)
+				    ovlap = ovlap - (0.5 * (xmax - xtop) *
+				        (ymax + 1.0 - 3.0 * hyfrac) +
+					(xtop - xmin) * yfrac)
+				else
+				    ovlap = ovlap + (0.5 * (xmax - xtop) *
+				        (ymax + 1.0 - 3.0 * hyfrac) +
+					(xtop - xmin) * yfrac)
+			     }
+
+			}
+		    }
+
+		    accum = accum + coeff[index+ii] * ovlap
+		    waccum = waccum + ovlap
+		}
+	    }
+
+	    if (waccum == 0.0)
+		zfit[i] = badval
+	    else
+		zfit[i] = accum / waccum
+	}
+end
+
+
+# II_BIDRIZ1 -- Procedure to evaluate the drizzle interpolant when xfrac and
+# yfrac are 1.0. The real array coeff contains the coefficients of the 2D
+# interpolant. The procedure assumes that 1 <= x <= nxpix and 1 <= y <= nypix
+# and that coeff[1+first_point] = datain[1,1]. Each x and y point is a set of 4
+# values describing the vertices of a quadrilateral in the input data. The
+# integration routine was adapted from the one developed by Bill Sparks at
+# ST and used the DITHER / DRIZZLE software. The 4 points describing the
+# corners of each quadrilateral integration region must be in order, e.g.
+# describe the vertices of a polygon in either CW or CCW order.
+ 
+procedure ii_bidriz1 (coeff, first_point, len_coeff, x, y, zfit, npts, badval)
+
+real	coeff[ARB]	# 1D coefficient array
+int	first_point	# offset of first data point
+int	len_coeff	# row length of coeff
+real	x[ARB]		# array of x values
+real	y[ARB]		# array of y values
+real	zfit[npts]	# array of interpolated values
+int	npts		# number of points to be evaluated
+real	badval		# undefined pixel value
+
+int	i, ii, jj, kk, index, nearax, nearbx, nearay, nearby
+real	px[5], py[5], dx, xmin, xmax, m, c, ymin, ymax, xtop
+real	ovlap, accum, waccum
+bool	negdx
+
+begin
+	do i = 1, npts {
+
+	    # Compute the limits of the integration in x and y.
+	    nearax = nint (min (x[4*i-3], x[4*i-2], x[4*i-1], x[4*i]))
+	    nearbx = nint (max (x[4*i-3], x[4*i-2], x[4*i-1], x[4*i]))
+	    nearay = nint (min (y[4*i-3], y[4*i-2], y[4*i-1], y[4*i]))
+	    nearby = nint (max (y[4*i-3], y[4*i-2], y[4*i-1], y[4*i]))
+
+	    # Initialize.
+	    accum = 0.0
+	    waccum = 0.0
+
+	    # Loop over all pixels which contribute to the integral.
+	    do jj = nearay, nearby {
+		index = first_point + (jj - 1) * len_coeff
+		do kk = 1, 4
+		    py[kk] = y[4*i+kk-4] - jj + 0.5
+		py[5] = py[1]
+		do ii = nearax, nearbx {
+
+		    # Transform the coordinates relative to a unit
+		    # square centered at the origin of the pixel. We
+		    # are going to approximate the new pixel area by
+		    # a quadilateral. Close the polygon.
+
+		    do kk = 1, 4
+			px[kk] = x[4*i+kk-4] - ii + 0.5
+		    px[5] = px[1]
+
+		    # Compute the area overlap of the output pixel with
+		    # the input pixels. 
+		    ovlap = 0.0
+		    do kk = 1, 4 {
+
+			# Check for vertical line segment.
+			dx = px[kk+1] - px[kk]
+			if (dx == 0.0)
+			    next
+
+			# Order the x integration limits.
+			if (px[kk] < px[kk+1]) {
+			    xmin = px[kk]
+			    xmax = px[kk+1]
+			} else {
+			    xmin = px[kk+1]
+			    xmax = px[kk]
+			}
+
+			# Check the x limits ignoring y for now.
+			if (xmin >= 1.0 || xmax <= 0.0)
+			    next
+			xmin = max (xmin, 0.0)
+			xmax = min (xmax, 1.0)
+
+			# Get basic info about the line y = mx + c.
+			if (dx < 0.0)
+			    negdx = true
+			else
+			    negdx = false
+			m = (py[kk+1] - py[kk]) / dx
+			c = py[kk] - m * px[kk]
+			ymin = m * xmin + c
+			ymax = m * xmax + c
+
+			# Trap segment entirely below axis.
+			if (ymin <= 0.0 && ymax <= 0.0)
+			    next
+
+			# Adjust bounds if segment crosses axis in order
+			# to exclude anything below the axis.
+			if (ymin < 0.0) {
+			    ymin = 0.0
+			    xmin = - c / m
+			}
+			if (ymax < 0.0) {
+			    ymax = 0.0
+			    xmax = - c / m
+			}
+
+			# There are four possibilities.
+
+			# Both y above 1.0. Line segment is entirely above
+			# square.
+			if (ymin >= 1.0 && ymax >= 1.0) {
+
+			    if (negdx)
+				ovlap = ovlap + (xmin - xmax)
+			    else
+				ovlap = ovlap + (xmax - xmin)
+
+			# Both y below 1.0. Segment is entirely within square.
+			} else if (ymin <= 1.0 && ymax <= 1.0) {
+
+			    if (negdx)
+				ovlap = ovlap + 0.5 * (xmin - xmax) *
+				    (ymax + ymin)
+			    else
+				ovlap = ovlap + 0.5 * (xmax - xmin) *
+				    (ymax + ymin)
+
+			# One of each. Segment must cross top of square.
+			} else {
+
+			    xtop = (1.0 - c) / m
+
+			    # insert precision check, e.g. possible pixel
+			    # overlap ? need to decide what action to take ...
+
+			    if (ymin < 1.0) {
+				if (negdx)
+				    ovlap = ovlap - (0.5 * (xtop - xmin) *
+				        (1.0 + ymin) + (xmax - xtop))
+				else
+				    ovlap = ovlap + (0.5 * (xtop - xmin) *
+				        (1.0 + ymin) + (xmax - xtop))
+			     } else {
+				if (negdx)
+				    ovlap = ovlap - (0.5 * (xmax - xtop) *
+				        (1.0 + ymax) + (xtop - xmin))
+				else
+				    ovlap = ovlap + (0.5 * (xmax - xtop) *
+				        (1.0 + ymax) + (xtop - xmin))
+			     }
+
+			}
+		    }
+
+		    accum = accum + coeff[index+ii] * ovlap
+		    waccum = waccum + ovlap
+		}
+	    }
+
+	    if (waccum == 0.0)
+		zfit[i] = badval
+	    else
+		zfit[i] = accum / waccum
+	}
+end
+
+
+# II_BIDRIZ0-- Procedure to evaluate the drizzle interpolant when xfrac and
+# yfrac are 0.0. The real array coeff contains the coefficients of the 2D
+# interpolant. The procedure assumes that 1 <= x <= nxpix and 1 <= y <= nypix
+# and that coeff[1+first_point] = datain[1,1]. Each x and y point is a set of 4
+# values describing the vertices of a quadrilateral in the input data. The
+# integration routine determines whether a pixel is in, out, on the edge
+# of or at a vertex of a polygon. The 4 points describing the corners of
+# each quadrilateral integration region must be in order, e.g.  describe
+# the vertices of a polygon in either CW or CCW order.
+# THIS ROUTINE IS NOT CURRENTLY BEING USED.
+ 
+procedure ii_bidriz0 (coeff, first_point, len_coeff, x, y, zfit, npts, badval)
+
+real	coeff[ARB]	# 1D coefficient array
+int	first_point	# offset of first data point
+int	len_coeff	# row length of coeff
+real	x[ARB]		# array of x values
+real	y[ARB]		# array of y values
+real	zfit[npts]	# array of interpolated values
+int	npts		# number of points to be evaluated
+real	badval		# the undefined pixel value
+
+bool	boundary, vertex
+int	i, jj, ii, kk, nearax, nearbx, nearay, nearby, ninter
+real	accum, waccum, px[5], py[5], lx, ld, u1, u2, u1u2, dx, dy, dd
+real	xi, ovlap, xmin, xmax
+
+begin
+	do i = 1, npts {
+
+	    # Compute the limits of the integration in x and y.
+	    nearax = nint (min (x[4*i-3], x[4*i-2], x[4*i-1], x[4*i]))
+	    nearbx = nint (max (x[4*i-3], x[4*i-2], x[4*i-1], x[4*i]))
+	    nearay = nint (min (y[4*i-3], y[4*i-2], y[4*i-1], y[4*i]))
+	    nearby = nint (max (y[4*i-3], y[4*i-2], y[4*i-1], y[4*i]))
+
+	    # Initialize.
+	    accum = 0.0
+	    waccum = 0.0
+
+	    # Loop over all pixels which contribute to the integral.
+	    do jj = nearay, nearby {
+		do ii = nearax, nearbx {
+
+		    # Transform the coordinates relative to a unit
+		    # square centered at the origin of the pixel. We
+		    # are going to approximate the new pixel area by
+		    # a quadilateral. Close the quadrilateral.
+
+		    do kk = 1, 4 {
+			px[kk] = x[4*i+kk-4] - ii + 0.5
+			py[kk] = y[4*i+kk-4] - jj + 0.5
+		    }
+		    px[5] = px[1]
+		    py[5] = py[1]
+
+		    # Initialize the integration.
+		    ovlap = 0.0
+		    ninter = 0
+
+		    # Define a line segment which begins at the point x = 0.5
+		    # y = 0.5 and runs parallel to the y axis.
+		    call alimr (px, 5, xmin, xmax)
+		    lx = xmax - xmin
+		    ld = 0.5 * lx
+		    u1 = -lx * py[1] + ld
+		    boundary = false
+		    vertex = false
+		    do kk = 2, 5 {
+
+		        u2 = -lx * py[kk] + ld
+			u1u2 = u1 * u2
+
+			# No intersection.
+			if (u1*u2 > 0.0) {
+			    ;
+
+			# Intersection with polygon line segment.
+			} else if (u1 != 0.0 && u2 != 0.0) {
+			    dy = py[kk-1] - py[kk]
+			    dx = px[kk-1] - px[kk]
+			    dd = px[kk-1] * py[kk] - py[kk-1] * px[kk]
+			    xi = (dx * ld - lx * dd) / (dy * lx)
+			    if (xi > 0.5)
+			        ninter = ninter + 1
+			    if (xi == 0.5)
+				boundary = true
+
+			# Collinearity.
+			} else if (u1 == 0.0 && u2 == 0.0) {
+			    xmin = min (px[kk-1], px[kk])
+			    xmax = max (px[kk-1], px[kk])
+			    if (xmin == 0.5 || xmax == 0.5)
+				vertex = true
+			    else if (xmin < 0.5 && xmax > 0.5)
+				boundary = true
+
+			# Vertex.
+			} else if (u1 != 0.0) {
+			    if (px[kk] == 0.5)
+				vertex = true
+			}
+
+			u1 = u2
+		    }
+
+		    if (vertex)
+			ovlap = 0.25
+		    else if (boundary)
+			ovlap = 0.5
+		    else if (mod (ninter, 2) == 0)
+			ovlap = 0.0
+		    else
+		        ovlap = 1.0
+		    waccum = waccum + ovlap
+		    accum = accum + ovlap *
+		        coeff[first_point+(jj-1)*len_coeff+ii]
+		}
+	    }
+
+	    if (waccum == 0.0)
+		zfit[i] = badval
+	    else
+		zfit[i] = accum / waccum
+	}
+
+end
diff --git a/math/iminterp/ii_cubspl.f b/math/iminterp/ii_cubspl.f
new file mode 100644
index 00000000..29407862
--- /dev/null
+++ b/math/iminterp/ii_cubspl.f
@@ -0,0 +1,119 @@
+      subroutine iicbsp (tau, c, n, ibcbeg, ibcend)
+c  from  * a practical guide to splines *  by c. de boor
+c     ************************	input  ***************************
+c     n = number of data points. assumed to be .ge. 2.
+c     (tau(i), c(1,i), i=1,...,n) = abscissae and ordinates of the
+c	 data points. tau is assumed to be strictly increasing.
+c     ibcbeg, ibcend = boundary condition indicators, and
+c     c(2,1), c(2,n) = boundary condition information. specifically,
+c	 ibcbeg = 0  means no boundary condition at tau(1) is given.
+c	    in this case, the not-a-knot condition is used, i.e. the
+c	    jump in the third derivative across tau(2) is forced to
+c	    zero, thus the first and the second cubic polynomial pieces
+c	    are made to coincide.)
+c	 ibcbeg = 1  means that the slope at tau(1) is made to equal
+c	    c(2,1), supplied by input.
+c	 ibcbeg = 2  means that the second derivative at tau(1) is
+c	    made to equal c(2,1), supplied by input.
+c	 ibcend = 0, 1, or 2 has analogous meaning concerning the
+c	    boundary condition at tau(n), with the additional infor-
+c	    mation taken from c(2,n).
+c     ***********************  output  **************************
+c     c(j,i), j=1,...,4; i=1,...,l (= n-1) = the polynomial coefficients
+c	 of the cubic interpolating spline with interior knots (or
+c	 joints) tau(2), ..., tau(n-1). precisely, in the interval
+c	 interval (tau(i), tau(i+1)), the spline f is given by
+c	    f(x) = c(1,i)+h*(c(2,i)+h*(c(3,i)+h*c(4,i)/3.)/2.)
+c	 where h = x - tau(i). the function program *ppvalu* may be
+c	 used to evaluate f or its derivatives from tau,c, l = n-1,
+c	 and k=4.
+      integer ibcbeg,ibcend,n,	 i,j,l,m
+      real c(4,n),tau(n),   divdf1,divdf3,dtau,g
+c****** a tridiagonal linear system for the unknown slopes s(i) of
+c  f  at tau(i), i=1,...,n, is generated and then solved by gauss elim-
+c  ination, with s(i) ending up in c(2,i), all i.
+c     c(3,.) and c(4,.) are used initially for temporary storage.
+      l = n-1
+compute first differences of tau sequence and store in c(3,.). also,
+compute first divided difference of data and store in c(4,.).
+      do 10 m=2,n
+	 c(3,m) = tau(m) - tau(m-1)
+   10	 c(4,m) = (c(1,m) - c(1,m-1))/c(3,m)
+construct first equation from the boundary condition, of the form
+c	      c(4,1)*s(1) + c(3,1)*s(2) = c(2,1)
+      if (ibcbeg-1)			11,15,16
+   11 if (n .gt. 2)			go to 12
+c     no condition at left end and n = 2.
+      c(4,1) = 1.
+      c(3,1) = 1.
+      c(2,1) = 2.*c(4,2)
+					go to 25
+c     not-a-knot condition at left end and n .gt. 2.
+   12 c(4,1) = c(3,3)
+      c(3,1) = c(3,2) + c(3,3)
+      c(2,1) =((c(3,2)+2.*c(3,1))*c(4,2)*c(3,3)+c(3,2)**2*c(4,3))/c(3,1)
+					go to 19
+c     slope prescribed at left end.
+   15 c(4,1) = 1.
+      c(3,1) = 0.
+					go to 18
+c     second derivative prescribed at left end.
+   16 c(4,1) = 2.
+      c(3,1) = 1.
+      c(2,1) = 3.*c(4,2) - c(3,2)/2.*c(2,1)
+   18 if(n .eq. 2)			go to 25
+c  if there are interior knots, generate the corresp. equations and car-
+c  ry out the forward pass of gauss elimination, after which the m-th
+c  equation reads    c(4,m)*s(m) + c(3,m)*s(m+1) = c(2,m).
+   19 do 20 m=2,l
+	 g = -c(3,m+1)/c(4,m-1)
+	 c(2,m) = g*c(2,m-1) + 3.*(c(3,m)*c(4,m+1)+c(3,m+1)*c(4,m))
+   20	 c(4,m) = g*c(3,m-1) + 2.*(c(3,m) + c(3,m+1))
+construct last equation from the second boundary condition, of the form
+c	    (-g*c(4,n-1))*s(n-1) + c(4,n)*s(n) = c(2,n)
+c     if slope is prescribed at right end, one can go directly to back-
+c     substitution, since c array happens to be set up just right for it
+c     at this point.
+      if (ibcend-1)			21,30,24
+   21 if (n .eq. 3 .and. ibcbeg .eq. 0) go to 22
+c     not-a-knot and n .ge. 3, and either n.gt.3 or  also not-a-knot at
+c     left end point.
+      g = c(3,n-1) + c(3,n)
+      c(2,n) = ((c(3,n)+2.*g)*c(4,n)*c(3,n-1)
+     *		  + c(3,n)**2*(c(1,n-1)-c(1,n-2))/c(3,n-1))/g
+      g = -g/c(4,n-1)
+      c(4,n) = c(3,n-1)
+					go to 29
+c     either (n=3 and not-a-knot also at left) or (n=2 and not not-a-
+c     knot at left end point).
+   22 c(2,n) = 2.*c(4,n)
+      c(4,n) = 1.
+					go to 28
+c     second derivative prescribed at right endpoint.
+   24 c(2,n) = 3.*c(4,n) + c(3,n)/2.*c(2,n)
+      c(4,n) = 2.
+					go to 28
+   25 if (ibcend-1)			26,30,24
+   26 if (ibcbeg .gt. 0)		go to 22
+c     not-a-knot at right endpoint and at left endpoint and n = 2.
+      c(2,n) = c(4,n)
+					go to 30
+   28 g = -1./c(4,n-1)
+complete forward pass of gauss elimination.
+   29 c(4,n) = g*c(3,n-1) + c(4,n)
+      c(2,n) = (g*c(2,n-1) + c(2,n))/c(4,n)
+carry out back substitution
+   30 j = l
+   40	 c(2,j) = (c(2,j) - c(3,j)*c(2,j+1))/c(4,j)
+	 j = j - 1
+	 if (j .gt. 0)			go to 40
+c****** generate cubic coefficients in each interval, i.e., the deriv.s
+c  at its left endpoint, from value and slope at its endpoints.
+      do 50 i=2,n
+	 dtau = c(3,i)
+	 divdf1 = (c(1,i) - c(1,i-1))/dtau
+	 divdf3 = c(2,i-1) + c(2,i) - 2.*divdf1
+	 c(3,i-1) = 2.*(divdf1 - c(2,i-1) - divdf3)/dtau
+   50	 c(4,i-1) = (divdf3/dtau)*(6./dtau)
+					return
+      end
diff --git a/math/iminterp/ii_eval.x b/math/iminterp/ii_eval.x
new file mode 100644
index 00000000..2e4cbb37
--- /dev/null
+++ b/math/iminterp/ii_eval.x
@@ -0,0 +1,430 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.  
+
+include <math.h>
+
+
+# II_NEAREST -- Procedure to evaluate the nearest neighbour interpolant.
+
+procedure ii_nearest (x, y, npts, data)
+
+real	x[ARB]		# x values, must be within [1,npts]
+real	y[ARB]		# interpolated values returned to user
+int	npts		# number of x values
+real	data[ARB]	# data to be interpolated
+
+int	i
+
+begin
+	do i = 1, npts
+	    y[i] = data[int(x[i] + 0.5)]
+end
+
+
+# II_LINEAR -- Procedure to evaluate the linear interpolant.
+
+procedure ii_linear (x, y, npts, data)
+
+real	x[ARB]		# x values, must be within [1,npts]
+real	y[ARB]		# interpolated values returned to user
+int	npts		# number of x values
+real	data[ARB]	# data to be interpolated
+
+int	i, nx
+
+begin
+	do i = 1, npts {
+	    nx = x[i]
+	    y[i] =  (x[i] - nx) * data[nx + 1] + (nx + 1 - x[i]) * data[nx]
+	}
+end
+
+
+# II_POLY3 -- Procedure to evaluate the cubic polynomial interpolant.
+
+procedure ii_poly3 (x, y, npts, data)
+
+real	x[ARB]		# x values, must be within [1,npts]
+real	y[ARB]		# interpolated values returned to user
+int	npts		# number of x values
+real	data[ARB]	# data to be interpolated from a[0] to a[npts+2]
+
+int	i, nx, nxold
+real	deltax, deltay, cd20, cd21
+
+begin
+	nxold = -1
+	do i = 1, npts {
+	    nx = x[i]
+	    deltax = x[i] - nx
+	    deltay = 1. - deltax
+
+	    if (nx != nxold) {
+		# second central differences:
+		cd20 = 1./6. * (data[nx+1] - 2. * data[nx] + data[nx-1])
+		cd21 = 1./6. * (data[nx+2] - 2. * data[nx+1] + data[nx])
+		nxold = nx
+	    }
+
+	    y[i] = deltax * (data[nx+1] + (deltax * deltax - 1.) * cd21) +
+		    deltay * (data[nx] + (deltay * deltay - 1.) * cd20)
+	}
+end
+
+
+# II_POLY5 -- Procedure to evaluate the fifth order polynomial interpolant.
+
+procedure ii_poly5 (x, y, npts, data)
+
+real	x[ARB]		# x values, must be within [1,npts]
+real	y[ARB]		# interpolated values returned to user
+int	npts		# number of x values
+real	data[ARB]	# data to be interpolated - from a[-1] to a[npts+3]
+
+int	i, nx, nxold
+real	deltax, deltay, cd20, cd21, cd40, cd41
+
+begin
+	nxold = -1
+	do i = 1, npts {
+	    nx = x[i]
+	    deltax = x[i] - nx
+	    deltay = 1. - deltax
+
+	    if (nx != nxold) {
+		cd20 = 1./6. * (data[nx+1] - 2. * data[nx] + data[nx-1])
+		cd21 = 1./6. * (data[nx+2] - 2. * data[nx+1] + data[nx])
+		# fourth central differences
+		cd40 = 1./120. * (data[nx-2] - 4. * data[nx-1] +
+			6. * data[nx] - 4. * data[nx+1] + data[nx+2])
+		cd41 = 1./120. * (data[nx-1] - 4. * data[nx] +
+			6. * data[nx+1] - 4. * data[nx+2] + data[nx+3])
+		nxold = nx
+	    }
+
+	    y[i] = deltax * (data[nx+1] + (deltax * deltax - 1.) *
+			 (cd21 + (deltax * deltax - 4.) * cd41)) +
+		   deltay * (data[nx] + (deltay * deltay - 1.) *
+			 (cd20 + (deltay * deltay - 4.) * cd40)) 
+	}
+end
+
+
+# II_SPLINE3 -- Procedure to evaluate the cubic spline interpolant.
+
+procedure ii_spline3 (x, y, npts, bcoeff)
+
+real	x[ARB]		# x values, must be within [1,npts]
+real	y[ARB]		# interpolated values returned to user
+int	npts		# number of x values
+real	bcoeff[ARB]	# basis spline coefficients - from a[0] to a[npts+1]
+
+int	i, nx, nxold
+real	deltax, c0, c1, c2, c3
+
+begin
+	nxold = -1
+	do i = 1, npts {
+	    nx = x[i]
+	    deltax = x[i] - nx
+
+	    if (nx != nxold) {
+		# convert b-spline coeff's to poly. coeff's
+		c0 = bcoeff[nx-1] + 4. * bcoeff[nx] + bcoeff[nx+1]
+		c1 = 3. * (bcoeff[nx+1] - bcoeff[nx-1])
+		c2 = 3. * (bcoeff[nx-1] - 2. * bcoeff[nx] + bcoeff[nx+1])
+		c3 = -bcoeff[nx-1] + 3. * bcoeff[nx] - 3. * bcoeff[nx+1] +
+		     bcoeff[nx+2]
+		nxold = nx
+	    }
+
+	    y[i] = c0 + deltax * (c1 + deltax * (c2 + deltax * c3))
+	}
+end
+
+
+# II_SINC -- Procedure to evaluate the sinc interpolant. The sinc
+# truncation length is nsinc. The taper is a cosbell function which is
+# approximated by a quartic polynomial which is valid for 0 <= x <= PI / 2
+# (Abramowitz and Stegun, 1972, Dover Publications, p 76). If the point to
+# be interpolated is less than mindx from a data point no interpolation is
+# done and the data point itself is returned.
+
+procedure ii_sinc (x, y, npts, data, npix, nsinc, mindx)
+
+real	x[ARB]		# x values, must be within [1,npts]
+real	y[ARB]		# interpolated values returned to user
+int	npts		# number of x values
+real	data[ARB]	# data to be interpolated
+int	npix		# number of data pixels
+int	nsinc		# sinc truncation length
+real	mindx		# interpolation minimum
+
+int	i, j, xc, minj, maxj, offj
+pointer	sp, taper
+real	dx, dxn, dx2, w1, sconst, a2, a4, sum, sumw
+
+begin
+	# Compute the constants for the cosine bell taper. 
+	sconst = (HALFPI / nsinc) ** 2
+	a2 = -0.49670
+	a4 = 0.03705
+
+	# Pre-compute the taper array. Incorporate the sign change portion
+	# of the sinc interpolator into the taper array.
+	call smark (sp)
+	call salloc (taper, 2 * nsinc + 1, TY_REAL)
+	if (mod (nsinc, 2) == 0)
+	    w1 = 1.0
+	else
+	    w1 = -1.0
+	do j = -nsinc,  nsinc {
+	    dx2 = sconst * j * j
+	    Memr[taper+j+nsinc] = w1 * (1.0 + a2 * dx2 + a4 * dx2 * dx2) ** 2
+	    w1 = -w1
+	}
+
+	do i = 1, npts {
+
+	    # Return zero outside of data.
+	    xc = nint (x[i])
+	    if (xc < 1 || xc > npix) {
+		y[i] = 0.
+		next
+	    }
+
+	    # Return the data value if x is too close to x[i].
+	    dx = x[i] - xc
+	    if (abs (dx) < mindx) {
+		y[i] = data[xc]
+		next
+	    }
+
+	    # Compute the limits of the true convolution.
+	    minj = max (1, xc - nsinc)
+	    maxj = min (npix, xc + nsinc)
+	    offj = -xc + nsinc
+
+	    # Do the convolution.
+	    sum = 0.0
+	    sumw = 0.0
+	    dxn = dx + xc
+	    do j = xc - nsinc, minj - 1 {
+		w1 = Memr[taper+j+offj] / (dxn - j) 
+		sum = sum + w1 * data[1]
+		sumw = sumw + w1
+	    }
+	    do j = minj, maxj {
+		w1 = Memr[taper+j+offj] / (dxn - j) 
+		sum = sum + w1 * data[j]
+		sumw = sumw + w1
+	    }
+	    do j = maxj + 1, xc + nsinc {
+		w1 = Memr[taper+j+offj] / (dxn - j) 
+		sum = sum + w1 * data[npix]
+		sumw = sumw + w1
+	    }
+
+	    # Compute value.
+	    y[i] = sum / sumw
+	}
+
+	call sfree (sp)
+end
+
+
+# II_LSINC -- Procedure to evaluate the sinc interpolant using a
+# precomputed look-up table. The sinc truncation length is nsinc. The taper
+# is a cosbell function which is  approximated by a quartic polynomial which
+# is valid for 0 <= x <= PI / 2 (Abramowitz and Stegun, 1972, Dover
+# Publications, p 76). If the point to be interpolated is less than mindx
+# from a data point no interpolation is done and the data point itself is
+# returned.
+
+procedure ii_lsinc (x, y, npts, data, npix, ltable, nconv, nincr, mindx)
+
+real	x[ARB]			# x values, must be within [1,npix]
+real	y[ARB]			# interpolated values returned to user
+int	npts			# number of x values
+real	data[ARB]		# data to be interpolated
+int	npix			# number of data pixels
+real	ltable[nconv,nincr]	# the sinc look-up table
+int	nconv			# sinc truncation length
+int	nincr			# the number of look-up table entries
+real	mindx			# interpolation minimum (don't use)
+
+int	i, j, nsinc, xc, lut, minj, maxj, offj
+real	dx, sum
+
+begin
+	nsinc = (nconv - 1) / 2
+	do i = 1, npts {
+
+	    # Return zero outside of data.
+	    xc = nint (x[i])
+	    if (xc < 1 || xc > npix) {
+		y[i] = 0.
+		next
+	    }
+
+	    # Return data point if dx is too small.
+	    dx = x[i] - xc
+	    if (abs (dx) < mindx) {
+		y[i] = data[xc]
+		next
+	    }
+
+	    # Find the correct look-up table entry.
+	    if (nincr == 1)
+		lut = 1
+	    else 
+		lut = nint ((-dx + 0.5) * (nincr - 1)) + 1
+		#lut = int ((-dx + 0.5) * (nincr - 1) + 0.5) + 1
+
+	    # Compute the convolution limits.
+	    minj = max (1, xc - nsinc)
+	    maxj = min (npix, xc + nsinc)
+	    offj = -xc + nsinc + 1
+
+	    # Do the convolution.
+	    sum = 0.0
+	    do j = xc - nsinc, minj - 1
+		sum = sum + ltable[j+offj,lut] * data[1]
+	    do j = minj, maxj
+		sum = sum + ltable[j+offj,lut] * data[j]
+	    do j = maxj + 1, xc + nsinc
+		sum = sum + ltable[j+offj,lut] * data[npix]
+
+	    # Compute the value.
+	    y[i] = sum
+	}
+end
+
+
+# II_DRIZ -- Procedure to evaluate the drizzle interpolant. 
+
+procedure ii_driz (x, y, npts, data, pixfrac, badval)
+
+real	x[ARB]		# x start and stop values, must be within [1,npts]
+real	y[ARB]		# interpolated values returned to user
+int	npts		# number of x values
+real	data[ARB]	# data to be interpolated
+real	pixfrac		# the drizzle pixel fraction
+real	badval		# value for undefined pixels
+
+int	i, j, neara, nearb
+real	hpixfrac, xa, xb, dx, accum, waccum
+
+begin
+	hpixfrac = pixfrac / 2.0
+	do i = 1, npts {
+
+	    # Define the interval of integration.
+	    xa = min (x[2*i-1], x[2*i])
+	    xb = max (x[2*i-1], x[2*i])
+	    neara = xa + 0.5
+	    nearb = xb + 0.5
+
+	    # Initialize the integration
+	    accum = 0.0
+	    waccum = 0.0
+	    if (neara == nearb) {
+
+	        dx = min (xb, nearb + hpixfrac) - max (xa, neara - hpixfrac)
+
+		if (dx > 0.0) {
+		    accum = accum + dx * data[neara]
+		    waccum = waccum + dx
+		}
+
+	    } else {
+
+		# first segement
+		dx = neara + hpixfrac - max (xa, neara - hpixfrac)
+
+		if (dx > 0.0) {
+		    accum = accum + dx * data[neara]
+		    waccum = waccum + dx
+		}
+
+		# interior segments.
+		do j = neara + 1, nearb - 1 {
+		    accum = accum + pixfrac * data[j]
+		    waccum = waccum + pixfrac
+		}
+
+		# last segment
+	        dx = min (xb, nearb + hpixfrac) - (nearb - hpixfrac)
+
+		if (dx > 0.0) {
+		    accum = accum + dx * data[nearb]
+		    waccum = waccum + dx
+		}
+	    }
+
+	    if (waccum == 0.0)
+		y[i] = badval
+	    else
+		y[i] = accum / waccum
+	}
+end
+
+
+# II_DRIZ1 -- Procedure to evaluate the drizzle interpolant in the case where
+# pixfrac = 1.0. 
+
+procedure ii_driz1 (x, y, npts, data, badval)
+
+real	x[ARB]		# x start and stop values, must be within [1,npts]
+real	y[ARB]		# interpolated values returned to user
+int	npts		# number of x values
+real	data[ARB]	# data to be interpolated
+real	badval		# undefined pixel value
+
+int	i, j, neara, nearb
+real	xa, xb, deltaxa, deltaxb, dx, accum, waccum
+
+begin
+	do i = 1, npts {
+
+	    # Define the interval of integration.
+	    xa = min (x[2*i-1], x[2*i])
+	    xb = max (x[2*i-1], x[2*i])
+	    neara = xa + 0.5
+	    nearb = xb + 0.5
+	    deltaxa = xa - neara
+	    deltaxb = xb - nearb
+
+	    # Only one segment involved.
+	    accum = 0.0
+	    waccum = 0.0
+	    if (neara == nearb) {
+
+		dx = deltaxb - deltaxa
+		accum = accum + dx * data[neara]
+		waccum = waccum + dx
+
+	    } else {
+
+		# First segment.
+		dx = 0.5 - deltaxa
+		accum = accum + dx * data[neara]
+		waccum = waccum + dx
+
+		# Middle segment.
+		do j = neara + 1, nearb - 1 {
+		    accum = accum + data[j]
+		    waccum = waccum + 1.0
+		}
+
+		# Last segment.
+		dx = deltaxb + 0.5
+		accum = accum + dx * data[nearb]
+		waccum = waccum + dx
+	    }
+
+	    if (waccum == 0.0)
+		y[i] = badval
+	    else
+		y[i] = accum / waccum
+	}
+end
diff --git a/math/iminterp/ii_greval.x b/math/iminterp/ii_greval.x
new file mode 100644
index 00000000..6b5d75b2
--- /dev/null
+++ b/math/iminterp/ii_greval.x
@@ -0,0 +1,859 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math.h>
+include <math/iminterp.h>
+
+# II_GRNEAREST -- Procedure to evaluate the nearest neighbour interpolant on
+# a rectangular grid. The procedure assumes that 1 <= x <= nxpix and
+# that 1 <= y <= nypix. The x and y vectors must be sorted in increasing
+# value of x and y such that x[i] < x[i+1] and y[i] < y[i+1]. The routine
+# outputs a grid of nxpix by nypix points using the coeff array where
+# coeff[1+first_point] = datain[1,1]
+
+procedure ii_grnearest (coeff, first_point, len_coeff, x, y, zfit, nxpts,
+		        nypts, len_zfit)
+
+real	coeff[ARB]		# 1D coefficient array
+int	first_point		# offset of first data point
+int	len_coeff		# row length of coeff 
+real	x[nxpts]		# array of x values
+real	y[nypts]		# array of y values
+real	zfit[len_zfit,ARB]	# array of interpolatedvalues
+int	nxpts			# number of x values
+int	nypts			# number of y values
+int	len_zfit		# row length of zfit
+
+int	ny
+int	index
+int	i, j
+pointer	sp, nx
+
+errchk	smark, salloc, sfree
+
+begin
+	call smark (sp)
+	call salloc (nx, nxpts, TY_INT)
+
+	# calculate the nearest x
+	do i = 1, nxpts
+	    Memi[nx+i-1] = x[i] + 0.5
+
+	# loop over the rows
+	do j = 1, nypts {
+
+	    # calculate pointer to the ny-th row of data
+	    ny = y[j] + 0.5
+	    index = first_point + (ny - 1) * len_coeff
+
+	    # loop over the columns
+	    do i = 1, nxpts
+		zfit[i,j] = coeff[index + Memi[nx+i-1]]
+	}
+
+	call sfree (sp)
+end
+
+
+# II_GRLINEAR -- Procedure to evaluate the bilinear interpolant
+# on a rectangular grid. The procedure assumes that 1 <= x <= nxpix and that
+# 1 <= y <= nypix. The x and y vectors are assumed to be sorted in increasing
+# order of x and y such that x[i] < x[i+1] and y[i] < y[i+1]. The routine 
+# produces a grid of nxpix * nypix evaluated points using the coeff array
+# where coeff[1+first_point] = datain[1,1].
+
+procedure ii_grlinear (coeff, first_point, len_coeff, x, y, zfit, nxpts,
+		       nypts, len_zfit)
+
+real	coeff[ARB]		# 1D array of coefficients
+int	first_point		# offset of first data point
+int	len_coeff		# row length of coeff
+real	x[nxpts]		# array of x values
+real	y[nypts]		# array of y values
+real	zfit[len_zfit,ARB]	# array of interpolated values
+int	nxpts			# number of x values
+int	nypts			# number of y values
+int	len_zfit		# row length of zfit
+
+int	i, j, ny
+int	nymin, nymax, nylines
+int	row_index, xindex
+pointer	sp, nx, sx, tx, work, lbuf1, lbuf2
+real	sy, ty
+
+errchk	smark, salloc, sfree
+
+begin
+	# calculate the x and y limits
+	nymin = y[1]
+	nymax = int (y[nypts]) + 1
+	nylines = nymax - nymin + 1
+
+	# allocate storage for work array
+	call smark (sp)
+	call salloc (nx, nxpts, TY_INT)
+	call salloc (sx, nxpts, TY_REAL)
+	call salloc (tx, nxpts, TY_REAL)
+	call salloc (work, nxpts * nylines, TY_REAL)
+
+	# initialize
+	call achtri (x, Memi[nx], nxpts)
+	do i = 1, nxpts {
+	    Memr[sx+i-1] = x[i] - Memi[nx+i-1]
+	    Memr[tx+i-1] = 1. - Memr[sx+i-1]
+	}
+
+	# for each value of y interpolate in x and store in work array
+	lbuf1 = work
+	do j = 1, nylines {
+
+	    # define pointer to appropriate row
+	    row_index = first_point + (j + nymin - 2) * len_coeff
+
+	    # interpolate in x at each y
+	    do i = 1, nxpts {
+		xindex = row_index + Memi[nx+i-1]
+		Memr[lbuf1+i-1] = Memr[tx+i-1] * coeff[xindex] +
+		    Memr[sx+i-1] * coeff[xindex+1]
+	    }
+
+	    lbuf1 = lbuf1 + nxpts
+	}
+
+	# at each x interpolate in y and store in temporary work array
+	do j = 1, nypts {
+
+	    ny = y[j]
+	    sy = y[j] - ny
+	    ty = 1. - sy
+
+	    lbuf1 = work + nxpts * (ny - nymin)
+	    lbuf2 = lbuf1 + nxpts
+
+	    call awsur (Memr[lbuf1], Memr[lbuf2], zfit[1,j], nxpts,
+		ty, sy)
+
+	}
+
+	# deallocate work space
+	call sfree (sp)
+end
+
+
+# II_GRPOLY3 -- Procedure to evaluate the bicubic polynomial interpolant
+# on a rectangular grid. The points to be evaluated are assumed
+# to lie in the range 1 <= x <= nxpix and 1 <= y <= nypix. The x and y vectors
+# are assumed to be sorted in increasing order of x and y such that
+# x[i] < x[i+1] and y[i] < y[i+1]. The interpolation is done using
+# Everett's central difference formula and separation of variables
+# and assuming that coeff[1+first_point] = datain[1,1].
+
+procedure ii_grpoly3 (coeff, first_point, len_coeff, x, y, zfit, nxpts, nypts,
+		      len_zfit)
+
+real	coeff[ARB]		# 1D array of coefficients
+int	first_point		# offset of first data point
+int	len_coeff		# length of row of coeffcient
+real	x[nxpts]		# array of x values
+real	y[nypts]		# array of y values
+real	zfit[len_zfit,ARB]	# array of interpolatedvalues
+int	nxpts			# number of x points
+int	nypts			# number of y points
+int	len_zfit		# row length of zfit
+
+int	nymin, nymax, nylines
+int	nxold, nyold
+int	row_index, xindex
+int	i, j, ny
+pointer	sp, nx, sx, sx2m1, tx, tx2m1, work
+pointer	lbuf, lbufp1, lbufp2, lbufm1
+real	cd20x, cd21x, cd20y, cd21y
+real	sy, ty, sy2m1, ty2m1
+
+errchk smark, salloc, sfree
+
+begin
+	# find y limits
+	nymin = int (y[1]) - 1
+	nymax = int (y[nypts]) + 2
+	nylines = nymax - nymin + 1
+
+	# allocate work space
+	call smark (sp)
+	call salloc (nx, nxpts, TY_INT)
+	call salloc (sx, nxpts, TY_REAL)
+	call salloc (sx2m1, nxpts, TY_REAL)
+	call salloc (tx, nxpts, TY_REAL)
+	call salloc (tx2m1, nxpts, TY_REAL) 
+	call salloc (work, nxpts * nylines, TY_REAL)
+
+	# initialize
+	call achtri (x, Memi[nx], nxpts)
+	do i = 1, nxpts {
+	    Memr[sx+i-1] = x[i] - Memi[nx+i-1]
+	    Memr[sx2m1+i-1] = Memr[sx+i-1] * Memr[sx+i-1] - 1.
+	    Memr[tx+i-1] = 1. - Memr[sx+i-1]
+	    Memr[tx2m1+i-1] = Memr[tx+i-1] * Memr[tx+i-1] - 1.
+	}
+
+	# for each value of y interpolate in x
+	lbuf = work
+	do j = 1, nylines {
+
+	    # calculate pointer to a row
+	    row_index = first_point + (j + nymin - 2) * len_coeff
+
+	    # interpolate in x at each y
+	    nxold = -1
+	    do i = 1, nxpts {
+
+		xindex= row_index + Memi[nx+i-1]
+
+		if (Memi[nx+i-1] != nxold) {
+		    #cd20x = 1./6. * (coeff[xindex+1] - 2. * coeff[xindex] +
+		           #coeff[xindex-1])
+		    #cd21x = 1./6. * (coeff[xindex+2] - 2. * coeff[xindex+1] +
+			    #coeff[xindex])
+		    cd20x = (coeff[xindex+1] - 2. * coeff[xindex] +
+		           coeff[xindex-1]) / 6.
+		    cd21x = (coeff[xindex+2] - 2. * coeff[xindex+1] +
+			    coeff[xindex]) / 6.0
+		}
+
+		Memr[lbuf+i-1] = Memr[sx+i-1] * (coeff[xindex+1] +
+		                Memr[sx2m1+i-1] * cd21x) +
+			        Memr[tx+i-1] * (coeff[xindex] +
+				Memr[tx2m1+i-1] * cd20x)
+
+		nxold = Memi[nx+i-1]
+	    }
+
+	    lbuf = lbuf + nxpts
+	}
+
+	# interpolate in y at each x
+	nyold = -1
+	do j = 1, nypts {
+
+	    ny = y[j]
+	    sy = y[j] - ny
+	    ty = 1. - sy
+	    sy2m1 = sy ** 2 - 1.
+	    ty2m1 = ty ** 2 - 1.
+
+	    lbuf = work + nxpts * (ny - nymin) 
+	    lbufm1 = lbuf - nxpts
+	    lbufp1 = lbuf + nxpts
+	    lbufp2 = lbufp1 + nxpts
+
+	    do i = 1, nxpts {
+
+		# calculate central differences in y
+		#if (nyold != ny) {
+		    #cd20y = 1./6. * (Memr[lbufp1+i-1] - 2. * Memr[lbuf+i-1] +
+			    #Memr[lbufm1+i-1])
+		    #cd21y = 1./6. * (Memr[lbufp2+i-1] - 2. *
+		    	    #Memr[lbufp1+i-1] + Memr[lbuf+i-1])
+		    cd20y = (Memr[lbufp1+i-1] - 2. * Memr[lbuf+i-1] +
+			    Memr[lbufm1+i-1]) / 6.0
+		    cd21y = (Memr[lbufp2+i-1] - 2. * Memr[lbufp1+i-1] +
+		    	    Memr[lbuf+i-1]) / 6.0
+		#}
+
+		# interpolate in y
+		zfit[i,j] =  sy * (Memr[lbufp1+i-1] + sy2m1 * cd21y) +
+			     ty * (Memr[lbuf+i-1] + ty2m1 * cd20y)
+
+	    }
+
+	    #nyold = ny
+	}
+
+	# free work space
+	call sfree (sp)
+end
+
+
+# II_GRPOLY5 -- Procedure to evaluate the biquintic polynomial interpolant
+# on a rectangular grid. The routine assumes that 1 <= x <= nxpix and
+# 1 <= y <= nypix.  The vectors x and y are assumed to be sorted in
+# increasing order such that x[i] < x[i+1] and y[i] < y[i+1]. The
+# interpolation is done using Everett's interpolation formula and
+# separation of variables and assuming that coeff[1+first_point] =
+# datain[1,1].
+
+procedure ii_grpoly5 (coeff, first_point, len_coeff, x, y, zfit, nxpts,
+		      nypts, len_zfit)
+
+real	coeff[ARB]		# 1D array of coefficients
+int	first_point		# offset of first data point
+int	len_coeff		# row length of coeff
+real	x[nxpts]		# array of x values
+real	y[nypts]		# array of y values
+real	zfit[len_zfit,ARB]	# array of fitted values
+int	nxpts			# number of x points
+int	nypts			# number of y points
+int	len_zfit		# row length of zfit
+
+int	nymax, nymin, nylines, nxold, nyold
+int	row_index, xindex
+int	i, j, ny
+pointer	sp, nx, sx, tx, sx2m1, sx2m4, tx2m1, tx2m4, work
+pointer	lbuf, lbufp1, lbufp2, lbufp3, lbufm1, lbufm2
+real	cd20x, cd21x, cd40x, cd41x
+real	cd20y, cd21y, cd40y, cd41y
+real	sy, ty, sy2m1, sy2m4, ty2m1, ty2m4
+
+errchk	smark, salloc, sfree
+
+begin
+	# find the y limits
+	nymin = int (y[1]) - 2
+	nymax = int (y[nypts]) + 3
+	nylines = nymax - nymin + 1
+
+	# allocate space
+	call smark (sp)
+	call salloc (nx, nxpts, TY_INT)
+	call salloc (sx, nxpts, TY_REAL)
+	call salloc (sx2m1, nxpts, TY_REAL)
+	call salloc (sx2m4, nxpts, TY_REAL)
+	call salloc (tx, nxpts, TY_REAL)
+	call salloc (tx2m1, nxpts, TY_REAL)
+	call salloc (tx2m4, nxpts, TY_REAL)
+	call salloc (work, nxpts * nylines, TY_REAL)
+
+	# intialize
+	call achtri (x, Memi[nx], nxpts)
+	do i = 1, nxpts {
+	    Memr[sx+i-1] = x[i] - Memi[nx+i-1]
+	    Memr[sx2m1+i-1] = Memr[sx+i-1] ** 2 - 1.
+	    Memr[sx2m4+i-1] = Memr[sx2m1+i-1] - 3.
+	    Memr[tx+i-1] = 1. - Memr[sx+i-1]
+	    Memr[tx2m1+i-1] = Memr[tx+i-1] ** 2 - 1.
+	    Memr[tx2m4+i-1] = Memr[tx2m1+i-1] - 3.
+	}
+
+
+	# for each value of y interpolate in x
+	lbuf = work
+	do j = 1, nylines {
+
+	    # calculate pointer to a row
+	    row_index = first_point + (j + nymin - 2) * len_coeff
+
+	    # interpolate in x at each y
+	    nxold = -1
+	    do i = 1, nxpts {
+
+		xindex = row_index + Memi[nx+i-1]
+
+		if (Memi[nx+i-1] != nxold) {
+		    #cd20x = 1./6. * (coeff[xindex+1] - 2. * coeff[xindex] +
+		            #coeff[xindex-1])
+		    #cd21x = 1./6. * (coeff[xindex+2] - 2. * coeff[xindex+1] +
+			    #coeff[xindex])
+		    cd20x = (coeff[xindex+1] - 2. * coeff[xindex] +
+		            coeff[xindex-1]) / 6.0
+		    cd21x = (coeff[xindex+2] - 2. * coeff[xindex+1] +
+			    coeff[xindex]) / 6.0
+		    #cd40x = 1./120. * (coeff[xindex-2] - 4. * coeff[xindex-1] +
+			    #6. * coeff[xindex] - 4. * coeff[xindex+1] +
+			    #coeff[xindex+2])
+		    #cd41x = 1./120. * (coeff[xindex-1] - 4. * coeff[xindex] +
+			    #6. * coeff[xindex+1] - 4. * coeff[xindex+2] +
+			    #coeff[xindex+3])
+		    cd40x = (coeff[xindex-2] - 4. * coeff[xindex-1] +
+			    6. * coeff[xindex] - 4. * coeff[xindex+1] +
+			    coeff[xindex+2]) / 120.0
+		    cd41x = (coeff[xindex-1] - 4. * coeff[xindex] +
+			    6. * coeff[xindex+1] - 4. * coeff[xindex+2] +
+			    coeff[xindex+3]) / 120.0
+		}
+
+		Memr[lbuf+i-1] = Memr[sx+i-1] * (coeff[xindex+1] +
+				 Memr[sx2m1+i-1] * (cd21x +
+				 Memr[sx2m4+i-1] * cd41x)) +
+			         Memr[tx+i-1] * (coeff[xindex] +
+				 Memr[tx2m1+i-1] * (cd20x +
+				 Memr[tx2m4+i-1] * cd40x))
+
+
+		nxold = Memi[nx+i-1]
+
+	    }
+
+	    lbuf = lbuf + nxpts
+	}
+
+	# at each x interpolate in y
+	nyold = -1
+	do j = 1, nypts {
+
+	    ny = y[j]
+	    sy = y[j] - ny
+	    sy2m1 = sy ** 2 - 1.
+	    sy2m4 = sy2m1 - 3.
+	    ty = 1. - sy
+	    ty2m1 = ty ** 2 - 1.
+	    ty2m4 = ty2m1 - 3.
+
+	    lbuf = work + nxpts * (ny - nymin)
+	    lbufp1 = lbuf + nxpts
+	    lbufp2 = lbufp1 + nxpts
+	    lbufp3 = lbufp2 + nxpts
+	    lbufm1 = lbuf - nxpts
+	    lbufm2 = lbufm1 - nxpts
+
+	    do i = 1, nxpts {
+
+		# calculate central differences
+		#if (nyold != ny) {
+		    #cd20y = 1./6. * (Memr[lbufp1+i-1] - 2. * Memr[lbuf+i-1] +
+			    #Memr[lbufm1+i-1])
+		    #cd21y = 1./6. * (Memr[lbufp2+i-1] - 2. *
+		    	    #Memr[lbufp1+i-1] + Memr[lbuf+i-1])
+		    cd20y = (Memr[lbufp1+i-1] - 2. * Memr[lbuf+i-1] +
+			    Memr[lbufm1+i-1]) / 6.
+		    cd21y = (Memr[lbufp2+i-1] - 2. *
+		    	    Memr[lbufp1+i-1] + Memr[lbuf+i-1]) / 6.
+		    #cd40y = 1./120. * (Memr[lbufm2+i-1] -
+		    	    #4. * Memr[lbufm1+i-1] + 6. * Memr[lbuf+i-1] -
+			    #4. * Memr[lbufp1+i-1] + Memr[lbufp2+i-1])
+		    #cd41y = 1./120. * (Memr[lbufm1+i-1] - 4. * 
+		    	    #Memr[lbuf+i-1] + 6. * Memr[lbufp1+i-1] - 4. *
+			    #Memr[lbufp2+i-1] + Memr[lbufp3+i-1])
+		    cd40y = (Memr[lbufm2+i-1] -
+		    	    4. * Memr[lbufm1+i-1] + 6. * Memr[lbuf+i-1] -
+			    4. * Memr[lbufp1+i-1] + Memr[lbufp2+i-1]) / 120.
+		    cd41y = (Memr[lbufm1+i-1] - 4. * 
+		    	    Memr[lbuf+i-1] + 6. * Memr[lbufp1+i-1] - 4. *
+			    Memr[lbufp2+i-1] + Memr[lbufp3+i-1]) / 120.0
+		#}
+
+		# interpolate in y
+		zfit[i,j] = sy * (Memr[lbufp1+i-1] + sy2m1 *
+			    (cd21y + sy2m4 * cd41y)) +
+			    ty * (Memr[lbuf+i-1] + ty2m1 *
+			    (cd20y + ty2m4 * cd40y))
+
+	    }
+
+	    #nyold = ny
+	}
+
+	# release work space
+	call sfree (sp)
+
+end
+
+
+# II_GRSPLINE3 -- Procedure to evaluate the bicubic spline interpolant
+# on a rectangular grid.  The program assumes that 1 <= x <= nxpix and
+# 1 <= y <= nypix. The routine assumes that x and y vectors are sorted
+# such that x[i] < x[i+1] and y[i] < y[i+1]. The interpolant is evaluated
+# by calculating the polynomial coefficients in x and y.
+
+procedure ii_grspline3 (coeff, first_point, len_coeff, x, y, zfit, nxpts,
+			nypts, len_zfit)
+
+real	coeff[ARB]		# 1D array of coefficients
+int	first_point		# offset of first data point
+int	len_coeff		# row length of coeff
+real	x[nxpts]		# array of x values
+real	y[nypts]		# array of y values
+real	zfit[len_zfit,ARB]	# array of interpolated values
+int	nxpts			# number of x values
+int	nypts			# number of y values
+int	len_zfit		# row length of zfit
+
+int	ny, nymin, nymax, nylines
+int	row_index, xindex
+int	i, j
+pointer	sp, nx, sx, tx, sx3, tx3, work, lbuf, lbufp1, lbufp2, lbufm1
+real	sy, ty, ty3, sy3
+
+errchk	smark, salloc, sfree
+
+begin
+	# find the y limits
+	nymin = int (y[1]) - 1
+	nymax = int (y[nypts]) + 2
+	nylines = nymax - nymin + 1
+
+	# allocate space for work array
+	call smark (sp)
+	call salloc (nx, nxpts, TY_INT)
+	call salloc (sx, nxpts, TY_REAL)
+	call salloc (sx3, nxpts, TY_REAL)
+	call salloc (tx, nxpts, TY_REAL)
+	call salloc (tx3, nxpts, TY_REAL)
+	call salloc (work, nylines * nxpts, TY_REAL)
+
+	# intialize
+	call achtri (x, Memi[nx], nxpts)
+	do j = 1, nxpts {
+	    Memr[sx+j-1] = x[j] - Memi[nx+j-1]
+	    Memr[tx+j-1] = 1. - Memr[sx+j-1]
+	}
+	call apowkr (Memr[sx], 3, Memr[sx3], nxpts)
+	call apowkr (Memr[tx], 3, Memr[tx3], nxpts)
+	do j = 1, nxpts {
+	    Memr[sx+j-1] = 1. + Memr[sx+j-1] * (3. + Memr[sx+j-1] *
+			   (3. - 3. * Memr[sx+j-1])) 
+	    Memr[tx+j-1] = 1. + Memr[tx+j-1] * (3. + Memr[tx+j-1] *
+			   (3. -  3. * Memr[tx+j-1])) 
+	}
+
+	# interpolate in x for each y
+	lbuf = work
+	do i = 1, nylines {
+
+	    # find appropriate row
+	    row_index = first_point + (i + nymin - 2) * len_coeff
+
+	    # x interpolation
+	    do j = 1, nxpts {
+
+		xindex = row_index + Memi[nx+j-1]
+		Memr[lbuf+j-1] = Memr[tx3+j-1] * coeff[xindex-1] +
+				 Memr[tx+j-1] * coeff[xindex] +
+				 Memr[sx+j-1] * coeff[xindex+1] +
+				 Memr[sx3+j-1] * coeff[xindex+2]
+	    }
+	    lbuf = lbuf + nxpts
+	}
+
+	# interpolate in y
+	do i = 1, nypts {
+
+	    ny = y[i]
+	    sy = y[i] - ny
+	    ty = 1. - sy
+	    sy3 = sy ** 3
+	    ty3 = ty ** 3
+	    sy = 1. + sy * (3. + sy * (3. - 3. * sy))
+	    ty = 1. + ty * (3. + ty * (3. - 3. * ty))
+
+	    lbuf = work + nxpts * (ny - nymin)
+	    lbufp1 = lbuf + nxpts
+	    lbufp2 = lbufp1 + nxpts
+	    lbufm1 = lbuf - nxpts
+
+	    do j = 1, nxpts
+		zfit[j,i] = ty3 * Memr[lbufm1+j-1] + ty * Memr[lbuf+j-1] +
+			    sy * Memr[lbufp1+j-1] + sy3 * Memr[lbufp2+j-1]
+	}
+
+	# release working space
+	call sfree (sp)
+end
+
+# II_GRSINC -- Procedure to evaluate the sinc interpolant on a rectangular
+# grid. The procedure assumes that 1 <= x <= nxpix and  that 1 <= y <= nypix.
+# The x and y vectors must be sorted in increasing value of x and y such that
+# x[i] < x[i+1] and y[i] < y[i+1]. The routine outputs a grid of nxpix by
+# nypix points using the coeff array where coeff[1+first_point] = datain[1,1]
+# The sinc truncation length is nsinc. The taper is a cosine bell function
+# which is approximated by a quartic polynomial which is valid for 0  <= x
+# <= PI / 2 (Abramowitz and Stegun 1972, Dover Publications, p 76). If the
+# point to be interpolated is less than mindx and mindy from a data point
+# no interpolation is done and the data point itself is returned.
+
+procedure ii_grsinc (coeff, first_point, len_coeff, len_array, x, y, zfit,
+		nxpts, nypts, len_zfit, nsinc, mindx, mindy)
+
+real	coeff[ARB]		# 1D coefficient array
+int	first_point		# offset of first data point
+int	len_coeff		# row length of coeff 
+int	len_array		# column length of coeff 
+real	x[nxpts]		# array of x values
+real	y[nypts]		# array of y values
+real	zfit[len_zfit,ARB]	# array of interpolatedvalues
+int	nxpts			# number of x values
+int	nypts			# number of y values
+int	len_zfit		# row length of zfit
+int	nsinc			# sinc interpolant truncation length
+real	mindx, mindy		# the precision of the interpolant.
+
+int	i, j, k, nconv, nymin, nymax, nylines
+int	ixy, index, minj, maxj, offj
+pointer	sp, taper, ac, ixn, work, pac, pwork, ppwork
+real	sconst, a2, a4, dxy, dxyn, dx2, axy, pxy, sumxy, fdxy
+
+begin
+	# Compute the limits of the convolution in y.
+	nconv = 2 * nsinc + 1
+	nymin = max (1, nint (y[1]) - nsinc)
+	#nymin = max (1, int (y[1]) - nsinc)
+	nymax = min (len_array, nint (y[nypts]) + nsinc)
+	#nymax = min (len_array, int (y[nypts]) + nsinc)
+	nylines = nymax - nymin + 1
+
+	# Allocate working space.
+	call smark (sp)
+	call salloc (taper, nconv, TY_REAL)
+	call salloc (ac, nconv * max (nxpts, nypts), TY_REAL)
+	call salloc (ixn, max (nxpts, nypts), TY_INT)
+	call salloc (work, nxpts * nylines, TY_REAL)
+
+	# Compute the parameters of the cosine bell taper.
+	sconst = (HALFPI / nsinc) ** 2
+	a2 = -0.49670
+	a4 = 0.03705
+	if (mod (nsinc, 2) == 0)
+	    fdxy = 1.0
+	else
+	    fdxy = -1.0
+	do i = -nsinc, nsinc {
+	    dx2 = sconst * i * i
+	    Memr[taper+i+nsinc] = fdxy * (1.0 + a2 * dx2 + a4 * dx2 * dx2) ** 2
+	    fdxy = -fdxy
+	}
+
+	# Compute the x interpolants for each shift in x.
+	pac = ac
+	do i = 1, nxpts {
+	    ixy = nint (x[i])
+	    Memi[ixn+i-1] = ixy
+	    dxy = x[i] - ixy
+	    #dxyn = -1 - nsinc - dxy
+	    dxyn = 1 + nsinc + dxy
+	    sumxy = 0.0
+	    do j = 1, nconv {
+		#axy = j + dxyn
+		axy = dxyn - j
+		if (axy == 0.0)
+		    pxy = 1.0
+		else if (dxy == 0.0)
+		    pxy = 0.0
+		else
+		    pxy = Memr[taper+j-1] / axy 
+		Memr[pac+j-1] = pxy
+		sumxy = sumxy + pxy
+	    }
+	    call adivkr (Memr[pac], sumxy, Memr[pac], nconv)
+	    pac = pac + nconv
+	}
+
+	# Do the convolutions in the x direction.
+	pwork = work
+	do k = nymin, nymax {
+	    index = first_point + (k - 1) * len_coeff
+	    pac = ac
+	    do i = 1, nxpts {
+		sumxy = 0.0
+		ixy = Memi[ixn+i-1]
+		minj = max (1, ixy - nsinc)
+		maxj = min (len_coeff, ixy + nsinc)
+		offj = -ixy + nsinc 
+		do j = ixy - nsinc, minj - 1
+		    sumxy = sumxy + Memr[pac+j+offj] * coeff[index+1] 
+		do j = minj, maxj
+		    sumxy = sumxy + Memr[pac+j+offj] * coeff[index+j] 
+		do j = maxj + 1, ixy + nsinc
+		    sumxy = sumxy + Memr[pac+j+offj] * coeff[index+len_coeff] 
+	        Memr[pwork+i-1] = sumxy
+		pac = pac + nconv
+	    }
+	    pwork = pwork + nxpts
+	}
+
+	# Compute the y interpolants for each shift in y.
+	pac = ac
+	do i = 1, nypts {
+	    ixy = nint (y[i])
+	    dxy = y[i] - ixy
+	    Memi[ixn+i-1] = ixy - nsinc - nymin + 1
+	    #dxyn = -1 - nsinc - dxy
+	    dxyn = 1 + nsinc + dxy
+	    sumxy = 0.0
+	    do j = 1, nconv {
+		#axy = j + dxyn
+		axy = dxyn - j
+		if (axy == 0.0)
+		    pxy = 1.0
+		else if (dxy == 0.0)
+		    pxy = 0.0
+		else
+		    pxy = Memr[taper+j-1] / axy 
+		Memr[pac+j-1] = pxy
+		sumxy = sumxy + pxy
+	    }
+	    call adivkr (Memr[pac], sumxy, Memr[pac], nconv)
+	    pac = pac + nconv
+	}
+
+	# Do the interpolation in y.
+	do k = 1, nxpts {
+	    pwork = work + k - 1
+	    pac = ac
+	    do i = 1, nypts {
+		ixy = min (nylines, max (1, Memi[ixn+i-1]))
+		ppwork = pwork + (ixy - 1) * nxpts
+		sumxy = 0.0
+		do j = 1, nconv {
+		    sumxy = sumxy + Memr[pac+j-1] * Memr[ppwork]
+		    ppwork = ppwork + nxpts
+		}
+		pac = pac + nconv
+		zfit[k,i] = sumxy 
+	    }
+	}
+
+	call sfree (sp)
+end
+
+
+# II_GRLSINC -- Procedure to evaluate the sinc interpolant on a rectangular
+# grid. The procedure assumes that 1 <= x <= nxpix and  that 1 <= y <= nypix.
+# The x and y vectors must be sorted in increasing value of x and y such that
+# x[i] < x[i+1] and y[i] < y[i+1]. The routine outputs a grid of nxpix by
+# nypix points using the coeff array where coeff[1+first_point] = datain[1,1]
+# The sinc truncation length is nsinc. The taper is a cosine bell function
+# which is approximated by a quartic polynomial which is valid for 0  <= x
+# <= PI / 2 (Abramowitz and Stegun 1972, Dover Publications, p 76). If the
+# point to be interpolated is less than mindx and mindy from a data point
+# no interpolation is done and the data point itself is returned.
+
+procedure ii_grlsinc (coeff, first_point, len_coeff, len_array, x, y, zfit,
+		nxpts, nypts, len_zfit, ltable, nconv, nxincr, nyincr,
+		mindx, mindy)
+
+real	coeff[ARB]				# 1D coefficient array
+int	first_point				# offset of first data point
+int	len_coeff				# row length of coeff 
+int	len_array				# column length of coeff 
+real	x[nxpts]				# array of x values
+real	y[nypts]				# array of y values
+real	zfit[len_zfit,ARB]			# array of interpolated values
+int	nxpts					# number of x values
+int	nypts					# number of y values
+int	len_zfit				# row length of zfit
+real	ltable[nconv,nconv,nxincr,nyincr]	# pre-computed sinc lut
+int	nconv					# sinc trunction full-width
+int	nxincr, nyincr				# resolution of look-up table
+real	mindx, mindy				# the precision of interpolant
+
+int	j
+pointer	sp, ytmp
+
+begin
+	# Allocate working space.
+	call smark (sp)
+	call salloc (ytmp, nxpts, TY_REAL)
+
+	do j = 1, nypts {
+	    call amovkr (y[j], Memr[ytmp], nxpts)
+	    call ii_bilsinc (coeff, first_point, len_coeff, len_array, x,
+	        Memr[ytmp], zfit[1,j], nxpts, ltable, nconv, nxincr, nyincr,
+		mindx, mindy)
+	}
+
+	call sfree (sp)
+end
+
+
+# II_GRDRIZ -- Procedure to evaluate the drizzle interpolant on a rectangular
+# grid. The procedure assumes that the x and y intervals are ordered from
+# smallest to largest
+
+procedure ii_grdriz (coeff, first_point, len_coeff, len_array, x, y, zfit,
+	nxpts, nypts, len_zfit, xfrac, yfrac, badval)
+
+real	coeff[ARB]		# 1D coefficient array
+int	first_point		# offset of first data point
+int	len_coeff		# row length of coeff 
+int	len_array		# column length of coeff 
+real	x[ARB]			# array of x values
+real	y[ARB]			# array of y values
+real	zfit[len_zfit,ARB]	# array of interpolatedvalues
+int	nxpts			# number of x values
+int	nypts			# number of y values
+int	len_zfit		# row length of zfit
+real	xfrac, yfrac		# the x and y pixel fractions
+real	badval			# bad value
+
+int	i, j, jj, nylmin, nylmax, nylines
+int	cindex, neara, nearb
+pointer	sp, work, xindex
+real	ymin, ymax, dy, accum, waccum, hyfrac
+
+begin
+	ymin = min (y[1], y[2])
+	ymax = max (y[2*nypts-1], y[2*nypts])
+	nylmin = int (ymin + 0.5) 
+	nylmax = int (ymax + 0.5)
+	nylines = nylmax - nylmin + 1
+
+	call smark (sp)
+	call salloc (work, nxpts * nylines, TY_REAL)
+
+	# For each in range y integrate in x.
+	cindex = 1 + first_point + (nylmin - 1) * len_coeff
+	xindex = work
+	do j = nylmin, nylmax {
+	    if (xfrac >= 1.0)
+	        call ii_driz1 (x, Memr[xindex], nxpts, coeff[cindex], badval)
+	    else
+	        call ii_driz (x, Memr[xindex], nxpts, coeff[cindex], xfrac,
+		    badval)
+	    xindex = xindex + nxpts
+	    cindex = cindex + len_coeff
+	}
+
+	# For each range in x integrate in y. This may need to be vectorized?
+	hyfrac = yfrac / 2.0
+	do i = 1, nxpts {
+
+	    xindex = work + i - 1
+
+	    do j = 1, nypts {
+
+		ymin = min (y[2*j-1], y[2*j])
+		ymax = max (y[2*j-1], y[2*j])
+		neara = ymin + 0.5
+		nearb = ymax + 0.5
+
+		accum = 0.0
+		waccum = 0.0
+		if (neara == nearb) {
+
+		    dy = min (ymax, nearb + hyfrac) - max (ymin,
+		       neara - hyfrac)
+		    if (dy > 0.0) {
+			accum = accum + dy * Memr[xindex+(neara-nylmin)*nxpts]
+			waccum = waccum + dy
+		    }
+
+		} else {
+
+		    # First segment.
+		    dy = neara + hyfrac - max (ymin, neara - hyfrac)
+		    if (dy > 0.0) {
+			accum = accum + dy * Memr[xindex+(neara-nylmin)*nxpts]
+			waccum = waccum + dy
+		    }
+
+		    # Interior segments.
+		    do jj = neara + 1, nearb - 1 {
+			accum = accum + yfrac * Memr[xindex+(jj-nylmin)*nxpts]
+			waccum = waccum + yfrac
+		    }
+
+		    # Last segment.
+		    dy = min (ymax, nearb + hyfrac) - (nearb - hyfrac)
+		    if (dy > 0.0) {
+			accum = accum + dy * Memr[xindex+(nearb-nylmin)*nxpts]
+			waccum = waccum + dy
+		    }
+		}
+
+		if (waccum <= 0.0)
+		    zfit[i,j] = 0.0
+		else
+		    zfit[i,j] = accum / waccum
+	    }
+	}
+
+	call sfree (sp)
+end
diff --git a/math/iminterp/ii_pc1deval.x b/math/iminterp/ii_pc1deval.x
new file mode 100644
index 00000000..7eca5304
--- /dev/null
+++ b/math/iminterp/ii_pc1deval.x
@@ -0,0 +1,291 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include	<math.h>
+include "im1interpdef.h"
+
+# IA_PCPOLY3 -- Calculate the coefficients of a 3rd order polynomial.
+
+procedure ia_pcpoly3 (x, datain, npts, pcoeff)
+
+real	x		# x value
+real	datain[ARB]	# array of input data
+int	npts		# number of data points
+real	pcoeff[ARB]	# array of polynomial coefficients
+
+int 	i, k, nearx, nterms
+real	temp[POLY3_ORDER]
+
+begin
+	nearx = x
+
+	# Check for edge problems.
+	k = 0
+	for(i = nearx - 1; i <= nearx + 2; i = i + 1) {
+	    k = k + 1
+
+	    # project data points into temporary array
+	    if (i < 1)
+		temp[k] = 2. * datain[1] - datain[2-i]
+	    else if (i > npts)
+		temp[k] = 2. * datain[npts] - datain[2*npts-i]
+	    else
+		temp[k] = datain[i]
+	}
+
+	nterms = 4
+
+	# Generate the difference table for Newton's form.
+	do k = 1, nterms - 1
+	    do i = 1, nterms - k
+		temp[i] = (temp[i+1] - temp[i]) / k
+	
+	# Shift to generate polynomial coefficients.
+	do k = nterms, 2, -1
+	    do i = 2, k
+		temp[i] = temp[i] + temp[i-1] * (k- i - nterms/2)
+	do i = 1, nterms
+	    pcoeff[i] = temp[nterms+1-i]
+end
+
+
+# IA_PCPOLY5 -- Calculate the coefficients of a fifth order polynomial.
+
+procedure ia_pcpoly5 (x, datain, npts, pcoeff)
+
+real	x		# x value
+real	datain[ARB]	# array of input data
+int	npts		# number of data points
+real	pcoeff[ARB]	# array of polynomial coefficients
+
+int 	i, k, nearx, nterms
+real	temp[POLY5_ORDER]
+
+begin
+	nearx = x
+
+	# Check for edge effects.
+	k = 0
+	for (i = nearx - 2; i <= nearx + 3; i = i + 1) {
+	    k = k + 1
+	    # project data points into temporary array
+	    if (i < 1)
+		temp[k] = 2. * datain[1] - datain[2-i]
+	    else if (i > npts)
+		temp[k] = 2. * datain[npts] - datain[2*npts-i]
+	    else
+		temp[k] = datain[i]
+	}
+
+	nterms = 6
+
+	# Generate difference table for Newton's form.
+	do k = 1, nterms - 1
+	    do i = 1, nterms - k
+		temp[i] = (temp[i+1] - temp[i]) / k
+	
+	# Shift to generate polynomial coefficients.
+	do k = nterms, 2, -1
+	    do i = 2, k
+		temp[i] = temp[i] + temp[i-1] * (k - i - nterms/2)
+	do i = 1, nterms
+	    pcoeff[i] = temp[nterms+1-i]
+end
+
+
+# IA_PCSPLINE3 -- Calculate the derivatives of a cubic spline.
+
+procedure ia_pcspline3 (x, datain, npts, pcoeff)
+
+real	x		# x value
+real	datain[ARB]	# data array
+int	npts		# number of data points
+real	pcoeff[ARB]	# array of polynomial coefficients
+
+int 	i, k, nearx, px
+real	temp[SPLPTS+3], bcoeff[SPLPTS+3]
+
+begin
+	nearx = x
+	k = 0
+
+	# Check for edge effects.
+	for (i = nearx - SPLPTS/2 + 1; i <= nearx + SPLPTS/2; i = i + 1) {
+	    if(i < 1 || i > npts)
+		;
+	    else {
+		k = k + 1
+		if (k == 1)
+		    px = nearx - i + 1
+		bcoeff[k+1] = datain[i]
+	    }
+	}
+
+	bcoeff[1] = 0.
+	bcoeff[k+2] = 0.
+
+	# Use special routine for cardinal splines.
+	call ii_spline (bcoeff, temp, k)
+
+	px = px + 1
+	bcoeff[k+3] = 0.
+
+	# Calculate polynomial coefficients.
+	pcoeff[1] = bcoeff[px-1] + 4. * bcoeff[px] + bcoeff[px+1]
+	pcoeff[2] = 3. * (bcoeff[px+1] - bcoeff[px-1])
+	pcoeff[3] = 3. * (bcoeff[px-1] - 2. * bcoeff[px] + bcoeff[px+1])
+	pcoeff[4] = -bcoeff[px-1] + 3. * bcoeff[px] - 3. * bcoeff[px+1] +
+				    bcoeff[px+2]
+end
+
+
+# II_SINCDER -- Evaluate derivatives of the sinc interpolator. If the
+# function value only is needed call ii_sinc. This routine computes only
+# the first two derivatives. The second  derivative is computed even if only
+# the first derivative is needed. The sinc truncation length is nsinc.
+# The taper is a cosbell function approximated by a quartic polynomial.
+# The data value is returned if x is closer to x[i] than mindx.
+
+procedure ii_sincder (x, der, nder, data, npix, nsinc, mindx)
+
+real	x		# x value
+real	der[ARB]	# derivatives to return
+int	nder		# number of derivatives
+real	data[npix]	# data to be interpolated
+int	npix		# number of pixels
+int	nsinc		# sinc truncation length
+real	mindx		# interpolation minimum
+
+int	i, j, xc
+real	dx, w, a, d, z, sconst, a2, a4, dx2, taper
+real	w1, w2, w3, u1, u2, u3, v1, v2, v3
+
+begin
+	# Return if no derivatives.
+	if (nder == 0)
+	    return
+
+	# Set derivatives intially to zero.
+	do i = 1, nder
+	    der[i] = 0.
+
+	# Return if outside data range.
+	xc = nint (x)
+	if (xc < 1 || xc > npix)
+	    return
+
+	# Call ii_sinc if only the function value is needed.
+	if (nder == 1) {
+	    call ii_sinc (x, der, 1, data, npix, nsinc, mindx)
+	    return
+	}
+
+        # Compute the constants for the cosine bell taper approximation.
+        sconst = (HALFPI / nsinc) ** 2
+        a2 = -0.49670
+        a4 = 0.03705
+
+	# Compute the derivatives by doing the required convolutions.
+	dx = x - xc
+	if (abs (dx) < mindx) {
+
+	    w = 1.
+	    d = data[xc]
+	    w1 = 1.; u1 = d * w1; v1 = w1
+	    w2 = 0.; u2 = 0.; v2 = 0.
+	    w3 = -1./3.; u3 = d * w3; v3 = w3
+
+	    # Derivative at the center of a pixel.
+	    do i = 1, nsinc {
+
+		w = -w
+		dx2 = sconst * i * i
+		taper = (1.0 + a2 * dx2 + a4 * dx2 * dx2) ** 2
+
+		j = xc - i
+		z = 1. / i
+		if (j >= 1)
+		    d = data[j]
+		else
+		    d = data[1]
+		w2 = w * z * taper
+		u2 = u2 + d * w2
+		v2 = v2 + w2
+		w3 = -2 * w2 * z
+		u3 = u3 + d * w3
+		v3 = v3 + w3
+
+		j = xc + i
+		if (j <= npix)
+		    d = data[j]
+		else
+		    d = data[npix]
+		w2 = -w * z * taper
+		u2 = u2 + d * w2
+		v2 = v2 + w2
+		w3 = 2 * w2 * z
+		u3 = u3 + d * w3
+		v3 = v3 + w3
+	    }
+
+	} else {
+
+	    w = 1.0
+	    a = 1 / tan (PI * dx)
+
+	    d = data[xc]
+	    z = 1. / dx
+	    w1 = w * z; u1 = d * w1; v1 = w1
+	    w2 = w1 * (a - z); u2 = d * w2; v2 = w2
+	    w3 = -w1 * (1 + 2 * z * (a - z)); u3 = d * w3; v3 = w3
+
+	    # Derivative off center of a pixel.
+	    do i = 1, nsinc {
+
+		w = -w
+		dx2 = sconst * i * i
+		taper = (1.0 + a2 * dx2 + a4 * dx2 * dx2) ** 2
+
+		j = xc - i
+		if (j >= 1)
+		    d = data[j]
+		else
+		    d = data[1]
+		z = 1. / (dx + i)
+		w1 = w * z * taper
+		u1 = u1 + d * w1
+		v1 = v1 + w1
+		w2 = w1 * (a - z)
+		u2 = u2 + d * w2
+		v2 = v2 + w2
+		w3 = -w1 * (1 + 2*z*(a-z))
+		u3 = u3 + d * w3
+		v3 = v3 + w3
+
+		j = xc + i
+		if (j <= npix)
+		    d = data[j]
+		else
+		    d = data[npix]
+		z = 1. / (dx - i)
+		w1 = w * z * taper
+		u1 = u1 + d * w1
+		v1 = v1 + w1
+		w2 = w1 * (a - z)
+		u2 = u2 + d * w2
+		v2 = v2 + w2
+		w3 = -w1 * (1 + 2*z*(a-z))
+		u3 = u3 + d * w3
+		v3 = v3 + w3
+	    }
+	}
+
+	# Compute the derivatives.
+	w1 = v1
+	w2 = v1 * w1
+	w3 = v1 * w2
+	der[1] = u1 / w1
+	if (nder > 1)
+	    der[2] = (u2 * v1 - u1 * v2) / w2
+	if (nder > 2)
+	    der[3] = u3 / w1 - 2*u2*v2 / w2 + 2*u1*v2*v2 / w3 - u1*v3 / w2
+end
diff --git a/math/iminterp/ii_pc2deval.x b/math/iminterp/ii_pc2deval.x
new file mode 100644
index 00000000..c26d2095
--- /dev/null
+++ b/math/iminterp/ii_pc2deval.x
@@ -0,0 +1,444 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math.h>
+
+# II_PCPOLY3 -- Procedure to evaluate the polynomial coefficients
+# of third order in x and y using Everetts formuala.
+
+procedure ii_pcpoly3 (coeff, index, len_coeff, pcoeff, len_pcoeff)
+
+real	coeff[ARB]		# 1D array of interpolant coeffcients
+int	index			# pointer into coeff array
+int	len_coeff		# row length of coeffcients
+real	pcoeff[len_pcoeff,ARB]	# polynomial coefficients
+int	len_pcoeff		# row length of pcoeff
+
+int	tptr
+int	i, j
+real	cd20, cd21, temp[4]
+
+begin
+	# determine polynomial coefficients in x
+	tptr = index
+	do i = 1, 4 {
+
+	    # calculate the central differences
+	    cd20 = 1./6. * (coeff[tptr+1] - 2. * coeff[tptr] + coeff[tptr-1])
+	    cd21 = 1./6. * (coeff[tptr+2] - 2. * coeff[tptr+1] + coeff[tptr])
+
+	    # calculate the polynomial coefficients in x at each y
+	    pcoeff[1,i] = coeff[tptr]
+	    pcoeff[2,i] = coeff[tptr+1] - coeff[tptr] - 2. * cd20 - cd21
+	    pcoeff[3,i] = 3. * cd20
+	    pcoeff[4,i] = cd21 - cd20
+
+	    tptr = tptr + len_coeff
+	}
+
+	# calculate polynomial coefficients in y
+	do j = 1, 4 {
+
+	    # calculate the central differences
+	    cd20 = 1./6. * (pcoeff[j,3] - 2. * pcoeff[j,2] + pcoeff[j,1])
+	    cd21 = 1./6. * (pcoeff[j,4] - 2. * pcoeff[j,3] + pcoeff[j,2])
+
+	    # calculate the final coefficients
+	    temp[1] = pcoeff[j,2] 
+	    temp[2] = pcoeff[j,3] - pcoeff[j,2] - 2. * cd20 - cd21
+	    temp[3] = 3. * cd20
+	    temp[4] = cd21 - cd20
+
+	    do i = 1, 4
+		pcoeff[j,i] = temp[i]
+	}
+end
+
+
+# II_PCPOLY5 -- Procedure to evaluate the polynomial coefficients
+# of fifth order in x and y using Everetts formuala.
+
+procedure ii_pcpoly5 (coeff, index, len_coeff, pcoeff, len_pcoeff)
+
+real	coeff[ARB]		# 1D array of interpolant coeffcients
+int	index			# pointer into coeff array
+int	len_coeff		# row length of coeffcients
+real	pcoeff[len_pcoeff,ARB]	# polynomial coefficients
+int	len_pcoeff		# row length of pcoeff array
+
+int	tptr
+int	i, j
+real	cd20, cd21, cd40, cd41, temp[6]
+
+begin
+	# determine polynomial coefficients in x
+	tptr = index
+	do i = 1, 6 {
+
+	    # calculate the central differences
+	    cd20 = 1./6. * (coeff[tptr+1] - 2. * coeff[tptr] + coeff[tptr-1])
+	    cd21 = 1./6. * (coeff[tptr+2] - 2. * coeff[tptr+1] + coeff[tptr])
+	    cd40 = 1./120. * (coeff[tptr-2] - 4. * coeff[tptr-1] +
+		   6. * coeff[tptr] - 4. * coeff[tptr+1] +
+		   coeff[tptr+2])
+	    cd41 = 1./120. * (coeff[tptr-1] - 4. * coeff[tptr] +
+		   6. * coeff[tptr+1] - 4. * coeff[tptr+2] +
+		   coeff[tptr+3])
+
+	    # calculate coefficients in x for each y
+	    pcoeff[1,i] = coeff[tptr]
+	    pcoeff[2,i] = coeff[tptr+1] - coeff[tptr] - 2. * cd20 - cd21 +
+			  6. * cd40 + 4. * cd41 
+	    pcoeff[3,i] = 3. * cd20 - 5. * cd40
+	    pcoeff[4,i] = cd21 - cd20 - 5. * (cd40 + cd41)
+	    pcoeff[5,i] = 5. * cd40
+	    pcoeff[6,i] = cd41 - cd40
+
+	    tptr = tptr + len_coeff
+	}
+
+	# calculate polynomial coefficients in y
+	do j = 1, 6 {
+
+	    # calculate the central differences
+	    cd20 = 1./6. * (pcoeff[j,4] - 2. * pcoeff[j,3] + pcoeff[j,2])
+	    cd21 = 1./6. * (pcoeff[j,5] - 2. * pcoeff[j,4] + pcoeff[j,3])
+	    cd40 = 1./120. * (pcoeff[j,1] - 4. * pcoeff[j,2] +
+	    	   6. * pcoeff[j,3] - 4. * pcoeff[j,4] + pcoeff[j,5])
+	    cd41 = 1./120. * (pcoeff[j,2] - 4. * pcoeff[j,3] +
+		   6. * pcoeff[j,4] - 4. * pcoeff[j,5] + pcoeff[j,6])
+
+	    # calculate the final coefficients
+	    temp[1] = pcoeff[j,3]
+	    temp[2] = pcoeff[j,4] - pcoeff[j,3] - 2. * cd20 - cd21 +
+		      6. * cd40 + 4. * cd41
+	    temp[3] = 3. * cd20 - 5. * cd40
+	    temp[4] = cd21 - cd20 - 5. * (cd40 + cd41)
+	    temp[5] = 5. * cd40
+	    temp[6] = cd41 - cd40
+
+	    do i = 1, 6
+		pcoeff[j,i] = temp[i]
+
+	}
+
+end
+
+
+# II_PCSPLINE3 -- Procedure to evaluate the polynomial coefficients
+# of bicubic spline.
+
+procedure ii_pcspline3 (coeff, index, len_coeff, pcoeff, len_pcoeff)
+
+real	coeff[ARB]		# 1D array of interpolant coeffcients
+int	index			# pointer into coeff array
+int	len_coeff		# row length of coeffcients
+real	pcoeff[len_pcoeff,ARB]	# polynomial coefficients
+int	len_pcoeff		# row length of pcoeff
+
+int	tptr
+int	i, j
+real	temp[4]
+
+begin
+	# determine polynomial coefficients in x
+	tptr = index
+	do i = 1, 4 {
+
+	    pcoeff[1,i] = coeff[tptr+1] + 4. * coeff[tptr] + coeff[tptr-1]
+	    pcoeff[2,i] = 3. * (coeff[tptr+1] - coeff[tptr-1])
+	    pcoeff[3,i] = 3. * (coeff[tptr-1] - 2. * coeff[tptr] +
+	    		  coeff[tptr+1])
+	    pcoeff[4,i] = -coeff[tptr-1] + 3. * coeff[tptr] -
+	    		  3. * coeff[tptr+1] + coeff[tptr+2]
+			    
+	    tptr = tptr + len_coeff
+	}
+
+	# calculate polynomial coefficients in y
+	do j = 1, 4 {
+
+	    temp[1] = pcoeff[j,3] + 4. * pcoeff[j,2] + pcoeff[j,1]
+	    temp[2] = 3. * (pcoeff[j,3] - pcoeff[j,1]) 
+	    temp[3] = 3. * (pcoeff[j,1] - 2. * pcoeff[j,2] + pcoeff[j,3])
+	    temp[4] = -pcoeff[j,1] + 3. * pcoeff[j,2] - 3. * pcoeff[j,3] +
+	    	      pcoeff[j,4]
+
+	    do i = 1, 4
+		pcoeff[j,i] = temp[i]
+	}
+end
+
+# II_BISINCDER -- Evaluate the derivatives of the 2D sinc interpolator. If the
+# function value only is needed call ii_bisinc. This routine computes only
+# the first 2 derivatives in x and y. The second derivative is computed
+# even if only the first derivative is needed. The sinc truncation length
+# is nsinc. The taper is a cosbell approximated by a quartic polynomial.
+# The data value if returned if x is closer to x[i] than mindx and  y is
+# closer to y[i]  than mindy.
+
+procedure ii_bisincder (x, y, der, nxder, nyder, len_der, coeff, first_point,
+	nxpix, nypix, nsinc, mindx, mindy)
+
+real	x, y			# the input x and y values
+real	der[len_der,ARB]	# the output derivatives array
+int	nxder, nyder		# the number of derivatives to compute
+int	len_der			# the width of the derivatives array
+real	coeff[ARB]		# the coefficient array
+int	first_point		# offset of first data point into the array
+int	nxpix, nypix		# size of the coefficient array
+int	nsinc			# the sinc truncation length
+real	mindx, mindy		# the precision of the sinc interpolant
+
+double	sumx, normx[3], normy[3], norm[3,3], sum[3,3]
+int	i, j, k, jj, kk, xc, yc, nconv, index
+int	minj, maxj, offj, mink, maxk, offk, last_point
+pointer	sp, ac, ar
+real	sconst, a2, a4, dx, dy, dxn, dyn, dx2, taper, sdx, ax, ay, ctanx, ctany
+real	zx, zy
+real	px[3], py[3]
+
+begin
+	# Return if no derivatives ar to be computed.
+	if (nxder == 0 || nyder == 0)
+	    return
+
+	# Initialize the derivatives to zero. 
+	do jj = 1, nyder {
+	    do kk = 1, nxder 
+		der[kk,jj] = 0.0
+	}
+
+	# Return if the data is outside range.
+	xc = nint (x)
+	yc = nint (y)
+	if (xc < 1 || xc > nxpix || yc < 1 || yc > nypix)
+	    return
+
+	# Call ii_bsinc if only the function value is requested.
+	if (nxder == 1 && nyder == 1) {
+	    call ii_bisinc (coeff, first_point, nxpix, nypix, x, y, der[1,1],
+		1, nsinc, mindx, mindy)
+	    return
+	}
+
+	# Compute the constants for the cosine bell taper approximation.
+	sconst = (HALFPI / nsinc) ** 2
+	a2 = -0.49670
+	a4 = 0.03705
+
+	# Allocate some working space.
+	nconv = 2 * nsinc + 1
+	call smark (sp)
+	call salloc (ac, 3 * nconv, TY_REAL)
+	call salloc (ar, 3 * nconv, TY_REAL)
+	call aclrr (Memr[ac], 3 * nconv)
+	call aclrr (Memr[ar], 3 * nconv)
+
+	# Initialize.
+	dx = x - xc
+	dy = y - yc
+	if (dx == 0.0)
+	    ctanx = 0.0
+	else
+	    ctanx = 1.0 / tan (PI * dx)
+	if (dy == 0.0)
+	    ctany = 0.0
+	else
+	    ctany = 1.0 / tan (PI * dy)
+	index = - 1 - nsinc
+	dxn = -1 - nsinc - dx
+	dyn = -1 - nsinc - dy
+	if (mod (nsinc, 2) == 0)
+	    sdx = 1.0
+	else
+	    sdx = -1.0
+	do jj = 1, 3 {
+	    normy[jj] = 0.0d0
+	    normx[jj] = 0.0d0
+	}
+
+	do i = 1, nconv {
+	    dx2 = sconst * (i + index) ** 2 
+	    taper = sdx * (1.0 + a2 * dx2 + a4 * dx2 * dx2) ** 2
+	    #ax = dxn + i
+	    #ay = dyn + i
+	    ax = -dxn - i
+	    ay = -dyn - i
+	    if (ax == 0.0) {
+		px[1] = 1.0
+		px[2] = 0.0
+		px[3] = - 1.0 / 3.0
+	    } else if (dx == 0.0) {
+		px[1] = 0.0
+		px[2] = 0.0
+		px[3] = 0.0
+	    } else {
+	        zx = 1.0 / ax
+		px[1] = taper * zx 
+		px[2] = px[1] * (ctanx - zx)
+		px[3] = -px[1] * (1.0 + 2.0 * zx * (ctanx - zx)) 
+	    }
+	    if (ay == 0.0) {
+		py[1] = 1.0
+		py[2] = 0.0
+		py[3] = - 1.0 / 3.0
+	    } else if (dy == 0.0) {
+		py[1] = 0.0
+		py[2] = 0.0
+		py[3] = 0.0
+	    } else {
+		zy = 1.0 / ay
+		py[1] = taper * zy
+		py[2] = py[1] * (ctany - zy)
+		py[3] = -py[1] * (1.0 + 2.0 * zy * (ctany - zy)) 
+	    }
+
+	    Memr[ac+i-1] = px[1]
+	    Memr[ac+nconv+i-1] = px[2]
+	    Memr[ac+2*nconv+i-1] = px[3]
+	    Memr[ar+i-1] = py[1]
+	    Memr[ar+nconv+i-1] = py[2]
+	    Memr[ar+2*nconv+i-1] = py[3]
+
+	    do jj = 1, 3 {
+		normx[jj] = normx[jj] + px[jj]
+		normy[jj] = normy[jj] + py[jj]
+	    }
+
+	    sdx = -sdx
+	}
+
+	# Normalize.
+	do jj = 1, 3 {
+	    do kk = 1, 3
+		norm[kk,jj] = normx[kk] * normy[jj]
+	}
+
+
+	# Do the convolution.
+        minj = max (1, yc - nsinc)
+        maxj = min (nypix, yc + nsinc)
+        mink = max (1, xc - nsinc)
+        maxk = min (nxpix, xc + nsinc)
+	do jj = 1, nyder {
+            offj = ar + (jj - 1) * nconv - yc + nsinc
+	    do kk = 1, nxder {
+                offk = ac + (kk - 1) * nconv - xc + nsinc
+		sum[kk,jj] = 0.0d0
+
+		# Do the convolutions.
+                do j = yc - nsinc, minj - 1 {
+                    sumx = 0.0d0
+                    do k = xc - nsinc, mink - 1
+                        sumx = sumx + Memr[k+offk] * coeff[first_point+1]
+                    do k = mink, maxk
+                        sumx = sumx + Memr[k+offk] * coeff[first_point+k]
+                    do k = maxk + 1, xc + nsinc
+                        sumx = sumx + Memr[k+offk] * coeff[first_point+nxpix]
+
+                    sum[kk,jj] = sum[kk,jj] + Memr[j+offj] * sumx
+                }
+
+
+                do j = minj, maxj {
+                    index = first_point + (j - 1) * nxpix
+                    sumx = 0.0d0
+                    do k = xc - nsinc, mink - 1
+                        sumx = sumx + Memr[k+offk] * coeff[index+1]
+                    do k = mink, maxk
+                        sumx = sumx + Memr[k+offk] * coeff[index+k]
+                    do k = maxk + 1, xc + nsinc
+                        sumx = sumx + Memr[k+offk] * coeff[index+nxpix]
+
+                    sum[kk,jj] = sum[kk,jj] + Memr[j+offj] * sumx
+                }
+
+                do j = maxj + 1, yc + nsinc {
+                    last_point = first_point + (nypix - 1) * nxpix
+                    sumx = 0.0d0
+                    do k = xc - nsinc, mink - 1
+                        sumx = sumx + Memr[k+offk] * coeff[last_point+1]
+                    do k = mink, maxk
+                        sumx = sumx + Memr[k+offk] * coeff[last_point+k]
+                    do k = maxk + 1, xc + nsinc
+                        sumx = sumx + Memr[k+offk] * coeff[last_point+nxpix]
+
+                    sum[kk,jj] = sum[kk,jj] + Memr[j+offj] * sumx
+                }
+
+	    }
+	}
+
+	# Build the derivatives.
+	der[1,1] = sum[1,1] / norm[1,1] 
+	if (nxder > 1)
+	    der[2,1] = sum[2,1] / norm[1,1] - (sum[1,1] * norm[2,1]) /
+	               norm[1,1] ** 2 
+	if (nxder > 2)
+	    der[3,1] = sum[3,1] / norm[1,1] - (norm[3,1] * sum[1,1] +
+	               2.0d0 * sum[2,1] * norm[2,1]) / norm[1,1] ** 2 +
+		       2.0d0 * sum[1,1] * norm[2,1] * norm[2,1] / norm[1,1] ** 3
+	if (nyder > 1) {
+	    der[1,2] = sum[1,2] / norm[1,1] - (sum[1,1] * norm[1,2]) /
+	               norm[1,1] ** 2 
+	    if (nxder > 1)
+		der[2,2] = sum[2,2] / norm[1,1] - (sum[2,1] * norm[1,2] +
+		           sum[1,2] * norm[2,1] + norm[2,2] * sum[1,1]) /
+			   norm[1,1] ** 2 + (2.0d0 * sum[1,1] * norm[2,1] *
+			   norm[1,2]) / norm[1,1] ** 3
+	    if (nxder > 2)
+		der[3,2] = sum[3,2] / norm[1,1] - (sum[3,1] * norm[1,2] +
+		           2.0 * norm[2,2] * sum[2,1] + 2.0 * sum[2,2] *
+			   norm[2,1] + norm[3,1] * sum[1,2] + norm[3,2] *
+			   sum[1,1]) / norm[1,1] ** 2 + (4.0 * norm[2,1] *
+			   sum[2,1] * norm[1,2] + 2.0 * norm[2,1] * sum[1,2] *
+			   norm[2,1] + 4.0 * norm[2,1] * norm[2,2] * sum[1,1] +
+			   2.0 * norm[3,1] * norm[1,2] * sum[1,1]) /
+			   norm[1,1] ** 3 - 6.0 * norm[2,1] * norm[2,1] *
+			   norm[1,2] * sum[1,1] / norm[1,1] ** 4
+
+	}
+	if (nyder > 2) {
+	    der[1,3] = sum[1,3] / norm[1,1] - (norm[1,3] * sum[1,1] +
+	               2.0d0 * sum[1,2] * norm[1,2]) / norm[1,1] ** 2 +
+		       2.0d0 * sum[1,1] * norm[1,2] * norm[1,2] / norm[1,1] ** 3
+	    if (nxder > 1)
+		der[2,3] = sum[2,3] / norm[1,1] - (sum[1,3] * norm[2,1] +
+		           2.0 * norm[2,2] * sum[1,2] + 2.0 * sum[2,2] *
+			   norm[1,2] + norm[1,3] * sum[2,1] + norm[2,3] *
+			   sum[1,1]) / norm[1,1] ** 2 + (4.0 * norm[1,2] *
+			   sum[1,2] * norm[2,1] + 2.0 * norm[1,2] * sum[2,1] *
+			   norm[1,2] + 4.0 * norm[1,2] * norm[2,2] * sum[1,1] +
+			   2.0 * norm[1,3] * norm[2,1] * sum[1,1]) /
+			   norm[1,1] ** 3 - 6.0 * norm[1,2] * norm[1,2] *
+			   norm[2,1] * sum[1,1] / norm[1,1] ** 4
+	    if (nxder > 2)
+		der[3,3] = sum[3,3] / norm[1,1] - (2.0 * sum[2,3] * norm[2,1] +
+		           norm[3,1] * sum[1,3] + 2.0 * norm[3,2] * sum[1,2] +
+			   4.0 * sum[2,2] * norm[2,2] + 2.0 * sum[3,2] *
+			   norm[1,2] + 2.0 * norm[2,3] * sum[2,1] + sum[3,1] *
+			   norm[1,3] + norm[3,3] * sum[1,1]) / norm[1,1] ** 2 +
+			   (2.0 * norm[2,1] * norm[2,1] * sum[1,3] + 8.0 *
+			   norm[2,1] * sum[1,2] * norm[2,2] + 8.0 * norm[2,1] *
+			   norm[1,2] * sum[2,2] + 4.0 * norm[2,1] * sum[2,1] *
+			   norm[1,3] + 4.0 * norm[2,1] * norm[2,3] * sum[1,1] +
+			   4.0 * norm[1,2] * sum[1,2] * norm[3,1] + 8.0 *
+			   norm[2,2] * sum[2,1] * norm[1,2] + 2.0 * norm[1,2] *
+			   norm[1,2] * sum[3,1] + 4.0 * norm[2,2] * norm[2,2] *
+			   sum[1,1] + 4.0 * norm[1,2] * norm[3,2] * sum[1,1] +
+			   2.0 * norm[1,3] * norm[3,1] * sum[1,1]) /
+			   norm[1,1] ** 3 - (12.0 * norm[2,1] * norm[2,1] *
+			   norm[1,2] * sum[1,2] + 12.0 * norm[2,1] * norm[1,2] *
+			   norm[1,2] * sum[2,1] + 24.0 * norm[2,1] * norm[1,2] *
+			   norm[2,2] * sum[1,1] + 6.0 * norm[2,1] * norm[2,1] *
+			   norm[1,3] * sum[1,1] + 6.0 * norm[1,2] * norm[1,2] *
+			   norm[3,1] * sum[1,1]) / norm[1,1] ** 4 + ( 24.0 *
+			   norm[1,2] * norm[1,2] * norm[2,1] * norm[2,1] *
+			   sum[1,1]) / norm[1,1] ** 5
+	}
+
+
+
+
+	call sfree (sp)
+end
diff --git a/math/iminterp/ii_polterp.x b/math/iminterp/ii_polterp.x
new file mode 100644
index 00000000..24216751
--- /dev/null
+++ b/math/iminterp/ii_polterp.x
@@ -0,0 +1,39 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im1interpdef.h"
+
+# II_POLTERP -- polynomial interpolator with x and y arrays given.
+# This algorithm is based on the Newton form as described in
+# C. de Boor's book, "A Practical Guide to Splines", 1978.
+# There is no error checking - this is meant to be used only by calls
+# from more complete routines that take care of such things.
+
+# Maximum number of terms is MAX_NDERIVS.
+
+real procedure ii_polterp (x, y, n, x0)
+
+real	x[ARB],y[ARB]	# x and y array
+real	x0		# desired x
+int	n		# number of points in x and y = number of
+			# terms in polynomial = order + 1
+
+int	k,i
+real	d[MAX_NDERIVS]
+
+begin
+
+	# Fill in entries for divided difference table.
+	do i = 1, n
+	    d[i] = y[i]
+
+	# Generate divided differences
+	do k = 1, n - 1
+	    do i = 1, n - k
+		d[i] = (d[i+1] - d[i])/(x[i+k] - x[i])
+
+	# Shift divided difference table to center on x0
+	do i = 2, n
+	    d[i] = d[i] + d[i-1] * (x0 - x[i])
+
+	return (d[n])
+end
diff --git a/math/iminterp/ii_sinctable.x b/math/iminterp/ii_sinctable.x
new file mode 100644
index 00000000..e062e9d0
--- /dev/null
+++ b/math/iminterp/ii_sinctable.x
@@ -0,0 +1,123 @@
+include <math.h>
+
+# II_SINCTABLE -- Compute the 1D sinc function look-up tables given the
+# width of the sinc function and the number of increments.
+
+procedure ii_sinctable (table, nconv, nincr, xshift)
+
+real	table[nconv,nincr]		#O the computed look-up table
+int	nconv				#I the sinc truncation length
+int	nincr				#I the number of look-up tables
+real	xshift				#I the shift of the look up table
+
+int	i, j, nsinc
+real	sconst, a2, a4, fsign, xsign, sum, dx, dx2, x, f
+
+begin
+	# Set up some constants.
+	nsinc = (nconv - 1) / 2
+	sconst = (HALFPI / nsinc) ** 2
+	a2 = -0.49670
+	a4 = 0.03705
+	if (mod (nsinc, 2) == 0)
+	    fsign = 1.0
+        else
+	    fsign = -1.0
+
+	# Create a one entry look-up table.
+	if (! IS_INDEFR(xshift)) {
+
+	    dx = xshift
+	    x = -nsinc - dx
+	    xsign = fsign
+	    sum = 0.0
+	    do j = 1, nconv {
+		if (x == 0.0)
+		    f = 1.0
+		else if (dx == 0.0)
+		    f = 0.0
+		else {
+		    dx2 = sconst * (j - nsinc - 1) ** 2
+		    f = xsign / x * (1.0 + a2 * dx2 + a4 * dx2 * dx2) ** 2
+		}
+		table[j,1] = f
+		sum = sum + f
+		x = x + 1.0
+		xsign = -xsign
+	    }
+	    do j = 1, nconv
+	        table[j,1] = table[j,1] / sum
+
+	# Create a multi-entry evenly spaced look-up table.
+	} else {
+
+	    do i = 1, nincr {
+	        dx = -0.5 + real (i - 1) / real (nincr - 1)
+	        x = -nsinc + dx
+		xsign = fsign
+	        sum = 0.0
+	        do j = 1, nconv {
+		    if ((x >= - 0.5 / (nincr - 1)) && (x < 0.5 / (nincr - 1)))
+		        f = 1.0
+		    else if ((dx >= -0.5 / (nincr - 1)) &&
+		        (dx < 0.5 / (nincr - 1)))
+		        f = 0.0
+		    else {
+		        dx2 = sconst * (j - nsinc - 1) ** 2
+		        f = xsign / x * (1.0 + a2 * dx2 + a4 * dx2 * dx2) ** 2
+		    }
+		    table[j,i] = f
+		    sum = sum + f
+		    x = x + 1.0
+		    xsign = -xsign
+	        }
+	        do j = 1, nconv
+		    table[j,i] = table[j,i] / sum
+	    }
+	}
+end
+
+
+# II_BISINCTABLE -- Compute the 2D sinc function look-up tables given the
+# width of the sinc function and the number of increments.
+
+procedure ii_bisinctable (table, nconv, nxincr, nyincr, xshift, yshift)
+
+real	table[nconv,nconv,nxincr,nyincr] #O the computed look-up table
+int	nconv				 #I the sinc truncation length
+int	nxincr, nyincr			 #I the number of look-up tables
+real	xshift, yshift			 #I the shift of the look up table
+
+int	j, ii, jj
+pointer	sp, fx, fy
+
+begin
+	# Allocate some working memory.
+	call smark (sp)
+	call salloc (fx, nconv * nxincr, TY_REAL)
+	call salloc (fy, nconv * nyincr, TY_REAL)
+
+	# Create a one entry look-up table.
+	if (! IS_INDEFR(xshift) && ! IS_INDEFR(yshift)) {
+
+	    call ii_sinctable (Memr[fx], nconv, 1, xshift)
+	    call ii_sinctable (Memr[fy], nconv, 1, yshift)
+	    do j = 1, nconv {
+		call amulkr (Memr[fx], Memr[fy+j-1], table[1,j,1,1], nconv)
+	    }
+
+	} else {
+
+	    call ii_sinctable (Memr[fx], nconv, nxincr, xshift)
+	    call ii_sinctable (Memr[fy], nconv, nyincr, yshift)
+	    do jj = 1, nyincr {
+		do ii = 1, nxincr {
+		    do j = 1, nconv
+			call amulkr (Memr[fx+(ii-1)*nconv],
+			    Memr[fy+(jj-1)*nconv+j-1], table[1,j,ii,jj], nconv)
+		}
+	    }
+	}
+
+	call sfree (sp)
+end
diff --git a/math/iminterp/ii_spline.x b/math/iminterp/ii_spline.x
new file mode 100644
index 00000000..c04a94de
--- /dev/null
+++ b/math/iminterp/ii_spline.x
@@ -0,0 +1,56 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# II_SPLINE -- This procedure fits uniformly spaced data with a cubic
+# spline. The spline is given as basis-spline coefficients that replace
+# the data values.
+# 
+# Storage at call time:
+#
+# bcoeff[1] = second derivative at x = 1
+# bcoeff[2] = first data point y[1]
+# bcoeff[3] = y[2]
+#
+# bcoeff[n+1] = y[n]
+# bcoeff[n+2] = second derivative at x = n
+#
+# Storage after call:
+#
+# bcoeff[1] ... bcoeff[n+2] = the n + 2 basis-spline coefficients for the
+# basis splines as defined in P.M. Prenter's book "Splines and Variational
+# Methods", Wiley, 1975.
+
+procedure ii_spline (bcoeff, diag, npts)
+
+real	bcoeff[ARB]	# data in and also bspline coefficients out
+real	diag[ARB]	# needed for offdiagnol matrix elements
+int	npts		# number of data points
+
+int	i
+
+begin
+        diag[1] = -2.
+        bcoeff[1] = bcoeff[1] / 6.
+
+        diag[2] = 0.
+        bcoeff[2] = (bcoeff[2] - bcoeff[1]) / 6.
+
+        # Gaussian elimination - diagnol below main is made zero
+        # and main diagnol is made all 1's
+        do i = 3, npts + 1 {
+            diag[i] = 1. / (4. - diag[i-1])
+            bcoeff[i] = diag[i] * (bcoeff[i] - bcoeff[i-1])
+        }
+
+        # Find last b spline coefficient first - overlay r.h.s.'s
+        bcoeff[npts+2] = ((diag[npts] + 2.) * bcoeff[npts+1] - bcoeff[npts] +
+		 bcoeff[npts+2] / 6.) / (1. + diag[npts+1] * (diag[npts] + 2.))
+
+        # back substitute filling in coefficients for b splines
+        # note bcoeff[npts+1] is evaluated correctly as can be checked 
+        # bcoeff[2] is already set since offdiagnol is 0.
+        do i = npts + 1, 3, -1
+            bcoeff[i] = bcoeff[i]  - diag[i] * bcoeff[i+1]
+
+        # evaluate bcoeff[1]
+        bcoeff[1] = bcoeff[1] + 2. * bcoeff[2] - bcoeff[3]
+end
diff --git a/math/iminterp/ii_spline2d.x b/math/iminterp/ii_spline2d.x
new file mode 100644
index 00000000..037e799c
--- /dev/null
+++ b/math/iminterp/ii_spline2d.x
@@ -0,0 +1,63 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# II_SPLINE2D -- This procedure calculates the univariate B-spline coefficients
+# for each row of data. The data are assumed to be uniformly spaced with a
+# spacing of 1. The first element of each row of data is assumed to contain
+# the second derivative of the data at x = 1. The nxpix + 2-th element of each
+# row is assumed to contain the second derivative of the function at x = nxpix.
+# Therfore if each row of data contains nxpix points, nxpix+2 B-spline
+# coefficients will be calculated. The univariate B-spline coefficients
+# for the i-th row of data are output to the i-th column of coeff.
+# Therefore two calls to II_SPLINE2D are required to calculate the 2D B-spline
+# coefficients.
+
+procedure ii_spline2d (data, coeff, nxpix, nvectors, len_data, len_coeff)
+
+real	data[len_data,ARB]	# input data array
+real	coeff[len_coeff,ARB]	# output array of univariate coefficients in x
+int	nxpix			# number of x data points
+int	nvectors		# number of univariate splines to calculate
+int	len_data		# row dimension of data
+int	len_coeff		# row dimension of coeff
+
+int	i, j
+pointer	diag
+
+errchk	malloc, mfree
+
+begin
+	# allocate space for off-diagonal elements
+	call malloc (diag, nxpix+1, TY_REAL)
+
+	# calculate off-diagonal elements by Gaussian elimination
+	Memr[diag] = -2.
+	Memr[diag+1] = 0.
+	do i = 3, nxpix + 1
+	    Memr[diag+i-1] = 1. / (4. - Memr[diag+i-2])
+
+	# loop over the nvectors rows of input data
+	do j = 1, nvectors {
+
+	    # copy the j-th row of data to the j-th column of coeff
+	    do i = 1, nxpix + 2
+		coeff[j,i] = data[i,j]
+
+	    # forward substitution
+	    coeff[j,1] = coeff[j,1] / 6.
+	    coeff[j,2] = (coeff[j,2] - coeff[j,1]) / 6.
+	    do i = 3, nxpix + 1
+		coeff[j,i] = Memr[diag+i-1] * (coeff[j,i] - coeff[j,i-1])
+
+	    # back subsitution
+	    coeff[j,nxpix+2] = ((Memr[diag+nxpix-1] + 2.) * coeff[j,nxpix+1] -
+		coeff[j,nxpix] + coeff[j,nxpix+2] / 6.) /
+		(1. + Memr[diag+nxpix] * (Memr[diag+nxpix-1] + 2.))
+	    do i = nxpix + 1, 3, - 1
+		coeff[j,i] = coeff[j,i] - Memr[diag+i-1] * coeff[j,i+1]
+	    coeff[j,1] = coeff[j,1] + 2. * coeff[j,2] - coeff[j,3]
+
+	}
+
+	# free space used for off-diagonal element storage
+	call mfree (diag, TY_REAL)
+end
diff --git a/math/iminterp/im1interpdef.h b/math/iminterp/im1interpdef.h
new file mode 100644
index 00000000..3e6c69e7
--- /dev/null
+++ b/math/iminterp/im1interpdef.h
@@ -0,0 +1,55 @@
+# Header file for asi package
+
+# set up the asi descriptor
+
+define	LEN_ASISTRUCT	10
+
+define	ASI_TYPE	Memi[$1]	# interpolator type
+define	ASI_NSINC	Memi[$1+1]	# sinc interpolator half-width
+define	ASI_NINCR	Memi[$1+2]	# number of sinc interpolator luts
+define	ASI_SHIFT	Memr[P2R($1+3)]	# sinc interpolator shift
+define	ASI_PIXFRAC	Memr[P2R($1+4)]	# pixel fraction for drizzle
+define	ASI_NCOEFF	Memi[$1+5]	# number of coefficients
+define	ASI_OFFSET	Memi[$1+6]	# offset of first data point
+define	ASI_COEFF	Memi[$1+7]	# pointer to coefficient array
+define	ASI_LTABLE	Memi[$1+8]	# pointer to sinc look-up table array
+define	ASI_BADVAL	Memr[P2R($1+9)]	# bad value for drizzle
+
+# define element of the coefficient array
+
+define	COEFF		Memr[P2P($1)]	# element of the coefficient matrix
+define	LTABLE		Memr[P2P($1)]	# element of the look-up table
+
+# define structure for ASISAVE and ASIRESTORE
+
+define	ASI_SAVETYPE	$1[1]
+define	ASI_SAVENSINC	$1[2]
+define	ASI_SAVENINCR	$1[3]
+define	ASI_SAVESHIFT	$1[4]
+define	ASI_SAVEPIXFRAC	$1[5]
+define	ASI_SAVENCOEFF	$1[6]
+define	ASI_SAVEOFFSET	$1[7]
+define	ASI_SAVEBADVAL	$1[8]
+define	ASI_SAVECOEFF	8
+
+# define the sinc function truncation length, taper and precision parameters
+# These should be identical to the definitions in im2interpdef.h.
+
+define	NSINC		15		# the sinc truncation length
+define	NINCR		20		# the number of sinc look-up tables
+define	DX		0.001		# sinc interpolation minimum
+define	PIXFRAC		1.0		# drizzle pixel fraction
+define	MIN_PIXFRAC	0.001		# the minimum drizzle pixel fraction
+define	BADVAL		0.0
+
+# define number of points used in spline interpolation for ARIEVAL, ARIDER
+# and ARBPIX
+
+define	SPLPTS		16
+
+# miscellaneous
+
+define	SPLINE3_ORDER	4
+define	POLY3_ORDER	4
+define	POLY5_ORDER	6
+define	MAX_NDERIVS	6
diff --git a/math/iminterp/im2interpdef.h b/math/iminterp/im2interpdef.h
new file mode 100644
index 00000000..6be7366d
--- /dev/null
+++ b/math/iminterp/im2interpdef.h
@@ -0,0 +1,63 @@
+# Internal definitions for the 2D interpolator structure
+
+define	LEN_MSISTRUCT	14
+
+define	MSI_TYPE	Memi[$1]	# interpolant type
+define	MSI_NSINC	Memi[$1+1]	# interpolant type
+define	MSI_NXINCR	Memi[$1+2]	# interpolant type
+define	MSI_NYINCR	Memi[$1+3]	# interpolant type
+define	MSI_XSHIFT	Memr[P2R($1+4)]	# x shift
+define	MSI_YSHIFT	Memr[P2R($1+5)]	# y shift
+define	MSI_XPIXFRAC	Memr[P2R($1+6)]	# x pixel fraction for drizzle
+define	MSI_YPIXFRAC	Memr[P2R($1+7)]	# y pixel fraction for drizzle
+define	MSI_NXCOEFF	Memi[$1+8]	# x dimension of coefficient array
+define	MSI_NYCOEFF	Memi[$1+9]	# y dimension of coefficient array
+define	MSI_COEFF	Memi[$1+10]	# pointer to coefficient array
+define	MSI_FSTPNT	Memi[$1+11]	# offset to first data point in coeff
+define	MSI_LTABLE	Memi[$1+12]	# offset to first data point in coeff
+define	MSI_BADVAL	Memr[P2R($1+13)]# undefined pixel value for drizzle
+
+# Definitions for msisave and msirestore
+
+define	MSI_SAVETYPE		$1[1]
+define	MSI_SAVENSINC		$1[2]
+define	MSI_SAVENXINCR		$1[3]
+define	MSI_SAVENYINCR		$1[4]
+define	MSI_SAVEXSHIFT		$1[5]
+define	MSI_SAVEYSHIFT		$1[6]
+define	MSI_SAVEXPIXFRAC	$1[7]
+define	MSI_SAVEYPIXFRAC	$1[8]
+define	MSI_SAVENXCOEFF		$1[9]
+define	MSI_SAVENYCOEFF		$1[10]
+define	MSI_SAVEFSTPNT		$1[11]
+define	MSI_SAVEBADVAL		$1[12]
+define	MSI_SAVECOEFF		12
+
+# Array element definitions
+# TEMP and DIAG for spline only
+
+define	COEFF		Memr[P2P($1)]	# element of coefficient array
+define	LTABLE		Memr[P2P($1)]	# element of look-up array
+define	TEMP		Memr[P2P($1)]	# element of temporary array
+define	DIAG		Memr[P2P($1)]	# element of diagonal
+
+# The since function truncation length, taper, and precision definitions
+# These should be identical to those in im1interpdef.h except for the DY
+# definition.
+
+define	NSINC		15
+define	NINCR		20
+define	DX		0.001
+define	DY		0.001
+define	PIXFRAC		1.0
+define	MIN_PIXFRAC	0.001
+define	BADVAL		0.0
+
+# miscellaneous defintions
+
+define	FNROWS		5		# maximum number or rows involved in
+					# boundary extension low side
+define	LNROWS		7		# maximum number of rows involved in
+					# high side boundary extension
+define	SPLPTS		16		# number of points for spline in mrieval
+define	MAX_NTERMS	6		# maximun number of terms in polynomials
diff --git a/math/iminterp/mkpkg b/math/iminterp/mkpkg
new file mode 100644
index 00000000..21941853
--- /dev/null
+++ b/math/iminterp/mkpkg
@@ -0,0 +1,53 @@
+# Image interpolator tools library.
+
+$checkout libiminterp.a ../
+$update   libiminterp.a
+$checkin  libiminterp.a ../
+$exit
+
+libiminterp.a:
+	arbpix.x	<math.h> im1interpdef.h <math/iminterp.h>
+	arider.x	im1interpdef.h <math/iminterp.h>
+	arieval.x	im1interpdef.h <math/iminterp.h>
+	asider.x	im1interpdef.h <math/iminterp.h>
+	asieval.x	im1interpdef.h <math/iminterp.h>
+	asifit.x	im1interpdef.h <math/iminterp.h>
+	asifree.x	im1interpdef.h
+	asigeti.x	im1interpdef.h <math/iminterp.h>
+	asigetr.x	im1interpdef.h <math/iminterp.h>
+	asigrl.x	im1interpdef.h <math/iminterp.h>
+	asiinit.x	im1interpdef.h <math/iminterp.h>
+	asisinit.x	im1interpdef.h <math/iminterp.h>
+	asirestore.x	im1interpdef.h <math/iminterp.h>
+	asisave.x	im1interpdef.h <math/iminterp.h>
+	asitype.x	im1interpdef.h <math/iminterp.h>
+	asivector.x	im1interpdef.h <math/iminterp.h>
+	ii_1dinteg.x	im1interpdef.h <math/iminterp.h>
+	ii_bieval.x	<math.h>	
+	ii_cubspl.f
+	ii_eval.x	<math.h>	
+	ii_greval.x	<math.h> <math/iminterp.h>
+	ii_pc1deval.x	<math.h> im1interpdef.h
+	ii_pc2deval.x	<math.h>	
+	ii_polterp.x	im1interpdef.h
+	ii_sinctable.x	<math.h>
+	ii_spline.x	
+	ii_spline2d.x	
+	mrider.x	im2interpdef.h <math/iminterp.h>
+	mrieval.x	im2interpdef.h <math/iminterp.h>
+	msider.x	im2interpdef.h <math/iminterp.h>
+	msieval.x	im2interpdef.h <math/iminterp.h>
+	msifit.x	im2interpdef.h <math/iminterp.h>
+	msifree.x	im2interpdef.h
+	msigeti.x	im2interpdef.h <math/iminterp.h>
+	msigetr.x	im2interpdef.h <math/iminterp.h>
+	msigrid.x	im2interpdef.h <math/iminterp.h>
+	msigrl.x	im2interpdef.h <math/iminterp.h> <mach.h>
+	msiinit.x	im2interpdef.h <math/iminterp.h>
+	msisinit.x	im2interpdef.h <math/iminterp.h>
+	msirestore.x	im2interpdef.h <math/iminterp.h>
+	msisave.x	im2interpdef.h <math/iminterp.h>
+	msisqgrl.x	im2interpdef.h <math/iminterp.h> <mach.h>
+	msivector.x	im2interpdef.h <math/iminterp.h>
+	msitype.x	im2interpdef.h <math/iminterp.h>
+	;
diff --git a/math/iminterp/mrider.x b/math/iminterp/mrider.x
new file mode 100644
index 00000000..8413df55
--- /dev/null
+++ b/math/iminterp/mrider.x
@@ -0,0 +1,420 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MRIDER -- Procedure to evaluate the derivatives of the interpolant
+# without the storage overhead required by the sequential version.
+# The derivatives are stored such that der[1,1] = the value of the
+# interpolant at x and y, der[2,1] = the first derivative in x and
+# der[2,1] = the first derivative in y.
+
+procedure mrider (x, y, datain, nxpix, nypix, len_datain, der, nxder, nyder,
+		    len_der, interp_type)
+
+real	x[ARB]				# x value
+real	y[ARB]				# y value
+real	datain[len_datain,ARB]		# data array
+int	nxpix				# number of x data points
+int	nypix				# number of y data points
+int	len_datain			# row length of datain
+real	der[len_der, ARB]		# array of derivatives
+int	nxder				# number of derivatives in x
+int	nyder				# number of derivatives in y
+int	len_der				# row length of der, len_der >= nxder
+int	interp_type			# interpolant type
+
+int	nx, ny, nxterms, nyterms, row_length
+int	index, xindex, yindex, first_row, last_row
+int	i, j, ii, jj, kx, ky
+pointer	tmp
+real	coeff[SPLPTS+3,SPLPTS+3], pcoeff[MAX_NTERMS,MAX_NTERMS]
+real	pctemp[MAX_NTERMS,MAX_NTERMS], sum[MAX_NTERMS]
+real	hold21, hold12, hold22, accum, deltax, deltay, tmpx[4], tmpy[4]
+real	xmin, xmax, ymin, ymax, sx, sy, tx, ty
+
+errchk	malloc, calloc, mfree
+
+begin
+	if (nxder < 1 || nyder < 1)
+	    return
+
+	# zero the derivatives
+	do j = 1, nyder {
+	    do i = 1, nxder
+		der[i,j] = 0.
+	}
+
+	switch (interp_type) {
+
+	case II_BINEAREST:
+
+	    der[1,1] = datain[int (x[1]+.5), int (y[1]+.5)]
+
+	    return
+
+	case II_BISINC, II_BILSINC:
+
+	    call ii_bisincder (x[1], y[1], der, nxder, nyder, len_der, datain,
+		0, len_datain, nypix, NSINC, DX, DY)
+
+	    return
+
+	case II_BILINEAR:
+
+	    nx = x[1]
+	    sx = x[1] - nx
+	    tx = 1. - sx
+
+	    ny = y[1]
+	    sy = y[1] - ny
+	    ty = 1. - sy
+
+	    # protect against the case where x = nxpix and/or y = nypix
+	    if (nx >= nxpix)
+		hold21 = 2. * datain[nx,ny] - datain[nx-1,ny]
+	    else
+		hold21 = datain[nx+1,ny]
+	    if (ny >= nypix)
+		hold12 = 2. * datain[nx,ny] - datain[nx,ny-1]
+	    else
+		hold12 = datain[nx,ny+1]
+	    if (nx >= nxpix && ny >= nypix)
+		hold22 = 2. * hold21 - (2. * datain[nx,ny-1] -
+			 datain[nx-1,ny-1])
+	    else if (nx >= nxpix)
+		hold22 = 2. * hold12 - datain[nx-1,ny+1] 
+	    else if (ny >= nypix)
+		hold 22 = 2. * hold21 - datain[nx+1,ny-1] 
+	    else
+		hold22 = datain[nx+1,ny+1]
+
+	    # evaluate the derivatives
+	    der[1,1] = tx * ty * datain[nx,ny] + sx * ty * hold21 +
+		    sy * tx * hold12 + sx * sy * hold22
+	    if (nxder > 1)
+		der[2,1] = - ty * datain[nx,ny] + ty * hold21 -
+			     sy * hold12 + sy * hold22
+	    if (nyder > 1)
+		der[1,2] = - tx * datain[nx,ny] - sx * hold21 +
+			     tx * hold12 + sx * hold22 
+	    if (nxder > 1 && nyder > 1)
+		der[2,2] = datain[nx,ny] - hold21 - hold12 + hold22
+
+
+	    return
+
+	case II_BIDRIZZLE:
+            call ii_bidriz1 (datain, 0, len_datain, x, y, der[1,1], 1, BADVAL)
+            if (nxder > 1) {
+                xmax = max (x[1], x[2], x[3], x[4])
+                xmin = min (x[1], x[2], x[3], x[4])
+                ymax = max (y[1], y[2], y[3], y[4])
+                ymin = min (y[1], y[2], y[3], y[4])
+                deltax = xmax - xmin
+                if (deltax == 0.0)
+                    der[2,1] = 0.0
+                else {
+                    tmpx[1] = xmin; tmpy[1] = ymin
+                    tmpx[2] = (xmax - xmin) / 2.0; tmpy[2] = ymin
+                    tmpx[3] = (xmax - xmin) / 2.0; tmpy[3] = ymax
+                    tmpx[4] = xmin; tmpy[4] = ymax
+                    call ii_bidriz1 (datain, 0, len_datain, tmpx, tmpy,
+			accum, 1, BADVAL)
+                    tmpx[1] = (xmax - xmin) / 2.0; tmpy[1] = ymin
+                    tmpx[2] = xmax; tmpy[2] = ymin
+                    tmpx[3] = xmax; tmpy[3] = ymax
+                    tmpx[4] = (xmax - xmin) / 2.0; tmpy[4] = ymax
+                    call ii_bidriz1 (datain, 0, len_datain, tmpx, tmpy,
+			der[2,1], 1, BADVAL)
+                    der[2,1] = 2.0 * (der[2,1] - accum) / deltax
+                }
+	    }
+            if (nyder > 1) {
+                deltay = ymax - ymin
+                if (deltay == 0.0)
+                    der[1,2] = 0.0
+                else {
+                    tmpx[1] = xmin; tmpy[1] =  ymin
+                    tmpx[2] = xmax; tmpy[2] = ymin
+                    tmpx[3] = xmax; tmpy[3] = (ymax - ymin) / 2.0
+                    tmpx[4] = xmin; tmpy[4] = (ymax - ymin) / 2.0
+                    call ii_bidriz1 (datain, 0, len_datain, tmpx, tmpy,
+		        accum, 1, BADVAL)
+                    tmpx[1] = xmin; tmpy[1] = (ymax - ymin) /  2.0
+                    tmpx[2] = xmax; tmpy[2] = (ymax - ymin) / 2.0
+                    tmpx[3] = xmax; tmpy[3] = ymax
+                    tmpx[4] = xmin; tmpy[4] = ymax
+                    call ii_bidriz1 (datain, 0, len_datain, tmpx, tmpy,
+			der[1,2], 1, BADVAL)
+                    der[1,2] = 2.0 * (der[1,2] - accum) / deltay
+                }
+            }
+
+	    return
+
+	case II_BIPOLY3:
+
+	    row_length = SPLPTS + 3
+
+	    nxterms = 4
+	    nyterms = 4
+
+	    nx = x[1]
+	    ny = y[1]
+
+	    sx = x[1] - nx
+	    sy = y[1] - ny
+
+	    # use boundary projection to extend the data rows
+	    yindex = 1
+	    for (j = ny - 1; j <= ny + 2; j = j + 1) {
+
+		# check that the data row is defined
+		if (j >= 1 && j <= nypix) {
+
+		    # extend the rows
+		    xindex = 1
+		    for (i = nx - 1; i <= nx + 2; i = i + 1) {
+			if (i < 1)
+			    coeff[xindex,yindex] = 2. * datain[1,j] -
+			    			  datain[2-i,j]
+			else if (i > nxpix)
+			    coeff[xindex,yindex] = 2. * datain[nxpix,j] -
+					   	  datain[2*nxpix-i,j] 
+			else
+			    coeff[xindex,yindex] = datain[i,j]
+			xindex = xindex + 1
+		    }
+		} else if (j == (nypix + 2)) {
+
+		    # allow for the final row
+		    xindex = 1
+		    for (i = nx - 1; i <= nx + 2; i = i + 1) {
+			if (i < 1)
+			    coeff[xindex,nyterms] = 2. * datain[1,nypix-2] -
+			    			  datain[2-i,nypix-2]
+			else if (i > nxpix)
+			    coeff[xindex,nyterms] = 2. * datain[nxpix,nypix-2] -
+					   	  datain[2*nxpix-i,nypix-2] 
+			else
+			    coeff[xindex,nyterms] = datain[i,nypix-2]
+			xindex = xindex + 1
+		    }
+
+		}
+
+		yindex = yindex + 1
+	    }
+
+
+	    # project columns
+	    first_row = max (1, 3 - ny)
+	    if (first_row > 1) {
+	        for (j = 1; j < first_row; j = j + 1)
+		    call awsur (coeff[1, first_row], coeff[1, 2*first_row-j],
+		    coeff[1,j], nxterms, 2., -1.)
+	    }
+
+	    last_row = min (nxterms, nypix - ny + 2)
+	    if (last_row < nxterms) {
+	        for (j = last_row + 1; j <= nxterms - 1; j = j + 1)
+		    call awsur (coeff[1,last_row], coeff[1,2*last_row-j],
+		    	        coeff[1,j], nxterms, 2., -1.)
+		if (last_row == 2)
+		    call awsur (coeff[1,last_row], coeff[1,4], coeff[1,4],
+				nxterms, 2., -1.)
+		else
+		    call awsur (coeff[1,last_row], coeff[1,2*last_row-4],
+				coeff[1,4], nxterms, 2., -1.)
+	    }
+
+	    # calculate the coefficients of the bicubic polynomial
+	    call ii_pcpoly3 (coeff, 2, row_length, pcoeff, MAX_NTERMS)
+
+	case II_BIPOLY5:
+	    row_length = SPLPTS + 3
+
+	    nxterms = 6
+	    nyterms = 6
+
+	    nx = x[1]
+	    ny = y[1]
+
+	    sx = x[1] - nx
+	    sy = y[1] - ny
+
+	    # extend rows of data
+	    yindex = 1
+	    for (j = ny - 2; j <= ny + 3; j = j + 1) {
+
+		# select the  rows containing data
+		if (j >= 1 && j <= nypix) {
+
+		    # extend the rows
+		    xindex = 1
+		    for (i = nx - 2; i <= nx + 3; i = i + 1) {
+			if (i < 1)
+			    coeff[xindex,yindex] = 2. * datain[1,j] -
+			    			  datain[2-i,j]
+			else if (i > nxpix)
+			    coeff[xindex,yindex] = 2. * datain[nxpix,j] -
+					   	  datain[2*nxpix-i,j] 
+			else
+			    coeff[xindex,yindex] = datain[i,j]
+			xindex = xindex + 1
+		    }
+
+		} else if (j == (ny + 3)) {
+
+		    # extend the rows
+		    xindex = 1
+		    for (i = nx - 2; i <= nx + 3; i = i + 1) {
+			if (i < 1)
+			    coeff[xindex,yindex] = 2. * datain[1,nypix-3] -
+			    			  datain[2-i,nypix-3]
+			else if (i > nxpix)
+			    coeff[xindex,yindex] = 2. * datain[nxpix,nypix-3] -
+					   	  datain[2*nxpix-i,nypix-3] 
+			else
+			    coeff[xindex,yindex] = datain[i,nypix-3]
+			xindex = xindex + 1
+		    }
+
+		}
+
+		yindex = yindex + 1
+	    }
+
+	    # project columns
+
+	    first_row = max (1, 4 - ny)
+	    if (first_row > 1) {
+	        for (j = 1; j < first_row; j = j + 1)
+		    call awsur (coeff[1,first_row], coeff[1,2*first_row-j],
+		    		coeff[1,j], nxterms, 2., -1.)
+	    }
+
+	    last_row = min (nxterms, nypix - ny + 3) 
+	    if (last_row < nxterms) {
+	        for (j = last_row + 1; j <= nxterms - 1; j = j + 1)
+		    call awsur (coeff[1,last_row], coeff[1,2*last_row-j],
+		    		coeff[1,j], nxterms, 2., -1.)
+		if (last_row == 3)
+		    call awsur (coeff[1,last_row], coeff[1,6], coeff[1,6],
+				nxterms, 2., -1.)
+		else
+		    call awsur (coeff[1,last_row], coeff[1,2*last_row-6],
+				coeff[1,6], nxterms, 2., -1.)
+	    }
+
+	    # caculate the polynomial coeffcients
+	    call ii_pcpoly5 (coeff, 3, row_length, pcoeff, MAX_NTERMS)
+
+
+	case II_BISPLINE3:
+	    row_length = SPLPTS + 3
+
+	    nxterms = 4
+	    nyterms = 4
+
+	    nx = x[1]
+	    ny = y[1]
+
+	    sx = x[1] - nx
+	    sy = y[1] - ny
+
+	    # allocate space for temporary array and 0 file
+	    call calloc (tmp, row_length * row_length, TY_REAL)
+
+	    ky = 0
+	    # maximum number of points used in each direction is SPLPTS
+	    for (j = ny - SPLPTS/2 + 1; j <= ny + SPLPTS/2; j = j + 1) {
+
+		if (j < 1 || j > nypix)
+		    ;
+		else {
+		    ky = ky + 1
+		    if (ky == 1)
+			yindex = ny - j + 1
+
+	    	    kx = 0
+		    for (i = nx - SPLPTS/2 + 1; i <= nx + SPLPTS/2; i = i + 1) {
+			if (i < 1 || i > nxpix)
+			    ;
+			else {
+			    kx = kx + 1
+			    if (kx == 1)
+				xindex = nx - i + 1
+			    coeff[kx+1,ky+1] = datain[i,j]
+			}
+		    }
+
+		    coeff[1,ky+1] = 0.
+		    coeff[kx+2,ky+1] = 0.
+		    coeff[kx+3,ky+1] = 0.
+
+		}
+	    }
+
+	    # zero out 1st and last 2 rows
+	    call amovkr (0., coeff[1,1], kx+3)
+	    call amovkr (0., coeff[1,ky+2], kx+3)
+	    call amovkr (0., coeff[1,ky+3],kx+3)
+
+	    # calculate the spline coefficients
+	    call ii_spline2d (coeff, Memr[tmp], kx, ky+2, row_length,
+			      row_length)
+	    call ii_spline2d (Memr[tmp], coeff, ky, kx+2, row_length,
+	    		      row_length)
+
+	    # calculate the polynomial coefficients
+	    index = (yindex - 1) * row_length + xindex + 1
+	    call ii_pcspline3 (coeff, index, row_length, pcoeff, MAX_NTERMS)
+
+	    # free space
+	    call mfree (tmp, TY_REAL)
+	}
+
+	# evaluate the derivatives of the higher order interpolants
+	do j = 1, nyder {
+
+	    # set pctemp
+	    do jj = nyterms, j, -1 {
+		do ii = 1, nxterms
+		    pctemp[ii,jj] = pcoeff[ii,jj]
+	    }
+
+	    do i = 1, nxder {
+
+		# accumulate the partial sums in x
+		do jj = nyterms, j, -1 {
+		    sum[jj] = pctemp[nxterms,jj]
+		    do ii = nxterms - 1, i, -1
+			sum[jj] = pctemp[ii,jj] + sum[jj] * sx
+		}
+
+		# accumulate the sum in y
+		accum = sum[nyterms]
+		do jj = nyterms - 1, j, -1
+		    accum = sum[jj] + accum * sy
+
+		# evaulate the derivative
+		der[i,j] = accum
+
+		# differentiate in x
+		do jj = nyterms, j, -1 {
+		    do ii = nxterms, i + 1, -1
+			pctemp[ii,jj] = (ii - i) * pctemp[ii,jj]
+		}
+
+	    }
+
+	    # differentiate in y
+	    do jj = 1, nxterms {
+		do ii = nyterms, j + 1, -1 
+		    pcoeff[jj,ii] = (ii - j) * pcoeff[jj,ii]
+	    }
+
+	}
+end
diff --git a/math/iminterp/mrieval.x b/math/iminterp/mrieval.x
new file mode 100644
index 00000000..6d89c456
--- /dev/null
+++ b/math/iminterp/mrieval.x
@@ -0,0 +1,303 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MRIEVAL -- Procedure to evaluate the 2D interpolant at a given value
+# of x and y. MRIEVAL allows the interpolation of a few interpolated
+# points without the computing time and storage required for the
+# sequential version. The routine assumes that 1 <= x <= nxpix and
+# 1 <= y <= nypix.
+
+real procedure mrieval (x, y, datain, nxpix, nypix, len_datain, interp_type)
+
+real	x[ARB]				# x value
+real	y[ARB]				# y value
+real	datain[len_datain,ARB]		# data array
+int	nxpix				# number of x data points
+int	nypix				# number of y data points
+int	len_datain			# row length of datain
+int	interp_type			# interpolant type
+
+int	nx, ny, nterms, row_length
+int	xindex, yindex, first_row, last_row
+int	kx, ky
+int	i, j
+pointer	tmp
+real	coeff[SPLPTS+3,SPLPTS+3]
+real	hold21, hold12, hold22
+real	sx, sy, tx, ty
+real	xval, yval, value
+errchk	malloc, calloc, mfree
+
+begin
+	switch (interp_type) {
+
+	case II_BINEAREST:
+	    return (datain[int (x[1]+0.5), int (y[1]+0.5)])
+
+	case II_BILINEAR:
+	    nx = x[1]
+	    sx = x[1] - nx
+	    tx = 1. - sx
+
+	    ny = y[1]
+	    sy = y[1] - ny
+	    ty = 1. - sy
+
+	    # protect against the case where x = nxpix and/or y = nypix
+	    if (nx >= nxpix)
+		hold21 = 2. * datain[nx,ny] - datain[nx-1,ny]
+	    else
+		hold21 = datain[nx+1,ny]
+	    if (ny >= nypix)
+		hold12 = 2. * datain[nx,ny] - datain[nx,ny-1]
+	    else
+		hold12 = datain[nx,ny+1]
+	    if (nx >= nxpix && ny >= nypix)
+		hold22 = 2. * hold21 - (2. * datain[nx,ny-1] -
+			 datain[nx-1,ny-1])
+	    else if (nx >= nxpix)
+		hold22 = 2. * hold12 - datain[nx-1,ny+1]
+	    else if (ny >= nypix)
+		hold22 = 2. * hold21 - datain[nx+1,ny-1]
+	    else
+		hold22 = datain[nx+1,ny+1]
+
+	    # evaluate the interpolant
+	    value = tx * ty * datain[nx,ny] + sx * ty * hold21 +
+		    sy * tx * hold12 + sx * sy * hold22
+
+	    return (value)
+
+	case II_BIDRIZZLE:
+	    call ii_bidriz1 (datain, 0, len_datain, x, y, value, 1, BADVAL)
+
+	    return (value)
+
+	case II_BIPOLY3:
+	    row_length = SPLPTS + 3
+	    nterms = 4
+	    nx = x[1]
+	    ny = y[1]
+
+	    # major problem is that near the edge the interior polynomial
+	    # must be defined
+
+	    # use boundary projection to extend the data rows
+	    yindex = 1
+	    for (j = ny - 1; j <= ny + 2; j = j + 1) {
+
+		# check that the data row is defined
+		if (j >= 1 && j <= nypix) {
+
+		    # extend the rows
+		    xindex = 1
+		    for (i = nx - 1; i <= nx + 2; i = i + 1) {
+			if (i < 1)
+			    coeff[xindex,yindex] = 2. * datain[1,j] -
+			    			  datain[2-i,j]
+			else if (i > nxpix)
+			    coeff[xindex,yindex] = 2. * datain[nxpix,j] -
+					   	  datain[2*nxpix-i,j] 
+			else
+			    coeff[xindex,yindex] = datain[i,j]
+			xindex = xindex + 1
+		    }
+
+		} else if (j == (ny + 2)) {
+
+		    # extend the rows
+		    xindex = 1
+		    for (i = nx - 1; i <= nx + 2; i = i + 1) {
+			if (i < 1)
+			    coeff[xindex,yindex] = 2. * datain[1,nypix-2] -
+			    			  datain[2-i,nypix-2]
+			else if (i > nxpix)
+			    coeff[xindex,yindex] = 2. * datain[nxpix,nypix-2] -
+					   	  datain[2*nxpix-i,nypix-2] 
+			else
+			    coeff[xindex,yindex] = datain[i,nypix-2]
+			xindex = xindex + 1
+		    }
+
+		}
+
+		yindex = yindex + 1
+	    }
+
+	    # project columns
+
+	    first_row = max (1, 3 - ny)
+	    if (first_row > 1) {
+	        for (j = 1; j < first_row; j = j + 1)
+		    call awsur (coeff[1, first_row], coeff[1, 2*first_row-j],
+		    coeff[1,j], nterms, 2., -1.)
+	    }
+
+	    last_row = min (nterms, nypix - ny + 2)
+	    if (last_row < nterms) {
+	        for (j = last_row + 1; j <= nterms - 1; j = j + 1)
+		    call awsur (coeff[1,last_row], coeff[1,2*last_row-j],
+		    	        coeff[1,j], nterms, 2., -1.)
+		if (last_row == 2)
+		    call awsur (coeff[1,last_row], coeff[1,4], coeff[1,4],
+				nterms, 2., -1.)
+		else
+		    call awsur (coeff[1,last_row], coeff[1,2*last_row-4],
+				coeff[1,4], nterms, 2., -1.)
+	    }
+
+
+	    # center the x value and call evaluation routine
+	    xval = 2 + (x[1] - nx)
+	    yval = 2 + (y[1] - ny)
+	    call ii_bipoly3 (coeff, 0, row_length, xval, yval, value, 1)
+
+	    return (value)
+
+	case II_BIPOLY5:
+	    row_length = SPLPTS + 3
+	    nterms = 6
+	    nx = x[1]
+	    ny = y[1]
+
+	    # major problem is to define interior polynomial near the edge
+
+	    # loop over the rows of data
+	    yindex = 1
+	    for (j = ny - 2; j <= ny + 3; j = j + 1) {
+
+		# select the  rows containing data
+		if (j >= 1 && j <= nypix) {
+
+		    # extend the rows
+		    xindex = 1
+		    for (i = nx - 2; i <= nx + 3; i = i + 1) {
+			if (i < 1)
+			    coeff[xindex,yindex] = 2. * datain[1,j] -
+			    			  datain[2-i,j]
+			else if (i > nxpix)
+			    coeff[xindex,yindex] = 2. * datain[nxpix,j] -
+					   	  datain[2*nxpix-i,j] 
+			else
+			    coeff[xindex,yindex] = datain[i,j]
+			xindex = xindex + 1
+		    }
+
+		} else if (j == (ny + 3)) {
+
+		    # extend the rows
+		    xindex = 1
+		    for (i = nx - 2; i <= nx + 3; i = i + 1) {
+			if (i < 1)
+			    coeff[xindex,yindex] = 2. * datain[1,nypix-3] -
+			    			  datain[2-i,nypix-3]
+			else if (i > nxpix)
+			    coeff[xindex,yindex] = 2. * datain[nxpix,nypix-3] -
+					   	  datain[2*nxpix-i,nypix-3] 
+			else
+			    coeff[xindex,yindex] = datain[i,nypix-3]
+			xindex = xindex + 1
+		    }
+
+		}
+
+		yindex = yindex + 1
+	    }
+
+	    # project columns
+
+	    first_row = max (1, 4 - ny)
+	    if (first_row > 1) {
+	        for (j = 1; j < first_row; j = j + 1)
+		    call awsur (coeff[1,first_row], coeff[1,2*first_row-j],
+		    		coeff[1,j], nterms, 2., -1.)
+	    }
+
+	    last_row = min (nterms, nypix - ny + 3) 
+	    if (last_row < nterms) {
+	        for (j = last_row + 1; j <= nterms - 1; j = j + 1)
+		    call awsur (coeff[1,last_row], coeff[1,2*last_row-j],
+		    		coeff[1,j], nterms, 2., -1.)
+		if (last_row == 3)
+		    call awsur (coeff[1,last_row], coeff[1,6], coeff[1,6],
+				nterms, 2., -1.)
+		else
+		    call awsur (coeff[1,last_row], coeff[1,2*last_row-6],
+				coeff[1,6], nterms, 2., -1.)
+	    }
+
+	    # call evaluation routine
+	    xval = 3 + (x[1] - nx)
+	    yval = 3 + (y[1] - ny)
+	    call ii_bipoly5 (coeff, 0, row_length, xval, yval, value, 1)
+
+	    return (value)
+
+	case II_BISPLINE3:
+	    row_length = SPLPTS + 3
+	    nx = x[1]
+	    ny = y[1]
+
+	    # allocate space for temporary array and 0 file
+	    call calloc (tmp, row_length * row_length, TY_REAL)
+
+	    ky = 0
+	    # maximum number of points used in each direction is SPLPTS
+	    for (j = ny - SPLPTS/2 + 1; j <= ny + SPLPTS/2; j = j + 1) {
+
+		if (j < 1 || j > nypix)
+		    ;
+		else {
+		    ky = ky + 1
+		    if (ky == 1)
+			yindex = ny - j + 1
+
+	    	    kx = 0
+		    for (i = nx - SPLPTS/2 + 1; i <= nx + SPLPTS/2; i = i + 1) {
+			if (i < 1 || i > nxpix)
+			    ;
+			else {
+			    kx = kx + 1
+			    if (kx == 1)
+				xindex = nx - i + 1
+			    coeff[kx+1,ky+1] = datain[i,j]
+			}
+		    }
+
+		    coeff[1,ky+1] = 0.
+		    coeff[kx+2,ky+1] = 0.
+		    coeff[kx+3,ky+1] = 0.
+
+		}
+	    }
+
+	    # zero out 1st and last 2 rows
+	    call amovkr (0., coeff[1,1], kx+3)
+	    call amovkr (0., coeff[1,ky+2], kx+3)
+	    call amovkr (0., coeff[1,ky+3],kx+3)
+
+	    # calculate the spline coefficients
+	    call ii_spline2d (coeff, Memr[tmp], kx, ky+2, row_length,
+			      row_length)
+	    call ii_spline2d (Memr[tmp], coeff, ky, kx+2, row_length,
+	    		      row_length)
+
+	    # evaluate spline
+	    xval = xindex + 1 + (x[1] - nx)
+	    yval = yindex + 1 + (y[1] - ny)
+	    call ii_bispline3 (coeff, 0, row_length, xval, yval, value, 1)
+
+	    # free space
+	    call mfree (tmp, TY_REAL)
+
+	    return (value)
+
+	case II_BISINC, II_BILSINC:
+	    call ii_bisinc (datain, 0, len_datain, nypix, x, y, value, 1,
+	        NSINC, DX, DY)
+
+	    return (value)
+	}
+end
diff --git a/math/iminterp/msider.x b/math/iminterp/msider.x
new file mode 100644
index 00000000..e66d9119
--- /dev/null
+++ b/math/iminterp/msider.x
@@ -0,0 +1,294 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MSIDER -- Calculate the derivatives of the interpolant. The derivative
+# der[i,j] = d f(x,y) / dx (i-1) dy (j-1). Therefore der[1,1] contains
+# the value of the interpolant, der[2,1] the 1st derivative in x and
+# der[1,2] the first derivative in y.
+
+procedure msider (msi, x, y, der, nxder, nyder, len_der)
+
+pointer	msi			# pointer to interpolant descriptor structure
+real	x[ARB]			# x value
+real	y[ARB]			# y value
+real	der[len_der,ARB]	# derivative array
+int	nxder			# number of x derivatives
+int	nyder			# number of y derivatives
+int	len_der			# row length of der, len_der >= nxder
+
+int	first_point, len_coeff
+int	nxterms, nyterms, nx, ny, nyd, nxd
+int	i, j, ii, jj
+real	sx, sy, tx, ty, xmin, xmax, ymin, ymax
+real	pcoeff[MAX_NTERMS,MAX_NTERMS], pctemp[MAX_NTERMS,MAX_NTERMS]
+real	sum[MAX_NTERMS], accum, deltax, deltay, tmpx[4], tmpy[4]
+pointer	index, ptr
+
+begin
+	if (nxder < 1 || nyder < 1)
+	    return
+
+	# set up coefficient array parameters
+	len_coeff = MSI_NXCOEFF(msi)
+	index = MSI_COEFF(msi) + MSI_FSTPNT(msi) - 1
+
+	# zero the derivatives
+	do j = 1, nyder {
+	    do i = 1, nxder
+		der[i,j] = 0.
+	}
+
+	# calculate the appropriate number of terms of the polynomials in
+	# x and y
+
+	switch (MSI_TYPE(msi)) {
+
+	case II_BINEAREST:
+
+	    nx = x[1] + 0.5
+	    ny = y[1] + 0.5
+
+	    ptr = index + (ny - 1) * len_coeff + nx
+	    der[1,1] = COEFF(ptr) 
+
+	    return
+
+	case II_BISINC, II_BILSINC:
+
+	    call ii_bisincder (x[1], y[1], der, nxder, nyder, len_der,
+	        COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi), MSI_NXCOEFF(msi),
+		MSI_NYCOEFF(msi), MSI_NSINC(msi), DX, DY)
+
+	    return
+
+	case II_BILINEAR:
+
+	    nx = x[1]
+	    ny = y[1]
+	    sx = x[1] - nx
+	    sy = y[1] - ny
+	    tx = 1. - sx
+	    ty = 1. - sy
+
+	    ptr = index + (ny - 1) * len_coeff + nx
+	    der[1,1] = tx * ty * COEFF(ptr) + sx * ty * COEFF(ptr+1) +
+		       sy * tx * COEFF(ptr+len_coeff) +
+		       sx * sy * COEFF(ptr+len_coeff+1)
+
+	    if (nxder > 1)
+		der[2,1] = -ty * COEFF(ptr) + ty * COEFF(ptr+1) -
+			   sy * COEFF(ptr+len_coeff) +
+			   sy * COEFF(ptr+len_coeff+1)
+
+	    if (nyder > 1)
+		der[1,2] = -tx * COEFF(ptr) - sx * COEFF(ptr+1) +
+			   tx * COEFF(ptr+len_coeff) +
+			   sx * COEFF(ptr+len_coeff+1)
+
+	    if (nyder > 1 && nxder > 1)
+		der[2,2] = COEFF(ptr) - COEFF(ptr+1) - COEFF(ptr+len_coeff) +
+			   COEFF(ptr+len_coeff+1)
+
+	    return
+
+	case II_BIDRIZZLE:
+            if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0)
+                call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+                    MSI_NXCOEFF(msi), x, y, der[1,1], 1, MSI_BADVAL(msi))
+            #else if (MSI_XPIXFRAC(msi) <= 0.0 && MSI_YPIXFRAC(msi) <= 0.0)
+                #call ii_bidriz0 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+                    #MSI_NXCOEFF(msi), x, y, der[1,1], 1, MSI_BADVAL(msi))
+            else
+                call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+                    MSI_NXCOEFF(msi), x, y, der[1,1], 1, MSI_XPIXFRAC(msi),
+                    MSI_YPIXFRAC(msi), MSI_BADVAL(msi))
+
+	    if (nxder > 1) {
+		xmax = max (x[1], x[2], x[3], x[4])
+		xmin = min (x[1], x[2], x[3], x[4])
+		ymax = max (y[1], y[2], y[3], y[4])
+		ymin = min (y[1], y[2], y[3], y[4])
+		deltax = xmax - xmin
+		if (deltax == 0.0)
+		    der[2,1] = 0.0
+		else {
+		    tmpx[1] = xmin; tmpy[1] = ymin
+		    tmpx[2] = (xmax - xmin) / 2.0; tmpy[2] = ymin
+		    tmpx[3] = (xmax - xmin) / 2.0; tmpy[3] = ymax
+		    tmpx[4] = xmin; tmpy[4] = ymax
+            	    if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0)
+                        call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+                            MSI_NXCOEFF(msi), tmpx, tmpy, accum, 1,
+			    MSI_BADVAL(msi))
+            	    #else if (MSI_XPIXFRAC(msi) <= 0.0 &&
+		        #MSI_YPIXFRAC(msi) <= 0.0)
+                        #call ii_bidriz0 (COEFF(MSI_COEFF(msi)),
+			    #MSI_FSTPNT(msi), MSI_NXCOEFF(msi), tmpx, tmpy,
+			    #accum, 1, MSI_BADVAL(msi))
+            	    else
+                        call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+                            MSI_NXCOEFF(msi), tmpx, tmpy, accum, 1,
+			    MSI_XPIXFRAC(msi), MSI_YPIXFRAC(msi),
+			    MSI_BADVAL(msi))
+		    tmpx[1] = (xmax - xmin) / 2.0; tmpy[1] = ymin
+		    tmpx[2] = xmax; tmpy[2] = ymin
+		    tmpx[3] = xmax; tmpy[3] = ymax
+		    tmpx[4] = (xmax - xmin) / 2.0; tmpy[4] = ymax
+            	    if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0)
+                        call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+                            MSI_NXCOEFF(msi), tmpx, tmpy, der[2,1], 1,
+			    MSI_BADVAL(msi))
+            	    #else if (MSI_XPIXFRAC(msi) <= 0.0 &&
+		        #MSI_YPIXFRAC(msi) <= 0.0)
+                        #call ii_bidriz0 (COEFF(MSI_COEFF(msi)),
+			    #MSI_FSTPNT(msi), MSI_NXCOEFF(msi), tmpx, tmpy,
+			    #der[2,1], 1, MSI_BADVAL(msi))
+            	    else
+                        call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+                            MSI_NXCOEFF(msi), tmpx, tmpy, der[2,1], 1,
+			    MSI_XPIXFRAC(msi), MSI_YPIXFRAC(msi),
+			    MSI_BADVAL(msi))
+		    der[2,1] = 2.0 * (der[2,1] - accum) / deltax
+		}
+	    }
+	    if (nyder > 1) {
+		deltay = ymax - ymin
+		if (deltay == 0.0)
+		    der[1,2] = 0.0
+		else {
+		    tmpx[1] = xmin; tmpy[1] =  ymin
+		    tmpx[2] = xmax; tmpy[2] = ymin
+		    tmpx[3] = xmax; tmpy[3] = (ymax - ymin) / 2.0
+		    tmpx[4] = xmin; tmpy[4] = (ymax - ymin) / 2.0
+            	    if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0)
+                        call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+                            MSI_NXCOEFF(msi), tmpx, tmpy, accum, 1,
+			    MSI_BADVAL(msi))
+            	    #else if (MSI_XPIXFRAC(msi) <= 0.0 &&
+		        #MSI_YPIXFRAC(msi) <= 0.0)
+                        #call ii_bidriz0 (COEFF(MSI_COEFF(msi)),
+			    #MSI_FSTPNT(msi), MSI_NXCOEFF(msi), tmpx, tmpy,
+			    #accum, 1, MSI_BADVAL(msi))
+            	    else
+                        call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+                            MSI_NXCOEFF(msi), tmpx, tmpy, accum, 1,
+			    MSI_XPIXFRAC(msi), MSI_YPIXFRAC(msi),
+			    MSI_BADVAL(msi))
+		    tmpx[1] = xmin; tmpy[1] = (ymax - ymin) /  2.0
+		    tmpx[2] = xmax; tmpy[2] = (ymax - ymin) / 2.0
+		    tmpx[3] = xmax; tmpy[3] = ymax
+		    tmpx[4] = xmin; tmpy[4] = ymax
+            	    if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0)
+                        call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+                            MSI_NXCOEFF(msi), tmpx, tmpy, der[1,2], 1,
+			    MSI_BADVAL(msi))
+            	    #else if (MSI_XPIXFRAC(msi) <= 0.0 &&
+		        #MSI_YPIXFRAC(msi) <= 0.0)
+                        #call ii_bidriz0 (COEFF(MSI_COEFF(msi)),
+			    #MSI_FSTPNT(msi), MSI_NXCOEFF(msi), tmpx, tmpy,
+			    #der[1,2], 1, MSI_BADVAL(msi))
+            	    else
+                        call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+                            MSI_NXCOEFF(msi), tmpx, tmpy, der[1,2], 1,
+			    MSI_XPIXFRAC(msi), MSI_YPIXFRAC(msi),
+			    MSI_BADVAL(msi))
+		    der[1,2] = 2.0 * (der[1,2] - accum) / deltay
+		}
+	    }
+
+	    return
+
+	case II_BIPOLY3:
+
+	    nxterms = 4
+	    nyterms = 4
+
+	    nxd = min (nxder, 4)
+	    nyd = min (nyder, 4) 
+
+	    nx = x[1]
+	    sx = x[1] - nx
+	    ny = y[1]
+	    sy = y[1] - ny
+
+	    first_point = MSI_FSTPNT(msi) + (ny - 2) * len_coeff + nx
+	    call ii_pcpoly3 (COEFF(MSI_COEFF(msi)), first_point, len_coeff,
+	    		     pcoeff, 6)
+
+	case II_BIPOLY5:
+
+	    nxterms = 6
+	    nyterms = 6
+
+	    nxd = min (nxder, 6)
+	    nyd = min (nyder, 6)
+
+	    nx = x[1]
+	    sx = x[1] - nx
+	    ny = y[1]
+	    sy = y[1] - ny
+
+	    first_point = MSI_FSTPNT(msi) + (ny - 3) * len_coeff + nx
+	    call ii_pcpoly5 (COEFF(MSI_COEFF(msi)), first_point, len_coeff,
+	    		    pcoeff, 6)
+
+	case II_BISPLINE3:
+
+	    nxterms = 4
+	    nyterms = 4
+
+	    nxd = min (nxder, 4)
+	    nyd = min (nyder, 4)
+
+	    nx = x[1]
+	    sx = x[1] - nx
+	    ny = y[1]
+	    sy = y[1] - ny
+
+	    first_point = MSI_FSTPNT(msi) + (ny - 2) * len_coeff + nx
+	    call ii_pcspline3 (COEFF(MSI_COEFF(msi)), first_point, len_coeff,
+	    			pcoeff, 6)
+	}
+
+	# evaluate the derivatives by nested multiplication
+	do j = 1, nyd {
+
+	    # set pctemp
+	    do jj =  nyterms, j, -1 {
+		do ii = 1, nxterms
+		    pctemp[ii,jj] = pcoeff[ii,jj]
+	    }
+
+	    do i = 1, nxd {
+
+		# accumulate the partial sums in x
+		do jj = nyterms, j, -1 {
+		    sum[jj] = pctemp[nxterms,jj]
+		    do ii = nxterms - 1, i, -1
+			sum[jj] = pctemp[ii,jj] + sum[jj] * sx
+		}
+
+		# accumulate the sum in y
+		accum = sum[nyterms]
+		do jj = nyterms - 1, j, -1
+		    accum = sum[jj] + accum * sy
+
+		# evaluate derivative
+		der[i,j] = accum
+
+		# differentiate in x
+		do jj = nyterms, j, -1 {
+		    do ii = nxterms, i + 1, -1
+		        pctemp[ii,jj] = (ii - i) * pctemp[ii,jj]
+		}
+	    }
+
+	    # differentiate in y
+	    do jj = 1, nxterms {
+		do ii = nyterms, j + 1, -1
+		    pcoeff[jj,ii] = (ii - j) * pcoeff[jj,ii]
+	    }
+	}
+end
diff --git a/math/iminterp/msieval.x b/math/iminterp/msieval.x
new file mode 100644
index 00000000..26af75b6
--- /dev/null
+++ b/math/iminterp/msieval.x
@@ -0,0 +1,74 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MSIEVAL -- Procedure to evaluate the interpolant at a single point.
+# The procedure assumes that 1 <= x <= nxpix and that 1 <= y <= nypix.
+# Checking for out of bounds pixels is the responsibility of the calling
+# program.
+
+real procedure msieval (msi, x, y)
+
+pointer	msi		# pointer to the interpolant descriptor
+real	x[ARB]		# x data value
+real	y[ARB]		# y data value
+
+real	value
+
+begin
+	switch (MSI_TYPE(msi)) {
+
+	case II_BINEAREST:
+	    call ii_binearest (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, value, 1)
+	    return (value)
+
+	case II_BILINEAR:
+	    call ii_bilinear (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, value, 1)
+	    return (value)
+
+	case II_BIPOLY3:
+	    call ii_bipoly3 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, value, 1)
+	    return (value)
+
+	case II_BIPOLY5:
+	    call ii_bipoly5 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, value, 1)
+	    return (value)
+
+	case II_BISPLINE3:
+	    call ii_bispline3 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, value, 1)
+	    return (value)
+
+	case II_BISINC:
+	    call ii_bisinc (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), MSI_NYCOEFF(msi), x, y, value, 1,
+		MSI_NSINC(msi), DX, DY)
+	    return (value)
+
+	case II_BILSINC:
+	    call ii_bilsinc (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), MSI_NYCOEFF(msi), x, y, value, 1,
+		LTABLE(MSI_LTABLE(msi)), 2 * MSI_NSINC(msi) + 1,
+		MSI_NXINCR(msi), MSI_NYINCR(msi), DX, DY)
+	    return (value)
+
+	case II_BIDRIZZLE:
+	    if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0) 
+	        call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	            MSI_NXCOEFF(msi), x, y, value, 1, MSI_BADVAL(msi))
+	    #else if (MSI_XPIXFRAC(msi) <= 0.0 && MSI_YPIXFRAC(msi) <= 0.0) 
+	        #call ii_bidriz0 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	            #MSI_NXCOEFF(msi), x, y, value, 1, MSI_BADVAL(msi))
+	    else
+	        call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	            MSI_NXCOEFF(msi), x, y, value, 1, MSI_XPIXFRAC(msi),
+		    MSI_YPIXFRAC(msi), MSI_BADVAL(msi))
+	    return (value)
+
+	}
+end
diff --git a/math/iminterp/msifit.x b/math/iminterp/msifit.x
new file mode 100644
index 00000000..27d861ff
--- /dev/null
+++ b/math/iminterp/msifit.x
@@ -0,0 +1,275 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MSIFIT -- MSIFIT calculates the coefficients of the interpolant.
+# With the exception of the bicubic spline interpolant the coefficients
+# are stored as the data points.  The 2D B-spline coefficients are
+# calculated using the routines II_SPLINE2D. MSIFIT checks that the
+# dimensions of the data array are appropriate for the interpolant selected
+# and allocates space for the coefficient array.
+# Boundary extension is performed using boundary projection.
+
+procedure msifit (msi, datain, nxpix, nypix, len_datain)
+
+pointer	msi			# pointer to interpolant descriptor structure
+real	datain[len_datain,ARB]	# data array
+int	nxpix			# number of points in the x dimension
+int	nypix			# number of points in the y dimension
+int	len_datain			# row length of datain
+
+int	i, j
+pointer	fptr, nptr, rptr
+pointer	tmp
+pointer	rptrf[FNROWS]
+pointer	rptrl[LNROWS]
+
+errchk	calloc, mfree
+
+begin
+	# check the row length of datain
+	if (len_datain < nxpix)
+	    call error (0, "MSIFIT: Row length of datain too small.")
+
+	# check that the number of data points in x and y is
+	# appropriate for the interpolant type selected and
+	# allocate space for the coefficient array allowing
+	# sufficient storage for boundary extension
+
+	switch (MSI_TYPE(msi)) {
+
+	case II_BINEAREST:
+
+	    if (nxpix < 1 || nypix < 1) {
+		call error (0, "MSIFIT: Too few data points.")
+		return
+	    } else {
+		MSI_NXCOEFF(msi) = nxpix
+		MSI_NYCOEFF(msi) = nypix
+		MSI_FSTPNT(msi) = 0
+		if (MSI_COEFF(msi) != NULL)
+		    call mfree (MSI_COEFF(msi), TY_REAL)
+		call malloc (MSI_COEFF(msi), nxpix * nypix, TY_REAL)
+	    }
+
+	case II_BILINEAR, II_BIDRIZZLE:
+
+	    if (nxpix < 2 || nypix < 2) {
+		call error (0, "MSIFIT: Too few data points.")
+		return
+	    } else {
+		MSI_NXCOEFF(msi) = nxpix + 1
+		MSI_NYCOEFF(msi) = nypix + 1
+		MSI_FSTPNT(msi) = 0
+		if (MSI_COEFF(msi) != NULL)
+		    call mfree (MSI_COEFF(msi), TY_REAL)
+		call malloc (MSI_COEFF(msi),
+			     MSI_NXCOEFF(msi) * MSI_NYCOEFF(msi), TY_REAL)
+	    }
+
+	case II_BIPOLY3:
+
+	    if (nxpix < 4 || nypix < 4) {
+		call error (0, "MSIFIT: Too few data points.")
+		return
+	    } else {
+		MSI_NXCOEFF(msi) = nxpix + 3
+		MSI_NYCOEFF(msi) = nypix + 3
+		MSI_FSTPNT(msi) = MSI_NXCOEFF(msi) + 1
+		if (MSI_COEFF(msi) != NULL)
+		    call mfree (MSI_COEFF(msi), TY_REAL)
+		call malloc (MSI_COEFF(msi),
+			     MSI_NXCOEFF(msi) * MSI_NYCOEFF(msi), TY_REAL)
+	    }
+
+	case II_BIPOLY5:
+
+	    if (nxpix < 6 || nypix < 6) {
+		call error (0, "MSIFIT: Too few data points.")
+		return
+	    } else {
+		MSI_NXCOEFF(msi) = nxpix + 5
+		MSI_NYCOEFF(msi) = nypix + 5
+		MSI_FSTPNT(msi) = 2 * MSI_NXCOEFF(msi) + 2
+		if (MSI_COEFF(msi) != NULL)
+		    call mfree (MSI_COEFF(msi), TY_REAL)
+		call malloc (MSI_COEFF(msi),
+			     MSI_NXCOEFF(msi) * MSI_NYCOEFF(msi), TY_REAL)
+	    }
+
+	case II_BISPLINE3:
+
+	    if (nxpix < 4 || nypix < 4) {
+		call error (0, "MSIFIT: Too few data points.")
+		return
+	    } else {
+		MSI_NXCOEFF(msi) = nxpix + 3
+		MSI_NYCOEFF(msi) = nypix + 3
+		MSI_FSTPNT(msi) = MSI_NXCOEFF(msi) + 1
+		if (MSI_COEFF(msi) != NULL)
+		    call mfree (MSI_COEFF(msi), TY_REAL)
+		call calloc (MSI_COEFF(msi),
+			     MSI_NXCOEFF(msi) * MSI_NYCOEFF(msi), TY_REAL)
+	    }
+
+	case II_BISINC, II_BILSINC:
+
+	    if (nxpix < 1 || nypix < 1) {
+		call error (0, "MSIFIT: Too few data points.")
+		return
+	    } else {
+		MSI_NXCOEFF(msi) = nxpix
+		MSI_NYCOEFF(msi) = nypix
+		MSI_FSTPNT(msi) = 0
+		if (MSI_COEFF(msi) != NULL)
+		    call mfree (MSI_COEFF(msi), TY_REAL)
+		call calloc (MSI_COEFF(msi), nxpix * nypix, TY_REAL)
+	    }
+
+	}
+
+	# index the coefficient pointer so that COEFF(fptr+1) points to the
+	# first data point in the coefficient array
+	fptr = MSI_COEFF(msi) - 1 + MSI_FSTPNT(msi)
+
+	# load data into coefficient array
+	rptr = fptr
+	do j = 1, nypix {
+	    call amovr (datain[1,j], COEFF(rptr+1), nxpix)
+	    rptr = rptr + MSI_NXCOEFF(msi)
+	}
+
+	# calculate the coefficients of the interpolant
+	# boundary extension is performed using boundary projection
+
+	switch (MSI_TYPE(msi)) {
+
+	case II_BINEAREST, II_BISINC, II_BILSINC:
+
+	    # no end conditions necessary, coefficients stored as data
+
+	case II_BILINEAR, II_BIDRIZZLE:
+
+	    # extend the rows
+	    rptr = fptr + nxpix
+	    do j = 1, nypix {
+		COEFF(rptr+1) = 2. * COEFF(rptr) - COEFF(rptr-1)
+		rptr = rptr + MSI_NXCOEFF(msi)
+	    }
+
+	    # define the pointers to the last, 2nd last and third last rows
+	    rptrl[1] = MSI_COEFF(msi) + (MSI_NYCOEFF(msi) - 1) *
+	    	       MSI_NXCOEFF(msi)
+	    do i = 2, 3
+		rptrl[i] = rptrl[i-1] - MSI_NXCOEFF(msi)
+
+	    # define the last row by extending the columns
+	    call awsur (COEFF(rptrl[2]), COEFF(rptrl[3]), COEFF(rptrl[1]),
+	    		MSI_NXCOEFF(msi), 2., -1.)
+	    
+	case II_BIPOLY3:
+
+	    # extend the rows
+	    rptr = fptr
+	    nptr = fptr + nxpix
+	    do j = 1, nypix {
+		COEFF(rptr) = 2. * COEFF(rptr+1) - COEFF(rptr+2)
+		COEFF(nptr+1) = 2. * COEFF(nptr) - COEFF(nptr-1)
+		COEFF(nptr+2) = 2. * COEFF(nptr) - COEFF(nptr-2)
+		rptr = rptr + MSI_NXCOEFF(msi)
+		nptr = nptr + MSI_NXCOEFF(msi)
+	    }
+
+	    # define pointers to first, second and third rows
+	    rptrf[1] = MSI_COEFF(msi) 
+	    do i = 2, 3
+		rptrf[i] = rptrf[i-1] + MSI_NXCOEFF(msi)
+
+	    # extend the columns, first row
+	    call awsur (COEFF(rptrf[2]), COEFF(rptrf[3]), COEFF(rptrf[1]),
+	    		MSI_NXCOEFF(msi), 2., -1.)
+	    
+	    # define the pointers to the last to fifth last rows
+	    rptrl[1] = MSI_COEFF(msi) + (MSI_NYCOEFF(msi) - 1) *
+	    	       MSI_NXCOEFF(msi) 
+	    do i = 2, 5
+		rptrl[i] = rptrl[i-1] - MSI_NXCOEFF(msi)
+
+	    # extend the columns, define 2nd last row
+	    call awsur (COEFF(rptrl[3]), COEFF(rptrl[4]), COEFF(rptrl[2]),
+	    		MSI_NXCOEFF(msi), 2., -1.)
+	    
+	    # extend the columns, define last row
+	    call awsur (COEFF(rptrl[3]), COEFF(rptrl[5]), COEFF(rptrl[1]),
+	    		MSI_NXCOEFF(msi), 2., -1.)
+	    
+	case II_BIPOLY5:
+
+	    # extend the rows
+	    rptr = fptr
+	    nptr = fptr + nxpix
+	    do j = 1, nypix {
+		COEFF(rptr-1) = 2. * COEFF(rptr+1) - COEFF(rptr+3)
+		COEFF(rptr) = 2. * COEFF(rptr+1) - COEFF(rptr+2)
+		COEFF(nptr+1) = 2. * COEFF(nptr) - COEFF(nptr-1)
+		COEFF(nptr+2) = 2. * COEFF(nptr) - COEFF(nptr-2)
+		COEFF(nptr+3) = 2. * COEFF(nptr) - COEFF(nptr-3)
+		rptr = rptr + MSI_NXCOEFF(msi)
+		nptr = nptr + MSI_NXCOEFF(msi)
+	    }
+
+	    # define pointers to first five rows
+	    rptrf[1] = MSI_COEFF(msi) 
+	    do i = 2, 5
+		rptrf[i] = rptrf[i-1] + MSI_NXCOEFF(msi)
+
+	    # extend the columns, define first row
+	    call awsur (COEFF(rptrf[3]), COEFF(rptrf[5]), COEFF(rptrf[1]),
+	    		MSI_NXCOEFF(msi), 2., -1.)
+	    
+	    # extend the columns, define second row
+	    call awsur (COEFF(rptrf[3]), COEFF(rptrf[4]), COEFF(rptrf[2]),
+	    		MSI_NXCOEFF(msi), 2., -1.)
+	    
+	    # define pointers last seven rows
+	    rptrl[1] = MSI_COEFF(msi) + (MSI_NYCOEFF(msi) - 1) *
+	    	       MSI_NXCOEFF(msi)
+	    do i = 2, 7
+		rptrl[i] = rptrl[i-1] - MSI_NXCOEFF(msi) 
+
+	    # extend the columns, last row
+	    call awsur (COEFF(rptrl[4]), COEFF(rptrl[7]), COEFF(rptrl[1]),
+	    		MSI_NXCOEFF(msi), 2., -1.)
+
+	    # extend the columns, 2nd last row
+	    call awsur (COEFF(rptrl[4]), COEFF(rptrl[6]), COEFF(rptrl[2]),
+	    		MSI_NXCOEFF(msi), 2., -1.)
+
+	    # extend the columns, 3rd last row
+	    call awsur (COEFF(rptrl[4]), COEFF(rptrl[5]), COEFF(rptrl[3]),
+	    		MSI_NXCOEFF(msi), 2., -1.)
+
+	case II_BISPLINE3:
+		
+	    # allocate space for a temporary work arrays
+	    call calloc (tmp, MSI_NXCOEFF(msi) * MSI_NYCOEFF(msi), TY_REAL)
+
+	    # the B-spline coefficients are calculated using the
+	    # natural end conditions, end coefficents are set to
+	    # zero
+
+	    # calculate the univariate B_spline coefficients in x
+	    call ii_spline2d (COEFF(MSI_COEFF(msi)), TEMP(tmp),
+	    	nxpix, MSI_NYCOEFF(msi), MSI_NXCOEFF(msi), MSI_NYCOEFF(msi))
+
+
+	    # calculate the univariate B-spline coefficients in y to
+	    # results of x interpolation
+	    call ii_spline2d (TEMP(tmp), COEFF(MSI_COEFF(msi)),
+	        nypix, MSI_NXCOEFF(msi), MSI_NYCOEFF(msi), MSI_NXCOEFF(msi))
+
+	    # deallocate storage for temporary arrays
+	    call mfree (tmp, TY_REAL)
+	}
+end
diff --git a/math/iminterp/msifree.x b/math/iminterp/msifree.x
new file mode 100644
index 00000000..0740e2ee
--- /dev/null
+++ b/math/iminterp/msifree.x
@@ -0,0 +1,21 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+
+# MSIFREE -- Procedure to deallocate the interpolant descriptor structure.
+
+procedure msifree (msi)
+
+pointer	msi		# pointer to the interpolant descriptor structure
+errchk	mfree
+
+begin
+	# free coefficient array
+	if (MSI_COEFF(msi) != NULL)
+	    call mfree (MSI_COEFF(msi), TY_REAL)
+	if (MSI_LTABLE(msi) != NULL)
+	    call mfree (MSI_LTABLE(msi), TY_REAL)
+
+	# free interpolant descriptor
+	call mfree (msi, TY_STRUCT)
+end
diff --git a/math/iminterp/msigeti.x b/math/iminterp/msigeti.x
new file mode 100644
index 00000000..5ff14bfc
--- /dev/null
+++ b/math/iminterp/msigeti.x
@@ -0,0 +1,24 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MSIGETI -- Procedure to fetch an asi integer parameter
+
+int procedure msigeti (msi, param)
+
+pointer	msi		# interpolant descriptor
+int	param		# parameter to be fetched
+
+begin
+	switch (param) {
+	case II_MSITYPE:
+	    return (MSI_TYPE(msi))
+	case II_MSINSAVE:
+	    return (MSI_NXCOEFF(msi) * MSI_NYCOEFF(msi) + MSI_SAVECOEFF)
+	case II_MSINSINC:
+	    return (MSI_NSINC(msi))
+	default:
+	    call error (0, "MSIGETI: Unknown MSI parameter.")
+	}
+end
diff --git a/math/iminterp/msigetr.x b/math/iminterp/msigetr.x
new file mode 100644
index 00000000..7fd66597
--- /dev/null
+++ b/math/iminterp/msigetr.x
@@ -0,0 +1,20 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MSIGETR -- Procedure to fetch an msi real parameter
+
+real procedure msigetr (msi, param)
+
+pointer	msi		# interpolant descriptor
+int	param		# parameter to be fetched
+
+begin
+	switch (param) {
+	case II_MSIBADVAL:
+	    return (MSI_BADVAL(msi))
+	default:
+	    call error (0, "MSIGETR: Unknown MSI parameter.")
+	}
+end
diff --git a/math/iminterp/msigrid.x b/math/iminterp/msigrid.x
new file mode 100644
index 00000000..01d114a2
--- /dev/null
+++ b/math/iminterp/msigrid.x
@@ -0,0 +1,65 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MSIGRID -- Procedure to evaluate the interpolant on a rectangular
+# grid. The procedure assumes that 1 <= x <= nxpix and 1 <= y <= nypix.
+# The x and y vectors must be ordered such that x[i] < x[i+1] and
+# y[i] < y[i+1].
+
+procedure msigrid (msi, x, y, zfit, nx, ny, len_zfit)
+
+pointer	msi 			# pointer to interpolant descriptor structure
+real	x[ARB]			# array of x values
+real	y[ARB]			# array of y values
+real	zfit[len_zfit,ARB]	# array of fitted values
+int	nx			# number of x points
+int	ny			# number of y points
+int	len_zfit		# row length of zfit
+
+errchk	ii_grnearest, ii_grlinear, ii_grpoly3, ii_grpoly5, ii_grspline3
+errchk	ii_grsinc, ii_grlsinc, ii_grdirz
+
+begin
+
+	switch (MSI_TYPE(msi)) {
+
+	case II_BINEAREST:
+	    call ii_grnearest (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, zfit, nx, ny, len_zfit)
+
+	case II_BILINEAR:
+	    call ii_grlinear (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, zfit, nx, ny, len_zfit)
+
+	case II_BIPOLY3:
+	    call ii_grpoly3 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, zfit, nx, ny, len_zfit)
+
+	case II_BIPOLY5:
+	    call ii_grpoly5 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, zfit, nx, ny, len_zfit)
+
+	case II_BISPLINE3:
+	    call ii_grspline3 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, zfit, nx, ny, len_zfit)
+
+	case II_BISINC:
+	    call ii_grsinc (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	       MSI_NXCOEFF(msi), MSI_NYCOEFF(msi), x, y, zfit, nx, ny, len_zfit,
+	       MSI_NSINC(msi), DX, DY)
+
+	case II_BILSINC:
+	    call ii_grlsinc (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	       MSI_NXCOEFF(msi), MSI_NYCOEFF(msi), x, y, zfit, nx, ny, len_zfit,
+	       LTABLE(MSI_LTABLE(msi)), 2 * MSI_NSINC(msi) + 1, MSI_NXINCR(msi),
+	       MSI_NYINCR(msi), DX, DY)
+
+	case II_BIDRIZZLE:
+	    call ii_grdriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), MSI_NYCOEFF(msi), x, y, zfit, nx, ny,
+		len_zfit, MSI_XPIXFRAC(msi), MSI_YPIXFRAC(msi),
+		MSI_BADVAL(msi))
+	}
+end
diff --git a/math/iminterp/msigrl.x b/math/iminterp/msigrl.x
new file mode 100644
index 00000000..7baeac34
--- /dev/null
+++ b/math/iminterp/msigrl.x
@@ -0,0 +1,238 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MSIGRL -- Procedure to integrate the 2D interpolant over a specified area.
+# The x and y arrays are assumed to describe a polygon which is the domain over
+# which the integration is to be performed. The x and y must describe a closed
+# curve and npts must be >= 4 with the last vertex equal to the first vertex.
+# The routine uses the technique of separation of variables. The restriction on
+# the polygon is that horizontal lines have at most one segment in common with
+# the domain of integration. Polygons which do not fit this restriction can be
+# split into one or more polygons before calling msigrl and the results can
+# then be summed.
+
+real procedure msigrl (msi, x, y, npts)
+
+pointer	msi		# pointer to the interpolant descriptor structure
+real	x[npts]		# array of x values
+real	y[npts]		# array of y values
+int	npts		# number of points which describe the boundary
+
+int	i, interp_type, nylmin, nylmax, offset
+pointer	x1lim, x2lim, xintegrl, ptr
+real	xmin, xmax, ymin, ymax, accum
+real	ii_1dinteg()
+
+begin
+	# set up 1D interpolant type
+	switch (MSI_TYPE(msi)) {
+	case II_BINEAREST:
+	    interp_type = II_NEAREST
+	case II_BILINEAR:
+	    interp_type = II_LINEAR
+	case II_BIDRIZZLE:
+	    interp_type = II_DRIZZLE
+	case II_BIPOLY3:
+	    interp_type = II_POLY3
+	case II_BIPOLY5:
+	    interp_type = II_POLY5
+	case II_BISPLINE3:
+	    interp_type = II_SPLINE3
+	case II_BISINC:
+	    interp_type = II_SINC
+	case II_BILSINC:
+	    interp_type = II_LSINC
+	}
+
+	# set up temporary storage for x limits and the x integrals
+	call calloc (x1lim, MSI_NYCOEFF(msi), TY_REAL)
+	call calloc (x2lim, MSI_NYCOEFF(msi), TY_REAL)
+	call calloc (xintegrl, MSI_NYCOEFF(msi), TY_REAL)
+
+	# offset of first data point from edge of coefficient array
+	offset = mod (MSI_FSTPNT(msi), MSI_NXCOEFF(msi)) 
+
+	# convert the (x,y) points which describe the polygon into
+	# two arrays of x limits x1lim and x2lim and two y limits ymin and ymax
+	call ii_find_limits (x, y, npts, 0, 0, MSI_NYCOEFF(msi),
+	    Memr[x1lim+offset], Memr[x2lim+offset], ymin, ymax, nylmin, nylmax)
+	nylmin = nylmin + offset
+	nylmax = nylmax + offset
+
+	# integrate in x
+	ptr = MSI_COEFF(msi) + offset + (nylmin - 1) * MSI_NXCOEFF(msi)
+	do i = nylmin, nylmax {
+	    xmin = min (Memr[x1lim+i-1], Memr[x2lim+i-1])
+	    xmax = max (Memr[x1lim+i-1], Memr[x2lim+i-1])
+	    Memr[xintegrl+i-1] = ii_1dinteg (COEFF(ptr), MSI_NXCOEFF(msi),
+	        xmin, xmax, interp_type, MSI_NSINC(msi), DX, MSI_XPIXFRAC(msi))
+	    ptr = ptr + MSI_NXCOEFF(msi)
+	}
+
+	# integrate in y
+	if (interp_type == II_SPLINE3) {
+	    call amulkr (Memr[xintegrl], 6.0, Memr[xintegrl], MSI_NYCOEFF(msi))
+	    accum = ii_1dinteg (Memr[xintegrl+offset], MSI_NYCOEFF(msi), ymin,
+	        ymax, II_NEAREST, MSI_NSINC(msi), DY, MSI_YPIXFRAC(msi))
+	} else {
+	    accum = ii_1dinteg (Memr[xintegrl+offset], MSI_NYCOEFF(msi), ymin,
+	        ymax, II_NEAREST, MSI_NSINC(msi), DY, MSI_YPIXFRAC(msi))
+	}
+
+	# free space
+	call mfree (xintegrl, TY_REAL)
+	call mfree (x1lim, TY_REAL)
+	call mfree (x2lim, TY_REAL)
+
+	return (accum)
+end
+
+
+# II_FIND_LIMITS -- Procedure to transform a set of (x,y)'s describing a
+# polygon into a set of limits.
+
+procedure ii_find_limits (x, y, npts, xboff, xeoff, max_nylines, x1lim, x2lim,
+ymin, ymax, nylmin, nylmax)
+
+real	x[npts]		# array of x values
+real	y[npts]		# array of y values
+int	npts		# number of data points
+int	xboff, xeoff	# boundary extension limits
+int	max_nylines	# max number of lines to integrate
+real	x1lim[ARB]	# array of x1 limits
+real	x2lim[ARB]	# array of x2 limits
+real	ymin		# minimum y value for integration
+real	ymax		# maximum y value for integration
+int	nylmin		# minimum line number for x integration
+int	nylmax		# maximum line number for x integration
+
+int	i, ninter
+pointer	sp, xintr, yintr
+real	xmin, xmax, lx, ld
+int	ii_pyclip()
+
+begin
+	call smark (sp)
+	call salloc (xintr, npts, TY_REAL)
+	call salloc (yintr, npts, TY_REAL)
+
+	# find x and y limits and their indicess
+	call alimr (x, npts, xmin, xmax)
+	call alimr (y, npts, ymin, ymax)
+
+	# calculate the line limits for integration 
+	nylmin = max (1, min (int (ymin + 0.5) - xboff, max_nylines))
+	nylmax = min (max_nylines, max (1, int (ymax + 0.5) + xeoff))
+
+	# initialize
+	lx = xmax - xmin
+
+	# calculate the limits
+	for (i = nylmin; i <= nylmax; i = i + 1) {
+
+	    if (ymin > i)
+	        ld = min (i + 0.5, ymax) * lx
+	    else if (ymax < i)
+	        ld = max (i - 0.5, ymin) * lx
+	    else
+	        ld = i * lx
+	    ninter = ii_pyclip (x, y, Memr[xintr], Memr[yintr], npts, lx, ld)
+	    if (ninter <= 0) {
+		x1lim[i] = xmin
+		x2lim[i] = xmin
+	    } else {
+		x1lim[i] = min (Memr[xintr], Memr[xintr+1])
+		x2lim[i] = max (Memr[xintr], Memr[xintr+1])
+	    }
+	}
+
+	call sfree (sp)
+end
+
+
+# II_YCLIP -- Procedure to determine the intersection points of a
+# horizontal image line with an arbitrary polygon.
+
+int procedure ii_pyclip (xver, yver, xintr, yintr, nver, lx, ld)
+
+real	xver[ARB]		# x vertex coords
+real	yver[ARB]		# y vertex coords
+real	xintr[ARB]		# x intersection coords
+real	yintr[ARB]		# y intersection coords
+int	nver			# number of vertices
+real	lx, ld 			# equation of image line
+
+int	i, nintr
+real	u1, u2, u1u2, dx, dy, dd, xa, ya, wa
+
+begin
+	nintr = 0
+	u1 = - lx * yver[1] + ld
+	do i = 2, nver {
+
+	    u2 = - lx * yver[i] + ld
+	    u1u2 = u1 * u2
+
+	    # Test whether polygon line segment intersects image line or not.
+	    if (u1u2 <= 0.0) {
+
+
+		# Compute the intersection coords.
+		if (u1 != 0.0 && u2 != 0.0) {
+
+		    dy = yver[i-1] - yver[i]
+		    dx = xver[i-1] - xver[i]
+		    dd = xver[i-1] * yver[i] - yver[i-1] * xver[i]
+		    xa = (dx * ld - lx * dd)
+		    ya = dy * ld 
+		    wa = dy * lx
+		    nintr = nintr + 1
+		    xintr[nintr] = xa / wa
+		    yintr[nintr] = ya / wa
+
+		# Test for collinearity.
+		} else if (u1 == 0.0 && u2 == 0.0) {
+
+		    nintr = nintr + 1
+		    xintr[nintr] = xver[i-1]
+		    yintr[nintr] = yver[i-1]
+		    nintr = nintr + 1
+		    xintr[nintr] = xver[i]
+		    yintr[nintr] = yver[i]
+
+		} else if (u1 != 0.0) {
+
+		    if (i == 1) {
+			dy = (yver[2] - yver[1])
+			dd = (yver[nver-1] - yver[1])
+		    } else if (i == nver) {
+			dy = (yver[2] - yver[nver])
+			dd = dy * (yver[nver-1] - yver[nver])
+		    } else {
+			dy = (yver[i+1] - yver[i])
+			dd = dy * (yver[i-1] - yver[i])
+		    }
+
+		    if (dy != 0.0) {
+			nintr = nintr + 1
+			xintr[nintr] = xver[i]
+			yintr[nintr] = yver[i]
+		    }
+
+		    if (dd > 0.0) {
+			nintr = nintr + 1
+			xintr[nintr] = xver[i]
+			yintr[nintr] = yver[i]
+		    }
+
+		}
+	    }
+
+	    u1 = u2
+	}
+
+	return (nintr)
+end
diff --git a/math/iminterp/msiinit.x b/math/iminterp/msiinit.x
new file mode 100644
index 00000000..895470e4
--- /dev/null
+++ b/math/iminterp/msiinit.x
@@ -0,0 +1,69 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include	<math/iminterp.h>
+
+# MSIINIT -- Procedure to initialize the sewquential 2D image interpolation
+# package.  MSIINIT checks that the interpolant is one of the permitted
+# types and allocates space for the interpolant descriptor structure.
+# MSIINIT returns the pointer to the interpolant descriptor structure.
+
+procedure msiinit (msi, interp_type)
+
+pointer	msi		# pointer to the interpolant descriptor structure
+int	interp_type	# interpolant type
+
+int	nconv
+errchk	malloc
+
+begin
+	if (interp_type < 1 || interp_type > II_NTYPES2D) {
+	    call error (0, "MSIINIT: Illegal interpolant.")
+	} else {
+	    call calloc (msi, LEN_MSISTRUCT, TY_STRUCT)
+	    MSI_TYPE(msi) = interp_type
+	    switch (interp_type) {
+	    case II_BILSINC:
+		MSI_NSINC(msi) = NSINC
+		MSI_NXINCR(msi) = NINCR
+		if (MSI_NXINCR(msi) > 1)
+		    MSI_NXINCR(msi) = MSI_NXINCR(msi) + 1
+		MSI_NYINCR(msi) = NINCR
+		if (MSI_NYINCR(msi) > 1)
+		    MSI_NYINCR(msi) = MSI_NYINCR(msi) + 1
+		MSI_XSHIFT(msi) = INDEFR
+		MSI_YSHIFT(msi) = INDEFR
+		nconv = 2 * MSI_NSINC(msi) + 1
+		call calloc (MSI_LTABLE(msi), nconv * MSI_NXINCR(msi) * nconv *
+		    MSI_NYINCR(msi), TY_REAL)
+		call ii_bisinctable (LTABLE(MSI_LTABLE(msi)), nconv,
+		    MSI_NXINCR(msi), MSI_NYINCR(msi), MSI_XSHIFT(msi),
+		    MSI_YSHIFT(msi))
+	    case II_BISINC:
+		MSI_NSINC(msi) = NSINC
+		MSI_NXINCR(msi) = 0
+		MSI_NYINCR(msi) = 0
+		MSI_XSHIFT(msi) = INDEFR
+		MSI_YSHIFT(msi) = INDEFR
+		MSI_LTABLE(msi) = NULL
+	    case II_BIDRIZZLE:
+		MSI_NSINC(msi) = 0
+		MSI_NXINCR(msi) = 0
+		MSI_NYINCR(msi) = 0
+		MSI_XSHIFT(msi) = INDEFR
+		MSI_YSHIFT(msi) = INDEFR
+		MSI_XPIXFRAC(msi) = PIXFRAC
+		MSI_YPIXFRAC(msi) = PIXFRAC
+		MSI_LTABLE(msi) = NULL
+	    default:
+		MSI_NSINC(msi) = 0
+		MSI_NXINCR(msi) = 0
+		MSI_NYINCR(msi) = 0
+		MSI_XSHIFT(msi) = INDEFR
+		MSI_YSHIFT(msi) = INDEFR
+		MSI_LTABLE(msi) = NULL
+	    }
+	    MSI_COEFF(msi) = NULL
+	    MSI_BADVAL(msi) = BADVAL
+	}
+end
diff --git a/math/iminterp/msirestore.x b/math/iminterp/msirestore.x
new file mode 100644
index 00000000..1a6b4c1c
--- /dev/null
+++ b/math/iminterp/msirestore.x
@@ -0,0 +1,50 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include	<math/iminterp.h>
+
+# MSIRESTORE -- Procedure to restore the interpolant stored by MSISAVE
+# for use by MSIEVAL, MSIVECTOR, MSIDER and MSIGRL.
+
+procedure msirestore (msi, interpolant)
+
+pointer	msi			# interpolant descriptor
+real	interpolant[ARB]	# array containing the interpolant
+
+int	interp_type, npix
+
+begin
+	interp_type = nint (MSI_SAVETYPE(interpolant))
+	if (interp_type < 1 || interp_type > II_NTYPES)
+	    call error (0, "MSIRESTORE: Unknown interpolant type.")
+
+	# allocate the interpolant descriptor structure and restore
+	# interpolant parameters
+	call malloc (msi, LEN_MSISTRUCT, TY_STRUCT)
+	MSI_TYPE(msi) = interp_type
+	MSI_NSINC(msi) = nint (MSI_SAVENSINC(interpolant))
+	MSI_NXINCR(msi) = nint (MSI_SAVENXINCR(interpolant))
+	MSI_NYINCR(msi) = nint (MSI_SAVENYINCR(interpolant))
+	MSI_XSHIFT(msi) = MSI_SAVEXSHIFT(interpolant)
+	MSI_YSHIFT(msi) = MSI_SAVEYSHIFT(interpolant)
+	MSI_XPIXFRAC(msi) = MSI_SAVEXPIXFRAC(interpolant)
+	MSI_YPIXFRAC(msi) = MSI_SAVEYPIXFRAC(interpolant)
+	MSI_NXCOEFF(msi) = nint (MSI_SAVENXCOEFF(interpolant))
+	MSI_NYCOEFF(msi) = nint (MSI_SAVENYCOEFF(interpolant))
+	MSI_FSTPNT(msi) = nint (MSI_SAVEFSTPNT(interpolant))
+	MSI_BADVAL(msi) = MSI_SAVEBADVAL(interpolant)
+
+	# allocate space for and restore coefficients
+	call malloc (MSI_COEFF(msi), MSI_NXCOEFF(msi) * MSI_NYCOEFF(msi),
+	    TY_REAL)
+	call amovr (interpolant[1+MSI_SAVECOEFF], COEFF(MSI_COEFF(msi)),
+	    MSI_NXCOEFF(msi) * MSI_NYCOEFF(msi))
+
+	# allocate space for and restore the look-up table
+	if (MSI_NXINCR(msi) > 0 && MSI_NYINCR(msi) > 0) {
+	    npix = (2.0 * MSI_NSINC(msi) + 1) ** 2 * MSI_NXINCR(msi) *
+		MSI_NYINCR(msi)
+	    call amovr (interpolant[1+MSI_SAVECOEFF+MSI_NXCOEFF(msi) *
+	        MSI_NYCOEFF(msi)], LTABLE(MSI_LTABLE(msi)), npix)
+	}
+end
diff --git a/math/iminterp/msisave.x b/math/iminterp/msisave.x
new file mode 100644
index 00000000..109e9698
--- /dev/null
+++ b/math/iminterp/msisave.x
@@ -0,0 +1,43 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MSISAVE -- Procedure to save the interpolant for later use by MSIEVAL,
+# MSIVECTOR, MSIDER and MSIGRL.
+
+procedure msisave (msi, interpolant)
+
+pointer	msi			# interpolant descriptor
+real	interpolant[ARB]	# array containing the interpolant
+
+int	npix
+
+begin
+	# save interpolant type, number of coefficients and position of
+	# first data point
+	MSI_SAVETYPE(interpolant) = MSI_TYPE(msi)
+	MSI_SAVENSINC(interpolant) = MSI_NSINC(msi)
+	MSI_SAVENXINCR(interpolant) = MSI_NXINCR(msi)
+	MSI_SAVENYINCR(interpolant) = MSI_NYINCR(msi)
+	MSI_SAVEXSHIFT(interpolant) = MSI_XSHIFT(msi)
+	MSI_SAVEYSHIFT(interpolant) = MSI_YSHIFT(msi)
+	MSI_SAVEXPIXFRAC(interpolant) = MSI_XPIXFRAC(msi)
+	MSI_SAVEYPIXFRAC(interpolant) = MSI_YPIXFRAC(msi)
+	MSI_SAVENXCOEFF(interpolant) = MSI_NXCOEFF(msi)
+	MSI_SAVENYCOEFF(interpolant) = MSI_NYCOEFF(msi)
+	MSI_SAVEFSTPNT(interpolant) = MSI_FSTPNT(msi)
+	MSI_SAVEBADVAL(interpolant) = MSI_BADVAL(msi)
+
+	# save coefficients
+	call amovr (COEFF(MSI_COEFF(msi)), interpolant[MSI_SAVECOEFF+1],
+	    MSI_NXCOEFF(msi) * MSI_NYCOEFF(msi))
+
+	# save look-up table
+	if (MSI_NXINCR(msi) > 0 && MSI_NYINCR(msi) > 0) {
+	    npix = (2 * MSI_NSINC(msi) + 1) ** 2 *
+	        MSI_NXINCR(msi) * MSI_NYINCR(msi)
+	    call amovr (LTABLE(MSI_LTABLE(msi)), interpolant[MSI_SAVECOEFF+1+
+	        MSI_NXCOEFF(msi) * MSI_NYCOEFF(msi)], npix)
+	}
+end
diff --git a/math/iminterp/msisinit.x b/math/iminterp/msisinit.x
new file mode 100644
index 00000000..6208331c
--- /dev/null
+++ b/math/iminterp/msisinit.x
@@ -0,0 +1,91 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include	<math/iminterp.h>
+
+# MSISINIT -- Procedure to initialize the sewquential 2D image interpolation
+# package.  MSISINIT checks that the interpolant is one of the permitted
+# types and allocates space for the interpolant descriptor structure.
+# MSIINIT returns the pointer to the interpolant descriptor structure.
+
+procedure msisinit (msi, interp_type, nsinc, nxincr, nyincr, xshift, yshift,
+	badval)
+
+pointer	msi		# pointer to the interpolant descriptor structure
+int	interp_type	# interpolant type
+int	nsinc		# nsinc interpolation width
+int	nxincr, nyincr	# number of look-up table elements in x and y
+real	xshift, yshift	# the x and y shifts
+real	badval		# undefined value for drizzle interpolant
+
+int	nconv
+errchk	malloc
+
+begin
+	if (interp_type < 1 || interp_type > II_NTYPES2D) {
+	    call error (0, "MSIINIT: Illegal interpolant.")
+	} else {
+	    call calloc (msi, LEN_MSISTRUCT, TY_STRUCT)
+	    MSI_TYPE(msi) = interp_type
+	    switch (interp_type) {
+
+	    case II_BILSINC:
+		MSI_NSINC(msi) = (nsinc - 1) / 2
+		MSI_NXINCR(msi) = nxincr
+		MSI_NYINCR(msi) = nyincr
+		if (nxincr > 1) {
+		    MSI_NXINCR(msi) = MSI_NXINCR(msi) + 1
+		    MSI_XSHIFT(msi) = INDEFR
+		} else {
+		    MSI_XSHIFT(msi) = xshift
+		}
+		if (nyincr > 1) {
+		    MSI_YSHIFT(msi) = INDEFR
+		    MSI_NYINCR(msi) = MSI_NYINCR(msi) + 1
+		} else {
+		    MSI_YSHIFT(msi) = yshift
+		}
+		MSI_XPIXFRAC(msi) = PIXFRAC
+		MSI_YPIXFRAC(msi) = PIXFRAC
+		nconv = 2 * MSI_NSINC(msi) + 1
+		call calloc (MSI_LTABLE(msi), nconv * MSI_NXINCR(msi) * nconv *
+		    MSI_NYINCR(msi), TY_REAL)
+		call ii_bisinctable (LTABLE(MSI_LTABLE(msi)), nconv,
+		    MSI_NXINCR(msi), MSI_NYINCR(msi), MSI_XSHIFT(msi),
+		    MSI_YSHIFT(msi))
+
+	    case II_BISINC:
+		MSI_NSINC(msi) = (nsinc - 1) / 2
+		MSI_NXINCR(msi) = 0
+		MSI_NYINCR(msi) = 0
+		MSI_XSHIFT(msi) = INDEFR
+		MSI_YSHIFT(msi) = INDEFR
+		MSI_XPIXFRAC(msi) = PIXFRAC
+		MSI_YPIXFRAC(msi) = PIXFRAC
+		MSI_LTABLE(msi) = NULL
+
+	    case II_BIDRIZZLE:
+		MSI_NSINC(msi) = 0
+		MSI_NXINCR(msi) = 0
+		MSI_NYINCR(msi) = 0
+		MSI_XSHIFT(msi) = INDEFR
+		MSI_YSHIFT(msi) = INDEFR
+		MSI_XPIXFRAC(msi) = max (MIN_PIXFRAC, min (xshift, 1.0))
+		MSI_YPIXFRAC(msi) = max (MIN_PIXFRAC, min (yshift, 1.0))
+		MSI_LTABLE(msi) = NULL
+
+	    default:
+		MSI_NSINC(msi) = 0
+		MSI_NXINCR(msi) = 0
+		MSI_NYINCR(msi) = 0
+		MSI_XSHIFT(msi) = INDEFR
+		MSI_YSHIFT(msi) = INDEFR
+		MSI_XPIXFRAC(msi) = PIXFRAC
+		MSI_YPIXFRAC(msi) = PIXFRAC
+		MSI_LTABLE(msi) = NULL
+
+	    }
+	    MSI_COEFF(msi) = NULL
+	    MSI_BADVAL(msi) = badval
+	}
+end
diff --git a/math/iminterp/msisqgrl.x b/math/iminterp/msisqgrl.x
new file mode 100644
index 00000000..82a3122b
--- /dev/null
+++ b/math/iminterp/msisqgrl.x
@@ -0,0 +1,96 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <mach.h>
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MSISQGRL -- Procedure to integrate the 2D interpolant over a rectangular
+# region.
+
+real procedure msisqgrl (msi, x1, x2, y1, y2)
+
+pointer	msi		# pointer to the interpolant descriptor structure
+real	x1, x2		# x integration limits
+real	y1, y2		# y integration limits
+
+int	i, interp_type, nylmin, nylmax, offset 
+pointer	xintegrl, ptr
+real	xmin, xmax, ymin, ymax, accum
+real	ii_1dinteg()
+
+begin
+	# set up 1D interpolant type to match 2-D interpolant
+	switch (MSI_TYPE(msi)) {
+	case II_BINEAREST:
+	    interp_type = II_NEAREST
+	case II_BILINEAR:
+	    interp_type = II_LINEAR
+	case II_BIDRIZZLE:
+	    interp_type = II_DRIZZLE
+	case II_BIPOLY3:
+	    interp_type = II_POLY3
+	case II_BIPOLY5:
+	    interp_type = II_POLY5
+	case II_BISPLINE3:
+	    interp_type = II_SPLINE3
+	case II_BISINC:
+	    interp_type = II_SINC
+	case II_BILSINC:
+	    interp_type = II_LSINC
+	}
+
+	# set up temporary storage for x integrals
+	call calloc (xintegrl, MSI_NYCOEFF(msi), TY_REAL)
+
+	# switch order of x integration at the end
+	xmin = x1
+	xmax = x2
+	if (x2 < x1) {
+	    xmax = x2
+	    xmin = x1
+	}
+
+	# switch order of y integration at end
+	ymin = y1
+	ymax = y2
+	if (y2 < y1) {
+	    ymax = y2
+	    ymin = y1
+	}
+
+	# find the appropriate range in y in the coeff array
+	offset = mod (MSI_FSTPNT(msi), MSI_NXCOEFF(msi)) 
+	nylmin = max (1, min (MSI_NYCOEFF(msi), int (ymin + 0.5))) 
+	nylmax = min (MSI_NYCOEFF(msi), max (1, int (ymax + 0.5)))
+	nylmin = nylmin + offset
+	nylmax = nylmax + offset
+
+	# integrate in x
+	ptr = MSI_COEFF(msi) + offset + (nylmin - 1) * MSI_NXCOEFF(msi)
+	do i = nylmin, nylmax {
+	    Memr[xintegrl+i-1] = ii_1dinteg (COEFF(ptr), MSI_NXCOEFF(msi),
+	        xmin, xmax, interp_type, MSI_NSINC(msi), DX, MSI_XPIXFRAC(msi))
+	    if (x2 < x1)
+		Memr[xintegrl+i-1] = - Memr[xintegrl+i-1]
+	    ptr = ptr + MSI_NXCOEFF(msi)
+	}
+
+	# integrate in y
+	if (interp_type == II_SPLINE3) {
+	    call amulkr (Memr[xintegrl], 6.0, Memr[xintegrl],
+	        MSI_NYCOEFF(msi))
+	    accum = ii_1dinteg (Memr[xintegrl+offset], MSI_NYCOEFF(msi),
+	        ymin, ymax, II_NEAREST, MSI_NSINC(msi), DY, MSI_YPIXFRAC(msi))
+	} else
+	    accum = ii_1dinteg (Memr[xintegrl+offset], MSI_NYCOEFF(msi),
+	        ymin, ymax, II_NEAREST, MSI_NSINC(msi), DY, MSI_YPIXFRAC(msi))
+
+	# free space
+	call mfree (xintegrl, TY_REAL)
+
+	# correct for integration error.
+	if (y2 < y1)
+	    return (-accum)
+	else
+	    return (accum)
+end
diff --git a/math/iminterp/msitype.x b/math/iminterp/msitype.x
new file mode 100644
index 00000000..27bea8ac
--- /dev/null
+++ b/math/iminterp/msitype.x
@@ -0,0 +1,97 @@
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MSITYPE -- Decode the interpolation string input by the user.
+
+procedure msitype (interpstr, interp_type, nsinc, nincr, shift)
+
+char	interpstr[ARB]			# the input interpolation string
+int	interp_type			# the interpolation type
+int	nsinc				# the sinc interpolation width
+int	nincr				# the sinc interpolation lut resolution
+real	shift				# the predefined shift / pixfrac
+
+int	ip
+pointer	sp, str
+int	strdic(), strncmp(), ctoi(), ctor()
+
+begin
+	call smark (sp)
+	call salloc (str, SZ_FNAME, TY_CHAR)
+	interp_type = strdic (interpstr, Memc[str], SZ_FNAME, II_BFUNCTIONS)
+
+	# Use the default interpolant parameters.
+	if (interp_type > 0) {
+	    switch (interp_type) {
+	    case II_BILSINC:
+		nsinc = 2 * NSINC + 1
+		nincr = NINCR
+		shift = INDEFR
+	    case II_BISINC:
+		nsinc = 2 * NSINC + 1
+		nincr = 0
+		shift = INDEFR
+	    case II_BIDRIZZLE:
+		nsinc = 0
+		nincr = 0
+		shift = PIXFRAC
+	    default:
+		nsinc = 0
+		nincr = 0
+		shift = INDEFR
+	    }
+
+	# Try to decode the look-up table sinc parameters.
+	} else if (strncmp (interpstr, "lsinc", 5) == 0) {
+	    ip = 6
+	    interp_type = II_BILSINC
+	    if (ctoi (interpstr, ip, nsinc) <= 0) {
+		nsinc = 2 * NSINC + 1
+		nincr = NINCR
+		shift = INDEFR
+	    } else {
+		if (interpstr[ip] == '[')
+		    ip = ip + 1
+		if (ctor (interpstr, ip, shift) <= 0)
+		    shift = INDEFR
+		if (IS_INDEFR(shift) || interpstr[ip] != ']') {
+		    nincr = NINCR
+		    shift = INDEFR
+		} else if (shift >= -0.5 && shift < 0.5) {
+		    nincr = 1
+		} else {
+		    nincr = nint (shift)
+		    shift = INDEFR
+		}
+	    }
+
+	# Try to decode the sinc parameters.
+	} else if (strncmp (interpstr, "sinc", 4) == 0) {
+	    ip = 5
+	    interp_type = II_BISINC
+	    if (ctoi (interpstr, ip, nsinc) <= 0)
+		nsinc = 2 * NSINC + 1
+	    nincr = 0
+	    shift = INDEFR
+	} else if (strncmp (interpstr, "drizzle", 7) == 0) {
+	    ip = 8
+	    if (interpstr[ip] == '[')
+		ip = ip + 1
+	    if (ctor (interpstr, ip, shift) <= 0)
+	        shift = PIXFRAC
+	    interp_type = II_DRIZZLE
+	    nsinc = 0
+	    nincr = 0
+	    if (interpstr[ip] != ']')
+		shift = PIXFRAC
+	    else if (shift < 0.0  || shift > 1.0)
+		shift = PIXFRAC
+	} else {
+	    interp_type = 0
+	    nsinc = 0
+	    nincr = 0
+	    shift = INDEFR
+	}
+
+	call sfree (sp)
+end
diff --git a/math/iminterp/msivector.x b/math/iminterp/msivector.x
new file mode 100644
index 00000000..dcc0915d
--- /dev/null
+++ b/math/iminterp/msivector.x
@@ -0,0 +1,65 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "im2interpdef.h"
+include <math/iminterp.h>
+
+# MSIVECTOR -- Procedure to evaluate the interpolant at an array of arbitrarily
+# spaced points. The routines assume that 1 <= x <= nxpix and 1 <= y <= nypix.
+# Checking for out of bounds pixels is the responsibility of the calling
+# program.
+
+procedure msivector (msi, x, y, zfit, npts)
+
+pointer	msi		# pointer to the interpolant descriptor structure
+real	x[ARB]		# array of x values
+real	y[ARB]		# array of y values
+real	zfit[npts]	# array of interpolated values
+int	npts		# number of points to be evaluated
+
+begin
+	switch (MSI_TYPE(msi)) {
+
+	case II_BINEAREST:
+	    call ii_binearest (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, zfit, npts)
+
+	case II_BILINEAR:
+	    call ii_bilinear (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, zfit, npts)
+
+	case II_BIPOLY3:
+	    call ii_bipoly3 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, zfit, npts)
+
+	case II_BIPOLY5:
+	    call ii_bipoly5 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, zfit, npts)
+
+	case II_BISPLINE3:
+	    call ii_bispline3 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), x, y, zfit, npts)
+
+	case II_BISINC:
+	    call ii_bisinc (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), MSI_NYCOEFF(msi), x, y, zfit, npts,
+		MSI_NSINC(msi), DX, DY)
+
+	case II_BILSINC:
+	    call ii_bilsinc (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	        MSI_NXCOEFF(msi), MSI_NYCOEFF(msi), x, y, zfit, npts,
+		LTABLE(MSI_LTABLE(msi)), 2 * MSI_NSINC(msi) + 1,
+		MSI_NXINCR(msi), MSI_NYINCR(msi), DX, DY)
+
+	case II_BIDRIZZLE:
+	    if (MSI_XPIXFRAC(msi) >= 1.0 && MSI_YPIXFRAC(msi) >= 1.0)
+	        call ii_bidriz1 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	            MSI_NXCOEFF(msi), x, y, zfit, npts, MSI_BADVAL(msi))
+	    #else if (MSI_XPIXFRAC(msi) <= 0.0 && MSI_YPIXFRAC(msi) <= 0.0)
+	        #call ii_bidriz0 (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	            #MSI_NXCOEFF(msi), x, y, zfit, npts, MSI_BADVAL(msi))
+	    else
+	        call ii_bidriz (COEFF(MSI_COEFF(msi)), MSI_FSTPNT(msi),
+	            MSI_NXCOEFF(msi), x, y, zfit, npts, MSI_XPIXFRAC(msi),
+		    MSI_YPIXFRAC(msi), MSI_BADVAL(msi))
+	}
+end
diff --git a/math/interp/Iinterp.hlp b/math/interp/Iinterp.hlp
new file mode 100644
index 00000000..527f0375
--- /dev/null
+++ b/math/interp/Iinterp.hlp
@@ -0,0 +1,293 @@
+
+.help INTERP Jan83 "Image Interpolation Package"
+.sh
+Introduction
+
+     One of the most common operations in image processing is interpolation.
+Due to the very large amount of data involved, efficiency is quite important,
+and the general purpose routines available from many sources cannot be used.
+
+
+The task of interpolating image data is simplified by the following
+considerations:
+.ls 4
+.ls o
+The pixels (data points) are equally spaced along a line or on a rectangular
+grid.
+.le
+.ls o
+There is no need for coordinate transformations.  The coordinates of a pixel
+or point to be interpolated are the same as the subscript of the pixel in the
+data array.  The coordinate of the first pixel in the array may be assumed
+to be 1.0, and the spacing between pixels is also 1.0.
+.le
+.le
+
+
+The task of interpolating image data is complicated by the following
+considerations:
+.ls
+.ls o
+We would like the "quality" of the interpolator to be something that can
+be set at run time by the user.  This is done by permitting the user to
+select the type of interpolator to be used, and the order of interpolation.
+The following interpolators will be provided:
+
+.nf
+    - nearest neighbor
+    - linear
+    - natural cubic spline
+    - divided differences, either 3rd or 5th order.
+.fi
+.le
+.ls o
+The interpolator must be able to deal with indefinite valued pixels.
+In the IRAF, an indefinite valued pixel has the special value INDEF.
+If the interpolator cannot return a meaningful interpolated value
+(due to the presence of indefinite pixels in the data, or because the
+coordinates of the point to be interpolated are out of bounds) the value
+INDEF should be returned instead.
+.le
+.le
+
+.sh
+Sequential Interpolation of One Dimensional Arrays
+
+     Ideally, we should be able to define a single set of procedures
+which can perform interpolation by any of the techniques mentioned above.
+The procedures for interpolating one dimensional arrays are optimized
+for the case where the entire array is to be sampled, probably in a sequential
+fashion.
+
+The following calls should suffice.  The package prefix is "asi", meaning
+array sequential interpolate, and the last three letters of each procedure
+name are used to describe the action performed by the procedure.  The
+interpolator is restricted to single precision real data, so there is no
+need for a type suffix.
+
+.ks
+.nf
+	asiset (coeff, interpolator_type, boundary_type)
+	asifit (data, npts, coeff)
+    y =	asival (x, coeff)			# evaluate y(x)
+	asider (x, derivs, nderiv, coeff)	# derivatives
+    v = asigrl (x1, x2, coeff)			# take integral
+.fi
+.ke
+
+Here, COEFF is a structure used to describe the interpolant, and 
+the interpolator type is chosen from the following set of options:
+
+.ks
+.nf
+	NEAREST		return value of nearest neighbor
+	LINEAR		linear interpolation
+	DIVDIF3		third order divided differences
+	DIVDIF5		fifth order divided differences
+	SPLINE3		cubic spline
+.fi
+.ke
+
+When the VAL procedure is called to evaluate the interpolant at a point X,
+the code must check to see if X is out of bounds.  If so, the type of value
+returned may be specified by the third and final argument to the SET procedure.
+
+.ks
+.nf
+	B_NEAREST	return nearest boundary (nb) value
+	B_INDEF		(default; return indefinite)
+	B_REFLECT	interpolate at abs(x)
+	B_WRAP		wrap around to opposite boundary
+	B_PROJECT	return y(nb) - (y(abs(x)) - y(nb))
+.fi
+.ke
+
+For example, the following subset preprocessor code fragment uses
+the array interpolation routines to shift a data array by a constant
+amount:
+
+
+.ks
+.nf
+	real	shift, coeff[NPIX+SZ_ASIHDR]
+	real	inrow[NPIX], outrow[NPIX], asival()
+	int	i, interpolator_type, boundary_type, clgeti()
+
+	begin
+		# get parameters from CL, setup interpolator
+		interpolator_type = clgeti ("interpolator")
+		boundary_type = clgeti ("boundary_type")
+		call asiset (coeff, interpolator_type, boundary_type)
+
+		[code to read pixels into inrow]
+		call asifit (inrow, NPIX, coeff)
+
+		do i = 1, NPIX			# do the interpolation
+		    outrow[i] = asival (i + shift, coeff)
+.fi
+.ke
+
+
+The array COEFF is actually a simple structure.  An initial call to ASISET
+is required to save the interpolator parameters in the COEFF structure.
+ASIFIT computes the coefficients of the interpolator curve, leaving the 
+coefficients in the appropriate part of the COEFF structure.  Thereafter,
+COEFF is read only.  ASIVAL evaluates the zeroth derivative of the curve
+at the given X coordinate.  ASIDER evaluates the first NDERIV derivatives
+at X, writing the values of these derivatives into the DERIVS output array.
+ASIGRL integrates the interpolant over the indicated range (returning INDEF
+if there are any indefinite pixels in that range).
+
+.ks
+.nf
+	    element			usage
+
+	       1		type of interpolator
+	       2		type of boundary condition
+	       3		number of pixels in x
+	       4		number of pixels in y
+	      5-9		reserved for future use
+	     10-N		coefficients
+
+		    The COEFF structure
+.fi
+.ke
+
+
+In the case of the nearest neighbor and linear interpolation algorithms,
+the coefficient array will contain the same data as the input data array.
+The cubic spline algorithm requires space for NPIX+2 b-spline coefficients.
+The space requirements of the divided differences algorithm are similar.
+The constant SZ_ASIHDR should allow enough space for the worst case.
+
+Note that both 3rd and 5th order divided differences interpolators are
+provided, but only the 3rd order (cubic) spline.  This is because the
+5th order spline is considerably harder than the cubic spline.  We can easily
+add a 5th order spline, or indeed a completely new algorithm such as the sinc
+function interpolator, without changing the calling sequences or data
+structures.
+
+.sh
+Random Interpolation of One Dimensional Arrays
+
+     If we wish only to interpolate a small region of an array, or a few
+points scattered along the array at random, or if memory space is more
+precious than execution speed, then a different sort of interpolator is
+desirable.  We can dispense with the coefficient array in this case, and
+operate directly on the data array.
+
+.ks
+.nf
+	ariset (interpolator_type, boundary_type)
+	arifit (data, npts)
+    y =	arival (x, data)
+	arider (x, derivs, nderiv, data)
+.fi
+.ke
+
+Since the number of points required to interpolate at a given X value
+is fixed, these routines are internally quite different than the sequential
+procedures.
+
+.sh
+Sequential Interpolation of Two Dimensional Arrays
+
+     None of the interpolation algorithms mentioned above are difficult
+to generalize to two dimensions.  The calling sequences should be kept as
+similar as possible.  The sequential two dimensional procedures are limited
+by the size of the two dimensional array which can be kept in memory, and 
+therefore are most useful for subrasters.  The COEFF array should be
+declared as a one dimensional array, even though it used to store a two
+dimensional array of coefficients.
+
+.ks
+.nf
+	msiset (coeff, interpolator_type), boundary_type)
+	msifit (data, nx, ny, coeff)
+    y =	msival (x, y, coeff)
+	msider (x, y, derivs, nderiv, coeff)
+.fi
+.ke
+
+Note that the coefficients of the bicubic spline are obtained by first
+doing a one dimensional spline fit to the rows of the data array, leaving
+the resultant coefficients in the rows of the coeff array, followed by
+a series of one dimensional fits to the coefficients in the coeff array.
+The row coefficients are overwritten by the coefficients of the tensor
+product spline.  Since all the work is done by the one dimensional spline
+fitting routine, little extra code is required to handle the two dimensional
+case.
+
+The bicubic spline is evaluated by summing the product C(i,j)*Bi(x)*Bj(y)
+at each of the sixteen coefficients contributing to the point (x,y).
+Once again, the one dimensional routines for evaluating the b-spline
+(the functions Bi(x) and Bj(y)) do most of the work.
+
+Although it is not required by very many applications, it would also
+be useful to be able to compute the surface integral of the interpolant
+over an arbitrary surface (this is useful for surface photometry
+applications).  Never having done this, I do not have any recommendations
+on how to set up the calling sequence.
+
+.sh
+Random Interpolation of Two Dimensional Arrays
+
+     The random interpolation procedures are particularly useful for two
+dimensional arrays due to the increased size of the arrays.  Also, if an
+application generally finds linear interpolation to be sufficient, and rarely
+uses a more expensive interpolator, the random routines will be more
+efficient overall.
+
+.ks
+.nf
+	mriset (interpolator_type, boundary_type)
+	msifit (data, nx, ny)
+    y = mrival (x, y, data)
+	mrider (x, y, derivs, nderiv, data)
+.fi
+.ke
+
+.sh
+Cardinal B-Splines
+
+     There are many different kinds of splines.  One of the best
+for the case where the data points are equally spaced is the cardinal spline.
+The so called "natural" end point conditions are probably the best one can
+do with noisy data.  Other end point conditions, such as not-a-knot, may be
+best for approximating analytic functions, but they are unreliable with
+noisy data.  The natural cubic cardinal spline is fitted by solving the
+following tridiagonal system of equations (Prenter, 1975).
+
+
+.ks
+.nf
+	/				  :		\
+	| 6  -12    6		          :	0	|
+	| 1    4    1		          :	y(1)	|
+	|      1    4    1		  :	y(2)	|
+	| 	     ...		  :		|
+	| 		1    4    1       :	y(n-1)	|
+	| 		     1    4    1  :	y(n)	|
+	| 		     6   -12   6  :	0	|
+	\				  :		/
+.fi
+.ke
+
+
+This matrix can most efficiently be solved by hardwiring the appropriate
+recursion relations into a procedure.  The problem of what to do when some
+of the Y(i) are indefinite has not yet been solved.
+
+The b-spline basis function used above is defined by
+
+.ks
+.nf
+	B(x) = (x-x1)**3				x:[x1,x2]
+	B(x) = 1 + 3(x-x2) + 3(x-x2)**2 - 3(x-x2)**3	x:[x2,x3]
+	B(x) = 1 + 3(x3-x) + 3(x3-x)**2 - 3(x3-x)**3	x:[x3,x4]
+	B(x) = (x4-x)**3				x:[x4,x5]
+.fi
+.ke
+
+where X1 through X4 are the X coordinates of the four b-spline
+coefficients contributing to the b-spline function at X.
diff --git a/math/interp/README b/math/interp/README
new file mode 100644
index 00000000..915afd6e
--- /dev/null
+++ b/math/interp/README
@@ -0,0 +1,7 @@
+Image interpolation package.  Contains interpolator routines specially
+designed to interpolate image data.  This interpolator task is characterized
+by data arrays in which the data points are equally spaced.  Data points
+and interpolation points are referenced simply by array index.  Indefinite
+valued pixels may be present in the data.  Since the interpolation routines
+will be applied to very large data arrays, efficiency is emphasized in these
+routines.
diff --git a/math/interp/arbpix.x b/math/interp/arbpix.x
new file mode 100644
index 00000000..0b61f3d2
--- /dev/null
+++ b/math/interp/arbpix.x
@@ -0,0 +1,203 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+.help
+		arbpix -- fix bad data
+
+Takes care of bad pixels by replacing the indef's with interpolated values.
+
+In order to replace bad points, the spline interpolator uses a limited
+data array, the maximum total length is given by SPLPTS.  
+
+The process is divided as follows:
+	1. Take care of points below first good point and above last good
+	   good point.
+	2. Load an array with only good points.
+	3. Interpolate that array.
+
+.endhelp
+
+procedure arbpix(datain,n,dataout,terptype)
+include "interpdef.h"
+include "asidef.h"
+
+real datain[ARB]		# data in array
+int n				# no. of data points
+real dataout[ARB]		# data out array - cannot be same as data in
+int terptype			# interpolator type - see interpdef.h
+
+int i, badnc 
+int k, ka, kb
+
+real iirbfval()
+
+begin
+
+	# count bad points
+	badnc = 0
+	do i = 1,n
+	    if (IS_INDEFR (datain[i]))
+		badnc = badnc + 1
+
+	# return if all bad or all good
+	if(badnc == n || badnc == 0)
+	    return
+
+	
+	# find first good point
+	for (ka = 1;  IS_INDEFR (datain[ka]);  ka = ka + 1)
+	    ;
+
+	# bad points below first good point are set at first value
+	do k = 1,ka-1
+	    dataout[k] = datain[ka]
+	
+	# find last good point
+	for (kb = n;  IS_INDEFR (datain[kb]);  kb = kb - 1)
+	    ;
+
+	# bad points beyond last good point get set at last value
+	do k = n, kb+1, -1
+	    dataout[k] = datain[kb]
+
+	# load the other points interpolating the bad points as needed
+	do k = ka, kb {
+	    if (!IS_INDEFR (datain[k]))		# good point
+		dataout[k] = datain[k]
+
+	    else 		# bad point -- generate interpolated value
+		dataout[k] = iirbfval(datain[ka],kb-ka+1,k-ka+1,terptype)
+	}
+
+end
+
+# This part fills a temporary array with good points that bracket the
+# bad point and calls the interpolating routine.
+
+real procedure iirbfval(y, n, k, terptype)
+
+real y[ARB]	# data_in array, y[1] and y[n] guaranteed to be good.
+int n		# length of data_in array.
+int k		# index of bad point to replace.
+int terptype
+
+int  j, jj,  pd, pu, tk, pns
+real td[SPLPTS], tx[SPLPTS]	# temporary arrays for interpolation
+
+real iirbint()
+
+begin
+	# The following test is done to improve speed.
+	# This code will work only if subroutines are implemented by
+	#    using static storage - i.e. the old internal values survive.
+	# This avoids reloading of temporary arrays if
+	#    there are consequetive bad points.
+
+	if (!IS_INDEFR (y[k-1])) {
+	    # set number of good points needed on each side of bad point
+	    switch (terptype) {
+	    case IT_NEAREST :
+		pns = 1
+	    case IT_LINEAR :
+		pns = 1
+	    case IT_POLY3 :
+		pns = 2
+	    case IT_POLY5 :
+		pns = 3
+	    case IT_SPLINE3 :
+		pns = SPLPTS / 2
+	    }
+
+	    # search down
+	    pd = 0
+	    for (j = k-1; j >= 1 && pd < pns; j = j-1)
+		if (!IS_INDEFR (y[j]))
+		    pd = pd + 1
+
+	    # load temp. arrays for values below our indef.
+	    tk = 0
+	    for(jj = j + 1; jj < k; jj = jj + 1)
+		if (!IS_INDEFR (y[jj])) {
+		    tk = tk + 1
+		    td[tk] = y[jj]
+		    tx[tk] = jj
+		}
+
+	     # search and load up from indef.
+	     pu = 0
+	     for (j = k + 1; j <= n && pu < pns; j = j + 1)
+		if (!IS_INDEFR (y[j])) {
+		     pu = pu + 1
+		     tk = tk + 1
+		     td[tk] = y[j]
+		     tx[tk] = j
+		 }
+	 }
+
+	 # return value interpolated from these arrays.
+	 return(iirbint(real(k), tx, td, tk, pd, terptype))
+
+end
+
+
+# This part interpolates the temporary arrays.
+# It does not represent a general purpose routine because the
+# previous part has determined the proper indices etc. so that
+# effort is not duplicated here.
+
+real procedure iirbint (x, tx, td, tk, pd, terptype)
+
+real	x		# point to interpolate
+real	tx[ARB]		# xvalues
+real	td[ARB]		# data values
+int 	tk		# size of data array
+int	pd		# index such that tx[pd] < x < tx[pd+1]
+int 	terptype
+
+int  i, ks, tpol
+real cc[4,SPLPTS]
+real h
+
+real iipol_terp()
+
+begin
+	switch (terptype) {
+
+	case IT_NEAREST :
+	    if (x - tx[1] > tx[2] - x)
+		return(td[2])
+	     else
+		return(td[1])
+
+	case IT_LINEAR :
+	    return(td[1] + (x - tx[1]) *
+			     (td[2] - td[1]) / (tx[2] - tx[1]))
+
+	case IT_SPLINE3 :
+	    do i = 1,tk
+		cc[1,i] = td[i]
+	    cc[2,1] = 0.
+	    cc[2,tk] = 0.
+
+	     # use spline routine from C. de Boor's book
+	     # A Practical Guide to Splines
+	     call cubspl(tx,cc,tk,2,2)
+	     h = x - tx[pd]
+	     return(cc[1,pd] + h * (cc[2,pd] + h *
+			       (cc[3,pd] + h * cc[4,pd]/3.)/2.))
+
+	default :	# one of the polynomial types
+	    # allow lower order if not enough points on one side
+	    tpol = tk
+	    ks = 1
+	    if (tk - pd < pd) {
+		tpol = 2 * (tk - pd)
+		ks = 2 * pd - tk + 1
+	    }
+	    if (tk - pd > pd)
+		tpol = 2 * pd
+
+	    # finally polynomial interpolate
+	    return(iipol_terp(tx[ks], td[ks], tpol, x))
+	}
+
+end
diff --git a/math/interp/arider.x b/math/interp/arider.x
new file mode 100644
index 00000000..fef55e0e
--- /dev/null
+++ b/math/interp/arider.x
@@ -0,0 +1,214 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+.help
+	arider -- random interpolator returns derivatives
+
+First looks at type of interpolator requested, then calls routine
+to evaluate.
+No error traps are included -- unreasonable values for the number of
+data points or the x position will either produce hard errors or garbage.
+
+.endhelp
+
+procedure arider(x, datain, n, derivs, nderiv,  interptype)
+include "interpdef.h"
+
+real	x		# need 1 <= x <= n
+real	datain[ARB]	# data values
+int	n		# number of data values
+real	derivs[ARB]	# derivatives out -- beware derivs[1] is 
+			#		function value
+int	nderiv		# total number of values returned in derivs
+int	interptype
+
+int	i, j, k, nt, nd, nx
+real	pc[6], ac, s
+
+begin
+	if(nderiv <= 0)
+	    return
+
+	# zero out derivs array
+	do i = 1, nderiv
+	    derivs[i] = 0.
+
+	switch (interptype) {
+	case IT_NEAREST :
+	    derivs[1] = datain[int(x + 0.5)]
+	    return
+	case IT_LINEAR :
+	    nx = x
+	    if( nx >= n )
+		nx = nx - 1
+	    derivs[1] = (x - nx) * datain[nx+1] + (nx + 1 - x) * datain[nx]
+	    if(nderiv >= 2)
+		derivs[2] = datain[nx+1] - datain[nx]
+	    return
+	# The other cases call subroutines to generate polynomial coeff.
+	case IT_POLY3 :
+	    call iidr_poly3(x, datain, n, pc)
+	    nt = 4
+	case IT_POLY5 :
+	    call iidr_poly5(x, datain, n, pc)
+	    nt = 6
+	case IT_SPLINE3 :
+	    call iidr_spline3(x, datain, n, pc)
+	    nt = 4
+	}
+
+	nx = x
+	s = x - nx
+	nd = nderiv
+	if (nderiv > nt)
+	    nd = nt
+
+	do k = 1,nd {	
+	    ac = pc[nt - k + 1]		# evluate using nested multiplication
+	    do j = nt - k, 1, -1
+		ac = pc[j] + s * ac
+
+	    derivs[k] = ac
+
+	    do j = 1, nt - k		# differentiate
+		pc[j] = j * pc[j + 1]
+	}
+end
+
+procedure iidr_poly3(x, datain, n, pc)
+
+real	x
+real	datain[ARB]
+int	n
+real	pc[ARB]
+
+int 	i, k, nx, nt
+real	a[4]
+
+begin
+
+	nx = x
+
+	# The major complication is that near the edge interior polynomial
+	# must somehow be defined.
+	k = 0
+	for(i = nx - 1; i <= nx + 2; i = i + 1){
+	    k = k + 1
+	    # project data points into temporary array
+	    if ( i < 1 )
+		a[k] = 2. * datain[1] - datain[2 - i]
+	    else if ( i > n )
+		a[k] = 2. * datain[n] - datain[2 * n - i]
+	    else
+		a[k] = datain[i]
+	}
+
+	nt = 4
+
+	# generate diffrence table for Newton's form
+	do k = 1, nt-1
+	    do i = 1, nt-k
+		a[i] = (a[i+1] - a[i]) / k
+	
+	# shift to generate polynomial coefficients
+	do k = nt,2,-1
+	    do i = 2,k
+		a[i] = a[i] + a[i-1] * (k - i - nt/2)
+	
+	do i = 1,nt
+	    pc[i] = a[nt+1-i]
+	
+	return
+
+end
+
+procedure iidr_poly5(x, datain, n, pc)
+
+real	x
+real	datain[ARB]
+int	n
+real	pc[ARB]
+
+int 	i, k, nx, nt
+real	a[6]
+
+begin
+
+	nx = x
+
+	# The major complication is that near the edge interior polynomial
+	# must somehow be defined.
+	k = 0
+	for(i = nx - 2; i <= nx + 3; i = i + 1){
+	    k = k + 1
+	    # project data points into temporary array
+	    if ( i < 1 )
+		a[k] = 2. * datain[1] - datain[2 - i]
+	    else if ( i > n )
+		a[k] = 2. * datain[n] - datain[2 * n - i]
+	    else
+		a[k] = datain[i]
+	}
+
+	nt = 6
+
+	# generate diffrence table for Newton's form
+	do k = 1, nt-1
+	    do i = 1, nt-k
+		a[i] = (a[i+1] - a[i]) / k
+	
+	# shift to generate polynomial coefficients
+	do k = nt,2,-1
+	    do i = 2,k
+		a[i] = a[i] + a[i-1] * (k - i - nt/2)
+	
+	do i = 1,nt
+	    pc[i] = a[nt+1-i]
+	
+	return
+
+end
+
+procedure iidr_spline3(x, datain, n, pc)
+
+real	x
+real	datain[ARB]
+int	n
+real	pc[ARB]
+
+int 	i, k, nx, px
+real	temp[SPLPTS+2], bcoeff[SPLPTS+2],  h
+
+begin
+
+	nx = x
+
+	h = x - nx
+	k = 0
+	# maximum number of points used is SPLPTS
+	for(i = nx - SPLPTS/2 + 1; i <= nx + SPLPTS/2; i = i + 1){
+	    if(i < 1 || i > n)
+		;
+	    else {
+		k = k + 1
+		if(k == 1)
+		    px = nx - i + 1
+		bcoeff[k+1] = datain[i]
+	    }
+	}
+
+	bcoeff[1] = 0.
+	bcoeff[k+2] = 0.
+
+	# Use special routine for cardinal splines.
+	call iif_spline(bcoeff, temp, k)
+
+	px = px + 1
+
+	pc[1] = bcoeff[px-1] + 4. * bcoeff[px] + bcoeff[px+1]
+	pc[2] = 3. * (bcoeff[px+1] - bcoeff[px-1])
+	pc[3] = 3. * (bcoeff[px-1] - 2. * bcoeff[px] + bcoeff[px+1])
+	pc[4] = -bcoeff[px-1] + 3. * bcoeff[px] - 3. * bcoeff[px+1] +
+				    bcoeff[px+2]
+		
+	return
+end
diff --git a/math/interp/arival.x b/math/interp/arival.x
new file mode 100644
index 00000000..50ee1c3e
--- /dev/null
+++ b/math/interp/arival.x
@@ -0,0 +1,124 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+.help
+		arival -- random interpolator returns value
+
+No error traps are included -- unreasonable values for the number of
+data points or the x position will either produce hard errors or garbage.
+This version is written in-line for speed.
+
+.endhelp
+
+real procedure arival(x, datain, n, interptype)
+include "interpdef.h"
+
+real	x		# need 1 <= x <= n
+real	datain[ARB]	# data values
+int	n		# number of data values
+int	interptype
+
+int 	i, k, nx, px
+real	a[6], cd20, cd21, cd40, cd41, s, t, h
+real	bcoeff[SPLPTS+2], temp[SPLPTS+2], pc[4]
+
+begin
+	switch (interptype) {
+	case IT_NEAREST :
+	    return(datain[int(x + 0.5)])
+	case IT_LINEAR :
+	    nx = x
+	    # protect against x = n case
+	    # else it will reference datain[n + 1]
+	    if(nx >= n)
+		nx = nx - 1
+	    return((x - nx) * datain[nx+1] + (nx + 1 - x) * datain[nx])
+	case IT_POLY3 :
+	    nx = x
+
+	    # The major complication is that near the edge interior polynomial
+	    # must somehow be defined.
+	    k = 0
+	    for(i = nx - 1; i <= nx + 2; i = i + 1){
+		k = k + 1
+		# project data points into temporary array
+		if ( i < 1 )
+		    a[k] = 2. * datain[1] - datain[2 - i]
+		else if ( i > n )
+		    a[k] = 2. * datain[n] - datain[2 * n - i]
+		else
+		    a[k] = datain[i]
+	    }
+
+	    s = x - nx
+	    t = 1. - s
+
+	    # second central differences
+	    cd20 = 1./6. * (a[3] - 2. * a[2] + a[1])
+	    cd21 = 1./6. * (a[4] - 2. * a[3] + a[2])
+
+	    return( s * (a[3] + (s * s - 1.) * cd21) +
+		    t * (a[2] + (t * t - 1.) * cd20) )
+	case IT_POLY5 :
+	    nx = x
+
+	    # The major complication is that near the edge interior polynomial
+	    # must somehow be defined.
+	    k = 0
+	    for(i = nx - 2; i <= nx + 3; i = i + 1){
+		k = k + 1
+		# project data points into temporary array
+		if ( i < 1 )
+		    a[k] = 2. * datain[1] - datain[2 - i]
+		else if ( i > n )
+		    a[k] = 2. * datain[n] - datain[2 * n - i]
+		else
+		    a[k] = datain[i]
+	    }
+
+	    s = x - nx
+	    t = 1. - s
+
+	    # second central differences
+	    cd20 = 1./6. * (a[4] - 2. * a[3] + a[2])
+	    cd21 = 1./6. * (a[5] - 2. * a[4] + a[3])
+
+	    # fourth central differences
+	    cd40 = 1./120. * (a[1] - 4. * a[2] + 6. * a[3] - 4. * a[4] + a[5])
+	    cd41 = 1./120. * (a[2] - 4. * a[3] + 6. * a[4] - 4. * a[5] + a[6])
+
+	    return( s * (a[4] + (s * s - 1.) * (cd21 + (s * s - 4.) * cd41)) +
+		    t * (a[3] + (t * t - 1.) * (cd20 + (t * t - 4.) * cd40)) )
+	case IT_SPLINE3 :
+	    nx = x
+
+	    h = x - nx
+	    k = 0
+	    # maximum number of points used is SPLPTS
+	    for(i = nx - SPLPTS/2 + 1; i <= nx + SPLPTS/2; i = i + 1){
+		if(i < 1 || i > n)
+		    ;
+		else {
+		    k = k + 1
+		    if(k == 1)
+			px = nx - i + 1
+		    bcoeff[k+1] = datain[i]
+		}
+	    }
+
+	    bcoeff[1] = 0.
+	    bcoeff[k+2] = 0.
+
+	    # Use special routine for cardinal splines.
+	    call iif_spline(bcoeff, temp, k)
+
+	    px = px + 1
+
+	    pc[1] = bcoeff[px-1] + 4. * bcoeff[px] + bcoeff[px+1]
+	    pc[2] = 3. * (bcoeff[px+1] - bcoeff[px-1])
+	    pc[3] = 3. * (bcoeff[px-1] - 2. * bcoeff[px] + bcoeff[px+1])
+	    pc[4] = -bcoeff[px-1] + 3. * bcoeff[px] - 3. * bcoeff[px+1] +
+					bcoeff[px+2]
+		    
+	    return(pc[1] + h * (pc[2] + h * (pc[3] + h * pc[4])))
+	}
+end
diff --git a/math/interp/asidef.h b/math/interp/asidef.h
new file mode 100644
index 00000000..9fd06084
--- /dev/null
+++ b/math/interp/asidef.h
@@ -0,0 +1,16 @@
+# defines for use with interpolator package
+# intended for internal consumption only
+# used to set up storage in coeff array
+
+define	TYPEI		coeff[1]	# code for interpolator type
+define	NPTS		coeff[2]	# no. of data points
+
+define	ITYPEI		int(coeff[1])
+define	INPTS		int(coeff[2])
+
+define ASITYPEERR	1
+define ASIFITERR	2
+
+define COFF		10		# offset into coeff array
+					# beware coeff[COFF - 2] is first
+					# location used !!
diff --git a/math/interp/asider.x b/math/interp/asider.x
new file mode 100644
index 00000000..2c9a2819
--- /dev/null
+++ b/math/interp/asider.x
@@ -0,0 +1,121 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+.help
+		procedure asider
+
+     This procedure finds derivatives assuming that x lands in
+array i.e. 1 <= x <= npts.
+It must be called by a routine that checks for out of bound references
+and takes care of bad points and checks to make sure that the number
+of derivatives requested is reasonable (max. is 5 derivatives or nder
+can be 6 at most and min. nder is 1)
+
+     This version assumes interior polynomial interpolants are stored as
+the data points with corections for bad points, and the spline interpolant
+is stored as a series of b-spline coefficients.
+
+     The storage and evaluation for nearest neighbor and linear interpolation
+are simpler so they are evaluated separately from other piecewise
+polynomials.
+.endhelp
+
+procedure asider(x,der,nder,coeff)
+include "interpdef.h"
+include "asidef.h"
+
+real x
+real coeff[ARB]
+int nder		# no. items returned = 1 + no. of deriv.
+
+real der[ARB]		# der[1] is value der[2] is f prime etc.
+
+int nx,n0,i,j,k,nt,nd
+real s,ac,pc[6],d[6]
+
+begin
+	do i = 1, nder   # return zero for derivatives that are zero
+	    der[i] = 0.
+
+	nt = 0    # nt is number of terms in case polynomial type
+
+	switch (ITYPEI)	{	# switch on interpolator type
+	
+	case IT_NEAREST :
+	    der[1] = (coeff[COFF + nint(x)])
+	    return
+
+	case IT_LINEAR :
+	    nx = x
+	    der[1] = (x - nx) * coeff[COFF + nx + 1] +
+		(nx + 1 - x) * coeff[COFF + nx]
+	    if ( nder > 1 )		# try to return exact number requested
+		der[2] = coeff[COFF + nx + 1] - coeff[COFF + nx]
+	    return
+
+	case IT_POLY3 :
+	    nt = 4
+
+	case IT_POLY5 :
+	    nt = 6
+
+	case IT_SPLINE3 :
+	    nt = 4
+
+	}
+
+	# falls through to here if interpolant is one of
+	# the higher order polynomial types or third order spline
+
+	nx = x
+	n0 = COFF + nx
+	s = x - nx
+
+	nd = nder		# no. of derivatives needed
+	if ( nder > nt )
+	    nd = nt
+
+	# generate polynomial coefficients, first for spline.
+	if (ITYPEI == IT_SPLINE3) {
+	    pc[1] = coeff[n0-1] + 4. * coeff[n0] + coeff[n0+1]
+	    pc[2] = 3. * (coeff[n0+1] - coeff[n0-1])
+	    pc[3] = 3. * (coeff[n0-1] - 2. * coeff[n0] + coeff[n0+1])
+	    pc[4] = -coeff[n0-1] + 3. * coeff[n0] - 3. * coeff[n0+1] +
+				    coeff[n0+2]
+		
+	} else {
+
+	# Newton's form written in line to get polynomial from data
+	    # load data
+	    do i = 1,nt
+		d[i] = coeff[n0 - nt/2 + i]
+
+	    # generate difference table
+	    do k = 1, nt-1
+		do i = 1,nt-k
+		    d[i] = (d[i+1] - d[i]) / k
+
+	    # shift to generate polynomial coefficients of (x - n0)
+	    do k = nt,2,-1
+		do i = 2,k
+		    d[i] = d[i] + d[i-1] * (k - i - nt/2)
+
+	    do i = 1,nt
+		pc[i] = d[nt + 1 - i]
+	}
+
+	do k = 1,nd {  # as loop progresses pc contains coefficients of
+			# higher and higher derivatives
+
+	    ac = pc[nt - k + 1]
+	    do j = nt - k, 1, -1	# evaluate using nested mult.
+		ac = pc[j] + s * ac
+
+	    der[k] = ac
+
+	    do j = 1,nt - k 	# differentiate polynomial
+		pc[j] = j * pc[j + 1]
+	}
+
+	return
+
+end
diff --git a/math/interp/asieva.x b/math/interp/asieva.x
new file mode 100644
index 00000000..bc5fcbb3
--- /dev/null
+++ b/math/interp/asieva.x
@@ -0,0 +1,38 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# procedure to evaluate interpolator at a sequence of ordered points
+# aasumes that all x_values land within [1,n].
+
+procedure asieva(x, y, n, coeff)
+include "interpdef.h"
+include "asidef.h"
+
+real x[ARB]			# ordered x array
+int n				# no. of points in x
+real coeff[ARB]
+
+real y[ARB]			# interpolated values
+
+begin
+	switch (ITYPEI)	{	# switch on interpolator type
+	
+	case IT_NEAREST :
+	    call iievne(x, y, n, coeff[COFF + 1])
+
+	case IT_LINEAR :
+	    call iievli(x, y, n, coeff[COFF + 1])
+
+	case IT_POLY3 :
+	    call iievp3(x, y, n, coeff[COFF + 1])
+
+	case IT_POLY5 :
+	    call iievp5(x, y, n, coeff[COFF + 1])
+
+	case IT_SPLINE3 :
+	    call iievs3(x, y, n, coeff[COFF + 1])
+
+	}
+
+	return
+
+end
diff --git a/math/interp/asifit.x b/math/interp/asifit.x
new file mode 100644
index 00000000..12b16b0f
--- /dev/null
+++ b/math/interp/asifit.x
@@ -0,0 +1,75 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+.help
+		asifit -- fit interpolator to data
+
+This version uses the "basis-spline" representation for the spline.
+It stores the data array itself for the polynomial interpolants.
+
+.endhelp
+
+procedure asifit(datain,n,coeff)
+include "interpdef.h"
+include "asidef.h"
+
+real datain[ARB]	# data array
+int n			# no. of data points
+real coeff[ARB]
+
+int i
+
+begin
+	NPTS = n
+
+	# error trap - check data array for size
+	switch (ITYPEI) {
+	case IT_SPLINE3:
+	    if(n < 4)
+		call error(ASIFITERR,"too few points for spline")
+	case IT_POLY5:
+	    if(n < 6)
+		call error(ASIFITERR,"too few points for poly5")
+	case IT_POLY3:
+	    if(n < 4)
+		call error(ASIFITERR,"too few points for poly3")
+	case IT_LINEAR:
+	    if(n < 2)
+		call error(ASIFITERR,"too few points for linear")
+	default:
+	    if(n < 1)
+		call error(ASIFITERR,"too few points for interpolation")
+
+	}
+
+	do i = 1,n
+	    coeff[COFF + i] = datain[i]
+
+
+	if (ITYPEI == IT_SPLINE3) {
+
+	    # specify natural end conditions - second deriv. zero
+	    coeff[COFF] = 0.
+	    coeff[COFF+n+1] = 0.
+
+	    # fit spline - generate b-spline coefficients.
+	    call iif_spline(coeff[COFF],coeff[COFF + n + 2],n)
+
+
+	} else {   # not the spline
+	    # We extend array to take care of values near edge.
+
+	    # Assign arbitrary values in case there are only a few points.
+	    for(i = n + 1; i < 5; i = i + 1)
+		coeff[COFF + i] = coeff[COFF + n]
+
+	    # Extend for worst case - poly 5 may need 3 extra points.
+	    do i = 1,3 {   # same recipe as project
+		coeff[COFF+1 - i] = 2. * coeff[COFF + 1] -
+			      coeff[COFF + 1 + i]
+		coeff[COFF+n + i] = 2. * coeff[COFF + n] -
+			      coeff[COFF + n - i]
+	    }
+	}
+
+	return
+end
diff --git a/math/interp/asigrl.x b/math/interp/asigrl.x
new file mode 100644
index 00000000..d528d0be
--- /dev/null
+++ b/math/interp/asigrl.x
@@ -0,0 +1,201 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+.help
+		procedure asigrl
+
+     This procedure finds the integral of the interpolant from a to b
+assuming both a and b land in the array.
+.endhelp
+
+real procedure asigrl(a,b,coeff)    # returns value of integral
+include "interpdef.h"
+include "asidef.h"
+
+real a,b		# integral limits
+real coeff[ARB]
+
+int na,nb,i,j,n0,nt
+real s,t,ac,xa,xb,pc[6]
+
+begin
+	xa = a
+	xb = b
+	if ( a > b ) {		# flip order and sign at end
+	    xa = b
+	    xb = a
+	}
+
+	na = xa
+	nb = xb
+	ac = 0.		# zero accumulator
+
+	# set number of terms
+	switch (ITYPEI) {		# switch on interpolator type
+	case IT_NEAREST :
+	    nt = 0
+	case IT_LINEAR :
+	    nt = 1
+	case IT_POLY3 :
+	    nt = 4
+	case IT_POLY5 :
+	    nt = 6
+	case IT_SPLINE3 :
+	    nt = 4
+	}
+
+	# NEAREST_NEIGHBOR and LINEAR are handled differently because of
+	# storage.  Also probably good for speed.
+
+	if (nt == 0) {		# NEAREST_NEIGHBOR
+	    # reset segment to center values
+	    na = xa + 0.5
+	    nb = xb + 0.5
+
+	    # set up for first segment
+	    s = xa - na
+
+	    # for clarity one segment case is handled separately
+	    if ( nb == na ) {	# only one segment involved
+		t = xb - nb
+		n0 = COFF + na
+		ac = ac + (t - s) * coeff[n0]
+	    } else {	# more than one segment
+
+		# first segment
+		n0 = COFF + na
+		ac = ac + (0.5 - s) * coeff[n0]
+
+		# middle segments
+		do j = na+1, nb-1 {
+		    n0 = COFF + j
+		    ac = ac + coeff[n0]
+		}
+
+		# last segment
+		n0 = COFF + nb
+		t = xb - nb
+		ac = ac + (t + 0.5) * coeff[n0]
+	    }
+
+	} else if (nt == 1) {	# LINEAR
+	    # set up for first segment
+	    s = xa - na
+
+	    # for clarity one segment case is handled separately
+	    if ( nb == na ) {	# only one segment involved
+		t = xb - nb
+		n0 = COFF + na
+		ac = ac + (t - s) * coeff[n0] +
+		     0.5 * (coeff[n0+1] - coeff[n0]) * (t*t - s*s)
+	    } else {	# more than one segment
+
+		# first segment
+		n0 = COFF + na
+		ac = ac + (1. - s) * coeff[n0] +
+		     0.5 * (coeff[n0+1] - coeff[n0]) * (1. - s*s)
+
+		# middle segments
+		do j = na+1, nb-1 {
+		    n0 = COFF + j
+		    ac = ac + 0.5 * (coeff[n0+1] + coeff[n0])
+		}
+
+		# last segment
+		n0 = COFF + nb
+		t = xb - nb
+		ac = ac + coeff[n0] * t + 0.5 *
+			(coeff[n0+1] - coeff[n0]) * t * t
+	    }
+
+	} else {		# A higher order interpolant
+
+	    # set up for first segment
+	    s = xa - na
+
+	    # for clarity one segment case is handled separately
+	    if ( nb == na ) {	# only one segment involved
+		t = xb - nb
+		n0 = COFF + na
+		call iigetpc(n0,pc,coeff)
+		do i = 1,nt
+		    ac = ac + (1./i) * pc[i] * (t ** i - s ** i)
+	    } else {	# more than one segment
+
+		# first segment
+		n0 = COFF + na
+		call iigetpc(n0,pc,coeff)
+		do i = 1,nt
+		    ac = ac + (1./i) * pc[i] * (1. - s ** i)
+
+		# middle segments
+		do j = na+1, nb-1 {
+		    n0 = COFF + j
+		    call iigetpc(n0,pc,coeff)
+		    do i = 1,nt
+			ac = ac + (1./i) * pc[i]
+		}
+
+		# last segment
+		n0 = COFF + nb
+		t = xb - nb
+		call iigetpc(n0,pc,coeff)
+		do i = 1,nt
+		    ac = ac + (1./i) * pc[i] * t ** i
+	    }
+	}
+
+	if ( a < b )
+	    return(ac)
+	else
+	    return(-ac)
+end
+
+	
+procedure iigetpc(n0, pc, coeff)	# generates polynomial coefficients
+					# if spline or poly3 or poly5
+
+int n0			# coefficients wanted for n0 < x n0 + 1
+real coeff[ARB]
+
+real pc[ARB]
+
+int i,k,nt
+real d[6]
+
+begin
+	# generate polynomial coefficients, first for spline.
+	if (ITYPEI == IT_SPLINE3) {
+	    pc[1] = coeff[n0-1] + 4. * coeff[n0] + coeff[n0+1]
+	    pc[2] = 3. * (coeff[n0+1] - coeff[n0-1])
+	    pc[3] = 3. * (coeff[n0-1] - 2. * coeff[n0] + coeff[n0+1])
+	    pc[4] = -coeff[n0-1] + 3. * coeff[n0] - 3. * coeff[n0+1] +
+				    coeff[n0+2]
+		
+	} else {
+	    if (ITYPEI == IT_POLY5)
+		nt = 6
+	    else	# must be POLY3
+		nt = 4
+
+	    # Newton's form written in line to get polynomial from data
+
+	    # load data
+	    do i = 1,nt
+		d[i] = coeff[n0 - nt/2 + i]
+
+	    # generate difference table
+	    do k = 1, nt-1
+		do i = 1,nt-k
+		    d[i] = (d[i+1] - d[i]) / k
+
+	    # shift to generate polynomial coefficients of (x - n0)
+	    do k = nt,2,-1
+		do i = 2,k
+		    d[i] = d[i] + d[i-1] * (k - i - 2)
+
+	    do i = 1,nt
+		pc[i] = d[nt + 1 - i]
+	}
+
+	return
+end
diff --git a/math/interp/asiset.x b/math/interp/asiset.x
new file mode 100644
index 00000000..126f4e39
--- /dev/null
+++ b/math/interp/asiset.x
@@ -0,0 +1,20 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# sets sequential interpolator type
+
+procedure asiset(coeff,interptype)
+include "interpdef.h"
+include "asidef.h"
+
+int interptype
+real coeff[ARB]
+
+begin
+
+	if(interptype <= 0 || interptype > ITNIT)
+	    call error(ASITYPEERR,"illegal interpolator type")
+	else
+	    TYPEI = interptype
+
+	return
+end
diff --git a/math/interp/asival.x b/math/interp/asival.x
new file mode 100644
index 00000000..56f18938
--- /dev/null
+++ b/math/interp/asival.x
@@ -0,0 +1,49 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+.help
+		procedure asival
+
+     This procedure finds interpolated value assuming that x lands in
+array i.e. 1 <= x < npts. 
+It must be called by a routine that checks for out of bound references
+and takes care of bad pixels.
+     This version assumes that the data are stored for polynomials and
+the spline appears as basis-spline coefficients.
+     Also the sequential evaluators are used to obtain the values in
+order to reduce the amount of duplicated code.
+.endhelp
+
+real procedure asival(x,coeff)
+include "interpdef.h"
+include "asidef.h"
+
+real x
+real coeff[ARB]
+
+real t
+
+begin
+	switch (ITYPEI)	{	# switch on interpolator type
+	
+	case IT_NEAREST :
+	    call iievne(x,t,1,coeff[COFF+1])
+	    return(t)
+
+	case IT_LINEAR :
+	    call iievli(x,t,1,coeff[COFF+1])
+	    return(t)
+
+	case IT_POLY3 :
+	    call iievp3(x,t,1,coeff[COFF+1])
+	    return(t)
+
+	case IT_POLY5 :
+	    call iievp5(x,t,1,coeff[COFF+1])
+	    return(t)
+
+	case IT_SPLINE3 :
+	    call iievs3(x,t,1,coeff[COFF+1])
+	    return(t)
+
+	}
+end
diff --git a/math/interp/bench.x b/math/interp/bench.x
new file mode 100644
index 00000000..539ddf67
--- /dev/null
+++ b/math/interp/bench.x
@@ -0,0 +1,55 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+
+include	"/usr/vesa/spec/terpdef.h"
+
+# Quickie benchmark, 1-d sequential image interpolators.
+
+define	MAX_PIXELS	2048
+define	SZ_NAME		20
+
+
+task	interp
+
+
+procedure interp()
+
+real	data[MAX_PIXELS], x[MAX_PIXELS], y[MAX_PIXELS]
+real	coeff[2 * MAX_PIXELS + SZ_ASI]
+char	interp_name[SZ_NAME]
+int	i, j, npix, nlines, interpolant
+bool	streq()
+int	clgeti()
+
+begin
+	npix = min (MAX_PIXELS, clgeti ("npix"))
+	nlines = npix				# square image
+	call clgstr ("interpolant", interp_name, SZ_NAME)
+
+	if (streq (interp_name, "nearest"))
+	    interpolant = IT_NEAR
+	else if (streq (interp_name, "linear"))
+	    interpolant = IT_LINEAR
+	else if (streq (interp_name, "poly3"))
+	    interpolant = IT_POLY3
+	else if (streq (interp_name, "poly5"))
+	    interpolant = IT_POLY5
+	else if (streq (interp_name, "spline3"))
+	    interpolant = IT_SPLINE3
+	else
+	    call error (0, "Unknown interpolant keyword")
+
+	call asiset (coeff, II_INIT, 0)
+	call asiset (coeff, II_INTERPOLANT, interpolant)
+	call asiset (coeff, II_ALLGOODPIX, YES)
+
+	do i = 1, npix {			# initialize data, x arrays
+	    data[i] = max(1.0, min(real(npix), real(i) + 0.15151))
+	    x[i] = i
+	}
+
+	do j = 1, nlines {			# interpolate npix ** 2
+	    call asifit (data, npix, coeff)
+	    call asieva (x, y, npix, coeff)
+	}
+end
diff --git a/math/interp/cubspl.f b/math/interp/cubspl.f
new file mode 100644
index 00000000..4bb54964
--- /dev/null
+++ b/math/interp/cubspl.f
@@ -0,0 +1,119 @@
+      subroutine cubspl ( tau, c, n, ibcbeg, ibcend )
+c  from  * a practical guide to splines *  by c. de boor
+c     ************************	input  ***************************
+c     n = number of data points. assumed to be .ge. 2.
+c     (tau(i), c(1,i), i=1,...,n) = abscissae and ordinates of the
+c	 data points. tau is assumed to be strictly increasing.
+c     ibcbeg, ibcend = boundary condition indicators, and
+c     c(2,1), c(2,n) = boundary condition information. specifically,
+c	 ibcbeg = 0  means no boundary condition at tau(1) is given.
+c	    in this case, the not-a-knot condition is used, i.e. the
+c	    jump in the third derivative across tau(2) is forced to
+c	    zero, thus the first and the second cubic polynomial pieces
+c	    are made to coincide.)
+c	 ibcbeg = 1  means that the slope at tau(1) is made to equal
+c	    c(2,1), supplied by input.
+c	 ibcbeg = 2  means that the second derivative at tau(1) is
+c	    made to equal c(2,1), supplied by input.
+c	 ibcend = 0, 1, or 2 has analogous meaning concerning the
+c	    boundary condition at tau(n), with the additional infor-
+c	    mation taken from c(2,n).
+c     ***********************  output  **************************
+c     c(j,i), j=1,...,4; i=1,...,l (= n-1) = the polynomial coefficients
+c	 of the cubic interpolating spline with interior knots (or
+c	 joints) tau(2), ..., tau(n-1). precisely, in the interval
+c	 interval (tau(i), tau(i+1)), the spline f is given by
+c	    f(x) = c(1,i)+h*(c(2,i)+h*(c(3,i)+h*c(4,i)/3.)/2.)
+c	 where h = x - tau(i). the function program *ppvalu* may be
+c	 used to evaluate f or its derivatives from tau,c, l = n-1,
+c	 and k=4.
+      integer ibcbeg,ibcend,n,	 i,j,l,m
+      real c(4,n),tau(n),   divdf1,divdf3,dtau,g
+c****** a tridiagonal linear system for the unknown slopes s(i) of
+c  f  at tau(i), i=1,...,n, is generated and then solved by gauss elim-
+c  ination, with s(i) ending up in c(2,i), all i.
+c     c(3,.) and c(4,.) are used initially for temporary storage.
+      l = n-1
+compute first differences of tau sequence and store in c(3,.). also,
+compute first divided difference of data and store in c(4,.).
+      do 10 m=2,n
+	 c(3,m) = tau(m) - tau(m-1)
+   10	 c(4,m) = (c(1,m) - c(1,m-1))/c(3,m)
+construct first equation from the boundary condition, of the form
+c	      c(4,1)*s(1) + c(3,1)*s(2) = c(2,1)
+      if (ibcbeg-1)			11,15,16
+   11 if (n .gt. 2)			go to 12
+c     no condition at left end and n = 2.
+      c(4,1) = 1.
+      c(3,1) = 1.
+      c(2,1) = 2.*c(4,2)
+					go to 25
+c     not-a-knot condition at left end and n .gt. 2.
+   12 c(4,1) = c(3,3)
+      c(3,1) = c(3,2) + c(3,3)
+      c(2,1) =((c(3,2)+2.*c(3,1))*c(4,2)*c(3,3)+c(3,2)**2*c(4,3))/c(3,1)
+					go to 19
+c     slope prescribed at left end.
+   15 c(4,1) = 1.
+      c(3,1) = 0.
+					go to 18
+c     second derivative prescribed at left end.
+   16 c(4,1) = 2.
+      c(3,1) = 1.
+      c(2,1) = 3.*c(4,2) - c(3,2)/2.*c(2,1)
+   18 if(n .eq. 2)			go to 25
+c  if there are interior knots, generate the corresp. equations and car-
+c  ry out the forward pass of gauss elimination, after which the m-th
+c  equation reads    c(4,m)*s(m) + c(3,m)*s(m+1) = c(2,m).
+   19 do 20 m=2,l
+	 g = -c(3,m+1)/c(4,m-1)
+	 c(2,m) = g*c(2,m-1) + 3.*(c(3,m)*c(4,m+1)+c(3,m+1)*c(4,m))
+   20	 c(4,m) = g*c(3,m-1) + 2.*(c(3,m) + c(3,m+1))
+construct last equation from the second boundary condition, of the form
+c	    (-g*c(4,n-1))*s(n-1) + c(4,n)*s(n) = c(2,n)
+c     if slope is prescribed at right end, one can go directly to back-
+c     substitution, since c array happens to be set up just right for it
+c     at this point.
+      if (ibcend-1)			21,30,24
+   21 if (n .eq. 3 .and. ibcbeg .eq. 0) go to 22
+c     not-a-knot and n .ge. 3, and either n.gt.3 or  also not-a-knot at
+c     left end point.
+      g = c(3,n-1) + c(3,n)
+      c(2,n) = ((c(3,n)+2.*g)*c(4,n)*c(3,n-1)
+     *		  + c(3,n)**2*(c(1,n-1)-c(1,n-2))/c(3,n-1))/g
+      g = -g/c(4,n-1)
+      c(4,n) = c(3,n-1)
+					go to 29
+c     either (n=3 and not-a-knot also at left) or (n=2 and not not-a-
+c     knot at left end point).
+   22 c(2,n) = 2.*c(4,n)
+      c(4,n) = 1.
+					go to 28
+c     second derivative prescribed at right endpoint.
+   24 c(2,n) = 3.*c(4,n) + c(3,n)/2.*c(2,n)
+      c(4,n) = 2.
+					go to 28
+   25 if (ibcend-1)			26,30,24
+   26 if (ibcbeg .gt. 0)		go to 22
+c     not-a-knot at right endpoint and at left endpoint and n = 2.
+      c(2,n) = c(4,n)
+					go to 30
+   28 g = -1./c(4,n-1)
+complete forward pass of gauss elimination.
+   29 c(4,n) = g*c(3,n-1) + c(4,n)
+      c(2,n) = (g*c(2,n-1) + c(2,n))/c(4,n)
+carry out back substitution
+   30 j = l
+   40	 c(2,j) = (c(2,j) - c(3,j)*c(2,j+1))/c(4,j)
+	 j = j - 1
+	 if (j .gt. 0)			go to 40
+c****** generate cubic coefficients in each interval, i.e., the deriv.s
+c  at its left endpoint, from value and slope at its endpoints.
+      do 50 i=2,n
+	 dtau = c(3,i)
+	 divdf1 = (c(1,i) - c(1,i-1))/dtau
+	 divdf3 = c(2,i-1) + c(2,i) - 2.*divdf1
+	 c(3,i-1) = 2.*(divdf1 - c(2,i-1) - divdf3)/dtau
+   50	 c(4,i-1) = (divdf3/dtau)*(6./dtau)
+					return
+      end
diff --git a/math/interp/iieval.x b/math/interp/iieval.x
new file mode 100644
index 00000000..87538525
--- /dev/null
+++ b/math/interp/iieval.x
@@ -0,0 +1,137 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+.help
+		procedures to evaluate interpolants
+
+     These procedures are seperated from the other programs in order
+to make it easier to optimise these in case it becomes necessary to
+obtain the fastest possible interpolants.  The interpolation package
+spends most of its time in these routines.
+.endhelp
+
+procedure iievne(x,y,n,a)   # nearest neighbor
+
+real	x[ARB]	# x values, must be within [1,n]
+real	y[ARB]	# interpolated values returned to user
+int	n	# number of x values
+real	a[ARB]	# data to be interpolated
+
+int	i
+
+begin
+	do i = 1, n
+	    y[i] = a[int(x[i] + 0.5)]
+	return
+end
+
+procedure iievli(x,y,n,a)   # linear
+
+real	x[ARB]	# x values, must be within [1,n]
+real	y[ARB]	# interpolated values returned to user
+int	n	# number of x values
+real	a[ARB]	# data to be interpolated
+
+int	i,nx
+
+begin
+	
+	do i = 1,n {
+	    nx = x[i]
+	    y[i] =  (x[i] - nx) * a[nx + 1] + (nx + 1 - x[i]) * a[nx]
+	}
+	return
+end
+
+procedure iievp3(x,y,n,a)   # interior third order polynomial
+
+real	x[ARB]	# x values, must be within [1,n]
+real	y[ARB]	# interpolated values returned to user
+int	n	# number of x values
+real	a[ARB]	# data to be interpolated from a[0] to a[n+2]
+
+int	i,nx,nxold
+real	s,t,cd20,cd21
+
+begin
+	nxold = -1
+	do i = 1,n {
+	    nx = x[i]
+	    s = x[i] - nx
+	    t = 1. - s
+	    if (nx != nxold) {
+
+		# second central differences:
+		cd20 = 1./6. * (a[nx+1] - 2. * a[nx] + a[nx-1])
+		cd21 = 1./6. * (a[nx+2] - 2. * a[nx+1] + a[nx])
+		nxold = nx
+	    }
+	    y[i] = s * (a[nx+1] + (s * s - 1.) * cd21) +
+		    t * (a[nx] + (t * t - 1.) * cd20)
+
+	}
+	return
+end
+
+procedure iievp5(x,y,n,a)   # interior fifth order polynomial
+
+real	x[ARB]	# x values, must be within [1,n]
+real	y[ARB]	# interpolated values returned to user
+int	n	# number of x values
+real	a[ARB]	# data to be interpolated - from a[-1] to a[n+3]
+
+int	i,nx,nxold
+real	s,t,cd20,cd21,cd40,cd41
+
+begin
+	nxold = -1
+	do i = 1,n {
+	    nx = x[i]
+	    s = x[i] - nx
+	    t = 1. - s
+	    if (nx != nxold) {
+		cd20 = 1./6. * (a[nx+1] - 2. * a[nx] + a[nx-1])
+		cd21 = 1./6. * (a[nx+2] - 2. * a[nx+1] + a[nx])
+
+		# fourth central differences
+		cd40 = 1./120. * (a[nx-2] - 4. * a[nx-1] +
+			6. * a[nx] - 4. * a[nx+1] + a[nx+2])
+		cd41 = 1./120. * (a[nx-1] - 4. * a[nx] +
+			6. * a[nx+1] - 4. * a[nx+2] + a[nx+3])
+		nxold = nx
+	    }
+	    y[i] = s * (a[nx+1] + (s * s - 1.) *
+			 (cd21 + (s * s - 4.) * cd41)) +
+		   t * (a[nx] + (t * t - 1.) *
+			 (cd20 + (t * t - 4.) * cd40)) 
+	}
+	return
+end
+
+procedure iievs3(x,y,n,a)   # cubic spline evaluator
+
+real	x[ARB]	# x values, must be within [1,n]
+real	y[ARB]	# interpolated values returned to user
+int	n	# number of x values
+real	a[ARB]	# basis spline coefficients - from a[0] to a[n+1]
+
+int	i,nx,nxold
+real	s,c0,c1,c2,c3
+
+begin
+	nxold = -1
+	do i = 1,n {
+	    nx = x[i]
+	    s = x[i] - nx
+	    if (nx != nxold) {
+
+		# convert b-spline coeff's to poly. coeff's
+		c0 = a[nx-1] + 4. * a[nx] + a[nx+1]
+		c1 = 3. * (a[nx+1] - a[nx-1])
+		c2 = 3. * (a[nx-1] - 2. * a[nx] + a[nx+1])
+		c3 = -a[nx-1] + 3. * a[nx] - 3. * a[nx+1] + a[nx+2]
+		nxold = nx
+	    }
+	    y[i] = c0 + s * (c1 + s * (c2 + s * c3) )
+	}
+	return
+end
diff --git a/math/interp/iif_spline.x b/math/interp/iif_spline.x
new file mode 100644
index 00000000..a8574e0b
--- /dev/null
+++ b/math/interp/iif_spline.x
@@ -0,0 +1,67 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+.help
+		procedure iif_spline
+
+     This fits uniformly spaced data with a cubic spline.  The spline is
+given as basis-spline coefficients that replace the data values.
+
+Storage at call time:
+
+b[1] = second derivative at x = 1
+b[2] = first data point y[1]
+b[3] = y[2]
+.
+.
+.
+b[n+1] = y[n]
+b[n+2] = second derivative at x = n
+
+Storage after call:
+
+b[1] ... b[n+2] = the n + 2 basis-spline coefficients for the basis splines
+    as defined in P. M. Prenter's book Splines and Variational Methods,
+    Wiley, 1975.
+
+.endhelp
+
+procedure iif_spline(b,d,n)
+
+real b[ARB]	# data in and also bspline coefficients out
+real d[ARB]     # needed for offdiagnol matrix elements
+int n           # number of data points
+
+int i
+
+begin
+    
+        d[1] = -2.
+        b[1] = b[1] / 6.
+
+        d[2] = 0.
+        b[2] = (b[2] - b[1]) / 6.
+
+        # Gaussian elimination - diagnol below main is made zero
+        # and main diagnol is made all 1's
+        do i = 3,n+1 {
+            d[i] = 1. / (4. - d[i-1])
+            b[i] = d[i] * (b[i] - b[i-1])
+        }
+
+        # Find last b spline coefficient first - overlay r.h.s.'s
+        b[n+2] = ( (d[n] + 2.) * b[n+1] - b[n] + b[n+2]/6.) / (1. +
+            d[n+1] * (d[n] + 2.))
+
+        # back substitute filling in coefficients for b splines
+        do i = n+1, 3, -1
+            b[i] = b[i]  - d[i] * b[i+1]
+
+        # note b[n+1] is evaluated correctly as can be checked 
+
+        # b[2] is already set since offdiagnol is 0.
+
+        # evaluate b[1]
+        b[1] = b[1] + 2. * b[2] - b[3]
+
+	return
+end
diff --git a/math/interp/iimail b/math/interp/iimail
new file mode 100644
index 00000000..69c19e9f
--- /dev/null
+++ b/math/interp/iimail
@@ -0,0 +1,213 @@
+From tody Wed Apr 20 18:50:45 1983
+Date: 20 Apr 1983 18:50-MST
+To: vesa
+Subject: ii comments
+Cc: tody
+
+I read through "tnotes1", and felt that enough information was conveyed
+to explain how the asi___ routines work, and how to use them.  It is
+good documentation for the package, though some sections are probably
+to technical for the general user, and should probably be moved to an
+appendix in the final documentation.
+
+I only have one minor suggestion, and that is that there seems little
+reason to abbreviate NEAR, REFL, and PROJ, since only three characters
+are saved in each case, and the other parameter names are all spelled out.
+
+I also looked at the code for ASIFIT.  I noticed that the recursion
+relations for the cubic spline are coded inline.  I suspect that this
+is actually LESS efficient than using a separate procedure, due to
+the complex coeff offset expressions appearing in the inner loops
+(unless the Fortran compiler does a very good job of optimizing loops).
+
+By using a separate procedure, for example, the statement
+
+	coeff[COFF+i] = coeff[off2+i] * (coeff[COFF+i] - coeff[COFF+i-1])
+
+can be converted to something like
+
+	bcoeff[i] = acoeff[i] * (bcoeff[i] - bcoeff[i-1])
+
+where in the main routine, there is a procedure call something like the
+following:
+
+	call fit_bspline3 (coeff[COFF], coeff[off2], ...)
+
+In other words, the routines that actually do the work do not need to
+know that everything is saved in a single coeff array.  This simplifies
+the code, as well as making it run faster on some machines.  The technique
+has an additional advantage: by isolating the compute bound code into
+a separate (small) procedure, it becomes easy to hand optimize that procedure
+in assembler, should we wish to do so.
+
+From tody Wed Apr 20 19:48:51 1983
+Date: 20 Apr 1983 19:48-MST
+To: vesa
+Subject: first benchmarks
+Cc: tody
+
+I ran some preliminary benchmarks on the asi code, assuming no bad pixels.
+The benchmark routine is in math/interp.  Results:
+
+512 by 512 image interpolation, no bad pixels, using ASIEVA:
+
+	nearest		47 (cpu seconds)
+	linear		22
+	poly3		50
+	poly5		89
+	spline3		94
+
+This is quite encouraging.  I expect that these timings can be decreased by
+a factor of from 3 to 5, given a good Fortran compiler (the current UNIX
+compiler is very poor), and possibly hand optimising critical sections of
+the code in assembler.
+
+The nearest neighbor timings don't make any sense (that should be the
+fastest interpolant).  Are you using sqrt, or something like that?
+The spline timings are worse than I expected, compared to poly3.  May
+be due to complex offset expressions, which F77 does not optimize.
+
+From tody Fri Feb 18 14:10:36 1983
+To: vesa
+Subject: x code
+Cc: tody
+
+
+We want to make IRAF source code as readable as possible, therefore there
+is a (currently unofficial) standard for ".x" code.  Your code is pretty
+close to the standard, but here are some things to consider:
+
+    (1)	It is preferable to enclose large blocks of documentation in
+	.help .. .endhelp sections, rather than making each line a comment.
+	This has two advantages: (1) it is awkward to edit text set off with
+	a # on each line, and (2) the help utilities can only extract
+	source code documentation which is set in help blocks.  It is not
+	necessary to use text formatter commands in help blocks, i.e.,
+	you can simply type it in as it will appear on the terminal.
+
+	In the same vein, it is better to put the discussion of the input
+	and output parameters in the help text, rather than in the
+	declarations section of the procedure.  Placing each input and
+	output parameter on a single line, followed at the right by a short
+	comment, gets the job done without cluttering up the declarations
+	section.  More extensive comments should be placed in the help text.
+
+
+    (2)	It is mostly up to the programmer to decide where to put whitespace
+	to make the structure of a program clearest.  Whitespace should
+	be inserted in a statement to make the important logical components
+	of the statement stand out.
+
+	In particular, there should be a space after every keyword, before
+	the left parenthesis.  If the statement is compound, the left brace
+	should be set off from the right paren by a space.  In short
+	expressions, operators should be set off by whitespace.
+
+	Adding whitespace between a function name and the left paren is
+	optional, as is whitespace between the elements of an argument list
+	(after commas).
+
+	Blank lines should be used to set off sections of code, just as
+	blank lines are used to separate paragraphs of text.
+
+	It is possible to overcomment code, making it hard to read.  If
+	more than a third of the lines in a procedure are comments, the
+	code is probably overcommented.  Place detailed discussion of the
+	algorithm in the help text.
+
+
+    (3)	Indenting structures by full tab stops is acceptable, but 4 space
+	indents are preferred (the code rapidly runs off the right side of
+	the screen if full tab indents are used, encouraging use of too
+	short identifiers and omission of whitespace).  The autoindent
+	feature of VI makes this easy (in .login file: 'set ai sw=4').
+
+
+    (4)	The standard form of the if .. else construct is
+	
+		if (expr) {
+		    stmt
+		} else {
+		    stmt
+
+	or (if "stmt" is several lines, and whitespace is desired)
+		
+		if (expr) {
+		    stmt
+
+		} else {
+		    stmt
+		
+	rather than
+
+		if (expr) {
+		    stmt
+		}
+		else {
+		    stmt
+
+From tody Fri Feb 18 15:21:33 1983
+Date: 18 Feb 1983 15:21-MST
+To: vesa
+Subject: spec changes
+Cc: tody
+
+
+Now that Garth, Harvey, Steve and others have had a chance to comment on the
+specs for the interpolator routines, it is time to make the final revisions
+to the specifications.  Often ones perspective on a problem changes when one
+actually begins coding, and even the most carefully prepared specifications
+need to be changed.  Please feel free to suggest further changes.
+
+
+Modifications
+
+    (1) Everyone wanted the interpolators to be able to generate estimated
+	values to replace indefinites (as an option).
+
+    (2)	Steve wanted sinc function interpolation added to the set of 
+	interpolators.  I would also like to try this for undersampled
+	CCD data.  A fairly high "order" (basis function size) seems
+	justified for this interpolant.
+
+    (3)	A surface integration routine is desired (MSIGRL).
+
+
+SET Routines
+
+    I think we should generalize the form of the "set" routines to permit
+options such as (1), and others we may wish to add in the future (such
+as telling the interpolator not to check for indefinites in the data).
+
+Set routines are also used in the FIO, IMIO, VSIO, and GIO packages in
+the program interface.  For example, in FIO, the number of buffers for a
+file could be set by a call of the form
+
+	call fset (fd, NBUFFERS, 2)
+
+The form of a set call is therefore
+
+	call ___set (object, parameter, value)
+
+i.e.,
+
+	call asiset (coeff, II_INTERPOLANT, II_DIVDIF3)
+	call asiset (coeff, II_TYBNDRY, II_NEAREST)
+	call asiset (coeff, II_REPLACE_INDEFS, YES)
+
+Note that the prefix "II_" must be added to all Image Interpolation
+defined parameters and parameter values.  This is unattractive, but necessary
+to avoid redefinitions of identifiers in other packages, such as IMIO (IMIO
+has the same boundary extension options as II).
+
+
+Surface Integration
+
+    I suggest the following calling sequence for the surface integration
+routine:
+
+	integral = msigrl (x, y, npts, coeff)
+
+where the surface to be integrated is defined by the closed curve {x[i],y[i]},
+where 1 <= i <= npts, defined by the caller.
+
diff --git a/math/interp/iipol_terp.x b/math/interp/iipol_terp.x
new file mode 100644
index 00000000..030d1964
--- /dev/null
+++ b/math/interp/iipol_terp.x
@@ -0,0 +1,41 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+.help
+		Procedure iipol_terp
+
+A polynomial interpolator with x and y arrays given.
+This algorithm is based on the Newton form as described in
+de Boor's book, A Practical Guide to Splines, 1978.
+There is no error checking - this is meant to be used only by calls
+from more complete routines that take care of such things.
+
+Maximum number of terms is 6.
+.endhelp
+
+real procedure iipol_terp(x,y,n,x0)
+
+real x[ARB],y[ARB]	# x and y array
+real x0			# desired x
+int n			# number of points in x and y = number of
+			# terms in polynomial = order + 1
+
+int k,i
+real d[6]
+
+begin
+
+	# Fill in entries for divided difference table.
+	do i = 1,n
+	    d[i] = y[i]
+
+	# Generate divided differences
+	do k = 1,n-1
+	    do i = 1,n-k
+		d[i] = (d[i+1] - d[i])/(x[i+k] - x[i])
+
+	# Shift divided difference table to center on x0
+	do i = 2,n
+	    d[i] = d[i] + d[i-1] * (x0 - x[i])
+
+	return(d[n])
+end
diff --git a/math/interp/interp.h b/math/interp/interp.h
new file mode 100644
index 00000000..e54fc1b5
--- /dev/null
+++ b/math/interp/interp.h
@@ -0,0 +1,19 @@
+# File of definitions for interpolator package.
+
+# Interpolator Types:
+
+define	IT_NEAREST	1
+define	IT_LINEAR	2
+define	IT_POLY3	3
+define	IT_POLY5	4
+define	IT_SPLINE3	5
+define	ITNIT		5	# number of types
+
+# Size of header etc. used for part of coeff dimension
+
+define	SZ_ASI			20
+
+# Total number of points used in spline interpolation of of bad pixels by
+# subroutine arbpix.
+
+define SPLPTS			16
diff --git a/math/interp/interpdef.h b/math/interp/interpdef.h
new file mode 100644
index 00000000..e54fc1b5
--- /dev/null
+++ b/math/interp/interpdef.h
@@ -0,0 +1,19 @@
+# File of definitions for interpolator package.
+
+# Interpolator Types:
+
+define	IT_NEAREST	1
+define	IT_LINEAR	2
+define	IT_POLY3	3
+define	IT_POLY5	4
+define	IT_SPLINE3	5
+define	ITNIT		5	# number of types
+
+# Size of header etc. used for part of coeff dimension
+
+define	SZ_ASI			20
+
+# Total number of points used in spline interpolation of of bad pixels by
+# subroutine arbpix.
+
+define SPLPTS			16
diff --git a/math/interp/mkpkg b/math/interp/mkpkg
new file mode 100644
index 00000000..55ab29c6
--- /dev/null
+++ b/math/interp/mkpkg
@@ -0,0 +1,21 @@
+# Old image interpolator tools library.
+
+$checkout libinterp.a lib$
+$update   libinterp.a
+$checkin  libinterp.a lib$
+$exit
+
+libinterp.a:
+	arbpix.x	interpdef.h asidef.h
+	arider.x	interpdef.h
+	arival.x	interpdef.h
+	asider.x	interpdef.h asidef.h
+	asieva.x	interpdef.h asidef.h
+	asifit.x	interpdef.h asidef.h
+	asigrl.x	interpdef.h asidef.h
+	asiset.x	interpdef.h asidef.h
+	asival.x	interpdef.h asidef.h
+	iieval.x        
+	iif_spline.x    
+	iipol_terp.x
+	;
diff --git a/math/interp/noteari b/math/interp/noteari
new file mode 100644
index 00000000..d42ed48b
--- /dev/null
+++ b/math/interp/noteari
@@ -0,0 +1,64 @@
+	Using the Random One Dimensional Interpolation Routines
+	A Quick Note for Programmers 
+
+
+I. GENERAL NOTES:
+
+	1. Defines are found in file interpdef.h.  The routines
+	   are in library interplib.a.
+
+	2. All pixels are assumed to be good. Except for routine
+	   arbpix.
+
+	3. This is for uniformly spaced data -- thus for the i-th
+	   data value, y[i], the corresponding x[i] = i by assumption.
+
+	4. All x references are assumed to land in the closed interval
+	   1 <= x <= NPTS, where NPTS is the number of points in the
+	   data array.  If x is outside this range, the result is
+	   not specified.
+
+
+II. PROCEDURES:
+
+
+  **** Subroutine to replace INDEF's with interpolated values.
+  *
+  *	arbpix (datain, n, dataout, interpolator_type)
+  *
+  *	real	datain[ARB]		# data_in array
+  *	int	n			# number of points in data_in
+  *	real	dataout[ARB]		# array out, may not be same as
+  *					# data_in
+  *	int	interpolator_type
+  *
+  *	    The interpolator type can be set to:
+  *
+  *		IT_NEAREST		nearest neighbor
+  *		IT_LINEAR		linear interpolation
+  *		IT_POLY3		interior polynomial 3rd order
+  *		IT_POLY5		interior polynomial 5th order
+  ****		IT_SPLINE3		cubic natural spline
+
+
+  **** Subroutine to return interpolated value
+  *
+  *	real arival (x, datain, n , interpolator_type)
+  *	
+  *	real	x
+  *	real	datain[ARB]		# data array
+  *	int	n			# number of points in data array
+  ****	int	interpolator_type	# see above
+  
+  
+  **** Subroutine to evaluate derivatives at a point.
+  *
+  *	arider (x, datain, n, derivs, nder, interpolator_type)
+  *
+  *	real	x
+  *	real	datain[ARB]		# data array
+  *	int	n			# number of points in data array
+  *	real	derivs[ARB]		# output array containing derivatives
+  *					# derivs[1] is function value
+  *	int	nder			# input:  nder - 1 derivs are evaluated
+  ****	int	interpolator_type	# see above
diff --git a/math/interp/noteasi b/math/interp/noteasi
new file mode 100644
index 00000000..ae22df83
--- /dev/null
+++ b/math/interp/noteasi
@@ -0,0 +1,101 @@
+	Using the Sequential One Dimensional Interpolation Routines
+	A Quick Note for Programmers 
+
+
+I. GENERAL NOTES:
+
+	1. Defines are found in file interpdef.h.  The routines
+	   are in library interplib.a.
+
+	2. All pixels are assumed to be good. Except for routine
+	   arbpix.
+
+	3. This is for uniformly spaced data -- thus for the i-th
+	   data value, y[i], the corresponding x[i] = i by assumption.
+
+	4. All x references are assumed to land in the closed interval
+	   1 <= x <= NPTS, where NPTS is the number of points in the
+	   data array.  If x is outside this range, the result is
+	   not specified.
+
+	5. A storage area and work space array must be provided.
+	   It is of type real and the size is 2 * NPTS + SZ_ASI
+
+	
+
+II. PROCEDURES:
+
+
+  **** Subroutine to replace INDEF's with interpolated values.
+  *
+  *	arbpix (datain, n, dataout, interpolator_type)
+  *
+  *	real	datain[ARB]		# data_in array
+  *	int	n			# number of points in data_in
+  *	real	dataout[ARB]		# array out, may not be same as
+  *					# data_in
+  *	int	interpolator_type
+  *
+  *	    The interpolator type can be set to:
+  *
+  *		IT_NEAREST		nearest neighbor
+  *		IT_LINEAR		linear interpolation
+  *		IT_POLY3		interior polynomial 3rd order
+  *		IT_POLY5		interior polynomial 5th order
+  ****		IT_SPLINE3		cubic natural spline
+
+
+  **** Subroutine to set interpolator type.
+  *
+  *	asiset(coeff,interpolator_type)
+  *
+  *	real	coeff[ARB]		# work + storage array, dimension
+  *					# 2 * NPTS + SZ_ASI
+  ****	int	interpolator_type	# see above
+
+
+  **** Subroutine to fit interpolator to data.
+  *
+  *	asifit (datain, npts, coeff)
+  *
+  *	real	datain[ARB]	# data array 
+  *	int	npts		# number of points in data array
+  ****	real	coeff[ARB]	# work+storage area dim 2*npts + SZ_ASI
+  
+  
+  **** Subroutine to return interpolated value after fitting.  
+  *
+  *	real asival (x, coeff)
+  *	
+  *	real	x
+  ****	real	coeff[ARB]
+  
+  
+  **** Subroutine to evaluate an ordered sequence of values.
+  *
+  *	asieva (x, y, n, coeff)
+  *
+  *	real	x[ARB]		# input array of x values
+  *	real	y[ARB]		# output array of interpolated values
+  *	int	n		# number of x values
+  ****	real	coeff[ARB]
+  
+  
+  **** Subroutine to evaluate derivatives at a point.
+  *
+  *	asider (x, derivs, nder, coeff)
+  *
+  *	real	x
+  *	real	derivs[ARB]	# output array containing derivatives
+  *				# derivs[1] is function value
+  *	int	nder		# input:  nder - 1 derivatives are evaluated
+  ****	real	coeff[ARB]
+  
+      
+  **** Subroutine to integrate the interpolated data.
+  *
+  *	real asigrl (a, b, coeff)
+  *
+  *	real	a		# lower limit
+  *	real	b		# upper limit
+  ****	real	coeff[ARB]
diff --git a/math/interp/notes3 b/math/interp/notes3
new file mode 100644
index 00000000..e7121c99
--- /dev/null
+++ b/math/interp/notes3
@@ -0,0 +1,216 @@
+	Notes on the Interpolator Package for IRAF Version 2
+
+	Some parts of the image interpolator package are available.
+This is a reminder of changes to the document TRP prepared by
+Doug Tody.  Also it is a place to keep track of why things were
+done the way they were.  The individual procedures (subroutines)
+will be discussed; making it easy to add, subtract and change things.
+
+**************************************************************************
+**									**
+**									**
+
+		GENERAL NOTES FOR 1-D PACKAGE:
+
+1. Handling of errors.
+
+	Some routines call the error routines of the IRAF package.
+	Logically it is reasonable to trap silly errors at certain points.
+	For instance if the interpolator type is set to a nonexistant type
+	an error call is generated.  
+
+	To the programmer, the two most important error features are:
+
+	1. All pixels are assumed to be good.
+
+	2. All x references are assumed to land in the closed interval
+	   1 <= x <= NPTS.
+	
+	Point 2 probably needs some explanation, because at first hand
+	it seems rather easy to test for x < 1 || x > NPTS and take
+	appropriate action.  There are two objections to including this
+	test.  First it is often possible to generate x values in such
+	a way that they are guaranteed to lie in the given interval.
+	Testing again within the interpolator package is a waste of
+	computer time.  Second the interpolator package becomes too large
+	if code is included to handle out of bounds references and such
+	code duplicates other parts of the IRAF package that handles
+	out of bound values.  The alternative is to return INDEF when
+	x is out of bounds.  This is not very appealing for many
+	routine applications such as picture shifting.
+
+2. Size of "coeff" array:
+
+	coeff is a real 1-d array of size  -- 2 * NPTS + SZ_ASI
+
+    where SZ_ASI is currently 30.  It, like the other defines needed for
+    the interp package, is available in the file -- terpdef.h .
+
+       This coeff array serves as work area for asifit, a structure to save
+    interpolator type, flags etc., an array to save data points or b-spline
+    coefficients as needed.
+
+   The polynomial interpolators are saved as the data points and the
+interpolation is done "on the fly".  Rather than compute polynomial
+coefficients before-hand, the interpolated value is calculated from
+the data values at time of request.  (The actual calculation is done
+by adding and multiplying things in an order suggested by Everett's
+interpolation formula rather than the polynomial coefficient form.
+The resulting values are the same up to differences due to numerical
+roundoff.  As a practical matter, all forms work except polynomials
+shifted far from the point of interest.  Polynomials shifted to a
+center far away suffer from bad roundoff errors.)
+
+   The splines must be calculated at a single pass because (formally)
+they are global (i.e use all of the data points).  The b-splines (b for
+basis) are just certain piecewise polynomials for solving the interpo-
+lation problem, it is convenient to calculate the coefficients of these
+b-splines and to save these in the array.
+
+3. Method of solution:
+
+**************************************************************************
+**									**
+**									**
+**									**
+			PROCEDURES:
+
+***************************************************************************
+
+	*****        asiset(coeff,interptype) 		       *****
+
+The interpolator type can be set to:
+
+	IT_NEAREST		nearest neighbor
+	IT_LINEAR		linear interpolation
+	IT_POLY3		interior polynomial 3rd order
+	IT_POLY5		interior polynomial 5th order
+	IT_SPLINE3		cubic natural spline
+
+Subroutines needed:
+
+	NONE
+
+
+
+*************************************************************************
+
+	*******		asifit (data, npts, coeff)            *****
+
+   This fits the interpolator to the data.  Takes care of bad points by
+replacing them with interpolated values to generate a
+uniformly spaced array.  For polynomial interpolators, this array is
+sent to the evaluation routines.  For the spline interpolator, the uniform
+array is fitted and the basis-spline coefficients are saved.
+
+Interior polynomial near boundary:
+   Array is extended according to choice of boundary conditions.
+Out of bounds values and values near the edge depend on choice of
+boundary conditions.
+
+Spline near boundary:
+   Natural (second derivative equals zero at edge) spline is fitted to
+data only.  The resulting function is reflected, wrapped etc. to generate
+out of bounds values.  Out of bounds values depend on choice of boundary
+conditions but values within the array near the edges do not.
+   For the wrap boundary condition, the one segment connecting point
+number n to point 1 is not generated by the spline fit.  Instead the
+polynomial that is continuous and has a continuous first and second
+derivative n is inserted.  In this one case, the first and second derivative
+are not continuous at 1.
+
+Replacing bad points:
+   The same kind of interpolator is used to replace bad points as that
+used to generate interpolated values.  The boundary conditions are not
+handled in the same manner.  Bad points near the edge are replaced by
+using lower order polynomial interpolators if there are not enough
+points on both sides of the bad point.  Bad points that are not
+straddled by good points are assigned the value of the nearest good
+point. This is done in the temporary array before the uniformly spaced
+interpolator is applied.
+
+subroutines needed:
+
+	real iipint(x,y,nterm,x0)
+		Returns interpolated value at x0 using polynomial with
+			<nterm> terms to connect the <nterm> data pairs
+			in x,y.
+
+	cubspl(tau,c,n,ibcbeg,ibcend)
+		Unmodified cubic spline interpolator for non-uniformly
+			spaced data taken from C. de Boor's book:
+			A Practical Guide to Splines, (1978
+			Springer-Verlag).
+
+	iifits(b,d,n)
+		Fits cubic spline to uniformly spaced array of y values
+			using a basis-spline representation for
+			the spline.
+
+
+
+*****************************************************************************
+
+	*****		y = asival (x, coeff)                  *****
+
+   Subroutine to return interpolated value after fitting.  
+
+Subroutines needed:
+
+	real iivalu (x, coeff)
+		Returns interpolated value assuming x is in array.  Also
+			has no code for bad point propagation.
+
+
+
+
+***************************************************************************
+
+	*****		asieva (x, y, n, coeff)                  *****
+
+   Given an ordered array of x values returns interpolated values in y.
+This is needed for speed.  Reduces number of subroutine calls per point,
+reduces the number of tests for out of bounds, and bad pixel
+propagation can be made more efficient.
+
+Subroutines needed:
+
+	real iivalu (x, coeff)
+
+
+
+**************************************************************************
+
+	*****		asider (x, derivs, nderiv, coeff)      *****
+
+   This evaluates derivatives at point x.  Returns the first
+nderiv - 1 derivatives.  derivs[1] is function value, derivs[2] is
+first derivative, derivs[3] is second derivative etc.
+   There is no check that nderiv is a reasonable value.  Polynomials
+have a limited number of non-zero derivatives, if more are asked for
+they come back as zero.
+
+Subroutines needed:
+
+	iivalu (x, coeff)
+
+	iiderv (x, derivs, nderiv, coeff)
+		Assumes x lands in array returns derivatives.  No handling
+			of bad points.
+
+****************************************************************************
+
+	******		integral = asigrl (a, b, coeff)           *******
+
+    This integrates the array from to a to b.  The boundary conditions are
+incorporated into the code so if function values can be returned from all
+points between a and b, the integral will be defined.  Thus for WRAP,
+REFLECT and PROJECT boundary conditions, the distance from a to b can be
+as large as 3 times the array length if a and b are chosen appropriately.
+For these boundary conditions, attempts to extend beyond +/- one cycle
+produce INDEF.
+
+Subroutines needed:
+
+	iiigrl (a, b, coeff)
+		returns integral when a and b land in array.
diff --git a/math/interp/overview b/math/interp/overview
new file mode 100644
index 00000000..4ad813ca
--- /dev/null
+++ b/math/interp/overview
@@ -0,0 +1,43 @@
+Interpolation Package
+
+	The routines here are intended to allow programmers to interpolate
+one dimensional arrays and two dimensional
+images in the IRAF system.  The routines are
+mathematical in nature and are not heavily tied into the IRAF package.
+The advantages of having locally written interpolators include the
+ability to optimize for uniformly spaced data and the possibility of
+adding features that are useful for the final application.  The
+one major feature that has been implemented is the ability to change
+the kind of interpolator used at run time by carrying along a variable
+that gives the interpolator type in the higher level code.
+
+	The kinds of interpolators include:
+		1. Nearest neighbor
+		2. Linear
+		3. Interior polynomial order = 3
+		4  Interior polynomial order = 5
+		5  Spline order = 3
+
+	The package is divided into array interpolators and image
+interpolators.  Within the array interpolators, there is further
+division into sequential and random interpolators.  The sequential
+interpolators are optimized for returning many values as is the
+case when an array is shifted or when an array is oversampled
+at many points in order to produce a smooth plot.  The random interpolators
+allow the evaluation of a few interpolated points without the computing
+time and storage overhead required for setting up the sequential version.
+
+	The original specification called for the interpolator package
+to deal with indefinite valued pixels and references out of bounds.
+A version of the array sequential interpolators was written that handled
+both situations allowing some options to the user.  The extension of
+these features to the two dimensional case becomes more dependent on
+details within IRAF and less mathematical in nature.  It would also
+duplicate other code within IRAF that deals with out of bound references.
+Finally the need to test for the various situations slows down the operation.
+So all features referring to indefinite valued pixels and out of bound
+references have been removed.  The user is responsible for ensuring that
+"x" values land within the array.  The code does not test to see if x
+is in bounds.  A routine has been added that interpolates
+an array with indefinites and returns an array with all legitimate
+real numbers.
diff --git a/math/interp/usernote b/math/interp/usernote
new file mode 100644
index 00000000..55483022
--- /dev/null
+++ b/math/interp/usernote
@@ -0,0 +1,118 @@
+	Using the Sequential One Dimensional Interpolation Routines
+	A Quick Note for Programmers 
+
+
+I. GENERAL NOTES:
+
+	1. Defines are found in file interpdef.h.  The routines
+	   are in library interplib.a.
+
+	2. All pixels are assumed to be good. Except for routine
+	   arbpix.
+
+	3. This is for uniformly spaced data -- thus for the i-th
+	   data value, y[i], the corresponding x[i] = i by assumption.
+
+	4. All x references are assumed to land in the closed interval
+	   1 <= x <= NPTS, where NPTS is the number of points in the
+	   data array.  If x is outside this range, the result is
+	   not specified.
+
+	5. A storage area and work space array must be provided.
+	   It is of type real and the size is 2 * NPTS + SZ_ASI
+
+	
+
+II. PROCEDURES:
+
+
+  **** Subroutine to select the interpolator type
+  *
+  *	interpolator_type = clginterp (param)
+  *
+  *	char	param[ARB]
+  *
+  *	     The parameter prompt string is sent to the CL and the
+  *	routine evaluates the returned string to select one of the
+  *	interpolator types given in interpdef.h.  The input string
+  *	may be one of the following with possible abbreviations:
+  *		nearest
+  *		linear
+  *		3rd order poly
+  *		5th order poly
+  ****		cubic spline
+
+
+  **** Subroutine to replace INDEF's with interpolated values.
+  *
+  *	arbpix (datain, n, dataout, interpolator_type)
+  *
+  *	real	datain[ARB]		# data_in array
+  *	int	n			# number of points in data_in
+  *	real	dataout[ARB]		# array out, may not be same as
+  *					# data_in
+  *	int	interpolator_type
+  *
+  *	    The interpolator type can be set to:
+  *
+  *		IT_NEAREST		nearest neighbor
+  *		IT_LINEAR		linear interpolation
+  *		IT_POLY3		interior polynomial 3rd order
+  *		IT_POLY5		interior polynomial 5th order
+  ****		IT_SPLINE3		cubic natural spline
+
+
+  **** Subroutine to set interpolator type.
+  *
+  *	asiset(coeff,interpolator_type)
+  *
+  *	real	coeff[ARB]		# work + storage array, dimension
+  *					# 2 * NPTS + SZ_ASI
+  ****	int	interpolator_type	# see above
+
+
+  **** Subroutine to fit interpolator to data.
+  *
+  *	asifit (datain, npts, coeff)
+  *
+  *	real	datain[ARB]	# data array 
+  *	int	npts		# number of points in data array
+  ****	real	coeff[ARB]	# work+storage area dim 2*npts + SZ_ASI
+  
+  
+  **** Subroutine to return interpolated value after fitting.  
+  *
+  *	real asival (x, coeff)
+  *	
+  *	real	x
+  ****	real	coeff[ARB]
+  
+  
+  **** Subroutine to evaluate an ordered sequence of values.
+  *
+  *	asieva (x, y, n, coeff)
+  *
+  *	real	x[ARB]		# input array of x values
+  *	real	y[ARB]		# output array of interpolated values
+  *	int	n		# number of x values
+  ****	real	coeff[ARB]
+  
+  
+  **** Subroutine to evaluate derivatives at a point.
+  *
+  *	asider (x, derivs, nder, coeff)
+  *
+  *	real	x
+  *	real	derivs[ARB]	# output array containing derivatives
+  *				# derivs[1] is function value
+  *	int	nder		# input:  nder - 1 derivatives are evaluated
+  ****	real	coeff[ARB]
+  
+      
+  **** Subroutine to integrate the interpolated data.
+  *
+  *	real asigrl (a, b, coeff)
+  *
+  *	real	a		# lower limit
+  *	real	b		# upper limit
+  ****	real	coeff[ARB]
diff --git a/math/llsq/README b/math/llsq/README
new file mode 100644
index 00000000..bfaabb58
--- /dev/null
+++ b/math/llsq/README
@@ -0,0 +1,33 @@
+This directory contains a collection of routines for solving linear least
+squares problems by the Singular Value Decomposition (SVD) method, as
+described in "Solving Least Squares Problems", by Charles L. Lawson and
+Richard J. Hanson, Prentice Hall, 1974.  The appendix of this book contains
+full listings of the Fortran codes, as well as a users guide.
+
+The numerical subroutines are in this directory.  The directory "progs"
+contains a number of examples of the use of these routines in Fortran programs.
+
+The numerical routines have been modified to eliminate the use of Fortran
+i/o for error conditions.  The integer status return IER has been added to
+all such routines, and the Fortran write statement(s) removed.  A successful
+call returns zero in IER, while an unsucessful call returns a positive integer
+error code, identifying the error.  The original codes are in the directory
+"original_f".
+
+The affected routines and the new calling sequences are as follows:
+
+      subroutine BNDSOL (mode,g,mdg,nb,ip,ir,x,n,rnorm,ier)
+      subroutine LDP	(g,mdg,m,n,h,x,xnorm,w,index,ier)
+      subroutine NNLS	(a,mda,m,n,b,x,rnorm,w,zz,index,ier)
+      subroutine SVDRS	(a,mda,mm,nn,b,mdb,nb,s,ier)
+
+The routines SVA and MFEOUT were not installed in the library, since they
+do extensive i/o, but have been modified to reflect the changes to the
+above subroutines.
+
+See "lsq.x" and "band.x" in progs/ for examples demonstrating the use
+of these routines in IRAF spp programs.
+
+20Nov82 D.Tody
+
+Oct85	Added comma after P edit descriptor in sva.f
diff --git a/math/llsq/bndacc.f b/math/llsq/bndacc.f
new file mode 100644
index 00000000..80b9914c
--- /dev/null
+++ b/math/llsq/bndacc.f
@@ -0,0 +1,74 @@
+      subroutine bndacc (g,mdg,nb,ip,ir,mt,jt)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   sequential algorithm for banded least squares problem..
+c	   accumulation phase.	    for solution phase use bndsol.
+c
+c     the calling program must set ir=1 and ip=1 before the first call
+c     to bndacc for a new case.
+c
+c     the second subscript of g( ) must be dimensioned at least
+c     nb+1 in the calling program.
+      dimension g(mdg,1)
+      zero=0.
+c
+c	       alg. steps 1-4 are performed external to this subroutine.
+c
+      nbp1=nb+1
+      if (mt.le.0) return
+c					      alg. step 5
+      if (jt.eq.ip) go to 70
+c					      alg. steps 6-7
+      if (jt.le.ir) go to 30
+c					      alg. steps 8-9
+      do 10 i=1,mt
+	ig1=jt+mt-i
+	ig2=ir+mt-i
+	do 10 j=1,nbp1
+   10	g(ig1,j)=g(ig2,j)
+c					      alg. step 10
+      ie=jt-ir
+      do 20 i=1,ie
+	ig=ir+i-1
+	do 20 j=1,nbp1
+   20	g(ig,j)=zero
+c					      alg. step 11
+      ir=jt
+c					      alg. step 12
+   30 mu=min0(nb-1,ir-ip-1)
+      if (mu.eq.0) go to 60
+c					      alg. step 13
+      do 50 l=1,mu
+c					      alg. step 14
+	k=min0(l,jt-ip)
+c					      alg. step 15
+	lp1=l+1
+	ig=ip+l
+	do 40 i=lp1,nb
+	  jg=i-k
+   40	  g(ig,jg)=g(ig,i)
+c					      alg. step 16
+	do 50 i=1,k
+	jg=nbp1-i
+   50	g(ig,jg)=zero
+c					      alg. step 17
+   60 ip=jt
+c					      alg. steps 18-19
+   70 mh=ir+mt-ip
+      kh=min0(nbp1,mh)
+c					      alg. step 20
+      do 80 i=1,kh
+   80	call h12 (1,i,max0(i+1,ir-ip+1),mh,g(ip,i),1,rho,
+     1		  g(ip,i+1),1,mdg,nbp1-i)
+c					      alg. step 21
+      ir=ip+kh
+c					      alg. step 22
+      if (kh.lt.nbp1) go to 100
+c					      alg. step 23
+      do 90 i=1,nb
+   90	g(ir-1,i)=zero
+c					      alg. step 24
+  100 continue
+c					      alg. step 25
+      return
+      end
diff --git a/math/llsq/bndsol.f b/math/llsq/bndsol.f
new file mode 100644
index 00000000..4c4bd973
--- /dev/null
+++ b/math/llsq/bndsol.f
@@ -0,0 +1,71 @@
+      subroutine bndsol (mode,g,mdg,nb,ip,ir,x,n,rnorm,ier)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   sequential solution of a banded least squares problem..
+c	   solution phase.   for the accumulation phase use bndacc.
+c
+c     mode = 1	   solve r*x=y	 where r and y are in the g( ) array
+c		   and x will be stored in the x( ) array.
+c	     2	   solve (r**t)*x=y   where r is in g( ),
+c		   y is initially in x( ), and x replaces y in x( ),
+c	     3	   solve r*x=y	 where r is in g( ).
+c		   y is initially in x( ), and x replaces y in x( ).
+c
+c     the second subscript of g( ) must be dimensioned at least
+c     nb+1 in the calling program.
+      dimension g(mdg,1),x(n)
+      zero=0.
+      ier = 0
+c
+      rnorm=zero
+      go to (10,90,50), mode
+c				    ********************* mode = 1
+c				    algc step 26
+   10	   do 20 j=1,n
+   20	   x(j)=g(j,nb+1)
+      rsq=zero
+      np1=n+1
+      irm1=ir-1
+      if (np1.gt.irm1) go to 40
+	   do 30 j=np1,irm1
+   30	   rsq=rsq+g(j,nb+1)**2
+      rnorm=sqrt(rsq)
+   40 continue
+c				    ********************* mode = 3
+c				    alg. step 27
+   50	   do 80 ii=1,n
+	   i=n+1-ii
+c				    alg. step 28
+	   s=zero
+	   l=max0(0,i-ip)
+c				    alg. step 29
+	   if (i.eq.n) go to 70
+c				    alg. step 30
+	   ie=min0(n+1-i,nb)
+		do 60 j=2,ie
+		jg=j+l
+		ix=i-1+j
+   60		s=s+g(i,jg)*x(ix)
+c				    alg. step 31
+   70	   if (g(i,l+1)) 80,130,80
+   80	   x(i)=(x(i)-s)/g(i,l+1)
+c				    alg. step 32
+      return
+c				    ********************* mode = 2
+   90	   do 120 j=1,n
+	   s=zero
+	   if (j.eq.1) go to 110
+	   i1=max0(1,j-nb+1)
+	   i2=j-1
+		do 100 i=i1,i2
+		l=j-i+1+max0(0,i-ip)
+  100		s=s+x(i)*g(i,l)
+  110	   l=max0(0,j-ip)
+	   if (g(j,l+1)) 120,130,120
+  120	   x(j)=(x(j)-s)/g(j,l+1)
+      return
+c
+c     error return: zero diagonal term in bndsol
+  130 ier = 1
+      return
+      end
diff --git a/math/llsq/diff.f b/math/llsq/diff.f
new file mode 100644
index 00000000..79dacb92
--- /dev/null
+++ b/math/llsq/diff.f
@@ -0,0 +1,6 @@
+      function diff(x,y)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 june 7
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+      diff=x-y
+      return
+      end
diff --git a/math/llsq/g1.f b/math/llsq/g1.f
new file mode 100644
index 00000000..5d44c50b
--- /dev/null
+++ b/math/llsq/g1.f
@@ -0,0 +1,33 @@
+      subroutine g1 (a,b,cos,sin,sig)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c
+c
+c     compute orthogonal rotation matrix..
+c     compute.. matrix	 (c, s) so that (c, s)(a) = (sqrt(a**2+b**2))
+c			 (-s,c) 	(-s,c)(b)   (	0	   )
+c     compute sig = sqrt(a**2+b**2)
+c	 sig is computed last to allow for the possibility that
+c	 sig may be in the same location as a or b .
+c
+      zero=0.
+      one=1.
+      if (abs(a).le.abs(b)) go to 10
+      xr=b/a
+      yr=sqrt(one+xr**2)
+      cos=sign(one/yr,a)
+      sin=cos*xr
+      sig=abs(a)*yr
+      return
+   10 if (b) 20,30,20
+   20 xr=a/b
+      yr=sqrt(one+xr**2)
+      sin=sign(one/yr,b)
+      cos=sin*xr
+      sig=abs(b)*yr
+      return
+   30 sig=zero
+      cos=zero
+      sin=one
+      return
+      end
diff --git a/math/llsq/g2.f b/math/llsq/g2.f
new file mode 100644
index 00000000..6f01a582
--- /dev/null
+++ b/math/llsq/g2.f
@@ -0,0 +1,9 @@
+      subroutine g2    (cos,sin,x,y)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1972 dec 15
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   apply the rotation computed by g1 to (x,y).
+      xr=cos*x+sin*y
+      y=-sin*x+cos*y
+      x=xr
+      return
+      end
diff --git a/math/llsq/gen.f b/math/llsq/gen.f
new file mode 100644
index 00000000..e7933d6d
--- /dev/null
+++ b/math/llsq/gen.f
@@ -0,0 +1,31 @@
+      function	 gen(anoise)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1972 dec 15
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   generate numbers for construction of test cases.
+      mi=891
+      mj=457
+      i=5
+      j=7
+      aj=0.
+c
+      if (anoise) 10,30,20
+   10 gen=0.
+      return
+c
+c     the sequence of values of j  is bounded between 1 and 996
+c     if initial j = 1,2,3,4,5,6,7,8, or 9, the period is 332
+c
+   20 j=j*mj
+      j=j-997*(j/997)
+      aj=j-498
+c     the sequence of values of i  is bounded between 1 and 999
+c     if initial i = 1,2,3,6,7, or 9,  the period will be 50
+c     if initial i = 4 or 8   the period will be 25
+c     if initial i = 5	      the period will be 10
+c
+   30 i=i*mi
+      i=i-1000*(i/1000)
+      ai=i-500
+      gen=ai+aj*anoise
+      return
+      end
diff --git a/math/llsq/h12.f b/math/llsq/h12.f
new file mode 100644
index 00000000..81daa629
--- /dev/null
+++ b/math/llsq/h12.f
@@ -0,0 +1,80 @@
+c     subroutine h12 (mode,lpivot,l1,m,u,iue,up,c,ice,icv,ncv)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c
+c     construction and/or application of a single
+c     householder transformation..     q = i + u*(u**t)/b
+c
+c     mode    = 1 or 2	 to select algorithm  h1  or  h2 .
+c     lpivot is the index of the pivot element.
+c     l1,m   if l1 .le. m   the transformation will be constructed to
+c	     zero elements indexed from l1 through m.	if l1 gt. m
+c	     the subroutine does an identity transformation.
+c     u(),iue,up    on entry to h1 u() contains the pivot vector.
+c		    iue is the storage increment between elements.
+c					on exit from h1 u() and up
+c		    contain quantities defining the vector u of the
+c		    householder transformation.   on entry to h2 u()
+c		    and up should contain quantities previously computed
+c		    by h1.  these will not be modified by h2.
+c     c()    on entry to h1 or h2 c() contains a matrix which will be
+c	     regarded as a set of vectors to which the householder
+c	     transformation is to be applied.  on exit c() contains the
+c	     set of transformed vectors.
+c     ice    storage increment between elements of vectors in c().
+c     icv    storage increment between vectors in c().
+c     ncv    number of vectors in c() to be transformed. if ncv .le. 0
+c	     no operations will be done on c().
+c
+      subroutine h12 (mode,lpivot,l1,m,u,iue,up,c,ice,icv,ncv)
+      dimension u(iue,m), c(1)
+      double precision sm,b
+      one=1.
+c
+      if (0.ge.lpivot.or.lpivot.ge.l1.or.l1.gt.m) return
+      cl=abs(u(1,lpivot))
+      if (mode.eq.2) go to 60
+c			     ****** construct the transformation. ******
+	  do 10 j=l1,m
+   10	  cl=amax1(abs(u(1,j)),cl)
+      if (cl) 130,130,20
+   20 clinv=one/cl
+      sm=(dble(u(1,lpivot))*clinv)**2
+	  do 30 j=l1,m
+   30	  sm=sm+(dble(u(1,j))*clinv)**2
+c			       convert dble. prec. sm to sngl. prec. sm1
+      sm1=sm
+      cl=cl*sqrt(sm1)
+      if (u(1,lpivot)) 50,50,40
+   40 cl=-cl
+   50 up=u(1,lpivot)-cl
+      u(1,lpivot)=cl
+      go to 70
+c	     ****** apply the transformation  i+u*(u**t)/b  to c. ******
+c
+   60 if (cl) 130,130,70
+   70 if (ncv.le.0) return
+      b=dble(up)*u(1,lpivot)
+c			b  must be nonpositive here.  if b = 0., return.
+c
+      if (b) 80,130,130
+   80 b=one/b
+      i2=1-icv+ice*(lpivot-1)
+      incr=ice*(l1-lpivot)
+	  do 120 j=1,ncv
+	  i2=i2+icv
+	  i3=i2+incr
+	  i4=i3
+	  sm=c(i2)*dble(up)
+	      do 90 i=l1,m
+	      sm=sm+c(i3)*dble(u(1,i))
+   90	      i3=i3+ice
+	  if (sm) 100,120,100
+  100	  sm=sm*b
+	  c(i2)=c(i2)+sm*dble(up)
+	      do 110 i=l1,m
+	      c(i4)=c(i4)+sm*dble(u(1,i))
+  110	      i4=i4+ice
+  120	  continue
+  130 return
+      end
diff --git a/math/llsq/hfti.f b/math/llsq/hfti.f
new file mode 100644
index 00000000..62dcebe4
--- /dev/null
+++ b/math/llsq/hfti.f
@@ -0,0 +1,136 @@
+      subroutine hfti (a,mda,m,n,b,mdb,nb,tau,krank,rnorm,h,g,ip)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   solve least squares problem using algorithm, hfti.
+c
+      dimension a(mda,n),b(mdb,nb),h(n),g(n),rnorm(nb)
+      integer ip(n)
+      double precision sm,dzero
+      szero=0.
+      dzero=0.d0
+      factor=0.001
+c
+      k=0
+      ldiag=min0(m,n)
+      if (ldiag.le.0) go to 270
+	  do 80 j=1,ldiag
+	  if (j.eq.1) go to 20
+c
+c     update squared column lengths and find lmax
+c    ..
+	  lmax=j
+	      do 10 l=j,n
+	      h(l)=h(l)-a(j-1,l)**2
+	      if (h(l).gt.h(lmax)) lmax=l
+   10	      continue
+	  if(diff(hmax+factor*h(lmax),hmax)) 20,20,50
+c
+c     compute squared column lengths and find lmax
+c    ..
+   20	  lmax=j
+	      do 40 l=j,n
+	      h(l)=0.
+		  do 30 i=j,m
+   30		  h(l)=h(l)+a(i,l)**2
+	      if (h(l).gt.h(lmax)) lmax=l
+   40	      continue
+	  hmax=h(lmax)
+c    ..
+c     lmax has been determined
+c
+c     do column interchanges if needed.
+c    ..
+   50	  continue
+	  ip(j)=lmax
+	  if (ip(j).eq.j) go to 70
+	      do 60 i=1,m
+	      tmp=a(i,j)
+	      a(i,j)=a(i,lmax)
+   60	      a(i,lmax)=tmp
+	  h(lmax)=h(j)
+c
+c     compute the j-th transformation and apply it to a and b.
+c    ..
+   70	  call h12 (1,j,j+1,m,a(1,j),1,h(j),a(1,j+1),1,mda,n-j)
+   80	  call h12 (2,j,j+1,m,a(1,j),1,h(j),b,1,mdb,nb)
+c
+c     determine the pseudorank, k, using the tolerance, tau.
+c    ..
+	  do 90 j=1,ldiag
+	  if (abs(a(j,j)).le.tau) go to 100
+   90	  continue
+      k=ldiag
+      go to 110
+  100 k=j-1
+  110 kp1=k+1
+c
+c     compute the norms of the residual vectors.
+c
+      if (nb.le.0) go to 140
+	  do 130 jb=1,nb
+	  tmp=szero
+	  if (kp1.gt.m) go to 130
+	      do 120 i=kp1,m
+  120	      tmp=tmp+b(i,jb)**2
+  130	  rnorm(jb)=sqrt(tmp)
+  140 continue
+c					    special for pseudorank = 0
+      if (k.gt.0) go to 160
+      if (nb.le.0) go to 270
+	  do 150 jb=1,nb
+	      do 150 i=1,n
+  150	      b(i,jb)=szero
+      go to 270
+c
+c     if the pseudorank is less than n compute householder
+c     decomposition of first k rows.
+c    ..
+  160 if (k.eq.n) go to 180
+	  do 170 ii=1,k
+	  i=kp1-ii
+  170	  call h12 (1,i,kp1,n,a(i,1),mda,g(i),a,mda,1,i-1)
+  180 continue
+c
+c
+      if (nb.le.0) go to 270
+	  do 260 jb=1,nb
+c
+c     solve the k by k triangular system.
+c    ..
+	      do 210 l=1,k
+	      sm=dzero
+	      i=kp1-l
+	      if (i.eq.k) go to 200
+	      ip1=i+1
+		  do 190 j=ip1,k
+  190		  sm=sm+a(i,j)*dble(b(j,jb))
+  200	      sm1=sm
+  210	      b(i,jb)=(b(i,jb)-sm1)/a(i,i)
+c
+c     complete computation of solution vector.
+c    ..
+	  if (k.eq.n) go to 240
+	      do 220 j=kp1,n
+  220	      b(j,jb)=szero
+	      do 230 i=1,k
+  230	      call h12 (2,i,kp1,n,a(i,1),mda,g(i),b(1,jb),1,mdb,1)
+c
+c      re-order the solution vector to compensate for the
+c      column interchanges.
+c    ..
+  240	      do 250 jj=1,ldiag
+	      j=ldiag+1-jj
+	      if (ip(j).eq.j) go to 250
+	      l=ip(j)
+	      tmp=b(l,jb)
+	      b(l,jb)=b(j,jb)
+	      b(j,jb)=tmp
+  250	      continue
+  260	  continue
+c    ..
+c     the solution vectors, x, are now
+c     in the first  n  rows of the array b(,).
+c
+  270 krank=k
+      return
+      end
diff --git a/math/llsq/ldp.f b/math/llsq/ldp.f
new file mode 100644
index 00000000..a083f35b
--- /dev/null
+++ b/math/llsq/ldp.f
@@ -0,0 +1,79 @@
+      subroutine ldp (g,mdg,m,n,h,x,xnorm,w,index,ier)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1974 mar 1
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c
+c	     **********  least distance programming  **********
+c
+      integer index(m)
+      dimension g(mdg,n), h(m), x(n), w(1)
+      zero=0.
+      one=1.
+      if (n.le.0) go to 120
+	  do 10 j=1,n
+   10	  x(j)=zero
+      xnorm=zero
+      if (m.le.0) go to 110
+c
+c     the declared dimension of w() must be at least (n+1)*(m+2)+2*m.
+c
+c      first (n+1)*m locs of w()   =  matrix e for problem nnls.
+c	next	 n+1 locs of w()   =  vector f for problem nnls.
+c	next	 n+1 locs of w()   =  vector z for problem nnls.
+c	next	   m locs of w()   =  vector y for problem nnls.
+c	next	   m locs of w()   =  vector wdual for problem nnls.
+c     copy g**t into first n rows and m columns of e.
+c     copy h**t into row n+1 of e.
+c
+      iw=0
+	  do 30 j=1,m
+	      do 20 i=1,n
+	      iw=iw+1
+   20	      w(iw)=g(j,i)
+	  iw=iw+1
+   30	  w(iw)=h(j)
+      if=iw+1
+c				 store n zeros followed by a one into f.
+	  do 40 i=1,n
+	  iw=iw+1
+   40	  w(iw)=zero
+      w(iw+1)=one
+c
+      np1=n+1
+      iz=iw+2
+      iy=iz+np1
+      iwdual=iy+m
+c
+      call nnls (w,np1,np1,m,w(if),w(iy),rnorm,w(iwdual),w(iz),index,
+     *		 ier)
+c		       use the following return if unsuccessful in nnls.
+      if (ier.ne.0) return
+      if (rnorm) 130,130,50
+   50 fac=one
+      iw=iy-1
+	  do 60 i=1,m
+	  iw=iw+1
+c				here we are using the solution vector y.
+   60	  fac=fac-h(i)*w(iw)
+c
+      if (diff(one+fac,one)) 130,130,70
+   70 fac=one/fac
+	  do 90 j=1,n
+	  iw=iy-1
+	      do 80 i=1,m
+	      iw=iw+1
+c				here we are using the solution vector y.
+   80	      x(j)=x(j)+g(i,j)*w(iw)
+   90	  x(j)=x(j)*fac
+	  do 100 j=1,n
+  100	  xnorm=xnorm+x(j)**2
+      xnorm=sqrt(xnorm)
+c			      successful return.
+  110 ier=0
+      return
+c			      error return.	  n .le. 0.
+  120 ier=2
+      return
+c			      returning with constraints not compatible.
+  130 ier=4
+      return
+      end
diff --git a/math/llsq/mfeout.f b/math/llsq/mfeout.f
new file mode 100644
index 00000000..fb439e40
--- /dev/null
+++ b/math/llsq/mfeout.f
@@ -0,0 +1,64 @@
+      subroutine mfeout (a,mda,m,n,names,mode)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   subroutine for matrix output with labeling.
+c
+c     a( )	   matrix to be output
+c		   mda	   first dimension of a array
+c		   m	     no. of rows in a matrix
+c		   n	     no. of cols in a matrix
+c     names()	   array of names.  if names(1) = 1h , the rest
+c		   of the names() array will be ignored.
+c     mode	   =1	for   4p8f15.0	format	for v matrix.
+c		   =2	for   8e15.8  format  for candidate solutions.
+c
+      dimension    a(mda,01)
+      integer names(m),ihead(2)
+      logical	notblk
+      data  maxcol/8/, iblank/1h /,ihead(1)/4h col/,ihead(2)/4hsoln/
+c
+      notblk=names(1).ne.iblank
+      if (m.le.0.or.n.le.0) return
+c
+      if (mode.eq.2) go to 10
+      write (6,70)
+      go to 20
+   10 write (6,80)
+   20 continue
+c
+      nblock=n/maxcol
+      last=n-nblock*maxcol
+      ncol=maxcol
+      j1=1
+c
+c			     main loop starts here
+c
+   30 if (nblock.gt.0) go to 40
+      if (last.le.0) return
+      ncol=last
+      last=0
+c
+   40 j2=j1+ncol-1
+      write (6,90) (ihead(mode),j,j=j1,j2)
+c
+	   do 60 i=1,m
+	   name=iblank
+	   if (notblk) name=names(i)
+c
+	   if (mode.eq.2) go to 50
+	   write (6,100) i,name,(a(i,j),j=j1,j2)
+	   go to 60
+   50	   write (6,110) i,name,(a(i,j),j=j1,j2)
+   60	   continue
+c
+      j1=j1+maxcol
+      nblock=nblock-1
+      go to 30
+c
+   70 format (45h0v-matrix of the singular value decomposition,
+     * 8h of a*d./47h (elements of v scaled up by a factor of 10**4))
+   80 format (35h0sequence of candidate solutions, x)
+   90 format (1h0,11x,8(6x,a4,i4,1x)/1x)
+  100 format (1x,i3,1x,a6,1x,4p8f15.0)
+  110 format (1x,i3,1x,a6,1x,8e15.8)
+      end
diff --git a/math/llsq/mkpkg b/math/llsq/mkpkg
new file mode 100644
index 00000000..1d2cf4a5
--- /dev/null
+++ b/math/llsq/mkpkg
@@ -0,0 +1,23 @@
+# Update Lawson's and Hanson's linear least squares package (LIBLLSQ).
+
+$checkout libllsq.a lib$
+$update   libllsq.a
+$checkin  libllsq.a lib$
+$exit
+
+libllsq.a:
+	bndacc.f
+	bndsol.f
+	diff.f
+	g1.f
+	g2.f
+	gen.f
+	h12.f
+	hfti.f
+	ldp.f
+	mfeout.f
+	nnls.f
+	qrbd.f
+	sva.f
+	svdrs.f
+	;
diff --git a/math/llsq/nnls.f b/math/llsq/nnls.f
new file mode 100644
index 00000000..58337147
--- /dev/null
+++ b/math/llsq/nnls.f
@@ -0,0 +1,276 @@
+c     subroutine nnls  (a,mda,m,n,b,x,rnorm,w,zz,index,ier)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 june 15
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c
+c	  **********   nonnegative least squares   **********
+c
+c     given an m by n matrix, a, and an m-vector, b,  compute an
+c     n-vector, x, which solves the least squares problem
+c
+c		       a * x = b  subject to x .ge. 0
+c
+c     a(),mda,m,n     mda is the first dimensioning parameter for the
+c		      array, a().   on entry a() contains the m by n
+c		      matrix, a.	   on exit a() contains
+c		      the product matrix, q*a , where q is an
+c		      m by m orthogonal matrix generated implicitly by
+c		      this subroutine.
+c     b()     on entry b() contains the m-vector, b.   on exit b() con-
+c	      tains q*b.
+c     x()     on entry x() need not be initialized.  on exit x() will
+c	      contain the solution vector.
+c     rnorm   on exit rnorm contains the euclidean norm of the
+c	      residual vector.
+c     w()     an n-array of working space.  on exit w() will contain
+c	      the dual solution vector.   w will satisfy w(i) = 0.
+c	      for all i in set p  and w(i) .le. 0. for all i in set z
+c     zz()     an m-array of working space.
+c     index()	  an integer working array of length at least n.
+c		  on exit the contents of this array define the sets
+c		  p and z as follows..
+c
+c		  index(1)   thru index(nsetp) = set p.
+c		  index(iz1) thru index(iz2)   = set z.
+c		  iz1 = nsetp + 1 = npp1
+c		  iz2 = n
+c     ier     this is a success-failure flag with the following
+c	      meanings.
+c	      0     the solution has been computed successfully.
+c	      2     the dimensions of the problem are bad.
+c		    either m .le. 0 or n .le. 0.
+c	      3     iteration count exceeded.  more than 3*n iterations.
+c
+      subroutine nnls (a,mda,m,n,b,x,rnorm,w,zz,index,ier)
+      dimension a(mda,n), b(m), x(n), w(n), zz(m)
+      integer index(n)
+      zero=0.
+      one=1.
+      two=2.
+      factor=0.01
+c
+      ier=0
+      if (m.gt.0.and.n.gt.0) go to 10
+      ier=2
+      return
+   10 iter=0
+      itmax=3*n
+c
+c		     initialize the arrays index() and x().
+c
+	  do 20 i=1,n
+	  x(i)=zero
+   20	  index(i)=i
+c
+      iz2=n
+      iz1=1
+      nsetp=0
+      npp1=1
+c			      ******  main loop begins here  ******
+   30 continue
+c		   quit if all coefficients are already in the solution.
+c			 or if m cols of a have been triangularized.
+c
+      if (iz1.gt.iz2.or.nsetp.ge.m) go to 350
+c
+c	  compute components of the dual (negative gradient) vector w().
+c
+	  do 50 iz=iz1,iz2
+	  j=index(iz)
+	  sm=zero
+	      do 40 l=npp1,m
+   40	      sm=sm+a(l,j)*b(l)
+   50	  w(j)=sm
+c				    find largest positive w(j).
+   60 wmax=zero
+	  do 70 iz=iz1,iz2
+	  j=index(iz)
+	  if (w(j).le.wmax) go to 70
+	  wmax=w(j)
+	  izmax=iz
+   70	  continue
+c
+c	      if wmax .le. 0. go to termination.
+c	      this indicates satisfaction of the kuhn-tucker conditions.
+c
+      if (wmax) 350,350,80
+   80 iz=izmax
+      j=index(iz)
+c
+c     the sign of w(j) is ok for j to be moved to set p.
+c     begin the transformation and check new diagonal element to avoid
+c     near linear dependence.
+c
+      asave=a(npp1,j)
+      call h12 (1,npp1,npp1+1,m,a(1,j),1,up,dummy,1,1,0)
+      unorm=zero
+      if (nsetp.eq.0) go to 100
+	  do 90 l=1,nsetp
+   90	  unorm=unorm+a(l,j)**2
+  100 unorm=sqrt(unorm)
+      if (diff(unorm+abs(a(npp1,j))*factor,unorm)) 130,130,110
+c
+c     col j is sufficiently independent.  copy b into zz, update zz and
+c   > solve for ztest ( = proposed new value for x(j) ).
+c
+  110	  do 120 l=1,m
+  120	  zz(l)=b(l)
+      call h12 (2,npp1,npp1+1,m,a(1,j),1,up,zz,1,1,1)
+      ztest=zz(npp1)/a(npp1,j)
+c
+c				      see if ztest is positive
+c     reject j as a candidate to be moved from set z to set p.
+c     restore a(npp1,j), set w(j)=0., and loop back to test dual
+c
+      if (ztest) 130,130,140
+c
+c     coeffs again.
+c
+  130 a(npp1,j)=asave
+      w(j)=zero
+      go to 60
+c
+c     the index  j=index(iz)  has been selected to be moved from
+c     set z to set p.	 update b,  update indices,  apply householder
+c     transformations to cols in new set z,  zero subdiagonal elts in
+c     col j,  set w(j)=0.
+c
+  140	  do 150 l=1,m
+  150	  b(l)=zz(l)
+c
+      index(iz)=index(iz1)
+      index(iz1)=j
+      iz1=iz1+1
+      nsetp=npp1
+      npp1=npp1+1
+c
+      if (iz1.gt.iz2) go to 170
+	  do 160 jz=iz1,iz2
+	  jj=index(jz)
+  160	  call h12 (2,nsetp,npp1,m,a(1,j),1,up,a(1,jj),1,mda,1)
+  170 continue
+c
+      if (nsetp.eq.m) go to 190
+	  do 180 l=npp1,m
+  180	  a(l,j)=zero
+  190 continue
+c
+      w(j)=zero
+c				 solve the triangular system.
+c				 store the solution temporarily in zz().
+      assign 200 to next
+      go to 400
+  200 continue
+c
+c			******	secondary loop begins here ******
+c
+c			   iteration counter.
+c
+  210 iter=iter+1
+      if (iter.le.itmax) go to 220
+         ier=3
+         go to 350
+  220 continue
+c
+c		     see if all new constrained coeffs are feasible.
+c				   if not compute alpha.
+c
+      alpha=two
+	  do 240 ip=1,nsetp
+	  l=index(ip)
+	  if (zz(ip)) 230,230,240
+c
+  230	  t=-x(l)/(zz(ip)-x(l))
+	  if (alpha.le.t) go to 240
+	  alpha=t
+	  jj=ip
+  240	  continue
+c
+c	   if all new constrained coeffs are feasible then alpha will
+c	   still = 2.	 if so exit from secondary loop to main loop.
+c
+      if (alpha.eq.two) go to 330
+c
+c	   otherwise use alpha which will be between 0. and 1. to
+c	   interpolate between the old x and the new zz.
+c
+	  do 250 ip=1,nsetp
+	  l=index(ip)
+  250	  x(l)=x(l)+alpha*(zz(ip)-x(l))
+c
+c	 modify a and b and the index arrays to move coefficient i
+c	 from set p to set z.
+c
+      i=index(jj)
+  260 x(i)=zero
+c
+      if (jj.eq.nsetp) go to 290
+      jj=jj+1
+	  do 280 j=jj,nsetp
+	  ii=index(j)
+	  index(j-1)=ii
+	  call g1 (a(j-1,ii),a(j,ii),cc,ss,a(j-1,ii))
+	  a(j,ii)=zero
+	      do 270 l=1,n
+	      if (l.ne.ii) call g2 (cc,ss,a(j-1,l),a(j,l))
+  270	      continue
+  280	  call g2 (cc,ss,b(j-1),b(j))
+  290 npp1=nsetp
+      nsetp=nsetp-1
+      iz1=iz1-1
+      index(iz1)=i
+c
+c	 see if the remaining coeffs in set p are feasible.  they should
+c	 be because of the way alpha was determined.
+c	 if any are infeasible it is due to round-off error.  any
+c	 that are nonpositive will be set to zero
+c	 and moved from set p to set z.
+c
+	  do 300 jj=1,nsetp
+	  i=index(jj)
+	  if (x(i)) 260,260,300
+  300	  continue
+c
+c	  copy b( ) into zz( ).  then solve again and loop back.
+c
+
+	  do 310 i=1,m
+  310	  zz(i)=b(i)
+      assign 320 to next
+      go to 400
+  320 continue
+      go to 210
+c		       ******  end of secondary loop  ******
+c
+  330	  do 340 ip=1,nsetp
+	  i=index(ip)
+  340	  x(i)=zz(ip)
+c	 all new coeffs are positive.  loop back to beginning.
+      go to 30
+c
+c			 ******  end of main loop  ******
+c
+c			 come to here for termination.
+c		      compute the norm of the final residual vector.
+c
+  350 sm=zero
+      if (npp1.gt.m) go to 370
+	  do 360 i=npp1,m
+  360	  sm=sm+b(i)**2
+      go to 390
+  370	  do 380 j=1,n
+  380	  w(j)=zero
+  390 rnorm=sqrt(sm)
+      return
+c
+c     the following block of code is used as an internal subroutine
+c     to solve the triangular system, putting the solution in zz().
+c
+  400	  do 430 l=1,nsetp
+	  ip=nsetp+1-l
+	  if (l.eq.1) go to 420
+	      do 410 ii=1,ip
+  410	      zz(ii)=zz(ii)-a(ii,jj)*zz(ip+1)
+  420	  jj=index(ip)
+  430	  zz(ip)=zz(ip)/a(ip,jj)
+      go to next, (200,320)
+      end
diff --git a/math/llsq/original_f/bndacc.f b/math/llsq/original_f/bndacc.f
new file mode 100644
index 00000000..80b9914c
--- /dev/null
+++ b/math/llsq/original_f/bndacc.f
@@ -0,0 +1,74 @@
+      subroutine bndacc (g,mdg,nb,ip,ir,mt,jt)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   sequential algorithm for banded least squares problem..
+c	   accumulation phase.	    for solution phase use bndsol.
+c
+c     the calling program must set ir=1 and ip=1 before the first call
+c     to bndacc for a new case.
+c
+c     the second subscript of g( ) must be dimensioned at least
+c     nb+1 in the calling program.
+      dimension g(mdg,1)
+      zero=0.
+c
+c	       alg. steps 1-4 are performed external to this subroutine.
+c
+      nbp1=nb+1
+      if (mt.le.0) return
+c					      alg. step 5
+      if (jt.eq.ip) go to 70
+c					      alg. steps 6-7
+      if (jt.le.ir) go to 30
+c					      alg. steps 8-9
+      do 10 i=1,mt
+	ig1=jt+mt-i
+	ig2=ir+mt-i
+	do 10 j=1,nbp1
+   10	g(ig1,j)=g(ig2,j)
+c					      alg. step 10
+      ie=jt-ir
+      do 20 i=1,ie
+	ig=ir+i-1
+	do 20 j=1,nbp1
+   20	g(ig,j)=zero
+c					      alg. step 11
+      ir=jt
+c					      alg. step 12
+   30 mu=min0(nb-1,ir-ip-1)
+      if (mu.eq.0) go to 60
+c					      alg. step 13
+      do 50 l=1,mu
+c					      alg. step 14
+	k=min0(l,jt-ip)
+c					      alg. step 15
+	lp1=l+1
+	ig=ip+l
+	do 40 i=lp1,nb
+	  jg=i-k
+   40	  g(ig,jg)=g(ig,i)
+c					      alg. step 16
+	do 50 i=1,k
+	jg=nbp1-i
+   50	g(ig,jg)=zero
+c					      alg. step 17
+   60 ip=jt
+c					      alg. steps 18-19
+   70 mh=ir+mt-ip
+      kh=min0(nbp1,mh)
+c					      alg. step 20
+      do 80 i=1,kh
+   80	call h12 (1,i,max0(i+1,ir-ip+1),mh,g(ip,i),1,rho,
+     1		  g(ip,i+1),1,mdg,nbp1-i)
+c					      alg. step 21
+      ir=ip+kh
+c					      alg. step 22
+      if (kh.lt.nbp1) go to 100
+c					      alg. step 23
+      do 90 i=1,nb
+   90	g(ir-1,i)=zero
+c					      alg. step 24
+  100 continue
+c					      alg. step 25
+      return
+      end
diff --git a/math/llsq/original_f/bndsol.f b/math/llsq/original_f/bndsol.f
new file mode 100644
index 00000000..05dd35d7
--- /dev/null
+++ b/math/llsq/original_f/bndsol.f
@@ -0,0 +1,70 @@
+      subroutine bndsol (mode,g,mdg,nb,ip,ir,x,n,rnorm)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   sequential solution of a banded least squares problem..
+c	   solution phase.   for the accumulation phase use bndacc.
+c
+c     mode = 1	   solve r*x=y	 where r and y are in the g( ) array
+c		   and x will be stored in the x( ) array.
+c	     2	   solve (r**t)*x=y   where r is in g( ),
+c		   y is initially in x( ), and x replaces y in x( ),
+c	     3	   solve r*x=y	 where r is in g( ).
+c		   y is initially in x( ), and x replaces y in x( ).
+c
+c     the second subscript of g( ) must be dimensioned at least
+c     nb+1 in the calling program.
+      dimension g(mdg,1),x(n)
+      zero=0.
+c
+      rnorm=zero
+      go to (10,90,50), mode
+c				    ********************* mode = 1
+c				    algc step 26
+   10	   do 20 j=1,n
+   20	   x(j)=g(j,nb+1)
+      rsq=zero
+      np1=n+1
+      irm1=ir-1
+      if (np1.gt.irm1) go to 40
+	   do 30 j=np1,irm1
+   30	   rsq=rsq+g(j,nb+1)**2
+      rnorm=sqrt(rsq)
+   40 continue
+c				    ********************* mode = 3
+c				    alg. step 27
+   50	   do 80 ii=1,n
+	   i=n+1-ii
+c				    alg. step 28
+	   s=zero
+	   l=max0(0,i-ip)
+c				    alg. step 29
+	   if (i.eq.n) go to 70
+c				    alg. step 30
+	   ie=min0(n+1-i,nb)
+		do 60 j=2,ie
+		jg=j+l
+		ix=i-1+j
+   60		s=s+g(i,jg)*x(ix)
+c				    alg. step 31
+   70	   if (g(i,l+1)) 80,130,80
+   80	   x(i)=(x(i)-s)/g(i,l+1)
+c				    alg. step 32
+      return
+c				    ********************* mode = 2
+   90	   do 120 j=1,n
+	   s=zero
+	   if (j.eq.1) go to 110
+	   i1=max0(1,j-nb+1)
+	   i2=j-1
+		do 100 i=i1,i2
+		l=j-i+1+max0(0,i-ip)
+  100		s=s+x(i)*g(i,l)
+  110	   l=max0(0,j-ip)
+	   if (g(j,l+1)) 120,130,120
+  120	   x(j)=(x(j)-s)/g(j,l+1)
+      return
+c
+  130 write (6,140) mode,i,j,l
+      stop
+  140 format (30h0zero diagonal term in bndsol.,12h mode,i,j,l=,4i6)
+      end
diff --git a/math/llsq/original_f/diff.f b/math/llsq/original_f/diff.f
new file mode 100644
index 00000000..79dacb92
--- /dev/null
+++ b/math/llsq/original_f/diff.f
@@ -0,0 +1,6 @@
+      function diff(x,y)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 june 7
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+      diff=x-y
+      return
+      end
diff --git a/math/llsq/original_f/g1.f b/math/llsq/original_f/g1.f
new file mode 100644
index 00000000..5d44c50b
--- /dev/null
+++ b/math/llsq/original_f/g1.f
@@ -0,0 +1,33 @@
+      subroutine g1 (a,b,cos,sin,sig)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c
+c
+c     compute orthogonal rotation matrix..
+c     compute.. matrix	 (c, s) so that (c, s)(a) = (sqrt(a**2+b**2))
+c			 (-s,c) 	(-s,c)(b)   (	0	   )
+c     compute sig = sqrt(a**2+b**2)
+c	 sig is computed last to allow for the possibility that
+c	 sig may be in the same location as a or b .
+c
+      zero=0.
+      one=1.
+      if (abs(a).le.abs(b)) go to 10
+      xr=b/a
+      yr=sqrt(one+xr**2)
+      cos=sign(one/yr,a)
+      sin=cos*xr
+      sig=abs(a)*yr
+      return
+   10 if (b) 20,30,20
+   20 xr=a/b
+      yr=sqrt(one+xr**2)
+      sin=sign(one/yr,b)
+      cos=sin*xr
+      sig=abs(b)*yr
+      return
+   30 sig=zero
+      cos=zero
+      sin=one
+      return
+      end
diff --git a/math/llsq/original_f/g2.f b/math/llsq/original_f/g2.f
new file mode 100644
index 00000000..6f01a582
--- /dev/null
+++ b/math/llsq/original_f/g2.f
@@ -0,0 +1,9 @@
+      subroutine g2    (cos,sin,x,y)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1972 dec 15
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   apply the rotation computed by g1 to (x,y).
+      xr=cos*x+sin*y
+      y=-sin*x+cos*y
+      x=xr
+      return
+      end
diff --git a/math/llsq/original_f/gen.f b/math/llsq/original_f/gen.f
new file mode 100644
index 00000000..98181a93
--- /dev/null
+++ b/math/llsq/original_f/gen.f
@@ -0,0 +1,28 @@
+      function	 gen(anoise)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1972 dec 15
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   generate numbers for construction of test cases.
+      if (anoise) 10,30,20
+   10 mi=891
+      mj=457
+      i=5
+      j=7
+      aj=0.
+      gen=0.
+      return
+c
+c     the sequence of values of j  is bounded between 1 and 996
+c     if initial j = 1,2,3,4,5,6,7,8, or 9, the period is 332
+   20 j=j*mj
+      j=j-997*(j/997)
+      aj=j-498
+c     the sequence of values of i  is bounded between 1 and 999
+c     if initial i = 1,2,3,6,7, or 9,  the period will be 50
+c     if initial i = 4 or 8   the period will be 25
+c     if initial i = 5	      the period will be 10
+   30 i=i*mi
+      i=i-1000*(i/1000)
+      ai=i-500
+      gen=ai+aj*anoise
+      return
+      end
diff --git a/math/llsq/original_f/h12.f b/math/llsq/original_f/h12.f
new file mode 100644
index 00000000..81daa629
--- /dev/null
+++ b/math/llsq/original_f/h12.f
@@ -0,0 +1,80 @@
+c     subroutine h12 (mode,lpivot,l1,m,u,iue,up,c,ice,icv,ncv)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c
+c     construction and/or application of a single
+c     householder transformation..     q = i + u*(u**t)/b
+c
+c     mode    = 1 or 2	 to select algorithm  h1  or  h2 .
+c     lpivot is the index of the pivot element.
+c     l1,m   if l1 .le. m   the transformation will be constructed to
+c	     zero elements indexed from l1 through m.	if l1 gt. m
+c	     the subroutine does an identity transformation.
+c     u(),iue,up    on entry to h1 u() contains the pivot vector.
+c		    iue is the storage increment between elements.
+c					on exit from h1 u() and up
+c		    contain quantities defining the vector u of the
+c		    householder transformation.   on entry to h2 u()
+c		    and up should contain quantities previously computed
+c		    by h1.  these will not be modified by h2.
+c     c()    on entry to h1 or h2 c() contains a matrix which will be
+c	     regarded as a set of vectors to which the householder
+c	     transformation is to be applied.  on exit c() contains the
+c	     set of transformed vectors.
+c     ice    storage increment between elements of vectors in c().
+c     icv    storage increment between vectors in c().
+c     ncv    number of vectors in c() to be transformed. if ncv .le. 0
+c	     no operations will be done on c().
+c
+      subroutine h12 (mode,lpivot,l1,m,u,iue,up,c,ice,icv,ncv)
+      dimension u(iue,m), c(1)
+      double precision sm,b
+      one=1.
+c
+      if (0.ge.lpivot.or.lpivot.ge.l1.or.l1.gt.m) return
+      cl=abs(u(1,lpivot))
+      if (mode.eq.2) go to 60
+c			     ****** construct the transformation. ******
+	  do 10 j=l1,m
+   10	  cl=amax1(abs(u(1,j)),cl)
+      if (cl) 130,130,20
+   20 clinv=one/cl
+      sm=(dble(u(1,lpivot))*clinv)**2
+	  do 30 j=l1,m
+   30	  sm=sm+(dble(u(1,j))*clinv)**2
+c			       convert dble. prec. sm to sngl. prec. sm1
+      sm1=sm
+      cl=cl*sqrt(sm1)
+      if (u(1,lpivot)) 50,50,40
+   40 cl=-cl
+   50 up=u(1,lpivot)-cl
+      u(1,lpivot)=cl
+      go to 70
+c	     ****** apply the transformation  i+u*(u**t)/b  to c. ******
+c
+   60 if (cl) 130,130,70
+   70 if (ncv.le.0) return
+      b=dble(up)*u(1,lpivot)
+c			b  must be nonpositive here.  if b = 0., return.
+c
+      if (b) 80,130,130
+   80 b=one/b
+      i2=1-icv+ice*(lpivot-1)
+      incr=ice*(l1-lpivot)
+	  do 120 j=1,ncv
+	  i2=i2+icv
+	  i3=i2+incr
+	  i4=i3
+	  sm=c(i2)*dble(up)
+	      do 90 i=l1,m
+	      sm=sm+c(i3)*dble(u(1,i))
+   90	      i3=i3+ice
+	  if (sm) 100,120,100
+  100	  sm=sm*b
+	  c(i2)=c(i2)+sm*dble(up)
+	      do 110 i=l1,m
+	      c(i4)=c(i4)+sm*dble(u(1,i))
+  110	      i4=i4+ice
+  120	  continue
+  130 return
+      end
diff --git a/math/llsq/original_f/hfti.f b/math/llsq/original_f/hfti.f
new file mode 100644
index 00000000..62dcebe4
--- /dev/null
+++ b/math/llsq/original_f/hfti.f
@@ -0,0 +1,136 @@
+      subroutine hfti (a,mda,m,n,b,mdb,nb,tau,krank,rnorm,h,g,ip)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   solve least squares problem using algorithm, hfti.
+c
+      dimension a(mda,n),b(mdb,nb),h(n),g(n),rnorm(nb)
+      integer ip(n)
+      double precision sm,dzero
+      szero=0.
+      dzero=0.d0
+      factor=0.001
+c
+      k=0
+      ldiag=min0(m,n)
+      if (ldiag.le.0) go to 270
+	  do 80 j=1,ldiag
+	  if (j.eq.1) go to 20
+c
+c     update squared column lengths and find lmax
+c    ..
+	  lmax=j
+	      do 10 l=j,n
+	      h(l)=h(l)-a(j-1,l)**2
+	      if (h(l).gt.h(lmax)) lmax=l
+   10	      continue
+	  if(diff(hmax+factor*h(lmax),hmax)) 20,20,50
+c
+c     compute squared column lengths and find lmax
+c    ..
+   20	  lmax=j
+	      do 40 l=j,n
+	      h(l)=0.
+		  do 30 i=j,m
+   30		  h(l)=h(l)+a(i,l)**2
+	      if (h(l).gt.h(lmax)) lmax=l
+   40	      continue
+	  hmax=h(lmax)
+c    ..
+c     lmax has been determined
+c
+c     do column interchanges if needed.
+c    ..
+   50	  continue
+	  ip(j)=lmax
+	  if (ip(j).eq.j) go to 70
+	      do 60 i=1,m
+	      tmp=a(i,j)
+	      a(i,j)=a(i,lmax)
+   60	      a(i,lmax)=tmp
+	  h(lmax)=h(j)
+c
+c     compute the j-th transformation and apply it to a and b.
+c    ..
+   70	  call h12 (1,j,j+1,m,a(1,j),1,h(j),a(1,j+1),1,mda,n-j)
+   80	  call h12 (2,j,j+1,m,a(1,j),1,h(j),b,1,mdb,nb)
+c
+c     determine the pseudorank, k, using the tolerance, tau.
+c    ..
+	  do 90 j=1,ldiag
+	  if (abs(a(j,j)).le.tau) go to 100
+   90	  continue
+      k=ldiag
+      go to 110
+  100 k=j-1
+  110 kp1=k+1
+c
+c     compute the norms of the residual vectors.
+c
+      if (nb.le.0) go to 140
+	  do 130 jb=1,nb
+	  tmp=szero
+	  if (kp1.gt.m) go to 130
+	      do 120 i=kp1,m
+  120	      tmp=tmp+b(i,jb)**2
+  130	  rnorm(jb)=sqrt(tmp)
+  140 continue
+c					    special for pseudorank = 0
+      if (k.gt.0) go to 160
+      if (nb.le.0) go to 270
+	  do 150 jb=1,nb
+	      do 150 i=1,n
+  150	      b(i,jb)=szero
+      go to 270
+c
+c     if the pseudorank is less than n compute householder
+c     decomposition of first k rows.
+c    ..
+  160 if (k.eq.n) go to 180
+	  do 170 ii=1,k
+	  i=kp1-ii
+  170	  call h12 (1,i,kp1,n,a(i,1),mda,g(i),a,mda,1,i-1)
+  180 continue
+c
+c
+      if (nb.le.0) go to 270
+	  do 260 jb=1,nb
+c
+c     solve the k by k triangular system.
+c    ..
+	      do 210 l=1,k
+	      sm=dzero
+	      i=kp1-l
+	      if (i.eq.k) go to 200
+	      ip1=i+1
+		  do 190 j=ip1,k
+  190		  sm=sm+a(i,j)*dble(b(j,jb))
+  200	      sm1=sm
+  210	      b(i,jb)=(b(i,jb)-sm1)/a(i,i)
+c
+c     complete computation of solution vector.
+c    ..
+	  if (k.eq.n) go to 240
+	      do 220 j=kp1,n
+  220	      b(j,jb)=szero
+	      do 230 i=1,k
+  230	      call h12 (2,i,kp1,n,a(i,1),mda,g(i),b(1,jb),1,mdb,1)
+c
+c      re-order the solution vector to compensate for the
+c      column interchanges.
+c    ..
+  240	      do 250 jj=1,ldiag
+	      j=ldiag+1-jj
+	      if (ip(j).eq.j) go to 250
+	      l=ip(j)
+	      tmp=b(l,jb)
+	      b(l,jb)=b(j,jb)
+	      b(j,jb)=tmp
+  250	      continue
+  260	  continue
+c    ..
+c     the solution vectors, x, are now
+c     in the first  n  rows of the array b(,).
+c
+  270 krank=k
+      return
+      end
diff --git a/math/llsq/original_f/ldp.f b/math/llsq/original_f/ldp.f
new file mode 100644
index 00000000..65d4c77e
--- /dev/null
+++ b/math/llsq/original_f/ldp.f
@@ -0,0 +1,79 @@
+      subroutine ldp (g,mdg,m,n,h,x,xnorm,w,index,mode)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1974 mar 1
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c
+c	     **********  least distance programming  **********
+c
+      integer index(m)
+      dimension g(mdg,n), h(m), x(n), w(1)
+      zero=0.
+      one=1.
+      if (n.le.0) go to 120
+	  do 10 j=1,n
+   10	  x(j)=zero
+      xnorm=zero
+      if (m.le.0) go to 110
+c
+c     the declared dimension of w() must be at least (n+1)*(m+2)+2*m.
+c
+c      first (n+1)*m locs of w()   =  matrix e for problem nnls.
+c	next	 n+1 locs of w()   =  vector f for problem nnls.
+c	next	 n+1 locs of w()   =  vector z for problem nnls.
+c	next	   m locs of w()   =  vector y for problem nnls.
+c	next	   m locs of w()   =  vector wdual for problem nnls.
+c     copy g**t into first n rows and m columns of e.
+c     copy h**t into row n+1 of e.
+c
+      iw=0
+	  do 30 j=1,m
+	      do 20 i=1,n
+	      iw=iw+1
+   20	      w(iw)=g(j,i)
+	  iw=iw+1
+   30	  w(iw)=h(j)
+      if=iw+1
+c				 store n zeros followed by a one into f.
+	  do 40 i=1,n
+	  iw=iw+1
+   40	  w(iw)=zero
+      w(iw+1)=one
+c
+      np1=n+1
+      iz=iw+2
+      iy=iz+np1
+      iwdual=iy+m
+c
+      call nnls (w,np1,np1,m,w(if),w(iy),rnorm,w(iwdual),w(iz),index,
+     *		 mode)
+c		       use the following return if unsuccessful in nnls.
+      if (mode.ne.1) return
+      if (rnorm) 130,130,50
+   50 fac=one
+      iw=iy-1
+	  do 60 i=1,m
+	  iw=iw+1
+c				here we are using the solution vector y.
+   60	  fac=fac-h(i)*w(iw)
+c
+      if (diff(one+fac,one)) 130,130,70
+   70 fac=one/fac
+	  do 90 j=1,n
+	  iw=iy-1
+	      do 80 i=1,m
+	      iw=iw+1
+c				here we are using the solution vector y.
+   80	      x(j)=x(j)+g(i,j)*w(iw)
+   90	  x(j)=x(j)*fac
+	  do 100 j=1,n
+  100	  xnorm=xnorm+x(j)**2
+      xnorm=sqrt(xnorm)
+c			      successful return.
+  110 mode=1
+      return
+c			      error return.	  n .le. 0.
+  120 mode=2
+      return
+c			      returning with constraints not compatible.
+  130 mode=4
+      return
+      end
diff --git a/math/llsq/original_f/nnls.f b/math/llsq/original_f/nnls.f
new file mode 100644
index 00000000..fb5aa767
--- /dev/null
+++ b/math/llsq/original_f/nnls.f
@@ -0,0 +1,278 @@
+c     subroutine nnls  (a,mda,m,n,b,x,rnorm,w,zz,index,mode)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 june 15
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c
+c	  **********   nonnegative least squares   **********
+c
+c     given an m by n matrix, a, and an m-vector, b,  compute an
+c     n-vector, x, which solves the least squares problem
+c
+c		       a * x = b  subject to x .ge. 0
+c
+c     a(),mda,m,n     mda is the first dimensioning parameter for the
+c		      array, a().   on entry a() contains the m by n
+c		      matrix, a.	   on exit a() contains
+c		      the product matrix, q*a , where q is an
+c		      m by m orthogonal matrix generated implicitly by
+c		      this subroutine.
+c     b()     on entry b() contains the m-vector, b.   on exit b() con-
+c	      tains q*b.
+c     x()     on entry x() need not be initialized.  on exit x() will
+c	      contain the solution vector.
+c     rnorm   on exit rnorm contains the euclidean norm of the
+c	      residual vector.
+c     w()     an n-array of working space.  on exit w() will contain
+c	      the dual solution vector.   w will satisfy w(i) = 0.
+c	      for all i in set p  and w(i) .le. 0. for all i in set z
+c     zz()     an m-array of working space.
+c     index()	  an integer working array of length at least n.
+c		  on exit the contents of this array define the sets
+c		  p and z as follows..
+c
+c		  index(1)   thru index(nsetp) = set p.
+c		  index(iz1) thru index(iz2)   = set z.
+c		  iz1 = nsetp + 1 = npp1
+c		  iz2 = n
+c     mode    this is a success-failure flag with the following
+c	      meanings.
+c	      1     the solution has been computed successfully.
+c	      2     the dimensions of the problem are bad.
+c		    either m .le. 0 or n .le. 0.
+c	      3    iteration count exceeded.  more than 3*n iterations.
+c
+      subroutine nnls (a,mda,m,n,b,x,rnorm,w,zz,index,mode)
+      dimension a(mda,n), b(m), x(n), w(n), zz(m)
+      integer index(n)
+      zero=0.
+      one=1.
+      two=2.
+      factor=0.01
+c
+      mode=1
+      if (m.gt.0.and.n.gt.0) go to 10
+      mode=2
+      return
+   10 iter=0
+      itmax=3*n
+c
+c		     initialize the arrays index() and x().
+c
+	  do 20 i=1,n
+	  x(i)=zero
+   20	  index(i)=i
+c
+      iz2=n
+      iz1=1
+      nsetp=0
+      npp1=1
+c			      ******  main loop begins here  ******
+   30 continue
+c		   quit if all coefficients are already in the solution.
+c			 or if m cols of a have been triangularized.
+c
+      if (iz1.gt.iz2.or.nsetp.ge.m) go to 350
+c
+c	  compute components of the dual (negative gradient) vector w().
+c
+	  do 50 iz=iz1,iz2
+	  j=index(iz)
+	  sm=zero
+	      do 40 l=npp1,m
+   40	      sm=sm+a(l,j)*b(l)
+   50	  w(j)=sm
+c				    find largest positive w(j).
+   60 wmax=zero
+	  do 70 iz=iz1,iz2
+	  j=index(iz)
+	  if (w(j).le.wmax) go to 70
+	  wmax=w(j)
+	  izmax=iz
+   70	  continue
+c
+c	      if wmax .le. 0. go to termination.
+c	      this indicates satisfaction of the kuhn-tucker conditions.
+c
+      if (wmax) 350,350,80
+   80 iz=izmax
+      j=index(iz)
+c
+c     the sign of w(j) is ok for j to be moved to set p.
+c     begin the transformation and check new diagonal element to avoid
+c     near linear dependence.
+c
+      asave=a(npp1,j)
+      call h12 (1,npp1,npp1+1,m,a(1,j),1,up,dummy,1,1,0)
+      unorm=zero
+      if (nsetp.eq.0) go to 100
+	  do 90 l=1,nsetp
+   90	  unorm=unorm+a(l,j)**2
+  100 unorm=sqrt(unorm)
+      if (diff(unorm+abs(a(npp1,j))*factor,unorm)) 130,130,110
+c
+c     col j is sufficiently independent.  copy b into zz, update zz and
+c   > solve for ztest ( = proposed new value for x(j) ).
+c
+  110	  do 120 l=1,m
+  120	  zz(l)=b(l)
+      call h12 (2,npp1,npp1+1,m,a(1,j),1,up,zz,1,1,1)
+      ztest=zz(npp1)/a(npp1,j)
+c
+c				      see if ztest is positive
+c     reject j as a candidate to be moved from set z to set p.
+c     restore a(npp1,j), set w(j)=0., and loop back to test dual
+c
+      if (ztest) 130,130,140
+c
+c     coeffs again.
+c
+  130 a(npp1,j)=asave
+      w(j)=zero
+      go to 60
+c
+c     the index  j=index(iz)  has been selected to be moved from
+c     set z to set p.	 update b,  update indices,  apply householder
+c     transformations to cols in new set z,  zero subdiagonal elts in
+c     col j,  set w(j)=0.
+c
+  140	  do 150 l=1,m
+  150	  b(l)=zz(l)
+c
+      index(iz)=index(iz1)
+      index(iz1)=j
+      iz1=iz1+1
+      nsetp=npp1
+      npp1=npp1+1
+c
+      if (iz1.gt.iz2) go to 170
+	  do 160 jz=iz1,iz2
+	  jj=index(jz)
+  160	  call h12 (2,nsetp,npp1,m,a(1,j),1,up,a(1,jj),1,mda,1)
+  170 continue
+c
+      if (nsetp.eq.m) go to 190
+	  do 180 l=npp1,m
+  180	  a(l,j)=zero
+  190 continue
+c
+      w(j)=zero
+c				 solve the triangular system.
+c				 store the solution temporarily in zz().
+      assign 200 to next
+      go to 400
+  200 continue
+c
+c			******	secondary loop begins here ******
+c
+c			   iteration counter.
+c
+  210 iter=iter+1
+      if (iter.le.itmax) go to 220
+      mode=3
+      write (6,440)
+      go to 350
+  220 continue
+c
+c		     see if all new constrained coeffs are feasible.
+c				   if not compute alpha.
+c
+      alpha=two
+	  do 240 ip=1,nsetp
+	  l=index(ip)
+	  if (zz(ip)) 230,230,240
+c
+  230	  t=-x(l)/(zz(ip)-x(l))
+	  if (alpha.le.t) go to 240
+	  alpha=t
+	  jj=ip
+  240	  continue
+c
+c	   if all new constrained coeffs are feasible then alpha will
+c	   still = 2.	 if so exit from secondary loop to main loop.
+c
+      if (alpha.eq.two) go to 330
+c
+c	   otherwise use alpha which will be between 0. and 1. to
+c	   interpolate between the old x and the new zz.
+c
+	  do 250 ip=1,nsetp
+	  l=index(ip)
+  250	  x(l)=x(l)+alpha*(zz(ip)-x(l))
+c
+c	 modify a and b and the index arrays to move coefficient i
+c	 from set p to set z.
+c
+      i=index(jj)
+  260 x(i)=zero
+c
+      if (jj.eq.nsetp) go to 290
+      jj=jj+1
+	  do 280 j=jj,nsetp
+	  ii=index(j)
+	  index(j-1)=ii
+	  call g1 (a(j-1,ii),a(j,ii),cc,ss,a(j-1,ii))
+	  a(j,ii)=zero
+	      do 270 l=1,n
+	      if (l.ne.ii) call g2 (cc,ss,a(j-1,l),a(j,l))
+  270	      continue
+  280	  call g2 (cc,ss,b(j-1),b(j))
+  290 npp1=nsetp
+      nsetp=nsetp-1
+      iz1=iz1-1
+      index(iz1)=i
+c
+c	 see if the remaining coeffs in set p are feasible.  they should
+c	 be because of the way alpha was determined.
+c	 if any are infeasible it is due to round-off error.  any
+c	 that are nonpositive will be set to zero
+c	 and moved from set p to set z.
+c
+	  do 300 jj=1,nsetp
+	  i=index(jj)
+	  if (x(i)) 260,260,300
+  300	  continue
+c
+c	  copy b( ) into zz( ).  then solve again and loop back.
+c
+
+	  do 310 i=1,m
+  310	  zz(i)=b(i)
+      assign 320 to next
+      go to 400
+  320 continue
+      go to 210
+c		       ******  end of secondary loop  ******
+c
+  330	  do 340 ip=1,nsetp
+	  i=index(ip)
+  340	  x(i)=zz(ip)
+c	 all new coeffs are positive.  loop back to beginning.
+      go to 30
+c
+c			 ******  end of main loop  ******
+c
+c			 come to here for termination.
+c		      compute the norm of the final residual vector.
+c
+  350 sm=zero
+      if (npp1.gt.m) go to 370
+	  do 360 i=npp1,m
+  360	  sm=sm+b(i)**2
+      go to 390
+  370	  do 380 j=1,n
+  380	  w(j)=zero
+  390 rnorm=sqrt(sm)
+      return
+c
+c     the following block of code is used as an internal subroutine
+c     to solve the triangular system, putting the solution in zz().
+c
+  400	  do 430 l=1,nsetp
+	  ip=nsetp+1-l
+	  if (l.eq.1) go to 420
+	      do 410 ii=1,ip
+  410	      zz(ii)=zz(ii)-a(ii,jj)*zz(ip+1)
+  420	  jj=index(ip)
+  430	  zz(ip)=zz(ip)/a(ip,jj)
+      go to next, (200,320)
+  440 format (35h0 nnls quitting on iteration count.)
+      end
diff --git a/math/llsq/original_f/qrbd.f b/math/llsq/original_f/qrbd.f
new file mode 100644
index 00000000..d9a12a24
--- /dev/null
+++ b/math/llsq/original_f/qrbd.f
@@ -0,0 +1,208 @@
+c     subroutine qrbd (ipass,q,e,nn,v,mdv,nrv,c,mdc,ncc)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   qr algorithm for singular values of a bidiagonal matrix.
+c
+c     the bidiagonal matrix
+c
+c			(q1,e2,0...    )
+c			(   q2,e3,0... )
+c		 d=	(	.      )
+c			(	  .   0)
+c			(	    .en)
+c			(	   0,qn)
+c
+c		  is pre and post multiplied by
+c		  elementary rotation matrices
+c		  ri and pi so that
+c
+c		  rk...r1*d*p1**(t)...pk**(t) = diag(s1,...,sn)
+c
+c		  to within working accuracy.
+c
+c  1. ei and qi occupy e(i) and q(i) as input.
+c
+c  2. rm...r1*c replaces 'c' in storage as output.
+c
+c  3. v*p1**(t)...pm**(t) replaces 'v' in storage as output.
+c
+c  4. si occupies q(i) as output.
+c
+c  5. the si's are nonincreasing and nonnegative.
+c
+c     this code is based on the paper and 'algol' code..
+c ref..
+c  1. reinsch,c.h. and golub,g.h. 'singular value decomposition
+c     and least squares solutions' (numer. math.), vol. 14,(1970).
+c
+      subroutine qrbd (ipass,q,e,nn,v,mdv,nrv,c,mdc,ncc)
+      logical wntv ,havers,fail
+      dimension q(nn),e(nn),v(mdv,nn),c(mdc,ncc)
+      zero=0.
+      one=1.
+      two=2.
+c
+      n=nn
+      ipass=1
+      if (n.le.0) return
+      n10=10*n
+      wntv=nrv.gt.0
+      havers=ncc.gt.0
+      fail=.false.
+      nqrs=0
+      e(1)=zero
+      dnorm=zero
+	   do 10 j=1,n
+   10	   dnorm=amax1(abs(q(j))+abs(e(j)),dnorm)
+	   do 200 kk=1,n
+	   k=n+1-kk
+c
+c     test for splitting or rank deficiencies..
+c	  first make test for last diagonal term, q(k), being small.
+   20	    if(k.eq.1) go to 50
+	    if(diff(dnorm+q(k),dnorm)) 50,25,50
+c
+c     since q(k) is small we will make a special pass to
+c     transform e(k) to zero.
+c
+   25	   cs=zero
+	   sn=-one
+		do 40 ii=2,k
+		i=k+1-ii
+		f=-sn*e(i+1)
+		e(i+1)=cs*e(i+1)
+		call g1 (q(i),f,cs,sn,q(i))
+c	  transformation constructed to zero position (i,k).
+c
+		if (.not.wntv) go to 40
+		     do 30 j=1,nrv
+   30		     call g2 (cs,sn,v(j,i),v(j,k))
+c	       accumulate rt. transformations in v.
+c
+   40		continue
+c
+c	  the matrix is now bidiagonal, and of lower order
+c	  since e(k) .eq. zero..
+c
+   50		do 60 ll=1,k
+		l=k+1-ll
+		if(diff(dnorm+e(l),dnorm)) 55,100,55
+   55		if(diff(dnorm+q(l-1),dnorm)) 60,70,60
+   60		continue
+c     this loop can't complete since e(1) = zero.
+c
+	   go to 100
+c
+c	  cancellation of e(l), l.gt.1.
+   70	   cs=zero
+	   sn=-one
+		do 90 i=l,k
+		f=-sn*e(i)
+		e(i)=cs*e(i)
+		if(diff(dnorm+f,dnorm)) 75,100,75
+   75		call g1 (q(i),f,cs,sn,q(i))
+		if (.not.havers) go to 90
+		     do 80 j=1,ncc
+   80		     call g2 (cs,sn,c(i,j),c(l-1,j))
+   90		continue
+c
+c	  test for convergence..
+  100	   z=q(k)
+	   if (l.eq.k) go to 170
+c
+c	  shift from bottom 2 by 2 minor of b**(t)*b.
+	   x=q(l)
+	   y=q(k-1)
+	   g=e(k-1)
+	   h=e(k)
+	   f=((y-z)*(y+z)+(g-h)*(g+h))/(two*h*y)
+	   g=sqrt(one+f**2)
+	   if (f.lt.zero) go to 110
+	   t=f+g
+	   go to 120
+  110	   t=f-g
+  120	   f=((x-z)*(x+z)+h*(y/t-h))/x
+c
+c	  next qr sweep..
+	   cs=one
+	   sn=one
+	   lp1=l+1
+		do 160 i=lp1,k
+		g=e(i)
+		y=q(i)
+		h=sn*g
+		g=cs*g
+		call g1 (f,h,cs,sn,e(i-1))
+		f=x*cs+g*sn
+		g=-x*sn+g*cs
+		h=y*sn
+		y=y*cs
+		if (.not.wntv) go to 140
+c
+c	       accumulate rotations (from the right) in 'v'
+		     do 130 j=1,nrv
+  130		     call g2 (cs,sn,v(j,i-1),v(j,i))
+  140		call g1 (f,h,cs,sn,q(i-1))
+		f=cs*g+sn*y
+		x=-sn*g+cs*y
+		if (.not.havers) go to 160
+		     do 150 j=1,ncc
+  150		     call g2 (cs,sn,c(i-1,j),c(i,j))
+c	       apply rotations from the left to
+c	       right hand sides in 'c'..
+c
+  160		continue
+	   e(l)=zero
+	   e(k)=f
+	   q(k)=x
+	   nqrs=nqrs+1
+	   if (nqrs.le.n10) go to 20
+c	   return to 'test for splitting'.
+c
+	   fail=.true.
+c     ..
+c     cutoff for convergence failure. 'nqrs' will be 2*n usually.
+  170	   if (z.ge.zero) go to 190
+	   q(k)=-z
+	   if (.not.wntv) go to 190
+		do 180 j=1,nrv
+  180		v(j,k)=-v(j,k)
+  190	   continue
+c	  convergence. q(k) is made nonnegative..
+c
+  200	   continue
+      if (n.eq.1) return
+	   do 210 i=2,n
+	   if (q(i).gt.q(i-1)) go to 220
+  210	   continue
+      if (fail) ipass=2
+      return
+c     ..
+c     every singular value is in order..
+  220	   do 270 i=2,n
+	   t=q(i-1)
+	   k=i-1
+		do 230 j=i,n
+		if (t.ge.q(j)) go to 230
+		t=q(j)
+		k=j
+  230		continue
+	   if (k.eq.i-1) go to 270
+	   q(k)=q(i-1)
+	   q(i-1)=t
+	   if (.not.havers) go to 250
+		do 240 j=1,ncc
+		t=c(i-1,j)
+		c(i-1,j)=c(k,j)
+  240		c(k,j)=t
+  250	   if (.not.wntv) go to 270
+		do 260 j=1,nrv
+		t=v(j,i-1)
+		v(j,i-1)=v(j,k)
+  260		v(j,k)=t
+  270	   continue
+c	  end of ordering algorithm.
+c
+      if (fail) ipass=2
+      return
+      end
diff --git a/math/llsq/original_f/sfeout.f b/math/llsq/original_f/sfeout.f
new file mode 100644
index 00000000..fb439e40
--- /dev/null
+++ b/math/llsq/original_f/sfeout.f
@@ -0,0 +1,64 @@
+      subroutine mfeout (a,mda,m,n,names,mode)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   subroutine for matrix output with labeling.
+c
+c     a( )	   matrix to be output
+c		   mda	   first dimension of a array
+c		   m	     no. of rows in a matrix
+c		   n	     no. of cols in a matrix
+c     names()	   array of names.  if names(1) = 1h , the rest
+c		   of the names() array will be ignored.
+c     mode	   =1	for   4p8f15.0	format	for v matrix.
+c		   =2	for   8e15.8  format  for candidate solutions.
+c
+      dimension    a(mda,01)
+      integer names(m),ihead(2)
+      logical	notblk
+      data  maxcol/8/, iblank/1h /,ihead(1)/4h col/,ihead(2)/4hsoln/
+c
+      notblk=names(1).ne.iblank
+      if (m.le.0.or.n.le.0) return
+c
+      if (mode.eq.2) go to 10
+      write (6,70)
+      go to 20
+   10 write (6,80)
+   20 continue
+c
+      nblock=n/maxcol
+      last=n-nblock*maxcol
+      ncol=maxcol
+      j1=1
+c
+c			     main loop starts here
+c
+   30 if (nblock.gt.0) go to 40
+      if (last.le.0) return
+      ncol=last
+      last=0
+c
+   40 j2=j1+ncol-1
+      write (6,90) (ihead(mode),j,j=j1,j2)
+c
+	   do 60 i=1,m
+	   name=iblank
+	   if (notblk) name=names(i)
+c
+	   if (mode.eq.2) go to 50
+	   write (6,100) i,name,(a(i,j),j=j1,j2)
+	   go to 60
+   50	   write (6,110) i,name,(a(i,j),j=j1,j2)
+   60	   continue
+c
+      j1=j1+maxcol
+      nblock=nblock-1
+      go to 30
+c
+   70 format (45h0v-matrix of the singular value decomposition,
+     * 8h of a*d./47h (elements of v scaled up by a factor of 10**4))
+   80 format (35h0sequence of candidate solutions, x)
+   90 format (1h0,11x,8(6x,a4,i4,1x)/1x)
+  100 format (1x,i3,1x,a6,1x,4p8f15.0)
+  110 format (1x,i3,1x,a6,1x,8e15.8)
+      end
diff --git a/math/llsq/original_f/sva.f b/math/llsq/original_f/sva.f
new file mode 100644
index 00000000..469a90ef
--- /dev/null
+++ b/math/llsq/original_f/sva.f
@@ -0,0 +1,193 @@
+      subroutine sva (a,mda,m,n,mdata,b,sing,names,iscale,d)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c		singular value analysis printout
+c
+c     iscale	   set by user to 1, 2, or 3 to select column scaling
+c		   option.
+c		   1   subr will use identity scaling and ignore the d()
+c		       array.
+c		   2   subr will scale nonzero cols to have unit euclide
+c		       length and will store reciprocal lengths of
+c		       original nonzero cols in d().
+c		   3   user supplies col scale factors in d(). subr
+c		       will mult col j by d(j) and remove the scaling
+c		       from the soln at the end.
+c
+      dimension  a(mda,n), b(m), sing(01),d(n)
+c     sing(3*n)
+      dimension names(n)
+      logical test
+      double precision	 sb, dzero
+      dzero=0.d0
+      one=1.
+      zero=0.
+      if (m.le.0 .or. n.le.0) return
+      np1=n+1
+      write (6,270)
+      write (6,260) m,n,mdata
+      go to (60,10,10), iscale
+c
+c     apply column scaling to a
+c
+   10	   do 50 j=1,n
+	   a1=d(j)
+	   go to (20,20,40), iscale
+   20	   sb=dzero
+		do 30 i=1,m
+   30		sb=sb+dble(a(i,j))**2
+	   a1=dsqrt(sb)
+	   if (a1.eq.zero) a1=one
+	   a1=one/a1
+	   d(j)=a1
+   40		do 50 i=1,m
+   50		a(i,j)=a(i,j)*a1
+      write (6,280) iscale,(d(j),j=1,n)
+      go to 70
+   60 continue
+      write (6,290)
+   70 continue
+c
+c     obtain  sing. value decomp. of scaled matrix.
+c
+c**********************************************************
+      call svdrs (a,mda,m,n,b,1,1,sing)
+c**********************************************************
+c
+c     print the v matrix.
+c
+      call mfeout (a,mda,n,n,names,1)
+      if (iscale.eq.1) go to 90
+c
+c     replace v by d*v in the array a()
+c
+	   do 80 i=1,n
+		do 80 j=1,n
+   80		a(i,j)=d(i)*a(i,j)
+c
+c     g  now in  b array.  v now in a array.
+c
+c
+c     obtain summary output.
+c
+   90 continue
+      write (6,220)
+c
+c     compute cumulative sums of squares of components of
+c     g and store them in sing(i), i=minmn+1,...,2*minmn+1
+c
+      sb=dzero
+      minmn=min0(m,n)
+      minmn1=minmn+1
+      if (m.eq.minmn) go to 110
+	   do 100 i=minmn1,m
+  100	   sb=sb+dble(b(i))**2
+  110 sing(2*minmn+1)=sb
+	   do 120 jj=1,minmn
+	   j=minmn+1-jj
+	   sb=sb+dble(b(j))**2
+	   js=minmn+j
+  120	   sing(js)=sb
+      a3=sing(minmn+1)
+      a4=sqrt(a3/float(max0(1,mdata)))
+      write (6,230) a3,a4
+c
+      nsol=0
+c
+c
+c
+	   do 160 k=1,minmn
+	   if (sing(k).eq.zero) go to 130
+	   nsol=k
+	   pi=b(k)/sing(k)
+	   a1=one/sing(k)
+	   a2=b(k)**2
+	   a3=sing(minmn1+k)
+	   a4=sqrt(a3/float(max0(1,mdata-k)))
+	   test=sing(k).ge.100..or.sing(k).lt..001
+	   if (test) write (6,240) k,sing(k),pi,a1,b(k),a2,a3,a4
+	   if (.not.test) write (6,250) k,sing(k),pi,a1,b(k),a2,a3,a4
+	   go to 140
+  130	   write (6,240) k,sing(k)
+	   pi=zero
+  140		do 150 i=1,n
+		a(i,k)=a(i,k)*pi
+  150		if (k.gt.1) a(i,k)=a(i,k)+a(i,k-1)
+  160	   continue
+c
+c     compute and print values of ynorm and rnorm.
+c
+      write (6,300)
+      j=0
+      ysq=zero
+      go to 180
+  170 j=j+1
+      ysq=ysq+(b(j)/sing(j))**2
+  180 ynorm=sqrt(ysq)
+      js=minmn1+j
+      rnorm=sqrt(sing(js))
+      yl=-1000.
+      if (ynorm.gt.0.) yl=alog10(ynorm)
+      rl=-1000.
+      if (rnorm.gt.0.) rl=alog10(rnorm)
+      write (6,310) j,ynorm,rnorm,yl,rl
+      if (j.lt.nsol) go to 170
+c
+c     compute values of xnorm and rnorm for a sequence of values of
+c     the levenberg-marquardt parameter.
+c
+      if (sing(1).eq.zero) go to 210
+      el=alog10(sing(1))+one
+      el2=alog10(sing(nsol))-one
+      del=(el2-el)/20.
+      ten=10.
+      aln10=alog(ten)
+      write (6,320)
+	   do 200 ie=1,21
+c     compute	     alamb=10.**el
+	   alamb=exp(aln10*el)
+	   ys=0.
+	   js=minmn1+nsol
+	   rs=sing(js)
+		do 190 i=1,minmn
+		sl=sing(i)**2+alamb**2
+		ys=ys+(b(i)*sing(i)/sl)**2
+		rs=rs+(b(i)*(alamb**2)/sl)**2
+  190		continue
+	   ynorm=sqrt(ys)
+	   rnorm=sqrt(rs)
+	   rl=-1000.
+	   if (rnorm.gt.zero) rl=alog10(rnorm)
+	   yl=-1000.
+	   if (ynorm.gt.zero) yl=alog10(ynorm)
+	   write (6,330) alamb,ynorm,rnorm,el,yl,rl
+	   el=el+del
+  200	   continue
+c
+c     print candidate solutions.
+c
+  210 if (nsol.ge.1) call mfeout (a,mda,n,nsol,names,2)
+      return
+  220 format (42h0 index  sing. value       p coef         ,48hrecip. s.
+     1v.             g coef            g**2  ,39h            c.s.s.
+     2    n.s.r.c.s.s.)
+  230 format (1h ,5x,1h0,88x,1pe15.4,1pe17.4)
+  240 format (1h ,i6,e12.4,1p(e15.4,4x,e15.4,4x,e15.4,4x,e15.4,4x,e15.4,
+     12x,e15.4))
+  250 format (1h ,i6,f12.4,1p(e15.4,4x,e15.4,4x,e15.4,4x,e15.4,4x,e15.4,
+     12x,e15.4))
+  260 format (5h0m = ,i6,8h,   n = ,i4,12h,   mdata = ,i8)
+  270 format (45h0singular value analysis of the least squares,42h probl
+     1em,  a*x=b,  scaled as  (a*d)*y=b  .)
+  280 format (19h0scaling option no.,i2,18h.  d is a diagonal,46h matrix
+     1 with the following diagonal elements../(5x,10e12.4))
+  290 format (50h0scaling option no. 1.   d is the identity matrix./1x)
+  300 format (6h0index,13x,28h         ynorm         rnorm,14x,28h  log1
+     10(ynorm)  log10(rnorm)/1x)
+  310 format (1h ,i4,14x,2e14.5,14x,2f14.5)
+  320 format (54h0norms of solution and residual vectors for a range of,
+     144h values of the levenberg-marquardt parameter,9h, lambda./1h0,4x
+     2,42h        lambda         ynorm         rnorm,42h log10(lambda)
+     3log10(ynorm)  log10(rnorm))
+  330 format (5x,3e14.5,3f14.5)
+      end
diff --git a/math/llsq/original_f/svdrs.f b/math/llsq/original_f/svdrs.f
new file mode 100644
index 00000000..66e488dc
--- /dev/null
+++ b/math/llsq/original_f/svdrs.f
@@ -0,0 +1,205 @@
+c     subroutine svdrs (a,mda,mm,nn,b,mdb,nb,s)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1974 mar 1
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   singular value decomposition also treating right side vector.
+c
+c     the array s occupies 3*n cells.
+c     a occupies m*n cells
+c     b occupies m*nb cells.
+c
+c     special singular value decomposition subroutine.
+c     we have the m x n matrix a and the system a*x=b to solve.
+c     either m .ge. n  or  m .lt. n is permitted.
+c			the singular value decomposition
+c     a = u*s*v**(t) is made in such a way that one gets
+c	 (1) the matrix v in the first n rows and columns of a.
+c	 (2) the diagonal matrix of ordered singular values in
+c	     the first n cells of the array s(ip), ip .ge. 3*n.
+c	 (3) the matrix product u**(t)*b=g gets placed back in b.
+c	 (4) the user must complete the solution and do his own
+c	     singular value analysis.
+c     *******
+c     give special
+c     treatment to rows and columns which are entirely zero.  this
+c     causes certain zero sing. vals. to appear as exact zeros rather
+c     than as about eta times the largest sing. val.   it similarly
+c     cleans up the associated columns of u and v.
+c     method..
+c      1. exchange cols of a to pack nonzero cols to the left.
+c	  set n = no. of nonzero cols.
+c	  use locations a(1,nn),a(1,nn-1),...,a(1,n+1) to record the
+c	  col permutations.
+c      2. exchange rows of a to pack nonzero rows to the top.
+c	  quit packing if find n nonzero rows.	make same row exchanges
+c	  in b.  set m so that all nonzero rows of the permuted a
+c	  are in first m rows.	if m .le. n then all m rows are
+c	  nonzero.  if m .gt. n then	  the first n rows are known
+c	  to be nonzero,and rows n+1 thru m may be zero or nonzero.
+c      3. apply original algorithm to the m by n problem.
+c      4. move permutation record from a(,) to s(i),i=n+1,...,nn.
+c      5. build v up from  n by n  to  nn by nn  by placing ones on
+c	  the diagonal and zeros elsewhere.  this is only partly done
+c	  explicitly.  it is completed during step 6.
+c      6. exchange rows of v to compensate for col exchanges of step 2.
+c      7. place zeros in  s(i),i=n+1,nn  to represent zero sing vals.
+c
+      subroutine svdrs (a,mda,mm,nn,b,mdb,nb,s)
+      dimension a(mda,nn),b(mdb,nb),s(nn,3)
+      zero=0.
+      one=1.
+c
+c			      begin.. special for zero rows and cols.
+c
+c			      pack the nonzero cols to the left
+c
+      n=nn
+      if (n.le.0.or.mm.le.0) return
+      j=n
+   10 continue
+	  do 20 i=1,mm
+	  if (a(i,j)) 50,20,50
+   20	  continue
+c
+c	  col j  is zero. exchange it with col n.
+c
+      if (j.eq.n) go to 40
+	  do 30 i=1,mm
+   30	  a(i,j)=a(i,n)
+   40 continue
+      a(1,n)=j
+      n=n-1
+   50 continue
+      j=j-1
+      if (j.ge.1) go to 10
+c			      if n=0 then a is entirely zero and svd
+c			      computation can be skipped
+      ns=0
+      if (n.eq.0) go to 240
+c			      pack nonzero rows to the top
+c			      quit packing if find n nonzero rows
+      i=1
+      m=mm
+   60 if (i.gt.n.or.i.ge.m) go to 150
+      if (a(i,i)) 90,70,90
+   70	  do 80 j=1,n
+	  if (a(i,j)) 90,80,90
+   80	  continue
+      go to 100
+   90 i=i+1
+      go to 60
+c			      row i is zero
+c			      exchange rows i and m
+  100 if(nb.le.0) go to 115
+	  do 110 j=1,nb
+	  t=b(i,j)
+	  b(i,j)=b(m,j)
+  110	  b(m,j)=t
+  115	  do 120 j=1,n
+  120	  a(i,j)=a(m,j)
+      if (m.gt.n) go to 140
+	  do 130 j=1,n
+  130	  a(m,j)=zero
+  140 continue
+c			      exchange is finished
+      m=m-1
+      go to 60
+c
+  150 continue
+c			      end.. special for zero rows and columns
+c			      begin.. svd algorithm
+c     method..
+c     (1)     reduce the matrix to upper bidiagonal form with
+c     householder transformations.
+c	   h(n)...h(1)aq(1)...q(n-2) = (d**t,0)**t
+c     where d is upper bidiagonal.
+c
+c     (2)     apply h(n)...h(1) to b.  here h(n)...h(1)*b replaces b
+c     in storage.
+c
+c     (3)     the matrix product w= q(1)...q(n-2) overwrites the first
+c     n rows of a in storage.
+c
+c     (4)     an svd for d is computed.  here k rotations ri and pi are
+c     computed so that
+c	   rk...r1*d*p1**(t)...pk**(t) = diag(s1,...,sm)
+c     to working accuracy.  the si are nonnegative and nonincreasing.
+c     here rk...r1*b overwrites b in storage while
+c     a*p1**(t)...pk**(t)  overwrites a in storage.
+c
+c     (5)     it follows that,with the proper definitions,
+c     u**(t)*b overwrites b, while v overwrites the first n row and
+c     columns of a.
+c
+      l=min0(m,n)
+c	      the following loop reduces a to upper bidiagonal and
+c	      also applies the premultiplying transformations to b.
+c
+	  do 170 j=1,l
+	  if (j.ge.m) go to 160
+	  call h12 (1,j,j+1,m,a(1,j),1,t,a(1,j+1),1,mda,n-j)
+	  call h12 (2,j,j+1,m,a(1,j),1,t,b,1,mdb,nb)
+  160	  if (j.ge.n-1) go to 170
+	  call h12 (1,j+1,j+2,n,a(j,1),mda,s(j,3),a(j+1,1),mda,1,m-j)
+  170	  continue
+c
+c     copy the bidiagonal matrix into the array s() for qrbd.
+c
+      if (n.eq.1) go to 190
+	  do 180 j=2,n
+	  s(j,1)=a(j,j)
+  180	  s(j,2)=a(j-1,j)
+  190 s(1,1)=a(1,1)
+c
+      ns=n
+      if (m.ge.n) go to 200
+      ns=m+1
+      s(ns,1)=zero
+      s(ns,2)=a(m,m+1)
+  200 continue
+c
+c     construct the explicit n by n product matrix, w=q1*q2*...*ql*i
+c     in the array a().
+c
+	  do 230 k=1,n
+	  i=n+1-k
+	  if(i.gt.min0(m,n-2)) go to 210
+	  call h12 (2,i+1,i+2,n,a(i,1),mda,s(i,3),a(1,i+1),1,mda,n-i)
+  210	      do 220 j=1,n
+  220	      a(i,j)=zero
+  230	  a(i,i)=one
+c
+c	   compute the svd of the bidiagonal matrix
+c
+      call qrbd (ipass,s(1,1),s(1,2),ns,a,mda,n,b,mdb,nb)
+c
+      go to (240,310), ipass
+  240 continue
+      if (ns.ge.n) go to 260
+      nsp1=ns+1
+	  do 250 j=nsp1,n
+  250	  s(j,1)=zero
+  260 continue
+      if (n.eq.nn) return
+      np1=n+1
+c				   move record of permutations
+c				   and store zeros
+	  do 280 j=np1,nn
+	  s(j,1)=a(1,j)
+	      do 270 i=1,n
+  270	      a(i,j)=zero
+  280	  continue
+c			      permute rows and set zero singular values.
+	  do 300 k=np1,nn
+	  i=s(k,1)
+	  s(k,1)=zero
+	      do 290 j=1,nn
+	      a(k,j)=a(i,j)
+  290	      a(i,j)=zero
+	  a(i,k)=one
+  300	  continue
+c			      end.. special for zero rows and columns
+      return
+  310 write (6,320)
+      stop
+  320 format (49h convergence failure in qr bidiagonal svd routine)
+      end
diff --git a/math/llsq/progs/README b/math/llsq/progs/README
new file mode 100644
index 00000000..e0c5a142
--- /dev/null
+++ b/math/llsq/progs/README
@@ -0,0 +1,5 @@
+
+This directory contains both Fortran and IRAF preprocessor programs
+demonstrating the use of the Lawson-Hanson llsq procedures.  The Fortran
+programs have not been modified to reflect the removal of Fortran i/o
+from the library procedures as installed in the IRAF llsq.a library.
diff --git a/math/llsq/progs/band.x b/math/llsq/progs/band.x
new file mode 100644
index 00000000..f65290ba
--- /dev/null
+++ b/math/llsq/progs/band.x
@@ -0,0 +1,70 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+
+define	MAXPTS		1024
+
+task	band
+
+# This procedure solves for the natural cubic spline which interpolates
+# the curve y[i] = 100., for i = 1 to n.  The matrix is of length n+2,
+# and has a bandwidth of 3.  Lawsons and Hansons routines BNDACC and 
+# BNDSOL (modified to return an error code IER) are used to solve the
+# system.  The computations are carried out in single precision.
+
+
+procedure band()
+
+real	g[MAXPTS,4], c[MAXPTS], rnorm
+int	ip, ir, i, n, ier, geti()
+real	marktime, cptime()
+
+begin
+	n = min (MAXPTS, geti ("npts"))
+	marktime = cptime()
+
+	ip = 1
+	ir = 1
+
+	g[ir,1] = 6.			# first row
+	g[ir,2] = -12.
+	g[ir,3] = 6.
+	g[ir,4] = 0.
+	call bndacc (g, MAXPTS, 3, ip, ir, 1, 1)
+
+	do i = 2, n-1 {			# tridiagonal elements
+	    g[ir,1] = 1.
+	    g[ir,2] = 4.
+	    g[ir,3] = 1.
+	    g[ir,4] = 100.
+	    call bndacc (g, MAXPTS, 3, ip, ir, 1, i-1)
+	}
+
+	g[ir,1] = 6.			# last row
+	g[ir,2] = -12.
+	g[ir,3] = 6.
+	g[ir,4] = 0.
+	call bndacc (g, MAXPTS, 3, ip, ir, 1, n-2)
+
+	call printf ("matrix accumulation took %8.2f cpu seconds\n")
+	    call pargr (cptime() - marktime)
+	marktime = cptime()
+
+					# solve for the b-spline coeff C
+	call bndsol (1, g, MAXPTS, 3, ip, ir, c, n, rnorm, ier)
+
+	call printf ("solution took %8.2f cpu seconds (rnorm=%g, ier=%d)\n")
+	    call pargr (cptime() - marktime)
+	    call pargr (rnorm)
+	    call pargi (ier)
+
+	call printf ("selected coefficients:\n")
+	for (i=1;  i <= n;) {		# print the first and last 4 coeff
+	    call printf ("%8d%15.6f\n")
+		call pargi (i)
+		call pargr (c[i])
+	    if (i == 4)
+		i = max(i+1, n-3)
+	    else
+		i = i + 1
+	}
+end
diff --git a/math/llsq/progs/data4 b/math/llsq/progs/data4
new file mode 100644
index 00000000..33bf1b08
--- /dev/null
+++ b/math/llsq/progs/data4
@@ -0,0 +1,15 @@
+  -.13405547  -.20162827  -.16930778  -.18971990  -.17387234	  -.4361
+  -.10379475  -.15766336  -.13346256  -.14848550  -.13597690	  -.3437
+  -.08779597  -.12883867  -.10683007  -.12011796  -.10932972	  -.2657
+   .02058554   .00335331  -.01641270   .00078606   .00271659	  -.0392
+  -.03248093  -.01876799   .00410639  -.01405894  -.01384391	   .0193
+   .05967662   .06667714   .04352153   .05740438   .05024962	   .0747
+   .06712457   .07352437   .04489770   .06471862   .05876455	   .0935
+   .08687186   .09368296   .05672327   .08141043   .07302320	   .1079
+   .02149662   .06222662   .07213486   .06200069   .05570931	   .1930
+   .06687407   .10344506   .09153849   .09508223   .08393667	   .2058
+   .15879069   .18088339   .11540692   .16160727   .14796479	   .2606
+   .17642887   .20361830   .13057860   .18385729   .17005549	   .3142
+   .11414080   .17259611   .14816471   .16007466   .14374096	   .3529
+   .07846038   .14669563   .14365800   .14003842   .12571177	   .3615
+   .10803175   .16994623   .14971519   .15885312   .14301547	   .3647
diff --git a/math/llsq/progs/lsq.x b/math/llsq/progs/lsq.x
new file mode 100644
index 00000000..ae002a16
--- /dev/null
+++ b/math/llsq/progs/lsq.x
@@ -0,0 +1,70 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+
+define	M	256
+define	N	256
+
+task	lsq
+
+# This procedure fits a natural cubic spline to an array of n data points.
+# The system being solved is a tridiagonal matrix of n+2 rows.  The system
+# is solved by Lawsons and Hansons routine HFTI, which solves a general
+# m by n linear system of equations.  This is enormous overkill for this
+# problem (see "band.x"), but serves to give timing estimates for the code.
+
+
+procedure lsq()
+
+real	a[M,N], b[M], tau, rnorm, h[N], g[N]
+int	krank, ip[N]
+int	i, j, m, n, geti()
+real	marktime, cptime()
+
+begin
+	m = min (M, geti ("npts"))	# size of matrix
+	n = min (N, m)
+	tau = 1e-6
+
+	do j = 1, n			# set up b-spline matrix
+	    do i = 1, m
+		a[i,j] = 0.
+
+	a[1,1] = 6.			# first row
+	a[1,2] = -12.
+	a[1,3] = 6.
+
+	a[m,n] = 6.			# last row
+	a[m,n-1] = -12.
+	a[m,n-2] = 6.
+
+	do j = 2, m-1 {			# tridiagonal elements
+	    a[j,j-1] = 1.
+	    a[j,j] = 4.
+	    a[j,j+1] = 1.
+	}
+
+	b[1] = 0.			# natural spline bndry conditions
+	b[m] = 0.
+
+	do i = 2, m-1			# set up data vector
+	    b[i] = 100.
+
+	marktime = cptime()
+	call hfti (a,M,m,n, b,1,1, tau, krank,rnorm, h,g,ip)
+
+	call printf ("took %8.2f cpu seconds (krank=%d, rnorm=%g)\n")
+	    call pargr (cptime() - marktime)
+	    call pargi (krank)
+	    call pargr (rnorm)
+
+	call printf ("selected coefficients:\n")
+	for (i=1;  i <= m;) {		# print first, last 4 coeff
+	    call printf ("%8d%15.5f\n")
+		call pargi (i)
+		call pargr (b[i])
+	    if (i == 4)
+		i = max(i+1, m-3)
+	    else
+		i = i + 1
+	}
+end
diff --git a/math/llsq/progs/prog1.f b/math/llsq/progs/prog1.f
new file mode 100644
index 00000000..13f64929
--- /dev/null
+++ b/math/llsq/progs/prog1.f
@@ -0,0 +1,124 @@
+c     prog1
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	 demonstrate algorithms hft and hs1 for solving least squares
+c     problems and algorithm cov for omputing the associated covariance
+c     matrices.
+c
+      dimension a(8,8),h(8),b(8)
+      real gen,anoise
+      double precision sm
+      data mda/8/
+c
+	   do 180 noise=1,2
+	   anoise=0.
+	   if (noise.eq.2) anoise=1.e-4
+	   write (6,230)
+	   write (6,240) anoise
+c     initialize the data generation function
+c    ..
+	   dummy=gen(-1.)
+		do 180 mn1=1,6,5
+		mn2=mn1+2
+		     do 180 m=mn1,mn2
+		     do 180 n=mn1,mn2
+		     np1=n+1
+		     write (6,250) m,n
+c     generate data
+c    ..
+			  do 10 i=1,m
+			       do 10 j=1,n
+   10			       a(i,j)=gen(anoise)
+			  do 20 i=1,m
+   20			  b(i)=gen(anoise)
+		     if(m .lt. n) go to 180
+c
+c     ******  begin algorithm hft  ******
+c    ..
+			  do 30 j=1,n
+   30		   call h12 (1,j,j+1,m,a(1,j),1,h(j),a(1,j+1),1,mda,n-j)
+c    ..
+c     the algorithm 'hft' is completed.
+c
+c     ******  begin algorithm hs1  ******
+c     apply the transformations  q(n)...q(1)=q to b
+c     replacing the previous contents of the array, b .
+c    ..
+			  do 40 j=1,n
+   40			      call h12 (2,j,j+1,m,a(1,j),1,h(j),b,1,1,1)
+c     solve the triangular system for the solution x.
+c     store x in the array, b .
+c    ..
+			  do 80 k=1,n
+			  i=np1-k
+			  sm=0.d0
+			  if (i.eq.n) go to 60
+			  ip1=i+1
+			       do 50 j=ip1,n
+   50			       sm=sm+a(i,j)*dble(b(j))
+   60			  if (a(i,i)) 80,70,80
+   70			  write (6,260)
+			  go to 180
+   80			  b(i)=(b(i)-sm)/a(i,i)
+c      compute length of residual vector.
+c     ..
+		     srsmsq=0.
+		     if (n.eq.m) go to 100
+		     mmn=m-n
+			  do 90 j=1,mmn
+			  npj=n+j
+   90			  srsmsq=srsmsq+b(npj)**2
+		     srsmsq=sqrt(srsmsq)
+c     ******  begin algorithm  cov  ******
+c     compute unscaled covariance matrix   ((a**t)*a)**(-1)
+c    ..
+  100			  do 110 j=1,n
+  110			  a(j,j)=1./a(j,j)
+		     if (n.eq.1) go to 140
+		     nm1=n-1
+			  do 130 i=1,nm1
+			  ip1=i+1
+			       do 130 j=ip1,n
+			       jm1=j-1
+			       sm=0.d0
+				    do 120 l=i,jm1
+  120				    sm=sm+a(i,l)*dble(a(l,j))
+  130			       a(i,j)=-sm*a(j,j)
+c    ..
+c     the upper triangle of a has been inverted
+c     upon itself.
+  140			  do 160 i=1,n
+			       do 160 j=i,n
+			       sm=0.d0
+				    do 150 l=j,n
+  150				    sm=sm+a(i,l)*dble(a(j,l))
+  160			       a(i,j)=sm
+c    ..
+c     the upper triangular part of the
+c     symmetric matrix (a**t*a)**(-1) has
+c     replaced the upper triangular part of
+c     the a array.
+		     write (6,200) (i,b(i),i=1,n)
+		     write (6,190) srsmsq
+		     write (6,210)
+			  do 170 i=1,n
+  170			  write (6,220) (i,j,a(i,j),j=i,n)
+  180		     continue
+      stop
+  190 format (1h0,8x,17hresidual length =,e12.4)
+  200 format (1h0,8x,34hestimated parameters,  x=a**(+)*b,,22h computed
+     1by 'hft,hs1'//(9x,i6,e16.8,i6,e16.8,i6,e16.8,i6,e16.8,i6,e16.8))
+  210 format (1h0,8x,31hcovariance matrix (unscaled) of,22h estimated pa
+     1rameters.,19h computed by 'cov'./1x)
+  220 format (9x,2i3,e16.8,2i3,e16.8,2i3,e16.8,2i3,e16.8,2i3,e16.8)
+  230 format (52h1 prog1.    this program demonstrates the algorithms,19
+     1h hft, hs1, and cov.//40h caution.. 'prog1' does no checking for ,
+     252hnear rank deficient matrices.  results in such cases,20h may be
+     3 meaningless.,/34h such cases are handled by 'prog2',11h or 'pro
+     4')
+  240 format (1h0,54hthe relative noise level of the generated data will
+     1 be,e16.4)
+  250 format (1h0////9h0   m   n/1x,2i4)
+  260 format (1h0,8x,36h******  terminating this case due to,37h a divis
+     1or being exactly zero. ******)
+      end
diff --git a/math/llsq/progs/prog2.f b/math/llsq/progs/prog2.f
new file mode 100644
index 00000000..5fb601cc
--- /dev/null
+++ b/math/llsq/progs/prog2.f
@@ -0,0 +1,125 @@
+c     prog2
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	 demonstrate algorithm	hfti  for solving least squares problems
+c     and algorithm  cov  for computing the associated unscaled
+c     covariance matrix.
+c
+      dimension a(8,8),h(8),b(8),g(8)
+      real gen,anoise
+      integer ip(8)
+      double precision sm
+      data mda /8/
+c
+	  do 180 noise=1,2
+	  anorm=500.
+	  anoise=0.
+	  tau=.5
+	  if (noise.eq.1) go to 10
+	  anoise=1.e-4
+	  tau=anorm*anoise*10.
+   10	  continue
+c     initialize the data generation function
+c    ..
+	  dummy=gen(-1.)
+	  write (6,230)
+	  write (6,240) anoise,anorm,tau
+c
+	      do 180 mn1=1,6,5
+	      mn2=mn1+2
+		  do 180 m=mn1,mn2
+		      do 180 n=mn1,mn2
+		      write (6,250) m,n
+c     generate data
+c    ..
+			  do 20 i=1,m
+			      do 20 j=1,n
+   20			      a(i,j)=gen(anoise)
+			  do 30 i=1,m
+   30			  b(i)=gen(anoise)
+c
+c     ****** call hfti	 ******
+c
+		      call hfti(a,mda,m,n,b,1,1,tau,krank,srsmsq,h,g,ip)
+c
+c
+		      write (6,260) krank
+		      write (6,200) (i,b(i),i=1,n)
+		      write (6,190) srsmsq
+		      if (krank.lt.n) go to 180
+c     ******  algorithm cov bigins here  ******
+c    ..
+			  do 40 j=1,n
+   40			  a(j,j)=1./a(j,j)
+		      if (n.eq.1) go to 70
+		      nm1=n-1
+			  do 60 i=1,nm1
+			  ip1=i+1
+			      do 60 j=ip1,n
+			      jm1=j-1
+			      sm=0.d0
+				  do 50 l=i,jm1
+   50				  sm=sm+a(i,l)*dble(a(l,j))
+   60			      a(i,j)=-sm*a(j,j)
+c    ..
+c     the upper triangle of a has been inverted
+c     upon itself.
+   70			  do 90 i=1,n
+			      do 90 j=i,n
+			      sm=0.d0
+				  do 80 l=j,n
+   80				  sm=sm+a(i,l)*dble(a(j,l))
+   90			      a(i,j)=sm
+		      if (n.lt.2) go to 160
+			  do 150 ii=2,n
+			  i=n+1-ii
+			  if (ip(i).eq.i) go to 150
+			  k=ip(i)
+			  tmp=a(i,i)
+			  a(i,i)=a(k,k)
+			  a(k,k)=tmp
+			  if (i.eq.1) go to 110
+			      do 100 l=2,i
+			      tmp=a(l-1,i)
+			      a(l-1,i)=a(l-1,k)
+  100			      a(l-1,k)=tmp
+  110			  ip1=i+1
+			  km1=k-1
+			  if (ip1.gt.km1) go to 130
+			      do 120 l=ip1,km1
+			      tmp=a(i,l)
+			      a(i,l)=a(l,k)
+  120			      a(l,k)=tmp
+  130			  if (k.eq.n) go to 150
+			  kp1=k+1
+			      do 140 l=kp1,n
+			      tmp=a(i,l)
+			      a(i,l)=a(k,l)
+  140			      a(k,l)=tmp
+  150			  continue
+  160		      continue
+c    ..
+c     covariance has been computed and repermuted.
+c     the upper triangular part of the
+c     symmetric matrix (a**t*a)**(-1) has
+c     replaced the upper triangular part of
+c     the a array.
+		      write (6,210)
+			  do 170 i=1,n
+  170			  write (6,220) (i,j,a(i,j),j=i,n)
+  180		      continue
+      stop
+  190 format (1h0,8x,17hresidual length =,e12.4)
+  200 format (1h0,8x,34hestimated parameters,  x=a**(+)*b,,22h computed
+     1by 'hfti'   //(9x,i6,e16.8,i6,e16.8,i6,e16.8,i6,e16.8,i6,e16.8))
+  210 format (1h0,8x,31hcovariance matrix (unscaled) of,22h estimated pa
+     1rameters.,19h computed by 'cov'./1x)
+  220 format (9x,2i3,e16.8,2i3,e16.8,2i3,e16.8,2i3,e16.8,2i3,e16.8)
+  230 format (52h1 prog2.     this program demonstates the algorithms,16
+     1h hfti  and  cov.)
+  240 format (1h0,54hthe relative noise level of the generated data will
+     1 be,e16.4/33h0the matrix norm is approximately,e12.4/43h0the absol
+     2ute pseudorank tolerance, tau, is,e12.4)
+  250 format (1h0////9h0   m   n/1x,2i4)
+  260 format (1h0,8x,12hpseudorank =,i4)
+      end
diff --git a/math/llsq/progs/prog3.f b/math/llsq/progs/prog3.f
new file mode 100644
index 00000000..290f8161
--- /dev/null
+++ b/math/llsq/progs/prog3.f
@@ -0,0 +1,138 @@
+c     prog3
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   demonstrate the use of subroutine   svdrs  to compute the
+c     singular value decomposition of a matrix, a, and solve a least
+c     squares problem,	a*x=b.
+c
+c     the s.v.d.  a= u*(s,0)**t*v**t is
+c     computed so that..
+c     (1)  u**t*b replaces the m+1 st. col. of	b.
+c
+c     (2)  u**t   replaces the m by m identity in
+c     the first m cols. of  b.
+c
+c     (3) v replaces the first n rows and cols.
+c     of a.
+c
+c     (4) the diagonal entries of the s matrix
+c     replace the first n entries of the array s.
+c
+c     the array s( ) must be dimensioned at least 3*n .
+c
+      dimension a(8,8),b(8,9),s(24),x(8),aa(8,8)
+      real gen,anoise
+      double precision sm
+      data mda,mdb/8,8/
+c
+      do 150 noise=1,2
+      anoise = 0.
+      rho = 1.e-3
+      if(noise .eq. 1) go to 5
+      anoise = 1.e-4
+      rho = 10. * anoise
+    5 continue
+      write(6,230)
+      write(6,240) anoise,rho
+c     initialize data generation function
+c    ..
+      dummy= gen(-1.)
+c
+	   do 150 mn1=1,6,5
+	   mn2=mn1+2
+		do 150 m=mn1,mn2
+		do 150 n=mn1,mn2
+		write (6,160) m,n
+		     do 20 i=1,m
+			  do 10 j=1,m
+   10			  b(i,j)=0.
+		     b(i,i)=1.
+			  do 20 j=1,n
+			  a(i,j)= gen(anoise)
+   20			  aa(i,j)=a(i,j)
+		     do 30 i=1,m
+   30		     b(i,m+1)= gen(anoise)
+c
+c     the arrays are now filled in..
+c     compute the s.v.d.
+c     ******************************************************
+		call svdrs (a,mda,m,n,b,mdb,m+1,s)
+c     ******************************************************
+c
+		write (6,170)
+		write (6,220) (i,s(i),i=1,n)
+		write (6,180)
+		write (6,220) (i,b(i,m+1),i=1,m)
+c
+c     test for disparity of ratio of singular values.
+c    ..
+		krank=n
+		tau=rho*s(1)
+		     do 40 i=1,n
+		     if (s(i).le.tau) go to 50
+   40		     continue
+		go to 55
+   50		krank=i-1
+   55 write(6,250) tau, krank
+c     compute solution vector assuming pseudorank is krank
+c     ..
+   60		     do 70 i=1,krank
+   70		     b(i,m+1)=b(i,m+1)/s(i)
+		     do 90 i=1,n
+		     sm=0.d0
+			  do 80 j=1,krank
+   80			  sm=sm+a(i,j)*dble(b(j,m+1))
+   90		     x(i)=sm
+c     compute predicted norm of residual vector.
+c     ..
+		srsmsq=0.
+		if (krank.eq.m) go to 110
+		kp1=krank+1
+		     do 100 i=kp1,m
+  100		     srsmsq=srsmsq+b(i,m+1)**2
+		srsmsq=sqrt(srsmsq)
+c
+  110		continue
+		write (6,190)
+		write (6,220) (i,x(i),i=1,n)
+		write (6,200) srsmsq
+c     compute the frobenius norm of  a**t- v*(s,0)*u**t.
+c
+c     compute  v*s  first.
+c
+		minmn=min0(m,n)
+		     do 120 j=1,minmn
+			  do 120 i=1,n
+  120			  a(i,j)=a(i,j)*s(j)
+		dn=0.
+		     do 140 j=1,m
+			  do 140 i=1,n
+			  sm=0.d0
+			       do 130 l=1,minmn
+  130			       sm=sm+a(i,l)*dble(b(l,j))
+c     computed difference of (i,j) th entry
+c     of  a**t-v*(s,0)*u**t.
+c     ..
+			  t=aa(j,i)-sm
+  140			  dn=dn+t**2
+		dn=sqrt(dn)/(sqrt(float(n))*s(1))
+		write (6,210) dn
+  150		continue
+      stop
+  160 format (1h0////9h0   m   n/1x,2i4)
+  170 format (1h0,8x,25hsingular values of matrix)
+  180 format (1h0,8x,30htransformed right side, u**t*b)
+  190 format (1h0,8x,33hestimated parameters,  x=a**(+)*b,21h computed b
+     1y 'svdrs' )
+  200 format (1h0,8x,24hresidual vector length =,e12.4)
+  210 format (1h0,8x,43hfrobenius norm (a-u*(s,0)**t*v**t)/(sqrt(n),
+     *22h*spectral norm of a) =,e12.4)
+  220 format (9x,i5,e16.8,i5,e16.8,i5,e16.8,i5,e16.8,i5,e16.8)
+  230 format(51h1prog3.     this program demonstrates the algorithm,
+     * 9h, svdrs. )
+  240 format(55h0the relative noise level of the generated data will be,
+     *e16.4/44h0the relative tolerance, rho, for pseudorank,
+     *17h determination is,e16.4)
+  250 format(1h0,8x,36habsolute pseudorank tolerance, tau =,
+     *e12.4,10x,12hpseudorank =,i5)
+      end
diff --git a/math/llsq/progs/prog4.f b/math/llsq/progs/prog4.f
new file mode 100644
index 00000000..090b1865
--- /dev/null
+++ b/math/llsq/progs/prog4.f
@@ -0,0 +1,22 @@
+c     prog4
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   demonstrate singular value analysis.
+c
+      dimension a(15,5),b(15),sing(15)
+      data names/1h /
+c
+      read (5,10) ((a(i,j),j=1,5),b(i),i=1,15)
+      write (6,20)
+      write (6,30) ((a(i,j),j=1,5),b(i),i=1,15)
+      write (6,40)
+c
+      call sva (a,15,15,5,15,b,sing,names,1,d)
+c
+      stop
+   10 format (6f12.0)
+   20 format (46h1prog4.    demonstrate singular value analysis/53h list
+     1ing of input matrix, a, and vector, b, follows..)
+   30 format (1h /(5f12.8,f20.4))
+   40 format (1h1)
+      end
diff --git a/math/llsq/progs/prog5.f b/math/llsq/progs/prog5.f
new file mode 100644
index 00000000..5484b846
--- /dev/null
+++ b/math/llsq/progs/prog5.f
@@ -0,0 +1,146 @@
+c     prog5
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   example of the use of subroutines bndacc and bndsol to solve
+c     sequentially the banded least squares problem which arises in
+c     spline curve fitting.
+c
+      dimension x(12),y(12),b(10),g(12,5),c(12),q(4),cov(12)
+c
+c	 define functions p1 and p2 to be used in constructing
+c	 cubic splines over uniformly spaced breakpoints.
+c
+      p1(t)=.25*t**2*t
+      p2(t)=-(1.-t)**2*(1.+t)*.75+1.
+      zero=0.
+c
+      write (6,230)
+      mdg=12
+      nband=4
+      m=12
+c				   set ordinates of data
+      y(1)=2.2
+      y(2)=4.0
+      y(3)=5.0
+      y(4)=4.6
+      y(5)=2.8
+      y(6)=2.7
+      y(7)=3.8
+      y(8)=5.1
+      y(9)=6.1
+      y(10)=6.3
+      y(11)=5.0
+      y(12)=2.0
+c				   set abcissas of data
+	   do 10 i=1,m
+   10	   x(i)=2*i
+c
+c     begin loop thru cases using increasing nos of breakpoints.
+c
+	   do 150 nbp=5,10
+	   nc=nbp+2
+c				   set breakpoints
+	   b(1)=x(1)
+	   b(nbp)=x(m)
+	   h=(b(nbp)-b(1))/float(nbp-1)
+	   if (nbp.le.2) go to 30
+		do 20 i=3,nbp
+   20		b(i-1)=b(i-2)+h
+   30	   continue
+	   write (6,240) nbp,(b(i),i=1,nbp)
+c
+c     initialize ir and ip before first call to bndacc.
+c
+	   ir=1
+	   ip=1
+	   i=1
+	   jt=1
+   40	   mt=0
+   50	   continue
+	   if (x(i).gt.b(jt+1)) go to 60
+c
+c			 set row  for ith data point
+c
+	   u=(x(i)-b(jt))/h
+	   ig=ir+mt
+	   g(ig,1)=p1(1.-u)
+	   g(ig,2)=p2(1.-u)
+	   g(ig,3)=p2(u)
+	   g(ig,4)=p1(u)
+	   g(ig,5)=y(i)
+	   mt=mt+1
+	   if (i.eq.m) go to 60
+	   i=i+1
+	   go to 50
+c
+c		    send block of data to processor
+c
+   60	   continue
+	   call bndacc (g,mdg,nband,ip,ir,mt,jt)
+	   if (i.eq.m) go to 70
+	   jt=jt+1
+	   go to 40
+c		    compute solution c()
+   70	   continue
+	   call bndsol (1,g,mdg,nband,ip,ir,c,nc,rnorm)
+c		   write solution coefficients
+	   write (6,180) (c(l),l=1,nc)
+	   write (6,210) rnorm
+c
+c	       compute and print x,y,yfit,r=y-yfit
+c
+	   write (6,160)
+	   jt=1
+		do 110 i=1,m
+   80		if (x(i).le.b(jt+1)) go to 90
+		jt=jt+1
+		go to 80
+c
+   90		u=(x(i)-b(jt))/h
+		q(1)=p1(1.-u)
+		q(2)=p2(1.-u)
+		q(3)=p2(u)
+		q(4)=p1(u)
+		yfit=zero
+		     do 100 l=1,4
+		     ic=jt-1+l
+  100		     yfit=yfit+c(ic)*q(l)
+		r=y(i)-yfit
+		write (6,170) i,x(i),y(i),yfit,r
+  110		continue
+c
+c     compute residual vector norm.
+c
+	   if (m.le.nc) go to 150
+	   sigsq=(rnorm**2)/float(m-nc)
+	   sigfac=sqrt(sigsq)
+	   write (6,220) sigfac
+	   write (6,200)
+c
+c     compute and print cols. of covariance.
+c
+		do 140 j=1,nc
+		     do 120 i=1,nc
+  120		     cov(i)=zero
+		cov(j)=1.
+		call bndsol (2,g,mdg,nband,ip,ir,cov,nc,rdummy)
+		call bndsol (3,g,mdg,nband,ip,ir,cov,nc,rdummy)
+c
+c    compute the jth col. of the covariance matrix.
+		     do 130 i=1,nc
+  130		     cov(i)=cov(i)*sigsq
+  140		write (6,190) (l,j,cov(l),l=1,nc)
+  150	   continue
+      stop
+  160 format (4h0  i,8x,1hx,10x,1hy,6x,4hyfit,4x,8hr=y-yfit/1x)
+  170 format (1x,i3,4x,f6.0,4x,f6.2,4x,f6.2,4x,f8.4)
+  180 format (4h0c =,10f10.5/(4x,10f10.5))
+  190 format (4(02x,2i5,e15.7))
+  200 format (46h0covariance matrix of the spline coefficients.)
+  210 format (9h0rnorm	=,e15.8)
+  220 format (9h0sigfac =,e15.8)
+  230 format (50h1prog5.    execute a sequence of cubic spline fits,27h
+     1to a discrete set of data.)
+  240 format (1x////,11h0new case..,/47h0number of breakpoints, includin
+     1g endpoints, is,i5/14h0breakpoints =,10f10.5,/(14x,10f10.5))
+      end
diff --git a/math/llsq/progs/prog6.f b/math/llsq/progs/prog6.f
new file mode 100644
index 00000000..71364ec4
--- /dev/null
+++ b/math/llsq/progs/prog6.f
@@ -0,0 +1,116 @@
+c     prog6
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 15
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   demonstrate the use of the subroutine   ldp	for least
+c     distance programming by solving the constrained line data fitting
+c     problem of chapter 23.
+c
+      dimension e(4,2), f(4), g(3,2), h(3), g2(3,2), h2(3), x(2), z(2),
+     1w(4)
+      dimension wldp(21), s(6), t(4)
+      integer index(3)
+c
+      write (6,110)
+      mde=4
+      mdgh=3
+c
+      me=4
+      mg=3
+      n=2
+c		 define the least squares and constraint matrices.
+      t(1)=0.25
+      t(2)=0.5
+      t(3)=0.5
+      t(4)=0.8
+c
+      w(1)=0.5
+      w(2)=0.6
+      w(3)=0.7
+      w(4)=1.2
+c
+	  do 10 i=1,me
+	  e(i,1)=t(i)
+	  e(i,2)=1.
+   10	  f(i)=w(i)
+c
+      g(1,1)=1.
+      g(1,2)=0.
+      g(2,1)=0.
+      g(2,2)=1.
+      g(3,1)=-1.
+      g(3,2)=-1.
+c
+      h(1)=0.
+      h(2)=0.
+      h(3)=-1.
+c
+c     compute the singular value decomposition of the matrix, e.
+c
+      call svdrs (e,mde,me,n,f,1,1,s)
+c
+      write (6,120) ((e(i,j),j=1,n),i=1,n)
+      write (6,130) f,(s(j),j=1,n)
+c
+c     generally rank determination and levenberg-marquardt
+c     stabilization could be inserted here.
+c
+c	 define the constraint matrix for the z coordinate system.
+	  do 30 i=1,mg
+	      do 30 j=1,n
+	      sm=0.
+		  do 20 l=1,n
+   20		  sm=sm+g(i,l)*e(l,j)
+   30	      g2(i,j)=sm/s(j)
+c	  define constraint rt side for the z coordinate system.
+	  do 50 i=1,mg
+	  sm=0.
+	      do 40 j=1,n
+   40	      sm=sm+g2(i,j)*f(j)
+   50	  h2(i)=h(i)-sm
+c
+      write (6,140) ((g2(i,j),j=1,n),i=1,mg)
+      write (6,150) h2
+c
+c			 solve the constrained problem in z-coordinates.
+c
+      call ldp (g2,mdgh,mg,n,h2,z,znorm,wldp,index,mode)
+c
+      write (6,200) mode,znorm
+      write (6,160) z
+c
+c		     transform back from z-coordinates to x-coordinates.
+	  do 60 j=1,n
+   60	  z(j)=(z(j)+f(j))/s(j)
+	  do 80 i=1,n
+	  sm=0.
+	      do 70 j=1,n
+   70	      sm=sm+e(i,j)*z(j)
+   80	  x(i)=sm
+      res=znorm**2
+      np1=n+1
+	  do 90 i=np1,me
+   90	  res=res+f(i)**2
+      res=sqrt(res)
+c				     compute the residuals.
+	  do 100 i=1,me
+  100	  f(i)=w(i)-x(1)*t(i)-x(2)
+      write (6,170) (x(j),j=1,n)
+      write (6,180) (i,f(i),i=1,me)
+      write (6,190) res
+      stop
+c
+  110 format (46h0prog6..  example of constrained curve fitting,26h usin
+     1g the subroutine ldp.,/43h0related intermediate quantities are giv
+     2en.)
+  120 format (10h0v =	   ,2f10.5/(10x,2f10.5))
+  130 format (10h0f tilda =,4f10.5/10h0s =	,2f10.5)
+  140 format (10h0g tilda =,2f10.5/(10x,2f10.5))
+  150 format (10h0h tilda =,3f10.5)
+  160 format (10h0z =	   ,2f10.5)
+  170 format (52h0the coeficients of the fitted line f(t)=x(1)*t+x(2),12
+     1h are x(1) = ,f10.5,14h	and x(2) = ,f10.5)
+  180 format (30h0the consecutive residuals are/1x,4(i10,f10.5))
+  190 format (23h0the residuals norm is ,f10.5)
+  200 format (18h0mode (from ldp) =,i3,2x,7hznorm =,f10.5)
+c
+      end
diff --git a/math/llsq/qrbd.f b/math/llsq/qrbd.f
new file mode 100644
index 00000000..d9a12a24
--- /dev/null
+++ b/math/llsq/qrbd.f
@@ -0,0 +1,208 @@
+c     subroutine qrbd (ipass,q,e,nn,v,mdv,nrv,c,mdc,ncc)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   qr algorithm for singular values of a bidiagonal matrix.
+c
+c     the bidiagonal matrix
+c
+c			(q1,e2,0...    )
+c			(   q2,e3,0... )
+c		 d=	(	.      )
+c			(	  .   0)
+c			(	    .en)
+c			(	   0,qn)
+c
+c		  is pre and post multiplied by
+c		  elementary rotation matrices
+c		  ri and pi so that
+c
+c		  rk...r1*d*p1**(t)...pk**(t) = diag(s1,...,sn)
+c
+c		  to within working accuracy.
+c
+c  1. ei and qi occupy e(i) and q(i) as input.
+c
+c  2. rm...r1*c replaces 'c' in storage as output.
+c
+c  3. v*p1**(t)...pm**(t) replaces 'v' in storage as output.
+c
+c  4. si occupies q(i) as output.
+c
+c  5. the si's are nonincreasing and nonnegative.
+c
+c     this code is based on the paper and 'algol' code..
+c ref..
+c  1. reinsch,c.h. and golub,g.h. 'singular value decomposition
+c     and least squares solutions' (numer. math.), vol. 14,(1970).
+c
+      subroutine qrbd (ipass,q,e,nn,v,mdv,nrv,c,mdc,ncc)
+      logical wntv ,havers,fail
+      dimension q(nn),e(nn),v(mdv,nn),c(mdc,ncc)
+      zero=0.
+      one=1.
+      two=2.
+c
+      n=nn
+      ipass=1
+      if (n.le.0) return
+      n10=10*n
+      wntv=nrv.gt.0
+      havers=ncc.gt.0
+      fail=.false.
+      nqrs=0
+      e(1)=zero
+      dnorm=zero
+	   do 10 j=1,n
+   10	   dnorm=amax1(abs(q(j))+abs(e(j)),dnorm)
+	   do 200 kk=1,n
+	   k=n+1-kk
+c
+c     test for splitting or rank deficiencies..
+c	  first make test for last diagonal term, q(k), being small.
+   20	    if(k.eq.1) go to 50
+	    if(diff(dnorm+q(k),dnorm)) 50,25,50
+c
+c     since q(k) is small we will make a special pass to
+c     transform e(k) to zero.
+c
+   25	   cs=zero
+	   sn=-one
+		do 40 ii=2,k
+		i=k+1-ii
+		f=-sn*e(i+1)
+		e(i+1)=cs*e(i+1)
+		call g1 (q(i),f,cs,sn,q(i))
+c	  transformation constructed to zero position (i,k).
+c
+		if (.not.wntv) go to 40
+		     do 30 j=1,nrv
+   30		     call g2 (cs,sn,v(j,i),v(j,k))
+c	       accumulate rt. transformations in v.
+c
+   40		continue
+c
+c	  the matrix is now bidiagonal, and of lower order
+c	  since e(k) .eq. zero..
+c
+   50		do 60 ll=1,k
+		l=k+1-ll
+		if(diff(dnorm+e(l),dnorm)) 55,100,55
+   55		if(diff(dnorm+q(l-1),dnorm)) 60,70,60
+   60		continue
+c     this loop can't complete since e(1) = zero.
+c
+	   go to 100
+c
+c	  cancellation of e(l), l.gt.1.
+   70	   cs=zero
+	   sn=-one
+		do 90 i=l,k
+		f=-sn*e(i)
+		e(i)=cs*e(i)
+		if(diff(dnorm+f,dnorm)) 75,100,75
+   75		call g1 (q(i),f,cs,sn,q(i))
+		if (.not.havers) go to 90
+		     do 80 j=1,ncc
+   80		     call g2 (cs,sn,c(i,j),c(l-1,j))
+   90		continue
+c
+c	  test for convergence..
+  100	   z=q(k)
+	   if (l.eq.k) go to 170
+c
+c	  shift from bottom 2 by 2 minor of b**(t)*b.
+	   x=q(l)
+	   y=q(k-1)
+	   g=e(k-1)
+	   h=e(k)
+	   f=((y-z)*(y+z)+(g-h)*(g+h))/(two*h*y)
+	   g=sqrt(one+f**2)
+	   if (f.lt.zero) go to 110
+	   t=f+g
+	   go to 120
+  110	   t=f-g
+  120	   f=((x-z)*(x+z)+h*(y/t-h))/x
+c
+c	  next qr sweep..
+	   cs=one
+	   sn=one
+	   lp1=l+1
+		do 160 i=lp1,k
+		g=e(i)
+		y=q(i)
+		h=sn*g
+		g=cs*g
+		call g1 (f,h,cs,sn,e(i-1))
+		f=x*cs+g*sn
+		g=-x*sn+g*cs
+		h=y*sn
+		y=y*cs
+		if (.not.wntv) go to 140
+c
+c	       accumulate rotations (from the right) in 'v'
+		     do 130 j=1,nrv
+  130		     call g2 (cs,sn,v(j,i-1),v(j,i))
+  140		call g1 (f,h,cs,sn,q(i-1))
+		f=cs*g+sn*y
+		x=-sn*g+cs*y
+		if (.not.havers) go to 160
+		     do 150 j=1,ncc
+  150		     call g2 (cs,sn,c(i-1,j),c(i,j))
+c	       apply rotations from the left to
+c	       right hand sides in 'c'..
+c
+  160		continue
+	   e(l)=zero
+	   e(k)=f
+	   q(k)=x
+	   nqrs=nqrs+1
+	   if (nqrs.le.n10) go to 20
+c	   return to 'test for splitting'.
+c
+	   fail=.true.
+c     ..
+c     cutoff for convergence failure. 'nqrs' will be 2*n usually.
+  170	   if (z.ge.zero) go to 190
+	   q(k)=-z
+	   if (.not.wntv) go to 190
+		do 180 j=1,nrv
+  180		v(j,k)=-v(j,k)
+  190	   continue
+c	  convergence. q(k) is made nonnegative..
+c
+  200	   continue
+      if (n.eq.1) return
+	   do 210 i=2,n
+	   if (q(i).gt.q(i-1)) go to 220
+  210	   continue
+      if (fail) ipass=2
+      return
+c     ..
+c     every singular value is in order..
+  220	   do 270 i=2,n
+	   t=q(i-1)
+	   k=i-1
+		do 230 j=i,n
+		if (t.ge.q(j)) go to 230
+		t=q(j)
+		k=j
+  230		continue
+	   if (k.eq.i-1) go to 270
+	   q(k)=q(i-1)
+	   q(i-1)=t
+	   if (.not.havers) go to 250
+		do 240 j=1,ncc
+		t=c(i-1,j)
+		c(i-1,j)=c(k,j)
+  240		c(k,j)=t
+  250	   if (.not.wntv) go to 270
+		do 260 j=1,nrv
+		t=v(j,i-1)
+		v(j,i-1)=v(j,k)
+  260		v(j,k)=t
+  270	   continue
+c	  end of ordering algorithm.
+c
+      if (fail) ipass=2
+      return
+      end
diff --git a/math/llsq/sva.f b/math/llsq/sva.f
new file mode 100644
index 00000000..ee7f893d
--- /dev/null
+++ b/math/llsq/sva.f
@@ -0,0 +1,198 @@
+      subroutine sva (a,mda,m,n,mdata,b,sing,names,iscale,d)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1973 jun 12
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c               singular value analysis printout
+c
+c     iscale       set by user to 1, 2, or 3 to select column scaling
+c                  option.
+c                  1   subr will use identity scaling and ignore the d()
+c                      array.
+c                  2   subr will scale nonzero cols to have unit euclide
+c                      length and will store reciprocal lengths of
+c                      original nonzero cols in d().
+c                  3   user supplies col scale factors in d(). subr
+c                      will mult col j by d(j) and remove the scaling
+c                      from the soln at the end.
+c
+      dimension  a(mda,n), b(m), sing(01),d(n)
+c     sing(3*n)
+      dimension names(n)
+      logical test
+      double precision   sb, dzero
+      dzero=0.d0
+      one=1.
+      zero=0.
+      if (m.le.0 .or. n.le.0) return
+      np1=n+1
+      write (6,270)
+      write (6,260) m,n,mdata
+      go to (60,10,10), iscale
+c
+c     apply column scaling to a
+c
+   10      do 50 j=1,n
+           a1=d(j)
+           go to (20,20,40), iscale
+   20      sb=dzero
+                do 30 i=1,m
+   30           sb=sb+dble(a(i,j))**2
+           a1=dsqrt(sb)
+           if (a1.eq.zero) a1=one
+           a1=one/a1
+           d(j)=a1
+   40           do 50 i=1,m
+   50           a(i,j)=a(i,j)*a1
+      write (6,280) iscale,(d(j),j=1,n)
+      go to 70
+   60 continue
+      write (6,290)
+   70 continue
+c
+c     obtain  sing. value decomp. of scaled matrix.
+c
+c**********************************************************
+      call svdrs (a,mda,m,n,b,1,1,sing,ier)
+      if (ier.eq.0) goto 75
+         write (6,295)
+         return
+   75 continue
+c**********************************************************
+c
+c     print the v matrix.
+c
+      call mfeout (a,mda,n,n,names,1)
+      if (iscale.eq.1) go to 90
+c
+c     replace v by d*v in the array a()
+c
+           do 80 i=1,n
+                do 80 j=1,n
+   80           a(i,j)=d(i)*a(i,j)
+c
+c     g  now in  b array.  v now in a array.
+c
+c
+c     obtain summary output.
+c
+   90 continue
+      write (6,220)
+c
+c     compute cumulative sums of squares of components of
+c     g and store them in sing(i), i=minmn+1,...,2*minmn+1
+c
+      sb=dzero
+      minmn=min0(m,n)
+      minmn1=minmn+1
+      if (m.eq.minmn) go to 110
+           do 100 i=minmn1,m
+  100      sb=sb+dble(b(i))**2
+  110 sing(2*minmn+1)=sb
+           do 120 jj=1,minmn
+           j=minmn+1-jj
+           sb=sb+dble(b(j))**2
+           js=minmn+j
+  120      sing(js)=sb
+      a3=sing(minmn+1)
+      a4=sqrt(a3/float(max0(1,mdata)))
+      write (6,230) a3,a4
+c
+      nsol=0
+c
+c
+c
+           do 160 k=1,minmn
+           if (sing(k).eq.zero) go to 130
+           nsol=k
+           pi=b(k)/sing(k)
+           a1=one/sing(k)
+           a2=b(k)**2
+           a3=sing(minmn1+k)
+           a4=sqrt(a3/float(max0(1,mdata-k)))
+           test=sing(k).ge.100..or.sing(k).lt..001
+           if (test) write (6,240) k,sing(k),pi,a1,b(k),a2,a3,a4
+           if (.not.test) write (6,250) k,sing(k),pi,a1,b(k),a2,a3,a4
+           go to 140
+  130      write (6,240) k,sing(k)
+           pi=zero
+  140           do 150 i=1,n
+                a(i,k)=a(i,k)*pi
+  150           if (k.gt.1) a(i,k)=a(i,k)+a(i,k-1)
+  160      continue
+c
+c     compute and print values of ynorm and rnorm.
+c
+      write (6,300)
+      j=0
+      ysq=zero
+      go to 180
+  170 j=j+1
+      ysq=ysq+(b(j)/sing(j))**2
+  180 ynorm=sqrt(ysq)
+      js=minmn1+j
+      rnorm=sqrt(sing(js))
+      yl=-1000.
+      if (ynorm.gt.0.) yl=alog10(ynorm)
+      rl=-1000.
+      if (rnorm.gt.0.) rl=alog10(rnorm)
+      write (6,310) j,ynorm,rnorm,yl,rl
+      if (j.lt.nsol) go to 170
+c
+c     compute values of xnorm and rnorm for a sequence of values of
+c     the levenberg-marquardt parameter.
+c
+      if (sing(1).eq.zero) go to 210
+      el=alog10(sing(1))+one
+      el2=alog10(sing(nsol))-one
+      del=(el2-el)/20.
+      ten=10.
+      aln10=alog(ten)
+      write (6,320)
+           do 200 ie=1,21
+c     compute        alamb=10.**el
+           alamb=exp(aln10*el)
+           ys=0.
+           js=minmn1+nsol
+           rs=sing(js)
+                do 190 i=1,minmn
+                sl=sing(i)**2+alamb**2
+                ys=ys+(b(i)*sing(i)/sl)**2
+                rs=rs+(b(i)*(alamb**2)/sl)**2
+  190           continue
+           ynorm=sqrt(ys)
+           rnorm=sqrt(rs)
+           rl=-1000.
+           if (rnorm.gt.zero) rl=alog10(rnorm)
+           yl=-1000.
+           if (ynorm.gt.zero) yl=alog10(ynorm)
+           write (6,330) alamb,ynorm,rnorm,el,yl,rl
+           el=el+del
+  200      continue
+c
+c     print candidate solutions.
+c
+  210 if (nsol.ge.1) call mfeout (a,mda,n,nsol,names,2)
+      return
+  220 format (42h0 index  sing. value       p coef         ,48hrecip. s.
+     1v.             g coef            g**2  ,
+     234h            c.s.s.    n.s.r.c.s.s.)
+  230 format (1h ,5x,1h0,88x,1pe15.4,1pe17.4)
+  240 format (1h ,i6,e12.4,1p,(e15.4,4x,e15.4,4x,e15.4,4x,e15.4,4x,e15.4
+     1,2x,e15.4))
+  250 format (1h ,i6,f12.4,1p,(e15.4,4x,e15.4,4x,e15.4,4x,e15.4,4x,e15.4
+     1,2x,e15.4))
+  260 format (5h0m = ,i6,8h,   n = ,i4,12h,   mdata = ,i8)
+  270 format (45h0singular value analysis of the least squares,42h probl
+     1em,  a*x=b,  scaled as  (a*d)*y=b  .)
+  280 format (19h0scaling option no.,i2,18h.  d is a diagonal,46h matrix
+     1 with the following diagonal elements../(5x,10e12.4))
+  290 format (50h0scaling option no. 1.   d is the identity matrix./1x)
+  295 format (49h convergence failure in qr bidiagonal svd routine)
+  300 format (6h0index,13x,28h         ynorm         rnorm,14x,28h  log1
+     10(ynorm)  log10(rnorm)/1x)
+  310 format (1h ,i4,14x,2e14.5,14x,2f14.5)
+  320 format (54h0norms of solution and residual vectors for a range of,
+     144h values of the levenberg-marquardt parameter,9h, lambda./1h0,4x
+     2,42h        lambda         ynorm         rnorm,
+     345h log10(lambda)     log10(ynorm)  log10(rnorm))
+  330 format (5x,3e14.5,3f14.5)
+      end
diff --git a/math/llsq/svdrs.f b/math/llsq/svdrs.f
new file mode 100644
index 00000000..46dba02d
--- /dev/null
+++ b/math/llsq/svdrs.f
@@ -0,0 +1,205 @@
+c     subroutine svdrs (a,mda,mm,nn,b,mdb,nb,s,ier)
+c     c.l.lawson and r.j.hanson, jet propulsion laboratory, 1974 mar 1
+c     to appear in 'solving least squares problems', prentice-hall, 1974
+c	   singular value decomposition also treating right side vector.
+c
+c     the array s occupies 3*n cells.
+c     a occupies m*n cells
+c     b occupies m*nb cells.
+c
+c     special singular value decomposition subroutine.
+c     we have the m x n matrix a and the system a*x=b to solve.
+c     either m .ge. n  or  m .lt. n is permitted.
+c			the singular value decomposition
+c     a = u*s*v**(t) is made in such a way that one gets
+c	 (1) the matrix v in the first n rows and columns of a.
+c	 (2) the diagonal matrix of ordered singular values in
+c	     the first n cells of the array s(ip), ip .ge. 3*n.
+c	 (3) the matrix product u**(t)*b=g gets placed back in b.
+c	 (4) the user must complete the solution and do his own
+c	     singular value analysis.
+c     *******
+c     give special
+c     treatment to rows and columns which are entirely zero.  this
+c     causes certain zero sing. vals. to appear as exact zeros rather
+c     than as about eta times the largest sing. val.   it similarly
+c     cleans up the associated columns of u and v.
+c     method..
+c      1. exchange cols of a to pack nonzero cols to the left.
+c	  set n = no. of nonzero cols.
+c	  use locations a(1,nn),a(1,nn-1),...,a(1,n+1) to record the
+c	  col permutations.
+c      2. exchange rows of a to pack nonzero rows to the top.
+c	  quit packing if find n nonzero rows.	make same row exchanges
+c	  in b.  set m so that all nonzero rows of the permuted a
+c	  are in first m rows.	if m .le. n then all m rows are
+c	  nonzero.  if m .gt. n then	  the first n rows are known
+c	  to be nonzero,and rows n+1 thru m may be zero or nonzero.
+c      3. apply original algorithm to the m by n problem.
+c      4. move permutation record from a(,) to s(i),i=n+1,...,nn.
+c      5. build v up from  n by n  to  nn by nn  by placing ones on
+c	  the diagonal and zeros elsewhere.  this is only partly done
+c	  explicitly.  it is completed during step 6.
+c      6. exchange rows of v to compensate for col exchanges of step 2.
+c      7. place zeros in  s(i),i=n+1,nn  to represent zero sing vals.
+c
+      subroutine svdrs (a,mda,mm,nn,b,mdb,nb,s,ier)
+      dimension a(mda,nn),b(mdb,nb),s(nn,3)
+      zero=0.
+      ier = 0
+      one=1.
+c
+c			      begin.. special for zero rows and cols.
+c
+c			      pack the nonzero cols to the left
+c
+      n=nn
+      if (n.le.0.or.mm.le.0) return
+      j=n
+   10 continue
+	  do 20 i=1,mm
+	  if (a(i,j)) 50,20,50
+   20	  continue
+c
+c	  col j  is zero. exchange it with col n.
+c
+      if (j.eq.n) go to 40
+	  do 30 i=1,mm
+   30	  a(i,j)=a(i,n)
+   40 continue
+      a(1,n)=j
+      n=n-1
+   50 continue
+      j=j-1
+      if (j.ge.1) go to 10
+c			      if n=0 then a is entirely zero and svd
+c			      computation can be skipped
+      ns=0
+      if (n.eq.0) go to 240
+c			      pack nonzero rows to the top
+c			      quit packing if find n nonzero rows
+      i=1
+      m=mm
+   60 if (i.gt.n.or.i.ge.m) go to 150
+      if (a(i,i)) 90,70,90
+   70	  do 80 j=1,n
+	  if (a(i,j)) 90,80,90
+   80	  continue
+      go to 100
+   90 i=i+1
+      go to 60
+c			      row i is zero
+c			      exchange rows i and m
+  100 if(nb.le.0) go to 115
+	  do 110 j=1,nb
+	  t=b(i,j)
+	  b(i,j)=b(m,j)
+  110	  b(m,j)=t
+  115	  do 120 j=1,n
+  120	  a(i,j)=a(m,j)
+      if (m.gt.n) go to 140
+	  do 130 j=1,n
+  130	  a(m,j)=zero
+  140 continue
+c			      exchange is finished
+      m=m-1
+      go to 60
+c
+  150 continue
+c			      end.. special for zero rows and columns
+c			      begin.. svd algorithm
+c     method..
+c     (1)     reduce the matrix to upper bidiagonal form with
+c     householder transformations.
+c	   h(n)...h(1)aq(1)...q(n-2) = (d**t,0)**t
+c     where d is upper bidiagonal.
+c
+c     (2)     apply h(n)...h(1) to b.  here h(n)...h(1)*b replaces b
+c     in storage.
+c
+c     (3)     the matrix product w= q(1)...q(n-2) overwrites the first
+c     n rows of a in storage.
+c
+c     (4)     an svd for d is computed.  here k rotations ri and pi are
+c     computed so that
+c	   rk...r1*d*p1**(t)...pk**(t) = diag(s1,...,sm)
+c     to working accuracy.  the si are nonnegative and nonincreasing.
+c     here rk...r1*b overwrites b in storage while
+c     a*p1**(t)...pk**(t)  overwrites a in storage.
+c
+c     (5)     it follows that,with the proper definitions,
+c     u**(t)*b overwrites b, while v overwrites the first n row and
+c     columns of a.
+c
+      l=min0(m,n)
+c	      the following loop reduces a to upper bidiagonal and
+c	      also applies the premultiplying transformations to b.
+c
+	  do 170 j=1,l
+	  if (j.ge.m) go to 160
+	  call h12 (1,j,j+1,m,a(1,j),1,t,a(1,j+1),1,mda,n-j)
+	  call h12 (2,j,j+1,m,a(1,j),1,t,b,1,mdb,nb)
+  160	  if (j.ge.n-1) go to 170
+	  call h12 (1,j+1,j+2,n,a(j,1),mda,s(j,3),a(j+1,1),mda,1,m-j)
+  170	  continue
+c
+c     copy the bidiagonal matrix into the array s() for qrbd.
+c
+      if (n.eq.1) go to 190
+	  do 180 j=2,n
+	  s(j,1)=a(j,j)
+  180	  s(j,2)=a(j-1,j)
+  190 s(1,1)=a(1,1)
+c
+      ns=n
+      if (m.ge.n) go to 200
+      ns=m+1
+      s(ns,1)=zero
+      s(ns,2)=a(m,m+1)
+  200 continue
+c
+c     construct the explicit n by n product matrix, w=q1*q2*...*ql*i
+c     in the array a().
+c
+	  do 230 k=1,n
+	  i=n+1-k
+	  if(i.gt.min0(m,n-2)) go to 210
+	  call h12 (2,i+1,i+2,n,a(i,1),mda,s(i,3),a(1,i+1),1,mda,n-i)
+  210	      do 220 j=1,n
+  220	      a(i,j)=zero
+  230	  a(i,i)=one
+c
+c	   compute the svd of the bidiagonal matrix
+c
+      call qrbd (ipass,s(1,1),s(1,2),ns,a,mda,n,b,mdb,nb)
+c
+      go to (240,310), ipass
+  240 continue
+      if (ns.ge.n) go to 260
+      nsp1=ns+1
+	  do 250 j=nsp1,n
+  250	  s(j,1)=zero
+  260 continue
+      if (n.eq.nn) return
+      np1=n+1
+c				   move record of permutations
+c				   and store zeros
+	  do 280 j=np1,nn
+	  s(j,1)=a(1,j)
+	      do 270 i=1,n
+  270	      a(i,j)=zero
+  280	  continue
+c			      permute rows and set zero singular values.
+	  do 300 k=np1,nn
+	  i=s(k,1)
+	  s(k,1)=zero
+	      do 290 j=1,nn
+	      a(k,j)=a(i,j)
+  290	      a(i,j)=zero
+	  a(i,k)=one
+  300	  continue
+c			      end.. special for zero rows and columns
+      return
+c     convergence failure in qr bidiagonal svd routine
+  310 ier = 1
+      end
diff --git a/math/math.hd b/math/math.hd
new file mode 100644
index 00000000..b5557997
--- /dev/null
+++ b/math/math.hd
@@ -0,0 +1,58 @@
+# Help directory file for the MATH package, a collection of mathematical
+# (numerical) packages.
+
+$bev		= "math$bevington/doc/"
+$curfit		= "math$curfit/doc/"
+$deboor		= "math$deboor/doc/"
+$gsurfit	= "math$gsurfit/doc/"
+$ieee		= "math$ieee/doc/"
+$iminterp	= "math$iminterp/doc/"
+$interp		= "math$interp/doc/"
+$llsq		= "math$llsq/doc/"
+$nlfit		= "math$nlfit/doc/"
+$slalib		= "math$slalib/doc/"
+$surfit		= "math$surfit/doc/"
+
+bevington	hlp = bev$bev.men,
+		sys = bev$bev.hlp,
+		pkg = bev$bev.hd
+
+curfit		hlp = curfit$curfit.men,
+		sys = curfit$curfit.hlp,
+		pkg = curfit$curfit.hd
+
+deboor		hlp = deboor$deboor.men,
+		sys = deboor$deboor.hlp,
+		pkg = deboor$deboor.hd
+
+ieee		hlp = ieee$ieee.men,
+		sys = ieee$ieee.hlp,
+		pkg = ieee$ieee.hd
+
+iminterp	hlp = iminterp$iminterp.men,
+		sys = iminterp$iminterp.hlp,
+		pkg = iminterp$iminterp.hd
+
+interp		hlp = interp$interp.men,
+		sys  = interp$interp.hlp,
+		pkg  = interp$interp.hd
+
+llsq		hlp = llsq$llsq.men,
+		sys = llsq$llsq.hlp,
+		pkg = llsq$llsq.hd
+
+nlfit		hlp = nlfit$nlfit.men,
+		sys = nlfit$nllmfit.hlp,
+		pkg = nlfit$nlfit.hd
+
+surfit		hlp = surfit$surfit.men,
+		sys = surfit$surfit.hlp,
+		pkg = surfit$surfit.hd
+
+gsurfit		hlp = gsurfit$gsurfit.men,
+		sys = gsurfit$gsurfit.hlp,
+		pkg = gsurfit$gsurfit.hd
+
+slalib		hlp = slalib$slalib.men,
+		sys = slalib$slalib.hlp,
+		pkg = slalib$slalib.hd
diff --git a/math/math.men b/math/math.men
new file mode 100644
index 00000000..c1f3c57c
--- /dev/null
+++ b/math/math.men
@@ -0,0 +1,11 @@
+      bevington - P.R. Bevington's statistical analysis package
+	 curfit - IRAF curve fitting package
+	 deboor - C.DeBoor's spline package
+	gsurfit - IRAF general surface fitting package
+	   ieee - IEEE signal processing routines
+       iminterp	- IRAF image interpolation package
+	 interp - Old 1D image interpolation routines
+	   llsq - Lawson's & Hanson's linear least squares package
+	  nlfit - IRAF Levenberg-Marquardt non-linear least squares package
+	 slalib - Starlink positional astronomy library
+	 surfit - IRAF image surface fitting package
diff --git a/math/minpack/chkder.f b/math/minpack/chkder.f
new file mode 100644
index 00000000..29578fc4
--- /dev/null
+++ b/math/minpack/chkder.f
@@ -0,0 +1,140 @@
+      subroutine chkder(m,n,x,fvec,fjac,ldfjac,xp,fvecp,mode,err)
+      integer m,n,ldfjac,mode
+      double precision x(n),fvec(m),fjac(ldfjac,n),xp(n),fvecp(m),
+     *                 err(m)
+c     **********
+c
+c     subroutine chkder
+c
+c     this subroutine checks the gradients of m nonlinear functions
+c     in n variables, evaluated at a point x, for consistency with
+c     the functions themselves. the user must call chkder twice,
+c     first with mode = 1 and then with mode = 2.
+c
+c     mode = 1. on input, x must contain the point of evaluation.
+c               on output, xp is set to a neighboring point.
+c
+c     mode = 2. on input, fvec must contain the functions and the
+c                         rows of fjac must contain the gradients
+c                         of the respective functions each evaluated
+c                         at x, and fvecp must contain the functions
+c                         evaluated at xp.
+c               on output, err contains measures of correctness of
+c                          the respective gradients.
+c
+c     the subroutine does not perform reliably if cancellation or
+c     rounding errors cause a severe loss of significance in the
+c     evaluation of a function. therefore, none of the components
+c     of x should be unusually small (in particular, zero) or any
+c     other value which may cause loss of significance.
+c
+c     the subroutine statement is
+c
+c       subroutine chkder(m,n,x,fvec,fjac,ldfjac,xp,fvecp,mode,err)
+c
+c     where
+c
+c       m is a positive integer input variable set to the number
+c         of functions.
+c
+c       n is a positive integer input variable set to the number
+c         of variables.
+c
+c       x is an input array of length n.
+c
+c       fvec is an array of length m. on input when mode = 2,
+c         fvec must contain the functions evaluated at x.
+c
+c       fjac is an m by n array. on input when mode = 2,
+c         the rows of fjac must contain the gradients of
+c         the respective functions evaluated at x.
+c
+c       ldfjac is a positive integer input parameter not less than m
+c         which specifies the leading dimension of the array fjac.
+c
+c       xp is an array of length n. on output when mode = 1,
+c         xp is set to a neighboring point of x.
+c
+c       fvecp is an array of length m. on input when mode = 2,
+c         fvecp must contain the functions evaluated at xp.
+c
+c       mode is an integer input variable set to 1 on the first call
+c         and 2 on the second. other values of mode are equivalent
+c         to mode = 1.
+c
+c       err is an array of length m. on output when mode = 2,
+c         err contains measures of correctness of the respective
+c         gradients. if there is no severe loss of significance,
+c         then if err(i) is 1.0 the i-th gradient is correct,
+c         while if err(i) is 0.0 the i-th gradient is incorrect.
+c         for values of err between 0.0 and 1.0, the categorization
+c         is less certain. in general, a value of err(i) greater
+c         than 0.5 indicates that the i-th gradient is probably
+c         correct, while a value of err(i) less than 0.5 indicates
+c         that the i-th gradient is probably incorrect.
+c
+c     subprograms called
+c
+c       minpack supplied ... dpmpar
+c
+c       fortran supplied ... dabs,dlog10,dsqrt
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,j
+      double precision eps,epsf,epslog,epsmch,factor,one,temp,zero
+      double precision dpmpar
+      data factor,one,zero /1.0d2,1.0d0,0.0d0/
+c
+c     epsmch is the machine precision.
+c
+      epsmch = dpmpar(1)
+c
+      eps = dsqrt(epsmch)
+c
+      if (mode .eq. 2) go to 20
+c
+c        mode = 1.
+c
+         do 10 j = 1, n
+            temp = eps*dabs(x(j))
+            if (temp .eq. zero) temp = eps
+            xp(j) = x(j) + temp
+   10       continue
+         go to 70
+   20 continue
+c
+c        mode = 2.
+c
+         epsf = factor*epsmch
+         epslog = dlog10(eps)
+         do 30 i = 1, m
+            err(i) = zero
+   30       continue
+         do 50 j = 1, n
+            temp = dabs(x(j))
+            if (temp .eq. zero) temp = one
+            do 40 i = 1, m
+               err(i) = err(i) + temp*fjac(i,j)
+   40          continue
+   50       continue
+         do 60 i = 1, m
+            temp = one
+            if (fvec(i) .ne. zero .and. fvecp(i) .ne. zero
+     *          .and. dabs(fvecp(i)-fvec(i)) .ge. epsf*dabs(fvec(i)))
+     *         temp = eps*dabs((fvecp(i)-fvec(i))/eps-err(i))
+     *                /(dabs(fvec(i)) + dabs(fvecp(i)))
+            err(i) = one
+            if (temp .gt. epsmch .and. temp .lt. eps)
+     *         err(i) = (dlog10(temp) - epslog)/epslog
+            if (temp .ge. eps) err(i) = zero
+   60       continue
+   70 continue
+c
+      return
+c
+c     last card of subroutine chkder.
+c
+      end
diff --git a/math/minpack/dogleg.f b/math/minpack/dogleg.f
new file mode 100644
index 00000000..b812f196
--- /dev/null
+++ b/math/minpack/dogleg.f
@@ -0,0 +1,177 @@
+      subroutine dogleg(n,r,lr,diag,qtb,delta,x,wa1,wa2)
+      integer n,lr
+      double precision delta
+      double precision r(lr),diag(n),qtb(n),x(n),wa1(n),wa2(n)
+c     **********
+c
+c     subroutine dogleg
+c
+c     given an m by n matrix a, an n by n nonsingular diagonal
+c     matrix d, an m-vector b, and a positive number delta, the
+c     problem is to determine the convex combination x of the
+c     gauss-newton and scaled gradient directions that minimizes
+c     (a*x - b) in the least squares sense, subject to the
+c     restriction that the euclidean norm of d*x be at most delta.
+c
+c     this subroutine completes the solution of the problem
+c     if it is provided with the necessary information from the
+c     qr factorization of a. that is, if a = q*r, where q has
+c     orthogonal columns and r is an upper triangular matrix,
+c     then dogleg expects the full upper triangle of r and
+c     the first n components of (q transpose)*b.
+c
+c     the subroutine statement is
+c
+c       subroutine dogleg(n,r,lr,diag,qtb,delta,x,wa1,wa2)
+c
+c     where
+c
+c       n is a positive integer input variable set to the order of r.
+c
+c       r is an input array of length lr which must contain the upper
+c         triangular matrix r stored by rows.
+c
+c       lr is a positive integer input variable not less than
+c         (n*(n+1))/2.
+c
+c       diag is an input array of length n which must contain the
+c         diagonal elements of the matrix d.
+c
+c       qtb is an input array of length n which must contain the first
+c         n elements of the vector (q transpose)*b.
+c
+c       delta is a positive input variable which specifies an upper
+c         bound on the euclidean norm of d*x.
+c
+c       x is an output array of length n which contains the desired
+c         convex combination of the gauss-newton direction and the
+c         scaled gradient direction.
+c
+c       wa1 and wa2 are work arrays of length n.
+c
+c     subprograms called
+c
+c       minpack-supplied ... dpmpar,enorm
+c
+c       fortran-supplied ... dabs,dmax1,dmin1,dsqrt
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,j,jj,jp1,k,l
+      double precision alpha,bnorm,epsmch,gnorm,one,qnorm,sgnorm,sum,
+     *                 temp,zero
+      double precision dpmpar,enorm
+      data one,zero /1.0d0,0.0d0/
+c
+c     epsmch is the machine precision.
+c
+      epsmch = dpmpar(1)
+c
+c     first, calculate the gauss-newton direction.
+c
+      jj = (n*(n + 1))/2 + 1
+      do 50 k = 1, n
+         j = n - k + 1
+         jp1 = j + 1
+         jj = jj - k
+         l = jj + 1
+         sum = zero
+         if (n .lt. jp1) go to 20
+         do 10 i = jp1, n
+            sum = sum + r(l)*x(i)
+            l = l + 1
+   10       continue
+   20    continue
+         temp = r(jj)
+         if (temp .ne. zero) go to 40
+         l = j
+         do 30 i = 1, j
+            temp = dmax1(temp,dabs(r(l)))
+            l = l + n - i
+   30       continue
+         temp = epsmch*temp
+         if (temp .eq. zero) temp = epsmch
+   40    continue
+         x(j) = (qtb(j) - sum)/temp
+   50    continue
+c
+c     test whether the gauss-newton direction is acceptable.
+c
+      do 60 j = 1, n
+         wa1(j) = zero
+         wa2(j) = diag(j)*x(j)
+   60    continue
+      qnorm = enorm(n,wa2)
+      if (qnorm .le. delta) go to 140
+c
+c     the gauss-newton direction is not acceptable.
+c     next, calculate the scaled gradient direction.
+c
+      l = 1
+      do 80 j = 1, n
+         temp = qtb(j)
+         do 70 i = j, n
+            wa1(i) = wa1(i) + r(l)*temp
+            l = l + 1
+   70       continue
+         wa1(j) = wa1(j)/diag(j)
+   80    continue
+c
+c     calculate the norm of the scaled gradient and test for
+c     the special case in which the scaled gradient is zero.
+c
+      gnorm = enorm(n,wa1)
+      sgnorm = zero
+      alpha = delta/qnorm
+      if (gnorm .eq. zero) go to 120
+c
+c     calculate the point along the scaled gradient
+c     at which the quadratic is minimized.
+c
+      do 90 j = 1, n
+         wa1(j) = (wa1(j)/gnorm)/diag(j)
+   90    continue
+      l = 1
+      do 110 j = 1, n
+         sum = zero
+         do 100 i = j, n
+            sum = sum + r(l)*wa1(i)
+            l = l + 1
+  100       continue
+         wa2(j) = sum
+  110    continue
+      temp = enorm(n,wa2)
+      sgnorm = (gnorm/temp)/temp
+c
+c     test whether the scaled gradient direction is acceptable.
+c
+      alpha = zero
+      if (sgnorm .ge. delta) go to 120
+c
+c     the scaled gradient direction is not acceptable.
+c     finally, calculate the point along the dogleg
+c     at which the quadratic is minimized.
+c
+      bnorm = enorm(n,qtb)
+      temp = (bnorm/gnorm)*(bnorm/qnorm)*(sgnorm/delta)
+      temp = temp - (delta/qnorm)*(sgnorm/delta)**2
+     *       + dsqrt((temp-(delta/qnorm))**2
+     *               +(one-(delta/qnorm)**2)*(one-(sgnorm/delta)**2))
+      alpha = ((delta/qnorm)*(one - (sgnorm/delta)**2))/temp
+  120 continue
+c
+c     form appropriate convex combination of the gauss-newton
+c     direction and the scaled gradient direction.
+c
+      temp = (one - alpha)*dmin1(sgnorm,delta)
+      do 130 j = 1, n
+         x(j) = temp*wa1(j) + alpha*x(j)
+  130    continue
+  140 continue
+      return
+c
+c     last card of subroutine dogleg.
+c
+      end
diff --git a/math/minpack/dpmpar.f b/math/minpack/dpmpar.f
new file mode 100644
index 00000000..776bf3d1
--- /dev/null
+++ b/math/minpack/dpmpar.f
@@ -0,0 +1,171 @@
+      double precision function dpmpar(i)
+      integer i
+c     **********
+c
+c     function dpmpar
+c
+c     This function provides double precision machine parameters
+c     when the appropriate set of data statements is activated (by
+c     removing the c from column 1) and all other data statements are
+c     rendered inactive. Most of the parameter values were obtained
+c     from the corresponding Bell Laboratories Port Library function.
+c
+c     The function statement is
+c
+c       double precision function dpmpar(i)
+c
+c     where
+c
+c       i is an integer input variable set to 1, 2, or 3 which
+c         selects the desired machine parameter. If the machine has
+c         t base b digits and its smallest and largest exponents are
+c         emin and emax, respectively, then these parameters are
+c
+c         dpmpar(1) = b**(1 - t), the machine precision,
+c
+c         dpmpar(2) = b**(emin - 1), the smallest magnitude,
+c
+c         dpmpar(3) = b**emax*(1 - b**(-t)), the largest magnitude.
+c
+c     Argonne National Laboratory. MINPACK Project. June 1983.
+c     Burton S. Garbow, Kenneth E. Hillstrom, Jorge J. More
+c
+c     **********
+      integer mcheps(4)
+      integer minmag(4)
+      integer maxmag(4)
+      double precision dmach(3)
+      equivalence (dmach(1),mcheps(1))
+      equivalence (dmach(2),minmag(1))
+      equivalence (dmach(3),maxmag(1))
+c
+c     Machine constants for the IBM 360/370 series,
+c     the Amdahl 470/V6, the ICL 2900, the Itel AS/6,
+c     the Xerox Sigma 5/7/9 and the Sel systems 85/86.
+c
+c     data mcheps(1),mcheps(2) / z34100000, z00000000 /
+c     data minmag(1),minmag(2) / z00100000, z00000000 /
+c     data maxmag(1),maxmag(2) / z7fffffff, zffffffff /
+c
+c     Machine constants for the Honeywell 600/6000 series.
+c
+c     data mcheps(1),mcheps(2) / o606400000000, o000000000000 /
+c     data minmag(1),minmag(2) / o402400000000, o000000000000 /
+c     data maxmag(1),maxmag(2) / o376777777777, o777777777777 /
+c
+c     Machine constants for the CDC 6000/7000 series.
+c
+c     data mcheps(1) / 15614000000000000000b /
+c     data mcheps(2) / 15010000000000000000b /
+c
+c     data minmag(1) / 00604000000000000000b /
+c     data minmag(2) / 00000000000000000000b /
+c
+c     data maxmag(1) / 37767777777777777777b /
+c     data maxmag(2) / 37167777777777777777b /
+c
+c     Machine constants for the PDP-10 (KA processor).
+c
+c     data mcheps(1),mcheps(2) / "114400000000, "000000000000 /
+c     data minmag(1),minmag(2) / "033400000000, "000000000000 /
+c     data maxmag(1),maxmag(2) / "377777777777, "344777777777 /
+c
+c     Machine constants for the PDP-10 (KI processor).
+c
+c     data mcheps(1),mcheps(2) / "104400000000, "000000000000 /
+c     data minmag(1),minmag(2) / "000400000000, "000000000000 /
+c     data maxmag(1),maxmag(2) / "377777777777, "377777777777 /
+c
+c     Machine constants for the PDP-11. 
+c
+c     data mcheps(1),mcheps(2) /   9472,      0 /
+c     data mcheps(3),mcheps(4) /      0,      0 /
+c
+c     data minmag(1),minmag(2) /    128,      0 /
+c     data minmag(3),minmag(4) /      0,      0 /
+c
+c     data maxmag(1),maxmag(2) /  32767,     -1 /
+c     data maxmag(3),maxmag(4) /     -1,     -1 /
+c
+c     Machine constants for the Burroughs 6700/7700 systems.
+c
+c     data mcheps(1) / o1451000000000000 /
+c     data mcheps(2) / o0000000000000000 /
+c
+c     data minmag(1) / o1771000000000000 /
+c     data minmag(2) / o7770000000000000 /
+c
+c     data maxmag(1) / o0777777777777777 /
+c     data maxmag(2) / o7777777777777777 /
+c
+c     Machine constants for the Burroughs 5700 system.
+c
+c     data mcheps(1) / o1451000000000000 /
+c     data mcheps(2) / o0000000000000000 /
+c
+c     data minmag(1) / o1771000000000000 /
+c     data minmag(2) / o0000000000000000 /
+c
+c     data maxmag(1) / o0777777777777777 /
+c     data maxmag(2) / o0007777777777777 /
+c
+c     Machine constants for the Burroughs 1700 system.
+c
+c     data mcheps(1) / zcc6800000 /
+c     data mcheps(2) / z000000000 /
+c
+c     data minmag(1) / zc00800000 /
+c     data minmag(2) / z000000000 /
+c
+c     data maxmag(1) / zdffffffff /
+c     data maxmag(2) / zfffffffff /
+c
+c     Machine constants for the Univac 1100 series.
+c
+c     data mcheps(1),mcheps(2) / o170640000000, o000000000000 /
+c     data minmag(1),minmag(2) / o000040000000, o000000000000 /
+c     data maxmag(1),maxmag(2) / o377777777777, o777777777777 /
+c
+c     Machine constants for the Data General Eclipse S/200.
+c
+c     Note - it may be appropriate to include the following card -
+c     static dmach(3)
+c
+c     data minmag/20k,3*0/,maxmag/77777k,3*177777k/
+c     data mcheps/32020k,3*0/
+c
+c     Machine constants for the Harris 220.
+c
+c     data mcheps(1),mcheps(2) / '20000000, '00000334 /
+c     data minmag(1),minmag(2) / '20000000, '00000201 /
+c     data maxmag(1),maxmag(2) / '37777777, '37777577 /
+c
+c     Machine constants for the Cray-1.
+c
+c     data mcheps(1) / 0376424000000000000000b /
+c     data mcheps(2) / 0000000000000000000000b /
+c
+c     data minmag(1) / 0200034000000000000000b /
+c     data minmag(2) / 0000000000000000000000b /
+c
+c     data maxmag(1) / 0577777777777777777777b /
+c     data maxmag(2) / 0000007777777777777776b /
+c
+c     Machine constants for the Prime 400.
+c
+c     data mcheps(1),mcheps(2) / :10000000000, :00000000123 /
+c     data minmag(1),minmag(2) / :10000000000, :00000100000 /
+c     data maxmag(1),maxmag(2) / :17777777777, :37777677776 /
+c
+c     Machine constants for the VAX-11.
+c
+      data mcheps(1),mcheps(2) /   9472,  0 /
+      data minmag(1),minmag(2) /    128,  0 /
+      data maxmag(1),maxmag(2) / -32769, -1 /
+c
+      dpmpar = dmach(i)
+      return
+c
+c     Last card of function dpmpar.
+c
+      end
diff --git a/math/minpack/enorm.f b/math/minpack/enorm.f
new file mode 100644
index 00000000..2cb5b607
--- /dev/null
+++ b/math/minpack/enorm.f
@@ -0,0 +1,108 @@
+      double precision function enorm(n,x)
+      integer n
+      double precision x(n)
+c     **********
+c
+c     function enorm
+c
+c     given an n-vector x, this function calculates the
+c     euclidean norm of x.
+c
+c     the euclidean norm is computed by accumulating the sum of
+c     squares in three different sums. the sums of squares for the
+c     small and large components are scaled so that no overflows
+c     occur. non-destructive underflows are permitted. underflows
+c     and overflows do not occur in the computation of the unscaled
+c     sum of squares for the intermediate components.
+c     the definitions of small, intermediate and large components
+c     depend on two constants, rdwarf and rgiant. the main
+c     restrictions on these constants are that rdwarf**2 not
+c     underflow and rgiant**2 not overflow. the constants
+c     given here are suitable for every known computer.
+c
+c     the function statement is
+c
+c       double precision function enorm(n,x)
+c
+c     where
+c
+c       n is a positive integer input variable.
+c
+c       x is an input array of length n.
+c
+c     subprograms called
+c
+c       fortran-supplied ... dabs,dsqrt
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i
+      double precision agiant,floatn,one,rdwarf,rgiant,s1,s2,s3,xabs,
+     *                 x1max,x3max,zero
+      data one,zero,rdwarf,rgiant /1.0d0,0.0d0,3.834d-20,1.304d19/
+      s1 = zero
+      s2 = zero
+      s3 = zero
+      x1max = zero
+      x3max = zero
+      floatn = n
+      agiant = rgiant/floatn
+      do 90 i = 1, n
+         xabs = dabs(x(i))
+         if (xabs .gt. rdwarf .and. xabs .lt. agiant) go to 70
+            if (xabs .le. rdwarf) go to 30
+c
+c              sum for large components.
+c
+               if (xabs .le. x1max) go to 10
+                  s1 = one + s1*(x1max/xabs)**2
+                  x1max = xabs
+                  go to 20
+   10          continue
+                  s1 = s1 + (xabs/x1max)**2
+   20          continue
+               go to 60
+   30       continue
+c
+c              sum for small components.
+c
+               if (xabs .le. x3max) go to 40
+                  s3 = one + s3*(x3max/xabs)**2
+                  x3max = xabs
+                  go to 50
+   40          continue
+                  if (xabs .ne. zero) s3 = s3 + (xabs/x3max)**2
+   50          continue
+   60       continue
+            go to 80
+   70    continue
+c
+c           sum for intermediate components.
+c
+            s2 = s2 + xabs**2
+   80    continue
+   90    continue
+c
+c     calculation of norm.
+c
+      if (s1 .eq. zero) go to 100
+         enorm = x1max*dsqrt(s1+(s2/x1max)/x1max)
+         go to 130
+  100 continue
+         if (s2 .eq. zero) go to 110
+            if (s2 .ge. x3max)
+     *         enorm = dsqrt(s2*(one+(x3max/s2)*(x3max*s3)))
+            if (s2 .lt. x3max)
+     *         enorm = dsqrt(x3max*((s2/x3max)+(x3max*s3)))
+            go to 120
+  110    continue
+            enorm = x3max*dsqrt(s3)
+  120    continue
+  130 continue
+      return
+c
+c     last card of function enorm.
+c
+      end
diff --git a/math/minpack/fdjac1.f b/math/minpack/fdjac1.f
new file mode 100644
index 00000000..aa058010
--- /dev/null
+++ b/math/minpack/fdjac1.f
@@ -0,0 +1,150 @@
+      subroutine fdjac1(fcn,n,x,fvec,fjac,ldfjac,iflag,ml,mu,epsfcn,
+     *                  wa1,wa2)
+      integer n,ldfjac,iflag,ml,mu
+      double precision epsfcn
+      double precision x(n),fvec(n),fjac(ldfjac,n),wa1(n),wa2(n)
+c     **********
+c
+c     subroutine fdjac1
+c
+c     this subroutine computes a forward-difference approximation
+c     to the n by n jacobian matrix associated with a specified
+c     problem of n functions in n variables. if the jacobian has
+c     a banded form, then function evaluations are saved by only
+c     approximating the nonzero terms.
+c
+c     the subroutine statement is
+c
+c       subroutine fdjac1(fcn,n,x,fvec,fjac,ldfjac,iflag,ml,mu,epsfcn,
+c                         wa1,wa2)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions. fcn must be declared
+c         in an external statement in the user calling
+c         program, and should be written as follows.
+c
+c         subroutine fcn(n,x,fvec,iflag)
+c         integer n,iflag
+c         double precision x(n),fvec(n)
+c         ----------
+c         calculate the functions at x and
+c         return this vector in fvec.
+c         ----------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of fdjac1.
+c         in this case set iflag to a negative integer.
+c
+c       n is a positive integer input variable set to the number
+c         of functions and variables.
+c
+c       x is an input array of length n.
+c
+c       fvec is an input array of length n which must contain the
+c         functions evaluated at x.
+c
+c       fjac is an output n by n array which contains the
+c         approximation to the jacobian matrix evaluated at x.
+c
+c       ldfjac is a positive integer input variable not less than n
+c         which specifies the leading dimension of the array fjac.
+c
+c       iflag is an integer variable which can be used to terminate
+c         the execution of fdjac1. see description of fcn.
+c
+c       ml is a nonnegative integer input variable which specifies
+c         the number of subdiagonals within the band of the
+c         jacobian matrix. if the jacobian is not banded, set
+c         ml to at least n - 1.
+c
+c       epsfcn is an input variable used in determining a suitable
+c         step length for the forward-difference approximation. this
+c         approximation assumes that the relative errors in the
+c         functions are of the order of epsfcn. if epsfcn is less
+c         than the machine precision, it is assumed that the relative
+c         errors in the functions are of the order of the machine
+c         precision.
+c
+c       mu is a nonnegative integer input variable which specifies
+c         the number of superdiagonals within the band of the
+c         jacobian matrix. if the jacobian is not banded, set
+c         mu to at least n - 1.
+c
+c       wa1 and wa2 are work arrays of length n. if ml + mu + 1 is at
+c         least n, then the jacobian is considered dense, and wa2 is
+c         not referenced.
+c
+c     subprograms called
+c
+c       minpack-supplied ... dpmpar
+c
+c       fortran-supplied ... dabs,dmax1,dsqrt
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,j,k,msum
+      double precision eps,epsmch,h,temp,zero
+      double precision dpmpar
+      data zero /0.0d0/
+c
+c     epsmch is the machine precision.
+c
+      epsmch = dpmpar(1)
+c
+      eps = dsqrt(dmax1(epsfcn,epsmch))
+      msum = ml + mu + 1
+      if (msum .lt. n) go to 40
+c
+c        computation of dense approximate jacobian.
+c
+         do 20 j = 1, n
+            temp = x(j)
+            h = eps*dabs(temp)
+            if (h .eq. zero) h = eps
+            x(j) = temp + h
+            call fcn(n,x,wa1,iflag)
+            if (iflag .lt. 0) go to 30
+            x(j) = temp
+            do 10 i = 1, n
+               fjac(i,j) = (wa1(i) - fvec(i))/h
+   10          continue
+   20       continue
+   30    continue
+         go to 110
+   40 continue
+c
+c        computation of banded approximate jacobian.
+c
+         do 90 k = 1, msum
+            do 60 j = k, n, msum
+               wa2(j) = x(j)
+               h = eps*dabs(wa2(j))
+               if (h .eq. zero) h = eps
+               x(j) = wa2(j) + h
+   60          continue
+            call fcn(n,x,wa1,iflag)
+            if (iflag .lt. 0) go to 100
+            do 80 j = k, n, msum
+               x(j) = wa2(j)
+               h = eps*dabs(wa2(j))
+               if (h .eq. zero) h = eps
+               do 70 i = 1, n
+                  fjac(i,j) = zero
+                  if (i .ge. j - mu .and. i .le. j + ml)
+     *               fjac(i,j) = (wa1(i) - fvec(i))/h
+   70             continue
+   80          continue
+   90       continue
+  100    continue
+  110 continue
+      return
+c
+c     last card of subroutine fdjac1.
+c
+      end
diff --git a/math/minpack/fdjac2.f b/math/minpack/fdjac2.f
new file mode 100644
index 00000000..218ab94c
--- /dev/null
+++ b/math/minpack/fdjac2.f
@@ -0,0 +1,107 @@
+      subroutine fdjac2(fcn,m,n,x,fvec,fjac,ldfjac,iflag,epsfcn,wa)
+      integer m,n,ldfjac,iflag
+      double precision epsfcn
+      double precision x(n),fvec(m),fjac(ldfjac,n),wa(m)
+c     **********
+c
+c     subroutine fdjac2
+c
+c     this subroutine computes a forward-difference approximation
+c     to the m by n jacobian matrix associated with a specified
+c     problem of m functions in n variables.
+c
+c     the subroutine statement is
+c
+c       subroutine fdjac2(fcn,m,n,x,fvec,fjac,ldfjac,iflag,epsfcn,wa)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions. fcn must be declared
+c         in an external statement in the user calling
+c         program, and should be written as follows.
+c
+c         subroutine fcn(m,n,x,fvec,iflag)
+c         integer m,n,iflag
+c         double precision x(n),fvec(m)
+c         ----------
+c         calculate the functions at x and
+c         return this vector in fvec.
+c         ----------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of fdjac2.
+c         in this case set iflag to a negative integer.
+c
+c       m is a positive integer input variable set to the number
+c         of functions.
+c
+c       n is a positive integer input variable set to the number
+c         of variables. n must not exceed m.
+c
+c       x is an input array of length n.
+c
+c       fvec is an input array of length m which must contain the
+c         functions evaluated at x.
+c
+c       fjac is an output m by n array which contains the
+c         approximation to the jacobian matrix evaluated at x.
+c
+c       ldfjac is a positive integer input variable not less than m
+c         which specifies the leading dimension of the array fjac.
+c
+c       iflag is an integer variable which can be used to terminate
+c         the execution of fdjac2. see description of fcn.
+c
+c       epsfcn is an input variable used in determining a suitable
+c         step length for the forward-difference approximation. this
+c         approximation assumes that the relative errors in the
+c         functions are of the order of epsfcn. if epsfcn is less
+c         than the machine precision, it is assumed that the relative
+c         errors in the functions are of the order of the machine
+c         precision.
+c
+c       wa is a work array of length m.
+c
+c     subprograms called
+c
+c       user-supplied ...... fcn
+c
+c       minpack-supplied ... dpmpar
+c
+c       fortran-supplied ... dabs,dmax1,dsqrt
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,j
+      double precision eps,epsmch,h,temp,zero
+      double precision dpmpar
+      data zero /0.0d0/
+c
+c     epsmch is the machine precision.
+c
+      epsmch = dpmpar(1)
+c
+      eps = dsqrt(dmax1(epsfcn,epsmch))
+      do 20 j = 1, n
+         temp = x(j)
+         h = eps*dabs(temp)
+         if (h .eq. zero) h = eps
+         x(j) = temp + h
+         call fcn(m,n,x,wa,iflag)
+         if (iflag .lt. 0) go to 30
+         x(j) = temp
+         do 10 i = 1, m
+            fjac(i,j) = (wa(i) - fvec(i))/h
+   10       continue
+   20    continue
+   30 continue
+      return
+c
+c     last card of subroutine fdjac2.
+c
+      end
diff --git a/math/minpack/hybrd.f b/math/minpack/hybrd.f
new file mode 100644
index 00000000..fc0b4c26
--- /dev/null
+++ b/math/minpack/hybrd.f
@@ -0,0 +1,459 @@
+      subroutine hybrd(fcn,n,x,fvec,xtol,maxfev,ml,mu,epsfcn,diag,
+     *                 mode,factor,nprint,info,nfev,fjac,ldfjac,r,lr,
+     *                 qtf,wa1,wa2,wa3,wa4)
+      integer n,maxfev,ml,mu,mode,nprint,info,nfev,ldfjac,lr
+      double precision xtol,epsfcn,factor
+      double precision x(n),fvec(n),diag(n),fjac(ldfjac,n),r(lr),
+     *                 qtf(n),wa1(n),wa2(n),wa3(n),wa4(n)
+      external fcn
+c     **********
+c
+c     subroutine hybrd
+c
+c     the purpose of hybrd is to find a zero of a system of
+c     n nonlinear functions in n variables by a modification
+c     of the powell hybrid method. the user must provide a
+c     subroutine which calculates the functions. the jacobian is
+c     then calculated by a forward-difference approximation.
+c
+c     the subroutine statement is
+c
+c       subroutine hybrd(fcn,n,x,fvec,xtol,maxfev,ml,mu,epsfcn,
+c                        diag,mode,factor,nprint,info,nfev,fjac,
+c                        ldfjac,r,lr,qtf,wa1,wa2,wa3,wa4)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions. fcn must be declared
+c         in an external statement in the user calling
+c         program, and should be written as follows.
+c
+c         subroutine fcn(n,x,fvec,iflag)
+c         integer n,iflag
+c         double precision x(n),fvec(n)
+c         ----------
+c         calculate the functions at x and
+c         return this vector in fvec.
+c         ---------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of hybrd.
+c         in this case set iflag to a negative integer.
+c
+c       n is a positive integer input variable set to the number
+c         of functions and variables.
+c
+c       x is an array of length n. on input x must contain
+c         an initial estimate of the solution vector. on output x
+c         contains the final estimate of the solution vector.
+c
+c       fvec is an output array of length n which contains
+c         the functions evaluated at the output x.
+c
+c       xtol is a nonnegative input variable. termination
+c         occurs when the relative error between two consecutive
+c         iterates is at most xtol.
+c
+c       maxfev is a positive integer input variable. termination
+c         occurs when the number of calls to fcn is at least maxfev
+c         by the end of an iteration.
+c
+c       ml is a nonnegative integer input variable which specifies
+c         the number of subdiagonals within the band of the
+c         jacobian matrix. if the jacobian is not banded, set
+c         ml to at least n - 1.
+c
+c       mu is a nonnegative integer input variable which specifies
+c         the number of superdiagonals within the band of the
+c         jacobian matrix. if the jacobian is not banded, set
+c         mu to at least n - 1.
+c
+c       epsfcn is an input variable used in determining a suitable
+c         step length for the forward-difference approximation. this
+c         approximation assumes that the relative errors in the
+c         functions are of the order of epsfcn. if epsfcn is less
+c         than the machine precision, it is assumed that the relative
+c         errors in the functions are of the order of the machine
+c         precision.
+c
+c       diag is an array of length n. if mode = 1 (see
+c         below), diag is internally set. if mode = 2, diag
+c         must contain positive entries that serve as
+c         multiplicative scale factors for the variables.
+c
+c       mode is an integer input variable. if mode = 1, the
+c         variables will be scaled internally. if mode = 2,
+c         the scaling is specified by the input diag. other
+c         values of mode are equivalent to mode = 1.
+c
+c       factor is a positive input variable used in determining the
+c         initial step bound. this bound is set to the product of
+c         factor and the euclidean norm of diag*x if nonzero, or else
+c         to factor itself. in most cases factor should lie in the
+c         interval (.1,100.). 100. is a generally recommended value.
+c
+c       nprint is an integer input variable that enables controlled
+c         printing of iterates if it is positive. in this case,
+c         fcn is called with iflag = 0 at the beginning of the first
+c         iteration and every nprint iterations thereafter and
+c         immediately prior to return, with x and fvec available
+c         for printing. if nprint is not positive, no special calls
+c         of fcn with iflag = 0 are made.
+c
+c       info is an integer output variable. if the user has
+c         terminated execution, info is set to the (negative)
+c         value of iflag. see description of fcn. otherwise,
+c         info is set as follows.
+c
+c         info = 0   improper input parameters.
+c
+c         info = 1   relative error between two consecutive iterates
+c                    is at most xtol.
+c
+c         info = 2   number of calls to fcn has reached or exceeded
+c                    maxfev.
+c
+c         info = 3   xtol is too small. no further improvement in
+c                    the approximate solution x is possible.
+c
+c         info = 4   iteration is not making good progress, as
+c                    measured by the improvement from the last
+c                    five jacobian evaluations.
+c
+c         info = 5   iteration is not making good progress, as
+c                    measured by the improvement from the last
+c                    ten iterations.
+c
+c       nfev is an integer output variable set to the number of
+c         calls to fcn.
+c
+c       fjac is an output n by n array which contains the
+c         orthogonal matrix q produced by the qr factorization
+c         of the final approximate jacobian.
+c
+c       ldfjac is a positive integer input variable not less than n
+c         which specifies the leading dimension of the array fjac.
+c
+c       r is an output array of length lr which contains the
+c         upper triangular matrix produced by the qr factorization
+c         of the final approximate jacobian, stored rowwise.
+c
+c       lr is a positive integer input variable not less than
+c         (n*(n+1))/2.
+c
+c       qtf is an output array of length n which contains
+c         the vector (q transpose)*fvec.
+c
+c       wa1, wa2, wa3, and wa4 are work arrays of length n.
+c
+c     subprograms called
+c
+c       user-supplied ...... fcn
+c
+c       minpack-supplied ... dogleg,dpmpar,enorm,fdjac1,
+c                            qform,qrfac,r1mpyq,r1updt
+c
+c       fortran-supplied ... dabs,dmax1,dmin1,min0,mod
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,iflag,iter,j,jm1,l,msum,ncfail,ncsuc,nslow1,nslow2
+      integer iwa(1)
+      logical jeval,sing
+      double precision actred,delta,epsmch,fnorm,fnorm1,one,pnorm,
+     *                 prered,p1,p5,p001,p0001,ratio,sum,temp,xnorm,
+     *                 zero
+      double precision dpmpar,enorm
+      data one,p1,p5,p001,p0001,zero
+     *     /1.0d0,1.0d-1,5.0d-1,1.0d-3,1.0d-4,0.0d0/
+c
+c     epsmch is the machine precision.
+c
+      epsmch = dpmpar(1)
+c
+      info = 0
+      iflag = 0
+      nfev = 0
+c
+c     check the input parameters for errors.
+c
+      if (n .le. 0 .or. xtol .lt. zero .or. maxfev .le. 0
+     *    .or. ml .lt. 0 .or. mu .lt. 0 .or. factor .le. zero
+     *    .or. ldfjac .lt. n .or. lr .lt. (n*(n + 1))/2) go to 300
+      if (mode .ne. 2) go to 20
+      do 10 j = 1, n
+         if (diag(j) .le. zero) go to 300
+   10    continue
+   20 continue
+c
+c     evaluate the function at the starting point
+c     and calculate its norm.
+c
+      iflag = 1
+      call fcn(n,x,fvec,iflag)
+      nfev = 1
+      if (iflag .lt. 0) go to 300
+      fnorm = enorm(n,fvec)
+c
+c     determine the number of calls to fcn needed to compute
+c     the jacobian matrix.
+c
+      msum = min0(ml+mu+1,n)
+c
+c     initialize iteration counter and monitors.
+c
+      iter = 1
+      ncsuc = 0
+      ncfail = 0
+      nslow1 = 0
+      nslow2 = 0
+c
+c     beginning of the outer loop.
+c
+   30 continue
+         jeval = .true.
+c
+c        calculate the jacobian matrix.
+c
+         iflag = 2
+         call fdjac1(fcn,n,x,fvec,fjac,ldfjac,iflag,ml,mu,epsfcn,wa1,
+     *               wa2)
+         nfev = nfev + msum
+         if (iflag .lt. 0) go to 300
+c
+c        compute the qr factorization of the jacobian.
+c
+         call qrfac(n,n,fjac,ldfjac,.false.,iwa,1,wa1,wa2,wa3)
+c
+c        on the first iteration and if mode is 1, scale according
+c        to the norms of the columns of the initial jacobian.
+c
+         if (iter .ne. 1) go to 70
+         if (mode .eq. 2) go to 50
+         do 40 j = 1, n
+            diag(j) = wa2(j)
+            if (wa2(j) .eq. zero) diag(j) = one
+   40       continue
+   50    continue
+c
+c        on the first iteration, calculate the norm of the scaled x
+c        and initialize the step bound delta.
+c
+         do 60 j = 1, n
+            wa3(j) = diag(j)*x(j)
+   60       continue
+         xnorm = enorm(n,wa3)
+         delta = factor*xnorm
+         if (delta .eq. zero) delta = factor
+   70    continue
+c
+c        form (q transpose)*fvec and store in qtf.
+c
+         do 80 i = 1, n
+            qtf(i) = fvec(i)
+   80       continue
+         do 120 j = 1, n
+            if (fjac(j,j) .eq. zero) go to 110
+            sum = zero
+            do 90 i = j, n
+               sum = sum + fjac(i,j)*qtf(i)
+   90          continue
+            temp = -sum/fjac(j,j)
+            do 100 i = j, n
+               qtf(i) = qtf(i) + fjac(i,j)*temp
+  100          continue
+  110       continue
+  120       continue
+c
+c        copy the triangular factor of the qr factorization into r.
+c
+         sing = .false.
+         do 150 j = 1, n
+            l = j
+            jm1 = j - 1
+            if (jm1 .lt. 1) go to 140
+            do 130 i = 1, jm1
+               r(l) = fjac(i,j)
+               l = l + n - i
+  130          continue
+  140       continue
+            r(l) = wa1(j)
+            if (wa1(j) .eq. zero) sing = .true.
+  150       continue
+c
+c        accumulate the orthogonal factor in fjac.
+c
+         call qform(n,n,fjac,ldfjac,wa1)
+c
+c        rescale if necessary.
+c
+         if (mode .eq. 2) go to 170
+         do 160 j = 1, n
+            diag(j) = dmax1(diag(j),wa2(j))
+  160       continue
+  170    continue
+c
+c        beginning of the inner loop.
+c
+  180    continue
+c
+c           if requested, call fcn to enable printing of iterates.
+c
+            if (nprint .le. 0) go to 190
+            iflag = 0
+            if (mod(iter-1,nprint) .eq. 0) call fcn(n,x,fvec,iflag)
+            if (iflag .lt. 0) go to 300
+  190       continue
+c
+c           determine the direction p.
+c
+            call dogleg(n,r,lr,diag,qtf,delta,wa1,wa2,wa3)
+c
+c           store the direction p and x + p. calculate the norm of p.
+c
+            do 200 j = 1, n
+               wa1(j) = -wa1(j)
+               wa2(j) = x(j) + wa1(j)
+               wa3(j) = diag(j)*wa1(j)
+  200          continue
+            pnorm = enorm(n,wa3)
+c
+c           on the first iteration, adjust the initial step bound.
+c
+            if (iter .eq. 1) delta = dmin1(delta,pnorm)
+c
+c           evaluate the function at x + p and calculate its norm.
+c
+            iflag = 1
+            call fcn(n,wa2,wa4,iflag)
+            nfev = nfev + 1
+            if (iflag .lt. 0) go to 300
+            fnorm1 = enorm(n,wa4)
+c
+c           compute the scaled actual reduction.
+c
+            actred = -one
+            if (fnorm1 .lt. fnorm) actred = one - (fnorm1/fnorm)**2
+c
+c           compute the scaled predicted reduction.
+c
+            l = 1
+            do 220 i = 1, n
+               sum = zero
+               do 210 j = i, n
+                  sum = sum + r(l)*wa1(j)
+                  l = l + 1
+  210             continue
+               wa3(i) = qtf(i) + sum
+  220          continue
+            temp = enorm(n,wa3)
+            prered = zero
+            if (temp .lt. fnorm) prered = one - (temp/fnorm)**2
+c
+c           compute the ratio of the actual to the predicted
+c           reduction.
+c
+            ratio = zero
+            if (prered .gt. zero) ratio = actred/prered
+c
+c           update the step bound.
+c
+            if (ratio .ge. p1) go to 230
+               ncsuc = 0
+               ncfail = ncfail + 1
+               delta = p5*delta
+               go to 240
+  230       continue
+               ncfail = 0
+               ncsuc = ncsuc + 1
+               if (ratio .ge. p5 .or. ncsuc .gt. 1)
+     *            delta = dmax1(delta,pnorm/p5)
+               if (dabs(ratio-one) .le. p1) delta = pnorm/p5
+  240       continue
+c
+c           test for successful iteration.
+c
+            if (ratio .lt. p0001) go to 260
+c
+c           successful iteration. update x, fvec, and their norms.
+c
+            do 250 j = 1, n
+               x(j) = wa2(j)
+               wa2(j) = diag(j)*x(j)
+               fvec(j) = wa4(j)
+  250          continue
+            xnorm = enorm(n,wa2)
+            fnorm = fnorm1
+            iter = iter + 1
+  260       continue
+c
+c           determine the progress of the iteration.
+c
+            nslow1 = nslow1 + 1
+            if (actred .ge. p001) nslow1 = 0
+            if (jeval) nslow2 = nslow2 + 1
+            if (actred .ge. p1) nslow2 = 0
+c
+c           test for convergence.
+c
+            if (delta .le. xtol*xnorm .or. fnorm .eq. zero) info = 1
+            if (info .ne. 0) go to 300
+c
+c           tests for termination and stringent tolerances.
+c
+            if (nfev .ge. maxfev) info = 2
+            if (p1*dmax1(p1*delta,pnorm) .le. epsmch*xnorm) info = 3
+            if (nslow2 .eq. 5) info = 4
+            if (nslow1 .eq. 10) info = 5
+            if (info .ne. 0) go to 300
+c
+c           criterion for recalculating jacobian approximation
+c           by forward differences.
+c
+            if (ncfail .eq. 2) go to 290
+c
+c           calculate the rank one modification to the jacobian
+c           and update qtf if necessary.
+c
+            do 280 j = 1, n
+               sum = zero
+               do 270 i = 1, n
+                  sum = sum + fjac(i,j)*wa4(i)
+  270             continue
+               wa2(j) = (sum - wa3(j))/pnorm
+               wa1(j) = diag(j)*((diag(j)*wa1(j))/pnorm)
+               if (ratio .ge. p0001) qtf(j) = sum
+  280          continue
+c
+c           compute the qr factorization of the updated jacobian.
+c
+            call r1updt(n,n,r,lr,wa1,wa2,wa3,sing)
+            call r1mpyq(n,n,fjac,ldfjac,wa2,wa3)
+            call r1mpyq(1,n,qtf,1,wa2,wa3)
+c
+c           end of the inner loop.
+c
+            jeval = .false.
+            go to 180
+  290    continue
+c
+c        end of the outer loop.
+c
+         go to 30
+  300 continue
+c
+c     termination, either normal or user imposed.
+c
+      if (iflag .lt. 0) info = iflag
+      iflag = 0
+      if (nprint .gt. 0) call fcn(n,x,fvec,iflag)
+      return
+c
+c     last card of subroutine hybrd.
+c
+      end
diff --git a/math/minpack/hybrd1.f b/math/minpack/hybrd1.f
new file mode 100644
index 00000000..c0a85927
--- /dev/null
+++ b/math/minpack/hybrd1.f
@@ -0,0 +1,123 @@
+      subroutine hybrd1(fcn,n,x,fvec,tol,info,wa,lwa)
+      integer n,info,lwa
+      double precision tol
+      double precision x(n),fvec(n),wa(lwa)
+      external fcn
+c     **********
+c
+c     subroutine hybrd1
+c
+c     the purpose of hybrd1 is to find a zero of a system of
+c     n nonlinear functions in n variables by a modification
+c     of the powell hybrid method. this is done by using the
+c     more general nonlinear equation solver hybrd. the user
+c     must provide a subroutine which calculates the functions.
+c     the jacobian is then calculated by a forward-difference
+c     approximation.
+c
+c     the subroutine statement is
+c
+c       subroutine hybrd1(fcn,n,x,fvec,tol,info,wa,lwa)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions. fcn must be declared
+c         in an external statement in the user calling
+c         program, and should be written as follows.
+c
+c         subroutine fcn(n,x,fvec,iflag)
+c         integer n,iflag
+c         double precision x(n),fvec(n)
+c         ----------
+c         calculate the functions at x and
+c         return this vector in fvec.
+c         ---------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of hybrd1.
+c         in this case set iflag to a negative integer.
+c
+c       n is a positive integer input variable set to the number
+c         of functions and variables.
+c
+c       x is an array of length n. on input x must contain
+c         an initial estimate of the solution vector. on output x
+c         contains the final estimate of the solution vector.
+c
+c       fvec is an output array of length n which contains
+c         the functions evaluated at the output x.
+c
+c       tol is a nonnegative input variable. termination occurs
+c         when the algorithm estimates that the relative error
+c         between x and the solution is at most tol.
+c
+c       info is an integer output variable. if the user has
+c         terminated execution, info is set to the (negative)
+c         value of iflag. see description of fcn. otherwise,
+c         info is set as follows.
+c
+c         info = 0   improper input parameters.
+c
+c         info = 1   algorithm estimates that the relative error
+c                    between x and the solution is at most tol.
+c
+c         info = 2   number of calls to fcn has reached or exceeded
+c                    200*(n+1).
+c
+c         info = 3   tol is too small. no further improvement in
+c                    the approximate solution x is possible.
+c
+c         info = 4   iteration is not making good progress.
+c
+c       wa is a work array of length lwa.
+c
+c       lwa is a positive integer input variable not less than
+c         (n*(3*n+13))/2.
+c
+c     subprograms called
+c
+c       user-supplied ...... fcn
+c
+c       minpack-supplied ... hybrd
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer index,j,lr,maxfev,ml,mode,mu,nfev,nprint
+      double precision epsfcn,factor,one,xtol,zero
+      data factor,one,zero /1.0d2,1.0d0,0.0d0/
+      info = 0
+c
+c     check the input parameters for errors.
+c
+      if (n .le. 0 .or. tol .lt. zero .or. lwa .lt. (n*(3*n + 13))/2)
+     *   go to 20
+c
+c     call hybrd.
+c
+      maxfev = 200*(n + 1)
+      xtol = tol
+      ml = n - 1
+      mu = n - 1
+      epsfcn = zero
+      mode = 2
+      do 10 j = 1, n
+         wa(j) = one
+   10    continue
+      nprint = 0
+      lr = (n*(n + 1))/2
+      index = 6*n + lr
+      call hybrd(fcn,n,x,fvec,xtol,maxfev,ml,mu,epsfcn,wa(1),mode,
+     *           factor,nprint,info,nfev,wa(index+1),n,wa(6*n+1),lr,
+     *           wa(n+1),wa(2*n+1),wa(3*n+1),wa(4*n+1),wa(5*n+1))
+      if (info .eq. 5) info = 4
+   20 continue
+      return
+c
+c     last card of subroutine hybrd1.
+c
+      end
diff --git a/math/minpack/hybrj.f b/math/minpack/hybrj.f
new file mode 100644
index 00000000..3070dad3
--- /dev/null
+++ b/math/minpack/hybrj.f
@@ -0,0 +1,440 @@
+      subroutine hybrj(fcn,n,x,fvec,fjac,ldfjac,xtol,maxfev,diag,mode,
+     *                 factor,nprint,info,nfev,njev,r,lr,qtf,wa1,wa2,
+     *                 wa3,wa4)
+      integer n,ldfjac,maxfev,mode,nprint,info,nfev,njev,lr
+      double precision xtol,factor
+      double precision x(n),fvec(n),fjac(ldfjac,n),diag(n),r(lr),
+     *                 qtf(n),wa1(n),wa2(n),wa3(n),wa4(n)
+c     **********
+c
+c     subroutine hybrj
+c
+c     the purpose of hybrj is to find a zero of a system of
+c     n nonlinear functions in n variables by a modification
+c     of the powell hybrid method. the user must provide a
+c     subroutine which calculates the functions and the jacobian.
+c
+c     the subroutine statement is
+c
+c       subroutine hybrj(fcn,n,x,fvec,fjac,ldfjac,xtol,maxfev,diag,
+c                        mode,factor,nprint,info,nfev,njev,r,lr,qtf,
+c                        wa1,wa2,wa3,wa4)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions and the jacobian. fcn must
+c         be declared in an external statement in the user
+c         calling program, and should be written as follows.
+c
+c         subroutine fcn(n,x,fvec,fjac,ldfjac,iflag)
+c         integer n,ldfjac,iflag
+c         double precision x(n),fvec(n),fjac(ldfjac,n)
+c         ----------
+c         if iflag = 1 calculate the functions at x and
+c         return this vector in fvec. do not alter fjac.
+c         if iflag = 2 calculate the jacobian at x and
+c         return this matrix in fjac. do not alter fvec.
+c         ---------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of hybrj.
+c         in this case set iflag to a negative integer.
+c
+c       n is a positive integer input variable set to the number
+c         of functions and variables.
+c
+c       x is an array of length n. on input x must contain
+c         an initial estimate of the solution vector. on output x
+c         contains the final estimate of the solution vector.
+c
+c       fvec is an output array of length n which contains
+c         the functions evaluated at the output x.
+c
+c       fjac is an output n by n array which contains the
+c         orthogonal matrix q produced by the qr factorization
+c         of the final approximate jacobian.
+c
+c       ldfjac is a positive integer input variable not less than n
+c         which specifies the leading dimension of the array fjac.
+c
+c       xtol is a nonnegative input variable. termination
+c         occurs when the relative error between two consecutive
+c         iterates is at most xtol.
+c
+c       maxfev is a positive integer input variable. termination
+c         occurs when the number of calls to fcn with iflag = 1
+c         has reached maxfev.
+c
+c       diag is an array of length n. if mode = 1 (see
+c         below), diag is internally set. if mode = 2, diag
+c         must contain positive entries that serve as
+c         multiplicative scale factors for the variables.
+c
+c       mode is an integer input variable. if mode = 1, the
+c         variables will be scaled internally. if mode = 2,
+c         the scaling is specified by the input diag. other
+c         values of mode are equivalent to mode = 1.
+c
+c       factor is a positive input variable used in determining the
+c         initial step bound. this bound is set to the product of
+c         factor and the euclidean norm of diag*x if nonzero, or else
+c         to factor itself. in most cases factor should lie in the
+c         interval (.1,100.). 100. is a generally recommended value.
+c
+c       nprint is an integer input variable that enables controlled
+c         printing of iterates if it is positive. in this case,
+c         fcn is called with iflag = 0 at the beginning of the first
+c         iteration and every nprint iterations thereafter and
+c         immediately prior to return, with x and fvec available
+c         for printing. fvec and fjac should not be altered.
+c         if nprint is not positive, no special calls of fcn
+c         with iflag = 0 are made.
+c
+c       info is an integer output variable. if the user has
+c         terminated execution, info is set to the (negative)
+c         value of iflag. see description of fcn. otherwise,
+c         info is set as follows.
+c
+c         info = 0   improper input parameters.
+c
+c         info = 1   relative error between two consecutive iterates
+c                    is at most xtol.
+c
+c         info = 2   number of calls to fcn with iflag = 1 has
+c                    reached maxfev.
+c
+c         info = 3   xtol is too small. no further improvement in
+c                    the approximate solution x is possible.
+c
+c         info = 4   iteration is not making good progress, as
+c                    measured by the improvement from the last
+c                    five jacobian evaluations.
+c
+c         info = 5   iteration is not making good progress, as
+c                    measured by the improvement from the last
+c                    ten iterations.
+c
+c       nfev is an integer output variable set to the number of
+c         calls to fcn with iflag = 1.
+c
+c       njev is an integer output variable set to the number of
+c         calls to fcn with iflag = 2.
+c
+c       r is an output array of length lr which contains the
+c         upper triangular matrix produced by the qr factorization
+c         of the final approximate jacobian, stored rowwise.
+c
+c       lr is a positive integer input variable not less than
+c         (n*(n+1))/2.
+c
+c       qtf is an output array of length n which contains
+c         the vector (q transpose)*fvec.
+c
+c       wa1, wa2, wa3, and wa4 are work arrays of length n.
+c
+c     subprograms called
+c
+c       user-supplied ...... fcn
+c
+c       minpack-supplied ... dogleg,dpmpar,enorm,
+c                            qform,qrfac,r1mpyq,r1updt
+c
+c       fortran-supplied ... dabs,dmax1,dmin1,mod
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,iflag,iter,j,jm1,l,ncfail,ncsuc,nslow1,nslow2
+      integer iwa(1)
+      logical jeval,sing
+      double precision actred,delta,epsmch,fnorm,fnorm1,one,pnorm,
+     *                 prered,p1,p5,p001,p0001,ratio,sum,temp,xnorm,
+     *                 zero
+      double precision dpmpar,enorm
+      data one,p1,p5,p001,p0001,zero
+     *     /1.0d0,1.0d-1,5.0d-1,1.0d-3,1.0d-4,0.0d0/
+c
+c     epsmch is the machine precision.
+c
+      epsmch = dpmpar(1)
+c
+      info = 0
+      iflag = 0
+      nfev = 0
+      njev = 0
+c
+c     check the input parameters for errors.
+c
+      if (n .le. 0 .or. ldfjac .lt. n .or. xtol .lt. zero
+     *    .or. maxfev .le. 0 .or. factor .le. zero
+     *    .or. lr .lt. (n*(n + 1))/2) go to 300
+      if (mode .ne. 2) go to 20
+      do 10 j = 1, n
+         if (diag(j) .le. zero) go to 300
+   10    continue
+   20 continue
+c
+c     evaluate the function at the starting point
+c     and calculate its norm.
+c
+      iflag = 1
+      call fcn(n,x,fvec,fjac,ldfjac,iflag)
+      nfev = 1
+      if (iflag .lt. 0) go to 300
+      fnorm = enorm(n,fvec)
+c
+c     initialize iteration counter and monitors.
+c
+      iter = 1
+      ncsuc = 0
+      ncfail = 0
+      nslow1 = 0
+      nslow2 = 0
+c
+c     beginning of the outer loop.
+c
+   30 continue
+         jeval = .true.
+c
+c        calculate the jacobian matrix.
+c
+         iflag = 2
+         call fcn(n,x,fvec,fjac,ldfjac,iflag)
+         njev = njev + 1
+         if (iflag .lt. 0) go to 300
+c
+c        compute the qr factorization of the jacobian.
+c
+         call qrfac(n,n,fjac,ldfjac,.false.,iwa,1,wa1,wa2,wa3)
+c
+c        on the first iteration and if mode is 1, scale according
+c        to the norms of the columns of the initial jacobian.
+c
+         if (iter .ne. 1) go to 70
+         if (mode .eq. 2) go to 50
+         do 40 j = 1, n
+            diag(j) = wa2(j)
+            if (wa2(j) .eq. zero) diag(j) = one
+   40       continue
+   50    continue
+c
+c        on the first iteration, calculate the norm of the scaled x
+c        and initialize the step bound delta.
+c
+         do 60 j = 1, n
+            wa3(j) = diag(j)*x(j)
+   60       continue
+         xnorm = enorm(n,wa3)
+         delta = factor*xnorm
+         if (delta .eq. zero) delta = factor
+   70    continue
+c
+c        form (q transpose)*fvec and store in qtf.
+c
+         do 80 i = 1, n
+            qtf(i) = fvec(i)
+   80       continue
+         do 120 j = 1, n
+            if (fjac(j,j) .eq. zero) go to 110
+            sum = zero
+            do 90 i = j, n
+               sum = sum + fjac(i,j)*qtf(i)
+   90          continue
+            temp = -sum/fjac(j,j)
+            do 100 i = j, n
+               qtf(i) = qtf(i) + fjac(i,j)*temp
+  100          continue
+  110       continue
+  120       continue
+c
+c        copy the triangular factor of the qr factorization into r.
+c
+         sing = .false.
+         do 150 j = 1, n
+            l = j
+            jm1 = j - 1
+            if (jm1 .lt. 1) go to 140
+            do 130 i = 1, jm1
+               r(l) = fjac(i,j)
+               l = l + n - i
+  130          continue
+  140       continue
+            r(l) = wa1(j)
+            if (wa1(j) .eq. zero) sing = .true.
+  150       continue
+c
+c        accumulate the orthogonal factor in fjac.
+c
+         call qform(n,n,fjac,ldfjac,wa1)
+c
+c        rescale if necessary.
+c
+         if (mode .eq. 2) go to 170
+         do 160 j = 1, n
+            diag(j) = dmax1(diag(j),wa2(j))
+  160       continue
+  170    continue
+c
+c        beginning of the inner loop.
+c
+  180    continue
+c
+c           if requested, call fcn to enable printing of iterates.
+c
+            if (nprint .le. 0) go to 190
+            iflag = 0
+            if (mod(iter-1,nprint) .eq. 0)
+     *         call fcn(n,x,fvec,fjac,ldfjac,iflag)
+            if (iflag .lt. 0) go to 300
+  190       continue
+c
+c           determine the direction p.
+c
+            call dogleg(n,r,lr,diag,qtf,delta,wa1,wa2,wa3)
+c
+c           store the direction p and x + p. calculate the norm of p.
+c
+            do 200 j = 1, n
+               wa1(j) = -wa1(j)
+               wa2(j) = x(j) + wa1(j)
+               wa3(j) = diag(j)*wa1(j)
+  200          continue
+            pnorm = enorm(n,wa3)
+c
+c           on the first iteration, adjust the initial step bound.
+c
+            if (iter .eq. 1) delta = dmin1(delta,pnorm)
+c
+c           evaluate the function at x + p and calculate its norm.
+c
+            iflag = 1
+            call fcn(n,wa2,wa4,fjac,ldfjac,iflag)
+            nfev = nfev + 1
+            if (iflag .lt. 0) go to 300
+            fnorm1 = enorm(n,wa4)
+c
+c           compute the scaled actual reduction.
+c
+            actred = -one
+            if (fnorm1 .lt. fnorm) actred = one - (fnorm1/fnorm)**2
+c
+c           compute the scaled predicted reduction.
+c
+            l = 1
+            do 220 i = 1, n
+               sum = zero
+               do 210 j = i, n
+                  sum = sum + r(l)*wa1(j)
+                  l = l + 1
+  210             continue
+               wa3(i) = qtf(i) + sum
+  220          continue
+            temp = enorm(n,wa3)
+            prered = zero
+            if (temp .lt. fnorm) prered = one - (temp/fnorm)**2
+c
+c           compute the ratio of the actual to the predicted
+c           reduction.
+c
+            ratio = zero
+            if (prered .gt. zero) ratio = actred/prered
+c
+c           update the step bound.
+c
+            if (ratio .ge. p1) go to 230
+               ncsuc = 0
+               ncfail = ncfail + 1
+               delta = p5*delta
+               go to 240
+  230       continue
+               ncfail = 0
+               ncsuc = ncsuc + 1
+               if (ratio .ge. p5 .or. ncsuc .gt. 1)
+     *            delta = dmax1(delta,pnorm/p5)
+               if (dabs(ratio-one) .le. p1) delta = pnorm/p5
+  240       continue
+c
+c           test for successful iteration.
+c
+            if (ratio .lt. p0001) go to 260
+c
+c           successful iteration. update x, fvec, and their norms.
+c
+            do 250 j = 1, n
+               x(j) = wa2(j)
+               wa2(j) = diag(j)*x(j)
+               fvec(j) = wa4(j)
+  250          continue
+            xnorm = enorm(n,wa2)
+            fnorm = fnorm1
+            iter = iter + 1
+  260       continue
+c
+c           determine the progress of the iteration.
+c
+            nslow1 = nslow1 + 1
+            if (actred .ge. p001) nslow1 = 0
+            if (jeval) nslow2 = nslow2 + 1
+            if (actred .ge. p1) nslow2 = 0
+c
+c           test for convergence.
+c
+            if (delta .le. xtol*xnorm .or. fnorm .eq. zero) info = 1
+            if (info .ne. 0) go to 300
+c
+c           tests for termination and stringent tolerances.
+c
+            if (nfev .ge. maxfev) info = 2
+            if (p1*dmax1(p1*delta,pnorm) .le. epsmch*xnorm) info = 3
+            if (nslow2 .eq. 5) info = 4
+            if (nslow1 .eq. 10) info = 5
+            if (info .ne. 0) go to 300
+c
+c           criterion for recalculating jacobian.
+c
+            if (ncfail .eq. 2) go to 290
+c
+c           calculate the rank one modification to the jacobian
+c           and update qtf if necessary.
+c
+            do 280 j = 1, n
+               sum = zero
+               do 270 i = 1, n
+                  sum = sum + fjac(i,j)*wa4(i)
+  270             continue
+               wa2(j) = (sum - wa3(j))/pnorm
+               wa1(j) = diag(j)*((diag(j)*wa1(j))/pnorm)
+               if (ratio .ge. p0001) qtf(j) = sum
+  280          continue
+c
+c           compute the qr factorization of the updated jacobian.
+c
+            call r1updt(n,n,r,lr,wa1,wa2,wa3,sing)
+            call r1mpyq(n,n,fjac,ldfjac,wa2,wa3)
+            call r1mpyq(1,n,qtf,1,wa2,wa3)
+c
+c           end of the inner loop.
+c
+            jeval = .false.
+            go to 180
+  290    continue
+c
+c        end of the outer loop.
+c
+         go to 30
+  300 continue
+c
+c     termination, either normal or user imposed.
+c
+      if (iflag .lt. 0) info = iflag
+      iflag = 0
+      if (nprint .gt. 0) call fcn(n,x,fvec,fjac,ldfjac,iflag)
+      return
+c
+c     last card of subroutine hybrj.
+c
+      end
diff --git a/math/minpack/hybrj1.f b/math/minpack/hybrj1.f
new file mode 100644
index 00000000..9f51c496
--- /dev/null
+++ b/math/minpack/hybrj1.f
@@ -0,0 +1,127 @@
+      subroutine hybrj1(fcn,n,x,fvec,fjac,ldfjac,tol,info,wa,lwa)
+      integer n,ldfjac,info,lwa
+      double precision tol
+      double precision x(n),fvec(n),fjac(ldfjac,n),wa(lwa)
+      external fcn
+c     **********
+c
+c     subroutine hybrj1
+c
+c     the purpose of hybrj1 is to find a zero of a system of
+c     n nonlinear functions in n variables by a modification
+c     of the powell hybrid method. this is done by using the
+c     more general nonlinear equation solver hybrj. the user
+c     must provide a subroutine which calculates the functions
+c     and the jacobian.
+c
+c     the subroutine statement is
+c
+c       subroutine hybrj1(fcn,n,x,fvec,fjac,ldfjac,tol,info,wa,lwa)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions and the jacobian. fcn must
+c         be declared in an external statement in the user
+c         calling program, and should be written as follows.
+c
+c         subroutine fcn(n,x,fvec,fjac,ldfjac,iflag)
+c         integer n,ldfjac,iflag
+c         double precision x(n),fvec(n),fjac(ldfjac,n)
+c         ----------
+c         if iflag = 1 calculate the functions at x and
+c         return this vector in fvec. do not alter fjac.
+c         if iflag = 2 calculate the jacobian at x and
+c         return this matrix in fjac. do not alter fvec.
+c         ---------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of hybrj1.
+c         in this case set iflag to a negative integer.
+c
+c       n is a positive integer input variable set to the number
+c         of functions and variables.
+c
+c       x is an array of length n. on input x must contain
+c         an initial estimate of the solution vector. on output x
+c         contains the final estimate of the solution vector.
+c
+c       fvec is an output array of length n which contains
+c         the functions evaluated at the output x.
+c
+c       fjac is an output n by n array which contains the
+c         orthogonal matrix q produced by the qr factorization
+c         of the final approximate jacobian.
+c
+c       ldfjac is a positive integer input variable not less than n
+c         which specifies the leading dimension of the array fjac.
+c
+c       tol is a nonnegative input variable. termination occurs
+c         when the algorithm estimates that the relative error
+c         between x and the solution is at most tol.
+c
+c       info is an integer output variable. if the user has
+c         terminated execution, info is set to the (negative)
+c         value of iflag. see description of fcn. otherwise,
+c         info is set as follows.
+c
+c         info = 0   improper input parameters.
+c
+c         info = 1   algorithm estimates that the relative error
+c                    between x and the solution is at most tol.
+c
+c         info = 2   number of calls to fcn with iflag = 1 has
+c                    reached 100*(n+1).
+c
+c         info = 3   tol is too small. no further improvement in
+c                    the approximate solution x is possible.
+c
+c         info = 4   iteration is not making good progress.
+c
+c       wa is a work array of length lwa.
+c
+c       lwa is a positive integer input variable not less than
+c         (n*(n+13))/2.
+c
+c     subprograms called
+c
+c       user-supplied ...... fcn
+c
+c       minpack-supplied ... hybrj
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer j,lr,maxfev,mode,nfev,njev,nprint
+      double precision factor,one,xtol,zero
+      data factor,one,zero /1.0d2,1.0d0,0.0d0/
+      info = 0
+c
+c     check the input parameters for errors.
+c
+      if (n .le. 0 .or. ldfjac .lt. n .or. tol .lt. zero
+     *    .or. lwa .lt. (n*(n + 13))/2) go to 20
+c
+c     call hybrj.
+c
+      maxfev = 100*(n + 1)
+      xtol = tol
+      mode = 2
+      do 10 j = 1, n
+         wa(j) = one
+   10    continue
+      nprint = 0
+      lr = (n*(n + 1))/2
+      call hybrj(fcn,n,x,fvec,fjac,ldfjac,xtol,maxfev,wa(1),mode,
+     *           factor,nprint,info,nfev,njev,wa(6*n+1),lr,wa(n+1),
+     *           wa(2*n+1),wa(3*n+1),wa(4*n+1),wa(5*n+1))
+      if (info .eq. 5) info = 4
+   20 continue
+      return
+c
+c     last card of subroutine hybrj1.
+c
+      end
diff --git a/math/minpack/lmder.f b/math/minpack/lmder.f
new file mode 100644
index 00000000..8797d8be
--- /dev/null
+++ b/math/minpack/lmder.f
@@ -0,0 +1,452 @@
+      subroutine lmder(fcn,m,n,x,fvec,fjac,ldfjac,ftol,xtol,gtol,
+     *                 maxfev,diag,mode,factor,nprint,info,nfev,njev,
+     *                 ipvt,qtf,wa1,wa2,wa3,wa4)
+      integer m,n,ldfjac,maxfev,mode,nprint,info,nfev,njev
+      integer ipvt(n)
+      double precision ftol,xtol,gtol,factor
+      double precision x(n),fvec(m),fjac(ldfjac,n),diag(n),qtf(n),
+     *                 wa1(n),wa2(n),wa3(n),wa4(m)
+c     **********
+c
+c     subroutine lmder
+c
+c     the purpose of lmder is to minimize the sum of the squares of
+c     m nonlinear functions in n variables by a modification of
+c     the levenberg-marquardt algorithm. the user must provide a
+c     subroutine which calculates the functions and the jacobian.
+c
+c     the subroutine statement is
+c
+c       subroutine lmder(fcn,m,n,x,fvec,fjac,ldfjac,ftol,xtol,gtol,
+c                        maxfev,diag,mode,factor,nprint,info,nfev,
+c                        njev,ipvt,qtf,wa1,wa2,wa3,wa4)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions and the jacobian. fcn must
+c         be declared in an external statement in the user
+c         calling program, and should be written as follows.
+c
+c         subroutine fcn(m,n,x,fvec,fjac,ldfjac,iflag)
+c         integer m,n,ldfjac,iflag
+c         double precision x(n),fvec(m),fjac(ldfjac,n)
+c         ----------
+c         if iflag = 1 calculate the functions at x and
+c         return this vector in fvec. do not alter fjac.
+c         if iflag = 2 calculate the jacobian at x and
+c         return this matrix in fjac. do not alter fvec.
+c         ----------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of lmder.
+c         in this case set iflag to a negative integer.
+c
+c       m is a positive integer input variable set to the number
+c         of functions.
+c
+c       n is a positive integer input variable set to the number
+c         of variables. n must not exceed m.
+c
+c       x is an array of length n. on input x must contain
+c         an initial estimate of the solution vector. on output x
+c         contains the final estimate of the solution vector.
+c
+c       fvec is an output array of length m which contains
+c         the functions evaluated at the output x.
+c
+c       fjac is an output m by n array. the upper n by n submatrix
+c         of fjac contains an upper triangular matrix r with
+c         diagonal elements of nonincreasing magnitude such that
+c
+c                t     t           t
+c               p *(jac *jac)*p = r *r,
+c
+c         where p is a permutation matrix and jac is the final
+c         calculated jacobian. column j of p is column ipvt(j)
+c         (see below) of the identity matrix. the lower trapezoidal
+c         part of fjac contains information generated during
+c         the computation of r.
+c
+c       ldfjac is a positive integer input variable not less than m
+c         which specifies the leading dimension of the array fjac.
+c
+c       ftol is a nonnegative input variable. termination
+c         occurs when both the actual and predicted relative
+c         reductions in the sum of squares are at most ftol.
+c         therefore, ftol measures the relative error desired
+c         in the sum of squares.
+c
+c       xtol is a nonnegative input variable. termination
+c         occurs when the relative error between two consecutive
+c         iterates is at most xtol. therefore, xtol measures the
+c         relative error desired in the approximate solution.
+c
+c       gtol is a nonnegative input variable. termination
+c         occurs when the cosine of the angle between fvec and
+c         any column of the jacobian is at most gtol in absolute
+c         value. therefore, gtol measures the orthogonality
+c         desired between the function vector and the columns
+c         of the jacobian.
+c
+c       maxfev is a positive integer input variable. termination
+c         occurs when the number of calls to fcn with iflag = 1
+c         has reached maxfev.
+c
+c       diag is an array of length n. if mode = 1 (see
+c         below), diag is internally set. if mode = 2, diag
+c         must contain positive entries that serve as
+c         multiplicative scale factors for the variables.
+c
+c       mode is an integer input variable. if mode = 1, the
+c         variables will be scaled internally. if mode = 2,
+c         the scaling is specified by the input diag. other
+c         values of mode are equivalent to mode = 1.
+c
+c       factor is a positive input variable used in determining the
+c         initial step bound. this bound is set to the product of
+c         factor and the euclidean norm of diag*x if nonzero, or else
+c         to factor itself. in most cases factor should lie in the
+c         interval (.1,100.).100. is a generally recommended value.
+c
+c       nprint is an integer input variable that enables controlled
+c         printing of iterates if it is positive. in this case,
+c         fcn is called with iflag = 0 at the beginning of the first
+c         iteration and every nprint iterations thereafter and
+c         immediately prior to return, with x, fvec, and fjac
+c         available for printing. fvec and fjac should not be
+c         altered. if nprint is not positive, no special calls
+c         of fcn with iflag = 0 are made.
+c
+c       info is an integer output variable. if the user has
+c         terminated execution, info is set to the (negative)
+c         value of iflag. see description of fcn. otherwise,
+c         info is set as follows.
+c
+c         info = 0  improper input parameters.
+c
+c         info = 1  both actual and predicted relative reductions
+c                   in the sum of squares are at most ftol.
+c
+c         info = 2  relative error between two consecutive iterates
+c                   is at most xtol.
+c
+c         info = 3  conditions for info = 1 and info = 2 both hold.
+c
+c         info = 4  the cosine of the angle between fvec and any
+c                   column of the jacobian is at most gtol in
+c                   absolute value.
+c
+c         info = 5  number of calls to fcn with iflag = 1 has
+c                   reached maxfev.
+c
+c         info = 6  ftol is too small. no further reduction in
+c                   the sum of squares is possible.
+c
+c         info = 7  xtol is too small. no further improvement in
+c                   the approximate solution x is possible.
+c
+c         info = 8  gtol is too small. fvec is orthogonal to the
+c                   columns of the jacobian to machine precision.
+c
+c       nfev is an integer output variable set to the number of
+c         calls to fcn with iflag = 1.
+c
+c       njev is an integer output variable set to the number of
+c         calls to fcn with iflag = 2.
+c
+c       ipvt is an integer output array of length n. ipvt
+c         defines a permutation matrix p such that jac*p = q*r,
+c         where jac is the final calculated jacobian, q is
+c         orthogonal (not stored), and r is upper triangular
+c         with diagonal elements of nonincreasing magnitude.
+c         column j of p is column ipvt(j) of the identity matrix.
+c
+c       qtf is an output array of length n which contains
+c         the first n elements of the vector (q transpose)*fvec.
+c
+c       wa1, wa2, and wa3 are work arrays of length n.
+c
+c       wa4 is a work array of length m.
+c
+c     subprograms called
+c
+c       user-supplied ...... fcn
+c
+c       minpack-supplied ... dpmpar,enorm,lmpar,qrfac
+c
+c       fortran-supplied ... dabs,dmax1,dmin1,dsqrt,mod
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,iflag,iter,j,l
+      double precision actred,delta,dirder,epsmch,fnorm,fnorm1,gnorm,
+     *                 one,par,pnorm,prered,p1,p5,p25,p75,p0001,ratio,
+     *                 sum,temp,temp1,temp2,xnorm,zero
+      double precision dpmpar,enorm
+      data one,p1,p5,p25,p75,p0001,zero
+     *     /1.0d0,1.0d-1,5.0d-1,2.5d-1,7.5d-1,1.0d-4,0.0d0/
+c
+c     epsmch is the machine precision.
+c
+      epsmch = dpmpar(1)
+c
+      info = 0
+      iflag = 0
+      nfev = 0
+      njev = 0
+c
+c     check the input parameters for errors.
+c
+      if (n .le. 0 .or. m .lt. n .or. ldfjac .lt. m
+     *    .or. ftol .lt. zero .or. xtol .lt. zero .or. gtol .lt. zero
+     *    .or. maxfev .le. 0 .or. factor .le. zero) go to 300
+      if (mode .ne. 2) go to 20
+      do 10 j = 1, n
+         if (diag(j) .le. zero) go to 300
+   10    continue
+   20 continue
+c
+c     evaluate the function at the starting point
+c     and calculate its norm.
+c
+      iflag = 1
+      call fcn(m,n,x,fvec,fjac,ldfjac,iflag)
+      nfev = 1
+      if (iflag .lt. 0) go to 300
+      fnorm = enorm(m,fvec)
+c
+c     initialize levenberg-marquardt parameter and iteration counter.
+c
+      par = zero
+      iter = 1
+c
+c     beginning of the outer loop.
+c
+   30 continue
+c
+c        calculate the jacobian matrix.
+c
+         iflag = 2
+         call fcn(m,n,x,fvec,fjac,ldfjac,iflag)
+         njev = njev + 1
+         if (iflag .lt. 0) go to 300
+c
+c        if requested, call fcn to enable printing of iterates.
+c
+         if (nprint .le. 0) go to 40
+         iflag = 0
+         if (mod(iter-1,nprint) .eq. 0)
+     *      call fcn(m,n,x,fvec,fjac,ldfjac,iflag)
+         if (iflag .lt. 0) go to 300
+   40    continue
+c
+c        compute the qr factorization of the jacobian.
+c
+         call qrfac(m,n,fjac,ldfjac,.true.,ipvt,n,wa1,wa2,wa3)
+c
+c        on the first iteration and if mode is 1, scale according
+c        to the norms of the columns of the initial jacobian.
+c
+         if (iter .ne. 1) go to 80
+         if (mode .eq. 2) go to 60
+         do 50 j = 1, n
+            diag(j) = wa2(j)
+            if (wa2(j) .eq. zero) diag(j) = one
+   50       continue
+   60    continue
+c
+c        on the first iteration, calculate the norm of the scaled x
+c        and initialize the step bound delta.
+c
+         do 70 j = 1, n
+            wa3(j) = diag(j)*x(j)
+   70       continue
+         xnorm = enorm(n,wa3)
+         delta = factor*xnorm
+         if (delta .eq. zero) delta = factor
+   80    continue
+c
+c        form (q transpose)*fvec and store the first n components in
+c        qtf.
+c
+         do 90 i = 1, m
+            wa4(i) = fvec(i)
+   90       continue
+         do 130 j = 1, n
+            if (fjac(j,j) .eq. zero) go to 120
+            sum = zero
+            do 100 i = j, m
+               sum = sum + fjac(i,j)*wa4(i)
+  100          continue
+            temp = -sum/fjac(j,j)
+            do 110 i = j, m
+               wa4(i) = wa4(i) + fjac(i,j)*temp
+  110          continue
+  120       continue
+            fjac(j,j) = wa1(j)
+            qtf(j) = wa4(j)
+  130       continue
+c
+c        compute the norm of the scaled gradient.
+c
+         gnorm = zero
+         if (fnorm .eq. zero) go to 170
+         do 160 j = 1, n
+            l = ipvt(j)
+            if (wa2(l) .eq. zero) go to 150
+            sum = zero
+            do 140 i = 1, j
+               sum = sum + fjac(i,j)*(qtf(i)/fnorm)
+  140          continue
+            gnorm = dmax1(gnorm,dabs(sum/wa2(l)))
+  150       continue
+  160       continue
+  170    continue
+c
+c        test for convergence of the gradient norm.
+c
+         if (gnorm .le. gtol) info = 4
+         if (info .ne. 0) go to 300
+c
+c        rescale if necessary.
+c
+         if (mode .eq. 2) go to 190
+         do 180 j = 1, n
+            diag(j) = dmax1(diag(j),wa2(j))
+  180       continue
+  190    continue
+c
+c        beginning of the inner loop.
+c
+  200    continue
+c
+c           determine the levenberg-marquardt parameter.
+c
+            call lmpar(n,fjac,ldfjac,ipvt,diag,qtf,delta,par,wa1,wa2,
+     *                 wa3,wa4)
+c
+c           store the direction p and x + p. calculate the norm of p.
+c
+            do 210 j = 1, n
+               wa1(j) = -wa1(j)
+               wa2(j) = x(j) + wa1(j)
+               wa3(j) = diag(j)*wa1(j)
+  210          continue
+            pnorm = enorm(n,wa3)
+c
+c           on the first iteration, adjust the initial step bound.
+c
+            if (iter .eq. 1) delta = dmin1(delta,pnorm)
+c
+c           evaluate the function at x + p and calculate its norm.
+c
+            iflag = 1
+            call fcn(m,n,wa2,wa4,fjac,ldfjac,iflag)
+            nfev = nfev + 1
+            if (iflag .lt. 0) go to 300
+            fnorm1 = enorm(m,wa4)
+c
+c           compute the scaled actual reduction.
+c
+            actred = -one
+            if (p1*fnorm1 .lt. fnorm) actred = one - (fnorm1/fnorm)**2
+c
+c           compute the scaled predicted reduction and
+c           the scaled directional derivative.
+c
+            do 230 j = 1, n
+               wa3(j) = zero
+               l = ipvt(j)
+               temp = wa1(l)
+               do 220 i = 1, j
+                  wa3(i) = wa3(i) + fjac(i,j)*temp
+  220             continue
+  230          continue
+            temp1 = enorm(n,wa3)/fnorm
+            temp2 = (dsqrt(par)*pnorm)/fnorm
+            prered = temp1**2 + temp2**2/p5
+            dirder = -(temp1**2 + temp2**2)
+c
+c           compute the ratio of the actual to the predicted
+c           reduction.
+c
+            ratio = zero
+            if (prered .ne. zero) ratio = actred/prered
+c
+c           update the step bound.
+c
+            if (ratio .gt. p25) go to 240
+               if (actred .ge. zero) temp = p5
+               if (actred .lt. zero)
+     *            temp = p5*dirder/(dirder + p5*actred)
+               if (p1*fnorm1 .ge. fnorm .or. temp .lt. p1) temp = p1
+               delta = temp*dmin1(delta,pnorm/p1)
+               par = par/temp
+               go to 260
+  240       continue
+               if (par .ne. zero .and. ratio .lt. p75) go to 250
+               delta = pnorm/p5
+               par = p5*par
+  250          continue
+  260       continue
+c
+c           test for successful iteration.
+c
+            if (ratio .lt. p0001) go to 290
+c
+c           successful iteration. update x, fvec, and their norms.
+c
+            do 270 j = 1, n
+               x(j) = wa2(j)
+               wa2(j) = diag(j)*x(j)
+  270          continue
+            do 280 i = 1, m
+               fvec(i) = wa4(i)
+  280          continue
+            xnorm = enorm(n,wa2)
+            fnorm = fnorm1
+            iter = iter + 1
+  290       continue
+c
+c           tests for convergence.
+c
+            if (dabs(actred) .le. ftol .and. prered .le. ftol
+     *          .and. p5*ratio .le. one) info = 1
+            if (delta .le. xtol*xnorm) info = 2
+            if (dabs(actred) .le. ftol .and. prered .le. ftol
+     *          .and. p5*ratio .le. one .and. info .eq. 2) info = 3
+            if (info .ne. 0) go to 300
+c
+c           tests for termination and stringent tolerances.
+c
+            if (nfev .ge. maxfev) info = 5
+            if (dabs(actred) .le. epsmch .and. prered .le. epsmch
+     *          .and. p5*ratio .le. one) info = 6
+            if (delta .le. epsmch*xnorm) info = 7
+            if (gnorm .le. epsmch) info = 8
+            if (info .ne. 0) go to 300
+c
+c           end of the inner loop. repeat if iteration unsuccessful.
+c
+            if (ratio .lt. p0001) go to 200
+c
+c        end of the outer loop.
+c
+         go to 30
+  300 continue
+c
+c     termination, either normal or user imposed.
+c
+      if (iflag .lt. 0) info = iflag
+      iflag = 0
+      if (nprint .gt. 0) call fcn(m,n,x,fvec,fjac,ldfjac,iflag)
+      return
+c
+c     last card of subroutine lmder.
+c
+      end
diff --git a/math/minpack/lmder1.f b/math/minpack/lmder1.f
new file mode 100644
index 00000000..d691940f
--- /dev/null
+++ b/math/minpack/lmder1.f
@@ -0,0 +1,156 @@
+      subroutine lmder1(fcn,m,n,x,fvec,fjac,ldfjac,tol,info,ipvt,wa,
+     *                  lwa)
+      integer m,n,ldfjac,info,lwa
+      integer ipvt(n)
+      double precision tol
+      double precision x(n),fvec(m),fjac(ldfjac,n),wa(lwa)
+      external fcn
+c     **********
+c
+c     subroutine lmder1
+c
+c     the purpose of lmder1 is to minimize the sum of the squares of
+c     m nonlinear functions in n variables by a modification of the
+c     levenberg-marquardt algorithm. this is done by using the more
+c     general least-squares solver lmder. the user must provide a
+c     subroutine which calculates the functions and the jacobian.
+c
+c     the subroutine statement is
+c
+c       subroutine lmder1(fcn,m,n,x,fvec,fjac,ldfjac,tol,info,
+c                         ipvt,wa,lwa)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions and the jacobian. fcn must
+c         be declared in an external statement in the user
+c         calling program, and should be written as follows.
+c
+c         subroutine fcn(m,n,x,fvec,fjac,ldfjac,iflag)
+c         integer m,n,ldfjac,iflag
+c         double precision x(n),fvec(m),fjac(ldfjac,n)
+c         ----------
+c         if iflag = 1 calculate the functions at x and
+c         return this vector in fvec. do not alter fjac.
+c         if iflag = 2 calculate the jacobian at x and
+c         return this matrix in fjac. do not alter fvec.
+c         ----------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of lmder1.
+c         in this case set iflag to a negative integer.
+c
+c       m is a positive integer input variable set to the number
+c         of functions.
+c
+c       n is a positive integer input variable set to the number
+c         of variables. n must not exceed m.
+c
+c       x is an array of length n. on input x must contain
+c         an initial estimate of the solution vector. on output x
+c         contains the final estimate of the solution vector.
+c
+c       fvec is an output array of length m which contains
+c         the functions evaluated at the output x.
+c
+c       fjac is an output m by n array. the upper n by n submatrix
+c         of fjac contains an upper triangular matrix r with
+c         diagonal elements of nonincreasing magnitude such that
+c
+c                t     t           t
+c               p *(jac *jac)*p = r *r,
+c
+c         where p is a permutation matrix and jac is the final
+c         calculated jacobian. column j of p is column ipvt(j)
+c         (see below) of the identity matrix. the lower trapezoidal
+c         part of fjac contains information generated during
+c         the computation of r.
+c
+c       ldfjac is a positive integer input variable not less than m
+c         which specifies the leading dimension of the array fjac.
+c
+c       tol is a nonnegative input variable. termination occurs
+c         when the algorithm estimates either that the relative
+c         error in the sum of squares is at most tol or that
+c         the relative error between x and the solution is at
+c         most tol.
+c
+c       info is an integer output variable. if the user has
+c         terminated execution, info is set to the (negative)
+c         value of iflag. see description of fcn. otherwise,
+c         info is set as follows.
+c
+c         info = 0  improper input parameters.
+c
+c         info = 1  algorithm estimates that the relative error
+c                   in the sum of squares is at most tol.
+c
+c         info = 2  algorithm estimates that the relative error
+c                   between x and the solution is at most tol.
+c
+c         info = 3  conditions for info = 1 and info = 2 both hold.
+c
+c         info = 4  fvec is orthogonal to the columns of the
+c                   jacobian to machine precision.
+c
+c         info = 5  number of calls to fcn with iflag = 1 has
+c                   reached 100*(n+1).
+c
+c         info = 6  tol is too small. no further reduction in
+c                   the sum of squares is possible.
+c
+c         info = 7  tol is too small. no further improvement in
+c                   the approximate solution x is possible.
+c
+c       ipvt is an integer output array of length n. ipvt
+c         defines a permutation matrix p such that jac*p = q*r,
+c         where jac is the final calculated jacobian, q is
+c         orthogonal (not stored), and r is upper triangular
+c         with diagonal elements of nonincreasing magnitude.
+c         column j of p is column ipvt(j) of the identity matrix.
+c
+c       wa is a work array of length lwa.
+c
+c       lwa is a positive integer input variable not less than 5*n+m.
+c
+c     subprograms called
+c
+c       user-supplied ...... fcn
+c
+c       minpack-supplied ... lmder
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer maxfev,mode,nfev,njev,nprint
+      double precision factor,ftol,gtol,xtol,zero
+      data factor,zero /1.0d2,0.0d0/
+      info = 0
+c
+c     check the input parameters for errors.
+c
+      if (n .le. 0 .or. m .lt. n .or. ldfjac .lt. m .or. tol .lt. zero
+     *    .or. lwa .lt. 5*n + m) go to 10
+c
+c     call lmder.
+c
+      maxfev = 100*(n + 1)
+      ftol = tol
+      xtol = tol
+      gtol = zero
+      mode = 1
+      nprint = 0
+      call lmder(fcn,m,n,x,fvec,fjac,ldfjac,ftol,xtol,gtol,maxfev,
+     *           wa(1),mode,factor,nprint,info,nfev,njev,ipvt,wa(n+1),
+     *           wa(2*n+1),wa(3*n+1),wa(4*n+1),wa(5*n+1))
+      if (info .eq. 8) info = 4
+   10 continue
+      return
+c
+c     last card of subroutine lmder1.
+c
+      end
diff --git a/math/minpack/lmdif.f b/math/minpack/lmdif.f
new file mode 100644
index 00000000..dd3d4ee2
--- /dev/null
+++ b/math/minpack/lmdif.f
@@ -0,0 +1,454 @@
+      subroutine lmdif(fcn,m,n,x,fvec,ftol,xtol,gtol,maxfev,epsfcn,
+     *                 diag,mode,factor,nprint,info,nfev,fjac,ldfjac,
+     *                 ipvt,qtf,wa1,wa2,wa3,wa4)
+      integer m,n,maxfev,mode,nprint,info,nfev,ldfjac
+      integer ipvt(n)
+      double precision ftol,xtol,gtol,epsfcn,factor
+      double precision x(n),fvec(m),diag(n),fjac(ldfjac,n),qtf(n),
+     *                 wa1(n),wa2(n),wa3(n),wa4(m)
+      external fcn
+c     **********
+c
+c     subroutine lmdif
+c
+c     the purpose of lmdif is to minimize the sum of the squares of
+c     m nonlinear functions in n variables by a modification of
+c     the levenberg-marquardt algorithm. the user must provide a
+c     subroutine which calculates the functions. the jacobian is
+c     then calculated by a forward-difference approximation.
+c
+c     the subroutine statement is
+c
+c       subroutine lmdif(fcn,m,n,x,fvec,ftol,xtol,gtol,maxfev,epsfcn,
+c                        diag,mode,factor,nprint,info,nfev,fjac,
+c                        ldfjac,ipvt,qtf,wa1,wa2,wa3,wa4)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions. fcn must be declared
+c         in an external statement in the user calling
+c         program, and should be written as follows.
+c
+c         subroutine fcn(m,n,x,fvec,iflag)
+c         integer m,n,iflag
+c         double precision x(n),fvec(m)
+c         ----------
+c         calculate the functions at x and
+c         return this vector in fvec.
+c         ----------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of lmdif.
+c         in this case set iflag to a negative integer.
+c
+c       m is a positive integer input variable set to the number
+c         of functions.
+c
+c       n is a positive integer input variable set to the number
+c         of variables. n must not exceed m.
+c
+c       x is an array of length n. on input x must contain
+c         an initial estimate of the solution vector. on output x
+c         contains the final estimate of the solution vector.
+c
+c       fvec is an output array of length m which contains
+c         the functions evaluated at the output x.
+c
+c       ftol is a nonnegative input variable. termination
+c         occurs when both the actual and predicted relative
+c         reductions in the sum of squares are at most ftol.
+c         therefore, ftol measures the relative error desired
+c         in the sum of squares.
+c
+c       xtol is a nonnegative input variable. termination
+c         occurs when the relative error between two consecutive
+c         iterates is at most xtol. therefore, xtol measures the
+c         relative error desired in the approximate solution.
+c
+c       gtol is a nonnegative input variable. termination
+c         occurs when the cosine of the angle between fvec and
+c         any column of the jacobian is at most gtol in absolute
+c         value. therefore, gtol measures the orthogonality
+c         desired between the function vector and the columns
+c         of the jacobian.
+c
+c       maxfev is a positive integer input variable. termination
+c         occurs when the number of calls to fcn is at least
+c         maxfev by the end of an iteration.
+c
+c       epsfcn is an input variable used in determining a suitable
+c         step length for the forward-difference approximation. this
+c         approximation assumes that the relative errors in the
+c         functions are of the order of epsfcn. if epsfcn is less
+c         than the machine precision, it is assumed that the relative
+c         errors in the functions are of the order of the machine
+c         precision.
+c
+c       diag is an array of length n. if mode = 1 (see
+c         below), diag is internally set. if mode = 2, diag
+c         must contain positive entries that serve as
+c         multiplicative scale factors for the variables.
+c
+c       mode is an integer input variable. if mode = 1, the
+c         variables will be scaled internally. if mode = 2,
+c         the scaling is specified by the input diag. other
+c         values of mode are equivalent to mode = 1.
+c
+c       factor is a positive input variable used in determining the
+c         initial step bound. this bound is set to the product of
+c         factor and the euclidean norm of diag*x if nonzero, or else
+c         to factor itself. in most cases factor should lie in the
+c         interval (.1,100.). 100. is a generally recommended value.
+c
+c       nprint is an integer input variable that enables controlled
+c         printing of iterates if it is positive. in this case,
+c         fcn is called with iflag = 0 at the beginning of the first
+c         iteration and every nprint iterations thereafter and
+c         immediately prior to return, with x and fvec available
+c         for printing. if nprint is not positive, no special calls
+c         of fcn with iflag = 0 are made.
+c
+c       info is an integer output variable. if the user has
+c         terminated execution, info is set to the (negative)
+c         value of iflag. see description of fcn. otherwise,
+c         info is set as follows.
+c
+c         info = 0  improper input parameters.
+c
+c         info = 1  both actual and predicted relative reductions
+c                   in the sum of squares are at most ftol.
+c
+c         info = 2  relative error between two consecutive iterates
+c                   is at most xtol.
+c
+c         info = 3  conditions for info = 1 and info = 2 both hold.
+c
+c         info = 4  the cosine of the angle between fvec and any
+c                   column of the jacobian is at most gtol in
+c                   absolute value.
+c
+c         info = 5  number of calls to fcn has reached or
+c                   exceeded maxfev.
+c
+c         info = 6  ftol is too small. no further reduction in
+c                   the sum of squares is possible.
+c
+c         info = 7  xtol is too small. no further improvement in
+c                   the approximate solution x is possible.
+c
+c         info = 8  gtol is too small. fvec is orthogonal to the
+c                   columns of the jacobian to machine precision.
+c
+c       nfev is an integer output variable set to the number of
+c         calls to fcn.
+c
+c       fjac is an output m by n array. the upper n by n submatrix
+c         of fjac contains an upper triangular matrix r with
+c         diagonal elements of nonincreasing magnitude such that
+c
+c                t     t           t
+c               p *(jac *jac)*p = r *r,
+c
+c         where p is a permutation matrix and jac is the final
+c         calculated jacobian. column j of p is column ipvt(j)
+c         (see below) of the identity matrix. the lower trapezoidal
+c         part of fjac contains information generated during
+c         the computation of r.
+c
+c       ldfjac is a positive integer input variable not less than m
+c         which specifies the leading dimension of the array fjac.
+c
+c       ipvt is an integer output array of length n. ipvt
+c         defines a permutation matrix p such that jac*p = q*r,
+c         where jac is the final calculated jacobian, q is
+c         orthogonal (not stored), and r is upper triangular
+c         with diagonal elements of nonincreasing magnitude.
+c         column j of p is column ipvt(j) of the identity matrix.
+c
+c       qtf is an output array of length n which contains
+c         the first n elements of the vector (q transpose)*fvec.
+c
+c       wa1, wa2, and wa3 are work arrays of length n.
+c
+c       wa4 is a work array of length m.
+c
+c     subprograms called
+c
+c       user-supplied ...... fcn
+c
+c       minpack-supplied ... dpmpar,enorm,fdjac2,lmpar,qrfac
+c
+c       fortran-supplied ... dabs,dmax1,dmin1,dsqrt,mod
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,iflag,iter,j,l
+      double precision actred,delta,dirder,epsmch,fnorm,fnorm1,gnorm,
+     *                 one,par,pnorm,prered,p1,p5,p25,p75,p0001,ratio,
+     *                 sum,temp,temp1,temp2,xnorm,zero
+      double precision dpmpar,enorm
+      data one,p1,p5,p25,p75,p0001,zero
+     *     /1.0d0,1.0d-1,5.0d-1,2.5d-1,7.5d-1,1.0d-4,0.0d0/
+c
+c     epsmch is the machine precision.
+c
+      epsmch = dpmpar(1)
+c
+      info = 0
+      iflag = 0
+      nfev = 0
+c
+c     check the input parameters for errors.
+c
+      if (n .le. 0 .or. m .lt. n .or. ldfjac .lt. m
+     *    .or. ftol .lt. zero .or. xtol .lt. zero .or. gtol .lt. zero
+     *    .or. maxfev .le. 0 .or. factor .le. zero) go to 300
+      if (mode .ne. 2) go to 20
+      do 10 j = 1, n
+         if (diag(j) .le. zero) go to 300
+   10    continue
+   20 continue
+c
+c     evaluate the function at the starting point
+c     and calculate its norm.
+c
+      iflag = 1
+      call fcn(m,n,x,fvec,iflag)
+      nfev = 1
+      if (iflag .lt. 0) go to 300
+      fnorm = enorm(m,fvec)
+c
+c     initialize levenberg-marquardt parameter and iteration counter.
+c
+      par = zero
+      iter = 1
+c
+c     beginning of the outer loop.
+c
+   30 continue
+c
+c        calculate the jacobian matrix.
+c
+         iflag = 2
+         call fdjac2(fcn,m,n,x,fvec,fjac,ldfjac,iflag,epsfcn,wa4)
+         nfev = nfev + n
+         if (iflag .lt. 0) go to 300
+c
+c        if requested, call fcn to enable printing of iterates.
+c
+         if (nprint .le. 0) go to 40
+         iflag = 0
+         if (mod(iter-1,nprint) .eq. 0) call fcn(m,n,x,fvec,iflag)
+         if (iflag .lt. 0) go to 300
+   40    continue
+c
+c        compute the qr factorization of the jacobian.
+c
+         call qrfac(m,n,fjac,ldfjac,.true.,ipvt,n,wa1,wa2,wa3)
+c
+c        on the first iteration and if mode is 1, scale according
+c        to the norms of the columns of the initial jacobian.
+c
+         if (iter .ne. 1) go to 80
+         if (mode .eq. 2) go to 60
+         do 50 j = 1, n
+            diag(j) = wa2(j)
+            if (wa2(j) .eq. zero) diag(j) = one
+   50       continue
+   60    continue
+c
+c        on the first iteration, calculate the norm of the scaled x
+c        and initialize the step bound delta.
+c
+         do 70 j = 1, n
+            wa3(j) = diag(j)*x(j)
+   70       continue
+         xnorm = enorm(n,wa3)
+         delta = factor*xnorm
+         if (delta .eq. zero) delta = factor
+   80    continue
+c
+c        form (q transpose)*fvec and store the first n components in
+c        qtf.
+c
+         do 90 i = 1, m
+            wa4(i) = fvec(i)
+   90       continue
+         do 130 j = 1, n
+            if (fjac(j,j) .eq. zero) go to 120
+            sum = zero
+            do 100 i = j, m
+               sum = sum + fjac(i,j)*wa4(i)
+  100          continue
+            temp = -sum/fjac(j,j)
+            do 110 i = j, m
+               wa4(i) = wa4(i) + fjac(i,j)*temp
+  110          continue
+  120       continue
+            fjac(j,j) = wa1(j)
+            qtf(j) = wa4(j)
+  130       continue
+c
+c        compute the norm of the scaled gradient.
+c
+         gnorm = zero
+         if (fnorm .eq. zero) go to 170
+         do 160 j = 1, n
+            l = ipvt(j)
+            if (wa2(l) .eq. zero) go to 150
+            sum = zero
+            do 140 i = 1, j
+               sum = sum + fjac(i,j)*(qtf(i)/fnorm)
+  140          continue
+            gnorm = dmax1(gnorm,dabs(sum/wa2(l)))
+  150       continue
+  160       continue
+  170    continue
+c
+c        test for convergence of the gradient norm.
+c
+         if (gnorm .le. gtol) info = 4
+         if (info .ne. 0) go to 300
+c
+c        rescale if necessary.
+c
+         if (mode .eq. 2) go to 190
+         do 180 j = 1, n
+            diag(j) = dmax1(diag(j),wa2(j))
+  180       continue
+  190    continue
+c
+c        beginning of the inner loop.
+c
+  200    continue
+c
+c           determine the levenberg-marquardt parameter.
+c
+            call lmpar(n,fjac,ldfjac,ipvt,diag,qtf,delta,par,wa1,wa2,
+     *                 wa3,wa4)
+c
+c           store the direction p and x + p. calculate the norm of p.
+c
+            do 210 j = 1, n
+               wa1(j) = -wa1(j)
+               wa2(j) = x(j) + wa1(j)
+               wa3(j) = diag(j)*wa1(j)
+  210          continue
+            pnorm = enorm(n,wa3)
+c
+c           on the first iteration, adjust the initial step bound.
+c
+            if (iter .eq. 1) delta = dmin1(delta,pnorm)
+c
+c           evaluate the function at x + p and calculate its norm.
+c
+            iflag = 1
+            call fcn(m,n,wa2,wa4,iflag)
+            nfev = nfev + 1
+            if (iflag .lt. 0) go to 300
+            fnorm1 = enorm(m,wa4)
+c
+c           compute the scaled actual reduction.
+c
+            actred = -one
+            if (p1*fnorm1 .lt. fnorm) actred = one - (fnorm1/fnorm)**2
+c
+c           compute the scaled predicted reduction and
+c           the scaled directional derivative.
+c
+            do 230 j = 1, n
+               wa3(j) = zero
+               l = ipvt(j)
+               temp = wa1(l)
+               do 220 i = 1, j
+                  wa3(i) = wa3(i) + fjac(i,j)*temp
+  220             continue
+  230          continue
+            temp1 = enorm(n,wa3)/fnorm
+            temp2 = (dsqrt(par)*pnorm)/fnorm
+            prered = temp1**2 + temp2**2/p5
+            dirder = -(temp1**2 + temp2**2)
+c
+c           compute the ratio of the actual to the predicted
+c           reduction.
+c
+            ratio = zero
+            if (prered .ne. zero) ratio = actred/prered
+c
+c           update the step bound.
+c
+            if (ratio .gt. p25) go to 240
+               if (actred .ge. zero) temp = p5
+               if (actred .lt. zero)
+     *            temp = p5*dirder/(dirder + p5*actred)
+               if (p1*fnorm1 .ge. fnorm .or. temp .lt. p1) temp = p1
+               delta = temp*dmin1(delta,pnorm/p1)
+               par = par/temp
+               go to 260
+  240       continue
+               if (par .ne. zero .and. ratio .lt. p75) go to 250
+               delta = pnorm/p5
+               par = p5*par
+  250          continue
+  260       continue
+c
+c           test for successful iteration.
+c
+            if (ratio .lt. p0001) go to 290
+c
+c           successful iteration. update x, fvec, and their norms.
+c
+            do 270 j = 1, n
+               x(j) = wa2(j)
+               wa2(j) = diag(j)*x(j)
+  270          continue
+            do 280 i = 1, m
+               fvec(i) = wa4(i)
+  280          continue
+            xnorm = enorm(n,wa2)
+            fnorm = fnorm1
+            iter = iter + 1
+  290       continue
+c
+c           tests for convergence.
+c
+            if (dabs(actred) .le. ftol .and. prered .le. ftol
+     *          .and. p5*ratio .le. one) info = 1
+            if (delta .le. xtol*xnorm) info = 2
+            if (dabs(actred) .le. ftol .and. prered .le. ftol
+     *          .and. p5*ratio .le. one .and. info .eq. 2) info = 3
+            if (info .ne. 0) go to 300
+c
+c           tests for termination and stringent tolerances.
+c
+            if (nfev .ge. maxfev) info = 5
+            if (dabs(actred) .le. epsmch .and. prered .le. epsmch
+     *          .and. p5*ratio .le. one) info = 6
+            if (delta .le. epsmch*xnorm) info = 7
+            if (gnorm .le. epsmch) info = 8
+            if (info .ne. 0) go to 300
+c
+c           end of the inner loop. repeat if iteration unsuccessful.
+c
+            if (ratio .lt. p0001) go to 200
+c
+c        end of the outer loop.
+c
+         go to 30
+  300 continue
+c
+c     termination, either normal or user imposed.
+c
+      if (iflag .lt. 0) info = iflag
+      iflag = 0
+      if (nprint .gt. 0) call fcn(m,n,x,fvec,iflag)
+      return
+c
+c     last card of subroutine lmdif.
+c
+      end
diff --git a/math/minpack/lmdif1.f b/math/minpack/lmdif1.f
new file mode 100644
index 00000000..70f8aae0
--- /dev/null
+++ b/math/minpack/lmdif1.f
@@ -0,0 +1,135 @@
+      subroutine lmdif1(fcn,m,n,x,fvec,tol,info,iwa,wa,lwa)
+      integer m,n,info,lwa
+      integer iwa(n)
+      double precision tol
+      double precision x(n),fvec(m),wa(lwa)
+      external fcn
+c     **********
+c
+c     subroutine lmdif1
+c
+c     the purpose of lmdif1 is to minimize the sum of the squares of
+c     m nonlinear functions in n variables by a modification of the
+c     levenberg-marquardt algorithm. this is done by using the more
+c     general least-squares solver lmdif. the user must provide a
+c     subroutine which calculates the functions. the jacobian is
+c     then calculated by a forward-difference approximation.
+c
+c     the subroutine statement is
+c
+c       subroutine lmdif1(fcn,m,n,x,fvec,tol,info,iwa,wa,lwa)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions. fcn must be declared
+c         in an external statement in the user calling
+c         program, and should be written as follows.
+c
+c         subroutine fcn(m,n,x,fvec,iflag)
+c         integer m,n,iflag
+c         double precision x(n),fvec(m)
+c         ----------
+c         calculate the functions at x and
+c         return this vector in fvec.
+c         ----------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of lmdif1.
+c         in this case set iflag to a negative integer.
+c
+c       m is a positive integer input variable set to the number
+c         of functions.
+c
+c       n is a positive integer input variable set to the number
+c         of variables. n must not exceed m.
+c
+c       x is an array of length n. on input x must contain
+c         an initial estimate of the solution vector. on output x
+c         contains the final estimate of the solution vector.
+c
+c       fvec is an output array of length m which contains
+c         the functions evaluated at the output x.
+c
+c       tol is a nonnegative input variable. termination occurs
+c         when the algorithm estimates either that the relative
+c         error in the sum of squares is at most tol or that
+c         the relative error between x and the solution is at
+c         most tol.
+c
+c       info is an integer output variable. if the user has
+c         terminated execution, info is set to the (negative)
+c         value of iflag. see description of fcn. otherwise,
+c         info is set as follows.
+c
+c         info = 0  improper input parameters.
+c
+c         info = 1  algorithm estimates that the relative error
+c                   in the sum of squares is at most tol.
+c
+c         info = 2  algorithm estimates that the relative error
+c                   between x and the solution is at most tol.
+c
+c         info = 3  conditions for info = 1 and info = 2 both hold.
+c
+c         info = 4  fvec is orthogonal to the columns of the
+c                   jacobian to machine precision.
+c
+c         info = 5  number of calls to fcn has reached or
+c                   exceeded 200*(n+1).
+c
+c         info = 6  tol is too small. no further reduction in
+c                   the sum of squares is possible.
+c
+c         info = 7  tol is too small. no further improvement in
+c                   the approximate solution x is possible.
+c
+c       iwa is an integer work array of length n.
+c
+c       wa is a work array of length lwa.
+c
+c       lwa is a positive integer input variable not less than
+c         m*n+5*n+m.
+c
+c     subprograms called
+c
+c       user-supplied ...... fcn
+c
+c       minpack-supplied ... lmdif
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer maxfev,mode,mp5n,nfev,nprint
+      double precision epsfcn,factor,ftol,gtol,xtol,zero
+      data factor,zero /1.0d2,0.0d0/
+      info = 0
+c
+c     check the input parameters for errors.
+c
+      if (n .le. 0 .or. m .lt. n .or. tol .lt. zero
+     *    .or. lwa .lt. m*n + 5*n + m) go to 10
+c
+c     call lmdif.
+c
+      maxfev = 200*(n + 1)
+      ftol = tol
+      xtol = tol
+      gtol = zero
+      epsfcn = zero
+      mode = 1
+      nprint = 0
+      mp5n = m + 5*n
+      call lmdif(fcn,m,n,x,fvec,ftol,xtol,gtol,maxfev,epsfcn,wa(1),
+     *           mode,factor,nprint,info,nfev,wa(mp5n+1),m,iwa,
+     *           wa(n+1),wa(2*n+1),wa(3*n+1),wa(4*n+1),wa(5*n+1))
+      if (info .eq. 8) info = 4
+   10 continue
+      return
+c
+c     last card of subroutine lmdif1.
+c
+      end
diff --git a/math/minpack/lmpar.f b/math/minpack/lmpar.f
new file mode 100644
index 00000000..26c422a7
--- /dev/null
+++ b/math/minpack/lmpar.f
@@ -0,0 +1,264 @@
+      subroutine lmpar(n,r,ldr,ipvt,diag,qtb,delta,par,x,sdiag,wa1,
+     *                 wa2)
+      integer n,ldr
+      integer ipvt(n)
+      double precision delta,par
+      double precision r(ldr,n),diag(n),qtb(n),x(n),sdiag(n),wa1(n),
+     *                 wa2(n)
+c     **********
+c
+c     subroutine lmpar
+c
+c     given an m by n matrix a, an n by n nonsingular diagonal
+c     matrix d, an m-vector b, and a positive number delta,
+c     the problem is to determine a value for the parameter
+c     par such that if x solves the system
+c
+c           a*x = b ,     sqrt(par)*d*x = 0 ,
+c
+c     in the least squares sense, and dxnorm is the euclidean
+c     norm of d*x, then either par is zero and
+c
+c           (dxnorm-delta) .le. 0.1*delta ,
+c
+c     or par is positive and
+c
+c           abs(dxnorm-delta) .le. 0.1*delta .
+c
+c     this subroutine completes the solution of the problem
+c     if it is provided with the necessary information from the
+c     qr factorization, with column pivoting, of a. that is, if
+c     a*p = q*r, where p is a permutation matrix, q has orthogonal
+c     columns, and r is an upper triangular matrix with diagonal
+c     elements of nonincreasing magnitude, then lmpar expects
+c     the full upper triangle of r, the permutation matrix p,
+c     and the first n components of (q transpose)*b. on output
+c     lmpar also provides an upper triangular matrix s such that
+c
+c            t   t                   t
+c           p *(a *a + par*d*d)*p = s *s .
+c
+c     s is employed within lmpar and may be of separate interest.
+c
+c     only a few iterations are generally needed for convergence
+c     of the algorithm. if, however, the limit of 10 iterations
+c     is reached, then the output par will contain the best
+c     value obtained so far.
+c
+c     the subroutine statement is
+c
+c       subroutine lmpar(n,r,ldr,ipvt,diag,qtb,delta,par,x,sdiag,
+c                        wa1,wa2)
+c
+c     where
+c
+c       n is a positive integer input variable set to the order of r.
+c
+c       r is an n by n array. on input the full upper triangle
+c         must contain the full upper triangle of the matrix r.
+c         on output the full upper triangle is unaltered, and the
+c         strict lower triangle contains the strict upper triangle
+c         (transposed) of the upper triangular matrix s.
+c
+c       ldr is a positive integer input variable not less than n
+c         which specifies the leading dimension of the array r.
+c
+c       ipvt is an integer input array of length n which defines the
+c         permutation matrix p such that a*p = q*r. column j of p
+c         is column ipvt(j) of the identity matrix.
+c
+c       diag is an input array of length n which must contain the
+c         diagonal elements of the matrix d.
+c
+c       qtb is an input array of length n which must contain the first
+c         n elements of the vector (q transpose)*b.
+c
+c       delta is a positive input variable which specifies an upper
+c         bound on the euclidean norm of d*x.
+c
+c       par is a nonnegative variable. on input par contains an
+c         initial estimate of the levenberg-marquardt parameter.
+c         on output par contains the final estimate.
+c
+c       x is an output array of length n which contains the least
+c         squares solution of the system a*x = b, sqrt(par)*d*x = 0,
+c         for the output par.
+c
+c       sdiag is an output array of length n which contains the
+c         diagonal elements of the upper triangular matrix s.
+c
+c       wa1 and wa2 are work arrays of length n.
+c
+c     subprograms called
+c
+c       minpack-supplied ... dpmpar,enorm,qrsolv
+c
+c       fortran-supplied ... dabs,dmax1,dmin1,dsqrt
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,iter,j,jm1,jp1,k,l,nsing
+      double precision dxnorm,dwarf,fp,gnorm,parc,parl,paru,p1,p001,
+     *                 sum,temp,zero
+      double precision dpmpar,enorm
+      data p1,p001,zero /1.0d-1,1.0d-3,0.0d0/
+c
+c     dwarf is the smallest positive magnitude.
+c
+      dwarf = dpmpar(2)
+c
+c     compute and store in x the gauss-newton direction. if the
+c     jacobian is rank-deficient, obtain a least squares solution.
+c
+      nsing = n
+      do 10 j = 1, n
+         wa1(j) = qtb(j)
+         if (r(j,j) .eq. zero .and. nsing .eq. n) nsing = j - 1
+         if (nsing .lt. n) wa1(j) = zero
+   10    continue
+      if (nsing .lt. 1) go to 50
+      do 40 k = 1, nsing
+         j = nsing - k + 1
+         wa1(j) = wa1(j)/r(j,j)
+         temp = wa1(j)
+         jm1 = j - 1
+         if (jm1 .lt. 1) go to 30
+         do 20 i = 1, jm1
+            wa1(i) = wa1(i) - r(i,j)*temp
+   20       continue
+   30    continue
+   40    continue
+   50 continue
+      do 60 j = 1, n
+         l = ipvt(j)
+         x(l) = wa1(j)
+   60    continue
+c
+c     initialize the iteration counter.
+c     evaluate the function at the origin, and test
+c     for acceptance of the gauss-newton direction.
+c
+      iter = 0
+      do 70 j = 1, n
+         wa2(j) = diag(j)*x(j)
+   70    continue
+      dxnorm = enorm(n,wa2)
+      fp = dxnorm - delta
+      if (fp .le. p1*delta) go to 220
+c
+c     if the jacobian is not rank deficient, the newton
+c     step provides a lower bound, parl, for the zero of
+c     the function. otherwise set this bound to zero.
+c
+      parl = zero
+      if (nsing .lt. n) go to 120
+      do 80 j = 1, n
+         l = ipvt(j)
+         wa1(j) = diag(l)*(wa2(l)/dxnorm)
+   80    continue
+      do 110 j = 1, n
+         sum = zero
+         jm1 = j - 1
+         if (jm1 .lt. 1) go to 100
+         do 90 i = 1, jm1
+            sum = sum + r(i,j)*wa1(i)
+   90       continue
+  100    continue
+         wa1(j) = (wa1(j) - sum)/r(j,j)
+  110    continue
+      temp = enorm(n,wa1)
+      parl = ((fp/delta)/temp)/temp
+  120 continue
+c
+c     calculate an upper bound, paru, for the zero of the function.
+c
+      do 140 j = 1, n
+         sum = zero
+         do 130 i = 1, j
+            sum = sum + r(i,j)*qtb(i)
+  130       continue
+         l = ipvt(j)
+         wa1(j) = sum/diag(l)
+  140    continue
+      gnorm = enorm(n,wa1)
+      paru = gnorm/delta
+      if (paru .eq. zero) paru = dwarf/dmin1(delta,p1)
+c
+c     if the input par lies outside of the interval (parl,paru),
+c     set par to the closer endpoint.
+c
+      par = dmax1(par,parl)
+      par = dmin1(par,paru)
+      if (par .eq. zero) par = gnorm/dxnorm
+c
+c     beginning of an iteration.
+c
+  150 continue
+         iter = iter + 1
+c
+c        evaluate the function at the current value of par.
+c
+         if (par .eq. zero) par = dmax1(dwarf,p001*paru)
+         temp = dsqrt(par)
+         do 160 j = 1, n
+            wa1(j) = temp*diag(j)
+  160       continue
+         call qrsolv(n,r,ldr,ipvt,wa1,qtb,x,sdiag,wa2)
+         do 170 j = 1, n
+            wa2(j) = diag(j)*x(j)
+  170       continue
+         dxnorm = enorm(n,wa2)
+         temp = fp
+         fp = dxnorm - delta
+c
+c        if the function is small enough, accept the current value
+c        of par. also test for the exceptional cases where parl
+c        is zero or the number of iterations has reached 10.
+c
+         if (dabs(fp) .le. p1*delta
+     *       .or. parl .eq. zero .and. fp .le. temp
+     *            .and. temp .lt. zero .or. iter .eq. 10) go to 220
+c
+c        compute the newton correction.
+c
+         do 180 j = 1, n
+            l = ipvt(j)
+            wa1(j) = diag(l)*(wa2(l)/dxnorm)
+  180       continue
+         do 210 j = 1, n
+            wa1(j) = wa1(j)/sdiag(j)
+            temp = wa1(j)
+            jp1 = j + 1
+            if (n .lt. jp1) go to 200
+            do 190 i = jp1, n
+               wa1(i) = wa1(i) - r(i,j)*temp
+  190          continue
+  200       continue
+  210       continue
+         temp = enorm(n,wa1)
+         parc = ((fp/delta)/temp)/temp
+c
+c        depending on the sign of the function, update parl or paru.
+c
+         if (fp .gt. zero) parl = dmax1(parl,par)
+         if (fp .lt. zero) paru = dmin1(paru,par)
+c
+c        compute an improved estimate for par.
+c
+         par = dmax1(parl,par+parc)
+c
+c        end of an iteration.
+c
+         go to 150
+  220 continue
+c
+c     termination.
+c
+      if (iter .eq. 0) par = zero
+      return
+c
+c     last card of subroutine lmpar.
+c
+      end
diff --git a/math/minpack/lmstr.f b/math/minpack/lmstr.f
new file mode 100644
index 00000000..d9a7893f
--- /dev/null
+++ b/math/minpack/lmstr.f
@@ -0,0 +1,466 @@
+      subroutine lmstr(fcn,m,n,x,fvec,fjac,ldfjac,ftol,xtol,gtol,
+     *                 maxfev,diag,mode,factor,nprint,info,nfev,njev,
+     *                 ipvt,qtf,wa1,wa2,wa3,wa4)
+      integer m,n,ldfjac,maxfev,mode,nprint,info,nfev,njev
+      integer ipvt(n)
+      logical sing
+      double precision ftol,xtol,gtol,factor
+      double precision x(n),fvec(m),fjac(ldfjac,n),diag(n),qtf(n),
+     *                 wa1(n),wa2(n),wa3(n),wa4(m)
+c     **********
+c
+c     subroutine lmstr
+c
+c     the purpose of lmstr is to minimize the sum of the squares of
+c     m nonlinear functions in n variables by a modification of
+c     the levenberg-marquardt algorithm which uses minimal storage.
+c     the user must provide a subroutine which calculates the
+c     functions and the rows of the jacobian.
+c
+c     the subroutine statement is
+c
+c       subroutine lmstr(fcn,m,n,x,fvec,fjac,ldfjac,ftol,xtol,gtol,
+c                        maxfev,diag,mode,factor,nprint,info,nfev,
+c                        njev,ipvt,qtf,wa1,wa2,wa3,wa4)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions and the rows of the jacobian.
+c         fcn must be declared in an external statement in the
+c         user calling program, and should be written as follows.
+c
+c         subroutine fcn(m,n,x,fvec,fjrow,iflag)
+c         integer m,n,iflag
+c         double precision x(n),fvec(m),fjrow(n)
+c         ----------
+c         if iflag = 1 calculate the functions at x and
+c         return this vector in fvec.
+c         if iflag = i calculate the (i-1)-st row of the
+c         jacobian at x and return this vector in fjrow.
+c         ----------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of lmstr.
+c         in this case set iflag to a negative integer.
+c
+c       m is a positive integer input variable set to the number
+c         of functions.
+c
+c       n is a positive integer input variable set to the number
+c         of variables. n must not exceed m.
+c
+c       x is an array of length n. on input x must contain
+c         an initial estimate of the solution vector. on output x
+c         contains the final estimate of the solution vector.
+c
+c       fvec is an output array of length m which contains
+c         the functions evaluated at the output x.
+c
+c       fjac is an output n by n array. the upper triangle of fjac
+c         contains an upper triangular matrix r such that
+c
+c                t     t           t
+c               p *(jac *jac)*p = r *r,
+c
+c         where p is a permutation matrix and jac is the final
+c         calculated jacobian. column j of p is column ipvt(j)
+c         (see below) of the identity matrix. the lower triangular
+c         part of fjac contains information generated during
+c         the computation of r.
+c
+c       ldfjac is a positive integer input variable not less than n
+c         which specifies the leading dimension of the array fjac.
+c
+c       ftol is a nonnegative input variable. termination
+c         occurs when both the actual and predicted relative
+c         reductions in the sum of squares are at most ftol.
+c         therefore, ftol measures the relative error desired
+c         in the sum of squares.
+c
+c       xtol is a nonnegative input variable. termination
+c         occurs when the relative error between two consecutive
+c         iterates is at most xtol. therefore, xtol measures the
+c         relative error desired in the approximate solution.
+c
+c       gtol is a nonnegative input variable. termination
+c         occurs when the cosine of the angle between fvec and
+c         any column of the jacobian is at most gtol in absolute
+c         value. therefore, gtol measures the orthogonality
+c         desired between the function vector and the columns
+c         of the jacobian.
+c
+c       maxfev is a positive integer input variable. termination
+c         occurs when the number of calls to fcn with iflag = 1
+c         has reached maxfev.
+c
+c       diag is an array of length n. if mode = 1 (see
+c         below), diag is internally set. if mode = 2, diag
+c         must contain positive entries that serve as
+c         multiplicative scale factors for the variables.
+c
+c       mode is an integer input variable. if mode = 1, the
+c         variables will be scaled internally. if mode = 2,
+c         the scaling is specified by the input diag. other
+c         values of mode are equivalent to mode = 1.
+c
+c       factor is a positive input variable used in determining the
+c         initial step bound. this bound is set to the product of
+c         factor and the euclidean norm of diag*x if nonzero, or else
+c         to factor itself. in most cases factor should lie in the
+c         interval (.1,100.). 100. is a generally recommended value.
+c
+c       nprint is an integer input variable that enables controlled
+c         printing of iterates if it is positive. in this case,
+c         fcn is called with iflag = 0 at the beginning of the first
+c         iteration and every nprint iterations thereafter and
+c         immediately prior to return, with x and fvec available
+c         for printing. if nprint is not positive, no special calls
+c         of fcn with iflag = 0 are made.
+c
+c       info is an integer output variable. if the user has
+c         terminated execution, info is set to the (negative)
+c         value of iflag. see description of fcn. otherwise,
+c         info is set as follows.
+c
+c         info = 0  improper input parameters.
+c
+c         info = 1  both actual and predicted relative reductions
+c                   in the sum of squares are at most ftol.
+c
+c         info = 2  relative error between two consecutive iterates
+c                   is at most xtol.
+c
+c         info = 3  conditions for info = 1 and info = 2 both hold.
+c
+c         info = 4  the cosine of the angle between fvec and any
+c                   column of the jacobian is at most gtol in
+c                   absolute value.
+c
+c         info = 5  number of calls to fcn with iflag = 1 has
+c                   reached maxfev.
+c
+c         info = 6  ftol is too small. no further reduction in
+c                   the sum of squares is possible.
+c
+c         info = 7  xtol is too small. no further improvement in
+c                   the approximate solution x is possible.
+c
+c         info = 8  gtol is too small. fvec is orthogonal to the
+c                   columns of the jacobian to machine precision.
+c
+c       nfev is an integer output variable set to the number of
+c         calls to fcn with iflag = 1.
+c
+c       njev is an integer output variable set to the number of
+c         calls to fcn with iflag = 2.
+c
+c       ipvt is an integer output array of length n. ipvt
+c         defines a permutation matrix p such that jac*p = q*r,
+c         where jac is the final calculated jacobian, q is
+c         orthogonal (not stored), and r is upper triangular.
+c         column j of p is column ipvt(j) of the identity matrix.
+c
+c       qtf is an output array of length n which contains
+c         the first n elements of the vector (q transpose)*fvec.
+c
+c       wa1, wa2, and wa3 are work arrays of length n.
+c
+c       wa4 is a work array of length m.
+c
+c     subprograms called
+c
+c       user-supplied ...... fcn
+c
+c       minpack-supplied ... dpmpar,enorm,lmpar,qrfac,rwupdt
+c
+c       fortran-supplied ... dabs,dmax1,dmin1,dsqrt,mod
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, dudley v. goetschel, kenneth e. hillstrom,
+c     jorge j. more
+c
+c     **********
+      integer i,iflag,iter,j,l
+      double precision actred,delta,dirder,epsmch,fnorm,fnorm1,gnorm,
+     *                 one,par,pnorm,prered,p1,p5,p25,p75,p0001,ratio,
+     *                 sum,temp,temp1,temp2,xnorm,zero
+      double precision dpmpar,enorm
+      data one,p1,p5,p25,p75,p0001,zero
+     *     /1.0d0,1.0d-1,5.0d-1,2.5d-1,7.5d-1,1.0d-4,0.0d0/
+c
+c     epsmch is the machine precision.
+c
+      epsmch = dpmpar(1)
+c
+      info = 0
+      iflag = 0
+      nfev = 0
+      njev = 0
+c
+c     check the input parameters for errors.
+c
+      if (n .le. 0 .or. m .lt. n .or. ldfjac .lt. n
+     *    .or. ftol .lt. zero .or. xtol .lt. zero .or. gtol .lt. zero
+     *    .or. maxfev .le. 0 .or. factor .le. zero) go to 340
+      if (mode .ne. 2) go to 20
+      do 10 j = 1, n
+         if (diag(j) .le. zero) go to 340
+   10    continue
+   20 continue
+c
+c     evaluate the function at the starting point
+c     and calculate its norm.
+c
+      iflag = 1
+      call fcn(m,n,x,fvec,wa3,iflag)
+      nfev = 1
+      if (iflag .lt. 0) go to 340
+      fnorm = enorm(m,fvec)
+c
+c     initialize levenberg-marquardt parameter and iteration counter.
+c
+      par = zero
+      iter = 1
+c
+c     beginning of the outer loop.
+c
+   30 continue
+c
+c        if requested, call fcn to enable printing of iterates.
+c
+         if (nprint .le. 0) go to 40
+         iflag = 0
+         if (mod(iter-1,nprint) .eq. 0) call fcn(m,n,x,fvec,wa3,iflag)
+         if (iflag .lt. 0) go to 340
+   40    continue
+c
+c        compute the qr factorization of the jacobian matrix
+c        calculated one row at a time, while simultaneously
+c        forming (q transpose)*fvec and storing the first
+c        n components in qtf.
+c
+         do 60 j = 1, n
+            qtf(j) = zero
+            do 50 i = 1, n
+               fjac(i,j) = zero
+   50          continue
+   60       continue
+         iflag = 2
+         do 70 i = 1, m
+            call fcn(m,n,x,fvec,wa3,iflag)
+            if (iflag .lt. 0) go to 340
+            temp = fvec(i)
+            call rwupdt(n,fjac,ldfjac,wa3,qtf,temp,wa1,wa2)
+            iflag = iflag + 1
+   70       continue
+         njev = njev + 1
+c
+c        if the jacobian is rank deficient, call qrfac to
+c        reorder its columns and update the components of qtf.
+c
+         sing = .false.
+         do 80 j = 1, n
+            if (fjac(j,j) .eq. zero) sing = .true.
+            ipvt(j) = j
+            wa2(j) = enorm(j,fjac(1,j))
+   80       continue
+         if (.not.sing) go to 130
+         call qrfac(n,n,fjac,ldfjac,.true.,ipvt,n,wa1,wa2,wa3)
+         do 120 j = 1, n
+            if (fjac(j,j) .eq. zero) go to 110
+            sum = zero
+            do 90 i = j, n
+               sum = sum + fjac(i,j)*qtf(i)
+   90          continue
+            temp = -sum/fjac(j,j)
+            do 100 i = j, n
+               qtf(i) = qtf(i) + fjac(i,j)*temp
+  100          continue
+  110       continue
+            fjac(j,j) = wa1(j)
+  120       continue
+  130    continue
+c
+c        on the first iteration and if mode is 1, scale according
+c        to the norms of the columns of the initial jacobian.
+c
+         if (iter .ne. 1) go to 170
+         if (mode .eq. 2) go to 150
+         do 140 j = 1, n
+            diag(j) = wa2(j)
+            if (wa2(j) .eq. zero) diag(j) = one
+  140       continue
+  150    continue
+c
+c        on the first iteration, calculate the norm of the scaled x
+c        and initialize the step bound delta.
+c
+         do 160 j = 1, n
+            wa3(j) = diag(j)*x(j)
+  160       continue
+         xnorm = enorm(n,wa3)
+         delta = factor*xnorm
+         if (delta .eq. zero) delta = factor
+  170    continue
+c
+c        compute the norm of the scaled gradient.
+c
+         gnorm = zero
+         if (fnorm .eq. zero) go to 210
+         do 200 j = 1, n
+            l = ipvt(j)
+            if (wa2(l) .eq. zero) go to 190
+            sum = zero
+            do 180 i = 1, j
+               sum = sum + fjac(i,j)*(qtf(i)/fnorm)
+  180          continue
+            gnorm = dmax1(gnorm,dabs(sum/wa2(l)))
+  190       continue
+  200       continue
+  210    continue
+c
+c        test for convergence of the gradient norm.
+c
+         if (gnorm .le. gtol) info = 4
+         if (info .ne. 0) go to 340
+c
+c        rescale if necessary.
+c
+         if (mode .eq. 2) go to 230
+         do 220 j = 1, n
+            diag(j) = dmax1(diag(j),wa2(j))
+  220       continue
+  230    continue
+c
+c        beginning of the inner loop.
+c
+  240    continue
+c
+c           determine the levenberg-marquardt parameter.
+c
+            call lmpar(n,fjac,ldfjac,ipvt,diag,qtf,delta,par,wa1,wa2,
+     *                 wa3,wa4)
+c
+c           store the direction p and x + p. calculate the norm of p.
+c
+            do 250 j = 1, n
+               wa1(j) = -wa1(j)
+               wa2(j) = x(j) + wa1(j)
+               wa3(j) = diag(j)*wa1(j)
+  250          continue
+            pnorm = enorm(n,wa3)
+c
+c           on the first iteration, adjust the initial step bound.
+c
+            if (iter .eq. 1) delta = dmin1(delta,pnorm)
+c
+c           evaluate the function at x + p and calculate its norm.
+c
+            iflag = 1
+            call fcn(m,n,wa2,wa4,wa3,iflag)
+            nfev = nfev + 1
+            if (iflag .lt. 0) go to 340
+            fnorm1 = enorm(m,wa4)
+c
+c           compute the scaled actual reduction.
+c
+            actred = -one
+            if (p1*fnorm1 .lt. fnorm) actred = one - (fnorm1/fnorm)**2
+c
+c           compute the scaled predicted reduction and
+c           the scaled directional derivative.
+c
+            do 270 j = 1, n
+               wa3(j) = zero
+               l = ipvt(j)
+               temp = wa1(l)
+               do 260 i = 1, j
+                  wa3(i) = wa3(i) + fjac(i,j)*temp
+  260             continue
+  270          continue
+            temp1 = enorm(n,wa3)/fnorm
+            temp2 = (dsqrt(par)*pnorm)/fnorm
+            prered = temp1**2 + temp2**2/p5
+            dirder = -(temp1**2 + temp2**2)
+c
+c           compute the ratio of the actual to the predicted
+c           reduction.
+c
+            ratio = zero
+            if (prered .ne. zero) ratio = actred/prered
+c
+c           update the step bound.
+c
+            if (ratio .gt. p25) go to 280
+               if (actred .ge. zero) temp = p5
+               if (actred .lt. zero)
+     *            temp = p5*dirder/(dirder + p5*actred)
+               if (p1*fnorm1 .ge. fnorm .or. temp .lt. p1) temp = p1
+               delta = temp*dmin1(delta,pnorm/p1)
+               par = par/temp
+               go to 300
+  280       continue
+               if (par .ne. zero .and. ratio .lt. p75) go to 290
+               delta = pnorm/p5
+               par = p5*par
+  290          continue
+  300       continue
+c
+c           test for successful iteration.
+c
+            if (ratio .lt. p0001) go to 330
+c
+c           successful iteration. update x, fvec, and their norms.
+c
+            do 310 j = 1, n
+               x(j) = wa2(j)
+               wa2(j) = diag(j)*x(j)
+  310          continue
+            do 320 i = 1, m
+               fvec(i) = wa4(i)
+  320          continue
+            xnorm = enorm(n,wa2)
+            fnorm = fnorm1
+            iter = iter + 1
+  330       continue
+c
+c           tests for convergence.
+c
+            if (dabs(actred) .le. ftol .and. prered .le. ftol
+     *          .and. p5*ratio .le. one) info = 1
+            if (delta .le. xtol*xnorm) info = 2
+            if (dabs(actred) .le. ftol .and. prered .le. ftol
+     *          .and. p5*ratio .le. one .and. info .eq. 2) info = 3
+            if (info .ne. 0) go to 340
+c
+c           tests for termination and stringent tolerances.
+c
+            if (nfev .ge. maxfev) info = 5
+            if (dabs(actred) .le. epsmch .and. prered .le. epsmch
+     *          .and. p5*ratio .le. one) info = 6
+            if (delta .le. epsmch*xnorm) info = 7
+            if (gnorm .le. epsmch) info = 8
+            if (info .ne. 0) go to 340
+c
+c           end of the inner loop. repeat if iteration unsuccessful.
+c
+            if (ratio .lt. p0001) go to 240
+c
+c        end of the outer loop.
+c
+         go to 30
+  340 continue
+c
+c     termination, either normal or user imposed.
+c
+      if (iflag .lt. 0) info = iflag
+      iflag = 0
+      if (nprint .gt. 0) call fcn(m,n,x,fvec,wa3,iflag)
+      return
+c
+c     last card of subroutine lmstr.
+c
+      end
diff --git a/math/minpack/lmstr1.f b/math/minpack/lmstr1.f
new file mode 100644
index 00000000..2fa8ee1c
--- /dev/null
+++ b/math/minpack/lmstr1.f
@@ -0,0 +1,156 @@
+      subroutine lmstr1(fcn,m,n,x,fvec,fjac,ldfjac,tol,info,ipvt,wa,
+     *                  lwa)
+      integer m,n,ldfjac,info,lwa
+      integer ipvt(n)
+      double precision tol
+      double precision x(n),fvec(m),fjac(ldfjac,n),wa(lwa)
+      external fcn
+c     **********
+c
+c     subroutine lmstr1
+c
+c     the purpose of lmstr1 is to minimize the sum of the squares of
+c     m nonlinear functions in n variables by a modification of
+c     the levenberg-marquardt algorithm which uses minimal storage.
+c     this is done by using the more general least-squares solver
+c     lmstr. the user must provide a subroutine which calculates
+c     the functions and the rows of the jacobian.
+c
+c     the subroutine statement is
+c
+c       subroutine lmstr1(fcn,m,n,x,fvec,fjac,ldfjac,tol,info,
+c                         ipvt,wa,lwa)
+c
+c     where
+c
+c       fcn is the name of the user-supplied subroutine which
+c         calculates the functions and the rows of the jacobian.
+c         fcn must be declared in an external statement in the
+c         user calling program, and should be written as follows.
+c
+c         subroutine fcn(m,n,x,fvec,fjrow,iflag)
+c         integer m,n,iflag
+c         double precision x(n),fvec(m),fjrow(n)
+c         ----------
+c         if iflag = 1 calculate the functions at x and
+c         return this vector in fvec.
+c         if iflag = i calculate the (i-1)-st row of the
+c         jacobian at x and return this vector in fjrow.
+c         ----------
+c         return
+c         end
+c
+c         the value of iflag should not be changed by fcn unless
+c         the user wants to terminate execution of lmstr1.
+c         in this case set iflag to a negative integer.
+c
+c       m is a positive integer input variable set to the number
+c         of functions.
+c
+c       n is a positive integer input variable set to the number
+c         of variables. n must not exceed m.
+c
+c       x is an array of length n. on input x must contain
+c         an initial estimate of the solution vector. on output x
+c         contains the final estimate of the solution vector.
+c
+c       fvec is an output array of length m which contains
+c         the functions evaluated at the output x.
+c
+c       fjac is an output n by n array. the upper triangle of fjac
+c         contains an upper triangular matrix r such that
+c
+c                t     t           t
+c               p *(jac *jac)*p = r *r,
+c
+c         where p is a permutation matrix and jac is the final
+c         calculated jacobian. column j of p is column ipvt(j)
+c         (see below) of the identity matrix. the lower triangular
+c         part of fjac contains information generated during
+c         the computation of r.
+c
+c       ldfjac is a positive integer input variable not less than n
+c         which specifies the leading dimension of the array fjac.
+c
+c       tol is a nonnegative input variable. termination occurs
+c         when the algorithm estimates either that the relative
+c         error in the sum of squares is at most tol or that
+c         the relative error between x and the solution is at
+c         most tol.
+c
+c       info is an integer output variable. if the user has
+c         terminated execution, info is set to the (negative)
+c         value of iflag. see description of fcn. otherwise,
+c         info is set as follows.
+c
+c         info = 0  improper input parameters.
+c
+c         info = 1  algorithm estimates that the relative error
+c                   in the sum of squares is at most tol.
+c
+c         info = 2  algorithm estimates that the relative error
+c                   between x and the solution is at most tol.
+c
+c         info = 3  conditions for info = 1 and info = 2 both hold.
+c
+c         info = 4  fvec is orthogonal to the columns of the
+c                   jacobian to machine precision.
+c
+c         info = 5  number of calls to fcn with iflag = 1 has
+c                   reached 100*(n+1).
+c
+c         info = 6  tol is too small. no further reduction in
+c                   the sum of squares is possible.
+c
+c         info = 7  tol is too small. no further improvement in
+c                   the approximate solution x is possible.
+c
+c       ipvt is an integer output array of length n. ipvt
+c         defines a permutation matrix p such that jac*p = q*r,
+c         where jac is the final calculated jacobian, q is
+c         orthogonal (not stored), and r is upper triangular.
+c         column j of p is column ipvt(j) of the identity matrix.
+c
+c       wa is a work array of length lwa.
+c
+c       lwa is a positive integer input variable not less than 5*n+m.
+c
+c     subprograms called
+c
+c       user-supplied ...... fcn
+c
+c       minpack-supplied ... lmstr
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, dudley v. goetschel, kenneth e. hillstrom,
+c     jorge j. more
+c
+c     **********
+      integer maxfev,mode,nfev,njev,nprint
+      double precision factor,ftol,gtol,xtol,zero
+      data factor,zero /1.0d2,0.0d0/
+      info = 0
+c
+c     check the input parameters for errors.
+c
+      if (n .le. 0 .or. m .lt. n .or. ldfjac .lt. n .or. tol .lt. zero
+     *    .or. lwa .lt. 5*n + m) go to 10
+c
+c     call lmstr.
+c
+      maxfev = 100*(n + 1)
+      ftol = tol
+      xtol = tol
+      gtol = zero
+      mode = 1
+      nprint = 0
+      call lmstr(fcn,m,n,x,fvec,fjac,ldfjac,ftol,xtol,gtol,maxfev,
+     *           wa(1),mode,factor,nprint,info,nfev,njev,ipvt,wa(n+1),
+     *           wa(2*n+1),wa(3*n+1),wa(4*n+1),wa(5*n+1))
+      if (info .eq. 8) info = 4
+   10 continue
+      return
+c
+c     last card of subroutine lmstr1.
+c
+      end
diff --git a/math/minpack/qform.f b/math/minpack/qform.f
new file mode 100644
index 00000000..087b2478
--- /dev/null
+++ b/math/minpack/qform.f
@@ -0,0 +1,95 @@
+      subroutine qform(m,n,q,ldq,wa)
+      integer m,n,ldq
+      double precision q(ldq,m),wa(m)
+c     **********
+c
+c     subroutine qform
+c
+c     this subroutine proceeds from the computed qr factorization of
+c     an m by n matrix a to accumulate the m by m orthogonal matrix
+c     q from its factored form.
+c
+c     the subroutine statement is
+c
+c       subroutine qform(m,n,q,ldq,wa)
+c
+c     where
+c
+c       m is a positive integer input variable set to the number
+c         of rows of a and the order of q.
+c
+c       n is a positive integer input variable set to the number
+c         of columns of a.
+c
+c       q is an m by m array. on input the full lower trapezoid in
+c         the first min(m,n) columns of q contains the factored form.
+c         on output q has been accumulated into a square matrix.
+c
+c       ldq is a positive integer input variable not less than m
+c         which specifies the leading dimension of the array q.
+c
+c       wa is a work array of length m.
+c
+c     subprograms called
+c
+c       fortran-supplied ... min0
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,j,jm1,k,l,minmn,np1
+      double precision one,sum,temp,zero
+      data one,zero /1.0d0,0.0d0/
+c
+c     zero out upper triangle of q in the first min(m,n) columns.
+c
+      minmn = min0(m,n)
+      if (minmn .lt. 2) go to 30
+      do 20 j = 2, minmn
+         jm1 = j - 1
+         do 10 i = 1, jm1
+            q(i,j) = zero
+   10       continue
+   20    continue
+   30 continue
+c
+c     initialize remaining columns to those of the identity matrix.
+c
+      np1 = n + 1
+      if (m .lt. np1) go to 60
+      do 50 j = np1, m
+         do 40 i = 1, m
+            q(i,j) = zero
+   40       continue
+         q(j,j) = one
+   50    continue
+   60 continue
+c
+c     accumulate q from its factored form.
+c
+      do 120 l = 1, minmn
+         k = minmn - l + 1
+         do 70 i = k, m
+            wa(i) = q(i,k)
+            q(i,k) = zero
+   70       continue
+         q(k,k) = one
+         if (wa(k) .eq. zero) go to 110
+         do 100 j = k, m
+            sum = zero
+            do 80 i = k, m
+               sum = sum + q(i,j)*wa(i)
+   80          continue
+            temp = sum/wa(k)
+            do 90 i = k, m
+               q(i,j) = q(i,j) - temp*wa(i)
+   90          continue
+  100       continue
+  110    continue
+  120    continue
+      return
+c
+c     last card of subroutine qform.
+c
+      end
diff --git a/math/minpack/qrfac.f b/math/minpack/qrfac.f
new file mode 100644
index 00000000..cb686086
--- /dev/null
+++ b/math/minpack/qrfac.f
@@ -0,0 +1,164 @@
+      subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa)
+      integer m,n,lda,lipvt
+      integer ipvt(lipvt)
+      logical pivot
+      double precision a(lda,n),rdiag(n),acnorm(n),wa(n)
+c     **********
+c
+c     subroutine qrfac
+c
+c     this subroutine uses householder transformations with column
+c     pivoting (optional) to compute a qr factorization of the
+c     m by n matrix a. that is, qrfac determines an orthogonal
+c     matrix q, a permutation matrix p, and an upper trapezoidal
+c     matrix r with diagonal elements of nonincreasing magnitude,
+c     such that a*p = q*r. the householder transformation for
+c     column k, k = 1,2,...,min(m,n), is of the form
+c
+c                           t
+c           i - (1/u(k))*u*u
+c
+c     where u has zeros in the first k-1 positions. the form of
+c     this transformation and the method of pivoting first
+c     appeared in the corresponding linpack subroutine.
+c
+c     the subroutine statement is
+c
+c       subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa)
+c
+c     where
+c
+c       m is a positive integer input variable set to the number
+c         of rows of a.
+c
+c       n is a positive integer input variable set to the number
+c         of columns of a.
+c
+c       a is an m by n array. on input a contains the matrix for
+c         which the qr factorization is to be computed. on output
+c         the strict upper trapezoidal part of a contains the strict
+c         upper trapezoidal part of r, and the lower trapezoidal
+c         part of a contains a factored form of q (the non-trivial
+c         elements of the u vectors described above).
+c
+c       lda is a positive integer input variable not less than m
+c         which specifies the leading dimension of the array a.
+c
+c       pivot is a logical input variable. if pivot is set true,
+c         then column pivoting is enforced. if pivot is set false,
+c         then no column pivoting is done.
+c
+c       ipvt is an integer output array of length lipvt. ipvt
+c         defines the permutation matrix p such that a*p = q*r.
+c         column j of p is column ipvt(j) of the identity matrix.
+c         if pivot is false, ipvt is not referenced.
+c
+c       lipvt is a positive integer input variable. if pivot is false,
+c         then lipvt may be as small as 1. if pivot is true, then
+c         lipvt must be at least n.
+c
+c       rdiag is an output array of length n which contains the
+c         diagonal elements of r.
+c
+c       acnorm is an output array of length n which contains the
+c         norms of the corresponding columns of the input matrix a.
+c         if this information is not needed, then acnorm can coincide
+c         with rdiag.
+c
+c       wa is a work array of length n. if pivot is false, then wa
+c         can coincide with rdiag.
+c
+c     subprograms called
+c
+c       minpack-supplied ... dpmpar,enorm
+c
+c       fortran-supplied ... dmax1,dsqrt,min0
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,j,jp1,k,kmax,minmn
+      double precision ajnorm,epsmch,one,p05,sum,temp,zero
+      double precision dpmpar,enorm
+      data one,p05,zero /1.0d0,5.0d-2,0.0d0/
+c
+c     epsmch is the machine precision.
+c
+      epsmch = dpmpar(1)
+c
+c     compute the initial column norms and initialize several arrays.
+c
+      do 10 j = 1, n
+         acnorm(j) = enorm(m,a(1,j))
+         rdiag(j) = acnorm(j)
+         wa(j) = rdiag(j)
+         if (pivot) ipvt(j) = j
+   10    continue
+c
+c     reduce a to r with householder transformations.
+c
+      minmn = min0(m,n)
+      do 110 j = 1, minmn
+         if (.not.pivot) go to 40
+c
+c        bring the column of largest norm into the pivot position.
+c
+         kmax = j
+         do 20 k = j, n
+            if (rdiag(k) .gt. rdiag(kmax)) kmax = k
+   20       continue
+         if (kmax .eq. j) go to 40
+         do 30 i = 1, m
+            temp = a(i,j)
+            a(i,j) = a(i,kmax)
+            a(i,kmax) = temp
+   30       continue
+         rdiag(kmax) = rdiag(j)
+         wa(kmax) = wa(j)
+         k = ipvt(j)
+         ipvt(j) = ipvt(kmax)
+         ipvt(kmax) = k
+   40    continue
+c
+c        compute the householder transformation to reduce the
+c        j-th column of a to a multiple of the j-th unit vector.
+c
+         ajnorm = enorm(m-j+1,a(j,j))
+         if (ajnorm .eq. zero) go to 100
+         if (a(j,j) .lt. zero) ajnorm = -ajnorm
+         do 50 i = j, m
+            a(i,j) = a(i,j)/ajnorm
+   50       continue
+         a(j,j) = a(j,j) + one
+c
+c        apply the transformation to the remaining columns
+c        and update the norms.
+c
+         jp1 = j + 1
+         if (n .lt. jp1) go to 100
+         do 90 k = jp1, n
+            sum = zero
+            do 60 i = j, m
+               sum = sum + a(i,j)*a(i,k)
+   60          continue
+            temp = sum/a(j,j)
+            do 70 i = j, m
+               a(i,k) = a(i,k) - temp*a(i,j)
+   70          continue
+            if (.not.pivot .or. rdiag(k) .eq. zero) go to 80
+            temp = a(j,k)/rdiag(k)
+            rdiag(k) = rdiag(k)*dsqrt(dmax1(zero,one-temp**2))
+            if (p05*(rdiag(k)/wa(k))**2 .gt. epsmch) go to 80
+            rdiag(k) = enorm(m-j,a(jp1,k))
+            wa(k) = rdiag(k)
+   80       continue
+   90       continue
+  100    continue
+         rdiag(j) = -ajnorm
+  110    continue
+      return
+c
+c     last card of subroutine qrfac.
+c
+      end
diff --git a/math/minpack/qrsolv.f b/math/minpack/qrsolv.f
new file mode 100644
index 00000000..f48954b3
--- /dev/null
+++ b/math/minpack/qrsolv.f
@@ -0,0 +1,193 @@
+      subroutine qrsolv(n,r,ldr,ipvt,diag,qtb,x,sdiag,wa)
+      integer n,ldr
+      integer ipvt(n)
+      double precision r(ldr,n),diag(n),qtb(n),x(n),sdiag(n),wa(n)
+c     **********
+c
+c     subroutine qrsolv
+c
+c     given an m by n matrix a, an n by n diagonal matrix d,
+c     and an m-vector b, the problem is to determine an x which
+c     solves the system
+c
+c           a*x = b ,     d*x = 0 ,
+c
+c     in the least squares sense.
+c
+c     this subroutine completes the solution of the problem
+c     if it is provided with the necessary information from the
+c     qr factorization, with column pivoting, of a. that is, if
+c     a*p = q*r, where p is a permutation matrix, q has orthogonal
+c     columns, and r is an upper triangular matrix with diagonal
+c     elements of nonincreasing magnitude, then qrsolv expects
+c     the full upper triangle of r, the permutation matrix p,
+c     and the first n components of (q transpose)*b. the system
+c     a*x = b, d*x = 0, is then equivalent to
+c
+c                  t       t
+c           r*z = q *b ,  p *d*p*z = 0 ,
+c
+c     where x = p*z. if this system does not have full rank,
+c     then a least squares solution is obtained. on output qrsolv
+c     also provides an upper triangular matrix s such that
+c
+c            t   t               t
+c           p *(a *a + d*d)*p = s *s .
+c
+c     s is computed within qrsolv and may be of separate interest.
+c
+c     the subroutine statement is
+c
+c       subroutine qrsolv(n,r,ldr,ipvt,diag,qtb,x,sdiag,wa)
+c
+c     where
+c
+c       n is a positive integer input variable set to the order of r.
+c
+c       r is an n by n array. on input the full upper triangle
+c         must contain the full upper triangle of the matrix r.
+c         on output the full upper triangle is unaltered, and the
+c         strict lower triangle contains the strict upper triangle
+c         (transposed) of the upper triangular matrix s.
+c
+c       ldr is a positive integer input variable not less than n
+c         which specifies the leading dimension of the array r.
+c
+c       ipvt is an integer input array of length n which defines the
+c         permutation matrix p such that a*p = q*r. column j of p
+c         is column ipvt(j) of the identity matrix.
+c
+c       diag is an input array of length n which must contain the
+c         diagonal elements of the matrix d.
+c
+c       qtb is an input array of length n which must contain the first
+c         n elements of the vector (q transpose)*b.
+c
+c       x is an output array of length n which contains the least
+c         squares solution of the system a*x = b, d*x = 0.
+c
+c       sdiag is an output array of length n which contains the
+c         diagonal elements of the upper triangular matrix s.
+c
+c       wa is a work array of length n.
+c
+c     subprograms called
+c
+c       fortran-supplied ... dabs,dsqrt
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,j,jp1,k,kp1,l,nsing
+      double precision cos,cotan,p5,p25,qtbpj,sin,sum,tan,temp,zero
+      data p5,p25,zero /5.0d-1,2.5d-1,0.0d0/
+c
+c     copy r and (q transpose)*b to preserve input and initialize s.
+c     in particular, save the diagonal elements of r in x.
+c
+      do 20 j = 1, n
+         do 10 i = j, n
+            r(i,j) = r(j,i)
+   10       continue
+         x(j) = r(j,j)
+         wa(j) = qtb(j)
+   20    continue
+c
+c     eliminate the diagonal matrix d using a givens rotation.
+c
+      do 100 j = 1, n
+c
+c        prepare the row of d to be eliminated, locating the
+c        diagonal element using p from the qr factorization.
+c
+         l = ipvt(j)
+         if (diag(l) .eq. zero) go to 90
+         do 30 k = j, n
+            sdiag(k) = zero
+   30       continue
+         sdiag(j) = diag(l)
+c
+c        the transformations to eliminate the row of d
+c        modify only a single element of (q transpose)*b
+c        beyond the first n, which is initially zero.
+c
+         qtbpj = zero
+         do 80 k = j, n
+c
+c           determine a givens rotation which eliminates the
+c           appropriate element in the current row of d.
+c
+            if (sdiag(k) .eq. zero) go to 70
+            if (dabs(r(k,k)) .ge. dabs(sdiag(k))) go to 40
+               cotan = r(k,k)/sdiag(k)
+               sin = p5/dsqrt(p25+p25*cotan**2)
+               cos = sin*cotan
+               go to 50
+   40       continue
+               tan = sdiag(k)/r(k,k)
+               cos = p5/dsqrt(p25+p25*tan**2)
+               sin = cos*tan
+   50       continue
+c
+c           compute the modified diagonal element of r and
+c           the modified element of ((q transpose)*b,0).
+c
+            r(k,k) = cos*r(k,k) + sin*sdiag(k)
+            temp = cos*wa(k) + sin*qtbpj
+            qtbpj = -sin*wa(k) + cos*qtbpj
+            wa(k) = temp
+c
+c           accumulate the tranformation in the row of s.
+c
+            kp1 = k + 1
+            if (n .lt. kp1) go to 70
+            do 60 i = kp1, n
+               temp = cos*r(i,k) + sin*sdiag(i)
+               sdiag(i) = -sin*r(i,k) + cos*sdiag(i)
+               r(i,k) = temp
+   60          continue
+   70       continue
+   80       continue
+   90    continue
+c
+c        store the diagonal element of s and restore
+c        the corresponding diagonal element of r.
+c
+         sdiag(j) = r(j,j)
+         r(j,j) = x(j)
+  100    continue
+c
+c     solve the triangular system for z. if the system is
+c     singular, then obtain a least squares solution.
+c
+      nsing = n
+      do 110 j = 1, n
+         if (sdiag(j) .eq. zero .and. nsing .eq. n) nsing = j - 1
+         if (nsing .lt. n) wa(j) = zero
+  110    continue
+      if (nsing .lt. 1) go to 150
+      do 140 k = 1, nsing
+         j = nsing - k + 1
+         sum = zero
+         jp1 = j + 1
+         if (nsing .lt. jp1) go to 130
+         do 120 i = jp1, nsing
+            sum = sum + r(i,j)*wa(i)
+  120       continue
+  130    continue
+         wa(j) = (wa(j) - sum)/sdiag(j)
+  140    continue
+  150 continue
+c
+c     permute the components of z back to components of x.
+c
+      do 160 j = 1, n
+         l = ipvt(j)
+         x(l) = wa(j)
+  160    continue
+      return
+c
+c     last card of subroutine qrsolv.
+c
+      end
diff --git a/math/minpack/r1mpyq.f b/math/minpack/r1mpyq.f
new file mode 100644
index 00000000..ec99b96c
--- /dev/null
+++ b/math/minpack/r1mpyq.f
@@ -0,0 +1,92 @@
+      subroutine r1mpyq(m,n,a,lda,v,w)
+      integer m,n,lda
+      double precision a(lda,n),v(n),w(n)
+c     **********
+c
+c     subroutine r1mpyq
+c
+c     given an m by n matrix a, this subroutine computes a*q where
+c     q is the product of 2*(n - 1) transformations
+c
+c           gv(n-1)*...*gv(1)*gw(1)*...*gw(n-1)
+c
+c     and gv(i), gw(i) are givens rotations in the (i,n) plane which
+c     eliminate elements in the i-th and n-th planes, respectively.
+c     q itself is not given, rather the information to recover the
+c     gv, gw rotations is supplied.
+c
+c     the subroutine statement is
+c
+c       subroutine r1mpyq(m,n,a,lda,v,w)
+c
+c     where
+c
+c       m is a positive integer input variable set to the number
+c         of rows of a.
+c
+c       n is a positive integer input variable set to the number
+c         of columns of a.
+c
+c       a is an m by n array. on input a must contain the matrix
+c         to be postmultiplied by the orthogonal matrix q
+c         described above. on output a*q has replaced a.
+c
+c       lda is a positive integer input variable not less than m
+c         which specifies the leading dimension of the array a.
+c
+c       v is an input array of length n. v(i) must contain the
+c         information necessary to recover the givens rotation gv(i)
+c         described above.
+c
+c       w is an input array of length n. w(i) must contain the
+c         information necessary to recover the givens rotation gw(i)
+c         described above.
+c
+c     subroutines called
+c
+c       fortran-supplied ... dabs,dsqrt
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more
+c
+c     **********
+      integer i,j,nmj,nm1
+      double precision cos,one,sin,temp
+      data one /1.0d0/
+c
+c     apply the first set of givens rotations to a.
+c
+      nm1 = n - 1
+      if (nm1 .lt. 1) go to 50
+      do 20 nmj = 1, nm1
+         j = n - nmj
+         if (dabs(v(j)) .gt. one) cos = one/v(j)
+         if (dabs(v(j)) .gt. one) sin = dsqrt(one-cos**2)
+         if (dabs(v(j)) .le. one) sin = v(j)
+         if (dabs(v(j)) .le. one) cos = dsqrt(one-sin**2)
+         do 10 i = 1, m
+            temp = cos*a(i,j) - sin*a(i,n)
+            a(i,n) = sin*a(i,j) + cos*a(i,n)
+            a(i,j) = temp
+   10       continue
+   20    continue
+c
+c     apply the second set of givens rotations to a.
+c
+      do 40 j = 1, nm1
+         if (dabs(w(j)) .gt. one) cos = one/w(j)
+         if (dabs(w(j)) .gt. one) sin = dsqrt(one-cos**2)
+         if (dabs(w(j)) .le. one) sin = w(j)
+         if (dabs(w(j)) .le. one) cos = dsqrt(one-sin**2)
+         do 30 i = 1, m
+            temp = cos*a(i,j) + sin*a(i,n)
+            a(i,n) = -sin*a(i,j) + cos*a(i,n)
+            a(i,j) = temp
+   30       continue
+   40    continue
+   50 continue
+      return
+c
+c     last card of subroutine r1mpyq.
+c
+      end
diff --git a/math/minpack/r1updt.f b/math/minpack/r1updt.f
new file mode 100644
index 00000000..e034973d
--- /dev/null
+++ b/math/minpack/r1updt.f
@@ -0,0 +1,207 @@
+      subroutine r1updt(m,n,s,ls,u,v,w,sing)
+      integer m,n,ls
+      logical sing
+      double precision s(ls),u(m),v(n),w(m)
+c     **********
+c
+c     subroutine r1updt
+c
+c     given an m by n lower trapezoidal matrix s, an m-vector u,
+c     and an n-vector v, the problem is to determine an
+c     orthogonal matrix q such that
+c
+c                   t
+c           (s + u*v )*q
+c
+c     is again lower trapezoidal.
+c
+c     this subroutine determines q as the product of 2*(n - 1)
+c     transformations
+c
+c           gv(n-1)*...*gv(1)*gw(1)*...*gw(n-1)
+c
+c     where gv(i), gw(i) are givens rotations in the (i,n) plane
+c     which eliminate elements in the i-th and n-th planes,
+c     respectively. q itself is not accumulated, rather the
+c     information to recover the gv, gw rotations is returned.
+c
+c     the subroutine statement is
+c
+c       subroutine r1updt(m,n,s,ls,u,v,w,sing)
+c
+c     where
+c
+c       m is a positive integer input variable set to the number
+c         of rows of s.
+c
+c       n is a positive integer input variable set to the number
+c         of columns of s. n must not exceed m.
+c
+c       s is an array of length ls. on input s must contain the lower
+c         trapezoidal matrix s stored by columns. on output s contains
+c         the lower trapezoidal matrix produced as described above.
+c
+c       ls is a positive integer input variable not less than
+c         (n*(2*m-n+1))/2.
+c
+c       u is an input array of length m which must contain the
+c         vector u.
+c
+c       v is an array of length n. on input v must contain the vector
+c         v. on output v(i) contains the information necessary to
+c         recover the givens rotation gv(i) described above.
+c
+c       w is an output array of length m. w(i) contains information
+c         necessary to recover the givens rotation gw(i) described
+c         above.
+c
+c       sing is a logical output variable. sing is set true if any
+c         of the diagonal elements of the output s are zero. otherwise
+c         sing is set false.
+c
+c     subprograms called
+c
+c       minpack-supplied ... dpmpar
+c
+c       fortran-supplied ... dabs,dsqrt
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, kenneth e. hillstrom, jorge j. more,
+c     john l. nazareth
+c
+c     **********
+      integer i,j,jj,l,nmj,nm1
+      double precision cos,cotan,giant,one,p5,p25,sin,tan,tau,temp,
+     *                 zero
+      double precision dpmpar
+      data one,p5,p25,zero /1.0d0,5.0d-1,2.5d-1,0.0d0/
+c
+c     giant is the largest magnitude.
+c
+      giant = dpmpar(3)
+c
+c     initialize the diagonal element pointer.
+c
+      jj = (n*(2*m - n + 1))/2 - (m - n)
+c
+c     move the nontrivial part of the last column of s into w.
+c
+      l = jj
+      do 10 i = n, m
+         w(i) = s(l)
+         l = l + 1
+   10    continue
+c
+c     rotate the vector v into a multiple of the n-th unit vector
+c     in such a way that a spike is introduced into w.
+c
+      nm1 = n - 1
+      if (nm1 .lt. 1) go to 70
+      do 60 nmj = 1, nm1
+         j = n - nmj
+         jj = jj - (m - j + 1)
+         w(j) = zero
+         if (v(j) .eq. zero) go to 50
+c
+c        determine a givens rotation which eliminates the
+c        j-th element of v.
+c
+         if (dabs(v(n)) .ge. dabs(v(j))) go to 20
+            cotan = v(n)/v(j)
+            sin = p5/dsqrt(p25+p25*cotan**2)
+            cos = sin*cotan
+            tau = one
+            if (dabs(cos)*giant .gt. one) tau = one/cos
+            go to 30
+   20    continue
+            tan = v(j)/v(n)
+            cos = p5/dsqrt(p25+p25*tan**2)
+            sin = cos*tan
+            tau = sin
+   30    continue
+c
+c        apply the transformation to v and store the information
+c        necessary to recover the givens rotation.
+c
+         v(n) = sin*v(j) + cos*v(n)
+         v(j) = tau
+c
+c        apply the transformation to s and extend the spike in w.
+c
+         l = jj
+         do 40 i = j, m
+            temp = cos*s(l) - sin*w(i)
+            w(i) = sin*s(l) + cos*w(i)
+            s(l) = temp
+            l = l + 1
+   40       continue
+   50    continue
+   60    continue
+   70 continue
+c
+c     add the spike from the rank 1 update to w.
+c
+      do 80 i = 1, m
+         w(i) = w(i) + v(n)*u(i)
+   80    continue
+c
+c     eliminate the spike.
+c
+      sing = .false.
+      if (nm1 .lt. 1) go to 140
+      do 130 j = 1, nm1
+         if (w(j) .eq. zero) go to 120
+c
+c        determine a givens rotation which eliminates the
+c        j-th element of the spike.
+c
+         if (dabs(s(jj)) .ge. dabs(w(j))) go to 90
+            cotan = s(jj)/w(j)
+            sin = p5/dsqrt(p25+p25*cotan**2)
+            cos = sin*cotan
+            tau = one
+            if (dabs(cos)*giant .gt. one) tau = one/cos
+            go to 100
+   90    continue
+            tan = w(j)/s(jj)
+            cos = p5/dsqrt(p25+p25*tan**2)
+            sin = cos*tan
+            tau = sin
+  100    continue
+c
+c        apply the transformation to s and reduce the spike in w.
+c
+         l = jj
+         do 110 i = j, m
+            temp = cos*s(l) + sin*w(i)
+            w(i) = -sin*s(l) + cos*w(i)
+            s(l) = temp
+            l = l + 1
+  110       continue
+c
+c        store the information necessary to recover the
+c        givens rotation.
+c
+         w(j) = tau
+  120    continue
+c
+c        test for zero diagonal elements in the output s.
+c
+         if (s(jj) .eq. zero) sing = .true.
+         jj = jj + (m - j + 1)
+  130    continue
+  140 continue
+c
+c     move w back into the last column of the output s.
+c
+      l = jj
+      do 150 i = n, m
+         s(l) = w(i)
+         l = l + 1
+  150    continue
+      if (s(jj) .eq. zero) sing = .true.
+      return
+c
+c     last card of subroutine r1updt.
+c
+      end
diff --git a/math/minpack/rwupdt.f b/math/minpack/rwupdt.f
new file mode 100644
index 00000000..05282b55
--- /dev/null
+++ b/math/minpack/rwupdt.f
@@ -0,0 +1,113 @@
+      subroutine rwupdt(n,r,ldr,w,b,alpha,cos,sin)
+      integer n,ldr
+      double precision alpha
+      double precision r(ldr,n),w(n),b(n),cos(n),sin(n)
+c     **********
+c
+c     subroutine rwupdt
+c
+c     given an n by n upper triangular matrix r, this subroutine
+c     computes the qr decomposition of the matrix formed when a row
+c     is added to r. if the row is specified by the vector w, then
+c     rwupdt determines an orthogonal matrix q such that when the
+c     n+1 by n matrix composed of r augmented by w is premultiplied
+c     by (q transpose), the resulting matrix is upper trapezoidal.
+c     the matrix (q transpose) is the product of n transformations
+c
+c           g(n)*g(n-1)* ... *g(1)
+c
+c     where g(i) is a givens rotation in the (i,n+1) plane which
+c     eliminates elements in the (n+1)-st plane. rwupdt also
+c     computes the product (q transpose)*c where c is the
+c     (n+1)-vector (b,alpha). q itself is not accumulated, rather
+c     the information to recover the g rotations is supplied.
+c
+c     the subroutine statement is
+c
+c       subroutine rwupdt(n,r,ldr,w,b,alpha,cos,sin)
+c
+c     where
+c
+c       n is a positive integer input variable set to the order of r.
+c
+c       r is an n by n array. on input the upper triangular part of
+c         r must contain the matrix to be updated. on output r
+c         contains the updated triangular matrix.
+c
+c       ldr is a positive integer input variable not less than n
+c         which specifies the leading dimension of the array r.
+c
+c       w is an input array of length n which must contain the row
+c         vector to be added to r.
+c
+c       b is an array of length n. on input b must contain the
+c         first n elements of the vector c. on output b contains
+c         the first n elements of the vector (q transpose)*c.
+c
+c       alpha is a variable. on input alpha must contain the
+c         (n+1)-st element of the vector c. on output alpha contains
+c         the (n+1)-st element of the vector (q transpose)*c.
+c
+c       cos is an output array of length n which contains the
+c         cosines of the transforming givens rotations.
+c
+c       sin is an output array of length n which contains the
+c         sines of the transforming givens rotations.
+c
+c     subprograms called
+c
+c       fortran-supplied ... dabs,dsqrt
+c
+c     argonne national laboratory. minpack project. march 1980.
+c     burton s. garbow, dudley v. goetschel, kenneth e. hillstrom,
+c     jorge j. more
+c
+c     **********
+      integer i,j,jm1
+      double precision cotan,one,p5,p25,rowj,tan,temp,zero
+      data one,p5,p25,zero /1.0d0,5.0d-1,2.5d-1,0.0d0/
+c
+      do 60 j = 1, n
+         rowj = w(j)
+         jm1 = j - 1
+c
+c        apply the previous transformations to
+c        r(i,j), i=1,2,...,j-1, and to w(j).
+c
+         if (jm1 .lt. 1) go to 20
+         do 10 i = 1, jm1
+            temp = cos(i)*r(i,j) + sin(i)*rowj
+            rowj = -sin(i)*r(i,j) + cos(i)*rowj
+            r(i,j) = temp
+   10       continue
+   20    continue
+c
+c        determine a givens rotation which eliminates w(j).
+c
+         cos(j) = one
+         sin(j) = zero
+         if (rowj .eq. zero) go to 50
+         if (dabs(r(j,j)) .ge. dabs(rowj)) go to 30
+            cotan = r(j,j)/rowj
+            sin(j) = p5/dsqrt(p25+p25*cotan**2)
+            cos(j) = sin(j)*cotan
+            go to 40
+   30    continue
+            tan = rowj/r(j,j)
+            cos(j) = p5/dsqrt(p25+p25*tan**2)
+            sin(j) = cos(j)*tan
+   40    continue
+c
+c        apply the current transformation to r(j,j), b(j), and alpha.
+c
+         r(j,j) = cos(j)*r(j,j) + sin(j)*rowj
+         temp = cos(j)*b(j) + sin(j)*alpha
+         alpha = -sin(j)*b(j) + cos(j)*alpha
+         b(j) = temp
+   50    continue
+   60    continue
+      return
+c
+c     last card of subroutine rwupdt.
+c
+      end
diff --git a/math/mkpkg b/math/mkpkg
new file mode 100644
index 00000000..47aa33d7
--- /dev/null
+++ b/math/mkpkg
@@ -0,0 +1,138 @@
+# Update the IRAF MATH libraries.
+
+$ifeq (hostid, unix)  !(clear;date)  $endif
+$call mathgen
+$echo "-------------- (done) -------------------"
+$ifeq (hostid, unix) !(date) $endif
+$exit
+
+# MATHGEN -- Update the math libraries.  The source for each library is
+# maintained in a separate subidrectory.  The binary libraries are in lib$.
+# To update a single library type "mkpkg" in the source directory for the
+# library, or type "mkpkg libname" in this directory, e.g. "mkpkg llsq".
+
+mathgen:
+	$call bev
+	$call curfit
+	$call deboor
+	$call gsurfit
+	# $call ieee
+	$call iminterp
+	$call interp
+	$call llsq
+	$call nlfit
+	$call slalib
+	$call surfit
+	$purge lib$
+	;
+
+bev:
+	$echo "-------------- LIBBEV -------------------"
+	$checkout libbev.a lib$
+	$update   libbev.a
+	$checkin  libbev.a lib$
+	;
+curfit:
+	$echo "-------------- LIBCURFIT ----------------"
+	$checkout libcurfit.a lib$
+	$update   libcurfit.a
+	$checkin  libcurfit.a lib$
+	;
+deboor:
+	$echo "-------------- LIBDEBOOR ----------------"
+	$checkout libdeboor.a lib$
+	$update   libdeboor.a
+	$checkin  libdeboor.a lib$
+	;
+gsurfit:
+	$echo "-------------- LIBGSURFIT ---------------"
+	$checkout libgsurfit.a lib$
+	$update   libgsurfit.a
+	$checkin  libgsurfit.a lib$
+	;
+ieee:
+	$echo "-------------- LIBIEEE ------------------"
+	$checkout libieee.a lib$
+	$update   libieee.a
+	$checkin  libieee.a lib$
+	;
+iminterp:
+	$echo "-------------- LIBIMINTERP --------------"
+	$checkout libiminterp.a lib$
+	$update   libiminterp.a
+	$checkin  libiminterp.a lib$
+	;
+interp:
+	$echo "-------------- LIBINTERP ----------------"
+	$checkout libinterp.a lib$
+	$update   libinterp.a
+	$checkin  libinterp.a lib$
+	;
+llsq:
+	$echo "-------------- LIBLLSQ ------------------"
+	$checkout libllsq.a lib$
+	$update   libllsq.a
+	$checkin  libllsq.a lib$
+	;
+nlfit:
+	$echo "-------------- LIBNLFIT -----------------"
+	$checkout libnlfit.a lib$
+	$update   libnlfit.a
+	$checkin  libnlfit.a lib$
+	;
+slalib:
+	$echo "-------------- LIBSLALIB ----------------"
+	$checkout libslalib.a lib$
+	$update   libslalib.a
+	$checkin  libslalib.a lib$
+	;
+surfit:
+	$echo "-------------- LIBSURFIT ----------------"
+	$checkout libsurfit.a lib$
+	$update   libsurfit.a
+	$checkin  libsurfit.a lib$
+	;
+
+libbev.a:				# Bevington routines
+	@bevington
+	;
+
+libcurfit.a:				# Curve fitting package
+	@curfit
+	;
+
+libdeboor.a:				# DeBoor spline package
+	@deboor
+	;
+
+libgsurfit.a:				# Generalized 2d surface fitting pkg
+	@gsurfit
+	;
+
+libieee.a:				# IEEE signal processing package
+	@ieee
+	;
+
+libiminterp.a:				# Image interpolation package
+	@iminterp
+	;
+
+libinterp.a:				# Obsolete version of iminterp pkg
+	@interp
+	;
+
+libllsq.a:				# Lawson and Hanson Least Squares pkg
+	@llsq
+	;
+
+libnlfit.a:                             # Levenberg-Marquardt fitting package
+	@nlfit
+	;
+
+libslalib.a:				# Starlink positional astronomy library
+	@slalib
+	;
+
+libsurfit.a:				# Surface fitting on an even grid
+	@surfit
+	;
diff --git a/math/nlfit/README b/math/nlfit/README
new file mode 100644
index 00000000..c47732af
--- /dev/null
+++ b/math/nlfit/README
@@ -0,0 +1,81 @@
+                      THE NLFIT PACKAGE
+
+This subdirectory contains the routines in the non-linear least squares
+fitting package NLFIT. NLFIT uses the Levenberg-Marquardt method  to
+to solve for the parameters of a user specified non-linear equation.
+The user must supply two routines. The first routine evaluates the function
+in terms of its parameters. The second routine evaluates the function and its
+derivatives in terms of its parameters.  The user must also supply initial
+guesses for the parameters and parameter increments, the list of
+parameters to be varied during the fitting processa, a fitting
+tolerance and the maximum number of iterations.
+
+The principal entry points into the NLFIT are listed below.
+
+	nlinit - Initialize the fitting routines
+       nlstati - Get the value of an integer NLFIT parameter
+        nlstat - Get the value of floating point NLFIT parameter
+	nlpget - Get the values of the fitted parameters
+	nlfree - Free memory allocated by nlinit
+	 nlfit - Fit the function
+	nleval - Evaluate the curve at a given point
+      nlvector - Evaluate the curve at an array of points 
+      nlerrors - Compute the fits statistics and errors in the parameters
+
+The calling sequences for the above routines are listed below. The [ird]
+stand for integer, real and double precision versions of each routine
+respectively.
+
+               nlinit[rd] (nl, address(fnc), address(dfnc), params, dparams,
+	            nparams, plist, nfparams, tol, itmax)
+        ival = nlstati (nl, param)
+     [rd]val = nlstat[rd] (nl, param)
+               nlpget[rd] (nl, params, nparams)
+               nlfree[rd] (nl)
+               nlfit[rd] (nl, x, z, w, npts, nvars, wtflag, ier)
+     [rd]val = nleval[rd] (nl, x, nvars)
+               nlvector[rd] (nl, x, zfit, npts, nvars)
+               nlerrors[rd] (nl, z, zfit, wts, npts, variance, chisqr, errors)
+
+The user supplied functions fnc and dfnc have the following calling
+sequences.
+	
+	       fnc (x, nvars, params, nparams, zfit)
+	      dfnc (x, nvars, params, dparams, nparams, zfit, derivs)
+
+    The address of the user supplied function can be determined with a
+call to locpr as in
+
+	      address = locpr (fnc)
+
+The user definitions for the NLFIT package can be found in the file 
+lib$math/nlfit.h and can be made available to user applications programs
+with the statement "include <math/nlfit.h>".
+
+The permitted values for the param argument in nlstat[ird] are the following.
+
+define	NLNPARAMS	integer		# Number of parameters
+define	NLNFPARAMS	integer         # Number of fitted parameters
+define	NLITMAX		integer		# Maximum number of iterations
+define	NLITER		integer		# Current number of iterations
+define	NLNPTS		integer         # Number of points
+define	NLSUMSQ		real/double	# Current reduced chi-squared
+define	NLOLDSQ		real/double     # Previous reduced chi-squared
+define	NLLAMBDA	real/double     # Value of lambda factor
+define	NLTOL		real/double	# Fitting tolerance in %chi-squared
+define	NLSCATTER	real/double     # Mean scatter in the fit
+
+The permitted values of the wtflag argument in nlfit[rd] are the following.
+
+define	WTS_USER			# User enters weights
+define	WTS_UNIFORM			# Equal weights
+define	WTS_CHISQ 			# Chi-squared weights
+define	WTS_SCATTER			# Weights include scatter term
+
+The permitted error values returned from nlfit[rd] are the following.
+
+define	DONE			0	# Solution converged
+define	SINGULAR		1	# Singular matrix
+define	NO_DEG_FREEDOM		2	# Too few points
+define	NOT_DONE		3	# Solution did not converge
+
diff --git a/math/nlfit/doc/nlerrors.hlp b/math/nlfit/doc/nlerrors.hlp
new file mode 100644
index 00000000..3b463c14
--- /dev/null
+++ b/math/nlfit/doc/nlerrors.hlp
@@ -0,0 +1,67 @@
+.help nlerrors Feb91 "Nlfit Package"
+.ih
+NAME
+nlerrors -- compute the fit statistics and errors in the parameters
+.ih
+SYNOPSIS
+nlerrors[rd] (nl, z, zfit, w, npts, variance, chisqr, errors)
+
+.nf
+pointer		nl		# curve descriptor
+real/double	z[npts]		# array of input function values
+real/double	zfit[npts]	# array of fitted function values
+real/double	w[npts]		# array of weights
+int		npts		# number of data points
+real/double	variance	# the computed variance of the fit
+real/double	chisqr		# the computed reduced chi-square of the fit
+real/double	errors[*]	# errors in the fitted parameters
+.fi
+.ih
+ARGUMENTS
+.ls nl     
+Pointer to the curve descriptor structure.
+.le
+.ls z   
+Array of function values.
+.le
+.ls zfit  
+Array of fitted function values.
+.le
+.ls w
+Array of weights.
+.le
+.ls npts
+The number of data points.
+.le
+.ls variance
+The computed variance of the fit.
+.le
+.ls chisqr
+The computed reduced chi-squared of the fit.
+.le
+.ls errors
+Array of errors in the computed parameters.
+.le
+.ih
+DESCRIPTION
+Compute the variance and reduced chi-squared of the fit and the
+errors in the fitted parameters.
+.ih
+NOTES
+The reduced chi-squared of the fit is the square root of the sum of the
+weighted squares of the residuals divided by the number of degrees of freedom.
+The variance of the fit is the square root of the sum of the
+squares of the residuals divided by the number of degrees of freedom.
+If the weighting is uniform, then the reduced chi-squared is equal to the
+variance of the fit.
+The error of the j-th parameter is the square root of the j-th diagonal
+element of the inverse of the data matrix. If the weighting is uniform,
+then the errors are scaled by the square root of the variance of the data.
+
+The zfit array can be computed by a call to the nlvector[rd] routine.
+The size of the array required to hold the output error array can be
+determined by a call to nlstati.
+.ih
+SEE ALSO
+nlvector,nlstat
+.endhelp
diff --git a/math/nlfit/doc/nleval.hlp b/math/nlfit/doc/nleval.hlp
new file mode 100644
index 00000000..f0bbb400
--- /dev/null
+++ b/math/nlfit/doc/nleval.hlp
@@ -0,0 +1,35 @@
+.help nleval Feb91 "Nlfit Package"
+.ih
+NAME
+nleval -- evaluate the fitted function at a single point
+.ih
+SYNOPSIS
+z = nleval[rd] (nl, x, nvars)
+
+.nf
+pointer		nl		# curve descriptor
+real/double	x[nvars]	# array of variables
+int		nvars		# the number of variables
+.fi
+.ih
+ARGUMENTS
+.ls nl    
+Pointer to the curve descriptor structure.
+.le
+.ls x   
+Array of variable values at which the curve is to be evaluated.
+.le
+.ls nvars
+The number of variables.
+.le
+.ih
+DESCRIPTION
+Evaluate the curve at the specified point. NLEVAL is a real or double
+function which returns the fitted z value.
+.ih
+NOTES
+NLEVAL uses the parameter array stored in the curve descriptor structure.
+.ih
+SEE ALSO
+nlvector
+.endhelp
diff --git a/math/nlfit/doc/nlfit.hd b/math/nlfit/doc/nlfit.hd
new file mode 100644
index 00000000..13bb3065
--- /dev/null
+++ b/math/nlfit/doc/nlfit.hd
@@ -0,0 +1,12 @@
+# Help directory for the NLFIT (non-linear least-squares fitting) package.
+
+$nlfit	= "math$nlfit/"
+
+nlerrors	hlp = nlerrors.hlp,	src = nlfit$nlerrorsr.x
+nleval		hlp = nleval.hlp,	src = nlfit$nlevalr.x
+nlinit		hlp = nlinit.hlp,	src = nlfit$nlinitr.x
+nlfit		hlp = nlfit.hlp,	src = nlfit$nlfitr.x
+nlfree		hlp = nlfree.hlp,	src = nlfit$nlfreer.x
+nlpget		hlp = nlpget.hlp,	src = nlfit$nlpgetr.x
+nlstat		hlp = nlstat.hlp,	src = nlfit$nlstatr.x
+nlvector	hlp = nlvector.hlp,	src = nlfit$nlvectorr.x
diff --git a/math/nlfit/doc/nlfit.hlp b/math/nlfit/doc/nlfit.hlp
new file mode 100644
index 00000000..8ed82512
--- /dev/null
+++ b/math/nlfit/doc/nlfit.hlp
@@ -0,0 +1,81 @@
+.help nlfit Feb91 "Nlfit Package"
+.ih
+NAME
+nlfit -- fit a curve to a set of data values
+.ih
+SYNOPSIS
+nlfit (nl, x, z, w, npts, nvars, wtflag, ier)
+
+.nf
+pointer		nl		# curve descriptor
+real/double	x[npts*nvars]	# variable values (stored as x[nvars,npts])
+real/double	z[npts]		# array of z values
+real/double	w[npts]		# array of weights
+int		npts		# number of data points
+int		wtflag		# type of weighting
+int		ier		# error code
+.fi
+.ih
+ARGUMENTS
+.ls nl    
+Pointer to the curve descriptor structure.
+.le
+.ls x    
+Array of x values.
+.le
+.ls z
+Array of function values.
+.le
+.ls w
+Array of weights.
+.le
+.ls npts
+The number of data points.
+.le
+.ls wtflag
+Type of weighting. The options are WTS_USER, WTS_UNIFORM, WTS_CHISQ and
+WTS_SCATTER. If wtflag = WTS_USER individual weights for each data point
+are supplied by the calling program and points with zero-valued weights are
+not included in the fit. If wtflag = WTS_UNIFORM, all weights are assigned
+values of 1. If wtflag = WTS_CHISQ the weights are set equal to the
+reciprocal of the function value. If wtflag = WTS_SCATTER the fitting
+routine adds a scatter term to the weights if the reduced chi-squared of
+the fit is significantly greater than 1.
+.le
+.ls ier
+Error code for the fit. The options are DONE, SINGULAR,
+NO_DEG_FREEDOM and NOT_DONE. If ier = SINGULAR, the numerical routines
+will compute a
+solution but one or more of the coefficients will be
+zero. If ier = NO_DEG_FREEDOM, there were too few data points to solve the
+matrix equations and the routine returns without fitting the data.
+If ier = NOT_DONE, the fit could not achieve the desired tolerance with
+the given input data in the specified maximum number of iterations.
+.le
+.ih
+DESCRIPTION
+NLFIT accumulate the data into the appropriate internal matrices and vectors
+and does the fit.
+.ih
+NOTES
+The permitted values of the input wtflag argument to nlfit[rd] are the
+following.
+
+.nf
+define	WTS_USER			# User enters weights
+define	WTS_UNIFORM			# Equal weights
+define	WTS_CHISQ 			# Chi-squared weights
+define	WTS_SCATTER			# Weights include scatter term
+.fi
+
+The permitted error values returned from nlfit[rd] are the following.
+
+.nf
+define	DONE			0	# Solution converged
+define	SINGULAR		1	# Singular matrix
+define	NO_DEG_FREEDOM		2	# Too few points
+define	NOT_DONE		3	# Solution did not converge
+.fi
+.ih
+SEE ALSO
+.endhelp
diff --git a/math/nlfit/doc/nlfit.men b/math/nlfit/doc/nlfit.men
new file mode 100644
index 00000000..5fb68623
--- /dev/null
+++ b/math/nlfit/doc/nlfit.men
@@ -0,0 +1,8 @@
+      nlerrors - Compute the fits statistics and errors in the parameters
+	 nlfit - Fit the function
+	nlfree - Free memory allocated by nlinit
+	nlinit - Initialize the fitting routines
+	nlpget - Get the values of the fitted parameters
+        nlstat - Get the value of an NLFIT parameter
+	nleval - Evaluate the curve at a given point
+      nlvector - Evaluate the curve at an array of points 
diff --git a/math/nlfit/doc/nlfree.hlp b/math/nlfit/doc/nlfree.hlp
new file mode 100644
index 00000000..9688d5e7
--- /dev/null
+++ b/math/nlfit/doc/nlfree.hlp
@@ -0,0 +1,26 @@
+.help nlfree Feb91 "Nlfit Package"
+.ih
+NAME
+nlfree -- free the curve descriptor structure
+.ih
+SYNOPSIS
+nlfree[rd] (nl)
+
+.nf
+pointer	nl	# curve descriptor
+.fi
+.ih
+ARGUMENTS
+.ls nl     
+Pointer to the curve descriptor structure.
+.le
+.ih
+DESCRIPTION
+Frees the curve descriptor structure.
+.ih
+NOTES
+NLFREE should be called after each curve fit.
+.ih
+SEE ALSO
+nlinit
+.endhelp
diff --git a/math/nlfit/doc/nlinit.hlp b/math/nlfit/doc/nlinit.hlp
new file mode 100644
index 00000000..94e5e5a9
--- /dev/null
+++ b/math/nlfit/doc/nlinit.hlp
@@ -0,0 +1,86 @@
+.help nlinit Feb91 "Nlfit Package"
+.ih
+NAME
+nlinit -- initialise curve descriptor
+.ih
+SYNOPSIS
+include <math/nlfit.h>
+
+nlinit[rd] (nl, fnc, dfnc, params, dparams, nparams, plist, nfparams,
+                tol, itmax)
+
+.nf
+pointer		nl		# curve descriptor
+int		fnc		# address of first user-supplied function
+int		dfnc		# address of second user-supplied function
+real/double	params[nparams]	# list of initial parameter values
+real/double	dparams[nparams]# list of parameter increments
+int		nparams		# number of parameters
+int		plist[nparams]	# list of parameters to be fit
+int		nfparams	# number of parameters to be fit
+real/double	tol		# fitting tolerance
+int		itmax		# maximum number of iterations
+.fi
+.ih
+ARGUMENTS
+.ls nl             
+Pointer to the curve descriptor structure.
+.le
+.ls fnc       
+The address of the user-supplied subroutine fncname for evaluating the function
+to be fit. The calling sequence of fncname is the following.
+
+.nf
+fncname (x, nvars, params, nparams, zfit)
+.fi
+.le
+.ls dfnc       
+The address of the user-supplied subroutine dfncname for evaluating the
+function to be fit and its derivatives with respect to the parameters.
+The calling sequence of dfncname is the following.
+
+.nf
+dfncname (x, nvars, params, dparams, nparams, zfit, derivs)
+.fi
+.le
+.ls params
+An array containing initial values of all the parameters, including both
+those to be fit and those that are to be held constant.
+.le
+.ls dparams
+An array parameter increment values over which the derivatives are to be
+computed empirically. If equations are supplied for the derivatives
+inside dfnc, the dparams array is not used.
+.le
+.ls nparams
+The total number of parameters in the user-supplied function.
+.le
+.ls plist
+The list of parameters to be fit. Plist is an integer array containing
+the indices of those parameters in params to be fit.
+.le
+.ls nfparams
+The total number of parameters to be fit.
+.le
+.ls tol   
+The fitting tolerance. If the difference in the chi-squared
+from one iteration to the next is less than the fitting tolerance
+times the current chi-squared, the fit has converged.
+.le
+.ls itmax
+The maximum number of fitting iterations. Itmax must be greater than
+or equal to 3.
+.le
+.ih
+DESCRIPTION
+Allocate space for the curve descriptor structure and the arrays and
+vectors used by the numerical routines. Initialize all arrays and vectors
+to zero. Return the curve descriptor to the calling routine.
+.ih
+NOTES
+NLINIT must be the first NLFIT routine called. NLINIT returns a NULL pointer
+if it encounters an illegal parameter list.
+.ih
+SEE ALSO
+nlfree
+.endhelp
diff --git a/math/nlfit/doc/nllmfit.hlp b/math/nlfit/doc/nllmfit.hlp
new file mode 100644
index 00000000..59309133
--- /dev/null
+++ b/math/nlfit/doc/nllmfit.hlp
@@ -0,0 +1,172 @@
+.help nlfit Feb91 "Math Package"
+.ih
+NAME
+nlfit -- Levenberg-Marquardt non-linear least-squares fitting package
+.ih
+SYNOPSIS
+The principal entry points into the NLFIT package are listed below.
+
+.nf
+	nlinit - Initialize the fitting routines
+        nlstat - Get the value of an NLFIT parameter
+	nlpget - Get the values of the fitted parameters
+	nlfree - Free memory allocated by nlinit
+	 nlfit - Fit the function
+	nleval - Evaluate the curve at a given point
+      nlvector - Evaluate the curve at an array of points 
+      nlerrors - Compute the fits statistics and errors in the parameters
+.fi
+
+The calling sequences for the above routines are listed below. The [ird]
+stand for integer, real and double precision versions of each routine
+respectively.
+
+.nf
+            nlinit[rd] (nl, address(fnc), address(dfnc), params, dparams,
+	        nparams, plist, nfparams, tol, itmax)
+        ival = nlstati (nl, param)
+  [rd]val = nlstat[rd] (nl, param)
+            nlpget[rd] (nl, params, nparams)
+            nlfree[rd] (nl)
+             nlfit[rd] (nl, x, z, w, npts, nvars, wtflag, ier)
+  [rd]val = nleval[rd] (nl, x, nvars)
+          nlvector[rd] (nl, x, zfit, npts, nvars)
+          nlerrors[rd] (nl, z, zfit, wts, npts, variance, chisqr, errors)
+.fi
+
+The user supplied functions fnc and dfnc must have the following form.
+	
+.nf
+	       fnc (x, nvars, params, nparams, zfit)
+	      dfnc (x, nvars, params, dparams, nparams, zfit, derivs)
+.fi
+
+The addresses of these functions can be obtained by a call to lcopr as
+follows.
+
+.nf
+		address = locpr (fnc)
+.fi
+
+.ih
+DESCRIPTION
+The NLFIT package provides a set of routines for fitting data to non-linear
+functions of several variables using least squares techniques.
+NLFIT uses the Levenberg-Marquardt
+method to solve for the parameters of a user specified non-linear equation.
+The user must supply two subroutines. The first subroutine evaluates the
+function in terms of its parameters. The second subroutine evaluates the
+function and its derivatives in terms of its parameters.  The user must
+also supply initial
+guesses for the parameters and parameter increments, the list of
+parameters to be varied during the fitting process, a fitting
+tolerance and the maximum number of iterations. 
+.ih
+NOTES
+The poackage definitions for NLFIT can be found in the file 
+lib$math/nlfit.h. In order to make these definitions available
+to the calling program, the user must insert the statement
+"include <math/nlfit.h>" inside the calling program.
+
+The permitted values for the param argument in nlstat[ird] are the following.
+
+.nf
+define	NLNPARAMS	integer		# Number of parameters
+define	NLNFPARAMS	integer         # Number of fitted parameters
+define	NLITMAX		integer		# Maximum number of iterations
+define	NLITER		integer		# Current number of iterations
+define	NLNPTS		integer         # Number of points
+define	NLSUMSQ		real/double	# Current reduced chi-squared
+define	NLOLDSQ		real/double     # Previous reduced chi-squared
+define	NLLAMBDA	real/double     # Value of lambda factor
+define	NLTOL		real/double	# Fitting tolerance in %chi-squared
+define	NLSCATTER	real/double     # Mean scatter in the fit
+.fi
+
+The permitted values of the wtflag argument in nlfit[rd] are the following.
+
+.nf
+define	WTS_USER			# User enters weights
+define	WTS_UNIFORM			# Equal weights
+define	WTS_CHISQ 			# Chi-squared weights
+define	WTS_SCATTER			# Weights include scatter term
+.fi
+
+The permitted error values returned from nlfit[rd] are the following.
+
+.nf
+define	DONE			0	# Solution converged
+define	SINGULAR		1	# Singular matrix
+define	NO_DEG_FREEDOM		2	# Too few points
+define	NOT_DONE		3	# Solution did not converge
+.fi
+.ih
+REFERENCES
+1. Bevington,P.R., 1969, Data Reduction and Error Analysis for the Physical
+Sciences, Chapter 11, page 235.
+
+2. Press, W.H. et al., 1986, Numerical Recipes: The Art of Scientific
+Computing, Chapter 14, page 523
+.ih
+EXAMPLES
+.nf
+Example 1: Fit a curve to the data using uniform weighting. Fit all the
+parameters.
+
+    # Include nlfit definitions
+    include <math/nlfit.h>
+
+    # Declare the variables
+    int	nparams, nfparams, itmax, npts, nvars, ier
+    int	plist[nparams]
+    real tol, variance, chisqr
+    real params[nparams], dparams[nparams], vars[nvars,npts], z[npts]
+    real w[npts], zfit[npts], errors[nparams]
+
+    # Declare the functions
+    extern fncname(), dfncname()
+    int	locpr()
+
+    begin
+            ... get data, set initial values of all parameters, parameter
+	    ... increments, tol and itmax
+
+            # Define list of variables to be fitted
+            nfparams = nparams
+            do i = 1, nparams
+	        plist[i] = i
+
+	    # Fit only parameters 1,3 and 5
+	    #nfparams = 3
+	    #plist[1] = 1
+	    #plist[2] = 3
+	    #plist[3] = 5
+
+            # Initialize the fitting routines
+            call nlinitr (nl, locpr (fncname), locpr (dfncname),
+	        params, dparams, nparams, plist, nfparams, tol, itmax)
+
+            # Fit the data
+            call nlfitr (nl, x, z, w, npts, nvars, WTS_UNIFORM, ier)
+            if (ier != DONE)
+	        ... take error action
+
+            # Compute the statistics of the fit
+            call nlvectorr (nl, x, zfit, npts, nvars)
+            call nlerrorsr (nl, z, zfit, wts, npts, variance, chisqr,
+	        errors)
+
+            # Get the values of the fitted parameters
+            call nlpgetr (nl, params, nparams)
+            call nlfreer (nl)
+
+            # Print the parameters and their errors.
+            do i = 1, nparams {
+	        call printf ("%d  %g  %g\n")
+	        call pargi (i)
+	        call pargr (params[i])
+	        call pargr (errors[i])
+	    }
+    end
+.fi
+.endhelp
diff --git a/math/nlfit/doc/nlpget.hlp b/math/nlfit/doc/nlpget.hlp
new file mode 100644
index 00000000..07f2ef5e
--- /dev/null
+++ b/math/nlfit/doc/nlpget.hlp
@@ -0,0 +1,38 @@
+.help nlpget Feb91 "Nlfit Package"
+
+.ih
+NAME
+nlpget -- get the number and values of the fitted parameters
+.ih
+SYNOPSIS
+nlpget[rd] (nl, params, nparams)
+
+.nf
+pointer		nl		# curve descriptor
+real/double	params[nparams]	# the parameters array
+int		nparams		# the number of parameters
+.fi
+.ih
+ARGUMENTS
+.ls nl
+Pointer to the curve descriptor.
+.le
+.ls params
+Array of fitted parameters.
+.le
+.ls nparameters
+The total number of parameters.
+.le
+.ih
+DESCRIPTION
+NLPGET fetches the parameters array and the number of parameters from the
+curve descriptor structure. All the parameters, both those that were
+fit and those that were held constant are output.
+.ih
+NOTES
+The array size required to hold the output parameters can be determined
+by a call to nlstati.
+.ih
+SEE ALSO
+nlstat
+.endhelp
diff --git a/math/nlfit/doc/nlstat.hlp b/math/nlfit/doc/nlstat.hlp
new file mode 100644
index 00000000..a745a663
--- /dev/null
+++ b/math/nlfit/doc/nlstat.hlp
@@ -0,0 +1,57 @@
+.help nlstat Feb91 "Nlfit Package"
+.ih
+NAME
+nlstat[ird] -- get an NLFIT parameter
+.ih
+SYNOPSIS
+include <math/nlfit.h>
+
+[ird]val = nlstat[ird] (nl, parameter)
+
+.nf
+pointer	nl		# curve descriptor
+int	parameter	# parameter to be returned
+.fi
+.ih
+ARGUMENTS
+.ls nl     
+The pointer to the curve descriptor structure.
+.le
+.ls parameter
+Parameter to be return.  Definitions in nlfit.h are:
+
+.nf
+NLNPARAMS	integer		# Number of parameters
+NLNFPARAMS	integer         # Number of fitted parameters
+NLITMAX		integer		# Maximum number of iterations
+NLITER		integer		# Current number of iterations
+NLNPTS		integer         # Number of points
+NLSUMSQ		real/double	# Current reduced chi-squared
+NLOLDSQ		real/double     # Previous reduced chi-squared
+NLLAMBDA	real/double     # Value of lambda factor
+NLTOL		real/double	# Fitting tolerance in %chi-squared
+NLSCATTER	real/double     # Mean scatter in the fit
+.fi
+.le
+.ih
+DESCRIPTION
+The values of integer, real or double  parameters are returned.
+The parameters include the number of parameters, the number of fitted
+parameters, the maximum number of iterations, the number of iterations,
+the total number of points, the current chi-squared, the previous
+chi-squared, the lambda factor, the fitting tolerance and the fitted
+scatter term.
+.ih
+EXAMPLES
+.nf
+include <math/nlfit.h>
+
+int	nlstati()
+
+call malloc (buf, nlstati (nl, NLNPARAMS), TY_REAL)
+call nlpgetr (nl, Memr[buf], nparams)
+.fi
+.ih
+SEE ALSO
+nlpget
+.endhelp
diff --git a/math/nlfit/doc/nlvector.hlp b/math/nlfit/doc/nlvector.hlp
new file mode 100644
index 00000000..98308cc3
--- /dev/null
+++ b/math/nlfit/doc/nlvector.hlp
@@ -0,0 +1,43 @@
+.help nlvector Feb91 "Nlfit Package"
+.ih
+NAME
+nlvector -- evaluate the fitted curve at a set of points
+.ih
+SYNOPSIS
+nlvector[rd] (nl, x, zfit, npts, nvars)
+
+.nf
+pointer		nl		# curve descriptor
+real/double	x[nvars*npts]	# array of variables stored as x[nvars,npts]
+real/double	zfit[npts]	# array of fitted function values
+int		npts		# number of data points
+int		nvars		# number of variables
+.fi
+.ih
+ARGUMENTS
+.ls nl   
+Pointer to the curve descriptor structure.
+.le
+.ls x     
+Array of variable values for all the data points.
+.le
+.ls zfit   
+Array of fitted function values.
+.le
+.ls npts   
+The number of data points at which the curve is to be evaluated.
+.le
+.ls nvars
+The number of variables in the fitted function.
+.le
+.ih
+DESCRIPTION
+Fit the curve to an array of data points.
+.ih
+NOTES
+NLVECTOR uses the coefficient array stored in the curfit descriptor
+structure.
+.ih
+SEE ALSO
+nleval
+.endhelp
diff --git a/math/nlfit/mkpkg b/math/nlfit/mkpkg
new file mode 100644
index 00000000..4573dfbf
--- /dev/null
+++ b/math/nlfit/mkpkg
@@ -0,0 +1,63 @@
+# The Non-linear Least-squares Fitting Package
+
+$checkout	libnlfit.a lib$
+$update		libnlfit.a
+$checkin	libnlfit.a lib$
+$exit
+
+tfiles:
+	$set	GEN = "$$generic -k -t rd"
+
+	$ifnewer (nlacpts.gx,  nlacptsr.x)	$(GEN) nlacpts.gx  $endif
+	$ifnewer (nlchomat.gx, nlchomatr.x)	$(GEN) nlchomat.gx $endif
+	$ifnewer (nldump.gx,   nldumpr.x)	$(GEN) nldump.gx   $endif
+	$ifnewer (nlerrors.gx, nlerrorsr.x)	$(GEN) nlerrors.gx $endif
+	$ifnewer (nleval.gx,   nlevalr.x)	$(GEN) nleval.gx   $endif
+	$ifnewer (nlfit.gx,    nlfitr.x)	$(GEN) nlfit.gx    $endif
+	$ifnewer (nlfitdef.gh, nlfitdefr.h)	$(GEN) nlfitdef.gh $endif
+	$ifnewer (nlfree.gx,   nlfreer.x)	$(GEN) nlfree.gx   $endif
+	$ifnewer (nlinit.gx,   nlinitr.x)	$(GEN) nlinit.gx   $endif
+	$ifnewer (nliter.gx,   nliterr.x)	$(GEN) nliter.gx   $endif
+	$ifnewer (nlpget.gx,   nlpgetr.x)	$(GEN) nlpget.gx   $endif
+	$ifnewer (nlsolve.gx,  nlsolver.x)	$(GEN) nlsolve.gx  $endif
+	$ifnewer (nlstat.gx,   nlstatr.x)	$(GEN) nlstat.gx   $endif
+	$ifnewer (nlvector.gx, nlvectorr.x)	$(GEN) nlvector.gx $endif
+	$ifnewer (nlzero.gx,   nlzeror.x)	$(GEN) nlzero.gx   $endif
+	;
+
+libnlfit.a:
+
+	$ifeq (USE_GENERIC, yes) $call tfiles $endif
+
+	nlacptsd.x	<math/nlfit.h>   "nlfitdefd.h"
+	nlacptsr.x	<math/nlfit.h>   "nlfitdefr.h"
+	nlchomatd.x	<math/nlfit.h>   "nlfitdefd.h" <mach.h>
+	nlchomatr.x	<math/nlfit.h>   "nlfitdefr.h" <mach.h>
+	nldumpd.x	"nlfitdefd.h"
+	nldumpr.x	"nlfitdefr.h"
+	nlerrmsg.x	<math/nlfit.h>
+	nlerrorsd.x	<math/nlfit.h>   "nlfitdefd.h" <mach.h>
+	nlerrorsr.x	<math/nlfit.h>   "nlfitdefr.h" <mach.h>
+	nlevald.x	<math/nlfit.h>   "nlfitdefd.h"
+	nlevalr.x	<math/nlfit.h>   "nlfitdefr.h"
+	nlfitd.x	<math/nlfit.h>   "nlfitdefd.h" <mach.h>
+	nlfitr.x	<math/nlfit.h>   "nlfitdefr.h" <mach.h>
+	nlfreed.x	"nlfitdefd.h"
+	nlfreer.x	"nlfitdefr.h"
+	nlinitd.x	"nlfitdefd.h"
+	nlinitr.x	"nlfitdefr.h"
+	nliterd.x	<math/nlfit.h>   "nlfitdefd.h" <mach.h>
+	nliterr.x	<math/nlfit.h>   "nlfitdefr.h" <mach.h>
+	nllist.x	
+	nlpgetd.x	"nlfitdefd.h"
+	nlpgetr.x	"nlfitdefr.h"
+	nlsolved.x	<math/nlfit.h>   "nlfitdefd.h"
+	nlsolver.x	<math/nlfit.h>   "nlfitdefr.h"
+	nlstati.x	<math/nlfit.h>   "nlfitdefr.h"
+	nlstatd.x	<math/nlfit.h>   "nlfitdefd.h"
+	nlstatr.x	<math/nlfit.h>   "nlfitdefr.h"
+	nlvectord.x	<math/nlfit.h>   "nlfitdefd.h"
+	nlvectorr.x	<math/nlfit.h>   "nlfitdefr.h"
+	nlzerod.x	"nlfitdefd.h"
+	nlzeror.x	"nlfitdefr.h"
+	;
diff --git a/math/nlfit/nlacpts.gx b/math/nlfit/nlacpts.gx
new file mode 100644
index 00000000..a9f947ba
--- /dev/null
+++ b/math/nlfit/nlacpts.gx
@@ -0,0 +1,111 @@
+include	<math/nlfit.h>
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+define	VAR	(($1 - 1) * $2 + 1)
+
+# NLACPTS - Accumulate a series of data points.
+
+PIXEL procedure nlacpts$t (nl, x, z, w, npts, nvars)
+
+pointer	nl		# pointer to nl fitting structure
+PIXEL	x[ARB]		# independent variables (npts * nvars)
+PIXEL	z[ARB]		# function values (npts)
+PIXEL	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+int	i, nfree
+PIXEL	sum, z0, dz
+
+begin
+	# Zero the accumulators.
+	call aclr$t (ALPHA(NL_ALPHA(nl)), NL_NFPARAMS(nl) ** 2)
+	call aclr$t (BETA(NL_BETA(nl)), NL_NFPARAMS(nl))
+
+	# Accumulate the points into the fit.
+	NL_NPTS (nl) = npts
+	sum = PIXEL(0.0)
+	do i = 1, npts {
+	    call zcall7 (NL_DFUNC(nl), x[VAR (i, nvars)], nvars,
+		PARAM(NL_PARAM(nl)), DPARAM(NL_DELPARAM(nl)), NL_NPARAMS(nl),
+		z0, DERIV(NL_DERIV(nl)))
+	    dz = z[i] - z0
+	    call nl_accum$t (DERIV(NL_DERIV(nl)), PLIST(NL_PLIST(nl)),
+		w[i], dz, NL_NFPARAMS(nl), ALPHA(NL_ALPHA(nl)), 
+		BETA(NL_BETA(nl)))
+	    sum = sum + w[i] * dz * dz
+	}
+
+	# Return the reduced chisqr.
+	nfree = NL_NPTS(nl) - NL_NFPARAMS(nl)
+	if (nfree <= 0)
+	    return (PIXEL (0.0))
+	else
+	    return (sum / nfree)
+end
+
+
+# NLRESID -- Recompute the residuals
+
+PIXEL procedure nlresid$t (nl, x, z, w, npts, nvars)
+
+pointer	nl		# pointer to nl fitting structure
+PIXEL	x[ARB]		# independent variables (npts * nvars)
+PIXEL	z[ARB]		# function values (npts)
+PIXEL	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+int	i, nfree
+PIXEL	sum, z0, dz
+
+begin
+	# Accumulate the residuals.
+	NL_NPTS(nl) = npts
+	sum = PIXEL (0.0)
+	do i = 1, npts {
+	    call zcall5 (NL_FUNC(nl), x[VAR (i, nvars)], nvars, TRY(NL_TRY(nl)),
+		NL_NPARAMS(nl), z0)
+	    dz = z[i] - z0
+	    sum = sum + dz * dz * w[i]
+	}
+
+	# Compute the reduced chisqr.
+	nfree = NL_NPTS(nl) - NL_NFPARAMS(nl)
+	if (nfree <= 0)
+	    return (PIXEL (0.0))
+	else
+	    return (sum / nfree)
+end
+
+
+# NL_ACCUM -- Accumulate a single point into the fit
+
+procedure nl_accum$t (deriv, list, w, dz, nfit, alpha, beta)
+
+PIXEL	deriv[ARB]	# derivatives
+int	list[ARB]	# list of active parameters
+PIXEL	w		# weight
+PIXEL	dz		# difference between data and model
+int	nfit		# number of fitted parameters
+PIXEL	alpha[nfit,ARB]	# alpha matrix
+PIXEL	beta[nfit]	# beta matrix
+
+int	i, j, k
+PIXEL	wt
+
+begin
+	do i = 1, nfit {
+	    wt = deriv[list[i]] * w
+	    k = 1
+	    do j = i, nfit {
+	        alpha[k,i] = alpha[k,i] + wt * deriv[list[j]]
+		k = k + 1
+	    }
+	    beta[i] = beta[i] + dz * wt
+	}
+end
diff --git a/math/nlfit/nlacptsd.x b/math/nlfit/nlacptsd.x
new file mode 100644
index 00000000..b08a897f
--- /dev/null
+++ b/math/nlfit/nlacptsd.x
@@ -0,0 +1,107 @@
+include	<math/nlfit.h>
+include "nlfitdefd.h"
+
+define	VAR	(($1 - 1) * $2 + 1)
+
+# NLACPTS - Accumulate a series of data points.
+
+double procedure nlacptsd (nl, x, z, w, npts, nvars)
+
+pointer	nl		# pointer to nl fitting structure
+double	x[ARB]		# independent variables (npts * nvars)
+double	z[ARB]		# function values (npts)
+double	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+int	i, nfree
+double	sum, z0, dz
+
+begin
+	# Zero the accumulators.
+	call aclrd (ALPHA(NL_ALPHA(nl)), NL_NFPARAMS(nl) ** 2)
+	call aclrd (BETA(NL_BETA(nl)), NL_NFPARAMS(nl))
+
+	# Accumulate the points into the fit.
+	NL_NPTS (nl) = npts
+	sum = double(0.0)
+	do i = 1, npts {
+	    call zcall7 (NL_DFUNC(nl), x[VAR (i, nvars)], nvars,
+		PARAM(NL_PARAM(nl)), DPARAM(NL_DELPARAM(nl)), NL_NPARAMS(nl),
+		z0, DERIV(NL_DERIV(nl)))
+	    dz = z[i] - z0
+	    call nl_accumd (DERIV(NL_DERIV(nl)), PLIST(NL_PLIST(nl)),
+		w[i], dz, NL_NFPARAMS(nl), ALPHA(NL_ALPHA(nl)), 
+		BETA(NL_BETA(nl)))
+	    sum = sum + w[i] * dz * dz
+	}
+
+	# Return the reduced chisqr.
+	nfree = NL_NPTS(nl) - NL_NFPARAMS(nl)
+	if (nfree <= 0)
+	    return (double (0.0))
+	else
+	    return (sum / nfree)
+end
+
+
+# NLRESID -- Recompute the residuals
+
+double procedure nlresidd (nl, x, z, w, npts, nvars)
+
+pointer	nl		# pointer to nl fitting structure
+double	x[ARB]		# independent variables (npts * nvars)
+double	z[ARB]		# function values (npts)
+double	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+int	i, nfree
+double	sum, z0, dz
+
+begin
+	# Accumulate the residuals.
+	NL_NPTS(nl) = npts
+	sum = double (0.0)
+	do i = 1, npts {
+	    call zcall5 (NL_FUNC(nl), x[VAR (i, nvars)], nvars, TRY(NL_TRY(nl)),
+		NL_NPARAMS(nl), z0)
+	    dz = z[i] - z0
+	    sum = sum + dz * dz * w[i]
+	}
+
+	# Compute the reduced chisqr.
+	nfree = NL_NPTS(nl) - NL_NFPARAMS(nl)
+	if (nfree <= 0)
+	    return (double (0.0))
+	else
+	    return (sum / nfree)
+end
+
+
+# NL_ACCUM -- Accumulate a single point into the fit
+
+procedure nl_accumd (deriv, list, w, dz, nfit, alpha, beta)
+
+double	deriv[ARB]	# derivatives
+int	list[ARB]	# list of active parameters
+double	w		# weight
+double	dz		# difference between data and model
+int	nfit		# number of fitted parameters
+double	alpha[nfit,ARB]	# alpha matrix
+double	beta[nfit]	# beta matrix
+
+int	i, j, k
+double	wt
+
+begin
+	do i = 1, nfit {
+	    wt = deriv[list[i]] * w
+	    k = 1
+	    do j = i, nfit {
+	        alpha[k,i] = alpha[k,i] + wt * deriv[list[j]]
+		k = k + 1
+	    }
+	    beta[i] = beta[i] + dz * wt
+	}
+end
diff --git a/math/nlfit/nlacptsr.x b/math/nlfit/nlacptsr.x
new file mode 100644
index 00000000..d68daf72
--- /dev/null
+++ b/math/nlfit/nlacptsr.x
@@ -0,0 +1,107 @@
+include	<math/nlfit.h>
+include "nlfitdefr.h"
+
+define	VAR	(($1 - 1) * $2 + 1)
+
+# NLACPTS - Accumulate a series of data points.
+
+real procedure nlacptsr (nl, x, z, w, npts, nvars)
+
+pointer	nl		# pointer to nl fitting structure
+real	x[ARB]		# independent variables (npts * nvars)
+real	z[ARB]		# function values (npts)
+real	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+int	i, nfree
+real	sum, z0, dz
+
+begin
+	# Zero the accumulators.
+	call aclrr (ALPHA(NL_ALPHA(nl)), NL_NFPARAMS(nl) ** 2)
+	call aclrr (BETA(NL_BETA(nl)), NL_NFPARAMS(nl))
+
+	# Accumulate the points into the fit.
+	NL_NPTS (nl) = npts
+	sum = real(0.0)
+	do i = 1, npts {
+	    call zcall7 (NL_DFUNC(nl), x[VAR (i, nvars)], nvars,
+		PARAM(NL_PARAM(nl)), DPARAM(NL_DELPARAM(nl)), NL_NPARAMS(nl),
+		z0, DERIV(NL_DERIV(nl)))
+	    dz = z[i] - z0
+	    call nl_accumr (DERIV(NL_DERIV(nl)), PLIST(NL_PLIST(nl)),
+		w[i], dz, NL_NFPARAMS(nl), ALPHA(NL_ALPHA(nl)), 
+		BETA(NL_BETA(nl)))
+	    sum = sum + w[i] * dz * dz
+	}
+
+	# Return the reduced chisqr.
+	nfree = NL_NPTS(nl) - NL_NFPARAMS(nl)
+	if (nfree <= 0)
+	    return (real (0.0))
+	else
+	    return (sum / nfree)
+end
+
+
+# NLRESID -- Recompute the residuals
+
+real procedure nlresidr (nl, x, z, w, npts, nvars)
+
+pointer	nl		# pointer to nl fitting structure
+real	x[ARB]		# independent variables (npts * nvars)
+real	z[ARB]		# function values (npts)
+real	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+int	i, nfree
+real	sum, z0, dz
+
+begin
+	# Accumulate the residuals.
+	NL_NPTS(nl) = npts
+	sum = real (0.0)
+	do i = 1, npts {
+	    call zcall5 (NL_FUNC(nl), x[VAR (i, nvars)], nvars, TRY(NL_TRY(nl)),
+		NL_NPARAMS(nl), z0)
+	    dz = z[i] - z0
+	    sum = sum + dz * dz * w[i]
+	}
+
+	# Compute the reduced chisqr.
+	nfree = NL_NPTS(nl) - NL_NFPARAMS(nl)
+	if (nfree <= 0)
+	    return (real (0.0))
+	else
+	    return (sum / nfree)
+end
+
+
+# NL_ACCUM -- Accumulate a single point into the fit
+
+procedure nl_accumr (deriv, list, w, dz, nfit, alpha, beta)
+
+real	deriv[ARB]	# derivatives
+int	list[ARB]	# list of active parameters
+real	w		# weight
+real	dz		# difference between data and model
+int	nfit		# number of fitted parameters
+real	alpha[nfit,ARB]	# alpha matrix
+real	beta[nfit]	# beta matrix
+
+int	i, j, k
+real	wt
+
+begin
+	do i = 1, nfit {
+	    wt = deriv[list[i]] * w
+	    k = 1
+	    do j = i, nfit {
+	        alpha[k,i] = alpha[k,i] + wt * deriv[list[j]]
+		k = k + 1
+	    }
+	    beta[i] = beta[i] + dz * wt
+	}
+end
diff --git a/math/nlfit/nlchomat.gx b/math/nlfit/nlchomat.gx
new file mode 100644
index 00000000..5a36c63c
--- /dev/null
+++ b/math/nlfit/nlchomat.gx
@@ -0,0 +1,130 @@
+include <mach.h>
+include <math/nlfit.h>
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+
+# NL_CHFAC -- Routine to calculate the Cholesky factorization of a
+# symmetric, positive semi-definite banded matrix. This routines was
+# adapted from the bchfac.f routine described in "A Practical Guide
+# to Splines", Carl de Boor (1978).
+
+procedure nl_chfac$t (matrix, nbands, nrows, matfac, ier)
+
+PIXEL   matrix[nbands, nrows]	# data matrix
+int	nbands			# number of bands
+int	nrows			# number of rows
+PIXEL   matfac[nbands, nrows]	# Cholesky factorization
+int	ier			# error code
+
+int	i, n, j, imax, jmax
+PIXEL   ratio
+
+begin
+	# Test for a single element matrix.
+	if (nrows == 1) {
+	    if (matrix[1,1] > PIXEL (0.0))
+	        matfac[1,1] = 1. / matrix[1,1]
+	    return
+	}
+		
+	# Copy the original matrix into matfac.
+	do n = 1, nrows {
+	    do j = 1, nbands
+		matfac[j,n] = matrix[j,n]
+	}
+
+	# Compute the factorization of the matrix.
+	do n = 1, nrows {
+
+	    # Test to see if matrix is singular.
+	    if (((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= EPSILON$T) {
+	    #if (((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= PIXEL(0.0)) {
+		do j = 1, nbands
+		    matfac[j,n] = PIXEL (0.0)
+		ier = SINGULAR
+		next
+	    }
+
+	    matfac[1,n] = PIXEL (1.0) / matfac[1,n]
+	    imax = min (nbands - 1, nrows - n)
+	    if (imax < 1)
+		next
+
+	    jmax = imax
+	    do i = 1, imax {
+		ratio = matfac[i+1,n] * matfac[1,n]
+		do j = 1, jmax
+		    matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
+		jmax = jmax - 1
+		matfac[i+1,n] = ratio
+	    }
+	}
+end
+
+
+# NL_CHSLV -- Solve the matrix whose Cholesky factorization was calculated in
+# NL_CHFAC for the coefficients. This routine was adapted from bchslv.f
+# described in "A Practical Guide to Splines", by Carl de Boor (1978).
+
+procedure nl_chslv$t (matfac, nbands, nrows, vector, coeff)
+
+PIXEL	matfac[nbands,nrows] 		# Cholesky factorization
+int	nbands				# number of bands
+int	nrows				# number of rows
+PIXEL	vector[nrows]			# right side of matrix equation
+PIXEL	coeff[nrows]			# coefficients
+
+int	i, n, j, jmax, nbndm1
+
+begin
+	# Test for a single element matrix.
+	if (nrows == 1) {
+	    coeff[1] = vector[1] * matfac[1,1]
+	    return
+	}
+
+	# Copy input vector to coefficients vector.
+	do i = 1, nrows
+	    coeff[i] = vector[i]
+
+	# Perform forward substitution.
+	nbndm1 = nbands - 1
+	do n = 1, nrows {
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+	        do j = 1, jmax
+		    coeff[j+n] = coeff[j+n] - matfac[j+1,n] * coeff[n]
+	    }
+	}
+
+	# Perform backward substitution.
+	for (n = nrows; n >= 1; n = n - 1) {
+	    coeff[n] = coeff[n] * matfac[1,n]
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+		do j = 1, jmax
+		    coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
+	    }
+	}
+end
+
+
+# NL_DAMP -- Procedure to add damping to matrix
+
+procedure nl_damp$t (inmatrix, outmatrix, constant, nbands, nrows)
+
+PIXEL	inmatrix[nbands,ARB]		# input matrix
+PIXEL	outmatrix[nbands,ARB]		# output matrix
+PIXEL	constant			# damping constant
+int	nbands, nrows			# dimensions of matrix
+
+int	i
+
+begin
+	do i = 1, nrows
+	    outmatrix[1,i] = inmatrix[1,i] * constant
+end
diff --git a/math/nlfit/nlchomatd.x b/math/nlfit/nlchomatd.x
new file mode 100644
index 00000000..775793ac
--- /dev/null
+++ b/math/nlfit/nlchomatd.x
@@ -0,0 +1,126 @@
+include <mach.h>
+include <math/nlfit.h>
+include "nlfitdefd.h"
+
+
+# NL_CHFAC -- Routine to calculate the Cholesky factorization of a
+# symmetric, positive semi-definite banded matrix. This routines was
+# adapted from the bchfac.f routine described in "A Practical Guide
+# to Splines", Carl de Boor (1978).
+
+procedure nl_chfacd (matrix, nbands, nrows, matfac, ier)
+
+double   matrix[nbands, nrows]	# data matrix
+int	nbands			# number of bands
+int	nrows			# number of rows
+double   matfac[nbands, nrows]	# Cholesky factorization
+int	ier			# error code
+
+int	i, n, j, imax, jmax
+double   ratio
+
+begin
+	# Test for a single element matrix.
+	if (nrows == 1) {
+	    if (matrix[1,1] > double (0.0))
+	        matfac[1,1] = 1. / matrix[1,1]
+	    return
+	}
+		
+	# Copy the original matrix into matfac.
+	do n = 1, nrows {
+	    do j = 1, nbands
+		matfac[j,n] = matrix[j,n]
+	}
+
+	# Compute the factorization of the matrix.
+	do n = 1, nrows {
+
+	    # Test to see if matrix is singular.
+	    if (((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= EPSILOND) {
+	    #if (((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= PIXEL(0.0)) {
+		do j = 1, nbands
+		    matfac[j,n] = double (0.0)
+		ier = SINGULAR
+		next
+	    }
+
+	    matfac[1,n] = double (1.0) / matfac[1,n]
+	    imax = min (nbands - 1, nrows - n)
+	    if (imax < 1)
+		next
+
+	    jmax = imax
+	    do i = 1, imax {
+		ratio = matfac[i+1,n] * matfac[1,n]
+		do j = 1, jmax
+		    matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
+		jmax = jmax - 1
+		matfac[i+1,n] = ratio
+	    }
+	}
+end
+
+
+# NL_CHSLV -- Solve the matrix whose Cholesky factorization was calculated in
+# NL_CHFAC for the coefficients. This routine was adapted from bchslv.f
+# described in "A Practical Guide to Splines", by Carl de Boor (1978).
+
+procedure nl_chslvd (matfac, nbands, nrows, vector, coeff)
+
+double	matfac[nbands,nrows] 		# Cholesky factorization
+int	nbands				# number of bands
+int	nrows				# number of rows
+double	vector[nrows]			# right side of matrix equation
+double	coeff[nrows]			# coefficients
+
+int	i, n, j, jmax, nbndm1
+
+begin
+	# Test for a single element matrix.
+	if (nrows == 1) {
+	    coeff[1] = vector[1] * matfac[1,1]
+	    return
+	}
+
+	# Copy input vector to coefficients vector.
+	do i = 1, nrows
+	    coeff[i] = vector[i]
+
+	# Perform forward substitution.
+	nbndm1 = nbands - 1
+	do n = 1, nrows {
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+	        do j = 1, jmax
+		    coeff[j+n] = coeff[j+n] - matfac[j+1,n] * coeff[n]
+	    }
+	}
+
+	# Perform backward substitution.
+	for (n = nrows; n >= 1; n = n - 1) {
+	    coeff[n] = coeff[n] * matfac[1,n]
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+		do j = 1, jmax
+		    coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
+	    }
+	}
+end
+
+
+# NL_DAMP -- Procedure to add damping to matrix
+
+procedure nl_dampd (inmatrix, outmatrix, constant, nbands, nrows)
+
+double	inmatrix[nbands,ARB]		# input matrix
+double	outmatrix[nbands,ARB]		# output matrix
+double	constant			# damping constant
+int	nbands, nrows			# dimensions of matrix
+
+int	i
+
+begin
+	do i = 1, nrows
+	    outmatrix[1,i] = inmatrix[1,i] * constant
+end
diff --git a/math/nlfit/nlchomatr.x b/math/nlfit/nlchomatr.x
new file mode 100644
index 00000000..09f3a7b3
--- /dev/null
+++ b/math/nlfit/nlchomatr.x
@@ -0,0 +1,126 @@
+include <mach.h>
+include <math/nlfit.h>
+include "nlfitdefr.h"
+
+
+# NL_CHFAC -- Routine to calculate the Cholesky factorization of a
+# symmetric, positive semi-definite banded matrix. This routines was
+# adapted from the bchfac.f routine described in "A Practical Guide
+# to Splines", Carl de Boor (1978).
+
+procedure nl_chfacr (matrix, nbands, nrows, matfac, ier)
+
+real   matrix[nbands, nrows]	# data matrix
+int	nbands			# number of bands
+int	nrows			# number of rows
+real   matfac[nbands, nrows]	# Cholesky factorization
+int	ier			# error code
+
+int	i, n, j, imax, jmax
+real   ratio
+
+begin
+	# Test for a single element matrix.
+	if (nrows == 1) {
+	    if (matrix[1,1] > real (0.0))
+	        matfac[1,1] = 1. / matrix[1,1]
+	    return
+	}
+		
+	# Copy the original matrix into matfac.
+	do n = 1, nrows {
+	    do j = 1, nbands
+		matfac[j,n] = matrix[j,n]
+	}
+
+	# Compute the factorization of the matrix.
+	do n = 1, nrows {
+
+	    # Test to see if matrix is singular.
+	    if (((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= EPSILONR) {
+	    #if (((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= PIXEL(0.0)) {
+		do j = 1, nbands
+		    matfac[j,n] = real (0.0)
+		ier = SINGULAR
+		next
+	    }
+
+	    matfac[1,n] = real (1.0) / matfac[1,n]
+	    imax = min (nbands - 1, nrows - n)
+	    if (imax < 1)
+		next
+
+	    jmax = imax
+	    do i = 1, imax {
+		ratio = matfac[i+1,n] * matfac[1,n]
+		do j = 1, jmax
+		    matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
+		jmax = jmax - 1
+		matfac[i+1,n] = ratio
+	    }
+	}
+end
+
+
+# NL_CHSLV -- Solve the matrix whose Cholesky factorization was calculated in
+# NL_CHFAC for the coefficients. This routine was adapted from bchslv.f
+# described in "A Practical Guide to Splines", by Carl de Boor (1978).
+
+procedure nl_chslvr (matfac, nbands, nrows, vector, coeff)
+
+real	matfac[nbands,nrows] 		# Cholesky factorization
+int	nbands				# number of bands
+int	nrows				# number of rows
+real	vector[nrows]			# right side of matrix equation
+real	coeff[nrows]			# coefficients
+
+int	i, n, j, jmax, nbndm1
+
+begin
+	# Test for a single element matrix.
+	if (nrows == 1) {
+	    coeff[1] = vector[1] * matfac[1,1]
+	    return
+	}
+
+	# Copy input vector to coefficients vector.
+	do i = 1, nrows
+	    coeff[i] = vector[i]
+
+	# Perform forward substitution.
+	nbndm1 = nbands - 1
+	do n = 1, nrows {
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+	        do j = 1, jmax
+		    coeff[j+n] = coeff[j+n] - matfac[j+1,n] * coeff[n]
+	    }
+	}
+
+	# Perform backward substitution.
+	for (n = nrows; n >= 1; n = n - 1) {
+	    coeff[n] = coeff[n] * matfac[1,n]
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+		do j = 1, jmax
+		    coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
+	    }
+	}
+end
+
+
+# NL_DAMP -- Procedure to add damping to matrix
+
+procedure nl_dampr (inmatrix, outmatrix, constant, nbands, nrows)
+
+real	inmatrix[nbands,ARB]		# input matrix
+real	outmatrix[nbands,ARB]		# output matrix
+real	constant			# damping constant
+int	nbands, nrows			# dimensions of matrix
+
+int	i
+
+begin
+	do i = 1, nrows
+	    outmatrix[1,i] = inmatrix[1,i] * constant
+end
diff --git a/math/nlfit/nldump.gx b/math/nlfit/nldump.gx
new file mode 100644
index 00000000..aa5899bd
--- /dev/null
+++ b/math/nlfit/nldump.gx
@@ -0,0 +1,164 @@
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+# NL_DUMP -- Dump NLFIT structure to a file
+
+procedure nl_dump$t (fd, nl)
+
+int	fd		# file descriptor
+pointer	nl		# NLFIT descriptor
+
+int	i, npars, nfpars
+
+begin
+	# Test NLFIT pointer
+	if (nl == NULL) {
+	    call fprintf (fd, "\n****** nl_dump: Null NLFIT pointer\n")
+	    call flush (fd)
+	    return
+	}
+
+	# File and NLFIT descriptors
+	call fprintf (fd, "\n****** nl_dump: (fd=%d), (nl=%d)\n")
+	    call pargi (fd)
+	    call pargi (nl)
+	call flush (fd)
+
+	# Dump function and derivative addresses
+	call fprintf (fd, "Fitting function pointer    = %d\n")
+	    call pargi (NL_FUNC (nl))
+	call fprintf (fd, "Derivative function pointer = %d\n")
+	    call pargi (NL_DFUNC (nl))
+	call flush (fd)
+
+	# Number of parameters
+	npars = NL_NPARAMS (nl)
+	nfpars = NL_NFPARAMS (nl)
+	call fprintf (fd, "Number of parameters        = %d\n")
+	    call pargi (npars)
+	call fprintf (fd, "Number of fitted parameters = %d\n")
+	    call pargi (nfpars)
+	call flush (fd)
+
+	# Fit parameters
+	call fprintf (fd, "Max number of iterations    = %d\n")
+	    call pargi (NL_ITMAX (nl))
+	call fprintf (fd, "Tolerance for convergence   = %g\n")
+	    call parg$t (NL_TOL (nl))
+	call flush (fd)
+
+	# Sums
+	call fprintf (fd, "Damping factor = %g\n")
+	    call parg$t (NL_LAMBDA (nl))
+	call fprintf (fd, "Sum of residuals squared last iteration = %g\n")
+	    call parg$t (NL_OLDSQ (nl))
+	call fprintf (fd, "Sum of residuals squared                = %g\n")
+	    call parg$t (NL_SUMSQ (nl))
+	call flush (fd)
+
+	# Counters
+	call fprintf (fd, "Iteration counter       = %d\n")
+	    call pargi (NL_ITER (nl))
+	call fprintf (fd, "Number of points in fit = %d\n")
+	    call pargi (NL_NPTS (nl))
+	call flush (fd)
+
+	# Parameter values
+	call fprintf (fd, "Parameter values (%d):\n")
+	    call pargi (NL_PARAM (nl))
+	if (NL_PARAM (nl) != NULL) {
+	    do i = 1, npars {
+		call fprintf (fd, "%d -> %g\n")
+		    call pargi (i)
+		    call parg$t (Mem$t[NL_PARAM (nl) + i - 1])
+	    }
+	} else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Parameter errors
+	call fprintf (fd, "Parameter errors (%d):\n")
+	    call pargi (NL_DPARAM (nl))
+	if (NL_DPARAM (nl) != NULL) {
+	    do i = 1, npars {
+		call fprintf (fd, "%d -> %g\n")
+		    call pargi (i)
+		    call parg$t (Mem$t[NL_DPARAM (nl) + i - 1])
+	    }
+	} else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Parameter list
+	call fprintf (fd, "Parameter list (%d):\n")
+	    call pargi (NL_PLIST (nl))
+	if (NL_PLIST (nl) != NULL) {
+	    do i = 1, npars {
+		call fprintf (fd, "%d -> %d\n")
+		    call pargi (i)
+		    call pargi (Memi[NL_PLIST (nl) + i - 1])
+	    }
+	} else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Alpha matrix
+	call fprintf (fd, "Alpha matrix (%d):\n")
+	    call pargi (NL_ALPHA (nl))
+	if (NL_ALPHA (nl) != NULL)
+	    call nl_adump$t (fd, Mem$t[NL_ALPHA (nl)], nfpars, nfpars)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Beta matrix
+	call fprintf (fd, "Beta matrix (%d):\n")
+	    call pargi (NL_BETA (nl))
+	if (NL_BETA (nl) != NULL)
+	    call nl_adump$t (fd, Mem$t[NL_BETA (nl)], nfpars, 1)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Covariance matrix
+	call fprintf (fd, "Covariance matrix (%d):\n")
+	    call pargi (NL_COVAR (nl))
+	if (NL_COVAR (nl) != NULL)
+	    call nl_adump$t (fd, Mem$t[NL_COVAR (nl)], nfpars, nfpars)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Cholesky factorization
+	call fprintf (fd, "Cholesky factorization matrix (%d):\n")
+	    call pargi (NL_CHOFAC (nl))
+	if (NL_CHOFAC (nl) != NULL)
+	    call nl_adump$t (fd, Mem$t[NL_CHOFAC (nl)], nfpars, nfpars)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+end
+
+
+# NL_ADUMP -- Dump array to file
+
+procedure nl_adump$t (fd, a, nrows, ncols)
+
+int	fd			# file descriptor
+PIXEL	a[nrows, ncols]		# array
+int	nrows, ncols		# dimension
+
+int	i, j
+
+begin
+	do i = 1, nrows {
+	    do j = 1, ncols {
+		call fprintf (fd, "%g  ")
+		    call parg$t (a[i, j])
+	    }
+	    call fprintf (fd, "\n")
+	}
+end
diff --git a/math/nlfit/nldumpd.x b/math/nlfit/nldumpd.x
new file mode 100644
index 00000000..f4c31d7d
--- /dev/null
+++ b/math/nlfit/nldumpd.x
@@ -0,0 +1,160 @@
+include "nlfitdefd.h"
+
+# NL_DUMP -- Dump NLFIT structure to a file
+
+procedure nl_dumpd (fd, nl)
+
+int	fd		# file descriptor
+pointer	nl		# NLFIT descriptor
+
+int	i, npars, nfpars
+
+begin
+	# Test NLFIT pointer
+	if (nl == NULL) {
+	    call fprintf (fd, "\n****** nl_dump: Null NLFIT pointer\n")
+	    call flush (fd)
+	    return
+	}
+
+	# File and NLFIT descriptors
+	call fprintf (fd, "\n****** nl_dump: (fd=%d), (nl=%d)\n")
+	    call pargi (fd)
+	    call pargi (nl)
+	call flush (fd)
+
+	# Dump function and derivative addresses
+	call fprintf (fd, "Fitting function pointer    = %d\n")
+	    call pargi (NL_FUNC (nl))
+	call fprintf (fd, "Derivative function pointer = %d\n")
+	    call pargi (NL_DFUNC (nl))
+	call flush (fd)
+
+	# Number of parameters
+	npars = NL_NPARAMS (nl)
+	nfpars = NL_NFPARAMS (nl)
+	call fprintf (fd, "Number of parameters        = %d\n")
+	    call pargi (npars)
+	call fprintf (fd, "Number of fitted parameters = %d\n")
+	    call pargi (nfpars)
+	call flush (fd)
+
+	# Fit parameters
+	call fprintf (fd, "Max number of iterations    = %d\n")
+	    call pargi (NL_ITMAX (nl))
+	call fprintf (fd, "Tolerance for convergence   = %g\n")
+	    call pargd (NL_TOL (nl))
+	call flush (fd)
+
+	# Sums
+	call fprintf (fd, "Damping factor = %g\n")
+	    call pargd (NL_LAMBDA (nl))
+	call fprintf (fd, "Sum of residuals squared last iteration = %g\n")
+	    call pargd (NL_OLDSQ (nl))
+	call fprintf (fd, "Sum of residuals squared                = %g\n")
+	    call pargd (NL_SUMSQ (nl))
+	call flush (fd)
+
+	# Counters
+	call fprintf (fd, "Iteration counter       = %d\n")
+	    call pargi (NL_ITER (nl))
+	call fprintf (fd, "Number of points in fit = %d\n")
+	    call pargi (NL_NPTS (nl))
+	call flush (fd)
+
+	# Parameter values
+	call fprintf (fd, "Parameter values (%d):\n")
+	    call pargi (NL_PARAM (nl))
+	if (NL_PARAM (nl) != NULL) {
+	    do i = 1, npars {
+		call fprintf (fd, "%d -> %g\n")
+		    call pargi (i)
+		    call pargd (Memd[NL_PARAM (nl) + i - 1])
+	    }
+	} else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Parameter errors
+	call fprintf (fd, "Parameter errors (%d):\n")
+	    call pargi (NL_DPARAM (nl))
+	if (NL_DPARAM (nl) != NULL) {
+	    do i = 1, npars {
+		call fprintf (fd, "%d -> %g\n")
+		    call pargi (i)
+		    call pargd (Memd[NL_DPARAM (nl) + i - 1])
+	    }
+	} else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Parameter list
+	call fprintf (fd, "Parameter list (%d):\n")
+	    call pargi (NL_PLIST (nl))
+	if (NL_PLIST (nl) != NULL) {
+	    do i = 1, npars {
+		call fprintf (fd, "%d -> %d\n")
+		    call pargi (i)
+		    call pargi (Memi[NL_PLIST (nl) + i - 1])
+	    }
+	} else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Alpha matrix
+	call fprintf (fd, "Alpha matrix (%d):\n")
+	    call pargi (NL_ALPHA (nl))
+	if (NL_ALPHA (nl) != NULL)
+	    call nl_adumpd (fd, Memd[NL_ALPHA (nl)], nfpars, nfpars)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Beta matrix
+	call fprintf (fd, "Beta matrix (%d):\n")
+	    call pargi (NL_BETA (nl))
+	if (NL_BETA (nl) != NULL)
+	    call nl_adumpd (fd, Memd[NL_BETA (nl)], nfpars, 1)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Covariance matrix
+	call fprintf (fd, "Covariance matrix (%d):\n")
+	    call pargi (NL_COVAR (nl))
+	if (NL_COVAR (nl) != NULL)
+	    call nl_adumpd (fd, Memd[NL_COVAR (nl)], nfpars, nfpars)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Cholesky factorization
+	call fprintf (fd, "Cholesky factorization matrix (%d):\n")
+	    call pargi (NL_CHOFAC (nl))
+	if (NL_CHOFAC (nl) != NULL)
+	    call nl_adumpd (fd, Memd[NL_CHOFAC (nl)], nfpars, nfpars)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+end
+
+
+# NL_ADUMP -- Dump array to file
+
+procedure nl_adumpd (fd, a, nrows, ncols)
+
+int	fd			# file descriptor
+double	a[nrows, ncols]		# array
+int	nrows, ncols		# dimension
+
+int	i, j
+
+begin
+	do i = 1, nrows {
+	    do j = 1, ncols {
+		call fprintf (fd, "%g  ")
+		    call pargd (a[i, j])
+	    }
+	    call fprintf (fd, "\n")
+	}
+end
diff --git a/math/nlfit/nldumpr.x b/math/nlfit/nldumpr.x
new file mode 100644
index 00000000..a81c6366
--- /dev/null
+++ b/math/nlfit/nldumpr.x
@@ -0,0 +1,160 @@
+include "nlfitdefr.h"
+
+# NL_DUMP -- Dump NLFIT structure to a file
+
+procedure nl_dumpr (fd, nl)
+
+int	fd		# file descriptor
+pointer	nl		# NLFIT descriptor
+
+int	i, npars, nfpars
+
+begin
+	# Test NLFIT pointer
+	if (nl == NULL) {
+	    call fprintf (fd, "\n****** nl_dump: Null NLFIT pointer\n")
+	    call flush (fd)
+	    return
+	}
+
+	# File and NLFIT descriptors
+	call fprintf (fd, "\n****** nl_dump: (fd=%d), (nl=%d)\n")
+	    call pargi (fd)
+	    call pargi (nl)
+	call flush (fd)
+
+	# Dump function and derivative addresses
+	call fprintf (fd, "Fitting function pointer    = %d\n")
+	    call pargi (NL_FUNC (nl))
+	call fprintf (fd, "Derivative function pointer = %d\n")
+	    call pargi (NL_DFUNC (nl))
+	call flush (fd)
+
+	# Number of parameters
+	npars = NL_NPARAMS (nl)
+	nfpars = NL_NFPARAMS (nl)
+	call fprintf (fd, "Number of parameters        = %d\n")
+	    call pargi (npars)
+	call fprintf (fd, "Number of fitted parameters = %d\n")
+	    call pargi (nfpars)
+	call flush (fd)
+
+	# Fit parameters
+	call fprintf (fd, "Max number of iterations    = %d\n")
+	    call pargi (NL_ITMAX (nl))
+	call fprintf (fd, "Tolerance for convergence   = %g\n")
+	    call pargr (NL_TOL (nl))
+	call flush (fd)
+
+	# Sums
+	call fprintf (fd, "Damping factor = %g\n")
+	    call pargr (NL_LAMBDA (nl))
+	call fprintf (fd, "Sum of residuals squared last iteration = %g\n")
+	    call pargr (NL_OLDSQ (nl))
+	call fprintf (fd, "Sum of residuals squared                = %g\n")
+	    call pargr (NL_SUMSQ (nl))
+	call flush (fd)
+
+	# Counters
+	call fprintf (fd, "Iteration counter       = %d\n")
+	    call pargi (NL_ITER (nl))
+	call fprintf (fd, "Number of points in fit = %d\n")
+	    call pargi (NL_NPTS (nl))
+	call flush (fd)
+
+	# Parameter values
+	call fprintf (fd, "Parameter values (%d):\n")
+	    call pargi (NL_PARAM (nl))
+	if (NL_PARAM (nl) != NULL) {
+	    do i = 1, npars {
+		call fprintf (fd, "%d -> %g\n")
+		    call pargi (i)
+		    call pargr (Memr[NL_PARAM (nl) + i - 1])
+	    }
+	} else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Parameter errors
+	call fprintf (fd, "Parameter errors (%d):\n")
+	    call pargi (NL_DPARAM (nl))
+	if (NL_DPARAM (nl) != NULL) {
+	    do i = 1, npars {
+		call fprintf (fd, "%d -> %g\n")
+		    call pargi (i)
+		    call pargr (Memr[NL_DPARAM (nl) + i - 1])
+	    }
+	} else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Parameter list
+	call fprintf (fd, "Parameter list (%d):\n")
+	    call pargi (NL_PLIST (nl))
+	if (NL_PLIST (nl) != NULL) {
+	    do i = 1, npars {
+		call fprintf (fd, "%d -> %d\n")
+		    call pargi (i)
+		    call pargi (Memi[NL_PLIST (nl) + i - 1])
+	    }
+	} else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Alpha matrix
+	call fprintf (fd, "Alpha matrix (%d):\n")
+	    call pargi (NL_ALPHA (nl))
+	if (NL_ALPHA (nl) != NULL)
+	    call nl_adumpr (fd, Memr[NL_ALPHA (nl)], nfpars, nfpars)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Beta matrix
+	call fprintf (fd, "Beta matrix (%d):\n")
+	    call pargi (NL_BETA (nl))
+	if (NL_BETA (nl) != NULL)
+	    call nl_adumpr (fd, Memr[NL_BETA (nl)], nfpars, 1)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Covariance matrix
+	call fprintf (fd, "Covariance matrix (%d):\n")
+	    call pargi (NL_COVAR (nl))
+	if (NL_COVAR (nl) != NULL)
+	    call nl_adumpr (fd, Memr[NL_COVAR (nl)], nfpars, nfpars)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+
+	# Cholesky factorization
+	call fprintf (fd, "Cholesky factorization matrix (%d):\n")
+	    call pargi (NL_CHOFAC (nl))
+	if (NL_CHOFAC (nl) != NULL)
+	    call nl_adumpr (fd, Memr[NL_CHOFAC (nl)], nfpars, nfpars)
+	else
+	    call fprintf (fd, "	Null pointer\n")
+	call flush (fd)
+end
+
+
+# NL_ADUMP -- Dump array to file
+
+procedure nl_adumpr (fd, a, nrows, ncols)
+
+int	fd			# file descriptor
+real	a[nrows, ncols]		# array
+int	nrows, ncols		# dimension
+
+int	i, j
+
+begin
+	do i = 1, nrows {
+	    do j = 1, ncols {
+		call fprintf (fd, "%g  ")
+		    call pargr (a[i, j])
+	    }
+	    call fprintf (fd, "\n")
+	}
+end
diff --git a/math/nlfit/nlerrmsg.x b/math/nlfit/nlerrmsg.x
new file mode 100644
index 00000000..e2b04b73
--- /dev/null
+++ b/math/nlfit/nlerrmsg.x
@@ -0,0 +1,24 @@
+include	<math/nlfit.h>
+
+# NLERRMSG -- Convert NLFIT error code into an error message.
+
+procedure nlerrmsg (ier, errmsg, maxch)
+
+int	ier			# NLFIT error code
+char	errmsg[maxch]		# output error message 
+int	maxch			# maximum number of chars
+
+begin
+	switch (ier) {
+	case DONE:
+	    call strcpy ("Solution converged", errmsg, maxch)
+	case SINGULAR:
+	    call strcpy ("Singular matrix", errmsg, maxch)
+	case NO_DEG_FREEDOM:
+	    call strcpy ("Too few points", errmsg, maxch)
+	case NOT_DONE:
+	    call strcpy ("Solution did not converge", errmsg, maxch)
+	default:
+	    call strcpy ("Unknown error code", errmsg, maxch)
+	}
+end
diff --git a/math/nlfit/nlerrors.gx b/math/nlfit/nlerrors.gx
new file mode 100644
index 00000000..061d2214
--- /dev/null
+++ b/math/nlfit/nlerrors.gx
@@ -0,0 +1,111 @@
+include <mach.h>
+include <math/nlfit.h>
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+define	COV	Mem$t[P2P($1)]	# element of COV
+
+
+# NLERRORS -- Procedure to calculate the reduced chi-squared of the fit
+# and the errors of the coefficients. First the variance
+# and the reduced chi-squared of the fit are estimated. If these two
+# quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+procedure nlerrors$t (nl, z, zfit, w, npts, variance, chisqr, errors)
+
+pointer	nl		# curve descriptor
+PIXEL	z[ARB]		# data points
+PIXEL	zfit[ARB]	# fitted data points
+PIXEL	w[ARB]		# array of weights
+int	npts		# number of points
+PIXEL	variance	# variance of the fit
+PIXEL	chisqr		# reduced chi-squared of fit (output)
+PIXEL	errors[ARB]	# errors in coefficients (output)
+
+int	i, n, nfree
+pointer	sp, covptr
+PIXEL   factor
+
+begin
+	# Allocate space for covariance vector.
+	call smark (sp)
+	call salloc (covptr, NL_NPARAMS(nl), TY_PIXEL)
+
+	# Estimate the variance and reduce chi-squared of the fit.
+	n = 0
+	variance = PIXEL (0.0)
+	chisqr = PIXEL (0.0)
+	do i = 1, npts {
+	    if (w[i] <= PIXEL (0.0))
+	        next
+	    factor = (z[i] - zfit[i]) ** 2
+	    variance = variance + factor
+	    chisqr = chisqr + factor * w[i]
+	    n = n + 1
+	}
+
+	# Calculate the reduced chi-squared.
+	nfree = n - NL_NFPARAMS(nl)
+	if (nfree  > 0) {
+	    variance = variance / nfree
+	    chisqr = chisqr / nfree
+	} else {
+	    variance = PIXEL (0.0)
+	    chisqr = PIXEL (0.0)
+	}
+
+	# If the variance equals the reduced chi_squared as in the case
+	# of uniform weights then scale the errors in the coefficients
+	# by the variance and not the reduced chi-squared
+
+	if (abs (chisqr - variance) <= EPSILON$T) {
+	    if (nfree > 0)
+		factor = chisqr
+	    else
+		factor = PIXEL (0.0)
+	} else
+	    factor = 1.
+
+	# Calculate the  errors in the coefficients.
+	call aclr$t (errors, NL_NPARAMS(nl))
+	call nlinvert$t (ALPHA(NL_ALPHA(nl)), CHOFAC(NL_CHOFAC(nl)),
+	    COV(covptr), errors, PLIST(NL_PLIST(nl)), NL_NFPARAMS(nl), factor)
+
+	call sfree (sp)
+end
+
+
+# NLINVERT -- Procedure to invert matrix and compute errors
+
+procedure nlinvert$t (alpha, chofac, cov, errors, list, nfit, variance)
+
+PIXEL	alpha[nfit,ARB]		# data matrix
+PIXEL	chofac[nfit, ARB]	# cholesky factorization
+PIXEL	cov[ARB]		# covariance vector
+PIXEL	errors[ARB]		# computed errors
+int	list[ARB]		# list of active parameters
+int	nfit			# number of fitted parameters
+PIXEL	variance		# variance of the fit
+
+int	i, ier
+
+begin
+	# Factorize the data matrix to determine the errors.
+	call nl_chfac$t (alpha, nfit, nfit, chofac, ier)
+
+	# Estimate the errors.
+	do i = 1, nfit {
+	    call aclr$t (cov, nfit)
+	    cov[i] = PIXEL (1.0)
+	    call nl_chslv$t (chofac, nfit, nfit, cov, cov)
+	    if (cov[i] >= PIXEL (0.0))
+	        errors[list[i]] = sqrt (cov[i] * variance)
+	    else
+		errors[list[i]] = PIXEL (0.0)
+	}
+end
diff --git a/math/nlfit/nlerrorsd.x b/math/nlfit/nlerrorsd.x
new file mode 100644
index 00000000..b23a7b36
--- /dev/null
+++ b/math/nlfit/nlerrorsd.x
@@ -0,0 +1,107 @@
+include <mach.h>
+include <math/nlfit.h>
+include "nlfitdefd.h"
+
+define	COV	Memd[P2P($1)]	# element of COV
+
+
+# NLERRORS -- Procedure to calculate the reduced chi-squared of the fit
+# and the errors of the coefficients. First the variance
+# and the reduced chi-squared of the fit are estimated. If these two
+# quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+procedure nlerrorsd (nl, z, zfit, w, npts, variance, chisqr, errors)
+
+pointer	nl		# curve descriptor
+double	z[ARB]		# data points
+double	zfit[ARB]	# fitted data points
+double	w[ARB]		# array of weights
+int	npts		# number of points
+double	variance	# variance of the fit
+double	chisqr		# reduced chi-squared of fit (output)
+double	errors[ARB]	# errors in coefficients (output)
+
+int	i, n, nfree
+pointer	sp, covptr
+double   factor
+
+begin
+	# Allocate space for covariance vector.
+	call smark (sp)
+	call salloc (covptr, NL_NPARAMS(nl), TY_DOUBLE)
+
+	# Estimate the variance and reduce chi-squared of the fit.
+	n = 0
+	variance = double (0.0)
+	chisqr = double (0.0)
+	do i = 1, npts {
+	    if (w[i] <= double (0.0))
+	        next
+	    factor = (z[i] - zfit[i]) ** 2
+	    variance = variance + factor
+	    chisqr = chisqr + factor * w[i]
+	    n = n + 1
+	}
+
+	# Calculate the reduced chi-squared.
+	nfree = n - NL_NFPARAMS(nl)
+	if (nfree  > 0) {
+	    variance = variance / nfree
+	    chisqr = chisqr / nfree
+	} else {
+	    variance = double (0.0)
+	    chisqr = double (0.0)
+	}
+
+	# If the variance equals the reduced chi_squared as in the case
+	# of uniform weights then scale the errors in the coefficients
+	# by the variance and not the reduced chi-squared
+
+	if (abs (chisqr - variance) <= EPSILOND) {
+	    if (nfree > 0)
+		factor = chisqr
+	    else
+		factor = double (0.0)
+	} else
+	    factor = 1.
+
+	# Calculate the  errors in the coefficients.
+	call aclrd (errors, NL_NPARAMS(nl))
+	call nlinvertd (ALPHA(NL_ALPHA(nl)), CHOFAC(NL_CHOFAC(nl)),
+	    COV(covptr), errors, PLIST(NL_PLIST(nl)), NL_NFPARAMS(nl), factor)
+
+	call sfree (sp)
+end
+
+
+# NLINVERT -- Procedure to invert matrix and compute errors
+
+procedure nlinvertd (alpha, chofac, cov, errors, list, nfit, variance)
+
+double	alpha[nfit,ARB]		# data matrix
+double	chofac[nfit, ARB]	# cholesky factorization
+double	cov[ARB]		# covariance vector
+double	errors[ARB]		# computed errors
+int	list[ARB]		# list of active parameters
+int	nfit			# number of fitted parameters
+double	variance		# variance of the fit
+
+int	i, ier
+
+begin
+	# Factorize the data matrix to determine the errors.
+	call nl_chfacd (alpha, nfit, nfit, chofac, ier)
+
+	# Estimate the errors.
+	do i = 1, nfit {
+	    call aclrd (cov, nfit)
+	    cov[i] = double (1.0)
+	    call nl_chslvd (chofac, nfit, nfit, cov, cov)
+	    if (cov[i] >= double (0.0))
+	        errors[list[i]] = sqrt (cov[i] * variance)
+	    else
+		errors[list[i]] = double (0.0)
+	}
+end
diff --git a/math/nlfit/nlerrorsr.x b/math/nlfit/nlerrorsr.x
new file mode 100644
index 00000000..40057b9c
--- /dev/null
+++ b/math/nlfit/nlerrorsr.x
@@ -0,0 +1,107 @@
+include <mach.h>
+include <math/nlfit.h>
+include "nlfitdefr.h"
+
+define	COV	Memr[P2P($1)]	# element of COV
+
+
+# NLERRORS -- Procedure to calculate the reduced chi-squared of the fit
+# and the errors of the coefficients. First the variance
+# and the reduced chi-squared of the fit are estimated. If these two
+# quantities are identical the variance is used to scale the errors
+# in the coefficients. The errors in the coefficients are proportional
+# to the inverse diagonal elements of MATRIX.
+
+procedure nlerrorsr (nl, z, zfit, w, npts, variance, chisqr, errors)
+
+pointer	nl		# curve descriptor
+real	z[ARB]		# data points
+real	zfit[ARB]	# fitted data points
+real	w[ARB]		# array of weights
+int	npts		# number of points
+real	variance	# variance of the fit
+real	chisqr		# reduced chi-squared of fit (output)
+real	errors[ARB]	# errors in coefficients (output)
+
+int	i, n, nfree
+pointer	sp, covptr
+real   factor
+
+begin
+	# Allocate space for covariance vector.
+	call smark (sp)
+	call salloc (covptr, NL_NPARAMS(nl), TY_REAL)
+
+	# Estimate the variance and reduce chi-squared of the fit.
+	n = 0
+	variance = real (0.0)
+	chisqr = real (0.0)
+	do i = 1, npts {
+	    if (w[i] <= real (0.0))
+	        next
+	    factor = (z[i] - zfit[i]) ** 2
+	    variance = variance + factor
+	    chisqr = chisqr + factor * w[i]
+	    n = n + 1
+	}
+
+	# Calculate the reduced chi-squared.
+	nfree = n - NL_NFPARAMS(nl)
+	if (nfree  > 0) {
+	    variance = variance / nfree
+	    chisqr = chisqr / nfree
+	} else {
+	    variance = real (0.0)
+	    chisqr = real (0.0)
+	}
+
+	# If the variance equals the reduced chi_squared as in the case
+	# of uniform weights then scale the errors in the coefficients
+	# by the variance and not the reduced chi-squared
+
+	if (abs (chisqr - variance) <= EPSILONR) {
+	    if (nfree > 0)
+		factor = chisqr
+	    else
+		factor = real (0.0)
+	} else
+	    factor = 1.
+
+	# Calculate the  errors in the coefficients.
+	call aclrr (errors, NL_NPARAMS(nl))
+	call nlinvertr (ALPHA(NL_ALPHA(nl)), CHOFAC(NL_CHOFAC(nl)),
+	    COV(covptr), errors, PLIST(NL_PLIST(nl)), NL_NFPARAMS(nl), factor)
+
+	call sfree (sp)
+end
+
+
+# NLINVERT -- Procedure to invert matrix and compute errors
+
+procedure nlinvertr (alpha, chofac, cov, errors, list, nfit, variance)
+
+real	alpha[nfit,ARB]		# data matrix
+real	chofac[nfit, ARB]	# cholesky factorization
+real	cov[ARB]		# covariance vector
+real	errors[ARB]		# computed errors
+int	list[ARB]		# list of active parameters
+int	nfit			# number of fitted parameters
+real	variance		# variance of the fit
+
+int	i, ier
+
+begin
+	# Factorize the data matrix to determine the errors.
+	call nl_chfacr (alpha, nfit, nfit, chofac, ier)
+
+	# Estimate the errors.
+	do i = 1, nfit {
+	    call aclrr (cov, nfit)
+	    cov[i] = real (1.0)
+	    call nl_chslvr (chofac, nfit, nfit, cov, cov)
+	    if (cov[i] >= real (0.0))
+	        errors[list[i]] = sqrt (cov[i] * variance)
+	    else
+		errors[list[i]] = real (0.0)
+	}
+end
diff --git a/math/nlfit/nleval.gx b/math/nlfit/nleval.gx
new file mode 100644
index 00000000..e116982b
--- /dev/null
+++ b/math/nlfit/nleval.gx
@@ -0,0 +1,25 @@
+include <math/nlfit.h>
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+
+# NLEVAL -- Evaluate the fit at a point.
+
+PIXEL procedure nleval$t (nl, x, nvars)
+
+pointer	nl		# nlfit descriptor
+PIXEL	x[ARB]		# x values
+int	nvars		# number of variables
+
+real	zfit
+
+begin
+	# Evaluate the function.
+	call zcall5 (NL_FUNC(nl), x, nvars, PARAM(NL_PARAM(nl)),
+	    NL_NPARAMS(nl), zfit)
+
+	return (zfit)
+end
diff --git a/math/nlfit/nlevald.x b/math/nlfit/nlevald.x
new file mode 100644
index 00000000..c7710acc
--- /dev/null
+++ b/math/nlfit/nlevald.x
@@ -0,0 +1,21 @@
+include <math/nlfit.h>
+include "nlfitdefd.h"
+
+
+# NLEVAL -- Evaluate the fit at a point.
+
+double procedure nlevald (nl, x, nvars)
+
+pointer	nl		# nlfit descriptor
+double	x[ARB]		# x values
+int	nvars		# number of variables
+
+real	zfit
+
+begin
+	# Evaluate the function.
+	call zcall5 (NL_FUNC(nl), x, nvars, PARAM(NL_PARAM(nl)),
+	    NL_NPARAMS(nl), zfit)
+
+	return (zfit)
+end
diff --git a/math/nlfit/nlevalr.x b/math/nlfit/nlevalr.x
new file mode 100644
index 00000000..4c68d865
--- /dev/null
+++ b/math/nlfit/nlevalr.x
@@ -0,0 +1,21 @@
+include <math/nlfit.h>
+include "nlfitdefr.h"
+
+
+# NLEVAL -- Evaluate the fit at a point.
+
+real procedure nlevalr (nl, x, nvars)
+
+pointer	nl		# nlfit descriptor
+real	x[ARB]		# x values
+int	nvars		# number of variables
+
+real	zfit
+
+begin
+	# Evaluate the function.
+	call zcall5 (NL_FUNC(nl), x, nvars, PARAM(NL_PARAM(nl)),
+	    NL_NPARAMS(nl), zfit)
+
+	return (zfit)
+end
diff --git a/math/nlfit/nlfit.gx b/math/nlfit/nlfit.gx
new file mode 100644
index 00000000..50dc0b21
--- /dev/null
+++ b/math/nlfit/nlfit.gx
@@ -0,0 +1,171 @@
+include <mach.h>
+include <math/nlfit.h>
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+# NLFIT -- Routine to perform a non-linear least squares fit. At least MINITER
+# iterations must be performed before the fit is complete.
+
+procedure nlfit$t (nl, x, z, w, npts, nvars, wtflag, stat)
+
+pointer	nl		# pointer to nlfit structure
+PIXEL	x[ARB]		# independent variables (npts * nvars)
+PIXEL	z[ARB]		# function values (npts)
+PIXEL	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+int	wtflag		# weighting type
+int	stat		# error code
+
+int	i, miniter, ier
+PIXEL	scatter, dscatter
+PIXEL	nlscatter$t()
+
+begin
+	# Initialize.
+	NL_ITER(nl) = 0
+	NL_LAMBDA(nl) = PIXEL (.001)
+	NL_REFSQ(nl) = PIXEL (0.0)
+	NL_SCATTER(nl) = PIXEL(0.0)
+
+	# Initialize the weights.
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    do i = 1, npts
+		w[i] = PIXEL (1.0)
+	case WTS_SCATTER:
+	    ;
+	case WTS_USER:
+	    ;
+	case WTS_CHISQ:
+	    do i = 1, npts {
+		if (z[i] > PIXEL (0.0))
+		    w[i] = PIXEL (1.0) / z[i]
+		else if (z[i] < PIXEL (0.0))
+		    w[i] = PIXEL (-1.0) / z[i]
+	        else
+	            w[i] = PIXEL (0.0)
+	    }
+	default:
+	    do i = 1, npts
+		w[i] = PIXEL (1.0)
+	}
+
+	# Initialize.
+	scatter = PIXEL(0.0)
+	if (wtflag == WTS_SCATTER)
+	    miniter = MINITER + 1
+	else
+	    miniter = MINITER
+
+	repeat {
+
+	    # Perform a single iteration.
+	    call nliter$t (nl, x, z, w, npts, nvars, ier)
+	    NL_ITER(nl) = NL_ITER(nl) + 1
+	    #call eprintf ("niter=%d refsq=%g oldsq=%g sumsq=%g\n")
+		#call pargi (NL_ITER(nl))
+		#call parg$t (NL_REFSQ(nl))
+		#call parg$t (NL_OLDSQ(nl))
+		#call parg$t (NL_SUMSQ(nl))
+	    stat = ier
+	    if (stat == NO_DEG_FREEDOM)
+	        break
+
+	    # Make the convergence checks.
+	    if (NL_ITER(nl) < miniter)
+		stat = NOT_DONE
+	    else if (NL_SUMSQ(nl) <= PIXEL (10.0) * EPSILON$T)
+		stat = DONE
+	    else if (NL_REFSQ(nl) < NL_SUMSQ(nl))
+		stat = NOT_DONE
+	    else if (((NL_REFSQ(nl) - NL_SUMSQ(nl)) / NL_SUMSQ(nl)) <
+	        NL_TOL(nl))
+		stat = DONE
+	    else
+		stat = NOT_DONE
+
+	    # Check for a singular solution.
+	    if (stat == DONE) {
+		if (ier == SINGULAR)
+		    stat = ier
+		break
+	    }
+
+	    # Quit if the lambda parameter goes to zero.
+	    if (NL_LAMBDA(nl) <= 0.0)
+		break
+
+	    # Check the number of iterations.
+	    if ((NL_ITER(nl) >= miniter) && (NL_ITER(nl) >= NL_ITMAX(nl)))
+		break
+
+	    # Adjust the weights if necessary.
+	    switch (wtflag) {
+	    case WTS_SCATTER:
+	        dscatter = nlscatter$t (nl, x, z, w, npts, nvars)
+		if ((NL_ITER(nl) >= MINITER) && (dscatter >= PIXEL (10.0) *
+		    EPSILON$T)) {
+		    do i = 1, npts {
+			if (w[i] <= PIXEL(0.0))
+			    w[i] = PIXEL(0.0)
+			else {
+		            w[i] = PIXEL(1.0) / (PIXEL(1.0) / w[i] + dscatter)
+			}
+		    }
+		    scatter = scatter + dscatter
+		}
+	    default:
+		;
+	    }
+
+	    # Get ready for next iteration.
+	    NL_REFSQ(nl) = min (NL_OLDSQ(nl), NL_SUMSQ(nl))
+	}
+
+	NL_SCATTER(nl) = NL_SCATTER(nl) + scatter
+end
+
+
+# NLSCATTER -- Routine to estimate the original scatter in the fit.
+
+PIXEL procedure nlscatter$t (nl, x, z, w, npts, nvars)
+
+pointer	nl		# Pointer to nl fitting structure
+PIXEL	x[ARB]		# independent variables (npts * nvars)
+PIXEL	z[ARB]		# function values (npts)
+PIXEL	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+pointer	sp, zfit, errors
+PIXEL	scatter, variance, chisqr
+int	nlstati()
+
+begin
+	# Allocate working memory.
+	call smark (sp)
+	call salloc (zfit, npts, TY_PIXEL)
+	call salloc (errors, nlstati (nl, NLNPARAMS), TY_PIXEL)
+
+	# Initialize
+	scatter = PIXEL (0.0)
+
+	# Compute the fit and the errors.
+	call nlvector$t (nl, x, Mem$t[zfit], npts, nvars)
+	call nlerrors$t (nl, z, Mem$t[zfit], w, npts, variance, chisqr,
+	    Mem$t[errors])
+
+	# Estimate the scatter.
+	if (chisqr <= PIXEL(0.0) || variance <= PIXEL(0.0))
+	    scatter = PIXEL (0.0)
+	else
+	    scatter = PIXEL(0.5) * variance * (chisqr - PIXEL(1.0)) / chisqr
+
+	call sfree (sp)
+
+	return (scatter)
+end
diff --git a/math/nlfit/nlfitd.x b/math/nlfit/nlfitd.x
new file mode 100644
index 00000000..975284ab
--- /dev/null
+++ b/math/nlfit/nlfitd.x
@@ -0,0 +1,167 @@
+include <mach.h>
+include <math/nlfit.h>
+include "nlfitdefd.h"
+
+# NLFIT -- Routine to perform a non-linear least squares fit. At least MINITER
+# iterations must be performed before the fit is complete.
+
+procedure nlfitd (nl, x, z, w, npts, nvars, wtflag, stat)
+
+pointer	nl		# pointer to nlfit structure
+double	x[ARB]		# independent variables (npts * nvars)
+double	z[ARB]		# function values (npts)
+double	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+int	wtflag		# weighting type
+int	stat		# error code
+
+int	i, miniter, ier
+double	scatter, dscatter
+double	nlscatterd()
+
+begin
+	# Initialize.
+	NL_ITER(nl) = 0
+	NL_LAMBDA(nl) = double (.001)
+	NL_REFSQ(nl) = double (0.0)
+	NL_SCATTER(nl) = double(0.0)
+
+	# Initialize the weights.
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    do i = 1, npts
+		w[i] = double (1.0)
+	case WTS_SCATTER:
+	    ;
+	case WTS_USER:
+	    ;
+	case WTS_CHISQ:
+	    do i = 1, npts {
+		if (z[i] > double (0.0))
+		    w[i] = double (1.0) / z[i]
+		else if (z[i] < double (0.0))
+		    w[i] = double (-1.0) / z[i]
+	        else
+	            w[i] = double (0.0)
+	    }
+	default:
+	    do i = 1, npts
+		w[i] = double (1.0)
+	}
+
+	# Initialize.
+	scatter = double(0.0)
+	if (wtflag == WTS_SCATTER)
+	    miniter = MINITER + 1
+	else
+	    miniter = MINITER
+
+	repeat {
+
+	    # Perform a single iteration.
+	    call nliterd (nl, x, z, w, npts, nvars, ier)
+	    NL_ITER(nl) = NL_ITER(nl) + 1
+	    #call eprintf ("niter=%d refsq=%g oldsq=%g sumsq=%g\n")
+		#call pargi (NL_ITER(nl))
+		#call parg$t (NL_REFSQ(nl))
+		#call parg$t (NL_OLDSQ(nl))
+		#call parg$t (NL_SUMSQ(nl))
+	    stat = ier
+	    if (stat == NO_DEG_FREEDOM)
+	        break
+
+	    # Make the convergence checks.
+	    if (NL_ITER(nl) < miniter)
+		stat = NOT_DONE
+	    else if (NL_SUMSQ(nl) <= double (10.0) * EPSILOND)
+		stat = DONE
+	    else if (NL_REFSQ(nl) < NL_SUMSQ(nl))
+		stat = NOT_DONE
+	    else if (((NL_REFSQ(nl) - NL_SUMSQ(nl)) / NL_SUMSQ(nl)) <
+	        NL_TOL(nl))
+		stat = DONE
+	    else
+		stat = NOT_DONE
+
+	    # Check for a singular solution.
+	    if (stat == DONE) {
+		if (ier == SINGULAR)
+		    stat = ier
+		break
+	    }
+
+	    # Quit if the lambda parameter goes to zero.
+	    if (NL_LAMBDA(nl) <= 0.0)
+		break
+
+	    # Check the number of iterations.
+	    if ((NL_ITER(nl) >= miniter) && (NL_ITER(nl) >= NL_ITMAX(nl)))
+		break
+
+	    # Adjust the weights if necessary.
+	    switch (wtflag) {
+	    case WTS_SCATTER:
+	        dscatter = nlscatterd (nl, x, z, w, npts, nvars)
+		if ((NL_ITER(nl) >= MINITER) && (dscatter >= double (10.0) *
+		    EPSILOND)) {
+		    do i = 1, npts {
+			if (w[i] <= double(0.0))
+			    w[i] = double(0.0)
+			else {
+		            w[i] = double(1.0) / (double(1.0) / w[i] + dscatter)
+			}
+		    }
+		    scatter = scatter + dscatter
+		}
+	    default:
+		;
+	    }
+
+	    # Get ready for next iteration.
+	    NL_REFSQ(nl) = min (NL_OLDSQ(nl), NL_SUMSQ(nl))
+	}
+
+	NL_SCATTER(nl) = NL_SCATTER(nl) + scatter
+end
+
+
+# NLSCATTER -- Routine to estimate the original scatter in the fit.
+
+double procedure nlscatterd (nl, x, z, w, npts, nvars)
+
+pointer	nl		# Pointer to nl fitting structure
+double	x[ARB]		# independent variables (npts * nvars)
+double	z[ARB]		# function values (npts)
+double	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+pointer	sp, zfit, errors
+double	scatter, variance, chisqr
+int	nlstati()
+
+begin
+	# Allocate working memory.
+	call smark (sp)
+	call salloc (zfit, npts, TY_DOUBLE)
+	call salloc (errors, nlstati (nl, NLNPARAMS), TY_DOUBLE)
+
+	# Initialize
+	scatter = double (0.0)
+
+	# Compute the fit and the errors.
+	call nlvectord (nl, x, Memd[zfit], npts, nvars)
+	call nlerrorsd (nl, z, Memd[zfit], w, npts, variance, chisqr,
+	    Memd[errors])
+
+	# Estimate the scatter.
+	if (chisqr <= double(0.0) || variance <= double(0.0))
+	    scatter = double (0.0)
+	else
+	    scatter = double(0.5) * variance * (chisqr - double(1.0)) / chisqr
+
+	call sfree (sp)
+
+	return (scatter)
+end
diff --git a/math/nlfit/nlfitdef.gh b/math/nlfit/nlfitdef.gh
new file mode 100644
index 00000000..62a542a8
--- /dev/null
+++ b/math/nlfit/nlfitdef.gh
@@ -0,0 +1,51 @@
+# The NLFIT data structure.
+
+# Structure length
+define	LEN_NLSTRUCT	35
+
+
+# Structure definition
+define  NL_TOL          Mem$t[P2$T($1+0)]   # Tolerance for convergence
+define  NL_LAMBDA       Mem$t[P2$T($1+2)]   # Damping factor
+define	NL_OLDSQ	Mem$t[P2$T($1+4)]   # Sum resid. squared last iter.
+define	NL_SUMSQ	Mem$t[P2$T($1+6)]   # Sum of residuals squared 
+define	NL_REFSQ	Mem$t[P2$T($1+8)]   # Reference sum of squares
+define	NL_SCATTER	Mem$t[P2$T($1+10)]  # Additional scatter
+
+define	NL_FUNC		Memi[$1+12]	# Fitting function
+define	NL_DFUNC	Memi[$1+13]	# Derivative function
+define	NL_NPARAMS	Memi[$1+14]	# Number of parameters
+define	NL_NFPARAMS	Memi[$1+15]	# Number of fitted parameters
+define	NL_ITMAX	Memi[$1+16]	# Max number of iterations
+define	NL_ITER		Memi[$1+17]	# Iteration counter
+define	NL_NPTS		Memi[$1+18]	# Number of points in fit
+
+define	NL_PARAM	Memi[$1+19]	# Pointer to parameter vector
+define	NL_OPARAM	Memi[$1+20]	# Pointer to orignal parameter vector
+define	NL_DPARAM	Memi[$1+21]	# Pointer to parameter change vector
+define	NL_DELPARAM	Memi[$1+22]	# Pointer to delta param vector
+define	NL_PLIST	Memi[$1+23]	# Pointer to parameter list
+define	NL_ALPHA	Memi[$1+24]	# Pointer to alpha matrix
+define	NL_COVAR	Memi[$1+25]	# Pointer to covariance matrix
+define	NL_BETA		Memi[$1+26]	# Pointer to beta matrix
+define	NL_TRY		Memi[$1+27]	# Pointer to trial vector
+define	NL_DERIV	Memi[$1+28]	# Pointer to derivatives
+define	NL_CHOFAC	Memi[$1+29]	# Pointer to Cholesky factorization
+
+# next free location	($1 + 30)
+
+# Access to buffers
+define	PLIST		Memi[$1]	# Parameter list
+define	OPARAM		Mem$t[P2P($1)]	# Original parameter vector
+define	PARAM		Mem$t[P2P($1)]	# Parameter vector
+define	DPARAM		Mem$t[P2P($1)]	# Parameter change vector
+define	ALPHA		Mem$t[P2P($1)]	# Alpha matrix
+define	BETA		Mem$t[P2P($1)]	# Beta matrix
+define	TRY		Mem$t[P2P($1)]	# Trial vector
+define	DERIV		Mem$t[P2P($1)]	# Derivatives
+define	CHOFAC		Mem$t[P2P($1)]	# Cholesky factorization
+define	COVAR		Mem$t[P2P($1)]	# Covariance matrix
+
+# Defined constants alter for tricky problems
+define	LAMBDAMAX	1000.0
+define	MINITER		3
diff --git a/math/nlfit/nlfitdefd.h b/math/nlfit/nlfitdefd.h
new file mode 100644
index 00000000..b5ed3bf3
--- /dev/null
+++ b/math/nlfit/nlfitdefd.h
@@ -0,0 +1,52 @@
+# The NLFIT data structure.
+
+# Structure length
+define	LEN_NLSTRUCT	35
+
+
+# Structure definition
+define  NL_TOL          Memd[P2D($1+0)]   # Tolerance for convergence
+define  NL_LAMBDA       Memd[P2D($1+2)]   # Damping factor
+define	NL_OLDSQ	Memd[P2D($1+4)]   # Sum resid. squared last iter.
+define	NL_SUMSQ	Memd[P2D($1+6)]   # Sum of residuals squared 
+define	NL_REFSQ	Memd[P2D($1+8)]   # Reference sum of squares
+define	NL_SCATTER	Memd[P2D($1+10)]  # Additional scatter
+
+define	NL_FUNC		Memi[$1+12]	# Fitting function
+define	NL_DFUNC	Memi[$1+13]	# Derivative function
+define	NL_NPARAMS	Memi[$1+14]	# Number of parameters
+define	NL_NFPARAMS	Memi[$1+15]	# Number of fitted parameters
+define	NL_ITMAX	Memi[$1+16]	# Max number of iterations
+define	NL_ITER		Memi[$1+17]	# Iteration counter
+define	NL_NPTS		Memi[$1+18]	# Number of points in fit
+
+define	NL_PARAM	Memi[$1+19]	# Pointer to parameter vector
+define	NL_OPARAM	Memi[$1+20]	# Pointer to orignal parameter vector
+define	NL_DPARAM	Memi[$1+21]	# Pointer to parameter change vector
+define	NL_DELPARAM	Memi[$1+22]	# Pointer to delta param vector
+define	NL_PLIST	Memi[$1+23]	# Pointer to parameter list
+define	NL_ALPHA	Memi[$1+24]	# Pointer to alpha matrix
+define	NL_COVAR	Memi[$1+25]	# Pointer to covariance matrix
+define	NL_BETA		Memi[$1+26]	# Pointer to beta matrix
+define	NL_TRY		Memi[$1+27]	# Pointer to trial vector
+define	NL_DERIV	Memi[$1+28]	# Pointer to derivatives
+define	NL_CHOFAC	Memi[$1+29]	# Pointer to Cholesky factorization
+
+# next free location	($1 + 30)
+
+# Access to buffers
+define	PLIST		Memi[$1]	# Parameter list
+define	OPARAM		Memd[$1]	# Original parameter vector
+define	PARAM		Memd[$1]	# Parameter vector
+define	DPARAM		Memd[$1]	# Parameter change vector
+define	ALPHA		Memd[$1]	# Alpha matrix
+define	BETA		Memd[$1]	# Beta matrix
+define	TRY		Memd[$1]	# Trial vector
+define	DERIV		Memd[$1]	# Derivatives
+define	CHOFAC		Memd[$1]	# Cholesky factorization
+define	COVAR		Memd[$1]	# Covariance matrix
+
+
+# Defined constants alter for tricky problems
+define	LAMBDAMAX	1000.0
+define	MINITER		3
diff --git a/math/nlfit/nlfitdefr.h b/math/nlfit/nlfitdefr.h
new file mode 100644
index 00000000..e3bf3ae0
--- /dev/null
+++ b/math/nlfit/nlfitdefr.h
@@ -0,0 +1,52 @@
+# The NLFIT data structure.
+
+# Structure length
+define	LEN_NLSTRUCT	35
+
+
+# Structure definition
+define  NL_TOL          Memr[P2R($1+0)]   # Tolerance for convergence
+define  NL_LAMBDA       Memr[P2R($1+2)]   # Damping factor
+define	NL_OLDSQ	Memr[P2R($1+4)]   # Sum resid. squared last iter.
+define	NL_SUMSQ	Memr[P2R($1+6)]   # Sum of residuals squared 
+define	NL_REFSQ	Memr[P2R($1+8)]   # Reference sum of squares
+define	NL_SCATTER	Memr[P2R($1+10)]  # Additional scatter
+
+define	NL_FUNC		Memi[$1+12]	# Fitting function
+define	NL_DFUNC	Memi[$1+13]	# Derivative function
+define	NL_NPARAMS	Memi[$1+14]	# Number of parameters
+define	NL_NFPARAMS	Memi[$1+15]	# Number of fitted parameters
+define	NL_ITMAX	Memi[$1+16]	# Max number of iterations
+define	NL_ITER		Memi[$1+17]	# Iteration counter
+define	NL_NPTS		Memi[$1+18]	# Number of points in fit
+
+define	NL_PARAM	Memi[$1+19]	# Pointer to parameter vector
+define	NL_OPARAM	Memi[$1+20]	# Pointer to orignal parameter vector
+define	NL_DPARAM	Memi[$1+21]	# Pointer to parameter change vector
+define	NL_DELPARAM	Memi[$1+22]	# Pointer to delta param vector
+define	NL_PLIST	Memi[$1+23]	# Pointer to parameter list
+define	NL_ALPHA	Memi[$1+24]	# Pointer to alpha matrix
+define	NL_COVAR	Memi[$1+25]	# Pointer to covariance matrix
+define	NL_BETA		Memi[$1+26]	# Pointer to beta matrix
+define	NL_TRY		Memi[$1+27]	# Pointer to trial vector
+define	NL_DERIV	Memi[$1+28]	# Pointer to derivatives
+define	NL_CHOFAC	Memi[$1+29]	# Pointer to Cholesky factorization
+
+# next free location	($1 + 30)
+
+# Access to buffers
+define	PLIST		Memi[$1]	# Parameter list
+define	OPARAM		Memr[$1]	# Original parameter vector
+define	PARAM		Memr[$1]	# Parameter vector
+define	DPARAM		Memr[$1]	# Parameter change vector
+define	ALPHA		Memr[$1]	# Alpha matrix
+define	BETA		Memr[$1]	# Beta matrix
+define	TRY		Memr[$1]	# Trial vector
+define	DERIV		Memr[$1]	# Derivatives
+define	CHOFAC		Memr[$1]	# Cholesky factorization
+define	COVAR		Memr[$1]	# Covariance matrix
+
+
+# Defined constants alter for tricky problems
+define	LAMBDAMAX	1000.0
+define	MINITER		3
diff --git a/math/nlfit/nlfitr.x b/math/nlfit/nlfitr.x
new file mode 100644
index 00000000..dc06b720
--- /dev/null
+++ b/math/nlfit/nlfitr.x
@@ -0,0 +1,167 @@
+include <mach.h>
+include <math/nlfit.h>
+include "nlfitdefr.h"
+
+# NLFIT -- Routine to perform a non-linear least squares fit. At least MINITER
+# iterations must be performed before the fit is complete.
+
+procedure nlfitr (nl, x, z, w, npts, nvars, wtflag, stat)
+
+pointer	nl		# pointer to nlfit structure
+real	x[ARB]		# independent variables (npts * nvars)
+real	z[ARB]		# function values (npts)
+real	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+int	wtflag		# weighting type
+int	stat		# error code
+
+int	i, miniter, ier
+real	scatter, dscatter
+real	nlscatterr()
+
+begin
+	# Initialize.
+	NL_ITER(nl) = 0
+	NL_LAMBDA(nl) = real (.001)
+	NL_REFSQ(nl) = real (0.0)
+	NL_SCATTER(nl) = real(0.0)
+
+	# Initialize the weights.
+	switch (wtflag) {
+	case WTS_UNIFORM:
+	    do i = 1, npts
+		w[i] = real (1.0)
+	case WTS_SCATTER:
+	    ;
+	case WTS_USER:
+	    ;
+	case WTS_CHISQ:
+	    do i = 1, npts {
+		if (z[i] > real (0.0))
+		    w[i] = real (1.0) / z[i]
+		else if (z[i] < real (0.0))
+		    w[i] = real (-1.0) / z[i]
+	        else
+	            w[i] = real (0.0)
+	    }
+	default:
+	    do i = 1, npts
+		w[i] = real (1.0)
+	}
+
+	# Initialize.
+	scatter = real(0.0)
+	if (wtflag == WTS_SCATTER)
+	    miniter = MINITER + 1
+	else
+	    miniter = MINITER
+
+	repeat {
+
+	    # Perform a single iteration.
+	    call nliterr (nl, x, z, w, npts, nvars, ier)
+	    NL_ITER(nl) = NL_ITER(nl) + 1
+	    #call eprintf ("niter=%d refsq=%g oldsq=%g sumsq=%g\n")
+		#call pargi (NL_ITER(nl))
+		#call parg$t (NL_REFSQ(nl))
+		#call parg$t (NL_OLDSQ(nl))
+		#call parg$t (NL_SUMSQ(nl))
+	    stat = ier
+	    if (stat == NO_DEG_FREEDOM)
+	        break
+
+	    # Make the convergence checks.
+	    if (NL_ITER(nl) < miniter)
+		stat = NOT_DONE
+	    else if (NL_SUMSQ(nl) <= real (10.0) * EPSILONR)
+		stat = DONE
+	    else if (NL_REFSQ(nl) < NL_SUMSQ(nl))
+		stat = NOT_DONE
+	    else if (((NL_REFSQ(nl) - NL_SUMSQ(nl)) / NL_SUMSQ(nl)) <
+	        NL_TOL(nl))
+		stat = DONE
+	    else
+		stat = NOT_DONE
+
+	    # Check for a singular solution.
+	    if (stat == DONE) {
+		if (ier == SINGULAR)
+		    stat = ier
+		break
+	    }
+
+	    # Quit if the lambda parameter goes to zero.
+	    if (NL_LAMBDA(nl) <= 0.0)
+		break
+
+	    # Check the number of iterations.
+	    if ((NL_ITER(nl) >= miniter) && (NL_ITER(nl) >= NL_ITMAX(nl)))
+		break
+
+	    # Adjust the weights if necessary.
+	    switch (wtflag) {
+	    case WTS_SCATTER:
+	        dscatter = nlscatterr (nl, x, z, w, npts, nvars)
+		if ((NL_ITER(nl) >= MINITER) && (dscatter >= real (10.0) *
+		    EPSILONR)) {
+		    do i = 1, npts {
+			if (w[i] <= real(0.0))
+			    w[i] = real(0.0)
+			else {
+		            w[i] = real(1.0) / (real(1.0) / w[i] + dscatter)
+			}
+		    }
+		    scatter = scatter + dscatter
+		}
+	    default:
+		;
+	    }
+
+	    # Get ready for next iteration.
+	    NL_REFSQ(nl) = min (NL_OLDSQ(nl), NL_SUMSQ(nl))
+	}
+
+	NL_SCATTER(nl) = NL_SCATTER(nl) + scatter
+end
+
+
+# NLSCATTER -- Routine to estimate the original scatter in the fit.
+
+real procedure nlscatterr (nl, x, z, w, npts, nvars)
+
+pointer	nl		# Pointer to nl fitting structure
+real	x[ARB]		# independent variables (npts * nvars)
+real	z[ARB]		# function values (npts)
+real	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+pointer	sp, zfit, errors
+real	scatter, variance, chisqr
+int	nlstati()
+
+begin
+	# Allocate working memory.
+	call smark (sp)
+	call salloc (zfit, npts, TY_REAL)
+	call salloc (errors, nlstati (nl, NLNPARAMS), TY_REAL)
+
+	# Initialize
+	scatter = real (0.0)
+
+	# Compute the fit and the errors.
+	call nlvectorr (nl, x, Memr[zfit], npts, nvars)
+	call nlerrorsr (nl, z, Memr[zfit], w, npts, variance, chisqr,
+	    Memr[errors])
+
+	# Estimate the scatter.
+	if (chisqr <= real(0.0) || variance <= real(0.0))
+	    scatter = real (0.0)
+	else
+	    scatter = real(0.5) * variance * (chisqr - real(1.0)) / chisqr
+
+	call sfree (sp)
+
+	return (scatter)
+end
diff --git a/math/nlfit/nlfree.gx b/math/nlfit/nlfree.gx
new file mode 100644
index 00000000..507dce57
--- /dev/null
+++ b/math/nlfit/nlfree.gx
@@ -0,0 +1,41 @@
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+# NLFREE -- Deallocate all assigned space
+
+procedure nlfree$t (nl)
+
+pointer	nl		# pointer to non-linear fitting structure
+
+errchk	mfree
+
+begin
+	if (nl == NULL)
+	    return
+	if (NL_PARAM(nl) != NULL)
+	    call mfree (NL_PARAM(nl), TY_PIXEL)
+	if (NL_OPARAM(nl) != NULL)
+	    call mfree (NL_OPARAM(nl), TY_PIXEL)
+	if (NL_DPARAM(nl) != NULL)
+	    call mfree (NL_DPARAM(nl), TY_PIXEL)
+	if (NL_DELPARAM(nl) != NULL)
+	    call mfree (NL_DELPARAM(nl), TY_PIXEL)
+	if (NL_PLIST(nl) != NULL)
+	    call mfree (NL_PLIST(nl), TY_INT)
+	if (NL_ALPHA(nl) != NULL)
+	    call mfree (NL_ALPHA(nl), TY_PIXEL)
+	if (NL_CHOFAC(nl) != NULL)
+	    call mfree (NL_CHOFAC(nl), TY_PIXEL)
+	if (NL_COVAR(nl) != NULL)
+	    call mfree (NL_COVAR(nl), TY_PIXEL)
+	if (NL_BETA(nl) != NULL)
+	    call mfree (NL_BETA(nl), TY_PIXEL)
+	if (NL_TRY(nl) != NULL)
+	    call mfree (NL_TRY(nl), TY_PIXEL)
+	if (NL_DERIV(nl) != NULL)
+	    call mfree (NL_DERIV(nl), TY_PIXEL)
+	call mfree (nl, TY_STRUCT)
+end
diff --git a/math/nlfit/nlfreed.x b/math/nlfit/nlfreed.x
new file mode 100644
index 00000000..56bcda62
--- /dev/null
+++ b/math/nlfit/nlfreed.x
@@ -0,0 +1,37 @@
+include "nlfitdefd.h"
+
+# NLFREE -- Deallocate all assigned space
+
+procedure nlfreed (nl)
+
+pointer	nl		# pointer to non-linear fitting structure
+
+errchk	mfree
+
+begin
+	if (nl == NULL)
+	    return
+	if (NL_PARAM(nl) != NULL)
+	    call mfree (NL_PARAM(nl), TY_DOUBLE)
+	if (NL_OPARAM(nl) != NULL)
+	    call mfree (NL_OPARAM(nl), TY_DOUBLE)
+	if (NL_DPARAM(nl) != NULL)
+	    call mfree (NL_DPARAM(nl), TY_DOUBLE)
+	if (NL_DELPARAM(nl) != NULL)
+	    call mfree (NL_DELPARAM(nl), TY_DOUBLE)
+	if (NL_PLIST(nl) != NULL)
+	    call mfree (NL_PLIST(nl), TY_INT)
+	if (NL_ALPHA(nl) != NULL)
+	    call mfree (NL_ALPHA(nl), TY_DOUBLE)
+	if (NL_CHOFAC(nl) != NULL)
+	    call mfree (NL_CHOFAC(nl), TY_DOUBLE)
+	if (NL_COVAR(nl) != NULL)
+	    call mfree (NL_COVAR(nl), TY_DOUBLE)
+	if (NL_BETA(nl) != NULL)
+	    call mfree (NL_BETA(nl), TY_DOUBLE)
+	if (NL_TRY(nl) != NULL)
+	    call mfree (NL_TRY(nl), TY_DOUBLE)
+	if (NL_DERIV(nl) != NULL)
+	    call mfree (NL_DERIV(nl), TY_DOUBLE)
+	call mfree (nl, TY_STRUCT)
+end
diff --git a/math/nlfit/nlfreer.x b/math/nlfit/nlfreer.x
new file mode 100644
index 00000000..639c4ecc
--- /dev/null
+++ b/math/nlfit/nlfreer.x
@@ -0,0 +1,37 @@
+include "nlfitdefr.h"
+
+# NLFREE -- Deallocate all assigned space
+
+procedure nlfreer (nl)
+
+pointer	nl		# pointer to non-linear fitting structure
+
+errchk	mfree
+
+begin
+	if (nl == NULL)
+	    return
+	if (NL_PARAM(nl) != NULL)
+	    call mfree (NL_PARAM(nl), TY_REAL)
+	if (NL_OPARAM(nl) != NULL)
+	    call mfree (NL_OPARAM(nl), TY_REAL)
+	if (NL_DPARAM(nl) != NULL)
+	    call mfree (NL_DPARAM(nl), TY_REAL)
+	if (NL_DELPARAM(nl) != NULL)
+	    call mfree (NL_DELPARAM(nl), TY_REAL)
+	if (NL_PLIST(nl) != NULL)
+	    call mfree (NL_PLIST(nl), TY_INT)
+	if (NL_ALPHA(nl) != NULL)
+	    call mfree (NL_ALPHA(nl), TY_REAL)
+	if (NL_CHOFAC(nl) != NULL)
+	    call mfree (NL_CHOFAC(nl), TY_REAL)
+	if (NL_COVAR(nl) != NULL)
+	    call mfree (NL_COVAR(nl), TY_REAL)
+	if (NL_BETA(nl) != NULL)
+	    call mfree (NL_BETA(nl), TY_REAL)
+	if (NL_TRY(nl) != NULL)
+	    call mfree (NL_TRY(nl), TY_REAL)
+	if (NL_DERIV(nl) != NULL)
+	    call mfree (NL_DERIV(nl), TY_REAL)
+	call mfree (nl, TY_STRUCT)
+end
diff --git a/math/nlfit/nlinit.gx b/math/nlfit/nlinit.gx
new file mode 100644
index 00000000..be6e436a
--- /dev/null
+++ b/math/nlfit/nlinit.gx
@@ -0,0 +1,66 @@
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+# NLINIT --  Initialize for non-linear fitting
+
+procedure nlinit$t (nl, fnc, dfnc, params, dparams, nparams, plist, nfparams,
+		    tol, itmax)
+
+pointer	nl		# pointer to nl fitting structure
+int	fnc		# fitting function address
+int	dfnc		# derivative function address
+PIXEL	params[ARB]	# initial values for the parameters
+PIXEL	dparams[ARB]	# initial guess at uncertainties in parameters
+int	nparams		# number of parameters
+int	plist[ARB]	# list of active parameters
+int	nfparams	# number of fitted parameters
+PIXEL	tol		# fitting tolerance
+int	itmax		# maximum number of iterations
+
+errchk	malloc, calloc, nl_list
+
+begin
+	# Allocate space for the non-linear package structure.
+	call calloc (nl, LEN_NLSTRUCT, TY_STRUCT)
+
+	# Store the addresses of the non-linear functions.
+	NL_FUNC(nl) = fnc
+	NL_DFUNC(nl) = dfnc
+
+	# Allocate temporary space for arrays.
+	call calloc (NL_ALPHA(nl), nfparams * nfparams, TY_PIXEL)
+	call calloc (NL_COVAR(nl), nfparams * nfparams, TY_PIXEL)
+	call calloc (NL_CHOFAC(nl), nfparams * nfparams, TY_PIXEL)
+	call calloc (NL_BETA(nl), nfparams, TY_PIXEL)
+
+	# Allocate space for parameter and trial parameter vectors.
+	call calloc (NL_DERIV(nl), nparams, TY_PIXEL)
+	call calloc (NL_PARAM(nl), nparams, TY_PIXEL)
+	call calloc (NL_OPARAM(nl), nparams, TY_PIXEL)
+	call calloc (NL_TRY(nl), nparams, TY_PIXEL)
+	call calloc (NL_DPARAM(nl), nparams, TY_PIXEL)
+	call calloc (NL_DELPARAM(nl), nparams, TY_PIXEL)
+	call calloc (NL_PLIST(nl), nparams, TY_INT)
+
+	# Initialize the parameters.
+	NL_NPARAMS(nl) = nparams
+	NL_NFPARAMS(nl) = nfparams
+	call amov$t (params, PARAM(NL_PARAM(nl)), nparams)
+	call amov$t (params, PARAM(NL_OPARAM(nl)), nparams)
+	call amov$t (dparams, DPARAM(NL_DELPARAM(nl)), nparams)
+	call amovi (plist, PLIST(NL_PLIST(nl)), nfparams)
+	NL_TOL(nl) = tol
+	NL_ITMAX(nl) = itmax
+	NL_SCATTER(nl) = PIXEL(0.0)
+
+	# Set up the parameter list.
+	iferr {
+	    call nl_list (PLIST(NL_PLIST(nl)), NL_NPARAMS(nl), NL_NFPARAMS(nl))
+	} then {
+	    call nlfree$t (nl)
+	    nl = NULL
+	}
+end
diff --git a/math/nlfit/nlinitd.x b/math/nlfit/nlinitd.x
new file mode 100644
index 00000000..16804764
--- /dev/null
+++ b/math/nlfit/nlinitd.x
@@ -0,0 +1,62 @@
+include "nlfitdefd.h"
+
+# NLINIT --  Initialize for non-linear fitting
+
+procedure nlinitd (nl, fnc, dfnc, params, dparams, nparams, plist, nfparams,
+		    tol, itmax)
+
+pointer	nl		# pointer to nl fitting structure
+int	fnc		# fitting function address
+int	dfnc		# derivative function address
+double	params[ARB]	# initial values for the parameters
+double	dparams[ARB]	# initial guess at uncertainties in parameters
+int	nparams		# number of parameters
+int	plist[ARB]	# list of active parameters
+int	nfparams	# number of fitted parameters
+double	tol		# fitting tolerance
+int	itmax		# maximum number of iterations
+
+errchk	malloc, calloc, nl_list
+
+begin
+	# Allocate space for the non-linear package structure.
+	call calloc (nl, LEN_NLSTRUCT, TY_STRUCT)
+
+	# Store the addresses of the non-linear functions.
+	NL_FUNC(nl) = fnc
+	NL_DFUNC(nl) = dfnc
+
+	# Allocate temporary space for arrays.
+	call calloc (NL_ALPHA(nl), nfparams * nfparams, TY_DOUBLE)
+	call calloc (NL_COVAR(nl), nfparams * nfparams, TY_DOUBLE)
+	call calloc (NL_CHOFAC(nl), nfparams * nfparams, TY_DOUBLE)
+	call calloc (NL_BETA(nl), nfparams, TY_DOUBLE)
+
+	# Allocate space for parameter and trial parameter vectors.
+	call calloc (NL_DERIV(nl), nparams, TY_DOUBLE)
+	call calloc (NL_PARAM(nl), nparams, TY_DOUBLE)
+	call calloc (NL_OPARAM(nl), nparams, TY_DOUBLE)
+	call calloc (NL_TRY(nl), nparams, TY_DOUBLE)
+	call calloc (NL_DPARAM(nl), nparams, TY_DOUBLE)
+	call calloc (NL_DELPARAM(nl), nparams, TY_DOUBLE)
+	call calloc (NL_PLIST(nl), nparams, TY_INT)
+
+	# Initialize the parameters.
+	NL_NPARAMS(nl) = nparams
+	NL_NFPARAMS(nl) = nfparams
+	call amovd (params, PARAM(NL_PARAM(nl)), nparams)
+	call amovd (params, PARAM(NL_OPARAM(nl)), nparams)
+	call amovd (dparams, DPARAM(NL_DELPARAM(nl)), nparams)
+	call amovi (plist, PLIST(NL_PLIST(nl)), nfparams)
+	NL_TOL(nl) = tol
+	NL_ITMAX(nl) = itmax
+	NL_SCATTER(nl) = double(0.0)
+
+	# Set up the parameter list.
+	iferr {
+	    call nl_list (PLIST(NL_PLIST(nl)), NL_NPARAMS(nl), NL_NFPARAMS(nl))
+	} then {
+	    call nlfreed (nl)
+	    nl = NULL
+	}
+end
diff --git a/math/nlfit/nlinitr.x b/math/nlfit/nlinitr.x
new file mode 100644
index 00000000..cb97f269
--- /dev/null
+++ b/math/nlfit/nlinitr.x
@@ -0,0 +1,62 @@
+include "nlfitdefr.h"
+
+# NLINIT --  Initialize for non-linear fitting
+
+procedure nlinitr (nl, fnc, dfnc, params, dparams, nparams, plist, nfparams,
+		    tol, itmax)
+
+pointer	nl		# pointer to nl fitting structure
+int	fnc		# fitting function address
+int	dfnc		# derivative function address
+real	params[ARB]	# initial values for the parameters
+real	dparams[ARB]	# initial guess at uncertainties in parameters
+int	nparams		# number of parameters
+int	plist[ARB]	# list of active parameters
+int	nfparams	# number of fitted parameters
+real	tol		# fitting tolerance
+int	itmax		# maximum number of iterations
+
+errchk	malloc, calloc, nl_list
+
+begin
+	# Allocate space for the non-linear package structure.
+	call calloc (nl, LEN_NLSTRUCT, TY_STRUCT)
+
+	# Store the addresses of the non-linear functions.
+	NL_FUNC(nl) = fnc
+	NL_DFUNC(nl) = dfnc
+
+	# Allocate temporary space for arrays.
+	call calloc (NL_ALPHA(nl), nfparams * nfparams, TY_REAL)
+	call calloc (NL_COVAR(nl), nfparams * nfparams, TY_REAL)
+	call calloc (NL_CHOFAC(nl), nfparams * nfparams, TY_REAL)
+	call calloc (NL_BETA(nl), nfparams, TY_REAL)
+
+	# Allocate space for parameter and trial parameter vectors.
+	call calloc (NL_DERIV(nl), nparams, TY_REAL)
+	call calloc (NL_PARAM(nl), nparams, TY_REAL)
+	call calloc (NL_OPARAM(nl), nparams, TY_REAL)
+	call calloc (NL_TRY(nl), nparams, TY_REAL)
+	call calloc (NL_DPARAM(nl), nparams, TY_REAL)
+	call calloc (NL_DELPARAM(nl), nparams, TY_REAL)
+	call calloc (NL_PLIST(nl), nparams, TY_INT)
+
+	# Initialize the parameters.
+	NL_NPARAMS(nl) = nparams
+	NL_NFPARAMS(nl) = nfparams
+	call amovr (params, PARAM(NL_PARAM(nl)), nparams)
+	call amovr (params, PARAM(NL_OPARAM(nl)), nparams)
+	call amovr (dparams, DPARAM(NL_DELPARAM(nl)), nparams)
+	call amovi (plist, PLIST(NL_PLIST(nl)), nfparams)
+	NL_TOL(nl) = tol
+	NL_ITMAX(nl) = itmax
+	NL_SCATTER(nl) = real(0.0)
+
+	# Set up the parameter list.
+	iferr {
+	    call nl_list (PLIST(NL_PLIST(nl)), NL_NPARAMS(nl), NL_NFPARAMS(nl))
+	} then {
+	    call nlfreer (nl)
+	    nl = NULL
+	}
+end
diff --git a/math/nlfit/nliter.gx b/math/nlfit/nliter.gx
new file mode 100644
index 00000000..7857f852
--- /dev/null
+++ b/math/nlfit/nliter.gx
@@ -0,0 +1,59 @@
+include <mach.h>
+include	<math/nlfit.h>
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+# NLITER - Routine to compute one iteration of the fitting process
+
+procedure nliter$t (nl, x, z, w, npts, nvars, ier)
+
+pointer	nl		# pointer to nl fitting structure
+PIXEL	x[ARB]		# independent variables (npts * nvars)
+PIXEL	z[ARB]		# function values (npts)
+PIXEL	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+int	ier		# error code
+
+int	i, index
+PIXEL	nlacpts$t(), nlresid$t()
+
+begin
+	# Do the initial accumulation.
+   	NL_OLDSQ(nl) = nlacpts$t (nl, x, z, w, npts, nvars)
+
+	# Set up temporary parameter array.
+	call amov$t (PARAM(NL_PARAM(nl)), TRY(NL_TRY(nl)), NL_NPARAMS(nl))
+
+	repeat {
+
+	    # Solve the matrix.
+	    call nlsolve$t (nl, ier)
+	    if (ier == NO_DEG_FREEDOM)
+	        return
+
+	    # Increment the parameters.
+	    do i = 1, NL_NFPARAMS(nl) {
+	        index = PLIST(NL_PLIST(nl)+i-1)
+	        TRY(NL_TRY(nl)+index-1) = TRY(NL_TRY(nl)+index-1) +
+		    DPARAM(NL_DPARAM(nl)+i-1)
+	    }
+
+	    # Reaccumulate the residuals and increment lambda.
+	    NL_SUMSQ(nl) = nlresid$t (nl, x, z, w, npts, nvars)
+	    #if (NL_OLDSQ(nl) > (NL_SUMSQ(nl) + NL_TOL(nl) * NL_SUMSQ(nl))) {
+	    if (NL_OLDSQ(nl) >= NL_SUMSQ(nl)) {
+		call amov$t (TRY(NL_TRY(nl)), PARAM(NL_PARAM(nl)),
+		    NL_NPARAMS(nl))
+		NL_LAMBDA(nl) = PIXEL (0.10) * NL_LAMBDA(nl)
+		break
+	    } else
+	        NL_LAMBDA(nl) = min (PIXEL(LAMBDAMAX),
+		    PIXEL (10.0) * NL_LAMBDA(nl))
+
+	} until (NL_LAMBDA(nl) <= PIXEL(0.0) ||
+	    NL_LAMBDA(nl) >= PIXEL(LAMBDAMAX))
+end
diff --git a/math/nlfit/nliterd.x b/math/nlfit/nliterd.x
new file mode 100644
index 00000000..418ab8fa
--- /dev/null
+++ b/math/nlfit/nliterd.x
@@ -0,0 +1,55 @@
+include <mach.h>
+include	<math/nlfit.h>
+include "nlfitdefd.h"
+
+# NLITER - Routine to compute one iteration of the fitting process
+
+procedure nliterd (nl, x, z, w, npts, nvars, ier)
+
+pointer	nl		# pointer to nl fitting structure
+double	x[ARB]		# independent variables (npts * nvars)
+double	z[ARB]		# function values (npts)
+double	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+int	ier		# error code
+
+int	i, index
+double	nlacptsd(), nlresidd()
+
+begin
+	# Do the initial accumulation.
+   	NL_OLDSQ(nl) = nlacptsd (nl, x, z, w, npts, nvars)
+
+	# Set up temporary parameter array.
+	call amovd (PARAM(NL_PARAM(nl)), TRY(NL_TRY(nl)), NL_NPARAMS(nl))
+
+	repeat {
+
+	    # Solve the matrix.
+	    call nlsolved (nl, ier)
+	    if (ier == NO_DEG_FREEDOM)
+	        return
+
+	    # Increment the parameters.
+	    do i = 1, NL_NFPARAMS(nl) {
+	        index = PLIST(NL_PLIST(nl)+i-1)
+	        TRY(NL_TRY(nl)+index-1) = TRY(NL_TRY(nl)+index-1) +
+		    DPARAM(NL_DPARAM(nl)+i-1)
+	    }
+
+	    # Reaccumulate the residuals and increment lambda.
+	    NL_SUMSQ(nl) = nlresidd (nl, x, z, w, npts, nvars)
+	    #if (NL_OLDSQ(nl) > (NL_SUMSQ(nl) + NL_TOL(nl) * NL_SUMSQ(nl))) {
+	    if (NL_OLDSQ(nl) >= NL_SUMSQ(nl)) {
+		call amovd (TRY(NL_TRY(nl)), PARAM(NL_PARAM(nl)),
+		    NL_NPARAMS(nl))
+		NL_LAMBDA(nl) = double (0.10) * NL_LAMBDA(nl)
+		break
+	    } else
+	        NL_LAMBDA(nl) = min (double(LAMBDAMAX),
+		    double (10.0) * NL_LAMBDA(nl))
+
+	} until (NL_LAMBDA(nl) <= double(0.0) ||
+	    NL_LAMBDA(nl) >= double(LAMBDAMAX))
+end
diff --git a/math/nlfit/nliterr.x b/math/nlfit/nliterr.x
new file mode 100644
index 00000000..cbc5a80a
--- /dev/null
+++ b/math/nlfit/nliterr.x
@@ -0,0 +1,55 @@
+include <mach.h>
+include	<math/nlfit.h>
+include "nlfitdefr.h"
+
+# NLITER - Routine to compute one iteration of the fitting process
+
+procedure nliterr (nl, x, z, w, npts, nvars, ier)
+
+pointer	nl		# pointer to nl fitting structure
+real	x[ARB]		# independent variables (npts * nvars)
+real	z[ARB]		# function values (npts)
+real	w[ARB]		# weights (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+int	ier		# error code
+
+int	i, index
+real	nlacptsr(), nlresidr()
+
+begin
+	# Do the initial accumulation.
+   	NL_OLDSQ(nl) = nlacptsr (nl, x, z, w, npts, nvars)
+
+	# Set up temporary parameter array.
+	call amovr (PARAM(NL_PARAM(nl)), TRY(NL_TRY(nl)), NL_NPARAMS(nl))
+
+	repeat {
+
+	    # Solve the matrix.
+	    call nlsolver (nl, ier)
+	    if (ier == NO_DEG_FREEDOM)
+	        return
+
+	    # Increment the parameters.
+	    do i = 1, NL_NFPARAMS(nl) {
+	        index = PLIST(NL_PLIST(nl)+i-1)
+	        TRY(NL_TRY(nl)+index-1) = TRY(NL_TRY(nl)+index-1) +
+		    DPARAM(NL_DPARAM(nl)+i-1)
+	    }
+
+	    # Reaccumulate the residuals and increment lambda.
+	    NL_SUMSQ(nl) = nlresidr (nl, x, z, w, npts, nvars)
+	    #if (NL_OLDSQ(nl) > (NL_SUMSQ(nl) + NL_TOL(nl) * NL_SUMSQ(nl))) {
+	    if (NL_OLDSQ(nl) >= NL_SUMSQ(nl)) {
+		call amovr (TRY(NL_TRY(nl)), PARAM(NL_PARAM(nl)),
+		    NL_NPARAMS(nl))
+		NL_LAMBDA(nl) = real (0.10) * NL_LAMBDA(nl)
+		break
+	    } else
+	        NL_LAMBDA(nl) = min (real(LAMBDAMAX),
+		    real (10.0) * NL_LAMBDA(nl))
+
+	} until (NL_LAMBDA(nl) <= real(0.0) ||
+	    NL_LAMBDA(nl) >= real(LAMBDAMAX))
+end
diff --git a/math/nlfit/nllist.x b/math/nlfit/nllist.x
new file mode 100644
index 00000000..d96351c9
--- /dev/null
+++ b/math/nlfit/nllist.x
@@ -0,0 +1,30 @@
+# NL_LIST -- Procedure to order the list used when the NLFIT structure
+# is initialized.
+
+procedure nl_list (list, nlist, nfit)
+
+int	list[ARB]		# list
+int	nlist			# number of elements in the list
+int	nfit			# number of active list elments
+
+int	i, j, nfitp1, ifound
+
+begin
+	nfitp1 = nfit + 1
+
+	do i = 1, nlist {
+	    ifound = 0
+	    do j = 1, nfit {
+		if (list[j] == i)
+		    ifound = ifound + 1
+	    }
+	    if (ifound == 0) {
+		list[nfitp1] = i
+		nfitp1 = nfitp1 + 1
+	    } else if (ifound > 1)
+	        call error (0, "Incorrect parameter ordering in plist")
+	}
+
+	if (nfitp1 != (nlist + 1))
+	    call error (0, "Incorrect parameter ordering in plist")
+end
diff --git a/math/nlfit/nlpget.gx b/math/nlfit/nlpget.gx
new file mode 100644
index 00000000..3a74fa6f
--- /dev/null
+++ b/math/nlfit/nlpget.gx
@@ -0,0 +1,18 @@
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+# NLPGET - Retreive parameter values
+
+procedure nlpget$t (nl, params, nparams)
+
+pointer	nl			# pointer to the nlfit structure
+PIXEL	params[ARB]		# parameter array
+int	nparams			# the number of the parameters
+
+begin
+	nparams = NL_NPARAMS(nl)
+	call amov$t (PARAM(NL_PARAM(nl)), params, nparams)
+end
diff --git a/math/nlfit/nlpgetd.x b/math/nlfit/nlpgetd.x
new file mode 100644
index 00000000..419bde09
--- /dev/null
+++ b/math/nlfit/nlpgetd.x
@@ -0,0 +1,14 @@
+include "nlfitdefd.h"
+
+# NLPGET - Retreive parameter values
+
+procedure nlpgetd (nl, params, nparams)
+
+pointer	nl			# pointer to the nlfit structure
+double	params[ARB]		# parameter array
+int	nparams			# the number of the parameters
+
+begin
+	nparams = NL_NPARAMS(nl)
+	call amovd (PARAM(NL_PARAM(nl)), params, nparams)
+end
diff --git a/math/nlfit/nlpgetr.x b/math/nlfit/nlpgetr.x
new file mode 100644
index 00000000..73fd7cbb
--- /dev/null
+++ b/math/nlfit/nlpgetr.x
@@ -0,0 +1,14 @@
+include "nlfitdefr.h"
+
+# NLPGET - Retreive parameter values
+
+procedure nlpgetr (nl, params, nparams)
+
+pointer	nl			# pointer to the nlfit structure
+real	params[ARB]		# parameter array
+int	nparams			# the number of the parameters
+
+begin
+	nparams = NL_NPARAMS(nl)
+	call amovr (PARAM(NL_PARAM(nl)), params, nparams)
+end
diff --git a/math/nlfit/nlsolve.gx b/math/nlfit/nlsolve.gx
new file mode 100644
index 00000000..a4055520
--- /dev/null
+++ b/math/nlfit/nlsolve.gx
@@ -0,0 +1,41 @@
+include <math/nlfit.h>
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+# NLSOLVE -- Procedure to solve nonlinear system
+
+procedure nlsolve$t (nl, ier)
+
+pointer	nl	# pointer to the nlfit structure
+int	ier	# error code
+
+int	nfree
+
+begin
+	# Make temporary arrays.
+	call amov$t (ALPHA(NL_ALPHA(nl)), COVAR(NL_COVAR(nl)),
+	    NL_NFPARAMS(nl) ** 2)
+	call amov$t (BETA(NL_BETA(nl)), DPARAM(NL_DPARAM(nl)), NL_NFPARAMS(nl))
+
+	# Add the lambda damping factor.
+	call nl_damp$t (COVAR(NL_COVAR(nl)), COVAR(NL_COVAR(nl)),
+	    (1.0 + NL_LAMBDA(nl)), NL_NFPARAMS(nl), NL_NFPARAMS(nl))
+
+	ier = OK
+	nfree = NL_NPTS(nl) - NL_NFPARAMS(nl)
+	if (nfree < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# Compute the factorization of the matrix.
+	call nl_chfac$t (COVAR(NL_COVAR(nl)), NL_NFPARAMS(nl), NL_NFPARAMS(nl),
+	    CHOFAC(NL_CHOFAC(nl)), ier)
+
+	# Solve the equations for the parameter increments.
+	call nl_chslv$t (CHOFAC(NL_CHOFAC(nl)), NL_NFPARAMS(nl), NL_NFPARAMS(nl),
+	    DPARAM(NL_DPARAM(nl)), DPARAM(NL_DPARAM(nl)))
+end
diff --git a/math/nlfit/nlsolved.x b/math/nlfit/nlsolved.x
new file mode 100644
index 00000000..77a43337
--- /dev/null
+++ b/math/nlfit/nlsolved.x
@@ -0,0 +1,37 @@
+include <math/nlfit.h>
+include "nlfitdefd.h"
+
+# NLSOLVE -- Procedure to solve nonlinear system
+
+procedure nlsolved (nl, ier)
+
+pointer	nl	# pointer to the nlfit structure
+int	ier	# error code
+
+int	nfree
+
+begin
+	# Make temporary arrays.
+	call amovd (ALPHA(NL_ALPHA(nl)), COVAR(NL_COVAR(nl)),
+	    NL_NFPARAMS(nl) ** 2)
+	call amovd (BETA(NL_BETA(nl)), DPARAM(NL_DPARAM(nl)), NL_NFPARAMS(nl))
+
+	# Add the lambda damping factor.
+	call nl_dampd (COVAR(NL_COVAR(nl)), COVAR(NL_COVAR(nl)),
+	    (1.0 + NL_LAMBDA(nl)), NL_NFPARAMS(nl), NL_NFPARAMS(nl))
+
+	ier = OK
+	nfree = NL_NPTS(nl) - NL_NFPARAMS(nl)
+	if (nfree < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# Compute the factorization of the matrix.
+	call nl_chfacd (COVAR(NL_COVAR(nl)), NL_NFPARAMS(nl), NL_NFPARAMS(nl),
+	    CHOFAC(NL_CHOFAC(nl)), ier)
+
+	# Solve the equations for the parameter increments.
+	call nl_chslvd (CHOFAC(NL_CHOFAC(nl)), NL_NFPARAMS(nl), NL_NFPARAMS(nl),
+	    DPARAM(NL_DPARAM(nl)), DPARAM(NL_DPARAM(nl)))
+end
diff --git a/math/nlfit/nlsolver.x b/math/nlfit/nlsolver.x
new file mode 100644
index 00000000..85d238d6
--- /dev/null
+++ b/math/nlfit/nlsolver.x
@@ -0,0 +1,37 @@
+include <math/nlfit.h>
+include "nlfitdefr.h"
+
+# NLSOLVE -- Procedure to solve nonlinear system
+
+procedure nlsolver (nl, ier)
+
+pointer	nl	# pointer to the nlfit structure
+int	ier	# error code
+
+int	nfree
+
+begin
+	# Make temporary arrays.
+	call amovr (ALPHA(NL_ALPHA(nl)), COVAR(NL_COVAR(nl)),
+	    NL_NFPARAMS(nl) ** 2)
+	call amovr (BETA(NL_BETA(nl)), DPARAM(NL_DPARAM(nl)), NL_NFPARAMS(nl))
+
+	# Add the lambda damping factor.
+	call nl_dampr (COVAR(NL_COVAR(nl)), COVAR(NL_COVAR(nl)),
+	    (1.0 + NL_LAMBDA(nl)), NL_NFPARAMS(nl), NL_NFPARAMS(nl))
+
+	ier = OK
+	nfree = NL_NPTS(nl) - NL_NFPARAMS(nl)
+	if (nfree < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# Compute the factorization of the matrix.
+	call nl_chfacr (COVAR(NL_COVAR(nl)), NL_NFPARAMS(nl), NL_NFPARAMS(nl),
+	    CHOFAC(NL_CHOFAC(nl)), ier)
+
+	# Solve the equations for the parameter increments.
+	call nl_chslvr (CHOFAC(NL_CHOFAC(nl)), NL_NFPARAMS(nl), NL_NFPARAMS(nl),
+	    DPARAM(NL_DPARAM(nl)), DPARAM(NL_DPARAM(nl)))
+end
diff --git a/math/nlfit/nlstat.gx b/math/nlfit/nlstat.gx
new file mode 100644
index 00000000..c17d5940
--- /dev/null
+++ b/math/nlfit/nlstat.gx
@@ -0,0 +1,30 @@
+include <math/nlfit.h>
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+# NLSTAT[RD] - Fetch an NLFIT real/double parameter
+
+PIXEL procedure nlstat$t (nl, param)
+
+pointer	nl		# pointer to NLFIT structure
+int	param		# parameter to be fetched
+
+begin
+	switch (param) {
+	case NLSUMSQ:
+	    return (NL_SUMSQ(nl))
+	case NLOLDSQ:
+	    return (NL_OLDSQ(nl))
+	case NLTOL:
+	    return (NL_TOL(nl))
+	case NLLAMBDA:
+	    return (NL_LAMBDA(nl))
+	case NLSCATTER:
+	    return (NL_SCATTER(nl))
+	default:
+	    return ($INDEF$T)
+	}
+end
diff --git a/math/nlfit/nlstatd.x b/math/nlfit/nlstatd.x
new file mode 100644
index 00000000..73661ce8
--- /dev/null
+++ b/math/nlfit/nlstatd.x
@@ -0,0 +1,26 @@
+include <math/nlfit.h>
+include "nlfitdefd.h"
+
+# NLSTAT[RD] - Fetch an NLFIT real/double parameter
+
+double procedure nlstatd (nl, param)
+
+pointer	nl		# pointer to NLFIT structure
+int	param		# parameter to be fetched
+
+begin
+	switch (param) {
+	case NLSUMSQ:
+	    return (NL_SUMSQ(nl))
+	case NLOLDSQ:
+	    return (NL_OLDSQ(nl))
+	case NLTOL:
+	    return (NL_TOL(nl))
+	case NLLAMBDA:
+	    return (NL_LAMBDA(nl))
+	case NLSCATTER:
+	    return (NL_SCATTER(nl))
+	default:
+	    return (INDEFD)
+	}
+end
diff --git a/math/nlfit/nlstati.x b/math/nlfit/nlstati.x
new file mode 100644
index 00000000..04c8cf27
--- /dev/null
+++ b/math/nlfit/nlstati.x
@@ -0,0 +1,26 @@
+include "nlfitdefr.h"
+include <math/nlfit.h>
+
+# NLSTATI - Fetch a NLFIT integer parameter
+
+int procedure nlstati (nl, param)
+
+pointer	nl		# pointer to NLFIT structure
+int	param		# parameter to be fetched
+
+begin
+	switch (param) {
+	case NLNPARAMS:
+	    return (NL_NPARAMS(nl))
+	case NLNFPARAMS:
+	    return (NL_NFPARAMS(nl))
+	case NLITMAX:
+	    return (NL_ITMAX(nl))
+	case NLITER:
+	    return (NL_ITER(nl))
+	case NLNPTS:
+	    return (NL_NPTS(nl))
+	default:
+	    return (INDEFI)
+	}
+end
diff --git a/math/nlfit/nlstatr.x b/math/nlfit/nlstatr.x
new file mode 100644
index 00000000..c6360017
--- /dev/null
+++ b/math/nlfit/nlstatr.x
@@ -0,0 +1,26 @@
+include <math/nlfit.h>
+include "nlfitdefr.h"
+
+# NLSTAT[RD] - Fetch an NLFIT real/double parameter
+
+real procedure nlstatr (nl, param)
+
+pointer	nl		# pointer to NLFIT structure
+int	param		# parameter to be fetched
+
+begin
+	switch (param) {
+	case NLSUMSQ:
+	    return (NL_SUMSQ(nl))
+	case NLOLDSQ:
+	    return (NL_OLDSQ(nl))
+	case NLTOL:
+	    return (NL_TOL(nl))
+	case NLLAMBDA:
+	    return (NL_LAMBDA(nl))
+	case NLSCATTER:
+	    return (NL_SCATTER(nl))
+	default:
+	    return (INDEFR)
+	}
+end
diff --git a/math/nlfit/nlvector.gx b/math/nlfit/nlvector.gx
new file mode 100644
index 00000000..f33d063c
--- /dev/null
+++ b/math/nlfit/nlvector.gx
@@ -0,0 +1,27 @@
+include	<math/nlfit.h>
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+define	VAR	(($1 - 1) * $2 + 1)
+
+# NLVECTOR -- Evaluate the fit for a series of data points.
+
+procedure nlvector$t (nl, x, zfit, npts, nvars)
+
+pointer	nl		# pointer to nl fitting structure
+PIXEL	x[ARB]		# independent variables (npts * nvars)
+PIXEL	zfit[ARB]	# function values (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+int	i
+
+begin
+	# Compute the fitted function.
+	do i = 1, npts
+	    call zcall5 (NL_FUNC(nl), x[VAR (i, nvars)], nvars,
+		PARAM(NL_PARAM(nl)), NL_NPARAMS(nl), zfit[i])
+end
diff --git a/math/nlfit/nlvectord.x b/math/nlfit/nlvectord.x
new file mode 100644
index 00000000..34bce9a5
--- /dev/null
+++ b/math/nlfit/nlvectord.x
@@ -0,0 +1,23 @@
+include	<math/nlfit.h>
+include "nlfitdefd.h"
+
+define	VAR	(($1 - 1) * $2 + 1)
+
+# NLVECTOR -- Evaluate the fit for a series of data points.
+
+procedure nlvectord (nl, x, zfit, npts, nvars)
+
+pointer	nl		# pointer to nl fitting structure
+double	x[ARB]		# independent variables (npts * nvars)
+double	zfit[ARB]	# function values (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+int	i
+
+begin
+	# Compute the fitted function.
+	do i = 1, npts
+	    call zcall5 (NL_FUNC(nl), x[VAR (i, nvars)], nvars,
+		PARAM(NL_PARAM(nl)), NL_NPARAMS(nl), zfit[i])
+end
diff --git a/math/nlfit/nlvectorr.x b/math/nlfit/nlvectorr.x
new file mode 100644
index 00000000..43450695
--- /dev/null
+++ b/math/nlfit/nlvectorr.x
@@ -0,0 +1,23 @@
+include	<math/nlfit.h>
+include "nlfitdefr.h"
+
+define	VAR	(($1 - 1) * $2 + 1)
+
+# NLVECTOR -- Evaluate the fit for a series of data points.
+
+procedure nlvectorr (nl, x, zfit, npts, nvars)
+
+pointer	nl		# pointer to nl fitting structure
+real	x[ARB]		# independent variables (npts * nvars)
+real	zfit[ARB]	# function values (npts)
+int	npts		# number of points
+int	nvars		# number of independent variables
+
+int	i
+
+begin
+	# Compute the fitted function.
+	do i = 1, npts
+	    call zcall5 (NL_FUNC(nl), x[VAR (i, nvars)], nvars,
+		PARAM(NL_PARAM(nl)), NL_NPARAMS(nl), zfit[i])
+end
diff --git a/math/nlfit/nlzero.gx b/math/nlfit/nlzero.gx
new file mode 100644
index 00000000..ffd1458b
--- /dev/null
+++ b/math/nlfit/nlzero.gx
@@ -0,0 +1,38 @@
+$if (datatype == r)
+include "nlfitdefr.h"
+$else
+include "nlfitdefd.h"
+$endif
+
+
+# NLZERO --  Zero the accumulators and reset the fitting parameter values to
+# their original values set by nlinit().
+
+procedure nlzero$t (nl)
+
+pointer	nl		# pointer to nl fitting structure
+
+int	nparams		# number of parameters
+int	nfparams	# number of fitted parameters
+
+begin
+	# Get number of parameters and fitting parameters.
+	nparams  = NL_NPARAMS(nl)
+	nfparams = NL_NFPARAMS(nl)
+
+	# Clear temporary array space.
+	call aclr$t (ALPHA(NL_ALPHA(nl)), nfparams * nfparams)
+	call aclr$t (COVAR(NL_COVAR(nl)), nfparams * nfparams)
+	call aclr$t (CHOFAC(NL_CHOFAC(nl)), nfparams * nfparams)
+	call aclr$t (BETA(NL_BETA(nl)), nfparams)
+
+	# Clear space for derivatives and trial parameter vectors.
+	call aclr$t (DERIV(NL_DERIV(nl)), nparams)
+	call aclr$t (TRY(NL_TRY(nl)), nparams)
+
+	# Reset parameters.
+	call amov$t (OPARAM(NL_OPARAM(nl)), PARAM(NL_PARAM(nl)), nparams)
+	call aclr$t (DPARAM(NL_DPARAM(nl)), nparams)
+
+	NL_SCATTER(nl) = PIXEL(0.0)
+end
diff --git a/math/nlfit/nlzerod.x b/math/nlfit/nlzerod.x
new file mode 100644
index 00000000..2ee86562
--- /dev/null
+++ b/math/nlfit/nlzerod.x
@@ -0,0 +1,34 @@
+include "nlfitdefd.h"
+
+
+# NLZERO --  Zero the accumulators and reset the fitting parameter values to
+# their original values set by nlinit().
+
+procedure nlzerod (nl)
+
+pointer	nl		# pointer to nl fitting structure
+
+int	nparams		# number of parameters
+int	nfparams	# number of fitted parameters
+
+begin
+	# Get number of parameters and fitting parameters.
+	nparams  = NL_NPARAMS(nl)
+	nfparams = NL_NFPARAMS(nl)
+
+	# Clear temporary array space.
+	call aclrd (ALPHA(NL_ALPHA(nl)), nfparams * nfparams)
+	call aclrd (COVAR(NL_COVAR(nl)), nfparams * nfparams)
+	call aclrd (CHOFAC(NL_CHOFAC(nl)), nfparams * nfparams)
+	call aclrd (BETA(NL_BETA(nl)), nfparams)
+
+	# Clear space for derivatives and trial parameter vectors.
+	call aclrd (DERIV(NL_DERIV(nl)), nparams)
+	call aclrd (TRY(NL_TRY(nl)), nparams)
+
+	# Reset parameters.
+	call amovd (OPARAM(NL_OPARAM(nl)), PARAM(NL_PARAM(nl)), nparams)
+	call aclrd (DPARAM(NL_DPARAM(nl)), nparams)
+
+	NL_SCATTER(nl) = double(0.0)
+end
diff --git a/math/nlfit/nlzeror.x b/math/nlfit/nlzeror.x
new file mode 100644
index 00000000..1cceba31
--- /dev/null
+++ b/math/nlfit/nlzeror.x
@@ -0,0 +1,34 @@
+include "nlfitdefr.h"
+
+
+# NLZERO --  Zero the accumulators and reset the fitting parameter values to
+# their original values set by nlinit().
+
+procedure nlzeror (nl)
+
+pointer	nl		# pointer to nl fitting structure
+
+int	nparams		# number of parameters
+int	nfparams	# number of fitted parameters
+
+begin
+	# Get number of parameters and fitting parameters.
+	nparams  = NL_NPARAMS(nl)
+	nfparams = NL_NFPARAMS(nl)
+
+	# Clear temporary array space.
+	call aclrr (ALPHA(NL_ALPHA(nl)), nfparams * nfparams)
+	call aclrr (COVAR(NL_COVAR(nl)), nfparams * nfparams)
+	call aclrr (CHOFAC(NL_CHOFAC(nl)), nfparams * nfparams)
+	call aclrr (BETA(NL_BETA(nl)), nfparams)
+
+	# Clear space for derivatives and trial parameter vectors.
+	call aclrr (DERIV(NL_DERIV(nl)), nparams)
+	call aclrr (TRY(NL_TRY(nl)), nparams)
+
+	# Reset parameters.
+	call amovr (OPARAM(NL_OPARAM(nl)), PARAM(NL_PARAM(nl)), nparams)
+	call aclrr (DPARAM(NL_DPARAM(nl)), nparams)
+
+	NL_SCATTER(nl) = real(0.0)
+end
diff --git a/math/slalib/Makefile.am b/math/slalib/Makefile.am
new file mode 100644
index 00000000..547240a7
--- /dev/null
+++ b/math/slalib/Makefile.am
@@ -0,0 +1,76 @@
+## Process this file with automake to produce Makefile.in
+
+cincludedir = $(includedir)/star
+dist_bin_SCRIPTS = sla_link sla_link_adam
+dist_pkgdata_DATA = SLA_CONDITIONS read.me
+
+EXTRA_DIST = Notes
+
+lib_LTLIBRARIES = libsla.la
+
+stardocs_DATA = @STAR_LATEX_DOCUMENTATION@
+
+libsla_la_SOURCES = \
+        $(PRIVATE_INCLUDES) \
+        $(PUBLIC_INCLUDES) \
+	$(F_ROUTINES) \
+	$(C_ROUTINES) \
+	$(FPP_ROUTINES)
+libsla_la_LIBADD = $(LTLIBOBJS)
+libsla_la_LDFLAGS = -version-info $(libsla_la_version_info)
+
+cinclude_HEADERS = $(PUBLIC_C_INCLUDES)
+
+# Make all library code position independent. This is handy for creating
+# shareable libraries from the static ones (Java JNI libraries).
+if !NOPIC
+libsla_la_FCFLAGS = $(AM_FCFLAGS) -prefer-pic
+endif
+
+PUBLIC_F_INCLUDES = 
+PUBLIC_C_INCLUDES = slalib.h 
+PRIVATE_INCLUDES = f77.h
+PUBLIC_INCLUDES = $(PUBLIC_F_INCLUDES) $(PUBLIC_C_INCLUDES)
+
+FPP_ROUTINES = \
+	random.F \
+	gresid.F
+
+C_ROUTINES = sla.c 
+
+F_ROUTINES = addet.f afin.f airmas.f altaz.f amp.f ampqk.f aop.f	\
+    aoppa.f aoppat.f aopqk.f atmdsp.f atms.f atmt.f av2m.f bear.f	\
+    caf2r.f caldj.f calyd.f cc2s.f cc62s.f cd2tf.f cldj.f clyd.f	\
+    combn.f cr2af.f cr2tf.f cs2c.f cs2c6.f ctf2d.f ctf2r.f daf2r.f	\
+    dafin.f dat.f dav2m.f dbear.f dbjin.f dc62s.f dcc2s.f dcmpf.f	\
+    dcs2c.f dd2tf.f de2h.f deuler.f dfltin.f dh2e.f dimxv.f djcal.f	\
+    djcl.f dm2av.f dmat.f dmoon.f dmxm.f dmxv.f dpav.f dr2af.f dr2tf.f	\
+    drange.f dranrm.f ds2c6.f ds2tp.f dsep.f dsepv.f dt.f dtf2d.f	\
+    dtf2r.f dtp2s.f dtp2v.f dtps2c.f dtpv2c.f dtt.f dv2tp.f dvdv.f	\
+    dvn.f dvxv.f e2h.f earth.f ecleq.f ecmat.f ecor.f eg50.f el2ue.f	\
+    epb.f epb2d.f epco.f epj.f epj2d.f epv.f eqecl.f eqeqx.f eqgal.f	\
+    etrms.f euler.f evp.f fitxy.f fk425.f fk45z.f fk524.f fk52h.f	\
+    fk54z.f fk5hz.f flotin.f galeq.f galsup.f ge50.f geoc.f gmst.f	\
+    gmsta.f h2e.f h2fk5.f hfk5z.f idchf.f idchi.f imxv.f intin.f	\
+    invf.f kbj.f m2av.f map.f mappa.f mapqk.f mapqkz.f moon.f mxm.f	\
+    mxv.f nut.f nutc.f nutc80.f oap.f oapqk.f obs.f pa.f pav.f pcd.f	\
+    pda2h.f pdq2h.f permut.f pertel.f pertue.f planel.f planet.f	\
+    plante.f plantu.f pm.f polmo.f prebn.f prec.f precl.f preces.f	\
+    prenut.f pv2el.f pv2ue.f pvobs.f pxy.f range.f ranorm.f rcc.f	\
+    rdplan.f refco.f refcoq.f refro.f refv.f refz.f rverot.f rvgalc.f	\
+    rvlg.f rvlsrd.f rvlsrk.f s2tp.f sep.f sepv.f smat.f subet.f		\
+    supgal.f svd.f svdcov.f svdsol.f tp2s.f tp2v.f tps2c.f tpv2c.f	\
+    ue2el.f ue2pv.f unpcd.f v2tp.f vdv.f veri.f vers.f vn.f vxv.f	\
+    wait.f xy2xy.f zd.f
+
+TESTS = sla_test slaTest
+check_PROGRAMS = sla_test slaTest
+
+sla_test_SOURCES = sla_test.f
+sla_test_LDADD = libsla.la
+
+slaTest_SOURCES = slaTest.c
+slaTest_LDADD   = libsla.la @FCLIBS@
+
+dist_starnews_DATA = sla.news
+DISTCLEANFILES = gresid.F random.F wait.f
diff --git a/math/slalib/Notes b/math/slalib/Notes
new file mode 100644
index 00000000..ffb5efca
--- /dev/null
+++ b/math/slalib/Notes
@@ -0,0 +1,23 @@
+
+SLALIB imported into CVS and autoconfed, January 2003.
+
+Platform-dependencies: there were three platform-dependent files, for
+random.f, gresid.f (both requiring a random number function) and
+wait.f (sleeps).  The original set of files had extensions alpha_OSF1,
+convex, ix86_Linux, mips, pcm, sun4, sun4_Solaris, and vax.  In each
+case, there were a number of files for unix-like platforms, one
+Windows/MSFortran (pcm) and one VAX one.  For random and gresid, the
+unix ones were largely the same, differing only in whether they called
+a function random() or ran(), and with different calls -- these could
+be handled using fpp.
+
+The Windows and VMS ones were sufficiently different that they've
+remained in separate files.  Each of the three has a __win file,
+specific to MSFortran (or to Windows, I'm not sure).  In each of the
+three cases, the __vms file is the original _vax file -- it's specific
+to VMS, not the VAX.  For random and gresid, the files are called
+random.fpp{__win,_dec_osf} even though there's nothing preprocessable
+in them.
+
+I _think_ I've got the __vms and __win dependencies right, but I've no
+way of testing them.
diff --git a/math/slalib/README b/math/slalib/README
new file mode 100644
index 00000000..606d3784
--- /dev/null
+++ b/math/slalib/README
@@ -0,0 +1,233 @@
+This directory contains the Fortran source for the SLALIB version 2.5-2
+routines. The SLALIB Fortran library has been made available to the IRAF
+project courtesy of Patrick Wallace of the Starlink project, the version
+distributed here is derived from the Starlink 2012 release in order to
+include the GPL'd version of the code.  All the documentation normally
+provided with the Starlink routines can be found in the doc subdirectory,
+and in the sun67.tex file.  See the 'read.me' and 'SLA_CONDITIONS' file
+in this directory for additional information and license restrictions.
+
+In order to complete the port to iraf the following name changes were
+made to the package routines. The package prefix was changed from "sla_"
+to "sl". Routines with root names that were longer than four characters
+have been renamed so that all the package routines have unique six
+character names. The complete name change list is shown below.
+A Unix sed script for implementing the changes automatically can be found
+in the file sedscript, using the editing commands in the files SED1,
+SED2, SED3.
+
+The machine dependent routines gresid, random, and wait have been removed
+from the IRAF version of SLALIB. The IRAF routines urand in osb$urand.x
+and tsleep in etc$tsleep.x can be used to replace the SLALIB routines
+random and wait.
+
+No other changes have been made to any of the routines. However a new
+routine precss.f has been added to the package. Precss.f is identical to
+preces.f except that the system argument is an integer code rather
+than a Fortran string. This avoids having to deal with Fortran strings
+and conversions in spp programs for this commonly used routine.
+
+The complete name translation list.
+
+sla_ADDET	slADET   
+sla_AFIN	slAFIN   
+sla_AIRMAS	slARMS   
+sla_ALTAZ	slALAZ   
+sla_AMP		slAMP   
+sla_AMPQK	slAMPQ   
+sla_AOP		slAOP   
+sla_AOPPA	slAOPA   
+sla_AOPPAT	slAOPT   
+sla_AOPQK	slAOPQ   
+sla__ATMS	slATMS   
+sla__ATMT	slATMT   
+sla_ATMDSP	slATMD   
+sla_AV2M	slAV2M   
+	
+sla_BEAR	slBEAR   
+	
+sla_CAF2R	slCAFR   
+sla_CALDJ	slCADJ   
+sla_CALYD	slCAYD   
+sla_CC2S	slCC2S   
+sla_CC62S	slC62S   
+sla_CD2TF	slCDTF   
+sla_CLDJ	slCLDJ   
+sla_CLYD	slCLYD   
+sla_CR2AF	slCRAF   
+sla_CR2TF	slCRTF   
+sla_CS2C	slCS2C   
+sla_CS2C6	slS2C6   
+sla_CTF2D	slCTFD   
+sla_CTF2R	slCTFR   
+	
+sla_DAF2R	slDAFR   
+sla_DAFIN	slDAFN   
+sla_DAT		slDAT   
+sla_DAV2M	slDAVM   
+sla_DBEAR	slDBER   
+sla_DBJIN	slDBJI   
+sla_DC62S	slDC6S   
+sla_DCC2S	slDC2S   
+sla_DCMPF	slDCMF   
+sla_DCS2C	slDS2C   
+sla_DD2TF	slDDTF   
+sla_DE2H	slDE2H   
+sla_DEULER	slDEUL   
+sla_DFLTIN	slDFLI   
+sla_DH2E	slDH2E   
+sla_DIMXV	slDIMV   
+sla_DJCAL	slDJCA   
+sla_DJCL	slDJCL   
+sla_DM2AV	slDMAV   
+sla_DMAT	slDMAT   
+sla_DMOON	slDMON   
+sla_DMXM	slDMXM   
+sla_DMXV	slDMXV   
+sla_DPAV	slDPAV
+sla_DR2AF	slDRAF   
+sla_DR2TF	slDRTF   
+sla_DRANGE	slDA1P   
+sla_DRANRM	slDA2P   
+sla_DS2C6	slDSC6   
+sla_DS2TP	slDSTP   
+sla_DSEP	slDSEP   
+sla_DT		slDT   
+sla_DTF2D	slDTFD   
+sla_DTF2R	slDTFR   
+sla_DTP2S	slDTPS   
+sla_DTP2V	slDTPV   
+sla_DTPS2C	slDPSC   
+sla_DTPV2C	slDPVC   
+sla_DTT		slDTT   
+sla_DV2TP	slDVTP   
+sla_DVDV	slDVDV   
+sla_DVN		slDVN   
+sla_DVXV	slDVXV   
+	
+sla_E2H		slE2H   
+sla_EARTH	slERTH   
+sla_ECLEQ	slECEQ   
+sla_ECMAT	slECMA   
+sla_ECOR	slECOR   
+sla_EG50	slEG50   
+sla_EL2UE       slELUE   
+sla_EPB		slEPB   
+sla_EPB2D	slEB2D   
+sla_EPCO	slEPCO   
+sla_EPJ		slEPJ   
+sla_EPJ2D	slEJ2D   
+sla_EQECL	slEQEC   
+sla_EQEQX	slEQEX   
+sla_EQGAL	slEQGA   
+sla_ETRMS	slETRM   
+sla_EULER	slEULR   
+sla_EVP		slEVP   
+	
+sla_FITXY	slFTXY   
+sla_FK425	slFK45   
+sla_FK45Z	slF45Z   
+sla_FK524	slFK54   
+sla_FK52H       slFK5H
+sla_FK54Z	slF54Z   
+sla_FK5HZ       slF5HZ
+sla_FLOTIN	slRFLI   
+	
+sla_GALEQ	slGAEQ   
+sla_GALSUP	slGASU   
+sla_GE50	slGE50   
+sla_GEOC	slGEOC   
+sla_GMST	slGMST   
+sla_GMSTA	slGMSA   
+
+sla_H2E		slH2E   
+sla_H2FK5       slHFK5
+sla_HFK5Z       slHF5Z
+	
+sla__IDCHI	slICHI   
+sla__IDCHF	slICHF   
+sla_IMXV	slIMXV   
+sla_INTIN	slINTI   
+sla_INVF	slINVF   
+	
+sla_KBJ		slKBJ   
+	
+sla_M2AV	slM2AV   
+sla_MAP		slMAP   
+sla_MAPPA	slMAPA   
+sla_MAPQK	slMAPQ   
+sla_MAPQKZ	slMAPZ   
+sla_MOON	slMOON   
+sla_MXM		slMXM   
+sla_MXV		slMXV   
+	
+sla_NUT		slNUT   
+sla_NUTC	slNUTC   
+	
+sla_OBS		slOBS   
+sla_OAP		slOAP   
+sla_OAPQK	slOAPQ   
+	
+sla_PA		slPA   
+sla_PAV		slPAV   
+sla_PCD		slPCD   
+sla_PDA2H	slPDAH   
+sla_PDQ2H	slPDQH   
+sla_PERTEL      slPRTL   
+sla_PERTUE      slPRTE   
+sla_PLANEL      slPLNE   
+sla_PLANET	slPLNT   
+sla_PLANTE      slPLTE   
+sla_PM		slPM   
+sla_POLMO       slPLMO
+sla_PREBN	slPRBN   
+sla_PREC	slPREC   
+sla_PRECES	slPRCE   
+sla_PRECL	slPREL   
+sla_PRECSS      slPRCS			# no SLALIB version
+sla_PRENUT	slPRNU   
+sla_PV2EL       slPVEL   
+sla_PV2UE       slPVUE   
+sla_PVOBS	slPVOB   
+sla_PXY		slPXY   
+	
+sla_RANGE	slRA1P   
+sla_RANORM	slRA2P   
+sla_RCC		slRCC   
+sla_RDPLAN	slRDPL   
+sla_REFCO	slRFCO   
+sla_REFCOQ      slRFCQ   
+sla_REFRO	slRFRO   
+sla_REFV	slREFV   
+sla_REFZ	slREFZ   
+sla_RVEROT	slRVER   
+sla_RVGALC	slRVGA   
+sla_RVLG	slRVLG   
+sla_RVLSRD	slRVLD   
+sla_RVLSRK	slRVLK   
+	
+sla_S2TP	slS2TP   
+sla_SEP		slSEP   
+sla_SMAT	slSMAT   
+sla_SUBET	slSUET   
+sla_SUPGAL	slSUGA   
+sla_SVD		slSVD   
+sla_SVDCOV	slSVDC   
+sla_SVDSOL	slSVDS   
+	
+sla_TP2S	slTP2S   
+sla_TP2V	slTP2V   
+sla_TPS2C	slTPSC   
+sla_TPV2C	slTPVC   
+	
+sla_UE2EL       slUEEL    
+sla_UE2PV       slUEPV    
+sla_UNPCD	slUPCD   
+	
+sla_V2TP	slV2TP   
+sla_VDV		slVDV   
+sla_VN		slVN   
+sla_VXV		slVXV   
+	
+sla_XY2XY	slXYXY   
+sla_ZD		slZD   
diff --git a/math/slalib/SED1 b/math/slalib/SED1
new file mode 100644
index 00000000..8fdff423
--- /dev/null
+++ b/math/slalib/SED1
@@ -0,0 +1,214 @@
+1,$s/sla_ADDET/slADET/g
+1,$s/sla_AFIN/slAFIN/g
+1,$s/sla_AIRMAS/slARMS/g
+1,$s/sla_ALTAZ/slALAZ/g
+1,$s/sla_AMPQK/slAMPQ/g
+1,$s/sla_AMP/slAMP/g
+1,$s/sla_AOPPAT/slAOPT/g
+1,$s/sla_AOPPA/slAOPA/g
+1,$s/sla_AOPQK/slAOPQ/g
+1,$s/sla_AOP/slAOP/g
+1,$s/sla_ATMDSP/slATMD/g
+1,$s/sla__ATMS/slATMS/g
+1,$s/sla__ATMT/slATMT/g
+1,$s/sla_AV2M/slAV2M/g
+
+1,$s/sla_BEAR/slBEAR/g
+
+1,$s/sla_CAF2R/slCAFR/g
+1,$s/sla_CALDJ/slCADJ/g
+1,$s/sla_CALYD/slCAYD/g
+1,$s/sla_CC2S/slCC2S/g
+1,$s/sla_CC62S/slC62S/g
+1,$s/sla_CD2TF/slCDTF/g
+1,$s/sla_CLDJ/slCLDJ/g
+1,$s/sla_CLYD/slCLYD/g
+1,$s/sla_CR2AF/slCRAF/g
+1,$s/sla_CR2TF/slCRTF/g
+1,$s/sla_CS2C6/slS2C6/g
+1,$s/sla_CS2C/slCS2C/g
+1,$s/sla_CTF2D/slCTFD/g
+1,$s/sla_CTF2R/slCTFR/g
+
+1,$s/sla_DAF2R/slDAFR/g
+1,$s/sla_DAFIN/slDAFN/g
+1,$s/sla_DAT/slDAT/g
+1,$s/sla_DAV2M/slDAVM/g
+1,$s/sla_DBEAR/slDBER/g
+1,$s/sla_DBJIN/slDBJI/g
+1,$s/sla_DC62S/slDC6S/g
+1,$s/sla_DCC2S/slDC2S/g
+1,$s/sla_DCMPF/slDCMF/g
+1,$s/sla_DCS2C/slDS2C/g
+1,$s/sla_DD2TF/slDDTF/g
+1,$s/sla_DE2H/slDE2H/g
+1,$s/sla_DEULER/slDEUL/g
+1,$s/sla_DFLTIN/slDFLI/g
+1,$s/sla_DH2E/slDH2E/g
+1,$s/sla_DIMXV/slDIMV/g
+1,$s/sla_DJCAL/slDJCA/g
+1,$s/sla_DJCL/slDJCL/g
+1,$s/sla_DM2AV/slDMAV/g
+1,$s/sla_DMAT/slDMAT/g
+1,$s/sla_DMOON/slDMON/g
+1,$s/sla_DMXM/slDMXM/g
+1,$s/sla_DMXV/slDMXV/g
+1,$s/sla_DPAV/slDPAV/g
+1,$s/sla_DR2AF/slDRAF/g
+1,$s/sla_DR2TF/slDRTF/g
+1,$s/sla_DRANGE/slDA1P/g
+1,$s/sla_DRANRM/slDA2P/g
+1,$s/sla_DS2C6/slDSC6/g
+1,$s/sla_DS2TP/slDSTP/g
+1,$s/sla_DSEP/slDSEP/g
+1,$s/sla_DTF2D/slDTFD/g
+1,$s/sla_DTF2R/slDTFR/g
+1,$s/sla_DTP2S/slDTPS/g
+1,$s/sla_DTP2V/slDTPV/g
+1,$s/sla_DTPS2C/slDPSC/g
+1,$s/sla_DTPV2C/slDPVC/g
+1,$s/sla_DTT/slDTT/g
+1,$s/sla_DT/slDT/g
+
+1,$s/sla_DV2TP/slDVTP/g
+1,$s/sla_DVDV/slDVDV/g
+1,$s/sla_DVN/slDVN/g
+1,$s/sla_DVXV/slDVXV/g
+
+1,$s/sla_E2H/slE2H/g
+1,$s/sla_EARTH/slERTH/g
+1,$s/sla_ECLEQ/slECEQ/g
+1,$s/sla_ECMAT/slECMA/g
+1,$s/sla_ECOR/slECOR/g
+1,$s/sla_EG50/slEG50/g
+1,$s/sla_EL2UE/slELUE/g
+1,$s/sla_EPB2D/slEB2D/g
+1,$s/sla_EPB/slEPB/g
+1,$s/sla_EPCO/slEPCO/g
+1,$s/sla_EPJ2D/slEJ2D/g
+1,$s/sla_EPJ/slEPJ/g
+1,$s/sla_EQECL/slEQEC/g
+1,$s/sla_EQEQX/slEQEX/g
+1,$s/sla_EQGAL/slEQGA/g
+1,$s/sla_ETRMS/slETRM/g
+1,$s/sla_EULER/slEULR/g
+1,$s/sla_EVP/slEVP/g
+
+1,$s/sla_FITXY/slFTXY/g
+1,$s/sla_FK425/slFK45/g
+1,$s/sla_FK45Z/slF45Z/g
+1,$s/sla_FK524/slFK54/g
+1,$s/sla_FK52H/slFK5H/g
+1,$s/sla_FK54Z/slF54Z/g
+1,$s/sla_FK5HZ/slF5HZ/g
+1,$s/sla_FLOTIN/slRFLI/g
+
+1,$s/sla_GALEQ/slGAEQ/g
+1,$s/sla_GALSUP/slGASU/g
+1,$s/sla_GE50/slGE50/g
+1,$s/sla_GEOC/slGEOC/g
+1,$s/sla_GMSTA/slGMSA/g
+1,$s/sla_GMST/slGMST/g
+1,$s/sla_GRESID/slGRES/g
+
+1,$s/sla_H2E/slH2E/g
+1,$s/sla_H2FK5/slHFK5/g
+1,$s/sla_HFK5Z/slHF5Z/g
+
+1,$s/sla__IDCHI/slICHI/g
+1,$s/sla__IDCHF/slICHF/g
+1,$s/sla_IMXV/slIMXV/g
+1,$s/sla_INTIN/slINTI/g
+1,$s/sla_INVF/slINVF/g
+
+1,$s/sla_KBJ/slKBJ/g
+
+1,$s/sla_M2AV/slM2AV/g
+1,$s/sla_MAPPA/slMAPA/g
+1,$s/sla_MAPQKZ/slMAPZ/g
+1,$s/sla_MAPQK/slMAPQ/g
+1,$s/sla_MAP/slMAP/g
+1,$s/sla_MOON/slMOON/g
+1,$s/sla_MXM/slMXM/g
+1,$s/sla_MXV/slMXV/g
+
+1,$s/sla_NUTC/slNUTC/g
+1,$s/sla_NUT/slNUT/g
+
+1,$s/sla_OAPQK/slOAPQ/g
+1,$s/sla_OAP/slOAP/g
+1,$s/sla_OBS/slOBS/g
+
+1,$s/sla_PA/slPA/g
+1,$s/sla_PAV/slPAV/g
+1,$s/sla_PCD/slPCD/g
+1,$s/sla_PDA2H/slPDAH/g
+1,$s/sla_PDQ2H/slPDQH/g
+1,$s/sla_PERTEL/slPRTL/g
+1,$s/sla_PERTUE/slPRTE/g
+1,$s/sla_PLANEL/slPLNE/g
+1,$s/sla_PLANET/slPLNT/g
+1,$s/sla_PLANTE/slPLTE/g
+1,$s/sla_PM/slPM/g
+1,$s/sla_POLMO/slPLMO/g
+1,$s/sla_PREBN/slPRBN/g
+1,$s/sla_PRECES/slPRCE/g
+1,$s/sla_PRECL/slPREL/g
+1,$s/sla_PREC/slPREC/g
+1,$s/sla_PRENUT/slPRNU/g
+1,$s/sla_PV2EL/slPVEL/g
+1,$s/sla_PV2UE/slPVUE/g
+1,$s/sla_PVOBS/slPVOB/g
+1,$s/sla_PXY/slPXY/g
+
+1,$s/sla_RANDOM/slRNDM/g
+1,$s/sla_RANGE/slRA1P/g
+1,$s/sla_RANORM/slRA2P/g
+1,$s/sla_RCC/slRCC/g
+1,$s/sla_RDPLAN/slRDPL/g
+1,$s/sla_REFCOQ/slRFCQ/g
+1,$s/sla_REFCO/slRFCO/g
+1,$s/sla_REFRO/slRFRO/g
+1,$s/sla_REFV/slREFV/g
+1,$s/sla_REFZ/slREFZ/g
+1,$s/sla_RVEROT/slRVER/g
+1,$s/sla_RVGALC/slRVGA/g
+1,$s/sla_RVLG/slRVLG/g
+1,$s/sla_RVLSRD/slRVLD/g
+1,$s/sla_RVLSRK/slRVLK/g
+
+1,$s/sla_S2TP/slS2TP/g
+1,$s/sla_SEP/slSEP/g
+1,$s/sla_SMAT/slSMAT/g
+1,$s/sla_SUBET/slSUET/g
+1,$s/sla_SUPGAL/slSUGA/g
+1,$s/sla_SVDCOV/slSVDC/g
+1,$s/sla_SVDSOL/slSVDS/g
+1,$s/sla_SVD/slSVD/g
+
+1,$s/sla_TP2S/slTP2S/g
+1,$s/sla_TP2V/slTP2V/g
+1,$s/sla_TPS2C/slTPSC/g
+1,$s/sla_TPV2C/slTPVC/g
+
+1,$s/sla_UE2EL/slUEEL/g
+1,$s/sla_UE2PV/slUEPV/g
+1,$s/sla_UNPCD/slUPCD/g
+
+1,$s/sla_V2TP/slV2TP/g
+1,$s/sla_VDV/slVDV/g
+1,$s/sla_VN/slVN/g
+1,$s/sla_VXV/slVXV/g
+
+1,$s/sla_WAIT/slWAIT/g
+1,$s/sla_XY2XY/slXYXY/g
+
+1,$s/sla_ZD/slZD/g
+
+
+1,$s/sla_COMBN/slCMBN/g
+1,$s/sla_EPV/slEPV/g
+1,$s/sla_PERMUT/slPERM/g
+1,$s/sla_PLANTU/slPLTU/g
+1,$s/sla_VERI/slVERI/g
+1,$s/sla_WAIT/slWAIT/g
diff --git a/math/slalib/SED2 b/math/slalib/SED2
new file mode 100644
index 00000000..e63ffd7a
--- /dev/null
+++ b/math/slalib/SED2
@@ -0,0 +1,132 @@
+1,$s/A D D E T/A D E T/g
+1,$s/A I R M A S/A R M S/g
+1,$s/A L T A Z/A L A Z/g
+1,$s/A M P Q K/A M P Q/g
+1,$s/A O P P A T/A O P T/g
+1,$s/A O P P A/A O P A/g
+1,$s/A O P Q K/A O P Q/g
+1,$s/A T M D S P/A T M D/g
+
+
+1,$s/C A F 2 R/C A F R/g
+1,$s/C A L D J/C A D J/g
+1,$s/C A L Y D/C A Y D/g
+1,$s/C C 6 2 S/C 6 2 S/g
+1,$s/C D 2 T F/C D T F/g
+1,$s/C R 2 A F/C R A F/g
+1,$s/C R 2 T F/C R T F/g
+1,$s/C S 2 C 6/S 2 C 6/g
+1,$s/C T F 2 D/C T F D/g
+1,$s/C T F 2 R/C T F R/g
+
+1,$s/D A F 2 R/D A F R/g
+1,$s/D A F I N/D A F N/g
+1,$s/D A V 2 M/D A V M/g
+1,$s/D B E A R/D B E R/g
+1,$s/D B J I N/D B J I/g
+1,$s/D C 6 2 S/D C 6 S/g
+1,$s/D C C 2 S/D C 2 S/g
+1,$s/D C M P F/D C M F/g
+1,$s/D C S 2 C/D S 2 C/g
+1,$s/D D 2 T F/D D T F/g
+1,$s/D E U L E R/D E U L/g
+1,$s/D F L T I N/D F L I/g
+1,$s/D I M X V/D I M V/g
+1,$s/D J C A L/D J C A/g
+1,$s/D M 2 A V/D M A V/g
+1,$s/D M O O N/D M O N/g
+1,$s/D R 2 A F/D R A F/g
+1,$s/D R 2 T F/D R T F/g
+1,$s/D R A N G E/D A 1 P/g
+1,$s/D R A N R M/D A 2 P/g
+1,$s/D S 2 C 6/D S C 6/g
+1,$s/D S 2 T P/D S T P/g
+1,$s/D T F 2 D/D T F D/g
+1,$s/D T F 2 R/D T F R/g
+1,$s/D T P 2 S/D T P S/g
+1,$s/D T P 2 V/D T P V/g
+1,$s/D T P S 2 C/D P S C/g
+1,$s/D T P V 2 C/D P V C/g
+1,$s/D V 2 T P/D V T P/g
+
+1,$s/E A R T H/E R T H/g
+1,$s/E C L E Q/E C E Q/g
+1,$s/E C M A T/E C M A/g
+1,$s/E L 2 U E/E L U E/g
+1,$s/E P B 2 D/E B 2 D/g
+1,$s/E P J 2 D/E J 2 D/g
+1,$s/E Q E C L/E Q E C/g
+1,$s/E Q E Q X/E Q E X/g
+1,$s/E Q G A L/E Q G A/g
+1,$s/E T R M S/E T R M/g
+1,$s/E U L E R/E U L R/g
+
+1,$s/F I T X Y/F T X Y/g
+1,$s/F K 4 2 5/F K 4 5/g
+1,$s/F K 4 5 Z/F 4 5 Z/g
+1,$s/F K 5 2 4/F K 5 4/g
+1,$s/F K 5 2 H/F K 5 H/g
+1,$s/F K 5 4 Z/F 5 4 Z/g
+1,$s/F K 5 H Z/F 5 H Z/g
+
+1,$s/F L O T I N/R F L I/g
+
+1,$s/G A L E Q/G A E Q/g
+1,$s/G A L S U P/G A S U/g
+1,$s/G M S T A/G M S A/g
+1,$s/G R E S I D/G R E S/g
+
+1,$s/H 2 F K 5/H F K 5/g
+1,$s/H F K 5 Z/H F 5 Z/g
+
+1,$s/I D C H I/I C H I/g
+1,$s/I D C H F/I C H F/g
+1,$s/I N T I N/I N T I/g
+
+1,$s/M A P P A/M A P A/g
+1,$s/M A P Q K Z/M A P Z/g
+1,$s/M A P Q K/M A P Q/g
+
+1,$s/O A P Q K/O A P Q/g
+
+1,$s/P D A 2 H/P D A H/g
+1,$s/P D Q 2 H/P D Q H/g
+1,$s/P E R T E L/P R T L/g
+1,$s/P E R T U E/P R T E/g
+1,$s/P L A N E L/P L N L/g
+1,$s/P L A N E T/P L N T/g
+1,$s/P L A N T E/P L T E/g
+1,$s/P O L M O/P L M O/g
+1,$s/P R E B N/P R B N/g
+1,$s/P R E C E S/P R C E/g
+1,$s/P R E C L/P R E L/g
+1,$s/P R E N U T/P R N U/g
+1,$s/P V 2 U E/P V U E/g
+1,$s/P V 2 E L/P V E L/g
+1,$s/P V O B S/P V O B/g
+
+1,$s/R A N D O M/R N D M/g
+1,$s/R A N G E/R A 1 P/g
+1,$s/R A N O R M/R A 2 P/g
+1,$s/R D P L A N/R D P L/g
+1,$s/R E F C O Q/R F C Q/g
+1,$s/R E F C O/R F C O/g
+1,$s/R E F R O/R F R O/g
+1,$s/R V E R O T/R V E R/g
+1,$s/R V G A L C/R V G A/g
+1,$s/R V L S R D/R V L D/g
+1,$s/R V L S R K/R V L K/g
+
+1,$s/S U B E T/S U E T/g
+1,$s/S U P G A L/S U G A/g
+1,$s/S V D C O V/S V D C/g
+1,$s/S V D S O L/S V D S/g
+
+1,$s/T P S 2 C/T P S C/g
+1,$s/T P V 2 C/T P V C/g
+
+1,$s/U E 2 E L/U E E L/g
+1,$s/U E 2 P V/U E P V/g
+1,$s/U N P C D/U P C D/g
+
+1,$s/X Y 2 X Y/X Y X Y/g
diff --git a/math/slalib/SLA_CONDITIONS b/math/slalib/SLA_CONDITIONS
new file mode 100644
index 00000000..2bc1e36b
--- /dev/null
+++ b/math/slalib/SLA_CONDITIONS
@@ -0,0 +1,280 @@
+		    GNU GENERAL PUBLIC LICENSE
+		       Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+                       51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+			    Preamble
+
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+   TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
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diff --git a/math/slalib/addet.f b/math/slalib/addet.f
new file mode 100644
index 00000000..4c58c8a8
--- /dev/null
+++ b/math/slalib/addet.f
@@ -0,0 +1,85 @@
+      SUBROUTINE slADET (RM, DM, EQ, RC, DC)
+*+
+*     - - - - - -
+*      A D E T
+*     - - - - - -
+*
+*  Add the E-terms (elliptic component of annual aberration)
+*  to a pre IAU 1976 mean place to conform to the old
+*  catalogue convention (double precision)
+*
+*  Given:
+*     RM,DM     dp     RA,Dec (radians) without E-terms
+*     EQ        dp     Besselian epoch of mean equator and equinox
+*
+*  Returned:
+*     RC,DC     dp     RA,Dec (radians) with E-terms included
+*
+*  Note:
+*
+*     Most star positions from pre-1984 optical catalogues (or
+*     derived from astrometry using such stars) embody the
+*     E-terms.  If it is necessary to convert a formal mean
+*     place (for example a pulsar timing position) to one
+*     consistent with such a star catalogue, then the RA,Dec
+*     should be adjusted using this routine.
+*
+*  Reference:
+*     Explanatory Supplement to the Astronomical Ephemeris,
+*     section 2D, page 48.
+*
+*  Called:  slETRM, slDS2C, slDC2S, slDA2P, slDA1P
+*
+*  P.T.Wallace   Starlink   18 March 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RM,DM,EQ,RC,DC
+
+      DOUBLE PRECISION slDA2P
+
+      DOUBLE PRECISION A(3),V(3)
+
+      INTEGER I
+
+
+
+*  E-terms vector
+      CALL slETRM(EQ,A)
+
+*  Spherical to Cartesian
+      CALL slDS2C(RM,DM,V)
+
+*  Include the E-terms
+      DO I=1,3
+         V(I)=V(I)+A(I)
+      END DO
+
+*  Cartesian to spherical
+      CALL slDC2S(V,RC,DC)
+
+*  Bring RA into conventional range
+      RC=slDA2P(RC)
+
+      END
diff --git a/math/slalib/afin.f b/math/slalib/afin.f
new file mode 100644
index 00000000..7e7fac4f
--- /dev/null
+++ b/math/slalib/afin.f
@@ -0,0 +1,120 @@
+      SUBROUTINE slAFIN (STRING, IPTR, A, J)
+*+
+*     - - - - -
+*      A F I N
+*     - - - - -
+*
+*  Sexagesimal character string to angle (single precision)
+*
+*  Given:
+*     STRING  c*(*)   string containing deg, arcmin, arcsec fields
+*     IPTR      i     pointer to start of decode (1st = 1)
+*
+*  Returned:
+*     IPTR      i     advanced past the decoded angle
+*     A         r     angle in radians
+*     J         i     status:  0 = OK
+*                             +1 = default, A unchanged
+*                             -1 = bad degrees      )
+*                             -2 = bad arcminutes   )  (note 3)
+*                             -3 = bad arcseconds   )
+*
+*  Example:
+*
+*    argument    before                           after
+*
+*    STRING      '-57 17 44.806  12 34 56.7'      unchanged
+*    IPTR        1                                16 (points to 12...)
+*    A           ?                                -1.00000
+*    J           ?                                0
+*
+*    A further call to slAFIN, without adjustment of IPTR, will
+*    decode the second angle, 12deg 34min 56.7sec.
+*
+*  Notes:
+*
+*     1)  The first three "fields" in STRING are degrees, arcminutes,
+*         arcseconds, separated by spaces or commas.  The degrees field
+*         may be signed, but not the others.  The decoding is carried
+*         out by the DFLTIN routine and is free-format.
+*
+*     2)  Successive fields may be absent, defaulting to zero.  For
+*         zero status, the only combinations allowed are degrees alone,
+*         degrees and arcminutes, and all three fields present.  If all
+*         three fields are omitted, a status of +1 is returned and A is
+*         unchanged.  In all other cases A is changed.
+*
+*     3)  Range checking:
+*
+*           The degrees field is not range checked.  However, it is
+*           expected to be integral unless the other two fields are
+*           absent.
+*
+*           The arcminutes field is expected to be 0-59, and integral if
+*           the arcseconds field is present.  If the arcseconds field
+*           is absent, the arcminutes is expected to be 0-59.9999...
+*
+*           The arcseconds field is expected to be 0-59.9999...
+*
+*     4)  Decoding continues even when a check has failed.  Under these
+*         circumstances the field takes the supplied value, defaulting
+*         to zero, and the result A is computed and returned.
+*
+*     5)  Further fields after the three expected ones are not treated
+*         as an error.  The pointer IPTR is left in the correct state
+*         for further decoding with the present routine or with DFLTIN
+*         etc.  See the example, above.
+*
+*     6)  If STRING contains hours, minutes, seconds instead of degrees
+*         etc, or if the required units are turns (or days) instead of
+*         radians, the result A should be multiplied as follows:
+*
+*           for        to obtain    multiply
+*           STRING     A in         A by
+*
+*           d ' "      radians      1       =  1.0
+*           d ' "      turns        1/2pi   =  0.1591549430918953358
+*           h m s      radians      15      =  15.0
+*           h m s      days         15/2pi  =  2.3873241463784300365
+*
+*  Called:  slDAFN
+*
+*  P.T.Wallace   Starlink   13 September 1990
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) STRING
+      INTEGER IPTR
+      REAL A
+      INTEGER J
+
+      DOUBLE PRECISION AD
+
+
+
+*  Call the double precision version
+      CALL slDAFN(STRING,IPTR,AD,J)
+      IF (J.LE.0) A=REAL(AD)
+
+      END
diff --git a/math/slalib/airmas.f b/math/slalib/airmas.f
new file mode 100644
index 00000000..aa9d08f0
--- /dev/null
+++ b/math/slalib/airmas.f
@@ -0,0 +1,76 @@
+      DOUBLE PRECISION FUNCTION slARMS (ZD)
+*+
+*     - - - - - - -
+*      A R M S
+*     - - - - - - -
+*
+*  Air mass at given zenith distance (double precision)
+*
+*  Given:
+*     ZD     d     Observed zenith distance (radians)
+*
+*  The result is an estimate of the air mass, in units of that
+*  at the zenith.
+*
+*  Notes:
+*
+*  1)  The "observed" zenith distance referred to above means "as
+*      affected by refraction".
+*
+*  2)  Uses Hardie's (1962) polynomial fit to Bemporad's data for
+*      the relative air mass, X, in units of thickness at the zenith
+*      as tabulated by Schoenberg (1929). This is adequate for all
+*      normal needs as it is accurate to better than 0.1% up to X =
+*      6.8 and better than 1% up to X = 10. Bemporad's tabulated
+*      values are unlikely to be trustworthy to such accuracy
+*      because of variations in density, pressure and other
+*      conditions in the atmosphere from those assumed in his work.
+*
+*  3)  The sign of the ZD is ignored.
+*
+*  4)  At zenith distances greater than about ZD = 87 degrees the
+*      air mass is held constant to avoid arithmetic overflows.
+*
+*  References:
+*     Hardie, R.H., 1962, in "Astronomical Techniques"
+*        ed. W.A. Hiltner, University of Chicago Press, p180.
+*     Schoenberg, E., 1929, Hdb. d. Ap.,
+*        Berlin, Julius Springer, 2, 268.
+*
+*  Original code by P.W.Hill, St Andrews
+*
+*  P.T.Wallace   Starlink   18 March 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION ZD
+
+      DOUBLE PRECISION SECZM1
+
+
+      SECZM1 = 1D0/(COS(MIN(1.52D0,ABS(ZD))))-1D0
+      slARMS = 1D0 + SECZM1*(0.9981833D0
+     :             - SECZM1*(0.002875D0 + 0.0008083D0*SECZM1))
+
+      END
diff --git a/math/slalib/altaz.f b/math/slalib/altaz.f
new file mode 100644
index 00000000..ca34a0d4
--- /dev/null
+++ b/math/slalib/altaz.f
@@ -0,0 +1,163 @@
+      SUBROUTINE slALAZ (HA, DEC, PHI,
+     :                      AZ, AZD, AZDD, EL, ELD, ELDD, PA, PAD, PADD)
+*+
+*     - - - - - -
+*      A L A Z
+*     - - - - - -
+*
+*  Positions, velocities and accelerations for an altazimuth
+*  telescope mount.
+*
+*  (double precision)
+*
+*  Given:
+*     HA      d     hour angle
+*     DEC     d     declination
+*     PHI     d     observatory latitude
+*
+*  Returned:
+*     AZ      d     azimuth
+*     AZD     d        "    velocity
+*     AZDD    d        "    acceleration
+*     EL      d     elevation
+*     ELD     d         "     velocity
+*     ELDD    d         "     acceleration
+*     PA      d     parallactic angle
+*     PAD     d         "      "   velocity
+*     PADD    d         "      "   acceleration
+*
+*  Notes:
+*
+*  1)  Natural units are used throughout.  HA, DEC, PHI, AZ, EL
+*      and ZD are in radians.  The velocities and accelerations
+*      assume constant declination and constant rate of change of
+*      hour angle (as for tracking a star);  the units of AZD, ELD
+*      and PAD are radians per radian of HA, while the units of AZDD,
+*      ELDD and PADD are radians per radian of HA squared.  To
+*      convert into practical degree- and second-based units:
+*
+*        angles * 360/2pi -> degrees
+*        velocities * (2pi/86400)*(360/2pi) -> degree/sec
+*        accelerations * ((2pi/86400)**2)*(360/2pi) -> degree/sec/sec
+*
+*      Note that the seconds here are sidereal rather than SI.  One
+*      sidereal second is about 0.99727 SI seconds.
+*
+*      The velocity and acceleration factors assume the sidereal
+*      tracking case.  Their respective numerical values are (exactly)
+*      1/240 and (approximately) 1/3300236.9.
+*
+*  2)  Azimuth is returned in the range 0-2pi;  north is zero,
+*      and east is +pi/2.  Elevation and parallactic angle are
+*      returned in the range +/-pi.  Parallactic angle is +ve for
+*      a star west of the meridian and is the angle NP-star-zenith.
+*
+*  3)  The latitude is geodetic as opposed to geocentric.  The
+*      hour angle and declination are topocentric.  Refraction and
+*      deficiencies in the telescope mounting are ignored.  The
+*      purpose of the routine is to give the general form of the
+*      quantities.  The details of a real telescope could profoundly
+*      change the results, especially close to the zenith.
+*
+*  4)  No range checking of arguments is carried out.
+*
+*  5)  In applications which involve many such calculations, rather
+*      than calling the present routine it will be more efficient to
+*      use inline code, having previously computed fixed terms such
+*      as sine and cosine of latitude, and (for tracking a star)
+*      sine and cosine of declination.
+*
+*  This revision:  29 October 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION HA,DEC,PHI,AZ,AZD,AZDD,EL,ELD,ELDD,PA,PAD,PADD
+
+      DOUBLE PRECISION DPI,D2PI,TINY
+      PARAMETER (DPI=3.1415926535897932384626433832795D0,
+     :           D2PI=6.283185307179586476925286766559D0,
+     :           TINY=1D-30)
+
+      DOUBLE PRECISION SH,CH,SD,CD,SP,CP,CHCD,SDCP,X,Y,Z,RSQ,R,A,E,C,S,
+     :                 Q,QD,AD,ED,EDR,ADD,EDD,QDD
+
+
+*  Useful functions
+      SH=SIN(HA)
+      CH=COS(HA)
+      SD=SIN(DEC)
+      CD=COS(DEC)
+      SP=SIN(PHI)
+      CP=COS(PHI)
+      CHCD=CH*CD
+      SDCP=SD*CP
+      X=-CHCD*SP+SDCP
+      Y=-SH*CD
+      Z=CHCD*CP+SD*SP
+      RSQ=X*X+Y*Y
+      R=SQRT(RSQ)
+
+*  Azimuth and elevation
+      IF (RSQ.EQ.0D0) THEN
+         A=0D0
+      ELSE
+         A=ATAN2(Y,X)
+      END IF
+      IF (A.LT.0D0) A=A+D2PI
+      E=ATAN2(Z,R)
+
+*  Parallactic angle
+      C=CD*SP-CH*SDCP
+      S=SH*CP
+      IF (C*C+S*S.GT.0) THEN
+         Q=ATAN2(S,C)
+      ELSE
+         Q=DPI-HA
+      END IF
+
+*  Velocities and accelerations (clamped at zenith/nadir)
+      IF (RSQ.LT.TINY) THEN
+         RSQ=TINY
+         R=SQRT(RSQ)
+      END IF
+      QD=-X*CP/RSQ
+      AD=SP+Z*QD
+      ED=CP*Y/R
+      EDR=ED/R
+      ADD=EDR*(Z*SP+(2D0-RSQ)*QD)
+      EDD=-R*QD*AD
+      QDD=EDR*(SP+2D0*Z*QD)
+
+*  Results
+      AZ=A
+      AZD=AD
+      AZDD=ADD
+      EL=E
+      ELD=ED
+      ELDD=EDD
+      PA=Q
+      PAD=QD
+      PADD=QDD
+
+      END
diff --git a/math/slalib/amp.f b/math/slalib/amp.f
new file mode 100644
index 00000000..d6aff8df
--- /dev/null
+++ b/math/slalib/amp.f
@@ -0,0 +1,89 @@
+      SUBROUTINE slAMP (RA, DA, DATE, EQ, RM, DM)
+*+
+*     - - - -
+*      A M P
+*     - - - -
+*
+*  Convert star RA,Dec from geocentric apparent to mean place
+*
+*  The mean coordinate system is the post IAU 1976 system,
+*  loosely called FK5.
+*
+*  Given:
+*     RA       d      apparent RA (radians)
+*     DA       d      apparent Dec (radians)
+*     DATE     d      TDB for apparent place (JD-2400000.5)
+*     EQ       d      equinox:  Julian epoch of mean place
+*
+*  Returned:
+*     RM       d      mean RA (radians)
+*     DM       d      mean Dec (radians)
+*
+*  References:
+*     1984 Astronomical Almanac, pp B39-B41.
+*     (also Lederle & Schwan, Astron. Astrophys. 134,
+*      1-6, 1984)
+*
+*  Notes:
+*
+*  1)  The distinction between the required TDB and TT is always
+*      negligible.  Moreover, for all but the most critical
+*      applications UTC is adequate.
+*
+*  2)  Iterative techniques are used for the aberration and light
+*      deflection corrections so that the routines slAMP (or
+*      slAMPQ) and slMAP (or slMAPQ) are accurate inverses;
+*      even at the edge of the Sun's disc the discrepancy is only
+*      about 1 nanoarcsecond.
+*
+*  3)  Where multiple apparent places are to be converted to mean
+*      places, for a fixed date and equinox, it is more efficient to
+*      use the slMAPA routine to compute the required parameters
+*      once, followed by one call to slAMPQ per star.
+*
+*  4)  The accuracy is sub-milliarcsecond, limited by the
+*      precession-nutation model (IAU 1976 precession, Shirai &
+*      Fukushima 2001 forced nutation and precession corrections).
+*
+*  5)  The accuracy is further limited by the routine slEVP, called
+*      by slMAPA, which computes the Earth position and velocity
+*      using the methods of Stumpff.  The maximum error is about
+*      0.3 mas.
+*
+*  Called:  slMAPA, slAMPQ
+*
+*  P.T.Wallace   Starlink   17 September 2001
+*
+*  Copyright (C) 2001 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RA,DA,DATE,EQ,RM,DM
+
+      DOUBLE PRECISION AMPRMS(21)
+
+
+
+      CALL slMAPA(EQ,DATE,AMPRMS)
+      CALL slAMPQ(RA,DA,AMPRMS,RM,DM)
+
+      END
diff --git a/math/slalib/ampqk.f b/math/slalib/ampqk.f
new file mode 100644
index 00000000..4bf95b69
--- /dev/null
+++ b/math/slalib/ampqk.f
@@ -0,0 +1,140 @@
+      SUBROUTINE slAMPQ (RA, DA, AMPRMS, RM, DM)
+*+
+*     - - - - - -
+*      A M P Q
+*     - - - - - -
+*
+*  Convert star RA,Dec from geocentric apparent to mean place
+*
+*  The mean coordinate system is the post IAU 1976 system,
+*  loosely called FK5.
+*
+*  Use of this routine is appropriate when efficiency is important
+*  and where many star positions are all to be transformed for
+*  one epoch and equinox.  The star-independent parameters can be
+*  obtained by calling the slMAPA routine.
+*
+*  Given:
+*     RA       d      apparent RA (radians)
+*     DA       d      apparent Dec (radians)
+*
+*     AMPRMS   d(21)  star-independent mean-to-apparent parameters:
+*
+*       (1)      time interval for proper motion (Julian years)
+*       (2-4)    barycentric position of the Earth (AU)
+*       (5-7)    heliocentric direction of the Earth (unit vector)
+*       (8)      (grav rad Sun)*2/(Sun-Earth distance)
+*       (9-11)   ABV: barycentric Earth velocity in units of c
+*       (12)     sqrt(1-v**2) where v=modulus(ABV)
+*       (13-21)  precession/nutation (3,3) matrix
+*
+*  Returned:
+*     RM       d      mean RA (radians)
+*     DM       d      mean Dec (radians)
+*
+*  References:
+*     1984 Astronomical Almanac, pp B39-B41.
+*     (also Lederle & Schwan, Astron. Astrophys. 134,
+*      1-6, 1984)
+*
+*  Note:
+*
+*     Iterative techniques are used for the aberration and
+*     light deflection corrections so that the routines
+*     slAMP (or slAMPQ) and slMAP (or slMAPQ) are
+*     accurate inverses;  even at the edge of the Sun's disc
+*     the discrepancy is only about 1 nanoarcsecond.
+*
+*  Called:  slDS2C, slDIMV, slDVDV, slDVN, slDC2S,
+*           slDA2P
+*
+*  P.T.Wallace   Starlink   7 May 2000
+*
+*  Copyright (C) 2000 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RA,DA,AMPRMS(21),RM,DM
+
+      INTEGER I,J
+
+      DOUBLE PRECISION GR2E,AB1,EHN(3),ABV(3),P3(3),P2(3),
+     :                 AB1P1,P1DV,P1DVP1,P1(3),W,PDE,PDEP1,P(3)
+
+      DOUBLE PRECISION slDVDV,slDA2P
+
+
+
+*  Unpack scalar and vector parameters
+      GR2E = AMPRMS(8)
+      AB1 = AMPRMS(12)
+      DO I=1,3
+         EHN(I) = AMPRMS(I+4)
+         ABV(I) = AMPRMS(I+8)
+      END DO
+
+*  Apparent RA,Dec to Cartesian
+      CALL slDS2C(RA,DA,P3)
+
+*  Precession and nutation
+      CALL slDIMV(AMPRMS(13),P3,P2)
+
+*  Aberration
+      AB1P1 = AB1+1D0
+      DO I=1,3
+         P1(I) = P2(I)
+      END DO
+      DO J=1,2
+         P1DV = slDVDV(P1,ABV)
+         P1DVP1 = 1D0+P1DV
+         W = 1D0+P1DV/AB1P1
+         DO I=1,3
+            P1(I) = (P1DVP1*P2(I)-W*ABV(I))/AB1
+         END DO
+         CALL slDVN(P1,P3,W)
+         DO I=1,3
+            P1(I) = P3(I)
+         END DO
+      END DO
+
+*  Light deflection
+      DO I=1,3
+         P(I) = P1(I)
+      END DO
+      DO J=1,5
+         PDE = slDVDV(P,EHN)
+         PDEP1 = 1D0+PDE
+         W = PDEP1-GR2E*PDE
+         DO I=1,3
+            P(I) = (PDEP1*P1(I)-GR2E*EHN(I))/W
+         END DO
+         CALL slDVN(P,P2,W)
+         DO I=1,3
+            P(I) = P2(I)
+         END DO
+      END DO
+
+*  Mean RA,Dec
+      CALL slDC2S(P,RM,DM)
+      RM = slDA2P(RM)
+
+      END
diff --git a/math/slalib/aop.f b/math/slalib/aop.f
new file mode 100644
index 00000000..0155deb1
--- /dev/null
+++ b/math/slalib/aop.f
@@ -0,0 +1,192 @@
+      SUBROUTINE slAOP ( RAP, DAP, DATE, DUT, ELONGM, PHIM, HM,
+     :                     XP, YP, TDK, PMB, RH, WL, TLR,
+     :                     AOB, ZOB, HOB, DOB, ROB )
+*+
+*     - - - -
+*      A O P
+*     - - - -
+*
+*  Apparent to observed place, for sources distant from the solar
+*  system.
+*
+*  Given:
+*     RAP    d      geocentric apparent right ascension
+*     DAP    d      geocentric apparent declination
+*     DATE   d      UTC date/time (Modified Julian Date, JD-2400000.5)
+*     DUT    d      delta UT:  UT1-UTC (UTC seconds)
+*     ELONGM d      mean longitude of the observer (radians, east +ve)
+*     PHIM   d      mean geodetic latitude of the observer (radians)
+*     HM     d      observer's height above sea level (metres)
+*     XP     d      polar motion x-coordinate (radians)
+*     YP     d      polar motion y-coordinate (radians)
+*     TDK    d      local ambient temperature (K; std=273.15D0)
+*     PMB    d      local atmospheric pressure (mb; std=1013.25D0)
+*     RH     d      local relative humidity (in the range 0D0-1D0)
+*     WL     d      effective wavelength (micron, e.g. 0.55D0)
+*     TLR    d      tropospheric lapse rate (K/metre, e.g. 0.0065D0)
+*
+*  Returned:
+*     AOB    d      observed azimuth (radians: N=0,E=90)
+*     ZOB    d      observed zenith distance (radians)
+*     HOB    d      observed Hour Angle (radians)
+*     DOB    d      observed Declination (radians)
+*     ROB    d      observed Right Ascension (radians)
+*
+*  Notes:
+*
+*   1)  This routine returns zenith distance rather than elevation
+*       in order to reflect the fact that no allowance is made for
+*       depression of the horizon.
+*
+*   2)  The accuracy of the result is limited by the corrections for
+*       refraction.  Providing the meteorological parameters are
+*       known accurately and there are no gross local effects, the
+*       predicted apparent RA,Dec should be within about 0.1 arcsec
+*       for a zenith distance of less than 70 degrees.  Even at a
+*       topocentric zenith distance of 90 degrees, the accuracy in
+*       elevation should be better than 1 arcmin;  useful results
+*       are available for a further 3 degrees, beyond which the
+*       slRFRO routine returns a fixed value of the refraction.
+*       The complementary routines slAOP (or slAOPQ) and slOAP
+*       (or slOAPQ) are self-consistent to better than 1 micro-
+*       arcsecond all over the celestial sphere.
+*
+*   3)  It is advisable to take great care with units, as even
+*       unlikely values of the input parameters are accepted and
+*       processed in accordance with the models used.
+*
+*   4)  "Apparent" place means the geocentric apparent right ascension
+*       and declination, which is obtained from a catalogue mean place
+*       by allowing for space motion, parallax, precession, nutation,
+*       annual aberration, and the Sun's gravitational lens effect.  For
+*       star positions in the FK5 system (i.e. J2000), these effects can
+*       be applied by means of the slMAP etc routines.  Starting from
+*       other mean place systems, additional transformations will be
+*       needed;  for example, FK4 (i.e. B1950) mean places would first
+*       have to be converted to FK5, which can be done with the
+*       slFK45 etc routines.
+*
+*   5)  "Observed" Az,El means the position that would be seen by a
+*       perfect theodolite located at the observer.  This is obtained
+*       from the geocentric apparent RA,Dec by allowing for Earth
+*       orientation and diurnal aberration, rotating from equator
+*       to horizon coordinates, and then adjusting for refraction.
+*       The HA,Dec is obtained by rotating back into equatorial
+*       coordinates, using the geodetic latitude corrected for polar
+*       motion, and is the position that would be seen by a perfect
+*       equatorial located at the observer and with its polar axis
+*       aligned to the Earth's axis of rotation (n.b. not to the
+*       refracted pole).  Finally, the RA is obtained by subtracting
+*       the HA from the local apparent ST.
+*
+*   6)  To predict the required setting of a real telescope, the
+*       observed place produced by this routine would have to be
+*       adjusted for the tilt of the azimuth or polar axis of the
+*       mounting (with appropriate corrections for mount flexures),
+*       for non-perpendicularity between the mounting axes, for the
+*       position of the rotator axis and the pointing axis relative
+*       to it, for tube flexure, for gear and encoder errors, and
+*       finally for encoder zero points.  Some telescopes would, of
+*       course, exhibit other properties which would need to be
+*       accounted for at the appropriate point in the sequence.
+*
+*   7)  This routine takes time to execute, due mainly to the
+*       rigorous integration used to evaluate the refraction.
+*       For processing multiple stars for one location and time,
+*       call slAOPA once followed by one call per star to slAOPQ.
+*       Where a range of times within a limited period of a few hours
+*       is involved, and the highest precision is not required, call
+*       slAOPA once, followed by a call to slAOPT each time the
+*       time changes, followed by one call per star to slAOPQ.
+*
+*   8)  The DATE argument is UTC expressed as an MJD.  This is,
+*       strictly speaking, wrong, because of leap seconds.  However,
+*       as long as the delta UT and the UTC are consistent there
+*       are no difficulties, except during a leap second.  In this
+*       case, the start of the 61st second of the final minute should
+*       begin a new MJD day and the old pre-leap delta UT should
+*       continue to be used.  As the 61st second completes, the MJD
+*       should revert to the start of the day as, simultaneously,
+*       the delta UTC changes by one second to its post-leap new value.
+*
+*   9)  The delta UT (UT1-UTC) is tabulated in IERS circulars and
+*       elsewhere.  It increases by exactly one second at the end of
+*       each UTC leap second, introduced in order to keep delta UT
+*       within +/- 0.9 seconds.
+*
+*  10)  IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.
+*       The longitude required by the present routine is east-positive,
+*       in accordance with geographical convention (and right-handed).
+*       In particular, note that the longitudes returned by the
+*       slOBS routine are west-positive, following astronomical
+*       usage, and must be reversed in sign before use in the present
+*       routine.
+*
+*  11)  The polar coordinates XP,YP can be obtained from IERS
+*       circulars and equivalent publications.  The maximum amplitude
+*       is about 0.3 arcseconds.  If XP,YP values are unavailable,
+*       use XP=YP=0D0.  See page B60 of the 1988 Astronomical Almanac
+*       for a definition of the two angles.
+*
+*  12)  The height above sea level of the observing station, HM,
+*       can be obtained from the Astronomical Almanac (Section J
+*       in the 1988 edition), or via the routine slOBS.  If P,
+*       the pressure in millibars, is available, an adequate
+*       estimate of HM can be obtained from the expression
+*
+*             HM ~ -29.3D0*TSL*LOG(P/1013.25D0).
+*
+*       where TSL is the approximate sea-level air temperature in K
+*       (see Astrophysical Quantities, C.W.Allen, 3rd edition,
+*       section 52).  Similarly, if the pressure P is not known,
+*       it can be estimated from the height of the observing
+*       station, HM, as follows:
+*
+*             P ~ 1013.25D0*EXP(-HM/(29.3D0*TSL)).
+*
+*       Note, however, that the refraction is nearly proportional to the
+*       pressure and that an accurate P value is important for precise
+*       work.
+*
+*  13)  The azimuths etc produced by the present routine are with
+*       respect to the celestial pole.  Corrections to the terrestrial
+*       pole can be computed using slPLMO.
+*
+*  Called:  slAOPA, slAOPQ
+*
+*  Last revision:   2 December 2005
+*
+*  Copyright P.T.Wallace.   All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RAP,DAP,DATE,DUT,ELONGM,PHIM,HM,
+     :                 XP,YP,TDK,PMB,RH,WL,TLR,AOB,ZOB,HOB,DOB,ROB
+
+      DOUBLE PRECISION AOPRMS(14)
+
+
+      CALL slAOPA(DATE,DUT,ELONGM,PHIM,HM,XP,YP,TDK,PMB,RH,WL,TLR,
+     :               AOPRMS)
+      CALL slAOPQ(RAP,DAP,AOPRMS,AOB,ZOB,HOB,DOB,ROB)
+
+      END
diff --git a/math/slalib/aoppa.f b/math/slalib/aoppa.f
new file mode 100644
index 00000000..a8d51ccc
--- /dev/null
+++ b/math/slalib/aoppa.f
@@ -0,0 +1,194 @@
+      SUBROUTINE slAOPA ( DATE, DUT, ELONGM, PHIM, HM,
+     :                       XP, YP, TDK, PMB, RH, WL, TLR, AOPRMS )
+*+
+*     - - - - - -
+*      A O P A
+*     - - - - - -
+*
+*  Precompute apparent to observed place parameters required by
+*  slAOPQ and slOAPQ.
+*
+*  Given:
+*     DATE   d      UTC date/time (modified Julian Date, JD-2400000.5)
+*     DUT    d      delta UT:  UT1-UTC (UTC seconds)
+*     ELONGM d      mean longitude of the observer (radians, east +ve)
+*     PHIM   d      mean geodetic latitude of the observer (radians)
+*     HM     d      observer's height above sea level (metres)
+*     XP     d      polar motion x-coordinate (radians)
+*     YP     d      polar motion y-coordinate (radians)
+*     TDK    d      local ambient temperature (K; std=273.15D0)
+*     PMB    d      local atmospheric pressure (mb; std=1013.25D0)
+*     RH     d      local relative humidity (in the range 0D0-1D0)
+*     WL     d      effective wavelength (micron, e.g. 0.55D0)
+*     TLR    d      tropospheric lapse rate (K/metre, e.g. 0.0065D0)
+*
+*  Returned:
+*     AOPRMS d(14)  star-independent apparent-to-observed parameters:
+*
+*       (1)      geodetic latitude (radians)
+*       (2,3)    sine and cosine of geodetic latitude
+*       (4)      magnitude of diurnal aberration vector
+*       (5)      height (HM)
+*       (6)      ambient temperature (TDK)
+*       (7)      pressure (PMB)
+*       (8)      relative humidity (RH)
+*       (9)      wavelength (WL)
+*       (10)     lapse rate (TLR)
+*       (11,12)  refraction constants A and B (radians)
+*       (13)     longitude + eqn of equinoxes + sidereal DUT (radians)
+*       (14)     local apparent sidereal time (radians)
+*
+*  Notes:
+*
+*   1)  It is advisable to take great care with units, as even
+*       unlikely values of the input parameters are accepted and
+*       processed in accordance with the models used.
+*
+*   2)  The DATE argument is UTC expressed as an MJD.  This is,
+*       strictly speaking, improper, because of leap seconds.  However,
+*       as long as the delta UT and the UTC are consistent there
+*       are no difficulties, except during a leap second.  In this
+*       case, the start of the 61st second of the final minute should
+*       begin a new MJD day and the old pre-leap delta UT should
+*       continue to be used.  As the 61st second completes, the MJD
+*       should revert to the start of the day as, simultaneously,
+*       the delta UTC changes by one second to its post-leap new value.
+*
+*   3)  The delta UT (UT1-UTC) is tabulated in IERS circulars and
+*       elsewhere.  It increases by exactly one second at the end of
+*       each UTC leap second, introduced in order to keep delta UT
+*       within +/- 0.9 seconds.
+*
+*   4)  IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.
+*       The longitude required by the present routine is east-positive,
+*       in accordance with geographical convention (and right-handed).
+*       In particular, note that the longitudes returned by the
+*       slOBS routine are west-positive, following astronomical
+*       usage, and must be reversed in sign before use in the present
+*       routine.
+*
+*   5)  The polar coordinates XP,YP can be obtained from IERS
+*       circulars and equivalent publications.  The maximum amplitude
+*       is about 0.3 arcseconds.  If XP,YP values are unavailable,
+*       use XP=YP=0D0.  See page B60 of the 1988 Astronomical Almanac
+*       for a definition of the two angles.
+*
+*   6)  The height above sea level of the observing station, HM,
+*       can be obtained from the Astronomical Almanac (Section J
+*       in the 1988 edition), or via the routine slOBS.  If P,
+*       the pressure in millibars, is available, an adequate
+*       estimate of HM can be obtained from the expression
+*
+*             HM ~ -29.3D0*TSL*LOG(P/1013.25D0).
+*
+*       where TSL is the approximate sea-level air temperature in K
+*       (see Astrophysical Quantities, C.W.Allen, 3rd edition,
+*       section 52).  Similarly, if the pressure P is not known,
+*       it can be estimated from the height of the observing
+*       station, HM, as follows:
+*
+*             P ~ 1013.25D0*EXP(-HM/(29.3D0*TSL)).
+*
+*       Note, however, that the refraction is nearly proportional to the
+*       pressure and that an accurate P value is important for precise
+*       work.
+*
+*   7)  Repeated, computationally-expensive, calls to slAOPA for
+*       times that are very close together can be avoided by calling
+*       slAOPA just once and then using slAOPT for the subsequent
+*       times.  Fresh calls to slAOPA will be needed only when
+*       changes in the precession have grown to unacceptable levels or
+*       when anything affecting the refraction has changed.
+*
+*  Called:  slGEOC, slRFCO, slEQEX, slAOPT
+*
+*  Last revision:   2 December 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,DUT,ELONGM,PHIM,HM,XP,YP,TDK,PMB,
+     :                 RH,WL,TLR,AOPRMS(14)
+
+      DOUBLE PRECISION slEQEX
+
+*  2Pi
+      DOUBLE PRECISION D2PI
+      PARAMETER (D2PI=6.283185307179586476925287D0)
+
+*  Seconds of time to radians
+      DOUBLE PRECISION S2R
+      PARAMETER (S2R=7.272205216643039903848712D-5)
+
+*  Speed of light (AU per day)
+      DOUBLE PRECISION C
+      PARAMETER (C=173.14463331D0)
+
+*  Ratio between solar and sidereal time
+      DOUBLE PRECISION SOLSID
+      PARAMETER (SOLSID=1.00273790935D0)
+
+      DOUBLE PRECISION CPHIM,XT,YT,ZT,XC,YC,ZC,ELONG,PHI,UAU,VAU
+
+
+
+*  Observer's location corrected for polar motion
+      CPHIM = COS(PHIM)
+      XT = COS(ELONGM)*CPHIM
+      YT = SIN(ELONGM)*CPHIM
+      ZT = SIN(PHIM)
+      XC = XT-XP*ZT
+      YC = YT+YP*ZT
+      ZC = XP*XT-YP*YT+ZT
+      IF (XC.EQ.0D0.AND.YC.EQ.0D0) THEN
+         ELONG = 0D0
+      ELSE
+         ELONG = ATAN2(YC,XC)
+      END IF
+      PHI = ATAN2(ZC,SQRT(XC*XC+YC*YC))
+      AOPRMS(1) = PHI
+      AOPRMS(2) = SIN(PHI)
+      AOPRMS(3) = COS(PHI)
+
+*  Magnitude of the diurnal aberration vector
+      CALL slGEOC(PHI,HM,UAU,VAU)
+      AOPRMS(4) = D2PI*UAU*SOLSID/C
+
+*  Copy the refraction parameters and compute the A & B constants
+      AOPRMS(5) = HM
+      AOPRMS(6) = TDK
+      AOPRMS(7) = PMB
+      AOPRMS(8) = RH
+      AOPRMS(9) = WL
+      AOPRMS(10) = TLR
+      CALL slRFCO(HM,TDK,PMB,RH,WL,PHI,TLR,1D-10,
+     :               AOPRMS(11),AOPRMS(12))
+
+*  Longitude + equation of the equinoxes + sidereal equivalent of DUT
+*  (ignoring change in equation of the equinoxes between UTC and TDB)
+      AOPRMS(13) = ELONG+slEQEX(DATE)+DUT*SOLSID*S2R
+
+*  Sidereal time
+      CALL slAOPT(DATE,AOPRMS)
+
+      END
diff --git a/math/slalib/aoppat.f b/math/slalib/aoppat.f
new file mode 100644
index 00000000..f086f7f7
--- /dev/null
+++ b/math/slalib/aoppat.f
@@ -0,0 +1,63 @@
+      SUBROUTINE slAOPT (DATE, AOPRMS)
+*+
+*     - - - - - - -
+*      A O P T
+*     - - - - - - -
+*
+*  Recompute the sidereal time in the apparent to observed place
+*  star-independent parameter block.
+*
+*  Given:
+*     DATE   d      UTC date/time (modified Julian Date, JD-2400000.5)
+*                   (see AOPPA source for comments on leap seconds)
+*
+*     AOPRMS d(14)  star-independent apparent-to-observed parameters
+*
+*       (1-12)   not required
+*       (13)     longitude + eqn of equinoxes + sidereal DUT
+*       (14)     not required
+*
+*  Returned:
+*     AOPRMS d(14)  star-independent apparent-to-observed parameters:
+*
+*       (1-13)   not changed
+*       (14)     local apparent sidereal time (radians)
+*
+*  For more information, see slAOPA.
+*
+*  Called:  slGMST
+*
+*  P.T.Wallace   Starlink   1 July 1993
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,AOPRMS(14)
+
+      DOUBLE PRECISION slGMST
+
+
+
+      AOPRMS(14) = slGMST(DATE)+AOPRMS(13)
+
+      END
diff --git a/math/slalib/aopqk.f b/math/slalib/aopqk.f
new file mode 100644
index 00000000..5e327d34
--- /dev/null
+++ b/math/slalib/aopqk.f
@@ -0,0 +1,260 @@
+      SUBROUTINE slAOPQ (RAP, DAP, AOPRMS, AOB, ZOB, HOB, DOB, ROB)
+*+
+*     - - - - - -
+*      A O P Q
+*     - - - - - -
+*
+*  Quick apparent to observed place (but see note 8, below, for
+*  remarks about speed).
+*
+*  Given:
+*     RAP    d      geocentric apparent right ascension
+*     DAP    d      geocentric apparent declination
+*     AOPRMS d(14)  star-independent apparent-to-observed parameters:
+*
+*       (1)      geodetic latitude (radians)
+*       (2,3)    sine and cosine of geodetic latitude
+*       (4)      magnitude of diurnal aberration vector
+*       (5)      height (HM)
+*       (6)      ambient temperature (T)
+*       (7)      pressure (P)
+*       (8)      relative humidity (RH)
+*       (9)      wavelength (WL)
+*       (10)     lapse rate (TLR)
+*       (11,12)  refraction constants A and B (radians)
+*       (13)     longitude + eqn of equinoxes + sidereal DUT (radians)
+*       (14)     local apparent sidereal time (radians)
+*
+*  Returned:
+*     AOB    d      observed azimuth (radians: N=0,E=90)
+*     ZOB    d      observed zenith distance (radians)
+*     HOB    d      observed Hour Angle (radians)
+*     DOB    d      observed Declination (radians)
+*     ROB    d      observed Right Ascension (radians)
+*
+*  Notes:
+*
+*   1)  This routine returns zenith distance rather than elevation
+*       in order to reflect the fact that no allowance is made for
+*       depression of the horizon.
+*
+*   2)  The accuracy of the result is limited by the corrections for
+*       refraction.  Providing the meteorological parameters are
+*       known accurately and there are no gross local effects, the
+*       observed RA,Dec predicted by this routine should be within
+*       about 0.1 arcsec for a zenith distance of less than 70 degrees.
+*       Even at a topocentric zenith distance of 90 degrees, the
+*       accuracy in elevation should be better than 1 arcmin;  useful
+*       results are available for a further 3 degrees, beyond which
+*       the slRFRO routine returns a fixed value of the refraction.
+*       The complementary routines slAOP (or slAOPQ) and sla_OaAP
+*       (or slOAPQ) are self-consistent to better than 1 micro-
+*       arcsecond all over the celestial sphere.
+*
+*   3)  It is advisable to take great care with units, as even
+*       unlikely values of the input parameters are accepted and
+*       processed in accordance with the models used.
+*
+*   4)  "Apparent" place means the geocentric apparent right ascension
+*       and declination, which is obtained from a catalogue mean place
+*       by allowing for space motion, parallax, precession, nutation,
+*       annual aberration, and the Sun's gravitational lens effect.  For
+*       star positions in the FK5 system (i.e. J2000), these effects can
+*       be applied by means of the slMAP etc routines.  Starting from
+*       other mean place systems, additional transformations will be
+*       needed;  for example, FK4 (i.e. B1950) mean places would first
+*       have to be converted to FK5, which can be done with the
+*       slFK45 etc routines.
+*
+*   5)  "Observed" Az,El means the position that would be seen by a
+*       perfect theodolite located at the observer.  This is obtained
+*       from the geocentric apparent RA,Dec by allowing for Earth
+*       orientation and diurnal aberration, rotating from equator
+*       to horizon coordinates, and then adjusting for refraction.
+*       The HA,Dec is obtained by rotating back into equatorial
+*       coordinates, using the geodetic latitude corrected for polar
+*       motion, and is the position that would be seen by a perfect
+*       equatorial located at the observer and with its polar axis
+*       aligned to the Earth's axis of rotation (n.b. not to the
+*       refracted pole).  Finally, the RA is obtained by subtracting
+*       the HA from the local apparent ST.
+*
+*   6)  To predict the required setting of a real telescope, the
+*       observed place produced by this routine would have to be
+*       adjusted for the tilt of the azimuth or polar axis of the
+*       mounting (with appropriate corrections for mount flexures),
+*       for non-perpendicularity between the mounting axes, for the
+*       position of the rotator axis and the pointing axis relative
+*       to it, for tube flexure, for gear and encoder errors, and
+*       finally for encoder zero points.  Some telescopes would, of
+*       course, exhibit other properties which would need to be
+*       accounted for at the appropriate point in the sequence.
+*
+*   7)  The star-independent apparent-to-observed-place parameters
+*       in AOPRMS may be computed by means of the slAOPA routine.
+*       If nothing has changed significantly except the time, the
+*       slAOPT routine may be used to perform the requisite
+*       partial recomputation of AOPRMS.
+*
+*   8)  At zenith distances beyond about 76 degrees, the need for
+*       special care with the corrections for refraction causes a
+*       marked increase in execution time.  Moreover, the effect
+*       gets worse with increasing zenith distance.  Adroit
+*       programming in the calling application may allow the
+*       problem to be reduced.  Prepare an alternative AOPRMS array,
+*       computed for zero air-pressure;  this will disable the
+*       refraction corrections and cause rapid execution.  Using
+*       this AOPRMS array, a preliminary call to the present routine
+*       will, depending on the application, produce a rough position
+*       which may be enough to establish whether the full, slow
+*       calculation (using the real AOPRMS array) is worthwhile.
+*       For example, there would be no need for the full calculation
+*       if the preliminary call had already established that the
+*       source was well below the elevation limits for a particular
+*       telescope.
+*
+*  9)   The azimuths etc produced by the present routine are with
+*       respect to the celestial pole.  Corrections to the terrestrial
+*       pole can be computed using slPLMO.
+*
+*  Called:  slDS2C, slREFZ, slRFRO, slDC2S, slDA2P
+*
+*  P.T.Wallace   Starlink   24 October 2003
+*
+*  Copyright (C) 2003 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RAP,DAP,AOPRMS(14),AOB,ZOB,HOB,DOB,ROB
+
+*  Breakpoint for fast/slow refraction algorithm:
+*  ZD greater than arctan(4), (see slRFCO routine)
+*  or vector Z less than cosine(arctan(Z)) = 1/sqrt(17)
+      DOUBLE PRECISION ZBREAK
+      PARAMETER (ZBREAK=0.242535625D0)
+
+      INTEGER I
+
+      DOUBLE PRECISION SPHI,CPHI,ST,V(3),XHD,YHD,ZHD,DIURAB,F,
+     :                 XHDT,YHDT,ZHDT,XAET,YAET,ZAET,AZOBS,
+     :                 ZDT,REFA,REFB,ZDOBS,DZD,DREF,CE,
+     :                 XAEO,YAEO,ZAEO,HMOBS,DCOBS,RAOBS
+
+      DOUBLE PRECISION slDA2P
+
+
+
+*  Sin, cos of latitude
+      SPHI = AOPRMS(2)
+      CPHI = AOPRMS(3)
+
+*  Local apparent sidereal time
+      ST = AOPRMS(14)
+
+*  Apparent RA,Dec to Cartesian -HA,Dec
+      CALL slDS2C(RAP-ST,DAP,V)
+      XHD = V(1)
+      YHD = V(2)
+      ZHD = V(3)
+
+*  Diurnal aberration
+      DIURAB = AOPRMS(4)
+      F = (1D0-DIURAB*YHD)
+      XHDT = F*XHD
+      YHDT = F*(YHD+DIURAB)
+      ZHDT = F*ZHD
+
+*  Cartesian -HA,Dec to Cartesian Az,El (S=0,E=90)
+      XAET = SPHI*XHDT-CPHI*ZHDT
+      YAET = YHDT
+      ZAET = CPHI*XHDT+SPHI*ZHDT
+
+*  Azimuth (N=0,E=90)
+      IF (XAET.EQ.0D0.AND.YAET.EQ.0D0) THEN
+         AZOBS = 0D0
+      ELSE
+         AZOBS = ATAN2(YAET,-XAET)
+      END IF
+
+*  Topocentric zenith distance
+      ZDT = ATAN2(SQRT(XAET*XAET+YAET*YAET),ZAET)
+
+*
+*  Refraction
+*  ----------
+
+*  Fast algorithm using two constant model
+      REFA = AOPRMS(11)
+      REFB = AOPRMS(12)
+      CALL slREFZ(ZDT,REFA,REFB,ZDOBS)
+
+*  Large zenith distance?
+      IF (COS(ZDOBS).LT.ZBREAK) THEN
+
+*     Yes: use rigorous algorithm
+
+*     Initialize loop (maximum of 10 iterations)
+         I = 1
+         DZD = 1D1
+         DO WHILE (ABS(DZD).GT.1D-10.AND.I.LE.10)
+
+*        Compute refraction using current estimate of observed ZD
+            CALL slRFRO(ZDOBS,AOPRMS(5),AOPRMS(6),AOPRMS(7),
+     :                     AOPRMS(8),AOPRMS(9),AOPRMS(1),
+     :                     AOPRMS(10),1D-8,DREF)
+
+*        Remaining discrepancy
+            DZD = ZDOBS+DREF-ZDT
+
+*        Update the estimate
+            ZDOBS = ZDOBS-DZD
+
+*        Increment the iteration counter
+            I = I+1
+         END DO
+      END IF
+
+*  To Cartesian Az/ZD
+      CE = SIN(ZDOBS)
+      XAEO = -COS(AZOBS)*CE
+      YAEO = SIN(AZOBS)*CE
+      ZAEO = COS(ZDOBS)
+
+*  Cartesian Az/ZD to Cartesian -HA,Dec
+      V(1) = SPHI*XAEO+CPHI*ZAEO
+      V(2) = YAEO
+      V(3) = -CPHI*XAEO+SPHI*ZAEO
+
+*  To spherical -HA,Dec
+      CALL slDC2S(V,HMOBS,DCOBS)
+
+*  Right Ascension
+      RAOBS = slDA2P(ST+HMOBS)
+
+*  Return the results
+      AOB = AZOBS
+      ZOB = ZDOBS
+      HOB = -HMOBS
+      DOB = DCOBS
+      ROB = RAOBS
+
+      END
diff --git a/math/slalib/atmdsp.f b/math/slalib/atmdsp.f
new file mode 100644
index 00000000..76d43261
--- /dev/null
+++ b/math/slalib/atmdsp.f
@@ -0,0 +1,141 @@
+      SUBROUTINE slATMD (TDK, PMB, RH, WL1, A1, B1, WL2, A2, B2)
+*+
+*     - - - - - - -
+*      A T M D
+*     - - - - - - -
+*
+*  Apply atmospheric-dispersion adjustments to refraction coefficients.
+*
+*  Given:
+*     TDK       d       ambient temperature, K
+*     PMB       d       ambient pressure, millibars
+*     RH        d       ambient relative humidity, 0-1
+*     WL1       d       reference wavelength, micrometre (0.4D0 recommended)
+*     A1        d       refraction coefficient A for wavelength WL1 (radians)
+*     B1        d       refraction coefficient B for wavelength WL1 (radians)
+*     WL2       d       wavelength for which adjusted A,B required
+*
+*  Returned:
+*     A2        d       refraction coefficient A for wavelength WL2 (radians)
+*     B2        d       refraction coefficient B for wavelength WL2 (radians)
+*
+*  Notes:
+*
+*  1  To use this routine, first call slRFCO specifying WL1 as the
+*     wavelength.  This yields refraction coefficients A1,B1, correct
+*     for that wavelength.  Subsequently, calls to slATMD specifying
+*     different wavelengths will produce new, slightly adjusted
+*     refraction coefficients which apply to the specified wavelength.
+*
+*  2  Most of the atmospheric dispersion happens between 0.7 micrometre
+*     and the UV atmospheric cutoff, and the effect increases strongly
+*     towards the UV end.  For this reason a blue reference wavelength
+*     is recommended, for example 0.4 micrometres.
+*
+*  3  The accuracy, for this set of conditions:
+*
+*        height above sea level    2000 m
+*                      latitude    29 deg
+*                      pressure    793 mb
+*                   temperature    17 degC
+*                      humidity    50%
+*                    lapse rate    0.0065 degC/m
+*          reference wavelength    0.4 micrometre
+*                star elevation    15 deg
+*
+*     is about 2.5 mas RMS between 0.3 and 1.0 micrometres, and stays
+*     within 4 mas for the whole range longward of 0.3 micrometres
+*     (compared with a total dispersion from 0.3 to 20.0 micrometres
+*     of about 11 arcsec).  These errors are typical for ordinary
+*     conditions and the given elevation;  in extreme conditions values
+*     a few times this size may occur, while at higher elevations the
+*     errors become much smaller.
+*
+*  4  If either wavelength exceeds 100 micrometres, the radio case
+*     is assumed and the returned refraction coefficients are the
+*     same as the given ones.  Note that radio refraction coefficients
+*     cannot be turned into optical values using this routine, nor
+*     vice versa.
+*
+*  5  The algorithm consists of calculation of the refractivity of the
+*     air at the observer for the two wavelengths, using the methods
+*     of the slRFRO routine, and then scaling of the two refraction
+*     coefficients according to classical refraction theory.  This
+*     amounts to scaling the A coefficient in proportion to (n-1) and
+*     the B coefficient almost in the same ratio (see R.M.Green,
+*     "Spherical Astronomy", Cambridge University Press, 1985).
+*
+*  Last revision   2 December 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION TDK,PMB,RH,WL1,A1,B1,WL2,A2,B2
+
+      DOUBLE PRECISION F,TDKOK,PMBOK,RHOK,
+     :                 PSAT,PWO,W1,WLOK,WLSQ,W2,DN1,DN2
+
+
+*  Check for radio wavelengths
+      IF (WL1.GT.100D0.OR.WL2.GT.100D0) THEN
+
+*     Radio: no dispersion
+         A2 = A1
+         B2 = B1
+      ELSE
+
+*     Optical: keep arguments within safe bounds
+         TDKOK = MIN(MAX(TDK,100D0),500D0)
+         PMBOK = MIN(MAX(PMB,0D0),10000D0)
+         RHOK = MIN(MAX(RH,0D0),1D0)
+
+*     Atmosphere parameters at the observer
+         PSAT = 10D0**(-8.7115D0+0.03477D0*TDKOK)
+         PWO = RHOK*PSAT
+         W1 = 11.2684D-6*PWO
+
+*     Refractivity at the observer for first wavelength
+         WLOK = MAX(WL1,0.1D0)
+         WLSQ = WLOK*WLOK
+         W2 = 77.5317D-6+(0.43909D-6+0.00367D-6/WLSQ)/WLSQ
+         DN1 = (W2*PMBOK-W1)/TDKOK
+
+*     Refractivity at the observer for second wavelength
+         WLOK = MAX(WL2,0.1D0)
+         WLSQ = WLOK*WLOK
+         W2 = 77.5317D-6+(0.43909D-6+0.00367D-6/WLSQ)/WLSQ
+         DN2 = (W2*PMBOK-W1)/TDKOK
+
+*     Scale the refraction coefficients (see Green 4.31, p93)
+         IF (DN1.NE.0D0) THEN
+            F = DN2/DN1
+            A2 = A1*F
+            B2 = B1*F
+            IF (DN1.NE.A1) B2=B2*(1D0+DN1*(DN1-DN2)/(2D0*(DN1-A1)))
+         ELSE
+            A2 = A1
+            B2 = B1
+         END IF
+      END IF
+
+      END
diff --git a/math/slalib/atms.f b/math/slalib/atms.f
new file mode 100644
index 00000000..fcee9c68
--- /dev/null
+++ b/math/slalib/atms.f
@@ -0,0 +1,58 @@
+      SUBROUTINE slATMS (RT, TT, DNT, GAMAL, R, DN, RDNDR)
+*+
+*     - - - - -
+*      A T M S
+*     - - - - -
+*
+*  Internal routine used by REFRO
+*
+*  Refractive index and derivative with respect to height for the
+*  stratosphere.
+*
+*  Given:
+*    RT      d    height of tropopause from centre of the Earth (metre)
+*    TT      d    temperature at the tropopause (K)
+*    DNT     d    refractive index at the tropopause
+*    GAMAL   d    constant of the atmospheric model = G*MD/R
+*    R       d    current distance from the centre of the Earth (metre)
+*
+*  Returned:
+*    DN      d    refractive index at R
+*    RDNDR   d    R * rate the refractive index is changing at R
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RT,TT,DNT,GAMAL,R,DN,RDNDR
+
+      DOUBLE PRECISION B,W
+
+
+      B = GAMAL/TT
+      W = (DNT-1D0)*EXP(-B*(R-RT))
+      DN = 1D0+W
+      RDNDR = -R*B*W
+
+      END
diff --git a/math/slalib/atmt.f b/math/slalib/atmt.f
new file mode 100644
index 00000000..4534e7ed
--- /dev/null
+++ b/math/slalib/atmt.f
@@ -0,0 +1,72 @@
+      SUBROUTINE slATMT (R0, T0, ALPHA, GAMM2, DELM2,
+     :                      C1, C2, C3, C4, C5, C6, R, T, DN, RDNDR)
+*+
+*     - - - - -
+*      A T M T
+*     - - - - -
+*
+*  Internal routine used by REFRO
+*
+*  Refractive index and derivative with respect to height for the
+*  troposphere.
+*
+*  Given:
+*    R0      d    height of observer from centre of the Earth (metre)
+*    T0      d    temperature at the observer (K)
+*    ALPHA   d    alpha          )
+*    GAMM2   d    gamma minus 2  ) see HMNAO paper
+*    DELM2   d    delta minus 2  )
+*    C1      d    useful term  )
+*    C2      d    useful term  )
+*    C3      d    useful term  ) see source
+*    C4      d    useful term  ) of slRFRO
+*    C5      d    useful term  )
+*    C6      d    useful term  )
+*    R       d    current distance from the centre of the Earth (metre)
+*
+*  Returned:
+*    T       d    temperature at R (K)
+*    DN      d    refractive index at R
+*    RDNDR   d    R * rate the refractive index is changing at R
+*
+*  Note that in the optical case C5 and C6 are zero.
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION R0,T0,ALPHA,GAMM2,DELM2,C1,C2,C3,C4,C5,C6,
+     :                 R,T,DN,RDNDR
+
+      DOUBLE PRECISION TT0,TT0GM2,TT0DM2
+
+
+      T = MAX(MIN(T0-ALPHA*(R-R0),320D0),100D0)
+      TT0 = T/T0
+      TT0GM2 = TT0**GAMM2
+      TT0DM2 = TT0**DELM2
+      DN = 1D0+(C1*TT0GM2-(C2-C5/T)*TT0DM2)*TT0
+      RDNDR = R*(-C3*TT0GM2+(C4-C6/TT0)*TT0DM2)
+
+      END
diff --git a/math/slalib/av2m.f b/math/slalib/av2m.f
new file mode 100644
index 00000000..69dab510
--- /dev/null
+++ b/math/slalib/av2m.f
@@ -0,0 +1,85 @@
+      SUBROUTINE slAV2M (AXVEC, RMAT)
+*+
+*     - - - - -
+*      A V 2 M
+*     - - - - -
+*
+*  Form the rotation matrix corresponding to a given axial vector.
+*
+*  (single precision)
+*
+*  A rotation matrix describes a rotation about some arbitrary axis,
+*  called the Euler axis.  The "axial vector" supplied to this routine
+*  has the same direction as the Euler axis, and its magnitude is the
+*  amount of rotation in radians.
+*
+*  Given:
+*    AXVEC  r(3)     axial vector (radians)
+*
+*  Returned:
+*    RMAT   r(3,3)   rotation matrix
+*
+*  If AXVEC is null, the unit matrix is returned.
+*
+*  The reference frame rotates clockwise as seen looking along
+*  the axial vector from the origin.
+*
+*  Last revision:   26 November 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL AXVEC(3),RMAT(3,3)
+
+      REAL X,Y,Z,PHI,S,C,W
+
+
+
+*  Rotation angle - magnitude of axial vector - and functions
+      X = AXVEC(1)
+      Y = AXVEC(2)
+      Z = AXVEC(3)
+      PHI = SQRT(X*X+Y*Y+Z*Z)
+      S = SIN(PHI)
+      C = COS(PHI)
+      W = 1.0-C
+
+*  Euler axis - direction of axial vector (perhaps null)
+      IF (PHI.NE.0.0) THEN
+         X = X/PHI
+         Y = Y/PHI
+         Z = Z/PHI
+      END IF
+
+*  Compute the rotation matrix
+      RMAT(1,1) = X*X*W+C
+      RMAT(1,2) = X*Y*W+Z*S
+      RMAT(1,3) = X*Z*W-Y*S
+      RMAT(2,1) = X*Y*W-Z*S
+      RMAT(2,2) = Y*Y*W+C
+      RMAT(2,3) = Y*Z*W+X*S
+      RMAT(3,1) = X*Z*W+Y*S
+      RMAT(3,2) = Y*Z*W-X*S
+      RMAT(3,3) = Z*Z*W+C
+
+      END
diff --git a/math/slalib/bear.f b/math/slalib/bear.f
new file mode 100644
index 00000000..e023d533
--- /dev/null
+++ b/math/slalib/bear.f
@@ -0,0 +1,60 @@
+      REAL FUNCTION slBEAR (A1, B1, A2, B2)
+*+
+*     - - - - -
+*      B E A R
+*     - - - - -
+*
+*  Bearing (position angle) of one point on a sphere relative to another
+*  (single precision)
+*
+*  Given:
+*     A1,B1    r    spherical coordinates of one point
+*     A2,B2    r    spherical coordinates of the other point
+*
+*  (The spherical coordinates are RA,Dec, Long,Lat etc, in radians.)
+*
+*  The result is the bearing (position angle), in radians, of point
+*  A2,B2 as seen from point A1,B1.  It is in the range +/- pi.  If
+*  A2,B2 is due east of A1,B1 the bearing is +pi/2.  Zero is returned
+*  if the two points are coincident.
+*
+*  P.T.Wallace   Starlink   23 March 1991
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL A1,B1,A2,B2
+
+      REAL DA,X,Y
+
+
+      DA=A2-A1
+      Y=SIN(DA)*COS(B2)
+      X=SIN(B2)*COS(B1)-COS(B2)*SIN(B1)*COS(DA)
+      IF (X.NE.0.0.OR.Y.NE.0.0) THEN
+         slBEAR=ATAN2(Y,X)
+      ELSE
+         slBEAR=0.0
+      END IF
+
+      END
diff --git a/math/slalib/caf2r.f b/math/slalib/caf2r.f
new file mode 100644
index 00000000..59a6c908
--- /dev/null
+++ b/math/slalib/caf2r.f
@@ -0,0 +1,75 @@
+      SUBROUTINE slCAFR (IDEG, IAMIN, ASEC, RAD, J)
+*+
+*     - - - - - -
+*      C A F R
+*     - - - - - -
+*
+*  Convert degrees, arcminutes, arcseconds to radians
+*  (single precision)
+*
+*  Given:
+*     IDEG        int       degrees
+*     IAMIN       int       arcminutes
+*     ASEC        real      arcseconds
+*
+*  Returned:
+*     RAD         real      angle in radians
+*     J           int       status:  0 = OK
+*                                    1 = IDEG outside range 0-359
+*                                    2 = IAMIN outside range 0-59
+*                                    3 = ASEC outside range 0-59.999...
+*
+*  Notes:
+*
+*  1)  The result is computed even if any of the range checks
+*      fail.
+*
+*  2)  The sign must be dealt with outside this routine.
+*
+*  P.T.Wallace   Starlink   23 August 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IDEG,IAMIN
+      REAL ASEC,RAD
+      INTEGER J
+
+*  Arc seconds to radians
+      REAL AS2R
+      PARAMETER (AS2R=0.484813681109535994E-5)
+
+
+
+*  Preset status
+      J=0
+
+*  Validate arcsec, arcmin, deg
+      IF (ASEC.LT.0.0.OR.ASEC.GE.60.0) J=3
+      IF (IAMIN.LT.0.OR.IAMIN.GT.59) J=2
+      IF (IDEG.LT.0.OR.IDEG.GT.359) J=1
+
+*  Compute angle
+      RAD=AS2R*(60.0*(60.0*REAL(IDEG)+REAL(IAMIN))+ASEC)
+
+      END
diff --git a/math/slalib/caldj.f b/math/slalib/caldj.f
new file mode 100644
index 00000000..34104ca8
--- /dev/null
+++ b/math/slalib/caldj.f
@@ -0,0 +1,75 @@
+      SUBROUTINE slCADJ (IY, IM, ID, DJM, J)
+*+
+*     - - - - - -
+*      C A D J
+*     - - - - - -
+*
+*  Gregorian Calendar to Modified Julian Date
+*
+*  (Includes century default feature:  use slCLDJ for years
+*   before 100AD.)
+*
+*  Given:
+*     IY,IM,ID     int    year, month, day in Gregorian calendar
+*
+*  Returned:
+*     DJM          dp     modified Julian Date (JD-2400000.5) for 0 hrs
+*     J            int    status:
+*                           0 = OK
+*                           1 = bad year   (MJD not computed)
+*                           2 = bad month  (MJD not computed)
+*                           3 = bad day    (MJD computed)
+*
+*  Acceptable years are 00-49, interpreted as 2000-2049,
+*                       50-99,     "       "  1950-1999,
+*                       100 upwards, interpreted literally.
+*
+*  Called:  slCLDJ
+*
+*  P.T.Wallace   Starlink   November 1985
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IY,IM,ID
+      DOUBLE PRECISION DJM
+      INTEGER J
+
+      INTEGER NY
+
+
+
+
+*  Default century if appropriate
+      IF (IY.GE.0.AND.IY.LE.49) THEN
+         NY=IY+2000
+      ELSE IF (IY.GE.50.AND.IY.LE.99) THEN
+         NY=IY+1900
+      ELSE
+         NY=IY
+      END IF
+
+*  Modified Julian Date
+      CALL slCLDJ(NY,IM,ID,DJM,J)
+
+      END
diff --git a/math/slalib/calyd.f b/math/slalib/calyd.f
new file mode 100644
index 00000000..0f65cb98
--- /dev/null
+++ b/math/slalib/calyd.f
@@ -0,0 +1,83 @@
+      SUBROUTINE slCAYD (IY, IM, ID, NY, ND, J)
+*+
+*     - - - - - -
+*      C A Y D
+*     - - - - - -
+*
+*  Gregorian calendar date to year and day in year (in a Julian
+*  calendar aligned to the 20th/21st century Gregorian calendar).
+*
+*  (Includes century default feature:  use slCLYD for years
+*   before 100AD.)
+*
+*  Given:
+*     IY,IM,ID   int    year, month, day in Gregorian calendar
+*                       (year may optionally omit the century)
+*  Returned:
+*     NY         int    year (re-aligned Julian calendar)
+*     ND         int    day in year (1 = January 1st)
+*     J          int    status:
+*                         0 = OK
+*                         1 = bad year (before -4711)
+*                         2 = bad month
+*                         3 = bad day (but conversion performed)
+*
+*  Notes:
+*
+*  1  This routine exists to support the low-precision routines
+*     slERTH, slMOON and slECOR.
+*
+*  2  Between 1900 March 1 and 2100 February 28 it returns answers
+*     which are consistent with the ordinary Gregorian calendar.
+*     Outside this range there will be a discrepancy which increases
+*     by one day for every non-leap century year.
+*
+*  3  Years in the range 50-99 are interpreted as 1950-1999, and
+*     years in the range 00-49 are interpreted as 2000-2049.
+*
+*  Called:  slCLYD
+*
+*  P.T.Wallace   Starlink   23 November 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IY,IM,ID,NY,ND,J
+
+      INTEGER I
+
+
+
+*  Default century if appropriate
+      IF (IY.GE.0.AND.IY.LE.49) THEN
+         I=IY+2000
+      ELSE IF (IY.GE.50.AND.IY.LE.99) THEN
+         I=IY+1900
+      ELSE
+         I=IY
+      END IF
+
+*  Perform the conversion
+      CALL slCLYD(I,IM,ID,NY,ND,J)
+
+      END
diff --git a/math/slalib/cc2s.f b/math/slalib/cc2s.f
new file mode 100644
index 00000000..c9187e3a
--- /dev/null
+++ b/math/slalib/cc2s.f
@@ -0,0 +1,70 @@
+      SUBROUTINE slCC2S (V, A, B)
+*+
+*     - - - - -
+*      C C 2 S
+*     - - - - -
+*
+*  Cartesian to spherical coordinates (single precision)
+*
+*  Given:
+*     V     r(3)   x,y,z vector
+*
+*  Returned:
+*     A,B   r      spherical coordinates in radians
+*
+*  The spherical coordinates are longitude (+ve anticlockwise looking
+*  from the +ve latitude pole) and latitude.  The Cartesian coordinates
+*  are right handed, with the x axis at zero longitude and latitude, and
+*  the z axis at the +ve latitude pole.
+*
+*  If V is null, zero A and B are returned.  At either pole, zero A is
+*  returned.
+*
+*  Last revision:   22 July 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL V(3),A,B
+
+      REAL X,Y,Z,R
+
+
+      X = V(1)
+      Y = V(2)
+      Z = V(3)
+      R = SQRT(X*X+Y*Y)
+
+      IF (R.EQ.0.0) THEN
+         A = 0.0
+      ELSE
+         A = ATAN2(Y,X)
+      END IF
+
+      IF (Z.EQ.0.0) THEN
+         B = 0.0
+      ELSE
+         B = ATAN2(Z,R)
+      END IF
+
+      END
diff --git a/math/slalib/cc62s.f b/math/slalib/cc62s.f
new file mode 100644
index 00000000..a3ad4f38
--- /dev/null
+++ b/math/slalib/cc62s.f
@@ -0,0 +1,100 @@
+      SUBROUTINE slC62S (V, A, B, R, AD, BD, RD)
+*+
+*     - - - - - -
+*      C 6 2 S
+*     - - - - - -
+*
+*  Conversion of position & velocity in Cartesian coordinates
+*  to spherical coordinates (single precision)
+*
+*  Given:
+*     V      r(6)   Cartesian position & velocity vector
+*
+*  Returned:
+*     A      r      longitude (radians)
+*     B      r      latitude (radians)
+*     R      r      radial coordinate
+*     AD     r      longitude derivative (radians per unit time)
+*     BD     r      latitude derivative (radians per unit time)
+*     RD     r      radial derivative
+*
+*  P.T.Wallace   Starlink   28 April 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL V(6),A,B,R,AD,BD,RD
+
+      REAL X,Y,Z,XD,YD,ZD,RXY2,RXY,R2,XYP
+
+
+
+*  Components of position/velocity vector
+      X=V(1)
+      Y=V(2)
+      Z=V(3)
+      XD=V(4)
+      YD=V(5)
+      ZD=V(6)
+
+*  Component of R in XY plane squared
+      RXY2=X*X+Y*Y
+
+*  Modulus squared
+      R2=RXY2+Z*Z
+
+*  Protection against null vector
+      IF (R2.EQ.0.0) THEN
+         X=XD
+         Y=YD
+         Z=ZD
+         RXY2=X*X+Y*Y
+         R2=RXY2+Z*Z
+      END IF
+
+*  Position and velocity in spherical coordinates
+      RXY=SQRT(RXY2)
+      XYP=X*XD+Y*YD
+      IF (RXY2.NE.0.0) THEN
+         A=ATAN2(Y,X)
+         B=ATAN2(Z,RXY)
+         AD=(X*YD-Y*XD)/RXY2
+         BD=(ZD*RXY2-Z*XYP)/(R2*RXY)
+      ELSE
+         A=0.0
+         IF (Z.NE.0.0) THEN
+            B=ATAN2(Z,RXY)
+         ELSE
+            B=0.0
+         END IF
+         AD=0.0
+         BD=0.0
+      END IF
+      R=SQRT(R2)
+      IF (R.NE.0.0) THEN
+         RD=(XYP+Z*ZD)/R
+      ELSE
+         RD=0.0
+      END IF
+
+      END
diff --git a/math/slalib/cd2tf.f b/math/slalib/cd2tf.f
new file mode 100644
index 00000000..87884372
--- /dev/null
+++ b/math/slalib/cd2tf.f
@@ -0,0 +1,73 @@
+      SUBROUTINE slCDTF (NDP, DAYS, SIGN, IHMSF)
+*+
+*     - - - - - -
+*      C D T F
+*     - - - - - -
+*
+*  Convert an interval in days into hours, minutes, seconds
+*
+*  (single precision)
+*
+*  Given:
+*     NDP       int      number of decimal places of seconds
+*     DAYS      real     interval in days
+*
+*  Returned:
+*     SIGN      char     '+' or '-'
+*     IHMSF     int(4)   hours, minutes, seconds, fraction
+*
+*  Notes:
+*
+*     1)  NDP less than zero is interpreted as zero.
+*
+*     2)  The largest useful value for NDP is determined by the size of
+*         DAYS, the format of REAL floating-point numbers on the target
+*         machine, and the risk of overflowing IHMSF(4).  On some
+*         architectures, for DAYS up to 1.0, the available floating-
+*         point precision corresponds roughly to NDP=3.  This is well
+*         below the ultimate limit of NDP=9 set by the capacity of a
+*         typical 32-bit IHMSF(4).
+*
+*     3)  The absolute value of DAYS may exceed 1.0.  In cases where it
+*         does not, it is up to the caller to test for and handle the
+*         case where DAYS is very nearly 1.0 and rounds up to 24 hours,
+*         by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+*
+*  Called:  slDDTF
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER NDP
+      REAL DAYS
+      CHARACTER SIGN*(*)
+      INTEGER IHMSF(4)
+
+
+
+*  Call double precision version
+      CALL slDDTF(NDP,DBLE(DAYS),SIGN,IHMSF)
+
+      END
diff --git a/math/slalib/cldj.f b/math/slalib/cldj.f
new file mode 100644
index 00000000..ed593ca3
--- /dev/null
+++ b/math/slalib/cldj.f
@@ -0,0 +1,95 @@
+      SUBROUTINE slCLDJ (IY, IM, ID, DJM, J)
+*+
+*     - - - - -
+*      C L D J
+*     - - - - -
+*
+*  Gregorian Calendar to Modified Julian Date
+*
+*  Given:
+*     IY,IM,ID     int    year, month, day in Gregorian calendar
+*
+*  Returned:
+*     DJM          dp     modified Julian Date (JD-2400000.5) for 0 hrs
+*     J            int    status:
+*                           0 = OK
+*                           1 = bad year   (MJD not computed)
+*                           2 = bad month  (MJD not computed)
+*                           3 = bad day    (MJD computed)
+*
+*  The year must be -4699 (i.e. 4700BC) or later.
+*
+*  The algorithm is adapted from Hatcher 1984 (QJRAS 25, 53-55).
+*
+*  Last revision:   27 July 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IY,IM,ID
+      DOUBLE PRECISION DJM
+      INTEGER J
+
+*  Month lengths in days
+      INTEGER MTAB(12)
+      DATA MTAB / 31,28,31,30,31,30,31,31,30,31,30,31 /
+
+
+
+*  Preset status.
+      J = 0
+
+*  Validate year.
+      IF ( IY .LT. -4699 ) THEN
+         J = 1
+      ELSE
+
+*     Validate month.
+         IF ( IM.GE.1 .AND. IM.LE.12 ) THEN
+
+*        Allow for leap year.
+            IF ( MOD(IY,4) .EQ. 0 ) THEN
+               MTAB(2) = 29
+            ELSE
+               MTAB(2) = 28
+            END IF
+            IF ( MOD(IY,100).EQ.0 .AND. MOD(IY,400).NE.0 )
+     :         MTAB(2) = 28
+
+*        Validate day.
+            IF ( ID.LT.1 .OR. ID.GT.MTAB(IM) ) J=3
+
+*        Modified Julian Date.
+            DJM = DBLE ( ( 1461 * ( IY - (12-IM)/10 + 4712 ) ) / 4
+     :               + ( 306 * MOD ( IM+9, 12 ) + 5 ) / 10
+     :               - ( 3 * ( ( IY - (12-IM)/10 + 4900 ) / 100 ) ) / 4
+     :               + ID - 2399904 )
+
+*        Bad month.
+         ELSE
+            J=2
+         END IF
+
+      END IF
+
+      END
diff --git a/math/slalib/clyd.f b/math/slalib/clyd.f
new file mode 100644
index 00000000..957a6ec8
--- /dev/null
+++ b/math/slalib/clyd.f
@@ -0,0 +1,119 @@
+      SUBROUTINE slCLYD (IY, IM, ID, NY, ND, JSTAT)
+*+
+*     - - - - -
+*      C L Y D
+*     - - - - -
+*
+*  Gregorian calendar to year and day in year (in a Julian calendar
+*  aligned to the 20th/21st century Gregorian calendar).
+*
+*  Given:
+*     IY,IM,ID   i    year, month, day in Gregorian calendar
+*
+*  Returned:
+*     NY         i    year (re-aligned Julian calendar)
+*     ND         i    day in year (1 = January 1st)
+*     JSTAT      i    status:
+*                       0 = OK
+*                       1 = bad year (before -4711)
+*                       2 = bad month
+*                       3 = bad day (but conversion performed)
+*
+*  Notes:
+*
+*  1  This routine exists to support the low-precision routines
+*     slERTH, slMOON and slECOR.
+*
+*  2  Between 1900 March 1 and 2100 February 28 it returns answers
+*     which are consistent with the ordinary Gregorian calendar.
+*     Outside this range there will be a discrepancy which increases
+*     by one day for every non-leap century year.
+*
+*  3  The essence of the algorithm is first to express the Gregorian
+*     date as a Julian Day Number and then to convert this back to
+*     a Julian calendar date, with day-in-year instead of month and
+*     day.  See 12.92-1 and 12.95-1 in the reference.
+*
+*  Reference:  Explanatory Supplement to the Astronomical Almanac,
+*              ed P.K.Seidelmann, University Science Books (1992),
+*              p604-606.
+*
+*  P.T.Wallace   Starlink   26 November 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IY,IM,ID,NY,ND,JSTAT
+
+      INTEGER I,J,K,L,N
+
+*  Month lengths in days
+      INTEGER MTAB(12)
+      DATA MTAB/31,28,31,30,31,30,31,31,30,31,30,31/
+
+
+
+*  Preset status
+      JSTAT=0
+
+*  Validate year
+      IF (IY.GE.-4711) THEN
+
+*     Validate month
+         IF (IM.GE.1.AND.IM.LE.12) THEN
+
+*        Allow for (Gregorian) leap year
+            IF (MOD(IY,4).EQ.0.AND.
+     :         (MOD(IY,100).NE.0.OR.MOD(IY,400).EQ.0)) THEN
+               MTAB(2)=29
+            ELSE
+               MTAB(2)=28
+            END IF
+
+*        Validate day
+            IF (ID.LT.1.OR.ID.GT.MTAB(IM)) JSTAT=3
+
+*        Perform the conversion
+            I=(14-IM)/12
+            K=IY-I
+            J=(1461*(K+4800))/4+(367*(IM-2+12*I))/12
+     :        -(3*((K+4900)/100))/4+ID-30660
+            K=(J-1)/1461
+            L=J-1461*K
+            N=(L-1)/365-L/1461
+            J=((80*(L-365*N+30))/2447)/11
+            I=N+J
+            ND=59+L-365*I+((4-N)/4)*(1-J)
+            NY=4*K+I-4716
+
+*        Bad month
+         ELSE
+            JSTAT=2
+         END IF
+      ELSE
+
+*     Bad year
+         JSTAT=1
+      END IF
+
+      END
diff --git a/math/slalib/combn.f b/math/slalib/combn.f
new file mode 100644
index 00000000..8f0dd64b
--- /dev/null
+++ b/math/slalib/combn.f
@@ -0,0 +1,160 @@
+      SUBROUTINE slCMBN ( NSEL, NCAND, LIST, J )
+*+
+*     - - - - - -
+*      C O M B N
+*     - - - - - -
+*
+*  Generate the next combination, a subset of a specified size chosen
+*  from a specified number of items.
+*
+*  Given:
+*     NSEL     i        number of items (subset size)
+*     NCAND    i        number of candidates (set size)
+*
+*  Given and returned:
+*     LIST     i(NSEL)  latest combination, LIST(1)=0 to initialize
+*
+*  Returned:
+*     J        i        status: -1 = illegal NSEL or NCAND
+*                                0 = OK
+*                               +1 = no more combinations available
+*
+*  Notes:
+*
+*  1) NSEL and NCAND must both be at least 1, and NSEL must be less
+*     than or equal to NCAND.
+*
+*  2) This routine returns, in the LIST array, a subset of NSEL integers
+*     chosen from the range 1 to NCAND inclusive, in ascending order.
+*     Before calling the routine for the first time, the caller must set
+*     the first element of the LIST array to zero (any value less than 1
+*     will do) to cause initialization.
+*
+*  2) The first combination to be generated is:
+*
+*        LIST(1)=1, LIST(2)=2, ..., LIST(NSEL)=NSEL
+*
+*     This is also the combination returned for the "finished" (J=1)
+*     case.
+*
+*     The final permutation to be generated is:
+*
+*        LIST(1)=NCAND, LIST(2)=NCAND-1, ..., LIST(NSEL)=NCAND-NSEL+1
+*
+*  3) If the "finished" (J=1) status is ignored, the routine
+*     continues to deliver combinations, the pattern repeating
+*     every NCAND!/(NSEL!*(NCAND-NSEL)!) calls.
+*
+*  4) The algorithm is by R.F.Warren-Smith (private communication).
+*
+*  P.T.Wallace   Starlink   25 August 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER NSEL,NCAND,LIST(NSEL),J
+
+      INTEGER I,LISTI,NMAX,M
+      LOGICAL MORE
+
+
+*  Validate, and set status.
+      IF (NSEL.LT.1.OR.NCAND.LT.1.OR.NSEL.GT.NCAND) THEN
+         J = -1
+         GO TO 9999
+      ELSE
+         J = 0
+      END IF
+
+*  Just starting?
+      IF (LIST(1).LT.1) THEN
+
+*     Yes: return 1,2,3...
+         DO I=1,NSEL
+            LIST(I) = I
+         END DO
+
+      ELSE
+
+*     No: find the first selection that we can increment.
+
+*     Start with the first list item.
+         I = 1
+
+*     Loop.
+         MORE = .TRUE.
+         DO WHILE (MORE)
+
+*        Current list item.
+            LISTI = LIST(I)
+
+*        Is this the final list item?
+            IF (I.GE.NSEL) THEN
+
+*           Yes:  comparison value is number of candidates plus one.
+               NMAX = NCAND+1
+            ELSE
+
+*           No:  comparison value is next list item.
+               NMAX = LIST(I+1)
+            END IF
+
+*        Can the current item be incremented?
+            IF (NMAX-LISTI.GT.1) THEN
+
+*           Yes:  increment it.
+               LIST(I) = LISTI+1
+
+*           Reinitialize the preceding items.
+               DO M=1,I-1
+                  LIST(M) = M
+               END DO
+
+*           Break.
+               MORE = .FALSE.
+            ELSE
+
+*           Can't increment the current item:  is it the final one?
+               IF (I.GE.NSEL) THEN
+
+*              Yes:  set the status.
+                  J = 1
+
+*              Restart the sequence.
+                  DO I=1,NSEL
+                     LIST(I) = I
+                  END DO
+
+*              Break.
+                  MORE = .FALSE.
+               ELSE
+
+*              No:  next list item.
+                  I = I+1
+               END IF
+            END IF
+         END DO
+      END IF
+ 9999 CONTINUE
+
+      END
diff --git a/math/slalib/configure.ac b/math/slalib/configure.ac
new file mode 100644
index 00000000..deeead59
--- /dev/null
+++ b/math/slalib/configure.ac
@@ -0,0 +1,134 @@
+dnl    Process this file with autoconf to produce a configure script
+AC_REVISION($Revision$)
+
+dnl    Initialisation: package name and version number
+AC_INIT(sla, 2.5-7, starlink@jiscmail.ac.uk)
+# Version-info specifications.  See SSN/78 for guidelines, and update the table
+# below for ANY change of version number.
+#
+# The library version numbers below match PTW's LIB_VERS 1.6 and 1.7
+# respectively, as it happens.  There is no need to continue this pattern
+# with any future changes, since these should respect the rather different
+# rules for the -version-info numbers.  Instead the PTW makefile LIB_VERS
+# changes should be regarded as guidelines for which changes are and are
+# not backwards-compatible.
+#
+#   Release    libsla.la
+#    2.4-12       6:0:0
+#    2.5-2        7:0:0
+AC_SUBST(libsla_la_version_info, 7:0:0)
+
+dnl    Require autoconf-2.50 at least
+AC_PREREQ(2.50)
+dnl    Require automake-1.8.2-starlink at least
+AM_INIT_AUTOMAKE(1.8.2-starlink)
+
+dnl    Sanity-check: name a file in the source directory -- if this
+dnl    isn't found then configure will complain
+AC_CONFIG_SRCDIR([sla_link])
+
+dnl    Include defaults for Starlink configurations
+STAR_DEFAULTS
+
+dnl    Find required versions of the programs we need for configuration
+AC_PROG_FC
+AC_PROG_FPP
+AC_PROG_LIBTOOL
+
+dnl    If --with-pic=no is set we should honour that.
+AM_CONDITIONAL(NOPIC, test x$pic_mode = xno)
+
+dnl    Platform-dependent/preprocessed sources.  This is slightly
+dnl    subtle: file random.F is a preprocessable file.  However,
+dnl    there are also versions available for VAX/VMS
+dnl    (random.F__vms) and Microsoft Fortran (random.F__win), and
+dnl    these are sufficiently distinct that it's not worth just
+dnl    configuring the function name.
+dnl
+dnl    The random and gresid VMS and Windows files have a .F
+dnl    extension: there's no preprocessable code in them, but they
+dnl    have to have the same name as the file which does have.
+dnl
+dnl    Problem: Is the code in the *__win files specific to Windows
+dnl    or to MSFortran?  Since you'd only get MSFortran on Windows, I
+dnl    suppose it's the former (or might as well be).
+dnl
+dnl    The __vms files will never be matched by this macro (will the
+dnl    __win files?), since config.guess doesn't cover VMS at all, but
+dnl    the following, as well as documenting the relationship, also
+dnl    causes the corresponding files to be included in the
+dnl    distribution, where they might be of use to someone.
+STAR_PLATFORM_SOURCES([random.F gresid.F wait.f],
+                      [__vms __win default])
+
+if cmp -s random.F random.Fdefault; then
+    # The unix version, to be configured
+    found_random=false
+    AC_CHECK_FUNCS([rand random], [found_random=true])
+    if $found_random; then
+        : OK
+    else
+        AC_LIBOBJ([rtl_random])
+    fi
+fi
+
+dnl    Conditional defining whether we build the thread-safe C wrappers
+AC_ARG_WITH([pthreads],
+            [ --with-pthreads   Build package with POSIX threads support],
+        if test "$withval" = "yes"; then
+           use_pthreads="yes"
+        else
+           use_pthreads="no"
+        fi,
+        use_pthreads="no")
+if test "$use_pthreads" = "yes"; then
+AC_CHECK_LIB([pthread], [pthread_create], ,[use_pthreads="no"])
+   if test "$use_pthreads" = "yes"; then
+      AC_DEFINE([USE_PTHREADS], [1], [Build with POSIX threads support])
+   fi
+fi
+
+dnl    Conditional defining whether we use CNF or not
+AC_ARG_WITH([cnf],
+            [ --with-cnf    Use Starlink CNF library for thread locking],
+        if test "$withval" = "yes"; then
+           use_cnf="yes"
+        else
+           use_cnf="no"
+        fi,
+        use_cnf="yes")
+if test "$use_cnf" = "yes"; then
+   AC_DEFINE([USE_CNF], [1], [Use Starlink CNF library for thread locking])
+fi
+
+STAR_CNF_COMPATIBLE_SYMBOLS
+
+dnl   We need this for the tests
+AC_FC_MAIN
+AC_FC_LIBRARY_LDFLAGS
+
+#  Perform the check that configures f77.h.in for the return type of REAL
+#  Fortran functions. On 64-bit g77 with f2c compatibility this is double
+#  not float.
+STAR_CNF_F2C_COMPATIBLE
+
+#  Determine type of Fortran character string lengths.
+STAR_CNF_TRAIL_TYPE
+
+AC_CONFIG_HEADERS([config.h])
+
+dnl    Declare the build and use dependencies for this package
+dnl    There are neither build nor use dependencies
+
+STAR_LATEX_DOCUMENTATION(sun67)
+
+dnl    Declare the build and use dependencies for this package
+dnl    NOTE, cnf should be a link dependency rather than a build
+dnl    dependency, but there is clearly a bug in starconf somewhere
+dbl    because making it a link dependency results in no CNF dependency
+dnl    being added to Makefile.dependencies.
+STAR_DECLARE_DEPENDENCIES([build],  [cnf])
+
+AC_CONFIG_FILES(Makefile component.xml vers.f veri.f f77.h)
+
+AC_OUTPUT
diff --git a/math/slalib/cr2af.f b/math/slalib/cr2af.f
new file mode 100644
index 00000000..f12058a1
--- /dev/null
+++ b/math/slalib/cr2af.f
@@ -0,0 +1,76 @@
+      SUBROUTINE slCRAF (NDP, ANGLE, SIGN, IDMSF)
+*+
+*     - - - - - -
+*      C R A F
+*     - - - - - -
+*
+*  Convert an angle in radians into degrees, arcminutes, arcseconds
+*  (single precision)
+*
+*  Given:
+*     NDP       int      number of decimal places of arcseconds
+*     ANGLE     real     angle in radians
+*
+*  Returned:
+*     SIGN      char     '+' or '-'
+*     IDMSF     int(4)   degrees, arcminutes, arcseconds, fraction
+*
+*  Notes:
+*
+*     1)  NDP less than zero is interpreted as zero.
+*
+*     2)  The largest useful value for NDP is determined by the size of
+*         ANGLE, the format of REAL floating-point numbers on the target
+*         machine, and the risk of overflowing IDMSF(4).  On some
+*         architectures, for ANGLE up to 2pi, the available floating-
+*         point precision corresponds roughly to NDP=3.  This is well
+*         below the ultimate limit of NDP=9 set by the capacity of a
+*         typical 32-bit IDMSF(4).
+*
+*     3)  The absolute value of ANGLE may exceed 2pi.  In cases where it
+*         does not, it is up to the caller to test for and handle the
+*         case where ANGLE is very nearly 2pi and rounds up to 360 deg,
+*         by testing for IDMSF(1)=360 and setting IDMSF(1-4) to zero.
+*
+*  Called:  slCDTF
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER NDP
+      REAL ANGLE
+      CHARACTER SIGN*(*)
+      INTEGER IDMSF(4)
+
+*  Hours to degrees * radians to turns
+      REAL F
+      PARAMETER (F=15.0/6.283185307179586476925287)
+
+
+
+*  Scale then use days to h,m,s routine
+      CALL slCDTF(NDP,ANGLE*F,SIGN,IDMSF)
+
+      END
diff --git a/math/slalib/cr2tf.f b/math/slalib/cr2tf.f
new file mode 100644
index 00000000..b23cbd2e
--- /dev/null
+++ b/math/slalib/cr2tf.f
@@ -0,0 +1,76 @@
+      SUBROUTINE slCRTF (NDP, ANGLE, SIGN, IHMSF)
+*+
+*     - - - - - -
+*      C R T F
+*     - - - - - -
+*
+*  Convert an angle in radians into hours, minutes, seconds
+*  (single precision)
+*
+*  Given:
+*     NDP       int      number of decimal places of seconds
+*     ANGLE     real     angle in radians
+*
+*  Returned:
+*     SIGN      char     '+' or '-'
+*     IHMSF     int(4)   hours, minutes, seconds, fraction
+*
+*  Notes:
+*
+*  1)  NDP less than zero is interpreted as zero.
+*
+*  2)  The largest useful value for NDP is determined by the size of
+*      ANGLE, the format of REAL floating-point numbers on the target
+*      machine, and the risk of overflowing IHMSF(4).  On some
+*      architectures, for ANGLE up to 2pi, the available floating-point
+*      precision corresponds roughly to NDP=3.  This is well below
+*      the ultimate limit of NDP=9 set by the capacity of a typical
+*      32-bit IHMSF(4).
+*
+*  3)  The absolute value of ANGLE may exceed 2pi.  In cases where it
+*      does not, it is up to the caller to test for and handle the
+*      case where ANGLE is very nearly 2pi and rounds up to 24 hours,
+*      by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+*
+*  Called:  slCDTF
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER NDP
+      REAL ANGLE
+      CHARACTER SIGN*(*)
+      INTEGER IHMSF(4)
+
+*  Turns to radians
+      REAL T2R
+      PARAMETER (T2R=6.283185307179586476925287)
+
+
+
+*  Scale then use days to h,m,s routine
+      CALL slCDTF(NDP,ANGLE/T2R,SIGN,IHMSF)
+
+      END
diff --git a/math/slalib/cs2c.f b/math/slalib/cs2c.f
new file mode 100644
index 00000000..a74ac4bd
--- /dev/null
+++ b/math/slalib/cs2c.f
@@ -0,0 +1,58 @@
+      SUBROUTINE slCS2C (A, B, V)
+*+
+*     - - - - -
+*      C S 2 C
+*     - - - - -
+*
+*  Spherical coordinates to direction cosines (single precision)
+*
+*  Given:
+*     A,B      real      spherical coordinates in radians
+*                           (RA,Dec), (long,lat) etc.
+*
+*  Returned:
+*     V        real(3)   x,y,z unit vector
+*
+*  The spherical coordinates are longitude (+ve anticlockwise looking
+*  from the +ve latitude pole) and latitude.  The Cartesian coordinates
+*  are right handed, with the x axis at zero longitude and latitude, and
+*  the z axis at the +ve latitude pole.
+*
+*  Last revision:   22 July 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL A,B,V(3)
+
+      REAL COSB
+
+
+
+      COSB = COS(B)
+
+      V(1) = COS(A)*COSB
+      V(2) = SIN(A)*COSB
+      V(3) = SIN(B)
+
+      END
diff --git a/math/slalib/cs2c6.f b/math/slalib/cs2c6.f
new file mode 100644
index 00000000..a8c4d402
--- /dev/null
+++ b/math/slalib/cs2c6.f
@@ -0,0 +1,73 @@
+      SUBROUTINE slS2C6 ( A, B, R, AD, BD, RD, V )
+*+
+*     - - - - - -
+*      S 2 C 6
+*     - - - - - -
+*
+*  Conversion of position & velocity in spherical coordinates
+*  to Cartesian coordinates (single precision)
+*
+*  Given:
+*     A     r      longitude (radians)
+*     B     r      latitude (radians)
+*     R     r      radial coordinate
+*     AD    r      longitude derivative (radians per unit time)
+*     BD    r      latitude derivative (radians per unit time)
+*     RD    r      radial derivative
+*
+*  Returned:
+*     V     r(6)   Cartesian position & velocity vector
+*
+*  Last revision:   11 September 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL A, B, R, AD, BD, RD, V(6)
+
+      REAL SA, CA, SB, CB, RCB, X, Y, RBD, W
+
+
+
+*  Useful functions.
+      SA = SIN(A)
+      CA = COS(A)
+      SB = SIN(B)
+      CB = COS(B)
+      RCB = R*CB
+      X = RCB*CA
+      Y = RCB*SA
+      RBD = R*BD
+      W = RBD*SB-CB*RD
+
+*  Position.
+      V(1) = X
+      V(2) = Y
+      V(3) = R*SB
+
+*  Velocity.
+      V(4) = -Y*AD-W*CA
+      V(5) = X*AD-W*SA
+      V(6) = RBD*CB+SB*RD
+
+      END
diff --git a/math/slalib/ctf2d.f b/math/slalib/ctf2d.f
new file mode 100644
index 00000000..a427c38d
--- /dev/null
+++ b/math/slalib/ctf2d.f
@@ -0,0 +1,74 @@
+      SUBROUTINE slCTFD (IHOUR, IMIN, SEC, DAYS, J)
+*+
+*     - - - - - -
+*      C T F D
+*     - - - - - -
+*
+*  Convert hours, minutes, seconds to days (single precision)
+*
+*  Given:
+*     IHOUR       int       hours
+*     IMIN        int       minutes
+*     SEC         real      seconds
+*
+*  Returned:
+*     DAYS        real      interval in days
+*     J           int       status:  0 = OK
+*                                    1 = IHOUR outside range 0-23
+*                                    2 = IMIN outside range 0-59
+*                                    3 = SEC outside range 0-59.999...
+*
+*  Notes:
+*
+*  1)  The result is computed even if any of the range checks
+*      fail.
+*
+*  2)  The sign must be dealt with outside this routine.
+*
+*  P.T.Wallace   Starlink   November 1984
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IHOUR,IMIN
+      REAL SEC,DAYS
+      INTEGER J
+
+*  Seconds per day
+      REAL D2S
+      PARAMETER (D2S=86400.0)
+
+
+
+*  Preset status
+      J=0
+
+*  Validate sec, min, hour
+      IF (SEC.LT.0.0.OR.SEC.GE.60.0) J=3
+      IF (IMIN.LT.0.OR.IMIN.GT.59) J=2
+      IF (IHOUR.LT.0.OR.IHOUR.GT.23) J=1
+
+*  Compute interval
+      DAYS=(60.0*(60.0*REAL(IHOUR)+REAL(IMIN))+SEC)/D2S
+
+      END
diff --git a/math/slalib/ctf2r.f b/math/slalib/ctf2r.f
new file mode 100644
index 00000000..fb841054
--- /dev/null
+++ b/math/slalib/ctf2r.f
@@ -0,0 +1,72 @@
+      SUBROUTINE slCTFR (IHOUR, IMIN, SEC, RAD, J)
+*+
+*     - - - - - -
+*      C T F R
+*     - - - - - -
+*
+*  Convert hours, minutes, seconds to radians (single precision)
+*
+*  Given:
+*     IHOUR       int       hours
+*     IMIN        int       minutes
+*     SEC         real      seconds
+*
+*  Returned:
+*     RAD         real      angle in radians
+*     J           int       status:  0 = OK
+*                                    1 = IHOUR outside range 0-23
+*                                    2 = IMIN outside range 0-59
+*                                    3 = SEC outside range 0-59.999...
+*
+*  Called:
+*     slCTFD
+*
+*  Notes:
+*
+*  1)  The result is computed even if any of the range checks
+*      fail.
+*
+*  2)  The sign must be dealt with outside this routine.
+*
+*  P.T.Wallace   Starlink   November 1984
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IHOUR,IMIN
+      REAL SEC,RAD
+      INTEGER J
+
+      REAL TURNS
+
+*  Turns to radians
+      REAL T2R
+      PARAMETER (T2R=6.283185307179586476925287)
+
+
+
+*  Convert to turns then radians
+      CALL slCTFD(IHOUR,IMIN,SEC,TURNS,J)
+      RAD=T2R*TURNS
+
+      END
diff --git a/math/slalib/daf2r.f b/math/slalib/daf2r.f
new file mode 100644
index 00000000..ddd07b74
--- /dev/null
+++ b/math/slalib/daf2r.f
@@ -0,0 +1,73 @@
+      SUBROUTINE slDAFR (IDEG, IAMIN, ASEC, RAD, J)
+*+
+*     - - - - - -
+*      D A F R
+*     - - - - - -
+*
+*  Convert degrees, arcminutes, arcseconds to radians
+*  (double precision)
+*
+*  Given:
+*     IDEG        int       degrees
+*     IAMIN       int       arcminutes
+*     ASEC        dp        arcseconds
+*
+*  Returned:
+*     RAD         dp        angle in radians
+*     J           int       status:  0 = OK
+*                                    1 = IDEG outside range 0-359
+*                                    2 = IAMIN outside range 0-59
+*                                    3 = ASEC outside range 0-59.999...
+*
+*  Notes:
+*     1)  The result is computed even if any of the range checks
+*         fail.
+*     2)  The sign must be dealt with outside this routine.
+*
+*  P.T.Wallace   Starlink   23 August 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IDEG,IAMIN
+      DOUBLE PRECISION ASEC,RAD
+      INTEGER J
+
+*  Arc seconds to radians
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+
+
+*  Preset status
+      J=0
+
+*  Validate arcsec, arcmin, deg
+      IF (ASEC.LT.0D0.OR.ASEC.GE.60D0) J=3
+      IF (IAMIN.LT.0.OR.IAMIN.GT.59) J=2
+      IF (IDEG.LT.0.OR.IDEG.GT.359) J=1
+
+*  Compute angle
+      RAD=AS2R*(60D0*(60D0*DBLE(IDEG)+DBLE(IAMIN))+ASEC)
+
+      END
diff --git a/math/slalib/dafin.f b/math/slalib/dafin.f
new file mode 100644
index 00000000..68ecc5f9
--- /dev/null
+++ b/math/slalib/dafin.f
@@ -0,0 +1,181 @@
+      SUBROUTINE slDAFN (STRING, IPTR, A, J)
+*+
+*     - - - - - -
+*      D A F N
+*     - - - - - -
+*
+*  Sexagesimal character string to angle (double precision)
+*
+*  Given:
+*     STRING  c*(*)   string containing deg, arcmin, arcsec fields
+*     IPTR      i     pointer to start of decode (1st = 1)
+*
+*  Returned:
+*     IPTR      i     advanced past the decoded angle
+*     A         d     angle in radians
+*     J         i     status:  0 = OK
+*                             +1 = default, A unchanged
+*                             -1 = bad degrees      )
+*                             -2 = bad arcminutes   )  (note 3)
+*                             -3 = bad arcseconds   )
+*
+*  Example:
+*
+*    argument    before                           after
+*
+*    STRING      '-57 17 44.806  12 34 56.7'      unchanged
+*    IPTR        1                                16 (points to 12...)
+*    A           ?                                -1.00000D0
+*    J           ?                                0
+*
+*    A further call to slDAFN, without adjustment of IPTR, will
+*    decode the second angle, 12deg 34min 56.7sec.
+*
+*  Notes:
+*
+*     1)  The first three "fields" in STRING are degrees, arcminutes,
+*         arcseconds, separated by spaces or commas.  The degrees field
+*         may be signed, but not the others.  The decoding is carried
+*         out by the DFLTIN routine and is free-format.
+*
+*     2)  Successive fields may be absent, defaulting to zero.  For
+*         zero status, the only combinations allowed are degrees alone,
+*         degrees and arcminutes, and all three fields present.  If all
+*         three fields are omitted, a status of +1 is returned and A is
+*         unchanged.  In all other cases A is changed.
+*
+*     3)  Range checking:
+*
+*           The degrees field is not range checked.  However, it is
+*           expected to be integral unless the other two fields are absent.
+*
+*           The arcminutes field is expected to be 0-59, and integral if
+*           the arcseconds field is present.  If the arcseconds field
+*           is absent, the arcminutes is expected to be 0-59.9999...
+*
+*           The arcseconds field is expected to be 0-59.9999...
+*
+*     4)  Decoding continues even when a check has failed.  Under these
+*         circumstances the field takes the supplied value, defaulting
+*         to zero, and the result A is computed and returned.
+*
+*     5)  Further fields after the three expected ones are not treated
+*         as an error.  The pointer IPTR is left in the correct state
+*         for further decoding with the present routine or with DFLTIN
+*         etc. See the example, above.
+*
+*     6)  If STRING contains hours, minutes, seconds instead of degrees
+*         etc, or if the required units are turns (or days) instead of
+*         radians, the result A should be multiplied as follows:
+*
+*           for        to obtain    multiply
+*           STRING     A in         A by
+*
+*           d ' "      radians      1       =  1D0
+*           d ' "      turns        1/2pi   =  0.1591549430918953358D0
+*           h m s      radians      15      =  15D0
+*           h m s      days         15/2pi  =  2.3873241463784300365D0
+*
+*  Called:  slDFLI
+*
+*  P.T.Wallace   Starlink   1 August 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) STRING
+      INTEGER IPTR
+      DOUBLE PRECISION A
+      INTEGER J
+
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=4.84813681109535993589914102358D-6)
+      INTEGER JF,JD,JM,JS
+      DOUBLE PRECISION DEG,ARCMIN,ARCSEC
+
+
+
+*  Preset the status to OK
+      JF=0
+
+*  Defaults
+      DEG=0D0
+      ARCMIN=0D0
+      ARCSEC=0D0
+
+*  Decode degrees, arcminutes, arcseconds
+      CALL slDFLI(STRING,IPTR,DEG,JD)
+      IF (JD.GT.1) THEN
+         JF=-1
+      ELSE
+         CALL slDFLI(STRING,IPTR,ARCMIN,JM)
+         IF (JM.LT.0.OR.JM.GT.1) THEN
+            JF=-2
+         ELSE
+            CALL slDFLI(STRING,IPTR,ARCSEC,JS)
+            IF (JS.LT.0.OR.JS.GT.1) THEN
+               JF=-3
+
+*        See if the combination of fields is credible
+            ELSE IF (JD.GT.0) THEN
+*           No degrees:  arcmin, arcsec ought also to be absent
+               IF (JM.EQ.0) THEN
+*              Suspect arcmin
+                  JF=-2
+               ELSE IF (JS.EQ.0) THEN
+*              Suspect arcsec
+                  JF=-3
+               ELSE
+*              All three fields absent
+                  JF=1
+               END IF
+*        Degrees present:  if arcsec present so ought arcmin to be
+            ELSE IF (JM.NE.0.AND.JS.EQ.0) THEN
+               JF=-3
+
+*        Tests for range and integrality
+
+*        Degrees
+            ELSE IF (JM.EQ.0.AND.DINT(DEG).NE.DEG) THEN
+               JF=-1
+*        Arcminutes
+            ELSE IF ((JS.EQ.0.AND.DINT(ARCMIN).NE.ARCMIN).OR.
+     :               ARCMIN.GE.60D0) THEN
+               JF=-2
+*        Arcseconds
+            ELSE IF (ARCSEC.GE.60D0) THEN
+               JF=-3
+            END IF
+         END IF
+      END IF
+
+*  Unless all three fields absent, compute angle value
+      IF (JF.LE.0) THEN
+         A=AS2R*(60D0*(60D0*ABS(DEG)+ARCMIN)+ARCSEC)
+         IF (JD.LT.0) A=-A
+      END IF
+
+*  Return the status
+      J=JF
+
+      END
diff --git a/math/slalib/dat.f b/math/slalib/dat.f
new file mode 100644
index 00000000..67620144
--- /dev/null
+++ b/math/slalib/dat.f
@@ -0,0 +1,232 @@
+      DOUBLE PRECISION FUNCTION slDAT (UTC)
+*+
+*     - - - -
+*      D A T
+*     - - - -
+*
+*  Increment to be applied to Coordinated Universal Time UTC to give
+*  International Atomic Time TAI (double precision)
+*
+*  Given:
+*     UTC      d      UTC date as a modified JD (JD-2400000.5)
+*
+*  Result:  TAI-UTC in seconds
+*
+*  Notes:
+*
+*  1  The UTC is specified to be a date rather than a time to indicate
+*     that care needs to be taken not to specify an instant which lies
+*     within a leap second.  Though in most cases UTC can include the
+*     fractional part, correct behaviour on the day of a leap second
+*     can only be guaranteed up to the end of the second 23:59:59.
+*
+*  2  For epochs from 1961 January 1 onwards, the expressions from the
+*     file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used.
+*
+*  3  The 5ms time step at 1961 January 1 is taken from 2.58.1 (p87) of
+*     the 1992 Explanatory Supplement.
+*
+*  4  UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper
+*     to call the routine with an earlier epoch.  However, if this
+*     is attempted, the TAI-UTC expression for the year 1960 is used.
+*
+*
+*     :-----------------------------------------:
+*     :                                         :
+*     :                IMPORTANT                :
+*     :                                         :
+*     :  This routine must be updated on each   :
+*     :     occasion that a leap second is      :
+*     :                announced                :
+*     :                                         :
+*     :  Latest leap second:  2012 July 1       :
+*     :                                         :
+*     :-----------------------------------------:
+*
+*  Last revision:   5 July 2008
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION UTC
+
+      DOUBLE PRECISION DT
+
+
+
+      IF (.FALSE.) THEN
+
+* - - - - - - - - - - - - - - - - - - - - - - *
+*  Add new code here on each occasion that a  *
+*  leap second is announced, and update the   *
+*  preamble comments appropriately.           *
+* - - - - - - - - - - - - - - - - - - - - - - *
+
+*     2012 July 1
+      ELSE IF (UTC.GE.56109D0) THEN
+         DT=35D0
+
+*     2009 January 1
+      ELSE IF (UTC.GE.54832D0) THEN
+         DT=34D0
+
+*     2006 January 1
+      ELSE IF (UTC.GE.53736D0) THEN
+         DT=33D0
+
+*     1999 January 1
+      ELSE IF (UTC.GE.51179D0) THEN
+         DT=32D0
+
+*     1997 July 1
+      ELSE IF (UTC.GE.50630D0) THEN
+         DT=31D0
+
+*     1996 January 1
+      ELSE IF (UTC.GE.50083D0) THEN
+         DT=30D0
+
+*     1994 July 1
+      ELSE IF (UTC.GE.49534D0) THEN
+         DT=29D0
+
+*     1993 July 1
+      ELSE IF (UTC.GE.49169D0) THEN
+         DT=28D0
+
+*     1992 July 1
+      ELSE IF (UTC.GE.48804D0) THEN
+         DT=27D0
+
+*     1991 January 1
+      ELSE IF (UTC.GE.48257D0) THEN
+         DT=26D0
+
+*     1990 January 1
+      ELSE IF (UTC.GE.47892D0) THEN
+         DT=25D0
+
+*     1988 January 1
+      ELSE IF (UTC.GE.47161D0) THEN
+         DT=24D0
+
+*     1985 July 1
+      ELSE IF (UTC.GE.46247D0) THEN
+         DT=23D0
+
+*     1983 July 1
+      ELSE IF (UTC.GE.45516D0) THEN
+         DT=22D0
+
+*     1982 July 1
+      ELSE IF (UTC.GE.45151D0) THEN
+         DT=21D0
+
+*     1981 July 1
+      ELSE IF (UTC.GE.44786D0) THEN
+         DT=20D0
+
+*     1980 January 1
+      ELSE IF (UTC.GE.44239D0) THEN
+         DT=19D0
+
+*     1979 January 1
+      ELSE IF (UTC.GE.43874D0) THEN
+         DT=18D0
+
+*     1978 January 1
+      ELSE IF (UTC.GE.43509D0) THEN
+         DT=17D0
+
+*     1977 January 1
+      ELSE IF (UTC.GE.43144D0) THEN
+         DT=16D0
+
+*     1976 January 1
+      ELSE IF (UTC.GE.42778D0) THEN
+         DT=15D0
+
+*     1975 January 1
+      ELSE IF (UTC.GE.42413D0) THEN
+         DT=14D0
+
+*     1974 January 1
+      ELSE IF (UTC.GE.42048D0) THEN
+         DT=13D0
+
+*     1973 January 1
+      ELSE IF (UTC.GE.41683D0) THEN
+         DT=12D0
+
+*     1972 July 1
+      ELSE IF (UTC.GE.41499D0) THEN
+         DT=11D0
+
+*     1972 January 1
+      ELSE IF (UTC.GE.41317D0) THEN
+         DT=10D0
+
+*     1968 February 1
+      ELSE IF (UTC.GE.39887D0) THEN
+         DT=4.2131700D0+(UTC-39126D0)*0.002592D0
+
+*     1966 January 1
+      ELSE IF (UTC.GE.39126D0) THEN
+         DT=4.3131700D0+(UTC-39126D0)*0.002592D0
+
+*     1965 September 1
+      ELSE IF (UTC.GE.39004D0) THEN
+         DT=3.8401300D0+(UTC-38761D0)*0.001296D0
+
+*     1965 July 1
+      ELSE IF (UTC.GE.38942D0) THEN
+         DT=3.7401300D0+(UTC-38761D0)*0.001296D0
+
+*     1965 March 1
+      ELSE IF (UTC.GE.38820D0) THEN
+         DT=3.6401300D0+(UTC-38761D0)*0.001296D0
+
+*     1965 January 1
+      ELSE IF (UTC.GE.38761D0) THEN
+         DT=3.5401300D0+(UTC-38761D0)*0.001296D0
+
+*     1964 September 1
+      ELSE IF (UTC.GE.38639D0) THEN
+         DT=3.4401300D0+(UTC-38761D0)*0.001296D0
+
+*     1964 April 1
+      ELSE IF (UTC.GE.38486D0) THEN
+         DT=3.3401300D0+(UTC-38761D0)*0.001296D0
+
+*     1964 January 1
+      ELSE IF (UTC.GE.38395D0) THEN
+         DT=3.2401300D0+(UTC-38761D0)*0.001296D0
+
+*     1963 November 1
+      ELSE IF (UTC.GE.38334D0) THEN
+         DT=1.9458580D0+(UTC-37665D0)*0.0011232D0
+
+*     1962 January 1
+      ELSE IF (UTC.GE.37665D0) THEN
+         DT=1.8458580D0+(UTC-37665D0)*0.0011232D0
+
+*     1961 August 1
+      ELSE IF (UTC.GE.37512D0) THEN
+         DT=1.3728180D0+(UTC-37300D0)*0.001296D0
+
+*     1961 January 1
+      ELSE IF (UTC.GE.37300D0) THEN
+         DT=1.4228180D0+(UTC-37300D0)*0.001296D0
+
+*     Before that
+      ELSE
+         DT=1.4178180D0+(UTC-37300D0)*0.001296D0
+
+      END IF
+
+      slDAT=DT
+
+      END
diff --git a/math/slalib/dav2m.f b/math/slalib/dav2m.f
new file mode 100644
index 00000000..7eb1f68b
--- /dev/null
+++ b/math/slalib/dav2m.f
@@ -0,0 +1,84 @@
+      SUBROUTINE slDAVM (AXVEC, RMAT)
+*+
+*     - - - - - -
+*      D A V M
+*     - - - - - -
+*
+*  Form the rotation matrix corresponding to a given axial vector.
+*  (double precision)
+*
+*  A rotation matrix describes a rotation about some arbitrary axis,
+*  called the Euler axis.  The "axial vector" supplied to this routine
+*  has the same direction as the Euler axis, and its magnitude is the
+*  amount of rotation in radians.
+*
+*  Given:
+*    AXVEC  d(3)     axial vector (radians)
+*
+*  Returned:
+*    RMAT   d(3,3)   rotation matrix
+*
+*  If AXVEC is null, the unit matrix is returned.
+*
+*  The reference frame rotates clockwise as seen looking along
+*  the axial vector from the origin.
+*
+*  Last revision:   26 November 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION AXVEC(3),RMAT(3,3)
+
+      DOUBLE PRECISION X,Y,Z,PHI,S,C,W
+
+
+
+*  Rotation angle - magnitude of axial vector - and functions
+      X = AXVEC(1)
+      Y = AXVEC(2)
+      Z = AXVEC(3)
+      PHI = SQRT(X*X+Y*Y+Z*Z)
+      S = SIN(PHI)
+      C = COS(PHI)
+      W = 1D0-C
+
+*  Euler axis - direction of axial vector (perhaps null)
+      IF (PHI.NE.0D0) THEN
+         X = X/PHI
+         Y = Y/PHI
+         Z = Z/PHI
+      END IF
+
+*  Compute the rotation matrix
+      RMAT(1,1) = X*X*W+C
+      RMAT(1,2) = X*Y*W+Z*S
+      RMAT(1,3) = X*Z*W-Y*S
+      RMAT(2,1) = X*Y*W-Z*S
+      RMAT(2,2) = Y*Y*W+C
+      RMAT(2,3) = Y*Z*W+X*S
+      RMAT(3,1) = X*Z*W+Y*S
+      RMAT(3,2) = Y*Z*W-X*S
+      RMAT(3,3) = Z*Z*W+C
+
+      END
diff --git a/math/slalib/dbear.f b/math/slalib/dbear.f
new file mode 100644
index 00000000..417c4bdf
--- /dev/null
+++ b/math/slalib/dbear.f
@@ -0,0 +1,60 @@
+      DOUBLE PRECISION FUNCTION slDBER (A1, B1, A2, B2)
+*+
+*     - - - - - -
+*      D B E R
+*     - - - - - -
+*
+*  Bearing (position angle) of one point on a sphere relative to another
+*  (double precision)
+*
+*  Given:
+*     A1,B1    d    spherical coordinates of one point
+*     A2,B2    d    spherical coordinates of the other point
+*
+*  (The spherical coordinates are RA,Dec, Long,Lat etc, in radians.)
+*
+*  The result is the bearing (position angle), in radians, of point
+*  A2,B2 as seen from point A1,B1.  It is in the range +/- pi.  If
+*  A2,B2 is due east of A1,B1 the bearing is +pi/2.  Zero is returned
+*  if the two points are coincident.
+*
+*  P.T.Wallace   Starlink   23 March 1991
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION A1,B1,A2,B2
+
+      DOUBLE PRECISION DA,X,Y
+
+
+      DA=A2-A1
+      Y=SIN(DA)*COS(B2)
+      X=SIN(B2)*COS(B1)-COS(B2)*SIN(B1)*COS(DA)
+      IF (X.NE.0D0.OR.Y.NE.0D0) THEN
+         slDBER=ATAN2(Y,X)
+      ELSE
+         slDBER=0D0
+      END IF
+
+      END
diff --git a/math/slalib/dbjin.f b/math/slalib/dbjin.f
new file mode 100644
index 00000000..6c4b31f5
--- /dev/null
+++ b/math/slalib/dbjin.f
@@ -0,0 +1,131 @@
+      SUBROUTINE slDBJI (STRING, NSTRT, DRESLT, J1, J2)
+*+
+*     - - - - - -
+*      D B J I
+*     - - - - - -
+*
+*  Convert free-format input into double precision floating point,
+*  using DFLTIN but with special syntax extensions.
+*
+*  The purpose of the syntax extensions is to help cope with mixed
+*  FK4 and FK5 data.  In addition to the syntax accepted by DFLTIN,
+*  the following two extensions are recognized by DBJIN:
+*
+*     1)  A valid non-null field preceded by the character 'B'
+*         (or 'b') is accepted.
+*
+*     2)  A valid non-null field preceded by the character 'J'
+*         (or 'j') is accepted.
+*
+*  The calling program is notified of the incidence of either of these
+*  extensions through an supplementary status argument.  The rest of
+*  the arguments are as for DFLTIN.
+*
+*  Given:
+*     STRING      char       string containing field to be decoded
+*     NSTRT       int        pointer to 1st character of field in string
+*
+*  Returned:
+*     NSTRT       int        incremented
+*     DRESLT      double     result
+*     J1          int        DFLTIN status: -1 = -OK
+*                                            0 = +OK
+*                                           +1 = null field
+*                                           +2 = error
+*     J2          int        syntax flag:  0 = normal DFLTIN syntax
+*                                         +1 = 'B' or 'b'
+*                                         +2 = 'J' or 'j'
+*
+*  Called:  slDFLI
+*
+*  For details of the basic syntax, see slDFLI.
+*
+*  P.T.Wallace   Starlink   23 November 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) STRING
+      INTEGER NSTRT
+      DOUBLE PRECISION DRESLT
+      INTEGER J1,J2
+
+      INTEGER J2A,LENSTR,NA,J1A,NB,J1B
+      CHARACTER C
+
+
+
+*   Preset syntax flag
+      J2A=0
+
+*   Length of string
+      LENSTR=LEN(STRING)
+
+*   Pointer to current character
+      NA=NSTRT
+
+*   Attempt normal decode
+      CALL slDFLI(STRING,NA,DRESLT,J1A)
+
+*   Proceed only if pointer still within string
+      IF (NA.GE.1.AND.NA.LE.LENSTR) THEN
+
+*      See if DFLTIN reported a null field
+         IF (J1A.EQ.1) THEN
+
+*         It did: examine character it stuck on
+            C=STRING(NA:NA)
+            IF (C.EQ.'B'.OR.C.EQ.'b') THEN
+*            'B' - provisionally note
+               J2A=1
+            ELSE IF (C.EQ.'J'.OR.C.EQ.'j') THEN
+*            'J' - provisionally note
+               J2A=2
+            END IF
+
+*         Following B or J, attempt to decode a number
+            IF (J2A.EQ.1.OR.J2A.EQ.2) THEN
+               NB=NA+1
+               CALL slDFLI(STRING,NB,DRESLT,J1B)
+
+*            If successful, copy pointer and status
+               IF (J1B.LE.0) THEN
+                  NA=NB
+                  J1A=J1B
+*            If not, forget about the B or J
+               ELSE
+                  J2A=0
+               END IF
+
+            END IF
+
+         END IF
+
+      END IF
+
+*   Return argument values and exit
+      NSTRT=NA
+      J1=J1A
+      J2=J2A
+
+      END
diff --git a/math/slalib/dc62s.f b/math/slalib/dc62s.f
new file mode 100644
index 00000000..7bb64e0d
--- /dev/null
+++ b/math/slalib/dc62s.f
@@ -0,0 +1,100 @@
+      SUBROUTINE slDC6S (V, A, B, R, AD, BD, RD)
+*+
+*     - - - - - -
+*      D C 6 S
+*     - - - - - -
+*
+*  Conversion of position & velocity in Cartesian coordinates
+*  to spherical coordinates (double precision)
+*
+*  Given:
+*     V      d(6)   Cartesian position & velocity vector
+*
+*  Returned:
+*     A      d      longitude (radians)
+*     B      d      latitude (radians)
+*     R      d      radial coordinate
+*     AD     d      longitude derivative (radians per unit time)
+*     BD     d      latitude derivative (radians per unit time)
+*     RD     d      radial derivative
+*
+*  P.T.Wallace   Starlink   28 April 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION V(6),A,B,R,AD,BD,RD
+
+      DOUBLE PRECISION X,Y,Z,XD,YD,ZD,RXY2,RXY,R2,XYP
+
+
+
+*  Components of position/velocity vector
+      X=V(1)
+      Y=V(2)
+      Z=V(3)
+      XD=V(4)
+      YD=V(5)
+      ZD=V(6)
+
+*  Component of R in XY plane squared
+      RXY2=X*X+Y*Y
+
+*  Modulus squared
+      R2=RXY2+Z*Z
+
+*  Protection against null vector
+      IF (R2.EQ.0D0) THEN
+         X=XD
+         Y=YD
+         Z=ZD
+         RXY2=X*X+Y*Y
+         R2=RXY2+Z*Z
+      END IF
+
+*  Position and velocity in spherical coordinates
+      RXY=SQRT(RXY2)
+      XYP=X*XD+Y*YD
+      IF (RXY2.NE.0D0) THEN
+         A=ATAN2(Y,X)
+         B=ATAN2(Z,RXY)
+         AD=(X*YD-Y*XD)/RXY2
+         BD=(ZD*RXY2-Z*XYP)/(R2*RXY)
+      ELSE
+         A=0D0
+         IF (Z.NE.0D0) THEN
+            B=ATAN2(Z,RXY)
+         ELSE
+            B=0D0
+         END IF
+         AD=0D0
+         BD=0D0
+      END IF
+      R=SQRT(R2)
+      IF (R.NE.0D0) THEN
+         RD=(XYP+Z*ZD)/R
+      ELSE
+         RD=0D0
+      END IF
+
+      END
diff --git a/math/slalib/dcc2s.f b/math/slalib/dcc2s.f
new file mode 100644
index 00000000..cbbbd625
--- /dev/null
+++ b/math/slalib/dcc2s.f
@@ -0,0 +1,70 @@
+      SUBROUTINE slDC2S (V, A, B)
+*+
+*     - - - - - -
+*      D C 2 S
+*     - - - - - -
+*
+*  Cartesian to spherical coordinates (double precision)
+*
+*  Given:
+*     V     d(3)   x,y,z vector
+*
+*  Returned:
+*     A,B   d      spherical coordinates in radians
+*
+*  The spherical coordinates are longitude (+ve anticlockwise looking
+*  from the +ve latitude pole) and latitude.  The Cartesian coordinates
+*  are right handed, with the x axis at zero longitude and latitude, and
+*  the z axis at the +ve latitude pole.
+*
+*  If V is null, zero A and B are returned.  At either pole, zero A is
+*  returned.
+*
+*  Last revision:   22 July 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION V(3),A,B
+
+      DOUBLE PRECISION X,Y,Z,R
+
+
+      X = V(1)
+      Y = V(2)
+      Z = V(3)
+      R = SQRT(X*X+Y*Y)
+
+      IF (R.EQ.0D0) THEN
+         A = 0D0
+      ELSE
+         A = ATAN2(Y,X)
+      END IF
+
+      IF (Z.EQ.0D0) THEN
+         B = 0D0
+      ELSE
+         B = ATAN2(Z,R)
+      END IF
+
+      END
diff --git a/math/slalib/dcmpf.f b/math/slalib/dcmpf.f
new file mode 100644
index 00000000..93d0d0c2
--- /dev/null
+++ b/math/slalib/dcmpf.f
@@ -0,0 +1,160 @@
+      SUBROUTINE slDCMF (COEFFS,XZ,YZ,XS,YS,PERP,ORIENT)
+*+
+*     - - - - - -
+*      D C M F
+*     - - - - - -
+*
+*  Decompose an [X,Y] linear fit into its constituent parameters:
+*  zero points, scales, nonperpendicularity and orientation.
+*
+*  Given:
+*     COEFFS  d(6)      transformation coefficients (see note)
+*
+*  Returned:
+*     XZ       d        x zero point
+*     YZ       d        y zero point
+*     XS       d        x scale
+*     YS       d        y scale
+*     PERP     d        nonperpendicularity (radians)
+*     ORIENT   d        orientation (radians)
+*
+*  Called:  slDA1P
+*
+*  The model relates two sets of [X,Y] coordinates as follows.
+*  Naming the elements of COEFFS:
+*
+*     COEFFS(1) = A
+*     COEFFS(2) = B
+*     COEFFS(3) = C
+*     COEFFS(4) = D
+*     COEFFS(5) = E
+*     COEFFS(6) = F
+*
+*  the model transforms coordinates [X1,Y1] into coordinates
+*  [X2,Y2] as follows:
+*
+*     X2 = A + B*X1 + C*Y1
+*     Y2 = D + E*X1 + F*Y1
+*
+*  The transformation can be decomposed into four steps:
+*
+*     1)  Zero points:
+*
+*             x' = XZ + X1
+*             y' = YZ + Y1
+*
+*     2)  Scales:
+*
+*             x'' = XS*x'
+*             y'' = YS*y'
+*
+*     3)  Nonperpendicularity:
+*
+*             x''' = cos(PERP/2)*x'' + sin(PERP/2)*y''
+*             y''' = sin(PERP/2)*x'' + cos(PERP/2)*y''
+*
+*     4)  Orientation:
+*
+*             X2 = cos(ORIENT)*x''' + sin(ORIENT)*y'''
+*             Y2 =-sin(ORIENT)*y''' + cos(ORIENT)*y'''
+*
+*  See also slFTXY, slPXY, slINVF, slXYXY
+*
+*  P.T.Wallace   Starlink   19 December 2001
+*
+*  Copyright (C) 2001 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION COEFFS(6),XZ,YZ,XS,YS,PERP,ORIENT
+
+      DOUBLE PRECISION A,B,C,D,E,F,RB2E2,RC2F2,XSC,YSC,P1,P2,P,WS,WC,
+     :                 OR,HP,SHP,CHP,SOR,COR,DET,X0,Y0,slDA1P
+
+
+
+*  Copy the six coefficients.
+      A = COEFFS(1)
+      B = COEFFS(2)
+      C = COEFFS(3)
+      D = COEFFS(4)
+      E = COEFFS(5)
+      F = COEFFS(6)
+
+*  Scales.
+      RB2E2 = SQRT(B*B+E*E)
+      RC2F2 = SQRT(C*C+F*F)
+      IF (B*F-C*E.GE.0D0) THEN
+         XSC = RB2E2
+      ELSE
+         B = -B
+         E = -E
+         XSC = -RB2E2
+      END IF
+      YSC = RC2F2
+
+*  Non-perpendicularity.
+      IF (C.NE.0D0.OR.F.NE.0D0) THEN
+         P1 = ATAN2(C,F)
+      ELSE
+         P1 = 0D0
+      END IF
+      IF (E.NE.0D0.OR.B.NE.0D0) THEN
+         P2 = ATAN2(E,B)
+      ELSE
+         P2 = 0D0
+      END IF
+      P = slDA1P(P1+P2)
+
+*  Orientation.
+      WS = C*RB2E2-E*RC2F2
+      WC = B*RC2F2+F*RB2E2
+      IF (WS.NE.0D0.OR.WC.NE.0D0) THEN
+         OR = ATAN2(WS,WC)
+      ELSE
+         OR = 0D0
+      END IF
+
+*  Zero points.
+      HP = P/2D0
+      SHP = SIN(HP)
+      CHP = COS(HP)
+      SOR = SIN(OR)
+      COR = COS(OR)
+      DET = XSC*YSC*(CHP+SHP)*(CHP-SHP)
+      IF (ABS(DET).GT.0D0) THEN
+         X0 = YSC*(A*(CHP*COR-SHP*SOR)-D*(CHP*SOR+SHP*COR))/DET
+         Y0 = XSC*(A*(CHP*SOR-SHP*COR)+D*(CHP*COR+SHP*SOR))/DET
+      ELSE
+         X0 = 0D0
+         Y0 = 0D0
+      END IF
+
+*  Results.
+      XZ = X0
+      YZ = Y0
+      XS = XSC
+      YS = YSC
+      PERP = P
+      ORIENT = OR
+
+      END
diff --git a/math/slalib/dcs2c.f b/math/slalib/dcs2c.f
new file mode 100644
index 00000000..59a70b98
--- /dev/null
+++ b/math/slalib/dcs2c.f
@@ -0,0 +1,57 @@
+      SUBROUTINE slDS2C (A, B, V)
+*+
+*     - - - - - -
+*      D S 2 C
+*     - - - - - -
+*
+*  Spherical coordinates to direction cosines (double precision)
+*
+*  Given:
+*     A,B       d      spherical coordinates in radians
+*                         (RA,Dec), (long,lat) etc.
+*
+*  Returned:
+*     V         d(3)   x,y,z unit vector
+*
+*  The spherical coordinates are longitude (+ve anticlockwise looking
+*  from the +ve latitude pole) and latitude.  The Cartesian coordinates
+*  are right handed, with the x axis at zero longitude and latitude, and
+*  the z axis at the +ve latitude pole.
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION A,B,V(3)
+
+      DOUBLE PRECISION COSB
+
+
+      COSB = COS(B)
+
+      V(1) = COS(A)*COSB
+      V(2) = SIN(A)*COSB
+      V(3) = SIN(B)
+
+      END
diff --git a/math/slalib/dd2tf.f b/math/slalib/dd2tf.f
new file mode 100644
index 00000000..e3227631
--- /dev/null
+++ b/math/slalib/dd2tf.f
@@ -0,0 +1,107 @@
+      SUBROUTINE slDDTF (NDP, DAYS, SIGN, IHMSF)
+*+
+*     - - - - - -
+*      D D T F
+*     - - - - - -
+*
+*  Convert an interval in days into hours, minutes, seconds
+*  (double precision)
+*
+*  Given:
+*     NDP      i      number of decimal places of seconds
+*     DAYS     d      interval in days
+*
+*  Returned:
+*     SIGN     c      '+' or '-'
+*     IHMSF    i(4)   hours, minutes, seconds, fraction
+*
+*  Notes:
+*
+*     1)  NDP less than zero is interpreted as zero.
+*
+*     2)  The largest useful value for NDP is determined by the size
+*         of DAYS, the format of DOUBLE PRECISION floating-point numbers
+*         on the target machine, and the risk of overflowing IHMSF(4).
+*         On some architectures, for DAYS up to 1D0, the available
+*         floating-point precision corresponds roughly to NDP=12.
+*         However, the practical limit is NDP=9, set by the capacity of
+*         a typical 32-bit IHMSF(4).
+*
+*     3)  The absolute value of DAYS may exceed 1D0.  In cases where it
+*         does not, it is up to the caller to test for and handle the
+*         case where DAYS is very nearly 1D0 and rounds up to 24 hours,
+*         by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER NDP
+      DOUBLE PRECISION DAYS
+      CHARACTER SIGN*(*)
+      INTEGER IHMSF(4)
+
+*  Days to seconds
+      DOUBLE PRECISION D2S
+      PARAMETER (D2S=86400D0)
+
+      INTEGER NRS,N
+      DOUBLE PRECISION RS,RM,RH,A,AH,AM,AS,AF
+
+
+
+*  Handle sign
+      IF (DAYS.GE.0D0) THEN
+         SIGN='+'
+      ELSE
+         SIGN='-'
+      END IF
+
+*  Field units in terms of least significant figure
+      NRS=1
+      DO N=1,NDP
+         NRS=NRS*10
+      END DO
+      RS=DBLE(NRS)
+      RM=RS*60D0
+      RH=RM*60D0
+
+*  Round interval and express in smallest units required
+      A=ANINT(RS*D2S*ABS(DAYS))
+
+*  Separate into fields
+      AH=AINT(A/RH)
+      A=A-AH*RH
+      AM=AINT(A/RM)
+      A=A-AM*RM
+      AS=AINT(A/RS)
+      AF=A-AS*RS
+
+*  Return results
+      IHMSF(1)=MAX(NINT(AH),0)
+      IHMSF(2)=MAX(MIN(NINT(AM),59),0)
+      IHMSF(3)=MAX(MIN(NINT(AS),59),0)
+      IHMSF(4)=MAX(NINT(MIN(AF,RS-1D0)),0)
+
+      END
diff --git a/math/slalib/de2h.f b/math/slalib/de2h.f
new file mode 100644
index 00000000..9d023e9f
--- /dev/null
+++ b/math/slalib/de2h.f
@@ -0,0 +1,107 @@
+      SUBROUTINE slDE2H (HA, DEC, PHI, AZ, EL)
+*+
+*     - - - - -
+*      D E 2 H
+*     - - - - -
+*
+*  Equatorial to horizon coordinates:  HA,Dec to Az,El
+*
+*  (double precision)
+*
+*  Given:
+*     HA      d     hour angle
+*     DEC     d     declination
+*     PHI     d     observatory latitude
+*
+*  Returned:
+*     AZ      d     azimuth
+*     EL      d     elevation
+*
+*  Notes:
+*
+*  1)  All the arguments are angles in radians.
+*
+*  2)  Azimuth is returned in the range 0-2pi;  north is zero,
+*      and east is +pi/2.  Elevation is returned in the range
+*      +/-pi/2.
+*
+*  3)  The latitude must be geodetic.  In critical applications,
+*      corrections for polar motion should be applied.
+*
+*  4)  In some applications it will be important to specify the
+*      correct type of hour angle and declination in order to
+*      produce the required type of azimuth and elevation.  In
+*      particular, it may be important to distinguish between
+*      elevation as affected by refraction, which would
+*      require the "observed" HA,Dec, and the elevation
+*      in vacuo, which would require the "topocentric" HA,Dec.
+*      If the effects of diurnal aberration can be neglected, the
+*      "apparent" HA,Dec may be used instead of the topocentric
+*      HA,Dec.
+*
+*  5)  No range checking of arguments is carried out.
+*
+*  6)  In applications which involve many such calculations, rather
+*      than calling the present routine it will be more efficient to
+*      use inline code, having previously computed fixed terms such
+*      as sine and cosine of latitude, and (for tracking a star)
+*      sine and cosine of declination.
+*
+*  P.T.Wallace   Starlink   9 July 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION HA,DEC,PHI,AZ,EL
+
+      DOUBLE PRECISION D2PI
+      PARAMETER (D2PI=6.283185307179586476925286766559D0)
+
+      DOUBLE PRECISION SH,CH,SD,CD,SP,CP,X,Y,Z,R,A
+
+
+*  Useful trig functions
+      SH=SIN(HA)
+      CH=COS(HA)
+      SD=SIN(DEC)
+      CD=COS(DEC)
+      SP=SIN(PHI)
+      CP=COS(PHI)
+
+*  Az,El as x,y,z
+      X=-CH*CD*SP+SD*CP
+      Y=-SH*CD
+      Z=CH*CD*CP+SD*SP
+
+*  To spherical
+      R=SQRT(X*X+Y*Y)
+      IF (R.EQ.0D0) THEN
+         A=0D0
+      ELSE
+         A=ATAN2(Y,X)
+      END IF
+      IF (A.LT.0D0) A=A+D2PI
+      AZ=A
+      EL=ATAN2(Z,R)
+
+      END
diff --git a/math/slalib/deuler.f b/math/slalib/deuler.f
new file mode 100644
index 00000000..1ae50acf
--- /dev/null
+++ b/math/slalib/deuler.f
@@ -0,0 +1,181 @@
+      SUBROUTINE slDEUL (ORDER, PHI, THETA, PSI, RMAT)
+*+
+*     - - - - - - -
+*      D E U L
+*     - - - - - - -
+*
+*  Form a rotation matrix from the Euler angles - three successive
+*  rotations about specified Cartesian axes (double precision)
+*
+*  Given:
+*    ORDER   c*(*)   specifies about which axes the rotations occur
+*    PHI     d       1st rotation (radians)
+*    THETA   d       2nd rotation (   "   )
+*    PSI     d       3rd rotation (   "   )
+*
+*  Returned:
+*    RMAT    d(3,3)  rotation matrix
+*
+*  A rotation is positive when the reference frame rotates
+*  anticlockwise as seen looking towards the origin from the
+*  positive region of the specified axis.
+*
+*  The characters of ORDER define which axes the three successive
+*  rotations are about.  A typical value is 'ZXZ', indicating that
+*  RMAT is to become the direction cosine matrix corresponding to
+*  rotations of the reference frame through PHI radians about the
+*  old Z-axis, followed by THETA radians about the resulting X-axis,
+*  then PSI radians about the resulting Z-axis.
+*
+*  The axis names can be any of the following, in any order or
+*  combination:  X, Y, Z, uppercase or lowercase, 1, 2, 3.  Normal
+*  axis labelling/numbering conventions apply;  the xyz (=123)
+*  triad is right-handed.  Thus, the 'ZXZ' example given above
+*  could be written 'zxz' or '313' (or even 'ZxZ' or '3xZ').  ORDER
+*  is terminated by length or by the first unrecognized character.
+*
+*  Fewer than three rotations are acceptable, in which case the later
+*  angle arguments are ignored.  If all rotations are zero, the
+*  identity matrix is produced.
+*
+*  P.T.Wallace   Starlink   23 May 1997
+*
+*  Copyright (C) 1997 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) ORDER
+      DOUBLE PRECISION PHI,THETA,PSI,RMAT(3,3)
+
+      INTEGER J,I,L,N,K
+      DOUBLE PRECISION RESULT(3,3),ROTN(3,3),ANGLE,S,C,W,WM(3,3)
+      CHARACTER AXIS
+
+
+
+*  Initialize result matrix
+      DO J=1,3
+         DO I=1,3
+            IF (I.NE.J) THEN
+               RESULT(I,J) = 0D0
+            ELSE
+               RESULT(I,J) = 1D0
+            END IF
+         END DO
+      END DO
+
+*  Establish length of axis string
+      L = LEN(ORDER)
+
+*  Look at each character of axis string until finished
+      DO N=1,3
+         IF (N.LE.L) THEN
+
+*        Initialize rotation matrix for the current rotation
+            DO J=1,3
+               DO I=1,3
+                  IF (I.NE.J) THEN
+                     ROTN(I,J) = 0D0
+                  ELSE
+                     ROTN(I,J) = 1D0
+                  END IF
+               END DO
+            END DO
+
+*        Pick up the appropriate Euler angle and take sine & cosine
+            IF (N.EQ.1) THEN
+               ANGLE = PHI
+            ELSE IF (N.EQ.2) THEN
+               ANGLE = THETA
+            ELSE
+               ANGLE = PSI
+            END IF
+            S = SIN(ANGLE)
+            C = COS(ANGLE)
+
+*        Identify the axis
+            AXIS = ORDER(N:N)
+            IF (AXIS.EQ.'X'.OR.
+     :          AXIS.EQ.'x'.OR.
+     :          AXIS.EQ.'1') THEN
+
+*           Matrix for x-rotation
+               ROTN(2,2) = C
+               ROTN(2,3) = S
+               ROTN(3,2) = -S
+               ROTN(3,3) = C
+
+            ELSE IF (AXIS.EQ.'Y'.OR.
+     :               AXIS.EQ.'y'.OR.
+     :               AXIS.EQ.'2') THEN
+
+*           Matrix for y-rotation
+               ROTN(1,1) = C
+               ROTN(1,3) = -S
+               ROTN(3,1) = S
+               ROTN(3,3) = C
+
+            ELSE IF (AXIS.EQ.'Z'.OR.
+     :               AXIS.EQ.'z'.OR.
+     :               AXIS.EQ.'3') THEN
+
+*           Matrix for z-rotation
+               ROTN(1,1) = C
+               ROTN(1,2) = S
+               ROTN(2,1) = -S
+               ROTN(2,2) = C
+
+            ELSE
+
+*           Unrecognized character - fake end of string
+               L = 0
+
+            END IF
+
+*        Apply the current rotation (matrix ROTN x matrix RESULT)
+            DO I=1,3
+               DO J=1,3
+                  W = 0D0
+                  DO K=1,3
+                     W = W+ROTN(I,K)*RESULT(K,J)
+                  END DO
+                  WM(I,J) = W
+               END DO
+            END DO
+            DO J=1,3
+               DO I=1,3
+                  RESULT(I,J) = WM(I,J)
+               END DO
+            END DO
+
+         END IF
+
+      END DO
+
+*  Copy the result
+      DO J=1,3
+         DO I=1,3
+            RMAT(I,J) = RESULT(I,J)
+         END DO
+      END DO
+
+      END
diff --git a/math/slalib/dfltin.f b/math/slalib/dfltin.f
new file mode 100644
index 00000000..7d514f39
--- /dev/null
+++ b/math/slalib/dfltin.f
@@ -0,0 +1,298 @@
+      SUBROUTINE slDFLI (STRING, NSTRT, DRESLT, JFLAG)
+*+
+*     - - - - - - -
+*      D F L I
+*     - - - - - - -
+*
+*  Convert free-format input into double precision floating point
+*
+*  Given:
+*     STRING     c     string containing number to be decoded
+*     NSTRT      i     pointer to where decoding is to start
+*     DRESLT     d     current value of result
+*
+*  Returned:
+*     NSTRT      i      advanced to next number
+*     DRESLT     d      result
+*     JFLAG      i      status: -1 = -OK, 0 = +OK, 1 = null, 2 = error
+*
+*  Notes:
+*
+*     1     The reason DFLTIN has separate OK status values for +
+*           and - is to enable minus zero to be detected.   This is
+*           of crucial importance when decoding mixed-radix numbers.
+*           For example, an angle expressed as deg, arcmin, arcsec
+*           may have a leading minus sign but a zero degrees field.
+*
+*     2     A TAB is interpreted as a space, and lowercase characters
+*           are interpreted as uppercase.
+*
+*     3     The basic format is the sequence of fields #^.^@#^, where
+*           # is a sign character + or -, ^ means a string of decimal
+*           digits, and @, which indicates an exponent, means D or E.
+*           Various combinations of these fields can be omitted, and
+*           embedded blanks are permissible in certain places.
+*
+*     4     Spaces:
+*
+*             .  Leading spaces are ignored.
+*
+*             .  Embedded spaces are allowed only after +, -, D or E,
+*                and after the decomal point if the first sequence of
+*                digits is absent.
+*
+*             .  Trailing spaces are ignored;  the first signifies
+*                end of decoding and subsequent ones are skipped.
+*
+*     5     Delimiters:
+*
+*             .  Any character other than +,-,0-9,.,D,E or space may be
+*                used to signal the end of the number and terminate
+*                decoding.
+*
+*             .  Comma is recognized by DFLTIN as a special case;  it
+*                is skipped, leaving the pointer on the next character.
+*                See 13, below.
+*
+*     6     Both signs are optional.  The default is +.
+*
+*     7     The mantissa ^.^ defaults to 1.
+*
+*     8     The exponent @#^ defaults to D0.
+*
+*     9     The strings of decimal digits may be of any length.
+*
+*     10    The decimal point is optional for whole numbers.
+*
+*     11    A "null result" occurs when the string of characters being
+*           decoded does not begin with +,-,0-9,.,D or E, or consists
+*           entirely of spaces.  When this condition is detected, JFLAG
+*           is set to 1 and DRESLT is left untouched.
+*
+*     12    NSTRT = 1 for the first character in the string.
+*
+*     13    On return from DFLTIN, NSTRT is set ready for the next
+*           decode - following trailing blanks and any comma.  If a
+*           delimiter other than comma is being used, NSTRT must be
+*           incremented before the next call to DFLTIN, otherwise
+*           all subsequent calls will return a null result.
+*
+*     14    Errors (JFLAG=2) occur when:
+*
+*             .  a +, -, D or E is left unsatisfied;  or
+*
+*             .  the decimal point is present without at least
+*                one decimal digit before or after it;  or
+*
+*             .  an exponent more than 100 has been presented.
+*
+*     15    When an error has been detected, NSTRT is left
+*           pointing to the character following the last
+*           one used before the error came to light.  This
+*           may be after the point at which a more sophisticated
+*           program could have detected the error.  For example,
+*           DFLTIN does not detect that '1D999' is unacceptable
+*           (on a computer where this is so) until the entire number
+*           has been decoded.
+*
+*     16    Certain highly unlikely combinations of mantissa &
+*           exponent can cause arithmetic faults during the
+*           decode, in some cases despite the fact that they
+*           together could be construed as a valid number.
+*
+*     17    Decoding is left to right, one pass.
+*
+*     18    See also FLOTIN and INTIN
+*
+*  Called:  slICHF
+*
+*  P.T.Wallace   Starlink   18 March 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) STRING
+      INTEGER NSTRT
+      DOUBLE PRECISION DRESLT
+      INTEGER JFLAG
+
+      INTEGER NPTR,MSIGN,NEXP,NDP,NVEC,NDIGIT,ISIGNX,J
+      DOUBLE PRECISION DMANT,DIGIT
+
+
+
+*  Current character
+      NPTR=NSTRT
+
+*  Set defaults: mantissa & sign, exponent & sign, decimal place count
+      DMANT=0D0
+      MSIGN=1
+      NEXP=0
+      ISIGNX=1
+      NDP=0
+
+*  Look for sign
+ 100  CONTINUE
+      CALL slICHF(STRING,NPTR,NVEC,NDIGIT,DIGIT)
+      GO TO ( 400,  100,  800,  500,  300,  200, 9110, 9100, 9110),NVEC
+*             0-9    SP   D/E    .     +     -     ,   ELSE   END
+
+*  Negative
+ 200  CONTINUE
+      MSIGN=-1
+
+*  Look for first leading decimal
+ 300  CONTINUE
+      CALL slICHF(STRING,NPTR,NVEC,NDIGIT,DIGIT)
+      GO TO ( 400, 300,  800,  500, 9200, 9200, 9200, 9200, 9210),NVEC
+*             0-9   SP   D/E    .     +     -     ,   ELSE   END
+
+*  Accept leading decimals
+ 400  CONTINUE
+      DMANT=DMANT*1D1+DIGIT
+      CALL slICHF(STRING,NPTR,NVEC,NDIGIT,DIGIT)
+      GO TO ( 400, 1310,  900,  600, 1300, 1300, 1300, 1300, 1310),NVEC
+*             0-9   SP    D/E    .     +     -     ,   ELSE   END
+
+*  Look for decimal when none preceded the point
+ 500  CONTINUE
+      CALL slICHF(STRING,NPTR,NVEC,NDIGIT,DIGIT)
+      GO TO ( 700, 500, 9200, 9200, 9200, 9200, 9200, 9200, 9210),NVEC
+*             0-9   SP   D/E    .     +     -     ,   ELSE   END
+
+*  Look for trailing decimals
+ 600  CONTINUE
+      CALL slICHF(STRING,NPTR,NVEC,NDIGIT,DIGIT)
+      GO TO ( 700, 1310,  900, 1300, 1300, 1300, 1300, 1300, 1310),NVEC
+*             0-9   SP    D/E    .     +     -     ,   ELSE   END
+
+*  Accept trailing decimals
+ 700  CONTINUE
+      NDP=NDP+1
+      DMANT=DMANT*1D1+DIGIT
+      GO TO 600
+
+*  Exponent symbol first in field: default mantissa to 1
+ 800  CONTINUE
+      DMANT=1D0
+
+*  Look for sign of exponent
+ 900  CONTINUE
+      CALL slICHF(STRING,NPTR,NVEC,NDIGIT,DIGIT)
+      GO TO (1200, 900, 9200, 9200, 1100, 1000, 9200, 9200, 9210),NVEC
+*             0-9   SP   D/E    .     +     -     ,   ELSE   END
+
+*  Exponent negative
+ 1000 CONTINUE
+      ISIGNX=-1
+
+*  Look for first digit of exponent
+ 1100 CONTINUE
+      CALL slICHF(STRING,NPTR,NVEC,NDIGIT,DIGIT)
+      GO TO (1200, 1100, 9200, 9200, 9200, 9200, 9200, 9200, 9210),NVEC
+*             0-9   SP    D/E    .     +     -     ,   ELSE   END
+
+*  Use exponent digit
+ 1200 CONTINUE
+      NEXP=NEXP*10+NDIGIT
+      IF (NEXP.GT.100) GO TO 9200
+
+*  Look for subsequent digits of exponent
+      CALL slICHF(STRING,NPTR,NVEC,NDIGIT,DIGIT)
+      GO TO (1200, 1310, 1300, 1300, 1300, 1300, 1300, 1300, 1310),NVEC
+*             0-9   SP    D/E    .     +     -     ,   ELSE   END
+
+*  Combine exponent and decimal place count
+ 1300 CONTINUE
+      NPTR=NPTR-1
+ 1310 CONTINUE
+      NEXP=NEXP*ISIGNX-NDP
+
+*  Skip if net exponent negative
+      IF (NEXP.LT.0) GO TO 1500
+
+*  Positive exponent: scale up
+ 1400 CONTINUE
+      IF (NEXP.LT.10) GO TO 1410
+      DMANT=DMANT*1D10
+      NEXP=NEXP-10
+      GO TO 1400
+ 1410 CONTINUE
+      IF (NEXP.LT.1) GO TO 1600
+      DMANT=DMANT*1D1
+      NEXP=NEXP-1
+      GO TO 1410
+
+*  Negative exponent: scale down
+ 1500 CONTINUE
+      IF (NEXP.GT.-10) GO TO 1510
+      DMANT=DMANT/1D10
+      NEXP=NEXP+10
+      GO TO 1500
+ 1510 CONTINUE
+      IF (NEXP.GT.-1) GO TO 1600
+      DMANT=DMANT/1D1
+      NEXP=NEXP+1
+      GO TO 1510
+
+*  Get result & status
+ 1600 CONTINUE
+      J=0
+      IF (MSIGN.EQ.1) GO TO 1610
+      J=-1
+      DMANT=-DMANT
+ 1610 CONTINUE
+      DRESLT=DMANT
+
+*  Skip to end of field
+ 1620 CONTINUE
+      CALL slICHF(STRING,NPTR,NVEC,NDIGIT,DIGIT)
+      GO TO (1720, 1620, 1720, 1720, 1720, 1720, 9900, 1720, 9900),NVEC
+*             0-9   SP    D/E    .     +     -     ,   ELSE   END
+
+ 1720 CONTINUE
+      NPTR=NPTR-1
+      GO TO 9900
+
+
+*  Exits
+
+*  Null field
+ 9100 CONTINUE
+      NPTR=NPTR-1
+ 9110 CONTINUE
+      J=1
+      GO TO 9900
+
+*  Errors
+ 9200 CONTINUE
+      NPTR=NPTR-1
+ 9210 CONTINUE
+      J=2
+
+*  Return
+ 9900 CONTINUE
+      NSTRT=NPTR
+      JFLAG=J
+
+      END
diff --git a/math/slalib/dh2e.f b/math/slalib/dh2e.f
new file mode 100644
index 00000000..0ef9946c
--- /dev/null
+++ b/math/slalib/dh2e.f
@@ -0,0 +1,101 @@
+      SUBROUTINE slDH2E (AZ, EL, PHI, HA, DEC)
+*+
+*     - - - - -
+*      D E 2 H
+*     - - - - -
+*
+*  Horizon to equatorial coordinates:  Az,El to HA,Dec
+*
+*  (double precision)
+*
+*  Given:
+*     AZ      d     azimuth
+*     EL      d     elevation
+*     PHI     d     observatory latitude
+*
+*  Returned:
+*     HA      d     hour angle
+*     DEC     d     declination
+*
+*  Notes:
+*
+*  1)  All the arguments are angles in radians.
+*
+*  2)  The sign convention for azimuth is north zero, east +pi/2.
+*
+*  3)  HA is returned in the range +/-pi.  Declination is returned
+*      in the range +/-pi/2.
+*
+*  4)  The latitude is (in principle) geodetic.  In critical
+*      applications, corrections for polar motion should be applied.
+*
+*  5)  In some applications it will be important to specify the
+*      correct type of elevation in order to produce the required
+*      type of HA,Dec.  In particular, it may be important to
+*      distinguish between the elevation as affected by refraction,
+*      which will yield the "observed" HA,Dec, and the elevation
+*      in vacuo, which will yield the "topocentric" HA,Dec.  If the
+*      effects of diurnal aberration can be neglected, the
+*      topocentric HA,Dec may be used as an approximation to the
+*      "apparent" HA,Dec.
+*
+*  6)  No range checking of arguments is done.
+*
+*  7)  In applications which involve many such calculations, rather
+*      than calling the present routine it will be more efficient to
+*      use inline code, having previously computed fixed terms such
+*      as sine and cosine of latitude.
+*
+*  P.T.Wallace   Starlink   21 February 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION AZ,EL,PHI,HA,DEC
+
+      DOUBLE PRECISION SA,CA,SE,CE,SP,CP,X,Y,Z,R
+
+
+*  Useful trig functions
+      SA=SIN(AZ)
+      CA=COS(AZ)
+      SE=SIN(EL)
+      CE=COS(EL)
+      SP=SIN(PHI)
+      CP=COS(PHI)
+
+*  HA,Dec as x,y,z
+      X=-CA*CE*SP+SE*CP
+      Y=-SA*CE
+      Z=CA*CE*CP+SE*SP
+
+*  To HA,Dec
+      R=SQRT(X*X+Y*Y)
+      IF (R.EQ.0D0) THEN
+         HA=0D0
+      ELSE
+         HA=ATAN2(Y,X)
+      END IF
+      DEC=ATAN2(Z,R)
+
+      END
diff --git a/math/slalib/dimxv.f b/math/slalib/dimxv.f
new file mode 100644
index 00000000..3eec08e4
--- /dev/null
+++ b/math/slalib/dimxv.f
@@ -0,0 +1,69 @@
+      SUBROUTINE slDIMV (DM, VA, VB)
+*+
+*     - - - - - -
+*      D I M V
+*     - - - - - -
+*
+*  Performs the 3-D backward unitary transformation:
+*
+*     vector VB = (inverse of matrix DM) * vector VA
+*
+*  (double precision)
+*
+*  (n.b.  the matrix must be unitary, as this routine assumes that
+*   the inverse and transpose are identical)
+*
+*  Given:
+*     DM       dp(3,3)    matrix
+*     VA       dp(3)      vector
+*
+*  Returned:
+*     VB       dp(3)      result vector
+*
+*  P.T.Wallace   Starlink   March 1986
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DM(3,3),VA(3),VB(3)
+
+      INTEGER I,J
+      DOUBLE PRECISION W,VW(3)
+
+
+
+*  Inverse of matrix DM * vector VA -> vector VW
+      DO J=1,3
+         W=0D0
+         DO I=1,3
+            W=W+DM(I,J)*VA(I)
+         END DO
+         VW(J)=W
+      END DO
+
+*  Vector VW -> vector VB
+      DO J=1,3
+         VB(J)=VW(J)
+      END DO
+
+      END
diff --git a/math/slalib/djcal.f b/math/slalib/djcal.f
new file mode 100644
index 00000000..31766d18
--- /dev/null
+++ b/math/slalib/djcal.f
@@ -0,0 +1,93 @@
+      SUBROUTINE slDJCA (NDP, DJM, IYMDF, J)
+*+
+*     - - - - - -
+*      D J C A
+*     - - - - - -
+*
+*  Modified Julian Date to Gregorian Calendar, expressed
+*  in a form convenient for formatting messages (namely
+*  rounded to a specified precision, and with the fields
+*  stored in a single array)
+*
+*  Given:
+*     NDP      i      number of decimal places of days in fraction
+*     DJM      d      modified Julian Date (JD-2400000.5)
+*
+*  Returned:
+*     IYMDF    i(4)   year, month, day, fraction in Gregorian
+*                     calendar
+*     J        i      status:  nonzero = out of range
+*
+*  Any date after 4701BC March 1 is accepted.
+*
+*  NDP should be 4 or less if internal overflows are to be avoided
+*  on machines which use 32-bit integers.
+*
+*  The algorithm is adapted from Hatcher 1984 (QJRAS 25, 53-55).
+*
+*  Last revision:   22 July 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER NDP
+      DOUBLE PRECISION DJM
+      INTEGER IYMDF(4),J
+
+      INTEGER NFD
+      DOUBLE PRECISION FD,DF,F,D
+      INTEGER JD,N4,ND10
+
+
+*  Validate.
+      IF ( DJM.LE.-2395520D0 .OR. DJM.GE.1D9 ) THEN
+         J = -1
+      ELSE
+         J = 0
+
+*     Denominator of fraction.
+         NFD = 10**MAX(NDP,0)
+         FD = DBLE(NFD)
+
+*     Round date and express in units of fraction.
+         DF = ANINT(DJM*FD)
+
+*     Separate day and fraction.
+         F = MOD(DF,FD)
+         IF (F.LT.0D0) F = F+FD
+         D = (DF-F)/FD
+
+*     Express day in Gregorian calendar.
+         JD = NINT(D)+2400001
+
+         N4 = 4*(JD+((2*((4*JD-17918)/146097)*3)/4+1)/2-37)
+         ND10 = 10*(MOD(N4-237,1461)/4)+5
+
+         IYMDF(1) = N4/1461-4712
+         IYMDF(2) = MOD(ND10/306+2,12)+1
+         IYMDF(3) = MOD(ND10,306)/10+1
+         IYMDF(4) = NINT(F)
+
+      END IF
+
+      END
diff --git a/math/slalib/djcl.f b/math/slalib/djcl.f
new file mode 100644
index 00000000..7164ea37
--- /dev/null
+++ b/math/slalib/djcl.f
@@ -0,0 +1,84 @@
+      SUBROUTINE slDJCL (DJM, IY, IM, ID, FD, J)
+*+
+*     - - - - -
+*      D J C L
+*     - - - - -
+*
+*  Modified Julian Date to Gregorian year, month, day,
+*  and fraction of a day.
+*
+*  Given:
+*     DJM      dp     modified Julian Date (JD-2400000.5)
+*
+*  Returned:
+*     IY       int    year
+*     IM       int    month
+*     ID       int    day
+*     FD       dp     fraction of day
+*     J        int    status:
+*                       0 = OK
+*                      -1 = unacceptable date (before 4701BC March 1)
+*
+*  The algorithm is adapted from Hatcher 1984 (QJRAS 25, 53-55).
+*
+*  Last revision:   22 July 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DJM
+      INTEGER IY,IM,ID
+      DOUBLE PRECISION FD
+      INTEGER J
+
+      DOUBLE PRECISION F,D
+      INTEGER JD,N4,ND10
+
+
+*  Check if date is acceptable.
+      IF ( DJM.LE.-2395520D0 .OR. DJM.GE.1D9 ) THEN
+         J = -1
+      ELSE
+         J = 0
+
+*     Separate day and fraction.
+         F = MOD(DJM,1D0)
+         IF (F.LT.0D0) F = F+1D0
+         D = ANINT(DJM-F)
+
+*     Express day in Gregorian calendar.
+         JD = NINT(D)+2400001
+
+         N4 = 4*(JD+((6*((4*JD-17918)/146097))/4+1)/2-37)
+         ND10 = 10*(MOD(N4-237,1461)/4)+5
+
+         IY = N4/1461-4712
+         IM = MOD(ND10/306+2,12)+1
+         ID = MOD(ND10,306)/10+1
+         FD = F
+
+         J=0
+
+      END IF
+
+      END
diff --git a/math/slalib/dm2av.f b/math/slalib/dm2av.f
new file mode 100644
index 00000000..5cabe620
--- /dev/null
+++ b/math/slalib/dm2av.f
@@ -0,0 +1,75 @@
+      SUBROUTINE slDMAV (RMAT, AXVEC)
+*+
+*     - - - - - -
+*      D M A V
+*     - - - - - -
+*
+*  From a rotation matrix, determine the corresponding axial vector.
+*  (double precision)
+*
+*  A rotation matrix describes a rotation about some arbitrary axis,
+*  called the Euler axis.  The "axial vector" returned by this routine
+*  has the same direction as the Euler axis, and its magnitude is the
+*  amount of rotation in radians.  (The magnitude and direction can be
+*  separated by means of the routine slDVN.)
+*
+*  Given:
+*    RMAT   d(3,3)   rotation matrix
+*
+*  Returned:
+*    AXVEC  d(3)     axial vector (radians)
+*
+*  The reference frame rotates clockwise as seen looking along
+*  the axial vector from the origin.
+*
+*  If RMAT is null, so is the result.
+*
+*  Last revision:   26 November 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RMAT(3,3),AXVEC(3)
+
+      DOUBLE PRECISION X,Y,Z,S2,C2,PHI,F
+
+
+
+      X = RMAT(2,3)-RMAT(3,2)
+      Y = RMAT(3,1)-RMAT(1,3)
+      Z = RMAT(1,2)-RMAT(2,1)
+      S2 = SQRT(X*X+Y*Y+Z*Z)
+      IF (S2.NE.0D0) THEN
+         C2 = RMAT(1,1)+RMAT(2,2)+RMAT(3,3)-1D0
+         PHI = ATAN2(S2,C2)
+         F = PHI/S2
+         AXVEC(1) = X*F
+         AXVEC(2) = Y*F
+         AXVEC(3) = Z*F
+      ELSE
+         AXVEC(1) = 0D0
+         AXVEC(2) = 0D0
+         AXVEC(3) = 0D0
+      END IF
+
+      END
diff --git a/math/slalib/dmat.f b/math/slalib/dmat.f
new file mode 100644
index 00000000..9209b062
--- /dev/null
+++ b/math/slalib/dmat.f
@@ -0,0 +1,158 @@
+      SUBROUTINE slDMAT (N, A, Y, D, JF, IW)
+*+
+*     - - - - -
+*      D M A T
+*     - - - - -
+*
+*  Matrix inversion & solution of simultaneous equations
+*  (double precision)
+*
+*  For the set of n simultaneous equations in n unknowns:
+*     A.Y = X
+*
+*  where:
+*     A is a non-singular N x N matrix
+*     Y is the vector of N unknowns
+*     X is the known vector
+*
+*  DMATRX computes:
+*     the inverse of matrix A
+*     the determinant of matrix A
+*     the vector of N unknowns
+*
+*  Arguments:
+*
+*     symbol  type   dimension           before              after
+*
+*       N      i                    no. of unknowns       unchanged
+*       A      d      (N,N)             matrix             inverse
+*       Y      d       (N)            known vector      solution vector
+*       D      d                           -             determinant
+*     * JF     i                           -           singularity flag
+*       IW     i       (N)                 -              workspace
+*
+*  * JF is the singularity flag.  If the matrix is non-singular, JF=0
+*    is returned.  If the matrix is singular, JF=-1 & D=0D0 are
+*    returned.  In the latter case, the contents of array A on return
+*    are undefined.
+*
+*  Algorithm:
+*     Gaussian elimination with partial pivoting.
+*
+*  Speed:
+*     Very fast.
+*
+*  Accuracy:
+*     Fairly accurate - errors 1 to 4 times those of routines optimized
+*     for accuracy.
+*
+*  P.T.Wallace   Starlink   4 December 2001
+*
+*  Copyright (C) 2001 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER N
+      DOUBLE PRECISION A(N,N),Y(N),D
+      INTEGER JF
+      INTEGER IW(N)
+
+      DOUBLE PRECISION SFA
+      PARAMETER (SFA=1D-20)
+
+      INTEGER K,IMX,I,J,NP1MK,KI
+      DOUBLE PRECISION AMX,T,AKK,YK,AIK
+
+
+      JF=0
+      D=1D0
+      DO K=1,N
+         AMX=DABS(A(K,K))
+         IMX=K
+         IF (K.NE.N) THEN
+            DO I=K+1,N
+               T=DABS(A(I,K))
+               IF (T.GT.AMX) THEN
+                  AMX=T
+                  IMX=I
+               END IF
+            END DO
+         END IF
+         IF (AMX.LT.SFA) THEN
+            JF=-1
+         ELSE
+            IF (IMX.NE.K) THEN
+               DO J=1,N
+                  T=A(K,J)
+                  A(K,J)=A(IMX,J)
+                  A(IMX,J)=T
+               END DO
+               T=Y(K)
+               Y(K)=Y(IMX)
+               Y(IMX)=T
+               D=-D
+            END IF
+            IW(K)=IMX
+            AKK=A(K,K)
+            D=D*AKK
+            IF (DABS(D).LT.SFA) THEN
+               JF=-1
+            ELSE
+               AKK=1D0/AKK
+               A(K,K)=AKK
+               DO J=1,N
+                  IF (J.NE.K) A(K,J)=A(K,J)*AKK
+               END DO
+               YK=Y(K)*AKK
+               Y(K)=YK
+               DO I=1,N
+                  AIK=A(I,K)
+                  IF (I.NE.K) THEN
+                     DO J=1,N
+                        IF (J.NE.K) A(I,J)=A(I,J)-AIK*A(K,J)
+                     END DO
+                     Y(I)=Y(I)-AIK*YK
+                  END IF
+               END DO
+               DO I=1,N
+                  IF (I.NE.K) A(I,K)=-A(I,K)*AKK
+               END DO
+            END IF
+         END IF
+      END DO
+      IF (JF.NE.0) THEN
+         D=0D0
+      ELSE
+         DO K=1,N
+            NP1MK=N+1-K
+            KI=IW(NP1MK)
+            IF (NP1MK.NE.KI) THEN
+               DO I=1,N
+                  T=A(I,NP1MK)
+                  A(I,NP1MK)=A(I,KI)
+                  A(I,KI)=T
+               END DO
+            END IF
+         END DO
+      END IF
+
+      END
diff --git a/math/slalib/dmoon.f b/math/slalib/dmoon.f
new file mode 100644
index 00000000..f16aadf1
--- /dev/null
+++ b/math/slalib/dmoon.f
@@ -0,0 +1,659 @@
+      SUBROUTINE slDMON (DATE, PV)
+*+
+*     - - - - - -
+*      D M O N
+*     - - - - - -
+*
+*  Approximate geocentric position and velocity of the Moon
+*  (double precision)
+*
+*  Given:
+*     DATE       D       TDB (loosely ET) as a Modified Julian Date
+*                                                    (JD-2400000.5)
+*
+*  Returned:
+*     PV         D(6)    Moon x,y,z,xdot,ydot,zdot, mean equator and
+*                                         equinox of date (AU, AU/s)
+*
+*  Notes:
+*
+*  1  This routine is a full implementation of the algorithm
+*     published by Meeus (see reference).
+*
+*  2  Meeus quotes accuracies of 10 arcsec in longitude, 3 arcsec in
+*     latitude and 0.2 arcsec in HP (equivalent to about 20 km in
+*     distance).  Comparison with JPL DE200 over the interval
+*     1960-2025 gives RMS errors of 3.7 arcsec and 83 mas/hour in
+*     longitude, 2.3 arcsec and 48 mas/hour in latitude, 11 km
+*     and 81 mm/s in distance.  The maximum errors over the same
+*     interval are 18 arcsec and 0.50 arcsec/hour in longitude,
+*     11 arcsec and 0.24 arcsec/hour in latitude, 40 km and 0.29 m/s
+*     in distance.
+*
+*  3  The original algorithm is expressed in terms of the obsolete
+*     timescale Ephemeris Time.  Either TDB or TT can be used, but
+*     not UT without incurring significant errors (30 arcsec at
+*     the present time) due to the Moon's 0.5 arcsec/sec movement.
+*
+*  4  The algorithm is based on pre IAU 1976 standards.  However,
+*     the result has been moved onto the new (FK5) equinox, an
+*     adjustment which is in any case much smaller than the
+*     intrinsic accuracy of the procedure.
+*
+*  5  Velocity is obtained by a complete analytical differentiation
+*     of the Meeus model.
+*
+*  Reference:
+*     Meeus, l'Astronomie, June 1984, p348.
+*
+*  P.T.Wallace   Starlink   22 January 1998
+*
+*  Copyright (C) 1998 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,PV(6)
+
+*  Degrees, arcseconds and seconds of time to radians
+      DOUBLE PRECISION D2R,DAS2R,DS2R
+      PARAMETER (D2R=0.0174532925199432957692369D0,
+     :           DAS2R=4.848136811095359935899141D-6,
+     :           DS2R=7.272205216643039903848712D-5)
+
+*  Seconds per Julian century (86400*36525)
+      DOUBLE PRECISION CJ
+      PARAMETER (CJ=3155760000D0)
+
+*  Julian epoch of B1950
+      DOUBLE PRECISION B1950
+      PARAMETER (B1950=1949.9997904423D0)
+
+*  Earth equatorial radius in AU ( = 6378.137 / 149597870 )
+      DOUBLE PRECISION ERADAU
+      PARAMETER (ERADAU=4.2635212653763D-5)
+
+      DOUBLE PRECISION T,THETA,SINOM,COSOM,DOMCOM,WA,DWA,WB,DWB,WOM,
+     :                 DWOM,SINWOM,COSWOM,V,DV,COEFF,EMN,EMPN,DN,FN,EN,
+     :                 DEN,DTHETA,FTHETA,EL,DEL,B,DB,BF,DBF,P,DP,SP,R,
+     :                 DR,X,Y,Z,XD,YD,ZD,SEL,CEL,SB,CB,RCB,RBD,W,EPJ,
+     :                 EQCOR,EPS,SINEPS,COSEPS,ES,EC
+      INTEGER N,I
+
+*
+*  Coefficients for fundamental arguments
+*
+*   at J1900:  T**0, T**1, T**2, T**3
+*   at epoch:  T**0, T**1
+*
+*  Units are degrees for position and Julian centuries for time
+*
+
+*  Moon's mean longitude
+      DOUBLE PRECISION ELP0,ELP1,ELP2,ELP3,ELP,DELP
+      PARAMETER (ELP0=270.434164D0,
+     :           ELP1=481267.8831D0,
+     :           ELP2=-0.001133D0,
+     :           ELP3=0.0000019D0)
+
+*  Sun's mean anomaly
+      DOUBLE PRECISION EM0,EM1,EM2,EM3,EM,DEM
+      PARAMETER (EM0=358.475833D0,
+     :           EM1=35999.0498D0,
+     :           EM2=-0.000150D0,
+     :           EM3=-0.0000033D0)
+
+*  Moon's mean anomaly
+      DOUBLE PRECISION EMP0,EMP1,EMP2,EMP3,EMP,DEMP
+      PARAMETER (EMP0=296.104608D0,
+     :           EMP1=477198.8491D0,
+     :           EMP2=0.009192D0,
+     :           EMP3=0.0000144D0)
+
+*  Moon's mean elongation
+      DOUBLE PRECISION D0,D1,D2,D3,D,DD
+      PARAMETER (D0=350.737486D0,
+     :           D1=445267.1142D0,
+     :           D2=-0.001436D0,
+     :           D3=0.0000019D0)
+
+*  Mean distance of the Moon from its ascending node
+      DOUBLE PRECISION F0,F1,F2,F3,F,DF
+      PARAMETER (F0=11.250889D0,
+     :           F1=483202.0251D0,
+     :           F2=-0.003211D0,
+     :           F3=-0.0000003D0)
+
+*  Longitude of the Moon's ascending node
+      DOUBLE PRECISION OM0,OM1,OM2,OM3,OM,DOM
+      PARAMETER (OM0=259.183275D0,
+     :           OM1=-1934.1420D0,
+     :           OM2=0.002078D0,
+     :           OM3=0.0000022D0)
+
+*  Coefficients for (dimensionless) E factor
+      DOUBLE PRECISION E1,E2,E,DE,ESQ,DESQ
+      PARAMETER (E1=-0.002495D0,E2=-0.00000752D0)
+
+*  Coefficients for periodic variations etc
+      DOUBLE PRECISION PAC,PA0,PA1
+      PARAMETER (PAC=0.000233D0,PA0=51.2D0,PA1=20.2D0)
+      DOUBLE PRECISION PBC
+      PARAMETER (PBC=-0.001778D0)
+      DOUBLE PRECISION PCC
+      PARAMETER (PCC=0.000817D0)
+      DOUBLE PRECISION PDC
+      PARAMETER (PDC=0.002011D0)
+      DOUBLE PRECISION PEC,PE0,PE1,PE2
+      PARAMETER (PEC=0.003964D0,
+     :                     PE0=346.560D0,PE1=132.870D0,PE2=-0.0091731D0)
+      DOUBLE PRECISION PFC
+      PARAMETER (PFC=0.001964D0)
+      DOUBLE PRECISION PGC
+      PARAMETER (PGC=0.002541D0)
+      DOUBLE PRECISION PHC
+      PARAMETER (PHC=0.001964D0)
+      DOUBLE PRECISION PIC
+      PARAMETER (PIC=-0.024691D0)
+      DOUBLE PRECISION PJC,PJ0,PJ1
+      PARAMETER (PJC=-0.004328D0,PJ0=275.05D0,PJ1=-2.30D0)
+      DOUBLE PRECISION CW1
+      PARAMETER (CW1=0.0004664D0)
+      DOUBLE PRECISION CW2
+      PARAMETER (CW2=0.0000754D0)
+
+*
+*  Coefficients for Moon position
+*
+*   Tx(N)       = coefficient of L, B or P term (deg)
+*   ITx(N,1-5)  = coefficients of M, M', D, F, E**n in argument
+*
+      INTEGER NL,NB,NP
+      PARAMETER (NL=50,NB=45,NP=31)
+      DOUBLE PRECISION TL(NL),TB(NB),TP(NP)
+      INTEGER ITL(5,NL),ITB(5,NB),ITP(5,NP)
+*
+*  Longitude
+*                                         M   M'  D   F   n
+      DATA TL( 1)/            +6.288750D0                     /,
+     :     (ITL(I, 1),I=1,5)/            +0, +1, +0, +0,  0   /
+      DATA TL( 2)/            +1.274018D0                     /,
+     :     (ITL(I, 2),I=1,5)/            +0, -1, +2, +0,  0   /
+      DATA TL( 3)/            +0.658309D0                     /,
+     :     (ITL(I, 3),I=1,5)/            +0, +0, +2, +0,  0   /
+      DATA TL( 4)/            +0.213616D0                     /,
+     :     (ITL(I, 4),I=1,5)/            +0, +2, +0, +0,  0   /
+      DATA TL( 5)/            -0.185596D0                     /,
+     :     (ITL(I, 5),I=1,5)/            +1, +0, +0, +0,  1   /
+      DATA TL( 6)/            -0.114336D0                     /,
+     :     (ITL(I, 6),I=1,5)/            +0, +0, +0, +2,  0   /
+      DATA TL( 7)/            +0.058793D0                     /,
+     :     (ITL(I, 7),I=1,5)/            +0, -2, +2, +0,  0   /
+      DATA TL( 8)/            +0.057212D0                     /,
+     :     (ITL(I, 8),I=1,5)/            -1, -1, +2, +0,  1   /
+      DATA TL( 9)/            +0.053320D0                     /,
+     :     (ITL(I, 9),I=1,5)/            +0, +1, +2, +0,  0   /
+      DATA TL(10)/            +0.045874D0                     /,
+     :     (ITL(I,10),I=1,5)/            -1, +0, +2, +0,  1   /
+      DATA TL(11)/            +0.041024D0                     /,
+     :     (ITL(I,11),I=1,5)/            -1, +1, +0, +0,  1   /
+      DATA TL(12)/            -0.034718D0                     /,
+     :     (ITL(I,12),I=1,5)/            +0, +0, +1, +0,  0   /
+      DATA TL(13)/            -0.030465D0                     /,
+     :     (ITL(I,13),I=1,5)/            +1, +1, +0, +0,  1   /
+      DATA TL(14)/            +0.015326D0                     /,
+     :     (ITL(I,14),I=1,5)/            +0, +0, +2, -2,  0   /
+      DATA TL(15)/            -0.012528D0                     /,
+     :     (ITL(I,15),I=1,5)/            +0, +1, +0, +2,  0   /
+      DATA TL(16)/            -0.010980D0                     /,
+     :     (ITL(I,16),I=1,5)/            +0, -1, +0, +2,  0   /
+      DATA TL(17)/            +0.010674D0                     /,
+     :     (ITL(I,17),I=1,5)/            +0, -1, +4, +0,  0   /
+      DATA TL(18)/            +0.010034D0                     /,
+     :     (ITL(I,18),I=1,5)/            +0, +3, +0, +0,  0   /
+      DATA TL(19)/            +0.008548D0                     /,
+     :     (ITL(I,19),I=1,5)/            +0, -2, +4, +0,  0   /
+      DATA TL(20)/            -0.007910D0                     /,
+     :     (ITL(I,20),I=1,5)/            +1, -1, +2, +0,  1   /
+      DATA TL(21)/            -0.006783D0                     /,
+     :     (ITL(I,21),I=1,5)/            +1, +0, +2, +0,  1   /
+      DATA TL(22)/            +0.005162D0                     /,
+     :     (ITL(I,22),I=1,5)/            +0, +1, -1, +0,  0   /
+      DATA TL(23)/            +0.005000D0                     /,
+     :     (ITL(I,23),I=1,5)/            +1, +0, +1, +0,  1   /
+      DATA TL(24)/            +0.004049D0                     /,
+     :     (ITL(I,24),I=1,5)/            -1, +1, +2, +0,  1   /
+      DATA TL(25)/            +0.003996D0                     /,
+     :     (ITL(I,25),I=1,5)/            +0, +2, +2, +0,  0   /
+      DATA TL(26)/            +0.003862D0                     /,
+     :     (ITL(I,26),I=1,5)/            +0, +0, +4, +0,  0   /
+      DATA TL(27)/            +0.003665D0                     /,
+     :     (ITL(I,27),I=1,5)/            +0, -3, +2, +0,  0   /
+      DATA TL(28)/            +0.002695D0                     /,
+     :     (ITL(I,28),I=1,5)/            -1, +2, +0, +0,  1   /
+      DATA TL(29)/            +0.002602D0                     /,
+     :     (ITL(I,29),I=1,5)/            +0, +1, -2, -2,  0   /
+      DATA TL(30)/            +0.002396D0                     /,
+     :     (ITL(I,30),I=1,5)/            -1, -2, +2, +0,  1   /
+      DATA TL(31)/            -0.002349D0                     /,
+     :     (ITL(I,31),I=1,5)/            +0, +1, +1, +0,  0   /
+      DATA TL(32)/            +0.002249D0                     /,
+     :     (ITL(I,32),I=1,5)/            -2, +0, +2, +0,  2   /
+      DATA TL(33)/            -0.002125D0                     /,
+     :     (ITL(I,33),I=1,5)/            +1, +2, +0, +0,  1   /
+      DATA TL(34)/            -0.002079D0                     /,
+     :     (ITL(I,34),I=1,5)/            +2, +0, +0, +0,  2   /
+      DATA TL(35)/            +0.002059D0                     /,
+     :     (ITL(I,35),I=1,5)/            -2, -1, +2, +0,  2   /
+      DATA TL(36)/            -0.001773D0                     /,
+     :     (ITL(I,36),I=1,5)/            +0, +1, +2, -2,  0   /
+      DATA TL(37)/            -0.001595D0                     /,
+     :     (ITL(I,37),I=1,5)/            +0, +0, +2, +2,  0   /
+      DATA TL(38)/            +0.001220D0                     /,
+     :     (ITL(I,38),I=1,5)/            -1, -1, +4, +0,  1   /
+      DATA TL(39)/            -0.001110D0                     /,
+     :     (ITL(I,39),I=1,5)/            +0, +2, +0, +2,  0   /
+      DATA TL(40)/            +0.000892D0                     /,
+     :     (ITL(I,40),I=1,5)/            +0, +1, -3, +0,  0   /
+      DATA TL(41)/            -0.000811D0                     /,
+     :     (ITL(I,41),I=1,5)/            +1, +1, +2, +0,  1   /
+      DATA TL(42)/            +0.000761D0                     /,
+     :     (ITL(I,42),I=1,5)/            -1, -2, +4, +0,  1   /
+      DATA TL(43)/            +0.000717D0                     /,
+     :     (ITL(I,43),I=1,5)/            -2, +1, +0, +0,  2   /
+      DATA TL(44)/            +0.000704D0                     /,
+     :     (ITL(I,44),I=1,5)/            -2, +1, -2, +0,  2   /
+      DATA TL(45)/            +0.000693D0                     /,
+     :     (ITL(I,45),I=1,5)/            +1, -2, +2, +0,  1   /
+      DATA TL(46)/            +0.000598D0                     /,
+     :     (ITL(I,46),I=1,5)/            -1, +0, +2, -2,  1   /
+      DATA TL(47)/            +0.000550D0                     /,
+     :     (ITL(I,47),I=1,5)/            +0, +1, +4, +0,  0   /
+      DATA TL(48)/            +0.000538D0                     /,
+     :     (ITL(I,48),I=1,5)/            +0, +4, +0, +0,  0   /
+      DATA TL(49)/            +0.000521D0                     /,
+     :     (ITL(I,49),I=1,5)/            -1, +0, +4, +0,  1   /
+      DATA TL(50)/            +0.000486D0                     /,
+     :     (ITL(I,50),I=1,5)/            +0, +2, -1, +0,  0   /
+*
+*  Latitude
+*                                         M   M'  D   F   n
+      DATA TB( 1)/            +5.128189D0                     /,
+     :     (ITB(I, 1),I=1,5)/            +0, +0, +0, +1,  0   /
+      DATA TB( 2)/            +0.280606D0                     /,
+     :     (ITB(I, 2),I=1,5)/            +0, +1, +0, +1,  0   /
+      DATA TB( 3)/            +0.277693D0                     /,
+     :     (ITB(I, 3),I=1,5)/            +0, +1, +0, -1,  0   /
+      DATA TB( 4)/            +0.173238D0                     /,
+     :     (ITB(I, 4),I=1,5)/            +0, +0, +2, -1,  0   /
+      DATA TB( 5)/            +0.055413D0                     /,
+     :     (ITB(I, 5),I=1,5)/            +0, -1, +2, +1,  0   /
+      DATA TB( 6)/            +0.046272D0                     /,
+     :     (ITB(I, 6),I=1,5)/            +0, -1, +2, -1,  0   /
+      DATA TB( 7)/            +0.032573D0                     /,
+     :     (ITB(I, 7),I=1,5)/            +0, +0, +2, +1,  0   /
+      DATA TB( 8)/            +0.017198D0                     /,
+     :     (ITB(I, 8),I=1,5)/            +0, +2, +0, +1,  0   /
+      DATA TB( 9)/            +0.009267D0                     /,
+     :     (ITB(I, 9),I=1,5)/            +0, +1, +2, -1,  0   /
+      DATA TB(10)/            +0.008823D0                     /,
+     :     (ITB(I,10),I=1,5)/            +0, +2, +0, -1,  0   /
+      DATA TB(11)/            +0.008247D0                     /,
+     :     (ITB(I,11),I=1,5)/            -1, +0, +2, -1,  1   /
+      DATA TB(12)/            +0.004323D0                     /,
+     :     (ITB(I,12),I=1,5)/            +0, -2, +2, -1,  0   /
+      DATA TB(13)/            +0.004200D0                     /,
+     :     (ITB(I,13),I=1,5)/            +0, +1, +2, +1,  0   /
+      DATA TB(14)/            +0.003372D0                     /,
+     :     (ITB(I,14),I=1,5)/            -1, +0, -2, +1,  1   /
+      DATA TB(15)/            +0.002472D0                     /,
+     :     (ITB(I,15),I=1,5)/            -1, -1, +2, +1,  1   /
+      DATA TB(16)/            +0.002222D0                     /,
+     :     (ITB(I,16),I=1,5)/            -1, +0, +2, +1,  1   /
+      DATA TB(17)/            +0.002072D0                     /,
+     :     (ITB(I,17),I=1,5)/            -1, -1, +2, -1,  1   /
+      DATA TB(18)/            +0.001877D0                     /,
+     :     (ITB(I,18),I=1,5)/            -1, +1, +0, +1,  1   /
+      DATA TB(19)/            +0.001828D0                     /,
+     :     (ITB(I,19),I=1,5)/            +0, -1, +4, -1,  0   /
+      DATA TB(20)/            -0.001803D0                     /,
+     :     (ITB(I,20),I=1,5)/            +1, +0, +0, +1,  1   /
+      DATA TB(21)/            -0.001750D0                     /,
+     :     (ITB(I,21),I=1,5)/            +0, +0, +0, +3,  0   /
+      DATA TB(22)/            +0.001570D0                     /,
+     :     (ITB(I,22),I=1,5)/            -1, +1, +0, -1,  1   /
+      DATA TB(23)/            -0.001487D0                     /,
+     :     (ITB(I,23),I=1,5)/            +0, +0, +1, +1,  0   /
+      DATA TB(24)/            -0.001481D0                     /,
+     :     (ITB(I,24),I=1,5)/            +1, +1, +0, +1,  1   /
+      DATA TB(25)/            +0.001417D0                     /,
+     :     (ITB(I,25),I=1,5)/            -1, -1, +0, +1,  1   /
+      DATA TB(26)/            +0.001350D0                     /,
+     :     (ITB(I,26),I=1,5)/            -1, +0, +0, +1,  1   /
+      DATA TB(27)/            +0.001330D0                     /,
+     :     (ITB(I,27),I=1,5)/            +0, +0, -1, +1,  0   /
+      DATA TB(28)/            +0.001106D0                     /,
+     :     (ITB(I,28),I=1,5)/            +0, +3, +0, +1,  0   /
+      DATA TB(29)/            +0.001020D0                     /,
+     :     (ITB(I,29),I=1,5)/            +0, +0, +4, -1,  0   /
+      DATA TB(30)/            +0.000833D0                     /,
+     :     (ITB(I,30),I=1,5)/            +0, -1, +4, +1,  0   /
+      DATA TB(31)/            +0.000781D0                     /,
+     :     (ITB(I,31),I=1,5)/            +0, +1, +0, -3,  0   /
+      DATA TB(32)/            +0.000670D0                     /,
+     :     (ITB(I,32),I=1,5)/            +0, -2, +4, +1,  0   /
+      DATA TB(33)/            +0.000606D0                     /,
+     :     (ITB(I,33),I=1,5)/            +0, +0, +2, -3,  0   /
+      DATA TB(34)/            +0.000597D0                     /,
+     :     (ITB(I,34),I=1,5)/            +0, +2, +2, -1,  0   /
+      DATA TB(35)/            +0.000492D0                     /,
+     :     (ITB(I,35),I=1,5)/            -1, +1, +2, -1,  1   /
+      DATA TB(36)/            +0.000450D0                     /,
+     :     (ITB(I,36),I=1,5)/            +0, +2, -2, -1,  0   /
+      DATA TB(37)/            +0.000439D0                     /,
+     :     (ITB(I,37),I=1,5)/            +0, +3, +0, -1,  0   /
+      DATA TB(38)/            +0.000423D0                     /,
+     :     (ITB(I,38),I=1,5)/            +0, +2, +2, +1,  0   /
+      DATA TB(39)/            +0.000422D0                     /,
+     :     (ITB(I,39),I=1,5)/            +0, -3, +2, -1,  0   /
+      DATA TB(40)/            -0.000367D0                     /,
+     :     (ITB(I,40),I=1,5)/            +1, -1, +2, +1,  1   /
+      DATA TB(41)/            -0.000353D0                     /,
+     :     (ITB(I,41),I=1,5)/            +1, +0, +2, +1,  1   /
+      DATA TB(42)/            +0.000331D0                     /,
+     :     (ITB(I,42),I=1,5)/            +0, +0, +4, +1,  0   /
+      DATA TB(43)/            +0.000317D0                     /,
+     :     (ITB(I,43),I=1,5)/            -1, +1, +2, +1,  1   /
+      DATA TB(44)/            +0.000306D0                     /,
+     :     (ITB(I,44),I=1,5)/            -2, +0, +2, -1,  2   /
+      DATA TB(45)/            -0.000283D0                     /,
+     :     (ITB(I,45),I=1,5)/            +0, +1, +0, +3,  0   /
+*
+*  Parallax
+*                                         M   M'  D   F   n
+      DATA TP( 1)/            +0.950724D0                     /,
+     :     (ITP(I, 1),I=1,5)/            +0, +0, +0, +0,  0   /
+      DATA TP( 2)/            +0.051818D0                     /,
+     :     (ITP(I, 2),I=1,5)/            +0, +1, +0, +0,  0   /
+      DATA TP( 3)/            +0.009531D0                     /,
+     :     (ITP(I, 3),I=1,5)/            +0, -1, +2, +0,  0   /
+      DATA TP( 4)/            +0.007843D0                     /,
+     :     (ITP(I, 4),I=1,5)/            +0, +0, +2, +0,  0   /
+      DATA TP( 5)/            +0.002824D0                     /,
+     :     (ITP(I, 5),I=1,5)/            +0, +2, +0, +0,  0   /
+      DATA TP( 6)/            +0.000857D0                     /,
+     :     (ITP(I, 6),I=1,5)/            +0, +1, +2, +0,  0   /
+      DATA TP( 7)/            +0.000533D0                     /,
+     :     (ITP(I, 7),I=1,5)/            -1, +0, +2, +0,  1   /
+      DATA TP( 8)/            +0.000401D0                     /,
+     :     (ITP(I, 8),I=1,5)/            -1, -1, +2, +0,  1   /
+      DATA TP( 9)/            +0.000320D0                     /,
+     :     (ITP(I, 9),I=1,5)/            -1, +1, +0, +0,  1   /
+      DATA TP(10)/            -0.000271D0                     /,
+     :     (ITP(I,10),I=1,5)/            +0, +0, +1, +0,  0   /
+      DATA TP(11)/            -0.000264D0                     /,
+     :     (ITP(I,11),I=1,5)/            +1, +1, +0, +0,  1   /
+      DATA TP(12)/            -0.000198D0                     /,
+     :     (ITP(I,12),I=1,5)/            +0, -1, +0, +2,  0   /
+      DATA TP(13)/            +0.000173D0                     /,
+     :     (ITP(I,13),I=1,5)/            +0, +3, +0, +0,  0   /
+      DATA TP(14)/            +0.000167D0                     /,
+     :     (ITP(I,14),I=1,5)/            +0, -1, +4, +0,  0   /
+      DATA TP(15)/            -0.000111D0                     /,
+     :     (ITP(I,15),I=1,5)/            +1, +0, +0, +0,  1   /
+      DATA TP(16)/            +0.000103D0                     /,
+     :     (ITP(I,16),I=1,5)/            +0, -2, +4, +0,  0   /
+      DATA TP(17)/            -0.000084D0                     /,
+     :     (ITP(I,17),I=1,5)/            +0, +2, -2, +0,  0   /
+      DATA TP(18)/            -0.000083D0                     /,
+     :     (ITP(I,18),I=1,5)/            +1, +0, +2, +0,  1   /
+      DATA TP(19)/            +0.000079D0                     /,
+     :     (ITP(I,19),I=1,5)/            +0, +2, +2, +0,  0   /
+      DATA TP(20)/            +0.000072D0                     /,
+     :     (ITP(I,20),I=1,5)/            +0, +0, +4, +0,  0   /
+      DATA TP(21)/            +0.000064D0                     /,
+     :     (ITP(I,21),I=1,5)/            -1, +1, +2, +0,  1   /
+      DATA TP(22)/            -0.000063D0                     /,
+     :     (ITP(I,22),I=1,5)/            +1, -1, +2, +0,  1   /
+      DATA TP(23)/            +0.000041D0                     /,
+     :     (ITP(I,23),I=1,5)/            +1, +0, +1, +0,  1   /
+      DATA TP(24)/            +0.000035D0                     /,
+     :     (ITP(I,24),I=1,5)/            -1, +2, +0, +0,  1   /
+      DATA TP(25)/            -0.000033D0                     /,
+     :     (ITP(I,25),I=1,5)/            +0, +3, -2, +0,  0   /
+      DATA TP(26)/            -0.000030D0                     /,
+     :     (ITP(I,26),I=1,5)/            +0, +1, +1, +0,  0   /
+      DATA TP(27)/            -0.000029D0                     /,
+     :     (ITP(I,27),I=1,5)/            +0, +0, -2, +2,  0   /
+      DATA TP(28)/            -0.000029D0                     /,
+     :     (ITP(I,28),I=1,5)/            +1, +2, +0, +0,  1   /
+      DATA TP(29)/            +0.000026D0                     /,
+     :     (ITP(I,29),I=1,5)/            -2, +0, +2, +0,  2   /
+      DATA TP(30)/            -0.000023D0                     /,
+     :     (ITP(I,30),I=1,5)/            +0, +1, -2, +2,  0   /
+      DATA TP(31)/            +0.000019D0                     /,
+     :     (ITP(I,31),I=1,5)/            -1, -1, +4, +0,  1   /
+
+
+
+*  Centuries since J1900
+      T=(DATE-15019.5D0)/36525D0
+
+*
+*  Fundamental arguments (radians) and derivatives (radians per
+*  Julian century) for the current epoch
+*
+
+*  Moon's mean longitude
+      ELP=D2R*MOD(ELP0+(ELP1+(ELP2+ELP3*T)*T)*T,360D0)
+      DELP=D2R*(ELP1+(2D0*ELP2+3D0*ELP3*T)*T)
+
+*  Sun's mean anomaly
+      EM=D2R*MOD(EM0+(EM1+(EM2+EM3*T)*T)*T,360D0)
+      DEM=D2R*(EM1+(2D0*EM2+3D0*EM3*T)*T)
+
+*  Moon's mean anomaly
+      EMP=D2R*MOD(EMP0+(EMP1+(EMP2+EMP3*T)*T)*T,360D0)
+      DEMP=D2R*(EMP1+(2D0*EMP2+3D0*EMP3*T)*T)
+
+*  Moon's mean elongation
+      D=D2R*MOD(D0+(D1+(D2+D3*T)*T)*T,360D0)
+      DD=D2R*(D1+(2D0*D2+3D0*D3*T)*T)
+
+*  Mean distance of the Moon from its ascending node
+      F=D2R*MOD(F0+(F1+(F2+F3*T)*T)*T,360D0)
+      DF=D2R*(F1+(2D0*F2+3D0*F3*T)*T)
+
+*  Longitude of the Moon's ascending node
+      OM=D2R*MOD(OM0+(OM1+(OM2+OM3*T)*T)*T,360D0)
+      DOM=D2R*(OM1+(2D0*OM2+3D0*OM3*T)*T)
+      SINOM=SIN(OM)
+      COSOM=COS(OM)
+      DOMCOM=DOM*COSOM
+
+*  Add the periodic variations
+      THETA=D2R*(PA0+PA1*T)
+      WA=SIN(THETA)
+      DWA=D2R*PA1*COS(THETA)
+      THETA=D2R*(PE0+(PE1+PE2*T)*T)
+      WB=PEC*SIN(THETA)
+      DWB=D2R*PEC*(PE1+2D0*PE2*T)*COS(THETA)
+      ELP=ELP+D2R*(PAC*WA+WB+PFC*SINOM)
+      DELP=DELP+D2R*(PAC*DWA+DWB+PFC*DOMCOM)
+      EM=EM+D2R*PBC*WA
+      DEM=DEM+D2R*PBC*DWA
+      EMP=EMP+D2R*(PCC*WA+WB+PGC*SINOM)
+      DEMP=DEMP+D2R*(PCC*DWA+DWB+PGC*DOMCOM)
+      D=D+D2R*(PDC*WA+WB+PHC*SINOM)
+      DD=DD+D2R*(PDC*DWA+DWB+PHC*DOMCOM)
+      WOM=OM+D2R*(PJ0+PJ1*T)
+      DWOM=DOM+D2R*PJ1
+      SINWOM=SIN(WOM)
+      COSWOM=COS(WOM)
+      F=F+D2R*(WB+PIC*SINOM+PJC*SINWOM)
+      DF=DF+D2R*(DWB+PIC*DOMCOM+PJC*DWOM*COSWOM)
+
+*  E-factor, and square
+      E=1D0+(E1+E2*T)*T
+      DE=E1+2D0*E2*T
+      ESQ=E*E
+      DESQ=2D0*E*DE
+
+*
+*  Series expansions
+*
+
+*  Longitude
+      V=0D0
+      DV=0D0
+      DO N=NL,1,-1
+         COEFF=TL(N)
+         EMN=DBLE(ITL(1,N))
+         EMPN=DBLE(ITL(2,N))
+         DN=DBLE(ITL(3,N))
+         FN=DBLE(ITL(4,N))
+         I=ITL(5,N)
+         IF (I.EQ.0) THEN
+            EN=1D0
+            DEN=0D0
+         ELSE IF (I.EQ.1) THEN
+            EN=E
+            DEN=DE
+         ELSE
+            EN=ESQ
+            DEN=DESQ
+         END IF
+         THETA=EMN*EM+EMPN*EMP+DN*D+FN*F
+         DTHETA=EMN*DEM+EMPN*DEMP+DN*DD+FN*DF
+         FTHETA=SIN(THETA)
+         V=V+COEFF*FTHETA*EN
+         DV=DV+COEFF*(COS(THETA)*DTHETA*EN+FTHETA*DEN)
+      END DO
+      EL=ELP+D2R*V
+      DEL=(DELP+D2R*DV)/CJ
+
+*  Latitude
+      V=0D0
+      DV=0D0
+      DO N=NB,1,-1
+         COEFF=TB(N)
+         EMN=DBLE(ITB(1,N))
+         EMPN=DBLE(ITB(2,N))
+         DN=DBLE(ITB(3,N))
+         FN=DBLE(ITB(4,N))
+         I=ITB(5,N)
+         IF (I.EQ.0) THEN
+            EN=1D0
+            DEN=0D0
+         ELSE IF (I.EQ.1) THEN
+            EN=E
+            DEN=DE
+         ELSE
+            EN=ESQ
+            DEN=DESQ
+         END IF
+         THETA=EMN*EM+EMPN*EMP+DN*D+FN*F
+         DTHETA=EMN*DEM+EMPN*DEMP+DN*DD+FN*DF
+         FTHETA=SIN(THETA)
+         V=V+COEFF*FTHETA*EN
+         DV=DV+COEFF*(COS(THETA)*DTHETA*EN+FTHETA*DEN)
+      END DO
+      BF=1D0-CW1*COSOM-CW2*COSWOM
+      DBF=CW1*DOM*SINOM+CW2*DWOM*SINWOM
+      B=D2R*V*BF
+      DB=D2R*(DV*BF+V*DBF)/CJ
+
+*  Parallax
+      V=0D0
+      DV=0D0
+      DO N=NP,1,-1
+         COEFF=TP(N)
+         EMN=DBLE(ITP(1,N))
+         EMPN=DBLE(ITP(2,N))
+         DN=DBLE(ITP(3,N))
+         FN=DBLE(ITP(4,N))
+         I=ITP(5,N)
+         IF (I.EQ.0) THEN
+            EN=1D0
+            DEN=0D0
+         ELSE IF (I.EQ.1) THEN
+            EN=E
+            DEN=DE
+         ELSE
+            EN=ESQ
+            DEN=DESQ
+         END IF
+         THETA=EMN*EM+EMPN*EMP+DN*D+FN*F
+         DTHETA=EMN*DEM+EMPN*DEMP+DN*DD+FN*DF
+         FTHETA=COS(THETA)
+         V=V+COEFF*FTHETA*EN
+         DV=DV+COEFF*(-SIN(THETA)*DTHETA*EN+FTHETA*DEN)
+      END DO
+      P=D2R*V
+      DP=D2R*DV/CJ
+
+*
+*  Transformation into final form
+*
+
+*  Parallax to distance (AU, AU/sec)
+      SP=SIN(P)
+      R=ERADAU/SP
+      DR=-R*DP*COS(P)/SP
+
+*  Longitude, latitude to x,y,z (AU)
+      SEL=SIN(EL)
+      CEL=COS(EL)
+      SB=SIN(B)
+      CB=COS(B)
+      RCB=R*CB
+      RBD=R*DB
+      W=RBD*SB-CB*DR
+      X=RCB*CEL
+      Y=RCB*SEL
+      Z=R*SB
+      XD=-Y*DEL-W*CEL
+      YD=X*DEL-W*SEL
+      ZD=RBD*CB+SB*DR
+
+*  Julian centuries since J2000
+      T=(DATE-51544.5D0)/36525D0
+
+*  Fricke equinox correction
+      EPJ=2000D0+T*100D0
+      EQCOR=DS2R*(0.035D0+0.00085D0*(EPJ-B1950))
+
+*  Mean obliquity (IAU 1976)
+      EPS=DAS2R*(84381.448D0+(-46.8150D0+(-0.00059D0+0.001813D0*T)*T)*T)
+
+*  To the equatorial system, mean of date, FK5 system
+      SINEPS=SIN(EPS)
+      COSEPS=COS(EPS)
+      ES=EQCOR*SINEPS
+      EC=EQCOR*COSEPS
+      PV(1)=X-EC*Y+ES*Z
+      PV(2)=EQCOR*X+Y*COSEPS-Z*SINEPS
+      PV(3)=Y*SINEPS+Z*COSEPS
+      PV(4)=XD-EC*YD+ES*ZD
+      PV(5)=EQCOR*XD+YD*COSEPS-ZD*SINEPS
+      PV(6)=YD*SINEPS+ZD*COSEPS
+
+      END
diff --git a/math/slalib/dmxm.f b/math/slalib/dmxm.f
new file mode 100644
index 00000000..0d319eef
--- /dev/null
+++ b/math/slalib/dmxm.f
@@ -0,0 +1,73 @@
+      SUBROUTINE slDMXM (A, B, C)
+*+
+*     - - - - -
+*      D M X M
+*     - - - - -
+*
+*  Product of two 3x3 matrices:
+*
+*      matrix C  =  matrix A  x  matrix B
+*
+*  (double precision)
+*
+*  Given:
+*      A      dp(3,3)        matrix
+*      B      dp(3,3)        matrix
+*
+*  Returned:
+*      C      dp(3,3)        matrix result
+*
+*  To comply with the ANSI Fortran 77 standard, A, B and C must
+*  be different arrays.  However, the routine is coded so as to
+*  work properly on many platforms even if this rule is violated.
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION A(3,3),B(3,3),C(3,3)
+
+      INTEGER I,J,K
+      DOUBLE PRECISION W,WM(3,3)
+
+
+*  Multiply into scratch matrix
+      DO I=1,3
+         DO J=1,3
+            W=0D0
+            DO K=1,3
+               W=W+A(I,K)*B(K,J)
+            END DO
+            WM(I,J)=W
+         END DO
+      END DO
+
+*  Return the result
+      DO J=1,3
+         DO I=1,3
+            C(I,J)=WM(I,J)
+         END DO
+      END DO
+
+      END
diff --git a/math/slalib/dmxv.f b/math/slalib/dmxv.f
new file mode 100644
index 00000000..28b8102d
--- /dev/null
+++ b/math/slalib/dmxv.f
@@ -0,0 +1,69 @@
+      SUBROUTINE slDMXV (DM, VA, VB)
+*+
+*     - - - - -
+*      D M X V
+*     - - - - -
+*
+*  Performs the 3-D forward unitary transformation:
+*
+*     vector VB = matrix DM * vector VA
+*
+*  (double precision)
+*
+*  Given:
+*     DM       dp(3,3)    matrix
+*     VA       dp(3)      vector
+*
+*  Returned:
+*     VB       dp(3)      result vector
+*
+*  To comply with the ANSI Fortran 77 standard, VA and VB must be
+*  different arrays.  However, the routine is coded so as to work
+*  properly on many platforms even if this rule is violated.
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DM(3,3),VA(3),VB(3)
+
+      INTEGER I,J
+      DOUBLE PRECISION W,VW(3)
+
+
+*  Matrix DM * vector VA -> vector VW
+      DO J=1,3
+         W=0D0
+         DO I=1,3
+            W=W+DM(J,I)*VA(I)
+         END DO
+         VW(J)=W
+      END DO
+
+*  Vector VW -> vector VB
+      DO J=1,3
+         VB(J)=VW(J)
+      END DO
+
+      END
diff --git a/math/slalib/doc/addet.hlp b/math/slalib/doc/addet.hlp
new file mode 100644
index 00000000..464dd86a
--- /dev/null
+++ b/math/slalib/doc/addet.hlp
@@ -0,0 +1,42 @@
+.help addet Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slADET (RM, DM, EQ, RC, DC)
+
+     - - - - - -
+      A D E T
+     - - - - - -
+
+  Add the E-terms (elliptic component of annual aberration)
+  to a pre IAU 1976 mean place to conform to the old
+  catalogue convention (double precision)
+
+  Given:
+     RM,DM     dp     RA,Dec (radians) without E-terms
+     EQ        dp     Besselian epoch of mean equator and equinox
+
+  Returned:
+     RC,DC     dp     RA,Dec (radians) with E-terms included
+
+  Note:
+
+     Most star positions from pre-1984 optical catalogues (or
+     derived from astrometry using such stars) embody the
+     E-terms.  If it is necessary to convert a formal mean
+     place (for example a pulsar timing position) to one
+     consistent with such a star catalogue, then the RA,Dec
+     should be adjusted using this routine.
+
+  Reference:
+     Explanatory Supplement to the Astronomical Ephemeris,
+     section 2D, page 48.
+
+  Called:  slETRM, slDS2C, slDC2S, slDA2P, slDA1P
+
+  P.T.Wallace   Starlink   18 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/afin.hlp b/math/slalib/doc/afin.hlp
new file mode 100644
index 00000000..f3c5a22c
--- /dev/null
+++ b/math/slalib/doc/afin.hlp
@@ -0,0 +1,91 @@
+.help afin Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slAFIN (STRING, IPTR, A, J)
+
+     - - - - -
+      A F I N
+     - - - - -
+
+  Sexagesimal character string to angle (single precision)
+
+  Given:
+     STRING  c*(*)   string containing deg, arcmin, arcsec fields
+     IPTR      i     pointer to start of decode (1st = 1)
+
+  Returned:
+     IPTR      i     advanced past the decoded angle
+     A         r     angle in radians
+     J         i     status:  0 = OK
+                             +1 = default, A unchanged
+                             -1 = bad degrees      )
+                             -2 = bad arcminutes   )  (note 3)
+                             -3 = bad arcseconds   )
+
+  Example:
+
+    argument    before                           after
+
+    STRING      '-57 17 44.806  12 34 56.7'      unchanged
+    IPTR        1                                16 (points to 12...)
+    A           ?                                -1.00000
+    J           ?                                0
+
+    A further call to slAFIN, without adjustment of IPTR, will
+    decode the second angle, 12deg 34min 56.7sec.
+
+  Notes:
+
+     1)  The first three "fields" in STRING are degrees, arcminutes,
+         arcseconds, separated by spaces or commas.  The degrees field
+         may be signed, but not the others.  The decoding is carried
+         out by the DFLTIN routine and is free-format.
+
+     2)  Successive fields may be absent, defaulting to zero.  For
+         zero status, the only combinations allowed are degrees alone,
+         degrees and arcminutes, and all three fields present.  If all
+         three fields are omitted, a status of +1 is returned and A is
+         unchanged.  In all other cases A is changed.
+
+     3)  Range checking:
+
+           The degrees field is not range checked.  However, it is
+           expected to be integral unless the other two fields are
+           absent.
+
+           The arcminutes field is expected to be 0-59, and integral if
+           the arcseconds field is present.  If the arcseconds field
+           is absent, the arcminutes is expected to be 0-59.9999...
+
+           The arcseconds field is expected to be 0-59.9999...
+
+     4)  Decoding continues even when a check has failed.  Under these
+         circumstances the field takes the supplied value, defaulting
+         to zero, and the result A is computed and returned.
+
+     5)  Further fields after the three expected ones are not treated
+         as an error.  The pointer IPTR is left in the correct state
+         for further decoding with the present routine or with DFLTIN
+         etc.  See the example, above.
+
+     6)  If STRING contains hours, minutes, seconds instead of degrees
+         etc, or if the required units are turns (or days) instead of
+         radians, the result A should be multiplied as follows:
+
+           for        to obtain    multiply
+           STRING     A in         A by
+
+           d ' "      radians      1       =  1.0
+           d ' "      turns        1/2pi   =  0.1591549430918953358
+           h m s      radians      15      =  15.0
+           h m s      days         15/2pi  =  2.3873241463784300365
+
+  Called:  slDAFN
+
+  P.T.Wallace   Starlink   13 September 1990
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/airmas.hlp b/math/slalib/doc/airmas.hlp
new file mode 100644
index 00000000..c347bb50
--- /dev/null
+++ b/math/slalib/doc/airmas.hlp
@@ -0,0 +1,51 @@
+.help airmas Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slARMS (ZD)
+
+     - - - - - - -
+      A R M S
+     - - - - - - -
+
+  Air mass at given zenith distance (double precision)
+
+  Given:
+     ZD     d     Observed zenith distance (radians)
+
+  The result is an estimate of the air mass, in units of that
+  at the zenith.
+
+  Notes:
+
+  1)  The "observed" zenith distance referred to above means "as
+      affected by refraction".
+
+  2)  Uses Hardie's (1962) polynomial fit to Bemporad's data for
+      the relative air mass, X, in units of thickness at the zenith
+      as tabulated by Schoenberg (1929). This is adequate for all
+      normal needs as it is accurate to better than 0.1% up to X =
+      6.8 and better than 1% up to X = 10. Bemporad's tabulated
+      values are unlikely to be trustworthy to such accuracy
+      because of variations in density, pressure and other
+      conditions in the atmosphere from those assumed in his work.
+
+  3)  The sign of the ZD is ignored.
+
+  4)  At zenith distances greater than about ZD = 87 degrees the
+      air mass is held constant to avoid arithmetic overflows.
+
+  References:
+     Hardie, R.H., 1962, in "Astronomical Techniques"
+        ed. W.A. Hiltner, University of Chicago Press, p180.
+     Schoenberg, E., 1929, Hdb. d. Ap.,
+        Berlin, Julius Springer, 2, 268.
+
+  Original code by P.W.Hill, St Andrews
+
+  P.T.Wallace   Starlink   18 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/altaz.hlp b/math/slalib/doc/altaz.hlp
new file mode 100644
index 00000000..0f701093
--- /dev/null
+++ b/math/slalib/doc/altaz.hlp
@@ -0,0 +1,79 @@
+.help altaz Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slALAZ (HA, DEC, PHI,
+     :                      AZ, AZD, AZDD, EL, ELD, ELDD, PA, PAD, PADD)
+
+     - - - - - -
+      A L A Z
+     - - - - - -
+
+  Positions, velocities and accelerations for an altazimuth
+  telescope mount.
+
+  (double precision)
+
+  Given:
+     HA      d     hour angle
+     DEC     d     declination
+     PHI     d     observatory latitude
+
+  Returned:
+     AZ      d     azimuth
+     AZD     d        "    velocity
+     AZDD    d        "    acceleration
+     EL      d     elevation
+     ELD     d         "     velocity
+     ELDD    d         "     acceleration
+     PA      d     parallactic angle
+     PAD     d         "      "   velocity
+     PADD    d         "      "   acceleration
+
+  Notes:
+
+  1)  Natural units are used throughout.  HA, DEC, PHI, AZ, EL
+      and ZD are in radians.  The velocities and accelerations
+      assume constant declination and constant rate of change of
+      hour angle (as for tracking a star);  the units of AZD, ELD
+      and PAD are radians per radian of HA, while the units of AZDD,
+      ELDD and PADD are radians per radian of HA squared.  To
+      convert into practical degree- and second-based units:
+
+        angles * 360/2pi -> degrees
+        velocities * (2pi/86400)*(360/2pi) -> degree/sec
+        accelerations * ((2pi/86400)**2)*(360/2pi) -> degree/sec/sec
+
+      Note that the seconds here are sidereal rather than SI.  One
+      sidereal second is about 0.99727 SI seconds.
+
+      The velocity and acceleration factors assume the sidereal
+      tracking case.  Their respective numerical values are (exactly)
+      1/240 and (approximately) 1/3300236.9.
+
+  2)  Azimuth is returned in the range 0-2pi;  north is zero,
+      and east is +pi/2.  Elevation and parallactic angle are
+      returned in the range +/-pi/2.  Position angle is +ve
+      for a star west of the meridian and is the angle NP-star-zenith.
+
+  3)  The latitude is geodetic as opposed to geocentric.  The
+      hour angle and declination are topocentric.  Refraction and
+      deficiencies in the telescope mounting are ignored.  The
+      purpose of the routine is to give the general form of the
+      quantities.  The details of a real telescope could profoundly
+      change the results, especially close to the zenith.
+
+  4)  No range checking of arguments is carried out.
+
+  5)  In applications which involve many such calculations, rather
+      than calling the present routine it will be more efficient to
+      use inline code, having previously computed fixed terms such
+      as sine and cosine of latitude, and (for tracking a star)
+      sine and cosine of declination.
+
+  P.T.Wallace   Starlink   14 March 1997
+
+  Copyright (C) 1997 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/amp.hlp b/math/slalib/doc/amp.hlp
new file mode 100644
index 00000000..f5d4dfc4
--- /dev/null
+++ b/math/slalib/doc/amp.hlp
@@ -0,0 +1,61 @@
+.help amp Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slAMP (RA, DA, DATE, EQ, RM, DM)
+
+     - - - -
+      A M P
+     - - - -
+
+  Convert star RA,Dec from geocentric apparent to mean place
+
+  The mean coordinate system is the post IAU 1976 system,
+  loosely called FK5.
+
+  Given:
+     RA       d      apparent RA (radians)
+     DA       d      apparent Dec (radians)
+     DATE     d      TDB for apparent place (JD-2400000.5)
+     EQ       d      equinox:  Julian epoch of mean place
+
+  Returned:
+     RM       d      mean RA (radians)
+     DM       d      mean Dec (radians)
+
+  References:
+     1984 Astronomical Almanac, pp B39-B41.
+     (also Lederle & Schwan, Astron. Astrophys. 134,
+      1-6, 1984)
+
+  Notes:
+
+  1)  The distinction between the required TDB and TT is
+      always negligible.  Moreover, for all but the most
+      critical applications UTC is adequate.
+
+  2)  The accuracy is limited by the routine slEVP, called
+      by slMAPA, which computes the Earth position and
+      velocity using the methods of Stumpff.  The maximum
+      error is about 0.3 milliarcsecond.
+
+  3)  Iterative techniques are used for the aberration and
+      light deflection corrections so that the routines
+      slAMP (or slAMPQ) and slMAP (or slMAPQ) are
+      accurate inverses;  even at the edge of the Sun's disc
+      the discrepancy is only about 1 nanoarcsecond.
+
+  4)  Where multiple apparent places are to be converted to
+      mean places, for a fixed date and equinox, it is more
+      efficient to use the slMAPA routine to compute the
+      required parameters once, followed by one call to
+      slAMPQ per star.
+
+  Called:  slMAPA, slAMPQ
+
+  P.T.Wallace   Starlink   19 January 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ampqk.hlp b/math/slalib/doc/ampqk.hlp
new file mode 100644
index 00000000..a4b8dee6
--- /dev/null
+++ b/math/slalib/doc/ampqk.hlp
@@ -0,0 +1,65 @@
+.help ampqk Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slAMPQ (RA, DA, AMPRMS, RM, DM)
+
+     - - - - - -
+      A M P Q
+     - - - - - -
+
+  Convert star RA,Dec from geocentric apparent to mean place
+
+  The mean coordinate system is the post IAU 1976 system,
+  loosely called FK5.
+
+  Use of this routine is appropriate when efficiency is important
+  and where many star positions are all to be transformed for
+  one epoch and equinox.  The star-independent parameters can be
+  obtained by calling the slMAPA routine.
+
+  Given:
+     RA       d      apparent RA (radians)
+     DA       d      apparent Dec (radians)
+
+     AMPRMS   d(21)  star-independent mean-to-apparent parameters:
+
+       (1)      time interval for proper motion (Julian years)
+       (2-4)    barycentric position of the Earth (AU)
+       (5-7)    heliocentric direction of the Earth (unit vector)
+       (8)      (grav rad Sun)*2/(Sun-Earth distance)
+       (9-11)   ABV: barycentric Earth velocity in units of c
+       (12)     sqrt(1-v**2) where v=modulus(ABV)
+       (13-21)  precession/nutation (3,3) matrix
+
+  Returned:
+     RM       d      mean RA (radians)
+     DM       d      mean Dec (radians)
+
+  References:
+     1984 Astronomical Almanac, pp B39-B41.
+     (also Lederle & Schwan, Astron. Astrophys. 134,
+      1-6, 1984)
+
+  Notes:
+
+  1)  The accuracy is limited by the routine slEVP, called
+      by slMAPA, which computes the Earth position and
+      velocity using the methods of Stumpff.  The maximum
+      error is about 0.3 milliarcsecond.
+
+  2)  Iterative techniques are used for the aberration and
+      light deflection corrections so that the routines
+      slAMP (or slAMPQ) and slMAP (or slMAPQ) are
+      accurate inverses;  even at the edge of the Sun's disc
+      the discrepancy is only about 1 nanoarcsecond.
+
+  Called:  slDS2C, slDIMV, slDVDV, slDVN, slDC2S,
+           slDA2P
+
+  P.T.Wallace   Starlink   21 June 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/aop.hlp b/math/slalib/doc/aop.hlp
new file mode 100644
index 00000000..dc3343bf
--- /dev/null
+++ b/math/slalib/doc/aop.hlp
@@ -0,0 +1,166 @@
+.help aop Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slAOP (RAP, DAP, DATE, DUT, ELONGM, PHIM, HM,
+     :                    XP, YP, TDK, PMB, RH, WL, TLR,
+     :                    AOB, ZOB, HOB, DOB, ROB)
+
+     - - - -
+      A O P
+     - - - -
+
+  Apparent to observed place, for optical sources distant from
+  the solar system.
+
+  Given:
+     RAP    d      geocentric apparent right ascension
+     DAP    d      geocentric apparent declination
+     DATE   d      UTC date/time (Modified Julian Date, JD-2400000.5)
+     DUT    d      delta UT:  UT1-UTC (UTC seconds)
+     ELONGM d      mean longitude of the observer (radians, east +ve)
+     PHIM   d      mean geodetic latitude of the observer (radians)
+     HM     d      observer's height above sea level (metres)
+     XP     d      polar motion x-coordinate (radians)
+     YP     d      polar motion y-coordinate (radians)
+     TDK    d      local ambient temperature (DegK; std=273.155D0)
+     PMB    d      local atmospheric pressure (mB; std=1013.25D0)
+     RH     d      local relative humidity (in the range 0D0-1D0)
+     WL     d      effective wavelength (micron, e.g. 0.55D0)
+     TLR    d      tropospheric lapse rate (DegK/metre, e.g. 0.0065D0)
+
+  Returned:
+     AOB    d      observed azimuth (radians: N=0,E=90)
+     ZOB    d      observed zenith distance (radians)
+     HOB    d      observed Hour Angle (radians)
+     DOB    d      observed Declination (radians)
+     ROB    d      observed Right Ascension (radians)
+
+  Notes:
+
+   1)  This routine returns zenith distance rather than elevation
+       in order to reflect the fact that no allowance is made for
+       depression of the horizon.
+
+   2)  The accuracy of the result is limited by the corrections for
+       refraction.  Providing the meteorological parameters are
+       known accurately and there are no gross local effects, the
+       predicted apparent RA,Dec should be within about 0.1 arcsec
+       for a zenith distance of less than 70 degrees.  Even at a
+       topocentric zenith distance of 90 degrees, the accuracy in
+       elevation should be better than 1 arcmin;  useful results
+       are available for a further 3 degrees, beyond which the
+       slRFRO routine returns a fixed value of the refraction.
+       The complementary routines slAOP (or slAOPQ) and slOAP
+       (or slOAPQ) are self-consistent to better than 1 micro-
+       arcsecond all over the celestial sphere.
+
+   3)  It is advisable to take great care with units, as even
+       unlikely values of the input parameters are accepted and
+       processed in accordance with the models used.
+
+   4)  "Apparent" place means the geocentric apparent right ascension
+       and declination, which is obtained from a catalogue mean place
+       by allowing for space motion, parallax, precession, nutation,
+       annual aberration, and the Sun's gravitational lens effect.  For
+       star positions in the FK5 system (i.e. J2000), these effects can
+       be applied by means of the slMAP etc routines.  Starting from
+       other mean place systems, additional transformations will be
+       needed;  for example, FK4 (i.e. B1950) mean places would first
+       have to be converted to FK5, which can be done with the
+       slFK45 etc routines.
+
+   5)  "Observed" Az,El means the position that would be seen by a
+       perfect theodolite located at the observer.  This is obtained
+       from the geocentric apparent RA,Dec by allowing for Earth
+       orientation and diurnal aberration, rotating from equator
+       to horizon coordinates, and then adjusting for refraction.
+       The HA,Dec is obtained by rotating back into equatorial
+       coordinates, using the geodetic latitude corrected for polar
+       motion, and is the position that would be seen by a perfect
+       equatorial located at the observer and with its polar axis
+       aligned to the Earth's axis of rotation (n.b. not to the
+       refracted pole).  Finally, the RA is obtained by subtracting
+       the HA from the local apparent ST.
+
+   6)  To predict the required setting of a real telescope, the
+       observed place produced by this routine would have to be
+       adjusted for the tilt of the azimuth or polar axis of the
+       mounting (with appropriate corrections for mount flexures),
+       for non-perpendicularity between the mounting axes, for the
+       position of the rotator axis and the pointing axis relative
+       to it, for tube flexure, for gear and encoder errors, and
+       finally for encoder zero points.  Some telescopes would, of
+       course, exhibit other properties which would need to be
+       accounted for at the appropriate point in the sequence.
+
+   7)  This routine takes time to execute, due mainly to the
+       rigorous integration used to evaluate the refraction.
+       For processing multiple stars for one location and time,
+       call slAOPA once followed by one call per star to slAOPQ.
+       Where a range of times within a limited period of a few hours
+       is involved, and the highest precision is not required, call
+       slAOPA once, followed by a call to slAOPT each time the
+       time changes, followed by one call per star to slAOPQ.
+
+   8)  The DATE argument is UTC expressed as an MJD.  This is,
+       strictly speaking, wrong, because of leap seconds.  However,
+       as long as the delta UT and the UTC are consistent there
+       are no difficulties, except during a leap second.  In this
+       case, the start of the 61st second of the final minute should
+       begin a new MJD day and the old pre-leap delta UT should
+       continue to be used.  As the 61st second completes, the MJD
+       should revert to the start of the day as, simultaneously,
+       the delta UTC changes by one second to its post-leap new value.
+
+   9)  The delta UT (UT1-UTC) is tabulated in IERS circulars and
+       elsewhere.  It increases by exactly one second at the end of
+       each UTC leap second, introduced in order to keep delta UT
+       within +/- 0.9 seconds.
+
+  10)  IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.
+       The longitude required by the present routine is east-positive,
+       in accordance with geographical convention (and right-handed).
+       In particular, note that the longitudes returned by the
+       slOBS routine are west-positive, following astronomical
+       usage, and must be reversed in sign before use in the present
+       routine.
+
+  11)  The polar coordinates XP,YP can be obtained from IERS
+       circulars and equivalent publications.  The maximum amplitude
+       is about 0.3 arcseconds.  If XP,YP values are unavailable,
+       use XP=YP=0D0.  See page B60 of the 1988 Astronomical Almanac
+       for a definition of the two angles.
+
+  12)  The height above sea level of the observing station, HM,
+       can be obtained from the Astronomical Almanac (Section J
+       in the 1988 edition), or via the routine slOBS.  If P,
+       the pressure in millibars, is available, an adequate
+       estimate of HM can be obtained from the expression
+
+             HM ~ -29.3D0*TSL*LOG(P/1013.25D0).
+
+       where TSL is the approximate sea-level air temperature in
+       deg K (see Astrophysical Quantities, C.W.Allen, 3rd edition,
+       section 52.)  Similarly, if the pressure P is not known,
+       it can be estimated from the height of the observing
+       station, HM as follows:
+
+             P ~ 1013.25D0*EXP(-HM/(29.3D0*TSL)).
+
+       Note, however, that the refraction is proportional to the
+       pressure and that an accurate P value is important for
+       precise work.
+
+  13)  The azimuths etc produced by the present routine are with
+       respect to the celestial pole.  Corrections to the terrestrial
+       pole can be computed using slPLMO.
+
+  Called:  slAOPA, slAOPQ
+
+  P.T.Wallace   Starlink   9 June 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/aoppa.hlp b/math/slalib/doc/aoppa.hlp
new file mode 100644
index 00000000..f96d835b
--- /dev/null
+++ b/math/slalib/doc/aoppa.hlp
@@ -0,0 +1,114 @@
+.help aoppa Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slAOPA (DATE, DUT, ELONGM, PHIM, HM,
+     :                      XP, YP, TDK, PMB, RH, WL, TLR, AOPRMS)
+
+     - - - - - -
+      A O P A
+     - - - - - -
+
+  Precompute apparent to observed place parameters required by
+  slAOPQ and slOAPQ.
+
+  Given:
+     DATE   d      UTC date/time (modified Julian Date, JD-2400000.5)
+     DUT    d      delta UT:  UT1-UTC (UTC seconds)
+     ELONGM d      mean longitude of the observer (radians, east +ve)
+     PHIM   d      mean geodetic latitude of the observer (radians)
+     HM     d      observer's height above sea level (metres)
+     XP     d      polar motion x-coordinate (radians)
+     YP     d      polar motion y-coordinate (radians)
+     TDK    d      local ambient temperature (DegK; std=273.155D0)
+     PMB    d      local atmospheric pressure (mB; std=1013.25D0)
+     RH     d      local relative humidity (in the range 0D0-1D0)
+     WL     d      effective wavelength (micron, e.g. 0.55D0)
+     TLR    d      tropospheric lapse rate (DegK/metre, e.g. 0.0065D0)
+
+  Returned:
+     AOPRMS d(14)  star-independent apparent-to-observed parameters:
+
+       (1)      geodetic latitude (radians)
+       (2,3)    sine and cosine of geodetic latitude
+       (4)      magnitude of diurnal aberration vector
+       (5)      height (HM)
+       (6)      ambient temperature (TDK)
+       (7)      pressure (PMB)
+       (8)      relative humidity (RH)
+       (9)      wavelength (WL)
+       (10)     lapse rate (TLR)
+       (11,12)  refraction constants A and B (radians)
+       (13)     longitude + eqn of equinoxes + sidereal DUT (radians)
+       (14)     local apparent sidereal time (radians)
+
+  Notes:
+
+   1)  It is advisable to take great care with units, as even
+       unlikely values of the input parameters are accepted and
+       processed in accordance with the models used.
+
+   2)  The DATE argument is UTC expressed as an MJD.  This is,
+       strictly speaking, improper, because of leap seconds.  However,
+       as long as the delta UT and the UTC are consistent there
+       are no difficulties, except during a leap second.  In this
+       case, the start of the 61st second of the final minute should
+       begin a new MJD day and the old pre-leap delta UT should
+       continue to be used.  As the 61st second completes, the MJD
+       should revert to the start of the day as, simultaneously,
+       the delta UTC changes by one second to its post-leap new value.
+
+   3)  The delta UT (UT1-UTC) is tabulated in IERS circulars and
+       elsewhere.  It increases by exactly one second at the end of
+       each UTC leap second, introduced in order to keep delta UT
+       within +/- 0.9 seconds.
+
+   4)  IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.
+       The longitude required by the present routine is east-positive,
+       in accordance with geographical convention (and right-handed).
+       In particular, note that the longitudes returned by the
+       slOBS routine are west-positive, following astronomical
+       usage, and must be reversed in sign before use in the present
+       routine.
+
+   5)  The polar coordinates XP,YP can be obtained from IERS
+       circulars and equivalent publications.  The maximum amplitude
+       is about 0.3 arcseconds.  If XP,YP values are unavailable,
+       use XP=YP=0D0.  See page B60 of the 1988 Astronomical Almanac
+       for a definition of the two angles.
+
+   6)  The height above sea level of the observing station, HM,
+       can be obtained from the Astronomical Almanac (Section J
+       in the 1988 edition), or via the routine slOBS.  If P,
+       the pressure in millibars, is available, an adequate
+       estimate of HM can be obtained from the expression
+
+             HM ~ -29.3D0*TSL*LOG(P/1013.25D0).
+
+       where TSL is the approximate sea-level air temperature in
+       deg K (see Astrophysical Quantities, C.W.Allen, 3rd edition,
+       section 52.)  Similarly, if the pressure P is not known,
+       it can be estimated from the height of the observing
+       station, HM as follows:
+
+             P ~ 1013.25D0*EXP(-HM/(29.3D0*TSL)).
+
+       Note, however, that the refraction is proportional to the
+       pressure and that an accurate P value is important for
+       precise work.
+
+   7)  Repeated, computationally-expensive, calls to slAOPA for
+       times that are very close together can be avoided by calling
+       slAOPA just once and then using slAOPT for the subsequent
+       times.  Fresh calls to slAOPA will be needed only when changes
+       in the precession have grown to unacceptable levels or when
+       anything affecting the refraction has changed.
+
+  Called:  slGEOC, slRFCO, slEQEX, slAOPT
+
+  P.T.Wallace   Starlink   9 June 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/aoppat.hlp b/math/slalib/doc/aoppat.hlp
new file mode 100644
index 00000000..c5d6f9c8
--- /dev/null
+++ b/math/slalib/doc/aoppat.hlp
@@ -0,0 +1,39 @@
+.help aoppat Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slAOPT (DATE, AOPRMS)
+
+     - - - - - - -
+      A O P T
+     - - - - - - -
+
+  Recompute the sidereal time in the apparent to observed place
+  star-independent parameter block.
+
+  Given:
+     DATE   d      UTC date/time (modified Julian Date, JD-2400000.5)
+                   (see AOPPA source for comments on leap seconds)
+
+     AOPRMS d(14)  star-independent apparent-to-observed parameters
+
+       (1-12)   not required
+       (13)     longitude + eqn of equinoxes + sidereal DUT
+       (14)     not required
+
+  Returned:
+     AOPRMS d(14)  star-independent apparent-to-observed parameters:
+
+       (1-13)   not changed
+       (14)     local apparent sidereal time (radians)
+
+  For more information, see slAOPA.
+
+  Called:  slGMST
+
+  P.T.Wallace   Starlink   1 July 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/aopqk.hlp b/math/slalib/doc/aopqk.hlp
new file mode 100644
index 00000000..aa916a5d
--- /dev/null
+++ b/math/slalib/doc/aopqk.hlp
@@ -0,0 +1,131 @@
+.help aopqk Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slAOPQ (RAP, DAP, AOPRMS, AOB, ZOB, HOB, DOB, ROB)
+
+     - - - - - -
+      A O P Q
+     - - - - - -
+
+  Quick apparent to observed place (but see note 8, below, for
+  remarks about speed).
+
+  Given:
+     RAP    d      geocentric apparent right ascension
+     DAP    d      geocentric apparent declination
+     AOPRMS d(14)  star-independent apparent-to-observed parameters:
+
+       (1)      geodetic latitude (radians)
+       (2,3)    sine and cosine of geodetic latitude
+       (4)      magnitude of diurnal aberration vector
+       (5)      height (HM)
+       (6)      ambient temperature (T)
+       (7)      pressure (P)
+       (8)      relative humidity (RH)
+       (9)      wavelength (WL)
+       (10)     lapse rate (TLR)
+       (11,12)  refraction constants A and B (radians)
+       (13)     longitude + eqn of equinoxes + sidereal DUT (radians)
+       (14)     local apparent sidereal time (radians)
+
+  Returned:
+     AOB    d      observed azimuth (radians: N=0,E=90)
+     ZOB    d      observed zenith distance (radians)
+     HOB    d      observed Hour Angle (radians)
+     DOB    d      observed Declination (radians)
+     ROB    d      observed Right Ascension (radians)
+
+  Notes:
+
+   1)  This routine returns zenith distance rather than elevation
+       in order to reflect the fact that no allowance is made for
+       depression of the horizon.
+
+   2)  The accuracy of the result is limited by the corrections for
+       refraction.  Providing the meteorological parameters are
+       known accurately and there are no gross local effects, the
+       observed RA,Dec predicted by this routine should be within
+       about 0.1 arcsec for a zenith distance of less than 70 degrees.
+       Even at a topocentric zenith distance of 90 degrees, the
+       accuracy in elevation should be better than 1 arcmin;  useful
+       results are available for a further 3 degrees, beyond which
+       the slaRefro routine returns a fixed value of the refraction.
+       The complementary routines slaAop (or slaAopqk) and slaOap
+       (or slaOapqk) are self-consistent to better than 1 micro-
+       arcsecond all over the celestial sphere.
+
+   3)  It is advisable to take great care with units, as even
+       unlikely values of the input parameters are accepted and
+       processed in accordance with the models used.
+
+   4)  "Apparent" place means the geocentric apparent right ascension
+       and declination, which is obtained from a catalogue mean place
+       by allowing for space motion, parallax, precession, nutation,
+       annual aberration, and the Sun's gravitational lens effect.  For
+       star positions in the FK5 system (i.e. J2000), these effects can
+       be applied by means of the slMAP etc routines.  Starting from
+       other mean place systems, additional transformations will be
+       needed;  for example, FK4 (i.e. B1950) mean places would first
+       have to be converted to FK5, which can be done with the
+       slFK45 etc routines.
+
+   5)  "Observed" Az,El means the position that would be seen by a
+       perfect theodolite located at the observer.  This is obtained
+       from the geocentric apparent RA,Dec by allowing for Earth
+       orientation and diurnal aberration, rotating from equator
+       to horizon coordinates, and then adjusting for refraction.
+       The HA,Dec is obtained by rotating back into equatorial
+       coordinates, using the geodetic latitude corrected for polar
+       motion, and is the position that would be seen by a perfect
+       equatorial located at the observer and with its polar axis
+       aligned to the Earth's axis of rotation (n.b. not to the
+       refracted pole).  Finally, the RA is obtained by subtracting
+       the HA from the local apparent ST.
+
+   6)  To predict the required setting of a real telescope, the
+       observed place produced by this routine would have to be
+       adjusted for the tilt of the azimuth or polar axis of the
+       mounting (with appropriate corrections for mount flexures),
+       for non-perpendicularity between the mounting axes, for the
+       position of the rotator axis and the pointing axis relative
+       to it, for tube flexure, for gear and encoder errors, and
+       finally for encoder zero points.  Some telescopes would, of
+       course, exhibit other properties which would need to be
+       accounted for at the appropriate point in the sequence.
+
+   7)  The star-independent apparent-to-observed-place parameters
+       in AOPRMS may be computed by means of the slAOPA routine.
+       If nothing has changed significantly except the time, the
+       slAOPT routine may be used to perform the requisite
+       partial recomputation of AOPRMS.
+
+   8)  At zenith distances beyond about 76 degrees, the need for
+       special care with the corrections for refraction causes a
+       marked increase in execution time.  Moreover, the effect
+       gets worse with increasing zenith distance.  Adroit
+       programming in the calling application may allow the
+       problem to be reduced.  Prepare an alternative AOPRMS array,
+       computed for zero air-pressure;  this will disable the
+       refraction corrections and cause rapid execution.  Using
+       this AOPRMS array, a preliminary call to the present routine
+       will, depending on the application, produce a rough position
+       which may be enough to establish whether the full, slow
+       calculation (using the real AOPRMS array) is worthwhile.
+       For example, there would be no need for the full calculation
+       if the preliminary call had already established that the
+       source was well below the elevation limits for a particular
+       telescope.
+
+  9)   The azimuths etc produced by the present routine are with
+       respect to the celestial pole.  Corrections to the terrestrial
+       pole can be computed using slPLMO.
+
+  Called:  slDS2C, slREFZ, slRFRO, slDC2S, slDA2P
+
+  P.T.Wallace   Starlink   22 February 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/atmdsp.hlp b/math/slalib/doc/atmdsp.hlp
new file mode 100644
index 00000000..eaa2b411
--- /dev/null
+++ b/math/slalib/doc/atmdsp.hlp
@@ -0,0 +1,75 @@
+.help atmdsp Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slATMD (TDK, PMB, RH, WL1, A1, B1, WL2, A2, B2)
+
+     - - - - - - -
+      A T M D
+     - - - - - - -
+
+  Apply atmospheric-dispersion adjustments to refraction coefficients.
+
+  Given:
+     TDK       d       ambient temperature, degrees K
+     PMB       d       ambient pressure, millibars
+     RH        d       ambient relative humidity, 0-1
+     WL1       d       reference wavelength, micrometre (0.4D0 recommended)
+     A1        d       refraction coefficient A for wavelength WL1 (radians)
+     B1        d       refraction coefficient B for wavelength WL1 (radians)
+     WL2       d       wavelength for which adjusted A,B required
+
+  Returned:
+     A2        d       refraction coefficient A for wavelength WL2 (radians)
+     B2        d       refraction coefficient B for wavelength WL2 (radians)
+
+  Notes:
+
+  1  To use this routine, first call slRFCO specifying WL1 as the
+     wavelength.  This yields refraction coefficients A1,B1, correct
+     for that wavelength.  Subsequently, calls to slATMD specifying
+     different wavelengths will produce new, slightly adjusted
+     refraction coefficients which apply to the specified wavelength.
+
+  2  Most of the atmospheric dispersion happens between 0.7 micrometre
+     and the UV atmospheric cutoff, and the effect increases strongly
+     towards the UV end.  For this reason a blue reference wavelength
+     is recommended, for example 0.4 micrometres.
+
+  3  The accuracy, for this set of conditions:
+
+        height above sea level    2000 m
+                      latitude    29 deg
+                      pressure    793 mB
+                   temperature    17 degC
+                      humidity    50%
+                    lapse rate    0.0065 degC/m
+          reference wavelength    0.4 micrometre
+                star elevation    15 deg
+
+     is about 2.5 mas RMS between 0.3 and 1.0 micrometres, and stays
+     within 4 mas for the whole range longward of 0.3 micrometres
+     (compared with a total dispersion from 0.3 to 20.0 micrometres
+     of about 11 arcsec).  These errors are typical for ordinary
+     conditions and the given elevation;  in extreme conditions values
+     a few times this size may occur, while at higher elevations the
+     errors become much smaller.
+
+  4  If either wavelength exceeds 100 micrometres, the radio case
+     is assumed and the returned refraction coefficients are the
+     same as the given ones.
+
+  5  The algorithm consists of calculation of the refractivity of the
+     air at the observer for the two wavelengths, using the methods
+     of the slRFRO routine, and then scaling of the two refraction
+     coefficients according to classical refraction theory.  This
+     amounts to scaling the A coefficient in proportion to (n-1) and
+     the B coefficient almost in the same ratio (see R.M.Green,
+     "Spherical Astronomy", Cambridge University Press, 1985).
+
+  P.T.Wallace   Starlink   6 October 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/av2m.hlp b/math/slalib/doc/av2m.hlp
new file mode 100644
index 00000000..0a98df84
--- /dev/null
+++ b/math/slalib/doc/av2m.hlp
@@ -0,0 +1,37 @@
+.help av2m Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slAV2M (AXVEC, RMAT)
+
+     - - - - -
+      A V 2 M
+     - - - - -
+
+  Form the rotation matrix corresponding to a given axial vector.
+
+  (single precision)
+
+  A rotation matrix describes a rotation about some arbitrary axis.
+  The axis is called the Euler axis, and the angle through which the
+  reference frame rotates is called the Euler angle.  The axial
+  vector supplied to this routine has the same direction as the
+  Euler axis, and its magnitude is the Euler angle in radians.
+
+  Given:
+    AXVEC  r(3)     axial vector (radians)
+
+  Returned:
+    RMAT   r(3,3)   rotation matrix
+
+  If AXVEC is null, the unit matrix is returned.
+
+  The reference frame rotates clockwise as seen looking along
+  the axial vector from the origin.
+
+  P.T.Wallace   Starlink   June 1989
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/bear.hlp b/math/slalib/doc/bear.hlp
new file mode 100644
index 00000000..97e4f13d
--- /dev/null
+++ b/math/slalib/doc/bear.hlp
@@ -0,0 +1,30 @@
+.help bear Jun99 "Slalib Package"
+.nf
+
+      REAL FUNCTION slBEAR (A1, B1, A2, B2)
+
+     - - - - -
+      B E A R
+     - - - - -
+
+  Bearing (position angle) of one point on a sphere relative to another
+  (single precision)
+
+  Given:
+     A1,B1    r    spherical coordinates of one point
+     A2,B2    r    spherical coordinates of the other point
+
+  (The spherical coordinates are RA,Dec, Long,Lat etc, in radians.)
+
+  The result is the bearing (position angle), in radians, of point
+  A2,B2 as seen from point A1,B1.  It is in the range +/- pi.  If
+  A2,B2 is due east of A1,B1 the bearing is +pi/2.  Zero is returned
+  if the two points are coincident.
+
+  P.T.Wallace   Starlink   23 March 1991
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/caf2r.hlp b/math/slalib/doc/caf2r.hlp
new file mode 100644
index 00000000..7533ff94
--- /dev/null
+++ b/math/slalib/doc/caf2r.hlp
@@ -0,0 +1,38 @@
+.help caf2r Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCAFR (IDEG, IAMIN, ASEC, RAD, J)
+
+     - - - - - -
+      C A F R
+     - - - - - -
+
+  Convert degrees, arcminutes, arcseconds to radians
+  (single precision)
+
+  Given:
+     IDEG        int       degrees
+     IAMIN       int       arcminutes
+     ASEC        real      arcseconds
+
+  Returned:
+     RAD         real      angle in radians
+     J           int       status:  0 = OK
+                                    1 = IDEG outside range 0-359
+                                    2 = IAMIN outside range 0-59
+                                    3 = ASEC outside range 0-59.999...
+
+  Notes:
+
+  1)  The result is computed even if any of the range checks
+      fail.
+
+  2)  The sign must be dealt with outside this routine.
+
+  P.T.Wallace   Starlink   23 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/caldj.hlp b/math/slalib/doc/caldj.hlp
new file mode 100644
index 00000000..1504c667
--- /dev/null
+++ b/math/slalib/doc/caldj.hlp
@@ -0,0 +1,38 @@
+.help caldj Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCADJ (IY, IM, ID, DJM, J)
+
+     - - - - - -
+      C A D J
+     - - - - - -
+
+  Gregorian Calendar to Modified Julian Date
+
+  (Includes century default feature:  use slCLDJ for years
+   before 100AD.)
+
+  Given:
+     IY,IM,ID     int    year, month, day in Gregorian calendar
+
+  Returned:
+     DJM          dp     modified Julian Date (JD-2400000.5) for 0 hrs
+     J            int    status:
+                           0 = OK
+                           1 = bad year   (MJD not computed)
+                           2 = bad month  (MJD not computed)
+                           3 = bad day    (MJD computed)
+
+  Acceptable years are 00-49, interpreted as 2000-2049,
+                       50-99,     "       "  1950-1999,
+                       100 upwards, interpreted literally.
+
+  Called:  slCLDJ
+
+  P.T.Wallace   Starlink   November 1985
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/calyd.hlp b/math/slalib/doc/calyd.hlp
new file mode 100644
index 00000000..7011cc41
--- /dev/null
+++ b/math/slalib/doc/calyd.hlp
@@ -0,0 +1,49 @@
+.help calyd Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCAYD (IY, IM, ID, NY, ND, J)
+
+     - - - - - -
+      C A Y D
+     - - - - - -
+
+  Gregorian calendar date to year and day in year (in a Julian
+  calendar aligned to the 20th/21st century Gregorian calendar).
+
+  (Includes century default feature:  use slCLYD for years
+   before 100AD.)
+
+  Given:
+     IY,IM,ID   int    year, month, day in Gregorian calendar
+                       (year may optionally omit the century)
+  Returned:
+     NY         int    year (re-aligned Julian calendar)
+     ND         int    day in year (1 = January 1st)
+     J          int    status:
+                         0 = OK
+                         1 = bad year (before -4711)
+                         2 = bad month
+                         3 = bad day (but conversion performed)
+
+  Notes:
+
+  1  This routine exists to support the low-precision routines
+     slERTH, slMOON and slECOR.
+
+  2  Between 1900 March 1 and 2100 February 28 it returns answers
+     which are consistent with the ordinary Gregorian calendar.
+     Outside this range there will be a discrepancy which increases
+     by one day for every non-leap century year.
+
+  3  Years in the range 50-99 are interpreted as 1950-1999, and
+     years in the range 00-49 are interpreted as 2000-2049.
+
+  Called:  slCLYD
+
+  P.T.Wallace   Starlink   23 November 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/cc2s.hlp b/math/slalib/doc/cc2s.hlp
new file mode 100644
index 00000000..8a16e76e
--- /dev/null
+++ b/math/slalib/doc/cc2s.hlp
@@ -0,0 +1,33 @@
+.help cc2s Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCC2S (V, A, B)
+
+     - - - - -
+      C C 2 S
+     - - - - -
+
+  Direction cosines to spherical coordinates (single precision)
+
+  Given:
+     V     r(3)   x,y,z vector
+
+  Returned:
+     A,B   r      spherical coordinates in radians
+
+  The spherical coordinates are longitude (+ve anticlockwise
+  looking from the +ve latitude pole) and latitude.  The
+  Cartesian coordinates are right handed, with the x axis
+  at zero longitude and latitude, and the z axis at the
+  +ve latitude pole.
+
+  If V is null, zero A and B are returned.
+  At either pole, zero A is returned.
+
+  P.T.Wallace   Starlink   July 1989
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/cc62s.hlp b/math/slalib/doc/cc62s.hlp
new file mode 100644
index 00000000..ffd20cb8
--- /dev/null
+++ b/math/slalib/doc/cc62s.hlp
@@ -0,0 +1,30 @@
+.help cc62s Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slC62S (V, A, B, R, AD, BD, RD)
+
+     - - - - - -
+      C 6 2 S
+     - - - - - -
+
+  Conversion of position & velocity in Cartesian coordinates
+  to spherical coordinates (single precision)
+
+  Given:
+     V      r(6)   Cartesian position & velocity vector
+
+  Returned:
+     A      r      longitude (radians)
+     B      r      latitude (radians)
+     R      r      radial coordinate
+     AD     r      longitude derivative (radians per unit time)
+     BD     r      latitude derivative (radians per unit time)
+     RD     r      radial derivative
+
+  P.T.Wallace   Starlink   28 April 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/cd2tf.hlp b/math/slalib/doc/cd2tf.hlp
new file mode 100644
index 00000000..52e66f62
--- /dev/null
+++ b/math/slalib/doc/cd2tf.hlp
@@ -0,0 +1,47 @@
+.help cd2tf Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCDTF (NDP, DAYS, SIGN, IHMSF)
+
+     - - - - - -
+      C D T F
+     - - - - - -
+
+  Convert an interval in days into hours, minutes, seconds
+
+  (single precision)
+
+  Given:
+     NDP       int      number of decimal places of seconds
+     DAYS      real     interval in days
+
+  Returned:
+     SIGN      char     '+' or '-'
+     IHMSF     int(4)   hours, minutes, seconds, fraction
+
+  Notes:
+
+     1)  NDP less than zero is interpreted as zero.
+
+     2)  The largest useful value for NDP is determined by the size of
+         DAYS, the format of REAL floating-point numbers on the target
+         machine, and the risk of overflowing IHMSF(4).  For example,
+         on the VAX, for DAYS up to 1.0, the available floating-point
+         precision corresponds roughly to NDP=3.  This is well below
+         the ultimate limit of NDP=9 set by the capacity of the 32-bit
+         integer IHMSF(4).
+
+     3)  The absolute value of DAYS may exceed 1.0.  In cases where it
+         does not, it is up to the caller to test for and handle the
+         case where DAYS is very nearly 1.0 and rounds up to 24 hours,
+         by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+
+  Called:  slDDTF
+
+  P.T.Wallace   Starlink   12 December 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/cldj.hlp b/math/slalib/doc/cldj.hlp
new file mode 100644
index 00000000..3f65adb1
--- /dev/null
+++ b/math/slalib/doc/cldj.hlp
@@ -0,0 +1,34 @@
+.help cldj Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCLDJ (IY, IM, ID, DJM, J)
+
+     - - - - -
+      C L D J
+     - - - - -
+
+  Gregorian Calendar to Modified Julian Date
+
+  Given:
+     IY,IM,ID     int    year, month, day in Gregorian calendar
+
+  Returned:
+     DJM          dp     modified Julian Date (JD-2400000.5) for 0 hrs
+     J            int    status:
+                           0 = OK
+                           1 = bad year   (MJD not computed)
+                           2 = bad month  (MJD not computed)
+                           3 = bad day    (MJD computed)
+
+  The year must be -4699 (i.e. 4700BC) or later.
+
+  The algorithm is derived from that of Hatcher 1984
+  (QJRAS 25, 53-55).
+
+  P.T.Wallace   Starlink   11 March 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/clyd.hlp b/math/slalib/doc/clyd.hlp
new file mode 100644
index 00000000..7afbe1aa
--- /dev/null
+++ b/math/slalib/doc/clyd.hlp
@@ -0,0 +1,50 @@
+.help clyd Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCLYD (IY, IM, ID, NY, ND, JSTAT)
+
+     - - - - -
+      C L Y D
+     - - - - -
+
+  Gregorian calendar to year and day in year (in a Julian calendar
+  aligned to the 20th/21st century Gregorian calendar).
+
+  Given:
+     IY,IM,ID   i    year, month, day in Gregorian calendar
+
+  Returned:
+     NY         i    year (re-aligned Julian calendar)
+     ND         i    day in year (1 = January 1st)
+     JSTAT      i    status:
+                       0 = OK
+                       1 = bad year (before -4711)
+                       2 = bad month
+                       3 = bad day (but conversion performed)
+
+  Notes:
+
+  1  This routine exists to support the low-precision routines
+     slERTH, slMOON and slECOR.
+
+  2  Between 1900 March 1 and 2100 February 28 it returns answers
+     which are consistent with the ordinary Gregorian calendar.
+     Outside this range there will be a discrepancy which increases
+     by one day for every non-leap century year.
+
+  3  The essence of the algorithm is first to express the Gregorian
+     date as a Julian Day Number and then to convert this back to
+     a Julian calendar date, with day-in-year instead of month and
+     day.  See 12.92-1 and 12.95-1 in the reference.
+
+  Reference:  Explanatory Supplement to the Astronomical Almanac,
+              ed P.K.Seidelmann, University Science Books (1992),
+              p604-606.
+
+  P.T.Wallace   Starlink   26 November 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/cr2af.hlp b/math/slalib/doc/cr2af.hlp
new file mode 100644
index 00000000..2a1863ca
--- /dev/null
+++ b/math/slalib/doc/cr2af.hlp
@@ -0,0 +1,46 @@
+.help cr2af Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCRAF (NDP, ANGLE, SIGN, IDMSF)
+
+     - - - - - -
+      C R A F
+     - - - - - -
+
+  Convert an angle in radians into degrees, arcminutes, arcseconds
+  (single precision)
+
+  Given:
+     NDP       int      number of decimal places of arcseconds
+     ANGLE     real     angle in radians
+
+  Returned:
+     SIGN      char     '+' or '-'
+     IDMSF     int(4)   degrees, arcminutes, arcseconds, fraction
+
+  Notes:
+
+     1)  NDP less than zero is interpreted as zero.
+
+     2)  The largest useful value for NDP is determined by the size of
+         ANGLE, the format of REAL floating-point numbers on the target
+         machine, and the risk of overflowing IDMSF(4).  For example,
+         on the VAX, for ANGLE up to 2pi, the available floating-point
+         precision corresponds roughly to NDP=3.  This is well below
+         the ultimate limit of NDP=9 set by the capacity of the 32-bit
+         integer IHMSF(4).
+
+     3)  The absolute value of ANGLE may exceed 2pi.  In cases where it
+         does not, it is up to the caller to test for and handle the
+         case where ANGLE is very nearly 2pi and rounds up to 360 deg,
+         by testing for IDMSF(1)=360 and setting IDMSF(1-4) to zero.
+
+  Called:  slCDTF
+
+  P.T.Wallace   Starlink   18 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/cr2tf.hlp b/math/slalib/doc/cr2tf.hlp
new file mode 100644
index 00000000..719db50e
--- /dev/null
+++ b/math/slalib/doc/cr2tf.hlp
@@ -0,0 +1,46 @@
+.help cr2tf Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCRTF (NDP, ANGLE, SIGN, IHMSF)
+
+     - - - - - -
+      C R T F
+     - - - - - -
+
+  Convert an angle in radians into hours, minutes, seconds
+  (single precision)
+
+  Given:
+     NDP       int      number of decimal places of seconds
+     ANGLE     real     angle in radians
+
+  Returned:
+     SIGN      char     '+' or '-'
+     IHMSF     int(4)   hours, minutes, seconds, fraction
+
+  Notes:
+
+  1)  NDP less than zero is interpreted as zero.
+
+  2)  The largest useful value for NDP is determined by the size of
+      ANGLE, the format of REAL floating-point numbers on the target
+      machine, and the risk of overflowing IHMSF(4).  For example,
+      on the VAX, for ANGLE up to 2pi, the available floating-point
+      precision corresponds roughly to NDP=3.  This is well below
+      the ultimate limit of NDP=9 set by the capacity of the 32-bit
+      integer IHMSF(4).
+
+  3)  The absolute value of ANGLE may exceed 2pi.  In cases where it
+      does not, it is up to the caller to test for and handle the
+      case where ANGLE is very nearly 2pi and rounds up to 24 hours,
+      by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+
+  Called:  slCDTF
+
+  P.T.Wallace   Starlink   18 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/cs2c.hlp b/math/slalib/doc/cs2c.hlp
new file mode 100644
index 00000000..df71c82c
--- /dev/null
+++ b/math/slalib/doc/cs2c.hlp
@@ -0,0 +1,31 @@
+.help cs2c Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCS2C (A, B, V)
+
+     - - - - -
+      C S 2 C
+     - - - - -
+
+  Spherical coordinates to direction cosines (single precision)
+
+  Given:
+     A,B      real      spherical coordinates in radians
+                        (RA,Dec), (Long,Lat) etc
+
+  Returned:
+     V        real(3)   x,y,z unit vector
+
+  The spherical coordinates are longitude (+ve anticlockwise
+  looking from the +ve latitude pole) and latitude.  The
+  Cartesian coordinates are right handed, with the x axis
+  at zero longitude and latitude, and the z axis at the
+  +ve latitude pole.
+
+  P.T.Wallace   Starlink   October 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/cs2c6.hlp b/math/slalib/doc/cs2c6.hlp
new file mode 100644
index 00000000..0b69377d
--- /dev/null
+++ b/math/slalib/doc/cs2c6.hlp
@@ -0,0 +1,30 @@
+.help cs2c6 Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slS2C6 (A, B, R, AD, BD, RD, V)
+
+     - - - - - -
+      S 2 C 6
+     - - - - - -
+
+  Conversion of position & velocity in spherical coordinates
+  to Cartesian coordinates (single precision)
+
+  Given:
+     A     r      longitude (radians)
+     B     r      latitude (radians)
+     R     r      radial coordinate
+     AD    r      longitude derivative (radians per unit time)
+     BD    r      latitude derivative (radians per unit time)
+     RD    r      radial derivative
+
+  Returned:
+     V     r(6)   Cartesian position & velocity vector
+
+  P.T.Wallace   Starlink   November 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ctf2d.hlp b/math/slalib/doc/ctf2d.hlp
new file mode 100644
index 00000000..e8c985c3
--- /dev/null
+++ b/math/slalib/doc/ctf2d.hlp
@@ -0,0 +1,37 @@
+.help ctf2d Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCTFD (IHOUR, IMIN, SEC, DAYS, J)
+
+     - - - - - -
+      C T F D
+     - - - - - -
+
+  Convert hours, minutes, seconds to days (single precision)
+
+  Given:
+     IHOUR       int       hours
+     IMIN        int       minutes
+     SEC         real      seconds
+
+  Returned:
+     DAYS        real      interval in days
+     J           int       status:  0 = OK
+                                    1 = IHOUR outside range 0-23
+                                    2 = IMIN outside range 0-59
+                                    3 = SEC outside range 0-59.999...
+
+  Notes:
+
+  1)  The result is computed even if any of the range checks
+      fail.
+
+  2)  The sign must be dealt with outside this routine.
+
+  P.T.Wallace   Starlink   November 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ctf2r.hlp b/math/slalib/doc/ctf2r.hlp
new file mode 100644
index 00000000..72a1fb56
--- /dev/null
+++ b/math/slalib/doc/ctf2r.hlp
@@ -0,0 +1,40 @@
+.help ctf2r Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slCTFR (IHOUR, IMIN, SEC, RAD, J)
+
+     - - - - - -
+      C T F R
+     - - - - - -
+
+  Convert hours, minutes, seconds to radians (single precision)
+
+  Given:
+     IHOUR       int       hours
+     IMIN        int       minutes
+     SEC         real      seconds
+
+  Returned:
+     RAD         real      angle in radians
+     J           int       status:  0 = OK
+                                    1 = IHOUR outside range 0-23
+                                    2 = IMIN outside range 0-59
+                                    3 = SEC outside range 0-59.999...
+
+  Called:
+     slCTFD
+
+  Notes:
+
+  1)  The result is computed even if any of the range checks
+      fail.
+
+  2)  The sign must be dealt with outside this routine.
+
+  P.T.Wallace   Starlink   November 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/daf2r.hlp b/math/slalib/doc/daf2r.hlp
new file mode 100644
index 00000000..f0cf7434
--- /dev/null
+++ b/math/slalib/doc/daf2r.hlp
@@ -0,0 +1,36 @@
+.help daf2r Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDAFR (IDEG, IAMIN, ASEC, RAD, J)
+
+     - - - - - -
+      D A F R
+     - - - - - -
+
+  Convert degrees, arcminutes, arcseconds to radians
+  (double precision)
+
+  Given:
+     IDEG        int       degrees
+     IAMIN       int       arcminutes
+     ASEC        dp        arcseconds
+
+  Returned:
+     RAD         dp        angle in radians
+     J           int       status:  0 = OK
+                                    1 = IDEG outside range 0-359
+                                    2 = IAMIN outside range 0-59
+                                    3 = ASEC outside range 0-59.999...
+
+  Notes:
+     1)  The result is computed even if any of the range checks
+         fail.
+     2)  The sign must be dealt with outside this routine.
+
+  P.T.Wallace   Starlink   23 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dafin.hlp b/math/slalib/doc/dafin.hlp
new file mode 100644
index 00000000..2fa24d5c
--- /dev/null
+++ b/math/slalib/doc/dafin.hlp
@@ -0,0 +1,90 @@
+.help dafin Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDAFN (STRING, IPTR, A, J)
+
+     - - - - - -
+      D A F N
+     - - - - - -
+
+  Sexagesimal character string to angle (double precision)
+
+  Given:
+     STRING  c*(*)   string containing deg, arcmin, arcsec fields
+     IPTR      i     pointer to start of decode (1st = 1)
+
+  Returned:
+     IPTR      i     advanced past the decoded angle
+     A         d     angle in radians
+     J         i     status:  0 = OK
+                             +1 = default, A unchanged
+                             -1 = bad degrees      )
+                             -2 = bad arcminutes   )  (note 3)
+                             -3 = bad arcseconds   )
+
+  Example:
+
+    argument    before                           after
+
+    STRING      '-57 17 44.806  12 34 56.7'      unchanged
+    IPTR        1                                16 (points to 12...)
+    A           ?                                -1.00000D0
+    J           ?                                0
+
+    A further call to slDAFN, without adjustment of IPTR, will
+    decode the second angle, 12deg 34min 56.7sec.
+
+  Notes:
+
+     1)  The first three "fields" in STRING are degrees, arcminutes,
+         arcseconds, separated by spaces or commas.  The degrees field
+         may be signed, but not the others.  The decoding is carried
+         out by the DFLTIN routine and is free-format.
+
+     2)  Successive fields may be absent, defaulting to zero.  For
+         zero status, the only combinations allowed are degrees alone,
+         degrees and arcminutes, and all three fields present.  If all
+         three fields are omitted, a status of +1 is returned and A is
+         unchanged.  In all other cases A is changed.
+
+     3)  Range checking:
+
+           The degrees field is not range checked.  However, it is
+           expected to be integral unless the other two fields are absent.
+
+           The arcminutes field is expected to be 0-59, and integral if
+           the arcseconds field is present.  If the arcseconds field
+           is absent, the arcminutes is expected to be 0-59.9999...
+
+           The arcseconds field is expected to be 0-59.9999...
+
+     4)  Decoding continues even when a check has failed.  Under these
+         circumstances the field takes the supplied value, defaulting
+         to zero, and the result A is computed and returned.
+
+     5)  Further fields after the three expected ones are not treated
+         as an error.  The pointer IPTR is left in the correct state
+         for further decoding with the present routine or with DFLTIN
+         etc. See the example, above.
+
+     6)  If STRING contains hours, minutes, seconds instead of degrees
+         etc, or if the required units are turns (or days) instead of
+         radians, the result A should be multiplied as follows:
+
+           for        to obtain    multiply
+           STRING     A in         A by
+
+           d ' "      radians      1       =  1D0
+           d ' "      turns        1/2pi   =  0.1591549430918953358D0
+           h m s      radians      15      =  15D0
+           h m s      days         15/2pi  =  2.3873241463784300365D0
+
+  Called:  slDFLI
+
+  P.T.Wallace   Starlink   1 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dat.hlp b/math/slalib/doc/dat.hlp
new file mode 100644
index 00000000..20777dc5
--- /dev/null
+++ b/math/slalib/doc/dat.hlp
@@ -0,0 +1,55 @@
+.help dat Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slDAT (UTC)
+
+     - - - -
+      D A T
+     - - - -
+
+  Increment to be applied to Coordinated Universal Time UTC to give
+  International Atomic Time TAI (double precision)
+
+  Given:
+     UTC      d      UTC date as a modified JD (JD-2400000.5)
+
+  Result:  TAI-UTC in seconds
+
+  Notes:
+
+  1  The UTC is specified to be a date rather than a time to indicate
+     that care needs to be taken not to specify an instant which lies
+     within a leap second.  Though in most cases UTC can include the
+     fractional part, correct behaviour on the day of a leap second
+     can only be guaranteed up to the end of the second 23:59:59.
+
+  2  For epochs from 1961 January 1 onwards, the expressions from the
+     file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used.
+
+  3  The 5ms timestep at 1961 January 1 is taken from 2.58.1 (p87) of
+     the 1992 Explanatory Supplement.
+
+  4  UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper
+     to call the routine with an earlier epoch.  However, if this
+     is attempted, the TAI-UTC expression for the year 1960 is used.
+
+
+     :-----------------------------------------:
+     :                                         :
+     :                IMPORTANT                :
+     :                                         :
+     :  This routine must be updated on each   :
+     :     occasion that a leap second is      :
+     :                announced                :
+     :                                         :
+     :  Latest leap second:  1999 January 1    :
+     :                                         :
+     :-----------------------------------------:
+
+  P.T.Wallace   Starlink   31 May 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dav2m.hlp b/math/slalib/doc/dav2m.hlp
new file mode 100644
index 00000000..26d5fae6
--- /dev/null
+++ b/math/slalib/doc/dav2m.hlp
@@ -0,0 +1,36 @@
+.help dav2m Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDAVM (AXVEC, RMAT)
+
+     - - - - - -
+      D A V M
+     - - - - - -
+
+  Form the rotation matrix corresponding to a given axial vector.
+  (double precision)
+
+  A rotation matrix describes a rotation about some arbitrary axis.
+  The axis is called the Euler axis, and the angle through which the
+  reference frame rotates is called the Euler angle.  The axial
+  vector supplied to this routine has the same direction as the
+  Euler axis, and its magnitude is the Euler angle in radians.
+
+  Given:
+    AXVEC  d(3)     axial vector (radians)
+
+  Returned:
+    RMAT   d(3,3)   rotation matrix
+
+  If AXVEC is null, the unit matrix is returned.
+
+  The reference frame rotates clockwise as seen looking along
+  the axial vector from the origin.
+
+  P.T.Wallace   Starlink   June 1989
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dbear.hlp b/math/slalib/doc/dbear.hlp
new file mode 100644
index 00000000..8d796e61
--- /dev/null
+++ b/math/slalib/doc/dbear.hlp
@@ -0,0 +1,30 @@
+.help dbear Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slDBER (A1, B1, A2, B2)
+
+     - - - - - -
+      D B E R
+     - - - - - -
+
+  Bearing (position angle) of one point on a sphere relative to another
+  (double precision)
+
+  Given:
+     A1,B1    d    spherical coordinates of one point
+     A2,B2    d    spherical coordinates of the other point
+
+  (The spherical coordinates are RA,Dec, Long,Lat etc, in radians.)
+
+  The result is the bearing (position angle), in radians, of point
+  A2,B2 as seen from point A1,B1.  It is in the range +/- pi.  If
+  A2,B2 is due east of A1,B1 the bearing is +pi/2.  Zero is returned
+  if the two points are coincident.
+
+  P.T.Wallace   Starlink   23 March 1991
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dbjin.hlp b/math/slalib/doc/dbjin.hlp
new file mode 100644
index 00000000..017333dd
--- /dev/null
+++ b/math/slalib/doc/dbjin.hlp
@@ -0,0 +1,52 @@
+.help dbjin Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDBJI (STRING, NSTRT, DRESLT, J1, J2)
+
+     - - - - - -
+      D B J I
+     - - - - - -
+
+  Convert free-format input into double precision floating point,
+  using DFLTIN but with special syntax extensions.
+
+  The purpose of the syntax extensions is to help cope with mixed
+  FK4 and FK5 data.  In addition to the syntax accepted by DFLTIN,
+  the following two extensions are recognized by DBJIN:
+
+     1)  A valid non-null field preceded by the character 'B'
+         (or 'b') is accepted.
+
+     2)  A valid non-null field preceded by the character 'J'
+         (or 'j') is accepted.
+
+  The calling program is notified of the incidence of either of these
+  extensions through an supplementary status argument.  The rest of
+  the arguments are as for DFLTIN.
+
+  Given:
+     STRING      char       string containing field to be decoded
+     NSTRT       int        pointer to 1st character of field in string
+
+  Returned:
+     NSTRT       int        incremented
+     DRESLT      double     result
+     J1          int        DFLTIN status: -1 = -OK
+                                            0 = +OK
+                                           +1 = null field
+                                           +2 = error
+     J2          int        syntax flag:  0 = normal DFLTIN syntax
+                                         +1 = 'B' or 'b'
+                                         +2 = 'J' or 'j'
+
+  Called:  slDFLI
+
+  For details of the basic syntax, see slDFLI.
+
+  P.T.Wallace   Starlink   23 November 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dc62s.hlp b/math/slalib/doc/dc62s.hlp
new file mode 100644
index 00000000..0294205b
--- /dev/null
+++ b/math/slalib/doc/dc62s.hlp
@@ -0,0 +1,30 @@
+.help dc62s Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDC6S (V, A, B, R, AD, BD, RD)
+
+     - - - - - -
+      D C 6 S
+     - - - - - -
+
+  Conversion of position & velocity in Cartesian coordinates
+  to spherical coordinates (double precision)
+
+  Given:
+     V      d(6)   Cartesian position & velocity vector
+
+  Returned:
+     A      d      longitude (radians)
+     B      d      latitude (radians)
+     R      d      radial coordinate
+     AD     d      longitude derivative (radians per unit time)
+     BD     d      latitude derivative (radians per unit time)
+     RD     d      radial derivative
+
+  P.T.Wallace   Starlink   28 April 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dcc2s.hlp b/math/slalib/doc/dcc2s.hlp
new file mode 100644
index 00000000..ace02cf7
--- /dev/null
+++ b/math/slalib/doc/dcc2s.hlp
@@ -0,0 +1,33 @@
+.help dcc2s Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDC2S (V, A, B)
+
+     - - - - - -
+      D C 2 S
+     - - - - - -
+
+  Direction cosines to spherical coordinates (double precision)
+
+  Given:
+     V     d(3)   x,y,z vector
+
+  Returned:
+     A,B   d      spherical coordinates in radians
+
+  The spherical coordinates are longitude (+ve anticlockwise
+  looking from the +ve latitude pole) and latitude.  The
+  Cartesian coordinates are right handed, with the x axis
+  at zero longitude and latitude, and the z axis at the
+  +ve latitude pole.
+
+  If V is null, zero A and B are returned.
+  At either pole, zero A is returned.
+
+  P.T.Wallace   Starlink   July 1989
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dcmpf.hlp b/math/slalib/doc/dcmpf.hlp
new file mode 100644
index 00000000..914addfd
--- /dev/null
+++ b/math/slalib/doc/dcmpf.hlp
@@ -0,0 +1,70 @@
+.help dcmpf Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDCMF (COEFFS,XZ,YZ,XS,YS,PERP,ORIENT)
+
+     - - - - - -
+      D C M F
+     - - - - - -
+
+  Decompose an [X,Y] linear fit into its constituent parameters:
+  zero points, scales, nonperpendicularity and orientation.
+
+  Given:
+     COEFFS  d(6)      transformation coefficients (see note)
+
+  Returned:
+     XZ       d        x zero point
+     YZ       d        y zero point
+     XS       d        x scale
+     YS       d        y scale
+     PERP     d        nonperpendicularity (radians)
+     ORIENT   d        orientation (radians)
+
+  The model relates two sets of [X,Y] coordinates as follows.
+  Naming the elements of COEFFS:
+
+     COEFFS(1) = A
+     COEFFS(2) = B
+     COEFFS(3) = C
+     COEFFS(4) = D
+     COEFFS(5) = E
+     COEFFS(6) = F
+
+  the model transforms coordinates [X1,Y1] into coordinates
+  [X2,Y2] as follows:
+
+     X2 = A + B*X1 + C*Y1
+     Y2 = D + E*X1 + F*Y1
+
+  The transformation can be decomposed into four steps:
+
+     1)  Zero points:
+
+             x' = XZ + X1
+             y' = YZ + Y1
+
+     2)  Scales:
+
+             x'' = XS*x'
+             y'' = YS*y'
+
+     3)  Nonperpendicularity:
+
+             x''' = cos(PERP/2)*x'' + sin(PERP/2)*y''
+             y''' = sin(PERP/2)*x'' + cos(PERP/2)*y''
+
+     4)  Orientation:
+
+             X2 = cos(ORIENT)*x''' + sin(ORIENT)*y'''
+             Y2 =-sin(ORIENT)*y''' + cos(ORIENT)*y'''
+
+  See also slFTXY, slPXY, slINVF, slXYXY
+
+  P.T.Wallace   Starlink   14 August 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dcs2c.hlp b/math/slalib/doc/dcs2c.hlp
new file mode 100644
index 00000000..50010ea4
--- /dev/null
+++ b/math/slalib/doc/dcs2c.hlp
@@ -0,0 +1,31 @@
+.help dcs2c Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDS2C (A, B, V)
+
+     - - - - - -
+      D S 2 C
+     - - - - - -
+
+  Spherical coordinates to direction cosines (double precision)
+
+  Given:
+     A,B       dp      spherical coordinates in radians
+                        (RA,Dec), (Long,Lat) etc
+
+  Returned:
+     V         dp(3)   x,y,z unit vector
+
+  The spherical coordinates are longitude (+ve anticlockwise
+  looking from the +ve latitude pole) and latitude.  The
+  Cartesian coordinates are right handed, with the x axis
+  at zero longitude and latitude, and the z axis at the
+  +ve latitude pole.
+
+  P.T.Wallace   Starlink   October 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dd2tf.hlp b/math/slalib/doc/dd2tf.hlp
new file mode 100644
index 00000000..124a7fcc
--- /dev/null
+++ b/math/slalib/doc/dd2tf.hlp
@@ -0,0 +1,44 @@
+.help dd2tf Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDDTF (NDP, DAYS, SIGN, IHMSF)
+
+     - - - - - -
+      D D T F
+     - - - - - -
+
+  Convert an interval in days into hours, minutes, seconds
+  (double precision)
+
+  Given:
+     NDP      i      number of decimal places of seconds
+     DAYS     d      interval in days
+
+  Returned:
+     SIGN     c      '+' or '-'
+     IHMSF    i(4)   hours, minutes, seconds, fraction
+
+  Notes:
+
+     1)  NDP less than zero is interpreted as zero.
+
+     2)  The largest useful value for NDP is determined by the size
+         of DAYS, the format of DOUBLE PRECISION floating-point numbers
+         on the target machine, and the risk of overflowing IHMSF(4).
+         For example, on the VAX, for DAYS up to 1D0, the available
+         floating-point precision corresponds roughly to NDP=12.
+         However, the practical limit is NDP=9, set by the capacity of
+         the 32-bit integer IHMSF(4).
+
+     3)  The absolute value of DAYS may exceed 1D0.  In cases where it
+         does not, it is up to the caller to test for and handle the
+         case where DAYS is very nearly 1D0 and rounds up to 24 hours,
+         by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+
+  P.T.Wallace   Starlink   19 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/de2h.hlp b/math/slalib/doc/de2h.hlp
new file mode 100644
index 00000000..7e5bcb06
--- /dev/null
+++ b/math/slalib/doc/de2h.hlp
@@ -0,0 +1,59 @@
+.help de2h Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDE2H (HA, DEC, PHI, AZ, EL)
+
+     - - - - -
+      D E 2 H
+     - - - - -
+
+  Equatorial to horizon coordinates:  HA,Dec to Az,El
+
+  (double precision)
+
+  Given:
+     HA      d     hour angle
+     DEC     d     declination
+     PHI     d     observatory latitude
+
+  Returned:
+     AZ      d     azimuth
+     EL      d     elevation
+
+  Notes:
+
+  1)  All the arguments are angles in radians.
+
+  2)  Azimuth is returned in the range 0-2pi;  north is zero,
+      and east is +pi/2.  Elevation is returned in the range
+      +/-pi/2.
+
+  3)  The latitude must be geodetic.  In critical applications,
+      corrections for polar motion should be applied.
+
+  4)  In some applications it will be important to specify the
+      correct type of hour angle and declination in order to
+      produce the required type of azimuth and elevation.  In
+      particular, it may be important to distinguish between
+      elevation as affected by refraction, which would
+      require the "observed" HA,Dec, and the elevation
+      in vacuo, which would require the "topocentric" HA,Dec.
+      If the effects of diurnal aberration can be neglected, the
+      "apparent" HA,Dec may be used instead of the topocentric
+      HA,Dec.
+
+  5)  No range checking of arguments is carried out.
+
+  6)  In applications which involve many such calculations, rather
+      than calling the present routine it will be more efficient to
+      use inline code, having previously computed fixed terms such
+      as sine and cosine of latitude, and (for tracking a star)
+      sine and cosine of declination.
+
+  P.T.Wallace   Starlink   9 July 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/deuler.hlp b/math/slalib/doc/deuler.hlp
new file mode 100644
index 00000000..1dc55844
--- /dev/null
+++ b/math/slalib/doc/deuler.hlp
@@ -0,0 +1,50 @@
+.help deuler Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDEUL (ORDER, PHI, THETA, PSI, RMAT)
+
+     - - - - - - -
+      D E U L
+     - - - - - - -
+
+  Form a rotation matrix from the Euler angles - three successive
+  rotations about specified Cartesian axes (double precision)
+
+  Given:
+    ORDER   c*(*)   specifies about which axes the rotations occur
+    PHI     d       1st rotation (radians)
+    THETA   d       2nd rotation (   "   )
+    PSI     d       3rd rotation (   "   )
+
+  Returned:
+    RMAT    d(3,3)  rotation matrix
+
+  A rotation is positive when the reference frame rotates
+  anticlockwise as seen looking towards the origin from the
+  positive region of the specified axis.
+
+  The characters of ORDER define which axes the three successive
+  rotations are about.  A typical value is 'ZXZ', indicating that
+  RMAT is to become the direction cosine matrix corresponding to
+  rotations of the reference frame through PHI radians about the
+  old Z-axis, followed by THETA radians about the resulting X-axis,
+  then PSI radians about the resulting Z-axis.
+
+  The axis names can be any of the following, in any order or
+  combination:  X, Y, Z, uppercase or lowercase, 1, 2, 3.  Normal
+  axis labeling/numbering conventions apply;  the xyz (=123)
+  triad is right-handed.  Thus, the 'ZXZ' example given above
+  could be written 'zxz' or '313' (or even 'ZxZ' or '3xZ').  ORDER
+  is terminated by length or by the first unrecognized character.
+
+  Fewer than three rotations are acceptable, in which case the later
+  angle arguments are ignored.  If all rotations are zero, the
+  identity matrix is produced.
+
+  P.T.Wallace   Starlink   23 May 1997
+
+  Copyright (C) 1997 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dfltin.hlp b/math/slalib/doc/dfltin.hlp
new file mode 100644
index 00000000..be42311f
--- /dev/null
+++ b/math/slalib/doc/dfltin.hlp
@@ -0,0 +1,118 @@
+.help dfltin Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDFLI (STRING, NSTRT, DRESLT, JFLAG)
+
+     - - - - - - -
+      D F L I
+     - - - - - - -
+
+  Convert free-format input into double precision floating point
+
+  Given:
+     STRING     c     string containing number to be decoded
+     NSTRT      i     pointer to where decoding is to start
+     DRESLT     d     current value of result
+
+  Returned:
+     NSTRT      i      advanced to next number
+     DRESLT     d      result
+     JFLAG      i      status: -1 = -OK, 0 = +OK, 1 = null, 2 = error
+
+  Notes:
+
+     1     The reason DFLTIN has separate OK status values for +
+           and - is to enable minus zero to be detected.   This is
+           of crucial importance when decoding mixed-radix numbers.
+           For example, an angle expressed as deg, arcmin, arcsec
+           may have a leading minus sign but a zero degrees field.
+
+     2     A TAB is interpreted as a space, and lowercase characters
+           are interpreted as uppercase.
+
+     3     The basic format is the sequence of fields #^.^@#^, where
+           # is a sign character + or -, ^ means a string of decimal
+           digits, and @, which indicates an exponent, means D or E.
+           Various combinations of these fields can be omitted, and
+           embedded blanks are permissible in certain places.
+
+     4     Spaces:
+
+             .  Leading spaces are ignored.
+
+             .  Embedded spaces are allowed only after +, -, D or E,
+                and after the decomal point if the first sequence of
+                digits is absent.
+
+             .  Trailing spaces are ignored;  the first signifies
+                end of decoding and subsequent ones are skipped.
+
+     5     Delimiters:
+
+             .  Any character other than +,-,0-9,.,D,E or space may be
+                used to signal the end of the number and terminate
+                decoding.
+
+             .  Comma is recognized by DFLTIN as a special case;  it
+                is skipped, leaving the pointer on the next character.
+                See 13, below.
+
+     6     Both signs are optional.  The default is +.
+
+     7     The mantissa ^.^ defaults to 1.
+
+     8     The exponent @#^ defaults to D0.
+
+     9     The strings of decimal digits may be of any length.
+
+     10    The decimal point is optional for whole numbers.
+
+     11    A "null result" occurs when the string of characters being
+           decoded does not begin with +,-,0-9,.,D or E, or consists
+           entirely of spaces.  When this condition is detected, JFLAG
+           is set to 1 and DRESLT is left untouched.
+
+     12    NSTRT = 1 for the first character in the string.
+
+     13    On return from DFLTIN, NSTRT is set ready for the next
+           decode - following trailing blanks and any comma.  If a
+           delimiter other than comma is being used, NSTRT must be
+           incremented before the next call to DFLTIN, otherwise
+           all subsequent calls will return a null result.
+
+     14    Errors (JFLAG=2) occur when:
+
+             .  a +, -, D or E is left unsatisfied;  or
+
+             .  the decimal point is present without at least
+                one decimal digit before or after it;  or
+
+             .  an exponent more than 100 has been presented.
+
+     15    When an error has been detected, NSTRT is left
+           pointing to the character following the last
+           one used before the error came to light.  This
+           may be after the point at which a more sophisticated
+           program could have detected the error.  For example,
+           DFLTIN does not detect that '1D999' is unacceptable
+           (on a computer where this is so) until the entire number
+           has been decoded.
+
+     16    Certain highly unlikely combinations of mantissa &
+           exponent can cause arithmetic faults during the
+           decode, in some cases despite the fact that they
+           together could be construed as a valid number.
+
+     17    Decoding is left to right, one pass.
+
+     18    See also FLOTIN and INTIN
+
+  Called:  slICHF
+
+  P.T.Wallace   Starlink   18 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dh2e.hlp b/math/slalib/doc/dh2e.hlp
new file mode 100644
index 00000000..965653c8
--- /dev/null
+++ b/math/slalib/doc/dh2e.hlp
@@ -0,0 +1,58 @@
+.help dh2e Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDH2E (AZ, EL, PHI, HA, DEC)
+
+     - - - - -
+      D E 2 H
+     - - - - -
+
+  Horizon to equatorial coordinates:  Az,El to HA,Dec
+
+  (double precision)
+
+  Given:
+     AZ      d     azimuth
+     EL      d     elevation
+     PHI     d     observatory latitude
+
+  Returned:
+     HA      d     hour angle
+     DEC     d     declination
+
+  Notes:
+
+  1)  All the arguments are angles in radians.
+
+  2)  The sign convention for azimuth is north zero, east +pi/2.
+
+  3)  HA is returned in the range +/-pi.  Declination is returned
+      in the range +/-pi/2.
+
+  4)  The latitude is (in principle) geodetic.  In critical
+      applications, corrections for polar motion should be applied.
+
+  5)  In some applications it will be important to specify the
+      correct type of elevation in order to produce the required
+      type of HA,Dec.  In particular, it may be important to
+      distinguish between the elevation as affected by refraction,
+      which will yield the "observed" HA,Dec, and the elevation
+      in vacuo, which will yield the "topocentric" HA,Dec.  If the
+      effects of diurnal aberration can be neglected, the
+      topocentric HA,Dec may be used as an approximation to the
+      "apparent" HA,Dec.
+
+  6)  No range checking of arguments is done.
+
+  7)  In applications which involve many such calculations, rather
+      than calling the present routine it will be more efficient to
+      use inline code, having previously computed fixed terms such
+      as sine and cosine of latitude.
+
+  P.T.Wallace   Starlink   21 February 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dimxv.hlp b/math/slalib/doc/dimxv.hlp
new file mode 100644
index 00000000..805f124a
--- /dev/null
+++ b/math/slalib/doc/dimxv.hlp
@@ -0,0 +1,32 @@
+.help dimxv Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDIMV (DM, VA, VB)
+
+     - - - - - -
+      D I M V
+     - - - - - -
+
+  Performs the 3-D backward unitary transformation:
+
+     vector VB = (inverse of matrix DM) * vector VA
+
+  (double precision)
+
+  (n.b.  the matrix must be unitary, as this routine assumes that
+   the inverse and transpose are identical)
+
+  Given:
+     DM       dp(3,3)    matrix
+     VA       dp(3)      vector
+
+  Returned:
+     VB       dp(3)      result vector
+
+  P.T.Wallace   Starlink   March 1986
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/djcal.hlp b/math/slalib/doc/djcal.hlp
new file mode 100644
index 00000000..d65c81bd
--- /dev/null
+++ b/math/slalib/doc/djcal.hlp
@@ -0,0 +1,38 @@
+.help djcal Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDJCA (NDP, DJM, IYMDF, J)
+
+     - - - - - -
+      D J C A
+     - - - - - -
+
+  Modified Julian Date to Gregorian Calendar, expressed
+  in a form convenient for formatting messages (namely
+  rounded to a specified precision, and with the fields
+  stored in a single array)
+
+  Given:
+     NDP      i      number of decimal places of days in fraction
+     DJM      d      modified Julian Date (JD-2400000.5)
+
+  Returned:
+     IYMDF    i(4)   year, month, day, fraction in Gregorian
+                     calendar
+     J        i      status:  nonzero = out of range
+
+  Any date after 4701BC March 1 is accepted.
+
+  NDP should be 4 or less if internal overflows are to be avoided
+  on machines which use 32-bit integers.
+
+  The algorithm is derived from that of Hatcher 1984
+  (QJRAS 25, 53-55).
+
+  P.T.Wallace   Starlink   27 April 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/djcl.hlp b/math/slalib/doc/djcl.hlp
new file mode 100644
index 00000000..a6327c1d
--- /dev/null
+++ b/math/slalib/doc/djcl.hlp
@@ -0,0 +1,34 @@
+.help djcl Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDJCL (DJM, IY, IM, ID, FD, J)
+
+     - - - - -
+      D J C L
+     - - - - -
+
+  Modified Julian Date to Gregorian year, month, day,
+  and fraction of a day.
+
+  Given:
+     DJM      dp     modified Julian Date (JD-2400000.5)
+
+  Returned:
+     IY       int    year
+     IM       int    month
+     ID       int    day
+     FD       dp     fraction of day
+     J        int    status:
+                       0 = OK
+                      -1 = unacceptable date (before 4701BC March 1)
+
+  The algorithm is derived from that of Hatcher 1984
+  (QJRAS 25, 53-55).
+
+  P.T.Wallace   Starlink   27 April 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dm2av.hlp b/math/slalib/doc/dm2av.hlp
new file mode 100644
index 00000000..6448b842
--- /dev/null
+++ b/math/slalib/doc/dm2av.hlp
@@ -0,0 +1,38 @@
+.help dm2av Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDMAV (RMAT, AXVEC)
+
+     - - - - - -
+      D M A V
+     - - - - - -
+
+  From a rotation matrix, determine the corresponding axial vector.
+  (double precision)
+
+  A rotation matrix describes a rotation about some arbitrary axis.
+  The axis is called the Euler axis, and the angle through which the
+  reference frame rotates is called the Euler angle.  The axial
+  vector returned by this routine has the same direction as the
+  Euler axis, and its magnitude is the Euler angle in radians.  (The
+  magnitude and direction can be separated by means of the routine
+  slDVN.)
+
+  Given:
+    RMAT   d(3,3)   rotation matrix
+
+  Returned:
+    AXVEC  d(3)     axial vector (radians)
+
+  The reference frame rotates clockwise as seen looking along
+  the axial vector from the origin.
+
+  If RMAT is null, so is the result.
+
+  P.T.Wallace   Starlink   24 December 1992
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dmat.hlp b/math/slalib/doc/dmat.hlp
new file mode 100644
index 00000000..7d496345
--- /dev/null
+++ b/math/slalib/doc/dmat.hlp
@@ -0,0 +1,58 @@
+.help dmat Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDMAT (N, A, Y, D, JF, IW)
+
+     - - - - -
+      D M A T
+     - - - - -
+
+  Matrix inversion & solution of simultaneous equations
+  (double precision)
+
+  For the set of n simultaneous equations in n unknowns:
+     A.Y = X
+
+  where:
+     A is a non-singular N x N matrix
+     Y is the vector of N unknowns
+     X is the known vector
+
+  DMATRX computes:
+     the inverse of matrix A
+     the determinant of matrix A
+     the vector of N unknowns
+
+  Arguments:
+
+     symbol  type   dimension           before              after
+
+       N      i                    no. of unknowns       unchanged
+       A      d      (N,N)             matrix             inverse
+       Y      d       (N)              vector            solution
+       D      d                           -             determinant
+     * JF     i                           -           singularity flag
+       IW     i       (N)                 -              workspace
+
+  *  JF is the singularity flag.  If the matrix is non-singular,
+    JF=0 is returned.  If the matrix is singular, JF=-1 & D=0D0 are
+    returned.  In the latter case, the contents of array A on return
+    are undefined.
+
+  Algorithm:
+     Gaussian elimination with partial pivoting.
+
+  Speed:
+     Very fast.
+
+  Accuracy:
+     Fairly accurate - errors 1 to 4 times those of routines optimized
+     for accuracy.
+
+  P.T.Wallace   Starlink   7 February 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dmoon.hlp b/math/slalib/doc/dmoon.hlp
new file mode 100644
index 00000000..5afe24ce
--- /dev/null
+++ b/math/slalib/doc/dmoon.hlp
@@ -0,0 +1,58 @@
+.help dmoon Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDMON (DATE, PV)
+
+     - - - - - -
+      D M O N
+     - - - - - -
+
+  Approximate geocentric position and velocity of the Moon
+  (double precision)
+
+  Given:
+     DATE       D       TDB (loosely ET) as a Modified Julian Date
+                                                    (JD-2400000.5)
+
+  Returned:
+     PV         D(6)    Moon x,y,z,xdot,ydot,zdot, mean equator and
+                                         equinox of date (AU, AU/s)
+
+  Notes:
+
+  1  This routine is a full implementation of the algorithm
+     published by Meeus (see reference).
+
+  2  Meeus quotes accuracies of 10 arcsec in longitude, 3 arcsec in
+     latitude and 0.2 arcsec in HP (equivalent to about 20 km in
+     distance).  Comparison with JPL DE200 over the interval
+     1960-2025 gives RMS errors of 3.7 arcsec and 83 mas/hour in
+     longitude, 2.3 arcsec and 48 mas/hour in latitude, 11 km
+     and 81 mm/s in distance.  The maximum errors over the same
+     interval are 18 arcsec and 0.50 arcsec/hour in longitude,
+     11 arcsec and 0.24 arcsec/hour in latitude, 40 km and 0.29 m/s
+     in distance. 
+
+  3  The original algorithm is expressed in terms of the obsolete
+     timescale Ephemeris Time.  Either TDB or TT can be used, but
+     not UT without incurring significant errors (30 arcsec at
+     the present time) due to the Moon's 0.5 arcsec/sec movement.
+
+  4  The algorithm is based on pre IAU 1976 standards.  However,
+     the result has been moved onto the new (FK5) equinox, an
+     adjustment which is in any case much smaller than the
+     intrinsic accuracy of the procedure.
+
+  5  Velocity is obtained by a complete analytical differentiation
+     of the Meeus model.
+
+  Reference:
+     Meeus, l'Astronomie, June 1984, p348.
+
+  P.T.Wallace   Starlink   22 January 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dmxm.hlp b/math/slalib/doc/dmxm.hlp
new file mode 100644
index 00000000..6eeea162
--- /dev/null
+++ b/math/slalib/doc/dmxm.hlp
@@ -0,0 +1,34 @@
+.help dmxm Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDMXM (A, B, C)
+
+     - - - - -
+      D M X M
+     - - - - -
+
+  Product of two 3x3 matrices:
+
+      matrix C  =  matrix A  x  matrix B
+
+  (double precision)
+
+  Given:
+      A      dp(3,3)        matrix
+      B      dp(3,3)        matrix
+
+  Returned:
+      C      dp(3,3)        matrix result
+
+  To comply with the ANSI Fortran 77 standard, A, B and C must
+  be different arrays.  However, the routine is coded so as to
+  work properly on the VAX and many other systems even if this
+  rule is violated.
+
+  P.T.Wallace   Starlink   5 April 1990
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dmxv.hlp b/math/slalib/doc/dmxv.hlp
new file mode 100644
index 00000000..025fd396
--- /dev/null
+++ b/math/slalib/doc/dmxv.hlp
@@ -0,0 +1,29 @@
+.help dmxv Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDMXV (DM, VA, VB)
+
+     - - - - -
+      D M X V
+     - - - - -
+
+  Performs the 3-D forward unitary transformation:
+
+     vector VB = matrix DM * vector VA
+
+  (double precision)
+
+  Given:
+     DM       dp(3,3)    matrix
+     VA       dp(3)      vector
+
+  Returned:
+     VB       dp(3)      result vector
+
+  P.T.Wallace   Starlink   March 1986
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dpav.hlp b/math/slalib/doc/dpav.hlp
new file mode 100644
index 00000000..d0111a2d
--- /dev/null
+++ b/math/slalib/doc/dpav.hlp
@@ -0,0 +1,38 @@
+.help dpav Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slDPAV ( V1, V2 )
+
+     - - - - -
+      D P A V
+     - - - - -
+
+  Position angle of one celestial direction with respect to another.
+
+  (double precision)
+
+  Given:
+     V1    d(3)    direction cosines of one point
+     V2    d(3)    direction cosines of the other point
+
+  (The coordinate frames correspond to RA,Dec, Long,Lat etc.)
+
+  The result is the bearing (position angle), in radians, of point
+  V2 with respect to point V1.  It is in the range +/- pi.  The
+  sense is such that if V2 is a small distance east of V1, the
+  bearing is about +pi/2.  Zero is returned if the two points
+  are coincident.
+
+  V1 and V2 need not be unit vectors.
+
+  The routine slDBER performs an equivalent function except
+  that the points are specified in the form of spherical
+  coordinates.
+
+  Patrick Wallace   Starlink   13 July 1997
+
+  Copyright (C) 1997 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dr2af.hlp b/math/slalib/doc/dr2af.hlp
new file mode 100644
index 00000000..b12d75c0
--- /dev/null
+++ b/math/slalib/doc/dr2af.hlp
@@ -0,0 +1,46 @@
+.help dr2af Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDRAF (NDP, ANGLE, SIGN, IDMSF)
+
+     - - - - - -
+      D R A F
+     - - - - - -
+
+  Convert an angle in radians to degrees, arcminutes, arcseconds
+  (double precision)
+
+  Given:
+     NDP      i      number of decimal places of arcseconds
+     ANGLE    d      angle in radians
+
+  Returned:
+     SIGN     c      '+' or '-'
+     IDMSF    i(4)   degrees, arcminutes, arcseconds, fraction
+
+  Notes:
+
+     1)  NDP less than zero is interpreted as zero.
+
+     2)  The largest useful value for NDP is determined by the size
+         of ANGLE, the format of DOUBLE PRECISION floating-point
+         numbers on the target machine, and the risk of overflowing
+         IDMSF(4).  For example, on the VAX, for ANGLE up to 2pi, the
+         available floating-point precision corresponds roughly to
+         NDP=12.  However, the practical limit is NDP=9, set by the
+         capacity of the 32-bit integer IDMSF(4).
+
+     3)  The absolute value of ANGLE may exceed 2pi.  In cases where it
+         does not, it is up to the caller to test for and handle the
+         case where ANGLE is very nearly 2pi and rounds up to 360 deg,
+         by testing for IDMSF(1)=360 and setting IDMSF(1-4) to zero.
+
+  Called:  slDDTF
+
+  P.T.Wallace   Starlink   19 March 1999
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dr2tf.hlp b/math/slalib/doc/dr2tf.hlp
new file mode 100644
index 00000000..49decabc
--- /dev/null
+++ b/math/slalib/doc/dr2tf.hlp
@@ -0,0 +1,46 @@
+.help dr2tf Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDRTF (NDP, ANGLE, SIGN, IHMSF)
+
+     - - - - - -
+      D R T F
+     - - - - - -
+
+  Convert an angle in radians to hours, minutes, seconds
+  (double precision)
+
+  Given:
+     NDP      i      number of decimal places of seconds
+     ANGLE    d      angle in radians
+
+  Returned:
+     SIGN     c      '+' or '-'
+     IHMSF    i(4)   hours, minutes, seconds, fraction
+
+  Notes:
+
+     1)  NDP less than zero is interpreted as zero.
+
+     2)  The largest useful value for NDP is determined by the size
+         of ANGLE, the format of DOUBLE PRECISION floating-point
+         numbers on the target machine, and the risk of overflowing
+         IHMSF(4).  For example, on the VAX, for ANGLE up to 2pi, the
+         available floating-point precision corresponds roughly to
+         NDP=12.  However, the practical limit is NDP=9, set by the
+         capacity of the 32-bit integer IHMSF(4).
+
+     3)  The absolute value of ANGLE may exceed 2pi.  In cases where it
+         does not, it is up to the caller to test for and handle the
+         case where ANGLE is very nearly 2pi and rounds up to 24 hours,
+         by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+
+  Called:  slDDTF
+
+  P.T.Wallace   Starlink   19 March 1999
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/drange.hlp b/math/slalib/doc/drange.hlp
new file mode 100644
index 00000000..025b6c08
--- /dev/null
+++ b/math/slalib/doc/drange.hlp
@@ -0,0 +1,23 @@
+.help drange Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slDA1P (ANGLE)
+
+     - - - - - - -
+      D A 1 P
+     - - - - - - -
+
+  Normalize angle into range +/- pi  (double precision)
+
+  Given:
+     ANGLE     dp      the angle in radians
+
+  The result (double precision) is ANGLE expressed in the range +/- pi.
+
+  P.T.Wallace   Starlink   23 November 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dranrm.hlp b/math/slalib/doc/dranrm.hlp
new file mode 100644
index 00000000..a479127e
--- /dev/null
+++ b/math/slalib/doc/dranrm.hlp
@@ -0,0 +1,24 @@
+.help dranrm Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slDA2P (ANGLE)
+
+     - - - - - - -
+      D A 2 P
+     - - - - - - -
+
+  Normalize angle into range 0-2 pi  (double precision)
+
+  Given:
+     ANGLE     dp      the angle in radians
+
+  The result is ANGLE expressed in the range 0-2 pi (double
+  precision).
+
+  P.T.Wallace   Starlink   23 November 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ds2c6.hlp b/math/slalib/doc/ds2c6.hlp
new file mode 100644
index 00000000..23d3442e
--- /dev/null
+++ b/math/slalib/doc/ds2c6.hlp
@@ -0,0 +1,32 @@
+.help ds2c6 Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDSC6 (A, B, R, AD, BD, RD, V)
+
+     - - - - - -
+      D S C 6
+     - - - - - -
+
+  Conversion of position & velocity in spherical coordinates
+  to Cartesian coordinates
+
+  (double precision)
+
+  Given:
+     A     dp      longitude (radians)
+     B     dp      latitude (radians)
+     R     dp      radial coordinate
+     AD    dp      longitude derivative (radians per unit time)
+     BD    dp      latitude derivative (radians per unit time)
+     RD    dp      radial derivative
+
+  Returned:
+     V     dp(6)   Cartesian position & velocity vector
+
+  P.T.Wallace   Starlink   10 July 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ds2tp.hlp b/math/slalib/doc/ds2tp.hlp
new file mode 100644
index 00000000..ff772145
--- /dev/null
+++ b/math/slalib/doc/ds2tp.hlp
@@ -0,0 +1,30 @@
+.help ds2tp Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDSTP (RA, DEC, RAZ, DECZ, XI, ETA, J)
+
+     - - - - - -
+      D S T P
+     - - - - - -
+
+  Projection of spherical coordinates onto tangent plane:
+  "gnomonic" projection - "standard coordinates" (double precision)
+
+  Given:
+     RA,DEC      dp   spherical coordinates of point to be projected
+     RAZ,DECZ    dp   spherical coordinates of tangent point
+
+  Returned:
+     XI,ETA      dp   rectangular coordinates on tangent plane
+     J           int  status:   0 = OK, star on tangent plane
+                                1 = error, star too far from axis
+                                2 = error, antistar on tangent plane
+                                3 = error, antistar too far from axis
+
+  P.T.Wallace   Starlink   18 July 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dsep.hlp b/math/slalib/doc/dsep.hlp
new file mode 100644
index 00000000..9b0f1117
--- /dev/null
+++ b/math/slalib/doc/dsep.hlp
@@ -0,0 +1,29 @@
+.help dsep Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slDSEP (A1, B1, A2, B2)
+
+     - - - - -
+      D S E P
+     - - - - -
+
+  Angle between two points on a sphere (double precision)
+
+  Given:
+     A1,B1    dp    spherical coordinates of one point
+     A2,B2    dp    spherical coordinates of the other point
+
+  (The spherical coordinates are RA,Dec, Long,Lat etc, in radians.)
+
+  The result is the angle, in radians, between the two points.  It
+  is always positive.
+
+  Called:  slDS2C
+
+  P.T.Wallace   Starlink   April 1985
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dt.hlp b/math/slalib/doc/dt.hlp
new file mode 100644
index 00000000..65ddca29
--- /dev/null
+++ b/math/slalib/doc/dt.hlp
@@ -0,0 +1,55 @@
+.help dt Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slDT (EPOCH)
+
+     - - -
+      D T
+     - - -
+
+  Estimate the offset between dynamical time and Universal Time
+  for a given historical epoch.
+
+  Given:
+     EPOCH       d        (Julian) epoch (e.g. 1850D0)
+
+  The result is a rough estimate of ET-UT (after 1984, TT-UT) at
+  the given epoch, in seconds.
+
+  Notes:
+
+  1  Depending on the epoch, one of three parabolic approximations
+     is used:
+
+      before 979    Stephenson & Morrison's 390 BC to AD 948 model
+      979 to 1708   Stephenson & Morrison's 948 to 1600 model
+      after 1708    McCarthy & Babcock's post-1650 model
+
+     The breakpoints are chosen to ensure continuity:  they occur
+     at places where the adjacent models give the same answer as
+     each other.
+
+  2  The accuracy is modest, with errors of up to 20 sec during
+     the interval since 1650, rising to perhaps 30 min by 1000 BC.
+     Comparatively accurate values from AD 1600 are tabulated in
+     the Astronomical Almanac (see section K8 of the 1995 AA).
+
+  3  The use of double-precision for both argument and result is
+     purely for compatibility with other SLALIB time routines.
+
+  4  The models used are based on a lunar tidal acceleration value
+     of -26.00 arcsec per century.
+
+  Reference:  Explanatory Supplement to the Astronomical Almanac,
+              ed P.K.Seidelmann, University Science Books (1992),
+              section 2.553, p83.  This contains references to
+              the Stephenson & Morrison and McCarthy & Babcock
+              papers.
+
+  P.T.Wallace   Starlink   1 March 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dtf2d.hlp b/math/slalib/doc/dtf2d.hlp
new file mode 100644
index 00000000..eef108f4
--- /dev/null
+++ b/math/slalib/doc/dtf2d.hlp
@@ -0,0 +1,36 @@
+.help dtf2d Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDTFD (IHOUR, IMIN, SEC, DAYS, J)
+
+     - - - - - -
+      D T F D
+     - - - - - -
+
+  Convert hours, minutes, seconds to days (double precision)
+
+  Given:
+     IHOUR       int       hours
+     IMIN        int       minutes
+     SEC         dp        seconds
+
+  Returned:
+     DAYS        dp        interval in days
+     J           int       status:  0 = OK
+                                    1 = IHOUR outside range 0-23
+                                    2 = IMIN outside range 0-59
+                                    3 = SEC outside range 0-59.999...
+
+  Notes:
+
+     1)  The result is computed even if any of the range checks fail.
+
+     2)  The sign must be dealt with outside this routine.
+
+  P.T.Wallace   Starlink   July 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dtf2r.hlp b/math/slalib/doc/dtf2r.hlp
new file mode 100644
index 00000000..ff3fcfbe
--- /dev/null
+++ b/math/slalib/doc/dtf2r.hlp
@@ -0,0 +1,39 @@
+.help dtf2r Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDTFR (IHOUR, IMIN, SEC, RAD, J)
+
+     - - - - - -
+      D T F R
+     - - - - - -
+
+  Convert hours, minutes, seconds to radians (double precision)
+
+  Given:
+     IHOUR       int       hours
+     IMIN        int       minutes
+     SEC         dp        seconds
+
+  Returned:
+     RAD         dp        angle in radians
+     J           int       status:  0 = OK
+                                    1 = IHOUR outside range 0-23
+                                    2 = IMIN outside range 0-59
+                                    3 = SEC outside range 0-59.999...
+
+  Called:
+     slDTFD
+
+  Notes:
+
+     1)  The result is computed even if any of the range checks fail.
+
+     2)  The sign must be dealt with outside this routine.
+
+  P.T.Wallace   Starlink   July 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dtp2s.hlp b/math/slalib/doc/dtp2s.hlp
new file mode 100644
index 00000000..73010651
--- /dev/null
+++ b/math/slalib/doc/dtp2s.hlp
@@ -0,0 +1,28 @@
+.help dtp2s Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDTPS (XI, ETA, RAZ, DECZ, RA, DEC)
+
+     - - - - - -
+      D T P S
+     - - - - - -
+
+  Transform tangent plane coordinates into spherical
+  (double precision)
+
+  Given:
+     XI,ETA      dp   tangent plane rectangular coordinates
+     RAZ,DECZ    dp   spherical coordinates of tangent point
+
+  Returned:
+     RA,DEC      dp   spherical coordinates (0-2pi,+/-pi/2)
+
+  Called:        slDA2P
+
+  P.T.Wallace   Starlink   24 July 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dtp2v.hlp b/math/slalib/doc/dtp2v.hlp
new file mode 100644
index 00000000..efd928ab
--- /dev/null
+++ b/math/slalib/doc/dtp2v.hlp
@@ -0,0 +1,40 @@
+.help dtp2v Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDTPV (XI, ETA, V0, V)
+
+     - - - - - -
+      D T P V
+     - - - - - -
+
+  Given the tangent-plane coordinates of a star and the direction
+  cosines of the tangent point, determine the direction cosines
+  of the star.
+
+  (double precision)
+
+  Given:
+     XI,ETA    d       tangent plane coordinates of star
+     V0        d(3)    direction cosines of tangent point
+
+  Returned:
+     V         d(3)    direction cosines of star
+
+  Notes:
+
+  1  If vector V0 is not of unit length, the returned vector V will
+     be wrong.
+
+  2  If vector V0 points at a pole, the returned vector V will be
+     based on the arbitrary assumption that the RA of the tangent
+     point is zero.
+
+  3  This routine is the Cartesian equivalent of the routine slDTPS.
+
+  P.T.Wallace   Starlink   11 February 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dtps2c.hlp b/math/slalib/doc/dtps2c.hlp
new file mode 100644
index 00000000..f0207d86
--- /dev/null
+++ b/math/slalib/doc/dtps2c.hlp
@@ -0,0 +1,58 @@
+.help dtps2c Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDPSC (XI, ETA, RA, DEC, RAZ1, DECZ1,
+     :                                         RAZ2, DECZ2, N)
+
+     - - - - - - -
+      D P S C
+     - - - - - - -
+
+  From the tangent plane coordinates of a star of known RA,Dec,
+  determine the RA,Dec of the tangent point.
+
+  (double precision)
+
+  Given:
+     XI,ETA      d    tangent plane rectangular coordinates
+     RA,DEC      d    spherical coordinates
+
+  Returned:
+     RAZ1,DECZ1  d    spherical coordinates of tangent point, solution 1
+     RAZ2,DECZ2  d    spherical coordinates of tangent point, solution 2
+     N           i    number of solutions:
+                        0 = no solutions returned (note 2)
+                        1 = only the first solution is useful (note 3)
+                        2 = both solutions are useful (note 3)
+
+  Notes:
+
+  1  The RAZ1 and RAZ2 values are returned in the range 0-2pi.
+
+  2  Cases where there is no solution can only arise near the poles.
+     For example, it is clearly impossible for a star at the pole
+     itself to have a non-zero XI value, and hence it is
+     meaningless to ask where the tangent point would have to be
+     to bring about this combination of XI and DEC.
+
+  3  Also near the poles, cases can arise where there are two useful
+     solutions.  The argument N indicates whether the second of the
+     two solutions returned is useful.  N=1 indicates only one useful
+     solution, the usual case;  under these circumstances, the second
+     solution corresponds to the "over-the-pole" case, and this is
+     reflected in the values of RAZ2 and DECZ2 which are returned.
+
+  4  The DECZ1 and DECZ2 values are returned in the range +/-pi, but
+     in the usual, non-pole-crossing, case, the range is +/-pi/2.
+
+  5  This routine is the spherical equivalent of the routine slDPVC.
+
+  Called:  slDA2P
+
+  P.T.Wallace   Starlink   5 June 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dtpv2c.hlp b/math/slalib/doc/dtpv2c.hlp
new file mode 100644
index 00000000..acc94985
--- /dev/null
+++ b/math/slalib/doc/dtpv2c.hlp
@@ -0,0 +1,51 @@
+.help dtpv2c Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDPVC (XI, ETA, V, V01, V02, N)
+
+     - - - - - - -
+      D P V C
+     - - - - - - -
+
+  Given the tangent-plane coordinates of a star and its direction
+  cosines, determine the direction cosines of the tangent-point.
+
+  (double precision)
+
+  Given:
+     XI,ETA    d       tangent plane coordinates of star
+     V         d(3)    direction cosines of star
+
+  Returned:
+     V01       d(3)    direction cosines of tangent point, solution 1
+     V02       d(3)    direction cosines of tangent point, solution 2
+     N         i       number of solutions:
+                         0 = no solutions returned (note 2)
+                         1 = only the first solution is useful (note 3)
+                         2 = both solutions are useful (note 3)
+
+  Notes:
+
+  1  The vector V must be of unit length or the result will be wrong.
+
+  2  Cases where there is no solution can only arise near the poles.
+     For example, it is clearly impossible for a star at the pole
+     itself to have a non-zero XI value, and hence it is meaningless
+     to ask where the tangent point would have to be.
+
+  3  Also near the poles, cases can arise where there are two useful
+     solutions.  The argument N indicates whether the second of the
+     two solutions returned is useful.  N=1 indicates only one useful
+     solution, the usual case;  under these circumstances, the second
+     solution can be regarded as valid if the vector V02 is interpreted
+     as the "over-the-pole" case.
+
+  4  This routine is the Cartesian equivalent of the routine slDPSC.
+
+  P.T.Wallace   Starlink   5 June 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dtt.hlp b/math/slalib/doc/dtt.hlp
new file mode 100644
index 00000000..67c2b1ae
--- /dev/null
+++ b/math/slalib/doc/dtt.hlp
@@ -0,0 +1,41 @@
+.help dtt Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slDTT (UTC)
+
+     - - - -
+      D T T
+     - - - -
+
+  Increment to be applied to Coordinated Universal Time UTC to give
+  Terrestrial Time TT (formerly Ephemeris Time ET)
+
+  (double precision)
+
+  Given:
+     UTC      d      UTC date as a modified JD (JD-2400000.5)
+
+  Result:  TT-UTC in seconds
+
+  Notes:
+
+  1  The UTC is specified to be a date rather than a time to indicate
+     that care needs to be taken not to specify an instant which lies
+     within a leap second.  Though in most cases UTC can include the
+     fractional part, correct behaviour on the day of a leap second
+     can only be guaranteed up to the end of the second 23:59:59.
+
+  2  Pre 1972 January 1 a fixed value of 10 + ET-TAI is returned.
+
+  3  See also the routine slDT, which roughly estimates ET-UT for
+     historical epochs.
+
+  Called:  slDAT
+
+  P.T.Wallace   Starlink   6 December 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dv2tp.hlp b/math/slalib/doc/dv2tp.hlp
new file mode 100644
index 00000000..6b927741
--- /dev/null
+++ b/math/slalib/doc/dv2tp.hlp
@@ -0,0 +1,42 @@
+.help dv2tp Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDVTP (V, V0, XI, ETA, J)
+
+     - - - - - -
+      D V T P
+     - - - - - -
+
+  Given the direction cosines of a star and of the tangent point,
+  determine the star's tangent-plane coordinates.
+
+  (double precision)
+
+  Given:
+     V         d(3)    direction cosines of star
+     V0        d(3)    direction cosines of tangent point
+
+  Returned:
+     XI,ETA    d       tangent plane coordinates of star
+     J         i       status:   0 = OK
+                                 1 = error, star too far from axis
+                                 2 = error, antistar on tangent plane
+                                 3 = error, antistar too far from axis
+
+  Notes:
+
+  1  If vector V0 is not of unit length, or if vector V is of zero
+     length, the results will be wrong.
+
+  2  If V0 points at a pole, the returned XI,ETA will be based on the
+     arbitrary assumption that the RA of the tangent point is zero.
+
+  3  This routine is the Cartesian equivalent of the routine slDSTP.
+
+  P.T.Wallace   Starlink   27 November 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dvdv.hlp b/math/slalib/doc/dvdv.hlp
new file mode 100644
index 00000000..d3c566dd
--- /dev/null
+++ b/math/slalib/doc/dvdv.hlp
@@ -0,0 +1,24 @@
+.help dvdv Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slDVDV (VA, VB)
+
+     - - - - -
+      D V D V
+     - - - - -
+
+  Scalar product of two 3-vectors  (double precision)
+
+  Given:
+      VA      dp(3)     first vector
+      VB      dp(3)     second vector
+
+  The result is the scalar product VA.VB (double precision)
+
+  P.T.Wallace   Starlink   November 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dvn.hlp b/math/slalib/doc/dvn.hlp
new file mode 100644
index 00000000..295937e6
--- /dev/null
+++ b/math/slalib/doc/dvn.hlp
@@ -0,0 +1,27 @@
+.help dvn Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDVN (V, UV, VM)
+
+     - - - -
+      D V N
+     - - - -
+
+  Normalizes a 3-vector also giving the modulus (double precision)
+
+  Given:
+     V       dp(3)      vector
+
+  Returned:
+     UV      dp(3)      unit vector in direction of V
+     VM      dp         modulus of V
+
+  If the modulus of V is zero, UV is set to zero as well
+
+  P.T.Wallace   Starlink   23 November 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/dvxv.hlp b/math/slalib/doc/dvxv.hlp
new file mode 100644
index 00000000..a7db5344
--- /dev/null
+++ b/math/slalib/doc/dvxv.hlp
@@ -0,0 +1,25 @@
+.help dvxv Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slDVXV (VA, VB, VC)
+
+     - - - - -
+      D V X V
+     - - - - -
+
+  Vector product of two 3-vectors  (double precision)
+
+  Given:
+      VA      dp(3)     first vector
+      VB      dp(3)     second vector
+
+  Returned:
+      VC      dp(3)     vector result
+
+  P.T.Wallace   Starlink   March 1986
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/e2h.hlp b/math/slalib/doc/e2h.hlp
new file mode 100644
index 00000000..f962d80a
--- /dev/null
+++ b/math/slalib/doc/e2h.hlp
@@ -0,0 +1,59 @@
+.help e2h Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slE2H (HA, DEC, PHI, AZ, EL)
+
+     - - - -
+      E 2 H
+     - - - -
+
+  Equatorial to horizon coordinates:  HA,Dec to Az,El
+
+  (single precision)
+
+  Given:
+     HA      r     hour angle
+     DEC     r     declination
+     PHI     r     observatory latitude
+
+  Returned:
+     AZ      r     azimuth
+     EL      r     elevation
+
+  Notes:
+
+  1)  All the arguments are angles in radians.
+
+  2)  Azimuth is returned in the range 0-2pi;  north is zero,
+      and east is +pi/2.  Elevation is returned in the range
+      +/-pi/2.
+
+  3)  The latitude must be geodetic.  In critical applications,
+      corrections for polar motion should be applied.
+
+  4)  In some applications it will be important to specify the
+      correct type of hour angle and declination in order to
+      produce the required type of azimuth and elevation.  In
+      particular, it may be important to distinguish between
+      elevation as affected by refraction, which would
+      require the "observed" HA,Dec, and the elevation
+      in vacuo, which would require the "topocentric" HA,Dec.
+      If the effects of diurnal aberration can be neglected, the
+      "apparent" HA,Dec may be used instead of the topocentric
+      HA,Dec.
+
+  5)  No range checking of arguments is carried out.
+
+  6)  In applications which involve many such calculations, rather
+      than calling the present routine it will be more efficient to
+      use inline code, having previously computed fixed terms such
+      as sine and cosine of latitude, and (for tracking a star)
+      sine and cosine of declination.
+
+  P.T.Wallace   Starlink   9 July 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/earth.hlp b/math/slalib/doc/earth.hlp
new file mode 100644
index 00000000..ea0eccd6
--- /dev/null
+++ b/math/slalib/doc/earth.hlp
@@ -0,0 +1,44 @@
+.help earth Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slERTH (IY, ID, FD, PV)
+
+     - - - - - -
+      E R T H
+     - - - - - -
+
+  Approximate heliocentric position and velocity of the Earth
+
+  Given:
+     IY       I       year
+     ID       I       day in year (1 = Jan 1st)
+     FD       R       fraction of day
+
+  Returned:
+     PV       R(6)    Earth position & velocity vector
+
+  Notes:
+
+  1  The date and time is TDB (loosely ET) in a Julian calendar
+     which has been aligned to the ordinary Gregorian
+     calendar for the interval 1900 March 1 to 2100 February 28.
+     The year and day can be obtained by calling slCAYD or
+     slCLYD.
+
+  2  The Earth heliocentric 6-vector is mean equator and equinox
+     of date.  Position part, PV(1-3), is in AU;  velocity part,
+     PV(4-6), is in AU/sec.
+
+  3  Max/RMS errors 1950-2050:
+       13/5 E-5 AU = 19200/7600 km in position
+       47/26 E-10 AU/s = 0.0070/0.0039 km/s in speed
+
+  4  More precise results are obtainable with the routine slEVP.
+
+  P.T.Wallace   Starlink   23 November 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ecleq.hlp b/math/slalib/doc/ecleq.hlp
new file mode 100644
index 00000000..02fc6c50
--- /dev/null
+++ b/math/slalib/doc/ecleq.hlp
@@ -0,0 +1,31 @@
+.help ecleq Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slECEQ (DL, DB, DATE, DR, DD)
+
+     - - - - - -
+      E C E Q
+     - - - - - -
+
+  Transformation from ecliptic coordinates to
+  J2000.0 equatorial coordinates (double precision)
+
+  Given:
+     DL,DB       dp      ecliptic longitude and latitude
+                           (mean of date, IAU 1980 theory, radians)
+     DATE        dp      TDB (loosely ET) as Modified Julian Date
+                                              (JD-2400000.5)
+  Returned:
+     DR,DD       dp      J2000.0 mean RA,Dec (radians)
+
+  Called:
+     slDS2C, slECMA, slDIMV, slPREC, slEPJ, slDC2S,
+     slDA2P, slDA1P
+
+  P.T.Wallace   Starlink   March 1986
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ecmat.hlp b/math/slalib/doc/ecmat.hlp
new file mode 100644
index 00000000..a9be4579
--- /dev/null
+++ b/math/slalib/doc/ecmat.hlp
@@ -0,0 +1,34 @@
+.help ecmat Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slECMA (DATE, RMAT)
+
+     - - - - - -
+      E C M A
+     - - - - - -
+
+  Form the equatorial to ecliptic rotation matrix - IAU 1980 theory
+  (double precision)
+
+  Given:
+     DATE     dp         TDB (loosely ET) as Modified Julian Date
+                                            (JD-2400000.5)
+  Returned:
+     RMAT     dp(3,3)    matrix
+
+  Reference:
+     Murray,C.A., Vectorial Astrometry, section 4.3.
+
+  Note:
+    The matrix is in the sense   V(ecl)  =  RMAT * V(equ);  the
+    equator, equinox and ecliptic are mean of date.
+
+  Called:  slDEUL
+
+  P.T.Wallace   Starlink   23 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ecor.hlp b/math/slalib/doc/ecor.hlp
new file mode 100644
index 00000000..07cf410f
--- /dev/null
+++ b/math/slalib/doc/ecor.hlp
@@ -0,0 +1,54 @@
+.help ecor Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slECOR (RM, DM, IY, ID, FD, RV, TL)
+
+     - - - - -
+      E C O R
+     - - - - -
+
+  Component of Earth orbit velocity and heliocentric
+  light time in a given direction (single precision)
+
+  Given:
+     RM,DM    real    mean RA, Dec of date (radians)
+     IY       int     year
+     ID       int     day in year (1 = Jan 1st)
+     FD       real    fraction of day
+
+  Returned:
+     RV       real    component of Earth orbital velocity (km/sec)
+     TL       real    component of heliocentric light time (sec)
+
+  Notes:
+
+  1  The date and time is TDB (loosely ET) in a Julian calendar
+     which has been aligned to the ordinary Gregorian
+     calendar for the interval 1900 March 1 to 2100 February 28.
+     The year and day can be obtained by calling slCAYD or
+     slCLYD.
+
+  2  Sign convention:
+
+     The velocity component is +ve when the Earth is receding from
+     the given point on the sky.  The light time component is +ve
+     when the Earth lies between the Sun and the given point on
+     the sky.
+
+  3  Accuracy:
+
+     The velocity component is usually within 0.004 km/s of the
+     correct value and is never in error by more than 0.007 km/s.
+     The error in light time correction is about 0.03s at worst,
+     but is usually better than 0.01s. For applications requiring
+     higher accuracy, see the slEVP routine.
+
+  Called:  slERTH, slCS2C, slVDV
+
+  P.T.Wallace   Starlink   24 November 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/eg50.hlp b/math/slalib/doc/eg50.hlp
new file mode 100644
index 00000000..da2c0fa3
--- /dev/null
+++ b/math/slalib/doc/eg50.hlp
@@ -0,0 +1,38 @@
+.help eg50 Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slEG50 (DR, DD, DL, DB)
+
+     - - - - -
+      E G 5 0
+     - - - - -
+
+  Transformation from B1950.0 'FK4' equatorial coordinates to
+  IAU 1958 galactic coordinates (double precision)
+
+  Given:
+     DR,DD       dp       B1950.0 'FK4' RA,Dec
+
+  Returned:
+     DL,DB       dp       galactic longitude and latitude L2,B2
+
+  (all arguments are radians)
+
+  Called:
+     slDS2C, slDMXV, slDC2S, slSUET, slDA2P, slDA1P
+
+  Note:
+     The equatorial coordinates are B1950.0 'FK4'.  Use the
+     routine slEQGA if conversion from J2000.0 coordinates
+     is required.
+
+  Reference:
+     Blaauw et al, Mon.Not.R.Astron.Soc.,121,123 (1960)
+
+  P.T.Wallace   Starlink   5 September 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/el2ue.hlp b/math/slalib/doc/el2ue.hlp
new file mode 100644
index 00000000..9271fff6
--- /dev/null
+++ b/math/slalib/doc/el2ue.hlp
@@ -0,0 +1,133 @@
+.help el2ue Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slELUE (DATE, JFORM, EPOCH, ORBINC, ANODE,
+     :                      PERIH, AORQ, E, AORL, DM,
+     :                      U, JSTAT)
+
+     - - - - - -
+      E L U E
+     - - - - - -
+
+  Transform conventional osculating orbital elements into "universal" form.
+
+  Given:
+     DATE     d       epoch (TT MJD) of osculation (Note 3)
+     JFORM    i       choice of element set (1-3, Note 6)
+     EPOCH    d       epoch (TT MJD) of the elements
+     ORBINC   d       inclination (radians)
+     ANODE    d       longitude of the ascending node (radians)
+     PERIH    d       longitude or argument of perihelion (radians)
+     AORQ     d       mean distance or perihelion distance (AU)
+     E        d       eccentricity
+     AORL     d       mean anomaly or longitude (radians, JFORM=1,2 only)
+     DM       d       daily motion (radians, JFORM=1 only)
+
+  Returned:
+     U        d(13)   universal orbital elements (Note 1)
+
+                (1)   combined mass (M+m)
+                (2)   total energy of the orbit (alpha)
+                (3)   reference (osculating) epoch (t0)
+              (4-6)   position at reference epoch (r0)
+              (7-9)   velocity at reference epoch (v0)
+               (10)   heliocentric distance at reference epoch
+               (11)   r0.v0
+               (12)   date (t)
+               (13)   universal eccentric anomaly (psi) of date, approx
+
+     JSTAT    i       status:  0 = OK
+                              -1 = illegal JFORM
+                              -2 = illegal E
+                              -3 = illegal AORQ
+                              -4 = illegal DM
+                              -5 = numerical error
+
+  Called:  slUEPV, slPVUE
+
+  Notes
+
+  1  The "universal" elements are those which define the orbit for the
+     purposes of the method of universal variables (see reference).
+     They consist of the combined mass of the two bodies, an epoch,
+     and the position and velocity vectors (arbitrary reference frame)
+     at that epoch.  The parameter set used here includes also various
+     quantities that can, in fact, be derived from the other
+     information.  This approach is taken to avoiding unnecessary
+     computation and loss of accuracy.  The supplementary quantities
+     are (i) alpha, which is proportional to the total energy of the
+     orbit, (ii) the heliocentric distance at epoch, (iii) the
+     outwards component of the velocity at the given epoch, (iv) an
+     estimate of psi, the "universal eccentric anomaly" at a given
+     date and (v) that date.
+
+  2  The companion routine is slUEPV.  This takes the set of numbers
+     that the present routine outputs and uses them to derive the
+     object's position and velocity.  A single prediction requires one
+     call to the present routine followed by one call to slUEPV;
+     for convenience, the two calls are packaged as the routine
+     slPLNE.  Multiple predictions may be made by again calling the
+     present routine once, but then calling slUEPV multiple times,
+     which is faster than multiple calls to slPLNE.
+
+  3  DATE is the epoch of osculation.  It is in the TT timescale
+     (formerly Ephemeris Time, ET) and is a Modified Julian Date
+     (JD-2400000.5).
+
+  4  The supplied orbital elements are with respect to the J2000
+     ecliptic and equinox.  The position and velocity parameters
+     returned in the array U are with respect to the mean equator and
+     equinox of epoch J2000, and are for the perihelion prior to the
+     specified epoch.
+
+  5  The universal elements returned in the array U are in canonical
+     units (solar masses, AU and canonical days).
+
+  6  Three different element-format options are available:
+
+     Option JFORM=1, suitable for the major planets:
+
+     EPOCH  = epoch of elements (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = longitude of perihelion, curly pi (radians)
+     AORQ   = mean distance, a (AU)
+     E      = eccentricity, e (range 0 to <1)
+     AORL   = mean longitude L (radians)
+     DM     = daily motion (radians)
+
+     Option JFORM=2, suitable for minor planets:
+
+     EPOCH  = epoch of elements (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = argument of perihelion, little omega (radians)
+     AORQ   = mean distance, a (AU)
+     E      = eccentricity, e (range 0 to <1)
+     AORL   = mean anomaly M (radians)
+
+     Option JFORM=3, suitable for comets:
+
+     EPOCH  = epoch of perihelion (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = argument of perihelion, little omega (radians)
+     AORQ   = perihelion distance, q (AU)
+     E      = eccentricity, e (range 0 to 10)
+
+  7  Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
+     not accessed.
+
+  8  The algorithm was originally adapted from the EPHSLA program of
+     D.H.P.Jones (private communication, 1996).  The method is based
+     on Stumpff's Universal Variables.
+
+  Reference:  Everhart & Pitkin, Am.J.Phys. 51, 712 (1983).
+
+  P.T.Wallace   Starlink   18 February 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/epb.hlp b/math/slalib/doc/epb.hlp
new file mode 100644
index 00000000..6c7ed368
--- /dev/null
+++ b/math/slalib/doc/epb.hlp
@@ -0,0 +1,27 @@
+.help epb Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slEPB (DATE)
+
+     - - - -
+      E P B
+     - - - -
+
+  Conversion of Modified Julian Date to Besselian Epoch
+  (double precision)
+
+  Given:
+     DATE     dp       Modified Julian Date (JD - 2400000.5)
+
+  The result is the Besselian Epoch.
+
+  Reference:
+     Lieske,J.H., 1979. Astron.Astrophys.,73,282.
+
+  P.T.Wallace   Starlink   February 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/epb2d.hlp b/math/slalib/doc/epb2d.hlp
new file mode 100644
index 00000000..b0ded162
--- /dev/null
+++ b/math/slalib/doc/epb2d.hlp
@@ -0,0 +1,27 @@
+.help epb2d Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slEB2D (EPB)
+
+     - - - - - -
+      E B 2 D
+     - - - - - -
+
+  Conversion of Besselian Epoch to Modified Julian Date
+  (double precision)
+
+  Given:
+     EPB      dp       Besselian Epoch
+
+  The result is the Modified Julian Date (JD - 2400000.5).
+
+  Reference:
+     Lieske,J.H., 1979. Astron.Astrophys.,73,282.
+
+  P.T.Wallace   Starlink   February 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/epco.hlp b/math/slalib/doc/epco.hlp
new file mode 100644
index 00000000..d92bfde2
--- /dev/null
+++ b/math/slalib/doc/epco.hlp
@@ -0,0 +1,40 @@
+.help epco Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slEPCO (K0, K, E)
+
+     - - - - -
+      E P C O
+     - - - - -
+
+  Convert an epoch into the appropriate form - 'B' or 'J'
+
+  Given:
+     K0    char    form of result:  'B'=Besselian, 'J'=Julian
+     K     char    form of given epoch:  'B' or 'J'
+     E     dp      epoch
+
+  Called:  slEPB, slEJ2D, slEPJ, slEB2D
+
+  Notes:
+
+     1) The result is always either equal to or very close to
+        the given epoch E.  The routine is required only in
+        applications where punctilious treatment of heterogeneous
+        mixtures of star positions is necessary.
+
+     2) K0 and K are not validated.  They are interpreted as follows:
+
+        o  If K0 and K are the same the result is E.
+        o  If K0 is 'B' or 'b' and K isn't, the conversion is J to B.
+        o  In all other cases, the conversion is B to J.
+
+        Note that K0 and K won't match if their cases differ.
+
+  P.T.Wallace   Starlink   5 September 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/epj.hlp b/math/slalib/doc/epj.hlp
new file mode 100644
index 00000000..34d47ec7
--- /dev/null
+++ b/math/slalib/doc/epj.hlp
@@ -0,0 +1,26 @@
+.help epj Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slEPJ (DATE)
+
+     - - - -
+      E P J
+     - - - -
+
+  Conversion of Modified Julian Date to Julian Epoch (double precision)
+
+  Given:
+     DATE     dp       Modified Julian Date (JD - 2400000.5)
+
+  The result is the Julian Epoch.
+
+  Reference:
+     Lieske,J.H., 1979. Astron.Astrophys.,73,282.
+
+  P.T.Wallace   Starlink   February 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/epj2d.hlp b/math/slalib/doc/epj2d.hlp
new file mode 100644
index 00000000..ceadf7ab
--- /dev/null
+++ b/math/slalib/doc/epj2d.hlp
@@ -0,0 +1,26 @@
+.help epj2d Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slEJ2D (EPJ)
+
+     - - - - - -
+      E J 2 D
+     - - - - - -
+
+  Conversion of Julian Epoch to Modified Julian Date (double precision)
+
+  Given:
+     EPJ      dp       Julian Epoch
+
+  The result is the Modified Julian Date (JD - 2400000.5).
+
+  Reference:
+     Lieske,J.H., 1979. Astron.Astrophys.,73,282.
+
+  P.T.Wallace   Starlink   February 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/eqecl.hlp b/math/slalib/doc/eqecl.hlp
new file mode 100644
index 00000000..a8266afe
--- /dev/null
+++ b/math/slalib/doc/eqecl.hlp
@@ -0,0 +1,31 @@
+.help eqecl Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slEQEC (DR, DD, DATE, DL, DB)
+
+     - - - - - -
+      E Q E C
+     - - - - - -
+
+  Transformation from J2000.0 equatorial coordinates to
+  ecliptic coordinates (double precision)
+
+  Given:
+     DR,DD       dp      J2000.0 mean RA,Dec (radians)
+     DATE        dp      TDB (loosely ET) as Modified Julian Date
+                                              (JD-2400000.5)
+  Returned:
+     DL,DB       dp      ecliptic longitude and latitude
+                         (mean of date, IAU 1980 theory, radians)
+
+  Called:
+     slDS2C, slPREC, slEPJ, slDMXV, slECMA, slDC2S,
+     slDA2P, slDA1P
+
+  P.T.Wallace   Starlink   March 1986
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/eqeqx.hlp b/math/slalib/doc/eqeqx.hlp
new file mode 100644
index 00000000..35da9ab4
--- /dev/null
+++ b/math/slalib/doc/eqeqx.hlp
@@ -0,0 +1,33 @@
+.help eqeqx Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slEQEX (DATE)
+
+     - - - - - -
+      E Q E X
+     - - - - - -
+
+  Equation of the equinoxes  (IAU 1994, double precision)
+
+  Given:
+     DATE    dp      TDB (loosely ET) as Modified Julian Date
+                                          (JD-2400000.5)
+
+  The result is the equation of the equinoxes (double precision)
+  in radians:
+
+     Greenwich apparent ST = GMST + slEQEX
+
+  References:  IAU Resolution C7, Recommendation 3 (1994)
+               Capitaine, N. & Gontier, A.-M., Astron. Astrophys.,
+               275, 645-650 (1993)
+               
+  Called:  slNUTC
+
+  Patrick Wallace   Starlink   23 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/eqgal.hlp b/math/slalib/doc/eqgal.hlp
new file mode 100644
index 00000000..1f37716f
--- /dev/null
+++ b/math/slalib/doc/eqgal.hlp
@@ -0,0 +1,38 @@
+.help eqgal Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slEQGA (DR, DD, DL, DB)
+
+     - - - - - -
+      E Q G A
+     - - - - - -
+
+  Transformation from J2000.0 equatorial coordinates to
+  IAU 1958 galactic coordinates (double precision)
+
+  Given:
+     DR,DD       dp       J2000.0 RA,Dec
+
+  Returned:
+     DL,DB       dp       galactic longitude and latitude L2,B2
+
+  (all arguments are radians)
+
+  Called:
+     slDS2C, slDMXV, slDC2S, slDA2P, slDA1P
+
+  Note:
+     The equatorial coordinates are J2000.0.  Use the routine
+     slEG50 if conversion from B1950.0 'FK4' coordinates is
+     required.
+
+  Reference:
+     Blaauw et al, Mon.Not.R.Astron.Soc.,121,123 (1960)
+
+  P.T.Wallace   Starlink   21 September 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/etrms.hlp b/math/slalib/doc/etrms.hlp
new file mode 100644
index 00000000..bc14b655
--- /dev/null
+++ b/math/slalib/doc/etrms.hlp
@@ -0,0 +1,35 @@
+.help etrms Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slETRM (EP, EV)
+
+     - - - - - -
+      E T R M
+     - - - - - -
+
+  Compute the E-terms (elliptic component of annual aberration)
+  vector (double precision)
+
+  Given:
+     EP      dp      Besselian epoch
+
+  Returned:
+     EV      dp(3)   E-terms as (dx,dy,dz)
+
+  Note the use of the J2000 aberration constant (20.49552 arcsec).
+  This is a reflection of the fact that the E-terms embodied in
+  existing star catalogues were computed from a variety of
+  aberration constants.  Rather than adopting one of the old
+  constants the latest value is used here.
+
+  References:
+     1  Smith, C.A. et al., 1989.  Astr.J. 97, 265.
+     2  Yallop, B.D. et al., 1989.  Astr.J. 97, 274.
+
+  P.T.Wallace   Starlink   23 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/euler.hlp b/math/slalib/doc/euler.hlp
new file mode 100644
index 00000000..7ae2fedc
--- /dev/null
+++ b/math/slalib/doc/euler.hlp
@@ -0,0 +1,52 @@
+.help euler Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slEULR (ORDER, PHI, THETA, PSI, RMAT)
+
+     - - - - - -
+      E U L R
+     - - - - - -
+
+  Form a rotation matrix from the Euler angles - three successive
+  rotations about specified Cartesian axes (single precision)
+
+  Given:
+    ORDER  c*(*)    specifies about which axes the rotations occur
+    PHI    r        1st rotation (radians)
+    THETA  r        2nd rotation (   "   )
+    PSI    r        3rd rotation (   "   )
+
+  Returned:
+    RMAT   r(3,3)   rotation matrix
+
+  A rotation is positive when the reference frame rotates
+  anticlockwise as seen looking towards the origin from the
+  positive region of the specified axis.
+
+  The characters of ORDER define which axes the three successive
+  rotations are about.  A typical value is 'ZXZ', indicating that
+  RMAT is to become the direction cosine matrix corresponding to
+  rotations of the reference frame through PHI radians about the
+  old Z-axis, followed by THETA radians about the resulting X-axis,
+  then PSI radians about the resulting Z-axis.
+
+  The axis names can be any of the following, in any order or
+  combination:  X, Y, Z, uppercase or lowercase, 1, 2, 3.  Normal
+  axis labeling/numbering conventions apply;  the xyz (=123)
+  triad is right-handed.  Thus, the 'ZXZ' example given above
+  could be written 'zxz' or '313' (or even 'ZxZ' or '3xZ').  ORDER
+  is terminated by length or by the first unrecognized character.
+
+  Fewer than three rotations are acceptable, in which case the later
+  angle arguments are ignored.  If all rotations are zero, the
+  identity matrix is produced.
+
+  Called:  slDEUL
+
+  P.T.Wallace   Starlink   23 May 1997
+
+  Copyright (C) 1997 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/evp.hlp b/math/slalib/doc/evp.hlp
new file mode 100644
index 00000000..e7fa04cf
--- /dev/null
+++ b/math/slalib/doc/evp.hlp
@@ -0,0 +1,66 @@
+.help evp Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slEVP (DATE, DEQX, DVB, DPB, DVH, DPH)
+
+     - - - -
+      E V P
+     - - - -
+
+  Barycentric and heliocentric velocity and position of the Earth
+
+  All arguments are double precision
+
+  Given:
+
+     DATE          TDB (loosely ET) as a Modified Julian Date
+                                         (JD-2400000.5)
+
+     DEQX          Julian Epoch (e.g. 2000.0D0) of mean equator and
+                   equinox of the vectors returned.  If DEQX .LE. 0D0,
+                   all vectors are referred to the mean equator and
+                   equinox (FK5) of epoch DATE.
+
+  Returned (all 3D Cartesian vectors):
+
+     DVB,DPB       barycentric velocity, position
+
+     DVH,DPH       heliocentric velocity, position
+
+  (Units are AU/s for velocity and AU for position)
+
+  Called:  slEPJ, slPREC
+
+  Accuracy:
+
+     The maximum deviations from the JPL DE96 ephemeris are as
+     follows:
+
+     barycentric velocity         0.42  m/s
+     barycentric position         6900  km
+
+     heliocentric velocity        0.42  m/s
+     heliocentric position        1600  km
+
+  This routine is adapted from the BARVEL and BARCOR
+  subroutines of P.Stumpff, which are described in
+  Astron. Astrophys. Suppl. Ser. 41, 1-8 (1980).  Most of the
+  changes are merely cosmetic and do not affect the results at
+  all.  However, some adjustments have been made so as to give
+  results that refer to the new (IAU 1976 'FK5') equinox
+  and precession, although the differences these changes make
+  relative to the results from Stumpff's original 'FK4' version
+  are smaller than the inherent accuracy of the algorithm.  One
+  minor shortcoming in the original routines that has NOT been
+  corrected is that better numerical accuracy could be achieved
+  if the various polynomial evaluations were nested.  Note also
+  that one of Stumpff's precession constants differs by 0.001 arcsec
+  from the value given in the Explanatory Supplement to the A.E.
+
+  P.T.Wallace   Starlink   21 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/fitxy.hlp b/math/slalib/doc/fitxy.hlp
new file mode 100644
index 00000000..814deb9f
--- /dev/null
+++ b/math/slalib/doc/fitxy.hlp
@@ -0,0 +1,76 @@
+.help fitxy Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slFTXY (ITYPE,NP,XYE,XYM,COEFFS,J)
+
+     - - - - - -
+      F T X Y
+     - - - - - -
+
+  Fit a linear model to relate two sets of [X,Y] coordinates.
+
+  Given:
+     ITYPE    i        type of model: 4 or 6 (note 1)
+     NP       i        number of samples (note 2)
+     XYE     d(2,np)   expected [X,Y] for each sample
+     XYM     d(2,np)   measured [X,Y] for each sample
+
+  Returned:
+     COEFFS  d(6)      coefficients of model (note 3)
+     J        i        status:  0 = OK
+                               -1 = illegal ITYPE
+                               -2 = insufficient data
+                               -3 = singular solution
+
+  Notes:
+
+  1)  ITYPE, which must be either 4 or 6, selects the type of model
+      fitted.  Both allowed ITYPE values produce a model COEFFS which
+      consists of six coefficients, namely the zero points and, for
+      each of XE and YE, the coefficient of XM and YM.  For ITYPE=6,
+      all six coefficients are independent, modelling squash and shear
+      as well as origin, scale, and orientation.  However, ITYPE=4
+      selects the "solid body rotation" option;  the model COEFFS
+      still consists of the same six coefficients, but now two of
+      them are used twice (appropriately signed).  Origin, scale
+      and orientation are still modelled, but not squash or shear -
+      the units of X and Y have to be the same.
+
+  2)  For NC=4, NP must be at least 2.  For NC=6, NP must be at
+      least 3.
+
+  3)  The model is returned in the array COEFFS.  Naming the
+      elements of COEFFS as follows:
+
+                  COEFFS(1) = A
+                  COEFFS(2) = B
+                  COEFFS(3) = C
+                  COEFFS(4) = D
+                  COEFFS(5) = E
+                  COEFFS(6) = F
+
+      the model is:
+
+            XE = A + B*XM + C*YM
+            YE = D + E*XM + F*YM
+
+      For the "solid body rotation" option (ITYPE=4), the
+      magnitudes of B and F, and of C and E, are equal.  The
+      signs of these coefficients depend on whether there is a
+      sign reversal between XE,YE and XM,YM;  fits are performed
+      with and without a sign reversal and the best one chosen.
+
+  4)  Error status values J=-1 and -2 leave COEFFS unchanged;
+      if J=-3 COEFFS may have been changed.
+
+  See also slPXY, slINVF, slXYXY, slDCMF
+
+  Called:  slDMAT, slDMXV
+
+  P.T.Wallace   Starlink   11 February 1991
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/fk425.hlp b/math/slalib/doc/fk425.hlp
new file mode 100644
index 00000000..808dcb7b
--- /dev/null
+++ b/math/slalib/doc/fk425.hlp
@@ -0,0 +1,81 @@
+.help fk425 Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slFK45 (R1950,D1950,DR1950,DD1950,P1950,V1950,
+     :                      R2000,D2000,DR2000,DD2000,P2000,V2000)
+
+     - - - - - -
+      F K 4 5
+     - - - - - -
+
+  Convert B1950.0 FK4 star data to J2000.0 FK5 (double precision)
+
+  This routine converts stars from the old, Bessel-Newcomb, FK4
+  system to the new, IAU 1976, FK5, Fricke system.  The precepts
+  of Smith et al (Ref 1) are followed, using the implementation
+  by Yallop et al (Ref 2) of a matrix method due to Standish.
+  Kinoshita's development of Andoyer's post-Newcomb precession is
+  used.  The numerical constants from Seidelmann et al (Ref 3) are
+  used canonically.
+
+  Given:  (all B1950.0,FK4)
+     R1950,D1950     dp    B1950.0 RA,Dec (rad)
+     DR1950,DD1950   dp    B1950.0 proper motions (rad/trop.yr)
+     P1950           dp    parallax (arcsec)
+     V1950           dp    radial velocity (km/s, +ve = moving away)
+
+  Returned:  (all J2000.0,FK5)
+     R2000,D2000     dp    J2000.0 RA,Dec (rad)
+     DR2000,DD2000   dp    J2000.0 proper motions (rad/Jul.yr)
+     P2000           dp    parallax (arcsec)
+     V2000           dp    radial velocity (km/s, +ve = moving away)
+
+  Notes:
+
+  1)  The proper motions in RA are dRA/dt rather than
+      cos(Dec)*dRA/dt, and are per year rather than per century.
+
+  2)  Conversion from Besselian epoch 1950.0 to Julian epoch
+      2000.0 only is provided for.  Conversions involving other
+      epochs will require use of the appropriate precession,
+      proper motion, and E-terms routines before and/or
+      after FK425 is called.
+
+  3)  In the FK4 catalogue the proper motions of stars within
+      10 degrees of the poles do not embody the differential
+      E-term effect and should, strictly speaking, be handled
+      in a different manner from stars outside these regions.
+      However, given the general lack of homogeneity of the star
+      data available for routine astrometry, the difficulties of
+      handling positions that may have been determined from
+      astrometric fields spanning the polar and non-polar regions,
+      the likelihood that the differential E-terms effect was not
+      taken into account when allowing for proper motion in past
+      astrometry, and the undesirability of a discontinuity in
+      the algorithm, the decision has been made in this routine to
+      include the effect of differential E-terms on the proper
+      motions for all stars, whether polar or not.  At epoch 2000,
+      and measuring on the sky rather than in terms of dRA, the
+      errors resulting from this simplification are less than
+      1 milliarcsecond in position and 1 milliarcsecond per
+      century in proper motion.
+
+  References:
+
+     1  Smith, C.A. et al, 1989.  "The transformation of astrometric
+        catalog systems to the equinox J2000.0".  Astron.J. 97, 265.
+
+     2  Yallop, B.D. et al, 1989.  "Transformation of mean star places
+        from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
+        Astron.J. 97, 274.
+
+     3  Seidelmann, P.K. (ed), 1992.  "Explanatory Supplement to
+        the Astronomical Almanac", ISBN 0-935702-68-7.
+
+  P.T.Wallace   Starlink   19 December 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/fk45z.hlp b/math/slalib/doc/fk45z.hlp
new file mode 100644
index 00000000..6994302f
--- /dev/null
+++ b/math/slalib/doc/fk45z.hlp
@@ -0,0 +1,83 @@
+.help fk45z Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slF45Z (R1950,D1950,BEPOCH,R2000,D2000)
+
+     - - - - - -
+      F 4 5 Z
+     - - - - - -
+
+  Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero
+  proper motion in the FK5 frame (double precision)
+
+  This routine converts stars from the old, Bessel-Newcomb, FK4
+  system to the new, IAU 1976, FK5, Fricke system, in such a
+  way that the FK5 proper motion is zero.  Because such a star
+  has, in general, a non-zero proper motion in the FK4 system,
+  the routine requires the epoch at which the position in the
+  FK4 system was determined.
+
+  The method is from Appendix 2 of Ref 1, but using the constants
+  of Ref 4.
+
+  Given:
+     R1950,D1950     dp    B1950.0 FK4 RA,Dec at epoch (rad)
+     BEPOCH          dp    Besselian epoch (e.g. 1979.3D0)
+
+  Returned:
+     R2000,D2000     dp    J2000.0 FK5 RA,Dec (rad)
+
+  Notes:
+
+  1)  The epoch BEPOCH is strictly speaking Besselian, but
+      if a Julian epoch is supplied the result will be
+      affected only to a negligible extent.
+
+  2)  Conversion from Besselian epoch 1950.0 to Julian epoch
+      2000.0 only is provided for.  Conversions involving other
+      epochs will require use of the appropriate precession,
+      proper motion, and E-terms routines before and/or
+      after FK45Z is called.
+
+  3)  In the FK4 catalogue the proper motions of stars within
+      10 degrees of the poles do not embody the differential
+      E-term effect and should, strictly speaking, be handled
+      in a different manner from stars outside these regions.
+      However, given the general lack of homogeneity of the star
+      data available for routine astrometry, the difficulties of
+      handling positions that may have been determined from
+      astrometric fields spanning the polar and non-polar regions,
+      the likelihood that the differential E-terms effect was not
+      taken into account when allowing for proper motion in past
+      astrometry, and the undesirability of a discontinuity in
+      the algorithm, the decision has been made in this routine to
+      include the effect of differential E-terms on the proper
+      motions for all stars, whether polar or not.  At epoch 2000,
+      and measuring on the sky rather than in terms of dRA, the
+      errors resulting from this simplification are less than
+      1 milliarcsecond in position and 1 milliarcsecond per
+      century in proper motion.
+
+  References:
+
+     1  Aoki,S., et al, 1983.  Astron.Astrophys., 128, 263.
+
+     2  Smith, C.A. et al, 1989.  "The transformation of astrometric
+        catalog systems to the equinox J2000.0".  Astron.J. 97, 265.
+
+     3  Yallop, B.D. et al, 1989.  "Transformation of mean star places
+        from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
+        Astron.J. 97, 274.
+
+     4  Seidelmann, P.K. (ed), 1992.  "Explanatory Supplement to
+        the Astronomical Almanac", ISBN 0-935702-68-7.
+
+  Called:  slDS2C, slEPJ, slEB2D, slDC2S, slDA2P
+
+  P.T.Wallace   Starlink   21 September 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/fk524.hlp b/math/slalib/doc/fk524.hlp
new file mode 100644
index 00000000..ed86273b
--- /dev/null
+++ b/math/slalib/doc/fk524.hlp
@@ -0,0 +1,81 @@
+.help fk524 Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slFK54 (R2000,D2000,DR2000,DD2000,P2000,V2000,
+     :                      R1950,D1950,DR1950,DD1950,P1950,V1950)
+
+     - - - - - -
+      F K 5 4
+     - - - - - -
+
+  Convert J2000.0 FK5 star data to B1950.0 FK4 (double precision)
+
+  This routine converts stars from the new, IAU 1976, FK5, Fricke
+  system, to the old, Bessel-Newcomb, FK4 system.  The precepts
+  of Smith et al (Ref 1) are followed, using the implementation
+  by Yallop et al (Ref 2) of a matrix method due to Standish.
+  Kinoshita's development of Andoyer's post-Newcomb precession is
+  used.  The numerical constants from Seidelmann et al (Ref 3) are
+  used canonically.
+
+  Given:  (all J2000.0,FK5)
+     R2000,D2000     dp    J2000.0 RA,Dec (rad)
+     DR2000,DD2000   dp    J2000.0 proper motions (rad/Jul.yr)
+     P2000           dp    parallax (arcsec)
+     V2000           dp    radial velocity (km/s, +ve = moving away)
+
+  Returned:  (all B1950.0,FK4)
+     R1950,D1950     dp    B1950.0 RA,Dec (rad)
+     DR1950,DD1950   dp    B1950.0 proper motions (rad/trop.yr)
+     P1950           dp    parallax (arcsec)
+     V1950           dp    radial velocity (km/s, +ve = moving away)
+
+  Notes:
+
+  1)  The proper motions in RA are dRA/dt rather than
+      cos(Dec)*dRA/dt, and are per year rather than per century.
+
+  2)  Note that conversion from Julian epoch 2000.0 to Besselian
+      epoch 1950.0 only is provided for.  Conversions involving
+      other epochs will require use of the appropriate precession,
+      proper motion, and E-terms routines before and/or after
+      FK524 is called.
+
+  3)  In the FK4 catalogue the proper motions of stars within
+      10 degrees of the poles do not embody the differential
+      E-term effect and should, strictly speaking, be handled
+      in a different manner from stars outside these regions.
+      However, given the general lack of homogeneity of the star
+      data available for routine astrometry, the difficulties of
+      handling positions that may have been determined from
+      astrometric fields spanning the polar and non-polar regions,
+      the likelihood that the differential E-terms effect was not
+      taken into account when allowing for proper motion in past
+      astrometry, and the undesirability of a discontinuity in
+      the algorithm, the decision has been made in this routine to
+      include the effect of differential E-terms on the proper
+      motions for all stars, whether polar or not.  At epoch 2000,
+      and measuring on the sky rather than in terms of dRA, the
+      errors resulting from this simplification are less than
+      1 milliarcsecond in position and 1 milliarcsecond per
+      century in proper motion.
+
+  References:
+
+     1  Smith, C.A. et al, 1989.  "The transformation of astrometric
+        catalog systems to the equinox J2000.0".  Astron.J. 97, 265.
+
+     2  Yallop, B.D. et al, 1989.  "Transformation of mean star places
+        from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
+        Astron.J. 97, 274.
+
+     3  Seidelmann, P.K. (ed), 1992.  "Explanatory Supplement to
+        the Astronomical Almanac", ISBN 0-935702-68-7.
+
+  P.T.Wallace   Starlink   19 December 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/fk52h.hlp b/math/slalib/doc/fk52h.hlp
new file mode 100644
index 00000000..ad7cb724
--- /dev/null
+++ b/math/slalib/doc/fk52h.hlp
@@ -0,0 +1,56 @@
+.help fk52h Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slFK5H (R5,D5,DR5,DD5,RH,DH,DRH,DDH)
+
+     - - - - - -
+      F K 5 H
+     - - - - - -
+
+  Transform FK5 (J2000) star data into the Hipparcos frame.
+
+  (double precision)
+
+  This routine transforms FK5 star positions and proper motions
+  into the frame of the Hipparcos catalogue.
+
+  Given (all FK5, equinox J2000, epoch J2000):
+     R5        d      RA (radians)
+     D5        d      Dec (radians)
+     DR5       d      proper motion in RA (dRA/dt, rad/Jyear)
+     DD5       d      proper motion in Dec (dDec/dt, rad/Jyear)
+
+  Returned (all Hipparcos, epoch J2000):
+     RH        d      RA (radians)
+     DH        d      Dec (radians)
+     DRH       d      proper motion in RA (dRA/dt, rad/Jyear)
+     DDH       d      proper motion in Dec (dDec/dt, rad/Jyear)
+
+  Called:  slDSC6, slDAVM, slDMXV, slDVXV, slDC6S
+
+  Notes:
+
+  1)  The proper motions in RA are dRA/dt rather than
+      cos(Dec)*dRA/dt, and are per year rather than per century.
+
+  2)  The FK5 to Hipparcos transformation consists of a pure
+      rotation and spin;  zonal errors in the FK5 catalogue are
+      not taken into account.
+
+  3)  The published orientation and spin components are interpreted
+      as "axial vectors".  An axial vector points at the pole of the
+      rotation and its length is the amount of rotation in radians.
+
+  4)  See also slHFK5, slF5HZ, slHF5Z.
+
+  Reference:
+
+     M.Feissel & F.Mignard, Astron. Astrophys. 331, L33-L36 (1998).
+
+  P.T.Wallace   Starlink   7 October 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/fk54z.hlp b/math/slalib/doc/fk54z.hlp
new file mode 100644
index 00000000..b453bad9
--- /dev/null
+++ b/math/slalib/doc/fk54z.hlp
@@ -0,0 +1,56 @@
+.help fk54z Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slF54Z (R2000,D2000,BEPOCH,
+     :                      R1950,D1950,DR1950,DD1950)
+
+     - - - - - -
+      F 5 4 Z
+     - - - - - -
+
+  Convert a J2000.0 FK5 star position to B1950.0 FK4 assuming
+  zero proper motion and parallax (double precision)
+
+  This routine converts star positions from the new, IAU 1976,
+  FK5, Fricke system to the old, Bessel-Newcomb, FK4 system.
+
+  Given:
+     R2000,D2000     dp    J2000.0 FK5 RA,Dec (rad)
+     BEPOCH          dp    Besselian epoch (e.g. 1950D0)
+
+  Returned:
+     R1950,D1950     dp    B1950.0 FK4 RA,Dec (rad) at epoch BEPOCH
+     DR1950,DD1950   dp    B1950.0 FK4 proper motions (rad/trop.yr)
+
+  Notes:
+
+  1)  The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
+
+  2)  Conversion from Julian epoch 2000.0 to Besselian epoch 1950.0
+      only is provided for.  Conversions involving other epochs will
+      require use of the appropriate precession routines before and
+      after this routine is called.
+
+  3)  Unlike in the slFK54 routine, the FK5 proper motions, the
+      parallax and the radial velocity are presumed zero.
+
+  4)  It is the intention that FK5 should be a close approximation
+      to an inertial frame, so that distant objects have zero proper
+      motion;  such objects have (in general) non-zero proper motion
+      in FK4, and this routine returns those fictitious proper
+      motions.
+
+  5)  The position returned by this routine is in the B1950
+      reference frame but at Besselian epoch BEPOCH.  For
+      comparison with catalogues the BEPOCH argument will
+      frequently be 1950D0.
+
+  Called:  slFK54, slPM
+
+  P.T.Wallace   Starlink   10 April 1990
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/fk5hz.hlp b/math/slalib/doc/fk5hz.hlp
new file mode 100644
index 00000000..4d5e5ab0
--- /dev/null
+++ b/math/slalib/doc/fk5hz.hlp
@@ -0,0 +1,54 @@
+.help fk5hz Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slF5HZ (R5,D5,EPOCH,RH,DH)
+
+     - - - - - -
+      F 5 H Z
+     - - - - - -
+
+  Transform an FK5 (J2000) star position into the frame of the
+  Hipparcos catalogue, assuming zero Hipparcos proper motion.
+
+  (double precision)
+
+  This routine converts a star position from the FK5 system to
+  the Hipparcos system, in such a way that the Hipparcos proper
+  motion is zero.  Because such a star has, in general, a non-zero
+  proper motion in the FK5 system, the routine requires the epoch
+  at which the position in the FK5 system was determined.
+
+  Given:
+     R5        d      FK5 RA (radians), equinox J2000, epoch EPOCH
+     D5        d      FK5 Dec (radians), equinox J2000, epoch EPOCH
+     EPOCH     d      Julian epoch (TDB)
+
+  Returned (all Hipparcos):
+     RH        d      RA (radians)
+     DH        d      Dec (radians)
+
+  Called:  slDS2C, slDAVM, slDIMV, slDMXV, slDC2S
+
+  Notes:
+
+  1)  The FK5 to Hipparcos transformation consists of a pure
+      rotation and spin;  zonal errors in the FK5 catalogue are
+      not taken into account.
+
+  2)  The published orientation and spin components are interpreted
+      as "axial vectors".  An axial vector points at the pole of the
+      rotation and its length is the amount of rotation in radians.
+
+  3)  See also slFK5H, slHFK5, slHF5Z.
+
+  Reference:
+
+     M.Feissel & F.Mignard, Astron. Astrophys. 331, L33-L36 (1998).
+
+  P.T.Wallace   Starlink   7 October 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/flotin.hlp b/math/slalib/doc/flotin.hlp
new file mode 100644
index 00000000..5e3d8bd6
--- /dev/null
+++ b/math/slalib/doc/flotin.hlp
@@ -0,0 +1,118 @@
+.help flotin Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slRFLI (STRING, NSTRT, RESLT, JFLAG)
+
+     - - - - - - -
+      R F L I
+     - - - - - - -
+
+  Convert free-format input into single precision floating point
+
+  Given:
+     STRING     c     string containing number to be decoded
+     NSTRT      i     pointer to where decoding is to start
+     RESLT      r     current value of result
+
+  Returned:
+     NSTRT      i      advanced to next number
+     RESLT      r      result
+     JFLAG      i      status: -1 = -OK, 0 = +OK, 1 = null, 2 = error
+
+  Called:  slDFLI
+
+  Notes:
+
+     1     The reason FLOTIN has separate OK status values for +
+           and - is to enable minus zero to be detected.   This is
+           of crucial importance when decoding mixed-radix numbers.
+           For example, an angle expressed as deg, arcmin, arcsec
+           may have a leading minus sign but a zero degrees field.
+
+     2     A TAB is interpreted as a space, and lowercase characters
+           are interpreted as uppercase.
+
+     3     The basic format is the sequence of fields #^.^@#^, where
+           # is a sign character + or -, ^ means a string of decimal
+           digits, and @, which indicates an exponent, means D or E.
+           Various combinations of these fields can be omitted, and
+           embedded blanks are permissible in certain places.
+
+     4     Spaces:
+
+             .  Leading spaces are ignored.
+
+             .  Embedded spaces are allowed only after +, -, D or E,
+                and after the decomal point if the first sequence of
+                digits is absent.
+
+             .  Trailing spaces are ignored;  the first signifies
+                end of decoding and subsequent ones are skipped.
+
+     5     Delimiters:
+
+             .  Any character other than +,-,0-9,.,D,E or space may be
+                used to signal the end of the number and terminate
+                decoding.
+
+             .  Comma is recognized by FLOTIN as a special case;  it
+                is skipped, leaving the pointer on the next character.
+                See 13, below.
+
+     6     Both signs are optional.  The default is +.
+
+     7     The mantissa ^.^ defaults to 1.
+
+     8     The exponent @#^ defaults to E0.
+
+     9     The strings of decimal digits may be of any length.
+
+     10    The decimal point is optional for whole numbers.
+
+     11    A "null result" occurs when the string of characters being
+           decoded does not begin with +,-,0-9,.,D or E, or consists
+           entirely of spaces.  When this condition is detected, JFLAG
+           is set to 1 and RESLT is left untouched.
+
+     12    NSTRT = 1 for the first character in the string.
+
+     13    On return from FLOTIN, NSTRT is set ready for the next
+           decode - following trailing blanks and any comma.  If a
+           delimiter other than comma is being used, NSTRT must be
+           incremented before the next call to FLOTIN, otherwise
+           all subsequent calls will return a null result.
+
+     14    Errors (JFLAG=2) occur when:
+
+             .  a +, -, D or E is left unsatisfied;  or
+
+             .  the decimal point is present without at least
+                one decimal digit before or after it;  or
+
+             .  an exponent more than 100 has been presented.
+
+     15    When an error has been detected, NSTRT is left
+           pointing to the character following the last
+           one used before the error came to light.  This
+           may be after the point at which a more sophisticated
+           program could have detected the error.  For example,
+           FLOTIN does not detect that '1E999' is unacceptable
+           (on a computer where this is so) until the entire number
+           has been decoded.
+
+     16    Certain highly unlikely combinations of mantissa &
+           exponent can cause arithmetic faults during the
+           decode, in some cases despite the fact that they
+           together could be construed as a valid number.
+
+     17    Decoding is left to right, one pass.
+
+     18    See also DFLTIN and INTIN
+
+  P.T.Wallace   Starlink   23 November 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/galeq.hlp b/math/slalib/doc/galeq.hlp
new file mode 100644
index 00000000..6bda60d1
--- /dev/null
+++ b/math/slalib/doc/galeq.hlp
@@ -0,0 +1,38 @@
+.help galeq Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slGAEQ (DL, DB, DR, DD)
+
+     - - - - - -
+      G A E Q
+     - - - - - -
+
+  Transformation from IAU 1958 galactic coordinates to
+  J2000.0 equatorial coordinates (double precision)
+
+  Given:
+     DL,DB       dp       galactic longitude and latitude L2,B2
+
+  Returned:
+     DR,DD       dp       J2000.0 RA,Dec
+
+  (all arguments are radians)
+
+  Called:
+     slDS2C, slDIMV, slDC2S, slDA2P, slDA1P
+
+  Note:
+     The equatorial coordinates are J2000.0.  Use the routine
+     slGE50 if conversion to B1950.0 'FK4' coordinates is
+     required.
+
+  Reference:
+     Blaauw et al, Mon.Not.R.Astron.Soc.,121,123 (1960)
+
+  P.T.Wallace   Starlink   21 September 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/galsup.hlp b/math/slalib/doc/galsup.hlp
new file mode 100644
index 00000000..497211ac
--- /dev/null
+++ b/math/slalib/doc/galsup.hlp
@@ -0,0 +1,43 @@
+.help galsup Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slGASU (DL, DB, DSL, DSB)
+
+     - - - - - - -
+      G A S U
+     - - - - - - -
+
+  Transformation from IAU 1958 galactic coordinates to
+  de Vaucouleurs supergalactic coordinates (double precision)
+
+  Given:
+     DL,DB       dp       galactic longitude and latitude L2,B2
+
+  Returned:
+     DSL,DSB     dp       supergalactic longitude and latitude
+
+  (all arguments are radians)
+
+  Called:
+     slDS2C, slDMXV, slDC2S, slDA2P, slDA1P
+
+  References:
+
+     de Vaucouleurs, de Vaucouleurs, & Corwin, Second Reference
+     Catalogue of Bright Galaxies, U. Texas, page 8.
+
+     Systems & Applied Sciences Corp., Documentation for the
+     machine-readable version of the above catalogue,
+     Contract NAS 5-26490.
+
+    (These two references give different values for the galactic
+     longitude of the supergalactic origin.  Both are wrong;  the
+     correct value is L2=137.37.)
+
+  P.T.Wallace   Starlink   25 January 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ge50.hlp b/math/slalib/doc/ge50.hlp
new file mode 100644
index 00000000..b064e834
--- /dev/null
+++ b/math/slalib/doc/ge50.hlp
@@ -0,0 +1,38 @@
+.help ge50 Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slGE50 (DL, DB, DR, DD)
+
+     - - - - -
+      G E 5 0
+     - - - - -
+
+  Transformation from IAU 1958 galactic coordinates to
+  B1950.0 'FK4' equatorial coordinates (double precision)
+
+  Given:
+     DL,DB       dp       galactic longitude and latitude L2,B2
+
+  Returned:
+     DR,DD       dp       B1950.0 'FK4' RA,Dec
+
+  (all arguments are radians)
+
+  Called:
+     slDS2C, slDIMV, slDC2S, slADET, slDA2P, slDA1P
+
+  Note:
+     The equatorial coordinates are B1950.0 'FK4'.  Use the
+     routine slGAEQ if conversion to J2000.0 coordinates
+     is required.
+
+  Reference:
+     Blaauw et al, Mon.Not.R.Astron.Soc.,121,123 (1960)
+
+  P.T.Wallace   Starlink   5 September 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/geoc.hlp b/math/slalib/doc/geoc.hlp
new file mode 100644
index 00000000..538474d1
--- /dev/null
+++ b/math/slalib/doc/geoc.hlp
@@ -0,0 +1,33 @@
+.help geoc Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slGEOC (P, H, R, Z)
+
+     - - - - -
+      G E O C
+     - - - - -
+
+  Convert geodetic position to geocentric (double precision)
+
+  Given:
+     P     dp     latitude (geodetic, radians)
+     H     dp     height above reference spheroid (geodetic, metres)
+
+  Returned:
+     R     dp     distance from Earth axis (AU)
+     Z     dp     distance from plane of Earth equator (AU)
+
+  Notes:
+     1)  Geocentric latitude can be obtained by evaluating ATAN2(Z,R).
+     2)  IAU 1976 constants are used.
+
+  Reference:
+     Green,R.M., Spherical Astronomy, CUP 1985, p98.
+
+  P.T.Wallace   Starlink   4th October 1989
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/gmst.hlp b/math/slalib/doc/gmst.hlp
new file mode 100644
index 00000000..7e58aec9
--- /dev/null
+++ b/math/slalib/doc/gmst.hlp
@@ -0,0 +1,41 @@
+.help gmst Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slGMST (UT1)
+
+     - - - - -
+      G M S T
+     - - - - -
+
+  Conversion from universal time to sidereal time (double precision)
+
+  Given:
+    UT1    dp     universal time (strictly UT1) expressed as
+                  modified Julian Date (JD-2400000.5)
+
+  The result is the Greenwich mean sidereal time (double
+  precision, radians).
+
+  The IAU 1982 expression (see page S15 of 1984 Astronomical
+  Almanac) is used, but rearranged to reduce rounding errors.
+  This expression is always described as giving the GMST at
+  0 hours UT.  In fact, it gives the difference between the
+  GMST and the UT, which happens to equal the GMST (modulo
+  24 hours) at 0 hours UT each day.  In this routine, the
+  entire UT is used directly as the argument for the
+  standard formula, and the fractional part of the UT is
+  added separately;  note that the factor 1.0027379... does
+  not appear.
+
+  See also the routine slGMSA, which delivers better numerical
+  precision by accepting the UT date and time as separate arguments.
+
+  Called:  slDA2P
+
+  P.T.Wallace   Starlink   14 September 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/gmsta.hlp b/math/slalib/doc/gmsta.hlp
new file mode 100644
index 00000000..e959d6cc
--- /dev/null
+++ b/math/slalib/doc/gmsta.hlp
@@ -0,0 +1,55 @@
+.help gmsta Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slGMSA (DATE, UT)
+
+     - - - - - -
+      G M S A
+     - - - - - -
+
+  Conversion from Universal Time to Greenwich mean sidereal time,
+  with rounding errors minimized.
+
+  double precision
+
+  Given:
+    DATE    d      UT1 date (MJD: integer part of JD-2400000.5))
+    UT      d      UT1 time (fraction of a day)
+
+  The result is the Greenwich mean sidereal time (double precision,
+  radians, in the range 0 to 2pi).
+
+  There is no restriction on how the UT is apportioned between the
+  DATE and UT arguments.  Either of the two arguments could, for
+  example, be zero and the entire date+time supplied in the other.
+  However, the routine is designed to deliver maximum accuracy when
+  the DATE argument is a whole number and the UT lies in the range
+  0 to 1 (or vice versa).
+
+  The algorithm is based on the IAU 1982 expression (see page S15 of
+  the 1984 Astronomical Almanac).  This is always described as giving
+  the GMST at 0 hours UT1.  In fact, it gives the difference between
+  the GMST and the UT, the steady 4-minutes-per-day drawing-ahead of
+  ST with respect to UT.  When whole days are ignored, the expression
+  happens to equal the GMST at 0 hours UT1 each day.
+
+  In this routine, the entire UT1 (the sum of the two arguments DATE
+  and UT) is used directly as the argument for the standard formula.
+  The UT1 is then added, but omitting whole days to conserve accuracy.
+
+  See also the routine slGMST, which accepts the UT as a single
+  argument.  Compared with slGMST, the extra numerical precision
+  delivered by the present routine is unlikely to be important in
+  an absolute sense, but may be useful when critically comparing
+  algorithms and in applications where two sidereal times close
+  together are differenced.
+
+  Called:  slDA2P
+
+  P.T.Wallace   Starlink   13 April 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/h2e.hlp b/math/slalib/doc/h2e.hlp
new file mode 100644
index 00000000..06fd4282
--- /dev/null
+++ b/math/slalib/doc/h2e.hlp
@@ -0,0 +1,58 @@
+.help h2e Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slH2E (AZ, EL, PHI, HA, DEC)
+
+     - - - - -
+      D E 2 H
+     - - - - -
+
+  Horizon to equatorial coordinates:  Az,El to HA,Dec
+
+  (single precision)
+
+  Given:
+     AZ      r     azimuth
+     EL      r     elevation
+     PHI     r     observatory latitude
+
+  Returned:
+     HA      r     hour angle
+     DEC     r     declination
+
+  Notes:
+
+  1)  All the arguments are angles in radians.
+
+  2)  The sign convention for azimuth is north zero, east +pi/2.
+
+  3)  HA is returned in the range +/-pi.  Declination is returned
+      in the range +/-pi/2.
+
+  4)  The latitude is (in principle) geodetic.  In critical
+      applications, corrections for polar motion should be applied.
+
+  5)  In some applications it will be important to specify the
+      correct type of elevation in order to produce the required
+      type of HA,Dec.  In particular, it may be important to
+      distinguish between the elevation as affected by refraction,
+      which will yield the "observed" HA,Dec, and the elevation
+      in vacuo, which will yield the "topocentric" HA,Dec.  If the
+      effects of diurnal aberration can be neglected, the
+      topocentric HA,Dec may be used as an approximation to the
+      "apparent" HA,Dec.
+
+  6)  No range checking of arguments is done.
+
+  7)  In applications which involve many such calculations, rather
+      than calling the present routine it will be more efficient to
+      use inline code, having previously computed fixed terms such
+      as sine and cosine of latitude.
+
+  P.T.Wallace   Starlink   21 February 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/h2fk5.hlp b/math/slalib/doc/h2fk5.hlp
new file mode 100644
index 00000000..158d9cfb
--- /dev/null
+++ b/math/slalib/doc/h2fk5.hlp
@@ -0,0 +1,57 @@
+.help h2fk5 Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slHFK5 (RH,DH,DRH,DDH,R5,D5,DR5,DD5)
+
+     - - - - - -
+      H F K 5
+     - - - - - -
+
+  Transform Hipparcos star data into the FK5 (J2000) system.
+
+  (double precision)
+
+  This routine transforms Hipparcos star positions and proper
+  motions into FK5 J2000.
+
+  Given (all Hipparcos, epoch J2000):
+     RH        d      RA (radians)
+     DH        d      Dec (radians)
+     DRH       d      proper motion in RA (dRA/dt, rad/Jyear)
+     DDH       d      proper motion in Dec (dDec/dt, rad/Jyear)
+
+  Returned (all FK5, equinox J2000, epoch J2000):
+     R5        d      RA (radians)
+     D5        d      Dec (radians)
+     DR5       d      proper motion in RA (dRA/dt, rad/Jyear)
+     DD5       d      proper motion in Dec (dDec/dt, rad/Jyear)
+
+  Called:  slDSC6, slDAVM, slDMXV, slDIMV, slDVXV,
+           slDC6S
+
+  Notes:
+
+  1)  The proper motions in RA are dRA/dt rather than
+      cos(Dec)*dRA/dt, and are per year rather than per century.
+
+  2)  The FK5 to Hipparcos transformation consists of a pure
+      rotation and spin;  zonal errors in the FK5 catalogue are
+      not taken into account.
+
+  3)  The published orientation and spin components are interpreted
+      as "axial vectors".  An axial vector points at the pole of the
+      rotation and its length is the amount of rotation in radians.
+
+  4)  See also slFK5H, slF5HZ, slHF5Z.
+
+  Reference:
+
+     M.Feissel & F.Mignard, Astron. Astrophys. 331, L33-L36 (1998).
+
+  P.T.Wallace   Starlink   7 October 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/hfk5z.hlp b/math/slalib/doc/hfk5z.hlp
new file mode 100644
index 00000000..a2bea786
--- /dev/null
+++ b/math/slalib/doc/hfk5z.hlp
@@ -0,0 +1,60 @@
+.help hfk5z Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slHF5Z (RH,DH,EPOCH,R5,D5,DR5,DD5)
+
+     - - - - - -
+      H F 5 Z
+     - - - - - -
+
+  Transform a Hipparcos star position into FK5 J2000, assuming
+  zero Hipparcos proper motion.
+
+  (double precision)
+
+  Given:
+     RH        d      Hipparcos RA (radians)
+     DH        d      Hipparcos Dec (radians)
+     EPOCH     d      Julian epoch (TDB)
+
+  Returned (all FK5, equinox J2000, epoch EPOCH):
+     R5        d      RA (radians)
+     D5        d      Dec (radians)
+
+  Called:  slDS2C, slDAVM, slDMXV, slDAVM, slDMXM,
+           slDIMV, slDVXV, slDC6S
+
+  Notes:
+
+  1)  The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
+
+  2)  The FK5 to Hipparcos transformation consists of a pure
+      rotation and spin;  zonal errors in the FK5 catalogue are
+      not taken into account.
+
+  3)  The published orientation and spin components are interpreted
+      as "axial vectors".  An axial vector points at the pole of the
+      rotation and its length is the amount of rotation in radians.
+
+  4)  It was the intention that Hipparcos should be a close
+      approximation to an inertial frame, so that distant objects
+      have zero proper motion;  such objects have (in general)
+      non-zero proper motion in FK5, and this routine returns those
+      fictitious proper motions.
+
+  5)  The position returned by this routine is in the FK5 J2000
+      reference frame but at Julian epoch EPOCH.
+
+  6)  See also slFK5H, slHFK5, slF5HZ.
+
+  Reference:
+
+     M.Feissel & F.Mignard, Astron. Astrophys. 331, L33-L36 (1998).
+
+  P.T.Wallace   Starlink   7 October 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/imxv.hlp b/math/slalib/doc/imxv.hlp
new file mode 100644
index 00000000..025c7122
--- /dev/null
+++ b/math/slalib/doc/imxv.hlp
@@ -0,0 +1,32 @@
+.help imxv Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slIMXV (RM, VA, VB)
+
+     - - - - -
+      I M X V
+     - - - - -
+
+  Performs the 3-D backward unitary transformation:
+
+     vector VB = (inverse of matrix RM) * vector VA
+
+  (single precision)
+
+  (n.b.  the matrix must be unitary, as this routine assumes that
+   the inverse and transpose are identical)
+
+  Given:
+     RM       real(3,3)    matrix
+     VA       real(3)      vector
+
+  Returned:
+     VB       real(3)      result vector
+
+  P.T.Wallace   Starlink   November 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/intin.hlp b/math/slalib/doc/intin.hlp
new file mode 100644
index 00000000..f0b0c8ee
--- /dev/null
+++ b/math/slalib/doc/intin.hlp
@@ -0,0 +1,90 @@
+.help intin Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slINTI (STRING, NSTRT, IRESLT, JFLAG)
+
+     - - - - - -
+      I N T I
+     - - - - - -
+
+  Convert free-format input into an integer
+
+  Given:
+     STRING     c     string containing number to be decoded
+     NSTRT      i     pointer to where decoding is to start
+     IRESLT     i     current value of result
+
+  Returned:
+     NSTRT      i      advanced to next number
+     IRESLT     i      result
+     JFLAG      i      status: -1 = -OK, 0 = +OK, 1 = null, 2 = error
+
+  Called:  slICHI
+
+  Notes:
+
+     1     The reason INTIN has separate OK status values for +
+           and - is to enable minus zero to be detected.   This is
+           of crucial importance when decoding mixed-radix numbers.
+           For example, an angle expressed as deg, arcmin, arcsec
+           may have a leading minus sign but a zero degrees field.
+
+     2     A TAB is interpreted as a space.
+
+     3     The basic format is the sequence of fields #^, where
+           # is a sign character + or -, and ^ means a string of
+           decimal digits.
+
+     4     Spaces:
+
+             .  Leading spaces are ignored.
+
+             .  Spaces between the sign and the number are allowed.
+
+             .  Trailing spaces are ignored;  the first signifies
+                end of decoding and subsequent ones are skipped.
+
+     5     Delimiters:
+
+             .  Any character other than +,-,0-9 or space may be
+                used to signal the end of the number and terminate
+                decoding.
+
+             .  Comma is recognized by INTIN as a special case;  it
+                is skipped, leaving the pointer on the next character.
+                See 9, below.
+
+     6     The sign is optional.  The default is +.
+
+     7     A "null result" occurs when the string of characters being
+           decoded does not begin with +,- or 0-9, or consists
+           entirely of spaces.  When this condition is detected, JFLAG
+           is set to 1 and IRESLT is left untouched.
+
+     8     NSTRT = 1 for the first character in the string.
+
+     9     On return from INTIN, NSTRT is set ready for the next
+           decode - following trailing blanks and any comma.  If a
+           delimiter other than comma is being used, NSTRT must be
+           incremented before the next call to INTIN, otherwise
+           all subsequent calls will return a null result.
+
+     10    Errors (JFLAG=2) occur when:
+
+             .  there is a + or - but no number;  or
+
+             .  the number is greater than BIG (defined below).
+
+     11    When an error has been detected, NSTRT is left
+           pointing to the character following the last
+           one used before the error came to light.
+
+     12    See also FLOTIN and DFLTIN.
+
+  P.T.Wallace   Starlink   27 April 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/invf.hlp b/math/slalib/doc/invf.hlp
new file mode 100644
index 00000000..e1d8588e
--- /dev/null
+++ b/math/slalib/doc/invf.hlp
@@ -0,0 +1,66 @@
+.help invf Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slINVF (FWDS,BKWDS,J)
+
+     - - - - -
+      I N V F
+     - - - - -
+
+  Invert a linear model of the type produced by the
+  slFTXY routine.
+
+  Given:
+     FWDS    d(6)      model coefficients
+
+  Returned:
+     BKWDS   d(6)      inverse model
+     J        i        status:  0 = OK, -1 = no inverse
+
+  The models relate two sets of [X,Y] coordinates as follows.
+  Naming the elements of FWDS:
+
+     FWDS(1) = A
+     FWDS(2) = B
+     FWDS(3) = C
+     FWDS(4) = D
+     FWDS(5) = E
+     FWDS(6) = F
+
+  where two sets of coordinates [X1,Y1] and [X2,Y1] are related
+  thus:
+
+     X2 = A + B*X1 + C*Y1
+     Y2 = D + E*X1 + F*Y1
+
+  the present routine generates a new set of coefficients:
+
+     BKWDS(1) = P
+     BKWDS(2) = Q
+     BKWDS(3) = R
+     BKWDS(4) = S
+     BKWDS(5) = T
+     BKWDS(6) = U
+
+  such that:
+
+     X1 = P + Q*X2 + R*Y2
+     Y1 = S + T*X2 + U*Y2
+
+  Two successive calls to slINVF will thus deliver a set
+  of coefficients equal to the starting values.
+
+  To comply with the ANSI Fortran standard, FWDS and BKWDS must
+  not be the same array, even though the routine is coded to
+  work on the VAX and most other computers even if this rule
+  is violated.
+
+  See also slFTXY, slPXY, slXYXY, slDCMF
+
+  P.T.Wallace   Starlink   11 April 1990
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/kbj.hlp b/math/slalib/doc/kbj.hlp
new file mode 100644
index 00000000..519868a7
--- /dev/null
+++ b/math/slalib/doc/kbj.hlp
@@ -0,0 +1,28 @@
+.help kbj Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slKBJ (JB, E, K, J)
+
+     - - - -
+      K B J
+     - - - -
+
+  Select epoch prefix 'B' or 'J'
+
+  Given:
+     JB     int     slDBJI prefix status:  0=none, 1='B', 2='J'
+     E      dp      epoch - Besselian or Julian
+
+  Returned:
+     K      char    'B' or 'J'
+     J      int     status:  0=OK
+
+  If JB=0, B is assumed for E < 1984D0, otherwise J.
+
+  P.T.Wallace   Starlink   31 July 1989
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/m2av.hlp b/math/slalib/doc/m2av.hlp
new file mode 100644
index 00000000..51d04343
--- /dev/null
+++ b/math/slalib/doc/m2av.hlp
@@ -0,0 +1,38 @@
+.help m2av Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slM2AV (RMAT, AXVEC)
+
+     - - - - -
+      M 2 A V
+     - - - - -
+
+  From a rotation matrix, determine the corresponding axial vector
+  (single precision)
+
+  A rotation matrix describes a rotation about some arbitrary axis.
+  The axis is called the Euler axis, and the angle through which the
+  reference frame rotates is called the Euler angle.  The axial
+  vector returned by this routine has the same direction as the
+  Euler axis, and its magnitude is the Euler angle in radians.  (The
+  magnitude and direction can be separated by means of the routine
+  slVN.)
+
+  Given:
+    RMAT   r(3,3)   rotation matrix
+
+  Returned:
+    AXVEC  r(3)     axial vector (radians)
+
+  The reference frame rotates clockwise as seen looking along
+  the axial vector from the origin.
+
+  If RMAT is null, so is the result.
+
+  P.T.Wallace   Starlink   11 April 1990
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/map.hlp b/math/slalib/doc/map.hlp
new file mode 100644
index 00000000..4a66189b
--- /dev/null
+++ b/math/slalib/doc/map.hlp
@@ -0,0 +1,65 @@
+.help map Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slMAP (RM, DM, PR, PD, PX, RV, EQ, DATE, RA, DA)
+
+     - - - -
+      M A P
+     - - - -
+
+  Transform star RA,Dec from mean place to geocentric apparent
+
+  The reference frames and timescales used are post IAU 1976.
+
+  References:
+     1984 Astronomical Almanac, pp B39-B41.
+     (also Lederle & Schwan, Astron. Astrophys. 134,
+      1-6, 1984)
+
+  Given:
+     RM,DM    dp     mean RA,Dec (rad)
+     PR,PD    dp     proper motions:  RA,Dec changes per Julian year
+     PX       dp     parallax (arcsec)
+     RV       dp     radial velocity (km/sec, +ve if receding)
+     EQ       dp     epoch and equinox of star data (Julian)
+     DATE     dp     TDB for apparent place (JD-2400000.5)
+
+  Returned:
+     RA,DA    dp     apparent RA,Dec (rad)
+
+  Called:
+     slMAPA       star-independent parameters
+     slMAPQ       quick mean to apparent
+
+  Notes:
+
+  1)  EQ is the Julian epoch specifying both the reference
+      frame and the epoch of the position - usually 2000.
+      For positions where the epoch and equinox are
+      different, use the routine slPM to apply proper
+      motion corrections before using this routine.
+
+  2)  The distinction between the required TDB and TT is
+      always negligible.  Moreover, for all but the most
+      critical applications UTC is adequate.
+
+  3)  The proper motions in RA are dRA/dt rather than
+      cos(Dec)*dRA/dt.
+
+  4)  This routine may be wasteful for some applications
+      because it recomputes the Earth position/velocity and
+      the precession/nutation matrix each time, and because
+      it allows for parallax and proper motion.  Where
+      multiple transformations are to be carried out for one
+      epoch, a faster method is to call the slMAPA routine
+      once and then either the slMAPQ routine (which includes
+      parallax and proper motion) or slMAPZ (which assumes
+      zero parallax and proper motion).
+
+  P.T.Wallace   Starlink   19 January 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/mappa.hlp b/math/slalib/doc/mappa.hlp
new file mode 100644
index 00000000..7a2bf727
--- /dev/null
+++ b/math/slalib/doc/mappa.hlp
@@ -0,0 +1,69 @@
+.help mappa Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slMAPA (EQ, DATE, AMPRMS)
+
+     - - - - - -
+      M A P A
+     - - - - - -
+
+  Compute star-independent parameters in preparation for
+  conversions between mean place and geocentric apparent place.
+
+  The parameters produced by this routine are required in the
+  parallax, light deflection, aberration, and precession/nutation
+  parts of the mean/apparent transformations.
+
+  The reference frames and timescales used are post IAU 1976.
+
+  Given:
+     EQ       d      epoch of mean equinox to be used (Julian)
+     DATE     d      TDB (JD-2400000.5)
+
+  Returned:
+     AMPRMS   d(21)  star-independent mean-to-apparent parameters:
+
+       (1)      time interval for proper motion (Julian years)
+       (2-4)    barycentric position of the Earth (AU)
+       (5-7)    heliocentric direction of the Earth (unit vector)
+       (8)      (grav rad Sun)*2/(Sun-Earth distance)
+       (9-11)   ABV: barycentric Earth velocity in units of c
+       (12)     sqrt(1-v**2) where v=modulus(ABV)
+       (13-21)  precession/nutation (3,3) matrix
+
+  References:
+     1984 Astronomical Almanac, pp B39-B41.
+     (also Lederle & Schwan, Astron. Astrophys. 134,
+      1-6, 1984)
+
+  Notes:
+
+  1)  For DATE, the distinction between the required TDB and TT
+      is always negligible.  Moreover, for all but the most
+      critical applications UTC is adequate.
+
+  2)  The accuracy of the routines using the parameters AMPRMS is
+      limited by the routine slEVP, used here to compute the
+      Earth position and velocity by the methods of Stumpff.
+      The maximum error in the resulting aberration corrections is
+      about 0.3 milliarcsecond.
+
+  3)  The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to
+      the mean equinox and equator of epoch EQ.
+
+  4)  The parameters AMPRMS produced by this routine are used by
+      slMAPQ and slMAPZ.
+
+  Called:
+     slEPJ         MDJ to Julian epoch
+     slEVP         earth position & velocity
+     slDVN         normalize vector
+     slPRNU      precession/nutation matrix
+
+  P.T.Wallace   Starlink   23 November 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/mapqk.hlp b/math/slalib/doc/mapqk.hlp
new file mode 100644
index 00000000..adfa1f3d
--- /dev/null
+++ b/math/slalib/doc/mapqk.hlp
@@ -0,0 +1,76 @@
+.help mapqk Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slMAPQ (RM, DM, PR, PD, PX, RV, AMPRMS, RA, DA)
+
+     - - - - - -
+      M A P Q
+     - - - - - -
+
+  Quick mean to apparent place:  transform a star RA,Dec from
+  mean place to geocentric apparent place, given the
+  star-independent parameters.
+
+  Use of this routine is appropriate when efficiency is important
+  and where many star positions, all referred to the same equator
+  and equinox, are to be transformed for one epoch.  The
+  star-independent parameters can be obtained by calling the
+  slMAPA routine.
+
+  If the parallax and proper motions are zero the slMAPZ
+  routine can be used instead.
+
+  The reference frames and timescales used are post IAU 1976.
+
+  Given:
+     RM,DM    d      mean RA,Dec (rad)
+     PR,PD    d      proper motions:  RA,Dec changes per Julian year
+     PX       d      parallax (arcsec)
+     RV       d      radial velocity (km/sec, +ve if receding)
+
+     AMPRMS   d(21)  star-independent mean-to-apparent parameters:
+
+       (1)      time interval for proper motion (Julian years)
+       (2-4)    barycentric position of the Earth (AU)
+       (5-7)    heliocentric direction of the Earth (unit vector)
+       (8)      (grav rad Sun)*2/(Sun-Earth distance)
+       (9-11)   barycentric Earth velocity in units of c
+       (12)     sqrt(1-v**2) where v=modulus(ABV)
+       (13-21)  precession/nutation (3,3) matrix
+
+  Returned:
+     RA,DA    d      apparent RA,Dec (rad)
+
+  References:
+     1984 Astronomical Almanac, pp B39-B41.
+     (also Lederle & Schwan, Astron. Astrophys. 134,
+      1-6, 1984)
+
+  Notes:
+
+  1)  The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to
+      the mean equinox and equator of epoch EQ.
+
+  2)  Strictly speaking, the routine is not valid for solar-system
+      sources, though the error will usually be extremely small.
+      However, to prevent gross errors in the case where the
+      position of the Sun is specified, the gravitational
+      deflection term is restrained within about 920 arcsec of the
+      centre of the Sun's disc.  The term has a maximum value of
+      about 1.85 arcsec at this radius, and decreases to zero as
+      the centre of the disc is approached.
+
+  Called:
+     slDS2C       spherical to Cartesian
+     slDVDV        dot product
+     slDMXV        matrix x vector
+     slDC2S       Cartesian to spherical
+     slDA2P      normalize angle 0-2Pi
+
+  P.T.Wallace   Starlink   23 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/mapqkz.hlp b/math/slalib/doc/mapqkz.hlp
new file mode 100644
index 00000000..2ca9b493
--- /dev/null
+++ b/math/slalib/doc/mapqkz.hlp
@@ -0,0 +1,68 @@
+.help mapqkz Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slMAPZ (RM, DM, AMPRMS, RA, DA)
+
+     - - - - - - -
+      M A P Z
+     - - - - - - -
+
+  Quick mean to apparent place:  transform a star RA,Dec from
+  mean place to geocentric apparent place, given the
+  star-independent parameters, and assuming zero parallax
+  and proper motion.
+
+  Use of this routine is appropriate when efficiency is important
+  and where many star positions, all with parallax and proper
+  motion either zero or already allowed for, and all referred to
+  the same equator and equinox, are to be transformed for one
+  epoch.  The star-independent parameters can be obtained by
+  calling the slMAPA routine.
+
+  The corresponding routine for the case of non-zero parallax
+  and proper motion is slMAPQ.
+
+  The reference frames and timescales used are post IAU 1976.
+
+  Given:
+     RM,DM    d      mean RA,Dec (rad)
+     AMPRMS   d(21)  star-independent mean-to-apparent parameters:
+
+       (1-4)    not used
+       (5-7)    heliocentric direction of the Earth (unit vector)
+       (8)      (grav rad Sun)*2/(Sun-Earth distance)
+       (9-11)   ABV: barycentric Earth velocity in units of c
+       (12)     sqrt(1-v**2) where v=modulus(ABV)
+       (13-21)  precession/nutation (3,3) matrix
+
+  Returned:
+     RA,DA    d      apparent RA,Dec (rad)
+
+  References:
+     1984 Astronomical Almanac, pp B39-B41.
+     (also Lederle & Schwan, Astron. Astrophys. 134,
+      1-6, 1984)
+
+  Notes:
+
+  1)  The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to the
+      mean equinox and equator of epoch EQ.
+
+  2)  Strictly speaking, the routine is not valid for solar-system
+      sources, though the error will usually be extremely small.
+      However, to prevent gross errors in the case where the
+      position of the Sun is specified, the gravitational
+      deflection term is restrained within about 920 arcsec of the
+      centre of the Sun's disc.  The term has a maximum value of
+      about 1.85 arcsec at this radius, and decreases to zero as
+      the centre of the disc is approached.
+
+  Called:  slDS2C, slDVDV, slDMXV, slDC2S, slDA2P
+
+  P.T.Wallace   Starlink   18 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/moon.hlp b/math/slalib/doc/moon.hlp
new file mode 100644
index 00000000..403984eb
--- /dev/null
+++ b/math/slalib/doc/moon.hlp
@@ -0,0 +1,59 @@
+.help moon Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slMOON (IY, ID, FD, PV)
+
+     - - - - -
+      M O O N
+     - - - - -
+
+  Approximate geocentric position and velocity of the Moon
+  (single precision).
+
+  Given:
+     IY       i       year
+     ID       i       day in year (1 = Jan 1st)
+     FD       r       fraction of day
+
+  Returned:
+     PV       r(6)    Moon position & velocity vector
+
+  Notes:
+
+  1  The date and time is TDB (loosely ET) in a Julian calendar
+     which has been aligned to the ordinary Gregorian
+     calendar for the interval 1900 March 1 to 2100 February 28.
+     The year and day can be obtained by calling slCAYD or
+     slCLYD.
+
+  2  The Moon 6-vector is Moon centre relative to Earth centre,
+     mean equator and equinox of date.  Position part, PV(1-3),
+     is in AU;  velocity part, PV(4-6), is in AU/sec.
+
+  3  The position is accurate to better than 0.5 arcminute
+     in direction and 1000 km in distance.  The velocity
+     is accurate to better than 0.5"/hour in direction and
+     4 m/s in distance.  (RMS figures with respect to JPL DE200
+     for the interval 1960-2025 are 14 arcsec and 0.2 arcsec/hour in
+     longitude, 9 arcsec and 0.2 arcsec/hour in latitude, 350 km and
+     2 m/s in distance.)  Note that the distance accuracy is
+     comparatively poor because this routine is principally intended
+     for computing topocentric direction.
+
+  4  This routine is only a partial implementation of the original
+     Meeus algorithm (reference below), which offers 4 times the
+     accuracy in direction and 30 times the accuracy in distance
+     when fully implemented (as it is in slDMON).
+
+  Reference:
+     Meeus, l'Astronomie, June 1984, p348.
+
+  Called:  slS2C6
+
+  P.T.Wallace   Starlink   8 December 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/mxm.hlp b/math/slalib/doc/mxm.hlp
new file mode 100644
index 00000000..7ee561e4
--- /dev/null
+++ b/math/slalib/doc/mxm.hlp
@@ -0,0 +1,33 @@
+.help mxm Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slMXM (A, B, C)
+
+     - - - -
+      M X M
+     - - - -
+
+  Product of two 3x3 matrices:
+      matrix C  =  matrix A  x  matrix B
+
+  (single precision)
+
+  Given:
+      A      real(3,3)        matrix
+      B      real(3,3)        matrix
+
+  Returned:
+      C      real(3,3)        matrix result
+
+  To comply with the ANSI Fortran 77 standard, A, B and C must
+  be different arrays.  However, the routine is coded so as to
+  work properly on the VAX and many other systems even if this
+  rule is violated.
+
+  P.T.Wallace   Starlink   5 April 1990
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/mxv.hlp b/math/slalib/doc/mxv.hlp
new file mode 100644
index 00000000..bacba504
--- /dev/null
+++ b/math/slalib/doc/mxv.hlp
@@ -0,0 +1,29 @@
+.help mxv Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slMXV (RM, VA, VB)
+
+     - - - -
+      M X V
+     - - - -
+
+  Performs the 3-D forward unitary transformation:
+
+     vector VB = matrix RM * vector VA
+
+  (single precision)
+
+  Given:
+     RM       real(3,3)    matrix
+     VA       real(3)      vector
+
+  Returned:
+     VB       real(3)      result vector
+
+  P.T.Wallace   Starlink   March 1986
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/nut.hlp b/math/slalib/doc/nut.hlp
new file mode 100644
index 00000000..95ea2ff0
--- /dev/null
+++ b/math/slalib/doc/nut.hlp
@@ -0,0 +1,34 @@
+.help nut Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slNUT (DATE, RMATN)
+
+     - - - -
+      N U T
+     - - - -
+
+  Form the matrix of nutation for a given date - IAU 1980 theory
+  (double precision)
+
+  References:
+     Final report of the IAU Working Group on Nutation,
+      chairman P.K.Seidelmann, 1980.
+     Kaplan,G.H., 1981, USNO circular no. 163, pA3-6.
+
+  Given:
+     DATE   dp         TDB (loosely ET) as Modified Julian Date
+                                           (=JD-2400000.5)
+  Returned:
+     RMATN  dp(3,3)    nutation matrix
+
+  The matrix is in the sense   V(true)  =  RMATN * V(mean)
+
+  Called:   slNUTC, slDEUL
+
+  P.T.Wallace   Starlink   1 January 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/nutc.hlp b/math/slalib/doc/nutc.hlp
new file mode 100644
index 00000000..b028219d
--- /dev/null
+++ b/math/slalib/doc/nutc.hlp
@@ -0,0 +1,33 @@
+.help nutc Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slNUTC (DATE, DPSI, DEPS, EPS0)
+
+     - - - - -
+      N U T C
+     - - - - -
+
+  Nutation:  longitude & obliquity components and mean
+  obliquity - IAU 1980 theory (double precision)
+
+  Given:
+
+     DATE        dp    TDB (loosely ET) as Modified Julian Date
+                                            (JD-2400000.5)
+  Returned:
+
+     DPSI,DEPS   dp    nutation in longitude,obliquity
+     EPS0        dp    mean obliquity
+
+  References:
+     Final report of the IAU Working Group on Nutation,
+      chairman P.K.Seidelmann, 1980.
+     Kaplan,G.H., 1981, USNO circular no. 163, pA3-6.
+
+  P.T.Wallace   Starlink   23 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/oap.hlp b/math/slalib/doc/oap.hlp
new file mode 100644
index 00000000..7322c0ee
--- /dev/null
+++ b/math/slalib/doc/oap.hlp
@@ -0,0 +1,163 @@
+.help oap Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slOAP (TYPE, OB1, OB2, DATE, DUT, ELONGM, PHIM,
+     :                    HM, XP, YP, TDK, PMB, RH, WL, TLR,
+     :                    RAP, DAP)
+
+     - - - -
+      O A P
+     - - - -
+
+  Observed to apparent place
+
+  Given:
+     TYPE   c*(*)  type of coordinates - 'R', 'H' or 'A' (see below)
+     OB1    d      observed Az, HA or RA (radians; Az is N=0,E=90)
+     OB2    d      observed ZD or Dec (radians)
+     DATE   d      UTC date/time (modified Julian Date, JD-2400000.5)
+     DUT    d      delta UT:  UT1-UTC (UTC seconds)
+     ELONGM d      mean longitude of the observer (radians, east +ve)
+     PHIM   d      mean geodetic latitude of the observer (radians)
+     HM     d      observer's height above sea level (metres)
+     XP     d      polar motion x-coordinate (radians)
+     YP     d      polar motion y-coordinate (radians)
+     TDK    d      local ambient temperature (DegK; std=273.155D0)
+     PMB    d      local atmospheric pressure (mB; std=1013.25D0)
+     RH     d      local relative humidity (in the range 0D0-1D0)
+     WL     d      effective wavelength (micron, e.g. 0.55D0)
+     TLR    d      tropospheric lapse rate (DegK/metre, e.g. 0.0065D0)
+
+  Returned:
+     RAP    d      geocentric apparent right ascension
+     DAP    d      geocentric apparent declination
+
+  Notes:
+
+  1)  Only the first character of the TYPE argument is significant.
+      'R' or 'r' indicates that OBS1 and OBS2 are the observed Right
+      Ascension and Declination;  'H' or 'h' indicates that they are
+      Hour Angle (West +ve) and Declination;  anything else ('A' or
+      'a' is recommended) indicates that OBS1 and OBS2 are Azimuth
+      (North zero, East is 90 deg) and zenith distance.  (Zenith
+      distance is used rather than elevation in order to reflect the
+      fact that no allowance is made for depression of the horizon.)
+
+  2)  The accuracy of the result is limited by the corrections for
+      refraction.  Providing the meteorological parameters are
+      known accurately and there are no gross local effects, the
+      predicted apparent RA,Dec should be within about 0.1 arcsec
+      for a zenith distance of less than 70 degrees.  Even at a
+      topocentric zenith distance of 90 degrees, the accuracy in
+      elevation should be better than 1 arcmin;  useful results
+      are available for a further 3 degrees, beyond which the
+      slRFRO routine returns a fixed value of the refraction.
+      The complementary routines slAOP (or slAOPQ) and slOAP
+      (or slOAPQ) are self-consistent to better than 1 micro-
+      arcsecond all over the celestial sphere.
+
+  3)  It is advisable to take great care with units, as even
+      unlikely values of the input parameters are accepted and
+      processed in accordance with the models used.
+
+  4)  "Observed" Az,El means the position that would be seen by a
+      perfect theodolite located at the observer.  This is
+      related to the observed HA,Dec via the standard rotation, using
+      the geodetic latitude (corrected for polar motion), while the
+      observed HA and RA are related simply through the local
+      apparent ST.  "Observed" RA,Dec or HA,Dec thus means the
+      position that would be seen by a perfect equatorial located
+      at the observer and with its polar axis aligned to the
+      Earth's axis of rotation (n.b. not to the refracted pole).
+      By removing from the observed place the effects of
+      atmospheric refraction and diurnal aberration, the
+      geocentric apparent RA,Dec is obtained.
+
+  5)  Frequently, mean rather than apparent RA,Dec will be required,
+      in which case further transformations will be necessary.  The
+      slAMP etc routines will convert the apparent RA,Dec produced
+      by the present routine into an "FK5" (J2000) mean place, by
+      allowing for the Sun's gravitational lens effect, annual
+      aberration, nutation and precession.  Should "FK4" (1950)
+      coordinates be needed, the routines slFK54 etc will also
+      need to be applied.
+
+  6)  To convert to apparent RA,Dec the coordinates read from a
+      real telescope, corrections would have to be applied for
+      encoder zero points, gear and encoder errors, tube flexure,
+      the position of the rotator axis and the pointing axis
+      relative to it, non-perpendicularity between the mounting
+      axes, and finally for the tilt of the azimuth or polar axis
+      of the mounting (with appropriate corrections for mount
+      flexures).  Some telescopes would, of course, exhibit other
+      properties which would need to be accounted for at the
+      appropriate point in the sequence.
+
+  7)  The star-independent apparent-to-observed-place parameters
+      in AOPRMS may be computed by means of the slAOPA routine.
+      If nothing has changed significantly except the time, the
+      slAOPT routine may be used to perform the requisite
+      partial recomputation of AOPRMS.
+
+  8)  The DATE argument is UTC expressed as an MJD.  This is,
+      strictly speaking, wrong, because of leap seconds.  However,
+      as long as the delta UT and the UTC are consistent there
+      are no difficulties, except during a leap second.  In this
+      case, the start of the 61st second of the final minute should
+      begin a new MJD day and the old pre-leap delta UT should
+      continue to be used.  As the 61st second completes, the MJD
+      should revert to the start of the day as, simultaneously,
+      the delta UTC changes by one second to its post-leap new value.
+
+  9)  The delta UT (UT1-UTC) is tabulated in IERS circulars and
+      elsewhere.  It increases by exactly one second at the end of
+      each UTC leap second, introduced in order to keep delta UT
+      within +/- 0.9 seconds.
+
+  10) IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.
+      The longitude required by the present routine is east-positive,
+      in accordance with geographical convention (and right-handed).
+      In particular, note that the longitudes returned by the
+      slOBS routine are west-positive, following astronomical
+      usage, and must be reversed in sign before use in the present
+      routine.
+
+  11) The polar coordinates XP,YP can be obtained from IERS
+      circulars and equivalent publications.  The maximum amplitude
+      is about 0.3 arcseconds.  If XP,YP values are unavailable,
+      use XP=YP=0D0.  See page B60 of the 1988 Astronomical Almanac
+      for a definition of the two angles.
+
+  12) The height above sea level of the observing station, HM,
+      can be obtained from the Astronomical Almanac (Section J
+      in the 1988 edition), or via the routine slOBS.  If P,
+      the pressure in millibars, is available, an adequate
+      estimate of HM can be obtained from the expression
+
+             HM ~ -29.3D0*TSL*LOG(P/1013.25D0).
+
+      where TSL is the approximate sea-level air temperature in
+      deg K (see Astrophysical Quantities, C.W.Allen, 3rd edition,
+      section 52.)  Similarly, if the pressure P is not known,
+      it can be estimated from the height of the observing
+      station, HM as follows:
+
+             P ~ 1013.25D0*EXP(-HM/(29.3D0*TSL)).
+
+      Note, however, that the refraction is proportional to the
+      pressure and that an accurate P value is important for
+      precise work.
+
+  13) The azimuths etc used by the present routine are with respect
+      to the celestial pole.  Corrections from the terrestrial pole
+      can be computed using slPLMO.
+
+  Called:  slAOPA, slOAPQ
+
+  P.T.Wallace   Starlink   9 June 1998
+
+  Copyright (C) 1998 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/oapqk.hlp b/math/slalib/doc/oapqk.hlp
new file mode 100644
index 00000000..70a37f86
--- /dev/null
+++ b/math/slalib/doc/oapqk.hlp
@@ -0,0 +1,114 @@
+.help oapqk Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slOAPQ (TYPE, OB1, OB2, AOPRMS, RAP, DAP)
+
+     - - - - - -
+      O A P Q
+     - - - - - -
+
+  Quick observed to apparent place
+
+  Given:
+     TYPE   c*(*)  type of coordinates - 'R', 'H' or 'A' (see below)
+     OB1    d      observed Az, HA or RA (radians; Az is N=0,E=90)
+     OB2    d      observed ZD or Dec (radians)
+     AOPRMS d(14)  star-independent apparent-to-observed parameters:
+
+       (1)      geodetic latitude (radians)
+       (2,3)    sine and cosine of geodetic latitude
+       (4)      magnitude of diurnal aberration vector
+       (5)      height (HM)
+       (6)      ambient temperature (T)
+       (7)      pressure (P)
+       (8)      relative humidity (RH)
+       (9)      wavelength (WL)
+       (10)     lapse rate (TLR)
+       (11,12)  refraction constants A and B (radians)
+       (13)     longitude + eqn of equinoxes + sidereal DUT (radians)
+       (14)     local apparent sidereal time (radians)
+
+  Returned:
+     RAP    d      geocentric apparent right ascension
+     DAP    d      geocentric apparent declination
+
+  Notes:
+
+  1)  Only the first character of the TYPE argument is significant.
+      'R' or 'r' indicates that OBS1 and OBS2 are the observed Right
+      Ascension and Declination;  'H' or 'h' indicates that they are
+      Hour Angle (West +ve) and Declination;  anything else ('A' or
+      'a' is recommended) indicates that OBS1 and OBS2 are Azimuth
+      (North zero, East is 90 deg) and zenith distance.  (Zenith
+      distance is used rather than elevation in order to reflect the
+      fact that no allowance is made for depression of the horizon.)
+
+  2)  The accuracy of the result is limited by the corrections for
+      refraction.  Providing the meteorological parameters are
+      known accurately and there are no gross local effects, the
+      predicted apparent RA,Dec should be within about 0.1 arcsec
+      for a zenith distance of less than 70 degrees.  Even at a
+      topocentric zenith distance of 90 degrees, the accuracy in
+      elevation should be better than 1 arcmin;  useful results
+      are available for a further 3 degrees, beyond which the
+      slRFRO routine returns a fixed value of the refraction.
+      The complementary routines slAOP (or slAOPQ) and slOAP
+      (or slOAPQ) are self-consistent to better than 1 micro-
+      arcsecond all over the celestial sphere.
+
+  3)  It is advisable to take great care with units, as even
+      unlikely values of the input parameters are accepted and
+      processed in accordance with the models used.
+
+  5)  "Observed" Az,El means the position that would be seen by a
+      perfect theodolite located at the observer.  This is
+      related to the observed HA,Dec via the standard rotation, using
+      the geodetic latitude (corrected for polar motion), while the
+      observed HA and RA are related simply through the local
+      apparent ST.  "Observed" RA,Dec or HA,Dec thus means the
+      position that would be seen by a perfect equatorial located
+      at the observer and with its polar axis aligned to the
+      Earth's axis of rotation (n.b. not to the refracted pole).
+      By removing from the observed place the effects of
+      atmospheric refraction and diurnal aberration, the
+      geocentric apparent RA,Dec is obtained.
+
+  5)  Frequently, mean rather than apparent RA,Dec will be required,
+      in which case further transformations will be necessary.  The
+      slAMP etc routines will convert the apparent RA,Dec produced
+      by the present routine into an "FK5" (J2000) mean place, by
+      allowing for the Sun's gravitational lens effect, annual
+      aberration, nutation and precession.  Should "FK4" (1950)
+      coordinates be needed, the routines slFK54 etc will also
+      need to be applied.
+
+  6)  To convert to apparent RA,Dec the coordinates read from a
+      real telescope, corrections would have to be applied for
+      encoder zero points, gear and encoder errors, tube flexure,
+      the position of the rotator axis and the pointing axis
+      relative to it, non-perpendicularity between the mounting
+      axes, and finally for the tilt of the azimuth or polar axis
+      of the mounting (with appropriate corrections for mount
+      flexures).  Some telescopes would, of course, exhibit other
+      properties which would need to be accounted for at the
+      appropriate point in the sequence.
+
+  7)  The star-independent apparent-to-observed-place parameters
+      in AOPRMS may be computed by means of the slAOPA routine.
+      If nothing has changed significantly except the time, the
+      slAOPT routine may be used to perform the requisite
+      partial recomputation of AOPRMS.
+
+  8) The azimuths etc used by the present routine are with respect
+     to the celestial pole.  Corrections from the terrestrial pole
+     can be computed using slPLMO.
+
+  Called:  slDS2C, slDC2S, slRFRO, slDA2P
+
+  P.T.Wallace   Starlink   23 June 1997
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/obs.hlp b/math/slalib/doc/obs.hlp
new file mode 100644
index 00000000..bce6404e
--- /dev/null
+++ b/math/slalib/doc/obs.hlp
@@ -0,0 +1,83 @@
+.help obs Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slOBS (N, C, NAME, W, P, H)
+
+     - - - -
+      O B S
+     - - - -
+
+  Parameters of selected groundbased observing stations
+
+  Given:
+     N       int     number specifying observing station
+
+  Either given or returned
+     C       c*(*)   identifier specifying observing station
+
+  Returned:
+     NAME    c*(*)   name of specified observing station
+     W       dp      longitude (radians, West +ve)
+     P       dp      geodetic latitude (radians, North +ve)
+     H       dp      height above sea level (metres)
+
+  Notes:
+
+     Station identifiers C may be up to 10 characters long,
+     and station names NAME may be up to 40 characters long.
+
+     C and N are alternative ways of specifying the observing
+     station.  The C option, which is the most generally useful,
+     may be selected by specifying an N value of zero or less.
+     If N is 1 or more, the parameters of the Nth station
+     in the currently supported list are interrogated, and
+     the station identifier C is returned as well as NAME, W,
+     P and H.
+
+     If the station parameters are not available, either because
+     the station identifier C is not recognized, or because an
+     N value greater than the number of stations supported is
+     given, a name of '?' is returned and C, W, P and H are left
+     in their current states.
+
+     Programs can obtain a list of all currently supported
+     stations by calling the routine repeatedly, with N=1,2,3...
+     When NAME='?' is seen, the list of stations has been
+     exhausted.
+
+     Station numbers, identifiers, names and other details are
+     subject to change and should not be hardwired into
+     application programs.
+
+     All station identifiers C are uppercase only;  lowercase
+     characters must be converted to uppercase by the calling
+     program.  The station names returned may contain both upper-
+     and lowercase.  All characters up to the first space are
+     checked;  thus an abbreviated ID will return the parameters
+     for the first station in the list which matches the
+     abbreviation supplied, and no station in the list will ever
+     contain embedded spaces.  C must not have leading spaces.
+
+     IMPORTANT -- BEWARE OF THE LONGITUDE SIGN CONVENTION.  The
+     longitude returned by slOBS is west-positive in accordance
+     with astronomical usage.  However, this sign convention is
+     left-handed and is the opposite of the one used by geographers;
+     elsewhere in SLALIB the preferable east-positive convention is
+     used.  In particular, note that for use in slAOP, slAOPA
+     and slOAP the sign of the longitude must be reversed.
+
+     Users are urged to inform the author of any improvements
+     they would like to see made.  For example:
+
+         typographical corrections
+         more accurate parameters
+         better station identifiers or names
+         additional stations
+
+  P.T.Wallace   Starlink   21 April 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pa.hlp b/math/slalib/doc/pa.hlp
new file mode 100644
index 00000000..a7ee7357
--- /dev/null
+++ b/math/slalib/doc/pa.hlp
@@ -0,0 +1,36 @@
+.help pa Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slPA (HA, DEC, PHI)
+
+     - - -
+      P A
+     - - -
+
+  HA, Dec to Parallactic Angle (double precision)
+
+  Given:
+     HA     d     hour angle in radians (geocentric apparent)
+     DEC    d     declination in radians (geocentric apparent)
+     PHI    d     observatory latitude in radians (geodetic)
+
+  The result is in the range -pi to +pi
+
+  Notes:
+
+  1)  The parallactic angle at a point in the sky is the position
+      angle of the vertical, i.e. the angle between the direction to
+      the pole and to the zenith.  In precise applications care must
+      be taken only to use geocentric apparent HA,Dec and to consider
+      separately the effects of atmospheric refraction and telescope
+      mount errors.
+
+  2)  At the pole a zero result is returned.
+
+  P.T.Wallace   Starlink   16 August 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pav.hlp b/math/slalib/doc/pav.hlp
new file mode 100644
index 00000000..a74d3ca3
--- /dev/null
+++ b/math/slalib/doc/pav.hlp
@@ -0,0 +1,40 @@
+.help pav Jun99 "Slalib Package"
+.nf
+
+      REAL FUNCTION slPAV ( V1, V2 )
+
+     - - - -
+      P A V
+     - - - -
+
+  Position angle of one celestial direction with respect to another.
+
+  (single precision)
+
+  Given:
+     V1    r(3)    direction cosines of one point
+     V2    r(3)    direction cosines of the other point
+
+  (The coordinate frames correspond to RA,Dec, Long,Lat etc.)
+
+  The result is the bearing (position angle), in radians, of point
+  V2 with respect to point V1.  It is in the range +/- pi.  The
+  sense is such that if V2 is a small distance east of V1, the
+  bearing is about +pi/2.  Zero is returned if the two points
+  are coincident.
+
+  V1 and V2 do not have to be unit vectors.
+
+  The routine slBEAR performs an equivalent function except
+  that the points are specified in the form of spherical
+  coordinates.
+
+  Called:  slDPAV
+
+  Patrick Wallace   Starlink   23 May 1997
+
+  Copyright (C) 1997 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pcd.hlp b/math/slalib/doc/pcd.hlp
new file mode 100644
index 00000000..dd6263a4
--- /dev/null
+++ b/math/slalib/doc/pcd.hlp
@@ -0,0 +1,51 @@
+.help pcd Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPCD (DISCO,X,Y)
+
+     - - - -
+      P C D
+     - - - -
+
+  Apply pincushion/barrel distortion to a tangent-plane [x,y].
+
+  Given:
+     DISCO    d      pincushion/barrel distortion coefficient
+     X,Y      d      tangent-plane coordinates
+
+  Returned:
+     X,Y      d      distorted coordinates
+
+  Notes:
+
+  1)  The distortion is of the form RP = R*(1 + C*R**2), where R is
+      the radial distance from the tangent point, C is the DISCO
+      argument, and RP is the radial distance in the presence of
+      the distortion.
+
+  2)  For pincushion distortion, C is +ve;  for barrel distortion,
+      C is -ve.
+
+  3)  For X,Y in units of one projection radius (in the case of
+      a photographic plate, the focal length), the following
+      DISCO values apply:
+
+          Geometry          DISCO
+
+          astrograph         0.0
+          Schmidt           -0.3333
+          AAT PF doublet  +147.069
+          AAT PF triplet  +178.585
+          AAT f/8          +21.20
+          JKT f/8          +13.32
+
+  4)  There is a companion routine, slUPCD, which performs
+      an approximately inverse operation.
+
+  P.T.Wallace   Starlink   31 December 1992
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pda2h.hlp b/math/slalib/doc/pda2h.hlp
new file mode 100644
index 00000000..6a5a7dc4
--- /dev/null
+++ b/math/slalib/doc/pda2h.hlp
@@ -0,0 +1,33 @@
+.help pda2h Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPDAH (P, D, A, H1, J1, H2, J2)
+
+     - - - - - -
+      P D A H
+     - - - - - -
+
+  Hour Angle corresponding to a given azimuth
+
+  (double precision)
+
+  Given:
+     P       d        latitude
+     D       d        declination
+     A       d        azimuth
+
+  Returned:
+     H1      d        hour angle:  first solution if any
+     J1      i        flag: 0 = solution 1 is valid
+     H2      d        hour angle:  second solution if any
+     J2      i        flag: 0 = solution 2 is valid
+
+  Called:  slDA1P
+
+  P.T.Wallace   Starlink   6 October 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pdq2h.hlp b/math/slalib/doc/pdq2h.hlp
new file mode 100644
index 00000000..cdb0702f
--- /dev/null
+++ b/math/slalib/doc/pdq2h.hlp
@@ -0,0 +1,33 @@
+.help pdq2h Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPDQH (P, D, Q, H1, J1, H2, J2)
+
+     - - - - - -
+      P D Q H
+     - - - - - -
+
+  Hour Angle corresponding to a given parallactic angle
+
+  (double precision)
+
+  Given:
+     P       d        latitude
+     D       d        declination
+     Q       d        parallactic angle
+
+  Returned:
+     H1      d        hour angle:  first solution if any
+     J1      i        flag: 0 = solution 1 is valid
+     H2      d        hour angle:  second solution if any
+     J2      i        flag: 0 = solution 2 is valid
+
+  Called:  slDA1P
+
+  P.T.Wallace   Starlink   6 October 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pertel.hlp b/math/slalib/doc/pertel.hlp
new file mode 100644
index 00000000..c1685eca
--- /dev/null
+++ b/math/slalib/doc/pertel.hlp
@@ -0,0 +1,121 @@
+.help pertel Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPRTL (JFORM, DATE0, DATE1,
+     :                 EPOCH0, ORBI0, ANODE0, PERIH0, AORQ0, E0, AM0,
+     :                 EPOCH1, ORBI1, ANODE1, PERIH1, AORQ1, E1, AM1,
+     :                       JSTAT)
+
+     - - - - - - -
+      P R T L
+     - - - - - - -
+
+  Update the osculating orbital elements of an asteroid or comet by
+  applying planetary perturbations.
+
+  Given (format and dates):
+     JFORM   i    choice of element set (2 or 3; Note 1)
+     DATE0   d    date of osculation (TT MJD) for the given elements
+     DATE1   d    date of osculation (TT MJD) for the updated elements
+
+  Given (the unperturbed elements):
+     EPOCH0  d    epoch (TT MJD) of the given element set (Note 2)
+     ORBI0   d    inclination (radians)
+     ANODE0  d    longitude of the ascending node (radians)
+     PERIH0  d    argument of perihelion (radians)
+     AORQ0   d    mean distance or perihelion distance (AU)
+     E0      d    eccentricity
+     AM0     d    mean anomaly (radians, JFORM=2 only)
+
+  Returned (the updated elements):
+     EPOCH1  d    epoch (TT MJD) of the updated element set (Note 2)
+     ORBI1   d    inclination (radians)
+     ANODE1  d    longitude of the ascending node (radians)
+     PERIH1  d    argument of perihelion (radians)
+     AORQ1   d    mean distance or perihelion distance (AU)
+     E1      d    eccentricity
+     AM1     d    mean anomaly (radians, JFORM=2 only)
+
+  Returned (status flag):
+     JSTAT   i    status: +102 = warning, distant epoch
+                          +101 = warning, large timespan ( > 100 years)
+                      +1 to +8 = coincident with major planet (Note 6)
+                             0 = OK
+                            -1 = illegal JFORM
+                            -2 = illegal E0
+                            -3 = illegal AORQ0
+                            -4 = internal error
+                            -5 = numerical error
+
+  Notes:
+
+  1  Two different element-format options are available:
+
+     Option JFORM=2, suitable for minor planets:
+
+     EPOCH   = epoch of elements (TT MJD)
+     ORBI    = inclination i (radians)
+     ANODE   = longitude of the ascending node, big omega (radians)
+     PERIH   = argument of perihelion, little omega (radians)
+     AORQ    = mean distance, a (AU)
+     E       = eccentricity, e
+     AM      = mean anomaly M (radians)
+
+     Option JFORM=3, suitable for comets:
+
+     EPOCH   = epoch of perihelion (TT MJD)
+     ORBI    = inclination i (radians)
+     ANODE   = longitude of the ascending node, big omega (radians)
+     PERIH   = argument of perihelion, little omega (radians)
+     AORQ    = perihelion distance, q (AU)
+     E       = eccentricity, e
+
+  2  DATE0, DATE1, EPOCH0 and EPOCH1 are all instants of time in
+     the TT timescale (formerly Ephemeris Time, ET), expressed
+     as Modified Julian Dates (JD-2400000.5).
+
+     DATE0 is the instant at which the given (i.e. unperturbed)
+     osculating elements are correct.
+
+     DATE1 is the specified instant at which the updated osculating
+     elements are correct.
+
+     EPOCH0 and EPOCH1 will be the same as DATE0 and DATE1
+     (respectively) for the JFORM=2 case, normally used for minor
+     planets.  For the JFORM=3 case, the two epochs will refer to
+     perihelion passage and so will not, in general, be the same as
+     DATE0 and/or DATE1 though they may be similar to one another.
+
+  3  The elements are with respect to the J2000 ecliptic and equinox.
+
+  4  Unused elements (AM0 and AM1 for JFORM=3) are not accessed.
+
+  5  See the slPRTE routine for details of the algorithm used.
+
+  6  This routine is not intended to be used for major planets, which
+     is why JFORM=1 is not available and why there is no opportunity
+     to specify either the longitude of perihelion or the daily
+     motion.  However, if JFORM=2 elements are somehow obtained for a
+     major planet and supplied to the routine, sensible results will,
+     in fact, be produced.  This happens because the slPRTE routine
+     that is called to perform the calculations checks the separation
+     between the body and each of the planets and interprets a
+     suspiciously small value (0.001 AU) as an attempt to apply it to
+     the planet concerned.  If this condition is detected, the
+     contribution from that planet is ignored, and the status is set to
+     the planet number (Mercury=1,...,Neptune=8) as a warning.
+
+  Reference:
+
+     Sterne, Theodore E., "An Introduction to Celestial Mechanics",
+     Interscience Publishers Inc., 1960.  Section 6.7, p199.
+
+  Called:  slELUE, slPRTE, slUEEL
+
+  P.T.Wallace   Starlink   14 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pertue.hlp b/math/slalib/doc/pertue.hlp
new file mode 100644
index 00000000..4f5cf166
--- /dev/null
+++ b/math/slalib/doc/pertue.hlp
@@ -0,0 +1,152 @@
+.help pertue Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPRTE (DATE, U, JSTAT)
+
+     - - - - - - -
+      P R T E
+     - - - - - - -
+
+  Update the universal elements of an asteroid or comet by applying
+  planetary perturbations.
+
+  Given:
+     DATE     d       final epoch (TT MJD) for the updated elements
+
+  Given and returned:
+     U        d(13)   universal elements (updated in place)
+
+                (1)   combined mass (M+m)
+                (2)   total energy of the orbit (alpha)
+                (3)   reference (osculating) epoch (t0)
+              (4-6)   position at reference epoch (r0)
+              (7-9)   velocity at reference epoch (v0)
+               (10)   heliocentric distance at reference epoch
+               (11)   r0.v0
+               (12)   date (t)
+               (13)   universal eccentric anomaly (psi) of date, approx
+
+  Returned:
+     JSTAT    i       status:
+                          +102 = warning, distant epoch
+                          +101 = warning, large timespan ( > 100 years)
+                      +1 to +8 = coincident with major planet (Note 5)
+                             0 = OK
+                            -1 = numerical error
+
+  Called:  slPLNT, slUEPV, slPVUE
+
+  Notes:
+
+  1  The "universal" elements are those which define the orbit for the
+     purposes of the method of universal variables (see reference 2).
+     They consist of the combined mass of the two bodies, an epoch,
+     and the position and velocity vectors (arbitrary reference frame)
+     at that epoch.  The parameter set used here includes also various
+     quantities that can, in fact, be derived from the other
+     information.  This approach is taken to avoiding unnecessary
+     computation and loss of accuracy.  The supplementary quantities
+     are (i) alpha, which is proportional to the total energy of the
+     orbit, (ii) the heliocentric distance at epoch, (iii) the
+     outwards component of the velocity at the given epoch, (iv) an
+     estimate of psi, the "universal eccentric anomaly" at a given
+     date and (v) that date.
+
+  2  The universal elements are with respect to the J2000 equator and
+     equinox.
+
+  3  The epochs DATE, U(3) and U(12) are all Modified Julian Dates
+     (JD-2400000.5).
+
+  4  The algorithm is a simplified form of Encke's method.  It takes as
+     a basis the unperturbed motion of the body, and numerically
+     integrates the perturbing accelerations from the major planets.
+     The expression used is essentially Sterne's 6.7-2 (reference 1).
+     Everhart and Pitkin (reference 2) suggest rectifying the orbit at
+     each integration step by propagating the new perturbed position
+     and velocity as the new universal variables.  In the present
+     routine the orbit is rectified less frequently than this, in order
+     to gain a slight speed advantage.  However, the rectification is
+     done directly in terms of position and velocity, as suggested by
+     Everhart and Pitkin, bypassing the use of conventional orbital
+     elements.
+
+     The f(q) part of the full Encke method is not used.  The purpose
+     of this part is to avoid subtracting two nearly equal quantities
+     when calculating the "indirect member", which takes account of the
+     small change in the Sun's attraction due to the slightly displaced
+     position of the perturbed body.  A simpler, direct calculation in
+     double precision proves to be faster and not significantly less
+     accurate.
+
+     Apart from employing a variable timestep, and occasionally
+     "rectifying the orbit" to keep the indirect member small, the
+     integration is done in a fairly straightforward way.  The
+     acceleration estimated for the middle of the timestep is assumed
+     to apply throughout that timestep;  it is also used in the
+     extrapolation of the perturbations to the middle of the next
+     timestep, to predict the new disturbed position.  There is no
+     iteration within a timestep.
+
+     Measures are taken to reach a compromise between execution time
+     and accuracy.  The starting-point is the goal of achieving
+     arcsecond accuracy for ordinary minor planets over a ten-year
+     timespan.  This goal dictates how large the timesteps can be,
+     which in turn dictates how frequently the unperturbed motion has
+     to be recalculated from the osculating elements.
+
+     Within predetermined limits, the timestep for the numerical
+     integration is varied in length in inverse proportion to the
+     magnitude of the net acceleration on the body from the major
+     planets.
+
+     The numerical integration requires estimates of the major-planet
+     motions.  Approximate positions for the major planets (Pluto
+     alone is omitted) are obtained from the routine slPLNT.  Two
+     levels of interpolation are used, to enhance speed without
+     significantly degrading accuracy.  At a low frequency, the routine
+     slPLNT is called to generate updated position+velocity "state
+     vectors".  The only task remaining to be carried out at the full
+     frequency (i.e. at each integration step) is to use the state
+     vectors to extrapolate the planetary positions.  In place of a
+     strictly linear extrapolation, some allowance is made for the
+     curvature of the orbit by scaling back the radius vector as the
+     linear extrapolation goes off at a tangent.
+
+     Various other approximations are made.  For example, perturbations
+     by Pluto and the minor planets are neglected, relativistic effects
+     are not taken into account and the Earth-Moon system is treated as
+     a single body.
+
+     In the interests of simplicity, the background calculations for
+     the major planets are carried out en masse.  The mean elements and
+     state vectors for all the planets are refreshed at the same time,
+     without regard for orbit curvature, mass or proximity.
+
+  5  This routine is not intended to be used for major planets.
+     However, if major-planet elements are supplied, sensible results
+     will, in fact, be produced.  This happens because the routine
+     checks the separation between the body and each of the planets and
+     interprets a suspiciously small value (0.001 AU) as an attempt to
+     apply the routine to the planet concerned.  If this condition is
+     detected, the contribution from that planet is ignored, and the
+     status is set to the planet number (Mercury=1,...,Neptune=8) as a
+     warning.
+
+  References:
+
+     1  Sterne, Theodore E., "An Introduction to Celestial Mechanics",
+        Interscience Publishers Inc., 1960.  Section 6.7, p199.
+
+     2  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
+
+  P.T.Wallace   Starlink   18 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/planel.hlp b/math/slalib/doc/planel.hlp
new file mode 100644
index 00000000..c5a0f02f
--- /dev/null
+++ b/math/slalib/doc/planel.hlp
@@ -0,0 +1,96 @@
+.help planel Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPLNE (DATE, JFORM, EPOCH, ORBINC, ANODE, PERIH,
+     :                       AORQ, E, AORL, DM, PV, JSTAT)
+
+     - - - - - - -
+      P L N L
+     - - - - - - -
+
+  Heliocentric position and velocity of a planet, asteroid or comet,
+  starting from orbital elements.
+
+  Given:
+     DATE      d      date, Modified Julian Date (JD - 2400000.5)
+     JFORM     i      choice of element set (1-3; Note 3)
+     EPOCH     d      epoch of elements (TT MJD)
+     ORBINC    d      inclination (radians)
+     ANODE     d      longitude of the ascending node (radians)
+     PERIH     d      longitude or argument of perihelion (radians)
+     AORQ      d      mean distance or perihelion distance (AU)
+     E         d      eccentricity
+     AORL      d      mean anomaly or longitude (radians, JFORM=1,2 only)
+     DM        d      daily motion (radians, JFORM=1 only)
+
+  Returned:
+     PV        d(6)   heliocentric x,y,z,xdot,ydot,zdot of date,
+                                       J2000 equatorial triad (AU,AU/s)
+     JSTAT     i      status:  0 = OK
+                              -1 = illegal JFORM
+                              -2 = illegal E
+                              -3 = illegal AORQ
+                              -4 = illegal DM
+                              -5 = numerical error
+
+  Called:  slELUE, slUEPV
+
+  Notes
+
+  1  DATE is the instant for which the prediction is required.  It is
+     in the TT timescale (formerly Ephemeris Time, ET) and is a
+     Modified Julian Date (JD-2400000.5).
+
+  2  The elements are with respect to the J2000 ecliptic and equinox.
+
+  3  Three different element-format options are available:
+
+     Option JFORM=1, suitable for the major planets:
+
+     EPOCH  = epoch of elements (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = longitude of perihelion, curly pi (radians)
+     AORQ   = mean distance, a (AU)
+     E      = eccentricity, e (range 0 to <1)
+     AORL   = mean longitude L (radians)
+     DM     = daily motion (radians)
+
+     Option JFORM=2, suitable for minor planets:
+
+     EPOCH  = epoch of elements (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = argument of perihelion, little omega (radians)
+     AORQ   = mean distance, a (AU)
+     E      = eccentricity, e (range 0 to <1)
+     AORL   = mean anomaly M (radians)
+
+     Option JFORM=3, suitable for comets:
+
+     EPOCH  = epoch of perihelion (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = argument of perihelion, little omega (radians)
+     AORQ   = perihelion distance, q (AU)
+     E      = eccentricity, e (range 0 to 10)
+
+  4  Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
+     not accessed.
+
+  5  The reference frame for the result is with respect to the mean
+     equator and equinox of epoch J2000.
+
+  6  The algorithm was originally adapted from the EPHSLA program of
+     D.H.P.Jones (private communication, 1996).  The method is based
+     on Stumpff's Universal Variables.
+
+  Reference:  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
+
+  P.T.Wallace   Starlink   18 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/planet.hlp b/math/slalib/doc/planet.hlp
new file mode 100644
index 00000000..3bdb7b9f
--- /dev/null
+++ b/math/slalib/doc/planet.hlp
@@ -0,0 +1,130 @@
+.help planet Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPLNT (DATE, NP, PV, JSTAT)
+
+     - - - - - - -
+      P L N T
+     - - - - - - -
+
+  Approximate heliocentric position and velocity of a specified
+  major planet.
+
+  Given:
+     DATE      d      Modified Julian Date (JD - 2400000.5)
+     NP        i      planet (1=Mercury, 2=Venus, 3=EMB ... 9=Pluto)
+
+  Returned:
+     PV        d(6)   heliocentric x,y,z,xdot,ydot,zdot, J2000
+                                           equatorial triad (AU,AU/s)
+     JSTAT     i      status: +1 = warning: date out of range
+                               0 = OK
+                              -1 = illegal NP (outside 1-9)
+                              -2 = solution didn't converge
+
+  Called:  slPLNE
+
+  Notes
+
+  1  The epoch, DATE, is in the TDB timescale and is a Modified
+     Julian Date (JD-2400000.5).
+
+  2  The reference frame is equatorial and is with respect to the
+     mean equinox and ecliptic of epoch J2000.
+
+  3  If an NP value outside the range 1-9 is supplied, an error
+     status (JSTAT = -1) is returned and the PV vector set to zeroes.
+
+  4  The algorithm for obtaining the mean elements of the planets
+     from Mercury to Neptune is due to J.L. Simon, P. Bretagnon,
+     J. Chapront, M. Chapront-Touze, G. Francou and J. Laskar
+     (Bureau des Longitudes, Paris).  The (completely different)
+     algorithm for calculating the ecliptic coordinates of Pluto
+     is by Meeus.
+
+  5  Comparisons of the present routine with the JPL DE200 ephemeris
+     give the following RMS errors over the interval 1960-2025:
+
+                      position (km)     speed (metre/sec)
+
+        Mercury            334               0.437
+        Venus             1060               0.855
+        EMB               2010               0.815
+        Mars              7690               1.98
+        Jupiter          71700               7.70
+        Saturn          199000              19.4
+        Uranus          564000              16.4
+        Neptune         158000              14.4
+        Pluto            36400               0.137
+
+     From comparisons with DE102, Simon et al quote the following
+     longitude accuracies over the interval 1800-2200:
+
+        Mercury                 4"
+        Venus                   5"
+        EMB                     6"
+        Mars                   17"
+        Jupiter                71"
+        Saturn                 81"
+        Uranus                 86"
+        Neptune                11"
+
+     In the case of Pluto, Meeus quotes an accuracy of 0.6 arcsec
+     in longitude and 0.2 arcsec in latitude for the period
+     1885-2099.
+
+     For all except Pluto, over the period 1000-3000 the accuracy
+     is better than 1.5 times that over 1800-2200.  Outside the
+     period 1000-3000 the accuracy declines.  For Pluto the
+     accuracy declines rapidly outside the period 1885-2099.
+     Outside these ranges (1885-2099 for Pluto, 1000-3000 for
+     the rest) a "date out of range" warning status (JSTAT=+1)
+     is returned.
+
+  6  The algorithms for (i) Mercury through Neptune and (ii) Pluto
+     are completely independent.  In the Mercury through Neptune
+     case, the present SLALIB implementation differs from the
+     original Simon et al Fortran code in the following respects.
+
+     *  The date is supplied as a Modified Julian Date rather
+        than a Julian Date (MJD = JD - 2400000.5).
+
+     *  The result is returned only in equatorial Cartesian form;
+        the ecliptic longitude, latitude and radius vector are not
+        returned.
+
+     *  The velocity is in AU per second, not AU per day.
+
+     *  Different error/warning status values are used.
+
+     *  Kepler's equation is not solved inline.
+
+     *  Polynomials in T are nested to minimize rounding errors.
+
+     *  Explicit double-precision constants are used to avoid
+        mixed-mode expressions.
+
+     *  There are other, cosmetic, changes to comply with
+        Starlink/SLALIB style guidelines.
+
+     None of the above changes affects the result significantly.
+
+  7  For NP=3 the result is for the Earth-Moon Barycentre.  To
+     obtain the heliocentric position and velocity of the Earth,
+     either use the SLALIB routine slEVP or call slDMON and
+     subtract 0.012150581 times the geocentric Moon vector from
+     the EMB vector produced by the present routine.  (The Moon
+     vector should be precessed to J2000 first, but this can
+     be omitted for modern epochs without introducing significant
+     inaccuracy.)
+
+  References:  Simon et al., Astron. Astrophys. 282, 663 (1994).
+               Meeus, Astronomical Algorithms, Willmann-Bell (1991).
+
+  P.T.Wallace   Starlink   27 May 1997
+
+  Copyright (C) 1997 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/plante.hlp b/math/slalib/doc/plante.hlp
new file mode 100644
index 00000000..a801ca51
--- /dev/null
+++ b/math/slalib/doc/plante.hlp
@@ -0,0 +1,97 @@
+.help plante Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPLTE (DATE, ELONG, PHI, JFORM, EPOCH,
+     :                       ORBINC, ANODE, PERIH, AORQ, E,
+     :                       AORL, DM, RA, DEC, R, JSTAT)
+
+     - - - - - - -
+      P L T E
+     - - - - - - -
+
+  Topocentric apparent RA,Dec of a Solar-System object whose
+  heliocentric orbital elements are known.
+
+  Given:
+     DATE      d     MJD of observation (JD - 2400000.5)
+     ELONG     d     observer's east longitude (radians)
+     PHI       d     observer's geodetic latitude (radians)
+     JFORM     i     choice of element set (1-3; Note 4)
+     EPOCH     d     epoch of elements (TT MJD)
+     ORBINC    d     inclination (radians)
+     ANODE     d     longitude of the ascending node (radians)
+     PERIH     d     longitude or argument of perihelion (radians)
+     AORQ      d     mean distance or perihelion distance (AU)
+     E         d     eccentricity
+     AORL      d     mean anomaly or longitude (radians, JFORM=1,2 only)
+     DM        d     daily motion (radians, JFORM=1 only )
+
+  Returned:
+     RA,DEC    d     RA, Dec (topocentric apparent, radians)
+     R         d     distance from observer (AU)
+     JSTAT     i     status:  0 = OK
+                             -1 = illegal JFORM
+                             -2 = illegal E
+                             -3 = illegal AORQ
+                             -4 = illegal DM
+                             -5 = numerical error
+
+  Notes:
+
+  1  DATE is the instant for which the prediction is required.  It is
+     in the TT timescale (formerly Ephemeris Time, ET) and is a
+     Modified Julian Date (JD-2400000.5).
+
+  2  The longitude and latitude allow correction for geocentric
+     parallax.  This is usually a small effect, but can become
+     important for Earth-crossing asteroids.  Geocentric positions
+     can be generated by appropriate use of routines slEVP and
+     slPLNE.
+
+  3  The elements are with respect to the J2000 ecliptic and equinox.
+
+  4  Three different element-format options are available:
+
+     Option JFORM=1, suitable for the major planets:
+
+     EPOCH  = epoch of elements (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = longitude of perihelion, curly pi (radians)
+     AORQ   = mean distance, a (AU)
+     E      = eccentricity, e
+     AORL   = mean longitude L (radians)
+     DM     = daily motion (radians)
+
+     Option JFORM=2, suitable for minor planets:
+
+     EPOCH  = epoch of elements (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = argument of perihelion, little omega (radians)
+     AORQ   = mean distance, a (AU)
+     E      = eccentricity, e
+     AORL   = mean anomaly M (radians)
+
+     Option JFORM=3, suitable for comets:
+
+     EPOCH  = epoch of perihelion (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = argument of perihelion, little omega (radians)
+     AORQ   = perihelion distance, q (AU)
+     E      = eccentricity, e
+
+  5  Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
+     not accessed.
+
+  Called: slGMST, slDT, slEPJ, slPVOB, slPRNU,
+          slPLNE, slDMXV, slDC2S, slDA2P
+
+  P.T.Wallace   Starlink   17 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pm.hlp b/math/slalib/doc/pm.hlp
new file mode 100644
index 00000000..a6d755ff
--- /dev/null
+++ b/math/slalib/doc/pm.hlp
@@ -0,0 +1,45 @@
+.help pm Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPM (R0, D0, PR, PD, PX, RV, EP0, EP1, R1, D1)
+
+     - - -
+      P M
+     - - -
+
+  Apply corrections for proper motion to a star RA,Dec
+  (double precision)
+
+  References:
+     1984 Astronomical Almanac, pp B39-B41.
+     (also Lederle & Schwan, Astron. Astrophys. 134,
+      1-6, 1984)
+
+  Given:
+     R0,D0    dp     RA,Dec at epoch EP0 (rad)
+     PR,PD    dp     proper motions:  RA,Dec changes per year of epoch
+     PX       dp     parallax (arcsec)
+     RV       dp     radial velocity (km/sec, +ve if receding)
+     EP0      dp     start epoch in years (e.g. Julian epoch)
+     EP1      dp     end epoch in years (same system as EP0)
+
+  Returned:
+     R1,D1    dp     RA,Dec at epoch EP1 (rad)
+
+  Called:
+     slDS2C       spherical to Cartesian
+     slDC2S       Cartesian to spherical
+     slDA2P      normalize angle 0-2Pi
+
+  Note:
+     The proper motions in RA are dRA/dt rather than
+     cos(Dec)*dRA/dt, and are in the same coordinate
+     system as R0,D0.
+
+  P.T.Wallace   Starlink   23 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/polmo.hlp b/math/slalib/doc/polmo.hlp
new file mode 100644
index 00000000..b3f68383
--- /dev/null
+++ b/math/slalib/doc/polmo.hlp
@@ -0,0 +1,87 @@
+.help polmo Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPLMO ( ELONGM, PHIM, XP, YP, ELONG, PHI, DAZ )
+
+     - - - - - -
+      P L M O
+     - - - - - -
+
+  Polar motion:  correct site longitude and latitude for polar
+  motion and calculate azimuth difference between celestial and
+  terrestrial poles.
+
+  Given:
+     ELONGM   d      mean longitude of the observer (radians, east +ve)
+     PHIM     d      mean geodetic latitude of the observer (radians)
+     XP       d      polar motion x-coordinate (radians)
+     YP       d      polar motion y-coordinate (radians)
+
+  Returned:
+     ELONG    d      true longitude of the observer (radians, east +ve)
+     PHI      d      true geodetic latitude of the observer (radians)
+     DAZ      d      azimuth correction (terrestrial-celestial, radians)
+
+  Notes:
+
+   1)  "Mean" longitude and latitude are the (fixed) values for the
+       site's location with respect to the IERS terrestrial reference
+       frame;  the latitude is geodetic.  TAKE CARE WITH THE LONGITUDE
+       SIGN CONVENTION.  The longitudes used by the present routine
+       are east-positive, in accordance with geographical convention
+       (and right-handed).  In particular, note that the longitudes
+       returned by the slOBS routine are west-positive, following
+       astronomical usage, and must be reversed in sign before use in
+       the present routine.
+
+   2)  XP and YP are the (changing) coordinates of the Celestial
+       Ephemeris Pole with respect to the IERS Reference Pole.
+       XP is positive along the meridian at longitude 0 degrees,
+       and YP is positive along the meridian at longitude
+       270 degrees (i.e. 90 degrees west).  Values for XP,YP can
+       be obtained from IERS circulars and equivalent publications;
+       the maximum amplitude observed so far is about 0.3 arcseconds.
+
+   3)  "True" longitude and latitude are the (moving) values for
+       the site's location with respect to the celestial ephemeris
+       pole and the meridian which corresponds to the Greenwich
+       apparent sidereal time.  The true longitude and latitude
+       link the terrestrial coordinates with the standard celestial
+       models (for precession, nutation, sidereal time etc).
+
+   4)  The azimuths produced by slAOP and slAOPQ are with
+       respect to due north as defined by the Celestial Ephemeris
+       Pole, and can therefore be called "celestial azimuths".
+       However, a telescope fixed to the Earth measures azimuth
+       essentially with respect to due north as defined by the
+       IERS Reference Pole, and can therefore be called "terrestrial
+       azimuth".  Uncorrected, this would manifest itself as a
+       changing "azimuth zero-point error".  The value DAZ is the
+       correction to be added to a celestial azimuth to produce
+       a terrestrial azimuth.
+
+   5)  The present routine is rigorous.  For most practical
+       purposes, the following simplified formulae provide an
+       adequate approximation:
+
+       ELONG = ELONGM+XP*COS(ELONGM)-YP*SIN(ELONGM)
+       PHI   = PHIM+(XP*SIN(ELONGM)+YP*COS(ELONGM))*TAN(PHIM)
+       DAZ   = -SQRT(XP*XP+YP*YP)*COS(ELONGM-ATAN2(XP,YP))/COS(PHIM)
+
+       An alternative formulation for DAZ is:
+
+       X = COS(ELONGM)*COS(PHIM)
+       Y = SIN(ELONGM)*COS(PHIM)
+       DAZ = ATAN2(-X*YP-Y*XP,X*X+Y*Y)
+
+   Reference:  Seidelmann, P.K. (ed), 1992.  "Explanatory Supplement
+               to the Astronomical Almanac", ISBN 0-935702-68-7,
+               sections 3.27, 4.25, 4.52.
+
+  P.T.Wallace   Starlink   22 February 1996
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/prebn.hlp b/math/slalib/doc/prebn.hlp
new file mode 100644
index 00000000..e2c1991b
--- /dev/null
+++ b/math/slalib/doc/prebn.hlp
@@ -0,0 +1,36 @@
+.help prebn Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPRBN (BEP0, BEP1, RMATP)
+
+     - - - - - -
+      P R B N
+     - - - - - -
+
+  Generate the matrix of precession between two epochs,
+  using the old, pre-IAU1976, Bessel-Newcomb model, using
+  Kinoshita's formulation (double precision)
+
+  Given:
+     BEP0    dp         beginning Besselian epoch
+     BEP1    dp         ending Besselian epoch
+
+  Returned:
+     RMATP  dp(3,3)    precession matrix
+
+  The matrix is in the sense   V(BEP1)  =  RMATP * V(BEP0)
+
+  Reference:
+     Kinoshita, H. (1975) 'Formulas for precession', SAO Special
+     Report No. 364, Smithsonian Institution Astrophysical
+     Observatory, Cambridge, Massachusetts.
+
+  Called:  slDEUL
+
+  P.T.Wallace   Starlink   23 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/prec.hlp b/math/slalib/doc/prec.hlp
new file mode 100644
index 00000000..4b12d918
--- /dev/null
+++ b/math/slalib/doc/prec.hlp
@@ -0,0 +1,53 @@
+.help prec Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPREC (EP0, EP1, RMATP)
+
+     - - - - -
+      P R E C
+     - - - - -
+
+  Form the matrix of precession between two epochs (IAU 1976, FK5)
+  (double precision)
+
+  Given:
+     EP0    dp         beginning epoch
+     EP1    dp         ending epoch
+
+  Returned:
+     RMATP  dp(3,3)    precession matrix
+
+  Notes:
+
+     1)  The epochs are TDB (loosely ET) Julian epochs.
+
+     2)  The matrix is in the sense   V(EP1)  =  RMATP * V(EP0)
+
+     3)  Though the matrix method itself is rigorous, the precession
+         angles are expressed through canonical polynomials which are
+         valid only for a limited time span.  There are also known
+         errors in the IAU precession rate.  The absolute accuracy
+         of the present formulation is better than 0.1 arcsec from
+         1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD,
+         and remains below 3 arcsec for the whole of the period
+         500BC to 3000AD.  The errors exceed 10 arcsec outside the
+         range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to
+         5600AD and exceed 1000 arcsec outside 6800BC to 8200AD.
+         The SLALIB routine slPREL implements a more elaborate
+         model which is suitable for problems spanning several
+         thousand years.
+
+  References:
+     Lieske,J.H., 1979. Astron.Astrophys.,73,282.
+      equations (6) & (7), p283.
+     Kaplan,G.H., 1981. USNO circular no. 163, pA2.
+
+  Called:  slDEUL
+
+  P.T.Wallace   Starlink   23 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/preces.hlp b/math/slalib/doc/preces.hlp
new file mode 100644
index 00000000..7652ea8a
--- /dev/null
+++ b/math/slalib/doc/preces.hlp
@@ -0,0 +1,47 @@
+.help preces Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPRCE (SYSTEM, EP0, EP1, RA, DC)
+
+     - - - - - - -
+      P R C E
+     - - - - - - -
+
+  Precession - either FK4 (Bessel-Newcomb, pre IAU 1976) or
+  FK5 (Fricke, post IAU 1976) as required.
+
+  Given:
+     SYSTEM     char   precession to be applied: 'FK4' or 'FK5'
+     EP0,EP1    dp     starting and ending epoch
+     RA,DC      dp     RA,Dec, mean equator & equinox of epoch EP0
+
+  Returned:
+     RA,DC      dp     RA,Dec, mean equator & equinox of epoch EP1
+
+  Called:    slDA2P, slPRBN, slPREC, slDS2C,
+             slDMXV, slDC2S
+
+  Notes:
+
+     1)  Lowercase characters in SYSTEM are acceptable.
+
+     2)  The epochs are Besselian if SYSTEM='FK4' and Julian if 'FK5'.
+         For example, to precess coordinates in the old system from
+         equinox 1900.0 to 1950.0 the call would be:
+             CALL slPRCE ('FK4', 1900D0, 1950D0, RA, DC)
+
+     3)  This routine will NOT correctly convert between the old and
+         the new systems - for example conversion from B1950 to J2000.
+         For these purposes see slFK45, slFK54, slF45Z and
+         slF54Z.
+
+     4)  If an invalid SYSTEM is supplied, values of -99D0,-99D0 will
+         be returned for both RA and DC.
+
+  P.T.Wallace   Starlink   20 April 1990
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/precl.hlp b/math/slalib/doc/precl.hlp
new file mode 100644
index 00000000..b715172a
--- /dev/null
+++ b/math/slalib/doc/precl.hlp
@@ -0,0 +1,47 @@
+.help precl Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPREL (EP0, EP1, RMATP)
+
+     - - - - - -
+      P R E L
+     - - - - - -
+
+  Form the matrix of precession between two epochs, using the
+  model of Simon et al (1994), which is suitable for long
+  periods of time.
+
+  (double precision)
+
+  Given:
+     EP0    dp         beginning epoch
+     EP1    dp         ending epoch
+
+  Returned:
+     RMATP  dp(3,3)    precession matrix
+
+  Notes:
+
+     1)  The epochs are TDB Julian epochs.
+
+     2)  The matrix is in the sense   V(EP1)  =  RMATP * V(EP0)
+
+     3)  The absolute accuracy of the model is limited by the
+         uncertainty in the general precession, about 0.3 arcsec per
+         1000 years.  The remainder of the formulation provides a
+         precision of 1 mas over the interval from 1000AD to 3000AD,
+         0.1 arcsec from 1000BC to 5000AD and 1 arcsec from
+         4000BC to 8000AD.
+
+  Reference:
+     Simon, J.L. et al., 1994. Astron.Astrophys., 282, 663-683.
+
+  Called:  slDEUL
+
+  P.T.Wallace   Starlink   23 August 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/precss.hlp b/math/slalib/doc/precss.hlp
new file mode 100644
index 00000000..ab244cf5
--- /dev/null
+++ b/math/slalib/doc/precss.hlp
@@ -0,0 +1,44 @@
+.help precss Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPRCS (SYSTEM, EP0, EP1, RA, DC)
+
+     - - - - - - -
+      P R C E
+     - - - - - - -
+
+  Precession - either FK4 (Bessel-Newcomb, pre IAU 1976) or
+  FK5 (Fricke, post IAU 1976) as required.
+
+  Given:
+     SYSTEM     int    precession to be applied: 1 = FK4 or 2 = FK5
+     EP0,EP1    dp     starting and ending epoch
+     RA,DC      dp     RA,Dec, mean equator & equinox of epoch EP0
+
+  Returned:
+     RA,DC      dp     RA,Dec, mean equator & equinox of epoch EP1
+
+  Called:    slDA2P, slPRBN, slPREC, slDS2C,
+             slDMXV, slDC2S
+
+  Notes:
+
+     1)  Lowercase characters in SYSTEM are acceptable.
+
+     2)  The epochs are Besselian if SYSTEM=FK4 and Julian if FK5.
+         For example, to precess coordinates in the old system from
+         equinox 1900.0 to 1950.0 the call would be:
+             CALL slPRCS (1, 1900D0, 1950D0, RA, DC)
+
+     3)  This routine will NOT correctly convert between the old and
+         the new systems - for example conversion from B1950 to J2000.
+         For these purposes see slFK45, slFK54, slF45Z and
+         slF54Z.
+
+     4)  If an invalid SYSTEM is supplied, values of -99D0,-99D0 will
+         be returned for both RA and DC.
+
+  P.T.Wallace   Starlink   20 April 1990
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/prenut.hlp b/math/slalib/doc/prenut.hlp
new file mode 100644
index 00000000..bbe3ceff
--- /dev/null
+++ b/math/slalib/doc/prenut.hlp
@@ -0,0 +1,35 @@
+.help prenut Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPRNU (EPOCH, DATE, RMATPN)
+
+     - - - - - - -
+      P R N U
+     - - - - - - -
+
+  Form the matrix of precession and nutation (IAU1976/FK5)
+  (double precision)
+
+  Given:
+     EPOCH   dp         Julian Epoch for mean coordinates
+     DATE    dp         Modified Julian Date (JD-2400000.5)
+                        for true coordinates
+
+  Returned:
+     RMATPN  dp(3,3)    combined precession/nutation matrix
+
+  Called:  slPREC, slEPJ, slNUT, slDMXM
+
+  Notes:
+
+  1)  The epoch and date are TDB (loosely ET).
+
+  2)  The matrix is in the sense   V(true)  =  RMATPN * V(mean)
+
+  P.T.Wallace   Starlink   April 1987
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pv2el.hlp b/math/slalib/doc/pv2el.hlp
new file mode 100644
index 00000000..ef027a38
--- /dev/null
+++ b/math/slalib/doc/pv2el.hlp
@@ -0,0 +1,145 @@
+.help pv2el Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPVEL (PV, DATE, PMASS, JFORMR,
+     :                      JFORM, EPOCH, ORBINC, ANODE, PERIH,
+     :                      AORQ, E, AORL, DM, JSTAT)
+
+     - - - - - -
+      P V E L
+     - - - - - -
+
+  Heliocentric osculating elements obtained from instantaneous position
+  and velocity.
+
+  Given:
+     PV        d(6)   heliocentric x,y,z,xdot,ydot,zdot of date,
+                      J2000 equatorial triad (AU,AU/s; Note 1)
+     DATE      d      date (TT Modified Julian Date = JD-2400000.5)
+     PMASS     d      mass of the planet (Sun=1; Note 2)
+     JFORMR    i      requested element set (1-3; Note 3)
+
+  Returned:
+     JFORM     d      element set actually returned (1-3; Note 4)
+     EPOCH     d      epoch of elements (TT MJD)
+     ORBINC    d      inclination (radians)
+     ANODE     d      longitude of the ascending node (radians)
+     PERIH     d      longitude or argument of perihelion (radians)
+     AORQ      d      mean distance or perihelion distance (AU)
+     E         d      eccentricity
+     AORL      d      mean anomaly or longitude (radians, JFORM=1,2 only)
+     DM        d      daily motion (radians, JFORM=1 only)
+     JSTAT     i      status:  0 = OK
+                              -1 = illegal PMASS
+                              -2 = illegal JFORMR
+                              -3 = position/velocity out of range
+
+  Notes
+
+  1  The PV 6-vector is with respect to the mean equator and equinox of
+     epoch J2000.  The orbital elements produced are with respect to
+     the J2000 ecliptic and mean equinox.
+
+  2  The mass, PMASS, is important only for the larger planets.  For
+     most purposes (e.g. asteroids) use 0D0.  Values less than zero
+     are illegal.
+
+  3  Three different element-format options are supported:
+
+     Option JFORM=1, suitable for the major planets:
+
+     EPOCH  = epoch of elements (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = longitude of perihelion, curly pi (radians)
+     AORQ   = mean distance, a (AU)
+     E      = eccentricity, e
+     AORL   = mean longitude L (radians)
+     DM     = daily motion (radians)
+
+     Option JFORM=2, suitable for minor planets:
+
+     EPOCH  = epoch of elements (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = argument of perihelion, little omega (radians)
+     AORQ   = mean distance, a (AU)
+     E      = eccentricity, e
+     AORL   = mean anomaly M (radians)
+
+     Option JFORM=3, suitable for comets:
+
+     EPOCH  = epoch of perihelion (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = argument of perihelion, little omega (radians)
+     AORQ   = perihelion distance, q (AU)
+     E      = eccentricity, e
+
+  4  It may not be possible to generate elements in the form
+     requested through JFORMR.  The caller is notified of the form
+     of elements actually returned by means of the JFORM argument:
+
+      JFORMR   JFORM     meaning
+
+        1        1       OK - elements are in the requested format
+        1        2       never happens
+        1        3       orbit not elliptical
+
+        2        1       never happens
+        2        2       OK - elements are in the requested format
+        2        3       orbit not elliptical
+
+        3        1       never happens
+        3        2       never happens
+        3        3       OK - elements are in the requested format
+
+  5  The arguments returned for each value of JFORM (cf Note 5: JFORM
+     may not be the same as JFORMR) are as follows:
+
+         JFORM         1              2              3
+         EPOCH         t0             t0             T
+         ORBINC        i              i              i
+         ANODE         Omega          Omega          Omega
+         PERIH         curly pi       omega          omega
+         AORQ          a              a              q
+         E             e              e              e
+         AORL          L              M              -
+         DM            n              -              -
+
+     where:
+
+         t0           is the epoch of the elements (MJD, TT)
+         T              "    epoch of perihelion (MJD, TT)
+         i              "    inclination (radians)
+         Omega          "    longitude of the ascending node (radians)
+         curly pi       "    longitude of perihelion (radians)
+         omega          "    argument of perihelion (radians)
+         a              "    mean distance (AU)
+         q              "    perihelion distance (AU)
+         e              "    eccentricity
+         L              "    longitude (radians, 0-2pi)
+         M              "    mean anomaly (radians, 0-2pi)
+         n              "    daily motion (radians)
+         -             means no value is set
+
+  6  At very small inclinations, the longitude of the ascending node
+     ANODE becomes indeterminate and under some circumstances may be
+     set arbitrarily to zero.  Similarly, if the orbit is close to
+     circular, the true anomaly becomes indeterminate and under some
+     circumstances may be set arbitrarily to zero.  In such cases,
+     the other elements are automatically adjusted to compensate,
+     and so the elements remain a valid description of the orbit.
+
+  Reference:  Sterne, Theodore E., "An Introduction to Celestial
+              Mechanics", Interscience Publishers, 1960
+
+  Called:  slDA2P
+
+  P.T.Wallace   Starlink   13 February 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pv2ue.hlp b/math/slalib/doc/pv2ue.hlp
new file mode 100644
index 00000000..776f877a
--- /dev/null
+++ b/math/slalib/doc/pv2ue.hlp
@@ -0,0 +1,70 @@
+.help pv2ue Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPVUE (PV, DATE, PMASS, U, JSTAT)
+
+     - - - - - -
+      P V U E
+     - - - - - -
+
+  Construct a universal element set based on an instantaneous position
+  and velocity.
+
+  Given:
+     PV        d(6)   heliocentric x,y,z,xdot,ydot,zdot of date,
+                      (AU,AU/s; Note 1)
+     DATE      d      date (TT Modified Julian Date = JD-2400000.5)
+     PMASS     d      mass of the planet (Sun=1; Note 2)
+
+  Returned:
+     U         d(13)  universal orbital elements (Note 3)
+
+                 (1)  combined mass (M+m)
+                 (2)  total energy of the orbit (alpha)
+                 (3)  reference (osculating) epoch (t0)
+               (4-6)  position at reference epoch (r0)
+               (7-9)  velocity at reference epoch (v0)
+                (10)  heliocentric distance at reference epoch
+                (11)  r0.v0
+                (12)  date (t)
+                (13)  universal eccentric anomaly (psi) of date, approx
+
+     JSTAT     i      status:  0 = OK
+                              -1 = illegal PMASS
+                              -2 = too close to Sun
+                              -3 = too slow
+
+  Notes
+
+  1  The PV 6-vector can be with respect to any chosen inertial frame,
+     and the resulting universal-element set will be with respect to
+     the same frame.  A common choice will be mean equator and ecliptic
+     of epoch J2000.
+
+  2  The mass, PMASS, is important only for the larger planets.  For
+     most purposes (e.g. asteroids) use 0D0.  Values less than zero
+     are illegal.
+
+  3  The "universal" elements are those which define the orbit for the
+     purposes of the method of universal variables (see reference).
+     They consist of the combined mass of the two bodies, an epoch,
+     and the position and velocity vectors (arbitrary reference frame)
+     at that epoch.  The parameter set used here includes also various
+     quantities that can, in fact, be derived from the other
+     information.  This approach is taken to avoiding unnecessary
+     computation and loss of accuracy.  The supplementary quantities
+     are (i) alpha, which is proportional to the total energy of the
+     orbit, (ii) the heliocentric distance at epoch, (iii) the
+     outwards component of the velocity at the given epoch, (iv) an
+     estimate of psi, the "universal eccentric anomaly" at a given
+     date and (v) that date.
+
+  Reference:  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
+
+  P.T.Wallace   Starlink   18 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pvobs.hlp b/math/slalib/doc/pvobs.hlp
new file mode 100644
index 00000000..607d73a5
--- /dev/null
+++ b/math/slalib/doc/pvobs.hlp
@@ -0,0 +1,31 @@
+.help pvobs Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPVOB (P, H, STL, PV)
+
+     - - - - - -
+      P V O B
+     - - - - - -
+
+  Position and velocity of an observing station (double precision)
+
+  Given:
+     P     dp     latitude (geodetic, radians)
+     H     dp     height above reference spheroid (geodetic, metres)
+     STL   dp     local apparent sidereal time (radians)
+
+  Returned:
+     PV    dp(6)  position/velocity 6-vector (AU, AU/s, true equator
+                                              and equinox of date)
+
+  Called:  slGEOC
+
+  IAU 1976 constants are used.
+
+  P.T.Wallace   Starlink   14 November 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/pxy.hlp b/math/slalib/doc/pxy.hlp
new file mode 100644
index 00000000..e2764150
--- /dev/null
+++ b/math/slalib/doc/pxy.hlp
@@ -0,0 +1,56 @@
+.help pxy Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slPXY (NP,XYE,XYM,COEFFS,XYP,XRMS,YRMS,RRMS)
+
+     - - - -
+      P X Y
+     - - - -
+
+  Given arrays of "expected" and "measured" [X,Y] coordinates, and a
+  linear model relating them (as produced by slFTXY), compute
+  the array of "predicted" coordinates and the RMS residuals.
+
+  Given:
+     NP       i        number of samples
+     XYE     d(2,np)   expected [X,Y] for each sample
+     XYM     d(2,np)   measured [X,Y] for each sample
+     COEFFS  d(6)      coefficients of model (see below)
+
+  Returned:
+     XYP     d(2,np)   predicted [X,Y] for each sample
+     XRMS     d        RMS in X
+     YRMS     d        RMS in Y
+     RRMS     d        total RMS (vector sum of XRMS and YRMS)
+
+  The model is supplied in the array COEFFS.  Naming the
+  elements of COEFF as follows:
+
+     COEFFS(1) = A
+     COEFFS(2) = B
+     COEFFS(3) = C
+     COEFFS(4) = D
+     COEFFS(5) = E
+     COEFFS(6) = F
+
+  the model is applied thus:
+
+     XP = A + B*XM + C*YM
+     YP = D + E*XM + F*YM
+
+  The residuals are (XP-XE) and (YP-YE).
+
+  If NP is less than or equal to zero, no coordinates are
+  transformed, and the RMS residuals are all zero.
+
+  See also slFTXY, slINVF, slXYXY, slDCMF
+
+  Called:  slXYXY
+
+  P.T.Wallace   Starlink   22 May 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/range.hlp b/math/slalib/doc/range.hlp
new file mode 100644
index 00000000..b65a1a92
--- /dev/null
+++ b/math/slalib/doc/range.hlp
@@ -0,0 +1,24 @@
+.help range Jun99 "Slalib Package"
+.nf
+
+      REAL FUNCTION slRA1P (ANGLE)
+
+     - - - - - -
+      R A 1 P
+     - - - - - -
+
+  Normalize angle into range +/- pi  (single precision)
+
+  Given:
+     ANGLE     dp      the angle in radians
+
+  The result is ANGLE expressed in the +/- pi (single
+  precision).
+
+  P.T.Wallace   Starlink   23 November 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ranorm.hlp b/math/slalib/doc/ranorm.hlp
new file mode 100644
index 00000000..5ee46937
--- /dev/null
+++ b/math/slalib/doc/ranorm.hlp
@@ -0,0 +1,24 @@
+.help ranorm Jun99 "Slalib Package"
+.nf
+
+      REAL FUNCTION slRA2P (ANGLE)
+
+     - - - - - - -
+      R A 2 P
+     - - - - - - -
+
+  Normalize angle into range 0-2 pi  (single precision)
+
+  Given:
+     ANGLE     dp      the angle in radians
+
+  The result is ANGLE expressed in the range 0-2 pi (single
+  precision).
+
+  P.T.Wallace   Starlink   23 November 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/rcc.hlp b/math/slalib/doc/rcc.hlp
new file mode 100644
index 00000000..fef7f578
--- /dev/null
+++ b/math/slalib/doc/rcc.hlp
@@ -0,0 +1,83 @@
+.help rcc Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slRCC (TDB, UT1, WL, U, V)
+
+     - - - -
+      R C C
+     - - - -
+
+  Relativistic clock correction:  the difference between proper time at
+  a point on the surface of the Earth and coordinate time in the Solar
+  System barycentric space-time frame of reference.
+
+  The proper time is Terrestrial Time TT;  the coordinate
+  time is an implementation of the Barycentric Dynamical Time TDB.
+
+  Given:
+    TDB   dp   coordinate time (MJD: JD-2400000.5)
+    UT1   dp   universal time (fraction of one day)
+    WL    dp   clock longitude (radians west)
+    U     dp   clock distance from Earth spin axis (km)
+    V     dp   clock distance north of Earth equatorial plane (km)
+
+  Returned:
+    The clock correction, TDB-TT, in seconds.  TDB may be considered
+    to be the coordinate time in the Solar System barycentre frame of
+    reference, and TT is the proper time given by clocks at mean sea
+    level on the Earth.
+
+    The result has a main (annual) sinusoidal term of amplitude
+    approximately 0.00166 seconds, plus planetary terms up to about
+    20 microseconds, and lunar and diurnal terms up to 2 microseconds.
+    The variation arises from the transverse Doppler effect and the
+    gravitational red-shift as the observer varies in speed and moves
+    through different gravitational potentials.
+
+  The argument TDB is, strictly, the barycentric coordinate time;
+  however, the terrestrial proper time (TT) can in practice be used.
+
+  The geocentric model is that of Fairhead & Bretagnon (1990), in its
+  full form.  It was supplied by Fairhead (private communication) as a
+  FORTRAN subroutine.  The original Fairhead routine used explicit
+  formulae, in such large numbers that problems were experienced with
+  certain compilers (Microsoft Fortran on PC aborted with stack
+  overflow, Convex compiled successfully but extremely slowly).  The
+  present implementation is a complete recoding, with the original
+  Fairhead coefficients held in a table.  To optimize arithmetic
+  precision, the terms are accumulated in reverse order, smallest
+  first.  A number of other coding changes were made, in order to match
+  the calling sequence of previous versions of the present routine, and
+  to comply with Starlink programming standards.  Under VAX/VMS, the
+  numerical results compared with those from the Fairhead form are
+  essentially unaffected by the changes, the differences being at the
+  10^-20 sec level.
+
+  The topocentric part of the model is from Moyer (1981) and
+  Murray (1983).
+
+  During the interval 1950-2050, the absolute accuracy is better
+  than +/- 3 nanoseconds relative to direct numerical integrations
+  using the JPL DE200/LE200 solar system ephemeris.
+
+  The IAU definition of TDB is that it must differ from TT only by
+  periodic terms.  Though practical, this is an imprecise definition
+  which ignores the existence of very long-period and secular effects
+  in the dynamics of the solar system.  As a consequence, different
+  implementations of TDB will, in general, differ in zero-point and
+  will drift linearly relative to one other.
+
+  References:
+    Bretagnon P, 1982 Astron. Astrophys., 114, 278-288.
+    Fairhead L & Bretagnon P, 1990, Astron. Astrophys., 229, 240-247.
+    Meeus J, 1984, l'Astronomie, 348-354.
+    Moyer T D, 1981, Cel. Mech., 23, 33.
+    Murray C A, 1983, Vectorial Astrometry, Adam Hilger.
+
+  P.T.Wallace   Starlink   10 November 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/rdplan.hlp b/math/slalib/doc/rdplan.hlp
new file mode 100644
index 00000000..5b9d560a
--- /dev/null
+++ b/math/slalib/doc/rdplan.hlp
@@ -0,0 +1,73 @@
+.help rdplan Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slRDPL (DATE, NP, ELONG, PHI, RA, DEC, DIAM)
+
+     - - - - - - -
+      R D P L
+     - - - - - - -
+
+  Approximate topocentric apparent RA,Dec of a planet, and its
+  angular diameter.
+
+  Given:
+     DATE        d       MJD of observation (JD - 2400000.5)
+     NP          i       planet: 1 = Mercury
+                                 2 = Venus
+                                 3 = Moon
+                                 4 = Mars
+                                 5 = Jupiter
+                                 6 = Saturn
+                                 7 = Uranus
+                                 8 = Neptune
+                                 9 = Pluto
+                              else = Sun
+     ELONG,PHI   d       observer's east longitude and geodetic
+                                               latitude (radians)
+
+  Returned:
+     RA,DEC      d        RA, Dec (topocentric apparent, radians)
+     DIAM        d        angular diameter (equatorial, radians)
+
+  Notes:
+
+  1  The date is in a dynamical timescale (TDB, formerly ET) and is
+     in the form of a Modified Julian Date (JD-2400000.5).  For all
+     practical purposes, TT can be used instead of TDB, and for many
+     applications UT will do (except for the Moon).
+
+  2  The longitude and latitude allow correction for geocentric
+     parallax.  This is a major effect for the Moon, but in the
+     context of the limited accuracy of the present routine its
+     effect on planetary positions is small (negligible for the
+     outer planets).  Geocentric positions can be generated by
+     appropriate use of the routines slDMON and slPLNT.
+
+  3  The direction accuracy (arcsec, 1000-3000AD) is of order:
+
+            Sun              5
+            Mercury          2
+            Venus           10
+            Moon            30
+            Mars            50
+            Jupiter         90
+            Saturn          90
+            Uranus          90
+            Neptune         10
+            Pluto            1   (1885-2099AD only)
+
+     The angular diameter accuracy is about 0.4% for the Moon,
+     and 0.01% or better for the Sun and planets.
+
+  See the slPLNT routine for references.
+
+  Called: slGMST, slDT, slEPJ, slDMON, slPVOB, slPRNU,
+          slPLNT, slDMXV, slDC2S, slDA2P
+
+  P.T.Wallace   Starlink   26 May 1997
+
+  Copyright (C) 1997 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/read.me b/math/slalib/doc/read.me
new file mode 100644
index 00000000..e7f5f358
--- /dev/null
+++ b/math/slalib/doc/read.me
@@ -0,0 +1,437 @@
+READ.ME
+
+Revision date 31 May 1999                          SLALIB Version 2.3-0
+
+-----------------------------------------------------------------------
+
+FILES IN THE ORIGINAL SOURCE DIRECTORY (VAX)
+
+   READ.ME           this file
+   *.FOR             Fortran source (separate modules)
+   *.OBS             ditto, but obsolete routines
+   *.NEW             ditto, but new and not yet ready for release
+   *.VAX             Fortran source for VAX/VMS
+   *.CNVX            Fortran source for Convex
+   *.MIPS            Fortran source for DECstation
+   *.SUN4            Fortran source for Sun SPARCstation
+   *.LNX             Fortran source for Linux
+   *.PCM             Microsoft Fortran source for PC
+   *.C               C functions needed for Linux version
+   PC.BAT            rebuilds PC version
+   REP.BAT           on PC, compiles one module and updates library
+   CREATE.COM        complete rebuild of VAX and Unix releases
+   PUT.COM           compile one module and update libraries
+   VAX_TO_UNIX.USH   script to complete transfer to Unix platforms
+   SLA.NEWS          NEWS item for latest release
+   MAKEFILE          Unix make file
+   MK                C-shell script to run make
+   SUN67.TEX         document
+
+FILES IN [.RELEASE] DIRECTORY ON VAX
+
+   SLALIB.OLB        object library
+   SLALIB.TLB        source library
+   SUN67.TEX         document
+
+FILES IN [.UNIX] DIRECTORY ON VAX
+
+   MAKEFILE          make file for DECstation and Sun SPARC
+   MK                C-shell script to run make
+   SLA.A             archive file containing everything else
+   VAX_TO_UNIX       script to complete transfer to Unix platforms
+   SLA.NEWS          NEWS item for latest release
+   SUN67.TEX         document
+
+FILES IN (INFORMAL) FTP DIRECTORIES
+
+   The files distributed informally through anonymous FTP may differ
+   slightly in both content and name from the ones listed above.  For
+   example the PC Fortran modules may be stored in archive files and
+   called xxx.f_pcm rather than XXX.PCM etc.
+
+-----------------------------------------------------------------------
+
+DISTRIBUTION - THIS DIRECTORY
+
+   Nothing from this directory needs to be distributed.
+
+DISTRIBUTION - [.RELEASE] DIRECTORY
+
+   SLALIB.*          SLALIB_DIR
+   SLA.NEWS          SLALIB_DIR
+   SUN67.TEX         DOCSDIR
+
+INSTRUCTIONS FOR SAVING SPACE
+
+   Extract from the SLALIB_DIR BACKUP save set only the file SLALIB.OLB.
+
+-----------------------------------------------------------------------
+
+PORTING FORTRAN SLALIB TO OTHER SYSTEMS
+
+FORTRAN SLALIB runs on VAX (VMS), PC (Linux+f2c), PC (Microsoft FORTRAN),
+Convex (ConvexOS), DECstation (Ultrix), DEC Alpha (OSF-1) and Sun
+SPARCstation (SunOS and Solaris).
+
+For most platforms, the required changes are confined to these routines:
+
+    sla_GRESID
+    sla_RANDOM
+    sla_WAIT
+
+VAX, CONVEX, DECSTATION/ALPHA, SUN & PC
+
+Versions suitable for the above platforms are supplied in the
+development directory as *.VAX, *,CNVX, *.MIPS, *.SUN4, *.PCM and
+*.LNX respectively.
+
+
+-----------------------------------------------------------------------
+
+LATEST RELEASE INFORMATION
+
+The latest release of SLALIB includes the following changes (most recent
+at the end):
+
+*  In sla_RCC, the topocentric term of coefficient 1.3184D-10 sec
+   had the wrong sign.  Minus is correct.
+
+*  The IAU decided in 1991 to rename the Terrestrial Dynamical
+   Time, TDT, which is now called "Terrestrial Time" or TT.
+   Appropriate changes have been made in the SLALIB documentation.
+   The same IAU resolutions introduced the timescales TCG and TCB;
+   there are at present no SLALIB routines to handle these new
+   timescales.
+
+*  The Keck 1 Telescope has been added to sla_OBS.
+
+*  The handling of the random-number seed in the PC versions of
+   sla_RANDOM and sla_GRESID was flawed and has been improved.
+
+*  The UTC leap second at the end of June 1993 has been added to the
+   routine sla_DAT.  Existing applications which call sla_DAT or
+   sla_DTT require relinking.
+
+*  Some unnecessary code in sla_AMPQK has been removed.
+
+*  Minor reorganization of the sla_REFRO code has led to an improvement
+   in speed of about 20%, and precautions have been taken against
+   potential arithmetic errors.
+
+*  There have been small revisions to sla_FK425 and sla_FK524.  The
+   results are not significantly affected, except in the pathological
+   case of large proper motion combined with immense distance, where
+   sla_FK524 could produce erroneous radial velocity values.  The
+   latest versions are close to the algorithms published in the 1992
+   Explanatory Supplement to the Astronomical Almanac.
+
+*  The leap second at the end of June 1994 has been added to sla_DAT.
+
+*  THE SLA_RVLSR ROUTINE HAS BEEN RETIRED.  Its place has been taken
+   by two new routines: sla_RVLSRK and sla_RVLSRD.  The original
+   sla_RVLSR had used a "kinematical" LSR.  When this was later changed
+   to a "dynamical" LSR for (what seemed liked good reasons at the time),
+   the small differences were noticed by spectral-line radio observers,
+   who had to fall back on old copies of the routine to remain consistent
+   with existing practice.  The new routines provide both sorts of LSR:
+   sla_RVLSRK uses a kinematical LSR and sla_RVLSRD uses the dynamical LSR.
+
+*  The sla_PA routine (computation of parallactic angle) used an
+   unnecessarily complicated formulation, which has been simplified.
+   The results are unaffected.
+
+*  The sla_ZD routine (computation of zenith distance) used a
+   straightforward cosine-formula-based method, which suffered from
+   decreased accuracy near the zenith.  A better, vector-derived,
+   formulation has been substituted, without materially affecting
+   the results.  Because sla_ZD is double precision, the old
+   formulation was always adequate;  however, had anyone transcribed
+   the code in single precision errors approaching 1 arcmin could
+   have resulted.  The new formulation delivers good results all
+   over the sky even in a single precision version.
+
+*  Routines have been added to transform equatorial coordinates
+   (HA,Dec) to horizon coordinates (Az,El) and back.  Single and
+   double precision are both supported.  The routines are called
+   sla_E2H, sla_DE2H, sla_H2E, sla_DH2E.
+
+*  A new routine has been added to the tangent-plane projection set.
+   The single and double precision versions are called sla_TPRD and
+   sla_DTPRD respectively.  Given the RA,Dec of a star and its
+   xi,eta coordinates, the routine determines the "plate centre".
+
+*  The existing routine sla_PREC for obtaining the precession matrix
+   uses the official IAU model and should continue to be used for
+   canonical purposes.  A new version, called sla_PRECL, uses a
+   more up-to-date model which delivers better accuracy, especially
+   over intervals of millennia.
+
+*  The routine sla_PVOBS was returning velocities in AU per sidereal
+   second rather than per UT second.  This has been corrected.  The
+   maximum error was equivalent to about 0.001 km/s.
+
+*  In sla_MAPQK and sla_MAPQKZ, the area within which the gravitional
+   light-deflection term is restrained has been extended from its
+   original 300 arcsec radius to about 920 arcsec, just inside the
+   Sun's disc.
+
+*  A chapter of explanation, with examples, has been added to SUN/67,
+   which has also undergone various cosmetic revisions.
+
+*  There were two discrepancies between the documentation of sla_DCMPF
+   (program comments and SUN/67) and the code.  The first was that the
+   formulae for the nonperpendicularity used PERP instead of PERP/2;
+   the documentation has been corrected.  The other was that the
+   documentation showed the zero point corrections being applied first,
+   whereas the code returned zero point corrections corresponding to
+   being applied last.  The code has been corrected to match the
+   documentation.
+
+*  The C module slaCldj gave incorrect answers for dates during
+   January and February.  The error, which did not affect the Fortran
+   version, has been corrected.
+
+*  THE CALL FOR TPRD AND DTPRD HAS BEEN CHANGED.  An integer status
+   argument has been added;  non-zero means the supplied RA,Dec
+   and Xi,Eta describe an impossible case.  (This can only happen
+   near the pole and with non-zero Xi.)  Also, a slightly neater
+   formulation has been introduced.
+
+*  Three new routines have been added.  ALTAZ takes a star's HA,Dec
+   and produces position, velocity and acceleration for azimuth,
+   elevation and parallactic angle.  PDA2H predicts the HA at which
+   a given azimuth will be reached.  PDQ2H does the same for
+   position angle.
+
+*  In the OBS routine, the wrong sign was returned for the Perkins
+   72 inch telescope at Lowell - fixed.
+
+*  A revised model for the equation of the equinoxes has been
+   installed in EQEQX, in line with recent IAU resolutions.  The
+   change amounts to less than 3 mas.
+
+*  A bug in DFLTIN has been corrected.  A negative number following
+   an E- or D-format number without intervening spaces lost its
+   sign.
+
+*  Four stations have been added to OBS:
+
+     TAUTENBERG  Tautenberg 1.34 metre Schmidt
+     PALOMAR48   Palomar 48-inch Schmidt
+     UKST        UK 1.2 metre Schmidt, Siding Spring
+     KISO        Kiso 1.05 metre Schmidt, Japan
+     ESOSCHMIDT  ESO 1 metre Schmidt, La Silla
+
+*  The EARTH and MOON routines could give an integer divide by zero
+   for years before 1 BC.  This has been corrected.
+
+*  CALYD (provided to support the EARTH and MOON routines) has been
+   upgraded to work outside the interval 1900 March 1 to
+   2100 February 28.  The status value indicating dates outside that
+   range has been dropped;  a new error value for year before -4711
+   has been introduced.
+
+*  A new routine, CLYD, has been added.  It is a version of CALYD
+   without the century-default feature and is to enable 1st-century
+   dates to be supplied to EARTH and MOON.
+
+*  Two new routines, PLANETS and RDPLAN, have been added, which
+   compute approximate planetary ephemerides.
+
+*  A new routine, DMOON, implements the same (Meeus) model as the
+   MOON routine, but in full and in double precision.  The time
+   argument is a straightforward MJD rather than MOON's year and
+   day-in-year.
+
+*  The REFRO code has been speeded up by a factor of two (and is
+   also clearer).
+
+*  REFV and REFZ have, in different ways, been made more accurate for
+   cases close to the horizon.  The improvement to REFV is relatively
+   modest, but REFZ is now capable of delivering useful results for
+   rise/set phenomena.
+
+*  AOPQK has been speeded up for low-elevation cases.
+
+*  Versions of the tangent-plane routines working directly in x,y,z
+   instead of spherical coordinates have been added.  They may be
+   faster in some applications.  The routines are DV2TP, V2TP, DTP2V,
+   TP2V, DTPXYZ, TPXYZ.
+
+*  The coordinates of the Australia Telescope Compact Array have been
+   added to OBS.  The name is 'ATCA'.
+
+*  Despite their recent introduction THE ROUTINES DTPRD, DTPXYZ, TPRD
+   AND TPXYZ HAVE BEEN WITHDRAWN.  They have been replaced by the new
+   routines DTPS2C, DTPV2C, TPS2C and TPV2C.  These are functionally
+   equivalent to the earlier routines but return two solutions instead
+   of one:  the second solution can arise near a pole.
+
+*  The UTC leap second at the end of 1995 has been added to sla_DAT.
+
+*  The refraction routine REFRO has been extensively revised.  The
+   principal motivation was to improve the radio predictions by
+   introducing better humidity models.  The models previously in
+   use had been entirely adequate for the optical case, for which
+   they had been devised, but improved models were required for
+   the radio case.  None of the changes significantly affects the
+   optical results with respect to the earlier version of the REFRO
+   routine.  For example, at 70 deg zenith distance the new version
+   agrees with the old version to better than 0.05 arcsec for any
+   reasonable combination of parameters.  However, the improved
+   water-vapour expressions do make a significant difference in the
+   radio band, at 70 deg zenith distance reaching almost 4 arcsec
+   for a hot, humid, low-altitude site during a period of low pressure.
+
+*  There was a bug in the (private) C version of RDPLAN.  The
+   answers were unaffected but there could be floating-point
+   problems on some platforms.
+
+*  A new routine has been added, GMSTA.  This gives greater numerical
+   precision than the existing GMST function by allowing the date and
+   time to be specified separately rather than as a single MJD.
+
+*  Measures taken in MAPQK to avoid trouble when processing Solar
+   positions had not been carried through into MAPQKZ.  The two
+   routines now use the same strategy.
+
+*  In REFRO, at zenith distances well beyond 90 deg and under some
+   conditions, it was possible to encounter arithmetic errors due to
+   failure of the tropospheric model-atmosphere to deliver sensible
+   temperatures.  This is inherent in the published algorithm.  To
+   avoid the problem, the temperature delivered by the model has been
+   constrained to the range 200 to 320 deg K.
+
+*  A new routine has been added, ATMDSP, for rapidly recalculating
+   the A,B refraction coefficients for different wavelengths.
+
+*  The first UTC leap-second date in the DAT routine was one day early.
+   This will have had no effect on the results for more recent epochs.
+
+*  The C version of OBS had some problems related to character string
+   handling.  A call using the "number" option retured an invalid
+   station ID, and station ID and name strings of the stipulated 10
+   and 40 character lengths were improperly terminated.
+
+*  A new routine, POLMO has been added.  This is a specialist tool
+   to do with Earth polar motion.
+
+*  DC62S and CC62S could give floating point errors if vectors in
+   unlikely units were supplied.  The handling of difficult cases
+   has been improved.
+
+*  Support for Linux has been added.
+
+*  The C version of REFRO was not re-entrant.  It is now;  there has
+   been a small (4%) speed penalty.
+
+*  RANDOM, GRESID and WAIT have been dropped from the C version.  They
+   could not easily be made re-entrant and posed perennial platform-
+   dependency problems.
+
+*  The value for the arcsec to radians factor in several routines
+   had an incorrect (and superfluous) 19th digit, which has been
+   removed.
+
+*  There was a minor bug in DV2TP and V2TP, to do with protection
+   against the special case where the tangent point is the pole.
+
+*  In OBS, the position of the Parkes radiotelescope has been revised,
+   and the ATNF Mopra observatory has been added.
+
+*  Two new routines have been added.  PAV (single precision) and DPAV
+   (double precision) are like BEAR and DBEAR but start with direction
+   cosines rather than spherical coordinates - they return the position
+   angle of one point with respect to the other.
+
+*  The C version of REFRO still wasn't re-entrant, but is now.
+
+*  The C version of DTF2D used to accept 60.0 in the seconds field;
+   this has been corrected.
+
+*  The PLANET and RDPLAN routines now include Pluto.  The ephemeris
+   is accurate (sub-arcsecond) but covers the 20th and 21st centuries
+   only.
+
+   !!!  IMPORTANT NOTE  !!!
+
+   RDPLAN used to interpret any planet number outside the range 1-8
+   as meaning the Sun.  The new version uses planet number 9.  Existing
+   programs using 9 for the Sun should be changed to use 0.  The rule
+   has not been changed, except that the range is now 1-9 instead of
+   1-8, as it is unlikely that the equivalent problem will arise in the
+   future.
+
+*  Two new routines have been added, PLANEL and PLANTE.  They are
+   analogues of PLANET and RDPLAN but for the case where orbital
+   elements are available.  They can be used for predicting the
+   positions of asteroids and comets, and, if up-to-date osculating
+   elements are supplied, more accurate positions for the major
+   planets than can be provided through the PLANET and RDPLAN
+   routines.
+
+*  The REFRO routine could give inaccurate results for low temperatures
+   (subzero C).  This was caused by over-cautious defensive programming,
+   which prevented the tropospheric temperature falling below 200 K.
+
+*  A new routine has been added, REFCOQ.  This calculates the coefficients
+   of a two-term refraction model.  It complements the existing REFCO
+   routine, being much faster at the expense of some accuracy.
+
+*  The 1997 July 1 UTC leap second has been added to the DAT routine.
+
+*  A bug in the C version of SVD (slaSvd) caused occasional false
+   indications of ill-conditioning.  The results of least-squares
+   fits do not seem to have been affected.  The Fortran version
+   (sla_SVD) did not have the bug.
+
+*  The Subaru telescope (Japanese National 8-metre telescope, Mauna Kea)
+   has been added to the OBS routine.
+
+*  The DAT routine has been extended back to the inception of UTC in
+   1960.
+
+*  The "earliest date possible" in DJCL was two days out (disagreeing
+   with DJCAL, which had the correct value).
+
+*  The GMSTA code has been improved.
+
+*  A new routine, PV2EL, takes a heliocentric J2000 equatorial position
+   and velocity and produces the equivalent set of osculating elements.
+
+*  The 1999 January 1 UTC leap second has been added to the DAT routine.
+
+*  Four new routines have been introduced which transform between the
+   FK5 system and the ICRS (Hipparcos) system.  FK52H and H2FK5 transform
+   star positions and proper motions from FK5 coordinates to Hipparcos
+   coordinates and vice versa.  FK5HZ and HFK5Z do the same but for the
+   case where the Hipparcos proper motions are zero.
+
+*  Six new routines have been introduced for dealing with orbital elements.
+   Four of them (sla_EL2UE, sla_PV2UE, sla_UE2EL and sla_UE2PV) provide
+   applications with direct access to the "universal variables" method
+   that was already being used internally.  Compared with using conventional
+   (angular) elements and solving Kepler's equation, the universal variables
+   approach has a number of advantages, including better handling of near-
+   parabolic orbits and greater efficiency.  The remaining two routines
+   (sla_PERTEL and sla_PERTUE) generate updated elements by applying
+   major-planet perturbations.  The new elements can then be used to
+   predict positions that are much more accurate.  For minor planets,
+   sub-arcsecond accuracy over a decade is achievable.
+
+*  Several observatory sites have been added to the OBS routine:  CFHT,
+   Keck 2, Gemini North, FCRAO, IRTF and CSO.  The coordinates for all
+   the Mauna Kea sites have been updated in accordance with recent aerial
+   photography results made available by the Institute for Astronomy,
+   University of Hawaii.
+
+*  A coding error in DAT produced incorrect results for dates in the
+   first 54 days of 1972.
+
+-----------------------------------------------------------------------
+
+
+ P.T.Wallace
+
+ ptw@star.rl.ac.uk
+ +44-1235-44-5372
diff --git a/math/slalib/doc/refco.hlp b/math/slalib/doc/refco.hlp
new file mode 100644
index 00000000..98be6d4c
--- /dev/null
+++ b/math/slalib/doc/refco.hlp
@@ -0,0 +1,54 @@
+.help refco Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slRFCO (HM, TDK, PMB, RH, WL, PHI, TLR, EPS,
+     :                      REFA, REFB)
+
+     - - - - - -
+      R F C O
+     - - - - - -
+
+  Determine the constants A and B in the atmospheric refraction
+  model dZ = A tan Z + B tan**3 Z.
+
+  Z is the "observed" zenith distance (i.e. affected by refraction)
+  and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo)
+  zenith distance.
+
+  Given:
+    HM      d     height of the observer above sea level (metre)
+    TDK     d     ambient temperature at the observer (deg K)
+    PMB     d     pressure at the observer (millibar)
+    RH      d     relative humidity at the observer (range 0-1)
+    WL      d     effective wavelength of the source (micrometre)
+    PHI     d     latitude of the observer (radian, astronomical)
+    TLR     d     temperature lapse rate in the troposphere (degK/metre)
+    EPS     d     precision required to terminate iteration (radian)
+
+  Returned:
+    REFA    d     tan Z coefficient (radian)
+    REFB    d     tan**3 Z coefficient (radian)
+
+  Called:  slRFRO
+
+  Notes:
+
+  1  Typical values for the TLR and EPS arguments might be 0.0065D0 and
+     1D-10 respectively.
+
+  2  The radio refraction is chosen by specifying WL > 100 micrometres.
+
+  3  The routine is a slower but more accurate alternative to the
+     slRFCQ routine.  The constants it produces give perfect
+     agreement with slRFRO at zenith distances arctan(1) (45 deg)
+     and arctan(4) (about 76 deg).  It achieves 0.5 arcsec accuracy
+     for ZD < 80 deg, 0.01 arcsec accuracy for ZD < 60 deg, and
+     0.001 arcsec accuracy for ZD < 45 deg.
+
+  P.T.Wallace   Starlink   3 June 1997
+
+  Copyright (C) 1997 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/refcoq.hlp b/math/slalib/doc/refcoq.hlp
new file mode 100644
index 00000000..153ed66e
--- /dev/null
+++ b/math/slalib/doc/refcoq.hlp
@@ -0,0 +1,167 @@
+.help refcoq Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slRFCQ (TDK, PMB, RH, WL, REFA, REFB)
+
+     - - - - - - -
+      R F C Q
+     - - - - - - -
+
+  Determine the constants A and B in the atmospheric refraction
+  model dZ = A tan Z + B tan**3 Z.  This is a fast alternative
+  to the slRFCO routine - see notes.
+
+  Z is the "observed" zenith distance (i.e. affected by refraction)
+  and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo)
+  zenith distance.
+
+  Given:
+    TDK      d      ambient temperature at the observer (deg K)
+    PMB      d      pressure at the observer (millibar)
+    RH       d      relative humidity at the observer (range 0-1)
+    WL       d      effective wavelength of the source (micrometre)
+
+  Returned:
+    REFA     d      tan Z coefficient (radian)
+    REFB     d      tan**3 Z coefficient (radian)
+
+  The radio refraction is chosen by specifying WL > 100 micrometres.
+
+  Notes:
+
+  1  The model is an approximation, for moderate zenith distances,
+     to the predictions of the slRFRO routine.  The approximation
+     is maintained across a range of conditions, and applies to
+     both optical/IR and radio.
+
+  2  The algorithm is a fast alternative to the slRFCO routine.
+     The latter calls the slRFRO routine itself:  this involves
+     integrations through a model atmosphere, and is costly in
+     processor time.  However, the model which is produced is precisely
+     correct for two zenith distance (45 degrees and about 76 degrees)
+     and at other zenith distances is limited in accuracy only by the
+     A tan Z + B tan**3 Z formulation itself.  The present routine
+     is not as accurate, though it satisfies most practical
+     requirements.
+
+  3  The model omits the effects of (i) height above sea level (apart
+     from the reduced pressure itself), (ii) latitude (i.e. the
+     flattening of the Earth) and (iii) variations in tropospheric
+     lapse rate.
+
+     The model was tested using the following range of conditions:
+
+       lapse rates 0.0055, 0.0065, 0.0075 deg/metre
+       latitudes 0, 25, 50, 75 degrees
+       heights 0, 2500, 5000 metres ASL
+       pressures mean for height -10% to +5% in steps of 5%
+       temperatures -10 deg to +20 deg with respect to 280 deg at SL
+       relative humidity 0, 0.5, 1
+       wavelengths 0.4, 0.6, ... 2 micron, + radio
+       zenith distances 15, 45, 75 degrees
+
+     The accuracy with respect to direct use of the slRFRO routine
+     was as follows:
+
+                            worst         RMS
+
+       optical/IR           62 mas       8 mas
+       radio               319 mas      49 mas
+
+     For this particular set of conditions:
+
+       lapse rate 0.0065 degK/metre
+       latitude 50 degrees
+       sea level
+       pressure 1005 mB
+       temperature 280.15 degK
+       humidity 80%
+       wavelength 5740 Angstroms
+
+     the results were as follows:
+
+       ZD        slRFRO   slRFCQ  Saastamoinen
+
+       10         10.27        10.27        10.27
+       20         21.19        21.20        21.19
+       30         33.61        33.61        33.60
+       40         48.82        48.83        48.81
+       45         58.16        58.18        58.16
+       50         69.28        69.30        69.27
+       55         82.97        82.99        82.95
+       60        100.51       100.54       100.50
+       65        124.23       124.26       124.20
+       70        158.63       158.68       158.61
+       72        177.32       177.37       177.31
+       74        200.35       200.38       200.32
+       76        229.45       229.43       229.42
+       78        267.44       267.29       267.41
+       80        319.13       318.55       319.10
+
+      deg        arcsec       arcsec       arcsec
+
+     The values for Saastamoinen's formula (which includes terms
+     up to tan^5) are taken from Hohenkerk and Sinclair (1985).
+
+     The results from the much slower but more accurate slRFCO
+     routine have not been included in the tabulation as they are
+     identical to those in the slRFRO column to the 0.01 arcsec
+     resolution used.
+
+  4  Outlandish input parameters are silently limited to mathematically
+     safe values.  Zero pressure is permissible, and causes zeroes to
+     be returned.
+
+  5  The algorithm draws on several sources, as follows:
+
+     a) The formula for the saturation vapour pressure of water as
+        a function of temperature and temperature is taken from
+        expressions A4.5-A4.7 of Gill (1982).
+
+     b) The formula for the water vapour pressure, given the
+        saturation pressure and the relative humidity, is from
+        Crane (1976), expression 2.5.5.
+
+     c) The refractivity of air is a function of temperature,
+        total pressure, water-vapour pressure and, in the case
+        of optical/IR but not radio, wavelength.  The formulae
+        for the two cases are developed from the Essen and Froome
+        expressions adopted in Resolution 1 of the 12th International
+        Geodesy Association General Assembly (1963).
+
+     The above three items are as used in the slRFRO routine.
+
+     d) The formula for beta, the ratio of the scale height of the
+        atmosphere to the geocentric distance of the observer, is
+        an adaption of expression 9 from Stone (1996).  The
+        adaptations, arrived at empirically, consist of (i) a
+        small adjustment to the coefficient and (ii) a humidity
+        term for the radio case only.
+
+     e) The formulae for the refraction constants as a function of
+        n-1 and beta are from Green (1987), expression 4.31.
+
+  References:
+
+     Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral
+     Atmosphere", Methods of Experimental Physics: Astrophysics 12B,
+     Academic Press, 1976.
+
+     Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press, 1982.
+
+     Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63, 1985.
+
+     International Geodesy Association General Assembly, Bulletin
+     Geodesique 70 p390, 1963.
+
+     Stone, Ronald C., P.A.S.P. 108 1051-1058, 1996.
+
+     Green, R.M., "Spherical Astronomy", Cambridge University Press, 1987.
+
+  P.T.Wallace   Starlink   4 June 1997
+
+  Copyright (C) 1997 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/refro.hlp b/math/slalib/doc/refro.hlp
new file mode 100644
index 00000000..8b66c95d
--- /dev/null
+++ b/math/slalib/doc/refro.hlp
@@ -0,0 +1,123 @@
+.help refro Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slRFRO (ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR,
+     :                      EPS, REF)
+
+     - - - - - -
+      R F R O
+     - - - - - -
+
+  Atmospheric refraction for radio and optical/IR wavelengths.
+
+  Given:
+    ZOBS    d  observed zenith distance of the source (radian)
+    HM      d  height of the observer above sea level (metre)
+    TDK     d  ambient temperature at the observer (deg K)
+    PMB     d  pressure at the observer (millibar)
+    RH      d  relative humidity at the observer (range 0-1)
+    WL      d  effective wavelength of the source (micrometre)
+    PHI     d  latitude of the observer (radian, astronomical)
+    TLR     d  temperature lapse rate in the troposphere (degK/metre)
+    EPS     d  precision required to terminate iteration (radian)
+
+  Returned:
+    REF     d  refraction: in vacuo ZD minus observed ZD (radian)
+
+  Notes:
+
+  1  A suggested value for the TLR argument is 0.0065D0.  The
+     refraction is significantly affected by TLR, and if studies
+     of the local atmosphere have been carried out a better TLR
+     value may be available.
+
+  2  A suggested value for the EPS argument is 1D-8.  The result is
+     usually at least two orders of magnitude more computationally
+     precise than the supplied EPS value.
+
+  3  The routine computes the refraction for zenith distances up
+     to and a little beyond 90 deg using the method of Hohenkerk
+     and Sinclair (NAO Technical Notes 59 and 63, subsequently adopted
+     in the Explanatory Supplement, 1992 edition - see section 3.281).
+
+  4  The code is a development of the optical/IR refraction subroutine
+     AREF of C.Hohenkerk (HMNAO, September 1984), with extensions to
+     support the radio case.  Apart from merely cosmetic changes, the
+     following modifications to the original HMNAO optical/IR refraction
+     code have been made:
+
+     .  The angle arguments have been changed to radians.
+
+     .  Any value of ZOBS is allowed (see note 6, below).
+
+     .  Other argument values have been limited to safe values.
+
+     .  Murray's values for the gas constants have been used
+        (Vectorial Astrometry, Adam Hilger, 1983).
+
+     .  The numerical integration phase has been rearranged for
+        extra clarity.
+
+     .  A better model for Ps(T) has been adopted (taken from
+        Gill, Atmosphere-Ocean Dynamics, Academic Press, 1982).
+
+     .  More accurate expressions for Pwo have been adopted
+        (again from Gill 1982).
+
+     .  Provision for radio wavelengths has been added using
+        expressions devised by A.T.Sinclair, RGO (private
+        communication 1989), based on the Essen & Froome
+        refractivity formula adopted in Resolution 1 of the
+        13th International Geodesy Association General Assembly
+        (Bulletin Geodesique 70 p390, 1963).
+
+     .  Various small changes have been made to gain speed.
+
+     None of the changes significantly affects the optical/IR results
+     with respect to the algorithm given in the 1992 Explanatory
+     Supplement.  For example, at 70 deg zenith distance the present
+     routine agrees with the ES algorithm to better than 0.05 arcsec
+     for any reasonable combination of parameters.  However, the
+     improved water-vapour expressions do make a significant difference
+     in the radio band, at 70 deg zenith distance reaching almost
+     4 arcsec for a hot, humid, low-altitude site during a period of
+     low pressure.
+
+  5  The radio refraction is chosen by specifying WL > 100 micrometres.
+     Because the algorithm takes no account of the ionosphere, the
+     accuracy deteriorates at low frequencies, below about 30 MHz.
+
+  6  Before use, the value of ZOBS is expressed in the range +/- pi.
+     If this ranged ZOBS is -ve, the result REF is computed from its
+     absolute value before being made -ve to match.  In addition, if
+     it has an absolute value greater than 93 deg, a fixed REF value
+     equal to the result for ZOBS = 93 deg is returned, appropriately
+     signed.
+
+  7  As in the original Hohenkerk and Sinclair algorithm, fixed values
+     of the water vapour polytrope exponent, the height of the
+     tropopause, and the height at which refraction is negligible are
+     used.
+
+  8  The radio refraction has been tested against work done by
+     Iain Coulson, JACH, (private communication 1995) for the
+     James Clerk Maxwell Telescope, Mauna Kea.  For typical conditions,
+     agreement at the 0.1 arcsec level is achieved for moderate ZD,
+     worsening to perhaps 0.5-1.0 arcsec at ZD 80 deg.  At hot and
+     humid sea-level sites the accuracy will not be as good.
+
+  9  It should be noted that the relative humidity RH is formally
+     defined in terms of "mixing ratio" rather than pressures or
+     densities as is often stated.  It is the mass of water per unit
+     mass of dry air divided by that for saturated air at the same
+     temperature and pressure (see Gill 1982).
+
+  Called:  slDA1P, slATMT, slATMS
+
+  P.T.Wallace   Starlink   3 June 1997
+
+  Copyright (C) 1997 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/refv.hlp b/math/slalib/doc/refv.hlp
new file mode 100644
index 00000000..104736a5
--- /dev/null
+++ b/math/slalib/doc/refv.hlp
@@ -0,0 +1,79 @@
+.help refv Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slREFV (VU, REFA, REFB, VR)
+
+     - - - - -
+      R E F V
+     - - - - -
+
+  Adjust an unrefracted Cartesian vector to include the effect of
+  atmospheric refraction, using the simple A tan Z + B tan**3 Z
+  model.
+
+  Given:
+    VU    dp    unrefracted position of the source (Az/El 3-vector)
+    REFA  dp    tan Z coefficient (radian)
+    REFB  dp    tan**3 Z coefficient (radian)
+
+  Returned:
+    VR    dp    refracted position of the source (Az/El 3-vector)
+
+  Notes:
+
+  1  This routine applies the adjustment for refraction in the
+     opposite sense to the usual one - it takes an unrefracted
+     (in vacuo) position and produces an observed (refracted)
+     position, whereas the A tan Z + B tan**3 Z model strictly
+     applies to the case where an observed position is to have the
+     refraction removed.  The unrefracted to refracted case is
+     harder, and requires an inverted form of the text-book
+     refraction models;  the algorithm used here is equivalent to
+     one iteration of the Newton-Raphson method applied to the above
+     formula.
+
+  2  Though optimized for speed rather than precision, the present
+     routine achieves consistency with the refracted-to-unrefracted
+     A tan Z + B tan**3 Z model at better than 1 micro-arcsecond within
+     30 degrees of the zenith and remains within 1 milliarcsecond to
+     beyond ZD 70 degrees.  The inherent accuracy of the model is, of
+     course, far worse than this - see the documentation for slRFCO
+     for more information.
+
+  3  At low elevations (below about 3 degrees) the refraction
+     correction is held back to prevent arithmetic problems and
+     wildly wrong results.  Over a wide range of observer heights
+     and corresponding temperatures and pressures, the following
+     levels of accuracy (arcsec) are achieved, relative to numerical
+     integration through a model atmosphere:
+
+              ZD    error
+
+              80      0.4
+              81      0.8
+              82      1.6
+              83      3
+              84      7
+              85     17
+              86     45
+              87    150
+              88    340
+              89    620
+              90   1100
+              91   1900         } relevant only to
+              92   3200         } high-elevation sites
+
+  4  See also the routine slREFZ, which performs the adjustment to
+     the zenith distance rather than in Cartesian Az/El coordinates.
+     The present routine is faster than slREFZ and, except very low down,
+     is equally accurate for all practical purposes.  However, beyond
+     about ZD 84 degrees slREFZ should be used, and for the utmost
+     accuracy iterative use of slRFRO should be considered.
+
+  P.T.Wallace   Starlink   26 December 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/refz.hlp b/math/slalib/doc/refz.hlp
new file mode 100644
index 00000000..5c91ab03
--- /dev/null
+++ b/math/slalib/doc/refz.hlp
@@ -0,0 +1,78 @@
+.help refz Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slREFZ (ZU, REFA, REFB, ZR)
+
+     - - - - -
+      R E F Z
+     - - - - -
+
+  Adjust an unrefracted zenith distance to include the effect of
+  atmospheric refraction, using the simple A tan Z + B tan**3 Z
+  model (plus special handling for large ZDs).
+
+  Given:
+    ZU    dp    unrefracted zenith distance of the source (radian)
+    REFA  dp    tan Z coefficient (radian)
+    REFB  dp    tan**3 Z coefficient (radian)
+
+  Returned:
+    ZR    dp    refracted zenith distance (radian)
+
+  Notes:
+
+  1  This routine applies the adjustment for refraction in the
+     opposite sense to the usual one - it takes an unrefracted
+     (in vacuo) position and produces an observed (refracted)
+     position, whereas the A tan Z + B tan**3 Z model strictly
+     applies to the case where an observed position is to have the
+     refraction removed.  The unrefracted to refracted case is
+     harder, and requires an inverted form of the text-book
+     refraction models;  the formula used here is based on the
+     Newton-Raphson method.  For the utmost numerical consistency
+     with the refracted to unrefracted model, two iterations are
+     carried out, achieving agreement at the 1D-11 arcseconds level
+     for a ZD of 80 degrees.  The inherent accuracy of the model
+     is, of course, far worse than this - see the documentation for
+     slRFCO for more information.
+
+  2  At ZD 83 degrees, the rapidly-worsening A tan Z + B tan**3 Z
+     model is abandoned and an empirical formula takes over.  Over a
+     wide range of observer heights and corresponding temperatures and
+     pressures, the following levels of accuracy (arcsec) are
+     typically achieved, relative to numerical integration through a
+     model atmosphere:
+
+              ZR    error
+
+              80      0.4
+              81      0.8
+              82      1.5
+              83      3.2
+              84      4.9
+              85      5.8
+              86      6.1
+              87      7.1
+              88     10
+              89     20
+              90     40
+              91    100         } relevant only to
+              92    200         } high-elevation sites
+
+     The high-ZD model is scaled to match the normal model at the
+     transition point;  there is no glitch.
+
+  3  Beyond 93 deg zenith distance, the refraction is held at its
+     93 deg value.
+
+  4  See also the routine slREFV, which performs the adjustment in
+     Cartesian Az/El coordinates, and with the emphasis on speed
+     rather than numerical accuracy.
+
+  P.T.Wallace   Starlink   19 September 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/rverot.hlp b/math/slalib/doc/rverot.hlp
new file mode 100644
index 00000000..5f61abd7
--- /dev/null
+++ b/math/slalib/doc/rverot.hlp
@@ -0,0 +1,40 @@
+.help rverot Jun99 "Slalib Package"
+.nf
+
+      REAL FUNCTION slRVER (PHI, RA, DA, ST)
+
+     - - - - - - -
+      R V E R
+     - - - - - - -
+
+  Velocity component in a given direction due to Earth rotation
+  (single precision)
+
+  Given:
+     PHI     real    latitude of observing station (geodetic)
+     RA,DA   real    apparent RA,DEC
+     ST      real    local apparent sidereal time
+
+  PHI, RA, DEC and ST are all in radians.
+
+  Result:
+     Component of Earth rotation in direction RA,DA (km/s)
+
+  Sign convention:
+     The result is +ve when the observatory is receding from the
+     given point on the sky.
+
+  Accuracy:
+     The simple algorithm used assumes a spherical Earth, of
+     a radius chosen to give results accurate to about 0.0005 km/s
+     for observing stations at typical latitudes and heights.  For
+     applications requiring greater precision, use the routine
+     slPVOB.
+
+  P.T.Wallace   Starlink   20 July 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/rvgalc.hlp b/math/slalib/doc/rvgalc.hlp
new file mode 100644
index 00000000..b0e2773e
--- /dev/null
+++ b/math/slalib/doc/rvgalc.hlp
@@ -0,0 +1,42 @@
+.help rvgalc Jun99 "Slalib Package"
+.nf
+
+      REAL FUNCTION slRVGA (R2000, D2000)
+
+     - - - - - - -
+      R V G A
+     - - - - - - -
+
+  Velocity component in a given direction due to the rotation
+  of the Galaxy (single precision)
+
+  Given:
+     R2000,D2000   real    J2000.0 mean RA,Dec (radians)
+
+  Result:
+     Component of dynamical LSR motion in direction R2000,D2000 (km/s)
+
+  Sign convention:
+     The result is +ve when the dynamical LSR is receding from the
+     given point on the sky.
+
+  Note:  The Local Standard of Rest used here is a point in the
+         vicinity of the Sun which is in a circular orbit around
+         the Galactic centre.  Sometimes called the "dynamical" LSR,
+         it is not to be confused with a "kinematical" LSR, which
+         is the mean standard of rest of star catalogues or stellar
+         populations.
+
+  Reference:  The orbital speed of 220 km/s used here comes from
+              Kerr & Lynden-Bell (1986), MNRAS, 221, p1023.
+
+  Called:
+     slCS2C, slVDV
+
+  P.T.Wallace   Starlink   23 March 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/rvlg.hlp b/math/slalib/doc/rvlg.hlp
new file mode 100644
index 00000000..e333c1e4
--- /dev/null
+++ b/math/slalib/doc/rvlg.hlp
@@ -0,0 +1,36 @@
+.help rvlg Jun99 "Slalib Package"
+.nf
+
+      REAL FUNCTION slRVLG (R2000, D2000)
+
+     - - - - -
+      R V L G
+     - - - - -
+
+  Velocity component in a given direction due to the combination
+  of the rotation of the Galaxy and the motion of the Galaxy
+  relative to the mean motion of the local group (single precision)
+
+  Given:
+     R2000,D2000   real    J2000.0 mean RA,Dec (radians)
+
+  Result:
+     Component of SOLAR motion in direction R2000,D2000 (km/s)
+
+  Sign convention:
+     The result is +ve when the Sun is receding from the
+     given point on the sky.
+
+  Reference:
+     IAU Trans 1976, 168, p201.
+
+  Called:
+     slCS2C, slVDV
+
+  P.T.Wallace   Starlink   June 1985
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/rvlsrd.hlp b/math/slalib/doc/rvlsrd.hlp
new file mode 100644
index 00000000..f7539867
--- /dev/null
+++ b/math/slalib/doc/rvlsrd.hlp
@@ -0,0 +1,51 @@
+.help rvlsrd Jun99 "Slalib Package"
+.nf
+
+      REAL FUNCTION slRVLD (R2000, D2000)
+
+     - - - - - - -
+      R V L D
+     - - - - - - -
+
+  Velocity component in a given direction due to the Sun's motion
+  with respect to the dynamical Local Standard of Rest.
+
+  (single precision)
+
+  Given:
+     R2000,D2000   r    J2000.0 mean RA,Dec (radians)
+
+  Result:
+     Component of "peculiar" solar motion in direction R2000,D2000 (km/s)
+
+  Sign convention:
+     The result is +ve when the Sun is receding from the given point on
+     the sky.
+
+  Note:  The Local Standard of Rest used here is the "dynamical" LSR,
+         a point in the vicinity of the Sun which is in a circular
+         orbit around the Galactic centre.  The Sun's motion with
+         respect to the dynamical LSR is called the "peculiar" solar
+         motion.
+
+         There is another type of LSR, called a "kinematical" LSR.  A
+         kinematical LSR is the mean standard of rest of specified star
+         catalogues or stellar populations, and several slightly
+         different kinematical LSRs are in use.  The Sun's motion with
+         respect to an agreed kinematical LSR is known as the "standard"
+         solar motion.  To obtain a radial velocity correction with
+         respect to an adopted kinematical LSR use the routine slRVLK.
+
+  Reference:  Delhaye (1965), in "Stars and Stellar Systems", vol 5,
+              p73.
+
+  Called:
+     slCS2C, slVDV
+
+  P.T.Wallace   Starlink   9 March 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/rvlsrk.hlp b/math/slalib/doc/rvlsrk.hlp
new file mode 100644
index 00000000..04cbca89
--- /dev/null
+++ b/math/slalib/doc/rvlsrk.hlp
@@ -0,0 +1,50 @@
+.help rvlsrk Jun99 "Slalib Package"
+.nf
+
+      REAL FUNCTION slRVLK (R2000, D2000)
+
+     - - - - - - -
+      R V L K
+     - - - - - - -
+
+  Velocity component in a given direction due to the Sun's motion
+  with respect to an adopted kinematic Local Standard of Rest.
+
+  (single precision)
+
+  Given:
+     R2000,D2000   r    J2000.0 mean RA,Dec (radians)
+
+  Result:
+     Component of "standard" solar motion in direction R2000,D2000 (km/s)
+
+  Sign convention:
+     The result is +ve when the Sun is receding from the given point on
+     the sky.
+
+  Note:  The Local Standard of Rest used here is one of several
+         "kinematical" LSRs in common use.  A kinematical LSR is the
+         mean standard of rest of specified star catalogues or stellar
+         populations.  The Sun's motion with respect to a kinematical
+         LSR is known as the "standard" solar motion.
+
+         There is another sort of LSR, the "dynamical" LSR, which is a
+         point in the vicinity of the Sun which is in a circular orbit
+         around the Galactic centre.  The Sun's motion with respect to
+         the dynamical LSR is called the "peculiar" solar motion.  To
+         obtain a radial velocity correction with respect to the
+         dynamical LSR use the routine slRVLD.
+
+  Reference:  Delhaye (1965), in "Stars and Stellar Systems", vol 5,
+              p73.
+
+  Called:
+     slCS2C, slVDV
+
+  P.T.Wallace   Starlink   11 March 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/s2tp.hlp b/math/slalib/doc/s2tp.hlp
new file mode 100644
index 00000000..fb92a6f9
--- /dev/null
+++ b/math/slalib/doc/s2tp.hlp
@@ -0,0 +1,31 @@
+.help s2tp Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slS2TP (RA, DEC, RAZ, DECZ, XI, ETA, J)
+
+     - - - - -
+      S 2 T P
+     - - - - -
+
+  Projection of spherical coordinates onto tangent plane:
+  "gnomonic" projection - "standard coordinates"
+  (single precision)
+
+  Given:
+     RA,DEC      real  spherical coordinates of point to be projected
+     RAZ,DECZ    real  spherical coordinates of tangent point
+
+  Returned:
+     XI,ETA      real  rectangular coordinates on tangent plane
+     J           int   status:   0 = OK, star on tangent plane
+                                 1 = error, star too far from axis
+                                 2 = error, antistar on tangent plane
+                                 3 = error, antistar too far from axis
+
+  P.T.Wallace   Starlink   18 July 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/sedscript b/math/slalib/doc/sedscript
new file mode 100755
index 00000000..3797f980
--- /dev/null
+++ b/math/slalib/doc/sedscript
@@ -0,0 +1,35 @@
+#!/bin/csh
+
+# EZSEDSCRIPT -- Script for automatically creating simple help for the
+# SLALIB FORTRAN routines.
+# 
+# First argument $1 is the month and year combined, e.g. Jun84
+
+foreach file (../*.f)
+    set rootfile = `basename $file .f`
+    set package = '"Slalib Package"'
+    set outfile = $rootfile.hlp
+    set d = `echo \$d`
+    set s = `echo \$s`
+    echo $outfile
+    echo "1i\\
+.help $rootfile $1 $package\\
+.nf\\
+\
+/^\*-/a\\
+\\
+.fi\\
+.endhelp\
+/^\*-/,$d\
+1,$s/^*+//\
+1,$s/^*//" > tmpfile
+    sed -f tmpfile $file > $outfile
+    rm tmpfile
+end
+
+rm atms.hlp
+rm atmt.hlp
+rm idchf.hlp
+rm idchi.hlp
+rm sla_test.hlp
+cp slalib.hlp.sav slalib.hlp
diff --git a/math/slalib/doc/sep.hlp b/math/slalib/doc/sep.hlp
new file mode 100644
index 00000000..71808737
--- /dev/null
+++ b/math/slalib/doc/sep.hlp
@@ -0,0 +1,29 @@
+.help sep Jun99 "Slalib Package"
+.nf
+
+      REAL FUNCTION slSEP (A1, B1, A2, B2)
+
+     - - - -
+      S E P
+     - - - -
+
+  Angle between two points on a sphere (single precision)
+
+  Given:
+     A1,B1    real    spherical coordinates of one point
+     A2,B2    real    spherical coordinates of the other point
+
+  (The spherical coordinates are RA,Dec, Long,Lat etc, in radians.)
+
+  The result is the angle, in radians, between the two points.  It
+  is always positive.
+
+  Called:  slCS2C
+
+  P.T.Wallace   Starlink   April 1985
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/sla.news b/math/slalib/doc/sla.news
new file mode 100644
index 00000000..541b6c8a
--- /dev/null
+++ b/math/slalib/doc/sla.news
@@ -0,0 +1,36 @@
+SLALIB_Version_2.3-0                                  Expiry 30 September 1999
+
+The latest releases of SLALIB include the following changes:
+
+*  The 1999 January 1 UTC leap second has been added to the DAT routine.
+
+*  Four new routines have been introduced which transform between the
+   FK5 system and the ICRS (Hipparcos) system.  FK52H and H2FK5 transform
+   star positions and proper motions from FK5 coordinates to Hipparcos
+   coordinates and vice versa.  FK5HZ and HFK5Z do the same but for the
+   case where the Hipparcos proper motions are zero.
+
+*  Six new routines have been introduced for dealing with orbital elements.
+   Four of them (sla_EL2UE, sla_PV2UE, sla_UE2EL and sla_UE2PV) provide
+   applications with direct access to the "universal variables" method
+   that was already being used internally.  Compared with using conventional
+   (angular) elements and solving Kepler's equation, the universal variables
+   approach has a number of advantages, including better handling of near-
+   parabolic orbits and greater efficiency.  The remaining two routines
+   (sla_PERTEL and sla_PERTUE) generate updated elements by applying
+   major-planet perturbations.  The new elements can then be used to
+   predict positions that are much more accurate.  For minor planets,
+   sub-arcsecond accuracy over a decade is achievable.
+
+*  Several observatory sites have been added to the OBS routine:  CFHT,
+   Keck 2, Gemini North, FCRAO, IRTF and CSO.  The coordinates for all
+   the Mauna Kea sites have been updated in accordance with recent aerial
+   photography results made available by the Institute for Astronomy,
+   University of Hawaii.
+ 
+ P.T.Wallace
+ 21 April 1999
+
+ ptw@star.rl.ac.uk
+ +44-1235-44-5372
+--------------------------------------------------------------------------
diff --git a/math/slalib/doc/slalib.hd b/math/slalib/doc/slalib.hd
new file mode 100644
index 00000000..35fe8ea0
--- /dev/null
+++ b/math/slalib/doc/slalib.hd
@@ -0,0 +1,183 @@
+# Help directory the SLALIB library
+
+$slalib		= "math$slalib/"
+
+addet		hlp=addet.hlp,		src=slalib$addet.f
+afin		hlp=afin.hlp,		src=slalib$afin.f
+airmas		hlp=airmas.hlp,		src=slalib$airmas.f
+altaz		hlp=altaz.hlp,		src=slalib$altaz.f
+amp		hlp=amp.hlp,		src=slalib$amp.f
+ampqk		hlp=ampqk.hlp,		src=slalib$ampqk.f
+aop		hlp=aop.hlp,		src=slalib$aop.f
+aoppa		hlp=aoppa.hlp,		src=slalib$aoppa.f
+aoppat		hlp=aoppat.hlp,		src=slalib$aoppat.f
+aopqk		hlp=aopqk.hlp,		src=slalib$aopqk.f
+atmdsp		hlp=atmdsp.hlp,		src=slalib$atmdsp.f
+av2m		hlp=av2m.hlp,		src=slalib$av2m.f
+bear		hlp=bear.hlp,		src=slalib$bear.f
+caf2r		hlp=caf2r.hlp,		src=slalib$caf2r.f
+caldj		hlp=caldj.hlp,		src=slalib$caldj.f
+calyd		hlp=calyd.hlp,		src=slalib$calyd.f
+cc2s		hlp=cc2s.hlp,		src=slalib$cc2s.f
+cc62s		hlp=cc62s.hlp,		src=slalib$cc62s.f
+cd2tf		hlp=cd2tf.hlp,		src=slalib$cd2tf.f
+cldj		hlp=cldj.hlp,		src=slalib$cldj.f
+clyd		hlp=clyd.hlp,		src=slalib$clyd.f
+cr2af		hlp=cr2af.hlp,		src=slalib$cr2af.f
+cr2tf		hlp=cr2tf.hlp,		src=slalib$cr2tf.f
+cs2c		hlp=cs2c.hlp,		src=slalib$cs2c.f
+cs2c6		hlp=cs2c6.hlp,		src=slalib$cs2c6.f
+ctf2d		hlp=ctf2d.hlp,		src=slalib$ctf2d.f
+ctf2r		hlp=ctf2r.hlp,		src=slalib$ctf2r.f
+daf2r		hlp=daf2r.hlp,		src=slalib$daf2r.f
+dafin		hlp=dafin.hlp,		src=slalib$dafin.f
+dat		hlp=dat.hlp,		src=slalib$dat.f
+dav2m		hlp=dav2m.hlp,		src=slalib$dav2m.f
+dbear		hlp=dbear.hlp,		src=slalib$dbear.f
+dbjin		hlp=dbjin.hlp,		src=slalib$dbjin.f
+dc62s		hlp=dc62s.hlp,		src=slalib$dc62s.f
+dcc2s		hlp=dcc2s.hlp,		src=slalib$dcc2s.f
+dcmpf		hlp=dcmpf.hlp,		src=slalib$dcmpf.f
+dcs2c		hlp=dcs2c.hlp,		src=slalib$dcs2c.f
+dd2tf		hlp=dd2tf.hlp,		src=slalib$dd2tf.f
+de2h		hlp=de2h.hlp,		src=slalib$de2h.f
+deuler		hlp=deuler.hlp,		src=slalib$deuler.f
+dfltin		hlp=dfltin.hlp,		src=slalib$dfltin.f
+dh2e		hlp=dh2e.hlp,		src=slalib$dh2e.f
+dimxv		hlp=dimxv.hlp,		src=slalib$dimxv.f
+djcal		hlp=djcal.hlp,		src=slalib$djcal.f
+djcl		hlp=djcl.hlp,		src=slalib$djcl.f
+dm2av		hlp=dm2av.hlp,		src=slalib$dm2av.f
+dmat		hlp=dmat.hlp,		src=slalib$dmat.f
+dmoon		hlp=dmoon.hlp,		src=slalib$dmoon.f
+dmxm		hlp=dmxm.hlp,		src=slalib$dmxm.f
+dmxv		hlp=dmxv.hlp,		src=slalib$dmxv.f
+dpav		hlp=dpav.hlp,		src=slalib$dpav.f
+dr2af		hlp=dr2af.hlp,		src=slalib$dr2af.f
+dr2tf		hlp=dr2tf.hlp,		src=slalib$dr2tf.f
+drange		hlp=drange.hlp,		src=slalib$drange.f
+dranrm		hlp=dranrm.hlp,		src=slalib$dranrm.f
+ds2c6		hlp=ds2c6.hlp,		src=slalib$ds2c6.f
+ds2tp		hlp=ds2tp.hlp,		src=slalib$ds2tp.f
+dsep		hlp=dsep.hlp,		src=slalib$dsep.f
+dt		hlp=dt.hlp,		src=slalib$dt.f
+dtf2d		hlp=dtf2d.hlp,		src=slalib$dtf2d.f
+dtf2r		hlp=dtf2r.hlp,		src=slalib$dtf2r.f
+dtp2s		hlp=dtp2s.hlp,		src=slalib$dtp2s.f
+dtp2v		hlp=dtp2v.hlp,		src=slalib$dtp2v.f
+dtps2c		hlp=dtps2c.hlp,		src=slalib$dtps2c.f
+dtpv2c		hlp=dtpv2c.hlp,		src=slalib$dtpv2c.f
+dtt		hlp=dtt.hlp,		src=slalib$dtt.f
+dv2tp		hlp=dv2tp.hlp,		src=slalib$dv2tp.f
+dvdv		hlp=dvdv.hlp,		src=slalib$dvdv.f
+dvn		hlp=dvn.hlp,		src=slalib$dvn.f
+dvxv		hlp=dvxv.hlp,		src=slalib$dvxv.f
+e2h		hlp=e2h.hlp,		src=slalib$e2h.f
+earth		hlp=earth.hlp,		src=slalib$earth.f
+ecleq		hlp=ecleq.hlp,		src=slalib$ecleq.f
+ecmat		hlp=ecmat.hlp,		src=slalib$ecmat.f
+ecor		hlp=ecor.hlp,		src=slalib$ecor.f
+eg50		hlp=eg50.hlp,		src=slalib$eg50.f
+el2ue		hlp=el2ue.hlp,		src=slalib$el2ue.f
+epb		hlp=epb.hlp,		src=slalib$epb.f
+epb2d		hlp=epb2d.hlp,		src=slalib$epb2d.f
+epco		hlp=epco.hlp,		src=slalib$epco.f
+epj		hlp=epj.hlp,		src=slalib$epj.f
+epj2d		hlp=epj2d.hlp,		src=slalib$epj2d.f
+eqecl		hlp=eqecl.hlp,		src=slalib$eqecl.f
+eqeqx		hlp=eqeqx.hlp,		src=slalib$eqeqx.f
+eqgal		hlp=eqgal.hlp,		src=slalib$eqgal.f
+etrms		hlp=etrms.hlp,		src=slalib$etrms.f
+euler		hlp=euler.hlp,		src=slalib$euler.f
+evp		hlp=evp.hlp,		src=slalib$evp.f
+fitxy		hlp=fitxy.hlp,		src=slalib$fitxy.f
+fk425		hlp=fk425.hlp,		src=slalib$fk425.f
+fk45z		hlp=fk45z.hlp,		src=slalib$fk45z.f
+fk524		hlp=fk524.hlp,		src=slalib$fk524.f
+fk54z		hlp=fk54z.hlp,		src=slalib$fk54z.f
+fk52h		hlp=fk52h.hlp,		src=slalib$fk52h.f
+fk5hz		hlp=fk5hz.hlp,		src=slalib$fk5hz.f
+flotin		hlp=flotin.hlp,		src=slalib$flotin.f
+galeq		hlp=galeq.hlp,		src=slalib$galeq.f
+galsup		hlp=galsup.hlp,		src=slalib$galsup.f
+ge50		hlp=ge50.hlp,		src=slalib$ge50.f
+geoc		hlp=geoc.hlp,		src=slalib$geoc.f
+gmst		hlp=gmst.hlp,		src=slalib$gmst.f
+gmsta		hlp=gmsta.hlp,		src=slalib$gmsta.f
+h2e		hlp=h2e.hlp,		src=slalib$h2e.f
+h2fk5		hlp=h2fk5.hlp,		src=slalib$h2fk5.f
+hfk5z		hlp=hfk5z.hlp,		src=slalib$hfk5z.f
+imxv		hlp=imxv.hlp,		src=slalib$imxv.f
+intin		hlp=intin.hlp,		src=slalib$intin.f
+invf		hlp=invf.hlp,		src=slalib$invf.f
+kbj		hlp=kbj.hlp,		src=slalib$kbj.f
+m2av		hlp=m2av.hlp,		src=slalib$m2av.f
+map		hlp=map.hlp,		src=slalib$map.f
+mappa		hlp=mappa.hlp,		src=slalib$mappa.f
+mapqk		hlp=mapqk.hlp,		src=slalib$mapqk.f
+mapqkz		hlp=mapqkz.hlp,		src=slalib$mapqkz.f
+moon		hlp=moon.hlp,		src=slalib$moon.f
+mxm		hlp=mxm.hlp,		src=slalib$mxm.f
+mxv		hlp=mxv.hlp,		src=slalib$mxv.f
+nut		hlp=nut.hlp,		src=slalib$nut.f
+nutc		hlp=nutc.hlp,		src=slalib$nutc.f
+oap		hlp=oap.hlp,		src=slalib$oap.f
+oapqk		hlp=oapqk.hlp,		src=slalib$oapqk.f
+obs		hlp=obs.hlp,		src=slalib$obs.f
+pa		hlp=pa.hlp,		src=slalib$pa.f
+pav		hlp=pav.hlp,		src=slalib$pav.f
+pcd		hlp=pcd.hlp,		src=slalib$pcd.f
+pda2h		hlp=pda2h.hlp,		src=slalib$pda2h.f
+pdq2h		hlp=pdq2h.hlp,		src=slalib$pdq2h.f
+pertel		hlp=pertel.hlp,         src=slalib$pertel.f
+pertue		hlp=pertue.hlp,         src=slalib$pertue.f
+planel		hlp=planel.hlp,		src=slalib$planel.f
+planet		hlp=planet.hlp,		src=slalib$planet.f
+plante		hlp=plante.hlp,		src=slalib$plante.f
+pm		hlp=pm.hlp,		src=slalib$pm.f
+polmo		hlp=polmo.hlp,		src=slalib$polmo.f
+prebn		hlp=prebn.hlp,		src=slalib$prebn.f
+prec		hlp=prec.hlp,		src=slalib$prec.f
+preces		hlp=preces.hlp,		src=slalib$preces.f
+precl		hlp=precl.hlp,		src=slalib$precl.f
+precss		hlp=precss.hlp,		src=slalib$precss.f
+prenut		hlp=prenut.hlp,		src=slalib$prenut.f
+pv2ue		hlp=pv2ue.hlp,		src=slalib$pv2ue.f
+pv2el		hlp=pv2el.hlp,		src=slalib$pv2el.f
+pvobs		hlp=pvobs.hlp,		src=slalib$pvobs.f
+pxy		hlp=pxy.hlp,		src=slalib$pxy.f
+range		hlp=range.hlp,		src=slalib$range.f
+ranorm		hlp=ranorm.hlp,		src=slalib$ranorm.f
+rcc		hlp=rcc.hlp,		src=slalib$rcc.f
+rdplan		hlp=rdplan.hlp,		src=slalib$rdplan.f
+refco		hlp=refco.hlp,		src=slalib$refco.f
+refcoq		hlp=refcoq.hlp,		src=slalib$refcoq.f
+refro		hlp=refro.hlp,		src=slalib$refro.f
+refv		hlp=refv.hlp,		src=slalib$refv.f
+refz		hlp=refz.hlp,		src=slalib$refz.f
+rverot		hlp=rverot.hlp,		src=slalib$rverot.f
+rvgalc		hlp=rvgalc.hlp,		src=slalib$rvgalc.f
+rvlg		hlp=rvlg.hlp,		src=slalib$rvlg.f
+rvlsrd		hlp=rvlsrd.hlp,		src=slalib$rvlsrd.f
+rvlsrk		hlp=rvlsrk.hlp,		src=slalib$rvlsrk.f
+s2tp		hlp=s2tp.hlp,		src=slalib$s2tp.f
+sep		hlp=sep.hlp,		src=slalib$sep.f
+smat		hlp=smat.hlp,		src=slalib$smat.f
+subet		hlp=subet.hlp,		src=slalib$subet.f
+supgal		hlp=supgal.hlp,		src=slalib$supgal.f
+svd		hlp=svd.hlp,		src=slalib$svd.f
+svdcov		hlp=svdcov.hlp,		src=slalib$svdcov.f
+svdsol		hlp=svdsol.hlp,		src=slalib$svdsol.f
+tp2s		hlp=tp2s.hlp,		src=slalib$tp2s.f
+tp2v		hlp=tp2v.hlp,		src=slalib$tp2v.f
+tps2c		hlp=tps2c.hlp,		src=slalib$tps2c.f
+tpv2c		hlp=tpv2c.hlp,		src=slalib$tpv2c.f
+ue2el		hlp=ue2el.hlp,		src=slalib$ue2el.f
+ue2pv		hlp=ue2pv.hlp,		src=slalib$ue2pv.f
+unpcd		hlp=unpcd.hlp,		src=slalib$unpcd.f
+v2tp		hlp=v2tp.hlp,		src=slalib$v2tp.f
+vdv		hlp=vdv.hlp,		src=slalib$vdv.f
+vn		hlp=vn.hlp,		src=slalib$vn.f
+vxv		hlp=vxv.hlp,		src=slalib$vxv.f
+xy2xy		hlp=xy2xy.hlp,		src=slalib$xy2xy.f
+zd		hlp=zd.hlp,		src=slalib$zd.f
diff --git a/math/slalib/doc/slalib.hlp b/math/slalib/doc/slalib.hlp
new file mode 100644
index 00000000..8da465cf
--- /dev/null
+++ b/math/slalib/doc/slalib.hlp
@@ -0,0 +1,591 @@
+.help slalib Nov95 "Immatch Package"
+.ih
+NAME
+slalib -- Starlink library of positional astronomy routines
+
+.ih
+DESCRIPTION
+SLALIB is a library of Fortran 77 routines intended to make accurate
+and reliable positional-astronomy applications easier to write. Most
+SLALIB library routines are concerned with astronomical position and time,
+but a number have wider trigonometrical, numerical or general applications.
+SLALIB contains routines covering the following topics: 1) string
+decoding and sexagesimal conversions, 2) angles, vectors and rotation
+matrices, 3) calendars and timescales, 4) precession and nutation, 5)
+proper motion, 6) FK4/5 and elliptic aberration, 7) geocentric coordinates,
+8) apparent and observed place, 9) azimuth and elevation, 10) refraction
+and air mass, 11) ecliptic, galactic, and supergalactic coordinates,
+12) ephemerides, 13) astrometry, and 14) numerical methods.
+
+The labels and calling sequences of the SLALIB are listed below grouped
+by function. To get more detailed help on any individual routine type
+the help command followed by the label, e.g the command "help flotin"
+will give detailed help on the subroutine slrfli.
+
+.ih
+STRING DECODING
+.nf
+ intin --  call subroutine slinti (string, nstrt, ireslt, jflag)
+       Convert free-format string into integer
+
+flotin --  call subroutine slrfli (string, nstrt, reslt, jflag)
+dfltin --  call subroutine sldfli (string, nstrt, dreslt, jflag)
+       Convert free-format string into floating point number
+
+  afin --  call subroutine slafin (string, iptr, a, j)
+ dafin --  call subroutine sldafn (string, iptr, a, j)
+       Convert free-format string from deg, armin, arcsec to radians
+.fi
+.ih
+SEXAGESIMAL CONVERSIONS
+.nf
+ ctf2d --  call subroutine slctfd (ihour, imin, sec, days, j)
+ dtf2d --  call subroutine sldtfd (ihour, imin, sec, days, j)
+       Hours, minutes, seconds to days
+
+ cd2tf --  call subroutine slcdtf (ndp, days, sign, ihmsf)
+ dd2tf --  call subroutine slddtf (ndp, days, sign, ihmsf)
+       Days to hours, minutes, and seconds
+
+ ctf2r --  call subroutine slctfr (ihour, imin, sec, rad, j)
+ dtf2r --  call subroutine sldtfr (ihour, imin, sec, rad, j)
+       Hours, minutes, seconds to radians
+
+ cr2tf --  call subroutine slcrtf (ndp, angle, sign, ihmsf)
+ dr2tf --  call subroutine sldrtf (ndp, angle, sign, ihmsf)
+       Radians to hours, minutes, seconds
+
+ caf2r --  call subroutine slcafr (ideg, iamin, asec, rad, j)
+ daf2r --  call subroutine sldafr (ideg, iamin, asec, rad, j)
+       Degrees, arcminutes, arcseconds to radians
+
+ cr2af --  call subroutine slcraf (ndp, angle, sign, idmsf)
+ dr2af --  call subroutine sldraf (ndp, angle, sign, idmsf)
+       Radians to degrees, arcminutes, arcseconds
+.fi
+.ih
+ANGLES, VECTORS AND ROTATION MATRICES
+.nf
+ range --  r = slra1p (angle)
+drange --  d = slda1p (angle)
+       Normalize angle into range [-pi,pi]
+
+ranorm --  r = slra2p (angle)
+dranrm --  d = slda2p (angle)
+       Normalize angle into range [0,2pi]
+
+  cs2c --  call subroutine slcs2c (a, b, v)
+ dcs2c --  call subroutine slds2c (a, b, v)
+       Spherical coordinates to [x,y,z]
+
+  cc2s --  call subroutine slcc2s (v, a, b)
+ dcc2s --  call subroutine sldc2s (v, a, b)
+       [x,y,z] to spherical coordinates
+
+   vdv --  r = slvdv (va, vb)
+  dvdv --  d = sldvdv (va, vb)
+       Scalar product of two 3-vectors
+
+   vxv --  call subroutine slvxv (va, vb, vc)
+  dvxv --  call subroutine sldvxv (va, vb, vc)
+       Vector product of two 3-vectors
+
+    vn --  call subroutine slvn (v, uv, vm)
+   dvn --  call subroutine sldvn (v, uv, vm)
+       Normalize a 3-vector also giving the modulus
+
+   sep --  s = slsep (a1, b1, a2, b2)
+  dsep --  d = sldsep (a1, b1, a2, b2)
+       Angle between two points on a sphere
+
+  bear --  s = slbear (a1, b1, a2, b2)
+ dbear --  d = sldber (a1, b1, a2, b2)
+   pav --  s = slpav (v1, v2)
+  dpav --  d = sldpav (v1, v2)
+       Direction of one point on a sphere seen from another
+
+ euler --  call subroutine sleulr (order, phi, theta, psi, rmat)
+deuler --  call subroutine sldeul (order, phi, theta, psi, rmat)
+       Form form rotation matrix from three Euler angles
+
+
+  av2m --  call subroutine slav2m (axvec, rmat)
+ dav2m --  call subroutine sldavm (axvec, rmat)
+       Form rotation matrix from axial vector
+
+  m2av --  call subroutine slm2av (rmat, axvec)
+ dm2av --  call subroutine sldmav (rmat, axvec)
+       Determine axial vector from rotation matrix
+
+  dmxv --  call subroutine sldmxv (dm, va, vb)
+   mxv --  call subroutine slmxv (rm, va, vb)
+       Rotate vector forwards
+
+  imxv --  call subroutine slimxv (rm, va, vb)
+ dimxv --  call subroutine sldimv (dm, va, vb)
+       Rotate vector backwards
+
+  dmxm --  call subroutine sldmxm (a, b, c)
+   mxm --  call subroutine slmxm (a, b, c)
+       Product of two 3X3 matrices
+
+ cs2c6 --  call subroutine sls2c6 (a, b, r, ad, bd, rd, v)
+ ds2c6 --  call subroutine sldsc6 (a, b, r, ad, bd, rd, v)
+       Conversion of position/velocity from spherical to Cartesian
+	   coordinates
+
+ cc62s --  call subroutine slc62s (v, a, b, r, ad, bd, rd)
+ dc62s --  call subroutine sldc6s (v, a, b, r, ad, bd, rd)
+       Conversion of position/velocity from Cartesian to spherical
+	   coordinates
+.fi
+.ih
+CALENDARS
+.nf
+  cldj --  call subroutine slcadj (iy, im, id, djm, j)
+       Gregorian calendar to Modified Julian Date
+
+ caldj --  call subroutine slcadj (iy, im, id, djm, j)
+       Gregorian calendar to Modified Julian Date, permitting century by
+	   default
+
+ djcal --  call subroutine sldjca (ndp, djm, iymdf, j)
+       Modified Julian Date to Gregorian calendar, in a from convenient
+	   for formatted output
+
+  djcl --  call subroutine sldjcl (djm, iy, im, id, fd, j)
+       Modified Julian Date to Gregorian Year, Month, Day, Fraction
+
+ calyd --  call subroutine slcayd (iy, im, id, ny, nd, j)
+       Calendar to year and day in year, permitting century default
+
+  clyd --  call subroutine slclyd (iy, im, id, ny, nd, jstat)
+       Calendar to year and day in year
+
+   epb --  d = slepb (date)
+       Modified Julian Date to Besselian Epoch
+
+ epb2d --  d = sleb2d (epb)
+       Besselian epoch to Modified Julian Date
+
+   epj --  d = slepj (date)
+       Modified Julian Date to Julian Epoch
+
+ epj2d --  d = slej2d (epj)
+       Julian epoch to Modified Julian Date
+.fi
+.fi
+.ih
+TIMESCALES
+.nf
+  gmst --  d = slgmst (ut1)
+       Conversion from Universal Time to siderial time
+
+ gmsta --  d = slgmsa (date, ut)
+       Conversion from Universal Time to siderial time, rounding errors
+	   minimized
+
+ eqeqx --  d = sleqex (date)
+       Equation of the equinoxes
+
+   dat --  d = sldat (utc)
+       Offset of Atomic Time from Coordinated Universal Time:
+	   TAI - UTC
+
+    dt --  d = sldt (epoch)
+       Approximate offset between dynamical time and universal time
+
+   dtt --  d = sldtt (utc)
+       Offset of Terrestrial Time from Coordinated Universal Time:
+	   TT - UTC
+
+   rcc --  d = slrcc (tdb, ut1, wl, u, v)
+       Relativistic clock correction: TDB - TT
+.fi
+.ih
+PRECESSION AND NUTATION
+.nf
+   nut --  call subroutine slnut (date, rmatn)
+       Nutation matrix
+
+  nutc --  call subroutine slnutc (date, dpsi, deps, eps0)
+       Longitude and obliquity components of nutation, mean obliquity
+
+  prec --  call subroutine slprec (ep0, ep1, rmatp)
+       Precession matrix (IAU)
+
+ precl --  call subroutine slprel (ep0, ep1, rmatp)
+       Precession matrix (suitable for long periods)
+
+prenut --  call subroutine slprnu (epoch, date, rmatpn)
+       Combined precession/nutation matrix
+
+ prebn --  call subroutine slprbn (bep0, bep1, rmatp)
+       Precession matrix (old system)
+
+preces --  call subroutine slprce (system, ep0, ep1, ra, dc)
+       Precession in either the old or new system, character string
+           ep0 and ep1
+
+precss --  call subroutine slprcs (system, ep0, ep1, ra, dc)
+       Precession in either the old or new system, integer ep0 and ep1
+.fi
+.fi
+.ih
+PROPER MOTION
+.nf
+    pm --  call subroutine slpm (r0, d0, pr, pd, px, rv, ep0, ep1, r1, d1)
+       Adjust for proper motion
+.fi
+.ih
+FK4/5/ICRS CONVERSIONS
+.nf
+ fk425 --  call subroutine slfk45 (r1950, d1950, dr1950, dd1950,
+           p1950, v1950, r2000, d2000, dr2000, dd2000, p2000, v2000)
+       Convert B1950.0 FK4 star data to J2000.0 FK5
+
+ fk45z --  call subroutine slf45z (r1950, d1950, bepoch, r2000, d2000)
+       Convert B1950.0 FK4 position to J2000.0 FK5 assuming zero proper
+	   motion in an inertial frame and no parallax
+
+ fk524 --  call subroutine slfk54 (r2000, d2000, dr2000, dd2000,
+           p2000, v2000, r1950, d1950, dr1950, dd1950, p1950, v1950)
+       Convert J2000.0 FK5 star data to B1950.0 FK4
+
+ fk54z --  call subroutine slf54z (r2000, d2000, bepoch, r1950, d1950,
+	   dr1950, dd1950)
+       Convert J2000.0 FK5 star data to B1950.0 FK4 assuming zero proper
+	   motion in an inertial frame and no parallax
+
+ fk52h --  call subroutine slfk5h (r5, d5, dr5, dd5, rh, dh, drh, ddh)
+       Convert J2000.0 FK5 star data to ICRS J2000.0 data
+
+ fk5hz --  call subroutine slf5hz (r5, d5, epoch, rh, dh)
+       Convert J2000.0 FK5 star data to ICRS J2000.0 data  assuming
+       no Hipparcos proper motion.
+
+ h2fk5 -- call subroutine slhfk5 (rh, dh, drh, ddh, r5, d5, dr5, dd5)
+       Convert ICRS J2000.0 data to J2000.0 Fk5 star data.
+
+ hfk5z -- call subroutine slhf5z (rh, dh, epoch, r5, d5)
+       Convert ICRS J2000.0 data to J2000.0 Fk5 star data assuming no
+       Hipparchos proper motion.
+
+ dbjin --  call subroutine sldbji (string, nstrt, dreslt, j1, j2)
+       Like dfltin but with extensions to accept leading 'B' and 'J'
+
+   kbj --  call subroutine slkbj (jb, e, k, j)
+       Select epoch prefix 'B' or 'J'
+
+  epco --  d = slepco (k0, k, e)
+       Convert an epoch into the appropriate form 'B' or 'J'
+.fi
+.ih
+ELLIPTIC ABERRATIONS
+.nf
+ etrms --  call subroutine sletrm (ep, ev)
+       E-terms
+
+ subet --  call subroutine slsuet (rc, dc, eq, rm, dm)
+       Remove the E-terms
+
+ addet --  call subroutine sladet (rm, dm, eq, rc, dc)
+       Add the E-terms
+.fi
+.ih
+GEOCENTRIC COORDINATES
+.nf
+   obs --  call subroutine slobs (n, c, name, w, p, h)
+       Interrogate list of observatory parameters
+
+  geoc --  call subroutine slgeoc (p, h, r, z)
+       Convert geodetic position to geocentric
+
+ pvobs --  call subroutine slpvob (p, h, stl, pv)
+       Position and velocity of observatory
+.fi
+.ih
+APPARENT AND OBSERVED PLACE
+.nf
+   map --  call subroutine slmap (rm, dm, pr, pd, px, rv, eq, date, ra, da)
+       Mean place to geocentric apparent place
+
+ mappa --  call subroutine slmapa (eq, date, amprms)
+       Precompute mean to apparent parameters
+
+ mapqk --  call subroutine slmapq (rm, dm, pr, pd, px, rv, amprms, ra, da)
+       Mean to apparent place using precomputed parameters
+
+mapqkz --  call subroutine slmapz (rm, dm, amprms, ra, da)
+       Mean to apparent place using precomputed parameters, for zero
+	   proper motion, parallax, and radial velocity
+
+   amp --  call subroutine slamp (ra, da, date, eq, rm, dm)
+       Geocentric apparent place to mean place
+
+ ampqk --  call subroutine slampq (ra, da, amprms, rm, dm)
+       Apparent to mean place using precomputed parameters
+
+   aop --  call subroutine slaop (rap, dap, date, dut, elongm, phim, hm,
+	   xp, yp, tdk, pmb, rh, wl, tlr, aob, zob, hob, dob, rob)
+       Apparent place to observed place
+
+ aoppa --  call subroutine slaopa (date, dut, elongm, phim, hm, xy, yp,
+	   tdk, pmb, rh, wl, tlr, aoprms)
+       Precompute apparent to observed parameters
+
+aoppat --  call subroutine slaopt (date, aoprms)
+       Update siderial time in apparent to observed parameters
+
+ aopqk --  call subroutine slaopq (rap, dap, aoprms, aob, zob, hob, dob, rob)
+       Apparent to observed using precomputed parameters
+
+   oap --  call subroutine sloap (type, ob1, ob2, date, dut, elongm, phim,
+	   xp, yp, tdk, pmb, rh, wl, tlr, rap, dap)
+       Observed to apparent
+
+ oapqk --  call subroutine sloapq (type, ob1, ob2, aoprms, rap, dap)
+       Observed to apparent using precomputed parameters
+
+ polmo -- call subroutine slplmo (elongim, phim, xp, yp, elong, phi, daz)
+       Correct site longitude and latitude for polar motion
+.fi
+.ih
+AZIMUTH AND ELEVATION
+.nf
+ altaz --  call subroutine slalaz (ha, dec, phi,
+       Positions, velocities, etc. for an altazimuth mount
+
+   e2h --  call subroutine sle2h (ha, dec, phi, az, el)
+  de2h --  call subroutine slde2h (ha, dec, phi, az, el)
+       Hour angle and declination to azimuth and elevation
+
+   h2e --  call subroutine slh2e (az, el, phi, ha, dec)
+  dh2e --  call subroutine sldh2e (az, el, phi, ha, dec)
+       Azimuth and elevation to hour angle and declination
+
+ pda2h --  call subroutine slpdah (p, d, a, h1, j1, h2, j2)
+       Hour angle corresponding to a given azimuth
+
+ pdq2h --  call subroutine slpdqh (p, d, q, h1, j1, h2, j2)
+       Hour angle corresponding to a given parallactic angle
+
+    pa --  d = slpa (ha, dec, phi)
+       Hour angle and declination to parallactic angle
+
+    zd --  d = slzd (ha, dec, phi)
+       Hour angle and declination to zenith distance
+.fi
+.ih
+REFRACTION AND AIR MASS
+.nf
+ refro --  call subroutine slrfro (zobs, hm, tdk, pmb, rh, wl, phi, tlr,
+	   eps, ref)
+       Change in zenith distance due to refraction
+
+ refco --  call subroutine slrfco (hm, tdk, pmb, rh, wl, phi, tlr, eps,
+	   refa, refb)
+       Constants for simple refraction model
+
+refcoq --  call subroutine slrfcq (tdk, pmb, rl, wl, refa, refb)
+       Constants for simple refraction model (quick version)
+
+atmdsp --  call subroutine slatmd (tdk, pmb, rh, wl1, a1, b1, wl2, a2, b2)
+       Adjust refraction constants for color
+
+  refz --  call subroutine slrefz (zu, refa, refb, zr)
+       Unrefracted to refracted zenith distance, simple model
+
+  refv --  call subroutine slrefv (vu, refa, refb, vr)
+       Unrefracted to refracted azimuth and elevation, simple model
+
+airmas --  d = slarms (zd)
+       Air mass
+.fi
+.ih
+ECLIPTIC COORDINATES
+.nf
+ ecmat --  call subroutine slecma (date, rmat)
+       Equatorial to ecliptic rotation matrix
+
+ eqecl --  call subroutine sleqec (dr, dd, date, dl, db)
+       J2000.0 FK5 to ecliptic coordinates
+
+ ecleq --  call subroutine sleceq (dl, db, date, dr, dd)
+       Ecliptic to J2000.0 FK5 coordinates
+.fi
+.ih
+GALACTIC COORDINATES
+.nf
+  eg50 --  call subroutine sleg50 (dr, dd, dl, db)
+       B1950.0 FK4 to galactic coordinates
+
+  ge50 --  call subroutine slge50 (dl, db, dr, dd)
+       Galactic to B1950.0 FK4 coordinates
+     
+ eqgal --  call subroutine sleqga (dr, dd, dl, db)
+       J2000.0 FK5 to galactic coordinates
+	   
+ galeq --  call subroutine slgaeq (dl, db, dr, dd)
+       Galactic to J2000.0 FK5 coordinates
+.fi
+.ih
+SUPERGALACTIC COORDINATES
+.nf
+galsup --  call subroutine slgasu (dl, db, dsl, dsb)
+       Galactic to supergalactic coordinates
+
+supgal --  call subroutine slsuga (dsl, dsb, dl, db)
+       Supergalactic to galactic coordinates
+.fi
+.ih
+EPHEMERIDES
+.nf
+ dmoon --  call subroutine sldmon (date, pv)
+       Approximate geocentric position and velocity of moon
+
+ earth --  call subroutine slerth (iy, id, fd, pv)
+       Approximate heliocentric position and velocity of earth
+
+   evp --  call subroutine slevp (date, deqx, dvb, dpb, dvh, dph)
+       Barycentric and heliocentric velocity and position of earth
+
+  moon --  call subroutine slmoon (iy, id, fd, pv)
+       Approximate geocentric position and velocity of moon
+
+planet --  call subroutine slplnt (date, np, pv, jstat)
+       Approximate heliocentric position and velocity of planet
+
+rdplan --  call subroutine slrdpl (date, np, elong, phi, ra, dec, diam)
+       Approximate topocentric apparent place of a planet
+
+planel --  call subroutine slplnl (date, jform, epoch, orbinc, anode,
+           perih, aorg, e, aorl, dm, pv, jstat)
+       Approximate heliocentric position and velocity of planet
+
+plante --  call subroutine slplte (date, elong, phi, jform, epoch, orbinc,
+	   anode, perih, aorq, e, aorl, dm, ra, dec, r, jstat)
+       Approximate topocentric apparent place of a planet
+
+ pv2el -- call subroutine slpvel (pv, date, pmass, jformr, jform, epoch,
+	  orbinc, anode, perih, aorg, e, aorl, dm, jstat) 
+       Convert J2000 position and velocity to equivalent osculating elements
+
+ el2ue -- call subroutine slelue (date, jform, epoch, orbinc, anode, perih,
+	  aorq, e, aorl, dm, u, jstat)
+       Convert conventional osculating orbital elements into universal
+       form.
+
+ ue2el -- call subroutine slueel (u, jformr, jform, epoch, orbinc, anode,
+	  perih, aorq, e, aorl, dm, jstat)
+       Convert universal elements into conventional heliocentric osculating
+       form.
+
+ pv2ue -- call subroutine slpvue (pv, date, pmass, u, jstat)
+       Construct a universal element set based on instantaneous position
+       and velocity.
+
+ ue2pv -- call subroutine sluepv (date, u, pv, jstat)
+       Compute heliocentric position and velocity of a planet, asteroid, or
+       comet, starting from orbital elements in the "universal variables"
+       form.
+
+pertel -- call subroutine slprtl (jform, date0, date1, epoch0, epoch1,
+	  orbi0, anode0, perih0, aorq0, e0, am0, epoch1, orbi1, anode1,
+	  perih1, aorq1m e1, am1, jstat)
+       Update the osculating elements of a comet or asteroid by applying
+       planetary perturbations.
+
+pertue -- call subroutine slprue (date, u, jstat)
+       Update universal elements of a comet or asteroid by applying planetary
+       perturbations.
+.fi
+.ih
+RADIAL VELOCITIES
+rverot --  s = slrver (phi, ra, da, st)
+       Velocity component due to rotation of the earth
+
+  ecor --  call subroutine slecor (rm, dm, iy, id, fd, rv, tl)
+       Components of velocity and light time due to earth orbital motion
+
+rvlsrd --  r = slrvld (r2000, d2000)
+       Velocity component due to solar motion wrt dynamical LSR
+
+rvlsrk --  r = slrvlk (r2000, d2000)
+       Velocity component due to solar motion wrt kinematical LSR
+
+rvgalc --  r = slrvga (r2000, d2000)
+       Velocity component due to rotation of the Galaxy
+
+  rvlg --  r = slrvlg (r2000, d2000)
+       Velocity component due to rotation and translation of the Galaxy,
+           relative to the mean motion of the local group
+.fi
+.ih
+ASTROMETRY
+.nf
+  s2tp --  call subroutine sls2tp (ra, dec, raz, decz, xi, eta, j)
+ ds2tp --  call subroutine sldstp (ra, dec, raz, decz, xi, eta, j)
+       Transform spherical into tangent plane coordinates
+
+  v2tp --  call subroutine slv2tp (v, v0, xi, eta, j)
+ dv2tp --  call subroutine sldvtp (v, v0, xi, eta, j)
+       Transform [x,y,z] into tangent plane coordinates
+
+  tp2s --  call subroutine sltp2s (xi, eta, raz, decz, ra, dec)
+ dtp2s --  call subroutine sldtps (xi, eta, raz, decz, ra, dec)
+       Transform tangent plane into spherical coordinates
+
+  tp2v --  call subroutine sltp2v (xi, eta, v0, v)
+ dtp2v --  call subroutine sldtpv (xi, eta, v0, v)
+       Transform tangent plane coordinates into [x,y,z]
+
+ tps2c --  call subroutine sltpsc (xi, eta, ra, dec, raz1, decz1,
+	   raz2, decz2, n)
+dtps2c --  call subroutine sldpsc (xi, eta, ra, dec, raz1, decz1,
+	   raz2, decz2, n)
+       Get plate center from tangent plane and spherical coordinates
+
+ tpv2c --  call subroutine sltpvc (xi, eta, v, v01, v02, n)
+dtpv2c --  call subroutine sldpvc (xi, eta, v, v01, v02, n)
+       Get plate center from [x,y,x] and tangent plane coordinates
+
+   pcd --  call subroutine slpcd (disco, x, y)
+       Apply pincushion/barrel distortion
+
+ unpcd --  call subroutine slupcd (disco, x, y)
+       Remove pincushion/barrel distortion
+
+ fitxy --  call subroutine slftxy (itype, np, xye, xym, coeffs, j)
+       Fit a linear model to relate two sets of [x,y] coordinates
+
+   pxy --  call subroutine slpxy (np, xye, xym, coeffs, xyp,
+           xrms, yrms, rrms)
+       Compute predicted coordinates and residuals
+
+  invf --  call subroutine slinvf (fwds, bkwds, j)
+       Invert a linear model
+
+ xy2xy --  call subroutine slxyxy (x1, y1, coeffs, x2, y2)
+       Transform one set of [x,y] coordinates
+
+ dcmpf --  call subroutine sldcmf (coeffs, xz, yz, xs, ys, perp, orient)
+       Decompose a linear fit into geometric parameters
+.fi
+.ih
+NUMERICAL METHODS
+.nf
+  smat --  call subroutine slsmat (n, a, y, d, jf, iw)
+  dmat --  call subroutine sldmat (n, a, y, d, jf, iw)
+       Matrix inversion and solution of simultaneous equations
+
+   svd --  call subroutine slsvd (m, n, mp, np, a, w, v, work, jstat)
+       Singular value decomposition of a matrix
+
+svdsol --  call subroutine slsvds (m, n, mp, np, b, u, w, v, work, x)
+       Solution from a given vector plus SVD
+
+svdcov --  call subroutine slsvdc (n, np, nc, w, v, work, cvm)
+       Covariance matrix from SVD
+.fi
+.endhelp
diff --git a/math/slalib/doc/slalib.hlp.sav b/math/slalib/doc/slalib.hlp.sav
new file mode 100644
index 00000000..8da465cf
--- /dev/null
+++ b/math/slalib/doc/slalib.hlp.sav
@@ -0,0 +1,591 @@
+.help slalib Nov95 "Immatch Package"
+.ih
+NAME
+slalib -- Starlink library of positional astronomy routines
+
+.ih
+DESCRIPTION
+SLALIB is a library of Fortran 77 routines intended to make accurate
+and reliable positional-astronomy applications easier to write. Most
+SLALIB library routines are concerned with astronomical position and time,
+but a number have wider trigonometrical, numerical or general applications.
+SLALIB contains routines covering the following topics: 1) string
+decoding and sexagesimal conversions, 2) angles, vectors and rotation
+matrices, 3) calendars and timescales, 4) precession and nutation, 5)
+proper motion, 6) FK4/5 and elliptic aberration, 7) geocentric coordinates,
+8) apparent and observed place, 9) azimuth and elevation, 10) refraction
+and air mass, 11) ecliptic, galactic, and supergalactic coordinates,
+12) ephemerides, 13) astrometry, and 14) numerical methods.
+
+The labels and calling sequences of the SLALIB are listed below grouped
+by function. To get more detailed help on any individual routine type
+the help command followed by the label, e.g the command "help flotin"
+will give detailed help on the subroutine slrfli.
+
+.ih
+STRING DECODING
+.nf
+ intin --  call subroutine slinti (string, nstrt, ireslt, jflag)
+       Convert free-format string into integer
+
+flotin --  call subroutine slrfli (string, nstrt, reslt, jflag)
+dfltin --  call subroutine sldfli (string, nstrt, dreslt, jflag)
+       Convert free-format string into floating point number
+
+  afin --  call subroutine slafin (string, iptr, a, j)
+ dafin --  call subroutine sldafn (string, iptr, a, j)
+       Convert free-format string from deg, armin, arcsec to radians
+.fi
+.ih
+SEXAGESIMAL CONVERSIONS
+.nf
+ ctf2d --  call subroutine slctfd (ihour, imin, sec, days, j)
+ dtf2d --  call subroutine sldtfd (ihour, imin, sec, days, j)
+       Hours, minutes, seconds to days
+
+ cd2tf --  call subroutine slcdtf (ndp, days, sign, ihmsf)
+ dd2tf --  call subroutine slddtf (ndp, days, sign, ihmsf)
+       Days to hours, minutes, and seconds
+
+ ctf2r --  call subroutine slctfr (ihour, imin, sec, rad, j)
+ dtf2r --  call subroutine sldtfr (ihour, imin, sec, rad, j)
+       Hours, minutes, seconds to radians
+
+ cr2tf --  call subroutine slcrtf (ndp, angle, sign, ihmsf)
+ dr2tf --  call subroutine sldrtf (ndp, angle, sign, ihmsf)
+       Radians to hours, minutes, seconds
+
+ caf2r --  call subroutine slcafr (ideg, iamin, asec, rad, j)
+ daf2r --  call subroutine sldafr (ideg, iamin, asec, rad, j)
+       Degrees, arcminutes, arcseconds to radians
+
+ cr2af --  call subroutine slcraf (ndp, angle, sign, idmsf)
+ dr2af --  call subroutine sldraf (ndp, angle, sign, idmsf)
+       Radians to degrees, arcminutes, arcseconds
+.fi
+.ih
+ANGLES, VECTORS AND ROTATION MATRICES
+.nf
+ range --  r = slra1p (angle)
+drange --  d = slda1p (angle)
+       Normalize angle into range [-pi,pi]
+
+ranorm --  r = slra2p (angle)
+dranrm --  d = slda2p (angle)
+       Normalize angle into range [0,2pi]
+
+  cs2c --  call subroutine slcs2c (a, b, v)
+ dcs2c --  call subroutine slds2c (a, b, v)
+       Spherical coordinates to [x,y,z]
+
+  cc2s --  call subroutine slcc2s (v, a, b)
+ dcc2s --  call subroutine sldc2s (v, a, b)
+       [x,y,z] to spherical coordinates
+
+   vdv --  r = slvdv (va, vb)
+  dvdv --  d = sldvdv (va, vb)
+       Scalar product of two 3-vectors
+
+   vxv --  call subroutine slvxv (va, vb, vc)
+  dvxv --  call subroutine sldvxv (va, vb, vc)
+       Vector product of two 3-vectors
+
+    vn --  call subroutine slvn (v, uv, vm)
+   dvn --  call subroutine sldvn (v, uv, vm)
+       Normalize a 3-vector also giving the modulus
+
+   sep --  s = slsep (a1, b1, a2, b2)
+  dsep --  d = sldsep (a1, b1, a2, b2)
+       Angle between two points on a sphere
+
+  bear --  s = slbear (a1, b1, a2, b2)
+ dbear --  d = sldber (a1, b1, a2, b2)
+   pav --  s = slpav (v1, v2)
+  dpav --  d = sldpav (v1, v2)
+       Direction of one point on a sphere seen from another
+
+ euler --  call subroutine sleulr (order, phi, theta, psi, rmat)
+deuler --  call subroutine sldeul (order, phi, theta, psi, rmat)
+       Form form rotation matrix from three Euler angles
+
+
+  av2m --  call subroutine slav2m (axvec, rmat)
+ dav2m --  call subroutine sldavm (axvec, rmat)
+       Form rotation matrix from axial vector
+
+  m2av --  call subroutine slm2av (rmat, axvec)
+ dm2av --  call subroutine sldmav (rmat, axvec)
+       Determine axial vector from rotation matrix
+
+  dmxv --  call subroutine sldmxv (dm, va, vb)
+   mxv --  call subroutine slmxv (rm, va, vb)
+       Rotate vector forwards
+
+  imxv --  call subroutine slimxv (rm, va, vb)
+ dimxv --  call subroutine sldimv (dm, va, vb)
+       Rotate vector backwards
+
+  dmxm --  call subroutine sldmxm (a, b, c)
+   mxm --  call subroutine slmxm (a, b, c)
+       Product of two 3X3 matrices
+
+ cs2c6 --  call subroutine sls2c6 (a, b, r, ad, bd, rd, v)
+ ds2c6 --  call subroutine sldsc6 (a, b, r, ad, bd, rd, v)
+       Conversion of position/velocity from spherical to Cartesian
+	   coordinates
+
+ cc62s --  call subroutine slc62s (v, a, b, r, ad, bd, rd)
+ dc62s --  call subroutine sldc6s (v, a, b, r, ad, bd, rd)
+       Conversion of position/velocity from Cartesian to spherical
+	   coordinates
+.fi
+.ih
+CALENDARS
+.nf
+  cldj --  call subroutine slcadj (iy, im, id, djm, j)
+       Gregorian calendar to Modified Julian Date
+
+ caldj --  call subroutine slcadj (iy, im, id, djm, j)
+       Gregorian calendar to Modified Julian Date, permitting century by
+	   default
+
+ djcal --  call subroutine sldjca (ndp, djm, iymdf, j)
+       Modified Julian Date to Gregorian calendar, in a from convenient
+	   for formatted output
+
+  djcl --  call subroutine sldjcl (djm, iy, im, id, fd, j)
+       Modified Julian Date to Gregorian Year, Month, Day, Fraction
+
+ calyd --  call subroutine slcayd (iy, im, id, ny, nd, j)
+       Calendar to year and day in year, permitting century default
+
+  clyd --  call subroutine slclyd (iy, im, id, ny, nd, jstat)
+       Calendar to year and day in year
+
+   epb --  d = slepb (date)
+       Modified Julian Date to Besselian Epoch
+
+ epb2d --  d = sleb2d (epb)
+       Besselian epoch to Modified Julian Date
+
+   epj --  d = slepj (date)
+       Modified Julian Date to Julian Epoch
+
+ epj2d --  d = slej2d (epj)
+       Julian epoch to Modified Julian Date
+.fi
+.fi
+.ih
+TIMESCALES
+.nf
+  gmst --  d = slgmst (ut1)
+       Conversion from Universal Time to siderial time
+
+ gmsta --  d = slgmsa (date, ut)
+       Conversion from Universal Time to siderial time, rounding errors
+	   minimized
+
+ eqeqx --  d = sleqex (date)
+       Equation of the equinoxes
+
+   dat --  d = sldat (utc)
+       Offset of Atomic Time from Coordinated Universal Time:
+	   TAI - UTC
+
+    dt --  d = sldt (epoch)
+       Approximate offset between dynamical time and universal time
+
+   dtt --  d = sldtt (utc)
+       Offset of Terrestrial Time from Coordinated Universal Time:
+	   TT - UTC
+
+   rcc --  d = slrcc (tdb, ut1, wl, u, v)
+       Relativistic clock correction: TDB - TT
+.fi
+.ih
+PRECESSION AND NUTATION
+.nf
+   nut --  call subroutine slnut (date, rmatn)
+       Nutation matrix
+
+  nutc --  call subroutine slnutc (date, dpsi, deps, eps0)
+       Longitude and obliquity components of nutation, mean obliquity
+
+  prec --  call subroutine slprec (ep0, ep1, rmatp)
+       Precession matrix (IAU)
+
+ precl --  call subroutine slprel (ep0, ep1, rmatp)
+       Precession matrix (suitable for long periods)
+
+prenut --  call subroutine slprnu (epoch, date, rmatpn)
+       Combined precession/nutation matrix
+
+ prebn --  call subroutine slprbn (bep0, bep1, rmatp)
+       Precession matrix (old system)
+
+preces --  call subroutine slprce (system, ep0, ep1, ra, dc)
+       Precession in either the old or new system, character string
+           ep0 and ep1
+
+precss --  call subroutine slprcs (system, ep0, ep1, ra, dc)
+       Precession in either the old or new system, integer ep0 and ep1
+.fi
+.fi
+.ih
+PROPER MOTION
+.nf
+    pm --  call subroutine slpm (r0, d0, pr, pd, px, rv, ep0, ep1, r1, d1)
+       Adjust for proper motion
+.fi
+.ih
+FK4/5/ICRS CONVERSIONS
+.nf
+ fk425 --  call subroutine slfk45 (r1950, d1950, dr1950, dd1950,
+           p1950, v1950, r2000, d2000, dr2000, dd2000, p2000, v2000)
+       Convert B1950.0 FK4 star data to J2000.0 FK5
+
+ fk45z --  call subroutine slf45z (r1950, d1950, bepoch, r2000, d2000)
+       Convert B1950.0 FK4 position to J2000.0 FK5 assuming zero proper
+	   motion in an inertial frame and no parallax
+
+ fk524 --  call subroutine slfk54 (r2000, d2000, dr2000, dd2000,
+           p2000, v2000, r1950, d1950, dr1950, dd1950, p1950, v1950)
+       Convert J2000.0 FK5 star data to B1950.0 FK4
+
+ fk54z --  call subroutine slf54z (r2000, d2000, bepoch, r1950, d1950,
+	   dr1950, dd1950)
+       Convert J2000.0 FK5 star data to B1950.0 FK4 assuming zero proper
+	   motion in an inertial frame and no parallax
+
+ fk52h --  call subroutine slfk5h (r5, d5, dr5, dd5, rh, dh, drh, ddh)
+       Convert J2000.0 FK5 star data to ICRS J2000.0 data
+
+ fk5hz --  call subroutine slf5hz (r5, d5, epoch, rh, dh)
+       Convert J2000.0 FK5 star data to ICRS J2000.0 data  assuming
+       no Hipparcos proper motion.
+
+ h2fk5 -- call subroutine slhfk5 (rh, dh, drh, ddh, r5, d5, dr5, dd5)
+       Convert ICRS J2000.0 data to J2000.0 Fk5 star data.
+
+ hfk5z -- call subroutine slhf5z (rh, dh, epoch, r5, d5)
+       Convert ICRS J2000.0 data to J2000.0 Fk5 star data assuming no
+       Hipparchos proper motion.
+
+ dbjin --  call subroutine sldbji (string, nstrt, dreslt, j1, j2)
+       Like dfltin but with extensions to accept leading 'B' and 'J'
+
+   kbj --  call subroutine slkbj (jb, e, k, j)
+       Select epoch prefix 'B' or 'J'
+
+  epco --  d = slepco (k0, k, e)
+       Convert an epoch into the appropriate form 'B' or 'J'
+.fi
+.ih
+ELLIPTIC ABERRATIONS
+.nf
+ etrms --  call subroutine sletrm (ep, ev)
+       E-terms
+
+ subet --  call subroutine slsuet (rc, dc, eq, rm, dm)
+       Remove the E-terms
+
+ addet --  call subroutine sladet (rm, dm, eq, rc, dc)
+       Add the E-terms
+.fi
+.ih
+GEOCENTRIC COORDINATES
+.nf
+   obs --  call subroutine slobs (n, c, name, w, p, h)
+       Interrogate list of observatory parameters
+
+  geoc --  call subroutine slgeoc (p, h, r, z)
+       Convert geodetic position to geocentric
+
+ pvobs --  call subroutine slpvob (p, h, stl, pv)
+       Position and velocity of observatory
+.fi
+.ih
+APPARENT AND OBSERVED PLACE
+.nf
+   map --  call subroutine slmap (rm, dm, pr, pd, px, rv, eq, date, ra, da)
+       Mean place to geocentric apparent place
+
+ mappa --  call subroutine slmapa (eq, date, amprms)
+       Precompute mean to apparent parameters
+
+ mapqk --  call subroutine slmapq (rm, dm, pr, pd, px, rv, amprms, ra, da)
+       Mean to apparent place using precomputed parameters
+
+mapqkz --  call subroutine slmapz (rm, dm, amprms, ra, da)
+       Mean to apparent place using precomputed parameters, for zero
+	   proper motion, parallax, and radial velocity
+
+   amp --  call subroutine slamp (ra, da, date, eq, rm, dm)
+       Geocentric apparent place to mean place
+
+ ampqk --  call subroutine slampq (ra, da, amprms, rm, dm)
+       Apparent to mean place using precomputed parameters
+
+   aop --  call subroutine slaop (rap, dap, date, dut, elongm, phim, hm,
+	   xp, yp, tdk, pmb, rh, wl, tlr, aob, zob, hob, dob, rob)
+       Apparent place to observed place
+
+ aoppa --  call subroutine slaopa (date, dut, elongm, phim, hm, xy, yp,
+	   tdk, pmb, rh, wl, tlr, aoprms)
+       Precompute apparent to observed parameters
+
+aoppat --  call subroutine slaopt (date, aoprms)
+       Update siderial time in apparent to observed parameters
+
+ aopqk --  call subroutine slaopq (rap, dap, aoprms, aob, zob, hob, dob, rob)
+       Apparent to observed using precomputed parameters
+
+   oap --  call subroutine sloap (type, ob1, ob2, date, dut, elongm, phim,
+	   xp, yp, tdk, pmb, rh, wl, tlr, rap, dap)
+       Observed to apparent
+
+ oapqk --  call subroutine sloapq (type, ob1, ob2, aoprms, rap, dap)
+       Observed to apparent using precomputed parameters
+
+ polmo -- call subroutine slplmo (elongim, phim, xp, yp, elong, phi, daz)
+       Correct site longitude and latitude for polar motion
+.fi
+.ih
+AZIMUTH AND ELEVATION
+.nf
+ altaz --  call subroutine slalaz (ha, dec, phi,
+       Positions, velocities, etc. for an altazimuth mount
+
+   e2h --  call subroutine sle2h (ha, dec, phi, az, el)
+  de2h --  call subroutine slde2h (ha, dec, phi, az, el)
+       Hour angle and declination to azimuth and elevation
+
+   h2e --  call subroutine slh2e (az, el, phi, ha, dec)
+  dh2e --  call subroutine sldh2e (az, el, phi, ha, dec)
+       Azimuth and elevation to hour angle and declination
+
+ pda2h --  call subroutine slpdah (p, d, a, h1, j1, h2, j2)
+       Hour angle corresponding to a given azimuth
+
+ pdq2h --  call subroutine slpdqh (p, d, q, h1, j1, h2, j2)
+       Hour angle corresponding to a given parallactic angle
+
+    pa --  d = slpa (ha, dec, phi)
+       Hour angle and declination to parallactic angle
+
+    zd --  d = slzd (ha, dec, phi)
+       Hour angle and declination to zenith distance
+.fi
+.ih
+REFRACTION AND AIR MASS
+.nf
+ refro --  call subroutine slrfro (zobs, hm, tdk, pmb, rh, wl, phi, tlr,
+	   eps, ref)
+       Change in zenith distance due to refraction
+
+ refco --  call subroutine slrfco (hm, tdk, pmb, rh, wl, phi, tlr, eps,
+	   refa, refb)
+       Constants for simple refraction model
+
+refcoq --  call subroutine slrfcq (tdk, pmb, rl, wl, refa, refb)
+       Constants for simple refraction model (quick version)
+
+atmdsp --  call subroutine slatmd (tdk, pmb, rh, wl1, a1, b1, wl2, a2, b2)
+       Adjust refraction constants for color
+
+  refz --  call subroutine slrefz (zu, refa, refb, zr)
+       Unrefracted to refracted zenith distance, simple model
+
+  refv --  call subroutine slrefv (vu, refa, refb, vr)
+       Unrefracted to refracted azimuth and elevation, simple model
+
+airmas --  d = slarms (zd)
+       Air mass
+.fi
+.ih
+ECLIPTIC COORDINATES
+.nf
+ ecmat --  call subroutine slecma (date, rmat)
+       Equatorial to ecliptic rotation matrix
+
+ eqecl --  call subroutine sleqec (dr, dd, date, dl, db)
+       J2000.0 FK5 to ecliptic coordinates
+
+ ecleq --  call subroutine sleceq (dl, db, date, dr, dd)
+       Ecliptic to J2000.0 FK5 coordinates
+.fi
+.ih
+GALACTIC COORDINATES
+.nf
+  eg50 --  call subroutine sleg50 (dr, dd, dl, db)
+       B1950.0 FK4 to galactic coordinates
+
+  ge50 --  call subroutine slge50 (dl, db, dr, dd)
+       Galactic to B1950.0 FK4 coordinates
+     
+ eqgal --  call subroutine sleqga (dr, dd, dl, db)
+       J2000.0 FK5 to galactic coordinates
+	   
+ galeq --  call subroutine slgaeq (dl, db, dr, dd)
+       Galactic to J2000.0 FK5 coordinates
+.fi
+.ih
+SUPERGALACTIC COORDINATES
+.nf
+galsup --  call subroutine slgasu (dl, db, dsl, dsb)
+       Galactic to supergalactic coordinates
+
+supgal --  call subroutine slsuga (dsl, dsb, dl, db)
+       Supergalactic to galactic coordinates
+.fi
+.ih
+EPHEMERIDES
+.nf
+ dmoon --  call subroutine sldmon (date, pv)
+       Approximate geocentric position and velocity of moon
+
+ earth --  call subroutine slerth (iy, id, fd, pv)
+       Approximate heliocentric position and velocity of earth
+
+   evp --  call subroutine slevp (date, deqx, dvb, dpb, dvh, dph)
+       Barycentric and heliocentric velocity and position of earth
+
+  moon --  call subroutine slmoon (iy, id, fd, pv)
+       Approximate geocentric position and velocity of moon
+
+planet --  call subroutine slplnt (date, np, pv, jstat)
+       Approximate heliocentric position and velocity of planet
+
+rdplan --  call subroutine slrdpl (date, np, elong, phi, ra, dec, diam)
+       Approximate topocentric apparent place of a planet
+
+planel --  call subroutine slplnl (date, jform, epoch, orbinc, anode,
+           perih, aorg, e, aorl, dm, pv, jstat)
+       Approximate heliocentric position and velocity of planet
+
+plante --  call subroutine slplte (date, elong, phi, jform, epoch, orbinc,
+	   anode, perih, aorq, e, aorl, dm, ra, dec, r, jstat)
+       Approximate topocentric apparent place of a planet
+
+ pv2el -- call subroutine slpvel (pv, date, pmass, jformr, jform, epoch,
+	  orbinc, anode, perih, aorg, e, aorl, dm, jstat) 
+       Convert J2000 position and velocity to equivalent osculating elements
+
+ el2ue -- call subroutine slelue (date, jform, epoch, orbinc, anode, perih,
+	  aorq, e, aorl, dm, u, jstat)
+       Convert conventional osculating orbital elements into universal
+       form.
+
+ ue2el -- call subroutine slueel (u, jformr, jform, epoch, orbinc, anode,
+	  perih, aorq, e, aorl, dm, jstat)
+       Convert universal elements into conventional heliocentric osculating
+       form.
+
+ pv2ue -- call subroutine slpvue (pv, date, pmass, u, jstat)
+       Construct a universal element set based on instantaneous position
+       and velocity.
+
+ ue2pv -- call subroutine sluepv (date, u, pv, jstat)
+       Compute heliocentric position and velocity of a planet, asteroid, or
+       comet, starting from orbital elements in the "universal variables"
+       form.
+
+pertel -- call subroutine slprtl (jform, date0, date1, epoch0, epoch1,
+	  orbi0, anode0, perih0, aorq0, e0, am0, epoch1, orbi1, anode1,
+	  perih1, aorq1m e1, am1, jstat)
+       Update the osculating elements of a comet or asteroid by applying
+       planetary perturbations.
+
+pertue -- call subroutine slprue (date, u, jstat)
+       Update universal elements of a comet or asteroid by applying planetary
+       perturbations.
+.fi
+.ih
+RADIAL VELOCITIES
+rverot --  s = slrver (phi, ra, da, st)
+       Velocity component due to rotation of the earth
+
+  ecor --  call subroutine slecor (rm, dm, iy, id, fd, rv, tl)
+       Components of velocity and light time due to earth orbital motion
+
+rvlsrd --  r = slrvld (r2000, d2000)
+       Velocity component due to solar motion wrt dynamical LSR
+
+rvlsrk --  r = slrvlk (r2000, d2000)
+       Velocity component due to solar motion wrt kinematical LSR
+
+rvgalc --  r = slrvga (r2000, d2000)
+       Velocity component due to rotation of the Galaxy
+
+  rvlg --  r = slrvlg (r2000, d2000)
+       Velocity component due to rotation and translation of the Galaxy,
+           relative to the mean motion of the local group
+.fi
+.ih
+ASTROMETRY
+.nf
+  s2tp --  call subroutine sls2tp (ra, dec, raz, decz, xi, eta, j)
+ ds2tp --  call subroutine sldstp (ra, dec, raz, decz, xi, eta, j)
+       Transform spherical into tangent plane coordinates
+
+  v2tp --  call subroutine slv2tp (v, v0, xi, eta, j)
+ dv2tp --  call subroutine sldvtp (v, v0, xi, eta, j)
+       Transform [x,y,z] into tangent plane coordinates
+
+  tp2s --  call subroutine sltp2s (xi, eta, raz, decz, ra, dec)
+ dtp2s --  call subroutine sldtps (xi, eta, raz, decz, ra, dec)
+       Transform tangent plane into spherical coordinates
+
+  tp2v --  call subroutine sltp2v (xi, eta, v0, v)
+ dtp2v --  call subroutine sldtpv (xi, eta, v0, v)
+       Transform tangent plane coordinates into [x,y,z]
+
+ tps2c --  call subroutine sltpsc (xi, eta, ra, dec, raz1, decz1,
+	   raz2, decz2, n)
+dtps2c --  call subroutine sldpsc (xi, eta, ra, dec, raz1, decz1,
+	   raz2, decz2, n)
+       Get plate center from tangent plane and spherical coordinates
+
+ tpv2c --  call subroutine sltpvc (xi, eta, v, v01, v02, n)
+dtpv2c --  call subroutine sldpvc (xi, eta, v, v01, v02, n)
+       Get plate center from [x,y,x] and tangent plane coordinates
+
+   pcd --  call subroutine slpcd (disco, x, y)
+       Apply pincushion/barrel distortion
+
+ unpcd --  call subroutine slupcd (disco, x, y)
+       Remove pincushion/barrel distortion
+
+ fitxy --  call subroutine slftxy (itype, np, xye, xym, coeffs, j)
+       Fit a linear model to relate two sets of [x,y] coordinates
+
+   pxy --  call subroutine slpxy (np, xye, xym, coeffs, xyp,
+           xrms, yrms, rrms)
+       Compute predicted coordinates and residuals
+
+  invf --  call subroutine slinvf (fwds, bkwds, j)
+       Invert a linear model
+
+ xy2xy --  call subroutine slxyxy (x1, y1, coeffs, x2, y2)
+       Transform one set of [x,y] coordinates
+
+ dcmpf --  call subroutine sldcmf (coeffs, xz, yz, xs, ys, perp, orient)
+       Decompose a linear fit into geometric parameters
+.fi
+.ih
+NUMERICAL METHODS
+.nf
+  smat --  call subroutine slsmat (n, a, y, d, jf, iw)
+  dmat --  call subroutine sldmat (n, a, y, d, jf, iw)
+       Matrix inversion and solution of simultaneous equations
+
+   svd --  call subroutine slsvd (m, n, mp, np, a, w, v, work, jstat)
+       Singular value decomposition of a matrix
+
+svdsol --  call subroutine slsvds (m, n, mp, np, b, u, w, v, work, x)
+       Solution from a given vector plus SVD
+
+svdcov --  call subroutine slsvdc (n, np, nc, w, v, work, cvm)
+       Covariance matrix from SVD
+.fi
+.endhelp
diff --git a/math/slalib/doc/slalib.men b/math/slalib/doc/slalib.men
new file mode 100644
index 00000000..2288c0aa
--- /dev/null
+++ b/math/slalib/doc/slalib.men
@@ -0,0 +1,179 @@
+    addet - add the E-terms to a pre IAU 1976 mean place
+     afin - convert a sexagesimal character string to radians (s.p.)
+   airmas - compute the airmass at a given zenith distance 
+    altaz - compute altazimuth positions, velocities, accelerations
+      amp - convert a geocentric apparent to post IAU 1976 mean place
+    ampqk - convert a geocentric apparent to post IAU 1976 mean place 
+      aop - convert an apparent to observed place 
+    aoppa - pre-compute the set of apparent to observed place parameters 
+   aoppat - recompute the apparent to observed place sidereal time parameter 
+    aopqk - convert an apparent to observed place
+   atmdsp - apply atmospheric dispersion terms to refraction coefficients 
+     av2m - compute a rotation matrix from an axial vector (s.p.)
+     bear - compute the bearing of a point on a sphere w.r.t. another
+    caf2r - convert degrees, arcminutes, and arcseconds to radians
+    caldj - convert a Gregorian calendar date to a modified Julian date
+    calyd - convert a Gregorian calendar date to a Julian calendar year, day 
+     cc2s - convert Cartesian to spherical coordinates (s.p.)
+    cc62s - convert a 6-vector from Cartesian to spherical coordinates 
+    cd2tf - convert an interval in days to hours, minutes, and seconds 
+     cldj - convert a Gregorian calendar date to a modified Julian date
+     clyd - convert a Gregorian calendar date a Julian calendar year, day
+    cr2af - convert radians to degrees, arcminutes, and arcseconds
+    cr2tf - convert radians to hours, minutes, and seconds 
+     cs2c - convert spherical to Cartesian coordinates (s.p.)
+    cs2c6 - convert spherical position/velocity  to Cartesian coordinates
+    ctf2d - convert hours, minutes, and seconds to days 
+    ctf2r - convert hours, minutes, and seconds to radians 
+    daf2r - convert degrees, arcminutes, and arcseconds to radians (d.p) 
+    dafin - convert a sexagesimal character string to radians (d.p.)
+      dat - compute difference between TAI and UTC in seconds 
+    dav2m - compute a rotation matrix from an axial vector (d.p)
+    dbear - compute the bearing of a point on a sphere w.r.t. another (d.p.)
+    dbjin - convert a character string to a Besselian/Julian epoch 
+    dc62s - convert Cartesian position/velocity to spherical coordinates (d.p.)
+    dcc2s - convert Cartesian to spherical coordinates  (d.p)
+    dcmpf - convert linear fit coefficients to geometric parameters 
+    dcs2c - convert spherical to Cartesian coordinates (d.p)
+    dd2tf - convert interval in days to hours, minutes, and seconds (d.p.)
+     de2h - convert hour angle and declination to azimuth and elevation (d.p.)
+   deuler - convert Euler angles to a rotation matrix (d.p.)
+   dfltin - convert a character string to a floating point number (d.p.)
+     dh2e - convert azimuth and elevation to hour angle and declination (d.p.)
+    dimxv - apply a 3D reverse rotation to a 3-vector (d.p.)
+    djcal - convert an MJD to a Gregorian calendar date 
+     djcl - convert an MJD to a Gregorian year, month, and day 
+    dm2av - convert a rotation matrix to an axial vector (d.p)
+     dmat - solve a set of simultaneous equations (d.p.)
+    dmoon - compute approximate geocentric position/velocity of moon (d.p.)
+     dmxm - compute the product of two 3X3 matrices (d.p.)
+     dmxv - multiple a 3-vector by a rotation matrix (d.p.)
+     dpav - compute the bearing of a point on a sphere w.r.t. another (d.p.)
+    dr2af - convert radians to degrees, arcminutes, and arcseconds (d.p)
+    dr2tf - convert radians to hours, minutes, and seconds (d.p.)
+   drange - normalize an angle to the range -pi <= angle <= pi (d.p.)
+   dranrm - normalize an angle to the range 0 <= angle <= 2pi (d.p.)
+    ds2c6 - convert spherical position/velocity to Cartesian coordinates (d.p.)
+    ds2tp - project spherical coordinates onto the tangent plane (d.p)
+     dsep - compute the angle between two points on a sphere (d.p.)
+       dt - estimate the approximate difference between ET and UT in seconds
+    dtf2d - convert hours, minutes, and seconds to days (d.p)
+    dtf2r - convert hours, minutes, and seconds to radians (d.p.)
+    dtp2s - convert tangent plane to spherical coordinates (d.p.)
+    dtp2v - convert tangent plane coordinates to direction cosines (d.p.)
+   dtps2c - compute the spherical coordinates of the tangent point (d.p.)
+   dtpv2c - compute the direction cosines of the tangent point (d.p.)
+      dtt - compute the difference between TT and UTC in seconds
+    dv2tp - convert direction cosines to tangent plane coordinates (d.p)
+     dvdv - compute the scalar product of 2 3-vectors (d.p.)
+      dvn - normalize a 3-vector and compute the modulus (d.p.)
+     dvxv - compute the vector product of 2 3-vectors (d.p.)
+      e2h - convert hour angle and declination to azimuth and elevation (d.p.)
+    earth - compute approximate heliocentric position/velocity of earth 
+    ecleq - convert from ecliptic to equatorial FK5 coordinates 
+    ecmat - compute the equatorial FK5 to ecliptic coordinates rotation matrix
+     ecor - compute rv of earth and time correction to sun in given direction
+     eg50 - convert equatorial FK4 to IAU 1958 galactic coordinates 
+    el2ue - convert osculating orbital elements into universal form
+      epb - convert an MJD to a Besselian epoch
+    epb2d - convert a Besselian epoch to an MJD
+     epco - convert a Besselian/Julian epoch to match a given epoch
+      epj - convert an MJD to a Julian epoch 
+    epj2d - convert a Julian epoch to an MJD
+    eqecl - convert equatorial FK5 to ecliptic coordinates
+    eqeqx - compute the equation of the equinoxes
+    eqgal - convert equatorial FK5 to IAU 1958 galactic coordinates
+    etrms - compute the E-terms vector 
+    euler - convert Euler angles to a rotation matrix (s.p.)
+      evp - compute the barycentric/heliocentric velocity/position of earth
+    fitxy - fit a linear model to 2 sets of [x,y] coordinates
+    fk425 - convert equatorial FK4 to FK5 coordinates
+    fk45z - convert equatorial FK4 to FK5 coordinates excluding proper motion 
+    fk524 - convert equatorial FK5 to FK4 coordinates
+    fk54z - convert equatorial FK5 to FK4 coordinates excluding proper motion
+    fk52h - convert equatorial FK5 to ICRS coordinates
+    fk5hz - Convert equatorial FK5 to ICRS coordinates (0 ICRS proper motions)
+   flotin - convert a character string to a floating point number
+    galeq - convert IAU 1958 galactic to equatorial FK5 coordinates
+   galsup - convert IAU 1958 galactic to deVaucouleurs supergalactic coordinates
+     ge50 - convert IAU 1958 galactic to equatorial FK4 coordinates 
+     geoc - convert geodetic to geocentric position 
+     gmst - convert from UT1 to GMST 
+    gmsta - convert from UT1 to GMST while minimizing rounding errors
+      h2e - convert azimuth and elevation to hour angle and declination (s.p.)
+    h2fk5 - Convert equatorial ICRS to FK5 coordinates
+    hfk5z - Convert equatorial ICRS to FK5 coordinates (0 ICRS proper motions)
+     imxv - apply a 3D reverse rotation to a 3-vector (s.p.) 
+    intin - convert a character string into an integer
+     invf - invert the linear model computed from 2 sets of [x,y] coordinates 
+      kbj - select the epoch prefix B or J
+     m2av - convert a rotation matrix to an axial vector (s.p.) 
+      map - convert a post IAU 1976 mean to geocentric apparent place  
+    mappa - precompute the set of mean to geocentric apparent place parameters 
+    mapqk - convert a post IAU 1976 mean to geocentric apparent place
+   mapqkz - convert a post IAU 1976 mean to geocentric apparent place 
+     moon - compute approximate geocentric position/velocity of moon 
+      mxm - compute the product of two 3X3 matrices (s.p.) 
+      mxv - multiply a 3-vector by a rotation matrix (s.p.) 
+      nut - compute the nutation matrix for a given date
+     nutc - compute the nutation components for a given date 
+      oap - convert from observed to apparent place 
+    oapqk - convert from observed to apparent place
+      obs - look up an entry in a list of groundbased observing stations 
+       pa - compute the parallactic angle from the hour angle and declination
+      pav - compute the bearing of a point on a sphere w.r.t. another
+      pcd - apply pincushion/barrel distortion to tangent plane coordinates 
+    pda2h - compute the hour angle corresponding to a given azimuth 
+    pdq2h - compute the hour angle corresponding to a given parallactic angle 
+   pertel - update osculating orbital elements by applying perturbations
+   pertue - update universal elements by applying perturbations
+   planel - compute the approximate heliocentric position/velocity of a planet 
+   planet - compute the approximate heliocentric position/velocity of a planet 
+   plante - compute approximate topocentric apparent position of a planet 
+       pm - apply the correction for proper motion to a star 
+    polmo - correct site longitude and latitude for polar motion
+    prebn - compute the FK4 matrix of precession between two epochs
+     prec - compute the FK5 matrix of precession between two epochs 
+   preces - precess coordinates in either the FK4 or FK5 systems 
+    precl - compute the longterm matrix of precession between two epochs 
+   precss - precess coordinates in either the FK4 or FK5 systems
+   prenut - compute the FK5 matrix of precession and nutation 
+    pv2el - convert J2000 position and velocity to osculating elements
+    pv2ue - convert instantaneous position and velocity to universal element set
+    pvobs - compute the geocentric position / velocity of an observing station 
+      pxy - apply a linear model to a set of expected and measured [x,y] 
+    range - normalize an angle to the range -pi <= angle <= pi (s.p.) 
+   ranorm - normalize an angle to the range 0 <= angle <= 2pi (s.p.) 
+      rcc - compute the difference between TDB and TT in seconds 
+   rdplan - compute approximate topocentric apparent position of a planet 
+    refco - compute the refraction coefficients 
+   refcoq - compute the refraction coefficients (fast version)
+    refro - compute the atmospheric refraction for optical and radio wavelengths
+     refv - apply the refraction correction to a Cartesian 3-vector 
+     refz - apply the refraction correction to a zenith distance 
+   rverot - compute the earth rotation velocity component in a given direction 
+   rvgalc - compute the dynamical LSR velocity component in a given direction 
+     rvlg - compute the solar velocity component in a given direction
+   rvlsrd - compute the peculiar solar velocity component in a given direction
+   rvlsrk - compute the standard solar velocity component in a given direction 
+     s2tp - project spherical coordinates onto the tangent plane (s.p.) 
+      sep - compute the angle between two points on a sphere (s.p.) 
+     smat - solve a set of simultaneous equations (s.p.) 
+    subet - remove the E-terms from a pre IAU 1976 catalog position
+   supgal - convert deVaucouleurs supergalactic to IAU 1958 galactic coordinates
+      svd - compute the SVD factorization of a matrix 
+   svdcov - compute the covariance matrix from the SVD factorization 
+   svdsol - solve a set of simultaneous equations using SVD factorization 
+     tp2s - convert tangent plane to spherical coordinates (s.p.) 
+     tp2v - convert tangent plane coordinates to direction cosines (s.p.) 
+    tps2c - compute the spherical coordinates of the tangent point (s.p.)
+    tpv2c - compute the direction cosines of the tangent point (s.p.) 
+    ue2el - convert universal elements into heliocentric osculating elements
+    ue2pv - compute heliocentric position and velocity from universal form
+    unpcd - remove pincushion/barrel distortion from distorted coordinates 
+     v2tp - convert direction cosines to tangent plane coordinates (s.p.) 
+      vdv - convert the scale production of two 3-vectors (s.p.)
+       vn - normalize a 3-vector and compute the modulus (s.p.) 
+      vxv - compute the vector product of two 3-vectors (s.p.) 
+    xy2xy - apply a computed linear model to a set of [x,y] 
+       zd -  convert hour angle and declination to zenith distance
diff --git a/math/slalib/doc/smat.hlp b/math/slalib/doc/smat.hlp
new file mode 100644
index 00000000..ad2b1f2d
--- /dev/null
+++ b/math/slalib/doc/smat.hlp
@@ -0,0 +1,60 @@
+.help smat Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slSMAT (N, A, Y, D, JF, IW)
+
+     - - - - -
+      S M A T
+     - - - - -
+
+  Matrix inversion & solution of simultaneous equations
+  (single precision)
+
+  For the set of n simultaneous equations in n unknowns:
+     A.Y = X
+
+  where:
+     A is a non-singular N x N matrix
+     Y is the vector of N unknowns
+     X is the known vector
+
+  SMATRX computes:
+     the inverse of matrix A
+     the determinant of matrix A
+     the vector of N unknowns
+
+  Arguments:
+
+     symbol  type dimension           before              after
+
+       N      int                 no. of unknowns       unchanged
+       A      real  (N,N)             matrix             inverse
+       Y      real   (N)              vector            solution
+       D      real                       -             determinant
+     * JF     int                        -           singularity flag
+       IW     int    (N)                 -              workspace
+
+  *  JF is the singularity flag.  If the matrix is non-singular,
+    JF=0 is returned.  If the matrix is singular, JF=-1 & D=0.0 are
+    returned.  In the latter case, the contents of array A on return
+    are undefined.
+
+  Algorithm:
+     Gaussian elimination with partial pivoting.
+
+  Speed:
+     Very fast.
+
+  Accuracy:
+     Fairly accurate - errors 1 to 4 times those of routines optimized
+     for accuracy.
+
+  Note:  replaces the obsolete slSMATRX routine.
+
+  P.T.Wallace   Starlink   10 September 1990
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/subet.hlp b/math/slalib/doc/subet.hlp
new file mode 100644
index 00000000..42d74ccf
--- /dev/null
+++ b/math/slalib/doc/subet.hlp
@@ -0,0 +1,41 @@
+.help subet Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slSUET (RC, DC, EQ, RM, DM)
+
+     - - - - - -
+      S U E T
+     - - - - - -
+
+  Remove the E-terms (elliptic component of annual aberration)
+  from a pre IAU 1976 catalogue RA,Dec to give a mean place
+  (double precision)
+
+  Given:
+     RC,DC     dp     RA,Dec (radians) with E-terms included
+     EQ        dp     Besselian epoch of mean equator and equinox
+
+  Returned:
+     RM,DM     dp     RA,Dec (radians) without E-terms
+
+  Called:
+     slETRM, slDS2C, sla_,DVDV, slDC2S, slDA2P
+
+  Explanation:
+     Most star positions from pre-1984 optical catalogues (or
+     derived from astrometry using such stars) embody the
+     E-terms.  This routine converts such a position to a
+     formal mean place (allowing, for example, comparison with a
+     pulsar timing position).
+
+  Reference:
+     Explanatory Supplement to the Astronomical Ephemeris,
+     section 2D, page 48.
+
+  P.T.Wallace   Starlink   10 May 1990
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/sun67.tex b/math/slalib/doc/sun67.tex
new file mode 100644
index 00000000..3e586f5e
--- /dev/null
+++ b/math/slalib/doc/sun67.tex
@@ -0,0 +1,12311 @@
+\documentclass[11pt,twoside]{article}
+\setcounter{tocdepth}{2}
+\pagestyle{myheadings}
+
+% -----------------------------------------------------------------------------
+% ? Document identification
+\newcommand{\stardoccategory}  {Starlink User Note}
+\newcommand{\stardocinitials}  {SUN}
+\newcommand{\stardocsource}    {sun67.44}
+\newcommand{\stardocnumber}    {67.44}
+\newcommand{\stardocauthors}   {P.\,T.\,Wallace}
+\newcommand{\stardocdate}      {29 April 1999}
+\newcommand{\stardoctitle}     {SLALIB --- Positional Astronomy Library}
+\newcommand{\stardocversion}   {2.3-0}
+\newcommand{\stardocmanual}    {Programmer's Manual}
+% ? End of document identification
+
+%%% Also see \nroutines definition later %%%
+
+% -----------------------------------------------------------------------------
+
+\newcommand{\stardocname}{\stardocinitials /\stardocnumber}
+\markright{\stardocname}
+\setlength{\textwidth}{160mm}
+\setlength{\textheight}{230mm}
+\setlength{\topmargin}{-2mm}
+\setlength{\oddsidemargin}{0mm}
+\setlength{\evensidemargin}{0mm}
+\setlength{\parindent}{0mm}
+\setlength{\parskip}{\medskipamount}
+\setlength{\unitlength}{1mm}
+
+% -----------------------------------------------------------------------------
+%  Hypertext definitions.
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+%  These are used by the LaTeX2HTML translator in conjunction with star2html.
+
+%  Comment.sty: version 2.0, 19 June 1992
+%  Selectively in/exclude pieces of text.
+%
+%  Author
+%    Victor Eijkhout                                      <eijkhout@cs.utk.edu>
+%    Department of Computer Science
+%    University Tennessee at Knoxville
+%    104 Ayres Hall
+%    Knoxville, TN 37996
+%    USA
+
+%  Do not remove the %\begin{rawtex} and %\end{rawtex} lines (used by
+%  star2html to signify raw TeX that latex2html cannot process).
+%\begin{rawtex}
+\makeatletter
+\def\makeinnocent#1{\catcode`#1=12 }
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+
+\def\ThrowAwayComment#1{\begingroup
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+      \fi \fi \html@next}
+}
+\makeatother
+
+\def\includecomment
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+\def\excludecomment
+ #1{\expandafter\def\csname#1\endcsname{\ThrowAwayComment{#1}}%
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+
+%  Define environments that ignore their contents.
+\excludecomment{comment}
+\excludecomment{rawhtml}
+\excludecomment{htmlonly}
+%\end{rawtex}
+
+%  Hypertext commands etc. This is a condensed version of the html.sty
+%  file supplied with LaTeX2HTML by: Nikos Drakos <nikos@cbl.leeds.ac.uk> &
+%  Jelle van Zeijl <jvzeijl@isou17.estec.esa.nl>. The LaTeX2HTML documentation
+%  should be consulted about all commands (and the environments defined above)
+%  except \xref and \xlabel which are Starlink specific.
+
+\newcommand{\htmladdnormallinkfoot}[2]{#1\footnote{#2}}
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+\newcommand{\htmlref}[2]{#1}
+\newcommand{\htmlimage}[1]{}
+\newcommand{\htmladdtonavigation}[1]{}
+
+%  Starlink cross-references and labels.
+\newcommand{\xref}[3]{#1}
+\newcommand{\xlabel}[1]{}
+
+%  LaTeX2HTML symbol.
+\newcommand{\latextohtml}{{\bf LaTeX}{2}{\tt{HTML}}}
+
+%  Define command to re-centre underscore for Latex and leave as normal
+%  for HTML (severe problems with \_ in tabbing environments and \_\_
+%  generally otherwise).
+\newcommand{\latex}[1]{#1}
+\newcommand{\setunderscore}{\renewcommand{\_}{{\tt\symbol{95}}}}
+\latex{\setunderscore}
+
+%  Redefine the \tableofcontents command. This procrastination is necessary
+%  to stop the automatic creation of a second table of contents page
+%  by latex2html.
+\newcommand{\latexonlytoc}[0]{\tableofcontents}
+
+% -----------------------------------------------------------------------------
+%  Debugging.
+%  =========
+%  Remove % on the following to debug links in the HTML version using Latex.
+
+% \newcommand{\hotlink}[2]{\fbox{\begin{tabular}[t]{@{}c@{}}#1\\\hline{\footnotesize #2}\end{tabular}}}
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+% -----------------------------------------------------------------------------
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+%------------------------------------------------------------------------------
+
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+
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+      #3
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+
+%  Replacement for HTML version (each routine in own subsection).
+\begin{htmlonly}
+   \renewcommand{\routine}[3]
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+  \multicolumn{1}{c}{#1} & {} & {#2}
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+
+\newcommand{\anote}[1]
+{
+  \goodbreak
+  \setlength{\oldspacing}{\topsep}
+  \setlength{\topsep}{0.3ex}
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+    \item[NOTE]:
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+  \setlength{\topsep}{\oldspacing}
+}
+
+\begin{htmlonly}
+   \renewcommand{\anote}[1]
+   {
+      \begin{description}
+      \item[NOTE:]
+          #1
+      \end{description}
+   }
+\end{htmlonly}
+
+\newcommand{\notes}[1]
+{
+  \goodbreak
+  \setlength{\oldspacing}{\topsep}
+  \setlength{\topsep}{0.3ex}
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+    \item[NOTES]:
+        #1
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+\begin{htmlonly}
+   \renewcommand{\notes}[1]
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+      \begin{description}
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+\end{htmlonly}
+
+\newcommand{\aref}[1]
+{
+  \goodbreak
+  \setlength{\oldspacing}{\topsep}
+  \setlength{\topsep}{0.3ex}
+  \begin{description}
+    \item[REFERENCE]:
+        #1
+  \end{description}
+  \setlength{\topsep}{\oldspacing}
+}
+
+\begin{htmlonly}
+   \newcommand{\aref}[1]
+   {
+     \begin{description}
+       \item[REFERENCE:]
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+     \end{description}
+   }
+\end{htmlonly}
+
+\newcommand{\refs}[1]
+{
+  \goodbreak
+  \setlength{\oldspacing}{\topsep}
+  \setlength{\topsep}{0.3ex}
+  \begin{description}
+    \item[REFERENCES]:
+        #1
+  \end{description}
+  \setlength{\topsep}{\oldspacing}
+}
+\begin{htmlonly}
+   \newcommand{\refs}[1]
+   {
+     \begin{description}
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+   }
+\end{htmlonly}
+
+\newcommand{\exampleitem}{\item [EXAMPLE]:}
+\begin{htmlonly}
+   \renewcommand{\exampleitem}{\item [EXAMPLE:]}
+\end{htmlonly}
+
+%------------------------------------------------------------------------------
+% ? End of document specific commands
+% -----------------------------------------------------------------------------
+%  Title Page.
+%  ===========
+\renewcommand{\thepage}{\roman{page}}
+\begin{document}
+\thispagestyle{empty}
+
+%  Latex document header.
+%  ======================
+\begin{latexonly}
+   CCLRC / {\sc Rutherford Appleton Laboratory} \hfill {\bf \stardocname}\\
+   {\large Particle Physics \& Astronomy Research Council}\\
+   {\large Starlink Project\\}
+   {\large \stardoccategory\ \stardocnumber}
+   \begin{flushright}
+   \stardocauthors\\
+   \stardocdate
+   \end{flushright}
+   \vspace{-4mm}
+   \rule{\textwidth}{0.5mm}
+   \vspace{5mm}
+   \begin{center}
+   {\Huge\bf  \stardoctitle \\ [2.5ex]}
+   {\LARGE\bf \stardocversion \\ [4ex]}
+   {\Huge\bf  \stardocmanual}
+   \end{center}
+   \vspace{5mm}
+
+% ? Heading for abstract if used.
+   \vspace{10mm}
+   \begin{center}
+      {\Large\bf Abstract}
+   \end{center}
+% ? End of heading for abstract.
+\end{latexonly}
+
+%  HTML documentation header.
+%  ==========================
+\begin{htmlonly}
+   \xlabel{}
+   \begin{rawhtml} <H1> \end{rawhtml}
+      \stardoctitle\\
+      \stardocversion\\
+      \stardocmanual
+   \begin{rawhtml} </H1> \end{rawhtml}
+
+% ? Add picture here if required.
+% ? End of picture
+
+   \begin{rawhtml} <P> <I> \end{rawhtml}
+   \stardoccategory \stardocnumber \\
+   \stardocauthors \\
+   \stardocdate
+   \begin{rawhtml} </I> </P> <H3> \end{rawhtml}
+      \htmladdnormallink{CCLRC}{http://www.cclrc.ac.uk} /
+      \htmladdnormallink{Rutherford Appleton Laboratory}
+                        {http://www.cclrc.ac.uk/ral} \\
+      \htmladdnormallink{Particle Physics \& Astronomy Research Council}
+                        {http://www.pparc.ac.uk} \\
+   \begin{rawhtml} </H3> <H2> \end{rawhtml}
+      \htmladdnormallink{Starlink Project}{http://star-www.rl.ac.uk/}
+   \begin{rawhtml} </H2> \end{rawhtml}
+   \htmladdnormallink{\htmladdimg{source.gif} Retrieve hardcopy}
+      {http://star-www.rl.ac.uk/cgi-bin/hcserver?\stardocsource}\\
+
+%  HTML document table of contents.
+%  ================================
+%  Add table of contents header and a navigation button to return to this
+%  point in the document (this should always go before the abstract \section).
+  \label{stardoccontents}
+  \begin{rawhtml}
+    <HR>
+    <H2>Contents</H2>
+  \end{rawhtml}
+  \renewcommand{\latexonlytoc}[0]{}
+  \htmladdtonavigation{\htmlref{\htmladdimg{contents_motif.gif}}
+        {stardoccontents}}
+
+% ? New section for abstract if used.
+  \section{\xlabel{abstract}Abstract}
+% ? End of new section for abstract
+\end{htmlonly}
+
+% -----------------------------------------------------------------------------
+% ? Document Abstract. (if used)
+%   ==================
+SLALIB is a library used by writers of positional-astronomy applications.
+Most of the \nroutines\ routines are concerned with astronomical position and time,
+but a number have wider trigonometrical, numerical or general applications.
+% ? End of document abstract
+% -----------------------------------------------------------------------------
+% ? Latex document Table of Contents (if used).
+%  ===========================================
+ \newpage
+ \begin{latexonly}
+   \setlength{\parskip}{0mm}
+   \latexonlytoc
+   \setlength{\parskip}{\medskipamount}
+   \markright{\stardocname}
+ \end{latexonly}
+% ? End of Latex document table of contents
+% -----------------------------------------------------------------------------
+\newpage
+\renewcommand{\thepage}{\arabic{page}}
+\setcounter{page}{1}
+
+\section{INTRODUCTION}
+\subsection{Purpose}
+SLALIB\footnote{The name isn't an acronym;
+it just stands for ``Subprogram Library~A''.}
+is a library of routines
+intended to make accurate and reliable positional-astronomy
+applications easier to write.
+Most SLALIB routines are concerned with astronomical position and time, but a
+number have wider trigonometrical, numerical or general applications.
+The applications ASTROM, COCO, RV and TPOINT
+all make extensive use of the SLALIB
+routines, as do a number of telescope control systems around the world.
+The SLALIB versions currently in service are written in
+Fortran~77 and run on VAX/VMS, several Unix platforms and PC.
+A generic ANSI~C version is also available from the author;  it is
+functionally similar to the Fortran version upon which the present
+document concentrates.
+
+\subsection{Example Application}
+Here is a simple example of an application program written
+using SLALIB calls:
+
+\begin{verbatim}
+         PROGRAM FK4FK5
+   *
+   *  Read a B1950 position from I/O unit 5 and reply on I/O unit 6
+   *  with the J2000 equivalent.  Enter a period to quit.
+   *
+         IMPLICIT NONE
+         CHARACTER C*80,S
+         INTEGER I,J,IHMSF(4),IDMSF(4)
+         DOUBLE PRECISION R4,D4,R5,D5
+         LOGICAL BAD
+
+   *   Loop until a period is entered
+         C = ' '
+         DO WHILE (C(:1).NE.'.')
+
+   *     Read h m s d ' "
+            READ (5,'(A)') C
+            IF (C(:1).NE.'.') THEN
+               BAD = .TRUE.
+
+   *        Decode the RA
+               I = 1
+               CALL sla_DAFIN(C,I,R4,J)
+               IF (J.EQ.0) THEN
+                  R4 = 15D0*R4
+
+   *           Decode the Dec
+                  CALL sla_DAFIN(C,I,D4,J)
+                  IF (J.EQ.0) THEN
+
+   *              FK4 to FK5
+                     CALL sla_FK45Z(R4,D4,1950D0,R5,D5)
+
+   *              Format and output the result
+                     CALL sla_DR2TF(2,R5,S,IHMSF)
+                     CALL sla_DR2AF(1,D5,S,IDMSF)
+                     WRITE (6,
+        :       '(1X,I2.2,2I3.2,''.'',I2.2,2X,A,I2.2,2I3.2,''.'',I1)')
+        :                                                     IHMSF,S,IDMSF
+                     BAD = .FALSE.
+                  END IF
+               END IF
+               IF (BAD) WRITE (6,'(1X,''?'')')
+            END IF
+         END DO
+
+         END
+\end{verbatim}
+In this example, SLALIB not only provides the complicated FK4 to
+FK5 transformation but also
+simplifies the tedious and error-prone tasks
+of decoding and formatting angles
+expressed as hours, minutes {\it etc}.  The
+example incorporates range checking, and avoids the
+notorious ``minus zero'' problem (an often-perpetrated bug where
+declinations between $0^{\circ}$ and $-1^{\circ}$ lose their minus
+sign).
+With a little extra elaboration and a few more calls to SLALIB,
+defaulting can be provided (enabling unused fields to
+be replaced with commas to avoid retyping), proper motions
+can be handled, different epochs can be specified, and
+so on.  See the program COCO (SUN/56) for further ideas.
+
+\subsection{Scope}
+SLALIB contains \nroutines\ routines covering the following topics:
+\begin{itemize}
+\item String Decoding,
+      Sexagesimal Conversions
+\item Angles, Vectors \& Rotation Matrices
+\item Calendars,
+      Timescales
+\item Precession \& Nutation
+\item Proper Motion
+\item FK4/FK5/Hipparcos,
+      Elliptic Aberration
+\item Geocentric Coordinates
+\item Apparent \& Observed Place
+\item Azimuth \& Elevation
+\item Refraction \& Air Mass
+\item Ecliptic,
+      Galactic,
+      Supergalactic Coordinates
+\item Ephemerides
+\item Astrometry
+\item Numerical Methods
+\end{itemize}
+
+\subsection{Objectives}
+SLALIB was designed to give application programmers
+a basic set of positional-astronomy tools which were
+accurate and easy to use.  To this end, the library is:
+\begin{itemize}
+\item Readily available, including source code and documentation.
+\item Supported and maintained.
+\item Portable -- coded in standard languages and available for
+multiple computers and operating systems.
+\item Thoroughly commented, both for maintainability and to
+assist those wishing to cannibalize the code.
+\item Stable.
+\item Trustworthy -- some care has gone into
+testing SLALIB, both by comparison with published data and
+by checks for internal consistency.
+\item Rigorous -- corners are not cut,
+even where the practical consequences would, as a rule, be
+negligible.
+\item Comprehensive, without including too many esoteric features
+required only by specialists.
+\item Practical -- almost all the routines have been written to
+satisfy real needs encountered during the development of
+real-life applications.
+\item Environment-independent -- the package is
+completely free of pauses, stops, I/O {\it etc}.
+\item Self-contained -- SLALIB calls no other libraries.
+\end{itemize}
+A few {\it caveats}:
+\begin{itemize}
+\item SLALIB does not pretend to be canonical.  It is in essence
+an anthology, and the adopted algorithms are liable
+to change as more up-to-date ones become available.
+\item The functions aren't orthogonal -- there are several
+cases of different
+routines doing similar things, and many examples where
+sequences of SLALIB calls have simply been packaged, all to
+make applications less trouble to write.
+\item There are omissions -- for example there are no
+routines for calculating physical ephemerides of
+Solar-System bodies.
+\item SLALIB is not homogeneous, though important subsets
+(for example the FK4/FK5 routines) are.
+\item The library is not foolproof.  You have to know what
+you are trying to do ({\it e.g.}\ by reading textbooks on positional
+astronomy), and it is the caller's responsibility to supply
+sensible arguments (although enough internal validation is done to
+avoid arithmetic errors).
+\item Without being written in a wasteful
+manner, SLALIB is nonetheless optimized for maintainability
+rather than speed.  In addition, there are many places
+where considerable simplification would be possible if some
+specified amount of accuracy could be sacrificed;  such
+compromises are left to the individual programmer and
+are not allowed to limit SLALIB's value as a source
+of comparison results.
+\end{itemize}
+
+\subsection{Fortran Version}
+The Fortran versions of SLALIB use ANSI Fortran~77 with a few
+commonplace extensions.  Just three out of the \nroutines\ routines require
+platform-specific techniques and accordingly are supplied
+in different forms.
+SLALIB has been implemented on the following platforms:
+VAX/VMS,
+PC (Microsoft Fortran, Linux),
+DECstation (Ultrix),
+DEC Alpha (DEC Unix),
+Sun (SunOS, Solaris),
+Hewlett Packard (HP-UX),
+CONVEX,
+Perkin-Elmer and
+Fujitsu.
+
+\subsection{C Version}
+An ANSI C version of SLALIB is available from the author
+but is not part of the Starlink release.
+The functionality of this (proprietary) C version closely matches
+that of the Starlink Fortran SLALIB, partly for the convenience of
+existing users of the Fortran version, some of whom have in the past
+implemented C ``wrappers''.  The function names
+cannot be the same as the Fortran versions because of potential
+linking problems when
+both forms of the library are present; the C routine which
+is the equivalent of (for example) {\tt SLA\_REFRO} is {\tt slaRefro}.
+The types of arguments follow the Fortran version, except
+that integers are {\tt int} rather than {\tt long}.
+Argument passing is by value
+(except for arrays and strings of course)
+for given arguments and by pointer for returned arguments.
+All the C functions are re-entrant.
+
+The Fortran routines {\tt sla\_GRESID}, {\tt sla\_RANDOM} and
+{\tt sla\_WAIT} have no C counterparts.
+
+Further details of the C version of SLALIB are available
+from the author.  The definitive guide to
+the calling sequences is the file {\tt slalib.h}.
+
+\subsection{Future Versions}
+The homogeneity and ease of use of SLALIB could perhaps be improved
+in the future
+by turning to C++ and object-oriented techniques.  For example ``celestial
+position'' could be a class and many of the transformations
+could happen automatically.  This requires further study and
+would almost certainly result in a complete redesign.
+Similarly,
+the impact of Fortran~90 has yet to be assessed.  Once compilers
+become widely available, some internal recoding may be worthwhile
+in order to simplify parts of the code.  However, as with C++,
+a redesign of the
+application interfaces will be needed if the capabilities of the
+new language are to be exploited to the full.
+
+\subsection{New Functions}
+In a package like SLALIB it is difficult to know how far to go.  Is it
+enough to provide the primitive operations, or should more
+complicated functions be packaged?  Is it worth encroaching on
+specialist areas, where individual experts have all written their
+own software already?  To what extent should CPU efficiency be
+an issue?  How much support of different numerical precisions is
+required?  And so on.
+
+In practice, almost all the routines in SLALIB are there because they were
+needed for some specific application, and this is likely to remain the
+pattern for any enhancements in the future.
+Suggestions for additional SLALIB routines should be addressed to the
+author.
+
+\subsection{Acknowledgements}
+SLALIB is descended from a package of routines written
+for the AAO 16-bit minicomputers
+in the mid-1970s.  The coming of the VAX
+allowed a much more comprehensive and thorough package
+to be designed for Starlink, especially important
+at a time when the adoption
+of the IAU 1976 resolutions meant that astronomers
+would have to cope with a mixture of reference frames,
+timescales and nomenclature.
+
+Much of the preparatory work on SLALIB was done by
+Althea~Wilkinson of Manchester University.
+During its development,
+Andrew~Murray,
+Catherine~Hohenkerk,
+Andrew~Sinclair,
+Bernard~Yallop
+and
+Brian~Emerson of Her Majesty's Nautical Almanac Office were consulted
+on many occasions; their advice was indispensable.
+I am especially grateful to
+Catherine~Hohenkerk
+for supplying preprints of papers, and test data. A number of
+enhancements to SLALIB were at the suggestion of
+Russell~Owen, University of Washington,
+Phil~Hill, St~Andrews University,
+Bill~Vacca, JILA, Boulder and
+Ron~Maddalena, NRAO.
+Mark~Calabretta, CSIRO Radiophysics, Sydney supplied changes to suit Convex.
+I am indebted to Derek~Jones (RGO) for providing algorithms for
+calculating 2-body orbital motion.
+
+The first C version of SLALIB was a hand-coded transcription
+of the Starlink Fortran version carried out by
+Steve~Eaton (University of Leeds) in the course of
+MSc work.  This was later
+enhanced by John~Straede (AAO) and Martin~Shepherd (Caltech).
+The current C SLALIB is a complete rewrite by the present author and
+includes a comprehensive validation suite.
+Additional comments on the C version came from Bob~Payne (NRAO) and
+Jeremy~Bailey (AAO).
+
+\section{LINKING}
+
+On Unix systems (Sun, DEC Alpha {\it etc.}):
+\begin{verse}
+{\tt \%~~f77 progname.o -L/star/lib `sla\_link` -o progname}
+\end{verse}
+(The above assumes that all Starlink directories have been added to
+the {\tt LD\_LIBRARY\_PATH} and {\tt PATH} environment variables
+as described in SUN/202.)
+
+On VAX/VMS:
+\begin{verse}
+{\tt \$~~LINK progname,SLALIB\_DIR:SLALIB/LIB}
+\end{verse}
+
+\pagebreak
+
+\section{SUBPROGRAM SPECIFICATIONS}
+%-----------------------------------------------------------------------
+\routine{SLA\_ADDET}{Add E-terms of Aberration}
+{
+ \action{Add the E-terms (elliptic component of annual aberration) to a
+  pre IAU 1976 mean place to conform to the old catalogue convention.}
+ \call{CALL sla\_ADDET (RM, DM, EQ, RC, DC)}
+}
+\args{GIVEN}
+{
+ \spec{RM,DM}{D}{\radec\ without E-terms (radians)} \\
+ \spec{EQ}{D}{Besselian epoch of mean equator and equinox}
+}
+\args{RETURNED}
+{
+ \spec{RC,DC}{D}{\radec\ with E-terms included (radians)}
+}
+\anote{Most star positions from pre-1984 optical catalogues (or
+       obtained by astrometry with respect to such stars) have the
+       E-terms built-in.  If it is necessary to convert a formal mean
+       place (for example a pulsar timing position) to one
+       consistent with such a star catalogue, then the 
+       \radec\ should be adjusted using this routine.}
+\aref{{\it Explanatory Supplement to the Astronomical Ephemeris},
+ section 2D, page 48.}
+%-----------------------------------------------------------------------
+\routine{SLA\_AFIN}{Sexagesimal character string to angle}
+{
+ \action{Decode a free-format sexagesimal string (degrees, arcminutes,
+         arcseconds) into a single precision floating point
+         number (radians).}
+ \call{CALL sla\_AFIN (STRING, NSTRT, RESLT, JF)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C*(*)}{string containing deg, arcmin, arcsec fields} \\
+ \spec{NSTRT}{I}{pointer to start of decode (beginning of STRING = 1)}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{advanced past the decoded angle} \\
+ \spec{RESLT}{R}{angle in radians} \\
+ \spec{JF}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em}   0 = OK} \\
+ \spec{}{}{\hspace{0.7em} $+1$ = default, RESLT unchanged (note 2)} \\
+ \spec{}{}{\hspace{0.7em} $-1$ = bad degrees (note 3)} \\
+ \spec{}{}{\hspace{0.7em} $-2$ = bad arcminutes (note 3)} \\
+ \spec{}{}{\hspace{0.7em} $-3$ = bad arcseconds (note 3)} \\
+}
+\goodbreak
+\setlength{\oldspacing}{\topsep}
+\setlength{\topsep}{0.3ex}
+\begin{description}
+ \exampleitem \\ [1.5ex]
+  \begin{tabular}{p{7em}p{15em}p{12em}}
+   {\it argument} & {\it before} & {\it after} \\ \\
+   STRING & $'$\verb*}-57 17 44.806  12 34 56.7}$'$ & unchanged \\
+   NSTRT & 1 & 16 ({\it i.e.}\ pointing to 12...) \\
+   RESLT & - & $-1.00000$ \\
+   JF & - & 0
+  \end{tabular}
+ \item A further call to sla\_AFIN, without adjustment of NSTRT, will
+       decode the second angle, \dms{12}{34}{56}{7}.
+\end{description}
+\setlength{\topsep}{\oldspacing}
+\notes
+{
+ \begin{enumerate}
+  \item The first three ``fields'' in STRING are degrees, arcminutes,
+   arcseconds, separated by spaces or commas.  The degrees field
+   may be signed, but not the others.  The decoding is carried
+   out by the sla\_DFLTIN routine and is free-format.
+  \item Successive fields may be absent, defaulting to zero.  For
+   zero status, the only combinations allowed are degrees alone,
+   degrees and arcminutes, and all three fields present.  If all
+   three fields are omitted, a status of +1 is returned and RESLT is
+   unchanged.  In all other cases RESLT is changed.
+  \item Range checking:
+   \begin{itemize}
+    \item The degrees field is not range checked.  However, it is
+     expected to be integral unless the other two fields are absent.
+    \item The arcminutes field is expected to be 0-59, and integral if
+     the arcseconds field is present.  If the arcseconds field
+     is absent, the arcminutes is expected to be 0-59.9999...
+    \item The arcseconds field is expected to be 0-59.9999...
+    \item Decoding continues even when a check has failed.  Under these
+     circumstances the field takes the supplied value, defaulting to
+     zero, and the result RESLT is computed and returned.
+   \end{itemize}
+   \item Further fields after the three expected ones are not treated as
+    an error.  The pointer NSTRT is left in the correct state for
+    further decoding with the present routine or with sla\_DFLTIN
+    {\it etc}.  See the example, above.
+   \item If STRING contains hours, minutes, seconds instead of
+    degrees {\it etc},
+    or if the required units are turns (or days) instead of radians,
+    the result RESLT should be multiplied as follows: \\ [1.5ex]
+    \begin{tabular}{p{6em}p{5em}p{15em}}
+    {\it for STRING} & {\it to obtain} & {\it multiply RESLT by} \\ \\
+    ${\circ}$~~\raisebox{-0.7ex}{$'$}~~\raisebox{-0.7ex}{$''$}
+     & radians & $1.0$ \\
+    ${\circ}$~~\raisebox{-0.7ex}{$'$}~~\raisebox{-0.7ex}{$''$}
+     & turns & $1/{2 \pi} = 0.1591549430918953358$ \\
+    h m s & radians & $15.0$ \\
+    h m s & days & $15/{2\pi} = 2.3873241463784300365$ \\
+   \end{tabular}
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AIRMAS}{Air Mass}
+{
+ \action{Air mass at given zenith distance (double precision).}
+ \call{D~=~sla\_AIRMAS (ZD)}
+}
+\args{GIVEN}
+{
+ \spec{ZD}{D}{observed zenith distance (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_AIRMAS}{D}{air mass (1 at zenith)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The {\it observed}\/ zenith distance referred to above means
+        ``as affected by refraction''.
+  \item The routine uses Hardie's (1962) polynomial fit to Bemporad's
+        data for the relative air mass, $X$, in units of thickness at the
+        zenith as tabulated by Schoenberg (1929). This is adequate for all
+        normal needs as it is accurate to better than
+        0.1\% up to $X = 6.8$ and better than 1\% up to $X = 10$.
+        Bemporad's tabulated values are unlikely to be trustworthy
+        to such accuracy
+        because of variations in density, pressure and other
+        conditions in the atmosphere from those assumed in his work.
+  \item The sign of the ZD is ignored.
+  \item At zenith distances greater than about $\zeta = 87^{\circ}$ the
+        air mass is held constant to avoid arithmetic overflows.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Hardie, R.H., 1962, in {\it Astronomical Techniques}\,
+        ed. W.A.\ Hiltner, University of Chicago Press, p180.
+  \item Schoenberg, E., 1929, Hdb.\ d.\ Ap.,
+        Berlin, Julius Springer, 2, 268.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_ALTAZ}{Velocities {\it etc.}\ for Altazimuth Mount}
+{
+ \action{Positions, velocities and accelerations for an altazimuth
+         telescope mount tracking a star (double precision).}
+ \call{CALL sla\_ALTAZ (\vtop{
+         \hbox{HA, DEC, PHI,}
+         \hbox{AZ, AZD, AZDD, EL, ELD, ELDD, PA, PAD, PADD)}}}
+}
+\args{GIVEN}
+{
+ \spec{HA}{D}{hour angle} \\
+ \spec{DEC}{D}{declination} \\
+ \spec{PHI}{D}{observatory latitude}
+}
+\args{RETURNED}
+{
+ \spec{AZ}{D}{azimuth} \\
+ \spec{AZD}{D}{azimuth velocity} \\
+ \spec{AZDD}{D}{azimuth acceleration} \\
+ \spec{EL}{D}{elevation} \\
+ \spec{ELD}{D}{elevation velocity} \\
+ \spec{ELDD}{D}{elevation acceleration} \\
+ \spec{PA}{D}{parallactic angle} \\
+ \spec{PAD}{D}{parallactic angle velocity} \\
+ \spec{PADD}{D}{parallactic angle acceleration}
+}
+\notes
+{
+ \begin{enumerate}
+  \setlength{\parskip}{\medskipamount}
+  \item Natural units are used throughout.  HA, DEC, PHI, AZ, EL
+        and ZD are in radians.  The velocities and accelerations
+        assume constant declination and constant rate of change of
+        hour angle (as for tracking a star);  the units of AZD, ELD
+        and PAD are radians per radian of HA, while the units of AZDD,
+        ELDD and PADD are radians per radian of HA squared.  To
+        convert into practical degree- and second-based units:
+
+        \begin{center}
+        \begin{tabular}{rlcl}
+                  angles & $\times 360/2\pi$ & $\rightarrow$ & degrees \\
+              velocities & $\times (2\pi/86400) \times (360/2\pi)$
+                                             & $\rightarrow$ & degree/sec \\
+           accelerations & $\times (2\pi/86400)^2 \times (360/2\pi)$
+                                             & $\rightarrow$ & degree/sec/sec \\
+        \end{tabular}
+        \end{center}
+
+        Note that the seconds here are sidereal rather than SI.  One
+        sidereal second is about 0.99727 SI seconds.
+
+        The velocity and acceleration factors assume the sidereal
+        tracking case.  Their respective numerical values are (exactly)
+        1/240 and (approximately) 1/3300236.9.
+  \item Azimuth is returned in the range $[\,0,2\pi\,]$;  north is zero,
+        and east is $+\pi/2$.  Elevation and parallactic angle are
+        returned in the range $\pm\pi/2$.  Position angle is +ve
+        for a star west of the meridian and is the angle NP--star--zenith.
+  \item The latitude is geodetic as opposed to geocentric.  The
+        hour angle and declination are topocentric.  Refraction and
+        deficiencies in the telescope mounting are ignored.  The
+        purpose of the routine is to give the general form of the
+        quantities.  The details of a real telescope could profoundly
+        change the results, especially close to the zenith.
+  \item No range checking of arguments is carried out.
+  \item In applications which involve many such calculations, rather
+        than calling the present routine it will be more efficient to
+        use inline code, having previously computed fixed terms such
+        as sine and cosine of latitude, and (for tracking a star)
+        sine and cosine of declination.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AMP}{Apparent to Mean}
+{
+ \action{Convert star \radec\ from geocentric apparent to
+         mean place (post IAU 1976).}
+ \call{CALL sla\_AMP (RA, DA, DATE, EQ, RM, DM)}
+}
+\args{GIVEN}
+{
+ \spec{RA,DA}{D}{apparent \radec\ (radians)} \\
+ \spec{DATE}{D}{TDB for apparent place (JD$-$2400000.5)} \\
+ \spec{EQ}{D}{equinox:  Julian epoch of mean place}
+}
+\args{RETURNED}
+{
+ \spec{RM,DM}{D}{mean \radec\ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The distinction between the required TDB and TT is
+        always negligible.  Moreover, for all but the most
+        critical applications UTC is adequate.
+  \item The accuracy is limited by the routine sla\_EVP, called
+        by sla\_MAPPA, which computes the Earth position and
+        velocity using the methods of Stumpff.  The maximum
+        error is about 0.3~milliarcsecond.
+  \item Iterative techniques are used for the aberration and
+        light deflection corrections so that the routines
+        sla\_AMP (or sla\_AMPQK) and sla\_MAP (or sla\_MAPQK) are
+        accurate inverses;  even at the edge of the Sun's disc
+        the discrepancy is only about 1~nanoarcsecond.
+  \item Where multiple apparent places are to be converted to
+        mean places, for a fixed date and equinox, it is more
+        efficient to use the sla\_MAPPA routine to compute the
+        required parameters once, followed by one call to
+        sla\_AMPQK per star.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AMPQK}{Quick Apparent to Mean}
+{
+ \action{Convert star \radec\ from geocentric apparent to mean place
+         (post IAU 1976).  Use of this routine is appropriate when
+         efficiency is important and where many star positions are
+         all to be transformed for one epoch and equinox.  The
+         star-independent parameters can be obtained by calling
+         the sla\_MAPPA routine.}
+ \call{CALL sla\_AMPQK (RA, DA, AMPRMS, RM, DM)}
+}
+\args{GIVEN}
+{
+ \spec{RA,DA}{D}{apparent \radec\ (radians)} \\
+ \spec{AMPRMS}{D(21)}{star-independent mean-to-apparent parameters:} \\
+ \specel   {(1)}     {time interval for proper motion (Julian years)} \\
+ \specel   {(2-4)}   {barycentric position of the Earth (AU)} \\
+ \specel   {(5-7)}   {heliocentric direction of the Earth (unit vector)} \\
+ \specel   {(8)}     {(gravitational radius of
+                      Sun)$\times 2 / $(Sun-Earth distance)} \\
+ \specel   {(9-11)}  {{\bf v}: barycentric Earth velocity in units of c} \\
+ \specel   {(12)}    {$\sqrt{1-\left|\mbox{\bf v}\right|^2}$} \\
+ \specel   {(13-21)} {precession/nutation $3\times3$ matrix}
+}
+\args{RETURNED}
+{
+ \spec{RM,DM}{D}{mean \radec\ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The accuracy is limited by the routine sla\_EVP, called
+        by sla\_MAPPA, which computes the Earth position and
+        velocity using the methods of Stumpff.  The maximum
+        error is about 0.3~milliarcsecond.
+  \item Iterative techniques are used for the aberration and
+        light deflection corrections so that the routines
+        sla\_AMP (or sla\_AMPQK) and sla\_MAP (or sla\_MAPQK) are
+        accurate inverses;  even at the edge of the Sun's disc
+        the discrepancy is only about 1~nanoarcsecond.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AOP}{Apparent to Observed}
+{
+ \action{Apparent to observed place, for optical sources distant from
+         the solar system.}
+ \call{CALL sla\_AOP (\vtop{
+         \hbox{RAP, DAP, DATE, DUT, ELONGM, PHIM, HM, XP, YP,}
+         \hbox{TDK, PMB, RH, WL, TLR, AOB, ZOB, HOB, DOB, ROB)}}}
+}
+\args{GIVEN}
+{
+ \spec{RAP,DAP}{D}{geocentric apparent \radec\ (radians)} \\
+ \spec{DATE}{D}{UTC date/time (Modified Julian Date, JD$-$2400000.5)} \\
+ \spec{DUT}{D}{$\Delta$UT:  UT1$-$UTC (UTC seconds)} \\
+ \spec{ELONGM}{D}{observer's mean longitude (radians, east +ve)} \\
+ \spec{PHIM}{D}{observer's mean geodetic latitude (radians)} \\
+ \spec{HM}{D}{observer's height above sea level (metres)} \\
+ \spec{XP,YP}{D}{polar motion \xy\ coordinates (radians)} \\
+ \spec{TDK}{D}{local ambient temperature (degrees K; std=273.155D0)} \\
+ \spec{PMB}{D}{local atmospheric pressure (mB; std=1013.25D0)} \\
+ \spec{RH}{D}{local relative humidity (in the range 0D0\,--\,1D0)} \\
+ \spec{WL}{D}{effective wavelength ($\mu{\rm m}$, {\it e.g.}\ 0.55D0)} \\
+ \spec{TLR}{D}{tropospheric lapse rate (degrees K per metre,
+                                              {\it e.g.}\ 0.0065D0)}
+}
+\args{RETURNED}
+{
+ \spec{AOB}{D}{observed azimuth (radians: N=0, E=$90^{\circ}$)} \\
+ \spec{ZOB}{D}{observed zenith distance (radians)} \\
+ \spec{HOB}{D}{observed Hour Angle (radians)} \\
+ \spec{DOB}{D}{observed $\delta$ (radians)} \\
+ \spec{ROB}{D}{observed $\alpha$ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine returns zenith distance rather than elevation
+        in order to reflect the fact that no allowance is made for
+        depression of the horizon.
+  \item The accuracy of the result is limited by the corrections for
+        refraction.  Providing the meteorological parameters are
+        known accurately and there are no gross local effects, the
+        predicted azimuth and elevation should be within about
+        \arcsec{0}{1} for $\zeta<70^{\circ}$.  Even
+        at a topocentric zenith distance of
+        $90^{\circ}$, the accuracy in elevation should be better than
+        1~arcminute;  useful results are available for a further
+        $3^{\circ}$, beyond which the sla\_REFRO routine returns a
+        fixed value of the refraction.  The complementary
+        routines sla\_AOP (or sla\_AOPQK) and sla\_OAP (or sla\_OAPQK)
+        are self-consistent to better than 1~microarcsecond all over
+        the celestial sphere.
+  \item It is advisable to take great care with units, as even
+        unlikely values of the input parameters are accepted and
+        processed in accordance with the models used.
+  \item {\it Apparent}\/ \radec\ means the geocentric apparent right ascension
+        and declination, which is obtained from a catalogue mean place
+        by allowing for space motion, parallax, precession, nutation,
+        annual aberration, and the Sun's gravitational lens effect.  For
+        star positions in the FK5 system ({\it i.e.}\ J2000), these effects can
+        be applied by means of the sla\_MAP {\it etc.}\ routines.  Starting from
+        other mean place systems, additional transformations will be
+        needed;  for example, FK4 ({\it i.e.}\ B1950) mean places would first
+        have to be converted to FK5, which can be done with the
+        sla\_FK425 {\it etc.}\ routines.
+  \item {\it Observed}\/ \azel\ means the position that would be seen by a
+        perfect theodolite located at the observer.  This is obtained
+        from the geocentric apparent \radec\ by allowing for Earth
+        orientation and diurnal aberration, rotating from equator
+        to horizon coordinates, and then adjusting for refraction.
+        The \hadec\ is obtained by rotating back into equatorial
+        coordinates, using the geodetic latitude corrected for polar
+        motion, and is the position that would be seen by a perfect
+        equatorial located at the observer and with its polar axis
+        aligned to the Earth's axis of rotation ({\it n.b.}\ not to the
+        refracted pole).  Finally, the $\alpha$ is obtained by subtracting
+        the {\it h}\/ from the local apparent ST.
+  \item To predict the required setting of a real telescope, the
+        observed place produced by this routine would have to be
+        adjusted for the tilt of the azimuth or polar axis of the
+        mounting (with appropriate corrections for mount flexures),
+        for non-perpendicularity between the mounting axes, for the
+        position of the rotator axis and the pointing axis relative
+        to it, for tube flexure, for gear and encoder errors, and
+        finally for encoder zero points.  Some telescopes would, of
+        course, exhibit other properties which would need to be
+        accounted for at the appropriate point in the sequence.
+  \item This routine takes time to execute, due mainly to the
+        rigorous integration used to evaluate the refraction.
+        For processing multiple stars for one location and time,
+        call sla\_AOPPA once followed by one call per star to sla\_AOPQK.
+        Where a range of times within a limited period of a few hours
+        is involved, and the highest precision is not required, call
+        sla\_AOPPA once, followed by a call to sla\_AOPPAT each time the
+        time changes, followed by one call per star to sla\_AOPQK.
+  \item The DATE argument is UTC expressed as an MJD.  This is,
+        strictly speaking, wrong, because of leap seconds.  However,
+        as long as the $\Delta$UT and the UTC are consistent there
+        are no difficulties, except during a leap second.  In this
+        case, the start of the 61st second of the final minute should
+        begin a new MJD day and the old pre-leap $\Delta$UT should
+        continue to be used.  As the 61st second completes, the MJD
+        should revert to the start of the day as, simultaneously,
+        the $\Delta$UT changes by one second to its post-leap new value.
+  \item The $\Delta$UT (UT1$-$UTC) is tabulated in IERS circulars and
+        elsewhere.  It increases by exactly one second at the end of
+        each UTC leap second, introduced in order to keep $\Delta$UT
+        within $\pm$\tsec{0}{9}.
+  \item IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.  The
+        longitude required by the present routine is {\bf east-positive},
+        in accordance with geographical convention (and right-handed).
+        In particular, note that the longitudes returned by the
+        sla\_OBS routine are west-positive (as in the {\it Astronomical
+        Almanac}\/ before 1984) and must be reversed in sign before use
+        in the present routine.
+  \item The polar coordinates XP,YP can be obtained from IERS
+        circulars and equivalent publications.  The
+        maximum amplitude is about \arcsec{0}{3}.  If XP,YP values
+        are unavailable, use XP=YP=0D0.  See page B60 of the 1988
+        {\it Astronomical Almanac}\/ for a definition of the two angles.
+  \item The height above sea level of the observing station, HM,
+        can be obtained from the {\it Astronomical Almanac}\/ (Section J
+        in the 1988 edition), or via the routine sla\_OBS.  If P,
+        the pressure in mB, is available, an adequate
+        estimate of HM can be obtained from the following expression:
+        \begin{quote}
+         {\tt HM=-29.3D0*TSL*LOG(P/1013.25D0)}
+        \end{quote}
+        where TSL is the approximate sea-level air temperature in degrees K
+        (see {\it Astrophysical Quantities}, C.W.Allen, 3rd~edition,
+        \S 52.)  Similarly, if the pressure P is not known,
+        it can be estimated from the height of the observing
+        station, HM as follows:
+        \begin{quote}
+         {\tt P=1013.25D0*EXP(-HM/(29.3D0*TSL))}
+        \end{quote}
+        Note, however, that the refraction is proportional to the
+        pressure and that an accurate P value is important for
+        precise work.
+  \item The azimuths {\it etc.}\ used by the present routine are with
+        respect to the celestial pole.  Corrections to the terrestrial pole
+        can be computed using sla\_POLMO.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AOPPA}{Appt-to-Obs Parameters}
+{
+ \action{Pre-compute the set of apparent to observed place parameters
+         required by the ``quick'' routines sla\_AOPQK and sla\_OAPQK.}
+ \call{CALL sla\_AOPPA (\vtop{
+          \hbox{DATE, DUT, ELONGM, PHIM, HM, XP, YP,}
+          \hbox{TDK, PMB, RH, WL, TLR, AOPRMS)}}}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{UTC date/time (Modified Julian Date, JD$-$2400000.5)} \\
+ \spec{DUT}{D}{$\Delta$UT:  UT1$-$UTC (UTC seconds)} \\
+ \spec{ELONGM}{D}{observer's mean longitude (radians, east +ve)} \\
+ \spec{PHIM}{D}{observer's mean geodetic latitude (radians)} \\
+ \spec{HM}{D}{observer's height above sea level (metres)} \\
+ \spec{XP,YP}{D}{polar motion \xy\ coordinates (radians)} \\
+ \spec{TDK}{D}{local ambient temperature (degrees K; std=273.155D0)} \\
+ \spec{PMB}{D}{local atmospheric pressure (mB; std=1013.25D0)} \\
+ \spec{RH}{D}{local relative humidity (in the range 0D0\,--\,1D0)} \\
+ \spec{WL}{D}{effective wavelength ($\mu{\rm m}$, {\it e.g.}\ 0.55D0)} \\
+ \spec{TLR}{D}{tropospheric lapse rate (degrees K per metre,
+                                              {\it e.g.}\ 0.0065D0)}
+}
+\args{RETURNED}
+{
+ \spec{AOPRMS}{D(14)}{star-independent apparent-to-observed parameters:} \\
+ \specel   {(1)}     {geodetic latitude (radians)} \\
+ \specel   {(2,3)}   {sine and cosine of geodetic latitude} \\
+ \specel   {(4)}     {magnitude of diurnal aberration vector} \\
+ \specel   {(5)}     {height (HM)} \\
+ \specel   {(6)}     {ambient temperature (TDK)} \\
+ \specel   {(7)}     {pressure (PMB)} \\
+ \specel   {(8)}     {relative humidity (RH)} \\
+ \specel   {(9)}     {wavelength (WL)} \\
+ \specel   {(10)}    {lapse rate (TLR)} \\
+ \specel   {(11,12)} {refraction constants A and B (radians)} \\
+ \specel   {(13)}    {longitude + eqn of equinoxes +
+                       ``sidereal $\Delta$UT'' (radians)} \\
+ \specel   {(14)}    {local apparent sidereal time (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item It is advisable to take great care with units, as even
+        unlikely values of the input parameters are accepted and
+        processed in accordance with the models used.
+  \item The DATE argument is UTC expressed as an MJD.  This is,
+        strictly speaking, wrong, because of leap seconds.  However,
+        as long as the $\Delta$UT and the UTC are consistent there
+        are no difficulties, except during a leap second.  In this
+        case, the start of the 61st second of the final minute should
+        begin a new MJD day and the old pre-leap $\Delta$UT should
+        continue to be used.  As the 61st second completes, the MJD
+        should revert to the start of the day as, simultaneously,
+        the $\Delta$UT changes by one second to its post-leap new value.
+  \item The $\Delta$UT (UT1$-$UTC) is tabulated in IERS circulars and
+        elsewhere.  It increases by exactly one second at the end of
+        each UTC leap second, introduced in order to keep $\Delta$UT
+        within $\pm$\tsec{0}{9}.  The ``sidereal $\Delta$UT'' which forms
+        part of AOPRMS(13) is the same quantity, but converted from solar
+        to sidereal seconds and expressed in radians.
+  \item IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.  The
+        longitude required by the present routine is {\bf east-positive},
+        in accordance with geographical convention (and right-handed).
+        In particular, note that the longitudes returned by the
+        sla\_OBS routine are west-positive (as in the {\it Astronomical
+        Almanac}\/ before 1984) and must be reversed in sign before use in
+        the present routine.
+  \item The polar coordinates XP,YP can be obtained from IERS
+        circulars and equivalent publications.  The
+        maximum amplitude is about \arcsec{0}{3}.  If XP,YP values
+        are unavailable, use XP=YP=0D0.  See page B60 of the 1988
+        {\it Astronomical Almanac}\/ for a definition of the two angles.
+  \item The height above sea level of the observing station, HM,
+        can be obtained from the {\it Astronomical Almanac}\/ (Section J
+        in the 1988 edition), or via the routine sla\_OBS.  If P,
+        the pressure in mB, is available, an adequate
+        estimate of HM can be obtained from the following expression:
+        \begin{quote}
+         {\tt HM=-29.3D0*TSL*LOG(P/1013.25D0)}
+        \end{quote}
+        where TSL is the approximate sea-level air temperature in degrees K
+        (see {\it Astrophysical Quantities}, C.W.Allen, 3rd~edition,
+        \S 52.)  Similarly, if the pressure P is not known,
+        it can be estimated from the height of the observing
+        station, HM as follows:
+        \begin{quote}
+         {\tt P=1013.25D0*EXP(-HM/(29.3D0*TSL))}
+        \end{quote}
+        Note, however, that the refraction is proportional to the
+        pressure and that an accurate P value is important for
+        precise work.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AOPPAT}{Update Appt-to-Obs Parameters}
+{
+ \action{Recompute the sidereal time in the apparent to observed place
+         star-independent parameter block.}
+ \call{CALL sla\_AOPPAT (DATE, AOPRMS)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{UTC date/time (Modified Julian Date, JD$-$2400000.5)} \\
+ \spec{AOPRMS}{D(14)}{star-independent apparent-to-observed parameters:} \\
+ \specel{(1-12)}{not required} \\
+ \specel{(13)}{longitude + eqn of equinoxes +
+               ``sidereal $\Delta$UT'' (radians)} \\
+ \specel{(14)}{not required}
+}
+\args{RETURNED}
+{
+ \spec{AOPRMS}{D(14)}{star-independent apparent-to-observed parameters:} \\
+ \specel{(1-13)}{not changed} \\
+ \specel{(14)}{local apparent sidereal time (radians)}
+}
+\anote{For more information, see sla\_AOPPA.}
+%-----------------------------------------------------------------------
+\routine{SLA\_AOPQK}{Quick Appt-to-Observed}
+{
+ \action{Quick apparent to observed place (but see Note~8, below).}
+ \call{CALL sla\_AOPQK (RAP, DAP, AOPRMS, AOB, ZOB, HOB, DOB, ROB)}
+}
+\args{GIVEN}
+{
+ \spec{RAP,DAP}{D}{geocentric apparent \radec\ (radians)} \\
+ \spec{AOPRMS}{D(14)}{star-independent apparent-to-observed parameters:} \\
+ \specel{(1)}{geodetic latitude (radians)} \\
+ \specel{(2,3)}{sine and cosine of geodetic latitude} \\
+ \specel{(4)}{magnitude of diurnal aberration vector} \\
+ \specel{(5)}{height (metres)} \\
+ \specel{(6)}{ambient temperature (degrees K)} \\
+ \specel{(7)}{pressure (mB)} \\
+ \specel{(8)}{relative humidity (0\,--\,1)} \\
+ \specel{(9)}{wavelength ($\mu{\rm m}$)} \\
+ \specel{(10)}{lapse rate (degrees K per metre)} \\
+ \specel{(11,12)}{refraction constants A and B (radians)} \\
+ \specel{(13)}{longitude + eqn of equinoxes +
+               ``sidereal $\Delta$UT'' (radians)} \\
+ \specel{(14)}{local apparent sidereal time (radians)}
+}
+\args{RETURNED}
+{
+ \spec{AOB}{D}{observed azimuth (radians: N=0, E=$90^{\circ}$)} \\
+ \spec{ZOB}{D}{observed zenith distance (radians)} \\
+ \spec{HOB}{D}{observed Hour Angle (radians)} \\
+ \spec{DOB}{D}{observed Declination (radians)} \\
+ \spec{ROB}{D}{observed Right Ascension (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine returns zenith distance rather than elevation
+        in order to reflect the fact that no allowance is made for
+        depression of the horizon.
+  \item The accuracy of the result is limited by the corrections for
+        refraction.  Providing the meteorological parameters are
+        known accurately and there are no gross local effects, the
+        predicted azimuth and elevation should be within about
+        \arcsec{0}{1} for $\zeta<70^{\circ}$.  Even
+        at a topocentric zenith distance of
+        $90^{\circ}$, the accuracy in elevation should be better than
+        1~arcminute;  useful results are available for a further
+        $3^{\circ}$, beyond which the sla\_REFRO routine returns a
+        fixed value of the refraction.  The complementary
+        routines sla\_AOP (or sla\_AOPQK) and sla\_OAP (or sla\_OAPQK)
+        are self-consistent to better than 1~microarcsecond all over
+        the celestial sphere.
+  \item It is advisable to take great care with units, as even
+        unlikely values of the input parameters are accepted and
+        processed in accordance with the models used.
+  \item {\it Apparent}\/ \radec\ means the geocentric apparent right ascension
+        and declination, which is obtained from a catalogue mean place
+        by allowing for space motion, parallax, precession, nutation,
+        annual aberration, and the Sun's gravitational lens effect.  For
+        star positions in the FK5 system ({\it i.e.}\ J2000), these effects can
+        be applied by means of the sla\_MAP {\it etc.}\ routines.  Starting from
+        other mean place systems, additional transformations will be
+        needed;  for example, FK4 ({\it i.e.}\ B1950) mean places would first
+        have to be converted to FK5, which can be done with the
+        sla\_FK425 {\it etc.}\ routines.
+  \item {\it Observed}\/ \azel\ means the position that would be seen by a
+        perfect theodolite located at the observer.  This is obtained
+        from the geocentric apparent \radec\ by allowing for Earth
+        orientation and diurnal aberration, rotating from equator
+        to horizon coordinates, and then adjusting for refraction.
+        The \hadec\ is obtained by rotating back into equatorial
+        coordinates, using the geodetic latitude corrected for polar
+        motion, and is the position that would be seen by a perfect
+        equatorial located at the observer and with its polar axis
+        aligned to the Earth's axis of rotation ({\it n.b.}\ not to the
+        refracted pole).  Finally, the $\alpha$ is obtained by subtracting
+        the {\it h}\/ from the local apparent ST.
+  \item To predict the required setting of a real telescope, the
+        observed place produced by this routine would have to be
+        adjusted for the tilt of the azimuth or polar axis of the
+        mounting (with appropriate corrections for mount flexures),
+        for non-perpendicularity between the mounting axes, for the
+        position of the rotator axis and the pointing axis relative
+        to it, for tube flexure, for gear and encoder errors, and
+        finally for encoder zero points.  Some telescopes would, of
+        course, exhibit other properties which would need to be
+        accounted for at the appropriate point in the sequence.
+  \item The star-independent apparent-to-observed-place parameters
+        in AOPRMS may be computed by means of the sla\_AOPPA routine.
+        If nothing has changed significantly except the time, the
+        sla\_AOPPAT routine may be used to perform the requisite
+        partial recomputation of AOPRMS.
+  \item The  ``sidereal $\Delta$UT'' which forms part of AOPRMS(13)
+        is UT1$-$UTC converted from solar to
+        sidereal seconds and expressed in radians.
+  \item At zenith distances beyond about $76^\circ$, the need for
+        special care with the corrections for refraction causes a
+        marked increase in execution time.  Moreover, the effect
+        gets worse with increasing zenith distance.  Adroit
+        programming in the calling application may allow the
+        problem to be reduced.  Prepare an alternative AOPRMS array,
+        computed for zero air-pressure;  this will disable the
+        refraction corrections and cause rapid execution.  Using
+        this AOPRMS array, a preliminary call to the present routine
+        will, depending on the application, produce a rough position
+        which may be enough to establish whether the full, slow
+        calculation (using the real AOPRMS array) is worthwhile.
+        For example, there would be no need for the full calculation
+        if the preliminary call had already established that the
+        source was well below the elevation limits for a particular
+        telescope.
+  \item The azimuths {\it etc.}\ used by the present routine are with
+        respect to the celestial pole.  Corrections to the terrestrial pole
+        can be computed using sla\_POLMO.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_ATMDSP}{Atmospheric Dispersion}
+{
+ \action{Apply atmospheric-dispersion adjustments to refraction coefficients.}
+ \call{CALL sla\_ATMDSP (TDK, PMB, RH, WL1, A1, B1, WL2, A2, B2)}
+}
+\args{GIVEN}
+{
+ \spec{TDK}{D}{ambient temperature at the observer (degrees K)} \\
+ \spec{PMB}{D}{pressure at the observer (mB)} \\
+ \spec{RH}{D}{relative humidity at the observer (range 0\,--\,1)} \\
+ \spec{WL1}{D}{base wavelength ($\mu{\rm m}$)} \\
+ \spec{A1}{D}{refraction coefficient A for wavelength WL1 (radians)} \\
+ \spec{B1}{D}{refraction coefficient B for wavelength WL1 (radians)} \\
+ \spec{WL2}{D}{wavelength for which adjusted A,B required ($\mu{\rm m}$)}
+}
+\args{RETURNED}
+{
+ \spec{A2}{D}{refraction coefficient A for wavelength WL2 (radians)} \\
+ \spec{B2}{D}{refraction coefficient B for wavelength WL2 (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item To use this routine, first call sla\_REFCO specifying WL1 as the
+        wavelength.  This yields refraction coefficients A1, B1, correct
+        for that wavelength.  Subsequently, calls to sla\_ATMDSP specifying
+        different wavelengths will produce new, slightly adjusted
+        refraction coefficients A2, B2, which apply to the specified wavelength.
+  \item Most of the atmospheric dispersion happens between $0.7\,\mu{\rm m}$
+        and the UV atmospheric cutoff, and the effect increases strongly
+        towards the UV end.  For this reason a blue reference wavelength
+        is recommended, for example $0.4\,\mu{\rm m}$.
+  \item The accuracy, for this set of conditions: \\[1pc]
+   \hspace*{5ex} \begin{tabular}{rcl}
+        height above sea level & ~ & 2000\,m \\
+                      latitude & ~ & $29^\circ$ \\
+                      pressure & ~ & 793\,mB \\
+                   temperature & ~ & $290^\circ$\,K \\
+                      humidity & ~ & 0.5 (50\%) \\
+                    lapse rate & ~ & $0.0065^\circ m^{-1}$ \\
+          reference wavelength & ~ & $0.4\,\mu{\rm m}$ \\
+                star elevation & ~ & $15^\circ$ \\
+                  \end{tabular}\\[1pc]
+        is about 2.5\,mas RMS between 0.3 and $1.0\,\mu{\rm m}$, and stays
+        within 4\,mas for the whole range longward of $0.3\,\mu{\rm m}$
+        (compared with a total dispersion from 0.3 to $20\,\mu{\rm m}$
+        of about \arcseci{11}).  These errors are typical for ordinary
+        conditions;  in extreme conditions values a few times this size
+        may occur.
+  \item If either wavelength exceeds $100\,\mu{\rm m}$, the radio case
+        is assumed and the returned refraction coefficients are the
+        same as the given ones.
+  \item The algorithm consists of calculation of the refractivity of the
+        air at the observer for the two wavelengths, using the methods
+        of the sla\_REFRO routine, and then scaling of the two refraction
+        coefficients according to classical refraction theory.  This
+        amounts to scaling the A coefficient in proportion to $(\mu-1)$ and
+        the B coefficient almost in the same ratio (see R.M.Green,
+        {\it Spherical Astronomy,}\/ Cambridge University Press, 1985).
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AV2M}{Rotation Matrix from Axial Vector}
+{
+ \action{Form the rotation matrix corresponding to a given axial vector
+         (single precision).}
+ \call{CALL sla\_AV2M (AXVEC, RMAT)}
+}
+\args{GIVEN}
+{
+ \spec{AXVEC}{R(3)}{axial vector (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RMAT}{R(3,3)}{rotation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A rotation matrix describes a rotation about some arbitrary axis.
+        The axis is called the {\it Euler axis}, and the angle through which the
+        reference frame rotates is called the Euler angle.  The axial
+        vector supplied to this routine has the same direction as the
+        Euler axis, and its magnitude is the Euler angle in radians.
+  \item If AXVEC is null, the unit matrix is returned.
+  \item The reference frame rotates clockwise as seen looking along
+        the axial vector from the origin.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_BEAR}{Direction Between Points on a Sphere}
+{
+ \action{Returns the bearing (position angle) of one point on a
+         sphere seen from another (single precision).}
+ \call{R~=~sla\_BEAR (A1, B1, A2, B2)}
+}
+\args{GIVEN}
+{
+ \spec{A1,B1}{R}{spherical coordinates of one point} \\
+ \spec{A2,B2}{R}{spherical coordinates of the other point}
+}
+\args{RETURNED}
+{
+ \spec{sla\_BEAR}{R}{bearing from first point to second}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The spherical coordinates are \radec,
+       $[\lambda,\phi]$ {\it etc.}, in radians.
+ \item The result is the bearing (position angle), in radians,
+       of point [A2,B2] as seen
+       from point [A1,B1].  It is in the range $\pm \pi$.  The sense
+       is such that if [A2,B2]
+       is a small distance due east of [A1,B1] the result
+       is about $+\pi/2$. Zero is returned
+       if the two points are coincident.
+ \item If either B-coordinate is outside the range $\pm\pi/2$, the
+       result may correspond to ``the long way round''.
+ \item The routine sla\_PAV performs an equivalent function except
+       that the points are specified in the form of Cartesian unit
+       vectors.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CAF2R}{Deg,Arcmin,Arcsec to Radians}
+{
+ \action{Convert degrees, arcminutes, arcseconds to radians
+         (single precision).}
+ \call{CALL sla\_CAF2R (IDEG, IAMIN, ASEC, RAD, J)}
+}
+\args{GIVEN}
+{
+ \spec{IDEG}{I}{degrees} \\
+ \spec{IAMIN}{I}{arcminutes} \\
+ \spec{ASEC}{R}{arcseconds}
+}
+\args{RETURNED}
+{
+ \spec{RAD}{R}{angle in radians} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 1 = IDEG outside range 0$-$359} \\
+ \spec{}{}{\hspace{1.5em} 2 = IAMIN outside range 0$-$59} \\
+ \spec{}{}{\hspace{1.5em} 3 = ASEC outside range 0$-$59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CALDJ}{Calendar Date to MJD}
+{
+ \action{Gregorian Calendar to Modified Julian Date, with century default.}
+ \call{CALL sla\_CALDJ (IY, IM, ID, DJM, J)}
+}
+\args{GIVEN}
+{
+ \spec{IY,IM,ID}{I}{year, month, day in Gregorian calendar}
+}
+\args{RETURNED}
+{
+ \spec{DJM}{D}{modified Julian Date (JD$-$2400000.5) for $0^{\rm h}$} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = bad year   (MJD not computed)} \\
+ \spec{}{}{\hspace{1.5em} 2 = bad month  (MJD not computed)} \\
+ \spec{}{}{\hspace{1.5em} 3 = bad day    (MJD computed)} \\
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine supports the {\it century default}\/ feature.
+        Acceptable years are:
+        \begin{itemize}
+         \item 00-49, interpreted as 2000\,--\,2049,
+         \item 50-99, interpreted as 1950\,--\,1999, and
+         \item 100 upwards, interpreted literally.
+        \end{itemize}
+        For 1-100AD use the routine sla\_CLDJ instead.
+  \item For year $n$BC use IY = $-(n-1)$.
+  \item When an invalid year or month is supplied (status J~=~1~or~2)
+        the MJD is {\bf not} computed.  When an invalid day is supplied
+        (status J~=~3) the MJD {\bf is} computed.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CALYD}{Calendar to Year, Day}
+{
+ \action{Gregorian calendar date to year and day in year, in a Julian
+         calendar aligned to the 20th/21st century Gregorian calendar,
+         with century default.}
+ \call{CALL sla\_CALYD (IY, IM, ID, NY, ND, J)}
+}
+\args{GIVEN}
+{
+ \spec{IY,IM,ID}{I}{year, month, day in Gregorian calendar:
+                    year may optionally omit the century}
+}
+\args{RETURNED}
+{
+ \spec{NY}{I}{year (re-aligned Julian calendar)} \\
+ \spec{ND}{I}{day in year (1 = January 1st)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em}  0 = OK} \\
+ \spec{}{}{\hspace{1.5em}  1 = bad year (before $-4711$)} \\
+ \spec{}{}{\hspace{1.5em}  2 = bad month} \\
+ \spec{}{}{\hspace{1.5em}  3 = bad day}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine supports the {\it century default}\/ feature.
+        Acceptable years are:
+        \begin{itemize}
+         \item 00-49, interpreted as 2000\,--\,2049,
+         \item 50-99, interpreted as 1950\,--\,1999, and
+         \item other years after -4712 , interpreted literally.
+        \end{itemize}
+        Use sla\_CLYD for years before 100AD.
+  \item The purpose of sla\_CALDJ is to support
+        sla\_EARTH, sla\_MOON and sla\_ECOR.
+  \item Between 1900~March~1 and 2100~February~28 it returns answers
+        which are consistent with the ordinary Gregorian calendar.
+        Outside this range there will be a discrepancy which increases
+        by one day for every non-leap century year.
+  \item When an invalid year or month is supplied (status J~=~1 or J~=~2)
+        the results are {\bf not} computed.  When a day is
+        supplied which is outside the conventional range (status J~=~3)
+        the results {\bf are} computed.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CC2S}{Cartesian to Spherical}
+{
+ \action{Cartesian coordinates to spherical coordinates (single precision).}
+ \call{CALL sla\_CC2S (V, A, B)}
+}
+\args{GIVEN}
+{
+ \spec{V}{R(3)}{\xyz\ vector}
+}
+\args{RETURNED}
+{
+ \spec{A,B}{R}{spherical coordinates in radians}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The spherical coordinates are longitude (+ve anticlockwise
+        looking from the +ve latitude pole) and latitude.  The
+        Cartesian coordinates are right handed, with the {\it x}-axis
+        at zero longitude and latitude, and the {\it z}-axis at the
+        +ve latitude pole.
+  \item If V is null, zero A and B are returned.
+  \item At either pole, zero A is returned.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CC62S}{Cartesian 6-Vector to Spherical}
+{
+ \action{Conversion of position \& velocity in Cartesian coordinates
+         to spherical coordinates (single precision).}
+ \call{CALL sla\_CC62S (V, A, B, R, AD, BD, RD)}
+}
+\args{GIVEN}
+{
+ \spec{V}{R(6)}{\xyzxyzd}
+}
+\args{RETURNED}
+{
+ \spec{A}{R}{longitude (radians) -- for example $\alpha$} \\
+ \spec{B}{R}{latitude (radians) -- for example $\delta$} \\
+ \spec{R}{R}{radial coordinate} \\
+ \spec{AD}{R}{longitude derivative (radians per unit time)} \\
+ \spec{BD}{R}{latitude derivative (radians per unit time)} \\
+ \spec{RD}{R}{radial derivative}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CD2TF}{Days to Hour,Min,Sec}
+{
+ \action{Convert an interval in days to hours, minutes, seconds
+         (single precision).}
+ \call{CALL sla\_CD2TF (NDP, DAYS, SIGN, IHMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of seconds} \\
+ \spec{DAYS}{R}{interval in days}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IHMSF}{I(4)}{hours, minutes, seconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size of
+        DAYS, the format of REAL floating-point numbers on the target
+        machine, and the risk of overflowing IHMSF(4).  For example,
+        on a VAX computer, for DAYS up to 1.0, the available floating-point
+        precision corresponds roughly to NDP=3.  This is well below
+        the ultimate limit of NDP=9 set by the capacity of the 32-bit
+        integer IHMSF(4).
+  \item The absolute value of DAYS may exceed 1.0.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where DAYS is very nearly 1.0 and rounds up to 24~hours,
+        by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+\end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CLDJ}{Calendar to MJD}
+{
+ \action{Gregorian Calendar to Modified Julian Date.}
+ \call{CALL sla\_CLDJ (IY, IM, ID, DJM, J)}
+}
+\args{GIVEN}
+{
+ \spec{IY,IM,ID}{I}{year, month, day in Gregorian calendar}
+}
+\args{RETURNED}
+{
+ \spec{DJM}{D}{modified Julian Date (JD$-$2400000.5) for $0^{\rm h}$} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = bad year} \\
+ \spec{}{}{\hspace{1.5em} 2 = bad month} \\
+ \spec{}{}{\hspace{1.5em} 3 = bad day}
+}
+\notes
+{
+ \begin{enumerate}
+  \item When an invalid year or month is supplied (status J~=~1~or~2)
+        the MJD is {\bf not} computed.  When an invalid day is supplied
+        (status J~=~3) the MJD {\bf is} computed.
+  \item The year must be $-$4699 ({\it i.e.}\ 4700BC) or later.
+        For year $n$BC use IY = $-(n-1)$.
+  \item An alternative to the present routine is sla\_CALDJ, which
+        accepts a year with the century missing.
+ \end{enumerate}
+}
+\aref{The algorithm is derived from that of Hatcher,
+      {\it Q.\,Jl.\,R.\,astr.\,Soc.}\ (1984) {\bf 25}, 53-55.}
+%-----------------------------------------------------------------------
+\routine{SLA\_CLYD}{Calendar to Year, Day}
+{
+ \action{Gregorian calendar date to year and day in year, in a Julian
+         calendar aligned to the 20th/21st century Gregorian calendar.}
+ \call{CALL sla\_CLYD (IY, IM, ID, NY, ND, J)}
+}
+\args{GIVEN}
+{
+ \spec{IY,IM,ID}{I}{year, month, day in Gregorian calendar}
+}
+\args{RETURNED}
+{
+ \spec{NY}{I}{year (re-aligned Julian calendar)} \\
+ \spec{ND}{I}{day in year (1 = January 1st)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em}  0 = OK} \\
+ \spec{}{}{\hspace{1.5em}  1 = bad year (before $-4711$)} \\
+ \spec{}{}{\hspace{1.5em}  2 = bad month} \\
+ \spec{}{}{\hspace{1.5em}  3 = bad day}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The purpose of sla\_CLYD is to support sla\_EARTH,
+        sla\_MOON and sla\_ECOR.
+  \item Between 1900~March~1 and 2100~February~28 it returns answers
+        which are consistent with the ordinary Gregorian calendar.
+        Outside this range there will be a discrepancy which increases
+        by one day for every non-leap century year.
+  \item When an invalid year or month is supplied (status J~=~1 or J~=~2)
+        the results are {\bf not} computed.  When a day is
+        supplied which is outside the conventional range (status J~=~3)
+        the results {\bf are} computed.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CR2AF}{Radians to Deg,Arcmin,Arcsec}
+{
+ \action{Convert an angle in radians to degrees, arcminutes,
+         arcseconds (single precision).}
+ \call{CALL sla\_CR2AF (NDP, ANGLE, SIGN, IDMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of arcseconds} \\
+ \spec{ANGLE}{R}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IDMSF}{I(4)}{degrees, arcminutes, arcseconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size of
+        ANGLE, the format of REAL floating-point numbers on the target
+        machine, and the risk of overflowing IDMSF(4).  For example,
+        on a VAX computer, for ANGLE up to $2\pi$, the available floating-point
+        precision corresponds roughly to NDP=3.  This is well below
+        the ultimate limit of NDP=9 set by the capacity of the 32-bit
+        integer IHMSF(4).
+  \item The absolute value of ANGLE may exceed $2\pi$.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where ANGLE is very nearly $2\pi$ and rounds up to $360^{\circ}$,
+        by testing for IDMSF(1)=360 and setting IDMSF(1-4) to zero.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CR2TF}{Radians to Hour,Min,Sec}
+{
+ \action{Convert an angle in radians to hours, minutes, seconds
+         (single precision).}
+ \call{CALL sla\_CR2TF (NDP, ANGLE, SIGN, IHMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of seconds} \\
+ \spec{ANGLE}{R}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IHMSF}{I(4)}{hours, minutes, seconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size of
+        ANGLE, the format of REAL floating-point numbers on the target
+        machine, and the risk of overflowing IHMSF(4).  For example,
+        on a VAX computer, for ANGLE up to $2\pi$, the available floating-point
+        precision corresponds roughly to NDP=3.  This is well below
+        the ultimate limit of NDP=9 set by the capacity of the 32-bit
+        integer IHMSF(4).
+  \item The absolute value of ANGLE may exceed $2\pi$.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where ANGLE is very nearly $2\pi$ and rounds up to 24~hours,
+        by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+\end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CS2C}{Spherical to Cartesian}
+{
+ \action{Spherical coordinates to Cartesian coordinates (single precision).}
+ \call{CALL sla\_CS2C (A, B, V)}
+}
+\args{GIVEN}
+{
+ \spec{A,B}{R}{spherical coordinates in radians: \radec\ {\it etc.}}
+}
+\args{RETURNED}
+{
+ \spec{V}{R(3)}{\xyz\ unit vector}
+}
+\anote{The spherical coordinates are longitude (+ve anticlockwise
+       looking from the +ve latitude pole) and latitude.  The
+       Cartesian coordinates are right handed, with the {\it x}-axis
+       at zero longitude and latitude, and the {\it z}-axis at the
+       +ve latitude pole.}
+%-----------------------------------------------------------------------
+\routine{SLA\_CS2C6}{Spherical Pos/Vel to Cartesian}
+{
+ \action{Conversion of position \& velocity in spherical coordinates
+         to Cartesian coordinates (single precision).}
+ \call{CALL sla\_CS2C6 (A, B, R, AD, BD, RD, V)}
+}
+\args{GIVEN}
+{
+ \spec{A}{R}{longitude (radians) -- for example $\alpha$} \\
+ \spec{B}{R}{latitude (radians) -- for example $\delta$} \\
+ \spec{R}{R}{radial coordinate} \\
+ \spec{AD}{R}{longitude derivative (radians per unit time)} \\
+ \spec{BD}{R}{latitude derivative (radians per unit time)} \\
+ \spec{RD}{R}{radial derivative}
+}
+\args{RETURNED}
+{
+ \spec{V}{R(6)}{\xyzxyzd}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CTF2D}{Hour,Min,Sec to Days}
+{
+ \action{Convert hours, minutes, seconds to days (single precision).}
+ \call{CALL sla\_CTF2D (IHOUR, IMIN, SEC, DAYS, J)}
+}
+\args{GIVEN}
+{
+ \spec{IHOUR}{I}{hours} \\
+ \spec{IMIN}{I}{minutes} \\
+ \spec{SEC}{R}{seconds}
+}
+\args{RETURNED}
+{
+ \spec{DAYS}{R}{interval in days} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = IHOUR outside range 0-23} \\
+ \spec{}{}{\hspace{1.5em} 2 = IMIN outside range 0-59} \\
+ \spec{}{}{\hspace{1.5em} 3 = SEC outside range 0-59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CTF2R}{Hour,Min,Sec to Radians}
+{
+ \action{Convert hours, minutes, seconds to radians (single precision).}
+ \call{CALL sla\_CTF2R (IHOUR, IMIN, SEC, RAD, J)}
+}
+\args{GIVEN}
+{
+ \spec{IHOUR}{I}{hours} \\
+ \spec{IMIN}{I}{minutes} \\
+ \spec{SEC}{R}{seconds}
+}
+\args{RETURNED}
+{
+ \spec{RAD}{R}{angle in radians} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = IHOUR outside range 0-23} \\
+ \spec{}{}{\hspace{1.5em} 2 = IMIN outside range 0-59} \\
+ \spec{}{}{\hspace{1.5em} 3 = SEC outside range 0-59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DAF2R}{Deg,Arcmin,Arcsec to Radians}
+{
+ \action{Convert degrees, arcminutes, arcseconds to radians
+  (double precision).}
+ \call{CALL sla\_DAF2R (IDEG, IAMIN, ASEC, RAD, J)}
+}
+\args{GIVEN}
+{
+ \spec{IDEG}{I}{degrees} \\
+ \spec{IAMIN}{I}{arcminutes} \\
+ \spec{ASEC}{D}{arcseconds}
+}
+\args{RETURNED}
+{
+ \spec{RAD}{D}{angle in radians} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 1 = IDEG outside range 0$-$359} \\
+ \spec{}{}{\hspace{1.5em} 2 = IAMIN outside range 0$-$59} \\
+ \spec{}{}{\hspace{1.5em} 3 = ASEC outside range 0$-$59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DAFIN}{Sexagesimal character string to angle}
+{
+ \action{Decode a free-format sexagesimal string (degrees, arcminutes,
+         arcseconds) into a double precision floating point
+         number (radians).}
+ \call{CALL sla\_DAFIN (STRING, NSTRT, DRESLT, JF)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C*(*)}{string containing deg, arcmin, arcsec fields} \\
+ \spec{NSTRT}{I}{pointer to start of decode (beginning of STRING = 1)}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{advanced past the decoded angle} \\
+ \spec{DRESLT}{D}{angle in radians} \\
+ \spec{JF}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em}   0 = OK} \\
+ \spec{}{}{\hspace{0.7em} $+1$ = default, DRESLT unchanged (note 2)} \\
+ \spec{}{}{\hspace{0.7em} $-1$ = bad degrees (note 3)} \\
+ \spec{}{}{\hspace{0.7em} $-2$ = bad arcminutes (note 3)} \\
+ \spec{}{}{\hspace{0.7em} $-3$ = bad arcseconds (note 3)} \\
+}
+\goodbreak
+\setlength{\oldspacing}{\topsep}
+\setlength{\topsep}{0.3ex}
+\begin{description}
+ \item [EXAMPLE]: \\ [1.5ex]
+  \begin{tabular}{p{7em}p{15em}p{12em}}
+   {\it argument} & {\it before} & {\it after} \\ \\
+   STRING & $'$\verb*}-57 17 44.806  12 34 56.7}$'$ & unchanged \\
+   NSTRT & 1 & 16 ({\it i.e.}\ pointing to 12...) \\
+   RESLT & - & $-1.00000${\tt D0} \\
+   JF & - & 0
+  \end{tabular}
+ \item A further call to sla\_DAFIN, without adjustment of NSTRT, will
+       decode the second angle, \dms{12}{34}{56}{7}.
+\end{description}
+\setlength{\topsep}{\oldspacing}
+\notes
+{
+ \begin{enumerate}
+  \item The first three ``fields'' in STRING are degrees, arcminutes,
+   arcseconds, separated by spaces or commas.  The degrees field
+   may be signed, but not the others.  The decoding is carried
+   out by the sla\_DFLTIN routine and is free-format.
+  \item Successive fields may be absent, defaulting to zero.  For
+   zero status, the only combinations allowed are degrees alone,
+   degrees and arcminutes, and all three fields present.  If all
+   three fields are omitted, a status of +1 is returned and DRESLT is
+   unchanged.  In all other cases DRESLT is changed.
+  \item Range checking:
+   \begin{itemize}
+    \item The degrees field is not range checked.  However, it is
+     expected to be integral unless the other two fields are absent.
+    \item The arcminutes field is expected to be 0-59, and integral if
+     the arcseconds field is present.  If the arcseconds field
+     is absent, the arcminutes is expected to be 0-59.9999...
+    \item The arcseconds field is expected to be 0-59.9999...
+    \item Decoding continues even when a check has failed.  Under these
+     circumstances the field takes the supplied value, defaulting to
+     zero, and the result DRESLT is computed and returned.
+   \end{itemize}
+   \item Further fields after the three expected ones are not treated as
+    an error.  The pointer NSTRT is left in the correct state for
+    further decoding with the present routine or with sla\_DFLTIN
+    {\it etc}.  See the example, above.
+   \item If STRING contains hours, minutes, seconds instead of
+    degrees {\it etc},
+    or if the required units are turns (or days) instead of radians,
+    the result DRESLT should be multiplied as follows: \\ [1.5ex]
+    \begin{tabular}{p{6em}p{5em}p{18em}}
+    {\it for STRING} & {\it to obtain} & {\it multiply DRESLT by} \\ \\
+    ${\circ}$~~\raisebox{-0.7ex}{$'$}~~\raisebox{-0.7ex}{$''$}
+     & radians & $1.0${\tt D0} \\
+    ${\circ}$~~\raisebox{-0.7ex}{$'$}~~\raisebox{-0.7ex}{$''$}
+     & turns & $1/{2 \pi} = 0.1591549430918953358${\tt D0} \\
+    h m s & radians & $15.0${\tt D0} \\
+    h m s & days & $15/{2\pi} = 2.3873241463784300365${\tt D0}
+   \end{tabular}
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_DAT}{TAI$-$UTC}
+{
+ \action{Increment to be applied to Coordinated Universal Time UTC to give
+         International Atomic Time TAI.}
+ \call{D~=~sla\_DAT (UTC)}
+}
+\args{GIVEN}
+{
+ \spec{UTC}{D}{UTC date as a modified JD (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DAT}{D}{TAI$-$UTC in seconds}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The UTC is specified to be a date rather than a time to indicate
+       that care needs to be taken not to specify an instant which lies
+       within a leap second.  Though in most cases UTC can include the
+       fractional part, correct behaviour on the day of a leap second
+       can be guaranteed only up to the end of the second
+       $23^{\rm h}\,59^{\rm m}\,59^{\rm s}$.
+ \item UTC began at 1960 January 1.  To specify a UTC prior to this
+       date would be meaningless;  in such cases the parameters
+       for the year 1960 are used by default.
+ \item This routine has to be updated on each occasion that a
+       leap second is announced, and programs using it relinked.
+       Refer to the program source code for information on when the
+       most recent leap second was added.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DAV2M}{Rotation Matrix from Axial Vector}
+{
+ \action{Form the rotation matrix corresponding to a given axial vector
+         (double precision).}
+ \call{CALL sla\_DAV2M (AXVEC, RMAT)}
+}
+\args{GIVEN}
+{
+ \spec{AXVEC}{D(3)}{axial vector (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RMAT}{D(3,3)}{rotation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A rotation matrix describes a rotation about some arbitrary axis.
+        The axis is called the {\it Euler axis}, and the angle through which the
+        reference frame rotates is called the {\it Euler angle}.  The axial
+        vector supplied to this routine has the same direction as the
+        Euler axis, and its magnitude is the Euler angle in radians.
+  \item If AXVEC is null, the unit matrix is returned.
+  \item The reference frame rotates clockwise as seen looking along
+        the axial vector from the origin.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DBEAR}{Direction Between Points on a Sphere}
+{
+ \action{Returns the bearing (position angle) of one point on a
+         sphere relative to another (double precision).}
+ \call{D~=~sla\_DBEAR (A1, B1, A2, B2)}
+}
+\args{GIVEN}
+{
+ \spec{A1,B1}{D}{spherical coordinates of one point} \\
+ \spec{A2,B2}{D}{spherical coordinates of the other point}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DBEAR}{D}{bearing from first point to second}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The spherical coordinates are \radec,
+       $[\lambda,\phi]$ {\it etc.}, in radians.
+ \item The result is the bearing (position angle), in radians,
+       of point [A2,B2] as seen
+       from point [A1,B1].  It is in the range $\pm \pi$.  The sense
+       is such that if [A2,B2]
+       is a small distance due east of [A1,B1] the result
+       is about $+\pi/2$. Zero is returned
+       if the two points are coincident.
+ \item If either B-coordinate is outside the range $\pm\pi/2$, the
+       result may correspond to ``the long way round''.
+ \item The routine sla\_DPAV performs an equivalent function except
+       that the points are specified in the form of Cartesian unit
+       vectors.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DBJIN}{Decode String to B/J Epoch (DP)}
+{
+ \action{Decode a character string into a DOUBLE PRECISION number,
+         with special provision for Besselian and Julian epochs.
+         The string syntax is as for sla\_DFLTIN, prefixed by
+         an optional `B' or `J'.}
+ \call{CALL sla\_DBJIN (STRING, NSTRT, DRESLT, J1, J2)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C}{string containing field to be decoded} \\
+ \spec{NSTRT}{I}{pointer to first character of field in string}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{incremented past the decoded field} \\
+ \spec{DRESLT}{D}{result} \\
+ \spec{J1}{I}{DFLTIN status:} \\
+ \spec{}{}{\hspace{0.7em} $-$1 = $-$OK} \\
+ \spec{}{}{\hspace{1.5em}   0 = +OK} \\
+ \spec{}{}{\hspace{1.5em}   1 = null field} \\
+ \spec{}{}{\hspace{1.5em}   2 = error} \\
+ \spec{J2}{I}{syntax flag:} \\
+ \spec{}{}{\hspace{1.5em}   0 = normal DFLTIN syntax} \\
+ \spec{}{}{\hspace{1.5em}   1 = `B' or `b'} \\
+ \spec{}{}{\hspace{1.5em}   2 = `J' or `j'}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The purpose of the syntax extensions is to help cope with mixed
+        FK4 and FK5 data, allowing fields such as `B1950' or `J2000'
+        to be decoded.
+  \item In addition to the syntax accepted by sla\_DFLTIN,
+        the following two extensions are recognized by sla\_DBJIN:
+        \begin{enumerate}
+         \item A valid non-null field preceded by the character `B'
+               (or `b') is accepted.
+         \item A valid non-null field preceded by the character `J'
+               (or `j') is accepted.
+         \end{enumerate}
+  \item The calling program is told of the `B' or `J' through an
+        supplementary status argument.  The rest of
+        the arguments are as for sla\_DFLTIN.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DC62S}{Cartesian 6-Vector to Spherical}
+{
+ \action{Conversion of position \& velocity in Cartesian coordinates
+         to spherical coordinates (double precision).}
+ \call{CALL sla\_DC62S (V, A, B, R, AD, BD, RD)}
+}
+\args{GIVEN}
+{
+ \spec{V}{D(6)}{\xyzxyzd}
+}
+\args{RETURNED}
+{
+ \spec{A}{D}{longitude (radians)} \\
+ \spec{B}{D}{latitude (radians)} \\
+ \spec{R}{D}{radial coordinate} \\
+ \spec{AD}{D}{longitude derivative (radians per unit time)} \\
+ \spec{BD}{D}{latitude derivative (radians per unit time)} \\
+ \spec{RD}{D}{radial derivative}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DCC2S}{Cartesian to Spherical}
+{
+ \action{Cartesian coordinates to spherical coordinates (double precision).}
+ \call{CALL sla\_DCC2S (V, A, B)}
+}
+\args{GIVEN}
+{
+ \spec{V}{D(3)}{\xyz\ vector}
+}
+\args{RETURNED}
+{
+ \spec{A,B}{D}{spherical coordinates in radians}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The spherical coordinates are longitude (+ve anticlockwise
+        looking from the +ve latitude pole) and latitude.  The
+        Cartesian coordinates are right handed, with the {\it x}-axis
+        at zero longitude and latitude, and the {\it z}-axis at the
+        +ve latitude pole.
+  \item If V is null, zero A and B are returned.
+  \item At either pole, zero A is returned.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DCMPF}{Interpret Linear Fit}
+{
+ \action{Decompose an \xy\ linear fit into its constituent parameters:
+         zero points, scales, nonperpendicularity and orientation.}
+ \call{CALL sla\_DCMPF (COEFFS,XZ,YZ,XS,YS,PERP,ORIENT)}
+}
+\args{GIVEN}
+{
+ \spec{COEFFS}{D(6)}{transformation coefficients (see note)}
+}
+\args{RETURNED}
+{
+ \spec{XZ}{D}{{\it x} zero point} \\
+ \spec{YZ}{D}{{\it y} zero point} \\
+ \spec{XS}{D}{{\it x} scale} \\
+ \spec{YS}{D}{{\it y} scale} \\
+ \spec{PERP}{D}{nonperpendicularity (radians)} \\
+ \spec{ORIENT}{D}{orientation (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The model relates two sets of \xy\ coordinates as follows.
+        Naming the six elements of COEFFS $a,b,c,d,e$ \& $f$,
+        the model transforms coordinates $[x_{1},y_{1}\,]$ into coordinates
+        $[x_{2},y_{2}\,]$ as follows:
+        \begin{verse}
+         $x_{2} = a + bx_{1} + cy_{1}$ \\
+         $y_{2} = d + ex_{1} + fy_{1}$
+        \end{verse}
+        The sla\_DCMPF routine decomposes this transformation
+        into four steps:
+        \begin{enumerate}
+        \item Zero points:
+              \begin{verse}
+               $x' = x_{1} + {\rm XZ}$ \\
+               $y' = y_{1} + {\rm YZ}$
+              \end{verse}
+        \item Scales:
+              \begin{verse}
+               $x'' = x' {\rm XS}$ \\
+               $y'' = y' {\rm YS}$
+              \end{verse}
+        \item Nonperpendicularity:
+              \begin{verse}
+               $x''' = + x'' \cos {\rm PERP}/2 + y'' \sin {\rm PERP}/2$ \\
+               $y''' = + x'' \sin {\rm PERP}/2 + y'' \cos {\rm PERP}/2$
+              \end{verse}
+        \item Orientation:
+              \begin{verse}
+               $x_{2} = + x''' \cos {\rm ORIENT} +
+                          y''' \sin {\rm ORIENT}$ \\
+               $y_{2} = - x''' \sin {\rm ORIENT} +
+                          y''' \cos {\rm ORIENT}$
+              \end{verse}
+        \end{enumerate}
+  \item See also sla\_FITXY, sla\_PXY, sla\_INVF, sla\_XY2XY.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DCS2C}{Spherical to Cartesian}
+{
+ \action{Spherical coordinates to Cartesian coordinates (double precision).}
+ \call{CALL sla\_DCS2C (A, B, V)}
+}
+\args{GIVEN}
+{
+ \spec{A,B}{D}{spherical coordinates in radians: \radec\ {\it etc.}}
+}
+\args{RETURNED}
+{
+ \spec{V}{D(3)}{\xyz\ unit vector}
+}
+\anote{The spherical coordinates are longitude (+ve anticlockwise
+       looking from the +ve latitude pole) and latitude.  The
+       Cartesian coordinates are right handed, with the {\it x}-axis
+       at zero longitude and latitude, and the {\it z}-axis at the
+       +ve latitude pole.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DD2TF}{Days to Hour,Min,Sec}
+{
+ \action{Convert an interval in days into hours, minutes, seconds
+         (double precision).}
+ \call{CALL sla\_DD2TF (NDP, DAYS, SIGN, IHMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of seconds} \\
+ \spec{DAYS}{D}{interval in days}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IHMSF}{I(4)}{hours, minutes, seconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size
+        of DAYS, the format of DOUBLE PRECISION floating-point numbers
+        on the target machine, and the risk of overflowing IHMSF(4).
+        For example, on a VAX computer, for DAYS up to 1D0, the available
+        floating-point precision corresponds roughly to NDP=12.  However,
+        the practical limit is NDP=9, set by the capacity of the 32-bit
+        integer IHMSF(4).
+  \item The absolute value of DAYS may exceed 1D0.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where DAYS is very nearly 1D0 and rounds up to 24~hours,
+        by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+\end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DE2H}{$h,\delta$ to Az,El}
+{
+ \action{Equatorial to horizon coordinates
+         (double precision).}
+ \call{CALL sla\_DE2H (HA, DEC, PHI, AZ, EL)}
+}
+\args{GIVEN}
+{
+ \spec{HA}{D}{hour angle (radians)} \\
+ \spec{DEC}{D}{declination (radians)} \\
+ \spec{PHI}{D}{latitude (radians)}
+}
+\args{RETURNED}
+{
+ \spec{AZ}{D}{azimuth (radians)} \\
+ \spec{EL}{D}{elevation (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Azimuth is returned in the range $0\!-\!2\pi$;  north is zero,
+        and east is $+\pi/2$.  Elevation is returned in the range
+        $\pm\pi$.
+  \item The latitude must be geodetic.  In critical applications,
+        corrections for polar motion should be applied.
+  \item In some applications it will be important to specify the
+        correct type of hour angle and declination in order to
+        produce the required type of azimuth and elevation.  In
+        particular, it may be important to distinguish between
+        elevation as affected by refraction, which would
+        require the {\it observed} \hadec, and the elevation
+        {\it in vacuo}, which would require the {\it topocentric}
+        \hadec.
+        If the effects of diurnal aberration can be neglected, the
+        {\it apparent} \hadec\ may be used instead of the topocentric
+        \hadec.
+  \item No range checking of arguments is carried out.
+  \item In applications which involve many such calculations, rather
+        than calling the present routine it will be more efficient to
+        use inline code, having previously computed fixed terms such
+        as sine and cosine of latitude, and (for tracking a star)
+        sine and cosine of declination.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DEULER}{Euler Angles to Rotation Matrix}
+{
+ \action{Form a rotation matrix from the Euler angles -- three
+         successive rotations about specified Cartesian axes
+         (double precision).}
+ \call{CALL sla\_DEULER (ORDER, PHI, THETA, PSI, RMAT)}
+}
+\args{GIVEN}
+{
+ \spec{ORDER}{C}{specifies about which axes the rotations occur} \\
+ \spec{PHI}{D}{1st rotation (radians)} \\
+ \spec{THETA}{D}{2nd rotation (radians)} \\
+ \spec{PSI}{D}{3rd rotation (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RMAT}{D(3,3)}{rotation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+ \item A rotation is positive when the reference frame rotates
+       anticlockwise as seen looking towards the origin from the
+       positive region of the specified axis.
+ \item The characters of ORDER define which axes the three successive
+       rotations are about.  A typical value is `ZXZ', indicating that
+       RMAT is to become the direction cosine matrix corresponding to
+       rotations of the reference frame through PHI radians about the
+       old {\it z}-axis, followed by THETA radians about the resulting
+       {\it x}-axis,
+       then PSI radians about the resulting {\it z}-axis.
+ \item The axis names can be any of the following, in any order or
+       combination:  X, Y, Z, uppercase or lowercase, 1, 2, 3.  Normal
+       axis labelling/numbering conventions apply;  the {\it xyz} ($\equiv123$)
+       triad is right-handed.  Thus, the `ZXZ' example given above
+       could be written `zxz' or `313' (or even `ZxZ' or `3xZ').  ORDER
+       is terminated by length or by the first unrecognized character.
+       Fewer than three rotations are acceptable, in which case the later
+       angle arguments are ignored.  Zero rotations produces a unit RMAT.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DFLTIN}{Decode a Double Precision Number}
+{
+ \action{Convert free-format input into double precision floating point.}
+ \call{CALL sla\_DFLTIN (STRING, NSTRT, DRESLT, JFLAG)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C}{string containing number to be decoded} \\
+ \spec{NSTRT}{I}{pointer to where decoding is to commence} \\
+ \spec{DRESLT}{D}{current value of result}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{advanced to next number} \\
+ \spec{DRESLT}{D}{result} \\
+ \spec{JFLAG}{I}{status: $-$1~=~$-$OK, 0~=~+OK, 1~=~null result, 2~=~error}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The reason sla\_DFLTIN has separate `OK' status values
+       for + and $-$ is to enable minus zero to be detected.
+       This is of crucial importance
+       when decoding mixed-radix numbers.  For example, an angle
+       expressed as degrees, arcminutes and arcseconds may have a
+       leading minus sign but a zero degrees field.
+ \item A TAB is interpreted as a space, and lowercase characters are
+       interpreted as uppercase.  {\it n.b.}\ The test for TAB is
+       ASCII-specific.
+ \item The basic format is the sequence of fields $\pm n.n x \pm n$,
+       where $\pm$ is a sign
+       character `+' or `$-$', $n$ means a string of decimal digits,
+       `.' is a decimal point, and $x$, which indicates an exponent,
+       means `D' or `E'.  Various combinations of these fields can be
+       omitted, and embedded blanks are permissible in certain places.
+ \item Spaces:
+       \begin{itemize}
+       \item Leading spaces are ignored.
+       \item Embedded spaces are allowed only after +, $-$, D or E,
+             and after the decimal point if the first sequence of
+             digits is absent.
+       \item Trailing spaces are ignored;  the first signifies
+             end of decoding and subsequent ones are skipped.
+       \end{itemize}
+ \item Delimiters:
+       \begin{itemize}
+       \item Any character other than +,$-$,0-9,.,D,E or space may be
+             used to signal the end of the number and terminate decoding.
+       \item Comma is recognized by sla\_DFLTIN as a special case; it
+             is skipped, leaving the pointer on the next character.  See
+             13, below.
+       \item Decoding will in all cases terminate if end of string
+             is reached.
+       \end{itemize}
+ \item Both signs are optional.  The default is +.
+ \item The mantissa $n.n$ defaults to unity.
+ \item The exponent $x\!\pm\!n$ defaults to `D0'.
+ \item The strings of decimal digits may be of any length.
+ \item The decimal point is optional for whole numbers.
+ \item A {\it null result}\/ occurs when the string of characters
+       being decoded does not begin with +,$-$,0-9,.,D or E, or
+       consists entirely of spaces.  When this condition is
+       detected, JFLAG is set to 1 and DRESLT is left untouched.
+ \item NSTRT = 1 for the first character in the string.
+ \item On return from sla\_DFLTIN, NSTRT is set ready for the next
+       decode -- following trailing blanks and any comma.  If a
+       delimiter other than comma is being used, NSTRT must be
+       incremented before the next call to sla\_DFLTIN, otherwise
+       all subsequent calls will return a null result.
+ \item Errors (JFLAG=2) occur when:
+       \begin{itemize}
+       \item a +, $-$, D or E is left unsatisfied; or
+       \item the decimal point is present without at least
+             one decimal digit before or after it; or
+       \item an exponent more than 100 has been presented.
+       \end{itemize}
+ \item When an error has been detected, NSTRT is left
+       pointing to the character following the last
+       one used before the error came to light.  This
+       may be after the point at which a more sophisticated
+       program could have detected the error.  For example,
+       sla\_DFLTIN does not detect that `1D999' is unacceptable
+       (on a computer where this is so) until the entire number
+       has been decoded.
+ \item Certain highly unlikely combinations of mantissa and
+       exponent can cause arithmetic faults during the
+       decode, in some cases despite the fact that they
+       together could be construed as a valid number.
+ \item Decoding is left to right, one pass.
+ \item See also sla\_FLOTIN and sla\_INTIN.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DH2E}{Az,El to $h,\delta$}
+{
+ \action{Horizon to equatorial coordinates
+         (double precision).}
+ \call{CALL sla\_DH2E (AZ, EL, PHI, HA, DEC)}
+}
+\args{GIVEN}
+{
+ \spec{AZ}{D}{azimuth (radians)} \\
+ \spec{EL}{D}{elevation (radians)} \\
+ \spec{PHI}{D}{latitude (radians)}
+}
+\args{RETURNED}
+{
+ \spec{HA}{D}{hour angle (radians)} \\
+ \spec{DEC}{D}{declination (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The sign convention for azimuth is north zero, east $+\pi/2$.
+  \item HA is returned in the range $\pm\pi$.  Declination is returned
+        in the range $\pm\pi$.
+  \item The latitude is (in principle) geodetic.  In critical
+        applications, corrections for polar motion should be applied
+        (see sla\_POLMO).
+  \item In some applications it will be important to specify the
+        correct type of elevation in order to produce the required
+        type of \hadec.  In particular, it may be important to
+        distinguish between the elevation as affected by refraction,
+        which will yield the {\it observed} \hadec, and the elevation
+        {\it in vacuo}, which will yield the {\it topocentric}
+        \hadec.  If the
+        effects of diurnal aberration can be neglected, the
+        topocentric \hadec\ may be used as an approximation to the
+        {\it apparent} \hadec.
+  \item No range checking of arguments is carried out.
+  \item In applications which involve many such calculations, rather
+        than calling the present routine it will be more efficient to
+        use inline code, having previously computed fixed terms such
+        as sine and cosine of latitude.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DIMXV}{Apply 3D Reverse Rotation}
+{
+ \action{Multiply a 3-vector by the inverse of a rotation
+         matrix (double precision).}
+ \call{CALL sla\_DIMXV (DM, VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{DM}{D(3,3)}{rotation matrix} \\
+ \spec{VA}{D(3)}{vector to be rotated}
+}
+\args{RETURNED}
+{
+ \spec{VB}{D(3)}{result vector}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine performs the operation:
+        \begin{verse}
+         {\bf b} = {\bf M}$^{T}\cdot${\bf a}
+        \end{verse}
+        where {\bf a} and {\bf b} are the 3-vectors VA and VB
+        respectively, and  {\bf M} is the $3\times3$ matrix DM.
+  \item The main function of this routine is apply an inverse
+        rotation;  under these circumstances, ${\bf \rm M}$ is
+        {\it orthogonal}, with its inverse the same as its transpose.
+  \item To comply with the ANSI Fortran 77 standard, VA and VB must
+        {\bf not} be the same array.  The routine is, in fact, coded
+        so as to work properly on the VAX and many other systems even
+        if this rule is violated, something that is {\bf not}, however,
+        recommended.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DJCAL}{MJD to Gregorian for Output}
+{
+ \action{Modified Julian Date to Gregorian Calendar Date, expressed
+         in a form convenient for formatting messages (namely
+         rounded to a specified precision, and with the fields
+         stored in a single array).}
+ \call{CALL sla\_DJCAL (NDP, DJM, IYMDF, J)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of days in fraction} \\
+ \spec{DJM}{D}{modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{IYMDF}{I(4)}{year, month, day, fraction in Gregorian calendar} \\
+ \spec{J}{I}{status:  nonzero = out of range}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Any date after 4701BC March 1 is accepted.
+  \item NDP should be 4 or less to avoid overflow on machines which
+        use 32-bit integers.
+ \end{enumerate}
+}
+\aref{The algorithm is derived from that of Hatcher,
+      {\it Q.\,Jl.\,R.\,astr.\,Soc.}\ (1984) {\bf 25}, 53-55.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DJCL}{MJD to Year,Month,Day,Frac}
+{
+ \action{Modified Julian Date to Gregorian year, month, day,
+         and fraction of a day.}
+ \call{CALL sla\_DJCL (DJM, IY, IM, ID, FD, J)}
+}
+\args{GIVEN}
+{
+ \spec{DJM}{D}{modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{IY}{I}{year} \\
+ \spec{IM}{I}{month} \\
+ \spec{ID}{I}{day} \\
+ \spec{FD}{D}{fraction of day} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{0.7em} $-$1 = unacceptable date (before 4701BC March 1)}
+}
+\aref{The algorithm is derived from that of Hatcher,
+      {\it Q.\,Jl.\,R.\,astr.\,Soc.}\ (1984) {\bf 25}, 53-55.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DM2AV}{Rotation Matrix to Axial Vector}
+{
+ \action{From a rotation matrix, determine the corresponding axial vector
+        (double precision).}
+ \call{CALL sla\_DM2AV (RMAT, AXVEC)}
+}
+\args{GIVEN}
+{
+ \spec{RMAT}{D(3,3)}{rotation matrix}
+}
+\args{RETURNED}
+{
+ \spec{AXVEC}{D(3)}{axial vector (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A rotation matrix describes a rotation about some arbitrary axis.
+        The axis is called the {\it Euler axis}, and the angle through
+        which the reference frame rotates is called the {\it Euler angle}.
+        The {\it axial vector}\/ returned by this routine has the same
+        direction as the Euler axis, and its magnitude is the Euler angle
+        in radians.
+  \item The magnitude and direction of the axial vector can be separated
+        by means of the routine sla\_DVN.
+  \item The reference frame rotates clockwise as seen looking along
+        the axial vector from the origin.
+  \item If RMAT is null, so is the result.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DMAT}{Solve Simultaneous Equations}
+{
+ \action{Matrix inversion and solution of simultaneous equations
+         (double precision).}
+ \call{CALL sla\_DMAT (N, A, Y, D, JF, IW)}
+}
+\args{GIVEN}
+{
+ \spec{N}{I}{number of unknowns} \\
+ \spec{A}{D(N,N)}{matrix} \\
+ \spec{Y}{D(N)}{vector}
+}
+\args{RETURNED}
+{
+ \spec{A}{D(N,N)}{matrix inverse} \\
+ \spec{Y}{D(N)}{solution} \\
+ \spec{D}{D}{determinant} \\
+ \spec{JF}{I}{singularity flag: 0=OK} \\
+ \spec{IW}{I(N)}{workspace}
+}
+\notes
+{
+ \begin{enumerate}
+  \item For the set of $n$ simultaneous linear equations in $n$ unknowns:
+        \begin{verse}
+         {\bf A}$\cdot${\bf y} = {\bf x}
+        \end{verse}
+        where:
+        \begin{itemize}
+         \item {\bf A} is a non-singular $n \times n$ matrix,
+         \item {\bf y} is the vector of $n$ unknowns, and
+         \item {\bf x} is the known vector,
+        \end{itemize}
+        sla\_DMAT computes:
+        \begin{itemize}
+         \item the inverse of matrix {\bf A},
+         \item the determinant of matrix {\bf A}, and
+         \item the vector of $n$ unknowns {\bf y}.
+        \end{itemize}
+        Argument N is the order $n$, A (given) is the matrix {\bf A},
+        Y (given) is the vector {\bf x} and Y (returned)
+        is the vector {\bf y}.
+        The argument A (returned) is the inverse matrix {\bf A}$^{-1}$,
+        and D is {\it det}\/({\bf A}).
+  \item JF is the singularity flag.  If the matrix is non-singular,
+        JF=0 is returned.  If the matrix is singular, JF=$-$1
+        and D=0D0 are returned.  In the latter case, the contents
+        of array A on return are undefined.
+  \item The algorithm is Gaussian elimination with partial pivoting.
+        This method is very fast;  some much slower algorithms can give
+        better accuracy, but only by a small factor.
+  \item This routine replaces the obsolete sla\_DMATRX.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DMOON}{Approx Moon Pos/Vel}
+{
+ \action{Approximate geocentric position and velocity of the Moon
+         (double precision).}
+ \call{CALL sla\_DMOON (DATE, PV)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (loosely ET) as a Modified Julian Date (JD$-$2400000.5)
+}
+}
+\args{RETURNED}
+{
+ \spec{PV}{D(6)}{Moon \xyzxyzd, mean equator and equinox
+                 of date (AU, AU~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine is a full implementation of the algorithm
+        published by Meeus (see reference).
+  \item Meeus quotes accuracies of \arcseci{10} in longitude,
+        \arcseci{3} in latitude and \arcsec{0}{2} arcsec in HP
+        (equivalent to about 20~km in distance).  Comparison with
+        JPL~DE200 over the interval 1960-2025 gives RMS errors of
+        \arcsec{3}{7} and 83~mas/hour in longitude,
+        \arcsec{2}{3} arcsec and 48~mas/hour in latitude,
+        11~km and 81~mm/s in distance.
+        The maximum errors over the same interval are
+        \arcseci{18} and \arcsec{0}{50}/hour in longitude,
+        \arcseci{11} and \arcsec{0}{24}/hour in latitude,
+        40~km and 0.29~m/s in distance.
+  \item The original algorithm is expressed in terms of the obsolete
+        timescale {\it Ephemeris Time}.  Either TDB or TT can be used,
+        but not UT without incurring significant errors (\arcseci{30} at
+        the present time) due to the Moon's \arcsec{0}{5}/s movement.
+  \item The algorithm is based on pre IAU 1976 standards.  However,
+        the result has been moved onto the new (FK5) equinox, an
+        adjustment which is in any case much smaller than the
+        intrinsic accuracy of the procedure.
+  \item Velocity is obtained by a complete analytical differentiation
+        of the Meeus model.
+ \end{enumerate}
+}
+\aref{Meeus, {\it l'Astronomie}, June 1984, p348.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DMXM}{Multiply $3\times3$ Matrices}
+{
+ \action{Product of two $3\times3$ matrices (double precision).}
+ \call{CALL sla\_DMXM (A, B, C)}
+}
+\args{GIVEN}
+{
+ \spec{A}{D(3,3)}{matrix {\bf A}} \\
+ \spec{B}{D(3,3)}{matrix {\bf B}}
+}
+\args{RETURNED}
+{
+ \spec{C}{D(3,3)}{matrix result: {\bf A}$\times${\bf B}}
+}
+\anote{To comply with the ANSI Fortran 77 standard, A, B and C must
+       be different arrays.  The routine is, in fact, coded
+       so as to work properly on the VAX and many other systems even
+       if this rule is violated, something that is {\bf not}, however,
+       recommended.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DMXV}{Apply 3D Rotation}
+{
+ \action{Multiply a 3-vector by a rotation matrix (double precision).}
+ \call{CALL sla\_DMXV (DM, VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{DM}{D(3,3)}{rotation matrix} \\
+ \spec{VA}{D(3)}{vector to be rotated}
+}
+\args{RETURNED}
+{
+ \spec{VB}{D(3)}{result vector}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine performs the operation:
+        \begin{verse}
+           {\bf b} = {\bf M}$\cdot${\bf a}
+        \end{verse}
+        where {\bf a} and {\bf b} are the 3-vectors VA and VB
+        respectively, and {\bf M} is the $3\times3$ matrix DM.
+  \item The main function of this routine is apply a
+        rotation;  under these circumstances, {\bf M} is a
+        {\it proper real orthogonal}\/ matrix.
+  \item To comply with the ANSI Fortran 77 standard, VA and VB must
+        {\bf not} be the same array.  The routine is, in fact, coded
+        so as to work properly on the VAX and many other systems even
+        if this rule is violated, something that is {\bf not}, however,
+        recommended.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DPAV}{Position-Angle Between Two Directions}
+{
+ \action{Returns the bearing (position angle) of one celestial
+         direction with respect to another (double precision).}
+ \call{D~=~sla\_DPAV (V1, V2)}
+}
+\args{GIVEN}
+{
+ \spec{V1}{D(3)}{direction cosines of one point} \\
+ \spec{V2}{D(3)}{directions cosines of the other point}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DPAV}{D}{position-angle of 2nd point with respect to 1st}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The coordinate frames correspond to \radec,
+       $[\lambda,\phi]$ {\it etc.}.
+ \item The result is the bearing (position angle), in radians,
+       of point V2 as seen
+       from point V1.  It is in the range $\pm \pi$.  The sense
+       is such that if V2
+       is a small distance due east of V1 the result
+       is about $+\pi/2$. Zero is returned
+       if the two points are coincident.
+ \item The routine sla\_DBEAR performs an equivalent function except
+       that the points are specified in the form of spherical coordinates.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_DR2AF}{Radians to Deg,Min,Sec,Frac}
+{
+ \action{Convert an angle in radians to degrees, arcminutes, arcseconds,
+         fraction (double precision).}
+ \call{CALL sla\_DR2AF (NDP, ANGLE, SIGN, IDMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of arcseconds} \\
+ \spec{ANGLE}{D}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IDMSF}{I(4)}{degrees, arcminutes, arcseconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size
+        of ANGLE, the format of DOUBLE~PRECISION floating-point numbers
+        on the target machine, and the risk of overflowing IDMSF(4).
+        For example, on a VAX computer, for ANGLE up to $2\pi$, the available
+        floating-point precision corresponds roughly to NDP=12.  However,
+        the practical limit is NDP=9, set by the capacity of the 32-bit
+        integer IDMSF(4).
+  \item The absolute value of ANGLE may exceed $2\pi$.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where ANGLE is very nearly $2\pi$ and rounds up to $360^{\circ}$,
+        by testing for IDMSF(1)=360 and setting IDMSF(1-4) to zero.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DR2TF}{Radians to Hour,Min,Sec,Frac}
+{
+ \action{Convert an angle in radians to hours, minutes, seconds,
+         fraction (double precision).}
+ \call{CALL sla\_DR2TF (NDP, ANGLE, SIGN, IHMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of seconds} \\
+ \spec{ANGLE}{D}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IHMSF}{I(4)}{hours, minutes, seconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size
+        of ANGLE, the format of DOUBLE PRECISION floating-point numbers
+        on the target machine, and the risk of overflowing IHMSF(4).
+        For example, on a VAX computer, for ANGLE up to $2\pi$, the available
+        floating-point precision corresponds roughly to NDP=12.  However,
+        the practical limit is NDP=9, set by the capacity of the 32-bit
+        integer IHMSF(4).
+  \item The absolute value of ANGLE may exceed $2\pi$.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where ANGLE is very nearly $2\pi$ and rounds up to 24~hours,
+        by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DRANGE}{Put Angle into Range $\pm\pi$}
+{
+ \action{Normalize an angle into the range $\pm\pi$ (double precision).}
+ \call{D~=~sla\_DRANGE (ANGLE)}
+}
+\args{GIVEN}
+{
+ \spec{ANGLE}{D}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DRANGE}{D}{ANGLE expressed in the range $\pm\pi$.}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DRANRM}{Put Angle into Range $0\!-\!2\pi$}
+{
+ \action{Normalize an angle into the range $0\!-\!2\pi$
+         (double precision).}
+ \call{D~=~sla\_DRANRM (ANGLE)}
+}
+\args{GIVEN}
+{
+ \spec{ANGLE}{D}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DRANRM}{D}{ANGLE expressed in the range $0\!-\!2\pi$}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DS2C6}{Spherical Pos/Vel to Cartesian}
+{
+ \action{Conversion of position \& velocity in spherical coordinates
+         to Cartesian coordinates (double precision).}
+ \call{CALL sla\_DS2C6 (A, B, R, AD, BD, RD, V)}
+}
+\args{GIVEN}
+{
+ \spec{A}{D}{longitude (radians) -- for example $\alpha$} \\
+ \spec{B}{D}{latitude (radians) -- for example $\delta$} \\
+ \spec{R}{D}{radial coordinate} \\
+ \spec{AD}{D}{longitude derivative (radians per unit time)} \\
+ \spec{BD}{D}{latitude derivative (radians per unit time)} \\
+ \spec{RD}{D}{radial derivative}
+}
+\args{RETURNED}
+{
+ \spec{V}{D(6)}{\xyzxyzd}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DS2TP}{Spherical to Tangent Plane}
+{
+ \action{Projection of spherical coordinates onto the tangent plane
+         (double precision).}
+ \call{CALL sla\_DS2TP (RA, DEC, RAZ, DECZ, XI, ETA, J)}
+}
+\args{GIVEN}
+{
+ \spec{RA,DEC}{D}{spherical coordinates of star (radians)} \\
+ \spec{RAZ,DECZ}{D}{spherical coordinates of tangent point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{XI,ETA}{D}{tangent plane coordinates (radians)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK, star on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 1 = error, star too far from axis} \\
+ \spec{}{}{\hspace{1.5em} 2 = error, antistar on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 3 = error, antistar too far from axis}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_DV2TP is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DSEP}{Angle Between 2 Points on Sphere}
+{
+ \action{Angle between two points on a sphere (double precision).}
+ \call{D~=~sla\_DSEP (A1, B1, A2, B2)}
+}
+\args{GIVEN}
+{
+ \spec{A1,B1}{D}{spherical coordinates of one point (radians)} \\
+ \spec{A2,B2}{D}{spherical coordinates of the other point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DSEP}{D}{angle between [A1,B1] and [A2,B2] in radians}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The spherical coordinates are right ascension and declination,
+        longitude and latitude, {\it etc.}, in radians.
+  \item The result is always positive.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DT}{Approximate ET minus UT}
+{
+ \action{Estimate $\Delta$T, the offset between dynamical time
+         and Universal Time, for a given historical epoch.}
+ \call{D~=~sla\_DT (EPOCH)}
+}
+\args{GIVEN}
+{
+ \spec{EPOCH}{D}{(Julian) epoch ({\it e.g.}\ 1850D0)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DT}{D}{approximate ET$-$UT (after 1984, TT$-$UT1) in seconds}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Depending on the epoch, one of three parabolic approximations
+        is used:
+\begin{tabbing}
+xx \= xxxxxxxxxxxxxxxxxx \= \kill
+\> before AD 979 \> Stephenson \& Morrison's 390 BC to AD 948 model \\
+\> AD 979 to AD 1708 \> Stephenson \& Morrison's AD 948 to AD 1600 model \\
+\> after AD 1708 \> McCarthy \& Babcock's post-1650 model
+\end{tabbing}
+        The breakpoints are chosen to ensure continuity:  they occur
+        at places where the adjacent models give the same answer as
+        each other.
+  \item The accuracy is modest, with errors of up to $20^{\rm s}$ during
+        the interval since 1650, rising to perhaps $30^{\rm m}$
+        by 1000~BC.  Comparatively accurate values from AD~1600
+        are tabulated in
+        the {\it Astronomical Almanac}\/ (see section K8 of the 1995
+        edition).
+  \item The use of {\tt DOUBLE PRECISION} for both argument and result is
+        simply for compatibility with other SLALIB time routines.
+  \item The models used are based on a lunar tidal acceleration value
+        of \arcsec{-26}{00} per century.
+ \end{enumerate}
+}
+\aref{Seidelmann, P.K.\ (ed), 1992.  {\it Explanatory
+      Supplement to the Astronomical Almanac,}\/ ISBN~0-935702-68-7.
+      This contains references to the papers by Stephenson \& Morrison
+      and by McCarthy \& Babcock which describe the models used here.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTF2D}{Hour,Min,Sec to Days}
+{
+ \action{Convert hours, minutes, seconds to days (double precision).}
+ \call{CALL sla\_DTF2D (IHOUR, IMIN, SEC, DAYS, J)}
+}
+\args{GIVEN}
+{
+ \spec{IHOUR}{I}{hours} \\
+ \spec{IMIN}{I}{minutes} \\
+ \spec{SEC}{D}{seconds}
+}
+\args{RETURNED}
+{
+ \spec{DAYS}{D}{interval in days} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = IHOUR outside range 0-23} \\
+ \spec{}{}{\hspace{1.5em} 2 = IMIN outside range 0-59} \\
+ \spec{}{}{\hspace{1.5em} 3 = SEC outside range 0-59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTF2R}{Hour,Min,Sec to Radians}
+{
+ \action{Convert hours, minutes, seconds to radians (double precision).}
+ \call{CALL sla\_DTF2R (IHOUR, IMIN, SEC, RAD, J)}
+}
+\args{GIVEN}
+{
+ \spec{IHOUR}{I}{hours} \\
+ \spec{IMIN}{I}{minutes} \\
+ \spec{SEC}{D}{seconds}
+}
+\args{RETURNED}
+{
+ \spec{RAD}{D}{angle in radians} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = IHOUR outside range 0-23} \\
+ \spec{}{}{\hspace{1.5em} 2 = IMIN outside range 0-59} \\
+ \spec{}{}{\hspace{1.5em} 3 = SEC outside range 0-59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTP2S}{Tangent Plane to Spherical}
+{
+ \action{Transform tangent plane coordinates into spherical
+         coordinates (double precision)}
+ \call{CALL sla\_DTP2S (XI, ETA, RAZ, DECZ, RA, DEC)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{D}{tangent plane rectangular coordinates (radians)} \\
+ \spec{RAZ,DECZ}{D}{spherical coordinates of tangent point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RA,DEC}{D}{spherical coordinates (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_DTP2V is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTP2V}{Tangent Plane to Direction Cosines}
+{
+ \action{Given the tangent-plane coordinates of a star and the direction
+         cosines of the tangent point, determine the direction cosines
+         of the star
+         (double precision).}
+ \call{CALL sla\_DTP2V (XI, ETA, V0, V)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{D}{tangent plane coordinates of star (radians)} \\
+ \spec{V0}{D(3)}{direction cosines of tangent point}
+}
+\args{RETURNED}
+{
+ \spec{V}{D(3)}{direction cosines of star}
+}
+\notes
+{
+ \begin{enumerate}
+  \item If vector V0 is not of unit length, the returned vector V will
+        be wrong.
+  \item If vector V0 points at a pole, the returned vector V will be
+        based on the arbitrary assumption that $\alpha=0$ at
+        the tangent point.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_DTP2S.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTPS2C}{Plate centre from $\xi,\eta$ and $\alpha,\delta$}
+{
+ \action{From the tangent plane coordinates of a star of known \radec,
+        determine the \radec\ of the tangent point (double precision)}
+ \call{CALL sla\_DTPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{D}{tangent plane rectangular coordinates (radians)} \\
+ \spec{RA,DEC}{D}{spherical coordinates (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RAZ1,DECZ1}{D}{spherical coordinates of tangent point,
+                      solution 1} \\
+ \spec{RAZ2,DECZ2}{D}{spherical coordinates of tangent point,
+                      solution 2} \\
+ \spec{N}{I}{number of solutions:} \\
+ \spec{}{}{\hspace{1em} 0 = no solutions returned  (note 2)} \\
+ \spec{}{}{\hspace{1em} 1 = only the first solution is useful (note 3)} \\
+ \spec{}{}{\hspace{1em} 2 = there are two useful solutions (note 3)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The RAZ1 and RAZ2 values returned are in the range $0\!-\!2\pi$.
+  \item Cases where there is no solution can only arise near the poles.
+        For example, it is clearly impossible for a star at the pole
+        itself to have a non-zero $\xi$ value, and hence it is
+        meaningless to ask where the tangent point would have to be
+        to bring about this combination of $\xi$ and $\delta$.
+  \item Also near the poles, cases can arise where there are two useful
+        solutions.  The argument N indicates whether the second of the
+        two solutions returned is useful.  N\,=\,1
+        indicates only one useful solution, the usual case;  under
+        these circumstances, the second solution corresponds to the
+        ``over-the-pole'' case, and this is reflected in the values
+        of RAZ2 and DECZ2 which are returned.
+  \item The DECZ1 and DECZ2 values returned are in the range $\pm\pi$,
+        but in the ordinary, non-pole-crossing, case, the range is
+        $\pm\pi/2$.
+  \item RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2 are all in radians.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_DTPV2C is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTPV2C}{Plate centre from $\xi,\eta$ and $x,y,z$}
+{
+ \action{From the tangent plane coordinates of a star of known
+         direction cosines, determine the direction cosines
+         of the tangent point (double precision)}
+ \call{CALL sla\_DTPV2C (XI, ETA, V, V01, V02, N)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{D}{tangent plane coordinates of star (radians)} \\
+ \spec{V}{D(3)}{direction cosines of star}
+}
+\args{RETURNED}
+{
+ \spec{V01}{D(3)}{direction cosines of tangent point, solution 1} \\
+ \spec{V01}{D(3)}{direction cosines of tangent point, solution 2} \\
+ \spec{N}{I}{number of solutions:} \\
+ \spec{}{}{\hspace{1em} 0 = no solutions returned  (note 2)} \\
+ \spec{}{}{\hspace{1em} 1 = only the first solution is useful (note 3)} \\
+ \spec{}{}{\hspace{1em} 2 = there are two useful solutions (note 3)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The vector V must be of unit length or the result will be wrong.
+  \item Cases where there is no solution can only arise near the poles.
+        For example, it is clearly impossible for a star at the pole
+        itself to have a non-zero XI value.
+  \item Also near the poles, cases can arise where there are two useful
+        solutions.  The argument N indicates whether the second of the
+        two solutions returned is useful.
+        N\,=\,1
+        indicates only one useful solution, the usual case;  under these
+        circumstances, the second solution can be regarded as valid if
+        the vector V02 is interpreted as the ``over-the-pole'' case.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_DTPS2C.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTT}{TT minus UTC}
+{
+ \action{Compute $\Delta$TT, the increment to be applied to
+         Coordinated Universal Time UTC to give
+         Terrestrial Time TT.}
+ \call{D~=~sla\_DTT (DJU)}
+}
+\args{GIVEN}
+{
+ \spec{DJU}{D}{UTC date as a modified JD (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DTT}{D}{TT$-$UTC in seconds}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The UTC is specified to be a date rather than a time to indicate
+        that care needs to be taken not to specify an instant which lies
+        within a leap second.  Though in most cases UTC can include the
+        fractional part, correct behaviour on the day of a leap second
+        can be guaranteed only up to the end of the second
+        $23^{\rm h}\,59^{\rm m}\,59^{\rm s}$.
+  \item Pre 1972 January 1 a fixed value of 10 + ET$-$TAI is returned.
+  \item TT is one interpretation of the defunct timescale
+        {\it Ephemeris Time}, ET.
+  \item See also the routine sla\_DT, which roughly estimates ET$-$UT for
+        historical epochs.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DV2TP}{Direction Cosines to Tangent Plane}
+{
+ \action{Given the direction cosines of a star and of the tangent point,
+         determine the star's tangent-plane coordinates
+         (double precision).}
+ \call{CALL sla\_DV2TP (V, V0, XI, ETA, J)}
+}
+\args{GIVEN}
+{
+ \spec{V}{D(3)}{direction cosines of star} \\
+ \spec{V0}{D(3)}{direction cosines of tangent point}
+}
+\args{RETURNED}
+{
+ \spec{XI,ETA}{D}{tangent plane coordinates (radians)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK, star on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 1 = error, star too far from axis} \\
+ \spec{}{}{\hspace{1.5em} 2 = error, antistar on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 3 = error, antistar too far from axis}
+}
+\notes
+{
+ \begin{enumerate}
+  \item If vector V0 is not of unit length, or if vector V is of zero
+        length, the results will be wrong.
+  \item If V0 points at a pole, the returned $\xi,\eta$
+        will be based on the
+        arbitrary assumption that $\alpha=0$ at the tangent point.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_DS2TP.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DVDV}{Scalar Product}
+{
+ \action{Scalar product of two 3-vectors (double precision).}
+ \call{D~=~sla\_DVDV (VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{VA}{D(3)}{first vector} \\
+ \spec{VB}{D(3)}{second vector}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DVDV}{D}{scalar product VA.VB}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DVN}{Normalize Vector}
+{
+ \action{Normalize a 3-vector, also giving the modulus (double precision).}
+ \call{CALL sla\_DVN (V, UV, VM)}
+}
+\args{GIVEN}
+{
+ \spec{V}{D(3)}{vector}
+}
+\args{RETURNED}
+{
+ \spec{UV}{D(3)}{unit vector in direction of V} \\
+ \spec{VM}{D}{modulus of V}
+}
+\anote{If the modulus of V is zero, UV is set to zero as well.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DVXV}{Vector Product}
+{
+ \action{Vector product of two 3-vectors (double precision).}
+ \call{CALL sla\_DVXV (VA, VB, VC)}
+}
+\args{GIVEN}
+{
+ \spec{VA}{D(3)}{first vector} \\
+ \spec{VB}{D(3)}{second vector}
+}
+\args{RETURNED}
+{
+ \spec{VC}{D(3)}{vector product VA$\times$VB}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_E2H}{$h,\delta$ to Az,El}
+{
+ \action{Equatorial to horizon coordinates
+         (single precision).}
+ \call{CALL sla\_DE2H (HA, DEC, PHI, AZ, EL)}
+}
+\args{GIVEN}
+{
+ \spec{HA}{R}{hour angle (radians)} \\
+ \spec{DEC}{R}{declination (radians)} \\
+ \spec{PHI}{R}{latitude (radians)}
+}
+\args{RETURNED}
+{
+ \spec{AZ}{R}{azimuth (radians)} \\
+ \spec{EL}{R}{elevation (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Azimuth is returned in the range $0\!-\!2\pi$;  north is zero,
+        and east is $+\pi/2$.  Elevation is returned in the range
+        $\pm\pi$.
+  \item The latitude must be geodetic.  In critical applications,
+        corrections for polar motion should be applied.
+  \item In some applications it will be important to specify the
+        correct type of hour angle and declination in order to
+        produce the required type of azimuth and elevation.  In
+        particular, it may be important to distinguish between
+        elevation as affected by refraction, which would
+        require the {\it observed} \hadec, and the elevation
+        {\it in vacuo}, which would require the {\it topocentric}
+        \hadec.
+        If the effects of diurnal aberration can be neglected, the
+        {\it apparent} \hadec\ may be used instead of the topocentric
+        \hadec.
+  \item No range checking of arguments is carried out.
+  \item In applications which involve many such calculations, rather
+        than calling the present routine it will be more efficient to
+        use inline code, having previously computed fixed terms such
+        as sine and cosine of latitude, and (for tracking a star)
+        sine and cosine of declination.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EARTH}{Approx Earth Pos/Vel}
+{
+ \action{Approximate heliocentric position and velocity of the Earth
+         (single precision).}
+ \call{CALL sla\_EARTH (IY, ID, FD, PV)}
+}
+\args{GIVEN}
+{
+ \spec{IY}{I}{year} \\
+ \spec{ID}{I}{day in year (1 = Jan 1st)} \\
+ \spec{FD}{R}{fraction of day}
+}
+\args{RETURNED}
+{
+ \spec{PV}{R(6)}{Earth \xyzxyzd\ (AU, AU~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The date and time is TDB (loosely ET) in a Julian calendar
+        which has been aligned to the ordinary Gregorian
+        calendar for the interval 1900~March~1 to 2100~February~28.
+        The year and day can be obtained by calling sla\_CALYD or
+        sla\_CLYD.
+  \item The Earth heliocentric 6-vector is referred to the
+        FK4 mean equator and equinox of date.
+  \item Maximum/RMS errors 1950-2050:
+        \begin{itemize}
+         \item 13/5~$\times10^{-5}$~AU = 19200/7600~km in position
+         \item 47/26~$\times10^{-10}$~AU~s$^{-1}$ =
+               0.0070/0.0039~km~s$^{-1}$ in speed
+        \end{itemize}
+  \item More accurate results are obtainable with the routine sla\_EVP.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_ECLEQ}{Ecliptic to Equatorial}
+{
+ \action{Transformation from ecliptic longitude and latitude to
+         J2000.0 \radec.}
+ \call{CALL sla\_ECLEQ (DL, DB, DATE, DR, DD)}
+}
+\args{GIVEN}
+{
+ \spec{DL,DB}{D}{ecliptic longitude and latitude
+                          (mean of date, IAU 1980 theory, radians)} \\
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date
+                                             (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{DR,DD}{D}{J2000.0 mean \radec\ (radians)}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_ECMAT}{Form $\alpha,\delta\rightarrow\lambda,\beta$ Matrix}
+{
+ \action{Form the equatorial to ecliptic rotation matrix (IAU 1980 theory).}
+ \call{CALL sla\_ECMAT (DATE, RMAT)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date
+                                           (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{RMAT}{D(3,3)}{rotation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item RMAT is matrix {\bf M} in the expression
+        {\bf v}$_{ecl}$~=~{\bf M}$\cdot${\bf v}$_{equ}$.
+  \item The equator, equinox and ecliptic are mean of date.
+ \end{enumerate}
+}
+\aref{Murray, C.A., {\it Vectorial Astrometry}, section 4.3.}
+%-----------------------------------------------------------------------
+\routine{SLA\_ECOR}{RV \& Time Corrns to Sun}
+{
+ \action{Component of Earth orbit velocity and heliocentric
+         light time in a given direction.}
+ \call{CALL sla\_ECOR (RM, DM, IY, ID, FD, RV, TL)}
+}
+\args{GIVEN}
+{
+ \spec{RM,DM}{R}{mean \radec\ of date (radians)} \\
+ \spec{IY}{I}{year} \\
+ \spec{ID}{I}{day in year (1 = Jan 1st)} \\
+ \spec{FD}{R}{fraction of day}
+}
+\args{RETURNED}
+{
+ \spec{RV}{R}{component of Earth orbital velocity (km~s$^{-1}$)} \\
+ \spec{TL}{R}{component of heliocentric light time (s)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The date and time is TDB (loosely ET) in a Julian calendar
+        which has been aligned to the ordinary Gregorian
+        calendar for the interval 1900 March 1 to 2100 February 28.
+        The year and day can be obtained by calling sla\_CALYD or
+        sla\_CLYD.
+  \item Sign convention:
+        \begin{itemize}
+         \item The velocity component is +ve when the
+               Earth is receding from
+               the given point on the sky.
+         \item The light time component is +ve
+               when the Earth lies between the Sun and
+               the given point on the sky.
+        \end{itemize}
+ \item Accuracy:
+       \begin{itemize}
+        \item The velocity component is usually within 0.004~km~s$^{-1}$
+              of the correct value and is never in error by more than
+              0.007~km~s$^{-1}$.
+        \item The error in light time correction is about
+              \tsec{0}{03} at worst,
+              but is usually better than \tsec{0}{01}.
+       \end{itemize}
+       For applications requiring higher accuracy, see the sla\_EVP routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EG50}{B1950 $\alpha,\delta$ to Galactic}
+{
+ \action{Transformation from B1950.0 FK4 equatorial coordinates to
+         IAU 1958 galactic coordinates.}
+ \call{CALL sla\_EG50 (DR, DD, DL, DB)}
+}
+\args{GIVEN}
+{
+ \spec{DR,DD}{D}{B1950.0 \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal\ (radians)}
+}
+\anote{The equatorial coordinates are B1950.0 FK4.  Use the
+       routine sla\_EQGAL if conversion from J2000.0 FK5 coordinates
+       is required.}
+\aref{Blaauw {\it et al.}, 1960, {\it Mon.Not.R.astr.Soc.},
+      {\bf 121}, 123.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EL2UE}{Conventional to Universal Elements}
+{
+ \action{Transform conventional osculating orbital elements
+         into ``universal'' form.}
+ \call{CALL sla\_EL2UE (\vtop{
+         \hbox{DATE, JFORM, EPOCH, ORBINC, ANODE,}
+         \hbox{PERIH, AORQ, E, AORL, DM,}
+         \hbox{U, JSTAT)}}}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{epoch (TT MJD) of osculation (Note~3)} \\
+ \spec{JFORM}{I}{choice of element set (1-3; Note~6)} \\
+ \spec{EPOCH}{D}{epoch of elements ($t_0$ or $T$, TT MJD)} \\
+ \spec{ORBINC}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH}{D}{longitude or argument of perihelion
+                            ($\varpi$ or $\omega$,} \\
+ \spec{}{}{\hspace{1.5em} radians)} \\
+ \spec{AORQ}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E}{D}{eccentricity ($e$)} \\
+ \spec{AORL}{D}{mean anomaly or longitude
+                               ($M$ or $L$, radians,} \\
+ \spec{}{}{\hspace{1.5em} JFORM=1,2 only)} \\
+ \spec{DM}{D}{daily motion ($n$, radians, JFORM=1 only)}
+}
+\args{RETURNED}
+{
+ \spec{U}{D(13)}{universal orbital elements (Note~1)} \\
+ \specel {(1)}     {combined mass ($M+m$)} \\
+ \specel {(2)}     {total energy of the orbit ($\alpha$)} \\
+ \specel {(3)}     {reference (osculating) epoch ($t_0$)} \\
+ \specel {(4-6)}   {position at reference epoch (${\rm \bf r}_0$)} \\
+ \specel {(7-9)}   {velocity at reference epoch (${\rm \bf v}_0$)} \\
+ \specel {(10)}    {heliocentric distance at reference epoch} \\
+ \specel {(11)}    {${\rm \bf r}_0.{\rm \bf v}_0$} \\
+ \specel {(12)}    {date ($t$)} \\
+ \specel {(13)}    {universal eccentric anomaly ($\psi$) of date,
+                    approx} \\ \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{1.95em}       0 = OK} \\
+ \spec{}{}{\hspace{1.2em}  $-$1 = illegal JFORM} \\
+ \spec{}{}{\hspace{1.2em}   $-$2 = illegal E} \\
+ \spec{}{}{\hspace{1.2em}   $-$3 = illegal AORQ} \\
+ \spec{}{}{\hspace{1.2em}   $-$4 = illegal DM} \\
+ \spec{}{}{\hspace{1.2em}   $-$5 = numerical error}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The ``universal'' elements are those which define the orbit for
+        the purposes of the method of universal variables (see reference).
+        They consist of the combined mass of the two bodies, an epoch,
+        and the position and velocity vectors (arbitrary reference frame)
+        at that epoch.  The parameter set used here includes also various
+        quantities that can, in fact, be derived from the other
+        information.  This approach is taken to avoiding unnecessary
+        computation and loss of accuracy.  The supplementary quantities
+        are (i)~$\alpha$, which is proportional to the total energy of the
+        orbit, (ii)~the heliocentric distance at epoch,
+        (iii)~the outwards component of the velocity at the given epoch,
+        (iv)~an estimate of $\psi$, the ``universal eccentric anomaly'' at a
+        given date and (v)~that date.
+  \item The companion routine is sla\_UE2PV.  This takes the set of numbers
+        that the present routine outputs and uses them to derive the
+        object's position and velocity.  A single prediction requires one
+        call to the present routine followed by one call to sla\_UE2PV;
+        for convenience, the two calls are packaged as the routine
+        sla\_PLANEL.  Multiple predictions may be made by again calling the
+        present routine once, but then calling sla\_UE2PV multiple times,
+        which is faster than multiple calls to sla\_PLANEL.
+  \item DATE is the epoch of osculation.  It is in the TT timescale
+        (formerly Ephemeris Time, ET) and is a Modified Julian Date
+        (JD$-$2400000.5).
+  \item The supplied orbital elements are with respect to the J2000
+        ecliptic and equinox.  The position and velocity parameters
+        returned in the array U are with respect to the mean equator and
+        equinox of epoch J2000, and are for the perihelion prior to the
+        specified epoch.
+  \item The universal elements returned in the array U are in canonical
+        units (solar masses, AU and canonical days).
+  \item Three different element-format options are supported, as
+        follows. \\
+
+        JFORM=1, suitable for the major planets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of elements $t_0$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> longitude of perihelion $\varpi$ (radians) \\
+        \> AORQ   \> = \> mean distance $a$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        \> AORL   \> = \> mean longitude $L$ (radians) \\
+        \> DM     \> = \> daily motion $n$ (radians)
+        \end{tabbing}
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of elements $t_0$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> mean distance $a$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        \> AORL   \> = \> mean anomaly $M$ (radians)
+        \end{tabbing}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of perihelion $T$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> perihelion distance $q$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e \leq 10 )$
+        \end{tabbing}
+  \item Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
+        not accessed.
+  \item The algorithm was originally adapted from the EPHSLA program of
+        D.\,H.\,P.\,Jones (private communication, 1996).  The method
+        is based on Stumpff's Universal Variables.
+ \end{enumerate}
+}
+\aref{Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.}
+%------------------------------------------------------------------------------
+\routine{SLA\_EPB}{MJD to Besselian Epoch}
+{
+ \action{Conversion of Modified Julian Date to Besselian Epoch.}
+ \call{D~=~sla\_EPB (DATE)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{Modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EPB}{D}{Besselian Epoch}
+}
+\aref{Lieske, J.H., 1979, {\it Astr.Astrophys.}\ {\bf 73}, 282.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EPB2D}{Besselian Epoch to MJD}
+{
+ \action{Conversion of Besselian Epoch to Modified Julian Date.}
+ \call{D~=~sla\_EPB2D (EPB)}
+}
+\args{GIVEN}
+{
+ \spec{EPB}{D}{Besselian Epoch}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EPB2D}{D}{Modified Julian Date (JD$-$2400000.5)}
+}
+\aref{Lieske, J.H., 1979. {\it Astr.Astrophys.}\ {\bf 73}, 282.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EPCO}{Convert Epoch to B or J}
+{
+ \action{Convert an epoch to Besselian or Julian to match another one.}
+ \call{D~=~sla\_EPCO (K0, K, E)}
+
+}
+\args{GIVEN}
+{
+ \spec{K0}{C}{form of result:  `B'=Besselian, `J'=Julian} \\
+ \spec{K}{C}{form of given epoch:  `B' or `J'} \\
+ \spec{E}{D}{epoch}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EPCO}{D}{the given epoch converted as necessary}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is always either equal to or very close to
+        the given epoch E.  The routine is required only in
+        applications where punctilious treatment of heterogeneous
+        mixtures of star positions is necessary.
+  \item K0 and K are not validated.  They are interpreted as follows:
+        \begin{itemize}
+         \item If K0 and K are the same, the result is E.
+         \item If K0 is `B' and K isn't, the conversion is J to B.
+         \item In all other cases, the conversion is B to J.
+        \end{itemize}
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EPJ}{MJD to Julian Epoch}
+{
+ \action{Convert Modified Julian Date to Julian Epoch.}
+ \call{D~=~sla\_EPJ (DATE)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{Modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EPJ}{D}{Julian Epoch}
+}
+\aref{Lieske, J.H., 1979.\ {\it Astr.Astrophys.}, {\bf 73}, 282.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EPJ2D}{Julian Epoch to MJD}
+{
+ \action{Convert Julian Epoch to Modified Julian Date.}
+ \call{D~=~sla\_EPJ2D (EPJ)}
+}
+\args{GIVEN}
+{
+ \spec{EPJ}{D}{Julian Epoch}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EPJ2D}{D}{Modified Julian Date (JD$-$2400000.5)}
+}
+\aref{Lieske, J.H., 1979.\ {\it Astr.Astrophys.}, {\bf 73}, 282.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EQECL}{J2000 $\alpha,\delta$ to Ecliptic}
+{
+ \action{Transformation from J2000.0 equatorial coordinates to
+         ecliptic longitude and latitude.}
+ \call{CALL sla\_EQECL (DR, DD, DATE, DL, DB)}
+}
+\args{GIVEN}
+{
+ \spec{DR,DD}{D}{J2000.0 mean \radec\ (radians)} \\
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{DL,DB}{D}{ecliptic longitude and latitude
+                        (mean of date, IAU 1980 theory, radians)}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EQEQX}{Equation of the Equinoxes}
+{
+ \action{Equation of the equinoxes (IAU 1994).}
+ \call{D~=~sla\_EQEQX (DATE)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EQEQX}{D}{The equation of the equinoxes (radians)}
+}
+\notes{
+ \begin{enumerate}
+  \item The equation of the equinoxes is defined here as GAST~$-$~GMST:
+        it is added to a {\it mean}\/ sidereal time to give the
+        {\it apparent}\/ sidereal time.
+  \item The change from the classic ``textbook'' expression
+        $\Delta\psi\,cos\,\epsilon$ occurred with IAU Resolution C7,
+        Recommendation~3 (1994).  The new formulation takes into
+        account cross-terms between the various precession and
+        nutation quantities, amounting to about 3~milliarcsec.
+        The transition from the old to the new model officially
+        takes place on 1997 February~27.
+ \end{enumerate}
+}
+\aref{Capitaine, N.\ \& Gontier, A.-M.\ (1993),
+      {\it Astron. Astrophys.},
+      {\bf 275}, 645-650.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EQGAL}{J2000 $\alpha,\delta$ to Galactic}
+{
+ \action{Transformation from J2000.0 FK5 equatorial coordinates to
+ IAU 1958 galactic coordinates.}
+ \call{CALL sla\_EQGAL (DR, DD, DL, DB)}
+}
+\args{GIVEN}
+{
+ \spec{DR,DD}{D}{J2000.0 \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal\ (radians)}
+}
+\anote{The equatorial coordinates are J2000.0 FK5.  Use the routine
+       sla\_EG50 if conversion from B1950.0 FK4 coordinates is required.}
+\aref{Blaauw {\it et al.}, 1960, {\it Mon.Not.R.astr.Soc.},
+      {\bf 121}, 123.}
+%-----------------------------------------------------------------------
+\routine{SLA\_ETRMS}{E-terms of Aberration}
+{
+ \action{Compute the E-terms vector -- the part of the annual
+         aberration which arises from the eccentricity of the
+         Earth's orbit.}
+ \call{CALL sla\_ETRMS (EP, EV)}
+}
+\args{GIVEN}
+{
+ \spec{EP}{D}{Besselian epoch}
+}
+\args{RETURNED}
+{
+ \spec{EV}{D(3)}{E-terms as $[\Delta x, \Delta y, \Delta z\,]$}
+}
+\anote{Note the use of the J2000 aberration constant (\arcsec{20}{49552}).
+       This is a reflection of the fact that the E-terms embodied in
+       existing star catalogues were computed from a variety of
+       aberration constants.  Rather than adopting one of the old
+       constants the latest value is used here.}
+\refs
+{
+ \begin{enumerate}
+  \item Smith, C.A.\ {\it et al.}, 1989.  {\it Astr.J.}\ {\bf 97}, 265.
+  \item Yallop, B.D.\ {\it et al.}, 1989.  {\it Astr.J.}\ {\bf 97}, 274.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EULER}{Rotation Matrix from Euler Angles}
+{
+ \action{Form a rotation matrix from the Euler angles -- three
+         successive rotations about specified Cartesian axes
+         (single precision).}
+ \call{CALL sla\_EULER (ORDER, PHI, THETA, PSI, RMAT)}
+}
+\args{GIVEN}
+{
+ \spec{ORDER}{C*(*)}{specifies about which axes the rotations occur} \\
+ \spec{PHI}{R}{1st rotation (radians)} \\
+ \spec{THETA}{R}{2nd rotation (radians)} \\
+ \spec{PSI}{R}{3rd rotation (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RMAT}{R(3,3)}{rotation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A rotation is positive when the reference frame rotates
+        anticlockwise as seen looking towards the origin from the
+        positive region of the specified axis.
+  \item The characters of ORDER define which axes the three successive
+        rotations are about.  A typical value is `ZXZ', indicating that
+        RMAT is to become the direction cosine matrix corresponding to
+        rotations of the reference frame through PHI radians about the
+        old {\it z}-axis, followed by THETA radians about the resulting
+        {\it x}-axis,
+        then PSI radians about the resulting {\it z}-axis.  In detail:
+        \begin{itemize}
+         \item The axis names can be any of the following, in any order or
+               combination:  X, Y, Z, uppercase or lowercase, 1, 2, 3.  Normal
+               axis labelling/numbering conventions apply;
+               the {\it xyz} ($\equiv123$)
+               triad is right-handed.  Thus, the `ZXZ' example given above
+               could be written `zxz' or `313' (or even `ZxZ' or `3xZ').
+         \item ORDER is terminated by length or by the first unrecognized
+               character.
+         \item Fewer than three rotations are acceptable, in which case
+               the later angle arguments are ignored.
+        \end{itemize}
+  \item Zero rotations produces a unit RMAT.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EVP}{Earth Position \& Velocity}
+{
+ \action{Barycentric and heliocentric velocity and position of the Earth.}
+ \call{CALL sla\_EVP (DATE, DEQX, DVB, DPB, DVH, DPH)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (formerly ET) as a Modified Julian Date
+                                        (JD$-$2400000.5)} \\
+ \spec{DEQX}{D}{Julian Epoch ({\it e.g.}\ 2000D0) of mean equator and
+                equinox of the vectors returned.  If DEQX~$<0$,
+                  all vectors are referred to the mean equator and
+                  equinox (FK5) of date DATE.}
+}
+\args{RETURNED}
+{
+ \spec{DVB}{D(3)}{barycentric \xyzd, AU~s$^{-1}$} \\
+ \spec{DPB}{D(3)}{barycentric \xyz, AU} \\
+ \spec{DVH}{D(3)}{heliocentric \xyzd, AU~s$^{-1}$} \\
+ \spec{DPH}{D(3)}{heliocentric \xyz, AU}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine is used when accuracy is more important
+        than CPU time, yet the extra complication of reading a
+        pre-computed ephemeris is not justified.  The maximum
+        deviations from the JPL~DE96 ephemeris are as follows:
+        \begin{itemize}
+         \item velocity (barycentric or heliocentric): 420~mm~s$^{-1}$
+         \item position (barycentric): 6900~km
+         \item position (heliocentric): 1600~km
+        \end{itemize}
+  \item The routine is an adaption of the BARVEL and BARCOR
+        subroutines of P.Stumpff, which are described in
+        {\it Astr.Astrophys.Suppl.Ser.}\ {\bf 41}, 1-8 (1980).
+        Most of the changes are merely cosmetic and do not affect
+        the results at all.  However, some adjustments have been
+        made so as to give results that refer to the new (IAU 1976
+        `FK5') equinox and precession, although the differences these
+        changes make relative to the results from Stumpff's original
+        `FK4' version are smaller than the inherent accuracy of the
+        algorithm.  One minor shortcoming in the original routines
+        that has {\bf not} been corrected is that slightly better
+        numerical accuracy could be achieved if the various polynomial
+        evaluations were to be so arranged that the smallest terms were
+        computed first.  Note also that one of Stumpff's precession
+        constants differs by \arcsec{0}{001} from the value given in the
+        {\it Explanatory Supplement}.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_FITXY}{Fit Linear Model to Two \xy\ Sets}
+{
+ \action{Fit a linear model to relate two sets of \xy\ coordinates.}
+ \call{CALL sla\_FITXY (ITYPE,NP,XYE,XYM,COEFFS,J)}
+}
+\args{GIVEN}
+{
+ \spec{ITYPE}{I}{type of model: 4 or 6 (note 1)} \\
+ \spec{NP}{I}{number of samples (note 2)} \\
+ \spec{XYE}{D(2,NP)}{expected \xy\ for each sample} \\
+ \spec{XYM}{D(2,NP)}{measured \xy\ for each sample}
+}
+\args{RETURNED}
+{
+ \spec{COEFFS}{D(6)}{coefficients of model (note 3)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{0.7em} $-$1 = illegal ITYPE} \\
+ \spec{}{}{\hspace{0.7em} $-$2 = insufficient data} \\
+ \spec{}{}{\hspace{0.7em} $-$3 = singular solution}
+}
+\notes
+{
+ \begin{enumerate}
+  \item ITYPE, which must be either 4 or 6, selects the type of model
+        fitted.  Both allowed ITYPE values produce a model COEFFS which
+        consists of six coefficients, namely the zero points and, for
+        each of XE and YE, the coefficient of XM and YM.  For ITYPE=6,
+        all six coefficients are independent, modelling squash and shear
+        as well as origin, scale, and orientation.  However, ITYPE=4
+        selects the {\it solid body rotation}\/ option;  the model COEFFS
+        still consists of the same six coefficients, but now two of
+        them are used twice (appropriately signed).  Origin, scale
+        and orientation are still modelled, but not squash or shear --
+        the units of X and Y have to be the same.
+  \item For NC=4, NP must be at least 2.  For NC=6, NP must be at
+        least 3.
+  \item The model is returned in the array COEFFS.  Naming the
+        six elements of COEFFS $a,b,c,d,e$ \& $f$,
+        the model transforms {\it measured}\/ coordinates
+        $[x_{m},y_{m}\,]$ into {\it expected}\/ coordinates
+        $[x_{e},y_{e}\,]$ as follows:
+        \begin{verse}
+         $x_{e} = a + bx_{m} + cy_{m}$ \\
+         $y_{e} = d + ex_{m} + fy_{m}$
+        \end{verse}
+        For the {\it solid body rotation}\/ option (ITYPE=4), the
+        magnitudes of $b$ and $f$, and of $c$ and $e$, are equal.  The
+        signs of these coefficients depend on whether there is a
+        sign reversal between $[x_{e},y_{e}]$ and $[x_{m},y_{m}]$;
+        fits are performed
+        with and without a sign reversal and the best one chosen.
+  \item Error status values J=$-$1 and $-$2 leave COEFFS unchanged;
+        if J=$-$3 COEFFS may have been changed.
+  \item See also sla\_PXY, sla\_INVF, sla\_XY2XY, sla\_DCMPF.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK425}{FK4 to FK5}
+{
+ \action{Convert B1950.0 FK4 star data to J2000.0 FK5.
+         This routine converts stars from the old, Bessel-Newcomb, FK4
+         system to the new, IAU~1976, FK5, Fricke system.  The precepts
+         of Smith~{\it et~al.}\ (see reference~1) are followed,
+         using the implementation
+         by Yallop~{\it et~al.}\ (reference~2) of a matrix method
+         due to Standish.
+         Kinoshita's development of Andoyer's post-Newcomb precession is
+         used.  The numerical constants from 
+         Seidelmann~{\it et~al.}\  (reference~3) are used canonically.}
+ \call{CALL sla\_FK425 (\vtop{
+         \hbox{R1950,D1950,DR1950,DD1950,P1950,V1950,}
+         \hbox{R2000,D2000,DR2000,DD2000,P2000,V2000)}}}
+}
+\args{GIVEN}
+{
+ \spec{R1950}{D}{B1950.0 $\alpha$ (radians)} \\
+ \spec{D1950}{D}{B1950.0 $\delta$ (radians)} \\
+ \spec{DR1950}{D}{B1950.0 proper motion in $\alpha$
+                              (radians per tropical year)} \\
+ \spec{DD1950}{D}{B1950.0 proper motion in $\delta$
+                              (radians per tropical year)} \\
+ \spec{P1950}{D}{B1950.0 parallax (arcsec)} \\
+ \spec{V1950}{D}{B1950.0 radial velocity (km~s$^{-1}$, +ve = moving away)}
+}
+\args{RETURNED}
+{
+ \spec{R2000}{D}{J2000.0 $\alpha$ (radians)} \\
+ \spec{D2000}{D}{J2000.0 $\delta$ (radians)} \\
+ \spec{DR2000}{D}{J2000.0 proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DD2000}{D}{J2000.0 proper motion in $\delta$
+                              (radians per Julian year)} \\
+ \spec{P2000}{D}{J2000.0 parallax (arcsec)} \\
+ \spec{V2000}{D}{J2000.0 radial velocity (km~s$^{-1}$, +ve = moving away)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item Conversion from Besselian epoch 1950.0 to Julian epoch
+        2000.0 only is provided for.  Conversions involving other
+        epochs will require use of the appropriate precession,
+        proper motion, and E-terms routines before and/or after FK425
+        is called.
+  \item In the FK4 catalogue the proper motions of stars within
+        $10^{\circ}$ of the poles do not include the {\it differential
+        E-terms}\/ effect and should, strictly speaking, be handled
+        in a different manner from stars outside these regions.
+        However, given the general lack of homogeneity of the star
+        data available for routine astrometry, the difficulties of
+        handling positions that may have been determined from
+        astrometric fields spanning the polar and non-polar regions,
+        the likelihood that the differential E-terms effect was not
+        taken into account when allowing for proper motion in past
+        astrometry, and the undesirability of a discontinuity in
+        the algorithm, the decision has been made in this routine to
+        include the effect of differential E-terms on the proper
+        motions for all stars, whether polar or not.  At epoch J2000,
+        and measuring on the sky rather than in terms of $\Delta\alpha$,
+        the errors resulting from this simplification are less than
+        1~milliarcsecond in position and 1~milliarcsecond per
+        century in proper motion.
+  \item See also sla\_FK45Z, sla\_FK524, sla\_FK54Z.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Smith, C.A.\ {\it et al.}, 1989.\  {\it Astr.J.}\ {\bf 97}, 265.
+  \item Yallop, B.D.\ {\it et al.}, 1989.\ {\it Astr.J.}\ {\bf 97}, 274.
+  \item Seidelmann, P.K.\ (ed), 1992.  {\it Explanatory
+        Supplement to the Astronomical Almanac,}\/ ISBN~0-935702-68-7.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK45Z}{FK4 to FK5, no P.M. or Parallax}
+{
+ \action{Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero
+         proper motion in the FK5 frame.
+         This routine converts stars from the old, Bessel-Newcomb, FK4
+         system to the new, IAU~1976, FK5, Fricke system, in such a
+         way that the FK5 proper motion is zero.  Because such a star
+         has, in general, a non-zero proper motion in the FK4 system,
+         the routine requires the epoch at which the position in the
+         FK4 system was determined.  The method is from appendix~2 of
+         reference~1, but using the constants of reference~4.}
+ \call{CALL sla\_FK45Z (R1950,D1950,BEPOCH,R2000,D2000)}
+}
+\args{GIVEN}
+{
+ \spec{R1950}{D}{B1950.0 FK4 $\alpha$ at epoch BEPOCH (radians)} \\
+ \spec{D1950}{D}{B1950.0 FK4 $\delta$ at epoch BEPOCH (radians)} \\
+ \spec{BEPOCH}{D}{Besselian epoch ({\it e.g.}\ 1979.3D0)}
+}
+\args{RETURNED}
+{
+ \spec{R2000}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D2000}{D}{J2000.0 FK5 $\delta$ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The epoch BEPOCH is strictly speaking Besselian, but
+        if a Julian epoch is supplied the result will be
+        affected only to a negligible extent.
+  \item Conversion from Besselian epoch 1950.0 to Julian epoch
+        2000.0 only is provided for.  Conversions involving other
+        epochs will require use of the appropriate precession,
+        proper motion, and E-terms routines before and/or
+        after FK45Z is called.
+  \item In the FK4 catalogue the proper motions of stars within
+        $10^{\circ}$ of the poles do not include the {\it differential
+        E-terms}\/ effect and should, strictly speaking, be handled
+        in a different manner from stars outside these regions.
+        However, given the general lack of homogeneity of the star
+        data available for routine astrometry, the difficulties of
+        handling positions that may have been determined from
+        astrometric fields spanning the polar and non-polar regions,
+        the likelihood that the differential E-terms effect was not
+        taken into account when allowing for proper motion in past
+        astrometry, and the undesirability of a discontinuity in
+        the algorithm, the decision has been made in this routine to
+        include the effect of differential E-terms on the proper
+        motions for all stars, whether polar or not.  At epoch 2000,
+        and measuring on the sky rather than in terms of $\Delta\alpha$,
+        the errors resulting from this simplification are less than
+        1~milliarcsecond in position and 1~milliarcsecond per
+        century in proper motion.
+  \item See also sla\_FK425, sla\_FK524, sla\_FK54Z.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Aoki, S., {\it et al.}, 1983.\ {\it Astr.Astrophys.}, {\bf 128}, 263.
+  \item Smith, C.A.\ {\it et al.}, 1989.\  {\it Astr.J.}\ {\bf 97}, 265.
+  \item Yallop, B.D.\ {\it et al.}, 1989.\ {\it Astr.J.}\ {\bf 97}, 274.
+  \item Seidelmann, P.K.\ (ed), 1992.  {\it Explanatory
+        Supplement to the Astronomical Almanac,}\/ ISBN~0-935702-68-7.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK524}{FK5 to FK4}
+{
+ \action{Convert J2000.0 FK5 star data to B1950.0 FK4.
+         This routine converts stars from the new, IAU~1976, FK5, Fricke
+         system, to the old, Bessel-Newcomb, FK4 system.
+         The precepts of Smith~{\it et~al.}\ (reference~1) are followed,
+         using the implementation by Yallop~{\it et~al.}\ (reference~2)
+         of a matrix method due to Standish.  Kinoshita's development of
+         Andoyer's post-Newcomb precession is used.  The numerical
+         constants from Seidelmann~{\it et~al.}\ (reference~3) are
+         used canonically.}
+ \call{CALL sla\_FK524 (\vtop{
+         \hbox{R2000,D2000,DR2000,DD2000,P2000,V2000,}
+         \hbox{R1950,D1950,DR1950,DD1950,P1950,V1950)}}}
+}
+\args{GIVEN}
+{
+ \spec{R2000}{D}{J2000.0 $\alpha$ (radians)} \\
+ \spec{D2000}{D}{J2000.0 $\delta$ (radians)} \\
+ \spec{DR2000}{D}{J2000.0 proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DD2000}{D}{J2000.0 proper motion in $\delta$
+                              (radians per Julian year)} \\
+ \spec{P2000}{D}{J2000.0 parallax (arcsec)} \\
+ \spec{V2000}{D}{J2000 radial velocity (km~s$^{-1}$, +ve = moving away)}
+}
+\args{RETURNED}
+{
+ \spec{R1950}{D}{B1950.0 $\alpha$ (radians)} \\
+ \spec{D1950}{D}{B1950.0 $\delta$ (radians)} \\
+ \spec{DR1950}{D}{B1950.0 proper motion in $\alpha$
+                              (radians per tropical year)} \\
+ \spec{DD1950}{D}{B1950.0 proper motion in $\delta$
+                              (radians per tropical year)} \\
+ \spec{P1950}{D}{B1950.0 parallax (arcsec)} \\
+ \spec{V1950}{D}{radial velocity (km~s$^{-1}$, +ve = moving away)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item Note that conversion from Julian epoch 2000.0 to Besselian
+        epoch 1950.0 only is provided for.  Conversions involving
+        other epochs will require use of the appropriate precession,
+        proper motion, and E-terms routines before and/or after
+        FK524 is called.
+  \item In the FK4 catalogue the proper motions of stars within
+        $10^{\circ}$ of the poles do not include the {\it differential
+        E-terms}\/ effect and should, strictly speaking, be handled
+        in a different manner from stars outside these regions.
+        However, given the general lack of homogeneity of the star
+        data available for routine astrometry, the difficulties of
+        handling positions that may have been determined from
+        astrometric fields spanning the polar and non-polar regions,
+        the likelihood that the differential E-terms effect was not
+        taken into account when allowing for proper motion in past
+        astrometry, and the undesirability of a discontinuity in
+        the algorithm, the decision has been made in this routine to
+        include the effect of differential E-terms on the proper
+        motions for all stars, whether polar or not.  At epoch 2000,
+        and measuring on the sky rather than in terms of $\Delta\alpha$,
+        the errors resulting from this simplification are less than
+        1~milliarcsecond in position and 1~milliarcsecond per
+        century in proper motion.
+  \item See also sla\_FK425, sla\_FK45Z, sla\_FK54Z.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Smith, C.A.\ {\it et al.}, 1989.\  {\it Astr.J.}\ {\bf 97}, 265.
+  \item Yallop, B.D.\ {\it et al.}, 1989.\ {\it Astr.J.}\ {\bf 97}, 274.
+  \item Seidelmann, P.K.\ (ed), 1992.  {\it Explanatory
+        Supplement to the Astronomical Almanac,}\/ ISBN~0-935702-68-7.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK52H}{FK5 to Hipparcos}
+{
+ \action{Transform an FK5 (J2000) position and proper motion
+         into the frame of the Hipparcos catalogue.}
+ \call{CALL sla\_FK52H (R5,D5,DR5,DD5,RH,DH,DRH,DDH)}
+}
+\args{GIVEN}
+{
+ \spec{R5}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D5}{D}{J2000.0 FK5 $\delta$ (radians)} \\
+ \spec{DR5}{D}{J2000.0 FK5 proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DD5}{D}{J2000.0 FK5 proper motion in $\delta$
+                              (radians per Julian year)}
+}
+\args{RETURNED}
+{
+ \spec{RH}{D}{Hipparcos $\alpha$ (radians)} \\
+ \spec{DH}{D}{Hipparcos $\delta$ (radians)} \\
+ \spec{DRH}{D}{Hipparcos proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DDH}{D}{Hipparcos proper motion in $\delta$
+                              (radians per Julian year)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item The FK5 to Hipparcos
+        transformation consists of a pure rotation and spin;
+        zonal errors in the FK5 catalogue are not taken into account.
+  \item The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin
+        values are as follows (see reference):
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~~~
+        \begin{tabular}{|r|r|r|} \hline
+        &
+        \multicolumn{1}{|c}{\it orientation} &
+        \multicolumn{1}{|c|}{\it ~~~spin~~~} \\ \hline
+        $x$ & $-19.9$~~~~ & ~$-0.30$~~ \\
+        $y$ &  $-9.1$~~~~ & ~$+0.60$~~ \\
+        $z$ & $+22.9$~~~~ & ~$+0.70$~~ \\ \hline
+        & {\it mas}~~~~~ & ~{\it mas/y}~ \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        These orientation and spin components are interpreted as
+        {\it axial vectors.}  An axial vector points at the pole of
+        the rotation and its length is the amount of rotation in radians.
+  \item See also sla\_FK5HZ, sla\_H2FK5, sla\_HFK5Z.
+ \end{enumerate}
+}
+\aref {Feissel, M.\ \& Mignard, F., 1998.,  {\it Astron.Astrophys.}\
+       {\bf 331}, L33-L36.}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK54Z}{FK5 to FK4, no P.M. or Parallax}
+{
+ \action{Convert a J2000.0 FK5 star position to B1950.0 FK4 assuming
+         FK5 zero proper motion and parallax.
+         This routine converts star positions from the new, IAU~1976,
+         FK5, Fricke system to the old, Bessel-Newcomb, FK4 system.}
+ \call{CALL sla\_FK54Z (R2000,D2000,BEPOCH,R1950,D1950,DR1950,DD1950)}
+}
+\args{GIVEN}
+{
+ \spec{R2000}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D2000}{D}{J2000.0 FK5 $\delta$ (radians)} \\
+ \spec{BEPOCH}{D}{Besselian epoch ({\it e.g.}\ 1950D0)}
+}
+\args{RETURNED}
+{
+ \spec{R1950}{D}{B1950.0 FK4 $\alpha$ at epoch BEPOCH (radians)} \\
+ \spec{D1950}{D}{B1950.0 FK4 $\delta$ at epoch BEPOCH (radians)} \\
+ \spec{DR1950}{D}{B1950.0 FK4 proper motion in $\alpha$
+                              (radians per tropical year)} \\
+ \spec{DD1950}{D}{B1950.0 FK4 proper motion in $\delta$
+                              (radians per tropical year)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item Conversion from Julian epoch 2000.0 to Besselian epoch 1950.0
+        only is provided for.  Conversions involving other epochs will
+        require use of the appropriate precession routines before and
+        after this routine is called.
+  \item Unlike in the sla\_FK524 routine, the FK5 proper motions, the
+        parallax and the radial velocity are presumed zero.
+  \item It was the intention that FK5 should be a close approximation
+        to an inertial frame, so that distant objects have zero proper
+        motion;  such objects have (in general) non-zero proper motion
+        in FK4, and this routine returns those {\it fictitious proper
+        motions}.
+  \item The position returned by this routine is in the B1950
+        reference frame but at Besselian epoch BEPOCH.  For
+        comparison with catalogues the BEPOCH argument will
+        frequently be 1950D0.
+  \item See also sla\_FK425, sla\_FK45Z, sla\_FK524.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK5HZ}{FK5 to Hipparcos, no P.M.}
+{
+ \action{Transform an FK5 (J2000) star position into the frame of the
+         Hipparcos catalogue, assuming zero Hipparcos proper motion.}
+ \call{CALL sla\_FK52H (R5,D5,EPOCH,RH,DH)}
+}
+\args{GIVEN}
+{
+ \spec{R5}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D5}{D}{J2000.0 FK5 $\delta$ (radians)} \\
+ \spec{EPOCH}{D}{Julian epoch (TDB)}
+}
+\args{RETURNED}
+{
+ \spec{RH}{D}{Hipparcos $\alpha$ (radians)} \\
+ \spec{DH}{D}{Hipparcos $\delta$ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item The FK5 to Hipparcos
+        transformation consists of a pure rotation and spin;
+        zonal errors in the FK5 catalogue are not taken into account.
+  \item The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin
+        values are as follows (see reference):
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~~~
+        \begin{tabular}{|r|r|r|} \hline
+        &
+        \multicolumn{1}{|c}{\it orientation} &
+        \multicolumn{1}{|c|}{\it ~~~spin~~~} \\ \hline
+        $x$ & $-19.9$~~~~ & ~$-0.30$~~ \\
+        $y$ &  $-9.1$~~~~ & ~$+0.60$~~ \\
+        $z$ & $+22.9$~~~~ & ~$+0.70$~~ \\ \hline
+        & {\it mas}~~~~~ & ~{\it mas/y}~ \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        These orientation and spin components are interpreted as
+        {\it axial vectors.}  An axial vector points at the pole of
+        the rotation and its length is the amount of rotation in radians.
+  \item See also sla\_FK52H, sla\_H2FK5, sla\_HFK5Z.
+ \end{enumerate}
+}
+\aref {Feissel, M.\ \& Mignard, F., 1998.,  {\it Astron.Astrophys.}\
+       {\bf 331}, L33-L36.}
+%-----------------------------------------------------------------------
+\routine{SLA\_FLOTIN}{Decode a Real Number}
+{
+ \action{Convert free-format input into single precision floating point.}
+ \call{CALL sla\_FLOTIN (STRING, NSTRT, RESLT, JFLAG)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C}{string containing number to be decoded} \\
+ \spec{NSTRT}{I}{pointer to where decoding is to commence} \\
+ \spec{RESLT}{R}{current value of result}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{advanced to next number} \\
+ \spec{RESLT}{R}{result} \\
+ \spec{JFLAG}{I}{status: $-$1~=~$-$OK, 0~=~+OK, 1~=~null result, 2~=~error}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The reason sla\_FLOTIN has separate `OK' status values
+       for + and $-$ is to enable minus zero to be detected.
+       This is of crucial importance
+       when decoding mixed-radix numbers.  For example, an angle
+       expressed as degrees, arcminutes and arcseconds may have a
+       leading minus sign but a zero degrees field.
+ \item A TAB is interpreted as a space, and lowercase characters are
+       interpreted as uppercase.  {\it n.b.}\ The test for TAB is
+       ASCII-specific.
+ \item The basic format is the sequence of fields $\pm n.n x \pm n$,
+       where $\pm$ is a sign
+       character `+' or `$-$', $n$ means a string of decimal digits,
+       `.' is a decimal point, and $x$, which indicates an exponent,
+       means `D' or `E'.  Various combinations of these fields can be
+       omitted, and embedded blanks are permissible in certain places.
+ \item Spaces:
+       \begin{itemize}
+       \item Leading spaces are ignored.
+       \item Embedded spaces are allowed only after +, $-$, D or E,
+             and after the decimal point if the first sequence of
+             digits is absent.
+       \item Trailing spaces are ignored;  the first signifies
+             end of decoding and subsequent ones are skipped.
+       \end{itemize}
+ \item Delimiters:
+       \begin{itemize}
+       \item Any character other than +,$-$,0-9,.,D,E or space may be
+             used to signal the end of the number and terminate decoding.
+       \item Comma is recognized by sla\_FLOTIN as a special case; it
+             is skipped, leaving the pointer on the next character.  See
+             13, below.
+       \item Decoding will in all cases terminate if end of string
+             is reached.
+       \end{itemize}
+ \item Both signs are optional.  The default is +.
+ \item The mantissa $n.n$ defaults to unity.
+ \item The exponent $x\!\pm\!n$ defaults to `E0'.
+ \item The strings of decimal digits may be of any length.
+ \item The decimal point is optional for whole numbers.
+ \item A {\it null result}\/ occurs when the string of characters
+       being decoded does not begin with +,$-$,0-9,.,D or E, or
+       consists entirely of spaces.  When this condition is
+       detected, JFLAG is set to 1 and RESLT is left untouched.
+ \item NSTRT = 1 for the first character in the string.
+ \item On return from sla\_FLOTIN, NSTRT is set ready for the next
+       decode -- following trailing blanks and any comma.  If a
+       delimiter other than comma is being used, NSTRT must be
+       incremented before the next call to sla\_FLOTIN, otherwise
+       all subsequent calls will return a null result.
+ \item Errors (JFLAG=2) occur when:
+       \begin{itemize}
+       \item a +, $-$, D or E is left unsatisfied; or
+       \item the decimal point is present without at least
+             one decimal digit before or after it; or
+       \item an exponent more than 100 has been presented.
+       \end{itemize}
+ \item When an error has been detected, NSTRT is left
+       pointing to the character following the last
+       one used before the error came to light.  This
+       may be after the point at which a more sophisticated
+       program could have detected the error.  For example,
+       sla\_FLOTIN does not detect that `1E999' is unacceptable
+       (on a computer where this is so)
+       until the entire number has been decoded.
+ \item Certain highly unlikely combinations of mantissa and
+       exponent can cause arithmetic faults during the
+       decode, in some cases despite the fact that they
+       together could be construed as a valid number.
+ \item Decoding is left to right, one pass.
+ \item See also sla\_DFLTIN and sla\_INTIN.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_GALEQ}{Galactic to J2000 $\alpha,\delta$}
+{
+ \action{Transformation from IAU 1958 galactic coordinates
+         to J2000.0 FK5 equatorial coordinates.}
+ \call{CALL sla\_GALEQ (DL, DB, DR, DD)}
+}
+\args{GIVEN}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal}
+}
+\args{RETURNED}
+{
+ \spec{DR,DD}{D}{J2000.0 \radec}
+}
+\notes
+{
+ \begin{enumerate}
+  \item All arguments are in radians.
+  \item The equatorial coordinates are J2000.0 FK5.  Use the routine
+        sla\_GE50 if conversion to B1950.0 FK4 coordinates is
+                           required.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_GALSUP}{Galactic to Supergalactic}
+{
+ \action{Transformation from IAU 1958 galactic coordinates to
+         de Vaucouleurs supergalactic coordinates.}
+ \call{CALL sla\_GALSUP (DL, DB, DSL, DSB)}
+}
+\args{GIVEN}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{DSL,DSB}{D}{supergalactic longitude and latitude (radians)}
+}
+\refs
+{
+ \begin{enumerate}
+  \item de Vaucouleurs, de Vaucouleurs, \& Corwin, {\it Second Reference
+    Catalogue of Bright Galaxies}, U.Texas, p8.
+  \item Systems \& Applied Sciences Corp., documentation for the
+        machine-readable version of the above catalogue,
+        Contract NAS 5-26490.
+ \end{enumerate}
+ (These two references give different values for the galactic
+ longitude of the supergalactic origin.  Both are wrong;  the
+ correct value is $l^{I\!I}=137.37$.)
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_GE50}{B1950 $\alpha,\delta$ to Galactic}
+{
+ \action{Transformation from IAU 1958 galactic coordinates to
+         B1950.0 FK4 equatorial coordinates.}
+ \call{CALL sla\_GE50 (DL, DB, DR, DD)}
+}
+\args{GIVEN}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal}
+}
+\args{RETURNED}
+{
+ \spec{DR,DD}{D}{B1950.0 \radec}
+}
+\notes
+{
+ \begin{enumerate}
+  \item All arguments are in radians.
+  \item The equatorial coordinates are B1950.0 FK4.  Use the
+        routine sla\_GALEQ if conversion to J2000.0 FK5 coordinates
+        is required.
+ \end{enumerate}
+}
+\aref{Blaauw {\it et al.}, 1960, {\it Mon.Not.R.astr.Soc.},
+      {\bf 121}, 123.}
+%-----------------------------------------------------------------------
+\routine{SLA\_GEOC}{Geodetic to Geocentric}
+{
+ \action{Convert geodetic position to geocentric.}
+ \call{CALL sla\_GEOC (P, H, R, Z)}
+}
+\args{GIVEN}
+{
+ \spec{P}{D}{latitude (geodetic, radians)} \\
+ \spec{H}{D}{height above reference spheroid (geodetic, metres)}
+}
+\args{RETURNED}
+{
+ \spec{R}{D}{distance from Earth axis (AU)} \\
+ \spec{Z}{D}{distance from plane of Earth equator (AU)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Geocentric latitude can be obtained by evaluating {\tt ATAN2(Z,R)}.
+  \item IAU 1976 constants are used.
+ \end{enumerate}
+}
+\aref{Green, R.M., 1985.\ {\it Spherical Astronomy}, Cambridge U.P., p98.}
+%-----------------------------------------------------------------------
+\routine{SLA\_GMST}{UT to GMST}
+{
+ \action{Conversion from universal time UT1 to Greenwich mean
+         sidereal time.}
+ \call{D~=~sla\_GMST (UT1)}
+}
+\args{GIVEN}
+{
+ \spec{UT1}{D}{universal time (strictly UT1) expressed as
+                 modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_GMST}{D}{Greenwich mean sidereal time (radians)}
+}
+\notes
+{
+  \begin{enumerate}
+       \item The IAU~1982 expression
+       (see page~S15 of the 1984 {\it Astronomical
+       Almanac})\/ is used, but rearranged to reduce rounding errors.  This
+       expression is always described as giving the GMST at $0^{\rm h}$UT;
+       in fact, it gives the difference between the
+       GMST and the UT, which happens to equal the GMST (modulo
+       24~hours) at $0^{\rm h}$UT each day.  In sla\_GMST, the
+       entire UT is used directly as the argument for the
+       canonical formula, and the fractional part of the UT is
+       added separately;  note that the factor $1.0027379\cdots$ does
+       not appear.
+       \item See also the routine sla\_GMSTA, which
+       delivers better numerical
+       precision by accepting the UT date and time as separate arguments.
+  \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_GMSTA}{UT to GMST (extra precision)}
+{
+ \action{Conversion from universal time UT1 to Greenwich Mean
+         sidereal time, with rounding errors minimized.}
+ \call{D~=~sla\_GMSTA (DATE, UT1)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{UT1 date as Modified Julian Date (integer part
+                of JD$-$2400000.5)} \\
+ \spec{UT1}{D}{UT1 time (fraction of a day)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_GMST}{D}{Greenwich mean sidereal time (radians)}
+}
+\notes
+{
+  \begin{enumerate}
+       \item The algorithm is derived from the IAU 1982 expression
+       (see page~S15 of the 1984 Astronomical Almanac).
+       \item There is no restriction on how the UT is apportioned between the
+       DATE and UT1 arguments.  Either of the two arguments could, for
+       example, be zero and the entire date\,+\,time supplied in the other.
+       However, the routine is designed to deliver maximum accuracy when
+       the DATE argument is a whole number and the UT1 argument
+       lies in the range $[\,0,\,1\,]$, or {\it vice versa}.
+       \item See also the routine sla\_GMST, which accepts the UT1 as a single
+       argument.  Compared with sla\_GMST, the extra numerical precision
+       delivered by the present routine is unlikely to be important in
+       an absolute sense, but may be useful when critically comparing
+       algorithms and in applications where two sidereal times close
+       together are differenced.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_GRESID}{Gaussian Residual}
+{
+ \action{Generate pseudo-random normal deviate or {\it Gaussian residual}.}
+ \call{R~=~sla\_GRESID (S)}
+}
+\args{GIVEN}
+{
+ \spec{S}{R}{standard deviation}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The results of many calls to this routine will be
+        normally distributed with mean zero and standard deviation S.
+  \item The Box-Muller algorithm is used.
+  \item The implementation is machine-dependent.
+ \end{enumerate}
+}
+\aref{Ahrens \& Dieter, 1972.\ {\it Comm.A.C.M.}\ {\bf 15}, 873.}
+%-----------------------------------------------------------------------
+\routine{SLA\_H2E}{Az,El to $h,\delta$}
+{
+ \action{Horizon to equatorial coordinates
+         (single precision).}
+ \call{CALL sla\_H2E (AZ, EL, PHI, HA, DEC)}
+}
+\args{GIVEN}
+{
+ \spec{AZ}{R}{azimuth (radians)} \\
+ \spec{EL}{R}{elevation (radians)} \\
+ \spec{PHI}{R}{latitude (radians)}
+}
+\args{RETURNED}
+{
+ \spec{HA}{R}{hour angle (radians)} \\
+ \spec{DEC}{R}{declination (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The sign convention for azimuth is north zero, east $+\pi/2$.
+  \item HA is returned in the range $\pm\pi$.  Declination is returned
+        in the range $\pm\pi$.
+  \item The latitude is (in principle) geodetic.  In critical
+        applications, corrections for polar motion should be applied
+        (see sla\_POLMO).
+  \item In some applications it will be important to specify the
+        correct type of elevation in order to produce the required
+        type of \hadec.  In particular, it may be important to
+        distinguish between the elevation as affected by refraction,
+        which will yield the {\it observed} \hadec, and the elevation
+        {\it in vacuo}, which will yield the {\it topocentric}
+        \hadec.  If the
+        effects of diurnal aberration can be neglected, the
+        topocentric \hadec\ may be used as an approximation to the
+        {\it apparent} \hadec.
+  \item No range checking of arguments is carried out.
+  \item In applications which involve many such calculations, rather
+        than calling the present routine it will be more efficient to
+        use inline code, having previously computed fixed terms such
+        as sine and cosine of latitude.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_H2FK5}{Hipparcos to FK5}
+{
+ \action{Transform a Hipparcos star position and proper motion
+         into the FK5 (J2000) frame.}
+ \call{CALL sla\_H2FK5 (RH,DH,DRH,DDH,R5,D5,DR5,DD5)}
+}
+\args{GIVEN}
+{
+ \spec{RH}{D}{Hipparcos $\alpha$ (radians)} \\
+ \spec{DH}{D}{Hipparcos $\delta$ (radians)} \\
+ \spec{DRH}{D}{Hipparcos proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DDH}{D}{Hipparcos proper motion in $\delta$
+                              (radians per Julian year)}
+}
+\args{RETURNED}
+{
+ \spec{R5}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D5}{D}{J2000.0 FK5 $\delta$ (radians)} \\
+ \spec{DR5}{D}{J2000.0 FK5 proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DD5}{D}{FK5 J2000.0 proper motion in $\delta$
+                              (radians per Julian year)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item The FK5 to Hipparcos
+        transformation consists of a pure rotation and spin;
+        zonal errors in the FK5 catalogue are not taken into account.
+  \item The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin
+        values are as follows (see reference):
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~~~
+        \begin{tabular}{|r|r|r|} \hline
+        &
+        \multicolumn{1}{|c}{\it orientation} &
+        \multicolumn{1}{|c|}{\it ~~~spin~~~} \\ \hline
+        $x$ & $-19.9$~~~~ & ~$-0.30$~~ \\
+        $y$ &  $-9.1$~~~~ & ~$+0.60$~~ \\
+        $z$ & $+22.9$~~~~ & ~$+0.70$~~ \\ \hline
+        & {\it mas}~~~~~ & ~{\it mas/y}~ \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        These orientation and spin components are interpreted as
+        {\it axial vectors.}  An axial vector points at the pole of
+        the rotation and its length is the amount of rotation in radians.
+  \item See also sla\_FK52H, sla\_FK5HZ, sla\_HFK5Z.
+ \end{enumerate}
+}
+\aref {Feissel, M.\ \& Mignard, F., 1998.,  {\it Astron.Astrophys.}\
+       {\bf 331}, L33-L36.}
+%-----------------------------------------------------------------------
+\routine{SLA\_HFK5Z}{Hipparcos to FK5, no P.M.}
+{
+ \action{Transform a Hipparcos star position
+         into the FK5 (J2000) frame assuming zero Hipparcos proper motion.}
+ \call{CALL sla\_HFK5Z (RH,DH,EPOCH,R5,D5,DR5,DD5)}
+}
+\args{GIVEN}
+{
+ \spec{RH}{D}{Hipparcos $\alpha$ (radians)} \\
+ \spec{DH}{D}{Hipparcos $\delta$ (radians)} \\
+ \spec{EPOCH}{D}{Julian epoch (TDB)}
+}
+\args{RETURNED}
+{
+ \spec{R5}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D5}{D}{J2000.0 FK5 $\delta$ (radians)} \\
+ \spec{DR5}{D}{J2000.0 FK5 proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DD5}{D}{FK5 J2000.0 proper motion in $\delta$
+                              (radians per Julian year)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item The FK5 to Hipparcos
+        transformation consists of a pure rotation and spin;
+        zonal errors in the FK5 catalogue are not taken into account.
+  \item The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin
+        values are as follows (see reference):
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~~~
+        \begin{tabular}{|r|r|r|} \hline
+        &
+        \multicolumn{1}{|c}{\it orientation} &
+        \multicolumn{1}{|c|}{\it ~~~spin~~~} \\ \hline
+        $x$ & $-19.9$~~~~ & ~$-0.30$~~ \\
+        $y$ &  $-9.1$~~~~ & ~$+0.60$~~ \\
+        $z$ & $+22.9$~~~~ & ~$+0.70$~~ \\ \hline
+        & {\it mas}~~~~~ & ~{\it mas/y}~ \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        These orientation and spin components are interpreted as
+        {\it axial vectors.}  An axial vector points at the pole of
+        the rotation and its length is the amount of rotation in radians.
+        The order of the rotations, which are very small,
+  \item It was the intention that Hipparcos should be a close
+        approximation to an inertial frame, so that distant objects
+        have zero proper motion;  such objects have (in general)
+        non-zero proper motion in FK5, and this routine returns those
+        {\it fictitious proper motions.}
+  \item The position returned by this routine is in the FK5 J2000
+        reference frame but at Julian epoch EPOCH.
+  \item See also sla\_FK52H, sla\_FK5HZ, sla\_H2FK5.
+ \end{enumerate}
+}
+\aref {Feissel, M.\ \& Mignard, F., 1998.,  {\it Astron.Astrophys.}\
+       {\bf 331}, L33-L36.}
+%-----------------------------------------------------------------------
+\routine{SLA\_IMXV}{Apply 3D Reverse Rotation}
+{
+ \action{Multiply a 3-vector by the inverse of a rotation
+         matrix (single precision).}
+ \call{CALL sla\_IMXV (RM, VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{RM}{R(3,3)}{rotation matrix} \\
+ \spec{VA}{R(3)}{vector to be rotated}
+}
+\args{RETURNED}
+{
+ \spec{VB}{R(3)}{result vector}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine performs the operation:
+        \begin{verse}
+         {\bf b} = {\bf M}$^{T}\cdot${\bf a}
+        \end{verse}
+        where {\bf a} and {\bf b} are the 3-vectors VA and VB
+        respectively, and {\bf M} is the $3\times3$ matrix RM.
+  \item The main function of this routine is apply an inverse
+        rotation;  under these circumstances, ${\bf M}$ is
+        {\it orthogonal}, with its inverse the same as its transpose.
+  \item To comply with the ANSI Fortran 77 standard, VA and VB must
+        {\bf not} be the same array.  The routine is, in fact, coded
+        so as to work properly on the VAX and many other systems even
+        if this rule is violated, something that is {\bf not}, however,
+        recommended.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_INTIN}{Decode an Integer Number}
+{
+ \action{Convert free-format input into an integer.}
+ \call{CALL sla\_INTIN (STRING, NSTRT, IRESLT, JFLAG)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C}{string containing number to be decoded} \\
+ \spec{NSTRT}{I}{pointer to where decoding is to commence} \\
+ \spec{IRESLT}{I}{current value of result}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{advanced to next number} \\
+ \spec{IRESLT}{I}{result} \\
+ \spec{JFLAG}{I}{status: $-$1 = $-$OK, 0~=~+OK, 1~=~null result, 2~=~error}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The reason sla\_INTIN has separate `OK' status values
+       for + and $-$ is to enable minus zero to be detected.
+       This is of crucial importance
+       when decoding mixed-radix numbers.  For example, an angle
+       expressed as degrees, arcminutes and arcseconds may have a
+       leading minus sign but a zero degrees field.
+ \item A TAB is interpreted as a space. {\it n.b.}\ The test for TAB is
+       ASCII-specific.
+ \item The basic format is the sequence of fields $\pm n$,
+       where $\pm$ is a sign
+       character `+' or `$-$', and $n$ means a string of decimal digits.
+ \item Spaces:
+       \begin{itemize}
+       \item Leading spaces are ignored.
+       \item Spaces between the sign and the number are allowed.
+       \item Trailing spaces are ignored;  the first signifies
+             end of decoding and subsequent ones are skipped.
+       \end{itemize}
+ \item Delimiters:
+       \begin{itemize}
+       \item Any character other than +,$-$,0-9 or space may be
+             used to signal the end of the number and terminate decoding.
+       \item Comma is recognized by sla\_INTIN as a special case; it
+             is skipped, leaving the pointer on the next character.  See
+             9, below.
+       \item Decoding will in all cases terminate if end of string
+             is reached.
+       \end{itemize}
+ \item The sign is optional.  The default is +.
+ \item A {\it null result}\/ occurs when the string of characters
+       being decoded does not begin with +,$-$ or 0-9, or
+       consists entirely of spaces.  When this condition is
+       detected, JFLAG is set to 1 and IRESLT is left untouched.
+ \item NSTRT = 1 for the first character in the string.
+ \item On return from sla\_INTIN, NSTRT is set ready for the next
+       decode -- following trailing blanks and any comma.  If a
+       delimiter other than comma is being used, NSTRT must be
+       incremented before the next call to sla\_INTIN, otherwise
+       all subsequent calls will return a null result.
+ \item Errors (JFLAG=2) occur when:
+       \begin{itemize}
+       \item there is a + or $-$ but no number; or
+       \item the number is greater than $2^{31}-1$.
+       \end{itemize}
+ \item When an error has been detected, NSTRT is left
+       pointing to the character following the last
+       one used before the error came to light.
+ \item See also sla\_FLOTIN and sla\_DFLTIN.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_INVF}{Invert Linear Model}
+{
+ \action{Invert a linear model of the type produced by the
+         sla\_FITXY routine.}
+ \call{CALL sla\_INVF (FWDS,BKWDS,J)}
+}
+\args{GIVEN}
+{
+ \spec{FWDS}{D(6)}{model coefficients}
+}
+\args{RETURNED}
+{
+ \spec{BKWDS}{D(6)}{inverse model} \\
+ \spec{J}{I}{status:  0 = OK, $-$1 = no inverse}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The models relate two sets of \xy\ coordinates as follows.
+        Naming the six elements of FWDS $a,b,c,d,e$ \& $f$,
+        where two sets of coordinates $[x_{1},y_{1}]$ and
+        $[x_{2},y_{2}\,]$ are related thus:
+        \begin{verse}
+         $x_{2} = a + bx_{1} + cy_{1}$ \\
+         $y_{2} = d + ex_{1} + fy_{1}$
+        \end{verse}
+        The present routine generates a new set of coefficients
+        $p,q,r,s,t$ \& $u$ (the array BKWDS) such that:
+        \begin{verse}
+         $x_{1} = p + qx_{2} + ry_{2}$ \\
+         $y_{1} = s + tx_{2} + uy_{2}$
+        \end{verse}
+  \item Two successive calls to this routine will deliver a set
+        of coefficients equal to the starting values.
+  \item To comply with the ANSI Fortran 77 standard, FWDS and BKWDS must
+        {\bf not} be the same array.  The routine is, in fact, coded
+        so as to work properly on the VAX and many other systems even
+        if this rule is violated, something that is {\bf not}, however,
+        recommended.
+  \item See also sla\_FITXY, sla\_PXY, sla\_XY2XY, sla\_DCMPF.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_KBJ}{Select Epoch Prefix}
+{
+ \action{Select epoch prefix `B' or `J'.}
+ \call{CALL sla\_KBJ (JB, E, K, J)}
+}
+\args{GIVEN}
+{
+ \spec{JB}{I}{sla\_DBJIN prefix status:  0=none, 1=`B', 2=`J'} \\
+ \spec{E}{D}{epoch -- Besselian or Julian}
+}
+\args{RETURNED}
+{
+ \spec{K}{C}{`B' or `J'} \\
+ \spec{J}{I}{status:  0=OK}
+}
+\anote{The routine is mainly intended for use in conjunction with the
+       sla\_DBJIN routine.  If the value of JB indicates that an explicit
+       B or J prefix was detected by sla\_DBJIN, a `B' or `J'
+       is returned to match.  If JB indicates that no explicit B or J
+       was supplied, the choice is made on the basis of the epoch
+       itself;  B is assumed for E $<1984$, otherwise J.}
+%-----------------------------------------------------------------------
+\routine{SLA\_M2AV}{Rotation Matrix to Axial Vector}
+{
+ \action{From a rotation matrix, determine the corresponding axial vector
+        (single precision).}
+ \call{CALL sla\_M2AV (RMAT, AXVEC)}
+}
+\args{GIVEN}
+{
+ \spec{RMAT}{R(3,3)}{rotation matrix}
+}
+\args{RETURNED}
+{
+ \spec{AXVEC}{R(3)}{axial vector (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A rotation matrix describes a rotation about some arbitrary axis.
+        The axis is called the {\it Euler axis}, and the angle through
+        which the reference frame rotates is called the {\it Euler angle}.
+        The {\it axial vector}\/ returned by this routine has the same
+        direction as the Euler axis, and its magnitude is the Euler angle
+        in radians.
+  \item The magnitude and direction of the axial vector can be separated
+        by means of the routine sla\_VN.
+  \item The reference frame rotates clockwise as seen looking along
+        the axial vector from the origin.
+  \item If RMAT is null, so is the result.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_MAP}{Mean to Apparent}
+{
+ \action{Transform star \radec\ from mean place to geocentric apparent.
+         The reference frames and timescales used are post IAU~1976.}
+ \call{CALL sla\_MAP (RM, DM, PR, PD, PX, RV, EQ, DATE, RA, DA)}
+}
+\args{GIVEN}
+{
+ \spec{RM,DM}{D}{mean \radec\ (radians)} \\
+ \spec{PR,PD}{D}{proper motions:  \radec\ changes per Julian year} \\
+ \spec{PX}{D}{parallax (arcsec)} \\
+ \spec{RV}{D}{radial velocity (km~s$^{-1}$, +ve if receding)} \\
+ \spec{EQ}{D}{epoch and equinox of star data (Julian)} \\
+ \spec{DATE}{D}{TDB for apparent place (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{RA,DA}{D}{apparent \radec\ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item EQ is the Julian epoch specifying both the reference
+        frame and the epoch of the position -- usually 2000.
+        For positions where the epoch and equinox are
+        different, use the routine sla\_PM to apply proper
+        motion corrections before using this routine.
+  \item The distinction between the required TDB and TT is
+        always negligible.  Moreover, for all but the most
+        critical applications UTC is adequate.
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item This routine may be wasteful for some applications
+        because it recomputes the Earth position/velocity and
+        the precession/nutation matrix each time, and because
+        it allows for parallax and proper motion.  Where
+        multiple transformations are to be carried out for one
+        epoch, a faster method is to call the sla\_MAPPA routine
+        once and then either the sla\_MAPQK routine (which includes
+        parallax and proper motion) or sla\_MAPQKZ (which assumes
+        zero parallax and FK5 proper motion).
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_MAPPA}{Mean to Apparent Parameters}
+{
+ \action{Compute star-independent parameters in preparation for
+         conversions between mean place and geocentric apparent place.
+         The parameters produced by this routine are required in the
+         parallax, light deflection, aberration, and precession/nutation
+         parts of the mean/apparent transformations.
+         The reference frames and timescales used are post IAU~1976.}
+ \call{CALL sla\_MAPPA (EQ, DATE, AMPRMS)}
+}
+\args{GIVEN}
+{
+ \spec{EQ}{D}{epoch of mean equinox to be used (Julian)} \\
+ \spec{DATE}{D}{TDB (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{AMPRMS}{D(21)}{star-independent mean-to-apparent parameters:} \\
+ \specel   {(1)}     {time interval for proper motion (Julian years)} \\
+ \specel   {(2-4)}   {barycentric position of the Earth (AU)} \\
+ \specel   {(5-7)}   {heliocentric direction of the Earth (unit vector)} \\
+ \specel   {(8)}     {(gravitational radius of
+                      Sun)$\times 2 / $(Sun-Earth distance)} \\
+ \specel   {(9-11)}  {{\bf v}: barycentric Earth velocity in units of c} \\
+ \specel   {(12)}    {$\sqrt{1-\left|\mbox{\bf v}\right|^2}$} \\
+ \specel   {(13-21)} {precession/nutation $3\times3$ matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item For DATE, the distinction between the required TDB and TT
+        is always negligible.  Moreover, for all but the most
+        critical applications UTC is adequate.
+  \item The accuracy of the routines using the parameters AMPRMS is
+        limited by the routine sla\_EVP, used here to compute the
+        Earth position and velocity by the methods of Stumpff.
+        The maximum error in the resulting aberration corrections is
+        about 0.3 milliarcsecond.
+  \item The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to
+        the mean equinox and equator of epoch EQ.
+  \item The parameters produced by this routine are used by
+        sla\_MAPQK and sla\_MAPQKZ.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_MAPQK}{Quick Mean to Apparent}
+{
+ \action{Quick mean to apparent place:  transform a star \radec\ from
+         mean place to geocentric apparent place, given the
+         star-independent parameters.  The reference frames and
+         timescales used are post IAU 1976.}
+ \call{CALL sla\_MAPQK (RM, DM, PR, PD, PX, RV, AMPRMS, RA, DA)}
+}
+\args{GIVEN}
+{
+ \spec{RM,DM}{D}{mean \radec\ (radians)} \\
+ \spec{PR,PD}{D}{proper motions:  \radec\ changes per Julian year} \\
+ \spec{PX}{D}{parallax (arcsec)} \\
+ \spec{RV}{D}{radial velocity (km~s$^{-1}$, +ve if receding)} \\
+ \spec{AMPRMS}{D(21)}{star-independent mean-to-apparent parameters:} \\
+ \specel   {(1)}     {time interval for proper motion (Julian years)} \\
+ \specel   {(2-4)}   {barycentric position of the Earth (AU)} \\
+ \specel   {(5-7)}   {heliocentric direction of the Earth (unit vector)} \\
+ \specel   {(8)}     {(gravitational radius of
+                      Sun)$\times 2 / $(Sun-Earth distance)} \\
+ \specel   {(9-11)}  {{\bf v}: barycentric Earth velocity in units of c} \\
+ \specel   {(12)}    {$\sqrt{1-\left|\mbox{\bf v}\right|^2}$} \\
+ \specel   {(13-21)} {precession/nutation $3\times3$ matrix}
+}
+\args{RETURNED}
+{
+ \spec{RA,DA}{D }{apparent \radec\ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Use of this routine is appropriate when efficiency is important
+        and where many star positions, all referred to the same equator
+        and equinox, are to be transformed for one epoch.  The
+        star-independent parameters can be obtained by calling the
+        sla\_MAPPA routine.
+  \item If the parallax and proper motions are zero the sla\_MAPQKZ
+        routine can be used instead.
+  \item The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to
+        the mean equinox and equator of epoch EQ.
+  \item Strictly speaking, the routine is not valid for solar-system
+        sources, though the error will usually be extremely small.
+        However, to prevent gross errors in the case where the
+        position of the Sun is specified, the gravitational
+        deflection term is restrained within about \arcseci{920} of the
+        centre of the Sun's disc.  The term has a maximum value of
+        about \arcsec{1}{85} at this radius, and decreases to zero as
+        the centre of the disc is approached.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_MAPQKZ}{Quick Mean-Appt, no PM {\it etc.}}
+{
+ \action{Quick mean to apparent place:  transform a star \radec\ from
+         mean place to geocentric apparent place, given the
+         star-independent parameters, and assuming zero parallax
+         and FK5 proper motion.
+         The reference frames and timescales used are post IAU~1976.}
+ \call{CALL sla\_MAPQKZ (RM, DM, AMPRMS, RA, DA)}
+}
+\args{GIVEN}
+{
+ \spec{RM,DM}{D}{mean \radec\ (radians)} \\
+ \spec{AMPRMS}{D(21)}{star-independent mean-to-apparent parameters:} \\
+ \specel   {(1)}     {time interval for proper motion (Julian years)} \\
+ \specel   {(2-4)}   {barycentric position of the Earth (AU)} \\
+ \specel   {(5-7)}   {heliocentric direction of the Earth (unit vector)} \\
+ \specel   {(8)}     {(gravitational radius of
+                      Sun)$\times 2 / $(Sun-Earth distance)} \\
+ \specel   {(9-11)}  {{\bf v}: barycentric Earth velocity in units of c} \\
+ \specel   {(12)}    {$\sqrt{1-\left|\mbox{\bf v}\right|^2}$} \\
+ \specel   {(13-21)} {precession/nutation $3\times3$ matrix}
+}
+\args{RETURNED}
+{
+ \spec{RA,DA}{D}{apparent \radec\ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Use of this routine is appropriate when efficiency is important
+        and where many star positions, all with parallax and proper
+        motion either zero or already allowed for, and all referred to
+        the same equator and equinox, are to be transformed for one
+        epoch.  The star-independent parameters can be obtained by
+        calling the sla\_MAPPA routine.
+  \item The corresponding routine for the case of non-zero parallax
+        and FK5 proper motion is sla\_MAPQK.
+  \item The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to the
+        mean equinox and equator of epoch EQ.
+  \item Strictly speaking, the routine is not valid for solar-system
+        sources, though the error will usually be extremely small.
+        However, to prevent gross errors in the case where the
+        position of the Sun is specified, the gravitational
+        deflection term is restrained within about \arcseci{920} of the
+        centre of the Sun's disc.  The term has a maximum value of
+        about \arcsec{1}{85} at this radius, and decreases to zero as
+        the centre of the disc is approached.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_MOON}{Approx Moon Pos/Vel}
+{
+ \action{Approximate geocentric position and velocity of the Moon
+         (single precision).}
+ \call{CALL sla\_MOON (IY, ID, FD, PV)}
+}
+\args{GIVEN}
+{
+ \spec{IY}{I}{year} \\
+ \spec{ID}{I}{day in year (1 = Jan 1st)} \\
+ \spec{FD}{R }{fraction of day}
+}
+\args{RETURNED}
+{
+ \spec{PV}{R(6)}{Moon \xyzxyzd, mean equator and equinox of
+                 date (AU, AU~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The date and time is TDB (loosely ET) in a Julian calendar
+        which has been aligned to the ordinary Gregorian
+        calendar for the interval 1900 March 1 to 2100 February 28.
+        The year and day can be obtained by calling sla\_CALYD or
+        sla\_CLYD.
+  \item The position is accurate to better than 0.5~arcminute
+        in direction and 1000~km in distance.  The velocity
+        is accurate to better than \arcsec{0}{5} per hour in direction
+        and 4~metres per socond in distance.  (RMS figures with respect
+        to JPL DE200 for the interval 1960-2025 are \arcseci{14} and
+        \arcsec{0}{2} per hour in longitude, \arcseci{9} and \arcsec{0}{2}
+        per hour in latitude, 350~km and 2~metres per second in distance.)
+        Note that the distance accuracy is comparatively poor because this
+        routine is principally intended for computing topocentric direction.
+  \item This routine is only a partial implementation of the original
+        Meeus algorithm (reference below), which offers 4 times the
+        accuracy in direction and 20 times the accuracy in distance
+        when fully implemented (as it is in sla\_DMOON).
+ \end{enumerate}
+}
+\aref{Meeus, {\it l'Astronomie}, June 1984, p348.}
+%-----------------------------------------------------------------------
+\routine{SLA\_MXM}{Multiply $3\times3$ Matrices}
+{
+ \action{Product of two $3\times3$ matrices (single precision).}
+ \call{CALL sla\_MXM (A, B, C)}
+}
+\args{GIVEN}
+{
+ \spec{A}{R(3,3)}{matrix {\bf A}} \\
+ \spec{B}{R(3,3)}{matrix {\bf B}}
+}
+\args{RETURNED}
+{
+ \spec{C}{R(3,3)}{matrix result: {\bf A}$\times${\bf B}}
+}
+\anote{To comply with the ANSI Fortran 77 standard, A, B and C must
+       be different arrays.  The routine is, in fact, coded
+       so as to work properly on the VAX and many other systems even
+       if this rule is violated, something that is {\bf not}, however,
+       recommended.}
+%-----------------------------------------------------------------------
+\routine{SLA\_MXV}{Apply 3D Rotation}
+{
+ \action{Multiply a 3-vector by a rotation matrix (single precision).}
+ \call{CALL sla\_MXV (RM, VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{RM}{R(3,3)}{rotation matrix} \\
+ \spec{VA}{R(3)}{vector to be rotated}
+}
+\args{RETURNED}
+{
+ \spec{VB}{R(3)}{result vector}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine performs the operation:
+        \begin{verse}
+         {\bf b} = {\bf M}$\cdot${\bf a}
+        \end{verse}
+        where {\bf a} and {\bf b} are the 3-vectors VA and VB
+        respectively, and {\bf M} is the $3\times3$ matrix RM.
+  \item The main function of this routine is apply a
+        rotation;  under these circumstances, ${\bf M}$ is a
+        {\it proper real orthogonal}\/ matrix.
+  \item To comply with the ANSI Fortran 77 standard, VA and VB must
+        {\bf not} be the same array.  The routine is, in fact, coded
+        so as to work properly on the VAX and many other systems even
+        if this rule is violated, something that is {\bf not}, however,
+        recommended.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_NUT}{Nutation Matrix}
+{
+ \action{Form the matrix of nutation (IAU 1980 theory) for a given date.}
+ \call{CALL sla\_NUT (DATE, RMATN)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date
+                                          (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{RMATN}{D(3,3)}{nutation matrix}
+}
+\anote{The matrix is in the sense:
+       \begin{verse}
+        {\bf v}$_{true}$ =  {\bf M}$\cdot${\bf v}$_{mean}$
+       \end{verse}
+       where {\bf v}$_{true}$ is the star vector relative to the
+       true equator and equinox of date, {\bf M} is the
+       $3\times3$ matrix RMATN and
+       {\bf v}$_{mean}$ is the star vector relative to the
+       mean equator and equinox of date.}
+\refs
+{
+ \begin{enumerate}
+  \item Final report of the IAU Working Group on Nutation,
+        chairman P.K.Seidelmann, 1980.
+  \item Kaplan, G.H., 1981.\ {\it USNO circular No.\ 163}, pA3-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_NUTC}{Nutation Components}
+{
+ \action{Nutation (IAU 1980 theory):  longitude \& obliquity
+         components, and mean obliquity.}
+ \call{CALL sla\_NUTC (DATE, DPSI, DEPS, EPS0)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date
+                                           (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{DPSI,DEPS}{D}{nutation in longitude and obliquity (radians)} \\
+ \spec{EPS0}{D}{mean obliquity (radians)}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Final report of the IAU Working Group on Nutation,
+        chairman P.K.Seidelmann, 1980.
+  \item Kaplan, G.H., 1981.\ {\it USNO circular no.\ 163}, pA3-6.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_OAP}{Observed to Apparent}
+{
+ \action{Observed to apparent place.}
+ \call{CALL sla\_OAP (\vtop{
+         \hbox{TYPE, OB1, OB2, DATE, DUT, ELONGM, PHIM,}
+         \hbox{HM, XP, YP, TDK, PMB, RH, WL, TLR, RAP, DAP)}}}
+}
+\args{GIVEN}
+{
+ \spec{TYPE}{C*(*)}{type of coordinates -- `R', `H' or `A' (see below)} \\
+ \spec{OB1}{D}{observed Az, HA or RA (radians; Az is N=0, E=$90^{\circ}$)} \\
+ \spec{OB2}{D}{observed zenith distance or $\delta$ (radians)} \\
+ \spec{DATE}{D }{UTC date/time (Modified Julian Date, JD$-$2400000.5)} \\
+ \spec{DUT}{D}{$\Delta$UT:  UT1$-$UTC (UTC seconds)} \\
+ \spec{ELONGM}{D}{observer's mean longitude (radians, east +ve)} \\
+ \spec{PHIM}{D}{observer's mean geodetic latitude (radians)} \\
+ \spec{HM}{D}{observer's height above sea level (metres)} \\
+ \spec{XP,YP}{D}{polar motion \xy\ coordinates (radians)} \\
+ \spec{TDK}{D}{local ambient temperature (degrees K; std=273.155D0)} \\
+ \spec{PMB}{D}{local atmospheric pressure (mB; std=1013.25D0)} \\
+ \spec{RH}{D}{local relative humidity (in the range 0D0\,--\,1D0)} \\
+ \spec{WL}{D}{effective wavelength ($\mu{\rm m}$, {\it e.g.}\ 0.55D0)} \\
+ \spec{TLR}{D}{tropospheric lapse rate (degrees K per metre,
+                                                {\it e.g.}\ 0.0065D0)}
+}
+\args{RETURNED}
+{
+ \spec{RAP,DAP}{D}{geocentric apparent \radec}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Only the first character of the TYPE argument is significant.
+        `R' or `r' indicates that OBS1 and OBS2 are the observed Right
+        Ascension and Declination;  `H' or `h' indicates that they are
+        Hour Angle (west +ve) and Declination; anything else (`A' or
+        `a' is recommended) indicates that OBS1 and OBS2 are Azimuth
+        (north zero, east is $90^{\circ}$) and Zenith Distance.  (Zenith
+        distance is used rather than elevation in order to reflect the
+        fact that no allowance is made for depression of the horizon.)
+  \item The accuracy of the result is limited by the corrections for
+        refraction.  Providing the meteorological parameters are
+        known accurately and there are no gross local effects, the
+        predicted azimuth and elevation should be within about
+        \arcsec{0}{1} for $\zeta<70^{\circ}$.  Even
+        at a topocentric zenith distance of
+        $90^{\circ}$, the accuracy in elevation should be better than
+        1~arcminute;  useful results are available for a further
+        $3^{\circ}$, beyond which the sla\_REFRO routine returns a
+        fixed value of the refraction.  The complementary
+        routines sla\_AOP (or sla\_AOPQK) and sla\_OAP (or sla\_OAPQK)
+        are self-consistent to better than 1~microarcsecond all over
+        the celestial sphere.
+  \item It is advisable to take great care with units, as even
+        unlikely values of the input parameters are accepted and
+        processed in accordance with the models used.
+  \item {\it Observed}\/ \azel\ means the position that would be seen by a
+        perfect theodolite located at the observer.  This is
+        related to the observed \hadec\ via the standard rotation, using
+        the geodetic latitude (corrected for polar motion), while the
+        observed HA and RA are related simply through the local
+        apparent ST.  {\it Observed}\/ \radec\ or \hadec\ thus means the
+        position that would be seen by a perfect equatorial located
+        at the observer and with its polar axis aligned to the
+        Earth's axis of rotation ({\it n.b.}\ not to the refracted pole).
+        By removing from the observed place the effects of
+        atmospheric refraction and diurnal aberration, the
+        geocentric apparent \radec\ is obtained.
+  \item Frequently, {\it mean}\/ rather than {\it apparent}\,
+        \radec\ will be required,
+        in which case further transformations will be necessary.  The
+        sla\_AMP {\it etc.}\ routines will convert
+        the apparent \radec\ produced
+        by the present routine into an FK5 J2000 mean place, by
+        allowing for the Sun's gravitational lens effect, annual
+        aberration, nutation and precession.  Should FK4 B1950
+        coordinates be needed, the routines sla\_FK524 {\it etc.}\ will also
+        need to be applied.
+  \item To convert to apparent \radec\ the coordinates read from a
+        real telescope, corrections would have to be applied for
+        encoder zero points, gear and encoder errors, tube flexure,
+        the position of the rotator axis and the pointing axis
+        relative to it, non-perpendicularity between the mounting
+        axes, and finally for the tilt of the azimuth or polar axis
+        of the mounting (with appropriate corrections for mount
+        flexures).  Some telescopes would, of course, exhibit other
+        properties which would need to be accounted for at the
+        appropriate point in the sequence.
+  \item The star-independent apparent-to-observed-place parameters
+        in AOPRMS may be computed by means of the sla\_AOPPA routine.
+        If nothing has changed significantly except the time, the
+        sla\_AOPPAT routine may be used to perform the requisite
+        partial recomputation of AOPRMS.
+  \item The DATE argument is UTC expressed as an MJD.  This is,
+        strictly speaking, wrong, because of leap seconds.  However,
+        as long as the $\Delta$UT and the UTC are consistent there
+        are no difficulties, except during a leap second.  In this
+        case, the start of the 61st second of the final minute should
+        begin a new MJD day and the old pre-leap $\Delta$UT should
+        continue to be used.  As the 61st second completes, the MJD
+        should revert to the start of the day as, simultaneously,
+        the $\Delta$UT changes by one second to its post-leap new value.
+  \item The $\Delta$UT (UT1$-$UTC) is tabulated in IERS circulars and
+        elsewhere.  It increases by exactly one second at the end of
+        each UTC leap second, introduced in order to keep $\Delta$UT
+        within $\pm$\tsec{0}{9}.
+  \item IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.  The
+        longitude required by the present routine is {\bf east-positive},
+        in accordance with geographical convention (and right-handed).
+        In particular, note that the longitudes returned by the
+        sla\_OBS routine are west-positive (as in the {\it Astronomical
+        Almanac}\/ before 1984) and must be reversed in sign before use
+        in the present routine.
+  \item The polar coordinates XP,YP can be obtained from IERS
+        circulars and equivalent publications.  The
+        maximum amplitude is about \arcsec{0}{3}.  If XP,YP values
+        are unavailable, use XP=YP=0D0.  See page B60 of the 1988
+        {\it Astronomical Almanac}\/ for a definition of the two angles.
+  \item The height above sea level of the observing station, HM,
+        can be obtained from the {\it Astronomical Almanac}\/ (Section J
+        in the 1988 edition), or via the routine sla\_OBS.  If P,
+        the pressure in mB, is available, an adequate
+        estimate of HM can be obtained from the following expression:
+        \begin{quote}
+         {\tt HM=-29.3D0*TSL*LOG(P/1013.25D0)}
+        \end{quote}
+        where TSL is the approximate sea-level air temperature in degrees K
+        (see {\it Astrophysical Quantities}, C.W.Allen, 3rd~edition,
+        \S 52.)  Similarly, if the pressure P is not known,
+        it can be estimated from the height of the observing
+        station, HM as follows:
+        \begin{quote}
+         {\tt P=1013.25D0*EXP(-HM/(29.3D0*TSL))}
+        \end{quote}
+        Note, however, that the refraction is proportional to the
+        pressure and that an accurate P value is important for
+        precise work.
+  \item The azimuths {\it etc.}\ used by the present routine are with
+        respect to the celestial pole.  Corrections from the terrestrial pole
+        can be computed using sla\_POLMO.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_OAPQK}{Quick Observed to Apparent}
+{
+ \action{Quick observed to apparent place.}
+ \call{CALL sla\_OAPQK (TYPE, OB1, OB2, AOPRMS, RAP, DAP)}
+}
+\args{GIVEN}
+{
+ \spec{TYPE}{C*(*)}{type of coordinates -- `R', `H' or `A' (see below)} \\
+ \spec{OB1}{D}{observed Az, HA or RA (radians; Az is N=0, E=$90^{\circ}$)} \\
+ \spec{OB2}{D}{observed zenith distance or $\delta$ (radians)} \\
+ \spec{AOPRMS}{D(14)}{star-independent apparent-to-observed parameters:} \\
+ \specel   {(1)}     {geodetic latitude (radians)} \\
+ \specel   {(2,3)}   {sine and cosine of geodetic latitude} \\
+ \specel   {(4)}     {magnitude of diurnal aberration vector} \\
+ \specel   {(5)}     {height (HM)} \\
+ \specel   {(6)}     {ambient temperature (TDK)} \\
+ \specel   {(7)}     {pressure (PMB)} \\
+ \specel   {(8)}     {relative humidity (RH)} \\
+ \specel   {(9)}     {wavelength (WL)} \\
+ \specel   {(10)}    {lapse rate (TLR)} \\
+ \specel   {(11,12)} {refraction constants A and B (radians)} \\
+ \specel   {(13)}    {longitude + eqn of equinoxes +
+                       ``sidereal $\Delta$UT'' (radians)} \\
+ \specel   {(14)}    {local apparent sidereal time (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RAP,DAP}{D}{geocentric apparent \radec}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Only the first character of the TYPE argument is significant.
+        `R' or `r' indicates that OBS1 and OBS2 are the observed Right
+        Ascension and Declination;  `H' or `h' indicates that they are
+        Hour Angle (west +ve) and Declination; anything else (`A' or
+        `a' is recommended) indicates that OBS1 and OBS2 are Azimuth
+        (north zero, east is $90^{\circ}$) and Zenith Distance.  (Zenith
+        distance is used rather than elevation in order to reflect the
+        fact that no allowance is made for depression of the horizon.)
+  \item The accuracy of the result is limited by the corrections for
+        refraction.  Providing the meteorological parameters are
+        known accurately and there are no gross local effects, the
+        predicted azimuth and elevation should be within about
+        \arcsec{0}{1} for $\zeta<70^{\circ}$.  Even
+        at a topocentric zenith distance of
+        $90^{\circ}$, the accuracy in elevation should be better than
+        1~arcminute;  useful results are available for a further
+        $3^{\circ}$, beyond which the sla\_REFRO routine returns a
+        fixed value of the refraction.  The complementary
+        routines sla\_AOP (or sla\_AOPQK) and sla\_OAP (or sla\_OAPQK)
+        are self-consistent to better than 1~microarcsecond all over
+        the celestial sphere.
+  \item It is advisable to take great care with units, as even
+        unlikely values of the input parameters are accepted and
+        processed in accordance with the models used.
+  \item {\it Observed}\/ \azel\ means the position that would be seen by a
+        perfect theodolite located at the observer.  This is
+        related to the observed \hadec\ via the standard rotation, using
+        the geodetic latitude (corrected for polar motion), while the
+        observed HA and RA are related simply through the local
+        apparent ST.  {\it Observed}\/ \radec\ or \hadec\ thus means the
+        position that would be seen by a perfect equatorial located
+        at the observer and with its polar axis aligned to the
+        Earth's axis of rotation ({\it n.b.}\ not to the refracted pole).
+        By removing from the observed place the effects of
+        atmospheric refraction and diurnal aberration, the
+        geocentric apparent \radec\ is obtained.
+  \item Frequently, {\it mean}\/ rather than {\it apparent}\,
+        \radec\ will be required,
+        in which case further transformations will be necessary.  The
+        sla\_AMP {\it etc.}\ routines will convert
+        the apparent \radec\ produced
+        by the present routine into an FK5 J2000 mean place, by
+        allowing for the Sun's gravitational lens effect, annual
+        aberration, nutation and precession.  Should FK4 B1950
+        coordinates be needed, the routines sla\_FK524 {\it etc.}\ will also
+        need to be applied.
+  \item To convert to apparent \radec\ the coordinates read from a
+        real telescope, corrections would have to be applied for
+        encoder zero points, gear and encoder errors, tube flexure,
+        the position of the rotator axis and the pointing axis
+        relative to it, non-perpendicularity between the mounting
+        axes, and finally for the tilt of the azimuth or polar axis
+        of the mounting (with appropriate corrections for mount
+        flexures).  Some telescopes would, of course, exhibit other
+        properties which would need to be accounted for at the
+        appropriate point in the sequence.
+  \item The star-independent apparent-to-observed-place parameters
+        in AOPRMS may be computed by means of the sla\_AOPPA routine.
+        If nothing has changed significantly except the time, the
+        sla\_AOPPAT routine may be used to perform the requisite
+        partial recomputation of AOPRMS.
+  \item The azimuths {\it etc.}\ used by the present routine are with
+        respect to the celestial pole.  Corrections from the terrestrial pole
+        can be computed using sla\_POLMO.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_OBS}{Observatory Parameters}
+{
+ \action{Look up an entry in a standard list of
+         groundbased observing stations parameters.}
+ \call{CALL sla\_OBS (N, C, NAME, W, P, H)}
+}
+\args{GIVEN}
+{
+ \spec{N}{I}{number specifying observing station}
+}
+\args{GIVEN or RETURNED}
+{
+ \spec{C}{C*(*)}{identifier specifying observing station}
+}
+\args{RETURNED}
+{
+ \spec{NAME}{C*(*)}{name of specified observing station} \\
+ \spec{W}{D}{longitude (radians, west +ve)} \\
+ \spec{P}{D}{geodetic latitude (radians, north +ve)} \\
+ \spec{H}{D}{height above sea level (metres)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Station identifiers C may be up to 10 characters long,
+        and station names NAME may be up to 40 characters long.
+  \item C and N are {\it alternative}\/ ways of specifying the observing
+        station.  The C option, which is the most generally useful,
+        may be selected by specifying an N value of zero or less.
+        If N is 1 or more, the parameters of the Nth station
+        in the currently supported list are interrogated, and
+        the station identifier C is returned as well as NAME, W,
+        P and H.
+  \item If the station parameters are not available, either because
+        the station identifier C is not recognized, or because an
+        N value greater than the number of stations supported is
+        given, a name of `?' is returned and W, P and H are left in
+        their current states.
+  \item Programs can obtain a list of all currently supported
+        stations by calling the routine repeatedly, with N=1,2,3...
+        When NAME=`?' is seen, the list of stations has been
+        exhausted.  The stations at the time of writing are listed
+        below.
+  \item Station numbers, identifiers, names and other details are
+        subject to change and should not be hardwired into
+        application programs.
+  \item All station identifiers C are uppercase only;  lower case
+        characters must be converted to uppercase by the calling
+        program.  The station names returned may contain both upper-
+        and lowercase.  All characters up to the first space are
+        checked;  thus an abbreviated ID will return the parameters
+        for the first station in the list which matches the
+        abbreviation supplied, and no station in the list will ever
+        contain embedded spaces.  C must not have leading spaces.
+  \item IMPORTANT -- BEWARE OF THE LONGITUDE SIGN CONVENTION.  The
+        longitude returned by sla\_OBS is
+        {\bf west-positive}, following the pre-1984 {\it Astronomical
+        Almanac}.  However, this sign convention is left-handed and is
+        the opposite of the one now used; elsewhere in
+        SLALIB the preferable east-positive convention is used.  In
+        particular, note that for use in sla\_AOP, sla\_AOPPA and
+        sla\_OAP the sign of the longitude must be reversed.
+  \item Users are urged to inform the author of any improvements
+        they would like to see made.  For example:
+        \begin{itemize}
+         \item typographical corrections
+         \item more accurate parameters
+         \item better station identifiers or names
+         \item additional stations
+        \end{itemize}
+ \end{enumerate}
+Stations supported by sla\_OBS at the time of writing:
+\begin{tabbing}
+xxxxxxxxxxxxxxxxx \= \kill
+{\it ID} \> {\it NAME} \\ \\
+AAT \> Anglo-Australian 3.9m Telescope \\
+ANU2.3 \> Siding Spring 2.3 metre \\
+APO3.5 \> Apache Point 3.5m \\
+ARECIBO \> Arecibo 1000 foot \\
+ATCA \> Australia Telescope Compact Array \\
+BLOEMF \> Bloemfontein 1.52 metre \\
+BOSQALEGRE \> Bosque Alegre 1.54 metre \\
+CAMB1MILE \> Cambridge 1 mile \\
+CAMB5KM \> Cambridge 5km \\
+CATALINA61 \> Catalina 61 inch \\
+CFHT \> Canada-France-Hawaii 3.6m Telescope \\
+CSO \> Caltech Sub-mm Observatory, Mauna Kea \\
+DAO72 \> DAO Victoria BC 1.85 metre \\
+DUNLAP74 \> David Dunlap 74 inch \\
+DUPONT \> Du Pont 2.5m Telescope, Las Campanas \\
+EFFELSBERG \> Effelsberg 100 metre \\
+ESO3.6 \> ESO 3.6 metre \\
+ESONTT \> ESO 3.5 metre NTT \\
+ESOSCHM \> ESO 1 metre Schmidt, La Silla \\
+FCRAO \> Five College Radio Astronomy Obs \\
+FLAGSTF61 \> USNO 61 inch astrograph, Flagstaff \\
+GBVA140 \> Greenbank 140 foot \\
+GBVA300 \> Greenbank 300 foot \\
+GEMININ \> Gemini North 8-m telescope \\
+HARVARD \> Harvard College Observatory 1.55m \\
+HPROV1.52 \> Haute Provence 1.52 metre \\
+HPROV1.93 \> Haute Provence 1.93 metre \\
+IRTF \> NASA IR Telescope Facility, Mauna Kea \\
+JCMT \> JCMT 15 metre \\
+JODRELL1 \> Jodrell Bank 250 foot \\
+KECK1 \> Keck 10m Telescope 1 \\
+KECK2 \> Keck 10m Telescope 2 \\
+KISO \> Kiso 1.05 metre Schmidt, Japan \\
+KOTTAMIA \> Kottamia 74 inch \\
+KPNO158 \> Kitt Peak 158 inch \\
+KPNO36FT \> Kitt Peak 36 foot \\
+KPNO84 \> Kitt Peak 84 inch \\
+KPNO90 \> Kitt Peak 90 inch \\
+LICK120 \> Lick 120 inch \\
+LOWELL72 \> Perkins 72 inch, Lowell \\
+LPO1 \> Jacobus Kapteyn 1m Telescope \\
+LPO2.5 \> Isaac Newton 2.5m Telescope \\
+LPO4.2 \> William Herschel 4.2m Telescope \\
+MAUNAK88 \> Mauna Kea 88 inch \\
+MCDONLD2.1 \> McDonald 2.1 metre \\
+MCDONLD2.7 \> McDonald 2.7 metre \\
+MMT \> MMT, Mt Hopkins \\
+MOPRA \> ATNF Mopra Observatory \\
+MTEKAR \> Mt Ekar 1.82 metre \\
+MTHOP1.5 \> Mt Hopkins 1.5 metre \\
+MTLEMMON60 \> Mt Lemmon 60 inch \\
+NOBEYAMA \> Nobeyama 45 metre \\
+OKAYAMA \> Okayama 1.88 metre \\
+PALOMAR200 \> Palomar 200 inch \\
+PALOMAR48 \> Palomar 48-inch Schmidt \\
+PALOMAR60 \> Palomar 60 inch \\
+PARKES \> Parkes 64 metre \\
+QUEBEC1.6 \> Quebec 1.6 metre \\
+SAAO74 \> Sutherland 74 inch \\
+SANPM83 \> San Pedro Martir 83 inch \\
+ST.ANDREWS \> St Andrews University Observatory \\
+STEWARD90 \> Steward 90 inch \\
+STROMLO74 \> Mount Stromlo 74 inch \\
+SUBARU \> Subaru 8 metre \\
+SUGARGROVE \> Sugar Grove 150 foot \\
+TAUTNBG \> Tautenburg 2 metre \\
+TAUTSCHM \> Tautenberg 1.34 metre Schmidt \\
+TIDBINBLA \> Tidbinbilla 64 metre \\
+TOLOLO1.5M \> Cerro Tololo 1.5 metre \\
+TOLOLO4M \> Cerro Tololo 4 metre \\
+UKIRT \> UK Infra Red Telescope \\
+UKST \> UK 1.2 metre Schmidt, Siding Spring \\
+USSR6 \> USSR 6 metre \\
+USSR600 \> USSR 600 foot \\
+VLA \> Very Large Array
+\end{tabbing}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PA}{$h,\delta$ to Parallactic Angle}
+{
+ \action{Hour angle and declination to parallactic angle
+         (double precision).}
+ \call{D~=~sla\_PA (HA, DEC, PHI)}
+}
+\args{GIVEN}
+{
+ \spec{HA}{D}{hour angle in radians (geocentric apparent)} \\
+ \spec{DEC}{D}{declination in radians (geocentric apparent)} \\
+ \spec{PHI}{D}{latitude in radians (geodetic)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_PA}{D}{parallactic angle (radians, in the range $\pm \pi$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The parallactic angle at a point in the sky is the position
+        angle of the vertical, {\it i.e.}\ the angle between the direction to
+        the pole and to the zenith.  In precise applications care must
+        be taken only to use geocentric apparent \hadec\ and to consider
+        separately the effects of atmospheric refraction and telescope
+        mount errors.
+  \item At the pole a zero result is returned.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PAV}{Position-Angle Between Two Directions}
+{
+ \action{Returns the bearing (position angle) of one celestial
+         direction with respect to another (single precision).}
+ \call{R~=~sla\_PAV (V1, V2)}
+}
+\args{GIVEN}
+{
+ \spec{V1}{R(3)}{direction cosines of one point} \\
+ \spec{V2}{R(3)}{directions cosines of the other point}
+}
+\args{RETURNED}
+{
+ \spec{sla\_PAV}{R}{position-angle of 2nd point with respect to 1st}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The coordinate frames correspond to \radec,
+       $[\lambda,\phi]$ {\it etc.}.
+ \item The result is the bearing (position angle), in radians,
+       of point V2 as seen
+       from point V1.  It is in the range $\pm \pi$.  The sense
+       is such that if V2
+       is a small distance due east of V1 the result
+       is about $+\pi/2$. Zero is returned
+       if the two points are coincident.
+ \item The routine sla\_BEAR performs an equivalent function except
+       that the points are specified in the form of spherical coordinates.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_PCD}{Apply Radial Distortion}
+{
+ \action{Apply pincushion/barrel distortion to a tangent-plane \xy.}
+ \call{CALL sla\_PCD (DISCO,X,Y)}
+}
+\args{GIVEN}
+{
+ \spec{DISCO}{D}{pincushion/barrel distortion coefficient} \\
+ \spec{X,Y}{D}{tangent-plane \xy}
+}
+\args{RETURNED}
+{
+ \spec{X,Y}{D}{distorted \xy}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The distortion is of the form $\rho = r (1 + c r^{2})$, where $r$ is
+        the radial distance from the tangent point, $c$ is the DISCO
+        argument, and $\rho$ is the radial distance in the presence of
+        the distortion.
+  \item For {\it pincushion}\/ distortion, C is +ve;  for
+        {\it barrel}\/ distortion, C is $-$ve.
+  \item For X,Y in units of one projection radius (in the case of
+        a photographic plate, the focal length), the following
+        DISCO values apply:
+
+        \vspace{2ex}
+
+        \hspace{5em}
+        \begin{tabular}{|l|c|} \hline
+         Geometry & DISCO \\ \hline \hline
+         astrograph & 0.0 \\ \hline
+         Schmidt & $-$0.3333 \\ \hline
+         AAT PF doublet & +147.069 \\ \hline
+         AAT PF triplet & +178.585 \\ \hline
+         AAT f/8 & +21.20 \\ \hline
+         JKT f/8 & +14.6 \\ \hline
+        \end{tabular}
+
+        \vspace{2ex}
+
+  \item There is a companion routine, sla\_UNPCD, which performs
+        an approximately inverse operation.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PDA2H}{H.A.\ for a Given Azimuth}
+{
+ \action{Hour Angle corresponding to a given azimuth (double precision).}
+ \call{CALL sla\_PDA2H (P, D, A, H1, J1, H2, J2)}
+}
+\args{GIVEN}
+{
+ \spec{P}{D}{latitude} \\
+ \spec{D}{D}{declination} \\
+ \spec{A}{D}{azimuth}
+}
+\args{RETURNED}
+{
+ \spec{H1}{D}{hour angle:  first solution if any} \\
+ \spec{J1}{I}{flag: 0 = solution 1 is valid} \\
+ \spec{H2}{D}{hour angle:  second solution if any} \\
+ \spec{J2}{I}{flag: 0 = solution 2 is valid}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PDQ2H}{H.A.\ for a Given P.A.}
+{
+ \action{Hour Angle corresponding to a given parallactic angle
+         (double precision).}
+ \call{CALL sla\_PDQ2H (P, D, Q, H1, J1, H2, J2)}
+}
+\args{GIVEN}
+{
+ \spec{P}{D}{latitude} \\
+ \spec{D}{D}{declination} \\
+ \spec{Q}{D}{azimuth}
+}
+\args{RETURNED}
+{
+ \spec{H1}{D}{hour angle:  first solution if any} \\
+ \spec{J1}{I}{flag: 0 = solution 1 is valid} \\
+ \spec{H2}{D}{hour angle:  second solution if any} \\
+ \spec{J2}{I}{flag: 0 = solution 2 is valid}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_PERTEL}{Perturbed Orbital Elements}
+{
+ \action{Update the osculating elements of an asteroid or comet by
+         applying planetary perturbations.}
+ \call{CALL sla\_PERTEL (\vtop{
+         \hbox{JFORM, DATE0, DATE1,}
+         \hbox{EPOCH0, ORBI0, ANODE0, PERIH0, AORQ0, E0, AM0,}
+         \hbox{EPOCH1, ORBI1, ANODE1, PERIH1, AORQ1, E1, AM1,}
+         \hbox{JSTAT)}}}
+}
+\args{GIVEN (format and dates)}
+{
+ \spec{JFORM}{I}{choice of element set (2 or 3; Note~1)} \\
+ \spec{DATE0}{D}{date of osculation (TT MJD) for the given} \\
+ \spec{}{}{\hspace{1.5em} elements} \\
+ \spec{DATE1}{D}{date of osculation (TT MJD) for the updated} \\
+ \spec{}{}{\hspace{1.5em} elements}
+}
+\args{GIVEN (the unperturbed elements)}
+{
+ \spec{EPOCH0}{D}{epoch of the given element set
+                            ($t_0$ or $T$, TT MJD;} \\
+ \spec{}{}{\hspace{1.5em} Note~2)} \\
+ \spec{ORBI0}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE0}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH0}{D}{argument of perihelion
+                            ($\omega$, radians)} \\
+ \spec{AORQ0}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E0}{D}{eccentricity ($e$)} \\
+ \spec{AM0}{D}{mean anomaly ($M$, radians, JFORM=2 only)}
+}
+\args{RETURNED (the updated elements)}
+{
+ \spec{EPOCH1}{D}{epoch of the updated element set
+                            ($t_0$ or $T$,} \\
+ \spec{}{}{\hspace{1.5em} TT MJD; Note~2)} \\
+ \spec{ORBI1}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE1}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH1}{D}{argument of perihelion
+                            ($\omega$, radians)} \\
+ \spec{AORQ1}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E1}{D}{eccentricity ($e$)} \\
+ \spec{AM1}{D}{mean anomaly ($M$, radians, JFORM=2 only)}
+}
+\args{RETURNED (status flag)}
+{
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{0.5em}+102 = warning, distant epoch} \\
+ \spec{}{}{\hspace{0.5em}+101 = warning, large timespan
+                                            ($>100$ years)} \\
+ \spec{}{}{\hspace{-1.3em}+1 to +8 = coincident with major planet
+                                                  (Note~6)} \\
+ \spec{}{}{\hspace{1.95em}       0 = OK} \\
+ \spec{}{}{\hspace{1.2em}    $-$1 = illegal JFORM} \\
+ \spec{}{}{\hspace{1.2em}    $-$2 = illegal E0} \\
+ \spec{}{}{\hspace{1.2em}    $-$3 = illegal AORQ0} \\
+ \spec{}{}{\hspace{1.2em}    $-$4 = internal error} \\
+ \spec{}{}{\hspace{1.2em}    $-$5 = numerical error}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Two different element-format options are supported, as follows. \\
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of elements $t_0$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> mean distance $a$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        \> AORL   \> = \> mean anomaly $M$ (radians)
+        \end{tabbing}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of perihelion $T$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> perihelion distance $q$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e \leq 10 )$
+        \end{tabbing}
+ \item DATE0, DATE1, EPOCH0 and EPOCH1 are all instants of time in
+       the TT timescale (formerly Ephemeris Time, ET), expressed
+       as Modified Julian Dates (JD$-$2400000.5).
+       \begin{itemize}
+       \item DATE0 is the instant at which the given
+             ({\it i.e.}\ unperturbed) osculating elements are correct.
+       \item DATE1 is the specified instant at which the updated osculating
+             elements are correct.
+       \item EPOCH0 and EPOCH1 will be the same as DATE0 and DATE1
+             (respectively) for the JFORM=2 case, normally used for minor
+             planets.  For the JFORM=3 case, the two epochs will refer to
+             perihelion passage and so will not, in general, be the same as
+             DATE0 and/or DATE1 though they may be similar to one another.
+       \end{itemize}
+ \item The elements are with respect to the J2000 ecliptic and mean equinox.
+ \item Unused elements (AM0 and AM1 for JFORM=3) are not accessed.
+ \item See the sla\_PERTUE routine for details of the algorithm used.
+ \item This routine is not intended to be used for major planets, which
+       is why JFORM=1 is not available and why there is no opportunity
+       to specify either the longitude of perihelion or the daily
+       motion.  However, if JFORM=2 elements are somehow obtained for a
+       major planet and supplied to the routine, sensible results will,
+       in fact, be produced.  This happens because the sla\_PERTUE routine
+       that is called to perform the calculations checks the separation
+       between the body and each of the planets and interprets a
+       suspiciously small value (0.001~AU) as an attempt to apply it to
+       the planet concerned.  If this condition is detected, the
+       contribution from that planet is ignored, and the status is set to
+       the planet number (Mercury=1,\ldots,Neptune=8) as a warning.
+ \end{enumerate}
+}
+\aref{Sterne, Theodore E., {\it An Introduction to Celestial Mechanics,}\/
+      Interscience Publishers, 1960.  Section 6.7, p199.}
+%------------------------------------------------------------------------------
+\routine{SLA\_PERTUE}{Perturbed Universal Elements}
+{
+ \action{Update the universal elements of an asteroid or comet by
+         applying planetary perturbations.}
+ \call{CALL sla\_PERTUE (DATE, U, JSTAT)}
+}
+\args{GIVEN}
+{
+ \spec{DATE1}{D}{final epoch (TT MJD) for the updated elements}
+}
+\args{GIVEN and RETURNED}
+{
+ \spec{U}{D(13)}{universal elements (updated in place)} \\
+ \specel {(1)}     {combined mass ($M+m$)} \\
+ \specel {(2)}     {total energy of the orbit ($\alpha$)} \\
+ \specel {(3)}     {reference (osculating) epoch ($t_0$)} \\
+ \specel {(4-6)}   {position at reference epoch (${\rm \bf r}_0$)} \\
+ \specel {(7-9)}   {velocity at reference epoch (${\rm \bf v}_0$)} \\
+ \specel {(10)}    {heliocentric distance at reference epoch} \\
+ \specel {(11)}    {${\rm \bf r}_0.{\rm \bf v_0}$} \\
+ \specel {(12)}    {date ($t$)} \\
+ \specel {(13)}    {universal eccentric anomaly ($\psi$) of date, approx}
+}
+\args{RETURNED}
+{
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{0.5em}+102 = warning, distant epoch} \\
+ \spec{}{}{\hspace{0.5em}+101 = warning, large timespan
+                                            ($>100$ years)} \\
+ \spec{}{}{\hspace{-1.3em}+1 to +8 = coincident with major planet
+                                                  (Note~5)} \\
+ \spec{}{}{\hspace{1.95em}       0 = OK} \\
+ \spec{}{}{\hspace{1.2em}    $-$1 = numerical error}
+}
+\notes
+{
+ \begin{enumerate}
+  \setlength{\parskip}{\medskipamount}
+  \item The ``universal'' elements are those which define the orbit for the
+        purposes of the method of universal variables (see reference 2).
+        They consist of the combined mass of the two bodies, an epoch,
+        and the position and velocity vectors (arbitrary reference frame)
+        at that epoch.  The parameter set used here includes also various
+        quantities that can, in fact, be derived from the other
+        information.  This approach is taken to avoiding unnecessary
+        computation and loss of accuracy.  The supplementary quantities
+        are (i)~$\alpha$, which is proportional to the total energy of the
+        orbit, (ii)~the heliocentric distance at epoch,
+        (iii)~the outwards component of the velocity at the given epoch,
+        (iv)~an estimate of $\psi$, the ``universal eccentric anomaly'' at a
+        given date and (v)~that date.
+  \item The universal elements are with respect to the J2000 equator and
+        equinox.
+  \item The epochs DATE, U(3) and U(12) are all Modified Julian Dates
+        (JD$-$2400000.5).
+  \item The algorithm is a simplified form of Encke's method.  It takes as
+        a basis the unperturbed motion of the body, and numerically
+        integrates the perturbing accelerations from the major planets.
+        The expression used is essentially Sterne's 6.7-2 (reference 1).
+        Everhart and Pitkin (reference 2) suggest rectifying the orbit at
+        each integration step by propagating the new perturbed position
+        and velocity as the new universal variables.  In the present
+        routine the orbit is rectified less frequently than this, in order
+        to gain a slight speed advantage.  However, the rectification is
+        done directly in terms of position and velocity, as suggested by
+        Everhart and Pitkin, bypassing the use of conventional orbital
+        elements.
+
+        The $f(q)$ part of the full Encke method is not used.  The purpose
+        of this part is to avoid subtracting two nearly equal quantities
+        when calculating the ``indirect member'', which takes account of the
+        small change in the Sun's attraction due to the slightly displaced
+        position of the perturbed body.  A simpler, direct calculation in
+        double precision proves to be faster and not significantly less
+        accurate.
+
+        Apart from employing a variable timestep, and occasionally
+        ``rectifying the orbit'' to keep the indirect member small, the
+        integration is done in a fairly straightforward way.  The
+        acceleration estimated for the middle of the timestep is assumed
+        to apply throughout that timestep;  it is also used in the
+        extrapolation of the perturbations to the middle of the next
+        timestep, to predict the new disturbed position.  There is no
+        iteration within a timestep.
+
+        Measures are taken to reach a compromise between execution time
+        and accuracy.  The starting-point is the goal of achieving
+        arcsecond accuracy for ordinary minor planets over a ten-year
+        timespan.  This goal dictates how large the timesteps can be,
+        which in turn dictates how frequently the unperturbed motion has
+        to be recalculated from the osculating elements.
+
+        Within predetermined limits, the timestep for the numerical
+        integration is varied in length in inverse proportion to the
+        magnitude of the net acceleration on the body from the major
+        planets.
+
+        The numerical integration requires estimates of the major-planet
+        motions.  Approximate positions for the major planets (Pluto
+        alone is omitted) are obtained from the routine sla\_PLANET.  Two
+        levels of interpolation are used, to enhance speed without
+        significantly degrading accuracy.  At a low frequency, the routine
+        sla\_PLANET is called to generate updated position+velocity ``state
+        vectors''.  The only task remaining to be carried out at the full
+        frequency ({\it i.e.}\ at each integration step) is to use the state
+        vectors to extrapolate the planetary positions.  In place of a
+        strictly linear extrapolation, some allowance is made for the
+        curvature of the orbit by scaling back the radius vector as the
+        linear extrapolation goes off at a tangent.
+
+        Various other approximations are made.  For example, perturbations
+        by Pluto and the minor planets are neglected, relativistic effects
+        are not taken into account and the Earth-Moon system is treated as
+        a single body.
+
+        In the interests of simplicity, the background calculations for
+        the major planets are carried out {\it en masse.}
+        The mean elements and
+        state vectors for all the planets are refreshed at the same time,
+        without regard for orbit curvature, mass or proximity.
+
+  \item This routine is not intended to be used for major planets.
+        However, if major-planet elements are supplied, sensible results
+        will, in fact, be produced.  This happens because the routine
+        checks the separation between the body and each of the planets and
+        interprets a suspiciously small value (0.001~AU) as an attempt to
+        apply the routine to the planet concerned.  If this condition
+        is detected, the
+        contribution from that planet is ignored, and the status is set to
+        the planet number (Mercury=1,\ldots,Neptune=8) as a warning.
+ \end{enumerate}
+}
+\refs{
+   \begin{enumerate}
+   \item Sterne, Theodore E., {\it An Introduction to Celestial Mechanics,}\/
+         Interscience Publishers, 1960.  Section 6.7, p199.
+   \item Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.
+   \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PLANEL}{Planet Position from Elements}
+{
+ \action{Heliocentric position and velocity of a planet,
+         asteroid or comet, starting from orbital elements.}
+ \call{CALL sla\_PLANEL (\vtop{
+         \hbox{DATE, JFORM, EPOCH, ORBINC, ANODE, PERIH,}
+         \hbox{AORQ, E, AORL, DM, PV, JSTAT)}}}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{Modified Julian Date (JD$-$2400000.5)} \\
+ \spec{JFORM}{I}{choice of element set (1-3, see Note~3, below)} \\
+ \spec{EPOCH}{D}{epoch of elements ($t_0$ or $T$, TT MJD)} \\
+ \spec{ORBINC}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH}{D}{longitude or argument of perihelion
+                            ($\varpi$ or $\omega$,} \\
+ \spec{}{}{\hspace{1.5em} radians)} \\
+ \spec{AORQ}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E}{D}{eccentricity ($e$)} \\
+ \spec{AORL}{D}{mean anomaly or longitude
+                               ($M$ or $L$, radians,} \\
+ \spec{}{}{\hspace{1.5em} JFORM=1,2 only)} \\
+ \spec{DM}{D}{daily motion ($n$, radians, JFORM=1 only)}
+}
+\args{RETURNED}
+{
+ \spec{PV}{D(6)}{heliocentric \xyzxyzd, equatorial, J2000} \\
+ \spec{}{}{\hspace{1.5em} (AU, AU/s)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal JFORM} \\
+ \spec{}{}{\hspace{1.5em} $-$2 = illegal E} \\
+ \spec{}{}{\hspace{1.5em} $-$3 = illegal AORQ} \\
+ \spec{}{}{\hspace{1.5em} $-$4 = illegal DM} \\
+ \spec{}{}{\hspace{1.5em} $-$5 = numerical error}
+}
+\notes
+{
+ \begin{enumerate}
+  \item DATE is the instant for which the prediction is
+        required.  It is in the TT timescale (formerly
+        Ephemeris Time, ET) and is a
+        Modified Julian Date (JD$-$2400000.5).
+  \item The elements are with respect to
+        the J2000 ecliptic and equinox.
+  \item Three different element-format options are available, as
+        follows. \\
+
+        JFORM=1, suitable for the major planets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of elements $t_0$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> longitude of perihelion $\varpi$ (radians) \\
+        \> AORQ   \> = \> mean distance $a$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        \> AORL   \> = \> mean longitude $L$ (radians) \\
+        \> DM     \> = \> daily motion $n$ (radians)
+        \end{tabbing}
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of elements $t_0$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> mean distance $a$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        \> AORL   \> = \> mean anomaly $M$ (radians)
+        \end{tabbing}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of perihelion $T$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> perihelion distance $q$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e \leq 10 )$
+        \end{tabbing}
+  \item Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
+        not accessed.
+  \item The reference frame for the result is equatorial and is with
+        respect to the mean equinox and ecliptic of epoch J2000.
+  \item The algorithm was originally adapted from the EPHSLA program of
+        D.\,H.\,P.\,Jones (private communication, 1996).  The method
+        is based on Stumpff's Universal Variables.
+ \end{enumerate}
+}
+\aref{Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.}
+%------------------------------------------------------------------------------
+\routine{SLA\_PLANET}{Planetary Ephemerides}
+{
+ \action{Approximate heliocentric position and velocity of a planet.}
+ \call{CALL sla\_PLANET (DATE, NP, PV, JSTAT)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{Modified Julian Date (JD$-$2400000.5)} \\
+ \spec{NP}{I}{planet:} \\
+ \spec{}{}{\hspace{1.5em} 1\,=\,Mercury} \\
+ \spec{}{}{\hspace{1.5em} 2\,=\,Venus} \\
+ \spec{}{}{\hspace{1.5em} 3\,=\,Earth-Moon Barycentre} \\
+ \spec{}{}{\hspace{1.5em} 4\,=\,Mars} \\
+ \spec{}{}{\hspace{1.5em} 5\,=\,Jupiter} \\
+ \spec{}{}{\hspace{1.5em} 6\,=\,Saturn} \\
+ \spec{}{}{\hspace{1.5em} 7\,=\,Uranus} \\
+ \spec{}{}{\hspace{1.5em} 8\,=\,Neptune} \\
+ \spec{}{}{\hspace{1.5em} 9\,=\,Pluto}
+}
+\args{RETURNED}
+{
+ \spec{PV}{D(6)}{heliocentric \xyzxyzd, equatorial, J2000} \\
+ \spec{}{}{\hspace{1.5em} (AU, AU/s)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} $+$1 = warning: date outside of range} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal NP (outside 1-9)} \\
+ \spec{}{}{\hspace{1.5em} $-$2 = solution didn't converge}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The epoch, DATE, is in the TDB timescale and is in the form
+        of a Modified Julian Date (JD$-$2400000.5).
+  \item The reference frame is equatorial and is with respect to
+        the mean equinox and ecliptic of epoch J2000.
+  \item If a planet number, NP, outside the range 1-9 is supplied, an error
+        status is returned (JSTAT~=~$-1$) and the PV vector
+        is set to zeroes.
+  \item The algorithm for obtaining the mean elements of the
+        planets from Mercury to Neptune is due to
+        J.\,L.\,Simon, P.\,Bretagnon, J.\,Chapront,
+        M.\,Chapront-Touze, G.\,Francou and J.\,Laskar (Bureau des
+        Longitudes, Paris, France).  The (completely different)
+        algorithm for calculating the ecliptic coordinates of
+        Pluto is by Meeus.
+  \item Comparisons of the present routine with the JPL DE200 ephemeris
+        give the following RMS errors over the interval 1960-2025:
+        \begin{tabbing}
+         xxxxx \= xxxxxxxxxxxxxxxxx \= xxxxxxxxxxxxxx \= \kill
+         \> \> {\it position (km)} \> {\it speed (metre/sec)} \\ \\
+         \> Mercury \> \hspace{2em}334 \> \hspace{2.5em}0.437 \\
+         \> Venus   \> \hspace{1.5em}1060 \> \hspace{2.5em}0.855 \\
+         \> EMB     \> \hspace{1.5em}2010 \> \hspace{2.5em}0.815 \\
+         \> Mars    \> \hspace{1.5em}7690 \> \hspace{2.5em}1.98 \\
+         \> Jupiter \> \hspace{1em}71700 \> \hspace{2.5em}7.70 \\
+         \> Saturn  \> \hspace{0.5em}199000 \> \hspace{2em}19.4 \\
+         \> Uranus  \> \hspace{0.5em}564000 \> \hspace{2em}16.4 \\
+         \> Neptune \> \hspace{0.5em}158000 \> \hspace{2em}14.4 \\
+         \> Pluto \> \hspace{1em}36400 \> \hspace{2.5em}0.137
+        \end{tabbing}
+        From comparisons with DE102, Simon {\it et al.}\/ quote the following
+        longitude accuracies over the interval 1800-2200:
+        \begin{tabbing}
+         xxxxx \= xxxxxxxxxxxxxxxxxxxx \= \kill
+         \> Mercury \> \hspace{0.5em}\arcseci{4} \\
+         \> Venus   \> \hspace{0.5em}\arcseci{5} \\
+         \> EMB     \> \hspace{0.5em}\arcseci{6} \\
+         \> Mars    \> \arcseci{17} \\
+         \> Jupiter \> \arcseci{71} \\
+         \> Saturn  \> \arcseci{81} \\
+         \> Uranus  \> \arcseci{86} \\
+         \> Neptune \> \arcseci{11}
+        \end{tabbing}
+        In the case of Pluto, Meeus quotes an accuracy of \arcsec{0}{6}
+        in longitude and \arcsec{0}{2} in latitude for the period
+        1885-2099.
+
+        For all except Pluto, over the period 1000-3000,
+        the accuracy is better than 1.5
+        times that over 1800-2200.  Outside the interval 1000-3000 the
+        accuracy declines.  For Pluto the accuracy declines rapidly
+        outside the period 1885-2099.  Outside these ranges
+        (1885-2099 for Pluto, 1000-3000 for the rest) a ``date out
+        of range'' warning status ({\tt JSTAT=+1}) is returned.
+  \item The algorithms for (i)~Mercury through Neptune and
+        (ii)~Pluto are completely independent.  In the Mercury
+        through Neptune case, the present SLALIB
+        implementation differs from the original
+        Simon {\it et al.}\/ Fortran code in the following respects:
+        \begin{itemize}
+         \item The date is supplied as a Modified Julian Date rather
+               a Julian Date (${\rm MJD} = ({\rm JD} - 2400000.5$).
+         \item The result is returned only in equatorial
+               Cartesian form;  the ecliptic
+               longitude, latitude and radius vector are not returned.
+         \item The velocity is in AU per second, not AU per day.
+         \item Different error/warning status values are used.
+         \item Kepler's Equation is not solved inline.
+         \item Polynomials in T are nested to minimize rounding errors.
+         \item Explicit double-precision constants are used to avoid
+               mixed-mode expressions.
+         \item There are other, cosmetic, changes to comply with
+               Starlink/SLALIB style guidelines.
+        \end{itemize}
+        None of the above changes affects the result significantly.
+  \item NP\,=\,3 the result is for the Earth-Moon Barycentre.  To
+        obtain the heliocentric position and velocity of the Earth,
+        either use the SLALIB routine sla\_EVP or call sla\_DMOON and
+        subtract 0.012150581 times the geocentric Moon vector from
+        the EMB vector produced by the present routine.  (The Moon
+        vector should be precessed to J2000 first, but this can
+        be omitted for modern epochs without introducing significant
+        inaccuracy.)
+ \end{enumerate}
+\refs
+{
+ \begin{enumerate}
+  \item Simon {\it et al.,}\/
+        Astron.\ Astrophys.\ {\bf 282}, 663 (1994).
+  \item Meeus, J.,
+        {\it Astronomical Algorithms,}\/ Willmann-Bell (1991).
+ \end{enumerate}
+}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_PLANTE}{\radec\ of Planet from Elements}
+{
+ \action{Topocentric apparent \radec\ of a Solar-System object whose
+         heliocentric orbital elements are known.}
+ \call{CALL sla\_PLANTE (\vtop{
+         \hbox{DATE, ELONG, PHI, JFORM, EPOCH, ORBINC, ANODE, PERIH,}
+         \hbox{AORQ, E, AORL, DM, RA, DEC, R, JSTAT)}}}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{MJD of observation (JD$-$2400000.5)} \\
+ \spec{ELONG,PHI}{D}{observer's longitude (east +ve) and latitude} \\
+ \spec{}{}{\hspace{1.5em} radians)} \\
+ \spec{JFORM}{I}{choice of element set (1-3, see Note~4, below)} \\
+ \spec{EPOCH}{D}{epoch of elements ($t_0$ or $T$, TT MJD)} \\
+ \spec{ORBINC}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH}{D}{longitude or argument of perihelion
+                            ($\varpi$ or $\omega$,} \\
+ \spec{}{}{\hspace{1.5em} radians)} \\
+ \spec{AORQ}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E}{D}{eccentricity ($e$)} \\
+ \spec{AORL}{D}{mean anomaly or longitude ($M$ or $L$,} \\
+  \spec{}{}{\hspace{1.5em} radians, JFORM=1,2 only)} \\
+ \spec{DM}{D}{daily motion ($n$, radians, JFORM=1 only)}
+}
+\args{RETURNED}
+{
+ \spec{RA,DEC}{D}{topocentric apparent \radec\ (radians)} \\
+ \spec{R}{D}{distance from observer (AU)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal JFORM} \\
+ \spec{}{}{\hspace{1.5em} $-$2 = illegal E} \\
+ \spec{}{}{\hspace{1.5em} $-$3 = illegal AORQ} \\
+ \spec{}{}{\hspace{1.5em} $-$4 = illegal DM} \\
+ \spec{}{}{\hspace{1.5em} $-$5 = numerical error}
+}
+\notes
+{
+ \begin{enumerate}
+  \item DATE is the instant for which the prediction is
+        required.  It is in the TT timescale (formerly
+        Ephemeris Time, ET) and is a
+        Modified Julian Date (JD$-$2400000.5).
+  \item The longitude and latitude allow correction for geocentric
+        parallax.  This is usually a small effect, but can become
+        important for Earth-crossing asteroids.  Geocentric positions
+        can be generated by appropriate use of the routines
+        sla\_EVP and sla\_PLANEL.
+  \item The elements are with respect to the J2000 ecliptic and equinox.
+  \item Three different element-format options are available, as
+        follows. \\
+
+        JFORM=1, suitable for the major planets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of elements $t_0$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> longitude of perihelion $\varpi$ (radians) \\
+        \> AORQ   \> = \> mean distance $a$ (AU) \\
+        \> E      \> = \> eccentricity $e$ \\
+        \> AORL   \> = \> mean longitude $L$ (radians) \\
+        \> DM     \> = \> daily motion $n$ (radians)
+        \end{tabbing}
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of elements $t_0$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> mean distance $a$ (AU) \\
+        \> E      \> = \> eccentricity $e$ \\
+        \> AORL   \> = \> mean anomaly $M$ (radians)
+        \end{tabbing}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of perihelion $T$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> perihelion distance $q$ (AU) \\
+        \> E      \> = \> eccentricity $e$
+        \end{tabbing}
+  \item Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
+        not accessed.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_PM}{Proper Motion}
+{
+ \action{Apply corrections for proper motion to a star \radec.}
+ \call{CALL sla\_PM (R0, D0, PR, PD, PX, RV, EP0, EP1, R1, D1)}
+}
+\args{GIVEN}
+{
+ \spec{R0,D0}{D}{\radec\ at epoch EP0 (radians)} \\
+ \spec{PR,PD}{D}{proper motions:  rate of change of 
+                 \radec\  (radians per year)} \\
+ \spec{PX}{D}{parallax (arcsec)} \\
+ \spec{RV}{D}{radial velocity (km~s$^{-1}$, +ve if receding)} \\
+ \spec{EP0}{D}{start epoch in years ({\it e.g.}\ Julian epoch)} \\
+ \spec{EP1}{D}{end epoch in years (same system as EP0)}
+}
+\args{RETURNED}
+{
+ \spec{R1,D1}{D}{\radec\ at epoch EP1 (radians)}
+}
+\anote{The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+       $\dot{\alpha}\cos\delta$, and are in the same coordinate
+       system as R0,D0.}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr. Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_POLMO}{Polar Motion}
+{
+ \action{Polar motion:  correct site longitude and latitude for polar
+         motion and calculate azimuth difference between celestial and
+         terrestrial poles.}
+ \call{CALL sla\_POLMO (ELONGM, PHIM, XP, YP, ELONG, PHI, DAZ)}
+}
+\args{GIVEN}
+{
+ \spec{ELONGM}{D}{mean longitude of the site (radians, east +ve)} \\
+ \spec{PHIM}{D}{mean geodetic latitude of the site (radians)} \\
+ \spec{XP}{D}{polar motion $x$-coordinate (radians)} \\
+ \spec{YP}{D}{polar motion $y$-coordinate (radians)}
+}
+\args{RETURNED}
+{
+ \spec{ELONG}{D}{true longitude of the site (radians, east +ve)} \\
+ \spec{PHI}{D}{true geodetic latitude of the site (radians)} \\
+ \spec{DAZ}{D}{azimuth correction (terrestrial$-$celestial, radians)}
+}
+\notes
+{
+\begin{enumerate}
+\item ``Mean'' longitude and latitude are the (fixed) values for the
+      site's location with respect to the IERS terrestrial reference
+      frame;  the latitude is geodetic.  TAKE CARE WITH THE LONGITUDE
+      SIGN CONVENTION.  The longitudes used by the present routine
+      are east-positive, in accordance with geographical convention
+      (and right-handed).  In particular, note that the longitudes
+      returned by the sla\_OBS routine are west-positive, following
+      astronomical usage, and must be reversed in sign before use in
+      the present routine.
+\item XP and YP are the (changing) coordinates of the Celestial
+      Ephemeris Pole with respect to the IERS Reference Pole.
+      XP is positive along the meridian at longitude $0^\circ$,
+      and YP is positive along the meridian at longitude
+      $270^\circ$ ({\it i.e.}\ $90^\circ$ west).  Values for XP,YP can
+      be obtained from IERS circulars and equivalent publications;
+      the maximum amplitude observed so far is about \arcsec{0}{3}.
+\item ``True'' longitude and latitude are the (moving) values for
+      the site's location with respect to the celestial ephemeris
+      pole and the meridian which corresponds to the Greenwich
+      apparent sidereal time.  The true longitude and latitude
+      link the terrestrial coordinates with the standard celestial
+      models (for precession, nutation, sidereal time {\it etc}).
+\item The azimuths produced by sla\_AOP and sla\_AOPQK are with
+      respect to due north as defined by the Celestial Ephemeris
+      Pole, and can therefore be called ``celestial azimuths''.
+      However, a telescope fixed to the Earth measures azimuth
+      essentially with respect to due north as defined by the
+      IERS Reference Pole, and can therefore be called ``terrestrial
+      azimuth''.  Uncorrected, this would manifest itself as a
+      changing ``azimuth zero-point error''.  The value DAZ is the
+      correction to be added to a celestial azimuth to produce
+      a terrestrial azimuth.
+\item The present routine is rigorous.  For most practical
+      purposes, the following simplified formulae provide an
+      adequate approximation: \\[2ex]
+      \hspace*{1em}\begin{tabular}{lll}
+        {\tt ELONG} & {\tt =} &
+             {\tt ELONGM+XP*COS(ELONGM)-YP*SIN(ELONGM)} \\
+        {\tt PHI  } & {\tt =} &
+             {\tt PHIM+(XP*SIN(ELONGM)+YP*COS(ELONGM))*TAN(PHIM)} \\
+        {\tt DAZ  } & {\tt =} &
+             {\tt -SQRT(XP*XP+YP*YP)*COS(ELONGM-ATAN2(XP,YP))/COS(PHIM)} \\
+      \end{tabular} \\[2ex]
+      An alternative formulation for DAZ is:\\[2ex]
+      \hspace*{1em}\begin{tabular}{lll}
+        {\tt X  } & {\tt =} & {\tt COS(ELONGM)*COS(PHIM)} \\
+        {\tt Y  } & {\tt =} & {\tt SIN(ELONGM)*COS(PHIM)} \\
+        {\tt DAZ} & {\tt =} & {\tt ATAN2(-X*YP-Y*XP,X*X+Y*Y)} \\
+      \end{tabular}
+\end{enumerate}
+}
+\aref{Seidelmann, P.K.\ (ed), 1992.  {\it Explanatory
+      Supplement to the Astronomical Almanac,}\/ ISBN~0-935702-68-7,
+      sections 3.27, 4.25, 4.52.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PREBN}{Precession Matrix (FK4)}
+{
+ \action{Generate the matrix of precession between two epochs,
+         using the old, pre IAU~1976, Bessel-Newcomb model, in
+         Andoyer's formulation.}
+ \call{CALL sla\_PREBN (BEP0, BEP1, RMATP)}
+}
+\args{GIVEN}
+{
+ \spec{BEP0}{D}{beginning Besselian epoch} \\
+ \spec{BEP1}{D}{ending Besselian epoch}
+}
+\args{RETURNED}
+{
+ \spec{RMATP}{D(3,3)}{precession matrix}
+}
+\anote{The matrix is in the sense:
+       \begin{verse}
+        {\bf v}$_{1}$ =  {\bf M}$\cdot${\bf v}$_{0}$
+       \end{verse}
+       where {\bf v}$_{1}$ is the star vector relative to the
+       mean equator and equinox of epoch BEP1, {\bf M} is the
+       $3\times3$ matrix RMATP and
+       {\bf v}$_{0}$ is the star vector relative to the
+       mean equator and equinox of epoch BEP0.}
+\aref{Smith {\it et al.}, 1989.\ {\it Astr.J.}\ {\bf 97}, 269.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PREC}{Precession Matrix (FK5)}
+{
+ \action{Form the matrix of precession between two epochs (IAU 1976, FK5).}
+ \call{CALL sla\_PREC (EP0, EP1, RMATP)}
+}
+\args{GIVEN}
+{
+ \spec{EP0}{D}{beginning epoch} \\
+ \spec{EP1}{D}{ending epoch}
+}
+\args{RETURNED}
+{
+ \spec{RMATP}{D(3,3)}{precession matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The epochs are TDB Julian epochs.
+  \item The matrix is in the sense:
+        \begin{verse}
+         {\bf v}$_{1}$ =  {\bf M}$\cdot${\bf v}$_{0}$
+        \end{verse}
+        where {\bf v}$_{1}$ is the star vector relative to the
+        mean equator and equinox of epoch EP1, {\bf M} is the
+        $3\times3$ matrix RMATP and
+        {\bf v}$_{0}$ is the star vector relative to the
+        mean equator and equinox of epoch EP0.
+  \item Though the matrix method itself is rigorous, the precession
+        angles are expressed through canonical polynomials which are
+        valid only for a limited time span.  There are also known
+        errors in the IAU precession rate.  The absolute accuracy
+        of the present formulation is better than \arcsec{0}{1} from
+        1960\,AD to 2040\,AD, better than \arcseci{1} from 1640\,AD to 2360\,AD,
+        and remains below \arcseci{3} for the whole of the period
+        500\,BC to 3000\,AD.  The errors exceed \arcseci{10} outside the
+        range 1200\,BC to 3900\,AD, exceed \arcseci{100} outside 4200\,BC to
+        5600\,AD and exceed \arcseci{1000} outside 6800\,BC to 8200\,AD.
+        The SLALIB routine sla\_PRECL implements a more elaborate
+        model which is suitable for problems spanning several
+        thousand years.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Lieske, J.H., 1979.\ {\it Astr.Astrophys.}\ {\bf 73}, 282;
+        equations 6 \& 7, p283.
+  \item Kaplan, G.H., 1981.\ {\it USNO circular no.\ 163}, pA2.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PRECES}{Precession}
+{
+ \action{Precession -- either the old ``FK4'' (Bessel-Newcomb, pre~IAU~1976)
+         or new ``FK5'' (Fricke, post~IAU~1976) as required.}
+ \call{CALL sla\_PRECES (SYSTEM, EP0, EP1, RA, DC)}
+}
+\args{GIVEN}
+{
+ \spec{SYSTEM}{C}{precession to be applied: `FK4' or `FK5'} \\
+ \spec{EP0,EP1}{D}{starting and ending epoch} \\
+ \spec{RA,DC}{D}{\radec, mean equator \& equinox of epoch EP0}
+}
+\args{RETURNED}
+{
+ \spec{RA,DC}{D}{\radec, mean equator \& equinox of epoch EP1}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Lowercase characters in SYSTEM are acceptable.
+  \item The epochs are Besselian if SYSTEM=`FK4' and Julian if `FK5'.
+        For example, to precess coordinates in the old system from
+        equinox 1900.0 to 1950.0 the call would be:
+        \begin{quote}
+         {\tt CALL sla\_PRECES ('FK4', 1900D0, 1950D0, RA, DC)}
+        \end{quote}
+  \item This routine will {\bf NOT} correctly convert between the old and
+        the new systems -- for example conversion from B1950 to J2000.
+        For these purposes see sla\_FK425, sla\_FK524, sla\_FK45Z and
+        sla\_FK54Z.
+  \item If an invalid SYSTEM is supplied, values of $-$99D0,$-$99D0 are
+        returned for both RA and DC.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PRECL}{Precession Matrix (latest)}
+{
+ \action{Form the matrix of precession between two epochs, using the
+         model of Simon {\it et al}.\ (1994), which is suitable for long
+         periods of time.}
+ \call{CALL sla\_PRECL (EP0, EP1, RMATP)}
+}
+\args{GIVEN}
+{
+ \spec{EP0}{D}{beginning epoch} \\
+ \spec{EP1}{D}{ending epoch}
+}
+\args{RETURNED}
+{
+ \spec{RMATP}{D(3,3)}{precession matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The epochs are TDB Julian epochs.
+  \item The matrix is in the sense:
+        \begin{verse}
+         {\bf v}$_{1}$ =  {\bf M}$\cdot${\bf v}$_{0}$
+        \end{verse}
+        where {\bf v}$_{1}$ is the star vector relative to the
+        mean equator and equinox of epoch EP1, {\bf M} is the
+        $3\times3$ matrix RMATP and
+        {\bf v}$_{0}$ is the star vector relative to the
+        mean equator and equinox of epoch EP0.
+  \item The absolute accuracy of the model is limited by the
+        uncertainty in the general precession, about \arcsec{0}{3} per
+        1000~years.  The remainder of the formulation provides a
+        precision of 1~milliarcsecond over the interval from 1000\,AD
+        to 3000\,AD, \arcsec{0}{1} from 1000\,BC to 5000\,AD and
+        \arcseci{1} from 4000\,BC to 8000\,AD.
+ \end{enumerate}
+}
+\aref{Simon, J.L.\ {\it et al}., 1994.\ {\it Astr.Astrophys.}\ {\bf 282},
+      663.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PRENUT}{Precession/Nutation Matrix}
+{
+ \action{Form the matrix of precession and nutation (IAU~1976, FK5).}
+ \call{CALL sla\_PRENUT (EPOCH, DATE, RMATPN)}
+}
+\args{GIVEN}
+{
+ \spec{EPOCH}{D}{Julian Epoch for mean coordinates} \\
+ \spec{DATE}{D}{Modified Julian Date (JD$-$2400000.5)
+                       for true coordinates}
+}
+\args{RETURNED}
+{
+ \spec{RMATPN}{D(3,3)}{combined precession/nutation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The epoch and date are TDB.
+  \item The matrix is in the sense:
+        \begin{verse}
+         {\bf v}$_{true}$ =  {\bf M}$\cdot${\bf v}$_{mean}$
+        \end{verse}
+        where {\bf v}$_{true}$ is the star vector relative to the
+        true equator and equinox of epoch DATE, {\bf M} is the
+        $3\times3$ matrix RMATPN and
+        {\bf v}$_{mean}$ is the star vector relative to the
+        mean equator and equinox of epoch EPOCH.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PV2EL}{Orbital Elements from Position/Velocity}
+{
+ \action{Heliocentric osculating elements obtained from instantaneous
+         position and velocity.}
+ \call{CALL sla\_PV2EL (\vtop{
+         \hbox{PV, DATE, PMASS, JFORMR, JFORM, EPOCH, ORBINC,}
+         \hbox{ANODE, PERIH, AORQ, E, AORL, DM, JSTAT)}}}
+}
+\args{GIVEN}
+{
+ \spec{PV}{D(6)}{heliocentric \xyzxyzd, equatorial, J2000} \\
+ \spec{}{}{\hspace{1.5em} (AU, AU/s; Note~1)} \\
+ \spec{DATE}{D}{date (TT Modified Julian Date = JD$-$2400000.5)} \\
+ \spec{PMASS}{D}{mass of the planet (Sun = 1; Note~2)} \\
+ \spec{JFORMR}{I}{requested element set (1-3; Note~3)}
+}
+\args{RETURNED}
+{
+ \spec{JFORM}{I}{element set actually returned (1-3; Note~4)} \\
+ \spec{EPOCH}{D}{epoch of elements ($t_0$ or $T$, TT MJD)} \\
+ \spec{ORBINC}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH}{D}{longitude or argument of perihelion
+                            ($\varpi$ or $\omega$,} \\
+ \spec{}{}{\hspace{1.5em} radians)} \\
+ \spec{AORQ}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E}{D}{eccentricity ($e$)} \\
+ \spec{AORL}{D}{mean anomaly or longitude
+                               ($M$ or $L$, radians,} \\
+ \spec{}{}{\hspace{1.5em} JFORM=1,2 only)} \\
+ \spec{DM}{D}{daily motion ($n$, radians, JFORM=1 only)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal PMASS} \\
+ \spec{}{}{\hspace{1.5em} $-$2 = illegal JFORMR} \\
+ \spec{}{}{\hspace{1.5em} $-$3 = position/velocity out of allowed range}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The PV 6-vector is with respect to the mean equator and equinox of
+        epoch J2000.  The orbital elements produced are with respect to
+        the J2000 ecliptic and mean equinox.
+  \item The mass, PMASS, is important only for the larger planets.  For
+        most purposes ({\it e.g.}~asteroids) use 0D0.  Values less than zero
+        are illegal.
+  \item Three different element-format options are supported, as
+        follows. \\
+
+        JFORM=1, suitable for the major planets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of elements $t_0$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> longitude of perihelion $\varpi$ (radians) \\
+        \> AORQ   \> = \> mean distance $a$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        \> AORL   \> = \> mean longitude $L$ (radians) \\
+        \> DM     \> = \> daily motion $n$ (radians)
+        \end{tabbing}
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of elements $t_0$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> mean distance $a$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        \> AORL   \> = \> mean anomaly $M$ (radians)
+        \end{tabbing}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of perihelion $T$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> perihelion distance $q$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e \leq 10 )$
+        \end{tabbing}
+  \item It may not be possible to generate elements in the form
+        requested through JFORMR.  The caller is notified of the form
+        of elements actually returned by means of the JFORM argument:
+
+        \begin{tabbing}
+        xx \= xxxxxxxxxx \= xxxxxxxxxxx \= \kill
+        \> JFORMR   \> JFORM   \> meaning \\ \\
+        \> ~~~~~1   \> ~~~~~1  \> OK: elements are in the requested format \\
+        \> ~~~~~1   \> ~~~~~2  \> never happens \\
+        \> ~~~~~1   \> ~~~~~3  \> orbit not elliptical \\
+        \> ~~~~~2   \> ~~~~~1  \> never happens \\
+        \> ~~~~~2   \> ~~~~~2  \> OK: elements are in the requested format \\
+        \> ~~~~~2   \> ~~~~~3  \> orbit not elliptical \\
+        \> ~~~~~3   \> ~~~~~1  \> never happens \\
+        \> ~~~~~3   \> ~~~~~2  \> never happens \\
+        \> ~~~~~3   \> ~~~~~3  \> OK: elements are in the requested format
+        \end{tabbing}
+  \item The arguments returned for each value of JFORM ({\it cf}\/ Note~5:
+        JFORM may not be the same as JFORMR) are as follows:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxxxxxx \= xxxxxx \= xxxxxx \= \kill
+        \> JFORM  \> 1        \> 2        \> 3 \\ \\
+        \> EPOCH  \> $t_0$    \> $t_0$    \> $T$ \\
+        \> ORBINC \> $i$      \> $i$      \> $i$ \\
+        \> ANODE  \> $\Omega$ \> $\Omega$ \> $\Omega$ \\
+        \> PERIH  \> $\varpi$ \> $\omega$ \> $\omega$ \\
+        \> AORQ   \> $a$      \> $a$      \> $q$ \\
+        \> E      \> $e$      \> $e$      \> $e$ \\
+        \> AORL   \> $L$      \> $M$      \> - \\
+        \> DM     \> $n$      \> -        \> -
+        \end{tabbing}
+
+        where:
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xxx \= \kill
+        \> $t_0$    \> is the epoch of the elements (MJD, TT) \\
+        \> $T$      \> is the epoch of perihelion (MJD, TT) \\
+        \> $i$      \> is the inclination (radians) \\
+        \> $\Omega$ \> is the longitude of the ascending node (radians) \\
+        \> $\varpi$ \> is the longitude of perihelion (radians) \\
+        \> $\omega$ \> is the argument of perihelion (radians) \\
+        \> $a$      \> is the mean distance (AU) \\
+        \> $q$      \> is the perihelion distance (AU) \\
+        \> $e$      \> is the eccentricity \\
+        \> $L$      \> is the longitude (radians, $0-2\pi$) \\
+        \> $M$      \> is the mean anomaly (radians, $0-2\pi$) \\
+        \> $n$      \> is the daily motion (radians) \\
+        \> - \> means no value is set
+        \end{tabbing}
+  \item At very small inclinations, the longitude of the ascending node
+        ANODE becomes indeterminate and under some circumstances may be
+        set arbitrarily to zero.  Similarly, if the orbit is close to
+        circular, the true anomaly becomes indeterminate and under some
+        circumstances may be set arbitrarily to zero.  In such cases,
+        the other elements are automatically adjusted to compensate,
+        and so the elements remain a valid description of the orbit.
+ \end{enumerate}
+}
+\aref{Sterne, Theodore E., {\it An Introduction to Celestial Mechanics,}\/
+      Interscience Publishers, 1960.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PV2UE}{Position/Velocity to Universal Elements}
+{
+ \action{Construct a universal element set based on an instantaneous
+         position and velocity.}
+ \call{CALL sla\_PV2UE (PV, DATE, PMASS, U, JSTAT)}
+}
+\args{GIVEN}
+{
+ \spec{PV}{D(6)}{heliocentric \xyzxyzd, equatorial, J2000} \\
+ \spec{}{}{\hspace{1.5em} (AU, AU/s; Note~1)} \\
+ \spec{DATE}{D}{date (TT Modified Julian Date = JD$-$2400000.5)} \\
+ \spec{PMASS}{D}{mass of the planet (Sun = 1; Note~2)}
+}
+\args{RETURNED}
+{
+ \spec{U}{D(13)}{universal orbital elements (Note~3)} \\
+ \specel {(1)}     {combined mass ($M+m$)} \\
+ \specel {(2)}     {total energy of the orbit ($\alpha$)} \\
+ \specel {(3)}     {reference (osculating) epoch ($t_0$)} \\
+ \specel {(4-6)}   {position at reference epoch (${\rm \bf r}_0$)} \\
+ \specel {(7-9)}   {velocity at reference epoch (${\rm \bf v}_0$)} \\
+ \specel {(10)}    {heliocentric distance at reference epoch} \\
+ \specel {(11)}    {${\rm \bf r}_0.{\rm \bf v}_0$} \\
+ \specel {(12)}    {date ($t$)} \\
+ \specel {(13)}    {universal eccentric anomaly ($\psi$) of date, approx} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{1.95em}      0 = OK} \\
+ \spec{}{}{\hspace{1.2em}    $-$1 = illegal PMASS} \\
+ \spec{}{}{\hspace{1.2em}    $-$2 = too close to Sun} \\
+ \spec{}{}{\hspace{1.2em}    $-$3 = too slow}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The PV 6-vector can be with respect to any chosen inertial frame,
+        and the resulting universal-element set will be with respect to
+        the same frame.  A common choice will be mean equator and ecliptic
+        of epoch J2000.
+  \item The mass, PMASS, is important only for the larger planets.  For
+        most purposes ({\it e.g.}~asteroids) use 0D0.  Values less than zero
+        are illegal.
+  \item The ``universal'' elements are those which define the orbit for the
+        purposes of the method of universal variables (see reference).
+        They consist of the combined mass of the two bodies, an epoch,
+        and the position and velocity vectors (arbitrary reference frame)
+        at that epoch.  The parameter set used here includes also various
+        quantities that can, in fact, be derived from the other
+        information.  This approach is taken to avoiding unnecessary
+        computation and loss of accuracy.  The supplementary quantities
+        are (i)~$\alpha$, which is proportional to the total energy of the
+        orbit, (ii)~the heliocentric distance at epoch,
+        (iii)~the outwards component of the velocity at the given epoch,
+        (iv)~an estimate of $\psi$, the ``universal eccentric anomaly'' at a
+        given date and (v)~that date.
+ \end{enumerate}
+}
+\aref{Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PVOBS}{Observatory Position \& Velocity}
+{
+ \action{Position and velocity of an observing station.}
+ \call{CALL sla\_PVOBS (P, H, STL, PV)}
+}
+\args{GIVEN}
+{
+ \spec{P}{D}{latitude (geodetic, radians)} \\
+ \spec{H}{D}{height above reference spheroid (geodetic, metres)} \\
+ \spec{STL}{D}{local apparent sidereal time (radians)}
+}
+\args{RETURNED}
+{
+ \spec{PV}{D(6)}{\xyzxyzd\ (AU, AU~s$^{-1}$, true equator and equinox
+                                                            of date)}
+}
+\anote{IAU 1976 constants are used.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PXY}{Apply Linear Model}
+{
+ \action{Given arrays of {\it expected}\/ and {\it measured}\,
+         \xy\ coordinates, and a
+         linear model relating them (as produced by sla\_FITXY), compute
+         the array of {\it predicted}\/ coordinates and the RMS residuals.}
+ \call{CALL sla\_PXY (NP,XYE,XYM,COEFFS,XYP,XRMS,YRMS,RRMS)}
+}
+\args{GIVEN}
+{
+ \spec{NP}{I}{number of samples} \\
+ \spec{XYE}{D(2,NP)}{expected \xy\ for each sample} \\
+ \spec{XYM}{D(2,NP)}{measured \xy\ for each sample} \\
+ \spec{COEFFS}{D(6)}{coefficients of model (see below)}
+}
+\args{RETURNED}
+{
+ \spec{XYP}{D(2,NP)}{predicted \xy\ for each sample} \\
+ \spec{XRMS}{D}{RMS in X} \\
+ \spec{YRMS}{D}{RMS in Y} \\
+ \spec{RRMS}{D }{total RMS (vector sum of XRMS and YRMS)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The model is supplied in the array COEFFS.  Naming the
+        six elements of COEFFS $a,b,c,d,e$ \& $f$,
+        the model transforms {\it measured}\/ coordinates
+        $[x_{m},y_{m}\,]$ into {\it predicted}\/ coordinates
+        $[x_{p},y_{p}\,]$ as follows:
+        \begin{verse}
+         $x_{p} = a + bx_{m} + cy_{m}$ \\
+         $y_{p} = d + ex_{m} + fy_{m}$
+        \end{verse}
+  \item The residuals are $(x_{p}-x_{e})$ and $(y_{p}-y_{e})$.
+  \item If NP is less than or equal to zero, no coordinates are
+        transformed, and the RMS residuals are all zero.
+  \item See also sla\_FITXY, sla\_INVF, sla\_XY2XY, sla\_DCMPF
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_RANDOM}{Random Number}
+{
+ \action{Generate pseudo-random real number in the range $0 \leq x < 1$.}
+ \call{R~=~sla\_RANDOM (SEED)}
+}
+\args{GIVEN}
+{
+ \spec{SEED}{R}{an arbitrary real number}
+}
+\args{RETURNED}
+{
+ \spec{SEED}{R}{a new arbitrary value} \\
+ \spec{sla\_RANDOM}{R}{Pseudo-random real number $0 \leq x < 1$.}
+}
+\anote{The implementation is machine-dependent.}
+%-----------------------------------------------------------------------
+\routine{SLA\_RANGE}{Put Angle into Range $\pm\pi$}
+{
+ \action{Normalize an angle into the range $\pm\pi$ (single precision).}
+ \call{R~=~sla\_RANGE (ANGLE)}
+}
+\args{GIVEN}
+{
+ \spec{ANGLE}{R}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RANGE}{R}{ANGLE expressed in the range $\pm\pi$.}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_RANORM}{Put Angle into Range $0\!-\!2\pi$}
+{
+ \action{Normalize an angle into the range $0\!-\!2\pi$ (single precision).}
+ \call{R~=~sla\_RANORM (ANGLE)}
+}
+\args{GIVEN}
+{
+ \spec{ANGLE}{R}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RANORM}{R}{ANGLE expressed in the range $0\!-\!2\pi$}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_RCC}{Barycentric Coordinate Time}
+{
+ \call{D~=~sla\_RCC (TDB, UT1, WL, U, V)}
+ \action{The relativistic clock correction TDB$-$TT, the
+         difference between {\it proper time}\,
+         on Earth and {\it coordinate time}\/ in the solar system barycentric
+         space-time frame of reference.  The proper time is TT;  the
+         coordinate time is {\it an implementation}\/ of TDB.}
+}
+\args{GIVEN}
+{
+ \spec{TDB}{D}{coordinate time (MJD: JD$-$2400000.5)} \\
+ \spec{UT1}{D}{universal time (fraction of one day)} \\
+ \spec{WL}{D}{clock longitude (radians west)} \\
+ \spec{U}{D}{clock distance from Earth spin axis (km)} \\
+ \spec{V}{D}{clock distance north of Earth equatorial plane (km)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RCC}{D}{TDB$-$TT (sec)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item TDB may be considered to
+        be the coordinate time in the solar system barycentre frame of
+        reference, and TT is the proper time given by clocks at mean sea
+        level on the Earth.
+  \item The result has a main (annual) sinusoidal term of amplitude
+        approximately 1.66ms, plus planetary terms up to about
+        20$\mu$s, and lunar and diurnal terms up to 2$\mu$s.  The
+        variation arises from the transverse Doppler effect and the
+        gravitational red-shift as the observer varies in speed and
+        moves through different gravitational potentials.
+  \item The argument TDB is, strictly, the barycentric coordinate time;
+        however, the terrestrial proper time (TT) can in practice be used.
+  \item The geocentric model is that of Fairhead \& Bretagnon (1990),
+        in its full
+        form.  It was supplied by Fairhead (private communication)
+        as a Fortran subroutine.  A number of coding changes were made to
+        this subroutine in order
+        match the calling sequence of previous versions of the present
+        routine, to comply with Starlink programming standards and to
+        avoid compilation problems on certain machines.  On the supported
+        computer types,
+        the numerical results are essentially unaffected by the
+        changes.  The topocentric model is from Moyer (1981) and Murray (1983).
+        During the interval 1950-2050, the absolute accuracy of the
+        geocentric model is better than $\pm3$~nanoseconds
+        relative to direct numerical integrations using the JPL DE200/LE200
+        solar system ephemeris.
+  \item The IAU definition of TDB is that it must differ from TT only by
+        periodic terms.  Though practical, this is an imprecise definition
+        which ignores the existence of very long-period and secular effects
+        in the dynamics of the solar system.  As a consequence, different
+        implementations of TDB will, in general, differ in zero-point and
+        will drift linearly relative to one other.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Fairhead, L.\ \& 
+        Bretagnon, P., 1990.\ {\it Astr.Astrophys.}\ {\bf 229}, 240-247.
+  \item Moyer, T.D., 1981.\ {\it Cel.Mech.}\ {\bf 23}, 33.
+  \item Murray, C.A., 1983,\ {\it Vectorial Astrometry}, Adam Hilger.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_RDPLAN}{Apparent \radec\ of Planet}
+{
+ \action{Approximate topocentric apparent \radec\ and angular
+         size of a planet.}
+ \call{CALL sla\_RDPLAN (DATE, NP, ELONG, PHI, RA, DEC, DIAM)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{MJD of observation (JD$-$2400000.5)} \\
+ \spec{NP}{I}{planet:} \\
+ \spec{}{}{\hspace{1.5em} 1\,=\,Mercury} \\
+ \spec{}{}{\hspace{1.5em} 2\,=\,Venus} \\
+ \spec{}{}{\hspace{1.5em} 3\,=\,Moon} \\
+ \spec{}{}{\hspace{1.5em} 4\,=\,Mars} \\
+ \spec{}{}{\hspace{1.5em} 5\,=\,Jupiter} \\
+ \spec{}{}{\hspace{1.5em} 6\,=\,Saturn} \\
+ \spec{}{}{\hspace{1.5em} 7\,=\,Uranus} \\
+ \spec{}{}{\hspace{1.5em} 8\,=\,Neptune} \\
+ \spec{}{}{\hspace{1.5em} 9\,=\,Pluto} \\
+ \spec{}{}{\hspace{0.44em} else\,=\,Sun} \\
+ \spec{ELONG,PHI}{D}{observer's longitude (east +ve) and latitude
+                     (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RA,DEC}{D}{topocentric apparent \radec\ (radians)} \\
+ \spec{DIAM}{D}{angular diameter (equatorial, radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The date is in a dynamical timescale (TDB, formerly ET)
+        and is in the form of a Modified
+        Julian Date (JD$-$2400000.5).  For all practical purposes, TT can
+        be used instead of TDB, and for many applications UT will do
+        (except for the Moon).
+  \item The longitude and latitude allow correction for geocentric
+        parallax.  This is a major effect for the Moon, but in the
+        context of the limited accuracy of the present routine its
+        effect on planetary positions is small (negligible for the
+        outer planets).  Geocentric positions can be generated by
+        appropriate use of the routines sla\_DMOON and sla\_PLANET.
+  \item The direction accuracy (arcsec, 1000-3000\,AD) is of order:
+        \begin{tabbing}
+         xxxxxxx \= xxxxxxxxxxxxxxxxxx \= \kill
+         \> Sun     \>  \hspace{0.5em}5 \\
+         \> Mercury \>  \hspace{0.5em}2 \\
+         \> Venus   \> 10 \\
+         \> Moon    \> 30 \\
+         \> Mars    \> 50 \\
+         \> Jupiter \> 90 \\
+         \> Saturn  \> 90 \\
+         \> Uranus  \> 90 \\
+         \> Neptune \> 10 \\
+         \> Pluto \> \hspace{0.5em}1~~~(1885-2099\,AD only)
+        \end{tabbing}
+        The angular diameter accuracy is about 0.4\% for the Moon,
+        and 0.01\% or better for the Sun and planets.
+        For more information on accuracy,
+        refer to the routines sla\_PLANET and sla\_DMOON,
+        which the present routine uses.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_REFCO}{Refraction Constants}
+{
+ \action{Determine the constants $a$ and $b$ in the
+         atmospheric refraction model
+         $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$,
+         where $\zeta$ is the {\it observed}\/ zenith distance
+         ({\it i.e.}\ affected by refraction) and $\Delta \zeta$ is
+         what to add to $\zeta$ to give the {\it topocentric}\,
+         ({\it i.e.\ in vacuo}) zenith distance.}
+ \call{CALL sla\_REFCO (HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REFA, REFB)}
+}
+\args{GIVEN}
+{
+ \spec{HM}{D}{height of the observer above sea level (metre)} \\
+ \spec{TDK}{D}{ambient temperature at the observer (degrees K)} \\
+ \spec{PMB}{D}{pressure at the observer (mB)} \\
+ \spec{RH}{D}{relative humidity at the observer (range 0\,--\,1)} \\
+ \spec{WL}{D}{effective wavelength of the source ($\mu{\rm m}$)} \\
+ \spec{PHI}{D}{latitude of the observer (radian, astronomical)} \\
+ \spec{TLR}{D}{temperature lapse rate in the troposphere
+                                     (degrees K per metre)} \\
+ \spec{EPS}{D}{precision required to terminate iteration (radian)}
+}
+\args{RETURNED}
+{
+ \spec{REFA}{D}{$\tan \zeta$ coefficient (radians)} \\
+ \spec{REFB}{D}{$\tan^{3} \zeta$ coefficient (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Suggested values for the TLR and EPS arguments are 0.0065D0 and
+        1D$-$8 respectively.
+  \item The radio refraction is chosen by specifying WL $>100$~$\mu{\rm m}$.
+  \item The routine is a slower but more accurate alternative to the
+        sla\_REFCOQ routine.  The constants it produces give perfect
+        agreement with sla\_REFRO at zenith distances
+        $\tan^{-1} 1$ ($45^\circ$) and $\tan^{-1} 4$ ($\sim 76^\circ$).
+        At other zenith distances, the model achieves:
+        \arcsec{0}{5} accuracy for $\zeta<80^{\circ}$,
+        \arcsec{0}{01} accuracy for $\zeta<60^{\circ}$, and
+        \arcsec{0}{001} accuracy for $\zeta<45^{\circ}$.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_REFCOQ}{Refraction Constants (fast)}
+{
+ \action{Determine the constants $a$ and $b$ in the
+         atmospheric refraction model
+         $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$,
+         where $\zeta$ is the {\it observed}\/ zenith distance
+         ({\it i.e.}\ affected by refraction) and $\Delta \zeta$ is
+         what to add to $\zeta$ to give the {\it topocentric}\,
+         ({\it i.e.\ in vacuo}) zenith distance. (This is a fast
+         alternative to the sla\_REFCO routine -- see notes.)}
+ \call{CALL sla\_REFCOQ (TDK, PMB, RH, WL, REFA, REFB)}
+}
+\args{GIVEN}
+{
+ \spec{TDK}{D}{ambient temperature at the observer (degrees K)} \\
+ \spec{PMB}{D}{pressure at the observer (mB)} \\
+ \spec{RH}{D}{relative humidity at the observer (range 0\,--\,1)} \\
+ \spec{WL}{D}{effective wavelength of the source ($\mu{\rm m}$)}
+}
+\args{RETURNED}
+{
+ \spec{REFA}{D}{$\tan \zeta$ coefficient (radians)} \\
+ \spec{REFB}{D}{$\tan^{3} \zeta$ coefficient (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The radio refraction is chosen by specifying WL $>100$~$\mu{\rm m}$.
+  \item The model is an approximation, for moderate zenith distances,
+        to the predictions of the sla\_REFRO routine.  The approximation
+        is maintained across a range of conditions, and applies to
+        both optical/IR and radio.
+  \item The algorithm is a fast alternative to the sla\_REFCO routine.
+        The latter calls the sla\_REFRO routine itself:  this involves
+        integrations through a model atmosphere, and is costly in
+        processor time.  However, the model which is produced is precisely
+        correct for two zenith distances ($45^\circ$ and $\sim\!76^\circ$)
+        and at other zenith distances is limited in accuracy only by the
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ formulation
+        itself.  The present routine is not as accurate, though it
+        satisfies most practical requirements.
+  \item The model omits the effects of (i)~height above sea level (apart
+        from the reduced pressure itself), (ii)~latitude ({\it i.e.}\ the
+        flattening of the Earth) and (iii)~variations in tropospheric
+        lapse rate.
+  \item The model has been tested using the following range of conditions:
+        \begin{itemize}
+        \item [$\cdot$] lapse rates 0.0055, 0.0065, 0.0075~degrees K per metre
+        \item [$\cdot$] latitudes $0^\circ$, $25^\circ$, $50^\circ$, $75^\circ$
+        \item [$\cdot$] heights 0, 2500, 5000 metres above sea level
+        \item [$\cdot$] pressures mean for height $-10$\% to $+5$\% in steps of $5$\%
+        \item [$\cdot$] temperatures $-10^\circ$ to $+20^\circ$ with respect to
+              $280^\circ$K at sea level
+        \item [$\cdot$] relative humidity 0, 0.5, 1
+        \item [$\cdot$] wavelength 0.4, 0.6, \ldots\ $2\mu{\rm m}$, + radio
+        \item [$\cdot$] zenith distances $15^\circ$, $45^\circ$, $75^\circ$
+        \end{itemize}
+        For the above conditions, the comparison with sla\_REFRO
+        was as follows:
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~
+        \begin{tabular}{|r|r|r|} \hline
+              & {\it worst} & {\it RMS} \\ \hline
+              optical/IR & 62 & 8 \\
+              radio & 319 & 49 \\ \hline
+              & mas & mas \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        For this particular set of conditions:
+        \begin{itemize}
+        \item [$\cdot$] lapse rate $6.5^\circ K km^{-1}$
+        \item [$\cdot$] latitude $50^\circ$
+        \item [$\cdot$] sea level
+        \item [$\cdot$] pressure 1005\,mB
+        \item [$\cdot$] temperature $7^\circ$C
+        \item [$\cdot$] humidity 80\%
+        \item [$\cdot$] wavelength 5740\,\.{A}
+        \end{itemize}
+        the results were as follows:
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~
+        \begin{tabular}{|r|r|r|r|} \hline
+        \multicolumn{1}{|c}{$\zeta$} &
+        \multicolumn{1}{|c}{sla\_REFRO} &
+        \multicolumn{1}{|c}{sla\_REFCOQ} &
+        \multicolumn{1}{|c|}{Saastamoinen} \\ \hline
+        10 &  10.27 &  10.27 &  10.27 \\
+        20 &  21.19 &  21.20 &  21.19 \\
+        30 &  33.61 &  33.61 &  33.60 \\
+        40 &  48.82 &  48.83 &  48.81 \\
+        45 &  58.16 &  58.18 &  58.16 \\
+        50 &  69.28 &  69.30 &  69.27 \\
+        55 &  82.97 &  82.99 &  82.95 \\
+        60 & 100.51 & 100.54 & 100.50 \\
+        65 & 124.23 & 124.26 & 124.20 \\
+        70 & 158.63 & 158.68 & 158.61 \\
+        72 & 177.32 & 177.37 & 177.31 \\
+        74 & 200.35 & 200.38 & 200.32 \\
+        76 & 229.45 & 229.43 & 229.42 \\
+        78 & 267.44 & 267.29 & 267.41 \\
+        80 & 319.13 & 318.55 & 319.10 \\ \hline
+        deg & arcsec & arcsec & arcsec \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        The values for Saastamoinen's formula (which includes terms
+        up to $\tan^5$) are taken from Hohenkerk and Sinclair (1985).
+
+        The results from the much slower but more accurate sla\_REFCO
+        routine have not been included in the tabulation as they are
+        identical to those in the sla\_REFRO column to the \arcsec{0}{01}
+        resolution used.
+  \item Outlandish input parameters are silently limited
+        to mathematically safe values.  Zero pressure is permissible,
+        and causes zeroes to be returned.
+  \item The algorithm draws on several sources, as follows:
+        \begin{itemize}
+        \item The formula for the saturation vapour pressure of water as
+              a function of temperature and temperature is taken from
+              expressions A4.5-A4.7 of Gill (1982).
+        \item The formula for the water vapour pressure, given the
+              saturation pressure and the relative humidity is from
+              Crane (1976), expression 2.5.5.
+        \item The refractivity of air is a function of temperature,
+              total pressure, water-vapour pressure and, in the case
+              of optical/IR but not radio, wavelength.  The formulae
+              for the two cases are developed from the Essen and Froome
+              expressions adopted in Resolution 1 of the 12th International
+              Geodesy Association General Assembly (1963).
+        \end{itemize}
+        The above three items are as used in the sla\_REFRO routine.
+        \begin{itemize}
+        \item The formula for $\beta~(=H_0/r_0)$ is
+              an adaption of expression 9 from Stone (1996).  The
+              adaptations, arrived at empirically, consist of (i)~a
+              small adjustment to the coefficient and (ii)~a humidity
+              term for the radio case only.
+        \item The formulae for the refraction constants as a function of
+              $n-1$ and $\beta$ are from Green (1987), expression 4.31.
+        \end{itemize}
+  \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Crane, R.K., Meeks, M.L.\ (ed), ``Refraction Effects in
+        the Neutral Atmosphere'',
+        {\it Methods of Experimental Physics: Astrophysics 12B,}\/
+        Academic Press, 1976.
+  \item Gill, Adrian E., {\it Atmosphere-Ocean Dynamics,}\/
+        Academic Press, 1982.
+  \item Hohenkerk, C.Y., \& Sinclair, A.T., NAO Technical Note
+        No.~63, 1985.
+  \item International Geodesy Association General Assembly, Bulletin
+        G\'{e}od\'{e}sique {\bf 70} p390, 1963.
+  \item Stone, Ronald C., P.A.S.P.~{\bf 108} 1051-1058, 1996.
+  \item Green, R.M., {\it Spherical Astronomy,}\/ Cambridge
+        University Press, 1987.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_REFRO}{Refraction}
+{
+ \action{Atmospheric refraction, for radio or optical/IR wavelengths.}
+ \call{CALL sla\_REFRO (ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REF)}
+}
+\args{GIVEN}
+{
+ \spec{ZOBS}{D}{observed zenith distance of the source (radians)} \\
+ \spec{HM}{D}{height of the observer above sea level (metre)} \\
+ \spec{TDK}{D}{ambient temperature at the observer (degrees K)} \\
+ \spec{PMB}{D}{pressure at the observer (mB)} \\
+ \spec{RH}{D}{relative humidity at the observer (range 0\,--\,1)} \\
+    \spec{WL}{D}{effective wavelength of the source ($\mu{\rm m}$)} \\
+ \spec{PHI}{D}{latitude of the observer (radian, astronomical)} \\
+ \spec{TLR}{D}{temperature lapse rate in the troposphere
+                                     (degrees K per metre)} \\
+ \spec{EPS}{D}{precision required to terminate iteration (radian)}
+}
+\args{RETURNED}
+{
+ \spec{REF}{D}{refraction: {\it in vacuo}\/ ZD minus observed ZD (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A suggested value for the TLR argument is 0.0065D0.  The
+        refraction is significantly affected by TLR, and if studies
+        of the local atmosphere have been carried out a better TLR
+        value may be available.
+  \item A suggested value for the EPS argument is 1D$-$8.  The result is
+        usually at least two orders of magnitude more computationally
+        precise than the supplied EPS value.
+  \item The routine computes the refraction for zenith distances up
+        to and a little beyond $90^\circ$ using the method of Hohenkerk
+        \& Sinclair (NAO Technical Notes 59 and 63, subsequently adopted
+        in the {\it Explanatory Supplement to the Astronomical Almanac,}\/
+        1992 -- see section 3.281).
+  \item The code is based on the AREF optical/IR refraction subroutine
+        of C.\,Hohenkerk (HMNAO, September 1984), with extensions to
+        support the radio case.  The modifications to the original HMNAO
+        optical/IR refraction code which affect the results are:
+        \begin{itemize}
+         \item Murray's values for the gas constants have been used
+               ({\it Vectorial Astrometry,}\/ Adam Hilger, 1983).
+         \item A better model for $P_s(T)$ has been adopted (taken from
+               Gill, {\it Atmosphere-Ocean Dynamics,}\/ Academic Press, 1982).
+         \item More accurate expressions for $Pw_o$ have been adopted
+               (again from Gill 1982).
+         \item Provision for radio wavelengths has been added using
+               expressions devised by A.\,T.\,Sinclair, RGO (private
+               communication 1989), based on the Essen \& Froome
+               refractivity formula adopted in Resolution~1 of the
+               12th International Geodesy Association General Assembly
+               (Bulletin G\'{e}od\'{e}sique {\bf 70} p390, 1963).
+        \end{itemize}
+        None of the changes significantly affects the optical/IR results
+        with respect to the algorithm given in the 1992 {\it Explanatory
+        Supplement.}\/  For example, at $70^\circ$ zenith distance the present
+        routine agrees with the ES algorithm to better than \arcsec{0}{05}
+        for any reasonable combination of parameters.  However, the
+        improved water-vapour expressions do make a significant difference
+        in the radio band, at $70^\circ$ zenith distance reaching almost
+        \arcseci{4} for a hot, humid, low-altitude site during a period of
+        low pressure.
+  \item The radio refraction is chosen by specifying WL $>100$~$\mu{\rm m}$.
+        Because the algorithm takes no account of the ionosphere, the
+        accuracy deteriorates at low frequencies, below about 30\,MHz.
+  \item Before use, the value of ZOBS is expressed in the range $\pm\pi$.
+        If this ranged ZOBS is negative, the result REF is computed from its
+        absolute value before being made negative to match.  In addition, if
+        it has an absolute value greater than $93^\circ$, a fixed REF value
+        equal to the result for ZOBS~$=93^\circ$ is returned, appropriately
+        signed.
+  \item As in the original Hohenkerk and Sinclair algorithm, fixed values
+        of the water vapour polytrope exponent, the height of the
+        tropopause, and the height at which refraction is negligible are
+        used.
+  \item The radio refraction has been tested against work done by
+        Iain~Coulson, JACH, (private communication 1995) for the
+        James Clerk Maxwell Telescope, Mauna Kea.  For typical conditions,
+        agreement at the \arcsec{0}{1} level is achieved for moderate ZD,
+        worsening to perhaps \arcsec{0}{5}\,--\,\arcsec{1}{0} at ZD $80^\circ$.
+        At hot and humid sea-level sites the accuracy will not be as good.
+  \item It should be noted that the relative humidity RH is formally
+        defined in terms of ``mixing ratio'' rather than pressures or
+        densities as is often stated.  It is the mass of water per unit
+        mass of dry air divided by that for saturated air at the same
+        temperature and pressure (see Gill 1982).  The familiar
+        $\nu=p_w/p_s$ or $\nu=\rho_w/\rho_s$ expressions can differ from
+        the formal definition by several percent, significant in the
+        radio case.
+  \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_REFV}{Apply Refraction to Vector}
+{
+ \action{Adjust an unrefracted Cartesian vector to include the effect of
+         atmospheric refraction, using the simple
+         $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model.}
+ \call{CALL sla\_REFV (VU, REFA, REFB, VR)}
+}
+\args{GIVEN}
+{
+ \spec{VU}{D}{unrefracted position of the source (\azel\ 3-vector)} \\
+ \spec{REFA}{D}{$\tan \zeta$ coefficient (radians)} \\
+ \spec{REFB}{D}{$\tan^{3} \zeta$ coefficient (radians)}
+}
+\args{RETURNED}
+{
+ \spec{VR}{D}{refracted position of the source (\azel\ 3-vector)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine applies the adjustment for refraction in the
+        opposite sense to the usual one -- it takes an unrefracted
+        ({\it in vacuo}\/) position and produces an observed (refracted)
+        position, whereas the
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$
+        model strictly
+        applies to the case where an observed position is to have the
+        refraction removed.  The unrefracted to refracted case is
+        harder, and requires an inverted form of the text-book
+        refraction models;  the algorithm used here is equivalent to
+        one iteration of the Newton-Raphson method applied to the
+        above formula.
+  \item Though optimized for speed rather than precision, the present
+        routine achieves consistency with the refracted-to-unrefracted
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$
+        model at better than 1~microarcsecond within
+        $30^\circ$ of the zenith and remains within 1~milliarcsecond to
+        $\zeta=70^\circ$.  The inherent accuracy of the model is, of
+        course, far worse than this -- see the documentation for sla\_REFCO
+        for more information.
+  \item At low elevations (below about $3^\circ$) the refraction
+        correction is held back to prevent arithmetic problems and
+        wildly wrong results.  Over a wide range of observer heights
+        and corresponding temperatures and pressures, the following
+        levels of accuracy are achieved, relative to numerical
+        integration through a model atmosphere:
+
+        \begin{center}
+        \begin{tabular}{ccl}
+              $\zeta_{obs}$ & {\it error} \\ \\
+              $80^\circ$ & \arcsec{0}{4}  \\
+              $81^\circ$ & \arcsec{0}{8}  \\
+              $82^\circ$ & \arcsec{1}{6}  \\
+              $83^\circ$ & \arcseci{3}    \\
+              $84^\circ$ & \arcseci{7}    \\
+              $85^\circ$ & \arcseci{17}   \\
+              $86^\circ$ & \arcseci{45}   \\
+              $87^\circ$ & \arcseci{150}  \\
+              $88^\circ$ & \arcseci{340}  \\
+              $89^\circ$ & \arcseci{620}  \\
+              $90^\circ$ & \arcseci{1100} \\
+              $91^\circ$ & \arcseci{1900} & $<$ high-altitude \\
+              $92^\circ$ & \arcseci{3200} & $<$ sites only \\
+        \end{tabular}
+        \end{center}
+  \item See also the routine sla\_REFZ, which performs the adjustment to
+        the zenith distance rather than in \xyz .
+        The present routine is faster than sla\_REFZ and,
+        except very low down,
+        is equally accurate for all practical purposes.  However, beyond
+        about $\zeta=84^\circ$ sla\_REFZ should be used, and for the utmost
+        accuracy iterative use of sla\_REFRO should be considered.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_REFZ}{Apply Refraction to ZD}
+{
+ \action{Adjust an unrefracted zenith distance to include the effect of
+         atmospheric refraction, using the simple
+         $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model.}
+ \call{CALL sla\_REFZ (ZU, REFA, REFB, ZR)}
+}
+\args{GIVEN}
+{
+ \spec{ZU}{D}{unrefracted zenith distance of the source (radians)} \\
+ \spec{REFA}{D}{$\tan \zeta$ coefficient (radians)} \\
+ \spec{REFB}{D}{$\tan^{3} \zeta$ coefficient (radians)}
+}
+\args{RETURNED}
+{
+ \spec{ZR}{D}{refracted zenith distance (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine applies the adjustment for refraction in the
+        opposite sense to the usual one -- it takes an unrefracted
+        ({\it in vacuo}\/) position and produces an observed (refracted)
+        position, whereas the
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$
+        model strictly
+        applies to the case where an observed position is to have the
+        refraction removed.  The unrefracted to refracted case is
+        harder, and requires an inverted form of the text-book
+        refraction models;  the formula used here is based on the
+        Newton-Raphson method.  For the utmost numerical consistency
+        with the refracted to unrefracted model, two iterations are
+        carried out, achieving agreement at the $10^{-11}$~arcsecond level
+        for $\zeta=80^\circ$.  The inherent accuracy of the model
+        is, of course, far worse than this -- see the documentation for
+        sla\_REFCO for more information.
+  \item At $\zeta=83^\circ$, the rapidly-worsening
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$
+        model is abandoned and an empirical formula takes over:
+
+          \[\Delta \zeta = F \left(
+  \frac{0^\circ\hspace{-0.37em}.\hspace{0.02em}55445
+                - 0^\circ\hspace{-0.37em}.\hspace{0.02em}01133 E
+                          + 0^\circ\hspace{-0.37em}.\hspace{0.02em}00202 E^2}
+             {1 + 0.28385 E +0.02390 E^2} \right) \]
+        where $E=90^\circ-\zeta_{true}$
+        and $F$ is a factor chosen to meet the
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$
+        formula at $\zeta=83^\circ$.  Over a
+        wide range of observer heights and corresponding temperatures and
+        pressures, the following levels of accuracy are achieved,
+        relative to numerical integration through a model atmosphere:
+
+        \begin{center}
+        \begin{tabular}{ccl}
+              $\zeta_{obs}$ & {\it error} \\ \\
+              $80^\circ$ & \arcsec{0}{4}  \\
+              $81^\circ$ & \arcsec{0}{8}  \\
+              $82^\circ$ & \arcsec{1}{5}  \\
+              $83^\circ$ & \arcsec{3}{2}  \\
+              $84^\circ$ & \arcsec{4}{9}  \\
+              $85^\circ$ & \arcsec{5}{8}  \\
+              $86^\circ$ & \arcsec{6}{1}  \\
+              $87^\circ$ & \arcsec{7}{1}  \\
+              $88^\circ$ & \arcseci{11}   \\
+              $89^\circ$ & \arcseci{21}   \\
+              $90^\circ$ & \arcseci{43}   \\
+              $91^\circ$ & \arcseci{92}  & $<$ high-altitude \\
+              $92^\circ$ & \arcseci{220} & $<$ sites only \\
+        \end{tabular}
+        \end{center}
+  \item See also the routine sla\_REFV, which performs the adjustment in
+        \xyz , and with the emphasis on speed rather than numerical accuracy.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_RVEROT}{RV Corrn to Earth Centre}
+{
+ \action{Velocity component in a given direction due to Earth rotation.}
+ \call{R~=~sla\_RVEROT (PHI, RA, DA, ST)}
+}
+\args{GIVEN}
+{
+ \spec{PHI}{R}{geodetic latitude of observing station (radians)} \\
+ \spec{RA,DA}{R}{apparent \radec\ (radians)} \\
+ \spec{ST}{R}{local apparent sidereal time (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RVEROT}{R}{Component of Earth rotation in
+                       direction RA,DA (km~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Sign convention: the result is positive when the observatory
+        is receding from the given point on the sky.
+  \item Accuracy: the simple algorithm used assumes a spherical Earth and
+        an observing station at sea level;  for actual observing
+        sites, the error is unlikely to be greater than 0.0005~km~s$^{-1}$.
+        For applications requiring greater precision, use the routine
+        sla\_PVOBS.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_RVGALC}{RV Corrn to Galactic Centre}
+{
+ \action{Velocity component in a given direction due to the rotation
+         of the Galaxy.}
+ \call{R~=~sla\_RVGALC (R2000, D2000)}
+}
+\args{GIVEN}
+{
+ \spec{R2000,D2000}{R}{J2000.0 mean \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RVGALC}{R}{Component of dynamical LSR motion in direction
+                       R2000,D2000 (km~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Sign convention: the result is positive when the LSR
+        is receding from the given point on the sky.
+  \item The Local Standard of Rest used here is a point in the
+        vicinity of the Sun which is in a circular orbit around
+        the Galactic centre.  Sometimes called the {\it dynamical}\/ LSR,
+        it is not to be confused with a {\it kinematical}\/ LSR, which
+        is the mean standard of rest of star catalogues or stellar
+        populations.
+  \item The dynamical LSR velocity due to Galactic rotation is assumed to
+        be 220~km~s$^{-1}$ towards $l^{I\!I}=90^{\circ}$,
+                                   $b^{I\!I}=0$.
+ \end{enumerate}
+}
+\aref{Kerr \& Lynden-Bell (1986), MNRAS, 221, p1023.}
+%-----------------------------------------------------------------------
+\routine{SLA\_RVLG}{RV Corrn to Local Group}
+{
+ \action{Velocity component in a given direction due to the combination
+         of the rotation of the Galaxy and the motion of the Galaxy
+         relative to the mean motion of the local group.}
+ \call{R~=~sla\_RVLG (R2000, D2000)}
+}
+\args{GIVEN}
+{
+ \spec{R2000,D2000}{R}{J2000.0 mean \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RVLG}{R}{Component of {\bf solar} ({\it n.b.})
+                     motion in direction R2000,D2000 (km~s$^{-1}$)}
+}
+\anote{Sign convention: the result is positive when
+       the Sun is receding from the given point on the sky.}
+\aref{{\it IAU Trans.}\ 1976.\ {\bf 16B}, p201.}
+%-----------------------------------------------------------------------
+\routine{SLA\_RVLSRD}{RV Corrn to Dynamical LSR}
+{
+ \action{Velocity component in a given direction due to the Sun's
+         motion with respect to the ``dynamical'' Local Standard of Rest.}
+ \call{R~=~sla\_RVLSRD (R2000, D2000)}
+}
+\args{GIVEN}
+{
+ \spec{R2000,D2000}{R}{J2000.0 mean \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RVLSRD}{R}{Component of {\it peculiar}\/ solar motion
+                      in direction R2000,D2000 (km~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Sign convention: the result is positive when
+        the Sun is receding from the given point on the sky.
+  \item The Local Standard of Rest used here is the {\it dynamical}\/ LSR,
+        a point in the vicinity of the Sun which is in a circular
+        orbit around the Galactic centre.  The Sun's motion with
+        respect to the dynamical LSR is called the {\it peculiar}\/ solar
+        motion.
+  \item There is another type of LSR, called a {\it kinematical}\/ LSR.  A
+        kinematical LSR is the mean standard of rest of specified star
+        catalogues or stellar populations, and several slightly
+        different kinematical LSRs are in use.  The Sun's motion with
+        respect to an agreed kinematical LSR is known as the
+        {\it standard}\/ solar motion.
+        The dynamical LSR is seldom used by observational astronomers,
+        who conventionally use a kinematical LSR such as the one implemented
+        in the routine sla\_RVLSRK.
+  \item The peculiar solar motion is from Delhaye (1965), in {\it Stars
+        and Stellar Systems}, vol~5, p73:  in Galactic Cartesian
+        coordinates (+9,+12,+7)~km~s$^{-1}$.
+        This corresponds to about 16.6~km~s$^{-1}$
+        towards Galactic coordinates $l^{I\!I}=53^{\circ},b^{I\!I}=+25^{\circ}$.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_RVLSRK}{RV Corrn to Kinematical LSR}
+{
+ \action{Velocity component in a given direction due to the Sun's
+         motion with respect to a kinematical Local Standard of Rest.}
+ \call{R~=~sla\_RVLSRK (R2000, D2000)}
+}
+\args{GIVEN}
+{
+ \spec{R2000,D2000}{R}{J2000.0 mean \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RVLSRK}{R}{Component of {\it standard}\/ solar motion
+                      in direction R2000,D2000 (km~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Sign convention: the result is positive when
+        the Sun is receding from the given point on the sky.
+  \item The Local Standard of Rest used here is one of several
+        {\it kinematical}\/ LSRs in common use.  A kinematical LSR is the
+        mean standard of rest of specified star catalogues or stellar
+        populations.  The Sun's motion with respect to a kinematical
+        LSR is known as the {\it standard}\/ solar motion.
+  \item There is another sort of LSR, seldom used by observational
+        astronomers, called the {\it dynamical}\/ LSR.  This is a
+        point in the vicinity of the Sun which is in a circular orbit
+        around the Galactic centre.  The Sun's motion with respect to
+        the dynamical LSR is called the {\it peculiar}\/ solar motion.  To
+        obtain a radial velocity correction with respect to the
+        dynamical LSR use the routine sla\_RVLSRD.
+  \item The adopted standard solar motion is 20~km~s$^{-1}$
+        towards $\alpha=18^{\rm h},\delta=+30^{\circ}$ (1900).
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Delhaye (1965), in {\it Stars and Stellar Systems}, vol~5, p73.
+  \item {\it Methods of Experimental Physics}\/ (ed Meeks), vol~12,
+        part~C, sec~6.1.5.2, p281.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_S2TP}{Spherical to Tangent Plane}
+{
+ \action{Projection of spherical coordinates onto the tangent plane
+         (single precision).}
+ \call{CALL sla\_S2TP (RA, DEC, RAZ, DECZ, XI, ETA, J)}
+}
+\args{GIVEN}
+{
+ \spec{RA,DEC}{R}{spherical coordinates of star (radians)} \\
+ \spec{RAZ,DECZ}{R}{spherical coordinates of tangent point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{XI,ETA}{R}{tangent plane coordinates (radians)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK, star on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 1 = error, star too far from axis} \\
+ \spec{}{}{\hspace{1.5em} 2 = error, antistar on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 3 = error, antistar too far from axis}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_V2TP is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_SEP}{Angle Between 2 Points on Sphere}
+{
+ \action{Angle between two points on a sphere (single precision).}
+ \call{R~=~sla\_SEP (A1, B1, A2, B2)}
+}
+\args{GIVEN}
+{
+ \spec{A1,B1}{R}{spherical coordinates of one point (radians)} \\
+ \spec{A2,B2}{R}{spherical coordinates of the other point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_SEP}{R}{angle between [A1,B1] and [A2,B2] in radians}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The spherical coordinates are right ascension and declination,
+  longitude and latitude, {\it etc.}\ in radians.
+  \item The result is always positive.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_SMAT}{Solve Simultaneous Equations}
+{
+ \action{Matrix inversion and solution of simultaneous equations
+         (single precision).}
+ \call{CALL sla\_SMAT (N, A, Y, D, JF, IW)}
+}
+\args{GIVEN}
+{
+ \spec{N}{I}{number of unknowns} \\
+ \spec{A}{R(N,N)}{matrix} \\
+ \spec{Y}{R(N)}{vector}
+}
+\args{RETURNED}
+{
+ \spec{A}{R(N,N)}{matrix inverse} \\
+ \spec{Y}{R(N)}{solution} \\
+ \spec{D}{R}{determinant} \\
+ \spec{JF}{I}{singularity flag: 0=OK} \\
+ \spec{IW}{I(N)}{workspace}
+}
+\notes
+{
+ \begin{enumerate}
+  \item For the set of $n$ simultaneous linear equations in $n$ unknowns:
+        \begin{verse}
+         {\bf A}$\cdot${\bf y} = {\bf x}
+        \end{verse}
+        where:
+        \begin{itemize}
+         \item {\bf A} is a non-singular $n \times n$ matrix,
+         \item {\bf y} is the vector of $n$ unknowns, and
+         \item {\bf x} is the known vector,
+        \end{itemize}
+        sla\_SMAT computes:
+        \begin{itemize}
+         \item the inverse of matrix {\bf A},
+         \item the determinant of matrix {\bf A}, and
+         \item the vector of $n$ unknowns {\bf y}.
+        \end{itemize}
+        Argument N is the order $n$, A (given) is the matrix {\bf A},
+        Y (given) is the vector {\bf x} and Y (returned)
+        is the vector {\bf y}.
+        The argument A (returned) is the inverse matrix {\bf A}$^{-1}$,
+        and D is {\it det}\/({\bf A}).
+  \item JF is the singularity flag.  If the matrix is non-singular,
+        JF=0 is returned.  If the matrix is singular, JF=$-$1
+        and D=0.0 are returned.  In the latter case, the contents
+        of array A on return are undefined.
+  \item The algorithm is Gaussian elimination with partial pivoting.
+        This method is very fast;  some much slower algorithms can give
+        better accuracy, but only by a small factor.
+  \item This routine replaces the obsolete sla\_SMATRX.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_SUBET}{Remove E-terms}
+{
+ \action{Remove the E-terms (elliptic component of annual aberration)
+         from a pre IAU~1976 catalogue \radec\ to give a mean place.}
+ \call{CALL sla\_SUBET (RC, DC, EQ, RM, DM)}
+}
+\args{GIVEN}
+{
+ \spec{RC,DC}{D}{\radec\ with E-terms included (radians)} \\
+ \spec{EQ}{D}{Besselian epoch of mean equator and equinox}
+}
+\args{RETURNED}
+{
+ \spec{RM,DM}{D}{\radec\ without E-terms (radians)}
+}
+\anote{Most star positions from pre-1984 optical catalogues (or
+       obtained by astrometry with respect to such stars) have the
+       E-terms built-in.  This routine converts such a position to a
+       formal mean place (allowing, for example, comparison with a
+       pulsar timing position).}
+\aref{{\it Explanatory Supplement to the Astronomical Ephemeris},
+      section 2D, page 48.}
+%-----------------------------------------------------------------------
+\routine{SLA\_SUPGAL}{Supergalactic to Galactic}
+{
+ \action{Transformation from de Vaucouleurs supergalactic coordinates
+         to IAU 1958 galactic coordinates.}
+ \call{CALL sla\_GALSUP (DL, DB, DSL, DSB)}
+}
+\args{GIVEN}
+{
+ \spec{DSL,DSB}{D}{supergalactic longitude and latitude (radians)}
+}
+\args{RETURNED}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal\ (radians)}
+}
+\refs
+{
+ \begin{enumerate}
+  \item de Vaucouleurs, de Vaucouleurs, \& Corwin, {\it Second Reference
+    Catalogue of Bright Galaxies}, U.Texas, p8.
+  \item Systems \& Applied Sciences Corp., documentation for the
+        machine-readable version of the above catalogue,
+        Contract NAS 5-26490.
+ \end{enumerate}
+ (These two references give different values for the galactic
+ longitude of the supergalactic origin.  Both are wrong;  the
+ correct value is $l^{I\!I}=137.37$.)
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_SVD}{Singular Value Decomposition}
+{
+ \action{Singular value decomposition.
+         This routine expresses a given matrix {\bf A} as the product of
+         three matrices {\bf U}, {\bf W}, {\bf V}$^{T}$:
+         \begin{tabbing}
+         XXXXXX \= \kill
+         \> {\bf A} = {\bf U} $\cdot$ {\bf W} $\cdot$ {\bf V}$^{T}$
+         \end{tabbing}
+         where:
+         \begin{tabbing}
+         XXXXXX \= XXXX \= \kill
+         \> {\bf A} \> is any $m$ (rows) $\times n$ (columns) matrix,
+                       where $m \geq n$ \\
+         \> {\bf U} \> is an $m \times n$ column-orthogonal matrix \\
+         \> {\bf W} \> is an $n \times n$ diagonal matrix with
+                       $w_{ii} \geq 0$ \\
+         \> {\bf V}$^{T}$ \> is the transpose of an $n \times n$
+                             orthogonal matrix
+\end{tabbing}
+}
+ \call{CALL sla\_SVD (M, N, MP, NP, A, W, V, WORK, JSTAT)}
+}
+\args{GIVEN}
+{
+ \spec{M,N}{I}{$m$, $n$, the numbers of rows and columns in matrix {\bf A}} \\
+ \spec{MP,NP}{I}{physical dimensions of array containing matrix {\bf A}} \\
+ \spec{A}{D(MP,NP)}{array containing $m \times n$ matrix {\bf A}}
+}
+\args{RETURNED}
+{
+ \spec{A}{D(MP,NP)}{array containing $m \times n$ column-orthogonal
+                    matrix {\bf U}} \\
+ \spec{W}{D(N)}{$n \times n$ diagonal matrix {\bf W}
+               (diagonal elements only)} \\
+ \spec{V}{D(NP,NP)}{array containing $n \times n$ orthogonal
+                    matrix {\bf V} ({\it n.b.}\ not {\bf V}$^{T}$)} \\
+ \spec{WORK}{D(N)}{workspace} \\
+ \spec{JSTAT}{I}{0~=~OK, $-$1~=~array A wrong shape, $>$0~=~index of W
+                 for which convergence failed (see note~3, below)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item M and N are the {\it logical}\/ dimensions of the
+        matrices and vectors concerned, which can be located in
+        arrays of larger {\it physical}\/ dimensions, given by MP and NP.
+  \item V contains matrix V, not the transpose of matrix V.
+  \item If the status JSTAT is greater than zero, this need not
+        necessarily be treated as a failure.  It means that, due to
+        chance properties of the matrix A, the QR transformation
+        phase of the routine did not fully converge in a predefined
+        number of iterations, something that very seldom occurs.
+        When this condition does arise, it is possible that the
+        elements of the diagonal matrix W have not been correctly
+        found.  However, in practice the results are likely to
+        be trustworthy.  Applications should report the condition
+        as a warning, but then proceed normally.
+ \end{enumerate}
+}
+\refs{The algorithm is an adaptation of the routine SVD in the {\it EISPACK}\,
+      library (Garbow~{\it et~al.}\ 1977, {\it EISPACK Guide Extension},
+      Springer Verlag), which is a FORTRAN~66 implementation of the Algol
+      routine SVD of Wilkinson \& Reinsch 1971 ({\it Handbook for Automatic
+      Computation}, vol~2, ed Bauer~{\it et~al.}, Springer Verlag).  These
+      references give full details of the algorithm used here.
+      A good account of the use of SVD in least squares problems is given
+      in {\it Numerical Recipes}\/ (Press~{\it et~al.}\ 1987, Cambridge
+      University Press), which includes another variant of the EISPACK code.}
+%-----------------------------------------------------------------------
+\routine{SLA\_SVDCOV}{Covariance Matrix from SVD}
+{
+ \action{From the {\bf W} and {\bf V} matrices from the SVD
+         factorization of a matrix
+         (as obtained from the sla\_SVD routine), obtain
+         the covariance matrix.}
+ \call{CALL sla\_SVDCOV (N, NP, NC, W, V, WORK, CVM)}
+}
+\args{GIVEN}
+{
+ \spec{N}{I}{$n$, the number of rows and columns in
+             matrices {\bf W} and {\bf V}} \\
+ \spec{NP}{I}{first dimension of array containing $n \times n$
+              matrix {\bf V}} \\
+ \spec{NC}{I}{first dimension of array CVM} \\
+ \spec{W}{D(N)}{$n \times n$ diagonal matrix {\bf W}
+                (diagonal elements only)} \\
+ \spec{V}{D(NP,NP)}{array containing $n \times n$ orthogonal matrix {\bf V}}
+}
+\args{RETURNED}
+{
+ \spec{WORK}{D(N)}{workspace} \\
+ \spec{CVM}{D(NC,NC)}{array to receive covariance matrix}
+}
+\aref{{\it Numerical Recipes}, section 14.3.}
+%-----------------------------------------------------------------------
+\routine{SLA\_SVDSOL}{Solution Vector from SVD}
+{
+ \action{From a given vector and the SVD of a matrix (as obtained from
+         the sla\_SVD routine), obtain the solution vector.
+         This routine solves the equation:
+         \begin{tabbing}
+         XXXXXX \= \kill
+         \> {\bf A} $\cdot$ {\bf x} = {\bf b}
+         \end{tabbing}
+         where:
+         \begin{tabbing}
+         XXXXXX \= XXXX \= \kill
+         \> {\bf A} \> is a given $m$ (rows) $\times n$ (columns)
+                       matrix, where $m \geq n$ \\
+         \> {\bf x} \> is the $n$-vector we wish to find, and \\
+         \> {\bf b} \> is a given $m$-vector
+         \end{tabbing}
+         by means of the {\it Singular Value Decomposition}\/ method (SVD).}
+ \call{CALL sla\_SVDSOL (M, N, MP, NP, B, U, W, V, WORK, X)}
+}
+\args{GIVEN}
+{
+ \spec{M,N}{I}{$m$, $n$, the numbers of rows and columns in matrix {\bf A}} \\
+ \spec{MP,NP}{I}{physical dimensions of array containing matrix {\bf A}} \\
+ \spec{B}{D(M)}{known vector {\bf b}} \\
+ \spec{U}{D(MP,NP)}{array containing $m \times n$ matrix {\bf U}} \\
+ \spec{W}{D(N)}{$n \times n$ diagonal matrix {\bf W}
+                (diagonal elements only)} \\
+ \spec{V}{D(NP,NP)}{array containing $n \times n$ orthogonal matrix {\bf V}}
+}
+\args{RETURNED}
+{
+ \spec{WORK}{D(N)}{workspace} \\
+ \spec{X}{D(N)}{unknown vector {\bf x}}
+}
+\notes
+{
+ \begin{enumerate}
+  \item In the Singular Value Decomposition method (SVD),
+        the matrix {\bf A} is first factorized (for example by
+        the routine sla\_SVD) into the following components:
+        \begin{tabbing}
+        XXXXXX \= \kill
+        \> {\bf A} = {\bf U} $\cdot$ {\bf W} $\cdot$ {\bf V}$^{T}$
+        \end{tabbing}
+        where:
+        \begin{tabbing}
+        XXXXXX \= XXXX \= \kill
+        \> {\bf A} \> is any $m$ (rows) $\times n$ (columns) matrix,
+                      where $m > n$ \\
+        \> {\bf U} \> is an $m \times n$ column-orthogonal matrix \\
+        \> {\bf W} \> is an $n \times n$ diagonal matrix with
+                      $w_{ii} \geq 0$ \\
+        \> {\bf V}$^{T}$ \> is the transpose of an $n \times n$
+                            orthogonal matrix
+        \end{tabbing}
+        Note that $m$ and $n$ are the {\it logical}\/ dimensions of the
+        matrices and vectors concerned, which can be located in
+        arrays of larger {\it physical}\/ dimensions MP and NP.
+        The solution is then found from the expression:
+        \begin{tabbing}
+        XXXXXX \= \kill
+        \> {\bf x} = {\bf V} $\cdot~[diag(1/${\bf W}$_{j})]
+           \cdot (${\bf U}$^{T} \cdot${\bf b})
+        \end{tabbing}
+  \item If matrix {\bf A} is square, and if the diagonal matrix {\bf W} is not
+        altered, the method is equivalent to conventional solution
+        of simultaneous equations.
+  \item If $m > n$, the result is a least-squares fit.
+  \item If the solution is poorly determined, this shows up in the
+        SVD factorization as very small or zero {\bf W}$_{j}$ values.  Where
+        a {\bf W}$_{j}$ value is small but non-zero it can be set to zero to
+        avoid ill effects.  The present routine detects such zero
+        {\bf W}$_{j}$ values and produces a sensible solution, with highly
+        correlated terms kept under control rather than being allowed
+        to elope to infinity, and with meaningful values for the
+       other terms.
+ \end{enumerate}
+}
+\aref{{\it Numerical Recipes}, section 2.9.}
+%-----------------------------------------------------------------------
+\routine{SLA\_TP2S}{Tangent Plane to Spherical}
+{
+ \action{Transform tangent plane coordinates into spherical
+         coordinates (single precision)}
+ \call{CALL sla\_TP2S (XI, ETA, RAZ, DECZ, RA, DEC)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{R}{tangent plane rectangular coordinates (radians)} \\
+ \spec{RAZ,DECZ}{R}{spherical coordinates of tangent point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RA,DEC}{R}{spherical coordinates (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_TP2V is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_TP2V}{Tangent Plane to Direction Cosines}
+{
+ \action{Given the tangent-plane coordinates of a star and the direction
+         cosines of the tangent point, determine the direction cosines
+         of the star
+         (single precision).}
+ \call{CALL sla\_TP2V (XI, ETA, V0, V)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{R}{tangent plane coordinates of star (radians)} \\
+ \spec{V0}{R(3)}{direction cosines of tangent point}
+}
+\args{RETURNED}
+{
+ \spec{V}{R(3)}{direction cosines of star}
+}
+\notes
+{
+ \begin{enumerate}
+  \item If vector V0 is not of unit length, the returned vector V will
+        be wrong.
+  \item If vector V0 points at a pole, the returned vector V will be
+        based on the arbitrary assumption that $\alpha=0$ at
+        the tangent point.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_TP2S.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_TPS2C}{Plate centre from $\xi,\eta$ and $\alpha,\delta$}
+{
+ \action{From the tangent plane coordinates of a star of known \radec,
+        determine the \radec\ of the tangent point (single precision)}
+ \call{CALL sla\_TPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{R}{tangent plane rectangular coordinates (radians)} \\
+ \spec{RA,DEC}{R}{spherical coordinates (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RAZ1,DECZ1}{R}{spherical coordinates of tangent point,
+                      solution 1} \\
+ \spec{RAZ2,DECZ2}{R}{spherical coordinates of tangent point,
+                      solution 2} \\
+ \spec{N}{I}{number of solutions:} \\
+ \spec{}{}{\hspace{1em} 0 = no solutions returned  (note 2)} \\
+ \spec{}{}{\hspace{1em} 1 = only the first solution is useful (note 3)} \\
+ \spec{}{}{\hspace{1em} 2 = there are two useful solutions (note 3)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The RAZ1 and RAZ2 values returned are in the range $0\!-\!2\pi$.
+  \item Cases where there is no solution can only arise near the poles.
+        For example, it is clearly impossible for a star at the pole
+        itself to have a non-zero $\xi$ value, and hence it is
+        meaningless to ask where the tangent point would have to be
+        to bring about this combination of $\xi$ and $\delta$.
+  \item Also near the poles, cases can arise where there are two useful
+        solutions.  The argument N indicates whether the second of the
+        two solutions returned is useful.  N\,=\,1
+        indicates only one useful solution, the usual case;  under
+        these circumstances, the second solution corresponds to the
+        ``over-the-pole'' case, and this is reflected in the values
+        of RAZ2 and DECZ2 which are returned.
+  \item The DECZ1 and DECZ2 values returned are in the range $\pm\pi$,
+        but in the ordinary, non-pole-crossing, case, the range is
+        $\pm\pi/2$.
+  \item RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2 are all in radians.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_TPV2C is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_TPV2C}{Plate centre from $\xi,\eta$ and $x,y,z$}
+{
+ \action{From the tangent plane coordinates of a star of known
+         direction cosines, determine the direction cosines
+         of the tangent point (single precision)}
+ \call{CALL sla\_TPV2C (XI, ETA, V, V01, V02, N)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{R}{tangent plane coordinates of star (radians)} \\
+ \spec{V}{R(3)}{direction cosines of star}
+}
+\args{RETURNED}
+{
+ \spec{V01}{R(3)}{direction cosines of tangent point, solution 1} \\
+ \spec{V01}{R(3)}{direction cosines of tangent point, solution 2} \\
+ \spec{N}{I}{number of solutions:} \\
+ \spec{}{}{\hspace{1em} 0 = no solutions returned  (note 2)} \\
+ \spec{}{}{\hspace{1em} 1 = only the first solution is useful (note 3)} \\
+ \spec{}{}{\hspace{1em} 2 = there are two useful solutions (note 3)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The vector V must be of unit length or the result will be wrong.
+  \item Cases where there is no solution can only arise near the poles.
+        For example, it is clearly impossible for a star at the pole
+        itself to have a non-zero XI value.
+  \item Also near the poles, cases can arise where there are two useful
+        solutions.  The argument N indicates whether the second of the
+        two solutions returned is useful.
+        N\,=\,1
+        indicates only one useful solution, the usual case;  under these
+        circumstances, the second solution can be regarded as valid if
+        the vector V02 is interpreted as the ``over-the-pole'' case.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_TPS2C.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_UE2EL}{Universal to Conventional Elements}
+{
+ \action{Transform universal elements into conventional heliocentric
+         osculating elements.}
+ \call{CALL sla\_UE2EL (\vtop{
+         \hbox{U, JFORMR,}
+         \hbox{JFORM, EPOCH, ORBINC, ANODE, PERIH,}
+         \hbox{AORQ, E, AORL, DM, JSTAT)}}}
+}
+\args{GIVEN}
+{
+ \spec{U}{D(13)}{universal orbital elements (updated; Note~1)} \\
+ \specel {(1)}     {combined mass ($M+m$)} \\
+ \specel {(2)}     {total energy of the orbit ($\alpha$)} \\
+ \specel {(3)}     {reference (osculating) epoch ($t_0$)} \\
+ \specel {(4-6)}   {position at reference epoch (${\rm \bf r}_0$)} \\
+ \specel {(7-9)}   {velocity at reference epoch (${\rm \bf v}_0$)} \\
+ \specel {(10)}    {heliocentric distance at reference epoch} \\
+ \specel {(11)}    {${\rm \bf r}_0.{\rm \bf v}_0$} \\
+ \specel {(12)}    {date ($t$)} \\
+ \specel {(13)}    {universal eccentric anomaly ($\psi$) of date, approx} \\ \\
+ \spec{JFORMR}{I}{requested element set (1-3; Note~3)}
+}
+\args{RETURNED}
+{
+ \spec{JFORM}{I}{element set actually returned (1-3; Note~4)} \\
+ \spec{EPOCH}{D}{epoch of elements ($t_0$ or $T$, TT MJD)} \\
+ \spec{ORBINC}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH}{D}{longitude or argument of perihelion
+                            ($\varpi$ or $\omega$,} \\
+ \spec{}{}{\hspace{1.5em} radians)} \\
+ \spec{AORQ}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E}{D}{eccentricity ($e$)} \\
+ \spec{AORL}{D}{mean anomaly or longitude
+                               ($M$ or $L$, radians,} \\
+ \spec{}{}{\hspace{1.5em} JFORM=1,2 only)} \\
+ \spec{DM}{D}{daily motion ($n$, radians, JFORM=1 only)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal PMASS} \\
+ \spec{}{}{\hspace{1.5em} $-$2 = illegal JFORMR} \\
+ \spec{}{}{\hspace{1.5em} $-$3 = position/velocity out of allowed range}
+}
+\notes
+{
+ \begin{enumerate}
+  \setlength{\parskip}{\medskipamount}
+  \item The ``universal'' elements are those which define the orbit for the
+        purposes of the method of universal variables (see reference 2).
+        They consist of the combined mass of the two bodies, an epoch,
+        and the position and velocity vectors (arbitrary reference frame)
+        at that epoch.  The parameter set used here includes also various
+        quantities that can, in fact, be derived from the other
+        information.  This approach is taken to avoiding unnecessary
+        computation and loss of accuracy.  The supplementary quantities
+        are (i)~$\alpha$, which is proportional to the total energy of the
+        orbit, (ii)~the heliocentric distance at epoch,
+        (iii)~the outwards component of the velocity at the given epoch,
+        (iv)~an estimate of $\psi$, the ``universal eccentric anomaly'' at a
+        given date and (v)~that date.
+  \item The universal elements are with respect to the mean equator and
+        equinox of epoch J2000.  The orbital elements produced are with
+        respect to the J2000 ecliptic and mean equinox.
+  \item Three different element-format options are supported, as
+        follows. \\
+
+        JFORM=1, suitable for the major planets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of elements $t_0$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> longitude of perihelion $\varpi$ (radians) \\
+        \> AORQ   \> = \> mean distance $a$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        \> AORL   \> = \> mean longitude $L$ (radians) \\
+        \> DM     \> = \> daily motion $n$ (radians)
+        \end{tabbing}
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of elements $t_0$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> mean distance $a$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        \> AORL   \> = \> mean anomaly $M$ (radians)
+        \end{tabbing}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xx \= \kill
+        \> EPOCH  \> = \> epoch of perihelion $T$ (TT MJD) \\
+        \> ORBINC \> = \> inclination $i$ (radians) \\
+        \> ANODE  \> = \> longitude of the ascending node $\Omega$ (radians) \\
+        \> PERIH  \> = \> argument of perihelion $\omega$ (radians) \\
+        \> AORQ   \> = \> perihelion distance $q$ (AU) \\
+        \> E      \> = \> eccentricity $e$ $( 0 \leq e \leq 10 )$
+        \end{tabbing}
+  \item It may not be possible to generate elements in the form
+        requested through JFORMR.  The caller is notified of the form
+        of elements actually returned by means of the JFORM argument:
+
+        \begin{tabbing}
+        xx \= xxxxxxxxxx \= xxxxxxxxxxx \= \kill
+        \> JFORMR   \> JFORM   \> meaning \\ \\
+        \> ~~~~~1   \> ~~~~~1  \> OK: elements are in the requested format \\
+        \> ~~~~~1   \> ~~~~~2  \> never happens \\
+        \> ~~~~~1   \> ~~~~~3  \> orbit not elliptical \\
+        \> ~~~~~2   \> ~~~~~1  \> never happens \\
+        \> ~~~~~2   \> ~~~~~2  \> OK: elements are in the requested format \\
+        \> ~~~~~2   \> ~~~~~3  \> orbit not elliptical \\
+        \> ~~~~~3   \> ~~~~~1  \> never happens \\
+        \> ~~~~~3   \> ~~~~~2  \> never happens \\
+        \> ~~~~~3   \> ~~~~~3  \> OK: elements are in the requested format
+        \end{tabbing}
+  \item The arguments returned for each value of JFORM ({\it cf}\/ Note~5:
+        JFORM may not be the same as JFORMR) are as follows:
+
+        \begin{tabbing}
+        xxx \= xxxxxxxxxxxx \= xxxxxx \= xxxxxx \= \kill
+        \> JFORM  \> 1        \> 2        \> 3 \\ \\
+        \> EPOCH  \> $t_0$    \> $t_0$    \> $T$ \\
+        \> ORBINC \> $i$      \> $i$      \> $i$ \\
+        \> ANODE  \> $\Omega$ \> $\Omega$ \> $\Omega$ \\
+        \> PERIH  \> $\varpi$ \> $\omega$ \> $\omega$ \\
+        \> AORQ   \> $a$      \> $a$      \> $q$ \\
+        \> E      \> $e$      \> $e$      \> $e$ \\
+        \> AORL   \> $L$      \> $M$      \> - \\
+        \> DM     \> $n$      \> -        \> -
+        \end{tabbing}
+
+        where:
+        \begin{tabbing}
+        xxx \= xxxxxxxx \= xxx \= \kill
+        \> $t_0$    \> is the epoch of the elements (MJD, TT) \\
+        \> $T$      \> is the epoch of perihelion (MJD, TT) \\
+        \> $i$      \> is the inclination (radians) \\
+        \> $\Omega$ \> is the longitude of the ascending node (radians) \\
+        \> $\varpi$ \> is the longitude of perihelion (radians) \\
+        \> $\omega$ \> is the argument of perihelion (radians) \\
+        \> $a$      \> is the mean distance (AU) \\
+        \> $q$      \> is the perihelion distance (AU) \\
+        \> $e$      \> is the eccentricity \\
+        \> $L$      \> is the longitude (radians, $0-2\pi$) \\
+        \> $M$      \> is the mean anomaly (radians, $0-2\pi$) \\
+        \> $n$      \> is the daily motion (radians) \\
+        \> - \> means no value is set
+        \end{tabbing}
+  \item At very small inclinations, the longitude of the ascending node
+        ANODE becomes indeterminate and under some circumstances may be
+        set arbitrarily to zero.  Similarly, if the orbit is close to
+        circular, the true anomaly becomes indeterminate and under some
+        circumstances may be set arbitrarily to zero.  In such cases,
+        the other elements are automatically adjusted to compensate,
+        and so the elements remain a valid description of the orbit.
+ \end{enumerate}
+}
+\refs{
+   \begin{enumerate}
+   \item Sterne, Theodore E., {\it An Introduction to Celestial Mechanics,}\/
+         Interscience Publishers, 1960.  Section 6.7, p199.
+   \item Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.
+   \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_UE2PV}{Pos/Vel from Universal Elements}
+{
+ \action{Heliocentric position and velocity of a planet, asteroid or comet,
+         starting from orbital elements in the ``universal variables'' form.}
+ \call{CALL sla\_UE2PV (DATE, U, PV, JSTAT)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{date (TT Modified Julian Date = JD$-$2400000.5)}
+}
+\args{GIVEN and RETURNED}
+{
+ \spec{U}{D(13)}{universal orbital elements (updated; Note~1)} \\
+ \specel {(1)}     {combined mass ($M+m$)} \\
+ \specel {(2)}     {total energy of the orbit ($\alpha$)} \\
+ \specel {(3)}     {reference (osculating) epoch ($t_0$)} \\
+ \specel {(4-6)}   {position at reference epoch (${\rm \bf r}_0$)} \\
+ \specel {(7-9)}   {velocity at reference epoch (${\rm \bf v}_0$)} \\
+ \specel {(10)}    {heliocentric distance at reference epoch} \\
+ \specel {(11)}    {${\rm \bf r}_0.{\rm \bf v}_0$} \\
+ \specel {(12)}    {date ($t$)} \\
+ \specel {(13)}    {universal eccentric anomaly ($\psi$) of date, approx}
+}
+\args{RETURNED}
+{
+ \spec{PV}{D(6)}{heliocentric \xyzxyzd, equatorial, J2000} \\
+ \spec{}{}{\hspace{1.5em} (AU, AU/s; Note~1)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{1.95em}      0 = OK} \\
+ \spec{}{}{\hspace{1.2em}    $-$1 = radius vector zero} \\
+ \spec{}{}{\hspace{1.2em}    $-2$ = failed to converge}
+}
+\notes
+{
+ \begin{enumerate}
+  \setlength{\parskip}{\medskipamount}
+  \item The ``universal'' elements are those which define the orbit for the
+        purposes of the method of universal variables (see reference).
+        They consist of the combined mass of the two bodies, an epoch,
+        and the position and velocity vectors (arbitrary reference frame)
+        at that epoch.  The parameter set used here includes also various
+        quantities that can, in fact, be derived from the other
+        information.  This approach is taken to avoiding unnecessary
+        computation and loss of accuracy.  The supplementary quantities
+        are (i)~$\alpha$, which is proportional to the total energy of the
+        orbit, (ii)~the heliocentric distance at epoch,
+        (iii)~the outwards component of the velocity at the given epoch,
+        (iv)~an estimate of $\psi$, the ``universal eccentric anomaly'' at a
+        given date and (v)~that date.
+  \item The companion routine is sla\_EL2UE.  This takes the conventional
+        orbital elements and transforms them into the set of numbers
+        needed by the present routine.  A single prediction requires one
+        one call to sla\_EL2UE followed by one call to the present routine;
+        for convenience, the two calls are packaged as the routine
+        sla\_PLANEL.  Multiple predictions may be made by again
+        calling sla\_EL2UE once, but then calling the present routine
+        multiple times, which is faster than multiple calls to sla\_PLANEL.
+
+        It is not obligatory to use sla\_EL2UE to obtain the parameters.
+        However, it should be noted that because sla\_EL2UE performs its
+        own validation, no checks on the contents of the array U are made
+        by the present routine.
+  \item DATE is the instant for which the prediction is required.  It is
+        in the TT timescale (formerly Ephemeris Time, ET) and is a
+        Modified Julian Date (JD$-$2400000.5).
+  \item The universal elements supplied in the array U are in canonical
+        units (solar masses, AU and canonical days).  The position and
+        velocity are not sensitive to the choice of reference frame.  The
+        sla\_EL2UE routine in fact produces coordinates with respect to the
+        J2000 equator and equinox.
+  \item The algorithm was originally adapted from the EPHSLA program of
+        D.\,H.\,P.\,Jones (private communication, 1996).  The method
+        is based on Stumpff's Universal Variables.
+ \end{enumerate}
+}
+\aref{Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.}
+%-----------------------------------------------------------------------
+\routine{SLA\_UNPCD}{Remove Radial Distortion}
+{
+ \action{Remove pincushion/barrel distortion from a distorted 
+         \xy\  to give tangent-plane \xy.}
+ \call{CALL sla\_UNPCD (DISCO,X,Y)}
+}
+\args{GIVEN}
+{
+ \spec{DISCO}{D}{pincushion/barrel distortion coefficient} \\
+ \spec{X,Y}{D}{distorted \xy}
+}
+\args{RETURNED}
+{
+ \spec{X,Y}{D}{tangent-plane \xy}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The distortion is of the form $\rho = r (1 + c r^{2})$, where $r$ is
+        the radial distance from the tangent point, $c$ is the DISCO
+        argument, and $\rho$ is the radial distance in the presence of
+        the distortion.
+  \item For {\it pincushion}\/ distortion, C is +ve;  for
+        {\it barrel}\/ distortion, C is $-$ve.
+  \item For X,Y in units of one projection radius (in the case of
+        a photographic plate, the focal length), the following
+        DISCO values apply:
+
+        \vspace{2ex}
+
+        \hspace{5em}
+        \begin{tabular}{|l|c|} \hline
+         Geometry & DISCO \\ \hline \hline
+         astrograph & 0.0 \\ \hline
+         Schmidt & $-$0.3333 \\ \hline
+         AAT PF doublet & +147.069 \\ \hline
+         AAT PF triplet & +178.585 \\ \hline
+         AAT f/8 & +21.20 \\ \hline
+         JKT f/8 & +14.6 \\ \hline
+        \end{tabular}
+
+        \vspace{2ex}
+
+  \item The present routine is an approximate inverse to the
+        companion routine sla\_PCD, obtained from two iterations
+        of Newton's method.  The mismatch between the sla\_PCD
+        and sla\_UNPCD is negligible for astrometric applications;
+        to reach 1~milliarcsec at the edge of the AAT triplet or
+        Schmidt field would require field diameters of \degree{2}{4}
+        and $42^{\circ}$ respectively.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_V2TP}{Direction Cosines to Tangent Plane}
+{
+ \action{Given the direction cosines of a star and of the tangent point,
+         determine the star's tangent-plane coordinates
+         (single precision).}
+ \call{CALL sla\_V2TP (V, V0, XI, ETA, J)}
+}
+\args{GIVEN}
+{
+ \spec{V}{R(3)}{direction cosines of star} \\
+ \spec{V0}{R(3)}{direction cosines of tangent point}
+}
+\args{RETURNED}
+{
+ \spec{XI,ETA}{R}{tangent plane coordinates (radians)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK, star on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 1 = error, star too far from axis} \\
+ \spec{}{}{\hspace{1.5em} 2 = error, antistar on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 3 = error, antistar too far from axis}
+}
+\notes
+{
+ \begin{enumerate}
+  \item If vector V0 is not of unit length, or if vector V is of zero
+        length, the results will be wrong.
+  \item If V0 points at a pole, the returned $\xi,\eta$
+        will be based on the
+        arbitrary assumption that $\alpha=0$ at the tangent point.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called 
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_S2TP.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_VDV}{Scalar Product}
+{
+ \action{Scalar product of two 3-vectors (single precision).}
+ \call{R~=~sla\_VDV (VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{VA}{R(3)}{first vector} \\
+ \spec{VB}{R(3)}{second vector}
+}
+\args{RETURNED}
+{
+ \spec{sla\_VDV}{R}{scalar product VA.VB}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_VN}{Normalize Vector}
+{
+ \action{Normalize a 3-vector, also giving the modulus (single precision).}
+ \call{CALL sla\_VN (V, UV, VM)}
+}
+\args{GIVEN}
+{
+ \spec{V}{R(3)}{vector}
+}
+\args{RETURNED}
+{
+ \spec{UV}{R(3)}{unit vector in direction of V} \\
+ \spec{VM}{R}{modulus of V}
+}
+\anote{If the modulus of V is zero, UV is set to zero as well.}
+%-----------------------------------------------------------------------
+\routine{SLA\_VXV}{Vector Product}
+{
+ \action{Vector product of two 3-vectors (single precision).}
+ \call{CALL sla\_VXV (VA, VB, VC)}
+}
+\args{GIVEN}
+{
+ \spec{VA}{R(3)}{first vector} \\
+ \spec{VB}{R(3)}{second vector}
+}
+\args{RETURNED}
+{
+ \spec{VC}{R(3)}{vector product VA$\times$VB}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_WAIT}{Time Delay}
+{
+ \action{Wait for a specified interval.}
+ \call{CALL sla\_WAIT (DELAY)}
+}
+\args{GIVEN}
+{
+ \spec{DELAY}{R}{delay in seconds}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The implementation is machine-specific.
+  \item The delay actually requested is restricted to the range
+        100ns-200s in the present implementation.
+  \item There is no guarantee of accuracy, though on almost all
+        types of computer the program will certainly not
+        resume execution {\it before}\/ the stated interval has
+        elapsed.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_XY2XY}{Apply Linear Model to an \xy}
+{
+ \action{Transform one \xy\ into another using a linear model of the type
+         produced by the sla\_FITXY routine.}
+ \call{CALL sla\_XY2XY (X1,Y1,COEFFS,X2,Y2)}
+}
+\args{GIVEN}
+{
+ \spec{X1,Y1}{D}{\xy\ before transformation} \\
+ \spec{COEFFS}{D(6)}{transformation coefficients (see note)}
+}
+\args{RETURNED}
+{
+ \spec{X2,Y2}{D}{\xy\ after transformation}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The model relates two sets of \xy\ coordinates as follows.
+        Naming the six elements of COEFFS $a,b,c,d,e$ \& $f$,
+        the present routine performs the transformation:
+        \begin{verse}
+          $x_{2} = a + bx_{1} + cy_{1}$ \\
+          $y_{2} = d + ex_{1} + fy_{1}$
+        \end{verse}
+  \item See also sla\_FITXY, sla\_PXY, sla\_INVF, sla\_DCMPF.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_ZD}{$h,\delta$ to Zenith Distance}
+{
+ \action{Hour angle and declination to zenith distance
+         (double precision).}
+ \call{D~=~sla\_ZD (HA, DEC, PHI)}
+}
+\args{GIVEN}
+{
+ \spec{HA}{D}{hour angle in radians} \\
+ \spec{DEC}{D}{declination in radians} \\
+ \spec{PHI}{D}{latitude in radians}
+}
+\args{RETURNED}
+{
+ \spec{sla\_ZD}{D}{zenith distance (radians, $0\!-\!\pi$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The latitude must be geodetic.  In critical applications,
+        corrections for polar motion should be applied (see sla\_POLMO).
+  \item In some applications it will be important to specify the
+        correct type of hour angle and declination in order to
+        produce the required type
+        of zenith distance.  In particular, it may be
+        important to distinguish between the zenith distance
+        as affected by refraction, which would require the
+        {\it observed}\/ \hadec, and the zenith distance {\it in vacuo},
+        which would require the {\it topocentric}\/ \hadec.  If
+        the effects of diurnal aberration can be neglected, the
+        {\it apparent}\/ \hadec\ may be used instead of the
+        {\it topocentric}\/ \hadec.
+  \item No range checking of arguments is done.
+  \item In applications which involve many zenith distance calculations,
+        rather than calling the present routine it will be more
+        efficient to use inline code, having previously computed fixed
+        terms such as sine and cosine of latitude, and perhaps sine and
+        cosine of declination.
+ \end{enumerate}
+}
+
+\pagebreak
+
+\section{EXPLANATION AND EXAMPLES}
+To guide the writer of positional-astronomy applications software,
+this final chapter puts the SLALIB routines into the context of
+astronomical phenomena and techniques, and presents a few
+``cookbook'' examples
+of the SLALIB calls in action.  The astronomical content of the chapter
+is not, of course, intended to be a substitute for specialist text-books on
+positional astronomy, but may help bridge the gap between
+such books and the SLALIB routines.  For further reading, the following
+cover a wide range of material and styles:
+\begin{itemize}
+\item {\it Explanatory Supplement to the Astronomical Almanac},
+      ed.\ P.\,Kenneth~Seidelmann (1992), University Science Books.
+\item {\it Vectorial Astrometry}, C.\,A.\,Murray (1983), Adam Hilger.
+\item {\it Spherical Astronomy}, Robin~M.\,Green (1985), Cambridge
+      University Press.
+\item {\it Spacecraft Attitude Determination and Control},
+      ed.\ James~R.\,Wertz (1986), Reidel.
+\item {\it Practical Astronomy with your Calculator},
+      Peter~Duffett-Smith (1981), Cambridge University Press.
+\end{itemize}
+Also of considerable value, though out of date in places, are:
+\begin{itemize}
+\item {\it Explanatory Supplement to the Astronomical Ephemeris
+      and the American Ephemeris and Nautical Almanac}, RGO/USNO (1974),
+      HMSO.
+\item {\it Textbook on Spherical Astronomy}, W.\,M.\,Smart (1977),
+      Cambridge University Press.
+\end{itemize}
+Only brief details of individual SLALIB routines are given here, and
+readers will find it useful to refer to the subprogram specifications
+elsewhere in this document.  The source code for the SLALIB routines
+(available in both Fortran and C) is also intended to be used as
+documentation.
+
+\subsection {Spherical Trigonometry}
+Celestial phenomena occur at such vast distances from the
+observer that for most practical purposes there is no need to
+work in 3D;  only the direction
+of a source matters, not how far away it is.  Things can
+therefore be viewed as if they were happening
+on the inside of sphere with the observer at the centre --
+the {\it celestial sphere}.  Problems involving
+positions and orientations in the sky can then be solved by
+using the formulae of {\it spherical trigonometry}, which
+apply to {\it spherical triangles}, the sides of which are
+{\it great circles}.
+
+Positions on the celestial sphere may be specified by using
+a spherical polar coordinate system, defined in terms of
+some fundamental plane and a line in that plane chosen to
+represent zero longitude.  Mathematicians usually work with the
+co-latitude, with zero at the principal pole, whereas most
+astronomical coordinate systems use latitude, reckoned plus and
+minus from the equator.
+Astronomical coordinate systems may be either right-handed
+({\it e.g.}\ right ascension and declination \radec,
+Galactic longitude and latitude \gal)
+or left-handed ({\it e.g.}\ hour angle and
+declination \hadec).  In some cases
+different conventions have been used in the past, a fruitful source of
+mistakes.  Azimuth and geographical longitude are examples;  azimuth
+is now generally reckoned north through east
+(making a left-handed system);  geographical longitude is now usually
+taken to increase eastwards (a right-handed system) but astronomers
+used to employ a west-positive convention.  In reports
+and program comments it is wise to spell out what convention
+is being used, if there is any possibility of confusion.
+
+When applying spherical trigonometry formulae, attention must be
+paid to
+rounding errors (for example it is a bad idea to find a
+small angle through its cosine) and to the possibility of
+problems close to poles.
+Also, if a formulation relies on inspection to establish
+the quadrant of the result, it is an indication that a vector-related
+method might be preferable.
+
+As well as providing many routines which work in terms of specific
+spherical coordinates such as \radec, SLALIB provides
+two routines which operate directly on generic spherical
+coordinates:
+sla\_SEP
+computes the separation between
+two points (the distance along a great circle) and
+sla\_BEAR
+computes the bearing (or {\it position angle})
+of one point seen from the other.  The routines
+sla\_DSEP
+and
+sla\_DBEAR
+are double precision equivalents.  As a simple demonstration
+of SLALIB, we will use these facilities to estimate the distance from
+London to Sydney and the initial compass heading:
+\goodbreak
+\begin{verbatim}
+            IMPLICIT NONE
+
+      *  Degrees to radians
+            REAL D2R
+            PARAMETER (D2R=0.01745329252)
+
+      *  Longitudes and latitudes (radians) for London and Sydney
+            REAL AL,BL,AS,BS
+            PARAMETER (AL=-0.2*D2R,BL=51.5*D2R,AS=151.2*D2R,BS=-33.9*D2R)
+
+      *  Earth radius in km (spherical approximation)
+            REAL RKM
+            PARAMETER (RKM=6375.0)
+
+            REAL sla_SEP,sla_BEAR
+
+
+      *  Distance and initial heading (N=0, E=90)
+            WRITE (*,'(1X,I5,'' km,'',I4,'' deg'')')
+           :    NINT(sla_SEP(AL,BL,AS,BS)*RKM),NINT(sla_BEAR(AL,BL,AS,BS)/D2R)
+
+            END
+\end{verbatim}
+\goodbreak
+(The result is 17011~km, $61^\circ$.)
+
+The routines
+sla\_PAV and
+sla\_DPAV
+are equivalents of sla\_BEAR and sla\_DBEAR but starting from
+direction-cosines instead of spherical coordinates.
+
+\subsubsection{Formatting angles}
+SLALIB has routines for decoding decimal numbers
+from character form and for converting angles to and from
+sexagesimal form (hours, minutes, seconds or degrees,
+arcminutes, arcseconds).  These apparently straightforward
+operations contain hidden traps which the SLALIB routines
+avoid.
+
+There are five routines for decoding numbers from a character
+string, such as might be entered using a keyboard.
+They all work in the same style, and successive calls
+can work their way along a single string decoding
+a sequence of numbers of assorted types.  Number
+fields can be separated by spaces or commas, and can be defaulted
+to previous values or to preset defaults.
+
+Three of the routines decode single numbers:
+sla\_INTIN
+(integer),
+sla\_FLOTIN
+(single precision floating point) and
+sla\_DFLTIN
+(double precision).  A minus sign can be
+detected even when the number is zero;  this avoids
+the frequently-encountered ``minus zero'' bug, where
+declinations {\it etc.}\ in
+the range $0^{\circ}$ to $-1^{\circ}$ mysteriously migrate to
+the range $0^{\circ}$ to $+1^{\circ}$.
+Here is an example (in Fortran) where we wish to
+read two numbers, and integer {\tt IX} and a real, {\tt Y},
+with {\tt X} defaulting to zero and {\tt Y} defaulting to
+{\tt X}:
+\goodbreak
+\begin{verbatim}
+            DOUBLE PRECISION Y
+            CHARACTER*80 A
+            INTEGER IX,I,J
+
+      *  Input the string to be decoded
+            READ (*,'(A)') A
+
+      *  Preset IX to its default value
+            IX = 0
+
+      *  Point to the start of the string
+            I = 1
+
+      *  Decode an integer
+            CALL sla_INTIN(A,I,IX,J)
+            IF (J.GT.1) GO TO ... (bad IX)
+
+      *  Preset Y to its default value
+            Y = DBLE(IX)
+
+      *  Decode a double precision number
+            CALL sla_DFLTIN(A,I,Y,J)
+            IF (J.GT.1) GO TO ... (bad Y)
+\end{verbatim}
+\goodbreak
+Two additional routines decode a 3-field sexagesimal number:
+sla\_AFIN
+(degrees, arcminutes, arcseconds to single
+precision radians) and
+sla\_DAFIN
+(the same but double precision).  They also
+work using other units such as hours {\it etc}.\ if
+you multiply the result by the appropriate factor.  An example
+Fortran program which uses
+sla\_DAFIN
+was given earlier, in section 1.2.
+
+SLALIB provides four routines for expressing an angle in radians
+in a preferred range.  The function
+sla\_RANGE
+expresses an angle
+in the range $\pm\pi$;
+sla\_RANORM
+expresses an angle in the range
+$0-2\pi$.  The functions
+sla\_DRANGE
+and
+sla\_DRANRM
+are double precision versions.
+
+Several routines
+(sla\_CTF2D,
+sla\_CR2AF
+{\it etc.}) are provided to convert
+angles to and from
+sexagesimal form (hours, minute, seconds or degrees,
+arcminutes and arcseconds).
+They avoid the common
+``converting from integer to real at the wrong time''
+bug, which produces angles like \hms{24}{59}{59}{999}.
+Here is a program which displays an hour angle
+stored in radians:
+\goodbreak
+\begin{verbatim}
+            DOUBLE PRECISION HA
+            CHARACTER SIGN
+            INTEGER IHMSF(4)
+            :
+            CALL sla_DR2TF(3,HA,SIGN,IHMSF)
+            WRITE (*,'(1X,A,3I3.2,''.'',I3.3)') SIGN,IHMSF
+\end{verbatim}
+\goodbreak
+
+\subsection {Vectors and Matrices}
+As an alternative to employing a spherical polar coordinate system,
+the direction of an object can be defined in terms of the sum of any
+three vectors as long as they are different and
+not coplanar.  In practice, three vectors at right angles are
+usually chosen, forming a system
+of {\it Cartesian coordinates}.  The {\it x}- and {\it y}-axes
+lie in the fundamental plane ({\it e.g.}\ the equator in the
+case of \radec), with the {\it x}-axis pointing to zero longitude.
+The {\it z}-axis is normal to the fundamental plane and points
+towards positive latitudes.  The {\it y}-axis can lie in either
+of the two possible directions, depending on whether the
+coordinate system is right-handed or left-handed.
+The three axes are sometimes called
+a {\it triad}.  For most applications involving arbitrarily
+distant objects such as stars, the vector which defines
+the direction concerned is constrained to have unit length.
+The {\it x}-, {\it y-} and {\it z-}components
+can be regarded as the scalar (dot) product of this vector
+onto the three axes of the triad in turn.  Because the vector
+is a unit vector,
+each of the three dot-products is simply the cosine of the angle
+between the unit vector and the axis concerned, and the
+{\it x}-, {\it y-} and {\it z-}components are sometimes
+called {\it direction cosines}.
+
+For some applications involving objects
+with the Solar System, unit vectors are inappropriate, and
+it is necessary to use vectors scaled in length-units such as
+AU, km {\it etc.}
+In these cases the origin of the coordinate system may not be
+the observer, but instead might be the Sun, the Solar-System
+barycentre, the centre of the Earth {\it etc.}  But whatever the application,
+the final direction in which the observer sees the object can be
+expressed as direction cosines.
+
+But where has this got us?  Instead of two numbers -- a longitude and
+a latitude -- we now have three numbers to look after
+-- the {\it x}-, {\it y-} and
+{\it z-}components -- whose quadratic sum we have somehow to contrive to
+be unity.  And, in addition to this apparent redundancy,
+most people find it harder to visualize
+problems in terms of \xyz\ than in $[\,\theta,\phi~]$.
+Despite these objections, the vector approach turns out to have
+significant advantages over the spherical trigonometry approach:
+\begin{itemize}
+\item Vector formulae tend to be much more succinct;  one vector
+      operation is the equivalent of strings of sines and cosines.
+\item The formulae are as a rule rigorous, even at the poles.
+\item Accuracy is maintained all over the celestial sphere.
+      When one Cartesian component is nearly unity and
+      therefore insensitive to direction, the others become small
+      and therefore more precise.
+\item Formulations usually deliver the quadrant of the result
+      without the need for any inspection (except within the
+      library function ATAN2).
+\end{itemize}
+A number of important transformations in positional
+astronomy turn out to be nothing more than changes of coordinate
+system, something which is especially convenient if
+the vector approach is used.  A direction with respect
+to one triad can be expressed relative to another triad simply
+by multiplying the \xyz\ column vector by the appropriate
+$3\times3$ orthogonal matrix
+(a tensor of Rank~2, or {\it dyadic}).  The three rows of this
+{\it rotation matrix}\/
+are the vectors in the old coordinate system of the three
+new axes, and the transformation amounts to obtaining the
+dot-product of the direction-vector with each of the three
+new axes.  Precession, nutation, \hadec\ to \azel,
+\radec\ to \gal\ and so on are typical examples of the
+technique.  A useful property of the rotation matrices
+is that they can be inverted simply by taking the transpose.
+
+The elements of these vectors and matrices are assorted combinations of
+the sines and cosines of the various angles involved (hour angle,
+declination and so on, depending on which transformation is
+being applied).  If you write out the matrix multiplications
+in full you get expressions which are essentially the same as the
+equivalent spherical trigonometry formulae.  Indeed, many of the
+standard formulae of spherical trigonometry are most easily
+derived by expressing the problem initially in
+terms of vectors.
+
+\subsubsection{Using vectors}
+SLALIB provides conversions between spherical and vector
+form
+(sla\_CS2C,
+sla\_CC2S
+{\it etc.}), plus an assortment
+of standard vector and matrix operations
+(sla\_VDV,
+sla\_MXV
+{\it etc.}).
+There are also routines
+(sla\_EULER
+{\it etc.}) for creating a rotation matrix
+from three {\it Euler angles}\/ (successive rotations about
+specified Cartesian axes).  Instead of Euler angles, a rotation
+matrix can be expressed as an {\it axial vector}\/ (the pole of the rotation,
+and the amount of rotation), and routines are provided for this
+(sla\_AV2M,
+sla\_M2AV
+{\it etc.}).
+
+Here is an example where spherical coordinates {\tt P1} and {\tt Q1}
+undergo a coordinate transformation and become {\tt P2} and {\tt Q2};
+the transformation consists of a rotation of the coordinate system
+through angles {\tt A}, {\tt B} and {\tt C} about the
+{\it z}, new {\it y}\/ and new {\it z}\/ axes respectively:
+\goodbreak
+\begin{verbatim}
+            REAL A,B,C,R(3,3),P1,Q1,V1(3),V2(3),P2,Q2
+             :
+      *  Create rotation matrix
+            CALL sla_EULER('ZYZ',A,B,C,R)
+
+      *  Transform position (P,Q) from spherical to Cartesian
+            CALL sla_CS2C(P1,Q1,V1)
+
+      *  Multiply by rotation matrix
+            CALL sla_MXV(R,V1,V2)
+
+      *  Back to spherical
+            CALL sla_CC2S(V2,P2,Q2)
+\end{verbatim}
+\goodbreak
+Small adjustments to the direction of a position
+vector are often most conveniently described in terms of
+$[\,\Delta x,\Delta y, \Delta z\,]$.  Adding the correction
+vector needs careful handling if the position
+vector is to remain of length unity, an advisable precaution which
+ensures that
+the \xyz\ components are always available to mean the cosines of
+the angles between the vector and the axis concerned.  Two types
+of shifts are commonly used,
+the first where a small vector of arbitrary direction is
+added to the unit vector, and the second where there is a displacement
+in the latitude coordinate (declination, elevation {\it etc.}) alone.
+
+For a shift produced by adding a small \xyz\ vector ${\bf D}$ to a
+unit vector ${\bf V1}$, the resulting vector ${\bf V2}$ has direction
+$<{\bf V1}+{\bf D}>$ but is no longer of unit length.  A better approximation
+is available if the result is multiplied by a scaling factor of
+$(1-{\bf D}\cdot{\bf V1})$, where the dot
+means scalar product.  In Fortran:
+\goodbreak
+\begin{verbatim}
+            F = (1D0-(DX*V1X+DY*V1Y+DZ*V1Z))
+            V2X = F*(V1X+DX)
+            V2Y = F*(V1Y+DY)
+            V2Z = F*(V1Z+DZ)
+\end{verbatim}
+\goodbreak
+\noindent
+The correction for diurnal aberration (discussed later) is
+an example of this form of shift.
+
+As an example of the second kind of displacement
+we will apply a small change in elevation $\delta E$ to an
+\azel\ direction vector.  The direction of the
+result can be obtained by making the allowable approximation
+${\tan \delta E\approx\delta E}$ and adding a adjustment
+vector of length $\delta E$ normal
+to the direction vector in the vertical plane containing the direction
+vector.  The $z$-component of the adjustment vector is
+$\delta E \cos E$,
+and the horizontal component is
+$\delta E \sin E$ which has then to be
+resolved into $x$ and $y$ in proportion to their current sizes. To
+approximate a unit vector more closely, a correction factor of
+$\cos \delta E$ can then be applied, which is nearly
+$(1-\delta E^2 /2)$ for
+small $\delta E$.  Expressed in Fortran, for initial vector
+{\tt V1X,V1Y,V1Z}, change in elevation {\tt DEL}
+(+ve $\equiv$ upwards), and result
+vector {\tt V2X,V2Y,V2Z}:
+\goodbreak
+\begin{verbatim}
+            COSDEL = 1DO-DEL*DEL/2D0
+            R1 = SQRT(V1X*V1X+V1Y*V1Y)
+            F = COSDEL*(R1-DEL*V1Z)/R1
+            V2X = F*V1X
+            V2Y = F*V1Y
+            V2Z = COSDEL*(V1Z+DEL*R1)
+\end{verbatim}
+\goodbreak
+An example of this type of shift is the correction for atmospheric
+refraction (see later).
+Depending on the relationship between $\delta E$ and $E$, special
+handling at the pole (the zenith for our example) may be required.
+
+SLALIB includes routines for the case where both a position
+and a velocity are involved.  The routines
+sla\_CS2C6
+and
+sla\_CC62S
+convert from $[\theta,\phi,\dot{\theta},\dot{\phi}]$
+to \xyzxyzd\ and back;
+sla\_DCS26
+and
+sla\_DC62S
+are double precision equivalents.
+
+\subsection {Celestial Coordinate Systems}
+SLALIB has routines to perform transformations
+of celestial positions between different spherical
+coordinate systems, including those shown in the following table:
+
+\begin{center}
+\begin{tabular}{|l|c|c|c|c|c|c|} \hline
+{\it system} & {\it symbols} & {\it longitude} & {\it latitude} &
+          {\it x-y plane} & {\it long.\ zero} & {\it RH/LH}
+\\ \hline \hline
+horizon & -- & azimuth & elevation & horizontal & north & L
+\\ \hline
+equatorial & $\alpha,\delta$ & R.A.\ & Dec.\ & equator & equinox & R
+\\ \hline
+local equ.\ & $h,\delta$ & H.A.\ & Dec.\ & equator & meridian & L
+\\ \hline
+ecliptic & $\lambda,\beta$ & ecl.\ long.\ & ecl.\ lat.\ &
+                                       ecliptic & equinox & R
+\\ \hline
+galactic & $l^{I\!I},b^{I\!I}$ & gal.\ long.\ & gal.\ lat.\ &
+                                       gal.\ equator & gal.\ centre & R
+\\ \hline
+supergalactic & SGL,SGB & SG long.\ & SG lat.\ &
+                                       SG equator & node w.\ gal.\ equ.\ & R
+\\ \hline
+\end{tabular}
+\end{center}
+Transformations between \hadec\ and \azel\ can be performed by
+calling
+sla\_E2H
+and
+sla\_H2E,
+or, in double precision,
+sla\_DE2H
+and
+sla\_DH2E.
+There is also a routine for obtaining
+zenith distance alone for a given \hadec,
+sla\_ZD,
+and one for determining the parallactic angle,
+sla\_PA.
+Three routines are included which relate to altazimuth telescope
+mountings.  For a given \hadec\ and latitude,
+sla\_ALTAZ
+returns the azimuth, elevation and parallactic angle, plus
+velocities and accelerations for sidereal tracking.
+The routines
+sla\_PDA2H
+and
+sla\_PDQ2H
+predict at what hour angle a given azimuth or
+parallactic angle will be reached.
+
+The routines
+sla\_EQECL
+and
+sla\_ECLEQ
+transform between ecliptic
+coordinates and \radec\/; there is also a routine for generating the
+equatorial to ecliptic rotation matrix for a given date:
+sla\_ECMAT.
+
+For conversion between Galactic coordinates and \radec\ there are
+two sets of routines, depending on whether the \radec\ is
+old-style, B1950, or new-style, J2000;
+sla\_EG50
+and
+sla\_GE50
+are \radec\ to \gal\ and {\it vice versa}\/ for the B1950 case, while
+sla\_EQGAL
+and
+sla\_GALEQ
+are the J2000 equivalents.
+
+Finally, the routines
+sla\_GALSUP
+and
+sla\_SUPGAL
+transform \gal\ to de~Vaucouleurs supergalactic longitude and latitude
+and {\it vice versa.}
+
+It should be appreciated that the table, above, constitutes
+a gross oversimplification.   Apparently
+simple concepts such as equator, equinox {\it etc.}\ are apt to be very hard to
+pin down precisely (polar motion, orbital perturbations \ldots) and
+some have several interpretations, all subtly different.  The various
+frames move in complicated ways with respect to one another or to
+the stars (themselves in motion).  And in some instances the
+coordinate system is slightly distorted, so that the
+ordinary rules of spherical trigonometry no longer strictly apply.
+
+These {\it caveats}\/
+apply particularly to the bewildering variety of different
+\radec\ systems that are in use.  Figure~1 shows how
+some of these systems are related, to one another and
+to the direction in which a celestial source actually
+appears in the sky.  At the top of the diagram are
+the various sorts of {\it mean place}\/
+found in star catalogues and papers;\footnote{One frame not included in
+Figure~1 is that of the Hipparcos catalogue.  This is currently the
+best available implementation in the optical of the {\it International
+Celestial Reference System}\/ (ICRS), which is based on extragalactic
+radio sources observed by VLBI.  The distinction between FK5 J2000
+and Hipparcos coordinates only becomes important when accuracies of
+50~mas or better are required.  More details are given in
+Section~4.14.} at the bottom is the
+{\it observed}\/ \azel, where a perfect theodolite would
+be pointed to see the source;  and in the body of
+the diagram are
+the intermediate processing steps and coordinate
+systems.  To help
+understand this diagram, and the SLALIB routines that can
+be used to carry out the various calculations, we will look at the coordinate
+systems involved, and the astronomical phenomena that
+affect them.
+
+\begin{figure}
+\begin{center}
+\begin{tabular}{|cccccc|}   \hline
+& & & & & \\
+\hspace{5em} & \hspace{5em} & \hspace{5em} &
+   \hspace{5em} & \hspace{5em} & \hspace{5em}  \\
+\multicolumn{2}{|c}{\hspace{0em}\fbox{\parbox{8.5em}{\center \vspace{-2ex}
+                                                   mean \radec, FK4, \\
+                                                   any equinox
+                                                   \vspace{0.5ex}}}} &
+ \multicolumn{2}{c}{\hspace{0em}\fbox{\parbox{8.5em}{\center \vspace{-2ex}
+                                                   mean \radec, FK4,
+                                                   no $\mu$, any equinox
+                                                   \vspace{0.5ex}}}} &
+\multicolumn{2}{c|}{\hspace{0em}\fbox{\parbox{8.5em}{\center \vspace{-2ex}
+                                                   mean \radec, FK5, \\
+                                                   any equinox
+                                                   \vspace{0.5ex}}}} \\
+& \multicolumn{2}{|c|}{} & \multicolumn{2}{c|}{} & \\
+\multicolumn{2}{|c}{space motion} & \multicolumn{1}{c|}{} & &
+   \multicolumn{2}{c|}{space motion} \\
+\multicolumn{2}{|c}{-- E-terms} &
+   \multicolumn{2}{c}{-- E-terms} & \multicolumn{1}{c|}{} & \\
+\multicolumn{2}{|c}{precess to B1950} & \multicolumn{2}{c}{precess to B1950} &
+   \multicolumn{2}{c|}{precess to J2000} \\
+\multicolumn{2}{|c}{+ E-terms} &
+   \multicolumn{2}{c}{+ E-terms} & \multicolumn{1}{c|}{} & \\
+\multicolumn{2}{|c}{FK4 to FK5, no $\mu$} &
+   \multicolumn{2}{c}{FK4 to FK5, no $\mu$} & \multicolumn{1}{c|}{} & \\
+\multicolumn{2}{|c}{parallax} & \multicolumn{1}{c|}{} & &
+   \multicolumn{2}{c|}{parallax} \\
+& \multicolumn{2}{|c|}{} & \multicolumn{2}{c|}{} & \\ \cline{2-5}
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{\parbox{18em}{\center \vspace{-2ex}
+                                   FK5, J2000, current epoch, geocentric
+                                          \vspace{0.5ex}}}} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{light deflection} & \\
+& \multicolumn{4}{c}{annual aberration} & \\
+& \multicolumn{4}{c}{precession/nutation} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{Apparent \radec}} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{Earth rotation} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{Apparent \hadec}} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{diurnal aberration} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{Topocentric \hadec}} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\hadec\ to \azel} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{Topocentric \azel}} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{refraction} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{Observed \azel}} & \\
+& & & & & \\
+& & & & & \\ \hline
+\end{tabular}
+\end{center}
+\vspace{-0.5ex}
+\caption{Relationship Between Celestial Coordinates}
+
+Star positions are published or catalogued using
+one of the mean \radec\ systems shown at
+the top.  The ``FK4'' systems
+were used before about 1980 and are usually
+equinox B1950.  The ``FK5'' system, equinox J2000, is now preferred,
+or rather its modern equivalent, the International Celestial Reference
+Frame (in the optical, the Hipparcos catalogue).
+The figure relates a star's mean \radec\ to the actual
+line-of-sight to the star.
+Note that for the conventional choices of equinox, namely
+B1950 or J2000, all of the precession and E-terms corrections
+are superfluous.
+\end{figure}
+
+\subsection{Precession and Nutation}
+{\it Right ascension and declination}, (\radec), are the names
+of the longitude and latitude in a spherical
+polar coordinate system based on the Earth's axis of rotation.
+The zero point of $\alpha$ is the point of intersection of
+the {\it celestial
+equator}\/ and the {\it ecliptic}\/ (the apparent path of the Sun
+through the year) where the Sun moves into the northern
+hemisphere.  This point is called the
+{\it first point of Aries},
+the {\it vernal equinox}\/ (with apologies to
+southern-hemisphere readers) or simply the {\it equinox}.\footnote{With
+the introduction of the International Celestial Reference System (ICRS), the
+connection between (i)~star coordinates and (ii)~the Earth's orientation
+and orbit has been broken.  However, the orientation of the
+International Celestial Reference Frame (ICRF) axes was, for convenience,
+chosen to match J2000 FK5, and for most practical purposes ICRF coordinates
+(for example entries in the Hipparcos catalogue) can be regarded as
+synonymous with J2000 FK5.  See Section 4.14 for further details.}
+
+This simple picture is unfortunately
+complicated by the difficulty of defining
+a suitable equator and equinox.  One problem is that the
+Sun's apparent motion is not completely regular, due to the
+ellipticity of the Earth's orbit and its continuous disturbance
+by the Moon and planets.  This is dealt with by
+separating the motion into (i)~a smooth and steady {\it mean Sun}\/
+and (ii)~a set of periodic corrections and perturbations; only the former
+is involved in establishing reference frames and timescales.
+A second, far larger problem, is that
+the celestial equator and the ecliptic
+are both moving with respect to the stars.
+These motions arise because of the gravitational
+interactions between the Earth and the other solar-system bodies.
+
+By far the largest effect is the
+so-called ``precession of the equinoxes'', where the Earth's
+rotation axis sweeps out a cone centred on the ecliptic
+pole, completing one revolution in about 26,000 years.  The
+cause of the motion is the torque exerted on the distorted and
+spinning Earth by the Sun and the Moon.  Consider the effect of the
+Sun alone, at or near the northern summer solstice.  The Sun
+`sees' the top (north pole) of the Earth tilted towards it
+(by about \degree{23}{5}, the {\it obliquity of the
+ecliptic}\/),
+and sees the nearer part of the Earth's equatorial bulge
+below centre and the further part above centre.
+Although the Earth is in free fall,
+the gravitational force on the nearer part of the
+equatorial bulge is greater than that on the further part, and
+so there is a net torque acting
+as if to eliminate the tilt.  Six months later the same thing
+is happening in reverse, except that the torque is still
+trying to eliminate the tilt.  In between (at the equinoxes) the
+torque shrinks to zero.  A torque acting on a spinning body
+is gyroscopically translated
+into a precessional motion of the spin axis at right-angles to the torque,
+and this happens to the Earth.
+The motion varies during the
+year, going through two maxima, but always acts in the
+same direction.  The Moon produces the same effect,
+adding a contribution to the precession which peaks twice
+per month.  The Moon's proximity to the Earth more than compensates
+for its smaller mass and gravitational attraction, so that it
+in fact contributes most of the precessional effect.
+
+The complex interactions between the three bodies produce a
+precessional motion that is wobbly rather than completely smooth.
+However, the main 26,000-year component is on such a grand scale that
+it dwarfs the remaining terms, the biggest of
+which has an amplitude of only \arcseci{17} and a period of
+about 18.6~years.  This difference of scale makes it convenient to treat
+these two components of the motion separately.  The main 26,000-year
+effect is called {\it luni-solar precession};  the smaller,
+faster, periodic terms are called the {\it nutation}.
+
+Note that precession and nutation are simply
+different frequency components of the same physical effect.  It is
+a common misconception that precession is caused
+by the Sun and nutation is caused by the Moon.  In fact
+the Moon is responsible for two-thirds of the precession, and,
+while it is true that much of the complex detail of the nutation is
+a reflection of the intricacies of the lunar orbit, there are
+nonetheless important solar terms in the nutation.
+
+In addition to and quite separate
+from the precession/nutation effect, the orbit of the Earth-Moon system
+is not fixed in orientation, a result of the attractions of the
+planets.  This slow (about \arcsec{0}{5}~per~year)
+secular rotation of the ecliptic about a slowly-moving diameter is called,
+confusingly, {\it planetary
+precession}\/ and, along with the luni-solar precession is
+included in the {\it general precession}.  The equator and
+ecliptic as affected by general precession
+are what define the various ``mean'' \radec\ reference frames.
+
+The models for precession and nutation come from a combination
+of observation and theory, and are subject to continuous
+refinement.  Nutation models in particular have reached a high
+degree of sophistication, taking into account such things as
+the non-rigidity of the Earth and the effects of
+the planets; SLALIB's nutation
+model (IAU~1980) involves 106 terms in each of $\psi$ (longitude)
+and $\epsilon$ (obliquity), some as small as \arcsec{0}{0001}.
+
+\subsubsection{SLALIB support for precession and nutation}
+SLALIB offers a choice of three precession models:
+\begin{itemize}
+\item The old Bessel-Newcomb, pre IAU~1976, ``FK4'' model, used for B1950
+      star positions and other pre-1984.0 purposes
+(sla\_PREBN).
+\item The new Fricke, IAU~1976, ``FK5'' model, used for J2000 star
+      positions and other post-1984.0 purposes
+(sla\_PREC).
+\item A model published by Simon {\it et al.}\ which is more accurate than
+      the IAU~1976 model and which is suitable for long
+      periods of time
+(sla\_PRECL).
+\end{itemize}
+In each case, the named SLALIB routine generates the $(3\times3)$
+{\it precession
+matrix}\/ for a given start and finish time.  For example,
+here is the Fortran code for generating the rotation
+matrix which describes the precession between the epochs
+J2000 and J1985.372 (IAU 1976 model):
+\goodbreak
+\begin{verbatim}
+            DOUBLE PRECISION PMAT(3,3)
+             :
+            CALL sla_PREC(2000D0,1985.372D0,PMAT)
+\end{verbatim}
+\goodbreak
+It is instructive to examine the resulting matrix:
+\goodbreak
+\begin{verbatim}
+            +0.9999936402  +0.0032709208  +0.0014214694
+            -0.0032709208  +0.9999946505  -0.0000023247
+            -0.0014214694  -0.0000023248  +0.9999989897
+\end{verbatim}
+\goodbreak
+Note that the diagonal elements are close to unity, and the
+other elements are small.  This shows that over an interval as
+short as 15~years the precession isn't going to move a
+position vector very far (in this case about \degree{0}{2}).
+
+For convenience, a direct \radec\ to \radec\ precession routine is
+also provided
+(sla\_PRECES),
+suitable for either the old or the new system (but not a
+mixture of the two).
+
+SLALIB provides only one nutation model, the new, IAU~1980 model,
+implemented in the routine
+sla\_NUTC.
+This returns the components of nutation
+in longitude and latitude (and also provides the obliquity) from
+which a nutation matrix can be generated by calling
+sla\_DEULER
+(and from which the {\it equation of the equinoxes}, described
+later, can be found).  Alternatively,
+the nutation matrix can be generated in a single call by using
+sla\_NUT.
+
+A rotation matrix for applying the entire precession/nutation
+transformation in one go can be generated by calling
+sla\_PRENUT.
+
+\subsection{Mean Places}
+The main effect of the precession/nutation is a steady increase of about
+\arcseci{50}/year in the ecliptic longitudes of the stars.  It is therefore
+essential, when reporting the position of an astronomical target, to
+qualify the coordinates with a date, or {\it epoch}.
+Specifying the epoch ties down the equator and
+equinox which define the \radec\ coordinate system that is
+being used.
+\footnote{An equinox is, however, not required for coordinates
+in the International Celestial Reference System.  Such coordinates must
+be labelled simply ``ICRS'', or the specific catalogue can be mentioned,
+such as ``Hipparcos'';  constructions such as ``Hipparcos, J2000'' are
+redundant and misleading.}  For simplicity, only
+the smooth and steady ``general
+precession'' part of the complete precession/nutation effect is
+included, thereby defining what is called the {\it mean}\/
+equator and equinox for the epoch concerned.  We say a star
+has a mean place of (for example)
+\hms{12}{07}{58}{09}~\dms{-19}{44}{37}{1} ``with respect to the mean equator
+and equinox of epoch J2000''.  The short way of saying
+this is ``\radec\ equinox J2000'' ({\bf not} ``\radec\ epoch J2000'', 
+which means something different to do with
+proper motion).
+
+\subsection{Epoch}
+The word ``epoch'' just means a moment in time, and can be supplied
+in a variety of forms, using different calendar systems and timescales.
+
+For the purpose of specifying the epochs associated with the
+mean place of a star, two conventions exist.  Both sorts of epoch
+superficially resemble years AD but are not tied to the civil
+(Gregorian) calendar;  to distinguish them from ordinary calendar-years
+there is often
+a ``.0'' suffix (as in ``1950.0''), although any other fractional
+part is perfectly legal ({\it e.g.}\ 1987.5).
+
+The older system,
+{\it Besselian epoch}, is defined in such a way that its units are
+tropical years of about 365.2422~days and its timescale is the
+obsolete {\it Ephemeris Time}.
+The start of the Besselian year is the moment
+when the ecliptic longitude of the mean Sun is
+$280^{\circ}$;  this happens near the start of the
+calendar year (which is why $280^{\circ}$ was chosen).
+
+The new system, {\it Julian epoch}, was adopted as
+part of the IAU~1976 revisions (about which more will be said
+in due course) and came formally into use at the
+beginning of 1984.  It uses the Julian year of exactly
+365.25~days; Julian epoch 2000 is defined to be 2000~January~1.5 in the
+TT timescale.
+
+For specifying mean places, various standard epochs are in use, the
+most common ones being Besselian epoch 1950.0 and Julian epoch 2000.0.
+To distinguish the two systems, Besselian epochs
+are now prefixed ``B'' and Julian epochs are prefixed ``J''.
+Epochs without an initial letter can be assumed to be Besselian
+if before 1984.0, otherwise Julian.  These details are supported by
+the SLALIB routines
+sla\_DBJIN
+(decodes numbers from a
+character string, accepting an optional leading B or J),
+sla\_KBJ
+(decides whether B or J depending on prefix or range) and
+sla\_EPCO
+(converts one epoch to match another).
+
+SLALIB has four routines for converting
+Besselian and Julian epochs into other forms.
+The functions
+sla\_EPB2D
+and
+sla\_EPJ2D
+convert Besselian and Julian epochs into MJD; the functions
+sla\_EPB
+and
+sla\_EPJ
+do the reverse.  For example, to express B1950 as a Julian epoch:
+\goodbreak
+\begin{verbatim}
+            DOUBLE PRECISION sla_EPJ,sla_EPB2D
+             :
+            WRITE (*,'(1X,''J'',F10.5)') sla_EPJ(sla_EPB2D(1950D0))
+\end{verbatim}
+\goodbreak
+(The answer is J1949.99979.)
+
+\subsection{Proper Motion}
+Stars in catalogues usually have, in addition to the 
+\radec\  coordinates, a {\it proper motion} $[\mu_\alpha,\mu_\delta]$.
+This is an intrinsic motion
+of the star across the background.  Very few stars have a
+proper motion which exceeds \arcseci{1}/year, and most are
+far below this level.  A star observed as part of normal
+astronomy research will, as a rule, have a proper motion
+which is unknown.
+
+Mean \radec\ and rate of change are not sufficient to pin
+down a star;  the epoch at which the \radec\ was or will
+be correct is also needed.  Note the distinction
+between the epoch which specifies the
+coordinate system and the epoch at which the star passed
+through the given \radec.  The full specification for a star
+is \radec, proper motions, equinox and epoch (plus something to
+identify which set of models for the precession {\it etc.}\ is 
+being used -- see the next section).
+For convenience, coordinates given in star catalogues are almost
+always adjusted to make the equinox and epoch the same -- for
+example B1950 in the case of the SAO~catalogue.
+
+SLALIB provides one routine to handle proper motion on its own,
+sla\_PM.
+Proper motion is also allowed for in various other
+routines as appropriate, for example
+sla\_MAP
+and
+sla\_FK425.
+Note that in all SLALIB routines which involve proper motion
+the units are radians per year and the
+$\alpha$ component is in the form $\dot{\alpha}$ ({\it i.e.}\ big
+numbers near the poles).
+Some star catalogues have proper motion per century, and
+in some catalogues the $\alpha$ component is in the form
+$\dot{\alpha}\cos\delta$ ({\it i.e.}\ angle on the sky).
+
+\subsection{Parallax and Radial Velocity}
+For the utmost accuracy and the nearest stars, allowance can
+be made for {\it annual parallax}\/ and for the effects of perspective
+on the proper motion.
+
+Parallax is appreciable only for nearby stars;  even
+the nearest, Proxima Centauri, is displaced from its average
+position by less than
+an arcsecond as the Earth revolves in its orbit.
+
+For stars with a known parallax, knowledge of the radial velocity
+allows the proper motion to be expressed as an actual space
+motion in 3~dimensions.  The proper motion is,
+in fact, a snapshot of the transverse component of the
+space motion, and in the case of nearby stars will
+change with time due to perspective.
+
+SLALIB does not provide facilities for handling parallax
+and radial-velocity on their own, but their contribution is
+allowed for in such routines as
+sla\_PM,
+sla\_MAP
+and
+sla\_FK425.
+Catalogue mean
+places do not include the effects of parallax and are therefore
+{\it barycentric};  when pointing telescopes {\it etc.}\ it is 
+usually most efficient to apply the slowly-changing
+parallax correction to the mean place of the target early on
+and to work with the {\it geocentric}\/ mean place.  This latter
+approach is implied in Figure~1.
+
+\subsection{Aberration}
+The finite speed of light combined with the motion of the observer
+around the Sun during the year causes apparent displacements of
+the positions of the stars.  The effect is called
+the {\it annual aberration} (or ``stellar''
+aberration).  Its maximum size, about \arcsec{20}{5},
+occurs for stars $90^{\circ}$ from the point towards which
+the Earth is headed as it orbits the Sun;  a star exactly in line with
+the Earth's motion is not displaced.  To receive the light of
+a star, the telescope has to be offset slightly in the direction of
+the Earth's motion.  A familiar analogy is the need to tilt your
+umbrella forward when on the move, to avoid getting wet.  This
+Newtonian model is,
+in fact, highly misleading in the context of light as opposed
+to rain, but happens to give the same answer as a relativistic
+treatment to first order (better than 1~milliarcsecond).
+
+Before the IAU 1976 resolutions, different
+values for the approximately
+\arcsec{20}{5} {\it aberration constant}\/ were employed
+at different times, and this can complicate comparisons
+between different catalogues.  Another complication comes from
+the so-called {\it E-terms of aberration},
+that small part of the annual aberration correction that is a
+function of the eccentricity of the Earth's orbit.  The E-terms,
+maximum amplitude about \arcsec{0}{3},
+happen to be approximately constant for a given star, and so they
+used to be incorporated in the catalogue \radec\/
+to reduce the labour of converting to and from apparent place.
+The E-terms can be removed from a catalogue \radec\/ by
+calling
+sla\_SUBET
+or applied (for example to allow a pulsar
+timing-position to be plotted on a B1950 finding chart)
+by calling
+sla\_ADDET;
+the E-terms vector itself can be obtained by calling
+sla\_ETRMS.
+Star positions post IAU 1976 are free of these distortions, and to
+apply corrections for annual aberration involves the actual
+barycentric velocity of the Earth rather than the use of
+canonical circular-orbit models.
+
+The annual aberration is the aberration correction for
+an imaginary observer at the Earth's centre.
+The motion of a real observer around the Earth's rotation axis in
+the course of the day makes a small extra contribution to the total
+aberration effect called the {\it diurnal aberration}.  Its
+maximum amplitude is about \arcsec{0}{2}.
+
+No SLALIB routine is provided for calculating the aberration on
+its own, though the required velocity vectors can be
+generated using
+sla\_EVP
+and
+sla\_GEOC.
+Annual and diurnal aberration are allowed for where required, for example in
+sla\_MAP
+{\it etc}.\ and
+sla\_AOP
+{\it etc}.  Note that this sort
+of aberration is different from the {\it planetary
+aberration}, which is the apparent displacement of a solar-system
+body, with respect to the ephemeris position, as a consequence
+of the motion of {\it both}\/ the Earth and the source.  The
+planetary aberration can be computed either by correcting the
+position of the solar-system body for light-time, followed by
+the ordinary stellar aberration correction, or more
+directly by expressing the position and velocity of the source
+in the observer's frame and correcting for light-time alone.
+
+\subsection{Different Sorts of Mean Place}
+A particularly confusing aspect of published mean places is that they
+are sensitive to the precise way they were determined.  A mean
+place is not directly observable, even with fundamental
+instruments such as transit circles, and to produce a mean
+place will involve relying on some existing star catalogue,
+for example the fundamental catalogues FK4 and FK5,
+and applying given mathematical models of precession, nutation,
+aberration and so on.
+Note in particular that no star catalogue,
+even a fundamental catalogue such as FK4 or
+FK5, defines a coordinate system, strictly speaking;
+it is merely a list of star positions and proper motions.
+However, once the stars from a given catalogue
+are used as position calibrators, {\it e.g.}\ for
+transit-circle observations or for plate reductions, then a
+broader sense of there being a coordinate grid naturally
+arises, and such phrases as ``in the system of
+the FK4'' can legitimately be employed.  However,
+there is no formal link between the
+two concepts -- no ``standard least squares fit'' between
+reality and the inevitably flawed catalogues.\footnote{This was
+true until the inception of the International Celestial Reference
+System, which is based on the idea of axes locked into the
+distant background.  The coordinates
+of the extragalactic sources which realize these
+axes have no individual significance; there is a ``no net rotation''
+condition which has to be satisfied each time any revisions take
+place.}  All such
+catalogues suffer at some level from systematic, zonal distortions
+of both the star positions and of the proper motions,
+and include measurement errors peculiar to individual
+stars.
+
+Many of these complications are of little significance except to
+specialists.  However, observational astronomers cannot
+escape exposure to at least the two main varieties of
+mean place, loosely called
+FK4 and FK5, and should be aware of
+certain pitfalls.  For most practical purposes the more recent
+system, FK5, is free of surprises and tolerates naive
+use well.  FK4, in contrast, contains two important traps:
+\begin{itemize}
+\item The FK4 system rotates at about
+      \arcsec{0}{5} per century relative to distant galaxies.
+      This is manifested as a systematic distortion in the
+      proper motions of all FK4-derived catalogues, which will
+      in turn pollute any astrometry done using those catalogues.
+      For example, FK4-based astrometry of a QSO using plates
+      taken decades apart will reveal a non-zero {\it fictitious proper
+      motion}, and any FK4 star which happens to have zero proper
+      motion is, in fact, slowly moving against the distant
+      background.  The FK4 frame rotates because it was
+      established before the nature of the Milky Way, and hence the
+      existence of systematic motions of nearby stars, had been
+      recognized.
+\item Star positions in the FK4 system are part-corrected for
+      annual aberration (see above) and embody the so-called
+      E-terms of aberration.
+\end{itemize}
+The change from the old FK4-based system to FK5
+occurred at the beginning
+of 1984 as part of a package of resolutions made by the IAU in 1976,
+along with the adoption of J2000 as the reference epoch.  Star
+positions in the newer, FK5, system are free from the E-terms, and
+the system is a much better approximation to an
+inertial frame (about five times better).
+
+It may occasionally be convenient to specify the FK4 fictitious proper
+motion directly.  In FK4, the centennial proper motion of (for example)
+a QSO is:
+
+$\mu_\alpha=-$\tsec{0}{015869}$
+          +(($\tsec{0}{029032}$~\sin \alpha
+            +$\tsec{0}{000340}$~\cos \alpha ) \sin \delta
+            -$\tsec{0}{000105}$~\cos \alpha
+            -$\tsec{0}{000083}$~\sin \alpha ) \sec \delta $ \\
+$\mu_\delta\,=+$\arcsec{0}{43549}$~\cos \alpha
+              -$\arcsec{0}{00510}$~\sin \alpha +
+              ($\arcsec{0}{00158}$~\sin \alpha
+              -$\arcsec{0}{00125}$~\cos \alpha ) \sin \delta
+              -$\arcsec{0}{00066}$~\cos \delta $
+
+\subsection{Mean Place Transformations}
+Figure~1 is based upon three varieties of mean \radec\ all of which are
+of practical significance to observing astronomers in the present era:
+\begin{itemize}
+   \item Old style (FK4) with known proper motion in the FK4
+         system, and with parallax and radial velocity either
+         known or assumed zero.
+   \item Old style (FK4) with zero proper motion in FK5,
+         and with parallax and radial velocity assumed zero.
+   \item New style (FK5) with proper motion, parallax and
+         radial velocity either known or assumed zero.
+\end{itemize}
+The figure outlines the steps required to convert positions in
+any of these systems to a J2000 \radec\ for the current
+epoch, as might be required in a telescope-control
+program for example.
+Most of the steps can be carried out by calling a single
+SLALIB routines;  there are other SLALIB routines which
+offer set-piece end-to-end transformation routines for common cases.
+Note, however, that SLALIB does not set out to provide the capability
+for arbitrary transformations of star-catalogue data
+between all possible systems of mean \radec.
+Only in the (common) cases of FK4, equinox and epoch B1950,
+to FK5, equinox and epoch J2000, and {\it vice versa}\/ are
+proper motion, parallax and radial velocity transformed
+along with the star position itself, the
+focus of SLALIB support.
+
+As an example of using SLALIB to transform mean places, here is
+a program which implements the top-left path of Figure~1.
+An FK4 \radec\ of arbitrary equinox and epoch and with
+known proper motion and
+parallax is transformed into an FK5 J2000 \radec\ for the current
+epoch.  As a test star we will use $\alpha=$\hms{16}{09}{55}{13},
+$\delta=$\dms{-75}{59}{27}{2}, equinox 1900, epoch 1963.087,
+$\mu_\alpha=$\tsec{-0}{0312}$/y$, $\mu_\delta=$\arcsec{+0}{103}$/y$,
+parallax = \arcsec{0}{062}, radial velocity = $-34.22$~km/s.  The
+epoch of observation is 1994.35.
+\goodbreak
+\begin{verbatim}
+            IMPLICIT NONE
+            DOUBLE PRECISION AS2R,S2R
+            PARAMETER (AS2R=4.8481368110953599D-6,S2R=7.2722052166430399D-5)
+            INTEGER J,I
+            DOUBLE PRECISION R0,D0,EQ0,EP0,PR,PD,PX,RV,EP1,R1,D1,R2,D2,R3,D3,
+           :                 R4,D4,R5,D5,R6,D6,EP1D,EP1B,W(3),EB(3),PXR,V(3)
+            DOUBLE PRECISION sla_EPB,sla_EPJ2D
+
+      *  RA, Dec etc of example star
+            CALL sla_DTF2R(16,09,55.13D0,R0,J)
+            CALL sla_DAF2R(75,59,27.2D0,D0,J)
+            D0=-D0
+            EQ0=1900D0
+            EP0=1963.087D0
+            PR=-0.0312D0*S2R
+            PD=+0.103D0*AS2R
+            PX=0.062D0
+            RV=-34.22D0
+            EP1=1994.35D0
+
+      *  Epoch of observation as MJD and Besselian epoch
+            EP1D=sla_EPJ2D(EP1)
+            EP1B=sla_EPB(EP1D)
+
+      *  Space motion to the current epoch
+            CALL sla_PM(R0,D0,PR,PD,PX,RV,EP0,EP1B,R1,D1)
+
+      *  Remove E-terms of aberration for the original equinox
+            CALL sla_SUBET(R1,D1,EQ0,R2,D2)
+
+      *  Precess to B1950
+            R3=R2
+            D3=D2
+            CALL sla_PRECES('FK4',EQ0,1950D0,R3,D3)
+
+      *  Add E-terms for the standard equinox B1950
+            CALL sla_ADDET(R3,D3,1950D0,R4,D4)
+
+      *  Transform to J2000, no proper motion
+            CALL sla_FK45Z(R4,D4,EP1B,R5,D5)
+
+      *  Parallax
+            CALL sla_EVP(sla_EPJ2D(EP1),2000D0,W,EB,W,W)
+            PXR=PX*AS2R
+            CALL sla_DCS2C(R5,D5,V)
+            DO I=1,3
+               V(I)=V(I)-PXR*EB(I)
+            END DO
+            CALL sla_DCC2S(V,R6,D6)
+             :
+\end{verbatim}
+\goodbreak
+It is interesting to look at how the \radec\ changes during the
+course of the calculation:
+\begin{tabbing}
+xxxxxxxxxxxxxx \= xxxxxxxxxxxxxxxxxxxxxxxxx \= x \= \kill
+\> {\tt 16 09 55.130 -75 59 27.20} \> \> {\it original equinox and epoch} \\
+\> {\tt 16 09 54.155 -75 59 23.98} \> \> {\it with space motion} \\
+\> {\tt 16 09 54.229 -75 59 24.18} \> \> {\it with old E-terms removed} \\
+\> {\tt 16 16 28.213 -76 06 54.57} \> \> {\it precessed to 1950.0} \\
+\> {\tt 16 16 28.138 -76 06 54.37} \> \> {\it with new E-terms} \\
+\> {\tt 16 23 07.901 -76 13 58.87} \> \> {\it J2000, current epoch} \\
+\> {\tt 16 23 07.907 -76 13 58.92} \> \> {\it including parallax}
+\end{tabbing}
+
+Other remarks about the above (unusually complicated) example:
+\begin{itemize}
+\item If the original equinox and epoch were B1950, as is quite
+      likely, then it would be unnecessary to treat space motions
+      and E-terms explicitly.  Transformation to FK5 J2000 could
+      be accomplished simply by calling
+sla\_FK425, after which
+      a call to
+sla\_PM and the parallax code would complete the
+      work.
+\item The rigorous treatment of the E-terms
+      has only a small effect on the result.  Such refinements
+      are, nevertheless, worthwhile in order to facilitate comparisons and
+      to increase the chances that star positions from different
+      suppliers are compatible.
+\item The FK4 to FK5 transformations,
+sla\_FK425
+      and
+sla\_FK45Z,
+      are not as is sometimes assumed simply 50 years of precession,
+      though this indeed accounts for most of the change.  The
+      transformations also include adjustments
+      to the equinox, a revised precession model, elimination of the
+      E-terms, a change to the proper-motion time unit and so on.
+      The reason there are two routines rather than just one
+      is that the FK4 frame rotates relative to the background, whereas
+      the FK5 frame is a much better approximation to an
+      inertial frame, and zero proper
+      motion in FK4 does not, therefore, mean zero proper motion in FK5.
+      SLALIB also provides two routines,
+sla\_FK524
+      and
+sla\_FK54Z,
+      to perform the inverse transformations.
+\item Some star catalogues (FK4 itself is one) were constructed using slightly
+      different procedures for the polar regions compared with
+      elsewhere.  SLALIB ignores this inhomogeneity and always
+      applies the standard
+      transformations irrespective of location on the celestial sphere.
+\end{itemize}
+
+\subsection {Mean Place to Apparent Place}
+The {\it geocentric apparent place}\/ of a source, or {\it apparent place}\/
+for short,
+is the \radec\ if viewed from the centre of the Earth,
+with respect to the true equator and equinox of date.
+Transformation of an FK5 mean \radec, equinox J2000,
+current epoch, to apparent place involves the following effects:
+\goodbreak
+\begin{itemize}
+   \item Light deflection -- the gravitational lens effect of
+         the sun.
+   \item Annual aberration.
+   \item Precession/nutation.
+\end{itemize}
+The {\it light deflection}\/ is seldom significant.  Its value
+at the limb of the Sun is about
+\arcsec{1}{74};  it falls off rapidly with distance from the
+Sun and has shrunk to about
+\arcsec{0}{02} at an elongation of $20^\circ$.
+
+As already described, the {\it annual aberration}\/
+is a function of the Earth's velocity
+relative to the solar system barycentre (available through the
+SLALIB routine
+sla\_EVP)
+and produces shifts of up to about \arcsec{20}{5}.
+
+The {\it precession/nutation}, from J2000 to the current epoch, is
+expressed by a rotation matrix which is available through the
+SLALIB routine
+sla\_PRENUT.
+
+The whole mean-to-apparent transformation can be done using the SLALIB
+routine
+sla\_MAP.  As a demonstration, here is a program which lists the
+{\it North Polar Distance}\/ ($90^\circ-\delta$) of Polaris for
+the decade of closest approach to the Pole:
+\goodbreak
+\begin{verbatim}
+            IMPLICIT NONE
+            DOUBLE PRECISION PI,PIBY2,D2R,S2R,AS2R
+            PARAMETER (PI=3.141592653589793238462643D0)
+            PARAMETER (D2R=PI/180D0,
+           :           PIBY2=PI/2D0,
+           :           S2R=PI/(12D0*3600D0),
+           :           AS2R=PI/(180D0*3600D0))
+            DOUBLE PRECISION RM,DM,PR,PD,DATE,RA,DA
+            INTEGER J,IDS,IDE,ID,IYMDF(4),I
+            DOUBLE PRECISION sla_EPJ2D
+
+            CALL sla_DTF2R(02,31,49.8131D0,RM,J)
+            CALL sla_DAF2R(89,15,50.661D0,DM,J)
+            PR=+21.7272D0*S2R/100D0
+            PD=-1.571D0*AS2R/100D0
+            WRITE (*,'(1X,'//
+           :            '''Polaris north polar distance (deg) 2096-2105''/)')
+            WRITE (*,'(4X,''Date'',7X''NPD''/)')
+            CALL sla_CLDJ(2096,1,1,DATE,J)
+            IDS=NINT(DATE)
+            CALL sla_CLDJ(2105,12,31,DATE,J)
+            IDE=NINT(DATE)
+            DO ID=IDS,IDE,10
+               DATE=DBLE(ID)
+               CALL sla_DJCAL(0,DATE,IYMDF,J)
+               CALL sla_MAP(RM,DM,PR,PD,0D0,0D0,2000D0,DATE,RA,DA)
+               WRITE (*,'(1X,I4,2I3.2,F9.5)') (IYMDF(I),I=1,3),(PIBY2-DA)/D2R
+            END DO
+
+            END
+\end{verbatim}
+\goodbreak
+For cases where the transformation has to be repeated for different
+times or for more than one star, the straightforward
+sla\_MAP
+approach is apt to be
+wasteful as both the Earth velocity and the
+precession/nutation matrix can be re-calculated relatively
+infrequently without ill effect.  A more efficient method is to
+perform the target-independent calculations only when necessary,
+by calling
+sla\_MAPPA,
+and then to use either
+sla\_MAPQKZ,
+when only the \radec\/ is known, or
+sla\_MAPQK,
+when full catalogue positions, including proper motion, parallax and
+radial velocity, are available.  How frequently to call
+sla\_MAPPA
+depends on the accuracy objectives;  once per
+night will deliver sub-arcsecond accuracy for example.
+
+The routines
+sla\_AMP
+and
+sla\_AMPQK
+allow the reverse transformation, from apparent to mean place.
+
+\subsection{Apparent Place to Observed Place}
+The {\it observed place}\/ of a source is its position as
+seen by a perfect theodolite at the location of the
+observer.  Transformation of an apparent \radec\ to observed 
+place involves the following effects:
+\goodbreak
+\begin{itemize}
+   \item \radec\ to \hadec.
+   \item Diurnal aberration.
+   \item \hadec\ to \azel.
+   \item Refraction.
+\end{itemize}
+The transformation from apparent \radec\ to
+apparent \hadec\ is made by allowing for
+{\it Earth rotation}\/ through the {\it sidereal time}, $\theta$:
+\[ h = \theta - \alpha \]
+For this equation to work, $\alpha$ must be the apparent right
+ascension for the time of observation, and $\theta$ must be
+the {\it local apparent sidereal time}.  The latter is obtained
+as follows:
+\begin{enumerate}
+\item from civil time obtain the coordinated universal time, UTC
+      (more later on this);
+\item add the UT1$-$UTC (typically a few tenths of a second) to
+      give the UT;
+\item from the UT compute the Greenwich mean sidereal time (using
+sla\_GMST);
+\item add the observer's (east) longitude, giving the local mean
+      sidereal time;
+\item add the equation of the equinoxes (using
+sla\_EQEQX).
+\end{enumerate}
+The {\it equation of the equinoxes}\/~($=\Delta\psi\cos\epsilon$ plus
+small terms)
+is the effect of nutation on the sidereal time.
+Its value is typically a second or less.  It is
+interesting to note that if the object of the exercise is to
+transform a mean place all the way into an observed place (very
+often the case),
+then the equation of the
+equinoxes and the longitude component of nutation can both be
+omitted, removing a great deal of computation.  However, SLALIB
+follows the normal convention and  works {\it via}\/ the apparent place.
+
+Note that for very precise work the observer's longitude should
+be corrected for {\it polar motion}.  This can be done with
+sla\_POLMO.
+The corrections are always less than about \arcsec{0}{3}, and
+are futile unless the position of the observer's telescope is known
+to better than a few metres.
+
+Tables of observed and
+predicted UT1$-$UTC corrections and polar motion data
+are published every few weeks by the International Earth Rotation Service.
+
+The transformation from apparent \hadec\ to {\it topocentric}\/
+\hadec\ consists of allowing for
+{\it diurnal aberration}.  This effect, maximum amplitude \arcsec{0}{2},
+was described earlier.  There is no specific SLALIB routine
+for computing the diurnal aberration,
+though the routines
+sla\_AOP {\it etc.}\
+include it, and the required velocity vector can be
+determined by calling
+sla\_GEOC.
+
+The next stage is the major coordinate rotation from local equatorial
+coordinates \hadec\ into horizon coordinates.  The SLALIB routines
+sla\_E2H
+{\it etc.}\ can be used for this.  For high-precision
+applications the mean geodetic latitude should be corrected for polar
+motion.
+
+\subsubsection{Refraction}
+The final correction is for atmospheric refraction.
+This effect, which depends on local meteorological conditions and
+the effective colour of the source/detector combination,
+increases the observed elevation of the source by a
+significant effect even at moderate zenith distances, and near the
+horizon by over \degree{0}{5}.  The amount of refraction can by
+computed by calling the SLALIB routine
+sla\_REFRO;
+however,
+this requires as input the observed zenith distance, which is what
+we are trying to predict.  For high precision it is
+therefore necessary to iterate, using the topocentric
+zenith distance as the initial estimate of the
+observed zenith distance.
+
+The full
+sla\_REFRO refraction calculation is onerous, and for
+zenith distances of less than, say, $75^{\circ}$ the following
+model can be used instead:
+
+\[ \zeta _{vac} \approx \zeta _{obs}
+                     + A \tan \zeta _{obs}
+                     + B \tan ^{3}\zeta _{obs} \]
+where $\zeta _{vac}$ is the topocentric
+zenith distance (i.e.\ {\it in vacuo}),
+$\zeta _{obs}$ is the observed
+zenith distance (i.e.\ affected by refraction), and $A$ and $B$ are
+constants, about \arcseci{60}
+and \arcsec{-0}{06} respectively for a sea-level site.
+The two constants can be calculated for a given set of conditions
+by calling either
+sla\_REFCO or
+sla\_REFCOQ.
+
+sla\_REFCO works by calling
+sla\_REFRO for two zenith distances and fitting $A$ and $B$
+to match.  The calculation is onerous, but delivers accurate
+results whatever the conditions.
+sla\_REFCOQ uses a direct formulation of $A$ and $B$ and
+is much faster;  it is slightly less accurate than
+sla\_REFCO but more than adequate for most practical purposes.
+
+Like the full refraction model, the two-term formulation works in the wrong
+direction for our purposes, predicting
+the {\it in vacuo}\/ (topocentric) zenith distance
+given the refracted (observed) zenith distance,
+rather than {\it vice versa}.  The obvious approach of
+interchanging $\zeta _{vac}$ and $\zeta _{obs}$ and
+reversing the signs, though approximately
+correct, gives avoidable errors which are just significant in
+some applications;  for
+example about \arcsec{0}{2} at $70^\circ$ zenith distance.  A
+much better result can easily be obtained, by using one Newton-Raphson
+iteration as follows:
+
+\[ \zeta _{obs} \approx \zeta _{vac}
+    - \frac{A \tan \zeta _{vac} + B \tan ^{3}\zeta _{vac}}
+    {1 + ( A + 3 B \tan ^{2}\zeta _{vac} ) \sec ^{2}\zeta _{vac}}\]
+
+The effect of refraction can be applied to an unrefracted
+zenith distance by calling
+sla\_REFZ or to an unrefracted
+\xyz\ by calling
+sla\_REFV.
+Over most of the sky these two routines deliver almost identical
+results, but beyond $\zeta=83^\circ$
+sla\_REFV
+becomes unacceptably inaccurate while
+sla\_REFZ
+remains usable.  (However
+sla\_REFV
+is significantly faster, which may be important in some applications.)
+SLALIB also provides a routine for computing the airmass, the function
+sla\_AIRMAS.
+
+The refraction ``constants'' returned by
+sla\_REFCO and
+sla\_REFCOQ
+are slightly affected by colour, especially at the blue end
+of the spectrum.  Where values for more than one
+wavelength are needed, rather than calling
+sla\_REFCO
+several times it is more efficient to call
+sla\_REFCO
+just once, for a selected ``base'' wavelength, and then to call
+sla\_ATMDSP
+once for each wavelength of interest.
+
+All the SLALIB refraction routines work for radio wavelengths as well
+as the optical/IR band.  The radio refraction is very dependent on
+humidity, and an accurate value must be supplied.  There is no
+wavelength dependence, however.  The choice of optical/IR or
+radio is made by specifying a wavelength greater than $100\mu m$
+for the radio case.
+
+\subsubsection{Efficiency considerations}
+The complete apparent place to observed place transformation
+can be carried out by calling
+sla\_AOP.
+For improved efficiency
+in cases of more than one star or a sequence of times, the
+target-independent calculations can be done once by
+calling
+sla\_AOPPA,
+the time can be updated by calling
+sla\_AOPPAT,
+and
+sla\_AOPQK
+can then be used to perform the
+apparent-to-observed transformation.  The reverse transformation
+is available through
+sla\_OAP
+and
+sla\_OAPQK.
+({\it n.b.}\ These routines use accurate but computationally-expensive
+refraction algorithms for zenith distances beyond about $76^\circ$.
+For many purposes, in-line code tailored to the accuracy requirements
+of the application will be preferable, for example ignoring UT1$-$UTC,
+omitting diurnal aberration and using
+sla\_REFZ
+to apply the refraction.)
+
+\subsection{The Hipparcos Catalogue and the ICRS}
+With effect from the beginning of 1998, the IAU adopted a new
+reference system to replace FK5 J2000.  The new system, called the
+International Celestial Reference System (ICRS), differs profoundly
+from all predecessors in that the link with solar-system dynamics
+was broken;  the ICRS axes are defined in terms of the directions
+of a set of extragalactic sources, not in terms of the mean equator and
+equinox at a given reference epoch.  Although the ICRS and FK5 coordinates
+of any given object are almost the same, the orientation of the new frame
+was essentially arbitrary, and the close match to FK5 J2000 was contrived
+purely for reasons of continuity and convenience.
+
+A distinction is made between the reference {\it system}\/ (the ICRS)
+and {\it frame}\/ (ICRF).  The ICRS is the set of prescriptions and
+conventions together with the modelling required to define, at any
+time, a triad of axes.  The ICRF is a practical realization, and
+currently consists of a catalogue of equatorial coordinates for 608
+extragalactic radio sources observed by VLBI.
+
+The best optical realization of the ICRF currently available is the
+Hipparcos catalogue.  The extragalactic sources were not directly
+observable by the Hipparcos satellite and so the link from Hipparcos
+to ICRF was established through a variety of indirect techniques: VLBI and
+conventional interferometry of radio stars, photographic astrometry
+and so on.  The Hipparcos frame is aligned to the ICRF to within about
+0.5~mas and 0.5~mas/year (at epoch 1991.25).
+
+The Hipparcos catalogue includes all of the FK5 stars, which has enabled
+the orientation and spin of the latter to be studied.  At epoch J2000,
+the misalignment of the FK5 frame with respect to Hipparcos
+(and hence ICRS) are about 32~mas and 1~mas/year respectively.
+Consequently, for many practical purposes, including pointing
+telescopes, the IAU 1976-1982 conventions on reference frames and
+Earth orientation remain adequate and there is no need to change to
+Hipparcos coordinates, new precession/nutation models and so on.
+However, for the most exacting astrometric applications, SLALIB
+provides some support for Hipparcos coordinates in the form of
+four new routines:
+sla\_FK52H and
+sla\_H2FK5,
+which transform FK5 positions and proper motions to the Hipparcos frame
+and {\it vice versa,}\/ and
+sla\_FK5HZ and
+sla\_HFK5Z,
+where the transformations are for stars whose Hipparcos proper motion is
+zero. 
+
+Further information on the ICRS can be found in the paper by M.\,Feissel
+and F.\,Mignard, Astron.\,Astrophys. 331, L33-L36 (1988).
+
+\subsection{Timescales}
+SLALIB provides for conversion between several timescales, and involves
+use of one or two others.  The full list is as follows:
+\begin{itemize}
+\item TAI: International Atomic Time
+\item UTC: Coordinated Universal Time
+\item UT: Universal Time
+\item GMST: Greenwich Mean Sidereal Time
+\item LAST: Local Apparent Sidereal Time
+\item TT: Terrestrial Time
+\item TDB: Barycentric Dynamical Time.
+\end{itemize}
+Three obsolete timescales should be mentioned here to avoid confusion.
+\begin{itemize}
+\item GMT: Greenwich Mean Time -- can mean either UTC or UT.
+\item ET: Ephemeris Time -- more or less the same as either TT or TDB.
+\item TDT: Terrestrial Dynamical Time -- former name of TT.
+\end{itemize}
+
+\subsubsection{Atomic Time: TAI}
+{\it International Atomic Time}\/ TAI is a laboratory timescale.  Its
+unit is the SI second, which is defined in terms of a
+defined number
+of wavelengths of the radiation produced by a certain electronic
+transition in the caesium 133 atom.  It
+is realized through a changing
+population of high-precision atomic clocks held
+at standards institutes in various countries.  There is an
+elaborate process of continuous intercomparison, leading to
+a weighted average of all the clocks involved.
+
+Though TAI shares the same second as the more familiar UTC, the
+two timescales are noticeably separated in epoch because of the
+build-up of leap seconds.  At the time of writing, UTC
+lags about half a minute behind TAI.
+
+For any given date, the difference TAI$-$UTC
+can be obtained by calling the SLALIB routine
+sla\_DAT.
+Note, however, that an up-to-date copy of the routine must be used if
+the most recent leap seconds are required.  For applications
+where this is critical, mechanisms independent of SLALIB
+and under local control must
+be set up;  in such cases
+sla\_DAT
+can be useful as an
+independent check, for test dates within the range of the
+available version.  Up-to-date information on TAI$-$UTC is available
+from {\tt ftp://maia.usno.navy.mil/ser7/tai-utc.dat}.
+
+\subsubsection{Universal Time: UTC, UT1}
+{\it Coordinated Universal Time}\/ UTC is the basis of civil timekeeping.
+Most time zones differ from UTC by an integer number
+of hours, though a few ({\it e.g.}\ parts of Canada and Australia) differ
+by $n+0.5$~hours.  The UTC second is the same as the SI second,
+as for TAI.  In the long term, UTC keeps in step with the
+Sun.  It does so even though the Earth's rotation is slightly
+variable (due to large scale movements of water and atmosphere
+among other things) by occasionally introducing a {\it leap
+second}.
+
+{\it Universal Time}\/ UT, or more specifically UT1,
+is in effect the mean solar time.  It is continuous
+({\it i.e.}\ there are no leap seconds) but has a variable
+rate because of the Earth's non-uniform rotation period.  It is
+needed for computing the sidereal time, an essential part of
+pointing a telescope at a celestial source.  To obtain UT1, you
+have to look up the value of UT1$-$UTC for the date concerned
+in tables published by the International Earth Rotation
+Service;  this quantity, kept in the range
+$\pm$\tsec{0}{9} by means of UTC leap
+seconds, is then added to the UTC.  The quantity UT1$-$UTC,
+which typically changes by 1 or 2~ms per day,
+can only be obtained by observation, though seasonal trends
+are known and the IERS listings are able to predict some way into
+the future with adequate accuracy for pointing telescopes.
+
+UTC leap seconds are introduced as necessary,
+usually at the end of December or June.
+On the average the solar day is slightly longer
+than the nominal 86,400~SI~seconds and so leap seconds are always positive;
+however, provision exists for negative leap seconds if needed.
+The form of a leap second can be seen from the
+following description of the end of June~1994:
+
+\hspace{3em}
+\begin{tabular}{clrccc} \\
+     &      &    &   UTC    & UT1$-$UTC  &    UT1       \\ \\
+1994 & June & 30 & 23 59 58 & $-0.218$ & 23 59 57.782 \\
+     &      &    & 23 59 59 & $-0.218$ & 23 59 58.782 \\
+     &      &    & 23 59 60 & $-0.218$ & 23 59 59.782 \\
+     & July &  1 & 00 00 00 & $+0.782$ & 00 00 00.782 \\
+     &      &    & 00 00 01 & $+0.782$ & 00 00 01.782 \\
+\end{tabular}
+
+Note that UTC has to be expressed as hours, minutes and
+seconds (or at least in seconds for a given date) if leap seconds
+are to be taken into account.  It is improper to express a UTC as a
+Julian Date, for example, because there will be an ambiguity
+during a leap second (in the above example,
+1994~June~30 \hms{23}{59}{60}{0} and
+1994~July~1 \hms{00}{00}{00}{0} would {\it both}\/ come out as
+MJD~49534.00000).  Although in the vast majority of
+cases this won't matter, there are potential problems in
+on-line data acquisition systems and in applications involving
+taking the difference between two times.  Note that although the routines
+sla\_DAT
+and
+sla\_DTT
+expect UTC in the form of an MJD, the meaning here is really a
+whole-number {\it date}\/ rather than a time.  Though the routines will accept
+a fractional part and will almost always function correctly, on a day
+which ends with a leap
+second incorrect results would be obtained during the leap second
+itself because by then the MJD would have moved into the next day.
+
+\subsubsection{Sidereal Time: GMST, LAST}
+Sidereal Time is the ``time of day'' relative to the
+stars rather than to the Sun.  After
+one sidereal day the stars come back to the same place in the
+sky, apart from sub-arcsecond precession effects.  Because the Earth
+rotates faster relative to the stars than to the Sun by one day
+per year, the sidereal second is shorter than the solar
+second; the ratio is about 0.9973.
+
+The {\it Greenwich Mean Sidereal Time}\/ GMST is
+linked to UT1 by a numerical formula which
+is implemented in the SLALIB routines
+sla\_GMST
+and
+sla\_GMSTA.
+There are, of course, no leap seconds in GMST, but the second
+changes in length along with the UT1 second, and also varies
+over long periods of time because of slow changes in the Earth's
+orbit.  This makes the timescale unsuitable for everything except
+predicting the apparent directions of celestial sources.
+
+The {\it Local Apparent Sidereal Time}\/ LAST is the apparent right
+ascension of the local meridian, from which the hour angle of any
+star can be determined knowing its $\alpha$.  It can be obtained from the
+GMST by adding the east longitude (corrected for polar motion
+in precise work) and the {\it equation of the equinoxes}.  The
+latter, already described, is an aspect of the nutation effect
+and can be predicted by calling the SLALIB routine
+sla\_EQEQX
+or, neglecting certain very small terms, by calling
+sla\_NUTC
+and using the expression $\Delta\psi\cos\epsilon$.
+
+\subsubsection{Dynamical Time: TT, TDB}
+Dynamical time is the independent variable in the theories
+which describe the motions of bodies in the solar system.  When
+you use published formulae which model the position of the
+Earth in its orbit, for example, or look up
+the Moon's position in a precomputed ephemeris, the date and time
+you use must be in terms of one of the dynamical timescales.  It
+is a common but understandable mistake to use UT directly, in which
+case the results will be about 1~minute out (in the present
+era).
+
+It is not hard to see why such timescales are necessary.
+UTC would clearly be unsuitable as the argument of an
+ephemeris because of leap seconds.
+A solar-system ephemeris based on UT1 or sidereal time would somehow
+have to include the unpredictable variations of the Earth's rotation.
+TAI would work, but eventually
+the ephemeris and the ensemble of atomic clocks would drift apart.
+In effect, the ephemeris {\it is}\/ a clock, with the bodies of
+the solar system the hands.
+
+Only two of the dynamical timescales are of any great importance to
+observational astronomers, TT and TDB.  (The obsolete
+timescale ET, ephemeris time, was more or less the same as TT.)
+
+{\it Terrestrial Time}\/ TT is
+the theoretical timescale of apparent geocentric ephemerides of solar
+system bodies.  It applies, in principle,
+to an Earthbound clock, at sea-level, and for practical purposes
+it is tied to
+Atomic Time TAI through the formula TT~$=$~TAI~$+$~\tsec{32}{184}.
+In practice, therefore, the units of TT are ordinary SI seconds, and
+the offset of \tsec{32}{184} with respect to TAI is fixed.
+The SLALIB routine
+sla\_DTT
+returns TT$-$UTC for a given UTC 
+({\it n.b.}\  sla\_DTT
+calls
+sla\_DAT,
+and the latter must be an up-to-date version if recent leap seconds are
+to be taken into account).
+
+{\it Barycentric Dynamical Time}\/ TDB differs from TT by an amount which
+cycles back and forth by a millisecond or two due to
+relativistic effects.  The variation is
+negligible for most purposes, but unless taken into
+account would swamp
+long-term analysis of pulse arrival times from the
+millisecond pulsars.  It is a consequence of
+the TT clock being on the Earth rather than in empty
+space:  the ellipticity of
+the Earth's orbit means that the TT clock's speed and
+gravitational potential vary slightly
+during the course of the year, and as a consequence
+its rate as seen from an outside observer
+varies due to transverse Doppler effect and gravitational
+redshift.  By definition, TDB and TT differ only
+by periodic terms, and the main effect
+is a sinusoidal variation of amplitude \tsec{0}{0016};  the
+largest planetary terms are nearly two orders of magnitude
+smaller.  The SLALIB routine
+sla\_RCC
+provides a model of
+TDB-TT accurate to a few nanoseconds.
+There are other dynamical timescales, not supported by
+SLALIB routines, which include allowance also for the secular terms.
+These timescales gain on TT and TDB by about \tsec{0}{0013}/day.
+
+For most purposes the more accessible TT is the timescale to use,
+for example when calling
+sla\_PRENUT
+to generate a precession/nutation matrix or when calling
+sla\_EVP
+to predict the
+Earth's position and velocity.  For some purposes TDB is the
+correct timescale, for example when interrogating the JPL planetary
+ephemeris (see {\it Starlink User Note~87}\/), though in most cases
+TT will be near enough and will involve less computation.
+
+Investigations of topocentric solar-system phenomena such as
+occultations and eclipses require solar time as well as dynamical
+time.  TT/TDB/ET is all that is required in order to compute the geocentric
+circumstances, but if horizon coordinates or geocentric parallax
+are to be tackled UT is also needed.  A rough estimate
+of $\Delta {\rm T} = {\rm ET} - {\rm UT}$ is
+available via the routine
+sla\_DT.
+For a given epoch ({\it e.g.}\ 1650) this returns an approximation
+to $\Delta {\rm T}$ in seconds.
+
+\subsection{Calendars}
+The ordinary {\it Gregorian Calendar Date},
+together with a time of day, can be
+used to express an epoch in any desired timescale.  For many purposes,
+however, a continuous count of days is more convenient, and for
+this purpose the system of {\it Julian Day Number}\/ can be used.
+JD zero is located about 7000~years ago, well before the
+historical era, and is formally defined in terms of Greenwich noon;
+Julian Day Number 2449444 began at noon on 1994 April~1.  {\it Julian Date}\/
+is the same system but with a fractional part appended;
+Julian Date 2449443.5 was the midnight on which 1994 April~1
+commenced.  Because of the unwieldy size of Julian Dates
+and the awkwardness of the half-day offset, it is
+accepted practice to remove the leading `24' and the trailing `.5',
+producing what is called the {\it Modified Julian Date}:
+MJD~=~JD$-2400000.5$.  SLALIB routines use MJD, as opposed to
+JD, throughout, largely to avoid loss of precision.
+1994 April~1 commenced at MJD~49443.0.
+
+Despite JD (and hence MJD) being defined in terms of (in effect)
+UT, the system can be used in conjunction with other timescales
+such as TAI, TT and TDB (and even sidereal time through the
+concept of {\it Greenwich Sidereal Date}).  However, it is improper
+to express a UTC as a JD or MJD because of leap seconds.
+
+SLALIB has six routines for converting to and from dates in
+the Gregorian calendar.  The routines
+sla\_CLDJ
+and
+sla\_CALDJ
+both convert a calendar date into an MJD, the former interpreting
+years between 0 and 99 as 1st century and the latter as late 20th or
+early 21st century.  The routines sla\_DJCL
+and
+sla\_DJCAL
+both convert an MJD into calendar year, month, day and fraction of a day;
+the latter performs rounding to a specified precision, important
+to avoid dates like `{\tt 94 04 01.***}' appearing in messages.
+Some of SLALIB's low-precision ephemeris routines
+(sla\_EARTH,
+sla\_MOON
+and
+sla\_ECOR)
+work in terms of year plus day-in-year (where
+day~1~=~January~1st, at least for the modern era).
+This form of date can be generated by
+calling
+sla\_CALYD
+(which defaults years 0-99 into 1950-2049)
+or
+sla\_CLYD
+(which covers the full range from prehistoric times).
+
+\subsection{Geocentric Coordinates}
+The location of the observer on the Earth is significant in a
+number of ways.  The most obvious, of course, is the effect of latitude
+on the observed \azel\ of a star.  Less obvious is the need to
+allow for geocentric parallax when finding the Moon with a
+telescope (and when doing high-precision work involving the
+Sun or planets), and the need to correct observed radial
+velocities and apparent pulsar periods for the effects
+of the Earth's rotation.
+
+The SLALIB routine
+sla\_OBS
+supplies details of groundbased observatories from an internal
+list.  This is useful when writing applications that apply to
+more than one observatory;  the user can enter a brief name,
+or browse through a list, and be spared the trouble of typing
+in the full latitude, longitude {\it etc}.  The following
+Fortran code returns the full name, longitude and latitude
+of a specified observatory:
+\goodbreak
+\begin{verbatim}
+            CHARACTER IDENT*10,NAME*40
+            DOUBLE PRECISION W,P,H
+             :
+            CALL sla_OBS(0,IDENT,NAME,W,P,H)
+            IF (NAME.EQ.'?') ...             (not recognized)
+\end{verbatim}
+\goodbreak
+(Beware of the longitude sign convention, which is west +ve
+for historical reasons.)  The following lists all
+the supported observatories:
+\goodbreak
+\begin{verbatim}
+             :
+            INTEGER N
+             :
+            N=1
+            NAME=' '
+            DO WHILE (NAME.NE.'?')
+               CALL sla_OBS(N,IDENT,NAME,W,P,H)
+               IF (NAME.NE.'?') THEN
+                  WRITE (*,'(1X,I3,4X,A,4X,A)') N,IDENT,NAME
+                  N=N+1
+               END IF
+            END DO
+\end{verbatim}
+\goodbreak
+The routine
+sla\_GEOC
+converts a {\it geodetic latitude}\/
+(one referred to the local horizon) to a geocentric position,
+taking into account the Earth's oblateness and also the height
+above sea level of the observer.  The results are expressed in
+vector form, namely as the distance of the observer from
+the spin axis and equator respectively.  The {\it geocentric
+latitude}\/ can be found be evaluating ATAN2 of the
+two numbers.  A full 3-D vector description of the position
+and velocity of the observer is available through the routine
+sla\_PVOBS.
+For a specified geodetic latitude, height above
+sea level, and local sidereal time,
+sla\_PVOBS
+generates a 6-element vector containing the position and
+velocity with respect to the true equator and equinox of
+date ({\it i.e.}\ compatible with apparent \radec).  For
+some applications it will be necessary to convert to a
+mean \radec\ frame (notably FK5, J2000) by multiplying
+elements 1-3 and 4-6 respectively with the appropriate
+precession matrix.  (In theory an additional correction to the
+velocity vector is needed to allow for differential precession,
+but this correction is always negligible.)
+
+See also the discussion of the routine
+sla\_RVEROT,
+later.
+
+\subsection{Ephemerides}
+SLALIB includes routines for generating positions and
+velocities of Solar-System bodies.  The accuracy objectives are
+modest, and the SLALIB facilities do not attempt
+to compete with precomputed ephemerides such as
+those provided by JPL, or with models containing
+thousands of terms.  It is also worth noting
+that SLALIB's very accurate star coordinate conversion
+routines are not strictly applicable to solar-system cases,
+though they are adequate for most practical purposes.
+
+Earth/Sun ephemerides can be generated using the routine
+sla\_EVP,
+which predicts Earth position and velocity with respect to both the
+solar-system barycentre and the
+Sun.  Maximum velocity error is 0.42~metres per second;  maximum
+heliocentric position error is 1600~km (about \arcseci{2}), with
+barycentric position errors about 4 times worse.
+(The Sun's position as
+seen from the Earth can, of course, be obtained simply by
+reversing the signs of the Cartesian components of the
+Earth\,:\,Sun vector.)
+
+Geocentric Moon ephemerides are available from
+sla\_DMOON,
+which predicts the Moon's position and velocity with respect to
+the Earth's centre.  Direction accuracy is usually better than
+10~km (\arcseci{5}) and distance accuracy a little worse.
+
+Lower-precision but faster predictions for the Sun and Moon
+can be made by calling
+sla\_EARTH
+and
+sla\_MOON.
+Both are single precision and accept dates in the form of
+year, day-in-year and fraction of day
+(starting from a calendar date you need to call
+sla\_CLYD
+or
+sla\_CALYD
+to get the required year and day).
+The
+sla\_EARTH
+routine returns the heliocentric position and velocity
+of the Earth's centre for the mean equator and
+equinox of date.  The accuracy is better than 20,000~km in position
+and 10~metres per second in speed.
+The
+position and velocity of the Moon with respect to the
+Earth's centre for the mean equator and ecliptic of date
+can be obtained by calling
+sla\_MOON.
+The positional accuracy is better than \arcseci{30} in direction
+and 1000~km in distance.
+
+Approximate ephemerides for all the major planets
+can be generated by calling
+sla\_PLANET
+or
+sla\_RDPLAN.  These routines offer arcminute accuracy (much
+better for the inner planets and for Pluto) over a span of several
+millennia (but only $\pm100$ years for Pluto).
+The routine
+sla\_PLANET produces heliocentric position and
+velocity in the form of equatorial \xyzxyzd\ for the
+mean equator and equinox of J2000.  The vectors
+produced by
+sla\_PLANET
+can be used in a variety of ways according to the
+requirements of the application concerned.  The routine
+sla\_RDPLAN
+uses
+sla\_PLANET
+and
+sla\_DMOON
+to deal with the common case of predicting
+a planet's apparent \radec\ and angular size as seen by a
+terrestrial observer.
+
+Note that in predicting the position in the sky of a solar-system body
+it is necessary to allow for geocentric parallax.  This correction
+is {\it essential}\/ in the case of the Moon, where the observer's
+position on the Earth can affect the Moon's \radec\ by up to
+$1^\circ$.  The calculation can most conveniently be done by calling
+sla\_PVOBS and subtracting the resulting 6-vector from the
+one produced by
+sla\_DMOON, as is demonstrated by the following example:
+\goodbreak
+\begin{verbatim}
+      *  Demonstrate the size of the geocentric parallax correction
+      *  in the case of the Moon.  The test example is for the AAT,
+      *  before midnight, in summer, near first quarter.
+
+            IMPLICIT NONE
+            CHARACTER NAME*40,SH,SD
+            INTEGER J,I,IHMSF(4),IDMSF(4)
+            DOUBLE PRECISION SLONGW,SLAT,H,DJUTC,FDUTC,DJUT1,DJTT,STL,
+           :                 RMATN(3,3),PMM(6),PMT(6),RM,DM,PVO(6),TL
+            DOUBLE PRECISION sla_DTT,sla_GMST,sla_EQEQX,sla_DRANRM
+
+      *  Get AAT longitude and latitude in radians and height in metres
+            CALL sla_OBS(0,'AAT',NAME,SLONGW,SLAT,H)
+
+      *  UTC (1992 January 13, 11 13 59) to MJD
+            CALL sla_CLDJ(1992,1,13,DJUTC,J)
+            CALL sla_DTF2D(11,13,59.0D0,FDUTC,J)
+            DJUTC=DJUTC+FDUTC
+
+      *  UT1 (UT1-UTC value of -0.152 sec is from IERS Bulletin B)
+            DJUT1=DJUTC+(-0.152D0)/86400D0
+
+      *  TT
+            DJTT=DJUTC+sla_DTT(DJUTC)/86400D0
+
+      *  Local apparent sidereal time
+            STL=sla_GMST(DJUT1)-SLONGW+sla_EQEQX(DJTT)
+
+      *  Geocentric position/velocity of Moon (mean of date)
+            CALL sla_DMOON(DJTT,PMM)
+
+      *  Nutation to true equinox of date
+            CALL sla_NUT(DJTT,RMATN)
+            CALL sla_DMXV(RMATN,PMM,PMT)
+            CALL sla_DMXV(RMATN,PMM(4),PMT(4))
+
+      *  Report geocentric HA,Dec
+            CALL sla_DCC2S(PMT,RM,DM)
+            CALL sla_DR2TF(2,sla_DRANRM(STL-RM),SH,IHMSF)
+            CALL sla_DR2AF(1,DM,SD,IDMSF)
+            WRITE (*,'(1X,'' geocentric:'',2X,A,I2.2,2I3.2,''.'',I2.2,'//
+           :                              '1X,A,I2.2,2I3.2,''.'',I1)')
+           :                                                SH,IHMSF,SD,IDMSF
+
+      *  Geocentric position of observer (true equator and equinox of date)
+            CALL sla_PVOBS(SLAT,H,STL,PVO)
+
+      *  Place origin at observer
+            DO I=1,6
+               PMT(I)=PMT(I)-PVO(I)
+            END DO
+
+      *  Allow for planetary aberration
+            TL=499.004782D0*SQRT(PMT(1)**2+PMT(2)**2+PMT(3)**2)
+            DO I=1,3
+               PMT(I)=PMT(I)-TL*PMT(I+3)
+            END DO
+
+      *  Report topocentric HA,Dec
+            CALL sla_DCC2S(PMT,RM,DM)
+            CALL sla_DR2TF(2,sla_DRANRM(STL-RM),SH,IHMSF)
+            CALL sla_DR2AF(1,DM,SD,IDMSF)
+            WRITE (*,'(1X,''topocentric:'',2X,A,I2.2,2I3.2,''.'',I2.2,'//
+           :                              '1X,A,I2.2,2I3.2,''.'',I1)')
+           :                                                SH,IHMSF,SD,IDMSF
+            END
+\end{verbatim}
+\goodbreak
+The output produced is as follows:
+\goodbreak
+\begin{verbatim}
+       geocentric:  +03 06 55.59 +15 03 39.0
+      topocentric:  +03 09 23.79 +15 40 51.5
+\end{verbatim}
+\goodbreak
+(An easier but
+less instructive method of estimating the topocentric apparent place of the
+Moon is to call the routine
+sla\_RDPLAN.)
+
+As an example of using
+sla\_PLANET,
+the following program estimates the geocentric separation
+between Venus and Jupiter during a close conjunction
+in 2\,BC, which is a star-of-Bethlehem candidate:
+\goodbreak
+\begin{verbatim}
+      *  Compute time and minimum geocentric apparent separation
+      *  between Venus and Jupiter during the close conjunction of 2 BC.
+
+            IMPLICIT NONE
+
+            DOUBLE PRECISION SEPMIN,DJD0,FD,DJD,DJDM,DF,PV(6),RMATP(3,3),
+           :                 PVM(6),PVE(6),TL,RV,DV,RJ,DJ,SEP
+            INTEGER IHOUR,IMIN,J,I,IHMIN,IMMIN
+            DOUBLE PRECISION sla_EPJ,sla_DSEP
+
+
+      *  Search for closest approach on the given day
+            DJD0=1720859.5D0
+            SEPMIN=1D10
+            DO IHOUR=20,22
+               DO IMIN=0,59
+                  CALL sla_DTF2D(IHOUR,IMIN,0D0,FD,J)
+
+      *        Julian date and MJD
+                  DJD=DJD0+FD
+                  DJDM=DJD-2400000.5D0
+
+      *        Earth to Moon (mean of date)
+                  CALL sla_DMOON(DJDM,PV)
+
+      *        Precess Moon position to J2000
+                  CALL sla_PRECL(sla_EPJ(DJDM),2000D0,RMATP)
+                  CALL sla_DMXV(RMATP,PV,PVM)
+
+      *        Sun to Earth-Moon Barycentre (mean J2000)
+                  CALL sla_PLANET(DJDM,3,PVE,J)
+
+      *        Correct from EMB to Earth
+                  DO I=1,3
+                     PV(I)=PVE(I)-0.012150581D0*PVM(I)
+                  END DO
+
+      *        Sun to Venus
+                  CALL sla_PLANET(DJDM,2,PV,J)
+
+      *        Earth to Venus
+                  DO I=1,6
+                     PV(I)=PV(I)-PVE(I)
+                  END DO
+
+      *        Light time to Venus (sec)
+                  TL=499.004782D0*SQRT((PV(1)-PVE(1))**2+
+           :                           (PV(2)-PVE(2))**2+
+           :                           (PV(3)-PVE(3))**2)
+
+      *        Extrapolate backwards in time by that much
+                  DO I=1,3
+                     PV(I)=PV(I)-TL*PV(I+3)
+                  END DO
+
+      *       To RA,Dec
+                  CALL sla_DCC2S(PV,RV,DV)
+
+      *        Same for Jupiter
+                  CALL sla_PLANET(DJDM,5,PV,J)
+                  DO I=1,6
+                     PV(I)=PV(I)-PVE(I)
+                  END DO
+                  TL=499.004782D0*SQRT((PV(1)-PVE(1))**2+
+           :                           (PV(2)-PVE(2))**2+
+           :                           (PV(3)-PVE(3))**2)
+                  DO I=1,3
+                     PV(I)=PV(I)-TL*PV(I+3)
+                  END DO
+                  CALL sla_DCC2S(PV,RJ,DJ)
+
+      *        Separation (arcsec)
+                  SEP=sla_DSEP(RV,DV,RJ,DJ)
+
+      *        Keep if smallest so far
+                  IF (SEP.LT.SEPMIN) THEN
+                     IHMIN=IHOUR
+                     IMMIN=IMIN
+                     SEPMIN=SEP
+                  END IF
+               END DO
+            END DO
+
+      *  Report
+            WRITE (*,'(1X,I2.2,'':'',I2.2,F6.1)') IHMIN,IMMIN,
+           :                                      206264.8062D0*SEPMIN
+
+            END
+\end{verbatim}
+\goodbreak
+The output produced (the Ephemeris Time on the day in question, and
+the closest approach in arcseconds) is as follows:
+\goodbreak
+\begin{verbatim}
+      21:19  33.7
+\end{verbatim}
+\goodbreak
+For comparison, accurate predictions based on the JPL DE\,102 ephemeris
+give a separation about \arcseci{8} less than
+the above estimate, occurring about half an hour earlier
+(see {\it Sky and Telescope,}\/ April~1987, p\,357).
+
+The following program demonstrates
+sla\_RDPLAN.
+\begin{verbatim}
+      *  For a given date, time and geographical location, output
+      *  a table of planetary positions and diameters.
+
+            IMPLICIT NONE
+            CHARACTER PNAMES(0:9)*7,B*80,S
+            INTEGER I,NP,IY,J,IM,ID,IHMSF(4),IDMSF(4)
+            DOUBLE PRECISION R2AS,FD,DJM,ELONG,PHI,RA,DEC,DIAM
+            PARAMETER (R2AS=206264.80625D0)
+            DATA PNAMES / 'Sun','Mercury','Venus','Moon','Mars','Jupiter',
+           :              'Saturn','Uranus','Neptune', 'Pluto' /
+
+
+      *  Loop until 'end' typed
+            B=' '
+            DO WHILE (B.NE.'END'.AND.B.NE.'end')
+
+      *     Get date, time and observer's location
+               PRINT *,'Date? (Y,M,D, Gregorian)'
+               READ (*,'(A)') B
+               IF (B.NE.'END'.AND.B.NE.'end') THEN
+                  I=1
+                  CALL sla_INTIN(B,I,IY,J)
+                  CALL sla_INTIN(B,I,IM,J)
+                  CALL sla_INTIN(B,I,ID,J)
+                  PRINT *,'Time? (H,M,S, dynamical)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,FD,J)
+                  FD=FD*2.3873241463784300365D0
+                  CALL sla_CLDJ(IY,IM,ID,DJM,J)
+                  DJM=DJM+FD
+                  PRINT *,'Longitude? (D,M,S, east +ve)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,ELONG,J)
+                  PRINT *,'Latitude? (D,M,S, (geodetic)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,PHI,J)
+
+      *        Loop planet by planet
+                  DO NP=0,8
+
+      *           Get RA,Dec and diameter
+                     CALL sla_RDPLAN(DJM,NP,ELONG,PHI,RA,DEC,DIAM)
+
+      *           One line of report
+                     CALL sla_DR2TF(2,RA,S,IHMSF)
+                     CALL sla_DR2AF(1,DEC,S,IDMSF)
+                     WRITE (*,
+           : '(1X,A,2X,3I3.2,''.'',I2.2,2X,A,I2.2,2I3.2,''.'',I1,F8.1)')
+           :                          PNAMES(NP),IHMSF,S,IDMSF,R2AS*DIAM
+
+      *           Next planet
+                  END DO
+                  PRINT *,' '
+               END IF
+
+      *     Next case
+            END DO
+
+            END
+\end{verbatim}
+Entering the following data (for 1927~June~29 at $5^{\rm h}\,25^{\rm m}$~ET
+and the position of Preston, UK.):
+\begin{verbatim}
+      1927 6 29
+      5 25
+      -2 42
+      53 46
+\end{verbatim}
+produces the following report:
+\begin{verbatim}
+      Sun       06 28 14.03  +23 17 17.5  1887.8
+      Mercury   08 08 58.62  +19 20 57.3     9.3
+      Venus     09 38 53.64  +15 35 32.9    22.8
+      Moon      06 28 18.30  +23 18 37.3  1903.9
+      Mars      09 06 49.34  +17 52 26.7     4.0
+      Jupiter   00 11 12.06  -00 10 57.5    41.1
+      Saturn    16 01 43.34  -18 36 55.9    18.2
+      Uranus    00 13 33.53  +00 39 36.0     3.5
+      Neptune   09 49 35.75  +13 38 40.8     2.2
+      Pluto     07 05 29.50  +21 25 04.2      .1
+\end{verbatim}
+Inspection of the Sun and Moon data reveals that
+a total solar eclipse is in progress.
+
+SLALIB also provides for the case where orbital elements (with respect
+to the J2000 equinox and ecliptic)
+are available.  This allows predictions to be made for minor-planets and
+(if you ignore non-gravitational effects)
+comets.  Furthermore, if major-planet elements for an epoch close to the date
+in question are available, more accurate predictions can be made than
+are offered by
+sla\_RDPLAN and
+sla\_PLANET.
+
+The SLALIB planetary-prediction
+routines that work with orbital elements are
+sla\_PLANTE (the orbital-elements equivalent of
+sla\_RDPLAN), which predicts the topocentric \radec, and
+sla\_PLANEL (the orbital-elements equivalent of
+sla\_PLANET), which predicts the heliocentric \xyzxyzd\ with respect to the
+J2000 equinox and equator.  In addition, the routine
+sla\_PV2EL does the inverse of
+sla\_PLANEL, transforming \xyzxyzd\ into {\it osculating elements.}
+
+Osculating elements describe the unperturbed 2-body orbit.  This is
+a good approximation to the actual orbit for a few weeks either
+side of the specified epoch, outside which perturbations due to
+the other bodies of the Solar System lead to
+increasing errors.  Given a minor planet's osculating elements for
+a particular date, predictions for a date even just
+100 days earlier or later
+are likely to be in error by several arcseconds.
+These errors can
+be reduced if new elements are generated which take account of
+the perturbations of the major planets, and this is what the routine
+sla\_PERTEL does.  Once
+sla\_PERTEL has been called, to provide osculating elements
+close to the required date, the elements can be passed to
+sla\_PLANEL or
+sla\_PLANTE in the normal way.  Predictions of arcsecond accuracy
+over a span of a decade or more are available using this
+technique.
+
+Three different combinations of orbital elements are
+provided for, matching the usual conventions
+for major planets, minor planets and
+comets respectively.  The choice is made through the
+argument {\tt JFORM}:\\
+
+\hspace{4em}
+\begin{tabular}{|c|c|c|} \hline
+{\tt JFORM=1} & {\tt JFORM=2} & {\tt JFORM=3} \\
+\hline \hline
+$t_0$ & $t_0$ & $T$ \\
+\hline
+$i$ & $i$ & $i$ \\
+\hline
+$\Omega$ & $\Omega$ & $\Omega$ \\
+\hline
+$\varpi$ & $\omega$ & $\omega$ \\
+\hline
+$a$ & $a$ & $q$ \\
+\hline
+$e$ & $e$ & $e$ \\
+\hline
+$L$ & $M$ & \\
+\hline
+$n$ & & \\
+\hline
+\end{tabular}\\[5ex]
+The symbols have the following meanings:
+\begin{tabbing}
+xxxxxxx \= xxxx \= \kill
+\> $t_0$ \> epoch at which the elements were correct \\
+\> $T$ \> epoch of perihelion passage \\
+\> $i$ \> inclination of the orbit \\
+\> $\Omega$ \> longitude of the ascending node \\
+\> $\varpi$ \> longitude of perihelion ($\varpi = \Omega + \omega$) \\
+\> $\omega$ \> argument of perihelion \\
+\> $a$ \> semi-major axis of the orbital ellipse \\
+\> $q$ \> perihelion distance \\
+\> $e$ \> orbital eccentricity \\
+\> $L$ \> mean longitude ($L = \varpi + M$) \\
+\> $M$ \> mean anomaly \\
+\> $n$ \> mean motion \\
+\end{tabbing}
+
+The mean motion, $n$, tells sla\_PLANEL the mass of the planet.
+If it is not available, it should be claculated
+from $n^2 a^3 = k^2 (1+m)$, where $k = 0.01720209895$ and
+m is the mass of the planet ($M_\odot = 1$); $a$ is in AU.
+
+Conventional elements are not the only way of specifying an orbit.
+The \xyzxyzd\ state vector is an equally valid specification,
+and the so-called {\it method of universal variables}\/ allows
+orbital calculations to be made directly, bypassing angular
+quantities and avoiding Kepler's Equation.  The universal-variables
+approach has various advantages, including better handling of
+near-parabolic cases and greater efficiency.
+SLALIB uses universal variables for its internal
+calculations and also offers a number of routines which
+applications can call.
+
+The universal elements are the \xyzxyzd\ and its epoch, plus the mass
+of the body.  The SLALIB routines supplement these elements with
+certain redundant values in order to
+avoid unnecessary recomputation when the elements are next used.
+
+The routines
+sla\_EL2UE and
+sla\_UE2EL transform conventional elements into the
+universal form and {\it vice versa.}
+The routine
+sla\_PV2UE takes an \xyzxyzd\ and forms the set of universal
+elements;
+sla\_UE2PV takes a set of universal elements and predicts the \xyzxyzd\
+for a specified epoch.
+The routine
+sla\_PERTUE provides updated universal elements,
+taking into account perturbations from the major planets.
+
+\subsection{Radial Velocity and Light-Time Corrections}
+When publishing high-resolution spectral observations
+it is necessary to refer them to a specified standard of rest.
+This involves knowing the component in the direction of the
+source of the velocity of the observer.  SLALIB provides a number
+of routines for this purpose, allowing observations to be
+referred to the Earth's centre, the Sun, a Local Standard of Rest
+(either dynamical or kinematical), the centre of the Galaxy, and
+the mean motion of the Local Group.
+
+The routine
+sla\_RVEROT
+corrects for the diurnal rotation of
+the observer around the Earth's axis.  This is always less than 0.5~km/s.
+
+No specific routine is provided to correct a radial velocity
+from geocentric to heliocentric, but this can easily be done by calling
+sla\_EVP
+as follows (array declarations {\it etc}.\ omitted):
+\goodbreak
+\begin{verbatim}
+             :
+      *  Star vector, J2000
+            CALL sla_DCS2C(RM,DM,V)
+
+      *  Earth/Sun velocity and position, J2000
+            CALL sla_EVP(TDB,2000D0,DVB,DPB,DVH,DPH)
+
+      *  Radial velocity correction due to Earth orbit (km/s)
+            VCORB = -sla_DVDV(V,DVH)*149.597870D6
+             :
+\end{verbatim}
+\goodbreak
+The maximum value of this correction is the Earth's orbital speed
+of about 30~km/s.  A related routine,
+sla\_ECOR,
+computes the light-time correction with respect to the Sun.  It
+would be used when reducing observations of a rapid variable-star
+for instance.
+Note, however, that the accuracy objectives for pulsar work are
+beyond the scope of these SLALIB routines, and even the superior
+sla\_EVP
+routine is unsuitable for arrival-time calculations of better
+than 25~millisecond accuracy.
+
+To remove the intrinsic $\sim20$~km/s motion of the Sun relative
+to other stars in the solar neighbourhood,
+a velocity correction to a
+{\it local standard of rest}\/ (LSR) is required.  There are
+opportunities for mistakes here.  There are two sorts of LSR,
+{\it dynamical}\/ and {\it kinematical}, and
+multiple definitions exist for the latter.  The
+dynamical LSR is a point near the Sun which is in a circular
+orbit around the Galactic centre;  the Sun has a ``peculiar''
+motion relative to the dynamical LSR.  A kinematical LSR is
+the mean standard of rest of specified star catalogues or stellar
+populations, and its precise definition depends on which
+catalogues or populations were used and how the analysis was
+carried out.  The Sun's motion with respect to a kinematical
+LSR is called the ``standard'' solar motion.  Radial
+velocity corrections to the dynamical LSR are produced by the routine
+sla\_RVLSRD
+and to the adopted kinematical LSR by
+sla\_RVLSRK.
+See the individual specifications for these routines for the
+precise definition of the LSR in each case.
+
+For extragalactic sources, the centre of the Galaxy can be used as
+a standard of rest.  The radial velocity correction from the
+dynamical LSR to the Galactic centre can be obtained by calling
+sla\_RVGALC.
+Its maximum value is 220~km/s.
+
+For very distant sources it is appropriate to work relative
+to the mean motion of the Local Group.  The routine for
+computing the radial velocity correction in this case is
+sla\_RVLG.
+Note that in this case the correction is with respect to the
+dynamical LSR, not the Galactic centre as might be expected.
+This conforms to the IAU definition, and confers immunity from
+revisions of the Galactic rotation speed.
+
+\subsection{Focal-Plane Astrometry}
+The relationship between the position of a star image in
+the focal plane of a telescope and the star's celestial
+coordinates is usually described in terms of the {\it tangent plane}\/
+or {\it gnomonic}\/ projection.  This is the projection produced
+by a pin-hole camera and is a good approximation to the projection
+geometry of a traditional large {\it f}\/-ratio astrographic refractor.
+SLALIB includes a group of routines which transform
+star positions between their observed places on the celestial
+sphere and their \xy\ coordinates in the tangent plane.  The
+spherical coordinate system does not have to be \radec\ but
+usually is.  The so-called {\it standard coordinates}\/ of a star
+are the tangent plane \xy, in radians, with respect to an origin
+at the tangent point, with the $y$-axis pointing north and
+the $x$-axis pointing east (in the direction of increasing $\alpha$).
+The factor relating the standard coordinates to
+the actual \xy\ coordinates in, say, millimetres is simply
+the focal length of the telescope.
+
+Given the \radec\ of the {\it plate centre}\/ (the tangent point)
+and the \radec\ of a star within the field, the standard
+coordinates can be determined by calling
+sla\_S2TP
+(single precision) or
+sla\_DS2TP
+(double precision).  The reverse transformation, where the
+\xy\ is known and we wish to find the \radec, is carried out by calling
+sla\_TP2S
+or
+sla\_DTP2S.
+Occasionally we know the both the \xy\ and the \radec\ of a 
+star and need to deduce the \radec\ of the tangent point;  
+this can be done by calling
+sla\_TPS2C
+or
+sla\_DTPS2C.
+(All of these transformations apply not just to \radec\ but to
+other spherical coordinate systems, of course.)
+Equivalent (and faster)
+routines are provided which work directly in \xyz\ instead of
+spherical coordinates:
+sla\_V2TP and
+sla\_DV2TP,
+sla\_TP2V and
+sla\_DTP2V,
+sla\_TPV2C and
+sla\_DTPV2C.
+
+Even at the best of times, the tangent plane projection is merely an
+approximation.  Some telescopes and cameras exhibit considerable pincushion
+or barrel distortion and some have a curved focal surface.
+For example, neither Schmidt cameras nor (especially)
+large reflecting telescopes with wide-field corrector lenses
+are adequately modelled by tangent-plane geometry.  In such
+cases, however, it is still possible to do most of the work
+using the (mathematically convenient) tangent-plane
+projection by inserting an extra step which applies or
+removes the distortion peculiar to the system concerned.
+A simple $r_1=r_0(1+Kr_0^2)$ law works well in the
+majority of cases; $r_0$ is the radial distance in the
+tangent plane, $r_1$ is the radial distance after adding
+the distortion, and $K$ is a constant which depends on the
+telescope ($\theta$ is unaffected).  The routine
+sla\_PCD
+applies the distortion to an \xy\ and
+sla\_UNPCD
+removes it.  For \xy\ in radians, $K$ values range from $-1/3$ for the
+tiny amount of barrel distortion in Schmidt geometry to several
+hundred for the serious pincushion distortion
+produced by wide-field correctors in big reflecting telescopes
+(the AAT prime focus triplet corrector is about $K=+178.6$).
+
+SLALIB includes a group of routines which can be put together
+to build a simple plate-reduction program.  The heart of the group is
+sla\_FITXY,
+which fits a linear model to relate two sets of \xy\ coordinates,
+in the case of a plate reduction the measured positions of the
+images of a set of
+reference stars and the standard
+coordinates derived from their catalogue positions.  The
+model is of the form:
+\[x_{p} = a + bx_{m} + cy_{m}\]
+\[y_{p} = d + ex_{m} + fy_{m}\]
+
+where the {\it p}\/ subscript indicates ``predicted'' coordinates
+(the model's approximation to the ideal ``expected'' coordinates) and the
+{\it m}\/ subscript indicates ``measured coordinates''.  The
+six coefficients {\it a--f}\/ can optionally be
+constrained to represent a ``solid body rotation'' free of
+any squash or shear distortions.  Without this constraint
+the model can, to some extent, accommodate effects like refraction,
+allowing mean places to be used directly and
+avoiding the extra complications of a
+full mean-apparent-observed transformation for each star.
+Having obtained the linear model,
+sla\_PXY
+can be used to process the set of measured and expected
+coordinates, giving the predicted coordinates and determining
+the RMS residuals in {\it x}\/ and {\it y}.
+The routine
+sla\_XY2XY
+transforms one \xy\ into another using the linear model.  A model
+can be inverted by calling
+sla\_INVF,
+and decomposed into zero points, scales, $x/y$ nonperpendicularity
+and orientation by calling
+sla\_DCMPF.
+
+\subsection{Numerical Methods}
+SLALIB contains a small number of simple, general-purpose
+numerical-methods routines.  They have no specific
+connection with positional astronomy but have proved useful in
+applications to do with simulation and fitting.
+
+At the heart of many simulation programs is the generation of
+pseudo-random numbers, evenly distributed in a given range:
+sla\_RANDOM
+does this.  Pseudo-random normal deviates, or ``Gaussian
+residuals'', are often required to simulate noise and
+can be generated by means of the function
+sla\_GRESID.
+Neither routine will pass super-sophisticated
+statistical tests, but they work adequately for most
+practical purposes and avoid the need to call non-standard
+library routines peculiar to one sort of computer.
+
+Applications which perform a least-squares fit using a traditional
+normal-equations methods can accomplish the required matrix-inversion
+by calling either
+sla\_SMAT
+(single precision) or
+sla\_DMAT
+(double).  A generally better way to perform such fits is
+to use singular value decomposition.  SLALIB provides a routine
+to do the decomposition itself,
+sla\_SVD,
+and two routines to use the results:
+sla\_SVDSOL
+generates the solution, and
+sla\_SVDCOV
+produces the covariance matrix.
+A simple demonstration of the use of the SLALIB SVD
+routines is given below.  It generates 500 simulated data
+points and fits them to a model which has 4 unknown coefficients.
+(The arrays in the example are sized to accept up to 1000
+points and 20 unknowns.)  The model is:
+\[ y = C_{1} +C_{2}x +C_{3}sin{x} +C_{4}cos{x} \]
+The test values for the four coefficients are
+$C_1\!=\!+50.0$,
+$C_2\!=\!-2.0$,
+$C_3\!=\!-10.0$ and
+$C_4\!=\!+25.0$.
+Gaussian noise, $\sigma=5.0$, is added to each ``observation''.
+\goodbreak
+\begin{verbatim}
+            IMPLICIT NONE
+
+      *  Sizes of arrays, physical and logical
+            INTEGER MP,NP,NC,M,N
+            PARAMETER (MP=1000,NP=10,NC=20,M=500,N=4)
+
+      *  The unknowns we are going to solve for
+            DOUBLE PRECISION C1,C2,C3,C4
+            PARAMETER (C1=50D0,C2=-2D0,C3=-10D0,C4=25D0)
+
+      *  Arrays
+            DOUBLE PRECISION A(MP,NP),W(NP),V(NP,NP),
+           :                 WORK(NP),B(MP),X(NP),CVM(NC,NC)
+
+            DOUBLE PRECISION VAL,BF1,BF2,BF3,BF4,SD2,D,VAR
+            REAL sla_GRESID
+            INTEGER I,J
+
+      *  Fill the design matrix
+            DO I=1,M
+
+      *     Dummy independent variable
+               VAL=DBLE(I)/10D0
+
+      *     The basis functions
+               BF1=1D0
+               BF2=VAL
+               BF3=SIN(VAL)
+               BF4=COS(VAL)
+
+      *     The observed value, including deliberate Gaussian noise
+               B(I)=C1*BF1+C2*BF2+C3*BF3+C4*BF4+DBLE(sla_GRESID(5.0))
+
+      *     Fill one row of the design matrix
+               A(I,1)=BF1
+               A(I,2)=BF2
+               A(I,3)=BF3
+               A(I,4)=BF4
+            END DO
+
+      *  Factorize the design matrix, solve and generate covariance matrix
+            CALL sla_SVD(M,N,MP,NP,A,W,V,WORK,J)
+            CALL sla_SVDSOL(M,N,MP,NP,B,A,W,V,WORK,X)
+            CALL sla_SVDCOV(N,NP,NC,W,V,WORK,CVM)
+
+      *  Compute the variance
+            SD2=0D0
+            DO I=1,M
+               VAL=DBLE(I)/10D0
+               BF1=1D0
+               BF2=VAL
+               BF3=SIN(VAL)
+               BF4=COS(VAL)
+               D=B(I)-(X(1)*BF1+X(2)*BF2+X(3)*BF3+X(4)*BF4)
+               SD2=SD2+D*D
+            END DO
+            VAR=SD2/DBLE(M)
+
+      *  Report the RMS and the solution
+            WRITE (*,'(1X,''RMS ='',F5.2/)') SQRT(VAR)
+            DO I=1,N
+               WRITE (*,'(1X,''C'',I1,'' ='',F7.3,'' +/-'',F6.3)')
+           :                                         I,X(I),SQRT(VAR*CVM(I,I))
+            END DO
+            END
+\end{verbatim}
+\goodbreak
+The program produces the following output:
+\goodbreak
+\begin{verbatim}
+            RMS = 4.88
+
+            C1 = 50.192 +/- 0.439
+            C2 = -2.002 +/- 0.015
+            C3 = -9.771 +/- 0.310
+            C4 = 25.275 +/- 0.310
+\end{verbatim}
+\goodbreak
+In this above example, essentially
+identical results would be obtained if the more
+commonplace normal-equations method had been used, and the large
+$1000\times20$ array would have been avoided.  However, the SVD method
+comes into its own when the opportunity is taken to edit the W-matrix
+(the so-called ``singular values'') in order to control
+possible ill-conditioning.  The procedure involves replacing with
+zeroes any W-elements smaller than a nominated value, for example
+0.001 times the largest W-element.  Small W-elements indicate
+ill-conditioning, which in the case of the normal-equations
+method would produce spurious large coefficient values and
+possible arithmetic overflows.  Using SVD, the effect on the solution
+of setting suspiciously small W-elements to zero is to restrain
+the offending coefficients from moving very far.  The
+fact that action was taken can be reported to show the program user that
+something is amiss.  Furthermore, if element W(J) was set to zero,
+the row numbers of the two biggest elements in the Jth column of the
+V-matrix identify the pair of solution coefficients that are
+dependent.
+
+A more detailed description of SVD and its use in least-squares
+problems would be out of place here, and the reader is urged
+to refer to the relevant sections of the book {\it Numerical Recipes}
+(Press {\it et al.}, Cambridge University Press, 1987).
+
+\pagebreak
+
+\section{SUMMARY OF CALLS}
+The basic trigonometrical and numerical facilities are supplied in both single
+and double precision versions.
+Most of the more esoteric position and time routines use double precision
+arguments only, even in cases where single precision would normally be adequate
+in practice.
+Certain routines with modest accuracy objectives are supplied in
+single precision versions only.
+In the calling sequences which follow, no attempt has been made
+to distinguish between single and double precision argument names,
+and frequently the same name is used on different occasions to
+mean different things.
+However, none of the routines uses a mixture of single and
+double precision arguments;  each routine is either wholly
+single precision or wholly double precision.
+
+In the classified list, below,
+{\it subroutine}\/ subprograms are those whose names and argument lists
+are preceded by `CALL', whereas {\it function}\/ subprograms are
+those beginning `R=' (when the result is REAL) or `D=' (when
+the result is DOUBLE~PRECISION).
+
+The list is, of course, merely for quick reference;  inexperienced
+users {\bf must} refer to the detailed specifications given later.
+In particular, {\bf don't guess} whether arguments are single or
+double precision; the result could be a program that happens to
+works on one sort of machine but not on another.
+
+\callhead{String Decoding}
+\begin{callset}
+\subp{CALL sla\_INTIN (STRING, NSTRT, IRESLT, JFLAG)}
+   Convert free-format string into integer
+\subq{CALL sla\_FLOTIN (STRING, NSTRT, RESLT, JFLAG)}
+     {CALL sla\_DFLTIN (STRING, NSTRT, DRESLT, JFLAG)}
+   Convert free-format string into floating-point number
+\subq{CALL sla\_AFIN (STRING, NSTRT, RESLT, JFLAG)}
+     {CALL sla\_DAFIN (STRING, NSTRT, DRESLT, JFLAG)}
+   Convert free-format string from deg,arcmin,arcsec to radians
+\end{callset}
+
+\callhead{Sexagesimal Conversions}
+\begin{callset}
+\subq{CALL sla\_CTF2D (IHOUR, IMIN, SEC, DAYS, J)}
+     {CALL sla\_DTF2D (IHOUR, IMIN, SEC, DAYS, J)}
+   Hours, minutes, seconds to days
+\subq{CALL sla\_CD2TF (NDP, DAYS, SIGN, IHMSF)}
+     {CALL sla\_DD2TF (NDP, DAYS, SIGN, IHMSF)}
+   Days to hours, minutes, seconds
+\subq{CALL sla\_CTF2R (IHOUR, IMIN, SEC, RAD, J)}
+     {CALL sla\_DTF2R (IHOUR, IMIN, SEC, RAD, J)}
+   Hours, minutes, seconds to radians
+\subq{CALL sla\_CR2TF (NDP, ANGLE, SIGN, IHMSF)}
+     {CALL sla\_DR2TF (NDP, ANGLE, SIGN, IHMSF)}
+   Radians to hours, minutes, seconds
+\subq{CALL sla\_CAF2R (IDEG, IAMIN, ASEC, RAD, J)}
+     {CALL sla\_DAF2R (IDEG, IAMIN, ASEC, RAD, J)}
+   Degrees, arcminutes, arcseconds to radians
+\subq{CALL sla\_CR2AF (NDP, ANGLE, SIGN, IDMSF)}
+     {CALL sla\_DR2AF (NDP, ANGLE, SIGN, IDMSF)}
+   Radians to degrees, arcminutes, arcseconds
+\end{callset}
+
+\callhead{Angles, Vectors and Rotation Matrices}
+\begin{callset}
+\subq{R~=~sla\_RANGE (ANGLE)}
+     {D~=~sla\_DRANGE (ANGLE)}
+   Normalize angle into range $\pm\pi$
+\subq{R~=~sla\_RANORM (ANGLE)}
+     {D~=~sla\_DRANRM (ANGLE)}
+   Normalize angle into range $0\!-\!2\pi$
+\subq{CALL sla\_CS2C (A, B, V)}
+     {CALL sla\_DCS2C (A, B, V)}
+   Spherical coordinates to \xyz
+\subq{CALL sla\_CC2S (V, A, B)}
+     {CALL sla\_DCC2S (V, A, B)}
+   \xyz\ to spherical coordinates
+\subq{R~=~sla\_VDV (VA, VB)}
+     {D~=~sla\_DVDV (VA, VB)}
+   Scalar product of two 3-vectors
+\subq{CALL sla\_VXV (VA, VB, VC)}
+     {CALL sla\_DVXV (VA, VB, VC)}
+   Vector product of two 3-vectors
+\subq{CALL sla\_VN (V, UV, VM)}
+     {CALL sla\_DVN (V, UV, VM)}
+   Normalize a 3-vector also giving the modulus
+\subq{R~=~sla\_SEP (A1, B1, A2, B2)}
+     {D~=~sla\_DSEP (A1, B1, A2, B2)}
+   Angle between two points on a sphere
+\subq{R~=~sla\_BEAR (A1, B1, A2, B2)}
+     {D~=~sla\_DBEAR (A1, B1, A2, B2)}
+   Direction of one point on a sphere seen from another
+\subq{R~=~sla\_PAV (V1, V2)}
+     {D~=~sla\_DPAV (V1, V2)}
+   Position-angle of one \xyz\ with respect to another
+\subq{CALL sla\_EULER (ORDER, PHI, THETA, PSI, RMAT)}
+     {CALL sla\_DEULER (ORDER, PHI, THETA, PSI, RMAT)}
+   Form rotation matrix from three Euler angles
+\subq{CALL sla\_AV2M (AXVEC, RMAT)}
+     {CALL sla\_DAV2M (AXVEC, RMAT)}
+   Form rotation matrix from axial vector
+\subq{CALL sla\_M2AV (RMAT, AXVEC)}
+     {CALL sla\_DM2AV (RMAT, AXVEC)}
+   Determine axial vector from rotation matrix
+\subq{CALL sla\_MXV (RM, VA, VB)}
+     {CALL sla\_DMXV (DM, VA, VB)}
+   Rotate vector forwards
+\subq{CALL sla\_IMXV (RM, VA, VB)}
+     {CALL sla\_DIMXV (DM, VA, VB)}
+   Rotate vector backwards
+\subq{CALL sla\_MXM (A, B, C)}
+     {CALL sla\_DMXM (A, B, C)}
+   Product of two 3x3 matrices
+\subq{CALL sla\_CS2C6 (A, B, R, AD, BD, RD, V)}
+     {CALL sla\_DS2C6 (A, B, R, AD, BD, RD, V)}
+   Conversion of position and velocity in spherical
+     coordinates to Cartesian coordinates
+\subq{CALL sla\_CC62S (V, A, B, R, AD, BD, RD)}
+     {CALL sla\_DC62S (V, A, B, R, AD, BD, RD)}
+   Conversion of position and velocity in Cartesian
+     coordinates to spherical coordinates
+\end{callset}
+
+\callhead{Calendars}
+\begin{callset}
+\subp{CALL sla\_CLDJ (IY, IM, ID, DJM, J)}
+   Gregorian Calendar to Modified Julian Date
+\subp{CALL sla\_CALDJ (IY, IM, ID, DJM, J)}
+   Gregorian Calendar to Modified Julian Date,
+     permitting century default
+\subp{CALL sla\_DJCAL (NDP, DJM, IYMDF, J)}
+   Modified Julian Date to Gregorian Calendar,
+     in a form convenient for formatted output
+\subp{CALL sla\_DJCL (DJM, IY, IM, ID, FD, J)}
+   Modified Julian Date to Gregorian Year, Month, Day, Fraction
+\subp{CALL sla\_CALYD (IY, IM, ID, NY, ND, J)}
+   Calendar to year and day in year, permitting century default
+\subp{CALL sla\_CLYD (IY, IM, ID, NY, ND, J)}
+   Calendar to year and day in year
+\subp{D~=~sla\_EPB (DATE)}
+   Modified Julian Date to Besselian Epoch
+\subp{D~=~sla\_EPB2D (EPB)}
+   Besselian Epoch to Modified Julian Date
+\subp{D~=~sla\_EPJ (DATE)}
+   Modified Julian Date to Julian Epoch
+\subp{D~=~sla\_EPJ2D (EPJ)}
+   Julian Epoch to Modified Julian Date
+\end{callset}
+
+\callhead{Timescales}
+\begin{callset}
+\subp{D~=~sla\_GMST (UT1)}
+   Conversion from Universal Time to sidereal time
+\subp{D~=~sla\_GMSTA (DATE, UT1)}
+   Conversion from Universal Time to sidereal time, rounding errors minimized
+\subp{D~=~sla\_EQEQX (DATE)}
+   Equation of the equinoxes
+\subp{D~=~sla\_DAT (DJU)}
+   Offset of Atomic Time from Coordinated Universal Time: TAI$-$UTC
+\subp{D~=~sla\_DT (EPOCH)}
+   Approximate offset between dynamical time and universal time
+\subp{D~=~sla\_DTT (DJU)}
+   Offset of Terrestrial Time from Coordinated Universal Time: TT$-$UTC
+\subp{D~=~sla\_RCC (TDB, UT1, WL, U, V)}
+   Relativistic clock correction: TDB$-$TT
+\end{callset}
+
+\callhead{Precession and Nutation}
+\begin{callset}
+\subp{CALL sla\_NUT (DATE, RMATN)}
+   Nutation matrix
+\subp{CALL sla\_NUTC (DATE, DPSI, DEPS, EPS0)}
+   Longitude and obliquity components of nutation, and
+     mean obliquity
+\subp{CALL sla\_PREC (EP0, EP1, RMATP)}
+   Precession matrix (IAU)
+\subp{CALL sla\_PRECL (EP0, EP1, RMATP)}
+   Precession matrix (suitable for long periods)
+\subp{CALL sla\_PRENUT (EPOCH, DATE, RMATPN)}
+   Combined precession/nutation matrix
+\subp{CALL sla\_PREBN (BEP0, BEP1, RMATP)}
+   Precession matrix, old system
+\subp{CALL sla\_PRECES (SYSTEM, EP0, EP1, RA, DC)}
+   Precession, in either the old or the new system
+\end{callset}
+
+\callhead{Proper Motion}
+\begin{callset}
+\subp{CALL sla\_PM (R0, D0, PR, PD, PX, RV, EP0, EP1, R1, D1)}
+   Adjust for proper motion
+\end{callset}
+
+\callhead{FK4/FK5/Hipparcos Conversions}
+\begin{callset}
+\subp{CALL sla\_FK425 (\vtop
+                       {\hbox{R1950, D1950, DR1950, DD1950, P1950, V1950,}
+                        \hbox{R2000, D2000, DR2000, DD2000, P2000, V2000)}}}
+   Convert B1950.0 FK4 star data to J2000.0 FK5
+\subp{CALL sla\_FK45Z (R1950, D1950, EPOCH, R2000, D2000)}
+   Convert B1950.0 FK4 position to J2000.0 FK5 assuming zero
+   FK5 proper motion and no parallax
+\subp{CALL sla\_FK524 (\vtop
+                       {\hbox{R2000, D2000, DR2000, DD2000, P2000, V2000,}
+                        \hbox{R1950, D1950, DR1950, DD1950, P1950, V1950)}}}
+   Convert J2000.0 FK5 star data to B1950.0 FK4
+\subp{CALL sla\_FK54Z (R2000, D2000, BEPOCH,
+               R1950, D1950, DR1950, DD1950)}
+   Convert J2000.0 FK5 position to B1950.0 FK4 assuming zero
+   FK5 proper motion and no parallax
+\subp{CALL sla\_FK52H (R5, D5, DR5, DD5, RH, DH, DRH, DDH)}
+   Convert J2000.0 FK5 star data to Hipparcos
+\subp{CALL sla\_FK5HZ (R5, D5, EPOCH, RH, DH )}
+   Convert J2000.0 FK5 position to Hipparcos assuming zero Hipparcos
+   proper motion
+\subp{CALL sla\_H2FK5 (RH, DH, DRH, DDH, R5, D5, DR5, DD5)}
+   Convert Hipparcos star data to J2000.0 FK5
+\subp{CALL sla\_HFK5Z (RH, DH, EPOCH, R5, D5, DR5, DD5)}
+   Convert Hipparcos position to J2000.0 FK5 assuming zero Hipparcos
+   proper motion
+\subp{CALL sla\_DBJIN (STRING, NSTRT, DRESLT, J1, J2)}
+   Like sla\_DFLTIN but with extensions to accept leading `B' and `J'
+\subp{CALL sla\_KBJ (JB, E, K, J)}
+   Select epoch prefix `B' or `J'
+\subp{D~=~sla\_EPCO (K0, K, E)}
+   Convert an epoch into the appropriate form -- `B' or `J'
+\end{callset}
+
+\callhead{Elliptic Aberration}
+\begin{callset}
+\subp{CALL sla\_ETRMS (EP, EV)}
+   E-terms
+\subp{CALL sla\_SUBET (RC, DC, EQ, RM, DM)}
+   Remove the E-terms
+\subp{CALL sla\_ADDET (RM, DM, EQ, RC, DC)}
+   Add the E-terms
+\end{callset}
+
+\callhead{Geographical and Geocentric Coordinates}
+\begin{callset}
+\subp{CALL sla\_OBS (NUMBER, ID, NAME, WLONG, PHI, HEIGHT)}
+   Interrogate list of observatory parameters
+\subp{CALL sla\_GEOC (P, H, R, Z)}
+   Convert geodetic position to geocentric
+\subp{CALL sla\_POLMO (ELONGM, PHIM, XP, YP, ELONG, PHI, DAZ)}
+   Polar motion
+\subp{CALL sla\_PVOBS (P, H, STL, PV)}
+   Position and velocity of observatory
+\end{callset}
+
+\callhead{Apparent and Observed Place}
+\begin{callset}
+\subp{CALL sla\_MAP (RM, DM, PR, PD, PX, RV, EQ, DATE, RA, DA)}
+   Mean place to geocentric apparent place
+\subp{CALL sla\_MAPPA (EQ, DATE, AMPRMS)}
+   Precompute mean to apparent parameters
+\subp{CALL sla\_MAPQK (RM, DM, PR, PD, PX, RV, AMPRMS, RA, DA)}
+   Mean to apparent using precomputed parameters
+\subp{CALL sla\_MAPQKZ (RM, DM, AMPRMS, RA, DA)}
+   Mean to apparent using precomputed parameters, for zero proper
+     motion, parallax and radial velocity
+\subp{CALL sla\_AMP (RA, DA, DATE, EQ, RM, DM)}
+   Geocentric apparent place to mean place
+\subp{CALL sla\_AMPQK (RA, DA, AOPRMS, RM, DM)}
+   Apparent to mean using precomputed parameters
+\subp{CALL sla\_AOP (\vtop
+                      {\hbox{RAP, DAP, UTC, DUT, ELONGM, PHIM, HM, XP, YP,}
+                       \hbox{TDK, PMB, RH, WL, TLR, AOB, ZOB, HOB, DOB, ROB)}}}
+   Apparent place to observed place
+\subp{CALL sla\_AOPPA (\vtop
+                        {\hbox{UTC, DUT, ELONGM, PHIM, HM, XP, YP,}
+                         \hbox{TDK, PMB, RH, WL, TLR, AOPRMS)}}}
+   Precompute apparent to observed parameters
+\subp{CALL sla\_AOPPAT (UTC, AOPRMS)}
+   Update sidereal time in apparent to observed parameters
+\subp{CALL sla\_AOPQK (RAP, DAP, AOPRMS, AOB, ZOB, HOB, DOB, ROB)}
+   Apparent to observed using precomputed parameters
+\subp{CALL sla\_OAP (\vtop
+                     {\hbox{TYPE, OB1, OB2, UTC, DUT, ELONGM, PHIM, HM, XP, YP,}
+                      \hbox{TDK, PMB, RH, WL, TLR, RAP, DAP)}}}
+   Observed to apparent
+\subp{CALL sla\_OAPQK (TYPE, OB1, OB2, AOPRMS, RA, DA)}
+   Observed to apparent using precomputed parameters
+\end{callset}
+
+\callhead{Azimuth and Elevation}
+\begin{callset}
+\subp{CALL sla\_ALTAZ (\vtop
+               {\hbox{HA, DEC, PHI,}
+                \hbox{AZ, AZD, AZDD, EL, ELD, ELDD, PA, PAD, PADD)}}}
+   Positions, velocities {\it etc.}\ for an altazimuth mount
+\subq{CALL sla\_E2H (HA, DEC, PHI, AZ, EL)}
+     {CALL sla\_DE2H (HA, DEC, PHI, AZ, EL)}
+   \hadec\ to \azel
+\subq{CALL sla\_H2E (AZ, EL, PHI, HA, DEC)}
+     {CALL sla\_DH2E (AZ, EL, PHI, HA, DEC)}
+   \azel\ to \hadec
+\subp{CALL sla\_PDA2H (P, D, A, H1, J1, H2, J2)}
+   Hour Angle corresponding to a given azimuth
+\subp{CALL sla\_PDQ2H (P, D, Q, H1, J1, H2, J2)}
+   Hour Angle corresponding to a given parallactic angle
+\subp{D~=~sla\_PA (HA, DEC, PHI)}
+   \hadec\ to parallactic angle
+\subp{D~=~sla\_ZD (HA, DEC, PHI)}
+   \hadec\ to zenith distance
+\end{callset}
+
+\callhead{Refraction and Air Mass}
+\begin{callset}
+\subp{CALL sla\_REFRO (ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REF)}
+   Change in zenith distance due to refraction
+\subp{CALL sla\_REFCO (HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REFA, REFB)}
+   Constants for simple refraction model (accurate)
+\subp{CALL sla\_REFCOQ (TDK, PMB, RH, WL, REFA, REFB)}
+   Constants for simple refraction model (fast)
+\subp{CALL sla\_ATMDSP ( TDK, PMB, RH, WL1, REFA1, REFB1, WL2, REFA2, REFB2 )}
+   Adjust refraction constants for colour
+\subp{CALL sla\_REFZ (ZU, REFA, REFB, ZR)}
+   Unrefracted to refracted ZD, simple model
+\subp{CALL sla\_REFV (VU, REFA, REFB, VR)}
+   Unrefracted to refracted \azel\ vector, simple model
+\subp{D~=~sla\_AIRMAS (ZD)}
+   Air mass
+\end{callset}
+
+\callhead{Ecliptic Coordinates}
+\begin{callset}
+\subp{CALL sla\_ECMAT (DATE, RMAT)}
+   Equatorial to ecliptic rotation matrix
+\subp{CALL sla\_EQECL (DR, DD, DATE, DL, DB)}
+   J2000.0 `FK5' to ecliptic coordinates
+\subp{CALL sla\_ECLEQ (DL, DB, DATE, DR, DD)}
+   Ecliptic coordinates to J2000.0 `FK5'
+\end{callset}
+
+\callhead{Galactic Coordinates}
+\begin{callset}
+\subp{CALL sla\_EG50 (DR, DD, DL, DB)}
+   B1950.0 `FK4' to galactic
+\subp{CALL sla\_GE50 (DL, DB, DR, DD)}
+   Galactic to B1950.0 `FK4'
+\subp{CALL sla\_EQGAL (DR, DD, DL, DB)}
+   J2000.0 `FK5' to galactic
+\subp{CALL sla\_GALEQ (DL, DB, DR, DD)}
+   Galactic to J2000.0 `FK5'
+\end{callset}
+
+\callhead{Supergalactic Coordinates}
+\begin{callset}
+\subp{CALL sla\_GALSUP (DL, DB, DSL, DSB)}
+   Galactic to supergalactic
+\subp{CALL sla\_SUPGAL (DSL, DSB, DL, DB)}
+   Supergalactic to galactic
+\end{callset}
+
+\callhead{Ephemerides}
+\begin{callset}
+\subp{CALL sla\_DMOON (DATE, PV)}
+   Approximate geocentric position and velocity of the Moon
+\subp{CALL sla\_EARTH (IY, ID, FD, PV)}
+   Approximate heliocentric position and velocity of the Earth
+\subp{CALL sla\_EVP (DATE, DEQX, DVB, DPB, DVH, DPH)}
+   Barycentric and heliocentric velocity and position of the Earth
+\subp{CALL sla\_MOON (IY, ID, FD, PV)}
+   Approximate geocentric position and velocity of the Moon
+\subp{CALL sla\_PLANET (DATE, NP, PV, JSTAT)}
+   Approximate heliocentric position and velocity of a planet
+\subp{CALL sla\_RDPLAN (DATE, NP, ELONG, PHI, RA, DEC, DIAM)}
+   Approximate topocentric apparent place of a planet
+\subp{CALL sla\_PLANEL (\vtop
+                       {\hbox{DATE, JFORM, EPOCH, ORBINC, ANODE, PERIH,}
+                      \hbox{AORQ, E, AORL, DM, PV, JSTAT)}}}
+   Heliocentric position and velocity of a planet, asteroid or
+   comet, starting from orbital elements
+\subp{CALL sla\_PLANTE (\vtop
+                       {\hbox{DATE, ELONG, PHI, JFORM, EPOCH, ORBINC, ANODE,}
+                      \hbox{PERIH, AORQ, E, AORL, DM, RA, DEC, R, JSTAT)}}}
+   Topocentric apparent place of a Solar-System object whose
+   heliocentric orbital elements are known
+\subp{CALL sla\_PV2EL (\vtop
+                      {\hbox{PV, DATE, PMASS, JFORMR, JFORM, EPOCH, ORBINC,}
+                     \hbox{ANODE, PERIH, AORQ, E, AORL, DM, JSTAT)}}}
+   Orbital elements of a planet from instantaneous position and velocity
+\subp{CALL sla\_PERTEL (\vtop
+                       {\hbox{JFORM, DATE0, DATE1,}
+                     \hbox{EPOCH0, ORBI0, ANODE0, PERIH0, AORQ0, E0, AM0,}
+                     \hbox{EPOCH1, ORBI1, ANODE1, PERIH1, AORQ1, E1, AM1,}
+                     \hbox{JSTAT)}}}
+   Update elements by applying perturbations
+\subp{CALL sla\_EL2UE (\vtop
+                      {\hbox{DATE, JFORM, EPOCH, ORBINC, ANODE,}
+                     \hbox{PERIH, AORQ, E, AORL, DM,}
+                     \hbox{U, JSTAT)}}}
+   Transform conventional elements to universal elements
+\subp{CALL sla\_UE2EL (\vtop
+                      {\hbox{U, JFORMR,}
+                     \hbox{JFORM, EPOCH, ORBINC, ANODE, PERIH,}
+                     \hbox{AORQ, E, AORL, DM, JSTAT)}}}
+   Transform universal elements to conventional elements
+\subp{CALL sla\_PV2UE (PV, DATE, PMASS, U, JSTAT)}
+   Package a position and velocity for use as universal elements
+\subp{CALL sla\_UE2PV (DATE, U, PV, JSTAT)}
+   Extract the position and velocity from universal elements
+\subp{CALL sla\_PERTUE (DATE, U, JSTAT)}
+   Update universal elements by applying perturbations
+\subp{R~=~sla\_RVEROT (PHI, RA, DA, ST)}
+   Velocity component due to rotation of the Earth
+\subp{CALL sla\_ECOR (RM, DM, IY, ID, FD, RV, TL)}
+   Components of velocity and light time due to Earth orbital motion
+\subp{R~=~sla\_RVLSRD (R2000, D2000)}
+   Velocity component due to solar motion wrt dynamical LSR
+\subp{R~=~sla\_RVLSRK (R2000, D2000)}
+   Velocity component due to solar motion wrt kinematical LSR
+\subp{R~=~sla\_RVGALC (R2000, D2000)}
+   Velocity component due to rotation of the Galaxy
+\subp{R~=~sla\_RVLG (R2000, D2000)}
+   Velocity component due to rotation and translation of the
+   Galaxy, relative to the mean motion of the local group
+\end{callset}
+
+\callhead{Astrometry}
+\begin{callset}
+\subq{CALL sla\_S2TP (RA, DEC, RAZ, DECZ, XI, ETA, J)}
+     {CALL sla\_DS2TP (RA, DEC, RAZ, DECZ, XI, ETA, J)}
+   Transform spherical coordinates into tangent plane
+\subq{CALL sla\_V2TP (V, V0, XI, ETA, J)}
+     {CALL sla\_DV2TP (V, V0, XI, ETA, J)}
+   Transform \xyz\ into tangent plane coordinates
+\subq{CALL sla\_DTP2S (XI, ETA, RAZ, DECZ, RA, DEC)}
+     {CALL sla\_TP2S (XI, ETA, RAZ, DECZ, RA, DEC)}
+   Transform tangent plane coordinates into spherical coordinates
+\subq{CALL sla\_DTP2V (XI, ETA, V0, V)}
+     {CALL sla\_TP2V (XI, ETA, V0, V)}
+   Transform tangent plane coordinates into \xyz
+\subq{CALL sla\_DTPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N)}
+     {CALL sla\_TPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N)}
+   Get plate centre from star \radec\ and tangent plane coordinates
+\subq{CALL sla\_DTPV2C (XI, ETA, V, V01, V02, N)}
+     {CALL sla\_TPV2C (XI, ETA, V, V01, V02, N)}
+   Get plate centre from star \xyz\ and tangent plane coordinates
+\subp{CALL sla\_PCD (DISCO, X, Y)}
+   Apply pincushion/barrel distortion
+\subp{CALL sla\_UNPCD (DISCO, X, Y)}
+   Remove pincushion/barrel distortion
+\subp{CALL sla\_FITXY (ITYPE, NP, XYE, XYM, COEFFS, J)}
+   Fit a linear model to relate two sets of \xy\ coordinates
+\subp{CALL sla\_PXY (NP, XYE, XYM, COEFFS, XYP, XRMS, YRMS, RRMS)}
+   Compute predicted coordinates and residuals
+\subp{CALL sla\_INVF (FWDS, BKWDS, J)}
+   Invert a linear model
+\subp{CALL sla\_XY2XY (X1, Y1, COEFFS, X2, Y2)}
+   Transform one \xy
+\subp{CALL sla\_DCMPF (COEFFS, XZ, YZ, XS, YS, PERP, ORIENT)}
+   Decompose a linear fit into scales {\it etc.}
+\end{callset}
+
+\callhead{Numerical Methods}
+\begin{callset}
+\subq{CALL sla\_SMAT (N, A, Y, D, JF, IW)}
+     {CALL sla\_DMAT (N, A, Y, D, JF, IW)}
+   Matrix inversion and solution of simultaneous equations
+\subp{CALL sla\_SVD (M, N, MP, NP, A, W, V, WORK, JSTAT)}
+   Singular value decomposition of a matrix
+\subp{CALL sla\_SVDSOL (M, N, MP, NP, B, U, W, V, WORK, X)}
+   Solution from given vector plus SVD
+\subp{CALL sla\_SVDCOV (N, NP, NC, W, V, WORK, CVM)}
+   Covariance matrix from SVD
+\subp{R~=~sla\_RANDOM (SEED)}
+   Generate pseudo-random real number in the range {$0 \leq x < 1$}
+\subp{R~=~sla\_GRESID (S)}
+   Generate pseudo-random normal deviate ($\equiv$ `Gaussian residual')
+\end{callset}
+
+\callhead{Real-time}
+\begin{callset}
+\subp{CALL sla\_WAIT (DELAY)}
+    Interval wait
+\end{callset}
+
+\end{document}
diff --git a/math/slalib/doc/supgal.hlp b/math/slalib/doc/supgal.hlp
new file mode 100644
index 00000000..aa260719
--- /dev/null
+++ b/math/slalib/doc/supgal.hlp
@@ -0,0 +1,43 @@
+.help supgal Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slSUGA (DSL, DSB, DL, DB)
+
+     - - - - - - -
+      S U G A
+     - - - - - - -
+
+  Transformation from de Vaucouleurs supergalactic coordinates
+  to IAU 1958 galactic coordinates (double precision)
+
+  Given:
+     DSL,DSB     dp       supergalactic longitude and latitude
+
+  Returned:
+     DL,DB       dp       galactic longitude and latitude L2,B2
+
+  (all arguments are radians)
+
+  Called:
+     slDS2C, slDIMV, slDC2S, slDA2P, slDA1P
+
+  References:
+
+     de Vaucouleurs, de Vaucouleurs, & Corwin, Second Reference
+     Catalogue of Bright Galaxies, U. Texas, page 8.
+
+     Systems & Applied Sciences Corp., Documentation for the
+     machine-readable version of the above catalogue,
+     Contract NAS 5-26490.
+
+    (These two references give different values for the galactic
+     longitude of the supergalactic origin.  Both are wrong;  the
+     correct value is L2=137.37.)
+
+  P.T.Wallace   Starlink   March 1986
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/svd.hlp b/math/slalib/doc/svd.hlp
new file mode 100644
index 00000000..14b87c43
--- /dev/null
+++ b/math/slalib/doc/svd.hlp
@@ -0,0 +1,73 @@
+.help svd Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slSVD (M, N, MP, NP, A, W, V, WORK, JSTAT)
+
+     - - - -
+      S V D
+     - - - -
+
+  Singular value decomposition  (double precision)
+
+  This routine expresses a given matrix A as the product of
+  three matrices U, W, V:
+
+     A = U x W x VT
+
+  Where:
+
+     A   is any M (rows) x N (columns) matrix, where M.GE.N
+     U   is an M x N column-orthogonal matrix
+     W   is an N x N diagonal matrix with W(I,I).GE.0
+     VT  is the transpose of an N x N orthogonal matrix
+
+     Note that M and N, above, are the LOGICAL dimensions of the
+     matrices and vectors concerned, which can be located in
+     arrays of larger PHYSICAL dimensions, given by MP and NP.
+
+  Given:
+     M,N    i         numbers of rows and columns in matrix A
+     MP,NP  i         physical dimensions of array containing matrix A
+     A      d(MP,NP)  array containing MxN matrix A
+
+  Returned:
+     A      d(MP,NP)  array containing MxN column-orthogonal matrix U
+     W      d(N)      NxN diagonal matrix W (diagonal elements only)
+     V      d(NP,NP)  array containing NxN orthogonal matrix V
+     WORK   d(N)      workspace
+     JSTAT  i         0 = OK, -1 = A wrong shape, >0 = index of W
+                      for which convergence failed.  See note 2, below.
+
+   Notes:
+
+   1)  V contains matrix V, not the transpose of matrix V.
+
+   2)  If the status JSTAT is greater than zero, this need not
+       necessarily be treated as a failure.  It means that, due to
+       chance properties of the matrix A, the QR transformation
+       phase of the routine did not fully converge in a predefined
+       number of iterations, something that very seldom occurs.
+       When this condition does arise, it is possible that the
+       elements of the diagonal matrix W have not been correctly
+       found.  However, in practice the results are likely to
+       be trustworthy.  Applications should report the condition
+       as a warning, but then proceed normally.
+
+  References:
+     The algorithm is an adaptation of the routine SVD in the EISPACK
+     library (Garbow et al 1977, EISPACK Guide Extension, Springer
+     Verlag), which is a FORTRAN 66 implementation of the Algol
+     routine SVD of Wilkinson & Reinsch 1971 (Handbook for Automatic
+     Computation, vol 2, ed Bauer et al, Springer Verlag).  These
+     references give full details of the algorithm used here.  A good
+     account of the use of SVD in least squares problems is given in
+     Numerical Recipes (Press et al 1986, Cambridge University Press),
+     which includes another variant of the EISPACK code.
+
+  P.T.Wallace   Starlink   22 December 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/svdcov.hlp b/math/slalib/doc/svdcov.hlp
new file mode 100644
index 00000000..48ce38df
--- /dev/null
+++ b/math/slalib/doc/svdcov.hlp
@@ -0,0 +1,35 @@
+.help svdcov Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slSVDC (N, NP, NC, W, V, WORK, CVM)
+
+     - - - - - - -
+      S V D C
+     - - - - - - -
+
+  From the W and V matrices from the SVD factorisation of a matrix
+  (as obtained from the slSVD routine), obtain the covariance matrix.
+
+  (double precision)
+
+  Given:
+     N      i         number of rows and columns in matrices W and V
+     NP     i         first dimension of array containing matrix V
+     NC     i         first dimension of array to receive CVM
+     W      d(N)      NxN diagonal matrix W (diagonal elements only)
+     V      d(NP,NP)  array containing NxN orthogonal matrix V
+
+  Returned:
+     WORK   d(N)      workspace
+     CVM    d(NC,NC)  array to receive covariance matrix
+
+  Reference:
+     Numerical Recipes, section 14.3.
+
+  P.T.Wallace   Starlink   December 1988
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/svdsol.hlp b/math/slalib/doc/svdsol.hlp
new file mode 100644
index 00000000..42513cfa
--- /dev/null
+++ b/math/slalib/doc/svdsol.hlp
@@ -0,0 +1,82 @@
+.help svdsol Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slSVDS (M, N, MP, NP, B, U, W, V, WORK, X)
+
+     - - - - - - -
+      S V D S
+     - - - - - - -
+
+  From a given vector and the SVD of a matrix (as obtained from
+  the SVD routine), obtain the solution vector (double precision)
+
+  This routine solves the equation:
+
+     A . x = b
+
+  where:
+
+     A   is a given M (rows) x N (columns) matrix, where M.GE.N
+     x   is the N-vector we wish to find
+     b   is a given M-vector
+
+  by means of the Singular Value Decomposition method (SVD).  In
+  this method, the matrix A is first factorised (for example by
+  the routine slSVD) into the following components:
+
+     A = U x W x VT
+
+  where:
+
+     A   is the M (rows) x N (columns) matrix
+     U   is an M x N column-orthogonal matrix
+     W   is an N x N diagonal matrix with W(I,I).GE.0
+     VT  is the transpose of an NxN orthogonal matrix
+
+     Note that M and N, above, are the LOGICAL dimensions of the
+     matrices and vectors concerned, which can be located in
+     arrays of larger PHYSICAL dimensions MP and NP.
+
+  The solution is found from the expression:
+
+     x = V . [diag(1/Wj)] . (transpose(U) . b)
+
+  Notes:
+
+  1)  If matrix A is square, and if the diagonal matrix W is not
+      adjusted, the method is equivalent to conventional solution
+      of simultaneous equations.
+
+  2)  If M>N, the result is a least-squares fit.
+
+  3)  If the solution is poorly determined, this shows up in the
+      SVD factorisation as very small or zero Wj values.  Where
+      a Wj value is small but non-zero it can be set to zero to
+      avoid ill effects.  The present routine detects such zero
+      Wj values and produces a sensible solution, with highly
+      correlated terms kept under control rather than being allowed
+      to elope to infinity, and with meaningful values for the
+      other terms.
+
+  Given:
+     M,N    i         numbers of rows and columns in matrix A
+     MP,NP  i         physical dimensions of array containing matrix A
+     B      d(M)      known vector b
+     U      d(MP,NP)  array containing MxN matrix U
+     W      d(N)      NxN diagonal matrix W (diagonal elements only)
+     V      d(NP,NP)  array containing NxN orthogonal matrix V
+
+  Returned:
+     WORK   d(N)      workspace
+     X      d(N)      unknown vector x
+
+  Reference:
+     Numerical Recipes, section 2.9.
+
+  P.T.Wallace   Starlink   29 October 1993
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/tp2s.hlp b/math/slalib/doc/tp2s.hlp
new file mode 100644
index 00000000..3cbf1c8e
--- /dev/null
+++ b/math/slalib/doc/tp2s.hlp
@@ -0,0 +1,28 @@
+.help tp2s Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slTP2S (XI, ETA, RAZ, DECZ, RA, DEC)
+
+     - - - - -
+      T P 2 S
+     - - - - -
+
+  Transform tangent plane coordinates into spherical
+  (single precision)
+
+  Given:
+     XI,ETA      real  tangent plane rectangular coordinates
+     RAZ,DECZ    real  spherical coordinates of tangent point
+
+  Returned:
+     RA,DEC      real  spherical coordinates (0-2pi,+/-pi/2)
+
+  Called:        slRA2P
+
+  P.T.Wallace   Starlink   24 July 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/tp2v.hlp b/math/slalib/doc/tp2v.hlp
new file mode 100644
index 00000000..e81c60d1
--- /dev/null
+++ b/math/slalib/doc/tp2v.hlp
@@ -0,0 +1,40 @@
+.help tp2v Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slTP2V (XI, ETA, V0, V)
+
+     - - - - -
+      T P 2 V
+     - - - - -
+
+  Given the tangent-plane coordinates of a star and the direction
+  cosines of the tangent point, determine the direction cosines
+  of the star.
+
+  (single precision)
+
+  Given:
+     XI,ETA    r       tangent plane coordinates of star
+     V0        r(3)    direction cosines of tangent point
+
+  Returned:
+     V         r(3)    direction cosines of star
+
+  Notes:
+
+  1  If vector V0 is not of unit length, the returned vector V will
+     be wrong.
+
+  2  If vector V0 points at a pole, the returned vector V will be
+     based on the arbitrary assumption that the RA of the tangent
+     point is zero.
+
+  3  This routine is the Cartesian equivalent of the routine slTP2S.
+
+  P.T.Wallace   Starlink   11 February 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/tps2c.hlp b/math/slalib/doc/tps2c.hlp
new file mode 100644
index 00000000..d1914ef2
--- /dev/null
+++ b/math/slalib/doc/tps2c.hlp
@@ -0,0 +1,58 @@
+.help tps2c Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slTPSC (XI, ETA, RA, DEC, RAZ1, DECZ1,
+     :                                        RAZ2, DECZ2, N)
+
+     - - - - - -
+      T P S C
+     - - - - - -
+
+  From the tangent plane coordinates of a star of known RA,Dec,
+  determine the RA,Dec of the tangent point.
+
+  (single precision)
+
+  Given:
+     XI,ETA      r    tangent plane rectangular coordinates
+     RA,DEC      r    spherical coordinates
+
+  Returned:
+     RAZ1,DECZ1  r    spherical coordinates of tangent point, solution 1
+     RAZ2,DECZ2  r    spherical coordinates of tangent point, solution 2
+     N           i    number of solutions:
+                        0 = no solutions returned (note 2)
+                        1 = only the first solution is useful (note 3)
+                        2 = both solutions are useful (note 3)
+
+  Notes:
+
+  1  The RAZ1 and RAZ2 values are returned in the range 0-2pi.
+
+  2  Cases where there is no solution can only arise near the poles.
+     For example, it is clearly impossible for a star at the pole
+     itself to have a non-zero XI value, and hence it is
+     meaningless to ask where the tangent point would have to be
+     to bring about this combination of XI and DEC.
+
+  3  Also near the poles, cases can arise where there are two useful
+     solutions.  The argument N indicates whether the second of the
+     two solutions returned is useful.  N=1 indicates only one useful
+     solution, the usual case;  under these circumstances, the second
+     solution corresponds to the "over-the-pole" case, and this is
+     reflected in the values of RAZ2 and DECZ2 which are returned.
+
+  4  The DECZ1 and DECZ2 values are returned in the range +/-pi, but
+     in the usual, non-pole-crossing, case, the range is +/-pi/2.
+
+  5  This routine is the spherical equivalent of the routine slDPVC.
+
+  Called:  slRA2P
+
+  P.T.Wallace   Starlink   5 June 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/tpv2c.hlp b/math/slalib/doc/tpv2c.hlp
new file mode 100644
index 00000000..7a1b688d
--- /dev/null
+++ b/math/slalib/doc/tpv2c.hlp
@@ -0,0 +1,51 @@
+.help tpv2c Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slTPVC (XI, ETA, V, V01, V02, N)
+
+     - - - - - -
+      T P V C
+     - - - - - -
+
+  Given the tangent-plane coordinates of a star and its direction
+  cosines, determine the direction cosines of the tangent-point.
+
+  (single precision)
+
+  Given:
+     XI,ETA    r       tangent plane coordinates of star
+     V         r(3)    direction cosines of star
+
+  Returned:
+     V01       r(3)    direction cosines of tangent point, solution 1
+     V02       r(3)    direction cosines of tangent point, solution 2
+     N         i       number of solutions:
+                         0 = no solutions returned (note 2)
+                         1 = only the first solution is useful (note 3)
+                         2 = both solutions are useful (note 3)
+
+  Notes:
+
+  1  The vector V must be of unit length or the result will be wrong.
+
+  2  Cases where there is no solution can only arise near the poles.
+     For example, it is clearly impossible for a star at the pole
+     itself to have a non-zero XI value, and hence it is meaningless
+     to ask where the tangent point would have to be.
+
+  3  Also near the poles, cases can arise where there are two useful
+     solutions.  The argument N indicates whether the second of the
+     two solutions returned is useful.  N=1 indicates only one useful
+     solution, the usual case;  under these circumstances, the second
+     solution can be regarded as valid if the vector V02 is interpreted
+     as the "over-the-pole" case.
+
+  4  This routine is the Cartesian equivalent of the routine slTPSC.
+
+  P.T.Wallace   Starlink   5 June 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ue2el.hlp b/math/slalib/doc/ue2el.hlp
new file mode 100644
index 00000000..6eb0996a
--- /dev/null
+++ b/math/slalib/doc/ue2el.hlp
@@ -0,0 +1,167 @@
+.help ue2el Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slUEEL (U, JFORMR,
+     :                      JFORM, EPOCH, ORBINC, ANODE, PERIH,
+     :                      AORQ, E, AORL, DM, JSTAT)
+
+     - - - - - -
+      U E E L
+     - - - - - -
+
+  Transform universal elements into conventional heliocentric
+  osculating elements.
+
+  Given:
+     U         d(13)  universal orbital elements (Note 1)
+
+                 (1)  combined mass (M+m)
+                 (2)  total energy of the orbit (alpha)
+                 (3)  reference (osculating) epoch (t0)
+               (4-6)  position at reference epoch (r0)
+               (7-9)  velocity at reference epoch (v0)
+                (10)  heliocentric distance at reference epoch
+                (11)  r0.v0
+                (12)  date (t)
+                (13)  universal eccentric anomaly (psi) of date, approx
+
+     JFORMR    i      requested element set (1-3; Note 3)
+
+  Returned:
+     JFORM     d      element set actually returned (1-3; Note 4)
+     EPOCH     d      epoch of elements (TT MJD)
+     ORBINC    d      inclination (radians)
+     ANODE     d      longitude of the ascending node (radians)
+     PERIH     d      longitude or argument of perihelion (radians)
+     AORQ      d      mean distance or perihelion distance (AU)
+     E         d      eccentricity
+     AORL      d      mean anomaly or longitude (radians, JFORM=1,2 only)
+     DM        d      daily motion (radians, JFORM=1 only)
+     JSTAT     i      status:  0 = OK
+                              -1 = illegal combined mass
+                              -2 = illegal JFORMR
+                              -3 = position/velocity out of range
+
+  Notes
+
+  1  The "universal" elements are those which define the orbit for the
+     purposes of the method of universal variables (see reference 2).
+     They consist of the combined mass of the two bodies, an epoch,
+     and the position and velocity vectors (arbitrary reference frame)
+     at that epoch.  The parameter set used here includes also various
+     quantities that can, in fact, be derived from the other
+     information.  This approach is taken to avoiding unnecessary
+     computation and loss of accuracy.  The supplementary quantities
+     are (i) alpha, which is proportional to the total energy of the
+     orbit, (ii) the heliocentric distance at epoch, (iii) the
+     outwards component of the velocity at the given epoch, (iv) an
+     estimate of psi, the "universal eccentric anomaly" at a given
+     date and (v) that date.
+
+  2  The universal elements are with respect to the mean equator and
+     equinox of epoch J2000.  The orbital elements produced are with
+     respect to the J2000 ecliptic and mean equinox.
+
+  3  Three different element-format options are supported:
+
+     Option JFORM=1, suitable for the major planets:
+
+     EPOCH  = epoch of elements (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = longitude of perihelion, curly pi (radians)
+     AORQ   = mean distance, a (AU)
+     E      = eccentricity, e
+     AORL   = mean longitude L (radians)
+     DM     = daily motion (radians)
+
+     Option JFORM=2, suitable for minor planets:
+
+     EPOCH  = epoch of elements (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = argument of perihelion, little omega (radians)
+     AORQ   = mean distance, a (AU)
+     E      = eccentricity, e
+     AORL   = mean anomaly M (radians)
+
+     Option JFORM=3, suitable for comets:
+
+     EPOCH  = epoch of perihelion (TT MJD)
+     ORBINC = inclination i (radians)
+     ANODE  = longitude of the ascending node, big omega (radians)
+     PERIH  = argument of perihelion, little omega (radians)
+     AORQ   = perihelion distance, q (AU)
+     E      = eccentricity, e
+
+  4  It may not be possible to generate elements in the form
+     requested through JFORMR.  The caller is notified of the form
+     of elements actually returned by means of the JFORM argument:
+
+      JFORMR   JFORM     meaning
+
+        1        1       OK - elements are in the requested format
+        1        2       never happens
+        1        3       orbit not elliptical
+
+        2        1       never happens
+        2        2       OK - elements are in the requested format
+        2        3       orbit not elliptical
+
+        3        1       never happens
+        3        2       never happens
+        3        3       OK - elements are in the requested format
+
+  5  The arguments returned for each value of JFORM (cf Note 6: JFORM
+     may not be the same as JFORMR) are as follows:
+
+         JFORM         1              2              3
+         EPOCH         t0             t0             T
+         ORBINC        i              i              i
+         ANODE         Omega          Omega          Omega
+         PERIH         curly pi       omega          omega
+         AORQ          a              a              q
+         E             e              e              e
+         AORL          L              M              -
+         DM            n              -              -
+
+     where:
+
+         t0           is the epoch of the elements (MJD, TT)
+         T              "    epoch of perihelion (MJD, TT)
+         i              "    inclination (radians)
+         Omega          "    longitude of the ascending node (radians)
+         curly pi       "    longitude of perihelion (radians)
+         omega          "    argument of perihelion (radians)
+         a              "    mean distance (AU)
+         q              "    perihelion distance (AU)
+         e              "    eccentricity
+         L              "    longitude (radians, 0-2pi)
+         M              "    mean anomaly (radians, 0-2pi)
+         n              "    daily motion (radians)
+         -             means no value is set
+
+  6  At very small inclinations, the longitude of the ascending node
+     ANODE becomes indeterminate and under some circumstances may be
+     set arbitrarily to zero.  Similarly, if the orbit is close to
+     circular, the true anomaly becomes indeterminate and under some
+     circumstances may be set arbitrarily to zero.  In such cases,
+     the other elements are automatically adjusted to compensate,
+     and so the elements remain a valid description of the orbit.
+
+  References:
+
+     1  Sterne, Theodore E., "An Introduction to Celestial Mechanics",
+        Interscience Publishers Inc., 1960.  Section 6.7, p199.
+
+     2  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
+
+  Called:  slPVEL
+
+  P.T.Wallace   Starlink   18 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/ue2pv.hlp b/math/slalib/doc/ue2pv.hlp
new file mode 100644
index 00000000..ed5c9609
--- /dev/null
+++ b/math/slalib/doc/ue2pv.hlp
@@ -0,0 +1,87 @@
+.help ue2pv Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slUEPV (DATE, U, PV, JSTAT)
+
+     - - - - - -
+      U E P V
+     - - - - - -
+
+  Heliocentric position and velocity of a planet, asteroid or comet,
+  starting from orbital elements in the "universal variables" form.
+
+  Given:
+     DATE     d       date, Modified Julian Date (JD-2400000.5)
+
+  Given and returned:
+     U        d(13)   universal orbital elements (updated; Note 1)
+
+       given    (1)   combined mass (M+m)
+         "      (2)   total energy of the orbit (alpha)
+         "      (3)   reference (osculating) epoch (t0)
+         "    (4-6)   position at reference epoch (r0)
+         "    (7-9)   velocity at reference epoch (v0)
+         "     (10)   heliocentric distance at reference epoch
+         "     (11)   r0.v0
+     returned  (12)   date (t)
+         "     (13)   universal eccentric anomaly (psi) of date
+
+  Returned:
+     PV       d(6)    position (AU) and velocity (AU/s)
+     JSTAT    i       status:  0 = OK
+                              -1 = radius vector zero
+                              -2 = failed to converge
+
+  Notes
+
+  1  The "universal" elements are those which define the orbit for the
+     purposes of the method of universal variables (see reference).
+     They consist of the combined mass of the two bodies, an epoch,
+     and the position and velocity vectors (arbitrary reference frame)
+     at that epoch.  The parameter set used here includes also various
+     quantities that can, in fact, be derived from the other
+     information.  This approach is taken to avoiding unnecessary
+     computation and loss of accuracy.  The supplementary quantities
+     are (i) alpha, which is proportional to the total energy of the
+     orbit, (ii) the heliocentric distance at epoch, (iii) the
+     outwards component of the velocity at the given epoch, (iv) an
+     estimate of psi, the "universal eccentric anomaly" at a given
+     date and (v) that date.
+
+  2  The companion routine is slELUE.  This takes the conventional
+     orbital elements and transforms them into the set of numbers
+     needed by the present routine.  A single prediction requires one
+     one call to slELUE followed by one call to the present routine;
+     for convenience, the two calls are packaged as the routine
+     slPLNE.  Multiple predictions may be made by again
+     calling slELUE once, but then calling the present routine
+     multiple times, which is faster than multiple calls to slPLNE.
+
+     It is not obligatory to use slELUE to obtain the parameters.
+     However, it should be noted that because slELUE performs its
+     own validation, no checks on the contents of the array U are made
+     by the present routine.
+
+  3  DATE is the instant for which the prediction is required.  It is
+     in the TT timescale (formerly Ephemeris Time, ET) and is a
+     Modified Julian Date (JD-2400000.5).
+
+  4  The universal elements supplied in the array U are in canonical
+     units (solar masses, AU and canonical days).  The position and
+     velocity are not sensitive to the choice of reference frame.  The
+     slELUE routine in fact produces coordinates with respect to the
+     J2000 equator and equinox.
+
+  5  The algorithm was originally adapted from the EPHSLA program of
+     D.H.P.Jones (private communication, 1996).  The method is based
+     on Stumpff's Universal Variables.
+
+  Reference:  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
+
+  P.T.Wallace   Starlink   19 March 1999
+
+  Copyright (C) 1999 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/unpcd.hlp b/math/slalib/doc/unpcd.hlp
new file mode 100644
index 00000000..26654492
--- /dev/null
+++ b/math/slalib/doc/unpcd.hlp
@@ -0,0 +1,57 @@
+.help unpcd Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slUPCD (DISCO,X,Y)
+
+     - - - - - -
+      U P C D
+     - - - - - -
+
+  Remove pincushion/barrel distortion from a distorted [x,y]
+  to give tangent-plane [x,y].
+
+  Given:
+     DISCO    d      pincushion/barrel distortion coefficient
+     X,Y      d      distorted coordinates
+
+  Returned:
+     X,Y      d      tangent-plane coordinates
+
+  Notes:
+
+  1)  The distortion is of the form RP = R*(1 + C*R**2), where R is
+      the radial distance from the tangent point, C is the DISCO
+      argument, and RP is the radial distance in the presence of
+      the distortion.
+
+  2)  For pincushion distortion, C is +ve;  for barrel distortion,
+      C is -ve.
+
+  3)  For X,Y in "radians" - units of one projection radius,
+      which in the case of a photograph is the focal length of
+      the camera - the following DISCO values apply:
+
+          Geometry          DISCO
+
+          astrograph         0.0
+          Schmidt           -0.3333
+          AAT PF doublet  +147.069
+          AAT PF triplet  +178.585
+          AAT f/8          +21.20
+          JKT f/8          +13.32
+
+  4)  The present routine is an approximate inverse to the
+      companion routine slPCD, obtained from two iterations
+      of Newton's method.  The mismatch between the slPCD and
+      slUPCD routines is negligible for astrometric applications;
+      to reach 1 milliarcsec at the edge of the AAT triplet or
+      Schmidt field would require field diameters of 2.4 degrees
+      and 42 degrees respectively.
+
+  P.T.Wallace   Starlink   1 August 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/v2tp.hlp b/math/slalib/doc/v2tp.hlp
new file mode 100644
index 00000000..6522e398
--- /dev/null
+++ b/math/slalib/doc/v2tp.hlp
@@ -0,0 +1,42 @@
+.help v2tp Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slV2TP (V, V0, XI, ETA, J)
+
+     - - - - -
+      V 2 T P
+     - - - - -
+
+  Given the direction cosines of a star and of the tangent point,
+  determine the star's tangent-plane coordinates.
+
+  (single precision)
+
+  Given:
+     V         r(3)    direction cosines of star
+     V0        r(3)    direction cosines of tangent point
+
+  Returned:
+     XI,ETA    r       tangent plane coordinates of star
+     J         i       status:   0 = OK
+                                 1 = error, star too far from axis
+                                 2 = error, antistar on tangent plane
+                                 3 = error, antistar too far from axis
+
+  Notes:
+
+  1  If vector V0 is not of unit length, or if vector V is of zero
+     length, the results will be wrong.
+
+  2  If V0 points at a pole, the returned XI,ETA will be based on the
+     arbitrary assumption that the RA of the tangent point is zero.
+
+  3  This routine is the Cartesian equivalent of the routine slS2TP.
+
+  P.T.Wallace   Starlink   27 November 1996
+
+  Copyright (C) 1996 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/vdv.hlp b/math/slalib/doc/vdv.hlp
new file mode 100644
index 00000000..526ce406
--- /dev/null
+++ b/math/slalib/doc/vdv.hlp
@@ -0,0 +1,24 @@
+.help vdv Jun99 "Slalib Package"
+.nf
+
+      REAL FUNCTION slVDV (VA, VB)
+
+     - - - -
+      V D V
+     - - - -
+
+  Scalar product of two 3-vectors  (single precision)
+
+  Given:
+      VA      real(3)     first vector
+      VB      real(3)     second vector
+
+  The result is the scalar product VA.VB (single precision)
+
+  P.T.Wallace   Starlink   November 1984
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/vn.hlp b/math/slalib/doc/vn.hlp
new file mode 100644
index 00000000..17b7b3ba
--- /dev/null
+++ b/math/slalib/doc/vn.hlp
@@ -0,0 +1,27 @@
+.help vn Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slVN (V, UV, VM)
+
+     - - -
+      V N
+     - - -
+
+  Normalizes a 3-vector also giving the modulus (single precision)
+
+  Given:
+     V       real(3)      vector
+
+  Returned:
+     UV      real(3)      unit vector in direction of V
+     VM      real         modulus of V
+
+  If the modulus of V is zero, UV is set to zero as well
+
+  P.T.Wallace   Starlink   23 November 1995
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/vxv.hlp b/math/slalib/doc/vxv.hlp
new file mode 100644
index 00000000..64272c33
--- /dev/null
+++ b/math/slalib/doc/vxv.hlp
@@ -0,0 +1,25 @@
+.help vxv Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slVXV (VA, VB, VC)
+
+     - - - -
+      V X V
+     - - - -
+
+  Vector product of two 3-vectors (single precision)
+
+  Given:
+      VA      real(3)     first vector
+      VB      real(3)     second vector
+
+  Returned:
+      VC      real(3)     vector result
+
+  P.T.Wallace   Starlink   March 1986
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/xy2xy.hlp b/math/slalib/doc/xy2xy.hlp
new file mode 100644
index 00000000..64ab43e2
--- /dev/null
+++ b/math/slalib/doc/xy2xy.hlp
@@ -0,0 +1,45 @@
+.help xy2xy Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slXYXY (X1,Y1,COEFFS,X2,Y2)
+
+     - - - - - -
+      X Y X Y
+     - - - - - -
+
+  Transform one [X,Y] into another using a linear model of the type
+  produced by the slFTXY routine.
+
+  Given:
+     X1       d        x-coordinate
+     Y1       d        y-coordinate
+     COEFFS  d(6)      transformation coefficients (see note)
+
+  Returned:
+     X2       d        x-coordinate
+     Y2       d        y-coordinate
+
+  The model relates two sets of [X,Y] coordinates as follows.
+  Naming the elements of COEFFS:
+
+     COEFFS(1) = A
+     COEFFS(2) = B
+     COEFFS(3) = C
+     COEFFS(4) = D
+     COEFFS(5) = E
+     COEFFS(6) = F
+
+  the present routine performs the transformation:
+
+     X2 = A + B*X1 + C*Y1
+     Y2 = D + E*X1 + F*Y1
+
+  See also slFTXY, slPXY, slINVF, slDCMF
+
+  P.T.Wallace   Starlink   5 December 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/doc/zd.hlp b/math/slalib/doc/zd.hlp
new file mode 100644
index 00000000..109b4d10
--- /dev/null
+++ b/math/slalib/doc/zd.hlp
@@ -0,0 +1,48 @@
+.help zd Jun99 "Slalib Package"
+.nf
+
+      DOUBLE PRECISION FUNCTION slZD (HA, DEC, PHI)
+
+     - - -
+      Z D
+     - - -
+
+  HA, Dec to Zenith Distance (double precision)
+
+  Given:
+     HA     d     Hour Angle in radians
+     DEC    d     declination in radians
+     PHI    d     observatory latitude in radians
+
+  The result is in the range 0 to pi.
+
+  Notes:
+
+  1)  The latitude must be geodetic.  In critical applications,
+      corrections for polar motion should be applied.
+
+  2)  In some applications it will be important to specify the
+      correct type of hour angle and declination in order to
+      produce the required type of zenith distance.  In particular,
+      it may be important to distinguish between the zenith distance
+      as affected by refraction, which would require the "observed"
+      HA,Dec, and the zenith distance in vacuo, which would require
+      the "topocentric" HA,Dec.  If the effects of diurnal aberration
+      can be neglected, the "apparent" HA,Dec may be used instead of
+      the topocentric HA,Dec.
+
+  3)  No range checking of arguments is done.
+
+  4)  In applications which involve many zenith distance calculations,
+      rather than calling the present routine it will be more efficient
+      to use inline code, having previously computed fixed terms such
+      as sine and cosine of latitude, and perhaps sine and cosine of
+      declination.
+
+  P.T.Wallace   Starlink   3 April 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp
diff --git a/math/slalib/dpav.f b/math/slalib/dpav.f
new file mode 100644
index 00000000..20de2742
--- /dev/null
+++ b/math/slalib/dpav.f
@@ -0,0 +1,82 @@
+      DOUBLE PRECISION FUNCTION slDPAV ( V1, V2 )
+*+
+*     - - - - -
+*      D P A V
+*     - - - - -
+*
+*  Position angle of one celestial direction with respect to another.
+*
+*  (double precision)
+*
+*  Given:
+*     V1    d(3)    direction cosines of one point
+*     V2    d(3)    direction cosines of the other point
+*
+*  (The coordinate frames correspond to RA,Dec, Long,Lat etc.)
+*
+*  The result is the bearing (position angle), in radians, of point
+*  V2 with respect to point V1.  It is in the range +/- pi.  The
+*  sense is such that if V2 is a small distance east of V1, the
+*  bearing is about +pi/2.  Zero is returned if the two points
+*  are coincident.
+*
+*  V1 and V2 need not be unit vectors.
+*
+*  The routine slDBER performs an equivalent function except
+*  that the points are specified in the form of spherical
+*  coordinates.
+*
+*  Last revision:   16 March 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION V1(3),V2(3)
+
+      DOUBLE PRECISION X1,Y1,Z1,W,X2,Y2,Z2,SQ,CQ
+
+
+
+*  The unit vector to point 1.
+      X1 = V1(1)
+      Y1 = V1(2)
+      Z1 = V1(3)
+      W = SQRT(X1*X1+Y1*Y1+Z1*Z1)
+      IF (W.NE.0D0) THEN
+         X1 = X1/W
+         Y1 = Y1/W
+         Z1 = Z1/W
+      END IF
+
+*  The vector to point 2.
+      X2 = V2(1)
+      Y2 = V2(2)
+      Z2 = V2(3)
+
+*  Position angle.
+      SQ = Y2*X1-X2*Y1
+      CQ = Z2*(X1*X1+Y1*Y1)-Z1*(X2*X1+Y2*Y1)
+      IF (SQ.EQ.0D0.AND.CQ.EQ.0D0) CQ=1D0
+      slDPAV = ATAN2(SQ,CQ)
+
+      END
diff --git a/math/slalib/dr2af.f b/math/slalib/dr2af.f
new file mode 100644
index 00000000..155f1f6b
--- /dev/null
+++ b/math/slalib/dr2af.f
@@ -0,0 +1,76 @@
+      SUBROUTINE slDRAF (NDP, ANGLE, SIGN, IDMSF)
+*+
+*     - - - - - -
+*      D R A F
+*     - - - - - -
+*
+*  Convert an angle in radians to degrees, arcminutes, arcseconds
+*  (double precision)
+*
+*  Given:
+*     NDP      i      number of decimal places of arcseconds
+*     ANGLE    d      angle in radians
+*
+*  Returned:
+*     SIGN     c      '+' or '-'
+*     IDMSF    i(4)   degrees, arcminutes, arcseconds, fraction
+*
+*  Notes:
+*
+*     1)  NDP less than zero is interpreted as zero.
+*
+*     2)  The largest useful value for NDP is determined by the size
+*         of ANGLE, the format of DOUBLE PRECISION floating-point
+*         numbers on the target machine, and the risk of overflowing
+*         IDMSF(4).  On some architectures, for ANGLE up to 2pi, the
+*         available floating-point precision corresponds roughly to
+*         NDP=12.  However, the practical limit is NDP=9, set by the
+*         capacity of a typical 32-bit IDMSF(4).
+*
+*     3)  The absolute value of ANGLE may exceed 2pi.  In cases where it
+*         does not, it is up to the caller to test for and handle the
+*         case where ANGLE is very nearly 2pi and rounds up to 360 deg,
+*         by testing for IDMSF(1)=360 and setting IDMSF(1-4) to zero.
+*
+*  Called:  slDDTF
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER NDP
+      DOUBLE PRECISION ANGLE
+      CHARACTER SIGN*(*)
+      INTEGER IDMSF(4)
+
+*  Hours to degrees * radians to turns
+      DOUBLE PRECISION F
+      PARAMETER (F=15D0/6.283185307179586476925287D0)
+
+
+
+*  Scale then use days to h,m,s routine
+      CALL slDDTF(NDP,ANGLE*F,SIGN,IDMSF)
+
+      END
diff --git a/math/slalib/dr2tf.f b/math/slalib/dr2tf.f
new file mode 100644
index 00000000..3f5edfbb
--- /dev/null
+++ b/math/slalib/dr2tf.f
@@ -0,0 +1,76 @@
+      SUBROUTINE slDRTF (NDP, ANGLE, SIGN, IHMSF)
+*+
+*     - - - - - -
+*      D R T F
+*     - - - - - -
+*
+*  Convert an angle in radians to hours, minutes, seconds
+*  (double precision)
+*
+*  Given:
+*     NDP      i      number of decimal places of seconds
+*     ANGLE    d      angle in radians
+*
+*  Returned:
+*     SIGN     c      '+' or '-'
+*     IHMSF    i(4)   hours, minutes, seconds, fraction
+*
+*  Notes:
+*
+*     1)  NDP less than zero is interpreted as zero.
+*
+*     2)  The largest useful value for NDP is determined by the size
+*         of ANGLE, the format of DOUBLE PRECISION floating-point
+*         numbers on the target machine, and the risk of overflowing
+*         IHMSF(4).  On some architectures, for ANGLE up to 2pi, the
+*         available floating-point precision corresponds roughly to
+*         NDP=12.  However, the practical limit is NDP=9, set by the
+*         capacity of a typical 32-bit IHMSF(4).
+*
+*     3)  The absolute value of ANGLE may exceed 2pi.  In cases where it
+*         does not, it is up to the caller to test for and handle the
+*         case where ANGLE is very nearly 2pi and rounds up to 24 hours,
+*         by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+*
+*  Called:  slDDTF
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER NDP
+      DOUBLE PRECISION ANGLE
+      CHARACTER SIGN*(*)
+      INTEGER IHMSF(4)
+
+*  Turns to radians
+      DOUBLE PRECISION T2R
+      PARAMETER (T2R=6.283185307179586476925287D0)
+
+
+
+*  Scale then use days to h,m,s routine
+      CALL slDDTF(NDP,ANGLE/T2R,SIGN,IHMSF)
+
+      END
diff --git a/math/slalib/drange.f b/math/slalib/drange.f
new file mode 100644
index 00000000..9f82c57e
--- /dev/null
+++ b/math/slalib/drange.f
@@ -0,0 +1,50 @@
+      DOUBLE PRECISION FUNCTION slDA1P (ANGLE)
+*+
+*     - - - - - - -
+*      D A 1 P
+*     - - - - - - -
+*
+*  Normalize angle into range +/- pi  (double precision)
+*
+*  Given:
+*     ANGLE     dp      the angle in radians
+*
+*  The result (double precision) is ANGLE expressed in the range +/- pi.
+*
+*  P.T.Wallace   Starlink   23 November 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION ANGLE
+
+      DOUBLE PRECISION DPI,D2PI
+      PARAMETER (DPI=3.141592653589793238462643D0)
+      PARAMETER (D2PI=6.283185307179586476925287D0)
+
+
+      slDA1P=MOD(ANGLE,D2PI)
+      IF (ABS(slDA1P).GE.DPI)
+     :          slDA1P=slDA1P-SIGN(D2PI,ANGLE)
+
+      END
diff --git a/math/slalib/dranrm.f b/math/slalib/dranrm.f
new file mode 100644
index 00000000..9325840c
--- /dev/null
+++ b/math/slalib/dranrm.f
@@ -0,0 +1,48 @@
+      DOUBLE PRECISION FUNCTION slDA2P (ANGLE)
+*+
+*     - - - - - - -
+*      D A 2 P
+*     - - - - - - -
+*
+*  Normalize angle into range 0-2 pi  (double precision)
+*
+*  Given:
+*     ANGLE     dp      the angle in radians
+*
+*  The result is ANGLE expressed in the range 0-2 pi.
+*
+*  Last revision:   22 July 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION ANGLE
+
+      DOUBLE PRECISION D2PI
+      PARAMETER (D2PI=6.283185307179586476925286766559D0)
+
+
+      slDA2P = MOD(ANGLE,D2PI)
+      IF (slDA2P.LT.0D0) slDA2P = slDA2P+D2PI
+
+      END
diff --git a/math/slalib/ds2c6.f b/math/slalib/ds2c6.f
new file mode 100644
index 00000000..7c7de506
--- /dev/null
+++ b/math/slalib/ds2c6.f
@@ -0,0 +1,75 @@
+      SUBROUTINE slDSC6 (A, B, R, AD, BD, RD, V)
+*+
+*     - - - - - -
+*      D S C 6
+*     - - - - - -
+*
+*  Conversion of position & velocity in spherical coordinates
+*  to Cartesian coordinates
+*
+*  (double precision)
+*
+*  Given:
+*     A     dp      longitude (radians)
+*     B     dp      latitude (radians)
+*     R     dp      radial coordinate
+*     AD    dp      longitude derivative (radians per unit time)
+*     BD    dp      latitude derivative (radians per unit time)
+*     RD    dp      radial derivative
+*
+*  Returned:
+*     V     dp(6)   Cartesian position & velocity vector
+*
+*  P.T.Wallace   Starlink   10 July 1993
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION A,B,R,AD,BD,RD,V(6)
+
+      DOUBLE PRECISION SA,CA,SB,CB,RCB,X,Y,RBD,W
+
+
+
+*  Useful functions
+      SA=SIN(A)
+      CA=COS(A)
+      SB=SIN(B)
+      CB=COS(B)
+      RCB=R*CB
+      X=RCB*CA
+      Y=RCB*SA
+      RBD=R*BD
+      W=RBD*SB-CB*RD
+
+*  Position
+      V(1)=X
+      V(2)=Y
+      V(3)=R*SB
+
+*  Velocity
+      V(4)=-Y*AD-W*CA
+      V(5)=X*AD-W*SA
+      V(6)=RBD*CB+SB*RD
+
+      END
diff --git a/math/slalib/ds2tp.f b/math/slalib/ds2tp.f
new file mode 100644
index 00000000..ee8104d7
--- /dev/null
+++ b/math/slalib/ds2tp.f
@@ -0,0 +1,85 @@
+      SUBROUTINE slDSTP (RA, DEC, RAZ, DECZ, XI, ETA, J)
+*+
+*     - - - - - -
+*      D S T P
+*     - - - - - -
+*
+*  Projection of spherical coordinates onto tangent plane:
+*  "gnomonic" projection - "standard coordinates" (double precision)
+*
+*  Given:
+*     RA,DEC      dp   spherical coordinates of point to be projected
+*     RAZ,DECZ    dp   spherical coordinates of tangent point
+*
+*  Returned:
+*     XI,ETA      dp   rectangular coordinates on tangent plane
+*     J           int  status:   0 = OK, star on tangent plane
+*                                1 = error, star too far from axis
+*                                2 = error, antistar on tangent plane
+*                                3 = error, antistar too far from axis
+*
+*  P.T.Wallace   Starlink   18 July 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RA,DEC,RAZ,DECZ,XI,ETA
+      INTEGER J
+
+      DOUBLE PRECISION SDECZ,SDEC,CDECZ,CDEC,
+     :                 RADIF,SRADIF,CRADIF,DENOM
+
+      DOUBLE PRECISION TINY
+      PARAMETER (TINY=1D-6)
+
+
+*  Trig functions
+      SDECZ=SIN(DECZ)
+      SDEC=SIN(DEC)
+      CDECZ=COS(DECZ)
+      CDEC=COS(DEC)
+      RADIF=RA-RAZ
+      SRADIF=SIN(RADIF)
+      CRADIF=COS(RADIF)
+
+*  Reciprocal of star vector length to tangent plane
+      DENOM=SDEC*SDECZ+CDEC*CDECZ*CRADIF
+
+*  Handle vectors too far from axis
+      IF (DENOM.GT.TINY) THEN
+         J=0
+      ELSE IF (DENOM.GE.0D0) THEN
+         J=1
+         DENOM=TINY
+      ELSE IF (DENOM.GT.-TINY) THEN
+         J=2
+         DENOM=-TINY
+      ELSE
+         J=3
+      END IF
+
+*  Compute tangent plane coordinates (even in dubious cases)
+      XI=CDEC*SRADIF/DENOM
+      ETA=(SDEC*CDECZ-CDEC*SDECZ*CRADIF)/DENOM
+
+      END
diff --git a/math/slalib/dsep.f b/math/slalib/dsep.f
new file mode 100644
index 00000000..6e7e9fff
--- /dev/null
+++ b/math/slalib/dsep.f
@@ -0,0 +1,61 @@
+      DOUBLE PRECISION FUNCTION slDSEP (A1, B1, A2, B2)
+*+
+*     - - - - -
+*      D S E P
+*     - - - - -
+*
+*  Angle between two points on a sphere.
+*
+*  (double precision)
+*
+*  Given:
+*     A1,B1    d     spherical coordinates of one point
+*     A2,B2    d     spherical coordinates of the other point
+*
+*  (The spherical coordinates are [RA,Dec], [Long,Lat] etc, in radians.)
+*
+*  The result is the angle, in radians, between the two points.  It
+*  is always positive.
+*
+*  Called:  slDS2C, slDSEPV
+*
+*  Last revision:   7 May 2000
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION A1,B1,A2,B2
+
+      DOUBLE PRECISION V1(3),V2(3)
+      DOUBLE PRECISION slDSEPV
+
+
+
+*  Convert coordinates from spherical to Cartesian.
+      CALL slDS2C(A1,B1,V1)
+      CALL slDS2C(A2,B2,V2)
+
+*  Angle between the vectors.
+      slDSEP = slDSEPV(V1,V2)
+
+      END
diff --git a/math/slalib/dsepv.f b/math/slalib/dsepv.f
new file mode 100644
index 00000000..6ff5d9d8
--- /dev/null
+++ b/math/slalib/dsepv.f
@@ -0,0 +1,77 @@
+      DOUBLE PRECISION FUNCTION slDSEPV (V1, V2)
+*+
+*     - - - - - -
+*      D S E P V
+*     - - - - - -
+*
+*  Angle between two vectors.
+*
+*  (double precision)
+*
+*  Given:
+*     V1      d(3)    first vector
+*     V2      d(3)    second vector
+*
+*  The result is the angle, in radians, between the two vectors.  It
+*  is always positive.
+*
+*  Notes:
+*
+*  1  There is no requirement for the vectors to be unit length.
+*
+*  2  If either vector is null, zero is returned.
+*
+*  3  The simplest formulation would use dot product alone.  However,
+*     this would reduce the accuracy for angles near zero and pi.  The
+*     algorithm uses both cross product and dot product, which maintains
+*     accuracy for all sizes of angle.
+*
+*  Called:  slDVXV, slDVN, slDVDV
+*
+*  Last revision:   14 June 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION V1(3),V2(3)
+
+      DOUBLE PRECISION V1XV2(3),WV(3),S,C
+      DOUBLE PRECISION slDVDV
+
+
+
+*  Modulus of cross product = sine multiplied by the two moduli.
+      CALL slDVXV(V1,V2,V1XV2)
+      CALL slDVN(V1XV2,WV,S)
+
+*  Dot product = cosine multiplied by the two moduli.
+      C = slDVDV(V1,V2)
+
+*  Angle between the vectors.
+      IF ( S.NE.0D0 .OR. C.NE.0D0 ) THEN
+         slDSEPV = ATAN2(S,C)
+      ELSE
+         slDSEPV = 0D0
+      END IF
+
+      END
diff --git a/math/slalib/dt.f b/math/slalib/dt.f
new file mode 100644
index 00000000..a012c677
--- /dev/null
+++ b/math/slalib/dt.f
@@ -0,0 +1,97 @@
+      DOUBLE PRECISION FUNCTION slDT (EPOCH)
+*+
+*     - - -
+*      D T
+*     - - -
+*
+*  Estimate the offset between dynamical time and Universal Time
+*  for a given historical epoch.
+*
+*  Given:
+*     EPOCH       d        (Julian) epoch (e.g. 1850D0)
+*
+*  The result is a rough estimate of ET-UT (after 1984, TT-UT) at
+*  the given epoch, in seconds.
+*
+*  Notes:
+*
+*  1  Depending on the epoch, one of three parabolic approximations
+*     is used:
+*
+*      before 979    Stephenson & Morrison's 390 BC to AD 948 model
+*      979 to 1708   Stephenson & Morrison's 948 to 1600 model
+*      after 1708    McCarthy & Babcock's post-1650 model
+*
+*     The breakpoints are chosen to ensure continuity:  they occur
+*     at places where the adjacent models give the same answer as
+*     each other.
+*
+*  2  The accuracy is modest, with errors of up to 20 sec during
+*     the interval since 1650, rising to perhaps 30 min by 1000 BC.
+*     Comparatively accurate values from AD 1600 are tabulated in
+*     the Astronomical Almanac (see section K8 of the 1995 AA).
+*
+*  3  The use of double-precision for both argument and result is
+*     purely for compatibility with other SLALIB time routines.
+*
+*  4  The models used are based on a lunar tidal acceleration value
+*     of -26.00 arcsec per century.
+*
+*  Reference:  Explanatory Supplement to the Astronomical Almanac,
+*              ed P.K.Seidelmann, University Science Books (1992),
+*              section 2.553, p83.  This contains references to
+*              the Stephenson & Morrison and McCarthy & Babcock
+*              papers.
+*
+*  P.T.Wallace   Starlink   1 March 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION EPOCH
+      DOUBLE PRECISION T,W,S
+
+
+*  Centuries since 1800
+      T=(EPOCH-1800D0)/100D0
+
+*  Select model
+      IF (EPOCH.GE.1708.185161980887D0) THEN
+
+*     Post-1708: use McCarthy & Babcock
+         W=T-0.19D0
+         S=5.156D0+13.3066D0*W*W
+      ELSE IF (EPOCH.GE.979.0258204760233D0) THEN
+
+*     979-1708: use Stephenson & Morrison's 948-1600 model
+         S=25.5D0*T*T
+      ELSE
+
+*     Pre-979: use Stephenson & Morrison's 390 BC to AD 948 model
+         S=1360.0D0+(320D0+44.3D0*T)*T
+      END IF
+
+*  Result
+      slDT=S
+
+      END
diff --git a/math/slalib/dtf2d.f b/math/slalib/dtf2d.f
new file mode 100644
index 00000000..757ed11e
--- /dev/null
+++ b/math/slalib/dtf2d.f
@@ -0,0 +1,73 @@
+      SUBROUTINE slDTFD (IHOUR, IMIN, SEC, DAYS, J)
+*+
+*     - - - - - -
+*      D T F D
+*     - - - - - -
+*
+*  Convert hours, minutes, seconds to days (double precision)
+*
+*  Given:
+*     IHOUR       int       hours
+*     IMIN        int       minutes
+*     SEC         dp        seconds
+*
+*  Returned:
+*     DAYS        dp        interval in days
+*     J           int       status:  0 = OK
+*                                    1 = IHOUR outside range 0-23
+*                                    2 = IMIN outside range 0-59
+*                                    3 = SEC outside range 0-59.999...
+*
+*  Notes:
+*
+*     1)  The result is computed even if any of the range checks fail.
+*
+*     2)  The sign must be dealt with outside this routine.
+*
+*  P.T.Wallace   Starlink   July 1984
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IHOUR,IMIN
+      DOUBLE PRECISION SEC,DAYS
+      INTEGER J
+
+*  Seconds per day
+      DOUBLE PRECISION D2S
+      PARAMETER (D2S=86400D0)
+
+
+
+*  Preset status
+      J=0
+
+*  Validate sec, min, hour
+      IF (SEC.LT.0D0.OR.SEC.GE.60D0) J=3
+      IF (IMIN.LT.0.OR.IMIN.GT.59) J=2
+      IF (IHOUR.LT.0.OR.IHOUR.GT.23) J=1
+
+*  Compute interval
+      DAYS=(60D0*(60D0*DBLE(IHOUR)+DBLE(IMIN))+SEC)/D2S
+
+      END
diff --git a/math/slalib/dtf2r.f b/math/slalib/dtf2r.f
new file mode 100644
index 00000000..f260e3e1
--- /dev/null
+++ b/math/slalib/dtf2r.f
@@ -0,0 +1,71 @@
+      SUBROUTINE slDTFR (IHOUR, IMIN, SEC, RAD, J)
+*+
+*     - - - - - -
+*      D T F R
+*     - - - - - -
+*
+*  Convert hours, minutes, seconds to radians (double precision)
+*
+*  Given:
+*     IHOUR       int       hours
+*     IMIN        int       minutes
+*     SEC         dp        seconds
+*
+*  Returned:
+*     RAD         dp        angle in radians
+*     J           int       status:  0 = OK
+*                                    1 = IHOUR outside range 0-23
+*                                    2 = IMIN outside range 0-59
+*                                    3 = SEC outside range 0-59.999...
+*
+*  Called:
+*     slDTFD
+*
+*  Notes:
+*
+*     1)  The result is computed even if any of the range checks fail.
+*
+*     2)  The sign must be dealt with outside this routine.
+*
+*  P.T.Wallace   Starlink   July 1984
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IHOUR,IMIN
+      DOUBLE PRECISION SEC,RAD
+      INTEGER J
+
+      DOUBLE PRECISION TURNS
+
+*  Turns to radians
+      DOUBLE PRECISION T2R
+      PARAMETER (T2R=6.283185307179586476925287D0)
+
+
+
+*  Convert to turns then radians
+      CALL slDTFD(IHOUR,IMIN,SEC,TURNS,J)
+      RAD=T2R*TURNS
+
+      END
diff --git a/math/slalib/dtp2s.f b/math/slalib/dtp2s.f
new file mode 100644
index 00000000..436057ea
--- /dev/null
+++ b/math/slalib/dtp2s.f
@@ -0,0 +1,60 @@
+      SUBROUTINE slDTPS (XI, ETA, RAZ, DECZ, RA, DEC)
+*+
+*     - - - - - -
+*      D T P S
+*     - - - - - -
+*
+*  Transform tangent plane coordinates into spherical
+*  (double precision)
+*
+*  Given:
+*     XI,ETA      dp   tangent plane rectangular coordinates
+*     RAZ,DECZ    dp   spherical coordinates of tangent point
+*
+*  Returned:
+*     RA,DEC      dp   spherical coordinates (0-2pi,+/-pi/2)
+*
+*  Called:        slDA2P
+*
+*  P.T.Wallace   Starlink   24 July 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION XI,ETA,RAZ,DECZ,RA,DEC
+
+      DOUBLE PRECISION slDA2P
+
+      DOUBLE PRECISION SDECZ,CDECZ,DENOM
+
+
+
+      SDECZ=SIN(DECZ)
+      CDECZ=COS(DECZ)
+
+      DENOM=CDECZ-ETA*SDECZ
+
+      RA=slDA2P(ATAN2(XI,DENOM)+RAZ)
+      DEC=ATAN2(SDECZ+ETA*CDECZ,SQRT(XI*XI+DENOM*DENOM))
+
+      END
diff --git a/math/slalib/dtp2v.f b/math/slalib/dtp2v.f
new file mode 100644
index 00000000..077df7a8
--- /dev/null
+++ b/math/slalib/dtp2v.f
@@ -0,0 +1,74 @@
+      SUBROUTINE slDTPV (XI, ETA, V0, V)
+*+
+*     - - - - - -
+*      D T P V
+*     - - - - - -
+*
+*  Given the tangent-plane coordinates of a star and the direction
+*  cosines of the tangent point, determine the direction cosines
+*  of the star.
+*
+*  (double precision)
+*
+*  Given:
+*     XI,ETA    d       tangent plane coordinates of star
+*     V0        d(3)    direction cosines of tangent point
+*
+*  Returned:
+*     V         d(3)    direction cosines of star
+*
+*  Notes:
+*
+*  1  If vector V0 is not of unit length, the returned vector V will
+*     be wrong.
+*
+*  2  If vector V0 points at a pole, the returned vector V will be
+*     based on the arbitrary assumption that the RA of the tangent
+*     point is zero.
+*
+*  3  This routine is the Cartesian equivalent of the routine slDTPS.
+*
+*  P.T.Wallace   Starlink   11 February 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION XI,ETA,V0(3),V(3)
+
+      DOUBLE PRECISION X,Y,Z,F,R
+
+
+      X=V0(1)
+      Y=V0(2)
+      Z=V0(3)
+      F=SQRT(1D0+XI*XI+ETA*ETA)
+      R=SQRT(X*X+Y*Y)
+      IF (R.EQ.0D0) THEN
+         R=1D-20
+         X=R
+      END IF
+      V(1)=(X-(XI*Y+ETA*X*Z)/R)/F
+      V(2)=(Y+(XI*X-ETA*Y*Z)/R)/F
+      V(3)=(Z+ETA*R)/F
+
+      END
diff --git a/math/slalib/dtps2c.f b/math/slalib/dtps2c.f
new file mode 100644
index 00000000..ce103804
--- /dev/null
+++ b/math/slalib/dtps2c.f
@@ -0,0 +1,109 @@
+      SUBROUTINE slDPSC (XI, ETA, RA, DEC, RAZ1, DECZ1,
+     :                                         RAZ2, DECZ2, N)
+*+
+*     - - - - - - -
+*      D P S C
+*     - - - - - - -
+*
+*  From the tangent plane coordinates of a star of known RA,Dec,
+*  determine the RA,Dec of the tangent point.
+*
+*  (double precision)
+*
+*  Given:
+*     XI,ETA      d    tangent plane rectangular coordinates
+*     RA,DEC      d    spherical coordinates
+*
+*  Returned:
+*     RAZ1,DECZ1  d    spherical coordinates of tangent point, solution 1
+*     RAZ2,DECZ2  d    spherical coordinates of tangent point, solution 2
+*     N           i    number of solutions:
+*                        0 = no solutions returned (note 2)
+*                        1 = only the first solution is useful (note 3)
+*                        2 = both solutions are useful (note 3)
+*
+*  Notes:
+*
+*  1  The RAZ1 and RAZ2 values are returned in the range 0-2pi.
+*
+*  2  Cases where there is no solution can only arise near the poles.
+*     For example, it is clearly impossible for a star at the pole
+*     itself to have a non-zero XI value, and hence it is
+*     meaningless to ask where the tangent point would have to be
+*     to bring about this combination of XI and DEC.
+*
+*  3  Also near the poles, cases can arise where there are two useful
+*     solutions.  The argument N indicates whether the second of the
+*     two solutions returned is useful.  N=1 indicates only one useful
+*     solution, the usual case;  under these circumstances, the second
+*     solution corresponds to the "over-the-pole" case, and this is
+*     reflected in the values of RAZ2 and DECZ2 which are returned.
+*
+*  4  The DECZ1 and DECZ2 values are returned in the range +/-pi, but
+*     in the usual, non-pole-crossing, case, the range is +/-pi/2.
+*
+*  5  This routine is the spherical equivalent of the routine slDPVC.
+*
+*  Called:  slDA2P
+*
+*  P.T.Wallace   Starlink   5 June 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION XI,ETA,RA,DEC,RAZ1,DECZ1,RAZ2,DECZ2
+      INTEGER N
+
+      DOUBLE PRECISION X2,Y2,SD,CD,SDF,R2,R,S,C
+
+      DOUBLE PRECISION slDA2P
+
+
+      X2=XI*XI
+      Y2=ETA*ETA
+      SD=SIN(DEC)
+      CD=COS(DEC)
+      SDF=SD*SQRT(1D0+X2+Y2)
+      R2=CD*CD*(1D0+Y2)-SD*SD*X2
+      IF (R2.GE.0D0) THEN
+         R=SQRT(R2)
+         S=SDF-ETA*R
+         C=SDF*ETA+R
+         IF (XI.EQ.0D0.AND.R.EQ.0D0) R=1D0
+         RAZ1=slDA2P(RA-ATAN2(XI,R))
+         DECZ1=ATAN2(S,C)
+         R=-R
+         S=SDF-ETA*R
+         C=SDF*ETA+R
+         RAZ2=slDA2P(RA-ATAN2(XI,R))
+         DECZ2=ATAN2(S,C)
+         IF (ABS(SDF).LT.1D0) THEN
+            N=1
+         ELSE
+            N=2
+         END IF
+      ELSE
+         N=0
+      END IF
+
+      END
diff --git a/math/slalib/dtpv2c.f b/math/slalib/dtpv2c.f
new file mode 100644
index 00000000..930ca9ff
--- /dev/null
+++ b/math/slalib/dtpv2c.f
@@ -0,0 +1,101 @@
+      SUBROUTINE slDPVC (XI, ETA, V, V01, V02, N)
+*+
+*     - - - - - - -
+*      D P V C
+*     - - - - - - -
+*
+*  Given the tangent-plane coordinates of a star and its direction
+*  cosines, determine the direction cosines of the tangent-point.
+*
+*  (double precision)
+*
+*  Given:
+*     XI,ETA    d       tangent plane coordinates of star
+*     V         d(3)    direction cosines of star
+*
+*  Returned:
+*     V01       d(3)    direction cosines of tangent point, solution 1
+*     V02       d(3)    direction cosines of tangent point, solution 2
+*     N         i       number of solutions:
+*                         0 = no solutions returned (note 2)
+*                         1 = only the first solution is useful (note 3)
+*                         2 = both solutions are useful (note 3)
+*
+*  Notes:
+*
+*  1  The vector V must be of unit length or the result will be wrong.
+*
+*  2  Cases where there is no solution can only arise near the poles.
+*     For example, it is clearly impossible for a star at the pole
+*     itself to have a non-zero XI value, and hence it is meaningless
+*     to ask where the tangent point would have to be.
+*
+*  3  Also near the poles, cases can arise where there are two useful
+*     solutions.  The argument N indicates whether the second of the
+*     two solutions returned is useful.  N=1 indicates only one useful
+*     solution, the usual case;  under these circumstances, the second
+*     solution can be regarded as valid if the vector V02 is interpreted
+*     as the "over-the-pole" case.
+*
+*  4  This routine is the Cartesian equivalent of the routine slDPSC.
+*
+*  P.T.Wallace   Starlink   5 June 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION XI,ETA,V(3),V01(3),V02(3)
+      INTEGER N
+
+      DOUBLE PRECISION X,Y,Z,RXY2,XI2,ETA2P1,SDF,R2,R,C
+
+
+      X=V(1)
+      Y=V(2)
+      Z=V(3)
+      RXY2=X*X+Y*Y
+      XI2=XI*XI
+      ETA2P1=ETA*ETA+1D0
+      SDF=Z*SQRT(XI2+ETA2P1)
+      R2=RXY2*ETA2P1-Z*Z*XI2
+      IF (R2.GT.0D0) THEN
+         R=SQRT(R2)
+         C=(SDF*ETA+R)/(ETA2P1*SQRT(RXY2*(R2+XI2)))
+         V01(1)=C*(X*R+Y*XI)
+         V01(2)=C*(Y*R-X*XI)
+         V01(3)=(SDF-ETA*R)/ETA2P1
+         R=-R
+         C=(SDF*ETA+R)/(ETA2P1*SQRT(RXY2*(R2+XI2)))
+         V02(1)=C*(X*R+Y*XI)
+         V02(2)=C*(Y*R-X*XI)
+         V02(3)=(SDF-ETA*R)/ETA2P1
+         IF (ABS(SDF).LT.1D0) THEN
+            N=1
+         ELSE
+            N=2
+         END IF
+      ELSE
+         N=0
+      END IF
+
+      END
diff --git a/math/slalib/dtt.f b/math/slalib/dtt.f
new file mode 100644
index 00000000..38e10ec8
--- /dev/null
+++ b/math/slalib/dtt.f
@@ -0,0 +1,64 @@
+      DOUBLE PRECISION FUNCTION slDTT (UTC)
+*+
+*     - - - -
+*      D T T
+*     - - - -
+*
+*  Increment to be applied to Coordinated Universal Time UTC to give
+*  Terrestrial Time TT (formerly Ephemeris Time ET)
+*
+*  (double precision)
+*
+*  Given:
+*     UTC      d      UTC date as a modified JD (JD-2400000.5)
+*
+*  Result:  TT-UTC in seconds
+*
+*  Notes:
+*
+*  1  The UTC is specified to be a date rather than a time to indicate
+*     that care needs to be taken not to specify an instant which lies
+*     within a leap second.  Though in most cases UTC can include the
+*     fractional part, correct behaviour on the day of a leap second
+*     can only be guaranteed up to the end of the second 23:59:59.
+*
+*  2  Pre 1972 January 1 a fixed value of 10 + ET-TAI is returned.
+*
+*  3  See also the routine slDT, which roughly estimates ET-UT for
+*     historical epochs.
+*
+*  Called:  slDAT
+*
+*  P.T.Wallace   Starlink   6 December 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION UTC
+
+      DOUBLE PRECISION slDAT
+
+
+      slDTT=32.184D0+slDAT(UTC)
+
+      END
diff --git a/math/slalib/dv2tp.f b/math/slalib/dv2tp.f
new file mode 100644
index 00000000..5d55f7f6
--- /dev/null
+++ b/math/slalib/dv2tp.f
@@ -0,0 +1,96 @@
+      SUBROUTINE slDVTP (V, V0, XI, ETA, J)
+*+
+*     - - - - - -
+*      D V T P
+*     - - - - - -
+*
+*  Given the direction cosines of a star and of the tangent point,
+*  determine the star's tangent-plane coordinates.
+*
+*  (double precision)
+*
+*  Given:
+*     V         d(3)    direction cosines of star
+*     V0        d(3)    direction cosines of tangent point
+*
+*  Returned:
+*     XI,ETA    d       tangent plane coordinates of star
+*     J         i       status:   0 = OK
+*                                 1 = error, star too far from axis
+*                                 2 = error, antistar on tangent plane
+*                                 3 = error, antistar too far from axis
+*
+*  Notes:
+*
+*  1  If vector V0 is not of unit length, or if vector V is of zero
+*     length, the results will be wrong.
+*
+*  2  If V0 points at a pole, the returned XI,ETA will be based on the
+*     arbitrary assumption that the RA of the tangent point is zero.
+*
+*  3  This routine is the Cartesian equivalent of the routine slDSTP.
+*
+*  P.T.Wallace   Starlink   27 November 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION V(3),V0(3),XI,ETA
+      INTEGER J
+
+      DOUBLE PRECISION X,Y,Z,X0,Y0,Z0,R2,R,W,D
+
+      DOUBLE PRECISION TINY
+      PARAMETER (TINY=1D-6)
+
+
+      X=V(1)
+      Y=V(2)
+      Z=V(3)
+      X0=V0(1)
+      Y0=V0(2)
+      Z0=V0(3)
+      R2=X0*X0+Y0*Y0
+      R=SQRT(R2)
+      IF (R.EQ.0D0) THEN
+         R=1D-20
+         X0=R
+      END IF
+      W=X*X0+Y*Y0
+      D=W+Z*Z0
+      IF (D.GT.TINY) THEN
+         J=0
+      ELSE IF (D.GE.0D0) THEN
+         J=1
+         D=TINY
+      ELSE IF (D.GT.-TINY) THEN
+         J=2
+         D=-TINY
+      ELSE
+         J=3
+      END IF
+      D=D*R
+      XI=(Y*X0-X*Y0)/D
+      ETA=(Z*R2-Z0*W)/D
+
+      END
diff --git a/math/slalib/dvdv.f b/math/slalib/dvdv.f
new file mode 100644
index 00000000..b80d5877
--- /dev/null
+++ b/math/slalib/dvdv.f
@@ -0,0 +1,45 @@
+      DOUBLE PRECISION FUNCTION slDVDV (VA, VB)
+*+
+*     - - - - -
+*      D V D V
+*     - - - - -
+*
+*  Scalar product of two 3-vectors  (double precision)
+*
+*  Given:
+*      VA      dp(3)     first vector
+*      VB      dp(3)     second vector
+*
+*  The result is the scalar product VA.VB (double precision)
+*
+*  P.T.Wallace   Starlink   November 1984
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION VA(3),VB(3)
+
+
+      slDVDV=VA(1)*VB(1)+VA(2)*VB(2)+VA(3)*VB(3)
+
+      END
diff --git a/math/slalib/dvn.f b/math/slalib/dvn.f
new file mode 100644
index 00000000..68774c77
--- /dev/null
+++ b/math/slalib/dvn.f
@@ -0,0 +1,70 @@
+      SUBROUTINE slDVN (V, UV, VM)
+*+
+*     - - - -
+*      D V N
+*     - - - -
+*
+*  Normalizes a 3-vector also giving the modulus (double precision)
+*
+*  Given:
+*     V       d(3)      vector
+*
+*  Returned:
+*     UV      d(3)      unit vector in direction of V
+*     VM      d         modulus of V
+*
+*  Notes:
+*
+*  1  If the modulus of V is zero, UV is set to zero as well.
+*
+*  2  To comply with the ANSI Fortran 77 standard, V and UV must be
+*     different arrays.  However, the routine is coded so as to work
+*     properly on most platforms even if this rule is violated.
+*
+*  Last revision:   22 July 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION V(3),UV(3),VM
+
+      INTEGER I
+      DOUBLE PRECISION W1,W2
+
+
+*  Modulus.
+      W1 = 0D0
+      DO I=1,3
+         W2 = V(I)
+         W1 = W1+W2*W2
+      END DO
+      W1 = SQRT(W1)
+      VM = W1
+
+*  Normalize the vector.
+      IF (W1.LE.0D0) W1 = 1D0
+      DO I=1,3
+         UV(I) = V(I)/W1
+      END DO
+
+      END
diff --git a/math/slalib/dvxv.f b/math/slalib/dvxv.f
new file mode 100644
index 00000000..1c422fb7
--- /dev/null
+++ b/math/slalib/dvxv.f
@@ -0,0 +1,57 @@
+      SUBROUTINE slDVXV (VA, VB, VC)
+*+
+*     - - - - -
+*      D V X V
+*     - - - - -
+*
+*  Vector product of two 3-vectors  (double precision)
+*
+*  Given:
+*      VA      dp(3)     first vector
+*      VB      dp(3)     second vector
+*
+*  Returned:
+*      VC      dp(3)     vector result
+*
+*  P.T.Wallace   Starlink   March 1986
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION VA(3),VB(3),VC(3)
+
+      DOUBLE PRECISION VW(3)
+      INTEGER I
+
+
+*  Form the vector product VA cross VB
+      VW(1)=VA(2)*VB(3)-VA(3)*VB(2)
+      VW(2)=VA(3)*VB(1)-VA(1)*VB(3)
+      VW(3)=VA(1)*VB(2)-VA(2)*VB(1)
+
+*  Return the result
+      DO I=1,3
+         VC(I)=VW(I)
+      END DO
+
+      END
diff --git a/math/slalib/e2h.f b/math/slalib/e2h.f
new file mode 100644
index 00000000..3905bbb7
--- /dev/null
+++ b/math/slalib/e2h.f
@@ -0,0 +1,107 @@
+      SUBROUTINE slE2H (HA, DEC, PHI, AZ, EL)
+*+
+*     - - - -
+*      E 2 H
+*     - - - -
+*
+*  Equatorial to horizon coordinates:  HA,Dec to Az,El
+*
+*  (single precision)
+*
+*  Given:
+*     HA      r     hour angle
+*     DEC     r     declination
+*     PHI     r     observatory latitude
+*
+*  Returned:
+*     AZ      r     azimuth
+*     EL      r     elevation
+*
+*  Notes:
+*
+*  1)  All the arguments are angles in radians.
+*
+*  2)  Azimuth is returned in the range 0-2pi;  north is zero,
+*      and east is +pi/2.  Elevation is returned in the range
+*      +/-pi/2.
+*
+*  3)  The latitude must be geodetic.  In critical applications,
+*      corrections for polar motion should be applied.
+*
+*  4)  In some applications it will be important to specify the
+*      correct type of hour angle and declination in order to
+*      produce the required type of azimuth and elevation.  In
+*      particular, it may be important to distinguish between
+*      elevation as affected by refraction, which would
+*      require the "observed" HA,Dec, and the elevation
+*      in vacuo, which would require the "topocentric" HA,Dec.
+*      If the effects of diurnal aberration can be neglected, the
+*      "apparent" HA,Dec may be used instead of the topocentric
+*      HA,Dec.
+*
+*  5)  No range checking of arguments is carried out.
+*
+*  6)  In applications which involve many such calculations, rather
+*      than calling the present routine it will be more efficient to
+*      use inline code, having previously computed fixed terms such
+*      as sine and cosine of latitude, and (for tracking a star)
+*      sine and cosine of declination.
+*
+*  P.T.Wallace   Starlink   9 July 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL HA,DEC,PHI,AZ,EL
+
+      REAL R2PI
+      PARAMETER (R2PI=6.283185307179586476925286766559)
+
+      REAL SH,CH,SD,CD,SP,CP,X,Y,Z,R,A
+
+
+*  Useful trig functions
+      SH=SIN(HA)
+      CH=COS(HA)
+      SD=SIN(DEC)
+      CD=COS(DEC)
+      SP=SIN(PHI)
+      CP=COS(PHI)
+
+*  Az,El as x,y,z
+      X=-CH*CD*SP+SD*CP
+      Y=-SH*CD
+      Z=CH*CD*CP+SD*SP
+
+*  To spherical
+      R=SQRT(X*X+Y*Y)
+      IF (R.EQ.0.0) THEN
+         A=0.0
+      ELSE
+         A=ATAN2(Y,X)
+      END IF
+      IF (A.LT.0.0) A=A+R2PI
+      AZ=A
+      EL=ATAN2(Z,R)
+
+      END
diff --git a/math/slalib/earth.f b/math/slalib/earth.f
new file mode 100644
index 00000000..5d2204af
--- /dev/null
+++ b/math/slalib/earth.f
@@ -0,0 +1,130 @@
+      SUBROUTINE slERTH (IY, ID, FD, PV)
+*+
+*     - - - - - -
+*      E R T H
+*     - - - - - -
+*
+*  Approximate heliocentric position and velocity of the Earth
+*
+*  Given:
+*     IY       I       year
+*     ID       I       day in year (1 = Jan 1st)
+*     FD       R       fraction of day
+*
+*  Returned:
+*     PV       R(6)    Earth position & velocity vector
+*
+*  Notes:
+*
+*  1  The date and time is TDB (loosely ET) in a Julian calendar
+*     which has been aligned to the ordinary Gregorian
+*     calendar for the interval 1900 March 1 to 2100 February 28.
+*     The year and day can be obtained by calling slCAYD or
+*     slCLYD.
+*
+*  2  The Earth heliocentric 6-vector is mean equator and equinox
+*     of date.  Position part, PV(1-3), is in AU;  velocity part,
+*     PV(4-6), is in AU/sec.
+*
+*  3  Max/RMS errors 1950-2050:
+*       13/5 E-5 AU = 19200/7600 km in position
+*       47/26 E-10 AU/s = 0.0070/0.0039 km/s in speed
+*
+*  4  More accurate results are obtainable with the routines slEVP
+*     and slEPV.
+*
+*  Last revision:   5 April 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IY,ID
+      REAL FD,PV(6)
+
+      INTEGER IY4
+      REAL TWOPI,SPEED,REMB,SEMB,YI,YF,T,ELM,GAMMA,EM,ELT,EPS0,
+     :     E,ESQ,V,R,ELMM,COSELT,SINEPS,COSEPS,W1,W2,SELMM,CELMM
+
+      PARAMETER (TWOPI=6.28318530718)
+
+*  Mean orbital speed of Earth, AU/s
+      PARAMETER (SPEED=1.9913E-7)
+
+*  Mean Earth:EMB distance and speed, AU and AU/s
+      PARAMETER (REMB=3.12E-5,SEMB=8.31E-11)
+
+
+
+*  Whole years & fraction of year, and years since J1900.0
+      YI=FLOAT(IY-1900)
+      IY4=MOD(MOD(IY,4)+4,4)
+      YF=(FLOAT(4*(ID-1/(IY4+1))-IY4-2)+4.0*FD)/1461.0
+      T=YI+YF
+
+*  Geometric mean longitude of Sun
+*  (cf 4.881627938+6.283319509911*T MOD 2PI)
+      ELM=MOD(4.881628+TWOPI*YF+0.00013420*T,TWOPI)
+
+*  Mean longitude of perihelion
+      GAMMA=4.908230+3.0005E-4*T
+
+*  Mean anomaly
+      EM=ELM-GAMMA
+
+*  Mean obliquity
+      EPS0=0.40931975-2.27E-6*T
+
+*  Eccentricity
+      E=0.016751-4.2E-7*T
+      ESQ=E*E
+
+*  True anomaly
+      V=EM+2.0*E*SIN(EM)+1.25*ESQ*SIN(2.0*EM)
+
+*  True ecliptic longitude
+      ELT=V+GAMMA
+
+*  True distance
+      R=(1.0-ESQ)/(1.0+E*COS(V))
+
+*  Moon's mean longitude
+      ELMM=MOD(4.72+83.9971*T,TWOPI)
+
+*  Useful functions
+      COSELT=COS(ELT)
+      SINEPS=SIN(EPS0)
+      COSEPS=COS(EPS0)
+      W1=-R*SIN(ELT)
+      W2=-SPEED*(COSELT+E*COS(GAMMA))
+      SELMM=SIN(ELMM)
+      CELMM=COS(ELMM)
+
+*  Earth position and velocity
+      PV(1)=-R*COSELT-REMB*CELMM
+      PV(2)=(W1-REMB*SELMM)*COSEPS
+      PV(3)=W1*SINEPS
+      PV(4)=SPEED*(SIN(ELT)+E*SIN(GAMMA))+SEMB*SELMM
+      PV(5)=(W2-SEMB*CELMM)*COSEPS
+      PV(6)=W2*SINEPS
+
+      END
diff --git a/math/slalib/ecleq.f b/math/slalib/ecleq.f
new file mode 100644
index 00000000..9c7d8ed3
--- /dev/null
+++ b/math/slalib/ecleq.f
@@ -0,0 +1,73 @@
+      SUBROUTINE slECEQ (DL, DB, DATE, DR, DD)
+*+
+*     - - - - - -
+*      E C E Q
+*     - - - - - -
+*
+*  Transformation from ecliptic coordinates to
+*  J2000.0 equatorial coordinates (double precision)
+*
+*  Given:
+*     DL,DB       dp      ecliptic longitude and latitude
+*                           (mean of date, IAU 1980 theory, radians)
+*     DATE        dp      TDB (loosely ET) as Modified Julian Date
+*                                              (JD-2400000.5)
+*  Returned:
+*     DR,DD       dp      J2000.0 mean RA,Dec (radians)
+*
+*  Called:
+*     slDS2C, slECMA, slDIMV, slPREC, slEPJ, slDC2S,
+*     slDA2P, slDA1P
+*
+*  P.T.Wallace   Starlink   March 1986
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DL,DB,DATE,DR,DD
+
+      DOUBLE PRECISION slEPJ,slDA2P,slDA1P
+
+      DOUBLE PRECISION RMAT(3,3),V1(3),V2(3)
+
+
+
+*  Spherical to Cartesian
+      CALL slDS2C(DL,DB,V1)
+
+*  Ecliptic to equatorial
+      CALL slECMA(DATE,RMAT)
+      CALL slDIMV(RMAT,V1,V2)
+
+*  Mean of date to J2000
+      CALL slPREC(2000D0,slEPJ(DATE),RMAT)
+      CALL slDIMV(RMAT,V2,V1)
+
+*  Cartesian to spherical
+      CALL slDC2S(V1,DR,DD)
+
+*  Express in conventional ranges
+      DR=slDA2P(DR)
+      DD=slDA1P(DD)
+
+      END
diff --git a/math/slalib/ecmat.f b/math/slalib/ecmat.f
new file mode 100644
index 00000000..8213dd8f
--- /dev/null
+++ b/math/slalib/ecmat.f
@@ -0,0 +1,70 @@
+      SUBROUTINE slECMA (DATE, RMAT)
+*+
+*     - - - - - -
+*      E C M A
+*     - - - - - -
+*
+*  Form the equatorial to ecliptic rotation matrix - IAU 1980 theory
+*  (double precision)
+*
+*  Given:
+*     DATE     dp         TDB (loosely ET) as Modified Julian Date
+*                                            (JD-2400000.5)
+*  Returned:
+*     RMAT     dp(3,3)    matrix
+*
+*  Reference:
+*     Murray,C.A., Vectorial Astrometry, section 4.3.
+*
+*  Note:
+*    The matrix is in the sense   V(ecl)  =  RMAT * V(equ);  the
+*    equator, equinox and ecliptic are mean of date.
+*
+*  Called:  slDEUL
+*
+*  P.T.Wallace   Starlink   23 August 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,RMAT(3,3)
+
+*  Arc seconds to radians
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+      DOUBLE PRECISION T,EPS0
+
+
+
+*  Interval between basic epoch J2000.0 and current epoch (JC)
+      T = (DATE-51544.5D0)/36525D0
+
+*  Mean obliquity
+      EPS0 = AS2R*
+     :   (84381.448D0+(-46.8150D0+(-0.00059D0+0.001813D0*T)*T)*T)
+
+*  Matrix
+      CALL slDEUL('X',EPS0,0D0,0D0,RMAT)
+
+      END
diff --git a/math/slalib/ecor.f b/math/slalib/ecor.f
new file mode 100644
index 00000000..5405bc7d
--- /dev/null
+++ b/math/slalib/ecor.f
@@ -0,0 +1,96 @@
+      SUBROUTINE slECOR (RM, DM, IY, ID, FD, RV, TL)
+*+
+*     - - - - -
+*      E C O R
+*     - - - - -
+*
+*  Component of Earth orbit velocity and heliocentric
+*  light time in a given direction (single precision)
+*
+*  Given:
+*     RM,DM    real    mean RA, Dec of date (radians)
+*     IY       int     year
+*     ID       int     day in year (1 = Jan 1st)
+*     FD       real    fraction of day
+*
+*  Returned:
+*     RV       real    component of Earth orbital velocity (km/sec)
+*     TL       real    component of heliocentric light time (sec)
+*
+*  Notes:
+*
+*  1  The date and time is TDB (loosely ET) in a Julian calendar
+*     which has been aligned to the ordinary Gregorian
+*     calendar for the interval 1900 March 1 to 2100 February 28.
+*     The year and day can be obtained by calling slCAYD or
+*     slCLYD.
+*
+*  2  Sign convention:
+*
+*     The velocity component is +ve when the Earth is receding from
+*     the given point on the sky.  The light time component is +ve
+*     when the Earth lies between the Sun and the given point on
+*     the sky.
+*
+*  3  Accuracy:
+*
+*     The velocity component is usually within 0.004 km/s of the
+*     correct value and is never in error by more than 0.007 km/s.
+*     The error in light time correction is about 0.03s at worst,
+*     but is usually better than 0.01s. For applications requiring
+*     higher accuracy, see the slEVP and slEPV routines.
+*
+*  Called:  slERTH, slCS2C, slVDV
+*
+*  Last revision:   5 April 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL RM,DM
+      INTEGER IY,ID
+      REAL FD,RV,TL
+
+      REAL slVDV
+
+      REAL PV(6),V(3),AUKM,AUSEC
+
+*  AU to km and light sec (1985 Almanac)
+      PARAMETER (AUKM=1.4959787066E8,
+     :           AUSEC=499.0047837)
+
+
+
+*  Sun:Earth position & velocity vector
+      CALL slERTH(IY,ID,FD,PV)
+
+*  Star position vector
+      CALL slCS2C(RM,DM,V)
+
+*  Velocity component
+      RV=-AUKM*slVDV(PV(4),V)
+
+*  Light time component
+      TL=AUSEC*slVDV(PV(1),V)
+
+      END
diff --git a/math/slalib/eg50.f b/math/slalib/eg50.f
new file mode 100644
index 00000000..85b65811
--- /dev/null
+++ b/math/slalib/eg50.f
@@ -0,0 +1,108 @@
+      SUBROUTINE slEG50 (DR, DD, DL, DB)
+*+
+*     - - - - -
+*      E G 5 0
+*     - - - - -
+*
+*  Transformation from B1950.0 'FK4' equatorial coordinates to
+*  IAU 1958 galactic coordinates (double precision)
+*
+*  Given:
+*     DR,DD       dp       B1950.0 'FK4' RA,Dec
+*
+*  Returned:
+*     DL,DB       dp       galactic longitude and latitude L2,B2
+*
+*  (all arguments are radians)
+*
+*  Called:
+*     slDS2C, slDMXV, slDC2S, slSUET, slDA2P, slDA1P
+*
+*  Note:
+*     The equatorial coordinates are B1950.0 'FK4'.  Use the
+*     routine slEQGA if conversion from J2000.0 coordinates
+*     is required.
+*
+*  Reference:
+*     Blaauw et al, Mon.Not.R.Astron.Soc.,121,123 (1960)
+*
+*  P.T.Wallace   Starlink   5 September 1993
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DR,DD,DL,DB
+
+      DOUBLE PRECISION slDA2P,slDA1P
+
+      DOUBLE PRECISION V1(3),V2(3),R,D
+
+*
+*  L2,B2 system of galactic coordinates
+*
+*  P = 192.25       RA of galactic north pole (mean B1950.0)
+*  Q =  62.6        inclination of galactic to mean B1950.0 equator
+*  R =  33          longitude of ascending node
+*
+*  P,Q,R are degrees
+*
+*
+*  Equatorial to galactic rotation matrix
+*
+*  The Euler angles are P, Q, 90-R, about the z then y then
+*  z axes.
+*
+*         +CP.CQ.SR-SP.CR     +SP.CQ.SR+CP.CR     -SQ.SR
+*
+*         -CP.CQ.CR-SP.SR     -SP.CQ.CR+CP.SR     +SQ.CR
+*
+*         +CP.SQ              +SP.SQ              +CQ
+*
+
+      DOUBLE PRECISION RMAT(3,3)
+      DATA RMAT(1,1),RMAT(1,2),RMAT(1,3),
+     :     RMAT(2,1),RMAT(2,2),RMAT(2,3),
+     :     RMAT(3,1),RMAT(3,2),RMAT(3,3) /
+     : -0.066988739415D0,-0.872755765852D0,-0.483538914632D0,
+     : +0.492728466075D0,-0.450346958020D0,+0.744584633283D0,
+     : -0.867600811151D0,-0.188374601723D0,+0.460199784784D0 /
+
+
+
+*  Remove E-terms
+      CALL slSUET(DR,DD,1950D0,R,D)
+
+*  Spherical to Cartesian
+      CALL slDS2C(R,D,V1)
+
+*  Rotate to galactic
+      CALL slDMXV(RMAT,V1,V2)
+
+*  Cartesian to spherical
+      CALL slDC2S(V2,DL,DB)
+
+*  Express angles in conventional ranges
+      DL=slDA2P(DL)
+      DB=slDA1P(DB)
+
+      END
diff --git a/math/slalib/el2ue.f b/math/slalib/el2ue.f
new file mode 100644
index 00000000..4edb620a
--- /dev/null
+++ b/math/slalib/el2ue.f
@@ -0,0 +1,329 @@
+      SUBROUTINE slELUE (DATE, JFORM, EPOCH, ORBINC, ANODE,
+     :                      PERIH, AORQ, E, AORL, DM,
+     :                      U, JSTAT)
+*+
+*     - - - - - -
+*      E L U E
+*     - - - - - -
+*
+*  Transform conventional osculating orbital elements into "universal"
+*  form.
+*
+*  Given:
+*     DATE    d      epoch (TT MJD) of osculation (Note 3)
+*     JFORM   i      choice of element set (1-3, Note 6)
+*     EPOCH   d      epoch (TT MJD) of the elements
+*     ORBINC  d      inclination (radians)
+*     ANODE   d      longitude of the ascending node (radians)
+*     PERIH   d      longitude or argument of perihelion (radians)
+*     AORQ    d      mean distance or perihelion distance (AU)
+*     E       d      eccentricity
+*     AORL    d      mean anomaly or longitude (radians, JFORM=1,2 only)
+*     DM      d      daily motion (radians, JFORM=1 only)
+*
+*  Returned:
+*     U       d(13)  universal orbital elements (Note 1)
+*
+*               (1)  combined mass (M+m)
+*               (2)  total energy of the orbit (alpha)
+*               (3)  reference (osculating) epoch (t0)
+*             (4-6)  position at reference epoch (r0)
+*             (7-9)  velocity at reference epoch (v0)
+*              (10)  heliocentric distance at reference epoch
+*              (11)  r0.v0
+*              (12)  date (t)
+*              (13)  universal eccentric anomaly (psi) of date, approx
+*
+*     JSTAT   i      status:  0 = OK
+*                            -1 = illegal JFORM
+*                            -2 = illegal E
+*                            -3 = illegal AORQ
+*                            -4 = illegal DM
+*                            -5 = numerical error
+*
+*  Called:  slUEPV, slPVUE
+*
+*  Notes
+*
+*  1  The "universal" elements are those which define the orbit for the
+*     purposes of the method of universal variables (see reference).
+*     They consist of the combined mass of the two bodies, an epoch,
+*     and the position and velocity vectors (arbitrary reference frame)
+*     at that epoch.  The parameter set used here includes also various
+*     quantities that can, in fact, be derived from the other
+*     information.  This approach is taken to avoiding unnecessary
+*     computation and loss of accuracy.  The supplementary quantities
+*     are (i) alpha, which is proportional to the total energy of the
+*     orbit, (ii) the heliocentric distance at epoch, (iii) the
+*     outwards component of the velocity at the given epoch, (iv) an
+*     estimate of psi, the "universal eccentric anomaly" at a given
+*     date and (v) that date.
+*
+*  2  The companion routine is slUEPV.  This takes the set of numbers
+*     that the present routine outputs and uses them to derive the
+*     object's position and velocity.  A single prediction requires one
+*     call to the present routine followed by one call to slUEPV;
+*     for convenience, the two calls are packaged as the routine
+*     slPLNE.  Multiple predictions may be made by again calling the
+*     present routine once, but then calling slUEPV multiple times,
+*     which is faster than multiple calls to slPLNE.
+*
+*  3  DATE is the epoch of osculation.  It is in the TT timescale
+*     (formerly Ephemeris Time, ET) and is a Modified Julian Date
+*     (JD-2400000.5).
+*
+*  4  The supplied orbital elements are with respect to the J2000
+*     ecliptic and equinox.  The position and velocity parameters
+*     returned in the array U are with respect to the mean equator and
+*     equinox of epoch J2000, and are for the perihelion prior to the
+*     specified epoch.
+*
+*  5  The universal elements returned in the array U are in canonical
+*     units (solar masses, AU and canonical days).
+*
+*  6  Three different element-format options are available:
+*
+*     Option JFORM=1, suitable for the major planets:
+*
+*     EPOCH  = epoch of elements (TT MJD)
+*     ORBINC = inclination i (radians)
+*     ANODE  = longitude of the ascending node, big omega (radians)
+*     PERIH  = longitude of perihelion, curly pi (radians)
+*     AORQ   = mean distance, a (AU)
+*     E      = eccentricity, e (range 0 to <1)
+*     AORL   = mean longitude L (radians)
+*     DM     = daily motion (radians)
+*
+*     Option JFORM=2, suitable for minor planets:
+*
+*     EPOCH  = epoch of elements (TT MJD)
+*     ORBINC = inclination i (radians)
+*     ANODE  = longitude of the ascending node, big omega (radians)
+*     PERIH  = argument of perihelion, little omega (radians)
+*     AORQ   = mean distance, a (AU)
+*     E      = eccentricity, e (range 0 to <1)
+*     AORL   = mean anomaly M (radians)
+*
+*     Option JFORM=3, suitable for comets:
+*
+*     EPOCH  = epoch of perihelion (TT MJD)
+*     ORBINC = inclination i (radians)
+*     ANODE  = longitude of the ascending node, big omega (radians)
+*     PERIH  = argument of perihelion, little omega (radians)
+*     AORQ   = perihelion distance, q (AU)
+*     E      = eccentricity, e (range 0 to 10)
+*
+*  7  Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
+*     not accessed.
+*
+*  8  The algorithm was originally adapted from the EPHSLA program of
+*     D.H.P.Jones (private communication, 1996).  The method is based
+*     on Stumpff's Universal Variables.
+*
+*  Reference:  Everhart & Pitkin, Am.J.Phys. 51, 712 (1983).
+*
+*  Last revision:   8 September 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE
+      INTEGER JFORM
+      DOUBLE PRECISION EPOCH,ORBINC,ANODE,PERIH,AORQ,E,AORL,DM,U(13)
+      INTEGER JSTAT
+
+*  Gaussian gravitational constant (exact)
+      DOUBLE PRECISION GCON
+      PARAMETER (GCON=0.01720209895D0)
+
+*  Sin and cos of J2000 mean obliquity (IAU 1976)
+      DOUBLE PRECISION SE,CE
+      PARAMETER (SE=0.3977771559319137D0,
+     :           CE=0.9174820620691818D0)
+
+      INTEGER J
+
+      DOUBLE PRECISION PHT,ARGPH,Q,W,CM,ALPHA,PHS,SW,CW,SI,CI,SO,CO,
+     :                 X,Y,Z,PX,PY,PZ,VX,VY,VZ,DT,FC,FP,PSI,
+     :                 UL(13),PV(6)
+
+
+
+*  Validate arguments.
+      IF (JFORM.LT.1.OR.JFORM.GT.3) THEN
+         JSTAT = -1
+         GO TO 9999
+      END IF
+      IF (E.LT.0D0.OR.E.GT.10D0.OR.(E.GE.1D0.AND.JFORM.NE.3)) THEN
+         JSTAT = -2
+         GO TO 9999
+      END IF
+      IF (AORQ.LE.0D0) THEN
+         JSTAT = -3
+         GO TO 9999
+      END IF
+      IF (JFORM.EQ.1.AND.DM.LE.0D0) THEN
+         JSTAT = -4
+         GO TO 9999
+      END IF
+
+*
+*  Transform elements into standard form:
+*
+*  PHT   = epoch of perihelion passage
+*  ARGPH = argument of perihelion (little omega)
+*  Q     = perihelion distance (q)
+*  CM    = combined mass, M+m (mu)
+
+      IF (JFORM.EQ.1) THEN
+
+*     Major planet.
+         PHT = EPOCH-(AORL-PERIH)/DM
+         ARGPH = PERIH-ANODE
+         Q = AORQ*(1D0-E)
+         W = DM/GCON
+         CM = W*W*AORQ*AORQ*AORQ
+
+      ELSE IF (JFORM.EQ.2) THEN
+
+*     Minor planet.
+         PHT = EPOCH-AORL*SQRT(AORQ*AORQ*AORQ)/GCON
+         ARGPH = PERIH
+         Q = AORQ*(1D0-E)
+         CM = 1D0
+
+      ELSE
+
+*     Comet.
+         PHT = EPOCH
+         ARGPH = PERIH
+         Q = AORQ
+         CM = 1D0
+
+      END IF
+
+*  The universal variable alpha.  This is proportional to the total
+*  energy of the orbit:  -ve for an ellipse, zero for a parabola,
+*  +ve for a hyperbola.
+
+      ALPHA = CM*(E-1D0)/Q
+
+*  Speed at perihelion.
+
+      PHS = SQRT(ALPHA+2D0*CM/Q)
+
+*  In a Cartesian coordinate system which has the x-axis pointing
+*  to perihelion and the z-axis normal to the orbit (such that the
+*  object orbits counter-clockwise as seen from +ve z), the
+*  perihelion position and velocity vectors are:
+*
+*    position   [Q,0,0]
+*    velocity   [0,PHS,0]
+*
+*  To express the results in J2000 equatorial coordinates we make a
+*  series of four rotations of the Cartesian axes:
+*
+*           axis      Euler angle
+*
+*     1      z        argument of perihelion (little omega)
+*     2      x        inclination (i)
+*     3      z        longitude of the ascending node (big omega)
+*     4      x        J2000 obliquity (epsilon)
+*
+*  In each case the rotation is clockwise as seen from the +ve end of
+*  the axis concerned.
+
+*  Functions of the Euler angles.
+      SW = SIN(ARGPH)
+      CW = COS(ARGPH)
+      SI = SIN(ORBINC)
+      CI = COS(ORBINC)
+      SO = SIN(ANODE)
+      CO = COS(ANODE)
+
+*  Position at perihelion (AU).
+      X = Q*CW
+      Y = Q*SW
+      Z = Y*SI
+      Y = Y*CI
+      PX = X*CO-Y*SO
+      Y = X*SO+Y*CO
+      PY = Y*CE-Z*SE
+      PZ = Y*SE+Z*CE
+
+*  Velocity at perihelion (AU per canonical day).
+      X = -PHS*SW
+      Y = PHS*CW
+      Z = Y*SI
+      Y = Y*CI
+      VX = X*CO-Y*SO
+      Y = X*SO+Y*CO
+      VY = Y*CE-Z*SE
+      VZ = Y*SE+Z*CE
+
+*  Time from perihelion to date (in Canonical Days: a canonical day
+*  is 58.1324409... days, defined as 1/GCON).
+
+      DT = (DATE-PHT)*GCON
+
+*  First approximation to the Universal Eccentric Anomaly, PSI,
+*  based on the circle (FC) and parabola (FP) values.
+
+      FC = DT/Q
+      W = (3D0*DT+SQRT(9D0*DT*DT+8D0*Q*Q*Q))**(1D0/3D0)
+      FP = W-2D0*Q/W
+      PSI = (1D0-E)*FC+E*FP
+
+*  Assemble local copy of element set.
+      UL(1) = CM
+      UL(2) = ALPHA
+      UL(3) = PHT
+      UL(4) = PX
+      UL(5) = PY
+      UL(6) = PZ
+      UL(7) = VX
+      UL(8) = VY
+      UL(9) = VZ
+      UL(10) = Q
+      UL(11) = 0D0
+      UL(12) = DATE
+      UL(13) = PSI
+
+*  Predict position+velocity at epoch of osculation.
+      CALL slUEPV(DATE,UL,PV,J)
+      IF (J.NE.0) GO TO 9010
+
+*  Convert back to universal elements.
+      CALL slPVUE(PV,DATE,CM-1D0,U,J)
+      IF (J.NE.0) GO TO 9010
+
+*  OK exit.
+      JSTAT = 0
+      GO TO 9999
+
+*  Quasi-impossible numerical errors.
+ 9010 CONTINUE
+      JSTAT = -5
+
+ 9999 CONTINUE
+      END
diff --git a/math/slalib/epb.f b/math/slalib/epb.f
new file mode 100644
index 00000000..8b492e27
--- /dev/null
+++ b/math/slalib/epb.f
@@ -0,0 +1,48 @@
+      DOUBLE PRECISION FUNCTION slEPB (DATE)
+*+
+*     - - - -
+*      E P B
+*     - - - -
+*
+*  Conversion of Modified Julian Date to Besselian Epoch
+*  (double precision)
+*
+*  Given:
+*     DATE     dp       Modified Julian Date (JD - 2400000.5)
+*
+*  The result is the Besselian Epoch.
+*
+*  Reference:
+*     Lieske,J.H., 1979. Astron.Astrophys.,73,282.
+*
+*  P.T.Wallace   Starlink   February 1984
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE
+
+
+      slEPB = 1900D0 + (DATE-15019.81352D0)/365.242198781D0
+
+      END
diff --git a/math/slalib/epb2d.f b/math/slalib/epb2d.f
new file mode 100644
index 00000000..e430c7fc
--- /dev/null
+++ b/math/slalib/epb2d.f
@@ -0,0 +1,48 @@
+      DOUBLE PRECISION FUNCTION slEB2D (EPB)
+*+
+*     - - - - - -
+*      E B 2 D
+*     - - - - - -
+*
+*  Conversion of Besselian Epoch to Modified Julian Date
+*  (double precision)
+*
+*  Given:
+*     EPB      dp       Besselian Epoch
+*
+*  The result is the Modified Julian Date (JD - 2400000.5).
+*
+*  Reference:
+*     Lieske,J.H., 1979. Astron.Astrophys.,73,282.
+*
+*  P.T.Wallace   Starlink   February 1984
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION EPB
+
+
+      slEB2D = 15019.81352D0 + (EPB-1900D0)*365.242198781D0
+
+      END
diff --git a/math/slalib/epco.f b/math/slalib/epco.f
new file mode 100644
index 00000000..fd6862bf
--- /dev/null
+++ b/math/slalib/epco.f
@@ -0,0 +1,69 @@
+      DOUBLE PRECISION FUNCTION slEPCO (K0, K, E)
+*+
+*     - - - - -
+*      E P C O
+*     - - - - -
+*
+*  Convert an epoch into the appropriate form - 'B' or 'J'
+*
+*  Given:
+*     K0    char    form of result:  'B'=Besselian, 'J'=Julian
+*     K     char    form of given epoch:  'B' or 'J'
+*     E     dp      epoch
+*
+*  Called:  slEPB, slEJ2D, slEPJ, slEB2D
+*
+*  Notes:
+*
+*     1) The result is always either equal to or very close to
+*        the given epoch E.  The routine is required only in
+*        applications where punctilious treatment of heterogeneous
+*        mixtures of star positions is necessary.
+*
+*     2) K0 and K are not validated.  They are interpreted as follows:
+*
+*        o  If K0 and K are the same the result is E.
+*        o  If K0 is 'B' or 'b' and K isn't, the conversion is J to B.
+*        o  In all other cases, the conversion is B to J.
+*
+*        Note that K0 and K won't match if their cases differ.
+*
+*  P.T.Wallace   Starlink   5 September 1993
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) K0,K
+      DOUBLE PRECISION E
+      DOUBLE PRECISION slEPB,slEJ2D,slEPJ,slEB2D
+
+
+      IF (K.EQ.K0) THEN
+         slEPCO=E
+      ELSE IF (K0.EQ.'B'.OR.K0.EQ.'b') THEN
+         slEPCO=slEPB(slEJ2D(E))
+      ELSE
+         slEPCO=slEPJ(slEB2D(E))
+      END IF
+
+      END
diff --git a/math/slalib/epj.f b/math/slalib/epj.f
new file mode 100644
index 00000000..cc8943db
--- /dev/null
+++ b/math/slalib/epj.f
@@ -0,0 +1,47 @@
+      DOUBLE PRECISION FUNCTION slEPJ (DATE)
+*+
+*     - - - -
+*      E P J
+*     - - - -
+*
+*  Conversion of Modified Julian Date to Julian Epoch (double precision)
+*
+*  Given:
+*     DATE     dp       Modified Julian Date (JD - 2400000.5)
+*
+*  The result is the Julian Epoch.
+*
+*  Reference:
+*     Lieske,J.H., 1979. Astron.Astrophys.,73,282.
+*
+*  P.T.Wallace   Starlink   February 1984
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE
+
+
+      slEPJ = 2000D0 + (DATE-51544.5D0)/365.25D0
+
+      END
diff --git a/math/slalib/epj2d.f b/math/slalib/epj2d.f
new file mode 100644
index 00000000..9754194b
--- /dev/null
+++ b/math/slalib/epj2d.f
@@ -0,0 +1,47 @@
+      DOUBLE PRECISION FUNCTION slEJ2D (EPJ)
+*+
+*     - - - - - -
+*      E J 2 D
+*     - - - - - -
+*
+*  Conversion of Julian Epoch to Modified Julian Date (double precision)
+*
+*  Given:
+*     EPJ      dp       Julian Epoch
+*
+*  The result is the Modified Julian Date (JD - 2400000.5).
+*
+*  Reference:
+*     Lieske,J.H., 1979. Astron.Astrophys.,73,282.
+*
+*  P.T.Wallace   Starlink   February 1984
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION EPJ
+
+
+      slEJ2D = 51544.5D0 + (EPJ-2000D0)*365.25D0
+
+      END
diff --git a/math/slalib/epv.f b/math/slalib/epv.f
new file mode 100644
index 00000000..dbea31b0
--- /dev/null
+++ b/math/slalib/epv.f
@@ -0,0 +1,2509 @@
+      SUBROUTINE slEPV ( DATE, PH, VH, PB, VB )
+*+
+*  - - - -
+*   E P V
+*  - - - -
+*
+*  Earth position and velocity, heliocentric and barycentric, with
+*  respect to the Barycentric Celestial Reference System.
+*
+*  Given:
+*     DATE      d         date, TDB Modified Julian Date (Note 1)
+*
+*  Returned:
+*     PH        d(3)      heliocentric Earth position (AU)
+*     VH        d(3)      heliocentric Earth velocity (AU,AU/day)
+*     PB        d(3)      barycentric Earth position (AU)
+*     VB        d(3)      barycentric Earth velocity (AU/day)
+*
+*  Notes:
+*
+*  1) The date is TDB as an MJD (=JD-2400000.5).  TT can be used instead
+*     of TDB in most applications.
+*
+*  2) On return, the arrays PH, VH, PV, PB contain the following:
+*
+*        PH(1)    x       }
+*        PH(2)    y       } heliocentric position, AU
+*        PH(3)    z       }
+*
+*        VH(1)    xdot    }
+*        VH(2)    ydot    } heliocentric velocity, AU/d
+*        VH(3)    zdot    }
+*
+*        PB(1)    x       }
+*        PB(2)    y       } barycentric position, AU
+*        PB(3)    z       }
+*
+*        VB(1)    xdot    }
+*        VB(2)    ydot    } barycentric velocity, AU/d
+*        VB(3)    zdot    }
+*
+*     The vectors are with respect to the Barycentric Celestial
+*     Reference System (BCRS); velocities are in AU per TDB day.
+*
+*  3) The routine is a SIMPLIFIED SOLUTION from the planetary theory
+*     VSOP2000 (X. Moisson, P. Bretagnon, 2001, Celes. Mechanics &
+*     Dyn. Astron., 80, 3/4, 205-213) and is an adaptation of original
+*     Fortran code supplied by P. Bretagnon (private comm., 2000).
+*
+*  4) Comparisons over the time span 1900-2100 with this simplified
+*     solution and the JPL DE405 ephemeris give the following results:
+*
+*                                RMS    max
+*           Heliocentric:
+*              position error    3.7   11.2   km
+*              velocity error    1.4    5.0   mm/s
+*
+*           Barycentric:
+*              position error    4.6   13.4   km
+*              velocity error    1.4    4.9   mm/s
+*
+*     The results deteriorate outside this time span.
+*
+*  5) The routine slEVP is faster but less accurate.  The present
+*     routine targets the case where high accuracy is more important
+*     than CPU time, yet the extra complication of reading a pre-
+*     computed ephemeris is not justified.
+*
+*  Last revision:   7 April 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-----------------------------------------------------------------------
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE, PH(3), VH(3), PB(3), VB(3)
+
+      DOUBLE PRECISION T, T2, XYZ, XYZD, A, B, C, CT, P, CP,
+     :                 HP(3), HV(3), BP(3), BV(3), X, Y, Z
+
+      INTEGER I, J, K
+
+*  Days per Julian year
+      DOUBLE PRECISION DJY
+      PARAMETER ( DJY = 365.25D0 )
+
+*  Reference epoch (J2000), MJD
+      DOUBLE PRECISION DJM0
+      PARAMETER ( DJM0 = 51544.5D0 )
+*
+*  Matrix elements for orienting the analytical model to DE405/ICRF.
+*
+*  The corresponding Euler angles are:
+*
+*                        d  '  "
+*    1st rotation    -  23 26 21.4091 about the x-axis  (obliquity)
+*    2nd rotation    +         0.0475 about the z-axis  (RA offset)
+*
+*  These were obtained empirically, by comparisons with DE405 over
+*  1900-2100.
+*
+      DOUBLE PRECISION AM12, AM13, AM21, AM22, AM23, AM32, AM33
+      PARAMETER ( AM12 = +0.000000211284D0,
+     :            AM13 = -0.000000091603D0,
+     :            AM21 = -0.000000230286D0,
+     :            AM22 = +0.917482137087D0,
+     :            AM23 = -0.397776982902D0,
+     :            AM32 = +0.397776982902D0,
+     :            AM33 = +0.917482137087D0 )
+
+*  ----------------------
+*  Ephemeris Coefficients
+*  ----------------------
+*
+*  The coefficients are stored in arrays of dimension (3,n,3).  There
+*  are separate sets of arrays for (i) the Sun to Earth vector and
+*  (ii) the Solar-System barycenter to Sun vector.  Each of these two
+*  sets contains separate arrays for the terms (n in number) in each
+*  power of time (in Julian years since J2000): T^0, T^1 and T^2.
+*  Within each array, all the Cartesian x-components, elements (i,j,1),
+*  appear first, followed by all the y-components, elements (i,j,2) and
+*  finally all the z-components, elements (i,j,3).  At the lowest level
+*  are groups of three coefficients.  The first coefficient in each
+*  group, element (1,j,k), is the amplitude of the term, the second,
+*  element (2,j,k), is the phase and the third, element (3,j,k), is the
+*  frequency.
+*
+*  The naming scheme is such that a block
+*
+*     DOUBLE PRECISION bn(3,Mbn,3)
+*
+*  applies to body b and time exponent n:
+*
+*    . b can be either E (Earth with respect to Sun) or S (Sun with
+*      respect to Solar-System Barycenter)
+*
+*    . n can be 0, 1 or 2, for T^0, T^1 or T^2
+*
+*  For example, array E2(3,ME2,3) contains the coefficients for
+*  the T^2 terms for the Sun-to-Earth vector.
+*
+*  There is no requirement for the X, Y and Z models for a particular
+*  block to use the same number of coefficients.  The number actually
+*  used is parameterized, the number of terms being used called NbnX,
+*  NbnY, and NbnZ respectively.  The parameter Mbn is the biggest of
+*  the three, and defines the array size.  Unused elements are not
+*  initialized and are never accessed.
+*
+
+      INTEGER NE0(3), NE0X, NE0Y, NE0Z, ME0,
+     :        NE1(3), NE1X, NE1Y, NE1Z, ME1,
+     :        NE2(3), NE2X, NE2Y, NE2Z, ME2,
+     :        NS0(3), NS0X, NS0Y, NS0Z, MS0,
+     :        NS1(3), NS1X, NS1Y, NS1Z, MS1,
+     :        NS2(3), NS2X, NS2Y, NS2Z, MS2
+
+      PARAMETER ( NE0X = 501, NE0Y = 501, NE0Z = 137, ME0 = NE0X,
+     :            NE1X =  79, NE1Y =  80, NE1Z =  12, ME1 = NE1Y,
+     :            NE2X =   5, NE2Y =   5, NE2Z =   3, ME2 = NE2X,
+     :            NS0X = 212, NS0Y = 213, NS0Z =  69, MS0 = NS0Y,
+     :            NS1X =  50, NS1Y =  50, NS1Z =  14, MS1 = NS1X,
+     :            NS2X =   9, NS2Y =   9, NS2Z =   2, MS2 = NS2X )
+
+      DOUBLE PRECISION E0(3,ME0,3), E1(3,ME1,3), E2(3,ME2,3),
+     :                 S0(3,MS0,3), S1(3,MS1,3), S2(3,MS2,3)
+
+      DATA NE0 / NE0X, NE0Y, NE0Z /
+      DATA NE1 / NE1X, NE1Y, NE1Z /
+      DATA NE2 / NE2X, NE2Y, NE2Z /
+      DATA NS0 / NS0X, NS0Y, NS0Z /
+      DATA NS1 / NS1X, NS1Y, NS1Z /
+      DATA NS2 / NS2X, NS2Y, NS2Z /
+
+*  Sun-to-Earth, T^0, X
+      DATA ((E0(I,J,1),I=1,3),J=  1, 10) /
+     :  0.9998292878132D+00, 0.1753485171504D+01, 0.6283075850446D+01,
+     :  0.8352579567414D-02, 0.1710344404582D+01, 0.1256615170089D+02,
+     :  0.5611445335148D-02, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.1046664295572D-03, 0.1667225416770D+01, 0.1884922755134D+02,
+     :  0.3110842534677D-04, 0.6687513390251D+00, 0.8399684731857D+02,
+     :  0.2552413503550D-04, 0.5830637358413D+00, 0.5296909721118D+00,
+     :  0.2137207845781D-04, 0.1092330954011D+01, 0.1577343543434D+01,
+     :  0.1680240182951D-04, 0.4955366134987D+00, 0.6279552690824D+01,
+     :  0.1679012370795D-04, 0.6153014091901D+01, 0.6286599010068D+01,
+     :  0.1445526946777D-04, 0.3472744100492D+01, 0.2352866153506D+01 /
+      DATA ((E0(I,J,1),I=1,3),J= 11, 20) /
+     :  0.1091038246184D-04, 0.3689845786119D+01, 0.5223693906222D+01,
+     :  0.9344399733932D-05, 0.6073934645672D+01, 0.1203646072878D+02,
+     :  0.8993182910652D-05, 0.3175705249069D+01, 0.1021328554739D+02,
+     :  0.5665546034116D-05, 0.2152484672246D+01, 0.1059381944224D+01,
+     :  0.6844146703035D-05, 0.1306964099750D+01, 0.5753384878334D+01,
+     :  0.7346610905565D-05, 0.4354980070466D+01, 0.3981490189893D+00,
+     :  0.6815396474414D-05, 0.2218229211267D+01, 0.4705732307012D+01,
+     :  0.6112787253053D-05, 0.5384788425458D+01, 0.6812766822558D+01,
+     :  0.4518120711239D-05, 0.6087604012291D+01, 0.5884926831456D+01,
+     :  0.4521963430706D-05, 0.1279424524906D+01, 0.6256777527156D+01 /
+      DATA ((E0(I,J,1),I=1,3),J= 21, 30) /
+     :  0.4497426764085D-05, 0.5369129144266D+01, 0.6309374173736D+01,
+     :  0.4062190566959D-05, 0.5436473303367D+00, 0.6681224869435D+01,
+     :  0.5412193480192D-05, 0.7867838528395D+00, 0.7755226100720D+00,
+     :  0.5469839049386D-05, 0.1461440311134D+01, 0.1414349524433D+02,
+     :  0.5205264083477D-05, 0.4432944696116D+01, 0.7860419393880D+01,
+     :  0.2149759935455D-05, 0.4502237496846D+01, 0.1150676975667D+02,
+     :  0.2279109618501D-05, 0.1239441308815D+01, 0.7058598460518D+01,
+     :  0.2259282939683D-05, 0.3272430985331D+01, 0.4694002934110D+01,
+     :  0.2558950271319D-05, 0.2265471086404D+01, 0.1216800268190D+02,
+     :  0.2561581447555D-05, 0.1454740653245D+01, 0.7099330490126D+00 /
+      DATA ((E0(I,J,1),I=1,3),J= 31, 40) /
+     :  0.1781441115440D-05, 0.2962068630206D+01, 0.7962980379786D+00,
+     :  0.1612005874644D-05, 0.1473255041006D+01, 0.5486777812467D+01,
+     :  0.1818630667105D-05, 0.3743903293447D+00, 0.6283008715021D+01,
+     :  0.1818601377529D-05, 0.6274174354554D+01, 0.6283142985870D+01,
+     :  0.1554475925257D-05, 0.1624110906816D+01, 0.2513230340178D+02,
+     :  0.2090948029241D-05, 0.5852052276256D+01, 0.1179062909082D+02,
+     :  0.2000176345460D-05, 0.4072093298513D+01, 0.1778984560711D+02,
+     :  0.1289535917759D-05, 0.5217019331069D+01, 0.7079373888424D+01,
+     :  0.1281135307881D-05, 0.4802054538934D+01, 0.3738761453707D+01,
+     :  0.1518229005692D-05, 0.8691914742502D+00, 0.2132990797783D+00 /
+      DATA ((E0(I,J,1),I=1,3),J= 41, 50) /
+     :  0.9450128579027D-06, 0.4601859529950D+01, 0.1097707878456D+02,
+     :  0.7781119494996D-06, 0.1844352816694D+01, 0.8827390247185D+01,
+     :  0.7733407759912D-06, 0.3582790154750D+01, 0.5507553240374D+01,
+     :  0.7350644318120D-06, 0.2695277788230D+01, 0.1589072916335D+01,
+     :  0.6535928827023D-06, 0.3651327986142D+01, 0.1176985366291D+02,
+     :  0.6324624183656D-06, 0.2241302375862D+01, 0.6262300422539D+01,
+     :  0.6298565300557D-06, 0.4407122406081D+01, 0.6303851278352D+01,
+     :  0.8587037089179D-06, 0.3024307223119D+01, 0.1672837615881D+03,
+     :  0.8299954491035D-06, 0.6192539428237D+01, 0.3340612434717D+01,
+     :  0.6311263503401D-06, 0.2014758795416D+01, 0.7113454667900D-02 /
+      DATA ((E0(I,J,1),I=1,3),J= 51, 60) /
+     :  0.6005646745452D-06, 0.3399500503397D+01, 0.4136910472696D+01,
+     :  0.7917715109929D-06, 0.2493386877837D+01, 0.6069776770667D+01,
+     :  0.7556958099685D-06, 0.4159491740143D+01, 0.6496374930224D+01,
+     :  0.6773228244949D-06, 0.4034162934230D+01, 0.9437762937313D+01,
+     :  0.5370708577847D-06, 0.1562219163734D+01, 0.1194447056968D+01,
+     :  0.5710804266203D-06, 0.2662730803386D+01, 0.6282095334605D+01,
+     :  0.5709824583726D-06, 0.3985828430833D+01, 0.6284056366286D+01,
+     :  0.5143950896447D-06, 0.1308144688689D+01, 0.6290189305114D+01,
+     :  0.5088010604546D-06, 0.5352817214804D+01, 0.6275962395778D+01,
+     :  0.4960369085172D-06, 0.2644267922349D+01, 0.6127655567643D+01 /
+      DATA ((E0(I,J,1),I=1,3),J= 61, 70) /
+     :  0.4803137891183D-06, 0.4008844192080D+01, 0.6438496133249D+01,
+     :  0.5731747768225D-06, 0.3794550174597D+01, 0.3154687086868D+01,
+     :  0.4735947960579D-06, 0.6107118308982D+01, 0.3128388763578D+01,
+     :  0.4808348796625D-06, 0.4771458618163D+01, 0.8018209333619D+00,
+     :  0.4115073743137D-06, 0.3327111335159D+01, 0.8429241228195D+01,
+     :  0.5230575889287D-06, 0.5305708551694D+01, 0.1336797263425D+02,
+     :  0.5133977889215D-06, 0.5784230738814D+01, 0.1235285262111D+02,
+     :  0.5065815825327D-06, 0.2052064793679D+01, 0.1185621865188D+02,
+     :  0.4339831593868D-06, 0.3644994195830D+01, 0.1726015463500D+02,
+     :  0.3952928638953D-06, 0.4930376436758D+01, 0.5481254917084D+01 /
+      DATA ((E0(I,J,1),I=1,3),J= 71, 80) /
+     :  0.4898498111942D-06, 0.4542084219731D+00, 0.9225539266174D+01,
+     :  0.4757490209328D-06, 0.3161126388878D+01, 0.5856477690889D+01,
+     :  0.4727701669749D-06, 0.6214993845446D+00, 0.2544314396739D+01,
+     :  0.3800966681863D-06, 0.3040132339297D+01, 0.4265981595566D+00,
+     :  0.3257301077939D-06, 0.8064977360087D+00, 0.3930209696940D+01,
+     :  0.3255810528674D-06, 0.1974147981034D+01, 0.2146165377750D+01,
+     :  0.3252029748187D-06, 0.2845924913135D+01, 0.4164311961999D+01,
+     :  0.3255505635308D-06, 0.3017900824120D+01, 0.5088628793478D+01,
+     :  0.2801345211990D-06, 0.6109717793179D+01, 0.1256967486051D+02,
+     :  0.3688987740970D-06, 0.2911550235289D+01, 0.1807370494127D+02 /
+      DATA ((E0(I,J,1),I=1,3),J= 81, 90) /
+     :  0.2475153429458D-06, 0.2179146025856D+01, 0.2629832328990D-01,
+     :  0.3033457749150D-06, 0.1994161050744D+01, 0.4535059491685D+01,
+     :  0.2186743763110D-06, 0.5125687237936D+01, 0.1137170464392D+02,
+     :  0.2764777032774D-06, 0.4822646860252D+00, 0.1256262854127D+02,
+     :  0.2199028768592D-06, 0.4637633293831D+01, 0.1255903824622D+02,
+     :  0.2046482824760D-06, 0.1467038733093D+01, 0.7084896783808D+01,
+     :  0.2611209147507D-06, 0.3044718783485D+00, 0.7143069561767D+02,
+     :  0.2286079656818D-06, 0.4764220356805D+01, 0.8031092209206D+01,
+     :  0.1855071202587D-06, 0.3383637774428D+01, 0.1748016358760D+01,
+     :  0.2324669506784D-06, 0.6189088449251D+01, 0.1831953657923D+02 /
+      DATA ((E0(I,J,1),I=1,3),J= 91,100) /
+     :  0.1709528015688D-06, 0.5874966729774D+00, 0.4933208510675D+01,
+     :  0.2168156875828D-06, 0.4302994009132D+01, 0.1044738781244D+02,
+     :  0.2106675556535D-06, 0.3800475419891D+01, 0.7477522907414D+01,
+     :  0.1430213830465D-06, 0.1294660846502D+01, 0.2942463415728D+01,
+     :  0.1388396901944D-06, 0.4594797202114D+01, 0.8635942003952D+01,
+     :  0.1922258844190D-06, 0.4943044543591D+00, 0.1729818233119D+02,
+     :  0.1888460058292D-06, 0.2426943912028D+01, 0.1561374759853D+03,
+     :  0.1789449386107D-06, 0.1582973303499D+00, 0.1592596075957D+01,
+     :  0.1360803685374D-06, 0.5197240440504D+01, 0.1309584267300D+02,
+     :  0.1504038014709D-06, 0.3120360916217D+01, 0.1649636139783D+02 /
+      DATA ((E0(I,J,1),I=1,3),J=101,110) /
+     :  0.1382769533389D-06, 0.6164702888205D+01, 0.7632943190217D+01,
+     :  0.1438059769079D-06, 0.1437423770979D+01, 0.2042657109477D+02,
+     :  0.1326303260037D-06, 0.3609688799679D+01, 0.1213955354133D+02,
+     :  0.1159244950540D-06, 0.5463018167225D+01, 0.5331357529664D+01,
+     :  0.1433118149136D-06, 0.6028909912097D+01, 0.7342457794669D+01,
+     :  0.1234623148594D-06, 0.3109645574997D+01, 0.6279485555400D+01,
+     :  0.1233949875344D-06, 0.3539359332866D+01, 0.6286666145492D+01,
+     :  0.9927196061299D-07, 0.1259321569772D+01, 0.7234794171227D+01,
+     :  0.1242302191316D-06, 0.1065949392609D+01, 0.1511046609763D+02,
+     :  0.1098402195201D-06, 0.2192508743837D+01, 0.1098880815746D+02 /
+      DATA ((E0(I,J,1),I=1,3),J=111,120) /
+     :  0.1158191395315D-06, 0.4054411278650D+01, 0.5729506548653D+01,
+     :  0.9048475596241D-07, 0.5429764748518D+01, 0.9623688285163D+01,
+     :  0.8889853269023D-07, 0.5046586206575D+01, 0.6148010737701D+01,
+     :  0.1048694242164D-06, 0.2628858030806D+01, 0.6836645152238D+01,
+     :  0.1112308378646D-06, 0.4177292719907D+01, 0.1572083878776D+02,
+     :  0.8631729709901D-07, 0.1601345232557D+01, 0.6418140963190D+01,
+     :  0.8527816951664D-07, 0.2463888997513D+01, 0.1471231707864D+02,
+     :  0.7892139456991D-07, 0.3154022088718D+01, 0.2118763888447D+01,
+     :  0.1051782905236D-06, 0.4795035816088D+01, 0.1349867339771D+01,
+     :  0.1048219943164D-06, 0.2952983395230D+01, 0.5999216516294D+01 /
+      DATA ((E0(I,J,1),I=1,3),J=121,130) /
+     :  0.7435760775143D-07, 0.5420547991464D+01, 0.6040347114260D+01,
+     :  0.9869574106949D-07, 0.3695646753667D+01, 0.6566935184597D+01,
+     :  0.9156886364226D-07, 0.3922675306609D+01, 0.5643178611111D+01,
+     :  0.7006834356188D-07, 0.1233968624861D+01, 0.6525804586632D+01,
+     :  0.9806170182601D-07, 0.1919542280684D+01, 0.2122839202813D+02,
+     :  0.9052289673607D-07, 0.4615902724369D+01, 0.4690479774488D+01,
+     :  0.7554200867893D-07, 0.1236863719072D+01, 0.1253985337760D+02,
+     :  0.8215741286498D-07, 0.3286800101559D+00, 0.1097355562493D+02,
+     :  0.7185178575397D-07, 0.5880942158367D+01, 0.6245048154254D+01,
+     :  0.7130726476180D-07, 0.7674871987661D+00, 0.6321103546637D+01 /
+      DATA ((E0(I,J,1),I=1,3),J=131,140) /
+     :  0.6650894461162D-07, 0.6987129150116D+00, 0.5327476111629D+01,
+     :  0.7396888823688D-07, 0.3576824794443D+01, 0.5368044267797D+00,
+     :  0.7420588884775D-07, 0.5033615245369D+01, 0.2354323048545D+02,
+     :  0.6141181642908D-07, 0.9449927045673D+00, 0.1296430071988D+02,
+     :  0.6373557924058D-07, 0.6206342280341D+01, 0.9517183207817D+00,
+     :  0.6359474329261D-07, 0.5036079095757D+01, 0.1990745094947D+01,
+     :  0.5740173582646D-07, 0.6105106371350D+01, 0.9555997388169D+00,
+     :  0.7019864084602D-07, 0.7237747359018D+00, 0.5225775174439D+00,
+     :  0.6398054487042D-07, 0.3976367969666D+01, 0.2407292145756D+02,
+     :  0.7797092650498D-07, 0.4305423910623D+01, 0.2200391463820D+02 /
+      DATA ((E0(I,J,1),I=1,3),J=141,150) /
+     :  0.6466760000900D-07, 0.3500136825200D+01, 0.5230807360890D+01,
+     :  0.7529417043890D-07, 0.3514779246100D+01, 0.1842262939178D+02,
+     :  0.6924571140892D-07, 0.2743457928679D+01, 0.1554202828031D+00,
+     :  0.6220798650222D-07, 0.2242598118209D+01, 0.1845107853235D+02,
+     :  0.5870209391853D-07, 0.2332832707527D+01, 0.6398972393349D+00,
+     :  0.6263953473888D-07, 0.2191105358956D+01, 0.6277552955062D+01,
+     :  0.6257781390012D-07, 0.4457559396698D+01, 0.6288598745829D+01,
+     :  0.5697304945123D-07, 0.3499234761404D+01, 0.1551045220144D+01,
+     :  0.6335438746791D-07, 0.6441691079251D+00, 0.5216580451554D+01,
+     :  0.6377258441152D-07, 0.2252599151092D+01, 0.5650292065779D+01 /
+      DATA ((E0(I,J,1),I=1,3),J=151,160) /
+     :  0.6484841818165D-07, 0.1992812417646D+01, 0.1030928125552D+00,
+     :  0.4735551485250D-07, 0.3744672082942D+01, 0.1431416805965D+02,
+     :  0.4628595996170D-07, 0.1334226211745D+01, 0.5535693017924D+00,
+     :  0.6258152336933D-07, 0.4395836159154D+01, 0.2608790314060D+02,
+     :  0.6196171366594D-07, 0.2587043007997D+01, 0.8467247584405D+02,
+     :  0.6159556952126D-07, 0.4782499769128D+01, 0.2394243902548D+03,
+     :  0.4987741172394D-07, 0.7312257619924D+00, 0.7771377146812D+02,
+     :  0.5459280703142D-07, 0.3001376372532D+01, 0.6179983037890D+01,
+     :  0.4863461189999D-07, 0.3767222128541D+01, 0.9027992316901D+02,
+     :  0.5349912093158D-07, 0.3663594450273D+01, 0.6386168663001D+01 /
+      DATA ((E0(I,J,1),I=1,3),J=161,170) /
+     :  0.5673725607806D-07, 0.4331187919049D+01, 0.6915859635113D+01,
+     :  0.4745485060512D-07, 0.5816195745518D+01, 0.6282970628506D+01,
+     :  0.4745379005326D-07, 0.8323672435672D+00, 0.6283181072386D+01,
+     :  0.4049002796321D-07, 0.3785023976293D+01, 0.6254626709878D+01,
+     :  0.4247084014515D-07, 0.2378220728783D+01, 0.7875671926403D+01,
+     :  0.4026912363055D-07, 0.2864103423269D+01, 0.6311524991013D+01,
+     :  0.4062935011774D-07, 0.2415408595975D+01, 0.3634620989887D+01,
+     :  0.5347771048509D-07, 0.3343479309801D+01, 0.2515860172507D+02,
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+     :  0.4009158925298D-08, 0.3500003416535D+01, 0.6244942932314D+01,
+     :  0.4784939596873D-08, 0.6196709413181D+01, 0.2929661536378D+02,
+     :  0.3983725022610D-08, 0.5103690031897D+01, 0.4274518229222D+01,
+     :  0.3870535232462D-08, 0.3187569587401D+01, 0.6321208768577D+01,
+     :  0.5140501213951D-08, 0.1668924357457D+01, 0.1232032006293D+02,
+     :  0.3849034819355D-08, 0.4445722510309D+01, 0.1726726808967D+02 /
+      DATA ((E0(I,J,1),I=1,3),J=361,370) /
+     :  0.4002383075060D-08, 0.5226224152423D+01, 0.7018952447668D+01,
+     :  0.3890719543549D-08, 0.4371166550274D+01, 0.1491901785440D+02,
+     :  0.4887084607881D-08, 0.5973556689693D+01, 0.1478866649112D+01,
+     :  0.3739939287592D-08, 0.2089084714600D+01, 0.6922973089781D+01,
+     :  0.5031925918209D-08, 0.4658371936827D+01, 0.1715706182245D+02,
+     :  0.4387748764954D-08, 0.4825580552819D+01, 0.2331413144044D+03,
+     :  0.4147398098865D-08, 0.3739003524998D+01, 0.1376059875786D+02,
+     :  0.3719089993586D-08, 0.1148941386536D+01, 0.6297302759782D+01,
+     :  0.3934238461056D-08, 0.1559893008343D+01, 0.7872148766781D+01,
+     :  0.3672471375622D-08, 0.5516145383612D+01, 0.6268848941110D+01 /
+      DATA ((E0(I,J,1),I=1,3),J=371,380) /
+     :  0.3768911277583D-08, 0.6116053700563D+01, 0.4157198507331D+01,
+     :  0.4033388417295D-08, 0.5076821746017D+01, 0.1567108171867D+02,
+     :  0.3764194617832D-08, 0.8164676232075D+00, 0.3185192151914D+01,
+     :  0.4840628226284D-08, 0.1360479453671D+01, 0.1252801878276D+02,
+     :  0.4949443923785D-08, 0.2725622229926D+01, 0.1617106187867D+03,
+     :  0.4117393089971D-08, 0.6054459628492D+00, 0.5642198095270D+01,
+     :  0.3925754020428D-08, 0.8570462135210D+00, 0.2139354194808D+02,
+     :  0.3630551757923D-08, 0.3552067338279D+01, 0.6294805223347D+01,
+     :  0.3627274802357D-08, 0.3096565085313D+01, 0.6271346477544D+01,
+     :  0.3806143885093D-08, 0.6367751709777D+00, 0.1725304118033D+02 /
+      DATA ((E0(I,J,1),I=1,3),J=381,390) /
+     :  0.4433254641565D-08, 0.4848461503937D+01, 0.7445550607224D+01,
+     :  0.3712319846576D-08, 0.1331950643655D+01, 0.4194847048887D+00,
+     :  0.3849847534783D-08, 0.4958368297746D+00, 0.9562891316684D+00,
+     :  0.3483955430165D-08, 0.2237215515707D+01, 0.1161697602389D+02,
+     :  0.3961912730982D-08, 0.3332402188575D+01, 0.2277943724828D+02,
+     :  0.3419978244481D-08, 0.5785600576016D+01, 0.1362553364512D+02,
+     :  0.3329417758177D-08, 0.9812676559709D-01, 0.1685848245639D+02,
+     :  0.4207206893193D-08, 0.9494780468236D+00, 0.2986433403208D+02,
+     :  0.3268548976410D-08, 0.1739332095686D+00, 0.5749861718712D+01,
+     :  0.3321880082685D-08, 0.1423354800666D+01, 0.6279143387820D+01 /
+      DATA ((E0(I,J,1),I=1,3),J=391,400) /
+     :  0.4503173010852D-08, 0.2314972675293D+00, 0.1385561574497D+01,
+     :  0.4316599090954D-08, 0.1012646782616D+00, 0.4176041334900D+01,
+     :  0.3283493323850D-08, 0.5233306881265D+01, 0.6287008313071D+01,
+     :  0.3164033542343D-08, 0.4005597257511D+01, 0.2099539292909D+02,
+     :  0.4159720956725D-08, 0.5365676242020D+01, 0.5905702259363D+01,
+     :  0.3565176892217D-08, 0.4284440620612D+01, 0.3932462625300D-02,
+     :  0.3514440950221D-08, 0.4270562636575D+01, 0.7335344340001D+01,
+     :  0.3540596871909D-08, 0.5953553201060D+01, 0.1234573916645D+02,
+     :  0.2960769905118D-08, 0.1115180417718D+01, 0.2670964694522D+02,
+     :  0.2962213739684D-08, 0.3863811918186D+01, 0.6408777551755D+00 /
+      DATA ((E0(I,J,1),I=1,3),J=401,410) /
+     :  0.3883556700251D-08, 0.1268617928302D+01, 0.6660449441528D+01,
+     :  0.2919225516346D-08, 0.4908605223265D+01, 0.1375773836557D+01,
+     :  0.3115158863370D-08, 0.3744519976885D+01, 0.3802769619140D-01,
+     :  0.4099438144212D-08, 0.4173244670532D+01, 0.4480965020977D+02,
+     :  0.2899531858964D-08, 0.5910601428850D+01, 0.2059724391010D+02,
+     :  0.3289733429855D-08, 0.2488050078239D+01, 0.1081813534213D+02,
+     :  0.3933075612875D-08, 0.1122363652883D+01, 0.3773735910827D+00,
+     :  0.3021403764467D-08, 0.4951973724904D+01, 0.2982630633589D+02,
+     :  0.2798598949757D-08, 0.5117057845513D+01, 0.1937891852345D+02,
+     :  0.3397421302707D-08, 0.6104159180476D+01, 0.6923953605621D+01 /
+      DATA ((E0(I,J,1),I=1,3),J=411,420) /
+     :  0.3720398002179D-08, 0.1184933429829D+01, 0.3066615496545D+02,
+     :  0.3598484186267D-08, 0.3505282086105D+01, 0.6147450479709D+01,
+     :  0.3694594027310D-08, 0.2286651088141D+01, 0.2636725487657D+01,
+     :  0.2680444152969D-08, 0.1871816775482D+00, 0.6816289982179D+01,
+     :  0.3497574865641D-08, 0.3143251755431D+01, 0.6418701221183D+01,
+     :  0.3130274129494D-08, 0.2462167316018D+01, 0.1235996607578D+02,
+     :  0.3241119069551D-08, 0.4256374004686D+01, 0.1652265972112D+02,
+     :  0.2601960842061D-08, 0.4970362941425D+01, 0.1045450126711D+02,
+     :  0.2690601527504D-08, 0.2372657824898D+01, 0.3163918923335D+00,
+     :  0.2908688152664D-08, 0.4232652627721D+01, 0.2828699048865D+02 /
+      DATA ((E0(I,J,1),I=1,3),J=421,430) /
+     :  0.3120456131875D-08, 0.3925747001137D+00, 0.2195415756911D+02,
+     :  0.3148855423384D-08, 0.3093478330445D+01, 0.1172006883645D+02,
+     :  0.3051044261017D-08, 0.5560948248212D+01, 0.6055599646783D+01,
+     :  0.2826006876660D-08, 0.5072790310072D+01, 0.5120601093667D+01,
+     :  0.3100034191711D-08, 0.4998530231096D+01, 0.1799603123222D+02,
+     :  0.2398771640101D-08, 0.2561739802176D+01, 0.6255674361143D+01,
+     :  0.2384002842728D-08, 0.4087420284111D+01, 0.6310477339748D+01,
+     :  0.2842146517568D-08, 0.2515048217955D+01, 0.5469525544182D+01,
+     :  0.2847674371340D-08, 0.5235326497443D+01, 0.1034429499989D+02,
+     :  0.2903722140764D-08, 0.1088200795797D+01, 0.6510552054109D+01 /
+      DATA ((E0(I,J,1),I=1,3),J=431,440) /
+     :  0.3187610710605D-08, 0.4710624424816D+01, 0.1693792562116D+03,
+     :  0.3048869992813D-08, 0.2857975896445D+00, 0.8390110365991D+01,
+     :  0.2860216950984D-08, 0.2241619020815D+01, 0.2243449970715D+00,
+     :  0.2701117683113D-08, 0.6651573305272D-01, 0.6129297044991D+01,
+     :  0.2509891590152D-08, 0.1285135324585D+01, 0.1044027435778D+02,
+     :  0.2623200252223D-08, 0.2981229834530D+00, 0.6436854655901D+01,
+     :  0.2622541669202D-08, 0.6122470726189D+01, 0.9380959548977D+01,
+     :  0.2818435667099D-08, 0.4251087148947D+01, 0.5934151399930D+01,
+     :  0.2365196797465D-08, 0.3465070460790D+01, 0.2470570524223D+02,
+     :  0.2358704646143D-08, 0.5791603815350D+01, 0.8671969964381D+01 /
+      DATA ((E0(I,J,1),I=1,3),J=441,450) /
+     :  0.2388299481390D-08, 0.4142483772941D+01, 0.7096626156709D+01,
+     :  0.1996041217224D-08, 0.2101901889496D+01, 0.1727188400790D+02,
+     :  0.2687593060336D-08, 0.1526689456959D+01, 0.7075506709219D+02,
+     :  0.2618913670810D-08, 0.2397684236095D+01, 0.6632000300961D+01,
+     :  0.2571523050364D-08, 0.5751929456787D+00, 0.6206810014183D+01,
+     :  0.2582135006946D-08, 0.5595464352926D+01, 0.4873985990671D+02,
+     :  0.2372530190361D-08, 0.5092689490655D+01, 0.1590676413561D+02,
+     :  0.2357178484712D-08, 0.4444363527851D+01, 0.3097883698531D+01,
+     :  0.2451590394723D-08, 0.3108251687661D+01, 0.6612329252343D+00,
+     :  0.2370045949608D-08, 0.2608133861079D+01, 0.3459636466239D+02 /
+      DATA ((E0(I,J,1),I=1,3),J=451,460) /
+     :  0.2268997267358D-08, 0.3639717753384D+01, 0.2844914056730D-01,
+     :  0.1731432137906D-08, 0.1741898445707D+00, 0.2019909489111D+02,
+     :  0.1629869741622D-08, 0.3902225646724D+01, 0.3035599730800D+02,
+     :  0.2206215801974D-08, 0.4971131250731D+01, 0.6281667977667D+01,
+     :  0.2205469554680D-08, 0.1677462357110D+01, 0.6284483723224D+01,
+     :  0.2148792362509D-08, 0.4236259604006D+01, 0.1980482729015D+02,
+     :  0.1873733657847D-08, 0.5926814998687D+01, 0.2876692439167D+02,
+     :  0.2026573758959D-08, 0.4349643351962D+01, 0.2449240616245D+02,
+     :  0.1807770325110D-08, 0.5700940482701D+01, 0.2045286941806D+02,
+     :  0.1881174408581D-08, 0.6601286363430D+00, 0.2358125818164D+02 /
+      DATA ((E0(I,J,1),I=1,3),J=461,470) /
+     :  0.1368023671690D-08, 0.2211098592752D+01, 0.2473415438279D+02,
+     :  0.1720017916280D-08, 0.4942488551129D+01, 0.1679593901136D+03,
+     :  0.1702427665131D-08, 0.1452233856386D+01, 0.3338575901272D+03,
+     :  0.1414032510054D-08, 0.5525357721439D+01, 0.1624205518357D+03,
+     :  0.1652626045364D-08, 0.4108794283624D+01, 0.8956999012000D+02,
+     :  0.1642957769686D-08, 0.7344335209984D+00, 0.5267006960365D+02,
+     :  0.1614952403624D-08, 0.3541213951363D+01, 0.3332657872986D+02,
+     :  0.1535988291188D-08, 0.4031094072151D+01, 0.3852657435933D+02,
+     :  0.1593193738177D-08, 0.4185136203609D+01, 0.2282781046519D+03,
+     :  0.1074569126382D-08, 0.1720485636868D+01, 0.8397383534231D+02 /
+      DATA ((E0(I,J,1),I=1,3),J=471,480) /
+     :  0.1074408214509D-08, 0.2758613420318D+01, 0.8401985929482D+02,
+     :  0.9700199670465D-09, 0.4216686842097D+01, 0.7826370942180D+02,
+     :  0.1258433517061D-08, 0.2575068876639D+00, 0.3115650189215D+03,
+     :  0.1240303229539D-08, 0.4800844956756D+00, 0.1784300471910D+03,
+     :  0.9018345948127D-09, 0.3896756361552D+00, 0.5886454391678D+02,
+     :  0.1135301432805D-08, 0.3700805023550D+00, 0.7842370451713D+02,
+     :  0.9215887951370D-09, 0.4364579276638D+01, 0.1014262087719D+03,
+     :  0.1055401054147D-08, 0.2156564222111D+01, 0.5660027930059D+02,
+     :  0.1008725979831D-08, 0.5454015785234D+01, 0.4245678405627D+02,
+     :  0.7217398104321D-09, 0.1597772562175D+01, 0.2457074661053D+03 /
+      DATA ((E0(I,J,1),I=1,3),J=481,490) /
+     :  0.6912033134447D-09, 0.5824090621461D+01, 0.1679936946371D+03,
+     :  0.6833881523549D-09, 0.3578778482835D+01, 0.6053048899753D+02,
+     :  0.4887304205142D-09, 0.3724362812423D+01, 0.9656299901946D+02,
+     :  0.5173709754788D-09, 0.5422427507933D+01, 0.2442876000072D+03,
+     :  0.4671353097145D-09, 0.2396106924439D+01, 0.1435713242844D+03,
+     :  0.5652608439480D-09, 0.2804028838685D+01, 0.8365903305582D+02,
+     :  0.5604061331253D-09, 0.1638816006247D+01, 0.8433466158131D+02,
+     :  0.4712723365400D-09, 0.8979003224474D+00, 0.3164282286739D+03,
+     :  0.4909967465112D-09, 0.3210426725516D+01, 0.4059982187939D+03,
+     :  0.4771358267658D-09, 0.5308027211629D+01, 0.1805255418145D+03 /
+      DATA ((E0(I,J,1),I=1,3),J=491,500) /
+     :  0.3943451445989D-09, 0.2195145341074D+01, 0.2568537517081D+03,
+     :  0.3952109120244D-09, 0.5081189491586D+01, 0.2449975330562D+03,
+     :  0.3788134594789D-09, 0.4345171264441D+01, 0.1568131045107D+03,
+     :  0.3738330190479D-09, 0.2613062847997D+01, 0.3948519331910D+03,
+     :  0.3099866678136D-09, 0.2846760817689D+01, 0.1547176098872D+03,
+     :  0.2002962716768D-09, 0.4921360989412D+01, 0.2268582385539D+03,
+     :  0.2198291338754D-09, 0.1130360117454D+00, 0.1658638954901D+03,
+     :  0.1491958330784D-09, 0.4228195232278D+01, 0.2219950288015D+03,
+     :  0.1475384076173D-09, 0.3005721811604D+00, 0.3052819430710D+03,
+     :  0.1661626624624D-09, 0.7830125621203D+00, 0.2526661704812D+03 /
+      DATA ((E0(I,J,1),I=1,3),J=501,NE0X) /
+     :  0.9015823460025D-10, 0.3807792942715D+01, 0.4171445043968D+03 /
+
+*  Sun-to-Earth, T^1, X
+      DATA ((E1(I,J,1),I=1,3),J=  1, 10) /
+     :  0.1234046326004D-05, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.5150068824701D-06, 0.6002664557501D+01, 0.1256615170089D+02,
+     :  0.1290743923245D-07, 0.5959437664199D+01, 0.1884922755134D+02,
+     :  0.1068615564952D-07, 0.2015529654209D+01, 0.6283075850446D+01,
+     :  0.2079619142538D-08, 0.1732960531432D+01, 0.6279552690824D+01,
+     :  0.2078009243969D-08, 0.4915604476996D+01, 0.6286599010068D+01,
+     :  0.6206330058856D-09, 0.3616457953824D+00, 0.4705732307012D+01,
+     :  0.5989335313746D-09, 0.3802607304474D+01, 0.6256777527156D+01,
+     :  0.5958495663840D-09, 0.2845866560031D+01, 0.6309374173736D+01,
+     :  0.4866923261539D-09, 0.5213203771824D+01, 0.7755226100720D+00 /
+      DATA ((E1(I,J,1),I=1,3),J= 11, 20) /
+     :  0.4267785823142D-09, 0.4368189727818D+00, 0.1059381944224D+01,
+     :  0.4610675141648D-09, 0.1837249181372D-01, 0.7860419393880D+01,
+     :  0.3626989993973D-09, 0.2161590545326D+01, 0.5753384878334D+01,
+     :  0.3563071194389D-09, 0.1452631954746D+01, 0.5884926831456D+01,
+     :  0.3557015642807D-09, 0.4470593393054D+01, 0.6812766822558D+01,
+     :  0.3210412089122D-09, 0.5195926078314D+01, 0.6681224869435D+01,
+     :  0.2875473577986D-09, 0.5916256610193D+01, 0.2513230340178D+02,
+     :  0.2842913681629D-09, 0.1149902426047D+01, 0.6127655567643D+01,
+     :  0.2751248215916D-09, 0.5502088574662D+01, 0.6438496133249D+01,
+     :  0.2481432881127D-09, 0.2921989846637D+01, 0.5486777812467D+01 /
+      DATA ((E1(I,J,1),I=1,3),J= 21, 30) /
+     :  0.2059885976560D-09, 0.3718070376585D+01, 0.7079373888424D+01,
+     :  0.2015522342591D-09, 0.5979395259740D+01, 0.6290189305114D+01,
+     :  0.1995364084253D-09, 0.6772087985494D+00, 0.6275962395778D+01,
+     :  0.1957436436943D-09, 0.2899210654665D+01, 0.5507553240374D+01,
+     :  0.1651609818948D-09, 0.6228206482192D+01, 0.1150676975667D+02,
+     :  0.1822980550699D-09, 0.1469348746179D+01, 0.1179062909082D+02,
+     :  0.1675223159760D-09, 0.3813910555688D+01, 0.7058598460518D+01,
+     :  0.1706491764745D-09, 0.3004380506684D+00, 0.7113454667900D-02,
+     :  0.1392952362615D-09, 0.1440393973406D+01, 0.7962980379786D+00,
+     :  0.1209868266342D-09, 0.4150425791727D+01, 0.4694002934110D+01 /
+      DATA ((E1(I,J,1),I=1,3),J= 31, 40) /
+     :  0.1009827202611D-09, 0.3290040429843D+01, 0.3738761453707D+01,
+     :  0.1047261388602D-09, 0.4229590090227D+01, 0.6282095334605D+01,
+     :  0.1047006652004D-09, 0.2418967680575D+01, 0.6284056366286D+01,
+     :  0.9609993143095D-10, 0.4627943659201D+01, 0.6069776770667D+01,
+     :  0.9590900593873D-10, 0.1894393939924D+01, 0.4136910472696D+01,
+     :  0.9146249188071D-10, 0.2010647519562D+01, 0.6496374930224D+01,
+     :  0.8545274480290D-10, 0.5529846956226D-01, 0.1194447056968D+01,
+     :  0.8224377881194D-10, 0.1254304102174D+01, 0.1589072916335D+01,
+     :  0.6183529510410D-10, 0.3360862168815D+01, 0.8827390247185D+01,
+     :  0.6259255147141D-10, 0.4755628243179D+01, 0.8429241228195D+01 /
+      DATA ((E1(I,J,1),I=1,3),J= 41, 50) /
+     :  0.5539291694151D-10, 0.5371746955142D+01, 0.4933208510675D+01,
+     :  0.7328259466314D-10, 0.4927699613906D+00, 0.4535059491685D+01,
+     :  0.6017835843560D-10, 0.5776682001734D-01, 0.1255903824622D+02,
+     :  0.7079827775243D-10, 0.4395059432251D+01, 0.5088628793478D+01,
+     :  0.5170358878213D-10, 0.5154062619954D+01, 0.1176985366291D+02,
+     :  0.4872301838682D-10, 0.6289611648973D+00, 0.6040347114260D+01,
+     :  0.5249869411058D-10, 0.5617272046949D+01, 0.3154687086868D+01,
+     :  0.4716172354411D-10, 0.3965901800877D+01, 0.5331357529664D+01,
+     :  0.4871214940964D-10, 0.4627507050093D+01, 0.1256967486051D+02,
+     :  0.4598076850751D-10, 0.6023631226459D+01, 0.6525804586632D+01 /
+      DATA ((E1(I,J,1),I=1,3),J= 51, 60) /
+     :  0.4562196089485D-10, 0.4138562084068D+01, 0.3930209696940D+01,
+     :  0.4325493872224D-10, 0.1330845906564D+01, 0.7632943190217D+01,
+     :  0.5673781176748D-10, 0.2558752615657D+01, 0.5729506548653D+01,
+     :  0.3961436642503D-10, 0.2728071734630D+01, 0.7234794171227D+01,
+     :  0.5101868209058D-10, 0.4113444965144D+01, 0.6836645152238D+01,
+     :  0.5257043167676D-10, 0.6195089830590D+01, 0.8031092209206D+01,
+     :  0.5076613989393D-10, 0.2305124132918D+01, 0.7477522907414D+01,
+     :  0.3342169352778D-10, 0.5415998155071D+01, 0.1097707878456D+02,
+     :  0.3545881983591D-10, 0.3727160564574D+01, 0.4164311961999D+01,
+     :  0.3364063738599D-10, 0.2901121049204D+00, 0.1137170464392D+02 /
+      DATA ((E1(I,J,1),I=1,3),J= 61, 70) /
+     :  0.3357039670776D-10, 0.1652229354331D+01, 0.5223693906222D+01,
+     :  0.4307412268687D-10, 0.4938909587445D+01, 0.1592596075957D+01,
+     :  0.3405769115435D-10, 0.2408890766511D+01, 0.3128388763578D+01,
+     :  0.3001926198480D-10, 0.4862239006386D+01, 0.1748016358760D+01,
+     :  0.2778264787325D-10, 0.5241168661353D+01, 0.7342457794669D+01,
+     :  0.2676159480666D-10, 0.3423593942199D+01, 0.2146165377750D+01,
+     :  0.2954273399939D-10, 0.1881721265406D+01, 0.5368044267797D+00,
+     :  0.3309362888795D-10, 0.1931525677349D+01, 0.8018209333619D+00,
+     :  0.2810283608438D-10, 0.2414659495050D+01, 0.5225775174439D+00,
+     :  0.3378045637764D-10, 0.4238019163430D+01, 0.1554202828031D+00 /
+      DATA ((E1(I,J,1),I=1,3),J= 71,NE1X) /
+     :  0.2558134979840D-10, 0.1828225235805D+01, 0.5230807360890D+01,
+     :  0.2273755578447D-10, 0.5858184283998D+01, 0.7084896783808D+01,
+     :  0.2294176037690D-10, 0.4514589779057D+01, 0.1726015463500D+02,
+     :  0.2533506099435D-10, 0.2355717851551D+01, 0.5216580451554D+01,
+     :  0.2716685375812D-10, 0.2221003625100D+01, 0.8635942003952D+01,
+     :  0.2419043435198D-10, 0.5955704951635D+01, 0.4690479774488D+01,
+     :  0.2521232544812D-10, 0.1395676848521D+01, 0.5481254917084D+01,
+     :  0.2630195021491D-10, 0.5727468918743D+01, 0.2629832328990D-01,
+     :  0.2548395840944D-10, 0.2628351859400D-03, 0.1349867339771D+01 /
+
+*  Sun-to-Earth, T^2, X
+      DATA ((E2(I,J,1),I=1,3),J=  1,NE2X) /
+     : -0.4143818297913D-10, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.2171497694435D-10, 0.4398225628264D+01, 0.1256615170089D+02,
+     :  0.9845398442516D-11, 0.2079720838384D+00, 0.6283075850446D+01,
+     :  0.9256833552682D-12, 0.4191264694361D+01, 0.1884922755134D+02,
+     :  0.1022049384115D-12, 0.5381133195658D+01, 0.8399684731857D+02 /
+
+*  Sun-to-Earth, T^0, Y
+      DATA ((E0(I,J,2),I=1,3),J=  1, 10) /
+     :  0.9998921098898D+00, 0.1826583913846D+00, 0.6283075850446D+01,
+     : -0.2442700893735D-01, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.8352929742915D-02, 0.1395277998680D+00, 0.1256615170089D+02,
+     :  0.1046697300177D-03, 0.9641423109763D-01, 0.1884922755134D+02,
+     :  0.3110841876663D-04, 0.5381140401712D+01, 0.8399684731857D+02,
+     :  0.2570269094593D-04, 0.5301016407128D+01, 0.5296909721118D+00,
+     :  0.2147389623610D-04, 0.2662510869850D+01, 0.1577343543434D+01,
+     :  0.1680344384050D-04, 0.5207904119704D+01, 0.6279552690824D+01,
+     :  0.1679117312193D-04, 0.4582187486968D+01, 0.6286599010068D+01,
+     :  0.1440512068440D-04, 0.1900688517726D+01, 0.2352866153506D+01 /
+      DATA ((E0(I,J,2),I=1,3),J= 11, 20) /
+     :  0.1135139664999D-04, 0.5273108538556D+01, 0.5223693906222D+01,
+     :  0.9345482571018D-05, 0.4503047687738D+01, 0.1203646072878D+02,
+     :  0.9007418719568D-05, 0.1605621059637D+01, 0.1021328554739D+02,
+     :  0.5671536712314D-05, 0.5812849070861D+00, 0.1059381944224D+01,
+     :  0.7451401861666D-05, 0.2807346794836D+01, 0.3981490189893D+00,
+     :  0.6393470057114D-05, 0.6029224133855D+01, 0.5753384878334D+01,
+     :  0.6814275881697D-05, 0.6472990145974D+00, 0.4705732307012D+01,
+     :  0.6113705628887D-05, 0.3813843419700D+01, 0.6812766822558D+01,
+     :  0.4503851367273D-05, 0.4527804370996D+01, 0.5884926831456D+01,
+     :  0.4522249141926D-05, 0.5991783029224D+01, 0.6256777527156D+01 /
+      DATA ((E0(I,J,2),I=1,3),J= 21, 30) /
+     :  0.4501794307018D-05, 0.3798703844397D+01, 0.6309374173736D+01,
+     :  0.5514927480180D-05, 0.3961257833388D+01, 0.5507553240374D+01,
+     :  0.4062862799995D-05, 0.5256247296369D+01, 0.6681224869435D+01,
+     :  0.5414900429712D-05, 0.5499032014097D+01, 0.7755226100720D+00,
+     :  0.5463153987424D-05, 0.6173092454097D+01, 0.1414349524433D+02,
+     :  0.5071611859329D-05, 0.2870244247651D+01, 0.7860419393880D+01,
+     :  0.2195112094455D-05, 0.2952338617201D+01, 0.1150676975667D+02,
+     :  0.2279139233919D-05, 0.5951775132933D+01, 0.7058598460518D+01,
+     :  0.2278386100876D-05, 0.4845456398785D+01, 0.4694002934110D+01,
+     :  0.2559088003308D-05, 0.6945321117311D+00, 0.1216800268190D+02 /
+      DATA ((E0(I,J,2),I=1,3),J= 31, 40) /
+     :  0.2561079286856D-05, 0.6167224608301D+01, 0.7099330490126D+00,
+     :  0.1792755796387D-05, 0.1400122509632D+01, 0.7962980379786D+00,
+     :  0.1818715656502D-05, 0.4703347611830D+01, 0.6283142985870D+01,
+     :  0.1818744924791D-05, 0.5086748900237D+01, 0.6283008715021D+01,
+     :  0.1554518791390D-05, 0.5331008042713D-01, 0.2513230340178D+02,
+     :  0.2063265737239D-05, 0.4283680484178D+01, 0.1179062909082D+02,
+     :  0.1497613520041D-05, 0.6074207826073D+01, 0.5486777812467D+01,
+     :  0.2000617940427D-05, 0.2501426281450D+01, 0.1778984560711D+02,
+     :  0.1289731195580D-05, 0.3646340599536D+01, 0.7079373888424D+01,
+     :  0.1282657998934D-05, 0.3232864804902D+01, 0.3738761453707D+01 /
+      DATA ((E0(I,J,2),I=1,3),J= 41, 50) /
+     :  0.1528915968658D-05, 0.5581433416669D+01, 0.2132990797783D+00,
+     :  0.1187304098432D-05, 0.5453576453694D+01, 0.9437762937313D+01,
+     :  0.7842782928118D-06, 0.2823953922273D+00, 0.8827390247185D+01,
+     :  0.7352892280868D-06, 0.1124369580175D+01, 0.1589072916335D+01,
+     :  0.6570189360797D-06, 0.2089154042840D+01, 0.1176985366291D+02,
+     :  0.6324967590410D-06, 0.6704855581230D+00, 0.6262300422539D+01,
+     :  0.6298289872283D-06, 0.2836414855840D+01, 0.6303851278352D+01,
+     :  0.6476686465855D-06, 0.4852433866467D+00, 0.7113454667900D-02,
+     :  0.8587034651234D-06, 0.1453511005668D+01, 0.1672837615881D+03,
+     :  0.8068948788113D-06, 0.9224087798609D+00, 0.6069776770667D+01 /
+      DATA ((E0(I,J,2),I=1,3),J= 51, 60) /
+     :  0.8353786011661D-06, 0.4631707184895D+01, 0.3340612434717D+01,
+     :  0.6009324532132D-06, 0.1829498827726D+01, 0.4136910472696D+01,
+     :  0.7558158559566D-06, 0.2588596800317D+01, 0.6496374930224D+01,
+     :  0.5809279504503D-06, 0.5516818853476D+00, 0.1097707878456D+02,
+     :  0.5374131950254D-06, 0.6275674734960D+01, 0.1194447056968D+01,
+     :  0.5711160507326D-06, 0.1091905956872D+01, 0.6282095334605D+01,
+     :  0.5710183170746D-06, 0.2415001635090D+01, 0.6284056366286D+01,
+     :  0.5144373590610D-06, 0.6020336443438D+01, 0.6290189305114D+01,
+     :  0.5103108927267D-06, 0.3775634564605D+01, 0.6275962395778D+01,
+     :  0.4960654697891D-06, 0.1073450946756D+01, 0.6127655567643D+01 /
+      DATA ((E0(I,J,2),I=1,3),J= 61, 70) /
+     :  0.4786385689280D-06, 0.2431178012310D+01, 0.6438496133249D+01,
+     :  0.6109911263665D-06, 0.5343356157914D+01, 0.3154687086868D+01,
+     :  0.4839898944024D-06, 0.5830833594047D-01, 0.8018209333619D+00,
+     :  0.4734822623919D-06, 0.4536080134821D+01, 0.3128388763578D+01,
+     :  0.4834741473290D-06, 0.2585090489754D+00, 0.7084896783808D+01,
+     :  0.5134858581156D-06, 0.4213317172603D+01, 0.1235285262111D+02,
+     :  0.5064004264978D-06, 0.4814418806478D+00, 0.1185621865188D+02,
+     :  0.3753476772761D-06, 0.1599953399788D+01, 0.8429241228195D+01,
+     :  0.4935264014283D-06, 0.2157417556873D+01, 0.2544314396739D+01,
+     :  0.3950929600897D-06, 0.3359394184254D+01, 0.5481254917084D+01 /
+      DATA ((E0(I,J,2),I=1,3),J= 71, 80) /
+     :  0.4895849789777D-06, 0.5165704376558D+01, 0.9225539266174D+01,
+     :  0.4215241688886D-06, 0.2065368800993D+01, 0.1726015463500D+02,
+     :  0.3796773731132D-06, 0.1468606346612D+01, 0.4265981595566D+00,
+     :  0.3114178142515D-06, 0.3615638079474D+01, 0.2146165377750D+01,
+     :  0.3260664220838D-06, 0.4417134922435D+01, 0.4164311961999D+01,
+     :  0.3976996123008D-06, 0.4700866883004D+01, 0.5856477690889D+01,
+     :  0.2801459672924D-06, 0.4538902060922D+01, 0.1256967486051D+02,
+     :  0.3638931868861D-06, 0.1334197991475D+01, 0.1807370494127D+02,
+     :  0.2487013269476D-06, 0.3749275558275D+01, 0.2629832328990D-01,
+     :  0.3034165481994D-06, 0.4236622030873D+00, 0.4535059491685D+01 /
+      DATA ((E0(I,J,2),I=1,3),J= 81, 90) /
+     :  0.2676278825586D-06, 0.5970848007811D+01, 0.3930209696940D+01,
+     :  0.2764903818918D-06, 0.5194636754501D+01, 0.1256262854127D+02,
+     :  0.2485149930507D-06, 0.1002434207846D+01, 0.5088628793478D+01,
+     :  0.2199305540941D-06, 0.3066773098403D+01, 0.1255903824622D+02,
+     :  0.2571106500435D-06, 0.7588312459063D+00, 0.1336797263425D+02,
+     :  0.2049751817158D-06, 0.3444977434856D+01, 0.1137170464392D+02,
+     :  0.2599707296297D-06, 0.1873128542205D+01, 0.7143069561767D+02,
+     :  0.1785018072217D-06, 0.5015891306615D+01, 0.1748016358760D+01,
+     :  0.2324833891115D-06, 0.4618271239730D+01, 0.1831953657923D+02,
+     :  0.1709711119545D-06, 0.5300003455669D+01, 0.4933208510675D+01 /
+      DATA ((E0(I,J,2),I=1,3),J= 91,100) /
+     :  0.2107159351716D-06, 0.2229819815115D+01, 0.7477522907414D+01,
+     :  0.1750333080295D-06, 0.6161485880008D+01, 0.1044738781244D+02,
+     :  0.2000598210339D-06, 0.2967357299999D+01, 0.8031092209206D+01,
+     :  0.1380920248681D-06, 0.3027007923917D+01, 0.8635942003952D+01,
+     :  0.1412460470299D-06, 0.6037597163798D+01, 0.2942463415728D+01,
+     :  0.1888459803001D-06, 0.8561476243374D+00, 0.1561374759853D+03,
+     :  0.1788370542585D-06, 0.4869736290209D+01, 0.1592596075957D+01,
+     :  0.1360893296167D-06, 0.3626411886436D+01, 0.1309584267300D+02,
+     :  0.1506846530160D-06, 0.1550975377427D+01, 0.1649636139783D+02,
+     :  0.1800913376176D-06, 0.2075826033190D+01, 0.1729818233119D+02 /
+      DATA ((E0(I,J,2),I=1,3),J=101,110) /
+     :  0.1436261390649D-06, 0.6148876420255D+01, 0.2042657109477D+02,
+     :  0.1220227114151D-06, 0.4382583879906D+01, 0.7632943190217D+01,
+     :  0.1337883603592D-06, 0.2036644327361D+01, 0.1213955354133D+02,
+     :  0.1159326650738D-06, 0.3892276994687D+01, 0.5331357529664D+01,
+     :  0.1352853128569D-06, 0.1447950649744D+01, 0.1673046366289D+02,
+     :  0.1433408296083D-06, 0.4457854692961D+01, 0.7342457794669D+01,
+     :  0.1234701666518D-06, 0.1538818147151D+01, 0.6279485555400D+01,
+     :  0.1234027192007D-06, 0.1968523220760D+01, 0.6286666145492D+01,
+     :  0.1244024091797D-06, 0.5779803499985D+01, 0.1511046609763D+02,
+     :  0.1097934945516D-06, 0.6210975221388D+00, 0.1098880815746D+02 /
+      DATA ((E0(I,J,2),I=1,3),J=111,120) /
+     :  0.1254611329856D-06, 0.2591963807998D+01, 0.1572083878776D+02,
+     :  0.1158247286784D-06, 0.2483612812670D+01, 0.5729506548653D+01,
+     :  0.9039078252960D-07, 0.3857554579796D+01, 0.9623688285163D+01,
+     :  0.9108024978836D-07, 0.5826368512984D+01, 0.7234794171227D+01,
+     :  0.8887068108436D-07, 0.3475694573987D+01, 0.6148010737701D+01,
+     :  0.8632374035438D-07, 0.3059070488983D-01, 0.6418140963190D+01,
+     :  0.7893186992967D-07, 0.1583194837728D+01, 0.2118763888447D+01,
+     :  0.8297650201172D-07, 0.8519770534637D+00, 0.1471231707864D+02,
+     :  0.1019759578988D-06, 0.1319598738732D+00, 0.1349867339771D+01,
+     :  0.1010037696236D-06, 0.9937860115618D+00, 0.6836645152238D+01 /
+      DATA ((E0(I,J,2),I=1,3),J=121,130) /
+     :  0.1047727548266D-06, 0.1382138405399D+01, 0.5999216516294D+01,
+     :  0.7351993881086D-07, 0.3833397851735D+01, 0.6040347114260D+01,
+     :  0.9868771092341D-07, 0.2124913814390D+01, 0.6566935184597D+01,
+     :  0.7007321959390D-07, 0.5946305343763D+01, 0.6525804586632D+01,
+     :  0.6861411679709D-07, 0.4574654977089D+01, 0.7238675589263D+01,
+     :  0.7554519809614D-07, 0.5949232686844D+01, 0.1253985337760D+02,
+     :  0.9541880448335D-07, 0.3495242990564D+01, 0.2122839202813D+02,
+     :  0.7185606722155D-07, 0.4310113471661D+01, 0.6245048154254D+01,
+     :  0.7131360871710D-07, 0.5480309323650D+01, 0.6321103546637D+01,
+     :  0.6651142021039D-07, 0.5411097713654D+01, 0.5327476111629D+01 /
+      DATA ((E0(I,J,2),I=1,3),J=131,140) /
+     :  0.8538618213667D-07, 0.1827849973951D+01, 0.1101510648075D+02,
+     :  0.8634954288044D-07, 0.5443584943349D+01, 0.5643178611111D+01,
+     :  0.7449415051484D-07, 0.2011535459060D+01, 0.5368044267797D+00,
+     :  0.7421047599169D-07, 0.3464562529249D+01, 0.2354323048545D+02,
+     :  0.6140694354424D-07, 0.5657556228815D+01, 0.1296430071988D+02,
+     :  0.6353525143033D-07, 0.3463816593821D+01, 0.1990745094947D+01,
+     :  0.6221964013447D-07, 0.1532259498697D+01, 0.9517183207817D+00,
+     :  0.5852480257244D-07, 0.1375396598875D+01, 0.9555997388169D+00,
+     :  0.6398637498911D-07, 0.2405645801972D+01, 0.2407292145756D+02,
+     :  0.7039744069878D-07, 0.5397541799027D+01, 0.5225775174439D+00 /
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+     :  0.5396992745159D-08, 0.1833502206373D+01, 0.6279789503410D+01,
+     :  0.6572913000726D-08, 0.3331122065824D+01, 0.1176433076753D+02,
+     :  0.5123421866413D-08, 0.2165327142679D+01, 0.1245594543367D+02,
+     :  0.5930495725999D-08, 0.2931146089284D+01, 0.6414617803568D+01 /
+      DATA ((E0(I,J,2),I=1,3),J=331,340) /
+     :  0.6431797403933D-08, 0.4134407994088D+01, 0.1350651127443D+00,
+     :  0.5003182207604D-08, 0.3805420303749D+01, 0.1096996532989D+02,
+     :  0.5587731032504D-08, 0.1082469260599D+01, 0.6062663316000D+01,
+     :  0.5935263407816D-08, 0.8384333678401D+00, 0.5326786718777D+01,
+     :  0.4756019827760D-08, 0.3552588749309D+01, 0.3104930017775D+01,
+     :  0.6599951172637D-08, 0.4320826409528D+01, 0.4087944051283D+02,
+     :  0.5902606868464D-08, 0.4811879454445D+01, 0.5849364236221D+01,
+     :  0.5921147809031D-08, 0.9942628922396D-01, 0.1581959461667D+01,
+     :  0.5505382581266D-08, 0.2466557607764D+01, 0.6503488384892D+01,
+     :  0.5353771071862D-08, 0.4551978748683D+01, 0.1735668374386D+03 /
+      DATA ((E0(I,J,2),I=1,3),J=341,350) /
+     :  0.5063282210946D-08, 0.5710812312425D+01, 0.1248988586463D+02,
+     :  0.5926120403383D-08, 0.1333998428358D+01, 0.2673594526851D+02,
+     :  0.5211016176149D-08, 0.4649315360760D+01, 0.2460261242967D+02,
+     :  0.5347075084894D-08, 0.5512754081205D+01, 0.4171425416666D+01,
+     :  0.4872609773574D-08, 0.1308025299938D+01, 0.5333900173445D+01,
+     :  0.4727711321420D-08, 0.2144908368062D+01, 0.7232251527446D+01,
+     :  0.6029426018652D-08, 0.5567259412084D+01, 0.3227113045244D+03,
+     :  0.4321485284369D-08, 0.5230667156451D+01, 0.9388005868221D+01,
+     :  0.4476406760553D-08, 0.6134081115303D+01, 0.5547199253223D+01,
+     :  0.5835268277420D-08, 0.4783808492071D+01, 0.7285056171570D+02 /
+      DATA ((E0(I,J,2),I=1,3),J=351,360) /
+     :  0.5172183602748D-08, 0.5161817911099D+01, 0.1884570439172D+02,
+     :  0.5693571465184D-08, 0.1381646203111D+01, 0.9723862754494D+02,
+     :  0.4060634965349D-08, 0.3876705259495D+00, 0.4274518229222D+01,
+     :  0.3967398770473D-08, 0.5029491776223D+01, 0.3496032717521D+01,
+     :  0.3943754005255D-08, 0.1923162955490D+01, 0.6244942932314D+01,
+     :  0.4781323427824D-08, 0.4633332586423D+01, 0.2929661536378D+02,
+     :  0.3871483781204D-08, 0.1616650009743D+01, 0.6321208768577D+01,
+     :  0.5141741733997D-08, 0.9817316704659D-01, 0.1232032006293D+02,
+     :  0.4002385978497D-08, 0.3656161212139D+01, 0.7018952447668D+01,
+     :  0.4901092604097D-08, 0.4404098713092D+01, 0.1478866649112D+01 /
+      DATA ((E0(I,J,2),I=1,3),J=361,370) /
+     :  0.3740932630345D-08, 0.5181188732639D+00, 0.6922973089781D+01,
+     :  0.4387283718538D-08, 0.3254859566869D+01, 0.2331413144044D+03,
+     :  0.5019197802033D-08, 0.3086773224677D+01, 0.1715706182245D+02,
+     :  0.3834931695175D-08, 0.2797882673542D+01, 0.1491901785440D+02,
+     :  0.3760413942497D-08, 0.2892676280217D+01, 0.1726726808967D+02,
+     :  0.3719717204628D-08, 0.5861046025739D+01, 0.6297302759782D+01,
+     :  0.4145623530149D-08, 0.2168239627033D+01, 0.1376059875786D+02,
+     :  0.3932788425380D-08, 0.6271811124181D+01, 0.7872148766781D+01,
+     :  0.3686377476857D-08, 0.3936853151404D+01, 0.6268848941110D+01,
+     :  0.3779077950339D-08, 0.1404148734043D+01, 0.4157198507331D+01 /
+      DATA ((E0(I,J,2),I=1,3),J=371,380) /
+     :  0.4091334550598D-08, 0.2452436180854D+01, 0.9779108567966D+01,
+     :  0.3926694536146D-08, 0.6102292739040D+01, 0.1098419223922D+02,
+     :  0.4841000253289D-08, 0.6072760457276D+01, 0.1252801878276D+02,
+     :  0.4949340130240D-08, 0.1154832815171D+01, 0.1617106187867D+03,
+     :  0.3761557737360D-08, 0.5527545321897D+01, 0.3185192151914D+01,
+     :  0.3647396268188D-08, 0.1525035688629D+01, 0.6271346477544D+01,
+     :  0.3932405074189D-08, 0.5570681040569D+01, 0.2139354194808D+02,
+     :  0.3631322501141D-08, 0.1981240601160D+01, 0.6294805223347D+01,
+     :  0.4130007425139D-08, 0.2050060880201D+01, 0.2195415756911D+02,
+     :  0.4433905965176D-08, 0.3277477970321D+01, 0.7445550607224D+01 /
+      DATA ((E0(I,J,2),I=1,3),J=381,390) /
+     :  0.3851814176947D-08, 0.5210690074886D+01, 0.9562891316684D+00,
+     :  0.3485807052785D-08, 0.6653274904611D+00, 0.1161697602389D+02,
+     :  0.3979772816991D-08, 0.1767941436148D+01, 0.2277943724828D+02,
+     :  0.3402607460500D-08, 0.3421746306465D+01, 0.1087398597200D+02,
+     :  0.4049993000926D-08, 0.1127144787547D+01, 0.3163918923335D+00,
+     :  0.3420511182382D-08, 0.4214794779161D+01, 0.1362553364512D+02,
+     :  0.3640772365012D-08, 0.5324905497687D+01, 0.1725304118033D+02,
+     :  0.3323037987501D-08, 0.6135761838271D+01, 0.6279143387820D+01,
+     :  0.4503141663637D-08, 0.1802305450666D+01, 0.1385561574497D+01,
+     :  0.4314560055588D-08, 0.4812299731574D+01, 0.4176041334900D+01 /
+      DATA ((E0(I,J,2),I=1,3),J=391,400) /
+     :  0.3294226949110D-08, 0.3657547059723D+01, 0.6287008313071D+01,
+     :  0.3215657197281D-08, 0.4866676894425D+01, 0.5749861718712D+01,
+     :  0.4129362656266D-08, 0.3809342558906D+01, 0.5905702259363D+01,
+     :  0.3137762976388D-08, 0.2494635174443D+01, 0.2099539292909D+02,
+     :  0.3514010952384D-08, 0.2699961831678D+01, 0.7335344340001D+01,
+     :  0.3327607571530D-08, 0.3318457714816D+01, 0.5436992986000D+01,
+     :  0.3541066946675D-08, 0.4382703582466D+01, 0.1234573916645D+02,
+     :  0.3216179847052D-08, 0.5271066317054D+01, 0.3802769619140D-01,
+     :  0.2959045059570D-08, 0.5819591585302D+01, 0.2670964694522D+02,
+     :  0.3884040326665D-08, 0.5980934960428D+01, 0.6660449441528D+01 /
+      DATA ((E0(I,J,2),I=1,3),J=401,410) /
+     :  0.2922027539886D-08, 0.3337290282483D+01, 0.1375773836557D+01,
+     :  0.4110846382042D-08, 0.5742978187327D+01, 0.4480965020977D+02,
+     :  0.2934508411032D-08, 0.2278075804200D+01, 0.6408777551755D+00,
+     :  0.3966896193000D-08, 0.5835747858477D+01, 0.3773735910827D+00,
+     :  0.3286695827610D-08, 0.5838898193902D+01, 0.3932462625300D-02,
+     :  0.3720643094196D-08, 0.1122212337858D+01, 0.1646033343740D+02,
+     :  0.3285508906174D-08, 0.9182250996416D+00, 0.1081813534213D+02,
+     :  0.3753880575973D-08, 0.5174761973266D+01, 0.5642198095270D+01,
+     :  0.3022129385587D-08, 0.3381611020639D+01, 0.2982630633589D+02,
+     :  0.2798569205621D-08, 0.3546193723922D+01, 0.1937891852345D+02 /
+      DATA ((E0(I,J,2),I=1,3),J=411,420) /
+     :  0.3397872070505D-08, 0.4533203197934D+01, 0.6923953605621D+01,
+     :  0.3708099772977D-08, 0.2756168198616D+01, 0.3066615496545D+02,
+     :  0.3599283541510D-08, 0.1934395469918D+01, 0.6147450479709D+01,
+     :  0.3688702753059D-08, 0.7149920971109D+00, 0.2636725487657D+01,
+     :  0.2681084724003D-08, 0.4899819493154D+01, 0.6816289982179D+01,
+     :  0.3495993460759D-08, 0.1572418915115D+01, 0.6418701221183D+01,
+     :  0.3130770324995D-08, 0.8912190180489D+00, 0.1235996607578D+02,
+     :  0.2744353821941D-08, 0.3800821940055D+01, 0.2059724391010D+02,
+     :  0.2842732906341D-08, 0.2644717440029D+01, 0.2828699048865D+02,
+     :  0.3046882682154D-08, 0.3987793020179D+01, 0.6055599646783D+01 /
+      DATA ((E0(I,J,2),I=1,3),J=421,430) /
+     :  0.2399072455143D-08, 0.9908826440764D+00, 0.6255674361143D+01,
+     :  0.2384306274204D-08, 0.2516149752220D+01, 0.6310477339748D+01,
+     :  0.2977324500559D-08, 0.5849195642118D+01, 0.1652265972112D+02,
+     :  0.3062835258972D-08, 0.1681660100162D+01, 0.1172006883645D+02,
+     :  0.3109682589231D-08, 0.5804143987737D+00, 0.2751146787858D+02,
+     :  0.2903920355299D-08, 0.5800768280123D+01, 0.6510552054109D+01,
+     :  0.2823221989212D-08, 0.9241118370216D+00, 0.5469525544182D+01,
+     :  0.3187949696649D-08, 0.3139776445735D+01, 0.1693792562116D+03,
+     :  0.2922559771655D-08, 0.3549440782984D+01, 0.2630839062450D+00,
+     :  0.2436302066603D-08, 0.4735540696319D+01, 0.3946258593675D+00 /
+      DATA ((E0(I,J,2),I=1,3),J=431,440) /
+     :  0.3049473043606D-08, 0.4998289124561D+01, 0.8390110365991D+01,
+     :  0.2863682575784D-08, 0.6709515671102D+00, 0.2243449970715D+00,
+     :  0.2641750517966D-08, 0.5410978257284D+01, 0.2986433403208D+02,
+     :  0.2704093466243D-08, 0.4778317207821D+01, 0.6129297044991D+01,
+     :  0.2445522177011D-08, 0.6009020662222D+01, 0.1171295538178D+02,
+     :  0.2623608810230D-08, 0.5010449777147D+01, 0.6436854655901D+01,
+     :  0.2079259704053D-08, 0.5980943768809D+01, 0.2019909489111D+02,
+     :  0.2820225596771D-08, 0.2679965110468D+01, 0.5934151399930D+01,
+     :  0.2365221950927D-08, 0.1894231148810D+01, 0.2470570524223D+02,
+     :  0.2359682077149D-08, 0.4220752950780D+01, 0.8671969964381D+01 /
+      DATA ((E0(I,J,2),I=1,3),J=441,450) /
+     :  0.2387577137206D-08, 0.2571783940617D+01, 0.7096626156709D+01,
+     :  0.1982102089816D-08, 0.5169765997119D+00, 0.1727188400790D+02,
+     :  0.2687502389925D-08, 0.6239078264579D+01, 0.7075506709219D+02,
+     :  0.2207751669135D-08, 0.2031184412677D+01, 0.4377611041777D+01,
+     :  0.2618370214274D-08, 0.8266079985979D+00, 0.6632000300961D+01,
+     :  0.2591951887361D-08, 0.8819350522008D+00, 0.4873985990671D+02,
+     :  0.2375055656248D-08, 0.3520944177789D+01, 0.1590676413561D+02,
+     :  0.2472019978911D-08, 0.1551431908671D+01, 0.6612329252343D+00,
+     :  0.2368157127199D-08, 0.4178610147412D+01, 0.3459636466239D+02,
+     :  0.1764846605693D-08, 0.1506764000157D+01, 0.1980094587212D+02 /
+      DATA ((E0(I,J,2),I=1,3),J=451,460) /
+     :  0.2291769608798D-08, 0.2118250611782D+01, 0.2844914056730D-01,
+     :  0.2209997316943D-08, 0.3363255261678D+01, 0.2666070658668D+00,
+     :  0.2292699097923D-08, 0.4200423956460D+00, 0.1484170571900D-02,
+     :  0.1629683015329D-08, 0.2331362582487D+01, 0.3035599730800D+02,
+     :  0.2206492862426D-08, 0.3400274026992D+01, 0.6281667977667D+01,
+     :  0.2205746568257D-08, 0.1066051230724D+00, 0.6284483723224D+01,
+     :  0.2026310767991D-08, 0.2779066487979D+01, 0.2449240616245D+02,
+     :  0.1762977622163D-08, 0.9951450691840D+00, 0.2045286941806D+02,
+     :  0.1368535049606D-08, 0.6402447365817D+00, 0.2473415438279D+02,
+     :  0.1720598775450D-08, 0.2303524214705D+00, 0.1679593901136D+03 /
+      DATA ((E0(I,J,2),I=1,3),J=461,470) /
+     :  0.1702429015449D-08, 0.6164622655048D+01, 0.3338575901272D+03,
+     :  0.1414033197685D-08, 0.3954561185580D+01, 0.1624205518357D+03,
+     :  0.1573768958043D-08, 0.2028286308984D+01, 0.3144167757552D+02,
+     :  0.1650705184447D-08, 0.2304040666128D+01, 0.5267006960365D+02,
+     :  0.1651087618855D-08, 0.2538461057280D+01, 0.8956999012000D+02,
+     :  0.1616409518983D-08, 0.5111054348152D+01, 0.3332657872986D+02,
+     :  0.1537175173581D-08, 0.5601130666603D+01, 0.3852657435933D+02,
+     :  0.1593191980553D-08, 0.2614340453411D+01, 0.2282781046519D+03,
+     :  0.1499480170643D-08, 0.3624721577264D+01, 0.2823723341956D+02,
+     :  0.1493807843235D-08, 0.4214569879008D+01, 0.2876692439167D+02 /
+      DATA ((E0(I,J,2),I=1,3),J=471,480) /
+     :  0.1074571199328D-08, 0.1496911744704D+00, 0.8397383534231D+02,
+     :  0.1074406983417D-08, 0.1187817671922D+01, 0.8401985929482D+02,
+     :  0.9757576855851D-09, 0.2655703035858D+01, 0.7826370942180D+02,
+     :  0.1258432887565D-08, 0.4969896184844D+01, 0.3115650189215D+03,
+     :  0.1240336343282D-08, 0.5192460776926D+01, 0.1784300471910D+03,
+     :  0.9016107005164D-09, 0.1960356923057D+01, 0.5886454391678D+02,
+     :  0.1135392360918D-08, 0.5082427809068D+01, 0.7842370451713D+02,
+     :  0.9216046089565D-09, 0.2793775037273D+01, 0.1014262087719D+03,
+     :  0.1061276615030D-08, 0.3726144311409D+01, 0.5660027930059D+02,
+     :  0.1010110596263D-08, 0.7404080708937D+00, 0.4245678405627D+02 /
+      DATA ((E0(I,J,2),I=1,3),J=481,490) /
+     :  0.7217424756199D-09, 0.2697449980577D-01, 0.2457074661053D+03,
+     :  0.6912003846756D-09, 0.4253296276335D+01, 0.1679936946371D+03,
+     :  0.6871814664847D-09, 0.5148072412354D+01, 0.6053048899753D+02,
+     :  0.4887158016343D-09, 0.2153581148294D+01, 0.9656299901946D+02,
+     :  0.5161802866314D-09, 0.3852750634351D+01, 0.2442876000072D+03,
+     :  0.5652599559057D-09, 0.1233233356270D+01, 0.8365903305582D+02,
+     :  0.4710812608586D-09, 0.5610486976767D+01, 0.3164282286739D+03,
+     :  0.4909977500324D-09, 0.1639629524123D+01, 0.4059982187939D+03,
+     :  0.4772641839378D-09, 0.3737100368583D+01, 0.1805255418145D+03,
+     :  0.4487562567153D-09, 0.1158417054478D+00, 0.8433466158131D+02 /
+      DATA ((E0(I,J,2),I=1,3),J=491,500) /
+     :  0.3943441230497D-09, 0.6243502862796D+00, 0.2568537517081D+03,
+     :  0.3952236913598D-09, 0.3510377382385D+01, 0.2449975330562D+03,
+     :  0.3788898363417D-09, 0.5916128302299D+01, 0.1568131045107D+03,
+     :  0.3738329328831D-09, 0.1042266763456D+01, 0.3948519331910D+03,
+     :  0.2451199165151D-09, 0.1166788435700D+01, 0.1435713242844D+03,
+     :  0.2436734402904D-09, 0.3254726114901D+01, 0.2268582385539D+03,
+     :  0.2213605274325D-09, 0.1687210598530D+01, 0.1658638954901D+03,
+     :  0.1491521204829D-09, 0.2657541786794D+01, 0.2219950288015D+03,
+     :  0.1474995329744D-09, 0.5013089805819D+01, 0.3052819430710D+03,
+     :  0.1661939475656D-09, 0.5495315428418D+01, 0.2526661704812D+03 /
+      DATA ((E0(I,J,2),I=1,3),J=501,NE0Y) /
+     :  0.9015946748003D-10, 0.2236989966505D+01, 0.4171445043968D+03 /
+
+*  Sun-to-Earth, T^1, Y
+      DATA ((E1(I,J,2),I=1,3),J=  1, 10) /
+     :  0.9304690546528D-06, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.5150715570663D-06, 0.4431807116294D+01, 0.1256615170089D+02,
+     :  0.1290825411056D-07, 0.4388610039678D+01, 0.1884922755134D+02,
+     :  0.4645466665386D-08, 0.5827263376034D+01, 0.6283075850446D+01,
+     :  0.2079625310718D-08, 0.1621698662282D+00, 0.6279552690824D+01,
+     :  0.2078189850907D-08, 0.3344713435140D+01, 0.6286599010068D+01,
+     :  0.6207190138027D-09, 0.5074049319576D+01, 0.4705732307012D+01,
+     :  0.5989826532569D-09, 0.2231842216620D+01, 0.6256777527156D+01,
+     :  0.5961360812618D-09, 0.1274975769045D+01, 0.6309374173736D+01,
+     :  0.4874165471016D-09, 0.3642277426779D+01, 0.7755226100720D+00 /
+      DATA ((E1(I,J,2),I=1,3),J= 11, 20) /
+     :  0.4283834034360D-09, 0.5148765510106D+01, 0.1059381944224D+01,
+     :  0.4652389287529D-09, 0.4715794792175D+01, 0.7860419393880D+01,
+     :  0.3751707476401D-09, 0.6617207370325D+00, 0.5753384878334D+01,
+     :  0.3559998806198D-09, 0.6155548875404D+01, 0.5884926831456D+01,
+     :  0.3558447558857D-09, 0.2898827297664D+01, 0.6812766822558D+01,
+     :  0.3211116927106D-09, 0.3625813502509D+01, 0.6681224869435D+01,
+     :  0.2875609914672D-09, 0.4345435813134D+01, 0.2513230340178D+02,
+     :  0.2843109704069D-09, 0.5862263940038D+01, 0.6127655567643D+01,
+     :  0.2744676468427D-09, 0.3926419475089D+01, 0.6438496133249D+01,
+     :  0.2481285237789D-09, 0.1351976572828D+01, 0.5486777812467D+01 /
+      DATA ((E1(I,J,2),I=1,3),J= 21, 30) /
+     :  0.2060338481033D-09, 0.2147556998591D+01, 0.7079373888424D+01,
+     :  0.2015822358331D-09, 0.4408358972216D+01, 0.6290189305114D+01,
+     :  0.2001195944195D-09, 0.5385829822531D+01, 0.6275962395778D+01,
+     :  0.1953667642377D-09, 0.1304933746120D+01, 0.5507553240374D+01,
+     :  0.1839744078713D-09, 0.6173567228835D+01, 0.1179062909082D+02,
+     :  0.1643334294845D-09, 0.4635942997523D+01, 0.1150676975667D+02,
+     :  0.1768051018652D-09, 0.5086283558874D+01, 0.7113454667900D-02,
+     :  0.1674874205489D-09, 0.2243332137241D+01, 0.7058598460518D+01,
+     :  0.1421445397609D-09, 0.6186899771515D+01, 0.7962980379786D+00,
+     :  0.1255163958267D-09, 0.5730238465658D+01, 0.4694002934110D+01 /
+      DATA ((E1(I,J,2),I=1,3),J= 31, 40) /
+     :  0.1013945281961D-09, 0.1726055228402D+01, 0.3738761453707D+01,
+     :  0.1047294335852D-09, 0.2658801228129D+01, 0.6282095334605D+01,
+     :  0.1047103879392D-09, 0.8481047835035D+00, 0.6284056366286D+01,
+     :  0.9530343962826D-10, 0.3079267149859D+01, 0.6069776770667D+01,
+     :  0.9604637611690D-10, 0.3258679792918D+00, 0.4136910472696D+01,
+     :  0.9153518537177D-10, 0.4398599886584D+00, 0.6496374930224D+01,
+     :  0.8562458214922D-10, 0.4772686794145D+01, 0.1194447056968D+01,
+     :  0.8232525360654D-10, 0.5966220721679D+01, 0.1589072916335D+01,
+     :  0.6150223411438D-10, 0.1780985591923D+01, 0.8827390247185D+01,
+     :  0.6272087858000D-10, 0.3184305429012D+01, 0.8429241228195D+01 /
+      DATA ((E1(I,J,2),I=1,3),J= 41, 50) /
+     :  0.5540476311040D-10, 0.3801260595433D+01, 0.4933208510675D+01,
+     :  0.7331901699361D-10, 0.5205948591865D+01, 0.4535059491685D+01,
+     :  0.6018528702791D-10, 0.4770139083623D+01, 0.1255903824622D+02,
+     :  0.5150530724804D-10, 0.3574796899585D+01, 0.1176985366291D+02,
+     :  0.6471933741811D-10, 0.2679787266521D+01, 0.5088628793478D+01,
+     :  0.5317460644174D-10, 0.9528763345494D+00, 0.3154687086868D+01,
+     :  0.4832187748783D-10, 0.5329322498232D+01, 0.6040347114260D+01,
+     :  0.4716763555110D-10, 0.2395235316466D+01, 0.5331357529664D+01,
+     :  0.4871509139861D-10, 0.3056663648823D+01, 0.1256967486051D+02,
+     :  0.4598417696768D-10, 0.4452762609019D+01, 0.6525804586632D+01 /
+      DATA ((E1(I,J,2),I=1,3),J= 51, 60) /
+     :  0.5674189533175D-10, 0.9879680872193D+00, 0.5729506548653D+01,
+     :  0.4073560328195D-10, 0.5939127696986D+01, 0.7632943190217D+01,
+     :  0.5040994945359D-10, 0.4549875824510D+01, 0.8031092209206D+01,
+     :  0.5078185134679D-10, 0.7346659893982D+00, 0.7477522907414D+01,
+     :  0.3769343537061D-10, 0.1071317188367D+01, 0.7234794171227D+01,
+     :  0.4980331365299D-10, 0.2500345341784D+01, 0.6836645152238D+01,
+     :  0.3458236594757D-10, 0.3825159450711D+01, 0.1097707878456D+02,
+     :  0.3578859493602D-10, 0.5299664791549D+01, 0.4164311961999D+01,
+     :  0.3370504646419D-10, 0.5002316301593D+01, 0.1137170464392D+02,
+     :  0.3299873338428D-10, 0.2526123275282D+01, 0.3930209696940D+01 /
+      DATA ((E1(I,J,2),I=1,3),J= 61, 70) /
+     :  0.4304917318409D-10, 0.3368078557132D+01, 0.1592596075957D+01,
+     :  0.3402418753455D-10, 0.8385495425800D+00, 0.3128388763578D+01,
+     :  0.2778460572146D-10, 0.3669905203240D+01, 0.7342457794669D+01,
+     :  0.2782710128902D-10, 0.2691664812170D+00, 0.1748016358760D+01,
+     :  0.2711725179646D-10, 0.4707487217718D+01, 0.5296909721118D+00,
+     :  0.2981760946340D-10, 0.3190260867816D+00, 0.5368044267797D+00,
+     :  0.2811672977772D-10, 0.3196532315372D+01, 0.7084896783808D+01,
+     :  0.2863454474467D-10, 0.2263240324780D+00, 0.5223693906222D+01,
+     :  0.3333464634051D-10, 0.3498451685065D+01, 0.8018209333619D+00,
+     :  0.3312991747609D-10, 0.5839154477412D+01, 0.1554202828031D+00 /
+      DATA ((E1(I,J,2),I=1,3),J= 71,NE1Y) /
+     :  0.2813255564006D-10, 0.8268044346621D+00, 0.5225775174439D+00,
+     :  0.2665098083966D-10, 0.3934021725360D+01, 0.5216580451554D+01,
+     :  0.2349795705216D-10, 0.5197620913779D+01, 0.2146165377750D+01,
+     :  0.2330352293961D-10, 0.2984999231807D+01, 0.1726015463500D+02,
+     :  0.2728001683419D-10, 0.6521679638544D+00, 0.8635942003952D+01,
+     :  0.2484061007669D-10, 0.3468955561097D+01, 0.5230807360890D+01,
+     :  0.2646328768427D-10, 0.1013724533516D+01, 0.2629832328990D-01,
+     :  0.2518630264831D-10, 0.6108081057122D+01, 0.5481254917084D+01,
+     :  0.2421901455384D-10, 0.1651097776260D+01, 0.1349867339771D+01,
+     :  0.6348533267831D-11, 0.3220226560321D+01, 0.8433466158131D+02 /
+
+*  Sun-to-Earth, T^2, Y
+      DATA ((E2(I,J,2),I=1,3),J=  1,NE2Y) /
+     :  0.5063375872532D-10, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.2173815785980D-10, 0.2827805833053D+01, 0.1256615170089D+02,
+     :  0.1010231999920D-10, 0.4634612377133D+01, 0.6283075850446D+01,
+     :  0.9259745317636D-12, 0.2620612076189D+01, 0.1884922755134D+02,
+     :  0.1022202095812D-12, 0.3809562326066D+01, 0.8399684731857D+02 /
+
+*  Sun-to-Earth, T^0, Z
+      DATA ((E0(I,J,3),I=1,3),J=  1, 10) /
+     :  0.2796207639075D-05, 0.3198701560209D+01, 0.8433466158131D+02,
+     :  0.1016042198142D-05, 0.5422360395913D+01, 0.5507553240374D+01,
+     :  0.8044305033647D-06, 0.3880222866652D+01, 0.5223693906222D+01,
+     :  0.4385347909274D-06, 0.3704369937468D+01, 0.2352866153506D+01,
+     :  0.3186156414906D-06, 0.3999639363235D+01, 0.1577343543434D+01,
+     :  0.2272412285792D-06, 0.3984738315952D+01, 0.1047747311755D+01,
+     :  0.1645620103007D-06, 0.3565412516841D+01, 0.5856477690889D+01,
+     :  0.1815836921166D-06, 0.4984507059020D+01, 0.6283075850446D+01,
+     :  0.1447461676364D-06, 0.3702753570108D+01, 0.9437762937313D+01,
+     :  0.1430760876382D-06, 0.3409658712357D+01, 0.1021328554739D+02 /
+      DATA ((E0(I,J,3),I=1,3),J= 11, 20) /
+     :  0.1120445753226D-06, 0.4829561570246D+01, 0.1414349524433D+02,
+     :  0.1090232840797D-06, 0.2080729178066D+01, 0.6812766822558D+01,
+     :  0.9715727346551D-07, 0.3476295881948D+01, 0.4694002934110D+01,
+     :  0.1036267136217D-06, 0.4056639536648D+01, 0.7109288135493D+02,
+     :  0.8752665271340D-07, 0.4448159519911D+01, 0.5753384878334D+01,
+     :  0.8331864956004D-07, 0.4991704044208D+01, 0.7084896783808D+01,
+     :  0.6901658670245D-07, 0.4325358994219D+01, 0.6275962395778D+01,
+     :  0.9144536848998D-07, 0.1141826375363D+01, 0.6620890113188D+01,
+     :  0.7205085037435D-07, 0.3624344170143D+01, 0.5296909721118D+00,
+     :  0.7697874654176D-07, 0.5554257458998D+01, 0.1676215758509D+03 /
+      DATA ((E0(I,J,3),I=1,3),J= 21, 30) /
+     :  0.5197545738384D-07, 0.6251760961735D+01, 0.1807370494127D+02,
+     :  0.5031345378608D-07, 0.2497341091913D+01, 0.4705732307012D+01,
+     :  0.4527110205840D-07, 0.2335079920992D+01, 0.6309374173736D+01,
+     :  0.4753355798089D-07, 0.7094148987474D+00, 0.5884926831456D+01,
+     :  0.4296951977516D-07, 0.1101916352091D+01, 0.6681224869435D+01,
+     :  0.3855341568387D-07, 0.1825495405486D+01, 0.5486777812467D+01,
+     :  0.5253930970990D-07, 0.4424740687208D+01, 0.7860419393880D+01,
+     :  0.4024630496471D-07, 0.5120498157053D+01, 0.1336797263425D+02,
+     :  0.4061069791453D-07, 0.6029771435451D+01, 0.3930209696940D+01,
+     :  0.3797883804205D-07, 0.4435193600836D+00, 0.3154687086868D+01 /
+      DATA ((E0(I,J,3),I=1,3),J= 31, 40) /
+     :  0.2933033225587D-07, 0.5124157356507D+01, 0.1059381944224D+01,
+     :  0.3503000930426D-07, 0.5421830162065D+01, 0.6069776770667D+01,
+     :  0.3670096214050D-07, 0.4582101667297D+01, 0.1219403291462D+02,
+     :  0.2905609437008D-07, 0.1926566420072D+01, 0.1097707878456D+02,
+     :  0.2466827821713D-07, 0.6090174539834D+00, 0.6496374930224D+01,
+     :  0.2691647295332D-07, 0.1393432595077D+01, 0.2200391463820D+02,
+     :  0.2150554667946D-07, 0.4308671715951D+01, 0.5643178611111D+01,
+     :  0.2237481922680D-07, 0.8133968269414D+00, 0.8635942003952D+01,
+     :  0.1817741038157D-07, 0.3755205127454D+01, 0.3340612434717D+01,
+     :  0.2227820762132D-07, 0.2759558596664D+01, 0.1203646072878D+02 /
+      DATA ((E0(I,J,3),I=1,3),J= 41, 50) /
+     :  0.1944713772307D-07, 0.5699645869121D+01, 0.1179062909082D+02,
+     :  0.1527340520662D-07, 0.1986749091746D+01, 0.3981490189893D+00,
+     :  0.1577282574914D-07, 0.3205017217983D+01, 0.5088628793478D+01,
+     :  0.1424738825424D-07, 0.6256747903666D+01, 0.2544314396739D+01,
+     :  0.1616563121701D-07, 0.2601671259394D+00, 0.1729818233119D+02,
+     :  0.1401210391692D-07, 0.4686939173506D+01, 0.7058598460518D+01,
+     :  0.1488726974214D-07, 0.2815862451372D+01, 0.2593412433514D+02,
+     :  0.1692626442388D-07, 0.4956894109797D+01, 0.1564752902480D+03,
+     :  0.1123571582910D-07, 0.2381192697696D+01, 0.3738761453707D+01,
+     :  0.9903308606317D-08, 0.4294851657684D+01, 0.9225539266174D+01 /
+      DATA ((E0(I,J,3),I=1,3),J= 51, 60) /
+     :  0.9174533187191D-08, 0.3075171510642D+01, 0.4164311961999D+01,
+     :  0.8645985631457D-08, 0.5477534821633D+00, 0.8429241228195D+01,
+     : -0.1085876492688D-07, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.9264309077815D-08, 0.5968571670097D+01, 0.7079373888424D+01,
+     :  0.8243116984954D-08, 0.1489098777643D+01, 0.1044738781244D+02,
+     :  0.8268102113708D-08, 0.3512977691983D+01, 0.1150676975667D+02,
+     :  0.9043613988227D-08, 0.1290704408221D+00, 0.1101510648075D+02,
+     :  0.7432912038789D-08, 0.1991086893337D+01, 0.2608790314060D+02,
+     :  0.8586233727285D-08, 0.4238357924414D+01, 0.2986433403208D+02,
+     :  0.7612230060131D-08, 0.2911090150166D+01, 0.4732030630302D+01 /
+      DATA ((E0(I,J,3),I=1,3),J= 61, 70) /
+     :  0.7097787751408D-08, 0.1908938392390D+01, 0.8031092209206D+01,
+     :  0.7640237040175D-08, 0.6129219000168D+00, 0.7962980379786D+00,
+     :  0.7070445688081D-08, 0.1380417036651D+01, 0.2146165377750D+01,
+     :  0.7690770957702D-08, 0.1680504249084D+01, 0.2122839202813D+02,
+     :  0.8051292542594D-08, 0.5127423484511D+01, 0.2942463415728D+01,
+     :  0.5902709104515D-08, 0.2020274190917D+01, 0.7755226100720D+00,
+     :  0.5134567496462D-08, 0.2606778676418D+01, 0.1256615170089D+02,
+     :  0.5525802046102D-08, 0.1613011769663D+01, 0.8018209333619D+00,
+     :  0.5880724784221D-08, 0.4604483417236D+01, 0.4690479774488D+01,
+     :  0.5211699081370D-08, 0.5718964114193D+01, 0.8827390247185D+01 /
+      DATA ((E0(I,J,3),I=1,3),J= 71, 80) /
+     :  0.4891849573562D-08, 0.3689658932196D+01, 0.2132990797783D+00,
+     :  0.5150246069997D-08, 0.4099769855122D+01, 0.6480980550449D+02,
+     :  0.5102434319633D-08, 0.5660834602509D+01, 0.3379454372902D+02,
+     :  0.5083405254252D-08, 0.9842221218974D+00, 0.4136910472696D+01,
+     :  0.4206562585682D-08, 0.1341363634163D+00, 0.3128388763578D+01,
+     :  0.4663249683579D-08, 0.8130132735866D+00, 0.5216580451554D+01,
+     :  0.4099474416530D-08, 0.5791497770644D+01, 0.4265981595566D+00,
+     :  0.4628251220767D-08, 0.1249802769331D+01, 0.1572083878776D+02,
+     :  0.5024068728142D-08, 0.4795684802743D+01, 0.6290189305114D+01,
+     :  0.5120234327758D-08, 0.3810420387208D+01, 0.5230807360890D+01 /
+      DATA ((E0(I,J,3),I=1,3),J= 81, 90) /
+     :  0.5524029815280D-08, 0.1029264714351D+01, 0.2397622045175D+03,
+     :  0.4757415718860D-08, 0.3528044781779D+01, 0.1649636139783D+02,
+     :  0.3915786131127D-08, 0.5593889282646D+01, 0.1589072916335D+01,
+     :  0.4869053149991D-08, 0.3299636454433D+01, 0.7632943190217D+01,
+     :  0.3649365703729D-08, 0.1286049002584D+01, 0.6206810014183D+01,
+     :  0.3992493949002D-08, 0.3100307589464D+01, 0.2515860172507D+02,
+     :  0.3320247477418D-08, 0.6212683940807D+01, 0.1216800268190D+02,
+     :  0.3287123739696D-08, 0.4699118445928D+01, 0.7234794171227D+01,
+     :  0.3472776811103D-08, 0.2630507142004D+01, 0.7342457794669D+01,
+     :  0.3423253294767D-08, 0.2946432844305D+01, 0.9623688285163D+01 /
+      DATA ((E0(I,J,3),I=1,3),J= 91,100) /
+     :  0.3896173898244D-08, 0.1224834179264D+01, 0.6438496133249D+01,
+     :  0.3388455337924D-08, 0.1543807616351D+01, 0.1494531617769D+02,
+     :  0.3062704716523D-08, 0.1191777572310D+01, 0.8662240327241D+01,
+     :  0.3270075600400D-08, 0.5483498767737D+01, 0.1194447056968D+01,
+     :  0.3101209215259D-08, 0.8000833804348D+00, 0.3772475342596D+02,
+     :  0.2780883347311D-08, 0.4077980721888D+00, 0.5863591145557D+01,
+     :  0.2903605931824D-08, 0.2617490302147D+01, 0.1965104848470D+02,
+     :  0.2682014743119D-08, 0.2634703158290D+01, 0.7238675589263D+01,
+     :  0.2534360108492D-08, 0.6102446114873D+01, 0.6836645152238D+01,
+     :  0.2392564882509D-08, 0.3681820208691D+01, 0.5849364236221D+01 /
+      DATA ((E0(I,J,3),I=1,3),J=101,110) /
+     :  0.2656667254856D-08, 0.6216045388886D+01, 0.6133512519065D+01,
+     :  0.2331242096773D-08, 0.5864949777744D+01, 0.4535059491685D+01,
+     :  0.2287898363668D-08, 0.4566628532802D+01, 0.7477522907414D+01,
+     :  0.2336944521306D-08, 0.2442722126930D+01, 0.1137170464392D+02,
+     :  0.3156632236269D-08, 0.1626628050682D+01, 0.2509084901204D+03,
+     :  0.2982612402766D-08, 0.2803604512609D+01, 0.1748016358760D+01,
+     :  0.2774031674807D-08, 0.4654002897158D+01, 0.8223916695780D+02,
+     :  0.2295236548638D-08, 0.4326518333253D+01, 0.3378142627421D+00,
+     :  0.2190714699873D-08, 0.4519614578328D+01, 0.2908881142201D+02,
+     :  0.2191495845045D-08, 0.3012626912549D+01, 0.1673046366289D+02 /
+      DATA ((E0(I,J,3),I=1,3),J=111,120) /
+     :  0.2492901628386D-08, 0.1290101424052D+00, 0.1543797956245D+03,
+     :  0.1993778064319D-08, 0.3864046799414D+01, 0.1778984560711D+02,
+     :  0.1898146479022D-08, 0.5053777235891D+01, 0.2042657109477D+02,
+     :  0.1918280127634D-08, 0.2222470192548D+01, 0.4165496312290D+02,
+     :  0.1916351061607D-08, 0.8719067257774D+00, 0.7737595720538D+02,
+     :  0.1834720181466D-08, 0.4031491098040D+01, 0.2358125818164D+02,
+     :  0.1249201523806D-08, 0.5938379466835D+01, 0.3301902111895D+02,
+     :  0.1477304050539D-08, 0.6544722606797D+00, 0.9548094718417D+02,
+     :  0.1264316431249D-08, 0.2059072853236D+01, 0.8399684731857D+02,
+     :  0.1203526495039D-08, 0.3644813532605D+01, 0.4558517281984D+02 /
+      DATA ((E0(I,J,3),I=1,3),J=121,130) /
+     :  0.9221681059831D-09, 0.3241815055602D+01, 0.7805158573086D+02,
+     :  0.7849278367646D-09, 0.5043812342457D+01, 0.5217580628120D+02,
+     :  0.7983392077387D-09, 0.5000024502753D+01, 0.1501922143975D+03,
+     :  0.7925395431654D-09, 0.1398734871821D-01, 0.9061773743175D+02,
+     :  0.7640473285886D-09, 0.5067111723130D+01, 0.4951538251678D+02,
+     :  0.5398937754482D-09, 0.5597382200075D+01, 0.1613385000004D+03,
+     :  0.5626247550193D-09, 0.2601338209422D+01, 0.7318837597844D+02,
+     :  0.5525197197855D-09, 0.5814832109256D+01, 0.1432335100216D+03,
+     :  0.5407629837898D-09, 0.3384820609076D+01, 0.3230491187871D+03,
+     :  0.3856739119801D-09, 0.1072391840473D+01, 0.2334791286671D+03 /
+      DATA ((E0(I,J,3),I=1,3),J=131,NE0Z) /
+     :  0.3856425239987D-09, 0.2369540393327D+01, 0.1739046517013D+03,
+     :  0.4350867755983D-09, 0.5255575751082D+01, 0.1620484330494D+03,
+     :  0.3844113924996D-09, 0.5482356246182D+01, 0.9757644180768D+02,
+     :  0.2854869155431D-09, 0.9573634763143D+00, 0.1697170704744D+03,
+     :  0.1719227671416D-09, 0.1887203025202D+01, 0.2265204242912D+03,
+     :  0.1527846879755D-09, 0.3982183931157D+01, 0.3341954043900D+03,
+     :  0.1128229264847D-09, 0.2787457156298D+01, 0.3119028331842D+03 /
+
+*  Sun-to-Earth, T^1, Z
+      DATA ((E1(I,J,3),I=1,3),J=  1, 10) /
+     :  0.2278290449966D-05, 0.3413716033863D+01, 0.6283075850446D+01,
+     :  0.5429458209830D-07, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.1903240492525D-07, 0.3370592358297D+01, 0.1256615170089D+02,
+     :  0.2385409276743D-09, 0.3327914718416D+01, 0.1884922755134D+02,
+     :  0.8676928342573D-10, 0.1824006811264D+01, 0.5223693906222D+01,
+     :  0.7765442593544D-10, 0.3888564279247D+01, 0.5507553240374D+01,
+     :  0.7066158332715D-10, 0.5194267231944D+01, 0.2352866153506D+01,
+     :  0.7092175288657D-10, 0.2333246960021D+01, 0.8399684731857D+02,
+     :  0.5357582213535D-10, 0.2224031176619D+01, 0.5296909721118D+00,
+     :  0.3828035865021D-10, 0.2156710933584D+01, 0.6279552690824D+01 /
+      DATA ((E1(I,J,3),I=1,3),J= 11,NE1Z) /
+     :  0.3824857220427D-10, 0.1529755219915D+01, 0.6286599010068D+01,
+     :  0.3286995181628D-10, 0.4879512900483D+01, 0.1021328554739D+02 /
+
+*  Sun-to-Earth, T^2, Z
+      DATA ((E2(I,J,3),I=1,3),J=  1,NE2Z) /
+     :  0.9722666114891D-10, 0.5152219582658D+01, 0.6283075850446D+01,
+     : -0.3494819171909D-11, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.6713034376076D-12, 0.6440188750495D+00, 0.1256615170089D+02 /
+
+*  SSB-to-Sun, T^0, X
+      DATA ((S0(I,J,1),I=1,3),J=  1, 10) /
+     :  0.4956757536410D-02, 0.3741073751789D+01, 0.5296909721118D+00,
+     :  0.2718490072522D-02, 0.4016011511425D+01, 0.2132990797783D+00,
+     :  0.1546493974344D-02, 0.2170528330642D+01, 0.3813291813120D-01,
+     :  0.8366855276341D-03, 0.2339614075294D+01, 0.7478166569050D-01,
+     :  0.2936777942117D-03, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.1201317439469D-03, 0.4090736353305D+01, 0.1059381944224D+01,
+     :  0.7578550887230D-04, 0.3241518088140D+01, 0.4265981595566D+00,
+     :  0.1941787367773D-04, 0.1012202064330D+01, 0.2061856251104D+00,
+     :  0.1889227765991D-04, 0.3892520416440D+01, 0.2204125344462D+00,
+     :  0.1937896968613D-04, 0.4797779441161D+01, 0.1495633313810D+00 /
+      DATA ((S0(I,J,1),I=1,3),J= 11, 20) /
+     :  0.1434506110873D-04, 0.3868960697933D+01, 0.5225775174439D+00,
+     :  0.1406659911580D-04, 0.4759766557397D+00, 0.5368044267797D+00,
+     :  0.1179022300202D-04, 0.7774961520598D+00, 0.7626583626240D-01,
+     :  0.8085864460959D-05, 0.3254654471465D+01, 0.3664874755930D-01,
+     :  0.7622752967615D-05, 0.4227633103489D+01, 0.3961708870310D-01,
+     :  0.6209171139066D-05, 0.2791828325711D+00, 0.7329749511860D-01,
+     :  0.4366435633970D-05, 0.4440454875925D+01, 0.1589072916335D+01,
+     :  0.3792124889348D-05, 0.5156393842356D+01, 0.7113454667900D-02,
+     :  0.3154548963402D-05, 0.6157005730093D+01, 0.4194847048887D+00,
+     :  0.3088359882942D-05, 0.2494567553163D+01, 0.6398972393349D+00 /
+      DATA ((S0(I,J,1),I=1,3),J= 21, 30) /
+     :  0.2788440902136D-05, 0.4934318747989D+01, 0.1102062672231D+00,
+     :  0.3039928456376D-05, 0.4895077702640D+01, 0.6283075850446D+01,
+     :  0.2272258457679D-05, 0.5278394064764D+01, 0.1030928125552D+00,
+     :  0.2162007057957D-05, 0.5802978019099D+01, 0.3163918923335D+00,
+     :  0.1767632855737D-05, 0.3415346595193D-01, 0.1021328554739D+02,
+     :  0.1349413459362D-05, 0.2001643230755D+01, 0.1484170571900D-02,
+     :  0.1170141900476D-05, 0.2424750491620D+01, 0.6327837846670D+00,
+     :  0.1054355266820D-05, 0.3123311487576D+01, 0.4337116142245D+00,
+     :  0.9800822461610D-06, 0.3026258088130D+01, 0.1052268489556D+01,
+     :  0.1091203749931D-05, 0.3157811670347D+01, 0.1162474756779D+01 /
+      DATA ((S0(I,J,1),I=1,3),J= 31, 40) /
+     :  0.6960236715913D-06, 0.8219570542313D+00, 0.1066495398892D+01,
+     :  0.5689257296909D-06, 0.1323052375236D+01, 0.9491756770005D+00,
+     :  0.6613172135802D-06, 0.2765348881598D+00, 0.8460828644453D+00,
+     :  0.6277702517571D-06, 0.5794064466382D+01, 0.1480791608091D+00,
+     :  0.6304884066699D-06, 0.7323555380787D+00, 0.2243449970715D+00,
+     :  0.4897850467382D-06, 0.3062464235399D+01, 0.3340612434717D+01,
+     :  0.3759148598786D-06, 0.4588290469664D+01, 0.3516457698740D-01,
+     :  0.3110520548195D-06, 0.1374299536572D+01, 0.6373574839730D-01,
+     :  0.3064708359780D-06, 0.4222267485047D+01, 0.1104591729320D-01,
+     :  0.2856347168241D-06, 0.3714202944973D+01, 0.1510475019529D+00 /
+      DATA ((S0(I,J,1),I=1,3),J= 41, 50) /
+     :  0.2840945514288D-06, 0.2847972875882D+01, 0.4110125927500D-01,
+     :  0.2378951599405D-06, 0.3762072563388D+01, 0.2275259891141D+00,
+     :  0.2714229481417D-06, 0.1036049980031D+01, 0.2535050500000D-01,
+     :  0.2323551717307D-06, 0.4682388599076D+00, 0.8582758298370D-01,
+     :  0.1881790512219D-06, 0.4790565425418D+01, 0.2118763888447D+01,
+     :  0.2261353968371D-06, 0.1669144912212D+01, 0.7181332454670D-01,
+     :  0.2214546389848D-06, 0.3937717281614D+01, 0.2968341143800D-02,
+     :  0.2184915594933D-06, 0.1129169845099D+00, 0.7775000683430D-01,
+     :  0.2000164937936D-06, 0.4030009638488D+01, 0.2093666171530D+00,
+     :  0.1966105136719D-06, 0.8745955786834D+00, 0.2172315424036D+00 /
+      DATA ((S0(I,J,1),I=1,3),J= 51, 60) /
+     :  0.1904742332624D-06, 0.5919743598964D+01, 0.2022531624851D+00,
+     :  0.1657399705031D-06, 0.2549141484884D+01, 0.7358765972222D+00,
+     :  0.1574070533987D-06, 0.5277533020230D+01, 0.7429900518901D+00,
+     :  0.1832261651039D-06, 0.3064688127777D+01, 0.3235053470014D+00,
+     :  0.1733615346569D-06, 0.3011432799094D+01, 0.1385174140878D+00,
+     :  0.1549124014496D-06, 0.4005569132359D+01, 0.5154640627760D+00,
+     :  0.1637044713838D-06, 0.1831375966632D+01, 0.8531963191132D+00,
+     :  0.1123420082383D-06, 0.1180270407578D+01, 0.1990721704425D+00,
+     :  0.1083754165740D-06, 0.3414101320863D+00, 0.5439178814476D+00,
+     :  0.1156638012655D-06, 0.6130479452594D+00, 0.5257585094865D+00 /
+      DATA ((S0(I,J,1),I=1,3),J= 61, 70) /
+     :  0.1142548785134D-06, 0.3724761948846D+01, 0.5336234347371D+00,
+     :  0.7921463895965D-07, 0.2435425589361D+01, 0.1478866649112D+01,
+     :  0.7428600285231D-07, 0.3542144398753D+01, 0.2164800718209D+00,
+     :  0.8323211246747D-07, 0.3525058072354D+01, 0.1692165728891D+01,
+     :  0.7257595116312D-07, 0.1364299431982D+01, 0.2101180877357D+00,
+     :  0.7111185833236D-07, 0.2460478875808D+01, 0.4155522422634D+00,
+     :  0.6868090383716D-07, 0.4397327670704D+01, 0.1173197218910D+00,
+     :  0.7226419974175D-07, 0.4042647308905D+01, 0.1265567569334D+01,
+     :  0.6955642383177D-07, 0.2865047906085D+01, 0.9562891316684D+00,
+     :  0.7492139296331D-07, 0.5014278994215D+01, 0.1422690933580D-01 /
+      DATA ((S0(I,J,1),I=1,3),J= 71, 80) /
+     :  0.6598363128857D-07, 0.2376730020492D+01, 0.6470106940028D+00,
+     :  0.7381147293385D-07, 0.3272990384244D+01, 0.1581959461667D+01,
+     :  0.6402909624032D-07, 0.5302290955138D+01, 0.9597935788730D-01,
+     :  0.6237454263857D-07, 0.5444144425332D+01, 0.7084920306520D-01,
+     :  0.5241198544016D-07, 0.4215359579205D+01, 0.5265099800692D+00,
+     :  0.5144463853918D-07, 0.1218916689916D+00, 0.5328719641544D+00,
+     :  0.5868164772299D-07, 0.2369402002213D+01, 0.7871412831580D-01,
+     :  0.6233195669151D-07, 0.1254922242403D+01, 0.2608790314060D+02,
+     :  0.6068463791422D-07, 0.5679713760431D+01, 0.1114304132498D+00,
+     :  0.4359361135065D-07, 0.6097219641646D+00, 0.1375773836557D+01 /
+      DATA ((S0(I,J,1),I=1,3),J= 81, 90) /
+     :  0.4686510366826D-07, 0.4786231041431D+01, 0.1143987543936D+00,
+     :  0.3758977287225D-07, 0.1167368068139D+01, 0.1596186371003D+01,
+     :  0.4282051974778D-07, 0.1519471064319D+01, 0.2770348281756D+00,
+     :  0.5153765386113D-07, 0.1860532322984D+01, 0.2228608264996D+00,
+     :  0.4575129387188D-07, 0.7632857887158D+00, 0.1465949902372D+00,
+     :  0.3326844933286D-07, 0.1298219485285D+01, 0.5070101000000D-01,
+     :  0.3748617450984D-07, 0.1046510321062D+01, 0.4903339079539D+00,
+     :  0.2816756661499D-07, 0.3434522346190D+01, 0.2991266627620D+00,
+     :  0.3412750405039D-07, 0.2523766270318D+01, 0.3518164938661D+00,
+     :  0.2655796761776D-07, 0.2904422260194D+01, 0.6256703299991D+00 /
+      DATA ((S0(I,J,1),I=1,3),J= 91,100) /
+     :  0.2963597929458D-07, 0.5923900431149D+00, 0.1099462426779D+00,
+     :  0.2539523734781D-07, 0.4851947722567D+01, 0.1256615170089D+02,
+     :  0.2283087914139D-07, 0.3400498595496D+01, 0.6681224869435D+01,
+     :  0.2321309799331D-07, 0.5789099148673D+01, 0.3368040641550D-01,
+     :  0.2549657649750D-07, 0.3991856479792D-01, 0.1169588211447D+01,
+     :  0.2290462303977D-07, 0.2788567577052D+01, 0.1045155034888D+01,
+     :  0.1945398522914D-07, 0.3290896998176D+01, 0.1155361302111D+01,
+     :  0.1849171512638D-07, 0.2698060129367D+01, 0.4452511715700D-02,
+     :  0.1647199834254D-07, 0.3016735644085D+01, 0.4408250688924D+00,
+     :  0.1529530765273D-07, 0.5573043116178D+01, 0.6521991896920D-01 /
+      DATA ((S0(I,J,1),I=1,3),J=101,110) /
+     :  0.1433199339978D-07, 0.1481192356147D+01, 0.9420622223326D+00,
+     :  0.1729134193602D-07, 0.1422817538933D+01, 0.2108507877249D+00,
+     :  0.1716463931346D-07, 0.3469468901855D+01, 0.2157473718317D+00,
+     :  0.1391206061378D-07, 0.6122436220547D+01, 0.4123712502208D+00,
+     :  0.1404746661924D-07, 0.1647765641936D+01, 0.4258542984690D-01,
+     :  0.1410452399455D-07, 0.5989729161964D+01, 0.2258291676434D+00,
+     :  0.1089828772168D-07, 0.2833705509371D+01, 0.4226656969313D+00,
+     :  0.1047374564948D-07, 0.5090690007331D+00, 0.3092784376656D+00,
+     :  0.1358279126532D-07, 0.5128990262836D+01, 0.7923417740620D-01,
+     :  0.1020456476148D-07, 0.9632772880808D+00, 0.1456308687557D+00 /
+      DATA ((S0(I,J,1),I=1,3),J=111,120) /
+     :  0.1033428735328D-07, 0.3223779318418D+01, 0.1795258541446D+01,
+     :  0.1412435841540D-07, 0.2410271572721D+01, 0.1525316725248D+00,
+     :  0.9722759371574D-08, 0.2333531395690D+01, 0.8434341241180D-01,
+     :  0.9657334084704D-08, 0.6199270974168D+01, 0.1272681024002D+01,
+     :  0.1083641148690D-07, 0.2864222292929D+01, 0.7032915397480D-01,
+     :  0.1067318403838D-07, 0.5833458866568D+00, 0.2123349582968D+00,
+     :  0.1062366201976D-07, 0.4307753989494D+01, 0.2142632012598D+00,
+     :  0.1236364149266D-07, 0.2873917870593D+01, 0.1847279083684D+00,
+     :  0.1092759489593D-07, 0.2959887266733D+01, 0.1370332435159D+00,
+     :  0.8912069362899D-08, 0.5141213702562D+01, 0.2648454860559D+01 /
+      DATA ((S0(I,J,1),I=1,3),J=121,130) /
+     :  0.9656467707970D-08, 0.4532182462323D+01, 0.4376440768498D+00,
+     :  0.8098386150135D-08, 0.2268906338379D+01, 0.2880807454688D+00,
+     :  0.7857714675000D-08, 0.4055544260745D+01, 0.2037373330570D+00,
+     :  0.7288455940646D-08, 0.5357901655142D+01, 0.1129145838217D+00,
+     :  0.9450595950552D-08, 0.4264926963939D+01, 0.5272426800584D+00,
+     :  0.9381718247537D-08, 0.7489366976576D-01, 0.5321392641652D+00,
+     :  0.7079052646038D-08, 0.1923311052874D+01, 0.6288513220417D+00,
+     :  0.9259004415344D-08, 0.2970256853438D+01, 0.1606092486742D+00,
+     :  0.8259801499742D-08, 0.3327056314697D+01, 0.8389694097774D+00,
+     :  0.6476334355779D-08, 0.2954925505727D+01, 0.2008557621224D+01 /
+      DATA ((S0(I,J,1),I=1,3),J=131,140) /
+     :  0.5984021492007D-08, 0.9138753105829D+00, 0.2042657109477D+02,
+     :  0.5989546863181D-08, 0.3244464082031D+01, 0.2111650433779D+01,
+     :  0.6233108606023D-08, 0.4995232638403D+00, 0.4305306221819D+00,
+     :  0.6877299149965D-08, 0.2834987233449D+01, 0.9561746721300D-02,
+     :  0.8311234227190D-08, 0.2202951835758D+01, 0.3801276407308D+00,
+     :  0.6599472832414D-08, 0.4478581462618D+01, 0.1063314406849D+01,
+     :  0.6160491096549D-08, 0.5145858696411D+01, 0.1368660381889D+01,
+     :  0.6164772043891D-08, 0.3762976697911D+00, 0.4234171675140D+00,
+     :  0.6363248684450D-08, 0.3162246718685D+01, 0.1253008786510D-01,
+     :  0.6448587520999D-08, 0.3442693302119D+01, 0.5287268506303D+00 /
+      DATA ((S0(I,J,1),I=1,3),J=141,150) /
+     :  0.6431662283977D-08, 0.8977549136606D+00, 0.5306550935933D+00,
+     :  0.6351223158474D-08, 0.4306447410369D+01, 0.5217580628120D+02,
+     :  0.5476721393451D-08, 0.3888529177855D+01, 0.2221856701002D+01,
+     :  0.5341772572619D-08, 0.2655560662512D+01, 0.7466759693650D-01,
+     :  0.5337055758302D-08, 0.5164990735946D+01, 0.7489573444450D-01,
+     :  0.5373120816787D-08, 0.6041214553456D+01, 0.1274714967946D+00,
+     :  0.5392351705426D-08, 0.9177763485932D+00, 0.1055449481598D+01,
+     :  0.6688495850205D-08, 0.3089608126937D+01, 0.2213766559277D+00,
+     :  0.5072003660362D-08, 0.4311316541553D+01, 0.2132517061319D+00,
+     :  0.5070726650455D-08, 0.5790675464444D+00, 0.2133464534247D+00 /
+      DATA ((S0(I,J,1),I=1,3),J=151,160) /
+     :  0.5658012950032D-08, 0.2703945510675D+01, 0.7287631425543D+00,
+     :  0.4835509924854D-08, 0.2975422976065D+01, 0.7160067364790D-01,
+     :  0.6479821978012D-08, 0.1324168733114D+01, 0.2209183458640D-01,
+     :  0.6230636494980D-08, 0.2860103632836D+01, 0.3306188016693D+00,
+     :  0.4649239516213D-08, 0.4832259763403D+01, 0.7796265773310D-01,
+     :  0.6487325792700D-08, 0.2726165825042D+01, 0.3884652414254D+00,
+     :  0.4682823682770D-08, 0.6966602455408D+00, 0.1073608853559D+01,
+     :  0.5704230804976D-08, 0.5669634104606D+01, 0.8731175355560D-01,
+     :  0.6125413585489D-08, 0.1513386538915D+01, 0.7605151500000D-01,
+     :  0.6035825038187D-08, 0.1983509168227D+01, 0.9846002785331D+00 /
+      DATA ((S0(I,J,1),I=1,3),J=161,170) /
+     :  0.4331123462303D-08, 0.2782892992807D+01, 0.4297791515992D+00,
+     :  0.4681107685143D-08, 0.5337232886836D+01, 0.2127790306879D+00,
+     :  0.4669105829655D-08, 0.5837133792160D+01, 0.2138191288687D+00,
+     :  0.5138823602365D-08, 0.3080560200507D+01, 0.7233337363710D-01,
+     :  0.4615856664534D-08, 0.1661747897471D+01, 0.8603097737811D+00,
+     :  0.4496916702197D-08, 0.2112508027068D+01, 0.7381754420900D-01,
+     :  0.4278479042945D-08, 0.5716528462627D+01, 0.7574578717200D-01,
+     :  0.3840525503932D-08, 0.6424172726492D+00, 0.3407705765729D+00,
+     :  0.4866636509685D-08, 0.4919244697715D+01, 0.7722995774390D-01,
+     :  0.3526100639296D-08, 0.2550821052734D+01, 0.6225157782540D-01 /
+      DATA ((S0(I,J,1),I=1,3),J=171,180) /
+     :  0.3939558488075D-08, 0.3939331491710D+01, 0.5268983110410D-01,
+     :  0.4041268772576D-08, 0.2275337571218D+01, 0.3503323232942D+00,
+     :  0.3948761842853D-08, 0.1999324200790D+01, 0.1451108196653D+00,
+     :  0.3258394550029D-08, 0.9121001378200D+00, 0.5296435984654D+00,
+     :  0.3257897048761D-08, 0.3428428660869D+01, 0.5297383457582D+00,
+     :  0.3842559031298D-08, 0.6132927720035D+01, 0.9098186128426D+00,
+     :  0.3109920095448D-08, 0.7693650193003D+00, 0.3932462625300D-02,
+     :  0.3132237775119D-08, 0.3621293854908D+01, 0.2346394437820D+00,
+     :  0.3942189421510D-08, 0.4841863659733D+01, 0.3180992042600D-02,
+     :  0.3796972285340D-08, 0.1814174994268D+01, 0.1862120789403D+00 /
+      DATA ((S0(I,J,1),I=1,3),J=181,190) /
+     :  0.3995640233688D-08, 0.1386990406091D+01, 0.4549093064213D+00,
+     :  0.2875013727414D-08, 0.9178318587177D+00, 0.1905464808669D+01,
+     :  0.3073719932844D-08, 0.2688923811835D+01, 0.3628624111593D+00,
+     :  0.2731016580075D-08, 0.1188259127584D+01, 0.2131850110243D+00,
+     :  0.2729549896546D-08, 0.3702160634273D+01, 0.2134131485323D+00,
+     :  0.3339372892449D-08, 0.7199163960331D+00, 0.2007689919132D+00,
+     :  0.2898833764204D-08, 0.1916709364999D+01, 0.5291709230214D+00,
+     :  0.2894536549362D-08, 0.2424043195547D+01, 0.5302110212022D+00,
+     :  0.3096872473843D-08, 0.4445894977497D+01, 0.2976424921901D+00,
+     :  0.2635672326810D-08, 0.3814366984117D+01, 0.1485980103780D+01 /
+      DATA ((S0(I,J,1),I=1,3),J=191,200) /
+     :  0.3649302697001D-08, 0.2924200596084D+01, 0.6044726378023D+00,
+     :  0.3127954585895D-08, 0.1842251648327D+01, 0.1084620721060D+00,
+     :  0.2616040173947D-08, 0.4155841921984D+01, 0.1258454114666D+01,
+     :  0.2597395859860D-08, 0.1158045978874D+00, 0.2103781122809D+00,
+     :  0.2593286172210D-08, 0.4771850408691D+01, 0.2162200472757D+00,
+     :  0.2481823585747D-08, 0.4608842558889D+00, 0.1062562936266D+01,
+     :  0.2742219550725D-08, 0.1538781127028D+01, 0.5651155736444D+00,
+     :  0.3199558469610D-08, 0.3226647822878D+00, 0.7036329877322D+00,
+     :  0.2666088542957D-08, 0.1967991731219D+00, 0.1400015846597D+00,
+     :  0.2397067430580D-08, 0.3707036669873D+01, 0.2125476091956D+00 /
+      DATA ((S0(I,J,1),I=1,3),J=201,210) /
+     :  0.2376570772738D-08, 0.1182086628042D+01, 0.2140505503610D+00,
+     :  0.2547228007887D-08, 0.4906256820629D+01, 0.1534957940063D+00,
+     :  0.2265575594114D-08, 0.3414949866857D+01, 0.2235935264888D+00,
+     :  0.2464381430585D-08, 0.4599122275378D+01, 0.2091065926078D+00,
+     :  0.2433408527044D-08, 0.2830751145445D+00, 0.2174915669488D+00,
+     :  0.2443605509076D-08, 0.4212046432538D+01, 0.1739420156204D+00,
+     :  0.2319779262465D-08, 0.9881978408630D+00, 0.7530171478090D-01,
+     :  0.2284622835465D-08, 0.5565347331588D+00, 0.7426161660010D-01,
+     :  0.2467268750783D-08, 0.5655708150766D+00, 0.2526561439362D+00,
+     :  0.2808513492782D-08, 0.1418405053408D+01, 0.5636314030725D+00 /
+      DATA ((S0(I,J,1),I=1,3),J=211,NS0X) /
+     :  0.2329528932532D-08, 0.4069557545675D+01, 0.1056200952181D+01,
+     :  0.9698639532817D-09, 0.1074134313634D+01, 0.7826370942180D+02 /
+
+*  SSB-to-Sun, T^1, X
+      DATA ((S1(I,J,1),I=1,3),J=  1, 10) /
+     : -0.1296310361520D-07, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.8975769009438D-08, 0.1128891609250D+01, 0.4265981595566D+00,
+     :  0.7771113441307D-08, 0.2706039877077D+01, 0.2061856251104D+00,
+     :  0.7538303866642D-08, 0.2191281289498D+01, 0.2204125344462D+00,
+     :  0.6061384579336D-08, 0.3248167319958D+01, 0.1059381944224D+01,
+     :  0.5726994235594D-08, 0.5569981398610D+01, 0.5225775174439D+00,
+     :  0.5616492836424D-08, 0.5057386614909D+01, 0.5368044267797D+00,
+     :  0.1010881584769D-08, 0.3473577116095D+01, 0.7113454667900D-02,
+     :  0.7259606157626D-09, 0.3651858593665D+00, 0.6398972393349D+00,
+     :  0.8755095026935D-09, 0.1662835408338D+01, 0.4194847048887D+00 /
+      DATA ((S1(I,J,1),I=1,3),J= 11, 20) /
+     :  0.5370491182812D-09, 0.1327673878077D+01, 0.4337116142245D+00,
+     :  0.5743773887665D-09, 0.4250200846687D+01, 0.2132990797783D+00,
+     :  0.4408103140300D-09, 0.3598752574277D+01, 0.1589072916335D+01,
+     :  0.3101892374445D-09, 0.4887822983319D+01, 0.1052268489556D+01,
+     :  0.3209453713578D-09, 0.9702272295114D+00, 0.5296909721118D+00,
+     :  0.3017228286064D-09, 0.5484462275949D+01, 0.1066495398892D+01,
+     :  0.3200700038601D-09, 0.2846613338643D+01, 0.1495633313810D+00,
+     :  0.2137637279911D-09, 0.5692163292729D+00, 0.3163918923335D+00,
+     :  0.1899686386727D-09, 0.2061077157189D+01, 0.2275259891141D+00,
+     :  0.1401994545308D-09, 0.4177771136967D+01, 0.1102062672231D+00 /
+      DATA ((S1(I,J,1),I=1,3),J= 21, 30) /
+     :  0.1578057810499D-09, 0.5782460597335D+01, 0.7626583626240D-01,
+     :  0.1237713253351D-09, 0.5705900866881D+01, 0.5154640627760D+00,
+     :  0.1313076837395D-09, 0.5163438179576D+01, 0.3664874755930D-01,
+     :  0.1184963304860D-09, 0.3054804427242D+01, 0.6327837846670D+00,
+     :  0.1238130878565D-09, 0.2317292575962D+01, 0.3961708870310D-01,
+     :  0.1015959527736D-09, 0.2194643645526D+01, 0.7329749511860D-01,
+     :  0.9017954423714D-10, 0.2868603545435D+01, 0.1990721704425D+00,
+     :  0.8668024955603D-10, 0.4923849675082D+01, 0.5439178814476D+00,
+     :  0.7756083930103D-10, 0.3014334135200D+01, 0.9491756770005D+00,
+     :  0.7536503401741D-10, 0.2704886279769D+01, 0.1030928125552D+00 /
+      DATA ((S1(I,J,1),I=1,3),J= 31, 40) /
+     :  0.5483308679332D-10, 0.6010983673799D+01, 0.8531963191132D+00,
+     :  0.5184339620428D-10, 0.1952704573291D+01, 0.2093666171530D+00,
+     :  0.5108658712030D-10, 0.2958575786649D+01, 0.2172315424036D+00,
+     :  0.5019424524650D-10, 0.1736317621318D+01, 0.2164800718209D+00,
+     :  0.4909312625978D-10, 0.3167216416257D+01, 0.2101180877357D+00,
+     :  0.4456638901107D-10, 0.7697579923471D+00, 0.3235053470014D+00,
+     :  0.4227030350925D-10, 0.3490910137928D+01, 0.6373574839730D-01,
+     :  0.4095456040093D-10, 0.5178888984491D+00, 0.6470106940028D+00,
+     :  0.4990537041422D-10, 0.3323887668974D+01, 0.1422690933580D-01,
+     :  0.4321170010845D-10, 0.4288484987118D+01, 0.7358765972222D+00 /
+      DATA ((S1(I,J,1),I=1,3),J= 41,NS1X) /
+     :  0.3544072091802D-10, 0.6021051579251D+01, 0.5265099800692D+00,
+     :  0.3480198638687D-10, 0.4600027054714D+01, 0.5328719641544D+00,
+     :  0.3440287244435D-10, 0.4349525970742D+01, 0.8582758298370D-01,
+     :  0.3330628322713D-10, 0.2347391505082D+01, 0.1104591729320D-01,
+     :  0.2973060707184D-10, 0.4789409286400D+01, 0.5257585094865D+00,
+     :  0.2932606766089D-10, 0.5831693799927D+01, 0.5336234347371D+00,
+     :  0.2876972310953D-10, 0.2692638514771D+01, 0.1173197218910D+00,
+     :  0.2827488278556D-10, 0.2056052487960D+01, 0.2022531624851D+00,
+     :  0.2515028239756D-10, 0.7411863262449D+00, 0.9597935788730D-01,
+     :  0.2853033744415D-10, 0.3948481024894D+01, 0.2118763888447D+01 /
+
+*  SSB-to-Sun, T^2, X
+      DATA ((S2(I,J,1),I=1,3),J=  1,NS2X) /
+     :  0.1603551636587D-11, 0.4404109410481D+01, 0.2061856251104D+00,
+     :  0.1556935889384D-11, 0.4818040873603D+00, 0.2204125344462D+00,
+     :  0.1182594414915D-11, 0.9935762734472D+00, 0.5225775174439D+00,
+     :  0.1158794583180D-11, 0.3353180966450D+01, 0.5368044267797D+00,
+     :  0.9597358943932D-12, 0.5567045358298D+01, 0.2132990797783D+00,
+     :  0.6511516579605D-12, 0.5630872420788D+01, 0.4265981595566D+00,
+     :  0.7419792747688D-12, 0.2156188581957D+01, 0.5296909721118D+00,
+     :  0.3951972655848D-12, 0.1981022541805D+01, 0.1059381944224D+01,
+     :  0.4478223877045D-12, 0.0000000000000D+00, 0.0000000000000D+00 /
+
+*  SSB-to-Sun, T^0, Y
+      DATA ((S0(I,J,2),I=1,3),J=  1, 10) /
+     :  0.4955392320126D-02, 0.2170467313679D+01, 0.5296909721118D+00,
+     :  0.2722325167392D-02, 0.2444433682196D+01, 0.2132990797783D+00,
+     :  0.1546579925346D-02, 0.5992779281546D+00, 0.3813291813120D-01,
+     :  0.8363140252966D-03, 0.7687356310801D+00, 0.7478166569050D-01,
+     :  0.3385792683603D-03, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.1201192221613D-03, 0.2520035601514D+01, 0.1059381944224D+01,
+     :  0.7587125720554D-04, 0.1669954006449D+01, 0.4265981595566D+00,
+     :  0.1964155361250D-04, 0.5707743963343D+01, 0.2061856251104D+00,
+     :  0.1891900364909D-04, 0.2320960679937D+01, 0.2204125344462D+00,
+     :  0.1937373433356D-04, 0.3226940689555D+01, 0.1495633313810D+00 /
+      DATA ((S0(I,J,2),I=1,3),J= 11, 20) /
+     :  0.1437139941351D-04, 0.2301626908096D+01, 0.5225775174439D+00,
+     :  0.1406267683099D-04, 0.5188579265542D+01, 0.5368044267797D+00,
+     :  0.1178703080346D-04, 0.5489483248476D+01, 0.7626583626240D-01,
+     :  0.8079835186041D-05, 0.1683751835264D+01, 0.3664874755930D-01,
+     :  0.7623253594652D-05, 0.2656400462961D+01, 0.3961708870310D-01,
+     :  0.6248667483971D-05, 0.4992775362055D+01, 0.7329749511860D-01,
+     :  0.4366353695038D-05, 0.2869706279678D+01, 0.1589072916335D+01,
+     :  0.3829101568895D-05, 0.3572131359950D+01, 0.7113454667900D-02,
+     :  0.3175733773908D-05, 0.4535372530045D+01, 0.4194847048887D+00,
+     :  0.3092437902159D-05, 0.9230153317909D+00, 0.6398972393349D+00 /
+      DATA ((S0(I,J,2),I=1,3),J= 21, 30) /
+     :  0.2874168812154D-05, 0.3363143761101D+01, 0.1102062672231D+00,
+     :  0.3040119321826D-05, 0.3324250895675D+01, 0.6283075850446D+01,
+     :  0.2699723308006D-05, 0.2917882441928D+00, 0.1030928125552D+00,
+     :  0.2134832683534D-05, 0.4220997202487D+01, 0.3163918923335D+00,
+     :  0.1770412139433D-05, 0.4747318496462D+01, 0.1021328554739D+02,
+     :  0.1377264209373D-05, 0.4305058462401D+00, 0.1484170571900D-02,
+     :  0.1127814538960D-05, 0.8538177240740D+00, 0.6327837846670D+00,
+     :  0.1055608090130D-05, 0.1551800742580D+01, 0.4337116142245D+00,
+     :  0.9802673861420D-06, 0.1459646735377D+01, 0.1052268489556D+01,
+     :  0.1090329461951D-05, 0.1587351228711D+01, 0.1162474756779D+01 /
+      DATA ((S0(I,J,2),I=1,3),J= 31, 40) /
+     :  0.6959590025090D-06, 0.5534442628766D+01, 0.1066495398892D+01,
+     :  0.5664914529542D-06, 0.6030673003297D+01, 0.9491756770005D+00,
+     :  0.6607787763599D-06, 0.4989507233927D+01, 0.8460828644453D+00,
+     :  0.6269725742838D-06, 0.4222951804572D+01, 0.1480791608091D+00,
+     :  0.6301889697863D-06, 0.5444316669126D+01, 0.2243449970715D+00,
+     :  0.4891042662861D-06, 0.1490552839784D+01, 0.3340612434717D+01,
+     :  0.3457083123290D-06, 0.3030475486049D+01, 0.3516457698740D-01,
+     :  0.3032559967314D-06, 0.2652038793632D+01, 0.1104591729320D-01,
+     :  0.2841133988903D-06, 0.1276744786829D+01, 0.4110125927500D-01,
+     :  0.2855564444432D-06, 0.2143368674733D+01, 0.1510475019529D+00 /
+      DATA ((S0(I,J,2),I=1,3),J= 41, 50) /
+     :  0.2765157135038D-06, 0.5444186109077D+01, 0.6373574839730D-01,
+     :  0.2382312465034D-06, 0.2190521137593D+01, 0.2275259891141D+00,
+     :  0.2808060365077D-06, 0.5735195064841D+01, 0.2535050500000D-01,
+     :  0.2332175234405D-06, 0.9481985524859D-01, 0.7181332454670D-01,
+     :  0.2322488199659D-06, 0.5180499361533D+01, 0.8582758298370D-01,
+     :  0.1881850258423D-06, 0.3219788273885D+01, 0.2118763888447D+01,
+     :  0.2196111392808D-06, 0.2366941159761D+01, 0.2968341143800D-02,
+     :  0.2183810335519D-06, 0.4825445110915D+01, 0.7775000683430D-01,
+     :  0.2002733093326D-06, 0.2457148995307D+01, 0.2093666171530D+00,
+     :  0.1967111767229D-06, 0.5586291545459D+01, 0.2172315424036D+00 /
+      DATA ((S0(I,J,2),I=1,3),J= 51, 60) /
+     :  0.1568473250543D-06, 0.3708003123320D+01, 0.7429900518901D+00,
+     :  0.1852528314300D-06, 0.4310638151560D+01, 0.2022531624851D+00,
+     :  0.1832111226447D-06, 0.1494665322656D+01, 0.3235053470014D+00,
+     :  0.1746805502310D-06, 0.1451378500784D+01, 0.1385174140878D+00,
+     :  0.1555730966650D-06, 0.1068040418198D+01, 0.7358765972222D+00,
+     :  0.1554883462559D-06, 0.2442579035461D+01, 0.5154640627760D+00,
+     :  0.1638380568746D-06, 0.2597913420625D+00, 0.8531963191132D+00,
+     :  0.1159938593640D-06, 0.5834512021280D+01, 0.1990721704425D+00,
+     :  0.1083427965695D-06, 0.5054033177950D+01, 0.5439178814476D+00,
+     :  0.1156480369431D-06, 0.5325677432457D+01, 0.5257585094865D+00 /
+      DATA ((S0(I,J,2),I=1,3),J= 61, 70) /
+     :  0.1141308860095D-06, 0.2153403923857D+01, 0.5336234347371D+00,
+     :  0.7913146470946D-07, 0.8642846847027D+00, 0.1478866649112D+01,
+     :  0.7439752463733D-07, 0.1970628496213D+01, 0.2164800718209D+00,
+     :  0.7280277104079D-07, 0.6073307250609D+01, 0.2101180877357D+00,
+     :  0.8319567719136D-07, 0.1954371928334D+01, 0.1692165728891D+01,
+     :  0.7137705549290D-07, 0.8904989440909D+00, 0.4155522422634D+00,
+     :  0.6900825396225D-07, 0.2825717714977D+01, 0.1173197218910D+00,
+     :  0.7245757216635D-07, 0.2481677513331D+01, 0.1265567569334D+01,
+     :  0.6961165696255D-07, 0.1292955312978D+01, 0.9562891316684D+00,
+     :  0.7571804456890D-07, 0.3427517575069D+01, 0.1422690933580D-01 /
+      DATA ((S0(I,J,2),I=1,3),J= 71, 80) /
+     :  0.6605425721904D-07, 0.8052192701492D+00, 0.6470106940028D+00,
+     :  0.7375477357248D-07, 0.1705076390088D+01, 0.1581959461667D+01,
+     :  0.7041664951470D-07, 0.4848356967891D+00, 0.9597935788730D-01,
+     :  0.6322199535763D-07, 0.3878069473909D+01, 0.7084920306520D-01,
+     :  0.5244380279191D-07, 0.2645560544125D+01, 0.5265099800692D+00,
+     :  0.5143125704988D-07, 0.4834486101370D+01, 0.5328719641544D+00,
+     :  0.5871866319373D-07, 0.7981472548900D+00, 0.7871412831580D-01,
+     :  0.6300822573871D-07, 0.5979398788281D+01, 0.2608790314060D+02,
+     :  0.6062154271548D-07, 0.4108655402756D+01, 0.1114304132498D+00,
+     :  0.4361912339976D-07, 0.5322624319280D+01, 0.1375773836557D+01 /
+      DATA ((S0(I,J,2),I=1,3),J= 81, 90) /
+     :  0.4417005920067D-07, 0.6240817359284D+01, 0.2770348281756D+00,
+     :  0.4686806749936D-07, 0.3214977301156D+01, 0.1143987543936D+00,
+     :  0.3758892132305D-07, 0.5879809634765D+01, 0.1596186371003D+01,
+     :  0.5151351332319D-07, 0.2893377688007D+00, 0.2228608264996D+00,
+     :  0.4554683578572D-07, 0.5475427144122D+01, 0.1465949902372D+00,
+     :  0.3442381385338D-07, 0.5992034796640D+01, 0.5070101000000D-01,
+     :  0.2831093954933D-07, 0.5367350273914D+01, 0.3092784376656D+00,
+     :  0.3756267090084D-07, 0.5758171285420D+01, 0.4903339079539D+00,
+     :  0.2816374679892D-07, 0.1863718700923D+01, 0.2991266627620D+00,
+     :  0.3419307025569D-07, 0.9524347534130D+00, 0.3518164938661D+00 /
+      DATA ((S0(I,J,2),I=1,3),J= 91,100) /
+     :  0.2904250494239D-07, 0.5304471615602D+01, 0.1099462426779D+00,
+     :  0.2471734511206D-07, 0.1297069793530D+01, 0.6256703299991D+00,
+     :  0.2539620831872D-07, 0.3281126083375D+01, 0.1256615170089D+02,
+     :  0.2281017868007D-07, 0.1829122133165D+01, 0.6681224869435D+01,
+     :  0.2275319473335D-07, 0.5797198160181D+01, 0.3932462625300D-02,
+     :  0.2547755368442D-07, 0.4752697708330D+01, 0.1169588211447D+01,
+     :  0.2285979669317D-07, 0.1223205292886D+01, 0.1045155034888D+01,
+     :  0.1913386560994D-07, 0.1757532993389D+01, 0.1155361302111D+01,
+     :  0.1809020525147D-07, 0.4246116108791D+01, 0.3368040641550D-01,
+     :  0.1649213300201D-07, 0.1445162890627D+01, 0.4408250688924D+00 /
+      DATA ((S0(I,J,2),I=1,3),J=101,110) /
+     :  0.1834972793932D-07, 0.1126917567225D+01, 0.4452511715700D-02,
+     :  0.1439550648138D-07, 0.6160756834764D+01, 0.9420622223326D+00,
+     :  0.1487645457041D-07, 0.4358761931792D+01, 0.4123712502208D+00,
+     :  0.1731729516660D-07, 0.6134456753344D+01, 0.2108507877249D+00,
+     :  0.1717747163567D-07, 0.1898186084455D+01, 0.2157473718317D+00,
+     :  0.1418190430374D-07, 0.4180286741266D+01, 0.6521991896920D-01,
+     :  0.1404844134873D-07, 0.7654053565412D-01, 0.4258542984690D-01,
+     :  0.1409842846538D-07, 0.4418612420312D+01, 0.2258291676434D+00,
+     :  0.1090948346291D-07, 0.1260615686131D+01, 0.4226656969313D+00,
+     :  0.1357577323612D-07, 0.3558248818690D+01, 0.7923417740620D-01 /
+      DATA ((S0(I,J,2),I=1,3),J=111,120) /
+     :  0.1018154061960D-07, 0.5676087241256D+01, 0.1456308687557D+00,
+     :  0.1412073972109D-07, 0.8394392632422D+00, 0.1525316725248D+00,
+     :  0.1030938326496D-07, 0.1653593274064D+01, 0.1795258541446D+01,
+     :  0.1180081567104D-07, 0.1285802592036D+01, 0.7032915397480D-01,
+     :  0.9708510575650D-08, 0.7631889488106D+00, 0.8434341241180D-01,
+     :  0.9637689663447D-08, 0.4630642649176D+01, 0.1272681024002D+01,
+     :  0.1068910429389D-07, 0.5294934032165D+01, 0.2123349582968D+00,
+     :  0.1063716179336D-07, 0.2736266800832D+01, 0.2142632012598D+00,
+     :  0.1234858713814D-07, 0.1302891146570D+01, 0.1847279083684D+00,
+     :  0.8912631189738D-08, 0.3570415993621D+01, 0.2648454860559D+01 /
+      DATA ((S0(I,J,2),I=1,3),J=121,130) /
+     :  0.1036378285534D-07, 0.4236693440949D+01, 0.1370332435159D+00,
+     :  0.9667798501561D-08, 0.2960768892398D+01, 0.4376440768498D+00,
+     :  0.8108314201902D-08, 0.6987781646841D+00, 0.2880807454688D+00,
+     :  0.7648364324628D-08, 0.2499017863863D+01, 0.2037373330570D+00,
+     :  0.7286136828406D-08, 0.3787426951665D+01, 0.1129145838217D+00,
+     :  0.9448237743913D-08, 0.2694354332983D+01, 0.5272426800584D+00,
+     :  0.9374276106428D-08, 0.4787121277064D+01, 0.5321392641652D+00,
+     :  0.7100226287462D-08, 0.3530238792101D+00, 0.6288513220417D+00,
+     :  0.9253056659571D-08, 0.1399478925664D+01, 0.1606092486742D+00,
+     :  0.6636432145504D-08, 0.3479575438447D+01, 0.1368660381889D+01 /
+      DATA ((S0(I,J,2),I=1,3),J=131,140) /
+     :  0.6469975312932D-08, 0.1383669964800D+01, 0.2008557621224D+01,
+     :  0.7335849729765D-08, 0.1243698166898D+01, 0.9561746721300D-02,
+     :  0.8743421205855D-08, 0.3776164289301D+01, 0.3801276407308D+00,
+     :  0.5993635744494D-08, 0.5627122113596D+01, 0.2042657109477D+02,
+     :  0.5981008479693D-08, 0.1674336636752D+01, 0.2111650433779D+01,
+     :  0.6188535145838D-08, 0.5214925208672D+01, 0.4305306221819D+00,
+     :  0.6596074017566D-08, 0.2907653268124D+01, 0.1063314406849D+01,
+     :  0.6630815126226D-08, 0.2127643669658D+01, 0.8389694097774D+00,
+     :  0.6156772830040D-08, 0.5082160803295D+01, 0.4234171675140D+00,
+     :  0.6446960563014D-08, 0.1872100916905D+01, 0.5287268506303D+00 /
+      DATA ((S0(I,J,2),I=1,3),J=141,150) /
+     :  0.6429324424668D-08, 0.5610276103577D+01, 0.5306550935933D+00,
+     :  0.6302232396465D-08, 0.1592152049607D+01, 0.1253008786510D-01,
+     :  0.6399244436159D-08, 0.2746214421532D+01, 0.5217580628120D+02,
+     :  0.5474965172558D-08, 0.2317666374383D+01, 0.2221856701002D+01,
+     :  0.5339293190692D-08, 0.1084724961156D+01, 0.7466759693650D-01,
+     :  0.5334733683389D-08, 0.3594106067745D+01, 0.7489573444450D-01,
+     :  0.5392665782110D-08, 0.5630254365606D+01, 0.1055449481598D+01,
+     :  0.6682075673789D-08, 0.1518480041732D+01, 0.2213766559277D+00,
+     :  0.5079130495960D-08, 0.2739765115711D+01, 0.2132517061319D+00,
+     :  0.5077759793261D-08, 0.5290711290094D+01, 0.2133464534247D+00 /
+      DATA ((S0(I,J,2),I=1,3),J=151,160) /
+     :  0.4832037368310D-08, 0.1404473217200D+01, 0.7160067364790D-01,
+     :  0.6463279674802D-08, 0.6038381695210D+01, 0.2209183458640D-01,
+     :  0.6240592771560D-08, 0.1290170653666D+01, 0.3306188016693D+00,
+     :  0.4672013521493D-08, 0.3261895939677D+01, 0.7796265773310D-01,
+     :  0.6500650750348D-08, 0.1154522312095D+01, 0.3884652414254D+00,
+     :  0.6344161389053D-08, 0.6206111545062D+01, 0.7605151500000D-01,
+     :  0.4682518370646D-08, 0.5409118796685D+01, 0.1073608853559D+01,
+     :  0.5329460015591D-08, 0.1202985784864D+01, 0.7287631425543D+00,
+     :  0.5701588675898D-08, 0.4098715257064D+01, 0.8731175355560D-01,
+     :  0.6030690867211D-08, 0.4132033218460D+00, 0.9846002785331D+00 /
+      DATA ((S0(I,J,2),I=1,3),J=161,170) /
+     :  0.4336256312655D-08, 0.1211415991827D+01, 0.4297791515992D+00,
+     :  0.4688498808975D-08, 0.3765479072409D+01, 0.2127790306879D+00,
+     :  0.4675578609335D-08, 0.4265540037226D+01, 0.2138191288687D+00,
+     :  0.4225578112158D-08, 0.5237566010676D+01, 0.3407705765729D+00,
+     :  0.5139422230028D-08, 0.1507173079513D+01, 0.7233337363710D-01,
+     :  0.4619995093571D-08, 0.9023957449848D-01, 0.8603097737811D+00,
+     :  0.4494776255461D-08, 0.5414930552139D+00, 0.7381754420900D-01,
+     :  0.4274026276788D-08, 0.4145735303659D+01, 0.7574578717200D-01,
+     :  0.5018141789353D-08, 0.3344408829055D+01, 0.3180992042600D-02,
+     :  0.4866163952181D-08, 0.3348534657607D+01, 0.7722995774390D-01 /
+      DATA ((S0(I,J,2),I=1,3),J=171,180) /
+     :  0.4111986020501D-08, 0.4198823597220D+00, 0.1451108196653D+00,
+     :  0.3356142784950D-08, 0.5609144747180D+01, 0.1274714967946D+00,
+     :  0.4070575554551D-08, 0.7028411059224D+00, 0.3503323232942D+00,
+     :  0.3257451857278D-08, 0.5624697983086D+01, 0.5296435984654D+00,
+     :  0.3256973703026D-08, 0.1857842076707D+01, 0.5297383457582D+00,
+     :  0.3830771508640D-08, 0.4562887279931D+01, 0.9098186128426D+00,
+     :  0.3725024005962D-08, 0.2358058692652D+00, 0.1084620721060D+00,
+     :  0.3136763921756D-08, 0.2049731526845D+01, 0.2346394437820D+00,
+     :  0.3795147256194D-08, 0.2432356296933D+00, 0.1862120789403D+00,
+     :  0.2877342229911D-08, 0.5631101279387D+01, 0.1905464808669D+01 /
+      DATA ((S0(I,J,2),I=1,3),J=181,190) /
+     :  0.3076931798805D-08, 0.1117615737392D+01, 0.3628624111593D+00,
+     :  0.2734765945273D-08, 0.5899826516955D+01, 0.2131850110243D+00,
+     :  0.2733405296885D-08, 0.2130562964070D+01, 0.2134131485323D+00,
+     :  0.2898552353410D-08, 0.3462387048225D+00, 0.5291709230214D+00,
+     :  0.2893736103681D-08, 0.8534352781543D+00, 0.5302110212022D+00,
+     :  0.3095717734137D-08, 0.2875061429041D+01, 0.2976424921901D+00,
+     :  0.2636190425832D-08, 0.2242512846659D+01, 0.1485980103780D+01,
+     :  0.3645512095537D-08, 0.1354016903958D+01, 0.6044726378023D+00,
+     :  0.2808173547723D-08, 0.6705114365631D-01, 0.6225157782540D-01,
+     :  0.2625012866888D-08, 0.4775705748482D+01, 0.5268983110410D-01 /
+      DATA ((S0(I,J,2),I=1,3),J=191,200) /
+     :  0.2572233995651D-08, 0.2638924216139D+01, 0.1258454114666D+01,
+     :  0.2604238824792D-08, 0.4826358927373D+01, 0.2103781122809D+00,
+     :  0.2596886385239D-08, 0.3200388483118D+01, 0.2162200472757D+00,
+     :  0.3228057304264D-08, 0.5384848409563D+01, 0.2007689919132D+00,
+     :  0.2481601798252D-08, 0.5173373487744D+01, 0.1062562936266D+01,
+     :  0.2745977498864D-08, 0.6250966149853D+01, 0.5651155736444D+00,
+     :  0.2669878833811D-08, 0.4906001352499D+01, 0.1400015846597D+00,
+     :  0.3203986611711D-08, 0.5034333010005D+01, 0.7036329877322D+00,
+     :  0.3354961227212D-08, 0.6108262423137D+01, 0.4549093064213D+00,
+     :  0.2400407324558D-08, 0.2135399294955D+01, 0.2125476091956D+00 /
+      DATA ((S0(I,J,2),I=1,3),J=201,210) /
+     :  0.2379905859802D-08, 0.5893721933961D+01, 0.2140505503610D+00,
+     :  0.2550844302187D-08, 0.3331940762063D+01, 0.1534957940063D+00,
+     :  0.2268824211001D-08, 0.1843418461035D+01, 0.2235935264888D+00,
+     :  0.2464700891204D-08, 0.3029548547230D+01, 0.2091065926078D+00,
+     :  0.2436814726024D-08, 0.4994717970364D+01, 0.2174915669488D+00,
+     :  0.2443623894745D-08, 0.2645102591375D+01, 0.1739420156204D+00,
+     :  0.2318701783838D-08, 0.5700547397897D+01, 0.7530171478090D-01,
+     :  0.2284448700256D-08, 0.5268898905872D+01, 0.7426161660010D-01,
+     :  0.2468848123510D-08, 0.5276280575078D+01, 0.2526561439362D+00,
+     :  0.2814052350303D-08, 0.6130168623475D+01, 0.5636314030725D+00 /
+      DATA ((S0(I,J,2),I=1,3),J=211,NS0Y) /
+     :  0.2243662755220D-08, 0.6631692457995D+00, 0.8886590321940D-01,
+     :  0.2330795855941D-08, 0.2499435487702D+01, 0.1056200952181D+01,
+     :  0.9757679038404D-09, 0.5796846023126D+01, 0.7826370942180D+02 /
+
+*  SSB-to-Sun, T^1, Y
+      DATA ((S1(I,J,2),I=1,3),J=  1, 10) /
+     :  0.8989047573576D-08, 0.5840593672122D+01, 0.4265981595566D+00,
+     :  0.7815938401048D-08, 0.1129664707133D+01, 0.2061856251104D+00,
+     :  0.7550926713280D-08, 0.6196589104845D+00, 0.2204125344462D+00,
+     :  0.6056556925895D-08, 0.1677494667846D+01, 0.1059381944224D+01,
+     :  0.5734142698204D-08, 0.4000920852962D+01, 0.5225775174439D+00,
+     :  0.5614341822459D-08, 0.3486722577328D+01, 0.5368044267797D+00,
+     :  0.1028678147656D-08, 0.1877141024787D+01, 0.7113454667900D-02,
+     :  0.7270792075266D-09, 0.5077167301739D+01, 0.6398972393349D+00,
+     :  0.8734141726040D-09, 0.9069550282609D-01, 0.4194847048887D+00,
+     :  0.5377371402113D-09, 0.6039381844671D+01, 0.4337116142245D+00 /
+      DATA ((S1(I,J,2),I=1,3),J= 11, 20) /
+     :  0.4729719431571D-09, 0.2153086311760D+01, 0.2132990797783D+00,
+     :  0.4458052820973D-09, 0.5059830025565D+01, 0.5296909721118D+00,
+     :  0.4406855467908D-09, 0.2027971692630D+01, 0.1589072916335D+01,
+     :  0.3101659310977D-09, 0.3317677981860D+01, 0.1052268489556D+01,
+     :  0.3016749232545D-09, 0.3913703482532D+01, 0.1066495398892D+01,
+     :  0.3198541352656D-09, 0.1275513098525D+01, 0.1495633313810D+00,
+     :  0.2142065389871D-09, 0.5301351614597D+01, 0.3163918923335D+00,
+     :  0.1902615247592D-09, 0.4894943352736D+00, 0.2275259891141D+00,
+     :  0.1613410990871D-09, 0.2449891130437D+01, 0.1102062672231D+00,
+     :  0.1576992165097D-09, 0.4211421447633D+01, 0.7626583626240D-01 /
+      DATA ((S1(I,J,2),I=1,3),J= 21, 30) /
+     :  0.1241637259894D-09, 0.4140803368133D+01, 0.5154640627760D+00,
+     :  0.1313974830355D-09, 0.3591920305503D+01, 0.3664874755930D-01,
+     :  0.1181697118258D-09, 0.1506314382788D+01, 0.6327837846670D+00,
+     :  0.1238239742779D-09, 0.7461405378404D+00, 0.3961708870310D-01,
+     :  0.1010107068241D-09, 0.6271010795475D+00, 0.7329749511860D-01,
+     :  0.9226316616509D-10, 0.1259158839583D+01, 0.1990721704425D+00,
+     :  0.8664946419555D-10, 0.3353244696934D+01, 0.5439178814476D+00,
+     :  0.7757230468978D-10, 0.1447677295196D+01, 0.9491756770005D+00,
+     :  0.7693168628139D-10, 0.1120509896721D+01, 0.1030928125552D+00,
+     :  0.5487897454612D-10, 0.4439380426795D+01, 0.8531963191132D+00 /
+      DATA ((S1(I,J,2),I=1,3),J= 31, 40) /
+     :  0.5196118677218D-10, 0.3788856619137D+00, 0.2093666171530D+00,
+     :  0.5110853339935D-10, 0.1386879372016D+01, 0.2172315424036D+00,
+     :  0.5027804534813D-10, 0.1647881805466D+00, 0.2164800718209D+00,
+     :  0.4922485922674D-10, 0.1594315079862D+01, 0.2101180877357D+00,
+     :  0.6155599524400D-10, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.4447147832161D-10, 0.5480720918976D+01, 0.3235053470014D+00,
+     :  0.4144691276422D-10, 0.1931371033660D+01, 0.6373574839730D-01,
+     :  0.4099950625452D-10, 0.5229611294335D+01, 0.6470106940028D+00,
+     :  0.5060541682953D-10, 0.1731112486298D+01, 0.1422690933580D-01,
+     :  0.4293615946300D-10, 0.2714571038925D+01, 0.7358765972222D+00 /
+      DATA ((S1(I,J,2),I=1,3),J= 41,NS1Y) /
+     :  0.3545659845763D-10, 0.4451041444634D+01, 0.5265099800692D+00,
+     :  0.3479112041196D-10, 0.3029385448081D+01, 0.5328719641544D+00,
+     :  0.3438516493570D-10, 0.2778507143731D+01, 0.8582758298370D-01,
+     :  0.3297341285033D-10, 0.7898709807584D+00, 0.1104591729320D-01,
+     :  0.2972585818015D-10, 0.3218785316973D+01, 0.5257585094865D+00,
+     :  0.2931707295017D-10, 0.4260731012098D+01, 0.5336234347371D+00,
+     :  0.2897198149403D-10, 0.1120753978101D+01, 0.1173197218910D+00,
+     :  0.2832293240878D-10, 0.4597682717827D+00, 0.2022531624851D+00,
+     :  0.2864348326612D-10, 0.2169939928448D+01, 0.9597935788730D-01,
+     :  0.2852714675471D-10, 0.2377659870578D+01, 0.2118763888447D+01 /
+
+*  SSB-to-Sun, T^2, Y
+      DATA ((S2(I,J,2),I=1,3),J=  1,NS2Y) /
+     :  0.1609114495091D-11, 0.2831096993481D+01, 0.2061856251104D+00,
+     :  0.1560330784946D-11, 0.5193058213906D+01, 0.2204125344462D+00,
+     :  0.1183535479202D-11, 0.5707003443890D+01, 0.5225775174439D+00,
+     :  0.1158183066182D-11, 0.1782400404928D+01, 0.5368044267797D+00,
+     :  0.1032868027407D-11, 0.4036925452011D+01, 0.2132990797783D+00,
+     :  0.6540142847741D-12, 0.4058241056717D+01, 0.4265981595566D+00,
+     :  0.7305236491596D-12, 0.6175401942957D+00, 0.5296909721118D+00,
+     : -0.5580725052968D-12, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.3946122651015D-12, 0.4108265279171D+00, 0.1059381944224D+01 /
+
+*  SSB-to-Sun, T^0, Z
+      DATA ((S0(I,J,3),I=1,3),J=  1, 10) /
+     :  0.1181255122986D-03, 0.4607918989164D+00, 0.2132990797783D+00,
+     :  0.1127777651095D-03, 0.4169146331296D+00, 0.5296909721118D+00,
+     :  0.4777754401806D-04, 0.4582657007130D+01, 0.3813291813120D-01,
+     :  0.1129354285772D-04, 0.5758735142480D+01, 0.7478166569050D-01,
+     : -0.1149543637123D-04, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.3298730512306D-05, 0.5978801994625D+01, 0.4265981595566D+00,
+     :  0.2733376706079D-05, 0.7665413691040D+00, 0.1059381944224D+01,
+     :  0.9426389657270D-06, 0.3710201265838D+01, 0.2061856251104D+00,
+     :  0.8187517749552D-06, 0.3390675605802D+00, 0.2204125344462D+00,
+     :  0.4080447871819D-06, 0.4552296640088D+00, 0.5225775174439D+00 /
+      DATA ((S0(I,J,3),I=1,3),J= 11, 20) /
+     :  0.3169973017028D-06, 0.3445455899321D+01, 0.5368044267797D+00,
+     :  0.2438098615549D-06, 0.5664675150648D+01, 0.3664874755930D-01,
+     :  0.2601897517235D-06, 0.1931894095697D+01, 0.1495633313810D+00,
+     :  0.2314558080079D-06, 0.3666319115574D+00, 0.3961708870310D-01,
+     :  0.1962549548002D-06, 0.3167411699020D+01, 0.7626583626240D-01,
+     :  0.2180518287925D-06, 0.1544420746580D+01, 0.7113454667900D-02,
+     :  0.1451382442868D-06, 0.1583756740070D+01, 0.1102062672231D+00,
+     :  0.1358439007389D-06, 0.5239941758280D+01, 0.6398972393349D+00,
+     :  0.1050585898028D-06, 0.2266958352859D+01, 0.3163918923335D+00,
+     :  0.1050029870186D-06, 0.2711495250354D+01, 0.4194847048887D+00 /
+      DATA ((S0(I,J,3),I=1,3),J= 21, 30) /
+     :  0.9934920679800D-07, 0.1116208151396D+01, 0.1589072916335D+01,
+     :  0.1048395331560D-06, 0.3408619600206D+01, 0.1021328554739D+02,
+     :  0.8370147196668D-07, 0.3810459401087D+01, 0.2535050500000D-01,
+     :  0.7989856510998D-07, 0.3769910473647D+01, 0.7329749511860D-01,
+     :  0.5441221655233D-07, 0.2416994903374D+01, 0.1030928125552D+00,
+     :  0.4610812906784D-07, 0.5858503336994D+01, 0.4337116142245D+00,
+     :  0.3923022803444D-07, 0.3354170010125D+00, 0.1484170571900D-02,
+     :  0.2610725582128D-07, 0.5410600646324D+01, 0.6327837846670D+00,
+     :  0.2455279767721D-07, 0.6120216681403D+01, 0.1162474756779D+01,
+     :  0.2375530706525D-07, 0.6055443426143D+01, 0.1052268489556D+01 /
+      DATA ((S0(I,J,3),I=1,3),J= 31, 40) /
+     :  0.1782967577553D-07, 0.3146108708004D+01, 0.8460828644453D+00,
+     :  0.1581687095238D-07, 0.6255496089819D+00, 0.3340612434717D+01,
+     :  0.1594657672461D-07, 0.3782604300261D+01, 0.1066495398892D+01,
+     :  0.1563448615040D-07, 0.1997775733196D+01, 0.2022531624851D+00,
+     :  0.1463624258525D-07, 0.1736316792088D+00, 0.3516457698740D-01,
+     :  0.1331585056673D-07, 0.4331941830747D+01, 0.9491756770005D+00,
+     :  0.1130634557637D-07, 0.6152017751825D+01, 0.2968341143800D-02,
+     :  0.1028949607145D-07, 0.2101792614637D+00, 0.2275259891141D+00,
+     :  0.1024074971618D-07, 0.4071833211074D+01, 0.5070101000000D-01,
+     :  0.8826956060303D-08, 0.4861633688145D+00, 0.2093666171530D+00 /
+      DATA ((S0(I,J,3),I=1,3),J= 41, 50) /
+     :  0.8572230171541D-08, 0.5268190724302D+01, 0.4110125927500D-01,
+     :  0.7649332643544D-08, 0.5134543417106D+01, 0.2608790314060D+02,
+     :  0.8581673291033D-08, 0.2920218146681D+01, 0.1480791608091D+00,
+     :  0.8430589300938D-08, 0.3604576619108D+01, 0.2172315424036D+00,
+     :  0.7776165501012D-08, 0.3772942249792D+01, 0.6373574839730D-01,
+     :  0.8311070234408D-08, 0.6200412329888D+01, 0.3235053470014D+00,
+     :  0.6927365212582D-08, 0.4543353113437D+01, 0.8531963191132D+00,
+     :  0.6791574208598D-08, 0.2882188406238D+01, 0.7181332454670D-01,
+     :  0.5593100811839D-08, 0.1776646892780D+01, 0.7429900518901D+00,
+     :  0.4553381853021D-08, 0.3949617611240D+01, 0.7775000683430D-01 /
+      DATA ((S0(I,J,3),I=1,3),J= 51, 60) /
+     :  0.5758000450068D-08, 0.3859251775075D+01, 0.1990721704425D+00,
+     :  0.4281283457133D-08, 0.1466294631206D+01, 0.2118763888447D+01,
+     :  0.4206935661097D-08, 0.5421776011706D+01, 0.1104591729320D-01,
+     :  0.4213751641837D-08, 0.3412048993322D+01, 0.2243449970715D+00,
+     :  0.5310506239878D-08, 0.5421641370995D+00, 0.5154640627760D+00,
+     :  0.3827450341320D-08, 0.8887314524995D+00, 0.1510475019529D+00,
+     :  0.4292435241187D-08, 0.1405043757194D+01, 0.1422690933580D-01,
+     :  0.3189780702289D-08, 0.1060049293445D+01, 0.1173197218910D+00,
+     :  0.3226611928069D-08, 0.6270858897442D+01, 0.2164800718209D+00,
+     :  0.2893897608830D-08, 0.5117563223301D+01, 0.6470106940028D+00 /
+      DATA ((S0(I,J,3),I=1,3),J= 61,NS0Z) /
+     :  0.3239852024578D-08, 0.4079092237983D+01, 0.2101180877357D+00,
+     :  0.2956892222200D-08, 0.1594917021704D+01, 0.3092784376656D+00,
+     :  0.2980177912437D-08, 0.5258787667564D+01, 0.4155522422634D+00,
+     :  0.3163725690776D-08, 0.3854589225479D+01, 0.8582758298370D-01,
+     :  0.2662262399118D-08, 0.3561326430187D+01, 0.5257585094865D+00,
+     :  0.2766689135729D-08, 0.3180732086830D+00, 0.1385174140878D+00,
+     :  0.2411600278464D-08, 0.3324798335058D+01, 0.5439178814476D+00,
+     :  0.2483527695131D-08, 0.4169069291947D+00, 0.5336234347371D+00,
+     :  0.7788777276590D-09, 0.1900569908215D+01, 0.5217580628120D+02 /
+
+*  SSB-to-Sun, T^1, Z
+      DATA ((S1(I,J,3),I=1,3),J=  1, 10) /
+     :  0.5444220475678D-08, 0.1803825509310D+01, 0.2132990797783D+00,
+     :  0.3883412695596D-08, 0.4668616389392D+01, 0.5296909721118D+00,
+     :  0.1334341434551D-08, 0.0000000000000D+00, 0.0000000000000D+00,
+     :  0.3730001266883D-09, 0.5401405918943D+01, 0.2061856251104D+00,
+     :  0.2894929197956D-09, 0.4932415609852D+01, 0.2204125344462D+00,
+     :  0.2857950357701D-09, 0.3154625362131D+01, 0.7478166569050D-01,
+     :  0.2499226432292D-09, 0.3657486128988D+01, 0.4265981595566D+00,
+     :  0.1937705443593D-09, 0.5740434679002D+01, 0.1059381944224D+01,
+     :  0.1374894396320D-09, 0.1712857366891D+01, 0.5368044267797D+00,
+     :  0.1217248678408D-09, 0.2312090870932D+01, 0.5225775174439D+00 /
+      DATA ((S1(I,J,3),I=1,3),J= 11,NS1Z) /
+     :  0.7961052740870D-10, 0.5283368554163D+01, 0.3813291813120D-01,
+     :  0.4979225949689D-10, 0.4298290471860D+01, 0.4194847048887D+00,
+     :  0.4388552286597D-10, 0.6145515047406D+01, 0.7113454667900D-02,
+     :  0.2586835212560D-10, 0.3019448001809D+01, 0.6398972393349D+00 /
+
+*  SSB-to-Sun, T^2, Z
+      DATA ((S2(I,J,3),I=1,3),J=  1,NS2Z) /
+     :  0.3749920358054D-12, 0.3230285558668D+01, 0.2132990797783D+00,
+     :  0.2735037220939D-12, 0.6154322683046D+01, 0.5296909721118D+00 /
+
+* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+*  Time since reference epoch, years.
+      T = ( DATE - DJM0 ) / DJY
+      T2 = T*T
+
+*  X then Y then Z.
+      DO K=1,3
+
+*     Initialize position and velocity component.
+         XYZ = 0D0
+         XYZD = 0D0
+
+*     ------------------------------------------------
+*     Obtain component of Sun to Earth ecliptic vector
+*     ------------------------------------------------
+
+*     Sun to Earth, T^0 terms.
+         DO J=1,NE0(K)
+            A = E0(1,J,K)
+            B = E0(2,J,K)
+            C = E0(3,J,K)
+            P = B + C*T
+            XYZ  = XYZ  + A*COS(P)
+            XYZD = XYZD - A*C*SIN(P)
+         END DO
+
+*     Sun to Earth, T^1 terms.
+         DO J=1,NE1(K)
+            A = E1(1,J,K)
+            B = E1(2,J,K)
+            C = E1(3,J,K)
+            CT = C*T
+            P = B + CT
+            CP = COS(P)
+            XYZ  = XYZ  + A*T*CP
+            XYZD = XYZD + A*(CP-CT*SIN(P))
+         END DO
+
+*     Sun to Earth, T^2 terms.
+         DO J=1,NE2(K)
+            A = E2(1,J,K)
+            B = E2(2,J,K)
+            C = E2(3,J,K)
+            CT = C*T
+            P = B + CT
+            CP = COS(P)
+            XYZ  = XYZ  + A*T2*CP
+            XYZD = XYZD + A*T*(2D0*CP-CT*SIN(P))
+         END DO
+
+*     Heliocentric Earth position and velocity component.
+         HP(K) = XYZ
+         HV(K) = XYZD / DJY
+
+*     ------------------------------------------------
+*     Obtain component of SSB to Earth ecliptic vector
+*     ------------------------------------------------
+
+*     SSB to Sun, T^0 terms.
+         DO J=1,NS0(K)
+            A = S0(1,J,K)
+            B = S0(2,J,K)
+            C = S0(3,J,K)
+            P = B + C*T
+            XYZ  = XYZ  + A*COS(P)
+            XYZD = XYZD - A*C*SIN(P)
+         END DO
+
+*     SSB to Sun, T^1 terms.
+         DO J=1,NS1(K)
+            A = S1(1,J,K)
+            B = S1(2,J,K)
+            C = S1(3,J,K)
+            CT = C*T
+            P = B + CT
+            CP = COS(P)
+            XYZ  = XYZ  + A*T*CP
+            XYZD = XYZD + A*(CP-CT*SIN(P))
+         END DO
+
+*     SSB to Sun, T^2 terms.
+         DO J=1,NS2(K)
+            A = S2(1,J,K)
+            B = S2(2,J,K)
+            C = S2(3,J,K)
+            CT = C*T
+            P = B + CT
+            CP = COS(P)
+            XYZ  = XYZ  + A*T2*CP
+            XYZD = XYZD + A*T*(2D0*CP-CT*SIN(P))
+         END DO
+
+*     Barycentric Earth position and velocity component.
+         BP(K) = XYZ
+         BV(K) = XYZD / DJY
+
+*     Next Cartesian component.
+      END DO
+
+*  Rotate from ecliptic to ICRS coordinates and return the results.
+      X = HP(1)
+      Y = HP(2)
+      Z = HP(3)
+      PH(1) =      X + AM12*Y + AM13*Z
+      PH(2) = AM21*X + AM22*Y + AM23*Z
+      PH(3) =          AM32*Y + AM33*Z
+      X = HV(1)
+      Y = HV(2)
+      Z = HV(3)
+      VH(1) =      X + AM12*Y + AM13*Z
+      VH(2) = AM21*X + AM22*Y + AM23*Z
+      VH(3) =          AM32*Y + AM33*Z
+      X = BP(1)
+      Y = BP(2)
+      Z = BP(3)
+      PB(1) =      X + AM12*Y + AM13*Z
+      PB(2) = AM21*X + AM22*Y + AM23*Z
+      PB(3) =          AM32*Y + AM33*Z
+      X = BV(1)
+      Y = BV(2)
+      Z = BV(3)
+      VB(1) =      X + AM12*Y + AM13*Z
+      VB(2) = AM21*X + AM22*Y + AM23*Z
+      VB(3) =          AM32*Y + AM33*Z
+
+      END
diff --git a/math/slalib/eqecl.f b/math/slalib/eqecl.f
new file mode 100644
index 00000000..d3e405a9
--- /dev/null
+++ b/math/slalib/eqecl.f
@@ -0,0 +1,73 @@
+      SUBROUTINE slEQEC (DR, DD, DATE, DL, DB)
+*+
+*     - - - - - -
+*      E Q E C
+*     - - - - - -
+*
+*  Transformation from J2000.0 equatorial coordinates to
+*  ecliptic coordinates (double precision)
+*
+*  Given:
+*     DR,DD       dp      J2000.0 mean RA,Dec (radians)
+*     DATE        dp      TDB (loosely ET) as Modified Julian Date
+*                                              (JD-2400000.5)
+*  Returned:
+*     DL,DB       dp      ecliptic longitude and latitude
+*                         (mean of date, IAU 1980 theory, radians)
+*
+*  Called:
+*     slDS2C, slPREC, slEPJ, slDMXV, slECMA, slDC2S,
+*     slDA2P, slDA1P
+*
+*  P.T.Wallace   Starlink   March 1986
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DR,DD,DATE,DL,DB
+
+      DOUBLE PRECISION slEPJ,slDA2P,slDA1P
+
+      DOUBLE PRECISION RMAT(3,3),V1(3),V2(3)
+
+
+
+*  Spherical to Cartesian
+      CALL slDS2C(DR,DD,V1)
+
+*  Mean J2000 to mean of date
+      CALL slPREC(2000D0,slEPJ(DATE),RMAT)
+      CALL slDMXV(RMAT,V1,V2)
+
+*  Equatorial to ecliptic
+      CALL slECMA(DATE,RMAT)
+      CALL slDMXV(RMAT,V2,V1)
+
+*  Cartesian to spherical
+      CALL slDC2S(V1,DL,DB)
+
+*  Express in conventional ranges
+      DL=slDA2P(DL)
+      DB=slDA1P(DB)
+
+      END
diff --git a/math/slalib/eqeqx.f b/math/slalib/eqeqx.f
new file mode 100644
index 00000000..915f40c3
--- /dev/null
+++ b/math/slalib/eqeqx.f
@@ -0,0 +1,75 @@
+      DOUBLE PRECISION FUNCTION slEQEX (DATE)
+*+
+*     - - - - - -
+*      E Q E X
+*     - - - - - -
+*
+*  Equation of the equinoxes  (IAU 1994, double precision)
+*
+*  Given:
+*     DATE    dp      TDB (loosely ET) as Modified Julian Date
+*                                          (JD-2400000.5)
+*
+*  The result is the equation of the equinoxes (double precision)
+*  in radians:
+*
+*     Greenwich apparent ST = GMST + slEQEX
+*
+*  References:  IAU Resolution C7, Recommendation 3 (1994)
+*               Capitaine, N. & Gontier, A.-M., Astron. Astrophys.,
+*               275, 645-650 (1993)
+*
+*  Called:  slNUTC
+*
+*  Patrick Wallace   Starlink   23 August 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE
+
+*  Turns to arc seconds and arc seconds to radians
+      DOUBLE PRECISION T2AS,AS2R
+      PARAMETER (T2AS=1296000D0,
+     :           AS2R=0.484813681109535994D-5)
+
+      DOUBLE PRECISION T,OM,DPSI,DEPS,EPS0
+
+
+
+*  Interval between basic epoch J2000.0 and current epoch (JC)
+      T=(DATE-51544.5D0)/36525D0
+
+*  Longitude of the mean ascending node of the lunar orbit on the
+*   ecliptic, measured from the mean equinox of date
+      OM=AS2R*(450160.280D0+(-5D0*T2AS-482890.539D0
+     :         +(7.455D0+0.008D0*T)*T)*T)
+
+*  Nutation
+      CALL slNUTC(DATE,DPSI,DEPS,EPS0)
+
+*  Equation of the equinoxes
+      slEQEX=DPSI*COS(EPS0)+AS2R*(0.00264D0*SIN(OM)+
+     :                               0.000063D0*SIN(OM+OM))
+
+      END
diff --git a/math/slalib/eqgal.f b/math/slalib/eqgal.f
new file mode 100644
index 00000000..eeb19f5d
--- /dev/null
+++ b/math/slalib/eqgal.f
@@ -0,0 +1,97 @@
+      SUBROUTINE slEQGA (DR, DD, DL, DB)
+*+
+*     - - - - - -
+*      E Q G A
+*     - - - - - -
+*
+*  Transformation from J2000.0 equatorial coordinates to
+*  IAU 1958 galactic coordinates (double precision)
+*
+*  Given:
+*     DR,DD       dp       J2000.0 RA,Dec
+*
+*  Returned:
+*     DL,DB       dp       galactic longitude and latitude L2,B2
+*
+*  (all arguments are radians)
+*
+*  Called:
+*     slDS2C, slDMXV, slDC2S, slDA2P, slDA1P
+*
+*  Note:
+*     The equatorial coordinates are J2000.0.  Use the routine
+*     slEG50 if conversion from B1950.0 'FK4' coordinates is
+*     required.
+*
+*  Reference:
+*     Blaauw et al, Mon.Not.R.Astron.Soc.,121,123 (1960)
+*
+*  P.T.Wallace   Starlink   21 September 1998
+*
+*  Copyright (C) 1998 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DR,DD,DL,DB
+
+      DOUBLE PRECISION slDA2P,slDA1P
+
+      DOUBLE PRECISION V1(3),V2(3)
+
+*
+*  L2,B2 system of galactic coordinates
+*
+*  P = 192.25       RA of galactic north pole (mean B1950.0)
+*  Q =  62.6        inclination of galactic to mean B1950.0 equator
+*  R =  33          longitude of ascending node
+*
+*  P,Q,R are degrees
+*
+*  Equatorial to galactic rotation matrix (J2000.0), obtained by
+*  applying the standard FK4 to FK5 transformation, for zero proper
+*  motion in FK5, to the columns of the B1950 equatorial to
+*  galactic rotation matrix:
+*
+      DOUBLE PRECISION RMAT(3,3)
+      DATA RMAT(1,1),RMAT(1,2),RMAT(1,3),
+     :     RMAT(2,1),RMAT(2,2),RMAT(2,3),
+     :     RMAT(3,1),RMAT(3,2),RMAT(3,3)/
+     : -0.054875539726D0,-0.873437108010D0,-0.483834985808D0,
+     : +0.494109453312D0,-0.444829589425D0,+0.746982251810D0,
+     : -0.867666135858D0,-0.198076386122D0,+0.455983795705D0/
+
+
+
+*  Spherical to Cartesian
+      CALL slDS2C(DR,DD,V1)
+
+*  Equatorial to galactic
+      CALL slDMXV(RMAT,V1,V2)
+
+*  Cartesian to spherical
+      CALL slDC2S(V2,DL,DB)
+
+*  Express in conventional ranges
+      DL=slDA2P(DL)
+      DB=slDA1P(DB)
+
+      END
diff --git a/math/slalib/etrms.f b/math/slalib/etrms.f
new file mode 100644
index 00000000..f596bf2c
--- /dev/null
+++ b/math/slalib/etrms.f
@@ -0,0 +1,80 @@
+      SUBROUTINE slETRM (EP, EV)
+*+
+*     - - - - - -
+*      E T R M
+*     - - - - - -
+*
+*  Compute the E-terms (elliptic component of annual aberration)
+*  vector (double precision)
+*
+*  Given:
+*     EP      dp      Besselian epoch
+*
+*  Returned:
+*     EV      dp(3)   E-terms as (dx,dy,dz)
+*
+*  Note the use of the J2000 aberration constant (20.49552 arcsec).
+*  This is a reflection of the fact that the E-terms embodied in
+*  existing star catalogues were computed from a variety of
+*  aberration constants.  Rather than adopting one of the old
+*  constants the latest value is used here.
+*
+*  References:
+*     1  Smith, C.A. et al., 1989.  Astr.J. 97, 265.
+*     2  Yallop, B.D. et al., 1989.  Astr.J. 97, 274.
+*
+*  P.T.Wallace   Starlink   23 August 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION EP,EV(3)
+
+*  Arcseconds to radians
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+      DOUBLE PRECISION T,E,E0,P,EK,CP
+
+
+
+*  Julian centuries since B1950
+      T=(EP-1950D0)*1.00002135903D-2
+
+*  Eccentricity
+      E=0.01673011D0-(0.00004193D0+0.000000126D0*T)*T
+
+*  Mean obliquity
+      E0=(84404.836D0-(46.8495D0+(0.00319D0+0.00181D0*T)*T)*T)*AS2R
+
+*  Mean longitude of perihelion
+      P=(1015489.951D0+(6190.67D0+(1.65D0+0.012D0*T)*T)*T)*AS2R
+
+*  E-terms
+      EK=E*20.49552D0*AS2R
+      CP=COS(P)
+      EV(1)= EK*SIN(P)
+      EV(2)=-EK*CP*COS(E0)
+      EV(3)=-EK*CP*SIN(E0)
+
+      END
diff --git a/math/slalib/euler.f b/math/slalib/euler.f
new file mode 100644
index 00000000..ff764cf6
--- /dev/null
+++ b/math/slalib/euler.f
@@ -0,0 +1,86 @@
+      SUBROUTINE slEULR (ORDER, PHI, THETA, PSI, RMAT)
+*+
+*     - - - - - -
+*      E U L R
+*     - - - - - -
+*
+*  Form a rotation matrix from the Euler angles - three successive
+*  rotations about specified Cartesian axes (single precision)
+*
+*  Given:
+*    ORDER  c*(*)    specifies about which axes the rotations occur
+*    PHI    r        1st rotation (radians)
+*    THETA  r        2nd rotation (   "   )
+*    PSI    r        3rd rotation (   "   )
+*
+*  Returned:
+*    RMAT   r(3,3)   rotation matrix
+*
+*  A rotation is positive when the reference frame rotates
+*  anticlockwise as seen looking towards the origin from the
+*  positive region of the specified axis.
+*
+*  The characters of ORDER define which axes the three successive
+*  rotations are about.  A typical value is 'ZXZ', indicating that
+*  RMAT is to become the direction cosine matrix corresponding to
+*  rotations of the reference frame through PHI radians about the
+*  old Z-axis, followed by THETA radians about the resulting X-axis,
+*  then PSI radians about the resulting Z-axis.
+*
+*  The axis names can be any of the following, in any order or
+*  combination:  X, Y, Z, uppercase or lowercase, 1, 2, 3.  Normal
+*  axis labelling/numbering conventions apply;  the xyz (=123)
+*  triad is right-handed.  Thus, the 'ZXZ' example given above
+*  could be written 'zxz' or '313' (or even 'ZxZ' or '3xZ').  ORDER
+*  is terminated by length or by the first unrecognized character.
+*
+*  Fewer than three rotations are acceptable, in which case the later
+*  angle arguments are ignored.  If all rotations are zero, the
+*  identity matrix is produced.
+*
+*  Called:  slDEUL
+*
+*  P.T.Wallace   Starlink   23 May 1997
+*
+*  Copyright (C) 1997 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) ORDER
+      REAL PHI,THETA,PSI,RMAT(3,3)
+
+      INTEGER J,I
+      DOUBLE PRECISION W(3,3)
+
+
+
+*  Compute matrix in double precision
+      CALL slDEUL(ORDER,DBLE(PHI),DBLE(THETA),DBLE(PSI),W)
+
+*  Copy the result
+      DO J=1,3
+         DO I=1,3
+            RMAT(I,J) = REAL(W(I,J))
+         END DO
+      END DO
+
+      END
diff --git a/math/slalib/evp.f b/math/slalib/evp.f
new file mode 100644
index 00000000..f1e6f555
--- /dev/null
+++ b/math/slalib/evp.f
@@ -0,0 +1,457 @@
+      SUBROUTINE slEVP (DATE, DEQX, DVB, DPB, DVH, DPH)
+*+
+*     - - - -
+*      E V P
+*     - - - -
+*
+*  Barycentric and heliocentric velocity and position of the Earth
+*
+*  All arguments are double precision
+*
+*  Given:
+*
+*     DATE          TDB (loosely ET) as a Modified Julian Date
+*                                         (JD-2400000.5)
+*
+*     DEQX          Julian Epoch (e.g. 2000.0D0) of mean equator and
+*                   equinox of the vectors returned.  If DEQX .LE. 0D0,
+*                   all vectors are referred to the mean equator and
+*                   equinox (FK5) of epoch DATE.
+*
+*  Returned (all 3D Cartesian vectors):
+*
+*     DVB,DPB       barycentric velocity, position (AU/s, AU)
+*     DVH,DPH       heliocentric velocity, position (AU/s, AU)
+*
+*  Called:  slEPJ, slPREC
+*
+*  Notes:
+*
+*  1  This routine is accurate enough for many purposes but faster and
+*     more compact than the slEPV routine.  The maximum deviations
+*     from the JPL DE96 ephemeris are as follows:
+*
+*       barycentric velocity         0.42  m/s
+*       barycentric position         6900  km
+*
+*       heliocentric velocity        0.42  m/s
+*       heliocentric position        1600  km
+*
+*  2  The routine is adapted from the BARVEL and BARCOR subroutines of
+*     Stumpff (1980).  Most of the changes are merely cosmetic and do
+*     not affect the results at all.  However, some adjustments have
+*     been made so as to give results that refer to the IAU 1976 'FK5'
+*     equinox and precession, although the differences these changes
+*     make relative to the results from Stumpff's original 'FK4' version
+*     are smaller than the inherent accuracy of the algorithm.  One
+*     minor shortcoming in the original routines that has NOT been
+*     corrected is that better numerical accuracy could be achieved if
+*     the various polynomial evaluations were nested.
+*
+*  Reference:
+*
+*    Stumpff, P., Astron.Astrophys.Suppl.Ser. 41, 1-8 (1980).
+*
+*  Last revision:   7 April 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,DEQX,DVB(3),DPB(3),DVH(3),DPH(3)
+
+      INTEGER IDEQ,I,J,K
+
+      REAL CC2PI,CCSEC3,CCSGD,CCKM,CCMLD,CCFDI,CCIM,T,TSQ,A,PERTL,
+     :     PERTLD,PERTR,PERTRD,COSA,SINA,ESQ,E,PARAM,TWOE,TWOG,G,
+     :     PHI,F,SINF,COSF,PHID,PSID,PERTP,PERTPD,TL,SINLM,COSLM,
+     :     SIGMA,B,PLON,POMG,PECC,FLATM,FLAT
+
+      DOUBLE PRECISION DC2PI,DS2R,DCSLD,DC1MME,DT,DTSQ,DLOCAL,DML,
+     :                 DEPS,DPARAM,DPSI,D1PDRO,DRD,DRLD,DTL,DSINLS,
+     :                 DCOSLS,DXHD,DYHD,DZHD,DXBD,DYBD,DZBD,DCOSEP,
+     :                 DSINEP,DYAHD,DZAHD,DYABD,DZABD,DR,
+     :                 DXH,DYH,DZH,DXB,DYB,DZB,DYAH,DZAH,DYAB,
+     :                 DZAB,DEPJ,DEQCOR,B1950
+
+      REAL SN(4),CCSEL(3,17),CCAMPS(5,15),CCSEC(3,4),CCAMPM(4,3),
+     :     CCPAMV(4),CCPAM(4),FORBEL(7),SORBEL(17),SINLP(4),COSLP(4)
+      EQUIVALENCE (SORBEL(1),E),(FORBEL(1),G)
+
+      DOUBLE PRECISION DCFEL(3,8),DCEPS(3),DCARGS(2,15),DCARGM(2,3),
+     :                 DPREMA(3,3),W,VW(3)
+
+      DOUBLE PRECISION slEPJ
+
+      PARAMETER (DC2PI=6.2831853071796D0,CC2PI=6.283185)
+      PARAMETER (DS2R=0.7272205216643D-4)
+      PARAMETER (B1950=1949.9997904423D0)
+
+*
+*   Constants DCFEL(I,K) of fast changing elements
+*                     I=1                I=2              I=3
+      DATA DCFEL/ 1.7400353D+00, 6.2833195099091D+02, 5.2796D-06,
+     :            6.2565836D+00, 6.2830194572674D+02,-2.6180D-06,
+     :            4.7199666D+00, 8.3997091449254D+03,-1.9780D-05,
+     :            1.9636505D-01, 8.4334662911720D+03,-5.6044D-05,
+     :            4.1547339D+00, 5.2993466764997D+01, 5.8845D-06,
+     :            4.6524223D+00, 2.1354275911213D+01, 5.6797D-06,
+     :            4.2620486D+00, 7.5025342197656D+00, 5.5317D-06,
+     :            1.4740694D+00, 3.8377331909193D+00, 5.6093D-06/
+
+*
+*   Constants DCEPS and CCSEL(I,K) of slowly changing elements
+*                      I=1           I=2           I=3
+      DATA DCEPS/  4.093198D-01,-2.271110D-04,-2.860401D-08 /
+      DATA CCSEL/  1.675104E-02,-4.179579E-05,-1.260516E-07,
+     :             2.220221E-01, 2.809917E-02, 1.852532E-05,
+     :             1.589963E+00, 3.418075E-02, 1.430200E-05,
+     :             2.994089E+00, 2.590824E-02, 4.155840E-06,
+     :             8.155457E-01, 2.486352E-02, 6.836840E-06,
+     :             1.735614E+00, 1.763719E-02, 6.370440E-06,
+     :             1.968564E+00, 1.524020E-02,-2.517152E-06,
+     :             1.282417E+00, 8.703393E-03, 2.289292E-05,
+     :             2.280820E+00, 1.918010E-02, 4.484520E-06,
+     :             4.833473E-02, 1.641773E-04,-4.654200E-07,
+     :             5.589232E-02,-3.455092E-04,-7.388560E-07,
+     :             4.634443E-02,-2.658234E-05, 7.757000E-08,
+     :             8.997041E-03, 6.329728E-06,-1.939256E-09,
+     :             2.284178E-02,-9.941590E-05, 6.787400E-08,
+     :             4.350267E-02,-6.839749E-05,-2.714956E-07,
+     :             1.348204E-02, 1.091504E-05, 6.903760E-07,
+     :             3.106570E-02,-1.665665E-04,-1.590188E-07/
+
+*
+*   Constants of the arguments of the short-period perturbations
+*   by the planets:   DCARGS(I,K)
+*                       I=1               I=2
+      DATA DCARGS/ 5.0974222D+00,-7.8604195454652D+02,
+     :             3.9584962D+00,-5.7533848094674D+02,
+     :             1.6338070D+00,-1.1506769618935D+03,
+     :             2.5487111D+00,-3.9302097727326D+02,
+     :             4.9255514D+00,-5.8849265665348D+02,
+     :             1.3363463D+00,-5.5076098609303D+02,
+     :             1.6072053D+00,-5.2237501616674D+02,
+     :             1.3629480D+00,-1.1790629318198D+03,
+     :             5.5657014D+00,-1.0977134971135D+03,
+     :             5.0708205D+00,-1.5774000881978D+02,
+     :             3.9318944D+00, 5.2963464780000D+01,
+     :             4.8989497D+00, 3.9809289073258D+01,
+     :             1.3097446D+00, 7.7540959633708D+01,
+     :             3.5147141D+00, 7.9618578146517D+01,
+     :             3.5413158D+00,-5.4868336758022D+02/
+
+*
+*   Amplitudes CCAMPS(N,K) of the short-period perturbations
+*           N=1          N=2          N=3          N=4          N=5
+      DATA CCAMPS/
+     : -2.279594E-5, 1.407414E-5, 8.273188E-6, 1.340565E-5,-2.490817E-7,
+     : -3.494537E-5, 2.860401E-7, 1.289448E-7, 1.627237E-5,-1.823138E-7,
+     :  6.593466E-7, 1.322572E-5, 9.258695E-6,-4.674248E-7,-3.646275E-7,
+     :  1.140767E-5,-2.049792E-5,-4.747930E-6,-2.638763E-6,-1.245408E-7,
+     :  9.516893E-6,-2.748894E-6,-1.319381E-6,-4.549908E-6,-1.864821E-7,
+     :  7.310990E-6,-1.924710E-6,-8.772849E-7,-3.334143E-6,-1.745256E-7,
+     : -2.603449E-6, 7.359472E-6, 3.168357E-6, 1.119056E-6,-1.655307E-7,
+     : -3.228859E-6, 1.308997E-7, 1.013137E-7, 2.403899E-6,-3.736225E-7,
+     :  3.442177E-7, 2.671323E-6, 1.832858E-6,-2.394688E-7,-3.478444E-7,
+     :  8.702406E-6,-8.421214E-6,-1.372341E-6,-1.455234E-6,-4.998479E-8,
+     : -1.488378E-6,-1.251789E-5, 5.226868E-7,-2.049301E-7, 0.0E0,
+     : -8.043059E-6,-2.991300E-6, 1.473654E-7,-3.154542E-7, 0.0E0,
+     :  3.699128E-6,-3.316126E-6, 2.901257E-7, 3.407826E-7, 0.0E0,
+     :  2.550120E-6,-1.241123E-6, 9.901116E-8, 2.210482E-7, 0.0E0,
+     : -6.351059E-7, 2.341650E-6, 1.061492E-6, 2.878231E-7, 0.0E0/
+
+*
+*   Constants of the secular perturbations in longitude
+*   CCSEC3 and CCSEC(N,K)
+*                      N=1           N=2           N=3
+      DATA CCSEC3/-7.757020E-08/,
+     :     CCSEC/  1.289600E-06, 5.550147E-01, 2.076942E+00,
+     :             3.102810E-05, 4.035027E+00, 3.525565E-01,
+     :             9.124190E-06, 9.990265E-01, 2.622706E+00,
+     :             9.793240E-07, 5.508259E+00, 1.559103E+01/
+
+*   Sidereal rate DCSLD in longitude, rate CCSGD in mean anomaly
+      DATA DCSLD/1.990987D-07/,
+     :     CCSGD/1.990969E-07/
+
+*   Some constants used in the calculation of the lunar contribution
+      DATA CCKM/3.122140E-05/,
+     :     CCMLD/2.661699E-06/,
+     :     CCFDI/2.399485E-07/
+
+*
+*   Constants DCARGM(I,K) of the arguments of the perturbations
+*   of the motion of the Moon
+*                       I=1               I=2
+      DATA DCARGM/  5.1679830D+00, 8.3286911095275D+03,
+     :              5.4913150D+00,-7.2140632838100D+03,
+     :              5.9598530D+00, 1.5542754389685D+04/
+
+*
+*   Amplitudes CCAMPM(N,K) of the perturbations of the Moon
+*            N=1          N=2           N=3           N=4
+      DATA CCAMPM/
+     :  1.097594E-01, 2.896773E-07, 5.450474E-02, 1.438491E-07,
+     : -2.223581E-02, 5.083103E-08, 1.002548E-02,-2.291823E-08,
+     :  1.148966E-02, 5.658888E-08, 8.249439E-03, 4.063015E-08/
+
+*
+*   CCPAMV(K)=A*M*DL/DT (planets), DC1MME=1-MASS(Earth+Moon)
+      DATA CCPAMV/8.326827E-11,1.843484E-11,1.988712E-12,1.881276E-12/
+      DATA DC1MME/0.99999696D0/
+
+*   CCPAM(K)=A*M(planets), CCIM=INCLINATION(Moon)
+      DATA CCPAM/4.960906E-3,2.727436E-3,8.392311E-4,1.556861E-3/
+      DATA CCIM/8.978749E-2/
+
+
+
+
+*
+*   EXECUTION
+*   ---------
+
+*   Control parameter IDEQ, and time arguments
+      IDEQ = 0
+      IF (DEQX.GT.0D0) IDEQ=1
+      DT = (DATE-15019.5D0)/36525D0
+      T = REAL(DT)
+      DTSQ = DT*DT
+      TSQ = REAL(DTSQ)
+
+*   Values of all elements for the instant DATE
+      DO K=1,8
+         DLOCAL = MOD(DCFEL(1,K)+DT*DCFEL(2,K)+DTSQ*DCFEL(3,K), DC2PI)
+         IF (K.EQ.1) THEN
+            DML = DLOCAL
+         ELSE
+            FORBEL(K-1) = REAL(DLOCAL)
+         END IF
+      END DO
+      DEPS = MOD(DCEPS(1)+DT*DCEPS(2)+DTSQ*DCEPS(3), DC2PI)
+      DO K=1,17
+         SORBEL(K) = MOD(CCSEL(1,K)+T*CCSEL(2,K)+TSQ*CCSEL(3,K),
+     :                   CC2PI)
+      END DO
+
+*   Secular perturbations in longitude
+      DO K=1,4
+         A = MOD(CCSEC(2,K)+T*CCSEC(3,K), CC2PI)
+         SN(K) = SIN(A)
+      END DO
+
+*   Periodic perturbations of the EMB (Earth-Moon barycentre)
+      PERTL =  CCSEC(1,1)          *SN(1) +CCSEC(1,2)*SN(2)+
+     :        (CCSEC(1,3)+T*CCSEC3)*SN(3) +CCSEC(1,4)*SN(4)
+      PERTLD = 0.0
+      PERTR = 0.0
+      PERTRD = 0.0
+      DO K=1,15
+         A = SNGL(MOD(DCARGS(1,K)+DT*DCARGS(2,K), DC2PI))
+         COSA = COS(A)
+         SINA = SIN(A)
+         PERTL = PERTL + CCAMPS(1,K)*COSA+CCAMPS(2,K)*SINA
+         PERTR = PERTR + CCAMPS(3,K)*COSA+CCAMPS(4,K)*SINA
+         IF (K.LT.11) THEN
+            PERTLD = PERTLD+
+     :               (CCAMPS(2,K)*COSA-CCAMPS(1,K)*SINA)*CCAMPS(5,K)
+            PERTRD = PERTRD+
+     :               (CCAMPS(4,K)*COSA-CCAMPS(3,K)*SINA)*CCAMPS(5,K)
+         END IF
+      END DO
+
+*   Elliptic part of the motion of the EMB
+      ESQ = E*E
+      DPARAM = 1D0-DBLE(ESQ)
+      PARAM = REAL(DPARAM)
+      TWOE = E+E
+      TWOG = G+G
+      PHI = TWOE*((1.0-ESQ*0.125)*SIN(G)+E*0.625*SIN(TWOG)
+     :          +ESQ*0.54166667*SIN(G+TWOG) )
+      F = G+PHI
+      SINF = SIN(F)
+      COSF = COS(F)
+      DPSI = DPARAM/(1D0+DBLE(E*COSF))
+      PHID = TWOE*CCSGD*((1.0+ESQ*1.5)*COSF+E*(1.25-SINF*SINF*0.5))
+      PSID = CCSGD*E*SINF/SQRT(PARAM)
+
+*   Perturbed heliocentric motion of the EMB
+      D1PDRO = 1D0+DBLE(PERTR)
+      DRD = D1PDRO*(DBLE(PSID)+DPSI*DBLE(PERTRD))
+      DRLD = D1PDRO*DPSI*(DCSLD+DBLE(PHID)+DBLE(PERTLD))
+      DTL = MOD(DML+DBLE(PHI)+DBLE(PERTL), DC2PI)
+      DSINLS = SIN(DTL)
+      DCOSLS = COS(DTL)
+      DXHD = DRD*DCOSLS-DRLD*DSINLS
+      DYHD = DRD*DSINLS+DRLD*DCOSLS
+
+*   Influence of eccentricity, evection and variation on the
+*   geocentric motion of the Moon
+      PERTL = 0.0
+      PERTLD = 0.0
+      PERTP = 0.0
+      PERTPD = 0.0
+      DO K=1,3
+         A = SNGL(MOD(DCARGM(1,K)+DT*DCARGM(2,K), DC2PI))
+         SINA = SIN(A)
+         COSA = COS(A)
+         PERTL = PERTL +CCAMPM(1,K)*SINA
+         PERTLD = PERTLD+CCAMPM(2,K)*COSA
+         PERTP = PERTP +CCAMPM(3,K)*COSA
+         PERTPD = PERTPD-CCAMPM(4,K)*SINA
+      END DO
+
+*   Heliocentric motion of the Earth
+      TL = FORBEL(2)+PERTL
+      SINLM = SIN(TL)
+      COSLM = COS(TL)
+      SIGMA = CCKM/(1.0+PERTP)
+      A = SIGMA*(CCMLD+PERTLD)
+      B = SIGMA*PERTPD
+      DXHD = DXHD+DBLE(A*SINLM)+DBLE(B*COSLM)
+      DYHD = DYHD-DBLE(A*COSLM)+DBLE(B*SINLM)
+      DZHD =     -DBLE(SIGMA*CCFDI*COS(FORBEL(3)))
+
+*   Barycentric motion of the Earth
+      DXBD = DXHD*DC1MME
+      DYBD = DYHD*DC1MME
+      DZBD = DZHD*DC1MME
+      DO K=1,4
+         PLON = FORBEL(K+3)
+         POMG = SORBEL(K+1)
+         PECC = SORBEL(K+9)
+         TL = MOD(PLON+2.0*PECC*SIN(PLON-POMG), CC2PI)
+         SINLP(K) = SIN(TL)
+         COSLP(K) = COS(TL)
+         DXBD = DXBD+DBLE(CCPAMV(K)*(SINLP(K)+PECC*SIN(POMG)))
+         DYBD = DYBD-DBLE(CCPAMV(K)*(COSLP(K)+PECC*COS(POMG)))
+         DZBD = DZBD-DBLE(CCPAMV(K)*SORBEL(K+13)*COS(PLON-SORBEL(K+5)))
+      END DO
+
+*   Transition to mean equator of date
+      DCOSEP = COS(DEPS)
+      DSINEP = SIN(DEPS)
+      DYAHD = DCOSEP*DYHD-DSINEP*DZHD
+      DZAHD = DSINEP*DYHD+DCOSEP*DZHD
+      DYABD = DCOSEP*DYBD-DSINEP*DZBD
+      DZABD = DSINEP*DYBD+DCOSEP*DZBD
+
+*   Heliocentric coordinates of the Earth
+      DR = DPSI*D1PDRO
+      FLATM = CCIM*SIN(FORBEL(3))
+      A = SIGMA*COS(FLATM)
+      DXH = DR*DCOSLS-DBLE(A*COSLM)
+      DYH = DR*DSINLS-DBLE(A*SINLM)
+      DZH =          -DBLE(SIGMA*SIN(FLATM))
+
+*   Barycentric coordinates of the Earth
+      DXB = DXH*DC1MME
+      DYB = DYH*DC1MME
+      DZB = DZH*DC1MME
+      DO K=1,4
+         FLAT = SORBEL(K+13)*SIN(FORBEL(K+3)-SORBEL(K+5))
+         A = CCPAM(K)*(1.0-SORBEL(K+9)*COS(FORBEL(K+3)-SORBEL(K+1)))
+         B = A*COS(FLAT)
+         DXB = DXB-DBLE(B*COSLP(K))
+         DYB = DYB-DBLE(B*SINLP(K))
+         DZB = DZB-DBLE(A*SIN(FLAT))
+      END DO
+
+*   Transition to mean equator of date
+      DYAH = DCOSEP*DYH-DSINEP*DZH
+      DZAH = DSINEP*DYH+DCOSEP*DZH
+      DYAB = DCOSEP*DYB-DSINEP*DZB
+      DZAB = DSINEP*DYB+DCOSEP*DZB
+
+*   Copy result components into vectors, correcting for FK4 equinox
+      DEPJ=slEPJ(DATE)
+      DEQCOR = DS2R*(0.035D0+0.00085D0*(DEPJ-B1950))
+      DVH(1) = DXHD-DEQCOR*DYAHD
+      DVH(2) = DYAHD+DEQCOR*DXHD
+      DVH(3) = DZAHD
+      DVB(1) = DXBD-DEQCOR*DYABD
+      DVB(2) = DYABD+DEQCOR*DXBD
+      DVB(3) = DZABD
+      DPH(1) = DXH-DEQCOR*DYAH
+      DPH(2) = DYAH+DEQCOR*DXH
+      DPH(3) = DZAH
+      DPB(1) = DXB-DEQCOR*DYAB
+      DPB(2) = DYAB+DEQCOR*DXB
+      DPB(3) = DZAB
+
+*   Was precession to another equinox requested?
+      IF (IDEQ.NE.0) THEN
+
+*     Yes: compute precession matrix from MJD DATE to Julian epoch DEQX
+         CALL slPREC(DEPJ,DEQX,DPREMA)
+
+*     Rotate DVH
+         DO J=1,3
+            W=0D0
+            DO I=1,3
+               W=W+DPREMA(J,I)*DVH(I)
+            END DO
+            VW(J)=W
+         END DO
+         DO J=1,3
+            DVH(J)=VW(J)
+         END DO
+
+*     Rotate DVB
+         DO J=1,3
+            W=0D0
+            DO I=1,3
+               W=W+DPREMA(J,I)*DVB(I)
+            END DO
+            VW(J)=W
+         END DO
+         DO J=1,3
+            DVB(J)=VW(J)
+         END DO
+
+*     Rotate DPH
+         DO J=1,3
+            W=0D0
+            DO I=1,3
+               W=W+DPREMA(J,I)*DPH(I)
+            END DO
+            VW(J)=W
+         END DO
+         DO J=1,3
+            DPH(J)=VW(J)
+         END DO
+
+*     Rotate DPB
+         DO J=1,3
+            W=0D0
+            DO I=1,3
+               W=W+DPREMA(J,I)*DPB(I)
+            END DO
+            VW(J)=W
+         END DO
+         DO J=1,3
+            DPB(J)=VW(J)
+         END DO
+      END IF
+
+      END
diff --git a/math/slalib/f77.h.in b/math/slalib/f77.h.in
new file mode 100644
index 00000000..43cab152
--- /dev/null
+++ b/math/slalib/f77.h.in
@@ -0,0 +1,956 @@
+/*
+*+
+*  Name:
+*     f77.h and cnf.h
+
+*  Purpose:
+*     C - FORTRAN interace macros and prototypes
+
+*  Language:
+*     C (part ANSI, part not)
+
+*  Type of Module:
+*     C include file
+
+*  Description:
+*     Including this file in SLALIB allows SLALIB to remain free of any
+*     dependencies on the rest of the Starlink Software Collection.
+*
+*     For historical reasons two files, F77.h and cnf.h are required
+*     but the have now been combined and for new code, only one is
+*     necessary.
+*
+*     This file defines the macros needed to write C functions that are
+*     designed to be called from FORTRAN programs, and to do so in a
+*     portable way. Arguments are normally passed by reference from a
+*     FORTRAN program, and so the F77 macros arrange for a pointer to
+*     all arguments to be available. This requires no work on most
+*     machines, but will actually generate the pointers on a machine
+*     that passes FORTRAN arguments by value.
+
+*  Notes:
+*     -  Macros are provided to handle the conversion of logical data
+*        values between the way that FORTRAN represents a value and the
+*        way that C represents it.
+*     -  Macros are provided to convert variables between the FORTRAN and
+*        C method of representing them. In most cases there is no
+*        conversion required, the macros just arrange for a pointer to
+*        the FORTRAN variable to be set appropriately. The possibility that
+*        FORTRAN and C might use different ways of representing integer
+*        and floating point values is considered remote, the macros are
+*        really only there for completeness and to assist in the automatic
+*        generation of C interfaces.
+*     -  For character variables the macros convert between
+*        the FORTRAN method of representing them (fixed length, blank
+*        filled strings) and the C method (variable length, null
+*        terminated strings) using calls to the CNF functions.
+
+*  Implementation Deficiencies:
+*     -  The macros support the K&R style of function definition, but
+*        this file may not work with all K&R compilers as it contains
+*        "#if defined" statements. These could be replaced with #ifdef's
+*        if necessary. This has not been done as is would make the code
+*        less clear and the need for support for K&R sytle definitions
+*        should disappear as ANSI compilers become the default.
+
+*  Copyright:
+*     Copyright (C) 1991, 1993 Science & Engineering Research Council.
+*     Copyright (C) 2006 Particle Physics and Astronomy Research Council.
+*     Copyright (C) 2011 Science and Technology Facilities Council.
+*     All Rights Reserved.
+
+*  Licence:
+*     This program is free software; you can redistribute it and/or
+*     modify it under the terms of the GNU General Public License as
+*     published by the Free Software Foundation; either version 2 of
+*     the License, or (at your option) any later version.
+*
+*     This program is distributed in the hope that it will be
+*     useful,but WITHOUT ANY WARRANTY; without even the implied
+*     warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
+*     PURPOSE. See the GNU General Public License for more details.
+*
+*     You should have received a copy of the GNU General Public License
+*     along with this program; if not, write to the Free Software
+*     Foundation, Inc., 51 Franklin Street,Fifth Floor, Boston, MA
+*     02110-1301, USA
+
+*  Authors:
+*     PMA: Peter Allan (Starlink, RAL)
+*     AJC: Alan Chipperfield (Starlink, RAL)
+*     DSB: David S Berry (JAC)
+*     PWD: Peter W. Draper (JAC, Durham University)
+*     {enter_new_authors_here}
+
+*  History:
+*     13-JUN-2006 (DSB):
+*        Original version, copied from AST.
+*     22-JUN-2006 (PWD):
+*        Updated to include changes that handle the return type of
+*        REAL functions (double, not float, on some platforms).
+*     13-JUL-2007 (PWD):
+*        Parameterise the type used for Fortran string lengths.
+*     11-MAY-2011 (DSB):
+*        Added F77_LOCK
+*     {enter_further_changes_here}
+*
+
+*  Bugs:
+*     {note_any_bugs_here}
+
+*-
+------------------------------------------------------------------------------
+*/
+#if !defined(CNF_MACROS)
+#define CNF_MACROS
+
+#include <stdlib.h>
+/*  This initial sections defines values for all macros. These are the	    */
+/*  values that are generally appropriate to an ANSI C compiler on Unix.    */
+/*  For macros that have different values on other systems, the macros	    */
+/*  should be undefined and then redefined in the system specific sections. */
+/*  At the end of this section, some macros are redefined if the compiler   */
+/*  is non-ANSI.							    */
+
+
+#if defined(__STDC__) || defined(VMS)
+#define CNF_CONST const
+#else
+#define CNF_CONST
+#endif
+
+/*  -----  Macros common to calling C from FORTRAN and FORTRAN from C  ---- */
+
+
+/*  ---  External Names  ---						    */
+
+/*  Macro to define the name of a Fortran routine or common block. This	    */
+/*  ends in an underscore on many Unix systems.				    */
+
+#define F77_EXTERNAL_NAME(X) X ## _
+
+
+/*  ---  Logical Values  ---						    */
+
+/*  Define the values that are used to represent the logical values TRUE    */
+/*  and FALSE in Fortran.						    */
+
+#define F77_TRUE 1
+#define F77_FALSE 0
+
+/*  Define macros that evaluate to C logical values, given a FORTRAN	    */
+/*  logical value.							    */
+
+#define F77_ISTRUE(X) ( X )
+#define F77_ISFALSE(X) ( !( X ) )
+
+
+/*  ---  Common Blocks  ---						    */
+
+/*  Macros used in referring to FORTRAN common blocks.			    */
+
+#define F77_BLANK_COMMON                _BLNK__
+#define F77_NAMED_COMMON(B)             F77_EXTERNAL_NAME(B)
+
+
+
+/*  ------------------  Calling C from FORTRAN  --------------------------- */
+
+
+/*  ---  Data Types  ---						    */
+
+/*  Define macros for all the Fortran data types (except COMPLEX, which is  */
+/*  not handled by this package).					    */
+
+#define F77_INTEGER_TYPE   int
+#define F77_REAL_TYPE      float
+#define F77_REAL_FUNCTION_TYPE      @REAL_FUNCTION_TYPE@
+#define F77_DOUBLE_TYPE    double
+#define F77_LOGICAL_TYPE   int
+#define F77_CHARACTER_TYPE char
+#define F77_BYTE_TYPE      signed char
+#define F77_WORD_TYPE      short int
+#define F77_UBYTE_TYPE     unsigned char
+#define F77_UWORD_TYPE     unsigned short int
+
+/*  Define macros for the type of a CHARACTER and CHARACTER_ARRAY argument  */
+#define F77_CHARACTER_ARG_TYPE char
+#define F77_CHARACTER_ARRAY_ARG_TYPE char
+
+/*  Define a macro to use when passing arguments that STARLINK FORTRAN	    */
+/*  treats as a pointer. From the point of view of C, this type should be   */
+/*  (void *), but it is declared as type unsigned int as we actually pass   */
+/*  an INTEGER from the FORTRAN routine. The distinction is important for   */
+/*  architectures where the size of an INTEGER is not the same as the size  */
+/*  of a pointer.							    */
+
+#define F77_POINTER_TYPE   unsigned int
+
+
+/*  ---  Subroutine Names  ---						    */
+
+/* This declares that the C function returns a value of void.		    */
+
+#define F77_SUBROUTINE(X)  void F77_EXTERNAL_NAME(X)
+
+
+/*  ---  Function Names  ---						    */
+
+/*  Macros to define the types and names of functions that return values.   */
+/*  Due the the different ways that function return values could be	    */
+/*  implemented, it is better not to use functions, but to stick to using   */
+/*  subroutines.							    */
+
+/*  Character functions are implemented, but in a way that cannot be	    */
+/*  guaranteed to be portable although it will work on VMS, SunOS, Ultrix   */
+/*  and DEC OSF/1. It would be better to return the character value as a    */
+/*  subroutine argument where possible, rather than use a character	    */
+/*  function.								    */
+
+#define F77_INTEGER_FUNCTION(X)   F77_INTEGER_TYPE F77_EXTERNAL_NAME(X)
+#define F77_REAL_FUNCTION(X)      F77_REAL_FUNCTION_TYPE F77_EXTERNAL_NAME(X)
+#define F77_DOUBLE_FUNCTION(X)    F77_DOUBLE_TYPE F77_EXTERNAL_NAME(X)
+#define F77_LOGICAL_FUNCTION(X)   F77_LOGICAL_TYPE F77_EXTERNAL_NAME(X)
+#define F77_CHARACTER_FUNCTION(X) void F77_EXTERNAL_NAME(X)
+#define F77_BYTE_FUNCTION(X)      F77_BYTE_TYPE F77_EXTERNAL_NAME(X)
+#define F77_WORD_FUNCTION(X)      F77_WORD_TYPE F77_EXTERNAL_NAME(X)
+#define F77_UBYTE_FUNCTION(X)     F77_UBYTE_TYPE F77_EXTERNAL_NAME(X)
+#define F77_UWORD_FUNCTION(X)     F77_UWORD_TYPE F77_EXTERNAL_NAME(X)
+#define F77_POINTER_FUNCTION(X)   F77_POINTER_TYPE F77_EXTERNAL_NAME(X)
+
+
+/*  ---  Character return value for a function  ---			    */
+
+#define CHARACTER_RETURN_VALUE(X) CHARACTER(X) TRAIL(X)
+#define CHARACTER_RETURN_ARG(X) CHARACTER_ARG(X) TRAIL_ARG(X)
+
+/*  ---  Dummy Arguments  ---						    */
+
+/*  Macros for defining subroutine arguments. All these macros take a	    */
+/*  single argument; the name of the parameter. On most systems, a numeric  */
+/*  argument is passed as a pointer.					    */
+
+#define INTEGER(X)     F77_INTEGER_TYPE *CNF_CONST X
+#define REAL(X)        F77_REAL_TYPE    *CNF_CONST X
+#define DOUBLE(X)      F77_DOUBLE_TYPE  *CNF_CONST X
+#define LOGICAL(X)     F77_LOGICAL_TYPE *CNF_CONST X
+#define BYTE(X)        F77_BYTE_TYPE    *CNF_CONST X
+#define WORD(X)        F77_WORD_TYPE    *CNF_CONST X
+#define UBYTE(X)       F77_UBYTE_TYPE   *CNF_CONST X
+#define UWORD(X)       F77_UWORD_TYPE   *CNF_CONST X
+
+/*  Pointer arguments. Define a pointer type for passing pointer values	    */
+/*  between subroutines.						    */
+
+#define POINTER(X)     F77_POINTER_TYPE *CNF_CONST X
+
+/*  EXTERNAL arguments. Define a passed subroutine or function name */
+#define SUBROUTINE(X)  void (*X)()
+#define INTEGER_FUNCTION(X)  F77_INTEGER_TYPE (*X)()
+#define REAL_FUNCTION(X)  F77_REAL_TYPE (*X)()
+#define DOUBLE_FUNCTION(X)  F77_DOUBLE_TYPE (*X)()
+#define LOGICAL_FUNCTION(X)  F77_LOGICAL_TYPE (*X)()
+#define CHARACTER_FUNCTION(X)  F77_CHARACTER_TYPE (*X)()
+#define BYTE_FUNCTION(X)  F77_BYTE_TYPE (*X)()
+#define WORD_FUNCTION(X)  F77_WORD_TYPE (*X)()
+#define UBYTE_FUNCTION(X)  F77_UBYTE_TYPE (*X)()
+#define UWORD_FUNCTION(X)  F77_UWORD_TYPE (*X)()
+#define POINTER_FUNCTION(X)  F77_POINTER_TYPE (*X)()
+
+/*  Array arguments.							    */
+
+#define INTEGER_ARRAY(X)     F77_INTEGER_TYPE *CNF_CONST X
+#define REAL_ARRAY(X)        F77_REAL_TYPE    *CNF_CONST X
+#define DOUBLE_ARRAY(X)      F77_DOUBLE_TYPE  *CNF_CONST X
+#define LOGICAL_ARRAY(X)     F77_LOGICAL_TYPE *CNF_CONST X
+#define BYTE_ARRAY(X)        F77_BYTE_TYPE    *CNF_CONST X
+#define WORD_ARRAY(X)        F77_WORD_TYPE    *CNF_CONST X
+#define UBYTE_ARRAY(X)       F77_UBYTE_TYPE   *CNF_CONST X
+#define UWORD_ARRAY(X)       F77_UWORD_TYPE   *CNF_CONST X
+
+#define POINTER_ARRAY(X)     F77_POINTER_TYPE *CNF_CONST X
+
+/*  Macros to handle character arguments.				    */
+
+/*  Character arguments can be passed in many ways. The purpose of these    */
+/*  macros and the GENPTR_CHARACTER macro (defined in the next section) is  */
+/*  to generate a pointer to a character variable called ARG and an integer */
+/*  ARG_length containing the length of ARG. If these two variables are	    */
+/*  available directly from the argument list of the routine, then the	    */
+/*  GENPTR_CHARACTER macro is null, otherwise it works on intermediate	    */
+/*  variables.								    */
+
+#define CHARACTER(X)             F77_CHARACTER_TYPE *CNF_CONST X
+#define TRAIL(X)                 ,@TRAIL_TYPE@ X ## _length
+#define CHARACTER_ARRAY(X)       F77_CHARACTER_TYPE *CNF_CONST X
+
+
+/*  ---  Getting Pointers to Arguments  ---				    */
+
+/*  Macros that ensure that a pointer to each argument is available for the */
+/*  programmer to use. Usually this means that these macros are null. On    */
+/*  VMS, a pointer to a character variable has to be generated. If a	    */
+/*  particular machine were to pass arguments by reference, rather than by  */
+/*  value, then these macros would construct the appropriate pointers.	    */
+
+#define GENPTR_INTEGER(X)
+#define GENPTR_REAL(X)
+#define GENPTR_DOUBLE(X)
+#define GENPTR_CHARACTER(X)
+#define GENPTR_LOGICAL(X)
+#define GENPTR_BYTE(X)
+#define GENPTR_WORD(X)
+#define GENPTR_UBYTE(X)
+#define GENPTR_UWORD(X)
+#define GENPTR_POINTER(X)
+
+#define GENPTR_INTEGER_ARRAY(X)
+#define GENPTR_REAL_ARRAY(X)
+#define GENPTR_DOUBLE_ARRAY(X)
+#define GENPTR_CHARACTER_ARRAY(X)
+#define GENPTR_LOGICAL_ARRAY(X)
+#define GENPTR_BYTE_ARRAY(X)
+#define GENPTR_WORD_ARRAY(X)
+#define GENPTR_UBYTE_ARRAY(X)
+#define GENPTR_UWORD_ARRAY(X)
+#define GENPTR_POINTER_ARRAY(X)
+
+#define GENPTR_SUBROUTINE(X)
+#define GENPTR_INTEGER_FUNCTION(X)
+#define GENPTR_REAL_FUNCTION(X)
+#define GENPTR_DOUBLE_FUNCTION(X)
+#define GENPTR_CHARACTER_FUNCTION(X)
+#define GENPTR_LOGICAL_FUNCTION(X)
+#define GENPTR_BYTE_FUNCTION(X)
+#define GENPTR_WORD_FUNCTION(X)
+#define GENPTR_UBYTE_FUNCTION(X)
+#define GENPTR_UWORD_FUNCTION(X)
+#define GENPTR_POINTER_FUNCTION(X)
+
+
+
+/*  ------------------  Calling FORTRAN from C  --------------------------- */
+
+
+/*  ---  Declare variables  ---						    */
+
+#define DECLARE_INTEGER(X) F77_INTEGER_TYPE X
+#define DECLARE_REAL(X)    F77_REAL_TYPE X
+#define DECLARE_DOUBLE(X)  F77_DOUBLE_TYPE X
+#define DECLARE_LOGICAL(X) F77_LOGICAL_TYPE X
+#define DECLARE_BYTE(X)    F77_BYTE_TYPE X
+#define DECLARE_WORD(X)    F77_WORD_TYPE X
+#define DECLARE_UBYTE(X)   F77_UBYTE_TYPE X
+#define DECLARE_UWORD(X)   F77_UWORD_TYPE X
+
+#define DECLARE_POINTER(X) F77_POINTER_TYPE X
+
+#define DECLARE_CHARACTER(X,L) F77_CHARACTER_TYPE X[L]; \
+   const int X##_length = L
+
+
+/*  ---  Declare arrays ---						    */
+
+#define DECLARE_INTEGER_ARRAY(X,D) F77_INTEGER_TYPE X[D]
+#define DECLARE_REAL_ARRAY(X,D)    F77_REAL_TYPE X[D]
+#define DECLARE_DOUBLE_ARRAY(X,D)  F77_DOUBLE_TYPE X[D]
+#define DECLARE_LOGICAL_ARRAY(X,D) F77_LOGICAL_TYPE X[D]
+#define DECLARE_BYTE_ARRAY(X,D)    F77_BYTE_TYPE X[D]
+#define DECLARE_WORD_ARRAY(X,D)    F77_WORD_TYPE X[D]
+#define DECLARE_UBYTE_ARRAY(X,D)   F77_UBYTE_TYPE X[D]
+#define DECLARE_UWORD_ARRAY(X,D)   F77_UWORD_TYPE X[D]
+#define DECLARE_POINTER_ARRAY(X,D) F77_POINTER_TYPE X[D]
+#define DECLARE_CHARACTER_ARRAY(X,L,D) F77_CHARACTER_TYPE X[D][L]; \
+   const int X##_length = L
+
+/*  ---  Declare and construct dynamic CHARACTER arguments ---                      */
+#define DECLARE_CHARACTER_DYN(X)   F77_CHARACTER_TYPE *X;\
+   int X##_length
+#define F77_CREATE_CHARACTER(X,L)  X=slaStringCreate(L);\
+   X##_length = (L>0?L:1)
+
+/* Declare Dynamic Fortran arrays */
+#define DECLARE_INTEGER_ARRAY_DYN(X) F77_INTEGER_TYPE *X
+#define DECLARE_REAL_ARRAY_DYN(X)    F77_REAL_TYPE *X
+#define DECLARE_DOUBLE_ARRAY_DYN(X)  F77_DOUBLE_TYPE *X
+#define DECLARE_LOGICAL_ARRAY_DYN(X) F77_LOGICAL_TYPE *X
+#define DECLARE_BYTE_ARRAY_DYN(X)    F77_BYTE_TYPE *X
+#define DECLARE_WORD_ARRAY_DYN(X)    F77_WORD_TYPE *X
+#define DECLARE_UBYTE_ARRAY_DYN(X)   F77_UBYTE_TYPE *X
+#define DECLARE_UWORD_ARRAY_DYN(X)   F77_UWORD_TYPE *X
+#define DECLARE_POINTER_ARRAY_DYN(X) F77_POINTER_TYPE *X
+#define DECLARE_CHARACTER_ARRAY_DYN(X)   F77_CHARACTER_TYPE *X;\
+   int X##_length
+
+/* Create arrays dynamic Fortran arrays for those types which require */
+/* Separate space for Fortran and C arrays                            */
+/* Character and logical are already defined                          */
+/* For most types there is nothing to do                              */
+#define F77_CREATE_CHARACTER_ARRAY(X,L,N) \
+        {int f77dims[1];f77dims[0]=N;X=cnfCrefa(L,1,f77dims);X##_length=L;}
+#define F77_CREATE_CHARACTER_ARRAY_M(X,L,N,D)  X=cnfCrefa(L,N,D);\
+   X##_length = L
+#define F77_CREATE_LOGICAL_ARRAY(X,N) \
+        {int f77dims[1];f77dims[0]=N;X=cnfCrela(1,f77dims);}
+#define F77_CREATE_LOGICAL_ARRAY_M(X,N,D) X=cnfCrela(N,D)
+#define F77_CREATE_INTEGER_ARRAY(X,N)
+#define F77_CREATE_REAL_ARRAY(X,N)
+#define F77_CREATE_DOUBLE_ARRAY(X,N)
+#define F77_CREATE_BYTE_ARRAY(X,N)
+#define F77_CREATE_UBYTE_ARRAY(X,N)
+#define F77_CREATE_WORD_ARRAY(X,N)
+#define F77_CREATE_UWORD_ARRAY(X,N)
+#define F77_CREATE_POINTER_ARRAY(X,N)\
+        X=(F77_POINTER_TYPE *) malloc(N*sizeof(F77_POINTER_TYPE))
+
+/* Associate Fortran arrays with C arrays                             */
+/* These macros ensure that there is space somewhere for the Fortran  */
+/* array. They are complemetary to the CREATE_type_ARRAY macros       */
+#define F77_ASSOC_CHARACTER_ARRAY(F,C)
+#define F77_ASSOC_LOGICAL_ARRAY(F,C)
+#define F77_ASSOC_INTEGER_ARRAY(F,C) F=C
+#define F77_ASSOC_REAL_ARRAY(F,C) F=C
+#define F77_ASSOC_DOUBLE_ARRAY(F,C) F=C
+#define F77_ASSOC_BYTE_ARRAY(F,C) F=C
+#define F77_ASSOC_UBYTE_ARRAY(F,C) F=C
+#define F77_ASSOC_WORD_ARRAY(F,C) F=C
+#define F77_ASSOC_UWORD_ARRAY(F,C) F=C
+#define F77_ASSOC_POINTER_ARRAY(F,C)
+
+/* Free created dynamic arrays */
+/* Character and logical are already defined */
+/* For most types there is nothing to do */
+#define F77_FREE_INTEGER(X)
+#define F77_FREE_REAL(X)
+#define F77_FREE_DOUBLE(X)
+#define F77_FREE_BYTE(X)
+#define F77_FREE_UBYTE(X)
+#define F77_FREE_WORD(X)
+#define F77_FREE_UWORD(X)
+#define F77_FREE_POINTER(X) cnfFree((void *)X);
+#define F77_FREE_CHARACTER(X) slaStringFree( X )
+#define F77_FREE_LOGICAL(X) cnfFree( (char *)X )
+
+/*  ---  IMPORT and EXPORT of values  --- */
+/* Export C variables to Fortran variables */
+#define F77_EXPORT_CHARACTER(C,F,L) slaStringExport(C,F,L)
+#define F77_EXPORT_DOUBLE(C,F) F=C
+#define F77_EXPORT_INTEGER(C,F) F=C
+#define F77_EXPORT_LOGICAL(C,F) F=C?F77_TRUE:F77_FALSE
+#define F77_EXPORT_REAL(C,F) F=C
+#define F77_EXPORT_BYTE(C,F) F=C
+#define F77_EXPORT_WORD(C,F) F=C
+#define F77_EXPORT_UBYTE(C,F) F=C
+#define F77_EXPORT_UWORD(C,F) F=C
+#define F77_EXPORT_POINTER(C,F) F=cnfFptr(C)
+#define F77_EXPORT_LOCATOR(C,F) cnfExpch(C,F,DAT__SZLOC)
+
+/* Allow for character strings to be NULL, protects strlen. Note this
+ * does not allow lengths to differ. */
+#define F77_CREATE_EXPORT_CHARACTER(C,F) \
+     if (C) { \
+        F77_CREATE_CHARACTER(F,strlen(C)); \
+        F77_EXPORT_CHARACTER(C,F,F##_length); \
+     } else { \
+        F77_CREATE_CHARACTER(F,1); \
+        F77_EXPORT_CHARACTER(" ",F,F##_length); \
+     }
+
+
+/* Export C arrays to Fortran */
+/* Arrays are assumed to be 1-d so just the number of elements is given  */
+/* This may be OK for n-d arrays also */
+/* CHARACTER arrays may be represented in C as arrays of arrays of char or */
+/* as arrays of pointers to char (the _P variant) */
+#define F77_EXPORT_CHARACTER_ARRAY(C,LC,F,LF,N) \
+        {int f77dims[1];f77dims[0]=N;cnfExprta(C,LC,F,LF,1,f77dims);}
+#define F77_EXPORT_CHARACTER_ARRAY_P(C,F,LF,N) \
+        {int f77dims[1];f77dims[0]=N;cnfExprtap(C,F,LF,1,f77dims);}
+#define F77_EXPORT_DOUBLE_ARRAY(C,F,N) F=(F77_DOUBLE_TYPE *)C
+#define F77_EXPORT_INTEGER_ARRAY(C,F,N) F=(F77_INTEGER_TYPE *)C
+#define F77_EXPORT_LOGICAL_ARRAY(C,F,N) \
+        {int f77dims[1];f77dims[0]=N;cnfExpla(C,F,1,f77dims);}
+#define F77_EXPORT_REAL_ARRAY(C,F,N) F=(F77_REAL_TYPE *)C
+#define F77_EXPORT_BYTE_ARRAY(C,F,N) F=(F77_BYTE_TYPE *)C
+#define F77_EXPORT_WORD_ARRAY(C,F,N) F=(F77_WORD_TYPE *)C
+#define F77_EXPORT_UBYTE_ARRAY(C,F,N) F=(F77_UBYTE_TYPE *)C
+#define F77_EXPORT_UWORD_ARRAY(C,F,N) F=(F77_UWORD_TYPE * )C
+#define F77_EXPORT_POINTER_ARRAY(C,F,N) \
+     {int f77i;for (f77i=0;f77i<N;f77i++)F[f77i]=cnfFptr(C[f77i]);}
+#define F77_EXPORT_LOCATOR_ARRAY(C,F,N) \
+        {int f77i;for (f77i=0;f77i<N;f77i++)cnfExpch(C,F,DAT__SZLOC);}
+
+/* Import Fortran variables to C */
+#define F77_IMPORT_CHARACTER(F,L,C) cnfImprt(F,L,C)
+#define F77_IMPORT_DOUBLE(F,C) C=F
+#define F77_IMPORT_INTEGER(F,C) C=F
+#define F77_IMPORT_LOGICAL(F,C) C=F77_ISTRUE(F)
+#define F77_IMPORT_REAL(F,C) C=F
+#define F77_IMPORT_BYTE(F,C) C=F
+#define F77_IMPORT_WORD(F,C) C=F
+#define F77_IMPORT_UBYTE(F,C) C=F
+#define F77_IMPORT_UWORD(F,C) C=F
+#define F77_IMPORT_POINTER(F,C) C=cnfCptr(F)
+#define F77_IMPORT_LOCATOR(F,C) cnfImpch(F,DAT__SZLOC,C)
+
+/* Import Fortran arrays to C */
+/* Arrays are assumed to be 1-d so just the number of elements is given  */
+/* This may be OK for n-d arrays also */
+/* CHARACTER arrays may be represented in C as arrays of arrays of char or */
+/* as arrays of pointers to char (the _P variant) */
+#define F77_IMPORT_CHARACTER_ARRAY(F,LF,C,LC,N) \
+        {int f77dims[1];f77dims[0]=N;cnfImprta(F,LF,C,LC,1,f77dims);}
+#define F77_IMPORT_CHARACTER_ARRAY_P(F,LF,C,LC,N) \
+        {int f77dims[1];f77dims[0]=N;cnfImprtap(F,LF,C,LC,1,f77dims);}
+#define F77_IMPORT_DOUBLE_ARRAY(F,C,N)
+#define F77_IMPORT_INTEGER_ARRAY(F,C,N)
+#define F77_IMPORT_LOGICAL_ARRAY(F,C,N) \
+        {int f77dims[1];f77dims[0]=N;cnfImpla(F,C,1,f77dims);}
+#define F77_IMPORT_REAL_ARRAY(F,C,N)
+#define F77_IMPORT_BYTE_ARRAY(F,C,N)
+#define F77_IMPORT_WORD_ARRAY(F,C,N)
+#define F77_IMPORT_UBYTE_ARRAY(F,C,N)
+#define F77_IMPORT_UWORD_ARRAY(F,C,N)
+#define F77_IMPORT_POINTER_ARRAY(F,C,N) \
+        {int f77i;for (f77i=0;f77i<N;f77i++)C[f77i]=cnfCptr(F[f77i]);}
+#define F77_IMPORT_LOCATOR_ARRAY(F,C,N) \
+        {int f77i;for (f77i=0;f77i<N;f77i++)cnfImpch(F,DAT__SZLOC,C);}
+
+/*  ---  Call a FORTRAN routine  ---					    */
+
+#define F77_CALL(X)  F77_EXTERNAL_NAME(X)
+
+
+/*  ---  Execute code synchronised by the CNF global mutex                  */
+#include <config.h>
+
+#if USE_CNF
+#define F77_LOCK(code) \
+   cnfLock(); \
+   code \
+   cnfUnlock();
+#else
+#define F77_LOCK(code) code
+#endif
+
+/*  ---  Pass arguments to a FORTRAN routine  ---			    */
+
+#define INTEGER_ARG(X)   X
+#define REAL_ARG(X)      X
+#define DOUBLE_ARG(X)    X
+#define LOGICAL_ARG(X)   X
+#define BYTE_ARG(X)      X
+#define WORD_ARG(X)      X
+#define UBYTE_ARG(X)     X
+#define UWORD_ARG(X)     X
+#define POINTER_ARG(X)   X
+#define CHARACTER_ARG(X) X
+#define TRAIL_ARG(X)     ,X##_length
+
+#define SUBROUTINE_ARG(X)  X
+#define INTEGER_FUNCTION_ARG(X)  X
+#define REAL_FUNCTION_ARG(X)  X
+#define DOUBLE_FUNCTION_ARG(X)  X
+#define LOGICAL_FUNCTION_ARG(X)  X
+#define CHARACTER_FUNCTION_ARG(X)  X
+#define BYTE_FUNCTION_ARG(X)  X
+#define WORD_FUNCTION_ARG(X)  X
+#define UBYTE_FUNCTION_ARG(X)  X
+#define UWORD_FUNCTION_ARG(X)  X
+#define POINTER_FUNCTION_ARG(X)  X
+
+#define INTEGER_ARRAY_ARG(X)   (F77_INTEGER_TYPE *)X
+#define REAL_ARRAY_ARG(X)      (F77_REAL_TYPE *)X
+#define DOUBLE_ARRAY_ARG(X)    (F77_DOUBLE_TYPE *)X
+#define LOGICAL_ARRAY_ARG(X)   (F77_LOGICAL_TYPE *)X
+#define BYTE_ARRAY_ARG(X)      (F77_BYTE_TYPE *)X
+#define WORD_ARRAY_ARG(X)      (F77_WORD_TYPE *)X
+#define UBYTE_ARRAY_ARG(X)     (F77_UBYTE_TYPE *)X
+#define UWORD_ARRAY_ARG(X)     (F77_UWORD_TYPE *)X
+#define POINTER_ARRAY_ARG(X)   (F77_POINTER_TYPE *)X
+#define CHARACTER_ARRAY_ARG(X) (F77_CHARACTER_ARRAY_ARG_TYPE *)X
+
+
+/* ------------------------ Non-ansi section ------------------------------ */
+
+/*  The difference between ANSI and non-ANSI compilers, as far as macro	    */
+/*  definition is concerned, is that non-ANSI compilers do not support the  */
+/*  token concatenation operator (##). To work around this, we use the fact */
+/*  that the null comment is preprocessed to produce no characters at all   */
+/*  by our non-ANSI compilers.						    */
+/*  This section does not deal with the fact that some non-ANSI compilers   */
+/*  cannot handle function prototypes. That is handled in the machine 	    */
+/*  specific sections.							    */
+
+#if !defined(__STDC__)
+
+/*  ---  External Name  ---						    */
+
+/*  Macro to define the name of a Fortran routine or common block. This	    */
+/*  ends in an underscore on many Unix systems.				    */
+
+#undef  F77_EXTERNAL_NAME
+#define F77_EXTERNAL_NAME(X) X/**/_
+
+
+/*  ---  Dummy Arguments  ---						    */
+
+/*  Macros to handle character dummy arguments.				    */
+
+#undef  TRAIL
+#define TRAIL(X) ,@TRAIL_TYPE@ X/**/_length
+
+
+/*  ---  Declare variables  ---						    */
+
+#undef  DECLARE_CHARACTER
+#define DECLARE_CHARACTER(X,L)         F77_CHARACTER_TYPE X[L]; \
+   const int X/**/_length = L
+#undef  DECLARE_CHARACTER_ARRAY
+#define DECLARE_CHARACTER_ARRAY(X,L,D) F77_CHARACTER_TYPE X[D][L]; \
+   const int X/**/_length = L
+#undef DECLARE_CHARACTER_DYN
+#define DECLARE_CHARACTER_DYN(X)   F77_CHARACTER_TYPE *X;\
+   int X/**/_length
+#undef DECLARE_CHARACTER_ARRAY_DYN
+#define DECLARE_CHARACTER_ARRAY_DYN(X)   F77_CHARACTER_TYPE *X;\
+   int X/**/_length
+#undef F77_CREATE_CHARACTER
+#define F77_CREATE_CHARACTER(X,L)  X=cnfCref(L);\
+   X/**/_length = L
+#undef F77_CREATE_CHARACTER_ARRAY
+#define F77_CREATE_CHARACTER_ARRAY(X,L,N) \
+        {int f77dims[1];f77dims[0]=N;X=cnfCrefa(L,1,f77dims);X/**/_length=L;}
+
+/*  ---  Pass arguments to a FORTRAN routine  ---			    */
+
+#undef  TRAIL_ARG
+#define TRAIL_ARG(X)     ,X/**/_length
+
+
+#endif  /* of non ANSI redefinitions					    */
+
+
+/* -----------------------------------------------------------------------  */
+
+/* The standard macros defined above are known to work with the following   */
+/* systems:								    */
+
+/*--------
+|   Sun   |
+---------*/
+
+/*  On SunOS, the ANSI definitions work with the acc and gcc compilers.     */
+/*  The cc compiler uses the non ANSI definitions. It also needs the K&R    */
+/*  definitions in the file kr.h.					    */
+/*  On Solaris, the standard definitions work with the cc compiler.	    */
+
+#if defined(sun)
+
+#if !defined(__STDC__)
+#if !defined(_F77_KR)
+#define _F77_KR
+#endif
+#endif
+
+#endif	/* Sun								    */
+
+/* -------------------- System dependent sections ------------------------- */
+
+/*------------
+|   VAX/VMS   |
+-------------*/
+
+/* Many macros need to be changed due to the way that VMS handles external  */
+/* names, passes character arguments and handles logical values.	    */
+
+
+#if defined(VMS)
+
+/*  ---  Data Types  ---						    */
+
+/*  Redefine the macro for the byte data type as signed is not valid syntax */
+/*  as the VMS compiler is not ANSI compliant.				    */
+
+#undef  F77_BYTE_TYPE
+#define F77_BYTE_TYPE      char
+
+
+/*  ---  External Names  ---						    */
+
+/*  Macro to define the name of a Fortran routine or common block.	    */
+/*  Fortran and C routines names are the same on VMS.			    */
+
+#undef  F77_EXTERNAL_NAME
+#define F77_EXTERNAL_NAME(X) X
+
+
+/*  ---  Dummy Arguments  ---						    */
+
+/*  Macros to handle character arguments.				    */
+/*  Character string arguments are pointers to character string descriptors */
+/*  and there are no trailing arguments.				    */
+
+#if( VMS != 0 )
+#include <descrip.h>
+#endif
+
+
+#undef  F77_CHARACTER_ARG_TYPE
+#define F77_CHARACTER_ARG_TYPE struct dsc$descriptor_s
+#undef  F77_CHARACTER_ARRAY_ARG_TYPE
+#define F77_CHARACTER_ARRAY_ARG_TYPE struct dsc$descriptor_a
+#undef  CHARACTER
+#define CHARACTER(X) F77_CHARACTER_ARG_TYPE *CNF_CONST X/**/_arg
+#undef  TRAIL
+#define TRAIL(X)
+#undef  CHARACTER_ARRAY
+#define CHARACTER_ARRAY(X)  F77_CHARACTER_ARRAY_ARG_TYPE *CNF_CONST X/**/_arg
+#undef  GENPTR_CHARACTER
+#define GENPTR_CHARACTER(X) \
+   F77_CHARACTER_TYPE *X = X/**/_arg->dsc$a_pointer; \
+   int X/**/_length = X/**/_arg->dsc$w_length;
+#undef  GENPTR_CHARACTER_ARRAY
+#define GENPTR_CHARACTER_ARRAY(X)   GENPTR_CHARACTER(X)
+
+
+/*  ---  Logical Values  ---						    */
+
+#undef  F77_TRUE
+#define F77_TRUE -1
+#undef  F77_ISTRUE
+#define F77_ISTRUE(X) ( (X)&1 )
+#undef  F77_ISFALSE
+#define F77_ISFALSE(X) ( ! ( (X)&1 ) )
+
+
+/*  ---  Common Blocks  ---						    */
+
+#undef  F77_BLANK_COMMON
+#define F77_BLANK_COMMON  $BLANK
+
+
+/*  ---  Declare Variables  ---						    */
+
+#undef  DECLARE_CHARACTER
+#define DECLARE_CHARACTER(X,L) \
+   F77_CHARACTER_TYPE X[L];    const int X/**/_length = L; \
+   F77_CHARACTER_ARG_TYPE X/**/_descr = \
+      { L, DSC$K_DTYPE_T, DSC$K_CLASS_S, X }; \
+   F77_CHARACTER_ARG_TYPE *X/**/_arg = &X/**/_descr
+#undef  DECLARE_CHARACTER_ARRAY
+#define DECLARE_CHARACTER_ARRAY(X,L,D) \
+   F77_CHARACTER_TYPE X[D][L]; const int X/**/_length = L; \
+   F77_CHARACTER_ARRAY_ARG_TYPE X/**/_descr = \
+      { L, DSC$K_DTYPE_T, DSC$K_CLASS_S, X }; \
+   F77_CHARACTER_ARRAY_ARG_TYPE *X/**/_arg = &X/**/_descr
+
+
+/*  ---  The dynamic allocation of character arguments  ---                 */
+#undef DECLARE_CHARACTER_DYN
+#define DECLARE_CHARACTER_DYN(X) int X/**/_length;\
+                                  F77_CHARACTER_ARG_TYPE *X/**/_arg;\
+                                  F77_CHARACTER_TYPE *X
+#undef DECLARE_CHARACTER_ARRAY_DYN
+#define DECLARE_CHARACTER_ARRAY_DYN(X) int X/**/_length;\
+                                  F77_CHARACTER_ARRAY_ARG_TYPE *X/**/_arg;\
+                                  F77_CHARACTER_TYPE *X
+#undef F77_CREATE_CHARACTER
+#define F77_CREATE_CHARACTER(X,L) X/**/_arg = cnfCref(L);\
+                                  X = X/**/_arg->dsc$a_pointer; \
+                                  X/**/_length = X/**/_arg->dsc$w_length
+#undef F77_CREATE_CHARACTER_ARRAY
+#define F77_CREATE_CHARACTER_ARRAY(X,L,N) \
+  {int f77dims[1];f77dims[0]=N;X/**/_arg=cnfCrefa(L,1,f77dims);X/**/_length=L;}
+#define F77_CREATE_CHARACTER_ARRAY_M(X,L,N,D) X/**/_arg = cnfCrefa(L,N,D);\
+                                  X = X/**/_arg->dsc$a_pointer; \
+                                  X/**/_length = X/**/_arg->dsc$w_length
+#undef F77_FREE_CHARACTER
+#define F77_FREE_CHARACTER(X)     slaStringFree( X/**/_arg )
+
+/*  ---  Pass arguments to a FORTRAN routine  ---			    */
+
+#undef  CHARACTER_ARG
+#define CHARACTER_ARG(X) X/**/_arg
+#undef  CHARACTER_ARRAY_ARG
+#define CHARACTER_ARRAY_ARG(X) X/**/_arg
+#undef  TRAIL_ARG
+#define TRAIL_ARG(X)
+
+#endif  /* VMS								    */
+
+/* -----------------------------------------------------------------------  */
+
+/*--------------------------
+|   DECstation Ultrix (cc)  |
+|   DECstation Ultrix (c89) |
+|   DECstation OSF/1        |
+|   Alpha OSF/1             |
+ --------------------------*/
+
+/* Do this complicated set of definitions as a single #if cannot be	    */
+/* continued across multiple lines.					    */
+
+#if defined(mips) && defined(ultrix)
+#define _dec_unix 1
+#endif
+#if defined(__mips) && defined(__ultrix)
+#define _dec_unix 1
+#endif
+#if defined(__mips__) && defined(__osf__)
+#define _dec_unix 1
+#endif
+#if defined(__alpha) && defined(__osf__)
+#define _dec_unix 1
+#endif
+
+#if _dec_unix
+
+/*  The macros for Ultrix are the same as the standard ones except for ones */
+/*  dealing with logical values. The ANSI definitions work with the c89	    */
+/*  compiler, and the non ANSI definitions work with the cc compiler.	    */
+/*  The same applies to DEC OSF/1, except that its cc compiler is ANSI	    */
+/*  compliant.								    */
+
+
+/*  ---  Logical Values  ---						    */
+
+/*  Redefine macros that evaluate to a C logical value, given a FORTRAN	    */
+/*  logical value. These definitions are only valid when used with the DEC  */
+/*  FORTRAN for RISC compiler. If you are using the earlier FORTRAN for	    */
+/*  RISC compiler from MIPS, then these macros should be deleted.	    */
+
+#undef  F77_TRUE
+#define F77_TRUE -1
+#undef  F77_ISTRUE
+#define F77_ISTRUE(X) ( (X)&1 )
+#undef  F77_ISFALSE
+#define F77_ISFALSE(X) ( ! ( (X)&1 ) )
+
+
+#endif  /* DEC Unix							    */
+
+/*
+*+
+*  Name:
+*     cnf.h
+
+*  Purpose:
+*     Function prototypes for cnf routines
+
+*  Language:
+*     ANSI C
+
+*  Type of Module:
+*     C include file
+
+*  Description:
+*     These are the prototype definitions for the functions in the CNF
+*     library. They are used used in mixing C and FORTRAN programs.
+
+*  Copyright:
+*     Copyright (C) 1991 Science & Engineering Research Council
+
+*  Authors:
+*     PMA: Peter Allan (Starlink, RAL)
+*     AJC: Alan Chipperfield (Starlink, RAL)
+*     {enter_new_authors_here}
+
+*  History:
+*     23-MAY-1991 (PMA):
+*        Original version.
+*     12-JAN-1996 (AJC):
+*        Add cnf_cref and cnf_freef
+*     14-JUN-1996 (AJC):
+*        Add cnf_crefa, imprta, exprta
+*                crela, impla, expla
+*     18-JUL-1996 (AJC):
+*        Add impch and expch
+*     17-MAR-1998 (AJC):
+*        Add imprtap and exprtap
+*     {enter_changes_here}
+
+*  Bugs:
+*     {note_any_bugs_here}
+
+*-
+------------------------------------------------------------------------------
+*/
+void *cnfCalloc( size_t, size_t );
+void cnfCopyf( const char *source_f, int source_len, char *dest_f,
+                int dest_len );
+void *cnfCptr( F77_POINTER_TYPE );
+char *cnfCreat( int length );
+F77_CHARACTER_ARG_TYPE *cnfCref( int length );
+F77_CHARACTER_ARG_TYPE *cnfCrefa( int length, int ndims, const int *dims );
+char *cnfCreib( const char *source_f, int source_len );
+char *cnfCreim( const char *source_f, int source_len );
+F77_LOGICAL_TYPE *cnfCrela( int ndims, const int *dims );
+void cnfExpch( const char *source_c, char *dest_f, int nchars );
+void cnfExpla( const int *source_c, F77_LOGICAL_TYPE *dest_f, int ndims,
+                const int *dims );
+void cnfExpn( const char *source_c, int max, char *dest_f, int dest_len );
+void cnfExprt( const char *source_c, char *dest_f, int dest_len );
+void cnfExprta( const char *source_c, int source_len, char *dest_f,
+                 int dest_len, int ndims, const int *dims );
+void cnfExprtap( char *const *source_c, char *dest_f, int dest_len,
+                  int ndims, const int *dims );
+F77_POINTER_TYPE cnfFptr( void *cpointer );
+void cnfFree( void * );
+void cnfFreef( F77_CHARACTER_ARG_TYPE *temp );
+void cnfImpb( const char *source_f, int source_len, char *dest_c );
+void cnfImpbn( const char *source_f, int source_len, int max, char *dest_c );
+void cnfImpch( const char *source_f, int nchars, char *dest_c );
+void cnfImpla( const F77_LOGICAL_TYPE *source_f, int *dest_c,
+                int ndims, const int *dims );
+void cnfImpn( const char *source_f, int source_len, int max, char *dest_c );
+void cnfImprt( const char *source_f, int source_len, char *dest_c );
+void cnfImprta( const char *source_f, int source_len, char *dest_c,
+                 int dest_len, int ndims, const int *dims );
+void cnfImprtap( const char *source_f, int source_len, char *const *dest_c,
+                  int dest_len, int ndims, const int *dims );
+int cnfLenc( const char *source_c );
+int cnfLenf( const char *source_f, int source_len );
+void *cnfMalloc( size_t );
+int cnfRegp( void * );
+void cnfUregp( void * );
+void cnfLock( void );
+void cnfUnlock( void );
+#endif
+
+#ifndef CNF_OLD_DEFINED
+#define CNF_OLD_DEFINED
+/* Define old names to be new names */
+#define cnf_calloc cnfCalloc
+#define cnf_copyf cnfCopyf
+#define cnf_cptr cnfCptr
+#define cnf_creat cnfCreat
+#define cnf_cref cnfCref
+#define cnf_crefa cnfCrefa
+#define cnf_creib cnfCreib
+#define cnf_creim cnfCreim
+#define cnf_crela cnfCrela
+#define cnf_expch cnfExpch
+#define cnf_expla cnfExpla
+#define cnf_expn cnfExpn
+#define cnf_exprt cnfExprt
+#define cnf_exprta cnfExprta
+#define cnf_exprtap cnfExprtap
+#define cnf_fptr cnfFptr
+#define cnf_free cnfFree
+#define cnf_freef cnfFreef
+#define cnf_impb cnfImpb
+#define cnf_impbn cnfImpbn
+#define cnf_impch cnfImpch
+#define cnf_impla cnfImpla
+#define cnf_impn cnfImpn
+#define cnf_imprt cnfImprt
+#define cnf_imprta cnfImprta
+#define cnf_imprtap cnfImprtap
+#define cnf_lenc cnfLenc
+#define cnf_lenf cnfLenf
+#define cnf_malloc cnfMalloc
+#define cnf_regp cnfRegp
+#define cnf_uregp cnfUregp
+
+#endif
diff --git a/math/slalib/fitxy.f b/math/slalib/fitxy.f
new file mode 100644
index 00000000..5060510e
--- /dev/null
+++ b/math/slalib/fitxy.f
@@ -0,0 +1,329 @@
+      SUBROUTINE slFTXY (ITYPE,NP,XYE,XYM,COEFFS,J)
+*+
+*     - - - - - -
+*      F T X Y
+*     - - - - - -
+*
+*  Fit a linear model to relate two sets of [X,Y] coordinates.
+*
+*  Given:
+*     ITYPE    i        type of model: 4 or 6 (note 1)
+*     NP       i        number of samples (note 2)
+*     XYE     d(2,np)   expected [X,Y] for each sample
+*     XYM     d(2,np)   measured [X,Y] for each sample
+*
+*  Returned:
+*     COEFFS  d(6)      coefficients of model (note 3)
+*     J        i        status:  0 = OK
+*                               -1 = illegal ITYPE
+*                               -2 = insufficient data
+*                               -3 = no solution
+*
+*  Notes:
+*
+*  1)  ITYPE, which must be either 4 or 6, selects the type of model
+*      fitted.  Both allowed ITYPE values produce a model COEFFS which
+*      consists of six coefficients, namely the zero points and, for
+*      each of XE and YE, the coefficient of XM and YM.  For ITYPE=6,
+*      all six coefficients are independent, modelling squash and shear
+*      as well as origin, scale, and orientation.  However, ITYPE=4
+*      selects the "solid body rotation" option;  the model COEFFS
+*      still consists of the same six coefficients, but now two of
+*      them are used twice (appropriately signed).  Origin, scale
+*      and orientation are still modelled, but not squash or shear -
+*      the units of X and Y have to be the same.
+*
+*  2)  For NC=4, NP must be at least 2.  For NC=6, NP must be at
+*      least 3.
+*
+*  3)  The model is returned in the array COEFFS.  Naming the
+*      elements of COEFFS as follows:
+*
+*                  COEFFS(1) = A
+*                  COEFFS(2) = B
+*                  COEFFS(3) = C
+*                  COEFFS(4) = D
+*                  COEFFS(5) = E
+*                  COEFFS(6) = F
+*
+*      the model is:
+*
+*            XE = A + B*XM + C*YM
+*            YE = D + E*XM + F*YM
+*
+*      For the "solid body rotation" option (ITYPE=4), the
+*      magnitudes of B and F, and of C and E, are equal.  The
+*      signs of these coefficients depend on whether there is a
+*      sign reversal between XE,YE and XM,YM;  fits are performed
+*      with and without a sign reversal and the best one chosen.
+*
+*  4)  Error status values J=-1 and -2 leave COEFFS unchanged;
+*      if J=-3 COEFFS may have been changed.
+*
+*  See also slPXY, slINVF, slXYXY, slDCMF
+*
+*  Called:  slDMAT, slDMXV
+*
+*  Last revision:   8 September 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER ITYPE,NP
+      DOUBLE PRECISION XYE(2,NP),XYM(2,NP),COEFFS(6)
+      INTEGER J
+
+      INTEGER I,JSTAT,IW(4),NSOL
+      DOUBLE PRECISION A,B,C,D,AOLD,BOLD,COLD,DOLD,SOLD,
+     :                 P,SXE,SXEXM,SXEYM,SYE,SYEYM,SYEXM,SXM,
+     :                 SYM,SXMXM,SXMYM,SYMYM,XE,YE,
+     :                 XM,YM,V(4),DM3(3,3),DM4(4,4),DET,
+     :                 SGN,SXXYY,SXYYX,SX2Y2,SDR2,XR,YR
+
+
+
+*  Preset the status
+      J=0
+
+*  Variable initializations to avoid compiler warnings
+      A = 0D0
+      B = 0D0
+      C = 0D0
+      D = 0D0
+      AOLD = 0D0
+      BOLD = 0D0
+      COLD = 0D0
+      DOLD = 0D0
+      SOLD = 0D0
+
+*  Float the number of samples
+      P=DBLE(NP)
+
+*  Check ITYPE
+      IF (ITYPE.EQ.6) THEN
+
+*
+*     Six-coefficient linear model
+*     ----------------------------
+
+*     Check enough samples
+         IF (NP.GE.3) THEN
+
+*     Form summations
+         SXE=0D0
+         SXEXM=0D0
+         SXEYM=0D0
+         SYE=0D0
+         SYEYM=0D0
+         SYEXM=0D0
+         SXM=0D0
+         SYM=0D0
+         SXMXM=0D0
+         SXMYM=0D0
+         SYMYM=0D0
+         DO I=1,NP
+            XE=XYE(1,I)
+            YE=XYE(2,I)
+            XM=XYM(1,I)
+            YM=XYM(2,I)
+            SXE=SXE+XE
+            SXEXM=SXEXM+XE*XM
+            SXEYM=SXEYM+XE*YM
+            SYE=SYE+YE
+            SYEYM=SYEYM+YE*YM
+            SYEXM=SYEXM+YE*XM
+            SXM=SXM+XM
+            SYM=SYM+YM
+            SXMXM=SXMXM+XM*XM
+            SXMYM=SXMYM+XM*YM
+            SYMYM=SYMYM+YM*YM
+         END DO
+
+*        Solve for A,B,C in  XE = A + B*XM + C*YM
+            V(1)=SXE
+            V(2)=SXEXM
+            V(3)=SXEYM
+            DM3(1,1)=P
+            DM3(1,2)=SXM
+            DM3(1,3)=SYM
+            DM3(2,1)=SXM
+            DM3(2,2)=SXMXM
+            DM3(2,3)=SXMYM
+            DM3(3,1)=SYM
+            DM3(3,2)=SXMYM
+            DM3(3,3)=SYMYM
+            CALL slDMAT(3,DM3,V,DET,JSTAT,IW)
+            IF (JSTAT.EQ.0) THEN
+               DO I=1,3
+                  COEFFS(I)=V(I)
+               END DO
+
+*           Solve for D,E,F in  YE = D + E*XM + F*YM
+               V(1)=SYE
+               V(2)=SYEXM
+               V(3)=SYEYM
+               CALL slDMXV(DM3,V,COEFFS(4))
+
+            ELSE
+
+*           No 6-coefficient solution possible
+               J=-3
+
+            END IF
+
+         ELSE
+
+*        Insufficient data for 6-coefficient fit
+            J=-2
+
+         END IF
+
+      ELSE IF (ITYPE.EQ.4) THEN
+
+*
+*     Four-coefficient solid body rotation model
+*     ------------------------------------------
+
+*     Check enough samples
+         IF (NP.GE.2) THEN
+
+*        Try two solutions, first without then with flip in X
+            DO NSOL=1,2
+               IF (NSOL.EQ.1) THEN
+                  SGN=1D0
+               ELSE
+                  SGN=-1D0
+               END IF
+
+*           Form summations
+               SXE=0D0
+               SXXYY=0D0
+               SXYYX=0D0
+               SYE=0D0
+               SXM=0D0
+               SYM=0D0
+               SX2Y2=0D0
+               DO I=1,NP
+                  XE=XYE(1,I)*SGN
+                  YE=XYE(2,I)
+                  XM=XYM(1,I)
+                  YM=XYM(2,I)
+                  SXE=SXE+XE
+                  SXXYY=SXXYY+XE*XM+YE*YM
+                  SXYYX=SXYYX+XE*YM-YE*XM
+                  SYE=SYE+YE
+                  SXM=SXM+XM
+                  SYM=SYM+YM
+                  SX2Y2=SX2Y2+XM*XM+YM*YM
+               END DO
+
+*
+*           Solve for A,B,C,D in:  +/- XE = A + B*XM - C*YM
+*                                    + YE = D + C*XM + B*YM
+               V(1)=SXE
+               V(2)=SXXYY
+               V(3)=SXYYX
+               V(4)=SYE
+               DM4(1,1)=P
+               DM4(1,2)=SXM
+               DM4(1,3)=-SYM
+               DM4(1,4)=0D0
+               DM4(2,1)=SXM
+               DM4(2,2)=SX2Y2
+               DM4(2,3)=0D0
+               DM4(2,4)=SYM
+               DM4(3,1)=SYM
+               DM4(3,2)=0D0
+               DM4(3,3)=-SX2Y2
+               DM4(3,4)=-SXM
+               DM4(4,1)=0D0
+               DM4(4,2)=SYM
+               DM4(4,3)=SXM
+               DM4(4,4)=P
+               CALL slDMAT(4,DM4,V,DET,JSTAT,IW)
+               IF (JSTAT.EQ.0) THEN
+                  A=V(1)
+                  B=V(2)
+                  C=V(3)
+                  D=V(4)
+
+*              Determine sum of radial errors squared
+                  SDR2=0D0
+                  DO I=1,NP
+                     XM=XYM(1,I)
+                     YM=XYM(2,I)
+                     XR=A+B*XM-C*YM-XYE(1,I)*SGN
+                     YR=D+C*XM+B*YM-XYE(2,I)
+                     SDR2=SDR2+XR*XR+YR*YR
+                  END DO
+
+               ELSE
+
+*              Singular: set flag
+                  SDR2=-1D0
+
+               END IF
+
+*           If first pass and non-singular, save variables
+               IF (NSOL.EQ.1.AND.JSTAT.EQ.0) THEN
+                  AOLD=A
+                  BOLD=B
+                  COLD=C
+                  DOLD=D
+                  SOLD=SDR2
+               END IF
+
+            END DO
+
+*        Pick the best of the two solutions
+            IF (SOLD.GE.0D0.AND.(SOLD.LE.SDR2.OR.NP.EQ.2)) THEN
+               COEFFS(1)=AOLD
+               COEFFS(2)=BOLD
+               COEFFS(3)=-COLD
+               COEFFS(4)=DOLD
+               COEFFS(5)=COLD
+               COEFFS(6)=BOLD
+            ELSE IF (JSTAT.EQ.0) THEN
+               COEFFS(1)=-A
+               COEFFS(2)=-B
+               COEFFS(3)=C
+               COEFFS(4)=D
+               COEFFS(5)=C
+               COEFFS(6)=B
+            ELSE
+
+*           No 4-coefficient fit possible
+               J=-3
+            END IF
+         ELSE
+
+*        Insufficient data for 4-coefficient fit
+            J=-2
+         END IF
+      ELSE
+
+*     Illegal ITYPE - not 4 or 6
+         J=-1
+      END IF
+
+      END
diff --git a/math/slalib/fk425.f b/math/slalib/fk425.f
new file mode 100644
index 00000000..40d5a615
--- /dev/null
+++ b/math/slalib/fk425.f
@@ -0,0 +1,267 @@
+      SUBROUTINE slFK45 (R1950,D1950,DR1950,DD1950,P1950,V1950,
+     :                      R2000,D2000,DR2000,DD2000,P2000,V2000)
+*+
+*     - - - - - -
+*      F K 4 5
+*     - - - - - -
+*
+*  Convert B1950.0 FK4 star data to J2000.0 FK5 (double precision)
+*
+*  This routine converts stars from the old, Bessel-Newcomb, FK4
+*  system to the new, IAU 1976, FK5, Fricke system.  The precepts
+*  of Smith et al (Ref 1) are followed, using the implementation
+*  by Yallop et al (Ref 2) of a matrix method due to Standish.
+*  Kinoshita's development of Andoyer's post-Newcomb precession is
+*  used.  The numerical constants from Seidelmann et al (Ref 3) are
+*  used canonically.
+*
+*  Given:  (all B1950.0,FK4)
+*     R1950,D1950     dp    B1950.0 RA,Dec (rad)
+*     DR1950,DD1950   dp    B1950.0 proper motions (rad/trop.yr)
+*     P1950           dp    parallax (arcsec)
+*     V1950           dp    radial velocity (km/s, +ve = moving away)
+*
+*  Returned:  (all J2000.0,FK5)
+*     R2000,D2000     dp    J2000.0 RA,Dec (rad)
+*     DR2000,DD2000   dp    J2000.0 proper motions (rad/Jul.yr)
+*     P2000           dp    parallax (arcsec)
+*     V2000           dp    radial velocity (km/s, +ve = moving away)
+*
+*  Notes:
+*
+*  1)  The proper motions in RA are dRA/dt rather than
+*      cos(Dec)*dRA/dt, and are per year rather than per century.
+*
+*  2)  Conversion from Besselian epoch 1950.0 to Julian epoch
+*      2000.0 only is provided for.  Conversions involving other
+*      epochs will require use of the appropriate precession,
+*      proper motion, and E-terms routines before and/or
+*      after FK425 is called.
+*
+*  3)  In the FK4 catalogue the proper motions of stars within
+*      10 degrees of the poles do not embody the differential
+*      E-term effect and should, strictly speaking, be handled
+*      in a different manner from stars outside these regions.
+*      However, given the general lack of homogeneity of the star
+*      data available for routine astrometry, the difficulties of
+*      handling positions that may have been determined from
+*      astrometric fields spanning the polar and non-polar regions,
+*      the likelihood that the differential E-terms effect was not
+*      taken into account when allowing for proper motion in past
+*      astrometry, and the undesirability of a discontinuity in
+*      the algorithm, the decision has been made in this routine to
+*      include the effect of differential E-terms on the proper
+*      motions for all stars, whether polar or not.  At epoch 2000,
+*      and measuring on the sky rather than in terms of dRA, the
+*      errors resulting from this simplification are less than
+*      1 milliarcsecond in position and 1 milliarcsecond per
+*      century in proper motion.
+*
+*  References:
+*
+*     1  Smith, C.A. et al, 1989.  "The transformation of astrometric
+*        catalog systems to the equinox J2000.0".  Astron.J. 97, 265.
+*
+*     2  Yallop, B.D. et al, 1989.  "Transformation of mean star places
+*        from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
+*        Astron.J. 97, 274.
+*
+*     3  Seidelmann, P.K. (ed), 1992.  "Explanatory Supplement to
+*        the Astronomical Almanac", ISBN 0-935702-68-7.
+*
+*  P.T.Wallace   Starlink   19 December 1993
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION R1950,D1950,DR1950,DD1950,P1950,V1950,
+     :                 R2000,D2000,DR2000,DD2000,P2000,V2000
+
+
+*  Miscellaneous
+      DOUBLE PRECISION R,D,UR,UD,PX,RV,SR,CR,SD,CD,W,WD
+      DOUBLE PRECISION X,Y,Z,XD,YD,ZD
+      DOUBLE PRECISION RXYSQ,RXYZSQ,RXY,RXYZ,SPXY,SPXYZ
+      INTEGER I,J
+
+*  Star position and velocity vectors
+      DOUBLE PRECISION R0(3),RD0(3)
+
+*  Combined position and velocity vectors
+      DOUBLE PRECISION V1(6),V2(6)
+
+*  2Pi
+      DOUBLE PRECISION D2PI
+      PARAMETER (D2PI=6.283185307179586476925287D0)
+
+*  Radians per year to arcsec per century
+      DOUBLE PRECISION PMF
+      PARAMETER (PMF=100D0*60D0*60D0*360D0/D2PI)
+
+*  Small number to avoid arithmetic problems
+      DOUBLE PRECISION TINY
+      PARAMETER (TINY=1D-30)
+
+
+*
+*  CANONICAL CONSTANTS  (see references)
+*
+
+*  Km per sec to AU per tropical century
+*  = 86400 * 36524.2198782 / 149597870
+      DOUBLE PRECISION VF
+      PARAMETER (VF=21.095D0)
+
+*  Constant vector and matrix (by columns)
+      DOUBLE PRECISION A(3),AD(3),EM(6,6)
+      DATA A,AD/ -1.62557D-6,  -0.31919D-6, -0.13843D-6,
+     :           +1.245D-3,    -1.580D-3,   -0.659D-3/
+
+      DATA (EM(I,1),I=1,6) / +0.9999256782D0,
+     :                       +0.0111820610D0,
+     :                       +0.0048579479D0,
+     :                       -0.000551D0,
+     :                       +0.238514D0,
+     :                       -0.435623D0 /
+
+      DATA (EM(I,2),I=1,6) / -0.0111820611D0,
+     :                       +0.9999374784D0,
+     :                       -0.0000271474D0,
+     :                       -0.238565D0,
+     :                       -0.002667D0,
+     :                       +0.012254D0 /
+
+      DATA (EM(I,3),I=1,6) / -0.0048579477D0,
+     :                       -0.0000271765D0,
+     :                       +0.9999881997D0,
+     :                       +0.435739D0,
+     :                       -0.008541D0,
+     :                       +0.002117D0 /
+
+      DATA (EM(I,4),I=1,6) / +0.00000242395018D0,
+     :                       +0.00000002710663D0,
+     :                       +0.00000001177656D0,
+     :                       +0.99994704D0,
+     :                       +0.01118251D0,
+     :                       +0.00485767D0 /
+
+      DATA (EM(I,5),I=1,6) / -0.00000002710663D0,
+     :                       +0.00000242397878D0,
+     :                       -0.00000000006582D0,
+     :                       -0.01118251D0,
+     :                       +0.99995883D0,
+     :                       -0.00002714D0 /
+
+      DATA (EM(I,6),I=1,6) / -0.00000001177656D0,
+     :                       -0.00000000006587D0,
+     :                       +0.00000242410173D0,
+     :                       -0.00485767D0,
+     :                       -0.00002718D0,
+     :                       +1.00000956D0 /
+
+
+
+*  Pick up B1950 data (units radians and arcsec/TC)
+      R=R1950
+      D=D1950
+      UR=DR1950*PMF
+      UD=DD1950*PMF
+      PX=P1950
+      RV=V1950
+
+*  Spherical to Cartesian
+      SR=SIN(R)
+      CR=COS(R)
+      SD=SIN(D)
+      CD=COS(D)
+
+      R0(1)=CR*CD
+      R0(2)=SR*CD
+      R0(3)=   SD
+
+      W=VF*RV*PX
+
+      RD0(1)=-SR*CD*UR-CR*SD*UD+W*R0(1)
+      RD0(2)= CR*CD*UR-SR*SD*UD+W*R0(2)
+      RD0(3)=             CD*UD+W*R0(3)
+
+*  Allow for e-terms and express as position+velocity 6-vector
+      W=R0(1)*A(1)+R0(2)*A(2)+R0(3)*A(3)
+      WD=R0(1)*AD(1)+R0(2)*AD(2)+R0(3)*AD(3)
+      DO I=1,3
+         V1(I)=R0(I)-A(I)+W*R0(I)
+         V1(I+3)=RD0(I)-AD(I)+WD*R0(I)
+      END DO
+
+*  Convert position+velocity vector to Fricke system
+      DO I=1,6
+         W=0D0
+         DO J=1,6
+            W=W+EM(I,J)*V1(J)
+         END DO
+         V2(I)=W
+      END DO
+
+*  Revert to spherical coordinates
+      X=V2(1)
+      Y=V2(2)
+      Z=V2(3)
+      XD=V2(4)
+      YD=V2(5)
+      ZD=V2(6)
+
+      RXYSQ=X*X+Y*Y
+      RXYZSQ=RXYSQ+Z*Z
+      RXY=SQRT(RXYSQ)
+      RXYZ=SQRT(RXYZSQ)
+
+      SPXY=X*XD+Y*YD
+      SPXYZ=SPXY+Z*ZD
+
+      IF (X.EQ.0D0.AND.Y.EQ.0D0) THEN
+         R=0D0
+      ELSE
+         R=ATAN2(Y,X)
+         IF (R.LT.0.0D0) R=R+D2PI
+      END IF
+      D=ATAN2(Z,RXY)
+
+      IF (RXY.GT.TINY) THEN
+         UR=(X*YD-Y*XD)/RXYSQ
+         UD=(ZD*RXYSQ-Z*SPXY)/(RXYZSQ*RXY)
+      END IF
+
+      IF (PX.GT.TINY) THEN
+         RV=SPXYZ/(PX*RXYZ*VF)
+         PX=PX/RXYZ
+      END IF
+
+*  Return results
+      R2000=R
+      D2000=D
+      DR2000=UR/PMF
+      DD2000=UD/PMF
+      V2000=RV
+      P2000=PX
+
+      END
diff --git a/math/slalib/fk45z.f b/math/slalib/fk45z.f
new file mode 100644
index 00000000..409d811b
--- /dev/null
+++ b/math/slalib/fk45z.f
@@ -0,0 +1,183 @@
+      SUBROUTINE slF45Z (R1950,D1950,BEPOCH,R2000,D2000)
+*+
+*     - - - - - -
+*      F 4 5 Z
+*     - - - - - -
+*
+*  Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero
+*  proper motion in the FK5 frame (double precision)
+*
+*  This routine converts stars from the old, Bessel-Newcomb, FK4
+*  system to the new, IAU 1976, FK5, Fricke system, in such a
+*  way that the FK5 proper motion is zero.  Because such a star
+*  has, in general, a non-zero proper motion in the FK4 system,
+*  the routine requires the epoch at which the position in the
+*  FK4 system was determined.
+*
+*  The method is from Appendix 2 of Ref 1, but using the constants
+*  of Ref 4.
+*
+*  Given:
+*     R1950,D1950     dp    B1950.0 FK4 RA,Dec at epoch (rad)
+*     BEPOCH          dp    Besselian epoch (e.g. 1979.3D0)
+*
+*  Returned:
+*     R2000,D2000     dp    J2000.0 FK5 RA,Dec (rad)
+*
+*  Notes:
+*
+*  1)  The epoch BEPOCH is strictly speaking Besselian, but
+*      if a Julian epoch is supplied the result will be
+*      affected only to a negligible extent.
+*
+*  2)  Conversion from Besselian epoch 1950.0 to Julian epoch
+*      2000.0 only is provided for.  Conversions involving other
+*      epochs will require use of the appropriate precession,
+*      proper motion, and E-terms routines before and/or
+*      after FK45Z is called.
+*
+*  3)  In the FK4 catalogue the proper motions of stars within
+*      10 degrees of the poles do not embody the differential
+*      E-term effect and should, strictly speaking, be handled
+*      in a different manner from stars outside these regions.
+*      However, given the general lack of homogeneity of the star
+*      data available for routine astrometry, the difficulties of
+*      handling positions that may have been determined from
+*      astrometric fields spanning the polar and non-polar regions,
+*      the likelihood that the differential E-terms effect was not
+*      taken into account when allowing for proper motion in past
+*      astrometry, and the undesirability of a discontinuity in
+*      the algorithm, the decision has been made in this routine to
+*      include the effect of differential E-terms on the proper
+*      motions for all stars, whether polar or not.  At epoch 2000,
+*      and measuring on the sky rather than in terms of dRA, the
+*      errors resulting from this simplification are less than
+*      1 milliarcsecond in position and 1 milliarcsecond per
+*      century in proper motion.
+*
+*  References:
+*
+*     1  Aoki,S., et al, 1983.  Astron.Astrophys., 128, 263.
+*
+*     2  Smith, C.A. et al, 1989.  "The transformation of astrometric
+*        catalog systems to the equinox J2000.0".  Astron.J. 97, 265.
+*
+*     3  Yallop, B.D. et al, 1989.  "Transformation of mean star places
+*        from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
+*        Astron.J. 97, 274.
+*
+*     4  Seidelmann, P.K. (ed), 1992.  "Explanatory Supplement to
+*        the Astronomical Almanac", ISBN 0-935702-68-7.
+*
+*  Called:  slDS2C, slEPJ, slEB2D, slDC2S, slDA2P
+*
+*  P.T.Wallace   Starlink   21 September 1998
+*
+*  Copyright (C) 1998 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION R1950,D1950,BEPOCH,R2000,D2000
+
+      DOUBLE PRECISION D2PI
+      PARAMETER (D2PI=6.283185307179586476925287D0)
+
+      DOUBLE PRECISION W
+      INTEGER I,J
+
+*  Position and position+velocity vectors
+      DOUBLE PRECISION R0(3),A1(3),V1(3),V2(6)
+
+*  Radians per year to arcsec per century
+      DOUBLE PRECISION PMF
+      PARAMETER (PMF=100D0*60D0*60D0*360D0/D2PI)
+
+*  Functions
+      DOUBLE PRECISION slEPJ,slEB2D,slDA2P
+
+*
+*  CANONICAL CONSTANTS  (see references)
+*
+
+*  Vectors A and Adot, and matrix M (only half of which is needed here)
+      DOUBLE PRECISION A(3),AD(3),EM(6,3)
+      DATA A,AD/ -1.62557D-6,  -0.31919D-6, -0.13843D-6,
+     :           +1.245D-3,    -1.580D-3,   -0.659D-3/
+
+      DATA (EM(I,1),I=1,6) / +0.9999256782D0,
+     :                       +0.0111820610D0,
+     :                       +0.0048579479D0,
+     :                       -0.000551D0,
+     :                       +0.238514D0,
+     :                       -0.435623D0 /
+
+      DATA (EM(I,2),I=1,6) / -0.0111820611D0,
+     :                       +0.9999374784D0,
+     :                       -0.0000271474D0,
+     :                       -0.238565D0,
+     :                       -0.002667D0,
+     :                       +0.012254D0 /
+
+      DATA (EM(I,3),I=1,6) / -0.0048579477D0,
+     :                       -0.0000271765D0,
+     :                       +0.9999881997D0,
+     :                       +0.435739D0,
+     :                       -0.008541D0,
+     :                       +0.002117D0 /
+
+
+
+*  Spherical to Cartesian
+      CALL slDS2C(R1950,D1950,R0)
+
+*  Adjust vector A to give zero proper motion in FK5
+      W=(BEPOCH-1950D0)/PMF
+      DO I=1,3
+         A1(I)=A(I)+W*AD(I)
+      END DO
+
+*  Remove e-terms
+      W=R0(1)*A1(1)+R0(2)*A1(2)+R0(3)*A1(3)
+      DO I=1,3
+         V1(I)=R0(I)-A1(I)+W*R0(I)
+      END DO
+
+*  Convert position vector to Fricke system
+      DO I=1,6
+         W=0D0
+         DO J=1,3
+            W=W+EM(I,J)*V1(J)
+         END DO
+         V2(I)=W
+      END DO
+
+*  Allow for fictitious proper motion in FK4
+      W=(slEPJ(slEB2D(BEPOCH))-2000D0)/PMF
+      DO I=1,3
+         V2(I)=V2(I)+W*V2(I+3)
+      END DO
+
+*  Revert to spherical coordinates
+      CALL slDC2S(V2,W,D2000)
+      R2000=slDA2P(W)
+
+      END
diff --git a/math/slalib/fk524.f b/math/slalib/fk524.f
new file mode 100644
index 00000000..49118030
--- /dev/null
+++ b/math/slalib/fk524.f
@@ -0,0 +1,275 @@
+      SUBROUTINE slFK54 (R2000,D2000,DR2000,DD2000,P2000,V2000,
+     :                      R1950,D1950,DR1950,DD1950,P1950,V1950)
+*+
+*     - - - - - -
+*      F K 5 4
+*     - - - - - -
+*
+*  Convert J2000.0 FK5 star data to B1950.0 FK4 (double precision)
+*
+*  This routine converts stars from the new, IAU 1976, FK5, Fricke
+*  system, to the old, Bessel-Newcomb, FK4 system.  The precepts
+*  of Smith et al (Ref 1) are followed, using the implementation
+*  by Yallop et al (Ref 2) of a matrix method due to Standish.
+*  Kinoshita's development of Andoyer's post-Newcomb precession is
+*  used.  The numerical constants from Seidelmann et al (Ref 3) are
+*  used canonically.
+*
+*  Given:  (all J2000.0,FK5)
+*     R2000,D2000     dp    J2000.0 RA,Dec (rad)
+*     DR2000,DD2000   dp    J2000.0 proper motions (rad/Jul.yr)
+*     P2000           dp    parallax (arcsec)
+*     V2000           dp    radial velocity (km/s, +ve = moving away)
+*
+*  Returned:  (all B1950.0,FK4)
+*     R1950,D1950     dp    B1950.0 RA,Dec (rad)
+*     DR1950,DD1950   dp    B1950.0 proper motions (rad/trop.yr)
+*     P1950           dp    parallax (arcsec)
+*     V1950           dp    radial velocity (km/s, +ve = moving away)
+*
+*  Notes:
+*
+*  1)  The proper motions in RA are dRA/dt rather than
+*      cos(Dec)*dRA/dt, and are per year rather than per century.
+*
+*  2)  Note that conversion from Julian epoch 2000.0 to Besselian
+*      epoch 1950.0 only is provided for.  Conversions involving
+*      other epochs will require use of the appropriate precession,
+*      proper motion, and E-terms routines before and/or after
+*      FK524 is called.
+*
+*  3)  In the FK4 catalogue the proper motions of stars within
+*      10 degrees of the poles do not embody the differential
+*      E-term effect and should, strictly speaking, be handled
+*      in a different manner from stars outside these regions.
+*      However, given the general lack of homogeneity of the star
+*      data available for routine astrometry, the difficulties of
+*      handling positions that may have been determined from
+*      astrometric fields spanning the polar and non-polar regions,
+*      the likelihood that the differential E-terms effect was not
+*      taken into account when allowing for proper motion in past
+*      astrometry, and the undesirability of a discontinuity in
+*      the algorithm, the decision has been made in this routine to
+*      include the effect of differential E-terms on the proper
+*      motions for all stars, whether polar or not.  At epoch 2000,
+*      and measuring on the sky rather than in terms of dRA, the
+*      errors resulting from this simplification are less than
+*      1 milliarcsecond in position and 1 milliarcsecond per
+*      century in proper motion.
+*
+*  References:
+*
+*     1  Smith, C.A. et al, 1989.  "The transformation of astrometric
+*        catalog systems to the equinox J2000.0".  Astron.J. 97, 265.
+*
+*     2  Yallop, B.D. et al, 1989.  "Transformation of mean star places
+*        from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
+*        Astron.J. 97, 274.
+*
+*     3  Seidelmann, P.K. (ed), 1992.  "Explanatory Supplement to
+*        the Astronomical Almanac", ISBN 0-935702-68-7.
+*
+*  P.T.Wallace   Starlink   19 December 1993
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION R2000,D2000,DR2000,DD2000,P2000,V2000,
+     :                 R1950,D1950,DR1950,DD1950,P1950,V1950
+
+
+*  Miscellaneous
+      DOUBLE PRECISION R,D,UR,UD,PX,RV
+      DOUBLE PRECISION SR,CR,SD,CD,X,Y,Z,W
+      DOUBLE PRECISION V1(6),V2(6)
+      DOUBLE PRECISION XD,YD,ZD
+      DOUBLE PRECISION RXYZ,WD,RXYSQ,RXY
+      INTEGER I,J
+
+*  2Pi
+      DOUBLE PRECISION D2PI
+      PARAMETER (D2PI=6.283185307179586476925287D0)
+
+*  Radians per year to arcsec per century
+      DOUBLE PRECISION PMF
+      PARAMETER (PMF=100D0*60D0*60D0*360D0/D2PI)
+
+*  Small number to avoid arithmetic problems
+      DOUBLE PRECISION TINY
+      PARAMETER (TINY=1D-30)
+
+*
+*  CANONICAL CONSTANTS  (see references)
+*
+
+*  Km per sec to AU per tropical century
+*  = 86400 * 36524.2198782 / 149597870
+      DOUBLE PRECISION VF
+      PARAMETER (VF=21.095D0)
+
+*  Constant vector and matrix (by columns)
+      DOUBLE PRECISION A(6),EMI(6,6)
+      DATA A/ -1.62557D-6,  -0.31919D-6, -0.13843D-6,
+     :        +1.245D-3,    -1.580D-3,   -0.659D-3/
+
+      DATA (EMI(I,1),I=1,6) / +0.9999256795D0,
+     :                        -0.0111814828D0,
+     :                        -0.0048590040D0,
+     :                        -0.000551D0,
+     :                        -0.238560D0,
+     :                        +0.435730D0 /
+
+      DATA (EMI(I,2),I=1,6) / +0.0111814828D0,
+     :                        +0.9999374849D0,
+     :                        -0.0000271557D0,
+     :                        +0.238509D0,
+     :                        -0.002667D0,
+     :                        -0.008541D0 /
+
+      DATA (EMI(I,3),I=1,6) / +0.0048590039D0,
+     :                        -0.0000271771D0,
+     :                        +0.9999881946D0,
+     :                        -0.435614D0,
+     :                        +0.012254D0,
+     :                        +0.002117D0 /
+
+      DATA (EMI(I,4),I=1,6) / -0.00000242389840D0,
+     :                        +0.00000002710544D0,
+     :                        +0.00000001177742D0,
+     :                        +0.99990432D0,
+     :                        -0.01118145D0,
+     :                        -0.00485852D0 /
+
+      DATA (EMI(I,5),I=1,6) / -0.00000002710544D0,
+     :                        -0.00000242392702D0,
+     :                        +0.00000000006585D0,
+     :                        +0.01118145D0,
+     :                        +0.99991613D0,
+     :                        -0.00002716D0 /
+
+      DATA (EMI(I,6),I=1,6) / -0.00000001177742D0,
+     :                        +0.00000000006585D0,
+     :                        -0.00000242404995D0,
+     :                        +0.00485852D0,
+     :                        -0.00002717D0,
+     :                        +0.99996684D0 /
+
+
+
+*  Pick up J2000 data (units radians and arcsec/JC)
+      R=R2000
+      D=D2000
+      UR=DR2000*PMF
+      UD=DD2000*PMF
+      PX=P2000
+      RV=V2000
+
+*  Spherical to Cartesian
+      SR=SIN(R)
+      CR=COS(R)
+      SD=SIN(D)
+      CD=COS(D)
+
+      X=CR*CD
+      Y=SR*CD
+      Z=   SD
+
+      W=VF*RV*PX
+
+      V1(1)=X
+      V1(2)=Y
+      V1(3)=Z
+
+      V1(4)=-UR*Y-CR*SD*UD+W*X
+      V1(5)= UR*X-SR*SD*UD+W*Y
+      V1(6)=         CD*UD+W*Z
+
+*  Convert position+velocity vector to BN system
+      DO I=1,6
+         W=0D0
+         DO J=1,6
+            W=W+EMI(I,J)*V1(J)
+         END DO
+         V2(I)=W
+      END DO
+
+*  Position vector components and magnitude
+      X=V2(1)
+      Y=V2(2)
+      Z=V2(3)
+      RXYZ=SQRT(X*X+Y*Y+Z*Z)
+
+*  Apply E-terms to position
+      W=X*A(1)+Y*A(2)+Z*A(3)
+      X=X+A(1)*RXYZ-W*X
+      Y=Y+A(2)*RXYZ-W*Y
+      Z=Z+A(3)*RXYZ-W*Z
+
+*  Recompute magnitude
+      RXYZ=SQRT(X*X+Y*Y+Z*Z)
+
+*  Apply E-terms to both position and velocity
+      X=V2(1)
+      Y=V2(2)
+      Z=V2(3)
+      W=X*A(1)+Y*A(2)+Z*A(3)
+      WD=X*A(4)+Y*A(5)+Z*A(6)
+      X=X+A(1)*RXYZ-W*X
+      Y=Y+A(2)*RXYZ-W*Y
+      Z=Z+A(3)*RXYZ-W*Z
+      XD=V2(4)+A(4)*RXYZ-WD*X
+      YD=V2(5)+A(5)*RXYZ-WD*Y
+      ZD=V2(6)+A(6)*RXYZ-WD*Z
+
+*  Convert to spherical
+      RXYSQ=X*X+Y*Y
+      RXY=SQRT(RXYSQ)
+
+      IF (X.EQ.0D0.AND.Y.EQ.0D0) THEN
+         R=0D0
+      ELSE
+         R=ATAN2(Y,X)
+         IF (R.LT.0.0D0) R=R+D2PI
+      END IF
+      D=ATAN2(Z,RXY)
+
+      IF (RXY.GT.TINY) THEN
+         UR=(X*YD-Y*XD)/RXYSQ
+         UD=(ZD*RXYSQ-Z*(X*XD+Y*YD))/((RXYSQ+Z*Z)*RXY)
+      END IF
+
+*  Radial velocity and parallax
+      IF (PX.GT.TINY) THEN
+         RV=(X*XD+Y*YD+Z*ZD)/(PX*VF*RXYZ)
+         PX=PX/RXYZ
+      END IF
+
+*  Return results
+      R1950=R
+      D1950=D
+      DR1950=UR/PMF
+      DD1950=UD/PMF
+      P1950=PX
+      V1950=RV
+
+      END
diff --git a/math/slalib/fk52h.f b/math/slalib/fk52h.f
new file mode 100644
index 00000000..4d9d42f8
--- /dev/null
+++ b/math/slalib/fk52h.f
@@ -0,0 +1,123 @@
+      SUBROUTINE slFK5H (R5,D5,DR5,DD5,RH,DH,DRH,DDH)
+*+
+*     - - - - - -
+*      F K 5 H
+*     - - - - - -
+*
+*  Transform FK5 (J2000) star data into the Hipparcos frame.
+*
+*  (double precision)
+*
+*  This routine transforms FK5 star positions and proper motions
+*  into the frame of the Hipparcos catalogue.
+*
+*  Given (all FK5, equinox J2000, epoch J2000):
+*     R5        d      RA (radians)
+*     D5        d      Dec (radians)
+*     DR5       d      proper motion in RA (dRA/dt, rad/Jyear)
+*     DD5       d      proper motion in Dec (dDec/dt, rad/Jyear)
+*
+*  Returned (all Hipparcos, epoch J2000):
+*     RH        d      RA (radians)
+*     DH        d      Dec (radians)
+*     DRH       d      proper motion in RA (dRA/dt, rad/Jyear)
+*     DDH       d      proper motion in Dec (dDec/dt, rad/Jyear)
+*
+*  Called:  slDSC6, slDAVM, slDMXV, slDVXV, slDC6S,
+*           slDA2P
+*
+*  Notes:
+*
+*  1)  The proper motions in RA are dRA/dt rather than
+*      cos(Dec)*dRA/dt, and are per year rather than per century.
+*
+*  2)  The FK5 to Hipparcos transformation consists of a pure
+*      rotation and spin;  zonal errors in the FK5 catalogue are
+*      not taken into account.
+*
+*  3)  The published orientation and spin components are interpreted
+*      as "axial vectors".  An axial vector points at the pole of the
+*      rotation and its length is the amount of rotation in radians.
+*
+*  4)  See also slHFK5, slF5HZ, slHF5Z.
+*
+*  Reference:
+*
+*     M.Feissel & F.Mignard, Astron. Astrophys. 331, L33-L36 (1998).
+*
+*  P.T.Wallace   Starlink   22 June 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION R5,D5,DR5,DD5,RH,DH,DRH,DDH
+
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+*  FK5 to Hipparcos orientation and spin (radians, radians/year)
+      DOUBLE PRECISION EPX,EPY,EPZ
+      DOUBLE PRECISION OMX,OMY,OMZ
+
+      PARAMETER ( EPX = -19.9D-3 * AS2R,
+     :            EPY =  -9.1D-3 * AS2R,
+     :            EPZ = +22.9D-3 * AS2R )
+
+      PARAMETER ( OMX = -0.30D-3 * AS2R,
+     :            OMY = +0.60D-3 * AS2R,
+     :            OMZ = +0.70D-3 * AS2R )
+
+      DOUBLE PRECISION PV5(6),ORTN(3),R5H(3,3),S5(3),VV(3),PVH(6),W,R,V
+      INTEGER I
+
+      DOUBLE PRECISION slDA2P
+
+
+
+*  FK5 barycentric position/velocity 6-vector (normalized).
+      CALL slDSC6(R5,D5,1D0,DR5,DD5,0D0,PV5)
+
+*  FK5 to Hipparcos orientation matrix.
+      ORTN(1) = EPX
+      ORTN(2) = EPY
+      ORTN(3) = EPZ
+      CALL slDAVM(ORTN,R5H)
+
+*  Hipparcos wrt FK5 spin vector.
+      S5(1) = OMX
+      S5(2) = OMY
+      S5(3) = OMZ
+
+*  Orient & spin the 6-vector into the Hipparcos frame.
+      CALL slDMXV(R5H,PV5,PVH)
+      CALL slDVXV(PV5,S5,VV)
+      DO I=1,3
+         VV(I) = PV5(I+3)+VV(I)
+      END DO
+      CALL slDMXV(R5H,VV,PVH(4))
+
+*  Hipparcos 6-vector to spherical.
+      CALL slDC6S(PVH,W,DH,R,DRH,DDH,V)
+      RH = slDA2P(W)
+
+      END
diff --git a/math/slalib/fk54z.f b/math/slalib/fk54z.f
new file mode 100644
index 00000000..69a93461
--- /dev/null
+++ b/math/slalib/fk54z.f
@@ -0,0 +1,87 @@
+      SUBROUTINE slF54Z (R2000,D2000,BEPOCH,
+     :                      R1950,D1950,DR1950,DD1950)
+*+
+*     - - - - - -
+*      F 5 4 Z
+*     - - - - - -
+*
+*  Convert a J2000.0 FK5 star position to B1950.0 FK4 assuming
+*  zero proper motion and parallax (double precision)
+*
+*  This routine converts star positions from the new, IAU 1976,
+*  FK5, Fricke system to the old, Bessel-Newcomb, FK4 system.
+*
+*  Given:
+*     R2000,D2000     dp    J2000.0 FK5 RA,Dec (rad)
+*     BEPOCH          dp    Besselian epoch (e.g. 1950D0)
+*
+*  Returned:
+*     R1950,D1950     dp    B1950.0 FK4 RA,Dec (rad) at epoch BEPOCH
+*     DR1950,DD1950   dp    B1950.0 FK4 proper motions (rad/trop.yr)
+*
+*  Notes:
+*
+*  1)  The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
+*
+*  2)  Conversion from Julian epoch 2000.0 to Besselian epoch 1950.0
+*      only is provided for.  Conversions involving other epochs will
+*      require use of the appropriate precession routines before and
+*      after this routine is called.
+*
+*  3)  Unlike in the slFK54 routine, the FK5 proper motions, the
+*      parallax and the radial velocity are presumed zero.
+*
+*  4)  It is the intention that FK5 should be a close approximation
+*      to an inertial frame, so that distant objects have zero proper
+*      motion;  such objects have (in general) non-zero proper motion
+*      in FK4, and this routine returns those fictitious proper
+*      motions.
+*
+*  5)  The position returned by this routine is in the B1950
+*      reference frame but at Besselian epoch BEPOCH.  For
+*      comparison with catalogues the BEPOCH argument will
+*      frequently be 1950D0.
+*
+*  Called:  slFK54, slPM
+*
+*  P.T.Wallace   Starlink   10 April 1990
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION R2000,D2000,BEPOCH,
+     :                 R1950,D1950,DR1950,DD1950
+
+      DOUBLE PRECISION R,D,PX,RV
+
+
+
+*  FK5 equinox J2000 (any epoch) to FK4 equinox B1950 epoch B1950
+      CALL slFK54(R2000,D2000,0D0,0D0,0D0,0D0,
+     :               R,D,DR1950,DD1950,PX,RV)
+
+*  Fictitious proper motion to epoch BEPOCH
+      CALL slPM(R,D,DR1950,DD1950,0D0,0D0,1950D0,BEPOCH,
+     :            R1950,D1950)
+
+      END
diff --git a/math/slalib/fk5hz.f b/math/slalib/fk5hz.f
new file mode 100644
index 00000000..0905376d
--- /dev/null
+++ b/math/slalib/fk5hz.f
@@ -0,0 +1,125 @@
+      SUBROUTINE slF5HZ (R5,D5,EPOCH,RH,DH)
+*+
+*     - - - - - -
+*      F 5 H Z
+*     - - - - - -
+*
+*  Transform an FK5 (J2000) star position into the frame of the
+*  Hipparcos catalogue, assuming zero Hipparcos proper motion.
+*
+*  (double precision)
+*
+*  This routine converts a star position from the FK5 system to
+*  the Hipparcos system, in such a way that the Hipparcos proper
+*  motion is zero.  Because such a star has, in general, a non-zero
+*  proper motion in the FK5 system, the routine requires the epoch
+*  at which the position in the FK5 system was determined.
+*
+*  Given:
+*     R5        d      FK5 RA (radians), equinox J2000, epoch EPOCH
+*     D5        d      FK5 Dec (radians), equinox J2000, epoch EPOCH
+*     EPOCH     d      Julian epoch (TDB)
+*
+*  Returned (all Hipparcos):
+*     RH        d      RA (radians)
+*     DH        d      Dec (radians)
+*
+*  Called:  slDS2C, slDAVM, slDIMV, slDMXV, slDC2S,
+*           slDA2P
+*
+*  Notes:
+*
+*  1)  The FK5 to Hipparcos transformation consists of a pure
+*      rotation and spin;  zonal errors in the FK5 catalogue are
+*      not taken into account.
+*
+*  2)  The published orientation and spin components are interpreted
+*      as "axial vectors".  An axial vector points at the pole of the
+*      rotation and its length is the amount of rotation in radians.
+*
+*  3)  See also slFK5H, slHFK5, slHF5Z.
+*
+*  Reference:
+*
+*     M.Feissel & F.Mignard, Astron. Astrophys. 331, L33-L36 (1998).
+*
+*  P.T.Wallace   Starlink   22 June 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION R5,D5,EPOCH,RH,DH
+
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+*  FK5 to Hipparcos orientation and spin (radians, radians/year)
+      DOUBLE PRECISION EPX,EPY,EPZ
+      DOUBLE PRECISION OMX,OMY,OMZ
+
+      PARAMETER ( EPX = -19.9D-3 * AS2R,
+     :            EPY =  -9.1D-3 * AS2R,
+     :            EPZ = +22.9D-3 * AS2R )
+
+      PARAMETER ( OMX = -0.30D-3 * AS2R,
+     :            OMY = +0.60D-3 * AS2R,
+     :            OMZ = +0.70D-3 * AS2R )
+
+      DOUBLE PRECISION P5E(3),ORTN(3),R5H(3,3),T,VST(3),RST(3,3),
+     :                 P5(3),PH(3),W
+
+      DOUBLE PRECISION slDA2P
+
+
+
+*  FK5 barycentric position vector.
+      CALL slDS2C(R5,D5,P5E)
+
+*  FK5 to Hipparcos orientation matrix.
+      ORTN(1) = EPX
+      ORTN(2) = EPY
+      ORTN(3) = EPZ
+      CALL slDAVM(ORTN,R5H)
+
+*  Time interval from epoch to J2000.
+      T = 2000D0-EPOCH
+
+*  Axial vector:  accumulated Hipparcos wrt FK5 spin over that interval.
+      VST(1) = OMX*T
+      VST(2) = OMY*T
+      VST(3) = OMZ*T
+
+*  Express the accumulated spin as a rotation matrix.
+      CALL slDAVM(VST,RST)
+
+*  Derotate the vector's FK5 axes back to epoch.
+      CALL slDIMV(RST,P5E,P5)
+
+*  Rotate the vector into the Hipparcos frame.
+      CALL slDMXV(R5H,P5,PH)
+
+*  Hipparcos vector to spherical.
+      CALL slDC2S(PH,W,DH)
+      RH = slDA2P(W)
+
+      END
diff --git a/math/slalib/flotin.f b/math/slalib/flotin.f
new file mode 100644
index 00000000..932580a3
--- /dev/null
+++ b/math/slalib/flotin.f
@@ -0,0 +1,146 @@
+      SUBROUTINE slRFLI (STRING, NSTRT, RESLT, JFLAG)
+*+
+*     - - - - - - -
+*      R F L I
+*     - - - - - - -
+*
+*  Convert free-format input into single precision floating point
+*
+*  Given:
+*     STRING     c     string containing number to be decoded
+*     NSTRT      i     pointer to where decoding is to start
+*     RESLT      r     current value of result
+*
+*  Returned:
+*     NSTRT      i      advanced to next number
+*     RESLT      r      result
+*     JFLAG      i      status: -1 = -OK, 0 = +OK, 1 = null, 2 = error
+*
+*  Called:  slDFLI
+*
+*  Notes:
+*
+*     1     The reason FLOTIN has separate OK status values for +
+*           and - is to enable minus zero to be detected.   This is
+*           of crucial importance when decoding mixed-radix numbers.
+*           For example, an angle expressed as deg, arcmin, arcsec
+*           may have a leading minus sign but a zero degrees field.
+*
+*     2     A TAB is interpreted as a space, and lowercase characters
+*           are interpreted as uppercase.
+*
+*     3     The basic format is the sequence of fields #^.^@#^, where
+*           # is a sign character + or -, ^ means a string of decimal
+*           digits, and @, which indicates an exponent, means D or E.
+*           Various combinations of these fields can be omitted, and
+*           embedded blanks are permissible in certain places.
+*
+*     4     Spaces:
+*
+*             .  Leading spaces are ignored.
+*
+*             .  Embedded spaces are allowed only after +, -, D or E,
+*                and after the decomal point if the first sequence of
+*                digits is absent.
+*
+*             .  Trailing spaces are ignored;  the first signifies
+*                end of decoding and subsequent ones are skipped.
+*
+*     5     Delimiters:
+*
+*             .  Any character other than +,-,0-9,.,D,E or space may be
+*                used to signal the end of the number and terminate
+*                decoding.
+*
+*             .  Comma is recognized by FLOTIN as a special case;  it
+*                is skipped, leaving the pointer on the next character.
+*                See 13, below.
+*
+*     6     Both signs are optional.  The default is +.
+*
+*     7     The mantissa ^.^ defaults to 1.
+*
+*     8     The exponent @#^ defaults to E0.
+*
+*     9     The strings of decimal digits may be of any length.
+*
+*     10    The decimal point is optional for whole numbers.
+*
+*     11    A "null result" occurs when the string of characters being
+*           decoded does not begin with +,-,0-9,.,D or E, or consists
+*           entirely of spaces.  When this condition is detected, JFLAG
+*           is set to 1 and RESLT is left untouched.
+*
+*     12    NSTRT = 1 for the first character in the string.
+*
+*     13    On return from FLOTIN, NSTRT is set ready for the next
+*           decode - following trailing blanks and any comma.  If a
+*           delimiter other than comma is being used, NSTRT must be
+*           incremented before the next call to FLOTIN, otherwise
+*           all subsequent calls will return a null result.
+*
+*     14    Errors (JFLAG=2) occur when:
+*
+*             .  a +, -, D or E is left unsatisfied;  or
+*
+*             .  the decimal point is present without at least
+*                one decimal digit before or after it;  or
+*
+*             .  an exponent more than 100 has been presented.
+*
+*     15    When an error has been detected, NSTRT is left
+*           pointing to the character following the last
+*           one used before the error came to light.  This
+*           may be after the point at which a more sophisticated
+*           program could have detected the error.  For example,
+*           FLOTIN does not detect that '1E999' is unacceptable
+*           (on a computer where this is so) until the entire number
+*           has been decoded.
+*
+*     16    Certain highly unlikely combinations of mantissa &
+*           exponent can cause arithmetic faults during the
+*           decode, in some cases despite the fact that they
+*           together could be construed as a valid number.
+*
+*     17    Decoding is left to right, one pass.
+*
+*     18    See also DFLTIN and INTIN
+*
+*  P.T.Wallace   Starlink   23 November 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) STRING
+      INTEGER NSTRT
+      REAL RESLT
+      INTEGER JFLAG
+
+      DOUBLE PRECISION DRESLT
+
+
+*  Call the double precision version
+      CALL slDFLI(STRING,NSTRT,DRESLT,JFLAG)
+      IF (JFLAG.LE.0) RESLT=REAL(DRESLT)
+
+      END
diff --git a/math/slalib/galeq.f b/math/slalib/galeq.f
new file mode 100644
index 00000000..e0010c8b
--- /dev/null
+++ b/math/slalib/galeq.f
@@ -0,0 +1,97 @@
+      SUBROUTINE slGAEQ (DL, DB, DR, DD)
+*+
+*     - - - - - -
+*      G A E Q
+*     - - - - - -
+*
+*  Transformation from IAU 1958 galactic coordinates to
+*  J2000.0 equatorial coordinates (double precision)
+*
+*  Given:
+*     DL,DB       dp       galactic longitude and latitude L2,B2
+*
+*  Returned:
+*     DR,DD       dp       J2000.0 RA,Dec
+*
+*  (all arguments are radians)
+*
+*  Called:
+*     slDS2C, slDIMV, slDC2S, slDA2P, slDA1P
+*
+*  Note:
+*     The equatorial coordinates are J2000.0.  Use the routine
+*     slGE50 if conversion to B1950.0 'FK4' coordinates is
+*     required.
+*
+*  Reference:
+*     Blaauw et al, Mon.Not.R.Astron.Soc.,121,123 (1960)
+*
+*  P.T.Wallace   Starlink   21 September 1998
+*
+*  Copyright (C) 1998 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DL,DB,DR,DD
+
+      DOUBLE PRECISION slDA2P,slDA1P
+
+      DOUBLE PRECISION V1(3),V2(3)
+
+*
+*  L2,B2 system of galactic coordinates
+*
+*  P = 192.25       RA of galactic north pole (mean B1950.0)
+*  Q =  62.6        inclination of galactic to mean B1950.0 equator
+*  R =  33          longitude of ascending node
+*
+*  P,Q,R are degrees
+*
+*  Equatorial to galactic rotation matrix (J2000.0), obtained by
+*  applying the standard FK4 to FK5 transformation, for zero proper
+*  motion in FK5, to the columns of the B1950 equatorial to
+*  galactic rotation matrix:
+*
+      DOUBLE PRECISION RMAT(3,3)
+      DATA RMAT(1,1),RMAT(1,2),RMAT(1,3),
+     :     RMAT(2,1),RMAT(2,2),RMAT(2,3),
+     :     RMAT(3,1),RMAT(3,2),RMAT(3,3)/
+     : -0.054875539726D0,-0.873437108010D0,-0.483834985808D0,
+     : +0.494109453312D0,-0.444829589425D0,+0.746982251810D0,
+     : -0.867666135858D0,-0.198076386122D0,+0.455983795705D0/
+
+
+
+*  Spherical to Cartesian
+      CALL slDS2C(DL,DB,V1)
+
+*  Galactic to equatorial
+      CALL slDIMV(RMAT,V1,V2)
+
+*  Cartesian to spherical
+      CALL slDC2S(V2,DR,DD)
+
+*  Express in conventional ranges
+      DR=slDA2P(DR)
+      DD=slDA1P(DD)
+
+      END
diff --git a/math/slalib/galsup.f b/math/slalib/galsup.f
new file mode 100644
index 00000000..afc9240c
--- /dev/null
+++ b/math/slalib/galsup.f
@@ -0,0 +1,97 @@
+      SUBROUTINE slGASU (DL, DB, DSL, DSB)
+*+
+*     - - - - - - -
+*      G A S U
+*     - - - - - - -
+*
+*  Transformation from IAU 1958 galactic coordinates to
+*  de Vaucouleurs supergalactic coordinates (double precision)
+*
+*  Given:
+*     DL,DB       dp       galactic longitude and latitude L2,B2
+*
+*  Returned:
+*     DSL,DSB     dp       supergalactic longitude and latitude
+*
+*  (all arguments are radians)
+*
+*  Called:
+*     slDS2C, slDMXV, slDC2S, slDA2P, slDA1P
+*
+*  References:
+*
+*     de Vaucouleurs, de Vaucouleurs, & Corwin, Second Reference
+*     Catalogue of Bright Galaxies, U. Texas, page 8.
+*
+*     Systems & Applied Sciences Corp., Documentation for the
+*     machine-readable version of the above catalogue,
+*     Contract NAS 5-26490.
+*
+*    (These two references give different values for the galactic
+*     longitude of the supergalactic origin.  Both are wrong;  the
+*     correct value is L2=137.37.)
+*
+*  P.T.Wallace   Starlink   25 January 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DL,DB,DSL,DSB
+
+      DOUBLE PRECISION slDA2P,slDA1P
+
+      DOUBLE PRECISION V1(3),V2(3)
+
+*
+*  System of supergalactic coordinates:
+*
+*    SGL   SGB        L2     B2      (deg)
+*     -    +90      47.37  +6.32
+*     0     0         -      0
+*
+*  Galactic to supergalactic rotation matrix:
+*
+      DOUBLE PRECISION RMAT(3,3)
+      DATA RMAT(1,1),RMAT(1,2),RMAT(1,3),
+     :     RMAT(2,1),RMAT(2,2),RMAT(2,3),
+     :     RMAT(3,1),RMAT(3,2),RMAT(3,3)/
+     : -0.735742574804D0,+0.677261296414D0,+0.000000000000D0,
+     : -0.074553778365D0,-0.080991471307D0,+0.993922590400D0,
+     : +0.673145302109D0,+0.731271165817D0,+0.110081262225D0/
+
+
+
+*  Spherical to Cartesian
+      CALL slDS2C(DL,DB,V1)
+
+*  Galactic to supergalactic
+      CALL slDMXV(RMAT,V1,V2)
+
+*  Cartesian to spherical
+      CALL slDC2S(V2,DSL,DSB)
+
+*  Express in conventional ranges
+      DSL=slDA2P(DSL)
+      DSB=slDA1P(DSB)
+
+      END
diff --git a/math/slalib/ge50.f b/math/slalib/ge50.f
new file mode 100644
index 00000000..a6a8afeb
--- /dev/null
+++ b/math/slalib/ge50.f
@@ -0,0 +1,108 @@
+      SUBROUTINE slGE50 (DL, DB, DR, DD)
+*+
+*     - - - - -
+*      G E 5 0
+*     - - - - -
+*
+*  Transformation from IAU 1958 galactic coordinates to
+*  B1950.0 'FK4' equatorial coordinates (double precision)
+*
+*  Given:
+*     DL,DB       dp       galactic longitude and latitude L2,B2
+*
+*  Returned:
+*     DR,DD       dp       B1950.0 'FK4' RA,Dec
+*
+*  (all arguments are radians)
+*
+*  Called:
+*     slDS2C, slDIMV, slDC2S, slADET, slDA2P, slDA1P
+*
+*  Note:
+*     The equatorial coordinates are B1950.0 'FK4'.  Use the
+*     routine slGAEQ if conversion to J2000.0 coordinates
+*     is required.
+*
+*  Reference:
+*     Blaauw et al, Mon.Not.R.Astron.Soc.,121,123 (1960)
+*
+*  P.T.Wallace   Starlink   5 September 1993
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DL,DB,DR,DD
+
+      DOUBLE PRECISION slDA2P,slDA1P
+
+      DOUBLE PRECISION V1(3),V2(3),R,D,RE,DE
+
+*
+*  L2,B2 system of galactic coordinates
+*
+*  P = 192.25       RA of galactic north pole (mean B1950.0)
+*  Q =  62.6        inclination of galactic to mean B1950.0 equator
+*  R =  33          longitude of ascending node
+*
+*  P,Q,R are degrees
+*
+*
+*  Equatorial to galactic rotation matrix
+*
+*  The Euler angles are P, Q, 90-R, about the z then y then
+*  z axes.
+*
+*         +CP.CQ.SR-SP.CR     +SP.CQ.SR+CP.CR     -SQ.SR
+*
+*         -CP.CQ.CR-SP.SR     -SP.CQ.CR+CP.SR     +SQ.CR
+*
+*         +CP.SQ              +SP.SQ              +CQ
+*
+
+      DOUBLE PRECISION RMAT(3,3)
+      DATA RMAT(1,1),RMAT(1,2),RMAT(1,3),
+     :     RMAT(2,1),RMAT(2,2),RMAT(2,3),
+     :     RMAT(3,1),RMAT(3,2),RMAT(3,3) /
+     : -0.066988739415D0,-0.872755765852D0,-0.483538914632D0,
+     : +0.492728466075D0,-0.450346958020D0,+0.744584633283D0,
+     : -0.867600811151D0,-0.188374601723D0,+0.460199784784D0 /
+
+
+
+*  Spherical to Cartesian
+      CALL slDS2C(DL,DB,V1)
+
+*  Rotate to mean B1950.0
+      CALL slDIMV(RMAT,V1,V2)
+
+*  Cartesian to spherical
+      CALL slDC2S(V2,R,D)
+
+*  Introduce E-terms
+      CALL slADET(R,D,1950D0,RE,DE)
+
+*  Express in conventional ranges
+      DR=slDA2P(RE)
+      DD=slDA1P(DE)
+
+      END
diff --git a/math/slalib/geoc.f b/math/slalib/geoc.f
new file mode 100644
index 00000000..470a1958
--- /dev/null
+++ b/math/slalib/geoc.f
@@ -0,0 +1,78 @@
+      SUBROUTINE slGEOC (P, H, R, Z)
+*+
+*     - - - - -
+*      G E O C
+*     - - - - -
+*
+*  Convert geodetic position to geocentric (double precision)
+*
+*  Given:
+*     P     dp     latitude (geodetic, radians)
+*     H     dp     height above reference spheroid (geodetic, metres)
+*
+*  Returned:
+*     R     dp     distance from Earth axis (AU)
+*     Z     dp     distance from plane of Earth equator (AU)
+*
+*  Notes:
+*
+*  1  Geocentric latitude can be obtained by evaluating ATAN2(Z,R).
+*
+*  2  IAU 1976 constants are used.
+*
+*  Reference:
+*
+*     Green,R.M., Spherical Astronomy, CUP 1985, p98.
+*
+*  Last revision:   22 July 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION P,H,R,Z
+
+*  Earth equatorial radius (metres)
+      DOUBLE PRECISION A0
+      PARAMETER (A0=6378140D0)
+
+*  Reference spheroid flattening factor and useful function
+      DOUBLE PRECISION F,B
+      PARAMETER (F=1D0/298.257D0,B=(1D0-F)**2)
+
+*  Astronomical unit in metres
+      DOUBLE PRECISION AU
+      PARAMETER (AU=1.49597870D11)
+
+      DOUBLE PRECISION SP,CP,C,S
+
+
+
+*  Geodetic to geocentric conversion
+      SP = SIN(P)
+      CP = COS(P)
+      C = 1D0/SQRT(CP*CP+B*SP*SP)
+      S = B*C
+      R = (A0*C+H)*CP/AU
+      Z = (A0*S+H)*SP/AU
+
+      END
diff --git a/math/slalib/gmst.f b/math/slalib/gmst.f
new file mode 100644
index 00000000..808ea382
--- /dev/null
+++ b/math/slalib/gmst.f
@@ -0,0 +1,78 @@
+      DOUBLE PRECISION FUNCTION slGMST (UT1)
+*+
+*     - - - - -
+*      G M S T
+*     - - - - -
+*
+*  Conversion from universal time to sidereal time (double precision)
+*
+*  Given:
+*    UT1    dp     universal time (strictly UT1) expressed as
+*                  modified Julian Date (JD-2400000.5)
+*
+*  The result is the Greenwich mean sidereal time (double
+*  precision, radians).
+*
+*  The IAU 1982 expression (see page S15 of 1984 Astronomical Almanac)
+*  is used, but rearranged to reduce rounding errors.  This expression
+*  is always described as giving the GMST at 0 hours UT.  In fact, it
+*  gives the difference between the GMST and the UT, which happens to
+*  equal the GMST (modulo 24 hours) at 0 hours UT each day.  In this
+*  routine, the entire UT is used directly as the argument for the
+*  standard formula, and the fractional part of the UT is added
+*  separately.  Note that the factor 1.0027379... does not appear in the
+*  IAU 1982 expression explicitly but in the form of the coefficient
+*  8640184.812866, which is 86400x36525x0.0027379...
+*
+*  See also the routine slGMSA, which delivers better numerical
+*  precision by accepting the UT date and time as separate arguments.
+*
+*  Called:  slDA2P
+*
+*  P.T.Wallace   Starlink   14 October 2001
+*
+*  Copyright (C) 2001 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION UT1
+
+      DOUBLE PRECISION slDA2P
+
+      DOUBLE PRECISION D2PI,S2R
+      PARAMETER (D2PI=6.283185307179586476925286766559D0,
+     :           S2R=7.272205216643039903848711535369D-5)
+
+      DOUBLE PRECISION TU
+
+
+
+*  Julian centuries from fundamental epoch J2000 to this UT
+      TU=(UT1-51544.5D0)/36525D0
+
+*  GMST at this UT
+      slGMST=slDA2P(MOD(UT1,1D0)*D2PI+
+     :                    (24110.54841D0+
+     :                    (8640184.812866D0+
+     :                    (0.093104D0-6.2D-6*TU)*TU)*TU)*S2R)
+
+      END
diff --git a/math/slalib/gmsta.f b/math/slalib/gmsta.f
new file mode 100644
index 00000000..31a92e99
--- /dev/null
+++ b/math/slalib/gmsta.f
@@ -0,0 +1,100 @@
+      DOUBLE PRECISION FUNCTION slGMSA (DATE, UT)
+*+
+*     - - - - - -
+*      G M S A
+*     - - - - - -
+*
+*  Conversion from Universal Time to Greenwich mean sidereal time,
+*  with rounding errors minimized.
+*
+*  double precision
+*
+*  Given:
+*    DATE    d      UT1 date (MJD: integer part of JD-2400000.5))
+*    UT      d      UT1 time (fraction of a day)
+*
+*  The result is the Greenwich mean sidereal time (double precision,
+*  radians, in the range 0 to 2pi).
+*
+*  There is no restriction on how the UT is apportioned between the
+*  DATE and UT arguments.  Either of the two arguments could, for
+*  example, be zero and the entire date+time supplied in the other.
+*  However, the routine is designed to deliver maximum accuracy when
+*  the DATE argument is a whole number and the UT lies in the range
+*  0 to 1 (or vice versa).
+*
+*  The algorithm is based on the IAU 1982 expression (see page S15 of
+*  the 1984 Astronomical Almanac).  This is always described as giving
+*  the GMST at 0 hours UT1.  In fact, it gives the difference between
+*  the GMST and the UT, the steady 4-minutes-per-day drawing-ahead of
+*  ST with respect to UT.  When whole days are ignored, the expression
+*  happens to equal the GMST at 0 hours UT1 each day.  Note that the
+*  factor 1.0027379... does not appear explicitly but in the form of
+*  the coefficient 8640184.812866, which is 86400x36525x0.0027379...
+*
+*  In this routine, the entire UT1 (the sum of the two arguments DATE
+*  and UT) is used directly as the argument for the standard formula.
+*  The UT1 is then added, but omitting whole days to conserve accuracy.
+*
+*  See also the routine slGMST, which accepts the UT as a single
+*  argument.  Compared with slGMST, the extra numerical precision
+*  delivered by the present routine is unlikely to be important in
+*  an absolute sense, but may be useful when critically comparing
+*  algorithms and in applications where two sidereal times close
+*  together are differenced.
+*
+*  Called:  slDA2P
+*
+*  P.T.Wallace   Starlink   14 October 2001
+*
+*  Copyright (C) 2001 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,UT
+
+*  Seconds of time to radians
+      DOUBLE PRECISION S2R
+      PARAMETER (S2R=7.272205216643039903848712D-5)
+
+      DOUBLE PRECISION D1,D2,T
+      DOUBLE PRECISION slDA2P
+
+
+*  Julian centuries since J2000.
+      IF (DATE.LT.UT) THEN
+         D1=DATE
+         D2=UT
+      ELSE
+         D1=UT
+         D2=DATE
+      END IF
+      T=(D1+(D2-51544.5D0))/36525D0
+
+*  GMST at this UT1.
+      slGMSA=slDA2P(S2R*(24110.54841D0+
+     :                         (8640184.812866D0+
+     :                         (0.093104D0
+     :                         -6.2D-6*T)*T)*T
+     :                         +86400D0*(MOD(D1,1D0)+MOD(D2,1D0))))
+
+      END
diff --git a/math/slalib/gresid.F__vms b/math/slalib/gresid.F__vms
new file mode 100644
index 00000000..7cb318fb
--- /dev/null
+++ b/math/slalib/gresid.F__vms
@@ -0,0 +1,89 @@
+      REAL FUNCTION sla_GRESID (S)
+*+
+*     - - - - - - -
+*      G R E S I D
+*     - - - - - - -
+*
+*  Generate pseudo-random normal deviate ( = 'Gaussian residual')
+*  (single precision)
+*
+*  !!! Version for VAX/VMS and DECstation !!!
+*
+*  Given:
+*     S      real     standard deviation
+*
+*  The results of many calls to this routine will be
+*  normally distributed with mean zero and standard deviation S.
+*
+*  The Box-Muller algorithm is used.  This is described in
+*  Numerical Recipes, section 7.2.
+*
+*  P.T.Wallace   Starlink   14 October 1991
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the 
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, 
+*    Boston, MA  02110-1301  USA
+*
+*-
+
+      IMPLICIT NONE
+
+      REAL S
+
+      REAL X,Y,R,W,GNEXT,G
+      INTEGER ISEED
+      LOGICAL FIRST
+
+      REAL RAN
+
+      SAVE GNEXT,ISEED,FIRST
+      DATA ISEED / 123456789 /
+      DATA FIRST / .TRUE. /
+
+
+
+*  Second normal deviate of the pair available?
+      IF (FIRST) THEN
+
+*     No - generate two random numbers inside unit circle
+         R = 2.0
+         DO WHILE (R.GE.1.0)
+
+*        Generate two random numbers in range +/- 1
+            X = 2.0*RAN(ISEED)-1.0
+            Y = 2.0*RAN(ISEED)-1.0
+
+*        Try again if not in unit circle
+            R = X*X+Y*Y
+         END DO
+
+*     Box-Muller transformation, generating two deviates
+         W = SQRT(-2.0*LOG(R)/MAX(R,1E-20))
+         GNEXT = X*W
+         G = Y*W
+
+*     Set flag to indicate availability of next deviate
+         FIRST = .FALSE.
+      ELSE
+
+*     Return second deviate of the pair & reset flag
+         G = GNEXT
+         FIRST = .TRUE.
+      END IF
+
+*  Scale the deviate by the required standard deviation
+      sla_GRESID = G*S
+
+      END
diff --git a/math/slalib/gresid.F__win b/math/slalib/gresid.F__win
new file mode 100644
index 00000000..af197dbd
--- /dev/null
+++ b/math/slalib/gresid.F__win
@@ -0,0 +1,90 @@
+      REAL FUNCTION sla_GRESID (S)
+*+
+*     - - - - - - -
+*      G R E S I D
+*     - - - - - - -
+*
+*  Generate pseudo-random normal deviate ( = 'Gaussian residual')
+*  (single precision)
+*
+*  Given:
+*     S      real     standard deviation
+*
+*  The results of many calls to this routine will be
+*  normally distributed with mean zero and standard deviation S.
+*
+*  The Box-Muller algorithm is used.  This is described in
+*  Numerical Recipes, section 7.2.
+*
+*  !!!  Microsoft Fortran dependent - calls the RAN routine   !!!
+*  !!!  To seed the random-number generator, either call the  !!!
+*  !!!  Microsoft SEED routine specifying some INTEGER*2      !!!
+*  !!!  seed or call the function sla_RANDOM specifying some  !!!
+*  !!!  REAL seed.                                            !!!
+*
+*  P.T.Wallace   Starlink   1 April 1993
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the 
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, 
+*    Boston, MA  02110-1301  USA
+*
+*-
+
+      IMPLICIT NONE
+
+      REAL S
+
+      REAL X,Y,RV,R,W,GNEXT,G
+      LOGICAL FIRST
+
+      SAVE GNEXT,RV,FIRST
+      DATA FIRST / .TRUE. /
+
+
+
+*  Second normal deviate of the pair available?
+      IF (FIRST) THEN
+
+*     No - generate two random numbers in range +/- 1
+ 1       CONTINUE
+         CALL RANDOM(RV)               !!! PC
+         X = 2.0*RV-1.0
+         CALL RANDOM(RV)               !!! PC
+         Y = 2.0*RV-1.0
+
+*     Try again if not in unit circle
+         R = X*X+Y*Y
+         IF (R.GE.1.0) GO TO 1
+
+*     Box-Muller transformation, generating two deviates
+         W = SQRT(-2.0*LOG(R)/MAX(R,1E-20))
+         GNEXT = X*W
+         G = Y*W
+
+*     Set flag to indicate availability of next deviate
+         FIRST = .FALSE.
+      ELSE
+
+*     Return second deviate of the pair & reset flag
+         G = GNEXT
+         FIRST = .TRUE.
+      END IF
+
+*  Scale the deviate by the required standard deviation
+      sla_GRESID = G*S
+
+      END
diff --git a/math/slalib/gresid.Fdefault b/math/slalib/gresid.Fdefault
new file mode 100644
index 00000000..e3b595ef
--- /dev/null
+++ b/math/slalib/gresid.Fdefault
@@ -0,0 +1,113 @@
+#include "config.h"
+      REAL FUNCTION sla_GRESID (S)
+*+
+*     - - - - - - -
+*      G R E S I D
+*     - - - - - - -
+*
+*  Generate pseudo-random normal deviate ( = 'Gaussian residual')
+*  (single precision)
+*
+*  Given:
+*     S      real     standard deviation
+*
+*  The results of many calls to this routine will be
+*  normally distributed with mean zero and standard deviation S.
+*
+*  The Box-Muller algorithm is used.  This is described in
+*  Numerical Recipes, section 7.2.
+*
+*  Called:  RAN or RAND (a REAL function returning a random variate --
+*           the precise function which is called depends on which functions
+*           are available when the library is built).  If neither of these
+*           is available, we use the local substitute RANDOM defined
+*           in rtl_random.c
+*
+*  P.T.Wallace   Starlink   14 October 1991
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the 
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, 
+*    Boston, MA  02110-1301  USA
+*-
+
+      IMPLICIT NONE
+
+      REAL S
+
+      REAL X,Y,R,W,GNEXT,G
+      LOGICAL FTF,FIRST
+
+#if HAVE_RAND
+      REAL RAND
+#elif HAVE_RANDOM
+      REAL RANDOM
+#else
+ error "Can't find random-number function"
+#endif
+
+      SAVE GNEXT,FTF,FIRST
+      DATA FTF,FIRST / .TRUE.,.TRUE. /
+
+      X = 0.0
+      Y = 0.0
+
+*  First time through, initialise the random-number generator
+#if HAVE_RAND
+      IF (FTF) THEN
+         X = RAND(123456789)
+         FTF = .FALSE.
+      END IF
+#endif
+
+*  Second normal deviate of the pair available?
+      IF (FIRST) THEN
+
+*     No - generate two random numbers inside unit circle
+         R = 2.0
+         DO WHILE (R.GE.1.0)
+
+*        Generate two random numbers in range +/- 1
+#if HAVE_RAND
+            X = 2.0*RAND(0)-1.0
+            Y = 2.0*RAND(0)-1.0
+#elif HAVE_RANDOM
+            X = 2.0*RAN(ISEED)-1.0
+            Y = 2.0*RAN(ISEED)-1.0
+#endif
+
+*        Try again if not in unit circle
+            R = X*X+Y*Y
+         END DO
+
+*     Box-Muller transformation, generating two deviates
+         W = SQRT(-2.0*LOG(R)/MAX(R,1E-20))
+         GNEXT = X*W
+         G = Y*W
+
+*     Set flag to indicate availability of next deviate
+         FIRST = .FALSE.
+      ELSE
+
+*     Return second deviate of the pair & reset flag
+         G = GNEXT
+         FIRST = .TRUE.
+      END IF
+
+*  Scale the deviate by the required standard deviation
+      sla_GRESID = G*S
+
+      END
diff --git a/math/slalib/h2e.f b/math/slalib/h2e.f
new file mode 100644
index 00000000..06016ce3
--- /dev/null
+++ b/math/slalib/h2e.f
@@ -0,0 +1,101 @@
+      SUBROUTINE slH2E ( AZ, EL, PHI, HA, DEC )
+*+
+*     - - - - -
+*      D E 2 H
+*     - - - - -
+*
+*  Horizon to equatorial coordinates:  Az,El to HA,Dec
+*
+*  (single precision)
+*
+*  Given:
+*     AZ      r     azimuth
+*     EL      r     elevation
+*     PHI     r     observatory latitude
+*
+*  Returned:
+*     HA      r     hour angle
+*     DEC     r     declination
+*
+*  Notes:
+*
+*  1)  All the arguments are angles in radians.
+*
+*  2)  The sign convention for azimuth is north zero, east +pi/2.
+*
+*  3)  HA is returned in the range +/-pi.  Declination is returned
+*      in the range +/-pi/2.
+*
+*  4)  The latitude is (in principle) geodetic.  In critical
+*      applications, corrections for polar motion should be applied.
+*
+*  5)  In some applications it will be important to specify the
+*      correct type of elevation in order to produce the required
+*      type of HA,Dec.  In particular, it may be important to
+*      distinguish between the elevation as affected by refraction,
+*      which will yield the "observed" HA,Dec, and the elevation
+*      in vacuo, which will yield the "topocentric" HA,Dec.  If the
+*      effects of diurnal aberration can be neglected, the
+*      topocentric HA,Dec may be used as an approximation to the
+*      "apparent" HA,Dec.
+*
+*  6)  No range checking of arguments is done.
+*
+*  7)  In applications which involve many such calculations, rather
+*      than calling the present routine it will be more efficient to
+*      use inline code, having previously computed fixed terms such
+*      as sine and cosine of latitude.
+*
+*  Last revision:   11 September 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL AZ, EL, PHI, HA, DEC
+
+      DOUBLE PRECISION SA, CA, SE, CE, SP, CP, X, Y, Z, R
+
+
+*  Useful trig functions.
+      SA = SIN(AZ)
+      CA = COS(AZ)
+      SE = SIN(EL)
+      CE = COS(EL)
+      SP = SIN(PHI)
+      CP = COS(PHI)
+
+*  HA,Dec as x,y,z.
+      X = -CA*CE*SP+SE*CP
+      Y = -SA*CE
+      Z = CA*CE*CP+SE*SP
+
+*  To HA,Dec.
+      R = SQRT(X*X+Y*Y)
+      IF (R.EQ.0.0) THEN
+         HA = 0.0
+      ELSE
+         HA = REAL(ATAN2(Y,X))
+      END IF
+      DEC = REAL(ATAN2(Z,R))
+
+      END
diff --git a/math/slalib/h2fk5.f b/math/slalib/h2fk5.f
new file mode 100644
index 00000000..74d71f39
--- /dev/null
+++ b/math/slalib/h2fk5.f
@@ -0,0 +1,127 @@
+      SUBROUTINE slHFK5 (RH,DH,DRH,DDH,R5,D5,DR5,DD5)
+*+
+*     - - - - - -
+*      H F K 5
+*     - - - - - -
+*
+*  Transform Hipparcos star data into the FK5 (J2000) system.
+*
+*  (double precision)
+*
+*  This routine transforms Hipparcos star positions and proper
+*  motions into FK5 J2000.
+*
+*  Given (all Hipparcos, epoch J2000):
+*     RH        d      RA (radians)
+*     DH        d      Dec (radians)
+*     DRH       d      proper motion in RA (dRA/dt, rad/Jyear)
+*     DDH       d      proper motion in Dec (dDec/dt, rad/Jyear)
+*
+*  Returned (all FK5, equinox J2000, epoch J2000):
+*     R5        d      RA (radians)
+*     D5        d      Dec (radians)
+*     DR5       d      proper motion in RA (dRA/dt, rad/Jyear)
+*     DD5       d      proper motion in Dec (dDec/dt, rad/Jyear)
+*
+*  Called:  slDSC6, slDAVM, slDMXV, slDIMV, slDVXV,
+*           slDC6S, slDA2P
+*
+*  Notes:
+*
+*  1)  The proper motions in RA are dRA/dt rather than
+*      cos(Dec)*dRA/dt, and are per year rather than per century.
+*
+*  2)  The FK5 to Hipparcos transformation consists of a pure
+*      rotation and spin;  zonal errors in the FK5 catalogue are
+*      not taken into account.
+*
+*  3)  The published orientation and spin components are interpreted
+*      as "axial vectors".  An axial vector points at the pole of the
+*      rotation and its length is the amount of rotation in radians.
+*
+*  4)  See also slFK5H, slF5HZ, slHF5Z.
+*
+*  Reference:
+*
+*     M.Feissel & F.Mignard, Astron. Astrophys. 331, L33-L36 (1998).
+*
+*  P.T.Wallace   Starlink   22 June 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RH,DH,DRH,DDH,R5,D5,DR5,DD5
+
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+*  FK5 to Hipparcos orientation and spin (radians, radians/year)
+      DOUBLE PRECISION EPX,EPY,EPZ
+      DOUBLE PRECISION OMX,OMY,OMZ
+
+      PARAMETER ( EPX = -19.9D-3 * AS2R,
+     :            EPY =  -9.1D-3 * AS2R,
+     :            EPZ = +22.9D-3 * AS2R )
+
+      PARAMETER ( OMX = -0.30D-3 * AS2R,
+     :            OMY = +0.60D-3 * AS2R,
+     :            OMZ = +0.70D-3 * AS2R )
+
+      DOUBLE PRECISION PVH(6),ORTN(3),R5H(3,3),S5(3),SH(3),VV(3),
+     :                 PV5(6),W,R,V
+      INTEGER I
+
+      DOUBLE PRECISION slDA2P
+
+
+
+*  Hipparcos barycentric position/velocity 6-vector (normalized).
+      CALL slDSC6(RH,DH,1D0,DRH,DDH,0D0,PVH)
+
+*  FK5 to Hipparcos orientation matrix.
+      ORTN(1) = EPX
+      ORTN(2) = EPY
+      ORTN(3) = EPZ
+      CALL slDAVM(ORTN,R5H)
+
+*  Hipparcos wrt FK5 spin vector.
+      S5(1) = OMX
+      S5(2) = OMY
+      S5(3) = OMZ
+
+*  Rotate the spin vector into the Hipparcos frame.
+      CALL slDMXV(R5H,S5,SH)
+
+*  De-orient & de-spin the 6-vector into FK5 J2000.
+      CALL slDIMV(R5H,PVH,PV5)
+      CALL slDVXV(PVH,SH,VV)
+      DO I=1,3
+         VV(I) = PVH(I+3)-VV(I)
+      END DO
+      CALL slDIMV(R5H,VV,PV5(4))
+
+*  FK5 6-vector to spherical.
+      CALL slDC6S(PV5,W,D5,R,DR5,DD5,V)
+      R5 = slDA2P(W)
+
+      END
diff --git a/math/slalib/hfk5z.f b/math/slalib/hfk5z.f
new file mode 100644
index 00000000..2f6d53b2
--- /dev/null
+++ b/math/slalib/hfk5z.f
@@ -0,0 +1,140 @@
+      SUBROUTINE slHF5Z (RH,DH,EPOCH,R5,D5,DR5,DD5)
+*+
+*     - - - - - -
+*      H F 5 Z
+*     - - - - - -
+*
+*  Transform a Hipparcos star position into FK5 J2000, assuming
+*  zero Hipparcos proper motion.
+*
+*  (double precision)
+*
+*  Given:
+*     RH        d      Hipparcos RA (radians)
+*     DH        d      Hipparcos Dec (radians)
+*     EPOCH     d      Julian epoch (TDB)
+*
+*  Returned (all FK5, equinox J2000, epoch EPOCH):
+*     R5        d      RA (radians)
+*     D5        d      Dec (radians)
+*
+*  Called:  slDS2C, slDAVM, slDMXV, slDMXM,
+*           slDIMV, slDVXV, slDC6S, slDA2P
+*
+*  Notes:
+*
+*  1)  The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
+*
+*  2)  The FK5 to Hipparcos transformation consists of a pure
+*      rotation and spin;  zonal errors in the FK5 catalogue are
+*      not taken into account.
+*
+*  3)  The published orientation and spin components are interpreted
+*      as "axial vectors".  An axial vector points at the pole of the
+*      rotation and its length is the amount of rotation in radians.
+*
+*  4)  It was the intention that Hipparcos should be a close
+*      approximation to an inertial frame, so that distant objects
+*      have zero proper motion;  such objects have (in general)
+*      non-zero proper motion in FK5, and this routine returns those
+*      fictitious proper motions.
+*
+*  5)  The position returned by this routine is in the FK5 J2000
+*      reference frame but at Julian epoch EPOCH.
+*
+*  6)  See also slFK5H, slHFK5, sla_FK5ZHZ.
+*
+*  Reference:
+*
+*     M.Feissel & F.Mignard, Astron. Astrophys. 331, L33-L36 (1998).
+*
+*  P.T.Wallace   Starlink   30 December 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RH,DH,EPOCH,R5,D5,DR5,DD5
+
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+*  FK5 to Hipparcos orientation and spin (radians, radians/year)
+      DOUBLE PRECISION EPX,EPY,EPZ
+      DOUBLE PRECISION OMX,OMY,OMZ
+
+      PARAMETER ( EPX = -19.9D-3 * AS2R,
+     :            EPY =  -9.1D-3 * AS2R,
+     :            EPZ = +22.9D-3 * AS2R )
+
+      PARAMETER ( OMX = -0.30D-3 * AS2R,
+     :            OMY = +0.60D-3 * AS2R,
+     :            OMZ = +0.70D-3 * AS2R )
+
+      DOUBLE PRECISION PH(3),ORTN(3),R5H(3,3),S5(3),SH(3),T,VST(3),
+     :                 RST(3,3),R5HT(3,3),PV5E(6),VV(3),W,R,V
+
+      DOUBLE PRECISION slDA2P
+
+
+
+*  Hipparcos barycentric position vector (normalized).
+      CALL slDS2C(RH,DH,PH)
+
+*  FK5 to Hipparcos orientation matrix.
+      ORTN(1) = EPX
+      ORTN(2) = EPY
+      ORTN(3) = EPZ
+      CALL slDAVM(ORTN,R5H)
+
+*  Hipparcos wrt FK5 spin vector.
+      S5(1) = OMX
+      S5(2) = OMY
+      S5(3) = OMZ
+
+*  Rotate the spin vector into the Hipparcos frame.
+      CALL slDMXV(R5H,S5,SH)
+
+*  Time interval from J2000 to epoch.
+      T = EPOCH-2000D0
+
+*  Axial vector:  accumulated Hipparcos wrt FK5 spin over that interval.
+      VST(1) = OMX*T
+      VST(2) = OMY*T
+      VST(3) = OMZ*T
+
+*  Express the accumulated spin as a rotation matrix.
+      CALL slDAVM(VST,RST)
+
+*  Rotation matrix:  accumulated spin, then FK5 to Hipparcos.
+      CALL slDMXM(R5H,RST,R5HT)
+
+*  De-orient & de-spin the vector into FK5 J2000 at epoch.
+      CALL slDIMV(R5HT,PH,PV5E)
+      CALL slDVXV(SH,PH,VV)
+      CALL slDIMV(R5HT,VV,PV5E(4))
+
+*  FK5 position/velocity 6-vector to spherical.
+      CALL slDC6S(PV5E,W,D5,R,DR5,DD5,V)
+      R5 = slDA2P(W)
+
+      END
diff --git a/math/slalib/idchf.f b/math/slalib/idchf.f
new file mode 100644
index 00000000..fa6e597b
--- /dev/null
+++ b/math/slalib/idchf.f
@@ -0,0 +1,112 @@
+      SUBROUTINE slICHF (STRING, NPTR, NVEC, NDIGIT, DIGIT)
+*+
+*     - - - - - -
+*      I C H F
+*     - - - - - -
+*
+*  Internal routine used by DFLTIN
+*
+*  Identify next character in string
+*
+*  Given:
+*     STRING      char        string
+*     NPTR        int         pointer to character to be identified
+*
+*  Returned:
+*     NPTR        int         incremented unless end of field
+*     NVEC        int         vector for identified character
+*     NDIGIT      int         0-9 if character was a numeral
+*     DIGIT       double      equivalent of NDIGIT
+*
+*     NVEC takes the following values:
+*
+*      1     0-9
+*      2     space or TAB   !!! n.b. ASCII TAB assumed !!!
+*      3     D,d,E or e
+*      4     .
+*      5     +
+*      6     -
+*      7     ,
+*      8     else
+*      9     outside field
+*
+*  If the character is not 0-9, NDIGIT and DIGIT are either not
+*  altered or are set to arbitrary values.
+*
+*  P.T.Wallace   Starlink   22 December 1992
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) STRING
+      INTEGER NPTR,NVEC,NDIGIT
+      DOUBLE PRECISION DIGIT
+
+      CHARACTER K
+      INTEGER NCHAR
+
+*  Character/vector tables
+      INTEGER NCREC
+      PARAMETER (NCREC=19)
+      CHARACTER KCTAB(NCREC)
+      INTEGER KVTAB(NCREC)
+      DATA KCTAB/'0','1','2','3','4','5','6','7','8','9',
+     :           ' ','D','d','E','e','.','+','-',','/
+      DATA KVTAB/10*1,2,4*3,4,5,6,7/
+
+
+*  Handle pointer outside field
+      IF (NPTR.LT.1.OR.NPTR.GT.LEN(STRING)) THEN
+         NVEC=9
+      ELSE
+
+*     Not end of field: identify the character
+         K=STRING(NPTR:NPTR)
+         DO NCHAR=1,NCREC
+            IF (K.EQ.KCTAB(NCHAR)) THEN
+
+*           Recognized
+               NVEC=KVTAB(NCHAR)
+               NDIGIT=NCHAR-1
+               DIGIT=DBLE(NDIGIT)
+               GO TO 2300
+            END IF
+         END DO
+
+*     Not recognized: check for TAB    !!! n.b. ASCII assumed !!!
+         IF (K.EQ.CHAR(9)) THEN
+
+*        TAB: treat as space
+            NVEC=2
+         ELSE
+
+*        Unrecognized
+            NVEC=8
+         END IF
+
+*     Increment pointer
+ 2300    CONTINUE
+         NPTR=NPTR+1
+      END IF
+
+      END
diff --git a/math/slalib/idchi.f b/math/slalib/idchi.f
new file mode 100644
index 00000000..99f8392d
--- /dev/null
+++ b/math/slalib/idchi.f
@@ -0,0 +1,109 @@
+      SUBROUTINE slICHI (STRING, NPTR, NVEC, DIGIT)
+*+
+*     - - - - - -
+*      I C H I
+*     - - - - - -
+*
+*  Internal routine used by INTIN
+*
+*  Identify next character in string
+*
+*  Given:
+*     STRING      char        string
+*     NPTR        int         pointer to character to be identified
+*
+*  Returned:
+*     NPTR        int         incremented unless end of field
+*     NVEC        int         vector for identified character
+*     DIGIT       double      double precision digit if 0-9
+*
+*     NVEC takes the following values:
+*
+*      1     0-9
+*      2     space or TAB   !!! n.b. ASCII TAB assumed !!!
+*      3     +
+*      4     -
+*      5     ,
+*      6     else
+*      7     outside string
+*
+*  If the character is not 0-9, DIGIT is either unaltered or
+*  is set to an arbitrary value.
+*
+*  P.T.Wallace   Starlink   22 December 1992
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) STRING
+      INTEGER NPTR,NVEC
+      DOUBLE PRECISION DIGIT
+
+      CHARACTER K
+      INTEGER NCHAR
+
+*  Character/vector tables
+      INTEGER NCREC
+      PARAMETER (NCREC=14)
+      CHARACTER KCTAB(NCREC)
+      INTEGER KVTAB(NCREC)
+      DATA KCTAB/'0','1','2','3','4','5','6','7','8','9',
+     :           ' ', '+','-',','/
+      DATA KVTAB/10*1,2,3,4,5/
+
+
+
+*  Handle pointer outside field
+      IF (NPTR.LT.1.OR.NPTR.GT.LEN(STRING)) THEN
+         NVEC=7
+      ELSE
+
+*     Not end of field: identify character
+         K=STRING(NPTR:NPTR)
+         DO NCHAR=1,NCREC
+            IF (K.EQ.KCTAB(NCHAR)) THEN
+
+*           Recognized
+               NVEC=KVTAB(NCHAR)
+               DIGIT=DBLE(NCHAR-1)
+               GO TO 2300
+            END IF
+         END DO
+
+*     Not recognized: check for TAB   !!! n.b. ASCII assumed !!!
+         IF (K.EQ.CHAR(9)) THEN
+
+*        TAB: treat as space
+            NVEC=2
+         ELSE
+
+*        Unrecognized
+            NVEC=6
+         END IF
+
+*     Increment pointer
+ 2300    CONTINUE
+         NPTR=NPTR+1
+      END IF
+
+      END
diff --git a/math/slalib/imxv.f b/math/slalib/imxv.f
new file mode 100644
index 00000000..804adef7
--- /dev/null
+++ b/math/slalib/imxv.f
@@ -0,0 +1,69 @@
+      SUBROUTINE slIMXV (RM, VA, VB)
+*+
+*     - - - - -
+*      I M X V
+*     - - - - -
+*
+*  Performs the 3-D backward unitary transformation:
+*
+*     vector VB = (inverse of matrix RM) * vector VA
+*
+*  (single precision)
+*
+*  (n.b.  the matrix must be unitary, as this routine assumes that
+*   the inverse and transpose are identical)
+*
+*  Given:
+*     RM       real(3,3)    matrix
+*     VA       real(3)      vector
+*
+*  Returned:
+*     VB       real(3)      result vector
+*
+*  P.T.Wallace   Starlink   November 1984
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL RM(3,3),VA(3),VB(3)
+
+      INTEGER I,J
+      REAL W,VW(3)
+
+
+
+*  Inverse of matrix RM * vector VA -> vector VW
+      DO J=1,3
+         W=0.0
+         DO I=1,3
+            W=W+RM(I,J)*VA(I)
+         END DO
+         VW(J)=W
+      END DO
+
+*  Vector VW -> vector VB
+      DO J=1,3
+         VB(J)=VW(J)
+      END DO
+
+      END
diff --git a/math/slalib/intin.f b/math/slalib/intin.f
new file mode 100644
index 00000000..669cb18d
--- /dev/null
+++ b/math/slalib/intin.f
@@ -0,0 +1,194 @@
+      SUBROUTINE slINTI (STRING, NSTRT, IRESLT, JFLAG)
+*+
+*     - - - - - -
+*      I N T I
+*     - - - - - -
+*
+*  Convert free-format input into an integer
+*
+*  Given:
+*     STRING     c     string containing number to be decoded
+*     NSTRT      i     pointer to where decoding is to start
+*     IRESLT     i     current value of result
+*
+*  Returned:
+*     NSTRT      i      advanced to next number
+*     IRESLT     i      result
+*     JFLAG      i      status: -1 = -OK, 0 = +OK, 1 = null, 2 = error
+*
+*  Called:  slICHI
+*
+*  Notes:
+*
+*     1     The reason INTIN has separate OK status values for +
+*           and - is to enable minus zero to be detected.   This is
+*           of crucial importance when decoding mixed-radix numbers.
+*           For example, an angle expressed as deg, arcmin, arcsec
+*           may have a leading minus sign but a zero degrees field.
+*
+*     2     A TAB is interpreted as a space.
+*
+*     3     The basic format is the sequence of fields #^, where
+*           # is a sign character + or -, and ^ means a string of
+*           decimal digits.
+*
+*     4     Spaces:
+*
+*             .  Leading spaces are ignored.
+*
+*             .  Spaces between the sign and the number are allowed.
+*
+*             .  Trailing spaces are ignored;  the first signifies
+*                end of decoding and subsequent ones are skipped.
+*
+*     5     Delimiters:
+*
+*             .  Any character other than +,-,0-9 or space may be
+*                used to signal the end of the number and terminate
+*                decoding.
+*
+*             .  Comma is recognized by INTIN as a special case;  it
+*                is skipped, leaving the pointer on the next character.
+*                See 9, below.
+*
+*     6     The sign is optional.  The default is +.
+*
+*     7     A "null result" occurs when the string of characters being
+*           decoded does not begin with +,- or 0-9, or consists
+*           entirely of spaces.  When this condition is detected, JFLAG
+*           is set to 1 and IRESLT is left untouched.
+*
+*     8     NSTRT = 1 for the first character in the string.
+*
+*     9     On return from INTIN, NSTRT is set ready for the next
+*           decode - following trailing blanks and any comma.  If a
+*           delimiter other than comma is being used, NSTRT must be
+*           incremented before the next call to INTIN, otherwise
+*           all subsequent calls will return a null result.
+*
+*     10    Errors (JFLAG=2) occur when:
+*
+*             .  there is a + or - but no number;  or
+*
+*             .  the number is greater than BIG (defined below).
+*
+*     11    When an error has been detected, NSTRT is left
+*           pointing to the character following the last
+*           one used before the error came to light.
+*
+*     12    See also FLOTIN and DFLTIN.
+*
+*  P.T.Wallace   Starlink   27 April 1998
+*
+*  Copyright (C) 1998 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) STRING
+      INTEGER NSTRT,IRESLT,JFLAG
+
+*  Maximum allowed value
+      DOUBLE PRECISION BIG
+      PARAMETER (BIG=2147483647D0)
+
+      INTEGER JPTR,MSIGN,NVEC,J
+      DOUBLE PRECISION DRES,DIGIT
+
+
+
+*  Current character
+      JPTR=NSTRT
+
+*  Set defaults
+      DRES=0D0
+      MSIGN=1
+
+*  Look for sign
+ 100  CONTINUE
+      CALL slICHI(STRING,JPTR,NVEC,DIGIT)
+      GO TO ( 400, 100,  300,  200, 9110, 9100, 9110),NVEC
+*             0-9   SP     +     -     ,   ELSE   END
+
+*  Negative
+ 200  CONTINUE
+      MSIGN=-1
+
+*  Look for first decimal
+ 300  CONTINUE
+      CALL slICHI(STRING,JPTR,NVEC,DIGIT)
+      GO TO ( 400, 300, 9200, 9200, 9200, 9200, 9210),NVEC
+*             0-9   SP     +     -     ,   ELSE   END
+
+*  Accept decimals
+ 400  CONTINUE
+      DRES=DRES*1D1+DIGIT
+
+*  Test for overflow
+      IF (DRES.GT.BIG) GO TO 9200
+
+*  Look for subsequent decimals
+      CALL slICHI(STRING,JPTR,NVEC,DIGIT)
+      GO TO ( 400, 1610, 1600, 1600, 1600, 1600, 1610),NVEC
+*             0-9   SP     +     -     ,   ELSE   END
+
+*  Get result & status
+ 1600 CONTINUE
+      JPTR=JPTR-1
+ 1610 CONTINUE
+      J=0
+      IF (MSIGN.EQ.1) GO TO 1620
+      J=-1
+      DRES=-DRES
+ 1620 CONTINUE
+      IRESLT=NINT(DRES)
+
+*  Skip to end of field
+ 1630 CONTINUE
+      CALL slICHI(STRING,JPTR,NVEC,DIGIT)
+      GO TO (1720, 1630, 1720, 1720, 9900, 1720, 9900),NVEC
+*             0-9   SP     +     -     ,   ELSE   END
+
+ 1720 CONTINUE
+      JPTR=JPTR-1
+      GO TO 9900
+
+*  Exits
+
+*  Null field
+ 9100 CONTINUE
+      JPTR=JPTR-1
+ 9110 CONTINUE
+      J=1
+      GO TO 9900
+
+*  Errors
+ 9200 CONTINUE
+      JPTR=JPTR-1
+ 9210 CONTINUE
+      J=2
+
+*  Return
+ 9900 CONTINUE
+      NSTRT=JPTR
+      JFLAG=J
+
+      END
diff --git a/math/slalib/invf.f b/math/slalib/invf.f
new file mode 100644
index 00000000..90eb83b9
--- /dev/null
+++ b/math/slalib/invf.f
@@ -0,0 +1,106 @@
+      SUBROUTINE slINVF (FWDS,BKWDS,J)
+*+
+*     - - - - -
+*      I N V F
+*     - - - - -
+*
+*  Invert a linear model of the type produced by the slFTXY routine.
+*
+*  Given:
+*     FWDS    d(6)      model coefficients
+*
+*  Returned:
+*     BKWDS   d(6)      inverse model
+*     J        i        status:  0 = OK, -1 = no inverse
+*
+*  The models relate two sets of [X,Y] coordinates as follows.
+*  Naming the elements of FWDS:
+*
+*     FWDS(1) = A
+*     FWDS(2) = B
+*     FWDS(3) = C
+*     FWDS(4) = D
+*     FWDS(5) = E
+*     FWDS(6) = F
+*
+*  where two sets of coordinates [X1,Y1] and [X2,Y1] are related
+*  thus:
+*
+*     X2 = A + B*X1 + C*Y1
+*     Y2 = D + E*X1 + F*Y1
+*
+*  the present routine generates a new set of coefficients:
+*
+*     BKWDS(1) = P
+*     BKWDS(2) = Q
+*     BKWDS(3) = R
+*     BKWDS(4) = S
+*     BKWDS(5) = T
+*     BKWDS(6) = U
+*
+*  such that:
+*
+*     X1 = P + Q*X2 + R*Y2
+*     Y1 = S + T*X2 + U*Y2
+*
+*  Two successive calls to slINVF will thus deliver a set
+*  of coefficients equal to the starting values.
+*
+*  To comply with the ANSI Fortran standard, FWDS and BKWDS must
+*  not be the same array, even though the routine is coded to
+*  work on many platforms even if this rule is violated.
+*
+*  See also slFTXY, slPXY, slXYXY, slDCMF
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION FWDS(6),BKWDS(6)
+      INTEGER J
+
+      DOUBLE PRECISION A,B,C,D,E,F,DET
+
+
+
+      A=FWDS(1)
+      B=FWDS(2)
+      C=FWDS(3)
+      D=FWDS(4)
+      E=FWDS(5)
+      F=FWDS(6)
+      DET=B*F-C*E
+      IF (DET.NE.0D0) THEN
+         BKWDS(1)=(C*D-A*F)/DET
+         BKWDS(2)=F/DET
+         BKWDS(3)=-C/DET
+         BKWDS(4)=(A*E-B*D)/DET
+         BKWDS(5)=-E/DET
+         BKWDS(6)=B/DET
+         J=0
+      ELSE
+         J=-1
+      END IF
+
+      END
diff --git a/math/slalib/kbj.f b/math/slalib/kbj.f
new file mode 100644
index 00000000..6d68a069
--- /dev/null
+++ b/math/slalib/kbj.f
@@ -0,0 +1,74 @@
+      SUBROUTINE slKBJ (JB, E, K, J)
+*+
+*     - - - -
+*      K B J
+*     - - - -
+*
+*  Select epoch prefix 'B' or 'J'
+*
+*  Given:
+*     JB     int     slDBJI prefix status:  0=none, 1='B', 2='J'
+*     E      dp      epoch - Besselian or Julian
+*
+*  Returned:
+*     K      char    'B' or 'J'
+*     J      int     status:  0=OK
+*
+*  If JB=0, B is assumed for E < 1984D0, otherwise J.
+*
+*  P.T.Wallace   Starlink   31 July 1989
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER JB
+      DOUBLE PRECISION E
+      CHARACTER K*(*)
+      INTEGER J
+
+*  Preset status
+      J=0
+
+*  If prefix given expressly, use it
+      IF (JB.EQ.1) THEN
+         K='B'
+      ELSE IF (JB.EQ.2) THEN
+         K='J'
+
+*  If no prefix, examine the epoch
+      ELSE IF (JB.EQ.0) THEN
+
+*     If epoch is pre-1984.0, assume Besselian;  otherwise Julian
+         IF (E.LT.1984D0) THEN
+            K='B'
+         ELSE
+            K='J'
+         END IF
+
+*  If illegal prefix, return error status
+      ELSE
+         K=' '
+         J=1
+      END IF
+
+      END
diff --git a/math/slalib/m2av.f b/math/slalib/m2av.f
new file mode 100644
index 00000000..7e2e0cdb
--- /dev/null
+++ b/math/slalib/m2av.f
@@ -0,0 +1,75 @@
+      SUBROUTINE slM2AV (RMAT, AXVEC)
+*+
+*     - - - - -
+*      M 2 A V
+*     - - - - -
+*
+*  From a rotation matrix, determine the corresponding axial vector
+*  (single precision)
+*
+*  A rotation matrix describes a rotation about some arbitrary axis,
+*  called the Euler axis.  The "axial vector" returned by this routine
+*  has the same direction as the Euler axis, and its magnitude is the
+*  amount of rotation in radians.  (The magnitude and direction can be
+*  separated by means of the routine slVN.)
+*
+*  Given:
+*    RMAT   r(3,3)   rotation matrix
+*
+*  Returned:
+*    AXVEC  r(3)     axial vector (radians)
+*
+*  The reference frame rotates clockwise as seen looking along
+*  the axial vector from the origin.
+*
+*  If RMAT is null, so is the result.
+*
+*  Last revision:   26 November 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL RMAT(3,3),AXVEC(3)
+
+      REAL X,Y,Z,S2,C2,PHI,F
+
+
+
+      X = RMAT(2,3)-RMAT(3,2)
+      Y = RMAT(3,1)-RMAT(1,3)
+      Z = RMAT(1,2)-RMAT(2,1)
+      S2 = SQRT(X*X+Y*Y+Z*Z)
+      IF (S2.NE.0.0) THEN
+         C2 = (RMAT(1,1)+RMAT(2,2)+RMAT(3,3)-1.0)
+         PHI = ATAN2(S2/2.0,C2/2.0)
+         F = PHI/S2
+         AXVEC(1) = X*F
+         AXVEC(2) = Y*F
+         AXVEC(3) = Z*F
+      ELSE
+         AXVEC(1) = 0.0
+         AXVEC(2) = 0.0
+         AXVEC(3) = 0.0
+      END IF
+
+      END
diff --git a/math/slalib/map.f b/math/slalib/map.f
new file mode 100644
index 00000000..5c019fcd
--- /dev/null
+++ b/math/slalib/map.f
@@ -0,0 +1,99 @@
+      SUBROUTINE slMAP (RM, DM, PR, PD, PX, RV, EQ, DATE, RA, DA)
+*+
+*     - - - -
+*      M A P
+*     - - - -
+*
+*  Transform star RA,Dec from mean place to geocentric apparent
+*
+*  The reference frames and timescales used are post IAU 1976.
+*
+*  References:
+*     1984 Astronomical Almanac, pp B39-B41.
+*     (also Lederle & Schwan, Astron. Astrophys. 134,
+*      1-6, 1984)
+*
+*  Given:
+*     RM,DM    dp     mean RA,Dec (rad)
+*     PR,PD    dp     proper motions:  RA,Dec changes per Julian year
+*     PX       dp     parallax (arcsec)
+*     RV       dp     radial velocity (km/sec, +ve if receding)
+*     EQ       dp     epoch and equinox of star data (Julian)
+*     DATE     dp     TDB for apparent place (JD-2400000.5)
+*
+*  Returned:
+*     RA,DA    dp     apparent RA,Dec (rad)
+*
+*  Called:
+*     slMAPA       star-independent parameters
+*     slMAPQ       quick mean to apparent
+*
+*  Notes:
+*
+*  1)  EQ is the Julian epoch specifying both the reference frame and
+*      the epoch of the position - usually 2000.  For positions where
+*      the epoch and equinox are different, use the routine slPM to
+*      apply proper motion corrections before using this routine.
+*
+*  2)  The distinction between the required TDB and TT is always
+*      negligible.  Moreover, for all but the most critical
+*      applications UTC is adequate.
+*
+*  3)  The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt.
+*
+*  4)  This routine may be wasteful for some applications because it
+*      recomputes the Earth position/velocity and the precession-
+*      nutation matrix each time, and because it allows for parallax
+*      and proper motion.  Where multiple transformations are to be
+*      carried out for one epoch, a faster method is to call the
+*      slMAPA routine once and then either the slMAPQ routine
+*      (which includes parallax and proper motion) or slMAPZ (which
+*      assumes zero parallax and proper motion).
+*
+*  5)  The accuracy is sub-milliarcsecond, limited by the
+*      precession-nutation model (IAU 1976 precession, Shirai &
+*      Fukushima 2001 forced nutation and precession corrections).
+*
+*  6)  The accuracy is further limited by the routine slEVP, called
+*      by slMAPA, which computes the Earth position and velocity
+*      using the methods of Stumpff.  The maximum error is about
+*      0.3 mas.
+*
+*  P.T.Wallace   Starlink   17 September 2001
+*
+*  Copyright (C) 2001 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RM,DM,PR,PD,PX,RV,EQ,DATE,RA,DA
+
+      DOUBLE PRECISION AMPRMS(21)
+
+
+
+*  Star-independent parameters
+      CALL slMAPA(EQ,DATE,AMPRMS)
+
+*  Mean to apparent
+      CALL slMAPQ(RM,DM,PR,PD,PX,RV,AMPRMS,RA,DA)
+
+      END
diff --git a/math/slalib/mappa.f b/math/slalib/mappa.f
new file mode 100644
index 00000000..d3d9c2ae
--- /dev/null
+++ b/math/slalib/mappa.f
@@ -0,0 +1,129 @@
+      SUBROUTINE slMAPA (EQ, DATE, AMPRMS)
+*+
+*     - - - - - -
+*      M A P A
+*     - - - - - -
+*
+*  Compute star-independent parameters in preparation for
+*  conversions between mean place and geocentric apparent place.
+*
+*  The parameters produced by this routine are required in the
+*  parallax, light deflection, aberration, and precession/nutation
+*  parts of the mean/apparent transformations.
+*
+*  The reference frames and timescales used are post IAU 1976.
+*
+*  Given:
+*     EQ       d      epoch of mean equinox to be used (Julian)
+*     DATE     d      TDB (JD-2400000.5)
+*
+*  Returned:
+*     AMPRMS   d(21)  star-independent mean-to-apparent parameters:
+*
+*       (1)      time interval for proper motion (Julian years)
+*       (2-4)    barycentric position of the Earth (AU)
+*       (5-7)    heliocentric direction of the Earth (unit vector)
+*       (8)      (grav rad Sun)*2/(Sun-Earth distance)
+*       (9-11)   ABV: barycentric Earth velocity in units of c
+*       (12)     sqrt(1-v**2) where v=modulus(ABV)
+*       (13-21)  precession/nutation (3,3) matrix
+*
+*  References:
+*     1984 Astronomical Almanac, pp B39-B41.
+*     (also Lederle & Schwan, Astron. Astrophys. 134,
+*      1-6, 1984)
+*
+*  Notes:
+*
+*  1)  For DATE, the distinction between the required TDB and TT
+*      is always negligible.  Moreover, for all but the most
+*      critical applications UTC is adequate.
+*
+*  2)  The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to
+*      the mean equinox and equator of epoch EQ.
+*
+*  3)  The parameters AMPRMS produced by this routine are used by
+*      slAMPQ, slMAPQ and slMAPZ.
+*
+*  4)  The accuracy is sub-milliarcsecond, limited by the
+*      precession-nutation model (IAU 1976 precession, Shirai &
+*      Fukushima 2001 forced nutation and precession corrections).
+*
+*  5)  A further limit to the accuracy of routines using the parameter
+*      array AMPRMS is imposed by the routine slEVP, used here to
+*      compute the Earth position and velocity by the methods of
+*      Stumpff.  The maximum error in the resulting aberration
+*      corrections is about 0.3 milliarcsecond.
+*
+*  Called:
+*     slEPJ         MDJ to Julian epoch
+*     slEVP         earth position & velocity
+*     slDVN         normalize vector
+*     slPRNU      precession/nutation matrix
+*
+*  P.T.Wallace   Starlink   24 October 2003
+*
+*  Copyright (C) 2003 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION EQ,DATE,AMPRMS(21)
+
+*  Light time for 1 AU (sec)
+      DOUBLE PRECISION CR
+      PARAMETER (CR=499.004782D0)
+
+*  Gravitational radius of the Sun x 2 (2*mu/c**2, AU)
+      DOUBLE PRECISION GR2
+      PARAMETER (GR2=2D0*9.87063D-9)
+
+      INTEGER I
+
+      DOUBLE PRECISION EBD(3),EHD(3),EH(3),E,VN(3),VM
+
+      DOUBLE PRECISION slEPJ
+
+
+
+*  Time interval for proper motion correction
+      AMPRMS(1) = slEPJ(DATE)-EQ
+
+*  Get Earth barycentric and heliocentric position and velocity
+      CALL slEVP(DATE,EQ,EBD,AMPRMS(2),EHD,EH)
+
+*  Heliocentric direction of earth (normalized) and modulus
+      CALL slDVN(EH,AMPRMS(5),E)
+
+*  Light deflection parameter
+      AMPRMS(8) = GR2/E
+
+*  Aberration parameters
+      DO I=1,3
+         AMPRMS(I+8) = EBD(I)*CR
+      END DO
+      CALL slDVN(AMPRMS(9),VN,VM)
+      AMPRMS(12) = SQRT(1D0-VM*VM)
+
+*  Precession/nutation matrix
+      CALL slPRNU(EQ,DATE,AMPRMS(13))
+
+      END
diff --git a/math/slalib/mapqk.f b/math/slalib/mapqk.f
new file mode 100644
index 00000000..0e1997ff
--- /dev/null
+++ b/math/slalib/mapqk.f
@@ -0,0 +1,160 @@
+      SUBROUTINE slMAPQ (RM, DM, PR, PD, PX, RV, AMPRMS, RA, DA)
+*+
+*     - - - - - -
+*      M A P Q
+*     - - - - - -
+*
+*  Quick mean to apparent place:  transform a star RA,Dec from
+*  mean place to geocentric apparent place, given the
+*  star-independent parameters.
+*
+*  Use of this routine is appropriate when efficiency is important
+*  and where many star positions, all referred to the same equator
+*  and equinox, are to be transformed for one epoch.  The
+*  star-independent parameters can be obtained by calling the
+*  slMAPA routine.
+*
+*  If the parallax and proper motions are zero the slMAPZ
+*  routine can be used instead.
+*
+*  The reference frames and timescales used are post IAU 1976.
+*
+*  Given:
+*     RM,DM    d      mean RA,Dec (rad)
+*     PR,PD    d      proper motions:  RA,Dec changes per Julian year
+*     PX       d      parallax (arcsec)
+*     RV       d      radial velocity (km/sec, +ve if receding)
+*
+*     AMPRMS   d(21)  star-independent mean-to-apparent parameters:
+*
+*       (1)      time interval for proper motion (Julian years)
+*       (2-4)    barycentric position of the Earth (AU)
+*       (5-7)    heliocentric direction of the Earth (unit vector)
+*       (8)      (grav rad Sun)*2/(Sun-Earth distance)
+*       (9-11)   barycentric Earth velocity in units of c
+*       (12)     sqrt(1-v**2) where v=modulus(ABV)
+*       (13-21)  precession/nutation (3,3) matrix
+*
+*  Returned:
+*     RA,DA    d      apparent RA,Dec (rad)
+*
+*  References:
+*     1984 Astronomical Almanac, pp B39-B41.
+*     (also Lederle & Schwan, Astron. Astrophys. 134,
+*      1-6, 1984)
+*
+*  Notes:
+*
+*  1)  The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to
+*      the mean equinox and equator of epoch EQ.
+*
+*  2)  Strictly speaking, the routine is not valid for solar-system
+*      sources, though the error will usually be extremely small.
+*      However, to prevent gross errors in the case where the
+*      position of the Sun is specified, the gravitational
+*      deflection term is restrained within about 920 arcsec of the
+*      centre of the Sun's disc.  The term has a maximum value of
+*      about 1.85 arcsec at this radius, and decreases to zero as
+*      the centre of the disc is approached.
+*
+*  Called:
+*     slDS2C       spherical to Cartesian
+*     slDVDV        dot product
+*     slDMXV        matrix x vector
+*     slDC2S       Cartesian to spherical
+*     slDA2P      normalize angle 0-2Pi
+*
+*  P.T.Wallace   Starlink   15 January 2000
+*
+*  Copyright (C) 2000 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RM,DM,PR,PD,PX,RV,AMPRMS(21),RA,DA
+
+*  Arc seconds to radians
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+*  Km/s to AU/year
+      DOUBLE PRECISION VF
+      PARAMETER (VF=0.21094502D0)
+
+      INTEGER I
+
+      DOUBLE PRECISION PMT,GR2E,AB1,EB(3),EHN(3),ABV(3),
+     :                 Q(3),PXR,W,EM(3),P(3),PN(3),PDE,PDEP1,
+     :                 P1(3),P1DV,P2(3),P3(3)
+
+      DOUBLE PRECISION slDVDV,slDA2P
+
+
+
+*  Unpack scalar and vector parameters
+      PMT = AMPRMS(1)
+      GR2E = AMPRMS(8)
+      AB1 = AMPRMS(12)
+      DO I=1,3
+         EB(I) = AMPRMS(I+1)
+         EHN(I) = AMPRMS(I+4)
+         ABV(I) = AMPRMS(I+8)
+      END DO
+
+*  Spherical to x,y,z
+      CALL slDS2C(RM,DM,Q)
+
+*  Space motion (radians per year)
+      PXR = PX*AS2R
+      W = VF*RV*PXR
+      EM(1) = -PR*Q(2)-PD*COS(RM)*SIN(DM)+W*Q(1)
+      EM(2) =  PR*Q(1)-PD*SIN(RM)*SIN(DM)+W*Q(2)
+      EM(3) =          PD*COS(DM)        +W*Q(3)
+
+*  Geocentric direction of star (normalized)
+      DO I=1,3
+         P(I) = Q(I)+PMT*EM(I)-PXR*EB(I)
+      END DO
+      CALL slDVN(P,PN,W)
+
+*  Light deflection (restrained within the Sun's disc)
+      PDE = slDVDV(PN,EHN)
+      PDEP1 = PDE+1D0
+      W = GR2E/MAX(PDEP1,1D-5)
+      DO I=1,3
+         P1(I) = PN(I)+W*(EHN(I)-PDE*PN(I))
+      END DO
+
+*  Aberration (normalization omitted)
+      P1DV = slDVDV(P1,ABV)
+      W = 1D0+P1DV/(AB1+1D0)
+      DO I=1,3
+         P2(I) = AB1*P1(I)+W*ABV(I)
+      END DO
+
+*  Precession and nutation
+      CALL slDMXV(AMPRMS(13),P2,P3)
+
+*  Geocentric apparent RA,Dec
+      CALL slDC2S(P3,RA,DA)
+      RA = slDA2P(RA)
+
+      END
diff --git a/math/slalib/mapqkz.f b/math/slalib/mapqkz.f
new file mode 100644
index 00000000..6409b22e
--- /dev/null
+++ b/math/slalib/mapqkz.f
@@ -0,0 +1,131 @@
+      SUBROUTINE slMAPZ (RM, DM, AMPRMS, RA, DA)
+*+
+*     - - - - - - -
+*      M A P Z
+*     - - - - - - -
+*
+*  Quick mean to apparent place:  transform a star RA,Dec from
+*  mean place to geocentric apparent place, given the
+*  star-independent parameters, and assuming zero parallax
+*  and proper motion.
+*
+*  Use of this routine is appropriate when efficiency is important
+*  and where many star positions, all with parallax and proper
+*  motion either zero or already allowed for, and all referred to
+*  the same equator and equinox, are to be transformed for one
+*  epoch.  The star-independent parameters can be obtained by
+*  calling the slMAPA routine.
+*
+*  The corresponding routine for the case of non-zero parallax
+*  and proper motion is slMAPQ.
+*
+*  The reference frames and timescales used are post IAU 1976.
+*
+*  Given:
+*     RM,DM    d      mean RA,Dec (rad)
+*     AMPRMS   d(21)  star-independent mean-to-apparent parameters:
+*
+*       (1-4)    not used
+*       (5-7)    heliocentric direction of the Earth (unit vector)
+*       (8)      (grav rad Sun)*2/(Sun-Earth distance)
+*       (9-11)   ABV: barycentric Earth velocity in units of c
+*       (12)     sqrt(1-v**2) where v=modulus(ABV)
+*       (13-21)  precession/nutation (3,3) matrix
+*
+*  Returned:
+*     RA,DA    d      apparent RA,Dec (rad)
+*
+*  References:
+*     1984 Astronomical Almanac, pp B39-B41.
+*     (also Lederle & Schwan, Astron. Astrophys. 134,
+*      1-6, 1984)
+*
+*  Notes:
+*
+*  1)  The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to the
+*      mean equinox and equator of epoch EQ.
+*
+*  2)  Strictly speaking, the routine is not valid for solar-system
+*      sources, though the error will usually be extremely small.
+*      However, to prevent gross errors in the case where the
+*      position of the Sun is specified, the gravitational
+*      deflection term is restrained within about 920 arcsec of the
+*      centre of the Sun's disc.  The term has a maximum value of
+*      about 1.85 arcsec at this radius, and decreases to zero as
+*      the centre of the disc is approached.
+*
+*  Called:  slDS2C, slDVDV, slDMXV, slDC2S, slDA2P
+*
+*  P.T.Wallace   Starlink   18 March 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RM,DM,AMPRMS(21),RA,DA
+
+      INTEGER I
+
+      DOUBLE PRECISION GR2E,AB1,EHN(3),ABV(3),
+     :                 P(3),PDE,PDEP1,W,P1(3),P1DV,
+     :                 P1DVP1,P2(3),P3(3)
+
+      DOUBLE PRECISION slDVDV,slDA2P
+
+
+
+
+*  Unpack scalar and vector parameters
+      GR2E = AMPRMS(8)
+      AB1 = AMPRMS(12)
+      DO I=1,3
+         EHN(I) = AMPRMS(I+4)
+         ABV(I) = AMPRMS(I+8)
+      END DO
+
+*  Spherical to x,y,z
+      CALL slDS2C(RM,DM,P)
+
+*  Light deflection
+      PDE = slDVDV(P,EHN)
+      PDEP1 = PDE+1D0
+      W = GR2E/MAX(PDEP1,1D-5)
+      DO I=1,3
+         P1(I) = P(I)+W*(EHN(I)-PDE*P(I))
+      END DO
+
+*  Aberration
+      P1DV = slDVDV(P1,ABV)
+      P1DVP1 = P1DV+1D0
+      W = 1D0+P1DV/(AB1+1D0)
+      DO I=1,3
+         P2(I) = (AB1*P1(I)+W*ABV(I))/P1DVP1
+      END DO
+
+*  Precession and nutation
+      CALL slDMXV(AMPRMS(13),P2,P3)
+
+*  Geocentric apparent RA,Dec
+      CALL slDC2S(P3,RA,DA)
+      RA = slDA2P(RA)
+
+      END
diff --git a/math/slalib/mkpkg b/math/slalib/mkpkg
new file mode 100644
index 00000000..d2f9203b
--- /dev/null
+++ b/math/slalib/mkpkg
@@ -0,0 +1,193 @@
+# SLALIB library routines
+
+$checkout libslalib.a lib$
+$update   libslalib.a
+$checkin  libslalib.a lib$
+$exit
+
+libslalib.a:
+	addet.f   
+	afin.f   
+	airmas.f   
+	altaz.f   
+	amp.f   
+	ampqk.f   
+	aop.f   
+	aoppa.f   
+	aoppat.f   
+	aopqk.f   
+	atmdsp.f   
+	atms.f   
+	atmt.f   
+	av2m.f   
+	bear.f   
+	caf2r.f   
+	caldj.f   
+	calyd.f   
+	cc2s.f   
+	cc62s.f   
+	cd2tf.f   
+	cldj.f   
+	clyd.f   
+	cr2af.f   
+	cr2tf.f   
+	cs2c.f   
+	cs2c6.f   
+	ctf2d.f   
+	ctf2r.f   
+	daf2r.f   
+	dafin.f   
+	dat.f   
+	dav2m.f   
+	dbear.f   
+	dbjin.f   
+	dc62s.f   
+	dcc2s.f   
+	dcmpf.f   
+	dcs2c.f   
+	dd2tf.f   
+	de2h.f   
+	deuler.f   
+	dfltin.f   
+	dh2e.f   
+	dimxv.f   
+	djcal.f   
+	djcl.f   
+	dm2av.f   
+	dmat.f   
+	dmoon.f   
+	dmxm.f   
+	dmxv.f   
+	dpav.f
+	dr2af.f   
+	dr2tf.f   
+	drange.f   
+	dranrm.f   
+	ds2c6.f   
+	ds2tp.f   
+	dsep.f   
+	dsepv.f   
+	dt.f   
+	dtf2d.f   
+	dtf2r.f   
+	dtp2s.f   
+	dtp2v.f   
+	dtps2c.f   
+	dtpv2c.f   
+	dtt.f   
+	dv2tp.f   
+	dvdv.f   
+	dvn.f   
+	dvxv.f   
+	e2h.f   
+	earth.f   
+	ecleq.f   
+	ecmat.f   
+	ecor.f   
+	eg50.f   
+	el2ue.f
+	epb.f   
+	epb2d.f   
+	epco.f   
+	epj.f   
+	epj2d.f   
+	eqecl.f   
+	eqeqx.f   
+	eqgal.f   
+	etrms.f   
+	euler.f   
+	evp.f   
+	fitxy.f   
+	fk425.f   
+	fk45z.f   
+	fk524.f   
+	fk54z.f   
+	fk52h.f
+	fk5hz.f
+	flotin.f   
+	galeq.f   
+	galsup.f   
+	ge50.f   
+	geoc.f   
+	gmst.f   
+	gmsta.f   
+	h2e.f   
+	h2fk5.f
+	hfk5z.f
+	idchf.f   
+	idchi.f   
+	imxv.f   
+	intin.f   
+	invf.f   
+	kbj.f   
+	m2av.f   
+	map.f   
+	mappa.f   
+	mapqk.f   
+	mapqkz.f   
+	moon.f   
+	mxm.f   
+	mxv.f   
+	nut.f   
+	nutc.f   
+	oap.f   
+	oapqk.f   
+	obs.f   
+	pa.f   
+	pav.f
+	pcd.f   
+	pda2h.f   
+	pdq2h.f   
+	pertel.f
+	pertue.f
+	planel.f
+	planet.f   
+	plante.f
+	pm.f   
+	polmo.f
+	prebn.f   
+	prec.f   
+	preces.f   
+	precl.f   
+	precss.f	# preces.f with an integer system argument
+	prenut.f   
+	pv2ue.f
+	pv2el.f
+	pvobs.f   
+	pxy.f   
+	range.f   
+	ranorm.f   
+	rcc.f   
+	rdplan.f   
+	refco.f   
+	refcoq.f
+	refro.f   
+	refv.f   
+	refz.f   
+	rverot.f   
+	rvgalc.f   
+	rvlg.f   
+	rvlsrd.f   
+	rvlsrk.f   
+	s2tp.f   
+	sep.f   
+	smat.f   
+	subet.f   
+	supgal.f   
+	svd.f   
+	svdcov.f   
+	svdsol.f   
+	tp2s.f   
+	tp2v.f   
+	tps2c.f   
+	tpv2c.f   
+	ue2el.f
+	ue2pv.f
+	unpcd.f   
+	v2tp.f   
+	vdv.f   
+	vn.f   
+	vxv.f   
+	xy2xy.f   
+	zd.f   
+	;
diff --git a/math/slalib/moon.f b/math/slalib/moon.f
new file mode 100644
index 00000000..c77395ee
--- /dev/null
+++ b/math/slalib/moon.f
@@ -0,0 +1,380 @@
+      SUBROUTINE slMOON (IY, ID, FD, PV)
+*+
+*     - - - - -
+*      M O O N
+*     - - - - -
+*
+*  Approximate geocentric position and velocity of the Moon
+*  (single precision).
+*
+*  Given:
+*     IY       i       year
+*     ID       i       day in year (1 = Jan 1st)
+*     FD       r       fraction of day
+*
+*  Returned:
+*     PV       r(6)    Moon position & velocity vector
+*
+*  Notes:
+*
+*  1  The date and time is TDB (loosely ET) in a Julian calendar
+*     which has been aligned to the ordinary Gregorian
+*     calendar for the interval 1900 March 1 to 2100 February 28.
+*     The year and day can be obtained by calling slCAYD or
+*     slCLYD.
+*
+*  2  The Moon 6-vector is Moon centre relative to Earth centre,
+*     mean equator and equinox of date.  Position part, PV(1-3),
+*     is in AU;  velocity part, PV(4-6), is in AU/sec.
+*
+*  3  The position is accurate to better than 0.5 arcminute
+*     in direction and 1000 km in distance.  The velocity
+*     is accurate to better than 0.5"/hour in direction and
+*     4 m/s in distance.  (RMS figures with respect to JPL DE200
+*     for the interval 1960-2025 are 14 arcsec and 0.2 arcsec/hour in
+*     longitude, 9 arcsec and 0.2 arcsec/hour in latitude, 350 km and
+*     2 m/s in distance.)  Note that the distance accuracy is
+*     comparatively poor because this routine is principally intended
+*     for computing topocentric direction.
+*
+*  4  This routine is only a partial implementation of the original
+*     Meeus algorithm (reference below), which offers 4 times the
+*     accuracy in direction and 30 times the accuracy in distance
+*     when fully implemented (as it is in slDMON).
+*
+*  Reference:
+*     Meeus, l'Astronomie, June 1984, p348.
+*
+*  Called:  slS2C6
+*
+*  P.T.Wallace   Starlink   8 December 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IY,ID
+      REAL FD,PV(6)
+
+      INTEGER ITP(4,4),ITL(4,39),ITB(4,29),I,IY4,N
+      REAL D2R,RATCON,ERADAU
+      REAL ELP0,ELP1,ELP1I,ELP1F
+      REAL EM0,EM1,EM1F
+      REAL EMP0,EMP1,EMP1I,EMP1F
+      REAL D0,D1,D1I,D1F
+      REAL F0,F1,F1I,F1F
+      REAL TL(39)
+      REAL TB(29)
+      REAL TP(4)
+      REAL YI,YF,T,ELP,EM,EMP,D,F,EL,ELD,COEFF,CEM,CEMP
+      REAL CD,CF,THETA,THETAD,B,BD,P,PD,SP,R,RD
+      REAL V(6),EPS,SINEPS,COSEPS
+
+*  Degrees to radians
+      PARAMETER (D2R=1.745329252E-2)
+
+*  Rate conversion factor:  D2R**2/(86400*365.25)
+      PARAMETER (RATCON=9.652743551E-12)
+
+*  Earth radius in AU:  6378.137/149597870
+      PARAMETER (ERADAU=4.2635212653763E-5)
+
+*
+*  Coefficients for fundamental arguments
+*
+*  Fixed term (deg), term in T (deg & whole revs + fraction per year)
+*
+*  Moon's mean longitude
+      DATA ELP0,ELP1,ELP1I,ELP1F /
+     :            270.434164, 4812.678831, 4680., 132.678831 /
+*
+*  Sun's mean anomaly
+      DATA EM0,EM1,EM1F /
+     :            358.475833,  359.990498,        359.990498 /
+*
+*  Moon's mean anomaly
+      DATA EMP0,EMP1,EMP1I,EMP1F /
+     :            296.104608, 4771.988491, 4680.,  91.988491 /
+*
+*  Moon's mean elongation
+      DATA D0,D1,D1I,D1F /
+     :            350.737486,  4452.671142, 4320., 132.671142 /
+*
+*  Mean distance of the Moon from its ascending node
+      DATA F0,F1,F1I,F1F /
+     :             11.250889, 4832.020251, 4680., 152.020251 /
+
+*
+*  Coefficients for Moon position
+*
+*   T(N)       = coefficient of term (deg)
+*   IT(N,1-4)  = coefficients of M, M', D, F in argument
+*
+*  Longitude
+*                                         M   M'  D   F
+      DATA TL( 1)/            +6.288750                     /,
+     :     (ITL(I, 1),I=1,4)/             0, +1,  0,  0     /
+      DATA TL( 2)/            +1.274018                     /,
+     :     (ITL(I, 2),I=1,4)/             0, -1, +2,  0     /
+      DATA TL( 3)/            +0.658309                     /,
+     :     (ITL(I, 3),I=1,4)/             0,  0, +2,  0     /
+      DATA TL( 4)/            +0.213616                     /,
+     :     (ITL(I, 4),I=1,4)/             0, +2,  0,  0     /
+      DATA TL( 5)/            -0.185596                     /,
+     :     (ITL(I, 5),I=1,4)/            +1,  0,  0,  0     /
+      DATA TL( 6)/            -0.114336                     /,
+     :     (ITL(I, 6),I=1,4)/             0,  0,  0, +2     /
+      DATA TL( 7)/            +0.058793                     /,
+     :     (ITL(I, 7),I=1,4)/             0, -2, +2,  0     /
+      DATA TL( 8)/            +0.057212                     /,
+     :     (ITL(I, 8),I=1,4)/            -1, -1, +2,  0     /
+      DATA TL( 9)/            +0.053320                     /,
+     :     (ITL(I, 9),I=1,4)/             0, +1, +2,  0     /
+      DATA TL(10)/            +0.045874                     /,
+     :     (ITL(I,10),I=1,4)/            -1,  0, +2,  0     /
+      DATA TL(11)/            +0.041024                     /,
+     :     (ITL(I,11),I=1,4)/            -1, +1,  0,  0     /
+      DATA TL(12)/            -0.034718                     /,
+     :     (ITL(I,12),I=1,4)/             0,  0, +1,  0     /
+      DATA TL(13)/            -0.030465                     /,
+     :     (ITL(I,13),I=1,4)/            +1, +1,  0,  0     /
+      DATA TL(14)/            +0.015326                     /,
+     :     (ITL(I,14),I=1,4)/             0,  0, +2, -2     /
+      DATA TL(15)/            -0.012528                     /,
+     :     (ITL(I,15),I=1,4)/             0, +1,  0, +2     /
+      DATA TL(16)/            -0.010980                     /,
+     :     (ITL(I,16),I=1,4)/             0, -1,  0, +2     /
+      DATA TL(17)/            +0.010674                     /,
+     :     (ITL(I,17),I=1,4)/             0, -1, +4,  0     /
+      DATA TL(18)/            +0.010034                     /,
+     :     (ITL(I,18),I=1,4)/             0, +3,  0,  0     /
+      DATA TL(19)/            +0.008548                     /,
+     :     (ITL(I,19),I=1,4)/             0, -2, +4,  0     /
+      DATA TL(20)/            -0.007910                     /,
+     :     (ITL(I,20),I=1,4)/            +1, -1, +2,  0     /
+      DATA TL(21)/            -0.006783                     /,
+     :     (ITL(I,21),I=1,4)/            +1,  0, +2,  0     /
+      DATA TL(22)/            +0.005162                     /,
+     :     (ITL(I,22),I=1,4)/             0, +1, -1,  0     /
+      DATA TL(23)/            +0.005000                     /,
+     :     (ITL(I,23),I=1,4)/            +1,  0, +1,  0     /
+      DATA TL(24)/            +0.004049                     /,
+     :     (ITL(I,24),I=1,4)/            -1, +1, +2,  0     /
+      DATA TL(25)/            +0.003996                     /,
+     :     (ITL(I,25),I=1,4)/             0, +2, +2,  0     /
+      DATA TL(26)/            +0.003862                     /,
+     :     (ITL(I,26),I=1,4)/             0,  0, +4,  0     /
+      DATA TL(27)/            +0.003665                     /,
+     :     (ITL(I,27),I=1,4)/             0, -3, +2,  0     /
+      DATA TL(28)/            +0.002695                     /,
+     :     (ITL(I,28),I=1,4)/            -1, +2,  0,  0     /
+      DATA TL(29)/            +0.002602                     /,
+     :     (ITL(I,29),I=1,4)/             0, +1, -2, -2     /
+      DATA TL(30)/            +0.002396                     /,
+     :     (ITL(I,30),I=1,4)/            -1, -2, +2,  0     /
+      DATA TL(31)/            -0.002349                     /,
+     :     (ITL(I,31),I=1,4)/             0, +1, +1,  0     /
+      DATA TL(32)/            +0.002249                     /,
+     :     (ITL(I,32),I=1,4)/            -2,  0, +2,  0     /
+      DATA TL(33)/            -0.002125                     /,
+     :     (ITL(I,33),I=1,4)/            +1, +2,  0,  0     /
+      DATA TL(34)/            -0.002079                     /,
+     :     (ITL(I,34),I=1,4)/            +2,  0,  0,  0     /
+      DATA TL(35)/            +0.002059                     /,
+     :     (ITL(I,35),I=1,4)/            -2, -1, +2,  0     /
+      DATA TL(36)/            -0.001773                     /,
+     :     (ITL(I,36),I=1,4)/             0, +1, +2, -2     /
+      DATA TL(37)/            -0.001595                     /,
+     :     (ITL(I,37),I=1,4)/             0,  0, +2, +2     /
+      DATA TL(38)/            +0.001220                     /,
+     :     (ITL(I,38),I=1,4)/            -1, -1, +4,  0     /
+      DATA TL(39)/            -0.001110                     /,
+     :     (ITL(I,39),I=1,4)/             0, +2,  0, +2     /
+*
+*  Latitude
+*                                         M   M'  D   F
+      DATA TB( 1)/            +5.128189                     /,
+     :     (ITB(I, 1),I=1,4)/             0,  0,  0, +1     /
+      DATA TB( 2)/            +0.280606                     /,
+     :     (ITB(I, 2),I=1,4)/             0, +1,  0, +1     /
+      DATA TB( 3)/            +0.277693                     /,
+     :     (ITB(I, 3),I=1,4)/             0, +1,  0, -1     /
+      DATA TB( 4)/            +0.173238                     /,
+     :     (ITB(I, 4),I=1,4)/             0,  0, +2, -1     /
+      DATA TB( 5)/            +0.055413                     /,
+     :     (ITB(I, 5),I=1,4)/             0, -1, +2, +1     /
+      DATA TB( 6)/            +0.046272                     /,
+     :     (ITB(I, 6),I=1,4)/             0, -1, +2, -1     /
+      DATA TB( 7)/            +0.032573                     /,
+     :     (ITB(I, 7),I=1,4)/             0,  0, +2, +1     /
+      DATA TB( 8)/            +0.017198                     /,
+     :     (ITB(I, 8),I=1,4)/             0, +2,  0, +1     /
+      DATA TB( 9)/            +0.009267                     /,
+     :     (ITB(I, 9),I=1,4)/             0, +1, +2, -1     /
+      DATA TB(10)/            +0.008823                     /,
+     :     (ITB(I,10),I=1,4)/             0, +2,  0, -1     /
+      DATA TB(11)/            +0.008247                     /,
+     :     (ITB(I,11),I=1,4)/            -1,  0, +2, -1     /
+      DATA TB(12)/            +0.004323                     /,
+     :     (ITB(I,12),I=1,4)/             0, -2, +2, -1     /
+      DATA TB(13)/            +0.004200                     /,
+     :     (ITB(I,13),I=1,4)/             0, +1, +2, +1     /
+      DATA TB(14)/            +0.003372                     /,
+     :     (ITB(I,14),I=1,4)/            -1,  0, -2, +1     /
+      DATA TB(15)/            +0.002472                     /,
+     :     (ITB(I,15),I=1,4)/            -1, -1, +2, +1     /
+      DATA TB(16)/            +0.002222                     /,
+     :     (ITB(I,16),I=1,4)/            -1,  0, +2, +1     /
+      DATA TB(17)/            +0.002072                     /,
+     :     (ITB(I,17),I=1,4)/            -1, -1, +2, -1     /
+      DATA TB(18)/            +0.001877                     /,
+     :     (ITB(I,18),I=1,4)/            -1, +1,  0, +1     /
+      DATA TB(19)/            +0.001828                     /,
+     :     (ITB(I,19),I=1,4)/             0, -1, +4, -1     /
+      DATA TB(20)/            -0.001803                     /,
+     :     (ITB(I,20),I=1,4)/            +1,  0,  0, +1     /
+      DATA TB(21)/            -0.001750                     /,
+     :     (ITB(I,21),I=1,4)/             0,  0,  0, +3     /
+      DATA TB(22)/            +0.001570                     /,
+     :     (ITB(I,22),I=1,4)/            -1, +1,  0, -1     /
+      DATA TB(23)/            -0.001487                     /,
+     :     (ITB(I,23),I=1,4)/             0,  0, +1, +1     /
+      DATA TB(24)/            -0.001481                     /,
+     :     (ITB(I,24),I=1,4)/            +1, +1,  0, +1     /
+      DATA TB(25)/            +0.001417                     /,
+     :     (ITB(I,25),I=1,4)/            -1, -1,  0, +1     /
+      DATA TB(26)/            +0.001350                     /,
+     :     (ITB(I,26),I=1,4)/            -1,  0,  0, +1     /
+      DATA TB(27)/            +0.001330                     /,
+     :     (ITB(I,27),I=1,4)/             0,  0, -1, +1     /
+      DATA TB(28)/            +0.001106                     /,
+     :     (ITB(I,28),I=1,4)/             0, +3,  0, +1     /
+      DATA TB(29)/            +0.001020                     /,
+     :     (ITB(I,29),I=1,4)/             0,  0, +4, -1     /
+*
+*  Parallax
+*                                         M   M'  D   F
+      DATA TP( 1)/            +0.051818                     /,
+     :     (ITP(I, 1),I=1,4)/             0, +1,  0,  0     /
+      DATA TP( 2)/            +0.009531                     /,
+     :     (ITP(I, 2),I=1,4)/             0, -1, +2,  0     /
+      DATA TP( 3)/            +0.007843                     /,
+     :     (ITP(I, 3),I=1,4)/             0,  0, +2,  0     /
+      DATA TP( 4)/            +0.002824                     /,
+     :     (ITP(I, 4),I=1,4)/             0, +2,  0,  0     /
+
+
+
+*  Whole years & fraction of year, and years since J1900.0
+      YI=FLOAT(IY-1900)
+      IY4=MOD(MOD(IY,4)+4,4)
+      YF=(FLOAT(4*(ID-1/(IY4+1))-IY4-2)+4.0*FD)/1461.0
+      T=YI+YF
+
+*  Moon's mean longitude
+      ELP=D2R*MOD(ELP0+ELP1I*YF+ELP1F*T,360.0)
+
+*  Sun's mean anomaly
+      EM=D2R*MOD(EM0+EM1F*T,360.0)
+
+*  Moon's mean anomaly
+      EMP=D2R*MOD(EMP0+EMP1I*YF+EMP1F*T,360.0)
+
+*  Moon's mean elongation
+      D=D2R*MOD(D0+D1I*YF+D1F*T,360.0)
+
+*  Mean distance of the moon from its ascending node
+      F=D2R*MOD(F0+F1I*YF+F1F*T,360.0)
+
+*  Longitude
+      EL=0.0
+      ELD=0.0
+      DO N=39,1,-1
+         COEFF=TL(N)
+         CEM=FLOAT(ITL(1,N))
+         CEMP=FLOAT(ITL(2,N))
+         CD=FLOAT(ITL(3,N))
+         CF=FLOAT(ITL(4,N))
+         THETA=CEM*EM+CEMP*EMP+CD*D+CF*F
+         THETAD=CEM*EM1+CEMP*EMP1+CD*D1+CF*F1
+         EL=EL+COEFF*SIN(THETA)
+         ELD=ELD+COEFF*COS(THETA)*THETAD
+      END DO
+      EL=EL*D2R+ELP
+      ELD=RATCON*(ELD+ELP1/D2R)
+
+*  Latitude
+      B=0.0
+      BD=0.0
+      DO N=29,1,-1
+         COEFF=TB(N)
+         CEM=FLOAT(ITB(1,N))
+         CEMP=FLOAT(ITB(2,N))
+         CD=FLOAT(ITB(3,N))
+         CF=FLOAT(ITB(4,N))
+         THETA=CEM*EM+CEMP*EMP+CD*D+CF*F
+         THETAD=CEM*EM1+CEMP*EMP1+CD*D1+CF*F1
+         B=B+COEFF*SIN(THETA)
+         BD=BD+COEFF*COS(THETA)*THETAD
+      END DO
+      B=B*D2R
+      BD=RATCON*BD
+
+*  Parallax
+      P=0.0
+      PD=0.0
+      DO N=4,1,-1
+         COEFF=TP(N)
+         CEM=FLOAT(ITP(1,N))
+         CEMP=FLOAT(ITP(2,N))
+         CD=FLOAT(ITP(3,N))
+         CF=FLOAT(ITP(4,N))
+         THETA=CEM*EM+CEMP*EMP+CD*D+CF*F
+         THETAD=CEM*EM1+CEMP*EMP1+CD*D1+CF*F1
+         P=P+COEFF*COS(THETA)
+         PD=PD-COEFF*SIN(THETA)*THETAD
+      END DO
+      P=(P+0.950724)*D2R
+      PD=RATCON*PD
+
+*  Transform parallax to distance (AU, AU/sec)
+      SP=SIN(P)
+      R=ERADAU/SP
+      RD=-R*PD/SP
+
+*  Longitude, latitude to x,y,z (AU)
+      CALL slS2C6(EL,B,R,ELD,BD,RD,V)
+
+*  Mean obliquity
+      EPS=D2R*(23.45229-0.00013*T)
+      SINEPS=SIN(EPS)
+      COSEPS=COS(EPS)
+
+*  Rotate Moon position and velocity into equatorial system
+      PV(1)=V(1)
+      PV(2)=V(2)*COSEPS-V(3)*SINEPS
+      PV(3)=V(2)*SINEPS+V(3)*COSEPS
+      PV(4)=V(4)
+      PV(5)=V(5)*COSEPS-V(6)*SINEPS
+      PV(6)=V(5)*SINEPS+V(6)*COSEPS
+
+      END
diff --git a/math/slalib/mxm.f b/math/slalib/mxm.f
new file mode 100644
index 00000000..1c00c632
--- /dev/null
+++ b/math/slalib/mxm.f
@@ -0,0 +1,72 @@
+      SUBROUTINE slMXM (A, B, C)
+*+
+*     - - - -
+*      M X M
+*     - - - -
+*
+*  Product of two 3x3 matrices:
+*      matrix C  =  matrix A  x  matrix B
+*
+*  (single precision)
+*
+*  Given:
+*      A      real(3,3)        matrix
+*      B      real(3,3)        matrix
+*
+*  Returned:
+*      C      real(3,3)        matrix result
+*
+*  To comply with the ANSI Fortran 77 standard, A, B and C must
+*  be different arrays.  However, the routine is coded so as to
+*  work properly on many platforms even if this rule is violated.
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL A(3,3),B(3,3),C(3,3)
+
+      INTEGER I,J,K
+      REAL W,WM(3,3)
+
+
+*  Multiply into scratch matrix
+      DO I=1,3
+         DO J=1,3
+            W=0.0
+            DO K=1,3
+               W=W+A(I,K)*B(K,J)
+            END DO
+            WM(I,J)=W
+         END DO
+      END DO
+
+*  Return the result
+      DO J=1,3
+         DO I=1,3
+            C(I,J)=WM(I,J)
+         END DO
+      END DO
+
+      END
diff --git a/math/slalib/mxv.f b/math/slalib/mxv.f
new file mode 100644
index 00000000..266c1f85
--- /dev/null
+++ b/math/slalib/mxv.f
@@ -0,0 +1,69 @@
+      SUBROUTINE slMXV (RM, VA, VB)
+*+
+*     - - - -
+*      M X V
+*     - - - -
+*
+*  Performs the 3-D forward unitary transformation:
+*
+*     vector VB = matrix RM * vector VA
+*
+*  (single precision)
+*
+*  Given:
+*     RM       real(3,3)    matrix
+*     VA       real(3)      vector
+*
+*  Returned:
+*     VB       real(3)      result vector
+*
+*  To comply with the ANSI Fortran 77 standard, VA and VB must be
+*  different arrays.  However, the routine is coded so as to work
+*  properly on many platforms even if this rule is violated.
+*
+*  Last revision:   26 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL RM(3,3),VA(3),VB(3)
+
+      INTEGER I,J
+      REAL W,VW(3)
+
+
+*  Matrix RM * vector VA -> vector VW
+      DO J=1,3
+         W=0.0
+         DO I=1,3
+            W=W+RM(J,I)*VA(I)
+         END DO
+         VW(J)=W
+      END DO
+
+*  Vector VW -> vector VB
+      DO J=1,3
+         VB(J)=VW(J)
+      END DO
+
+      END
diff --git a/math/slalib/newnames b/math/slalib/newnames
new file mode 100644
index 00000000..f91c9c86
--- /dev/null
+++ b/math/slalib/newnames
@@ -0,0 +1,205 @@
+sla_ADDET	slADET   
+sla_AFIN	slAFIN   
+sla_AIRMAS	slARMS   
+sla_ALTAZ	slALAZ   
+sla_AMP		slAMP   
+sla_AMPQK	slAMPQ   
+sla_AOP		slAOP   
+sla_AOPPA	slAOPA   
+sla_AOPPAT	slAOPT   
+sla_AOPQK	slAOPQ   
+sla__ATMS	slATMS   
+sla__ATMT	slATMT   
+sla_ATMDSP	slATMD   
+sla_AV2M	slAV2M   
+	
+sla_BEAR	slBEAR   
+	
+sla_CAF2R	slCAFR   
+sla_CALDJ	slCADJ   
+sla_CALYD	slCAYD   
+sla_CC2S	slCC2S   
+sla_CC62S	slC62S   
+sla_CD2TF	slCDTF   
+sla_CLDJ	slCLDJ   
+sla_CLYD	slCLYD   
+sla_CR2AF	slCRAF   
+sla_CR2TF	slCRTF   
+sla_CS2C	slCS2C   
+sla_CS2C6	slS2C6   
+sla_CTF2D	slCTFD   
+sla_CTF2R	slCTFR   
+	
+sla_DAF2R	slDAFR   
+sla_DAFIN	slDAFN   
+sla_DAT		slDAT   
+sla_DAV2M	slDAVM   
+sla_DBEAR	slDBER   
+sla_DBJIN	slDBJI   
+sla_DC62S	slDC6S   
+sla_DCC2S	slDC2S   
+sla_DCMPF	slDCMF   
+sla_DCS2C	slDS2C   
+sla_DD2TF	slDDTF   
+sla_DE2H	slDE2H   
+sla_DEULER	slDEUL   
+sla_DFLTIN	slDFLI   
+sla_DH2E	slDH2E   
+sla_DIMXV	slDIMV   
+sla_DJCAL	slDJCA   
+sla_DJCL	slDJCL   
+sla_DM2AV	slDMAV   
+sla_DMAT	slDMAT   
+sla_DMOON	slDMON   
+sla_DMXM	slDMXM   
+sla_DMXV	slDMXV   
+sla_DPAV	slDPAV   
+sla_DR2AF	slDRAF   
+sla_DR2TF	slDRTF   
+sla_DRANGE	slDA1P   
+sla_DRANRM	slDA2P   
+sla_DS2C6	slDSC6   
+sla_DS2TP	slDSTP   
+sla_DSEP	slDSEP   
+sla_DT		slDT   
+sla_DTF2D	slDTFD   
+sla_DTF2R	slDTFR   
+sla_DTP2S	slDTPS   
+sla_DTP2V	slDTPV   
+sla_DTPS2C	slDPSC   
+sla_DTPV2C	slDPVC   
+sla_DTT		slDTT   
+sla_DV2TP	slDVTP   
+sla_DVDV	slDVDV   
+sla_DVN		slDVN   
+sla_DVXV	slDVXV   
+	
+sla_E2H		slE2H   
+sla_EARTH	slERTH   
+sla_ECLEQ	slECEQ   
+sla_ECMAT	slECMA   
+sla_ECOR	slECOR   
+sla_EG50	slEG50   
+sla_EL2UE       slELUE   
+sla_EPB		slEPB   
+sla_EPB2D	slEB2D   
+sla_EPCO	slEPCO   
+sla_EPJ		slEPJ   
+sla_EPJ2D	slEJ2D   
+sla_EQECL	slEQEC   
+sla_EQEQX	slEQEX   
+sla_EQGAL	slEQGA   
+sla_ETRMS	slETRM   
+sla_EULER	slEULR   
+sla_EVP		slEVP   
+	
+sla_FITXY	slFTXY   
+sla_FK425	slFK45   
+sla_FK45Z	slF45Z   
+sla_FK524	slFK54   
+sla_FK52H	slFK5H   
+sla_FK54Z	slF54Z   
+sla_FK5HZ	slF5HZ   
+sla_FLOTIN	slRFLI   
+	
+sla_GALEQ	slGAEQ   
+sla_GALSUP	slGASU   
+sla_GE50	slGE50   
+sla_GEOC	slGEOC   
+sla_GMST	slGMST   
+sla_GMSTA	slGMSA   
+sla_GRESID	slGRES   
+	
+sla_H2E		slH2E   
+sla_H2FK5       slHFK5   
+sla_HFK5Z       slHF5Z      
+	
+sla__IDCHI	slICHI   
+sla__IDCHF	slICHF   
+sla_IMXV	slIMXV   
+sla_INTIN	slINTI   
+sla_INVF	slINVF   
+	
+sla_KBJ		slKBJ   
+	
+sla_M2AV	slM2AV   
+sla_MAP		slMAP   
+sla_MAPPA	slMAPA   
+sla_MAPQK	slMAPQ   
+sla_MAPQKZ	slMAPZ   
+sla_MOON	slMOON   
+sla_MXM		slMXM   
+sla_MXV		slMXV   
+	
+sla_NUT		slNUT   
+sla_NUTC	slNUTC   
+	
+sla_OBS		slOBS   
+sla_OAP		slOAP   
+sla_OAPQK	slOAPQ   
+	
+sla_PA		slPA   
+sla_PAV		slPAV   
+sla_PCD		slPCD   
+sla_PDA2H	slPDAH   
+sla_PDQ2H	slPDQH   
+sla_PERTEL      slPRTL   
+sla_PERTUE      slPRTE   
+sla_PLANEL      slPLNE   
+sla_PLANET	slPLNT   
+sla_PLANTE      slPLTE   
+sla_PM		slPM   
+sla_POLMO       slPLMO
+sla_PREBN	slPRBN   
+sla_PREC	slPREC   
+sla_PRECES	slPRCE   
+sla_PRECL	slPREL   
+sla_PRENUT	slPRNU   
+sla_PV2EL       slPVEL   
+sla_PV2UE       slPVUE   
+sla_PVOBS	slPVOB   
+sla_PXY		slPXY   
+	
+sla_RANDOM	slRNDM   
+sla_RANGE	slRA1P   
+sla_RANORM	slRA2P   
+sla_RCC		slRCC   
+sla_RDPLAN	slRDPL   
+sla_REFCO	slRFCO   
+sla_REFCOQ	slRFCQ   
+sla_REFRO	slRFRO   
+sla_REFV	slREFV   
+sla_REFZ	slREFZ   
+sla_RVEROT	slRVER   
+sla_RVGALC	slRVGA   
+sla_RVLG	slRVLG   
+sla_RVLSRD	slRVLD   
+sla_RVLSRK	slRVLK   
+	
+sla_S2TP	slS2TP   
+sla_SEP		slSEP   
+sla_SMAT	slSMAT   
+sla_SUBET	slSUET   
+sla_SUPGAL	slSUGA   
+sla_SVD		slSVD   
+sla_SVDCOV	slSVDC   
+sla_SVDSOL	slSVDS   
+	
+sla_TP2S	slTP2S   
+sla_TP2V	slTP2V   
+sla_TPS2C	slTPSC   
+sla_TPV2C	slTPVC   
+	
+sla_UE2EL       slUEEL   
+sla_UE2PV       slUEPV   
+sla_UNPCD	slUPCD   
+	
+sla_V2TP	slV2TP   
+sla_VDV		slVDV   
+sla_VN		slVN   
+sla_VXV		slVXV   
+	
+sla_WAIT	slWAIT   
+	
+sla_XY2XY	slXYXY   
+sla_ZD		slZD   
diff --git a/math/slalib/nut.f b/math/slalib/nut.f
new file mode 100644
index 00000000..b3cbf192
--- /dev/null
+++ b/math/slalib/nut.f
@@ -0,0 +1,76 @@
+      SUBROUTINE slNUT (DATE, RMATN)
+*+
+*     - - - -
+*      N U T
+*     - - - -
+*
+*  Form the matrix of nutation for a given date - Shirai & Fukushima
+*  2001 theory (double precision)
+*
+*  Reference:
+*     Shirai, T. & Fukushima, T., Astron.J. 121, 3270-3283 (2001).
+*
+*  Given:
+*     DATE    d          TDB (loosely ET) as Modified Julian Date
+*                                           (=JD-2400000.5)
+*  Returned:
+*     RMATN   d(3,3)     nutation matrix
+*
+*  Notes:
+*
+*  1  The matrix is in the sense  v(true) = rmatn * v(mean) .
+*     where v(true) is the star vector relative to the true equator and
+*     equinox of date and v(mean) is the star vector relative to the
+*     mean equator and equinox of date.
+*
+*  2  The matrix represents forced nutation (but not free core
+*     nutation) plus corrections to the IAU~1976 precession model.
+*
+*  3  Earth attitude predictions made by combining the present nutation
+*     matrix with IAU~1976 precession are accurate to 1~mas (with
+*     respect to the ICRS) for a few decades around 2000.
+*
+*  4  The distinction between the required TDB and TT is always
+*     negligible.  Moreover, for all but the most critical applications
+*     UTC is adequate.
+*
+*  Called:   slNUTC, slDEUL
+*
+*  Last revision:   1 December 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,RMATN(3,3)
+
+      DOUBLE PRECISION DPSI,DEPS,EPS0
+
+
+
+*  Nutation components and mean obliquity
+      CALL slNUTC(DATE,DPSI,DEPS,EPS0)
+
+*  Rotation matrix
+      CALL slDEUL('XZX',EPS0,-DPSI,-(EPS0+DEPS),RMATN)
+
+      END
diff --git a/math/slalib/nutc.f b/math/slalib/nutc.f
new file mode 100644
index 00000000..95affe1b
--- /dev/null
+++ b/math/slalib/nutc.f
@@ -0,0 +1,831 @@
+      SUBROUTINE slNUTC (DATE, DPSI, DEPS, EPS0)
+*+
+*     - - - - -
+*      N U T C
+*     - - - - -
+*
+*  Nutation:  longitude & obliquity components and mean obliquity,
+*  using the Shirai & Fukushima (2001) theory.
+*
+*  Given:
+*     DATE        d    TDB (loosely ET) as Modified Julian Date
+*                                            (JD-2400000.5)
+*  Returned:
+*     DPSI,DEPS   d    nutation in longitude,obliquity
+*     EPS0        d    mean obliquity
+*
+*  Notes:
+*
+*  1  The routine predicts forced nutation (but not free core nutation)
+*     plus corrections to the IAU 1976 precession model.
+*
+*  2  Earth attitude predictions made by combining the present nutation
+*     model with IAU 1976 precession are accurate to 1 mas (with respect
+*     to the ICRF) for a few decades around 2000.
+*
+*  3  The slNUTC80 routine is the equivalent of the present routine
+*     but using the IAU 1980 nutation theory.  The older theory is less
+*     accurate, leading to errors as large as 350 mas over the interval
+*     1900-2100, mainly because of the error in the IAU 1976 precession.
+*
+*  References:
+*
+*     Shirai, T. & Fukushima, T., Astron.J. 121, 3270-3283 (2001).
+*
+*     Fukushima, T., Astron.Astrophys. 244, L11 (1991).
+*
+*     Simon, J. L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
+*     Francou, G. & Laskar, J., Astron.Astrophys. 282, 663 (1994).
+*
+*  This revision:   24 November 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,DPSI,DEPS,EPS0
+
+*  Degrees to radians
+      DOUBLE PRECISION DD2R
+      PARAMETER (DD2R=1.745329251994329576923691D-2)
+
+*  Arc seconds to radians
+      DOUBLE PRECISION DAS2R
+      PARAMETER (DAS2R=4.848136811095359935899141D-6)
+
+*  Arc seconds in a full circle
+      DOUBLE PRECISION TURNAS
+      PARAMETER (TURNAS=1296000D0)
+
+*  Reference epoch (J2000), MJD
+      DOUBLE PRECISION DJM0
+      PARAMETER (DJM0=51544.5D0 )
+
+*  Days per Julian century
+      DOUBLE PRECISION DJC
+      PARAMETER (DJC=36525D0)
+
+      INTEGER I,J
+      DOUBLE PRECISION T,EL,ELP,F,D,OM,VE,MA,JU,SA,THETA,C,S,DP,DE
+
+*  Number of terms in the nutation model
+      INTEGER NTERMS
+      PARAMETER (NTERMS=194)
+
+*  The SF2001 forced nutation model
+      INTEGER NA(9,NTERMS)
+      DOUBLE PRECISION PSI(4,NTERMS), EPS(4,NTERMS)
+
+*  Coefficients of fundamental angles
+      DATA ( ( NA(I,J), I=1,9 ), J=1,10 ) /
+     :    0,   0,   0,   0,  -1,   0,   0,   0,   0,
+     :    0,   0,   2,  -2,   2,   0,   0,   0,   0,
+     :    0,   0,   2,   0,   2,   0,   0,   0,   0,
+     :    0,   0,   0,   0,  -2,   0,   0,   0,   0,
+     :    0,   1,   0,   0,   0,   0,   0,   0,   0,
+     :    0,   1,   2,  -2,   2,   0,   0,   0,   0,
+     :    1,   0,   0,   0,   0,   0,   0,   0,   0,
+     :    0,   0,   2,   0,   1,   0,   0,   0,   0,
+     :    1,   0,   2,   0,   2,   0,   0,   0,   0,
+     :    0,  -1,   2,  -2,   2,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=11,20 ) /
+     :    0,   0,   2,  -2,   1,   0,   0,   0,   0,
+     :   -1,   0,   2,   0,   2,   0,   0,   0,   0,
+     :   -1,   0,   0,   2,   0,   0,   0,   0,   0,
+     :    1,   0,   0,   0,   1,   0,   0,   0,   0,
+     :    1,   0,   0,   0,  -1,   0,   0,   0,   0,
+     :   -1,   0,   2,   2,   2,   0,   0,   0,   0,
+     :    1,   0,   2,   0,   1,   0,   0,   0,   0,
+     :   -2,   0,   2,   0,   1,   0,   0,   0,   0,
+     :    0,   0,   0,   2,   0,   0,   0,   0,   0,
+     :    0,   0,   2,   2,   2,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=21,30 ) /
+     :    2,   0,   0,  -2,   0,   0,   0,   0,   0,
+     :    2,   0,   2,   0,   2,   0,   0,   0,   0,
+     :    1,   0,   2,  -2,   2,   0,   0,   0,   0,
+     :   -1,   0,   2,   0,   1,   0,   0,   0,   0,
+     :    2,   0,   0,   0,   0,   0,   0,   0,   0,
+     :    0,   0,   2,   0,   0,   0,   0,   0,   0,
+     :    0,   1,   0,   0,   1,   0,   0,   0,   0,
+     :   -1,   0,   0,   2,   1,   0,   0,   0,   0,
+     :    0,   2,   2,  -2,   2,   0,   0,   0,   0,
+     :    0,   0,   2,  -2,   0,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=31,40 ) /
+     :   -1,   0,   0,   2,  -1,   0,   0,   0,   0,
+     :    0,   1,   0,   0,  -1,   0,   0,   0,   0,
+     :    0,   2,   0,   0,   0,   0,   0,   0,   0,
+     :   -1,   0,   2,   2,   1,   0,   0,   0,   0,
+     :    1,   0,   2,   2,   2,   0,   0,   0,   0,
+     :    0,   1,   2,   0,   2,   0,   0,   0,   0,
+     :   -2,   0,   2,   0,   0,   0,   0,   0,   0,
+     :    0,   0,   2,   2,   1,   0,   0,   0,   0,
+     :    0,  -1,   2,   0,   2,   0,   0,   0,   0,
+     :    0,   0,   0,   2,   1,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=41,50 ) /
+     :    1,   0,   2,  -2,   1,   0,   0,   0,   0,
+     :    2,   0,   0,  -2,  -1,   0,   0,   0,   0,
+     :    2,   0,   2,  -2,   2,   0,   0,   0,   0,
+     :    2,   0,   2,   0,   1,   0,   0,   0,   0,
+     :    0,   0,   0,   2,  -1,   0,   0,   0,   0,
+     :    0,  -1,   2,  -2,   1,   0,   0,   0,   0,
+     :   -1,  -1,   0,   2,   0,   0,   0,   0,   0,
+     :    2,   0,   0,  -2,   1,   0,   0,   0,   0,
+     :    1,   0,   0,   2,   0,   0,   0,   0,   0,
+     :    0,   1,   2,  -2,   1,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=51,60 ) /
+     :    1,  -1,   0,   0,   0,   0,   0,   0,   0,
+     :   -2,   0,   2,   0,   2,   0,   0,   0,   0,
+     :    0,  -1,   0,   2,   0,   0,   0,   0,   0,
+     :    3,   0,   2,   0,   2,   0,   0,   0,   0,
+     :    0,   0,   0,   1,   0,   0,   0,   0,   0,
+     :    1,  -1,   2,   0,   2,   0,   0,   0,   0,
+     :    1,   0,   0,  -1,   0,   0,   0,   0,   0,
+     :   -1,  -1,   2,   2,   2,   0,   0,   0,   0,
+     :   -1,   0,   2,   0,   0,   0,   0,   0,   0,
+     :    2,   0,   0,   0,  -1,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=61,70 ) /
+     :    0,  -1,   2,   2,   2,   0,   0,   0,   0,
+     :    1,   1,   2,   0,   2,   0,   0,   0,   0,
+     :    2,   0,   0,   0,   1,   0,   0,   0,   0,
+     :    1,   1,   0,   0,   0,   0,   0,   0,   0,
+     :    1,   0,  -2,   2,  -1,   0,   0,   0,   0,
+     :    1,   0,   2,   0,   0,   0,   0,   0,   0,
+     :   -1,   1,   0,   1,   0,   0,   0,   0,   0,
+     :    1,   0,   0,   0,   2,   0,   0,   0,   0,
+     :   -1,   0,   1,   0,   1,   0,   0,   0,   0,
+     :    0,   0,   2,   1,   2,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=71,80 ) /
+     :   -1,   1,   0,   1,   1,   0,   0,   0,   0,
+     :   -1,   0,   2,   4,   2,   0,   0,   0,   0,
+     :    0,  -2,   2,  -2,   1,   0,   0,   0,   0,
+     :    1,   0,   2,   2,   1,   0,   0,   0,   0,
+     :    1,   0,   0,   0,  -2,   0,   0,   0,   0,
+     :   -2,   0,   2,   2,   2,   0,   0,   0,   0,
+     :    1,   1,   2,  -2,   2,   0,   0,   0,   0,
+     :   -2,   0,   2,   4,   2,   0,   0,   0,   0,
+     :   -1,   0,   4,   0,   2,   0,   0,   0,   0,
+     :    2,   0,   2,  -2,   1,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=81,90 ) /
+     :    1,   0,   0,  -1,  -1,   0,   0,   0,   0,
+     :    2,   0,   2,   2,   2,   0,   0,   0,   0,
+     :    1,   0,   0,   2,   1,   0,   0,   0,   0,
+     :    3,   0,   0,   0,   0,   0,   0,   0,   0,
+     :    0,   0,   2,  -2,  -1,   0,   0,   0,   0,
+     :    3,   0,   2,  -2,   2,   0,   0,   0,   0,
+     :    0,   0,   4,  -2,   2,   0,   0,   0,   0,
+     :   -1,   0,   0,   4,   0,   0,   0,   0,   0,
+     :    0,   1,   2,   0,   1,   0,   0,   0,   0,
+     :    0,   0,   2,  -2,   3,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=91,100 ) /
+     :   -2,   0,   0,   4,   0,   0,   0,   0,   0,
+     :   -1,  -1,   0,   2,   1,   0,   0,   0,   0,
+     :   -2,   0,   2,   0,  -1,   0,   0,   0,   0,
+     :    0,   0,   2,   0,  -1,   0,   0,   0,   0,
+     :    0,  -1,   2,   0,   1,   0,   0,   0,   0,
+     :    0,   1,   0,   0,   2,   0,   0,   0,   0,
+     :    0,   0,   2,  -1,   2,   0,   0,   0,   0,
+     :    2,   1,   0,  -2,   0,   0,   0,   0,   0,
+     :    0,   0,   2,   4,   2,   0,   0,   0,   0,
+     :   -1,  -1,   0,   2,  -1,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=101,110 ) /
+     :   -1,   1,   0,   2,   0,   0,   0,   0,   0,
+     :    1,  -1,   0,   0,   1,   0,   0,   0,   0,
+     :    0,  -1,   2,  -2,   0,   0,   0,   0,   0,
+     :    0,   1,   0,   0,  -2,   0,   0,   0,   0,
+     :    1,  -1,   2,   2,   2,   0,   0,   0,   0,
+     :    1,   0,   0,   2,  -1,   0,   0,   0,   0,
+     :   -1,   1,   2,   2,   2,   0,   0,   0,   0,
+     :    3,   0,   2,   0,   1,   0,   0,   0,   0,
+     :    0,   1,   2,   2,   2,   0,   0,   0,   0,
+     :    1,   0,   2,  -2,   0,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=111,120 ) /
+     :   -1,   0,  -2,   4,  -1,   0,   0,   0,   0,
+     :   -1,  -1,   2,   2,   1,   0,   0,   0,   0,
+     :    0,  -1,   2,   2,   1,   0,   0,   0,   0,
+     :    2,  -1,   2,   0,   2,   0,   0,   0,   0,
+     :    0,   0,   0,   2,   2,   0,   0,   0,   0,
+     :    1,  -1,   2,   0,   1,   0,   0,   0,   0,
+     :   -1,   1,   2,   0,   2,   0,   0,   0,   0,
+     :    0,   1,   0,   2,   0,   0,   0,   0,   0,
+     :    0,   1,   2,  -2,   0,   0,   0,   0,   0,
+     :    0,   3,   2,  -2,   2,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=121,130 ) /
+     :    0,   0,   0,   1,   1,   0,   0,   0,   0,
+     :   -1,   0,   2,   2,   0,   0,   0,   0,   0,
+     :    2,   1,   2,   0,   2,   0,   0,   0,   0,
+     :    1,   1,   0,   0,   1,   0,   0,   0,   0,
+     :    2,   0,   0,   2,   0,   0,   0,   0,   0,
+     :    1,   1,   2,   0,   1,   0,   0,   0,   0,
+     :   -1,   0,   0,   2,   2,   0,   0,   0,   0,
+     :    1,   0,  -2,   2,   0,   0,   0,   0,   0,
+     :    0,  -1,   0,   2,  -1,   0,   0,   0,   0,
+     :   -1,   0,   1,   0,   2,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=131,140 ) /
+     :    0,   1,   0,   1,   0,   0,   0,   0,   0,
+     :    1,   0,  -2,   2,  -2,   0,   0,   0,   0,
+     :    0,   0,   0,   1,  -1,   0,   0,   0,   0,
+     :    1,  -1,   0,   0,  -1,   0,   0,   0,   0,
+     :    0,   0,   0,   4,   0,   0,   0,   0,   0,
+     :    1,  -1,   0,   2,   0,   0,   0,   0,   0,
+     :    1,   0,   2,   1,   2,   0,   0,   0,   0,
+     :    1,   0,   2,  -1,   2,   0,   0,   0,   0,
+     :   -1,   0,   0,   2,  -2,   0,   0,   0,   0,
+     :    0,   0,   2,   1,   1,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=141,150 ) /
+     :   -1,   0,   2,   0,  -1,   0,   0,   0,   0,
+     :   -1,   0,   2,   4,   1,   0,   0,   0,   0,
+     :    0,   0,   2,   2,   0,   0,   0,   0,   0,
+     :    1,   1,   2,  -2,   1,   0,   0,   0,   0,
+     :    0,   0,   1,   0,   1,   0,   0,   0,   0,
+     :   -1,   0,   2,  -1,   1,   0,   0,   0,   0,
+     :   -2,   0,   2,   2,   1,   0,   0,   0,   0,
+     :    2,  -1,   0,   0,   0,   0,   0,   0,   0,
+     :    4,   0,   2,   0,   2,   0,   0,   0,   0,
+     :    2,   1,   2,  -2,   2,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=151,160 ) /
+     :    0,   1,   2,   1,   2,   0,   0,   0,   0,
+     :    1,   0,   4,  -2,   2,   0,   0,   0,   0,
+     :    1,   1,   0,   0,  -1,   0,   0,   0,   0,
+     :   -2,   0,   2,   4,   1,   0,   0,   0,   0,
+     :    2,   0,   2,   0,   0,   0,   0,   0,   0,
+     :   -1,   0,   1,   0,   0,   0,   0,   0,   0,
+     :    1,   0,   0,   1,   0,   0,   0,   0,   0,
+     :    0,   1,   0,   2,   1,   0,   0,   0,   0,
+     :   -1,   0,   4,   0,   1,   0,   0,   0,   0,
+     :   -1,   0,   0,   4,   1,   0,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=161,170 ) /
+     :    2,   0,   2,   2,   1,   0,   0,   0,   0,
+     :    2,   1,   0,   0,   0,   0,   0,   0,   0,
+     :    0,   0,   5,  -5,   5,  -3,   0,   0,   0,
+     :    0,   0,   0,   0,   0,   0,   0,   2,   0,
+     :    0,   0,   1,  -1,   1,   0,   0,  -1,   0,
+     :    0,   0,  -1,   1,  -1,   1,   0,   0,   0,
+     :    0,   0,  -1,   1,   0,   0,   2,   0,   0,
+     :    0,   0,   3,  -3,   3,   0,   0,  -1,   0,
+     :    0,   0,  -8,   8,  -7,   5,   0,   0,   0,
+     :    0,   0,  -1,   1,  -1,   0,   2,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=171,180 ) /
+     :    0,   0,  -2,   2,  -2,   2,   0,   0,   0,
+     :    0,   0,  -6,   6,  -6,   4,   0,   0,   0,
+     :    0,   0,  -2,   2,  -2,   0,   8,  -3,   0,
+     :    0,   0,   6,  -6,   6,   0,  -8,   3,   0,
+     :    0,   0,   4,  -4,   4,  -2,   0,   0,   0,
+     :    0,   0,  -3,   3,  -3,   2,   0,   0,   0,
+     :    0,   0,   4,  -4,   3,   0,  -8,   3,   0,
+     :    0,   0,  -4,   4,  -5,   0,   8,  -3,   0,
+     :    0,   0,   0,   0,   0,   2,   0,   0,   0,
+     :    0,   0,  -4,   4,  -4,   3,   0,   0,   0 /
+      DATA ( ( NA(I,J), I=1,9 ), J=181,190 ) /
+     :    0,   1,  -1,   1,  -1,   0,   0,   1,   0,
+     :    0,   0,   0,   0,   0,   0,   0,   1,   0,
+     :    0,   0,   1,  -1,   1,   1,   0,   0,   0,
+     :    0,   0,   2,  -2,   2,   0,  -2,   0,   0,
+     :    0,  -1,  -7,   7,  -7,   5,   0,   0,   0,
+     :   -2,   0,   2,   0,   2,   0,   0,  -2,   0,
+     :   -2,   0,   2,   0,   1,   0,   0,  -3,   0,
+     :    0,   0,   2,  -2,   2,   0,   0,  -2,   0,
+     :    0,   0,   1,  -1,   1,   0,   0,   1,   0,
+     :    0,   0,   0,   0,   0,   0,   0,   0,   2 /
+      DATA ( ( NA(I,J), I=1,9 ), J=191,NTERMS ) /
+     :    0,   0,   0,   0,   0,   0,   0,   0,   1,
+     :    2,   0,  -2,   0,  -2,   0,   0,   3,   0,
+     :    0,   0,   1,  -1,   1,   0,   0,  -2,   0,
+     :    0,   0,  -7,   7,  -7,   5,   0,   0,   0 /
+
+*  Nutation series: longitude
+      DATA ( ( PSI(I,J), I=1,4 ), J=1,10 ) /
+     :  3341.5D0, 17206241.8D0,  3.1D0, 17409.5D0,
+     : -1716.8D0, -1317185.3D0,  1.4D0,  -156.8D0,
+     :   285.7D0,  -227667.0D0,  0.3D0,   -23.5D0,
+     :   -68.6D0,  -207448.0D0,  0.0D0,   -21.4D0,
+     :   950.3D0,   147607.9D0, -2.3D0,  -355.0D0,
+     :   -66.7D0,   -51689.1D0,  0.2D0,   122.6D0,
+     :  -108.6D0,    71117.6D0,  0.0D0,     7.0D0,
+     :    35.6D0,   -38740.2D0,  0.1D0,   -36.2D0,
+     :    85.4D0,   -30127.6D0,  0.0D0,    -3.1D0,
+     :     9.0D0,    21583.0D0,  0.1D0,   -50.3D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=11,20 ) /
+     :    22.1D0,    12822.8D0,  0.0D0,    13.3D0,
+     :     3.4D0,    12350.8D0,  0.0D0,     1.3D0,
+     :   -21.1D0,    15699.4D0,  0.0D0,     1.6D0,
+     :     4.2D0,     6313.8D0,  0.0D0,     6.2D0,
+     :   -22.8D0,     5796.9D0,  0.0D0,     6.1D0,
+     :    15.7D0,    -5961.1D0,  0.0D0,    -0.6D0,
+     :    13.1D0,    -5159.1D0,  0.0D0,    -4.6D0,
+     :     1.8D0,     4592.7D0,  0.0D0,     4.5D0,
+     :   -17.5D0,     6336.0D0,  0.0D0,     0.7D0,
+     :    16.3D0,    -3851.1D0,  0.0D0,    -0.4D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=21,30 ) /
+     :    -2.8D0,     4771.7D0,  0.0D0,     0.5D0,
+     :    13.8D0,    -3099.3D0,  0.0D0,    -0.3D0,
+     :     0.2D0,     2860.3D0,  0.0D0,     0.3D0,
+     :     1.4D0,     2045.3D0,  0.0D0,     2.0D0,
+     :    -8.6D0,     2922.6D0,  0.0D0,     0.3D0,
+     :    -7.7D0,     2587.9D0,  0.0D0,     0.2D0,
+     :     8.8D0,    -1408.1D0,  0.0D0,     3.7D0,
+     :     1.4D0,     1517.5D0,  0.0D0,     1.5D0,
+     :    -1.9D0,    -1579.7D0,  0.0D0,     7.7D0,
+     :     1.3D0,    -2178.6D0,  0.0D0,    -0.2D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=31,40 ) /
+     :    -4.8D0,     1286.8D0,  0.0D0,     1.3D0,
+     :     6.3D0,     1267.2D0,  0.0D0,    -4.0D0,
+     :    -1.0D0,     1669.3D0,  0.0D0,    -8.3D0,
+     :     2.4D0,    -1020.0D0,  0.0D0,    -0.9D0,
+     :     4.5D0,     -766.9D0,  0.0D0,     0.0D0,
+     :    -1.1D0,      756.5D0,  0.0D0,    -1.7D0,
+     :    -1.4D0,    -1097.3D0,  0.0D0,    -0.5D0,
+     :     2.6D0,     -663.0D0,  0.0D0,    -0.6D0,
+     :     0.8D0,     -714.1D0,  0.0D0,     1.6D0,
+     :     0.4D0,     -629.9D0,  0.0D0,    -0.6D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=41,50 ) /
+     :     0.3D0,      580.4D0,  0.0D0,     0.6D0,
+     :    -1.6D0,      577.3D0,  0.0D0,     0.5D0,
+     :    -0.9D0,      644.4D0,  0.0D0,     0.0D0,
+     :     2.2D0,     -534.0D0,  0.0D0,    -0.5D0,
+     :    -2.5D0,      493.3D0,  0.0D0,     0.5D0,
+     :    -0.1D0,     -477.3D0,  0.0D0,    -2.4D0,
+     :    -0.9D0,      735.0D0,  0.0D0,    -1.7D0,
+     :     0.7D0,      406.2D0,  0.0D0,     0.4D0,
+     :    -2.8D0,      656.9D0,  0.0D0,     0.0D0,
+     :     0.6D0,      358.0D0,  0.0D0,     2.0D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=51,60 ) /
+     :    -0.7D0,      472.5D0,  0.0D0,    -1.1D0,
+     :    -0.1D0,     -300.5D0,  0.0D0,     0.0D0,
+     :    -1.2D0,      435.1D0,  0.0D0,    -1.0D0,
+     :     1.8D0,     -289.4D0,  0.0D0,     0.0D0,
+     :     0.6D0,     -422.6D0,  0.0D0,     0.0D0,
+     :     0.8D0,     -287.6D0,  0.0D0,     0.6D0,
+     :   -38.6D0,     -392.3D0,  0.0D0,     0.0D0,
+     :     0.7D0,     -281.8D0,  0.0D0,     0.6D0,
+     :     0.6D0,     -405.7D0,  0.0D0,     0.0D0,
+     :    -1.2D0,      229.0D0,  0.0D0,     0.2D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=61,70 ) /
+     :     1.1D0,     -264.3D0,  0.0D0,     0.5D0,
+     :    -0.7D0,      247.9D0,  0.0D0,    -0.5D0,
+     :    -0.2D0,      218.0D0,  0.0D0,     0.2D0,
+     :     0.6D0,     -339.0D0,  0.0D0,     0.8D0,
+     :    -0.7D0,      198.7D0,  0.0D0,     0.2D0,
+     :    -1.5D0,      334.0D0,  0.0D0,     0.0D0,
+     :     0.1D0,      334.0D0,  0.0D0,     0.0D0,
+     :    -0.1D0,     -198.1D0,  0.0D0,     0.0D0,
+     :  -106.6D0,        0.0D0,  0.0D0,     0.0D0,
+     :    -0.5D0,      165.8D0,  0.0D0,     0.0D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=71,80 ) /
+     :     0.0D0,      134.8D0,  0.0D0,     0.0D0,
+     :     0.9D0,     -151.6D0,  0.0D0,     0.0D0,
+     :     0.0D0,     -129.7D0,  0.0D0,     0.0D0,
+     :     0.8D0,     -132.8D0,  0.0D0,    -0.1D0,
+     :     0.5D0,     -140.7D0,  0.0D0,     0.0D0,
+     :    -0.1D0,      138.4D0,  0.0D0,     0.0D0,
+     :     0.0D0,      129.0D0,  0.0D0,    -0.3D0,
+     :     0.5D0,     -121.2D0,  0.0D0,     0.0D0,
+     :    -0.3D0,      114.5D0,  0.0D0,     0.0D0,
+     :    -0.1D0,      101.8D0,  0.0D0,     0.0D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=81,90 ) /
+     :    -3.6D0,     -101.9D0,  0.0D0,     0.0D0,
+     :     0.8D0,     -109.4D0,  0.0D0,     0.0D0,
+     :     0.2D0,      -97.0D0,  0.0D0,     0.0D0,
+     :    -0.7D0,      157.3D0,  0.0D0,     0.0D0,
+     :     0.2D0,      -83.3D0,  0.0D0,     0.0D0,
+     :    -0.3D0,       93.3D0,  0.0D0,     0.0D0,
+     :    -0.1D0,       92.1D0,  0.0D0,     0.0D0,
+     :    -0.5D0,      133.6D0,  0.0D0,     0.0D0,
+     :    -0.1D0,       81.5D0,  0.0D0,     0.0D0,
+     :     0.0D0,      123.9D0,  0.0D0,     0.0D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=91,100 ) /
+     :    -0.3D0,      128.1D0,  0.0D0,     0.0D0,
+     :     0.1D0,       74.1D0,  0.0D0,    -0.3D0,
+     :    -0.2D0,      -70.3D0,  0.0D0,     0.0D0,
+     :    -0.4D0,       66.6D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -66.7D0,  0.0D0,     0.0D0,
+     :    -0.7D0,       69.3D0,  0.0D0,    -0.3D0,
+     :     0.0D0,      -70.4D0,  0.0D0,     0.0D0,
+     :    -0.1D0,      101.5D0,  0.0D0,     0.0D0,
+     :     0.5D0,      -69.1D0,  0.0D0,     0.0D0,
+     :    -0.2D0,       58.5D0,  0.0D0,     0.2D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=101,110 ) /
+     :     0.1D0,      -94.9D0,  0.0D0,     0.2D0,
+     :     0.0D0,       52.9D0,  0.0D0,    -0.2D0,
+     :     0.1D0,       86.7D0,  0.0D0,    -0.2D0,
+     :    -0.1D0,      -59.2D0,  0.0D0,     0.2D0,
+     :     0.3D0,      -58.8D0,  0.0D0,     0.1D0,
+     :    -0.3D0,       49.0D0,  0.0D0,     0.0D0,
+     :    -0.2D0,       56.9D0,  0.0D0,    -0.1D0,
+     :     0.3D0,      -50.2D0,  0.0D0,     0.0D0,
+     :    -0.2D0,       53.4D0,  0.0D0,    -0.1D0,
+     :     0.1D0,      -76.5D0,  0.0D0,     0.0D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=111,120 ) /
+     :    -0.2D0,       45.3D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -46.8D0,  0.0D0,     0.0D0,
+     :     0.2D0,      -44.6D0,  0.0D0,     0.0D0,
+     :     0.2D0,      -48.7D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -46.8D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -42.0D0,  0.0D0,     0.0D0,
+     :     0.0D0,       46.4D0,  0.0D0,    -0.1D0,
+     :     0.2D0,      -67.3D0,  0.0D0,     0.1D0,
+     :     0.0D0,      -65.8D0,  0.0D0,     0.2D0,
+     :    -0.1D0,      -43.9D0,  0.0D0,     0.3D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=121,130 ) /
+     :     0.0D0,      -38.9D0,  0.0D0,     0.0D0,
+     :    -0.3D0,       63.9D0,  0.0D0,     0.0D0,
+     :    -0.2D0,       41.2D0,  0.0D0,     0.0D0,
+     :     0.0D0,      -36.1D0,  0.0D0,     0.2D0,
+     :    -0.3D0,       58.5D0,  0.0D0,     0.0D0,
+     :    -0.1D0,       36.1D0,  0.0D0,     0.0D0,
+     :     0.0D0,      -39.7D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -57.7D0,  0.0D0,     0.0D0,
+     :    -0.2D0,       33.4D0,  0.0D0,     0.0D0,
+     :    36.4D0,        0.0D0,  0.0D0,     0.0D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=131,140 ) /
+     :    -0.1D0,       55.7D0,  0.0D0,    -0.1D0,
+     :     0.1D0,      -35.4D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -31.0D0,  0.0D0,     0.0D0,
+     :    -0.1D0,       30.1D0,  0.0D0,     0.0D0,
+     :    -0.3D0,       49.2D0,  0.0D0,     0.0D0,
+     :    -0.2D0,       49.1D0,  0.0D0,     0.0D0,
+     :    -0.1D0,       33.6D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -33.5D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -31.0D0,  0.0D0,     0.0D0,
+     :    -0.1D0,       28.0D0,  0.0D0,     0.0D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=141,150 ) /
+     :     0.1D0,      -25.2D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -26.2D0,  0.0D0,     0.0D0,
+     :    -0.2D0,       41.5D0,  0.0D0,     0.0D0,
+     :     0.0D0,       24.5D0,  0.0D0,     0.1D0,
+     :   -16.2D0,        0.0D0,  0.0D0,     0.0D0,
+     :     0.0D0,      -22.3D0,  0.0D0,     0.0D0,
+     :     0.0D0,       23.1D0,  0.0D0,     0.0D0,
+     :    -0.1D0,       37.5D0,  0.0D0,     0.0D0,
+     :     0.2D0,      -25.7D0,  0.0D0,     0.0D0,
+     :     0.0D0,       25.2D0,  0.0D0,     0.0D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=151,160 ) /
+     :     0.1D0,      -24.5D0,  0.0D0,     0.0D0,
+     :    -0.1D0,       24.3D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -20.7D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -20.8D0,  0.0D0,     0.0D0,
+     :    -0.2D0,       33.4D0,  0.0D0,     0.0D0,
+     :    32.9D0,        0.0D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -32.6D0,  0.0D0,     0.0D0,
+     :     0.0D0,       19.9D0,  0.0D0,     0.0D0,
+     :    -0.1D0,       19.6D0,  0.0D0,     0.0D0,
+     :     0.0D0,      -18.7D0,  0.0D0,     0.0D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=161,170 ) /
+     :     0.1D0,      -19.0D0,  0.0D0,     0.0D0,
+     :     0.1D0,      -28.6D0,  0.0D0,     0.0D0,
+     :     4.0D0,      178.8D0,-11.8D0,     0.3D0,
+     :    39.8D0,     -107.3D0, -5.6D0,    -1.0D0,
+     :     9.9D0,      164.0D0, -4.1D0,     0.1D0,
+     :    -4.8D0,     -135.3D0, -3.4D0,    -0.1D0,
+     :    50.5D0,       75.0D0,  1.4D0,    -1.2D0,
+     :    -1.1D0,      -53.5D0,  1.3D0,     0.0D0,
+     :   -45.0D0,       -2.4D0, -0.4D0,     6.6D0,
+     :   -11.5D0,      -61.0D0, -0.9D0,     0.4D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=171,180 ) /
+     :     4.4D0,      -68.4D0, -3.4D0,     0.0D0,
+     :     7.7D0,      -47.1D0, -4.7D0,    -1.0D0,
+     :   -42.9D0,      -12.6D0, -1.2D0,     4.2D0,
+     :   -42.8D0,       12.7D0, -1.2D0,    -4.2D0,
+     :    -7.6D0,      -44.1D0,  2.1D0,    -0.5D0,
+     :   -64.1D0,        1.7D0,  0.2D0,     4.5D0,
+     :    36.4D0,      -10.4D0,  1.0D0,     3.5D0,
+     :    35.6D0,       10.2D0,  1.0D0,    -3.5D0,
+     :    -1.7D0,       39.5D0,  2.0D0,     0.0D0,
+     :    50.9D0,       -8.2D0, -0.8D0,    -5.0D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=181,190 ) /
+     :     0.0D0,       52.3D0,  1.2D0,     0.0D0,
+     :   -42.9D0,      -17.8D0,  0.4D0,     0.0D0,
+     :     2.6D0,       34.3D0,  0.8D0,     0.0D0,
+     :    -0.8D0,      -48.6D0,  2.4D0,    -0.1D0,
+     :    -4.9D0,       30.5D0,  3.7D0,     0.7D0,
+     :     0.0D0,      -43.6D0,  2.1D0,     0.0D0,
+     :     0.0D0,      -25.4D0,  1.2D0,     0.0D0,
+     :     2.0D0,       40.9D0, -2.0D0,     0.0D0,
+     :    -2.1D0,       26.1D0,  0.6D0,     0.0D0,
+     :    22.6D0,       -3.2D0, -0.5D0,    -0.5D0 /
+      DATA ( ( PSI(I,J), I=1,4 ), J=191,NTERMS ) /
+     :    -7.6D0,       24.9D0, -0.4D0,    -0.2D0,
+     :    -6.2D0,       34.9D0,  1.7D0,     0.3D0,
+     :     2.0D0,       17.4D0, -0.4D0,     0.1D0,
+     :    -3.9D0,       20.5D0,  2.4D0,     0.6D0 /
+
+*  Nutation series: obliquity
+      DATA ( ( EPS(I,J), I=1,4 ), J=1,10 ) /
+     : 9205365.8D0, -1506.2D0,  885.7D0, -0.2D0,
+     :  573095.9D0,  -570.2D0, -305.0D0, -0.3D0,
+     :   97845.5D0,   147.8D0,  -48.8D0, -0.2D0,
+     :  -89753.6D0,    28.0D0,   46.9D0,  0.0D0,
+     :    7406.7D0,  -327.1D0,  -18.2D0,  0.8D0,
+     :   22442.3D0,   -22.3D0,  -67.6D0,  0.0D0,
+     :    -683.6D0,    46.8D0,    0.0D0,  0.0D0,
+     :   20070.7D0,    36.0D0,    1.6D0,  0.0D0,
+     :   12893.8D0,    39.5D0,   -6.2D0,  0.0D0,
+     :   -9593.2D0,    14.4D0,   30.2D0, -0.1D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=11,20 ) /
+     :   -6899.5D0,     4.8D0,   -0.6D0,  0.0D0,
+     :   -5332.5D0,    -0.1D0,    2.7D0,  0.0D0,
+     :    -125.2D0,    10.5D0,    0.0D0,  0.0D0,
+     :   -3323.4D0,    -0.9D0,   -0.3D0,  0.0D0,
+     :    3142.3D0,     8.9D0,    0.3D0,  0.0D0,
+     :    2552.5D0,     7.3D0,   -1.2D0,  0.0D0,
+     :    2634.4D0,     8.8D0,    0.2D0,  0.0D0,
+     :   -2424.4D0,     1.6D0,   -0.4D0,  0.0D0,
+     :    -123.3D0,     3.9D0,    0.0D0,  0.0D0,
+     :    1642.4D0,     7.3D0,   -0.8D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=21,30 ) /
+     :      47.9D0,     3.2D0,    0.0D0,  0.0D0,
+     :    1321.2D0,     6.2D0,   -0.6D0,  0.0D0,
+     :   -1234.1D0,    -0.3D0,    0.6D0,  0.0D0,
+     :   -1076.5D0,    -0.3D0,    0.0D0,  0.0D0,
+     :     -61.6D0,     1.8D0,    0.0D0,  0.0D0,
+     :     -55.4D0,     1.6D0,    0.0D0,  0.0D0,
+     :     856.9D0,    -4.9D0,   -2.1D0,  0.0D0,
+     :    -800.7D0,    -0.1D0,    0.0D0,  0.0D0,
+     :     685.1D0,    -0.6D0,   -3.8D0,  0.0D0,
+     :     -16.9D0,    -1.5D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=31,40 ) /
+     :     695.7D0,     1.8D0,    0.0D0,  0.0D0,
+     :     642.2D0,    -2.6D0,   -1.6D0,  0.0D0,
+     :      13.3D0,     1.1D0,   -0.1D0,  0.0D0,
+     :     521.9D0,     1.6D0,    0.0D0,  0.0D0,
+     :     325.8D0,     2.0D0,   -0.1D0,  0.0D0,
+     :    -325.1D0,    -0.5D0,    0.9D0,  0.0D0,
+     :      10.1D0,     0.3D0,    0.0D0,  0.0D0,
+     :     334.5D0,     1.6D0,    0.0D0,  0.0D0,
+     :     307.1D0,     0.4D0,   -0.9D0,  0.0D0,
+     :     327.2D0,     0.5D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=41,50 ) /
+     :    -304.6D0,    -0.1D0,    0.0D0,  0.0D0,
+     :     304.0D0,     0.6D0,    0.0D0,  0.0D0,
+     :    -276.8D0,    -0.5D0,    0.1D0,  0.0D0,
+     :     268.9D0,     1.3D0,    0.0D0,  0.0D0,
+     :     271.8D0,     1.1D0,    0.0D0,  0.0D0,
+     :     271.5D0,    -0.4D0,   -0.8D0,  0.0D0,
+     :      -5.2D0,     0.5D0,    0.0D0,  0.0D0,
+     :    -220.5D0,     0.1D0,    0.0D0,  0.0D0,
+     :     -20.1D0,     0.3D0,    0.0D0,  0.0D0,
+     :    -191.0D0,     0.1D0,    0.5D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=51,60 ) /
+     :      -4.1D0,     0.3D0,    0.0D0,  0.0D0,
+     :     130.6D0,    -0.1D0,    0.0D0,  0.0D0,
+     :       3.0D0,     0.3D0,    0.0D0,  0.0D0,
+     :     122.9D0,     0.8D0,    0.0D0,  0.0D0,
+     :       3.7D0,    -0.3D0,    0.0D0,  0.0D0,
+     :     123.1D0,     0.4D0,   -0.3D0,  0.0D0,
+     :     -52.7D0,    15.3D0,    0.0D0,  0.0D0,
+     :     120.7D0,     0.3D0,   -0.3D0,  0.0D0,
+     :       4.0D0,    -0.3D0,    0.0D0,  0.0D0,
+     :     126.5D0,     0.5D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=61,70 ) /
+     :     112.7D0,     0.5D0,   -0.3D0,  0.0D0,
+     :    -106.1D0,    -0.3D0,    0.3D0,  0.0D0,
+     :    -112.9D0,    -0.2D0,    0.0D0,  0.0D0,
+     :       3.6D0,    -0.2D0,    0.0D0,  0.0D0,
+     :     107.4D0,     0.3D0,    0.0D0,  0.0D0,
+     :     -10.9D0,     0.2D0,    0.0D0,  0.0D0,
+     :      -0.9D0,     0.0D0,    0.0D0,  0.0D0,
+     :      85.4D0,     0.0D0,    0.0D0,  0.0D0,
+     :       0.0D0,   -88.8D0,    0.0D0,  0.0D0,
+     :     -71.0D0,    -0.2D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=71,80 ) /
+     :     -70.3D0,     0.0D0,    0.0D0,  0.0D0,
+     :      64.5D0,     0.4D0,    0.0D0,  0.0D0,
+     :      69.8D0,     0.0D0,    0.0D0,  0.0D0,
+     :      66.1D0,     0.4D0,    0.0D0,  0.0D0,
+     :     -61.0D0,    -0.2D0,    0.0D0,  0.0D0,
+     :     -59.5D0,    -0.1D0,    0.0D0,  0.0D0,
+     :     -55.6D0,     0.0D0,    0.2D0,  0.0D0,
+     :      51.7D0,     0.2D0,    0.0D0,  0.0D0,
+     :     -49.0D0,    -0.1D0,    0.0D0,  0.0D0,
+     :     -52.7D0,    -0.1D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=81,90 ) /
+     :     -49.6D0,     1.4D0,    0.0D0,  0.0D0,
+     :      46.3D0,     0.4D0,    0.0D0,  0.0D0,
+     :      49.6D0,     0.1D0,    0.0D0,  0.0D0,
+     :      -5.1D0,     0.1D0,    0.0D0,  0.0D0,
+     :     -44.0D0,    -0.1D0,    0.0D0,  0.0D0,
+     :     -39.9D0,    -0.1D0,    0.0D0,  0.0D0,
+     :     -39.5D0,    -0.1D0,    0.0D0,  0.0D0,
+     :      -3.9D0,     0.1D0,    0.0D0,  0.0D0,
+     :     -42.1D0,    -0.1D0,    0.0D0,  0.0D0,
+     :     -17.2D0,     0.1D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=91,100 ) /
+     :      -2.3D0,     0.1D0,    0.0D0,  0.0D0,
+     :     -39.2D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -38.4D0,     0.1D0,    0.0D0,  0.0D0,
+     :      36.8D0,     0.2D0,    0.0D0,  0.0D0,
+     :      34.6D0,     0.1D0,    0.0D0,  0.0D0,
+     :     -32.7D0,     0.3D0,    0.0D0,  0.0D0,
+     :      30.4D0,     0.0D0,    0.0D0,  0.0D0,
+     :       0.4D0,     0.1D0,    0.0D0,  0.0D0,
+     :      29.3D0,     0.2D0,    0.0D0,  0.0D0,
+     :      31.6D0,     0.1D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=101,110 ) /
+     :       0.8D0,    -0.1D0,    0.0D0,  0.0D0,
+     :     -27.9D0,     0.0D0,    0.0D0,  0.0D0,
+     :       2.9D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -25.3D0,     0.0D0,    0.0D0,  0.0D0,
+     :      25.0D0,     0.1D0,    0.0D0,  0.0D0,
+     :      27.5D0,     0.1D0,    0.0D0,  0.0D0,
+     :     -24.4D0,    -0.1D0,    0.0D0,  0.0D0,
+     :      24.9D0,     0.2D0,    0.0D0,  0.0D0,
+     :     -22.8D0,    -0.1D0,    0.0D0,  0.0D0,
+     :       0.9D0,    -0.1D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=111,120 ) /
+     :      24.4D0,     0.1D0,    0.0D0,  0.0D0,
+     :      23.9D0,     0.1D0,    0.0D0,  0.0D0,
+     :      22.5D0,     0.1D0,    0.0D0,  0.0D0,
+     :      20.8D0,     0.1D0,    0.0D0,  0.0D0,
+     :      20.1D0,     0.0D0,    0.0D0,  0.0D0,
+     :      21.5D0,     0.1D0,    0.0D0,  0.0D0,
+     :     -20.0D0,     0.0D0,    0.0D0,  0.0D0,
+     :       1.4D0,     0.0D0,    0.0D0,  0.0D0,
+     :      -0.2D0,    -0.1D0,    0.0D0,  0.0D0,
+     :      19.0D0,     0.0D0,   -0.1D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=121,130 ) /
+     :      20.5D0,     0.0D0,    0.0D0,  0.0D0,
+     :      -2.0D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -17.6D0,    -0.1D0,    0.0D0,  0.0D0,
+     :      19.0D0,     0.0D0,    0.0D0,  0.0D0,
+     :      -2.4D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -18.4D0,    -0.1D0,    0.0D0,  0.0D0,
+     :      17.1D0,     0.0D0,    0.0D0,  0.0D0,
+     :       0.4D0,     0.0D0,    0.0D0,  0.0D0,
+     :      18.4D0,     0.1D0,    0.0D0,  0.0D0,
+     :       0.0D0,    17.4D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=131,140 ) /
+     :      -0.6D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -15.4D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -16.8D0,    -0.1D0,    0.0D0,  0.0D0,
+     :      16.3D0,     0.0D0,    0.0D0,  0.0D0,
+     :      -2.0D0,     0.0D0,    0.0D0,  0.0D0,
+     :      -1.5D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -14.3D0,    -0.1D0,    0.0D0,  0.0D0,
+     :      14.4D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -13.4D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -14.3D0,    -0.1D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=141,150 ) /
+     :     -13.7D0,     0.0D0,    0.0D0,  0.0D0,
+     :      13.1D0,     0.1D0,    0.0D0,  0.0D0,
+     :      -1.7D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -12.8D0,     0.0D0,    0.0D0,  0.0D0,
+     :       0.0D0,   -14.4D0,    0.0D0,  0.0D0,
+     :      12.4D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -12.0D0,     0.0D0,    0.0D0,  0.0D0,
+     :      -0.8D0,     0.0D0,    0.0D0,  0.0D0,
+     :      10.9D0,     0.1D0,    0.0D0,  0.0D0,
+     :     -10.8D0,     0.0D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=151,160 ) /
+     :      10.5D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -10.4D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -11.2D0,     0.0D0,    0.0D0,  0.0D0,
+     :      10.5D0,     0.1D0,    0.0D0,  0.0D0,
+     :      -1.4D0,     0.0D0,    0.0D0,  0.0D0,
+     :       0.0D0,     0.1D0,    0.0D0,  0.0D0,
+     :       0.7D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -10.3D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -10.0D0,     0.0D0,    0.0D0,  0.0D0,
+     :       9.6D0,     0.0D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=161,170 ) /
+     :       9.4D0,     0.1D0,    0.0D0,  0.0D0,
+     :       0.6D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -87.7D0,     4.4D0,   -0.4D0, -6.3D0,
+     :      46.3D0,    22.4D0,    0.5D0, -2.4D0,
+     :      15.6D0,    -3.4D0,    0.1D0,  0.4D0,
+     :       5.2D0,     5.8D0,    0.2D0, -0.1D0,
+     :     -30.1D0,    26.9D0,    0.7D0,  0.0D0,
+     :      23.2D0,    -0.5D0,    0.0D0,  0.6D0,
+     :       1.0D0,    23.2D0,    3.4D0,  0.0D0,
+     :     -12.2D0,    -4.3D0,    0.0D0,  0.0D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=171,180 ) /
+     :      -2.1D0,    -3.7D0,   -0.2D0,  0.1D0,
+     :     -18.6D0,    -3.8D0,   -0.4D0,  1.8D0,
+     :       5.5D0,   -18.7D0,   -1.8D0, -0.5D0,
+     :      -5.5D0,   -18.7D0,    1.8D0, -0.5D0,
+     :      18.4D0,    -3.6D0,    0.3D0,  0.9D0,
+     :      -0.6D0,     1.3D0,    0.0D0,  0.0D0,
+     :      -5.6D0,   -19.5D0,    1.9D0,  0.0D0,
+     :       5.5D0,   -19.1D0,   -1.9D0,  0.0D0,
+     :     -17.3D0,    -0.8D0,    0.0D0,  0.9D0,
+     :      -3.2D0,    -8.3D0,   -0.8D0,  0.3D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=181,190 ) /
+     :      -0.1D0,     0.0D0,    0.0D0,  0.0D0,
+     :      -5.4D0,     7.8D0,   -0.3D0,  0.0D0,
+     :     -14.8D0,     1.4D0,    0.0D0,  0.3D0,
+     :      -3.8D0,     0.4D0,    0.0D0, -0.2D0,
+     :      12.6D0,     3.2D0,    0.5D0, -1.5D0,
+     :       0.1D0,     0.0D0,    0.0D0,  0.0D0,
+     :     -13.6D0,     2.4D0,   -0.1D0,  0.0D0,
+     :       0.9D0,     1.2D0,    0.0D0,  0.0D0,
+     :     -11.9D0,    -0.5D0,    0.0D0,  0.3D0,
+     :       0.4D0,    12.0D0,    0.3D0, -0.2D0 /
+      DATA ( ( EPS(I,J), I=1,4 ), J=191,NTERMS ) /
+     :       8.3D0,     6.1D0,   -0.1D0,  0.1D0,
+     :       0.0D0,     0.0D0,    0.0D0,  0.0D0,
+     :       0.4D0,   -10.8D0,    0.3D0,  0.0D0,
+     :       9.6D0,     2.2D0,    0.3D0, -1.2D0 /
+
+
+
+*  Interval between fundamental epoch J2000.0 and given epoch (JC).
+      T = (DATE-DJM0)/DJC
+
+*  Mean anomaly of the Moon.
+      EL  = 134.96340251D0*DD2R+
+     :      MOD(T*(1717915923.2178D0+
+     :          T*(        31.8792D0+
+     :          T*(         0.051635D0+
+     :          T*(       - 0.00024470D0)))),TURNAS)*DAS2R
+
+*  Mean anomaly of the Sun.
+      ELP = 357.52910918D0*DD2R+
+     :      MOD(T*( 129596581.0481D0+
+     :          T*(       - 0.5532D0+
+     :          T*(         0.000136D0+
+     :          T*(       - 0.00001149D0)))),TURNAS)*DAS2R
+
+*  Mean argument of the latitude of the Moon.
+      F   =  93.27209062D0*DD2R+
+     :      MOD(T*(1739527262.8478D0+
+     :          T*(      - 12.7512D0+
+     :          T*(      -  0.001037D0+
+     :          T*(         0.00000417D0)))),TURNAS)*DAS2R
+
+*  Mean elongation of the Moon from the Sun.
+      D   = 297.85019547D0*DD2R+
+     :      MOD(T*(1602961601.2090D0+
+     :          T*(       - 6.3706D0+
+     :          T*(         0.006539D0+
+     :          T*(       - 0.00003169D0)))),TURNAS)*DAS2R
+
+*  Mean longitude of the ascending node of the Moon.
+      OM  = 125.04455501D0*DD2R+
+     :      MOD(T*( - 6962890.5431D0+
+     :          T*(         7.4722D0+
+     :          T*(         0.007702D0+
+     :          T*(       - 0.00005939D0)))),TURNAS)*DAS2R
+
+*  Mean longitude of Venus.
+      VE    = 181.97980085D0*DD2R+MOD(210664136.433548D0*T,TURNAS)*DAS2R
+
+*  Mean longitude of Mars.
+      MA    = 355.43299958D0*DD2R+MOD( 68905077.493988D0*T,TURNAS)*DAS2R
+
+*  Mean longitude of Jupiter.
+      JU    =  34.35151874D0*DD2R+MOD( 10925660.377991D0*T,TURNAS)*DAS2R
+
+*  Mean longitude of Saturn.
+      SA    =  50.07744430D0*DD2R+MOD(  4399609.855732D0*T,TURNAS)*DAS2R
+
+*  Geodesic nutation (Fukushima 1991) in microarcsec.
+      DP = -153.1D0*SIN(ELP)-1.9D0*SIN(2D0*ELP)
+      DE = 0D0
+
+*  Shirai & Fukushima (2001) nutation series.
+      DO J=NTERMS,1,-1
+         THETA = DBLE(NA(1,J))*EL+
+     :           DBLE(NA(2,J))*ELP+
+     :           DBLE(NA(3,J))*F+
+     :           DBLE(NA(4,J))*D+
+     :           DBLE(NA(5,J))*OM+
+     :           DBLE(NA(6,J))*VE+
+     :           DBLE(NA(7,J))*MA+
+     :           DBLE(NA(8,J))*JU+
+     :           DBLE(NA(9,J))*SA
+         C = COS(THETA)
+         S = SIN(THETA)
+         DP = DP+(PSI(1,J)+PSI(3,J)*T)*C+(PSI(2,J)+PSI(4,J)*T)*S
+         DE = DE+(EPS(1,J)+EPS(3,J)*T)*C+(EPS(2,J)+EPS(4,J)*T)*S
+      END DO
+
+*  Change of units, and addition of the precession correction.
+      DPSI = (DP*1D-6-0.042888D0-0.29856D0*T)*DAS2R
+      DEPS = (DE*1D-6-0.005171D0-0.02408D0*T)*DAS2R
+
+*  Mean obliquity of date (Simon et al. 1994).
+      EPS0 = (84381.412D0+
+     :         (-46.80927D0+
+     :          (-0.000152D0+
+     :           (0.0019989D0+
+     :          (-0.00000051D0+
+     :          (-0.000000025D0)*T)*T)*T)*T)*T)*DAS2R
+
+      END
diff --git a/math/slalib/nutc80.f b/math/slalib/nutc80.f
new file mode 100644
index 00000000..4d27e331
--- /dev/null
+++ b/math/slalib/nutc80.f
@@ -0,0 +1,476 @@
+      SUBROUTINE slNUTC80 (DATE, DPSI, DEPS, EPS0)
+*+
+*     - - - - - - -
+*      N U T C 8 0
+*     - - - - - - -
+*
+*  Nutation:  longitude & obliquity components and mean obliquity,
+*  using the IAU 1980 theory (double precision)
+*
+*  Given:
+*     DATE        d     TDB (loosely ET) as Modified Julian Date
+*                                            (JD-2400000.5)
+*  Returned:
+*     DPSI,DEPS   d     nutation in longitude,obliquity
+*     EPS0        d     mean obliquity
+*
+*  Called:  slDA1P
+*
+*  Notes:
+*
+*  1  Earth attitude predictions made by combining the present nutation
+*     model with IAU 1976 precession are accurate to 0.35 arcsec over
+*     the interval 1900-2100.  (The accuracy is much better near the
+*     middle of the interval.)
+*
+*  2  The slNUTC routine is the equivalent of the present routine
+*     but using the Shirai & Fukushima 2001 forced nutation theory
+*     (SF2001).  The newer theory is more accurate than IAU 1980,
+*     within 1 mas (with respect to the ICRF) for a few decades around
+*     2000.  The improvement is mainly because of the corrections to the
+*     IAU 1976 precession that the SF2001 theory includes.
+*
+*  References:
+*     Final report of the IAU Working Group on Nutation,
+*      chairman P.K.Seidelmann, 1980.
+*     Kaplan,G.H., 1981, USNO circular no. 163, pA3-6.
+*
+*  P.T.Wallace   Starlink   7 October 2001
+*
+*  Copyright (C) 2001 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,DPSI,DEPS,EPS0
+
+      DOUBLE PRECISION T2AS,AS2R,U2R
+      DOUBLE PRECISION T,EL,EL2,EL3
+      DOUBLE PRECISION ELP,ELP2
+      DOUBLE PRECISION F,F2,F4
+      DOUBLE PRECISION D,D2,D4
+      DOUBLE PRECISION OM,OM2
+      DOUBLE PRECISION DP,DE
+      DOUBLE PRECISION A
+
+      DOUBLE PRECISION slDA1P
+
+
+*  Turns to arc seconds
+      PARAMETER (T2AS=1296000D0)
+*  Arc seconds to radians
+      PARAMETER (AS2R=0.484813681109535994D-5)
+*  Units of 0.0001 arcsec to radians
+      PARAMETER (U2R=AS2R/1D4)
+
+
+
+
+*  Interval between basic epoch J2000.0 and current epoch (JC)
+      T=(DATE-51544.5D0)/36525D0
+
+*
+*  FUNDAMENTAL ARGUMENTS in the FK5 reference system
+*
+
+*  Mean longitude of the Moon minus mean longitude of the Moon's perigee
+      EL=slDA1P(AS2R*(485866.733D0+(1325D0*T2AS+715922.633D0
+     :                   +(31.310D0+0.064D0*T)*T)*T))
+
+*  Mean longitude of the Sun minus mean longitude of the Sun's perigee
+      ELP=slDA1P(AS2R*(1287099.804D0+(99D0*T2AS+1292581.224D0
+     :                   +(-0.577D0-0.012D0*T)*T)*T))
+
+*  Mean longitude of the Moon minus mean longitude of the Moon's node
+      F=slDA1P(AS2R*(335778.877D0+(1342D0*T2AS+295263.137D0
+     :                   +(-13.257D0+0.011D0*T)*T)*T))
+
+*  Mean elongation of the Moon from the Sun
+      D=slDA1P(AS2R*(1072261.307D0+(1236D0*T2AS+1105601.328D0
+     :                   +(-6.891D0+0.019D0*T)*T)*T))
+
+*  Longitude of the mean ascending node of the lunar orbit on the
+*   ecliptic, measured from the mean equinox of date
+      OM=slDA1P(AS2R*(450160.280D0+(-5D0*T2AS-482890.539D0
+     :                   +(7.455D0+0.008D0*T)*T)*T))
+
+*  Multiples of arguments
+      EL2=EL+EL
+      EL3=EL2+EL
+      ELP2=ELP+ELP
+      F2=F+F
+      F4=F2+F2
+      D2=D+D
+      D4=D2+D2
+      OM2=OM+OM
+
+
+*
+*  SERIES FOR THE NUTATION
+*
+      DP=0D0
+      DE=0D0
+
+*  106
+      DP=DP+SIN(ELP+D)
+*  105
+      DP=DP-SIN(F2+D4+OM2)
+*  104
+      DP=DP+SIN(EL2+D2)
+*  103
+      DP=DP-SIN(EL-F2+D2)
+*  102
+      DP=DP-SIN(EL+ELP-D2+OM)
+*  101
+      DP=DP-SIN(-ELP+F2+OM)
+*  100
+      DP=DP-SIN(EL-F2-D2)
+*  99
+      DP=DP-SIN(ELP+D2)
+*  98
+      DP=DP-SIN(F2-D+OM2)
+*  97
+      DP=DP-SIN(-F2+OM)
+*  96
+      DP=DP+SIN(-EL-ELP+D2+OM)
+*  95
+      DP=DP+SIN(ELP+F2+OM)
+*  94
+      DP=DP-SIN(EL+F2-D2)
+*  93
+      DP=DP+SIN(EL3+F2-D2+OM2)
+*  92
+      DP=DP+SIN(F4-D2+OM2)
+*  91
+      DP=DP-SIN(EL+D2+OM)
+*  90
+      DP=DP-SIN(EL2+F2+D2+OM2)
+*  89
+      A=EL2+F2-D2+OM
+      DP=DP+SIN(A)
+      DE=DE-COS(A)
+*  88
+      DP=DP+SIN(EL-ELP-D2)
+*  87
+      DP=DP+SIN(-EL+F4+OM2)
+*  86
+      A=-EL2+F2+D4+OM2
+      DP=DP-SIN(A)
+      DE=DE+COS(A)
+*  85
+      A=EL+F2+D2+OM
+      DP=DP-SIN(A)
+      DE=DE+COS(A)
+*  84
+      A=EL+ELP+F2-D2+OM2
+      DP=DP+SIN(A)
+      DE=DE-COS(A)
+*  83
+      DP=DP-SIN(EL2-D4)
+*  82
+      A=-EL+F2+D4+OM2
+      DP=DP-2D0*SIN(A)
+      DE=DE+COS(A)
+*  81
+      A=-EL2+F2+D2+OM2
+      DP=DP+SIN(A)
+      DE=DE-COS(A)
+*  80
+      DP=DP-SIN(EL-D4)
+*  79
+      A=-EL+OM2
+      DP=DP+SIN(A)
+      DE=DE-COS(A)
+*  78
+      A=F2+D+OM2
+      DP=DP+2D0*SIN(A)
+      DE=DE-COS(A)
+*  77
+      DP=DP+2D0*SIN(EL3)
+*  76
+      A=EL+OM2
+      DP=DP-2D0*SIN(A)
+      DE=DE+COS(A)
+*  75
+      A=EL2+OM
+      DP=DP+2D0*SIN(A)
+      DE=DE-COS(A)
+*  74
+      A=-EL+F2-D2+OM
+      DP=DP-2D0*SIN(A)
+      DE=DE+COS(A)
+*  73
+      A=EL+ELP+F2+OM2
+      DP=DP+2D0*SIN(A)
+      DE=DE-COS(A)
+*  72
+      A=-ELP+F2+D2+OM2
+      DP=DP-3D0*SIN(A)
+      DE=DE+COS(A)
+*  71
+      A=EL3+F2+OM2
+      DP=DP-3D0*SIN(A)
+      DE=DE+COS(A)
+*  70
+      A=-EL2+OM
+      DP=DP-2D0*SIN(A)
+      DE=DE+COS(A)
+*  69
+      A=-EL-ELP+F2+D2+OM2
+      DP=DP-3D0*SIN(A)
+      DE=DE+COS(A)
+*  68
+      A=EL-ELP+F2+OM2
+      DP=DP-3D0*SIN(A)
+      DE=DE+COS(A)
+*  67
+      DP=DP+3D0*SIN(EL+F2)
+*  66
+      DP=DP-3D0*SIN(EL+ELP)
+*  65
+      DP=DP-4D0*SIN(D)
+*  64
+      DP=DP+4D0*SIN(EL-F2)
+*  63
+      DP=DP-4D0*SIN(ELP-D2)
+*  62
+      A=EL2+F2+OM
+      DP=DP-5D0*SIN(A)
+      DE=DE+3D0*COS(A)
+*  61
+      DP=DP+5D0*SIN(EL-ELP)
+*  60
+      A=-D2+OM
+      DP=DP-5D0*SIN(A)
+      DE=DE+3D0*COS(A)
+*  59
+      A=EL+F2-D2+OM
+      DP=DP+6D0*SIN(A)
+      DE=DE-3D0*COS(A)
+*  58
+      A=F2+D2+OM
+      DP=DP-7D0*SIN(A)
+      DE=DE+3D0*COS(A)
+*  57
+      A=D2+OM
+      DP=DP-6D0*SIN(A)
+      DE=DE+3D0*COS(A)
+*  56
+      A=EL2+F2-D2+OM2
+      DP=DP+6D0*SIN(A)
+      DE=DE-3D0*COS(A)
+*  55
+      DP=DP+6D0*SIN(EL+D2)
+*  54
+      A=EL+F2+D2+OM2
+      DP=DP-8D0*SIN(A)
+      DE=DE+3D0*COS(A)
+*  53
+      A=-ELP+F2+OM2
+      DP=DP-7D0*SIN(A)
+      DE=DE+3D0*COS(A)
+*  52
+      A=ELP+F2+OM2
+      DP=DP+7D0*SIN(A)
+      DE=DE-3D0*COS(A)
+*  51
+      DP=DP-7D0*SIN(EL+ELP-D2)
+*  50
+      A=-EL+F2+D2+OM
+      DP=DP-10D0*SIN(A)
+      DE=DE+5D0*COS(A)
+*  49
+      A=EL-D2+OM
+      DP=DP-13D0*SIN(A)
+      DE=DE+7D0*COS(A)
+*  48
+      A=-EL+D2+OM
+      DP=DP+16D0*SIN(A)
+      DE=DE-8D0*COS(A)
+*  47
+      A=-EL+F2+OM
+      DP=DP+21D0*SIN(A)
+      DE=DE-10D0*COS(A)
+*  46
+      DP=DP+26D0*SIN(F2)
+      DE=DE-COS(F2)
+*  45
+      A=EL2+F2+OM2
+      DP=DP-31D0*SIN(A)
+      DE=DE+13D0*COS(A)
+*  44
+      A=EL+F2-D2+OM2
+      DP=DP+29D0*SIN(A)
+      DE=DE-12D0*COS(A)
+*  43
+      DP=DP+29D0*SIN(EL2)
+      DE=DE-COS(EL2)
+*  42
+      A=F2+D2+OM2
+      DP=DP-38D0*SIN(A)
+      DE=DE+16D0*COS(A)
+*  41
+      A=EL+F2+OM
+      DP=DP-51D0*SIN(A)
+      DE=DE+27D0*COS(A)
+*  40
+      A=-EL+F2+D2+OM2
+      DP=DP-59D0*SIN(A)
+      DE=DE+26D0*COS(A)
+*  39
+      A=-EL+OM
+      DP=DP+(-58D0-0.1D0*T)*SIN(A)
+      DE=DE+32D0*COS(A)
+*  38
+      A=EL+OM
+      DP=DP+(63D0+0.1D0*T)*SIN(A)
+      DE=DE-33D0*COS(A)
+*  37
+      DP=DP+63D0*SIN(D2)
+      DE=DE-2D0*COS(D2)
+*  36
+      A=-EL+F2+OM2
+      DP=DP+123D0*SIN(A)
+      DE=DE-53D0*COS(A)
+*  35
+      A=EL-D2
+      DP=DP-158D0*SIN(A)
+      DE=DE-COS(A)
+*  34
+      A=EL+F2+OM2
+      DP=DP-301D0*SIN(A)
+      DE=DE+(129D0-0.1D0*T)*COS(A)
+*  33
+      A=F2+OM
+      DP=DP+(-386D0-0.4D0*T)*SIN(A)
+      DE=DE+200D0*COS(A)
+*  32
+      DP=DP+(712D0+0.1D0*T)*SIN(EL)
+      DE=DE-7D0*COS(EL)
+*  31
+      A=F2+OM2
+      DP=DP+(-2274D0-0.2D0*T)*SIN(A)
+      DE=DE+(977D0-0.5D0*T)*COS(A)
+*  30
+      DP=DP-SIN(ELP+F2-D2)
+*  29
+      DP=DP+SIN(-EL+D+OM)
+*  28
+      DP=DP+SIN(ELP+OM2)
+*  27
+      DP=DP-SIN(ELP-F2+D2)
+*  26
+      DP=DP+SIN(-F2+D2+OM)
+*  25
+      DP=DP+SIN(EL2+ELP-D2)
+*  24
+      DP=DP-4D0*SIN(EL-D)
+*  23
+      A=ELP+F2-D2+OM
+      DP=DP+4D0*SIN(A)
+      DE=DE-2D0*COS(A)
+*  22
+      A=EL2-D2+OM
+      DP=DP+4D0*SIN(A)
+      DE=DE-2D0*COS(A)
+*  21
+      A=-ELP+F2-D2+OM
+      DP=DP-5D0*SIN(A)
+      DE=DE+3D0*COS(A)
+*  20
+      A=-EL2+D2+OM
+      DP=DP-6D0*SIN(A)
+      DE=DE+3D0*COS(A)
+*  19
+      A=-ELP+OM
+      DP=DP-12D0*SIN(A)
+      DE=DE+6D0*COS(A)
+*  18
+      A=ELP2+F2-D2+OM2
+      DP=DP+(-16D0+0.1D0*T)*SIN(A)
+      DE=DE+7D0*COS(A)
+*  17
+      A=ELP+OM
+      DP=DP-15D0*SIN(A)
+      DE=DE+9D0*COS(A)
+*  16
+      DP=DP+(17D0-0.1D0*T)*SIN(ELP2)
+*  15
+      DP=DP-22D0*SIN(F2-D2)
+*  14
+      A=EL2-D2
+      DP=DP+48D0*SIN(A)
+      DE=DE+COS(A)
+*  13
+      A=F2-D2+OM
+      DP=DP+(129D0+0.1D0*T)*SIN(A)
+      DE=DE-70D0*COS(A)
+*  12
+      A=-ELP+F2-D2+OM2
+      DP=DP+(217D0-0.5D0*T)*SIN(A)
+      DE=DE+(-95D0+0.3D0*T)*COS(A)
+*  11
+      A=ELP+F2-D2+OM2
+      DP=DP+(-517D0+1.2D0*T)*SIN(A)
+      DE=DE+(224D0-0.6D0*T)*COS(A)
+*  10
+      DP=DP+(1426D0-3.4D0*T)*SIN(ELP)
+      DE=DE+(54D0-0.1D0*T)*COS(ELP)
+*  9
+      A=F2-D2+OM2
+      DP=DP+(-13187D0-1.6D0*T)*SIN(A)
+      DE=DE+(5736D0-3.1D0*T)*COS(A)
+*  8
+      DP=DP+SIN(EL2-F2+OM)
+*  7
+      A=-ELP2+F2-D2+OM
+      DP=DP-2D0*SIN(A)
+      DE=DE+1D0*COS(A)
+*  6
+      DP=DP-3D0*SIN(EL-ELP-D)
+*  5
+      A=-EL2+F2+OM2
+      DP=DP-3D0*SIN(A)
+      DE=DE+1D0*COS(A)
+*  4
+      DP=DP+11D0*SIN(EL2-F2)
+*  3
+      A=-EL2+F2+OM
+      DP=DP+46D0*SIN(A)
+      DE=DE-24D0*COS(A)
+*  2
+      DP=DP+(2062D0+0.2D0*T)*SIN(OM2)
+      DE=DE+(-895D0+0.5D0*T)*COS(OM2)
+*  1
+      DP=DP+(-171996D0-174.2D0*T)*SIN(OM)
+      DE=DE+(92025D0+8.9D0*T)*COS(OM)
+
+*  Convert results to radians
+      DPSI=DP*U2R
+      DEPS=DE*U2R
+
+*  Mean obliquity
+      EPS0=AS2R*(84381.448D0+
+     :           (-46.8150D0+
+     :           (-0.00059D0+
+     :           0.001813D0*T)*T)*T)
+
+      END
diff --git a/math/slalib/oap.f b/math/slalib/oap.f
new file mode 100644
index 00000000..1e851d50
--- /dev/null
+++ b/math/slalib/oap.f
@@ -0,0 +1,193 @@
+      SUBROUTINE slOAP ( TYPE, OB1, OB2, DATE, DUT, ELONGM, PHIM,
+     :                     HM, XP, YP, TDK, PMB, RH, WL, TLR,
+     :                     RAP, DAP )
+*+
+*     - - - -
+*      O A P
+*     - - - -
+*
+*  Observed to apparent place.
+*
+*  Given:
+*     TYPE   c*(*)  type of coordinates - 'R', 'H' or 'A' (see below)
+*     OB1    d      observed Az, HA or RA (radians; Az is N=0,E=90)
+*     OB2    d      observed ZD or Dec (radians)
+*     DATE   d      UTC date/time (modified Julian Date, JD-2400000.5)
+*     DUT    d      delta UT:  UT1-UTC (UTC seconds)
+*     ELONGM d      mean longitude of the observer (radians, east +ve)
+*     PHIM   d      mean geodetic latitude of the observer (radians)
+*     HM     d      observer's height above sea level (metres)
+*     XP     d      polar motion x-coordinate (radians)
+*     YP     d      polar motion y-coordinate (radians)
+*     TDK    d      local ambient temperature (K; std=273.15D0)
+*     PMB    d      local atmospheric pressure (mb; std=1013.25D0)
+*     RH     d      local relative humidity (in the range 0D0-1D0)
+*     WL     d      effective wavelength (micron, e.g. 0.55D0)
+*     TLR    d      tropospheric lapse rate (K/metre, e.g. 0.0065D0)
+*
+*  Returned:
+*     RAP    d      geocentric apparent right ascension
+*     DAP    d      geocentric apparent declination
+*
+*  Notes:
+*
+*  1)  Only the first character of the TYPE argument is significant.
+*      'R' or 'r' indicates that OBS1 and OBS2 are the observed right
+*      ascension and declination;  'H' or 'h' indicates that they are
+*      hour angle (west +ve) and declination;  anything else ('A' or
+*      'a' is recommended) indicates that OBS1 and OBS2 are azimuth
+*      (north zero, east 90 deg) and zenith distance.  (Zenith
+*      distance is used rather than elevation in order to reflect the
+*      fact that no allowance is made for depression of the horizon.)
+*
+*  2)  The accuracy of the result is limited by the corrections for
+*      refraction.  Providing the meteorological parameters are
+*      known accurately and there are no gross local effects, the
+*      predicted apparent RA,Dec should be within about 0.1 arcsec
+*      for a zenith distance of less than 70 degrees.  Even at a
+*      topocentric zenith distance of 90 degrees, the accuracy in
+*      elevation should be better than 1 arcmin;  useful results
+*      are available for a further 3 degrees, beyond which the
+*      slRFRO routine returns a fixed value of the refraction.
+*      The complementary routines slAOP (or slAOPQ) and slOAP
+*      (or slOAPQ) are self-consistent to better than 1 micro-
+*      arcsecond all over the celestial sphere.
+*
+*  3)  It is advisable to take great care with units, as even
+*      unlikely values of the input parameters are accepted and
+*      processed in accordance with the models used.
+*
+*  4)  "Observed" Az,El means the position that would be seen by a
+*      perfect theodolite located at the observer.  This is
+*      related to the observed HA,Dec via the standard rotation, using
+*      the geodetic latitude (corrected for polar motion), while the
+*      observed HA and RA are related simply through the local
+*      apparent ST.  "Observed" RA,Dec or HA,Dec thus means the
+*      position that would be seen by a perfect equatorial located
+*      at the observer and with its polar axis aligned to the
+*      Earth's axis of rotation (n.b. not to the refracted pole).
+*      By removing from the observed place the effects of
+*      atmospheric refraction and diurnal aberration, the
+*      geocentric apparent RA,Dec is obtained.
+*
+*  5)  Frequently, mean rather than apparent RA,Dec will be required,
+*      in which case further transformations will be necessary.  The
+*      slAMP etc routines will convert the apparent RA,Dec produced
+*      by the present routine into an "FK5" (J2000) mean place, by
+*      allowing for the Sun's gravitational lens effect, annual
+*      aberration, nutation and precession.  Should "FK4" (1950)
+*      coordinates be needed, the routines slFK54 etc will also
+*      need to be applied.
+*
+*  6)  To convert to apparent RA,Dec the coordinates read from a
+*      real telescope, corrections would have to be applied for
+*      encoder zero points, gear and encoder errors, tube flexure,
+*      the position of the rotator axis and the pointing axis
+*      relative to it, non-perpendicularity between the mounting
+*      axes, and finally for the tilt of the azimuth or polar axis
+*      of the mounting (with appropriate corrections for mount
+*      flexures).  Some telescopes would, of course, exhibit other
+*      properties which would need to be accounted for at the
+*      appropriate point in the sequence.
+*
+*  7)  This routine takes time to execute, due mainly to the rigorous
+*      integration used to evaluate the refraction.  For processing
+*      multiple stars for one location and time, call slAOPA once
+*      followed by one call per star to slOAPQ.  Where a range of
+*      times within a limited period of a few hours is involved, and the
+*      highest precision is not required, call slAOPA once, followed
+*      by a call to slAOPT each time the time changes, followed by
+*      one call per star to slOAPQ.
+*
+*  8)  The DATE argument is UTC expressed as an MJD.  This is, strictly
+*      speaking, wrong, because of leap seconds.  However, as long as
+*      the delta UT and the UTC are consistent there are no
+*      difficulties, except during a leap second.  In this case, the
+*      start of the 61st second of the final minute should begin a new
+*      MJD day and the old pre-leap delta UT should continue to be used.
+*      As the 61st second completes, the MJD should revert to the start
+*      of the day as, simultaneously, the delta UTC changes by one
+*      second to its post-leap new value.
+*
+*  9)  The delta UT (UT1-UTC) is tabulated in IERS circulars and
+*      elsewhere.  It increases by exactly one second at the end of
+*      each UTC leap second, introduced in order to keep delta UT
+*      within +/- 0.9 seconds.
+*
+*  10) IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.
+*      The longitude required by the present routine is east-positive,
+*      in accordance with geographical convention (and right-handed).
+*      In particular, note that the longitudes returned by the
+*      slOBS routine are west-positive, following astronomical
+*      usage, and must be reversed in sign before use in the present
+*      routine.
+*
+*  11) The polar coordinates XP,YP can be obtained from IERS
+*      circulars and equivalent publications.  The maximum amplitude
+*      is about 0.3 arcseconds.  If XP,YP values are unavailable,
+*      use XP=YP=0D0.  See page B60 of the 1988 Astronomical Almanac
+*      for a definition of the two angles.
+*
+*  12) The height above sea level of the observing station, HM,
+*      can be obtained from the Astronomical Almanac (Section J
+*      in the 1988 edition), or via the routine slOBS.  If P,
+*      the pressure in millibars, is available, an adequate
+*      estimate of HM can be obtained from the expression
+*
+*             HM ~ -29.3D0*TSL*LOG(P/1013.25D0).
+*
+*      where TSL is the approximate sea-level air temperature in K
+*      (see Astrophysical Quantities, C.W.Allen, 3rd edition,
+*      section 52).  Similarly, if the pressure P is not known,
+*      it can be estimated from the height of the observing
+*      station, HM, as follows:
+*
+*             P ~ 1013.25D0*EXP(-HM/(29.3D0*TSL)).
+*
+*      Note, however, that the refraction is nearly proportional to the
+*      pressure and that an accurate P value is important for precise
+*      work.
+*
+*  13) The azimuths etc. used by the present routine are with respect
+*      to the celestial pole.  Corrections from the terrestrial pole
+*      can be computed using slPLMO.
+*
+*  Called:  slAOPA, slOAPQ
+*
+*  Last revision:   2 December 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) TYPE
+      DOUBLE PRECISION OB1,OB2,DATE,DUT,ELONGM,PHIM,HM,
+     :                 XP,YP,TDK,PMB,RH,WL,TLR,RAP,DAP
+
+      DOUBLE PRECISION AOPRMS(14)
+
+
+      CALL slAOPA(DATE,DUT,ELONGM,PHIM,HM,XP,YP,TDK,PMB,RH,WL,TLR,
+     :               AOPRMS)
+      CALL slOAPQ(TYPE,OB1,OB2,AOPRMS,RAP,DAP)
+
+      END
diff --git a/math/slalib/oapqk.f b/math/slalib/oapqk.f
new file mode 100644
index 00000000..7e8a2bb5
--- /dev/null
+++ b/math/slalib/oapqk.f
@@ -0,0 +1,251 @@
+      SUBROUTINE slOAPQ (TYPE, OB1, OB2, AOPRMS, RAP, DAP)
+*+
+*     - - - - - -
+*      O A P Q
+*     - - - - - -
+*
+*  Quick observed to apparent place
+*
+*  Given:
+*     TYPE   c*(*)  type of coordinates - 'R', 'H' or 'A' (see below)
+*     OB1    d      observed Az, HA or RA (radians; Az is N=0,E=90)
+*     OB2    d      observed ZD or Dec (radians)
+*     AOPRMS d(14)  star-independent apparent-to-observed parameters:
+*
+*       (1)      geodetic latitude (radians)
+*       (2,3)    sine and cosine of geodetic latitude
+*       (4)      magnitude of diurnal aberration vector
+*       (5)      height (HM)
+*       (6)      ambient temperature (T)
+*       (7)      pressure (P)
+*       (8)      relative humidity (RH)
+*       (9)      wavelength (WL)
+*       (10)     lapse rate (TLR)
+*       (11,12)  refraction constants A and B (radians)
+*       (13)     longitude + eqn of equinoxes + sidereal DUT (radians)
+*       (14)     local apparent sidereal time (radians)
+*
+*  Returned:
+*     RAP    d      geocentric apparent right ascension
+*     DAP    d      geocentric apparent declination
+*
+*  Notes:
+*
+*  1)  Only the first character of the TYPE argument is significant.
+*      'R' or 'r' indicates that OBS1 and OBS2 are the observed right
+*      ascension and declination;  'H' or 'h' indicates that they are
+*      hour angle (west +ve) and declination;  anything else ('A' or
+*      'a' is recommended) indicates that OBS1 and OBS2 are azimuth
+*      (north zero, east 90 deg) and zenith distance.  (Zenith distance
+*      is used rather than elevation in order to reflect the fact that
+*      no allowance is made for depression of the horizon.)
+*
+*  2)  The accuracy of the result is limited by the corrections for
+*      refraction.  Providing the meteorological parameters are
+*      known accurately and there are no gross local effects, the
+*      predicted apparent RA,Dec should be within about 0.1 arcsec
+*      for a zenith distance of less than 70 degrees.  Even at a
+*      topocentric zenith distance of 90 degrees, the accuracy in
+*      elevation should be better than 1 arcmin;  useful results
+*      are available for a further 3 degrees, beyond which the
+*      slRFRO routine returns a fixed value of the refraction.
+*      The complementary routines slAOP (or slAOPQ) and slOAP
+*      (or slOAPQ) are self-consistent to better than 1 micro-
+*      arcsecond all over the celestial sphere.
+*
+*  3)  It is advisable to take great care with units, as even
+*      unlikely values of the input parameters are accepted and
+*      processed in accordance with the models used.
+*
+*  5)  "Observed" Az,El means the position that would be seen by a
+*      perfect theodolite located at the observer.  This is
+*      related to the observed HA,Dec via the standard rotation, using
+*      the geodetic latitude (corrected for polar motion), while the
+*      observed HA and RA are related simply through the local
+*      apparent ST.  "Observed" RA,Dec or HA,Dec thus means the
+*      position that would be seen by a perfect equatorial located
+*      at the observer and with its polar axis aligned to the
+*      Earth's axis of rotation (n.b. not to the refracted pole).
+*      By removing from the observed place the effects of
+*      atmospheric refraction and diurnal aberration, the
+*      geocentric apparent RA,Dec is obtained.
+*
+*  5)  Frequently, mean rather than apparent RA,Dec will be required,
+*      in which case further transformations will be necessary.  The
+*      slAMP etc routines will convert the apparent RA,Dec produced
+*      by the present routine into an "FK5" (J2000) mean place, by
+*      allowing for the Sun's gravitational lens effect, annual
+*      aberration, nutation and precession.  Should "FK4" (1950)
+*      coordinates be needed, the routines slFK54 etc will also
+*      need to be applied.
+*
+*  6)  To convert to apparent RA,Dec the coordinates read from a
+*      real telescope, corrections would have to be applied for
+*      encoder zero points, gear and encoder errors, tube flexure,
+*      the position of the rotator axis and the pointing axis
+*      relative to it, non-perpendicularity between the mounting
+*      axes, and finally for the tilt of the azimuth or polar axis
+*      of the mounting (with appropriate corrections for mount
+*      flexures).  Some telescopes would, of course, exhibit other
+*      properties which would need to be accounted for at the
+*      appropriate point in the sequence.
+*
+*  7)  The star-independent apparent-to-observed-place parameters
+*      in AOPRMS may be computed by means of the slAOPA routine.
+*      If nothing has changed significantly except the time, the
+*      slAOPT routine may be used to perform the requisite
+*      partial recomputation of AOPRMS.
+*
+*  8) The azimuths etc used by the present routine are with respect
+*     to the celestial pole.  Corrections from the terrestrial pole
+*     can be computed using slPLMO.
+*
+*  Called:  slDS2C, slDC2S, slRFRO, slDA2P
+*
+*  Last revision:   29 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) TYPE
+      DOUBLE PRECISION OB1,OB2,AOPRMS(14),RAP,DAP
+
+*  Breakpoint for fast/slow refraction algorithm:
+*  ZD greater than arctan(4), (see slRFCO routine)
+*  or vector Z less than cosine(arctan(Z)) = 1/sqrt(17)
+      DOUBLE PRECISION ZBREAK
+      PARAMETER (ZBREAK=0.242535625D0)
+
+      CHARACTER C
+      DOUBLE PRECISION C1,C2,SPHI,CPHI,ST,CE,XAEO,YAEO,ZAEO,V(3),
+     :                 XMHDO,YMHDO,ZMHDO,AZ,SZ,ZDO,TZ,DREF,ZDT,
+     :                 XAET,YAET,ZAET,XMHDA,YMHDA,ZMHDA,DIURAB,F,HMA
+
+      DOUBLE PRECISION slDA2P
+
+
+
+*  Coordinate type
+      C = TYPE(1:1)
+
+*  Coordinates
+      C1 = OB1
+      C2 = OB2
+
+*  Sin, cos of latitude
+      SPHI = AOPRMS(2)
+      CPHI = AOPRMS(3)
+
+*  Local apparent sidereal time
+      ST = AOPRMS(14)
+
+*  Standardise coordinate type
+      IF (C.EQ.'R'.OR.C.EQ.'r') THEN
+         C = 'R'
+      ELSE IF (C.EQ.'H'.OR.C.EQ.'h') THEN
+         C = 'H'
+      ELSE
+         C = 'A'
+      END IF
+
+*  If Az,ZD convert to Cartesian (S=0,E=90)
+      IF (C.EQ.'A') THEN
+         CE = SIN(C2)
+         XAEO = -COS(C1)*CE
+         YAEO = SIN(C1)*CE
+         ZAEO = COS(C2)
+      ELSE
+
+*     If RA,Dec convert to HA,Dec
+         IF (C.EQ.'R') THEN
+            C1 = ST-C1
+         END IF
+
+*     To Cartesian -HA,Dec
+         CALL slDS2C(-C1,C2,V)
+         XMHDO = V(1)
+         YMHDO = V(2)
+         ZMHDO = V(3)
+
+*     To Cartesian Az,El (S=0,E=90)
+         XAEO = SPHI*XMHDO-CPHI*ZMHDO
+         YAEO = YMHDO
+         ZAEO = CPHI*XMHDO+SPHI*ZMHDO
+      END IF
+
+*  Azimuth (S=0,E=90)
+      IF (XAEO.NE.0D0.OR.YAEO.NE.0D0) THEN
+         AZ = ATAN2(YAEO,XAEO)
+      ELSE
+         AZ = 0D0
+      END IF
+
+*  Sine of observed ZD, and observed ZD
+      SZ = SQRT(XAEO*XAEO+YAEO*YAEO)
+      ZDO = ATAN2(SZ,ZAEO)
+
+*
+*  Refraction
+*  ----------
+
+*  Large zenith distance?
+      IF (ZAEO.GE.ZBREAK) THEN
+
+*     Fast algorithm using two constant model
+         TZ = SZ/ZAEO
+         DREF = (AOPRMS(11)+AOPRMS(12)*TZ*TZ)*TZ
+
+      ELSE
+
+*     Rigorous algorithm for large ZD
+         CALL slRFRO(ZDO,AOPRMS(5),AOPRMS(6),AOPRMS(7),AOPRMS(8),
+     :                  AOPRMS(9),AOPRMS(1),AOPRMS(10),1D-8,DREF)
+      END IF
+
+      ZDT = ZDO+DREF
+
+*  To Cartesian Az,ZD
+      CE = SIN(ZDT)
+      XAET = COS(AZ)*CE
+      YAET = SIN(AZ)*CE
+      ZAET = COS(ZDT)
+
+*  Cartesian Az,ZD to Cartesian -HA,Dec
+      XMHDA = SPHI*XAET+CPHI*ZAET
+      YMHDA = YAET
+      ZMHDA = -CPHI*XAET+SPHI*ZAET
+
+*  Diurnal aberration
+      DIURAB = -AOPRMS(4)
+      F = (1D0-DIURAB*YMHDA)
+      V(1) = F*XMHDA
+      V(2) = F*(YMHDA+DIURAB)
+      V(3) = F*ZMHDA
+
+*  To spherical -HA,Dec
+      CALL slDC2S(V,HMA,DAP)
+
+*  Right Ascension
+      RAP = slDA2P(ST+HMA)
+
+      END
diff --git a/math/slalib/obs.f b/math/slalib/obs.f
new file mode 100644
index 00000000..5aad21d1
--- /dev/null
+++ b/math/slalib/obs.f
@@ -0,0 +1,943 @@
+      SUBROUTINE slOBS (N, C, NAME, W, P, H)
+*+
+*     - - - -
+*      O B S
+*     - - - -
+*
+*  Parameters of selected groundbased observing stations
+*
+*  Given:
+*     N       int     number specifying observing station
+*
+*  Either given or returned
+*     C       c*(*)   identifier specifying observing station
+*
+*  Returned:
+*     NAME    c*(*)   name of specified observing station
+*     W       dp      longitude (radians, West +ve)
+*     P       dp      geodetic latitude (radians, North +ve)
+*     H       dp      height above sea level (metres)
+*
+*  Notes:
+*
+*     Station identifiers C may be up to 10 characters long,
+*     and station names NAME may be up to 40 characters long.
+*
+*     C and N are alternative ways of specifying the observing
+*     station.  The C option, which is the most generally useful,
+*     may be selected by specifying an N value of zero or less.
+*     If N is 1 or more, the parameters of the Nth station
+*     in the currently supported list are interrogated, and
+*     the station identifier C is returned as well as NAME, W,
+*     P and H.
+*
+*     If the station parameters are not available, either because
+*     the station identifier C is not recognized, or because an
+*     N value greater than the number of stations supported is
+*     given, a name of '?' is returned and C, W, P and H are left
+*     in their current states.
+*
+*     Programs can obtain a list of all currently supported
+*     stations by calling the routine repeatedly, with N=1,2,3...
+*     When NAME='?' is seen, the list of stations has been
+*     exhausted.
+*
+*     Station numbers, identifiers, names and other details are
+*     subject to change and should not be hardwired into
+*     application programs.
+*
+*     All station identifiers C are uppercase only;  lowercase
+*     characters must be converted to uppercase by the calling
+*     program.  The station names returned may contain both upper-
+*     and lowercase.  All characters up to the first space are
+*     checked;  thus an abbreviated ID will return the parameters
+*     for the first station in the list which matches the
+*     abbreviation supplied, and no station in the list will ever
+*     contain embedded spaces.  C must not have leading spaces.
+*
+*     IMPORTANT -- BEWARE OF THE LONGITUDE SIGN CONVENTION.  The
+*     longitude returned by slOBS is west-positive in accordance
+*     with astronomical usage.  However, this sign convention is
+*     left-handed and is the opposite of the one used by geographers;
+*     elsewhere in SLALIB the preferable east-positive convention is
+*     used.  In particular, note that for use in slAOP, slAOPA
+*     and slOAP the sign of the longitude must be reversed.
+*
+*     Users are urged to inform the author of any improvements
+*     they would like to see made.  For example:
+*
+*         typographical corrections
+*         more accurate parameters
+*         better station identifiers or names
+*         additional stations
+*
+*  P.T.Wallace   Starlink   15 March 2002
+*
+*  Copyright (C) 2002 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER N
+      CHARACTER C*(*),NAME*(*)
+      DOUBLE PRECISION W,P,H
+
+      INTEGER NMAX,M,NS,I
+      CHARACTER*10 CC
+
+      DOUBLE PRECISION AS2R,WEST,NORTH,EAST,SOUTH
+      INTEGER ID,IAM
+      REAL AS
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+*  Table of station identifiers
+      PARAMETER (NMAX=83)
+      CHARACTER*10 CTAB(NMAX)
+      DATA CTAB  (1) /'AAT       '/
+      DATA CTAB  (2) /'LPO4.2    '/
+      DATA CTAB  (3) /'LPO2.5    '/
+      DATA CTAB  (4) /'LPO1      '/
+      DATA CTAB  (5) /'LICK120   '/
+      DATA CTAB  (6) /'MMT       '/
+      DATA CTAB  (7) /'DAO72     '/
+      DATA CTAB  (8) /'DUPONT    '/
+      DATA CTAB  (9) /'MTHOP1.5  '/
+      DATA CTAB (10) /'STROMLO74 '/
+      DATA CTAB (11) /'ANU2.3    '/
+      DATA CTAB (12) /'GBVA140   '/
+      DATA CTAB (13) /'TOLOLO4M  '/
+      DATA CTAB (14) /'TOLOLO1.5M'/
+      DATA CTAB (15) /'TIDBINBLA '/
+      DATA CTAB (16) /'BLOEMF    '/
+      DATA CTAB (17) /'BOSQALEGRE'/
+      DATA CTAB (18) /'FLAGSTF61 '/
+      DATA CTAB (19) /'LOWELL72  '/
+      DATA CTAB (20) /'HARVARD   '/
+      DATA CTAB (21) /'OKAYAMA   '/
+      DATA CTAB (22) /'KPNO158   '/
+      DATA CTAB (23) /'KPNO90    '/
+      DATA CTAB (24) /'KPNO84    '/
+      DATA CTAB (25) /'KPNO36FT  '/
+      DATA CTAB (26) /'KOTTAMIA  '/
+      DATA CTAB (27) /'ESO3.6    '/
+      DATA CTAB (28) /'MAUNAK88  '/
+      DATA CTAB (29) /'UKIRT     '/
+      DATA CTAB (30) /'QUEBEC1.6 '/
+      DATA CTAB (31) /'MTEKAR    '/
+      DATA CTAB (32) /'MTLEMMON60'/
+      DATA CTAB (33) /'MCDONLD2.7'/
+      DATA CTAB (34) /'MCDONLD2.1'/
+      DATA CTAB (35) /'PALOMAR200'/
+      DATA CTAB (36) /'PALOMAR60 '/
+      DATA CTAB (37) /'DUNLAP74  '/
+      DATA CTAB (38) /'HPROV1.93 '/
+      DATA CTAB (39) /'HPROV1.52 '/
+      DATA CTAB (40) /'SANPM83   '/
+      DATA CTAB (41) /'SAAO74    '/
+      DATA CTAB (42) /'TAUTNBG   '/
+      DATA CTAB (43) /'CATALINA61'/
+      DATA CTAB (44) /'STEWARD90 '/
+      DATA CTAB (45) /'USSR6     '/
+      DATA CTAB (46) /'ARECIBO   '/
+      DATA CTAB (47) /'CAMB5KM   '/
+      DATA CTAB (48) /'CAMB1MILE '/
+      DATA CTAB (49) /'EFFELSBERG'/
+      DATA CTAB (50) /'GBVA300   '/
+      DATA CTAB (51) /'JODRELL1  '/
+      DATA CTAB (52) /'PARKES    '/
+      DATA CTAB (53) /'VLA       '/
+      DATA CTAB (54) /'SUGARGROVE'/
+      DATA CTAB (55) /'USSR600   '/
+      DATA CTAB (56) /'NOBEYAMA  '/
+      DATA CTAB (57) /'JCMT      '/
+      DATA CTAB (58) /'ESONTT    '/
+      DATA CTAB (59) /'ST.ANDREWS'/
+      DATA CTAB (60) /'APO3.5    '/
+      DATA CTAB (61) /'KECK1     '/
+      DATA CTAB (62) /'TAUTSCHM  '/
+      DATA CTAB (63) /'PALOMAR48 '/
+      DATA CTAB (64) /'UKST      '/
+      DATA CTAB (65) /'KISO      '/
+      DATA CTAB (66) /'ESOSCHM   '/
+      DATA CTAB (67) /'ATCA      '/
+      DATA CTAB (68) /'MOPRA     '/
+      DATA CTAB (69) /'SUBARU    '/
+      DATA CTAB (70) /'CFHT      '/
+      DATA CTAB (71) /'KECK2     '/
+      DATA CTAB (72) /'GEMININ   '/
+      DATA CTAB (73) /'FCRAO     '/
+      DATA CTAB (74) /'IRTF      '/
+      DATA CTAB (75) /'CSO       '/
+      DATA CTAB (76) /'VLT1      '/
+      DATA CTAB (77) /'VLT2      '/
+      DATA CTAB (78) /'VLT3      '/
+      DATA CTAB (79) /'VLT4      '/
+      DATA CTAB (80) /'GEMINIS   '/
+      DATA CTAB (81) /'KOSMA3M   '/
+      DATA CTAB (82) /'MAGELLAN1 '/
+      DATA CTAB (83) /'MAGELLAN2 '/
+
+*  Degrees, arcminutes, arcseconds to radians
+      WEST(ID,IAM,AS)=AS2R*(DBLE(60*(60*ID+IAM))+DBLE(AS))
+      NORTH(ID,IAM,AS)=WEST(ID,IAM,AS)
+      EAST(ID,IAM,AS)=-WEST(ID,IAM,AS)
+      SOUTH(ID,IAM,AS)=-WEST(ID,IAM,AS)
+
+
+
+
+*  Station specified by number or identifier?
+      IF (N.GT.0) THEN
+
+*     Station specified by number
+         M=N
+         IF (M.LE.NMAX) C=CTAB(M)
+
+      ELSE
+
+*     Station specified by identifier:  determine corresponding number
+         CC=C
+         DO NS=1,NMAX
+            DO I=1,10
+               IF (CC(I:I).EQ.' ') GO TO 5
+               IF (CC(I:I).NE.CTAB(NS)(I:I)) GO TO 1
+            END DO
+            GO TO 5
+ 1          CONTINUE
+         END DO
+         NS=NMAX+1
+ 5       CONTINUE
+         IF (C(1:1).NE.' ') THEN
+            M=NS
+         ELSE
+            M=NMAX+1
+         END IF
+
+      END IF
+
+*
+*  Return parameters of Mth station
+*  --------------------------------
+
+      GO TO (10,20,30,40,50,60,70,80,90,100,
+     :       110,120,130,140,150,160,170,180,190,200,
+     :       210,220,230,240,250,260,270,280,290,300,
+     :       310,320,330,340,350,360,370,380,390,400,
+     :       410,420,430,440,450,460,470,480,490,500,
+     :       510,520,530,540,550,560,570,580,590,600,
+     :       610,620,630,640,650,660,670,680,690,700,
+     :       710,720,730,740,750,760,770,780,790,800,
+     :       810,820,830) M
+      GO TO 9000
+
+*  AAT (Observer's Guide)                                            AAT
+ 10   CONTINUE
+      NAME='Anglo-Australian 3.9m Telescope'
+      W=EAST(149,03,57.91)
+      P=SOUTH(31,16,37.34)
+      H=1164D0
+      GO TO 9999
+
+*  WHT (Gemini, April 1987)                                       LPO4.2
+ 20   CONTINUE
+      NAME='William Herschel 4.2m Telescope'
+      W=WEST(17,52,53.9)
+      P=NORTH(28,45,38.1)
+      H=2332D0
+      GO TO 9999
+
+*  INT (Gemini, April 1987)                                       LPO2.5
+ 30   CONTINUE
+      NAME='Isaac Newton 2.5m Telescope'
+      W=WEST(17,52,39.5)
+      P=NORTH(28,45,43.2)
+      H=2336D0
+      GO TO 9999
+
+*  JKT (Gemini, April 1987)                                         LPO1
+ 40   CONTINUE
+      NAME='Jacobus Kapteyn 1m Telescope'
+      W=WEST(17,52,41.2)
+      P=NORTH(28,45,39.9)
+      H=2364D0
+      GO TO 9999
+
+*  Lick 120" (S.L.Allen, private communication, 2002)            LICK120
+ 50   CONTINUE
+      NAME='Lick 120 inch'
+      W=WEST(121,38,13.689)
+      P=NORTH(37,20,34.931)
+      H=1286D0
+      GO TO 9999
+
+*  MMT 6.5m conversion (MMT Observatory website)                     MMT
+ 60   CONTINUE
+      NAME='MMT 6.5m, Mt Hopkins'
+      W=WEST(110,53,04.4)
+      P=NORTH(31,41,19.6)
+      H=2608D0
+      GO TO 9999
+
+*  Victoria B.C. 1.85m (1984 Almanac)                              DAO72
+ 70   CONTINUE
+      NAME='DAO Victoria BC 1.85 metre'
+      W=WEST(123,25,01.18)
+      P=NORTH(48,31,11.9)
+      H=238D0
+      GO TO 9999
+
+*  Las Campanas (1983 Almanac)                                    DUPONT
+ 80   CONTINUE
+      NAME='Du Pont 2.5m Telescope, Las Campanas'
+      W=WEST(70,42,9.)
+      P=SOUTH(29,00,11.)
+      H=2280D0
+      GO TO 9999
+
+*  Mt Hopkins 1.5m (1983 Almanac)                               MTHOP1.5
+ 90   CONTINUE
+      NAME='Mt Hopkins 1.5 metre'
+      W=WEST(110,52,39.00)
+      P=NORTH(31,40,51.4)
+      H=2344D0
+      GO TO 9999
+
+*  Mt Stromlo 74" (1983 Almanac)                               STROMLO74
+ 100  CONTINUE
+      NAME='Mount Stromlo 74 inch'
+      W=EAST(149,00,27.59)
+      P=SOUTH(35,19,14.3)
+      H=767D0
+      GO TO 9999
+
+*  ANU 2.3m, SSO (Gary Hovey)                                     ANU2.3
+ 110  CONTINUE
+      NAME='Siding Spring 2.3 metre'
+      W=EAST(149,03,40.3)
+      P=SOUTH(31,16,24.1)
+      H=1149D0
+      GO TO 9999
+
+*  Greenbank 140' (1983 Almanac)                                 GBVA140
+ 120  CONTINUE
+      NAME='Greenbank 140 foot'
+      W=WEST(79,50,09.61)
+      P=NORTH(38,26,15.4)
+      H=881D0
+      GO TO 9999
+
+*  Cerro Tololo 4m (1982 Almanac)                               TOLOLO4M
+ 130  CONTINUE
+      NAME='Cerro Tololo 4 metre'
+      W=WEST(70,48,53.6)
+      P=SOUTH(30,09,57.8)
+      H=2235D0
+      GO TO 9999
+
+*  Cerro Tololo 1.5m (1982 Almanac)                           TOLOLO1.5M
+ 140  CONTINUE
+      NAME='Cerro Tololo 1.5 metre'
+      W=WEST(70,48,54.5)
+      P=SOUTH(30,09,56.3)
+      H=2225D0
+      GO TO 9999
+
+*  Tidbinbilla 64m (1982 Almanac)                              TIDBINBLA
+ 150  CONTINUE
+      NAME='Tidbinbilla 64 metre'
+      W=EAST(148,58,48.20)
+      P=SOUTH(35,24,14.3)
+      H=670D0
+      GO TO 9999
+
+*  Bloemfontein 1.52m (1981 Almanac)                              BLOEMF
+ 160  CONTINUE
+      NAME='Bloemfontein 1.52 metre'
+      W=EAST(26,24,18.)
+      P=SOUTH(29,02,18.)
+      H=1387D0
+      GO TO 9999
+
+*  Bosque Alegre 1.54m (1981 Almanac)                         BOSQALEGRE
+ 170  CONTINUE
+      NAME='Bosque Alegre 1.54 metre'
+      W=WEST(64,32,48.0)
+      P=SOUTH(31,35,53.)
+      H=1250D0
+      GO TO 9999
+
+*  USNO 61" astrographic reflector, Flagstaff (1981 Almanac)   FLAGSTF61
+ 180  CONTINUE
+      NAME='USNO 61 inch astrograph, Flagstaff'
+      W=WEST(111,44,23.6)
+      P=NORTH(35,11,02.5)
+      H=2316D0
+      GO TO 9999
+
+*  Lowell 72" (1981 Almanac)                                    LOWELL72
+ 190  CONTINUE
+      NAME='Perkins 72 inch, Lowell'
+      W=WEST(111,32,09.3)
+      P=NORTH(35,05,48.6)
+      H=2198D0
+      GO TO 9999
+
+*  Harvard 1.55m (1981 Almanac)                                  HARVARD
+ 200  CONTINUE
+      NAME='Harvard College Observatory 1.55m'
+      W=WEST(71,33,29.32)
+      P=NORTH(42,30,19.0)
+      H=185D0
+      GO TO 9999
+
+*  Okayama 1.88m (1981 Almanac)                                  OKAYAMA
+ 210  CONTINUE
+      NAME='Okayama 1.88 metre'
+      W=EAST(133,35,47.29)
+      P=NORTH(34,34,26.1)
+      H=372D0
+      GO TO 9999
+
+*  Kitt Peak Mayall 4m (1981 Almanac)                            KPNO158
+ 220  CONTINUE
+      NAME='Kitt Peak 158 inch'
+      W=WEST(111,35,57.61)
+      P=NORTH(31,57,50.3)
+      H=2120D0
+      GO TO 9999
+
+*  Kitt Peak 90 inch (1981 Almanac)                               KPNO90
+ 230  CONTINUE
+      NAME='Kitt Peak 90 inch'
+      W=WEST(111,35,58.24)
+      P=NORTH(31,57,46.9)
+      H=2071D0
+      GO TO 9999
+
+*  Kitt Peak 84 inch (1981 Almanac)                               KPNO84
+ 240  CONTINUE
+      NAME='Kitt Peak 84 inch'
+      W=WEST(111,35,51.56)
+      P=NORTH(31,57,29.2)
+      H=2096D0
+      GO TO 9999
+
+*  Kitt Peak 36 foot (1981 Almanac)                             KPNO36FT
+ 250  CONTINUE
+      NAME='Kitt Peak 36 foot'
+      W=WEST(111,36,51.12)
+      P=NORTH(31,57,12.1)
+      H=1939D0
+      GO TO 9999
+
+*  Kottamia 74" (1981 Almanac)                                  KOTTAMIA
+ 260  CONTINUE
+      NAME='Kottamia 74 inch'
+      W=EAST(31,49,30.)
+      P=NORTH(29,55,54.)
+      H=476D0
+      GO TO 9999
+
+*  La Silla 3.6m (1981 Almanac)                                   ESO3.6
+ 270  CONTINUE
+      NAME='ESO 3.6 metre'
+      W=WEST(70,43,36.)
+      P=SOUTH(29,15,36.)
+      H=2428D0
+      GO TO 9999
+
+*  Mauna Kea 88 inch                                            MAUNAK88
+*  (IfA website, Richard Wainscoat)
+ 280  CONTINUE
+      NAME='Mauna Kea 88 inch'
+      W=WEST(155,28,09.96)
+      P=NORTH(19,49,22.77)
+      H=4213.6D0
+      GO TO 9999
+
+*  UKIRT (IfA website, Richard Wainscoat)                          UKIRT
+ 290  CONTINUE
+      NAME='UK Infra Red Telescope'
+      W=WEST(155,28,13.18)
+      P=NORTH(19,49,20.75)
+      H=4198.5D0
+      GO TO 9999
+
+*  Quebec 1.6m (1981 Almanac)                                  QUEBEC1.6
+ 300  CONTINUE
+      NAME='Quebec 1.6 metre'
+      W=WEST(71,09,09.7)
+      P=NORTH(45,27,20.6)
+      H=1114D0
+      GO TO 9999
+
+*  Mt Ekar 1.82m (1981 Almanac)                                   MTEKAR
+ 310  CONTINUE
+      NAME='Mt Ekar 1.82 metre'
+      W=EAST(11,34,15.)
+      P=NORTH(45,50,48.)
+      H=1365D0
+      GO TO 9999
+
+*  Mt Lemmon 60" (1981 Almanac)                               MTLEMMON60
+ 320  CONTINUE
+      NAME='Mt Lemmon 60 inch'
+      W=WEST(110,42,16.9)
+      P=NORTH(32,26,33.9)
+      H=2790D0
+      GO TO 9999
+
+*  Mt Locke 2.7m (1981 Almanac)                               MCDONLD2.7
+ 330  CONTINUE
+      NAME='McDonald 2.7 metre'
+      W=WEST(104,01,17.60)
+      P=NORTH(30,40,17.7)
+      H=2075D0
+      GO TO 9999
+
+*  Mt Locke 2.1m (1981 Almanac)                               MCDONLD2.1
+ 340  CONTINUE
+      NAME='McDonald 2.1 metre'
+      W=WEST(104,01,20.10)
+      P=NORTH(30,40,17.7)
+      H=2075D0
+      GO TO 9999
+
+*  Palomar 200" (1981 Almanac)                                PALOMAR200
+ 350  CONTINUE
+      NAME='Palomar 200 inch'
+      W=WEST(116,51,50.)
+      P=NORTH(33,21,22.)
+      H=1706D0
+      GO TO 9999
+
+*  Palomar 60" (1981 Almanac)                                  PALOMAR60
+ 360  CONTINUE
+      NAME='Palomar 60 inch'
+      W=WEST(116,51,31.)
+      P=NORTH(33,20,56.)
+      H=1706D0
+      GO TO 9999
+
+*  David Dunlap 74" (1981 Almanac)                              DUNLAP74
+ 370  CONTINUE
+      NAME='David Dunlap 74 inch'
+      W=WEST(79,25,20.)
+      P=NORTH(43,51,46.)
+      H=244D0
+      GO TO 9999
+
+*  Haute Provence 1.93m (1981 Almanac)                         HPROV1.93
+ 380  CONTINUE
+      NAME='Haute Provence 1.93 metre'
+      W=EAST(5,42,46.75)
+      P=NORTH(43,55,53.3)
+      H=665D0
+      GO TO 9999
+
+*  Haute Provence 1.52m (1981 Almanac)                         HPROV1.52
+ 390  CONTINUE
+      NAME='Haute Provence 1.52 metre'
+      W=EAST(5,42,43.82)
+      P=NORTH(43,56,00.2)
+      H=667D0
+      GO TO 9999
+
+*  San Pedro Martir 83" (1981 Almanac)                           SANPM83
+ 400  CONTINUE
+      NAME='San Pedro Martir 83 inch'
+      W=WEST(115,27,47.)
+      P=NORTH(31,02,38.)
+      H=2830D0
+      GO TO 9999
+
+*  Sutherland 74" (1981 Almanac)                                  SAAO74
+ 410  CONTINUE
+      NAME='Sutherland 74 inch'
+      W=EAST(20,48,44.3)
+      P=SOUTH(32,22,43.4)
+      H=1771D0
+      GO TO 9999
+
+*  Tautenburg 2m (1981 Almanac)                                  TAUTNBG
+ 420  CONTINUE
+      NAME='Tautenburg 2 metre'
+      W=EAST(11,42,45.)
+      P=NORTH(50,58,51.)
+      H=331D0
+      GO TO 9999
+
+*  Catalina 61" (1981 Almanac)                                CATALINA61
+ 430  CONTINUE
+      NAME='Catalina 61 inch'
+      W=WEST(110,43,55.1)
+      P=NORTH(32,25,00.7)
+      H=2510D0
+      GO TO 9999
+
+*  Steward 90" (1981 Almanac)                                  STEWARD90
+ 440  CONTINUE
+      NAME='Steward 90 inch'
+      W=WEST(111,35,58.24)
+      P=NORTH(31,57,46.9)
+      H=2071D0
+      GO TO 9999
+
+*  Russian 6m (1981 Almanac)                                       USSR6
+ 450  CONTINUE
+      NAME='USSR 6 metre'
+      W=EAST(41,26,30.0)
+      P=NORTH(43,39,12.)
+      H=2100D0
+      GO TO 9999
+
+*  Arecibo 1000' (1981 Almanac)                                  ARECIBO
+ 460  CONTINUE
+      NAME='Arecibo 1000 foot'
+      W=WEST(66,45,11.1)
+      P=NORTH(18,20,36.6)
+      H=496D0
+      GO TO 9999
+
+*  Cambridge 5km (1981 Almanac)                                  CAMB5KM
+ 470  CONTINUE
+      NAME='Cambridge 5km'
+      W=EAST(0,02,37.23)
+      P=NORTH(52,10,12.2)
+      H=17D0
+      GO TO 9999
+
+*  Cambridge 1 mile (1981 Almanac)                             CAMB1MILE
+ 480  CONTINUE
+      NAME='Cambridge 1 mile'
+      W=EAST(0,02,21.64)
+      P=NORTH(52,09,47.3)
+      H=17D0
+      GO TO 9999
+
+*  Bonn 100m (1981 Almanac)                                   EFFELSBERG
+ 490  CONTINUE
+      NAME='Effelsberg 100 metre'
+      W=EAST(6,53,01.5)
+      P=NORTH(50,31,28.6)
+      H=366D0
+      GO TO 9999
+
+*  Greenbank 300' (1981 Almanac)                        GBVA300 (R.I.P.)
+ 500  CONTINUE
+      NAME='Greenbank 300 foot'
+      W=WEST(79,50,56.36)
+      P=NORTH(38,25,46.3)
+      H=894D0
+      GO TO 9999
+
+*  Jodrell Bank Mk 1 (1981 Almanac)                             JODRELL1
+ 510  CONTINUE
+      NAME='Jodrell Bank 250 foot'
+      W=WEST(2,18,25.)
+      P=NORTH(53,14,10.5)
+      H=78D0
+      GO TO 9999
+
+*  Australia Telescope Parkes Observatory                         PARKES
+*  (Peter te Lintel Hekkert)
+ 520  CONTINUE
+      NAME='Parkes 64 metre'
+      W=EAST(148,15,44.3591)
+      P=SOUTH(32,59,59.8657)
+      H=391.79D0
+      GO TO 9999
+
+*  VLA (1981 Almanac)                                                VLA
+ 530  CONTINUE
+      NAME='Very Large Array'
+      W=WEST(107,37,03.82)
+      P=NORTH(34,04,43.5)
+      H=2124D0
+      GO TO 9999
+
+*  Sugar Grove 150' (1981 Almanac)                            SUGARGROVE
+ 540  CONTINUE
+      NAME='Sugar Grove 150 foot'
+      W=WEST(79,16,23.)
+      P=NORTH(38,31,14.)
+      H=705D0
+      GO TO 9999
+
+*  Russian 600' (1981 Almanac)                                   USSR600
+ 550  CONTINUE
+      NAME='USSR 600 foot'
+      W=EAST(41,35,25.5)
+      P=NORTH(43,49,32.)
+      H=973D0
+      GO TO 9999
+
+*  Nobeyama 45 metre mm dish (based on 1981 Almanac entry)      NOBEYAMA
+ 560  CONTINUE
+      NAME='Nobeyama 45 metre'
+      W=EAST(138,29,12.)
+      P=NORTH(35,56,19.)
+      H=1350D0
+      GO TO 9999
+
+*  James Clerk Maxwell 15 metre mm telescope, Mauna Kea             JCMT
+*  From GPS measurements on 11Apr2007 for eSMA setup (R. Tilanus)
+ 570  CONTINUE
+      NAME='JCMT 15 metre'
+      W=WEST(155,28,37.30)
+      P=NORTH(19,49,22.22)
+      H=4124.75D0
+      GO TO 9999
+
+*  ESO 3.5 metre NTT, La Silla (K.Wirenstrand)                    ESONTT
+ 580  CONTINUE
+      NAME='ESO 3.5 metre NTT'
+      W=WEST(70,43,07.)
+      P=SOUTH(29,15,30.)
+      H=2377D0
+      GO TO 9999
+
+*  St Andrews University Observatory (1982 Almanac)           ST.ANDREWS
+ 590  CONTINUE
+      NAME='St Andrews'
+      W=WEST(2,48,52.5)
+      P=NORTH(56,20,12.)
+      H=30D0
+      GO TO 9999
+
+*  Apache Point 3.5 metre (R.Owen)                                APO3.5
+ 600  CONTINUE
+      NAME='Apache Point 3.5m'
+      W=WEST(105,49,11.56)
+      P=NORTH(32,46,48.96)
+      H=2809D0
+      GO TO 9999
+
+*  W.M.Keck Observatory, Telescope 1                               KECK1
+*  (William Lupton)
+ 610  CONTINUE
+      NAME='Keck 10m Telescope #1'
+      W=WEST(155,28,28.99)
+      P=NORTH(19,49,33.41)
+      H=4160D0
+      GO TO 9999
+
+*  Tautenberg Schmidt (1983 Almanac)                            TAUTSCHM
+ 620  CONTINUE
+      NAME='Tautenberg 1.34 metre Schmidt'
+      W=EAST(11,42,45.0)
+      P=NORTH(50,58,51.0)
+      H=331D0
+      GO TO 9999
+
+*  Palomar Schmidt (1981 Almanac)                              PALOMAR48
+ 630  CONTINUE
+      NAME='Palomar 48-inch Schmidt'
+      W=WEST(116,51,32.0)
+      P=NORTH(33,21,26.0)
+      H=1706D0
+      GO TO 9999
+
+*  UK Schmidt, Siding Spring (1983 Almanac)                         UKST
+ 640  CONTINUE
+      NAME='UK 1.2 metre Schmidt, Siding Spring'
+      W=EAST(149,04,12.8)
+      P=SOUTH(31,16,27.8)
+      H=1145D0
+      GO TO 9999
+
+*  Kiso Schmidt, Japan (1981 Almanac)                               KISO
+ 650  CONTINUE
+      NAME='Kiso 1.05 metre Schmidt, Japan'
+      W=EAST(137,37,42.2)
+      P=NORTH(35,47,38.7)
+      H=1130D0
+      GO TO 9999
+
+*  ESO Schmidt, La Silla (1981 Almanac)                          ESOSCHM
+ 660  CONTINUE
+      NAME='ESO 1 metre Schmidt, La Silla'
+      W=WEST(70,43,46.5)
+      P=SOUTH(29,15,25.8)
+      H=2347D0
+      GO TO 9999
+
+*  Australia Telescope Compact Array                                ATCA
+*  (WGS84 coordinates of Station 35, Mark Calabretta)
+ 670  CONTINUE
+      NAME='Australia Telescope Compact Array'
+      W=EAST(149,33,00.500)
+      P=SOUTH(30,18,46.385)
+      H=236.9D0
+      GO TO 9999
+
+*  Australia Telescope Mopra Observatory                           MOPRA
+*  (Peter te Lintel Hekkert)
+ 680  CONTINUE
+      NAME='ATNF Mopra Observatory'
+      W=EAST(149,05,58.732)
+      P=SOUTH(31,16,04.451)
+      H=850D0
+      GO TO 9999
+
+*  Subaru telescope, Mauna Kea                                     SUBARU
+*  (IfA website, Richard Wainscoat)
+ 690  CONTINUE
+      NAME='Subaru 8m telescope'
+      W=WEST(155,28,33.67)
+      P=NORTH(19,49,31.81)
+      H=4163D0
+      GO TO 9999
+
+*  Canada-France-Hawaii Telescope, Mauna Kea                         CFHT
+*  (IfA website, Richard Wainscoat)
+ 700  CONTINUE
+      NAME='Canada-France-Hawaii 3.6m Telescope'
+      W=WEST(155,28,07.95)
+      P=NORTH(19,49,30.91)
+      H=4204.1D0
+      GO TO 9999
+
+*  W.M.Keck Observatory, Telescope 2                                KECK2
+*  (William Lupton)
+ 710  CONTINUE
+      NAME='Keck 10m Telescope #2'
+      W=WEST(155,28,27.24)
+      P=NORTH(19,49,35.62)
+      H=4159.6D0
+      GO TO 9999
+
+*  Gemini North, Mauna Kea                                        GEMININ
+*  (IfA website, Richard Wainscoat)
+ 720  CONTINUE
+      NAME='Gemini North 8-m telescope'
+      W=WEST(155,28,08.57)
+      P=NORTH(19,49,25.69)
+      H=4213.4D0
+      GO TO 9999
+
+*  Five College Radio Astronomy Observatory                        FCRAO
+*  (Tim Jenness)
+ 730  CONTINUE
+      NAME='Five College Radio Astronomy Obs'
+      W=WEST(72,20,42.0)
+      P=NORTH(42,23,30.0)
+      H=314D0
+      GO TO 9999
+
+*  NASA Infra Red Telescope Facility                                IRTF
+*  (IfA website, Richard Wainscoat)
+ 740  CONTINUE
+      NAME='NASA IR Telescope Facility, Mauna Kea'
+      W=WEST(155,28,19.20)
+      P=NORTH(19,49,34.39)
+      H=4168.1D0
+      GO TO 9999
+
+*  Caltech Submillimeter Observatory                                 CSO
+*  (IfA website, Richard Wainscoat; height estimated)
+ 750  CONTINUE
+      NAME='Caltech Sub-mm Observatory, Mauna Kea'
+      W=WEST(155,28,31.79)
+      P=NORTH(19,49,20.78)
+      H=4080D0
+      GO TO 9999
+
+* ESO VLT, UT1                                                       VLT1
+* (ESO website, VLT Whitebook Chapter 2)
+ 760  CONTINUE
+      NAME='ESO VLT, Paranal, Chile: UT1'
+      W=WEST(70,24,11.642)
+      P=SOUTH(24,37,33.117)
+      H=2635.43
+      GO TO 9999
+
+* ESO VLT, UT2                                                       VLT2
+* (ESO website, VLT Whitebook Chapter 2)
+ 770  CONTINUE
+      NAME='ESO VLT, Paranal, Chile: UT2'
+      W=WEST(70,24,10.855)
+      P=SOUTH(24,37,31.465)
+      H=2635.43
+      GO TO 9999
+
+* ESO VLT, UT3                                                       VLT3
+* (ESO website, VLT Whitebook Chapter 2)
+ 780  CONTINUE
+      NAME='ESO VLT, Paranal, Chile: UT3'
+      W=WEST(70,24,09.896)
+      P=SOUTH(24,37,30.300)
+      H=2635.43
+      GO TO 9999
+
+* ESO VLT, UT4                                                       VLT4
+* (ESO website, VLT Whitebook Chapter 2)
+ 790  CONTINUE
+      NAME='ESO VLT, Paranal, Chile: UT4'
+      W=WEST(70,24,08.000)
+      P=SOUTH(24,37,31.000)
+      H=2635.43
+      GO TO 9999
+
+*  Gemini South, Cerro Pachon                                     GEMINIS
+*  (GPS readings by Patrick Wallace)
+ 800  CONTINUE
+      NAME='Gemini South 8-m telescope'
+      W=WEST(70,44,11.5)
+      P=SOUTH(30,14,26.7)
+      H=2738D0
+      GO TO 9999
+
+*  Cologne Observatory for Submillimeter Astronomy (KOSMA)        KOSMA3M
+*  (Holger Jakob)
+ 810  CONTINUE
+      NAME='KOSMA 3m telescope, Gornergrat'
+      W=EAST(7,47,3.48)
+      P=NORTH(45,58,59.772)
+      H=3141D0
+      GO TO 9999
+
+*  Magellan 1, 6.5m telescope at Las Campanas, Chile            MAGELLAN1
+*  (Skip Schaller)
+ 820  CONTINUE
+      NAME='Magellan 1, 6.5m, Las Campanas'
+      W=WEST(70,41,31.9)
+      P=SOUTH(29,00,51.7)
+      H=2408D0
+      GO TO 9999
+
+*  Magellan 2, 6.5m telescope at Las Campanas, Chile            MAGELLAN2
+*  (Skip Schaller)
+ 830  CONTINUE
+      NAME='Magellan 2, 6.5m, Las Campanas'
+      W=WEST(70,41,33.5)
+      P=SOUTH(29,00,50.3)
+      H=2408D0
+      GO TO 9999
+
+*  Unrecognized station
+ 9000 CONTINUE
+      NAME='?'
+
+*  Exit
+ 9999 CONTINUE
+
+      END
diff --git a/math/slalib/pa.f b/math/slalib/pa.f
new file mode 100644
index 00000000..88d21105
--- /dev/null
+++ b/math/slalib/pa.f
@@ -0,0 +1,64 @@
+      DOUBLE PRECISION FUNCTION slPA (HA, DEC, PHI)
+*+
+*     - - -
+*      P A
+*     - - -
+*
+*  HA, Dec to Parallactic Angle (double precision)
+*
+*  Given:
+*     HA     d     hour angle in radians (geocentric apparent)
+*     DEC    d     declination in radians (geocentric apparent)
+*     PHI    d     observatory latitude in radians (geodetic)
+*
+*  The result is in the range -pi to +pi
+*
+*  Notes:
+*
+*  1)  The parallactic angle at a point in the sky is the position
+*      angle of the vertical, i.e. the angle between the direction to
+*      the pole and to the zenith.  In precise applications care must
+*      be taken only to use geocentric apparent HA,Dec and to consider
+*      separately the effects of atmospheric refraction and telescope
+*      mount errors.
+*
+*  2)  At the pole a zero result is returned.
+*
+*  P.T.Wallace   Starlink   16 August 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION HA,DEC,PHI
+
+      DOUBLE PRECISION CP,SQSZ,CQSZ
+
+
+
+      CP=COS(PHI)
+      SQSZ=CP*SIN(HA)
+      CQSZ=SIN(PHI)*COS(DEC)-CP*SIN(DEC)*COS(HA)
+      IF (SQSZ.EQ.0D0.AND.CQSZ.EQ.0D0) CQSZ=1D0
+      slPA=ATAN2(SQSZ,CQSZ)
+
+      END
diff --git a/math/slalib/pav.f b/math/slalib/pav.f
new file mode 100644
index 00000000..6e6af8a3
--- /dev/null
+++ b/math/slalib/pav.f
@@ -0,0 +1,71 @@
+      REAL FUNCTION slPAV ( V1, V2 )
+*+
+*     - - - -
+*      P A V
+*     - - - -
+*
+*  Position angle of one celestial direction with respect to another.
+*
+*  (single precision)
+*
+*  Given:
+*     V1    r(3)    direction cosines of one point
+*     V2    r(3)    direction cosines of the other point
+*
+*  (The coordinate frames correspond to RA,Dec, Long,Lat etc.)
+*
+*  The result is the bearing (position angle), in radians, of point
+*  V2 with respect to point V1.  It is in the range +/- pi.  The
+*  sense is such that if V2 is a small distance east of V1, the
+*  bearing is about +pi/2.  Zero is returned if the two points
+*  are coincident.
+*
+*  V1 and V2 do not have to be unit vectors.
+*
+*  The routine slBEAR performs an equivalent function except
+*  that the points are specified in the form of spherical
+*  coordinates.
+*
+*  Called:  slDPAV
+*
+*  Last revision:   11 September 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL V1(3), V2(3)
+
+      INTEGER I
+      DOUBLE PRECISION D1(3), D2(3)
+
+      DOUBLE PRECISION slDPAV
+
+
+*  Call the double precision version.
+      DO I=1,3
+         D1(I) = V1(I)
+         D2(I) = V2(I)
+      END DO
+      slPAV = REAL(slDPAV(D1,D2))
+
+      END
diff --git a/math/slalib/pcd.f b/math/slalib/pcd.f
new file mode 100644
index 00000000..cef1dbf7
--- /dev/null
+++ b/math/slalib/pcd.f
@@ -0,0 +1,77 @@
+      SUBROUTINE slPCD (DISCO,X,Y)
+*+
+*     - - - -
+*      P C D
+*     - - - -
+*
+*  Apply pincushion/barrel distortion to a tangent-plane [x,y].
+*
+*  Given:
+*     DISCO    d      pincushion/barrel distortion coefficient
+*     X,Y      d      tangent-plane coordinates
+*
+*  Returned:
+*     X,Y      d      distorted coordinates
+*
+*  Notes:
+*
+*  1)  The distortion is of the form RP = R*(1 + C*R**2), where R is
+*      the radial distance from the tangent point, C is the DISCO
+*      argument, and RP is the radial distance in the presence of
+*      the distortion.
+*
+*  2)  For pincushion distortion, C is +ve;  for barrel distortion,
+*      C is -ve.
+*
+*  3)  For X,Y in units of one projection radius (in the case of
+*      a photographic plate, the focal length), the following
+*      DISCO values apply:
+*
+*          Geometry          DISCO
+*
+*          astrograph         0.0
+*          Schmidt           -0.3333
+*          AAT PF doublet  +147.069
+*          AAT PF triplet  +178.585
+*          AAT f/8          +21.20
+*          JKT f/8          +13.32
+*
+*  4)  There is a companion routine, slUPCD, which performs the
+*      inverse operation.
+*
+*  P.T.Wallace   Starlink   3 September 2000
+*
+*  Copyright (C) 2000 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DISCO,X,Y
+
+      DOUBLE PRECISION F
+
+
+
+      F=1D0+DISCO*(X*X+Y*Y)
+      X=X*F
+      Y=Y*F
+
+      END
diff --git a/math/slalib/pda2h.f b/math/slalib/pda2h.f
new file mode 100644
index 00000000..ea8a3425
--- /dev/null
+++ b/math/slalib/pda2h.f
@@ -0,0 +1,118 @@
+      SUBROUTINE slPDAH (P, D, A, H1, J1, H2, J2)
+*+
+*     - - - - - -
+*      P D A H
+*     - - - - - -
+*
+*  Hour Angle corresponding to a given azimuth
+*
+*  (double precision)
+*
+*  Given:
+*     P       d        latitude
+*     D       d        declination
+*     A       d        azimuth
+*
+*  Returned:
+*     H1      d        hour angle:  first solution if any
+*     J1      i        flag: 0 = solution 1 is valid
+*     H2      d        hour angle:  second solution if any
+*     J2      i        flag: 0 = solution 2 is valid
+*
+*  Called:  slDA1P
+*
+*  P.T.Wallace   Starlink   6 October 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION P,D,A,H1
+      INTEGER J1
+      DOUBLE PRECISION H2
+      INTEGER J2
+
+      DOUBLE PRECISION DPI
+      PARAMETER (DPI=3.141592653589793238462643D0)
+      DOUBLE PRECISION D90
+      PARAMETER (D90=DPI/2D0)
+      DOUBLE PRECISION TINY
+      PARAMETER (TINY=1D-12)
+      DOUBLE PRECISION PN,AN,DN,SA,CA,SASP,QT,QB,HPT,T
+      DOUBLE PRECISION slDA1P
+
+
+*  Preset status flags to OK
+      J1=0
+      J2=0
+
+*  Adjust latitude, azimuth, declination to avoid critical values
+      PN=slDA1P(P)
+      IF (ABS(ABS(PN)-D90).LT.TINY) THEN
+         PN=PN-SIGN(TINY,PN)
+      ELSE IF (ABS(PN).LT.TINY) THEN
+         PN=TINY
+      END IF
+      AN=slDA1P(A)
+      IF (ABS(ABS(AN)-DPI).LT.TINY) THEN
+         AN=AN-SIGN(TINY,AN)
+      ELSE IF (ABS(AN).LT.TINY) THEN
+         AN=TINY
+      END IF
+      DN=slDA1P(D)
+      IF (ABS(ABS(DN)-ABS(P)).LT.TINY) THEN
+         DN=DN-SIGN(TINY,DN)
+      ELSE IF (ABS(ABS(DN)-D90).LT.TINY) THEN
+         DN=DN-SIGN(TINY,DN)
+      ELSE IF (ABS(DN).LT.TINY) THEN
+         DN=TINY
+      END IF
+
+*  Useful functions
+      SA=SIN(AN)
+      CA=COS(AN)
+      SASP=SA*SIN(PN)
+
+*  Quotient giving sin(h+t)
+      QT=SIN(DN)*SA*COS(PN)
+      QB=COS(DN)*SQRT(CA*CA+SASP*SASP)
+
+*  Any solutions?
+      IF (ABS(QT).LE.QB) THEN
+
+*     Yes: find h+t and t
+         HPT=ASIN(QT/QB)
+         T=ATAN2(SASP,-CA)
+
+*     The two solutions
+         H1=slDA1P(HPT-T)
+         H2=slDA1P(-HPT-(T+DPI))
+
+*     Reject unless h and A different signs
+         IF (H1*AN.GT.0D0) J1=-1
+         IF (H2*AN.GT.0D0) J2=-1
+      ELSE
+         J1=-1
+         J2=-1
+      END IF
+
+      END
diff --git a/math/slalib/pdq2h.f b/math/slalib/pdq2h.f
new file mode 100644
index 00000000..678bb3d7
--- /dev/null
+++ b/math/slalib/pdq2h.f
@@ -0,0 +1,116 @@
+      SUBROUTINE slPDQH (P, D, Q, H1, J1, H2, J2)
+*+
+*     - - - - - -
+*      P D Q H
+*     - - - - - -
+*
+*  Hour Angle corresponding to a given parallactic angle
+*
+*  (double precision)
+*
+*  Given:
+*     P       d        latitude
+*     D       d        declination
+*     Q       d        parallactic angle
+*
+*  Returned:
+*     H1      d        hour angle:  first solution if any
+*     J1      i        flag: 0 = solution 1 is valid
+*     H2      d        hour angle:  second solution if any
+*     J2      i        flag: 0 = solution 2 is valid
+*
+*  Called:  slDA1P
+*
+*  P.T.Wallace   Starlink   6 October 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION P,D,Q,H1
+      INTEGER J1
+      DOUBLE PRECISION H2
+      INTEGER J2
+
+      DOUBLE PRECISION DPI
+      PARAMETER (DPI=3.141592653589793238462643D0)
+      DOUBLE PRECISION D90
+      PARAMETER (D90=DPI/2D0)
+      DOUBLE PRECISION TINY
+      PARAMETER (TINY=1D-12)
+      DOUBLE PRECISION PN,QN,DN,SQ,CQ,SQSD,QT,QB,HPT,T
+      DOUBLE PRECISION slDA1P
+
+
+*  Preset status flags to OK
+      J1=0
+      J2=0
+
+*  Adjust latitude, declination, parallactic angle to avoid critical values
+      PN=slDA1P(P)
+      IF (ABS(ABS(PN)-D90).LT.TINY) THEN
+         PN=PN-SIGN(TINY,PN)
+      ELSE IF (ABS(PN).LT.TINY) THEN
+         PN=TINY
+      END IF
+      QN=slDA1P(Q)
+      IF (ABS(ABS(QN)-DPI).LT.TINY) THEN
+         QN=QN-SIGN(TINY,QN)
+      ELSE IF (ABS(QN).LT.TINY) THEN
+         QN=TINY
+      END IF
+      DN=slDA1P(D)
+      IF (ABS(ABS(D)-ABS(P)).LT.TINY) THEN
+         DN=DN-SIGN(TINY,DN)
+      ELSE IF (ABS(ABS(D)-D90).LT.TINY) THEN
+         DN=DN-SIGN(TINY,DN)
+      END IF
+
+*  Useful functions
+      SQ=SIN(QN)
+      CQ=COS(QN)
+      SQSD=SQ*SIN(DN)
+
+*  Quotient giving sin(h+t)
+      QT=SIN(PN)*SQ*COS(DN)
+      QB=COS(PN)*SQRT(CQ*CQ+SQSD*SQSD)
+
+*  Any solutions?
+      IF (ABS(QT).LE.QB) THEN
+
+*     Yes: find h+t and t
+         HPT=ASIN(QT/QB)
+         T=ATAN2(SQSD,CQ)
+
+*     The two solutions
+         H1=slDA1P(HPT-T)
+         H2=slDA1P(-HPT-(T+DPI))
+
+*     Reject if h and Q different signs
+         IF (H1*QN.LT.0D0) J1=-1
+         IF (H2*QN.LT.0D0) J2=-1
+      ELSE
+         J1=-1
+         J2=-1
+      END IF
+
+      END
diff --git a/math/slalib/permut.f b/math/slalib/permut.f
new file mode 100644
index 00000000..b5aee8b7
--- /dev/null
+++ b/math/slalib/permut.f
@@ -0,0 +1,160 @@
+      SUBROUTINE slPERM ( N, ISTATE, IORDER, J )
+*+
+*     - - - - - - -
+*      P E R M U T
+*     - - - - - - -
+*
+*  Generate the next permutation of a specified number of items.
+*
+*  Given:
+*     N         i      number of items:  there will be N! permutations
+*
+*  Given and returned:
+*     ISTATE    i(N)   state, ISTATE(1)=-1 to initialize
+*
+*  Returned:
+*     IORDER    i(N)   next permutation of numbers 1,2,...,N
+*     J         i      status: -1 = illegal N (zero or less is illegal)
+*                               0 = OK
+*                              +1 = no more permutations available
+*
+*  Notes:
+*
+*  1) This routine returns, in the IORDER array, the integers 1 to N
+*     inclusive, in an order that depends on the current contents of
+*     the ISTATE array.  Before calling the routine for the first
+*     time, the caller must set the first element of the ISTATE array
+*     to -1 (any negative number will do) to cause the ISTATE array
+*     to be fully initialized.
+*
+*  2) The first permutation to be generated is:
+*
+*          IORDER(1)=N, IORDER(2)=N-1, ..., IORDER(N)=1
+*
+*     This is also the permutation returned for the "finished"
+*     (J=1) case.
+*
+*     The final permutation to be generated is:
+*
+*          IORDER(1)=1, IORDER(2)=2, ..., IORDER(N)=N
+*
+*  3) If the "finished" (J=1) status is ignored, the routine continues
+*     to deliver permutations, the pattern repeating every N! calls.
+*
+*  Last revision:   19 February 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER N,IORDER(N),ISTATE(N),J
+
+      INTEGER I,IP1,ISLOT,ISKIP
+
+
+*  -------------
+*  Preliminaries
+*  -------------
+
+*  Validate, and set status.
+      IF (N.LT.1) THEN
+         J = -1
+         GO TO 9999
+      ELSE
+         J = 0
+      END IF
+
+*  If just starting, initialize state array
+      IF (ISTATE(1).LT.0) THEN
+         ISTATE(1) = -1
+         DO I=2,N
+            ISTATE(I) = 0
+         END DO
+      END IF
+
+*  --------------------------
+*  Increment the state number
+*  --------------------------
+
+*  The state number, maintained in the ISTATE array, is a mixed-radix
+*  number with N! states.  The least significant digit, with a radix of
+*  1, is in ISTATE(1).  The next digit, in ISTATE(2), has a radix of 2,
+*  and so on.
+
+*  Increment the least-significant digit of the state number.
+      ISTATE(1) = ISTATE(1)+1
+
+*  Digit by digit starting with the least significant.
+      DO I=1,N
+
+*     Carry?
+         IF (ISTATE(I).GE.I) THEN
+
+*        Yes:  reset the current digit.
+            ISTATE(I) = 0
+
+*        Overflow?
+            IF (I.GE.N) THEN
+
+*           Yes:  there are no more permutations.
+               J = 1
+            ELSE
+
+*           No:  carry.
+               IP1 = I+1
+               ISTATE(IP1) = ISTATE(IP1)+1
+            END IF
+         END IF
+      END DO
+
+*  -------------------------------------------------------------------
+*  Translate the state number into the corresponding permutation order
+*  -------------------------------------------------------------------
+
+*  Initialize the order array.  All but one element will be overwritten.
+      DO I=1,N
+         IORDER(I) = 1
+      END DO
+
+*  Look at each state number digit, starting with the most significant.
+      DO I=N,2,-1
+
+*     Initialize the position where the new number will go.
+         ISLOT = 0
+
+*     The state number digit says which unfilled slot is to be used.
+         DO ISKIP=0,ISTATE(I)
+
+*        Increment the slot number until an unused slot is found.
+            ISLOT = ISLOT+1
+            DO WHILE (IORDER(ISLOT).GT.1)
+               ISLOT = ISLOT+1
+            END DO
+         END DO
+
+*     Store the number in the permutation order array.
+         IORDER(ISLOT) = I
+      END DO
+
+ 9999 CONTINUE
+
+      END
diff --git a/math/slalib/pertel.f b/math/slalib/pertel.f
new file mode 100644
index 00000000..06bf3c42
--- /dev/null
+++ b/math/slalib/pertel.f
@@ -0,0 +1,182 @@
+      SUBROUTINE slPRTL (JFORM, DATE0, DATE1,
+     :                 EPOCH0, ORBI0, ANODE0, PERIH0, AORQ0, E0, AM0,
+     :                 EPOCH1, ORBI1, ANODE1, PERIH1, AORQ1, E1, AM1,
+     :                       JSTAT)
+*+
+*     - - - - - - -
+*      P R T L
+*     - - - - - - -
+*
+*  Update the osculating orbital elements of an asteroid or comet by
+*  applying planetary perturbations.
+*
+*  Given (format and dates):
+*     JFORM   i    choice of element set (2 or 3; Note 1)
+*     DATE0   d    date of osculation (TT MJD) for the given elements
+*     DATE1   d    date of osculation (TT MJD) for the updated elements
+*
+*  Given (the unperturbed elements):
+*     EPOCH0  d    epoch (TT MJD) of the given element set (Note 2)
+*     ORBI0   d    inclination (radians)
+*     ANODE0  d    longitude of the ascending node (radians)
+*     PERIH0  d    argument of perihelion (radians)
+*     AORQ0   d    mean distance or perihelion distance (AU)
+*     E0      d    eccentricity
+*     AM0     d    mean anomaly (radians, JFORM=2 only)
+*
+*  Returned (the updated elements):
+*     EPOCH1  d    epoch (TT MJD) of the updated element set (Note 2)
+*     ORBI1   d    inclination (radians)
+*     ANODE1  d    longitude of the ascending node (radians)
+*     PERIH1  d    argument of perihelion (radians)
+*     AORQ1   d    mean distance or perihelion distance (AU)
+*     E1      d    eccentricity
+*     AM1     d    mean anomaly (radians, JFORM=2 only)
+*
+*  Returned (status flag):
+*     JSTAT   i    status: +102 = warning, distant epoch
+*                          +101 = warning, large timespan ( > 100 years)
+*                     +1 to +10 = coincident with planet (Note 6)
+*                             0 = OK
+*                            -1 = illegal JFORM
+*                            -2 = illegal E0
+*                            -3 = illegal AORQ0
+*                            -4 = internal error
+*                            -5 = numerical error
+*
+*  Notes:
+*
+*  1  Two different element-format options are available:
+*
+*     Option JFORM=2, suitable for minor planets:
+*
+*     EPOCH   = epoch of elements (TT MJD)
+*     ORBI    = inclination i (radians)
+*     ANODE   = longitude of the ascending node, big omega (radians)
+*     PERIH   = argument of perihelion, little omega (radians)
+*     AORQ    = mean distance, a (AU)
+*     E       = eccentricity, e
+*     AM      = mean anomaly M (radians)
+*
+*     Option JFORM=3, suitable for comets:
+*
+*     EPOCH   = epoch of perihelion (TT MJD)
+*     ORBI    = inclination i (radians)
+*     ANODE   = longitude of the ascending node, big omega (radians)
+*     PERIH   = argument of perihelion, little omega (radians)
+*     AORQ    = perihelion distance, q (AU)
+*     E       = eccentricity, e
+*
+*  2  DATE0, DATE1, EPOCH0 and EPOCH1 are all instants of time in
+*     the TT timescale (formerly Ephemeris Time, ET), expressed
+*     as Modified Julian Dates (JD-2400000.5).
+*
+*     DATE0 is the instant at which the given (i.e. unperturbed)
+*     osculating elements are correct.
+*
+*     DATE1 is the specified instant at which the updated osculating
+*     elements are correct.
+*
+*     EPOCH0 and EPOCH1 will be the same as DATE0 and DATE1
+*     (respectively) for the JFORM=2 case, normally used for minor
+*     planets.  For the JFORM=3 case, the two epochs will refer to
+*     perihelion passage and so will not, in general, be the same as
+*     DATE0 and/or DATE1 though they may be similar to one another.
+*
+*  3  The elements are with respect to the J2000 ecliptic and equinox.
+*
+*  4  Unused elements (AM0 and AM1 for JFORM=3) are not accessed.
+*
+*  5  See the slPRTE routine for details of the algorithm used.
+*
+*  6  This routine is not intended to be used for major planets, which
+*     is why JFORM=1 is not available and why there is no opportunity
+*     to specify either the longitude of perihelion or the daily
+*     motion.  However, if JFORM=2 elements are somehow obtained for a
+*     major planet and supplied to the routine, sensible results will,
+*     in fact, be produced.  This happens because the slPRTE routine
+*     that is called to perform the calculations checks the separation
+*     between the body and each of the planets and interprets a
+*     suspiciously small value (0.001 AU) as an attempt to apply it to
+*     the planet concerned.  If this condition is detected, the
+*     contribution from that planet is ignored, and the status is set to
+*     the planet number (1-10 = Mercury, Venus, EMB, Mars, Jupiter,
+*     Saturn, Uranus, Neptune, Earth, Moon) as a warning.
+*
+*  Reference:
+*
+*     Sterne, Theodore E., "An Introduction to Celestial Mechanics",
+*     Interscience Publishers Inc., 1960.  Section 6.7, p199.
+*
+*  Called:  slELUE, slPRTE, slUEEL
+*
+*  This revision:   19 June 2004
+*
+*  Copyright (C) 2004 P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+      INTEGER JFORM
+      DOUBLE PRECISION DATE0,DATE1,
+     :                 EPOCH0,ORBI0,ANODE0,PERIH0,AORQ0,E0,AM0,
+     :                 EPOCH1,ORBI1,ANODE1,PERIH1,AORQ1,E1,AM1
+      INTEGER JSTAT
+
+      DOUBLE PRECISION U(13),DM
+      INTEGER J,JF
+
+
+
+*  Check that the elements are either minor-planet or comet format.
+      IF (JFORM.LT.2.OR.JFORM.GT.3) THEN
+         JSTAT = -1
+         GO TO 9999
+      ELSE
+
+*     Provisionally set the status to OK.
+         JSTAT = 0
+      END IF
+
+*  Transform the elements from conventional to universal form.
+      CALL slELUE(DATE0,JFORM,EPOCH0,ORBI0,ANODE0,PERIH0,
+     :               AORQ0,E0,AM0,0D0,U,J)
+      IF (J.NE.0) THEN
+         JSTAT = J
+         GO TO 9999
+      END IF
+
+*  Update the universal elements.
+      CALL slPRTE(DATE1,U,J)
+      IF (J.GT.0) THEN
+         JSTAT = J
+      ELSE IF (J.LT.0) THEN
+         JSTAT = -5
+         GO TO 9999
+      END IF
+
+*  Transform from universal to conventional elements.
+      CALL slUEEL(U,JFORM,
+     :               JF, EPOCH1, ORBI1, ANODE1, PERIH1,
+     :               AORQ1, E1, AM1, DM, J)
+      IF (JF.NE.JFORM.OR.J.NE.0) JSTAT=-5
+
+ 9999 CONTINUE
+      END
diff --git a/math/slalib/pertue.f b/math/slalib/pertue.f
new file mode 100644
index 00000000..fc9683c5
--- /dev/null
+++ b/math/slalib/pertue.f
@@ -0,0 +1,644 @@
+      SUBROUTINE slPRTE (DATE, U, JSTAT)
+*+
+*     - - - - - - -
+*      P R T E
+*     - - - - - - -
+*
+*  Update the universal elements of an asteroid or comet by applying
+*  planetary perturbations.
+*
+*  Given:
+*     DATE     d       final epoch (TT MJD) for the updated elements
+*
+*  Given and returned:
+*     U        d(13)   universal elements (updated in place)
+*
+*                (1)   combined mass (M+m)
+*                (2)   total energy of the orbit (alpha)
+*                (3)   reference (osculating) epoch (t0)
+*              (4-6)   position at reference epoch (r0)
+*              (7-9)   velocity at reference epoch (v0)
+*               (10)   heliocentric distance at reference epoch
+*               (11)   r0.v0
+*               (12)   date (t)
+*               (13)   universal eccentric anomaly (psi) of date, approx
+*
+*  Returned:
+*     JSTAT    i       status:
+*                          +102 = warning, distant epoch
+*                          +101 = warning, large timespan ( > 100 years)
+*                     +1 to +10 = coincident with major planet (Note 5)
+*                             0 = OK
+*                            -1 = numerical error
+*
+*  Called:  slEPJ, slPLNT, slPVUE, slUEPV, slEPV,
+*           slPREC, slDMON, slDMXV
+*
+*  Notes:
+*
+*  1  The "universal" elements are those which define the orbit for the
+*     purposes of the method of universal variables (see reference 2).
+*     They consist of the combined mass of the two bodies, an epoch,
+*     and the position and velocity vectors (arbitrary reference frame)
+*     at that epoch.  The parameter set used here includes also various
+*     quantities that can, in fact, be derived from the other
+*     information.  This approach is taken to avoiding unnecessary
+*     computation and loss of accuracy.  The supplementary quantities
+*     are (i) alpha, which is proportional to the total energy of the
+*     orbit, (ii) the heliocentric distance at epoch, (iii) the
+*     outwards component of the velocity at the given epoch, (iv) an
+*     estimate of psi, the "universal eccentric anomaly" at a given
+*     date and (v) that date.
+*
+*  2  The universal elements are with respect to the J2000 equator and
+*     equinox.
+*
+*  3  The epochs DATE, U(3) and U(12) are all Modified Julian Dates
+*     (JD-2400000.5).
+*
+*  4  The algorithm is a simplified form of Encke's method.  It takes as
+*     a basis the unperturbed motion of the body, and numerically
+*     integrates the perturbing accelerations from the major planets.
+*     The expression used is essentially Sterne's 6.7-2 (reference 1).
+*     Everhart and Pitkin (reference 2) suggest rectifying the orbit at
+*     each integration step by propagating the new perturbed position
+*     and velocity as the new universal variables.  In the present
+*     routine the orbit is rectified less frequently than this, in order
+*     to gain a slight speed advantage.  However, the rectification is
+*     done directly in terms of position and velocity, as suggested by
+*     Everhart and Pitkin, bypassing the use of conventional orbital
+*     elements.
+*
+*     The f(q) part of the full Encke method is not used.  The purpose
+*     of this part is to avoid subtracting two nearly equal quantities
+*     when calculating the "indirect member", which takes account of the
+*     small change in the Sun's attraction due to the slightly displaced
+*     position of the perturbed body.  A simpler, direct calculation in
+*     double precision proves to be faster and not significantly less
+*     accurate.
+*
+*     Apart from employing a variable timestep, and occasionally
+*     "rectifying the orbit" to keep the indirect member small, the
+*     integration is done in a fairly straightforward way.  The
+*     acceleration estimated for the middle of the timestep is assumed
+*     to apply throughout that timestep;  it is also used in the
+*     extrapolation of the perturbations to the middle of the next
+*     timestep, to predict the new disturbed position.  There is no
+*     iteration within a timestep.
+*
+*     Measures are taken to reach a compromise between execution time
+*     and accuracy.  The starting-point is the goal of achieving
+*     arcsecond accuracy for ordinary minor planets over a ten-year
+*     timespan.  This goal dictates how large the timesteps can be,
+*     which in turn dictates how frequently the unperturbed motion has
+*     to be recalculated from the osculating elements.
+*
+*     Within predetermined limits, the timestep for the numerical
+*     integration is varied in length in inverse proportion to the
+*     magnitude of the net acceleration on the body from the major
+*     planets.
+*
+*     The numerical integration requires estimates of the major-planet
+*     motions.  Approximate positions for the major planets (Pluto
+*     alone is omitted) are obtained from the routine slPLNT.  Two
+*     levels of interpolation are used, to enhance speed without
+*     significantly degrading accuracy.  At a low frequency, the routine
+*     slPLNT is called to generate updated position+velocity "state
+*     vectors".  The only task remaining to be carried out at the full
+*     frequency (i.e. at each integration step) is to use the state
+*     vectors to extrapolate the planetary positions.  In place of a
+*     strictly linear extrapolation, some allowance is made for the
+*     curvature of the orbit by scaling back the radius vector as the
+*     linear extrapolation goes off at a tangent.
+*
+*     Various other approximations are made.  For example, perturbations
+*     by Pluto and the minor planets are neglected and relativistic
+*     effects are not taken into account.
+*
+*     In the interests of simplicity, the background calculations for
+*     the major planets are carried out en masse.  The mean elements and
+*     state vectors for all the planets are refreshed at the same time,
+*     without regard for orbit curvature, mass or proximity.
+*
+*     The Earth-Moon system is treated as a single body when the body is
+*     distant but as separate bodies when closer to the EMB than the
+*     parameter RNE, which incurs a time penalty but improves accuracy
+*     for near-Earth objects.
+*
+*  5  This routine is not intended to be used for major planets.
+*     However, if major-planet elements are supplied, sensible results
+*     will, in fact, be produced.  This happens because the routine
+*     checks the separation between the body and each of the planets and
+*     interprets a suspiciously small value (0.001 AU) as an attempt to
+*     apply the routine to the planet concerned.  If this condition is
+*     detected, the contribution from that planet is ignored, and the
+*     status is set to the planet number (1-10 = Mercury, Venus, EMB,
+*     Mars, Jupiter, Saturn, Uranus, Neptune, Earth, Moon) as a warning.
+*
+*  References:
+*
+*     1  Sterne, Theodore E., "An Introduction to Celestial Mechanics",
+*        Interscience Publishers Inc., 1960.  Section 6.7, p199.
+*
+*     2  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
+*
+*  Last revision:   27 December 2004
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+      DOUBLE PRECISION DATE,U(13)
+      INTEGER JSTAT
+
+*  Distance from EMB at which Earth and Moon are treated separately
+      DOUBLE PRECISION RNE
+      PARAMETER (RNE=1D0)
+
+*  Coincidence with major planet distance
+      DOUBLE PRECISION COINC
+      PARAMETER (COINC=0.0001D0)
+
+*  Coefficient relating timestep to perturbing force
+      DOUBLE PRECISION TSC
+      PARAMETER (TSC=1D-4)
+
+*  Minimum and maximum timestep (days)
+      DOUBLE PRECISION TSMIN,TSMAX
+      PARAMETER (TSMIN=0.01D0,TSMAX=10D0)
+
+*  Age limit for major-planet state vector (days)
+      DOUBLE PRECISION AGEPMO
+      PARAMETER (AGEPMO=5D0)
+
+*  Age limit for major-planet mean elements (days)
+      DOUBLE PRECISION AGEPEL
+      PARAMETER (AGEPEL=50D0)
+
+*  Margin for error when deciding whether to renew the planetary data
+      DOUBLE PRECISION TINY
+      PARAMETER (TINY=1D-6)
+
+*  Age limit for the body's osculating elements (before rectification)
+      DOUBLE PRECISION AGEBEL
+      PARAMETER (AGEBEL=100D0)
+
+*  Gaussian gravitational constant (exact) and square
+      DOUBLE PRECISION GCON,GCON2
+      PARAMETER (GCON=0.01720209895D0,GCON2=GCON*GCON)
+
+*  The final epoch
+      DOUBLE PRECISION TFINAL
+
+*  The body's current universal elements
+      DOUBLE PRECISION UL(13)
+
+*  Current reference epoch
+      DOUBLE PRECISION T0
+
+*  Timespan from latest orbit rectification to final epoch (days)
+      DOUBLE PRECISION TSPAN
+
+*  Time left to go before integration is complete
+      DOUBLE PRECISION TLEFT
+
+*  Time direction flag: +1=forwards, -1=backwards
+      DOUBLE PRECISION FB
+
+*  First-time flag
+      LOGICAL FIRST
+
+*
+*  The current perturbations
+*
+*  Epoch (days relative to current reference epoch)
+      DOUBLE PRECISION RTN
+*  Position (AU)
+      DOUBLE PRECISION PERP(3)
+*  Velocity (AU/d)
+      DOUBLE PRECISION PERV(3)
+*  Acceleration (AU/d/d)
+      DOUBLE PRECISION PERA(3)
+*
+
+*  Length of current timestep (days), and half that
+      DOUBLE PRECISION TS,HTS
+
+*  Epoch of middle of timestep
+      DOUBLE PRECISION T
+
+*  Epoch of planetary mean elements
+      DOUBLE PRECISION TPEL
+
+*  Planet number (1=Mercury, 2=Venus, 3=EMB...8=Neptune)
+      INTEGER NP
+
+*  Planetary universal orbital elements
+      DOUBLE PRECISION UP(13,8)
+
+*  Epoch of planetary state vectors
+      DOUBLE PRECISION TPMO
+
+*  State vectors for the major planets (AU,AU/s)
+      DOUBLE PRECISION PVIN(6,8)
+
+*  Earth velocity and position vectors (AU,AU/s)
+      DOUBLE PRECISION VB(3),PB(3),VH(3),PE(3)
+
+*  Moon geocentric state vector (AU,AU/s) and position part
+      DOUBLE PRECISION PVM(6),PM(3)
+
+*  Date to J2000 de-precession matrix
+      DOUBLE PRECISION PMAT(3,3)
+
+*
+*  Correction terms for extrapolated major planet vectors
+*
+*  Sun-to-planet distances squared multiplied by 3
+      DOUBLE PRECISION R2X3(8)
+*  Sunward acceleration terms, G/2R^3
+      DOUBLE PRECISION GC(8)
+*  Tangential-to-circular correction factor
+      DOUBLE PRECISION FC
+*  Radial correction factor due to Sunwards acceleration
+      DOUBLE PRECISION FG
+*
+
+*  The body's unperturbed and perturbed state vectors (AU,AU/s)
+      DOUBLE PRECISION PV0(6),PV(6)
+
+*  The body's perturbed and unperturbed heliocentric distances (AU) cubed
+      DOUBLE PRECISION R03,R3
+
+*  The perturbating accelerations, indirect and direct
+      DOUBLE PRECISION FI(3),FD(3)
+
+*  Sun-to-planet vector, and distance cubed
+      DOUBLE PRECISION RHO(3),RHO3
+
+*  Body-to-planet vector, and distance cubed
+      DOUBLE PRECISION DELTA(3),DELTA3
+
+*  Miscellaneous
+      INTEGER I,J
+      DOUBLE PRECISION R2,W,DT,DT2,R,FT
+      LOGICAL NE
+
+      DOUBLE PRECISION slEPJ
+
+*  Planetary inverse masses, Mercury through Neptune then Earth and Moon
+      DOUBLE PRECISION AMAS(10)
+      DATA AMAS / 6023600D0, 408523.5D0, 328900.5D0, 3098710D0,
+     :            1047.355D0, 3498.5D0, 22869D0, 19314D0,
+     :            332946.038D0, 27068709D0 /
+
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*----------------------------------------------------------------------*
+
+
+*  Preset the status to OK.
+      JSTAT = 0
+
+*  Copy the final epoch.
+      TFINAL = DATE
+
+*  Copy the elements (which will be periodically updated).
+      DO I=1,13
+         UL(I) = U(I)
+      END DO
+
+*  Initialize the working reference epoch.
+      T0=UL(3)
+
+*  Total timespan (days) and hence time left.
+      TSPAN = TFINAL-T0
+      TLEFT = TSPAN
+
+*  Warn if excessive.
+      IF (ABS(TSPAN).GT.36525D0) JSTAT=101
+
+*  Time direction: +1 for forwards, -1 for backwards.
+      FB = SIGN(1D0,TSPAN)
+
+*  Initialize relative epoch for start of current timestep.
+      RTN = 0D0
+
+*  Reset the perturbations (position, velocity, acceleration).
+      DO I=1,3
+         PERP(I) = 0D0
+         PERV(I) = 0D0
+         PERA(I) = 0D0
+      END DO
+
+*  Set "first iteration" flag.
+      FIRST = .TRUE.
+
+*  Step through the time left.
+      DO WHILE (FB*TLEFT.GT.0D0)
+
+*     Magnitude of current acceleration due to planetary attractions.
+         IF (FIRST) THEN
+            TS = TSMIN
+         ELSE
+            R2 = 0D0
+            DO I=1,3
+               W = FD(I)
+               R2 = R2+W*W
+            END DO
+            W = SQRT(R2)
+
+*        Use the acceleration to decide how big a timestep can be tolerated.
+            IF (W.NE.0D0) THEN
+               TS = MIN(TSMAX,MAX(TSMIN,TSC/W))
+            ELSE
+               TS = TSMAX
+            END IF
+         END IF
+         TS = TS*FB
+
+*     Override if final epoch is imminent.
+         TLEFT = TSPAN-RTN
+         IF (ABS(TS).GT.ABS(TLEFT)) TS=TLEFT
+
+*     Epoch of middle of timestep.
+         HTS = TS/2D0
+         T = T0+RTN+HTS
+
+*     Is it time to recompute the major-planet elements?
+         IF (FIRST.OR.ABS(T-TPEL)-AGEPEL.GE.TINY) THEN
+
+*        Yes: go forward in time by just under the maximum allowed.
+            TPEL = T+FB*AGEPEL
+
+*        Compute the state vector for the new epoch.
+            DO NP=1,8
+               CALL slPLNT(TPEL,NP,PV,J)
+
+*           Warning if remote epoch, abort if error.
+               IF (J.EQ.1) THEN
+                  JSTAT = 102
+               ELSE IF (J.NE.0) THEN
+                  GO TO 9010
+               END IF
+
+*           Transform the vector into universal elements.
+               CALL slPVUE(PV,TPEL,0D0,UP(1,NP),J)
+               IF (J.NE.0) GO TO 9010
+            END DO
+         END IF
+
+*     Is it time to recompute the major-planet motions?
+         IF (FIRST.OR.ABS(T-TPMO)-AGEPMO.GE.TINY) THEN
+
+*        Yes: look ahead.
+            TPMO = T+FB*AGEPMO
+
+*        Compute the motions of each planet (AU,AU/d).
+            DO NP=1,8
+
+*           The planet's position and velocity (AU,AU/s).
+               CALL slUEPV(TPMO,UP(1,NP),PVIN(1,NP),J)
+               IF (J.NE.0) GO TO 9010
+
+*           Scale velocity to AU/d.
+               DO J=4,6
+                  PVIN(J,NP) = PVIN(J,NP)*86400D0
+               END DO
+
+*           Precompute also the extrapolation correction terms.
+               R2 = 0D0
+               DO I=1,3
+                  W = PVIN(I,NP)
+                  R2 = R2+W*W
+               END DO
+               R2X3(NP) = R2*3D0
+               GC(NP) = GCON2/(2D0*R2*SQRT(R2))
+            END DO
+         END IF
+
+*     Reset the first-time flag.
+         FIRST = .FALSE.
+
+*     Unperturbed motion of the body at middle of timestep (AU,AU/s).
+         CALL slUEPV(T,UL,PV0,J)
+         IF (J.NE.0) GO TO 9010
+
+*     Perturbed position of the body (AU) and heliocentric distance cubed.
+         R2 = 0D0
+         DO I=1,3
+            W = PV0(I)+PERP(I)+(PERV(I)+PERA(I)*HTS/2D0)*HTS
+            PV(I) = W
+            R2 = R2+W*W
+         END DO
+         R3 = R2*SQRT(R2)
+
+*     The body's unperturbed heliocentric distance cubed.
+         R2 = 0D0
+         DO I=1,3
+            W = PV0(I)
+            R2 = R2+W*W
+         END DO
+         R03 = R2*SQRT(R2)
+
+*     Compute indirect and initialize direct parts of the perturbation.
+         DO I=1,3
+            FI(I) = PV0(I)/R03-PV(I)/R3
+            FD(I) = 0D0
+         END DO
+
+*     Ready to compute the direct planetary effects.
+
+*     Reset the "near-Earth" flag.
+         NE = .FALSE.
+
+*     Interval from state-vector epoch to middle of current timestep.
+         DT = T-TPMO
+         DT2 = DT*DT
+
+*     Planet by planet, including separate Earth and Moon.
+         DO NP=1,10
+
+*        Which perturbing body?
+            IF (NP.LE.8) THEN
+
+*           Planet: compute the extrapolation in longitude (squared).
+               R2 = 0D0
+               DO J=4,6
+                  W = PVIN(J,NP)*DT
+                  R2 = R2+W*W
+               END DO
+
+*           Hence the tangential-to-circular correction factor.
+               FC = 1D0+R2/R2X3(NP)
+
+*           The radial correction factor due to the inwards acceleration.
+               FG = 1D0-GC(NP)*DT2
+
+*           Planet's position.
+               DO I=1,3
+                  RHO(I) = FG*(PVIN(I,NP)+FC*PVIN(I+3,NP)*DT)
+               END DO
+
+            ELSE IF (NE) THEN
+
+*           Near-Earth and either Earth or Moon.
+
+               IF (NP.EQ.9) THEN
+
+*              Earth: position.
+                  CALL slEPV(T,PE,VH,PB,VB)
+                  DO I=1,3
+                     RHO(I) = PE(I)
+                  END DO
+
+               ELSE
+
+*              Moon: position.
+                  CALL slPREC(slEPJ(T),2000D0,PMAT)
+                  CALL slDMON(T,PVM)
+                  CALL slDMXV(PMAT,PVM,PM)
+                  DO I=1,3
+                     RHO(I) = PM(I)+PE(I)
+                  END DO
+               END IF
+            END IF
+
+*        Proceed unless Earth or Moon and not the near-Earth case.
+            IF (NP.LE.8.OR.NE) THEN
+
+*           Heliocentric distance cubed.
+               R2 = 0D0
+               DO I=1,3
+                  W = RHO(I)
+                  R2 = R2+W*W
+               END DO
+               R = SQRT(R2)
+               RHO3 = R2*R
+
+*           Body-to-planet vector, and distance.
+               R2 = 0D0
+               DO I=1,3
+                  W = RHO(I)-PV(I)
+                  DELTA(I) = W
+                  R2 = R2+W*W
+               END DO
+               R = SQRT(R2)
+
+*           If this is the EMB, set the near-Earth flag appropriately.
+               IF (NP.EQ.3.AND.R.LT.RNE) NE = .TRUE.
+
+*           Proceed unless EMB and this is the near-Earth case.
+               IF (.NOT.(NE.AND.NP.EQ.3)) THEN
+
+*              If too close, ignore this planet and set a warning.
+                  IF (R.LT.COINC) THEN
+                     JSTAT = NP
+
+                  ELSE
+
+*                 Accumulate "direct" part of perturbation acceleration.
+                     DELTA3 = R2*R
+                     W = AMAS(NP)
+                     DO I=1,3
+                        FD(I) = FD(I)+(DELTA(I)/DELTA3-RHO(I)/RHO3)/W
+                     END DO
+                  END IF
+               END IF
+            END IF
+         END DO
+
+*     Update the perturbations to the end of the timestep.
+         RTN = RTN+TS
+         DO I=1,3
+            W = (FI(I)+FD(I))*GCON2
+            FT = W*TS
+            PERP(I) = PERP(I)+(PERV(I)+FT/2D0)*TS
+            PERV(I) = PERV(I)+FT
+            PERA(I) = W
+         END DO
+
+*     Time still to go.
+         TLEFT = TSPAN-RTN
+
+*     Is it either time to rectify the orbit or the last time through?
+         IF (ABS(RTN).GE.AGEBEL.OR.FB*TLEFT.LE.0D0) THEN
+
+*        Yes: update to the end of the current timestep.
+            T0 = T0+RTN
+            RTN = 0D0
+
+*        The body's unperturbed motion (AU,AU/s).
+            CALL slUEPV(T0,UL,PV0,J)
+            IF (J.NE.0) GO TO 9010
+
+*        Add and re-initialize the perturbations.
+            DO I=1,3
+               J = I+3
+               PV(I) = PV0(I)+PERP(I)
+               PV(J) = PV0(J)+PERV(I)/86400D0
+               PERP(I) = 0D0
+               PERV(I) = 0D0
+               PERA(I) = FD(I)*GCON2
+            END DO
+
+*        Use the position and velocity to set up new universal elements.
+            CALL slPVUE(PV,T0,0D0,UL,J)
+            IF (J.NE.0) GO TO 9010
+
+*        Adjust the timespan and time left.
+            TSPAN = TFINAL-T0
+            TLEFT = TSPAN
+         END IF
+
+*     Next timestep.
+      END DO
+
+*  Return the updated universal-element set.
+      DO I=1,13
+         U(I) = UL(I)
+      END DO
+
+*  Finished.
+      GO TO 9999
+
+*  Miscellaneous numerical error.
+ 9010 CONTINUE
+      JSTAT = -1
+
+ 9999 CONTINUE
+      END
diff --git a/math/slalib/planel.f b/math/slalib/planel.f
new file mode 100644
index 00000000..666a4036
--- /dev/null
+++ b/math/slalib/planel.f
@@ -0,0 +1,184 @@
+      SUBROUTINE slPLNE (DATE, JFORM, EPOCH, ORBINC, ANODE, PERIH,
+     :                       AORQ, E, AORL, DM, PV, JSTAT)
+*+
+*     - - - - - - -
+*      P L N L
+*     - - - - - - -
+*
+*  Heliocentric position and velocity of a planet, asteroid or comet,
+*  starting from orbital elements.
+*
+*  Given:
+*     DATE     d     date, Modified Julian Date (JD - 2400000.5, Note 1)
+*     JFORM    i     choice of element set (1-3; Note 3)
+*     EPOCH    d     epoch of elements (TT MJD, Note 4)
+*     ORBINC   d     inclination (radians)
+*     ANODE    d     longitude of the ascending node (radians)
+*     PERIH    d     longitude or argument of perihelion (radians)
+*     AORQ     d     mean distance or perihelion distance (AU)
+*     E        d     eccentricity
+*     AORL     d     mean anomaly or longitude (radians, JFORM=1,2 only)
+*     DM       d     daily motion (radians, JFORM=1 only)
+*
+*  Returned:
+*     PV       d(6)  heliocentric x,y,z,xdot,ydot,zdot of date,
+*                                     J2000 equatorial triad (AU,AU/s)
+*     JSTAT    i     status:  0 = OK
+*                            -1 = illegal JFORM
+*                            -2 = illegal E
+*                            -3 = illegal AORQ
+*                            -4 = illegal DM
+*                            -5 = numerical error
+*
+*  Called:  slELUE, slUEPV
+*
+*  Notes
+*
+*  1  DATE is the instant for which the prediction is required.  It is
+*     in the TT timescale (formerly Ephemeris Time, ET) and is a
+*     Modified Julian Date (JD-2400000.5).
+*
+*  2  The elements are with respect to the J2000 ecliptic and equinox.
+*
+*  3  A choice of three different element-set options is available:
+*
+*     Option JFORM = 1, suitable for the major planets:
+*
+*       EPOCH  = epoch of elements (TT MJD)
+*       ORBINC = inclination i (radians)
+*       ANODE  = longitude of the ascending node, big omega (radians)
+*       PERIH  = longitude of perihelion, curly pi (radians)
+*       AORQ   = mean distance, a (AU)
+*       E      = eccentricity, e (range 0 to <1)
+*       AORL   = mean longitude L (radians)
+*       DM     = daily motion (radians)
+*
+*     Option JFORM = 2, suitable for minor planets:
+*
+*       EPOCH  = epoch of elements (TT MJD)
+*       ORBINC = inclination i (radians)
+*       ANODE  = longitude of the ascending node, big omega (radians)
+*       PERIH  = argument of perihelion, little omega (radians)
+*       AORQ   = mean distance, a (AU)
+*       E      = eccentricity, e (range 0 to <1)
+*       AORL   = mean anomaly M (radians)
+*
+*     Option JFORM = 3, suitable for comets:
+*
+*       EPOCH  = epoch of elements and perihelion (TT MJD)
+*       ORBINC = inclination i (radians)
+*       ANODE  = longitude of the ascending node, big omega (radians)
+*       PERIH  = argument of perihelion, little omega (radians)
+*       AORQ   = perihelion distance, q (AU)
+*       E      = eccentricity, e (range 0 to 10)
+*
+*     Unused arguments (DM for JFORM=2, AORL and DM for JFORM=3) are not
+*     accessed.
+*
+*  4  Each of the three element sets defines an unperturbed heliocentric
+*     orbit.  For a given epoch of observation, the position of the body
+*     in its orbit can be predicted from these elements, which are
+*     called "osculating elements", using standard two-body analytical
+*     solutions.  However, due to planetary perturbations, a given set
+*     of osculating elements remains usable for only as long as the
+*     unperturbed orbit that it describes is an adequate approximation
+*     to reality.  Attached to such a set of elements is a date called
+*     the "osculating epoch", at which the elements are, momentarily,
+*     a perfect representation of the instantaneous position and
+*     velocity of the body.
+*
+*     Therefore, for any given problem there are up to three different
+*     epochs in play, and it is vital to distinguish clearly between
+*     them:
+*
+*     . The epoch of observation:  the moment in time for which the
+*       position of the body is to be predicted.
+*
+*     . The epoch defining the position of the body:  the moment in time
+*       at which, in the absence of purturbations, the specified
+*       position (mean longitude, mean anomaly, or perihelion) is
+*       reached.
+*
+*     . The osculating epoch:  the moment in time at which the given
+*       elements are correct.
+*
+*     For the major-planet and minor-planet cases it is usual to make
+*     the epoch that defines the position of the body the same as the
+*     epoch of osculation.  Thus, only two different epochs are
+*     involved:  the epoch of the elements and the epoch of observation.
+*
+*     For comets, the epoch of perihelion fixes the position in the
+*     orbit and in general a different epoch of osculation will be
+*     chosen.  Thus, all three types of epoch are involved.
+*
+*     For the present routine:
+*
+*     . The epoch of observation is the argument DATE.
+*
+*     . The epoch defining the position of the body is the argument
+*       EPOCH.
+*
+*     . The osculating epoch is not used and is assumed to be close
+*       enough to the epoch of observation to deliver adequate accuracy.
+*       If not, a preliminary call to slPRTL may be used to update
+*       the element-set (and its associated osculating epoch) by
+*       applying planetary perturbations.
+*
+*  5  The reference frame for the result is with respect to the mean
+*     equator and equinox of epoch J2000.
+*
+*  6  The algorithm was originally adapted from the EPHSLA program of
+*     D.H.P.Jones (private communication, 1996).  The method is based
+*     on Stumpff's Universal Variables.
+*
+*  Reference:  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
+*
+*  P.T.Wallace   Starlink   31 December 2002
+*
+*  Copyright (C) 2002 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE
+      INTEGER JFORM
+      DOUBLE PRECISION EPOCH,ORBINC,ANODE,PERIH,AORQ,E,AORL,DM,PV(6)
+      INTEGER JSTAT
+
+      DOUBLE PRECISION U(13)
+      INTEGER J
+
+
+
+*  Validate elements and convert to "universal variables" parameters.
+      CALL slELUE(DATE,JFORM,
+     :               EPOCH,ORBINC,ANODE,PERIH,AORQ,E,AORL,DM,U,J)
+
+*  Determine the position and velocity.
+      IF (J.EQ.0) THEN
+         CALL slUEPV(DATE,U,PV,J)
+         IF (J.NE.0) J=-5
+      END IF
+
+*  Wrap up.
+      JSTAT = J
+
+      END
diff --git a/math/slalib/planet.f b/math/slalib/planet.f
new file mode 100644
index 00000000..02590c65
--- /dev/null
+++ b/math/slalib/planet.f
@@ -0,0 +1,725 @@
+      SUBROUTINE slPLNT (DATE, NP, PV, JSTAT)
+*+
+*     - - - - - - -
+*      P L N T
+*     - - - - - - -
+*
+*  Approximate heliocentric position and velocity of a specified
+*  major planet.
+*
+*  Given:
+*     DATE      d      Modified Julian Date (JD - 2400000.5)
+*     NP        i      planet (1=Mercury, 2=Venus, 3=EMB ... 9=Pluto)
+*
+*  Returned:
+*     PV        d(6)   heliocentric x,y,z,xdot,ydot,zdot, J2000
+*                                           equatorial triad (AU,AU/s)
+*     JSTAT     i      status: +1 = warning: date out of range
+*                               0 = OK
+*                              -1 = illegal NP (outside 1-9)
+*                              -2 = solution didn't converge
+*
+*  Called:  slPLNE
+*
+*  Notes
+*
+*  1  The epoch, DATE, is in the TDB timescale and is a Modified
+*     Julian Date (JD-2400000.5).
+*
+*  2  The reference frame is equatorial and is with respect to the
+*     mean equinox and ecliptic of epoch J2000.
+*
+*  3  If an NP value outside the range 1-9 is supplied, an error
+*     status (JSTAT = -1) is returned and the PV vector set to zeroes.
+*
+*  4  The algorithm for obtaining the mean elements of the planets
+*     from Mercury to Neptune is due to J.L. Simon, P. Bretagnon,
+*     J. Chapront, M. Chapront-Touze, G. Francou and J. Laskar
+*     (Bureau des Longitudes, Paris).  The (completely different)
+*     algorithm for calculating the ecliptic coordinates of Pluto
+*     is by Meeus.
+*
+*  5  Comparisons of the present routine with the JPL DE200 ephemeris
+*     give the following RMS errors over the interval 1960-2025:
+*
+*                      position (km)     speed (metre/sec)
+*
+*        Mercury            334               0.437
+*        Venus             1060               0.855
+*        EMB               2010               0.815
+*        Mars              7690               1.98
+*        Jupiter          71700               7.70
+*        Saturn          199000              19.4
+*        Uranus          564000              16.4
+*        Neptune         158000              14.4
+*        Pluto            36400               0.137
+*
+*     From comparisons with DE102, Simon et al quote the following
+*     longitude accuracies over the interval 1800-2200:
+*
+*        Mercury                 4"
+*        Venus                   5"
+*        EMB                     6"
+*        Mars                   17"
+*        Jupiter                71"
+*        Saturn                 81"
+*        Uranus                 86"
+*        Neptune                11"
+*
+*     In the case of Pluto, Meeus quotes an accuracy of 0.6 arcsec
+*     in longitude and 0.2 arcsec in latitude for the period
+*     1885-2099.
+*
+*     For all except Pluto, over the period 1000-3000 the accuracy
+*     is better than 1.5 times that over 1800-2200.  Outside the
+*     period 1000-3000 the accuracy declines.  For Pluto the
+*     accuracy declines rapidly outside the period 1885-2099.
+*     Outside these ranges (1885-2099 for Pluto, 1000-3000 for
+*     the rest) a "date out of range" warning status (JSTAT=+1)
+*     is returned.
+*
+*  6  The algorithms for (i) Mercury through Neptune and (ii) Pluto
+*     are completely independent.  In the Mercury through Neptune
+*     case, the present SLALIB implementation differs from the
+*     original Simon et al Fortran code in the following respects.
+*
+*     *  The date is supplied as a Modified Julian Date rather
+*        than a Julian Date (MJD = JD - 2400000.5).
+*
+*     *  The result is returned only in equatorial Cartesian form;
+*        the ecliptic longitude, latitude and radius vector are not
+*        returned.
+*
+*     *  The velocity is in AU per second, not AU per day.
+*
+*     *  Different error/warning status values are used.
+*
+*     *  Kepler's equation is not solved inline.
+*
+*     *  Polynomials in T are nested to minimize rounding errors.
+*
+*     *  Explicit double-precision constants are used to avoid
+*        mixed-mode expressions.
+*
+*     *  There are other, cosmetic, changes to comply with
+*        Starlink/SLALIB style guidelines.
+*
+*     None of the above changes affects the result significantly.
+*
+*  7  For NP=3 the result is for the Earth-Moon Barycentre.  To
+*     obtain the heliocentric position and velocity of the Earth,
+*     either use the SLALIB routine slEVP (or slEPV) or call
+*     slDMON and subtract 0.012150581 times the geocentric Moon
+*     vector from the EMB vector produced by the present routine.
+*     (The Moon vector should be precessed to J2000 first, but this
+*     can be omitted for modern epochs without introducing significant
+*     inaccuracy.)
+*
+*  References:  Simon et al., Astron. Astrophys. 282, 663 (1994).
+*               Meeus, Astronomical Algorithms, Willmann-Bell (1991).
+*
+*  This revision:  19 June 2004
+*
+*  Copyright (C) 2004 P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE
+      INTEGER NP
+      DOUBLE PRECISION PV(6)
+      INTEGER JSTAT
+
+*  2Pi, deg to radians, arcsec to radians
+      DOUBLE PRECISION D2PI,D2R,AS2R
+      PARAMETER (D2PI=6.283185307179586476925286766559D0,
+     :           D2R=0.017453292519943295769236907684886D0,
+     :           AS2R=4.848136811095359935899141023579D-6)
+
+*  Gaussian gravitational constant (exact)
+      DOUBLE PRECISION GCON
+      PARAMETER (GCON=0.01720209895D0)
+
+*  Seconds per Julian century
+      DOUBLE PRECISION SPC
+      PARAMETER (SPC=36525D0*86400D0)
+
+*  Sin and cos of J2000 mean obliquity (IAU 1976)
+      DOUBLE PRECISION SE,CE
+      PARAMETER (SE=0.3977771559319137D0,
+     :           CE=0.9174820620691818D0)
+
+      INTEGER I,J,IJSP(3,43)
+      DOUBLE PRECISION AMAS(8),A(3,8),DLM(3,8),E(3,8),
+     :                 PI(3,8),DINC(3,8),OMEGA(3,8),
+     :                 DKP(9,8),CA(9,8),SA(9,8),
+     :                 DKQ(10,8),CLO(10,8),SLO(10,8),
+     :                 T,DA,DE,DPE,DI,DO,DMU,ARGA,ARGL,DM,
+     :                 AB(2,3,43),DJ0,DS0,DP0,DL0,DLD0,DB0,DR0,
+     :                 DJ,DS,DP,DJD,DSD,DPD,WLBR(3),WLBRD(3),
+     :                 WJ,WS,WP,AL,ALD,SAL,CAL,
+     :                 AC,BC,DL,DLD,DB,DBD,DR,DRD,
+     :                 SL,CL,SB,CB,SLCB,CLCB,X,Y,Z,XD,YD,ZD
+
+*  -----------------------
+*  Mercury through Neptune
+*  -----------------------
+
+*  Planetary inverse masses
+      DATA AMAS / 6023600D0,408523.5D0,328900.5D0,3098710D0,
+     :            1047.355D0,3498.5D0,22869D0,19314D0 /
+
+*
+*  Tables giving the mean Keplerian elements, limited to T**2 terms:
+*
+*         A       semi-major axis (AU)
+*         DLM     mean longitude (degree and arcsecond)
+*         E       eccentricity
+*         PI      longitude of the perihelion (degree and arcsecond)
+*         DINC    inclination (degree and arcsecond)
+*         OMEGA   longitude of the ascending node (degree and arcsecond)
+*
+      DATA A /
+     :  0.3870983098D0,             0D0,      0D0,
+     :  0.7233298200D0,             0D0,      0D0,
+     :  1.0000010178D0,             0D0,      0D0,
+     :  1.5236793419D0,           3D-10,      0D0,
+     :  5.2026032092D0,       19132D-10,  -39D-10,
+     :  9.5549091915D0, -0.0000213896D0,  444D-10,
+     : 19.2184460618D0,       -3716D-10,  979D-10,
+     : 30.1103868694D0,      -16635D-10,  686D-10 /
+*
+      DATA DLM /
+     : 252.25090552D0, 5381016286.88982D0,  -1.92789D0,
+     : 181.97980085D0, 2106641364.33548D0,   0.59381D0,
+     : 100.46645683D0, 1295977422.83429D0,  -2.04411D0,
+     : 355.43299958D0,  689050774.93988D0,   0.94264D0,
+     :  34.35151874D0,  109256603.77991D0, -30.60378D0,
+     :  50.07744430D0,   43996098.55732D0,  75.61614D0,
+     : 314.05500511D0,   15424811.93933D0,  -1.75083D0,
+     : 304.34866548D0,    7865503.20744D0,   0.21103D0/
+*
+      DATA E /
+     : 0.2056317526D0,  0.0002040653D0,      -28349D-10,
+     : 0.0067719164D0, -0.0004776521D0,       98127D-10,
+     : 0.0167086342D0, -0.0004203654D0, -0.0000126734D0,
+     : 0.0934006477D0,  0.0009048438D0,      -80641D-10,
+     : 0.0484979255D0,  0.0016322542D0, -0.0000471366D0,
+     : 0.0555481426D0, -0.0034664062D0, -0.0000643639D0,
+     : 0.0463812221D0, -0.0002729293D0,  0.0000078913D0,
+     : 0.0094557470D0,  0.0000603263D0,            0D0 /
+*
+      DATA PI /
+     :  77.45611904D0,  5719.11590D0,   -4.83016D0,
+     : 131.56370300D0,   175.48640D0, -498.48184D0,
+     : 102.93734808D0, 11612.35290D0,   53.27577D0,
+     : 336.06023395D0, 15980.45908D0,  -62.32800D0,
+     :  14.33120687D0,  7758.75163D0,  259.95938D0,
+     :  93.05723748D0, 20395.49439D0,  190.25952D0,
+     : 173.00529106D0,  3215.56238D0,  -34.09288D0,
+     :  48.12027554D0,  1050.71912D0,   27.39717D0 /
+*
+      DATA DINC /
+     : 7.00498625D0, -214.25629D0,   0.28977D0,
+     : 3.39466189D0,  -30.84437D0, -11.67836D0,
+     :          0D0,  469.97289D0,  -3.35053D0,
+     : 1.84972648D0, -293.31722D0,  -8.11830D0,
+     : 1.30326698D0,  -71.55890D0,  11.95297D0,
+     : 2.48887878D0,   91.85195D0, -17.66225D0,
+     : 0.77319689D0,  -60.72723D0,   1.25759D0,
+     : 1.76995259D0,    8.12333D0,   0.08135D0 /
+*
+      DATA OMEGA /
+     :  48.33089304D0,  -4515.21727D0,  -31.79892D0,
+     :  76.67992019D0, -10008.48154D0,  -51.32614D0,
+     : 174.87317577D0,  -8679.27034D0,   15.34191D0,
+     :  49.55809321D0, -10620.90088D0, -230.57416D0,
+     : 100.46440702D0,   6362.03561D0,  326.52178D0,
+     : 113.66550252D0,  -9240.19942D0,  -66.23743D0,
+     :  74.00595701D0,   2669.15033D0,  145.93964D0,
+     : 131.78405702D0,   -221.94322D0,   -0.78728D0 /
+*
+*  Tables for trigonometric terms to be added to the mean elements
+*  of the semi-major axes.
+*
+      DATA DKP /
+     : 69613, 75645, 88306, 59899, 15746, 71087, 142173,  3086,    0,
+     : 21863, 32794, 26934, 10931, 26250, 43725,  53867, 28939,    0,
+     : 16002, 21863, 32004, 10931, 14529, 16368,  15318, 32794,    0,
+     : 6345,   7818, 15636,  7077,  8184, 14163,   1107,  4872,    0,
+     : 1760,   1454,  1167,   880,   287,  2640,     19,  2047, 1454,
+     :  574,      0,   880,   287,    19,  1760,   1167,   306,  574,
+     :  204,      0,   177,  1265,     4,   385,    200,   208,  204,
+     :    0,    102,   106,     4,    98,  1367,    487,   204,    0 /
+*
+      DATA CA /
+     :      4,    -13,    11,    -9,    -9,    -3,    -1,     4,    0,
+     :   -156,     59,   -42,     6,    19,   -20,   -10,   -12,    0,
+     :     64,   -152,    62,    -8,    32,   -41,    19,   -11,    0,
+     :    124,    621,  -145,   208,    54,   -57,    30,    15,    0,
+     : -23437,  -2634,  6601,  6259, -1507, -1821,  2620, -2115,-1489,
+     :  62911,-119919, 79336, 17814,-24241, 12068,  8306, -4893, 8902,
+     : 389061,-262125,-44088,  8387,-22976, -2093,  -615, -9720, 6633,
+     :-412235,-157046,-31430, 37817, -9740,   -13, -7449,  9644,    0 /
+*
+      DATA SA /
+     :     -29,    -1,     9,     6,    -6,     5,     4,     0,    0,
+     :     -48,  -125,   -26,   -37,    18,   -13,   -20,    -2,    0,
+     :    -150,   -46,    68,    54,    14,    24,   -28,    22,    0,
+     :    -621,   532,  -694,   -20,   192,   -94,    71,   -73,    0,
+     :  -14614,-19828, -5869,  1881, -4372, -2255,   782,   930,  913,
+     :  139737,     0, 24667, 51123, -5102,  7429, -4095, -1976,-9566,
+     : -138081,     0, 37205,-49039,-41901,-33872,-27037,-12474,18797,
+     :       0, 28492,133236, 69654, 52322,-49577,-26430, -3593,    0 /
+*
+*  Tables giving the trigonometric terms to be added to the mean
+*  elements of the mean longitudes.
+*
+      DATA DKQ /
+     :  3086, 15746, 69613, 59899, 75645, 88306, 12661, 2658,  0,   0,
+     : 21863, 32794, 10931,    73,  4387, 26934,  1473, 2157,  0,   0,
+     :    10, 16002, 21863, 10931,  1473, 32004,  4387,   73,  0,   0,
+     :    10,  6345,  7818,  1107, 15636,  7077,  8184,  532, 10,   0,
+     :    19,  1760,  1454,   287,  1167,   880,   574, 2640, 19,1454,
+     :    19,   574,   287,   306,  1760,    12,    31,   38, 19, 574,
+     :     4,   204,   177,     8,    31,   200,  1265,  102,  4, 204,
+     :     4,   102,   106,     8,    98,  1367,   487,  204,  4, 102 /
+*
+      DATA CLO /
+     :     21,   -95, -157,   41,   -5,   42,   23,   30,     0,    0,
+     :   -160,  -313, -235,   60,  -74,  -76,  -27,   34,     0,    0,
+     :   -325,  -322,  -79,  232,  -52,   97,   55,  -41,     0,    0,
+     :   2268,  -979,  802,  602, -668,  -33,  345,  201,   -55,    0,
+     :   7610, -4997,-7689,-5841,-2617, 1115, -748, -607,  6074,  354,
+     : -18549, 30125,20012, -730,  824,   23, 1289, -352,-14767,-2062,
+     :-135245,-14594, 4197,-4030,-5630,-2898, 2540, -306,  2939, 1986,
+     :  89948,  2103, 8963, 2695, 3682, 1648,  866, -154, -1963, -283 /
+*
+      DATA SLO /
+     :   -342,   136,  -23,   62,   66,  -52,  -33,   17,     0,    0,
+     :    524,  -149,  -35,  117,  151,  122,  -71,  -62,     0,    0,
+     :   -105,  -137,  258,   35, -116,  -88, -112,  -80,     0,    0,
+     :    854,  -205, -936, -240,  140, -341,  -97, -232,   536,    0,
+     : -56980,  8016, 1012, 1448,-3024,-3710,  318,  503,  3767,  577,
+     : 138606,-13478,-4964, 1441,-1319,-1482,  427, 1236, -9167,-1918,
+     :  71234,-41116, 5334,-4935,-1848,   66,  434,-1748,  3780, -701,
+     : -47645, 11647, 2166, 3194,  679,    0, -244, -419, -2531,   48 /
+
+*  -----
+*  Pluto
+*  -----
+
+*
+*  Coefficients for fundamental arguments:  mean longitudes
+*  (degrees) and mean rate of change of longitude (degrees per
+*  Julian century) for Jupiter, Saturn and Pluto
+*
+      DATA DJ0, DJD / 34.35D0, 3034.9057D0 /
+      DATA DS0, DSD / 50.08D0, 1222.1138D0 /
+      DATA DP0, DPD / 238.96D0, 144.9600D0 /
+
+*  Coefficients for latitude, longitude, radius vector
+      DATA DL0,DLD0 / 238.956785D0, 144.96D0 /
+      DATA DB0 / -3.908202D0 /
+      DATA DR0 / 40.7247248D0 /
+
+*
+*  Coefficients for periodic terms (Meeus's Table 36.A)
+*
+*  The coefficients for term n in the series are:
+*
+*    IJSP(1,n)     J
+*    IJSP(2,n)     S
+*    IJSP(3,n)     P
+*    AB(1,1,n)     longitude sine (degrees)
+*    AB(2,1,n)     longitude cosine (degrees)
+*    AB(1,2,n)     latitude sine (degrees)
+*    AB(2,2,n)     latitude cosine (degrees)
+*    AB(1,3,n)     radius vector sine (AU)
+*    AB(2,3,n)     radius vector cosine (AU)
+*
+      DATA (IJSP(I, 1),I=1,3),((AB(J,I, 1),J=1,2),I=1,3) /
+     :                             0,  0,  1,
+     :            -19798886D-6,  19848454D-6,
+     :             -5453098D-6, -14974876D-6,
+     :             66867334D-7,  68955876D-7 /
+      DATA (IJSP(I, 2),I=1,3),((AB(J,I, 2),J=1,2),I=1,3) /
+     :                             0,  0,  2,
+     :               897499D-6,  -4955707D-6,
+     :              3527363D-6,   1672673D-6,
+     :            -11826086D-7,   -333765D-7 /
+      DATA (IJSP(I, 3),I=1,3),((AB(J,I, 3),J=1,2),I=1,3) /
+     :                             0,  0,  3,
+     :               610820D-6,   1210521D-6,
+     :             -1050939D-6,    327763D-6,
+     :              1593657D-7,  -1439953D-7 /
+      DATA (IJSP(I, 4),I=1,3),((AB(J,I, 4),J=1,2),I=1,3) /
+     :                             0,  0,  4,
+     :              -341639D-6,   -189719D-6,
+     :               178691D-6,   -291925D-6,
+     :               -18948D-7,    482443D-7 /
+      DATA (IJSP(I, 5),I=1,3),((AB(J,I, 5),J=1,2),I=1,3) /
+     :                             0,  0,  5,
+     :               129027D-6,    -34863D-6,
+     :                18763D-6,    100448D-6,
+     :               -66634D-7,    -85576D-7 /
+      DATA (IJSP(I, 6),I=1,3),((AB(J,I, 6),J=1,2),I=1,3) /
+     :                             0,  0,  6,
+     :               -38215D-6,     31061D-6,
+     :               -30594D-6,    -25838D-6,
+     :                30841D-7,     -5765D-7 /
+      DATA (IJSP(I, 7),I=1,3),((AB(J,I, 7),J=1,2),I=1,3) /
+     :                             0,  1, -1,
+     :                20349D-6,     -9886D-6,
+     :                 4965D-6,     11263D-6,
+     :                -6140D-7,     22254D-7 /
+      DATA (IJSP(I, 8),I=1,3),((AB(J,I, 8),J=1,2),I=1,3) /
+     :                             0,  1,  0,
+     :                -4045D-6,     -4904D-6,
+     :                  310D-6,      -132D-6,
+     :                 4434D-7,      4443D-7 /
+      DATA (IJSP(I, 9),I=1,3),((AB(J,I, 9),J=1,2),I=1,3) /
+     :                             0,  1,  1,
+     :                -5885D-6,     -3238D-6,
+     :                 2036D-6,      -947D-6,
+     :                -1518D-7,       641D-7 /
+      DATA (IJSP(I,10),I=1,3),((AB(J,I,10),J=1,2),I=1,3) /
+     :                             0,  1,  2,
+     :                -3812D-6,      3011D-6,
+     :                   -2D-6,      -674D-6,
+     :                   -5D-7,       792D-7 /
+      DATA (IJSP(I,11),I=1,3),((AB(J,I,11),J=1,2),I=1,3) /
+     :                             0,  1,  3,
+     :                 -601D-6,      3468D-6,
+     :                 -329D-6,      -563D-6,
+     :                  518D-7,       518D-7 /
+      DATA (IJSP(I,12),I=1,3),((AB(J,I,12),J=1,2),I=1,3) /
+     :                             0,  2, -2,
+     :                 1237D-6,       463D-6,
+     :                  -64D-6,        39D-6,
+     :                  -13D-7,      -221D-7 /
+      DATA (IJSP(I,13),I=1,3),((AB(J,I,13),J=1,2),I=1,3) /
+     :                             0,  2, -1,
+     :                 1086D-6,      -911D-6,
+     :                  -94D-6,       210D-6,
+     :                  837D-7,      -494D-7 /
+      DATA (IJSP(I,14),I=1,3),((AB(J,I,14),J=1,2),I=1,3) /
+     :                             0,  2,  0,
+     :                  595D-6,     -1229D-6,
+     :                   -8D-6,      -160D-6,
+     :                 -281D-7,       616D-7 /
+      DATA (IJSP(I,15),I=1,3),((AB(J,I,15),J=1,2),I=1,3) /
+     :                             1, -1,  0,
+     :                 2484D-6,      -485D-6,
+     :                 -177D-6,       259D-6,
+     :                  260D-7,      -395D-7 /
+      DATA (IJSP(I,16),I=1,3),((AB(J,I,16),J=1,2),I=1,3) /
+     :                             1, -1,  1,
+     :                  839D-6,     -1414D-6,
+     :                   17D-6,       234D-6,
+     :                 -191D-7,      -396D-7 /
+      DATA (IJSP(I,17),I=1,3),((AB(J,I,17),J=1,2),I=1,3) /
+     :                             1,  0, -3,
+     :                 -964D-6,      1059D-6,
+     :                  582D-6,      -285D-6,
+     :                -3218D-7,       370D-7 /
+      DATA (IJSP(I,18),I=1,3),((AB(J,I,18),J=1,2),I=1,3) /
+     :                             1,  0, -2,
+     :                -2303D-6,     -1038D-6,
+     :                 -298D-6,       692D-6,
+     :                 8019D-7,     -7869D-7 /
+      DATA (IJSP(I,19),I=1,3),((AB(J,I,19),J=1,2),I=1,3) /
+     :                             1,  0, -1,
+     :                 7049D-6,       747D-6,
+     :                  157D-6,       201D-6,
+     :                  105D-7,     45637D-7 /
+      DATA (IJSP(I,20),I=1,3),((AB(J,I,20),J=1,2),I=1,3) /
+     :                             1,  0,  0,
+     :                 1179D-6,      -358D-6,
+     :                  304D-6,       825D-6,
+     :                 8623D-7,      8444D-7 /
+      DATA (IJSP(I,21),I=1,3),((AB(J,I,21),J=1,2),I=1,3) /
+     :                             1,  0,  1,
+     :                  393D-6,       -63D-6,
+     :                 -124D-6,       -29D-6,
+     :                 -896D-7,      -801D-7 /
+      DATA (IJSP(I,22),I=1,3),((AB(J,I,22),J=1,2),I=1,3) /
+     :                             1,  0,  2,
+     :                  111D-6,      -268D-6,
+     :                   15D-6,         8D-6,
+     :                  208D-7,      -122D-7 /
+      DATA (IJSP(I,23),I=1,3),((AB(J,I,23),J=1,2),I=1,3) /
+     :                             1,  0,  3,
+     :                  -52D-6,      -154D-6,
+     :                    7D-6,        15D-6,
+     :                 -133D-7,        65D-7 /
+      DATA (IJSP(I,24),I=1,3),((AB(J,I,24),J=1,2),I=1,3) /
+     :                             1,  0,  4,
+     :                  -78D-6,       -30D-6,
+     :                    2D-6,         2D-6,
+     :                  -16D-7,         1D-7 /
+      DATA (IJSP(I,25),I=1,3),((AB(J,I,25),J=1,2),I=1,3) /
+     :                             1,  1, -3,
+     :                  -34D-6,       -26D-6,
+     :                    4D-6,         2D-6,
+     :                  -22D-7,         7D-7 /
+      DATA (IJSP(I,26),I=1,3),((AB(J,I,26),J=1,2),I=1,3) /
+     :                             1,  1, -2,
+     :                  -43D-6,         1D-6,
+     :                    3D-6,         0D-6,
+     :                   -8D-7,        16D-7 /
+      DATA (IJSP(I,27),I=1,3),((AB(J,I,27),J=1,2),I=1,3) /
+     :                             1,  1, -1,
+     :                  -15D-6,        21D-6,
+     :                    1D-6,        -1D-6,
+     :                    2D-7,         9D-7 /
+      DATA (IJSP(I,28),I=1,3),((AB(J,I,28),J=1,2),I=1,3) /
+     :                             1,  1,  0,
+     :                   -1D-6,        15D-6,
+     :                    0D-6,        -2D-6,
+     :                   12D-7,         5D-7 /
+      DATA (IJSP(I,29),I=1,3),((AB(J,I,29),J=1,2),I=1,3) /
+     :                             1,  1,  1,
+     :                    4D-6,         7D-6,
+     :                    1D-6,         0D-6,
+     :                    1D-7,        -3D-7 /
+      DATA (IJSP(I,30),I=1,3),((AB(J,I,30),J=1,2),I=1,3) /
+     :                             1,  1,  3,
+     :                    1D-6,         5D-6,
+     :                    1D-6,        -1D-6,
+     :                    1D-7,         0D-7 /
+      DATA (IJSP(I,31),I=1,3),((AB(J,I,31),J=1,2),I=1,3) /
+     :                             2,  0, -6,
+     :                    8D-6,         3D-6,
+     :                   -2D-6,        -3D-6,
+     :                    9D-7,         5D-7 /
+      DATA (IJSP(I,32),I=1,3),((AB(J,I,32),J=1,2),I=1,3) /
+     :                             2,  0, -5,
+     :                   -3D-6,         6D-6,
+     :                    1D-6,         2D-6,
+     :                    2D-7,        -1D-7 /
+      DATA (IJSP(I,33),I=1,3),((AB(J,I,33),J=1,2),I=1,3) /
+     :                             2,  0, -4,
+     :                    6D-6,       -13D-6,
+     :                   -8D-6,         2D-6,
+     :                   14D-7,        10D-7 /
+      DATA (IJSP(I,34),I=1,3),((AB(J,I,34),J=1,2),I=1,3) /
+     :                             2,  0, -3,
+     :                   10D-6,        22D-6,
+     :                   10D-6,        -7D-6,
+     :                  -65D-7,        12D-7 /
+      DATA (IJSP(I,35),I=1,3),((AB(J,I,35),J=1,2),I=1,3) /
+     :                             2,  0, -2,
+     :                  -57D-6,       -32D-6,
+     :                    0D-6,        21D-6,
+     :                  126D-7,      -233D-7 /
+      DATA (IJSP(I,36),I=1,3),((AB(J,I,36),J=1,2),I=1,3) /
+     :                             2,  0, -1,
+     :                  157D-6,       -46D-6,
+     :                    8D-6,         5D-6,
+     :                  270D-7,      1068D-7 /
+      DATA (IJSP(I,37),I=1,3),((AB(J,I,37),J=1,2),I=1,3) /
+     :                             2,  0,  0,
+     :                   12D-6,       -18D-6,
+     :                   13D-6,        16D-6,
+     :                  254D-7,       155D-7 /
+      DATA (IJSP(I,38),I=1,3),((AB(J,I,38),J=1,2),I=1,3) /
+     :                             2,  0,  1,
+     :                   -4D-6,         8D-6,
+     :                   -2D-6,        -3D-6,
+     :                  -26D-7,        -2D-7 /
+      DATA (IJSP(I,39),I=1,3),((AB(J,I,39),J=1,2),I=1,3) /
+     :                             2,  0,  2,
+     :                   -5D-6,         0D-6,
+     :                    0D-6,         0D-6,
+     :                    7D-7,         0D-7 /
+      DATA (IJSP(I,40),I=1,3),((AB(J,I,40),J=1,2),I=1,3) /
+     :                             2,  0,  3,
+     :                    3D-6,         4D-6,
+     :                    0D-6,         1D-6,
+     :                  -11D-7,         4D-7 /
+      DATA (IJSP(I,41),I=1,3),((AB(J,I,41),J=1,2),I=1,3) /
+     :                             3,  0, -2,
+     :                   -1D-6,        -1D-6,
+     :                    0D-6,         1D-6,
+     :                    4D-7,       -14D-7 /
+      DATA (IJSP(I,42),I=1,3),((AB(J,I,42),J=1,2),I=1,3) /
+     :                             3,  0, -1,
+     :                    6D-6,        -3D-6,
+     :                    0D-6,         0D-6,
+     :                   18D-7,        35D-7 /
+      DATA (IJSP(I,43),I=1,3),((AB(J,I,43),J=1,2),I=1,3) /
+     :                             3,  0,  0,
+     :                   -1D-6,        -2D-6,
+     :                    0D-6,         1D-6,
+     :                   13D-7,         3D-7 /
+
+
+*  Validate the planet number.
+      IF (NP.LT.1.OR.NP.GT.9) THEN
+         JSTAT=-1
+         DO I=1,6
+            PV(I)=0D0
+         END DO
+      ELSE
+
+*     Separate algorithms for Pluto and the rest.
+         IF (NP.NE.9) THEN
+
+*        -----------------------
+*        Mercury through Neptune
+*        -----------------------
+
+*        Time: Julian millennia since J2000.
+            T=(DATE-51544.5D0)/365250D0
+
+*        OK status unless remote epoch.
+            IF (ABS(T).LE.1D0) THEN
+               JSTAT=0
+            ELSE
+               JSTAT=1
+            END IF
+
+*        Compute the mean elements.
+            DA=A(1,NP)+(A(2,NP)+A(3,NP)*T)*T
+            DL=(3600D0*DLM(1,NP)+(DLM(2,NP)+DLM(3,NP)*T)*T)*AS2R
+            DE=E(1,NP)+(E(2,NP)+E(3,NP)*T)*T
+            DPE=MOD((3600D0*PI(1,NP)+(PI(2,NP)+PI(3,NP)*T)*T)*AS2R,D2PI)
+            DI=(3600D0*DINC(1,NP)+(DINC(2,NP)+DINC(3,NP)*T)*T)*AS2R
+            DO=MOD((3600D0*OMEGA(1,NP)
+     :                        +(OMEGA(2,NP)+OMEGA(3,NP)*T)*T)*AS2R,D2PI)
+
+*        Apply the trigonometric terms.
+            DMU=0.35953620D0*T
+            DO J=1,8
+               ARGA=DKP(J,NP)*DMU
+               ARGL=DKQ(J,NP)*DMU
+               DA=DA+(CA(J,NP)*COS(ARGA)+SA(J,NP)*SIN(ARGA))*1D-7
+               DL=DL+(CLO(J,NP)*COS(ARGL)+SLO(J,NP)*SIN(ARGL))*1D-7
+            END DO
+            ARGA=DKP(9,NP)*DMU
+            DA=DA+T*(CA(9,NP)*COS(ARGA)+SA(9,NP)*SIN(ARGA))*1D-7
+            DO J=9,10
+               ARGL=DKQ(J,NP)*DMU
+               DL=DL+T*(CLO(J,NP)*COS(ARGL)+SLO(J,NP)*SIN(ARGL))*1D-7
+            END DO
+            DL=MOD(DL,D2PI)
+
+*        Daily motion.
+            DM=GCON*SQRT((1D0+1D0/AMAS(NP))/(DA*DA*DA))
+
+*        Make the prediction.
+            CALL slPLNE(DATE,1,DATE,DI,DO,DPE,DA,DE,DL,DM,PV,J)
+            IF (J.LT.0) JSTAT=-2
+
+         ELSE
+
+*        -----
+*        Pluto
+*        -----
+
+*        Time: Julian centuries since J2000.
+            T=(DATE-51544.5D0)/36525D0
+
+*        OK status unless remote epoch.
+            IF (T.GE.-1.15D0.AND.T.LE.1D0) THEN
+               JSTAT=0
+            ELSE
+               JSTAT=1
+            END IF
+
+*        Fundamental arguments (radians).
+            DJ=(DJ0+DJD*T)*D2R
+            DS=(DS0+DSD*T)*D2R
+            DP=(DP0+DPD*T)*D2R
+
+*        Initialize coefficients and derivatives.
+            DO I=1,3
+               WLBR(I)=0D0
+               WLBRD(I)=0D0
+            END DO
+
+*        Term by term through Meeus Table 36.A.
+            DO J=1,43
+
+*           Argument and derivative (radians, radians per century).
+               WJ=DBLE(IJSP(1,J))
+               WS=DBLE(IJSP(2,J))
+               WP=DBLE(IJSP(3,J))
+               AL=WJ*DJ+WS*DS+WP*DP
+               ALD=(WJ*DJD+WS*DSD+WP*DPD)*D2R
+
+*           Functions of argument.
+               SAL=SIN(AL)
+               CAL=COS(AL)
+
+*           Periodic terms in longitude, latitude, radius vector.
+               DO I=1,3
+
+*              A and B coefficients (deg, AU).
+                  AC=AB(1,I,J)
+                  BC=AB(2,I,J)
+
+*              Periodic terms (deg, AU, deg/Jc, AU/Jc).
+                  WLBR(I)=WLBR(I)+AC*SAL+BC*CAL
+                  WLBRD(I)=WLBRD(I)+(AC*CAL-BC*SAL)*ALD
+               END DO
+            END DO
+
+*        Heliocentric longitude and derivative (radians, radians/sec).
+            DL=(DL0+DLD0*T+WLBR(1))*D2R
+            DLD=(DLD0+WLBRD(1))*D2R/SPC
+
+*        Heliocentric latitude and derivative (radians, radians/sec).
+            DB=(DB0+WLBR(2))*D2R
+            DBD=WLBRD(2)*D2R/SPC
+
+*        Heliocentric radius vector and derivative (AU, AU/sec).
+            DR=DR0+WLBR(3)
+            DRD=WLBRD(3)/SPC
+
+*        Functions of latitude, longitude, radius vector.
+            SL=SIN(DL)
+            CL=COS(DL)
+            SB=SIN(DB)
+            CB=COS(DB)
+            SLCB=SL*CB
+            CLCB=CL*CB
+
+*        Heliocentric vector and derivative, J2000 ecliptic and equinox.
+            X=DR*CLCB
+            Y=DR*SLCB
+            Z=DR*SB
+            XD=DRD*CLCB-DR*(CL*SB*DBD+SLCB*DLD)
+            YD=DRD*SLCB+DR*(-SL*SB*DBD+CLCB*DLD)
+            ZD=DRD*SB+DR*CB*DBD
+
+*        Transform to J2000 equator and equinox.
+            PV(1)=X
+            PV(2)=Y*CE-Z*SE
+            PV(3)=Y*SE+Z*CE
+            PV(4)=XD
+            PV(5)=YD*CE-ZD*SE
+            PV(6)=YD*SE+ZD*CE
+         END IF
+      END IF
+
+      END
diff --git a/math/slalib/plante.f b/math/slalib/plante.f
new file mode 100644
index 00000000..585e764d
--- /dev/null
+++ b/math/slalib/plante.f
@@ -0,0 +1,251 @@
+      SUBROUTINE slPLTE (DATE, ELONG, PHI, JFORM, EPOCH,
+     :                       ORBINC, ANODE, PERIH, AORQ, E,
+     :                       AORL, DM, RA, DEC, R, JSTAT)
+*+
+*     - - - - - - -
+*      P L T E
+*     - - - - - - -
+*
+*  Topocentric apparent RA,Dec of a Solar-System object whose
+*  heliocentric orbital elements are known.
+*
+*  Given:
+*     DATE     d     MJD of observation (JD - 2400000.5, Notes 1,5)
+*     ELONG    d     observer's east longitude (radians, Note 2)
+*     PHI      d     observer's geodetic latitude (radians, Note 2)
+*     JFORM    i     choice of element set (1-3; Notes 3-6)
+*     EPOCH    d     epoch of elements (TT MJD, Note 5)
+*     ORBINC   d     inclination (radians)
+*     ANODE    d     longitude of the ascending node (radians)
+*     PERIH    d     longitude or argument of perihelion (radians)
+*     AORQ     d     mean distance or perihelion distance (AU)
+*     E        d     eccentricity
+*     AORL     d     mean anomaly or longitude (radians, JFORM=1,2 only)
+*     DM       d     daily motion (radians, JFORM=1 only )
+*
+*  Returned:
+*     RA,DEC   d     RA, Dec (topocentric apparent, radians)
+*     R        d     distance from observer (AU)
+*     JSTAT    i     status:  0 = OK
+*                            -1 = illegal JFORM
+*                            -2 = illegal E
+*                            -3 = illegal AORQ
+*                            -4 = illegal DM
+*                            -5 = numerical error
+*
+*  Called: slELUE, slPLTU
+*
+*  Notes:
+*
+*  1  DATE is the instant for which the prediction is required.  It is
+*     in the TT timescale (formerly Ephemeris Time, ET) and is a
+*     Modified Julian Date (JD-2400000.5).
+*
+*  2  The longitude and latitude allow correction for geocentric
+*     parallax.  This is usually a small effect, but can become
+*     important for near-Earth asteroids.  Geocentric positions can be
+*     generated by appropriate use of routines slEVP (or slEPV) and
+*     slPLNE.
+*
+*  3  The elements are with respect to the J2000 ecliptic and equinox.
+*
+*  4  A choice of three different element-set options is available:
+*
+*     Option JFORM = 1, suitable for the major planets:
+*
+*       EPOCH  = epoch of elements (TT MJD)
+*       ORBINC = inclination i (radians)
+*       ANODE  = longitude of the ascending node, big omega (radians)
+*       PERIH  = longitude of perihelion, curly pi (radians)
+*       AORQ   = mean distance, a (AU)
+*       E      = eccentricity, e (range 0 to <1)
+*       AORL   = mean longitude L (radians)
+*       DM     = daily motion (radians)
+*
+*     Option JFORM = 2, suitable for minor planets:
+*
+*       EPOCH  = epoch of elements (TT MJD)
+*       ORBINC = inclination i (radians)
+*       ANODE  = longitude of the ascending node, big omega (radians)
+*       PERIH  = argument of perihelion, little omega (radians)
+*       AORQ   = mean distance, a (AU)
+*       E      = eccentricity, e (range 0 to <1)
+*       AORL   = mean anomaly M (radians)
+*
+*     Option JFORM = 3, suitable for comets:
+*
+*       EPOCH  = epoch of elements and perihelion (TT MJD)
+*       ORBINC = inclination i (radians)
+*       ANODE  = longitude of the ascending node, big omega (radians)
+*       PERIH  = argument of perihelion, little omega (radians)
+*       AORQ   = perihelion distance, q (AU)
+*       E      = eccentricity, e (range 0 to 10)
+*
+*     Unused arguments (DM for JFORM=2, AORL and DM for JFORM=3) are not
+*     accessed.
+*
+*  5  Each of the three element sets defines an unperturbed heliocentric
+*     orbit.  For a given epoch of observation, the position of the body
+*     in its orbit can be predicted from these elements, which are
+*     called "osculating elements", using standard two-body analytical
+*     solutions.  However, due to planetary perturbations, a given set
+*     of osculating elements remains usable for only as long as the
+*     unperturbed orbit that it describes is an adequate approximation
+*     to reality.  Attached to such a set of elements is a date called
+*     the "osculating epoch", at which the elements are, momentarily,
+*     a perfect representation of the instantaneous position and
+*     velocity of the body.
+*
+*     Therefore, for any given problem there are up to three different
+*     epochs in play, and it is vital to distinguish clearly between
+*     them:
+*
+*     . The epoch of observation:  the moment in time for which the
+*       position of the body is to be predicted.
+*
+*     . The epoch defining the position of the body:  the moment in time
+*       at which, in the absence of purturbations, the specified
+*       position (mean longitude, mean anomaly, or perihelion) is
+*       reached.
+*
+*     . The osculating epoch:  the moment in time at which the given
+*       elements are correct.
+*
+*     For the major-planet and minor-planet cases it is usual to make
+*     the epoch that defines the position of the body the same as the
+*     epoch of osculation.  Thus, only two different epochs are
+*     involved:  the epoch of the elements and the epoch of observation.
+*
+*     For comets, the epoch of perihelion fixes the position in the
+*     orbit and in general a different epoch of osculation will be
+*     chosen.  Thus, all three types of epoch are involved.
+*
+*     For the present routine:
+*
+*     . The epoch of observation is the argument DATE.
+*
+*     . The epoch defining the position of the body is the argument
+*       EPOCH.
+*
+*     . The osculating epoch is not used and is assumed to be close
+*       enough to the epoch of observation to deliver adequate accuracy.
+*       If not, a preliminary call to slPRTL may be used to update
+*       the element-set (and its associated osculating epoch) by
+*       applying planetary perturbations.
+*
+*  6  Two important sources for orbital elements are Horizons, operated
+*     by the Jet Propulsion Laboratory, Pasadena, and the Minor Planet
+*     Center, operated by the Center for Astrophysics, Harvard.
+*
+*     The JPL Horizons elements (heliocentric, J2000 ecliptic and
+*     equinox) correspond to SLALIB arguments as follows.
+*
+*       Major planets:
+*
+*         JFORM  = 1
+*         EPOCH  = JDCT-2400000.5D0
+*         ORBINC = IN (in radians)
+*         ANODE  = OM (in radians)
+*         PERIH  = OM+W (in radians)
+*         AORQ   = A
+*         E      = EC
+*         AORL   = MA+OM+W (in radians)
+*         DM     = N (in radians)
+*
+*         Epoch of osculation = JDCT-2400000.5D0
+*
+*       Minor planets:
+*
+*         JFORM  = 2
+*         EPOCH  = JDCT-2400000.5D0
+*         ORBINC = IN (in radians)
+*         ANODE  = OM (in radians)
+*         PERIH  = W (in radians)
+*         AORQ   = A
+*         E      = EC
+*         AORL   = MA (in radians)
+*
+*         Epoch of osculation = JDCT-2400000.5D0
+*
+*       Comets:
+*
+*         JFORM  = 3
+*         EPOCH  = Tp-2400000.5D0
+*         ORBINC = IN (in radians)
+*         ANODE  = OM (in radians)
+*         PERIH  = W (in radians)
+*         AORQ   = QR
+*         E      = EC
+*
+*         Epoch of osculation = JDCT-2400000.5D0
+*
+*     The MPC elements correspond to SLALIB arguments as follows.
+*
+*       Minor planets:
+*
+*         JFORM  = 2
+*         EPOCH  = Epoch-2400000.5D0
+*         ORBINC = Incl. (in radians)
+*         ANODE  = Node (in radians)
+*         PERIH  = Perih. (in radians)
+*         AORQ   = a
+*         E      = e
+*         AORL   = M (in radians)
+*
+*         Epoch of osculation = Epoch-2400000.5D0
+*
+*       Comets:
+*
+*         JFORM  = 3
+*         EPOCH  = T-2400000.5D0
+*         ORBINC = Incl. (in radians)
+*         ANODE  = Node. (in radians)
+*         PERIH  = Perih. (in radians)
+*         AORQ   = q
+*         E      = e
+*
+*         Epoch of osculation = Epoch-2400000.5D0
+*
+*  This revision:  19 June 2004
+*
+*  Copyright (C) 2004 P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,ELONG,PHI
+      INTEGER JFORM
+      DOUBLE PRECISION EPOCH,ORBINC,ANODE,PERIH,AORQ,E,
+     :                 AORL,DM,RA,DEC,R
+      INTEGER JSTAT
+
+      DOUBLE PRECISION U(13)
+
+
+*  Transform conventional elements to universal elements.
+      CALL slELUE(DATE,
+     :               JFORM,EPOCH,ORBINC,ANODE,PERIH,AORQ,E,AORL,DM,
+     :               U,JSTAT)
+
+*  If successful, make the prediction.
+      IF (JSTAT.EQ.0) CALL slPLTU(DATE,ELONG,PHI,U,RA,DEC,R,JSTAT)
+
+      END
diff --git a/math/slalib/plantu.f b/math/slalib/plantu.f
new file mode 100644
index 00000000..81e65148
--- /dev/null
+++ b/math/slalib/plantu.f
@@ -0,0 +1,156 @@
+      SUBROUTINE slPLTU (DATE, ELONG, PHI, U, RA, DEC, R, JSTAT)
+*+
+*     - - - - - - -
+*      P L A N T U
+*     - - - - - - -
+*
+*  Topocentric apparent RA,Dec of a Solar-System object whose
+*  heliocentric universal elements are known.
+*
+*  Given:
+*     DATE      d     TT MJD of observation (JD - 2400000.5)
+*     ELONG     d     observer's east longitude (radians)
+*     PHI       d     observer's geodetic latitude (radians)
+*     U       d(13)   universal elements
+*
+*               (1)   combined mass (M+m)
+*               (2)   total energy of the orbit (alpha)
+*               (3)   reference (osculating) epoch (t0)
+*             (4-6)   position at reference epoch (r0)
+*             (7-9)   velocity at reference epoch (v0)
+*              (10)   heliocentric distance at reference epoch
+*              (11)   r0.v0
+*              (12)   date (t)
+*              (13)   universal eccentric anomaly (psi) of date, approx
+*
+*  Returned:
+*     RA,DEC    d     RA, Dec (topocentric apparent, radians)
+*     R         d     distance from observer (AU)
+*     JSTAT     i     status:  0 = OK
+*                             -1 = radius vector zero
+*                             -2 = failed to converge
+*
+*  Called: slGMST, slDT, slEPJ, slEPV, slUEPV, slPRNU,
+*          slDMXV, slPVOB, slDC2S, slDA2P
+*
+*  Notes:
+*
+*  1  DATE is the instant for which the prediction is required.  It is
+*     in the TT timescale (formerly Ephemeris Time, ET) and is a
+*     Modified Julian Date (JD-2400000.5).
+*
+*  2  The longitude and latitude allow correction for geocentric
+*     parallax.  This is usually a small effect, but can become
+*     important for near-Earth asteroids.  Geocentric positions can be
+*     generated by appropriate use of routines slEPV (or slEVP) and
+*     slUEPV.
+*
+*  3  The "universal" elements are those which define the orbit for the
+*     purposes of the method of universal variables (see reference 2).
+*     They consist of the combined mass of the two bodies, an epoch,
+*     and the position and velocity vectors (arbitrary reference frame)
+*     at that epoch.  The parameter set used here includes also various
+*     quantities that can, in fact, be derived from the other
+*     information.  This approach is taken to avoiding unnecessary
+*     computation and loss of accuracy.  The supplementary quantities
+*     are (i) alpha, which is proportional to the total energy of the
+*     orbit, (ii) the heliocentric distance at epoch, (iii) the
+*     outwards component of the velocity at the given epoch, (iv) an
+*     estimate of psi, the "universal eccentric anomaly" at a given
+*     date and (v) that date.
+*
+*  4  The universal elements are with respect to the J2000 equator and
+*     equinox.
+*
+*     1  Sterne, Theodore E., "An Introduction to Celestial Mechanics",
+*        Interscience Publishers Inc., 1960.  Section 6.7, p199.
+*
+*     2  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
+*
+*  Last revision:   19 February 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,ELONG,PHI,U(13),RA,DEC,R
+      INTEGER JSTAT
+
+*  Light time for unit distance (sec)
+      DOUBLE PRECISION TAU
+      PARAMETER (TAU=499.004782D0)
+
+      INTEGER I
+      DOUBLE PRECISION DVB(3),DPB(3),VSG(6),VSP(6),V(6),RMAT(3,3),
+     :                 VGP(6),STL,VGO(6),DX,DY,DZ,D,TL
+      DOUBLE PRECISION slGMST,slDT,slEPJ,slDA2P
+
+
+
+*  Sun to geocentre (J2000, velocity in AU/s).
+      CALL slEPV(DATE,VSG,VSG(4),DPB,DVB)
+      DO I=4,6
+         VSG(I)=VSG(I)/86400D0
+      END DO
+
+*  Sun to planet (J2000).
+      CALL slUEPV(DATE,U,VSP,JSTAT)
+
+*  Geocentre to planet (J2000).
+      DO I=1,6
+         V(I)=VSP(I)-VSG(I)
+      END DO
+
+*  Precession and nutation to date.
+      CALL slPRNU(2000D0,DATE,RMAT)
+      CALL slDMXV(RMAT,V,VGP)
+      CALL slDMXV(RMAT,V(4),VGP(4))
+
+*  Geocentre to observer (date).
+      STL=slGMST(DATE-slDT(slEPJ(DATE))/86400D0)+ELONG
+      CALL slPVOB(PHI,0D0,STL,VGO)
+
+*  Observer to planet (date).
+      DO I=1,6
+         V(I)=VGP(I)-VGO(I)
+      END DO
+
+*  Geometric distance (AU).
+      DX=V(1)
+      DY=V(2)
+      DZ=V(3)
+      D=SQRT(DX*DX+DY*DY+DZ*DZ)
+
+*  Light time (sec).
+      TL=TAU*D
+
+*  Correct position for planetary aberration
+      DO I=1,3
+         V(I)=V(I)-TL*V(I+3)
+      END DO
+
+*  To RA,Dec.
+      CALL slDC2S(V,RA,DEC)
+      RA=slDA2P(RA)
+      R=D
+
+      END
diff --git a/math/slalib/pm.f b/math/slalib/pm.f
new file mode 100644
index 00000000..903f92a8
--- /dev/null
+++ b/math/slalib/pm.f
@@ -0,0 +1,98 @@
+      SUBROUTINE slPM (R0, D0, PR, PD, PX, RV, EP0, EP1, R1, D1)
+*+
+*     - - -
+*      P M
+*     - - -
+*
+*  Apply corrections for proper motion to a star RA,Dec
+*  (double precision)
+*
+*  References:
+*     1984 Astronomical Almanac, pp B39-B41.
+*     (also Lederle & Schwan, Astron. Astrophys. 134,
+*      1-6, 1984)
+*
+*  Given:
+*     R0,D0    dp     RA,Dec at epoch EP0 (rad)
+*     PR,PD    dp     proper motions:  RA,Dec changes per year of epoch
+*     PX       dp     parallax (arcsec)
+*     RV       dp     radial velocity (km/sec, +ve if receding)
+*     EP0      dp     start epoch in years (e.g. Julian epoch)
+*     EP1      dp     end epoch in years (same system as EP0)
+*
+*  Returned:
+*     R1,D1    dp     RA,Dec at epoch EP1 (rad)
+*
+*  Called:
+*     slDS2C       spherical to Cartesian
+*     slDC2S       Cartesian to spherical
+*     slDA2P      normalize angle 0-2Pi
+*
+*  Notes:
+*
+*  1  The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt,
+*     and are in the same coordinate system as R0,D0.
+*
+*  2  If the available proper motions are pre-FK5 they will be per
+*     tropical year rather than per Julian year, and so the epochs
+*     must both be Besselian rather than Julian.  In such cases, a
+*     scaling factor of 365.2422D0/365.25D0 should be applied to the
+*     radial velocity before use.
+*
+*  P.T.Wallace   Starlink   19 January 2000
+*
+*  Copyright (C) 2000 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION R0,D0,PR,PD,PX,RV,EP0,EP1,R1,D1
+
+*  Km/s to AU/year multiplied by arcseconds to radians
+      DOUBLE PRECISION VFR
+      PARAMETER (VFR=(365.25D0*86400D0/149597870D0)*4.8481368111D-6)
+
+      INTEGER I
+      DOUBLE PRECISION slDA2P
+      DOUBLE PRECISION W,EM(3),T,P(3)
+
+
+
+*  Spherical to Cartesian
+      CALL slDS2C(R0,D0,P)
+
+*  Space motion (radians per year)
+      W=VFR*RV*PX
+      EM(1)=-PR*P(2)-PD*COS(R0)*SIN(D0)+W*P(1)
+      EM(2)= PR*P(1)-PD*SIN(R0)*SIN(D0)+W*P(2)
+      EM(3)=         PD*COS(D0)        +W*P(3)
+
+*  Apply the motion
+      T=EP1-EP0
+      DO I=1,3
+         P(I)=P(I)+T*EM(I)
+      END DO
+
+*  Cartesian to spherical
+      CALL slDC2S(P,R1,D1)
+      R1=slDA2P(R1)
+
+      END
diff --git a/math/slalib/polmo.f b/math/slalib/polmo.f
new file mode 100644
index 00000000..c82f2132
--- /dev/null
+++ b/math/slalib/polmo.f
@@ -0,0 +1,159 @@
+      SUBROUTINE slPLMO ( ELONGM, PHIM, XP, YP, ELONG, PHI, DAZ )
+*+
+*     - - - - - -
+*      P L M O
+*     - - - - - -
+*
+*  Polar motion:  correct site longitude and latitude for polar
+*  motion and calculate azimuth difference between celestial and
+*  terrestrial poles.
+*
+*  Given:
+*     ELONGM   d      mean longitude of the observer (radians, east +ve)
+*     PHIM     d      mean geodetic latitude of the observer (radians)
+*     XP       d      polar motion x-coordinate (radians)
+*     YP       d      polar motion y-coordinate (radians)
+*
+*  Returned:
+*     ELONG    d      true longitude of the observer (radians, east +ve)
+*     PHI      d      true geodetic latitude of the observer (radians)
+*     DAZ      d      azimuth correction (terrestrial-celestial, radians)
+*
+*  Notes:
+*
+*   1)  "Mean" longitude and latitude are the (fixed) values for the
+*       site's location with respect to the IERS terrestrial reference
+*       frame;  the latitude is geodetic.  TAKE CARE WITH THE LONGITUDE
+*       SIGN CONVENTION.  The longitudes used by the present routine
+*       are east-positive, in accordance with geographical convention
+*       (and right-handed).  In particular, note that the longitudes
+*       returned by the slOBS routine are west-positive, following
+*       astronomical usage, and must be reversed in sign before use in
+*       the present routine.
+*
+*   2)  XP and YP are the (changing) coordinates of the Celestial
+*       Ephemeris Pole with respect to the IERS Reference Pole.
+*       XP is positive along the meridian at longitude 0 degrees,
+*       and YP is positive along the meridian at longitude
+*       270 degrees (i.e. 90 degrees west).  Values for XP,YP can
+*       be obtained from IERS circulars and equivalent publications;
+*       the maximum amplitude observed so far is about 0.3 arcseconds.
+*
+*   3)  "True" longitude and latitude are the (moving) values for
+*       the site's location with respect to the celestial ephemeris
+*       pole and the meridian which corresponds to the Greenwich
+*       apparent sidereal time.  The true longitude and latitude
+*       link the terrestrial coordinates with the standard celestial
+*       models (for precession, nutation, sidereal time etc).
+*
+*   4)  The azimuths produced by slAOP and slAOPQ are with
+*       respect to due north as defined by the Celestial Ephemeris
+*       Pole, and can therefore be called "celestial azimuths".
+*       However, a telescope fixed to the Earth measures azimuth
+*       essentially with respect to due north as defined by the
+*       IERS Reference Pole, and can therefore be called "terrestrial
+*       azimuth".  Uncorrected, this would manifest itself as a
+*       changing "azimuth zero-point error".  The value DAZ is the
+*       correction to be added to a celestial azimuth to produce
+*       a terrestrial azimuth.
+*
+*   5)  The present routine is rigorous.  For most practical
+*       purposes, the following simplified formulae provide an
+*       adequate approximation:
+*
+*       ELONG = ELONGM+XP*COS(ELONGM)-YP*SIN(ELONGM)
+*       PHI   = PHIM+(XP*SIN(ELONGM)+YP*COS(ELONGM))*TAN(PHIM)
+*       DAZ   = -SQRT(XP*XP+YP*YP)*COS(ELONGM-ATAN2(XP,YP))/COS(PHIM)
+*
+*       An alternative formulation for DAZ is:
+*
+*       X = COS(ELONGM)*COS(PHIM)
+*       Y = SIN(ELONGM)*COS(PHIM)
+*       DAZ = ATAN2(-X*YP-Y*XP,X*X+Y*Y)
+*
+*   Reference:  Seidelmann, P.K. (ed), 1992.  "Explanatory Supplement
+*               to the Astronomical Almanac", ISBN 0-935702-68-7,
+*               sections 3.27, 4.25, 4.52.
+*
+*  P.T.Wallace   Starlink   30 November 2000
+*
+*  Copyright (C) 2000 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION ELONGM,PHIM,XP,YP,ELONG,PHI,DAZ
+
+      DOUBLE PRECISION SEL,CEL,SPH,CPH,XM,YM,ZM,XNM,YNM,ZNM,
+     :                 SXP,CXP,SYP,CYP,ZW,XT,YT,ZT,XNT,YNT
+
+
+
+*  Site mean longitude and mean geodetic latitude as a Cartesian vector
+      SEL=SIN(ELONGM)
+      CEL=COS(ELONGM)
+      SPH=SIN(PHIM)
+      CPH=COS(PHIM)
+
+      XM=CEL*CPH
+      YM=SEL*CPH
+      ZM=SPH
+
+*  Rotate site vector by polar motion, Y-component then X-component
+      SXP=SIN(XP)
+      CXP=COS(XP)
+      SYP=SIN(YP)
+      CYP=COS(YP)
+
+      ZW=(-YM*SYP+ZM*CYP)
+
+      XT=XM*CXP-ZW*SXP
+      YT=YM*CYP+ZM*SYP
+      ZT=XM*SXP+ZW*CXP
+
+*  Rotate also the geocentric direction of the terrestrial pole (0,0,1)
+      XNM=-SXP*CYP
+      YNM=SYP
+      ZNM=CXP*CYP
+
+      CPH=SQRT(XT*XT+YT*YT)
+      IF (CPH.EQ.0D0) XT=1D0
+      SEL=YT/CPH
+      CEL=XT/CPH
+
+*  Return true longitude and true geodetic latitude of site
+      IF (XT.NE.0D0.OR.YT.NE.0D0) THEN
+         ELONG=ATAN2(YT,XT)
+      ELSE
+         ELONG=0D0
+      END IF
+      PHI=ATAN2(ZT,CPH)
+
+*  Return current azimuth of terrestrial pole seen from site position
+      XNT=(XNM*CEL+YNM*SEL)*ZT-ZNM*CPH
+      YNT=-XNM*SEL+YNM*CEL
+      IF (XNT.NE.0D0.OR.YNT.NE.0D0) THEN
+         DAZ=ATAN2(-YNT,-XNT)
+      ELSE
+         DAZ=0D0
+      END IF
+
+      END
diff --git a/math/slalib/prebn.f b/math/slalib/prebn.f
new file mode 100644
index 00000000..0c46f592
--- /dev/null
+++ b/math/slalib/prebn.f
@@ -0,0 +1,80 @@
+      SUBROUTINE slPRBN (BEP0, BEP1, RMATP)
+*+
+*     - - - - - -
+*      P R B N
+*     - - - - - -
+*
+*  Generate the matrix of precession between two epochs,
+*  using the old, pre-IAU1976, Bessel-Newcomb model, using
+*  Kinoshita's formulation (double precision)
+*
+*  Given:
+*     BEP0    dp         beginning Besselian epoch
+*     BEP1    dp         ending Besselian epoch
+*
+*  Returned:
+*     RMATP  dp(3,3)    precession matrix
+*
+*  The matrix is in the sense   V(BEP1)  =  RMATP * V(BEP0)
+*
+*  Reference:
+*     Kinoshita, H. (1975) 'Formulas for precession', SAO Special
+*     Report No. 364, Smithsonian Institution Astrophysical
+*     Observatory, Cambridge, Massachusetts.
+*
+*  Called:  slDEUL
+*
+*  P.T.Wallace   Starlink   23 August 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION BEP0,BEP1,RMATP(3,3)
+
+*  Arc seconds to radians
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+      DOUBLE PRECISION BIGT,T,TAS2R,W,ZETA,Z,THETA
+
+
+
+*  Interval between basic epoch B1850.0 and beginning epoch in TC
+      BIGT = (BEP0-1850D0)/100D0
+
+*  Interval over which precession required, in tropical centuries
+      T = (BEP1-BEP0)/100D0
+
+*  Euler angles
+      TAS2R = T*AS2R
+      W = 2303.5548D0+(1.39720D0+0.000059D0*BIGT)*BIGT
+
+      ZETA = (W+(0.30242D0-0.000269D0*BIGT+0.017996D0*T)*T)*TAS2R
+      Z = (W+(1.09478D0+0.000387D0*BIGT+0.018324D0*T)*T)*TAS2R
+      THETA = (2005.1125D0+(-0.85294D0-0.000365D0*BIGT)*BIGT+
+     :        (-0.42647D0-0.000365D0*BIGT-0.041802D0*T)*T)*TAS2R
+
+*  Rotation matrix
+      CALL slDEUL('ZYZ',-ZETA,THETA,-Z,RMATP)
+
+      END
diff --git a/math/slalib/prec.f b/math/slalib/prec.f
new file mode 100644
index 00000000..e8eadce7
--- /dev/null
+++ b/math/slalib/prec.f
@@ -0,0 +1,97 @@
+      SUBROUTINE slPREC (EP0, EP1, RMATP)
+*+
+*     - - - - -
+*      P R E C
+*     - - - - -
+*
+*  Form the matrix of precession between two epochs (IAU 1976, FK5)
+*  (double precision)
+*
+*  Given:
+*     EP0    dp         beginning epoch
+*     EP1    dp         ending epoch
+*
+*  Returned:
+*     RMATP  dp(3,3)    precession matrix
+*
+*  Notes:
+*
+*     1)  The epochs are TDB (loosely ET) Julian epochs.
+*
+*     2)  The matrix is in the sense   V(EP1)  =  RMATP * V(EP0)
+*
+*     3)  Though the matrix method itself is rigorous, the precession
+*         angles are expressed through canonical polynomials which are
+*         valid only for a limited time span.  There are also known
+*         errors in the IAU precession rate.  The absolute accuracy
+*         of the present formulation is better than 0.1 arcsec from
+*         1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD,
+*         and remains below 3 arcsec for the whole of the period
+*         500BC to 3000AD.  The errors exceed 10 arcsec outside the
+*         range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to
+*         5600AD and exceed 1000 arcsec outside 6800BC to 8200AD.
+*         The SLALIB routine slPREL implements a more elaborate
+*         model which is suitable for problems spanning several
+*         thousand years.
+*
+*  References:
+*     Lieske,J.H., 1979. Astron.Astrophys.,73,282.
+*      equations (6) & (7), p283.
+*     Kaplan,G.H., 1981. USNO circular no. 163, pA2.
+*
+*  Called:  slDEUL
+*
+*  P.T.Wallace   Starlink   23 August 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION EP0,EP1,RMATP(3,3)
+
+*  Arc seconds to radians
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+      DOUBLE PRECISION T0,T,TAS2R,W,ZETA,Z,THETA
+
+
+
+*  Interval between basic epoch J2000.0 and beginning epoch (JC)
+      T0 = (EP0-2000D0)/100D0
+
+*  Interval over which precession required (JC)
+      T = (EP1-EP0)/100D0
+
+*  Euler angles
+      TAS2R = T*AS2R
+      W = 2306.2181D0+(1.39656D0-0.000139D0*T0)*T0
+
+      ZETA = (W+((0.30188D0-0.000344D0*T0)+0.017998D0*T)*T)*TAS2R
+      Z = (W+((1.09468D0+0.000066D0*T0)+0.018203D0*T)*T)*TAS2R
+      THETA = ((2004.3109D0+(-0.85330D0-0.000217D0*T0)*T0)
+     :        +((-0.42665D0-0.000217D0*T0)-0.041833D0*T)*T)*TAS2R
+
+*  Rotation matrix
+      CALL slDEUL('ZYZ',-ZETA,THETA,-Z,RMATP)
+
+      END
diff --git a/math/slalib/preces.f b/math/slalib/preces.f
new file mode 100644
index 00000000..9c2aec25
--- /dev/null
+++ b/math/slalib/preces.f
@@ -0,0 +1,102 @@
+      SUBROUTINE slPRCE (SYSTEM, EP0, EP1, RA, DC)
+*+
+*     - - - - - - -
+*      P R C E
+*     - - - - - - -
+*
+*  Precession - either FK4 (Bessel-Newcomb, pre IAU 1976) or
+*  FK5 (Fricke, post IAU 1976) as required.
+*
+*  Given:
+*     SYSTEM     char   precession to be applied: 'FK4' or 'FK5'
+*     EP0,EP1    dp     starting and ending epoch
+*     RA,DC      dp     RA,Dec, mean equator & equinox of epoch EP0
+*
+*  Returned:
+*     RA,DC      dp     RA,Dec, mean equator & equinox of epoch EP1
+*
+*  Called:    slDA2P, slPRBN, slPREC, slDS2C,
+*             slDMXV, slDC2S
+*
+*  Notes:
+*
+*     1)  Lowercase characters in SYSTEM are acceptable.
+*
+*     2)  The epochs are Besselian if SYSTEM='FK4' and Julian if 'FK5'.
+*         For example, to precess coordinates in the old system from
+*         equinox 1900.0 to 1950.0 the call would be:
+*             CALL slPRCE ('FK4', 1900D0, 1950D0, RA, DC)
+*
+*     3)  This routine will NOT correctly convert between the old and
+*         the new systems - for example conversion from B1950 to J2000.
+*         For these purposes see slFK45, slFK54, slF45Z and
+*         slF54Z.
+*
+*     4)  If an invalid SYSTEM is supplied, values of -99D0,-99D0 will
+*         be returned for both RA and DC.
+*
+*  P.T.Wallace   Starlink   20 April 1990
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER SYSTEM*(*)
+      DOUBLE PRECISION EP0,EP1,RA,DC
+
+      DOUBLE PRECISION PM(3,3),V1(3),V2(3)
+      CHARACTER SYSUC*3
+
+      DOUBLE PRECISION slDA2P
+
+
+
+
+*  Convert to uppercase and validate SYSTEM
+      SYSUC=SYSTEM
+      IF (SYSUC(1:1).EQ.'f') SYSUC(1:1)='F'
+      IF (SYSUC(2:2).EQ.'k') SYSUC(2:2)='K'
+      IF (SYSUC.NE.'FK4'.AND.SYSUC.NE.'FK5') THEN
+         RA=-99D0
+         DC=-99D0
+      ELSE
+
+*     Generate appropriate precession matrix
+         IF (SYSUC.EQ.'FK4') THEN
+            CALL slPRBN(EP0,EP1,PM)
+         ELSE
+            CALL slPREC(EP0,EP1,PM)
+         END IF
+
+*     Convert RA,Dec to x,y,z
+         CALL slDS2C(RA,DC,V1)
+
+*     Precess
+         CALL slDMXV(PM,V1,V2)
+
+*     Back to RA,Dec
+         CALL slDC2S(V2,RA,DC)
+         RA=slDA2P(RA)
+
+      END IF
+
+      END
diff --git a/math/slalib/precl.f b/math/slalib/precl.f
new file mode 100644
index 00000000..55bb839e
--- /dev/null
+++ b/math/slalib/precl.f
@@ -0,0 +1,143 @@
+      SUBROUTINE slPREL (EP0, EP1, RMATP)
+*+
+*     - - - - - -
+*      P R E L
+*     - - - - - -
+*
+*  Form the matrix of precession between two epochs, using the
+*  model of Simon et al (1994), which is suitable for long
+*  periods of time.
+*
+*  (double precision)
+*
+*  Given:
+*     EP0    dp         beginning epoch
+*     EP1    dp         ending epoch
+*
+*  Returned:
+*     RMATP  dp(3,3)    precession matrix
+*
+*  Notes:
+*
+*     1)  The epochs are TDB Julian epochs.
+*
+*     2)  The matrix is in the sense   V(EP1)  =  RMATP * V(EP0)
+*
+*     3)  The absolute accuracy of the model is limited by the
+*         uncertainty in the general precession, about 0.3 arcsec per
+*         1000 years.  The remainder of the formulation provides a
+*         precision of 1 mas over the interval from 1000AD to 3000AD,
+*         0.1 arcsec from 1000BC to 5000AD and 1 arcsec from
+*         4000BC to 8000AD.
+*
+*  Reference:
+*     Simon, J.L. et al., 1994. Astron.Astrophys., 282, 663-683.
+*
+*  Called:  slDEUL
+*
+*  P.T.Wallace   Starlink   23 August 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION EP0,EP1,RMATP(3,3)
+
+*  Arc seconds to radians
+      DOUBLE PRECISION AS2R
+      PARAMETER (AS2R=0.484813681109535994D-5)
+
+      DOUBLE PRECISION T0,T,TAS2R,W,ZETA,Z,THETA
+
+
+
+*  Interval between basic epoch J2000.0 and beginning epoch (1000JY)
+      T0 = (EP0-2000D0)/1000D0
+
+*  Interval over which precession required (1000JY)
+      T = (EP1-EP0)/1000D0
+
+*  Euler angles
+      TAS2R = T*AS2R
+      W =      23060.9097D0+
+     :          (139.7459D0+
+     :           (-0.0038D0+
+     :           (-0.5918D0+
+     :           (-0.0037D0+
+     :             0.0007D0*T0)*T0)*T0)*T0)*T0
+
+      ZETA =   (W+(30.2226D0+
+     :            (-0.2523D0+
+     :            (-0.3840D0+
+     :            (-0.0014D0+
+     :              0.0007D0*T0)*T0)*T0)*T0+
+     :            (18.0183D0+
+     :            (-0.1326D0+
+     :             (0.0006D0+
+     :              0.0005D0*T0)*T0)*T0+
+     :            (-0.0583D0+
+     :            (-0.0001D0+
+     :              0.0007D0*T0)*T0+
+     :            (-0.0285D0+
+     :            (-0.0002D0)*T)*T)*T)*T)*T)*TAS2R
+
+      Z =     (W+(109.5270D0+
+     :             (0.2446D0+
+     :            (-1.3913D0+
+     :            (-0.0134D0+
+     :              0.0026D0*T0)*T0)*T0)*T0+
+     :            (18.2667D0+
+     :            (-1.1400D0+
+     :            (-0.0173D0+
+     :              0.0044D0*T0)*T0)*T0+
+     :            (-0.2821D0+
+     :            (-0.0093D0+
+     :              0.0032D0*T0)*T0+
+     :            (-0.0301D0+
+     :              0.0006D0*T0
+     :             -0.0001D0*T)*T)*T)*T)*T)*TAS2R
+
+      THETA =  (20042.0207D0+
+     :           (-85.3131D0+
+     :            (-0.2111D0+
+     :             (0.3642D0+
+     :             (0.0008D0+
+     :            (-0.0005D0)*T0)*T0)*T0)*T0)*T0+
+     :           (-42.6566D0+
+     :            (-0.2111D0+
+     :             (0.5463D0+
+     :             (0.0017D0+
+     :            (-0.0012D0)*T0)*T0)*T0)*T0+
+     :           (-41.8238D0+
+     :             (0.0359D0+
+     :             (0.0027D0+
+     :            (-0.0001D0)*T0)*T0)*T0+
+     :            (-0.0731D0+
+     :             (0.0019D0+
+     :              0.0009D0*T0)*T0+
+     :            (-0.0127D0+
+     :              0.0011D0*T0+0.0004D0*T)*T)*T)*T)*T)*TAS2R
+
+*  Rotation matrix
+      CALL slDEUL('ZYZ',-ZETA,THETA,-Z,RMATP)
+
+      END
diff --git a/math/slalib/precss.f b/math/slalib/precss.f
new file mode 100644
index 00000000..c18707dc
--- /dev/null
+++ b/math/slalib/precss.f
@@ -0,0 +1,76 @@
+      SUBROUTINE slPRCS (SYSTEM, EP0, EP1, RA, DC)
+*+
+*     - - - - - - -
+*      P R C E
+*     - - - - - - -
+*
+*  Precession - either FK4 (Bessel-Newcomb, pre IAU 1976) or
+*  FK5 (Fricke, post IAU 1976) as required.
+*
+*  Given:
+*     SYSTEM     int    precession to be applied: 1 = FK4 or 2 = FK5
+*     EP0,EP1    dp     starting and ending epoch
+*     RA,DC      dp     RA,Dec, mean equator & equinox of epoch EP0
+*
+*  Returned:
+*     RA,DC      dp     RA,Dec, mean equator & equinox of epoch EP1
+*
+*  Called:    slDA2P, slPRBN, slPREC, slDS2C,
+*             slDMXV, slDC2S
+*
+*  Notes:
+*
+*     1)  Lowercase characters in SYSTEM are acceptable.
+*
+*     2)  The epochs are Besselian if SYSTEM=FK4 and Julian if FK5.
+*         For example, to precess coordinates in the old system from
+*         equinox 1900.0 to 1950.0 the call would be:
+*             CALL slPRCS (1, 1900D0, 1950D0, RA, DC)
+*
+*     3)  This routine will NOT correctly convert between the old and
+*         the new systems - for example conversion from B1950 to J2000.
+*         For these purposes see slFK45, slFK54, slF45Z and
+*         slF54Z.
+*
+*     4)  If an invalid SYSTEM is supplied, values of -99D0,-99D0 will
+*         be returned for both RA and DC.
+*
+*  P.T.Wallace   Starlink   20 April 1990
+*-
+
+      IMPLICIT NONE
+
+      INTEGER SYSTEM
+      DOUBLE PRECISION EP0,EP1,RA,DC
+
+      DOUBLE PRECISION PM(3,3),V1(3),V2(3)
+
+      DOUBLE PRECISION slDA2P
+
+
+*  Convert to uppercase and validate SYSTEM
+      IF (SYSTEM.NE.1.AND.SYSTEM.NE.2) THEN
+         RA=-99D0
+         DC=-99D0
+      ELSE
+
+*     Generate appropriate precession matrix
+         IF (SYSTEM.EQ.1) THEN
+            CALL slPRBN(EP0,EP1,PM)
+         ELSE
+            CALL slPREC(EP0,EP1,PM)
+         END IF
+
+*     Convert RA,Dec to x,y,z
+         CALL slDS2C(RA,DC,V1)
+
+*     Precess
+         CALL slDMXV(PM,V1,V2)
+
+*     Back to RA,Dec
+         CALL slDC2S(V2,RA,DC)
+         RA=slDA2P(RA)
+
+      END IF
+
+      END
diff --git a/math/slalib/precss.f.sav b/math/slalib/precss.f.sav
new file mode 100644
index 00000000..c18707dc
--- /dev/null
+++ b/math/slalib/precss.f.sav
@@ -0,0 +1,76 @@
+      SUBROUTINE slPRCS (SYSTEM, EP0, EP1, RA, DC)
+*+
+*     - - - - - - -
+*      P R C E
+*     - - - - - - -
+*
+*  Precession - either FK4 (Bessel-Newcomb, pre IAU 1976) or
+*  FK5 (Fricke, post IAU 1976) as required.
+*
+*  Given:
+*     SYSTEM     int    precession to be applied: 1 = FK4 or 2 = FK5
+*     EP0,EP1    dp     starting and ending epoch
+*     RA,DC      dp     RA,Dec, mean equator & equinox of epoch EP0
+*
+*  Returned:
+*     RA,DC      dp     RA,Dec, mean equator & equinox of epoch EP1
+*
+*  Called:    slDA2P, slPRBN, slPREC, slDS2C,
+*             slDMXV, slDC2S
+*
+*  Notes:
+*
+*     1)  Lowercase characters in SYSTEM are acceptable.
+*
+*     2)  The epochs are Besselian if SYSTEM=FK4 and Julian if FK5.
+*         For example, to precess coordinates in the old system from
+*         equinox 1900.0 to 1950.0 the call would be:
+*             CALL slPRCS (1, 1900D0, 1950D0, RA, DC)
+*
+*     3)  This routine will NOT correctly convert between the old and
+*         the new systems - for example conversion from B1950 to J2000.
+*         For these purposes see slFK45, slFK54, slF45Z and
+*         slF54Z.
+*
+*     4)  If an invalid SYSTEM is supplied, values of -99D0,-99D0 will
+*         be returned for both RA and DC.
+*
+*  P.T.Wallace   Starlink   20 April 1990
+*-
+
+      IMPLICIT NONE
+
+      INTEGER SYSTEM
+      DOUBLE PRECISION EP0,EP1,RA,DC
+
+      DOUBLE PRECISION PM(3,3),V1(3),V2(3)
+
+      DOUBLE PRECISION slDA2P
+
+
+*  Convert to uppercase and validate SYSTEM
+      IF (SYSTEM.NE.1.AND.SYSTEM.NE.2) THEN
+         RA=-99D0
+         DC=-99D0
+      ELSE
+
+*     Generate appropriate precession matrix
+         IF (SYSTEM.EQ.1) THEN
+            CALL slPRBN(EP0,EP1,PM)
+         ELSE
+            CALL slPREC(EP0,EP1,PM)
+         END IF
+
+*     Convert RA,Dec to x,y,z
+         CALL slDS2C(RA,DC,V1)
+
+*     Precess
+         CALL slDMXV(PM,V1,V2)
+
+*     Back to RA,Dec
+         CALL slDC2S(V2,RA,DC)
+         RA=slDA2P(RA)
+
+      END IF
+
+      END
diff --git a/math/slalib/prenut.f b/math/slalib/prenut.f
new file mode 100644
index 00000000..4e2bb8cb
--- /dev/null
+++ b/math/slalib/prenut.f
@@ -0,0 +1,67 @@
+      SUBROUTINE slPRNU (EPOCH, DATE, RMATPN)
+*+
+*     - - - - - - -
+*      P R N U
+*     - - - - - - -
+*
+*  Form the matrix of precession and nutation (SF2001)
+*  (double precision)
+*
+*  Given:
+*     EPOCH   dp         Julian Epoch for mean coordinates
+*     DATE    dp         Modified Julian Date (JD-2400000.5)
+*                        for true coordinates
+*
+*  Returned:
+*     RMATPN  dp(3,3)    combined precession/nutation matrix
+*
+*  Called:  slPREC, slEPJ, slNUT, slDMXM
+*
+*  Notes:
+*
+*  1)  The epoch and date are TDB (loosely ET).  TT will do, or even
+*      UTC.
+*
+*  2)  The matrix is in the sense   V(true) = RMATPN * V(mean)
+*
+*  Last revision:   3 December 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION EPOCH,DATE,RMATPN(3,3)
+
+      DOUBLE PRECISION RMATP(3,3),RMATN(3,3),slEPJ
+
+
+
+*  Precession
+      CALL slPREC(EPOCH,slEPJ(DATE),RMATP)
+
+*  Nutation
+      CALL slNUT(DATE,RMATN)
+
+*  Combine the matrices:  PN = N x P
+      CALL slDMXM(RMATN,RMATP,RMATPN)
+
+      END
diff --git a/math/slalib/pv2el.f b/math/slalib/pv2el.f
new file mode 100644
index 00000000..b8db2d25
--- /dev/null
+++ b/math/slalib/pv2el.f
@@ -0,0 +1,380 @@
+      SUBROUTINE slPVEL (PV, DATE, PMASS, JFORMR,
+     :                      JFORM, EPOCH, ORBINC, ANODE, PERIH,
+     :                      AORQ, E, AORL, DM, JSTAT)
+*+
+*     - - - - - -
+*      P V E L
+*     - - - - - -
+*
+*  Heliocentric osculating elements obtained from instantaneous position
+*  and velocity.
+*
+*  Given:
+*     PV        d(6)   heliocentric x,y,z,xdot,ydot,zdot of date,
+*                      J2000 equatorial triad (AU,AU/s; Note 1)
+*     DATE      d      date (TT Modified Julian Date = JD-2400000.5)
+*     PMASS     d      mass of the planet (Sun=1; Note 2)
+*     JFORMR    i      requested element set (1-3; Note 3)
+*
+*  Returned:
+*     JFORM     d      element set actually returned (1-3; Note 4)
+*     EPOCH     d      epoch of elements (TT MJD)
+*     ORBINC    d      inclination (radians)
+*     ANODE     d      longitude of the ascending node (radians)
+*     PERIH     d      longitude or argument of perihelion (radians)
+*     AORQ      d      mean distance or perihelion distance (AU)
+*     E         d      eccentricity
+*     AORL      d      mean anomaly or longitude (radians, JFORM=1,2 only)
+*     DM        d      daily motion (radians, JFORM=1 only)
+*     JSTAT     i      status:  0 = OK
+*                              -1 = illegal PMASS
+*                              -2 = illegal JFORMR
+*                              -3 = position/velocity out of range
+*
+*  Notes
+*
+*  1  The PV 6-vector is with respect to the mean equator and equinox of
+*     epoch J2000.  The orbital elements produced are with respect to
+*     the J2000 ecliptic and mean equinox.
+*
+*  2  The mass, PMASS, is important only for the larger planets.  For
+*     most purposes (e.g. asteroids) use 0D0.  Values less than zero
+*     are illegal.
+*
+*  3  Three different element-format options are supported:
+*
+*     Option JFORM=1, suitable for the major planets:
+*
+*     EPOCH  = epoch of elements (TT MJD)
+*     ORBINC = inclination i (radians)
+*     ANODE  = longitude of the ascending node, big omega (radians)
+*     PERIH  = longitude of perihelion, curly pi (radians)
+*     AORQ   = mean distance, a (AU)
+*     E      = eccentricity, e
+*     AORL   = mean longitude L (radians)
+*     DM     = daily motion (radians)
+*
+*     Option JFORM=2, suitable for minor planets:
+*
+*     EPOCH  = epoch of elements (TT MJD)
+*     ORBINC = inclination i (radians)
+*     ANODE  = longitude of the ascending node, big omega (radians)
+*     PERIH  = argument of perihelion, little omega (radians)
+*     AORQ   = mean distance, a (AU)
+*     E      = eccentricity, e
+*     AORL   = mean anomaly M (radians)
+*
+*     Option JFORM=3, suitable for comets:
+*
+*     EPOCH  = epoch of perihelion (TT MJD)
+*     ORBINC = inclination i (radians)
+*     ANODE  = longitude of the ascending node, big omega (radians)
+*     PERIH  = argument of perihelion, little omega (radians)
+*     AORQ   = perihelion distance, q (AU)
+*     E      = eccentricity, e
+*
+*  4  It may not be possible to generate elements in the form
+*     requested through JFORMR.  The caller is notified of the form
+*     of elements actually returned by means of the JFORM argument:
+*
+*      JFORMR   JFORM     meaning
+*
+*        1        1       OK - elements are in the requested format
+*        1        2       never happens
+*        1        3       orbit not elliptical
+*
+*        2        1       never happens
+*        2        2       OK - elements are in the requested format
+*        2        3       orbit not elliptical
+*
+*        3        1       never happens
+*        3        2       never happens
+*        3        3       OK - elements are in the requested format
+*
+*  5  The arguments returned for each value of JFORM (cf Note 5: JFORM
+*     may not be the same as JFORMR) are as follows:
+*
+*         JFORM         1              2              3
+*         EPOCH         t0             t0             T
+*         ORBINC        i              i              i
+*         ANODE         Omega          Omega          Omega
+*         PERIH         curly pi       omega          omega
+*         AORQ          a              a              q
+*         E             e              e              e
+*         AORL          L              M              -
+*         DM            n              -              -
+*
+*     where:
+*
+*         t0           is the epoch of the elements (MJD, TT)
+*         T              "    epoch of perihelion (MJD, TT)
+*         i              "    inclination (radians)
+*         Omega          "    longitude of the ascending node (radians)
+*         curly pi       "    longitude of perihelion (radians)
+*         omega          "    argument of perihelion (radians)
+*         a              "    mean distance (AU)
+*         q              "    perihelion distance (AU)
+*         e              "    eccentricity
+*         L              "    longitude (radians, 0-2pi)
+*         M              "    mean anomaly (radians, 0-2pi)
+*         n              "    daily motion (radians)
+*         -             means no value is set
+*
+*  6  At very small inclinations, the longitude of the ascending node
+*     ANODE becomes indeterminate and under some circumstances may be
+*     set arbitrarily to zero.  Similarly, if the orbit is close to
+*     circular, the true anomaly becomes indeterminate and under some
+*     circumstances may be set arbitrarily to zero.  In such cases,
+*     the other elements are automatically adjusted to compensate,
+*     and so the elements remain a valid description of the orbit.
+*
+*  7  The osculating epoch for the returned elements is the argument
+*     DATE.
+*
+*  Reference:  Sterne, Theodore E., "An Introduction to Celestial
+*              Mechanics", Interscience Publishers, 1960
+*
+*  Called:  slDA2P
+*
+*  Last revision:   8 September 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION PV(6),DATE,PMASS
+      INTEGER JFORMR,JFORM
+      DOUBLE PRECISION EPOCH,ORBINC,ANODE,PERIH,AORQ,E,AORL,DM
+      INTEGER JSTAT
+
+*  Seconds to days
+      DOUBLE PRECISION DAY
+      PARAMETER (DAY=86400D0)
+
+*  Gaussian gravitational constant (exact)
+      DOUBLE PRECISION GCON
+      PARAMETER (GCON=0.01720209895D0)
+
+*  Sin and cos of J2000 mean obliquity (IAU 1976)
+      DOUBLE PRECISION SE,CE
+      PARAMETER (SE=0.3977771559319137D0,
+     :           CE=0.9174820620691818D0)
+
+*  Minimum allowed distance (AU) and speed (AU/day)
+      DOUBLE PRECISION RMIN,VMIN
+      PARAMETER (RMIN=1D-3,VMIN=1D-8)
+
+*  How close to unity the eccentricity has to be to call it a parabola
+      DOUBLE PRECISION PARAB
+      PARAMETER (PARAB=1D-8)
+
+      DOUBLE PRECISION X,Y,Z,XD,YD,ZD,R,V2,V,RDV,GMU,HX,HY,HZ,
+     :                 HX2PY2,H2,H,OI,BIGOM,AR,ECC,S,C,AT,U,OM,
+     :                 GAR3,EM1,EP1,HAT,SHAT,CHAT,AE,AM,DN,PL,
+     :                 EL,Q,TP,THAT,THHF,F
+
+      INTEGER JF
+
+      DOUBLE PRECISION slDA2P
+
+
+*  Validate arguments PMASS and JFORMR.
+      IF (PMASS.LT.0D0) THEN
+         JSTAT = -1
+         GO TO 999
+      END IF
+      IF (JFORMR.LT.1.OR.JFORMR.GT.3) THEN
+         JSTAT = -2
+         GO TO 999
+      END IF
+
+*  Provisionally assume the elements will be in the chosen form.
+      JF = JFORMR
+
+*  Rotate the position from equatorial to ecliptic coordinates.
+      X = PV(1)
+      Y = PV(2)*CE+PV(3)*SE
+      Z = -PV(2)*SE+PV(3)*CE
+
+*  Rotate the velocity similarly, scaling to AU/day.
+      XD = DAY*PV(4)
+      YD = DAY*(PV(5)*CE+PV(6)*SE)
+      ZD = DAY*(-PV(5)*SE+PV(6)*CE)
+
+*  Distance and speed.
+      R = SQRT(X*X+Y*Y+Z*Z)
+      V2 = XD*XD+YD*YD+ZD*ZD
+      V = SQRT(V2)
+
+*  Reject unreasonably small values.
+      IF (R.LT.RMIN.OR.V.LT.VMIN) THEN
+         JSTAT = -3
+         GO TO 999
+      END IF
+
+*  R dot V.
+      RDV = X*XD+Y*YD+Z*ZD
+
+*  Mu.
+      GMU = (1D0+PMASS)*GCON*GCON
+
+*  Vector angular momentum per unit reduced mass.
+      HX = Y*ZD-Z*YD
+      HY = Z*XD-X*ZD
+      HZ = X*YD-Y*XD
+
+*  Areal constant.
+      HX2PY2 = HX*HX+HY*HY
+      H2 = HX2PY2+HZ*HZ
+      H = SQRT(H2)
+
+*  Inclination.
+      OI = ATAN2(SQRT(HX2PY2),HZ)
+
+*  Longitude of ascending node.
+      IF (HX.NE.0D0.OR.HY.NE.0D0) THEN
+         BIGOM = ATAN2(HX,-HY)
+      ELSE
+         BIGOM=0D0
+      END IF
+
+*  Reciprocal of mean distance etc.
+      AR = 2D0/R-V2/GMU
+
+*  Eccentricity.
+      ECC = SQRT(MAX(1D0-AR*H2/GMU,0D0))
+
+*  True anomaly.
+      S = H*RDV
+      C = H2-R*GMU
+      IF (S.NE.0D0.OR.C.NE.0D0) THEN
+         AT = ATAN2(S,C)
+      ELSE
+         AT = 0D0
+      END IF
+
+*  Argument of the latitude.
+      S = SIN(BIGOM)
+      C = COS(BIGOM)
+      U = ATAN2((-X*S+Y*C)*COS(OI)+Z*SIN(OI),X*C+Y*S)
+
+*  Argument of perihelion.
+      OM = U-AT
+
+*  Capture near-parabolic cases.
+      IF (ABS(ECC-1D0).LT.PARAB) ECC=1D0
+
+*  Comply with JFORMR = 1 or 2 only if orbit is elliptical.
+      IF (ECC.GE.1D0) JF=3
+
+*  Functions.
+      GAR3 = GMU*AR*AR*AR
+      EM1 = ECC-1D0
+      EP1 = ECC+1D0
+      HAT = AT/2D0
+      SHAT = SIN(HAT)
+      CHAT = COS(HAT)
+
+*  Variable initializations to avoid compiler warnings.
+      AM = 0D0
+      DN = 0D0
+      PL = 0D0
+      EL = 0D0
+      Q = 0D0
+      TP = 0D0
+
+*  Ellipse?
+      IF (ECC.LT.1D0 ) THEN
+
+*     Eccentric anomaly.
+         AE = 2D0*ATAN2(SQRT(-EM1)*SHAT,SQRT(EP1)*CHAT)
+
+*     Mean anomaly.
+         AM = AE-ECC*SIN(AE)
+
+*     Daily motion.
+         DN = SQRT(GAR3)
+      END IF
+
+*  "Major planet" element set?
+      IF (JF.EQ.1) THEN
+
+*     Longitude of perihelion.
+         PL = BIGOM+OM
+
+*     Longitude at epoch.
+         EL = PL+AM
+      END IF
+
+*  "Comet" element set?
+      IF (JF.EQ.3) THEN
+
+*     Perihelion distance.
+         Q = H2/(GMU*EP1)
+
+*     Ellipse, parabola, hyperbola?
+         IF (ECC.LT.1D0) THEN
+
+*        Ellipse: epoch of perihelion.
+            TP = DATE-AM/DN
+         ELSE
+
+*        Parabola or hyperbola: evaluate tan ( ( true anomaly ) / 2 )
+            THAT = SHAT/CHAT
+            IF (ECC.EQ.1D0) THEN
+
+*           Parabola: epoch of perihelion.
+               TP = DATE-THAT*(1D0+THAT*THAT/3D0)*H*H2/(2D0*GMU*GMU)
+            ELSE
+
+*           Hyperbola: epoch of perihelion.
+               THHF = SQRT(EM1/EP1)*THAT
+               F = LOG(1D0+THHF)-LOG(1D0-THHF)
+               TP = DATE-(ECC*SINH(F)-F)/SQRT(-GAR3)
+            END IF
+         END IF
+      END IF
+
+*  Return the appropriate set of elements.
+      JFORM = JF
+      ORBINC = OI
+      ANODE = slDA2P(BIGOM)
+      E = ECC
+      IF (JF.EQ.1) THEN
+         PERIH = slDA2P(PL)
+         AORL = slDA2P(EL)
+         DM = DN
+      ELSE
+         PERIH = slDA2P(OM)
+         IF (JF.EQ.2) AORL = slDA2P(AM)
+      END IF
+      IF (JF.NE.3) THEN
+         EPOCH = DATE
+         AORQ = 1D0/AR
+      ELSE
+         EPOCH = TP
+         AORQ = Q
+      END IF
+      JSTAT = 0
+
+ 999  CONTINUE
+      END
diff --git a/math/slalib/pv2ue.f b/math/slalib/pv2ue.f
new file mode 100644
index 00000000..a2a686ab
--- /dev/null
+++ b/math/slalib/pv2ue.f
@@ -0,0 +1,168 @@
+      SUBROUTINE slPVUE (PV, DATE, PMASS, U, JSTAT)
+*+
+*     - - - - - -
+*      P V U E
+*     - - - - - -
+*
+*  Construct a universal element set based on an instantaneous position
+*  and velocity.
+*
+*  Given:
+*     PV        d(6)   heliocentric x,y,z,xdot,ydot,zdot of date,
+*                      (AU,AU/s; Note 1)
+*     DATE      d      date (TT Modified Julian Date = JD-2400000.5)
+*     PMASS     d      mass of the planet (Sun=1; Note 2)
+*
+*  Returned:
+*     U         d(13)  universal orbital elements (Note 3)
+*
+*                 (1)  combined mass (M+m)
+*                 (2)  total energy of the orbit (alpha)
+*                 (3)  reference (osculating) epoch (t0)
+*               (4-6)  position at reference epoch (r0)
+*               (7-9)  velocity at reference epoch (v0)
+*                (10)  heliocentric distance at reference epoch
+*                (11)  r0.v0
+*                (12)  date (t)
+*                (13)  universal eccentric anomaly (psi) of date, approx
+*
+*     JSTAT     i      status:  0 = OK
+*                              -1 = illegal PMASS
+*                              -2 = too close to Sun
+*                              -3 = too slow
+*
+*  Notes
+*
+*  1  The PV 6-vector can be with respect to any chosen inertial frame,
+*     and the resulting universal-element set will be with respect to
+*     the same frame.  A common choice will be mean equator and ecliptic
+*     of epoch J2000.
+*
+*  2  The mass, PMASS, is important only for the larger planets.  For
+*     most purposes (e.g. asteroids) use 0D0.  Values less than zero
+*     are illegal.
+*
+*  3  The "universal" elements are those which define the orbit for the
+*     purposes of the method of universal variables (see reference).
+*     They consist of the combined mass of the two bodies, an epoch,
+*     and the position and velocity vectors (arbitrary reference frame)
+*     at that epoch.  The parameter set used here includes also various
+*     quantities that can, in fact, be derived from the other
+*     information.  This approach is taken to avoiding unnecessary
+*     computation and loss of accuracy.  The supplementary quantities
+*     are (i) alpha, which is proportional to the total energy of the
+*     orbit, (ii) the heliocentric distance at epoch, (iii) the
+*     outwards component of the velocity at the given epoch, (iv) an
+*     estimate of psi, the "universal eccentric anomaly" at a given
+*     date and (v) that date.
+*
+*  Reference:  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
+*
+*  P.T.Wallace   Starlink   18 March 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION PV(6),DATE,PMASS,U(13)
+      INTEGER JSTAT
+
+*  Gaussian gravitational constant (exact)
+      DOUBLE PRECISION GCON
+      PARAMETER (GCON=0.01720209895D0)
+
+*  Canonical days to seconds
+      DOUBLE PRECISION CD2S
+      PARAMETER (CD2S=GCON/86400D0)
+
+*  Minimum allowed distance (AU) and speed (AU per canonical day)
+      DOUBLE PRECISION RMIN,VMIN
+      PARAMETER (RMIN=1D-3,VMIN=1D-3)
+
+      DOUBLE PRECISION T0,CM,X,Y,Z,XD,YD,ZD,R,V2,V,ALPHA,RDV
+
+
+*  Reference epoch.
+      T0 = DATE
+
+*  Combined mass (mu=M+m).
+      IF (PMASS.LT.0D0) GO TO 9010
+      CM = 1D0+PMASS
+
+*  Unpack the state vector, expressing velocity in AU per canonical day.
+      X = PV(1)
+      Y = PV(2)
+      Z = PV(3)
+      XD = PV(4)/CD2S
+      YD = PV(5)/CD2S
+      ZD = PV(6)/CD2S
+
+*  Heliocentric distance, and speed.
+      R = SQRT(X*X+Y*Y+Z*Z)
+      V2 = XD*XD+YD*YD+ZD*ZD
+      V = SQRT(V2)
+
+*  Reject unreasonably small values.
+      IF (R.LT.RMIN) GO TO 9020
+      IF (V.LT.VMIN) GO TO 9030
+
+*  Total energy of the orbit.
+      ALPHA = V2-2D0*CM/R
+
+*  Outward component of velocity.
+      RDV = X*XD+Y*YD+Z*ZD
+
+*  Construct the universal-element set.
+      U(1) = CM
+      U(2) = ALPHA
+      U(3) = T0
+      U(4) = X
+      U(5) = Y
+      U(6) = Z
+      U(7) = XD
+      U(8) = YD
+      U(9) = ZD
+      U(10) = R
+      U(11) = RDV
+      U(12) = T0
+      U(13) = 0D0
+
+*  Exit.
+      JSTAT = 0
+      GO TO 9999
+
+*  Negative PMASS.
+ 9010 CONTINUE
+      JSTAT = -1
+      GO TO 9999
+
+*  Too close.
+ 9020 CONTINUE
+      JSTAT = -2
+      GO TO 9999
+
+*  Too slow.
+ 9030 CONTINUE
+      JSTAT = -3
+
+ 9999 CONTINUE
+      END
diff --git a/math/slalib/pvobs.f b/math/slalib/pvobs.f
new file mode 100644
index 00000000..143704c3
--- /dev/null
+++ b/math/slalib/pvobs.f
@@ -0,0 +1,77 @@
+      SUBROUTINE slPVOB (P, H, STL, PV)
+*+
+*     - - - - - -
+*      P V O B
+*     - - - - - -
+*
+*  Position and velocity of an observing station (double precision)
+*
+*  Given:
+*     P     dp     latitude (geodetic, radians)
+*     H     dp     height above reference spheroid (geodetic, metres)
+*     STL   dp     local apparent sidereal time (radians)
+*
+*  Returned:
+*     PV    dp(6)  position/velocity 6-vector (AU, AU/s, true equator
+*                                              and equinox of date)
+*
+*  Called:  slGEOC
+*
+*  IAU 1976 constants are used.
+*
+*  P.T.Wallace   Starlink   14 November 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION P,H,STL,PV(6)
+
+      DOUBLE PRECISION R,Z,S,C,V
+
+*  Mean sidereal rate (at J2000) in radians per (UT1) second
+      DOUBLE PRECISION SR
+      PARAMETER (SR=7.292115855306589D-5)
+
+
+
+*  Geodetic to geocentric conversion
+      CALL slGEOC(P,H,R,Z)
+
+*  Functions of ST
+      S=SIN(STL)
+      C=COS(STL)
+
+*  Speed
+      V=SR*R
+
+*  Position
+      PV(1)=R*C
+      PV(2)=R*S
+      PV(3)=Z
+
+*  Velocity
+      PV(4)=-V*S
+      PV(5)=V*C
+      PV(6)=0D0
+
+      END
diff --git a/math/slalib/pxy.f b/math/slalib/pxy.f
new file mode 100644
index 00000000..6b67089b
--- /dev/null
+++ b/math/slalib/pxy.f
@@ -0,0 +1,110 @@
+      SUBROUTINE slPXY (NP,XYE,XYM,COEFFS,XYP,XRMS,YRMS,RRMS)
+*+
+*     - - - -
+*      P X Y
+*     - - - -
+*
+*  Given arrays of "expected" and "measured" [X,Y] coordinates, and a
+*  linear model relating them (as produced by slFTXY), compute
+*  the array of "predicted" coordinates and the RMS residuals.
+*
+*  Given:
+*     NP       i        number of samples
+*     XYE     d(2,np)   expected [X,Y] for each sample
+*     XYM     d(2,np)   measured [X,Y] for each sample
+*     COEFFS  d(6)      coefficients of model (see below)
+*
+*  Returned:
+*     XYP     d(2,np)   predicted [X,Y] for each sample
+*     XRMS     d        RMS in X
+*     YRMS     d        RMS in Y
+*     RRMS     d        total RMS (vector sum of XRMS and YRMS)
+*
+*  The model is supplied in the array COEFFS.  Naming the
+*  elements of COEFF as follows:
+*
+*     COEFFS(1) = A
+*     COEFFS(2) = B
+*     COEFFS(3) = C
+*     COEFFS(4) = D
+*     COEFFS(5) = E
+*     COEFFS(6) = F
+*
+*  the model is applied thus:
+*
+*     XP = A + B*XM + C*YM
+*     YP = D + E*XM + F*YM
+*
+*  The residuals are (XP-XE) and (YP-YE).
+*
+*  If NP is less than or equal to zero, no coordinates are
+*  transformed, and the RMS residuals are all zero.
+*
+*  See also slFTXY, slINVF, slXYXY, slDCMF
+*
+*  Called:  slXYXY
+*
+*  P.T.Wallace   Starlink   22 May 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER NP
+      DOUBLE PRECISION XYE(2,NP),XYM(2,NP),COEFFS(6),
+     :                 XYP(2,NP),XRMS,YRMS,RRMS
+
+      INTEGER I
+      DOUBLE PRECISION SDX2,SDY2,XP,YP,DX,DY,DX2,DY2,P
+
+
+
+*  Initialize summations
+      SDX2=0D0
+      SDY2=0D0
+
+*  Loop by sample
+      DO I=1,NP
+
+*     Transform "measured" [X,Y] to "predicted" [X,Y]
+         CALL slXYXY(XYM(1,I),XYM(2,I),COEFFS,XP,YP)
+         XYP(1,I)=XP
+         XYP(2,I)=YP
+
+*     Compute residuals in X and Y, and update summations
+         DX=XYE(1,I)-XP
+         DY=XYE(2,I)-YP
+         DX2=DX*DX
+         DY2=DY*DY
+         SDX2=SDX2+DX2
+         SDY2=SDY2+DY2
+
+*     Next sample
+      END DO
+
+*  Compute RMS values
+      P=MAX(1D0,DBLE(NP))
+      XRMS=SQRT(SDX2/P)
+      YRMS=SQRT(SDY2/P)
+      RRMS=SQRT(XRMS*XRMS+YRMS*YRMS)
+
+      END
diff --git a/math/slalib/random.F__vms b/math/slalib/random.F__vms
new file mode 100644
index 00000000..b57b5fc9
--- /dev/null
+++ b/math/slalib/random.F__vms
@@ -0,0 +1,69 @@
+      REAL FUNCTION sla_RANDOM (SEED)
+*+
+*     - - - - - - -
+*      R A N D O M
+*     - - - - - - -
+*
+*  Generate pseudo-random real number in the range 0 <= X < 1.
+*  (single precision)
+*
+*  !!!  Version for VAX/VMS and DECstation !!!
+*
+*  Given:
+*     SEED     real     an arbitrary real number
+*
+*  Notes:
+*
+*  1)  The result is a pseudo-random REAL number in the range
+*      0 <= sla_RANDOM < 1.
+*
+*  2)  SEED is used first time through only.
+*
+*  Called:  RAN (a REAL function from the DEC Fortran Library)
+*
+*  P.T.Wallace   Starlink   14 October 1991
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the 
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, 
+*    Boston, MA  02110-1301  USA
+*
+*-
+
+      IMPLICIT NONE
+
+      REAL SEED
+
+      REAL RAN
+
+      REAL AS
+      INTEGER ISEED
+      LOGICAL FIRST
+      SAVE FIRST
+      DATA FIRST /.TRUE./
+
+
+
+*  If first time, turn SEED into a large, odd integer
+      IF (FIRST) THEN
+         AS=ABS(SEED)+1.0
+         ISEED=NINT(AS/10.0**(NINT(ALOG10(AS))-6))
+         IF (MOD(ISEED,2).EQ.0) ISEED=ISEED+1
+         FIRST=.FALSE.
+      END IF
+
+*  Next pseudo-random number
+      sla_RANDOM=RAN(ISEED)
+
+      END
diff --git a/math/slalib/random.F__win b/math/slalib/random.F__win
new file mode 100644
index 00000000..9cd77fac
--- /dev/null
+++ b/math/slalib/random.F__win
@@ -0,0 +1,59 @@
+      REAL FUNCTION sla_RANDOM (XSEED)
+*+
+*     - - - - - - -
+*      R A N D O M
+*     - - - - - - -
+*
+*  Generate pseudo-random real number in the range 0 <= X < 1.
+*
+*  (single precision)
+*
+*  !!!  Microsoft Fortran dependent  !!!
+*
+*  Given (but used first time only):
+*     XSEED    real     an arbitrary real number
+*
+*  The value returned is a pseudo-random number such that
+*  0 <= sla_RANDOM < 1.
+*
+*  Called:  RANDOM (Microsoft run-time library)
+*
+*  P.T.Wallace   Starlink   7 November 2003
+*
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the 
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, 
+*    Boston, MA  02110-1301  USA
+*
+*-
+
+      IMPLICIT NONE
+
+      REAL XSEED
+
+      REAL X
+      LOGICAL FIRST
+      SAVE FIRST
+      DATA FIRST /.TRUE./
+
+
+      IF (FIRST) THEN
+         CALL SEED(NINT(MOD(XSEED*1.234E7,32E3)))  ! Microsoft Fortran
+         FIRST=.FALSE.
+      END IF
+      CALL RANDOM(X)                               ! Microsoft Fortran
+      sla_RANDOM=X
+
+      END
diff --git a/math/slalib/random.Fdefault b/math/slalib/random.Fdefault
new file mode 100644
index 00000000..9a79cb6c
--- /dev/null
+++ b/math/slalib/random.Fdefault
@@ -0,0 +1,87 @@
+#include "config.h"
+      REAL FUNCTION sla_RANDOM (SEED)
+*+
+*     - - - - - - -
+*      R A N D O M
+*     - - - - - - -
+*
+*  Generate pseudo-random real number in the range 0 <= X < 1.
+*  (single precision)
+*
+*
+*  Given:
+*     SEED     real     an arbitrary real number
+*
+*  Notes:
+*
+*  1)  The result is a pseudo-random REAL number in the range
+*      0 <= sla_RANDOM < 1.
+*
+*  2)  SEED is used first time through only.
+*
+*  Called:  RAN or RAND (a REAL function returning a random variate --
+*           the precise function which is called depends on which functions
+*           are available when the library is built).  If neither of these
+*           is available, we use the local substitute RANDOM defined
+*           in rtl_random.c
+*
+*  P.T.Wallace   Starlink   14 October 1991
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the 
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, 
+*    Boston, MA  02110-1301  USA
+*-
+
+      IMPLICIT NONE
+
+      REAL SEED
+
+#if HAVE_RAND
+      REAL RAND
+#elif HAVE_RANDOM
+      REAL RANDOM
+#else
+ error "Can't find random-number function"
+#endif
+
+      REAL AS
+      INTEGER ISEED
+      LOGICAL FIRST
+      SAVE FIRST
+      DATA FIRST /.TRUE./
+
+
+
+*  If first time, turn SEED into a large, odd integer
+      IF (FIRST) THEN
+         AS=ABS(SEED)+1.0
+         ISEED=NINT(AS/10.0**(NINT(ALOG10(AS))-6))
+         IF (MOD(ISEED,2).EQ.0) ISEED=ISEED+1
+         FIRST=.FALSE.
+#if HAVE_RAND
+         AS = RAND(ISEED)
+#endif
+      ELSE
+         ISEED=0
+      END IF
+
+*  Next pseudo-random number
+#if HAVE_RAND
+      sla_RANDOM=RAND(0)
+#elif HAVE_RANDOM
+      sla_RANDOM=RANDOM(ISEED)
+#endif
+
+      END
diff --git a/math/slalib/range.f b/math/slalib/range.f
new file mode 100644
index 00000000..fa927043
--- /dev/null
+++ b/math/slalib/range.f
@@ -0,0 +1,51 @@
+      REAL FUNCTION slRA1P (ANGLE)
+*+
+*     - - - - - -
+*      R A 1 P
+*     - - - - - -
+*
+*  Normalize angle into range +/- pi  (single precision)
+*
+*  Given:
+*     ANGLE     dp      the angle in radians
+*
+*  The result is ANGLE expressed in the +/- pi (single
+*  precision).
+*
+*  P.T.Wallace   Starlink   23 November 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL ANGLE
+
+      REAL API,A2PI
+      PARAMETER (API=3.141592653589793238462643)
+      PARAMETER (A2PI=6.283185307179586476925287)
+
+
+      slRA1P=MOD(ANGLE,A2PI)
+      IF (ABS(slRA1P).GE.API)
+     :          slRA1P=slRA1P-SIGN(A2PI,ANGLE)
+
+      END
diff --git a/math/slalib/ranorm.f b/math/slalib/ranorm.f
new file mode 100644
index 00000000..77f4b781
--- /dev/null
+++ b/math/slalib/ranorm.f
@@ -0,0 +1,49 @@
+      REAL FUNCTION slRA2P (ANGLE)
+*+
+*     - - - - - - -
+*      R A 2 P
+*     - - - - - - -
+*
+*  Normalize angle into range 0-2 pi  (single precision)
+*
+*  Given:
+*     ANGLE     dp      the angle in radians
+*
+*  The result is ANGLE expressed in the range 0-2 pi (single
+*  precision).
+*
+*  P.T.Wallace   Starlink   23 November 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL ANGLE
+
+      REAL A2PI
+      PARAMETER (A2PI=6.283185307179586476925287)
+
+
+      slRA2P=MOD(ANGLE,A2PI)
+      IF (slRA2P.LT.0.0) slRA2P=slRA2P+A2PI
+
+      END
diff --git a/math/slalib/rcc.f b/math/slalib/rcc.f
new file mode 100644
index 00000000..a07a6d82
--- /dev/null
+++ b/math/slalib/rcc.f
@@ -0,0 +1,1110 @@
+      DOUBLE PRECISION FUNCTION slRCC (TDB, UT1, WL, U, V)
+*+
+*     - - - -
+*      R C C
+*     - - - -
+*
+*  Relativistic clock correction:  the difference between proper time at
+*  a point on the surface of the Earth and coordinate time in the Solar
+*  System barycentric space-time frame of reference.
+*
+*  The proper time is terrestrial time, TT;  the coordinate time is an
+*  implementation of barycentric dynamical time, TDB.
+*
+*  Given:
+*    TDB      d     TDB (MJD: JD-2400000.5)
+*    UT1      d     universal time (fraction of one day)
+*    WL       d     clock longitude (radians west)
+*    U        d     clock distance from Earth spin axis (km)
+*    V        d     clock distance north of Earth equatorial plane (km)
+*
+*  Returned:
+*    The clock correction, TDB-TT, in seconds:
+*
+*    .  TDB is coordinate time in the solar system barycentre frame
+*       of reference, in units chosen to eliminate the scale difference
+*       with respect to terrestrial time.
+*
+*    .  TT is the proper time for clocks at mean sea level on the
+*       Earth.
+*
+*  Notes:
+*
+*  1  The argument TDB is, strictly, the barycentric coordinate time;
+*     however, the terrestrial time TT can in practice be used without
+*     any significant loss of accuracy.
+*
+*  2  The result returned by slRCC comprises a main (annual)
+*     sinusoidal term of amplitude approximately 0.00166 seconds, plus
+*     planetary and lunar terms up to about 20 microseconds, and diurnal
+*     terms up to 2 microseconds.  The variation arises from the
+*     transverse Doppler effect and the gravitational red-shift as the
+*     observer varies in speed and moves through different gravitational
+*     potentials.
+*
+*  3  The geocentric model is that of Fairhead & Bretagnon (1990), in
+*     its full form.  It was supplied by Fairhead (private
+*     communication) as a FORTRAN subroutine.  The original Fairhead
+*     routine used explicit formulae, in such large numbers that
+*     problems were experienced with certain compilers (Microsoft
+*     Fortran on PC aborted with stack overflow, Convex compiled
+*     successfully but extremely slowly).  The present implementation is
+*     a complete recoding, with the original Fairhead coefficients held
+*     in a table.  To optimise arithmetic precision, the terms are
+*     accumulated in reverse order, smallest first.  A number of other
+*     coding changes were made, in order to match the calling sequence
+*     of previous versions of the present routine, and to comply with
+*     Starlink programming standards.  The numerical results compared
+*     with those from the Fairhead form are essentially unaffected by
+*     the changes, the differences being at the 10^-20 sec level.
+*
+*  4  The topocentric part of the model is from Moyer (1981) and
+*     Murray (1983).  It is an approximation to the expression
+*     ( v / c ) . ( r / c ), where v is the barycentric velocity of
+*     the Earth, r is the geocentric position of the observer and
+*     c is the speed of light.
+*
+*  5  During the interval 1950-2050, the absolute accuracy of is better
+*     than +/- 3 nanoseconds relative to direct numerical integrations
+*     using the JPL DE200/LE200 solar system ephemeris.
+*
+*  6  The IAU definition of TDB was that it must differ from TT only by
+*     periodic terms.  Though practical, this is an imprecise definition
+*     which ignores the existence of very long-period and secular
+*     effects in the dynamics of the solar system.  As a consequence,
+*     different implementations of TDB will, in general, differ in zero-
+*     point and will drift linearly relative to one other.
+*
+*  7  TDB was, in principle, superseded by new coordinate timescales
+*     which the IAU introduced in 1991:  geocentric coordinate time,
+*     TCG, and barycentric coordinate time, TCB.  However, slRCC
+*     can be used to implement the periodic part of TCB-TCG.
+*
+*  References:
+*
+*  1  Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247
+*     (1990).
+*
+*  2  Moyer, T.D., Cel.Mech., 23, 33 (1981).
+*
+*  3  Murray, C.A., Vectorial Astrometry, Adam Hilger (1983).
+*
+*  4  Seidelmann, P.K. et al, Explanatory Supplement to the
+*     Astronomical Almanac, Chapter 2, University Science Books
+*     (1992).
+*
+*  5  Simon J.L., Bretagnon P., Chapront J., Chapront-Touze M.,
+*     Francou G. & Laskar J., Astron.Astrophys., 282, 663-683 (1994).
+*
+*  P.T.Wallace   Starlink   7 May 2000
+*
+*  Copyright (C) 2000 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION TDB,UT1,WL,U,V
+
+      DOUBLE PRECISION D2PI,D2R
+      PARAMETER (D2PI=6.283185307179586476925287D0,
+     :           D2R=0.0174532925199432957692369D0)
+
+      DOUBLE PRECISION T,TSOL,W,ELSUN,EMSUN,D,ELJ,ELS,
+     :                 WT,W0,W1,W2,W3,W4,WF,WJ
+
+* -----------------------------------------------------------------------
+*
+*  Fairhead and Bretagnon canonical coefficients
+*
+*  787 sets of three coefficients.
+*
+*  Each set is amplitude (microseconds)
+*              frequency (radians per Julian millennium since J2000),
+*              phase (radians).
+*
+*  Sets   1-474 are the T**0 terms,
+*   "   475-679  "   "  T**1   "
+*   "   680-764  "   "  T**2   "
+*   "   765-784  "   "  T**3   "
+*   "   785-787  "   "  T**4   "  .
+*
+      DOUBLE PRECISION FAIRHD(3,787)
+      INTEGER I,J
+      DATA ((FAIRHD(I,J),I=1,3),J=  1, 10) /
+     : 1656.674564D-6,    6283.075849991D0, 6.240054195D0,
+     :   22.417471D-6,    5753.384884897D0, 4.296977442D0,
+     :   13.839792D-6,   12566.151699983D0, 6.196904410D0,
+     :    4.770086D-6,     529.690965095D0, 0.444401603D0,
+     :    4.676740D-6,    6069.776754553D0, 4.021195093D0,
+     :    2.256707D-6,     213.299095438D0, 5.543113262D0,
+     :    1.694205D-6,      -3.523118349D0, 5.025132748D0,
+     :    1.554905D-6,   77713.771467920D0, 5.198467090D0,
+     :    1.276839D-6,    7860.419392439D0, 5.988822341D0,
+     :    1.193379D-6,    5223.693919802D0, 3.649823730D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J= 11, 20) /
+     :    1.115322D-6,    3930.209696220D0, 1.422745069D0,
+     :    0.794185D-6,   11506.769769794D0, 2.322313077D0,
+     :    0.447061D-6,      26.298319800D0, 3.615796498D0,
+     :    0.435206D-6,    -398.149003408D0, 4.349338347D0,
+     :    0.600309D-6,    1577.343542448D0, 2.678271909D0,
+     :    0.496817D-6,    6208.294251424D0, 5.696701824D0,
+     :    0.486306D-6,    5884.926846583D0, 0.520007179D0,
+     :    0.432392D-6,      74.781598567D0, 2.435898309D0,
+     :    0.468597D-6,    6244.942814354D0, 5.866398759D0,
+     :    0.375510D-6,    5507.553238667D0, 4.103476804D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J= 21, 30) /
+     :    0.243085D-6,    -775.522611324D0, 3.651837925D0,
+     :    0.173435D-6,   18849.227549974D0, 6.153743485D0,
+     :    0.230685D-6,    5856.477659115D0, 4.773852582D0,
+     :    0.203747D-6,   12036.460734888D0, 4.333987818D0,
+     :    0.143935D-6,    -796.298006816D0, 5.957517795D0,
+     :    0.159080D-6,   10977.078804699D0, 1.890075226D0,
+     :    0.119979D-6,      38.133035638D0, 4.551585768D0,
+     :    0.118971D-6,    5486.777843175D0, 1.914547226D0,
+     :    0.116120D-6,    1059.381930189D0, 0.873504123D0,
+     :    0.137927D-6,   11790.629088659D0, 1.135934669D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J= 31, 40) /
+     :    0.098358D-6,    2544.314419883D0, 0.092793886D0,
+     :    0.101868D-6,   -5573.142801634D0, 5.984503847D0,
+     :    0.080164D-6,     206.185548437D0, 2.095377709D0,
+     :    0.079645D-6,    4694.002954708D0, 2.949233637D0,
+     :    0.062617D-6,      20.775395492D0, 2.654394814D0,
+     :    0.075019D-6,    2942.463423292D0, 4.980931759D0,
+     :    0.064397D-6,    5746.271337896D0, 1.280308748D0,
+     :    0.063814D-6,    5760.498431898D0, 4.167901731D0,
+     :    0.048042D-6,    2146.165416475D0, 1.495846011D0,
+     :    0.048373D-6,     155.420399434D0, 2.251573730D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J= 41, 50) /
+     :    0.058844D-6,     426.598190876D0, 4.839650148D0,
+     :    0.046551D-6,      -0.980321068D0, 0.921573539D0,
+     :    0.054139D-6,   17260.154654690D0, 3.411091093D0,
+     :    0.042411D-6,    6275.962302991D0, 2.869567043D0,
+     :    0.040184D-6,      -7.113547001D0, 3.565975565D0,
+     :    0.036564D-6,    5088.628839767D0, 3.324679049D0,
+     :    0.040759D-6,   12352.852604545D0, 3.981496998D0,
+     :    0.036507D-6,     801.820931124D0, 6.248866009D0,
+     :    0.036955D-6,    3154.687084896D0, 5.071801441D0,
+     :    0.042732D-6,     632.783739313D0, 5.720622217D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J= 51, 60) /
+     :    0.042560D-6,  161000.685737473D0, 1.270837679D0,
+     :    0.040480D-6,   15720.838784878D0, 2.546610123D0,
+     :    0.028244D-6,   -6286.598968340D0, 5.069663519D0,
+     :    0.033477D-6,    6062.663207553D0, 4.144987272D0,
+     :    0.034867D-6,     522.577418094D0, 5.210064075D0,
+     :    0.032438D-6,    6076.890301554D0, 0.749317412D0,
+     :    0.030215D-6,    7084.896781115D0, 3.389610345D0,
+     :    0.029247D-6,  -71430.695617928D0, 4.183178762D0,
+     :    0.033529D-6,    9437.762934887D0, 2.404714239D0,
+     :    0.032423D-6,    8827.390269875D0, 5.541473556D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J= 61, 70) /
+     :    0.027567D-6,    6279.552731642D0, 5.040846034D0,
+     :    0.029862D-6,   12139.553509107D0, 1.770181024D0,
+     :    0.022509D-6,   10447.387839604D0, 1.460726241D0,
+     :    0.020937D-6,    8429.241266467D0, 0.652303414D0,
+     :    0.020322D-6,     419.484643875D0, 3.735430632D0,
+     :    0.024816D-6,   -1194.447010225D0, 1.087136918D0,
+     :    0.025196D-6,    1748.016413067D0, 2.901883301D0,
+     :    0.021691D-6,   14143.495242431D0, 5.952658009D0,
+     :    0.017673D-6,    6812.766815086D0, 3.186129845D0,
+     :    0.022567D-6,    6133.512652857D0, 3.307984806D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J= 71, 80) /
+     :    0.016155D-6,   10213.285546211D0, 1.331103168D0,
+     :    0.014751D-6,    1349.867409659D0, 4.308933301D0,
+     :    0.015949D-6,    -220.412642439D0, 4.005298270D0,
+     :    0.015974D-6,   -2352.866153772D0, 6.145309371D0,
+     :    0.014223D-6,   17789.845619785D0, 2.104551349D0,
+     :    0.017806D-6,      73.297125859D0, 3.475975097D0,
+     :    0.013671D-6,    -536.804512095D0, 5.971672571D0,
+     :    0.011942D-6,    8031.092263058D0, 2.053414715D0,
+     :    0.014318D-6,   16730.463689596D0, 3.016058075D0,
+     :    0.012462D-6,     103.092774219D0, 1.737438797D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J= 81, 90) /
+     :    0.010962D-6,       3.590428652D0, 2.196567739D0,
+     :    0.015078D-6,   19651.048481098D0, 3.969480770D0,
+     :    0.010396D-6,     951.718406251D0, 5.717799605D0,
+     :    0.011707D-6,   -4705.732307544D0, 2.654125618D0,
+     :    0.010453D-6,    5863.591206116D0, 1.913704550D0,
+     :    0.012420D-6,    4690.479836359D0, 4.734090399D0,
+     :    0.011847D-6,    5643.178563677D0, 5.489005403D0,
+     :    0.008610D-6,    3340.612426700D0, 3.661698944D0,
+     :    0.011622D-6,    5120.601145584D0, 4.863931876D0,
+     :    0.010825D-6,     553.569402842D0, 0.842715011D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J= 91,100) /
+     :    0.008666D-6,    -135.065080035D0, 3.293406547D0,
+     :    0.009963D-6,     149.563197135D0, 4.870690598D0,
+     :    0.009858D-6,    6309.374169791D0, 1.061816410D0,
+     :    0.007959D-6,     316.391869657D0, 2.465042647D0,
+     :    0.010099D-6,     283.859318865D0, 1.942176992D0,
+     :    0.007147D-6,    -242.728603974D0, 3.661486981D0,
+     :    0.007505D-6,    5230.807466803D0, 4.920937029D0,
+     :    0.008323D-6,   11769.853693166D0, 1.229392026D0,
+     :    0.007490D-6,   -6256.777530192D0, 3.658444681D0,
+     :    0.009370D-6,  149854.400134205D0, 0.673880395D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=101,110) /
+     :    0.007117D-6,      38.027672636D0, 5.294249518D0,
+     :    0.007857D-6,   12168.002696575D0, 0.525733528D0,
+     :    0.007019D-6,    6206.809778716D0, 0.837688810D0,
+     :    0.006056D-6,     955.599741609D0, 4.194535082D0,
+     :    0.008107D-6,   13367.972631107D0, 3.793235253D0,
+     :    0.006731D-6,    5650.292110678D0, 5.639906583D0,
+     :    0.007332D-6,      36.648562930D0, 0.114858677D0,
+     :    0.006366D-6,    4164.311989613D0, 2.262081818D0,
+     :    0.006858D-6,    5216.580372801D0, 0.642063318D0,
+     :    0.006919D-6,    6681.224853400D0, 6.018501522D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=111,120) /
+     :    0.006826D-6,    7632.943259650D0, 3.458654112D0,
+     :    0.005308D-6,   -1592.596013633D0, 2.500382359D0,
+     :    0.005096D-6,   11371.704689758D0, 2.547107806D0,
+     :    0.004841D-6,    5333.900241022D0, 0.437078094D0,
+     :    0.005582D-6,    5966.683980335D0, 2.246174308D0,
+     :    0.006304D-6,   11926.254413669D0, 2.512929171D0,
+     :    0.006603D-6,   23581.258177318D0, 5.393136889D0,
+     :    0.005123D-6,      -1.484472708D0, 2.999641028D0,
+     :    0.004648D-6,    1589.072895284D0, 1.275847090D0,
+     :    0.005119D-6,    6438.496249426D0, 1.486539246D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=121,130) /
+     :    0.004521D-6,    4292.330832950D0, 6.140635794D0,
+     :    0.005680D-6,   23013.539539587D0, 4.557814849D0,
+     :    0.005488D-6,      -3.455808046D0, 0.090675389D0,
+     :    0.004193D-6,    7234.794256242D0, 4.869091389D0,
+     :    0.003742D-6,    7238.675591600D0, 4.691976180D0,
+     :    0.004148D-6,    -110.206321219D0, 3.016173439D0,
+     :    0.004553D-6,   11499.656222793D0, 5.554998314D0,
+     :    0.004892D-6,    5436.993015240D0, 1.475415597D0,
+     :    0.004044D-6,    4732.030627343D0, 1.398784824D0,
+     :    0.004164D-6,   12491.370101415D0, 5.650931916D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=131,140) /
+     :    0.004349D-6,   11513.883316794D0, 2.181745369D0,
+     :    0.003919D-6,   12528.018664345D0, 5.823319737D0,
+     :    0.003129D-6,    6836.645252834D0, 0.003844094D0,
+     :    0.004080D-6,   -7058.598461315D0, 3.690360123D0,
+     :    0.003270D-6,      76.266071276D0, 1.517189902D0,
+     :    0.002954D-6,    6283.143160294D0, 4.447203799D0,
+     :    0.002872D-6,      28.449187468D0, 1.158692983D0,
+     :    0.002881D-6,     735.876513532D0, 0.349250250D0,
+     :    0.003279D-6,    5849.364112115D0, 4.893384368D0,
+     :    0.003625D-6,    6209.778724132D0, 1.473760578D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=141,150) /
+     :    0.003074D-6,     949.175608970D0, 5.185878737D0,
+     :    0.002775D-6,    9917.696874510D0, 1.030026325D0,
+     :    0.002646D-6,   10973.555686350D0, 3.918259169D0,
+     :    0.002575D-6,   25132.303399966D0, 6.109659023D0,
+     :    0.003500D-6,     263.083923373D0, 1.892100742D0,
+     :    0.002740D-6,   18319.536584880D0, 4.320519510D0,
+     :    0.002464D-6,     202.253395174D0, 4.698203059D0,
+     :    0.002409D-6,       2.542797281D0, 5.325009315D0,
+     :    0.003354D-6,  -90955.551694697D0, 1.942656623D0,
+     :    0.002296D-6,    6496.374945429D0, 5.061810696D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=151,160) /
+     :    0.003002D-6,    6172.869528772D0, 2.797822767D0,
+     :    0.003202D-6,   27511.467873537D0, 0.531673101D0,
+     :    0.002954D-6,   -6283.008539689D0, 4.533471191D0,
+     :    0.002353D-6,     639.897286314D0, 3.734548088D0,
+     :    0.002401D-6,   16200.772724501D0, 2.605547070D0,
+     :    0.003053D-6,  233141.314403759D0, 3.029030662D0,
+     :    0.003024D-6,   83286.914269554D0, 2.355556099D0,
+     :    0.002863D-6,   17298.182327326D0, 5.240963796D0,
+     :    0.002103D-6,   -7079.373856808D0, 5.756641637D0,
+     :    0.002303D-6,   83996.847317911D0, 2.013686814D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=161,170) /
+     :    0.002303D-6,   18073.704938650D0, 1.089100410D0,
+     :    0.002381D-6,      63.735898303D0, 0.759188178D0,
+     :    0.002493D-6,    6386.168624210D0, 0.645026535D0,
+     :    0.002366D-6,       3.932153263D0, 6.215885448D0,
+     :    0.002169D-6,   11015.106477335D0, 4.845297676D0,
+     :    0.002397D-6,    6243.458341645D0, 3.809290043D0,
+     :    0.002183D-6,    1162.474704408D0, 6.179611691D0,
+     :    0.002353D-6,    6246.427287062D0, 4.781719760D0,
+     :    0.002199D-6,    -245.831646229D0, 5.956152284D0,
+     :    0.001729D-6,    3894.181829542D0, 1.264976635D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=171,180) /
+     :    0.001896D-6,   -3128.388765096D0, 4.914231596D0,
+     :    0.002085D-6,      35.164090221D0, 1.405158503D0,
+     :    0.002024D-6,   14712.317116458D0, 2.752035928D0,
+     :    0.001737D-6,    6290.189396992D0, 5.280820144D0,
+     :    0.002229D-6,     491.557929457D0, 1.571007057D0,
+     :    0.001602D-6,   14314.168113050D0, 4.203664806D0,
+     :    0.002186D-6,     454.909366527D0, 1.402101526D0,
+     :    0.001897D-6,   22483.848574493D0, 4.167932508D0,
+     :    0.001825D-6,   -3738.761430108D0, 0.545828785D0,
+     :    0.001894D-6,    1052.268383188D0, 5.817167450D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=181,190) /
+     :    0.001421D-6,      20.355319399D0, 2.419886601D0,
+     :    0.001408D-6,   10984.192351700D0, 2.732084787D0,
+     :    0.001847D-6,   10873.986030480D0, 2.903477885D0,
+     :    0.001391D-6,   -8635.942003763D0, 0.593891500D0,
+     :    0.001388D-6,      -7.046236698D0, 1.166145902D0,
+     :    0.001810D-6,  -88860.057071188D0, 0.487355242D0,
+     :    0.001288D-6,   -1990.745017041D0, 3.913022880D0,
+     :    0.001297D-6,   23543.230504682D0, 3.063805171D0,
+     :    0.001335D-6,    -266.607041722D0, 3.995764039D0,
+     :    0.001376D-6,   10969.965257698D0, 5.152914309D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=191,200) /
+     :    0.001745D-6,  244287.600007027D0, 3.626395673D0,
+     :    0.001649D-6,   31441.677569757D0, 1.952049260D0,
+     :    0.001416D-6,    9225.539273283D0, 4.996408389D0,
+     :    0.001238D-6,    4804.209275927D0, 5.503379738D0,
+     :    0.001472D-6,    4590.910180489D0, 4.164913291D0,
+     :    0.001169D-6,    6040.347246017D0, 5.841719038D0,
+     :    0.001039D-6,    5540.085789459D0, 2.769753519D0,
+     :    0.001004D-6,    -170.672870619D0, 0.755008103D0,
+     :    0.001284D-6,   10575.406682942D0, 5.306538209D0,
+     :    0.001278D-6,      71.812653151D0, 4.713486491D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=201,210) /
+     :    0.001321D-6,   18209.330263660D0, 2.624866359D0,
+     :    0.001297D-6,   21228.392023546D0, 0.382603541D0,
+     :    0.000954D-6,    6282.095528923D0, 0.882213514D0,
+     :    0.001145D-6,    6058.731054289D0, 1.169483931D0,
+     :    0.000979D-6,    5547.199336460D0, 5.448375984D0,
+     :    0.000987D-6,   -6262.300454499D0, 2.656486959D0,
+     :    0.001070D-6, -154717.609887482D0, 1.827624012D0,
+     :    0.000991D-6,    4701.116501708D0, 4.387001801D0,
+     :    0.001155D-6,     -14.227094002D0, 3.042700750D0,
+     :    0.001176D-6,     277.034993741D0, 3.335519004D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=211,220) /
+     :    0.000890D-6,   13916.019109642D0, 5.601498297D0,
+     :    0.000884D-6,   -1551.045222648D0, 1.088831705D0,
+     :    0.000876D-6,    5017.508371365D0, 3.969902609D0,
+     :    0.000806D-6,   15110.466119866D0, 5.142876744D0,
+     :    0.000773D-6,   -4136.910433516D0, 0.022067765D0,
+     :    0.001077D-6,     175.166059800D0, 1.844913056D0,
+     :    0.000954D-6,   -6284.056171060D0, 0.968480906D0,
+     :    0.000737D-6,    5326.786694021D0, 4.923831588D0,
+     :    0.000845D-6,    -433.711737877D0, 4.749245231D0,
+     :    0.000819D-6,    8662.240323563D0, 5.991247817D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=221,230) /
+     :    0.000852D-6,     199.072001436D0, 2.189604979D0,
+     :    0.000723D-6,   17256.631536341D0, 6.068719637D0,
+     :    0.000940D-6,    6037.244203762D0, 6.197428148D0,
+     :    0.000885D-6,   11712.955318231D0, 3.280414875D0,
+     :    0.000706D-6,   12559.038152982D0, 2.824848947D0,
+     :    0.000732D-6,    2379.164473572D0, 2.501813417D0,
+     :    0.000764D-6,   -6127.655450557D0, 2.236346329D0,
+     :    0.000908D-6,     131.541961686D0, 2.521257490D0,
+     :    0.000907D-6,   35371.887265976D0, 3.370195967D0,
+     :    0.000673D-6,    1066.495477190D0, 3.876512374D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=231,240) /
+     :    0.000814D-6,   17654.780539750D0, 4.627122566D0,
+     :    0.000630D-6,      36.027866677D0, 0.156368499D0,
+     :    0.000798D-6,     515.463871093D0, 5.151962502D0,
+     :    0.000798D-6,     148.078724426D0, 5.909225055D0,
+     :    0.000806D-6,     309.278322656D0, 6.054064447D0,
+     :    0.000607D-6,     -39.617508346D0, 2.839021623D0,
+     :    0.000601D-6,     412.371096874D0, 3.984225404D0,
+     :    0.000646D-6,   11403.676995575D0, 3.852959484D0,
+     :    0.000704D-6,   13521.751441591D0, 2.300991267D0,
+     :    0.000603D-6,  -65147.619767937D0, 4.140083146D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=241,250) /
+     :    0.000609D-6,   10177.257679534D0, 0.437122327D0,
+     :    0.000631D-6,    5767.611978898D0, 4.026532329D0,
+     :    0.000576D-6,   11087.285125918D0, 4.760293101D0,
+     :    0.000674D-6,   14945.316173554D0, 6.270510511D0,
+     :    0.000726D-6,    5429.879468239D0, 6.039606892D0,
+     :    0.000710D-6,   28766.924424484D0, 5.672617711D0,
+     :    0.000647D-6,   11856.218651625D0, 3.397132627D0,
+     :    0.000678D-6,   -5481.254918868D0, 6.249666675D0,
+     :    0.000618D-6,   22003.914634870D0, 2.466427018D0,
+     :    0.000738D-6,    6134.997125565D0, 2.242668890D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=251,260) /
+     :    0.000660D-6,     625.670192312D0, 5.864091907D0,
+     :    0.000694D-6,    3496.032826134D0, 2.668309141D0,
+     :    0.000531D-6,    6489.261398429D0, 1.681888780D0,
+     :    0.000611D-6, -143571.324284214D0, 2.424978312D0,
+     :    0.000575D-6,   12043.574281889D0, 4.216492400D0,
+     :    0.000553D-6,   12416.588502848D0, 4.772158039D0,
+     :    0.000689D-6,    4686.889407707D0, 6.224271088D0,
+     :    0.000495D-6,    7342.457780181D0, 3.817285811D0,
+     :    0.000567D-6,    3634.621024518D0, 1.649264690D0,
+     :    0.000515D-6,   18635.928454536D0, 3.945345892D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=261,270) /
+     :    0.000486D-6,    -323.505416657D0, 4.061673868D0,
+     :    0.000662D-6,   25158.601719765D0, 1.794058369D0,
+     :    0.000509D-6,     846.082834751D0, 3.053874588D0,
+     :    0.000472D-6,  -12569.674818332D0, 5.112133338D0,
+     :    0.000461D-6,    6179.983075773D0, 0.513669325D0,
+     :    0.000641D-6,   83467.156352816D0, 3.210727723D0,
+     :    0.000520D-6,   10344.295065386D0, 2.445597761D0,
+     :    0.000493D-6,   18422.629359098D0, 1.676939306D0,
+     :    0.000478D-6,    1265.567478626D0, 5.487314569D0,
+     :    0.000472D-6,     -18.159247265D0, 1.999707589D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=271,280) /
+     :    0.000559D-6,   11190.377900137D0, 5.783236356D0,
+     :    0.000494D-6,    9623.688276691D0, 3.022645053D0,
+     :    0.000463D-6,    5739.157790895D0, 1.411223013D0,
+     :    0.000432D-6,   16858.482532933D0, 1.179256434D0,
+     :    0.000574D-6,   72140.628666286D0, 1.758191830D0,
+     :    0.000484D-6,   17267.268201691D0, 3.290589143D0,
+     :    0.000550D-6,    4907.302050146D0, 0.864024298D0,
+     :    0.000399D-6,      14.977853527D0, 2.094441910D0,
+     :    0.000491D-6,     224.344795702D0, 0.878372791D0,
+     :    0.000432D-6,   20426.571092422D0, 6.003829241D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=281,290) /
+     :    0.000481D-6,    5749.452731634D0, 4.309591964D0,
+     :    0.000480D-6,    5757.317038160D0, 1.142348571D0,
+     :    0.000485D-6,    6702.560493867D0, 0.210580917D0,
+     :    0.000426D-6,    6055.549660552D0, 4.274476529D0,
+     :    0.000480D-6,    5959.570433334D0, 5.031351030D0,
+     :    0.000466D-6,   12562.628581634D0, 4.959581597D0,
+     :    0.000520D-6,   39302.096962196D0, 4.788002889D0,
+     :    0.000458D-6,   12132.439962106D0, 1.880103788D0,
+     :    0.000470D-6,   12029.347187887D0, 1.405611197D0,
+     :    0.000416D-6,   -7477.522860216D0, 1.082356330D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=291,300) /
+     :    0.000449D-6,   11609.862544012D0, 4.179989585D0,
+     :    0.000465D-6,   17253.041107690D0, 0.353496295D0,
+     :    0.000362D-6,   -4535.059436924D0, 1.583849576D0,
+     :    0.000383D-6,   21954.157609398D0, 3.747376371D0,
+     :    0.000389D-6,      17.252277143D0, 1.395753179D0,
+     :    0.000331D-6,   18052.929543158D0, 0.566790582D0,
+     :    0.000430D-6,   13517.870106233D0, 0.685827538D0,
+     :    0.000368D-6,   -5756.908003246D0, 0.731374317D0,
+     :    0.000330D-6,   10557.594160824D0, 3.710043680D0,
+     :    0.000332D-6,   20199.094959633D0, 1.652901407D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=301,310) /
+     :    0.000384D-6,   11933.367960670D0, 5.827781531D0,
+     :    0.000387D-6,   10454.501386605D0, 2.541182564D0,
+     :    0.000325D-6,   15671.081759407D0, 2.178850542D0,
+     :    0.000318D-6,     138.517496871D0, 2.253253037D0,
+     :    0.000305D-6,    9388.005909415D0, 0.578340206D0,
+     :    0.000352D-6,    5749.861766548D0, 3.000297967D0,
+     :    0.000311D-6,    6915.859589305D0, 1.693574249D0,
+     :    0.000297D-6,   24072.921469776D0, 1.997249392D0,
+     :    0.000363D-6,    -640.877607382D0, 5.071820966D0,
+     :    0.000323D-6,   12592.450019783D0, 1.072262823D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=311,320) /
+     :    0.000341D-6,   12146.667056108D0, 4.700657997D0,
+     :    0.000290D-6,    9779.108676125D0, 1.812320441D0,
+     :    0.000342D-6,    6132.028180148D0, 4.322238614D0,
+     :    0.000329D-6,    6268.848755990D0, 3.033827743D0,
+     :    0.000374D-6,   17996.031168222D0, 3.388716544D0,
+     :    0.000285D-6,    -533.214083444D0, 4.687313233D0,
+     :    0.000338D-6,    6065.844601290D0, 0.877776108D0,
+     :    0.000276D-6,      24.298513841D0, 0.770299429D0,
+     :    0.000336D-6,   -2388.894020449D0, 5.353796034D0,
+     :    0.000290D-6,    3097.883822726D0, 4.075291557D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=321,330) /
+     :    0.000318D-6,     709.933048357D0, 5.941207518D0,
+     :    0.000271D-6,   13095.842665077D0, 3.208912203D0,
+     :    0.000331D-6,    6073.708907816D0, 4.007881169D0,
+     :    0.000292D-6,     742.990060533D0, 2.714333592D0,
+     :    0.000362D-6,   29088.811415985D0, 3.215977013D0,
+     :    0.000280D-6,   12359.966151546D0, 0.710872502D0,
+     :    0.000267D-6,   10440.274292604D0, 4.730108488D0,
+     :    0.000262D-6,     838.969287750D0, 1.327720272D0,
+     :    0.000250D-6,   16496.361396202D0, 0.898769761D0,
+     :    0.000325D-6,   20597.243963041D0, 0.180044365D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=331,340) /
+     :    0.000268D-6,    6148.010769956D0, 5.152666276D0,
+     :    0.000284D-6,    5636.065016677D0, 5.655385808D0,
+     :    0.000301D-6,    6080.822454817D0, 2.135396205D0,
+     :    0.000294D-6,    -377.373607916D0, 3.708784168D0,
+     :    0.000236D-6,    2118.763860378D0, 1.733578756D0,
+     :    0.000234D-6,    5867.523359379D0, 5.575209112D0,
+     :    0.000268D-6, -226858.238553767D0, 0.069432392D0,
+     :    0.000265D-6,  167283.761587465D0, 4.369302826D0,
+     :    0.000280D-6,   28237.233459389D0, 5.304829118D0,
+     :    0.000292D-6,   12345.739057544D0, 4.096094132D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=341,350) /
+     :    0.000223D-6,   19800.945956225D0, 3.069327406D0,
+     :    0.000301D-6,   43232.306658416D0, 6.205311188D0,
+     :    0.000264D-6,   18875.525869774D0, 1.417263408D0,
+     :    0.000304D-6,   -1823.175188677D0, 3.409035232D0,
+     :    0.000301D-6,     109.945688789D0, 0.510922054D0,
+     :    0.000260D-6,     813.550283960D0, 2.389438934D0,
+     :    0.000299D-6,  316428.228673312D0, 5.384595078D0,
+     :    0.000211D-6,    5756.566278634D0, 3.789392838D0,
+     :    0.000209D-6,    5750.203491159D0, 1.661943545D0,
+     :    0.000240D-6,   12489.885628707D0, 5.684549045D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=351,360) /
+     :    0.000216D-6,    6303.851245484D0, 3.862942261D0,
+     :    0.000203D-6,    1581.959348283D0, 5.549853589D0,
+     :    0.000200D-6,    5642.198242609D0, 1.016115785D0,
+     :    0.000197D-6,     -70.849445304D0, 4.690702525D0,
+     :    0.000227D-6,    6287.008003254D0, 2.911891613D0,
+     :    0.000197D-6,     533.623118358D0, 1.048982898D0,
+     :    0.000205D-6,   -6279.485421340D0, 1.829362730D0,
+     :    0.000209D-6,  -10988.808157535D0, 2.636140084D0,
+     :    0.000208D-6,    -227.526189440D0, 4.127883842D0,
+     :    0.000191D-6,     415.552490612D0, 4.401165650D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=361,370) /
+     :    0.000190D-6,   29296.615389579D0, 4.175658539D0,
+     :    0.000264D-6,   66567.485864652D0, 4.601102551D0,
+     :    0.000256D-6,   -3646.350377354D0, 0.506364778D0,
+     :    0.000188D-6,   13119.721102825D0, 2.032195842D0,
+     :    0.000185D-6,    -209.366942175D0, 4.694756586D0,
+     :    0.000198D-6,   25934.124331089D0, 3.832703118D0,
+     :    0.000195D-6,    4061.219215394D0, 3.308463427D0,
+     :    0.000234D-6,    5113.487598583D0, 1.716090661D0,
+     :    0.000188D-6,    1478.866574064D0, 5.686865780D0,
+     :    0.000222D-6,   11823.161639450D0, 1.942386641D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=371,380) /
+     :    0.000181D-6,   10770.893256262D0, 1.999482059D0,
+     :    0.000171D-6,    6546.159773364D0, 1.182807992D0,
+     :    0.000206D-6,      70.328180442D0, 5.934076062D0,
+     :    0.000169D-6,   20995.392966449D0, 2.169080622D0,
+     :    0.000191D-6,   10660.686935042D0, 5.405515999D0,
+     :    0.000228D-6,   33019.021112205D0, 4.656985514D0,
+     :    0.000184D-6,   -4933.208440333D0, 3.327476868D0,
+     :    0.000220D-6,    -135.625325010D0, 1.765430262D0,
+     :    0.000166D-6,   23141.558382925D0, 3.454132746D0,
+     :    0.000191D-6,    6144.558353121D0, 5.020393445D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=381,390) /
+     :    0.000180D-6,    6084.003848555D0, 0.602182191D0,
+     :    0.000163D-6,   17782.732072784D0, 4.960593133D0,
+     :    0.000225D-6,   16460.333529525D0, 2.596451817D0,
+     :    0.000222D-6,    5905.702242076D0, 3.731990323D0,
+     :    0.000204D-6,     227.476132789D0, 5.636192701D0,
+     :    0.000159D-6,   16737.577236597D0, 3.600691544D0,
+     :    0.000200D-6,    6805.653268085D0, 0.868220961D0,
+     :    0.000187D-6,   11919.140866668D0, 2.629456641D0,
+     :    0.000161D-6,     127.471796607D0, 2.862574720D0,
+     :    0.000205D-6,    6286.666278643D0, 1.742882331D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=391,400) /
+     :    0.000189D-6,     153.778810485D0, 4.812372643D0,
+     :    0.000168D-6,   16723.350142595D0, 0.027860588D0,
+     :    0.000149D-6,   11720.068865232D0, 0.659721876D0,
+     :    0.000189D-6,    5237.921013804D0, 5.245313000D0,
+     :    0.000143D-6,    6709.674040867D0, 4.317625647D0,
+     :    0.000146D-6,    4487.817406270D0, 4.815297007D0,
+     :    0.000144D-6,    -664.756045130D0, 5.381366880D0,
+     :    0.000175D-6,    5127.714692584D0, 4.728443327D0,
+     :    0.000162D-6,    6254.626662524D0, 1.435132069D0,
+     :    0.000187D-6,   47162.516354635D0, 1.354371923D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=401,410) /
+     :    0.000146D-6,   11080.171578918D0, 3.369695406D0,
+     :    0.000180D-6,    -348.924420448D0, 2.490902145D0,
+     :    0.000148D-6,     151.047669843D0, 3.799109588D0,
+     :    0.000157D-6,    6197.248551160D0, 1.284375887D0,
+     :    0.000167D-6,     146.594251718D0, 0.759969109D0,
+     :    0.000133D-6,   -5331.357443741D0, 5.409701889D0,
+     :    0.000154D-6,      95.979227218D0, 3.366890614D0,
+     :    0.000148D-6,   -6418.140930027D0, 3.384104996D0,
+     :    0.000128D-6,   -6525.804453965D0, 3.803419985D0,
+     :    0.000130D-6,   11293.470674356D0, 0.939039445D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=411,420) /
+     :    0.000152D-6,   -5729.506447149D0, 0.734117523D0,
+     :    0.000138D-6,     210.117701700D0, 2.564216078D0,
+     :    0.000123D-6,    6066.595360816D0, 4.517099537D0,
+     :    0.000140D-6,   18451.078546566D0, 0.642049130D0,
+     :    0.000126D-6,   11300.584221356D0, 3.485280663D0,
+     :    0.000119D-6,   10027.903195729D0, 3.217431161D0,
+     :    0.000151D-6,    4274.518310832D0, 4.404359108D0,
+     :    0.000117D-6,    6072.958148291D0, 0.366324650D0,
+     :    0.000165D-6,   -7668.637425143D0, 4.298212528D0,
+     :    0.000117D-6,   -6245.048177356D0, 5.379518958D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=421,430) /
+     :    0.000130D-6,   -5888.449964932D0, 4.527681115D0,
+     :    0.000121D-6,    -543.918059096D0, 6.109429504D0,
+     :    0.000162D-6,    9683.594581116D0, 5.720092446D0,
+     :    0.000141D-6,    6219.339951688D0, 0.679068671D0,
+     :    0.000118D-6,   22743.409379516D0, 4.881123092D0,
+     :    0.000129D-6,    1692.165669502D0, 0.351407289D0,
+     :    0.000126D-6,    5657.405657679D0, 5.146592349D0,
+     :    0.000114D-6,     728.762966531D0, 0.520791814D0,
+     :    0.000120D-6,      52.596639600D0, 0.948516300D0,
+     :    0.000115D-6,      65.220371012D0, 3.504914846D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=431,440) /
+     :    0.000126D-6,    5881.403728234D0, 5.577502482D0,
+     :    0.000158D-6,  163096.180360983D0, 2.957128968D0,
+     :    0.000134D-6,   12341.806904281D0, 2.598576764D0,
+     :    0.000151D-6,   16627.370915377D0, 3.985702050D0,
+     :    0.000109D-6,    1368.660252845D0, 0.014730471D0,
+     :    0.000131D-6,    6211.263196841D0, 0.085077024D0,
+     :    0.000146D-6,    5792.741760812D0, 0.708426604D0,
+     :    0.000146D-6,     -77.750543984D0, 3.121576600D0,
+     :    0.000107D-6,    5341.013788022D0, 0.288231904D0,
+     :    0.000138D-6,    6281.591377283D0, 2.797450317D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=441,450) /
+     :    0.000113D-6,   -6277.552925684D0, 2.788904128D0,
+     :    0.000115D-6,    -525.758811831D0, 5.895222200D0,
+     :    0.000138D-6,    6016.468808270D0, 6.096188999D0,
+     :    0.000139D-6,   23539.707386333D0, 2.028195445D0,
+     :    0.000146D-6,   -4176.041342449D0, 4.660008502D0,
+     :    0.000107D-6,   16062.184526117D0, 4.066520001D0,
+     :    0.000142D-6,   83783.548222473D0, 2.936315115D0,
+     :    0.000128D-6,    9380.959672717D0, 3.223844306D0,
+     :    0.000135D-6,    6205.325306007D0, 1.638054048D0,
+     :    0.000101D-6,    2699.734819318D0, 5.481603249D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=451,460) /
+     :    0.000104D-6,    -568.821874027D0, 2.205734493D0,
+     :    0.000103D-6,    6321.103522627D0, 2.440421099D0,
+     :    0.000119D-6,    6321.208885629D0, 2.547496264D0,
+     :    0.000138D-6,    1975.492545856D0, 2.314608466D0,
+     :    0.000121D-6,     137.033024162D0, 4.539108237D0,
+     :    0.000123D-6,   19402.796952817D0, 4.538074405D0,
+     :    0.000119D-6,   22805.735565994D0, 2.869040566D0,
+     :    0.000133D-6,   64471.991241142D0, 6.056405489D0,
+     :    0.000129D-6,     -85.827298831D0, 2.540635083D0,
+     :    0.000131D-6,   13613.804277336D0, 4.005732868D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=461,470) /
+     :    0.000104D-6,    9814.604100291D0, 1.959967212D0,
+     :    0.000112D-6,   16097.679950283D0, 3.589026260D0,
+     :    0.000123D-6,    2107.034507542D0, 1.728627253D0,
+     :    0.000121D-6,   36949.230808424D0, 6.072332087D0,
+     :    0.000108D-6,  -12539.853380183D0, 3.716133846D0,
+     :    0.000113D-6,   -7875.671863624D0, 2.725771122D0,
+     :    0.000109D-6,    4171.425536614D0, 4.033338079D0,
+     :    0.000101D-6,    6247.911759770D0, 3.441347021D0,
+     :    0.000113D-6,    7330.728427345D0, 0.656372122D0,
+     :    0.000113D-6,   51092.726050855D0, 2.791483066D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=471,480) /
+     :    0.000106D-6,    5621.842923210D0, 1.815323326D0,
+     :    0.000101D-6,     111.430161497D0, 5.711033677D0,
+     :    0.000103D-6,     909.818733055D0, 2.812745443D0,
+     :    0.000101D-6,    1790.642637886D0, 1.965746028D0,
+
+*  T
+     :  102.156724D-6,    6283.075849991D0, 4.249032005D0,
+     :    1.706807D-6,   12566.151699983D0, 4.205904248D0,
+     :    0.269668D-6,     213.299095438D0, 3.400290479D0,
+     :    0.265919D-6,     529.690965095D0, 5.836047367D0,
+     :    0.210568D-6,      -3.523118349D0, 6.262738348D0,
+     :    0.077996D-6,    5223.693919802D0, 4.670344204D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=481,490) /
+     :    0.054764D-6,    1577.343542448D0, 4.534800170D0,
+     :    0.059146D-6,      26.298319800D0, 1.083044735D0,
+     :    0.034420D-6,    -398.149003408D0, 5.980077351D0,
+     :    0.032088D-6,   18849.227549974D0, 4.162913471D0,
+     :    0.033595D-6,    5507.553238667D0, 5.980162321D0,
+     :    0.029198D-6,    5856.477659115D0, 0.623811863D0,
+     :    0.027764D-6,     155.420399434D0, 3.745318113D0,
+     :    0.025190D-6,    5746.271337896D0, 2.980330535D0,
+     :    0.022997D-6,    -796.298006816D0, 1.174411803D0,
+     :    0.024976D-6,    5760.498431898D0, 2.467913690D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=491,500) /
+     :    0.021774D-6,     206.185548437D0, 3.854787540D0,
+     :    0.017925D-6,    -775.522611324D0, 1.092065955D0,
+     :    0.013794D-6,     426.598190876D0, 2.699831988D0,
+     :    0.013276D-6,    6062.663207553D0, 5.845801920D0,
+     :    0.011774D-6,   12036.460734888D0, 2.292832062D0,
+     :    0.012869D-6,    6076.890301554D0, 5.333425680D0,
+     :    0.012152D-6,    1059.381930189D0, 6.222874454D0,
+     :    0.011081D-6,      -7.113547001D0, 5.154724984D0,
+     :    0.010143D-6,    4694.002954708D0, 4.044013795D0,
+     :    0.009357D-6,    5486.777843175D0, 3.416081409D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=501,510) /
+     :    0.010084D-6,     522.577418094D0, 0.749320262D0,
+     :    0.008587D-6,   10977.078804699D0, 2.777152598D0,
+     :    0.008628D-6,    6275.962302991D0, 4.562060226D0,
+     :    0.008158D-6,    -220.412642439D0, 5.806891533D0,
+     :    0.007746D-6,    2544.314419883D0, 1.603197066D0,
+     :    0.007670D-6,    2146.165416475D0, 3.000200440D0,
+     :    0.007098D-6,      74.781598567D0, 0.443725817D0,
+     :    0.006180D-6,    -536.804512095D0, 1.302642751D0,
+     :    0.005818D-6,    5088.628839767D0, 4.827723531D0,
+     :    0.004945D-6,   -6286.598968340D0, 0.268305170D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=511,520) /
+     :    0.004774D-6,    1349.867409659D0, 5.808636673D0,
+     :    0.004687D-6,    -242.728603974D0, 5.154890570D0,
+     :    0.006089D-6,    1748.016413067D0, 4.403765209D0,
+     :    0.005975D-6,   -1194.447010225D0, 2.583472591D0,
+     :    0.004229D-6,     951.718406251D0, 0.931172179D0,
+     :    0.005264D-6,     553.569402842D0, 2.336107252D0,
+     :    0.003049D-6,    5643.178563677D0, 1.362634430D0,
+     :    0.002974D-6,    6812.766815086D0, 1.583012668D0,
+     :    0.003403D-6,   -2352.866153772D0, 2.552189886D0,
+     :    0.003030D-6,     419.484643875D0, 5.286473844D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=521,530) /
+     :    0.003210D-6,      -7.046236698D0, 1.863796539D0,
+     :    0.003058D-6,    9437.762934887D0, 4.226420633D0,
+     :    0.002589D-6,   12352.852604545D0, 1.991935820D0,
+     :    0.002927D-6,    5216.580372801D0, 2.319951253D0,
+     :    0.002425D-6,    5230.807466803D0, 3.084752833D0,
+     :    0.002656D-6,    3154.687084896D0, 2.487447866D0,
+     :    0.002445D-6,   10447.387839604D0, 2.347139160D0,
+     :    0.002990D-6,    4690.479836359D0, 6.235872050D0,
+     :    0.002890D-6,    5863.591206116D0, 0.095197563D0,
+     :    0.002498D-6,    6438.496249426D0, 2.994779800D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=531,540) /
+     :    0.001889D-6,    8031.092263058D0, 3.569003717D0,
+     :    0.002567D-6,     801.820931124D0, 3.425611498D0,
+     :    0.001803D-6,  -71430.695617928D0, 2.192295512D0,
+     :    0.001782D-6,       3.932153263D0, 5.180433689D0,
+     :    0.001694D-6,   -4705.732307544D0, 4.641779174D0,
+     :    0.001704D-6,   -1592.596013633D0, 3.997097652D0,
+     :    0.001735D-6,    5849.364112115D0, 0.417558428D0,
+     :    0.001643D-6,    8429.241266467D0, 2.180619584D0,
+     :    0.001680D-6,      38.133035638D0, 4.164529426D0,
+     :    0.002045D-6,    7084.896781115D0, 0.526323854D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=541,550) /
+     :    0.001458D-6,    4292.330832950D0, 1.356098141D0,
+     :    0.001437D-6,      20.355319399D0, 3.895439360D0,
+     :    0.001738D-6,    6279.552731642D0, 0.087484036D0,
+     :    0.001367D-6,   14143.495242431D0, 3.987576591D0,
+     :    0.001344D-6,    7234.794256242D0, 0.090454338D0,
+     :    0.001438D-6,   11499.656222793D0, 0.974387904D0,
+     :    0.001257D-6,    6836.645252834D0, 1.509069366D0,
+     :    0.001358D-6,   11513.883316794D0, 0.495572260D0,
+     :    0.001628D-6,    7632.943259650D0, 4.968445721D0,
+     :    0.001169D-6,     103.092774219D0, 2.838496795D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=551,560) /
+     :    0.001162D-6,    4164.311989613D0, 3.408387778D0,
+     :    0.001092D-6,    6069.776754553D0, 3.617942651D0,
+     :    0.001008D-6,   17789.845619785D0, 0.286350174D0,
+     :    0.001008D-6,     639.897286314D0, 1.610762073D0,
+     :    0.000918D-6,   10213.285546211D0, 5.532798067D0,
+     :    0.001011D-6,   -6256.777530192D0, 0.661826484D0,
+     :    0.000753D-6,   16730.463689596D0, 3.905030235D0,
+     :    0.000737D-6,   11926.254413669D0, 4.641956361D0,
+     :    0.000694D-6,    3340.612426700D0, 2.111120332D0,
+     :    0.000701D-6,    3894.181829542D0, 2.760823491D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=561,570) /
+     :    0.000689D-6,    -135.065080035D0, 4.768800780D0,
+     :    0.000700D-6,   13367.972631107D0, 5.760439898D0,
+     :    0.000664D-6,    6040.347246017D0, 1.051215840D0,
+     :    0.000654D-6,    5650.292110678D0, 4.911332503D0,
+     :    0.000788D-6,    6681.224853400D0, 4.699648011D0,
+     :    0.000628D-6,    5333.900241022D0, 5.024608847D0,
+     :    0.000755D-6,    -110.206321219D0, 4.370971253D0,
+     :    0.000628D-6,    6290.189396992D0, 3.660478857D0,
+     :    0.000635D-6,   25132.303399966D0, 4.121051532D0,
+     :    0.000534D-6,    5966.683980335D0, 1.173284524D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=571,580) /
+     :    0.000543D-6,    -433.711737877D0, 0.345585464D0,
+     :    0.000517D-6,   -1990.745017041D0, 5.414571768D0,
+     :    0.000504D-6,    5767.611978898D0, 2.328281115D0,
+     :    0.000485D-6,    5753.384884897D0, 1.685874771D0,
+     :    0.000463D-6,    7860.419392439D0, 5.297703006D0,
+     :    0.000604D-6,     515.463871093D0, 0.591998446D0,
+     :    0.000443D-6,   12168.002696575D0, 4.830881244D0,
+     :    0.000570D-6,     199.072001436D0, 3.899190272D0,
+     :    0.000465D-6,   10969.965257698D0, 0.476681802D0,
+     :    0.000424D-6,   -7079.373856808D0, 1.112242763D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=581,590) /
+     :    0.000427D-6,     735.876513532D0, 1.994214480D0,
+     :    0.000478D-6,   -6127.655450557D0, 3.778025483D0,
+     :    0.000414D-6,   10973.555686350D0, 5.441088327D0,
+     :    0.000512D-6,    1589.072895284D0, 0.107123853D0,
+     :    0.000378D-6,   10984.192351700D0, 0.915087231D0,
+     :    0.000402D-6,   11371.704689758D0, 4.107281715D0,
+     :    0.000453D-6,    9917.696874510D0, 1.917490952D0,
+     :    0.000395D-6,     149.563197135D0, 2.763124165D0,
+     :    0.000371D-6,    5739.157790895D0, 3.112111866D0,
+     :    0.000350D-6,   11790.629088659D0, 0.440639857D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=591,600) /
+     :    0.000356D-6,    6133.512652857D0, 5.444568842D0,
+     :    0.000344D-6,     412.371096874D0, 5.676832684D0,
+     :    0.000383D-6,     955.599741609D0, 5.559734846D0,
+     :    0.000333D-6,    6496.374945429D0, 0.261537984D0,
+     :    0.000340D-6,    6055.549660552D0, 5.975534987D0,
+     :    0.000334D-6,    1066.495477190D0, 2.335063907D0,
+     :    0.000399D-6,   11506.769769794D0, 5.321230910D0,
+     :    0.000314D-6,   18319.536584880D0, 2.313312404D0,
+     :    0.000424D-6,    1052.268383188D0, 1.211961766D0,
+     :    0.000307D-6,      63.735898303D0, 3.169551388D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=601,610) /
+     :    0.000329D-6,      29.821438149D0, 6.106912080D0,
+     :    0.000357D-6,    6309.374169791D0, 4.223760346D0,
+     :    0.000312D-6,   -3738.761430108D0, 2.180556645D0,
+     :    0.000301D-6,     309.278322656D0, 1.499984572D0,
+     :    0.000268D-6,   12043.574281889D0, 2.447520648D0,
+     :    0.000257D-6,   12491.370101415D0, 3.662331761D0,
+     :    0.000290D-6,     625.670192312D0, 1.272834584D0,
+     :    0.000256D-6,    5429.879468239D0, 1.913426912D0,
+     :    0.000339D-6,    3496.032826134D0, 4.165930011D0,
+     :    0.000283D-6,    3930.209696220D0, 4.325565754D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=611,620) /
+     :    0.000241D-6,   12528.018664345D0, 3.832324536D0,
+     :    0.000304D-6,    4686.889407707D0, 1.612348468D0,
+     :    0.000259D-6,   16200.772724501D0, 3.470173146D0,
+     :    0.000238D-6,   12139.553509107D0, 1.147977842D0,
+     :    0.000236D-6,    6172.869528772D0, 3.776271728D0,
+     :    0.000296D-6,   -7058.598461315D0, 0.460368852D0,
+     :    0.000306D-6,   10575.406682942D0, 0.554749016D0,
+     :    0.000251D-6,   17298.182327326D0, 0.834332510D0,
+     :    0.000290D-6,    4732.030627343D0, 4.759564091D0,
+     :    0.000261D-6,    5884.926846583D0, 0.298259862D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=621,630) /
+     :    0.000249D-6,    5547.199336460D0, 3.749366406D0,
+     :    0.000213D-6,   11712.955318231D0, 5.415666119D0,
+     :    0.000223D-6,    4701.116501708D0, 2.703203558D0,
+     :    0.000268D-6,    -640.877607382D0, 0.283670793D0,
+     :    0.000209D-6,    5636.065016677D0, 1.238477199D0,
+     :    0.000193D-6,   10177.257679534D0, 1.943251340D0,
+     :    0.000182D-6,    6283.143160294D0, 2.456157599D0,
+     :    0.000184D-6,    -227.526189440D0, 5.888038582D0,
+     :    0.000182D-6,   -6283.008539689D0, 0.241332086D0,
+     :    0.000228D-6,   -6284.056171060D0, 2.657323816D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=631,640) /
+     :    0.000166D-6,    7238.675591600D0, 5.930629110D0,
+     :    0.000167D-6,    3097.883822726D0, 5.570955333D0,
+     :    0.000159D-6,    -323.505416657D0, 5.786670700D0,
+     :    0.000154D-6,   -4136.910433516D0, 1.517805532D0,
+     :    0.000176D-6,   12029.347187887D0, 3.139266834D0,
+     :    0.000167D-6,   12132.439962106D0, 3.556352289D0,
+     :    0.000153D-6,     202.253395174D0, 1.463313961D0,
+     :    0.000157D-6,   17267.268201691D0, 1.586837396D0,
+     :    0.000142D-6,   83996.847317911D0, 0.022670115D0,
+     :    0.000152D-6,   17260.154654690D0, 0.708528947D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=641,650) /
+     :    0.000144D-6,    6084.003848555D0, 5.187075177D0,
+     :    0.000135D-6,    5756.566278634D0, 1.993229262D0,
+     :    0.000134D-6,    5750.203491159D0, 3.457197134D0,
+     :    0.000144D-6,    5326.786694021D0, 6.066193291D0,
+     :    0.000160D-6,   11015.106477335D0, 1.710431974D0,
+     :    0.000133D-6,    3634.621024518D0, 2.836451652D0,
+     :    0.000134D-6,   18073.704938650D0, 5.453106665D0,
+     :    0.000134D-6,    1162.474704408D0, 5.326898811D0,
+     :    0.000128D-6,    5642.198242609D0, 2.511652591D0,
+     :    0.000160D-6,     632.783739313D0, 5.628785365D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=651,660) /
+     :    0.000132D-6,   13916.019109642D0, 0.819294053D0,
+     :    0.000122D-6,   14314.168113050D0, 5.677408071D0,
+     :    0.000125D-6,   12359.966151546D0, 5.251984735D0,
+     :    0.000121D-6,    5749.452731634D0, 2.210924603D0,
+     :    0.000136D-6,    -245.831646229D0, 1.646502367D0,
+     :    0.000120D-6,    5757.317038160D0, 3.240883049D0,
+     :    0.000134D-6,   12146.667056108D0, 3.059480037D0,
+     :    0.000137D-6,    6206.809778716D0, 1.867105418D0,
+     :    0.000141D-6,   17253.041107690D0, 2.069217456D0,
+     :    0.000129D-6,   -7477.522860216D0, 2.781469314D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=661,670) /
+     :    0.000116D-6,    5540.085789459D0, 4.281176991D0,
+     :    0.000116D-6,    9779.108676125D0, 3.320925381D0,
+     :    0.000129D-6,    5237.921013804D0, 3.497704076D0,
+     :    0.000113D-6,    5959.570433334D0, 0.983210840D0,
+     :    0.000122D-6,    6282.095528923D0, 2.674938860D0,
+     :    0.000140D-6,     -11.045700264D0, 4.957936982D0,
+     :    0.000108D-6,   23543.230504682D0, 1.390113589D0,
+     :    0.000106D-6,  -12569.674818332D0, 0.429631317D0,
+     :    0.000110D-6,    -266.607041722D0, 5.501340197D0,
+     :    0.000115D-6,   12559.038152982D0, 4.691456618D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=671,680) /
+     :    0.000134D-6,   -2388.894020449D0, 0.577313584D0,
+     :    0.000109D-6,   10440.274292604D0, 6.218148717D0,
+     :    0.000102D-6,    -543.918059096D0, 1.477842615D0,
+     :    0.000108D-6,   21228.392023546D0, 2.237753948D0,
+     :    0.000101D-6,   -4535.059436924D0, 3.100492232D0,
+     :    0.000103D-6,      76.266071276D0, 5.594294322D0,
+     :    0.000104D-6,     949.175608970D0, 5.674287810D0,
+     :    0.000101D-6,   13517.870106233D0, 2.196632348D0,
+     :    0.000100D-6,   11933.367960670D0, 4.056084160D0,
+     :    4.322990D-6,    6283.075849991D0, 2.642893748D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=681,690) /
+     :    0.406495D-6,       0.000000000D0, 4.712388980D0,
+     :    0.122605D-6,   12566.151699983D0, 2.438140634D0,
+     :    0.019476D-6,     213.299095438D0, 1.642186981D0,
+     :    0.016916D-6,     529.690965095D0, 4.510959344D0,
+     :    0.013374D-6,      -3.523118349D0, 1.502210314D0,
+     :    0.008042D-6,      26.298319800D0, 0.478549024D0,
+     :    0.007824D-6,     155.420399434D0, 5.254710405D0,
+     :    0.004894D-6,    5746.271337896D0, 4.683210850D0,
+     :    0.004875D-6,    5760.498431898D0, 0.759507698D0,
+     :    0.004416D-6,    5223.693919802D0, 6.028853166D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=691,700) /
+     :    0.004088D-6,      -7.113547001D0, 0.060926389D0,
+     :    0.004433D-6,   77713.771467920D0, 3.627734103D0,
+     :    0.003277D-6,   18849.227549974D0, 2.327912542D0,
+     :    0.002703D-6,    6062.663207553D0, 1.271941729D0,
+     :    0.003435D-6,    -775.522611324D0, 0.747446224D0,
+     :    0.002618D-6,    6076.890301554D0, 3.633715689D0,
+     :    0.003146D-6,     206.185548437D0, 5.647874613D0,
+     :    0.002544D-6,    1577.343542448D0, 6.232904270D0,
+     :    0.002218D-6,    -220.412642439D0, 1.309509946D0,
+     :    0.002197D-6,    5856.477659115D0, 2.407212349D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=701,710) /
+     :    0.002897D-6,    5753.384884897D0, 5.863842246D0,
+     :    0.001766D-6,     426.598190876D0, 0.754113147D0,
+     :    0.001738D-6,    -796.298006816D0, 2.714942671D0,
+     :    0.001695D-6,     522.577418094D0, 2.629369842D0,
+     :    0.001584D-6,    5507.553238667D0, 1.341138229D0,
+     :    0.001503D-6,    -242.728603974D0, 0.377699736D0,
+     :    0.001552D-6,    -536.804512095D0, 2.904684667D0,
+     :    0.001370D-6,    -398.149003408D0, 1.265599125D0,
+     :    0.001889D-6,   -5573.142801634D0, 4.413514859D0,
+     :    0.001722D-6,    6069.776754553D0, 2.445966339D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=711,720) /
+     :    0.001124D-6,    1059.381930189D0, 5.041799657D0,
+     :    0.001258D-6,     553.569402842D0, 3.849557278D0,
+     :    0.000831D-6,     951.718406251D0, 2.471094709D0,
+     :    0.000767D-6,    4694.002954708D0, 5.363125422D0,
+     :    0.000756D-6,    1349.867409659D0, 1.046195744D0,
+     :    0.000775D-6,     -11.045700264D0, 0.245548001D0,
+     :    0.000597D-6,    2146.165416475D0, 4.543268798D0,
+     :    0.000568D-6,    5216.580372801D0, 4.178853144D0,
+     :    0.000711D-6,    1748.016413067D0, 5.934271972D0,
+     :    0.000499D-6,   12036.460734888D0, 0.624434410D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=721,730) /
+     :    0.000671D-6,   -1194.447010225D0, 4.136047594D0,
+     :    0.000488D-6,    5849.364112115D0, 2.209679987D0,
+     :    0.000621D-6,    6438.496249426D0, 4.518860804D0,
+     :    0.000495D-6,   -6286.598968340D0, 1.868201275D0,
+     :    0.000456D-6,    5230.807466803D0, 1.271231591D0,
+     :    0.000451D-6,    5088.628839767D0, 0.084060889D0,
+     :    0.000435D-6,    5643.178563677D0, 3.324456609D0,
+     :    0.000387D-6,   10977.078804699D0, 4.052488477D0,
+     :    0.000547D-6,  161000.685737473D0, 2.841633844D0,
+     :    0.000522D-6,    3154.687084896D0, 2.171979966D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=731,740) /
+     :    0.000375D-6,    5486.777843175D0, 4.983027306D0,
+     :    0.000421D-6,    5863.591206116D0, 4.546432249D0,
+     :    0.000439D-6,    7084.896781115D0, 0.522967921D0,
+     :    0.000309D-6,    2544.314419883D0, 3.172606705D0,
+     :    0.000347D-6,    4690.479836359D0, 1.479586566D0,
+     :    0.000317D-6,     801.820931124D0, 3.553088096D0,
+     :    0.000262D-6,     419.484643875D0, 0.606635550D0,
+     :    0.000248D-6,    6836.645252834D0, 3.014082064D0,
+     :    0.000245D-6,   -1592.596013633D0, 5.519526220D0,
+     :    0.000225D-6,    4292.330832950D0, 2.877956536D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=741,750) /
+     :    0.000214D-6,    7234.794256242D0, 1.605227587D0,
+     :    0.000205D-6,    5767.611978898D0, 0.625804796D0,
+     :    0.000180D-6,   10447.387839604D0, 3.499954526D0,
+     :    0.000229D-6,     199.072001436D0, 5.632304604D0,
+     :    0.000214D-6,     639.897286314D0, 5.960227667D0,
+     :    0.000175D-6,    -433.711737877D0, 2.162417992D0,
+     :    0.000209D-6,     515.463871093D0, 2.322150893D0,
+     :    0.000173D-6,    6040.347246017D0, 2.556183691D0,
+     :    0.000184D-6,    6309.374169791D0, 4.732296790D0,
+     :    0.000227D-6,  149854.400134205D0, 5.385812217D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=751,760) /
+     :    0.000154D-6,    8031.092263058D0, 5.120720920D0,
+     :    0.000151D-6,    5739.157790895D0, 4.815000443D0,
+     :    0.000197D-6,    7632.943259650D0, 0.222827271D0,
+     :    0.000197D-6,      74.781598567D0, 3.910456770D0,
+     :    0.000138D-6,    6055.549660552D0, 1.397484253D0,
+     :    0.000149D-6,   -6127.655450557D0, 5.333727496D0,
+     :    0.000137D-6,    3894.181829542D0, 4.281749907D0,
+     :    0.000135D-6,    9437.762934887D0, 5.979971885D0,
+     :    0.000139D-6,   -2352.866153772D0, 4.715630782D0,
+     :    0.000142D-6,    6812.766815086D0, 0.513330157D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=761,770) /
+     :    0.000120D-6,   -4705.732307544D0, 0.194160689D0,
+     :    0.000131D-6,  -71430.695617928D0, 0.000379226D0,
+     :    0.000124D-6,    6279.552731642D0, 2.122264908D0,
+     :    0.000108D-6,   -6256.777530192D0, 0.883445696D0,
+     :    0.143388D-6,    6283.075849991D0, 1.131453581D0,
+     :    0.006671D-6,   12566.151699983D0, 0.775148887D0,
+     :    0.001480D-6,     155.420399434D0, 0.480016880D0,
+     :    0.000934D-6,     213.299095438D0, 6.144453084D0,
+     :    0.000795D-6,     529.690965095D0, 2.941595619D0,
+     :    0.000673D-6,    5746.271337896D0, 0.120415406D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=771,780) /
+     :    0.000672D-6,    5760.498431898D0, 5.317009738D0,
+     :    0.000389D-6,    -220.412642439D0, 3.090323467D0,
+     :    0.000373D-6,    6062.663207553D0, 3.003551964D0,
+     :    0.000360D-6,    6076.890301554D0, 1.918913041D0,
+     :    0.000316D-6,     -21.340641002D0, 5.545798121D0,
+     :    0.000315D-6,    -242.728603974D0, 1.884932563D0,
+     :    0.000278D-6,     206.185548437D0, 1.266254859D0,
+     :    0.000238D-6,    -536.804512095D0, 4.532664830D0,
+     :    0.000185D-6,     522.577418094D0, 4.578313856D0,
+     :    0.000245D-6,   18849.227549974D0, 0.587467082D0 /
+      DATA ((FAIRHD(I,J),I=1,3),J=781,787) /
+     :    0.000180D-6,     426.598190876D0, 5.151178553D0,
+     :    0.000200D-6,     553.569402842D0, 5.355983739D0,
+     :    0.000141D-6,    5223.693919802D0, 1.336556009D0,
+     :    0.000104D-6,    5856.477659115D0, 4.239842759D0,
+     :    0.003826D-6,    6283.075849991D0, 5.705257275D0,
+     :    0.000303D-6,   12566.151699983D0, 5.407132842D0,
+     :    0.000209D-6,     155.420399434D0, 1.989815753D0 /
+* -----------------------------------------------------------------------
+
+
+
+*  Time since J2000.0 in Julian millennia.
+      T=(TDB-51544.5D0)/365250D0
+
+* -------------------- Topocentric terms -------------------------------
+
+*  Convert UT1 to local solar time in radians.
+      TSOL = MOD(UT1,1D0)*D2PI - WL
+
+*  FUNDAMENTAL ARGUMENTS:  Simon et al 1994
+
+*  Combine time argument (millennia) with deg/arcsec factor.
+      W = T / 3600D0
+
+*  Sun Mean Longitude.
+      ELSUN = MOD(280.46645683D0+1296027711.03429D0*W,360D0)*D2R
+
+*  Sun Mean Anomaly.
+      EMSUN = MOD(357.52910918D0+1295965810.481D0*W,360D0)*D2R
+
+*  Mean Elongation of Moon from Sun.
+      D = MOD(297.85019547D0+16029616012.090D0*W,360D0)*D2R
+
+*  Mean Longitude of Jupiter.
+      ELJ = MOD(34.35151874D0+109306899.89453D0*W,360D0)*D2R
+
+*  Mean Longitude of Saturn.
+      ELS = MOD(50.07744430D0+44046398.47038D0*W,360D0)*D2R
+
+*  TOPOCENTRIC TERMS:  Moyer 1981 and Murray 1983.
+      WT =  +0.00029D-10*U*SIN(TSOL+ELSUN-ELS)
+     :      +0.00100D-10*U*SIN(TSOL-2D0*EMSUN)
+     :      +0.00133D-10*U*SIN(TSOL-D)
+     :      +0.00133D-10*U*SIN(TSOL+ELSUN-ELJ)
+     :      -0.00229D-10*U*SIN(TSOL+2D0*ELSUN+EMSUN)
+     :      -0.0220 D-10*V*COS(ELSUN+EMSUN)
+     :      +0.05312D-10*U*SIN(TSOL-EMSUN)
+     :      -0.13677D-10*U*SIN(TSOL+2D0*ELSUN)
+     :      -1.3184 D-10*V*COS(ELSUN)
+     :      +3.17679D-10*U*SIN(TSOL)
+
+* --------------- Fairhead model ---------------------------------------
+
+*  T**0
+      W0=0D0
+      DO I=474,1,-1
+         W0=W0+FAIRHD(1,I)*SIN(FAIRHD(2,I)*T+FAIRHD(3,I))
+      END DO
+
+*  T**1
+      W1=0D0
+      DO I=679,475,-1
+         W1=W1+FAIRHD(1,I)*SIN(FAIRHD(2,I)*T+FAIRHD(3,I))
+      END DO
+
+*  T**2
+      W2=0D0
+      DO I=764,680,-1
+         W2=W2+FAIRHD(1,I)*SIN(FAIRHD(2,I)*T+FAIRHD(3,I))
+      END DO
+
+*  T**3
+      W3=0D0
+      DO I=784,765,-1
+         W3=W3+FAIRHD(1,I)*SIN(FAIRHD(2,I)*T+FAIRHD(3,I))
+      END DO
+
+*  T**4
+      W4=0D0
+      DO I=787,785,-1
+         W4=W4+FAIRHD(1,I)*SIN(FAIRHD(2,I)*T+FAIRHD(3,I))
+      END DO
+
+*  Multiply by powers of T and combine.
+      WF=T*(T*(T*(T*W4+W3)+W2)+W1)+W0
+
+*  Adjustments to use JPL planetary masses instead of IAU.
+      WJ=     0.00065D-6  * SIN(   6069.776754D0   *T + 4.021194D0   ) +
+     :        0.00033D-6  * SIN(    213.299095D0   *T + 5.543132D0   ) +
+     :      (-0.00196D-6  * SIN(   6208.294251D0   *T + 5.696701D0   ))+
+     :      (-0.00173D-6  * SIN(     74.781599D0   *T + 2.435900D0   ))+
+     :        0.03638D-6*T*T
+
+* -----------------------------------------------------------------------
+
+*  Final result:  TDB-TT in seconds.
+      slRCC=WT+WF+WJ
+
+      END
diff --git a/math/slalib/rdplan.f b/math/slalib/rdplan.f
new file mode 100644
index 00000000..95ba3ef8
--- /dev/null
+++ b/math/slalib/rdplan.f
@@ -0,0 +1,201 @@
+      SUBROUTINE slRDPL (DATE, NP, ELONG, PHI, RA, DEC, DIAM)
+*+
+*     - - - - - - -
+*      R D P L
+*     - - - - - - -
+*
+*  Approximate topocentric apparent RA,Dec of a planet, and its
+*  angular diameter.
+*
+*  Given:
+*     DATE        d       MJD of observation (JD - 2400000.5)
+*     NP          i       planet: 1 = Mercury
+*                                 2 = Venus
+*                                 3 = Moon
+*                                 4 = Mars
+*                                 5 = Jupiter
+*                                 6 = Saturn
+*                                 7 = Uranus
+*                                 8 = Neptune
+*                                 9 = Pluto
+*                              else = Sun
+*     ELONG,PHI   d       observer's east longitude and geodetic
+*                                               latitude (radians)
+*
+*  Returned:
+*     RA,DEC      d        RA, Dec (topocentric apparent, radians)
+*     DIAM        d        angular diameter (equatorial, radians)
+*
+*  Notes:
+*
+*  1  The date is in a dynamical timescale (TDB, formerly ET) and is
+*     in the form of a Modified Julian Date (JD-2400000.5).  For all
+*     practical purposes, TT can be used instead of TDB, and for many
+*     applications UT will do (except for the Moon).
+*
+*  2  The longitude and latitude allow correction for geocentric
+*     parallax.  This is a major effect for the Moon, but in the
+*     context of the limited accuracy of the present routine its
+*     effect on planetary positions is small (negligible for the
+*     outer planets).  Geocentric positions can be generated by
+*     appropriate use of the routines slDMON and slPLNT.
+*
+*  3  The direction accuracy (arcsec, 1000-3000AD) is of order:
+*
+*            Sun              5
+*            Mercury          2
+*            Venus           10
+*            Moon            30
+*            Mars            50
+*            Jupiter         90
+*            Saturn          90
+*            Uranus          90
+*            Neptune         10
+*            Pluto            1   (1885-2099AD only)
+*
+*     The angular diameter accuracy is about 0.4% for the Moon,
+*     and 0.01% or better for the Sun and planets.
+*
+*  See the slPLNT routine for references.
+*
+*  Called: slGMST, slDT, slEPJ, slDMON, slPVOB, slPRNU,
+*          slPLNT, slDMXV, slDC2S, slDA2P
+*
+*  P.T.Wallace   Starlink   26 May 1997
+*
+*  Copyright (C) 1997 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE
+      INTEGER NP
+      DOUBLE PRECISION ELONG,PHI,RA,DEC,DIAM
+
+*  AU in km
+      DOUBLE PRECISION AUKM
+      PARAMETER (AUKM=1.49597870D8)
+
+*  Light time for unit distance (sec)
+      DOUBLE PRECISION TAU
+      PARAMETER (TAU=499.004782D0)
+
+      INTEGER IP,J,I
+      DOUBLE PRECISION EQRAU(0:9),STL,VGM(6),V(6),RMAT(3,3),
+     :                 VSE(6),VSG(6),VSP(6),VGO(6),DX,DY,DZ,R,TL
+      DOUBLE PRECISION slGMST,slDT,slEPJ,slDA2P
+
+*  Equatorial radii (km)
+      DATA EQRAU / 696000D0,2439.7D0,6051.9D0,1738D0,3397D0,71492D0,
+     :             60268D0,25559D0,24764D0,1151D0 /
+
+
+
+*  Classify NP
+      IP=NP
+      IF (IP.LT.0.OR.IP.GT.9) IP=0
+
+*  Approximate local ST
+      STL=slGMST(DATE-slDT(slEPJ(DATE))/86400D0)+ELONG
+
+*  Geocentre to Moon (mean of date)
+      CALL slDMON(DATE,V)
+
+*  Nutation to true of date
+      CALL slNUT(DATE,RMAT)
+      CALL slDMXV(RMAT,V,VGM)
+      CALL slDMXV(RMAT,V(4),VGM(4))
+
+*  Moon?
+      IF (IP.EQ.3) THEN
+
+*     Yes: geocentre to Moon (true of date)
+         DO I=1,6
+            V(I)=VGM(I)
+         END DO
+      ELSE
+
+*     No: precession/nutation matrix, J2000 to date
+         CALL slPRNU(2000D0,DATE,RMAT)
+
+*     Sun to Earth-Moon Barycentre (J2000)
+         CALL slPLNT(DATE,3,V,J)
+
+*     Precession and nutation to date
+         CALL slDMXV(RMAT,V,VSE)
+         CALL slDMXV(RMAT,V(4),VSE(4))
+
+*     Sun to geocentre (true of date)
+         DO I=1,6
+            VSG(I)=VSE(I)-0.012150581D0*VGM(I)
+         END DO
+
+*     Sun?
+         IF (IP.EQ.0) THEN
+
+*        Yes: geocentre to Sun
+            DO I=1,6
+               V(I)=-VSG(I)
+            END DO
+         ELSE
+
+*        No: Sun to Planet (J2000)
+            CALL slPLNT(DATE,IP,V,J)
+
+*        Precession and nutation to date
+            CALL slDMXV(RMAT,V,VSP)
+            CALL slDMXV(RMAT,V(4),VSP(4))
+
+*        Geocentre to planet
+            DO I=1,6
+               V(I)=VSP(I)-VSG(I)
+            END DO
+         END IF
+      END IF
+
+*  Refer to origin at the observer
+      CALL slPVOB(PHI,0D0,STL,VGO)
+      DO I=1,6
+         V(I)=V(I)-VGO(I)
+      END DO
+
+*  Geometric distance (AU)
+      DX=V(1)
+      DY=V(2)
+      DZ=V(3)
+      R=SQRT(DX*DX+DY*DY+DZ*DZ)
+
+*  Light time (sec)
+      TL=TAU*R
+
+*  Correct position for planetary aberration
+      DO I=1,3
+         V(I)=V(I)-TL*V(I+3)
+      END DO
+
+*  To RA,Dec
+      CALL slDC2S(V,RA,DEC)
+      RA=slDA2P(RA)
+
+*  Angular diameter (radians)
+      DIAM=2D0*ASIN(EQRAU(IP)/(R*AUKM))
+
+      END
diff --git a/math/slalib/read.me b/math/slalib/read.me
new file mode 100644
index 00000000..0b216cb6
--- /dev/null
+++ b/math/slalib/read.me
@@ -0,0 +1,443 @@
+READ.ME
+
+Revision date 14 June 2005                         SLALIB Version 2.5-2
+
+-----------------------------------------------------------------------
+
+FILES IN THE ORIGINAL SOURCE DIRECTORY (UNIX)
+
+   read.me           this file
+   *.f               Fortran source (separate modules)
+   *.vax             Fortran source for VAX/VMS
+   *.cnvx            Fortran source for Convex
+   *.mips            Fortran source for DECstation
+   *.sun4            Fortran source for Sun SPARCstation
+   *.lnx             Fortran source for Linux
+   *.pcm             Microsoft Fortran source for PC
+   *.c               C functions needed for Linux version
+   sla.news          NEWS item for latest release
+   make_file         Unix make file
+   mk                C-shell script to run make
+   sun67.tex         document
+
+-----------------------------------------------------------------------
+
+    Copyright (C) 1995-2005 Rutherford Appleton Laboratory
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
+
+
+-----------------------------------------------------------------------
+
+PORTING FORTRAN SLALIB TO OTHER SYSTEMS
+
+FORTRAN SLALIB runs on VAX (VMS), PC (Linux+f2c), PC (Microsoft FORTRAN),
+Convex (ConvexOS), DECstation (Ultrix), DEC Alpha (OSF-1) and Sun
+SPARCstation (SunOS and Solaris).
+
+For most platforms, the required changes are confined to these routines:
+
+    sla_GRESID
+    sla_RANDOM
+    sla_WAIT
+
+VAX, CONVEX, DECSTATION/ALPHA, SUN & PC
+
+Versions suitable for the above platforms are supplied in the
+development directory as *.vax, *,cnvx, *.mips, *.sun4, *.pcm and
+*.lnx respectively.
+
+
+-----------------------------------------------------------------------
+
+LATEST RELEASE INFORMATION
+
+The latest release of SLALIB includes the following changes (most recent
+at the end):
+
+*  In sla_RCC, the topocentric term of coefficient 1.3184D-10 sec
+   had the wrong sign.  Minus is correct.
+
+*  The IAU decided in 1991 to rename the Terrestrial Dynamical
+   Time, TDT, which is now called "Terrestrial Time" or TT.
+   Appropriate changes have been made in the SLALIB documentation.
+   The same IAU resolutions introduced the timescales TCG and TCB;
+   there are at present no SLALIB routines to handle these new
+   timescales.
+
+*  The Keck 1 Telescope has been added to sla_OBS.
+
+*  The handling of the random-number seed in the PC versions of
+   sla_RANDOM and sla_GRESID was flawed and has been improved.
+
+*  The UTC leap second at the end of June 1993 has been added to the
+   routine sla_DAT.  Existing applications which call sla_DAT or
+   sla_DTT require relinking.
+
+*  Some unnecessary code in sla_AMPQK has been removed.
+
+*  Minor reorganization of the sla_REFRO code has led to an improvement
+   in speed of about 20%, and precautions have been taken against
+   potential arithmetic errors.
+
+*  There have been small revisions to sla_FK425 and sla_FK524.  The
+   results are not significantly affected, except in the pathological
+   case of large proper motion combined with immense distance, where
+   sla_FK524 could produce erroneous radial velocity values.  The
+   latest versions are close to the algorithms published in the 1992
+   Explanatory Supplement to the Astronomical Almanac.
+
+*  The leap second at the end of June 1994 has been added to sla_DAT.
+
+*  THE SLA_RVLSR ROUTINE HAS BEEN RETIRED.  Its place has been taken
+   by two new routines: sla_RVLSRK and sla_RVLSRD.  The original
+   sla_RVLSR had used a "kinematical" LSR.  When this was later changed
+   to a "dynamical" LSR for (what seemed liked good reasons at the time),
+   the small differences were noticed by spectral-line radio observers,
+   who had to fall back on old copies of the routine to remain consistent
+   with existing practice.  The new routines provide both sorts of LSR:
+   sla_RVLSRK uses a kinematical LSR and sla_RVLSRD uses the dynamical LSR.
+
+*  The sla_PA routine (computation of parallactic angle) used an
+   unnecessarily complicated formulation, which has been simplified.
+   The results are unaffected.
+
+*  The sla_ZD routine (computation of zenith distance) used a
+   straightforward cosine-formula-based method, which suffered from
+   decreased accuracy near the zenith.  A better, vector-derived,
+   formulation has been substituted, without materially affecting
+   the results.  Because sla_ZD is double precision, the old
+   formulation was always adequate;  however, had anyone transcribed
+   the code in single precision errors approaching 1 arcmin could
+   have resulted.  The new formulation delivers good results all
+   over the sky even in a single precision version.
+
+*  Routines have been added to transform equatorial coordinates
+   (HA,Dec) to horizon coordinates (Az,El) and back.  Single and
+   double precision are both supported.  The routines are called
+   sla_E2H, sla_DE2H, sla_H2E, sla_DH2E.
+
+*  A new routine has been added to the tangent-plane projection set.
+   The single and double precision versions are called sla_TPRD and
+   sla_DTPRD respectively.  Given the RA,Dec of a star and its
+   xi,eta coordinates, the routine determines the "plate centre".
+
+*  The existing routine sla_PREC for obtaining the precession matrix
+   uses the official IAU model and should continue to be used for
+   canonical purposes.  A new version, called sla_PRECL, uses a
+   more up-to-date model which delivers better accuracy, especially
+   over intervals of millennia.
+
+*  The routine sla_PVOBS was returning velocities in AU per sidereal
+   second rather than per UT second.  This has been corrected.  The
+   maximum error was equivalent to about 0.001 km/s.
+
+*  In sla_MAPQK and sla_MAPQKZ, the area within which the gravitional
+   light-deflection term is restrained has been extended from its
+   original 300 arcsec radius to about 920 arcsec, just inside the
+   Sun's disc.
+
+*  A chapter of explanation, with examples, has been added to SUN/67,
+   which has also undergone various cosmetic revisions.
+
+*  There were two discrepancies between the documentation of sla_DCMPF
+   (program comments and SUN/67) and the code.  The first was that the
+   formulae for the nonperpendicularity used PERP instead of PERP/2;
+   the documentation has been corrected.  The other was that the
+   documentation showed the zero point corrections being applied first,
+   whereas the code returned zero point corrections corresponding to
+   being applied last.  The code has been corrected to match the
+   documentation.
+
+*  The C module slaCldj gave incorrect answers for dates during
+   January and February.  The error, which did not affect the Fortran
+   version, has been corrected.
+
+*  THE CALLS FOR sla_TPRD AND sla_DTPRD HAS BEEN CHANGED.  An integer
+   status argument has been added;  non-zero means the supplied RA,Dec
+   and Xi,Eta describe an impossible case.  (This can only happen
+   near the pole and with non-zero Xi.)  Also, a slightly neater
+   formulation has been introduced.
+
+*  Three new routines have been added.  sla_ALTAZ takes a star's HA,Dec
+   and produces position, velocity and acceleration for azimuth,
+   elevation and parallactic angle.  sla_PDA2H predicts the HA at which
+   a given azimuth will be reached.  sla_PDQ2H does the same for
+   position angle.
+
+*  In the sla_OBS routine, the wrong sign was returned for the Perkins
+   72 inch telescope at Lowell - fixed.
+
+*  A revised model for the equation of the equinoxes has been
+   installed in sla_EQEQX, in line with recent IAU resolutions.  The
+   change amounts to less than 3 mas.
+
+*  A bug in sla_DFLTIN has been corrected.  A negative number following
+   an E- or D-format number without intervening spaces lost its sign.
+
+*  Four stations have been added to sla_OBS:
+
+     TAUTENBERG  Tautenberg 1.34 metre Schmidt
+     PALOMAR48   Palomar 48-inch Schmidt
+     UKST        UK 1.2 metre Schmidt, Siding Spring
+     KISO        Kiso 1.05 metre Schmidt, Japan
+     ESOSCHMIDT  ESO 1 metre Schmidt, La Silla
+
+*  The sla_EARTH and sla_MOON routines could give an integer divide by zero
+   for years before 1 BC.  This has been corrected.
+
+*  sla_CALYD (provided to support the sla_EARTH and sla_MOON routines)
+   has been upgraded to work outside the interval 1900 March 1 to
+   2100 February 28.  The status value indicating dates outside that
+   range has been dropped;  a new error value for year before -4711
+   has been introduced.
+
+*  A new routine, sla_CLYD, has been added.  It is a version of sla_CALYD
+   without the century-default feature and is to enable 1st-century
+   dates to be supplied to sla_EARTH and sla_MOON.
+
+*  Two new routines, sla_PLANET and sla_RDPLAN, have been added, which
+   compute approximate planetary ephemerides.
+
+*  A new routine, sla_DMOON, implements the same (Meeus) model as the
+   sla_MOON routine, but in full and in double precision.  The time
+   argument is a straightforward MJD rather than sla_MOON's year and
+   day-in-year.
+
+*  The sla_REFRO code has been speeded up by a factor of two (and is
+   also clearer).
+
+*  sla_REFV and sla_REFZ have, in different ways, been made more accurate
+   for cases close to the horizon.  The improvement to sla_REFV is
+   relatively modest, but sla_REFZ is now capable of delivering useful
+   results for rise/set phenomena.
+
+*  sla_AOPQK has been speeded up for low-elevation cases.
+
+*  Versions of the tangent-plane routines working directly in x,y,z
+   instead of spherical coordinates have been added.  They may be
+   faster in some applications.  The routines are sla_DV2TP, sla_V2TP,
+   sla_DTP2V, sla_TP2V, sla_DTPXYZ, sla_TPXYZ.
+
+*  The coordinates of the Australia Telescope Compact Array have been
+   added to sla_OBS.  The name is 'ATCA'.
+
+*  Despite their recent introduction THE ROUTINES sla_DTPRD, sla_DTPXYZ,
+   sla_TPRD AND sla_TPXYZ HAVE BEEN WITHDRAWN.  They have been replaced
+   by the new routines sla_DTPS2C, sla_DTPV2C, sla_TPS2C and sla_TPV2C.
+   These are functionally equivalent to the earlier routines but return
+   two solutions instead of one:  the second solution can arise near a
+   pole.
+
+*  The UTC leap second at the end of 1995 has been added to sla_DAT.
+
+*  The refraction routine sla_REFRO has been extensively revised.  The
+   principal motivation was to improve the radio predictions by
+   introducing better humidity models.  The models previously in
+   use had been entirely adequate for the optical case, for which
+   they had been devised, but improved models were required for
+   the radio case.  None of the changes significantly affects the
+   optical results with respect to the earlier version of the sla_REFRO
+   routine.  For example, at 70 deg zenith distance the new version
+   agrees with the old version to better than 0.05 arcsec for any
+   reasonable combination of parameters.  However, the improved
+   water-vapour expressions do make a significant difference in the
+   radio band, at 70 deg zenith distance reaching almost 4 arcsec
+   for a hot, humid, low-altitude site during a period of low pressure.
+
+*  There was a bug in slaRdplan, the (private) C version of sla_RDPLAN.
+   The answers were unaffected but there could be floating-point
+   problems on some platforms.
+
+*  A new routine has been added, sla_GMSTA.  This gives greater numerical
+   precision than the existing GMST function by allowing the date and
+   time to be specified separately rather than as a single MJD.
+
+*  Measures taken in sla_MAPQK to avoid trouble when processing Solar
+   positions had not been carried through into sla_MAPQKZ.  The two
+   routines now use the same strategy.
+
+*  In sla_REFRO, at zenith distances well beyond 90 deg and under some
+   conditions, it was possible to encounter arithmetic errors due to
+   failure of the tropospheric model-atmosphere to deliver sensible
+   temperatures.  This is inherent in the published algorithm.  To
+   avoid the problem, the temperature delivered by the model has been
+   constrained to the range 200 to 320 deg K.
+
+*  A new routine has been added, sla_ATMDSP, for rapidly recalculating
+   the A,B refraction coefficients for different wavelengths.
+
+*  The first UTC leap-second date in the sla_DAT routine was one day early.
+   This will have had no effect on the results for more recent epochs.
+
+*  slaObs, the C version of sla_OBS, had some problems related to character
+   string handling.  A call using the "number" option retured an invalid
+   station ID, and station ID and name strings of the stipulated 10
+   and 40 character lengths were improperly terminated.
+
+*  A new routine, sla_POLMO has been added.  This is a specialist tool
+   to do with Earth polar motion.
+
+*  sla_DC62S and sla_CC62S could give floating point errors if vectors in
+   unlikely units were supplied.  The handling of difficult cases  has
+   been improved.
+
+*  Support for Linux has been added.
+
+*  slaRefreo, the C version of sla_REFRO, was not re-entrant.  It is now;
+   there has been a small (4%) speed penalty.
+
+*  The C routines slaRandom, slaGresid and slaWait have been dropped.
+   They could not easily be made re-entrant and posed perennial platform-
+   dependency problems.
+
+*  The value for the arcsec to radians factor in several routines
+   had an incorrect (and superfluous) 19th digit, which has been
+   removed.
+
+*  There was a minor bug in sla_DV2TP and sla_V2TP, to do with protection
+   against the special case where the tangent point is the pole.
+
+*  In sla_OBS, the position of the Parkes radiotelescope has been revised,
+   and the ATNF Mopra observatory has been added.
+
+*  Two new routines have been added.  sla_PAV (single precision) and
+   sla_DPAV (double precision) are like sla_BEAR and sla_DBEAR but start
+   with direction cosines rather than spherical coordinates - they return
+   the position angle of one point with respect to the other.
+
+*  slaRefro, the C version of sla_REFRO, still wasn't re-entrant, but is
+   now.
+
+*  slaDtf2d, the C version of sla_DTF2D, used to accept 60.0 in the seconds
+   field;  this has been corrected.
+
+*  The sla_PLANET and sla_RDPLAN routines now include Pluto.  The ephemeris
+   is accurate (sub-arcsecond) but covers the 20th and 21st centuries
+   only.
+
+   !!!  IMPORTANT NOTE  !!!
+
+   sla_RDPLAN used to interpret any planet number outside the range 1-8
+   as meaning the Sun.  The new version uses planet number 9.  Existing
+   programs using 9 for the Sun should be changed to use 0.  The rule
+   has not been changed, except that the range is now 1-9 instead of
+   1-8, as it is unlikely that the equivalent problem will arise in the
+   future.
+
+*  Two new routines have been added, sla_PLANEL and sla_PLANTE.  They are
+   analogues of sla_PLANET and sla_RDPLAN but for the case where orbital
+   elements are available.  They can be used for predicting the
+   positions of asteroids and comets, and, if up-to-date osculating
+   elements are supplied, more accurate positions for the major
+   planets than can be provided through the sla_PLANET and sla_RDPLAN
+   routines.
+
+*  The sla_REFRO routine could give inaccurate results for low temperatures
+   (subzero C).  This was caused by over-cautious defensive programming,
+   which prevented the tropospheric temperature falling below 200 K.
+
+*  A new routine has been added, sla_REFCOQ.  This calculates the coefficients
+   of a two-term refraction model.  It complements the existing sla_REFCO
+   routine, being much faster at the expense of some accuracy.
+
+*  The 1997 July 1 UTC leap second has been added to the sla_DAT routine.
+
+*  A bug in slaSvd, the C version of sla_SVD, caused occasional false
+   indications of ill-conditioning.  The results of least-squares
+   fits do not seem to have been affected.  The Fortran version did not
+   have the bug.
+
+*  The Subaru telescope (Japanese National 8-metre telescope, Mauna Kea)
+   has been added to the sla_OBS routine.
+
+*  The sla_DAT routine has been extended back to the inception of UTC in
+   1960.
+
+*  The "earliest date possible" in DJCL sla_was two days out (disagreeing
+   with sla_DJCAL, which had the correct value).
+
+*  The sla_GMSTA code has been improved.
+
+*  A new routine, sla_PV2EL, takes a heliocentric J2000 equatorial position
+   and velocity and produces the equivalent set of osculating elements.
+
+*  The 1999 January 1 UTC leap second has been added to the sla_DAT routine.
+
+*  Four new routines have been introduced which transform between the
+   FK5 system and the ICRS (Hipparcos) system.  sla_FK52H and sla_H2FK5
+   transform star positions and proper motions from FK5 coordinates to
+   Hipparcos coordinates and vice versa.  sla_FK5HZ and sla_HFK5Z do the
+   same but for the case where the Hipparcos proper motions are zero.
+
+*  Six new routines have been introduced for dealing with orbital elements.
+   Four of them (sla_EL2UE, sla_PV2UE, sla_UE2EL and sla_UE2PV) provide
+   applications with direct access to the "universal variables" method
+   that was already being used internally.  Compared with using conventional
+   (angular) elements and solving Kepler's equation, the universal variables
+   approach has a number of advantages, including better handling of near-
+   parabolic orbits and greater efficiency.  The remaining two routines
+   (sla_PERTEL and sla_PERTUE) generate updated elements by applying
+   major-planet perturbations.  The new elements can then be used to
+   predict positions that are much more accurate.  For minor planets,
+   sub-arcsecond accuracy over a decade is achievable.
+
+*  Several observatory sites have been added to the OBS routine:  CFHT,
+   Keck 2, Gemini North, FCRAO, IRTF and CSO.  The coordinates for all
+   the Mauna Kea sites have been updated in accordance with recent aerial
+   photography results made available by the Institute for Astronomy,
+   University of Hawaii.
+
+*  A bug in sla_DAT has been corrected.  It used to give incorrect
+   results for dates in the first 54 days of 1972.
+
+*  There are new routines for generating permutations (sla_PERMUT) and
+   combinations (sla_COMBN).
+ 
+*  There was a bug in sla_PM for star data using Julian epochs (i.e. all
+   modern data).  The treatment of radial velocity was correct for
+   Besselian epochs but wrong for Julian epochs.  This had only a tiny
+   effect on a handful of nearby stars.  The new version assumes Julian
+   epochs when interpreting the radial velocity.  If the data are old-
+   style, using Besselian epochs, you have to scale the radial velocity
+   by 365.2422/365.25 first.
+
+*  There was a bug in sla_RCC which meant the diurnal terms were being
+   calculated incorrectly, leading to errors of up to about 4 microsec.
+
+*  Two new routines have been added, sla_DSEPV and sla_SEPV.  These are
+   analogues of the existing routines sla_DSEP and sla_SEP, but accept
+   [x,y,z] vectors instead of spherical coordinates.
+
+*  The sla_UNPCD routine used to be approximate but now is rigorous.
+
+*  The four VLTs and Gemini South have been added to sla_OBS.
+
+*  An additional Earth position/velocity routine, sla_EPV, has been
+   added.  It is bigger and slower than sla_EVP but much more accurate.
+   Position accuracy is a few km;  velocity accuracy is a few mm/s.
+   The sla_PERTUE and sla_PLANTU routines now call this routine in
+   order to deliver better predictions for near-Earth objects.
+
+*  There was a bug in sla_DSEPV.  For the unique case of two precisely
+   antipodal vectors zero was returned instead of pi.
+
+-----------------------------------------------------------------------
+
+
+ P.T.Wallace
+
+ ptw@star.rl.ac.uk
+ +44-1235-44-5372
diff --git a/math/slalib/refco.f b/math/slalib/refco.f
new file mode 100644
index 00000000..f03a30fa
--- /dev/null
+++ b/math/slalib/refco.f
@@ -0,0 +1,88 @@
+      SUBROUTINE slRFCO ( HM, TDK, PMB, RH, WL, PHI, TLR, EPS,
+     :                       REFA, REFB )
+*+
+*     - - - - - -
+*      R F C O
+*     - - - - - -
+*
+*  Determine the constants A and B in the atmospheric refraction
+*  model dZ = A tan Z + B tan**3 Z.
+*
+*  Z is the "observed" zenith distance (i.e. affected by refraction)
+*  and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo)
+*  zenith distance.
+*
+*  Given:
+*    HM      d     height of the observer above sea level (metre)
+*    TDK     d     ambient temperature at the observer (K)
+*    PMB     d     pressure at the observer (millibar)
+*    RH      d     relative humidity at the observer (range 0-1)
+*    WL      d     effective wavelength of the source (micrometre)
+*    PHI     d     latitude of the observer (radian, astronomical)
+*    TLR     d     temperature lapse rate in the troposphere (K/metre)
+*    EPS     d     precision required to terminate iteration (radian)
+*
+*  Returned:
+*    REFA    d     tan Z coefficient (radian)
+*    REFB    d     tan**3 Z coefficient (radian)
+*
+*  Called:  slRFRO
+*
+*  Notes:
+*
+*  1  Typical values for the TLR and EPS arguments might be 0.0065D0 and
+*     1D-10 respectively.
+*
+*  2  The radio refraction is chosen by specifying WL > 100 micrometres.
+*
+*  3  The routine is a slower but more accurate alternative to the
+*     slRFCQ routine.  The constants it produces give perfect
+*     agreement with slRFRO at zenith distances arctan(1) (45 deg)
+*     and arctan(4) (about 76 deg).  It achieves 0.5 arcsec accuracy
+*     for ZD < 80 deg, 0.01 arcsec accuracy for ZD < 60 deg, and
+*     0.001 arcsec accuracy for ZD < 45 deg.
+*
+*  P.T.Wallace   Starlink   22 May 2004
+*
+*  Copyright (C) 2004 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION HM,TDK,PMB,RH,WL,PHI,TLR,EPS,REFA,REFB
+
+      DOUBLE PRECISION ATN1,ATN4,R1,R2
+
+*  Sample zenith distances: arctan(1) and arctan(4)
+      PARAMETER (ATN1=0.7853981633974483D0,
+     :           ATN4=1.325817663668033D0)
+
+
+
+*  Determine refraction for the two sample zenith distances
+      CALL slRFRO(ATN1,HM,TDK,PMB,RH,WL,PHI,TLR,EPS,R1)
+      CALL slRFRO(ATN4,HM,TDK,PMB,RH,WL,PHI,TLR,EPS,R2)
+
+*  Solve for refraction constants
+      REFA = (64D0*R1-R2)/60D0
+      REFB = (R2-4D0*R1)/60D0
+
+      END
diff --git a/math/slalib/refcoq.f b/math/slalib/refcoq.f
new file mode 100644
index 00000000..76e40341
--- /dev/null
+++ b/math/slalib/refcoq.f
@@ -0,0 +1,227 @@
+      SUBROUTINE slRFCQ ( TDK, PMB, RH, WL, REFA, REFB )
+*+
+*     - - - - - - -
+*      R F C Q
+*     - - - - - - -
+*
+*  Determine the constants A and B in the atmospheric refraction
+*  model dZ = A tan Z + B tan**3 Z.  This is a fast alternative
+*  to the slRFCO routine - see notes.
+*
+*  Z is the "observed" zenith distance (i.e. affected by refraction)
+*  and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo)
+*  zenith distance.
+*
+*  Given:
+*    TDK      d      ambient temperature at the observer (K)
+*    PMB      d      pressure at the observer (millibar)
+*    RH       d      relative humidity at the observer (range 0-1)
+*    WL       d      effective wavelength of the source (micrometre)
+*
+*  Returned:
+*    REFA     d      tan Z coefficient (radian)
+*    REFB     d      tan**3 Z coefficient (radian)
+*
+*  The radio refraction is chosen by specifying WL > 100 micrometres.
+*
+*  Notes:
+*
+*  1  The model is an approximation, for moderate zenith distances,
+*     to the predictions of the slRFRO routine.  The approximation
+*     is maintained across a range of conditions, and applies to
+*     both optical/IR and radio.
+*
+*  2  The algorithm is a fast alternative to the slRFCO routine.
+*     The latter calls the slRFRO routine itself:  this involves
+*     integrations through a model atmosphere, and is costly in
+*     processor time.  However, the model which is produced is precisely
+*     correct for two zenith distance (45 degrees and about 76 degrees)
+*     and at other zenith distances is limited in accuracy only by the
+*     A tan Z + B tan**3 Z formulation itself.  The present routine
+*     is not as accurate, though it satisfies most practical
+*     requirements.
+*
+*  3  The model omits the effects of (i) height above sea level (apart
+*     from the reduced pressure itself), (ii) latitude (i.e. the
+*     flattening of the Earth) and (iii) variations in tropospheric
+*     lapse rate.
+*
+*     The model was tested using the following range of conditions:
+*
+*       lapse rates 0.0055, 0.0065, 0.0075 K/metre
+*       latitudes 0, 25, 50, 75 degrees
+*       heights 0, 2500, 5000 metres ASL
+*       pressures mean for height -10% to +5% in steps of 5%
+*       temperatures -10 deg to +20 deg with respect to 280 deg at SL
+*       relative humidity 0, 0.5, 1
+*       wavelengths 0.4, 0.6, ... 2 micron, + radio
+*       zenith distances 15, 45, 75 degrees
+*
+*     The accuracy with respect to direct use of the slRFRO routine
+*     was as follows:
+*
+*                            worst         RMS
+*
+*       optical/IR           62 mas       8 mas
+*       radio               319 mas      49 mas
+*
+*     For this particular set of conditions:
+*
+*       lapse rate 0.0065 K/metre
+*       latitude 50 degrees
+*       sea level
+*       pressure 1005 mb
+*       temperature 280.15 K
+*       humidity 80%
+*       wavelength 5740 Angstroms
+*
+*     the results were as follows:
+*
+*       ZD        slRFRO   slRFCQ  Saastamoinen
+*
+*       10         10.27        10.27        10.27
+*       20         21.19        21.20        21.19
+*       30         33.61        33.61        33.60
+*       40         48.82        48.83        48.81
+*       45         58.16        58.18        58.16
+*       50         69.28        69.30        69.27
+*       55         82.97        82.99        82.95
+*       60        100.51       100.54       100.50
+*       65        124.23       124.26       124.20
+*       70        158.63       158.68       158.61
+*       72        177.32       177.37       177.31
+*       74        200.35       200.38       200.32
+*       76        229.45       229.43       229.42
+*       78        267.44       267.29       267.41
+*       80        319.13       318.55       319.10
+*
+*      deg        arcsec       arcsec       arcsec
+*
+*     The values for Saastamoinen's formula (which includes terms
+*     up to tan^5) are taken from Hohenkerk and Sinclair (1985).
+*
+*     The results from the much slower but more accurate slRFCO
+*     routine have not been included in the tabulation as they are
+*     identical to those in the slRFRO column to the 0.01 arcsec
+*     resolution used.
+*
+*  4  Outlandish input parameters are silently limited to mathematically
+*     safe values.  Zero pressure is permissible, and causes zeroes to
+*     be returned.
+*
+*  5  The algorithm draws on several sources, as follows:
+*
+*     a) The formula for the saturation vapour pressure of water as
+*        a function of temperature and temperature is taken from
+*        expressions A4.5-A4.7 of Gill (1982).
+*
+*     b) The formula for the water vapour pressure, given the
+*        saturation pressure and the relative humidity, is from
+*        Crane (1976), expression 2.5.5.
+*
+*     c) The refractivity of air is a function of temperature,
+*        total pressure, water-vapour pressure and, in the case
+*        of optical/IR but not radio, wavelength.  The formulae
+*        for the two cases are developed from Hohenkerk & Sinclair
+*        (1985) and Rueger (2002).
+*
+*     The above three items are as used in the slRFRO routine.
+*
+*     d) The formula for beta, the ratio of the scale height of the
+*        atmosphere to the geocentric distance of the observer, is
+*        an adaption of expression 9 from Stone (1996).  The
+*        adaptations, arrived at empirically, consist of (i) a
+*        small adjustment to the coefficient and (ii) a humidity
+*        term for the radio case only.
+*
+*     e) The formulae for the refraction constants as a function of
+*        n-1 and beta are from Green (1987), expression 4.31.
+*
+*  References:
+*
+*     Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral
+*     Atmosphere", Methods of Experimental Physics: Astrophysics 12B,
+*     Academic Press, 1976.
+*
+*     Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press, 1982.
+*
+*     Green, R.M., "Spherical Astronomy", Cambridge University Press, 1987.
+*
+*     Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63, 1985.
+*
+*     Rueger, J.M., "Refractive Index Formulae for Electronic Distance
+*     Measurement with Radio and Millimetre Waves", in Unisurv Report
+*     S-68, School of Surveying and Spatial Information Systems,
+*     University of New South Wales, Sydney, Australia, 2002.
+*
+*     Stone, Ronald C., P.A.S.P. 108 1051-1058, 1996.
+*
+*  Last revision:   2 December 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION TDK,PMB,RH,WL,REFA,REFB
+
+      LOGICAL OPTIC
+      DOUBLE PRECISION T,P,R,W,TDC,PS,PW,WLSQ,GAMMA,BETA
+
+
+
+*  Decide whether optical/IR or radio case:  switch at 100 microns.
+      OPTIC = WL.LE.100D0
+
+*  Restrict parameters to safe values.
+      T = MIN(MAX(TDK,100D0),500D0)
+      P = MIN(MAX(PMB,0D0),10000D0)
+      R = MIN(MAX(RH,0D0),1D0)
+      W = MIN(MAX(WL,0.1D0),1D6)
+
+*  Water vapour pressure at the observer.
+      IF (P.GT.0D0) THEN
+         TDC = T-273.15D0
+         PS = 10D0**((0.7859D0+0.03477D0*TDC)/(1D0+0.00412D0*TDC))*
+     :                                    (1D0+P*(4.5D-6+6D-10*TDC*TDC))
+         PW = R*PS/(1D0-(1D0-R)*PS/P)
+      ELSE
+         PW = 0D0
+      END IF
+
+*  Refractive index minus 1 at the observer.
+      IF (OPTIC) THEN
+         WLSQ = W*W
+         GAMMA = ((77.53484D-6+(4.39108D-7+3.666D-9/WLSQ)/WLSQ)*P
+     :                                                 -11.2684D-6*PW)/T
+      ELSE
+         GAMMA = (77.6890D-6*P-(6.3938D-6-0.375463D0/T)*PW)/T
+      END IF
+
+*  Formula for beta adapted from Stone, with empirical adjustments.
+      BETA=4.4474D-6*T
+      IF (.NOT.OPTIC) BETA=BETA-0.0074D0*PW*BETA
+
+*  Refraction constants from Green.
+      REFA = GAMMA*(1D0-BETA)
+      REFB = -GAMMA*(BETA-GAMMA/2D0)
+
+      END
diff --git a/math/slalib/refro.f b/math/slalib/refro.f
new file mode 100644
index 00000000..3a93264e
--- /dev/null
+++ b/math/slalib/refro.f
@@ -0,0 +1,402 @@
+      SUBROUTINE slRFRO ( ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR,
+     :                       EPS, REF )
+*+
+*     - - - - - -
+*      R F R O
+*     - - - - - -
+*
+*  Atmospheric refraction for radio and optical/IR wavelengths.
+*
+*  Given:
+*    ZOBS    d  observed zenith distance of the source (radian)
+*    HM      d  height of the observer above sea level (metre)
+*    TDK     d  ambient temperature at the observer (K)
+*    PMB     d  pressure at the observer (millibar)
+*    RH      d  relative humidity at the observer (range 0-1)
+*    WL      d  effective wavelength of the source (micrometre)
+*    PHI     d  latitude of the observer (radian, astronomical)
+*    TLR     d  temperature lapse rate in the troposphere (K/metre)
+*    EPS     d  precision required to terminate iteration (radian)
+*
+*  Returned:
+*    REF     d  refraction: in vacuo ZD minus observed ZD (radian)
+*
+*  Notes:
+*
+*  1  A suggested value for the TLR argument is 0.0065D0.  The
+*     refraction is significantly affected by TLR, and if studies
+*     of the local atmosphere have been carried out a better TLR
+*     value may be available.  The sign of the supplied TLR value
+*     is ignored.
+*
+*  2  A suggested value for the EPS argument is 1D-8.  The result is
+*     usually at least two orders of magnitude more computationally
+*     precise than the supplied EPS value.
+*
+*  3  The routine computes the refraction for zenith distances up
+*     to and a little beyond 90 deg using the method of Hohenkerk
+*     and Sinclair (NAO Technical Notes 59 and 63, subsequently adopted
+*     in the Explanatory Supplement, 1992 edition - see section 3.281).
+*
+*  4  The code is a development of the optical/IR refraction subroutine
+*     AREF of C.Hohenkerk (HMNAO, September 1984), with extensions to
+*     support the radio case.  Apart from merely cosmetic changes, the
+*     following modifications to the original HMNAO optical/IR refraction
+*     code have been made:
+*
+*     .  The angle arguments have been changed to radians.
+*
+*     .  Any value of ZOBS is allowed (see note 6, below).
+*
+*     .  Other argument values have been limited to safe values.
+*
+*     .  Murray's values for the gas constants have been used
+*        (Vectorial Astrometry, Adam Hilger, 1983).
+*
+*     .  The numerical integration phase has been rearranged for
+*        extra clarity.
+*
+*     .  A better model for Ps(T) has been adopted (taken from
+*        Gill, Atmosphere-Ocean Dynamics, Academic Press, 1982).
+*
+*     .  More accurate expressions for Pwo have been adopted
+*        (again from Gill 1982).
+*
+*     .  The formula for the water vapour pressure, given the
+*        saturation pressure and the relative humidity, is from
+*        Crane (1976), expression 2.5.5.
+*
+*     .  Provision for radio wavelengths has been added using
+*        expressions devised by A.T.Sinclair, RGO (private
+*        communication 1989).  The refractivity model currently
+*        used is from J.M.Rueger, "Refractive Index Formulae for
+*        Electronic Distance Measurement with Radio and Millimetre
+*        Waves", in Unisurv Report S-68 (2002), School of Surveying
+*        and Spatial Information Systems, University of New South
+*        Wales, Sydney, Australia.
+*
+*     .  The optical refractivity for dry air is from Resolution 3 of
+*        the International Association of Geodesy adopted at the XXIIth
+*        General Assembly in Birmingham, UK, 1999.
+*
+*     .  Various small changes have been made to gain speed.
+*
+*  5  The radio refraction is chosen by specifying WL > 100 micrometres.
+*     Because the algorithm takes no account of the ionosphere, the
+*     accuracy deteriorates at low frequencies, below about 30 MHz.
+*
+*  6  Before use, the value of ZOBS is expressed in the range +/- pi.
+*     If this ranged ZOBS is -ve, the result REF is computed from its
+*     absolute value before being made -ve to match.  In addition, if
+*     it has an absolute value greater than 93 deg, a fixed REF value
+*     equal to the result for ZOBS = 93 deg is returned, appropriately
+*     signed.
+*
+*  7  As in the original Hohenkerk and Sinclair algorithm, fixed values
+*     of the water vapour polytrope exponent, the height of the
+*     tropopause, and the height at which refraction is negligible are
+*     used.
+*
+*  8  The radio refraction has been tested against work done by
+*     Iain Coulson, JACH, (private communication 1995) for the
+*     James Clerk Maxwell Telescope, Mauna Kea.  For typical conditions,
+*     agreement at the 0.1 arcsec level is achieved for moderate ZD,
+*     worsening to perhaps 0.5-1.0 arcsec at ZD 80 deg.  At hot and
+*     humid sea-level sites the accuracy will not be as good.
+*
+*  9  It should be noted that the relative humidity RH is formally
+*     defined in terms of "mixing ratio" rather than pressures or
+*     densities as is often stated.  It is the mass of water per unit
+*     mass of dry air divided by that for saturated air at the same
+*     temperature and pressure (see Gill 1982).
+*
+*  10 The algorithm is designed for observers in the troposphere.  The
+*     supplied temperature, pressure and lapse rate are assumed to be
+*     for a point in the troposphere and are used to define a model
+*     atmosphere with the tropopause at 11km altitude and a constant
+*     temperature above that.  However, in practice, the refraction
+*     values returned for stratospheric observers, at altitudes up to
+*     25km, are quite usable.
+*
+*  Called:  slDA1P, slATMT, slATMS
+*
+*  Last revision:   5 December 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION ZOBS,HM,TDK,PMB,RH,WL,PHI,TLR,EPS,REF
+
+*
+*  Fixed parameters
+*
+      DOUBLE PRECISION D93,GCR,DMD,DMW,S,DELTA,HT,HS
+      INTEGER ISMAX
+*  93 degrees in radians
+      PARAMETER (D93=1.623156204D0)
+*  Universal gas constant
+      PARAMETER (GCR=8314.32D0)
+*  Molecular weight of dry air
+      PARAMETER (DMD=28.9644D0)
+*  Molecular weight of water vapour
+      PARAMETER (DMW=18.0152D0)
+*  Mean Earth radius (metre)
+      PARAMETER (S=6378120D0)
+*  Exponent of temperature dependence of water vapour pressure
+      PARAMETER (DELTA=18.36D0)
+*  Height of tropopause (metre)
+      PARAMETER (HT=11000D0)
+*  Upper limit for refractive effects (metre)
+      PARAMETER (HS=80000D0)
+*  Numerical integration: maximum number of strips.
+      PARAMETER (ISMAX=16384)
+
+      INTEGER IS,K,N,I,J
+      LOGICAL OPTIC,LOOP
+      DOUBLE PRECISION ZOBS1,ZOBS2,HMOK,TDKOK,PMBOK,RHOK,WLOK,ALPHA,
+     :                 TOL,WLSQ,GB,A,GAMAL,GAMMA,GAMM2,DELM2,
+     :                 TDC,PSAT,PWO,W,
+     :                 C1,C2,C3,C4,C5,C6,R0,TEMPO,DN0,RDNDR0,SK0,F0,
+     :                 RT,TT,DNT,RDNDRT,SINE,ZT,FT,DNTS,RDNDRP,ZTS,FTS,
+     :                 RS,DNS,RDNDRS,ZS,FS,REFOLD,Z0,ZRANGE,FB,FF,FO,FE,
+     :                 H,R,SZ,RG,DR,TG,DN,RDNDR,T,F,REFP,REFT
+
+      DOUBLE PRECISION slDA1P
+
+*  The refraction integrand
+      DOUBLE PRECISION REFI
+      REFI(DN,RDNDR) = RDNDR/(DN+RDNDR)
+
+
+
+*  Transform ZOBS into the normal range.
+      ZOBS1 = slDA1P(ZOBS)
+      ZOBS2 = MIN(ABS(ZOBS1),D93)
+
+*  Keep other arguments within safe bounds.
+      HMOK = MIN(MAX(HM,-1D3),HS)
+      TDKOK = MIN(MAX(TDK,100D0),500D0)
+      PMBOK = MIN(MAX(PMB,0D0),10000D0)
+      RHOK = MIN(MAX(RH,0D0),1D0)
+      WLOK = MAX(WL,0.1D0)
+      ALPHA = MIN(MAX(ABS(TLR),0.001D0),0.01D0)
+
+*  Tolerance for iteration.
+      TOL = MIN(MAX(ABS(EPS),1D-12),0.1D0)/2D0
+
+*  Decide whether optical/IR or radio case - switch at 100 microns.
+      OPTIC = WLOK.LE.100D0
+
+*  Set up model atmosphere parameters defined at the observer.
+      WLSQ = WLOK*WLOK
+      GB = 9.784D0*(1D0-0.0026D0*COS(PHI+PHI)-0.00000028D0*HMOK)
+      IF (OPTIC) THEN
+         A = (287.6155D0+(1.62887D0+0.01360D0/WLSQ)/WLSQ)
+     :                                              *273.15D-6/1013.25D0
+      ELSE
+         A = 77.6890D-6
+      END IF
+      GAMAL = (GB*DMD)/GCR
+      GAMMA = GAMAL/ALPHA
+      GAMM2 = GAMMA-2D0
+      DELM2 = DELTA-2D0
+      TDC = TDKOK-273.15D0
+      PSAT = 10D0**((0.7859D0+0.03477D0*TDC)/(1D0+0.00412D0*TDC))*
+     :                                (1D0+PMBOK*(4.5D-6+6D-10*TDC*TDC))
+      IF (PMBOK.GT.0D0) THEN
+         PWO = RHOK*PSAT/(1D0-(1D0-RHOK)*PSAT/PMBOK)
+      ELSE
+         PWO = 0D0
+      END IF
+      W = PWO*(1D0-DMW/DMD)*GAMMA/(DELTA-GAMMA)
+      C1 = A*(PMBOK+W)/TDKOK
+      IF (OPTIC) THEN
+         C2 = (A*W+11.2684D-6*PWO)/TDKOK
+      ELSE
+         C2 = (A*W+6.3938D-6*PWO)/TDKOK
+      END IF
+      C3 = (GAMMA-1D0)*ALPHA*C1/TDKOK
+      C4 = (DELTA-1D0)*ALPHA*C2/TDKOK
+      IF (OPTIC) THEN
+         C5 = 0D0
+         C6 = 0D0
+      ELSE
+         C5 = 375463D-6*PWO/TDKOK
+         C6 = C5*DELM2*ALPHA/(TDKOK*TDKOK)
+      END IF
+
+*  Conditions at the observer.
+      R0 = S+HMOK
+      CALL slATMT(R0,TDKOK,ALPHA,GAMM2,DELM2,C1,C2,C3,C4,C5,C6,
+     :                                              R0,TEMPO,DN0,RDNDR0)
+      SK0 = DN0*R0*SIN(ZOBS2)
+      F0 = REFI(DN0,RDNDR0)
+
+*  Conditions in the troposphere at the tropopause.
+      RT = S+MAX(HT,HMOK)
+      CALL slATMT(R0,TDKOK,ALPHA,GAMM2,DELM2,C1,C2,C3,C4,C5,C6,
+     :                                                 RT,TT,DNT,RDNDRT)
+      SINE = SK0/(RT*DNT)
+      ZT = ATAN2(SINE,SQRT(MAX(1D0-SINE*SINE,0D0)))
+      FT = REFI(DNT,RDNDRT)
+
+*  Conditions in the stratosphere at the tropopause.
+      CALL slATMS(RT,TT,DNT,GAMAL,RT,DNTS,RDNDRP)
+      SINE = SK0/(RT*DNTS)
+      ZTS = ATAN2(SINE,SQRT(MAX(1D0-SINE*SINE,0D0)))
+      FTS = REFI(DNTS,RDNDRP)
+
+*  Conditions at the stratosphere limit.
+      RS = S+HS
+      CALL slATMS(RT,TT,DNT,GAMAL,RS,DNS,RDNDRS)
+      SINE = SK0/(RS*DNS)
+      ZS = ATAN2(SINE,SQRT(MAX(1D0-SINE*SINE,0D0)))
+      FS = REFI(DNS,RDNDRS)
+
+*  Variable initialization to avoid compiler warning.
+      REFT = 0D0
+
+*  Integrate the refraction integral in two parts;  first in the
+*  troposphere (K=1), then in the stratosphere (K=2).
+
+      DO K = 1,2
+
+*     Initialize previous refraction to ensure at least two iterations.
+         REFOLD = 1D0
+
+*     Start off with 8 strips.
+         IS = 8
+
+*     Start Z, Z range, and start and end values.
+         IF (K.EQ.1) THEN
+            Z0 = ZOBS2
+            ZRANGE = ZT-Z0
+            FB = F0
+            FF = FT
+         ELSE
+            Z0 = ZTS
+            ZRANGE = ZS-Z0
+            FB = FTS
+            FF = FS
+         END IF
+
+*     Sums of odd and even values.
+         FO = 0D0
+         FE = 0D0
+
+*     First time through the loop we have to do every point.
+         N = 1
+
+*     Start of iteration loop (terminates at specified precision).
+         LOOP = .TRUE.
+         DO WHILE (LOOP)
+
+*        Strip width.
+            H = ZRANGE/DBLE(IS)
+
+*        Initialize distance from Earth centre for quadrature pass.
+            IF (K.EQ.1) THEN
+               R = R0
+            ELSE
+               R = RT
+            END IF
+
+*        One pass (no need to compute evens after first time).
+            DO I=1,IS-1,N
+
+*           Sine of observed zenith distance.
+               SZ = SIN(Z0+H*DBLE(I))
+
+*           Find R (to the nearest metre, maximum four iterations).
+               IF (SZ.GT.1D-20) THEN
+                  W = SK0/SZ
+                  RG = R
+                  DR = 1D6
+                  J = 0
+                  DO WHILE (ABS(DR).GT.1D0.AND.J.LT.4)
+                     J=J+1
+                     IF (K.EQ.1) THEN
+                        CALL slATMT(R0,TDKOK,ALPHA,GAMM2,DELM2,
+     :                                 C1,C2,C3,C4,C5,C6,RG,TG,DN,RDNDR)
+                     ELSE
+                        CALL slATMS(RT,TT,DNT,GAMAL,RG,DN,RDNDR)
+                     END IF
+                     DR = (RG*DN-W)/(DN+RDNDR)
+                     RG = RG-DR
+                  END DO
+                  R = RG
+               END IF
+
+*           Find the refractive index and integrand at R.
+               IF (K.EQ.1) THEN
+                  CALL slATMT(R0,TDKOK,ALPHA,GAMM2,DELM2,
+     :                                   C1,C2,C3,C4,C5,C6,R,T,DN,RDNDR)
+               ELSE
+                  CALL slATMS(RT,TT,DNT,GAMAL,R,DN,RDNDR)
+               END IF
+               F = REFI(DN,RDNDR)
+
+*           Accumulate odd and (first time only) even values.
+               IF (N.EQ.1.AND.MOD(I,2).EQ.0) THEN
+                  FE = FE+F
+               ELSE
+                  FO = FO+F
+               END IF
+            END DO
+
+*        Evaluate the integrand using Simpson's Rule.
+            REFP = H*(FB+4D0*FO+2D0*FE+FF)/3D0
+
+*        Has the required precision been achieved (or can't be)?
+            IF (ABS(REFP-REFOLD).GT.TOL.AND.IS.LT.ISMAX) THEN
+
+*           No: prepare for next iteration.
+
+*           Save current value for convergence test.
+               REFOLD = REFP
+
+*           Double the number of strips.
+               IS = IS+IS
+
+*           Sum of all current values = sum of next pass's even values.
+               FE = FE+FO
+
+*           Prepare for new odd values.
+               FO = 0D0
+
+*           Skip even values next time.
+               N = 2
+            ELSE
+
+*           Yes: save troposphere component and terminate the loop.
+               IF (K.EQ.1) REFT = REFP
+               LOOP = .FALSE.
+            END IF
+         END DO
+      END DO
+
+*  Result.
+      REF = REFT+REFP
+      IF (ZOBS1.LT.0D0) REF = -REF
+
+      END
diff --git a/math/slalib/refv.f b/math/slalib/refv.f
new file mode 100644
index 00000000..42a5f1f6
--- /dev/null
+++ b/math/slalib/refv.f
@@ -0,0 +1,129 @@
+      SUBROUTINE slREFV (VU, REFA, REFB, VR)
+*+
+*     - - - - -
+*      R E F V
+*     - - - - -
+*
+*  Adjust an unrefracted Cartesian vector to include the effect of
+*  atmospheric refraction, using the simple A tan Z + B tan**3 Z
+*  model.
+*
+*  Given:
+*    VU    dp    unrefracted position of the source (Az/El 3-vector)
+*    REFA  dp    tan Z coefficient (radian)
+*    REFB  dp    tan**3 Z coefficient (radian)
+*
+*  Returned:
+*    VR    dp    refracted position of the source (Az/El 3-vector)
+*
+*  Notes:
+*
+*  1  This routine applies the adjustment for refraction in the
+*     opposite sense to the usual one - it takes an unrefracted
+*     (in vacuo) position and produces an observed (refracted)
+*     position, whereas the A tan Z + B tan**3 Z model strictly
+*     applies to the case where an observed position is to have the
+*     refraction removed.  The unrefracted to refracted case is
+*     harder, and requires an inverted form of the text-book
+*     refraction models;  the algorithm used here is equivalent to
+*     one iteration of the Newton-Raphson method applied to the above
+*     formula.
+*
+*  2  Though optimized for speed rather than precision, the present
+*     routine achieves consistency with the refracted-to-unrefracted
+*     A tan Z + B tan**3 Z model at better than 1 microarcsecond within
+*     30 degrees of the zenith and remains within 1 milliarcsecond to
+*     beyond ZD 70 degrees.  The inherent accuracy of the model is, of
+*     course, far worse than this - see the documentation for slRFCO
+*     for more information.
+*
+*  3  At low elevations (below about 3 degrees) the refraction
+*     correction is held back to prevent arithmetic problems and
+*     wildly wrong results.  For optical/IR wavelengths, over a wide
+*     range of observer heights and corresponding temperatures and
+*     pressures, the following levels of accuracy (arcsec, worst case)
+*     are achieved, relative to numerical integration through a model
+*     atmosphere:
+*
+*              ZD    error
+*
+*              80      0.7
+*              81      1.3
+*              82      2.5
+*              83      5
+*              84     10
+*              85     20
+*              86     55
+*              87    160
+*              88    360
+*              89    640
+*              90   1100
+*              91   1700         } relevant only to
+*              92   2600         } high-elevation sites
+*
+*     The results for radio are slightly worse over most of the range,
+*     becoming significantly worse below ZD=88 and unusable beyond
+*     ZD=90.
+*
+*  4  See also the routine slREFZ, which performs the adjustment to
+*     the zenith distance rather than in Cartesian Az/El coordinates.
+*     The present routine is faster than slREFZ and, except very low down,
+*     is equally accurate for all practical purposes.  However, beyond
+*     about ZD 84 degrees slREFZ should be used, and for the utmost
+*     accuracy iterative use of slRFRO should be considered.
+*
+*  P.T.Wallace   Starlink   10 April 2004
+*
+*  Copyright (C) 2004 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION VU(3),REFA,REFB,VR(3)
+
+      DOUBLE PRECISION X,Y,Z1,Z,ZSQ,RSQ,R,WB,WT,D,CD,F
+
+
+
+*  Initial estimate = unrefracted vector
+      X = VU(1)
+      Y = VU(2)
+      Z1 = VU(3)
+
+*  Keep correction approximately constant below about 3 deg elevation
+      Z = MAX(Z1,0.05D0)
+
+*  One Newton-Raphson iteration
+      ZSQ = Z*Z
+      RSQ = X*X+Y*Y
+      R = SQRT(RSQ)
+      WB = REFB*RSQ/ZSQ
+      WT = (REFA+WB)/(1D0+(REFA+3D0*WB)*(ZSQ+RSQ)/ZSQ)
+      D = WT*R/Z
+      CD = 1D0-D*D/2D0
+      F = CD*(1D0-WT)
+
+*  Post-refraction x,y,z
+      VR(1) = X*F
+      VR(2) = Y*F
+      VR(3) = CD*(Z+D*R)+(Z1-Z)
+
+      END
diff --git a/math/slalib/refz.f b/math/slalib/refz.f
new file mode 100644
index 00000000..6bdae80f
--- /dev/null
+++ b/math/slalib/refz.f
@@ -0,0 +1,170 @@
+      SUBROUTINE slREFZ (ZU, REFA, REFB, ZR)
+*+
+*     - - - - -
+*      R E F Z
+*     - - - - -
+*
+*  Adjust an unrefracted zenith distance to include the effect of
+*  atmospheric refraction, using the simple A tan Z + B tan**3 Z
+*  model (plus special handling for large ZDs).
+*
+*  Given:
+*    ZU    dp    unrefracted zenith distance of the source (radian)
+*    REFA  dp    tan Z coefficient (radian)
+*    REFB  dp    tan**3 Z coefficient (radian)
+*
+*  Returned:
+*    ZR    dp    refracted zenith distance (radian)
+*
+*  Notes:
+*
+*  1  This routine applies the adjustment for refraction in the
+*     opposite sense to the usual one - it takes an unrefracted
+*     (in vacuo) position and produces an observed (refracted)
+*     position, whereas the A tan Z + B tan**3 Z model strictly
+*     applies to the case where an observed position is to have the
+*     refraction removed.  The unrefracted to refracted case is
+*     harder, and requires an inverted form of the text-book
+*     refraction models;  the formula used here is based on the
+*     Newton-Raphson method.  For the utmost numerical consistency
+*     with the refracted to unrefracted model, two iterations are
+*     carried out, achieving agreement at the 1D-11 arcseconds level
+*     for a ZD of 80 degrees.  The inherent accuracy of the model
+*     is, of course, far worse than this - see the documentation for
+*     slRFCO for more information.
+*
+*  2  At ZD 83 degrees, the rapidly-worsening A tan Z + B tan^3 Z
+*     model is abandoned and an empirical formula takes over.  For
+*     optical/IR wavelengths, over a wide range of observer heights and
+*     corresponding temperatures and pressures, the following levels of
+*     accuracy (arcsec, worst case) are achieved, relative to numerical
+*     integration through a model atmosphere:
+*
+*              ZR    error
+*
+*              80      0.7
+*              81      1.3
+*              82      2.4
+*              83      4.7
+*              84      6.2
+*              85      6.4
+*              86      8
+*              87     10
+*              88     15
+*              89     30
+*              90     60
+*              91    150         } relevant only to
+*              92    400         } high-elevation sites
+*
+*     For radio wavelengths the errors are typically 50% larger than
+*     the optical figures and by ZD 85 deg are twice as bad, worsening
+*     rapidly below that.  To maintain 1 arcsec accuracy down to ZD=85
+*     at the Green Bank site, Condon (2004) has suggested amplifying
+*     the amount of refraction predicted by slREFZ below 10.8 deg
+*     elevation by the factor (1+0.00195*(10.8-E_t)), where E_t is the
+*     unrefracted elevation in degrees.
+*
+*     The high-ZD model is scaled to match the normal model at the
+*     transition point;  there is no glitch.
+*
+*  3  Beyond 93 deg zenith distance, the refraction is held at its
+*     93 deg value.
+*
+*  4  See also the routine slREFV, which performs the adjustment in
+*     Cartesian Az/El coordinates, and with the emphasis on speed
+*     rather than numerical accuracy.
+*
+*  Reference:
+*
+*     Condon,J.J., Refraction Corrections for the GBT, PTCS/PN/35.2,
+*     NRAO Green Bank, 2004.
+*
+*  P.T.Wallace   Starlink   9 April 2004
+*
+*  Copyright (C) 2004 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION ZU,REFA,REFB,ZR
+
+*  Radians to degrees
+      DOUBLE PRECISION R2D
+      PARAMETER (R2D=57.29577951308232D0)
+
+*  Largest usable ZD (deg)
+      DOUBLE PRECISION D93
+      PARAMETER (D93=93D0)
+
+*  Coefficients for high ZD model (used beyond ZD 83 deg)
+      DOUBLE PRECISION C1,C2,C3,C4,C5
+      PARAMETER (C1=+0.55445D0,
+     :           C2=-0.01133D0,
+     :           C3=+0.00202D0,
+     :           C4=+0.28385D0,
+     :           C5=+0.02390D0)
+
+*  ZD at which one model hands over to the other (radians)
+      DOUBLE PRECISION Z83
+      PARAMETER (Z83=83D0/R2D)
+
+*  High-ZD-model prediction (deg) for that point
+      DOUBLE PRECISION REF83
+      PARAMETER (REF83=(C1+C2*7D0+C3*49D0)/(1D0+C4*7D0+C5*49D0))
+
+      DOUBLE PRECISION ZU1,ZL,S,C,T,TSQ,TCU,REF,E,E2
+
+
+
+*  Perform calculations for ZU or 83 deg, whichever is smaller
+      ZU1 = MIN(ZU,Z83)
+
+*  Functions of ZD
+      ZL = ZU1
+      S = SIN(ZL)
+      C = COS(ZL)
+      T = S/C
+      TSQ = T*T
+      TCU = T*TSQ
+
+*  Refracted ZD (mathematically to better than 1 mas at 70 deg)
+      ZL = ZL-(REFA*T+REFB*TCU)/(1D0+(REFA+3D0*REFB*TSQ)/(C*C))
+
+*  Further iteration
+      S = SIN(ZL)
+      C = COS(ZL)
+      T = S/C
+      TSQ = T*T
+      TCU = T*TSQ
+      REF = ZU1-ZL+
+     :          (ZL-ZU1+REFA*T+REFB*TCU)/(1D0+(REFA+3D0*REFB*TSQ)/(C*C))
+
+*  Special handling for large ZU
+      IF (ZU.GT.ZU1) THEN
+         E = 90D0-MIN(D93,ZU*R2D)
+         E2 = E*E
+         REF = (REF/REF83)*(C1+C2*E+C3*E2)/(1D0+C4*E+C5*E2)
+      END IF
+
+*  Return refracted ZD
+      ZR = ZU-REF
+
+      END
diff --git a/math/slalib/rtl_random.c b/math/slalib/rtl_random.c
new file mode 100644
index 00000000..a8730c0c
--- /dev/null
+++ b/math/slalib/rtl_random.c
@@ -0,0 +1,33 @@
+#include <stdlib.h>
+
+float
+random_ ( int *iseed )
+/*
+**  - - - - - - -
+**   r a n d o m
+**  - - - - - - -
+**
+**  Generate pseudo-random real number in the range 0 <= x < 1.
+**
+**  (single precision)
+**
+**  This function is designed to replace the Fortran->C interface routine
+**  random(3f) on systems which do not have this library (for example Linux)
+**
+**  Fortran call:   X = RANDOM(ISEED)
+**
+**  Given:
+**     iseed     int     seed value
+**
+**     If iseed !=0  random-number generator is initialised and first number
+**                   is returned.
+**        iseed == 0 next number in the sequence is returned
+**
+**  B.K.McIlwrath    Starlink   12 January 1996
+*/
+{
+   if( *iseed != 0 )
+      srand(*iseed);
+
+   return (float) rand() / (float) RAND_MAX;
+}
diff --git a/math/slalib/rverot.f b/math/slalib/rverot.f
new file mode 100644
index 00000000..3fc5ab50
--- /dev/null
+++ b/math/slalib/rverot.f
@@ -0,0 +1,66 @@
+      REAL FUNCTION slRVER (PHI, RA, DA, ST)
+*+
+*     - - - - - - -
+*      R V E R
+*     - - - - - - -
+*
+*  Velocity component in a given direction due to Earth rotation
+*  (single precision)
+*
+*  Given:
+*     PHI     real    latitude of observing station (geodetic)
+*     RA,DA   real    apparent RA,DEC
+*     ST      real    local apparent sidereal time
+*
+*  PHI, RA, DEC and ST are all in radians.
+*
+*  Result:
+*     Component of Earth rotation in direction RA,DA (km/s)
+*
+*  Sign convention:
+*     The result is +ve when the observatory is receding from the
+*     given point on the sky.
+*
+*  Accuracy:
+*     The simple algorithm used assumes a spherical Earth, of
+*     a radius chosen to give results accurate to about 0.0005 km/s
+*     for observing stations at typical latitudes and heights.  For
+*     applications requiring greater precision, use the routine
+*     slPVOB.
+*
+*  P.T.Wallace   Starlink   20 July 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL PHI,RA,DA,ST
+
+*  Nominal mean sidereal speed of Earth equator in km/s (the actual
+*  value is about 0.4651)
+      REAL ESPEED
+      PARAMETER (ESPEED=0.4655)
+
+
+      slRVER=ESPEED*COS(PHI)*SIN(ST-RA)*COS(DA)
+
+      END
diff --git a/math/slalib/rvgalc.f b/math/slalib/rvgalc.f
new file mode 100644
index 00000000..173c7d92
--- /dev/null
+++ b/math/slalib/rvgalc.f
@@ -0,0 +1,87 @@
+      REAL FUNCTION slRVGA (R2000, D2000)
+*+
+*     - - - - - - -
+*      R V G A
+*     - - - - - - -
+*
+*  Velocity component in a given direction due to the rotation
+*  of the Galaxy (single precision)
+*
+*  Given:
+*     R2000,D2000   real    J2000.0 mean RA,Dec (radians)
+*
+*  Result:
+*     Component of dynamical LSR motion in direction R2000,D2000 (km/s)
+*
+*  Sign convention:
+*     The result is +ve when the dynamical LSR is receding from the
+*     given point on the sky.
+*
+*  Note:  The Local Standard of Rest used here is a point in the
+*         vicinity of the Sun which is in a circular orbit around
+*         the Galactic centre.  Sometimes called the "dynamical" LSR,
+*         it is not to be confused with a "kinematical" LSR, which
+*         is the mean standard of rest of star catalogues or stellar
+*         populations.
+*
+*  Reference:  The orbital speed of 220 km/s used here comes from
+*              Kerr & Lynden-Bell (1986), MNRAS, 221, p1023.
+*
+*  Called:
+*     slCS2C, slVDV
+*
+*  P.T.Wallace   Starlink   23 March 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL R2000,D2000
+
+      REAL VA(3), VB(3)
+
+      REAL slVDV
+
+*
+*  LSR velocity due to Galactic rotation
+*
+*  Speed = 220 km/s
+*  Apex  = L2,B2  90deg, 0deg
+*        = RA,Dec  21 12 01.1  +48 19 47  J2000.0
+*
+*  This is expressed in the form of a J2000.0 x,y,z vector:
+*
+*      VA(1) = X = -SPEED*COS(RA)*COS(DEC)
+*      VA(2) = Y = -SPEED*SIN(RA)*COS(DEC)
+*      VA(3) = Z = -SPEED*SIN(DEC)
+
+      DATA VA / -108.70408, +97.86251, -164.33610 /
+
+
+
+*  Convert given J2000 RA,Dec to x,y,z
+      CALL slCS2C(R2000,D2000,VB)
+
+*  Compute dot product with LSR motion vector
+      slRVGA=slVDV(VA,VB)
+
+      END
diff --git a/math/slalib/rvlg.f b/math/slalib/rvlg.f
new file mode 100644
index 00000000..cc3076e6
--- /dev/null
+++ b/math/slalib/rvlg.f
@@ -0,0 +1,82 @@
+      REAL FUNCTION slRVLG (R2000, D2000)
+*+
+*     - - - - -
+*      R V L G
+*     - - - - -
+*
+*  Velocity component in a given direction due to the combination
+*  of the rotation of the Galaxy and the motion of the Galaxy
+*  relative to the mean motion of the local group (single precision)
+*
+*  Given:
+*     R2000,D2000   real    J2000.0 mean RA,Dec (radians)
+*
+*  Result:
+*     Component of SOLAR motion in direction R2000,D2000 (km/s)
+*
+*  Sign convention:
+*     The result is +ve when the Sun is receding from the
+*     given point on the sky.
+*
+*  Reference:
+*     IAU Trans 1976, 168, p201.
+*
+*  Called:
+*     slCS2C, slVDV
+*
+*  P.T.Wallace   Starlink   June 1985
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL R2000,D2000
+
+      REAL VA(3), VB(3)
+
+      REAL slVDV
+
+*
+*  Solar velocity due to Galactic rotation and translation
+*
+*  Speed = 300 km/s
+*
+*  Apex  = L2,B2  90deg, 0deg
+*        = RA,Dec  21 12 01.1  +48 19 47  J2000.0
+*
+*  This is expressed in the form of a J2000.0 x,y,z vector:
+*
+*      VA(1) = X = -SPEED*COS(RA)*COS(DEC)
+*      VA(2) = Y = -SPEED*SIN(RA)*COS(DEC)
+*      VA(3) = Z = -SPEED*SIN(DEC)
+
+      DATA VA / -148.23284, +133.44888, -224.09467 /
+
+
+
+*  Convert given J2000 RA,Dec to x,y,z
+      CALL slCS2C(R2000,D2000,VB)
+
+*  Compute dot product with Solar motion vector
+      slRVLG=slVDV(VA,VB)
+
+      END
diff --git a/math/slalib/rvlsrd.f b/math/slalib/rvlsrd.f
new file mode 100644
index 00000000..720d6c9c
--- /dev/null
+++ b/math/slalib/rvlsrd.f
@@ -0,0 +1,96 @@
+      REAL FUNCTION slRVLD (R2000, D2000)
+*+
+*     - - - - - - -
+*      R V L D
+*     - - - - - - -
+*
+*  Velocity component in a given direction due to the Sun's motion
+*  with respect to the dynamical Local Standard of Rest.
+*
+*  (single precision)
+*
+*  Given:
+*     R2000,D2000   r    J2000.0 mean RA,Dec (radians)
+*
+*  Result:
+*     Component of "peculiar" solar motion in direction R2000,D2000 (km/s)
+*
+*  Sign convention:
+*     The result is +ve when the Sun is receding from the given point on
+*     the sky.
+*
+*  Note:  The Local Standard of Rest used here is the "dynamical" LSR,
+*         a point in the vicinity of the Sun which is in a circular
+*         orbit around the Galactic centre.  The Sun's motion with
+*         respect to the dynamical LSR is called the "peculiar" solar
+*         motion.
+*
+*         There is another type of LSR, called a "kinematical" LSR.  A
+*         kinematical LSR is the mean standard of rest of specified star
+*         catalogues or stellar populations, and several slightly
+*         different kinematical LSRs are in use.  The Sun's motion with
+*         respect to an agreed kinematical LSR is known as the "standard"
+*         solar motion.  To obtain a radial velocity correction with
+*         respect to an adopted kinematical LSR use the routine slRVLK.
+*
+*  Reference:  Delhaye (1965), in "Stars and Stellar Systems", vol 5,
+*              p73.
+*
+*  Called:
+*     slCS2C, slVDV
+*
+*  P.T.Wallace   Starlink   9 March 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL R2000,D2000
+
+      REAL VA(3), VB(3)
+
+      REAL slVDV
+
+*
+*  Peculiar solar motion from Delhaye 1965: in Galactic Cartesian
+*  coordinates (+9,+12,+7) km/s.  This corresponds to about 16.6 km/s
+*  towards Galactic coordinates L2 = 53 deg, B2 = +25 deg, or RA,Dec
+*  17 49 58.7 +28 07 04 J2000.
+*
+*  The solar motion is expressed here in the form of a J2000.0
+*  equatorial Cartesian vector:
+*
+*      VA(1) = X = -SPEED*COS(RA)*COS(DEC)
+*      VA(2) = Y = -SPEED*SIN(RA)*COS(DEC)
+*      VA(3) = Z = -SPEED*SIN(DEC)
+
+      DATA VA / +0.63823, +14.58542, -7.80116 /
+
+
+
+*  Convert given J2000 RA,Dec to x,y,z
+      CALL slCS2C(R2000,D2000,VB)
+
+*  Compute dot product with solar motion vector
+      slRVLD=slVDV(VA,VB)
+
+      END
diff --git a/math/slalib/rvlsrk.f b/math/slalib/rvlsrk.f
new file mode 100644
index 00000000..52b3db95
--- /dev/null
+++ b/math/slalib/rvlsrk.f
@@ -0,0 +1,95 @@
+      REAL FUNCTION slRVLK (R2000, D2000)
+*+
+*     - - - - - - -
+*      R V L K
+*     - - - - - - -
+*
+*  Velocity component in a given direction due to the Sun's motion
+*  with respect to an adopted kinematic Local Standard of Rest.
+*
+*  (single precision)
+*
+*  Given:
+*     R2000,D2000   r    J2000.0 mean RA,Dec (radians)
+*
+*  Result:
+*     Component of "standard" solar motion in direction R2000,D2000 (km/s)
+*
+*  Sign convention:
+*     The result is +ve when the Sun is receding from the given point on
+*     the sky.
+*
+*  Note:  The Local Standard of Rest used here is one of several
+*         "kinematical" LSRs in common use.  A kinematical LSR is the
+*         mean standard of rest of specified star catalogues or stellar
+*         populations.  The Sun's motion with respect to a kinematical
+*         LSR is known as the "standard" solar motion.
+*
+*         There is another sort of LSR, the "dynamical" LSR, which is a
+*         point in the vicinity of the Sun which is in a circular orbit
+*         around the Galactic centre.  The Sun's motion with respect to
+*         the dynamical LSR is called the "peculiar" solar motion.  To
+*         obtain a radial velocity correction with respect to the
+*         dynamical LSR use the routine slRVLD.
+*
+*  Reference:  Delhaye (1965), in "Stars and Stellar Systems", vol 5,
+*              p73.
+*
+*  Called:
+*     slCS2C, slVDV
+*
+*  P.T.Wallace   Starlink   11 March 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL R2000,D2000
+
+      REAL VA(3), VB(3)
+
+      REAL slVDV
+
+*
+*  Standard solar motion (from Methods of Experimental Physics, ed Meeks,
+*  vol 12, part C, sec 6.1.5.2, p281):
+*
+*  20 km/s towards RA 18h Dec +30d (1900).
+*
+*  The solar motion is expressed here in the form of a J2000.0
+*  equatorial Cartesian vector:
+*
+*      VA(1) = X = -SPEED*COS(RA)*COS(DEC)
+*      VA(2) = Y = -SPEED*SIN(RA)*COS(DEC)
+*      VA(3) = Z = -SPEED*SIN(DEC)
+
+      DATA VA / -0.29000, +17.31726, -10.00141 /
+
+
+
+*  Convert given J2000 RA,Dec to x,y,z
+      CALL slCS2C(R2000,D2000,VB)
+
+*  Compute dot product with solar motion vector
+      slRVLK=slVDV(VA,VB)
+
+      END
diff --git a/math/slalib/s2tp.f b/math/slalib/s2tp.f
new file mode 100644
index 00000000..ca187db2
--- /dev/null
+++ b/math/slalib/s2tp.f
@@ -0,0 +1,85 @@
+      SUBROUTINE slS2TP (RA, DEC, RAZ, DECZ, XI, ETA, J)
+*+
+*     - - - - -
+*      S 2 T P
+*     - - - - -
+*
+*  Projection of spherical coordinates onto tangent plane:
+*  "gnomonic" projection - "standard coordinates"
+*  (single precision)
+*
+*  Given:
+*     RA,DEC      real  spherical coordinates of point to be projected
+*     RAZ,DECZ    real  spherical coordinates of tangent point
+*
+*  Returned:
+*     XI,ETA      real  rectangular coordinates on tangent plane
+*     J           int   status:   0 = OK, star on tangent plane
+*                                 1 = error, star too far from axis
+*                                 2 = error, antistar on tangent plane
+*                                 3 = error, antistar too far from axis
+*
+*  P.T.Wallace   Starlink   18 July 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL RA,DEC,RAZ,DECZ,XI,ETA
+      INTEGER J
+
+      REAL SDECZ,SDEC,CDECZ,CDEC,RADIF,SRADIF,CRADIF,DENOM
+
+      REAL TINY
+      PARAMETER (TINY=1E-6)
+
+
+*  Trig functions
+      SDECZ=SIN(DECZ)
+      SDEC=SIN(DEC)
+      CDECZ=COS(DECZ)
+      CDEC=COS(DEC)
+      RADIF=RA-RAZ
+      SRADIF=SIN(RADIF)
+      CRADIF=COS(RADIF)
+
+*  Reciprocal of star vector length to tangent plane
+      DENOM=SDEC*SDECZ+CDEC*CDECZ*CRADIF
+
+*  Handle vectors too far from axis
+      IF (DENOM.GT.TINY) THEN
+         J=0
+      ELSE IF (DENOM.GE.0.0) THEN
+         J=1
+         DENOM=TINY
+      ELSE IF (DENOM.GT.-TINY) THEN
+         J=2
+         DENOM=-TINY
+      ELSE
+         J=3
+      END IF
+
+*  Compute tangent plane coordinates (even in dubious cases)
+      XI=CDEC*SRADIF/DENOM
+      ETA=(SDEC*CDECZ-CDEC*SDECZ*CRADIF)/DENOM
+
+      END
diff --git a/math/slalib/sedscript b/math/slalib/sedscript
new file mode 100755
index 00000000..046d7e1d
--- /dev/null
+++ b/math/slalib/sedscript
@@ -0,0 +1,17 @@
+#!/bin/csh
+
+# SEDSCRIPT -- Script for editing/renaming the SLALIB FORTRAN routines
+
+# Make the appropriate name changes and add IRAF copyright
+foreach file (*.f)
+    echo $file
+    sed -f SED1 $file > tempfile.f
+    rm $file
+    mv tempfile.f $file
+    sed -f SED2 $file > tempfile.f
+    rm $file
+    mv tempfile.f $file
+end
+
+# Restore IRAF version of the preces.f file from a save version.
+cp precss.f.sav precss.f
diff --git a/math/slalib/sep.f b/math/slalib/sep.f
new file mode 100644
index 00000000..100de493
--- /dev/null
+++ b/math/slalib/sep.f
@@ -0,0 +1,56 @@
+      REAL FUNCTION slSEP (A1, B1, A2, B2)
+*+
+*     - - - -
+*      S E P
+*     - - - -
+*
+*  Angle between two points on a sphere.
+*
+*  (single precision)
+*
+*  Given:
+*     A1,B1    r     spherical coordinates of one point
+*     A2,B2    r     spherical coordinates of the other point
+*
+*  (The spherical coordinates are [RA,Dec], [Long,Lat] etc, in radians.)
+*
+*  The result is the angle, in radians, between the two points.  It
+*  is always positive.
+*
+*  Called:  slDSEP
+*
+*  Last revision:   7 May 2000
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL A1,B1,A2,B2
+
+      DOUBLE PRECISION slDSEP
+
+
+
+*  Use double precision version.
+      slSEP = REAL(slDSEP(DBLE(A1),DBLE(B1),DBLE(A2),DBLE(B2)))
+
+      END
diff --git a/math/slalib/sepv.f b/math/slalib/sepv.f
new file mode 100644
index 00000000..c1c867ce
--- /dev/null
+++ b/math/slalib/sepv.f
@@ -0,0 +1,71 @@
+      REAL FUNCTION slSEPV (V1, V2)
+*+
+*     - - - - -
+*      S E P V
+*     - - - - -
+*
+*  Angle between two vectors.
+*
+*  (single precision)
+*
+*  Given:
+*     V1      r(3)    first vector
+*     V2      r(3)    second vector
+*
+*  The result is the angle, in radians, between the two vectors.  It
+*  is always positive.
+*
+*  Notes:
+*
+*  1  There is no requirement for the vectors to be unit length.
+*
+*  2  If either vector is null, zero is returned.
+*
+*  3  The simplest formulation would use dot product alone.  However,
+*     this would reduce the accuracy for angles near zero and pi.  The
+*     algorithm uses both cross product and dot product, which maintains
+*     accuracy for all sizes of angle.
+*
+*  Called:  slDSEPV
+*
+*  Last revision:   7 May 2000
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL V1(3),V2(3)
+
+      INTEGER I
+      DOUBLE PRECISION DV1(3),DV2(3)
+      DOUBLE PRECISION slDSEPV
+
+
+
+*  Use double precision version.
+      DO I=1,3
+         DV1(I) = DBLE(V1(I))
+         DV2(I) = DBLE(V2(I))
+      END DO
+      slSEPV = REAL(slDSEPV(DV1,DV2))
+
+      END
diff --git a/math/slalib/sla.c b/math/slalib/sla.c
new file mode 100644
index 00000000..10bfde3c
--- /dev/null
+++ b/math/slalib/sla.c
@@ -0,0 +1,2338 @@
+/*
+*  Name:
+*     sla.c
+
+*  Purpose:
+*     Implement a C interface to the Fortran SLALIB library.
+
+*  Description:
+*     This file implements a C interface to the Fortran version of the
+*     SLALIB library.
+
+*  Notes:
+*     This interface only supports a subset of the functions provided by
+*     SLALIB. It should be extended as and when necessary.
+
+*  Copyright:
+*     Copyright (C) 1996-2006 Council for the Central Laboratory of the
+*     Research Councils. Copyright (C) 2007-2008 Science and Technology
+*     Facilities Council. All Rights Reserved.
+
+*  Licence:
+*     This program is free software; you can redistribute it and/or
+*     modify it under the terms of the GNU General Public Licence as
+*     published by the Free Software Foundation; either version 2 of
+*     the Licence, or (at your option) any later version.
+*
+*     This program is distributed in the hope that it will be
+*     useful,but WITHOUT ANY WARRANTY; without even the implied
+*     warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
+*     PURPOSE. See the GNU General Public Licence for more details.
+*
+*     You should have received a copy of the GNU General Public Licence
+*     along with this program; if not, write to the Free Software
+*     Foundation, Inc., 51 Franklin Street,Fifth Floor, Boston, MA
+*     02110-1301, USA
+
+*  Authors:
+*     RFWS: R.F. Warren-Smith (STARLINK)
+*     DSB: David S. Berry (STARLINK)
+*     TIMJ: Tim Jenness (JAC, Hawaii)
+*     PWD: Peter W. Draper (Durham University)
+
+*  History:
+*     12-NOV-1996 (RFWS):
+*        Original version.
+*     28-APR-1997 (RFWS):
+*        Added SLA_DJCAL.
+*     26-SEP-1997 (DSB):
+*        Added SLA_DD2TF, SLA_DJCL.
+*     21-JUN-2001 (DSB):
+*        Added SLA_DBEAR, SLA_DVDV.
+*     23-AUG-2001 (DSB):
+*        Added SLA_SVD and SLA_SVDSOL
+*     11-NOV-2002 (DSB):
+*        Added SLA_RVEROT, SLA_GMST, SLA_EQEQX, SLA_RVLSRK, SLA_RVLSRD,
+*        SLA_RVLG, SLA_RVGALC.
+*     11-JUN-2003 (DSB):
+*        Added SLA_GEOC, SLA_HFK5Z and SLA_FK5HZ.
+*     2-DEC-2004 (DSB):
+*        Added SLA_DEULER.
+*     29-SEP-2005 (DSB):
+*        Added SLA_DE2H and SLA_DH2E
+*     12-JUN-2006 (DSB):
+*        Moved from AST to SLALIB.
+*     25-JUN-2006 (TIMJ):
+*        Add SLA_AIRMAS.
+*     07-AUG-2006 (TIMJ):
+*        Import cnfImprt from CNF.
+*        Add SLA_OBS
+*     08-AUG-2006 (TIMJ):
+*        Add SLA_PA
+*     12-DEC-2006 (TIMJ):
+*        Add SLA_DTT and SLA_DAT
+*     21-DEC-2006 (TIMJ):
+*        Add SLA_RDPLAN
+*     03-APR-2007 (TIMJ):
+*        Add SLA_DR2TF
+*     14-DEC-2007 (TIMJ):
+*        Add slaDafin, Add slaMap
+*     12-MAR-2008 (TIMJ):
+*        Add slaOap, slaDr2af, slaAmp, slaPertel, slaPlanet, slaCldj
+*        to enable elements test.
+*     14-JUL-2008 (TIMJ):
+*        Allowed to use const.
+*     30-JUL-2008 (TIMJ):
+*        Add slaDs2tp
+*     10-FEB-2012 (DSB):
+*        Added slaPvobs
+*-
+*/
+
+/* Header files. */
+/* ============= */
+#include "f77.h"                 /* FORTRAN <-> C interface macros (SUN/209) */
+#include "slalib.h"              /* Prototypes for C SLALIB functions */
+#include <stdlib.h>              /* Malloc etc */
+#include <string.h>              /* string manipulation */
+
+
+/* Functions needed to avoid a dependence on CNF. */
+/* ============================================== */
+
+static void slaStringExport( const char *source_c, char *dest_f, int dest_len ) {
+/*
+*+
+*  Name:
+*     slaStringExport
+
+*  Purpose:
+*     Export a C string to a FORTRAN string.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     void slaStringExport( const char *source_c, char *dest_f, int dest_len )
+
+*  Description:
+*     This function creates a FORTRAN string from a C string, storing
+*     it in the supplied memory. If the C string is shorter than the
+*     space allocated for the FORTRAN string, then it is padded with
+*     blanks. If the C string is longer than the space allocated for
+*     the FORTRAN string, then the string is truncated.
+
+*  Parameters:
+*     source_c
+*        A pointer to the input C string.
+*     dest_f
+*        A pointer to the output FORTRAN string.
+*     dest_len
+*        The length of the output FORTRAN string.
+
+*  Notes:
+*     - This function is potentially platform-specific. For example,
+*     if FORTRAN strings were passed by descriptor, then the
+*     descriptor address would be passed as "dest_f" and this must
+*     then be used to locate the actual FORTRAN character data.
+*     - This function is equivalent to cnfExprt but is included here to
+*     avoid SLALIB becoming dependent on CNF.
+*-
+*/
+
+/* Local Variables:*/
+   int i;                        /* Loop counter for characters */
+
+/* Check the supplied pointers. */
+   if ( !source_c || !dest_f ) return;
+
+/* Copy the characters of the input C string to the output FORTRAN
+   string, taking care not to go beyond the end of the FORTRAN
+   string.*/
+   for ( i = 0; source_c[ i ] && ( i < dest_len ); i++ ) {
+      dest_f[ i ] = source_c[ i ];
+   }
+
+/* Fill the rest of the output FORTRAN string with blanks. */
+   for ( ; i < dest_len; i++ ) dest_f[ i ] = ' ';
+}
+
+static void slaStringImport( const char *source_f, int source_len, char *dest_c )
+
+/*
+*+
+*  Name:
+*     slaStringImportt
+
+*  Purpose:
+*     Import a FORTRAN string into a C string
+
+*  Type:
+*     Protected function.
+
+*  Language:
+*     ANSI C
+
+*  Invocation:
+*     slaStringImport( source_f, source_len, dest_c )
+
+*  Description:
+*     Import a FORTRAN string into a C string, discarding trailing
+*     blanks. The NUL character is appended to the C string after
+*     the last non-blank character. The input string and output string
+*     pointers can point to the same location if the string is to be
+*     modified in place (but care must be taken to allow for the additional
+*     C terminator when allocating memory).
+
+*  Arguments:
+*     const char *source_f (Given)
+*        A pointer to the input FORTRAN string
+*     int source_len (Given)
+*        The length of the input FORTRAN string
+*     char *dest_c (Returned via pointer)
+*        A pointer to the output C string. Can be same as source.
+
+*  Notes:
+*     -  No check is made that there is sufficient space allocated to
+*        the C string to hold the FORTRAN string and a terminating null.
+*        It is responsibility of the programmer to check this.
+*     -  This function is equivalent to cnfImprt but is included here to
+*        avoid SLALIB becoming dependent on CNF.
+
+*  Authors:
+*     PMA: Peter Allan (Starlink, RAL)
+*     AJC: Alan Chipperfield (Starlink, RAL)
+*     TIMJ: Tim Jenness (JAC, Hawaii)
+*     {enter_new_authors_here}
+
+*  History:
+*     27-MAR-1991 (PMA):
+*        Original version.
+*     22-MAY-1996 (AJC):
+*        Correct description re trailing blanks
+*     24-SEP-1998 (AJC):
+*        Specify const char * for input strings
+*     25-NOV-2005 (TIMJ):
+*        Allow the strings to be identical
+*     {enter_changes_here}
+
+*-
+
+*...........................................................................*/
+
+{
+/* Local Variables:							    */
+
+   int i;			 /* Loop counter			    */
+
+
+/* Find the last non blank character in the input FORTRAN string.	    */
+
+   for( i = source_len - 1 ; ( i >= 0 ) && ( source_f[i] == ' ' ) ; i-- )
+      ;
+
+/* Put a null character at the end of the output C string.		    */
+
+   dest_c[i+1] = '\0';
+
+/* Copy the characters from the input FORTRAN string to the output C	    */
+/* string if the strings are different.				      	    */
+
+   if (dest_c != source_f ) {
+     memmove( dest_c, source_f, (size_t)i+1 );
+   }
+}
+
+/* Allocate string buffer dynamically. Taken from cnfCref.
+   See cnfCref for more details.
+*/
+
+static F77_CHARACTER_ARG_TYPE *slaStringCreate( int length ) {
+  /* Local Variables:                                                         */
+   F77_CHARACTER_ARG_TYPE *ptr;  /* A pointer to the string allocated       */
+
+/* Allocate the space.                                                      */
+   ptr = (F77_CHARACTER_ARG_TYPE *)
+       malloc( (size_t)( ( length > 0 ) ? length : 1 ) );
+
+/* Check for malloc returning a null value. If it does not, set the string  */
+/* to the null character.                                                   */
+   if ( ptr != 0 ) {
+       ptr[0] = '\0';
+   }
+
+   return( ptr );
+}
+
+/* Free space allocate by slaStringCreate. Take from cnfFreef */
+
+static void slaStringFree ( F77_CHARACTER_ARG_TYPE * temp ) {
+  free( temp );
+}
+
+
+/* SLALIB wrapper implementations. */
+/* =============================== */
+/* Fortran routine prototype. */
+F77_SUBROUTINE(sla_addet)( DOUBLE(RM),
+                           DOUBLE(DM),
+                           DOUBLE(EQ),
+                           DOUBLE(RC),
+                           DOUBLE(DC) );
+
+/* C interface implementation. */
+void slaAddet ( double rm, double dm, double eq, double *rc, double *dc ) {
+   DECLARE_DOUBLE(RM);
+   DECLARE_DOUBLE(DM);
+   DECLARE_DOUBLE(EQ);
+   DECLARE_DOUBLE(RC);
+   DECLARE_DOUBLE(DC);
+   RM = rm;
+   DM = dm;
+   EQ = eq;
+   F77_LOCK( F77_CALL(sla_addet)( DOUBLE_ARG(&RM),
+                        DOUBLE_ARG(&DM),
+                        DOUBLE_ARG(&EQ),
+                        DOUBLE_ARG(&RC),
+                        DOUBLE_ARG(&DC) ); )
+   *rc = RC;
+   *dc = DC;
+}
+
+/* etc... */
+F77_SUBROUTINE(sla_ampqk)( DOUBLE(RA),
+                           DOUBLE(DA),
+                           DOUBLE_ARRAY(AMPRMS),
+                           DOUBLE(RM),
+                           DOUBLE(DM) );
+
+void slaAmpqk ( double ra, double da, double amprms[21],
+                double *rm, double *dm ) {
+   DECLARE_DOUBLE(RA);
+   DECLARE_DOUBLE(DA);
+   DECLARE_DOUBLE_ARRAY(AMPRMS,21);
+   DECLARE_DOUBLE(RM);
+   DECLARE_DOUBLE(DM);
+   int i;
+   RA = ra;
+   DA = da;
+   for ( i = 0; i < 21; i++ ) AMPRMS[ i ] = amprms[ i ];
+   F77_LOCK( F77_CALL(sla_ampqk)( DOUBLE_ARG(&RA),
+                        DOUBLE_ARG(&DA),
+                        DOUBLE_ARRAY_ARG(AMPRMS),
+                        DOUBLE_ARG(&RM),
+                        DOUBLE_ARG(&DM) ); )
+   *rm = RM;
+   *dm = DM;
+}
+
+F77_DOUBLE_FUNCTION(sla_airmas)( DOUBLE(ZD) );
+
+double slaAirmas( double zd ) {
+  DECLARE_DOUBLE(ZD);
+  double result;
+  ZD = zd;
+  F77_LOCK( result = F77_CALL(sla_airmas)( DOUBLE_ARG(&ZD) ); )
+  return result;
+}
+
+F77_SUBROUTINE(sla_caldj)( INTEGER(IY),
+                           INTEGER(IM),
+                           INTEGER(ID),
+                           DOUBLE(DJM),
+                           INTEGER(J) );
+
+void slaCaldj ( int iy, int im, int id, double *djm, int *j ) {
+   DECLARE_INTEGER(IY);
+   DECLARE_INTEGER(IM);
+   DECLARE_INTEGER(ID);
+   DECLARE_DOUBLE(DJM);
+   DECLARE_INTEGER(J);
+   IY = iy;
+   IM = im;
+   ID = id;
+   F77_LOCK( F77_CALL(sla_caldj)( INTEGER_ARG(&IY),
+                        INTEGER_ARG(&IM),
+                        INTEGER_ARG(&ID),
+                        DOUBLE_ARG(&DJM),
+                        INTEGER_ARG(&J) ); )
+   *djm = DJM;
+   *j = J;
+}
+
+F77_SUBROUTINE(sla_daf2r)( INTEGER(IDEG),
+                           INTEGER(IAMIN),
+                           DOUBLE(ASEC),
+                           DOUBLE(RAD),
+                           INTEGER(J) );
+
+void slaDaf2r ( int ideg, int iamin, double asec, double *rad, int *j ) {
+   DECLARE_INTEGER(IDEG);
+   DECLARE_INTEGER(IAMIN);
+   DECLARE_DOUBLE(ASEC);
+   DECLARE_DOUBLE(RAD);
+   DECLARE_INTEGER(J);
+   IDEG = ideg;
+   IAMIN = iamin;
+   ASEC = asec;
+   F77_LOCK( F77_CALL(sla_daf2r)( INTEGER_ARG(&IDEG),
+                        INTEGER_ARG(&IAMIN),
+                        DOUBLE_ARG(&ASEC),
+                        DOUBLE_ARG(&RAD),
+                        INTEGER_ARG(&J) ); )
+   *rad = RAD;
+   *j = J;
+}
+
+F77_SUBROUTINE(sla_dav2m)( DOUBLE_ARRAY(AXVEC),
+                           DOUBLE_ARRAY(RMAT) );
+
+void slaDav2m ( double axvec[3], double rmat[3][3] ) {
+   DECLARE_DOUBLE_ARRAY(AXVEC,3);
+   DECLARE_DOUBLE_ARRAY(RMAT,9);
+   int i;
+   int j;
+   for ( i = 0; i < 3; i++ ) AXVEC[ i ] = axvec[ i ];
+   F77_LOCK( F77_CALL(sla_dav2m)( DOUBLE_ARRAY_ARG(AXVEC),
+                        DOUBLE_ARRAY_ARG(RMAT) ); )
+   for ( i = 0; i < 3; i++ ) {
+      for ( j = 0; j < 3; j++ ) rmat[ i ][ j ] = RMAT[ i + 3 * j ];
+   }
+}
+
+F77_SUBROUTINE(sla_dcc2s)( DOUBLE_ARRAY(V),
+                           DOUBLE(A),
+                           DOUBLE(B) );
+
+void slaDcc2s ( double v[3], double *a, double *b ) {
+   DECLARE_DOUBLE_ARRAY(V,3);
+   DECLARE_DOUBLE(A);
+   DECLARE_DOUBLE(B);
+   int i;
+   for ( i = 0; i < 3; i++ ) V[ i ] = v[ i ];
+   F77_LOCK( F77_CALL(sla_dcc2s)( DOUBLE_ARRAY_ARG(V),
+                        DOUBLE_ARG(&A),
+                        DOUBLE_ARG(&B) ); )
+   *a = A;
+   *b = B;
+}
+
+F77_SUBROUTINE(sla_dcs2c)( DOUBLE(A),
+                           DOUBLE(B),
+                           DOUBLE_ARRAY(V) );
+
+void slaDcs2c ( double a, double b, double v[3] ) {
+   DECLARE_DOUBLE(A);
+   DECLARE_DOUBLE(B);
+   DECLARE_DOUBLE_ARRAY(V,3);
+   int i;
+   A = a;
+   B = b;
+   F77_LOCK( F77_CALL(sla_dcs2c)( DOUBLE_ARG(&A),
+                        DOUBLE_ARG(&B),
+                        DOUBLE_ARRAY_ARG(V) ); )
+   for ( i = 0; i < 3; i++ ) v[ i ] = V[ i ];
+}
+
+F77_SUBROUTINE(sla_dd2tf)( INTEGER(NDP),
+                           DOUBLE(DAYS),
+                           CHARACTER(SIGN),
+                           INTEGER_ARRAY(IHMSF)
+                           TRAIL(SIGN) );
+
+void slaDd2tf ( int ndp, double days, char *sign, int ihmsf[4] ) {
+   DECLARE_INTEGER(NDP);
+   DECLARE_DOUBLE(DAYS);
+   DECLARE_CHARACTER(SIGN,2);
+   DECLARE_INTEGER_ARRAY(IHMSF,4);
+   int i;
+
+   NDP = ndp;
+   DAYS = days;
+   F77_LOCK( F77_CALL(sla_dd2tf)( INTEGER_ARG(&NDP),
+                        DOUBLE_ARG(&DAYS),
+                        CHARACTER_ARG(SIGN),
+                        INTEGER_ARRAY_ARG(IHMSF)
+                        TRAIL_ARG(SIGN) ); )
+   sign[0] = SIGN[0];
+   sign[1] = 0;
+   for ( i = 0; i < 4; i++ ) ihmsf[ i ] = IHMSF[ i ];
+}
+
+F77_SUBROUTINE(sla_dr2tf)( INTEGER(NDP),
+                           DOUBLE(ANGLE),
+                           CHARACTER(SIGN),
+                           INTEGER_ARRAY(IHMSF)
+                           TRAIL(SIGN) );
+
+void
+slaDr2tf( int ndp, double angle, char * sign, int ihmsf[4] )  {
+  DECLARE_INTEGER(NDP);
+  DECLARE_DOUBLE(ANGLE);
+  DECLARE_CHARACTER(SIGN,2);
+  DECLARE_INTEGER_ARRAY(IHMSF,4);
+  int i;
+
+  NDP = ndp;
+  ANGLE = angle;
+  F77_LOCK( F77_CALL(sla_dr2tf)( INTEGER_ARG(&NDP),
+		       DOUBLE_ARG(&ANGLE),
+		       CHARACTER_ARG(SIGN),
+		       INTEGER_ARRAY_ARG(IHMSF)
+		       TRAIL_ARG(SIGN) ); )
+  sign[0] = SIGN[0];
+  sign[1] = 0;
+  for ( i = 0; i < 4; i++ ) ihmsf[ i ] = IHMSF[ i ];
+}
+
+F77_SUBROUTINE(sla_dr2af)( INTEGER(NDP),
+                           DOUBLE(ANGLE),
+                           CHARACTER(SIGN),
+                           INTEGER_ARRAY(IDMSF)
+                           TRAIL(SIGN) );
+
+void
+slaDr2af( int ndp, double angle, char * sign, int idmsf[4] )  {
+  DECLARE_INTEGER(NDP);
+  DECLARE_DOUBLE(ANGLE);
+  DECLARE_CHARACTER(SIGN,2);
+  DECLARE_INTEGER_ARRAY(IDMSF,4);
+  int i;
+
+  NDP = ndp;
+  ANGLE = angle;
+  F77_LOCK( F77_CALL(sla_dr2af)( INTEGER_ARG(&NDP),
+		       DOUBLE_ARG(&ANGLE),
+		       CHARACTER_ARG(SIGN),
+		       INTEGER_ARRAY_ARG(IDMSF)
+		       TRAIL_ARG(SIGN) ); )
+  sign[0] = SIGN[0];
+  sign[1] = 0;
+  for ( i = 0; i < 4; i++ ) idmsf[ i ] = IDMSF[ i ];
+}
+
+F77_SUBROUTINE(sla_dimxv)( DOUBLE_ARRAY(DM),
+                           DOUBLE_ARRAY(VA),
+                           DOUBLE_ARRAY(VB) );
+
+void slaDimxv ( double dm[3][3], double va[3], double vb[3] ) {
+   DECLARE_DOUBLE_ARRAY(DM,9);
+   DECLARE_DOUBLE_ARRAY(VA,3);
+   DECLARE_DOUBLE_ARRAY(VB,3);
+   int i;
+   int j;
+   for ( i = 0; i < 3; i++ ) {
+      for ( j = 0; j < 3; j++ ) DM[ i + j * 3 ] = dm[ i ][ j ];
+      VA[ i ] = va[ i ];
+   }
+   F77_LOCK( F77_CALL(sla_dimxv)( DOUBLE_ARRAY_ARG(DM),
+                        DOUBLE_ARRAY_ARG(VA),
+                        DOUBLE_ARRAY_ARG(VB) ); )
+   for ( i = 0; i < 3; i++ ) vb[ i ] = VB[ i ];
+}
+
+F77_SUBROUTINE(sla_djcal)( INTEGER(NDP),
+                           DOUBLE(DJM),
+                           INTEGER_ARRAY(IYMDF),
+                           INTEGER(J) );
+
+void slaDjcal ( int ndp, double djm, int iymdf[ 4 ], int *j ) {
+   DECLARE_INTEGER(NDP);
+   DECLARE_DOUBLE(DJM);
+   DECLARE_INTEGER_ARRAY(IYMDF,4);
+   DECLARE_INTEGER(J);
+   int i;
+
+   NDP = ndp;
+   DJM = djm;
+   F77_LOCK( F77_CALL(sla_djcal)( INTEGER_ARG(&NDP),
+                        DOUBLE_ARG(&DJM),
+                        INTEGER_ARRAY_ARG(IYMDF),
+                        INTEGER_ARG(&J) ); )
+   for ( i = 0; i < 4; i++ ) iymdf[ i ] = IYMDF[ i ];
+   *j = J;
+}
+
+F77_SUBROUTINE(sla_djcl)( DOUBLE(DJM),
+                          INTEGER(IY),
+                          INTEGER(IM),
+                          INTEGER(ID),
+                          DOUBLE(FD),
+                          INTEGER(J) );
+
+void slaDjcl ( double djm, int *iy, int *im, int *id, double *fd, int *j ) {
+   DECLARE_DOUBLE(DJM);
+   DECLARE_INTEGER(IY);
+   DECLARE_INTEGER(IM);
+   DECLARE_INTEGER(ID);
+   DECLARE_DOUBLE(FD);
+   DECLARE_INTEGER(J);
+
+   DJM = djm;
+   F77_LOCK( F77_CALL(sla_djcl)( DOUBLE_ARG(&DJM),
+                       INTEGER_ARG(&IY),
+                       INTEGER_ARG(&IM),
+                       INTEGER_ARG(&ID),
+                       DOUBLE_ARG(&FD),
+                       INTEGER_ARG(&J) ); )
+   *iy = IY;
+   *im = IM;
+   *id = ID;
+   *fd = FD;
+   *j = J;
+}
+
+F77_SUBROUTINE(sla_dmat)( INTEGER(N),
+                          DOUBLE_ARRAY(A),
+                          DOUBLE_ARRAY(Y),
+                          DOUBLE(D),
+                          INTEGER(JF),
+                          INTEGER_ARRAY(IW) );
+
+void slaDmat ( int n, double *a, double *y, double *d, int *jf, int *iw ) {
+   DECLARE_INTEGER(N);
+   F77_DOUBLE_TYPE *A;
+   F77_DOUBLE_TYPE *Y;
+   DECLARE_DOUBLE(D);
+   DECLARE_INTEGER(JF);
+   F77_INTEGER_TYPE *IW;
+   int i;
+   int j;
+   A = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) ( n * n ) );
+   Y = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) n );
+   if ( sizeof( F77_INTEGER_TYPE ) > sizeof( int ) ) {
+      IW = malloc( sizeof( F77_INTEGER_TYPE ) * (size_t) n );
+   } else {
+      IW = (F77_INTEGER_TYPE *) iw;
+   }
+   if ( IW ) {
+      N = n;
+      for ( i = 0; i < n; i++ ) {
+         for ( j = 0; j < n; j++ ) A[ i + n * j ] = a[ n * i + j ];
+         Y[ i ] = y[ i ];
+      }
+      F77_LOCK( F77_CALL(sla_dmat)( INTEGER_ARG(&N), DOUBLE_ARRAY_ARG(A),
+                          DOUBLE_ARRAY_ARG(Y), DOUBLE_ARG(&D),
+                          INTEGER_ARG(&JF), INTEGER_ARG(IW) ); )
+      for ( i = 0; i < n; i++ ) {
+         for ( j = 0; j < n; j++ ) a[ n * i + j ] = A[ i + n * j ];
+         y[ i ] = Y[ i ];
+      }
+      *d = D;
+      *jf = JF;
+   }
+   free( A );
+   free( Y );
+   if ( sizeof( F77_INTEGER_TYPE ) > sizeof( int ) ) free( IW );
+}
+
+F77_SUBROUTINE(sla_dmxm)( DOUBLE_ARRAY(A),
+                          DOUBLE_ARRAY(B),
+                          DOUBLE_ARRAY(C) );
+
+void slaDmxm ( double a[3][3], double b[3][3], double c[3][3] ) {
+   DECLARE_DOUBLE_ARRAY(A,9);
+   DECLARE_DOUBLE_ARRAY(B,9);
+   DECLARE_DOUBLE_ARRAY(C,9);
+   int i;
+   int j;
+   for ( i = 0; i < 3; i++ ) {
+      for ( j = 0; j < 3; j++ ) {
+         A[ i + 3 * j ] = a[ i ][ j ];
+         B[ i + 3 * j ] = b[ i ][ j ];
+      }
+   }
+   F77_LOCK( F77_CALL(sla_dmxm)( DOUBLE_ARRAY_ARG(A),
+                       DOUBLE_ARRAY_ARG(B),
+                       DOUBLE_ARRAY_ARG(C) ); )
+   for ( i = 0; i < 3; i++ ) {
+      for ( j = 0; j < 3; j++ ) c[ i ][ j ] = C[ i + 3 * j ];
+   }
+}
+
+F77_SUBROUTINE(sla_dmxv)( DOUBLE_ARRAY(DM),
+                          DOUBLE_ARRAY(VA),
+                          DOUBLE_ARRAY(VB) );
+
+void slaDmxv ( double dm[3][3], double va[3], double vb[3] ) {
+   DECLARE_DOUBLE_ARRAY(DM,9);
+   DECLARE_DOUBLE_ARRAY(VA,3);
+   DECLARE_DOUBLE_ARRAY(VB,3);
+   int i;
+   int j;
+   for ( i = 0; i < 3; i++ ) {
+      for ( j = 0; j < 3; j++ ) DM[ i + 3 * j ] = dm[ i ][ j ];
+      VA[ i ] = va[ i ];
+   }
+   F77_LOCK( F77_CALL(sla_dmxv)( DOUBLE_ARRAY_ARG(DM),
+                       DOUBLE_ARRAY_ARG(VA),
+                       DOUBLE_ARRAY_ARG(VB) ); )
+   for ( i = 0; i < 3; i++ ) vb[ i ] = VB[ i ];
+}
+
+F77_DOUBLE_FUNCTION(sla_dbear)( DOUBLE(A1), DOUBLE(B1),
+                                DOUBLE(A2), DOUBLE(B2) );
+
+double slaDbear ( double a1, double b1, double a2, double b2  ) {
+   DECLARE_DOUBLE(A1);
+   DECLARE_DOUBLE(B1);
+   DECLARE_DOUBLE(A2);
+   DECLARE_DOUBLE(B2);
+   double result;
+   A1 = a1;
+   B1 = b1;
+   A2 = a2;
+   B2 = b2;
+   F77_LOCK( result = F77_CALL(sla_dbear)( DOUBLE_ARG(&A1), DOUBLE_ARG(&B1),
+                                 DOUBLE_ARG(&A2), DOUBLE_ARG(&B2) ); )
+   return result;
+}
+
+F77_DOUBLE_FUNCTION(sla_drange)( DOUBLE(ANGLE) );
+
+double slaDrange ( double angle ) {
+   DECLARE_DOUBLE(ANGLE);
+   double result;
+   ANGLE = angle;
+   F77_LOCK( result = F77_CALL(sla_drange)( DOUBLE_ARG(&ANGLE) ); )
+   return result;
+}
+
+F77_DOUBLE_FUNCTION(sla_dranrm)( DOUBLE(ANGLE) );
+
+double slaDranrm ( double angle ) {
+   DECLARE_DOUBLE(ANGLE);
+   double result;
+   ANGLE = angle;
+   F77_LOCK( result = F77_CALL(sla_dranrm)( DOUBLE_ARG(&ANGLE) ); )
+   return result;
+}
+
+F77_DOUBLE_FUNCTION(sla_dsep)( DOUBLE(A1),
+                               DOUBLE(B1),
+                               DOUBLE(A2),
+                               DOUBLE(B2) );
+
+double slaDsep ( double a1, double b1, double a2, double b2 ) {
+   DECLARE_DOUBLE(A1);
+   DECLARE_DOUBLE(B1);
+   DECLARE_DOUBLE(A2);
+   DECLARE_DOUBLE(B2);
+   double result;
+   A1 = a1;
+   B1 = b1;
+   A2 = a2;
+   B2 = b2;
+   F77_LOCK( result = F77_CALL(sla_dsep)( DOUBLE_ARG(&A1),
+                                DOUBLE_ARG(&B1),
+                                DOUBLE_ARG(&A2),
+                                DOUBLE_ARG(&B2) ); )
+   return result;
+}
+
+F77_SUBROUTINE(sla_ds2tp)( DOUBLE(RA), DOUBLE(DEC),
+                           DOUBLE(RAZ), DOUBLE(DECZ),
+                           DOUBLE(XI), DOUBLE(ETA),
+                           INTEGER(J) );
+
+void slaDs2tp ( double ra, double dec, double raz, double decz, double * xi, double * eta, int* j ) {
+
+  DECLARE_DOUBLE(RA);
+  DECLARE_DOUBLE(DEC);
+  DECLARE_DOUBLE(RAZ);
+  DECLARE_DOUBLE(DECZ);
+  DECLARE_DOUBLE(XI);
+  DECLARE_DOUBLE(ETA);
+  DECLARE_INTEGER(J);
+
+  F77_EXPORT_DOUBLE(ra, RA);
+  F77_EXPORT_DOUBLE(dec, DEC);
+  F77_EXPORT_DOUBLE(raz, RAZ);
+  F77_EXPORT_DOUBLE(decz, DECZ);
+
+  F77_LOCK( F77_CALL(sla_ds2tp)( DOUBLE_ARG(&RA),
+                       DOUBLE_ARG(&DEC),
+                       DOUBLE_ARG(&RAZ),
+                       DOUBLE_ARG(&DECZ),
+                       DOUBLE_ARG(&XI),
+                       DOUBLE_ARG(&ETA),
+                       INTEGER_ARG(&J) ); )
+
+  F77_IMPORT_DOUBLE(XI, *xi);
+  F77_IMPORT_DOUBLE(ETA, *eta);
+  F77_IMPORT_DOUBLE(J, *j);
+
+}
+
+F77_DOUBLE_FUNCTION(sla_dvdv)( DOUBLE_ARRAY(VA),
+                               DOUBLE_ARRAY(VB) );
+
+double slaDvdv( double va[3], double vb[3] ) {
+   DECLARE_DOUBLE_ARRAY(VA,3);
+   DECLARE_DOUBLE_ARRAY(VB,3);
+   double result;
+   int i;
+   for ( i = 0; i < 3; i++ ) {
+      VA[ i ] = va[ i ];
+      VB[ i ] = vb[ i ];
+   }
+   F77_LOCK( result = F77_CALL(sla_dvdv)( DOUBLE_ARRAY_ARG(VA),
+                                DOUBLE_ARRAY_ARG(VB) ); )
+   return result;
+}
+
+F77_SUBROUTINE(sla_dtf2d)( INTEGER(IHOUR),
+                           INTEGER(IMIN),
+                           DOUBLE(SEC),
+                           DOUBLE(DAYS),
+                           INTEGER(J) );
+
+void slaDtf2d ( int ihour, int imin, double sec, double *days, int *j ) {
+   DECLARE_INTEGER(IHOUR);
+   DECLARE_INTEGER(IMIN);
+   DECLARE_DOUBLE(SEC);
+   DECLARE_DOUBLE(DAYS);
+   DECLARE_INTEGER(J);
+   IHOUR = ihour;
+   IMIN = imin;
+   SEC = sec;
+   F77_LOCK( F77_CALL(sla_dtf2d)( INTEGER_ARG(&IHOUR),
+                        INTEGER_ARG(&IMIN),
+                        DOUBLE_ARG(&SEC),
+                        DOUBLE_ARG(&DAYS),
+                        INTEGER_ARG(&J) ); )
+   *days = DAYS;
+   *j = J;
+}
+
+F77_SUBROUTINE(sla_dtf2r)( INTEGER(IHOUR),
+                           INTEGER(IMIN),
+                           DOUBLE(SEC),
+                           DOUBLE(RAD),
+                           INTEGER(J) );
+
+void slaDtf2r ( int ihour, int imin, double sec, double *rad, int *j ) {
+   DECLARE_INTEGER(IHOUR);
+   DECLARE_INTEGER(IMIN);
+   DECLARE_DOUBLE(SEC);
+   DECLARE_DOUBLE(RAD);
+   DECLARE_INTEGER(J);
+   IHOUR = ihour;
+   IMIN = imin;
+   SEC = sec;
+   F77_LOCK( F77_CALL(sla_dtf2r)( INTEGER_ARG(&IHOUR),
+                        INTEGER_ARG(&IMIN),
+                        DOUBLE_ARG(&SEC),
+                        DOUBLE_ARG(&RAD),
+                        INTEGER_ARG(&J) ); )
+   *rad = RAD;
+   *j = J;
+}
+
+F77_DOUBLE_FUNCTION(sla_dt)( DOUBLE(EPOCH) );
+
+double slaDt ( double epoch )
+{
+    DECLARE_DOUBLE(EPOCH);
+    double result;
+    EPOCH = epoch;
+    F77_LOCK( result = F77_CALL(sla_dt)( DOUBLE_ARG(&EPOCH) ); )
+    return result;
+}
+
+F77_SUBROUTINE(sla_dvn)( DOUBLE_ARRAY(V),
+                         DOUBLE_ARRAY(UV),
+                         DOUBLE(VM) );
+
+void slaDvn ( double v[3], double uv[3], double *vm ) {
+   DECLARE_DOUBLE_ARRAY(V,3);
+   DECLARE_DOUBLE_ARRAY(UV,3);
+   DECLARE_DOUBLE(VM);
+   int i;
+   for ( i = 0; i < 3; i++ ) V[ i ] = v[ i ];
+   F77_LOCK( F77_CALL(sla_dvn)( DOUBLE_ARRAY_ARG(V),
+                      DOUBLE_ARRAY_ARG(UV),
+                      DOUBLE_ARG(&VM) ); )
+   for ( i = 0; i < 3; i++ ) uv[ i ] = UV[ i ];
+   *vm = VM;
+}
+
+F77_SUBROUTINE(sla_dvxv)( DOUBLE_ARRAY(VA),
+                          DOUBLE_ARRAY(VB),
+                          DOUBLE_ARRAY(VC) );
+
+void slaDvxv ( double va[3], double vb[3], double vc[3] ) {
+   DECLARE_DOUBLE_ARRAY(VA,3);
+   DECLARE_DOUBLE_ARRAY(VB,3);
+   DECLARE_DOUBLE_ARRAY(VC,3);
+   int i;
+   for ( i = 0; i < 3; i++ ) {
+      VA[ i ] = va[ i ];
+      VB[ i ] = vb[ i ];
+   }
+   F77_LOCK( F77_CALL(sla_dvxv)( DOUBLE_ARRAY_ARG(VA),
+                       DOUBLE_ARRAY_ARG(VB),
+                       DOUBLE_ARRAY_ARG(VC) ); )
+   for ( i = 0; i < 3; i++ ) vc[ i ] = VC[ i ];
+}
+
+F77_SUBROUTINE(sla_ecmat)( DOUBLE(DATE),
+                           DOUBLE_ARRAY(RMAT) );
+
+void slaEcmat ( double date, double rmat[3][3] ) {
+   DECLARE_DOUBLE(DATE);
+   DECLARE_DOUBLE_ARRAY(RMAT,9);
+   int i;
+   int j;
+   DATE = date;
+   F77_LOCK( F77_CALL(sla_ecmat)( DOUBLE_ARG(&DATE),
+                        DOUBLE_ARRAY_ARG(RMAT) ); )
+   for ( i = 0; i < 3; i++ ) {
+      for ( j = 0; j < 3; j++ ) rmat[ i ][ j ] = RMAT[ i + 3 * j ];
+   }
+}
+
+F77_DOUBLE_FUNCTION(sla_epb)( DOUBLE(DATE) );
+
+double slaEpb ( double date ) {
+   DECLARE_DOUBLE(DATE);
+   double result;
+   DATE = date;
+   F77_LOCK( result = F77_CALL(sla_epb)( DOUBLE_ARG(&DATE) ); )
+   return result;
+}
+
+F77_DOUBLE_FUNCTION(sla_epb2d)( DOUBLE(EPB) );
+
+double slaEpb2d ( double epb ) {
+   DECLARE_DOUBLE(EPB);
+   double result;
+   EPB = epb;
+   F77_LOCK( result = F77_CALL(sla_epb2d)( DOUBLE_ARG(&EPB) ); )
+   return result;
+}
+
+F77_DOUBLE_FUNCTION(sla_epj)( DOUBLE(DATE) );
+
+double slaEpj ( double date ) {
+   DECLARE_DOUBLE(DATE);
+   double result;
+   DATE = date;
+   F77_LOCK( result = F77_CALL(sla_epj)( DOUBLE_ARG(&DATE) ); )
+   return result;
+}
+
+F77_DOUBLE_FUNCTION(sla_epj2d)( DOUBLE(EPJ) );
+
+double slaEpj2d ( double epj ) {
+   DECLARE_DOUBLE(EPJ);
+   double result;
+   EPJ = epj;
+   F77_LOCK( result = F77_CALL(sla_epj2d)( DOUBLE_ARG(&EPJ) ); )
+   return result;
+}
+
+F77_DOUBLE_FUNCTION(sla_eqeqx)( DOUBLE(DATE) );
+
+double slaEqeqx ( double date ) {
+   DECLARE_DOUBLE(DATE);
+   double result;
+   DATE = date;
+   F77_LOCK( result = F77_CALL(sla_eqeqx)( DOUBLE_ARG(&DATE) ); )
+   return result;
+}
+
+F77_SUBROUTINE(sla_eqgal)( DOUBLE(DR),
+                           DOUBLE(DD),
+                           DOUBLE(DL),
+                           DOUBLE(DB) );
+
+void slaEqgal ( double dr, double dd, double *dl, double *db ) {
+   DECLARE_DOUBLE(DR);
+   DECLARE_DOUBLE(DD);
+   DECLARE_DOUBLE(DL);
+   DECLARE_DOUBLE(DB);
+   DR = dr;
+   DD = dd;
+   F77_LOCK( F77_CALL(sla_eqgal)( DOUBLE_ARG(&DR),
+                        DOUBLE_ARG(&DD),
+                        DOUBLE_ARG(&DL),
+                        DOUBLE_ARG(&DB) ); )
+   *dl = DL;
+   *db = DB;
+}
+
+F77_SUBROUTINE(sla_fk45z)( DOUBLE(R1950),
+                           DOUBLE(D1950),
+                           DOUBLE(BEPOCH),
+                           DOUBLE(R2000),
+                           DOUBLE(D2000) );
+
+void slaFk45z ( double r1950, double d1950, double bepoch,
+                double *r2000, double *d2000 ) {
+   DECLARE_DOUBLE(R1950);
+   DECLARE_DOUBLE(D1950);
+   DECLARE_DOUBLE(BEPOCH);
+   DECLARE_DOUBLE(R2000);
+   DECLARE_DOUBLE(D2000);
+   R1950 = r1950;
+   D1950 = d1950;
+   BEPOCH = bepoch;
+   F77_LOCK( F77_CALL(sla_fk45z)( DOUBLE_ARG(&R1950),
+                        DOUBLE_ARG(&D1950),
+                        DOUBLE_ARG(&BEPOCH),
+                        DOUBLE_ARG(&R2000),
+                        DOUBLE_ARG(&D2000) ); )
+   *r2000 = R2000;
+   *d2000 = D2000;
+}
+
+F77_SUBROUTINE(sla_fk54z)( DOUBLE(R2000),
+                           DOUBLE(D2000),
+                           DOUBLE(BEPOCH),
+                           DOUBLE(R1950),
+                           DOUBLE(D1950),
+                           DOUBLE(DR1950),
+                           DOUBLE(DD1950) );
+
+void slaFk54z ( double r2000, double d2000, double bepoch,
+                double *r1950, double *d1950,
+                double *dr1950, double *dd1950 ) {
+   DECLARE_DOUBLE(R2000);
+   DECLARE_DOUBLE(D2000);
+   DECLARE_DOUBLE(BEPOCH);
+   DECLARE_DOUBLE(R1950);
+   DECLARE_DOUBLE(D1950);
+   DECLARE_DOUBLE(DR1950);
+   DECLARE_DOUBLE(DD1950);
+   R2000 = r2000;
+   D2000 = d2000;
+   BEPOCH = bepoch;
+   F77_LOCK( F77_CALL(sla_fk54z)( DOUBLE_ARG(&R2000),
+                        DOUBLE_ARG(&D2000),
+                        DOUBLE_ARG(&BEPOCH),
+                        DOUBLE_ARG(&R1950),
+                        DOUBLE_ARG(&D1950),
+                        DOUBLE_ARG(&DR1950),
+                        DOUBLE_ARG(&DD1950) ); )
+   *r1950 = R1950;
+   *d1950 = D1950;
+   *dr1950 = DR1950;
+   *dd1950 = DD1950;
+}
+
+F77_SUBROUTINE(sla_galeq)( DOUBLE(DL),
+                           DOUBLE(DB),
+                           DOUBLE(DR),
+                           DOUBLE(DD) );
+
+void slaGaleq ( double dl, double db, double *dr, double *dd ) {
+   DECLARE_DOUBLE(DL);
+   DECLARE_DOUBLE(DB);
+   DECLARE_DOUBLE(DR);
+   DECLARE_DOUBLE(DD);
+   DL = dl;
+   DB = db;
+   F77_LOCK( F77_CALL(sla_galeq)( DOUBLE_ARG(&DL),
+                        DOUBLE_ARG(&DB),
+                        DOUBLE_ARG(&DR),
+                        DOUBLE_ARG(&DD) ); )
+   *dr = DR;
+   *dd = DD;
+}
+
+F77_SUBROUTINE(sla_galsup)( DOUBLE(DL),
+                            DOUBLE(DB),
+                            DOUBLE(DSL),
+                            DOUBLE(DSB) );
+
+void slaGalsup ( double dl, double db, double *dsl, double *dsb ) {
+   DECLARE_DOUBLE(DL);
+   DECLARE_DOUBLE(DB);
+   DECLARE_DOUBLE(DSL);
+   DECLARE_DOUBLE(DSB);
+   DL = dl;
+   DB = db;
+   F77_LOCK( F77_CALL(sla_galsup)( DOUBLE_ARG(&DL),
+                         DOUBLE_ARG(&DB),
+                         DOUBLE_ARG(&DSL),
+                         DOUBLE_ARG(&DSB) ); )
+   *dsl = DSL;
+   *dsb = DSB;
+}
+
+F77_DOUBLE_FUNCTION(sla_gmst)( DOUBLE(UT1) );
+
+double slaGmst ( double ut1 ) {
+   DECLARE_DOUBLE(UT1);
+   double result;
+   UT1 = ut1;
+   F77_LOCK( result = F77_CALL(sla_gmst)( DOUBLE_ARG(&UT1) ); )
+   return result;
+}
+
+F77_SUBROUTINE(sla_mappa)( DOUBLE(EQ),
+                           DOUBLE(DATE),
+                           DOUBLE_ARRAY(AMPRMS) );
+
+void slaMappa ( double eq, double date, double amprms[21] ) {
+   DECLARE_DOUBLE(EQ);
+   DECLARE_DOUBLE(DATE);
+   DECLARE_DOUBLE_ARRAY(AMPRMS,21);
+   int i;
+   EQ = eq;
+   DATE = date;
+   F77_LOCK( F77_CALL(sla_mappa)( DOUBLE_ARG(&EQ),
+                        DOUBLE_ARG(&DATE),
+                        DOUBLE_ARRAY_ARG(AMPRMS) ); )
+   for ( i = 0; i < 21; i++ ) amprms[ i ] = AMPRMS[ i ];
+}
+
+F77_SUBROUTINE(sla_map)(DOUBLE(RM), DOUBLE(DM),
+			DOUBLE(PR), DOUBLE(PD),
+			DOUBLE(PX),
+			DOUBLE(RV),
+			DOUBLE(EQ),
+			DOUBLE(DATE),
+			DOUBLE(RA), DOUBLE(DA) );
+
+void
+slaMap( double rm, double dm, double pr, double pd, double px,
+	double rv, double eq, double date, double * ra, double * da ) {
+  DECLARE_DOUBLE(RM);
+  DECLARE_DOUBLE(DM);
+  DECLARE_DOUBLE(PR);
+  DECLARE_DOUBLE(PD);
+  DECLARE_DOUBLE(PX);
+  DECLARE_DOUBLE(RV);
+  DECLARE_DOUBLE(EQ);
+  DECLARE_DOUBLE(DATE);
+  DECLARE_DOUBLE(RA);
+  DECLARE_DOUBLE(DA);
+
+  F77_EXPORT_DOUBLE(rm,RM);
+  F77_EXPORT_DOUBLE(dm,DM);
+  F77_EXPORT_DOUBLE(pr,PR);
+  F77_EXPORT_DOUBLE(pd,PD);
+  F77_EXPORT_DOUBLE(px,PX);
+  F77_EXPORT_DOUBLE(rv,RV);
+  F77_EXPORT_DOUBLE(eq,EQ);
+  F77_EXPORT_DOUBLE(date,DATE);
+
+  F77_LOCK( F77_CALL(sla_map)( DOUBLE_ARG(&RM),
+		     DOUBLE_ARG(&DM),
+		     DOUBLE_ARG(&PR),
+		     DOUBLE_ARG(&PD),
+		     DOUBLE_ARG(&PX),
+		     DOUBLE_ARG(&RV),
+		     DOUBLE_ARG(&EQ),
+		     DOUBLE_ARG(&DATE),
+		     DOUBLE_ARG(&RA),
+		     DOUBLE_ARG(&DA)
+		     ); )
+
+
+  F77_IMPORT_DOUBLE(RA, *ra);
+  F77_IMPORT_DOUBLE(DA, *da);
+}
+
+
+F77_SUBROUTINE(sla_mapqkz)( DOUBLE(RM),
+                            DOUBLE(DM),
+                            DOUBLE_ARRAY(AMPRMS),
+                            DOUBLE(RA),
+                            DOUBLE(DA) );
+
+void slaMapqkz ( double rm, double dm, double amprms[21],
+                 double *ra, double *da ) {
+   DECLARE_DOUBLE(RM);
+   DECLARE_DOUBLE(DM);
+   DECLARE_DOUBLE_ARRAY(AMPRMS,21);
+   DECLARE_DOUBLE(RA);
+   DECLARE_DOUBLE(DA);
+   int i;
+   RM = rm;
+   DM = dm;
+   for ( i = 0; i < 21; i++ ) AMPRMS[ i ] = amprms[ i ];
+   F77_LOCK( F77_CALL(sla_mapqkz)( DOUBLE_ARG(&RM),
+                         DOUBLE_ARG(&DM),
+                         DOUBLE_ARRAY_ARG(AMPRMS),
+                         DOUBLE_ARG(&RA),
+                         DOUBLE_ARG(&DA) ); )
+   *ra = RA;
+   *da = DA;
+}
+
+F77_SUBROUTINE(sla_mapqk)( DOUBLE(RM),
+                           DOUBLE(DM),
+                           DOUBLE(PR),
+                           DOUBLE(PD),
+                           DOUBLE(PX),
+                           DOUBLE(RV),
+                           DOUBLE_ARRAY(AMPRMS),
+                           DOUBLE(RA),
+                           DOUBLE(DA) );
+
+void slaMapqk ( double rm, double dm, double pr, double pd,
+                double px, double rv, double amprms[21],
+                double *ra, double *da ) {
+   DECLARE_DOUBLE(RM);
+   DECLARE_DOUBLE(DM);
+   DECLARE_DOUBLE(PR);
+   DECLARE_DOUBLE(PD);
+   DECLARE_DOUBLE(PX);
+   DECLARE_DOUBLE(RV);
+   DECLARE_DOUBLE_ARRAY(AMPRMS,21);
+   DECLARE_DOUBLE(RA);
+   DECLARE_DOUBLE(DA);
+   int i;
+   RM = rm;
+   DM = dm;
+   PR = pr;
+   PD = pd;
+   PX = px;
+   RV = rv;
+   for ( i = 0; i < 21; i++ ) AMPRMS[ i ] = amprms[ i ];
+   F77_LOCK( F77_CALL(sla_mapqk)( DOUBLE_ARG(&RM),
+                         DOUBLE_ARG(&DM),
+                         DOUBLE_ARG(&PR),
+                         DOUBLE_ARG(&PD),
+                         DOUBLE_ARG(&PX),
+                         DOUBLE_ARG(&RV),
+                         DOUBLE_ARRAY_ARG(AMPRMS),
+                         DOUBLE_ARG(&RA),
+                         DOUBLE_ARG(&DA) ); )
+   *ra = RA;
+   *da = DA;
+}
+
+F77_SUBROUTINE(sla_prebn)( DOUBLE(BEP0),
+                           DOUBLE(BEP1),
+                           DOUBLE_ARRAY(RMATP) );
+
+void slaPrebn ( double bep0, double bep1, double rmatp[3][3] ) {
+   DECLARE_DOUBLE(BEP0);
+   DECLARE_DOUBLE(BEP1);
+   DECLARE_DOUBLE_ARRAY(RMATP,9);
+   int i;
+   int j;
+   BEP0 = bep0;
+   BEP1 = bep1;
+   F77_LOCK( F77_CALL(sla_prebn)( DOUBLE_ARG(&BEP0),
+                        DOUBLE_ARG(&BEP1),
+                        DOUBLE_ARRAY_ARG(RMATP) ); )
+   for ( i = 0; i < 3; i++ ) {
+      for ( j = 0; j < 3; j++ ) rmatp[ i ][ j ] = RMATP[ i + 3 * j ];
+   }
+}
+
+F77_SUBROUTINE(sla_prec)( DOUBLE(EP0),
+                          DOUBLE(EP1),
+                          DOUBLE_ARRAY(RMATP) );
+
+void slaPrec ( double ep0, double ep1, double rmatp[3][3] ) {
+   DECLARE_DOUBLE(EP0);
+   DECLARE_DOUBLE(EP1);
+   DECLARE_DOUBLE_ARRAY(RMATP,9);
+   int i;
+   int j;
+   EP0 = ep0;
+   EP1 = ep1;
+   F77_LOCK( F77_CALL(sla_prec)( DOUBLE_ARG(&EP0),
+                       DOUBLE_ARG(&EP1),
+                       DOUBLE_ARRAY_ARG(RMATP) ); )
+   for ( i = 0; i < 3; i++ ) {
+      for ( j = 0; j < 3; j++ ) rmatp[ i ][ j ] = RMATP[ i + 3 * j ];
+   }
+}
+
+F77_REAL_FUNCTION(sla_rverot)( REAL(PHI),
+                               REAL(RA),
+                               REAL(DEC),
+                               REAL(ST) );
+
+float slaRverot ( float phi, float ra, float dec, float st ) {
+   DECLARE_REAL(PHI);
+   DECLARE_REAL(RA);
+   DECLARE_REAL(DEC);
+   DECLARE_REAL(ST);
+   float result;
+   PHI = phi;
+   RA = ra;
+   DEC = dec;
+   ST = st;
+   F77_LOCK( result = F77_CALL(sla_rverot)( REAL_ARG(&PHI),
+                                  REAL_ARG(&RA),
+                                  REAL_ARG(&DEC),
+                                  REAL_ARG(&ST) ); )
+   return result;
+}
+
+F77_REAL_FUNCTION(sla_rvgalc)( REAL(RA),
+                               REAL(DEC) );
+
+float slaRvgalc ( float ra, float dec ) {
+   DECLARE_REAL(RA);
+   DECLARE_REAL(DEC);
+   float result;
+   RA = ra;
+   DEC = dec;
+   F77_LOCK( result = F77_CALL(sla_rvgalc)( REAL_ARG(&RA),
+                                  REAL_ARG(&DEC) ); )
+   return result;
+}
+
+F77_REAL_FUNCTION(sla_rvlg)( REAL(RA),
+                             REAL(DEC) );
+
+float slaRvlg ( float ra, float dec ) {
+   DECLARE_REAL(RA);
+   DECLARE_REAL(DEC);
+   float result;
+   RA = ra;
+   DEC = dec;
+   F77_LOCK( result = F77_CALL(sla_rvlg)( REAL_ARG(&RA),
+                                REAL_ARG(&DEC) ); )
+   return result;
+}
+
+F77_REAL_FUNCTION(sla_rvlsrd)( REAL(RA),
+                               REAL(DEC) );
+
+float slaRvlsrd ( float ra, float dec ) {
+   DECLARE_REAL(RA);
+   DECLARE_REAL(DEC);
+   float result;
+   RA = ra;
+   DEC = dec;
+   F77_LOCK( result = F77_CALL(sla_rvlsrd)( REAL_ARG(&RA),
+                                  REAL_ARG(&DEC) ); )
+   return result;
+}
+
+F77_REAL_FUNCTION(sla_rvlsrk)( REAL(RA),
+                               REAL(DEC) );
+
+float slaRvlsrk ( float ra, float dec ) {
+   DECLARE_REAL(RA);
+   DECLARE_REAL(DEC);
+   float result;
+   RA = ra;
+   DEC = dec;
+   F77_LOCK( result = F77_CALL(sla_rvlsrk)( REAL_ARG(&RA),
+                                  REAL_ARG(&DEC) ); )
+   return result;
+}
+
+
+F77_SUBROUTINE(sla_subet)( DOUBLE(RC),
+                           DOUBLE(DC),
+                           DOUBLE(EQ),
+                           DOUBLE(RM),
+                           DOUBLE(DM) );
+
+void slaSubet ( double rc, double dc, double eq, double *rm, double *dm ) {
+   DECLARE_DOUBLE(RC);
+   DECLARE_DOUBLE(DC);
+   DECLARE_DOUBLE(EQ);
+   DECLARE_DOUBLE(RM);
+   DECLARE_DOUBLE(DM);
+   RC = rc;
+   DC = dc;
+   EQ = eq;
+   F77_LOCK( F77_CALL(sla_subet)( DOUBLE_ARG(&RC),
+                        DOUBLE_ARG(&DC),
+                        DOUBLE_ARG(&EQ),
+                        DOUBLE_ARG(&RM),
+                        DOUBLE_ARG(&DM) ); )
+   *rm = RM;
+   *dm = DM;
+}
+
+F77_SUBROUTINE(sla_supgal)( DOUBLE(DSL),
+                            DOUBLE(DSB),
+                            DOUBLE(DL),
+                            DOUBLE(DB) );
+
+void slaSupgal ( double dsl, double dsb, double *dl, double *db ) {
+   DECLARE_DOUBLE(DSL);
+   DECLARE_DOUBLE(DSB);
+   DECLARE_DOUBLE(DL);
+   DECLARE_DOUBLE(DB);
+   DSL = dsl;
+   DSB = dsb;
+   F77_LOCK( F77_CALL(sla_supgal)( DOUBLE_ARG(&DSL),
+                         DOUBLE_ARG(&DSB),
+                         DOUBLE_ARG(&DL),
+                         DOUBLE_ARG(&DB) ); )
+   *dl = DL;
+   *db = DB;
+}
+
+
+
+F77_SUBROUTINE(sla_svd)( INTEGER(M),
+                         INTEGER(N),
+                         INTEGER(MP),
+                         INTEGER(NP),
+                         DOUBLE_ARRAY(A),
+                         DOUBLE_ARRAY(W),
+                         DOUBLE_ARRAY(V),
+                         DOUBLE_ARRAY(WORK),
+                         INTEGER(JSTAT) );
+
+void slaSvd ( int m, int n, int mp, int np,
+              double *a, double *w, double *v, double *work,
+              int *jstat ){
+   DECLARE_INTEGER(M);
+   DECLARE_INTEGER(N);
+   DECLARE_INTEGER(MP);
+   DECLARE_INTEGER(NP);
+   F77_DOUBLE_TYPE *A;
+   F77_DOUBLE_TYPE *W;
+   F77_DOUBLE_TYPE *V;
+   F77_DOUBLE_TYPE *WORK;
+   DECLARE_INTEGER(JSTAT);
+
+
+   int i;
+   int j;
+
+   A = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) ( mp * np ) );
+   W = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) n );
+   V = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) ( np * np ) );
+   WORK = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) n );
+
+   if ( WORK ) {
+      M = m;
+      N = n;
+      MP = mp;
+      NP = np;
+
+      for ( i = 0; i < m; i++ ) {
+         for ( j = 0; j < n; j++ ) A[ i + mp * j ] = a[ np * i + j ];
+      }
+
+      F77_LOCK( F77_CALL(sla_svd)( INTEGER_ARG(&M),
+                         INTEGER_ARG(&N),
+                         INTEGER_ARG(&MP),
+                         INTEGER_ARG(&NP),
+                         DOUBLE_ARRAY_ARG(A),
+                         DOUBLE_ARRAY_ARG(W),
+                         DOUBLE_ARRAY_ARG(V),
+                         DOUBLE_ARRAY_ARG(WORK),
+                         INTEGER_ARG(&JSTAT) ); )
+
+
+      for ( i = 0; i < m; i++ ) {
+         for ( j = 0; j < n; j++ ) a[ np * i + j ] = A[ i + mp * j ];
+      }
+
+      for ( i = 0; i < n; i++ ) {
+         w[ i ] = W[ i ];
+         work[ i ] = WORK[ i ];
+         for ( j = 0; j < n; j++ ) v[ np * i + j ] = V[ i + np * j ];
+      }
+
+      *jstat = JSTAT;
+   }
+
+   free( A );
+   free( W );
+   free( V );
+   free( WORK );
+}
+
+F77_SUBROUTINE(sla_svdsol)( INTEGER(M),
+                         INTEGER(N),
+                         INTEGER(MP),
+                         INTEGER(NP),
+                         DOUBLE_ARRAY(B),
+                         DOUBLE_ARRAY(U),
+                         DOUBLE_ARRAY(W),
+                         DOUBLE_ARRAY(V),
+                         DOUBLE_ARRAY(WORK),
+                         DOUBLE_ARRAY(X) );
+
+void slaSvdsol ( int m, int n, int mp, int np,
+                 double *b, double *u, double *w, double *v,
+                 double *work, double *x ){
+
+   DECLARE_INTEGER(M);
+   DECLARE_INTEGER(N);
+   DECLARE_INTEGER(MP);
+   DECLARE_INTEGER(NP);
+   F77_DOUBLE_TYPE *B;
+   F77_DOUBLE_TYPE *U;
+   F77_DOUBLE_TYPE *W;
+   F77_DOUBLE_TYPE *V;
+   F77_DOUBLE_TYPE *WORK;
+   F77_DOUBLE_TYPE *X;
+
+   int i;
+   int j;
+
+   B = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) ( m ) );
+   U = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) ( mp * np ) );
+   W = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) n );
+   V = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) ( np * np ) );
+   WORK = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) n );
+   X = malloc( sizeof( F77_DOUBLE_TYPE ) * (size_t) n );
+
+   if ( X ) {
+      M = m;
+      N = n;
+      MP = mp;
+      NP = np;
+
+      for ( i = 0; i < m; i++ ) {
+         B[ i ] = b[ i ];
+         for ( j = 0; j < n; j++ ) U[ i + mp * j ] = u[ np * i + j ];
+      }
+      for ( i = 0; i < n; i++ ) {
+         W[ i ] = w[ i ];
+         for ( j = 0; j < n; j++ ) V[ i + np * j ] = v[ np * i + j ];
+      }
+
+      F77_LOCK( F77_CALL(sla_svdsol)( INTEGER_ARG(&M),
+                         INTEGER_ARG(&N),
+                         INTEGER_ARG(&MP),
+                         INTEGER_ARG(&NP),
+                         DOUBLE_ARRAY_ARG(B),
+                         DOUBLE_ARRAY_ARG(U),
+                         DOUBLE_ARRAY_ARG(W),
+                         DOUBLE_ARRAY_ARG(V),
+                         DOUBLE_ARRAY_ARG(WORK),
+                         DOUBLE_ARRAY_ARG(X) ); )
+
+      for ( i = 0; i < n; i++ ) {
+         x[ i ] = X[ i ];
+         work[ i ] = WORK[ i ];
+      }
+   }
+
+   free( B );
+   free( U );
+   free( W );
+   free( V );
+   free( WORK );
+   free( X );
+}
+
+
+
+F77_SUBROUTINE(sla_evp)( DOUBLE(DATE),
+                         DOUBLE(DEQX),
+                         DOUBLE_ARRAY(DVB),
+                         DOUBLE_ARRAY(DPB),
+                         DOUBLE_ARRAY(DVH),
+                         DOUBLE_ARRAY(DPH) );
+
+void slaEvp ( double date, double deqx, double dvb[3], double dpb[3],
+              double dvh[3], double dph[3] ) {
+   DECLARE_DOUBLE(DATE);
+   DECLARE_DOUBLE(DEQX);
+   DECLARE_DOUBLE_ARRAY(DVB,3);
+   DECLARE_DOUBLE_ARRAY(DPB,3);
+   DECLARE_DOUBLE_ARRAY(DVH,3);
+   DECLARE_DOUBLE_ARRAY(DPH,3);
+
+   int i;
+   DATE = date;
+   DEQX = deqx;
+   F77_LOCK( F77_CALL(sla_evp)( DOUBLE_ARG(&DATE),
+                      DOUBLE_ARG(&DEQX),
+                      DOUBLE_ARRAY_ARG(DVB),
+                      DOUBLE_ARRAY_ARG(DPB),
+                      DOUBLE_ARRAY_ARG(DVH),
+                      DOUBLE_ARRAY_ARG(DPH) ); )
+   for ( i = 0; i < 3; i++ ) {
+      dvb[ i ] = DVB[ i ];
+      dpb[ i ] = DPB[ i ];
+      dvh[ i ] = DVH[ i ];
+      dph[ i ] = DPH[ i ];
+   }
+
+}
+
+F77_SUBROUTINE(sla_fk5hz)( DOUBLE(R5),
+                           DOUBLE(D5),
+                           DOUBLE(JEPOCH),
+                           DOUBLE(RH),
+                           DOUBLE(DH) );
+
+void slaFk5hz ( double r5, double d5, double jepoch,
+                double *rh, double *dh ) {
+   DECLARE_DOUBLE(R5);
+   DECLARE_DOUBLE(D5);
+   DECLARE_DOUBLE(JEPOCH);
+   DECLARE_DOUBLE(RH);
+   DECLARE_DOUBLE(DH);
+   R5 = r5;
+   D5 = d5;
+   JEPOCH = jepoch;
+   F77_LOCK( F77_CALL(sla_fk5hz)( DOUBLE_ARG(&R5),
+                        DOUBLE_ARG(&D5),
+                        DOUBLE_ARG(&JEPOCH),
+                        DOUBLE_ARG(&RH),
+                        DOUBLE_ARG(&DH) ); )
+   *rh = RH;
+   *dh = DH;
+}
+
+F77_SUBROUTINE(sla_hfk5z)( DOUBLE(RH),
+                           DOUBLE(DH),
+                           DOUBLE(JEPOCH),
+                           DOUBLE(R5),
+                           DOUBLE(D5),
+                           DOUBLE(DR5),
+                           DOUBLE(DD5) );
+
+void slaHfk5z ( double rh, double dh, double jepoch,
+                double *r5, double *d5,
+                double *dr5, double *dd5 ) {
+   DECLARE_DOUBLE(RH);
+   DECLARE_DOUBLE(DH);
+   DECLARE_DOUBLE(JEPOCH);
+   DECLARE_DOUBLE(R5);
+   DECLARE_DOUBLE(D5);
+   DECLARE_DOUBLE(DR5);
+   DECLARE_DOUBLE(DD5);
+   RH = rh;
+   DH = dh;
+   JEPOCH = jepoch;
+   F77_LOCK( F77_CALL(sla_hfk5z)( DOUBLE_ARG(&RH),
+                        DOUBLE_ARG(&DH),
+                        DOUBLE_ARG(&JEPOCH),
+                        DOUBLE_ARG(&R5),
+                        DOUBLE_ARG(&D5),
+                        DOUBLE_ARG(&DR5),
+                        DOUBLE_ARG(&DD5) ); )
+   *r5 = R5;
+   *d5 = D5;
+   *dr5 = DR5;
+   *dd5 = DD5;
+}
+
+F77_SUBROUTINE(sla_geoc)( DOUBLE(P),
+                          DOUBLE(H),
+                          DOUBLE(R),
+                          DOUBLE(Z) );
+
+void slaGeoc ( double p, double h, double *r, double *z ) {
+   DECLARE_DOUBLE(P);
+   DECLARE_DOUBLE(H);
+   DECLARE_DOUBLE(R);
+   DECLARE_DOUBLE(Z);
+   P = p;
+   H = h;
+   F77_LOCK( F77_CALL(sla_geoc)( DOUBLE_ARG(&P),
+                       DOUBLE_ARG(&H),
+                       DOUBLE_ARG(&R),
+                       DOUBLE_ARG(&Z) ); )
+   *r = R;
+   *z = Z;
+}
+
+F77_SUBROUTINE(sla_deuler)( CHARACTER(ORDER),
+                            DOUBLE(PHI),
+                            DOUBLE(THETA),
+                            DOUBLE(PSI),
+                            DOUBLE_ARRAY(RMAT)
+                            TRAIL(ORDER) );
+
+void slaDeuler ( const char *order, double phi, double theta, double psi,
+                 double rmat[3][3] ) {
+
+   DECLARE_CHARACTER(ORDER,4);
+   DECLARE_DOUBLE(PHI);
+   DECLARE_DOUBLE(THETA);
+   DECLARE_DOUBLE(PSI);
+   DECLARE_DOUBLE_ARRAY(RMAT,9);
+   int i,j;
+
+   PHI   = phi;
+   THETA = theta;
+   PSI   = psi;
+
+   slaStringExport( order, ORDER, 4 );
+
+   F77_LOCK( F77_CALL (sla_deuler) ( CHARACTER_ARG(ORDER),
+                           DOUBLE_ARG(&PHI),
+                           DOUBLE_ARG(&THETA),
+                           DOUBLE_ARG(&PSI),
+                           DOUBLE_ARRAY_ARG(RMAT)
+                           TRAIL_ARG(ORDER) ); )
+
+   for ( i = 0; i < 3; i++ ) {
+      for ( j = 0; j < 3; j++ ) rmat[ i ][ j ] = RMAT[ i + 3 * j ];
+   }
+
+}
+
+F77_SUBROUTINE(sla_de2h)( DOUBLE(HA),
+                          DOUBLE(DEC),
+                          DOUBLE(PHI),
+                          DOUBLE(AZ),
+                          DOUBLE(EL) );
+
+void slaDe2h ( double ha, double dec, double phi, double *az, double *el ) {
+   DECLARE_DOUBLE(HA);
+   DECLARE_DOUBLE(DEC);
+   DECLARE_DOUBLE(PHI);
+   DECLARE_DOUBLE(AZ);
+   DECLARE_DOUBLE(EL);
+   HA = ha;
+   DEC = dec;
+   PHI = phi;
+   F77_LOCK( F77_CALL(sla_de2h)( DOUBLE_ARG(&HA),
+                       DOUBLE_ARG(&DEC),
+                       DOUBLE_ARG(&PHI),
+                       DOUBLE_ARG(&AZ),
+                       DOUBLE_ARG(&EL) ); )
+   *az = AZ;
+   *el = EL;
+}
+
+F77_SUBROUTINE(sla_dh2e)( DOUBLE(AZ),
+                          DOUBLE(EL),
+                          DOUBLE(PHI),
+                          DOUBLE(HA),
+                          DOUBLE(DEC) );
+
+void slaDh2e ( double az, double el, double phi, double *ha, double *dec ) {
+   DECLARE_DOUBLE(AZ);
+   DECLARE_DOUBLE(EL);
+   DECLARE_DOUBLE(PHI);
+   DECLARE_DOUBLE(HA);
+   DECLARE_DOUBLE(DEC);
+   AZ = az;
+   EL = el;
+   PHI = phi;
+   F77_LOCK( F77_CALL(sla_dh2e)( DOUBLE_ARG(&AZ),
+                       DOUBLE_ARG(&EL),
+                       DOUBLE_ARG(&PHI),
+                       DOUBLE_ARG(&HA),
+                       DOUBLE_ARG(&DEC) ); )
+   *ha = HA;
+   *dec = DEC;
+}
+
+
+F77_SUBROUTINE(sla_obs)( INTEGER(I),
+			 CHARACTER(C),
+			 CHARACTER(NAME),
+			 DOUBLE(W),
+			 DOUBLE(P),
+			 DOUBLE(H)
+			 TRAIL(C)
+			 TRAIL(NAME) );
+
+/* Note that SLA insists that "c" has space for 10 characters + nul
+   and "name" has space for 40 characters + nul */
+
+void
+slaObs( int n, char *c, char *name, double *w, double *p, double *h  ) {
+
+  DECLARE_INTEGER( N );
+  DECLARE_CHARACTER( C, 10 );
+  DECLARE_CHARACTER( NAME, 40 );
+  DECLARE_DOUBLE( W );
+  DECLARE_DOUBLE( P );
+  DECLARE_DOUBLE( H );
+
+  if (n < 1) {
+    /* C needs to be imported */
+    slaStringExport( c, C, 10 );
+  } else {
+    /* initialise C */
+    slaStringExport( "", C, 10 );
+  }
+  F77_EXPORT_INTEGER( n, N );
+
+  /* w, p and h are not touched on error but for consistency this means
+     we copy the current values to Fortran so that we can correctly copy
+     back the result. */
+  F77_EXPORT_DOUBLE( *w, W );
+  F77_EXPORT_DOUBLE( *p, P );
+  F77_EXPORT_DOUBLE( *h, H );
+
+  /* call the routine */
+  F77_LOCK( F77_CALL(sla_obs)( INTEGER_ARG(&N),
+		     CHARACTER_ARG(C),
+		     CHARACTER_ARG(NAME),
+		     DOUBLE_ARG(&W),
+		     DOUBLE_ARG(&P),
+		     DOUBLE_ARG(&H)
+		     TRAIL_ARG(C)
+		     TRAIL_ARG(NAME) ); )
+
+  /* extract results */
+  slaStringImport( NAME, 40, name );
+  if (n > 0 && name[0] != '?') {
+    /* only do this if we know we used a numeric input and if the result
+       for the NAME is not '?' (since we are not allowed to alter the string
+       in that case). This allows people
+       to call slaObs with a string constant */
+    slaStringImport( C, 10, c );
+  }
+  F77_IMPORT_DOUBLE( W, *w );
+  F77_IMPORT_DOUBLE( P, *p );
+  F77_IMPORT_DOUBLE( H, *h );
+
+}
+
+F77_DOUBLE_FUNCTION(sla_pa)( DOUBLE(HA), DOUBLE(DEC), DOUBLE(PHI) );
+
+double
+slaPa ( double ha, double dec, double phi ) {
+  DECLARE_DOUBLE(HA);
+  DECLARE_DOUBLE(DEC);
+  DECLARE_DOUBLE(PHI);
+  DECLARE_DOUBLE(RETVAL);
+  double retval;
+
+  F77_EXPORT_DOUBLE( ha, HA );
+  F77_EXPORT_DOUBLE( dec, DEC );
+  F77_EXPORT_DOUBLE( phi, PHI );
+
+  F77_LOCK( RETVAL = F77_CALL(sla_pa)( DOUBLE_ARG(&HA), DOUBLE_ARG(&DEC), DOUBLE_ARG(&PHI)); )
+
+  F77_IMPORT_DOUBLE( RETVAL, retval );
+  return retval;
+}
+
+F77_DOUBLE_FUNCTION(sla_dtt)( DOUBLE(UTC) );
+
+double
+slaDtt( double utc ) {
+  DECLARE_DOUBLE(UTC);
+  DECLARE_DOUBLE(RETVAL);
+  double retval;
+
+  F77_EXPORT_DOUBLE( utc, UTC );
+  F77_LOCK( RETVAL = F77_CALL(sla_dtt)( DOUBLE_ARG(&UTC) ); )
+
+  F77_IMPORT_DOUBLE( RETVAL, retval );
+  return retval;
+}
+
+F77_DOUBLE_FUNCTION(sla_dat)( DOUBLE(UTC) );
+
+double
+slaDat( double utc ) {
+  DECLARE_DOUBLE(UTC);
+  DECLARE_DOUBLE(RETVAL);
+  double retval;
+
+  F77_EXPORT_DOUBLE( utc, UTC );
+  F77_LOCK( RETVAL = F77_CALL(sla_dat)( DOUBLE_ARG(&UTC) ); )
+
+  F77_IMPORT_DOUBLE( RETVAL, retval );
+  return retval;
+}
+
+F77_SUBROUTINE(sla_rdplan)(DOUBLE(DATE), INTEGER(I), DOUBLE(ELONG), DOUBLE(PHI),
+			   DOUBLE(RA), DOUBLE(DEC), DOUBLE(DIAM) );
+
+void
+slaRdplan( double date, int i, double elong, double phi,
+	   double * ra, double * dec, double * diam ) {
+  DECLARE_DOUBLE(DATE);
+  DECLARE_INTEGER(I);
+  DECLARE_DOUBLE(ELONG);
+  DECLARE_DOUBLE(PHI);
+  DECLARE_DOUBLE(RA);
+  DECLARE_DOUBLE(DEC);
+  DECLARE_DOUBLE(DIAM);
+
+  F77_EXPORT_DOUBLE( date, DATE );
+  F77_EXPORT_INTEGER( i, I );
+  F77_EXPORT_DOUBLE( elong, ELONG );
+  F77_EXPORT_DOUBLE( phi, PHI );
+
+  F77_LOCK( F77_CALL(sla_rdplan)( DOUBLE_ARG(&DATE),
+			INTEGER_ARG(&I),
+			DOUBLE_ARG(&ELONG),
+			DOUBLE_ARG(&PHI),
+			DOUBLE_ARG(&RA),
+			DOUBLE_ARG(&DEC),
+			DOUBLE_ARG(&DIAM)); )
+
+  F77_IMPORT_DOUBLE( RA, *ra );
+  F77_IMPORT_DOUBLE( DEC, *dec );
+  F77_IMPORT_DOUBLE( DIAM, *diam );
+}
+
+F77_SUBROUTINE(sla_dafin)( CHARACTER(STRING), INTEGER(IPTR), DOUBLE(A),
+			   INTEGER(J) TRAIL(STRING) );
+
+void
+slaDafin( const char * string, int * iptr, double *a, int *j ) {
+
+  DECLARE_CHARACTER_DYN(STRING);
+  DECLARE_DOUBLE(A);
+  DECLARE_INTEGER(IPTR);
+  DECLARE_INTEGER(J);
+
+  F77_EXPORT_INTEGER( *iptr, IPTR );
+  F77_CREATE_EXPORT_CHARACTER( string, STRING );
+
+  F77_LOCK( F77_CALL(sla_dafin)( CHARACTER_ARG(STRING), INTEGER_ARG(&IPTR),
+		       DOUBLE_ARG(&A), INTEGER_ARG(&J) TRAIL_ARG(STRING) ); )
+
+  F77_IMPORT_INTEGER(IPTR, *iptr );
+  F77_IMPORT_INTEGER(J, *j );
+  F77_IMPORT_DOUBLE(A, *a );
+  F77_FREE_CHARACTER(STRING);
+
+}
+
+F77_SUBROUTINE(sla_oap)( CHARACTER(TYPE),
+                         DOUBLE(OB1),
+                         DOUBLE(OB2),
+                         DOUBLE(DATE),
+                         DOUBLE(DUT),
+                         DOUBLE(ELONGM),
+                         DOUBLE(PHIM),
+                         DOUBLE(HM),
+                         DOUBLE(XP),
+                         DOUBLE(YP),
+                         DOUBLE(TDK),
+                         DOUBLE(PMB),
+                         DOUBLE(RH),
+                         DOUBLE(WL),
+                         DOUBLE(TLR),
+                         DOUBLE(RAP),
+                         DOUBLE(DAP)
+                         TRAIL(TYPE) );
+
+void slaOap ( const char *type, double ob1, double ob2, double date,
+              double dut, double elongm, double phim, double hm,
+              double xp, double yp, double tdk, double pmb,
+              double rh, double wl, double tlr,
+              double *rap, double *dap ) {
+  DECLARE_CHARACTER(TYPE,1);
+  DECLARE_DOUBLE(OB1);
+  DECLARE_DOUBLE(OB2);
+  DECLARE_DOUBLE(DATE);
+  DECLARE_DOUBLE(DUT);
+  DECLARE_DOUBLE(ELONGM);
+  DECLARE_DOUBLE(PHIM);
+  DECLARE_DOUBLE(HM);
+  DECLARE_DOUBLE(XP);
+  DECLARE_DOUBLE(YP);
+  DECLARE_DOUBLE(TDK);
+  DECLARE_DOUBLE(PMB);
+  DECLARE_DOUBLE(RH);
+  DECLARE_DOUBLE(WL);
+  DECLARE_DOUBLE(TLR);
+  DECLARE_DOUBLE(RAP);
+  DECLARE_DOUBLE(DAP);
+
+  slaStringExport( type, TYPE, 1 );
+  OB1 = ob1;
+  OB2 = ob2;
+  DATE = date;
+  DUT  = dut;
+  ELONGM = elongm;
+  PHIM = phim;
+  HM = hm;
+  XP = xp;
+  YP = yp;
+  TDK = tdk;
+  PMB = pmb;
+  RH = rh;
+  WL = wl;
+  TLR = tlr;
+
+  F77_LOCK( F77_CALL(sla_oap)( CHARACTER_ARG(TYPE),
+                     DOUBLE_ARG(&OB1), DOUBLE_ARG(&OB2),
+                     DOUBLE_ARG(&DATE), DOUBLE_ARG(&DUT),
+                     DOUBLE_ARG(&ELONGM), DOUBLE_ARG(&PHIM),
+                     DOUBLE_ARG(&HM), DOUBLE_ARG(&XP),
+                     DOUBLE_ARG(&YP), DOUBLE_ARG(&TDK),
+                     DOUBLE_ARG(&PMB), DOUBLE_ARG(&RH),
+                     DOUBLE_ARG(&WL), DOUBLE_ARG(&TLR),
+                     DOUBLE_ARG(&RAP), DOUBLE_ARG(&DAP)
+                     TRAIL_ARG(TYPE) ); )
+
+  *rap = RAP;
+  *dap = DAP;
+
+}
+
+F77_SUBROUTINE(sla_amp)( DOUBLE(RA),
+                         DOUBLE(DA),
+                         DOUBLE(DATE),
+                         DOUBLE(EQ),
+                         DOUBLE(RM),
+                         DOUBLE(DM)
+                         );
+
+void slaAmp( double ra, double da, double date, double eq,
+             double *rm, double *dm) {
+
+  DECLARE_DOUBLE(RA);
+  DECLARE_DOUBLE(DA);
+  DECLARE_DOUBLE(DATE);
+  DECLARE_DOUBLE(EQ);
+  DECLARE_DOUBLE(RM);
+  DECLARE_DOUBLE(DM);
+
+  RA = ra;
+  DA = da;
+  DATE = date;
+  EQ = eq;
+
+  F77_LOCK( F77_CALL(sla_amp)( DOUBLE_ARG(&RA),
+                     DOUBLE_ARG(&DA),
+                     DOUBLE_ARG(&DATE),
+                     DOUBLE_ARG(&EQ),
+                     DOUBLE_ARG(&RM),
+                     DOUBLE_ARG(&DM)); )
+
+  *rm = RM;
+  *dm = DM;
+
+}
+
+F77_SUBROUTINE(sla_aop)(
+                         DOUBLE(RAP),
+                         DOUBLE(DAP),
+                         DOUBLE(DATE),
+                         DOUBLE(DUT),
+                         DOUBLE(ELONGM),
+                         DOUBLE(PHIM),
+                         DOUBLE(HM),
+                         DOUBLE(XP),
+                         DOUBLE(YP),
+                         DOUBLE(TDK),
+                         DOUBLE(PMB),
+                         DOUBLE(RH),
+                         DOUBLE(WL),
+                         DOUBLE(TLR),
+                         DOUBLE(AOB),
+                         DOUBLE(ZOB),
+                         DOUBLE(HOB),
+                         DOUBLE(DOB),
+                         DOUBLE(ROB) );
+
+void slaAop ( double rap, double dap, double date, double dut,
+              double elongm, double phim, double hm, double xp,
+              double yp, double tdk, double pmb, double rh,
+              double wl, double tlr,
+              double *aob, double *zob, double *hob,
+              double *dob, double *rob ) {
+
+    DECLARE_DOUBLE(RAP);
+    DECLARE_DOUBLE(DAP);
+    DECLARE_DOUBLE(DATE);
+    DECLARE_DOUBLE(DUT);
+    DECLARE_DOUBLE(ELONGM);
+    DECLARE_DOUBLE(PHIM);
+    DECLARE_DOUBLE(HM);
+    DECLARE_DOUBLE(XP);
+    DECLARE_DOUBLE(YP);
+    DECLARE_DOUBLE(TDK);
+    DECLARE_DOUBLE(PMB);
+    DECLARE_DOUBLE(RH);
+    DECLARE_DOUBLE(WL);
+    DECLARE_DOUBLE(TLR);
+    DECLARE_DOUBLE(AOB);
+    DECLARE_DOUBLE(ZOB);
+    DECLARE_DOUBLE(HOB);
+    DECLARE_DOUBLE(DOB);
+    DECLARE_DOUBLE(ROB);
+
+    RAP = rap;
+    DAP = dap;
+    DATE = date;
+    DUT  = dut;
+    ELONGM = elongm;
+    PHIM = phim;
+    HM = hm;
+    XP = xp;
+    YP = yp;
+    TDK = tdk;
+    PMB = pmb;
+    RH = rh;
+    WL = wl;
+    TLR = tlr;
+
+    F77_LOCK( F77_CALL(sla_aop)(
+                      DOUBLE_ARG(&RAP),
+                      DOUBLE_ARG(&DAP),
+                      DOUBLE_ARG(&DATE),
+                      DOUBLE_ARG(&DUT),
+                      DOUBLE_ARG(&ELONGM),
+                      DOUBLE_ARG(&PHIM),
+                      DOUBLE_ARG(&HM),
+                      DOUBLE_ARG(&XP),
+                      DOUBLE_ARG(&YP),
+                      DOUBLE_ARG(&TDK),
+                      DOUBLE_ARG(&PMB),
+                      DOUBLE_ARG(&RH),
+                      DOUBLE_ARG(&WL),
+                      DOUBLE_ARG(&TLR),
+                      DOUBLE_ARG(&AOB),
+                      DOUBLE_ARG(&ZOB),
+                      DOUBLE_ARG(&HOB),
+                      DOUBLE_ARG(&DOB),
+                      DOUBLE_ARG(&ROB) ); )
+
+    *aob = AOB;
+    *zob = ZOB;
+    *hob = HOB;
+    *dob = DOB;
+    *rob = ROB;
+}
+
+F77_SUBROUTINE(sla_cldj)( INTEGER(IY),
+                          INTEGER(IM),
+                          INTEGER(ID),
+                          DOUBLE(DJM),
+                          INTEGER(I) );
+
+void
+slaCldj( int iy, int im, int id, double * djm, int *i ) {
+  DECLARE_INTEGER(IY);
+  DECLARE_INTEGER(IM);
+  DECLARE_INTEGER(ID);
+  DECLARE_DOUBLE(DJM);
+  DECLARE_INTEGER(I);
+
+  IY = iy;
+  IM = im;
+  ID = id;
+
+  F77_LOCK( F77_CALL(sla_cldj)( INTEGER_ARG(&IY),
+                      INTEGER_ARG(&IM),
+                      INTEGER_ARG(&ID),
+                      DOUBLE_ARG(&DJM),
+                      INTEGER_ARG(&I) ); )
+
+  *djm = DJM;
+  *i = I;
+
+}
+
+F77_SUBROUTINE(sla_pertel)( INTEGER(JFORM),
+                            DOUBLE(DATE0),
+                            DOUBLE(DATE1),
+                            DOUBLE(EPOCH0),
+                            DOUBLE(ORBI0),
+                            DOUBLE(ANODE0),
+                            DOUBLE(PERIH0),
+                            DOUBLE(AORQ0),
+                            DOUBLE(E0),
+                            DOUBLE(AM0),
+                            DOUBLE(EPOCH1),
+                            DOUBLE(ORBI1),
+                            DOUBLE(ANODE1),
+                            DOUBLE(PERIH1),
+                            DOUBLE(AORQ1),
+                            DOUBLE(E1),
+                            DOUBLE(AM1),
+                            INTEGER(JSTAT) );
+
+void slaPertel (int jform, double date0, double date1,
+                double epoch0, double orbi0, double anode0,
+                double perih0, double aorq0, double e0, double am0,
+                double *epoch1, double *orbi1, double *anode1,
+                double *perih1, double *aorq1, double *e1, double *am1,
+                int *jstat ) {
+
+  DECLARE_INTEGER(JFORM);
+  DECLARE_DOUBLE(DATE0);
+  DECLARE_DOUBLE(DATE1);
+  DECLARE_DOUBLE(EPOCH0);
+  DECLARE_DOUBLE(ORBI0);
+  DECLARE_DOUBLE(ANODE0);
+  DECLARE_DOUBLE(PERIH0);
+  DECLARE_DOUBLE(AORQ0);
+  DECLARE_DOUBLE(E0);
+  DECLARE_DOUBLE(AM0);
+  DECLARE_DOUBLE(EPOCH1);
+  DECLARE_DOUBLE(ORBI1);
+  DECLARE_DOUBLE(ANODE1);
+  DECLARE_DOUBLE(PERIH1);
+  DECLARE_DOUBLE(AORQ1);
+  DECLARE_DOUBLE(E1);
+  DECLARE_DOUBLE(AM1);
+  DECLARE_INTEGER(JSTAT);
+
+  JFORM = jform;
+  DATE0 = date0;
+  DATE1 = date1;
+  EPOCH0 = epoch0;
+  ORBI0 = orbi0;
+  ANODE0 = anode0;
+  PERIH0 = perih0;
+  AORQ0 = aorq0;
+  E0 = e0;
+  AM0 = am0;
+
+  F77_LOCK( F77_CALL(sla_pertel)( INTEGER_ARG(&JFORM),
+                       DOUBLE_ARG(&DATE0),
+                       DOUBLE_ARG(&DATE1),
+                       DOUBLE_ARG(&EPOCH0),
+                       DOUBLE_ARG(&ORBI0),
+                       DOUBLE_ARG(&ANODE0),
+                       DOUBLE_ARG(&PERIH0),
+                       DOUBLE_ARG(&AORQ0),
+                       DOUBLE_ARG(&E0),
+                       DOUBLE_ARG(&AM0),
+                       DOUBLE_ARG(&EPOCH1),
+                       DOUBLE_ARG(&ORBI1),
+                       DOUBLE_ARG(&ANODE1),
+                       DOUBLE_ARG(&PERIH1),
+                       DOUBLE_ARG(&AORQ1),
+                       DOUBLE_ARG(&E1),
+                       DOUBLE_ARG(&AM1),
+                       INTEGER_ARG(&JSTAT) ); )
+
+  *epoch1 = EPOCH1;
+  *orbi1 = ORBI1;
+  *anode1 = ANODE1;
+  *perih1 = PERIH1;
+  *aorq1 = AORQ1;
+  *e1 = E1;
+  *am1 = AM1;
+  *jstat = JSTAT;
+
+}
+
+F77_SUBROUTINE(sla_plante)(DOUBLE(DATE),
+                           DOUBLE(ELONG),
+                           DOUBLE(PHI),
+                           INTEGER(JFORM),
+                           DOUBLE(EPOCH),
+                           DOUBLE(ORBINC),
+                           DOUBLE(ANODE),
+                           DOUBLE(PERIH),
+                           DOUBLE(AORQ),
+                           DOUBLE(E),
+                           DOUBLE(AORL),
+                           DOUBLE(DM),
+                           DOUBLE(RA),
+                           DOUBLE(DEC),
+                           DOUBLE(R),
+                           INTEGER(JSTAT) );
+
+void slaPlante ( double date, double elong, double phi, int jform,
+                 double epoch, double orbinc, double anode, double perih,
+                 double aorq, double e, double aorl, double dm,
+                 double *ra, double *dec, double *r, int *jstat ) {
+
+  DECLARE_DOUBLE(DATE);
+  DECLARE_DOUBLE(ELONG);
+  DECLARE_DOUBLE(PHI);
+  DECLARE_INTEGER(JFORM);
+  DECLARE_DOUBLE(EPOCH);
+  DECLARE_DOUBLE(ORBINC);
+  DECLARE_DOUBLE(ANODE);
+  DECLARE_DOUBLE(PERIH);
+  DECLARE_DOUBLE(AORQ);
+  DECLARE_DOUBLE(E);
+  DECLARE_DOUBLE(AORL);
+  DECLARE_DOUBLE(DM);
+  DECLARE_DOUBLE(RA);
+  DECLARE_DOUBLE(DEC);
+  DECLARE_DOUBLE(R);
+  DECLARE_INTEGER(JSTAT);
+
+  DATE = date;
+  ELONG = elong;
+  PHI = phi;
+  JFORM = jform;
+  EPOCH = epoch;
+  ORBINC = orbinc;
+  ANODE = anode;
+  PERIH = perih;
+  AORQ = aorq;
+  E = e;
+  AORL = aorl;
+  DM = dm;
+
+  F77_LOCK( F77_CALL(sla_plante)( DOUBLE_ARG(&EPOCH),
+                       DOUBLE_ARG(&ELONG),
+                       DOUBLE_ARG(&PHI),
+                       INTEGER_ARG(&JFORM),
+                       DOUBLE_ARG(&EPOCH),
+                       DOUBLE_ARG(&ORBINC),
+                       DOUBLE_ARG(&ANODE),
+                       DOUBLE_ARG(&PERIH),
+                       DOUBLE_ARG(&AORQ),
+                       DOUBLE_ARG(&E),
+                       DOUBLE_ARG(&AORL),
+                       DOUBLE_ARG(&DM),
+                       DOUBLE_ARG(&RA),
+                       DOUBLE_ARG(&DEC),
+                       DOUBLE_ARG(&R),
+                       INTEGER_ARG(&JSTAT) ); )
+
+  *ra = RA;
+  *dec = DEC;
+  *r = R;
+  *jstat = JSTAT;
+
+}
+
+F77_SUBROUTINE(sla_preces)(CHARACTER(SYS),
+                           DOUBLE(EP0),
+			   DOUBLE(EP1),
+                           DOUBLE(RA),
+                           DOUBLE(DC)
+			   TRAIL(SYS) );
+
+void slaPreces ( const char sys[3], double ep0, double ep1,
+                 double *ra, double *dc ) {
+
+  DECLARE_CHARACTER(SYS,3);
+  DECLARE_DOUBLE(EP0);
+  DECLARE_DOUBLE(EP1);
+  DECLARE_DOUBLE(RA);
+  DECLARE_DOUBLE(DC);
+
+  slaStringExport( sys, SYS, 3 );
+  EP0 = ep0;
+  EP1 = ep1;
+  RA = *ra;
+  DC = *dc;
+
+  F77_LOCK( F77_CALL(sla_preces)( CHARACTER_ARG(SYS),
+				  DOUBLE_ARG(&EP0),
+				  DOUBLE_ARG(&EP1),
+				  DOUBLE_ARG(&RA),
+				  DOUBLE_ARG(&DC)
+				  TRAIL_ARG(SYS) ); )
+
+  *ra = RA;
+  *dc = DC;
+
+}
+
+
+F77_SUBROUTINE(sla_pvobs)( DOUBLE(P),
+			   DOUBLE(H),
+                           DOUBLE(STL),
+                           DOUBLE_ARRAY(PV) );
+
+void slaPvobs( double p, double h, double stl, double pv[6] ){
+   DECLARE_DOUBLE(P);
+   DECLARE_DOUBLE(H);
+   DECLARE_DOUBLE(STL);
+   DECLARE_DOUBLE_ARRAY(PV,6);
+
+   int i;
+   P = p;
+   H = h;
+   STL = stl;
+   F77_LOCK( F77_CALL(sla_pvobs)( DOUBLE_ARG(&P),
+                                  DOUBLE_ARG(&H),
+                                  DOUBLE_ARG(&STL),
+                                  DOUBLE_ARRAY_ARG(PV) ); )
+   for( i = 0; i < 6; i++ ) pv[ i ] = PV[ i ];
+}
+
diff --git a/math/slalib/sla.news b/math/slalib/sla.news
new file mode 100644
index 00000000..e395c6e5
--- /dev/null
+++ b/math/slalib/sla.news
@@ -0,0 +1,88 @@
+#     23-SEP-2005 (PTW):
+#        Suppression of compiler warnings.
+#        Improved sla_UE2PV.
+#        Package version number changed to 2.5-4.
+
+SLALIB_Version_2.5.5
+
+* The SLALIB C wrapper now optionally uses the CNF library to serialise
+calls from C to Fortran, there-by ensuring that the C functions are
+thread-safe. This dependency on CNF can be switched off by configuring
+SLALIB with the "--without-cnf" option, in which case CNF will not be
+used and the C wrappers will not be thread-safe.
+
+SLALIB_Version_2.5.4
+
+* Changes to sla_EL2UE, sla_FITXY, sla_PV2EL, sla_REFRO, sla_UE2PV and
+  sla_SVD to avoid warnings if compiled with -Wall and -g -O.
+
+* Changes to sla_UE2PV to improve convergence in high-eccentricity
+  cases.
+
+SLALIB_Version_2.5.3                                  Expiry 30 June 2006
+
+* 2006 January 1 leap second added to sla_DAT.
+
+SLALIB_Version_2.5.2                                  Expiry 31 March 2006
+
+* Bug-fix to sla_DSEPV.  Precisely antipodal vectors returned zero
+  instead of pi.
+
+SLALIB_Version_2.5.1                                  Expiry 31 March 2006
+
+* An additional Earth position/velocity routine, sla_EPV, has been
+  added.  It is bigger and slower than sla_EVP but much more accurate.
+  Position accuracy is a few km;  velocity accuracy is a few mm/s.
+  The sla_PERTUE and sla_PLANTU routines now call this routine in
+  order to deliver better predictions for near-Earth objects.
+
+SLALIB_Version_2.4-14                              Expiry 31 December 2005
+
+* Cosmetic changes to about 20% of the routines.
+
+* Updated optical refraction model in REFCOQ and REFRO.
+
+SLALIB_Version_2.4-12
+
+* SLALIB has been autoconfed and integrated into the new Starlink build
+  system.
+
+* It has been released under the Gnu General Public License
+
+SLALIB_Version_2.4-11                                 Expiry 31 March 2004
+
+The latest releases of SLALIB include the following changes:
+
+* A new routine PLANTU has been added.  It predicts the topocentric
+  apparent RA,Dec of a solar-system body given the Universal Elements.
+  It is a Universal-Elements counterpart to PLANTE, which uses
+  conventional spherical elements (and which now calls PLANTU).
+
+* The documentation for the suite of heliocentric orbital elements
+  routines has been improved to make it easier and more obvious how
+  to use of elements from JPL Horizons and from the Minor Planet
+  Center.
+
+  Confusion over epochs has often arisen, because the epoch of osculation
+  (when the elements are momentarily correct) is completely separate from
+  the epochs that locate a body in its orbit, the former having a role
+  only when appying perturbations.  Part of the reason for this confusion
+  is that for major and minor planets it is conventional to adopt the
+  same epoch for (i) osculation and (ii) computing the anomaly or longitude
+  that fixes the body, even though they could in principle be different.
+  For the comet case this convention is impossible because the choice of
+  perihelion dictates the epoch fixing the body, and hence the existence
+  of (and need for) two independent concepts of epoch is exposed.
+
+  The SLALIB routines in question, especially slaPlante, now have extra
+  explanation dealing with the three distinct epochs (date of observation,
+  fixing the body, and osculation) and also some notes dealing with JPL
+  and MPC elements.  Additionally, a table has been added to SUN/67
+  showing how to use the JPL and MPC elements.
+
+ P.T.Wallace
+ 8 April 2005
+
+ ptw@tpsoft.demon.co.uk
+ +44-1235-531198
+--------------------------------------------------------------------------
diff --git a/math/slalib/slaTest.c b/math/slalib/slaTest.c
new file mode 100644
index 00000000..ab684558
--- /dev/null
+++ b/math/slalib/slaTest.c
@@ -0,0 +1,112 @@
+/*
+ *+
+ *  Name:
+ *     slaTest
+
+ *  Purpose:
+ *     Test C interface to SLA
+
+ *  Language:
+ *     Starlink ANSI C
+
+ *  Description:
+ *     Provides a simple test of the C interface. Test coverage is not
+ *     complete because not all Fortran routines have wrappers.
+
+ *  Copyright:
+ *     Copyright (C) 2006 Particle Physics and Engineering Research Council
+
+ *  Licence:
+ *     This program is free software; you can redistribute it and/or
+ *     modify it under the terms of the GNU General Public License as
+ *     published by the Free Software Foundation; either version 2 of
+ *     the License, or (at your option) any later version.
+ *
+ *     This program is distributed in the hope that it will be
+ *     useful,but WITHOUT ANY WARRANTY; without even the implied
+ *     warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
+ *     PURPOSE. See the GNU General Public License for more details.
+ *
+ *     You should have received a copy of the GNU General Public License
+ *     along with this program; if not, write to the Free Software
+ *     Foundation, Inc., 51 Franklin Street,Fifth Floor, Boston, MA
+ *     02110-1301, USA
+
+ *  Authors:
+ *     TIMJ: Tim Jenness (JAC, Hawaii)
+ *     {enter_new_authors_here}
+
+ *  History:
+ *     07-AUG-2006 (TIMJ):
+ *       Original version.
+
+ *-
+ */
+
+#if HAVE_CONFIG_H
+#  include <config.h>
+#endif
+
+#include <stdlib.h>
+#include <stdio.h>
+#include <string.h>
+#include "slalib.h"
+
+#if HAVE_FC_MAIN
+void FC_MAIN ( void );
+void FC_MAIN ( ) {}
+#endif
+
+
+int main ( void ) {
+  double w, p, h;
+  char telname[41];
+  char telshort[11];
+  int  exstatus = EXIT_SUCCESS;
+
+
+  /* call slaObs - initialise to recognisable state */
+  w = 0.0; p = 0.0; h = -1.0;
+
+  /* first call by short name */
+  slaObs( 0, "JCMT", telname, &w, &p, &h );
+  if ( h == -1.0 ) {
+    printf( "Error obtaining information on JCMT\n");
+    exstatus = EXIT_FAILURE;
+  } else {
+    printf( "Telescope JCMT is '%s' w = %f, p = %f, h = %f\n",
+	    telname, w, p, h);
+  }
+
+  /* call by index */
+  h = -1.0; w = 0.0; p = 0.0;
+  slaObs( 1, telshort, telname, &w, &p, &h );
+  if (h == -1.0 ) {
+    printf( "Error obtaining information on telescope 1\n");
+    exstatus = EXIT_FAILURE;
+  } else {
+    printf( "Telescope 1 is '%s' aka '%s' w = %f, p = %f, h = %f\n",
+	    telshort, telname, w, p, h);
+  }
+
+  /* deliberately fail - with bad index */
+  h = -1.0; w = 0.0; p = 0.0; strcpy( telshort, "unknown" );
+  slaObs( 100000, telshort, telname, &w, &p, &h );
+  if (h != -1.0 || telname[0] != '?') {
+    printf("Attempt to decode unfeasibly large telescope index should have failed\n");
+    printf("Got this result:  Tel: '%s' aka '%s', w=%f p=%f h=%f\n", telshort,
+	   telname, w, p, h);
+    exstatus = EXIT_FAILURE;
+  }
+
+  /* deliberately fail - with bad name */
+  h = -1.0; w = 0.0; p = 0.0;
+  slaObs( 0, "AFakeTel", telname, &w, &p, &h );
+  if (h != -1.0 || telname[0] != '?') {
+    printf("Attempt to decode unknown telescope should have failed\n");
+    printf("Got this result:  Tel: '%s', w=%f p=%f h=%f\n", telname, w, p, h);
+    exstatus = EXIT_FAILURE;
+  }
+
+  return exstatus;
+}
diff --git a/math/slalib/sla_link b/math/slalib/sla_link
new file mode 100755
index 00000000..941abfac
--- /dev/null
+++ b/math/slalib/sla_link
@@ -0,0 +1 @@
+echo -lsla `cnf_link`
diff --git a/math/slalib/sla_link_adam b/math/slalib/sla_link_adam
new file mode 100755
index 00000000..a5e757b3
--- /dev/null
+++ b/math/slalib/sla_link_adam
@@ -0,0 +1 @@
+echo -lsla `cnf_link_adam`
diff --git a/math/slalib/sla_test.f b/math/slalib/sla_test.f
new file mode 100644
index 00000000..4edaf093
--- /dev/null
+++ b/math/slalib/sla_test.f
@@ -0,0 +1,6655 @@
+      PROGRAM SLA_TEST
+*+
+*  - - - - - - - - -
+*   S L A _ T E S T
+*  - - - - - - - - -
+*
+*  Validate the slalib library.
+*
+*  Each slalib function is tested to some useful but in most cases
+*  not exhaustive level.  Successful completion is signalled by an
+*  absence of output messages.  Failure of a given function or
+*  group of functions results in error messages.
+*
+*  Any messages go to standard output.
+*
+*  Adapted from original C code by P.T.Wallace.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink and P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+      INTEGER EXITSTATUS
+
+
+*  Preset the status to success.
+      STATUS = .TRUE.
+
+*  Test all the slalib functions.
+      CALL T_ADDET ( STATUS )
+      CALL T_AFIN ( STATUS )
+      CALL T_AIRMAS ( STATUS )
+      CALL T_ALTAZ ( STATUS )
+      CALL T_AMP ( STATUS )
+      CALL T_AOP ( STATUS )
+      CALL T_BEAR ( STATUS )
+      CALL T_CAF2R ( STATUS )
+      CALL T_CALDJ ( STATUS )
+      CALL T_CALYD ( STATUS )
+      CALL T_CC2S ( STATUS )
+      CALL T_CC62S ( STATUS )
+      CALL T_CD2TF ( STATUS )
+      CALL T_CLDJ ( STATUS )
+      CALL T_CR2AF ( STATUS )
+      CALL T_CR2TF ( STATUS )
+      CALL T_CS2C6 ( STATUS )
+      CALL T_CTF2D ( STATUS )
+      CALL T_CTF2R ( STATUS )
+      CALL T_DAT ( STATUS )
+      CALL T_DBJIN ( STATUS )
+      CALL T_DJCAL ( STATUS )
+      CALL T_DMAT ( STATUS )
+      CALL T_E2H ( STATUS )
+      CALL T_EARTH ( STATUS )
+      CALL T_ECLEQ ( STATUS )
+      CALL T_ECMAT ( STATUS )
+      CALL T_ECOR ( STATUS )
+      CALL T_EG50 ( STATUS )
+      CALL T_EPB ( STATUS )
+      CALL T_EPB2D ( STATUS )
+      CALL T_EPCO ( STATUS )
+      CALL T_EPJ ( STATUS )
+      CALL T_EPJ2D ( STATUS )
+      CALL T_EQECL ( STATUS )
+      CALL T_EQEQX ( STATUS )
+      CALL T_EQGAL ( STATUS )
+      CALL T_ETRMS ( STATUS )
+      CALL T_EVP ( STATUS )
+      CALL T_FITXY ( STATUS )
+      CALL T_FK425 ( STATUS )
+      CALL T_FK45Z ( STATUS )
+      CALL T_FK524 ( STATUS )
+      CALL T_FK52H ( STATUS )
+      CALL T_FK54Z ( STATUS )
+      CALL T_FLOTIN ( STATUS )
+      CALL T_GALEQ ( STATUS )
+      CALL T_GALSUP ( STATUS )
+      CALL T_GE50 ( STATUS )
+      CALL T_GMST ( STATUS )
+      CALL T_INTIN ( STATUS )
+      CALL T_KBJ ( STATUS )
+      CALL T_MAP ( STATUS )
+      CALL T_MOON ( STATUS )
+      CALL T_NUT ( STATUS )
+      CALL T_OBS ( STATUS )
+      CALL T_PA ( STATUS )
+      CALL T_PCD ( STATUS )
+      CALL T_PDA2H ( STATUS )
+      CALL T_PDQ2H ( STATUS )
+      CALL T_PERCOM ( STATUS )
+      CALL T_PLANET ( STATUS )
+      CALL T_PM ( STATUS )
+      CALL T_POLMO ( STATUS )
+      CALL T_PREBN ( STATUS )
+      CALL T_PREC ( STATUS )
+      CALL T_PRECES ( STATUS )
+      CALL T_PRENUT ( STATUS )
+      CALL T_PVOBS ( STATUS )
+      CALL T_RANGE ( STATUS )
+      CALL T_RANORM ( STATUS )
+      CALL T_RCC ( STATUS )
+      CALL T_REF ( STATUS )
+      CALL T_RV ( STATUS )
+      CALL T_SEP ( STATUS )
+      CALL T_SMAT ( STATUS )
+      CALL T_SUPGAL ( STATUS )
+      CALL T_SVD ( STATUS )
+      CALL T_TP ( STATUS )
+      CALL T_TPV ( STATUS )
+      CALL T_VECMAT ( STATUS )
+      CALL T_ZD ( STATUS )
+
+*  Report any errors and set up an appropriate exit status.  Set the
+*  EXITSTATUS to 0 on success, 1 on any error -- Unix-style.  The
+*  EXIT intrinsic is non-standard but common (which is portable enough
+*  for a regression test).
+
+      IF ( STATUS ) THEN
+         WRITE (*,'(1X,''SLALIB validation OK!'')')
+         EXITSTATUS = 0
+      ELSE
+         WRITE (*,'(1X,''SLALIB validation failed!'')')
+         EXITSTATUS = 1
+      ENDIF
+
+      CALL EXIT(EXITSTATUS)
+
+      END
+
+      SUBROUTINE VCS ( S, SOK, FUNC, TEST, STATUS )
+*+
+*  - - - -
+*   V C S
+*  - - - -
+*
+*  Validate a character string result.
+*
+*  Internal routine used by sla_TEST program.
+*
+*  Given:
+*     S        CHARACTER    string produced by routine under test
+*     SOK      CHARACTER    correct value
+*     FUNC     CHARACTER    name of routine under test
+*     TEST     CHARACTER    name of individual test (or ' ')
+*
+*  Given and returned:
+*     STATUS   LOGICAL      set to .FALSE. if test fails
+*
+*  Called:  ERR
+*
+*  Last revision:   25 May 2002
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) S, SOK, FUNC, TEST
+      LOGICAL STATUS
+
+
+      IF ( S .NE. SOK ) THEN
+         CALL ERR ( FUNC, TEST, STATUS )
+         WRITE (*,'(1X,''  expected ='',6X,''"'',A,''"'')') SOK
+         WRITE (*,'(1X,''  actual =  '',6X,''"'',A,''"'')') S
+      END IF
+
+      END
+
+      SUBROUTINE VIV ( IVAL, IVALOK, FUNC, TEST, STATUS )
+*+
+*  - - - -
+*   V I V
+*  - - - -
+*
+*  Validate an integer result.
+*
+*  Internal routine used by sla_TEST program.
+*
+*  Given:
+*     IVAL     INTEGER      value computed by routine under test
+*     IVALOK   INTEGER      correct value
+*     FUNC     CHARACTER    name of routine under test
+*     TEST     CHARACTER    name of individual test (or ' ')
+*
+*  Given and returned:
+*     STATUS   LOGICAL      set to .FALSE. if test fails
+*
+*  Called:  ERR
+*
+*  Last revision:   25 May 2002
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER IVAL, IVALOK
+      CHARACTER*(*) FUNC, TEST
+      LOGICAL STATUS
+
+
+      IF ( IVAL .NE. IVALOK ) THEN
+         CALL ERR ( FUNC, TEST, STATUS )
+         WRITE (*,'(1X,''  expected ='',I10)') IVALOK
+         WRITE (*,'(1X,''  actual =  '',I10)') IVAL
+      END IF
+
+      END
+
+      SUBROUTINE VLV ( IVAL, IVALOK, FUNC, TEST, STATUS )
+*+
+*  - - - -
+*   V L V
+*  - - - -
+*
+*  Validate a long result.
+*
+*  Internal routine used by sla_TEST program.
+*
+*  Given:
+*     IVAL     INTEGER*4    value computed by routine under test
+*     IVALOK   INTEGER*4    correct value
+*     FUNC     CHARACTER    name of routine under test
+*     TEST     CHARACTER    name of individual test (or ' ')
+*
+*  Given and returned:
+*     STATUS   LOGICAL      set to .FALSE. if test fails
+*
+*  Called:  ERR
+*
+*  Last revision:   25 May 2002
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER*4 IVAL, IVALOK
+      CHARACTER*(*) FUNC, TEST
+      LOGICAL STATUS
+
+
+      IF ( IVAL .NE. IVALOK ) THEN
+         CALL ERR ( FUNC, TEST, STATUS )
+         WRITE (*,'(1X,''  expected ='',I10)') IVALOK
+         WRITE (*,'(1X,''  actual =  '',I10)') IVAL
+      END IF
+
+      END
+
+      SUBROUTINE VVD ( VAL, VALOK, DVAL, FUNC, TEST, STATUS )
+*+
+*  - - - -
+*   V V D
+*  - - - -
+*
+*  Validate a double result.
+*
+*  Internal routine used by sla_TEST program.
+*
+*  Given:
+*     VAL      DOUBLE       value computed by routine under test
+*     VALOK    DOUBLE       correct value
+*     DVAL     DOUBLE       maximum allowable error
+*     FUNC     CHARACTER    name of routine under test
+*     TEST     CHARACTER    name of individual test (or ' ')
+*
+*  Given and returned:
+*     STATUS   LOGICAL      set to .FALSE. if test fails
+*
+*  Called:  ERR
+*
+*  Last revision:   25 May 2002
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION VAL, VALOK, DVAL
+      CHARACTER*(*) FUNC, TEST
+      LOGICAL STATUS
+
+
+      IF ( DABS ( VAL - VALOK ) .GT. DVAL ) THEN
+         CALL ERR ( FUNC, TEST, STATUS )
+         WRITE (*,'(1X,''  expected ='',G30.19)') VALOK
+         WRITE (*,'(1X,''  actual =  '',G30.19)') VAL
+      END IF
+
+      END
+
+      SUBROUTINE ERR ( FUNC, TEST, STATUS )
+*+
+*  - - - -
+*   E R R
+*  - - - -
+*
+*  Report a failed test.
+*
+*  Internal routine used by sla_TEST program.
+*
+*  Given:
+*     FUNC     CHARACTER    name of routine under test
+*     TEST     CHARACTER    name of individual test (or ' ')
+*
+*  Given and returned:
+*     STATUS   LOGICAL      set to .FALSE.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER*(*) FUNC, TEST
+      LOGICAL STATUS
+
+
+      WRITE (*,'(1X,A,'' test '',A,'' fails:'')') FUNC, TEST
+      STATUS = .FALSE.
+
+      END
+
+      SUBROUTINE T_ADDET ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ A D E T
+*  - - - - - - - -
+*
+*  Test slADET, slSUET routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slADET, VVD, slSUET.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION RM, DM, EQ, R1, D1, R2, D2
+
+      RM = 2D0
+      DM = -1D0
+      EQ = 1975D0
+
+      CALL slADET ( RM, DM, EQ, R1, D1 )
+      CALL VVD ( R1 - RM, 2.983864874295250D-6, 1D-12, 'slADET',
+     :           'R', STATUS )
+      CALL VVD ( D1 - DM, 2.379650804185118D-7, 1D-12, 'slADET',
+     :           'D', STATUS )
+
+      CALL slSUET ( R1, D1, EQ, R2, D2 )
+      CALL VVD ( R2 - RM, 0D0, 1D-12, 'slSUET', 'R', STATUS )
+      CALL VVD ( D2 - DM, 0D0, 1D-12, 'slSUET', 'D', STATUS )
+
+      END
+
+      SUBROUTINE T_AFIN ( STATUS )
+*+
+*  - - - - - - -
+*   T _ A F I N
+*  - - - - - - -
+*
+*  Test slAFIN and slDAFN routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slAFIN, VIV, VVD, slDAFN.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER I, J
+      REAL F
+      DOUBLE PRECISION D
+      CHARACTER*12 S
+      DATA S /'12 34 56.7 |'/
+
+
+      I = 1
+      CALL slAFIN (S, I, F, J)
+      CALL VIV ( I, 12, 'slAFIN', 'I', STATUS )
+      CALL VVD ( DBLE( F ), 0.2196045986911432D0, 1D-6, 'slAFIN',
+     :           'A', STATUS )
+      CALL VIV ( J, 0, 'slAFIN', 'J', STATUS )
+
+      I = 1
+      CALL slDAFN (S, I, D, J)
+      CALL VIV ( I, 12, 'slDAFN', 'I', STATUS )
+      CALL VVD ( D, 0.2196045986911432D0, 1D-12, 'slDAFN', 'A',
+     :           STATUS )
+      CALL VIV ( J, 0, 'slDAFN', 'J', STATUS )
+
+      END
+
+      SUBROUTINE T_AIRMAS ( STATUS )
+*+
+*  - - - - - - - - -
+*   T _ A R M S
+*  - - - - - - - - -
+*
+*  Test slARMS routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called: VVD, slARMS.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slARMS
+
+
+      CALL VVD ( slARMS ( 1.2354D0 ), 3.015698990074724D0,
+     :           1D-12, 'slARMS', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_ALTAZ ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ A L A Z
+*  - - - - - - - -
+*
+*  Test slALAZ routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slALAZ, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION AZ, AZD, AZDD, EL, ELD, ELDD, PA, PAD, PADD
+
+      CALL slALAZ ( 0.7D0, -0.7D0, -0.65D0,
+     :                 AZ, AZD, AZDD, EL, ELD, ELDD, PA, PAD, PADD )
+
+      CALL VVD ( AZ, 4.400560746660174D0, 1D-12, 'slALAZ',
+     :           'AZ', STATUS )
+      CALL VVD ( AZD, -0.2015438937145421D0, 1D-13, 'slALAZ',
+     :           'AZD', STATUS )
+      CALL VVD ( AZDD, -0.4381266949668748D0, 1D-13, 'slALAZ',
+     :           'AZDD', STATUS )
+      CALL VVD ( EL, 1.026646506651396D0, 1D-12, 'slALAZ',
+     :           'EL', STATUS )
+      CALL VVD ( ELD, -0.7576920683826450D0, 1D-13, 'slALAZ',
+     :           'ELD', STATUS )
+      CALL VVD ( ELDD, 0.04922465406857453D0, 1D-14, 'slALAZ',
+     :           'ELDD', STATUS )
+      CALL VVD ( PA, 1.707639969653937D0, 1D-12, 'slALAZ',
+     :           'PA', STATUS )
+      CALL VVD ( PAD, 0.4717832355365627D0, 1D-13, 'slALAZ',
+     :           'PAD', STATUS )
+      CALL VVD ( PADD, -0.2957914128185515D0, 1D-13, 'slALAZ',
+     :           'PADD', STATUS )
+
+      END
+
+      SUBROUTINE T_AMP ( STATUS )
+*+
+*  - - - - - -
+*   T _ A M P
+*  - - - - - -
+*
+*  Test slAMP, slMAPA, slAMPQ routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slAMP, VVD.
+*
+*  Last revision:   16 November 2001
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION RM, DM
+
+      CALL slAMP ( 2.345D0, -1.234D0, 50100D0, 1990D0, RM, DM )
+      CALL VVD ( RM, 2.344472180027961D0, 1D-11, 'slAMP', 'R',
+     :           STATUS )
+      CALL VVD ( DM, -1.233573099847705D0, 1D-11, 'slAMP', 'D',
+     :           STATUS )
+
+      END
+
+      SUBROUTINE T_AOP ( STATUS )
+*+
+*  - - - - - -
+*   T _ A O P
+*  - - - - - -
+*
+*  Test slAOP, slAOPA, slAOPQ, slOAP, slOAPQ,
+*  slAOPT routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slAOP, VVD, slAOPA, slAOPQ, slOAP, slOAPQ,
+*  slAOPT.
+*
+*  Defined in slamac.h:  DS2R
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER I
+      DOUBLE PRECISION DS2R
+      DOUBLE PRECISION RAP, DAP, DATE, DUT, ELONGM, PHIM, HM, XP, YP,
+     :    TDK, PMB, RH, WL, TLR, AOB, ZOB, HOB, DOB, ROB, AOPRMS(14)
+
+      PARAMETER (DS2R =
+     :      7.2722052166430399038487115353692196393452995355905D-5)
+
+      DAP = -0.1234D0
+      DATE = 51000.1D0
+      DUT = 25D0
+      ELONGM = 2.1D0
+      PHIM = 0.5D0
+      HM = 3000D0
+      XP = -0.5D-6
+      YP = 1D-6
+      TDK = 280D0
+      PMB = 550D0
+      RH = 0.6D0
+      TLR = 0.006D0
+
+      DO I = 1, 3
+
+         IF ( I .EQ. 1 ) THEN
+            RAP = 2.7D0
+            WL = 0.45D0
+            ELSE IF ( I .EQ. 2 ) THEN
+                RAP = 2.345D0
+            ELSE
+                WL = 1D6
+         END IF
+
+         CALL slAOP ( RAP, DAP, DATE, DUT, ELONGM, PHIM, HM, XP, YP,
+     :                  TDK, PMB, RH, WL, TLR, AOB, ZOB, HOB, DOB, ROB )
+
+         IF ( I .EQ. 1 ) THEN
+            CALL VVD ( AOB, 1.812817787123283034D0, 1D-10, 'slAOP',
+     :                 'lo aob', STATUS )
+            CALL VVD ( ZOB, 1.393860816635714034D0, 1D-10, 'slAOP',
+     :                 'lo zob', STATUS )
+            CALL VVD ( HOB, -1.297808009092456683D0, 1D-10, 'slAOP',
+     :                 'lo hob', STATUS )
+            CALL VVD ( DOB, -0.122967060534561D0, 1D-10, 'slAOP',
+     :                 'lo dob', STATUS )
+            CALL VVD ( ROB, 2.699270287872084D0, 1D-10, 'slAOP',
+     :                    'lo rob', STATUS )
+         ELSE IF ( I .EQ. 2 ) THEN
+            CALL VVD ( AOB, 2.019928026670621442D0, 1D-10, 'slAOP',
+     :                 'aob/o', STATUS )
+            CALL VVD ( ZOB, 1.101316172427482466D0, 1D-10, 'slAOP',
+     :                 'zob/o', STATUS )
+            CALL VVD ( HOB, -0.9432923558497740862D0, 1D-10, 'slAOP',
+     :                 'hob/o', STATUS )
+            CALL VVD ( DOB, -0.1232144708194224D0, 1D-10, 'slAOP',
+     :                 'dob/o', STATUS )
+            CALL VVD ( ROB, 2.344754634629428D0, 1D-10, 'slAOP',
+     :                 'rob/o', STATUS )
+         ELSE
+            CALL VVD ( AOB, 2.019928026670621442D0, 1D-10, 'slAOP',
+     :                 'aob/r', STATUS )
+            CALL VVD ( ZOB, 1.101267532198003760D0, 1D-10, 'slAOP',
+     :                 'zob/r', STATUS )
+            CALL VVD ( HOB, -0.9432533138143315937D0, 1D-10, 'slAOP',
+     :                 'hob/r', STATUS )
+            CALL VVD ( DOB, -0.1231850665614878D0, 1D-10, 'slAOP',
+     :                 'dob/r', STATUS )
+            CALL VVD ( ROB, 2.344715592593984D0, 1D-10, 'slAOP',
+     :                 'rob/r', STATUS )
+         END IF
+      END DO
+
+      DATE = 48000.3D0
+      WL = 0.45D0
+
+      CALL slAOPA ( DATE, DUT, ELONGM, PHIM, HM, XP, YP, TDK,
+     :                 PMB, RH, WL, TLR, AOPRMS )
+      CALL VVD ( AOPRMS(1), 0.4999993892136306D0, 1D-13, 'slAOPA',
+     :           '1', STATUS )
+      CALL VVD ( AOPRMS(2), 0.4794250025886467D0, 1D-13, 'slAOPA',
+     :           '2', STATUS )
+      CALL VVD ( AOPRMS(3), 0.8775828547167932D0, 1D-13, 'slAOPA',
+     :           '3', STATUS )
+      CALL VVD ( AOPRMS(4), 1.363180872136126D-6, 1D-13, 'slAOPA',
+     :           '4', STATUS )
+      CALL VVD ( AOPRMS(5), 3000D0, 1D-10, 'slAOPA', '5',
+     :           STATUS )
+      CALL VVD ( AOPRMS(6), 280D0, 1D-11, 'slAOPA', '6',
+     :           STATUS )
+      CALL VVD ( AOPRMS(7), 550D0, 1D-11, 'slAOPA', '7',
+     :           STATUS )
+      CALL VVD ( AOPRMS(8), 0.6D0, 1D-13, 'slAOPA', '8',
+     :           STATUS )
+      CALL VVD ( AOPRMS(9), 0.45D0, 1D-13, 'slAOPA', '9',
+     :           STATUS )
+      CALL VVD ( AOPRMS(10), 0.006D0, 1D-15, 'slAOPA', '10',
+     :           STATUS )
+      CALL VVD ( AOPRMS(11), 0.0001562803328459898D0, 1D-13,
+     :           'slAOPA', '11', STATUS )
+      CALL VVD ( AOPRMS(12), -1.792293660141D-7, 1D-13,
+     :           'slAOPA', '12', STATUS )
+      CALL VVD ( AOPRMS(13), 2.101874231495843D0, 1D-13,
+     :           'slAOPA', '13', STATUS )
+      CALL VVD ( AOPRMS(14), 7.601916802079765D0, 1D-8,
+     :           'slAOPA', '14', STATUS )
+
+      CALL slOAP ( 'R', 1.6D0, -1.01D0, DATE, DUT, ELONGM, PHIM,
+     :               HM, XP, YP, TDK, PMB, RH, WL, TLR, RAP, DAP )
+      CALL VVD ( RAP, 1.601197569844787D0, 1D-10, 'slOAP',
+     :           'Rr', STATUS )
+      CALL VVD ( DAP, -1.012528566544262D0, 1D-10, 'slOAP',
+     :           'Rd', STATUS )
+      CALL slOAP ( 'H', -1.234D0, 2.34D0, DATE, DUT, ELONGM, PHIM,
+     :               HM, XP, YP, TDK, PMB, RH, WL, TLR, RAP, DAP )
+      CALL VVD ( RAP, 5.693087688154886463D0, 1D-10, 'slOAP',
+     :           'Hr', STATUS )
+      CALL VVD ( DAP, 0.8010281167405444D0, 1D-10, 'slOAP',
+     :           'Hd', STATUS )
+      CALL slOAP ( 'A', 6.1D0, 1.1D0, DATE, DUT, ELONGM, PHIM,
+     :               HM, XP, YP, TDK, PMB, RH, WL, TLR, RAP, DAP )
+      CALL VVD ( RAP, 5.894305175192448940D0, 1D-10, 'slOAP',
+     :           'Ar', STATUS )
+      CALL VVD ( DAP, 1.406150707974922D0, 1D-10, 'slOAP',
+     :           'Ad', STATUS )
+
+      CALL slOAPQ ( 'R', 2.1D0, -0.345D0, AOPRMS, RAP, DAP )
+      CALL VVD ( RAP, 2.10023962776202D0, 1D-10, 'slOAPQ',
+     :           'Rr', STATUS )
+      CALL VVD ( DAP, -0.3452428692888919D0, 1D-10, 'slOAPQ',
+     :           'Rd', STATUS )
+      CALL slOAPQ ( 'H', -0.01D0, 1.03D0, AOPRMS, RAP, DAP )
+      CALL VVD ( RAP, 1.328731933634564995D0, 1D-10, 'slOAPQ',
+     :           'Hr', STATUS )
+      CALL VVD ( DAP, 1.030091538647746D0, 1D-10, 'slOAPQ',
+     :           'Hd', STATUS )
+      CALL slOAPQ ( 'A', 4.321D0, 0.987D0, AOPRMS, RAP, DAP )
+      CALL VVD ( RAP, 0.4375507112075065923D0, 1D-10, 'slOAPQ',
+     :           'Ar', STATUS )
+      CALL VVD ( DAP, -0.01520898480744436D0, 1D-10, 'slOAPQ',
+     :           'Ad', STATUS )
+
+      CALL slAOPT ( DATE + DS2R, AOPRMS )
+      CALL VVD ( AOPRMS(14), 7.602374979243502D0, 1D-8, 'slAOPT',
+     :           ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_BEAR ( STATUS )
+*+
+*  - - - - - - -
+*   T _ B E A R
+*  - - - - - - -
+*
+*  Test slBEAR, slDBER, slDPAV, slPAV routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  VVD, slBEAR, slDBER,
+*           slDS2C, slPAV, slDPAV.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER I
+      REAL F1(3), F2(3)
+      REAL slBEAR, slPAV
+      DOUBLE PRECISION D1(3), D2(3)
+      DOUBLE PRECISION A1, B1, A2, B2
+      DOUBLE PRECISION slDBER, slDPAV
+
+
+      A1 = 1.234D0
+      B1 = -0.123D0
+      A2 = 2.345D0
+      B2 = 0.789D0
+
+      CALL VVD ( DBLE( slBEAR ( SNGL( A1 ), SNGL( B1 ), SNGL( A2 ),
+     :           SNGL( B2 ) ) ), 0.7045970341781791D0, 1D-6,
+     :           'slBEAR', ' ', STATUS )
+      CALL VVD ( slDBER ( A1, B1, A2, B2 ), 0.7045970341781791D0,
+     :           1D-12, 'slDBER', ' ', STATUS )
+      CALL slDS2C ( A1, B1, D1 )
+      CALL slDS2C ( A2, B2, D2 )
+
+      DO I = 1, 3
+        F1(I) = SNGL( D1(I) )
+        F2(I) = SNGL( D2(I) )
+      END DO
+
+      CALL VVD ( DBLE( slPAV ( F1, F2 ) ), 0.7045970341781791D0,
+     :           1D-6, 'slPAV', ' ', STATUS )
+      CALL VVD ( slDPAV ( D1, D2 ), 0.7045970341781791D0,
+     :           1D-12, 'slDPAV', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_CAF2R ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ C A F R
+*  - - - - - - - -
+*
+*  Test slCAFR, slDAFR routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slCAFR, VVD, VIV, slDAFR.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J
+      REAL R
+      DOUBLE PRECISION DR
+
+      CALL slCAFR ( 76, 54, 32.1E0, R, J )
+      CALL VVD ( DBLE( R ), 1.342313819975276D0, 1D-6, 'slCAFR',
+     :           'R', STATUS )
+      CALL VIV ( J, 0, 'slCAFR', 'J', STATUS )
+      CALL slDAFR ( 76, 54, 32.1D0, DR, J )
+      CALL VVD ( DR, 1.342313819975276D0, 1D-12, 'slDAFR',
+     :           'R', STATUS )
+      CALL VIV ( J, 0, 'slCAFR', 'J', STATUS )
+
+      END
+
+      SUBROUTINE T_CALDJ ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ C A D J
+*  - - - - - - - -
+*
+*  Test slCADJ routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slCADJ, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J
+      DOUBLE PRECISION DJM
+
+      CALL slCADJ ( 1999, 12, 31, DJM, J )
+      CALL VVD ( DJM, 51543D0, 0D0, 'slCADJ', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_CALYD ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ C A Y D
+*  - - - - - - - -
+*
+*  Test slCAYD and slCLYD routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slCAYD, slCLYD, VIV.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER NY, ND, J
+
+      CALL slCAYD ( 46, 4, 30, NY, ND, J )
+      CALL VIV ( NY, 2046, 'slCAYD', 'Y', STATUS )
+      CALL VIV ( ND, 120, 'slCAYD', 'D', STATUS )
+      CALL VIV ( J, 0, 'slCAYD', 'J', STATUS )
+      CALL slCLYD ( -5000, 1, 1, NY, ND, J )
+      CALL VIV ( J, 1, 'slCLYD', 'illegal year', STATUS )
+      CALL slCLYD ( 1900, 0, 1, NY, ND, J )
+      CALL VIV ( J, 2, 'slCLYD', 'illegal month', STATUS )
+      CALL slCLYD ( 1900, 2, 29, NY, ND, J)
+      CALL VIV ( NY, 1900, 'slCLYD', 'illegal day (Y)', STATUS )
+      CALL VIV ( ND, 61, 'slCLYD', 'illegal day (D)', STATUS )
+      CALL VIV ( J, 3, 'slCLYD', 'illegal day (J)', STATUS )
+      CALL slCLYD ( 2000, 2, 29, NY, ND, J )
+      CALL VIV ( NY, 2000, 'slCLYD', 'Y', STATUS )
+      CALL VIV ( ND, 60, 'slCLYD', 'D', STATUS )
+      CALL VIV ( J, 0, 'slCLYD', 'J', STATUS )
+
+      END
+
+      SUBROUTINE T_CC2S ( STATUS )
+*+
+*  - - - - - - -
+*   T _ C C 2 S
+*  - - - - - - -
+*
+*  Test slCC2S, slDC2S routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slCC2S, VVD, slDC2S.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      REAL V(3), A, B
+      DOUBLE PRECISION DV(3), DA, DB
+
+      DATA V/100.0, -50.0, 25.0/
+      DATA DV/100D0, -50D0, 25D0/
+
+      CALL slCC2S ( V, A, B )
+      CALL VVD ( DBLE( A), -0.4636476090008061D0, 1D-6, 'slCC2S',
+     :           'A', STATUS )
+      CALL VVD ( DBLE( B ), 0.2199879773954594D0, 1D-6, 'slCC2S',
+     :           'B', STATUS )
+
+      CALL slDC2S ( DV, DA, DB )
+      CALL VVD ( DA, -0.4636476090008061D0, 1D-12, 'slDC2S',
+     :           'A', STATUS )
+      CALL VVD ( DB, 0.2199879773954594D0, 1D-12, 'slDC2S',
+     :           'B', STATUS )
+
+      END
+
+      SUBROUTINE T_CC62S ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ C 6 2 S
+*  - - - - - - - -
+*
+*  Test slC62S, slDC6S routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slC62S, VVD, slDC6S.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      REAL V(6), A, B, R, AD, BD, RD
+      DOUBLE PRECISION DV(6), DA, DB, DR, DAD, DBD, DRD
+
+      DATA V/100.0, -50.0, 25.0, -0.1, 0.2, 0.7/
+      DATA DV/100D0, -50D0, 25D0, -0.1D0, 0.2D0, 0.7D0/
+
+      CALL slC62S ( V, A, B, R, AD, BD, RD )
+      CALL VVD ( DBLE( A ), -0.4636476090008061D0, 1D-6, 'slC62S',
+     :           'A', STATUS )
+      CALL VVD ( DBLE( B ), 0.2199879773954594D0, 1D-6, 'slC62S',
+     :           'B', STATUS )
+      CALL VVD ( DBLE( R ), 114.564392373896D0, 1D-3, 'slC62S',
+     :           'R', STATUS )
+      CALL VVD ( DBLE( AD ), 0.001200000000000000D0, 1D-9, 'slC62S',
+     :           'AD', STATUS )
+      CALL VVD ( DBLE( BD ), 0.006303582107999407D0, 1D-8, 'slC62S',
+     :           'BD', STATUS )
+      CALL VVD ( DBLE( RD ), -0.02182178902359925D0, 1D-7, 'slC62S',
+     :           'RD', STATUS )
+
+      CALL slDC6S ( DV, DA, DB, DR, DAD, DBD, DRD )
+      CALL VVD ( DA, -0.4636476090008061D0, 1D-6, 'slDC6S',
+     :           'A', STATUS )
+      CALL VVD ( DB, 0.2199879773954594D0, 1D-6, 'slDC6S',
+     :           'B', STATUS )
+      CALL VVD ( DR, 114.564392373896D0, 1D-9, 'slDC6S',
+     :           'R', STATUS )
+      CALL VVD ( DAD, 0.001200000000000000D0, 1D-15, 'slDC6S',
+     :           'AD', STATUS )
+      CALL VVD ( DBD, 0.006303582107999407D0, 1D-14, 'slDC6S',
+     :           'BD', STATUS )
+      CALL VVD ( DRD, -0.02182178902359925D0, 1D-13, 'slDC6S',
+     :           'RD', STATUS )
+
+      END
+
+      SUBROUTINE T_CD2TF ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ C D T F
+*  - - - - - - - -
+*
+*  Test slCDTF, slDDTF routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slCDTF, VIV, VVD, slDDTF.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER IHMSF(4)
+      CHARACTER S
+
+      CALL slCDTF ( 4, -0.987654321E0, S, IHMSF )
+      CALL VIV ( ICHAR( S ), ICHAR( '-' ), 'slCDTF', 'S', STATUS )
+      CALL VIV ( IHMSF(1), 23, 'slCDTF', '(1)', STATUS )
+      CALL VIV ( IHMSF(2), 42, 'slCDTF', '(2)', STATUS )
+      CALL VIV ( IHMSF(3), 13, 'slCDTF', '(3)', STATUS )
+      CALL VVD ( DFLOAT( IHMSF(4) ), 3333D0, 1000D0, 'slCDTF',
+     :           '(4)', STATUS )
+
+      CALL slDDTF ( 4, -0.987654321D0, S, IHMSF )
+      CALL VIV ( ICHAR( S ), ICHAR( '-' ), 'slDDTF', 'S', STATUS )
+      CALL VIV ( IHMSF(1), 23, 'slDDTF', '(1)', STATUS )
+      CALL VIV ( IHMSF(2), 42, 'slDDTF', '(2)', STATUS )
+      CALL VIV ( IHMSF(3), 13, 'slDDTF', '(3)', STATUS )
+      CALL VIV ( IHMSF(4), 3333, 'slDDTF', '(4)', STATUS )
+
+      END
+
+      SUBROUTINE T_CLDJ ( STATUS )
+*+
+*  - - - - - - -
+*   T _ C L D J
+*  - - - - - - -
+*
+*  Test slCLDJ routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slCLDJ, VVD, VIV.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J
+      DOUBLE PRECISION D
+
+      CALL slCLDJ ( 1899, 12, 31, D, J )
+      CALL VVD ( D, 15019D0, 0D0, 'slCLDJ', 'D', STATUS )
+      CALL VIV ( J, 0, 'slCLDJ', 'J', STATUS )
+
+      END
+
+      SUBROUTINE T_CR2AF ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ C R A F
+*  - - - - - - - -
+*
+*  Test slCRAF, slDRAF routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slCRAF, VIV, VVD, slDRAF.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER IDMSF(4)
+      CHARACTER S
+
+      CALL slCRAF ( 4, 2.345E0, S, IDMSF )
+      CALL VIV ( ICHAR( S ), ICHAR( '+' ), 'slCRAF', 'S', STATUS )
+      CALL VIV ( IDMSF(1), 134, 'slCRAF', '(1)', STATUS )
+      CALL VIV ( IDMSF(2), 21, 'slCRAF', '(2)', STATUS )
+      CALL VIV ( IDMSF(3), 30, 'slCRAF', '(3)', STATUS )
+      CALL VVD ( DBLE( IDMSF(4) ), 9706D0, 1000D0, 'slCRAF',
+     :           '(4)', STATUS )
+
+      CALL slDRAF ( 4, 2.345D0, S, IDMSF )
+      CALL VIV ( ICHAR( S ), ICHAR( '+' ), 'slDRAF', 'S', STATUS )
+      CALL VIV ( IDMSF(1), 134, 'slDRAF', '(1)', STATUS )
+      CALL VIV ( IDMSF(2), 21, 'slDRAF', '(2)', STATUS )
+      CALL VIV ( IDMSF(3), 30, 'slDRAF', '(3)', STATUS )
+      CALL VIV ( IDMSF(4), 9706, 'slDRAF', '(4)', STATUS )
+
+      END
+
+      SUBROUTINE T_CR2TF ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ C R T F
+*  - - - - - - - -
+*
+*  Test slCRTF, slDRTF routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slCRTF, VIV, VVD, slDRTF.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER IHMSF(4)
+      CHARACTER S
+
+      CALL slCRTF ( 4, -3.01234E0, S, IHMSF )
+      CALL VIV ( ICHAR( S ), ICHAR( '-' ), 'slCRTF', 'S', STATUS )
+      CALL VIV ( IHMSF(1), 11, 'slCRTF', '(1)', STATUS )
+      CALL VIV ( IHMSF(2), 30, 'slCRTF', '(2)', STATUS )
+      CALL VIV ( IHMSF(3), 22, 'slCRTF', '(3)', STATUS )
+      CALL VVD ( DBLE( IHMSF(4) ), 6484D0, 1000D0, 'slCRTF',
+     :           '(4)', STATUS )
+
+      CALL slDRTF ( 4, -3.01234D0, S, IHMSF )
+      CALL VIV ( ICHAR( S ), ICHAR( '-' ), 'slDRTF', 'S', STATUS )
+      CALL VIV ( IHMSF(1), 11, 'slDRTF', '(1)', STATUS )
+      CALL VIV ( IHMSF(2), 30, 'slDRTF', '(2)', STATUS )
+      CALL VIV ( IHMSF(3), 22, 'slDRTF', '(3)', STATUS )
+      CALL VIV ( IHMSF(4), 6484, 'slDRTF', '(4)', STATUS )
+
+      END
+
+      SUBROUTINE T_CS2C6 ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ S 2 C 6
+*  - - - - - - - -
+*
+*  Test slS2C6, slDSC6 routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slS2C6, VVD, slDSC6.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      REAL V(6)
+      DOUBLE PRECISION DV(6)
+
+      CALL slS2C6( -3.21E0, 0.123E0, 0.456E0, -7.8E-6, 9.01E-6,
+     :                -1.23E-5, V )
+      CALL VVD ( DBLE( V(1) ), -0.4514964673880165D0,
+     :           1D-6, 'slS2C6', 'X', STATUS )
+      CALL VVD ( DBLE( V(2) ),  0.03093394277342585D0,
+     :           1D-6, 'slS2C6', 'Y', STATUS )
+      CALL VVD ( DBLE( V(3) ),  0.05594668105108779D0,
+     :           1D-6, 'slS2C6', 'Z', STATUS )
+      CALL VVD ( DBLE( V(4) ),  1.292270850663260D-5,
+     :           1D-6, 'slS2C6', 'XD', STATUS )
+      CALL VVD ( DBLE( V(5) ),  2.652814182060692D-6,
+     :           1D-6, 'slS2C6', 'YD', STATUS )
+      CALL VVD ( DBLE( V(6) ),  2.568431853930293D-6,
+     :           1D-6, 'slS2C6', 'ZD', STATUS )
+
+      CALL slDSC6( -3.21D0, 0.123D0, 0.456D0, -7.8D-6, 9.01D-6,
+     :                -1.23D-5, DV )
+      CALL VVD ( DV(1), -0.4514964673880165D0, 1D-12, 'slDSC6',
+     :           'X', STATUS )
+      CALL VVD ( DV(2),  0.03093394277342585D0, 1D-12, 'slDSC6',
+     :           'Y', STATUS )
+      CALL VVD ( DV(3),  0.05594668105108779D0, 1D-12, 'slDSC6',
+     :           'Z', STATUS )
+      CALL VVD ( DV(4),  1.292270850663260D-5, 1D-12, 'slDSC6',
+     :           'XD', STATUS )
+      CALL VVD ( DV(5),  2.652814182060692D-6, 1D-12, 'slDSC6',
+     :           'YD', STATUS )
+      CALL VVD ( DV(6),  2.568431853930293D-6, 1D-12, 'slDSC6',
+     :           'ZD', STATUS )
+
+      END
+
+      SUBROUTINE T_CTF2D ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ C T F D
+*  - - - - - - - -
+*
+*  Test slCTFD, slDTFD routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slCTFD, VVD, VIV, slDTFD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J
+      REAL D
+      DOUBLE PRECISION DD
+
+      CALL slCTFD (23, 56, 59.1E0, D, J)
+      CALL VVD ( DBLE( D ), 0.99790625D0, 1D-6, 'slCTFD',
+     :           'D', STATUS )
+      CALL VIV ( J, 0, 'slCTFD', 'J', STATUS )
+
+      CALL slDTFD (23, 56, 59.1D0, DD, J)
+      CALL VVD ( DD, 0.99790625D0, 1D-12, 'slDTFD', 'D', STATUS )
+      CALL VIV ( J, 0, 'slDTFD', 'J', STATUS )
+
+      END
+
+      SUBROUTINE T_CTF2R ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ C T F R
+*  - - - - - - - -
+*
+*  Test slCTFR, slDTFR routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slCTFR, VVD, VIV, slDTFR.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J
+      REAL R
+      DOUBLE PRECISION DR
+
+      CALL slCTFR (23, 56, 59.1E0, R, J)
+      CALL VVD ( DBLE( R ), 6.270029887942679D0, 1D-6, 'slCTFR',
+     :           'R', STATUS )
+      CALL VIV ( J, 0, 'slCTFR', 'J', STATUS )
+
+      CALL slDTFR (23, 56, 59.1D0, DR, J)
+      CALL VVD ( DR, 6.270029887942679D0, 1D-12, 'slDTFR',
+     :           'R', STATUS )
+      CALL VIV ( J, 0, 'slDTFR', 'J', STATUS )
+
+      END
+
+      SUBROUTINE T_DAT ( STATUS )
+*+
+*  - - - - - -
+*   T _ D A T
+*  - - - - - -
+*
+*  Test slDAT, slDTT, slDT routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slDAT, slDTT, slDT, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slDAT, slDTT, slDT
+
+
+      CALL VVD ( slDAT ( 43900D0 ), 18D0, 0D0, 'slDAT',
+     :           ' ', STATUS )
+      CALL VVD ( slDTT ( 40404D0 ), 39.709746D0, 1D-12, 'slDTT',
+     :           ' ', STATUS )
+      CALL VVD ( slDT ( 500D0 ), 4686.7D0, 1D-10, 'slDT',
+     :           '500', STATUS )
+      CALL VVD ( slDT ( 1400D0 ), 408D0, 1D-11, 'slDT',
+     :           '1400', STATUS )
+      CALL VVD ( slDT ( 1950D0 ), 27.99145626D0, 1D-12, 'slDT',
+     :           '1950', STATUS )
+
+      END
+
+      SUBROUTINE T_DBJIN ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ D B J I
+*  - - - - - - - -
+*
+*  Test slDBJI routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slDBJI, VVD, VIV.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER I, JA, JB
+      DOUBLE PRECISION D
+      CHARACTER*32 S
+      DATA S /'  B1950, , J 2000, B1975 JE     '/
+
+      I = 1
+      D = 0D0
+
+      CALL slDBJI ( S, I, D, JA, JB )
+      CALL VIV ( I, 9, 'slDBJI', 'I1', STATUS )
+      CALL VVD ( D, 1950D0, 0D0, 'slDBJI', 'D1', STATUS )
+      CALL VIV ( JA, 0, 'slDBJI', 'JA1', STATUS )
+      CALL VIV ( JB, 1, 'slDBJI', 'JB1', STATUS )
+
+      CALL slDBJI ( S, I, D, JA, JB )
+      CALL VIV ( I, 11, 'slDBJI', 'I2', STATUS )
+      CALL VVD ( D, 1950D0, 0D0, 'slDBJI', 'D2', STATUS )
+      CALL VIV ( JA, 1, 'slDBJI', 'JA2', STATUS )
+      CALL VIV ( JB, 0, 'slDBJI', 'JB2', STATUS )
+
+      CALL slDBJI ( S, I, D, JA, JB )
+      CALL VIV ( I, 19, 'slDBJI', 'I3', STATUS )
+      CALL VVD ( D, 2000D0, 0D0, 'slDBJI', 'D3', STATUS )
+      CALL VIV ( JA, 0, 'slDBJI', 'JA3', STATUS )
+      CALL VIV ( JB, 2, 'slDBJI', 'JB3', STATUS )
+
+      CALL slDBJI ( S, I, D, JA, JB )
+      CALL VIV ( I, 26, 'slDBJI', 'I4', STATUS )
+      CALL VVD ( D, 1975D0, 0D0, 'slDBJI', 'D4', STATUS )
+      CALL VIV ( JA, 0, 'slDBJI', 'JA4', STATUS )
+      CALL VIV ( JB, 1, 'slDBJI', 'JB4', STATUS )
+
+      CALL slDBJI ( S, I, D, JA, JB )
+      CALL VIV ( I, 26, 'slDBJI', 'I5', STATUS )
+      CALL VVD ( D, 1975D0, 0D0, 'slDBJI', 'D5', STATUS )
+      CALL VIV ( JA, 1, 'slDBJI', 'JA5', STATUS )
+      CALL VIV ( JB, 0, 'slDBJI', 'JB5', STATUS )
+
+      END
+
+      SUBROUTINE T_DJCAL ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ D J C A
+*  - - - - - - - -
+*
+*  Test slDJCA, slDJCL routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slDJCA, VIV.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER IYDMF(4), J, IY, IM, ID
+      DOUBLE PRECISION DJM
+      DOUBLE PRECISION F
+
+      DJM = 50123.9999D0
+
+      CALL slDJCA ( 4, DJM, IYDMF, J )
+      CALL VIV ( IYDMF(1), 1996, 'slDJCA', 'Y', STATUS )
+      CALL VIV ( IYDMF(2), 2, 'slDJCA', 'M', STATUS )
+      CALL VIV ( IYDMF(3), 10, 'slDJCA', 'D', STATUS )
+      CALL VIV ( IYDMF(4), 9999, 'slDJCA', 'F', STATUS )
+      CALL VIV ( J, 0, 'slDJCA', 'J', STATUS )
+
+      CALL slDJCL ( DJM, IY, IM, ID, F, J )
+      CALL VIV ( IY, 1996, 'slDJCL', 'Y', STATUS )
+      CALL VIV ( IM, 2, 'slDJCL', 'M', STATUS )
+      CALL VIV ( ID, 10, 'slDJCL', 'D', STATUS )
+      CALL VVD ( F, 0.9999D0, 1D-7, 'slDJCL', 'F', STATUS )
+      CALL VIV ( J, 0, 'slDJCL', 'J', STATUS )
+
+      END
+
+      SUBROUTINE T_DMAT ( STATUS )
+*+
+*  - - - - - - -
+*   T _ D M A T
+*  - - - - - - -
+*
+*  Test slDMAT routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slDMAT, VVD, VIV.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J, IW(3)
+      DOUBLE PRECISION DA(3,3)
+      DOUBLE PRECISION DV(3)
+      DOUBLE PRECISION DD
+
+      DATA DA/2.22D0,     1.6578D0,     1.380522D0,
+     :        1.6578D0,   1.380522D0,   1.22548578D0,
+     :        1.380522D0, 1.22548578D0, 1.1356276122D0/
+      DATA DV/2.28625D0, 1.7128825D0, 1.429432225D0/
+
+      CALL slDMAT ( 3, DA, DV, DD, J, IW )
+
+      CALL VVD ( DA(1,1), 18.02550629769198D0,
+     :           1D-10, 'slDMAT', 'A(1,1)', STATUS )
+      CALL VVD ( DA(1,2), -52.16386644917280607D0,
+     :           1D-10, 'slDMAT', 'A(1,2)', STATUS )
+      CALL VVD ( DA(1,3), 34.37875949717850495D0,
+     :           1D-10, 'slDMAT', 'A(1,3)', STATUS )
+      CALL VVD ( DA(2,1), -52.16386644917280607D0,
+     :           1D-10, 'slDMAT', 'A(2,1)', STATUS )
+      CALL VVD ( DA(2,2), 168.1778099099805627D0,
+     :           1D-10, 'slDMAT', 'A(2,2)', STATUS )
+      CALL VVD ( DA(2,3), -118.0722869694232670D0,
+     :           1D-10, 'slDMAT', 'A(2,3)', STATUS )
+      CALL VVD ( DA(3,1), 34.37875949717850495D0,
+     :           1D-10, 'slDMAT', 'A(3,1)', STATUS )
+      CALL VVD ( DA(3,2), -118.0722869694232670D0,
+     :           1D-10, 'slDMAT', 'A(3,2)', STATUS )
+      CALL VVD ( DA(3,3), 86.50307003740151262D0,
+     :           1D-10, 'slDMAT', 'A(3,3)', STATUS )
+      CALL VVD ( DV(1), 1.002346480763383D0,
+     :           1D-12, 'slDMAT', 'V(1)', STATUS )
+      CALL VVD ( DV(2), 0.03285594016974583489D0,
+     :           1D-12, 'slDMAT', 'V(2)', STATUS )
+      CALL VVD ( DV(3), 0.004760688414885247309D0,
+     :           1D-12, 'slDMAT', 'V(3)', STATUS )
+      CALL VVD ( DD, 0.003658344147359863D0,
+     :           1D-12, 'slDMAT', 'D', STATUS )
+      CALL VIV ( J, 0, 'slDMAT', 'J', STATUS )
+
+      END
+
+      SUBROUTINE T_E2H ( STATUS )
+*+
+*  - - - - - - -
+*   T _ E 2 H
+*  - - - - - - -
+*
+*  Test slE2H, slDE2H, slH2E, slDH2E routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  All the above plus VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      REAL H, D, P, A, E
+      DOUBLE PRECISION DH, DD, DP, DA, DE
+
+      DH = -0.3D0
+      DD = -1.1D0
+      DP = -0.7D0
+
+      H = SNGL( DH )
+      D = SNGL( DD )
+      P = SNGL( DP )
+
+      CALL slDE2H ( DH, DD, DP, DA, DE )
+      CALL VVD ( DA, 2.820087515852369D0, 1D-12, 'slDE2H',
+     :           'AZ', STATUS )
+      CALL VVD ( DE, 1.132711866443304D0, 1D-12, 'slDE2H',
+     :           'El', STATUS )
+
+      CALL slE2H ( H, D, P, A, E )
+      CALL VVD ( DBLE( A ), 2.820087515852369D0, 1D-6, 'slE2H',
+     :           'AZ', STATUS )
+      CALL VVD ( DBLE( E ), 1.132711866443304D0, 1D-6, 'slE2H',
+     :           'El', STATUS )
+
+      CALL slDH2E ( DA, DE, DP, DH, DD )
+      CALL VVD ( DH, -0.3D0, 1D-12, 'slDH2E', 'HA', STATUS )
+      CALL VVD ( DD, -1.1D0, 1D-12, 'slDH2E', 'DEC', STATUS )
+
+      CALL slH2E ( A, E, P, H, D )
+      CALL VVD ( DBLE( H ), -0.3D0, 1D-6, 'slH2E',
+     :           'HA', STATUS )
+      CALL VVD ( DBLE( D ), -1.1D0, 1D-6, 'slH2E',
+     :           'DEC', STATUS )
+
+      END
+
+      SUBROUTINE T_EARTH ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ E R T H
+*  - - - - - - - -
+*
+*  Test slERTH routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slERTH, VVD.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      REAL PV(6)
+
+      CALL slERTH ( 1978, 174, 0.87E0, PV )
+
+      CALL VVD ( DBLE( PV(1) ), 3.590867086D-2, 1D-6, 'slERTH',
+     :           'PV(1)', STATUS )
+      CALL VVD ( DBLE( PV(2) ), -9.319285116D-1, 1D-6, 'slERTH',
+     :           'PV(2)', STATUS )
+      CALL VVD ( DBLE( PV(3) ), -4.041039435D-1, 1D-6, 'slERTH',
+     :           'PV(3)', STATUS )
+      CALL VVD ( DBLE( PV(4) ), 1.956930055D-7, 1D-13, 'slERTH',
+     :           'PV(4)', STATUS )
+      CALL VVD ( DBLE( PV(5) ), 5.743797400D-9, 1D-13, 'slERTH',
+     :           'PV(5)', STATUS )
+      CALL VVD ( DBLE( PV(6) ), 2.512001677D-9, 1D-13, 'slERTH',
+     :           'PV(6)', STATUS )
+
+      END
+
+      SUBROUTINE T_ECLEQ ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ E C E Q
+*  - - - - - - - -
+*
+*  Test slECEQ routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slECEQ, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION R, D
+
+      CALL slECEQ ( 1.234D0, -0.123D0, 43210D0, R, D )
+
+      CALL VVD ( R, 1.229910118208851D0, 1D-12, 'slECEQ',
+     :           'RA', STATUS )
+      CALL VVD ( D, 0.2638461400411088D0, 1D-12, 'slECEQ',
+     :           'DEC', STATUS )
+
+      END
+
+      SUBROUTINE T_ECMAT ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ E C M A
+*  - - - - - - - -
+*
+*  Test slECMA routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slECMA, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION RM(3,3)
+
+      CALL slECMA ( 41234D0, RM )
+
+      CALL VVD ( RM(1,1), 1D0, 1D-12, 'slECMA',
+     :           '(1,1)', STATUS )
+      CALL VVD ( RM(1,2), 0D0, 1D-12, 'slECMA',
+     :           '(1,2)', STATUS )
+      CALL VVD ( RM(1,3), 0D0, 1D-12, 'slECMA',
+     :           '(1,3)', STATUS )
+      CALL VVD ( RM(2,1), 0D0, 1D-12, 'slECMA',
+     :           '(2,1)', STATUS )
+      CALL VVD ( RM(2,2), 0.917456575085716D0, 1D-12, 'slECMA',
+     :           '(2,2)', STATUS )
+      CALL VVD ( RM(2,3), 0.397835937079581D0, 1D-12, 'slECMA',
+     :           '(2,3)', STATUS )
+      CALL VVD ( RM(3,1), 0D0, 1D-12, 'slECMA',
+     :           '(3,1)', STATUS )
+      CALL VVD ( RM(3,2), -0.397835937079581D0, 1D-12, 'slECMA',
+     :           '(3,2)', STATUS )
+      CALL VVD ( RM(3,3), 0.917456575085716D0, 1D-12, 'slECMA',
+     :           '(3,3)', STATUS )
+
+      END
+
+      SUBROUTINE T_ECOR ( STATUS )
+*+
+*  - - - - - - -
+*   T _ E C O R
+*  - - - - - - -
+*
+*  Test slECOR routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slECOR, VVD.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      REAL RV, Tl
+
+      CALL slECOR ( 2.345E0, -0.567E0, 1995, 306, 0.037E0, RV, Tl )
+
+      CALL VVD ( DBLE( RV ), -19.182460D0, 1D-3, 'slECOR',
+     :           'RV', STATUS )
+      CALL VVD ( DBLE( Tl ), -120.36632D0, 1D-2, 'slECOR',
+     :           'Tl', STATUS )
+
+      END
+
+      SUBROUTINE T_EG50 ( STATUS )
+*+
+*  - - - - - - -
+*   T _ E G 5 0
+*  - - - - - - -
+*
+*  Test slEG50 routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slEG50, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION DL, DB
+
+      CALL slEG50 ( 3.012D0, 1.234D0, DL, DB )
+
+      CALL VVD ( DL, 2.305557953813397D0, 1D-12, 'slEG50',
+     :           'L', STATUS )
+      CALL VVD ( DB, 0.7903600886585871D0, 1D-12, 'slEG50',
+     :           'B', STATUS )
+
+      END
+
+      SUBROUTINE T_EPB ( STATUS )
+
+*+
+*  - - - - - -
+*   T _ E P B
+*  - - - - - -
+*
+*  Test slEPB routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slEPB, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slEPB
+
+
+      CALL VVD ( slEPB ( 45123D0 ), 1982.419793168669D0, 1D-8,
+     :           'slEPB', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_EPB2D ( STATUS )
+*+
+*  - - - - - - -
+*   T _ E B 2 D
+*  - - - - - - -
+*
+*  Test slEB2D routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slEB2D, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slEB2D
+
+
+      CALL VVD ( slEB2D ( 1975.5D0 ), 42595.5995279655D0, 1D-7,
+     :           'slEB2D', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_EPCO ( STATUS )
+*+
+*  - - - - - - -
+*   T _ E P C O
+*  - - - - - - -
+*
+*  Test slEPCO routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slEPCO, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slEPCO
+
+
+      CALL VVD ( slEPCO ( 'B', 'J', 2000D0 ), 2000.001277513665D0,
+     :           1D-7, 'slEPCO', 'BJ', STATUS )
+      CALL VVD ( slEPCO ( 'J', 'B', 1950D0 ), 1949.999790442300D0,
+     :           1D-7, 'slEPCO', 'JB', STATUS )
+      CALL VVD ( slEPCO ( 'J', 'J', 2000D0 ), 2000D0,
+     :           1D-7, 'slEPCO', 'JJ', STATUS )
+
+      END
+
+      SUBROUTINE T_EPJ ( STATUS )
+*+
+*  - - - - - -
+*   T _ E P J
+*  - - - - - -
+*
+*  Test slEPJ routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slEPJ, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slEPJ
+
+
+      CALL VVD ( slEPJ ( 42999D0 ), 1976.603696098563D0,
+     :           1D-7, 'slEPJ', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_EPJ2D ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ E J 2 D
+*  - - - - - - - -
+*
+*  Test slEJ2D routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slEJ2D, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slEJ2D
+
+
+      CALL VVD ( slEJ2D ( 2010.077D0 ), 55225.124250D0,
+     :           1D-6, 'slEJ2D', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_EQECL ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ E Q E C
+*  - - - - - - - -
+*
+*  Test slEQEC routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slEQEC, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION DL, DB
+
+      CALL slEQEC ( 0.789D0, -0.123D0, 46555D0, DL, DB )
+
+      CALL VVD ( DL, 0.7036566430349022D0, 1D-12, 'slEQEC',
+     :           'L', STATUS )
+      CALL VVD ( DB, -0.4036047164116848D0, 1D-12, 'slEQEC',
+     :           'B', STATUS )
+
+      END
+
+      SUBROUTINE T_EQEQX ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ E Q E X
+*  - - - - - - - -
+*
+*  Test slEQEX routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slEQEX, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slEQEX
+
+
+      CALL VVD ( slEQEX ( 41234D0 ), 5.376047445838358596D-5,
+     :           1D-17, 'slEQEX', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_EQGAL ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ E Q G A
+*  - - - - - - - -
+*
+*  Test slEQGA routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slEQGA, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION DL, DB
+
+      CALL slEQGA ( 5.67D0, -1.23D0, DL, DB )
+
+      CALL VVD ( DL, 5.612270780904526D0, 1D-12, 'slEQGA',
+     :           'DL', STATUS )
+      CALL VVD ( DB, -0.6800521449061520D0, 1D-12, 'slEQGA',
+     :           'DB', STATUS )
+
+      END
+
+      SUBROUTINE T_ETRMS ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ E T R M
+*  - - - - - - - -
+*
+*  Test slETRM routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slETRM, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION EV(3)
+
+      CALL slETRM ( 1976.9D0, EV )
+
+      CALL VVD ( EV(1), -1.621617102537041D-6, 1D-18, 'slETRM',
+     :           'X', STATUS )
+      CALL VVD ( EV(2), -3.310070088507914D-7, 1D-18, 'slETRM',
+     :           'Y', STATUS )
+      CALL VVD ( EV(3), -1.435296627515719D-7, 1D-18, 'slETRM',
+     :           'Z', STATUS )
+
+      END
+
+      SUBROUTINE T_EVP ( STATUS )
+*+
+*  - - - - - -
+*   T _ E V P
+*  - - - - - -
+*
+*  Test slEVP and slEPV routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slEVP, slEPV, VVD.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION DVB(3), DPB(3), DVH(3), DPH(3)
+
+      CALL slEVP ( 50100D0, 1990D0, DVB, DPB, DVH, DPH )
+
+      CALL VVD ( DVB(1), -1.807210068604058436D-7, 1D-14, 'slEVP',
+     :           'DVB(X)', STATUS )
+      CALL VVD ( DVB(2), -8.385891022440320D-8, 1D-14, 'slEVP',
+     :           'DVB(Y)', STATUS )
+      CALL VVD ( DVB(3), -3.635846882638055D-8, 1D-14, 'slEVP',
+     :           'DVB(Z)', STATUS )
+      CALL VVD ( DPB(1), -0.4515615297360333D0, 1D-7, 'slEVP',
+     :           'DPB(X)', STATUS )
+      CALL VVD ( DPB(2),  0.8103788166239596D0, 1D-7, 'slEVP',
+     :           'DPB(Y)', STATUS )
+      CALL VVD ( DPB(3),  0.3514505204144827D0, 1D-7, 'slEVP',
+     :           'DPB(Z)', STATUS )
+      CALL VVD ( DVH(1), -1.806354061156890855D-7, 1D-14, 'slEVP',
+     :           'DVH(X)', STATUS )
+      CALL VVD ( DVH(2), -8.383798678086174D-8, 1D-14, 'slEVP',
+     :           'DVH(Y)', STATUS )
+      CALL VVD ( DVH(3), -3.635185843644782D-8, 1D-14, 'slEVP',
+     :           'DVH(Z)', STATUS )
+      CALL VVD ( DPH(1), -0.4478571659918565D0, 1D-7, 'slEVP',
+     :           'DPH(X)', STATUS )
+      CALL VVD ( DPH(2),  0.8036439916076232D0, 1D-7, 'slEVP',
+     :           'DPH(Y)', STATUS )
+      CALL VVD ( DPH(3),  0.3484298459102053D0, 1D-7, 'slEVP',
+     :           'DPH(Z)', STATUS )
+
+      CALL slEPV ( 53411.52501161D0, DPH, DVH, DPB, DVB )
+
+      CALL VVD ( DPH(1), -0.7757238809297653D0, 1D-12, 'slEPV',
+     :           'DPH(X)', STATUS )
+      CALL VVD ( DPH(2), +0.5598052241363390D0, 1D-12, 'slEPV',
+     :           'DPH(Y)', STATUS )
+      CALL VVD ( DPH(3), +0.2426998466481708D0, 1D-12, 'slEPV',
+     :           'DPH(Z)', STATUS )
+      CALL VVD ( DVH(1), -0.0109189182414732D0, 1D-12, 'slEPV',
+     :           'DVH(X)', STATUS )
+      CALL VVD ( DVH(2), -0.0124718726844084D0, 1D-12, 'slEPV',
+     :           'DVH(Y)', STATUS )
+      CALL VVD ( DVH(3), -0.0054075694180650D0, 1D-12, 'slEPV',
+     :           'DVH(Z)', STATUS )
+      CALL VVD ( DPB(1), -0.7714104440491060D0, 1D-12, 'slEPV',
+     :           'DPB(X)', STATUS )
+      CALL VVD ( DPB(2), +0.5598412061824225D0, 1D-12, 'slEPV',
+     :           'DPB(Y)', STATUS )
+      CALL VVD ( DPB(3), +0.2425996277722475D0, 1D-12, 'slEPV',
+     :           'DPB(Z)', STATUS )
+      CALL VVD ( DVB(1), -0.0109187426811683D0, 1D-12, 'slEPV',
+     :           'DVB(X)', STATUS )
+      CALL VVD ( DVB(2), -0.0124652546173285D0, 1D-12, 'slEPV',
+     :           'DVB(Y)', STATUS )
+      CALL VVD ( DVB(3), -0.0054047731809662D0, 1D-12, 'slEPV',
+     :           'DVB(Z)', STATUS )
+
+      END
+
+      SUBROUTINE T_FITXY ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ F T X Y
+*  - - - - - - - -
+*
+*  Test slFTXY, slPXY, slINVF, slXYXY, slDCMF routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slFTXY, VVD, VIV, slPXY, slINVF, slXYXY, slDCMF.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J, NPTS
+
+      PARAMETER (NPTS = 8)
+
+      DOUBLE PRECISION XYE(2,NPTS)
+      DOUBLE PRECISION XYM(2,NPTS)
+      DOUBLE PRECISION COEFFS(6), XYP(2,NPTS), XRMS, YRMS, RRMS,
+     :    BKWDS(6), X2, Y2, XZ, YZ, XS, YS, PERP, ORIENT
+
+      DATA XYE/-23.4D0, -12.1D0,   32D0,  -15.3D0,
+     :          10.9D0,  23.7D0,   -3D0,   16.1D0,
+     :          45D0,  32.5D0,    8.6D0,  -17D0,
+     :          15.3D0,  10D0,  121.7D0,   -3.8D0/
+      DATA XYM/-23.41D0, 12.12D0,  32.03D0,  15.34D0,
+     :          10.93D0,-23.72D0,  -3.01D0, -16.10D0,
+     :          44.90D0,-32.46D0,   8.55D0,  17.02D0,
+     :          15.31D0,-10.07D0, 120.92D0,   3.81D0/
+
+*  Fit a 4-coeff linear model to relate two sets of (x,y) coordinates.
+
+      CALL slFTXY ( 4, NPTS, XYE, XYM, COEFFS, J )
+      CALL VVD ( COEFFS(1), -7.938263381515947D-3,
+     :           1D-12, 'slFTXY', '4/1', STATUS )
+      CALL VVD ( COEFFS(2), 1.004640925187200D0,
+     :           1D-12, 'slFTXY', '4/2', STATUS )
+      CALL VVD ( COEFFS(3), 3.976948048238268D-4,
+     :           1D-12, 'slFTXY', '4/3', STATUS )
+      CALL VVD ( COEFFS(4), -2.501031681585021D-2,
+     :           1D-12, 'slFTXY', '4/4', STATUS )
+      CALL VVD ( COEFFS(5), 3.976948048238268D-4,
+     :           1D-12, 'slFTXY', '4/5', STATUS )
+      CALL VVD ( COEFFS(6), -1.004640925187200D0,
+     :           1D-12, 'slFTXY', '4/6', STATUS )
+      CALL VIV ( J, 0, 'slFTXY', '4/J', STATUS )
+
+*  Same but 6-coeff.
+
+      CALL slFTXY ( 6, NPTS, XYE, XYM, COEFFS, J )
+      CALL VVD ( COEFFS(1), -2.617232551841476D-2,
+     :           1D-12, 'slFTXY', '6/1', STATUS )
+      CALL VVD ( COEFFS(2), 1.005634905041421D0,
+     :           1D-12, 'slFTXY', '6/2', STATUS )
+      CALL VVD ( COEFFS(3), 2.133045023329208D-3,
+     :           1D-12, 'slFTXY', '6/3', STATUS )
+      CALL VVD ( COEFFS(4), 3.846993364417779909D-3,
+     :           1D-12, 'slFTXY', '6/4', STATUS )
+      CALL VVD ( COEFFS(5), 1.301671386431460D-4,
+     :           1D-12, 'slFTXY', '6/5', STATUS )
+      CALL VVD ( COEFFS(6), -0.9994827065693964D0,
+     :           1D-12, 'slFTXY', '6/6', STATUS )
+      CALL VIV ( J, 0, 'slFTXY', '6/J', STATUS )
+
+*  Compute predicted coordinates and residuals.
+
+      CALL slPXY ( NPTS, XYE, XYM, COEFFS, XYP, XRMS, YRMS, RRMS )
+      CALL VVD ( XYP(1,1), -23.542232946855340D0,
+     :           1D-12, 'slPXY', 'X1', STATUS )
+      CALL VVD ( XYP(2,1), -12.11293062297230597D0,
+     :           1D-12, 'slPXY', 'Y1', STATUS )
+      CALL VVD ( XYP(1,2), 32.217034593616180D0,
+     :           1D-12, 'slPXY', 'X2', STATUS )
+      CALL VVD ( XYP(2,2), -15.324048471959370D0,
+     :           1D-12, 'slPXY', 'Y2', STATUS )
+      CALL VVD ( XYP(1,3), 10.914821358630950D0,
+     :           1D-12, 'slPXY', 'X3', STATUS )
+      CALL VVD ( XYP(2,3), 23.712999520015880D0,
+     :           1D-12, 'slPXY', 'Y3', STATUS )
+      CALL VVD ( XYP(1,4), -3.087475414568693D0,
+     :           1D-12, 'slPXY', 'X4', STATUS )
+      CALL VVD ( XYP(2,4), 16.09512676604438414D0,
+     :           1D-12, 'slPXY', 'Y4', STATUS )
+      CALL VVD ( XYP(1,5), 45.05759626938414666D0,
+     :           1D-12, 'slPXY', 'X5', STATUS )
+      CALL VVD ( XYP(2,5), 32.45290015313210889D0,
+     :           1D-12, 'slPXY', 'Y5', STATUS )
+      CALL VVD ( XYP(1,6), 8.608310538882801D0,
+     :           1D-12, 'slPXY', 'X6', STATUS )
+      CALL VVD ( XYP(2,6), -17.006235743411300D0,
+     :           1D-12, 'slPXY', 'Y6', STATUS )
+      CALL VVD ( XYP(1,7), 15.348618307280820D0,
+     :           1D-12, 'slPXY', 'X7', STATUS )
+      CALL VVD ( XYP(2,7), 10.07063070741086835D0,
+     :           1D-12, 'slPXY', 'Y7', STATUS )
+      CALL VVD ( XYP(1,8), 121.5833272936291482D0,
+     :           1D-12, 'slPXY', 'X8', STATUS )
+      CALL VVD ( XYP(2,8), -3.788442308260240D0,
+     :           1D-12, 'slPXY', 'Y8', STATUS )
+      CALL VVD ( XRMS ,0.1087247110488075D0,
+     :           1D-13, 'slPXY', 'XRMS', STATUS )
+      CALL VVD ( YRMS, 0.03224481175794666D0,
+     :           1D-13, 'slPXY', 'YRMS', STATUS )
+      CALL VVD ( RRMS, 0.1134054261398109D0,
+     :           1D-13, 'slPXY', 'RRMS', STATUS )
+
+*  Invert the model.
+
+      CALL slINVF ( COEFFS, BKWDS, J )
+      CALL VVD ( BKWDS(1), 0.02601750208015891D0,
+     :           1D-12, 'slINVF', '1', status)
+      CALL VVD ( BKWDS(2), 0.9943963945040283D0,
+     :           1D-12, 'slINVF', '2', status)
+      CALL VVD ( BKWDS(3), 0.002122190075497872D0,
+     :           1D-12, 'slINVF', '3', status)
+      CALL VVD ( BKWDS(4), 0.003852372795357474353D0,
+     :           1D-12, 'slINVF', '4', status)
+      CALL VVD ( BKWDS(5), 0.0001295047252932767D0,
+     :           1D-12, 'slINVF', '5', status)
+      CALL VVD ( BKWDS(6), -1.000517284779212D0,
+     :           1D-12, 'slINVF', '6', status)
+      CALL VIV ( J, 0, 'slINVF', 'J', STATUS )
+
+*  Transform one x,y.
+
+      CALL slXYXY ( 44.5D0, 32.5D0, COEFFS, X2, Y2 )
+      CALL VVD ( X2, 44.793904912083030D0,
+     :           1D-11, 'slXYXY', 'X', status)
+      CALL VVD ( Y2, -32.473548532471330D0,
+     :           1D-11, 'slXYXY', 'Y', status)
+
+*  Decompose the fit into scales etc.
+
+      CALL slDCMF ( COEFFS, XZ, YZ, XS, YS, PERP, ORIENT )
+      CALL VVD ( XZ, -0.0260175020801628646D0,
+     :           1D-12, 'slDCMF', 'XZ', status)
+      CALL VVD ( YZ, -0.003852372795357474353D0,
+     :           1D-12, 'slDCMF', 'YZ', status)
+      CALL VVD ( XS, -1.00563491346569D0,
+     :           1D-12, 'slDCMF', 'XS', status)
+      CALL VVD ( YS, 0.999484982684761D0,
+     :           1D-12, 'slDCMF', 'YS', status)
+      CALL VVD ( PERP,-0.002004707996156263D0,
+     :           1D-12, 'slDCMF', 'P', status)
+      CALL VVD ( ORIENT, 3.14046086182333D0,
+     :           1D-12, 'slDCMF', 'O', status)
+
+      END
+
+      SUBROUTINE T_FK425 ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ F K 4 5
+*  - - - - - - - -
+*
+*  Test slFK45 routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slFK45.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION R2000, D2000, DR2000, DD2000, P2000, V2000
+
+      CALL slFK45 ( 1.234D0, -0.123D0, -1D-5, 2D-6, 0.5D0,
+     :                 20D0, R2000, D2000, DR2000, DD2000, P2000,
+     :                 V2000 )
+
+      CALL VVD ( R2000, 1.244117554618727D0, 1D-12, 'slFK45',
+     :           'R', STATUS )
+      CALL VVD ( D2000, -0.1213164254458709D0, 1D-12, 'slFK45',
+     :           'D', STATUS )
+      CALL VVD ( DR2000, -9.964265838268711D-6, 1D-17, 'slFK45',
+     :           'DR', STATUS )
+      CALL VVD ( DD2000, 2.038065265773541D-6, 1D-17, 'slFK45',
+     :           'DD', STATUS )
+      CALL VVD ( P2000, 0.4997443812415410D0, 1D-12, 'slFK45',
+     :           'P', STATUS )
+      CALL VVD ( V2000, 20.010460915421010D0, 1D-11, 'slFK45',
+     :           'V', STATUS )
+
+      END
+
+      SUBROUTINE T_FK45Z ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ F 4 5 Z
+*  - - - - - - - -
+*
+*  Test slF45Z routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slF45Z.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION R2000, D2000
+
+      CALL slF45Z ( 1.234D0, -0.123D0, 1984D0, R2000, D2000 )
+
+      CALL VVD ( R2000, 1.244616510731691D0, 1D-12, 'slF45Z',
+     :           'R', STATUS )
+      CALL VVD ( D2000, -0.1214185839586555D0, 1D-12, 'slF45Z',
+     :           'D', STATUS )
+
+      END
+
+      SUBROUTINE T_FK524 ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ F K 5 4
+*  - - - - - - - -
+*
+*  Test slFK54 routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slFK54.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION R1950, D1950, DR1950, DD1950, P1950, V1950
+
+      CALL slFK54 ( 4.567D0, -1.23D0, -3D-5, 8D-6, 0.29D0,
+     :                 -35D0, R1950, D1950, DR1950, DD1950, P1950,
+     :                 V1950 )
+
+      CALL VVD ( R1950, 4.543778603272084D0, 1D-12, 'slFK54',
+     :           'R', STATUS )
+      CALL VVD ( D1950, -1.229642790187574D0, 1D-12, 'slFK54',
+     :           'D', STATUS )
+      CALL VVD ( DR1950, -2.957873121769244D-5, 1D-17, 'slFK54',
+     :           'DR', STATUS )
+      CALL VVD ( DD1950, 8.117725309659079D-6, 1D-17, 'slFK54',
+     :           'DD', STATUS )
+      CALL VVD ( P1950, 0.2898494999992917D0, 1D-12, 'slFK54',
+     :           'P', STATUS )
+      CALL VVD ( V1950, -35.026862824252680D0, 1D-11, 'slFK54',
+     :           'V', STATUS )
+
+      END
+
+      SUBROUTINE T_FK52H ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ F K 5 H
+*  - - - - - - - -
+*
+*  Test slFK5H, slHFK5, slF5HZ, slHF5Z routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slFK54, slHFK5.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION R5, D5, DR5, DD5, RH, DH, DRH, DDH
+
+      CALL slFK5H ( 1.234D0, -0.987D0, 1D-6, -2D-6, RH, DH, DRH,
+     :                 DDH )
+      CALL VVD ( RH, 1.234000000272122558D0, 1D-13, 'slFK5H',
+     :           'R', STATUS )
+      CALL VVD ( DH, -0.9869999235218543959D0, 1D-13, 'slFK5H',
+     :           'D', STATUS )
+      CALL VVD ( DRH, 0.000000993178295D0, 1D-13, 'slFK5H',
+     :           'DR', STATUS )
+      CALL VVD ( DDH, -0.000001997665915D0, 1D-13, 'slFK5H',
+     :           'DD', STATUS )
+      CALL slHFK5 ( RH, DH, DRH, DDH, r5, D5, DR5, DD5 )
+      CALL VVD ( R5, 1.234D0, 1D-13, 'slHFK5', 'R', STATUS )
+      CALL VVD ( D5, -0.987D0, 1D-13, 'slHFK5', 'D', STATUS )
+      CALL VVD ( DR5, 1D-6, 1D-13, 'slHFK5', 'DR', STATUS )
+      CALL VVD ( DD5, -2D-6, 1D-13, 'slHFK5', 'DD', STATUS )
+      CALL slF5HZ ( 1.234D0, -0.987D0, 1980D0, RH, DH )
+      CALL VVD ( RH, 1.234000136713611301D0, 1D-13, 'slF5HZ',
+     :           'R', STATUS )
+      CALL VVD ( DH, -0.9869999702020807601D0, 1D-13, 'slF5HZ',
+     :           'D', STATUS )
+      CALL slHF5Z ( RH, DH, 1980D0, R5, D5, DR5, DD5 )
+      CALL VVD ( R5, 1.234D0, 1D-13, 'slHF5Z', 'R', STATUS )
+      CALL VVD ( D5, -0.987D0, 1D-13, 'slHF5Z', 'D', STATUS )
+      CALL VVD ( DR5, 0.000000006822074D0, 1D-13, 'slHF5Z',
+     :           'DR', STATUS )
+      CALL VVD ( DD5, -0.000000002334012D0, 1D-13, 'slHF5Z',
+     :           'DD', STATUS )
+
+      END
+
+      SUBROUTINE T_FK54Z ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ F 5 4 Z
+*  - - - - - - - -
+*
+*  Test slF54Z routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slF54Z.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION R1950, D1950, DR1950, DD1950
+
+      CALL slF54Z ( 0.001D0, -1.55D0, 1900D0, R1950, D1950,
+     :                 DR1950, DD1950 )
+
+      CALL VVD ( R1950, 6.271585543439484D0, 1D-12, 'slF54Z',
+     :           'R', STATUS )
+      CALL VVD ( D1950, -1.554861715330319D0, 1D-12, 'slF54Z',
+     :           'D', STATUS )
+      CALL VVD ( DR1950, -4.175410876044916011D-8, 1D-20, 'slF54Z',
+     :           'DR', STATUS )
+      CALL VVD ( DD1950, 2.118595098308522D-8, 1D-20, 'slF54Z',
+     :           'DD', STATUS )
+
+      END
+
+      SUBROUTINE T_FLOTIN ( STATUS )
+*+
+*  - - - - - - - - -
+*   T _ R F L I
+*  - - - - - - - - -
+*
+*  Test slRFLI, slDFLI routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slRFLI, VVD, VIV, slDFLI.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER I, J
+      REAL FV
+      DOUBLE PRECISION DV
+      CHARACTER*33 S
+      DATA S /'  12.345, , -0 1E3-4 2000  E     '/
+
+      I = 1
+      FV = 0.0
+
+      CALL slRFLI ( S, I, FV, J )
+      CALL VIV ( I, 10, 'slRFLI', 'V5', STATUS )
+      CALL VVD ( DBLE( FV ), 12.345D0, 1D-5, 'slRFLI',
+     :           'V1', STATUS )
+      CALL VIV ( J, 0, 'slRFLI', 'J1', STATUS )
+
+      CALL slRFLI ( S, I, FV, J )
+      CALL VIV ( I, 12, 'slRFLI', 'I2', STATUS )
+      CALL VVD ( DBLE( FV ), 12.345D0, 1D-5, 'slRFLI',
+     :           'V2', STATUS )
+      CALL VIV ( J, 1, 'slRFLI', 'J2', STATUS )
+
+      CALL slRFLI ( S, I, FV, J )
+      CALL VIV ( I, 16, 'slRFLI', 'I3', STATUS )
+      CALL VVD ( DBLE( FV ), 0D0, 0D0, 'slRFLI', 'V3', STATUS )
+      CALL VIV ( J, -1, 'slRFLI', 'J3', STATUS )
+
+      CALL slRFLI ( S, I, FV, J )
+      CALL VIV ( I, 19, 'slRFLI', 'I4', STATUS )
+      CALL VVD ( DBLE( FV), 1000D0, 0D0, 'slRFLI', 'V4', STATUS )
+      CALL VIV ( J, 0, 'slRFLI', 'J4', STATUS )
+
+      CALL slRFLI ( S, I, FV, J )
+      CALL VIV ( I, 22, 'slRFLI', 'I5', STATUS )
+      CALL VVD ( DBLE( FV ), -4D0, 0D0, 'slRFLI', 'V5', STATUS )
+      CALL VIV ( J, -1, 'slRFLI', 'J5', STATUS )
+
+      CALL slRFLI ( S, I, FV, J )
+      CALL VIV ( I, 28, 'slRFLI', 'I6', STATUS )
+      CALL VVD ( DBLE( FV ), 2000D0, 0D0, 'slRFLI',
+     :           'V6', STATUS )
+      CALL VIV ( J, 0, 'slRFLI', 'J6', STATUS )
+
+      CALL slRFLI ( S, I, FV, J )
+      CALL VIV ( I, 34, 'slRFLI', 'I7', STATUS )
+      CALL VVD ( DBLE( FV ), 2000D0, 0D0, 'slRFLI',
+     :           'V7', STATUS )
+      CALL VIV ( J, 2, 'slRFLI', 'J7', STATUS )
+
+      I = 1
+      DV = 0D0
+
+      CALL slDFLI ( S, I, DV, J )
+      CALL VIV ( I, 10, 'slDFLI', 'I1', STATUS )
+      CALL VVD ( DV, 12.345D0, 1D-12, 'slDFLI', 'V1', STATUS )
+      CALL VIV ( J, 0, 'slDFLI', 'J1', STATUS )
+
+      CALL slDFLI ( S, I, DV, J )
+      CALL VIV ( I, 12, 'slDFLI', 'I2', STATUS )
+      CALL VVD ( DV, 12.345D0, 1D-12, 'slDFLI', 'V2', STATUS )
+      CALL VIV ( J, 1, 'slDFLI', 'J2', STATUS )
+
+      CALL slDFLI ( S, I, DV, J )
+      CALL VIV ( I, 16, 'slDFLI', 'I3', STATUS )
+      CALL VVD ( DV, 0D0, 0D0, 'slDFLI', 'V3', STATUS )
+      CALL VIV ( J, -1, 'slDFLI', 'J3', STATUS )
+
+      CALL slDFLI ( S, I, DV, J )
+      CALL VIV ( I, 19, 'slDFLI', 'I4', STATUS )
+      CALL VVD ( DV, 1000D0, 0D0, 'slDFLI', 'V4', STATUS )
+      CALL VIV ( J, 0, 'slDFLI', 'J4', STATUS )
+
+      CALL slDFLI ( S, I, DV, J )
+      CALL VIV ( I, 22, 'slDFLI', 'I5', STATUS )
+      CALL VVD ( DV, -4D0, 0D0, 'slDFLI', 'V5', STATUS )
+      CALL VIV ( J, -1, 'slDFLI', 'J5', STATUS )
+
+      CALL slDFLI ( S, I, DV, J )
+      CALL VIV ( I, 28, 'slDFLI', 'I6', STATUS )
+      CALL VVD ( DV, 2000D0, 0D0, 'slDFLI', 'V6', STATUS )
+      CALL VIV ( J, 0, 'slDFLI', 'J6', STATUS )
+
+      CALL slDFLI ( S, I, DV, J )
+      CALL VIV ( I, 34, 'slDFLI', 'I7', STATUS )
+      CALL VVD ( DV, 2000D0, 0D0, 'slDFLI', 'V7', STATUS )
+      CALL VIV ( J, 2, 'slDFLI', 'J7', STATUS )
+
+      END
+
+      SUBROUTINE T_GALEQ ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ G A E Q
+*  - - - - - - - -
+*
+*  Test slGAEQ routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slGAEQ, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION DR, DD
+
+      CALL slGAEQ ( 5.67D0, -1.23D0, DR, DD )
+
+      CALL VVD ( DR, 0.04729270418071426D0, 1D-12, 'slGAEQ',
+     :           'DR', STATUS )
+      CALL VVD ( DD, -0.7834003666745548D0, 1D-12, 'slGAEQ',
+     :           'DD', STATUS )
+
+      END
+
+      SUBROUTINE T_GALSUP ( STATUS )
+*+
+*  - - - - - - - - -
+*   T _ G A S U
+*  - - - - - - - - -
+*
+*  Test slGASU routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slGASU, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION DSL, DSB
+
+      CALL slGASU ( 6.1D0, -1.4D0, DSL, DSB )
+
+      CALL VVD ( DSL, 4.567933268859171D0, 1D-12, 'slGASU',
+     :           'DSL', STATUS )
+      CALL VVD ( DSB, -0.01862369899731829D0, 1D-12, 'slGASU',
+     :           'DSB', STATUS )
+
+      END
+
+      SUBROUTINE T_GE50 ( STATUS )
+*+
+*  - - - - - - -
+*   T _ G E 5 0
+*  - - - - - - -
+*
+*  Test slGE50 routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slGE50, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION DR, DD
+
+      CALL slGE50 ( 6.1D0, -1.55D0, DR, DD )
+
+      CALL VVD ( DR, 0.1966825219934508D0, 1D-12, 'slGE50',
+     :           'DR', STATUS )
+      CALL VVD ( DD, -0.4924752701678960D0, 1D-12, 'slGE50',
+     :           'DD', STATUS )
+
+      END
+
+      SUBROUTINE T_GMST ( STATUS )
+*+
+*  - - - - - - -
+*   T _ G M S T
+*  - - - - - - -
+*
+*  Test slGMST and slGMSA routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slGMST, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slGMST, slGMSA
+
+
+      CALL VVD ( slGMST ( 43999.999D0 ), 3.9074971356487318D0,
+     :           1D-9, 'slGMST', ' ', STATUS )
+      CALL VVD ( slGMSA ( 43999D0, 0.999D0 ),
+     :           3.9074971356487318D0, 1D-12, 'slGMSA', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_INTIN ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ I N T I
+*  - - - - - - - -
+*
+*  Test slINTI routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slINTI, VIV.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER*4 N
+      INTEGER I, J
+      CHARACTER*28 S
+      DATA S /'  -12345, , -0  2000  +     '/
+
+      I = 1
+      N = 0
+
+      CALL slINTI ( S, I, N, J )
+      CALL VIV ( I, 10, 'slINTI', 'I1', STATUS )
+      CALL VLV ( N, -12345, 'slINTI', 'V1', STATUS )
+      CALL VIV ( J, -1, 'slINTI', 'J1', STATUS )
+
+      CALL slINTI ( S, I, N, J )
+      CALL VIV ( I, 12, 'slINTI', 'I2', STATUS )
+      CALL VLV ( N, -12345, 'slINTI', 'V2', STATUS )
+      CALL VIV ( J, 1, 'slINTI', 'J2', STATUS )
+
+      CALL slINTI ( S, I, N, J )
+      CALL VIV ( I, 17, 'slINTI', 'I3', STATUS )
+      CALL VLV ( N, 0, 'slINTI', 'V3', STATUS )
+      CALL VIV ( J, -1, 'slINTI', 'J3', STATUS )
+
+      CALL slINTI ( S, I, N, J )
+      CALL VIV ( I, 23, 'slINTI', 'I4', STATUS )
+      CALL VLV ( N, 2000, 'slINTI', 'V4', STATUS )
+      CALL VIV ( J, 0, 'slINTI', 'J4', STATUS )
+
+      CALL slINTI ( S, I, N, J )
+      CALL VIV ( I, 29, 'slINTI', 'I5', STATUS )
+      CALL VLV ( N, 2000, 'slINTI', 'V5', STATUS )
+      CALL VIV ( J, 2, 'slINTI', 'J5', STATUS )
+
+      END
+
+      SUBROUTINE T_KBJ ( STATUS )
+*+
+*  - - - - - -
+*   T _ K B J
+*  - - - - - -
+*
+*  Test slKBJ routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slKBJ, VCS, VIV.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J
+      DOUBLE PRECISION E
+      CHARACTER K
+      DATA K /'?'/
+
+      E = 1950D0
+      CALL slKBJ ( -1, E, K, J )
+      CALL VCS ( K, ' ', 'slKBJ', 'JB1', STATUS )
+      CALL VIV ( J, 1, 'slKBJ', 'J1', STATUS )
+      CALL slKBJ ( 0, E, K, J )
+      CALL VCS ( K, 'B', 'slKBJ', 'JB2', STATUS )
+      CALL VIV ( J, 0, 'slKBJ', 'J2', STATUS )
+      CALL slKBJ ( 1, E, K, J )
+      CALL VCS ( K, 'B', 'slKBJ', 'JB3', STATUS )
+      CALL VIV ( J, 0, 'slKBJ', 'J3', STATUS )
+      CALL slKBJ ( 2, E, K, J )
+      CALL VCS ( K, 'J', 'slKBJ', 'JB4', STATUS )
+      CALL VIV ( J, 0, 'slKBJ', 'J4', STATUS )
+      CALL slKBJ ( 3, E, K, J )
+      CALL VCS ( K, ' ', 'slKBJ', 'JB5', STATUS )
+      CALL VIV ( J, 1, 'slKBJ', 'J5', STATUS )
+
+      E = 2000D0
+      CALL slKBJ ( 0, E, K, J )
+      CALL VCS ( K, 'J', 'slKBJ', 'JB6', STATUS )
+      CALL VIV ( J, 0, 'slKBJ', 'J6', STATUS )
+      CALL slKBJ ( 1, E, K, J )
+      CALL VCS ( K, 'B', 'slKBJ', 'jB7', STATUS )
+      CALL VIV ( J, 0, 'slKBJ', 'J7', STATUS )
+      CALL slKBJ ( 2, E, K, J )
+      CALL VCS ( K, 'J', 'slKBJ', 'JB8', STATUS )
+      CALL VIV ( J, 0, 'slKBJ', 'J8', STATUS )
+
+      END
+
+      SUBROUTINE T_MAP ( STATUS )
+*+
+*  - - - - - -
+*   T _ M A P
+*  - - - - - -
+*
+*  Test slMAP, slMAPA, slMAPQ, slMAPZ routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slMAP, slMAPA, slMAPQ, slMAPZ, VVD.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION RA, DA, AMPRMS(21)
+
+      CALL slMAP ( 6.123D0, -0.999D0, 1.23D-5, -0.987D-5,
+     :               0.123D0, 32.1D0, 1999D0, 43210.9D0, RA, DA )
+
+      CALL VVD ( RA, 6.117130429775647D0, 1D-12, 'slMAP',
+     :           'RA', STATUS )
+      CALL VVD ( DA, -1.000880769038632D0, 1D-12, 'slMAP',
+     :           'DA', STATUS )
+
+      CALL slMAPA ( 2020D0, 45012.3D0, AMPRMS )
+
+      CALL VVD ( AMPRMS(1), -37.884188911704310D0,
+     :           1D-11, 'slMAPA', 'AMPRMS(1)', STATUS )
+      CALL VVD ( AMPRMS(2),  -0.7888341859486424D0,
+     :           1D-7, 'slMAPA', 'AMPRMS(2)', STATUS )
+      CALL VVD ( AMPRMS(3),   0.5405321789059870D0,
+     :           1D-7, 'slMAPA', 'AMPRMS(3)', STATUS )
+      CALL VVD ( AMPRMS(4),   0.2340784267119091D0,
+     :           1D-7, 'slMAPA', 'AMPRMS(4)', STATUS )
+      CALL VVD ( AMPRMS(5),  -0.8067807553217332071D0,
+     :           1D-7, 'slMAPA', 'AMPRMS(5)', STATUS )
+      CALL VVD ( AMPRMS(6),   0.5420884771236513880D0,
+     :           1D-7, 'slMAPA', 'AMPRMS(6)', STATUS )
+      CALL VVD ( AMPRMS(7),   0.2350423277034460899D0,
+     :           1D-7, 'slMAPA', 'AMPRMS(7)', STATUS )
+      CALL VVD ( AMPRMS(8),   1.999729469227807D-8,
+     :           1D-12, 'slMAPA', 'AMPRMS(8)', STATUS )
+      CALL VVD ( AMPRMS(9),  -6.035531043691568494D-5,
+     :           1D-12, 'slMAPA', 'AMPRMS(9)', STATUS )
+      CALL VVD ( AMPRMS(10), -7.381891582591552377D-5,
+     :           1D-11, 'slMAPA', 'AMPRMS(10)', STATUS )
+      CALL VVD ( AMPRMS(11), -3.200897749853207412D-5,
+     :           1D-11, 'slMAPA', 'AMPRMS(11)', STATUS )
+      CALL VVD ( AMPRMS(12),  0.9999999949417148D0,
+     :           1D-11, 'slMAPA', 'AMPRMS(12)', STATUS )
+      CALL VVD ( AMPRMS(13),  0.9999566751478850D0,
+     :           1D-11, 'slMAPA', 'AMPRMS(13)', STATUS )
+      CALL VVD ( AMPRMS(14), -8.537361890149777D-3,
+     :           1D-11, 'slMAPA', 'AMPRMS(14)', STATUS )
+      CALL VVD ( AMPRMS(15), -3.709619811228171D-3,
+     :           1D-11, 'slMAPA', 'AMPRMS(15)', STATUS )
+      CALL VVD ( AMPRMS(16), 8.537308717676752D-3,
+     :           1D-11, 'slMAPA', 'AMPRMS(16)', STATUS )
+      CALL VVD ( AMPRMS(17),  0.9999635560607690D0,
+     :           1D-11, 'slMAPA', 'AMPRMS(17)', STATUS )
+      CALL VVD ( AMPRMS(18), -3.016886324169151D-5,
+     :           1D-11, 'slMAPA', 'AMPRMS(18)', STATUS )
+      CALL VVD ( AMPRMS(19),  3.709742180572510D-3,
+     :           1D-11, 'slMAPA', 'AMPRMS(19)', STATUS )
+      CALL VVD ( AMPRMS(20), -1.502613373498668D-6,
+     :           1D-11, 'slMAPA', 'AMPRMS(20)', STATUS )
+      CALL VVD ( AMPRMS(21),  0.9999931188816729D0,
+     :           1D-11, 'slMAPA', 'AMPRMS(21)', STATUS )
+
+      CALL slMAPQ ( 1.234D0, -0.987D0, -1.2D-5, -0.99D0,
+     :                 0.75D0, -23.4D0, AMPRMS, RA, DA )
+
+      CALL VVD ( RA, 1.223337584930993D0, 1D-11, 'slMAPQ',
+     :           'RA', STATUS )
+      CALL VVD ( DA, 0.5558838650379129D0, 1D-11, 'slMAPQ',
+     :           'DA', STATUS )
+
+      CALL slMAPZ ( 6.012D0, 1.234D0, AMPRMS, RA, DA )
+
+      CALL VVD ( RA, 6.006091119756597D0, 1D-11, 'slMAPZ',
+     :           'RA', STATUS )
+      CALL VVD ( DA, 1.23045846622498D0, 1D-11, 'slMAPZ',
+     :           'DA', STATUS )
+
+      END
+
+      SUBROUTINE T_MOON ( STATUS )
+*+
+*  - - - - - - -
+*   T _ M O O N
+*  - - - - - - -
+*
+*  Test slMOON and slDMON routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slMOON, slDMON, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      REAL PV(6)
+
+      CALL slMOON ( 1999, 365, 0.9E0, PV )
+
+      CALL VVD ( DBLE( PV(1) ), -2.155729505970773D-3, 1D-6,
+     :           'slMOON', '(1)', STATUS )
+      CALL VVD ( DBLE( PV(2) ), -1.538107758633427D-3, 1D-6,
+     :           'slMOON', '(2)', STATUS )
+      CALL VVD ( DBLE( PV(3) ), -4.003940552689305D-4, 1D-6 ,
+     :           'slMOON', '(3)', STATUS )
+      CALL VVD ( DBLE( PV(4) ),  3.629209419071314D-9, 1D-12,
+     :           'slMOON', '(4)', STATUS )
+      CALL VVD ( DBLE( PV(5) ), -4.989667166259157D-9, 1D-12,
+     :           'slMOON', '(5)', STATUS )
+      CALL VVD ( DBLE( PV(6) ), -2.160752457288307D-9, 1D-12,
+     :           'slMOON', '(6)', STATUS )
+
+      END
+
+      SUBROUTINE T_NUT ( STATUS )
+*+
+*  - - - - - -
+*   T _ N U T
+*  - - - - - -
+*
+*  Test slNUT, slNUTC, slNUTC80 routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slNUT, slNUTC, VVD.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION RMATN(3,3), DPSI, DEPS, EPS0
+
+      CALL slNUT ( 46012.34D0, RMATN )
+
+      CALL VVD ( RMATN(1,1),  9.999999969492166D-1, 1D-12,
+     :           'slNUT', '(1,1)', STATUS )
+      CALL VVD ( RMATN(1,2),  7.166577986249302D-5, 1D-12,
+     :           'slNUT', '(1,2)', STATUS )
+      CALL VVD ( RMATN(1,3),  3.107382973077677D-5, 1D-12,
+     :           'slNUT', '(1,3)', STATUS )
+      CALL VVD ( RMATN(2,1), -7.166503970900504D-5, 1D-12,
+     :           'slNUT', '(2,1)', STATUS )
+      CALL VVD ( RMATN(2,2),  9.999999971483732D-1, 1D-12,
+     :           'slNUT', '(2,2)', STATUS )
+      CALL VVD ( RMATN(2,3), -2.381965032461830D-5, 1D-12,
+     :           'slNUT', '(2,3)', STATUS )
+      CALL VVD ( RMATN(3,1), -3.107553669598237D-5, 1D-12,
+     :           'slNUT', '(3,1)', STATUS )
+      CALL VVD ( RMATN(3,2),  2.381742334472628D-5, 1D-12,
+     :           'slNUT', '(3,2)', STATUS )
+      CALL VVD ( RMATN(3,3),  9.999999992335206818D-1, 1D-12,
+     :           'slNUT', '(3,3)', STATUS )
+
+      CALL slNUTC ( 50123.4D0, DPSI, DEPS, EPS0 )
+
+      CALL VVD ( DPSI, 3.523550954747999709D-5, 1D-17, 'slNUTC',
+     :           'DPSI', STATUS )
+      CALL VVD ( DEPS, -4.143371566683342D-5, 1D-17, 'slNUTC',
+     :           'DEPS', STATUS )
+      CALL VVD ( EPS0, 0.4091014592901651D0, 1D-12, 'slNUTC',
+     :           'EPS0', STATUS )
+
+      CALL slNUTC80 ( 50123.4D0, DPSI, DEPS, EPS0 )
+
+      CALL VVD ( DPSI, 3.537714281665945321D-5, 1D-17, 'slNUTC80',
+     :           'DPSI', STATUS )
+      CALL VVD ( DEPS, -4.140590085987148317D-5, 1D-17, 'slNUTC80',
+     :           'DEPS', STATUS )
+      CALL VVD ( EPS0, 0.4091016349007751D0, 1D-12, 'slNUTC80',
+     :           'EPS0', STATUS )
+
+      END
+
+      SUBROUTINE T_OBS ( STATUS )
+*+
+*  - - - - - -
+*   T _ O B S
+*  - - - - - -
+*
+*  Test slOBS routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slOBS, err, VVD.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER N
+      DOUBLE PRECISION W, P, H
+      CHARACTER*10 C
+      CHARACTER*40 NAME
+
+      N = 0
+      C = 'MMT'
+      CALL slOBS ( N, C, NAME, W, P, H )
+      CALL VCS ( C, 'MMT', 'slOBS', '1/C', STATUS )
+      CALL VCS ( NAME, 'MMT 6.5m, Mt Hopkins', 'slOBS', '1/NAME',
+     :           STATUS )
+      CALL VVD ( W, 1.935300584055477D0, 1D-8, 'slOBS',
+     :           '1/W', STATUS )
+      CALL VVD ( P, 0.5530735081550342238D0, 1D-10, 'slOBS',
+     :           '1/P', STATUS )
+      CALL VVD ( H, 2608D0, 1D-10, 'slOBS',
+     :           '1/H', STATUS )
+
+      N = 61
+      CALL slOBS ( N, C, NAME, W, P, H )
+      CALL VCS ( C, 'KECK1', 'slOBS', '2/C', STATUS )
+      CALL VCS ( NAME, 'Keck 10m Telescope #1', 'slOBS',
+     :           '2/NAME', STATUS )
+      CALL VVD ( W, 2.713545757918895D0, 1D-8, 'slOBS',
+     :           '2/W', STATUS )
+      CALL VVD ( P, 0.3460280563536619D0, 1D-8, 'slOBS',
+     :           '2/P', STATUS )
+      CALL VVD ( H, 4160D0, 1D-10, 'slOBS',
+     :           '2/H', STATUS )
+
+      N = 83
+      CALL slOBS ( N, C, NAME, W, P, H )
+      CALL VCS ( C, 'MAGELLAN2', 'slOBS', '3/C', STATUS )
+      CALL VCS ( NAME, 'Magellan 2, 6.5m, Las Campanas',
+     :           'slOBS', '3/NAME', STATUS )
+      CALL VVD ( W, 1.233819305534497D0, 1D-8, 'slOBS',
+     :           '3/W', STATUS )
+      CALL VVD ( P, -0.506389344359954D0, 1D-8, 'slOBS',
+     :           '3/P', STATUS )
+      CALL VVD ( H, 2408D0, 1D-10, 'slOBS',
+     :           '3/H', STATUS )
+
+      N = 84
+      CALL slOBS ( N, C, NAME, W, P, H )
+      CALL VCS ( NAME, '?', 'slOBS', '4/NAME', STATUS )
+
+      END
+
+      SUBROUTINE T_PA ( STATUS )
+*+
+*  - - - - -
+*   T _ P A
+*  - - - - -
+*
+*  Test slPA routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slPA, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slPA
+
+
+      CALL VVD ( slPA ( -1.567D0, 1.5123D0, 0.987D0 ),
+     :           -1.486288540423851D0, 1D-12, 'slPA', ' ', STATUS )
+      CALL VVD ( slPA ( 0D0, 0.789D0, 0.789D0 ),
+     :           0D0, 0D0, 'slPA', 'zenith', STATUS )
+
+      END
+
+      SUBROUTINE T_PCD ( STATUS )
+*+
+*  - - - - - -
+*   T _ P C D
+*  - - - - - -
+*
+*  Test slPCD, slUPCD routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slPCD, VVD, slUPCD.
+*
+*  Last revision:   4 September 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION DISCO, X, Y
+
+      DISCO = 178.585D0
+      X = 0.0123D0
+      Y = -0.00987D0
+
+      CALL slPCD ( DISCO, X, Y )
+      CALL VVD ( X, 0.01284630845735895D0, 1D-14, 'slPCD',
+     :           'X', STATUS )
+      CALL VVD ( Y, -0.01030837922553926D0, 1D-14, 'slPCD',
+     :           'Y', STATUS )
+
+      CALL slUPCD ( DISCO, X, Y )
+      CALL VVD ( X, 0.0123D0, 1D-14, 'slUPCD',
+     :           'X', STATUS )
+      CALL VVD ( Y, -0.00987D0, 1D-14, 'slUPCD',
+     :           'Y', STATUS )
+
+      END
+
+      SUBROUTINE T_PDA2H ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ P D A H
+*  - - - - - - - -
+*
+*  Test slPDAH routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slPDAH, VVD.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J1, J2
+      DOUBLE PRECISION H1, H2
+
+      CALL slPDAH ( -0.51D0, -1.31D0, 3.1D0, H1, J1, H2, J2 )
+      CALL VVD ( H1, -0.1161784556585304927D0, 1D-14, 'slPDAH',
+     :           'H1', STATUS )
+      CALL VIV ( J1, 0, 'slPDAH', 'J1', STATUS )
+      CALL VVD ( H2, -2.984787179226459D0, 1D-13, 'slPDAH',
+     :           'H2', STATUS )
+      CALL VIV ( J2, 0, 'slPDAH', 'J2', STATUS )
+
+      END
+
+      SUBROUTINE T_PDQ2H ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ P D Q H
+*  - - - - - - - -
+*
+*  Test slPDQH routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slPDQH, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J1, J2
+      DOUBLE PRECISION H1, H2
+
+      CALL slPDQH ( 0.9D0, 0.2D0, 0.1D0, H1, J1, H2, J2 )
+      CALL VVD ( H1, 0.1042809894435257D0, 1D-14, 'slPDQH',
+     :           'H1', STATUS )
+      CALL VIV ( J1, 0, 'slPDQH', 'J1', STATUS )
+      CALL VVD ( H2, 2.997450098818439D0, 1D-13, 'slPDQH',
+     :           'H2', STATUS )
+      CALL VIV ( J2, 0, 'slPDQH', 'J2', STATUS )
+
+      END
+
+      SUBROUTINE T_PERCOM ( STATUS )
+*+
+*  - - - - - - - - -
+*   T _ P E R C O M
+*  - - - - - - - - -
+*
+*  Test slCMBN, slPERM routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slCMBN, VIV, slPERM.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER LIST(3), I, J, ISTATE(4), IORDER(4)
+
+      LIST(1) = 0
+
+      DO I = 1, 11
+         CALL slCMBN ( 3, 5, LIST, J )
+      END DO
+
+      CALL VIV ( J, 1, 'slCMBN', 'J', STATUS )
+      CALL VIV ( LIST(1), 1, 'slCMBN', 'LIST(1)', STATUS )
+      CALL VIV ( LIST(2), 2, 'slCMBN', 'LIST(2)', STATUS )
+      CALL VIV ( LIST(3), 3, 'slCMBN', 'LIST(3)', STATUS )
+
+      ISTATE(1) = -1
+
+      DO I = 1, 25
+         CALL slPERM ( 4, ISTATE, IORDER, J )
+      END DO
+
+      CALL VIV ( J, 1, 'slPERM', 'J', STATUS )
+      CALL VIV ( IORDER(1), 4, 'slPERM', 'IORDER(1)', STATUS )
+      CALL VIV ( IORDER(2), 3, 'slPERM', 'IORDER(2)', STATUS )
+      CALL VIV ( IORDER(3), 2, 'slPERM', 'IORDER(3)', STATUS )
+      CALL VIV ( IORDER(4), 1, 'slPERM', 'IORDER(4)', STATUS )
+
+      END
+
+      SUBROUTINE T_PLANET ( STATUS )
+*+
+*  - - - - - - - - -
+*   T _ P L N T
+*  - - - - - - - - -
+*
+*  Test slELUE, slPRTL, slPRTE, slPLNE, slPLNT,
+*  slPLTE, slPLTU, slPVEL, slPVUE, slRDPL, slUEEL
+*  and slUEPV routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slELUE, slPRTL, slPRTE, slPLNE, slPLNT,
+*           slPLTE, slPLTU, slPVEL, slPVUE, slRDPL,
+*           slUEEL, slUEPV, VIV, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J, JFORM
+      DOUBLE PRECISION U(13), PV(6), RA, DEC, R, DIAM, EPOCH, ORBINC,
+     :    ANODE, PERIH, AORQ, E, AORL, DM
+
+
+      CALL slELUE ( 50000D0, 1, 49000D0, 0.1D0, 2D0, 0.2D0,
+     :                 3D0, 0.05D0, 3D0, 0.003312D0, U, J )
+      CALL VVD ( U(1), 1.000878908362435284D0, 1D-12, 'slELUE',
+     :           'U(1)', STATUS )
+      CALL VVD ( U(2), -0.3336263027874777288D0, 1D-12, 'slELUE',
+     :           'U(2)', STATUS )
+      CALL VVD ( U(3), 50000D0, 1D-12, 'slELUE',
+     :           'U(3)', STATUS )
+      CALL VVD ( U(4), 2.840425801310305210D0, 1D-12, 'slELUE',
+     :           'U(4)', STATUS )
+      CALL VVD ( U(5), 0.1264380368035014224D0, 1D-12, 'slELUE',
+     :           'U(5)', STATUS )
+      CALL VVD ( U(6), -0.2287711835229143197D0, 1D-12, 'slELUE',
+     :           'U(6)', STATUS )
+      CALL VVD ( U(7), -0.01301062595106185195D0, 1D-12, 'slELUE',
+     :           'U(7)', STATUS )
+      CALL VVD ( U(8), 0.5657102158104651697D0, 1D-12, 'slELUE',
+     :           'U(8)', STATUS )
+      CALL VVD ( U(9), 0.2189745287281794885D0, 1D-12, 'slELUE',
+     :           'U(9)', STATUS )
+      CALL VVD ( U(10), 2.852427310959998500D0, 1D-12, 'slELUE',
+     :           'U(10)', STATUS )
+      CALL VVD ( U(11), -0.01552349065435120900D0, 1D-12, 'slELUE',
+     :           'U(11)', STATUS )
+      CALL VVD ( U(12), 50000D0, 1D-12, 'slELUE',
+     :           'U(12)', STATUS )
+      CALL VVD ( U(13), 0D0, 1D-12, 'slELUE',
+     :           'U(13)', STATUS )
+      CALL VIV ( J, 0, 'slELUE', 'J', STATUS )
+
+      CALL slPRTL ( 2, 43000D0, 43200D0, 43000D0,
+     :                  0.2D0, 3D0, 4D0, 5D0, 0.02D0, 6D0,
+     :                  EPOCH, ORBINC, ANODE, PERIH, AORQ, E, AORL, J )
+      CALL VVD ( EPOCH, 43200D0, 1D-10, 'slPRTL',
+     :           'EPOCH', STATUS )
+      CALL VVD ( ORBINC, 0.1995661466545422381D0, 1D-7, 'slPRTL',
+     :           'ORBINC', STATUS )
+      CALL VVD ( ANODE, 2.998052737821591215D0, 1D-7, 'slPRTL',
+     :           'ANODE', STATUS )
+      CALL VVD ( PERIH, 4.009516448441143636D0, 1D-6, 'slPRTL',
+     :           'PERIH', STATUS )
+      CALL VVD ( AORQ, 5.014216294790922323D0, 1D-7, 'slPRTL',
+     :           'AORQ', STATUS )
+      CALL VVD ( E, 0.02281386258309823607D0, 1D-7, 'slPRTL',
+     :           'E', STATUS )
+      CALL VVD ( AORL, 0.01735248648779583748D0, 1D-6, 'slPRTL',
+     :           'AORL', STATUS )
+      CALL VIV ( J, 0, 'slPRTL', 'J', STATUS )
+
+      CALL slPRTE ( 50100D0, U, J )
+      CALL VVD ( U(1), 1.000000000000000D0, 1D-12, 'slPRTE',
+     :           'U(1)', STATUS )
+      CALL VVD ( U(2), -0.3329769417028020949D0, 1D-11, 'slPRTE',
+     :           'U(2)', STATUS )
+      CALL VVD ( U(3), 50100D0, 1D-12, 'slPRTE',
+     :           'U(3)', STATUS )
+      CALL VVD ( U(4), 2.638884303608524597D0, 1D-11, 'slPRTE',
+     :           'U(4)', STATUS )
+      CALL VVD ( U(5), 1.070994304747824305D0, 1D-11, 'slPRTE',
+     :           'U(5)', STATUS )
+      CALL VVD ( U(6), 0.1544112080167568589D0, 1D-11, 'slPRTE',
+     :           'U(6)', STATUS )
+      CALL VVD ( U(7), -0.2188240619161439344D0, 1D-11, 'slPRTE',
+     :           'U(7)', STATUS )
+      CALL VVD ( U(8), 0.5207557453451906385D0, 1D-11, 'slPRTE',
+     :           'U(8)', STATUS )
+      CALL VVD ( U(9), 0.2217782439275216936D0, 1D-11, 'slPRTE',
+     :           'U(9)', STATUS )
+      CALL VVD ( U(10), 2.852118859689216658D0, 1D-11, 'slPRTE',
+     :           'U(10)', STATUS )
+      CALL VVD ( U(11), 0.01452010174371893229D0, 1D-11, 'slPRTE',
+     :           'U(11)', STATUS )
+      CALL VVD ( U(12), 50100D0, 1D-12, 'slPRTE',
+     :           'U(12)', STATUS )
+      CALL VVD ( U(13), 0D0, 1D-12, 'slPRTE',
+     :           'U(13)', STATUS )
+      CALL VIV ( J, 0, 'slPRTE', 'J', STATUS )
+
+      CALL slPLNE ( 50600D0, 2, 50500D0, 0.1D0, 3D0, 5D0,
+     :                  2D0, 0.3D0, 4D0, 0D0, PV, J )
+      CALL VVD ( PV(1), 1.947628959288897677D0, 1D-12, 'slPLNE',
+     :           'PV(1)', STATUS )
+      CALL VVD ( PV(2), -1.013736058752235271D0, 1D-12, 'slPLNE',
+     :           'PV(2)', STATUS )
+      CALL VVD ( PV(3), -0.3536409947732733647D0, 1D-12, 'slPLNE',
+     :           'PV(3)', STATUS )
+      CALL VVD ( PV(4), 2.742247411571786194D-8, 1D-19, 'slPLNE',
+     :           'PV(4)', STATUS )
+      CALL VVD ( PV(5), 1.170467244079075911D-7, 1D-19, 'slPLNE',
+     :           'PV(5)', STATUS )
+      CALL VVD ( PV(6), 3.709878268217564005D-8, 1D-19, 'slPLNE',
+     :           'PV(6)', STATUS )
+      CALL VIV ( J, 0, 'slPLNE', 'J', STATUS )
+
+      CALL slPLNT ( 1D6, 0, PV, J )
+      CALL VVD ( PV(1), 0D0, 0D0, 'slPLNT',
+     :           'PV(1) 1', STATUS )
+      CALL VVD ( PV(2), 0D0, 0D0, 'slPLNT',
+     :           'PV(2) 1', STATUS )
+      CALL VVD ( PV(3), 0D0, 0D0, 'slPLNT',
+     :           'PV(3) 1', STATUS )
+      CALL VVD ( PV(4), 0D0, 0D0, 'slPLNT',
+     :           'PV(4) 1', STATUS )
+      CALL VVD ( PV(5), 0D0, 0D0, 'slPLNT',
+     :           'PV(5) 1', STATUS )
+      CALL VVD ( PV(6), 0D0, 0D0, 'slPLNT',
+     :           'PV(6) 1', STATUS )
+      CALL VIV ( J, -1, 'slPLNT', 'J 1', STATUS )
+
+      CALL slPLNT ( 1D6, 10, PV, J )
+      CALL VIV ( J, -1, 'slPLNT', 'J 2', STATUS )
+
+      CALL slPLNT ( -320000D0, 3, PV, J )
+      CALL VVD ( PV(1), 0.9308038666827242603D0, 1D-11, 'slPLNT',
+     :           'PV(1) 3', STATUS )
+      CALL VVD ( PV(2), 0.3258319040252137618D0, 1D-11, 'slPLNT',
+     :           'PV(2) 3', STATUS )
+      CALL VVD ( PV(3), 0.1422794544477122021D0, 1D-11, 'slPLNT',
+     :           'PV(3) 3', STATUS )
+      CALL VVD ( PV(4), -7.441503423889371696D-8, 1D-17, 'slPLNT',
+     :           'PV(4) 3', STATUS )
+      CALL VVD ( PV(5), 1.699734557528650689D-7, 1D-17, 'slPLNT',
+     :           'PV(5) 3', STATUS )
+      CALL VVD ( PV(6), 7.415505123001430864D-8, 1D-17, 'slPLNT',
+     :           'PV(6) 3', STATUS )
+      CALL VIV ( J, 1, 'slPLNT', 'J 3', STATUS )
+
+      CALL slPLNT ( 43999.9D0, 1, PV, J )
+      CALL VVD ( PV(1), 0.2945293959257422246D0, 1D-11, 'slPLNT',
+     :           'PV(1) 4', STATUS )
+      CALL VVD ( PV(2), -0.2452204176601052181D0, 1D-11, 'slPLNT',
+     :           'PV(2) 4', STATUS )
+      CALL VVD ( PV(3), -0.1615427700571978643D0, 1D-11, 'slPLNT',
+     :           'PV(3) 4', STATUS )
+      CALL VVD ( PV(4), 1.636421147459047057D-7, 1D-18, 'slPLNT',
+     :           'PV(4) 4', STATUS )
+      CALL VVD ( PV(5), 2.252949422574889753D-7, 1D-18, 'slPLNT',
+     :           'PV(5) 4', STATUS )
+      CALL VVD ( PV(6), 1.033542799062371839D-7, 1D-18, 'slPLNT',
+     :           'PV(6) 4', STATUS )
+      CALL VIV ( J, 0, 'slPLNT', 'J 4', STATUS )
+
+      CALL slPLTE ( 50600D0, -1.23D0, 0.456D0, 2, 50500D0,
+     :                  0.1D0, 3D0, 5D0, 2D0, 0.3D0, 4D0,
+     :                  0D0, RA, DEC, R, J )
+      CALL VVD ( RA, 6.222958101333794007D0, 1D-10, 'slPLTE',
+     :           'RA', STATUS )
+      CALL VVD ( DEC, 0.01142220305739771601D0, 1D-10, 'slPLTE',
+     :           'DEC', STATUS )
+      CALL VVD ( R, 2.288902494080167624D0, 1D-8, 'slPLTE',
+     :           'R', STATUS )
+      CALL VIV ( J, 0, 'slPLTE', 'J', STATUS )
+
+      U(1) = 1.0005D0
+      U(2) = -0.3D0
+      U(3) = 55000D0
+      U(4) = 2.8D0
+      U(5) = 0.1D0
+      U(6) = -0.2D0
+      U(7) = -0.01D0
+      U(8) = 0.5D0
+      U(9) = 0.22D0
+      U(10) = 2.8D0
+      U(11) = -0.015D0
+      U(12) = 55001D0
+      U(13) = 0D0
+
+      CALL slPLTU ( 55001D0, -1.23D0, 0.456D0, U, RA, DEC, R, J )
+      CALL VVD ( RA, 0.3531814831241686647D0, 1D-9, 'slPLTU',
+     :           'RA', STATUS )
+      CALL VVD ( DEC, 0.06940344580567131328D0, 1D-9, 'slPLTU',
+     :           'DEC', STATUS )
+      CALL VVD ( R, 3.031687170873274464D0, 1D-8, 'slPLTU',
+     :           'R', STATUS )
+      CALL VIV ( J, 0, 'slPLTU', 'J', STATUS )
+
+      PV(1) = 0.3D0
+      PV(2) = -0.2D0
+      PV(3) = 0.1D0
+      PV(4) = -0.9D-7
+      PV(5) = 0.8D-7
+      PV(6) = -0.7D-7
+      CALL slPVEL ( PV, 50000D0, 0.00006D0, 1,
+     :                 JFORM, EPOCH, ORBINC, ANODE, PERIH,
+     :                 AORQ, E, AORL, DM, J )
+      CALL VIV ( JFORM, 1, 'slPVEL', 'JFORM', STATUS )
+      CALL VVD ( EPOCH, 50000D0, 1D-10, 'slPVEL',
+     :           'EPOCH', STATUS )
+      CALL VVD ( ORBINC, 1.52099895268912D0, 1D-12, 'slPVEL',
+     :           'ORBINC', STATUS )
+      CALL VVD ( ANODE, 2.720503180538650D0, 1D-12, 'slPVEL',
+     :           'ANODE', STATUS )
+      CALL VVD ( PERIH, 2.194081512031836D0, 1D-12, 'slPVEL',
+     :           'PERIH', STATUS )
+      CALL VVD ( AORQ, 0.2059371035373771D0, 1D-12, 'slPVEL',
+     :           'AORQ', STATUS )
+      CALL VVD ( E, 0.9866822985810528D0, 1D-12, 'slPVEL',
+     :           'E', STATUS )
+      CALL VVD ( AORL, 0.2012758344836794D0, 1D-12, 'slPVEL',
+     :           'AORL', STATUS )
+      CALL VVD ( DM, 0.1840740507951820D0, 1D-12, 'slPVEL',
+     :           'DM', STATUS )
+      CALL VIV ( J, 0, 'slPVEL', 'J', STATUS )
+
+      CALL slPVUE ( PV, 50000D0, 0.00006D0, U, J )
+      CALL VVD ( U(1), 1.00006D0, 1D-12, 'slPVUE',
+     :           'U(1)', STATUS )
+      CALL VVD ( U(2), -4.856142884511782D0, 1D-12, 'slPVUE',
+     :           'U(2)', STATUS )
+      CALL VVD ( U(3), 50000D0, 1D-12, 'slPVUE',
+     :           'U(3)', STATUS )
+      CALL VVD ( U(4), 0.3D0, 1D-12, 'slPVUE',
+     :           'U(4)', STATUS )
+      CALL VVD ( U(5), -0.2D0, 1D-12, 'slPVUE',
+     :           'U(5)', STATUS )
+      CALL VVD ( U(6), 0.1D0, 1D-12, 'slPVUE',
+     :           'U(6)', STATUS )
+      CALL VVD ( U(7), -0.4520378601821727D0, 1D-12, 'slPVUE',
+     :           'U(7)', STATUS )
+      CALL VVD ( U(8), 0.4018114312730424D0, 1D-12, 'slPVUE',
+     :           'U(8)', STATUS )
+      CALL VVD ( U(9), -.3515850023639121D0, 1D-12, 'slPVUE',
+     :           'U(9)', STATUS )
+      CALL VVD ( U(10), 0.3741657386773941D0, 1D-12, 'slPVUE',
+     :           'U(10)', STATUS )
+      CALL VVD ( U(11), -0.2511321445456515D0, 1D-12, 'slPVUE',
+     :           'U(11)', STATUS )
+      CALL VVD ( U(12), 50000D0, 1D-12, 'slPVUE',
+     :           'U(12)', STATUS )
+      CALL VVD ( U(13), 0D0, 1D-12, 'slPVUE',
+     :           'U(13)', STATUS )
+      CALL VIV ( J, 0, 'slPVUE', 'J', STATUS )
+
+      CALL slRDPL ( 40999.9D0, 0, 0.1D0, -0.9D0, RA, DEC, DIAM )
+      CALL VVD ( RA, 5.772270359389275837D0, 1D-7, 'slRDPL',
+     :           'RA 0', STATUS )
+      CALL VVD ( DEC, -0.2089207338795416192D0, 1D-7, 'slRDPL',
+     :           'DEC 0', STATUS )
+      CALL VVD ( DIAM, 9.415338935229717875D-3, 1D-14, 'slRDPL',
+     :           'DIAM 0', STATUS )
+      CALL slRDPL ( 41999.9D0, 1, 1.1D0, -0.9D0, RA, DEC, DIAM )
+      CALL VVD ( RA, 3.866363420052936653D0, 1D-7, 'slRDPL',
+     :           'RA 1', STATUS )
+      CALL VVD ( DEC, -0.2594430577550113130D0, 1D-7, 'slRDPL',
+     :           'DEC 1', STATUS )
+      CALL VVD ( DIAM, 4.638468996795023071D-5, 1D-14, 'slRDPL',
+     :           'DIAM 1', STATUS )
+      CALL slRDPL ( 42999.9D0, 2, 2.1D0, 0.9D0, RA, DEC, DIAM )
+      CALL VVD ( RA, 2.695383203184077378D0, 1D-7, 'slRDPL',
+     :           'RA 2', STATUS )
+      CALL VVD ( DEC, 0.2124044506294805126D0, 1D-7, 'slRDPL',
+     :           'DEC 2', STATUS )
+      CALL VVD ( DIAM, 4.892222838681000389D-5, 1D-14, 'slRDPL',
+     :           'DIAM 2', STATUS )
+      CALL slRDPL ( 43999.9D0, 3, 3.1D0, 0.9D0, RA, DEC, DIAM )
+      CALL VVD ( RA, 2.908326678461540165D0, 1D-7, 'slRDPL',
+     :           'RA 3', STATUS )
+      CALL VVD ( DEC, 0.08729783126905579385D0, 1D-7, 'slRDPL',
+     :           'DEC 3', STATUS )
+      CALL VVD ( DIAM, 8.581305866034962476D-3, 1D-14, 'slRDPL',
+     :           'DIAM 3', STATUS )
+      CALL slRDPL ( 44999.9D0, 4, -0.1D0, 1.1D0, RA, DEC, DIAM )
+      CALL VVD ( RA, 3.429840787472851721D0, 1D-7, 'slRDPL',
+     :           'RA 4', STATUS )
+      CALL VVD ( DEC, -0.06979851055261161013D0, 1D-7, 'slRDPL',
+     :           'DEC 4', STATUS )
+      CALL VVD ( DIAM, 4.540536678439300199D-5, 1D-14, 'slRDPL',
+     :           'DIAM 4', STATUS )
+      CALL slRDPL ( 45999.9D0, 5, -1.1D0, 0.1D0, RA, DEC, DIAM )
+      CALL VVD ( RA, 4.864669466449422548D0, 1D-7, 'slRDPL',
+     :           'RA 5', STATUS )
+      CALL VVD ( DEC, -0.4077714497908953354D0, 1D-7, 'slRDPL',
+     :           'DEC 5', STATUS )
+      CALL VVD ( DIAM, 1.727945579027815576D-4, 1D-14, 'slRDPL',
+     :           'DIAM 5', STATUS )
+      CALL slRDPL ( 46999.9D0, 6, -2.1D0, -0.1D0, RA, DEC, DIAM )
+      CALL VVD ( RA, 4.432929829176388766D0, 1D-7, 'slRDPL',
+     :           'RA 6', STATUS )
+      CALL VVD ( DEC, -0.3682820877854730530D0, 1D-7, 'slRDPL',
+     :           'DEC 6', STATUS )
+      CALL VVD ( DIAM, 8.670829016099083311D-5, 1D-14, 'slRDPL',
+     :           'DIAM 6', STATUS )
+      CALL slRDPL ( 47999.9D0, 7, -3.1D0, -1.1D0, RA, DEC, DIAM )
+      CALL VVD ( RA, 4.894972492286818487D0, 1D-7, 'slRDPL',
+     :           'RA 7', STATUS )
+      CALL VVD ( DEC, -0.4084068901053653125D0, 1D-7, 'slRDPL',
+     :           'DEC 7', STATUS )
+      CALL VVD ( DIAM, 1.793916783975974163D-5, 1D-14, 'slRDPL',
+     :           'DIAM 7', STATUS )
+      CALL slRDPL ( 48999.9D0, 8, 0D0, 0D0, RA, DEC, DIAM )
+      CALL VVD ( RA, 5.066050284760144000D0, 1D-7, 'slRDPL',
+     :           'RA 8', STATUS )
+      CALL VVD ( DEC, -0.3744690779683850609D0, 1D-7, 'slRDPL',
+     :           'DEC 8', STATUS )
+      CALL VVD ( DIAM, 1.062210086082700563D-5, 1D-14, 'slRDPL',
+     :           'DIAM 8', STATUS )
+      CALL slRDPL ( 49999.9D0, 9, 0D0, 0D0, RA, DEC, DIAM )
+      CALL VVD ( RA, 4.179543143097200945D0, 1D-7, 'slRDPL',
+     :           'RA 9', STATUS )
+      CALL VVD ( DEC, -0.1258021632894033300D0, 1D-7, 'slRDPL',
+     :           'DEC 9', STATUS )
+      CALL VVD ( DIAM, 5.034057475664904352D-7, 1D-14, 'slRDPL',
+     :           'DIAM 9', STATUS )
+
+      CALL slUEEL ( U, 1, JFORM, EPOCH, ORBINC, ANODE, PERIH,
+     :                 AORQ, E, AORL, DM, J )
+      CALL VIV ( JFORM, 1, 'slUEEL', 'JFORM', STATUS )
+      CALL VVD ( EPOCH, 50000.00000000000D0, 1D-10, 'slPVEL',
+     :           'EPOCH', STATUS )
+      CALL VVD ( ORBINC, 1.520998952689120D0, 1D-12, 'slUEEL',
+     :           'ORBINC', STATUS )
+      CALL VVD ( ANODE, 2.720503180538650D0, 1D-12, 'slUEEL',
+     :           'ANODE', STATUS )
+      CALL VVD ( PERIH, 2.194081512031836D0, 1D-12, 'slUEEL',
+     :           'PERIH', STATUS )
+      CALL VVD ( AORQ, 0.2059371035373771D0, 1D-12, 'slUEEL',
+     :           'AORQ', STATUS )
+      CALL VVD ( E, 0.9866822985810528D0, 1D-12, 'slUEEL',
+     :           'E', STATUS )
+      CALL VVD ( AORL, 0.2012758344836794D0, 1D-12, 'slUEEL',
+     :           'AORL', STATUS )
+      CALL VIV ( J, 0, 'slUEEL', 'J', STATUS )
+
+      CALL slUEPV ( 50010D0, U, PV, J )
+      CALL VVD ( U(1), 1.00006D0, 1D-12, 'slUEPV',
+     :           'U(1)', STATUS )
+      CALL VVD ( U(2), -4.856142884511782111D0, 1D-12, 'slUEPV',
+     :           'U(2)', STATUS )
+      CALL VVD ( U(3), 50000D0, 1D-12, 'slUEPV',
+     :           'U(3)', STATUS )
+      CALL VVD ( U(4), 0.3D0, 1D-12, 'slUEPV',
+     :           'U(4)', STATUS )
+      CALL VVD ( U(5), -0.2D0, 1D-12, 'slUEPV',
+     :           'U(5)', STATUS )
+      CALL VVD ( U(6), 0.1D0, 1D-12, 'slUEPV',
+     :           'U(6)', STATUS )
+      CALL VVD ( U(7), -0.4520378601821727110D0, 1D-12, 'slUEPV',
+     :           'U(7)', STATUS )
+      CALL VVD ( U(8), 0.4018114312730424097D0, 1D-12, 'slUEPV',
+     :           'U(8)', STATUS )
+      CALL VVD ( U(9), -0.3515850023639121085D0, 1D-12, 'slUEPV',
+     :           'U(9)', STATUS )
+      CALL VVD ( U(10), 0.3741657386773941386D0, 1D-12, 'slUEPV',
+     :           'U(10)', STATUS )
+      CALL VVD ( U(11), -0.2511321445456515061D0, 1D-12, 'slUEPV',
+     :           'U(11)', STATUS )
+      CALL VVD ( U(12), 50010.00000000000D0, 1D-12, 'slUEPV',
+     :           'U(12)', STATUS )
+      CALL VVD ( U(13), 0.7194308220038886856D0, 1D-12, 'slUEPV',
+     :           'U(13)', STATUS )
+      CALL VVD ( PV(1), 0.07944764084631667011D0, 1D-12, 'slUEPV',
+     :           'PV(1)', STATUS )
+      CALL VVD ( PV(2), -0.04118141077419014775D0, 1D-12, 'slUEPV',
+     :           'PV(2)', STATUS )
+      CALL VVD ( PV(3), 0.002915180702063625400D0, 1D-12, 'slUEPV',
+     :           'PV(3)', STATUS )
+      CALL VVD ( PV(4), -0.6890132370721108608D-6, 1D-18,'slUEPV',
+     :           'PV(4)', STATUS )
+      CALL VVD ( PV(5), 0.4326690733487621457D-6, 1D-18, 'slUEPV',
+     :           'PV(5)', STATUS )
+      CALL VVD ( PV(6), -0.1763249096254134306D-6, 1D-18, 'slUEPV',
+     :           'PV(6)', STATUS )
+      CALL VIV ( J, 0, 'slUEPV', 'J', STATUS )
+
+      END
+
+      SUBROUTINE T_PM ( STATUS )
+*+
+*  - - - - -
+*   T _ P M
+*  - - - - -
+*
+*  Test slPM routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slPM, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION R1, D1
+
+      CALL slPM ( 5.43D0, -0.87D0, -0.33D-5, 0.77D-5, 0.7D0,
+     :              50.3D0*365.2422D0/365.25D0, 1899D0, 1943D0,
+     :              R1, D1 )
+      CALL VVD ( R1, 5.429855087793875D0, 1D-12, 'slPM',
+     :           'R', STATUS )
+      CALL VVD ( D1, -0.8696617307805072D0, 1D-12, 'slPM',
+     :           'D', STATUS )
+
+      END
+
+      SUBROUTINE T_POLMO ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ P L M O
+*  - - - - - - - -
+*
+*  Test slPLMO routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slPLMO, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION ELONG, PHI, DAZ
+
+      CALL slPLMO ( 0.7D0, -0.5D0, 1D-6, -2D-6, ELONG, PHI, DAZ )
+
+      CALL VVD ( ELONG,  0.7000004837322044D0, 1D-12, 'slPLMO',
+     :           'ELONG', STATUS )
+      CALL VVD ( PHI, -0.4999979467222241D0, 1D-12, 'slPLMO',
+     :           'PHI', STATUS )
+      CALL VVD ( DAZ,  1.008982781275728D-6, 1D-12, 'slPLMO',
+     :           'DAZ', STATUS )
+
+      END
+
+      SUBROUTINE T_PREBN ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ P R B N
+*  - - - - - - - -
+*
+*  Test slPRBN routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slPRBN, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION RMATP(3,3)
+
+      CALL slPRBN ( 1925D0, 1975D0, RMATP )
+
+      CALL VVD ( RMATP(1,1),  9.999257613786738D-1, 1D-12,
+     :           'slPRBN', '(1,1)', STATUS )
+      CALL VVD ( RMATP(1,2), -1.117444640880939D-2, 1D-12,
+     :           'slPRBN', '(1,2)', STATUS )
+      CALL VVD ( RMATP(1,3), -4.858341150654265D-3, 1D-12,
+     :           'slPRBN', '(1,3)', STATUS )
+      CALL VVD ( RMATP(2,1),  1.117444639746558D-2, 1D-12,
+     :           'slPRBN', '(2,1)', STATUS )
+      CALL VVD ( RMATP(2,2),  9.999375635561940D-1, 1D-12,
+     :           'slPRBN', '(2,2)', STATUS )
+      CALL VVD ( RMATP(2,3), -2.714797892626396D-5, 1D-12,
+     :           'slPRBN', '(2,3)', STATUS )
+      CALL VVD ( RMATP(3,1),  4.858341176745641D-3, 1D-12,
+     :           'slPRBN', '(3,1)', STATUS )
+      CALL VVD ( RMATP(3,2), -2.714330927085065D-5, 1D-12,
+     :           'slPRBN', '(3,2)', STATUS )
+      CALL VVD ( RMATP(3,3),  9.999881978224798D-1, 1D-12,
+     :           'slPRBN', '(3,3)', STATUS )
+
+      END
+
+      SUBROUTINE T_PREC ( STATUS )
+*+
+*  - - - - - - -
+*   T _ P R E C
+*  - - - - - - -
+*
+*  Test slPREC and slPREL routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slPREC, slPREL, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION RMATP(3,3)
+
+      CALL slPREC ( 1925D0, 1975D0, RMATP )
+
+      CALL VVD ( RMATP(1,1),  9.999257249850045D-1, 1D-12,
+     :           'slPREC', '(1,1)', STATUS )
+      CALL VVD ( RMATP(1,2), -1.117719859160180D-2, 1D-12,
+     :           'slPREC', '(1,2)', STATUS )
+      CALL VVD ( RMATP(1,3), -4.859500474027002D-3, 1D-12,
+     :           'slPREC', '(1,3)', STATUS )
+      CALL VVD ( RMATP(2,1),  1.117719858025860D-2, 1D-12,
+     :           'slPREC', '(2,1)', STATUS )
+      CALL VVD ( RMATP(2,2),  9.999375327960091D-1, 1D-12,
+     :           'slPREC', '(2,2)', STATUS )
+      CALL VVD ( RMATP(2,3), -2.716114374174549D-5, 1D-12,
+     :           'slPREC', '(2,3)', STATUS )
+      CALL VVD ( RMATP(3,1),  4.859500500117173D-3, 1D-12,
+     :           'slPREC', '(3,1)', STATUS )
+      CALL VVD ( RMATP(3,2), -2.715647545167383D-5, 1D-12,
+     :           'slPREC', '(3,2)', STATUS )
+      CALL VVD ( RMATP(3,3),  9.999881921889954D-1, 1D-12,
+     :           'slPREC', '(3,3)', STATUS )
+
+      CALL slPREL ( 1925D0, 1975D0, RMATP )
+
+      CALL VVD ( RMATP(1,1),  9.999257331781050D-1, 1D-12,
+     :           'slPREC', '(1,1)', STATUS )
+      CALL VVD ( RMATP(1,2), -1.117658038434041D-2, 1D-12,
+     :           'slPREC', '(1,2)', STATUS )
+      CALL VVD ( RMATP(1,3), -4.859236477249598D-3, 1D-12,
+     :           'slPREC', '(1,3)', STATUS )
+      CALL VVD ( RMATP(2,1),  1.117658037299592D-2, 1D-12,
+     :           'slPREC', '(2,1)', STATUS )
+      CALL VVD ( RMATP(2,2),  9.999375397061558D-1, 1D-12,
+     :           'slPREC', '(2,2)', STATUS )
+      CALL VVD ( RMATP(2,3), -2.715816653174189D-5, 1D-12,
+     :           'slPREC', '(2,3)', STATUS )
+      CALL VVD ( RMATP(3,1),  4.859236503342703D-3, 1D-12,
+     :           'slPREC', '(3,1)', STATUS )
+      CALL VVD ( RMATP(3,2), -2.715349745834860D-5, 1D-12,
+     :           'slPREC', '(3,2)', STATUS )
+      CALL VVD ( RMATP(3,3),  9.999881934719490D-1, 1D-12,
+     :           'slPREC', '(3,3)', STATUS )
+
+      END
+
+      SUBROUTINE T_PRECES ( STATUS )
+*+
+*  - - - - - - - - -
+*   T _ P R C E
+*  - - - - - - - - -
+*
+*  Test slPRCE routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slPRCE, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION RA, DC
+
+      RA = 6.28D0
+      DC = -1.123D0
+      CALL slPRCE ( 'FK4', 1925D0, 1950D0, RA, DC )
+      CALL VVD ( RA,  0.002403604864728447D0, 1D-12, 'slPRCE',
+     :           'R', STATUS )
+      CALL VVD ( DC, -1.120570643322045D0, 1D-12, 'slPRCE',
+     :           'D', STATUS )
+
+      RA = 0.0123D0
+      DC = 1.0987D0
+      CALL slPRCE ( 'FK5', 2050D0, 1990D0, RA, DC )
+      CALL VVD ( RA, 6.282003602708382D0, 1D-12, 'slPRCE',
+     :           'R', STATUS )
+      CALL VVD ( DC, 1.092870326188383D0, 1D-12, 'slPRCE',
+     :           'D', STATUS )
+
+      END
+
+      SUBROUTINE T_PRENUT ( STATUS )
+*+
+*  - - - - - - - - -
+*   P R N U
+*  - - - - - - - - -
+*
+*  Test slPRNU routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slPRNU, VVD.
+*
+*  Last revision:   16 November 2001
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION RMATPN(3,3)
+
+      CALL slPRNU ( 1985D0, 50123.4567D0, RMATPN )
+
+      CALL VVD ( RMATPN(1,1),  9.999962358680738D-1, 1D-12,
+     :           'slPRNU', '(1,1)', STATUS )
+      CALL VVD ( RMATPN(1,2), -2.516417057665452D-3, 1D-12,
+     :           'slPRNU', '(1,2)', STATUS )
+      CALL VVD ( RMATPN(1,3), -1.093569785342370D-3, 1D-12,
+     :           'slPRNU', '(1,3)', STATUS )
+      CALL VVD ( RMATPN(2,1),  2.516462370370876D-3, 1D-12,
+     :           'slPRNU', '(2,1)', STATUS )
+      CALL VVD ( RMATPN(2,2),  9.999968329010883D-1, 1D-12,
+     :           'slPRNU', '(2,2)', STATUS )
+      CALL VVD ( RMATPN(2,3),  4.006159587358310D-5, 1D-12,
+     :           'slPRNU', '(2,3)', STATUS )
+      CALL VVD ( RMATPN(3,1),  1.093465510215479D-3, 1D-12,
+     :           'slPRNU', '(3,1)', STATUS )
+      CALL VVD ( RMATPN(3,2), -4.281337229063151D-5, 1D-12,
+     :           'slPRNU', '(3,2)', STATUS )
+      CALL VVD ( RMATPN(3,3),  9.999994012499173D-1, 1D-12,
+     :           'slPRNU', '(3,3)', STATUS )
+
+      END
+
+      SUBROUTINE T_PVOBS ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ P V O B
+*  - - - - - - - -
+*
+*  Test slPVOB routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slPVOB, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION PV(6)
+
+      CALL slPVOB ( 0.5123D0, 3001D0, -0.567D0, PV )
+
+      CALL VVD ( PV(1), 0.3138647803054939D-4, 1D-16, 'slPVOB',
+     :           '(1)', STATUS )
+      CALL VVD ( PV(2),-0.1998515596527082D-4, 1D-16, 'slPVOB',
+     :           '(2)', STATUS )
+      CALL VVD ( PV(3), 0.2078572043443275D-4, 1D-16, 'slPVOB',
+     :           '(3)', STATUS )
+      CALL VVD ( PV(4), 0.1457340726851264D-8, 1D-20, 'slPVOB',
+     :           '(4)', STATUS )
+      CALL VVD ( PV(5), 0.2288738340888011D-8, 1D-20, 'slPVOB',
+     :           '(5)', STATUS )
+      CALL VVD ( PV(6), 0D0, 0D0, 'slPVOB',
+     :           '(6)', STATUS )
+
+      END
+
+      SUBROUTINE T_RANGE ( STATUS )
+*+
+*  - - - - - - - -
+*   T _ R A 1 P
+*  - - - - - - - -
+*
+*  Test slRA1P, slDA1P routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slRA1P, VVD, slDA1P.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      REAL slRA1P
+      DOUBLE PRECISION slDA1P
+
+
+      CALL VVD ( DBLE( slRA1P ( -4.0 ) ), 2.283185307179586D0,
+     :           1D-6, 'slRA1P', ' ', STATUS )
+      CALL VVD ( slDA1P ( -4D0 ), 2.283185307179586D0,
+     :           1D-12, 'slDA1P', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_RANORM ( STATUS )
+*+
+*  - - - - - - - - -
+*   T _ R A 2 P
+*  - - - - - - - - -
+*
+*  Test slRA2P, slDA2P routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slRA2P, VVD, slDA2P.
+*
+*  Last revision:   22 October 2006
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      REAL slRA2P
+      DOUBLE PRECISION slDA2P
+
+
+      CALL VVD ( DBLE( slRA2P ( -0.1E0 ) ), 6.183185307179587D0,
+     :           1D-5, 'slRA2P', '1', STATUS )
+      CALL VVD ( slDA2P ( -0.1D0 ), 6.183185307179587D0,
+     :           1D-12, 'slDA2P', '2', STATUS )
+
+      END
+
+      SUBROUTINE T_RCC ( STATUS )
+*+
+*  - - - - - -
+*   T _ R C C
+*  - - - - - -
+*
+*  Test slRCC routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slRCC, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slRCC
+
+
+      CALL VVD ( slRCC ( 48939.123D0, 0.76543D0, 5.0123D0,
+     :                     5525.242D0, 3190D0 ),
+     :           -1.280131613589158D-3, 1D-15, 'slRCC', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_REF ( STATUS )
+*+
+*  - - - - - -
+*   T _ R E F
+*  - - - - - -
+*
+*  Test slRFRO, slRFCO, slATMD, slREFV, slREFZ routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slRFRO, VVD, slRFCO, slRFCQ, slATMD,
+*           slDS2C, slREFV, slREFZ.
+*
+*  Last revision:   17 January 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION REF, REFA, REFB, REFA2, REFB2, VU(3), VR(3), ZR
+
+      CALL slRFRO ( 1.4D0, 3456.7D0, 280D0, 678.9D0, 0.9D0, 0.55D0,
+     :                 -0.3D0, 0.006D0, 1D-9, REF )
+      CALL VVD ( REF, 0.00106715763018568D0, 1D-12, 'slRFRO',
+     :           'O', STATUS )
+
+      CALL slRFRO ( 1.4D0, 3456.7D0, 280D0, 678.9D0, 0.9D0, 1000D0,
+     :                 -0.3D0, 0.006D0, 1D-9, REF )
+      CALL VVD ( REF, 0.001296416185295403D0, 1D-12, 'slRFRO',
+     :           'R', STATUS )
+
+      CALL slRFCQ ( 275.9D0, 709.3D0, 0.9D0, 101D0, REFA, REFB )
+      CALL VVD ( REFA, 2.324736903790639D-4, 1D-12, 'slRFCQ',
+     :           'A/R', STATUS )
+      CALL VVD ( REFB, -2.442884551059D-7, 1D-15, 'slRFCQ',
+     :           'B/R', STATUS )
+
+      CALL slRFCO ( 2111.1D0, 275.9D0, 709.3D0, 0.9D0, 101D0,
+     :                 -1.03D0, 0.0067D0, 1D-12, REFA, REFB )
+      CALL VVD ( REFA, 2.324673985217244D-4, 1D-12, 'slRFCO',
+     :           'A/R', STATUS )
+      CALL VVD ( REFB, -2.265040682496D-7, 1D-15, 'slRFCO',
+     :           'B/R', STATUS )
+
+      CALL slRFCQ ( 275.9D0, 709.3D0, 0.9D0, 0.77D0, REFA, REFB )
+      CALL VVD ( REFA, 2.007406521596588D-4, 1D-12, 'slRFCQ',
+     :           'A', STATUS )
+      CALL VVD ( REFB, -2.264210092590D-7, 1D-15, 'slRFCQ',
+     :           'B', STATUS )
+
+      CALL slRFCO ( 2111.1D0, 275.9D0, 709.3D0, 0.9D0, 0.77D0,
+     :                 -1.03D0, 0.0067D0, 1D-12, REFA, REFB )
+      CALL VVD ( REFA, 2.007202720084551D-4, 1D-12, 'slRFCO',
+     :           'A', STATUS )
+      CALL VVD ( REFB, -2.223037748876D-7, 1D-15, 'slRFCO',
+     :           'B', STATUS )
+
+      CALL slATMD ( 275.9D0, 709.3D0, 0.9D0, 0.77D0,
+     :                  REFA, REFB, 0.5D0, REFA2, REFB2 )
+      CALL VVD ( REFA2, 2.034523658888048D-4, 1D-12, 'slATMD',
+     :           'A', STATUS )
+      CALL VVD ( REFB2, -2.250855362179D-7, 1D-15, 'slATMD',
+     :           'B', STATUS )
+
+      CALL slDS2C ( 0.345D0, 0.456D0, VU )
+      CALL slREFV ( VU, REFA, REFB, VR )
+      CALL VVD ( VR(1), 0.8447487047790478D0, 1D-12, 'slREFV',
+     :           'X1', STATUS )
+      CALL VVD ( VR(2), 0.3035794890562339D0, 1D-12, 'slREFV',
+     :           'Y1', STATUS )
+      CALL VVD ( VR(3), 0.4407256738589851D0, 1D-12, 'slREFV',
+     :           'Z1', STATUS )
+
+      CALL slDS2C ( 3.7D0, 0.03D0, VU )
+      CALL slREFV ( VU, REFA, REFB, VR )
+      CALL VVD ( VR(1), -0.8476187691681673D0, 1D-12, 'slREFV',
+     :           'X2', STATUS )
+      CALL VVD ( VR(2), -0.5295354802804889D0, 1D-12, 'slREFV',
+     :           'Y2', STATUS )
+      CALL VVD ( VR(3), 0.0322914582168426D0, 1D-12, 'slREFV',
+     :           'Z2', STATUS )
+
+      CALL slREFZ ( 0.567D0, REFA, REFB, ZR )
+      CALL VVD ( ZR, 0.566872285910534D0, 1D-12, 'slREFZ',
+     :           'hi el', STATUS )
+
+      CALL slREFZ ( 1.55D0, REFA, REFB, ZR )
+      CALL VVD ( ZR, 1.545697350690958D0, 1D-12, 'slREFZ',
+     :           'lo el', STATUS )
+
+      END
+
+      SUBROUTINE T_RV ( STATUS )
+*+
+*  - - - - -
+*   T _ R V
+*  - - - - -
+*
+*  Test slRVER, slRVGA, slRVLG, slRVLD, slRVLK routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called: VVD, slRVER, slRVGA, slRVLG, slRVLD, slRVLK.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      REAL slRVER, slRVGA, slRVLG, slRVLD, slRVLK
+
+
+      CALL VVD ( DBLE( slRVER ( -0.777E0, 5.67E0, -0.3E0,
+     :           3.19E0 ) ), -0.1948098355075913D0, 1D-6,
+     :           'slRVER', ' ', STATUS )
+      CALL VVD ( DBLE( slRVGA ( 1.11E0, -0.99E0 ) ),
+     :           158.9630759840254D0, 1D-3, 'slRVGA', ' ', STATUS )
+      CALL VVD ( DBLE( slRVLG ( 3.97E0, 1.09E0 ) ),
+     :           -197.818762175363D0, 1D-3, 'slRVLG', ' ', STATUS )
+      CALL VVD ( DBLE( slRVLD ( 6.01E0, 0.1E0 ) ),
+     :           -4.082811335150567D0, 1D-4, 'slRVLD', ' ', STATUS )
+      CALL VVD ( DBLE( slRVLK ( 6.01E0, 0.1E0 ) ),
+     :           -5.925180579830265D0, 1D-4, 'slRVLK', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_SEP ( STATUS )
+*+
+*  - - - - - - -
+*   T _ S E P
+*  - - - - - - -
+*
+*  Test slDSEP, slDSEPV, slSEP, slSEPV routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slDSEP, slSEP, VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER I
+      REAL slSEP, slSEPV
+      REAL R1(3), R2(3), AR1, BR1, AR2, BR2
+      DOUBLE PRECISION slDSEP, slDSEPV
+      DOUBLE PRECISION D1(3), D2(3), AD1, BD1, AD2, BD2
+
+
+      R1(1) = 1.0
+      R1(2) = 0.1
+      R1(3) = 0.2
+      R2(1) = -3.0
+      R2(2) = 1E-3
+      R2(3) = 0.2
+
+      DO I = 1, 3
+         D1(I) = DBLE( R1(I) )
+         D2(I) = DBLE( R2(I) )
+      END DO
+
+      CALL slDC2S ( D1, AD1, BD1 )
+      CALL slDC2S ( D2, AD2, BD2 )
+
+      AR1 = SNGL( AD1 )
+      BR1 = SNGL( BD1 )
+      AR2 = SNGL( AD2 )
+      BR2 = SNGL( BD2 )
+
+      CALL VVD ( slDSEP ( AD1, BD1, AD2, BD2 ),
+     :           2.8603919190246608D0, 1D-7, 'slDSEP', ' ', STATUS )
+      CALL VVD ( DBLE( slSEP ( AR1, BR1, AR2, BR2 ) ),
+     :           2.8603919190246608D0, 1D-4, 'slSEP', ' ', STATUS )
+      CALL VVD ( slDSEPV ( D1, D2 ),
+     :           2.8603919190246608D0, 1D-7, 'slDSEPV', ' ', STATUS )
+      CALL VVD ( DBLE( slSEPV ( R1, R2 ) ),
+     :           2.8603919190246608D0, 1D-4, 'slSEPV', ' ', STATUS )
+
+      END
+
+      SUBROUTINE T_SMAT ( STATUS )
+*+
+*  - - - - - - -
+*   T _ S M A T
+*  - - - - - - -
+*
+*  Test slSMAT routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slSMAT, VVD, VIV.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J, IW(3)
+      REAL A(3,3)
+      REAL V(3)
+      REAL D
+
+      DATA A/2.22E0,     1.6578E0,     1.380522E0,
+     :       1.6578E0,   1.380522E0,   1.22548578E0,
+     :       1.380522E0, 1.22548578E0, 1.1356276122E0/
+      DATA V/2.28625E0,  1.7128825E0,  1.429432225E0/
+
+
+      CALL slSMAT ( 3, A, V, D, J, IW )
+
+      CALL VVD ( DBLE( A(1,1) ), 18.02550629769198D0,
+     :           1D-2, 'slSMAT', 'A(0,0)', STATUS )
+      CALL VVD ( DBLE( A(1,2) ), -52.16386644917481D0,
+     :           1D-2, 'slSMAT', 'A(0,1)', STATUS )
+      CALL VVD ( DBLE( A(1,3) ), 34.37875949717994D0,
+     :           1D-2, 'slSMAT', 'A(0,2)', STATUS )
+      CALL VVD ( DBLE( A(2,1) ), -52.16386644917477D0,
+     :           1D-2, 'slSMAT', 'A(1,0)', STATUS )
+      CALL VVD ( DBLE( A(2,2) ), 168.1778099099869D0,
+     :           1D-1, 'slSMAT', 'A(1,1)', STATUS )
+      CALL VVD ( DBLE( A(2,3) ), -118.0722869694278D0,
+     :           1D-2, 'slSMAT', 'A(1,2)', STATUS )
+      CALL VVD ( DBLE( A(3,1) ), 34.37875949717988D0,
+     :           1D-2, 'slSMAT', 'A(2,0)', STATUS )
+      CALL VVD ( DBLE( A(3,2) ), -118.07228696942770D0,
+     :           1D-2, 'slSMAT', 'A(2,1)', STATUS )
+      CALL VVD ( DBLE( A(3,3) ), 86.50307003740468D0,
+     :           1D-2, 'slSMAT', 'A(2,2)', STATUS )
+      CALL VVD ( DBLE( V(1) ), 1.002346480763383D0,
+     :           1D-4, 'slSMAT', 'V(1)', STATUS )
+      CALL VVD ( DBLE( V(2) ), 0.0328559401697292D0,
+     :           1D-4, 'slSMAT', 'V(2)', STATUS )
+      CALL VVD ( DBLE( V(3) ), 0.004760688414898454D0,
+     :           1D-4, 'slSMAT', 'V(3)', STATUS )
+      CALL VVD ( DBLE( D ), 0.003658344147359863D0,
+     :           1D-4, 'slSMAT', 'D', STATUS )
+      CALL VIV ( J, 0, 'slSMAT', 'J', STATUS )
+
+      END
+
+      SUBROUTINE T_SUPGAL ( STATUS )
+*+
+*  - - - - - - - - -
+*   T _ S U G A
+*  - - - - - - - - -
+*
+*  Test slSUGA routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slSUGA, VVD.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION DL, DB
+
+      CALL slSUGA ( 6.1D0, -1.4D0, Dl, DB )
+
+      CALL VVD ( DL, 3.798775860769474D0, 1D-12, 'slSUGA',
+     :           'DL', STATUS )
+      CALL VVD ( DB, -0.1397070490669407D0, 1D-12, 'slSUGA',
+     :           'DB', STATUS )
+
+      END
+
+      SUBROUTINE T_SVD ( STATUS )
+*+
+*  - - - - - -
+*   T _ S V D
+*  - - - - - -
+*
+*  Test slSVD, slSVDS, slSVDC routines.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  slSVD, VVD, slSVDS, slSVDC.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER M, N
+      INTEGER I, J
+      INTEGER MP, NP, NC
+
+      PARAMETER (MP = 10)
+      PARAMETER (NP = 6)
+      PARAMETER (NC = 7)
+
+      DOUBLE PRECISION A(MP,NP), W(NP), V(NP,NP), WORK(NP),
+     :                  B(MP), X(NP), C(NC,NC)
+      DOUBLE PRECISION VAL
+
+      M = 5
+      N = 4
+
+      DO I = 1, M
+         VAL = DFLOAT( ( I ) ) / 2D0
+         B(I) = 23D0 - 3D0 * VAL - 11D0 * DSIN ( VAL ) +
+     :          13D0 * DCOS ( VAL )
+         A(I,1) = 1D0
+         A(I,2) = VAL
+         A(I,3) = DSIN ( VAL )
+         A(I,4) = DCOS ( VAL )
+      END DO
+
+      CALL slSVD ( M, N, MP, NP, A, W, V, WORK, J )
+
+*  Allow U and V to have reversed signs.
+      IF (A(1,1) .GT. 0D0) THEN
+         DO I = 1, M
+            DO J = 1, N
+               A(I,J) = - A(I,J)
+               V(I,J) = - V(I,J)
+            END DO
+         END DO
+      END IF
+
+      CALL VVD ( A(1,1), -0.21532492989299D0, 1D-12, 'slSVD',
+     :           'A(1,1)', STATUS )
+      CALL VVD ( A(1,2),  0.67675050651267D0, 1D-12, 'slSVD',
+     :           'A(1,2)', STATUS )
+      CALL VVD ( A(1,3), -0.37267876361644D0, 1D-12, 'slSVD',
+     :           'A(1,3)', STATUS )
+      CALL VVD ( A(1,4),  0.58330405917160D0, 1D-12, 'slSVD',
+     :           'A(1,4)', STATUS )
+      CALL VVD ( A(2,1), -0.33693420368121D0, 1D-12, 'slSVD',
+     :           'A(2,1)', STATUS )
+      CALL VVD ( A(2,2),  0.48011695963936D0, 1D-12, 'slSVD',
+     :           'A(2,2)', STATUS )
+      CALL VVD ( A(2,3),  0.62656568539705D0, 1D-12, 'slSVD',
+     :           'A(2,3)', STATUS )
+      CALL VVD ( A(2,4), -0.17479918328198D0, 1D-12, 'slSVD',
+     :           'A(2,4)', STATUS )
+      CALL VVD ( A(3,1), -0.44396825906047D0, 1D-12, 'slSVD',
+     :           'A(3,1)', STATUS )
+      CALL VVD ( A(3,2),  0.18255923809825D0, 1D-12, 'slSVD',
+     :           'A(3,2)', STATUS )
+      CALL VVD ( A(3,3),  0.02228154115994D0, 1D-12, 'slSVD',
+     :           'A(3,3)', STATUS )
+      CALL VVD ( A(3,4), -0.51743308030238D0, 1D-12, 'slSVD',
+     :           'A(3,4)', STATUS )
+      CALL VVD ( A(4,1), -0.53172583816951D0, 1D-12, 'slSVD',
+     :           'A(4,1)', STATUS )
+      CALL VVD ( A(4,2), -0.16537863535943D0, 1D-12, 'slSVD',
+     :           'A(4,2)', STATUS )
+      CALL VVD ( A(4,3), -0.61134201569990D0, 1D-12, 'slSVD',
+     :           'A(4,3)', STATUS )
+      CALL VVD ( A(4,4), -0.28871221824912D0, 1D-12, 'slSVD',
+     :           'A(4,4)', STATUS )
+      CALL VVD ( A(5,1), -0.60022523682867D0, 1D-12, 'slSVD',
+     :           'A(5,1)', STATUS )
+      CALL VVD ( A(5,2), -0.50081781972404D0, 1D-12, 'slSVD',
+     :           'A(5,2)', STATUS )
+      CALL VVD ( A(5,3),  0.30706750690326D0, 1D-12, 'slSVD',
+     :           'A(5,3)', STATUS )
+      CALL VVD ( A(5,4),  0.52736124480318D0, 1D-12, 'slSVD',
+     :           'A(5,4)', STATUS )
+
+      CALL VVD ( W(1), 4.57362714220621D0, 1D-12, 'slSVD',
+     :           'W(1)', STATUS )
+      CALL VVD ( W(2), 1.64056393111226D0, 1D-12, 'slSVD',
+     :           'W(2)', STATUS )
+      CALL VVD ( W(3), 0.03999179717447D0, 1D-12, 'slSVD',
+     :           'W(3)', STATUS )
+      CALL VVD ( W(4), 0.37267332634218D0, 1D-12, 'slSVD',
+     :           'W(4)', STATUS )
+
+      CALL VVD ( V(1,1), -0.46531525230679D0, 1D-12, 'slSVD',
+     :           'V(1,1)', STATUS )
+      CALL VVD ( V(1,2),  0.41036514115630D0, 1D-12, 'slSVD',
+     :           'V(1,2)', STATUS )
+      CALL VVD ( V(1,3), -0.70279526907678D0, 1D-12, 'slSVD',
+     :           'V(1,3)', STATUS )
+      CALL VVD ( V(1,4),  0.34808185338758D0, 1D-12, 'slSVD',
+     :           'V(1,4)', STATUS )
+      CALL VVD ( V(2,1), -0.80342444002914D0, 1D-12, 'slSVD',
+     :           'V(2,1)', STATUS )
+      CALL VVD ( V(2,2), -0.29896472833787D0, 1D-12, 'slSVD',
+     :           'V(2,2)', STATUS )
+      CALL VVD ( V(2,3),  0.46592932810178D0, 1D-12, 'slSVD',
+     :           'V(2,3)', STATUS )
+      CALL VVD ( V(2,4),  0.21917828721921D0, 1D-12, 'slSVD',
+     :           'V(2,4)', STATUS )
+      CALL VVD ( V(3,1), -0.36564497020801D0, 1D-12, 'slSVD',
+     :           'V(3,1)', STATUS )
+      CALL VVD ( V(3,2),  0.28066812941896D0, 1D-12, 'slSVD',
+     :           'V(3,2)', STATUS )
+      CALL VVD ( V(3,3), -0.03324480702665D0, 1D-12, 'slSVD',
+     :           'V(3,3)', STATUS )
+      CALL VVD ( V(3,4), -0.88680546891402D0, 1D-12, 'slSVD',
+     :           'V(3,4)', STATUS )
+      CALL VVD ( V(4,1),  0.06553350971918D0, 1D-12, 'slSVD',
+     :           'V(4,1)', STATUS )
+      CALL VVD ( V(4,2),  0.81452191085452D0, 1D-12, 'slSVD',
+     :           'V(4,2)', STATUS )
+      CALL VVD ( V(4,3),  0.53654771808636D0, 1D-12, 'slSVD',
+     :           'V(4,3)', STATUS )
+      CALL VVD ( V(4,4),  0.21065602782287D0, 1D-12, 'slSVD',
+     :           'V(4,4)', STATUS )
+
+      CALL slSVDS ( M, N, MP, NP, B, A, W, V, WORK, X )
+
+      CALL VVD ( X(1),  23D0, 1D-12, 'slSVDS', 'X(1)', STATUS )
+      CALL VVD ( X(2),  -3D0, 1D-12, 'slSVDS', 'X(2)', STATUS )
+      CALL VVD ( X(3), -11D0, 1D-12, 'slSVDS', 'X(3)', STATUS )
+      CALL VVD ( X(4),  13D0, 1D-12, 'slSVDS', 'X(4)', STATUS )
+
+      CALL slSVDC ( N, NP, NC, W, V, WORK, C )
+
+      CALL VVD ( C(1,1),  309.77269378273270D0, 1D-10,
+     :           'slSVDC', 'C(1,1)', STATUS )
+      CALL VVD ( C(1,2), -204.22043941662150D0, 1D-10,
+     :           'slSVDC', 'C(1,2)', STATUS )
+      CALL VVD ( C(1,3),   12.43704316907477D0, 1D-10,
+     :           'slSVDC', 'C(1,3)', STATUS )
+      CALL VVD ( C(1,4), -235.12299986206710D0, 1D-10,
+     :           'slSVDC', 'C(1,4)', STATUS )
+      CALL VVD ( C(2,1), -204.22043941662150D0, 1D-10,
+     :           'slSVDC', 'C(2,1)', STATUS )
+      CALL VVD ( C(2,2),  136.14695961108110D0, 1D-10,
+     :           'slSVDC', 'C(2,2)', STATUS )
+      CALL VVD ( C(2,3),  -11.10167446246327D0, 1D-10,
+     :           'slSVDC', 'C(2,3)', STATUS )
+      CALL VVD ( C(2,4),  156.54937371198730D0, 1D-10,
+     :           'slSVDC', 'C(2,4)', STATUS )
+      CALL VVD ( C(3,1),   12.43704316907477D0, 1D-10,
+     :           'slSVDC', 'C(3,1)', STATUS )
+      CALL VVD ( C(3,2),  -11.10167446246327D0, 1D-10,
+     :           'slSVDC', 'C(3,2)', STATUS )
+      CALL VVD ( C(3,3),    6.38909830090602D0, 1D-10,
+     :           'slSVDC', 'C(3,3)', STATUS )
+      CALL VVD ( C(3,4),  -12.41424302586736D0, 1D-10,
+     :           'slSVDC', 'C(3,4)', STATUS )
+      CALL VVD ( C(4,1), -235.12299986206710D0, 1D-10,
+     :           'slSVDC', 'C(4,1)', STATUS )
+      CALL VVD ( C(4,2),  156.54937371198730D0, 1D-10,
+     :           'slSVDC', 'C(4,2)', STATUS )
+      CALL VVD ( C(4,3),  -12.41424302586736D0, 1D-10,
+     :           'slSVDC', 'C(4,3)', STATUS )
+      CALL VVD ( C(4,4),  180.56719842359560D0, 1D-10,
+     :           'slSVDC', 'C(4,4)', STATUS )
+
+      END
+
+      SUBROUTINE T_TP ( STATUS )
+*+
+*  - - - - - -
+*   T _ T P
+*  - - - - - -
+*
+*  Test spherical tangent-planD-projection routines:
+*
+*       slS2TP      slDSTP     slDPSC
+*       slTP2S      slDTPS     slTPSC
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  all the above, plus VVD and VIV.
+*
+*  Last revision:   10 July 2000
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J
+      REAL R0, D0, R1, D1, X, Y, R2, D2, R01, D01, R02, D02
+      DOUBLE PRECISION DR0, DD0, DR1, DD1, DX, DY, DR2, DD2, DR01,
+     :                 DD01, DR02, DD02
+
+      R0 = 3.1E0
+      D0 = -0.9E0
+      R1 = R0 + 0.2E0
+      D1 = D0 - 0.1E0
+      CALL slS2TP ( R1, D1, R0, D0, X, Y, J )
+      CALL VVD ( DBLE( X ), 0.1086112301590404D0, 1D-6, 'slS2TP',
+     :           'X', STATUS )
+      CALL VVD ( DBLE( Y ), -0.1095506200711452D0, 1D-6, 'slS2TP',
+     :           'Y', STATUS )
+      CALL VIV ( J, 0, 'slS2TP', 'J', STATUS )
+      CALL slTP2S ( X, Y, R0, D0, R2, D2 )
+      CALL VVD ( DBLE( ( R2 - R1 ) ), 0D0, 1D-6, 'slTP2S',
+     :           'R', STATUS )
+      CALL VVD ( DBLE( ( D2 - D1 ) ), 0D0, 1D-6, 'slTP2S',
+     :           'D', STATUS )
+      CALL slTPSC ( X, Y, R2, D2, R01, D01, R02, D02, J )
+      CALL VVD ( DBLE( R01 ),  3.1D0, 1D-6, 'slTPSC',
+     :           'R1', STATUS )
+      CALL VVD ( DBLE( D01 ), -0.9D0, 1D-6, 'slTPSC',
+     :           'D1', STATUS )
+      CALL VVD ( DBLE( R02 ), 0.3584073464102072D0, 1D-6, 'slTPSC',
+     :           'R2', STATUS )
+      CALL VVD ( DBLE( D02 ), -2.023361658234722D0, 1D-6, 'slTPSC',
+     :           'D2', STATUS )
+      CALL VIV ( J, 1, 'slTPSC', 'N', STATUS )
+
+      DR0 = 3.1D0
+      DD0 = -0.9D0
+      DR1 = DR0 + 0.2D0
+      DD1 = DD0 - 0.1D0
+      CALL slDSTP ( DR1, DD1, DR0, DD0, DX, DY, J )
+      CALL VVD ( DX, 0.1086112301590404D0, 1D-12, 'slDSTP',
+     :           'X', STATUS )
+      CALL VVD ( DY, -0.1095506200711452D0, 1D-12, 'slDSTP',
+     :           'Y', STATUS )
+      CALL VIV ( J, 0, 'slDSTP', 'J', STATUS )
+      CALL slDTPS ( DX, DY, DR0, DD0, DR2, DD2 )
+      CALL VVD ( DR2 - DR1, 0D0, 1D-12, 'slDTPS', 'R', STATUS )
+      CALL VVD ( DD2 - DD1, 0D0, 1D-12, 'slDTPS', 'D', STATUS )
+      CALL slDPSC ( DX, DY, DR2, DD2, DR01, DD01, DR02, DD02, J )
+      CALL VVD ( DR01,  3.1D0, 1D-12, 'slDPSC', 'R1', STATUS )
+      CALL VVD ( DD01, -0.9D0, 1D-12, 'slDPSC', 'D1', STATUS )
+      CALL VVD ( DR02, 0.3584073464102072D0, 1D-12, 'slDPSC',
+     :           'R2', STATUS )
+      CALL VVD ( DD02, -2.023361658234722D0, 1D-12, 'slDPSC',
+     :           'D2', STATUS )
+      CALL VIV ( J, 1, 'slDPSC', 'N', STATUS )
+
+      END
+
+      SUBROUTINE T_TPV ( STATUS )
+*+
+*  - - - - - -
+*   T _ T P V
+*  - - - - - -
+*
+*  Test Cartesian tangent-planD-projection routines:
+*
+*       slTP2V      slV2TP      slTPVC
+*       slDTPV     slDVTP     slDPVC
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  all the above, plus VVD and VIV.
+*
+*  Last revision:   21 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER J
+      REAL RXI, RETA, RV(3), RV0(3), RTXI, RTETA, RTV(3),
+     :     RTV01(3), RTV02(3)
+      DOUBLE PRECISION XI, ETA, X, Y, Z, V(3), V0(3), TXI, TETA,
+     :                 TV(3), TV01(3), TV02(3)
+
+      XI = -0.1D0
+      ETA = 0.055D0
+      RXI = SNGL( XI )
+      RETA = SNGL( ETA )
+
+      X = -0.7D0
+      Y = -0.13D0
+      Z = DSQRT ( 1D0 - X * X - Y * Y )
+      RV(1) = SNGL( X )
+      RV(2) = SNGL( Y )
+      RV(3) = SNGL( Z )
+      V(1) = X
+      V(2) = Y
+      V(3) = Z
+
+      X = -0.72D0
+      Y = -0.16D0
+      Z = DSQRT ( 1D0 - X * X - Y * Y )
+      RV0(1) = SNGL( X )
+      RV0(2) = SNGL( Y )
+      RV0(3) = SNGL( Z )
+      V0(1) = X
+      V0(2) = Y
+      V0(3) = Z
+
+      CALL slTP2V ( RXI, RETA, RV0, RTV )
+      CALL VVD ( DBLE( RTV(1) ), -0.700887428128D0, 1D-6, 'slTP2V',
+     :           'V(1)', STATUS )
+      CALL VVD ( DBLE( RTV(2) ), -0.05397407D0, 1D-6, 'slTP2V',
+     :           'V(2)', STATUS )
+      CALL VVD ( DBLE( RTV(3) ),  0.711226836562D0, 1D-6, 'slTP2V',
+     :           'V(3)', STATUS )
+
+      CALL slDTPV ( XI, ETA, V0, TV )
+      CALL VVD ( TV(1), -0.7008874281280771D0, 1D-13, 'slDTPV',
+     :           'V(1)', STATUS )
+      CALL VVD ( TV(2), -0.05397406827952735D0, 1D-13, 'slDTPV',
+     :           'V(2)', STATUS )
+      CALL VVD ( TV(3), 0.7112268365615617D0, 1D-13, 'slDTPV',
+     :           'V(3)', STATUS )
+
+      CALL slV2TP ( RV, RV0, RTXI, RTETA, J)
+      CALL VVD ( DBLE( RTXI ), -0.02497229197D0, 1D-6, 'slV2TP',
+     :           'XI', STATUS )
+      CALL VVD ( DBLE( RTETA ), 0.03748140764D0, 1D-6, 'slV2TP',
+     :           'ETA', STATUS )
+      CALL VIV ( J, 0, 'slV2TP', 'J', STATUS )
+
+      CALL slDVTP ( V, V0, TXI, TETA, J )
+      CALL VVD ( TXI, -0.02497229197023852D0, 1D-13, 'slDVTP',
+     :           'XI', STATUS )
+      CALL VVD ( TETA, 0.03748140764224765D0, 1D-13, 'slDVTP',
+     :           'ETA', STATUS )
+      CALL VIV ( J, 0, 'slDVTP', 'J', STATUS )
+
+      CALL slTPVC ( RXI, RETA, RV, RTV01, RTV02, J )
+      CALL VVD ( DBLE( RTV01(1) ), -0.7074573732537283D0, 1D-6,
+     :           'slTPVC', 'V01(1)', STATUS )
+      CALL VVD ( DBLE( RTV01(2) ), -0.2372965765309941D0, 1D-6,
+     :           'slTPVC', 'V01(2)', STATUS )
+      CALL VVD ( DBLE( RTV01(3) ), 0.6657284730245545D0, 1D-6,
+     :           'slTPVC', 'V01(3)', STATUS )
+      CALL VVD ( DBLE( RTV02(1) ), -0.6680480104758149D0, 1D-6,
+     :           'slTPVC', 'V02(1)', STATUS )
+      CALL VVD ( DBLE( RTV02(2) ), -0.02915588494045333D0, 1D-6,
+     :           'slTPVC', 'V02(2)', STATUS )
+      CALL VVD ( DBLE( RTV02(3) ), 0.7435467638774610D0, 1D-6,
+     :           'slTPVC', 'V02(3)', STATUS )
+      CALL VIV ( J, 1, 'slTPVC', 'N', STATUS )
+
+      CALL slDPVC ( XI, ETA, V, TV01, TV02, J )
+      CALL VVD ( TV01(1), -0.7074573732537283D0, 1D-13, 'slDPVC',
+     :           'V01(1)', STATUS )
+      CALL VVD ( TV01(2), -0.2372965765309941D0, 1D-13, 'slDPVC',
+     :           'V01(2)', STATUS )
+      CALL VVD ( TV01(3), 0.6657284730245545D0, 1D-13, 'slDPVC',
+     :           'V01(3)', STATUS )
+      CALL VVD ( TV02(1), -0.6680480104758149D0, 1D-13, 'slDPVC',
+     :           'V02(1)', STATUS )
+      CALL VVD ( TV02(2), -0.02915588494045333D0, 1D-13, 'slDPVC',
+     :           'V02(2)', STATUS )
+      CALL VVD ( TV02(3), 0.7435467638774610D0, 1D-13, 'slDPVC',
+     :           'V02(3)', STATUS )
+      CALL VIV ( J, 1, 'slDPVC', 'N', STATUS )
+
+      END
+
+      SUBROUTINE T_VECMAT ( STATUS )
+*+
+*  - - - - - - - - -
+*   T _ V E C M A
+*  - - - - - - - - -
+*
+*  Test all the 3-vector and 3x3 matrix routines:
+*
+*          slAV2M     slDAVM
+*          slCC2S     slDC2S
+*          slCS2C     slDS2C
+*          slEULR    slDEUL
+*          slIMXV     slDIMV
+*          slM2AV     slDMAV
+*          slMXM      slDMXM
+*          slMXV      slDMXV
+*          slVDV      slDVDV
+*          slVN       slDVN
+*          slVXV      slDVXV
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called:  all the above, plus VVD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      INTEGER I
+      REAL slVDV
+      REAL AV(3), RM1(3,3), RM2(3,3), RM(3,3), V1(3), V2(3),
+     :   V3(3), V4(3), V5(3), VM, V6(3), V7(3)
+      DOUBLE PRECISION slDVDV
+      DOUBLE PRECISION DAV(3), DRM1(3,3), DRM2(3,3), DRM(3,3),
+     :                 DV1(3), DV2(3), DV3(3), DV4(3), DV5(3),
+     :                 DVM, DV6(3), DV7(3)
+
+
+*  Make a rotation matrix.
+      AV(1) = -0.123E0
+      AV(2) = 0.0987E0
+      AV(3) = 0.0654E0
+      CALL slAV2M ( AV, RM1 )
+      CALL VVD ( DBLE( RM1(1,1) ), 0.9930075842721269D0,
+     :           1D-6, 'slAV2M', '11', STATUS )
+      CALL VVD ( DBLE( RM1(1,2) ), 0.05902743090199868D0,
+     :           1D-6, 'slAV2M', '12', STATUS )
+      CALL VVD ( DBLE( RM1(1,3) ), -0.1022335560329612D0,
+     :           1D-6, 'slAV2M', '13', STATUS )
+      CALL VVD ( DBLE( RM1(2,1) ), -0.07113807138648245D0,
+     :           1D-6, 'slAV2M', '21', STATUS )
+      CALL VVD ( DBLE( RM1(2,2) ), 0.9903204657727545D0,
+     :           1D-6, 'slAV2M', '22', STATUS )
+      CALL VVD ( DBLE( RM1(2,3) ), -0.1191836812279541D0,
+     :           1D-6, 'slAV2M', '23', STATUS )
+      CALL VVD ( DBLE( RM1(3,1) ), 0.09420887631983825D0,
+     :           1D-6, 'slAV2M', '31', STATUS )
+      CALL VVD ( DBLE( RM1(3,2) ), 0.1256229973879967D0,
+     :           1D-6, 'slAV2M', '32', STATUS )
+      CALL VVD ( DBLE( RM1(3,3) ), 0.9875948309655174D0,
+     :           1D-6, 'slAV2M', '33', STATUS )
+
+*  Make another.
+      CALL slEULR ( 'YZY', 2.345E0, -0.333E0, 2.222E0, RM2 )
+      CALL VVD ( DBLE( RM2(1,1) ), -0.1681574770810878D0,
+     :           1D-6, 'slEULR', '11', STATUS )
+      CALL VVD ( DBLE( RM2(1,2) ), 0.1981362273264315D0,
+     :           1D-6, 'slEULR', '12', STATUS )
+      CALL VVD ( DBLE( RM2(1,3) ), 0.9656423242187410D0,
+     :           1D-6, 'slEULR', '13', STATUS )
+      CALL VVD ( DBLE( RM2(2,1) ), -0.2285369373983370D0,
+     :           1D-6, 'slEULR', '21', STATUS )
+      CALL VVD ( DBLE( RM2(2,2) ), 0.9450659587140423D0,
+     :           1D-6, 'slEULR', '22', STATUS )
+      CALL VVD ( DBLE( RM2(2,3) ), -0.2337117924378156D0,
+     :           1D-6, 'slEULR', '23', STATUS )
+      CALL VVD ( DBLE( RM2(3,1) ), -0.9589024617479674D0,
+     :           1D-6, 'slEULR', '31', STATUS )
+      CALL VVD ( DBLE( RM2(3,2) ), -0.2599853247796050D0,
+     :           1D-6, 'slEULR', '32', STATUS )
+      CALL VVD ( DBLE( RM2(3,3) ), -0.1136384607117296D0,
+     :           1D-6, 'slEULR', '33', STATUS )
+
+*  Combine them.
+      CALL slMXM ( RM2, RM1, RM )
+      CALL VVD ( DBLE( RM(1,1) ), -0.09010460088585805D0,
+     :           1D-6, 'slMXM', '11', STATUS )
+      CALL VVD ( DBLE( RM(1,2) ), 0.3075993402463796D0,
+     :           1D-6, 'slMXM', '12', STATUS )
+      CALL VVD ( DBLE( RM(1,3) ), 0.9472400998581048D0,
+     :           1D-6, 'slMXM', '13', STATUS )
+      CALL VVD ( DBLE( RM(2,1) ), -0.3161868071070688D0,
+     :           1D-6, 'slMXM', '21', STATUS )
+      CALL VVD ( DBLE( RM(2,2) ), 0.8930686362478707D0,
+     :           1D-6, 'slMXM', '22', STATUS )
+      CALL VVD ( DBLE( RM(2,3) ),-0.3200848543149236D0,
+     :           1D-6, 'slMXM', '23', STATUS )
+      CALL VVD ( DBLE( RM(3,1) ),-0.9444083141897035D0,
+     :           1D-6, 'slMXM', '31', STATUS )
+      CALL VVD ( DBLE( RM(3,2) ),-0.3283459407855694D0,
+     :           1D-6, 'slMXM', '32', STATUS )
+      CALL VVD ( DBLE( RM(3,3) ), 0.01678926022795169D0,
+     :           1D-6, 'slMXM', '33', STATUS )
+
+*  Create a vector.
+      CALL slCS2C ( 3.0123E0, -0.999E0, V1 )
+      CALL VVD ( DBLE( V1(1) ), -0.5366267667260525D0,
+     :           1D-6, 'slCS2C', 'X', STATUS )
+      CALL VVD ( DBLE( V1(2) ), 0.06977111097651444D0,
+     :           1D-6, 'slCS2C', 'Y', STATUS )
+      CALL VVD ( DBLE( V1(3) ), -0.8409302618566215D0,
+     :           1D-6, 'slCS2C', 'Z', STATUS )
+
+*  Rotate it using the two matrices sequentially.
+      CALL slMXV ( RM1, V1, V2 )
+      CALL slMXV ( RM2, V2, V3 )
+      CALL VVD ( DBLE( V3(1) ), -0.7267487768696160D0,
+     :           1D-6, 'slMXV', 'X', STATUS )
+      CALL VVD ( DBLE( V3(2) ), 0.5011537352639822D0,
+     :           1D-6, 'slMXV', 'Y', STATUS )
+      CALL VVD ( DBLE( V3(3) ), 0.4697671220397141D0,
+     :           1D-6, 'slMXV', 'Z', STATUS )
+
+*  Derotate it using the combined matrix.
+      CALL slIMXV ( RM, V3, V4 )
+      CALL VVD ( DBLE( V4(1) ), -0.5366267667260526D0,
+     :           1D-6, 'slIMXV', 'X', STATUS )
+      CALL VVD ( DBLE( V4(2) ), 0.06977111097651445D0,
+     :           1D-6, 'slIMXV', 'Y', STATUS )
+      CALL VVD ( DBLE( V4(3) ), -0.8409302618566215D0,
+     :           1D-6, 'slIMXV', 'Z', STATUS )
+
+*  Convert the combined matrix into an axial vector.
+      CALL slM2AV ( RM, V5 )
+      CALL VVD ( DBLE( V5(1) ), 0.006889040510209034D0,
+     :           1D-6, 'slM2AV', 'X', STATUS )
+      CALL VVD ( DBLE( V5(2) ), -1.577473205461961D0,
+     :           1D-6, 'slM2AV', 'Y', STATUS )
+      CALL VVD ( DBLE( V5(3) ), 0.5201843672856759D0,
+     :           1D-6, 'slM2AV', 'Z', STATUS )
+
+*  Multiply it by a scalar and then normalize.
+      DO I = 1, 3
+         V5(I) = V5(I) * 1000.0
+      END DO
+
+      CALL slVN ( V5, V6, VM )
+      CALL VVD ( DBLE( V6(1) ), 0.004147420704640065D0,
+     :           1D-6, 'slVN', 'X', STATUS )
+      CALL VVD ( DBLE( V6(2) ), -0.9496888606842218D0,
+     :           1D-6, 'slVN', 'Y', STATUS )
+      CALL VVD ( DBLE( V6(3) ), 0.3131674740355448D0,
+     :           1D-6, 'slVN', 'Z', STATUS )
+      CALL VVD ( DBLE( VM ), 1661.042127339937D0,
+     :           1D-3, 'slVN', 'M', STATUS )
+
+*  Dot product with the original vector.
+      CALL VVD ( DBLE( slVDV ( V6, V1 ) ),
+     :           -0.3318384698006295D0, 1D-6, 'slVN', ' ', STATUS )
+
+*  Cross product with the original vector.
+      CALL slVXV (V6, V1, V7 )
+      CALL VVD ( DBLE( V7(1) ), 0.7767720597123304D0,
+     :           1D-6, 'slVXV', 'X', STATUS )
+      CALL VVD ( DBLE( V7(2) ), -0.1645663574562769D0,
+     :           1D-6, 'slVXV', 'Y', STATUS )
+      CALL VVD ( DBLE( V7(3) ), -0.5093390925544726D0,
+     :           1D-6, 'slVXV', 'Z', STATUS )
+
+*  Same in double precision.
+
+      DAV(1) = -0.123D0
+      DAV(2) = 0.0987D0
+      DAV(3) = 0.0654D0
+      CALL slDAVM ( DAV, DRM1 )
+      CALL VVD ( DRM1(1,1), 0.9930075842721269D0, 1D-12,
+     :           'slDAVM', '11', STATUS )
+      CALL VVD ( DRM1(1,2), 0.05902743090199868D0, 1D-12,
+     :           'slDAVM', '12', STATUS )
+      CALL VVD ( DRM1(1,3), -0.1022335560329612D0, 1D-12,
+     :           'slDAVM', '13', STATUS )
+      CALL VVD ( DRM1(2,1), -0.07113807138648245D0, 1D-12,
+     :           'slDAVM', '21', STATUS )
+      CALL VVD ( DRM1(2,2), 0.9903204657727545D0, 1D-12,
+     :           'slDAVM', '22', STATUS )
+      CALL VVD ( DRM1(2,3), -0.1191836812279541D0, 1D-12,
+     :           'slDAVM', '23', STATUS )
+      CALL VVD ( DRM1(3,1), 0.09420887631983825D0, 1D-12,
+     :           'slDAVM', '31', STATUS )
+      CALL VVD ( DRM1(3,2), 0.1256229973879967D0, 1D-12,
+     :           'slDAVM', '32', STATUS )
+      CALL VVD ( DRM1(3,3), 0.9875948309655174D0, 1D-12,
+     :           'slDAVM', '33', STATUS )
+
+      CALL slDEUL ( 'YZY', 2.345D0, -0.333D0, 2.222D0, DRM2 )
+      CALL VVD ( DRM2(1,1), -0.1681574770810878D0, 1D-12,
+     :           'slDEUL', '11', STATUS )
+      CALL VVD ( DRM2(1,2), 0.1981362273264315D0, 1D-12,
+     :           'slDEUL', '12', STATUS )
+      CALL VVD ( DRM2(1,3), 0.9656423242187410D0, 1D-12,
+     :           'slDEUL', '13', STATUS )
+      CALL VVD ( DRM2(2,1), -0.2285369373983370D0, 1D-12,
+     :           'slDEUL', '21', STATUS )
+      CALL VVD ( DRM2(2,2), 0.9450659587140423D0, 1D-12,
+     :           'slDEUL', '22', STATUS )
+      CALL VVD ( DRM2(2,3), -0.2337117924378156D0, 1D-12,
+     :           'slDEUL', '23', STATUS )
+      CALL VVD ( DRM2(3,1), -0.9589024617479674D0, 1D-12,
+     :           'slDEUL', '31', STATUS )
+      CALL VVD ( DRM2(3,2), -0.2599853247796050D0, 1D-12,
+     :           'slDEUL', '32', STATUS )
+      CALL VVD ( DRM2(3,3), -0.1136384607117296D0, 1D-12,
+     :           'slDEUL', '33', STATUS )
+
+      CALL slDMXM ( DRM2, DRM1, DRM )
+      CALL VVD ( DRM(1,1), -0.09010460088585805D0, 1D-12,
+     :           'slDMXM', '11', STATUS )
+      CALL VVD ( DRM(1,2), 0.3075993402463796D0, 1D-12,
+     :           'slDMXM', '12', STATUS )
+      CALL VVD ( DRM(1,3), 0.9472400998581048D0, 1D-12,
+     :           'slDMXM', '13', STATUS )
+      CALL VVD ( DRM(2,1), -0.3161868071070688D0, 1D-12,
+     :           'slDMXM', '21', STATUS )
+      CALL VVD ( DRM(2,2), 0.8930686362478707D0, 1D-12,
+     :           'slDMXM', '22', STATUS )
+      CALL VVD ( DRM(2,3), -0.3200848543149236D0, 1D-12,
+     :           'slDMXM', '23', STATUS )
+      CALL VVD ( DRM(3,1), -0.9444083141897035D0, 1D-12,
+     :           'slDMXM', '31', STATUS )
+      CALL VVD ( DRM(3,2), -0.3283459407855694D0, 1D-12,
+     :           'slDMXM', '32', STATUS )
+      CALL VVD ( DRM(3,3), 0.01678926022795169D0, 1D-12,
+     :           'slDMXM', '33', STATUS )
+
+      CALL slDS2C ( 3.0123D0, -0.999D0, DV1 )
+      CALL VVD ( DV1(1), -0.5366267667260525D0, 1D-12,
+     :           'slDS2C', 'X', STATUS )
+      CALL VVD ( DV1(2), 0.06977111097651444D0, 1D-12,
+     :           'slDS2C', 'Y', STATUS )
+      CALL VVD ( DV1(3), -0.8409302618566215D0, 1D-12,
+     :           'slDS2C', 'Z', STATUS )
+
+      CALL slDMXV ( DRM1, DV1, DV2 )
+      CALL slDMXV ( DRM2, DV2, DV3 )
+      CALL VVD ( DV3(1), -0.7267487768696160D0, 1D-12,
+     :           'slDMXV', 'X', STATUS )
+      CALL VVD ( DV3(2), 0.5011537352639822D0, 1D-12,
+     :           'slDMXV', 'Y', STATUS )
+      CALL VVD ( DV3(3), 0.4697671220397141D0, 1D-12,
+     :           'slDMXV', 'Z', STATUS )
+
+      CALL slDIMV ( DRM, DV3, DV4 )
+      CALL VVD ( DV4(1), -0.5366267667260526D0, 1D-12,
+     :           'slDIMV', 'X', STATUS )
+      CALL VVD ( DV4(2), 0.06977111097651445D0, 1D-12,
+     :           'slDIMV', 'Y', STATUS )
+      CALL VVD ( DV4(3), -0.8409302618566215D0, 1D-12,
+     :           'slDIMV', 'Z', STATUS )
+
+      CALL slDMAV ( DRM, DV5 )
+      CALL VVD ( DV5(1), 0.006889040510209034D0, 1D-12,
+     :           'slDMAV', 'X', STATUS )
+      CALL VVD ( DV5(2), -1.577473205461961D0, 1D-12,
+     :           'slDMAV', 'Y', STATUS )
+      CALL VVD ( DV5(3), 0.5201843672856759D0, 1D-12,
+     :           'slDMAV', 'Z', STATUS )
+
+      DO I = 1, 3
+         DV5(I) = DV5(I) * 1000D0
+      END DO
+
+      CALL slDVN ( DV5, DV6, DVM )
+      CALL VVD ( DV6(1), 0.004147420704640065D0, 1D-12,
+     :           'slDVN', 'X', STATUS )
+      CALL VVD ( DV6(2), -0.9496888606842218D0, 1D-12,
+     :           'slDVN', 'Y', STATUS )
+      CALL VVD ( DV6(3), 0.3131674740355448D0, 1D-12,
+     :           'slDVN', 'Z', STATUS )
+      CALL VVD ( DVM, 1661.042127339937D0, 1D-9, 'slDVN',
+     :           'M', STATUS )
+
+      CALL VVD ( slDVDV ( DV6, DV1 ), -0.3318384698006295D0,
+     :           1D-12, 'slDVN', ' ', STATUS )
+
+      CALL slDVXV (DV6, DV1, DV7 )
+      CALL VVD ( DV7(1), 0.7767720597123304D0, 1D-12,
+     :           'slDVXV', 'X', STATUS )
+      CALL VVD ( DV7(2), -0.1645663574562769D0, 1D-12,
+     :           'slDVXV', 'Y', STATUS )
+      CALL VVD ( DV7(3), -0.5093390925544726D0, 1D-12,
+     :           'slDVXV', 'Z', STATUS )
+
+      END
+
+      SUBROUTINE T_ZD ( STATUS )
+*+
+*  - - - - -
+*   T _ Z D
+*  - - - - -
+*
+*  Test slZD routine.
+*
+*  Returned:
+*     STATUS    LOGICAL     .TRUE. = success, .FALSE. = fail
+*
+*  Called: VVD, slZD.
+*
+*  Last revision:   22 October 2005
+*
+*  Copyright CLRC/Starlink.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+*    Boston, MA  02111-1307  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      LOGICAL STATUS
+
+      DOUBLE PRECISION slZD
+
+
+      CALL VVD ( slZD ( -1.023D0, -0.876D0, -0.432D0 ),
+     :           0.8963914139430839D0, 1D-12, 'slZD', ' ', STATUS )
+
+      END
diff --git a/math/slalib/slalib.h b/math/slalib/slalib.h
new file mode 100644
index 00000000..bf804c4f
--- /dev/null
+++ b/math/slalib/slalib.h
@@ -0,0 +1,509 @@
+#ifndef SLALIBHDEF
+#define SLALIBHDEF
+/*
+**  Author:
+**    Patrick Wallace  (ptw@tpsoft.demon.co.uk)
+**
+**  License:
+**    This program is free software; you can redistribute it and/or modify
+**    it under the terms of the GNU General Public License as published by
+**    the Free Software Foundation; either version 2 of the License, or
+**    (at your option) any later version.
+**
+**    This program is distributed in the hope that it will be useful,
+**    but WITHOUT ANY WARRANTY; without even the implied warranty of
+**    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+**    GNU General Public License for more details.
+**
+**    You should have received a copy of the GNU General Public License
+**    along with this program; if not, write to the Free Software
+**    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301
+**    USA.
+**
+**  Last revision:   10 December 2002
+**
+*/
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <math.h>
+
+void slaAddet ( double rm, double dm, double eq, double *rc, double *dc );
+
+void slaAfin ( const char *string, int *iptr, float *a, int *j );
+
+double slaAirmas ( double zd );
+
+void slaAltaz ( double ha, double dec, double phi,
+                double *az, double *azd, double *azdd,
+                double *el, double *eld, double *eldd,
+                double *pa, double *pad, double *padd );
+
+void slaAmp ( double ra, double da, double date, double eq,
+              double *rm, double *dm );
+
+void slaAmpqk ( double ra, double da, double amprms[21],
+                double *rm, double *dm );
+
+void slaAop ( double rap, double dap, double date, double dut,
+              double elongm, double phim, double hm, double xp,
+              double yp, double tdk, double pmb, double rh,
+              double wl, double tlr,
+              double *aob, double *zob, double *hob,
+              double *dob, double *rob );
+
+void slaAoppa ( double date, double dut, double elongm, double phim,
+                double hm, double xp, double yp, double tdk, double pmb,
+                double rh, double wl, double tlr, double aoprms[14] );
+
+void slaAoppat ( double date, double aoprms[14] );
+
+void slaAopqk ( double rap, double dap, double aoprms[14],
+                double *aob, double *zob, double *hob,
+                double *dob, double *rob );
+
+void slaAtmdsp ( double tdk, double pmb, double rh, double wl1,
+                 double a1, double b1, double wl2, double *a2, double *b2 );
+
+void slaAv2m ( float axvec[3], float rmat[3][3] );
+
+float slaBear ( float a1, float b1, float a2, float b2 );
+
+void slaCaf2r ( int ideg, int iamin, float asec, float *rad, int *j );
+
+void slaCaldj ( int iy, int im, int id, double *djm, int *j );
+
+void slaCalyd ( int iy, int im, int id, int *ny, int *nd, int *j );
+
+void slaCc2s ( float v[3], float *a, float *b );
+
+void slaCc62s ( float v[6], float *a, float *b, float *r,
+                float *ad, float *bd, float *rd );
+
+void slaCd2tf ( int ndp, float days, char *sign, int ihmsf[4] );
+
+void slaCldj ( int iy, int im, int id, double *djm, int *j );
+
+void slaClyd ( int iy, int im, int id, int *ny, int *nd, int *jstat );
+
+void slaCombn ( int nsel, int ncand, int list[], int *j );
+
+void slaCr2af ( int ndp, float angle, char *sign, int idmsf[4] );
+
+void slaCr2tf ( int ndp, float angle, char *sign, int ihmsf[4] );
+
+void slaCs2c ( float a, float b, float v[3] );
+
+void slaCs2c6 ( float a, float b, float r, float ad,
+                float bd, float rd, float v[6] );
+
+void slaCtf2d ( int ihour, int imin, float sec, float *days, int *j );
+
+void slaCtf2r ( int ihour, int imin, float sec, float *rad, int *j );
+
+void slaDaf2r ( int ideg, int iamin, double asec, double *rad, int *j );
+
+void slaDafin ( const char *string, int *iptr, double *a, int *j );
+
+double slaDat ( double dju );
+
+void slaDav2m ( double axvec[3], double rmat[3][3] );
+
+double slaDbear ( double a1, double b1, double a2, double b2 );
+
+void slaDbjin ( const char *string, int *nstrt,
+                double *dreslt, int *jf1, int *jf2 );
+
+void slaDc62s ( double v[6], double *a, double *b, double *r,
+                double *ad, double *bd, double *rd );
+
+void slaDcc2s ( double v[3], double *a, double *b );
+
+void slaDcmpf ( double coeffs[6], double *xz, double *yz, double *xs,
+                double *ys, double *perp, double *orient );
+
+void slaDcs2c ( double a, double b, double v[3] );
+
+void slaDd2tf ( int ndp, double days, char *sign, int ihmsf[4] );
+
+void slaDe2h ( double ha, double dec, double phi,
+               double *az, double *el );
+
+void slaDeuler ( const char *order, double phi, double theta, double psi,
+                 double rmat[3][3] );
+
+void slaDfltin ( const char *string, int *nstrt, double *dreslt, int *jflag );
+
+void slaDh2e ( double az, double el, double phi, double *ha, double *dec);
+
+void slaDimxv ( double dm[3][3], double va[3], double vb[3] );
+
+void slaDjcal ( int ndp, double djm, int iymdf[4], int *j );
+
+void slaDjcl ( double djm, int *iy, int *im, int *id, double *fd, int *j );
+
+void slaDm2av ( double rmat[3][3], double axvec[3] );
+
+void slaDmat ( int n, double *a, double *y, double *d, int *jf, int *iw );
+
+void slaDmoon ( double date, double pv[6] );
+
+void slaDmxm ( double a[3][3], double b[3][3], double c[3][3] );
+
+void slaDmxv ( double dm[3][3], double va[3], double vb[3] );
+
+double slaDpav ( double v1[3], double v2[3] );
+
+void slaDr2af ( int ndp, double angle, char *sign, int idmsf[4] );
+
+void slaDr2tf ( int ndp, double angle, char *sign, int ihmsf[4] );
+
+double slaDrange ( double angle );
+
+double slaDranrm ( double angle );
+
+void slaDs2c6 ( double a, double b, double r, double ad, double bd,
+                double rd, double v[6] );
+
+void slaDs2tp ( double ra, double dec, double raz, double decz,
+                double *xi, double *eta, int *j );
+
+double slaDsep ( double a1, double b1, double a2, double b2 );
+
+double slaDsepv ( double v1[3], double v2[3] );
+
+double slaDt ( double epoch );
+
+void slaDtf2d ( int ihour, int imin, double sec, double *days, int *j );
+
+void slaDtf2r ( int ihour, int imin, double sec, double *rad, int *j );
+
+void slaDtp2s ( double xi, double eta, double raz, double decz,
+                double *ra, double *dec );
+
+void slaDtp2v ( double xi, double eta, double v0[3], double v[3] );
+
+void slaDtps2c ( double xi, double eta, double ra, double dec,
+                 double *raz1, double *decz1,
+                 double *raz2, double *decz2, int *n );
+
+void slaDtpv2c ( double xi, double eta, double v[3],
+                 double v01[3], double v02[3], int *n );
+
+double slaDtt ( double dju );
+
+void slaDv2tp ( double v[3], double v0[3], double *xi, double *eta, int *j );
+
+double slaDvdv ( double va[3], double vb[3] );
+
+void slaDvn ( double v[3], double uv[3], double *vm );
+
+void slaDvxv ( double va[3], double vb[3], double vc[3] );
+
+void slaE2h ( float ha, float dec, float phi, float *az, float *el );
+
+void slaEarth ( int iy, int id, float fd, float posvel[6] );
+
+void slaEcleq ( double dl, double db, double date, double *dr, double *dd );
+
+void slaEcmat ( double date, double rmat[3][3] );
+
+void slaEcor ( float rm, float dm, int iy, int id, float fd,
+               float *rv, float *tl );
+
+void slaEg50 ( double dr, double dd, double *dl, double *db );
+
+void slaEl2ue ( double date, int jform, double epoch, double orbinc,
+                double anode, double perih, double aorq, double e,
+                double aorl, double dm, double u[], int *jstat );
+
+double slaEpb ( double date );
+
+double slaEpb2d ( double epb );
+
+double slaEpco ( char k0, char k, double e );
+
+double slaEpj ( double date );
+
+double slaEpj2d ( double epj );
+
+void slaEqecl ( double dr, double dd, double date, double *dl, double *db );
+
+double slaEqeqx ( double date );
+
+void slaEqgal ( double dr, double dd, double *dl, double *db );
+
+void slaEtrms ( double ep, double ev[3] );
+
+void slaEuler ( const char *order, float phi, float theta, float psi,
+                float rmat[3][3] );
+
+void slaEvp ( double date, double deqx,
+              double dvb[3], double dpb[3],
+              double dvh[3], double dph[3] );
+
+void slaFitxy ( int itype, int np, double xye[][2], double xym[][2],
+                double coeffs[6], int *j );
+
+void slaFk425 ( double r1950, double d1950, double dr1950,
+                double dd1950, double p1950, double v1950,
+                double *r2000, double *d2000, double *dr2000,
+                double *dd2000, double *p2000, double *v2000 );
+
+void slaFk45z ( double r1950, double d1950, double bepoch,
+                double *r2000, double *d2000 );
+
+void slaFk524 ( double r2000, double d2000, double dr2000,
+                double dd2000, double p2000, double v2000,
+                double *r1950, double *d1950, double *dr1950,
+                double *dd1950, double *p1950, double *v1950 );
+
+void slaFk52h ( double r5, double d5, double dr5, double dd5,
+                double *dr, double *dh, double *drh, double *ddh );
+
+void slaFk54z ( double r2000, double d2000, double bepoch,
+                double *r1950, double *d1950,
+                double *dr1950, double *dd1950 );
+
+void slaFk5hz ( double r5, double d5, double epoch,
+                double *rh, double *dh );
+
+void slaFlotin ( const char *string, int *nstrt, float *reslt, int *jflag );
+
+void slaGaleq ( double dl, double db, double *dr, double *dd );
+
+void slaGalsup ( double dl, double db, double *dsl, double *dsb );
+
+void slaGe50 ( double dl, double db, double *dr, double *dd );
+
+void slaGeoc ( double p, double h, double *r, double *z );
+
+double slaGmst ( double ut1 );
+
+double slaGmsta ( double date, double ut1 );
+
+void slaH2e ( float az, float el, float phi, float *ha, float *dec );
+
+void slaH2fk5 ( double dr, double dh, double drh, double ddh,
+                double *r5, double *d5, double *dr5, double *dd5 );
+
+void slaHfk5z ( double rh, double dh, double epoch,
+                double *r5, double *d5, double *dr5, double *dd5 );
+
+void slaImxv ( float rm[3][3], float va[3], float vb[3] );
+
+void slaInt2in ( const char *string, int *nstrt, int *ireslt, int *jflag );
+
+void slaIntin ( const char *string, int *nstrt, long *ireslt, int *jflag );
+
+void slaInvf ( double fwds[6], double bkwds[6], int *j );
+
+void slaKbj ( int jb, double e, char *k, int *j );
+
+void slaM2av ( float rmat[3][3], float axvec[3] );
+
+void slaMap ( double rm, double dm, double pr, double pd,
+              double px, double rv, double eq, double date,
+              double *ra, double *da );
+
+void slaMappa ( double eq, double date, double amprms[21] );
+
+void slaMapqk ( double rm, double dm, double pr, double pd,
+                double px, double rv, double amprms[21],
+                double *ra, double *da );
+
+void slaMapqkz ( double rm, double dm, double amprms[21],
+                 double *ra, double *da );
+
+void slaMoon ( int iy, int id, float fd, float posvel[6] );
+
+void slaMxm ( float a[3][3], float b[3][3], float c[3][3] );
+
+void slaMxv ( float rm[3][3], float va[3], float vb[3] );
+
+void slaNut ( double date, double rmatn[3][3] );
+
+void slaNutc ( double date, double *dpsi, double *deps, double *eps0 );
+
+void slaNutc80 ( double date, double *dpsi, double *deps, double *eps0 );
+
+void slaOap ( const char *type, double ob1, double ob2, double date,
+              double dut, double elongm, double phim, double hm,
+              double xp, double yp, double tdk, double pmb,
+              double rh, double wl, double tlr,
+              double *rap, double *dap );
+
+void slaOapqk ( const char *type, double ob1, double ob2, double aoprms[14],
+                double *rap, double *dap );
+
+void slaObs ( int n, char *c, char *name, double *w, double *p, double *h );
+
+double slaPa ( double ha, double dec, double phi );
+
+double slaPav ( float v1[3], float v2[3] );
+
+void slaPcd ( double disco, double *x, double *y );
+
+void slaPda2h ( double p, double d, double a,
+                double *h1, int *j1, double *h2, int *j2 );
+
+void slaPdq2h ( double p, double d, double q,
+                double *h1, int *j1, double *h2, int *j2 );
+
+void slaPermut ( int n, int istate[], int iorder[], int *j );
+
+void slaPertel (int jform, double date0, double date1,
+                double epoch0, double orbi0, double anode0,
+                double perih0, double aorq0, double e0, double am0,
+                double *epoch1, double *orbi1, double *anode1,
+                double *perih1, double *aorq1, double *e1, double *am1,
+                int *jstat );
+
+void slaPertue ( double date, double u[], int *jstat );
+
+void slaPlanel ( double date, int jform, double epoch, double orbinc,
+                 double anode, double perih, double aorq,  double e,
+                 double aorl, double dm, double pv[6], int *jstat );
+
+void slaPlanet ( double date, int np, double pv[6], int *j );
+
+void slaPlante ( double date, double elong, double phi, int jform,
+                 double epoch, double orbinc, double anode, double perih,
+                 double aorq, double e, double aorl, double dm,
+                 double *ra, double *dec, double *r, int *jstat );
+
+void slaPlantu ( double date, double elong, double phi, double u[],
+                 double *ra, double *dec, double *r, int *jstat );
+
+void slaPm ( double r0, double d0, double pr, double pd,
+             double px, double rv, double ep0, double ep1,
+             double *r1, double *d1 );
+
+void slaPolmo ( double elongm, double phim, double xp, double yp,
+                double *elong, double *phi, double *daz );
+
+void slaPrebn ( double bep0, double bep1, double rmatp[3][3] );
+
+void slaPrec ( double ep0, double ep1, double rmatp[3][3] );
+
+void slaPrecl ( double ep0, double ep1, double rmatp[3][3] );
+
+void slaPreces ( const char sys[3], double ep0, double ep1,
+                 double *ra, double *dc );
+
+void slaPrenut ( double epoch, double date, double rmatpn[3][3] );
+
+void slaPv2el ( double pv[], double date, double pmass, int jformr,
+                int *jform, double *epoch, double *orbinc,
+                double *anode, double *perih, double *aorq, double *e,
+                double *aorl, double *dm, int *jstat );
+
+void slaPv2ue ( double pv[], double date, double pmass,
+                double u[], int *jstat );
+
+void slaPvobs ( double p, double h, double stl, double pv[6] );
+
+void slaPxy ( int np, double xye[][2], double xym[][2],
+              double coeffs[6],
+              double xyp[][2], double *xrms, double *yrms, double *rrms );
+
+float slaRange ( float angle );
+
+float slaRanorm ( float angle );
+
+double slaRcc ( double tdb, double ut1, double wl, double u, double v );
+
+void slaRdplan ( double date, int np, double elong, double phi,
+                 double *ra, double *dec, double *diam );
+
+void slaRefco ( double hm, double tdk, double pmb, double rh,
+                double wl, double phi, double tlr, double eps,
+                double *refa, double *refb );
+
+void slaRefcoq ( double tdk, double pmb, double rh, double wl,
+                double *refa, double *refb );
+
+void slaRefro ( double zobs, double hm, double tdk, double pmb,
+                double rh, double wl, double phi, double tlr, double eps,
+                double *ref );
+
+void slaRefv ( double vu[3], double refa, double refb, double vr[3] );
+
+void slaRefz ( double zu, double refa, double refb, double *zr );
+
+float slaRverot ( float phi, float ra, float da, float st );
+
+float slaRvgalc ( float r2000, float d2000 );
+
+float slaRvlg ( float r2000, float d2000 );
+
+float slaRvlsrd ( float r2000, float d2000 );
+
+float slaRvlsrk ( float r2000, float d2000 );
+
+void slaS2tp ( float ra, float dec, float raz, float decz,
+               float *xi, float *eta, int *j );
+
+float slaSep ( float a1, float b1, float a2, float b2 );
+
+float slaSepv ( float v1[3], float v2[3] );
+
+void slaSmat ( int n, float *a, float *y, float *d, int *jf, int *iw );
+
+void slaSubet ( double rc, double dc, double eq,
+                double *rm, double *dm );
+
+void slaSupgal ( double dsl, double dsb, double *dl, double *db );
+
+void slaSvd ( int m, int n, int mp, int np,
+              double *a, double *w, double *v, double *work,
+              int *jstat );
+
+void slaSvdcov ( int n, int np, int nc,
+                 double *w, double *v, double *work, double *cvm );
+
+void slaSvdsol ( int m, int n, int mp, int np,
+                 double *b, double *u, double *w, double *v,
+                 double *work, double *x );
+
+void slaTp2s ( float xi, float eta, float raz, float decz,
+               float *ra, float *dec );
+
+void slaTp2v ( float xi, float eta, float v0[3], float v[3] );
+
+void slaTps2c ( float xi, float eta, float ra, float dec,
+                float *raz1, float *decz1,
+                float *raz2, float *decz2, int *n );
+
+void slaTpv2c ( float xi, float eta, float v[3],
+                float v01[3], float v02[3], int *n );
+
+void slaUe2el ( double u[], int jformr,
+                int *jform, double *epoch, double *orbinc,
+                double *anode, double *perih, double *aorq, double *e,
+                double *aorl, double *dm, int *jstat );
+
+void slaUe2pv ( double date, double u[], double pv[], int *jstat );
+
+void slaUnpcd ( double disco, double *x, double *y );
+
+void slaV2tp ( float v[3], float v0[3], float *xi, float *eta, int *j );
+
+float slaVdv ( float va[3], float vb[3] );
+
+void slaVn ( float v[3], float uv[3], float *vm );
+
+void slaVxv ( float va[3], float vb[3], float vc[3] );
+
+void slaXy2xy ( double x1, double y1, double coeffs[6],
+                double *x2, double *y2 );
+
+double slaZd ( double ha, double dec, double phi );
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/math/slalib/smat.f b/math/slalib/smat.f
new file mode 100644
index 00000000..bd922c55
--- /dev/null
+++ b/math/slalib/smat.f
@@ -0,0 +1,159 @@
+      SUBROUTINE slSMAT (N, A, Y, D, JF, IW)
+*+
+*     - - - - -
+*      S M A T
+*     - - - - -
+*
+*  Matrix inversion & solution of simultaneous equations
+*  (single precision)
+*
+*  For the set of n simultaneous equations in n unknowns:
+*     A.Y = X
+*
+*  where:
+*     A is a non-singular N x N matrix
+*     Y is the vector of N unknowns
+*     X is the known vector
+*
+*  SMATRX computes:
+*     the inverse of matrix A
+*     the determinant of matrix A
+*     the vector of N unknowns
+*
+*  Arguments:
+*
+*     symbol  type dimension           before              after
+*
+*       N      int                 no. of unknowns       unchanged
+*       A      real  (N,N)             matrix             inverse
+*       Y      real   (N)              vector            solution
+*       D      real                       -             determinant
+*     * JF     int                        -           singularity flag
+*       IW     int    (N)                 -              workspace
+*
+*  *  JF is the singularity flag.  If the matrix is non-singular,
+*    JF=0 is returned.  If the matrix is singular, JF=-1 & D=0.0 are
+*    returned.  In the latter case, the contents of array A on return
+*    are undefined.
+*
+*  Algorithm:
+*     Gaussian elimination with partial pivoting.
+*
+*  Speed:
+*     Very fast.
+*
+*  Accuracy:
+*     Fairly accurate - errors 1 to 4 times those of routines optimised
+*     for accuracy.
+*
+*  Note:  replaces the obsolete slSMATRX routine.
+*
+*  P.T.Wallace   Starlink   10 September 1990
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER N
+      REAL A(N,N),Y(N),D
+      INTEGER JF
+      INTEGER IW(N)
+
+      REAL SFA
+      PARAMETER (SFA=1E-20)
+
+      INTEGER K,IMX,I,J,NP1MK,KI
+      REAL AMX,T,AKK,YK,AIK
+
+
+      JF=0
+      D=1.0
+      DO K=1,N
+         AMX=ABS(A(K,K))
+         IMX=K
+         IF (K.NE.N) THEN
+            DO I=K+1,N
+               T=ABS(A(I,K))
+               IF (T.GT.AMX) THEN
+                  AMX=T
+                  IMX=I
+               END IF
+            END DO
+         END IF
+         IF (AMX.LT.SFA) THEN
+            JF=-1
+         ELSE
+            IF (IMX.NE.K) THEN
+               DO J=1,N
+                  T=A(K,J)
+                  A(K,J)=A(IMX,J)
+                  A(IMX,J)=T
+               END DO
+               T=Y(K)
+               Y(K)=Y(IMX)
+               Y(IMX)=T
+               D=-D
+            END IF
+            IW(K)=IMX
+            AKK=A(K,K)
+            D=D*AKK
+            IF (ABS(D).LT.SFA) THEN
+               JF=-1
+            ELSE
+               AKK=1.0/AKK
+               A(K,K)=AKK
+               DO J=1,N
+                  IF (J.NE.K) A(K,J)=A(K,J)*AKK
+               END DO
+               YK=Y(K)*AKK
+               Y(K)=YK
+               DO I=1,N
+                  AIK=A(I,K)
+                  IF (I.NE.K) THEN
+                     DO J=1,N
+                        IF (J.NE.K) A(I,J)=A(I,J)-AIK*A(K,J)
+                     END DO
+                     Y(I)=Y(I)-AIK*YK
+                  END IF
+               END DO
+               DO I=1,N
+                  IF (I.NE.K) A(I,K)=-A(I,K)*AKK
+               END DO
+            END IF
+         END IF
+      END DO
+      IF (JF.NE.0) THEN
+         D=0.0
+      ELSE
+         DO K=1,N
+            NP1MK=N+1-K
+            KI=IW(NP1MK)
+            IF (NP1MK.NE.KI) THEN
+               DO I=1,N
+                  T=A(I,NP1MK)
+                  A(I,NP1MK)=A(I,KI)
+                  A(I,KI)=T
+               END DO
+            END IF
+         END DO
+      END IF
+      END
diff --git a/math/slalib/subet.f b/math/slalib/subet.f
new file mode 100644
index 00000000..04ed6f9d
--- /dev/null
+++ b/math/slalib/subet.f
@@ -0,0 +1,84 @@
+      SUBROUTINE slSUET (RC, DC, EQ, RM, DM)
+*+
+*     - - - - - -
+*      S U E T
+*     - - - - - -
+*
+*  Remove the E-terms (elliptic component of annual aberration)
+*  from a pre IAU 1976 catalogue RA,Dec to give a mean place
+*  (double precision)
+*
+*  Given:
+*     RC,DC     dp     RA,Dec (radians) with E-terms included
+*     EQ        dp     Besselian epoch of mean equator and equinox
+*
+*  Returned:
+*     RM,DM     dp     RA,Dec (radians) without E-terms
+*
+*  Called:
+*     slETRM, slDS2C, sla_,DVDV, slDC2S, slDA2P
+*
+*  Explanation:
+*     Most star positions from pre-1984 optical catalogues (or
+*     derived from astrometry using such stars) embody the
+*     E-terms.  This routine converts such a position to a
+*     formal mean place (allowing, for example, comparison with a
+*     pulsar timing position).
+*
+*  Reference:
+*     Explanatory Supplement to the Astronomical Ephemeris,
+*     section 2D, page 48.
+*
+*  P.T.Wallace   Starlink   10 May 1990
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION RC,DC,EQ,RM,DM
+
+      DOUBLE PRECISION slDA2P,slDVDV
+      DOUBLE PRECISION A(3),V(3),F
+
+      INTEGER I
+
+
+
+*  E-terms
+      CALL slETRM(EQ,A)
+
+*  Spherical to Cartesian
+      CALL slDS2C(RC,DC,V)
+
+*  Include the E-terms
+      F=1D0+slDVDV(V,A)
+      DO I=1,3
+         V(I)=F*V(I)-A(I)
+      END DO
+
+*  Cartesian to spherical
+      CALL slDC2S(V,RM,DM)
+
+*  Bring RA into conventional range
+      RM=slDA2P(RM)
+
+      END
diff --git a/math/slalib/sun67.tex b/math/slalib/sun67.tex
new file mode 100644
index 00000000..ab9c7ba9
--- /dev/null
+++ b/math/slalib/sun67.tex
@@ -0,0 +1,13140 @@
+\documentclass[11pt,twoside]{article}
+\setcounter{tocdepth}{2}
+\pagestyle{myheadings}
+
+% -----------------------------------------------------------------------------
+% ? Document identification
+\newcommand{\stardoccategory}  {Starlink User Note}
+\newcommand{\stardocinitials}  {SUN}
+\newcommand{\stardocsource}    {sun67.70}
+\newcommand{\stardocnumber}    {67.70}
+\newcommand{\stardocauthors}   {P.\,T.\,Wallace}
+\newcommand{\stardocdate}      {19 December 2005}
+\newcommand{\stardoctitle}     {SLALIB --- Positional Astronomy Library}
+\newcommand{\stardocversion}   {2.5-3}
+\newcommand{\stardocmanual}    {Programmer's Manual}
+% ? End of document identification
+
+%%% Also see \nroutines definition later %%%
+
+% -----------------------------------------------------------------------------
+
+\newcommand{\stardocname}{\stardocinitials /\stardocnumber}
+\markright{\stardocname}
+
+%----------------------------------------------------
+% Comment out unwanted definitions to suit stationery
+
+\setlength{\textwidth}{160mm}       %
+\setlength{\textheight}{230mm}      % European A4
+\setlength{\topmargin}{-5mm}        %
+
+%\setlength{\textwidth}{167mm}       %
+%\setlength{\textheight}{220mm}      % US Letter
+%\setlength{\topmargin}{-10mm}       %
+
+%
+%----------------------------------------------------
+
+\setlength{\textwidth}{160mm}
+\setlength{\textheight}{230mm}
+\setlength{\topmargin}{-2mm}
+\setlength{\oddsidemargin}{0mm}
+\setlength{\evensidemargin}{0mm}
+\setlength{\parindent}{0mm}
+\setlength{\parskip}{\medskipamount}
+\setlength{\unitlength}{1mm}
+
+% -----------------------------------------------------------------------------
+%  Hypertext definitions.
+%  ======================
+%  These are used by the LaTeX2HTML translator in conjunction with star2html.
+
+%  Comment.sty: version 2.0, 19 June 1992
+%  Selectively in/exclude pieces of text.
+%
+%  Author
+%    Victor Eijkhout                                      <eijkhout@cs.utk.edu>
+%    Department of Computer Science
+%    University Tennessee at Knoxville
+%    104 Ayres Hall
+%    Knoxville, TN 37996
+%    USA
+
+%  Do not remove the %begin{latexonly} and %end{latexonly} lines (used by
+%  star2html to signify raw TeX that latex2html cannot process).
+%begin{latexonly}
+\makeatletter
+\def\makeinnocent#1{\catcode`#1=12 }
+\def\csarg#1#2{\expandafter#1\csname#2\endcsname}
+
+\def\ThrowAwayComment#1{\begingroup
+    \def\CurrentComment{#1}%
+    \let\do\makeinnocent \dospecials
+    \makeinnocent\^^L% and whatever other special cases
+    \endlinechar`\^^M \catcode`\^^M=12 \xComment}
+{\catcode`\^^M=12 \endlinechar=-1 %
+ \gdef\xComment#1^^M{\def\test{#1}
+      \csarg\ifx{PlainEnd\CurrentComment Test}\test
+          \let\html@next\endgroup
+      \else \csarg\ifx{LaLaEnd\CurrentComment Test}\test
+            \edef\html@next{\endgroup\noexpand\end{\CurrentComment}}
+      \else \let\html@next\xComment
+      \fi \fi \html@next}
+}
+\makeatother
+
+\def\includecomment
+ #1{\expandafter\def\csname#1\endcsname{}%
+    \expandafter\def\csname end#1\endcsname{}}
+\def\excludecomment
+ #1{\expandafter\def\csname#1\endcsname{\ThrowAwayComment{#1}}%
+    {\escapechar=-1\relax
+     \csarg\xdef{PlainEnd#1Test}{\string\\end#1}%
+     \csarg\xdef{LaLaEnd#1Test}{\string\\end\string\{#1\string\}}%
+    }}
+
+%  Define environments that ignore their contents.
+\excludecomment{comment}
+\excludecomment{rawhtml}
+\excludecomment{htmlonly}
+
+%  Hypertext commands etc. This is a condensed version of the html.sty
+%  file supplied with LaTeX2HTML by: Nikos Drakos <nikos@cbl.leeds.ac.uk> &
+%  Jelle van Zeijl <jvzeijl@isou17.estec.esa.nl>. The LaTeX2HTML documentation
+%  should be consulted about all commands (and the environments defined above)
+%  except \xref and \xlabel which are Starlink specific.
+
+\newcommand{\htmladdnormallinkfoot}[2]{#1\footnote{#2}}
+\newcommand{\htmladdnormallink}[2]{#1}
+\newcommand{\htmladdimg}[1]{}
+\newenvironment{latexonly}{}{}
+\newcommand{\hyperref}[4]{#2\ref{#4}#3}
+\newcommand{\htmlref}[2]{#1}
+\newcommand{\htmlimage}[1]{}
+\newcommand{\htmladdtonavigation}[1]{}
+\newcommand{\latexhtml}[2]{#1}
+\newcommand{\html}[1]{}
+
+%  Starlink cross-references and labels.
+\newcommand{\xref}[3]{#1}
+\newcommand{\xlabel}[1]{}
+
+%  LaTeX2HTML symbol.
+\newcommand{\latextohtml}{{\bf LaTeX}{2}{\tt{HTML}}}
+
+%  Define command to re-centre underscore for Latex and leave as normal
+%  for HTML (severe problems with \_ in tabbing environments and \_\_
+%  generally otherwise).
+\newcommand{\latex}[1]{#1}
+\newcommand{\setunderscore}{\renewcommand{\_}{{\tt\symbol{95}}}}
+\latex{\setunderscore}
+
+% -----------------------------------------------------------------------------
+%  Debugging.
+%  =========
+%  Remove % on the following to debug links in the HTML version using Latex.
+
+% \newcommand{\hotlink}[2]{\fbox{\begin{tabular}[t]{@{}c@{}}#1\\\hline{\footnotesize #2}\end{tabular}}}
+% \renewcommand{\htmladdnormallinkfoot}[2]{\hotlink{#1}{#2}}
+% \renewcommand{\htmladdnormallink}[2]{\hotlink{#1}{#2}}
+% \renewcommand{\hyperref}[4]{\hotlink{#1}{\S\ref{#4}}}
+% \renewcommand{\htmlref}[2]{\hotlink{#1}{\S\ref{#2}}}
+% \renewcommand{\xref}[3]{\hotlink{#1}{#2 -- #3}}
+%end{latexonly}
+% -----------------------------------------------------------------------------
+% ? Document specific \newcommand or \newenvironment commands.
+%------------------------------------------------------------------------------
+
+\newcommand{\nroutines} {188}
+\newcommand{\radec}     {$[\,\alpha,\delta\,]$}
+\newcommand{\hadec}     {$[\,h,\delta\,]$}
+\newcommand{\xieta}     {$[\,\xi,\eta\,]$}
+\newcommand{\azel}      {$[\,Az,El~]$}
+\newcommand{\ecl}       {$[\,\lambda,\beta~]$}
+\newcommand{\gal}       {$[\,l^{I\!I},b^{I\!I}\,]$}
+\newcommand{\xy}        {$[\,x,y\,]$}
+\newcommand{\xyz}       {$[\,x,y,z\,]$}
+\newcommand{\xyzd}      {$[\,\dot{x},\dot{y},\dot{z}\,]$}
+\newcommand{\xyzxyzd}   {$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$}
+\newcommand{\degree}[2] {$#1^{\circ}
+                        \hspace{-0.37em}.\hspace{0.02em}#2$}
+
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+\begin{htmlonly}
+   \newcommand{\arcsec}[2] {
+      {$#1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.#2$}
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+\end{htmlonly}
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+%------------------------------------------------------------------------------
+% ? End of document specific commands
+% -----------------------------------------------------------------------------
+%  Title Page.
+%  ===========
+\renewcommand{\thepage}{\roman{page}}
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+\thispagestyle{empty}
+
+%  Latex document header.
+%  ======================
+\begin{latexonly}
+   CCLRC / {\sc Rutherford Appleton Laboratory} \hfill {\bf \stardocname}\\
+   {\large Particle Physics \& Astronomy Research Council}\\
+   {\large Starlink Project\\}
+   {\large \stardoccategory\ \stardocnumber}
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+   \stardocdate
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+   {\Huge\bf  \stardocmanual}
+   \end{center}
+   \vspace{5mm}
+
+% ? Heading for abstract if used.
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+   \begin{center}
+      {\Large\bf Abstract}
+   \end{center}
+% ? End of heading for abstract.
+\end{latexonly}
+
+%  HTML documentation header.
+%  ==========================
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+      \htmladdnormallink{CCLRC}{http://www.cclrc.ac.uk} /
+      \htmladdnormallink{Rutherford Appleton Laboratory}
+                        {http://www.cclrc.ac.uk} \\
+      \htmladdnormallink{Particle Physics \& Astronomy Research Council}
+                        {http://www.pparc.ac.uk} \\
+   \begin{rawhtml} </H3> <H2> \end{rawhtml}
+      \htmladdnormallink{Starlink Project}{http://www.starlink.ac.uk/}
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+    <H2>Contents</H2>
+  \end{rawhtml}
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+  \section{\xlabel{abstract}Abstract}
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+\end{htmlonly}
+
+% -----------------------------------------------------------------------------
+% ? Document Abstract. (if used)
+%   ==================
+SLALIB is a library used by writers of positional-astronomy applications.
+Most of the \nroutines\ routines are concerned with astronomical position
+and time,
+but a number have wider trigonometrical, numerical or general applications.
+% ? End of document abstract
+% -----------------------------------------------------------------------------
+% ? Latex document Table of Contents (if used).
+%  ===========================================
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+ \begin{latexonly}
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+   \setlength{\parskip}{\medskipamount}
+   \markright{\stardocname}
+ \end{latexonly}
+% ? End of Latex document table of contents
+% -----------------------------------------------------------------------------
+\newpage
+\renewcommand{\thepage}{\arabic{page}}
+\setcounter{page}{1}
+
+\section{INTRODUCTION}
+\subsection{Purpose}
+SLALIB\footnote{The name isn't an acronym;
+it just stands for ``Subprogram Library~A''.}
+is a library of routines
+intended to make accurate and reliable positional-astronomy
+applications easier to write.
+Most SLALIB routines are concerned with astronomical position and time, but a
+number have wider trigonometrical, numerical or general applications.
+The applications ASTROM, COCO, RV and TPOINT
+all make extensive use of the SLALIB
+routines, as do a number of telescope control systems around the world.
+The SLALIB versions currently in service are written in
+Fortran~77 and run on VAX/VMS, several Unix platforms and PC.
+A proprietary ANSI~C version is also available from the author;  it is
+functionally similar to the Fortran version upon which the present
+document concentrates.
+
+\subsection{Example Application}
+Here is a simple example of an application program written
+using SLALIB calls:
+
+\begin{verbatim}
+         PROGRAM FK4FK5
+   *
+   *  Read a B1950 position from I/O unit 5 and reply on I/O unit 6
+   *  with the J2000 equivalent.  Enter a period to quit.
+   *
+         IMPLICIT NONE
+         CHARACTER C*80,S
+         INTEGER I,J,IHMSF(4),IDMSF(4)
+         DOUBLE PRECISION R4,D4,R5,D5
+         LOGICAL BAD
+
+   *   Loop until a period is entered
+         C = ' '
+         DO WHILE (C(:1).NE.'.')
+
+   *     Read h m s d ' "
+            READ (5,'(A)') C
+            IF (C(:1).NE.'.') THEN
+               BAD = .TRUE.
+
+   *        Decode the RA
+               I = 1
+               CALL sla_DAFIN(C,I,R4,J)
+               IF (J.EQ.0) THEN
+                  R4 = 15D0*R4
+
+   *           Decode the Dec
+                  CALL sla_DAFIN(C,I,D4,J)
+                  IF (J.EQ.0) THEN
+
+   *              FK4 to FK5
+                     CALL sla_FK45Z(R4,D4,1950D0,R5,D5)
+
+   *              Format and output the result
+                     CALL sla_DR2TF(2,R5,S,IHMSF)
+                     CALL sla_DR2AF(1,D5,S,IDMSF)
+                     WRITE (6,
+        :       '(1X,I2.2,2I3.2,''.'',I2.2,2X,A,I2.2,2I3.2,''.'',I1)')
+        :                                                     IHMSF,S,IDMSF
+                     BAD = .FALSE.
+                  END IF
+               END IF
+               IF (BAD) WRITE (6,'(1X,''?'')')
+            END IF
+         END DO
+
+         END
+\end{verbatim}
+In this example, SLALIB not only provides the complicated FK4 to
+FK5 transformation but also
+simplifies the tedious and error-prone tasks
+of decoding and formatting angles
+expressed as hours, minutes {\it etc}.  The
+example incorporates range checking, and avoids the
+notorious ``minus zero'' problem (an often-perpetrated bug where
+declinations between $0^{\circ}$ and $-1^{\circ}$ lose their minus
+sign).
+With a little extra elaboration and a few more calls to SLALIB,
+defaulting can be provided (enabling unused fields to
+be replaced with commas to avoid retyping), proper motions
+can be handled, different epochs can be specified, and
+so on.  See the program COCO (SUN/56) for further ideas.
+
+\subsection{Scope}
+SLALIB contains \nroutines\ routines covering the following topics:
+\begin{itemize}
+\item String Decoding,
+      Sexagesimal Conversions
+\item Angles, Vectors \& Rotation Matrices
+\item Calendars,
+      Time Scales
+\item Precession \& Nutation
+\item Proper Motion
+\item FK4/FK5/Hipparcos,
+      Elliptic Aberration
+\item Geocentric Coordinates
+\item Apparent \& Observed Place
+\item Azimuth \& Elevation
+\item Refraction \& Air Mass
+\item Ecliptic,
+      Galactic,
+      Supergalactic Coordinates
+\item Ephemerides
+\item Astrometry
+\item Numerical Methods
+\end{itemize}
+
+\subsection{Objectives}
+SLALIB was designed to give application programmers
+a basic set of positional-astronomy tools which were
+accurate and easy to use.  To this end, the library is:
+\begin{itemize}
+\item Readily available, including source code and documentation.
+\item Supported and maintained.
+\item Portable -- coded in standard languages and available for
+multiple computers and operating systems.
+\item Thoroughly commented, both for maintainability and to
+assist those wishing to cannibalize the code.
+\item Stable.
+\item Trustworthy -- some care has gone into
+testing SLALIB, both by comparison with published data and
+by checks for internal consistency.
+\item Rigorous -- corners are not cut,
+even where the practical consequences would, as a rule, be
+negligible.
+\item Comprehensive, without including too many esoteric features
+required only by specialists.
+\item Practical -- almost all the routines have been written to
+satisfy real needs encountered during the development of
+real-life applications.
+\item Environment-independent -- the package is
+completely free of pauses, stops, I/O {\it etc}.
+\item Self-contained -- SLALIB calls no other libraries.
+\end{itemize}
+A few {\it caveats}:
+\begin{itemize}
+\item SLALIB does not pretend to be canonical.  It is in essence
+an anthology, and the adopted algorithms are liable
+to change as more up-to-date ones become available.
+\item The functions aren't orthogonal -- there are several
+cases of different
+routines doing similar things, and many examples where
+sequences of SLALIB calls have simply been packaged, all to
+make applications less trouble to write.
+\item There are omissions -- for example there are no
+routines for calculating physical ephemerides of
+Solar-System bodies.
+\item SLALIB is not homogeneous, though important subsets
+(for example the FK4/FK5 routines) are.
+\item The library is not foolproof.  You have to know what
+you are trying to do ({\it e.g.}\ by reading textbooks on positional
+astronomy), and it is the caller's responsibility to supply
+sensible arguments (although enough internal validation is done to
+avoid arithmetic errors).
+\item Without being written in a wasteful
+manner, SLALIB is nonetheless optimized for maintainability
+rather than speed.  In addition, there are many places
+where considerable simplification would be possible if some
+specified amount of accuracy could be sacrificed;  such
+compromises are left to the individual programmer and
+are not allowed to limit SLALIB's value as a source
+of comparison results.
+\end{itemize}
+
+\subsection{Fortran Version}
+The Fortran versions of SLALIB use ANSI Fortran~77 with a few
+commonplace extensions.  Just three out of the \nroutines\ routines require
+platform-specific techniques and accordingly are supplied
+in different forms.
+SLALIB has been implemented on the following platforms:
+VAX/VMS,
+PC (Microsoft Fortran, Linux),
+DECstation (Ultrix),
+DEC Alpha (DEC Unix),
+Sun (SunOS, Solaris),
+Hewlett Packard (HP-UX),
+CONVEX,
+Perkin-Elmer and
+Fujitsu.
+
+\subsection{C Version}
+An ANSI C version of SLALIB is available from the author
+but is not part of the Starlink release.
+The functionality of this (proprietary) C version closely matches
+that of the Starlink Fortran SLALIB, partly for the convenience of
+existing users of the Fortran version, some of whom have in the past
+implemented C ``wrappers''.  The function names
+cannot be the same as the Fortran versions because of potential
+linking problems when
+both forms of the library are present; the C routine which
+is the equivalent of (for example) {\tt SLA\_REFRO} is {\tt slaRefro}.
+The types of arguments follow the Fortran version, except
+that integers are {\tt int} rather than {\tt long} (the one
+exception being
+{\tt slaIntin}, which returns a {\tt long}
+and is supplemented by an additional routine,
+not present in the Fortran SLALIB, called {\tt slaInt2in}, which returns
+an {\tt int}).
+Argument passing is by value
+(except for arrays and strings of course)
+for given arguments and by pointer for returned arguments.
+All the C functions are re-entrant.
+
+The Fortran routines {\tt sla\_GRESID}, {\tt sla\_RANDOM} and
+{\tt sla\_WAIT} have no C counterparts.
+
+Further details of the C version of SLALIB are available
+from the author.  The definitive guide to
+the calling sequences is the file {\tt slalib.h}.
+
+\subsection{Future Versions}
+The homogeneity and ease of use of SLALIB could perhaps be improved
+in the future by turning to object-oriented techniques, in particular
+through the C++ and Java languages.  For example ``celestial
+position'' could be a class and many of the transformations
+could happen automatically.  This requires further study and
+would result in a complete redesign.  Various attempts have been
+made to do this, but none as yet has the author's seal of
+approval.  Furthermore,
+the impact of Fortran~90 has yet to be assessed.  Should compilers
+become widely available, some internal recoding may be worthwhile
+in order to simplify parts of the code.  However, as with C++,
+a redesign of the
+application interfaces will be needed if the capabilities of the
+new language are to be exploited to the full.
+
+\subsection{New Functions}
+In a package like SLALIB it is difficult to know how far to go.  Is it
+enough to provide the primitive operations, or should more
+complicated functions be packaged?  Is it worth encroaching on
+specialist areas, where individual experts have all written their
+own software already?  To what extent should CPU efficiency be
+an issue?  How much support of different numerical precisions is
+required?  And so on.
+
+In practice, almost all the routines in SLALIB are there because they were
+needed for some specific application, and this is likely to remain the
+pattern for any enhancements in the future.
+Suggestions for additional SLALIB routines should be addressed to the
+author.
+
+\subsection{Acknowledgements}
+SLALIB is descended from a package of routines written
+for the AAO 16-bit minicomputers
+in the mid-1970s.  The coming of the VAX
+allowed a much more comprehensive and thorough package
+to be designed for Starlink, especially important
+at a time when the adoption
+of the IAU 1976 resolutions meant that astronomers
+would have to cope with a mixture of reference frames,
+time scales and nomenclature.
+
+Much of the preparatory work on SLALIB was done by
+Althea~Wilkinson of Manchester University.
+During its development,
+Andrew~Murray,
+Catherine~Hohenkerk,
+Andrew~Sinclair,
+Bernard~Yallop
+and
+Brian~Emerson of Her Majesty's Nautical Almanac Office were consulted
+on many occasions; their advice was indispensable.
+I am especially grateful to
+Catherine~Hohenkerk
+for supplying preprints of papers, and test data. A number of
+enhancements to SLALIB were at the suggestion of
+Russell~Owen, University of Washington,
+the late Phil~Hill, St~Andrews University,
+Bill~Vacca, JILA, Boulder and
+Ron~Maddalena, NRAO.
+Mark~Calabretta, CSIRO Radiophysics, Sydney supplied changes to suit Convex.
+I am indebted to Derek~Jones (RGO) for introducing me to the
+``universal variables'' method of calculating orbits.
+
+The first C version of SLALIB was a hand-coded transcription
+of the Starlink Fortran version carried out by
+Steve~Eaton (University of Leeds) in the course of
+MSc work.  This was later
+enhanced by John~Straede (AAO) and Martin~Shepherd (Caltech).
+The current C SLALIB is a complete rewrite by the present author and
+includes a comprehensive validation suite.
+Additional comments on the C version came from Bob~Payne (NRAO) and
+Jeremy~Bailey (AAO).
+
+\section{LINKING}
+
+On Unix systems (Linux, Sun, DEC Alpha {\it etc.}):
+\begin{verse}
+{\tt \%~~f77 progname.o -L/star/lib `sla\_link` -o progname}
+\end{verse}
+(The above assumes that all Starlink directories have been added to
+the {\tt LD\_LIBRARY\_PATH} and {\tt PATH} environment variables
+as described in SUN/202.)
+
+\pagebreak
+
+\section{SUBPROGRAM SPECIFICATIONS}
+%-----------------------------------------------------------------------
+\routine{SLA\_ADDET}{Add E-terms of Aberration}
+{
+ \action{Add the E-terms (elliptic component of annual aberration) to a
+  pre IAU 1976 mean place to conform to the old catalogue convention.}
+ \call{CALL sla\_ADDET (RM, DM, EQ, RC, DC)}
+}
+\args{GIVEN}
+{
+ \spec{RM,DM}{D}{\radec\ without E-terms (radians)} \\
+ \spec{EQ}{D}{Besselian epoch of mean equator and equinox}
+}
+\args{RETURNED}
+{
+ \spec{RC,DC}{D}{\radec\ with E-terms included (radians)}
+}
+\anote{Most star positions from pre-1984 optical catalogues (or
+       obtained by astrometry with respect to such stars) have the
+       E-terms built-in.  If it is necessary to convert a formal mean
+       place (for example a pulsar timing position) to one
+       consistent with such a star catalogue, then the
+       \radec\ should be adjusted using this routine.}
+\aref{{\it Explanatory Supplement to the Astronomical Ephemeris},
+ section 2D, page 48.}
+%-----------------------------------------------------------------------
+\routine{SLA\_AFIN}{Sexagesimal character string to angle}
+{
+ \action{Decode a free-format sexagesimal string (degrees, arcminutes,
+         arcseconds) into a single precision floating point
+         number (radians).}
+ \call{CALL sla\_AFIN (STRING, NSTRT, RESLT, JF)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C*(*)}{string containing deg, arcmin, arcsec fields} \\
+ \spec{NSTRT}{I}{pointer to start of decode (beginning of STRING = 1)}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{advanced past the decoded angle} \\
+ \spec{RESLT}{R}{angle in radians} \\
+ \spec{JF}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em}   0 = OK} \\
+ \spec{}{}{\hspace{0.7em} $+1$ = default, RESLT unchanged (note 2)} \\
+ \spec{}{}{\hspace{0.7em} $-1$ = bad degrees (note 3)} \\
+ \spec{}{}{\hspace{0.7em} $-2$ = bad arcminutes (note 3)} \\
+ \spec{}{}{\hspace{0.7em} $-3$ = bad arcseconds (note 3)} \\
+}
+\goodbreak
+\setlength{\oldspacing}{\topsep}
+\setlength{\topsep}{0.3ex}
+\begin{description}
+ \exampleitem \\ [1.5ex]
+  \begin{tabular}{lll}
+   {\it argument} & {\it before} & {\it after} \\ \\
+   STRING & $'$\verb*#-57 17 44.806  12 34 56.7#$'$ & unchanged \\
+   NSTRT & 1 & 16 ({\it i.e.}\ pointing to 12...) \\
+   RESLT & - & $-1.00000$ \\
+   JF & - & 0
+  \end{tabular}
+\end{description}
+A further call to sla\_AFIN, without adjustment of NSTRT, will
+decode the second angle, \dms{12}{34}{56}{7}.
+\setlength{\topsep}{\oldspacing}
+\notes
+{
+ \begin{enumerate}
+  \item The first three ``fields'' in STRING are degrees, arcminutes,
+   arcseconds, separated by spaces or commas.  The degrees field
+   may be signed, but not the others.  The decoding is carried
+   out by the sla\_DFLTIN routine and is free-format.
+  \item Successive fields may be absent, defaulting to zero.  For
+   zero status, the only combinations allowed are degrees alone,
+   degrees and arcminutes, and all three fields present.  If all
+   three fields are omitted, a status of +1 is returned and RESLT is
+   unchanged.  In all other cases RESLT is changed.
+  \item Range checking:
+   \begin{itemize}
+    \item The degrees field is not range checked.  However, it is
+     expected to be integral unless the other two fields are absent.
+    \item The arcminutes field is expected to be 0-59, and integral if
+     the arcseconds field is present.  If the arcseconds field
+     is absent, the arcminutes is expected to be 0-59.9999...
+    \item The arcseconds field is expected to be 0-59.9999...
+    \item Decoding continues even when a check has failed.  Under these
+     circumstances the field takes the supplied value, defaulting to
+     zero, and the result RESLT is computed and returned.
+   \end{itemize}
+   \item Further fields after the three expected ones are not treated as
+    an error.  The pointer NSTRT is left in the correct state for
+    further decoding with the present routine or with sla\_DFLTIN
+    {\it etc}.  See the example, above.
+   \item If STRING contains hours, minutes, seconds instead of
+    degrees {\it etc},
+    or if the required units are turns (or days) instead of radians,
+    the result RESLT should be multiplied as follows: \\ [1.5ex]
+    \begin{tabular}{lll}
+    {\it for STRING} & {\it to obtain} & {\it multiply RESLT by} \\ \\
+    ${\circ}$~~\raisebox{-0.7ex}{$'$}~~\raisebox{-0.7ex}{$''$}
+     & radians & $1.0$ \\
+    ${\circ}$~~\raisebox{-0.7ex}{$'$}~~\raisebox{-0.7ex}{$''$}
+     & turns & $1/{2 \pi} = 0.1591549430918953358$ \\
+    h m s & radians & $15.0$ \\
+    h m s & days & $15/{2\pi} = 2.3873241463784300365$ \\
+   \end{tabular}
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AIRMAS}{Air Mass}
+{
+ \action{Air mass at given zenith distance (double precision).}
+ \call{D~=~sla\_AIRMAS (ZD)}
+}
+\args{GIVEN}
+{
+ \spec{ZD}{D}{observed zenith distance (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_AIRMAS}{D}{air mass (1 at zenith)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The {\it observed}\/ zenith distance referred to above means
+        ``as affected by refraction''.
+  \item The routine uses Hardie's (1962) polynomial fit to Bemporad's
+        data for the relative air mass, $X$, in units of thickness at the
+        zenith as tabulated by Schoenberg (1929). This is adequate for all
+        normal needs as it is accurate to better than
+        0.1\% up to $X = 6.8$ and better than 1\% up to $X = 10$.
+        Bemporad's tabulated values are unlikely to be trustworthy
+        to such accuracy
+        because of variations in density, pressure and other
+        conditions in the atmosphere from those assumed in his work.
+  \item The sign of the ZD is ignored.
+  \item At zenith distances greater than about $\zeta = 87^{\circ}$ the
+        air mass is held constant to avoid arithmetic overflows.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Hardie, R.H., 1962, in {\it Astronomical Techniques}\,
+        ed. W.A.\ Hiltner, University of Chicago Press, p180.
+  \item Schoenberg, E., 1929, Hdb.\ d.\ Ap.,
+        Berlin, Julius Springer, 2, 268.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_ALTAZ}{Velocities {\it etc.}\ for Altazimuth Mount}
+{
+ \action{Positions, velocities and accelerations for an altazimuth
+         telescope mount that is tracking a star (double precision).}
+ \call{CALL sla\_ALTAZ (\vtop{
+         \hbox{HA, DEC, PHI,}
+         \hbox{AZ, AZD, AZDD, EL, ELD, ELDD, PA, PAD, PADD)}}}
+}
+\args{GIVEN}
+{
+ \spec{HA}{D}{hour angle} \\
+ \spec{DEC}{D}{declination} \\
+ \spec{PHI}{D}{observatory latitude}
+}
+\args{RETURNED}
+{
+ \spec{AZ}{D}{azimuth} \\
+ \spec{AZD}{D}{azimuth velocity} \\
+ \spec{AZDD}{D}{azimuth acceleration} \\
+ \spec{EL}{D}{elevation} \\
+ \spec{ELD}{D}{elevation velocity} \\
+ \spec{ELDD}{D}{elevation acceleration} \\
+ \spec{PA}{D}{parallactic angle} \\
+ \spec{PAD}{D}{parallactic angle velocity} \\
+ \spec{PADD}{D}{parallactic angle acceleration}
+}
+\notes
+{
+ \begin{enumerate}
+  \setlength{\parskip}{\medskipamount}
+  \item Natural units are used throughout.  HA, DEC, PHI, AZ, EL
+        and ZD are in radians.  The velocities and accelerations
+        assume constant declination and constant rate of change of
+        hour angle (as for tracking a star);  the units of AZD, ELD
+        and PAD are radians per radian of HA, while the units of AZDD,
+        ELDD and PADD are radians per radian of HA squared.  To
+        convert into practical degree- and second-based units:
+
+        \begin{center}
+        \begin{tabular}{rlcl}
+                  angles & $\times 360/2\pi$ & $\rightarrow$ & degrees \\
+              velocities & $\times (2\pi/86400) \times (360/2\pi)$
+                                             & $\rightarrow$ & degree/sec \\
+           accelerations & $\times (2\pi/86400)^2 \times (360/2\pi)$
+                                             & $\rightarrow$ & degree/sec/sec \\
+        \end{tabular}
+        \end{center}
+
+        Note that the seconds here are sidereal rather than SI.  One
+        sidereal second is about 0.99727 SI seconds.
+
+        The velocity and acceleration factors assume the sidereal
+        tracking case.  Their respective numerical values are (exactly)
+        1/240 and (approximately) 1/3300236.9.
+  \item Azimuth is returned in the range $[\,0,2\pi\,]$;  north is zero,
+        and east is $+\pi/2$.  Elevation and parallactic angle are
+        returned in the range $\pm\pi$.  Position angle is +ve
+        for a star west of the meridian and is the angle NP--star--zenith.
+  \item The latitude is geodetic as opposed to geocentric.  The
+        hour angle and declination are topocentric.  Refraction and
+        deficiencies in the telescope mounting are ignored.  The
+        purpose of the routine is to give the general form of the
+        quantities.  The details of a real telescope could profoundly
+        change the results, especially close to the zenith.
+  \item No range checking of arguments is carried out.
+  \item In applications which involve many such calculations, rather
+        than calling the present routine it will be more efficient to
+        use inline code, having previously computed fixed terms such
+        as sine and cosine of latitude, and (for tracking a star)
+        sine and cosine of declination.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AMP}{Apparent to Mean}
+{
+ \action{Convert star \radec\ from geocentric apparent to
+         mean place (post IAU 1976).}
+ \call{CALL sla\_AMP (RA, DA, DATE, EQ, RM, DM)}
+}
+\args{GIVEN}
+{
+ \spec{RA,DA}{D}{apparent \radec\ (radians)} \\
+ \spec{DATE}{D}{TDB for apparent place (JD$-$2400000.5)} \\
+ \spec{EQ}{D}{equinox:  Julian epoch of mean place}
+}
+\args{RETURNED}
+{
+ \spec{RM,DM}{D}{mean \radec\ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The distinction between the required TDB and TT is
+        always negligible.  Moreover, for all but the most
+        critical applications UTC is adequate.
+  \item Iterative techniques are used for the aberration and
+        light deflection corrections so that the routines
+        sla\_AMP (or sla\_AMPQK) and sla\_MAP (or sla\_MAPQK) are
+        accurate inverses;  even at the edge of the Sun's disc
+        the discrepancy is only about 1~nanoarcsecond.
+  \item Where multiple apparent places are to be converted to
+        mean places, for a fixed date and equinox, it is more
+        efficient to use the sla\_MAPPA routine to compute the
+        required parameters once, followed by one call to
+        sla\_AMPQK per star.
+  \item For EQ=2000D0,
+        the agreement with ICRS sub-mas, limited by the
+        precession-nutation model (IAU 1976 precession, Shirai \&
+        Fukushima 2001 forced nutation and precession corrections).
+  \item The accuracy is further limited by the routine sla\_EVP, called
+        by sla\_MAPPA, which computes the Earth position and
+        velocity using the methods of Stumpff.  The maximum
+        error is about 0.3~milliarcsecond.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AMPQK}{Quick Apparent to Mean}
+{
+ \action{Convert star \radec\ from geocentric apparent to mean place
+         (post IAU 1976).  Use of this routine is appropriate when
+         efficiency is important and where many star positions are
+         all to be transformed for one epoch and equinox.  The
+         star-independent parameters can be obtained by calling
+         the sla\_MAPPA routine.}
+ \call{CALL sla\_AMPQK (RA, DA, AMPRMS, RM, DM)}
+}
+\args{GIVEN}
+{
+ \spec{RA,DA}{D}{apparent \radec\ (radians)} \\
+ \spec{AMPRMS}{D(21)}{star-independent mean-to-apparent parameters:} \\
+ \specel   {(1)}     {time interval for proper motion (Julian years)} \\
+ \specel   {(2-4)}   {barycentric position of the Earth (AU)} \\
+ \specel   {(5-7)}   {heliocentric direction of the Earth (unit vector)} \\
+ \specel   {(8)}     {(gravitational radius of
+                      Sun)$\times 2 / $(Sun-Earth distance)} \\
+ \specel   {(9-11)}  {{\bf v}: barycentric Earth velocity in units of c} \\
+ \specel   {(12)}    {$\sqrt{1-\left|\mbox{\bf v}\right|^2}$} \\
+ \specel   {(13-21)} {precession-nutation $3\times3$ matrix}
+}
+\args{RETURNED}
+{
+ \spec{RM,DM}{D}{mean \radec\ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Iterative techniques are used for the aberration and
+        light deflection corrections so that the routines
+        sla\_AMP (or sla\_AMPQK) and sla\_MAP (or sla\_MAPQK) are
+        accurate inverses;  even at the edge of the Sun's disc
+        the discrepancy is only about 1~nanoarcsecond.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AOP}{Apparent to Observed}
+{
+ \action{Apparent to observed place, for sources distant from
+         the solar system.}
+ \call{CALL sla\_AOP (\vtop{
+         \hbox{RAP, DAP, DATE, DUT, ELONGM, PHIM, HM, XP, YP,}
+         \hbox{TDK, PMB, RH, WL, TLR, AOB, ZOB, HOB, DOB, ROB)}}}
+}
+\args{GIVEN}
+{
+ \spec{RAP,DAP}{D}{geocentric apparent \radec\ (radians)} \\
+ \spec{DATE}{D}{UTC date/time (Modified Julian Date, JD$-$2400000.5)} \\
+ \spec{DUT}{D}{$\Delta$UT:  UT1$-$UTC (UTC seconds)} \\
+ \spec{ELONGM}{D}{observer's mean longitude (radians, east +ve)} \\
+ \spec{PHIM}{D}{observer's mean geodetic latitude (radians)} \\
+ \spec{HM}{D}{observer's height above sea level (metres)} \\
+ \spec{XP,YP}{D}{polar motion \xy\ coordinates (radians)} \\
+ \spec{TDK}{D}{local ambient temperature (K; std=273.15D0)} \\
+ \spec{PMB}{D}{local atmospheric pressure (mb; std=1013.25D0)} \\
+ \spec{RH}{D}{local relative humidity (in the range 0D0\,--\,1D0)} \\
+ \spec{WL}{D}{effective wavelength ($\mu{\rm m}$, {\it e.g.}\ 0.55D0)} \\
+ \spec{TLR}{D}{tropospheric lapse rate (K per metre,
+                                              {\it e.g.}\ 0.0065D0)}
+}
+\args{RETURNED}
+{
+ \spec{AOB}{D}{observed azimuth (radians: N=0, E=$90^{\circ}$)} \\
+ \spec{ZOB}{D}{observed zenith distance (radians)} \\
+ \spec{HOB}{D}{observed Hour Angle (radians)} \\
+ \spec{DOB}{D}{observed $\delta$ (radians)} \\
+ \spec{ROB}{D}{observed $\alpha$ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine returns zenith distance rather than elevation
+        in order to reflect the fact that no allowance is made for
+        depression of the horizon.
+  \item The accuracy of the result is limited by the corrections for
+        refraction.  Providing the meteorological parameters are
+        known accurately and there are no gross local effects, the
+        predicted azimuth and elevation should be within about
+        \arcsec{0}{1} for $\zeta<70^{\circ}$.  Even
+        at a topocentric zenith distance of
+        $90^{\circ}$, the accuracy in elevation should be better than
+        1~arcminute;  useful results are available for a further
+        $3^{\circ}$, beyond which the sla\_REFRO routine returns a
+        fixed value of the refraction.  The complementary
+        routines sla\_AOP (or sla\_AOPQK) and sla\_OAP (or sla\_OAPQK)
+        are self-consistent to better than 1~microarcsecond all over
+        the celestial sphere.
+  \item It is advisable to take great care with units, as even
+        unlikely values of the input parameters are accepted and
+        processed in accordance with the models used.
+  \item {\it Apparent}\/ \radec\ means the geocentric apparent
+        right ascension
+        and declination, which is obtained from a catalogue mean place
+        by allowing for space motion, parallax, the Sun's gravitational
+        lens effect, annual aberration, and precession-nutation.  For
+        star positions in the FK5 system ({\it i.e.}\ J2000), these
+        effects can
+        be applied by means of the sla\_MAP {\it etc.}\ routines.
+        Starting from
+        other mean place systems, additional transformations will be
+        needed;  for example, FK4 ({\it i.e.}\ B1950) mean places would
+        first have to be converted to FK5, which can be done with the
+        sla\_FK425 {\it etc.}\ routines.
+  \item {\it Observed}\/ \azel\ means the position that would be seen by a
+        perfect theodolite located at the observer.  This is obtained
+        from the geocentric apparent \radec\ by allowing for Earth
+        orientation and diurnal aberration, rotating from equator
+        to horizon coordinates, and then adjusting for refraction.
+        The \hadec\ is obtained by rotating back into equatorial
+        coordinates, using the geodetic latitude corrected for polar
+        motion, and is the position that would be seen by a perfect
+        equatorial located at the observer and with its polar axis
+        aligned to the Earth's axis of rotation ({\it n.b.}\ not to the
+        refracted pole).  Finally, the $\alpha$ is obtained by subtracting
+        the {\it h}\/ from the local apparent ST.
+  \item To predict the required setting of a real telescope, the
+        observed place produced by this routine would have to be
+        adjusted for the tilt of the azimuth or polar axis of the
+        mounting (with appropriate corrections for mount flexures),
+        for non-perpendicularity between the mounting axes, for the
+        position of the rotator axis and the pointing axis relative
+        to it, for tube flexure, for gear and encoder errors, and
+        finally for encoder zero points.  Some telescopes would, of
+        course, exhibit other properties which would need to be
+        accounted for at the appropriate point in the sequence.
+  \item This routine takes time to execute, due mainly to the
+        rigorous integration used to evaluate the refraction.
+        For processing multiple stars for one location and time,
+        call sla\_AOPPA once followed by one call per star to sla\_AOPQK.
+        Where a range of times within a limited period of a few hours
+        is involved, and the highest precision is not required, call
+        sla\_AOPPA once, followed by a call to sla\_AOPPAT each time the
+        time changes, followed by one call per star to sla\_AOPQK.
+  \item The DATE argument is UTC expressed as an MJD.  This is,
+        strictly speaking, wrong, because of leap seconds.  However,
+        as long as the $\Delta$UT and the UTC are consistent there
+        are no difficulties, except during a leap second.  In this
+        case, the start of the 61st second of the final minute should
+        begin a new MJD day and the old pre-leap $\Delta$UT should
+        continue to be used.  As the 61st second completes, the MJD
+        should revert to the start of the day as, simultaneously,
+        the $\Delta$UT changes by one second to its post-leap new value.
+  \item The $\Delta$UT (UT1$-$UTC) is tabulated in IERS circulars and
+        elsewhere.  It increases by exactly one second at the end of
+        each UTC leap second, introduced in order to keep $\Delta$UT
+        within $\pm$\tsec{0}{9}.
+  \item IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.  The
+        longitude required by the present routine is {\bf east-positive},
+        in accordance with geographical convention (and right-handed).
+        In particular, note that the longitudes returned by the
+        sla\_OBS routine are west-positive (as in the {\it Astronomical
+        Almanac}\/ before 1984) and must be reversed in sign before use
+        in the present routine.
+  \item The polar coordinates XP,YP can be obtained from IERS
+        circulars and equivalent publications.  The
+        maximum amplitude is about \arcsec{0}{3}.  If XP,YP values
+        are unavailable, use XP=YP=0D0.  See page B60 of the 1988
+        {\it Astronomical Almanac}\/ for a definition of the two angles.
+  \item The height above sea level of the observing station, HM,
+        can be obtained from the {\it Astronomical Almanac}\/ (Section J
+        in the 1988 edition), or via the routine sla\_OBS.  If P,
+        the pressure in millibars, is available, an adequate
+        estimate of HM can be obtained from the following expression:
+        \begin{quote}
+         {\tt HM=-29.3D0*TSL*LOG(P/1013.25D0)}
+        \end{quote}
+        where TSL is the approximate sea-level air temperature in K
+        (see {\it Astrophysical Quantities}, C.W.Allen, 3rd~edition,
+        \S 52).  Similarly, if the pressure P is not known,
+        it can be estimated from the height of the observing
+        station, HM as follows:
+        \begin{quote}
+         {\tt P=1013.25D0*EXP(-HM/(29.3D0*TSL))}
+        \end{quote}
+        Note, however, that the refraction is nearly proportional to the
+        pressure and that an accurate P value is important for
+        precise work.
+  \item The azimuths {\it etc.}\ used by the present routine are with
+        respect to the celestial pole.  Corrections to the terrestrial pole
+        can be computed using sla\_POLMO.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AOPPA}{Appt-to-Obs Parameters}
+{
+ \action{Pre-compute the set of apparent to observed place parameters
+         required by the ``quick'' routines sla\_AOPQK and sla\_OAPQK.}
+ \call{CALL sla\_AOPPA (\vtop{
+          \hbox{DATE, DUT, ELONGM, PHIM, HM, XP, YP,}
+          \hbox{TDK, PMB, RH, WL, TLR, AOPRMS)}}}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{UTC date/time (Modified Julian Date, JD$-$2400000.5)} \\
+ \spec{DUT}{D}{$\Delta$UT:  UT1$-$UTC (UTC seconds)} \\
+ \spec{ELONGM}{D}{observer's mean longitude (radians, east +ve)} \\
+ \spec{PHIM}{D}{observer's mean geodetic latitude (radians)} \\
+ \spec{HM}{D}{observer's height above sea level (metres)} \\
+ \spec{XP,YP}{D}{polar motion \xy\ coordinates (radians)} \\
+ \spec{TDK}{D}{local ambient temperature (K; std=273.15D0)} \\
+ \spec{PMB}{D}{local atmospheric pressure (mb; std=1013.25D0)} \\
+ \spec{RH}{D}{local relative humidity (in the range 0D0\,--\,1D0)} \\
+ \spec{WL}{D}{effective wavelength ($\mu{\rm m}$, {\it e.g.}\ 0.55D0)} \\
+ \spec{TLR}{D}{tropospheric lapse rate (K per metre,
+                                              {\it e.g.}\ 0.0065D0)}
+}
+\args{RETURNED}
+{
+ \spec{AOPRMS}{D(14)}{star-independent apparent-to-observed parameters:} \\
+ \specel   {(1)}     {geodetic latitude (radians)} \\
+ \specel   {(2,3)}   {sine and cosine of geodetic latitude} \\
+ \specel   {(4)}     {magnitude of diurnal aberration vector} \\
+ \specel   {(5)}     {height (HM)} \\
+ \specel   {(6)}     {ambient temperature (TDK)} \\
+ \specel   {(7)}     {pressure (PMB)} \\
+ \specel   {(8)}     {relative humidity (RH)} \\
+ \specel   {(9)}     {wavelength (WL)} \\
+ \specel   {(10)}    {lapse rate (TLR)} \\
+ \specel   {(11,12)} {refraction constants A and B (radians)} \\
+ \specel   {(13)}    {longitude + eqn of equinoxes +
+                       ``sidereal $\Delta$UT'' (radians)} \\
+ \specel   {(14)}    {local apparent sidereal time (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item It is advisable to take great care with units, as even
+        unlikely values of the input parameters are accepted and
+        processed in accordance with the models used.
+  \item The DATE argument is UTC expressed as an MJD.  This is,
+        strictly speaking, wrong, because of leap seconds.  However,
+        as long as the $\Delta$UT and the UTC are consistent there
+        are no difficulties, except during a leap second.  In this
+        case, the start of the 61st second of the final minute should
+        begin a new MJD day and the old pre-leap $\Delta$UT should
+        continue to be used.  As the 61st second completes, the MJD
+        should revert to the start of the day as, simultaneously,
+        the $\Delta$UT changes by one second to its post-leap new value.
+  \item The $\Delta$UT (UT1$-$UTC) is tabulated in IERS circulars and
+        elsewhere.  It increases by exactly one second at the end of
+        each UTC leap second, introduced in order to keep $\Delta$UT
+        within $\pm$\tsec{0}{9}.  The ``sidereal $\Delta$UT'' which forms
+        part of AOPRMS(13) is the same quantity, but converted from solar
+        to sidereal seconds and expressed in radians.
+  \item IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.  The
+        longitude required by the present routine is {\bf east-positive},
+        in accordance with geographical convention (and right-handed).
+        In particular, note that the longitudes returned by the
+        sla\_OBS routine are west-positive (as in the {\it Astronomical
+        Almanac}\/ before 1984) and must be reversed in sign before use in
+        the present routine.
+  \item The polar coordinates XP,YP can be obtained from IERS
+        circulars and equivalent publications.  The
+        maximum amplitude is about \arcsec{0}{3}.  If XP,YP values
+        are unavailable, use XP=YP=0D0.  See page B60 of the 1988
+        {\it Astronomical Almanac}\/ for a definition of the two angles.
+  \item The height above sea level of the observing station, HM,
+        can be obtained from the {\it Astronomical Almanac}\/ (Section J
+        in the 1988 edition), or via the routine sla\_OBS.  If P,
+        the pressure in millibars, is available, an adequate
+        estimate of HM can be obtained from the following expression:
+        \begin{quote}
+         {\tt HM=-29.3D0*TSL*LOG(P/1013.25D0)}
+        \end{quote}
+        where TSL is the approximate sea-level air temperature in K
+        (see {\it Astrophysical Quantities}, C.W.Allen, 3rd~edition,
+        \S 52).  Similarly, if the pressure P is not known,
+        it can be estimated from the height of the observing
+        station, HM as follows:
+        \begin{quote}
+         {\tt P=1013.25D0*EXP(-HM/(29.3D0*TSL))}
+        \end{quote}
+        Note, however, that the refraction is nearly proportional to the
+        pressure and that an accurate P value is important for
+        precise work.
+  \item Repeated, computationally-expensive, calls to sla\_AOPPA for
+        times that are very close together can be avoided by calling
+        sla\_AOPPA just once and then using sla\_AOPPAT for the subsequent
+        times.  Fresh calls to sla\_AOPPA will be needed only when changes
+        in the precession have grown to unacceptable levels or when
+        anything affecting the refraction has changed.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AOPPAT}{Update Appt-to-Obs Parameters}
+{
+ \action{Recompute the sidereal time in the apparent to observed place
+         star-independent parameter block.}
+ \call{CALL sla\_AOPPAT (DATE, AOPRMS)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{UTC date/time (Modified Julian Date, JD$-$2400000.5)} \\
+ \spec{AOPRMS}{D(14)}{star-independent apparent-to-observed parameters:} \\
+ \specel{(1-12)}{not required} \\
+ \specel{(13)}{longitude + eqn of equinoxes +
+               ``sidereal $\Delta$UT'' (radians)} \\
+ \specel{(14)}{not required}
+}
+\args{RETURNED}
+{
+ \spec{AOPRMS}{D(14)}{star-independent apparent-to-observed parameters:} \\
+ \specel{(1-13)}{not changed} \\
+ \specel{(14)}{local apparent sidereal time (radians)}
+}
+\anote{For more information, see sla\_AOPPA.}
+%-----------------------------------------------------------------------
+\routine{SLA\_AOPQK}{Quick Appt-to-Observed}
+{
+ \action{Quick apparent to observed place (but see Note~8, below).}
+ \call{CALL sla\_AOPQK (RAP, DAP, AOPRMS, AOB, ZOB, HOB, DOB, ROB)}
+}
+\args{GIVEN}
+{
+ \spec{RAP,DAP}{D}{geocentric apparent \radec\ (radians)} \\
+ \spec{AOPRMS}{D(14)}{star-independent apparent-to-observed parameters:} \\
+ \specel{(1)}{geodetic latitude (radians)} \\
+ \specel{(2,3)}{sine and cosine of geodetic latitude} \\
+ \specel{(4)}{magnitude of diurnal aberration vector} \\
+ \specel{(5)}{height (metres)} \\
+ \specel{(6)}{ambient temperature (K)} \\
+ \specel{(7)}{pressure (mb)} \\
+ \specel{(8)}{relative humidity (0\,--\,1)} \\
+ \specel{(9)}{wavelength ($\mu{\rm m}$)} \\
+ \specel{(10)}{lapse rate (K per metre)} \\
+ \specel{(11,12)}{refraction constants A and B (radians)} \\
+ \specel{(13)}{longitude + eqn of equinoxes +
+               ``sidereal $\Delta$UT'' (radians)} \\
+ \specel{(14)}{local apparent sidereal time (radians)}
+}
+\args{RETURNED}
+{
+ \spec{AOB}{D}{observed azimuth (radians: N=0, E=$90^{\circ}$)} \\
+ \spec{ZOB}{D}{observed zenith distance (radians)} \\
+ \spec{HOB}{D}{observed Hour Angle (radians)} \\
+ \spec{DOB}{D}{observed Declination (radians)} \\
+ \spec{ROB}{D}{observed Right Ascension (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine returns zenith distance rather than elevation
+        in order to reflect the fact that no allowance is made for
+        depression of the horizon.
+  \item The accuracy of the result is limited by the corrections for
+        refraction.  Providing the meteorological parameters are
+        known accurately and there are no gross local effects, the
+        predicted azimuth and elevation should be within about
+        \arcsec{0}{1} for $\zeta<70^{\circ}$.  Even
+        at a topocentric zenith distance of
+        $90^{\circ}$, the accuracy in elevation should be better than
+        1~arcminute;  useful results are available for a further
+        $3^{\circ}$, beyond which the sla\_REFRO routine returns a
+        fixed value of the refraction.  The complementary
+        routines sla\_AOP (or sla\_AOPQK) and sla\_OAP (or sla\_OAPQK)
+        are self-consistent to better than 1~microarcsecond all over
+        the celestial sphere.
+  \item It is advisable to take great care with units, as even
+        unlikely values of the input parameters are accepted and
+        processed in accordance with the models used.
+  \item {\it Apparent}\/ \radec\ means the geocentric apparent right ascension
+        and declination, which is obtained from a catalogue mean place
+        by allowing for space motion, parallax, the Sun's gravitational
+        lens effect, annual aberration and precession-nutation.  For
+        star positions in the FK5 system ({\it i.e.}\ J2000), these effects can
+        be applied by means of the sla\_MAP {\it etc.}\ routines.  Starting from
+        other mean place systems, additional transformations will be
+        needed;  for example, FK4 ({\it i.e.}\ B1950) mean places would first
+        have to be converted to FK5, which can be done with the
+        sla\_FK425 {\it etc.}\ routines.
+  \item {\it Observed}\/ \azel\ means the position that would be seen by a
+        perfect theodolite located at the observer.  This is obtained
+        from the geocentric apparent \radec\ by allowing for Earth
+        orientation and diurnal aberration, rotating from equator
+        to horizon coordinates, and then adjusting for refraction.
+        The \hadec\ is obtained by rotating back into equatorial
+        coordinates, using the geodetic latitude corrected for polar
+        motion, and is the position that would be seen by a perfect
+        equatorial located at the observer and with its polar axis
+        aligned to the Earth's axis of rotation ({\it n.b.}\ not to the
+        refracted pole).  Finally, the $\alpha$ is obtained by subtracting
+        the {\it h}\/ from the local apparent ST.
+  \item To predict the required setting of a real telescope, the
+        observed place produced by this routine would have to be
+        adjusted for the tilt of the azimuth or polar axis of the
+        mounting (with appropriate corrections for mount flexures),
+        for non-perpendicularity between the mounting axes, for the
+        position of the rotator axis and the pointing axis relative
+        to it, for tube flexure, for gear and encoder errors, and
+        finally for encoder zero points.  Some telescopes would, of
+        course, exhibit other properties which would need to be
+        accounted for at the appropriate point in the sequence.
+  \item The star-independent apparent-to-observed-place parameters
+        in AOPRMS may be computed by means of the sla\_AOPPA routine.
+        If nothing has changed significantly except the time, the
+        sla\_AOPPAT routine may be used to perform the requisite
+        partial recomputation of AOPRMS.
+  \item At zenith distances beyond about $76^\circ$, the need for
+        special care with the corrections for refraction causes a
+        marked increase in execution time.  Moreover, the effect
+        gets worse with increasing zenith distance.  Adroit
+        programming in the calling application may allow the
+        problem to be reduced.  Prepare an alternative AOPRMS array,
+        computed for zero air-pressure;  this will disable the
+        refraction corrections and cause rapid execution.  Using
+        this AOPRMS array, a preliminary call to the present routine
+        will, depending on the application, produce a rough position
+        which may be enough to establish whether the full, slow
+        calculation (using the real AOPRMS array) is worthwhile.
+        For example, there would be no need for the full calculation
+        if the preliminary call had already established that the
+        source was well below the elevation limits for a particular
+        telescope.
+  \item The azimuths {\it etc.}\ used by the present routine are with
+        respect to the celestial pole.  Corrections to the terrestrial pole
+        can be computed using sla\_POLMO.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_ATMDSP}{Atmospheric Dispersion}
+{
+ \action{Apply atmospheric-dispersion adjustments to refraction coefficients.}
+ \call{CALL sla\_ATMDSP (TDK, PMB, RH, WL1, A1, B1, WL2, A2, B2)}
+}
+\args{GIVEN}
+{
+ \spec{TDK}{D}{ambient temperature at the observer (K)} \\
+ \spec{PMB}{D}{pressure at the observer (mb)} \\
+ \spec{RH}{D}{relative humidity at the observer (range 0\,--\,1)} \\
+ \spec{WL1}{D}{base wavelength ($\mu{\rm m}$)} \\
+ \spec{A1}{D}{refraction coefficient A for wavelength WL1 (radians)} \\
+ \spec{B1}{D}{refraction coefficient B for wavelength WL1 (radians)} \\
+ \spec{WL2}{D}{wavelength for which adjusted A,B required ($\mu{\rm m}$)}
+}
+\args{RETURNED}
+{
+ \spec{A2}{D}{refraction coefficient A for wavelength WL2 (radians)} \\
+ \spec{B2}{D}{refraction coefficient B for wavelength WL2 (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item To use this routine, first call sla\_REFCO specifying WL1 as the
+        wavelength.  This yields refraction coefficients A1, B1, correct
+        for that wavelength.  Subsequently, calls to sla\_ATMDSP specifying
+        different wavelengths will produce new, slightly adjusted
+        refraction coefficients A2, B2, which apply to the specified wavelength.
+  \item Most of the atmospheric dispersion happens between $0.7\,\mu{\rm m}$
+        and the UV atmospheric cutoff, and the effect increases strongly
+        towards the UV end.  For this reason a blue reference wavelength
+        is recommended, for example $0.4\,\mu{\rm m}$.
+  \item The accuracy, for this set of conditions: \\[1pc]
+   \hspace*{5ex} \begin{tabular}{rcl}
+        height above sea level & ~ & 2000\,m \\
+                      latitude & ~ & $29^\circ$ \\
+                      pressure & ~ & 793\,mb \\
+                   temperature & ~ & $290^\circ$\,K \\
+                      humidity & ~ & 0.5 (50\%) \\
+                    lapse rate & ~ & $0.0065^\circ m^{-1}$ \\
+          reference wavelength & ~ & $0.4\,\mu{\rm m}$ \\
+                star elevation & ~ & $15^\circ$ \\
+                  \end{tabular}\\[1pc]
+        is about 2.5\,mas RMS between 0.3 and $1.0\,\mu{\rm m}$, and stays
+        within 4\,mas for the whole range longward of $0.3\,\mu{\rm m}$
+        (compared with a total dispersion from 0.3 to $20\,\mu{\rm m}$
+        of about \arcseci{11}).  These errors are typical for ordinary
+        conditions;  in extreme conditions values a few times this size
+        may occur.
+  \item If either wavelength exceeds $100\,\mu{\rm m}$, the radio case
+        is assumed and the returned refraction coefficients are the
+        same as the given ones. Note that radio refraction coefficients
+        cannot be turned into optical values using this routine, nor
+        vice versa.
+  \item The algorithm consists of calculation of the refractivity of the
+        air at the observer for the two wavelengths, using the methods
+        of the sla\_REFRO routine, and then scaling of the two refraction
+        coefficients according to classical refraction theory.  This
+        amounts to scaling the A coefficient in proportion to $(\mu-1)$ and
+        the B coefficient almost in the same ratio (see R.M.Green,
+        {\it Spherical Astronomy,}\/ Cambridge University Press, 1985).
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_AV2M}{Rotation Matrix from Axial Vector}
+{
+ \action{Form the rotation matrix corresponding to a given axial vector
+         (single precision).}
+ \call{CALL sla\_AV2M (AXVEC, RMAT)}
+}
+\args{GIVEN}
+{
+ \spec{AXVEC}{R(3)}{axial vector (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RMAT}{R(3,3)}{rotation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A rotation matrix describes a rotation about some
+        arbitrary axis, called the Euler axis.  The
+        {\it axial vector} supplied to this routine
+        has the same direction as the Euler axis, and its
+        magnitude is the amount of rotation in radians.
+  \item If AXVEC is null, the unit matrix is returned.
+  \item The reference frame rotates clockwise as seen looking along
+        the axial vector from the origin.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_BEAR}{Direction Between Points on a Sphere}
+{
+ \action{Returns the bearing (position angle) of one point on a
+         sphere seen from another (single precision).}
+ \call{R~=~sla\_BEAR (A1, B1, A2, B2)}
+}
+\args{GIVEN}
+{
+ \spec{A1,B1}{R}{spherical coordinates of one point} \\
+ \spec{A2,B2}{R}{spherical coordinates of the other point}
+}
+\args{RETURNED}
+{
+ \spec{sla\_BEAR}{R}{bearing from first point to second}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The spherical coordinates are \radec,
+       $[\lambda,\phi]$ {\it etc.}, in radians.
+ \item The result is the bearing (position angle), in radians,
+       of point [A2,B2] as seen
+       from point [A1,B1].  It is in the range $\pm \pi$.  The sense
+       is such that if [A2,B2]
+       is a small distance due east of [A1,B1] the result
+       is about $+\pi/2$. Zero is returned
+       if the two points are coincident.
+ \item If either B-coordinate is outside the range $\pm\pi/2$, the
+       result may correspond to ``the long way round''.
+ \item The routine sla\_PAV performs an equivalent function except
+       that the points are specified in the form of Cartesian unit
+       vectors.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CAF2R}{Deg,Arcmin,Arcsec to Radians}
+{
+ \action{Convert degrees, arcminutes, arcseconds to radians
+         (single precision).}
+ \call{CALL sla\_CAF2R (IDEG, IAMIN, ASEC, RAD, J)}
+}
+\args{GIVEN}
+{
+ \spec{IDEG}{I}{degrees} \\
+ \spec{IAMIN}{I}{arcminutes} \\
+ \spec{ASEC}{R}{arcseconds}
+}
+\args{RETURNED}
+{
+ \spec{RAD}{R}{angle in radians} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 1 = IDEG outside range 0$-$359} \\
+ \spec{}{}{\hspace{1.5em} 2 = IAMIN outside range 0$-$59} \\
+ \spec{}{}{\hspace{1.5em} 3 = ASEC outside range 0$-$59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CALDJ}{Calendar Date to MJD}
+{
+ \action{Gregorian Calendar to Modified Julian Date, with century default.}
+ \call{CALL sla\_CALDJ (IY, IM, ID, DJM, J)}
+}
+\args{GIVEN}
+{
+ \spec{IY,IM,ID}{I}{year, month, day in Gregorian calendar}
+}
+\args{RETURNED}
+{
+ \spec{DJM}{D}{modified Julian Date (JD$-$2400000.5) for $0^{\rm h}$} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = bad year   (MJD not computed)} \\
+ \spec{}{}{\hspace{1.5em} 2 = bad month  (MJD not computed)} \\
+ \spec{}{}{\hspace{1.5em} 3 = bad day    (MJD computed)} \\
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine supports the {\it century default}\/ feature.
+        Acceptable years are:
+        \begin{itemize}
+         \item 00-49, interpreted as 2000\,--\,2049,
+         \item 50-99, interpreted as 1950\,--\,1999, and
+         \item 100 upwards, interpreted literally.
+        \end{itemize}
+        For 1-100AD use the routine sla\_CLDJ instead.
+  \item For year $n$BC use IY = $-(n-1)$.
+  \item When an invalid year or month is supplied (status J~=~1~or~2)
+        the MJD is {\bf not} computed.  When an invalid day is supplied
+        (status J~=~3) the MJD {\bf is} computed.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CALYD}{Calendar to Year, Day}
+{
+ \action{Gregorian calendar date to year and day in year, in a Julian
+         calendar aligned to the 20th/21st century Gregorian calendar,
+         with century default.}
+ \call{CALL sla\_CALYD (IY, IM, ID, NY, ND, J)}
+}
+\args{GIVEN}
+{
+ \spec{IY,IM,ID}{I}{year, month, day in Gregorian calendar:
+                    year may optionally omit the century}
+}
+\args{RETURNED}
+{
+ \spec{NY}{I}{year (re-aligned Julian calendar)} \\
+ \spec{ND}{I}{day in year (1 = January 1st)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em}  0 = OK} \\
+ \spec{}{}{\hspace{1.5em}  1 = bad year (before $-4711$)} \\
+ \spec{}{}{\hspace{1.5em}  2 = bad month} \\
+ \spec{}{}{\hspace{1.5em}  3 = bad day}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine supports the {\it century default}\/ feature.
+        Acceptable years are:
+        \begin{itemize}
+         \item 00-49, interpreted as 2000\,--\,2049,
+         \item 50-99, interpreted as 1950\,--\,1999, and
+         \item other years after $-4712$, interpreted literally.
+        \end{itemize}
+        Use sla\_CLYD for years before 100AD.
+  \item The purpose of sla\_CALDJ is to support
+        sla\_EARTH, sla\_MOON and sla\_ECOR.
+  \item Between 1900~March~1 and 2100~February~28 it returns answers
+        which are consistent with the ordinary Gregorian calendar.
+        Outside this range there will be a discrepancy which increases
+        by one day for every non-leap century year.
+  \item When an invalid year or month is supplied (status J~=~1 or J~=~2)
+        the results are {\bf not} computed.  When a day is
+        supplied which is outside the conventional range (status J~=~3)
+        the results {\bf are} computed.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CC2S}{Cartesian to Spherical}
+{
+ \action{Cartesian coordinates to spherical coordinates (single precision).}
+ \call{CALL sla\_CC2S (V, A, B)}
+}
+\args{GIVEN}
+{
+ \spec{V}{R(3)}{\xyz\ vector}
+}
+\args{RETURNED}
+{
+ \spec{A,B}{R}{spherical coordinates in radians}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The spherical coordinates are longitude (+ve anticlockwise
+        looking from the +ve latitude pole) and latitude.  The
+        Cartesian coordinates are right handed, with the {\it x}-axis
+        at zero longitude and latitude, and the {\it z}-axis at the
+        +ve latitude pole.
+  \item If V is null, zero A and B are returned.
+  \item At either pole, zero A is returned.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CC62S}{Cartesian 6-Vector to Spherical}
+{
+ \action{Conversion of position \& velocity in Cartesian coordinates
+         to spherical coordinates (single precision).}
+ \call{CALL sla\_CC62S (V, A, B, R, AD, BD, RD)}
+}
+\args{GIVEN}
+{
+ \spec{V}{R(6)}{\xyzxyzd}
+}
+\args{RETURNED}
+{
+ \spec{A}{R}{longitude (radians) -- for example $\alpha$} \\
+ \spec{B}{R}{latitude (radians) -- for example $\delta$} \\
+ \spec{R}{R}{radial coordinate} \\
+ \spec{AD}{R}{longitude derivative (radians per unit time)} \\
+ \spec{BD}{R}{latitude derivative (radians per unit time)} \\
+ \spec{RD}{R}{radial derivative}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CD2TF}{Days to Hour,Min,Sec}
+{
+ \action{Convert an interval in days to hours, minutes, seconds
+         (single precision).}
+ \call{CALL sla\_CD2TF (NDP, DAYS, SIGN, IHMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of seconds} \\
+ \spec{DAYS}{R}{interval in days}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IHMSF}{I(4)}{hours, minutes, seconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size of
+        DAYS, the format of REAL floating-point numbers on the target
+        machine, and the risk of overflowing IHMSF(4).  On some
+        architectures, for DAYS up to 1.0,
+        the available floating-point
+        precision corresponds roughly to NDP=3.  This is well
+        below the ultimate limit of NDP=9 set by the capacity of a
+        typical 32-bit IHMSF(4).
+  \item The absolute value of DAYS may exceed 1.0.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where DAYS is very nearly 1.0 and rounds up to 24~hours,
+        by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+\end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CLDJ}{Calendar to MJD}
+{
+ \action{Gregorian Calendar to Modified Julian Date.}
+ \call{CALL sla\_CLDJ (IY, IM, ID, DJM, J)}
+}
+\args{GIVEN}
+{
+ \spec{IY,IM,ID}{I}{year, month, day in Gregorian calendar}
+}
+\args{RETURNED}
+{
+ \spec{DJM}{D}{modified Julian Date (JD$-$2400000.5) for $0^{\rm h}$} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = bad year} \\
+ \spec{}{}{\hspace{1.5em} 2 = bad month} \\
+ \spec{}{}{\hspace{1.5em} 3 = bad day}
+}
+\notes
+{
+ \begin{enumerate}
+  \item When an invalid year or month is supplied (status J~=~1~or~2)
+        the MJD is {\bf not} computed.  When an invalid day is supplied
+        (status J~=~3) the MJD {\bf is} computed.
+  \item The year must be $-$4699 ({\it i.e.}\ 4700BC) or later.
+        For year $n$BC use IY = $-(n-1)$.
+  \item An alternative to the present routine is sla\_CALDJ, which
+        accepts a year with the century missing.
+ \end{enumerate}
+}
+\aref{The algorithm is adapted from Hatcher,
+      {\it Q.\,Jl.\,R.\,astr.\,Soc.}\ (1984) {\bf 25}, 53-55.}
+%-----------------------------------------------------------------------
+\routine{SLA\_CLYD}{Calendar to Year, Day}
+{
+ \action{Gregorian calendar date to year and day in year, in a Julian
+         calendar aligned to the 20th/21st century Gregorian calendar.}
+ \call{CALL sla\_CLYD (IY, IM, ID, NY, ND, J)}
+}
+\args{GIVEN}
+{
+ \spec{IY,IM,ID}{I}{year, month, day in Gregorian calendar}
+}
+\args{RETURNED}
+{
+ \spec{NY}{I}{year (re-aligned Julian calendar)} \\
+ \spec{ND}{I}{day in year (1 = January 1st)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em}  0 = OK} \\
+ \spec{}{}{\hspace{1.5em}  1 = bad year (before $-4711$)} \\
+ \spec{}{}{\hspace{1.5em}  2 = bad month} \\
+ \spec{}{}{\hspace{1.5em}  3 = bad day}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The purpose of sla\_CLYD is to support sla\_EARTH,
+        sla\_MOON and sla\_ECOR.
+  \item Between 1900~March~1 and 2100~February~28 it returns answers
+        which are consistent with the ordinary Gregorian calendar.
+        Outside this range there will be a discrepancy which increases
+        by one day for every non-leap century year.
+  \item When an invalid year or month is supplied (status J~=~1 or J~=~2)
+        the results are {\bf not} computed.  When a day is
+        supplied which is outside the conventional range (status J~=~3)
+        the results {\bf are} computed.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_COMBN}{Next Combination}
+{
+ \action{Generate the next combination, a subset of a specified size chosen
+         from a specified number of items.}
+ \call{CALL sla\_COMBN (NSEL, NCAND, LIST, J)}
+}
+\args{GIVEN}
+{
+ \spec{NSEL}{I}{number of items (subset size)} \\
+ \spec{NCAND}{I}{number of candidates (set size)}
+}
+\args{GIVEN and RETURNED}
+{
+ \spec{LIST}{I(NSEL)}{latest combination, LIST(1)=0 to initialize}
+}
+\args{RETURNED}
+{
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal NSEL or NCAND} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $+$1 = no more combinations available}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NSEL and NCAND must both be at least 1, and NSEL must be less
+        than or equal to NCAND.
+  \item This routine returns, in the LIST array, a subset of NSEL integers
+        chosen from the range 1 to NCAND inclusive, in ascending order.
+        Before calling the routine for the first time, the caller must set
+        the first element of the LIST array to zero (any value less than 1
+        will do) to cause initialization.
+  \item The first combination to be generated is:
+        \begin{verse}
+            LIST(1)=1, LIST(2)=2, \ldots, LIST(NSEL)=NSEL
+        \end{verse}
+        This is also the combination returned for the ``finished'' (J=1) case.
+        The final permutation to be generated is:
+        \begin{verse}
+           LIST(1)=NCAND, LIST(2)=NCAND$-$1, \ldots, \\
+           ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~LIST(NSEL)=NCAND$-$NSEL+1
+        \end{verse}
+  \item If the ``finished'' (J=1) status is ignored, the routine
+        continues to deliver combinations, the pattern repeating
+        every NCAND!/(NSEL!(NCAND$-$NSEL)!) calls.
+  \item The algorithm is by R.\,F.\,Warren-Smith (private communication).
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CR2AF}{Radians to Deg,Arcmin,Arcsec}
+{
+ \action{Convert an angle in radians to degrees, arcminutes,
+         arcseconds (single precision).}
+ \call{CALL sla\_CR2AF (NDP, ANGLE, SIGN, IDMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of arcseconds} \\
+ \spec{ANGLE}{R}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IDMSF}{I(4)}{degrees, arcminutes, arcseconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size of
+        ANGLE, the format of REAL floating-point numbers on the target
+        machine, and the risk of overflowing IDMSF(4).  On some
+        architectures, for ANGLE up to 2pi,
+        the available floating-point
+        precision corresponds roughly to NDP=3.  This is well
+        below the ultimate limit of NDP=9 set by the capacity of a
+        typical 32-bit IDMSF(4).
+  \item The absolute value of ANGLE may exceed $2\pi$.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where ANGLE is very nearly $2\pi$ and rounds up to $360^{\circ}$,
+        by testing for IDMSF(1)=360 and setting IDMSF(1-4) to zero.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CR2TF}{Radians to Hour,Min,Sec}
+{
+ \action{Convert an angle in radians to hours, minutes, seconds
+         (single precision).}
+ \call{CALL sla\_CR2TF (NDP, ANGLE, SIGN, IHMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of seconds} \\
+ \spec{ANGLE}{R}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IHMSF}{I(4)}{hours, minutes, seconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size of
+        ANGLE, the format of REAL floating-point numbers on the target
+        machine, and the risk of overflowing IHMSF(4).  On some
+        architectures, for ANGLE up to 2pi,
+        the available floating-point
+        precision corresponds roughly to NDP=3.  This is well below
+        the ultimate limit of NDP=9 set by the capacity of a typical
+        32-bit IHMSF(4).
+  \item The absolute value of ANGLE may exceed $2\pi$.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where ANGLE is very nearly $2\pi$ and rounds up to 24~hours,
+        by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+\end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CS2C}{Spherical to Cartesian}
+{
+ \action{Spherical coordinates to Cartesian coordinates (single precision).}
+ \call{CALL sla\_CS2C (A, B, V)}
+}
+\args{GIVEN}
+{
+ \spec{A,B}{R}{spherical coordinates in radians: \radec\ {\it etc.}}
+}
+\args{RETURNED}
+{
+ \spec{V}{R(3)}{\xyz\ unit vector}
+}
+\anote{The spherical coordinates are longitude (+ve anticlockwise
+       looking from the +ve latitude pole) and latitude.  The
+       Cartesian coordinates are right handed, with the {\it x}-axis
+       at zero longitude and latitude, and the {\it z}-axis at the
+       +ve latitude pole.}
+%-----------------------------------------------------------------------
+\routine{SLA\_CS2C6}{Spherical Pos/Vel to Cartesian}
+{
+ \action{Conversion of position \& velocity in spherical coordinates
+         to Cartesian coordinates (single precision).}
+ \call{CALL sla\_CS2C6 (A, B, R, AD, BD, RD, V)}
+}
+\args{GIVEN}
+{
+ \spec{A}{R}{longitude (radians) -- for example $\alpha$} \\
+ \spec{B}{R}{latitude (radians) -- for example $\delta$} \\
+ \spec{R}{R}{radial coordinate} \\
+ \spec{AD}{R}{longitude derivative (radians per unit time)} \\
+ \spec{BD}{R}{latitude derivative (radians per unit time)} \\
+ \spec{RD}{R}{radial derivative}
+}
+\args{RETURNED}
+{
+ \spec{V}{R(6)}{\xyzxyzd}
+}
+\anote{The spherical coordinates are longitude (+ve anticlockwise
+       looking from the +ve latitude pole) and latitude.  The
+       Cartesian coordinates are right handed, with the {\it x}-axis
+       at zero longitude and latitude, and the {\it z}-axis at the
+       +ve latitude pole.}
+%-----------------------------------------------------------------------
+\routine{SLA\_CTF2D}{Hour,Min,Sec to Days}
+{
+ \action{Convert hours, minutes, seconds to days (single precision).}
+ \call{CALL sla\_CTF2D (IHOUR, IMIN, SEC, DAYS, J)}
+}
+\args{GIVEN}
+{
+ \spec{IHOUR}{I}{hours} \\
+ \spec{IMIN}{I}{minutes} \\
+ \spec{SEC}{R}{seconds}
+}
+\args{RETURNED}
+{
+ \spec{DAYS}{R}{interval in days} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = IHOUR outside range 0-23} \\
+ \spec{}{}{\hspace{1.5em} 2 = IMIN outside range 0-59} \\
+ \spec{}{}{\hspace{1.5em} 3 = SEC outside range 0-59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_CTF2R}{Hour,Min,Sec to Radians}
+{
+ \action{Convert hours, minutes, seconds to radians (single precision).}
+ \call{CALL sla\_CTF2R (IHOUR, IMIN, SEC, RAD, J)}
+}
+\args{GIVEN}
+{
+ \spec{IHOUR}{I}{hours} \\
+ \spec{IMIN}{I}{minutes} \\
+ \spec{SEC}{R}{seconds}
+}
+\args{RETURNED}
+{
+ \spec{RAD}{R}{angle in radians} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = IHOUR outside range 0-23} \\
+ \spec{}{}{\hspace{1.5em} 2 = IMIN outside range 0-59} \\
+ \spec{}{}{\hspace{1.5em} 3 = SEC outside range 0-59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DAF2R}{Deg,Arcmin,Arcsec to Radians}
+{
+ \action{Convert degrees, arcminutes, arcseconds to radians
+  (double precision).}
+ \call{CALL sla\_DAF2R (IDEG, IAMIN, ASEC, RAD, J)}
+}
+\args{GIVEN}
+{
+ \spec{IDEG}{I}{degrees} \\
+ \spec{IAMIN}{I}{arcminutes} \\
+ \spec{ASEC}{D}{arcseconds}
+}
+\args{RETURNED}
+{
+ \spec{RAD}{D}{angle in radians} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 1 = IDEG outside range 0$-$359} \\
+ \spec{}{}{\hspace{1.5em} 2 = IAMIN outside range 0$-$59} \\
+ \spec{}{}{\hspace{1.5em} 3 = ASEC outside range 0$-$59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DAFIN}{Sexagesimal character string to angle}
+{
+ \action{Decode a free-format sexagesimal string (degrees, arcminutes,
+         arcseconds) into a double precision floating point
+         number (radians).}
+ \call{CALL sla\_DAFIN (STRING, NSTRT, DRESLT, JF)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C*(*)}{string containing deg, arcmin, arcsec fields} \\
+ \spec{NSTRT}{I}{pointer to start of decode (beginning of STRING = 1)}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{advanced past the decoded angle} \\
+ \spec{DRESLT}{D}{angle in radians} \\
+ \spec{JF}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em}   0 = OK} \\
+ \spec{}{}{\hspace{0.7em} $+1$ = default, DRESLT unchanged (note 2)} \\
+ \spec{}{}{\hspace{0.7em} $-1$ = bad degrees (note 3)} \\
+ \spec{}{}{\hspace{0.7em} $-2$ = bad arcminutes (note 3)} \\
+ \spec{}{}{\hspace{0.7em} $-3$ = bad arcseconds (note 3)} \\
+}
+\goodbreak
+\setlength{\oldspacing}{\topsep}
+\setlength{\topsep}{0.3ex}
+\begin{description}
+ \item [EXAMPLE]: \\ [1.5ex]
+  \begin{tabular}{lll}
+   {\it argument} & {\it before} & {\it after} \\ \\
+   STRING & $'$\verb*}-57 17 44.806  12 34 56.7}$'$ & unchanged \\
+   NSTRT & 1 & 16 ({\it i.e.}\ pointing to 12...) \\
+   RESLT & - & $-1.00000${\tt D0} \\
+   JF & - & 0
+  \end{tabular}
+ \item A further call to sla\_DAFIN, without adjustment of NSTRT, will
+       decode the second angle, \dms{12}{34}{56}{7}.
+\end{description}
+\setlength{\topsep}{\oldspacing}
+\notes
+{
+ \begin{enumerate}
+  \item The first three ``fields'' in STRING are degrees, arcminutes,
+   arcseconds, separated by spaces or commas.  The degrees field
+   may be signed, but not the others.  The decoding is carried
+   out by the sla\_DFLTIN routine and is free-format.
+  \item Successive fields may be absent, defaulting to zero.  For
+   zero status, the only combinations allowed are degrees alone,
+   degrees and arcminutes, and all three fields present.  If all
+   three fields are omitted, a status of +1 is returned and DRESLT is
+   unchanged.  In all other cases DRESLT is changed.
+  \item Range checking:
+   \begin{itemize}
+    \item The degrees field is not range checked.  However, it is
+     expected to be integral unless the other two fields are absent.
+    \item The arcminutes field is expected to be 0-59, and integral if
+     the arcseconds field is present.  If the arcseconds field
+     is absent, the arcminutes is expected to be 0-59.9999...
+    \item The arcseconds field is expected to be 0-59.9999...
+    \item Decoding continues even when a check has failed.  Under these
+     circumstances the field takes the supplied value, defaulting to
+     zero, and the result DRESLT is computed and returned.
+   \end{itemize}
+   \item Further fields after the three expected ones are not treated as
+    an error.  The pointer NSTRT is left in the correct state for
+    further decoding with the present routine or with sla\_DFLTIN
+    {\it etc}.  See the example, above.
+   \item If STRING contains hours, minutes, seconds instead of
+    degrees {\it etc},
+    or if the required units are turns (or days) instead of radians,
+    the result DRESLT should be multiplied as follows: \\ [1.5ex]
+    \begin{tabular}{lll}
+    {\it for STRING} & {\it to obtain} & {\it multiply DRESLT by} \\ \\
+    ${\circ}$~~\raisebox{-0.7ex}{$'$}~~\raisebox{-0.7ex}{$''$}
+     & radians & $1.0D0$ \\
+    ${\circ}$~~\raisebox{-0.7ex}{$'$}~~\raisebox{-0.7ex}{$''$}
+     & turns & $1/{2 \pi} = 0.1591549430918953358D0$ \\
+    h m s & radians & $15.0D0$ \\
+    h m s & days & $15/{2\pi} = 2.3873241463784300365D0$
+   \end{tabular}
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_DAT}{TAI$-$UTC}
+{
+ \action{Increment to be applied to Coordinated Universal Time UTC to give
+         International Atomic Time TAI.}
+ \call{D~=~sla\_DAT (UTC)}
+}
+\args{GIVEN}
+{
+ \spec{UTC}{D}{UTC date as a modified JD (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DAT}{D}{TAI$-$UTC in seconds}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The UTC is specified to be a date rather than a time to indicate
+       that care needs to be taken not to specify an instant which lies
+       within a leap second.  Though in most cases UTC can include the
+       fractional part, correct behaviour on the day of a leap second
+       can be guaranteed only up to the end of the second
+       $23^{\rm h}\,59^{\rm m}\,59^{\rm s}$.
+ \item For epochs from 1961 January 1 onwards, the expressions from the
+       file {\tt ftp://maia.usno.navy.mil/ser7/tai-utc.dat} are used.
+       A 5ms time step at 1961~January~1 is taken from 2.58.1 (p87) of
+       the 1992 Explanatory Supplement.
+ \item UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper
+       to call the routine with an earlier epoch.  However, if this
+       is attempted, the TAI$-$UTC expression for the year 1960 is used.
+ \item This routine has to be updated on each occasion that a
+       leap second is announced, and programs using it relinked.
+       Refer to the program source code for information on when the
+       most recent leap second was added.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DAV2M}{Rotation Matrix from Axial Vector}
+{
+ \action{Form the rotation matrix corresponding to a given axial vector
+         (double precision).}
+ \call{CALL sla\_DAV2M (AXVEC, RMAT)}
+}
+\args{GIVEN}
+{
+ \spec{AXVEC}{D(3)}{axial vector (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RMAT}{D(3,3)}{rotation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A rotation matrix describes a rotation about some
+        arbitrary axis, called the Euler axis.  The
+        {\it axial vector} supplied to this routine
+        has the same direction as the Euler axis, and its
+        magnitude is the amount of rotation in radians.
+  \item If AXVEC is null, the unit matrix is returned.
+  \item The reference frame rotates clockwise as seen looking along
+        the axial vector from the origin.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DBEAR}{Direction Between Points on a Sphere}
+{
+ \action{Returns the bearing (position angle) of one point on a
+         sphere relative to another (double precision).}
+ \call{D~=~sla\_DBEAR (A1, B1, A2, B2)}
+}
+\args{GIVEN}
+{
+ \spec{A1,B1}{D}{spherical coordinates of one point} \\
+ \spec{A2,B2}{D}{spherical coordinates of the other point}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DBEAR}{D}{bearing from first point to second}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The spherical coordinates are \radec,
+       $[\lambda,\phi]$ {\it etc.}, in radians.
+ \item The result is the bearing (position angle), in radians,
+       of point [A2,B2] as seen
+       from point [A1,B1].  It is in the range $\pm \pi$.  The sense
+       is such that if [A2,B2]
+       is a small distance due east of [A1,B1] the result
+       is about $+\pi/2$. Zero is returned
+       if the two points are coincident.
+ \item If either B-coordinate is outside the range $\pm\pi/2$, the
+       result may correspond to ``the long way round''.
+ \item The routine sla\_DPAV performs an equivalent function except
+       that the points are specified in the form of Cartesian
+       vectors.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DBJIN}{Decode String to B/J Epoch (DP)}
+{
+ \action{Decode a character string into a DOUBLE PRECISION number,
+         with special provision for Besselian and Julian epochs.
+         The string syntax is as for sla\_DFLTIN, prefixed by
+         an optional `B' or `J'.}
+ \call{CALL sla\_DBJIN (STRING, NSTRT, DRESLT, J1, J2)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C}{string containing field to be decoded} \\
+ \spec{NSTRT}{I}{pointer to first character of field in string}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{incremented past the decoded field} \\
+ \spec{DRESLT}{D}{result} \\
+ \spec{J1}{I}{DFLTIN status:} \\
+ \spec{}{}{\hspace{0.7em} $-$1 = $-$OK} \\
+ \spec{}{}{\hspace{1.5em}   0 = +OK} \\
+ \spec{}{}{\hspace{1.5em}   1 = null field} \\
+ \spec{}{}{\hspace{1.5em}   2 = error} \\
+ \spec{J2}{I}{syntax flag:} \\
+ \spec{}{}{\hspace{1.5em}   0 = normal DFLTIN syntax} \\
+ \spec{}{}{\hspace{1.5em}   1 = `B' or `b'} \\
+ \spec{}{}{\hspace{1.5em}   2 = `J' or `j'}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The purpose of the syntax extensions is to help cope with mixed
+        FK4 and FK5 data, allowing fields such as `B1950' or `J2000'
+        to be decoded.
+  \item In addition to the syntax accepted by sla\_DFLTIN,
+        the following two extensions are recognized by sla\_DBJIN:
+        \begin{enumerate}
+         \item A valid non-null field preceded by the character `B'
+               (or `b') is accepted.
+         \item A valid non-null field preceded by the character `J'
+               (or `j') is accepted.
+         \end{enumerate}
+  \item The calling program is told of the `B' or `J' through an
+        supplementary status argument.  The rest of
+        the arguments are as for sla\_DFLTIN.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DC62S}{Cartesian 6-Vector to Spherical}
+{
+ \action{Conversion of position \& velocity in Cartesian coordinates
+         to spherical coordinates (double precision).}
+ \call{CALL sla\_DC62S (V, A, B, R, AD, BD, RD)}
+}
+\args{GIVEN}
+{
+ \spec{V}{D(6)}{\xyzxyzd}
+}
+\args{RETURNED}
+{
+ \spec{A}{D}{longitude (radians)} \\
+ \spec{B}{D}{latitude (radians)} \\
+ \spec{R}{D}{radial coordinate} \\
+ \spec{AD}{D}{longitude derivative (radians per unit time)} \\
+ \spec{BD}{D}{latitude derivative (radians per unit time)} \\
+ \spec{RD}{D}{radial derivative}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DCC2S}{Cartesian to Spherical}
+{
+ \action{Cartesian coordinates to spherical coordinates (double precision).}
+ \call{CALL sla\_DCC2S (V, A, B)}
+}
+\args{GIVEN}
+{
+ \spec{V}{D(3)}{\xyz\ vector}
+}
+\args{RETURNED}
+{
+ \spec{A,B}{D}{spherical coordinates in radians}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The spherical coordinates are longitude (+ve anticlockwise
+        looking from the +ve latitude pole) and latitude.  The
+        Cartesian coordinates are right handed, with the {\it x}-axis
+        at zero longitude and latitude, and the {\it z}-axis at the
+        +ve latitude pole.
+  \item If V is null, zero A and B are returned.
+  \item At either pole, zero A is returned.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DCMPF}{Interpret Linear Fit}
+{
+ \action{Decompose an \xy\ linear fit into its constituent parameters:
+         zero points, scales, nonperpendicularity and orientation.}
+ \call{CALL sla\_DCMPF (COEFFS,XZ,YZ,XS,YS,PERP,ORIENT)}
+}
+\args{GIVEN}
+{
+ \spec{COEFFS}{D(6)}{transformation coefficients (see note)}
+}
+\args{RETURNED}
+{
+ \spec{XZ}{D}{{\it x} zero point} \\
+ \spec{YZ}{D}{{\it y} zero point} \\
+ \spec{XS}{D}{{\it x} scale} \\
+ \spec{YS}{D}{{\it y} scale} \\
+ \spec{PERP}{D}{nonperpendicularity (radians)} \\
+ \spec{ORIENT}{D}{orientation (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The model relates two sets of \xy\ coordinates as follows.
+        Naming the six elements of COEFFS $a,b,c,d,e$ \& $f$,
+        the model transforms coordinates $[x_{1},y_{1}\,]$ into coordinates
+        $[x_{2},y_{2}\,]$ as follows:
+        \begin{verse}
+         $x_{2} = a + bx_{1} + cy_{1}$ \\
+         $y_{2} = d + ex_{1} + fy_{1}$
+        \end{verse}
+        The sla\_DCMPF routine decomposes this transformation
+        into four steps:
+        \begin{enumerate}
+        \item Zero points:
+              \begin{verse}
+               $x' = x_{1} + {\rm XZ}$ \\
+               $y' = y_{1} + {\rm YZ}$
+              \end{verse}
+        \item Scales:
+              \begin{verse}
+               $x'' = x' {\rm XS}$ \\
+               $y'' = y' {\rm YS}$
+              \end{verse}
+        \item Nonperpendicularity:
+              \begin{verse}
+               $x''' = + x'' \cos {\rm PERP}/2 + y'' \sin {\rm PERP}/2$ \\
+               $y''' = + x'' \sin {\rm PERP}/2 + y'' \cos {\rm PERP}/2$
+              \end{verse}
+        \item Orientation:
+              \begin{verse}
+               $x_{2} = + x''' \cos {\rm ORIENT} +
+                          y''' \sin {\rm ORIENT}$ \\
+               $y_{2} = - x''' \sin {\rm ORIENT} +
+                          y''' \cos {\rm ORIENT}$
+              \end{verse}
+        \end{enumerate}
+  \item See also sla\_FITXY, sla\_PXY, sla\_INVF, sla\_XY2XY.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DCS2C}{Spherical to Cartesian}
+{
+ \action{Spherical coordinates to Cartesian coordinates (double precision).}
+ \call{CALL sla\_DCS2C (A, B, V)}
+}
+\args{GIVEN}
+{
+ \spec{A,B}{D}{spherical coordinates in radians: \radec\ {\it etc.}}
+}
+\args{RETURNED}
+{
+ \spec{V}{D(3)}{\xyz\ unit vector}
+}
+\anote{The spherical coordinates are longitude (+ve anticlockwise
+       looking from the +ve latitude pole) and latitude.  The
+       Cartesian coordinates are right handed, with the {\it x}-axis
+       at zero longitude and latitude, and the {\it z}-axis at the
+       +ve latitude pole.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DD2TF}{Days to Hour,Min,Sec}
+{
+ \action{Convert an interval in days into hours, minutes, seconds
+         (double precision).}
+ \call{CALL sla\_DD2TF (NDP, DAYS, SIGN, IHMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of seconds} \\
+ \spec{DAYS}{D}{interval in days}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IHMSF}{I(4)}{hours, minutes, seconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size
+        of DAYS, the format of DOUBLE PRECISION floating-point numbers
+        on the target machine, and the risk of overflowing IHMSF(4).
+        On some architectures, for DAYS up to 1D0, the available
+        floating-point precision corresponds roughly to NDP=12.
+        However, the practical limit is NDP=9, set by the capacity of
+        a typical 32-bit IHMSF(4).
+  \item The absolute value of DAYS may exceed 1D0.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where DAYS is very nearly 1D0 and rounds up to 24~hours,
+        by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+\end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DE2H}{$h,\delta$ to Az,El}
+{
+ \action{Equatorial to horizon coordinates
+         (double precision).}
+ \call{CALL sla\_DE2H (HA, DEC, PHI, AZ, EL)}
+}
+\args{GIVEN}
+{
+ \spec{HA}{D}{hour angle (radians)} \\
+ \spec{DEC}{D}{declination (radians)} \\
+ \spec{PHI}{D}{latitude (radians)}
+}
+\args{RETURNED}
+{
+ \spec{AZ}{D}{azimuth (radians)} \\
+ \spec{EL}{D}{elevation (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Azimuth is returned in the range $0\!-\!2\pi$;  north is zero,
+        and east is $+\pi/2$.  Elevation is returned in the range
+        $\pm\pi$.
+  \item The latitude must be geodetic.  In critical applications,
+        corrections for polar motion should be applied.
+  \item In some applications it will be important to specify the
+        correct type of hour angle and declination in order to
+        produce the required type of azimuth and elevation.  In
+        particular, it may be important to distinguish between
+        elevation as affected by refraction, which would
+        require the {\it observed} \hadec, and the elevation
+        {\it in vacuo}, which would require the {\it topocentric}
+        \hadec.
+        If the effects of diurnal aberration can be neglected, the
+        {\it apparent} \hadec\ may be used instead of the topocentric
+        \hadec.
+  \item No range checking of arguments is carried out.
+  \item In applications which involve many such calculations, rather
+        than calling the present routine it will be more efficient to
+        use inline code, having previously computed fixed terms such
+        as sine and cosine of latitude, and (for tracking a star)
+        sine and cosine of declination.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DEULER}{Euler Angles to Rotation Matrix}
+{
+ \action{Form a rotation matrix from the Euler angles -- three
+         successive rotations about specified Cartesian axes
+         (double precision).}
+ \call{CALL sla\_DEULER (ORDER, PHI, THETA, PSI, RMAT)}
+}
+\args{GIVEN}
+{
+ \spec{ORDER}{C}{specifies about which axes the rotations occur} \\
+ \spec{PHI}{D}{1st rotation (radians)} \\
+ \spec{THETA}{D}{2nd rotation (radians)} \\
+ \spec{PSI}{D}{3rd rotation (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RMAT}{D(3,3)}{rotation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+ \item A rotation is positive when the reference frame rotates
+       anticlockwise as seen looking towards the origin from the
+       positive region of the specified axis.
+ \item The characters of ORDER define which axes the three successive
+       rotations are about.  A typical value is `ZXZ', indicating that
+       RMAT is to become the direction cosine matrix corresponding to
+       rotations of the reference frame through PHI radians about the
+       old {\it z}-axis, followed by THETA radians about the resulting
+       {\it x}-axis,
+       then PSI radians about the resulting {\it z}-axis.
+ \item The axis names can be any of the following, in any order or
+       combination:  X, Y, Z, uppercase or lowercase, 1, 2, 3.  Normal
+       axis labelling/numbering conventions apply;  the {\it xyz} ($\equiv123$)
+       triad is right-handed.  Thus, the `ZXZ' example given above
+       could be written `zxz' or `313' (or even `ZxZ' or `3xZ').  ORDER
+       is terminated by length or by the first unrecognized character.
+       Fewer than three rotations are acceptable, in which case the later
+       angle arguments are ignored.  Zero rotations produces
+       the identity RMAT.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DFLTIN}{Decode a Double Precision Number}
+{
+ \action{Convert free-format input into double precision floating point.}
+ \call{CALL sla\_DFLTIN (STRING, NSTRT, DRESLT, JFLAG)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C}{string containing number to be decoded} \\
+ \spec{NSTRT}{I}{pointer to where decoding is to commence} \\
+ \spec{DRESLT}{D}{current value of result}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{advanced to next number} \\
+ \spec{DRESLT}{D}{result} \\
+ \spec{JFLAG}{I}{status: $-$1~=~$-$OK, 0~=~+OK, 1~=~null result, 2~=~error}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The reason sla\_DFLTIN has separate `OK' status values
+       for + and $-$ is to enable minus zero to be detected.
+       This is of crucial importance
+       when decoding mixed-radix numbers.  For example, an angle
+       expressed as degrees, arcminutes and arcseconds may have a
+       leading minus sign but a zero degrees field.
+ \item A TAB is interpreted as a space, and lowercase characters are
+       interpreted as uppercase.  {\it n.b.}\ The test for TAB is
+       ASCII-specific.
+ \item The basic format is the sequence of fields $\pm n.n x \pm n$,
+       where $\pm$ is a sign
+       character `+' or `$-$', $n$ means a string of decimal digits,
+       `.' is a decimal point, and $x$, which indicates an exponent,
+       means `D' or `E'.  Various combinations of these fields can be
+       omitted, and embedded blanks are permissible in certain places.
+ \item Spaces:
+       \begin{itemize}
+       \item Leading spaces are ignored.
+       \item Embedded spaces are allowed only after +, $-$, D or E,
+             and after the decimal point if the first sequence of
+             digits is absent.
+       \item Trailing spaces are ignored;  the first signifies
+             end of decoding and subsequent ones are skipped.
+       \end{itemize}
+ \item Delimiters:
+       \begin{itemize}
+       \item Any character other than +,$-$,0-9,.,D,E or space may be
+             used to signal the end of the number and terminate decoding.
+       \item Comma is recognized by sla\_DFLTIN as a special case; it
+             is skipped, leaving the pointer on the next character.  See
+             13, below.
+       \item Decoding will in all cases terminate if end of string
+             is reached.
+       \end{itemize}
+ \item Both signs are optional.  The default is +.
+ \item The mantissa $n.n$ defaults to unity.
+ \item The exponent $x\!\pm\!n$ defaults to `D0'.
+ \item The strings of decimal digits may be of any length.
+ \item The decimal point is optional for whole numbers.
+ \item A {\it null result}\/ occurs when the string of characters
+       being decoded does not begin with +,$-$,0-9,.,D or E, or
+       consists entirely of spaces.  When this condition is
+       detected, JFLAG is set to 1 and DRESLT is left untouched.
+ \item NSTRT = 1 for the first character in the string.
+ \item On return from sla\_DFLTIN, NSTRT is set ready for the next
+       decode -- following trailing blanks and any comma.  If a
+       delimiter other than comma is being used, NSTRT must be
+       incremented before the next call to sla\_DFLTIN, otherwise
+       all subsequent calls will return a null result.
+ \item Errors (JFLAG=2) occur when:
+       \begin{itemize}
+       \item a +, $-$, D or E is left unsatisfied; or
+       \item the decimal point is present without at least
+             one decimal digit before or after it; or
+       \item an exponent more than 100 has been presented.
+       \end{itemize}
+ \item When an error has been detected, NSTRT is left
+       pointing to the character following the last
+       one used before the error came to light.  This
+       may be after the point at which a more sophisticated
+       program could have detected the error.  For example,
+       sla\_DFLTIN does not detect that `1D999' is unacceptable
+       (on a computer where this is so) until the entire number
+       has been decoded.
+ \item Certain highly unlikely combinations of mantissa and
+       exponent can cause arithmetic faults during the
+       decode, in some cases despite the fact that they
+       together could be construed as a valid number.
+ \item Decoding is left to right, one pass.
+ \item See also sla\_FLOTIN and sla\_INTIN.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DH2E}{Az,El to $h,\delta$}
+{
+ \action{Horizon to equatorial coordinates
+         (double precision).}
+ \call{CALL sla\_DH2E (AZ, EL, PHI, HA, DEC)}
+}
+\args{GIVEN}
+{
+ \spec{AZ}{D}{azimuth (radians)} \\
+ \spec{EL}{D}{elevation (radians)} \\
+ \spec{PHI}{D}{latitude (radians)}
+}
+\args{RETURNED}
+{
+ \spec{HA}{D}{hour angle (radians)} \\
+ \spec{DEC}{D}{declination (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The sign convention for azimuth is north zero, east $+\pi/2$.
+  \item HA is returned in the range $\pm\pi$.  Declination is returned
+        in the range $\pm\pi/2$.
+  \item The latitude is (in principle) geodetic.  In critical
+        applications, corrections for polar motion should be applied
+        (see sla\_POLMO).
+  \item In some applications it will be important to specify the
+        correct type of elevation in order to produce the required
+        type of \hadec.  In particular, it may be important to
+        distinguish between the elevation as affected by refraction,
+        which will yield the {\it observed} \hadec, and the elevation
+        {\it in vacuo}, which will yield the {\it topocentric}
+        \hadec.  If the
+        effects of diurnal aberration can be neglected, the
+        topocentric \hadec\ may be used as an approximation to the
+        {\it apparent} \hadec.
+  \item No range checking of arguments is carried out.
+  \item In applications which involve many such calculations, rather
+        than calling the present routine it will be more efficient to
+        use inline code, having previously computed fixed terms such
+        as sine and cosine of latitude.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DIMXV}{Apply 3D Reverse Rotation}
+{
+ \action{Multiply a 3-vector by the inverse of a rotation
+         matrix (double precision).}
+ \call{CALL sla\_DIMXV (DM, VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{DM}{D(3,3)}{rotation matrix} \\
+ \spec{VA}{D(3)}{vector to be rotated}
+}
+\args{RETURNED}
+{
+ \spec{VB}{D(3)}{result vector}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine performs the operation:
+        \begin{verse}
+         {\bf b} = {\bf M}$^{T}\cdot${\bf a}
+        \end{verse}
+        where {\bf a} and {\bf b} are the 3-vectors VA and VB
+        respectively, and  {\bf M} is the $3\times3$ matrix DM.
+  \item The main function of this routine is apply an inverse
+        rotation;  under these circumstances, ${\bf M}$ is
+        {\it orthogonal}, with its inverse the same as its transpose.
+  \item To comply with the ANSI Fortran 77 standard, VA and VB must
+        {\bf not} be the same array.  The routine is, in fact, coded
+        so as to work properly on the VAX and many other systems even
+        if this rule is violated, something that is {\bf not}, however,
+        recommended.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DJCAL}{MJD to Gregorian for Output}
+{
+ \action{Modified Julian Date to Gregorian Calendar Date, expressed
+         in a form convenient for formatting messages (namely
+         rounded to a specified precision, and with the fields
+         stored in a single array).}
+ \call{CALL sla\_DJCAL (NDP, DJM, IYMDF, J)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of days in fraction} \\
+ \spec{DJM}{D}{modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{IYMDF}{I(4)}{year, month, day, fraction in Gregorian calendar} \\
+ \spec{J}{I}{status:  nonzero = out of range}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Any date after 4701BC March 1 is accepted.
+  \item Large NDP values risk internal overflows.  It is typically safe
+        to use up to NDP=4.
+ \end{enumerate}
+}
+\aref{The algorithm is adapted from Hatcher,
+      {\it Q.\,Jl.\,R.\,astr.\,Soc.}\ (1984) {\bf 25}, 53-55.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DJCL}{MJD to Year,Month,Day,Frac}
+{
+ \action{Modified Julian Date to Gregorian year, month, day,
+         and fraction of a day.}
+ \call{CALL sla\_DJCL (DJM, IY, IM, ID, FD, J)}
+}
+\args{GIVEN}
+{
+ \spec{DJM}{D}{modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{IY}{I}{year} \\
+ \spec{IM}{I}{month} \\
+ \spec{ID}{I}{day} \\
+ \spec{FD}{D}{fraction of day} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em}0~=~OK} \\
+ \spec{}{}{\hspace{0.7em}$-$1~= unacceptable date} \\
+ \spec{}{}{\hspace{0.7em}~~~~~~~~~~~~(before 4701\,BC~March~1)}
+}
+\aref{The algorithm is adapted from Hatcher,
+      {\it Q.\,Jl.\,R.\,astr.\,Soc.}\ (1984) {\bf 25}, 53-55.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DM2AV}{Rotation Matrix to Axial Vector}
+{
+ \action{From a rotation matrix, determine the corresponding axial vector
+        (double precision).}
+ \call{CALL sla\_DM2AV (RMAT, AXVEC)}
+}
+\args{GIVEN}
+{
+ \spec{RMAT}{D(3,3)}{rotation matrix}
+}
+\args{RETURNED}
+{
+ \spec{AXVEC}{D(3)}{axial vector (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A rotation matrix describes a rotation about some arbitrary axis,
+        called the Euler axis.  The {\it axial vector} returned by
+        this routine has the same direction as the Euler axis, and its
+        magnitude is the amount of rotation in radians.
+  \item The magnitude and direction of the axial vector can be separated
+        by means of the routine sla\_DVN.
+  \item The reference frame rotates clockwise as seen looking along
+        the axial vector from the origin.
+  \item If RMAT is null, so is the result.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DMAT}{Solve Simultaneous Equations}
+{
+ \action{Matrix inversion and solution of simultaneous equations
+         (double precision).}
+ \call{CALL sla\_DMAT (N, A, Y, D, JF, IW)}
+}
+\args{GIVEN}
+{
+ \spec{N}{I}{number of unknowns} \\
+ \spec{A}{D(N,N)}{matrix} \\
+ \spec{Y}{D(N)}{vector}
+}
+\args{RETURNED}
+{
+ \spec{A}{D(N,N)}{matrix inverse} \\
+ \spec{Y}{D(N)}{solution} \\
+ \spec{D}{D}{determinant} \\
+ \spec{JF}{I}{singularity flag: 0=OK} \\
+ \spec{IW}{I(N)}{workspace}
+}
+\notes
+{
+ \begin{enumerate}
+  \item For the set of $n$ simultaneous linear equations in $n$ unknowns:
+        \begin{verse}
+         {\bf A}$\cdot${\bf y} = {\bf x}
+        \end{verse}
+        where:
+        \begin{itemize}
+         \item {\bf A} is a non-singular $n \times n$ matrix,
+         \item {\bf y} is the vector of $n$ unknowns, and
+         \item {\bf x} is the known vector,
+        \end{itemize}
+        sla\_DMAT computes:
+        \begin{itemize}
+         \item the inverse of matrix {\bf A},
+         \item the determinant of matrix {\bf A}, and
+         \item the vector of $n$ unknowns {\bf y}.
+        \end{itemize}
+        Argument N is the order $n$, A (given) is the matrix {\bf A},
+        Y (given) is the vector {\bf x} and Y (returned)
+        is the vector {\bf y}.
+        The argument A (returned) is the inverse matrix {\bf A}$^{-1}$,
+        and D is {\it det}\/({\bf A}).
+  \item JF is the singularity flag.  If the matrix is non-singular,
+        JF=0 is returned.  If the matrix is singular, JF=$-$1
+        and D=0D0 are returned.  In the latter case, the contents
+        of array A on return are undefined.
+  \item The algorithm is Gaussian elimination with partial pivoting.
+        This method is very fast;  some much slower algorithms can give
+        better accuracy, but only by a small factor.
+  \item This routine replaces the obsolete sla\_DMATRX.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DMOON}{Approx Moon Pos/Vel}
+{
+ \action{Approximate geocentric position and velocity of the Moon
+         (double precision).}
+ \call{CALL sla\_DMOON (DATE, PV)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (loosely ET) as a Modified Julian Date (JD$-$2400000.5)
+}
+}
+\args{RETURNED}
+{
+ \spec{PV}{D(6)}{Moon \xyzxyzd, mean equator and equinox
+                 of date (AU, AU~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine is a full implementation of the algorithm
+        published by Meeus (see reference).
+  \item Meeus quotes accuracies of \arcseci{10} in longitude,
+        \arcseci{3} in latitude and \arcsec{0}{2} arcsec in HP
+        (equivalent to about 20~km in distance).  Comparison with
+        JPL~DE200 over the interval 1960-2025 gives RMS errors of
+        \arcsec{3}{7} and 83~mas/hour in longitude,
+        \arcsec{2}{3} arcsec and 48~mas/hour in latitude,
+        11~km and 81~mm/s in distance.
+        The maximum errors over the same interval are
+        \arcseci{18} and \arcsec{0}{50}/hour in longitude,
+        \arcseci{11} and \arcsec{0}{24}/hour in latitude,
+        40~km and 0.29~m/s in distance.
+  \item The original algorithm is expressed in terms of the obsolete
+        time scale {\it Ephemeris Time}.  Either TDB or TT can be used,
+        but not UT without incurring significant errors (\arcseci{30} at
+        the present time) due to the Moon's \arcsec{0}{5}/s movement.
+  \item The algorithm is based on pre IAU 1976 standards.  However,
+        the result has been moved onto the new (FK5) equinox, an
+        adjustment which is in any case much smaller than the
+        intrinsic accuracy of the procedure.
+  \item Velocity is obtained by a complete analytical differentiation
+        of the Meeus model.
+ \end{enumerate}
+}
+\aref{Meeus, {\it l'Astronomie}, June 1984, p348.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DMXM}{Multiply $3\times3$ Matrices}
+{
+ \action{Product of two $3\times3$ matrices (double precision).}
+ \call{CALL sla\_DMXM (A, B, C)}
+}
+\args{GIVEN}
+{
+ \spec{A}{D(3,3)}{matrix {\bf A}} \\
+ \spec{B}{D(3,3)}{matrix {\bf B}}
+}
+\args{RETURNED}
+{
+ \spec{C}{D(3,3)}{matrix result: {\bf A}$\times${\bf B}}
+}
+\anote{To comply with the ANSI Fortran 77 standard, A, B and C must
+       be different arrays.  However, the routine is coded so as to
+       work properly on many platforms even if this rule is violated,
+       something that is {\bf not}, however, recommended.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DMXV}{Apply 3D Rotation}
+{
+ \action{Multiply a 3-vector by a rotation matrix (double precision).}
+ \call{CALL sla\_DMXV (DM, VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{DM}{D(3,3)}{rotation matrix} \\
+ \spec{VA}{D(3)}{vector to be rotated}
+}
+\args{RETURNED}
+{
+ \spec{VB}{D(3)}{result vector}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine performs the operation:
+        \begin{verse}
+           {\bf b} = {\bf M}$\cdot${\bf a}
+        \end{verse}
+        where {\bf a} and {\bf b} are the 3-vectors VA and VB
+        respectively, and {\bf M} is the $3\times3$ matrix DM.
+  \item The main function of this routine is apply a
+        rotation;  under these circumstances, {\bf M} is a
+        {\it proper real orthogonal}\/ matrix.
+  \item To comply with the ANSI Fortran 77 standard, VA and VB must
+        {\bf not} be the same array.  The routine is, in fact, coded
+        so as to work properly with many Fortran compilers even
+        if this rule is violated, something that is {\bf not}, however,
+        recommended.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DPAV}{Position-Angle Between Two Directions}
+{
+ \action{Returns the bearing (position angle) of one celestial
+         direction with respect to another (double precision).}
+ \call{D~=~sla\_DPAV (V1, V2)}
+}
+\args{GIVEN}
+{
+ \spec{V1}{D(3)}{vector to one point} \\
+ \spec{V2}{D(3)}{vector to the other point}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DPAV}{D}{position-angle of 2nd point with respect to 1st}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The coordinate frames correspond to \radec,
+       $[\lambda,\phi]$ {\it etc.}.
+ \item The result is the bearing (position angle), in radians,
+       of point V2 as seen
+       from point V1.  It is in the range $\pm \pi$.  The sense
+       is such that if V2
+       is a small distance due east of V1 the result
+       is about $+\pi/2$. Zero is returned
+       if the two points are coincident.
+ \item There is no requirement for either vector to be of unit length.
+ \item The routine sla\_DBEAR performs an equivalent function except
+       that the points are specified in the form of spherical coordinates.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_DR2AF}{Radians to Deg,Min,Sec,Frac}
+{
+ \action{Convert an angle in radians to degrees, arcminutes, arcseconds,
+         fraction (double precision).}
+ \call{CALL sla\_DR2AF (NDP, ANGLE, SIGN, IDMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of arcseconds} \\
+ \spec{ANGLE}{D}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IDMSF}{I(4)}{degrees, arcminutes, arcseconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size
+        of ANGLE, the format of DOUBLE PRECISION floating-point
+        numbers on the target machine, and the risk of overflowing
+        IDMSF(4).  On some architectures, for ANGLE up to 2pi, the
+        available floating-point precision corresponds roughly to
+        NDP=12.  However, the practical limit is NDP=9, set by the
+        capacity of a typical 32-bit IDMSF(4).
+  \item The absolute value of ANGLE may exceed $2\pi$.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where ANGLE is very nearly $2\pi$ and rounds up to $360^{\circ}$,
+        by testing for IDMSF(1)=360 and setting IDMSF(1-4) to zero.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DR2TF}{Radians to Hour,Min,Sec,Frac}
+{
+ \action{Convert an angle in radians to hours, minutes, seconds,
+         fraction (double precision).}
+ \call{CALL sla\_DR2TF (NDP, ANGLE, SIGN, IHMSF)}
+}
+\args{GIVEN}
+{
+ \spec{NDP}{I}{number of decimal places of seconds} \\
+ \spec{ANGLE}{D}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{SIGN}{C}{`+' or `$-$'} \\
+ \spec{IHMSF}{I(4)}{hours, minutes, seconds, fraction}
+}
+\notes
+{
+ \begin{enumerate}
+  \item NDP less than zero is interpreted as zero.
+  \item The largest useful value for NDP is determined by the size
+        of ANGLE, the format of DOUBLE PRECISION floating-point
+        numbers on the target machine, and the risk of overflowing
+        IHMSF(4).  On some architectures, for ANGLE up to 2pi, the
+        available floating-point precision corresponds roughly to
+        NDP=12.  However, the practical limit is NDP=9, set by the
+        capacity of a typical 32-bit IHMSF(4).
+  \item The absolute value of ANGLE may exceed $2\pi$.  In cases where it
+        does not, it is up to the caller to test for and handle the
+        case where ANGLE is very nearly $2\pi$ and rounds up to 24~hours,
+        by testing for IHMSF(1)=24 and setting IHMSF(1-4) to zero.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DRANGE}{Put Angle into Range $\pm\pi$}
+{
+ \action{Normalize an angle into the range $\pm\pi$ (double precision).}
+ \call{D~=~sla\_DRANGE (ANGLE)}
+}
+\args{GIVEN}
+{
+ \spec{ANGLE}{D}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DRANGE}{D}{ANGLE expressed in the range $\pm\pi$.}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DRANRM}{Put Angle into Range $0\!-\!2\pi$}
+{
+ \action{Normalize an angle into the range $0\!-\!2\pi$
+         (double precision).}
+ \call{D~=~sla\_DRANRM (ANGLE)}
+}
+\args{GIVEN}
+{
+ \spec{ANGLE}{D}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DRANRM}{D}{ANGLE expressed in the range $0\!-\!2\pi$}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DS2C6}{Spherical Pos/Vel to Cartesian}
+{
+ \action{Conversion of position \& velocity in spherical coordinates
+         to Cartesian coordinates (double precision).}
+ \call{CALL sla\_DS2C6 (A, B, R, AD, BD, RD, V)}
+}
+\args{GIVEN}
+{
+ \spec{A}{D}{longitude (radians) -- for example $\alpha$} \\
+ \spec{B}{D}{latitude (radians) -- for example $\delta$} \\
+ \spec{R}{D}{radial coordinate} \\
+ \spec{AD}{D}{longitude derivative (radians per unit time)} \\
+ \spec{BD}{D}{latitude derivative (radians per unit time)} \\
+ \spec{RD}{D}{radial derivative}
+}
+\args{RETURNED}
+{
+ \spec{V}{D(6)}{\xyzxyzd}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DS2TP}{Spherical to Tangent Plane}
+{
+ \action{Projection of spherical coordinates onto the tangent plane
+         (double precision).}
+ \call{CALL sla\_DS2TP (RA, DEC, RAZ, DECZ, XI, ETA, J)}
+}
+\args{GIVEN}
+{
+ \spec{RA,DEC}{D}{spherical coordinates of star (radians)} \\
+ \spec{RAZ,DECZ}{D}{spherical coordinates of tangent point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{XI,ETA}{D}{tangent plane coordinates (radians)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK, star on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 1 = error, star too far from axis} \\
+ \spec{}{}{\hspace{1.5em} 2 = error, antistar on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 3 = error, antistar too far from axis}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_DV2TP is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DSEP}{Angle Between 2 Points on Sphere}
+{
+ \action{Angle between two points on a sphere (double precision).}
+ \call{D~=~sla\_DSEP (A1, B1, A2, B2)}
+}
+\args{GIVEN}
+{
+ \spec{A1,B1}{D}{spherical coordinates of one point (radians)} \\
+ \spec{A2,B2}{D}{spherical coordinates of the other point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DSEP}{D}{angle between [A1,B1] and [A2,B2] in radians}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The spherical coordinates are right ascension and declination,
+        longitude and latitude, {\it etc.}, in radians.
+  \item The result is always positive.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DSEPV}{Angle Between 2 Vectors}
+{
+ \action{Angle between two vectors (double precision).}
+ \call{D~=~sla\_DSEPV (V1, V2)}
+}
+\args{GIVEN}
+{
+ \spec{V1}{D(3)}{first vector} \\
+ \spec{V2}{D(3)}{second vector}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DSEPV}{D}{angle between V1 and V2 in radians}
+}
+\notes
+{
+ \begin{enumerate}
+  \item There is no requirement for either vector to be of unit length.
+  \item If either vector is null, zero is returned.
+  \item The result is always positive.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DT}{Approximate ET minus UT}
+{
+ \action{Estimate $\Delta$T, the offset between dynamical time
+         and Universal Time, for a given historical epoch.}
+ \call{D~=~sla\_DT (EPOCH)}
+}
+\args{GIVEN}
+{
+ \spec{EPOCH}{D}{(Julian) epoch ({\it e.g.}\ 1850D0)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DT}{D}{approximate ET$-$UT (after 1984, TT$-$UT1) in seconds}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Depending on the epoch, one of three parabolic approximations
+        is used:
+
+\begin{tabular}{lll}
+& before AD 979 & Stephenson \& Morrison's 390 BC to AD 948 model \\
+& AD 979 to AD 1708 & Stephenson \& Morrison's AD 948 to AD 1600 model \\
+& after AD 1708 & McCarthy \& Babcock's post-1650 model
+\end{tabular}
+
+        The breakpoints are chosen to ensure continuity:  they occur
+        at places where the adjacent models give the same answer as
+        each other.
+  \item The accuracy is modest, with errors of up to $20^{\rm s}$ during
+        the interval since 1650, rising to perhaps $30^{\rm m}$
+        by 1000~BC.  Comparatively accurate values from AD~1600
+        are tabulated in
+        the {\it Astronomical Almanac}\/ (see section K8 of the 1995
+        edition).
+  \item The use of {\tt DOUBLE PRECISION} for both argument and result is
+        simply for compatibility with other SLALIB time routines.
+  \item The models used are based on a lunar tidal acceleration value
+        of \arcsec{-26}{00} per century.
+ \end{enumerate}
+}
+\aref{Seidelmann, P.K.\ (ed), 1992.  {\it Explanatory
+      Supplement to the Astronomical Almanac,}\/ ISBN~0-935702-68-7.
+      This contains references to the papers by Stephenson \& Morrison
+      and by McCarthy \& Babcock which describe the models used here.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTF2D}{Hour,Min,Sec to Days}
+{
+ \action{Convert hours, minutes, seconds to days (double precision).}
+ \call{CALL sla\_DTF2D (IHOUR, IMIN, SEC, DAYS, J)}
+}
+\args{GIVEN}
+{
+ \spec{IHOUR}{I}{hours} \\
+ \spec{IMIN}{I}{minutes} \\
+ \spec{SEC}{D}{seconds}
+}
+\args{RETURNED}
+{
+ \spec{DAYS}{D}{interval in days} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = IHOUR outside range 0-23} \\
+ \spec{}{}{\hspace{1.5em} 2 = IMIN outside range 0-59} \\
+ \spec{}{}{\hspace{1.5em} 3 = SEC outside range 0-59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTF2R}{Hour,Min,Sec to Radians}
+{
+ \action{Convert hours, minutes, seconds to radians (double precision).}
+ \call{CALL sla\_DTF2R (IHOUR, IMIN, SEC, RAD, J)}
+}
+\args{GIVEN}
+{
+ \spec{IHOUR}{I}{hours} \\
+ \spec{IMIN}{I}{minutes} \\
+ \spec{SEC}{D}{seconds}
+}
+\args{RETURNED}
+{
+ \spec{RAD}{D}{angle in radians} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{1.5em} 1 = IHOUR outside range 0-23} \\
+ \spec{}{}{\hspace{1.5em} 2 = IMIN outside range 0-59} \\
+ \spec{}{}{\hspace{1.5em} 3 = SEC outside range 0-59.999$\cdots$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is computed even if any of the range checks fail.
+  \item The sign must be dealt with outside this routine.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTP2S}{Tangent Plane to Spherical}
+{
+ \action{Transform tangent plane coordinates into spherical
+         coordinates (double precision)}
+ \call{CALL sla\_DTP2S (XI, ETA, RAZ, DECZ, RA, DEC)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{D}{tangent plane rectangular coordinates (radians)} \\
+ \spec{RAZ,DECZ}{D}{spherical coordinates of tangent point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RA,DEC}{D}{spherical coordinates (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_DTP2V is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTP2V}{Tangent Plane to Direction Cosines}
+{
+ \action{Given the tangent-plane coordinates of a star and the direction
+         cosines of the tangent point, determine the direction cosines
+         of the star
+         (double precision).}
+ \call{CALL sla\_DTP2V (XI, ETA, V0, V)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{D}{tangent plane coordinates of star (radians)} \\
+ \spec{V0}{D(3)}{direction cosines of tangent point}
+}
+\args{RETURNED}
+{
+ \spec{V}{D(3)}{direction cosines of star}
+}
+\notes
+{
+ \begin{enumerate}
+  \item If vector V0 is not of unit length, the returned vector V will
+        be wrong.
+  \item If vector V0 points at a pole, the returned vector V will be
+        based on the arbitrary assumption that $\alpha=0$ at
+        the tangent point.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_DTP2S.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTPS2C}{Plate centre from $\xi,\eta$ and $\alpha,\delta$}
+{
+ \action{From the tangent plane coordinates of a star of known \radec,
+        determine the \radec\ of the tangent point (double precision)}
+ \call{CALL sla\_DTPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{D}{tangent plane rectangular coordinates (radians)} \\
+ \spec{RA,DEC}{D}{spherical coordinates (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RAZ1,DECZ1}{D}{spherical coordinates of tangent point,
+                      solution 1} \\
+ \spec{RAZ2,DECZ2}{D}{spherical coordinates of tangent point,
+                      solution 2} \\
+ \spec{N}{I}{number of solutions:} \\
+ \spec{}{}{\hspace{1em} 0 = no solutions returned  (note 2)} \\
+ \spec{}{}{\hspace{1em} 1 = only the first solution is useful (note 3)} \\
+ \spec{}{}{\hspace{1em} 2 = there are two useful solutions (note 3)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The RAZ1 and RAZ2 values returned are in the range $0\!-\!2\pi$.
+  \item Cases where there is no solution can only arise near the poles.
+        For example, it is clearly impossible for a star at the pole
+        itself to have a non-zero $\xi$ value, and hence it is
+        meaningless to ask where the tangent point would have to be
+        to bring about this combination of $\xi$ and $\delta$.
+  \item Also near the poles, cases can arise where there are two useful
+        solutions.  The argument N indicates whether the second of the
+        two solutions returned is useful.  N\,=\,1
+        indicates only one useful solution, the usual case;  under
+        these circumstances, the second solution corresponds to the
+        ``over-the-pole'' case, and this is reflected in the values
+        of RAZ2 and DECZ2 which are returned.
+  \item The DECZ1 and DECZ2 values returned are in the range $\pm\pi$,
+        but in the ordinary, non-pole-crossing, case, the range is
+        $\pm\pi/2$.
+  \item RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2 are all in radians.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_DTPV2C is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTPV2C}{Plate centre from $\xi,\eta$ and $x,y,z$}
+{
+ \action{From the tangent plane coordinates of a star of known
+         direction cosines, determine the direction cosines
+         of the tangent point (double precision)}
+ \call{CALL sla\_DTPV2C (XI, ETA, V, V01, V02, N)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{D}{tangent plane coordinates of star (radians)} \\
+ \spec{V}{D(3)}{direction cosines of star}
+}
+\args{RETURNED}
+{
+ \spec{V01}{D(3)}{direction cosines of tangent point, solution 1} \\
+ \spec{V02}{D(3)}{direction cosines of tangent point, solution 2} \\
+ \spec{N}{I}{number of solutions:} \\
+ \spec{}{}{\hspace{1em} 0 = no solutions returned  (note 2)} \\
+ \spec{}{}{\hspace{1em} 1 = only the first solution is useful (note 3)} \\
+ \spec{}{}{\hspace{1em} 2 = there are two useful solutions (note 3)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The vector V must be of unit length or the result will be wrong.
+  \item Cases where there is no solution can only arise near the poles.
+        For example, it is clearly impossible for a star at the pole
+        itself to have a non-zero XI value.
+  \item Also near the poles, cases can arise where there are two useful
+        solutions.  The argument N indicates whether the second of the
+        two solutions returned is useful.
+        N\,=\,1
+        indicates only one useful solution, the usual case;  under these
+        circumstances, the second solution can be regarded as valid if
+        the vector V02 is interpreted as the ``over-the-pole'' case.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_DTPS2C.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DTT}{TT minus UTC}
+{
+ \action{Compute $\Delta$TT, the increment to be applied to
+         Coordinated Universal Time UTC to give
+         Terrestrial Time TT.}
+ \call{D~=~sla\_DTT (DJU)}
+}
+\args{GIVEN}
+{
+ \spec{DJU}{D}{UTC date as a modified JD (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DTT}{D}{TT$-$UTC in seconds}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The UTC is specified to be a date rather than a time to indicate
+        that care needs to be taken not to specify an instant which lies
+        within a leap second.  Though in most cases UTC can include the
+        fractional part, correct behaviour on the day of a leap second
+        can be guaranteed only up to the end of the second
+        $23^{\rm h}\,59^{\rm m}\,59^{\rm s}$.
+  \item Pre 1972 January 1 a fixed value of 10 + ET$-$TAI is returned.
+  \item TT is one interpretation of the defunct time scale
+        {\it Ephemeris Time}, ET.
+  \item See also the routine sla\_DT, which roughly estimates ET$-$UT for
+        historical epochs.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DV2TP}{Direction Cosines to Tangent Plane}
+{
+ \action{Given the direction cosines of a star and of the tangent point,
+         determine the star's tangent-plane coordinates
+         (double precision).}
+ \call{CALL sla\_DV2TP (V, V0, XI, ETA, J)}
+}
+\args{GIVEN}
+{
+ \spec{V}{D(3)}{direction cosines of star} \\
+ \spec{V0}{D(3)}{direction cosines of tangent point}
+}
+\args{RETURNED}
+{
+ \spec{XI,ETA}{D}{tangent plane coordinates (radians)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK, star on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 1 = error, star too far from axis} \\
+ \spec{}{}{\hspace{1.5em} 2 = error, antistar on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 3 = error, antistar too far from axis}
+}
+\notes
+{
+ \begin{enumerate}
+  \item If vector V0 is not of unit length, or if vector V is of zero
+        length, the results will be wrong.
+  \item If V0 points at a pole, the returned $\xi,\eta$
+        will be based on the
+        arbitrary assumption that $\alpha=0$ at the tangent point.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_DS2TP.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DVDV}{Scalar Product}
+{
+ \action{Scalar product of two 3-vectors (double precision).}
+ \call{D~=~sla\_DVDV (VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{VA}{D(3)}{first vector} \\
+ \spec{VB}{D(3)}{second vector}
+}
+\args{RETURNED}
+{
+ \spec{sla\_DVDV}{D}{scalar product VA.VB}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_DVN}{Normalize Vector}
+{
+ \action{Normalize a 3-vector, also giving the modulus (double precision).}
+ \call{CALL sla\_DVN (V, UV, VM)}
+}
+\args{GIVEN}
+{
+ \spec{V}{D(3)}{vector}
+}
+\args{RETURNED}
+{
+ \spec{UV}{D(3)}{unit vector in direction of V} \\
+ \spec{VM}{D}{modulus of V}
+}
+\anote{If the modulus of V is zero, UV is set to zero as well.}
+%-----------------------------------------------------------------------
+\routine{SLA\_DVXV}{Vector Product}
+{
+ \action{Vector product of two 3-vectors (double precision).}
+ \call{CALL sla\_DVXV (VA, VB, VC)}
+}
+\args{GIVEN}
+{
+ \spec{VA}{D(3)}{first vector} \\
+ \spec{VB}{D(3)}{second vector}
+}
+\args{RETURNED}
+{
+ \spec{VC}{D(3)}{vector product VA$\times$VB}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_E2H}{$h,\delta$ to Az,El}
+{
+ \action{Equatorial to horizon coordinates
+         (single precision).}
+ \call{CALL sla\_DE2H (HA, DEC, PHI, AZ, EL)}
+}
+\args{GIVEN}
+{
+ \spec{HA}{R}{hour angle (radians)} \\
+ \spec{DEC}{R}{declination (radians)} \\
+ \spec{PHI}{R}{latitude (radians)}
+}
+\args{RETURNED}
+{
+ \spec{AZ}{R}{azimuth (radians)} \\
+ \spec{EL}{R}{elevation (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Azimuth is returned in the range $0\!-\!2\pi$;  north is zero,
+        and east is $+\pi/2$.  Elevation is returned in the range
+        $\pm\pi$.
+  \item The latitude must be geodetic.  In critical applications,
+        corrections for polar motion should be applied.
+  \item In some applications it will be important to specify the
+        correct type of hour angle and declination in order to
+        produce the required type of azimuth and elevation.  In
+        particular, it may be important to distinguish between
+        elevation as affected by refraction, which would
+        require the {\it observed} \hadec, and the elevation
+        {\it in vacuo}, which would require the {\it topocentric}
+        \hadec.
+        If the effects of diurnal aberration can be neglected, the
+        {\it apparent} \hadec\ may be used instead of the topocentric
+        \hadec.
+  \item No range checking of arguments is carried out.
+  \item In applications which involve many such calculations, rather
+        than calling the present routine it will be more efficient to
+        use inline code, having previously computed fixed terms such
+        as sine and cosine of latitude, and (for tracking a star)
+        sine and cosine of declination.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EARTH}{Approx Earth Pos/Vel}
+{
+ \action{Approximate heliocentric position and velocity of the Earth
+         (single precision).}
+ \call{CALL sla\_EARTH (IY, ID, FD, PV)}
+}
+\args{GIVEN}
+{
+ \spec{IY}{I}{year} \\
+ \spec{ID}{I}{day in year (1 = Jan 1st)} \\
+ \spec{FD}{R}{fraction of day}
+}
+\args{RETURNED}
+{
+ \spec{PV}{R(6)}{Earth \xyzxyzd\ (AU, AU~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The date and time is TDB (loosely ET) in a Julian calendar
+        which has been aligned to the ordinary Gregorian
+        calendar for the interval 1900~March~1 to 2100~February~28.
+        The year and day can be obtained by calling sla\_CALYD or
+        sla\_CLYD.
+  \item The Earth heliocentric 6-vector is referred to the
+        FK4 mean equator and equinox of date.
+  \item Maximum/RMS errors 1950-2050:
+        \begin{itemize}
+         \item 13/5~$\times10^{-5}$~AU = 19200/7600~km in position
+         \item 47/26~$\times10^{-10}$~AU~s$^{-1}$ =
+               0.0070/0.0039~km~s$^{-1}$ in speed
+        \end{itemize}
+  \item More accurate results are obtainable with the routines sla\_EVP
+        and sla\_EPV.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_ECLEQ}{Ecliptic to Equatorial}
+{
+ \action{Transformation from ecliptic longitude and latitude to
+         J2000.0 \radec.}
+ \call{CALL sla\_ECLEQ (DL, DB, DATE, DR, DD)}
+}
+\args{GIVEN}
+{
+ \spec{DL,DB}{D}{ecliptic longitude and latitude
+                          (mean of date, IAU 1980 theory, radians)} \\
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date
+                                             (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{DR,DD}{D}{J2000.0 mean \radec\ (radians)}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_ECMAT}{Form $\alpha,\delta\rightarrow\lambda,\beta$ Matrix}
+{
+ \action{Form the equatorial to ecliptic rotation matrix (IAU 1980 theory).}
+ \call{CALL sla\_ECMAT (DATE, RMAT)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date
+                                           (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{RMAT}{D(3,3)}{rotation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item RMAT is matrix {\bf M} in the expression
+        {\bf v}$_{ecl}$~=~{\bf M}$\cdot${\bf v}$_{equ}$.
+  \item The equator, equinox and ecliptic are mean of date.
+ \end{enumerate}
+}
+\aref{Murray, C.A., {\it Vectorial Astrometry}, section 4.3.}
+%-----------------------------------------------------------------------
+\routine{SLA\_ECOR}{RV \& Time Corrns to Sun}
+{
+ \action{Component of Earth orbit velocity and heliocentric
+         light time in a given direction.}
+ \call{CALL sla\_ECOR (RM, DM, IY, ID, FD, RV, TL)}
+}
+\args{GIVEN}
+{
+ \spec{RM,DM}{R}{mean \radec\ of date (radians)} \\
+ \spec{IY}{I}{year} \\
+ \spec{ID}{I}{day in year (1 = Jan 1st)} \\
+ \spec{FD}{R}{fraction of day}
+}
+\args{RETURNED}
+{
+ \spec{RV}{R}{component of Earth orbital velocity (km~s$^{-1}$)} \\
+ \spec{TL}{R}{component of heliocentric light time (s)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The date and time is TDB (loosely ET) in a Julian calendar
+        which has been aligned to the ordinary Gregorian
+        calendar for the interval 1900 March 1 to 2100 February 28.
+        The year and day can be obtained by calling sla\_CALYD or
+        sla\_CLYD.
+  \item Sign convention:
+        \begin{itemize}
+         \item The velocity component is +ve when the
+               Earth is receding from
+               the given point on the sky.
+         \item The light time component is +ve
+               when the Earth lies between the Sun and
+               the given point on the sky.
+        \end{itemize}
+ \item Accuracy:
+       \begin{itemize}
+        \item The velocity component is usually within 0.004~km~s$^{-1}$
+              of the correct value and is never in error by more than
+              0.007~km~s$^{-1}$.
+        \item The error in light time correction is about
+              \tsec{0}{03} at worst,
+              but is usually better than \tsec{0}{01}.
+       \end{itemize}
+       For applications requiring higher accuracy, see the sla\_EVP
+       and sla\_EPV routines.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EG50}{B1950 $\alpha,\delta$ to Galactic}
+{
+ \action{Transformation from B1950.0 FK4 equatorial coordinates to
+         IAU 1958 galactic coordinates.}
+ \call{CALL sla\_EG50 (DR, DD, DL, DB)}
+}
+\args{GIVEN}
+{
+ \spec{DR,DD}{D}{B1950.0 \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal\ (radians)}
+}
+\anote{The equatorial coordinates are B1950.0 FK4.  Use the
+       routine sla\_EQGAL if conversion from J2000.0 FK5 coordinates
+       is required.}
+\aref{Blaauw {\it et al.}, 1960, {\it Mon.Not.R.astr.Soc.},
+      {\bf 121}, 123.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EL2UE}{Conventional to Universal Elements}
+{
+ \action{Transform conventional osculating orbital elements
+         into ``universal'' form.}
+ \call{CALL sla\_EL2UE (\vtop{
+         \hbox{DATE, JFORM, EPOCH, ORBINC, ANODE,}
+         \hbox{PERIH, AORQ, E, AORL, DM,}
+         \hbox{U, JSTAT)}}}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{epoch (TT MJD) of osculation (Note~3)} \\
+ \spec{JFORM}{I}{choice of element set (1-3; Note~6)} \\
+ \spec{EPOCH}{D}{epoch of elements ($t_0$ or $T$, TT MJD)} \\
+ \spec{ORBINC}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH}{D}{longitude or argument of perihelion
+                            ($\varpi$ or $\omega$,} \\
+ \spec{}{}{\hspace{1.5em} radians)} \\
+ \spec{AORQ}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E}{D}{eccentricity ($e$)} \\
+ \spec{AORL}{D}{mean anomaly or longitude
+                               ($M$ or $L$, radians,} \\
+ \spec{}{}{\hspace{1.5em} JFORM=1,2 only)} \\
+ \spec{DM}{D}{daily motion ($n$, radians, JFORM=1 only)}
+}
+\args{RETURNED}
+{
+ \spec{U}{D(13)}{universal orbital elements (Note~1)} \\
+ \specel {(1)}     {combined mass ($M+m$)} \\
+ \specel {(2)}     {total energy of the orbit ($\alpha$)} \\
+ \specel {(3)}     {reference (osculating) epoch ($t_0$)} \\
+ \specel {(4-6)}   {position at reference epoch (${\rm \bf r}_0$)} \\
+ \specel {(7-9)}   {velocity at reference epoch (${\rm \bf v}_0$)} \\
+ \specel {(10)}    {heliocentric distance at reference epoch} \\
+ \specel {(11)}    {${\rm \bf r}_0.{\rm \bf v}_0$} \\
+ \specel {(12)}    {date ($t$)} \\
+ \specel {(13)}    {universal eccentric anomaly ($\psi$) of date,
+                    approx} \\ \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{1.95em}       0 = OK} \\
+ \spec{}{}{\hspace{1.2em}  $-$1 = illegal JFORM} \\
+ \spec{}{}{\hspace{1.2em}   $-$2 = illegal E} \\
+ \spec{}{}{\hspace{1.2em}   $-$3 = illegal AORQ} \\
+ \spec{}{}{\hspace{1.2em}   $-$4 = illegal DM} \\
+ \spec{}{}{\hspace{1.2em}   $-$5 = numerical error}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The ``universal'' elements are those which define the orbit for
+        the purposes of the method of universal variables (see reference).
+        They consist of the combined mass of the two bodies, an epoch,
+        and the position and velocity vectors (arbitrary reference frame)
+        at that epoch.  The parameter set used here includes also various
+        quantities that can, in fact, be derived from the other
+        information.  This approach is taken to avoiding unnecessary
+        computation and loss of accuracy.  The supplementary quantities
+        are (i)~$\alpha$, which is proportional to the total energy of the
+        orbit, (ii)~the heliocentric distance at epoch,
+        (iii)~the outwards component of the velocity at the given epoch,
+        (iv)~an estimate of $\psi$, the ``universal eccentric anomaly'' at a
+        given date and (v)~that date.
+  \item The companion routine is sla\_UE2PV.  This takes the set of numbers
+        that the present routine outputs and uses them to derive the
+        object's position and velocity.  A single prediction requires one
+        call to the present routine followed by one call to sla\_UE2PV;
+        for convenience, the two calls are packaged as the routine
+        sla\_PLANEL.  Multiple predictions may be made by again calling the
+        present routine once, but then calling sla\_UE2PV multiple times,
+        which is faster than multiple calls to sla\_PLANEL.
+  \item DATE is the epoch of osculation.  It is in the TT time scale
+        (formerly Ephemeris Time, ET) and is a Modified Julian Date
+        (JD$-$2400000.5).
+  \item The supplied orbital elements are with respect to the J2000
+        ecliptic and equinox.  The position and velocity parameters
+        returned in the array U are with respect to the mean equator and
+        equinox of epoch J2000, and are for the perihelion prior to the
+        specified epoch.
+  \item The universal elements returned in the array U are in canonical
+        units (solar masses, AU and canonical days).
+  \item Three different element-format options are supported, as
+        follows. \\
+
+        JFORM=1, suitable for the major planets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of elements $t_0$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & longitude of perihelion $\varpi$ (radians) \\
+        & AORQ   & = & mean distance $a$ (AU) \\
+        & E      & = & eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        & AORL   & = & mean longitude $L$ (radians) \\
+        & DM     & = & daily motion $n$ (radians)
+        \end{tabular}
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of elements $t_0$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & mean distance $a$ (AU) \\
+        & E      & = & eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        & AORL   & = & mean anomaly $M$ (radians)
+        \end{tabular}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of perihelion $T$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & perihelion distance $q$ (AU) \\
+        & E      & = & eccentricity $e$ $( 0 \leq e \leq 10 )$
+        \end{tabular}
+
+  \item Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
+        not accessed.
+  \item The algorithm was originally adapted from the EPHSLA program of
+        D.\,H.\,P.\,Jones (private communication, 1996).  The method
+        is based on Stumpff's Universal Variables.
+ \end{enumerate}
+}
+\aref{Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.}
+%------------------------------------------------------------------------------
+\routine{SLA\_EPB}{MJD to Besselian Epoch}
+{
+ \action{Conversion of Modified Julian Date to Besselian Epoch.}
+ \call{D~=~sla\_EPB (DATE)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{Modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EPB}{D}{Besselian Epoch}
+}
+\aref{Lieske, J.H., 1979, {\it Astr.Astrophys.}\ {\bf 73}, 282.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EPB2D}{Besselian Epoch to MJD}
+{
+ \action{Conversion of Besselian Epoch to Modified Julian Date.}
+ \call{D~=~sla\_EPB2D (EPB)}
+}
+\args{GIVEN}
+{
+ \spec{EPB}{D}{Besselian Epoch}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EPB2D}{D}{Modified Julian Date (JD$-$2400000.5)}
+}
+\aref{Lieske, J.H., 1979. {\it Astr.Astrophys.}\ {\bf 73}, 282.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EPCO}{Convert Epoch to B or J}
+{
+ \action{Convert an epoch to Besselian or Julian to match another one.}
+ \call{D~=~sla\_EPCO (K0, K, E)}
+
+}
+\args{GIVEN}
+{
+ \spec{K0}{C}{form of result:  `B'=Besselian, `J'=Julian} \\
+ \spec{K}{C}{form of given epoch:  `B' or `J'} \\
+ \spec{E}{D}{epoch}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EPCO}{D}{the given epoch converted as necessary}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The result is always either equal to or very close to
+        the given epoch E.  The routine is required only in
+        applications where punctilious treatment of heterogeneous
+        mixtures of star positions is necessary.
+  \item K0 and K are not validated.  They are interpreted as follows:
+        \begin{itemize}
+         \item If K0 and K are the same, the result is E.
+         \item If K0 is `B' and K isn't, the conversion is J to B.
+         \item In all other cases, the conversion is B to J.
+        \end{itemize}
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EPJ}{MJD to Julian Epoch}
+{
+ \action{Convert Modified Julian Date to Julian Epoch.}
+ \call{D~=~sla\_EPJ (DATE)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{Modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EPJ}{D}{Julian Epoch}
+}
+\aref{Lieske, J.H., 1979.\ {\it Astr.Astrophys.}, {\bf 73}, 282.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EPJ2D}{Julian Epoch to MJD}
+{
+ \action{Convert Julian Epoch to Modified Julian Date.}
+ \call{D~=~sla\_EPJ2D (EPJ)}
+}
+\args{GIVEN}
+{
+ \spec{EPJ}{D}{Julian Epoch}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EPJ2D}{D}{Modified Julian Date (JD$-$2400000.5)}
+}
+\aref{Lieske, J.H., 1979.\ {\it Astr.Astrophys.}, {\bf 73}, 282.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EPV}{Earth Position \& Velocity (high accuracy)}
+{
+ \action{Earth position and velocity, heliocentric and barycentric,
+         with respect to the Barycentric Celestial Reference System.}
+ \call{CALL sla\_EPV (DATE, PH, VH, PB, VB)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB Modified Julian Date (Note~1)}
+}
+\args{RETURNED}
+{
+ \spec{PH}{D(3)}{heliocentric \xyz, AU} \\
+ \spec{VH}{D(3)}{heliocentric \xyzd, AU~d$^{-1}$} \\
+ \spec{PB}{D(3)}{barycentric \xyz, AU} \\
+ \spec{VB}{D(3)}{barycentric \xyzd, AU~d$^{-1}$}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The date is TDB as MJD (=JD$-$2400000.5).  TT can be used
+        instead of TDB in most applications.
+  \item The vectors are with respect to the Barycentric Celestial
+        Reference System (BCRS).  Positions are in AU;  velocities are in
+        AU per TDB day.
+  \item The routine is a {\it simplified solution}\/ from the planetary
+        theory VSOP2000 (X.\,Moisson, P.\,Bretagnon, 2001, Celes. Mechanics
+        \& Dyn. Astron., {\bf 80}, 3/4, 205-213) and is an adaptation of
+        original Fortran code supplied by P.\,Bretagnon (private
+        communication, 2000).
+  \item Comparisons over the time span 1900-2100 with this simplified
+        solution and the JPL DE405 ephemeris give the following results:
+
+        \begin{tabular}{lllll}
+        &               & RMS & max \\
+        & Heliocentric: \\
+        & ~~~~~position error & 3.7 & 11.2 & km \\
+        & ~~~~~velocity error & 1.4 & ~5.0 & mm/s \\
+        & Barycentric: \\
+        & ~~~~~position error & 4.6 & 13.4 & km \\
+        & ~~~~~velocity error & 1.4 & ~4.9 & mm/s
+        \end{tabular}
+
+        The results deteriorate outside this time span.
+  \item The routine sla\_EVP is faster but less accurate.
+        The present routine targets the case where high
+        accuracy is more important
+        than CPU time, yet the extra complication of reading a
+        pre-computed ephemeris is not justified.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EQECL}{J2000 $\alpha,\delta$ to Ecliptic}
+{
+ \action{Transformation from J2000.0 equatorial coordinates to
+         ecliptic longitude and latitude.}
+ \call{CALL sla\_EQECL (DR, DD, DATE, DL, DB)}
+}
+\args{GIVEN}
+{
+ \spec{DR,DD}{D}{J2000.0 mean \radec\ (radians)} \\
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{DL,DB}{D}{ecliptic longitude and latitude
+                        (mean of date, IAU 1980 theory, radians)}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EQEQX}{Equation of the Equinoxes}
+{
+ \action{Equation of the equinoxes (IAU 1994).}
+ \call{D~=~sla\_EQEQX (DATE)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_EQEQX}{D}{The equation of the equinoxes (radians)}
+}
+\notes{
+ \begin{enumerate}
+  \item The equation of the equinoxes is defined here as GAST~$-$~GMST:
+        it is added to a {\it mean}\/ sidereal time to give the
+        {\it apparent}\/ sidereal time.
+  \item The change from the classic ``textbook'' expression
+        $\Delta\psi\,cos\,\epsilon$ occurred with IAU Resolution C7,
+        Recommendation~3 (1994).  The new formulation takes into
+        account cross-terms between the various precession and
+        nutation quantities, amounting to about 3~milliarcsec.
+        The transition from the old to the new model officially
+        took place on 1997 February~27.
+ \end{enumerate}
+}
+\aref{Capitaine, N.\ \& Gontier, A.-M.\ (1993),
+      {\it Astron. Astrophys.},
+      {\bf 275}, 645-650.}
+%-----------------------------------------------------------------------
+\routine{SLA\_EQGAL}{J2000 $\alpha,\delta$ to Galactic}
+{
+ \action{Transformation from J2000.0 FK5 equatorial coordinates to
+ IAU 1958 galactic coordinates.}
+ \call{CALL sla\_EQGAL (DR, DD, DL, DB)}
+}
+\args{GIVEN}
+{
+ \spec{DR,DD}{D}{J2000.0 \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal\ (radians)}
+}
+\anote{The equatorial coordinates are J2000.0 FK5.  Use the routine
+       sla\_EG50 if conversion from B1950.0 FK4 coordinates is required.}
+\aref{Blaauw {\it et al.}, 1960, {\it Mon.Not.R.astr.Soc.},
+      {\bf 121}, 123.}
+%-----------------------------------------------------------------------
+\routine{SLA\_ETRMS}{E-terms of Aberration}
+{
+ \action{Compute the E-terms vector -- the part of the annual
+         aberration which arises from the eccentricity of the
+         Earth's orbit.}
+ \call{CALL sla\_ETRMS (EP, EV)}
+}
+\args{GIVEN}
+{
+ \spec{EP}{D}{Besselian epoch}
+}
+\args{RETURNED}
+{
+ \spec{EV}{D(3)}{E-terms as $[\Delta x, \Delta y, \Delta z\,]$}
+}
+\anote{Note the use of the J2000 aberration constant (\arcsec{20}{49552}).
+       This is a reflection of the fact that the E-terms embodied in
+       existing star catalogues were computed from a variety of
+       aberration constants.  Rather than adopting one of the old
+       constants the latest value is used here.}
+\refs
+{
+ \begin{enumerate}
+  \item Smith, C.A.\ {\it et al.}, 1989.  {\it Astr.J.}\ {\bf 97}, 265.
+  \item Yallop, B.D.\ {\it et al.}, 1989.  {\it Astr.J.}\ {\bf 97}, 274.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EULER}{Rotation Matrix from Euler Angles}
+{
+ \action{Form a rotation matrix from the Euler angles -- three
+         successive rotations about specified Cartesian axes
+         (single precision).}
+ \call{CALL sla\_EULER (ORDER, PHI, THETA, PSI, RMAT)}
+}
+\args{GIVEN}
+{
+ \spec{ORDER}{C*(*)}{specifies about which axes the rotations occur} \\
+ \spec{PHI}{R}{1st rotation (radians)} \\
+ \spec{THETA}{R}{2nd rotation (radians)} \\
+ \spec{PSI}{R}{3rd rotation (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RMAT}{R(3,3)}{rotation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A rotation is positive when the reference frame rotates
+        anticlockwise as seen looking towards the origin from the
+        positive region of the specified axis.
+  \item The characters of ORDER define which axes the three successive
+        rotations are about.  A typical value is `ZXZ', indicating that
+        RMAT is to become the direction cosine matrix corresponding to
+        rotations of the reference frame through PHI radians about the
+        old {\it z}-axis, followed by THETA radians about the resulting
+        {\it x}-axis,
+        then PSI radians about the resulting {\it z}-axis.  In detail:
+        \begin{itemize}
+         \item The axis names can be any of the following, in any order or
+               combination:  X, Y, Z, uppercase or lowercase, 1, 2, 3.  Normal
+               axis labelling/numbering conventions apply;
+               the {\it xyz} ($\equiv123$)
+               triad is right-handed.  Thus, the `ZXZ' example given above
+               could be written `zxz' or `313' (or even `ZxZ' or `3xZ').
+         \item ORDER is terminated by length or by the first unrecognized
+               character.
+         \item Fewer than three rotations are acceptable, in which case
+               the later angle arguments are ignored.
+        \end{itemize}
+  \item Zero rotations produces the identity RMAT.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_EVP}{Earth Position \& Velocity}
+{
+ \action{Barycentric and heliocentric velocity and position of the Earth.}
+ \call{CALL sla\_EVP (DATE, DEQX, DVB, DPB, DVH, DPH)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (formerly ET) as a Modified Julian Date
+                                        (JD$-$2400000.5)} \\
+ \spec{DEQX}{D}{Julian Epoch ({\it e.g.}\ 2000D0) of mean equator and
+                equinox of the vectors returned.  If DEQX~$<0$,
+                  all vectors are referred to the mean equator and
+                  equinox (FK5) of date DATE.}
+}
+\args{RETURNED}
+{
+ \spec{DVB}{D(3)}{barycentric \xyzd, AU~s$^{-1}$} \\
+ \spec{DPB}{D(3)}{barycentric \xyz, AU} \\
+ \spec{DVH}{D(3)}{heliocentric \xyzd, AU~s$^{-1}$} \\
+ \spec{DPH}{D(3)}{heliocentric \xyz, AU}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine is accurate enough for many purposes but faster
+        and more compact than the sla\_EPV routine.  The maximum
+        deviations from the JPL~DE96 ephemeris are as follows:
+        \begin{itemize}
+         \item velocity (barycentric or heliocentric): 420~mm~s$^{-1}$
+         \item position (barycentric): 6900~km
+         \item position (heliocentric): 1600~km
+        \end{itemize}
+  \item The routine is adapted from the BARVEL and BARCOR
+        subroutines of Stumpff (1980).
+        Most of the changes are merely cosmetic and do not affect
+        the results at all.  However, some adjustments have been
+        made so as to give results that refer to the IAU 1976
+        `FK5' equinox and precession, although the differences these
+        changes make relative to the results from Stumpff's original
+        `FK4' version are smaller than the inherent accuracy of the
+        algorithm.  One minor shortcoming in the original routines
+        that has {\bf not} been corrected is that slightly better
+        numerical accuracy could be achieved if the various polynomial
+        evaluations were to be so arranged that the smallest terms were
+        computed first.
+ \end{enumerate}
+}
+\aref {Stumpff, P., 1980.,  {\it Astron.Astrophys.Suppl.Ser.}\
+       {\bf 41}, 1-8.}
+%-----------------------------------------------------------------------
+\routine{SLA\_FITXY}{Fit Linear Model to Two \xy\ Sets}
+{
+ \action{Fit a linear model to relate two sets of \xy\ coordinates.}
+ \call{CALL sla\_FITXY (ITYPE, NP, XYE, XYM, COEFFS, J)}
+}
+\args{GIVEN}
+{
+ \spec{ITYPE}{I}{type of model: 4 or 6 (note 1)} \\
+ \spec{NP}{I}{number of samples (note 2)} \\
+ \spec{XYE}{D(2,NP)}{expected \xy\ for each sample} \\
+ \spec{XYM}{D(2,NP)}{measured \xy\ for each sample}
+}
+\args{RETURNED}
+{
+ \spec{COEFFS}{D(6)}{coefficients of model (note 3)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK} \\
+ \spec{}{}{\hspace{0.7em} $-$1 = illegal ITYPE} \\
+ \spec{}{}{\hspace{0.7em} $-$2 = insufficient data} \\
+ \spec{}{}{\hspace{0.7em} $-$3 = singular solution}
+}
+\notes
+{
+ \begin{enumerate}
+  \item ITYPE, which must be either 4 or 6, selects the type of model
+        fitted.  Both allowed ITYPE values produce a model COEFFS which
+        consists of six coefficients, namely the zero points and, for
+        each of XE and YE, the coefficient of XM and YM.  For ITYPE=6,
+        all six coefficients are independent, modelling squash and shear
+        as well as origin, scale, and orientation.  However, ITYPE=4
+        selects the {\it solid body rotation}\/ option;  the model COEFFS
+        still consists of the same six coefficients, but now two of
+        them are used twice (appropriately signed).  Origin, scale
+        and orientation are still modelled, but not squash or shear --
+        the units of X and Y have to be the same.
+  \item For NC=4, NP must be at least 2.  For NC=6, NP must be at
+        least 3.
+  \item The model is returned in the array COEFFS.  Naming the
+        six elements of COEFFS $a,b,c,d,e$ \& $f$,
+        the model transforms {\it measured}\/ coordinates
+        $[x_{m},y_{m}\,]$ into {\it expected}\/ coordinates
+        $[x_{e},y_{e}\,]$ as follows:
+        \begin{verse}
+         $x_{e} = a + bx_{m} + cy_{m}$ \\
+         $y_{e} = d + ex_{m} + fy_{m}$
+        \end{verse}
+        For the {\it solid body rotation}\/ option (ITYPE=4), the
+        magnitudes of $b$ and $f$, and of $c$ and $e$, are equal.  The
+        signs of these coefficients depend on whether there is a
+        sign reversal between $[x_{e},y_{e}]$ and $[x_{m},y_{m}]$;
+        fits are performed
+        with and without a sign reversal and the best one chosen.
+  \item Error status values J=$-$1 and $-$2 leave COEFFS unchanged;
+        if J=$-$3 COEFFS may have been changed.
+  \item See also sla\_PXY, sla\_INVF, sla\_XY2XY, sla\_DCMPF.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK425}{FK4 to FK5}
+{
+ \action{Convert B1950.0 FK4 star data to J2000.0 FK5.
+         This routine converts stars from the old, Bessel-Newcomb, FK4
+         system to the new, IAU~1976, FK5, Fricke system.  The precepts
+         of Smith~{\it et~al.}\ (see reference~1) are followed,
+         using the implementation
+         by Yallop~{\it et~al.}\ (reference~2) of a matrix method
+         due to Standish.
+         Kinoshita's development of Andoyer's post-Newcomb precession is
+         used.  The numerical constants from
+         Seidelmann~{\it et~al.}\  (reference~3) are used canonically.}
+ \call{CALL sla\_FK425 (\vtop{
+         \hbox{R1950,D1950,DR1950,DD1950,P1950,V1950,}
+         \hbox{R2000,D2000,DR2000,DD2000,P2000,V2000)}}}
+}
+\args{GIVEN}
+{
+ \spec{R1950}{D}{B1950.0 $\alpha$ (radians)} \\
+ \spec{D1950}{D}{B1950.0 $\delta$ (radians)} \\
+ \spec{DR1950}{D}{B1950.0 proper motion in $\alpha$
+                              (radians per tropical year)} \\
+ \spec{DD1950}{D}{B1950.0 proper motion in $\delta$
+                              (radians per tropical year)} \\
+ \spec{P1950}{D}{B1950.0 parallax (arcsec)} \\
+ \spec{V1950}{D}{B1950.0 radial velocity (km~s$^{-1}$, +ve = moving away)}
+}
+\args{RETURNED}
+{
+ \spec{R2000}{D}{J2000.0 $\alpha$ (radians)} \\
+ \spec{D2000}{D}{J2000.0 $\delta$ (radians)} \\
+ \spec{DR2000}{D}{J2000.0 proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DD2000}{D}{J2000.0 proper motion in $\delta$
+                              (radians per Julian year)} \\
+ \spec{P2000}{D}{J2000.0 parallax (arcsec)} \\
+ \spec{V2000}{D}{J2000.0 radial velocity (km~s$^{-1}$, +ve = moving away)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item Conversion from Besselian epoch 1950.0 to Julian epoch
+        2000.0 only is provided for.  Conversions involving other
+        epochs will require use of the appropriate precession,
+        proper motion, and E-terms routines before and/or after FK425
+        is called.
+  \item In the FK4 catalogue the proper motions of stars within
+        $10^{\circ}$ of the poles do not include the {\it differential
+        E-terms}\/ effect and should, strictly speaking, be handled
+        in a different manner from stars outside these regions.
+        However, given the general lack of homogeneity of the star
+        data available for routine astrometry, the difficulties of
+        handling positions that may have been determined from
+        astrometric fields spanning the polar and non-polar regions,
+        the likelihood that the differential E-terms effect was not
+        taken into account when allowing for proper motion in past
+        astrometry, and the undesirability of a discontinuity in
+        the algorithm, the decision has been made in this routine to
+        include the effect of differential E-terms on the proper
+        motions for all stars, whether polar or not.  At epoch J2000,
+        and measuring on the sky rather than in terms of $\Delta\alpha$,
+        the errors resulting from this simplification are less than
+        1~milliarcsecond in position and 1~milliarcsecond per
+        century in proper motion.
+  \item See also sla\_FK45Z, sla\_FK524, sla\_FK54Z.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Smith, C.A.\ {\it et al.}, 1989.\  {\it Astr.J.}\ {\bf 97}, 265.
+  \item Yallop, B.D.\ {\it et al.}, 1989.\ {\it Astr.J.}\ {\bf 97}, 274.
+  \item Seidelmann, P.K.\ (ed), 1992.  {\it Explanatory
+        Supplement to the Astronomical Almanac,}\/ ISBN~0-935702-68-7.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK45Z}{FK4 to FK5, no P.M. or Parallax}
+{
+ \action{Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero
+         proper motion in the FK5 frame.
+         This routine converts stars from the old, Bessel-Newcomb, FK4
+         system to the new, IAU~1976, FK5, Fricke system, in such a
+         way that the FK5 proper motion is zero.  Because such a star
+         has, in general, a non-zero proper motion in the FK4 system,
+         the routine requires the epoch at which the position in the
+         FK4 system was determined.  The method is from appendix~2 of
+         reference~1, but using the constants of reference~4.}
+ \call{CALL sla\_FK45Z (R1950, D1950, BEPOCH, R2000, D2000)}
+}
+\args{GIVEN}
+{
+ \spec{R1950}{D}{B1950.0 FK4 $\alpha$ at epoch BEPOCH (radians)} \\
+ \spec{D1950}{D}{B1950.0 FK4 $\delta$ at epoch BEPOCH (radians)} \\
+ \spec{BEPOCH}{D}{Besselian epoch ({\it e.g.}\ 1979.3D0)}
+}
+\args{RETURNED}
+{
+ \spec{R2000}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D2000}{D}{J2000.0 FK5 $\delta$ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The epoch BEPOCH is strictly speaking Besselian, but
+        if a Julian epoch is supplied the result will be
+        affected only to a negligible extent.
+  \item Conversion from Besselian epoch 1950.0 to Julian epoch
+        2000.0 only is provided for.  Conversions involving other
+        epochs will require use of the appropriate precession,
+        proper motion, and E-terms routines before and/or
+        after FK45Z is called.
+  \item In the FK4 catalogue the proper motions of stars within
+        $10^{\circ}$ of the poles do not include the {\it differential
+        E-terms}\/ effect and should, strictly speaking, be handled
+        in a different manner from stars outside these regions.
+        However, given the general lack of homogeneity of the star
+        data available for routine astrometry, the difficulties of
+        handling positions that may have been determined from
+        astrometric fields spanning the polar and non-polar regions,
+        the likelihood that the differential E-terms effect was not
+        taken into account when allowing for proper motion in past
+        astrometry, and the undesirability of a discontinuity in
+        the algorithm, the decision has been made in this routine to
+        include the effect of differential E-terms on the proper
+        motions for all stars, whether polar or not.  At epoch 2000,
+        and measuring on the sky rather than in terms of $\Delta\alpha$,
+        the errors resulting from this simplification are less than
+        1~milliarcsecond in position and 1~milliarcsecond per
+        century in proper motion.
+  \item See also sla\_FK425, sla\_FK524, sla\_FK54Z.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Aoki, S., {\it et al.}, 1983.\ {\it Astr.Astrophys.}, {\bf 128}, 263.
+  \item Smith, C.A.\ {\it et al.}, 1989.\  {\it Astr.J.}\ {\bf 97}, 265.
+  \item Yallop, B.D.\ {\it et al.}, 1989.\ {\it Astr.J.}\ {\bf 97}, 274.
+  \item Seidelmann, P.K.\ (ed), 1992.  {\it Explanatory
+        Supplement to the Astronomical Almanac,}\/ ISBN~0-935702-68-7.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK524}{FK5 to FK4}
+{
+ \action{Convert J2000.0 FK5 star data to B1950.0 FK4.
+         This routine converts stars from the new, IAU~1976, FK5, Fricke
+         system, to the old, Bessel-Newcomb, FK4 system.
+         The precepts of Smith~{\it et~al.}\ (reference~1) are followed,
+         using the implementation by Yallop~{\it et~al.}\ (reference~2)
+         of a matrix method due to Standish.  Kinoshita's development of
+         Andoyer's post-Newcomb precession is used.  The numerical
+         constants from Seidelmann~{\it et~al.}\ (reference~3) are
+         used canonically.}
+ \call{CALL sla\_FK524 (\vtop{
+         \hbox{R2000, D2000, DR2000, DD2000, P2000, V2000,}
+         \hbox{R1950, D1950, DR1950, DD1950, P1950, V1950)}}}
+}
+\args{GIVEN}
+{
+ \spec{R2000}{D}{J2000.0 $\alpha$ (radians)} \\
+ \spec{D2000}{D}{J2000.0 $\delta$ (radians)} \\
+ \spec{DR2000}{D}{J2000.0 proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DD2000}{D}{J2000.0 proper motion in $\delta$
+                              (radians per Julian year)} \\
+ \spec{P2000}{D}{J2000.0 parallax (arcsec)} \\
+ \spec{V2000}{D}{J2000 radial velocity (km~s$^{-1}$, +ve = moving away)}
+}
+\args{RETURNED}
+{
+ \spec{R1950}{D}{B1950.0 $\alpha$ (radians)} \\
+ \spec{D1950}{D}{B1950.0 $\delta$ (radians)} \\
+ \spec{DR1950}{D}{B1950.0 proper motion in $\alpha$
+                              (radians per tropical year)} \\
+ \spec{DD1950}{D}{B1950.0 proper motion in $\delta$
+                              (radians per tropical year)} \\
+ \spec{P1950}{D}{B1950.0 parallax (arcsec)} \\
+ \spec{V1950}{D}{radial velocity (km~s$^{-1}$, +ve = moving away)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item Note that conversion from Julian epoch 2000.0 to Besselian
+        epoch 1950.0 only is provided for.  Conversions involving
+        other epochs will require use of the appropriate precession,
+        proper motion, and E-terms routines before and/or after
+        FK524 is called.
+  \item In the FK4 catalogue the proper motions of stars within
+        $10^{\circ}$ of the poles do not include the {\it differential
+        E-terms}\/ effect and should, strictly speaking, be handled
+        in a different manner from stars outside these regions.
+        However, given the general lack of homogeneity of the star
+        data available for routine astrometry, the difficulties of
+        handling positions that may have been determined from
+        astrometric fields spanning the polar and non-polar regions,
+        the likelihood that the differential E-terms effect was not
+        taken into account when allowing for proper motion in past
+        astrometry, and the undesirability of a discontinuity in
+        the algorithm, the decision has been made in this routine to
+        include the effect of differential E-terms on the proper
+        motions for all stars, whether polar or not.  At epoch 2000,
+        and measuring on the sky rather than in terms of $\Delta\alpha$,
+        the errors resulting from this simplification are less than
+        1~milliarcsecond in position and 1~milliarcsecond per
+        century in proper motion.
+  \item See also sla\_FK425, sla\_FK45Z, sla\_FK54Z.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Smith, C.A.\ {\it et al.}, 1989.\  {\it Astr.J.}\ {\bf 97}, 265.
+  \item Yallop, B.D.\ {\it et al.}, 1989.\ {\it Astr.J.}\ {\bf 97}, 274.
+  \item Seidelmann, P.K.\ (ed), 1992.  {\it Explanatory
+        Supplement to the Astronomical Almanac,}\/ ISBN~0-935702-68-7.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK52H}{FK5 to Hipparcos}
+{
+ \action{Transform an FK5 (J2000) position and proper motion
+         into the frame of the Hipparcos catalogue.}
+ \call{CALL sla\_FK52H (R5, D5, DR5, DD5, RH, DH, DRH, DDH)}
+}
+\args{GIVEN}
+{
+ \spec{R5}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D5}{D}{J2000.0 FK5 $\delta$ (radians)} \\
+ \spec{DR5}{D}{J2000.0 FK5 proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DD5}{D}{J2000.0 FK5 proper motion in $\delta$
+                              (radians per Julian year)}
+}
+\args{RETURNED}
+{
+ \spec{RH}{D}{Hipparcos $\alpha$ (radians)} \\
+ \spec{DH}{D}{Hipparcos $\delta$ (radians)} \\
+ \spec{DRH}{D}{Hipparcos proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DDH}{D}{Hipparcos proper motion in $\delta$
+                              (radians per Julian year)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item The FK5 to Hipparcos
+        transformation consists of a pure rotation and spin;
+        zonal errors in the FK5 catalogue are not taken into account.
+  \item The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin
+        values are as follows (see reference):
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~~~
+        \begin{tabular}{|r|r|r|} \hline
+        &
+        \multicolumn{1}{|c}{\it orientation} &
+        \multicolumn{1}{|c|}{\it ~~~spin~~~} \\ \hline
+        $x$ & $-19.9$~~~~ & ~$-0.30$~~ \\
+        $y$ &  $-9.1$~~~~ & ~$+0.60$~~ \\
+        $z$ & $+22.9$~~~~ & ~$+0.70$~~ \\ \hline
+        & {\it mas}~~~~~ & ~{\it mas/y}~ \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        These orientation and spin components are interpreted as
+        {\it axial vectors.}  An axial vector points at the pole of
+        the rotation and its length is the amount of rotation in radians.
+  \item See also sla\_FK5HZ, sla\_H2FK5, sla\_HFK5Z.
+ \end{enumerate}
+}
+\aref {Feissel, M.\ \& Mignard, F., 1998.,  {\it Astron.Astrophys.}\
+       {\bf 331}, L33-L36.}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK54Z}{FK5 to FK4, no P.M. or Parallax}
+{
+ \action{Convert a J2000.0 FK5 star position to B1950.0 FK4 assuming
+         FK5 zero proper motion and parallax.
+         This routine converts star positions from the new, IAU~1976,
+         FK5, Fricke system to the old, Bessel-Newcomb, FK4 system.}
+ \call{CALL sla\_FK54Z (R2000, D2000, BEPOCH, R1950, D1950, DR1950, DD1950)}
+}
+\args{GIVEN}
+{
+ \spec{R2000}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D2000}{D}{J2000.0 FK5 $\delta$ (radians)} \\
+ \spec{BEPOCH}{D}{Besselian epoch ({\it e.g.}\ 1950D0)}
+}
+\args{RETURNED}
+{
+ \spec{R1950}{D}{B1950.0 FK4 $\alpha$ at epoch BEPOCH (radians)} \\
+ \spec{D1950}{D}{B1950.0 FK4 $\delta$ at epoch BEPOCH (radians)} \\
+ \spec{DR1950}{D}{B1950.0 FK4 proper motion in $\alpha$
+                              (radians per tropical year)} \\
+ \spec{DD1950}{D}{B1950.0 FK4 proper motion in $\delta$
+                              (radians per tropical year)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item Conversion from Julian epoch 2000.0 to Besselian epoch 1950.0
+        only is provided for.  Conversions involving other epochs will
+        require use of the appropriate precession routines before and
+        after this routine is called.
+  \item Unlike in the sla\_FK524 routine, the FK5 proper motions, the
+        parallax and the radial velocity are presumed zero.
+  \item It was the intention that FK5 should be a close approximation
+        to an inertial frame, so that distant objects have zero proper
+        motion;  such objects have (in general) non-zero proper motion
+        in FK4, and this routine returns those {\it fictitious proper
+        motions}.
+  \item The position returned by this routine is in the B1950
+        reference frame but at Besselian epoch BEPOCH.  For
+        comparison with catalogues the BEPOCH argument will
+        frequently be 1950D0.
+  \item See also sla\_FK425, sla\_FK45Z, sla\_FK524.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_FK5HZ}{FK5 to Hipparcos, no P.M.}
+{
+ \action{Transform an FK5 (J2000) star position into the frame of the
+         Hipparcos catalogue, assuming zero Hipparcos proper motion.}
+ \call{CALL sla\_FK5HZ (R5, D5, EPOCH, RH, DH)}
+}
+\args{GIVEN}
+{
+ \spec{R5}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D5}{D}{J2000.0 FK5 $\delta$ (radians)} \\
+ \spec{EPOCH}{D}{Julian epoch (TDB)}
+}
+\args{RETURNED}
+{
+ \spec{RH}{D}{Hipparcos $\alpha$ (radians)} \\
+ \spec{DH}{D}{Hipparcos $\delta$ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item The FK5 to Hipparcos
+        transformation consists of a pure rotation and spin;
+        zonal errors in the FK5 catalogue are not taken into account.
+  \item The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin
+        values are as follows (see reference):
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~~~
+        \begin{tabular}{|r|r|r|} \hline
+        &
+        \multicolumn{1}{|c}{\it orientation} &
+        \multicolumn{1}{|c|}{\it ~~~spin~~~} \\ \hline
+        $x$ & $-19.9$~~~~ & ~$-0.30$~~ \\
+        $y$ &  $-9.1$~~~~ & ~$+0.60$~~ \\
+        $z$ & $+22.9$~~~~ & ~$+0.70$~~ \\ \hline
+        & {\it mas}~~~~~ & ~{\it mas/y}~ \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        These orientation and spin components are interpreted as
+        {\it axial vectors.}  An axial vector points at the pole of
+        the rotation and its length is the amount of rotation in radians.
+  \item See also sla\_FK52H, sla\_H2FK5, sla\_HFK5Z.
+ \end{enumerate}
+}
+\aref {Feissel, M.\ \& Mignard, F., 1998.,  {\it Astron.Astrophys.}\
+       {\bf 331}, L33-L36.}
+%-----------------------------------------------------------------------
+\routine{SLA\_FLOTIN}{Decode a Real Number}
+{
+ \action{Convert free-format input into single precision floating point.}
+ \call{CALL sla\_FLOTIN (STRING, NSTRT, RESLT, JFLAG)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C}{string containing number to be decoded} \\
+ \spec{NSTRT}{I}{pointer to where decoding is to commence} \\
+ \spec{RESLT}{R}{current value of result}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{advanced to next number} \\
+ \spec{RESLT}{R}{result} \\
+ \spec{JFLAG}{I}{status: $-$1~=~$-$OK, 0~=~+OK, 1~=~null result, 2~=~error}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The reason sla\_FLOTIN has separate `OK' status values
+       for + and $-$ is to enable minus zero to be detected.
+       This is of crucial importance
+       when decoding mixed-radix numbers.  For example, an angle
+       expressed as degrees, arcminutes and arcseconds may have a
+       leading minus sign but a zero degrees field.
+ \item A TAB is interpreted as a space, and lowercase characters are
+       interpreted as uppercase.  {\it n.b.}\ The test for TAB is
+       ASCII-specific.
+ \item The basic format is the sequence of fields $\pm n.n x \pm n$,
+       where $\pm$ is a sign
+       character `+' or `$-$', $n$ means a string of decimal digits,
+       `.' is a decimal point, and $x$, which indicates an exponent,
+       means `D' or `E'.  Various combinations of these fields can be
+       omitted, and embedded blanks are permissible in certain places.
+ \item Spaces:
+       \begin{itemize}
+       \item Leading spaces are ignored.
+       \item Embedded spaces are allowed only after +, $-$, D or E,
+             and after the decimal point if the first sequence of
+             digits is absent.
+       \item Trailing spaces are ignored;  the first signifies
+             end of decoding and subsequent ones are skipped.
+       \end{itemize}
+ \item Delimiters:
+       \begin{itemize}
+       \item Any character other than +,$-$,0-9,.,D,E or space may be
+             used to signal the end of the number and terminate decoding.
+       \item Comma is recognized by sla\_FLOTIN as a special case; it
+             is skipped, leaving the pointer on the next character.  See
+             13, below.
+       \item Decoding will in all cases terminate if end of string
+             is reached.
+       \end{itemize}
+ \item Both signs are optional.  The default is +.
+ \item The mantissa $n.n$ defaults to unity.
+ \item The exponent $x\!\pm\!n$ defaults to `E0'.
+ \item The strings of decimal digits may be of any length.
+ \item The decimal point is optional for whole numbers.
+ \item A {\it null result}\/ occurs when the string of characters
+       being decoded does not begin with +,$-$,0-9,.,D or E, or
+       consists entirely of spaces.  When this condition is
+       detected, JFLAG is set to 1 and RESLT is left untouched.
+ \item NSTRT = 1 for the first character in the string.
+ \item On return from sla\_FLOTIN, NSTRT is set ready for the next
+       decode -- following trailing blanks and any comma.  If a
+       delimiter other than comma is being used, NSTRT must be
+       incremented before the next call to sla\_FLOTIN, otherwise
+       all subsequent calls will return a null result.
+ \item Errors (JFLAG=2) occur when:
+       \begin{itemize}
+       \item a +, $-$, D or E is left unsatisfied; or
+       \item the decimal point is present without at least
+             one decimal digit before or after it; or
+       \item an exponent more than 100 has been presented.
+       \end{itemize}
+ \item When an error has been detected, NSTRT is left
+       pointing to the character following the last
+       one used before the error came to light.  This
+       may be after the point at which a more sophisticated
+       program could have detected the error.  For example,
+       sla\_FLOTIN does not detect that `1E999' is unacceptable
+       (on a computer where this is so)
+       until the entire number has been decoded.
+ \item Certain highly unlikely combinations of mantissa and
+       exponent can cause arithmetic faults during the
+       decode, in some cases despite the fact that they
+       together could be construed as a valid number.
+ \item Decoding is left to right, one pass.
+ \item See also sla\_DFLTIN and sla\_INTIN.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_GALEQ}{Galactic to J2000 $\alpha,\delta$}
+{
+ \action{Transformation from IAU 1958 galactic coordinates
+         to J2000.0 FK5 equatorial coordinates.}
+ \call{CALL sla\_GALEQ (DL, DB, DR, DD)}
+}
+\args{GIVEN}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal}
+}
+\args{RETURNED}
+{
+ \spec{DR,DD}{D}{J2000.0 \radec}
+}
+\notes
+{
+ \begin{enumerate}
+  \item All arguments are in radians.
+  \item The equatorial coordinates are J2000.0 FK5.  Use the routine
+        sla\_GE50 if conversion to B1950.0 FK4 coordinates is
+                           required.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_GALSUP}{Galactic to Supergalactic}
+{
+ \action{Transformation from IAU 1958 galactic coordinates to
+         de Vaucouleurs supergalactic coordinates.}
+ \call{CALL sla\_GALSUP (DL, DB, DSL, DSB)}
+}
+\args{GIVEN}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{DSL,DSB}{D}{supergalactic longitude and latitude (radians)}
+}
+\refs
+{
+ \begin{enumerate}
+  \item de Vaucouleurs, de Vaucouleurs, \& Corwin, {\it Second Reference
+    Catalogue of Bright Galaxies}, U.Texas, p8.
+  \item Systems \& Applied Sciences Corp., documentation for the
+        machine-readable version of the above catalogue,
+        Contract NAS 5-26490.
+ \end{enumerate}
+ (These two references give different values for the galactic
+ longitude of the supergalactic origin.  Both are wrong;  the
+ correct value is $l^{I\!I}=137.37$.)
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_GE50}{Galactic to B1950 $\alpha,\delta$}
+{
+ \action{Transformation from IAU 1958 galactic coordinates to
+         B1950.0 FK4 equatorial coordinates.}
+ \call{CALL sla\_GE50 (DL, DB, DR, DD)}
+}
+\args{GIVEN}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal}
+}
+\args{RETURNED}
+{
+ \spec{DR,DD}{D}{B1950.0 \radec}
+}
+\notes
+{
+ \begin{enumerate}
+  \item All arguments are in radians.
+  \item The equatorial coordinates are B1950.0 FK4.  Use the
+        routine sla\_GALEQ if conversion to J2000.0 FK5 coordinates
+        is required.
+ \end{enumerate}
+}
+\aref{Blaauw {\it et al.}, 1960, {\it Mon.Not.R.astr.Soc.},
+      {\bf 121}, 123.}
+%-----------------------------------------------------------------------
+\routine{SLA\_GEOC}{Geodetic to Geocentric}
+{
+ \action{Convert geodetic position to geocentric.}
+ \call{CALL sla\_GEOC (P, H, R, Z)}
+}
+\args{GIVEN}
+{
+ \spec{P}{D}{latitude (geodetic, radians)} \\
+ \spec{H}{D}{height above reference spheroid (geodetic, metres)}
+}
+\args{RETURNED}
+{
+ \spec{R}{D}{distance from Earth axis (AU)} \\
+ \spec{Z}{D}{distance from plane of Earth equator (AU)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Geocentric latitude can be obtained by evaluating {\tt ATAN2(Z,R)}.
+  \item IAU 1976 constants are used.
+ \end{enumerate}
+}
+\aref{Green, R.M., 1985.\ {\it Spherical Astronomy}, Cambridge U.P., p98.}
+%-----------------------------------------------------------------------
+\routine{SLA\_GMST}{UT to GMST}
+{
+ \action{Conversion from universal time UT1 to Greenwich mean
+         sidereal time.}
+ \call{D~=~sla\_GMST (UT1)}
+}
+\args{GIVEN}
+{
+ \spec{UT1}{D}{universal time (strictly UT1) expressed as
+                 modified Julian Date (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_GMST}{D}{Greenwich mean sidereal time (radians)}
+}
+\notes
+{
+  \begin{enumerate}
+       \item The IAU~1982 expression
+       (see page~S15 of the 1984 {\it Astronomical
+       Almanac})\/ is used, but rearranged to reduce rounding errors.  This
+       expression is always described as giving the GMST at $0^{\rm h}$UT;
+       in fact, it gives the difference between the
+       GMST and the UT, which happens to equal the GMST (modulo
+       24~hours) at $0^{\rm h}$UT each day.  In sla\_GMST, the
+       entire UT is used directly as the argument for the
+       canonical formula, and the fractional part of the UT is
+       added separately;  note that the factor $1.0027379\cdots$ does
+       not appear.
+       \item See also the routine sla\_GMSTA, which
+       delivers better numerical
+       precision by accepting the UT date and time as separate arguments.
+  \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_GMSTA}{UT to GMST (extra precision)}
+{
+ \action{Conversion from universal time UT1 to Greenwich mean
+         sidereal time, with rounding errors minimized.}
+ \call{D~=~sla\_GMSTA (DATE, UT1)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{UT1 date as Modified Julian Date (integer part
+                of JD$-$2400000.5)} \\
+ \spec{UT1}{D}{UT1 time (fraction of a day)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_GMST}{D}{Greenwich mean sidereal time (radians)}
+}
+\notes
+{
+  \begin{enumerate}
+       \item The algorithm is derived from the IAU 1982 expression
+       (see page~S15 of the 1984 Astronomical Almanac).
+       \item There is no restriction on how the UT is apportioned between the
+       DATE and UT1 arguments.  Either of the two arguments could, for
+       example, be zero and the entire date\,+\,time supplied in the other.
+       However, the routine is designed to deliver maximum accuracy when
+       the DATE argument is a whole number and the UT1 argument
+       lies in the range $[\,0,\,1\,]$, or {\it vice versa}.
+       \item See also the routine sla\_GMST, which accepts the UT1 as a single
+       argument.  Compared with sla\_GMST, the extra numerical precision
+       delivered by the present routine is unlikely to be important in
+       an absolute sense, but may be useful when critically comparing
+       algorithms and in applications where two sidereal times close
+       together are differenced.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_GRESID}{Gaussian Residual}
+{
+ \action{Generate pseudo-random normal deviate or {\it Gaussian residual}.}
+ \call{R~=~sla\_GRESID (S)}
+}
+\args{GIVEN}
+{
+ \spec{S}{R}{standard deviation}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The results of many calls to this routine will be
+        normally distributed with mean zero and standard deviation S.
+  \item The Box-Muller algorithm is used.
+  \item The implementation is machine-dependent.
+ \end{enumerate}
+}
+\aref{Ahrens \& Dieter, 1972.\ {\it Comm.A.C.M.}\ {\bf 15}, 873.}
+%-----------------------------------------------------------------------
+\routine{SLA\_H2E}{Az,El to $h,\delta$}
+{
+ \action{Horizon to equatorial coordinates
+         (single precision).}
+ \call{CALL sla\_H2E (AZ, EL, PHI, HA, DEC)}
+}
+\args{GIVEN}
+{
+ \spec{AZ}{R}{azimuth (radians)} \\
+ \spec{EL}{R}{elevation (radians)} \\
+ \spec{PHI}{R}{latitude (radians)}
+}
+\args{RETURNED}
+{
+ \spec{HA}{R}{hour angle (radians)} \\
+ \spec{DEC}{R}{declination (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The sign convention for azimuth is north zero, east $+\pi/2$.
+  \item HA is returned in the range $\pm\pi$.  Declination is returned
+        in the range $\pm\pi$.
+  \item The latitude is (in principle) geodetic.  In critical
+        applications, corrections for polar motion should be applied
+        (see sla\_POLMO).
+  \item In some applications it will be important to specify the
+        correct type of elevation in order to produce the required
+        type of \hadec.  In particular, it may be important to
+        distinguish between the elevation as affected by refraction,
+        which will yield the {\it observed} \hadec, and the elevation
+        {\it in vacuo}, which will yield the {\it topocentric}
+        \hadec.  If the
+        effects of diurnal aberration can be neglected, the
+        topocentric \hadec\ may be used as an approximation to the
+        {\it apparent} \hadec.
+  \item No range checking of arguments is carried out.
+  \item In applications which involve many such calculations, rather
+        than calling the present routine it will be more efficient to
+        use inline code, having previously computed fixed terms such
+        as sine and cosine of latitude.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_H2FK5}{Hipparcos to FK5}
+{
+ \action{Transform a Hipparcos star position and proper motion
+         into the FK5 (J2000) frame.}
+ \call{CALL sla\_H2FK5 (RH, DH, DRH, DDH, R5, D5, DR5, DD5)}
+}
+\args{GIVEN}
+{
+ \spec{RH}{D}{Hipparcos $\alpha$ (radians)} \\
+ \spec{DH}{D}{Hipparcos $\delta$ (radians)} \\
+ \spec{DRH}{D}{Hipparcos proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DDH}{D}{Hipparcos proper motion in $\delta$
+                              (radians per Julian year)}
+}
+\args{RETURNED}
+{
+ \spec{R5}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D5}{D}{J2000.0 FK5 $\delta$ (radians)} \\
+ \spec{DR5}{D}{J2000.0 FK5 proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DD5}{D}{FK5 J2000.0 proper motion in $\delta$
+                              (radians per Julian year)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item The FK5 to Hipparcos
+        transformation consists of a pure rotation and spin;
+        zonal errors in the FK5 catalogue are not taken into account.
+  \item The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin
+        values are as follows (see reference):
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~~~
+        \begin{tabular}{|r|r|r|} \hline
+        &
+        \multicolumn{1}{|c}{\it orientation} &
+        \multicolumn{1}{|c|}{\it ~~~spin~~~} \\ \hline
+        $x$ & $-19.9$~~~~ & ~$-0.30$~~ \\
+        $y$ &  $-9.1$~~~~ & ~$+0.60$~~ \\
+        $z$ & $+22.9$~~~~ & ~$+0.70$~~ \\ \hline
+        & {\it mas}~~~~~ & ~{\it mas/y}~ \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        These orientation and spin components are interpreted as
+        {\it axial vectors.}  An axial vector points at the pole of
+        the rotation and its length is the amount of rotation in radians.
+  \item See also sla\_FK52H, sla\_FK5HZ, sla\_HFK5Z.
+ \end{enumerate}
+}
+\aref {Feissel, M.\ \& Mignard, F., 1998.,  {\it Astron.Astrophys.}\
+       {\bf 331}, L33-L36.}
+%-----------------------------------------------------------------------
+\routine{SLA\_HFK5Z}{Hipparcos to FK5, no P.M.}
+{
+ \action{Transform a Hipparcos star position
+         into the FK5 (J2000) frame assuming zero Hipparcos proper motion.}
+ \call{CALL sla\_HFK5Z (RH, DH, EPOCH, R5, D5, DR5, DD5)}
+}
+\args{GIVEN}
+{
+ \spec{RH}{D}{Hipparcos $\alpha$ (radians)} \\
+ \spec{DH}{D}{Hipparcos $\delta$ (radians)} \\
+ \spec{EPOCH}{D}{Julian epoch (TDB)}
+}
+\args{RETURNED}
+{
+ \spec{R5}{D}{J2000.0 FK5 $\alpha$ (radians)} \\
+ \spec{D5}{D}{J2000.0 FK5 $\delta$ (radians)} \\
+ \spec{DR5}{D}{J2000.0 FK5 proper motion in $\alpha$
+                              (radians per Julian year)} \\
+ \spec{DD5}{D}{FK5 J2000.0 proper motion in $\delta$
+                              (radians per Julian year)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item The FK5 to Hipparcos
+        transformation consists of a pure rotation and spin;
+        zonal errors in the FK5 catalogue are not taken into account.
+  \item The adopted epoch J2000.0 FK5 to Hipparcos orientation and spin
+        values are as follows (see reference):
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~~~
+        \begin{tabular}{|r|r|r|} \hline
+        &
+        \multicolumn{1}{|c}{\it orientation} &
+        \multicolumn{1}{|c|}{\it ~~~spin~~~} \\ \hline
+        $x$ & $-19.9$~~~~ & ~$-0.30$~~ \\
+        $y$ &  $-9.1$~~~~ & ~$+0.60$~~ \\
+        $z$ & $+22.9$~~~~ & ~$+0.70$~~ \\ \hline
+        & {\it mas}~~~~~ & ~{\it mas/y}~ \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        These orientation and spin components are interpreted as
+        {\it axial vectors.}  An axial vector points at the pole of
+        the rotation and its length is the amount of rotation in radians.
+  \item It was the intention that Hipparcos should be a close
+        approximation to an inertial frame, so that distant objects
+        have zero proper motion;  such objects have (in general)
+        non-zero proper motion in FK5, and this routine returns those
+        {\it fictitious proper motions.}
+  \item The position returned by this routine is in the FK5 J2000
+        reference frame but at Julian epoch EPOCH.
+  \item See also sla\_FK52H, sla\_FK5HZ, sla\_H2FK5.
+ \end{enumerate}
+}
+\aref {Feissel, M.\ \& Mignard, F., 1998.,  {\it Astron.Astrophys.}\
+       {\bf 331}, L33-L36.}
+%-----------------------------------------------------------------------
+\routine{SLA\_IMXV}{Apply 3D Reverse Rotation}
+{
+ \action{Multiply a 3-vector by the inverse of a rotation
+         matrix (single precision).}
+ \call{CALL sla\_IMXV (RM, VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{RM}{R(3,3)}{rotation matrix} \\
+ \spec{VA}{R(3)}{vector to be rotated}
+}
+\args{RETURNED}
+{
+ \spec{VB}{R(3)}{result vector}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine performs the operation:
+        \begin{verse}
+         {\bf b} = {\bf M}$^{T}\cdot${\bf a}
+        \end{verse}
+        where {\bf a} and {\bf b} are the 3-vectors VA and VB
+        respectively, and {\bf M} is the $3\times3$ matrix RM.
+  \item The main function of this routine is apply an inverse
+        rotation;  under these circumstances, ${\bf M}$ is
+        {\it orthogonal}, with its inverse the same as its transpose.
+  \item To comply with the ANSI Fortran 77 standard, VA and VB must
+        {\bf not} be the same array.  The routine is, in fact, coded
+        so as to work properly on the VAX and many other systems even
+        if this rule is violated, something that is {\bf not}, however,
+        recommended.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_INTIN}{Decode an Integer Number}
+{
+ \action{Convert free-format input into an integer.}
+ \call{CALL sla\_INTIN (STRING, NSTRT, IRESLT, JFLAG)}
+}
+\args{GIVEN}
+{
+ \spec{STRING}{C}{string containing number to be decoded} \\
+ \spec{NSTRT}{I}{pointer to where decoding is to commence} \\
+ \spec{IRESLT}{I}{current value of result}
+}
+\args{RETURNED}
+{
+ \spec{NSTRT}{I}{advanced to next number} \\
+ \spec{IRESLT}{I}{result} \\
+ \spec{JFLAG}{I}{status: $-$1 = $-$OK, 0~=~+OK, 1~=~null result, 2~=~error}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The reason sla\_INTIN has separate `OK' status values
+       for + and $-$ is to enable minus zero to be detected.
+       This is of crucial importance
+       when decoding mixed-radix numbers.  For example, an angle
+       expressed as degrees, arcminutes and arcseconds may have a
+       leading minus sign but a zero degrees field.
+ \item A TAB is interpreted as a space. {\it n.b.}\ The test for TAB is
+       ASCII-specific.
+ \item The basic format is the sequence of fields $\pm n$,
+       where $\pm$ is a sign
+       character `+' or `$-$', and $n$ means a string of decimal digits.
+ \item Spaces:
+       \begin{itemize}
+       \item Leading spaces are ignored.
+       \item Spaces between the sign and the number are allowed.
+       \item Trailing spaces are ignored;  the first signifies
+             end of decoding and subsequent ones are skipped.
+       \end{itemize}
+ \item Delimiters:
+       \begin{itemize}
+       \item Any character other than +,$-$,0-9 or space may be
+             used to signal the end of the number and terminate decoding.
+       \item Comma is recognized by sla\_INTIN as a special case; it
+             is skipped, leaving the pointer on the next character.  See
+             9, below.
+       \item Decoding will in all cases terminate if end of string
+             is reached.
+       \end{itemize}
+ \item The sign is optional.  The default is +.
+ \item A {\it null result}\/ occurs when the string of characters
+       being decoded does not begin with +,$-$ or 0-9, or
+       consists entirely of spaces.  When this condition is
+       detected, JFLAG is set to 1 and IRESLT is left untouched.
+ \item NSTRT = 1 for the first character in the string.
+ \item On return from sla\_INTIN, NSTRT is set ready for the next
+       decode -- following trailing blanks and any comma.  If a
+       delimiter other than comma is being used, NSTRT must be
+       incremented before the next call to sla\_INTIN, otherwise
+       all subsequent calls will return a null result.
+ \item Errors (JFLAG=2) occur when:
+       \begin{itemize}
+       \item there is a + or $-$ but no number; or
+       \item the number is greater than $2^{31}-1$.
+       \end{itemize}
+ \item When an error has been detected, NSTRT is left
+       pointing to the character following the last
+       one used before the error came to light.
+ \item See also sla\_FLOTIN and sla\_DFLTIN.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_INVF}{Invert Linear Model}
+{
+ \action{Invert a linear model of the type produced by the
+         sla\_FITXY routine.}
+ \call{CALL sla\_INVF (FWDS,BKWDS,J)}
+}
+\args{GIVEN}
+{
+ \spec{FWDS}{D(6)}{model coefficients}
+}
+\args{RETURNED}
+{
+ \spec{BKWDS}{D(6)}{inverse model} \\
+ \spec{J}{I}{status:  0 = OK, $-$1 = no inverse}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The models relate two sets of \xy\ coordinates as follows.
+        Naming the six elements of FWDS $a,b,c,d,e$ \& $f$,
+        where two sets of coordinates $[x_{1},y_{1}]$ and
+        $[x_{2},y_{2}\,]$ are related thus:
+        \begin{verse}
+         $x_{2} = a + bx_{1} + cy_{1}$ \\
+         $y_{2} = d + ex_{1} + fy_{1}$
+        \end{verse}
+        The present routine generates a new set of coefficients
+        $p,q,r,s,t$ \& $u$ (the array BKWDS) such that:
+        \begin{verse}
+         $x_{1} = p + qx_{2} + ry_{2}$ \\
+         $y_{1} = s + tx_{2} + uy_{2}$
+        \end{verse}
+  \item Two successive calls to this routine will deliver a set
+        of coefficients equal to the starting values.
+  \item To comply with the ANSI Fortran 77 standard, FWDS and BKWDS must
+        {\bf not} be the same array.  The routine is, in fact, coded
+        so as to work properly with many Fortran compilers even
+        if this rule is violated, something that is {\bf not}, however,
+        recommended.
+  \item See also sla\_FITXY, sla\_PXY, sla\_XY2XY, sla\_DCMPF.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_KBJ}{Select Epoch Prefix}
+{
+ \action{Select epoch prefix `B' or `J'.}
+ \call{CALL sla\_KBJ (JB, E, K, J)}
+}
+\args{GIVEN}
+{
+ \spec{JB}{I}{sla\_DBJIN prefix status:  0=none, 1=`B', 2=`J'} \\
+ \spec{E}{D}{epoch -- Besselian or Julian}
+}
+\args{RETURNED}
+{
+ \spec{K}{C}{`B' or `J'} \\
+ \spec{J}{I}{status:  0=OK}
+}
+\anote{The routine is mainly intended for use in conjunction with the
+       sla\_DBJIN routine.  If the value of JB indicates that an explicit
+       B or J prefix was detected by sla\_DBJIN, a `B' or `J'
+       is returned to match.  If JB indicates that no explicit B or J
+       was supplied, the choice is made on the basis of the epoch
+       itself;  B is assumed for E $<1984$, otherwise J.}
+%-----------------------------------------------------------------------
+\routine{SLA\_M2AV}{Rotation Matrix to Axial Vector}
+{
+ \action{From a rotation matrix, determine the corresponding axial vector
+        (single precision).}
+ \call{CALL sla\_M2AV (RMAT, AXVEC)}
+}
+\args{GIVEN}
+{
+ \spec{RMAT}{R(3,3)}{rotation matrix}
+}
+\args{RETURNED}
+{
+ \spec{AXVEC}{R(3)}{axial vector (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A rotation matrix describes a rotation about some arbitrary axis,
+        called the Euler axis.  The {\it axial vector} returned by
+        this routine has the same direction as the Euler axis, and its
+        magnitude is the amount of rotation in radians.
+  \item The magnitude and direction of the axial vector can be separated
+        by means of the routine sla\_VN.
+  \item The reference frame rotates clockwise as seen looking along
+        the axial vector from the origin.
+  \item If RMAT is null, so is the result.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_MAP}{Mean to Apparent}
+{
+ \action{Transform star \radec\ from mean place to geocentric apparent.
+         The reference frames and time scales used are post IAU~1976.}
+ \call{CALL sla\_MAP (RM, DM, PR, PD, PX, RV, EQ, DATE, RA, DA)}
+}
+\args{GIVEN}
+{
+ \spec{RM,DM}{D}{mean \radec\ (radians)} \\
+ \spec{PR,PD}{D}{proper motions:  \radec\ changes per Julian year} \\
+ \spec{PX}{D}{parallax (arcsec)} \\
+ \spec{RV}{D}{radial velocity (km~s$^{-1}$, +ve if receding)} \\
+ \spec{EQ}{D}{epoch and equinox of star data (Julian)} \\
+ \spec{DATE}{D}{TDB for apparent place (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{RA,DA}{D}{apparent \radec\ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item EQ is the Julian epoch specifying both the reference
+        frame and the epoch of the position -- usually 2000.
+        For positions where the epoch and equinox are
+        different, use the routine sla\_PM to apply proper
+        motion corrections before using this routine.
+  \item The distinction between the required TDB and TT is
+        always negligible.  Moreover, for all but the most
+        critical applications UTC is adequate.
+  \item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+        $\dot{\alpha}\cos\delta$, and are per year rather than per century.
+  \item This routine may be wasteful for some applications
+        because it recomputes the Earth position/velocity and
+        the precession-nutation matrix each time, and because
+        it allows for parallax and proper motion.  Where
+        multiple transformations are to be carried out for one
+        epoch, a faster method is to call the sla\_MAPPA routine
+        once and then either the sla\_MAPQK routine (which includes
+        parallax and proper motion) or sla\_MAPQKZ (which assumes
+        zero parallax and FK5 proper motion).
+  \item The accuracy, starting from ICRS star data,
+        is limited to about 1~mas by the
+        precession-nutation model used, SF2001.
+        A different precession-nutation model
+        can be introduced by using sla\_MAPPA and sla\_MAPQK (see
+        the previous note) and replacing the precession-nutation
+        matrix into the parameter array directly.
+  \item The accuracy is further limited by the routine sla\_EVP, called
+        by sla\_MAPPA, which computes the Earth position and
+        velocity using the methods of Stumpff.  The maximum
+        error is about 0.3~milliarcsecond.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_MAPPA}{Mean to Apparent Parameters}
+{
+ \action{Compute star-independent parameters in preparation for
+         conversions between mean place and geocentric apparent place.
+         The parameters produced by this routine are required in the
+         parallax, light deflection, aberration, and precession-nutation
+         parts of the mean/apparent transformations.
+         The reference frames and time scales used are post IAU~1976.}
+ \call{CALL sla\_MAPPA (EQ, DATE, AMPRMS)}
+}
+\args{GIVEN}
+{
+ \spec{EQ}{D}{epoch of mean equinox to be used (Julian)} \\
+ \spec{DATE}{D}{TDB (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{AMPRMS}{D(21)}{star-independent mean-to-apparent parameters:} \\
+ \specel   {(1)}     {time interval for proper motion (Julian years)} \\
+ \specel   {(2-4)}   {barycentric position of the Earth (AU)} \\
+ \specel   {(5-7)}   {heliocentric direction of the Earth (unit vector)} \\
+ \specel   {(8)}     {(gravitational radius of
+                      Sun)$\times 2 / $(Sun-Earth distance)} \\
+ \specel   {(9-11)}  {{\bf v}: barycentric Earth velocity in units of c} \\
+ \specel   {(12)}    {$\sqrt{1-\left|\mbox{\bf v}\right|^2}$} \\
+ \specel   {(13-21)} {precession-nutation $3\times3$ matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item For DATE, the distinction between the required TDB and TT
+        is always negligible.  Moreover, for all but the most
+        critical applications UTC is adequate.
+  \item The vectors AMPRMS(2-4) and AMPRMS(5-7) are
+        (in essence) referred to
+        the mean equinox and equator of epoch EQ.  For
+        EQ=2000D0, they are referred to the ICRS.
+  \item The parameters produced by this routine are used by
+        sla\_MAPQK, sla\_MAPQKZ and sla\_AMPQK.
+  \item The accuracy, starting from ICRS star data,
+        is limited to about 1~mas by the precession-nutation
+        model used, SF2001.  A different precession-nutation model
+        can be introduced by first calling the present routine
+        and then replacing the precession-nutation
+        matrix in AMPRMS(13-21) directly.
+  \item A further limit to the accuracy of routines using the
+        parameter array AMPRMS is
+        imposed by the routine sla\_EVP, used here to compute the
+        Earth position and velocity by the methods of Stumpff.
+        The maximum error in the resulting aberration corrections is
+        about 0.3 milliarcsecond.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_MAPQK}{Quick Mean to Apparent}
+{
+ \action{Quick mean to apparent place:  transform a star \radec\ from
+         mean place to geocentric apparent place, given the
+         star-independent parameters.  The reference frames and
+         time scales used are post IAU~1976.}
+ \call{CALL sla\_MAPQK (RM, DM, PR, PD, PX, RV, AMPRMS, RA, DA)}
+}
+\args{GIVEN}
+{
+ \spec{RM,DM}{D}{mean \radec\ (radians)} \\
+ \spec{PR,PD}{D}{proper motions:  \radec\ changes per Julian year} \\
+ \spec{PX}{D}{parallax (arcsec)} \\
+ \spec{RV}{D}{radial velocity (km~s$^{-1}$, +ve if receding)} \\
+ \spec{AMPRMS}{D(21)}{star-independent mean-to-apparent parameters:} \\
+ \specel   {(1)}     {time interval for proper motion (Julian years)} \\
+ \specel   {(2-4)}   {barycentric position of the Earth (AU)} \\
+ \specel   {(5-7)}   {heliocentric direction of the Earth (unit vector)} \\
+ \specel   {(8)}     {(gravitational radius of
+                      Sun)$\times 2 / $(Sun-Earth distance)} \\
+ \specel   {(9-11)}  {{\bf v}: barycentric Earth velocity in units of c} \\
+ \specel   {(12)}    {$\sqrt{1-\left|\mbox{\bf v}\right|^2}$} \\
+ \specel   {(13-21)} {precession-nutation $3\times3$ matrix}
+}
+\args{RETURNED}
+{
+ \spec{RA,DA}{D }{apparent \radec\ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Use of this routine is appropriate when efficiency is important
+        and where many star positions, all referred to the same equator
+        and equinox, are to be transformed for one epoch.  The
+        star-independent parameters can be obtained by calling the
+        sla\_MAPPA routine.
+  \item If the parallax and proper motions are zero the sla\_MAPQKZ
+        routine can be used instead.
+  \item The vectors AMPRMS(2-4) and AMPRMS(5-7) are
+        (in essence) referred to
+        the mean equinox and equator of epoch EQ.  For
+        EQ=2000D0, they are referred to the ICRS.
+  \item Strictly speaking, the routine is not valid for solar-system
+        sources, though the error will usually be extremely small.
+        However, to prevent gross errors in the case where the
+        position of the Sun is specified, the gravitational
+        deflection term is restrained within about \arcseci{920} of the
+        centre of the Sun's disc.  The term has a maximum value of
+        about \arcsec{1}{85} at this radius, and decreases to zero as
+        the centre of the disc is approached.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_MAPQKZ}{Quick Mean-Appt, no PM {\it etc.}}
+{
+ \action{Quick mean to apparent place:  transform a star \radec\ from
+         mean place to geocentric apparent place, given the
+         star-independent parameters, and assuming zero parallax
+         and FK5 proper motion.
+         The reference frames and time scales used are post IAU~1976.}
+ \call{CALL sla\_MAPQKZ (RM, DM, AMPRMS, RA, DA)}
+}
+\args{GIVEN}
+{
+ \spec{RM,DM}{D}{mean \radec\ (radians)} \\
+ \spec{AMPRMS}{D(21)}{star-independent mean-to-apparent parameters:} \\
+ \specel   {(1)}     {time interval for proper motion (Julian years)} \\
+ \specel   {(2-4)}   {barycentric position of the Earth (AU)} \\
+ \specel   {(5-7)}   {heliocentric direction of the Earth (unit vector)} \\
+ \specel   {(8)}     {(gravitational radius of
+                      Sun)$\times 2 / $(Sun-Earth distance)} \\
+ \specel   {(9-11)}  {{\bf v}: barycentric Earth velocity in units of c} \\
+ \specel   {(12)}    {$\sqrt{1-\left|\mbox{\bf v}\right|^2}$} \\
+ \specel   {(13-21)} {precession-nutation $3\times3$ matrix}
+}
+\args{RETURNED}
+{
+ \spec{RA,DA}{D}{apparent \radec\ (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Use of this routine is appropriate when efficiency is important
+        and where many star positions, all with parallax and proper
+        motion either zero or already allowed for, and all referred to
+        the same equator and equinox, are to be transformed for one
+        epoch.  The star-independent parameters can be obtained by
+        calling the sla\_MAPPA routine.
+  \item The corresponding routine for the case of non-zero parallax
+        and FK5 proper motion is sla\_MAPQK.
+  \item The vectors AMPRMS(2-4) and AMPRMS(5-7) are
+        (in essence) referred to
+        the mean equinox and equator of epoch EQ.  For
+        EQ=2000D0, they are referred to the ICRS.
+  \item Strictly speaking, the routine is not valid for solar-system
+        sources, though the error will usually be extremely small.
+        However, to prevent gross errors in the case where the
+        position of the Sun is specified, the gravitational
+        deflection term is restrained within about \arcseci{920} of the
+        centre of the Sun's disc.  The term has a maximum value of
+        about \arcsec{1}{85} at this radius, and decreases to zero as
+        the centre of the disc is approached.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr.Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_MOON}{Approx Moon Pos/Vel}
+{
+ \action{Approximate geocentric position and velocity of the Moon
+         (single precision).}
+ \call{CALL sla\_MOON (IY, ID, FD, PV)}
+}
+\args{GIVEN}
+{
+ \spec{IY}{I}{year} \\
+ \spec{ID}{I}{day in year (1 = Jan 1st)} \\
+ \spec{FD}{R }{fraction of day}
+}
+\args{RETURNED}
+{
+ \spec{PV}{R(6)}{Moon \xyzxyzd, mean equator and equinox of
+                 date (AU, AU~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The date and time is TDB (loosely ET) in a Julian calendar
+        which has been aligned to the ordinary Gregorian
+        calendar for the interval 1900 March 1 to 2100 February 28.
+        The year and day can be obtained by calling sla\_CALYD or
+        sla\_CLYD.
+  \item The position is accurate to better than 0.5~arcminute
+        in direction and 1000~km in distance.  The velocity
+        is accurate to better than \arcsec{0}{5} per hour in direction
+        and 4~metres per second in distance.  (RMS figures with respect
+        to JPL DE200 for the interval 1960-2025 are \arcseci{14} and
+        \arcsec{0}{2} per hour in longitude, \arcseci{9} and \arcsec{0}{2}
+        per hour in latitude, 350~km and 2~metres per second in distance.)
+        Note that the distance accuracy is comparatively poor because this
+        routine is principally intended for computing topocentric direction.
+  \item This routine is only a partial implementation of the original
+        Meeus algorithm (reference below), which offers 4 times the
+        accuracy in direction and 20 times the accuracy in distance
+        when fully implemented (as it is in sla\_DMOON).
+ \end{enumerate}
+}
+\aref{Meeus, {\it l'Astronomie}, June 1984, p348.}
+%-----------------------------------------------------------------------
+\routine{SLA\_MXM}{Multiply $3\times3$ Matrices}
+{
+ \action{Product of two $3\times3$ matrices (single precision).}
+ \call{CALL sla\_MXM (A, B, C)}
+}
+\args{GIVEN}
+{
+ \spec{A}{R(3,3)}{matrix {\bf A}} \\
+ \spec{B}{R(3,3)}{matrix {\bf B}}
+}
+\args{RETURNED}
+{
+ \spec{C}{R(3,3)}{matrix result: {\bf A}$\times${\bf B}}
+}
+\anote{To comply with the ANSI Fortran 77 standard, A, B and C must
+       be different arrays.  The routine is, in fact, coded
+       so as to work properly with many Fortran compilers even
+       if this rule is violated, something that is {\bf not}, however,
+       recommended.}
+%-----------------------------------------------------------------------
+\routine{SLA\_MXV}{Apply 3D Rotation}
+{
+ \action{Multiply a 3-vector by a rotation matrix (single precision).}
+ \call{CALL sla\_MXV (RM, VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{RM}{R(3,3)}{rotation matrix} \\
+ \spec{VA}{R(3)}{vector to be rotated}
+}
+\args{RETURNED}
+{
+ \spec{VB}{R(3)}{result vector}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine performs the operation:
+        \begin{verse}
+         {\bf b} = {\bf M}$\cdot${\bf a}
+        \end{verse}
+        where {\bf a} and {\bf b} are the 3-vectors VA and VB
+        respectively, and {\bf M} is the $3\times3$ matrix RM.
+  \item The main function of this routine is apply a
+        rotation;  under these circumstances, ${\bf M}$ is a
+        {\it proper real orthogonal}\/ matrix.
+  \item To comply with the ANSI Fortran 77 standard, VA and VB must
+        {\bf not} be the same array.  The routine is, in fact, coded
+        so as to work properly with many Fortran compilers even
+        if this rule is violated, something that is {\bf not}, however,
+        recommended.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_NUT}{Nutation Matrix}
+{
+ \action{Form the matrix of nutation (SF2001 theory) for a given date.}
+ \call{CALL sla\_NUT (DATE, RMATN)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date
+                                          (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{RMATN}{D(3,3)}{nutation matrix}
+}
+\notes{
+ \begin{enumerate}
+  \item The matrix is in the sense:
+        \begin{verse}
+         ${\bf v}_{true} = {\bf M}\times{\bf v}_{mean}$
+        \end{verse}
+        where ${\bf v}_{true}$ is the star vector relative to the
+        true equator and equinox of date, {\bf M} is the
+        $3\times3$ matrix {\tt rmatn} and
+        ${\bf v}_{mean}$ is the star vector relative to the
+        mean equator and equinox of date.
+  \item The matrix represents forced nutation (but not free core nutation)
+        plus corrections to the IAU~1976 precession model.
+  \item Earth attitude predictions made by combining the present nutation
+        matrix with IAU~1976 precession are accurate to 1~mas (with respect
+        to the ICRS) for a few decades around 2000.
+  \item The distinction between the required TDB and TT is
+        always negligible.  Moreover, for all but the most
+        critical applications UTC is adequate.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Kaplan, G.H., 1981.\ {\it USNO circular No.\ 163}, pA3-6.
+  \item Shirai, T. \& Fukushima, T., 2001, Astron.J., {\bf 121},
+        3270-3283.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_NUTC}{Nutation Components}
+{
+ \action{Nutation (SF2001 theory):  longitude \& obliquity
+         components, and mean obliquity.}
+ \call{CALL sla\_NUTC (DATE, DPSI, DEPS, EPS0)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date
+                                           (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{DPSI,DEPS}{D}{nutation in longitude and obliquity (radians)} \\
+ \spec{EPS0}{D}{mean obliquity (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The routine predicts forced nutation (but not free core nutation)
+        plus corrections to the IAU~1976 precession model.
+  \item Earth attitude predictions made by combining the present nutation
+        model with IAU~1976 precession are accurate to 1~mas (with respect
+        to the ICRS) for a few decades around 2000.
+  \item The slaNutc80 routine is the equivalent of the present routine
+        but using the IAU 1980 nutation theory.  The older theory is less
+        accurate, leading to errors as large as 350~mas over the interval
+        1900-2100, mainly because of the error in the IAU~1976 precession.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Shirai, T. \& Fukushima, T., Astron.J.\ 121, 3270-3283 (2001).
+  \item Fukushima, T., Astron.Astrophys.\ 244, L11 (1991).
+  \item Simon, J. L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
+        Francou, G. \& Laskar, J., Astron.Astrophys.\ 282, 663 (1994).
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_NUTC80}{Nutation Components, IAU 1980}
+{
+ \action{Nutation (IAU 1980 theory):  longitude \& obliquity
+         components, and mean obliquity.}
+ \call{CALL sla\_NUTC80 (DATE, DPSI, DEPS, EPS0)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TDB (formerly ET) as Modified Julian Date
+                                           (JD$-$2400000.5)}
+}
+\args{RETURNED}
+{
+ \spec{DPSI,DEPS}{D}{nutation in longitude and obliquity (radians)} \\
+ \spec{EPS0}{D}{mean obliquity (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The IAU 1980 theory used in the present function has
+        errors as large as 350~mas over the interval
+        1900-2100, mainly because of the error in the IAU~1976
+        precession.  For more accurate results, either the corrections
+        published in IERS {\it Bulletin~B}\/
+        must be applied, or the
+        sla\_NUTC function can be used.  The latter is based upon the
+        more recent SF2001 nutation theory and is of better
+        than 1\,mas accuracy.
+  \item The distinction between the required TDB and TT is
+        always negligible.  Moreover, for all but the most
+        critical applications UTC is adequate.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Final report of the IAU Working Group on Nutation,
+        chairman P.K.Seidelmann, 1980.
+  \item Kaplan, G.H., 1981.\ {\it USNO circular no.\ 163}, pA3-6.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_OAP}{Observed to Apparent}
+{
+ \action{Observed to apparent place.}
+ \call{CALL sla\_OAP (\vtop{
+         \hbox{TYPE, OB1, OB2, DATE, DUT, ELONGM, PHIM,}
+         \hbox{HM, XP, YP, TDK, PMB, RH, WL, TLR, RAP, DAP)}}}
+}
+\args{GIVEN}
+{
+ \spec{TYPE}{C*(*)}{type of coordinates -- `R', `H' or `A' (see below)} \\
+ \spec{OB1}{D}{observed Az, HA or RA (radians; Az is N=0, E=$90^{\circ}$)} \\
+ \spec{OB2}{D}{observed zenith distance or $\delta$ (radians)} \\
+ \spec{DATE}{D }{UTC date/time (Modified Julian Date, JD$-$2400000.5)} \\
+ \spec{DUT}{D}{$\Delta$UT:  UT1$-$UTC (UTC seconds)} \\
+ \spec{ELONGM}{D}{observer's mean longitude (radians, east +ve)} \\
+ \spec{PHIM}{D}{observer's mean geodetic latitude (radians)} \\
+ \spec{HM}{D}{observer's height above sea level (metres)} \\
+ \spec{XP,YP}{D}{polar motion \xy\ coordinates (radians)} \\
+ \spec{TDK}{D}{local ambient temperature (K; std=273.15D0)} \\
+ \spec{PMB}{D}{local atmospheric pressure (mb; std=1013.25D0)} \\
+ \spec{RH}{D}{local relative humidity (in the range 0D0\,--\,1D0)} \\
+ \spec{WL}{D}{effective wavelength ($\mu{\rm m}$, {\it e.g.}\ 0.55D0)} \\
+ \spec{TLR}{D}{tropospheric lapse rate (K per metre,
+                                                {\it e.g.}\ 0.0065D0)}
+}
+\args{RETURNED}
+{
+ \spec{RAP,DAP}{D}{geocentric apparent \radec}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Only the first character of the TYPE argument is significant.
+        `R' or `r' indicates that OBS1 and OBS2 are the observed right
+        ascension and declination;  `H' or `h' indicates that they are
+        hour angle (west +ve) and declination; anything else (`A' or
+        `a' is recommended) indicates that OBS1 and OBS2 are azimuth
+        (north zero, east $90^{\circ}$) and zenith distance.  (Zenith
+        distance is used rather than elevation in order to reflect the
+        fact that no allowance is made for depression of the horizon.)
+  \item The accuracy of the result is limited by the corrections for
+        refraction.  Providing the meteorological parameters are
+        known accurately and there are no gross local effects, the
+        predicted azimuth and elevation should be within about
+        \arcsec{0}{1} for $\zeta<70^{\circ}$.  Even
+        at a topocentric zenith distance of
+        $90^{\circ}$, the accuracy in elevation should be better than
+        1~arcminute;  useful results are available for a further
+        $3^{\circ}$, beyond which the sla\_REFRO routine returns a
+        fixed value of the refraction.  The complementary
+        routines sla\_AOP (or sla\_AOPQK) and sla\_OAP (or sla\_OAPQK)
+        are self-consistent to better than 1~microarcsecond all over
+        the celestial sphere.
+  \item It is advisable to take great care with units, as even
+        unlikely values of the input parameters are accepted and
+        processed in accordance with the models used.
+  \item {\it Observed}\/ \azel\ means the position that would be seen by a
+        perfect theodolite located at the observer.  This is
+        related to the observed \hadec\ via the standard rotation, using
+        the geodetic latitude (corrected for polar motion), while the
+        observed HA and RA are related simply through the local
+        apparent ST.  {\it Observed}\/ \radec\ or \hadec\ thus means the
+        position that would be seen by a perfect equatorial located
+        at the observer and with its polar axis aligned to the
+        Earth's axis of rotation ({\it n.b.}\ not to the refracted pole).
+        By removing from the observed place the effects of
+        atmospheric refraction and diurnal aberration, the
+        geocentric apparent \radec\ is obtained.
+  \item Frequently, {\it mean}\/ rather than {\it apparent}\,
+        \radec\ will be required,
+        in which case further transformations will be necessary.  The
+        sla\_AMP {\it etc.}\ routines will convert
+        the apparent \radec\ produced
+        by the present routine into an FK5 J2000 mean place, by
+        allowing for the Sun's gravitational lens effect, annual
+        aberration, nutation and precession.  Should FK4 B1950
+        coordinates be required, the routines sla\_FK524 {\it etc.}\ will also
+        have to be applied.
+  \item To convert to apparent \radec\ the coordinates read from a
+        real telescope, corrections would have to be applied for
+        encoder zero points, gear and encoder errors, tube flexure,
+        the position of the rotator axis and the pointing axis
+        relative to it, non-perpendicularity between the mounting
+        axes, and finally for the tilt of the azimuth or polar axis
+        of the mounting (with appropriate corrections for mount
+        flexures).  Some telescopes would, of course, exhibit other
+        properties which would need to be accounted for at the
+        appropriate point in the sequence.
+  \item This routine takes time to execute, due mainly to the
+        rigorous integration used to evaluate the refraction.
+        For processing multiple stars for one location and time,
+        call sla\_AOPPA once followed by one call per star to sla\_OAPQK.
+        Where a range of times within a limited period of a few hours
+        is involved, and the highest precision is not required, call
+        sla\_AOPPA once, followed by a call to sla\_AOPPAT each time the
+        time changes, followed by one call per star to sla\_OAPQK.
+  \item The DATE argument is UTC expressed as an MJD.  This is,
+        strictly speaking, wrong, because of leap seconds.  However,
+        as long as the $\Delta$UT and the UTC are consistent there
+        are no difficulties, except during a leap second.  In this
+        case, the start of the 61st second of the final minute should
+        begin a new MJD day and the old pre-leap $\Delta$UT should
+        continue to be used.  As the 61st second completes, the MJD
+        should revert to the start of the day as, simultaneously,
+        the $\Delta$UT changes by one second to its post-leap new value.
+  \item The $\Delta$UT (UT1$-$UTC) is tabulated in IERS circulars and
+        elsewhere.  It increases by exactly one second at the end of
+        each UTC leap second, introduced in order to keep $\Delta$UT
+        within $\pm$\tsec{0}{9}.
+  \item IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.  The
+        longitude required by the present routine is {\bf east-positive},
+        in accordance with geographical convention (and right-handed).
+        In particular, note that the longitudes returned by the
+        sla\_OBS routine are west-positive (as in the {\it Astronomical
+        Almanac}\/ before 1984) and must be reversed in sign before use
+        in the present routine.
+  \item The polar coordinates XP,YP can be obtained from IERS
+        circulars and equivalent publications.  The
+        maximum amplitude is about \arcsec{0}{3}.  If XP,YP values
+        are unavailable, use XP=YP=0D0.  See page B60 of the 1988
+        {\it Astronomical Almanac}\/ for a definition of the two angles.
+  \item The height above sea level of the observing station, HM,
+        can be obtained from the {\it Astronomical Almanac}\/ (Section J
+        in the 1988 edition), or via the routine sla\_OBS.  If P,
+        the pressure in mb, is available, an adequate
+        estimate of HM can be obtained from the following expression:
+        \begin{quote}
+         {\tt HM=-29.3D0*TSL*LOG(P/1013.25D0)}
+        \end{quote}
+        where TSL is the approximate sea-level air temperature in K
+        (see {\it Astrophysical Quantities}, C.W.Allen, 3rd~edition,
+        \S 52).  Similarly, if the pressure P is not known,
+        it can be estimated from the height of the observing
+        station, HM as follows:
+        \begin{quote}
+         {\tt P=1013.25D0*EXP(-HM/(29.3D0*TSL))}
+        \end{quote}
+        Note, however, that the refraction is nearly proportional to the
+        pressure and that an accurate P value is important for
+        precise work.
+  \item The azimuths {\it etc.}\ used by the present routine are with
+        respect to the celestial pole.  Corrections from the terrestrial pole
+        can be computed using sla\_POLMO.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_OAPQK}{Quick Observed to Apparent}
+{
+ \action{Quick observed to apparent place.}
+ \call{CALL sla\_OAPQK (TYPE, OB1, OB2, AOPRMS, RAP, DAP)}
+}
+\args{GIVEN}
+{
+ \spec{TYPE}{C*(*)}{type of coordinates -- `R', `H' or `A' (see below)} \\
+ \spec{OB1}{D}{observed Az, HA or RA (radians; Az is N=0, E=$90^{\circ}$)} \\
+ \spec{OB2}{D}{observed zenith distance or $\delta$ (radians)} \\
+ \spec{AOPRMS}{D(14)}{star-independent apparent-to-observed parameters:} \\
+ \specel   {(1)}     {geodetic latitude (radians)} \\
+ \specel   {(2,3)}   {sine and cosine of geodetic latitude} \\
+ \specel   {(4)}     {magnitude of diurnal aberration vector} \\
+ \specel   {(5)}     {height (HM)} \\
+ \specel   {(6)}     {ambient temperature (TDK)} \\
+ \specel   {(7)}     {pressure (PMB)} \\
+ \specel   {(8)}     {relative humidity (RH)} \\
+ \specel   {(9)}     {wavelength (WL)} \\
+ \specel   {(10)}    {lapse rate (TLR)} \\
+ \specel   {(11,12)} {refraction constants A and B (radians)} \\
+ \specel   {(13)}    {longitude + eqn of equinoxes +
+                       ``sidereal $\Delta$UT'' (radians)} \\
+ \specel   {(14)}    {local apparent sidereal time (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RAP,DAP}{D}{geocentric apparent \radec}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Only the first character of the TYPE argument is significant.
+        `R' or `r' indicates that OBS1 and OBS2 are the observed right
+        ascension and declination;  `H' or `h' indicates that they are
+        hour angle (west +ve) and declination; anything else (`A' or
+        `a' is recommended) indicates that OBS1 and OBS2 are Azimuth
+        (north zero, east $90^{\circ}$) and zenith distance.  (Zenith
+        distance is used rather than elevation in order to reflect the
+        fact that no allowance is made for depression of the horizon.)
+  \item The accuracy of the result is limited by the corrections for
+        refraction.  Providing the meteorological parameters are
+        known accurately and there are no gross local effects, the
+        predicted azimuth and elevation should be within about
+        \arcsec{0}{1} for $\zeta<70^{\circ}$.  Even
+        at a topocentric zenith distance of
+        $90^{\circ}$, the accuracy in elevation should be better than
+        1~arcminute;  useful results are available for a further
+        $3^{\circ}$, beyond which the sla\_REFRO routine returns a
+        fixed value of the refraction.  The complementary
+        routines sla\_AOP (or sla\_AOPQK) and sla\_OAP (or sla\_OAPQK)
+        are self-consistent to better than 1~microarcsecond all over
+        the celestial sphere.
+  \item It is advisable to take great care with units, as even
+        unlikely values of the input parameters are accepted and
+        processed in accordance with the models used.
+  \item {\it Observed}\/ \azel\ means the position that would be seen by a
+        perfect theodolite located at the observer.  This is
+        related to the observed \hadec\ via the standard rotation, using
+        the geodetic latitude (corrected for polar motion), while the
+        observed HA and RA are related simply through the local
+        apparent ST.  {\it Observed}\/ \radec\ or \hadec\ thus means the
+        position that would be seen by a perfect equatorial located
+        at the observer and with its polar axis aligned to the
+        Earth's axis of rotation ({\it n.b.}\ not to the refracted pole).
+        By removing from the observed place the effects of
+        atmospheric refraction and diurnal aberration, the
+        geocentric apparent \radec\ is obtained.
+  \item Frequently, {\it mean}\/ rather than {\it apparent}\,
+        \radec\ will be required,
+        in which case further transformations will be necessary.  The
+        sla\_AMP {\it etc.}\ routines will convert
+        the apparent \radec\ produced
+        by the present routine into an FK5 J2000 mean place, by
+        allowing for the Sun's gravitational lens effect, annual
+        aberration, nutation and precession.  Should FK4 B1950
+        coordinates be required, the routines sla\_FK524 {\it etc.}\ will also
+        have to be applied.
+  \item To convert to apparent \radec\ the coordinates read from a
+        real telescope, corrections would have to be applied for
+        encoder zero points, gear and encoder errors, tube flexure,
+        the position of the rotator axis and the pointing axis
+        relative to it, non-perpendicularity between the mounting
+        axes, and finally for the tilt of the azimuth or polar axis
+        of the mounting (with appropriate corrections for mount
+        flexures).  Some telescopes would, of course, exhibit other
+        properties which would need to be accounted for at the
+        appropriate point in the sequence.
+  \item The star-independent apparent-to-observed-place parameters
+        in AOPRMS may be computed by means of the sla\_AOPPA routine.
+        If nothing has changed significantly except the time, the
+        sla\_AOPPAT routine may be used to perform the requisite
+        partial recomputation of AOPRMS.
+  \item The azimuths {\it etc.}\ used by the present routine are with
+        respect to the celestial pole.  Corrections from the terrestrial pole
+        can be computed using sla\_POLMO.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_OBS}{Observatory Parameters}
+{
+ \action{Look up an entry in a standard list of
+         groundbased observing stations parameters.}
+ \call{CALL sla\_OBS (N, C, NAME, W, P, H)}
+}
+\args{GIVEN}
+{
+ \spec{N}{I}{number specifying observing station}
+}
+\args{GIVEN or RETURNED}
+{
+ \spec{C}{C*(*)}{identifier specifying observing station}
+}
+\args{RETURNED}
+{
+ \spec{NAME}{C*(*)}{name of specified observing station} \\
+ \spec{W}{D}{longitude (radians, west +ve)} \\
+ \spec{P}{D}{geodetic latitude (radians, north +ve)} \\
+ \spec{H}{D}{height above sea level (metres)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Station identifiers C may be up to 10 characters long,
+        and station names NAME may be up to 40 characters long.
+  \item C and N are {\it alternative}\/ ways of specifying the observing
+        station.  The C option, which is the most generally useful,
+        may be selected by specifying an N value of zero or less.
+        If N is 1 or more, the parameters of the Nth station
+        in the currently supported list are interrogated, and
+        the station identifier C is returned as well as NAME, W,
+        P and H.
+  \item If the station parameters are not available, either because
+        the station identifier C is not recognized, or because an
+        N value greater than the number of stations supported is
+        given, a name of `?' is returned and W, P and H are left in
+        their current states.
+  \item Programs can obtain a list of all currently supported
+        stations by calling the routine repeatedly, with N=1,2,3...
+        When NAME=`?' is seen, the list of stations has been
+        exhausted.  The stations at the time of writing are listed
+        below.
+  \item Station numbers, identifiers, names and other details are
+        subject to change and should not be hardwired into
+        application programs.
+  \item All station identifiers C are uppercase only;  lower case
+        characters must be converted to uppercase by the calling
+        program.  The station names returned may contain both upper-
+        and lowercase.  All characters up to the first space are
+        checked;  thus an abbreviated ID will return the parameters
+        for the first station in the list which matches the
+        abbreviation supplied, and no station in the list will ever
+        contain embedded spaces.  C must not have leading spaces.
+  \item IMPORTANT -- BEWARE OF THE LONGITUDE SIGN CONVENTION.  The
+        longitude returned by sla\_OBS is
+        {\bf west-positive}, following the pre-1984 {\it Astronomical
+        Almanac}.  However, this sign convention is left-handed and is
+        the opposite of the one now used; elsewhere in
+        SLALIB the preferable east-positive convention is used.  In
+        particular, note that for use in sla\_AOP, sla\_AOPPA and
+        sla\_OAP the sign of the longitude must be reversed.
+  \item Users are urged to inform the author of any improvements
+        they would like to see made.  For example:
+        \begin{itemize}
+         \item typographical corrections
+         \item more accurate parameters
+         \item better station identifiers or names
+         \item additional stations
+        \end{itemize}
+ \end{enumerate}
+Stations supported by sla\_OBS at the time of writing:
+
+\begin{tabbing}
+xxxxxxxxxxxxxxxxx \= \kill
+{\it ID} \> {\it NAME} \\ \\
+AAT \> Anglo-Australian 3.9m Telescope \\
+ANU2.3 \> Siding Spring 2.3m \\
+APO3.5 \> Apache Point 3.5m \\
+ARECIBO \> Arecibo 1000 foot \\
+ATCA \> Australia Telescope Compact Array \\
+BLOEMF \> Bloemfontein 1.52m \\
+BOSQALEGRE \> Bosque Alegre 1.54m \\
+CAMB1MILE \> Cambridge 1 mile \\
+CAMB5KM \> Cambridge 5 km \\
+CATALINA61 \> Catalina 61 inch \\
+CFHT \> Canada-France-Hawaii 3.6m Telescope \\
+CSO \> Caltech Sub-mm Observatory, Mauna Kea \\
+DAO72 \> DAO Victoria BC 1.85m \\
+DUNLAP74 \> David Dunlap 74 inch \\
+DUPONT \> Du Pont 2.5m Telescope, Las Campanas \\
+EFFELSBERG \> Effelsberg 100m \\
+ESO3.6 \> ESO 3.6m \\
+ESONTT \> ESO 3.5m NTT \\
+ESOSCHM \> ESO 1m Schmidt, La Silla \\
+FCRAO \> Five College Radio Astronomy Obs \\
+FLAGSTF61 \> USNO 61 inch astrograph, Flagstaff \\
+GBVA140 \> Greenbank 140 foot \\
+GBVA300 \> Greenbank 300 foot \\
+GEMININ \> Gemini North 8m \\
+GEMINIS \> Gemini South 8m \\
+HARVARD \> Harvard College Observatory 1.55m \\
+HPROV1.52 \> Haute Provence 1.52m \\
+HPROV1.93 \> Haute Provence 1.93m \\
+IRTF \> NASA IR Telescope Facility, Mauna Kea \\
+JCMT \> JCMT 15m \\
+JODRELL1 \> Jodrell Bank 250 foot \\
+KECK1 \> Keck 10m Telescope 1 \\
+KECK2 \> Keck 10m Telescope 2 \\
+KISO \> Kiso 1.05m Schmidt, Japan \\
+KOSMA3M \> Cologne Submillimeter Observatory 3m \\
+KOTTAMIA \> Kottamia 74 inch \\
+KPNO158 \> Kitt Peak 158 inch \\
+KPNO36FT \> Kitt Peak 36 foot \\
+KPNO84 \> Kitt Peak 84 inch \\
+KPNO90 \> Kitt Peak 90 inch \\
+LICK120 \> Lick 120 inch \\
+LOWELL72 \> Perkins 72 inch, Lowell \\
+LPO1 \> Jacobus Kapteyn 1m Telescope \\
+LPO2.5 \> Isaac Newton 2.5m Telescope \\
+LPO4.2 \> William Herschel 4.2m Telescope \\
+MAGELLAN1 \> Magellan 1, 6.5m, Las Campanas \\
+MAGELLAN2 \> Magellan 2, 6.5m, Las Campanas \\
+MAUNAK88 \> Mauna Kea 88 inch \\
+MCDONLD2.1 \> McDonald 2.1m \\
+MCDONLD2.7 \> McDonald 2.7m \\
+MMT \> MMT, Mt Hopkins \\
+MOPRA \> ATNF Mopra Observatory \\
+MTEKAR \> Mt Ekar 1.82m \\
+MTHOP1.5 \> Mt Hopkins 1.5m \\
+MTLEMMON60 \> Mt Lemmon 60 inch \\
+NOBEYAMA \> Nobeyama 45m \\
+OKAYAMA \> Okayama 1.88m \\
+PALOMAR200 \> Palomar 200 inch \\
+PALOMAR48 \> Palomar 48-inch Schmidt \\
+PALOMAR60 \> Palomar 60 inch \\
+PARKES \> Parkes 64m \\
+QUEBEC1.6 \> Quebec 1.6m \\
+SAAO74 \> Sutherland 74 inch \\
+SANPM83 \> San Pedro Martir 83 inch \\
+ST.ANDREWS \> St Andrews University Observatory \\
+STEWARD90 \> Steward 90 inch \\
+STROMLO74 \> Mount Stromlo 74 inch \\
+SUBARU \> Subaru 8m \\
+SUGARGROVE \> Sugar Grove 150 foot \\
+TAUTNBG \> Tautenburg 2m \\
+TAUTSCHM \> Tautenberg 1.34m Schmidt \\
+TIDBINBLA \> Tidbinbilla 64m \\
+TOLOLO1.5M \> Cerro Tololo 1.5m \\
+TOLOLO4M \> Cerro Tololo 4m \\
+UKIRT \> UK Infra Red Telescope \\
+UKST \> UK 1.2m Schmidt, Siding Spring \\
+USSR6 \> USSR 6m \\
+USSR600 \> USSR 600 foot \\
+VLA \> Very Large Array \\
+VLT1 \> ESO VLT 8m, UT1 \\
+VLT2 \> ESO VLT 8m, UT2 \\
+VLT3 \> ESO VLT 8m, UT3 \\
+VLT4 \> ESO VLT 8m, UT4
+\end{tabbing}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PA}{$h,\delta$ to Parallactic Angle}
+{
+ \action{Hour angle and declination to parallactic angle
+         (double precision).}
+ \call{D~=~sla\_PA (HA, DEC, PHI)}
+}
+\args{GIVEN}
+{
+ \spec{HA}{D}{hour angle in radians (geocentric apparent)} \\
+ \spec{DEC}{D}{declination in radians (geocentric apparent)} \\
+ \spec{PHI}{D}{latitude in radians (geodetic)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_PA}{D}{parallactic angle (radians, in the range $\pm \pi$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The parallactic angle at a point in the sky is the position
+        angle of the vertical, {\it i.e.}\ the angle between the direction to
+        the pole and to the zenith.  In precise applications care must
+        be taken only to use geocentric apparent \hadec\ and to consider
+        separately the effects of atmospheric refraction and telescope
+        mount errors.
+  \item At the pole a zero result is returned.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PAV}{Position-Angle Between Two Directions}
+{
+ \action{Returns the bearing (position angle) of one celestial
+         direction with respect to another (single precision).}
+ \call{R~=~sla\_PAV (V1, V2)}
+}
+\args{GIVEN}
+{
+ \spec{V1}{R(3)}{vector to one point} \\
+ \spec{V2}{R(3)}{vector to the other point}
+}
+\args{RETURNED}
+{
+ \spec{sla\_PAV}{R}{position-angle of 2nd point with respect to 1st}
+}
+\notes
+{
+ \begin{enumerate}
+ \item The coordinate frames correspond to \radec,
+       $[\lambda,\phi]$ {\it etc.}.
+ \item The result is the bearing (position angle), in radians,
+       of point V2 as seen
+       from point V1.  It is in the range $\pm \pi$.  The sense
+       is such that if V2
+       is a small distance due east of V1 the result
+       is about $+\pi/2$. Zero is returned
+       if the two points are coincident.
+ \item There is no requirement for either vector to be of unit length.
+ \item The routine sla\_BEAR performs an equivalent function except
+       that the points are specified in the form of spherical coordinates.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_PCD}{Apply Radial Distortion}
+{
+ \action{Apply pincushion/barrel distortion to a tangent-plane \xy.}
+ \call{CALL sla\_PCD (DISCO,X,Y)}
+}
+\args{GIVEN}
+{
+ \spec{DISCO}{D}{pincushion/barrel distortion coefficient} \\
+ \spec{X,Y}{D}{tangent-plane \xy}
+}
+\args{RETURNED}
+{
+ \spec{X,Y}{D}{distorted \xy}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The distortion is of the form $\rho = r (1 + c r^{2})$, where $r$ is
+        the radial distance from the tangent point, $c$ is the DISCO
+        argument, and $\rho$ is the radial distance in the presence of
+        the distortion.
+  \item For {\it pincushion}\/ distortion, C is +ve;  for
+        {\it barrel}\/ distortion, C is $-$ve.
+  \item For X,Y in units of one projection radius (in the case of
+        a photographic plate, the focal length), the following
+        DISCO values apply:
+
+        \vspace{2ex}
+
+        \hspace{5em}
+        \begin{tabular}{|l|c|} \hline
+         Geometry & DISCO \\ \hline \hline
+         astrograph & 0.0 \\ \hline
+         Schmidt & $-$0.3333 \\ \hline
+         AAT PF doublet & +147.069 \\ \hline
+         AAT PF triplet & +178.585 \\ \hline
+         AAT f/8 & +21.20 \\ \hline
+         JKT f/8 & +14.6 \\ \hline
+        \end{tabular}
+
+        \vspace{2ex}
+
+  \item There is a companion routine, sla\_UNPCD, which performs the
+        inverse operation.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PDA2H}{H.A.\ for a Given Azimuth}
+{
+ \action{Hour Angle corresponding to a given azimuth (double precision).}
+ \call{CALL sla\_PDA2H (P, D, A, H1, J1, H2, J2)}
+}
+\args{GIVEN}
+{
+ \spec{P}{D}{latitude} \\
+ \spec{D}{D}{declination} \\
+ \spec{A}{D}{azimuth}
+}
+\args{RETURNED}
+{
+ \spec{H1}{D}{hour angle:  first solution if any} \\
+ \spec{J1}{I}{flag: 0 = solution 1 is valid} \\
+ \spec{H2}{D}{hour angle:  second solution if any} \\
+ \spec{J2}{I}{flag: 0 = solution 2 is valid}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PDQ2H}{H.A.\ for a Given P.A.}
+{
+ \action{Hour Angle corresponding to a given parallactic angle
+         (double precision).}
+ \call{CALL sla\_PDQ2H (P, D, Q, H1, J1, H2, J2)}
+}
+\args{GIVEN}
+{
+ \spec{P}{D}{latitude} \\
+ \spec{D}{D}{declination} \\
+ \spec{Q}{D}{azimuth}
+}
+\args{RETURNED}
+{
+ \spec{H1}{D}{hour angle:  first solution if any} \\
+ \spec{J1}{I}{flag: 0 = solution 1 is valid} \\
+ \spec{H2}{D}{hour angle:  second solution if any} \\
+ \spec{J2}{I}{flag: 0 = solution 2 is valid}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PERMUT}{Next Permutation}
+{
+ \action{Generate the next permutation of a specified number of items.}
+ \call{CALL sla\_PERMUT (N, ISTATE, IORDER, J)}
+}
+\args{GIVEN}
+{
+ \spec{N}{I}{number of items:  there will be N! permutations} \\
+ \spec{ISTATE}{I(N)}{state, ISTATE(1)$=-1$ to initialize}
+}
+\args{RETURNED}
+{
+ \spec{ISTATE}{I(N)}{state, updated ready for next time} \\
+ \spec{IORDER}{I(N)}{next permutation of numbers 1,2,\ldots,N} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal N (zero or less is illegal)} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $+$1 = no more permutations available}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine returns, in the IORDER array, the integers 1 to N
+        inclusive, in an order that depends on the current contents of
+        the ISTATE array.  Before calling the routine for the first
+        time, the caller must set the first element of the ISTATE array
+        to $-1$ (any negative number will do) to cause the ISTATE array
+        to be fully initialized.
+  \item The first permutation to be generated is:
+        \begin{verse}
+           IORDER(1)=N, IORDER(2)=N-1, ..., IORDER(N)=1
+        \end{verse}
+        This is also the permutation returned for the ``finished'' (J=1) case.
+        The final permutation to be generated is:
+        \begin{verse}
+           IORDER(1)=1, IORDER(2)=2, ..., IORDER(N)=N
+        \end{verse}
+  \item If the ``finished'' (J=1) status is ignored, the routine continues
+        to deliver permutations, the pattern repeating every~N!\,~calls.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_PERTEL}{Perturbed Orbital Elements}
+{
+ \action{Update the osculating elements of an asteroid or comet by
+         applying planetary perturbations.}
+ \call{CALL sla\_PERTEL (\vtop{
+         \hbox{JFORM, DATE0, DATE1,}
+         \hbox{EPOCH0, ORBI0, ANODE0, PERIH0, AORQ0, E0, AM0,}
+         \hbox{EPOCH1, ORBI1, ANODE1, PERIH1, AORQ1, E1, AM1,}
+         \hbox{JSTAT)}}}
+}
+\args{GIVEN (format and dates)}
+{
+ \spec{JFORM}{I}{choice of element set (2 or 3; Note~1)} \\
+ \spec{DATE0}{D}{date of osculation (TT MJD) for the given} \\
+ \spec{}{}{\hspace{1.5em} elements} \\
+ \spec{DATE1}{D}{date of osculation (TT MJD) for the updated} \\
+ \spec{}{}{\hspace{1.5em} elements}
+}
+\args{GIVEN (the unperturbed elements)}
+{
+ \spec{EPOCH0}{D}{epoch of the given element set
+                            ($t_0$ or $T$, TT MJD;} \\
+ \spec{}{}{\hspace{1.5em} Note~2)} \\
+ \spec{ORBI0}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE0}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH0}{D}{argument of perihelion
+                            ($\omega$, radians)} \\
+ \spec{AORQ0}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E0}{D}{eccentricity ($e$)} \\
+ \spec{AM0}{D}{mean anomaly ($M$, radians, JFORM=2 only)}
+}
+\args{RETURNED (the updated elements)}
+{
+ \spec{EPOCH1}{D}{epoch of the updated element set
+                            ($t_0$ or $T$,} \\
+ \spec{}{}{\hspace{1.5em} TT MJD; Note~2)} \\
+ \spec{ORBI1}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE1}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH1}{D}{argument of perihelion
+                            ($\omega$, radians)} \\
+ \spec{AORQ1}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E1}{D}{eccentricity ($e$)} \\
+ \spec{AM1}{D}{mean anomaly ($M$, radians, JFORM=2 only)}
+}
+\args{RETURNED (status flag)}
+{
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{0.5em}+102 = warning, distant epoch} \\
+ \spec{}{}{\hspace{0.5em}+101 = warning, large timespan
+                                            ($>100$ years)} \\
+ \spec{}{}{\hspace{-1.8em}+1 to +10 = coincident with major planet
+                                                  (Note~6)} \\
+ \spec{}{}{\hspace{1.95em}       0 = OK} \\
+ \spec{}{}{\hspace{1.2em}    $-$1 = illegal JFORM} \\
+ \spec{}{}{\hspace{1.2em}    $-$2 = illegal E0} \\
+ \spec{}{}{\hspace{1.2em}    $-$3 = illegal AORQ0} \\
+ \spec{}{}{\hspace{1.2em}    $-$4 = internal error} \\
+ \spec{}{}{\hspace{1.2em}    $-$5 = numerical error}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Two different element-format options are supported, as follows. \\
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of elements $t_0$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & mean distance $a$ (AU) \\
+        & E      & = & eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        & AORL   & = & mean anomaly $M$ (radians)
+        \end{tabular}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of perihelion $T$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & perihelion distance $q$ (AU) \\
+        & E      & = & eccentricity $e$ $( 0 \leq e \leq 10 )$
+        \end{tabular}
+
+ \item DATE0, DATE1, EPOCH0 and EPOCH1 are all instants of time in
+       the TT time scale (formerly Ephemeris Time, ET), expressed
+       as Modified Julian Dates (JD$-$2400000.5).
+       \begin{itemize}
+       \item DATE0 is the instant at which the given
+             ({\it i.e.}\ unperturbed) osculating elements are correct.
+       \item DATE1 is the specified instant at which the updated osculating
+             elements are correct.
+       \item EPOCH0 and EPOCH1 will be the same as DATE0 and DATE1
+             (respectively) for the JFORM=2 case, normally used for minor
+             planets.  For the JFORM=3 case, the two epochs will refer to
+             perihelion passage and so will not, in general, be the same as
+             DATE0 and/or DATE1 though they may be similar to one another.
+       \end{itemize}
+ \item The elements are with respect to the J2000 ecliptic and mean equinox.
+ \item Unused elements (AM0 and AM1 for JFORM=3) are not accessed.
+ \item See the sla\_PERTUE routine for details of the algorithm used.
+ \item This routine is not intended to be used for major planets, which
+       is why JFORM=1 is not available and why there is no opportunity
+       to specify either the longitude of perihelion or the daily
+       motion.  However, if JFORM=2 elements are somehow obtained for a
+       major planet and supplied to the routine, sensible results will,
+       in fact, be produced.  This happens because the sla\_PERTUE routine
+       that is called to perform the calculations checks the separation
+       between the body and each of the planets and interprets a
+       suspiciously small value (0.001~AU) as an attempt to apply it to
+       the planet concerned.  If this condition is detected, the
+       contribution from that planet is ignored, and the status is set to
+       the planet number (1--10 = Mercury, Venus, EMB, Mars, Jupiter,
+       Saturn, Uranus, Neptune, Earth, Moon) as a warning.
+ \end{enumerate}
+}
+\aref{Sterne, Theodore E., {\it An Introduction to Celestial Mechanics,}\/
+      Interscience Publishers, 1960.  Section 6.7, p199.}
+%------------------------------------------------------------------------------
+\routine{SLA\_PERTUE}{Perturbed Universal Elements}
+{
+ \action{Update the universal elements of an asteroid or comet by
+         applying planetary perturbations.}
+ \call{CALL sla\_PERTUE (DATE, U, JSTAT)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{final epoch (TT MJD) for the updated elements}
+}
+\args{GIVEN and RETURNED}
+{
+ \spec{U}{D(13)}{universal elements (updated in place)} \\
+ \specel {(1)}     {combined mass ($M+m$)} \\
+ \specel {(2)}     {total energy of the orbit ($\alpha$)} \\
+ \specel {(3)}     {reference (osculating) epoch ($t_0$)} \\
+ \specel {(4-6)}   {position at reference epoch (${\rm \bf r}_0$)} \\
+ \specel {(7-9)}   {velocity at reference epoch (${\rm \bf v}_0$)} \\
+ \specel {(10)}    {heliocentric distance at reference epoch} \\
+ \specel {(11)}    {${\rm \bf r}_0.{\rm \bf v_0}$} \\
+ \specel {(12)}    {date ($t$)} \\
+ \specel {(13)}    {universal eccentric anomaly ($\psi$) of date, approx}
+}
+\args{RETURNED}
+{
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{0.5em}+102 = warning, distant epoch} \\
+ \spec{}{}{\hspace{0.5em}+101 = warning, large timespan
+                                            ($>100$ years)} \\
+ \spec{}{}{\hspace{-1.8em}+1 to +10 = coincident with major planet
+                                                  (Note~5)} \\
+ \spec{}{}{\hspace{1.95em}       0 = OK} \\
+ \spec{}{}{\hspace{1.2em}    $-$1 = numerical error}
+}
+\notes
+{
+ \begin{enumerate}
+  \setlength{\parskip}{\medskipamount}
+  \item The ``universal'' elements are those which define the orbit for the
+        purposes of the method of universal variables (see reference 2).
+        They consist of the combined mass of the two bodies, an epoch,
+        and the position and velocity vectors (arbitrary reference frame)
+        at that epoch.  The parameter set used here includes also various
+        quantities that can, in fact, be derived from the other
+        information.  This approach is taken to avoiding unnecessary
+        computation and loss of accuracy.  The supplementary quantities
+        are (i)~$\alpha$, which is proportional to the total energy of the
+        orbit, (ii)~the heliocentric distance at epoch,
+        (iii)~the outwards component of the velocity at the given epoch,
+        (iv)~an estimate of $\psi$, the ``universal eccentric anomaly'' at a
+        given date and (v)~that date.
+
+  \item The universal elements are with respect to the J2000 equator and
+        equinox.
+
+  \item The epochs DATE, U(3) and U(12) are all Modified Julian Dates
+        (JD$-$2400000.5).
+
+  \item The algorithm is a simplified form of Encke's method.  It takes as
+        a basis the unperturbed motion of the body, and numerically
+        integrates the perturbing accelerations from the major planets.
+        The expression used is essentially Sterne's 6.7-2 (reference 1).
+        Everhart \& Pitkin (reference 2) suggest rectifying the orbit at
+        each integration step by propagating the new perturbed position
+        and velocity as the new universal variables.  In the present
+        routine the orbit is rectified less frequently than this, in order
+        to gain a slight speed advantage.  However, the rectification is
+        done directly in terms of position and velocity, as suggested by
+        Everhart \& Pitkin, bypassing the use of conventional orbital
+        elements.
+
+        The $f(q)$ part of the full Encke method is not used.  The purpose
+        of this part is to avoid subtracting two nearly equal quantities
+        when calculating the ``indirect member'', which takes account of the
+        small change in the Sun's attraction due to the slightly displaced
+        position of the perturbed body.  A simpler, direct calculation in
+        double precision proves to be faster and not significantly less
+        accurate.
+
+        Apart from employing a variable timestep, and occasionally
+        ``rectifying the orbit'' to keep the indirect member small, the
+        integration is done in a fairly straightforward way.  The
+        acceleration estimated for the middle of the timestep is assumed
+        to apply throughout that timestep;  it is also used in the
+        extrapolation of the perturbations to the middle of the next
+        timestep, to predict the new disturbed position.  There is no
+        iteration within a timestep.
+
+        Measures are taken to reach a compromise between execution time
+        and accuracy.  The starting-point is the goal of achieving
+        arcsecond accuracy for ordinary minor planets over a ten-year
+        timespan.  This goal dictates how large the timesteps can be,
+        which in turn dictates how frequently the unperturbed motion has
+        to be recalculated from the osculating elements.
+
+        Within predetermined limits, the timestep for the numerical
+        integration is varied in length in inverse proportion to the
+        magnitude of the net acceleration on the body from the major
+        planets.
+
+        The numerical integration requires estimates of the major-planet
+        motions.  Approximate positions for the major planets (Pluto
+        alone is omitted) are obtained from the routine sla\_PLANET.  Two
+        levels of interpolation are used, to enhance speed without
+        significantly degrading accuracy.  At a low frequency, the routine
+        sla\_PLANET is called to generate updated position+velocity ``state
+        vectors''.  The only task remaining to be carried out at the full
+        frequency ({\it i.e.}\ at each integration step) is to use the state
+        vectors to extrapolate the planetary positions.  In place of a
+        strictly linear extrapolation, some allowance is made for the
+        curvature of the orbit by scaling back the radius vector as the
+        linear extrapolation goes off at a tangent.
+
+        Various other approximations are made.  For example, perturbations
+        by Pluto and the minor planets are neglected and relativistic
+        effects are not taken into account.
+
+        In the interests of simplicity, the background calculations for
+        the major planets are carried out {\it en masse.}
+        The mean elements and
+        state vectors for all the planets are refreshed at the same time,
+        without regard for orbit curvature, mass or proximity.
+
+        The Earth-Moon system is treated as a single body when the body is
+        distant but as separate bodies when closer to the EMB than the
+        parameter RNE, which incurs a time penalty but improves accuracy
+        for near-Earth objects.
+
+  \item This routine is not intended to be used for major planets.
+        However, if major-planet elements are supplied, sensible results
+        will, in fact, be produced.  This happens because the routine
+        checks the separation between the body and each of the planets and
+        interprets a suspiciously small value (0.001~AU) as an attempt to
+        apply the routine to the planet concerned.  If this condition
+        is detected, the
+        contribution from that planet is ignored, and the status is set to
+        the planet number (1--10 = Mercury, Venus, EMB,
+        Mars, Jupiter, Saturn, Uranus, Neptune, Earth, Moon) as a warning.
+ \end{enumerate}
+}
+\refs{
+   \begin{enumerate}
+   \item Sterne, Theodore E., {\it An Introduction to Celestial Mechanics,}\/
+         Interscience Publishers, 1960.  Section 6.7, p199.
+   \item Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.
+   \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PLANEL}{Planet Position from Elements}
+{
+ \action{Heliocentric position and velocity of a planet,
+         asteroid or comet, starting from orbital elements.}
+ \call{CALL sla\_PLANEL (\vtop{
+         \hbox{DATE, JFORM, EPOCH, ORBINC, ANODE, PERIH,}
+         \hbox{AORQ, E, AORL, DM, PV, JSTAT)}}}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TT MJD of observation (JD$-$2400000.5,} \\
+ \spec{}{}{\hspace{1.5em} Note~1)} \\
+ \spec{JFORM}{I}{choice of element set (1-3, Note~3)} \\
+ \spec{EPOCH}{D}{epoch of elements ($t_0$ or $T$, TT MJD, Note~4)} \\
+ \spec{ORBINC}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH}{D}{longitude or argument of perihelion
+                            ($\varpi$ or $\omega$,} \\
+ \spec{}{}{\hspace{1.5em} radians)} \\
+ \spec{AORQ}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E}{D}{eccentricity ($e$)} \\
+ \spec{AORL}{D}{mean anomaly or longitude
+                               ($M$ or $L$, radians,} \\
+ \spec{}{}{\hspace{1.5em} JFORM=1,2 only)} \\
+ \spec{DM}{D}{daily motion ($n$, radians, JFORM=1 only)}
+}
+\args{RETURNED}
+{
+ \spec{PV}{D(6)}{heliocentric \xyzxyzd, equatorial, J2000} \\
+ \spec{}{}{\hspace{1.5em} (AU, AU/s)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal JFORM} \\
+ \spec{}{}{\hspace{1.5em} $-$2 = illegal E} \\
+ \spec{}{}{\hspace{1.5em} $-$3 = illegal AORQ} \\
+ \spec{}{}{\hspace{1.5em} $-$4 = illegal DM} \\
+ \spec{}{}{\hspace{1.5em} $-$5 = numerical error}
+}
+\notes
+{
+ \begin{enumerate}
+  \item DATE is the instant for which the prediction is required.  It is
+        in the TT time scale (formerly Ephemeris Time, ET) and is a
+        Modified Julian Date (JD$-$2400000.5).
+  \item The elements are with respect to the J2000 ecliptic and equinox.
+  \item A choice of three different element-format options is available, as
+        follows. \\
+
+        JFORM=1, suitable for the major planets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of elements $t_0$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & longitude of perihelion $\varpi$ (radians) \\
+        & AORQ   & = & mean distance $a$ (AU) \\
+        & E      & = & eccentricity $e$ \\
+        & AORL   & = & mean longitude $L$ (radians) \\
+        & DM     & = & daily motion $n$ (radians)
+        \end{tabular}
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of elements $t_0$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & mean distance $a$ (AU) \\
+        & E      & = & eccentricity $e$ \\
+        & AORL   & = & mean anomaly $M$ (radians)
+        \end{tabular}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of perihelion $T$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & perihelion distance $q$ (AU) \\
+        & E      & = & eccentricity $e$
+        \end{tabular}
+
+        Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
+        not accessed.
+
+  \item Each of the three element sets defines an unperturbed heliocentric
+        orbit.  For a given epoch of observation, the position of the body
+        in its orbit can be predicted from these elements, which are
+        called {\it osculating elements,}\/
+        using standard two-body analytical
+        solutions.  However, due to planetary perturbations, a given set
+        of osculating elements remains usable for only as long as the
+        unperturbed orbit that it describes is an adequate approximation
+        to reality.  Attached to such a set of elements is a date called
+        the {\it osculating epoch,}\/
+        at which the elements are, momentarily,
+        a perfect representation of the instantaneous position and
+        velocity of the body.
+
+        \vspace{1ex}
+
+        Therefore, for any given problem there are up to three different
+        epochs in play, and it is vital to distinguish clearly between
+        them:
+        \begin{itemize}
+        \item The epoch of observation:  the moment in time for which the
+              position of the body is to be predicted.
+        \item The epoch defining the position of the body:  the moment
+              in time at which, in the absence of purturbations, the
+              specified position---mean longitude, mean anomaly, or
+              perihelion---is reached.
+        \item The osculating epoch:  the moment in time at which the
+              given elements are correct.
+        \end{itemize}
+        For the major-planet and minor-planet cases it is usual to make
+        the epoch that defines the position of the body the same as the
+        epoch of osculation.  Thus, only two different epochs are
+        involved:  the epoch of the elements and the epoch of observation.
+        For comets, the epoch of perihelion fixes the position in the
+        orbit and in general a different epoch of osculation will be
+        chosen.  Thus, all three types of epoch are involved.
+
+        \vspace{1ex}
+
+        \goodbreak
+        For the present routine:
+        \begin{itemize}
+        \item The epoch of observation is the argument DATE.
+        \item The epoch defining the position of the body is the argument
+              EPOCH.
+        \item The osculating epoch is not used and is assumed to be
+              close enough to the epoch of observation to deliver
+              adequate accuracy. If not, a preliminary call to
+              sla\_PERTEL may be used to update the element-set (and
+              its associated osculating epoch) by
+              applying planetary perturbations.
+        \end{itemize}
+  \item The reference frame for the result is equatorial and is with
+        respect to the mean equinox and ecliptic of epoch J2000.
+  \item The algorithm was originally adapted from the EPHSLA program of
+        D.\,H.\,P.\,Jones (private communication, 1996).  The method
+        is based on Stumpff's Universal Variables.
+ \end{enumerate}
+}
+\aref{Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.}
+%------------------------------------------------------------------------------
+\routine{SLA\_PLANET}{Planetary Ephemerides}
+{
+ \action{Approximate heliocentric position and velocity of a planet.}
+ \call{CALL sla\_PLANET (DATE, NP, PV, JSTAT)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{Modified Julian Date (JD$-$2400000.5)} \\
+ \spec{NP}{I}{planet:} \\
+ \spec{}{}{\hspace{1.5em} 1\,=\,Mercury} \\
+ \spec{}{}{\hspace{1.5em} 2\,=\,Venus} \\
+ \spec{}{}{\hspace{1.5em} 3\,=\,Earth-Moon Barycentre} \\
+ \spec{}{}{\hspace{1.5em} 4\,=\,Mars} \\
+ \spec{}{}{\hspace{1.5em} 5\,=\,Jupiter} \\
+ \spec{}{}{\hspace{1.5em} 6\,=\,Saturn} \\
+ \spec{}{}{\hspace{1.5em} 7\,=\,Uranus} \\
+ \spec{}{}{\hspace{1.5em} 8\,=\,Neptune} \\
+ \spec{}{}{\hspace{1.5em} 9\,=\,Pluto}
+}
+\args{RETURNED}
+{
+ \spec{PV}{D(6)}{heliocentric \xyzxyzd, equatorial, J2000} \\
+ \spec{}{}{\hspace{1.5em} (AU, AU/s)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} $+$1 = warning: date outside of range} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal NP (outside 1-9)} \\
+ \spec{}{}{\hspace{1.5em} $-$2 = solution didn't converge}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The epoch, DATE, is in the TDB time scale and is in the form
+        of a Modified Julian Date (JD$-$2400000.5).
+  \item The reference frame is equatorial and is with respect to
+        the mean equinox and ecliptic of epoch J2000.
+  \item If a planet number, NP, outside the range 1-9 is supplied, an error
+        status is returned (JSTAT~=~$-1$) and the PV vector
+        is set to zeroes.
+  \item The algorithm for obtaining the mean elements of the
+        planets from Mercury to Neptune is due to
+        J.\,L.\,Simon, P.\,Bretagnon, J.\,Chapront,
+        M.\,Chapront-Touze, G.\,Francou and J.\,Laskar (Bureau des
+        Longitudes, Paris, France).  The (completely different)
+        algorithm for calculating the ecliptic coordinates of
+        Pluto is by Meeus.
+  \item Comparisons of the present routine with the JPL DE200 ephemeris
+        give the following RMS errors over the interval 1960-2025:
+
+        \begin{tabular}{llll}
+         & & {\it position (km)} & {\it speed (metre/sec)} \\ \\
+         & Mercury & \hspace{2em}334 & \hspace{2.5em}0.437 \\
+         & Venus   & \hspace{1.5em}1060 & \hspace{2.5em}0.855 \\
+         & EMB     & \hspace{1.5em}2010 & \hspace{2.5em}0.815 \\
+         & Mars    & \hspace{1.5em}7690 & \hspace{2.5em}1.98 \\
+         & Jupiter & \hspace{1em}71700 & \hspace{2.5em}7.70 \\
+         & Saturn  & \hspace{0.5em}199000 & \hspace{2em}19.4 \\
+         & Uranus  & \hspace{0.5em}564000 & \hspace{2em}16.4 \\
+         & Neptune & \hspace{0.5em}158000 & \hspace{2em}14.4 \\
+         & Pluto & \hspace{1em}36400 & \hspace{2.5em}0.137
+        \end{tabular}
+
+        From comparisons with DE102, Simon {\it et al.}\/ quote the following
+        longitude accuracies over the interval 1800-2200:
+
+        \begin{tabular}{lll}
+         & Mercury & \hspace{0.5em}\arcseci{4} \\
+         & Venus   & \hspace{0.5em}\arcseci{5} \\
+         & EMB     & \hspace{0.5em}\arcseci{6} \\
+         & Mars    & \arcseci{17} \\
+         & Jupiter & \arcseci{71} \\
+         & Saturn  & \arcseci{81} \\
+         & Uranus  & \arcseci{86} \\
+         & Neptune & \arcseci{11}
+        \end{tabular}
+
+        In the case of Pluto, Meeus quotes an accuracy of \arcsec{0}{6}
+        in longitude and \arcsec{0}{2} in latitude for the period
+        1885-2099.
+
+        For all except Pluto, over the period 1000-3000,
+        the accuracy is better than 1.5
+        times that over 1800-2200.  Outside the interval 1000-3000 the
+        accuracy declines.  For Pluto the accuracy declines rapidly
+        outside the period 1885-2099.  Outside these ranges
+        (1885-2099 for Pluto, 1000-3000 for the rest) a ``date out
+        of range'' warning status ({\tt JSTAT=+1}) is returned.
+  \item The algorithms for (i)~Mercury through Neptune and
+        (ii)~Pluto are completely independent.  In the Mercury
+        through Neptune case, the present SLALIB
+        implementation differs from the original
+        Simon {\it et al.}\/ Fortran code in the following respects:
+        \begin{itemize}
+         \item The date is supplied as a Modified Julian Date rather
+               a Julian Date (${\rm MJD} = ({\rm JD} - 2400000.5$).
+         \item The result is returned only in equatorial
+               Cartesian form;  the ecliptic
+               longitude, latitude and radius vector are not returned.
+         \item The velocity is in AU per second, not AU per day.
+         \item Different error/warning status values are used.
+         \item Kepler's Equation is not solved inline.
+         \item Polynomials in T are nested to minimize rounding errors.
+         \item Explicit double-precision constants are used to avoid
+               mixed-mode expressions.
+         \item There are other, cosmetic, changes to comply with
+               Starlink/SLALIB style guidelines.
+        \end{itemize}
+        None of the above changes affects the result significantly.
+  \item For NP\,=\,3 the result is for the Earth-Moon Barycentre.  To
+        obtain the heliocentric position and velocity of the Earth,
+        either use the SLALIB routine sla\_EVP (or sla\_EPV)
+        or call sla\_DMOON and
+        subtract 0.012150581 times the geocentric Moon vector from
+        the EMB vector produced by the present routine.  (The Moon
+        vector should be precessed to J2000 first, but this can
+        be omitted for modern epochs without introducing significant
+        inaccuracy.)
+ \end{enumerate}
+\refs
+{
+ \begin{enumerate}
+  \item Simon {\it et al.,}\/
+        Astron.\ Astrophys.\ {\bf 282}, 663 (1994).
+  \item Meeus, J.,
+        {\it Astronomical Algorithms,}\/ Willmann-Bell (1991).
+ \end{enumerate}
+}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_PLANTE}{\radec\ of Planet from Elements}
+{
+ \action{Topocentric apparent \radec\ of a Solar-System object whose
+         heliocentric orbital elements are known.}
+ \call{CALL sla\_PLANTE (\vtop{
+         \hbox{DATE, ELONG, PHI, JFORM, EPOCH, ORBINC, ANODE, PERIH,}
+         \hbox{AORQ, E, AORL, DM, RA, DEC, R, JSTAT)}}}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TT MJD of observation (JD$-$2400000.5,} \\
+ \spec{}{}{\hspace{1.5em} Notes~1,5)} \\
+ \spec{ELONG,PHI}{D}{observer's longitude (east +ve) and latitude} \\
+ \spec{}{}{\hspace{1.5em} (radians, Note~2)} \\
+ \spec{JFORM}{I}{choice of element set (1-3, Notes~3-6)} \\
+ \spec{EPOCH}{D}{epoch of elements ($t_0$ or $T$, TT MJD, Note~5)} \\
+ \spec{ORBINC}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH}{D}{longitude or argument of perihelion
+                            ($\varpi$ or $\omega$,} \\
+ \spec{}{}{\hspace{1.5em} radians)} \\
+ \spec{AORQ}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E}{D}{eccentricity ($e$)} \\
+ \spec{AORL}{D}{mean anomaly or longitude ($M$ or $L$, radians,} \\
+  \spec{}{}{\hspace{1.5em} JFORM=1,2 only)} \\
+ \spec{DM}{D}{daily motion ($n$, radians, JFORM=1 only)}
+}
+\args{RETURNED}
+{
+ \spec{RA,DEC}{D}{topocentric apparent \radec\ (radians)} \\
+ \spec{R}{D}{distance from observer (AU)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal JFORM} \\
+ \spec{}{}{\hspace{1.5em} $-$2 = illegal E} \\
+ \spec{}{}{\hspace{1.5em} $-$3 = illegal AORQ} \\
+ \spec{}{}{\hspace{1.5em} $-$4 = illegal DM} \\
+ \spec{}{}{\hspace{1.5em} $-$5 = numerical error}
+}
+\notes
+{
+ \begin{enumerate}
+  \item DATE is the instant for which the prediction is
+        required.  It is in the TT time scale (formerly
+        Ephemeris Time, ET) and is a
+        Modified Julian Date (JD$-$2400000.5).
+  \item The longitude and latitude allow correction for geocentric
+        parallax.  This is usually a small effect, but can become
+        important for near-Earth asteroids.  Geocentric positions
+        can be generated by appropriate use of the routines
+        sla\_EVP (or sla\_EPV) and sla\_PLANEL.
+  \item The elements are with respect to the J2000 ecliptic and equinox.
+  \item A choice of three different element-format options is available, as
+        follows. \\
+
+        JFORM=1, suitable for the major planets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of elements $t_0$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & longitude of perihelion $\varpi$ (radians) \\
+        & AORQ   & = & mean distance $a$ (AU) \\
+        & E      & = & eccentricity $e$ \\
+        & AORL   & = & mean longitude $L$ (radians) \\
+        & DM     & = & daily motion $n$ (radians)
+        \end{tabular}
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of elements $t_0$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & mean distance $a$ (AU) \\
+        & E      & = & eccentricity $e$ \\
+        & AORL   & = & mean anomaly $M$ (radians)
+        \end{tabular}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of perihelion $T$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & perihelion distance $q$ (AU) \\
+        & E      & = & eccentricity $e$
+        \end{tabular}
+
+        Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
+        not accessed.
+
+  \item Each of the three element sets defines an unperturbed heliocentric
+        orbit.  For a given epoch of observation, the position of the body
+        in its orbit can be predicted from these elements, which are
+        called {\it osculating elements,}\/
+        using standard two-body analytical
+        solutions.  However, due to planetary perturbations, a given set
+        of osculating elements remains usable for only as long as the
+        unperturbed orbit that it describes is an adequate approximation
+        to reality.  Attached to such a set of elements is a date called
+        the {\it osculating epoch,}\/
+        at which the elements are, momentarily,
+        a perfect representation of the instantaneous position and
+        velocity of the body.
+
+        \vspace{1ex}
+
+        Therefore, for any given problem there are up to three different
+        epochs in play, and it is vital to distinguish clearly between
+        them:
+        \begin{itemize}
+        \item The epoch of observation:  the moment in time for which the
+              position of the body is to be predicted.
+        \item The epoch defining the position of the body:  the moment
+              in time at which, in the absence of purturbations, the
+              specified position---mean longitude, mean anomaly, or
+              perihelion---is reached.
+        \item The osculating epoch:  the moment in time at which the
+              given elements are correct.
+        \end{itemize}
+        For the major-planet and minor-planet cases it is usual to make
+        the epoch that defines the position of the body the same as the
+        epoch of osculation.  Thus, only two different epochs are
+        involved:  the epoch of the elements and the epoch of observation.
+        For comets, the epoch of perihelion fixes the position in the
+        orbit and in general a different epoch of osculation will be
+        chosen.  Thus, all three types of epoch are involved.
+
+        \vspace{1ex}
+
+        \goodbreak
+        For the present routine:
+        \begin{itemize}
+        \item The epoch of observation is the argument DATE.
+        \item The epoch defining the position of the body is the argument
+              EPOCH.
+        \item The osculating epoch is not used and is assumed to be
+              close enough to the epoch of observation to deliver
+              adequate accuracy. If not, a preliminary call to
+              sla\_PERTEL may be used to update the element-set (and
+              its associated osculating epoch) by
+              applying planetary perturbations.
+        \end{itemize}
+  \item Two important sources for orbital elements are {\it Horizons,}\/
+        operated by the Jet Propulsion Laboratory, Pasadena,
+        and the {\it Minor Planet Center,}\/ operated by the Center for
+        Astrophysics, Harvard.  For further details, see Section~\ref{ephem}.
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_PLANTU}{\radec\ from Universal Elements}
+{
+ \action{Topocentric apparent \radec\ of a Solar-System object whose
+         heliocentric universal orbital elements are known.}
+ \call{CALL sla\_PLANTU (DATE, ELONG, PHI, U, RA, DEC, R, JSTAT)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{TT MJD of observation (JD$-$2400000.5)} \\
+ \spec{ELONG,PHI}{D}{observer's longitude (east +ve) and latitude} \\
+ \spec{}{}{\hspace{1.5em} radians)}
+}
+\args{GIVEN and RETURNED}
+{
+ \spec{U}{D(13)}{universal orbital elements} \\
+ \specel {(1)}     {combined mass ($M+m$)} \\
+ \specel {(2)}     {total energy of the orbit ($\alpha$)} \\
+ \specel {(3)}     {reference (osculating) epoch ($t_0$)} \\
+ \specel {(4-6)}   {position at reference epoch (${\rm \bf r}_0$)} \\
+ \specel {(7-9)}   {velocity at reference epoch (${\rm \bf v}_0$)} \\
+ \specel {(10)}    {heliocentric distance at reference epoch} \\
+ \specel {(11)}    {${\rm \bf r}_0.{\rm \bf v_0}$} \\
+ \specel {(12)}    {date ($t$)} \\
+ \specel {(13)}    {universal eccentric anomaly ($\psi$) of date, approx}
+}
+\args{RETURNED}
+{
+ \spec{RA,DEC}{D}{topocentric apparent \radec\ (radians)} \\
+ \spec{R}{D}{distance from observer (AU)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = radius vector zero} \\
+ \spec{}{}{\hspace{1.5em} $-$2 = failed to converge}
+}
+\notes
+{
+ \begin{enumerate}
+  \item DATE is the instant for which the prediction is
+        required.  It is in the TT time scale (formerly
+        Ephemeris Time, ET) and is a
+        Modified Julian Date (JD$-$2400000.5).
+  \item The longitude and latitude allow correction for geocentric
+        parallax.  This is usually a small effect, but can become
+        important for near-Earth asteroids.  Geocentric positions
+        can be generated by appropriate use of the routines
+        sla\_EVP (or sla\_EPV) and sla\_UE2PV.
+  \item The ``universal'' elements are those which define the orbit for the
+        purposes of the method of universal variables (see reference 2).
+        They consist of the combined mass of the two bodies, an epoch,
+        and the position and velocity vectors (arbitrary reference frame)
+        at that epoch.  The parameter set used here includes also various
+        quantities that can, in fact, be derived from the other
+        information.  This approach is taken to avoiding unnecessary
+        computation and loss of accuracy.  The supplementary quantities
+        are (i)~$\alpha$, which is proportional to the total energy of the
+        orbit, (ii)~the heliocentric distance at epoch,
+        (iii)~the outwards component of the velocity at the given epoch,
+        (iv)~an estimate of $\psi$, the ``universal eccentric anomaly'' at a
+        given date and (v)~that date.
+  \item The universal elements are with respect to the J2000 ecliptic
+        and equinox.
+ \end{enumerate}
+}
+\refs{
+   \begin{enumerate}
+   \item Sterne, Theodore E., {\it An Introduction to Celestial Mechanics,}\/
+         Interscience Publishers, 1960.  Section 6.7, p199.
+   \item Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.
+   \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_PM}{Proper Motion}
+{
+ \action{Apply corrections for proper motion to a star \radec.}
+ \call{CALL sla\_PM (R0, D0, PR, PD, PX, RV, EP0, EP1, R1, D1)}
+}
+\args{GIVEN}
+{
+ \spec{R0,D0}{D}{\radec\ at epoch EP0 (radians)} \\
+ \spec{PR,PD}{D}{proper motions:  rate of change of
+                 \radec\  (radians per year)} \\
+ \spec{PX}{D}{parallax (arcsec)} \\
+ \spec{RV}{D}{radial velocity (km~s$^{-1}$, +ve if receding)} \\
+ \spec{EP0}{D}{start epoch in years ({\it e.g.}\ Julian epoch)} \\
+ \spec{EP1}{D}{end epoch in years (same system as EP0)}
+}
+\args{RETURNED}
+{
+ \spec{R1,D1}{D}{\radec\ at epoch EP1 (radians)}
+}
+\notes
+{
+\begin{enumerate}
+\item The $\alpha$ proper motions are $\dot{\alpha}$ rather than
+      $\dot{\alpha}\cos\delta$, and are in the same coordinate
+      system as R0,D0.
+\item If the available proper motions are pre-FK5 they will be per
+      tropical year rather than per Julian year, and so the epochs
+      must both be Besselian rather than Julian.  In such cases, a
+      scaling factor of 365.2422D0/365.25D0 should be applied to the
+      radial velocity before use also.
+\end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item 1984 {\it Astronomical Almanac}, pp B39-B41.
+  \item Lederle \& Schwan, 1984.\ {\it Astr. Astrophys.}\ {\bf 134}, 1-6.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_POLMO}{Polar Motion}
+{
+ \action{Polar motion:  correct site longitude and latitude for polar
+         motion and calculate azimuth difference between celestial and
+         terrestrial poles.}
+ \call{CALL sla\_POLMO (ELONGM, PHIM, XP, YP, ELONG, PHI, DAZ)}
+}
+\args{GIVEN}
+{
+ \spec{ELONGM}{D}{mean longitude of the site (radians, east +ve)} \\
+ \spec{PHIM}{D}{mean geodetic latitude of the site (radians)} \\
+ \spec{XP}{D}{polar motion $x$-coordinate (radians)} \\
+ \spec{YP}{D}{polar motion $y$-coordinate (radians)}
+}
+\args{RETURNED}
+{
+ \spec{ELONG}{D}{true longitude of the site (radians, east +ve)} \\
+ \spec{PHI}{D}{true geodetic latitude of the site (radians)} \\
+ \spec{DAZ}{D}{azimuth correction (terrestrial$-$celestial, radians)}
+}
+\notes
+{
+\begin{enumerate}
+\item ``Mean'' longitude and latitude are the (fixed) values for the
+      site's location with respect to the IERS terrestrial reference
+      frame;  the latitude is geodetic.  TAKE CARE WITH THE LONGITUDE
+      SIGN CONVENTION.  The longitudes used by the present routine
+      are east-positive, in accordance with geographical convention
+      (and right-handed).  In particular, note that the longitudes
+      returned by the sla\_OBS routine are west-positive, following
+      astronomical usage, and must be reversed in sign before use in
+      the present routine.
+\item XP and YP are the (changing) coordinates of the Celestial
+      Ephemeris Pole with respect to the IERS Reference Pole.
+      XP is positive along the meridian at longitude $0^\circ$,
+      and YP is positive along the meridian at longitude
+      $270^\circ$ ({\it i.e.}\ $90^\circ$ west).  Values for XP,YP can
+      be obtained from IERS circulars and equivalent publications;
+      the maximum amplitude observed so far is about \arcsec{0}{3}.
+\item ``True'' longitude and latitude are the (moving) values for
+      the site's location with respect to the celestial ephemeris
+      pole and the meridian which corresponds to the Greenwich
+      apparent sidereal time.  The true longitude and latitude
+      link the terrestrial coordinates with the standard celestial
+      models (for precession, nutation, sidereal time {\it etc}).
+\item The azimuths produced by sla\_AOP and sla\_AOPQK are with
+      respect to due north as defined by the Celestial Ephemeris
+      Pole, and can therefore be called ``celestial azimuths''.
+      However, a telescope fixed to the Earth measures azimuth
+      essentially with respect to due north as defined by the
+      IERS Reference Pole, and can therefore be called ``terrestrial
+      azimuth''.  Uncorrected, this would manifest itself as a
+      changing ``azimuth zero-point error''.  The value DAZ is the
+      correction to be added to a celestial azimuth to produce
+      a terrestrial azimuth.
+\item The present routine is rigorous.  For most practical
+      purposes, the following simplified formulae provide an
+      adequate approximation: \\[2ex]
+      \hspace*{1em}\begin{tabular}{lll}
+        {\tt ELONG} & {\tt =} &
+             {\tt ELONGM+XP*COS(ELONGM)-YP*SIN(ELONGM)} \\
+        {\tt PHI  } & {\tt =} &
+             {\tt PHIM+(XP*SIN(ELONGM)+YP*COS(ELONGM))*TAN(PHIM)} \\
+        {\tt DAZ  } & {\tt =} &
+             {\tt -SQRT(XP*XP+YP*YP)*COS(ELONGM-ATAN2(XP,YP))/COS(PHIM)} \\
+      \end{tabular} \\[2ex]
+      An alternative formulation for DAZ is:\\[2ex]
+      \hspace*{1em}\begin{tabular}{lll}
+        {\tt X  } & {\tt =} & {\tt COS(ELONGM)*COS(PHIM)} \\
+        {\tt Y  } & {\tt =} & {\tt SIN(ELONGM)*COS(PHIM)} \\
+        {\tt DAZ} & {\tt =} & {\tt ATAN2(-X*YP-Y*XP,X*X+Y*Y)} \\
+      \end{tabular}
+\end{enumerate}
+}
+\aref{Seidelmann, P.K.\ (ed), 1992.  {\it Explanatory
+      Supplement to the Astronomical Almanac,}\/ ISBN~0-935702-68-7,
+      sections 3.27, 4.25, 4.52.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PREBN}{Precession Matrix (FK4)}
+{
+ \action{Generate the matrix of precession between two epochs,
+         using the old, pre IAU~1976, Bessel-Newcomb model, in
+         Andoyer's formulation.}
+ \call{CALL sla\_PREBN (BEP0, BEP1, RMATP)}
+}
+\args{GIVEN}
+{
+ \spec{BEP0}{D}{beginning Besselian epoch} \\
+ \spec{BEP1}{D}{ending Besselian epoch}
+}
+\args{RETURNED}
+{
+ \spec{RMATP}{D(3,3)}{precession matrix}
+}
+\anote{The matrix is in the sense:
+       \begin{verse}
+        {\bf v}$_{1}$ =  {\bf M}$\cdot${\bf v}$_{0}$
+       \end{verse}
+       where {\bf v}$_{1}$ is the star vector relative to the
+       mean equator and equinox of epoch BEP1, {\bf M} is the
+       $3\times3$ matrix RMATP and
+       {\bf v}$_{0}$ is the star vector relative to the
+       mean equator and equinox of epoch BEP0.}
+\aref{Smith {\it et al.}, 1989.\ {\it Astr.J.}\ {\bf 97}, 269.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PREC}{Precession Matrix (FK5)}
+{
+ \action{Form the matrix of precession between two epochs (IAU 1976, FK5).}
+ \call{CALL sla\_PREC (EP0, EP1, RMATP)}
+}
+\args{GIVEN}
+{
+ \spec{EP0}{D}{beginning epoch} \\
+ \spec{EP1}{D}{ending epoch}
+}
+\args{RETURNED}
+{
+ \spec{RMATP}{D(3,3)}{precession matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The epochs are TDB Julian epochs.
+  \item The matrix is in the sense:
+        \begin{verse}
+         {\bf v}$_{1}$ =  {\bf M}$\cdot${\bf v}$_{0}$
+        \end{verse}
+        where {\bf v}$_{1}$ is the star vector relative to the
+        mean equator and equinox of epoch EP1, {\bf M} is the
+        $3\times3$ matrix RMATP and
+        {\bf v}$_{0}$ is the star vector relative to the
+        mean equator and equinox of epoch EP0.
+  \item Though the matrix method itself is rigorous, the precession
+        angles are expressed through canonical polynomials which are
+        valid only for a limited time span.  There are also known
+        errors in the IAU precession rate.  The absolute accuracy
+        of the present formulation is better than \arcsec{0}{1} from
+        1960\,AD to 2040\,AD, better than \arcseci{1} from 1640\,AD to 2360\,AD,
+        and remains below \arcseci{3} for the whole of the period
+        500\,BC to 3000\,AD.  The errors exceed \arcseci{10} outside the
+        range 1200\,BC to 3900\,AD, exceed \arcseci{100} outside 4200\,BC to
+        5600\,AD and exceed \arcseci{1000} outside 6800\,BC to 8200\,AD.
+        The SLALIB routine sla\_PRECL implements a more elaborate
+        model which is suitable for problems spanning several
+        thousand years.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Lieske, J.H., 1979.\ {\it Astr.Astrophys.}\ {\bf 73}, 282;
+        equations 6 \& 7, p283.
+  \item Kaplan, G.H., 1981.\ {\it USNO circular no.\ 163}, pA2.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PRECES}{Precession}
+{
+ \action{Precession -- either the old ``FK4'' (Bessel-Newcomb, pre~IAU~1976)
+         or new ``FK5'' (Fricke, post~IAU~1976) as required.}
+ \call{CALL sla\_PRECES (SYSTEM, EP0, EP1, RA, DC)}
+}
+\args{GIVEN}
+{
+ \spec{SYSTEM}{C}{precession to be applied: `FK4' or `FK5'} \\
+ \spec{EP0,EP1}{D}{starting and ending epoch} \\
+ \spec{RA,DC}{D}{\radec, mean equator \& equinox of epoch EP0}
+}
+\args{RETURNED}
+{
+ \spec{RA,DC}{D}{\radec, mean equator \& equinox of epoch EP1}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Lowercase characters in SYSTEM are acceptable.
+  \item The epochs are Besselian if SYSTEM=`FK4' and Julian if `FK5'.
+        For example, to precess coordinates in the old system from
+        equinox 1900.0 to 1950.0 the call would be:
+        \begin{quote}
+         {\tt CALL sla\_PRECES ('FK4', 1900D0, 1950D0, RA, DC)}
+        \end{quote}
+  \item This routine will {\bf NOT} correctly convert between the old and
+        the new systems -- for example conversion from B1950 to J2000.
+        For these purposes see sla\_FK425, sla\_FK524, sla\_FK45Z and
+        sla\_FK54Z.
+  \item If an invalid SYSTEM is supplied, values of $-$99D0,$-$99D0 are
+        returned for both RA and DC.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PRECL}{Precession Matrix (latest)}
+{
+ \action{Form the matrix of precession between two epochs, using the
+         model of Simon {\it et al}.\ (1994), which is suitable for long
+         periods of time.}
+ \call{CALL sla\_PRECL (EP0, EP1, RMATP)}
+}
+\args{GIVEN}
+{
+ \spec{EP0}{D}{beginning epoch} \\
+ \spec{EP1}{D}{ending epoch}
+}
+\args{RETURNED}
+{
+ \spec{RMATP}{D(3,3)}{precession matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The epochs are TDB Julian epochs.
+  \item The matrix is in the sense:
+        \begin{verse}
+         {\bf v}$_{1}$ =  {\bf M}$\cdot${\bf v}$_{0}$
+        \end{verse}
+        where {\bf v}$_{1}$ is the star vector relative to the
+        mean equator and equinox of epoch EP1, {\bf M} is the
+        $3\times3$ matrix RMATP and
+        {\bf v}$_{0}$ is the star vector relative to the
+        mean equator and equinox of epoch EP0.
+  \item The absolute accuracy of the model is limited by the
+        uncertainty in the general precession, about \arcsec{0}{3} per
+        1000~years.  The remainder of the formulation provides a
+        precision of 1~milliarcsecond over the interval from 1000\,AD
+        to 3000\,AD, \arcsec{0}{1} from 1000\,BC to 5000\,AD and
+        \arcseci{1} from 4000\,BC to 8000\,AD.
+ \end{enumerate}
+}
+\aref{Simon, J.L.\ {\it et al}., 1994.\ {\it Astr.Astrophys.}\ {\bf 282},
+      663.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PRENUT}{Precession-Nutation Matrix}
+{
+ \action{Form the matrix of precession and nutation (SF2001).}
+ \call{CALL sla\_PRENUT (EPOCH, DATE, RMATPN)}
+}
+\args{GIVEN}
+{
+ \spec{EPOCH}{D}{Julian Epoch for mean coordinates} \\
+ \spec{DATE}{D}{Modified Julian Date (JD$-$2400000.5)
+                       for true coordinates}
+}
+\args{RETURNED}
+{
+ \spec{RMATPN}{D(3,3)}{combined precession-nutation matrix}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The epoch and date are TDB.  TT (or even UTC) will do.
+  \item The matrix is in the sense:
+        \begin{verse}
+         {\bf v}$_{true}$ =  {\bf M}$\cdot${\bf v}$_{mean}$
+        \end{verse}
+        where {\bf v}$_{true}$ is the star vector relative to the
+        true equator and equinox of epoch DATE, {\bf M} is the
+        $3\times3$ matrix RMATPN and
+        {\bf v}$_{mean}$ is the star vector relative to the
+        mean equator and equinox of epoch EPOCH.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_PV2EL}{Orbital Elements from Position/Velocity}
+{
+ \action{Heliocentric osculating elements obtained from instantaneous
+         position and velocity.}
+ \call{CALL sla\_PV2EL (\vtop{
+         \hbox{PV, DATE, PMASS, JFORMR, JFORM, EPOCH, ORBINC,}
+         \hbox{ANODE, PERIH, AORQ, E, AORL, DM, JSTAT)}}}
+}
+\args{GIVEN}
+{
+ \spec{PV}{D(6)}{heliocentric \xyzxyzd, equatorial, J2000} \\
+ \spec{}{}{\hspace{1.5em} (AU, AU/s; Note~1)} \\
+ \spec{DATE}{D}{date (TT Modified Julian Date = JD$-$2400000.5)} \\
+ \spec{PMASS}{D}{mass of the planet (Sun = 1; Note~2)} \\
+ \spec{JFORMR}{I}{requested element set (1-3; Note~3)}
+}
+\args{RETURNED}
+{
+ \spec{JFORM}{I}{element set actually returned (1-3; Note~4)} \\
+ \spec{EPOCH}{D}{epoch of elements ($t_0$ or $T$, TT MJD)} \\
+ \spec{ORBINC}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH}{D}{longitude or argument of perihelion
+                            ($\varpi$ or $\omega$,} \\
+ \spec{}{}{\hspace{1.5em} radians)} \\
+ \spec{AORQ}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E}{D}{eccentricity ($e$)} \\
+ \spec{AORL}{D}{mean anomaly or longitude
+                               ($M$ or $L$, radians,} \\
+ \spec{}{}{\hspace{1.5em} JFORM=1,2 only)} \\
+ \spec{DM}{D}{daily motion ($n$, radians, JFORM=1 only)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal PMASS} \\
+ \spec{}{}{\hspace{1.5em} $-$2 = illegal JFORMR} \\
+ \spec{}{}{\hspace{1.5em} $-$3 = position/velocity out of allowed range}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The PV 6-vector is with respect to the mean equator and equinox of
+        epoch J2000.  The orbital elements produced are with respect to
+        the J2000 ecliptic and mean equinox.
+  \item The mass, PMASS, is important only for the larger planets.  For
+        most purposes ({\it e.g.}~asteroids) use 0D0.  Values less than zero
+        are illegal.
+  \item Three different element-format options are supported, as
+        follows. \\
+
+        JFORM=1, suitable for the major planets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of elements $t_0$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & longitude of perihelion $\varpi$ (radians) \\
+        & AORQ   & = & mean distance $a$ (AU) \\
+        & E      & = & eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        & AORL   & = & mean longitude $L$ (radians) \\
+        & DM     & = & daily motion $n$ (radians)
+        \end{tabular}
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of elements $t_0$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & mean distance $a$ (AU) \\
+        & E      & = & eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        & AORL   & = & mean anomaly $M$ (radians)
+        \end{tabular}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of perihelion $T$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & perihelion distance $q$ (AU) \\
+        & E      & = & eccentricity $e$ $( 0 \leq e \leq 10 )$
+        \end{tabular}
+
+  \item It may not be possible to generate elements in the form
+        requested through JFORMR.  The caller is notified of the form
+        of elements actually returned by means of the JFORM argument:
+
+        \begin{tabular}{llll}
+        & JFORMR   & JFORM   & meaning \\ \\
+        & ~~~~~1   & ~~~~~1  & OK: elements are in the requested format \\
+        & ~~~~~1   & ~~~~~2  & never happens \\
+        & ~~~~~1   & ~~~~~3  & orbit not elliptical \\
+        & ~~~~~2   & ~~~~~1  & never happens \\
+        & ~~~~~2   & ~~~~~2  & OK: elements are in the requested format \\
+        & ~~~~~2   & ~~~~~3  & orbit not elliptical \\
+        & ~~~~~3   & ~~~~~1  & never happens \\
+        & ~~~~~3   & ~~~~~2  & never happens \\
+        & ~~~~~3   & ~~~~~3  & OK: elements are in the requested format
+        \end{tabular}
+
+  \item The arguments returned for each value of JFORM ({\it cf.}\/ Note~5:
+        JFORM may not be the same as JFORMR) are as follows:
+
+        \begin{tabular}{lllll}
+        & JFORM  & 1        & 2        & 3 \\ \\
+        & EPOCH  & $t_0$    & $t_0$    & $T$ \\
+        & ORBINC & $i$      & $i$      & $i$ \\
+        & ANODE  & $\Omega$ & $\Omega$ & $\Omega$ \\
+        & PERIH  & $\varpi$ & $\omega$ & $\omega$ \\
+        & AORQ   & $a$      & $a$      & $q$ \\
+        & E      & $e$      & $e$      & $e$ \\
+        & AORL   & $L$      & $M$      & - \\
+        & DM     & $n$      & -        & -
+        \end{tabular}
+
+        where:
+
+        \begin{tabular}{lll}
+        & $t_0$    & is the epoch of the elements (MJD, TT) \\
+        & $T$      & is the epoch of perihelion (MJD, TT) \\
+        & $i$      & is the inclination (radians) \\
+        & $\Omega$ & is the longitude of the ascending node (radians) \\
+        & $\varpi$ & is the longitude of perihelion (radians) \\
+        & $\omega$ & is the argument of perihelion (radians) \\
+        & $a$      & is the mean distance (AU) \\
+        & $q$      & is the perihelion distance (AU) \\
+        & $e$      & is the eccentricity \\
+        & $L$      & is the longitude (radians, $0-2\pi$) \\
+        & $M$      & is the mean anomaly (radians, $0-2\pi$) \\
+        & $n$      & is the daily motion (radians) \\
+        & - & means no value is set
+        \end{tabular}
+
+  \item At very small inclinations, the longitude of the ascending node
+        ANODE becomes indeterminate and under some circumstances may be
+        set arbitrarily to zero.  Similarly, if the orbit is close to
+        circular, the true anomaly becomes indeterminate and under some
+        circumstances may be set arbitrarily to zero.  In such cases,
+        the other elements are automatically adjusted to compensate,
+        and so the elements remain a valid description of the orbit.
+  \item The osculating epoch for the returned elements is the argument
+        DATE.
+ \end{enumerate}
+}
+\aref{Sterne, Theodore E., {\it An Introduction to Celestial Mechanics,}\/
+      Interscience Publishers, 1960.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PV2UE}{Position/Velocity to Universal Elements}
+{
+ \action{Construct a universal element set based on an instantaneous
+         position and velocity.}
+ \call{CALL sla\_PV2UE (PV, DATE, PMASS, U, JSTAT)}
+}
+\args{GIVEN}
+{
+ \spec{PV}{D(6)}{heliocentric \xyzxyzd, equatorial, J2000} \\
+ \spec{}{}{\hspace{1.5em} (AU, AU/s; Note~1)} \\
+ \spec{DATE}{D}{date (TT Modified Julian Date = JD$-$2400000.5)} \\
+ \spec{PMASS}{D}{mass of the planet (Sun = 1; Note~2)}
+}
+\args{RETURNED}
+{
+ \spec{U}{D(13)}{universal orbital elements (Note~3)} \\
+ \specel {(1)}     {combined mass ($M+m$)} \\
+ \specel {(2)}     {total energy of the orbit ($\alpha$)} \\
+ \specel {(3)}     {reference (osculating) epoch ($t_0$)} \\
+ \specel {(4-6)}   {position at reference epoch (${\rm \bf r}_0$)} \\
+ \specel {(7-9)}   {velocity at reference epoch (${\rm \bf v}_0$)} \\
+ \specel {(10)}    {heliocentric distance at reference epoch} \\
+ \specel {(11)}    {${\rm \bf r}_0.{\rm \bf v}_0$} \\
+ \specel {(12)}    {date ($t$)} \\
+ \specel {(13)}    {universal eccentric anomaly ($\psi$) of date, approx} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{1.95em}      0 = OK} \\
+ \spec{}{}{\hspace{1.2em}    $-$1 = illegal PMASS} \\
+ \spec{}{}{\hspace{1.2em}    $-$2 = too close to Sun} \\
+ \spec{}{}{\hspace{1.2em}    $-$3 = too slow}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The PV 6-vector can be with respect to any chosen inertial frame,
+        and the resulting universal-element set will be with respect to
+        the same frame.  A common choice will be mean equator and ecliptic
+        of epoch J2000.
+  \item The mass, PMASS, is important only for the larger planets.  For
+        most purposes ({\it e.g.}~asteroids) use 0D0.  Values less than zero
+        are illegal.
+  \item The ``universal'' elements are those which define the orbit for the
+        purposes of the method of universal variables (see reference).
+        They consist of the combined mass of the two bodies, an epoch,
+        and the position and velocity vectors (arbitrary reference frame)
+        at that epoch.  The parameter set used here includes also various
+        quantities that can, in fact, be derived from the other
+        information.  This approach is taken to avoiding unnecessary
+        computation and loss of accuracy.  The supplementary quantities
+        are (i)~$\alpha$, which is proportional to the total energy of the
+        orbit, (ii)~the heliocentric distance at epoch,
+        (iii)~the outwards component of the velocity at the given epoch,
+        (iv)~an estimate of $\psi$, the ``universal eccentric anomaly'' at a
+        given date and (v)~that date.
+ \end{enumerate}
+}
+\aref{Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PVOBS}{Observatory Position \& Velocity}
+{
+ \action{Position and velocity of an observing station.}
+ \call{CALL sla\_PVOBS (P, H, STL, PV)}
+}
+\args{GIVEN}
+{
+ \spec{P}{D}{latitude (geodetic, radians)} \\
+ \spec{H}{D}{height above reference spheroid (geodetic, metres)} \\
+ \spec{STL}{D}{local apparent sidereal time (radians)}
+}
+\args{RETURNED}
+{
+ \spec{PV}{D(6)}{\xyzxyzd\ (AU, AU~s$^{-1}$, true equator and equinox
+                                                            of date)}
+}
+\anote{IAU 1976 constants are used.}
+%-----------------------------------------------------------------------
+\routine{SLA\_PXY}{Apply Linear Model}
+{
+ \action{Given arrays of {\it expected}\/ and {\it measured}\,
+         \xy\ coordinates, and a
+         linear model relating them (as produced by sla\_FITXY), compute
+         the array of {\it predicted}\/ coordinates and the RMS residuals.}
+ \call{CALL sla\_PXY (NP,XYE,XYM,COEFFS,XYP,XRMS,YRMS,RRMS)}
+}
+\args{GIVEN}
+{
+ \spec{NP}{I}{number of samples} \\
+ \spec{XYE}{D(2,NP)}{expected \xy\ for each sample} \\
+ \spec{XYM}{D(2,NP)}{measured \xy\ for each sample} \\
+ \spec{COEFFS}{D(6)}{coefficients of model (see below)}
+}
+\args{RETURNED}
+{
+ \spec{XYP}{D(2,NP)}{predicted \xy\ for each sample} \\
+ \spec{XRMS}{D}{RMS in X} \\
+ \spec{YRMS}{D}{RMS in Y} \\
+ \spec{RRMS}{D }{total RMS (vector sum of XRMS and YRMS)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The model is supplied in the array COEFFS.  Naming the
+        six elements of COEFFS $a,b,c,d,e$ \& $f$,
+        the model transforms {\it measured}\/ coordinates
+        $[x_{m},y_{m}\,]$ into {\it predicted}\/ coordinates
+        $[x_{p},y_{p}\,]$ as follows:
+        \begin{verse}
+         $x_{p} = a + bx_{m} + cy_{m}$ \\
+         $y_{p} = d + ex_{m} + fy_{m}$
+        \end{verse}
+  \item The residuals are $(x_{p}-x_{e})$ and $(y_{p}-y_{e})$.
+  \item If NP is less than or equal to zero, no coordinates are
+        transformed, and the RMS residuals are all zero.
+  \item See also sla\_FITXY, sla\_INVF, sla\_XY2XY, sla\_DCMPF
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_RANDOM}{Random Number}
+{
+ \action{Generate pseudo-random real number in the range $0 \leq x < 1$.}
+ \call{R~=~sla\_RANDOM (SEED)}
+}
+\args{GIVEN}
+{
+ \spec{SEED}{R}{an arbitrary real number}
+}
+\args{RETURNED}
+{
+ \spec{SEED}{R}{a new arbitrary value} \\
+ \spec{sla\_RANDOM}{R}{Pseudo-random real number $0 \leq x < 1$.}
+}
+\anote{The implementation is machine-dependent.}
+%-----------------------------------------------------------------------
+\routine{SLA\_RANGE}{Put Angle into Range $\pm\pi$}
+{
+ \action{Normalize an angle into the range $\pm\pi$ (single precision).}
+ \call{R~=~sla\_RANGE (ANGLE)}
+}
+\args{GIVEN}
+{
+ \spec{ANGLE}{R}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RANGE}{R}{ANGLE expressed in the range $\pm\pi$.}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_RANORM}{Put Angle into Range $0\!-\!2\pi$}
+{
+ \action{Normalize an angle into the range $0\!-\!2\pi$ (single precision).}
+ \call{R~=~sla\_RANORM (ANGLE)}
+}
+\args{GIVEN}
+{
+ \spec{ANGLE}{R}{angle in radians}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RANORM}{R}{ANGLE expressed in the range $0\!-\!2\pi$}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_RCC}{Barycentric Coordinate Time}
+{
+ \call{D~=~sla\_RCC (TDB, UT1, WL, U, V)}
+ \action{The relativistic clock correction:
+         the difference between {\it proper time}\/ at
+         a point on the Earth and
+         {\it coordinate time}\/ in the solar
+         system barycentric space-time frame of reference.
+         The proper time is Terrestrial Time, TT;
+         the coordinate time is an implementation of Barycentric
+         Dynamical Time, TDB.}
+}
+\args{GIVEN}
+{
+ \spec{TDB}{D}{TDB (MJD: JD$-$2400000.5)} \\
+ \spec{UT1}{D}{universal time (fraction of one day)} \\
+ \spec{WL}{D}{clock longitude (radians west)} \\
+ \spec{U}{D}{clock distance from Earth spin axis (km)} \\
+ \spec{V}{D}{clock distance north of Earth equatorial plane (km)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RCC}{D}{TDB$-$TT (sec; Note 1)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item TDB is coordinate time in the solar system barycentre frame
+        of reference, in units chosen to eliminate the scale difference
+        with respect to terrestrial time.  TT is the proper
+        time for clocks at mean sea level on the Earth.
+  \item The number returned by sla\_RCC comprises
+        a main (annual) sinusoidal term of amplitude
+        approximately 1.66ms, plus lunar and planetary terms up to about
+        20$\mu$s, and diurnal terms up to 2$\mu$s.  The
+        variation arises from the transverse Doppler effect and the
+        gravitational red-shift as the observer varies in speed and
+        moves through different gravitational potentials.
+  \item The argument TDB is, strictly, the barycentric coordinate time;
+        however, the terrestrial time (TT) can in practice be used without
+        significant loss of accuracy.
+  \item The geocentric model is that of Fairhead \& Bretagnon (1990), in
+        its full form.  It was supplied by Fairhead (private communication)
+        as a Fortran subroutine.  A number of coding changes were made to
+        this subroutine in order
+        match the calling sequence of previous versions of the present
+        routine, to comply with Starlink programming standards and to
+        avoid compilation problems on certain machines.  The
+        numerical results are essentially unaffected by the
+        changes.
+  \item The topocentric model is from Moyer (1981) and Murray (1983).
+        It is an approximation to the expression
+        \[\frac{{\bf v}_e \cdot ( {\bf x} - {\bf x}_e )}{c^2}\]
+        where ${\bf v}_e$ is the barycentric velocity of
+        the Earth, ${\bf x}$ and ${\bf x}_e$ are the barycentric positions
+        of the observer and the Earth respectively, and
+        c is the speed of light.
+        It can be disabled, if necessary, by setting the arguments
+        U and V to zero.
+  \item During the interval 1950-2050, the absolute accuracy
+        is better than $\pm3$~nanoseconds
+        relative to direct numerical integrations using the JPL DE200/LE200
+        solar system ephemeris.
+  \item The IAU 1976 definition of TDB was that it must differ from TT only by
+        periodic terms.  Though practical, this is an imprecise definition
+        which ignores the existence of very long-period and secular effects
+        in the dynamics of the solar system.  As a consequence, different
+        implementations of TDB will, in general, differ in zero-point and
+        will drift linearly relative to one other.  In 1991 the IAU introduced
+        new time scales designed to overcome these objections:  geocentric coordinate
+        time, TCG, and barycentric coordinate time, TCB.  In principle, therefore,
+        TDB is obsolete.  However, sla\_RCC
+        can be used to implement the periodic part of TCB$-$TCG.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Fairhead,\,L., \& Bretagnon,\,P., {\it Astron.\,Astrophys.,}\/
+        {\bf 229}, 240-247 (1990).
+  \item Moyer,\,T.D., {\it Cel.\,Mech.,}\/ {\bf 23}, 33 (1981).
+  \item Murray,\,C.A., {\it Vectorial Astrometry,}\/ Adam Hilger (1983).
+  \item Seidelmann,\,P.K.\ {\it et al,}\/ {\it Explanatory Supplement to the
+        Astronomical Almanac,}\/ Chapter 2, University Science Books
+        (1992).
+  \item Simon,\,J.L., Bretagnon,\,P., Chapront,\,J., Chapront-Touze,\,M.,
+        Francou,\,G.\ \& Laskar,\,J., {\it Astron.Astrophys.,}\/
+        {\bf 282}, 663-683 (1994).
+ \end{enumerate}
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_RDPLAN}{Apparent \radec\ of Planet}
+{
+ \action{Approximate topocentric apparent \radec\ and angular
+         size of a planet.}
+ \call{CALL sla\_RDPLAN (DATE, NP, ELONG, PHI, RA, DEC, DIAM)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{MJD of observation (JD$-$2400000.5)} \\
+ \spec{NP}{I}{planet:} \\
+ \spec{}{}{\hspace{1.5em} 1\,=\,Mercury} \\
+ \spec{}{}{\hspace{1.5em} 2\,=\,Venus} \\
+ \spec{}{}{\hspace{1.5em} 3\,=\,Moon} \\
+ \spec{}{}{\hspace{1.5em} 4\,=\,Mars} \\
+ \spec{}{}{\hspace{1.5em} 5\,=\,Jupiter} \\
+ \spec{}{}{\hspace{1.5em} 6\,=\,Saturn} \\
+ \spec{}{}{\hspace{1.5em} 7\,=\,Uranus} \\
+ \spec{}{}{\hspace{1.5em} 8\,=\,Neptune} \\
+ \spec{}{}{\hspace{1.5em} 9\,=\,Pluto} \\
+ \spec{}{}{\hspace{0.44em} else\,=\,Sun} \\
+ \spec{ELONG,PHI}{D}{observer's longitude (east +ve) and latitude
+                     (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RA,DEC}{D}{topocentric apparent \radec\ (radians)} \\
+ \spec{DIAM}{D}{angular diameter (equatorial, radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The date is in a dynamical time scale (TDB, formerly ET)
+        and is in the form of a Modified
+        Julian Date (JD$-$2400000.5).  For all practical purposes, TT can
+        be used instead of TDB, and for many applications UT will do
+        (except for the Moon).
+  \item The longitude and latitude allow correction for geocentric
+        parallax.  This is a major effect for the Moon, but in the
+        context of the limited accuracy of the present routine its
+        effect on planetary positions is small (negligible for the
+        outer planets).  Geocentric positions can be generated by
+        appropriate use of the routines sla\_DMOON and sla\_PLANET.
+  \item The direction accuracy (arcsec, 1000-3000\,AD) is of order:
+
+        \begin{tabular}{lll}
+         & Sun     &  \hspace{0.5em}5 \\
+         & Mercury &  \hspace{0.5em}2 \\
+         & Venus   & 10 \\
+         & Moon    & 30 \\
+         & Mars    & 50 \\
+         & Jupiter & 90 \\
+         & Saturn  & 90 \\
+         & Uranus  & 90 \\
+         & Neptune & 10 \\
+         & Pluto & \hspace{0.5em}1~~~(1885-2099\,AD only)
+        \end{tabular}
+
+        The angular diameter accuracy is about 0.4\% for the Moon,
+        and 0.01\% or better for the Sun and planets.
+        For more information on accuracy,
+        refer to the routines sla\_PLANET and sla\_DMOON,
+        which the present routine uses.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_REFCO}{Refraction Constants}
+{
+ \action{Determine the constants $a$ and $b$ in the
+         atmospheric refraction model
+         $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$,
+         where $\zeta$ is the {\it observed}\/ zenith distance
+         ({\it i.e.}\ affected by refraction) and $\Delta \zeta$ is
+         what to add to $\zeta$ to give the {\it topocentric}\,
+         ({\it i.e.\ in vacuo}) zenith distance.}
+ \call{CALL sla\_REFCO (HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REFA, REFB)}
+}
+\args{GIVEN}
+{
+ \spec{HM}{D}{height of the observer above sea level (metre)} \\
+ \spec{TDK}{D}{ambient temperature at the observer K)} \\
+ \spec{PMB}{D}{pressure at the observer (mb)} \\
+ \spec{RH}{D}{relative humidity at the observer (range 0\,--\,1)} \\
+ \spec{WL}{D}{effective wavelength of the source ($\mu{\rm m}$)} \\
+ \spec{PHI}{D}{latitude of the observer (radian, astronomical)} \\
+ \spec{TLR}{D}{temperature lapse rate in the troposphere
+                                     ( K per metre)} \\
+ \spec{EPS}{D}{precision required to terminate iteration (radian)}
+}
+\args{RETURNED}
+{
+ \spec{REFA}{D}{$\tan \zeta$ coefficient (radians)} \\
+ \spec{REFB}{D}{$\tan^{3} \zeta$ coefficient (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Suggested values for the TLR and EPS arguments are 0.0065D0 and
+        1D$-$8 respectively.  The signs of both are immaterial.
+  \item The radio refraction is chosen by specifying WL $>100$~$\mu{\rm m}$.
+  \item The routine is a slower but more accurate alternative to the
+        sla\_REFCOQ routine.  The constants it produces give perfect
+        agreement with sla\_REFRO at zenith distances
+        $\tan^{-1} 1$ ($45^\circ$) and $\tan^{-1} 4$ ($\sim 76^\circ$).
+        At other zenith distances, the model achieves:
+        \arcsec{0}{5} accuracy for $\zeta<80^{\circ}$,
+        \arcsec{0}{01} accuracy for $\zeta<60^{\circ}$, and
+        \arcsec{0}{001} accuracy for $\zeta<45^{\circ}$.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_REFCOQ}{Refraction Constants (fast)}
+{
+ \action{Determine the constants $a$ and $b$ in the
+         atmospheric refraction model
+         $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$,
+         where $\zeta$ is the {\it observed}\/ zenith distance
+         ({\it i.e.}\ affected by refraction) and $\Delta \zeta$ is
+         what to add to $\zeta$ to give the {\it topocentric}\,
+         ({\it i.e.\ in vacuo}) zenith distance. (This is a fast
+         alternative to the sla\_REFCO routine -- see notes.)}
+ \call{CALL sla\_REFCOQ (TDK, PMB, RH, WL, REFA, REFB)}
+}
+\args{GIVEN}
+{
+ \spec{TDK}{D}{ambient temperature at the observer (K)} \\
+ \spec{PMB}{D}{pressure at the observer (mb)} \\
+ \spec{RH}{D}{relative humidity at the observer (range 0\,--\,1)} \\
+ \spec{WL}{D}{effective wavelength of the source ($\mu{\rm m}$)}
+}
+\args{RETURNED}
+{
+ \spec{REFA}{D}{$\tan \zeta$ coefficient (radians)} \\
+ \spec{REFB}{D}{$\tan^{3} \zeta$ coefficient (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The radio refraction is chosen by specifying WL $>100$~$\mu{\rm m}$.
+  \item The model is an approximation, for moderate zenith distances,
+        to the predictions of the sla\_REFRO routine.  The approximation
+        is maintained across a range of conditions, and applies to
+        both optical/IR and radio.
+  \item The algorithm is a fast alternative to the sla\_REFCO routine.
+        The latter calls the sla\_REFRO routine itself:  this involves
+        integrations through a model atmosphere, and is costly in
+        processor time.  However, the model which is produced is precisely
+        correct for two zenith distances ($45^\circ$ and $\sim\!76^\circ$)
+        and at other zenith distances is limited in accuracy only by the
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ formulation
+        itself.  The present routine is not as accurate, though it
+        satisfies most practical requirements.
+  \item The model omits the effects of (i)~height above sea level (apart
+        from the reduced pressure itself), (ii)~latitude ({\it i.e.}\ the
+        flattening of the Earth) and (iii)~variations in tropospheric
+        lapse rate.
+  \item The model has been tested using the following range of conditions:
+        \begin{itemize}
+        \item [$\cdot$] lapse rates 0.0055, 0.0065, 0.0075~K per metre
+        \item [$\cdot$] latitudes $0^\circ$, $25^\circ$, $50^\circ$, $75^\circ$
+        \item [$\cdot$] heights 0, 2500, 5000 metres above sea level
+        \item [$\cdot$] pressures mean for height $-10$\% to $+5$\% in steps of $5$\%
+        \item [$\cdot$] temperatures $-10^\circ$ to $+20^\circ$ with respect to
+              $280$K at sea level
+        \item [$\cdot$] relative humidity 0, 0.5, 1
+        \item [$\cdot$] wavelength 0.4, 0.6, \ldots\ $2\mu{\rm m}$, + radio
+        \item [$\cdot$] zenith distances $15^\circ$, $45^\circ$, $75^\circ$
+        \end{itemize}
+        For the above conditions, the comparison with sla\_REFRO
+        was as follows:
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~
+        \begin{tabular}{|r|r|r|} \hline
+              & {\it worst} & {\it RMS} \\ \hline
+              optical/IR & 62 & 8 \\
+              radio & 319 & 49 \\ \hline
+              & mas & mas \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        For this particular set of conditions:
+        \begin{itemize}
+        \item [$\cdot$] lapse rate 6.5 K km$^{-1}$
+        \item [$\cdot$] latitude $50^\circ$
+        \item [$\cdot$] sea level
+        \item [$\cdot$] pressure 1005\,mb
+        \item [$\cdot$] temperature $7^\circ$C
+        \item [$\cdot$] humidity 80\%
+        \item [$\cdot$] wavelength 5740\,\.{A}
+        \end{itemize}
+        the results were as follows:
+
+        \vspace{2ex}
+
+        ~~~~~~~~~~
+        \begin{tabular}{|r|r|r|r|} \hline
+        \multicolumn{1}{|c}{$\zeta$} &
+        \multicolumn{1}{|c}{sla\_REFRO} &
+        \multicolumn{1}{|c}{sla\_REFCOQ} &
+        \multicolumn{1}{|c|}{Saastamoinen} \\ \hline
+        10 &  10.27 &  10.27 &  10.27 \\
+        20 &  21.19 &  21.20 &  21.19 \\
+        30 &  33.61 &  33.61 &  33.60 \\
+        40 &  48.82 &  48.83 &  48.81 \\
+        45 &  58.16 &  58.18 &  58.16 \\
+        50 &  69.28 &  69.30 &  69.27 \\
+        55 &  82.97 &  82.99 &  82.95 \\
+        60 & 100.51 & 100.54 & 100.50 \\
+        65 & 124.23 & 124.26 & 124.20 \\
+        70 & 158.63 & 158.68 & 158.61 \\
+        72 & 177.32 & 177.37 & 177.31 \\
+        74 & 200.35 & 200.38 & 200.32 \\
+        76 & 229.45 & 229.43 & 229.42 \\
+        78 & 267.44 & 267.29 & 267.41 \\
+        80 & 319.13 & 318.55 & 319.10 \\ \hline
+        deg & arcsec & arcsec & arcsec \\ \hline
+        \end{tabular}
+
+        \vspace{3ex}
+
+        The values for Saastamoinen's formula (which includes terms
+        up to $\tan^5$) are taken from Hohenkerk \& Sinclair (1985).
+
+        The results from the much slower but more accurate sla\_REFCO
+        routine have not been included in the tabulation as they are
+        identical to those in the sla\_REFRO column to the \arcsec{0}{01}
+        resolution used.
+  \item Outlandish input parameters are silently limited
+        to mathematically safe values.  Zero pressure is permissible,
+        and causes zeroes to be returned.
+  \item The algorithm draws on several sources, as follows:
+        \begin{itemize}
+        \item The formula for the saturation vapour pressure of water as
+              a function of temperature and temperature is taken from
+              expressions A4.5-A4.7 of Gill (1982).
+        \item The formula for the water vapour pressure, given the
+              saturation pressure and the relative humidity is from
+              Crane (1976), expression 2.5.5.
+        \item The refractivity of air is a function of temperature,
+              total pressure, water-vapour pressure and, in the case
+              of optical/IR but not radio, wavelength.  The formulae
+              for the two cases are developed from Hohenkerk \& Sinclair
+              (1985) and Rueger (2002).
+        \item The formula for $\beta~(=H_0/r_0)$ is
+              an adaption of expression 9 from Stone (1996).  The
+              adaptations, arrived at empirically, consist of (i)~a
+              small adjustment to the coefficient and (ii)~a humidity
+              term for the radio case only.
+        \item The formulae for the refraction constants as a function of
+              $n-1$ and $\beta$ are from Green (1987), expression 4.31.
+        \end{itemize}
+        The first three items are as used in the sla\_REFRO routine.
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Crane, R.K., Meeks, M.L.\ (ed), ``Refraction Effects in
+        the Neutral Atmosphere'',
+        {\it Methods of Experimental Physics: Astrophysics 12B,}\/
+        Academic Press, 1976.
+  \item Gill, Adrian E., {\it Atmosphere-Ocean Dynamics,}\/
+        Academic Press, 1982.
+  \item Green, R.M., {\it Spherical Astronomy,}\/ Cambridge
+        University Press, 1987.
+  \item Hohenkerk, C.Y., \& Sinclair, A.T., NAO Technical Note
+        No.~63, 1985.
+  \item Rueger, J.M., {\it Refractive Index Formulae for
+        Electronic Distance Measurement with Radio and Millimetre
+        Waves}, in Unisurv Report S-68, School of Surveying
+        and Spatial Information Systems, University of New South
+        Wales, Sydney, Australia, 2002.
+  \item Stone, Ronald C., P.A.S.P.~{\bf 108} 1051-1058, 1996.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_REFRO}{Refraction}
+{
+ \action{Atmospheric refraction, for radio or optical/IR wavelengths.}
+ \call{CALL sla\_REFRO (ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REF)}
+}
+\args{GIVEN}
+{
+ \spec{ZOBS}{D}{observed zenith distance of the source (radians)} \\
+ \spec{HM}{D}{height of the observer above sea level (metre)} \\
+ \spec{TDK}{D}{ambient temperature at the observer (K)} \\
+ \spec{PMB}{D}{pressure at the observer (mb)} \\
+ \spec{RH}{D}{relative humidity at the observer (range 0\,--\,1)} \\
+    \spec{WL}{D}{effective wavelength of the source ($\mu{\rm m}$)} \\
+ \spec{PHI}{D}{latitude of the observer (radian, astronomical)} \\
+ \spec{TLR}{D}{temperature lapse rate in the troposphere
+                                     (K per metre)} \\
+ \spec{EPS}{D}{precision required to terminate iteration (radian)}
+}
+\args{RETURNED}
+{
+ \spec{REF}{D}{refraction: {\it in vacuo}\/ ZD minus observed ZD (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item A suggested value for the TLR argument is 0.0065D0 (sign immaterial).
+        The refraction is significantly affected by TLR, and if studies
+        of the local atmosphere have been carried out a better TLR
+        value may be available.
+  \item A suggested value for the EPS argument is 1D$-$8.  The result is
+        usually at least two orders of magnitude more computationally
+        precise than the supplied EPS value.
+  \item The routine computes the refraction for zenith distances up
+        to and a little beyond $90^\circ$ using the method of Hohenkerk
+        \& Sinclair (NAO Technical Notes 59 and 63, subsequently adopted
+        in the {\it Explanatory Supplement to the Astronomical Almanac,}\/
+        1992 -- see section 3.281).
+ \item The code is based on the {\tt AREF}
+       optical/IR refraction subroutine
+       (HMNAO, September 1984, RGO: Hohenkerk 1985),
+       with extensions to
+       support the radio case.  The modifications to the original HMNAO
+       optical/IR refraction code which affect the results are:
+       \begin{itemize}
+        \item The angle arguments have been changed to radians,
+              any value of ZOBS is allowed (see Note~6, below) and
+              other argument values have been limited to safe values.
+        \item Revised values for the gas constants are used, from
+              Murray (1983).
+        \item A better model for $P_s(T)$ has been adopted,
+              from Gill (1982).
+        \item More accurate expressions for $Pw_o$ have been adopted
+              (again from Gill 1982).
+        \item The formula for the water vapour pressure, given the
+              saturation pressure and the relative humidity, is from
+              Crane (1976), expression 2.5.5.
+        \item Provision for radio wavelengths has been added using
+              expressions devised by A.\,T.\,Sinclair, RGO (Sinclair 1989).
+              The refractivity model is from Rueger (2002).
+        \item The optical refractivity for dry air is from IAG (1999).
+       \end{itemize}
+  \item The radio refraction is chosen by specifying WL $>100$~$\mu{\rm m}$.
+        Because the algorithm takes no account of the ionosphere, the
+        accuracy deteriorates at low frequencies, below about 30\,MHz.
+  \item Before use, the value of ZOBS is expressed in the range $\pm\pi$.
+        If this ranged ZOBS is negative, the result REF is computed from its
+        absolute value before being made negative to match.  In addition, if
+        it has an absolute value greater than $93^\circ$, a fixed REF value
+        equal to the result for ZOBS~$=93^\circ$ is returned, appropriately
+        signed.
+  \item As in the original Hohenkerk \& Sinclair algorithm, fixed values
+        of the water vapour polytrope exponent, the height of the
+        tropopause, and the height at which refraction is negligible are
+        used.
+  \item The radio refraction has been tested against work done by
+        Iain~Coulson, JACH, (private communication 1995) for the
+        James Clerk Maxwell Telescope, Mauna Kea.  For typical conditions,
+        agreement at the \arcsec{0}{1} level is achieved for moderate ZD,
+        worsening to perhaps \arcsec{0}{5}\,--\,\arcsec{1}{0} at ZD $80^\circ$.
+        At hot and humid sea-level sites the accuracy will not be as good.
+  \item It should be noted that the relative humidity RH is formally
+        defined in terms of ``mixing ratio'' rather than pressures or
+        densities as is often stated.  It is the mass of water per unit
+        mass of dry air divided by that for saturated air at the same
+        temperature and pressure (see Gill 1982).  The familiar
+        $\nu=p_w/p_s$ or $\nu=\rho_w/\rho_s$ expressions can differ from
+        the formal definition by several percent, significant in the
+        radio case.
+  \item The algorithm is designed for observers in the troposphere.  The
+        supplied temperature, pressure and lapse rate are assumed to be
+        for a point in the troposphere and are used to define a model
+        atmosphere with the tropopause at 11km altitude and a constant
+        temperature above that.  However, in practice, the refraction
+        values returned for stratospheric observers, at altitudes up to
+        25km, are quite usable.
+  \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Coulsen, I.\ 1995, private communication.
+  \item Crane, R.K., Meeks, M.L.\ (ed), 1976,
+        ``Refraction Effects in the Neutral Atmosphere'',
+        {\it Methods of Experimental Physics: Astrophysics 12B},
+        Academic Press.
+  \item Gill, Adrian E.\ 1982, {\it Atmosphere-Ocean Dynamics},
+        Academic Press.
+  \item Hohenkerk, C.Y.\ 1985, private communication.
+  \item Hohenkerk, C.Y., \& Sinclair, A.T.\ 1985,
+        {\it NAO Technical Note}\/
+        No.~63, Royal Greenwich Observatory.
+  \item International Association of Geodesy,
+        XXIIth General Assembly, Birmingham, UK, 1999,
+        Resolution 3.
+  \item Murray, C.A.\ 1983, {\it Vectorial Astrometry,}
+        Adam Hilger, Bristol.
+  \item Seidelmann,\,P.K.\ {\it et al.}\ 1992,
+        {\it Explanatory Supplement to the
+        Astronomical Almanac}, Chapter 3, University Science Books.
+  \item Rueger, J.M.\ 2002, {\it Refractive Index Formulae for
+        Electronic Distance Measurement with Radio and Millimetre
+        Waves}, in Unisurv Report S-68, School of Surveying
+        and Spatial Information Systems, University of New South
+        Wales, Sydney, Australia.
+  \item Sinclair, A.T.\ 1989, private communication.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_REFV}{Apply Refraction to Vector}
+{
+ \action{Adjust an unrefracted Cartesian vector to include the effect of
+         atmospheric refraction, using the simple
+         $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model.}
+ \call{CALL sla\_REFV (VU, REFA, REFB, VR)}
+}
+\args{GIVEN}
+{
+ \spec{VU}{D}{unrefracted position of the source (\azel\ 3-vector)} \\
+ \spec{REFA}{D}{$\tan \zeta$ coefficient (radians)} \\
+ \spec{REFB}{D}{$\tan^{3} \zeta$ coefficient (radians)}
+}
+\args{RETURNED}
+{
+ \spec{VR}{D}{refracted position of the source (\azel\ 3-vector)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine applies the adjustment for refraction in the
+        opposite sense to the usual one -- it takes an unrefracted
+        ({\it in vacuo}\/) position and produces an observed (refracted)
+        position, whereas the
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$
+        model strictly
+        applies to the case where an observed position is to have the
+        refraction removed.  The unrefracted to refracted case is
+        harder, and requires an inverted form of the text-book
+        refraction models;  the algorithm used here is equivalent to
+        one iteration of the Newton-Raphson method applied to the
+        above formula.
+  \item Though optimized for speed rather than precision, the present
+        routine achieves consistency with the refracted-to-unrefracted
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$
+        model at better than 1~microarcsecond within
+        $30^\circ$ of the zenith and remains within 1~milliarcsecond to
+        $\zeta=70^\circ$.  The inherent accuracy of the model is, of
+        course, far worse than this -- see the documentation for sla\_REFCO
+        for more information.
+  \item At low elevations (below about $3^\circ$) the refraction
+        correction is held back to prevent arithmetic problems and
+        wildly wrong results.  For optical/IR wavelengths, over a wide
+        range of observer heights and corresponding temperatures and
+        pressures, the following levels of accuracy (worst case)
+        are achieved, relative to numerical integration through a model
+        atmosphere:
+        \begin{center}
+        \begin{tabular}{ccl}
+              $\zeta_{obs}$ & {\it error} \\ \\
+              $80^\circ$ & \arcsec{0}{7}  \\
+              $81^\circ$ & \arcsec{1}{3}  \\
+              $82^\circ$ & \arcsec{2}{5}  \\
+              $83^\circ$ & \arcseci{5}    \\
+              $84^\circ$ & \arcseci{10}    \\
+              $85^\circ$ & \arcseci{20}   \\
+              $86^\circ$ & \arcseci{55}   \\
+              $87^\circ$ & \arcseci{160}  \\
+              $88^\circ$ & \arcseci{360}  \\
+              $89^\circ$ & \arcseci{640}  \\
+              $90^\circ$ & \arcseci{1100} \\
+              $91^\circ$ & \arcseci{1700} & $<$ high-altitude \\
+              $92^\circ$ & \arcseci{2600} & $<$ sites only \\
+        \end{tabular}
+        \end{center}
+        The results for radio are slightly worse over most of the range,
+        becoming significantly worse below $\zeta = 88^\circ$
+        and unusable beyond $\zeta = 90^\circ$.
+  \item See also the routine sla\_REFZ, which performs the adjustment to
+        the zenith distance rather than in \xyz.
+        The present routine is faster than sla\_REFZ and,
+        except very low down,
+        is equally accurate for all practical purposes.  However, beyond
+        about $\zeta=84^\circ$ sla\_REFZ should be used, and for the utmost
+        accuracy iterative use of sla\_REFRO should be considered.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_REFZ}{Apply Refraction to ZD}
+{
+ \action{Adjust an unrefracted zenith distance to include the effect of
+         atmospheric refraction, using the simple
+         $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$ model.}
+ \call{CALL sla\_REFZ (ZU, REFA, REFB, ZR)}
+}
+\args{GIVEN}
+{
+ \spec{ZU}{D}{unrefracted zenith distance of the source (radians)} \\
+ \spec{REFA}{D}{$\tan \zeta$ coefficient (radians)} \\
+ \spec{REFB}{D}{$\tan^{3} \zeta$ coefficient (radians)}
+}
+\args{RETURNED}
+{
+ \spec{ZR}{D}{refracted zenith distance (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item This routine applies the adjustment for refraction in the
+        opposite sense to the usual one -- it takes an unrefracted
+        ({\it in vacuo}\/) position and produces an observed (refracted)
+        position, whereas the
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$
+        model strictly
+        applies to the case where an observed position is to have the
+        refraction removed.  The unrefracted to refracted case is
+        harder, and requires an inverted form of the text-book
+        refraction models;  the formula used here is based on the
+        Newton-Raphson method.  For the utmost numerical consistency
+        with the refracted to unrefracted model, two iterations are
+        carried out, achieving agreement at the $10^{-11}$~arcsecond level
+        for $\zeta=80^\circ$.  The inherent accuracy of the model
+        is, of course, far worse than this -- see the documentation for
+        sla\_REFCO for more information.
+  \item At $\zeta=83^\circ$, the rapidly-worsening
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$
+        model is abandoned and an empirical formula takes over:
+
+          \[\Delta \zeta = F \left(
+  \frac{0^\circ\hspace{-0.37em}.\hspace{0.02em}55445
+                - 0^\circ\hspace{-0.37em}.\hspace{0.02em}01133 E
+                          + 0^\circ\hspace{-0.37em}.\hspace{0.02em}00202 E^2}
+             {1 + 0.28385 E +0.02390 E^2} \right) \]
+        where $E=90^\circ-\zeta_{true}$
+        and $F$ is a factor chosen to meet the
+        $\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$
+        formula at $\zeta=83^\circ$.
+
+        For optical/IR wavelengths, over a wide range of observer heights
+        and corresponding temperatures and pressures, the following levels
+        of accuracy (worst case) are achieved,
+        relative to numerical integration through a model atmosphere:
+
+        \begin{center}
+        \begin{tabular}{ccl}
+              $\zeta_{obs}$ & {\it error} \\ \\
+              $80^\circ$ & \arcsec{0}{7}  \\
+              $81^\circ$ & \arcsec{1}{3}  \\
+              $82^\circ$ & \arcsec{2}{4}  \\
+              $83^\circ$ & \arcsec{4}{7}  \\
+              $84^\circ$ & \arcsec{6}{2}  \\
+              $85^\circ$ & \arcsec{6}{4}  \\
+              $86^\circ$ & \arcseci{8}    \\
+              $87^\circ$ & \arcseci{10}   \\
+              $88^\circ$ & \arcseci{15}   \\
+              $89^\circ$ & \arcseci{30}   \\
+              $90^\circ$ & \arcseci{60}   \\
+              $91^\circ$ & \arcseci{150} & $<$ high-altitude \\
+              $92^\circ$ & \arcseci{400} & $<$ sites only \\
+        \end{tabular}
+        \end{center}
+        For radio wavelengths the errors are typically 50\% larger than
+        the optical figures and by $\zeta = 85^\circ$ are twice as bad,
+        worsening rapidly below that.  To maintain \arcseci{1} accuracy
+        down to $\zeta = 85^\circ$ at the Green Bank site, Condon (2004)
+        has suggested amplifying the amount of refraction predicted by
+        sla\_REFZ below \degree{10}{8} elevation by the factor
+        $(1+0.00195*(10.8-E_{topo}))$, where $E_{topo}$ is the
+        unrefracted elevation in degrees.
+
+        The high-ZD model is scaled to match the normal model at the
+        transition point;  there is no glitch.
+  \item See also the routine sla\_REFV, which performs the adjustment in
+        \xyz , and with the emphasis on speed rather than numerical accuracy.
+ \end{enumerate}
+}
+\aref{Condon,\,J.J., {\it Refraction Corrections for the GBT,} PTCS/PN/35.2,
+      NRAO Green Bank, 2004.}
+%-----------------------------------------------------------------------
+\routine{SLA\_RVEROT}{RV Corrn to Earth Centre}
+{
+ \action{Velocity component in a given direction due to Earth rotation.}
+ \call{R~=~sla\_RVEROT (PHI, RA, DA, ST)}
+}
+\args{GIVEN}
+{
+ \spec{PHI}{R}{geodetic latitude of observing station (radians)} \\
+ \spec{RA,DA}{R}{apparent \radec\ (radians)} \\
+ \spec{ST}{R}{local apparent sidereal time (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RVEROT}{R}{Component of Earth rotation in
+                       direction [RA,DA]~(km~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Sign convention: the result is positive when the observatory
+        is receding from the given point on the sky.
+  \item Accuracy: the simple algorithm used assumes a spherical Earth and
+        an observing station at sea level;  for actual observing
+        sites, the error is unlikely to be greater than 0.0005~km~s$^{-1}$.
+        For applications requiring greater accuracy, use the routine
+        sla\_PVOBS.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_RVGALC}{RV Corrn to Galactic Centre}
+{
+ \action{Velocity component in a given direction due to the rotation
+         of the Galaxy.}
+ \call{R~=~sla\_RVGALC (R2000, D2000)}
+}
+\args{GIVEN}
+{
+ \spec{R2000,D2000}{R}{J2000.0 mean \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RVGALC}{R}{Component of dynamical LSR motion in direction
+                       R2000,D2000 (km~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Sign convention: the result is positive when the LSR
+        is receding from the given point on the sky.
+  \item The Local Standard of Rest used here is a point in the
+        vicinity of the Sun which is in a circular orbit around
+        the Galactic centre.  Sometimes called the {\it dynamical}\/ LSR,
+        it is not to be confused with a {\it kinematical}\/ LSR, which
+        is the mean standard of rest of star catalogues or stellar
+        populations.
+  \item The dynamical LSR velocity due to Galactic rotation is assumed to
+        be 220~km~s$^{-1}$ towards $l^{I\!I}=90^{\circ}$,
+                                   $b^{I\!I}=0$.
+ \end{enumerate}
+}
+\aref{Kerr \& Lynden-Bell (1986), MNRAS, 221, p1023.}
+%-----------------------------------------------------------------------
+\routine{SLA\_RVLG}{RV Corrn to Local Group}
+{
+ \action{Velocity component in a given direction due to the combination
+         of the rotation of the Galaxy and the motion of the Galaxy
+         relative to the mean motion of the local group.}
+ \call{R~=~sla\_RVLG (R2000, D2000)}
+}
+\args{GIVEN}
+{
+ \spec{R2000,D2000}{R}{J2000.0 mean \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RVLG}{R}{Component of {\bf solar} ({\it n.b.})
+                     motion in direction R2000,D2000 (km~s$^{-1}$)}
+}
+\anote{Sign convention: the result is positive when
+       the Sun is receding from the given point on the sky.}
+\aref{{\it IAU Trans.}\ 1976.\ {\bf 16B}, p201.}
+%-----------------------------------------------------------------------
+\routine{SLA\_RVLSRD}{RV Corrn to Dynamical LSR}
+{
+ \action{Velocity component in a given direction due to the Sun's
+         motion with respect to the ``dynamical'' Local Standard of Rest.}
+ \call{R~=~sla\_RVLSRD (R2000, D2000)}
+}
+\args{GIVEN}
+{
+ \spec{R2000,D2000}{R}{J2000.0 mean \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RVLSRD}{R}{Component of {\it peculiar}\/ solar motion
+                      in direction R2000,D2000 (km~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Sign convention: the result is positive when
+        the Sun is receding from the given point on the sky.
+  \item The Local Standard of Rest used here is the {\it dynamical}\/ LSR,
+        a point in the vicinity of the Sun which is in a circular
+        orbit around the Galactic centre.  The Sun's motion with
+        respect to the dynamical LSR is called the {\it peculiar}\/ solar
+        motion.
+  \item There is another type of LSR, called a {\it kinematical}\/ LSR.  A
+        kinematical LSR is the mean standard of rest of specified star
+        catalogues or stellar populations, and several slightly
+        different kinematical LSRs are in use.  The Sun's motion with
+        respect to an agreed kinematical LSR is known as the
+        {\it standard}\/ solar motion.
+        The dynamical LSR is seldom used by observational astronomers,
+        who conventionally use a kinematical LSR such as the one implemented
+        in the routine sla\_RVLSRK.
+  \item The peculiar solar motion is from Delhaye (1965), in {\it Stars
+        and Stellar Systems}, vol~5, p73:  in Galactic Cartesian
+        coordinates (+9,+12,+7)~km~s$^{-1}$.
+        This corresponds to about 16.6~km~s$^{-1}$
+        towards Galactic coordinates $l^{I\!I}=53^{\circ},b^{I\!I}=+25^{\circ}$.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_RVLSRK}{RV Corrn to Kinematical LSR}
+{
+ \action{Velocity component in a given direction due to the Sun's
+         motion with respect to a kinematical Local Standard of Rest.}
+ \call{R~=~sla\_RVLSRK (R2000, D2000)}
+}
+\args{GIVEN}
+{
+ \spec{R2000,D2000}{R}{J2000.0 mean \radec\ (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_RVLSRK}{R}{Component of {\it standard}\/ solar motion
+                      in direction R2000,D2000 (km~s$^{-1}$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item Sign convention: the result is positive when
+        the Sun is receding from the given point on the sky.
+  \item The Local Standard of Rest used here is one of several
+        {\it kinematical}\/ LSRs in common use.  A kinematical LSR is the
+        mean standard of rest of specified star catalogues or stellar
+        populations.  The Sun's motion with respect to a kinematical
+        LSR is known as the {\it standard}\/ solar motion.
+  \item There is another sort of LSR, seldom used by observational
+        astronomers, called the {\it dynamical}\/ LSR.  This is a
+        point in the vicinity of the Sun which is in a circular orbit
+        around the Galactic centre.  The Sun's motion with respect to
+        the dynamical LSR is called the {\it peculiar}\/ solar motion.  To
+        obtain a radial velocity correction with respect to the
+        dynamical LSR use the routine sla\_RVLSRD.
+  \item The adopted standard solar motion is 20~km~s$^{-1}$
+        towards $\alpha=18^{\rm h},\delta=+30^{\circ}$ (1900).
+ \end{enumerate}
+}
+\refs
+{
+ \begin{enumerate}
+  \item Delhaye (1965), in {\it Stars and Stellar Systems}, vol~5, p73.
+  \item {\it Methods of Experimental Physics}\/ (ed Meeks), vol~12,
+        part~C, sec~6.1.5.2, p281.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_S2TP}{Spherical to Tangent Plane}
+{
+ \action{Projection of spherical coordinates onto the tangent plane
+         (single precision).}
+ \call{CALL sla\_S2TP (RA, DEC, RAZ, DECZ, XI, ETA, J)}
+}
+\args{GIVEN}
+{
+ \spec{RA,DEC}{R}{spherical coordinates of star (radians)} \\
+ \spec{RAZ,DECZ}{R}{spherical coordinates of tangent point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{XI,ETA}{R}{tangent plane coordinates (radians)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK, star on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 1 = error, star too far from axis} \\
+ \spec{}{}{\hspace{1.5em} 2 = error, antistar on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 3 = error, antistar too far from axis}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_V2TP is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_SEP}{Angle Between 2 Points on Sphere}
+{
+ \action{Angle between two points on a sphere (single precision).}
+ \call{R~=~sla\_SEP (A1, B1, A2, B2)}
+}
+\args{GIVEN}
+{
+ \spec{A1,B1}{R}{spherical coordinates of one point (radians)} \\
+ \spec{A2,B2}{R}{spherical coordinates of the other point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{sla\_SEP}{R}{angle between [A1,B1] and [A2,B2] in radians}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The spherical coordinates are right ascension and declination,
+  longitude and latitude, {\it etc.}\ in radians.
+  \item The result is always positive.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_SEPV}{Angle Between 2 Vectors}
+{
+ \action{Angle between two vectors (single precision).}
+ \call{R~=~sla\_SEPV (V1, V2)}
+}
+\args{GIVEN}
+{
+ \spec{V1}{R(3)}{first vector} \\
+ \spec{V2}{R(3)}{second vector}
+}
+\args{RETURNED}
+{
+ \spec{sla\_SEPV}{R}{angle between V1 and V2 in radians}
+}
+\notes
+{
+ \begin{enumerate}
+  \item There is no requirement for either vector to be of unit length.
+  \item If either vector is null, zero is returned.
+  \item The result is always positive.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_SMAT}{Solve Simultaneous Equations}
+{
+ \action{Matrix inversion and solution of simultaneous equations
+         (single precision).}
+ \call{CALL sla\_SMAT (N, A, Y, D, JF, IW)}
+}
+\args{GIVEN}
+{
+ \spec{N}{I}{number of unknowns} \\
+ \spec{A}{R(N,N)}{matrix} \\
+ \spec{Y}{R(N)}{vector}
+}
+\args{RETURNED}
+{
+ \spec{A}{R(N,N)}{matrix inverse} \\
+ \spec{Y}{R(N)}{solution} \\
+ \spec{D}{R}{determinant} \\
+ \spec{JF}{I}{singularity flag: 0=OK} \\
+ \spec{IW}{I(N)}{workspace}
+}
+\notes
+{
+ \begin{enumerate}
+  \item For the set of $n$ simultaneous linear equations in $n$ unknowns:
+        \begin{verse}
+         {\bf A}$\cdot${\bf y} = {\bf x}
+        \end{verse}
+        where:
+        \begin{itemize}
+         \item {\bf A} is a non-singular $n \times n$ matrix,
+         \item {\bf y} is the vector of $n$ unknowns, and
+         \item {\bf x} is the known vector,
+        \end{itemize}
+        sla\_SMAT computes:
+        \begin{itemize}
+         \item the inverse of matrix {\bf A},
+         \item the determinant of matrix {\bf A}, and
+         \item the vector of $n$ unknowns {\bf y}.
+        \end{itemize}
+        Argument N is the order $n$, A (given) is the matrix {\bf A},
+        Y (given) is the vector {\bf x} and Y (returned)
+        is the vector {\bf y}.
+        The argument A (returned) is the inverse matrix {\bf A}$^{-1}$,
+        and D is {\it det}\/({\bf A}).
+  \item JF is the singularity flag.  If the matrix is non-singular,
+        JF=0 is returned.  If the matrix is singular, JF=$-$1
+        and D=0.0 are returned.  In the latter case, the contents
+        of array A on return are undefined.
+  \item The algorithm is Gaussian elimination with partial pivoting.
+        This method is very fast;  some much slower algorithms can give
+        better accuracy, but only by a small factor.
+  \item This routine replaces the obsolete sla\_SMATRX.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_SUBET}{Remove E-terms}
+{
+ \action{Remove the E-terms (elliptic component of annual aberration)
+         from a pre IAU~1976 catalogue \radec\ to give a mean place.}
+ \call{CALL sla\_SUBET (RC, DC, EQ, RM, DM)}
+}
+\args{GIVEN}
+{
+ \spec{RC,DC}{D}{\radec\ with E-terms included (radians)} \\
+ \spec{EQ}{D}{Besselian epoch of mean equator and equinox}
+}
+\args{RETURNED}
+{
+ \spec{RM,DM}{D}{\radec\ without E-terms (radians)}
+}
+\anote{Most star positions from pre-1984 optical catalogues (or
+       obtained by astrometry with respect to such stars) have the
+       E-terms built-in.  This routine converts such a position to a
+       formal mean place (allowing, for example, comparison with a
+       pulsar timing position).}
+\aref{{\it Explanatory Supplement to the Astronomical Ephemeris},
+      section 2D, page 48.}
+%-----------------------------------------------------------------------
+\routine{SLA\_SUPGAL}{Supergalactic to Galactic}
+{
+ \action{Transformation from de Vaucouleurs supergalactic coordinates
+         to IAU 1958 galactic coordinates.}
+ \call{CALL sla\_SUPGAL (DSL, DSB, DL, DB)}
+}
+\args{GIVEN}
+{
+ \spec{DSL,DSB}{D}{supergalactic longitude and latitude (radians)}
+}
+\args{RETURNED}
+{
+ \spec{DL,DB}{D}{galactic longitude and latitude \gal\ (radians)}
+}
+\refs
+{
+ \begin{enumerate}
+  \item de Vaucouleurs, de Vaucouleurs, \& Corwin, {\it Second Reference
+    Catalogue of Bright Galaxies}, U.Texas, p8.
+  \item Systems \& Applied Sciences Corp., documentation for the
+        machine-readable version of the above catalogue,
+        Contract NAS 5-26490.
+ \end{enumerate}
+ (These two references give different values for the galactic
+ longitude of the supergalactic origin.  Both are wrong;  the
+ correct value is $l^{I\!I}=137.37$.)
+}
+%------------------------------------------------------------------------------
+\routine{SLA\_SVD}{Singular Value Decomposition}
+{
+ \action{Singular value decomposition.
+         This routine expresses a given matrix {\bf A} as the product of
+         three matrices {\bf U}, {\bf W}, {\bf V}$^{T}$:
+
+         \begin{tabular}{ll}
+         & {\bf A} = {\bf U} $\cdot$ {\bf W} $\cdot$ {\bf V}$^{T}$
+         \end{tabular}
+
+         where:
+
+         \begin{tabular}{lll}
+         & {\bf A} & is any $m$ (rows) $\times n$ (columns) matrix,
+                       where $m \geq n$ \\
+         & {\bf U} & is an $m \times n$ column-orthogonal matrix \\
+         & {\bf W} & is an $n \times n$ diagonal matrix with
+                       $w_{ii} \geq 0$ \\
+         & {\bf V}$^{T}$ & is the transpose of an $n \times n$
+                             orthogonal matrix
+         \end{tabular}
+}
+ \call{CALL sla\_SVD (M, N, MP, NP, A, W, V, WORK, JSTAT)}
+}
+\args{GIVEN}
+{
+ \spec{M,N}{I}{$m$, $n$, the numbers of rows and columns in matrix {\bf A}} \\
+ \spec{MP,NP}{I}{physical dimensions of array containing matrix {\bf A}} \\
+ \spec{A}{D(MP,NP)}{array containing $m \times n$ matrix {\bf A}}
+}
+\args{RETURNED}
+{
+ \spec{A}{D(MP,NP)}{array containing $m \times n$ column-orthogonal
+                    matrix {\bf U}} \\
+ \spec{W}{D(N)}{$n \times n$ diagonal matrix {\bf W}
+               (diagonal elements only)} \\
+ \spec{V}{D(NP,NP)}{array containing $n \times n$ orthogonal
+                    matrix {\bf V} ({\it n.b.}\ not {\bf V}$^{T}$)} \\
+ \spec{WORK}{D(N)}{workspace} \\
+ \spec{JSTAT}{I}{0~=~OK, $-$1~=~array A wrong shape, $>$0~=~index of W
+                 for which convergence failed (see note~3, below)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item M and N are the {\it logical}\/ dimensions of the
+        matrices and vectors concerned, which can be located in
+        arrays of larger {\it physical}\/ dimensions, given by MP and NP.
+  \item V contains matrix V, not the transpose of matrix V.
+  \item If the status JSTAT is greater than zero, this need not
+        necessarily be treated as a failure.  It means that, due to
+        chance properties of the matrix A, the QR transformation
+        phase of the routine did not fully converge in a predefined
+        number of iterations, something that very seldom occurs.
+        When this condition does arise, it is possible that the
+        elements of the diagonal matrix W have not been correctly
+        found.  However, in practice the results are likely to
+        be trustworthy.  Applications should report the condition
+        as a warning, but then proceed normally.
+ \end{enumerate}
+}
+\refs{The algorithm is an adaptation of the routine SVD in the {\it EISPACK}\,
+      library (Garbow~{\it et~al.}\ 1977, {\it EISPACK Guide Extension},
+      Springer Verlag), which is a FORTRAN~66 implementation of the Algol
+      routine SVD of Wilkinson \& Reinsch 1971 ({\it Handbook for Automatic
+      Computation}, vol~2, ed Bauer~{\it et~al.}, Springer Verlag).  These
+      references give full details of the algorithm used here.
+      A good account of the use of SVD in least squares problems is given
+      in {\it Numerical Recipes}\/ (Press~{\it et~al.}\ 1987, Cambridge
+      University Press), which includes another variant of the EISPACK code.}
+%-----------------------------------------------------------------------
+\routine{SLA\_SVDCOV}{Covariance Matrix from SVD}
+{
+ \action{From the {\bf W} and {\bf V} matrices from the SVD
+         factorization of a matrix
+         (as obtained from the sla\_SVD routine), obtain
+         the covariance matrix.}
+ \call{CALL sla\_SVDCOV (N, NP, NC, W, V, WORK, CVM)}
+}
+\args{GIVEN}
+{
+ \spec{N}{I}{$n$, the number of rows and columns in
+             matrices {\bf W} and {\bf V}} \\
+ \spec{NP}{I}{first dimension of array containing $n \times n$
+              matrix {\bf V}} \\
+ \spec{NC}{I}{first dimension of array CVM} \\
+ \spec{W}{D(N)}{$n \times n$ diagonal matrix {\bf W}
+                (diagonal elements only)} \\
+ \spec{V}{D(NP,NP)}{array containing $n \times n$ orthogonal matrix {\bf V}}
+}
+\args{RETURNED}
+{
+ \spec{WORK}{D(N)}{workspace} \\
+ \spec{CVM}{D(NC,NC)}{array to receive covariance matrix}
+}
+\aref{{\it Numerical Recipes}, section 14.3.}
+%-----------------------------------------------------------------------
+\routine{SLA\_SVDSOL}{Solution Vector from SVD}
+{
+ \action{From a given vector and the SVD of a matrix (as obtained from
+         the sla\_SVD routine), obtain the solution vector.
+         This routine solves the equation:
+
+         \begin{tabular}{ll}
+         & {\bf A} $\cdot$ {\bf x} = {\bf b}
+         \end{tabular}
+
+         where:
+
+         \begin{tabular}{lll}
+         & {\bf A} & is a given $m$ (rows) $\times n$ (columns)
+                       matrix, where $m \geq n$ \\
+         & {\bf x} & is the $n$-vector we wish to find, and \\
+         & {\bf b} & is a given $m$-vector
+         \end{tabular}
+
+         by means of the {\it Singular Value Decomposition}\/ method (SVD).}
+ \call{CALL sla\_SVDSOL (M, N, MP, NP, B, U, W, V, WORK, X)}
+}
+\args{GIVEN}
+{
+ \spec{M,N}{I}{$m$, $n$, the numbers of rows and columns in matrix {\bf A}} \\
+ \spec{MP,NP}{I}{physical dimensions of array containing matrix {\bf A}} \\
+ \spec{B}{D(M)}{known vector {\bf b}} \\
+ \spec{U}{D(MP,NP)}{array containing $m \times n$ matrix {\bf U}} \\
+ \spec{W}{D(N)}{$n \times n$ diagonal matrix {\bf W}
+                (diagonal elements only)} \\
+ \spec{V}{D(NP,NP)}{array containing $n \times n$ orthogonal matrix {\bf V}}
+}
+\args{RETURNED}
+{
+ \spec{WORK}{D(N)}{workspace} \\
+ \spec{X}{D(N)}{unknown vector {\bf x}}
+}
+\notes
+{
+ \begin{enumerate}
+  \item In the Singular Value Decomposition method (SVD),
+        the matrix {\bf A} is first factorized (for example by
+        the routine sla\_SVD) into the following components:
+
+        \begin{tabular}{ll}
+        & {\bf A} = {\bf U} $\cdot$ {\bf W} $\cdot$ {\bf V}$^{T}$
+        \end{tabular}
+
+        where:
+
+        \begin{tabular}{lll}
+        & {\bf A} & is any $m$ (rows) $\times n$ (columns) matrix,
+                      where $m > n$ \\
+        & {\bf U} & is an $m \times n$ column-orthogonal matrix \\
+        & {\bf W} & is an $n \times n$ diagonal matrix with
+                      $w_{ii} \geq 0$ \\
+        & {\bf V}$^{T}$ & is the transpose of an $n \times n$
+                            orthogonal matrix
+        \end{tabular}
+
+        Note that $m$ and $n$ are the {\it logical}\/ dimensions of the
+        matrices and vectors concerned, which can be located in
+        arrays of larger {\it physical}\/ dimensions MP and NP.
+        The solution is then found from the expression:
+
+        \begin{tabular}{ll}
+        & {\bf x} = {\bf V} $\cdot~[diag(1/${\bf W}$_{j})]
+           \cdot (${\bf U}$^{T} \cdot${\bf b})
+        \end{tabular}
+
+  \item If matrix {\bf A} is square, and if the diagonal matrix {\bf W} is not
+        altered, the method is equivalent to conventional solution
+        of simultaneous equations.
+  \item If $m > n$, the result is a least-squares fit.
+  \item If the solution is poorly determined, this shows up in the
+        SVD factorization as very small or zero {\bf W}$_{j}$ values.  Where
+        a {\bf W}$_{j}$ value is small but non-zero it can be set to zero to
+        avoid ill effects.  The present routine detects such zero
+        {\bf W}$_{j}$ values and produces a sensible solution, with highly
+        correlated terms kept under control rather than being allowed
+        to elope to infinity, and with meaningful values for the
+       other terms.
+ \end{enumerate}
+}
+\aref{{\it Numerical Recipes}, section 2.9.}
+%-----------------------------------------------------------------------
+\routine{SLA\_TP2S}{Tangent Plane to Spherical}
+{
+ \action{Transform tangent plane coordinates into spherical
+         coordinates (single precision)}
+ \call{CALL sla\_TP2S (XI, ETA, RAZ, DECZ, RA, DEC)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{R}{tangent plane rectangular coordinates (radians)} \\
+ \spec{RAZ,DECZ}{R}{spherical coordinates of tangent point (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RA,DEC}{R}{spherical coordinates (radians)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_TP2V is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_TP2V}{Tangent Plane to Direction Cosines}
+{
+ \action{Given the tangent-plane coordinates of a star and the direction
+         cosines of the tangent point, determine the direction cosines
+         of the star
+         (single precision).}
+ \call{CALL sla\_TP2V (XI, ETA, V0, V)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{R}{tangent plane coordinates of star (radians)} \\
+ \spec{V0}{R(3)}{direction cosines of tangent point}
+}
+\args{RETURNED}
+{
+ \spec{V}{R(3)}{direction cosines of star}
+}
+\notes
+{
+ \begin{enumerate}
+  \item If vector V0 is not of unit length, the returned vector V will
+        be wrong.
+  \item If vector V0 points at a pole, the returned vector V will be
+        based on the arbitrary assumption that $\alpha=0$ at
+        the tangent point.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_TP2S.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_TPS2C}{Plate centre from $\xi,\eta$ and $\alpha,\delta$}
+{
+ \action{From the tangent plane coordinates of a star of known \radec,
+        determine the \radec\ of the tangent point (single precision)}
+ \call{CALL sla\_TPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{R}{tangent plane rectangular coordinates (radians)} \\
+ \spec{RA,DEC}{R}{spherical coordinates (radians)}
+}
+\args{RETURNED}
+{
+ \spec{RAZ1,DECZ1}{R}{spherical coordinates of tangent point,
+                      solution 1} \\
+ \spec{RAZ2,DECZ2}{R}{spherical coordinates of tangent point,
+                      solution 2} \\
+ \spec{N}{I}{number of solutions:} \\
+ \spec{}{}{\hspace{1em} 0 = no solutions returned  (note 2)} \\
+ \spec{}{}{\hspace{1em} 1 = only the first solution is useful (note 3)} \\
+ \spec{}{}{\hspace{1em} 2 = there are two useful solutions (note 3)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The RAZ1 and RAZ2 values returned are in the range $0\!-\!2\pi$.
+  \item Cases where there is no solution can only arise near the poles.
+        For example, it is clearly impossible for a star at the pole
+        itself to have a non-zero $\xi$ value, and hence it is
+        meaningless to ask where the tangent point would have to be
+        to bring about this combination of $\xi$ and $\delta$.
+  \item Also near the poles, cases can arise where there are two useful
+        solutions.  The argument N indicates whether the second of the
+        two solutions returned is useful.  N\,=\,1
+        indicates only one useful solution, the usual case;  under
+        these circumstances, the second solution corresponds to the
+        ``over-the-pole'' case, and this is reflected in the values
+        of RAZ2 and DECZ2 which are returned.
+  \item The DECZ1 and DECZ2 values returned are in the range $\pm\pi$,
+        but in the ordinary, non-pole-crossing, case, the range is
+        $\pm\pi/2$.
+  \item RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2 are all in radians.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item When working in \xyz\ rather than spherical coordinates, the
+        equivalent Cartesian routine sla\_TPV2C is available.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_TPV2C}{Plate centre from $\xi,\eta$ and $x,y,z$}
+{
+ \action{From the tangent plane coordinates of a star of known
+         direction cosines, determine the direction cosines
+         of the tangent point (single precision)}
+ \call{CALL sla\_TPV2C (XI, ETA, V, V01, V02, N)}
+}
+\args{GIVEN}
+{
+ \spec{XI,ETA}{R}{tangent plane coordinates of star (radians)} \\
+ \spec{V}{R(3)}{direction cosines of star}
+}
+\args{RETURNED}
+{
+ \spec{V01}{R(3)}{direction cosines of tangent point, solution 1} \\
+ \spec{V01}{R(3)}{direction cosines of tangent point, solution 2} \\
+ \spec{N}{I}{number of solutions:} \\
+ \spec{}{}{\hspace{1em} 0 = no solutions returned  (note 2)} \\
+ \spec{}{}{\hspace{1em} 1 = only the first solution is useful (note 3)} \\
+ \spec{}{}{\hspace{1em} 2 = there are two useful solutions (note 3)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The vector V must be of unit length or the result will be wrong.
+  \item Cases where there is no solution can only arise near the poles.
+        For example, it is clearly impossible for a star at the pole
+        itself to have a non-zero XI value.
+  \item Also near the poles, cases can arise where there are two useful
+        solutions.  The argument N indicates whether the second of the
+        two solutions returned is useful.
+        N\,=\,1
+        indicates only one useful solution, the usual case;  under these
+        circumstances, the second solution can be regarded as valid if
+        the vector V02 is interpreted as the ``over-the-pole'' case.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_TPS2C.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_UE2EL}{Universal to Conventional Elements}
+{
+ \action{Transform universal elements into conventional heliocentric
+         osculating elements.}
+ \call{CALL sla\_UE2EL (\vtop{
+         \hbox{U, JFORMR,}
+         \hbox{JFORM, EPOCH, ORBINC, ANODE, PERIH,}
+         \hbox{AORQ, E, AORL, DM, JSTAT)}}}
+}
+\args{GIVEN}
+{
+ \spec{U}{D(13)}{universal orbital elements (updated; Note~1)} \\
+ \specel {(1)}     {combined mass ($M+m$)} \\
+ \specel {(2)}     {total energy of the orbit ($\alpha$)} \\
+ \specel {(3)}     {reference (osculating) epoch ($t_0$)} \\
+ \specel {(4-6)}   {position at reference epoch (${\rm \bf r}_0$)} \\
+ \specel {(7-9)}   {velocity at reference epoch (${\rm \bf v}_0$)} \\
+ \specel {(10)}    {heliocentric distance at reference epoch} \\
+ \specel {(11)}    {${\rm \bf r}_0.{\rm \bf v}_0$} \\
+ \specel {(12)}    {date ($t$)} \\
+ \specel {(13)}    {universal eccentric anomaly ($\psi$) of date, approx} \\ \\
+ \spec{JFORMR}{I}{requested element set (1-3; Note~3)}
+}
+\args{RETURNED}
+{
+ \spec{JFORM}{I}{element set actually returned (1-3; Note~4)} \\
+ \spec{EPOCH}{D}{epoch of elements ($t_0$ or $T$, TT MJD)} \\
+ \spec{ORBINC}{D}{inclination ($i$, radians)} \\
+ \spec{ANODE}{D}{longitude of the ascending node ($\Omega$, radians)} \\
+ \spec{PERIH}{D}{longitude or argument of perihelion
+                            ($\varpi$ or $\omega$,} \\
+ \spec{}{}{\hspace{1.5em} radians)} \\
+ \spec{AORQ}{D}{mean distance or perihelion distance ($a$ or $q$, AU)} \\
+ \spec{E}{D}{eccentricity ($e$)} \\
+ \spec{AORL}{D}{mean anomaly or longitude
+                               ($M$ or $L$, radians,} \\
+ \spec{}{}{\hspace{1.5em} JFORM=1,2 only)} \\
+ \spec{DM}{D}{daily motion ($n$, radians, JFORM=1 only)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{2.3em}    0 = OK} \\
+ \spec{}{}{\hspace{1.5em} $-$1 = illegal PMASS} \\
+ \spec{}{}{\hspace{1.5em} $-$2 = illegal JFORMR} \\
+ \spec{}{}{\hspace{1.5em} $-$3 = position/velocity out of allowed range}
+}
+\notes
+{
+ \begin{enumerate}
+  \setlength{\parskip}{\medskipamount}
+  \item The ``universal'' elements are those which define the orbit for the
+        purposes of the method of universal variables (see reference 2).
+        They consist of the combined mass of the two bodies, an epoch,
+        and the position and velocity vectors (arbitrary reference frame)
+        at that epoch.  The parameter set used here includes also various
+        quantities that can, in fact, be derived from the other
+        information.  This approach is taken to avoiding unnecessary
+        computation and loss of accuracy.  The supplementary quantities
+        are (i)~$\alpha$, which is proportional to the total energy of the
+        orbit, (ii)~the heliocentric distance at epoch,
+        (iii)~the outwards component of the velocity at the given epoch,
+        (iv)~an estimate of $\psi$, the ``universal eccentric anomaly'' at a
+        given date and (v)~that date.
+  \item The universal elements are with respect to the mean equator and
+        equinox of epoch J2000.  The orbital elements produced are with
+        respect to the J2000 ecliptic and mean equinox.
+  \item Three different element-format options are supported, as
+        follows. \\
+
+        JFORM=1, suitable for the major planets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of elements $t_0$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & longitude of perihelion $\varpi$ (radians) \\
+        & AORQ   & = & mean distance $a$ (AU) \\
+        & E      & = & eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        & AORL   & = & mean longitude $L$ (radians) \\
+        & DM     & = & daily motion $n$ (radians)
+        \end{tabular}
+
+        JFORM=2, suitable for minor planets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of elements $t_0$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & mean distance $a$ (AU) \\
+        & E      & = & eccentricity $e$ $( 0 \leq e < 1 )$ \\
+        & AORL   & = & mean anomaly $M$ (radians)
+        \end{tabular}
+
+        JFORM=3, suitable for comets:
+
+        \begin{tabular}{llll}
+        & EPOCH  & = & epoch of perihelion $T$ (TT MJD) \\
+        & ORBINC & = & inclination $i$ (radians) \\
+        & ANODE  & = & longitude of the ascending node $\Omega$ (radians) \\
+        & PERIH  & = & argument of perihelion $\omega$ (radians) \\
+        & AORQ   & = & perihelion distance $q$ (AU) \\
+        & E      & = & eccentricity $e$ $( 0 \leq e \leq 10 )$
+        \end{tabular}
+
+  \item It may not be possible to generate elements in the form
+        requested through JFORMR.  The caller is notified of the form
+        of elements actually returned by means of the JFORM argument:
+
+        \begin{tabular}{llll}
+        & JFORMR   & JFORM   & meaning \\ \\
+        & ~~~~~1   & ~~~~~1  & OK: elements are in the requested format \\
+        & ~~~~~1   & ~~~~~2  & never happens \\
+        & ~~~~~1   & ~~~~~3  & orbit not elliptical \\
+        & ~~~~~2   & ~~~~~1  & never happens \\
+        & ~~~~~2   & ~~~~~2  & OK: elements are in the requested format \\
+        & ~~~~~2   & ~~~~~3  & orbit not elliptical \\
+        & ~~~~~3   & ~~~~~1  & never happens \\
+        & ~~~~~3   & ~~~~~2  & never happens \\
+        & ~~~~~3   & ~~~~~3  & OK: elements are in the requested format
+        \end{tabular}
+
+  \item The arguments returned for each value of JFORM ({\it cf.}\/ Note~5:
+        JFORM may not be the same as JFORMR) are as follows:
+
+        \begin{tabular}{lllll}
+        & JFORM  & 1        & 2        & 3 \\ \\
+        & EPOCH  & $t_0$    & $t_0$    & $T$ \\
+        & ORBINC & $i$      & $i$      & $i$ \\
+        & ANODE  & $\Omega$ & $\Omega$ & $\Omega$ \\
+        & PERIH  & $\varpi$ & $\omega$ & $\omega$ \\
+        & AORQ   & $a$      & $a$      & $q$ \\
+        & E      & $e$      & $e$      & $e$ \\
+        & AORL   & $L$      & $M$      & - \\
+        & DM     & $n$      & -        & -
+        \end{tabular}
+
+        where:
+
+        \begin{tabular}{lll}
+        & $t_0$    & is the epoch of the elements (MJD, TT) \\
+        & $T$      & is the epoch of perihelion (MJD, TT) \\
+        & $i$      & is the inclination (radians) \\
+        & $\Omega$ & is the longitude of the ascending node (radians) \\
+        & $\varpi$ & is the longitude of perihelion (radians) \\
+        & $\omega$ & is the argument of perihelion (radians) \\
+        & $a$      & is the mean distance (AU) \\
+        & $q$      & is the perihelion distance (AU) \\
+        & $e$      & is the eccentricity \\
+        & $L$      & is the longitude (radians, $0-2\pi$) \\
+        & $M$      & is the mean anomaly (radians, $0-2\pi$) \\
+        & $n$      & is the daily motion (radians) \\
+        & - & means no value is set
+        \end{tabular}
+
+  \item At very small inclinations, the longitude of the ascending node
+        ANODE becomes indeterminate and under some circumstances may be
+        set arbitrarily to zero.  Similarly, if the orbit is close to
+        circular, the true anomaly becomes indeterminate and under some
+        circumstances may be set arbitrarily to zero.  In such cases,
+        the other elements are automatically adjusted to compensate,
+        and so the elements remain a valid description of the orbit.
+ \end{enumerate}
+}
+\refs{
+   \begin{enumerate}
+   \item Sterne, Theodore E., {\it An Introduction to Celestial Mechanics,}\/
+         Interscience Publishers, 1960.  Section 6.7, p199.
+   \item Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.
+   \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_UE2PV}{Pos/Vel from Universal Elements}
+{
+ \action{Heliocentric position and velocity of a planet, asteroid or comet,
+         starting from orbital elements in the ``universal variables'' form.}
+ \call{CALL sla\_UE2PV (DATE, U, PV, JSTAT)}
+}
+\args{GIVEN}
+{
+ \spec{DATE}{D}{date (TT Modified Julian Date = JD$-$2400000.5)}
+}
+\args{GIVEN and RETURNED}
+{
+ \spec{U}{D(13)}{universal orbital elements (updated; Note~1)} \\
+ \specel {(1)}     {combined mass ($M+m$)} \\
+ \specel {(2)}     {total energy of the orbit ($\alpha$)} \\
+ \specel {(3)}     {reference (osculating) epoch ($t_0$)} \\
+ \specel {(4-6)}   {position at reference epoch (${\rm \bf r}_0$)} \\
+ \specel {(7-9)}   {velocity at reference epoch (${\rm \bf v}_0$)} \\
+ \specel {(10)}    {heliocentric distance at reference epoch} \\
+ \specel {(11)}    {${\rm \bf r}_0.{\rm \bf v}_0$} \\
+ \specel {(12)}    {date ($t$)} \\
+ \specel {(13)}    {universal eccentric anomaly ($\psi$) of date, approx}
+}
+\args{RETURNED}
+{
+ \spec{PV}{D(6)}{heliocentric \xyzxyzd, equatorial, J2000} \\
+ \spec{}{}{\hspace{1.5em} (AU, AU/s; Note~1)} \\
+ \spec{JSTAT}{I}{status:} \\
+ \spec{}{}{\hspace{1.95em}      0 = OK} \\
+ \spec{}{}{\hspace{1.2em}    $-$1 = radius vector zero} \\
+ \spec{}{}{\hspace{1.2em}    $-2$ = failed to converge}
+}
+\notes
+{
+ \begin{enumerate}
+  \setlength{\parskip}{\medskipamount}
+  \item The ``universal'' elements are those which define the orbit for the
+        purposes of the method of universal variables (see reference).
+        They consist of the combined mass of the two bodies, an epoch,
+        and the position and velocity vectors (arbitrary reference frame)
+        at that epoch.  The parameter set used here includes also various
+        quantities that can, in fact, be derived from the other
+        information.  This approach is taken to avoiding unnecessary
+        computation and loss of accuracy.  The supplementary quantities
+        are (i)~$\alpha$, which is proportional to the total energy of the
+        orbit, (ii)~the heliocentric distance at epoch,
+        (iii)~the outwards component of the velocity at the given epoch,
+        (iv)~an estimate of $\psi$, the ``universal eccentric anomaly'' at a
+        given date and (v)~that date.
+  \item The companion routine is sla\_EL2UE.  This takes the conventional
+        orbital elements and transforms them into the set of numbers
+        needed by the present routine.  A single prediction requires one
+        one call to sla\_EL2UE followed by one call to the present routine;
+        for convenience, the two calls are packaged as the routine
+        sla\_PLANEL.  Multiple predictions may be made by again
+        calling sla\_EL2UE once, but then calling the present routine
+        multiple times, which is faster than multiple calls to sla\_PLANEL.
+
+        It is not obligatory to use sla\_EL2UE to obtain the parameters.
+        However, it should be noted that because sla\_EL2UE performs its
+        own validation, no checks on the contents of the array U are made
+        by the present routine.
+  \item DATE is the instant for which the prediction is required.  It is
+        in the TT time scale (formerly Ephemeris Time, ET) and is a
+        Modified Julian Date (JD$-$2400000.5).
+  \item The universal elements supplied in the array U are in canonical
+        units (solar masses, AU and canonical days).  The position and
+        velocity are not sensitive to the choice of reference frame.  The
+        sla\_EL2UE routine in fact produces coordinates with respect to the
+        J2000 equator and equinox.
+  \item The algorithm was originally adapted from the EPHSLA program of
+        D.\,H.\,P.\,Jones (private communication, 1996).  The method
+        is based on Stumpff's Universal Variables.
+ \end{enumerate}
+}
+\aref{Everhart, E. \& Pitkin, E.T., Am.~J.~Phys.~51, 712, 1983.}
+%-----------------------------------------------------------------------
+\routine{SLA\_UNPCD}{Remove Radial Distortion}
+{
+ \action{Remove pincushion/barrel distortion from a distorted
+         \xy\  to give tangent-plane \xy.}
+ \call{CALL sla\_UNPCD (DISCO,X,Y)}
+}
+\args{GIVEN}
+{
+ \spec{DISCO}{D}{pincushion/barrel distortion coefficient} \\
+ \spec{X,Y}{D}{distorted \xy}
+}
+\args{RETURNED}
+{
+ \spec{X,Y}{D}{tangent-plane \xy}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The distortion is of the form $\rho = r (1 + c r^{2})$, where $r$ is
+        the radial distance from the tangent point, $c$ is the DISCO
+        argument, and $\rho$ is the radial distance in the presence of
+        the distortion.
+  \item For {\it pincushion}\/ distortion, C is +ve;  for
+        {\it barrel}\/ distortion, C is $-$ve.
+  \item For X,Y in units of one projection radius (in the case of
+        a photographic plate, the focal length), the following
+        DISCO values apply:
+
+        \vspace{2ex}
+
+        \hspace{5em}
+        \begin{tabular}{|l|c|} \hline
+         Geometry & DISCO \\ \hline \hline
+         astrograph & 0.0 \\ \hline
+         Schmidt & $-$0.3333 \\ \hline
+         AAT PF doublet & +147.069 \\ \hline
+         AAT PF triplet & +178.585 \\ \hline
+         AAT f/8 & +21.20 \\ \hline
+         JKT f/8 & +14.6 \\ \hline
+        \end{tabular}
+
+        \vspace{2ex}
+
+  \item The present routine is a rigorous inverse of the companion
+        routine sla\_PCD.  The expression for $\rho$ in Note~1
+        is rewritten in the form $x^3 + ax + b = 0$ and solved by
+        standard techniques.
+
+  \item Cases where the cubic has multiple real roots can sometimes
+        occur, corresponding to extreme instances of barrel distortion
+        where up to three different undistorted \xy s all produce the
+        same distorted \xy.  However, only one solution is returned,
+        the one that produces the smallest change in \xy.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_V2TP}{Direction Cosines to Tangent Plane}
+{
+ \action{Given the direction cosines of a star and of the tangent point,
+         determine the star's tangent-plane coordinates
+         (single precision).}
+ \call{CALL sla\_V2TP (V, V0, XI, ETA, J)}
+}
+\args{GIVEN}
+{
+ \spec{V}{R(3)}{direction cosines of star} \\
+ \spec{V0}{R(3)}{direction cosines of tangent point}
+}
+\args{RETURNED}
+{
+ \spec{XI,ETA}{R}{tangent plane coordinates (radians)} \\
+ \spec{J}{I}{status:} \\
+ \spec{}{}{\hspace{1.5em} 0 = OK, star on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 1 = error, star too far from axis} \\
+ \spec{}{}{\hspace{1.5em} 2 = error, antistar on tangent plane} \\
+ \spec{}{}{\hspace{1.5em} 3 = error, antistar too far from axis}
+}
+\notes
+{
+ \begin{enumerate}
+  \item If vector V0 is not of unit length, or if vector V is of zero
+        length, the results will be wrong.
+  \item If V0 points at a pole, the returned $\xi,\eta$
+        will be based on the
+        arbitrary assumption that $\alpha=0$ at the tangent point.
+  \item The projection is called the {\it gnomonic}\/ projection;  the
+        Cartesian coordinates \xieta\ are called
+        {\it standard coordinates.}\/  The latter
+        are in units of the distance from the tangent plane to the projection
+        point, {\it i.e.}\ radians near the origin.
+  \item This routine is the Cartesian equivalent of the routine sla\_S2TP.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_VDV}{Scalar Product}
+{
+ \action{Scalar product of two 3-vectors (single precision).}
+ \call{R~=~sla\_VDV (VA, VB)}
+}
+\args{GIVEN}
+{
+ \spec{VA}{R(3)}{first vector} \\
+ \spec{VB}{R(3)}{second vector}
+}
+\args{RETURNED}
+{
+ \spec{sla\_VDV}{R}{scalar product VA.VB}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_VN}{Normalize Vector}
+{
+ \action{Normalize a 3-vector, also giving the modulus (single precision).}
+ \call{CALL sla\_VN (V, UV, VM)}
+}
+\args{GIVEN}
+{
+ \spec{V}{R(3)}{vector}
+}
+\args{RETURNED}
+{
+ \spec{UV}{R(3)}{unit vector in direction of V} \\
+ \spec{VM}{R}{modulus of V}
+}
+\anote{If the modulus of V is zero, UV is set to zero as well.}
+%-----------------------------------------------------------------------
+\routine{SLA\_VXV}{Vector Product}
+{
+ \action{Vector product of two 3-vectors (single precision).}
+ \call{CALL sla\_VXV (VA, VB, VC)}
+}
+\args{GIVEN}
+{
+ \spec{VA}{R(3)}{first vector} \\
+ \spec{VB}{R(3)}{second vector}
+}
+\args{RETURNED}
+{
+ \spec{VC}{R(3)}{vector product VA$\times$VB}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_WAIT}{Time Delay}
+{
+ \action{Wait for a specified interval.}
+ \call{CALL sla\_WAIT (DELAY)}
+}
+\args{GIVEN}
+{
+ \spec{DELAY}{R}{delay in seconds}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The implementation is machine-specific.
+  \item The delay actually requested is restricted to the range
+        100ns-200s in the present implementation.
+  \item There is no guarantee of accuracy, though on almost all
+        types of computer the program will certainly not
+        resume execution {\it before}\/ the stated interval has
+        elapsed.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_XY2XY}{Apply Linear Model to an \xy}
+{
+ \action{Transform one \xy\ into another using a linear model of the type
+         produced by the sla\_FITXY routine.}
+ \call{CALL sla\_XY2XY (X1, Y1, COEFFS, X2, Y2)}
+}
+\args{GIVEN}
+{
+ \spec{X1,Y1}{D}{\xy\ before transformation} \\
+ \spec{COEFFS}{D(6)}{transformation coefficients (see note)}
+}
+\args{RETURNED}
+{
+ \spec{X2,Y2}{D}{\xy\ after transformation}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The model relates two sets of \xy\ coordinates as follows.
+        Naming the six elements of COEFFS $a,b,c,d,e$ \& $f$,
+        the present routine performs the transformation:
+        \begin{verse}
+          $x_{2} = a + bx_{1} + cy_{1}$ \\
+          $y_{2} = d + ex_{1} + fy_{1}$
+        \end{verse}
+  \item See also sla\_FITXY, sla\_PXY, sla\_INVF, sla\_DCMPF.
+ \end{enumerate}
+}
+%-----------------------------------------------------------------------
+\routine{SLA\_ZD}{$h,\delta$ to Zenith Distance}
+{
+ \action{Hour angle and declination to zenith distance
+         (double precision).}
+ \call{D~=~sla\_ZD (HA, DEC, PHI)}
+}
+\args{GIVEN}
+{
+ \spec{HA}{D}{hour angle in radians} \\
+ \spec{DEC}{D}{declination in radians} \\
+ \spec{PHI}{D}{latitude in radians}
+}
+\args{RETURNED}
+{
+ \spec{sla\_ZD}{D}{zenith distance (radians, $0\!-\!\pi$)}
+}
+\notes
+{
+ \begin{enumerate}
+  \item The latitude must be geodetic.  In critical applications,
+        corrections for polar motion should be applied (see sla\_POLMO).
+  \item In some applications it will be important to specify the
+        correct type of hour angle and declination in order to
+        produce the required type
+        of zenith distance.  In particular, it may be
+        important to distinguish between the zenith distance
+        as affected by refraction, which would require the
+        {\it observed}\/ \hadec, and the zenith distance {\it in vacuo},
+        which would require the {\it topocentric}\/ \hadec.  If
+        the effects of diurnal aberration can be neglected, the
+        {\it apparent}\/ \hadec\ may be used instead of the
+        {\it topocentric}\/ \hadec.
+  \item No range checking of arguments is done.
+  \item In applications which involve many zenith distance calculations,
+        rather than calling the present routine it will be more
+        efficient to use inline code, having previously computed fixed
+        terms such as sine and cosine of latitude, and perhaps sine and
+        cosine of declination.
+ \end{enumerate}
+}
+\vfill
+\pagebreak
+
+\section{EXPLANATION AND EXAMPLES}
+To guide the writer of positional-astronomy applications software,
+this final chapter puts the SLALIB routines into the context of
+astronomical phenomena and techniques, and presents a few
+``cookbook'' examples
+of the SLALIB calls in action.  The astronomical content of the chapter
+is not, of course, intended to be a substitute for specialist text-books on
+positional astronomy, but may help bridge the gap between
+such books and the SLALIB routines.  For further reading, the following
+cover a wide range of material and styles:
+\begin{itemize}
+\item {\it Explanatory Supplement to the Astronomical Almanac},
+      ed.\ P.\,Kenneth~Seidelmann (1992), University Science Books.
+\item {\it Vectorial Astrometry}, C.\,A.\,Murray (1983), Adam Hilger.
+\item {\it Spherical Astronomy}, Robin~M.\,Green (1985), Cambridge
+      University Press.
+\item {\it Spacecraft Attitude Determination and Control},
+      ed.\ James~R.\,Wertz (1986), Reidel.
+\item {\it Practical Astronomy with your Calculator},
+      Peter~Duffett-Smith (1981), Cambridge University Press.
+\end{itemize}
+Also of considerable value, though out of date in places, are:
+\begin{itemize}
+\item {\it Explanatory Supplement to the Astronomical Ephemeris
+      and the American Ephemeris and Nautical Almanac}, RGO/USNO (1974),
+      HMSO.
+\item {\it Textbook on Spherical Astronomy}, W.\,M.\,Smart (1977),
+      Cambridge University Press.
+\end{itemize}
+Only brief details of individual SLALIB routines are given here, and
+readers will find it useful to refer to the subprogram specifications
+elsewhere in this document.  The source code for the SLALIB routines
+(available in both Fortran and C) is also intended to be used as
+documentation.
+
+\subsection {Spherical Trigonometry}
+Celestial phenomena occur at such vast distances from the
+observer that for most practical purposes there is no need to
+work in 3D;  only the direction
+of a source matters, not how far away it is.  Things can
+therefore be viewed as if they were happening
+on the inside of sphere with the observer at the centre --
+the {\it celestial sphere}.  Problems involving
+positions and orientations in the sky can then be solved by
+using the formulae of {\it spherical trigonometry}, which
+apply to {\it spherical triangles}, the sides of which are
+{\it great circles}.
+
+Positions on the celestial sphere may be specified by using
+a spherical polar coordinate system, defined in terms of
+some fundamental plane and a line in that plane chosen to
+represent zero longitude.  Mathematicians usually work with the
+co-latitude, with zero at the principal pole, whereas most
+astronomical coordinate systems use latitude, reckoned plus and
+minus from the equator.
+Astronomical coordinate systems may be either right-handed
+({\it e.g.}\ right ascension and declination \radec,
+Galactic longitude and latitude \gal)
+or left-handed ({\it e.g.}\ hour angle and
+declination \hadec).  In some cases
+different conventions have been used in the past, a fruitful source of
+mistakes.  Azimuth and geographical longitude are examples;  azimuth
+is now generally reckoned north through east
+(making a left-handed system);  geographical longitude is now usually
+taken to increase eastwards (a right-handed system) but astronomers
+used to employ a west-positive convention.  In reports
+and program comments it is wise to spell out what convention
+is being used, if there is any possibility of confusion.
+
+When applying spherical trigonometry formulae, attention must be
+paid to
+rounding errors (for example it is a bad idea to find a
+small angle through its cosine) and to the possibility of
+problems close to poles.
+Also, if a formulation relies on inspection to establish
+the quadrant of the result, it is an indication that a vector-related
+method might be preferable.
+
+As well as providing many routines which work in terms of specific
+spherical coordinates such as \radec, SLALIB provides
+two routines which operate directly on generic spherical
+coordinates:
+sla\_SEP
+computes the separation between
+two points (the distance along a great circle) and
+sla\_BEAR
+computes the bearing (or {\it position angle})
+of one point seen from the other.  The routines
+sla\_DSEP
+and
+sla\_DBEAR
+are double precision equivalents.  As a simple demonstration
+of SLALIB, we will use these facilities to estimate the distance from
+London to Sydney and the initial compass heading:
+\goodbreak
+\begin{verbatim}
+            IMPLICIT NONE
+
+      *  Degrees to radians
+            REAL D2R
+            PARAMETER (D2R=0.01745329252)
+
+      *  Longitudes and latitudes (radians) for London and Sydney
+            REAL AL,BL,AS,BS
+            PARAMETER (AL=-0.2*D2R,BL=51.5*D2R,AS=151.2*D2R,BS=-33.9*D2R)
+
+      *  Earth radius in km (spherical approximation)
+            REAL RKM
+            PARAMETER (RKM=6375.0)
+
+            REAL sla_SEP,sla_BEAR
+
+
+      *  Distance and initial heading (N=0, E=90)
+            WRITE (*,'(1X,I5,'' km,'',I4,'' deg'')')
+           :    NINT(sla_SEP(AL,BL,AS,BS)*RKM),NINT(sla_BEAR(AL,BL,AS,BS)/D2R)
+
+            END
+\end{verbatim}
+\goodbreak
+(The result is 17011~km, $61^\circ$.)
+
+The routines
+sla\_SEPV,
+sla\_DSEPV,
+sla\_PAV,
+sla\_DPAV
+are equivalents of sla\_SEP, sla\_DSEP, sla\_BEAR and sla\_DBEAR
+but starting from vectors
+instead of spherical coordinates.
+
+\subsubsection{Formatting angles}
+SLALIB has routines for decoding decimal numbers
+from character form and for converting angles to and from
+sexagesimal form (hours, minutes, seconds or degrees,
+arcminutes, arcseconds).  These apparently straightforward
+operations contain hidden traps which the SLALIB routines
+avoid.
+
+There are five routines for decoding numbers from a character
+string, such as might be entered using a keyboard.
+They all work in the same style, and successive calls
+can work their way along a single string decoding
+a sequence of numbers of assorted types.  Number
+fields can be separated by spaces or commas, and can be defaulted
+to previous values or to preset defaults.
+
+Three of the routines decode single numbers:
+sla\_INTIN
+(integer),
+sla\_FLOTIN
+(single precision floating point) and
+sla\_DFLTIN
+(double precision).  A minus sign can be
+detected even when the number is zero;  this avoids
+the frequently-encountered ``minus zero'' bug, where
+declinations {\it etc.}\ in
+the range $0^{\circ}$ to $-1^{\circ}$ mysteriously migrate to
+the range $0^{\circ}$ to $+1^{\circ}$.
+Here is an example (in Fortran) where we wish to
+read two numbers, an integer {\tt IX} and a real, {\tt Y},
+with {\tt IX} defaulting to zero and {\tt Y} defaulting to
+{\tt IX}:
+\goodbreak
+\begin{verbatim}
+            DOUBLE PRECISION Y
+            CHARACTER*80 A
+            INTEGER IX,I,J
+
+      *  Input the string to be decoded
+            READ (*,'(A)') A
+
+      *  Preset IX to its default value
+            IX = 0
+
+      *  Point to the start of the string
+            I = 1
+
+      *  Decode an integer
+            CALL sla_INTIN(A,I,IX,J)
+            IF (J.GT.1) GO TO ... (bad IX)
+
+      *  Preset Y to its default value
+            Y = DBLE(IX)
+
+      *  Decode a double precision number
+            CALL sla_DFLTIN(A,I,Y,J)
+            IF (J.GT.1) GO TO ... (bad Y)
+\end{verbatim}
+\goodbreak
+Two additional routines decode a 3-field sexagesimal number:
+sla\_AFIN
+(degrees, arcminutes, arcseconds to single
+precision radians) and
+sla\_DAFIN
+(the same but double precision).  They also
+work using other units such as hours {\it etc}.\ if
+you multiply the result by the appropriate factor.  An example
+Fortran program which uses
+sla\_DAFIN
+was given earlier, in section 1.2.
+
+SLALIB provides four routines for expressing an angle in radians
+in a preferred range.  The function
+sla\_RANGE
+expresses an angle
+in the range $\pm\pi$;
+sla\_RANORM
+expresses an angle in the range
+$0-2\pi$.  The functions
+sla\_DRANGE
+and
+sla\_DRANRM
+are double precision versions.
+
+Several routines
+(sla\_CTF2D,
+sla\_CR2AF
+{\it etc.}) are provided to convert
+angles to and from
+sexagesimal form (hours, minute, seconds or degrees,
+arcminutes and arcseconds).
+They avoid the common
+``converting from integer to real at the wrong time''
+bug, which produces angles like \hms{24}{59}{59}{999}.
+Here is a program which displays an hour angle
+stored in radians:
+\goodbreak
+\begin{verbatim}
+            DOUBLE PRECISION HA
+            CHARACTER SIGN
+            INTEGER IHMSF(4)
+            :
+            CALL sla_DR2TF(3,HA,SIGN,IHMSF)
+            WRITE (*,'(1X,A,3I3.2,''.'',I3.3)') SIGN,IHMSF
+\end{verbatim}
+\goodbreak
+
+\subsection {Vectors and Matrices}
+As an alternative to employing a spherical polar coordinate system,
+the direction of an object can be defined in terms of the sum of any
+three vectors as long as they are different and
+not coplanar.  In practice, three vectors at right angles are
+usually chosen, forming a system
+of {\it Cartesian coordinates}.  The {\it x}- and {\it y}-axes
+lie in the fundamental plane ({\it e.g.}\ the equator in the
+case of \radec), with the {\it x}-axis pointing to zero longitude.
+The {\it z}-axis is normal to the fundamental plane and points
+towards positive latitudes.  The {\it y}-axis can lie in either
+of the two possible directions, depending on whether the
+coordinate system is right-handed or left-handed.
+The three axes are sometimes called
+a {\it triad}.  For most applications involving arbitrarily
+distant objects such as stars, the vector which defines
+the direction concerned is constrained to have unit length.
+The {\it x}-, {\it y-} and {\it z-}components
+can be regarded as the scalar (dot) product of this vector
+onto the three axes of the triad in turn.  Because the vector
+is a unit vector,
+each of the three dot-products is simply the cosine of the angle
+between the unit vector and the axis concerned, and the
+{\it x}-, {\it y-} and {\it z-}components are sometimes
+called {\it direction cosines}.
+
+For some applications, including those involving objects
+within the Solar System, unit vectors are inappropriate, and
+it is necessary to use vectors scaled in length-units such as
+AU, km {\it etc.}
+In these cases the origin of the coordinate system may not be
+the observer, but instead might be the Sun, the Solar-System
+barycentre, the centre of the Earth {\it etc.}  But whatever the application,
+the final direction in which the observer sees the object can be
+expressed as direction cosines.
+
+But where has this got us?  Instead of two numbers -- a longitude and
+a latitude -- we now have three numbers to look after
+-- the {\it x}-, {\it y-} and
+{\it z-}components -- whose quadratic sum we have somehow to contrive to
+be unity.  And, in addition to this apparent redundancy,
+most people find it harder to visualize
+problems in terms of \xyz\ than in $[\,\theta,\phi~]$.
+Despite these objections, the vector approach turns out to have
+significant advantages over the spherical trigonometry approach:
+\begin{itemize}
+\item Vector formulae tend to be much more succinct;  one vector
+      operation is the equivalent of strings of sines and cosines.
+\item The formulae are as a rule rigorous, even at the poles.
+\item Accuracy is maintained all over the celestial sphere.
+      When one Cartesian component is nearly unity and
+      therefore insensitive to direction, the others become small
+      and therefore more precise.
+\item Formulations usually deliver the quadrant of the result
+      without the need for any inspection (except within the
+      library function ATAN2).
+\end{itemize}
+A number of important transformations in positional
+astronomy turn out to be nothing more than changes of coordinate
+system, something which is especially convenient if
+the vector approach is used.  A direction with respect
+to one triad can be expressed relative to another triad simply
+by multiplying the \xyz\ column vector by the appropriate
+$3\times3$ orthogonal matrix
+(a tensor of Rank~2, or {\it dyadic}).  The three rows of this
+{\it rotation matrix}\/
+are the vectors in the old coordinate system of the three
+new axes, and the transformation amounts to obtaining the
+dot-product of the direction-vector with each of the three
+new axes.  Precession, nutation, \hadec\ to \azel,
+\radec\ to \gal\ and so on are typical examples of the
+technique.  A useful property of the rotation matrices
+is that they can be inverted simply by taking the transpose.
+
+The elements of these vectors and matrices are assorted combinations of
+the sines and cosines of the various angles involved (hour angle,
+declination and so on, depending on which transformation is
+being applied).  If you write out the matrix multiplications
+in full you get expressions which are essentially the same as the
+equivalent spherical trigonometry formulae.  Indeed, many of the
+standard formulae of spherical trigonometry are most easily
+derived by expressing the problem initially in
+terms of vectors.
+
+\subsubsection{Using vectors}
+SLALIB provides conversions between spherical and vector
+form
+(sla\_CS2C,
+sla\_CC2S
+{\it etc.}), plus an assortment
+of standard vector and matrix operations
+(sla\_VDV,
+sla\_MXV
+{\it etc.}).
+There are also routines
+(sla\_EULER
+{\it etc.}) for creating a rotation matrix
+from three {\it Euler angles}\/ (successive rotations about
+specified Cartesian axes).  Instead of Euler angles, a rotation
+matrix can be expressed as an {\it axial vector}\/ (the pole of the rotation,
+and the amount of rotation), and routines are provided for this
+(sla\_AV2M,
+sla\_M2AV
+{\it etc.}).
+
+Here is an example where spherical coordinates {\tt P1} and {\tt Q1}
+undergo a coordinate transformation and become {\tt P2} and {\tt Q2};
+the transformation consists of a rotation of the coordinate system
+through angles {\tt A}, {\tt B} and {\tt C} about the
+{\it z}, new {\it y}\/ and new {\it z}\/ axes respectively:
+\goodbreak
+\begin{verbatim}
+            REAL A,B,C,R(3,3),P1,Q1,V1(3),V2(3),P2,Q2
+             :
+      *  Create rotation matrix
+            CALL sla_EULER('ZYZ',A,B,C,R)
+
+      *  Transform position (P1,Q1) from spherical to Cartesian
+            CALL sla_CS2C(P1,Q1,V1)
+
+      *  Apply the rotation
+            CALL sla_MXV(R,V1,V2)
+
+      *  Back to spherical
+            CALL sla_CC2S(V2,P2,Q2)
+\end{verbatim}
+\goodbreak
+Small adjustments to the direction of a position
+vector are often most conveniently described in terms of
+$[\,\Delta x,\Delta y, \Delta z\,]$.  Adding the correction
+vector needs careful handling if the position
+vector is to remain of length unity, an advisable precaution which
+ensures that
+the \xyz\ components are always available to mean the cosines of
+the angles between the vector and the axis concerned.  Two types
+of shifts are commonly used,
+the first where a small vector of arbitrary direction is
+added to the unit vector, and the second where there is a displacement
+in the latitude coordinate (declination, elevation {\it etc.}) alone.
+
+For a shift produced by adding a small \xyz\ vector ${\bf d}$ to a
+unit vector ${\bf v}_1$, the resulting vector ${\bf v}_2$ has direction
+$<{\bf v}_1+{\bf d}>$ but is no longer of unit length.  A better approximation
+is available if the result is multiplied by a scaling factor of
+$(1-{\bf d}\cdot{\bf v}_1)$, where the dot
+means scalar product.  In Fortran:
+\goodbreak
+\begin{verbatim}
+            F = (1D0-(DX*V1X+DY*V1Y+DZ*V1Z))
+            V2X = F*(V1X+DX)
+            V2Y = F*(V1Y+DY)
+            V2Z = F*(V1Z+DZ)
+\end{verbatim}
+\goodbreak
+\noindent
+The correction for diurnal aberration (discussed later) is
+an example of this form of shift.
+
+As an example of the second kind of displacement
+we will apply a small change in elevation $\delta E$ to an
+\azel\ direction vector.  The direction of the
+result can be obtained by making the allowable approximation
+${\tan \delta E\approx\delta E}$ and adding a adjustment
+vector of length $\delta E$ normal
+to the direction vector in the vertical plane containing the direction
+vector.  The $z$-component of the adjustment vector is
+$\delta E \cos E$,
+and the horizontal component is
+$\delta E \sin E$ which has then to be
+resolved into $x$ and $y$ in proportion to their current sizes. To
+approximate a unit vector more closely, a correction factor of
+$\cos \delta E$ can then be applied, which is nearly
+$(1-\delta E^2 /2)$ for
+small $\delta E$.  Expressed in Fortran, for initial vector
+{\tt V1X,V1Y,V1Z}, change in elevation {\tt DEL}
+(+ve $\equiv$ upwards), and result
+vector {\tt V2X,V2Y,V2Z}:
+\goodbreak
+\begin{verbatim}
+            COSDEL = 1D0-DEL*DEL/2D0
+            R1 = SQRT(V1X*V1X+V1Y*V1Y)
+            F = COSDEL*(R1-DEL*V1Z)/R1
+            V2X = F*V1X
+            V2Y = F*V1Y
+            V2Z = COSDEL*(V1Z+DEL*R1)
+\end{verbatim}
+\goodbreak
+An example of this type of shift is the correction for atmospheric
+refraction (see later).
+Depending on the relationship between $\delta E$ and $E$, special
+handling at the pole (the zenith for our example) may be required.
+
+SLALIB includes routines for the case where both a position
+and a velocity are involved.  The routines
+sla\_CS2C6
+and
+sla\_CC62S
+convert from $[\theta,\phi,\dot{\theta},\dot{\phi}]$
+to \xyzxyzd\ and back;
+sla\_DS2C6
+and
+sla\_DC62S
+are double precision equivalents.
+
+\subsection {Celestial Coordinate Systems}
+SLALIB has routines to perform transformations
+of celestial positions between different spherical
+coordinate systems, including those shown in the following table:
+
+\begin{center}
+\begin{tabular}{|l|c|c|c|c|c|c|} \hline
+{\it system} & {\it symbols} & {\it longitude} & {\it latitude} &
+          {\it x-y plane} & {\it long.\ zero} & {\it RH/LH}
+\\ \hline \hline
+horizon & -- & azimuth & elevation & horizontal & north & L
+\\ \hline
+equatorial & $\alpha,\delta$ & R.A.\ & Dec.\ & equator & equinox & R
+\\ \hline
+local equ.\ & $h,\delta$ & H.A.\ & Dec.\ & equator & meridian & L
+\\ \hline
+ecliptic & $\lambda,\beta$ & ecl.\ long.\ & ecl.\ lat.\ &
+                                       ecliptic & equinox & R
+\\ \hline
+galactic & $l^{I\!I},b^{I\!I}$ & gal.\ long.\ & gal.\ lat.\ &
+                                       gal.\ equator & gal.\ centre & R
+\\ \hline
+supergalactic & SGL,SGB & SG long.\ & SG lat.\ &
+                                       SG equator & node w.\ gal.\ equ.\ & R
+\\ \hline
+\end{tabular}
+\end{center}
+Transformations between \hadec\ and \azel\ can be performed by
+calling
+sla\_E2H
+and
+sla\_H2E,
+or, in double precision,
+sla\_DE2H
+and
+sla\_DH2E.
+There is also a routine for obtaining
+zenith distance alone for a given \hadec,
+sla\_ZD,
+and one for determining the parallactic angle,
+sla\_PA.
+Three routines are included which relate to altazimuth telescope
+mountings.  For a given \hadec\ and latitude,
+sla\_ALTAZ
+returns the azimuth, elevation and parallactic angle, plus
+velocities and accelerations for sidereal tracking.
+The routines
+sla\_PDA2H
+and
+sla\_PDQ2H
+predict at what hour angle a given azimuth or
+parallactic angle will be reached.
+
+The routines
+sla\_EQECL
+and
+sla\_ECLEQ
+transform between ecliptic
+coordinates and \radec\/; there is also a routine for generating the
+equatorial to ecliptic rotation matrix for a given date:
+sla\_ECMAT.
+
+For conversion between Galactic coordinates and \radec\ there are
+two sets of routines, depending on whether the \radec\ is
+old-style, B1950, or new-style, J2000;
+sla\_EG50
+and
+sla\_GE50
+are \radec\ to \gal\ and {\it vice versa}\/ for the B1950 case, while
+sla\_EQGAL
+and
+sla\_GALEQ
+are the J2000 equivalents.
+
+Finally, the routines
+sla\_GALSUP
+and
+sla\_SUPGAL
+transform \gal\ to de~Vaucouleurs supergalactic longitude and latitude
+and {\it vice versa.}
+
+It should be appreciated that the table, above, constitutes
+a gross oversimplification.   Apparently
+simple concepts such as equator, equinox {\it etc.}\ are apt to be very hard to
+pin down precisely (polar motion, orbital perturbations \ldots) and
+some have several interpretations, all subtly different.  The various
+frames move in complicated ways with respect to one another or to
+the stars (themselves in motion).  And in some instances the
+coordinate system is slightly distorted, so that the
+ordinary rules of spherical trigonometry no longer strictly apply.
+
+These {\it caveats}\/
+apply particularly to the bewildering variety of different
+\radec\ systems that are in use.  Figure~1 shows how
+some of these systems are related, to one another and
+to the direction in which a celestial source actually
+appears in the sky.  At the top of the diagram are
+the various sorts of {\it mean place}\/
+found in star catalogues and papers;\footnote{One frame not included in
+Figure~1 is that of the Hipparcos catalogue.  This is currently the
+best available implementation in the optical of the {\it International
+Celestial Reference System}\/ (ICRS), which is based on extragalactic
+radio sources observed by VLBI.  The distinction between FK5 J2000
+and Hipparcos coordinates only becomes important when accuracies of
+50~mas or better are required.  More details are given in
+Section~4.14.} at the bottom is the
+{\it observed}\/ \azel, where a perfect theodolite would
+be pointed to see the source;  and in the body of
+the diagram are
+the intermediate processing steps and coordinate
+systems.  To help
+understand this diagram, and the SLALIB routines that can
+be used to carry out the various calculations, we will look at the coordinate
+systems involved, and the astronomical phenomena that
+affect them.
+
+\begin{figure}
+\begin{center}
+\begin{tabular}{|cccccc|}   \hline
+& & & & & \\
+\hspace{5em} & \hspace{5em} & \hspace{5em} &
+   \hspace{5em} & \hspace{5em} & \hspace{5em}  \\
+\multicolumn{2}{|c}{\hspace{0em}\fbox{\parbox{8.5em}{\center \vspace{-2ex}
+                                                   mean \radec, FK4, \\
+                                                   any equinox
+                                                   \vspace{0.5ex}}}} &
+ \multicolumn{2}{c}{\hspace{0em}\fbox{\parbox{8.5em}{\center \vspace{-2ex}
+                                                   mean \radec, FK4,
+                                                   no $\mu$, any equinox
+                                                   \vspace{0.5ex}}}} &
+\multicolumn{2}{c|}{\hspace{0em}\fbox{\parbox{8.5em}{\center \vspace{-2ex}
+                                                   mean \radec, FK5, \\
+                                                   any equinox
+                                                   \vspace{0.5ex}}}} \\
+& \multicolumn{2}{|c|}{} & \multicolumn{2}{c|}{} & \\
+\multicolumn{2}{|c}{space motion} & \multicolumn{1}{c|}{} & &
+   \multicolumn{2}{c|}{space motion} \\
+\multicolumn{2}{|c}{-- E-terms} &
+   \multicolumn{2}{c}{-- E-terms} & \multicolumn{1}{c|}{} & \\
+\multicolumn{2}{|c}{precess to B1950} & \multicolumn{2}{c}{precess to B1950} &
+   \multicolumn{2}{c|}{precess to J2000} \\
+\multicolumn{2}{|c}{+ E-terms} &
+   \multicolumn{2}{c}{+ E-terms} & \multicolumn{1}{c|}{} & \\
+\multicolumn{2}{|c}{FK4 to FK5, no $\mu$} &
+   \multicolumn{2}{c}{FK4 to FK5, no $\mu$} & \multicolumn{1}{c|}{} & \\
+\multicolumn{2}{|c}{parallax} & \multicolumn{1}{c|}{} & &
+   \multicolumn{2}{c|}{parallax} \\
+& \multicolumn{2}{|c|}{} & \multicolumn{2}{c|}{} & \\ \cline{2-5}
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{\parbox{18em}{\center \vspace{-2ex}
+                                   FK5, J2000, current epoch, geocentric
+                                          \vspace{0.5ex}}}} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{light deflection} & \\
+& \multicolumn{4}{c}{annual aberration} & \\
+& \multicolumn{4}{c}{precession-nutation} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{Apparent \radec}} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{Earth rotation} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{Apparent \hadec}} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{diurnal aberration} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{Topocentric \hadec}} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\hadec\ to \azel} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{Topocentric \azel}} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{refraction} & \\
+\multicolumn{3}{|c|}{} & & & \\
+& \multicolumn{4}{c}{\fbox{Observed \azel}} & \\
+& & & & & \\
+& & & & & \\ \hline
+\end{tabular}
+\end{center}
+\vspace{-0.5ex}
+\caption{\bf Relationship Between Celestial Coordinates}
+
+Star positions are published or catalogued using
+one of the mean \radec\ systems shown at
+the top.  The ``FK4'' systems
+were used before about 1980 and are usually
+equinox B1950.  The ``FK5'' system, equinox J2000, is now preferred,
+or rather its modern equivalent, the International Celestial Reference
+Frame (in the optical, the Hipparcos catalogue).
+The figure relates a star's mean \radec\ to the actual
+line-of-sight to the star.
+Note that for the conventional choices of equinox, namely
+B1950 or J2000, all of the precession and E-terms corrections
+are superfluous.
+\end{figure}
+
+\subsection{Precession and Nutation}
+{\it Right ascension and declination}, (\radec), are the names
+of the longitude and latitude in a spherical
+polar coordinate system based on the Earth's axis of rotation.
+The zero point of $\alpha$ is the point of intersection of
+the {\it celestial
+equator}\/ and the {\it ecliptic}\/ (the apparent path of the Sun
+through the year) where the Sun moves into the northern
+hemisphere.  This point is called the
+{\it first point of Aries},
+the {\it vernal equinox}\/ (with apologies to
+southern-hemisphere readers) or simply the {\it equinox}.\footnote{With
+the introduction of the International Celestial Reference System (ICRS), the
+connection between (i)~star coordinates and (ii)~the Earth's orientation
+and orbit has been broken.  However, the orientation of the
+International Celestial Reference Frame (ICRF) axes was, for convenience,
+chosen to match J2000 FK5, and for most practical purposes ICRF coordinates
+(for example entries in the Hipparcos catalogue) can be regarded as
+synonymous with J2000 FK5.  See Section 4.14 for further details.}
+
+This simple picture is unfortunately
+complicated by the difficulty of defining
+a suitable equator and equinox.  One problem is that the
+Sun's apparent diurnal and annual
+motions are not completely regular, due to the
+ellipticity of the Earth's orbit and its continuous disturbance
+by the Moon and planets.  This is dealt with by
+separating the motion into (i)~a smooth and steady {\it mean Sun}\/
+and (ii)~a set of periodic corrections and perturbations; only the former
+is involved in establishing reference systems and time scales.
+A second, far larger problem, is that
+the celestial equator and the ecliptic
+are both moving with respect to the stars.
+These motions arise because of the gravitational
+interactions between the Earth and the other solar-system bodies.
+
+By far the largest effect is the
+so-called ``precession of the equinoxes'', where the Earth's
+rotation axis sweeps out a cone centred on the ecliptic
+pole, completing one revolution in about 26,000 years.  The
+cause of the motion is the torque exerted on the distorted and
+spinning Earth by the Sun and the Moon.  Consider the effect of the
+Sun alone, at or near the northern summer solstice.  The Sun
+`sees' the top (north pole) of the Earth tilted towards it
+(by about \degree{23}{5}, the {\it obliquity of the
+ecliptic}\/),
+and sees the nearer part of the Earth's equatorial bulge
+below centre and the further part above centre.
+Although the Earth is in free fall,
+the gravitational force on the nearer part of the
+equatorial bulge is greater than that on the further part, and
+so there is a net torque acting
+as if to eliminate the tilt.  Six months later the same thing
+is happening in reverse, except that the torque is still
+trying to eliminate the tilt.  In between (at the equinoxes) the
+torque shrinks to zero.  A torque acting on a spinning body
+is gyroscopically translated
+into a precessional motion of the spin axis at right-angles to the torque,
+and this happens to the Earth.
+The motion varies during the
+year, going through two maxima, but always acts in the
+same direction.  The Moon produces the same effect,
+adding a contribution to the precession which peaks twice
+per month.  The Moon's proximity to the Earth more than compensates
+for its smaller mass and gravitational attraction, so that it
+in fact contributes most of the precessional effect.
+
+The complex interactions between the three bodies produce a
+precessional motion that is wobbly rather than completely smooth.
+However, the main 26,000-year component is on such a grand scale that
+it dwarfs the remaining terms, the biggest of
+which has an amplitude of only \arcseci{11} and a period of
+about 18.6~years.  This difference of scale makes it convenient to treat
+these two components of the motion separately.  The main 26,000-year
+effect is called {\it luni-solar precession};  the smaller,
+faster, periodic terms are called the {\it nutation}.
+
+Note that precession and nutation are simply
+different frequency components of the same physical effect.  It is
+a common misconception that precession is caused
+by the Sun and nutation is caused by the Moon.  In fact
+the Moon is responsible for two-thirds of the precession, and,
+while it is true that much of the complex detail of the nutation is
+a reflection of the intricacies of the lunar orbit, there are
+nonetheless important solar terms in the nutation.
+
+In addition to and quite separate
+from the precession-nutation effect, the orbit of the Earth-Moon system
+is not fixed in orientation, a result of the attractions of the
+planets.  This slow (about \arcsec{0}{5}~per~year)
+secular rotation of the ecliptic about a slowly-moving diameter is called,
+confusingly, {\it planetary
+precession}\/ and, along with the luni-solar precession is
+included in the {\it general precession}.  The equator and
+ecliptic as affected by general precession
+are what define the various ``mean'' \radec\ reference frames.
+
+The models for precession and nutation come from a combination
+of observation and theory, and are subject to continuous
+refinement.  Nutation models in particular have reached a high
+degree of sophistication, taking into account such things as
+the non-rigidity of the Earth and the effects of
+the planets; SLALIB's nutation
+model (SF2001) involves 194 terms in each of $\psi$ (longitude)
+and $\epsilon$ (obliquity), some as small as a few microarcseconds.
+
+\subsubsection{SLALIB support for precession and nutation}
+SLALIB offers a choice of three precession models:
+\begin{itemize}
+\item The old Bessel-Newcomb, pre IAU~1976, ``FK4'' model, used for B1950
+      star positions and other pre-1984.0 purposes
+(sla\_PREBN).
+\item The new Fricke, IAU~1976, ``FK5'' model, used for J2000 star
+      positions and other post-1984.0 purposes
+(sla\_PREC).
+\item A model published by Simon {\it et al.}\ which is more accurate than
+      the IAU~1976 model and which is suitable for long
+      periods of time
+(sla\_PRECL).
+\end{itemize}
+In each case, the named SLALIB routine generates the $(3\times3)$
+{\it precession
+matrix}\/ for a given start and finish time.  For example,
+here is the Fortran code for generating the rotation
+matrix which describes the precession between the epochs
+J2000 and J1985.372 (IAU 1976 model):
+\goodbreak
+\begin{verbatim}
+            DOUBLE PRECISION PMAT(3,3)
+             :
+            CALL sla_PREC(2000D0,1985.372D0,PMAT)
+\end{verbatim}
+\goodbreak
+It is instructive to examine the resulting matrix:
+\goodbreak
+\begin{verbatim}
+            +0.9999936402  +0.0032709208  +0.0014214694
+            -0.0032709208  +0.9999946505  -0.0000023247
+            -0.0014214694  -0.0000023248  +0.9999989897
+\end{verbatim}
+\goodbreak
+Note that the diagonal elements are close to unity, and the
+other elements are small.  This shows that over an interval as
+short as 15~years the precession isn't going to move a
+position vector very far (in this case about \degree{0}{2}).
+
+For convenience, a direct \radec\ to \radec\ precession routine is
+also provided
+(sla\_PRECES),
+suitable for either the old or the new system (but not a
+mixture of the two).
+
+SLALIB provides two nutation models, the old IAU~1980 model,
+implemented in the routine
+slaNutc80, and a much more accurate newer theory, SF2001,
+implemented in the routine
+slaNutc.
+Both return the components of nutation
+in longitude and latitude (and also provide the obliquity) from
+which a nutation matrix can be generated by calling
+slaDeuler
+(and from which the {\it equation of the equinoxes}, described
+later, can be found).  Alternatively,
+the SF2001 nutation matrix can be generated in a single call by using
+slaNut.  The SF2001 nutation theory includes components that correct
+for errors in the IAU~1976 precession and also for the
+$\sim 23\,$mas
+displacement between the mean J2000 and ICRS coordinate systems,
+achieving a final accuracy well under 1\,mas in the present era.
+
+A rotation matrix for applying the entire precession-nutation
+transformation in one go can be generated by calling
+sla\_PRENUT.
+
+\subsection{Mean Places}
+From a classical standpoint,
+the main effect of the precession-nutation is an increase of about
+\arcseci{50}/year in the ecliptic longitudes of the stars.  It is therefore
+essential, when reporting the position of an astronomical target, to
+qualify the coordinates with a date, or {\it epoch}.
+Specifying the epoch ties down the equator and
+equinox which define the \radec\ coordinate system that is
+being used.
+\footnote{An equinox is, however, not required for coordinates
+in the International Celestial Reference System.  Such coordinates must
+be labelled simply ``ICRS'', or the specific catalogue can be mentioned,
+such as ``Hipparcos'';  constructions such as ``Hipparcos, J2000'' are
+redundant and misleading.}  For simplicity, only
+the smooth and steady ``precession'' part of the
+complete precession-nutation effect is
+included, thereby defining what is called the {\it mean}\/
+equator and equinox for the epoch concerned.  We say a star
+has a mean place of (for example)
+\hms{12}{07}{58}{09}~\dms{-19}{44}{37}{1} ``with respect to the mean equator
+and equinox of epoch J2000''.  The short way of saying
+this is ``\radec\ equinox J2000'' ({\bf not} ``\radec\ epoch J2000'',
+which means something different to do with
+proper motion).
+
+\subsection{Epoch}
+The word ``epoch'' just means a significant
+moment in time, and can be supplied
+in a variety of forms, using different calendar systems and time scales.
+
+For the purpose of specifying the epochs associated with the
+mean place of a star, two conventions exist.  Both sorts of epoch
+superficially resemble years AD but are not tied to the civil
+(Gregorian) calendar;  to distinguish them from ordinary calendar-years
+there is often
+a ``.0'' suffix (as in ``1950.0''), although any other fractional
+part is perfectly legal ({\it e.g.}\ 1987.5).
+
+The older system,
+{\it Besselian epoch}, is defined in such a way that its units are
+tropical years of about 365.2422~days and its time scale is the
+obsolete {\it Ephemeris Time}.
+The start of the Besselian year is the moment
+when the ecliptic longitude of the mean Sun is
+$280^{\circ}$;  this happens near the start of the
+calendar year (which is why $280^{\circ}$ was chosen).
+
+The new system, {\it Julian epoch}, was adopted as
+part of the IAU~1976 revisions (about which more will be said
+in due course) and came formally into use at the
+beginning of 1984.  It uses the Julian year of exactly
+365.25~days; Julian epoch 2000 is defined to be 2000~January~1.5 in the
+TT time scale.
+
+For specifying mean places, various standard epochs are in use, the
+most common ones being Besselian epoch 1950.0 and Julian epoch 2000.0.
+To distinguish the two systems, Besselian epochs
+are now prefixed ``B'' and Julian epochs are prefixed ``J''.
+Epochs without an initial letter can be assumed to be Besselian
+if before 1984.0, otherwise Julian.  These details are supported by
+the SLALIB routines
+sla\_DBJIN
+(decodes numbers from a
+character string, accepting an optional leading B or J),
+sla\_KBJ
+(decides whether B or J depending on prefix or range) and
+sla\_EPCO
+(converts one epoch to match another).
+
+SLALIB has four routines for converting
+Besselian and Julian epochs into other forms.
+The functions
+sla\_EPB2D
+and
+sla\_EPJ2D
+convert Besselian and Julian epochs into MJD; the functions
+sla\_EPB
+and
+sla\_EPJ
+do the reverse.  For example, to express B1950 as a Julian epoch:
+\goodbreak
+\begin{verbatim}
+            DOUBLE PRECISION sla_EPJ,sla_EPB2D
+             :
+            WRITE (*,'(1X,''J'',F10.5)') sla_EPJ(sla_EPB2D(1950D0))
+\end{verbatim}
+\goodbreak
+(The answer is J1949.99979.)
+
+\subsection{Proper Motion}
+Stars in catalogues usually have, in addition to the
+\radec\  coordinates, a {\it proper motion} $[\mu_\alpha,\mu_\delta]$.
+This is an intrinsic motion
+of the star across the background.  Very few stars have a
+proper motion which exceeds \arcseci{1}/year, and most are
+far below this level.  A star observed as part of normal
+astronomy research will, as a rule, have a proper motion
+which is unknown.
+
+Mean \radec\ and rate of change are not sufficient to pin
+down a star;  the epoch at which the \radec\ was or will
+be correct is also needed.  Note the distinction
+between the epoch which specifies the
+coordinate system and the epoch at which the star passed
+through the given \radec.  The full specification for a star
+is \radec, proper motions, equinox and epoch (plus something to
+identify which set of models for the precession {\it etc.}\ is
+being used -- see the next section).
+For convenience, coordinates given in star catalogues are almost
+always adjusted to make the equinox and epoch the same -- for
+example B1950 in the case of the SAO~catalogue.
+
+SLALIB provides one routine to handle proper motion on its own,
+sla\_PM.
+Proper motion is also allowed for in various other
+routines as appropriate, for example
+sla\_MAP
+and
+sla\_FK425.
+Note that in all SLALIB routines which involve proper motion
+the units are radians per year and the
+$\alpha$ component is in the form $\dot{\alpha}$ ({\it i.e.}\ big
+numbers near the poles).
+Some star catalogues have proper motion per century, and
+in some catalogues the $\alpha$ component is in the form
+$\dot{\alpha}\cos\delta$ ({\it i.e.}\ angle on the sky).
+
+\subsection{Parallax and Radial Velocity}
+For the utmost accuracy and the nearest stars, allowance can
+be made for {\it annual parallax}\/ and for the effects of perspective
+on the proper motion.
+
+Parallax is appreciable only for nearby stars;  even
+the nearest, Proxima Centauri, is displaced from its average
+position by less than
+an arcsecond as the Earth revolves in its orbit.
+
+For stars with a known parallax, knowledge of the radial velocity
+allows the proper motion to be expressed as an actual space
+motion in 3~dimensions.  The proper motion is,
+in fact, a snapshot of the transverse component of the
+space motion, and in the case of nearby stars will
+change with time due to perspective.
+
+SLALIB does not provide facilities for handling parallax
+and radial-velocity on their own, but their contribution is
+allowed for in such routines as
+sla\_PM,
+sla\_MAP
+and
+sla\_FK425.
+Catalogue mean
+places do not include the effects of parallax and are therefore
+{\it barycentric};  when pointing telescopes {\it etc.}\ it is
+usually most efficient to apply the slowly-changing
+parallax correction to the mean place of the target early on
+and to work with the {\it geocentric}\/ mean place.  This latter
+approach is implied in Figure~1.
+
+\subsection{Aberration}
+The finite speed of light combined with the motion of the observer
+around the Sun during the year causes apparent displacements of
+the positions of the stars.  The effect is called
+the {\it annual aberration} (or ``stellar''
+aberration).  Its maximum size, about \arcsec{20}{5},
+occurs for stars $90^{\circ}$ from the point towards which
+the Earth is headed as it orbits the Sun;  a star exactly in line with
+the Earth's motion is not displaced.  To receive the light of
+a star, the telescope has to be offset slightly in the direction of
+the Earth's motion.  A familiar analogy is the need to tilt your
+umbrella forward when on the move, to avoid getting wet.  This
+classical model is,
+in fact, misleading in the context of light as opposed
+to rain, but happens to give the same answer as a relativistic
+treatment to first order (better than 1~milliarcsecond).
+
+Before the IAU 1976 resolutions, different
+values for the approximately
+\arcsec{20}{5} {\it aberration constant}\/ were employed
+at different times, and this can complicate comparisons
+between different catalogues.  Another complication comes from
+the so-called {\it E-terms of aberration},
+that small part of the annual aberration correction that is a
+function of the eccentricity of the Earth's orbit.  The E-terms,
+maximum amplitude about \arcsec{0}{3},
+happen to be approximately constant for a given star, and so they
+used to be incorporated in the catalogue \radec\/
+to reduce the labour of converting to and from apparent place.
+The E-terms can be removed from a catalogue \radec\/ by
+calling
+sla\_SUBET
+or applied (for example to allow a pulsar
+timing-position to be plotted on a B1950 finding chart)
+by calling
+sla\_ADDET;
+the E-terms vector itself can be obtained by calling
+sla\_ETRMS.
+Star positions post IAU 1976 are free of these distortions, and to
+apply corrections for annual aberration involves the actual
+barycentric velocity of the Earth rather than the use of
+canonical circular-orbit models.
+
+The annual aberration is the aberration correction for
+an imaginary observer at the Earth's centre.
+The motion of a real observer around the Earth's rotation axis in
+the course of the day makes a small extra contribution to the total
+aberration effect called the {\it diurnal aberration}.  Its
+maximum amplitude is about \arcsec{0}{3}.
+
+No SLALIB routine is provided for calculating the aberration on
+its own, though the required velocity vectors can be
+generated using
+sla\_EVP (or
+sla\_EPV)
+and
+sla\_GEOC.
+Annual and diurnal aberration are allowed for where required, for example in
+sla\_MAP
+{\it etc}.\ and
+sla\_AOP
+{\it etc}.  Note that this sort
+of aberration is different from the {\it planetary
+aberration}, which is the apparent displacement of a solar-system
+body, with respect to the ephemeris position, as a consequence
+of the motion of {\it both}\/ the Earth and the source.  The
+planetary aberration can be computed either by correcting the
+position of the solar-system body for light-time, followed by
+the ordinary stellar aberration correction, or more
+directly by expressing the position and velocity of the source
+in the observer's frame and correcting for light-time alone.
+
+\subsection{Different Sorts of Mean Place}
+A confusing aspect of the mean places used in the
+pre-ICRS era is that they
+are sensitive to the precise way they were determined.  A mean
+place is not directly observable, even with fundamental
+instruments such as transit circles, and to produce one
+will involve relying on some existing star catalogue,
+for example the fundamental catalogues FK4 and FK5,
+and applying given mathematical models of precession, nutation,
+aberration and so on.
+Note in particular that no star catalogue,
+even a fundamental catalogue such as FK4 or
+FK5, defines a coordinate system, strictly speaking;
+it is merely a list of star positions and proper motions.
+However, once the stars from a given catalogue
+are used as position calibrators, {\it e.g.}\ for
+transit-circle observations or for plate reductions, then a
+broader sense of there being a coordinate grid naturally
+arises, and such phrases as ``in the system of
+the FK4'' can legitimately be employed.  However,
+there is no formal link between the
+two concepts -- no ``standard least squares fit'' between
+reality and the inevitably flawed catalogues.
+All such
+catalogues suffer at some level from systematic, zonal distortions
+of both the star positions and of the proper motions,
+and include measurement errors peculiar to individual
+stars.
+
+Many of these complications are of little significance except to
+specialists.  However, observational astronomers cannot
+escape exposure to at least the two main varieties of
+mean place, loosely called
+FK4 and FK5, and should be aware of
+certain pitfalls.  For most practical purposes the more recent
+system, FK5, is free of surprises and tolerates naive
+use well.  FK4, in contrast, contains two important traps:
+\begin{itemize}
+\item The FK4 system rotates at about
+      \arcsec{0}{5} per century relative to distant galaxies.
+      This is manifested as a systematic distortion in the
+      proper motions of all FK4-derived catalogues, which will
+      in turn pollute any astrometry done using those catalogues.
+      For example, FK4-based astrometry of a QSO using plates
+      taken decades apart will reveal a non-zero {\it fictitious proper
+      motion}, and any FK4 star which happens to have zero proper
+      motion is, in fact, slowly moving against the distant
+      background.  The FK4 frame rotates because it was
+      established before the nature of the Milky Way, and hence the
+      existence of systematic motions of nearby stars, had been
+      recognized.
+\item Star positions in the FK4 system are part-corrected for
+      annual aberration (see above) and embody the so-called
+      E-terms of aberration.
+\end{itemize}
+The change from the old FK4-based system to FK5
+occurred at the beginning
+of 1984 as part of a package of resolutions made by the IAU in 1976,
+along with the adoption of J2000 as the reference epoch.  Star
+positions in the newer, FK5, system are free from the E-terms, and
+the system is a much better approximation to an
+inertial frame -- about five times better (and ICRS is hundreds
+of times better still).
+
+It may occasionally be convenient to specify the FK4 fictitious proper
+motion directly.  In FK4, the centennial proper motion of (for example)
+a QSO is:
+
+$\mu_\alpha=-$\tsec{0}{015869}$
+          +(($\tsec{0}{029032}$~\sin \alpha
+            +$\tsec{0}{000340}$~\cos \alpha ) \sin \delta
+            -$\tsec{0}{000105}$~\cos \alpha
+            -$\tsec{0}{000083}$~\sin \alpha ) \sec \delta $ \\
+$\mu_\delta\,=+$\arcsec{0}{43549}$~\cos \alpha
+              -$\arcsec{0}{00510}$~\sin \alpha +
+              ($\arcsec{0}{00158}$~\sin \alpha
+              -$\arcsec{0}{00125}$~\cos \alpha ) \sin \delta
+              -$\arcsec{0}{00066}$~\cos \delta $
+
+\subsection{Mean Place Transformations}
+Figure~1 is based upon three varieties of mean \radec\ all of which are
+of practical significance to observing astronomers in the present era:
+\begin{itemize}
+   \item Old style (FK4) with known proper motion in the FK4
+         system, and with parallax and radial velocity either
+         known or assumed zero.
+   \item Old style (FK4) with zero proper motion in FK5,
+         and with parallax and radial velocity assumed zero.
+   \item New style (FK5 or, loosely, ICRS)
+         with proper motion, parallax and
+         radial velocity either known or assumed zero.
+\end{itemize}
+The figure outlines the steps required to convert positions in
+any of these systems to a J2000 \radec\ for the current
+epoch, as might be required in a telescope-control
+program for example.
+Most of the steps can be carried out by calling a single
+SLALIB routine;  there are other SLALIB routines which
+offer set-piece end-to-end transformation routines for common cases.
+Note, however, that SLALIB does not set out to provide the capability
+for arbitrary transformations of star-catalogue data
+between all possible systems of mean \radec.
+Only in the (common) cases of FK4, equinox and epoch B1950,
+to FK5, equinox and epoch J2000, and {\it vice versa}\/ are
+proper motion, parallax and radial velocity transformed
+along with the star position itself, the
+focus of SLALIB support.
+
+As an example of using SLALIB to transform mean places, here is
+Fortran code that implements the top-left path of Figure~1.
+An FK4 \radec\ of arbitrary equinox and epoch and with
+known proper motion and
+parallax is transformed into an FK5 J2000 \radec\ for the current
+epoch.  As a test star we will use $\alpha=$\hms{16}{09}{55}{13},
+$\delta=$\dms{-75}{59}{27}{2}, equinox 1900, epoch 1963.087,
+$\mu_\alpha=$\tsec{-0}{0312}$/y$, $\mu_\delta=$\arcsec{+0}{103}$/y$,
+parallax = \arcsec{0}{062}, radial velocity = $-34.22$~km/s.  The
+date of observation is 1994.35.
+\goodbreak
+\begin{verbatim}
+            IMPLICIT NONE
+            DOUBLE PRECISION AS2R,S2R
+            PARAMETER (AS2R=4.8481368110953599D-6,S2R=7.2722052166430399D-5)
+            INTEGER J,I
+            DOUBLE PRECISION R0,D0,EQ0,EP0,PR,PD,PX,RV,EP1,R1,D1,R2,D2,R3,D3,
+           :                 R4,D4,R5,D5,R6,D6,EP1D,EP1B,W(3),EB(3),PXR,V(3)
+            DOUBLE PRECISION sla_EPB,sla_EPJ2D
+
+      *  RA, Dec etc of example star
+            CALL sla_DTF2R(16,09,55.13D0,R0,J)
+            CALL sla_DAF2R(75,59,27.2D0,D0,J)
+            D0=-D0
+            EQ0=1900D0
+            EP0=1963.087D0
+            PR=-0.0312D0*S2R
+            PD=+0.103D0*AS2R
+            PX=0.062D0
+            RV=-34.22D0
+            EP1=1994.35D0
+
+      *  Epoch of observation as MJD and Besselian epoch
+            EP1D=sla_EPJ2D(EP1)
+            EP1B=sla_EPB(EP1D)
+
+      *  Space motion to the current epoch
+            CALL sla_PM(R0,D0,PR,PD,PX,RV,EP0,EP1B,R1,D1)
+
+      *  Remove E-terms of aberration for the original equinox
+            CALL sla_SUBET(R1,D1,EQ0,R2,D2)
+
+      *  Precess to B1950
+            R3=R2
+            D3=D2
+            CALL sla_PRECES('FK4',EQ0,1950D0,R3,D3)
+
+      *  Add E-terms for the standard equinox B1950
+            CALL sla_ADDET(R3,D3,1950D0,R4,D4)
+
+      *  Transform to J2000, no proper motion
+            CALL sla_FK45Z(R4,D4,EP1B,R5,D5)
+
+      *  Parallax
+            CALL sla_EVP(sla_EPJ2D(EP1),2000D0,W,EB,W,W)
+            PXR=PX*AS2R
+            CALL sla_DCS2C(R5,D5,V)
+            DO I=1,3
+               V(I)=V(I)-PXR*EB(I)
+            END DO
+            CALL sla_DCC2S(V,R6,D6)
+             :
+\end{verbatim}
+\goodbreak
+It is interesting to look at how the \radec\ changes during the
+course of the calculation:
+\begin{tabbing}
+xxxxxxxxxxxxxx \= xxxxxxxxxxxxxxxxxxxxxxxxx \= x \= \kill
+\> {\tt 16 09 55.130 -75 59 27.20} \> \> {\it original equinox and epoch} \\
+\> {\tt 16 09 54.155 -75 59 23.98} \> \> {\it with space motion} \\
+\> {\tt 16 09 54.229 -75 59 24.18} \> \> {\it with old E-terms removed} \\
+\> {\tt 16 16 28.213 -76 06 54.57} \> \> {\it precessed to 1950.0} \\
+\> {\tt 16 16 28.138 -76 06 54.37} \> \> {\it with new E-terms} \\
+\> {\tt 16 23 07.901 -76 13 58.87} \> \> {\it J2000, current epoch} \\
+\> {\tt 16 23 07.907 -76 13 58.92} \> \> {\it including parallax}
+\end{tabbing}
+
+Other remarks about the above (unusually complicated) example:
+\begin{itemize}
+\item If the original equinox and epoch were B1950, as is quite
+      likely, then it would be unnecessary to treat space motions
+      and E-terms explicitly.  Transformation to FK5 J2000 could
+      be accomplished simply by calling
+sla\_FK425, after which
+      a call to
+sla\_PM and the parallax code would complete the
+      work.
+\item The rigorous treatment of the E-terms
+      has only a small effect on the result.  Such refinements
+      are, nevertheless, worthwhile in order to facilitate comparisons and
+      to increase the chances that star positions from different
+      suppliers are compatible.
+\item The FK4 to FK5 transformations,
+sla\_FK425
+      and
+sla\_FK45Z,
+      are not as is sometimes assumed simply 50 years of precession,
+      though this indeed accounts for most of the change.  The
+      transformations also include adjustments
+      to the equinox, a revised precession model, elimination of the
+      E-terms, a change to the proper-motion time unit and so on.
+      The reason there are two routines rather than just one
+      is that the FK4 frame rotates relative to the background, whereas
+      the FK5 frame is a much better approximation to an
+      inertial frame, and zero proper
+      motion in FK4 does not, therefore, mean zero proper motion in FK5.
+      SLALIB also provides two routines,
+sla\_FK524
+      and
+sla\_FK54Z,
+      to perform the inverse transformations.
+\item Some star catalogues (FK4 itself is one) were constructed using slightly
+      different procedures for the polar regions compared with
+      elsewhere.  SLALIB ignores this inhomogeneity and always
+      applies the standard
+      transformations, irrespective of location on the celestial sphere.
+\end{itemize}
+
+\subsection {Mean Place to Apparent Place}
+The {\it geocentric apparent place}\/ of a source, or {\it apparent place}\/
+for short,
+is the \radec\ if viewed from the centre of the Earth,
+with respect to the true equator and equinox of date.
+Transformation of an FK5 mean \radec, equinox J2000,
+current epoch, to apparent place involves the following effects:
+\goodbreak
+\begin{itemize}
+   \item Light deflection -- the gravitational lens effect of
+         the sun.
+   \item Annual aberration.
+   \item Precession-nutation.
+\end{itemize}
+The {\it light deflection}\/ is seldom significant.  Its value
+at the limb of the Sun is about
+\arcsec{1}{74};  it falls off rapidly with distance from the
+Sun and has shrunk to about
+\arcsec{0}{02} at an elongation of $20^\circ$.
+
+As already described, the {\it annual aberration}\/
+is a function of the Earth's velocity
+relative to the solar system barycentre (available through the
+SLALIB routines
+sla\_EVP and
+sla\_EPV)
+and produces shifts of up to about \arcsec{20}{5}.
+
+The {\it precession-nutation}, from J2000 to the current epoch, is
+expressed by a rotation matrix which is available through the
+SLALIB routine
+sla\_PRENUT.
+
+The whole mean-to-apparent transformation can be done using the SLALIB
+routine
+sla\_MAP.  As a demonstration, here is a program which lists the
+{\it North Polar Distance}\/ ($90^\circ-\delta$) of Polaris for
+the decade of closest approach to the Pole:
+\goodbreak
+\begin{verbatim}
+            IMPLICIT NONE
+            DOUBLE PRECISION PI,PIBY2,D2R,S2R,AS2R
+            PARAMETER (PI=3.141592653589793238462643D0)
+            PARAMETER (D2R=PI/180D0,
+           :           PIBY2=PI/2D0,
+           :           S2R=PI/(12D0*3600D0),
+           :           AS2R=PI/(180D0*3600D0))
+            DOUBLE PRECISION RM,DM,PR,PD,DATE,RA,DA
+            INTEGER J,IDS,IDE,ID,IYMDF(4),I
+
+            CALL sla_DTF2R(02,31,49.8131D0,RM,J)
+            CALL sla_DAF2R(89,15,50.661D0,DM,J)
+            PR=+21.7272D0*S2R/100D0
+            PD=-1.571D0*AS2R/100D0
+            WRITE (*,'(1X,'//
+           :            '''Polaris north polar distance (deg) 2096-2105''/)')
+            WRITE (*,'(4X,''Date'',7X''NPD''/)')
+            CALL sla_CLDJ(2096,1,1,DATE,J)
+            IDS=NINT(DATE)
+            CALL sla_CLDJ(2105,12,31,DATE,J)
+            IDE=NINT(DATE)
+            DO ID=IDS,IDE,10
+               DATE=DBLE(ID)
+               CALL sla_DJCAL(0,DATE,IYMDF,J)
+               CALL sla_MAP(RM,DM,PR,PD,0D0,0D0,2000D0,DATE,RA,DA)
+               WRITE (*,'(1X,I4,2I3.2,F9.5)') (IYMDF(I),I=1,3),(PIBY2-DA)/D2R
+            END DO
+
+            END
+\end{verbatim}
+\goodbreak
+For cases where the transformation has to be repeated for different
+times or for more than one star, the straightforward
+sla\_MAP
+approach is apt to be
+wasteful as both the Earth velocity and the
+precession-nutation matrix can be re-calculated relatively
+infrequently without ill effect.  A more efficient method is to
+perform the target-independent calculations only when necessary,
+by calling
+sla\_MAPPA,
+and then to use either
+sla\_MAPQKZ,
+when only the \radec\/ is known, or
+sla\_MAPQK,
+when full catalogue positions, including proper motion, parallax and
+radial velocity, are available.  How frequently to call
+sla\_MAPPA
+depends on the accuracy objectives;  once per
+night will deliver sub-arcsecond accuracy for example.
+
+The routines
+sla\_AMP
+and
+sla\_AMPQK
+allow the reverse transformation, from apparent to mean place.
+
+\subsection{Apparent Place to Observed Place}
+The {\it observed place}\/ of a source is its position as
+seen by a perfect theodolite at the location of the
+observer.  Transformation of an apparent \radec\ to observed
+place involves the following effects:
+\goodbreak
+\begin{itemize}
+   \item \radec\ to \hadec.
+   \item Diurnal aberration.
+   \item \hadec\ to \azel.
+   \item Refraction.
+\end{itemize}
+The transformation from apparent \radec\ to
+apparent \hadec\ is made by allowing for
+{\it Earth rotation}\/ through the {\it sidereal time}, $\theta$:
+\[ h = \theta - \alpha \]
+For this equation to work, $\alpha$ must be the apparent right
+ascension for the time of observation, and $\theta$ must be
+the {\it local apparent sidereal time}.  The latter is obtained
+as follows:
+\begin{enumerate}
+\item from civil time obtain the coordinated universal time, UTC
+      (more later on this);
+\item add the UT1$-$UTC (typically a few tenths of a second) to
+      give the UT;
+\item from the UT compute the Greenwich mean sidereal time (using
+sla\_GMST);
+\item add the observer's (east) longitude, giving the local mean
+      sidereal time;
+\item add the equation of the equinoxes (using
+sla\_EQEQX).
+\end{enumerate}
+The {\it equation of the equinoxes}\/~($=\Delta\psi\cos\epsilon$ plus
+small terms)
+is the effect of nutation on the sidereal time.
+Its value is typically a second or less.  It is
+interesting to note that if the object of the exercise is to
+transform a mean place all the way into an observed place (very
+often the case),
+then the equation of the
+equinoxes and the longitude component of nutation can both be
+omitted, removing a great deal of computation.  However, SLALIB
+follows the normal convention and  works {\it via}\/ the apparent place.
+
+Note that for very precise work the observer's longitude should
+be corrected for {\it polar motion}.  This can be done with
+sla\_POLMO.
+The corrections are always less than about \arcsec{0}{3}, and
+are futile unless the position of the observer's telescope is known
+to better than a few metres.
+
+Tables of observed and
+predicted UT1$-$UTC corrections and polar motion data
+are published every few weeks by the International Earth Rotation Service.
+
+The transformation from apparent \hadec\ to {\it topocentric}\/
+\hadec\ consists of allowing for
+{\it diurnal aberration}.  This effect, maximum amplitude \arcsec{0}{2},
+was described earlier.  There is no specific SLALIB routine
+for computing the diurnal aberration,
+though the routines
+sla\_AOP {\it etc.}\
+include it, and the required velocity vector can be
+determined by calling
+sla\_GEOC.
+
+The next stage is the major coordinate rotation from local equatorial
+coordinates \hadec\ into horizon coordinates.  The SLALIB routines
+sla\_E2H
+{\it etc.}\ can be used for this.  For high-precision
+applications the mean geodetic latitude should be corrected for polar
+motion.
+
+\subsubsection{Refraction}
+The final correction is for atmospheric refraction.
+This effect, which depends on local meteorological conditions and
+the effective colour of the source/detector combination,
+increases the observed elevation of the source by a
+significant effect even at moderate zenith distances, and near the
+horizon by over \degree{0}{5}.  The amount of refraction can by
+computed by calling the SLALIB routine
+sla\_REFRO;
+however,
+this requires as input the observed zenith distance, which is what
+we are trying to predict.  For high precision it is
+therefore necessary to iterate, using the topocentric
+zenith distance as the initial estimate of the
+observed zenith distance.
+
+The full
+sla\_REFRO refraction calculation is onerous, and for
+zenith distances of less than, say, $75^{\circ}$ the following
+model can be used instead:
+
+\[ \zeta _{vac} \approx \zeta _{obs}
+                     + A \tan \zeta _{obs}
+                     + B \tan ^{3}\zeta _{obs} \]
+where $\zeta _{vac}$ is the topocentric
+zenith distance (i.e.\ {\it in vacuo}),
+$\zeta _{obs}$ is the observed
+zenith distance (i.e.\ affected by refraction), and $A$ and $B$ are
+constants, about \arcseci{60}
+and \arcsec{-0}{06} respectively for a sea-level site.
+The two constants can be calculated for a given set of conditions
+by calling either
+sla\_REFCO or
+sla\_REFCOQ.
+
+sla\_REFCO works by calling
+sla\_REFRO for two zenith distances and fitting $A$ and $B$
+to match.  The calculation is onerous, but delivers accurate
+results whatever the conditions.
+sla\_REFCOQ uses a direct formulation of $A$ and $B$ and
+is much faster;  it is slightly less accurate than
+sla\_REFCO but more than adequate for most practical purposes.
+
+Like the full refraction model, the two-term formulation works in the wrong
+direction for our purposes, predicting
+the {\it in vacuo}\/ (topocentric) zenith distance
+given the refracted (observed) zenith distance,
+rather than {\it vice versa}.  The obvious approach of
+interchanging $\zeta _{vac}$ and $\zeta _{obs}$ and
+reversing the signs, though approximately
+correct, gives avoidable errors which are just significant in
+some applications;  for
+example about \arcsec{0}{2} at $70^\circ$ zenith distance.  A
+much better result can easily be obtained, by using one Newton-Raphson
+iteration as follows:
+
+\[ \zeta _{obs} \approx \zeta _{vac}
+    - \frac{A \tan \zeta _{vac} + B \tan ^{3}\zeta _{vac}}
+    {1 + ( A + 3 B \tan ^{2}\zeta _{vac} ) \sec ^{2}\zeta _{vac}}\]
+
+The effect of refraction can be applied to an unrefracted
+zenith distance by calling
+sla\_REFZ or to an unrefracted
+\xyz\ by calling
+sla\_REFV.
+Over most of the sky these two routines deliver almost identical
+results, but beyond $\zeta=83^\circ$
+sla\_REFV
+becomes unacceptably inaccurate while
+sla\_REFZ
+remains usable.  (However
+sla\_REFV
+is significantly faster, which may be important in some applications.)
+SLALIB also provides a routine for computing the airmass, the function
+sla\_AIRMAS.
+
+The refraction ``constants'' returned by
+sla\_REFCO and
+sla\_REFCOQ
+are slightly affected by colour, especially at the blue end
+of the spectrum.  Where values for more than one
+wavelength are needed, rather than calling
+sla\_REFCO
+several times it is more efficient to call
+sla\_REFCO
+just once, for a selected ``base'' wavelength, and then to call
+sla\_ATMDSP
+once for each wavelength of interest.
+
+All the SLALIB refraction routines work for radio wavelengths as well
+as the optical/IR band.  The radio refraction is very dependent on
+humidity, and an accurate value must be supplied.  There is no
+wavelength dependence, however.  The choice of optical/IR or
+radio is made by specifying a wavelength greater than $100\mu {\rm m}$
+for the radio case.
+
+\subsubsection{Efficiency considerations}
+The complete apparent place to observed place transformation
+can be carried out by calling
+sla\_AOP.
+For improved efficiency
+in cases of more than one star or a sequence of times, the
+target-independent calculations can be done once by
+calling
+sla\_AOPPA,
+the time can be updated by calling
+sla\_AOPPAT,
+and
+sla\_AOPQK
+can then be used to perform the
+apparent-to-observed transformation.  The reverse transformation
+is available through
+sla\_OAP
+and
+sla\_OAPQK.
+({\it n.b.}\ These routines use accurate but computationally-expensive
+refraction algorithms for zenith distances beyond about $76^\circ$.
+For many purposes, in-line code tailored to the accuracy requirements
+of the application will be preferable, for example ignoring
+polar motion,
+omitting diurnal aberration and using
+sla\_REFZ
+to apply the refraction.)
+
+\subsection{The Hipparcos Catalogue and the ICRS}
+With effect from the beginning of 1998, the IAU adopted a new
+reference system to replace FK5 J2000.  The new system, called the
+International Celestial Reference System (ICRS), differs profoundly
+from all predecessors in that the link with solar-system dynamics
+was broken;  the ICRS axes are defined in terms of the coordinates
+of a set of extragalactic sources, not in terms of the mean equator and
+equinox at a given reference epoch.  Although the ICRS and FK5 coordinates
+of any given object are almost the same, the orientation of the new frame
+was essentially arbitrary, and the close match to FK5 J2000 was contrived
+purely for reasons of continuity and convenience.
+
+A distinction is made between the reference {\it system}\/ (the ICRS)
+and {\it frame}\/ (ICRF).  The ICRS is the set of prescriptions and
+conventions together with the modelling required to define, at any
+time, a triad of axes.  The ICRF is a practical realization, and
+currently consists of a catalogue of equatorial coordinates for 608
+extragalactic radio sources observed by VLBI.
+
+The best optical realization of the ICRF currently available is the
+Hipparcos catalogue.  The extragalactic sources were not directly
+observable by the Hipparcos satellite and so the link from Hipparcos
+to ICRF was established through a variety of indirect techniques: VLBI and
+conventional interferometry of radio stars, photographic astrometry
+and so on.  The Hipparcos frame is aligned to the ICRF to within about
+0.5~mas and 0.5~mas/year (at epoch 1991.25).
+
+The Hipparcos catalogue includes all of the FK5 stars, which has enabled
+the orientation and spin of the latter to be studied.  At epoch J2000,
+the misalignment of the FK5 frame with respect to Hipparcos
+(and hence ICRS) are about 32~mas and 1~mas/year respectively.
+Consequently, for many practical purposes, including pointing
+telescopes, the IAU 1976-1982 conventions on reference frames and
+Earth orientation remain adequate and there is no need to change to
+Hipparcos coordinates, new precession-nutation models and so on.
+However, for the most exacting astrometric applications, SLALIB
+provides some support for Hipparcos coordinates in the form of
+four new routines:
+sla\_FK52H and
+sla\_H2FK5,
+which transform FK5 positions and proper motions to the Hipparcos frame
+and {\it vice versa,}\/ and
+sla\_FK5HZ and
+sla\_HFK5Z,
+where the transformations are for stars whose Hipparcos proper motion is
+zero.
+
+Further information on the ICRS can be found in the paper by M.\,Feissel
+and F.\,Mignard, Astron.\,Astrophys. 331, L33-L36 (1988).
+
+\subsection{Time Scales}
+
+SLALIB provides for transformation between several time scales, and involves
+use of one or two others.  The full list is as follows:
+\begin{itemize}
+\item TAI: International Atomic Time
+\item UTC: Coordinated Universal Time
+\item TT: Terrestrial Time
+\item TDB: Barycentric Dynamical Time.
+\item UT: Universal Time
+\item GMST: Greenwich mean sidereal time
+\item GAST (or GST): Greenwich apparent sidereal time.
+\item LAST: local apparent sidereal time
+\end{itemize}
+Strictly speaking, UT and the sidereal times are not {\it times}\/ in
+the physics sense, but {\it angles}\/ that describe Earth rotation.
+
+Three obsolete time scales should be mentioned here to avoid confusion.
+\begin{itemize}
+\item GMT: Greenwich Mean Time -- can mean either UTC or UT.
+\item ET: Ephemeris Time -- more or less the same as either TT or TDB.
+\item TDT: Terrestrial Dynamical Time -- former name of TT.
+\end{itemize}
+
+time scales that have no SLALIB support at present:
+\begin{itemize}
+\item Any form of local civil time (BST, PDT {\it etc.})
+\item TCG: geocentric coordinate time.
+\item TCB: barycentric coordinate time.
+\end{itemize}
+
+\subsubsection{Atomic Time: TAI}
+{\it International Atomic Time,} TAI, is a ``laboratory''
+time scale with no link to astronomical observations
+except in an historical sense.  Its
+unit is the SI second, which is defined in terms of a
+specific number
+of wavelengths of the radiation produced by a certain electronic
+transition in the caesium 133 atom.  It
+is realized through a changing
+population of high-precision atomic clocks held
+at standards institutes in various countries.  There is an
+elaborate process of continuous intercomparison, leading to
+a weighted average of all the clocks involved.
+
+Though TAI shares the same second as the more familiar UTC, the
+two time scales are noticeably separated in epoch because of the
+build-up of leap seconds (see the next section).
+At the time of writing, UTC
+lags over half a minute behind TAI.
+
+For any given date, the difference TAI$-$UTC
+can be obtained by calling the SLALIB function
+sla\_DAT.
+Note, however, that an up-to-date copy of the function must be used if
+the most recent leap seconds are required.  For applications
+where this is critical, mechanisms independent of SLALIB
+and under local control must
+be set up;  in such cases
+sla\_DAT
+can be useful as an
+independent check, for test dates within the range of the
+available version.  Up-to-date information on TAI$-$UTC is available
+from {\tt ftp://maia.usno.navy.mil/ser7/tai-utc.dat}.
+
+\subsubsection{Universal Time: UT, UTC}
+\label{UTC}
+{\it Universal Time,} UT, or more specifically UT1,
+is in effect mean solar time and is really an expression
+of Earth rotation rather than a measure of time.
+Originally
+defined in terms of a point in the sky called ``the fictitious
+mean Sun'', UT is now defined through its relationship
+with Earth rotation angle
+(formerly sidereal time).
+Because the Earth's rotation rate is slightly irregular and
+gradually decreasing,\footnote{The Earth is slowing
+down because of tidal effects.  The SI
+second reflects the length-of-day in the mid-19th century, when
+the astronomical observations that established modern timekeeping
+were being made.  Since then,
+the average length-of-day has increased by roughly 2~ms.
+Superimposed in this gradual slowdown are
+variations (seasonal and decadal) that are geophysical in origin,
+notably due to large scale movements of water and atmosphere.
+Because of
+conservation of angular momentum, as the Earth's rotation-rate
+decreases, the Moon moves farther away.  In 50 billion years the
+distance of the Moon will be at a maximum, 44\% greater than now, at
+which stage day and month will both equal 47 present days.}
+the UT second is not precisely
+matched to the SI second.  This makes UT itself unsuitable for
+use as a time scale.
+
+That role is instead taken by
+{\it Coordinated Universal Time,} UTC, which is clock-based and
+is the foundation of civil timekeeping.
+Most time zones differ from UTC by an integer number
+of hours, though a few ({\it e.g.}\ parts of Canada and Australia) differ
+by $n+0.5$~hours.  Since its introduction, UTC has been kept
+roughly in step with UT by a variety of adjustments that are
+agreed in advance and then carried out in a coordinated manner by
+the timekeeping communities of different countries---hence the
+name.  Though rate
+changes were used in the past, nowadays all such adjustments
+are made by occasionally inserting
+a whole second.  This procedure is called
+a {\it leap second}.  Because the day length is now slightly longer
+than 86400 SI seconds, a leap second amounts to stopping the UTC
+clock for a second to let the Earth catch up.
+
+You need UT1 in order to point a telescope or antenna at a
+celestial target.  To obtain it
+starting from UTC, you
+have to look up the value of UT1$-$UTC for the date concerned
+in tables published by the International Earth Rotation and
+reference frames
+Service;  this quantity, kept in the range
+$\pm$\tsec{0}{9} by means of leap
+seconds, is then added to the UTC.  The quantity UT1$-$UTC,
+which typically changes by of order 1~ms per day,
+can be obtained only by observation (VLBI using
+extragalactic radio sources), though seasonal trends
+are well known and the IERS listings are able to predict some way into
+the future with adequate accuracy for pointing telescopes.
+
+UTC leap seconds are introduced as necessary,
+usually at the end of December or June.
+Because on the average the solar day is slightly longer
+than the nominal 86,400~SI~seconds, leap seconds are always positive;
+however, provision exists for negative leap seconds if needed.
+The form of a leap second can be seen from the
+following description of the end of June~1994:
+
+\hspace{3em}
+\begin{tabular}{clrccc} \\
+     &      &    &   UTC    & UT1$-$UTC  &    UT1       \\ \\
+1994 & June & 30 & 23 59 58 & $-0.218$ & 23 59 57.782 \\
+     &      &    & 23 59 59 & $-0.218$ & 23 59 58.782 \\
+     &      &    & 23 59 60 & $-0.218$ & 23 59 59.782 \\
+     & July &  1 & 00 00 00 & $+0.782$ & 00 00 00.782 \\
+     &      &    & 00 00 01 & $+0.782$ & 00 00 01.782 \\
+\end{tabular}
+\goodbreak
+
+Note that UTC has to be expressed as hours, minutes and
+seconds (or at least in seconds for a given date) if leap seconds
+are to be taken into account in the
+correct manner.
+It is improper to express a UTC as a
+Julian Date, for example, because there will be an ambiguity
+during a leap second (in the above example,
+1994~June~30 \hms{23}{59}{60}{0} and
+1994~July~1 \hms{00}{00}{00}{0} would {\it both}\/ come out as
+MJD~49534.00000).  Although in the vast majority of
+cases this won't matter, there are potential problems in
+on-line data acquisition systems and in applications involving
+taking the difference between two times.  Note that although the functions
+sla\_DAT
+and
+sla\_DTT
+expect UTC in the form of an MJD, the meaning here is really a
+whole-number {\it date}\/ rather than a time.
+Though the functions will accept
+a fractional part and will almost always function correctly, on a day
+which ends with a leap
+second incorrect results would be obtained during the leap second
+itself because by then the MJD would have moved into the next day.
+
+\subsubsection{Sidereal Time: GMST, LAST {\it etc.}}
+Sidereal time is like the time of day but relative to the
+stars rather than to the Sun.  After
+one sidereal day the stars come back to the same place in the
+sky, apart from sub-arcsecond precession effects.  Because the Earth
+rotates faster relative to the stars than to the Sun by one day
+per year, the sidereal second is shorter than the solar
+second; the ratio is about 0.9973.
+
+The {\it Greenwich mean sidereal time,} GMST, is
+linked to UT1 by a numerical formula which
+is implemented in the SLALIB functions
+sla\_GMST
+and
+sla\_GMSTA.
+There are, of course, no leap seconds in GMST, but the sidereal
+second (measured in SI seconds)
+changes in length along with the UT1 second, and also varies
+over long periods of time because of slow changes in the Earth's
+orbit.  This makes sidereal time unsuitable for everything except
+predicting the apparent directions of celestial sources, in other
+words as an angle rather than a time.
+
+The {\it local apparent sidereal time,} LAST, is the apparent right
+ascension of the local meridian, from which the hour angle of any
+star can be determined knowing its right
+ascension.  LAST can be obtained from the
+GMST by adding the east longitude (corrected for polar motion
+in precise work) and the {\it equation of the equinoxes}.  The
+latter, already described, is an aspect of the nutation effect
+and can be predicted by calling the SLALIB function
+sla\_EQEQX
+or, neglecting certain very small terms, by calling
+sla\_NUTC
+and using the expression $\Delta\psi\cos\epsilon$.
+
+GAST, or plain GST, is GMST plus the equation of the equinoxes.
+
+\subsubsection{Dynamical Time: TT, TDB}
+Dynamical time (formerly Ephemeris Time, ET)
+is the independent variable in the theories
+which describe the motions of bodies in the solar system.  When
+using published formulae or
+tables that model the position of the
+Earth in its orbit, for example, or look up
+the Moon's position in a precomputed ephemeris, the date and time
+must be in terms of one of the dynamical time scales.  It
+is a common but understandable mistake to use UTC directly, in which
+case the results will be over a minute out (at the time of writing).
+
+It is not hard to see why such time scales are necessary.
+UTC would clearly be unsuitable as the argument of an
+ephemeris because of leap seconds.
+A solar-system ephemeris based on UT1 or sidereal time would somehow
+have to include the unpredictable variations of the Earth's rotation.
+TAI would work, but in principle
+the ephemeris and the ensemble of atomic clocks would
+eventually drift apart.
+In effect, the ephemeris {\it is}\/ a clock, with the bodies of
+the solar system the hands from which the ephemeris time is read.
+
+Only two of the dynamical time scales are of any great importance to
+observational astronomers, TT and TDB.
+
+{\it Terrestrial Time,} TT, is
+the theoretical time scale of apparent geocentric ephemerides of solar
+system bodies.  It applies to clocks at sea-level, and for practical purposes
+it is tied to
+Atomic Time TAI through the formula TT~$=$~TAI~$+$~\tsec{32}{184}.
+In practice, therefore, the units of TT are ordinary SI seconds, and
+the offset of \tsec{32}{184} with respect to TAI is fixed.
+The SLALIB function
+sla\_DTT
+returns TT$-$UTC for a given UTC
+({\it n.b.}~sla\_DTT
+calls
+sla\_DTT,
+and the latter must be an up-to-date version if recent leap seconds are
+to be taken into account).
+
+{\it Barycentric Dynamical Time,} TDB, is a
+{\it coordinate time,} suitable
+for labelling events that are most simply described in a context
+where the bodies of the solar system
+are absent.  Applications include
+the emission of pulsar radiation and the motions of the
+solar-system bodies themselves.  When the readings of the
+observer's TT clock are labelled using such a
+coordinate time, differences
+are seen because the clock is affected by its
+speed in the barycentric coordinate system
+and the gravitational potential in which it is immersed.  Equivalently,
+observations of pulsars
+expressed in TT would display similar variations (quite
+apart from the familiar light-time effects).
+
+TDB is defined in such a way that it keeps close to TT
+on the average, with the relativistic effects emerging as
+quasi-periodic differences of maximum amplitude rather less
+than 2\,ms.  This is
+negligible for many purposes, so that TT can act as
+a perfectly adequate surrogate for TDB in most cases,
+but unless taken into
+account would swamp
+long-term analysis of pulse arrival times from the
+millisecond pulsars.
+
+Most of the variation between TDB and TT comes from the ellipticity of
+the Earth's orbit;  the TT clock's speed and
+gravitational potential vary slightly
+during the course of the year, and as a consequence
+its rate as seen from an outside observer
+varies due to transverse Doppler effect and gravitational
+redshift.  The main component is a sinusoidal variation of
+amplitude \tsec{0}{0017};  higher harmonics, and terms
+caused by Moon and planets, lie two orders of magnitude below
+this dominant annual term.  Diurnal (topocentric) terms, a
+function of UT, are $2\,\mu$s or less.
+
+The IAU 1976 resolution defined TDB by
+stipulating that TDB$-$TT consists of periodic terms only.
+This provided
+a good qualitative description, but turned out to
+contain hidden assumptions about the form of the
+solar-system ephemeris and hence lacked dynamical
+rigour.  A later resolution, in 1991, introduced new
+coordinate time scales, TCG and TCB, and identified TDB as a
+linear transformation of one of them (TCB) with a rate
+chosen not to drift from TT on the average.  Unfortunately
+even this improved definition has proved to
+contin ambiguities.  The SLALIB
+sla\_RCC function implements TDB in the way that is
+most consistent with the 1976 definition and
+with existing practice.  It provides a model of
+TDB$-$TT accurate to a few nanoseconds.
+
+Unlike TDB, the IAU 1991 coordinate time scales TCG and TCB
+(not supported by SLALIB functions at present)
+do not have their rates adjusted to track TT and consequently
+gain on TT and TDB, by about
+\tsec{0}{02}/year and \tsec{0}{5}/year respectively.
+
+As already pointed out, the distinction between TT and TDB is
+of no practical importance for most purposes.  For
+example when calling
+sla\_PRENUT
+to generate a precession-nutation matrix, or when calling
+sla\_EVP or
+sla\_EPV
+to predict the
+Earth's position and velocity, the time argument is strictly
+TDB, but TT is entirely adequate and will require much
+less computation.
+
+The time scale used by the JPL solar-system ephemerides is called
+$T_{eph}$ and is numerically the same as TDB.
+
+Predictions of topocentric solar-system phenomena such as
+occultations and eclipses require solar time UT as well as dynamical
+time.  TT/TDB/ET is all that is required in order to compute the geocentric
+circumstances, but if horizon coordinates or geocentric parallax
+are to be tackled UT is also needed.  A rough estimate
+of $\Delta {\rm T} = {\rm ET} - {\rm UT}$ is
+available via the function
+sla\_DT.
+For a given epoch ({\it e.g.}\ 1650) this returns an approximation
+to $\Delta {\rm T}$ in seconds.
+
+
+
+
+\subsection{Calendars}
+The ordinary {\it Gregorian Calendar Date},
+together with a time of day, can be
+used to express an epoch in any desired time scale.  For many purposes,
+however, a continuous count of days is more convenient, and for
+this purpose the system of {\it Julian Day Number}\/ can be used.
+JD zero is located about 7000~years ago, well before the
+historical era, and is formally defined in terms of Greenwich noon;
+for example Julian Day Number 2449444 began at noon
+on 1994 April~1.  {\it Julian Date}\/
+is the same system but with a fractional part appended;
+Julian Date 2449443.5 was the midnight on which 1994 April~1
+commenced.  Because of the unwieldy size of Julian Dates
+and the awkwardness of the half-day offset, it is
+accepted practice to remove the leading `24' and the trailing `.5',
+producing what is called the {\it Modified Julian Date}:
+MJD~=~JD$-2400000.5$.  SLALIB routines use MJD, as opposed to
+JD, throughout, largely to avoid loss of precision.
+1994 April~1 commenced at MJD~49443.0.
+
+Despite JD (and hence MJD) being defined in terms of (in effect)
+UT, the system can be used in conjunction with other time scales
+such as TAI, TT and TDB (and even sidereal time through the
+concept of {\it Greenwich Sidereal Date}).  However, it is improper
+to express a UTC as a JD or MJD because of leap seconds.
+
+SLALIB has six routines for converting to and from dates in
+the Gregorian calendar.  The routines
+sla\_CLDJ
+and
+sla\_CALDJ
+both convert a calendar date into an MJD, the former interpreting
+years between 0 and 99 as 1st century and the latter as late 20th or
+early 21st century.  The routines sla\_DJCL
+and
+sla\_DJCAL
+both convert an MJD into calendar year, month, day and fraction of a day;
+the latter performs rounding to a specified precision, important
+to avoid dates like `{\tt 2005 04 01.***}' appearing in messages.
+Some of SLALIB's low-precision ephemeris routines
+(sla\_EARTH,
+sla\_MOON
+and
+sla\_ECOR)
+work in terms of year plus day-in-year (where
+day~1~=~January~1st, at least for the modern era).
+This form of date can be generated by
+calling
+sla\_CALYD
+(which defaults years 0-99 into 1950-2049)
+or
+sla\_CLYD
+(which covers the full range from prehistoric times).
+
+\subsection{Geocentric Coordinates}
+The location of the observer on the Earth is significant in a
+number of ways.  The most obvious, of course, is the effect of
+longitude and latitude
+on the observed \azel\ of a star.  Less obvious is the need to
+allow for geocentric parallax when finding the Moon with a
+telescope (and when doing high-precision work involving the
+Sun or planets), and the need to correct observed radial
+velocities and apparent pulsar periods for the effects
+of the Earth's rotation.
+
+The SLALIB routine
+sla\_OBS
+supplies details of groundbased observatories from an internal
+list.  This is useful when writing applications that apply to
+more than one observatory;  the user can enter a brief name,
+or browse through a list, and be spared the trouble of typing
+in the full latitude, longitude {\it etc}.  The following
+Fortran code returns the full name, longitude and latitude
+of a specified observatory:
+\goodbreak
+\begin{verbatim}
+            CHARACTER IDENT*10,NAME*40
+            DOUBLE PRECISION W,P,H
+             :
+            CALL sla_OBS(0,IDENT,NAME,W,P,H)
+            IF (NAME.EQ.'?') ...             (not recognized)
+\end{verbatim}
+\goodbreak
+(Beware of the longitude sign convention, which is west +ve
+for historical reasons.)  The following lists all
+the supported observatories:
+\goodbreak
+\begin{verbatim}
+             :
+            INTEGER N
+             :
+            N=1
+            NAME=' '
+            DO WHILE (NAME.NE.'?')
+               CALL sla_OBS(N,IDENT,NAME,W,P,H)
+               IF (NAME.NE.'?') THEN
+                  WRITE (*,'(1X,I3,4X,A,4X,A)') N,IDENT,NAME
+                  N=N+1
+               END IF
+            END DO
+\end{verbatim}
+\goodbreak
+The routine
+sla\_GEOC
+converts a {\it geodetic latitude}\/
+(one referred to the local horizon) to a geocentric position,
+taking into account the Earth's oblateness and also the height
+above sea level of the observer.  The results are expressed in
+vector form, namely as the distance of the observer from
+the spin axis and equator respectively.  The {\it geocentric
+latitude}\/ can be found be evaluating ATAN2 of the
+two numbers.  A full 3-D vector description of the position
+and velocity of the observer is available through the routine
+sla\_PVOBS.
+For a specified geodetic latitude, height above
+sea level, and local sidereal time,
+sla\_PVOBS
+generates a 6-element vector containing the position and
+velocity with respect to the true equator and equinox of
+date ({\it i.e.}\ compatible with apparent \radec).  For
+some applications it will be necessary to convert to a
+mean \radec\ frame (notably FK5, J2000) by multiplying
+elements 1-3 and 4-6 respectively with the appropriate
+precession matrix.  (In theory an additional correction to the
+velocity vector is needed to allow for differential precession,
+but this correction is always negligible.)
+
+See also the discussion of the routine
+sla\_RVEROT,
+later.
+
+\label{ephem}
+\subsection{Ephemerides}
+SLALIB includes routines for generating positions and
+velocities of Solar-System bodies.  The accuracy objectives are
+modest, and the SLALIB facilities do not attempt
+to compete with precomputed ephemerides such as
+those provided by JPL, or with models containing
+thousands of terms.  It is also worth noting
+that SLALIB's very accurate star coordinate conversion
+routines are not strictly applicable to solar-system cases,
+though they are adequate for most practical purposes.
+
+Earth/Sun ephemerides can be generated using the routines
+sla\_EVP and
+sla\_EPV,
+each of which predict Earth position and velocity with respect to both the
+solar-system barycentre and the
+Sun.  The two routines offer different trade-offs between
+accuracy and execution time.  For most purposes,
+sla\_EVP is adequate:
+maximum velocity error is 0.42~metres per second;  maximum
+heliocentric position error is 1600~km (equivalent to
+about \arcseci{2} at 1~AU), with
+barycentric position errors about 4 times worse.
+The larger and slower
+sla\_EPV
+delivers $3\sigma$ results of 0.005~metres per second in velocity
+and 15~km in position, and is particularly useful when predicting
+apparent directions of near-Earth objects.
+(The Sun's position as
+seen from the Earth can, of course, be obtained simply by
+reversing the signs of the Cartesian components of the
+Earth\,:\,Sun vector.)
+
+Geocentric Moon ephemerides are available from
+sla\_DMOON,
+which predicts the Moon's position and velocity with respect to
+the Earth's centre.  Direction accuracy is usually better than
+10~km (\arcseci{5}) and distance accuracy a little worse.
+
+Lower-precision but faster predictions for the Sun and Moon
+can be made by calling
+sla\_EARTH
+and
+sla\_MOON.
+Both are single precision and accept dates in the form of
+year, day-in-year and fraction of day
+(starting from a calendar date you need to call
+sla\_CLYD
+or
+sla\_CALYD
+to get the required year and day).
+The
+sla\_EARTH
+routine returns the heliocentric position and velocity
+of the Earth's centre for the mean equator and
+equinox of date.  The accuracy is better than 20,000~km in position
+and 10~metres per second in speed.
+The
+position and velocity of the Moon with respect to the
+Earth's centre for the mean equator and ecliptic of date
+can be obtained by calling
+sla\_MOON.
+The positional accuracy is better than \arcseci{30} in direction
+and 1000~km in distance.
+
+Approximate ephemerides for all the major planets
+can be generated by calling
+sla\_PLANET
+or
+sla\_RDPLAN.  These routines offer arcminute accuracy (much
+better for the inner planets and for Pluto) over a span of several
+millennia (but only $\pm100$ years for Pluto).
+The routine
+sla\_PLANET produces heliocentric position and
+velocity in the form of equatorial \xyzxyzd\ for the
+mean equator and equinox of J2000.  The vectors
+produced by
+sla\_PLANET
+can be used in a variety of ways according to the
+requirements of the application concerned.  The routine
+sla\_RDPLAN
+uses
+sla\_PLANET
+and
+sla\_DMOON
+to deal with the common case of predicting
+a planet's apparent \radec\ and angular size as seen by a
+terrestrial observer.
+
+Note that in predicting the position in the sky of a solar-system body
+it is necessary to allow for geocentric parallax.  This correction
+is {\it essential}\/ in the case of the Moon, where the observer's
+position on the Earth can affect the Moon's \radec\ by up to
+$1^\circ$.  The calculation can most conveniently be done by calling
+sla\_PVOBS and subtracting the resulting 6-vector from the
+one produced by
+sla\_DMOON, as is demonstrated by the following example:
+\goodbreak
+\begin{verbatim}
+      *  Demonstrate the size of the geocentric parallax correction
+      *  in the case of the Moon.  The test example is for the AAT,
+      *  before midnight, in summer, near first quarter.
+
+            IMPLICIT NONE
+            CHARACTER NAME*40,SH,SD
+            INTEGER J,I,IHMSF(4),IDMSF(4)
+            DOUBLE PRECISION SLONGW,SLAT,H,DJUTC,FDUTC,DJUT1,DJTT,STL,
+           :                 RMATN(3,3),PMM(6),PMT(6),RM,DM,PVO(6),TL
+            DOUBLE PRECISION sla_DTT,sla_GMST,sla_EQEQX,sla_DRANRM
+
+      *  Get AAT longitude and latitude in radians and height in metres
+            CALL sla_OBS(0,'AAT',NAME,SLONGW,SLAT,H)
+
+      *  UTC (1992 January 13, 11 13 59) to MJD
+            CALL sla_CLDJ(1992,1,13,DJUTC,J)
+            CALL sla_DTF2D(11,13,59.0D0,FDUTC,J)
+            DJUTC=DJUTC+FDUTC
+
+      *  UT1 (UT1-UTC value of -0.152 sec is from IERS Bulletin B)
+            DJUT1=DJUTC+(-0.152D0)/86400D0
+
+      *  TT
+            DJTT=DJUTC+sla_DTT(DJUTC)/86400D0
+
+      *  Local apparent sidereal time
+            STL=sla_GMST(DJUT1)-SLONGW+sla_EQEQX(DJTT)
+
+      *  Geocentric position/velocity of Moon (mean of date)
+            CALL sla_DMOON(DJTT,PMM)
+
+      *  Nutation to true equinox of date
+            CALL sla_NUT(DJTT,RMATN)
+            CALL sla_DMXV(RMATN,PMM,PMT)
+            CALL sla_DMXV(RMATN,PMM(4),PMT(4))
+
+      *  Report geocentric HA,Dec
+            CALL sla_DCC2S(PMT,RM,DM)
+            CALL sla_DR2TF(2,sla_DRANRM(STL-RM),SH,IHMSF)
+            CALL sla_DR2AF(1,DM,SD,IDMSF)
+            WRITE (*,'(1X,'' geocentric:'',2X,A,I2.2,2I3.2,''.'',I2.2,'//
+           :                              '1X,A,I2.2,2I3.2,''.'',I1)')
+           :                                                SH,IHMSF,SD,IDMSF
+
+      *  Geocentric position of observer (true equator and equinox of date)
+            CALL sla_PVOBS(SLAT,H,STL,PVO)
+
+      *  Place origin at observer
+            DO I=1,6
+               PMT(I)=PMT(I)-PVO(I)
+            END DO
+
+      *  Allow for planetary aberration
+            TL=499.004782D0*SQRT(PMT(1)**2+PMT(2)**2+PMT(3)**2)
+            DO I=1,3
+               PMT(I)=PMT(I)-TL*PMT(I+3)
+            END DO
+
+      *  Report topocentric HA,Dec
+            CALL sla_DCC2S(PMT,RM,DM)
+            CALL sla_DR2TF(2,sla_DRANRM(STL-RM),SH,IHMSF)
+            CALL sla_DR2AF(1,DM,SD,IDMSF)
+            WRITE (*,'(1X,''topocentric:'',2X,A,I2.2,2I3.2,''.'',I2.2,'//
+           :                              '1X,A,I2.2,2I3.2,''.'',I1)')
+           :                                                SH,IHMSF,SD,IDMSF
+            END
+\end{verbatim}
+\goodbreak
+The output produced is as follows:
+\goodbreak
+\begin{verbatim}
+       geocentric:  +03 06 55.55 +15 03 38.8
+      topocentric:  +03 09 23.76 +15 40 51.4
+\end{verbatim}
+\goodbreak
+(An easier but
+less instructive method of estimating the topocentric apparent place of the
+Moon is to call the routine
+sla\_RDPLAN.)
+
+As an example of using
+sla\_PLANET,
+the following program estimates the geocentric separation
+between Venus and Jupiter during a close conjunction
+in 2\,BC, which is a star-of-Bethlehem candidate:
+\goodbreak
+\begin{verbatim}
+      *  Compute time and minimum geocentric apparent separation
+      *  between Venus and Jupiter during the close conjunction of 2 BC.
+
+            IMPLICIT NONE
+
+            DOUBLE PRECISION SEPMIN,DJD0,FD,DJD,DJDM,PV(6),RMATP(3,3),
+           :                 PVM(6),PVE(6),TL,RV,DV,RJ,DJ,SEP
+            INTEGER IHOUR,IMIN,J,I,IHMIN,IMMIN
+            DOUBLE PRECISION sla_EPJ,sla_DSEP
+
+
+      *  Search for closest approach on the given day
+            DJD0=1720859.5D0
+            SEPMIN=1D10
+            DO IHOUR=20,22
+               DO IMIN=0,59
+                  CALL sla_DTF2D(IHOUR,IMIN,0D0,FD,J)
+
+      *        Julian date and MJD
+                  DJD=DJD0+FD
+                  DJDM=DJD-2400000.5D0
+
+      *        Earth to Moon (mean of date)
+                  CALL sla_DMOON(DJDM,PV)
+
+      *        Precess Moon position to J2000
+                  CALL sla_PRECL(sla_EPJ(DJDM),2000D0,RMATP)
+                  CALL sla_DMXV(RMATP,PV,PVM)
+
+      *        Sun to Earth-Moon Barycentre (mean J2000)
+                  CALL sla_PLANET(DJDM,3,PVE,J)
+
+      *        Correct from EMB to Earth
+                  DO I=1,3
+                     PVE(I)=PVE(I)-0.012150581D0*PVM(I)
+                  END DO
+
+      *        Sun to Venus
+                  CALL sla_PLANET(DJDM,2,PV,J)
+
+      *        Earth to Venus
+                  DO I=1,6
+                     PV(I)=PV(I)-PVE(I)
+                  END DO
+
+      *        Light time to Venus (sec)
+                  TL=499.004782D0*SQRT((PV(1)-PVE(1))**2+
+           :                           (PV(2)-PVE(2))**2+
+           :                           (PV(3)-PVE(3))**2)
+
+      *        Extrapolate backwards in time by that much
+                  DO I=1,3
+                     PV(I)=PV(I)-TL*PV(I+3)
+                  END DO
+
+      *        To RA,Dec
+                  CALL sla_DCC2S(PV,RV,DV)
+
+      *        Same for Jupiter
+                  CALL sla_PLANET(DJDM,5,PV,J)
+                  DO I=1,6
+                     PV(I)=PV(I)-PVE(I)
+                  END DO
+                  TL=499.004782D0*SQRT((PV(1)-PVE(1))**2+
+           :                           (PV(2)-PVE(2))**2+
+           :                           (PV(3)-PVE(3))**2)
+                  DO I=1,3
+                     PV(I)=PV(I)-TL*PV(I+3)
+                  END DO
+                  CALL sla_DCC2S(PV,RJ,DJ)
+
+      *        Separation (arcsec)
+                  SEP=sla_DSEP(RV,DV,RJ,DJ)
+
+      *        Keep if smallest so far
+                  IF (SEP.LT.SEPMIN) THEN
+                     IHMIN=IHOUR
+                     IMMIN=IMIN
+                     SEPMIN=SEP
+                  END IF
+               END DO
+            END DO
+
+      *  Report
+            WRITE (*,'(1X,I2.2,'':'',I2.2,F6.1)') IHMIN,IMMIN,
+           :                                      206264.8062D0*SEPMIN
+
+            END
+\end{verbatim}
+\goodbreak
+The output produced (the Ephemeris Time on the day in question, and
+the closest approach in arcseconds) is as follows:
+\goodbreak
+\begin{verbatim}
+      21:16  33.3
+\end{verbatim}
+\goodbreak
+For comparison, accurate JPL predictions
+give a separation \arcseci{8} less than
+the above estimate, occurring $30^{\rm m}$ earlier
+(see {\it Sky and Telescope,}\/ April~1987, p\,357).
+
+The following program demonstrates
+sla\_RDPLAN.
+\begin{verbatim}
+      *  For a given date, time and geographical location, output
+      *  a table of planetary positions and diameters.
+
+            IMPLICIT NONE
+            CHARACTER PNAMES(0:9)*7,B*80,S
+            INTEGER I,NP,IY,J,IM,ID,IHMSF(4),IDMSF(4)
+            DOUBLE PRECISION D15B2P,R2AS,FD,DJM,ELONG,PHI,RA,DEC,DIAM
+            PARAMETER (D15B2P=2.3873241463784300365D0,
+           :           R2AS=206264.80625D0)
+            DATA PNAMES / 'Sun','Mercury','Venus','Moon','Mars','Jupiter',
+           :              'Saturn','Uranus','Neptune', 'Pluto' /
+
+
+      *  Loop until 'end' typed
+            B=' '
+            DO WHILE (B.NE.'END'.AND.B.NE.'end')
+
+      *     Get date, time and observer's location
+               PRINT *,'Date? (Y,M,D, Gregorian)'
+               READ (*,'(A)') B
+               IF (B.NE.'END'.AND.B.NE.'end') THEN
+                  I=1
+                  CALL sla_INTIN(B,I,IY,J)
+                  CALL sla_INTIN(B,I,IM,J)
+                  CALL sla_INTIN(B,I,ID,J)
+                  PRINT *,'Time? (H,M,S, dynamical)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,FD,J)
+                  FD=FD*D15B2P
+                  CALL sla_CLDJ(IY,IM,ID,DJM,J)
+                  DJM=DJM+FD
+                  PRINT *,'Longitude? (D,M,S, east +ve)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,ELONG,J)
+                  PRINT *,'Latitude? (D,M,S, geodetic)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,PHI,J)
+
+      *        Loop planet by planet
+                  DO NP=0,9
+
+      *           Get RA,Dec and diameter
+                     CALL sla_RDPLAN(DJM,NP,ELONG,PHI,RA,DEC,DIAM)
+
+      *           One line of report
+                     CALL sla_DR2TF(2,RA,S,IHMSF)
+                     CALL sla_DR2AF(1,DEC,S,IDMSF)
+                     WRITE (*,
+           : '(1X,A,2X,3I3.2,''.'',I2.2,2X,A,I2.2,2I3.2,''.'',I1,F8.1)')
+           :                          PNAMES(NP),IHMSF,S,IDMSF,R2AS*DIAM
+
+      *           Next planet
+                  END DO
+                  PRINT *,' '
+               END IF
+
+      *     Next case
+            END DO
+
+            END
+\end{verbatim}
+Entering the following data (for 1927~June~29 at $5^{\rm h}\,25^{\rm m}$~ET
+and the position of Preston, UK):
+\begin{verbatim}
+      1927 6 29
+      5 25
+      -2 42
+      53 46
+\end{verbatim}
+produces the following report:
+\begin{verbatim}
+      Sun       06 28 14.03  +23 17 17.3  1887.8
+      Mercury   08 08 58.60  +19 20 57.1     9.3
+      Venus     09 38 53.61  +15 35 32.8    22.8
+      Moon      06 28 15.95  +23 17 21.3  1902.3
+      Mars      09 06 49.33  +17 52 26.6     4.0
+      Jupiter   00 11 12.08  -00 10 57.5    41.1
+      Saturn    16 01 43.35  -18 36 55.9    18.2
+      Uranus    00 13 33.54  +00 39 36.1     3.5
+      Neptune   09 49 35.76  +13 38 40.8     2.2
+      Pluto     07 05 29.51  +21 25 04.2     0.1
+\end{verbatim}
+Inspection of the Sun and Moon data reveals that
+a total solar eclipse is in progress.
+
+SLALIB also provides for the case where orbital elements (with respect
+to the J2000 equinox and ecliptic)
+are available.  This allows predictions to be made for minor-planets and
+(if you ignore non-gravitational effects)
+comets.  Furthermore, if major-planet elements for an epoch close to the date
+in question are available, more accurate predictions can be made than
+are offered by
+sla\_RDPLAN and
+sla\_PLANET.
+
+The SLALIB planetary-prediction
+routines that work with orbital elements are
+sla\_PLANTE (the orbital-elements equivalent of
+sla\_RDPLAN), which predicts the topocentric \radec, and
+sla\_PLANEL (the orbital-elements equivalent of
+sla\_PLANET), which predicts the heliocentric \xyzxyzd\ with respect to the
+J2000 equinox and equator.  In addition, the routine
+sla\_PV2EL does the inverse of
+sla\_PLANEL, transforming \xyzxyzd\ into {\it osculating elements.}
+
+Osculating elements describe the unperturbed 2-body orbit.  Depending
+on accuracy requirements, this unperturbed orbit is an
+adequate approximation to the actual orbit for a few weeks either
+side of the specified epoch, outside which perturbations due to
+the other bodies of the Solar System lead to
+increasing errors.  Given a minor planet's osculating elements for
+a particular date, predictions for a date only
+100 days earlier or later
+are likely to be in error by several arcseconds.
+These errors can
+be reduced if new elements are generated which take account of
+the perturbations of the major planets, and this is what the routine
+sla\_PERTEL does.  Once
+sla\_PERTEL has been called, to provide osculating elements
+close to the required date, the elements can be passed to
+sla\_PLANEL or
+sla\_PLANTE in the normal way.  Predictions of arcsecond accuracy
+over a span of a decade or more are available using this
+technique.
+
+Three different combinations of orbital elements are
+provided for, matching the usual conventions
+for major planets, minor planets and
+comets respectively.  The choice is made through the
+argument {\tt JFORM}:
+
+\vspace{1ex}
+\hspace{3em}
+\begin{tabular}{|c|c|c|} \hline
+{\tt JFORM=1} & {\tt JFORM=2} & {\tt JFORM=3} \\
+\hline \hline
+$t_0$ & $t_0$ & $T$ \\
+\hline
+$i$ & $i$ & $i$ \\
+\hline
+$\Omega$ & $\Omega$ & $\Omega$ \\
+\hline
+$\varpi$ & $\omega$ & $\omega$ \\
+\hline
+$a$ & $a$ & $q$ \\
+\hline
+$e$ & $e$ & $e$ \\
+\hline
+$L$ & $M$ & \\
+\hline
+$n$ & & \\
+\hline
+\end{tabular}\\[2ex]
+The symbols have the following meanings:
+
+\vspace{-1ex}
+
+\begin{tabular}{lll}
+& $t_0$ & epoch of osculation \\
+& $T$ & epoch of perihelion passage \\
+& $i$ & inclination of the orbit \\
+& $\Omega$ & longitude of the ascending node \\
+& $\varpi$ & longitude of perihelion ($\varpi = \Omega + \omega$) \\
+& $\omega$ & argument of perihelion \\
+& $a$ & semi-major axis of the orbital ellipse \\
+& $q$ & perihelion distance \\
+& $e$ & orbital eccentricity \\
+& $L$ & mean longitude ($L = \varpi + M$) \\
+& $M$ & mean anomaly \\
+& $n$ & mean motion \\
+\end{tabular}
+
+The mean motion, $n$, tells
+sla\_PLANEL the mass of the planet.
+If it is not available, it should be calculated
+from $n^2 a^3 = k^2 (1+m)$, where $k = 0.01720209895$ and
+m is the mass of the planet ($M_\odot = 1$); $a$ is in AU.
+
+Note that for any given problem there are up to three different
+epochs in play, and it is vital to distinguish clearly between
+them:
+\begin{itemize}
+\item The epoch of observation:  the moment in time for which the
+      position of the body is to be predicted.
+\item The epoch defining the position of the body:  the moment in time
+      at which, in the absence of purturbations, the specified
+      position---mean longitude, mean anomaly, or perihelion---is
+      reached.
+\item The epoch of osculation:  the moment in time at which the given
+      elements precisely specify the body's position and velocity.
+\end{itemize}
+
+For the major-planet and minor-planet cases it is usual to make
+the epoch that defines the position of the body the same as the
+epoch of osculation.  Thus, for planets (major and
+minor) only two different epochs are
+involved:  the epoch of the elements and the epoch of observation.
+For comets, the epoch of perihelion fixes the position in the
+orbit and in general a different epoch of osculation will be
+chosen.  Thus, for comets all three types of epoch are involved.
+How many of the three elements are present in a given SLALIB
+argument list depends on the routine concerned.
+
+Two important sources for orbital elements are the {\it Horizons}\/
+service, operated by the Jet Propulsion Laboratory, Pasadena,
+and the Minor Planet Center, operated by the Center for
+Astrophysics, Harvard.
+The JPL elements (heliocentric, J2000 ecliptic and
+equinox) and MPC elements
+correspond to SLALIB arguments as shown in the following table,
+where ``(rad)'' means conversion from degrees to radians, and
+``(MJD)'' means ``subtract {\tt 2400000.5D0}'':
+
+\vspace{2ex}
+
+\begin{small}
+\begin{tabular}{|c||c|c|c||c|c|} \hline
+{\it SLALIB } & \multicolumn{3}{c||}{\it JPL}
+ & \multicolumn{2}{c|}{\it MPC} \\
+argument & major planet & minor planet & comet & minor planet & comet \\
+\hline \hline
+{\tt JFORM} & {\tt 1} & {\tt 2} & {\tt 3} & {\tt 2} & {\tt 3} \\
+{\tt EPOCH} & {\tt JDCT} (MJD) & {\tt JDCT} (MJD) & {\tt Tp} (MJD) &
+                                    {\tt Epoch} (MJD) & {\tt T} (MJD) \\
+{\tt ORBINC} & {\tt IN} (rad) & {\tt IN} (rad) & {\tt IN} (rad) &
+                                {\tt Incl.} (rad) & {\tt Incl.} (rad) \\
+{\tt ANODE} & {\tt OM} (rad) & {\tt OM} (rad) & {\tt OM} (rad) &
+                                 {\tt Node} (rad) & {\tt Node.} (rad) \\
+{\tt PERIH} & {\tt OM+W} (rad) & {\tt W} (rad) & {\tt W} (rad) &
+                              {\tt Perih.} (rad) & {\tt Perih.} (rad) \\
+{\tt AORQ} & {\tt A} & {\tt A} & {\tt QR} & {\tt a} & {\tt q} \\
+{\tt E} & {\tt EC} & {\tt EC} & {\tt EC} & {\tt e} & {\tt e} \\
+{\tt AORL} & {\tt MA+OM+W} (rad) & {\tt MA} (rad) & & {\tt M} (rad) & \\
+{\tt DM} & {\tt N} (rad) & & & & \\  \hline
+epoch of osculation & {\tt JDCT} (MJD)
+                    & {\tt JDCT} (MJD)
+                    & {\tt JDCT} (MJD)
+                    & {\tt Epoch} (MJD)
+                    & {\tt Epoch} (MJD) \\
+\hline
+\end{tabular}
+\end{small}\\[3ex]
+
+Conventional elements are not the only way of specifying an orbit.
+The \xyzxyzd\ state vector is an equally valid specification,
+and the so-called {\it method of universal variables}\/ allows
+orbital calculations to be made directly, bypassing angular
+quantities and avoiding Kepler's Equation.  The universal-variables
+approach has various advantages, including better handling of
+near-parabolic cases and greater efficiency.
+SLALIB uses universal variables for its internal
+calculations and also offers a number of routines which
+applications can call.
+
+The universal elements are the \xyzxyzd\ and its epoch, plus the mass
+of the body.  The SLALIB routines supplement these elements with
+certain redundant values in order to
+avoid unnecessary recomputation when the elements are next used.
+
+The routines
+sla\_EL2UE and
+sla\_UE2EL transform conventional elements into the
+universal form and {\it vice versa.}
+The routine
+sla\_PV2UE takes an \xyzxyzd\ and forms the set of universal
+elements;
+sla\_UE2PV takes a set of universal elements and predicts the \xyzxyzd\
+for a specified epoch.
+The routine
+sla\_PERTUE provides updated universal elements,
+taking into account perturbations from the major planets.
+Starting with universal elements, the routine
+sla\_PLANTU (the universal elements equivalent of
+sla\_PLANTE) predicts topocentric \radec.
+
+\subsection{Radial Velocity and Light-Time Corrections}
+When publishing high-resolution spectral observations
+it is necessary to refer them to a specified standard of rest.
+This involves knowing the component in the direction of the
+source of the velocity of the observer.  SLALIB provides a number
+of routines for this purpose, allowing observations to be
+referred to the Earth's centre, the Sun, a Local Standard of Rest
+(either dynamical or kinematical), the centre of the Galaxy, and
+the mean motion of the Local Group.
+
+The routine
+sla\_RVEROT
+corrects for the diurnal rotation of
+the observer around the Earth's axis.  This is always less than 0.5~km/s.
+
+No specific routine is provided to correct a radial velocity
+from geocentric to heliocentric, but this can easily be done by calling
+sla\_EVP
+as follows (array declarations {\it etc}.\ omitted):
+\goodbreak
+\begin{verbatim}
+             :
+      *  Star vector, J2000
+            CALL sla_DCS2C(RM,DM,V)
+
+      *  Earth/Sun velocity and position, J2000
+            CALL sla_EVP(TDB,2000D0,DVB,DPB,DVH,DPH)
+
+      *  Radial velocity correction due to Earth orbit (km/s)
+            VCORB = -sla_DVDV(V,DVH)*149.597870D6
+             :
+\end{verbatim}
+\goodbreak
+The maximum value of this correction is the Earth's orbital speed
+of about 30~km/s.  A related routine,
+sla\_ECOR,
+computes the light-time correction with respect to the Sun.  It
+would be used when reducing observations of a rapid variable-star
+for instance.
+For pulsar work the
+sla\_EVP routine is not sufficiently accurate for
+phase predictions, being limited to about 25~ms.  The
+alternative sla\_EPV routine will deliver pulse arrival times
+accurate to 50~$\mu$s, but is significantly slower.
+
+To remove the intrinsic $\sim20$~km/s motion of the Sun relative
+to other stars in the solar neighbourhood,
+a velocity correction to a
+{\it local standard of rest}\/ (LSR) is required.  There are
+opportunities for mistakes here.  There are two sorts of LSR,
+{\it dynamical}\/ and {\it kinematical}, and
+multiple definitions exist for the latter.  The
+dynamical LSR is a point near the Sun which is in a circular
+orbit around the Galactic centre;  the Sun has a ``peculiar''
+motion relative to the dynamical LSR.  A kinematical LSR is
+the mean standard of rest of specified star catalogues or stellar
+populations, and its precise definition depends on which
+catalogues or populations were used and how the analysis was
+carried out.  The Sun's motion with respect to a kinematical
+LSR is called the ``standard'' solar motion.  Radial
+velocity corrections to the dynamical LSR are produced by the routine
+sla\_RVLSRD
+and to the adopted kinematical LSR by
+sla\_RVLSRK.
+See the individual specifications for these routines for the
+precise definition of the LSR in each case.
+
+For extragalactic sources, the centre of the Galaxy can be used as
+a standard of rest.  The radial velocity correction from the
+dynamical LSR to the Galactic centre can be obtained by calling
+sla\_RVGALC.
+Its maximum value is 220~km/s.
+
+For very distant sources it is appropriate to work relative
+to the mean motion of the Local Group.  The routine for
+computing the radial velocity correction in this case is
+sla\_RVLG.
+Note that in this case the correction is with respect to the
+dynamical LSR, not the Galactic centre as might be expected.
+This conforms to the IAU definition, and confers immunity from
+revisions of the Galactic rotation speed.
+
+\subsection{Focal-Plane Astrometry}
+The relationship between the position of a star image in
+the focal plane of a telescope and the star's celestial
+coordinates is usually described in terms of the {\it tangent plane}\/
+or {\it gnomonic}\/ projection.  This is the projection produced
+by a pin-hole camera and is a good approximation to the projection
+geometry of a traditional large {\it f}\/-ratio astrographic refractor.
+SLALIB includes a group of routines which transform
+star positions between their observed places on the celestial
+sphere and their \xy\ coordinates in the tangent plane.  The
+spherical coordinate system does not have to be \radec\ but
+usually is.  The so-called {\it standard coordinates}\/ of a star
+are the tangent plane \xy, in radians, with respect to an origin
+at the tangent point, with the $y$-axis pointing north and
+the $x$-axis pointing east (in the direction of increasing $\alpha$).
+The factor relating the standard coordinates to
+the actual \xy\ coordinates in, say, millimetres is simply
+the focal length of the telescope.
+
+Given the \radec\ of the {\it plate centre}\/ (the tangent point)
+and the \radec\ of a star within the field, the standard
+coordinates can be determined by calling
+sla\_S2TP
+(single precision) or
+sla\_DS2TP
+(double precision).  The reverse transformation, where the
+\xy\ is known and we wish to find the \radec, is carried out by calling
+sla\_TP2S
+or
+sla\_DTP2S.
+Occasionally we know the both the \xy\ and the \radec\ of a
+star and need to deduce the \radec\ of the tangent point;
+this can be done by calling
+sla\_TPS2C
+or
+sla\_DTPS2C.
+(All of these transformations apply not just to \radec\ but to
+other spherical coordinate systems, of course.)
+Equivalent (and faster)
+routines are provided which work directly in \xyz\ instead of
+spherical coordinates:
+sla\_V2TP and
+sla\_DV2TP,
+sla\_TP2V and
+sla\_DTP2V,
+sla\_TPV2C and
+sla\_DTPV2C.
+
+Even at the best of times, the tangent plane projection is merely an
+approximation.  Some telescopes and cameras exhibit considerable pincushion
+or barrel distortion and some have a curved focal surface.
+For example, neither Schmidt cameras nor (especially)
+large reflecting telescopes with wide-field corrector lenses
+are adequately modelled by tangent-plane geometry.  In such
+cases, however, it is still possible to do most of the work
+using the (mathematically convenient) tangent-plane
+projection by inserting an extra step which applies or
+removes the distortion peculiar to the system concerned.
+A simple $r_1=r_0(1+Kr_0^2)$ law works well in the
+majority of cases; $r_0$ is the radial distance in the
+tangent plane, $r_1$ is the radial distance after adding
+the distortion, and $K$ is a constant which depends on the
+telescope ($\theta$ is unaffected).  The routine
+sla\_PCD
+applies the distortion to an \xy\ and
+sla\_UNPCD
+removes it.  For \xy\ in radians, $K$ values range from $-1/3$ for the
+tiny amount of barrel distortion in Schmidt geometry to several
+hundred for the serious pincushion distortion
+produced by wide-field correctors in big reflecting telescopes
+(the AAT prime focus triplet corrector is about $K=+178.6$).
+
+SLALIB includes a group of routines which can be put together
+to build a simple plate-reduction program.  The heart of the group is
+sla\_FITXY,
+which fits a linear model to relate two sets of \xy\ coordinates,
+in the case of a plate reduction the measured positions of the
+images of a set of
+reference stars and the standard
+coordinates derived from their catalogue positions.  The
+model is of the form:
+\[x_{p} = a + bx_{m} + cy_{m}\]
+\[y_{p} = d + ex_{m} + fy_{m}\]
+
+where the {\it p}\/ subscript indicates ``predicted'' coordinates
+(the model's approximation to the ideal ``expected'' coordinates) and the
+{\it m}\/ subscript indicates ``measured coordinates''.  The
+six coefficients {\it a--f}\/ can optionally be
+constrained to represent a ``solid body rotation'' free of
+any squash or shear distortions.  Without this constraint
+the model can, to some extent, accommodate effects like refraction,
+allowing mean places to be used directly and
+avoiding the extra complications of a
+full mean-apparent-observed transformation for each star.
+Having obtained the linear model,
+sla\_PXY
+can be used to process the set of measured and expected
+coordinates, giving the predicted coordinates and determining
+the RMS residuals in {\it x}\/ and {\it y}.
+The routine
+sla\_XY2XY
+transforms one \xy\ into another using the linear model.  A model
+can be inverted by calling
+sla\_INVF,
+and decomposed into zero points, scales, $x/y$ nonperpendicularity
+and orientation by calling
+sla\_DCMPF.
+
+\subsection{Numerical Methods}
+SLALIB contains a small number of simple, general-purpose
+numerical-methods routines.  They have no specific
+connection with positional astronomy but have proved useful in
+applications to do with simulation and fitting.
+
+At the heart of many simulation programs is the generation of
+pseudo-random numbers, evenly distributed in a given range:
+sla\_RANDOM
+does this.  Pseudo-random normal deviates, or ``Gaussian
+residuals'', are often required to simulate noise and
+can be generated by means of the function
+sla\_GRESID.
+Neither routine will pass super-sophisticated
+statistical tests, but they work adequately for most
+practical purposes and avoid the need to call non-standard
+library routines peculiar to one sort of computer.
+
+Applications which perform a least-squares fit using a traditional
+normal-equations methods can accomplish the required matrix-inversion
+by calling either
+sla\_SMAT
+(single precision) or
+sla\_DMAT
+(double).  A generally better way to perform such fits is
+to use singular value decomposition.  SLALIB provides a routine
+to do the decomposition itself,
+sla\_SVD,
+and two routines to use the results:
+sla\_SVDSOL
+generates the solution, and
+sla\_SVDCOV
+produces the covariance matrix.
+A simple demonstration of the use of the SLALIB SVD
+routines is given below.  It generates 500 simulated data
+points and fits them to a model which has 4 unknown coefficients.
+(The arrays in the example are sized to accept up to 1000
+points and 20 unknowns.)  The model is:
+\[ y = C_{1} +C_{2}x +C_{3}sin{x} +C_{4}cos{x} \]
+The test values for the four coefficients are
+$C_1\!=\!+50.0$,
+$C_2\!=\!-2.0$,
+$C_3\!=\!-10.0$ and
+$C_4\!=\!+25.0$.
+Gaussian noise, $\sigma=5.0$, is added to each ``observation''.
+\goodbreak
+\begin{verbatim}
+            IMPLICIT NONE
+
+      *  Sizes of arrays, physical and logical
+            INTEGER MP,NP,NC,M,N
+            PARAMETER (MP=1000,NP=10,NC=20,M=500,N=4)
+
+      *  The unknowns we are going to solve for
+            DOUBLE PRECISION C1,C2,C3,C4
+            PARAMETER (C1=50D0,C2=-2D0,C3=-10D0,C4=25D0)
+
+      *  Arrays
+            DOUBLE PRECISION A(MP,NP),W(NP),V(NP,NP),
+           :                 WORK(NP),B(MP),X(NP),CVM(NC,NC)
+
+            DOUBLE PRECISION VAL,BF1,BF2,BF3,BF4,SD2,D,VAR
+            REAL sla_GRESID
+            INTEGER I,J
+
+      *  Fill the design matrix
+            DO I=1,M
+
+      *     Dummy independent variable
+               VAL=DBLE(I)/10D0
+
+      *     The basis functions
+               BF1=1D0
+               BF2=VAL
+               BF3=SIN(VAL)
+               BF4=COS(VAL)
+
+      *     The observed value, including deliberate Gaussian noise
+               B(I)=C1*BF1+C2*BF2+C3*BF3+C4*BF4+DBLE(sla_GRESID(5.0))
+
+      *     Fill one row of the design matrix
+               A(I,1)=BF1
+               A(I,2)=BF2
+               A(I,3)=BF3
+               A(I,4)=BF4
+            END DO
+
+      *  Factorize the design matrix, solve and generate covariance matrix
+            CALL sla_SVD(M,N,MP,NP,A,W,V,WORK,J)
+            CALL sla_SVDSOL(M,N,MP,NP,B,A,W,V,WORK,X)
+            CALL sla_SVDCOV(N,NP,NC,W,V,WORK,CVM)
+
+      *  Compute the variance
+            SD2=0D0
+            DO I=1,M
+               VAL=DBLE(I)/10D0
+               BF1=1D0
+               BF2=VAL
+               BF3=SIN(VAL)
+               BF4=COS(VAL)
+               D=B(I)-(X(1)*BF1+X(2)*BF2+X(3)*BF3+X(4)*BF4)
+               SD2=SD2+D*D
+            END DO
+            VAR=SD2/DBLE(M)
+
+      *  Report the RMS and the solution
+            WRITE (*,'(1X,''RMS ='',F5.2/)') SQRT(VAR)
+            DO I=1,N
+               WRITE (*,'(1X,''C'',I1,'' ='',F7.3,'' +/-'',F6.3)')
+           :                                         I,X(I),SQRT(VAR*CVM(I,I))
+            END DO
+            END
+\end{verbatim}
+\goodbreak
+The program produces output like the following:
+\goodbreak
+\begin{verbatim}
+            RMS = 4.88
+
+            C1 = 50.192 +/- 0.439
+            C2 = -2.002 +/- 0.015
+            C3 = -9.771 +/- 0.310
+            C4 = 25.275 +/- 0.310
+\end{verbatim}
+\goodbreak
+In this above example, essentially
+identical results would be obtained if the more
+commonplace normal-equations method had been used, and the large
+$1000\times20$ array would have been avoided.  However, the SVD method
+comes into its own when the opportunity is taken to edit the W-matrix
+(the so-called ``singular values'') in order to control
+possible ill-conditioning.  The procedure involves replacing with
+zeroes any W-elements smaller than a nominated value, for example
+0.001 times the largest W-element.  Small W-elements indicate
+ill-conditioning, which in the case of the normal-equations
+method would produce spurious large coefficient values and
+possible arithmetic overflows.  Using SVD, the effect on the solution
+of setting suspiciously small W-elements to zero is to restrain
+the offending coefficients from moving very far.  The
+fact that action was taken can be reported to show the program user that
+something is amiss.  Furthermore, if element W(J) was set to zero,
+the row numbers of the two biggest elements in the Jth column of the
+V-matrix identify the pair of solution coefficients that are
+dependent.
+
+A more detailed description of SVD and its use in least-squares
+problems would be out of place here, and the reader is urged
+to refer to the relevant sections of the book {\it Numerical Recipes}
+(Press {\it et al.}, Cambridge University Press, 1987).
+
+The routines
+sla\_COMBN
+and
+sla\_PERMUT
+are useful for problems which involve combinations (different subsets)
+and permutations (different orders).
+Both return the next in a sequence of results, cycling through all the
+possible results as the routine is called repeatedly.
+
+\vfill
+
+\pagebreak
+
+\section{SUMMARY OF CALLS}
+The basic trigonometrical and numerical facilities are supplied in both single
+and double precision versions.
+Most of the more esoteric position and time routines use double precision
+arguments only, even in cases where single precision would normally be adequate
+in practice.
+Certain routines with modest accuracy objectives are supplied in
+single precision versions only.
+In the calling sequences which follow, no attempt has been made
+to distinguish between single and double precision argument names,
+and frequently the same name is used on different occasions to
+mean different things.
+However, none of the routines uses a mixture of single and
+double precision arguments;  each routine is either wholly
+single precision or wholly double precision.
+
+In the classified list, below,
+{\it subroutine}\/ subprograms are those whose names and argument lists
+are preceded by `CALL', whereas {\it function}\/ subprograms are
+those beginning `R=' (when the result is REAL) or `D=' (when
+the result is DOUBLE~PRECISION).
+
+The list is, of course, merely for quick reference;  inexperienced
+users {\bf must} refer to the detailed specifications given later.
+In particular, {\bf don't guess} whether arguments are single or
+double precision; the result could be a program that happens to
+works on one sort of machine but not on another.
+
+\callhead{String Decoding}
+\begin{callset}
+\subp{CALL sla\_INTIN (STRING, NSTRT, IRESLT, JFLAG)}
+   Convert free-format string into integer
+\subq{CALL sla\_FLOTIN (STRING, NSTRT, RESLT, JFLAG)}
+     {CALL sla\_DFLTIN (STRING, NSTRT, DRESLT, JFLAG)}
+   Convert free-format string into floating-point number
+\subq{CALL sla\_AFIN (STRING, NSTRT, RESLT, JFLAG)}
+     {CALL sla\_DAFIN (STRING, NSTRT, DRESLT, JFLAG)}
+   Convert free-format string from deg,arcmin,arcsec to radians
+\end{callset}
+
+\callhead{Sexagesimal Conversions}
+\begin{callset}
+\subq{CALL sla\_CTF2D (IHOUR, IMIN, SEC, DAYS, J)}
+     {CALL sla\_DTF2D (IHOUR, IMIN, SEC, DAYS, J)}
+   Hours, minutes, seconds to days
+\subq{CALL sla\_CD2TF (NDP, DAYS, SIGN, IHMSF)}
+     {CALL sla\_DD2TF (NDP, DAYS, SIGN, IHMSF)}
+   Days to hours, minutes, seconds
+\subq{CALL sla\_CTF2R (IHOUR, IMIN, SEC, RAD, J)}
+     {CALL sla\_DTF2R (IHOUR, IMIN, SEC, RAD, J)}
+   Hours, minutes, seconds to radians
+\subq{CALL sla\_CR2TF (NDP, ANGLE, SIGN, IHMSF)}
+     {CALL sla\_DR2TF (NDP, ANGLE, SIGN, IHMSF)}
+   Radians to hours, minutes, seconds
+\subq{CALL sla\_CAF2R (IDEG, IAMIN, ASEC, RAD, J)}
+     {CALL sla\_DAF2R (IDEG, IAMIN, ASEC, RAD, J)}
+   Degrees, arcminutes, arcseconds to radians
+\subq{CALL sla\_CR2AF (NDP, ANGLE, SIGN, IDMSF)}
+     {CALL sla\_DR2AF (NDP, ANGLE, SIGN, IDMSF)}
+   Radians to degrees, arcminutes, arcseconds
+\end{callset}
+
+\callhead{Angles, Vectors and Rotation Matrices}
+\begin{callset}
+\subq{R~=~sla\_RANGE (ANGLE)}
+     {D~=~sla\_DRANGE (ANGLE)}
+   Normalize angle into range $\pm\pi$
+\subq{R~=~sla\_RANORM (ANGLE)}
+     {D~=~sla\_DRANRM (ANGLE)}
+   Normalize angle into range $0\!-\!2\pi$
+\subq{CALL sla\_CS2C (A, B, V)}
+     {CALL sla\_DCS2C (A, B, V)}
+   Spherical coordinates to \xyz
+\subq{CALL sla\_CC2S (V, A, B)}
+     {CALL sla\_DCC2S (V, A, B)}
+   \xyz\ to spherical coordinates
+\subq{R~=~sla\_VDV (VA, VB)}
+     {D~=~sla\_DVDV (VA, VB)}
+   Scalar product of two 3-vectors
+\subq{CALL sla\_VXV (VA, VB, VC)}
+     {CALL sla\_DVXV (VA, VB, VC)}
+   Vector product of two 3-vectors
+\subq{CALL sla\_VN (V, UV, VM)}
+     {CALL sla\_DVN (V, UV, VM)}
+   Normalize a 3-vector also giving the modulus
+\subq{R~=~sla\_SEP (A1, B1, A2, B2)}
+     {D~=~sla\_DSEP (A1, B1, A2, B2)}
+   Angle between two points on a sphere
+\subq{R~=~sla\_SEPV (V1, V2)}
+     {D~=~sla\_DSEPV (V1, V2)}
+   Angle between two \xyz\ vectors
+\subq{R~=~sla\_BEAR (A1, B1, A2, B2)}
+     {D~=~sla\_DBEAR (A1, B1, A2, B2)}
+   Direction of one point on a sphere seen from another
+\subq{R~=~sla\_PAV (V1, V2)}
+     {D~=~sla\_DPAV (V1, V2)}
+   Position-angle of one \xyz\ with respect to another
+\subq{CALL sla\_EULER (ORDER, PHI, THETA, PSI, RMAT)}
+     {CALL sla\_DEULER (ORDER, PHI, THETA, PSI, RMAT)}
+   Form rotation matrix from three Euler angles
+\subq{CALL sla\_AV2M (AXVEC, RMAT)}
+     {CALL sla\_DAV2M (AXVEC, RMAT)}
+   Form rotation matrix from axial vector
+\subq{CALL sla\_M2AV (RMAT, AXVEC)}
+     {CALL sla\_DM2AV (RMAT, AXVEC)}
+   Determine axial vector from rotation matrix
+\subq{CALL sla\_MXV (RM, VA, VB)}
+     {CALL sla\_DMXV (DM, VA, VB)}
+   Rotate vector forwards
+\subq{CALL sla\_IMXV (RM, VA, VB)}
+     {CALL sla\_DIMXV (DM, VA, VB)}
+   Rotate vector backwards
+\subq{CALL sla\_MXM (A, B, C)}
+     {CALL sla\_DMXM (A, B, C)}
+   Product of two 3x3 matrices
+\subq{CALL sla\_CS2C6 (A, B, R, AD, BD, RD, V)}
+     {CALL sla\_DS2C6 (A, B, R, AD, BD, RD, V)}
+   Conversion of position and velocity in spherical
+     coordinates to Cartesian coordinates
+\subq{CALL sla\_CC62S (V, A, B, R, AD, BD, RD)}
+     {CALL sla\_DC62S (V, A, B, R, AD, BD, RD)}
+   Conversion of position and velocity in Cartesian
+     coordinates to spherical coordinates
+\end{callset}
+
+\callhead{Calendars}
+\begin{callset}
+\subp{CALL sla\_CLDJ (IY, IM, ID, DJM, J)}
+   Gregorian Calendar to Modified Julian Date
+\subp{CALL sla\_CALDJ (IY, IM, ID, DJM, J)}
+   Gregorian Calendar to Modified Julian Date,
+     permitting century default
+\subp{CALL sla\_DJCAL (NDP, DJM, IYMDF, J)}
+   Modified Julian Date to Gregorian Calendar,
+     in a form convenient for formatted output
+\subp{CALL sla\_DJCL (DJM, IY, IM, ID, FD, J)}
+   Modified Julian Date to Gregorian Year, Month, Day, Fraction
+\subp{CALL sla\_CALYD (IY, IM, ID, NY, ND, J)}
+   Calendar to year and day in year, permitting century default
+\subp{CALL sla\_CLYD (IY, IM, ID, NY, ND, J)}
+   Calendar to year and day in year
+\subp{D~=~sla\_EPB (DATE)}
+   Modified Julian Date to Besselian Epoch
+\subp{D~=~sla\_EPB2D (EPB)}
+   Besselian Epoch to Modified Julian Date
+\subp{D~=~sla\_EPJ (DATE)}
+   Modified Julian Date to Julian Epoch
+\subp{D~=~sla\_EPJ2D (EPJ)}
+   Julian Epoch to Modified Julian Date
+\end{callset}
+
+\callhead{Time Scales}
+\begin{callset}
+\subp{D~=~sla\_GMST (UT1)}
+   Conversion from Universal Time to sidereal time
+\subp{D~=~sla\_GMSTA (DATE, UT1)}
+   Conversion from Universal Time to sidereal time, rounding errors minimized
+\subp{D~=~sla\_EQEQX (DATE)}
+   Equation of the equinoxes
+\subp{D~=~sla\_DAT (DJU)}
+   Offset of Atomic Time from Coordinated Universal Time: TAI$-$UTC
+\subp{D~=~sla\_DT (EPOCH)}
+   Approximate offset between dynamical time and universal time
+\subp{D~=~sla\_DTT (DJU)}
+   Offset of Terrestrial Time from Coordinated Universal Time: TT$-$UTC
+\subp{D~=~sla\_RCC (TDB, UT1, WL, U, V)}
+   Relativistic clock correction: TDB$-$TT
+\end{callset}
+
+\callhead{Precession and Nutation}
+\begin{callset}
+\subp{CALL sla\_NUT (DATE, RMATN)}
+   Nutation matrix
+\subp{CALL sla\_NUTC (DATE, DPSI, DEPS, EPS0)}
+   Longitude and obliquity components of nutation, and
+     mean obliquity
+\subp{CALL sla\_NUTC80 (DATE, DPSI, DEPS, EPS0)}
+   Longitude and obliquity components of nutation, and
+     mean obliquity, IAU 1980
+\subp{CALL sla\_PREC (EP0, EP1, RMATP)}
+   Precession matrix (IAU)
+\subp{CALL sla\_PRECL (EP0, EP1, RMATP)}
+   Precession matrix (suitable for long periods)
+\subp{CALL sla\_PRENUT (EPOCH, DATE, RMATPN)}
+   Combined precession-nutation matrix
+\subp{CALL sla\_PREBN (BEP0, BEP1, RMATP)}
+   Precession matrix, old system
+\subp{CALL sla\_PRECES (SYSTEM, EP0, EP1, RA, DC)}
+   Precession, in either the old or the new system
+\end{callset}
+
+\callhead{Proper Motion}
+\begin{callset}
+\subp{CALL sla\_PM (R0, D0, PR, PD, PX, RV, EP0, EP1, R1, D1)}
+   Adjust for proper motion
+\end{callset}
+
+\callhead{FK4/FK5/Hipparcos Conversions}
+\begin{callset}
+\subp{CALL sla\_FK425 (\vtop
+                       {\hbox{R1950, D1950, DR1950, DD1950, P1950, V1950,}
+                        \hbox{R2000, D2000, DR2000, DD2000, P2000, V2000)}}}
+   Convert B1950.0 FK4 star data to J2000.0 FK5
+\subp{CALL sla\_FK45Z (R1950, D1950, EPOCH, R2000, D2000)}
+   Convert B1950.0 FK4 position to J2000.0 FK5 assuming zero
+   FK5 proper motion and no parallax
+\subp{CALL sla\_FK524 (\vtop
+                       {\hbox{R2000, D2000, DR2000, DD2000, P2000, V2000,}
+                        \hbox{R1950, D1950, DR1950, DD1950, P1950, V1950)}}}
+   Convert J2000.0 FK5 star data to B1950.0 FK4
+\subp{CALL sla\_FK54Z (R2000, D2000, BEPOCH,
+               R1950, D1950, DR1950, DD1950)}
+   Convert J2000.0 FK5 position to B1950.0 FK4 assuming zero
+   FK5 proper motion and no parallax
+\subp{CALL sla\_FK52H (R5, D5, DR5, DD5, RH, DH, DRH, DDH)}
+   Convert J2000.0 FK5 star data to Hipparcos
+\subp{CALL sla\_FK5HZ (R5, D5, EPOCH, RH, DH )}
+   Convert J2000.0 FK5 position to Hipparcos assuming zero Hipparcos
+   proper motion
+\subp{CALL sla\_H2FK5 (RH, DH, DRH, DDH, R5, D5, DR5, DD5)}
+   Convert Hipparcos star data to J2000.0 FK5
+\subp{CALL sla\_HFK5Z (RH, DH, EPOCH, R5, D5, DR5, DD5)}
+   Convert Hipparcos position to J2000.0 FK5 assuming zero Hipparcos
+   proper motion
+\subp{CALL sla\_DBJIN (STRING, NSTRT, DRESLT, J1, J2)}
+   Like sla\_DFLTIN but with extensions to accept leading `B' and `J'
+\subp{CALL sla\_KBJ (JB, E, K, J)}
+   Select epoch prefix `B' or `J'
+\subp{D~=~sla\_EPCO (K0, K, E)}
+   Convert an epoch into the appropriate form -- `B' or `J'
+\end{callset}
+
+\callhead{Elliptic Aberration}
+\begin{callset}
+\subp{CALL sla\_ETRMS (EP, EV)}
+   E-terms
+\subp{CALL sla\_SUBET (RC, DC, EQ, RM, DM)}
+   Remove the E-terms
+\subp{CALL sla\_ADDET (RM, DM, EQ, RC, DC)}
+   Add the E-terms
+\end{callset}
+
+\callhead{Geographical and Geocentric Coordinates}
+\begin{callset}
+\subp{CALL sla\_OBS (NUMBER, ID, NAME, WLONG, PHI, HEIGHT)}
+   Interrogate list of observatory parameters
+\subp{CALL sla\_GEOC (P, H, R, Z)}
+   Convert geodetic position to geocentric
+\subp{CALL sla\_POLMO (ELONGM, PHIM, XP, YP, ELONG, PHI, DAZ)}
+   Polar motion
+\subp{CALL sla\_PVOBS (P, H, STL, PV)}
+   Position and velocity of observatory
+\end{callset}
+
+\callhead{Apparent and Observed Place}
+\begin{callset}
+\subp{CALL sla\_MAP (RM, DM, PR, PD, PX, RV, EQ, DATE, RA, DA)}
+   Mean place to geocentric apparent place
+\subp{CALL sla\_MAPPA (EQ, DATE, AMPRMS)}
+   Precompute mean to apparent parameters
+\subp{CALL sla\_MAPQK (RM, DM, PR, PD, PX, RV, AMPRMS, RA, DA)}
+   Mean to apparent using precomputed parameters
+\subp{CALL sla\_MAPQKZ (RM, DM, AMPRMS, RA, DA)}
+   Mean to apparent using precomputed parameters, for zero proper
+     motion, parallax and radial velocity
+\subp{CALL sla\_AMP (RA, DA, DATE, EQ, RM, DM)}
+   Geocentric apparent place to mean place
+\subp{CALL sla\_AMPQK (RA, DA, AMPRMS, RM, DM)}
+   Apparent to mean using precomputed parameters
+\subp{CALL sla\_AOP (\vtop
+                      {\hbox{RAP, DAP, UTC, DUT, ELONGM, PHIM, HM, XP, YP,}
+                       \hbox{TDK, PMB, RH, WL, TLR, AOB, ZOB, HOB, DOB, ROB)}}}
+   Apparent place to observed place
+\subp{CALL sla\_AOPPA (\vtop
+                        {\hbox{UTC, DUT, ELONGM, PHIM, HM, XP, YP,}
+                         \hbox{TDK, PMB, RH, WL, TLR, AOPRMS)}}}
+   Precompute apparent to observed parameters
+\subp{CALL sla\_AOPPAT (UTC, AOPRMS)}
+   Update sidereal time in apparent to observed parameters
+\subp{CALL sla\_AOPQK (RAP, DAP, AOPRMS, AOB, ZOB, HOB, DOB, ROB)}
+   Apparent to observed using precomputed parameters
+\subp{CALL sla\_OAP (\vtop
+                     {\hbox{TYPE, OB1, OB2, UTC, DUT, ELONGM, PHIM, HM, XP, YP,}
+                      \hbox{TDK, PMB, RH, WL, TLR, RAP, DAP)}}}
+   Observed to apparent
+\subp{CALL sla\_OAPQK (TYPE, OB1, OB2, AOPRMS, RA, DA)}
+   Observed to apparent using precomputed parameters
+\end{callset}
+
+\callhead{Azimuth and Elevation}
+\begin{callset}
+\subp{CALL sla\_ALTAZ (\vtop
+               {\hbox{HA, DEC, PHI,}
+                \hbox{AZ, AZD, AZDD, EL, ELD, ELDD, PA, PAD, PADD)}}}
+   Positions, velocities {\it etc.}\ for an altazimuth mount
+\subq{CALL sla\_E2H (HA, DEC, PHI, AZ, EL)}
+     {CALL sla\_DE2H (HA, DEC, PHI, AZ, EL)}
+   \hadec\ to \azel
+\subq{CALL sla\_H2E (AZ, EL, PHI, HA, DEC)}
+     {CALL sla\_DH2E (AZ, EL, PHI, HA, DEC)}
+   \azel\ to \hadec
+\subp{CALL sla\_PDA2H (P, D, A, H1, J1, H2, J2)}
+   Hour Angle corresponding to a given azimuth
+\subp{CALL sla\_PDQ2H (P, D, Q, H1, J1, H2, J2)}
+   Hour Angle corresponding to a given parallactic angle
+\subp{D~=~sla\_PA (HA, DEC, PHI)}
+   \hadec\ to parallactic angle
+\subp{D~=~sla\_ZD (HA, DEC, PHI)}
+   \hadec\ to zenith distance
+\end{callset}
+
+\callhead{Refraction and Air Mass}
+\begin{callset}
+\subp{CALL sla\_REFRO (ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REF)}
+   Change in zenith distance due to refraction
+\subp{CALL sla\_REFCO (HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REFA, REFB)}
+   Constants for simple refraction model (accurate)
+\subp{CALL sla\_REFCOQ (TDK, PMB, RH, WL, REFA, REFB)}
+   Constants for simple refraction model (fast)
+\subp{CALL sla\_ATMDSP ( TDK, PMB, RH, WL1, REFA1, REFB1, WL2, REFA2, REFB2 )}
+   Adjust refraction constants for colour
+\subp{CALL sla\_REFZ (ZU, REFA, REFB, ZR)}
+   Unrefracted to refracted ZD, simple model
+\subp{CALL sla\_REFV (VU, REFA, REFB, VR)}
+   Unrefracted to refracted \azel\ vector, simple model
+\subp{D~=~sla\_AIRMAS (ZD)}
+   Air mass
+\end{callset}
+
+\callhead{Ecliptic Coordinates}
+\begin{callset}
+\subp{CALL sla\_ECMAT (DATE, RMAT)}
+   Equatorial to ecliptic rotation matrix
+\subp{CALL sla\_EQECL (DR, DD, DATE, DL, DB)}
+   J2000.0 `FK5' to ecliptic coordinates
+\subp{CALL sla\_ECLEQ (DL, DB, DATE, DR, DD)}
+   Ecliptic coordinates to J2000.0 `FK5'
+\end{callset}
+
+\callhead{Galactic Coordinates}
+\begin{callset}
+\subp{CALL sla\_EG50 (DR, DD, DL, DB)}
+   B1950.0 `FK4' to galactic
+\subp{CALL sla\_GE50 (DL, DB, DR, DD)}
+   Galactic to B1950.0 `FK4'
+\subp{CALL sla\_EQGAL (DR, DD, DL, DB)}
+   J2000.0 `FK5' to galactic
+\subp{CALL sla\_GALEQ (DL, DB, DR, DD)}
+   Galactic to J2000.0 `FK5'
+\end{callset}
+
+\callhead{Supergalactic Coordinates}
+\begin{callset}
+\subp{CALL sla\_GALSUP (DL, DB, DSL, DSB)}
+   Galactic to supergalactic
+\subp{CALL sla\_SUPGAL (DSL, DSB, DL, DB)}
+   Supergalactic to galactic
+\end{callset}
+
+\callhead{Ephemerides}
+\begin{callset}
+\subp{CALL sla\_DMOON (DATE, PV)}
+   Approximate geocentric position and velocity of the Moon
+\subp{CALL sla\_EARTH (IY, ID, FD, PV)}
+   Approximate heliocentric position and velocity of the Earth
+\subp{CALL sla\_EPV (DATE, DPH, DVH, DPB, DVB )}
+   Heliocentric and barycentric position and velocity of the Earth
+\subp{CALL sla\_EVP (DATE, DEQX, DVB, DPB, DVH, DPH)}
+   Barycentric and heliocentric velocity and position of the Earth
+\subp{CALL sla\_MOON (IY, ID, FD, PV)}
+   Approximate geocentric position and velocity of the Moon
+\subp{CALL sla\_PLANET (DATE, NP, PV, JSTAT)}
+   Approximate heliocentric position and velocity of a planet
+\subp{CALL sla\_RDPLAN (DATE, NP, ELONG, PHI, RA, DEC, DIAM)}
+   Approximate topocentric apparent place of a planet
+\subp{CALL sla\_PLANEL (\vtop
+                       {\hbox{DATE, JFORM, EPOCH, ORBINC, ANODE, PERIH,}
+                      \hbox{AORQ, E, AORL, DM, PV, JSTAT)}}}
+   Heliocentric position and velocity of a planet, asteroid or
+   comet, starting from orbital elements
+\subp{CALL sla\_PLANTE (\vtop
+                       {\hbox{DATE, ELONG, PHI, JFORM, EPOCH, ORBINC, ANODE,}
+                      \hbox{PERIH, AORQ, E, AORL, DM, RA, DEC, R, JSTAT)}}}
+   Topocentric apparent place of a Solar-System object whose
+   heliocentric orbital elements are known
+\subp{CALL sla\_PLANTU (DATE, ELONG, PHI, U, RA, DEC, R, JSTAT)}
+   Topocentric apparent place of a Solar-System object whose
+   heliocentric universal orbital elements are known
+\subp{CALL sla\_PV2EL (\vtop
+                      {\hbox{PV, DATE, PMASS, JFORMR, JFORM, EPOCH, ORBINC,}
+                     \hbox{ANODE, PERIH, AORQ, E, AORL, DM, JSTAT)}}}
+   Orbital elements of a planet from instantaneous position and velocity
+\subp{CALL sla\_PERTEL (\vtop
+                       {\hbox{JFORM, DATE0, DATE1,}
+                     \hbox{EPOCH0, ORBI0, ANODE0, PERIH0, AORQ0, E0, AM0,}
+                     \hbox{EPOCH1, ORBI1, ANODE1, PERIH1, AORQ1, E1, AM1,}
+                     \hbox{JSTAT)}}}
+   Update elements by applying perturbations
+\subp{CALL sla\_EL2UE (\vtop
+                      {\hbox{DATE, JFORM, EPOCH, ORBINC, ANODE,}
+                     \hbox{PERIH, AORQ, E, AORL, DM,}
+                     \hbox{U, JSTAT)}}}
+   Transform conventional elements to universal elements
+\subp{CALL sla\_UE2EL (\vtop
+                      {\hbox{U, JFORMR,}
+                     \hbox{JFORM, EPOCH, ORBINC, ANODE, PERIH,}
+                     \hbox{AORQ, E, AORL, DM, JSTAT)}}}
+   Transform universal elements to conventional elements
+\subp{CALL sla\_PV2UE (PV, DATE, PMASS, U, JSTAT)}
+   Package a position and velocity for use as universal elements
+\subp{CALL sla\_UE2PV (DATE, U, PV, JSTAT)}
+   Extract the position and velocity from universal elements
+\subp{CALL sla\_PERTUE (DATE, U, JSTAT)}
+   Update universal elements by applying perturbations
+\subp{R~=~sla\_RVEROT (PHI, RA, DA, ST)}
+   Velocity component due to rotation of the Earth
+\subp{CALL sla\_ECOR (RM, DM, IY, ID, FD, RV, TL)}
+   Components of velocity and light time due to Earth orbital motion
+\subp{R~=~sla\_RVLSRD (R2000, D2000)}
+   Velocity component due to solar motion wrt dynamical LSR
+\subp{R~=~sla\_RVLSRK (R2000, D2000)}
+   Velocity component due to solar motion wrt kinematical LSR
+\subp{R~=~sla\_RVGALC (R2000, D2000)}
+   Velocity component due to rotation of the Galaxy
+\subp{R~=~sla\_RVLG (R2000, D2000)}
+   Velocity component due to rotation and translation of the
+   Galaxy, relative to the mean motion of the local group
+\end{callset}
+
+\callhead{Astrometry}
+\begin{callset}
+\subq{CALL sla\_S2TP (RA, DEC, RAZ, DECZ, XI, ETA, J)}
+     {CALL sla\_DS2TP (RA, DEC, RAZ, DECZ, XI, ETA, J)}
+   Transform spherical coordinates into tangent plane
+\subq{CALL sla\_V2TP (V, V0, XI, ETA, J)}
+     {CALL sla\_DV2TP (V, V0, XI, ETA, J)}
+   Transform \xyz\ into tangent plane coordinates
+\subq{CALL sla\_DTP2S (XI, ETA, RAZ, DECZ, RA, DEC)}
+     {CALL sla\_TP2S (XI, ETA, RAZ, DECZ, RA, DEC)}
+   Transform tangent plane coordinates into spherical coordinates
+\subq{CALL sla\_DTP2V (XI, ETA, V0, V)}
+     {CALL sla\_TP2V (XI, ETA, V0, V)}
+   Transform tangent plane coordinates into \xyz
+\subq{CALL sla\_DTPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N)}
+     {CALL sla\_TPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N)}
+   Get plate centre from star \radec\ and tangent plane coordinates
+\subq{CALL sla\_DTPV2C (XI, ETA, V, V01, V02, N)}
+     {CALL sla\_TPV2C (XI, ETA, V, V01, V02, N)}
+   Get plate centre from star \xyz\ and tangent plane coordinates
+\subp{CALL sla\_PCD (DISCO, X, Y)}
+   Apply pincushion/barrel distortion
+\subp{CALL sla\_UNPCD (DISCO, X, Y)}
+   Remove pincushion/barrel distortion
+\subp{CALL sla\_FITXY (ITYPE, NP, XYE, XYM, COEFFS, J)}
+   Fit a linear model to relate two sets of \xy\ coordinates
+\subp{CALL sla\_PXY (NP, XYE, XYM, COEFFS, XYP, XRMS, YRMS, RRMS)}
+   Compute predicted coordinates and residuals
+\subp{CALL sla\_INVF (FWDS, BKWDS, J)}
+   Invert a linear model
+\subp{CALL sla\_XY2XY (X1, Y1, COEFFS, X2, Y2)}
+   Transform one \xy
+\subp{CALL sla\_DCMPF (COEFFS, XZ, YZ, XS, YS, PERP, ORIENT)}
+   Decompose a linear fit into scales {\it etc.}
+\end{callset}
+
+\callhead{Numerical Methods}
+\begin{callset}
+\subp{CALL sla\_COMBN (NSEL, NCAND, LIST, J)}
+   Next combination (subset from a specified number of items)
+\subp{CALL sla\_PERMUT (N, ISTATE, IORDER, J)}
+   Next permutation of a specified number of items
+\subq{CALL sla\_SMAT (N, A, Y, D, JF, IW)}
+     {CALL sla\_DMAT (N, A, Y, D, JF, IW)}
+   Matrix inversion and solution of simultaneous equations
+\subp{CALL sla\_SVD (M, N, MP, NP, A, W, V, WORK, JSTAT)}
+   Singular value decomposition of a matrix
+\subp{CALL sla\_SVDSOL (M, N, MP, NP, B, U, W, V, WORK, X)}
+   Solution from given vector plus SVD
+\subp{CALL sla\_SVDCOV (N, NP, NC, W, V, WORK, CVM)}
+   Covariance matrix from SVD
+\subp{R~=~sla\_RANDOM (SEED)}
+   Generate pseudo-random real number in the range {$0 \leq x < 1$}
+\subp{R~=~sla\_GRESID (S)}
+   Generate pseudo-random normal deviate ($\equiv$ `Gaussian residual')
+\end{callset}
+
+\callhead{Real-time}
+\begin{callset}
+\subp{CALL sla\_WAIT (DELAY)}
+    Interval wait
+\end{callset}
+
+\end{document}
diff --git a/math/slalib/supgal.f b/math/slalib/supgal.f
new file mode 100644
index 00000000..4df6b10d
--- /dev/null
+++ b/math/slalib/supgal.f
@@ -0,0 +1,97 @@
+      SUBROUTINE slSUGA (DSL, DSB, DL, DB)
+*+
+*     - - - - - - -
+*      S U G A
+*     - - - - - - -
+*
+*  Transformation from de Vaucouleurs supergalactic coordinates
+*  to IAU 1958 galactic coordinates (double precision)
+*
+*  Given:
+*     DSL,DSB     dp       supergalactic longitude and latitude
+*
+*  Returned:
+*     DL,DB       dp       galactic longitude and latitude L2,B2
+*
+*  (all arguments are radians)
+*
+*  Called:
+*     slDS2C, slDIMV, slDC2S, slDA2P, slDA1P
+*
+*  References:
+*
+*     de Vaucouleurs, de Vaucouleurs, & Corwin, Second Reference
+*     Catalogue of Bright Galaxies, U. Texas, page 8.
+*
+*     Systems & Applied Sciences Corp., Documentation for the
+*     machine-readable version of the above catalogue,
+*     Contract NAS 5-26490.
+*
+*    (These two references give different values for the galactic
+*     longitude of the supergalactic origin.  Both are wrong;  the
+*     correct value is L2=137.37.)
+*
+*  P.T.Wallace   Starlink   March 1986
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DSL,DSB,DL,DB
+
+      DOUBLE PRECISION slDA2P,slDA1P
+
+      DOUBLE PRECISION V1(3),V2(3)
+
+*
+*  System of supergalactic coordinates:
+*
+*    SGL   SGB        L2     B2      (deg)
+*     -    +90      47.37  +6.32
+*     0     0         -      0
+*
+*  Galactic to supergalactic rotation matrix:
+*
+      DOUBLE PRECISION RMAT(3,3)
+      DATA RMAT(1,1),RMAT(1,2),RMAT(1,3),
+     :     RMAT(2,1),RMAT(2,2),RMAT(2,3),
+     :     RMAT(3,1),RMAT(3,2),RMAT(3,3)/
+     : -0.735742574804D0,+0.677261296414D0,+0.000000000000D0,
+     : -0.074553778365D0,-0.080991471307D0,+0.993922590400D0,
+     : +0.673145302109D0,+0.731271165817D0,+0.110081262225D0/
+
+
+
+*  Spherical to Cartesian
+      CALL slDS2C(DSL,DSB,V1)
+
+*  Supergalactic to galactic
+      CALL slDIMV(RMAT,V1,V2)
+
+*  Cartesian to spherical
+      CALL slDC2S(V2,DL,DB)
+
+*  Express in conventional ranges
+      DL=slDA2P(DL)
+      DB=slDA1P(DB)
+
+      END
diff --git a/math/slalib/svd.f b/math/slalib/svd.f
new file mode 100644
index 00000000..59f53cfd
--- /dev/null
+++ b/math/slalib/svd.f
@@ -0,0 +1,401 @@
+      SUBROUTINE slSVD (M, N, MP, NP, A, W, V, WORK, JSTAT)
+*+
+*     - - - -
+*      S V D
+*     - - - -
+*
+*  Singular value decomposition  (double precision)
+*
+*  This routine expresses a given matrix A as the product of
+*  three matrices U, W, V:
+*
+*     A = U x W x VT
+*
+*  Where:
+*
+*     A   is any M (rows) x N (columns) matrix, where M.GE.N
+*     U   is an M x N column-orthogonal matrix
+*     W   is an N x N diagonal matrix with W(I,I).GE.0
+*     VT  is the transpose of an N x N orthogonal matrix
+*
+*     Note that M and N, above, are the LOGICAL dimensions of the
+*     matrices and vectors concerned, which can be located in
+*     arrays of larger PHYSICAL dimensions, given by MP and NP.
+*
+*  Given:
+*     M,N    i         numbers of rows and columns in matrix A
+*     MP,NP  i         physical dimensions of array containing matrix A
+*     A      d(MP,NP)  array containing MxN matrix A
+*
+*  Returned:
+*     A      d(MP,NP)  array containing MxN column-orthogonal matrix U
+*     W      d(N)      NxN diagonal matrix W (diagonal elements only)
+*     V      d(NP,NP)  array containing NxN orthogonal matrix V
+*     WORK   d(N)      workspace
+*     JSTAT  i         0 = OK, -1 = A wrong shape, >0 = index of W
+*                      for which convergence failed.  See note 2, below.
+*
+*   Notes:
+*
+*   1)  V contains matrix V, not the transpose of matrix V.
+*
+*   2)  If the status JSTAT is greater than zero, this need not
+*       necessarily be treated as a failure.  It means that, due to
+*       chance properties of the matrix A, the QR transformation
+*       phase of the routine did not fully converge in a predefined
+*       number of iterations, something that very seldom occurs.
+*       When this condition does arise, it is possible that the
+*       elements of the diagonal matrix W have not been correctly
+*       found.  However, in practice the results are likely to
+*       be trustworthy.  Applications should report the condition
+*       as a warning, but then proceed normally.
+*
+*  References:
+*     The algorithm is an adaptation of the routine SVD in the EISPACK
+*     library (Garbow et al 1977, EISPACK Guide Extension, Springer
+*     Verlag), which is a FORTRAN 66 implementation of the Algol
+*     routine SVD of Wilkinson & Reinsch 1971 (Handbook for Automatic
+*     Computation, vol 2, ed Bauer et al, Springer Verlag).  These
+*     references give full details of the algorithm used here.  A good
+*     account of the use of SVD in least squares problems is given in
+*     Numerical Recipes (Press et al 1986, Cambridge University Press),
+*     which includes another variant of the EISPACK code.
+*
+*  Last revision:   8 September 2005
+*
+*  Copyright P.T.Wallace.  All rights reserved.
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER M,N,MP,NP
+      DOUBLE PRECISION A(MP,NP),W(N),V(NP,NP),WORK(N)
+      INTEGER JSTAT
+
+*  Maximum number of iterations in QR phase
+      INTEGER ITMAX
+      PARAMETER (ITMAX=30)
+
+      INTEGER L,L1,I,K,J,K1,ITS,I1
+      LOGICAL CANCEL
+      DOUBLE PRECISION G,SCALE,AN,S,X,F,H,C,Y,Z
+
+
+
+*  Variable initializations to avoid compiler warnings.
+      L = 0
+      L1 = 0
+
+*  Check that the matrix is the right shape
+      IF (M.LT.N) THEN
+
+*     No:  error status
+         JSTAT = -1
+
+      ELSE
+
+*     Yes:  preset the status to OK
+         JSTAT = 0
+
+*
+*     Householder reduction to bidiagonal form
+*     ----------------------------------------
+
+         G = 0D0
+         SCALE = 0D0
+         AN = 0D0
+         DO I=1,N
+            L = I+1
+            WORK(I) = SCALE*G
+            G = 0D0
+            S = 0D0
+            SCALE = 0D0
+            IF (I.LE.M) THEN
+               DO K=I,M
+                  SCALE = SCALE+ABS(A(K,I))
+               END DO
+               IF (SCALE.NE.0D0) THEN
+                  DO K=I,M
+                     X = A(K,I)/SCALE
+                     A(K,I) = X
+                     S = S+X*X
+                  END DO
+                  F = A(I,I)
+                  G = -SIGN(SQRT(S),F)
+                  H = F*G-S
+                  A(I,I) = F-G
+                  IF (I.NE.N) THEN
+                     DO J=L,N
+                        S = 0D0
+                        DO K=I,M
+                           S = S+A(K,I)*A(K,J)
+                        END DO
+                        F = S/H
+                        DO K=I,M
+                           A(K,J) = A(K,J)+F*A(K,I)
+                        END DO
+                     END DO
+                  END IF
+                  DO K=I,M
+                     A(K,I) = SCALE*A(K,I)
+                  END DO
+               END IF
+            END IF
+            W(I) = SCALE*G
+            G = 0D0
+            S = 0D0
+            SCALE = 0D0
+            IF (I.LE.M .AND. I.NE.N) THEN
+               DO K=L,N
+                  SCALE = SCALE+ABS(A(I,K))
+               END DO
+               IF (SCALE.NE.0D0) THEN
+                  DO K=L,N
+                     X = A(I,K)/SCALE
+                     A(I,K) = X
+                     S = S+X*X
+                  END DO
+                  F = A(I,L)
+                  G = -SIGN(SQRT(S),F)
+                  H = F*G-S
+                  A(I,L) = F-G
+                  DO K=L,N
+                     WORK(K) = A(I,K)/H
+                  END DO
+                  IF (I.NE.M) THEN
+                     DO J=L,M
+                        S = 0D0
+                        DO K=L,N
+                           S = S+A(J,K)*A(I,K)
+                        END DO
+                        DO K=L,N
+                           A(J,K) = A(J,K)+S*WORK(K)
+                        END DO
+                     END DO
+                  END IF
+                  DO K=L,N
+                     A(I,K) = SCALE*A(I,K)
+                  END DO
+               END IF
+            END IF
+
+*        Overestimate of largest column norm for convergence test
+            AN = MAX(AN,ABS(W(I))+ABS(WORK(I)))
+
+         END DO
+
+*
+*     Accumulation of right-hand transformations
+*     ------------------------------------------
+
+         DO I=N,1,-1
+            IF (I.NE.N) THEN
+               IF (G.NE.0D0) THEN
+                  DO J=L,N
+                     V(J,I) = (A(I,J)/A(I,L))/G
+                  END DO
+                  DO J=L,N
+                     S = 0D0
+                     DO K=L,N
+                        S = S+A(I,K)*V(K,J)
+                     END DO
+                     DO K=L,N
+                        V(K,J) = V(K,J)+S*V(K,I)
+                     END DO
+                  END DO
+               END IF
+               DO J=L,N
+                  V(I,J) = 0D0
+                  V(J,I) = 0D0
+               END DO
+            END IF
+            V(I,I) = 1D0
+            G = WORK(I)
+            L = I
+         END DO
+
+*
+*     Accumulation of left-hand transformations
+*     -----------------------------------------
+
+         DO I=N,1,-1
+            L = I+1
+            G = W(I)
+            IF (I.NE.N) THEN
+               DO J=L,N
+                  A(I,J) = 0D0
+               END DO
+            END IF
+            IF (G.NE.0D0) THEN
+               IF (I.NE.N) THEN
+                  DO J=L,N
+                     S = 0D0
+                     DO K=L,M
+                        S = S+A(K,I)*A(K,J)
+                     END DO
+                     F = (S/A(I,I))/G
+                     DO K=I,M
+                        A(K,J) = A(K,J)+F*A(K,I)
+                     END DO
+                  END DO
+               END IF
+               DO J=I,M
+                  A(J,I) = A(J,I)/G
+               END DO
+            ELSE
+               DO J=I,M
+                  A(J,I) = 0D0
+               END DO
+            END IF
+            A(I,I) = A(I,I)+1D0
+         END DO
+
+*
+*     Diagonalisation of the bidiagonal form
+*     --------------------------------------
+
+         DO K=N,1,-1
+            K1 = K-1
+
+*        Iterate until converged
+            ITS = 0
+            DO WHILE (ITS.LT.ITMAX)
+               ITS = ITS+1
+
+*           Test for splitting into submatrices
+               CANCEL = .TRUE.
+               DO L=K,1,-1
+                  L1 = L-1
+                  IF (AN+ABS(WORK(L)).EQ.AN) THEN
+                     CANCEL = .FALSE.
+                     GO TO 10
+                  END IF
+*              (Following never attempted for L=1 because WORK(1) is zero)
+                  IF (AN+ABS(W(L1)).EQ.AN) GO TO 10
+               END DO
+ 10            CONTINUE
+
+*           Cancellation of WORK(L) if L>1
+               IF (CANCEL) THEN
+                  C = 0D0
+                  S = 1D0
+                  DO I=L,K
+                     F = S*WORK(I)
+                     IF (AN+ABS(F).EQ.AN) GO TO 20
+                     G = W(I)
+                     H = SQRT(F*F+G*G)
+                     W(I) = H
+                     C = G/H
+                     S = -F/H
+                     DO J=1,M
+                        Y = A(J,L1)
+                        Z = A(J,I)
+                        A(J,L1) = Y*C+Z*S
+                        A(J,I) = -Y*S+Z*C
+                     END DO
+                  END DO
+ 20               CONTINUE
+               END IF
+
+*           Converged?
+               Z = W(K)
+               IF (L.EQ.K) THEN
+
+*              Yes:  stop iterating
+                  ITS = ITMAX
+
+*              Ensure singular values non-negative
+                  IF (Z.LT.0D0) THEN
+                     W(K) = -Z
+                     DO J=1,N
+                        V(J,K) = -V(J,K)
+                     END DO
+                  END IF
+               ELSE
+
+*              Not converged yet:  set status if iteration limit reached
+                  IF (ITS.EQ.ITMAX) JSTAT = K
+
+*              Shift from bottom 2x2 minor
+                  X = W(L)
+                  Y = W(K1)
+                  G = WORK(K1)
+                  H = WORK(K)
+                  F = ((Y-Z)*(Y+Z)+(G-H)*(G+H))/(2D0*H*Y)
+                  IF (ABS(F).LE.1D15) THEN
+                     G = SQRT(F*F+1D0)
+                  ELSE
+                     G = ABS(F)
+                  END IF
+                  F = ((X-Z)*(X+Z)+H*(Y/(F+SIGN(G,F))-H))/X
+
+*              Next QR transformation
+                  C = 1D0
+                  S = 1D0
+                  DO I1=L,K1
+                     I = I1+1
+                     G = WORK(I)
+                     Y = W(I)
+                     H = S*G
+                     G = C*G
+                     Z = SQRT(F*F+H*H)
+                     WORK(I1) = Z
+                     IF (Z.NE.0D0) THEN
+                        C = F/Z
+                        S = H/Z
+                     ELSE
+                        C = 1D0
+                        S = 0D0
+                     END IF
+                     F = X*C+G*S
+                     G = -X*S+G*C
+                     H = Y*S
+                     Y = Y*C
+                     DO J=1,N
+                        X = V(J,I1)
+                        Z = V(J,I)
+                        V(J,I1) = X*C+Z*S
+                        V(J,I) = -X*S+Z*C
+                     END DO
+                     Z = SQRT(F*F+H*H)
+                     W(I1) = Z
+                     IF (Z.NE.0D0) THEN
+                        C = F/Z
+                        S = H/Z
+                     END IF
+                     F = C*G+S*Y
+                     X = -S*G+C*Y
+                     DO J=1,M
+                        Y = A(J,I1)
+                        Z = A(J,I)
+                        A(J,I1) = Y*C+Z*S
+                        A(J,I) = -Y*S+Z*C
+                     END DO
+                  END DO
+                  WORK(L) = 0D0
+                  WORK(K) = F
+                  W(K) = X
+               END IF
+            END DO
+         END DO
+      END IF
+
+      END
diff --git a/math/slalib/svdcov.f b/math/slalib/svdcov.f
new file mode 100644
index 00000000..02a6be0e
--- /dev/null
+++ b/math/slalib/svdcov.f
@@ -0,0 +1,78 @@
+      SUBROUTINE slSVDC (N, NP, NC, W, V, WORK, CVM)
+*+
+*     - - - - - - -
+*      S V D C
+*     - - - - - - -
+*
+*  From the W and V matrices from the SVD factorisation of a matrix
+*  (as obtained from the slSVD routine), obtain the covariance matrix.
+*
+*  (double precision)
+*
+*  Given:
+*     N      i         number of rows and columns in matrices W and V
+*     NP     i         first dimension of array containing matrix V
+*     NC     i         first dimension of array to receive CVM
+*     W      d(N)      NxN diagonal matrix W (diagonal elements only)
+*     V      d(NP,NP)  array containing NxN orthogonal matrix V
+*
+*  Returned:
+*     WORK   d(N)      workspace
+*     CVM    d(NC,NC)  array to receive covariance matrix
+*
+*  Reference:
+*     Numerical Recipes, section 14.3.
+*
+*  P.T.Wallace   Starlink   December 1988
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER N,NP,NC
+      DOUBLE PRECISION W(N),V(NP,NP),WORK(N),CVM(NC,NC)
+
+      INTEGER I,J,K
+      DOUBLE PRECISION S
+
+
+
+      DO I=1,N
+         S=W(I)
+         IF (S.NE.0D0) THEN
+            WORK(I)=1D0/(S*S)
+         ELSE
+            WORK(I)=0D0
+         END IF
+      END DO
+      DO I=1,N
+         DO J=1,I
+            S=0D0
+            DO K=1,N
+               S=S+V(I,K)*V(J,K)*WORK(K)
+            END DO
+            CVM(I,J)=S
+            CVM(J,I)=S
+         END DO
+      END DO
+
+      END
diff --git a/math/slalib/svdsol.f b/math/slalib/svdsol.f
new file mode 100644
index 00000000..53209f2d
--- /dev/null
+++ b/math/slalib/svdsol.f
@@ -0,0 +1,127 @@
+      SUBROUTINE slSVDS (M, N, MP, NP, B, U, W, V, WORK, X)
+*+
+*     - - - - - - -
+*      S V D S
+*     - - - - - - -
+*
+*  From a given vector and the SVD of a matrix (as obtained from
+*  the SVD routine), obtain the solution vector (double precision)
+*
+*  This routine solves the equation:
+*
+*     A . x = b
+*
+*  where:
+*
+*     A   is a given M (rows) x N (columns) matrix, where M.GE.N
+*     x   is the N-vector we wish to find
+*     b   is a given M-vector
+*
+*  by means of the Singular Value Decomposition method (SVD).  In
+*  this method, the matrix A is first factorised (for example by
+*  the routine slSVD) into the following components:
+*
+*     A = U x W x VT
+*
+*  where:
+*
+*     A   is the M (rows) x N (columns) matrix
+*     U   is an M x N column-orthogonal matrix
+*     W   is an N x N diagonal matrix with W(I,I).GE.0
+*     VT  is the transpose of an NxN orthogonal matrix
+*
+*     Note that M and N, above, are the LOGICAL dimensions of the
+*     matrices and vectors concerned, which can be located in
+*     arrays of larger PHYSICAL dimensions MP and NP.
+*
+*  The solution is found from the expression:
+*
+*     x = V . [diag(1/Wj)] . (transpose(U) . b)
+*
+*  Notes:
+*
+*  1)  If matrix A is square, and if the diagonal matrix W is not
+*      adjusted, the method is equivalent to conventional solution
+*      of simultaneous equations.
+*
+*  2)  If M>N, the result is a least-squares fit.
+*
+*  3)  If the solution is poorly determined, this shows up in the
+*      SVD factorisation as very small or zero Wj values.  Where
+*      a Wj value is small but non-zero it can be set to zero to
+*      avoid ill effects.  The present routine detects such zero
+*      Wj values and produces a sensible solution, with highly
+*      correlated terms kept under control rather than being allowed
+*      to elope to infinity, and with meaningful values for the
+*      other terms.
+*
+*  Given:
+*     M,N    i         numbers of rows and columns in matrix A
+*     MP,NP  i         physical dimensions of array containing matrix A
+*     B      d(M)      known vector b
+*     U      d(MP,NP)  array containing MxN matrix U
+*     W      d(N)      NxN diagonal matrix W (diagonal elements only)
+*     V      d(NP,NP)  array containing NxN orthogonal matrix V
+*
+*  Returned:
+*     WORK   d(N)      workspace
+*     X      d(N)      unknown vector x
+*
+*  Reference:
+*     Numerical Recipes, section 2.9.
+*
+*  P.T.Wallace   Starlink   29 October 1993
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      INTEGER M,N,MP,NP
+      DOUBLE PRECISION B(M),U(MP,NP),W(N),V(NP,NP),WORK(N),X(N)
+
+      INTEGER J,I,JJ
+      DOUBLE PRECISION S
+
+
+
+*  Calculate [diag(1/Wj)] . transpose(U) . b (or zero for zero Wj)
+      DO J=1,N
+         S=0D0
+         IF (W(J).NE.0D0) THEN
+            DO I=1,M
+               S=S+U(I,J)*B(I)
+            END DO
+            S=S/W(J)
+         END IF
+         WORK(J)=S
+      END DO
+
+*  Multiply by matrix V to get result
+      DO J=1,N
+         S=0D0
+         DO JJ=1,N
+            S=S+V(J,JJ)*WORK(JJ)
+         END DO
+         X(J)=S
+      END DO
+
+      END
diff --git a/math/slalib/tp2s.f b/math/slalib/tp2s.f
new file mode 100644
index 00000000..f8d31895
--- /dev/null
+++ b/math/slalib/tp2s.f
@@ -0,0 +1,60 @@
+      SUBROUTINE slTP2S (XI, ETA, RAZ, DECZ, RA, DEC)
+*+
+*     - - - - -
+*      T P 2 S
+*     - - - - -
+*
+*  Transform tangent plane coordinates into spherical
+*  (single precision)
+*
+*  Given:
+*     XI,ETA      real  tangent plane rectangular coordinates
+*     RAZ,DECZ    real  spherical coordinates of tangent point
+*
+*  Returned:
+*     RA,DEC      real  spherical coordinates (0-2pi,+/-pi/2)
+*
+*  Called:        slRA2P
+*
+*  P.T.Wallace   Starlink   24 July 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL XI,ETA,RAZ,DECZ,RA,DEC
+
+      REAL slRA2P
+
+      REAL SDECZ,CDECZ,DENOM
+
+
+
+      SDECZ=SIN(DECZ)
+      CDECZ=COS(DECZ)
+
+      DENOM=CDECZ-ETA*SDECZ
+
+      RA=slRA2P(ATAN2(XI,DENOM)+RAZ)
+      DEC=ATAN2(SDECZ+ETA*CDECZ,SQRT(XI*XI+DENOM*DENOM))
+
+      END
diff --git a/math/slalib/tp2v.f b/math/slalib/tp2v.f
new file mode 100644
index 00000000..ba2ff7dd
--- /dev/null
+++ b/math/slalib/tp2v.f
@@ -0,0 +1,74 @@
+      SUBROUTINE slTP2V (XI, ETA, V0, V)
+*+
+*     - - - - -
+*      T P 2 V
+*     - - - - -
+*
+*  Given the tangent-plane coordinates of a star and the direction
+*  cosines of the tangent point, determine the direction cosines
+*  of the star.
+*
+*  (single precision)
+*
+*  Given:
+*     XI,ETA    r       tangent plane coordinates of star
+*     V0        r(3)    direction cosines of tangent point
+*
+*  Returned:
+*     V         r(3)    direction cosines of star
+*
+*  Notes:
+*
+*  1  If vector V0 is not of unit length, the returned vector V will
+*     be wrong.
+*
+*  2  If vector V0 points at a pole, the returned vector V will be
+*     based on the arbitrary assumption that the RA of the tangent
+*     point is zero.
+*
+*  3  This routine is the Cartesian equivalent of the routine slTP2S.
+*
+*  P.T.Wallace   Starlink   11 February 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL XI,ETA,V0(3),V(3)
+
+      REAL X,Y,Z,F,R
+
+
+      X=V0(1)
+      Y=V0(2)
+      Z=V0(3)
+      F=SQRT(1.0+XI*XI+ETA*ETA)
+      R=SQRT(X*X+Y*Y)
+      IF (R.EQ.0.0) THEN
+         R=1E-20
+         X=R
+      END IF
+      V(1)=(X-(XI*Y+ETA*X*Z)/R)/F
+      V(2)=(Y+(XI*X-ETA*Y*Z)/R)/F
+      V(3)=(Z+ETA*R)/F
+
+      END
diff --git a/math/slalib/tps2c.f b/math/slalib/tps2c.f
new file mode 100644
index 00000000..80873699
--- /dev/null
+++ b/math/slalib/tps2c.f
@@ -0,0 +1,109 @@
+      SUBROUTINE slTPSC (XI, ETA, RA, DEC, RAZ1, DECZ1,
+     :                                        RAZ2, DECZ2, N)
+*+
+*     - - - - - -
+*      T P S C
+*     - - - - - -
+*
+*  From the tangent plane coordinates of a star of known RA,Dec,
+*  determine the RA,Dec of the tangent point.
+*
+*  (single precision)
+*
+*  Given:
+*     XI,ETA      r    tangent plane rectangular coordinates
+*     RA,DEC      r    spherical coordinates
+*
+*  Returned:
+*     RAZ1,DECZ1  r    spherical coordinates of tangent point, solution 1
+*     RAZ2,DECZ2  r    spherical coordinates of tangent point, solution 2
+*     N           i    number of solutions:
+*                        0 = no solutions returned (note 2)
+*                        1 = only the first solution is useful (note 3)
+*                        2 = both solutions are useful (note 3)
+*
+*  Notes:
+*
+*  1  The RAZ1 and RAZ2 values are returned in the range 0-2pi.
+*
+*  2  Cases where there is no solution can only arise near the poles.
+*     For example, it is clearly impossible for a star at the pole
+*     itself to have a non-zero XI value, and hence it is
+*     meaningless to ask where the tangent point would have to be
+*     to bring about this combination of XI and DEC.
+*
+*  3  Also near the poles, cases can arise where there are two useful
+*     solutions.  The argument N indicates whether the second of the
+*     two solutions returned is useful.  N=1 indicates only one useful
+*     solution, the usual case;  under these circumstances, the second
+*     solution corresponds to the "over-the-pole" case, and this is
+*     reflected in the values of RAZ2 and DECZ2 which are returned.
+*
+*  4  The DECZ1 and DECZ2 values are returned in the range +/-pi, but
+*     in the usual, non-pole-crossing, case, the range is +/-pi/2.
+*
+*  5  This routine is the spherical equivalent of the routine slDPVC.
+*
+*  Called:  slRA2P
+*
+*  P.T.Wallace   Starlink   5 June 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL XI,ETA,RA,DEC,RAZ1,DECZ1,RAZ2,DECZ2
+      INTEGER N
+
+      REAL X2,Y2,SD,CD,SDF,R2,R,S,C
+
+      REAL slRA2P
+
+
+      X2=XI*XI
+      Y2=ETA*ETA
+      SD=SIN(DEC)
+      CD=COS(DEC)
+      SDF=SD*SQRT(1.0+X2+Y2)
+      R2=CD*CD*(1.0+Y2)-SD*SD*X2
+      IF (R2.GE.0.0) THEN
+         R=SQRT(R2)
+         S=SDF-ETA*R
+         C=SDF*ETA+R
+         IF (XI.EQ.0.0.AND.R.EQ.0.0) R=1.0
+         RAZ1=slRA2P(RA-ATAN2(XI,R))
+         DECZ1=ATAN2(S,C)
+         R=-R
+         S=SDF-ETA*R
+         C=SDF*ETA+R
+         RAZ2=slRA2P(RA-ATAN2(XI,R))
+         DECZ2=ATAN2(S,C)
+         IF (ABS(SDF).LT.1.0) THEN
+            N=1
+         ELSE
+            N=2
+         END IF
+      ELSE
+         N=0
+      END IF
+
+      END
diff --git a/math/slalib/tpv2c.f b/math/slalib/tpv2c.f
new file mode 100644
index 00000000..2c01fe73
--- /dev/null
+++ b/math/slalib/tpv2c.f
@@ -0,0 +1,101 @@
+      SUBROUTINE slTPVC (XI, ETA, V, V01, V02, N)
+*+
+*     - - - - - -
+*      T P V C
+*     - - - - - -
+*
+*  Given the tangent-plane coordinates of a star and its direction
+*  cosines, determine the direction cosines of the tangent-point.
+*
+*  (single precision)
+*
+*  Given:
+*     XI,ETA    r       tangent plane coordinates of star
+*     V         r(3)    direction cosines of star
+*
+*  Returned:
+*     V01       r(3)    direction cosines of tangent point, solution 1
+*     V02       r(3)    direction cosines of tangent point, solution 2
+*     N         i       number of solutions:
+*                         0 = no solutions returned (note 2)
+*                         1 = only the first solution is useful (note 3)
+*                         2 = both solutions are useful (note 3)
+*
+*  Notes:
+*
+*  1  The vector V must be of unit length or the result will be wrong.
+*
+*  2  Cases where there is no solution can only arise near the poles.
+*     For example, it is clearly impossible for a star at the pole
+*     itself to have a non-zero XI value, and hence it is meaningless
+*     to ask where the tangent point would have to be.
+*
+*  3  Also near the poles, cases can arise where there are two useful
+*     solutions.  The argument N indicates whether the second of the
+*     two solutions returned is useful.  N=1 indicates only one useful
+*     solution, the usual case;  under these circumstances, the second
+*     solution can be regarded as valid if the vector V02 is interpreted
+*     as the "over-the-pole" case.
+*
+*  4  This routine is the Cartesian equivalent of the routine slTPSC.
+*
+*  P.T.Wallace   Starlink   5 June 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL XI,ETA,V(3),V01(3),V02(3)
+      INTEGER N
+
+      REAL X,Y,Z,RXY2,XI2,ETA2P1,SDF,R2,R,C
+
+
+      X=V(1)
+      Y=V(2)
+      Z=V(3)
+      RXY2=X*X+Y*Y
+      XI2=XI*XI
+      ETA2P1=ETA*ETA+1.0
+      SDF=Z*SQRT(XI2+ETA2P1)
+      R2=RXY2*ETA2P1-Z*Z*XI2
+      IF (R2.GT.0.0) THEN
+         R=SQRT(R2)
+         C=(SDF*ETA+R)/(ETA2P1*SQRT(RXY2*(R2+XI2)))
+         V01(1)=C*(X*R+Y*XI)
+         V01(2)=C*(Y*R-X*XI)
+         V01(3)=(SDF-ETA*R)/ETA2P1
+         R=-R
+         C=(SDF*ETA+R)/(ETA2P1*SQRT(RXY2*(R2+XI2)))
+         V02(1)=C*(X*R+Y*XI)
+         V02(2)=C*(Y*R-X*XI)
+         V02(3)=(SDF-ETA*R)/ETA2P1
+         IF (ABS(SDF).LT.1.0) THEN
+            N=1
+         ELSE
+            N=2
+         END IF
+      ELSE
+         N=0
+      END IF
+
+      END
diff --git a/math/slalib/ue2el.f b/math/slalib/ue2el.f
new file mode 100644
index 00000000..303c63f6
--- /dev/null
+++ b/math/slalib/ue2el.f
@@ -0,0 +1,212 @@
+      SUBROUTINE slUEEL (U, JFORMR,
+     :                      JFORM, EPOCH, ORBINC, ANODE, PERIH,
+     :                      AORQ, E, AORL, DM, JSTAT)
+*+
+*     - - - - - -
+*      U E E L
+*     - - - - - -
+*
+*  Transform universal elements into conventional heliocentric
+*  osculating elements.
+*
+*  Given:
+*     U         d(13)  universal orbital elements (Note 1)
+*
+*                 (1)  combined mass (M+m)
+*                 (2)  total energy of the orbit (alpha)
+*                 (3)  reference (osculating) epoch (t0)
+*               (4-6)  position at reference epoch (r0)
+*               (7-9)  velocity at reference epoch (v0)
+*                (10)  heliocentric distance at reference epoch
+*                (11)  r0.v0
+*                (12)  date (t)
+*                (13)  universal eccentric anomaly (psi) of date, approx
+*
+*     JFORMR    i      requested element set (1-3; Note 3)
+*
+*  Returned:
+*     JFORM     d      element set actually returned (1-3; Note 4)
+*     EPOCH     d      epoch of elements (TT MJD)
+*     ORBINC    d      inclination (radians)
+*     ANODE     d      longitude of the ascending node (radians)
+*     PERIH     d      longitude or argument of perihelion (radians)
+*     AORQ      d      mean distance or perihelion distance (AU)
+*     E         d      eccentricity
+*     AORL      d      mean anomaly or longitude (radians, JFORM=1,2 only)
+*     DM        d      daily motion (radians, JFORM=1 only)
+*     JSTAT     i      status:  0 = OK
+*                              -1 = illegal combined mass
+*                              -2 = illegal JFORMR
+*                              -3 = position/velocity out of range
+*
+*  Notes
+*
+*  1  The "universal" elements are those which define the orbit for the
+*     purposes of the method of universal variables (see reference 2).
+*     They consist of the combined mass of the two bodies, an epoch,
+*     and the position and velocity vectors (arbitrary reference frame)
+*     at that epoch.  The parameter set used here includes also various
+*     quantities that can, in fact, be derived from the other
+*     information.  This approach is taken to avoiding unnecessary
+*     computation and loss of accuracy.  The supplementary quantities
+*     are (i) alpha, which is proportional to the total energy of the
+*     orbit, (ii) the heliocentric distance at epoch, (iii) the
+*     outwards component of the velocity at the given epoch, (iv) an
+*     estimate of psi, the "universal eccentric anomaly" at a given
+*     date and (v) that date.
+*
+*  2  The universal elements are with respect to the mean equator and
+*     equinox of epoch J2000.  The orbital elements produced are with
+*     respect to the J2000 ecliptic and mean equinox.
+*
+*  3  Three different element-format options are supported:
+*
+*     Option JFORM=1, suitable for the major planets:
+*
+*     EPOCH  = epoch of elements (TT MJD)
+*     ORBINC = inclination i (radians)
+*     ANODE  = longitude of the ascending node, big omega (radians)
+*     PERIH  = longitude of perihelion, curly pi (radians)
+*     AORQ   = mean distance, a (AU)
+*     E      = eccentricity, e
+*     AORL   = mean longitude L (radians)
+*     DM     = daily motion (radians)
+*
+*     Option JFORM=2, suitable for minor planets:
+*
+*     EPOCH  = epoch of elements (TT MJD)
+*     ORBINC = inclination i (radians)
+*     ANODE  = longitude of the ascending node, big omega (radians)
+*     PERIH  = argument of perihelion, little omega (radians)
+*     AORQ   = mean distance, a (AU)
+*     E      = eccentricity, e
+*     AORL   = mean anomaly M (radians)
+*
+*     Option JFORM=3, suitable for comets:
+*
+*     EPOCH  = epoch of perihelion (TT MJD)
+*     ORBINC = inclination i (radians)
+*     ANODE  = longitude of the ascending node, big omega (radians)
+*     PERIH  = argument of perihelion, little omega (radians)
+*     AORQ   = perihelion distance, q (AU)
+*     E      = eccentricity, e
+*
+*  4  It may not be possible to generate elements in the form
+*     requested through JFORMR.  The caller is notified of the form
+*     of elements actually returned by means of the JFORM argument:
+*
+*      JFORMR   JFORM     meaning
+*
+*        1        1       OK - elements are in the requested format
+*        1        2       never happens
+*        1        3       orbit not elliptical
+*
+*        2        1       never happens
+*        2        2       OK - elements are in the requested format
+*        2        3       orbit not elliptical
+*
+*        3        1       never happens
+*        3        2       never happens
+*        3        3       OK - elements are in the requested format
+*
+*  5  The arguments returned for each value of JFORM (cf Note 6: JFORM
+*     may not be the same as JFORMR) are as follows:
+*
+*         JFORM         1              2              3
+*         EPOCH         t0             t0             T
+*         ORBINC        i              i              i
+*         ANODE         Omega          Omega          Omega
+*         PERIH         curly pi       omega          omega
+*         AORQ          a              a              q
+*         E             e              e              e
+*         AORL          L              M              -
+*         DM            n              -              -
+*
+*     where:
+*
+*         t0           is the epoch of the elements (MJD, TT)
+*         T              "    epoch of perihelion (MJD, TT)
+*         i              "    inclination (radians)
+*         Omega          "    longitude of the ascending node (radians)
+*         curly pi       "    longitude of perihelion (radians)
+*         omega          "    argument of perihelion (radians)
+*         a              "    mean distance (AU)
+*         q              "    perihelion distance (AU)
+*         e              "    eccentricity
+*         L              "    longitude (radians, 0-2pi)
+*         M              "    mean anomaly (radians, 0-2pi)
+*         n              "    daily motion (radians)
+*         -             means no value is set
+*
+*  6  At very small inclinations, the longitude of the ascending node
+*     ANODE becomes indeterminate and under some circumstances may be
+*     set arbitrarily to zero.  Similarly, if the orbit is close to
+*     circular, the true anomaly becomes indeterminate and under some
+*     circumstances may be set arbitrarily to zero.  In such cases,
+*     the other elements are automatically adjusted to compensate,
+*     and so the elements remain a valid description of the orbit.
+*
+*  References:
+*
+*     1  Sterne, Theodore E., "An Introduction to Celestial Mechanics",
+*        Interscience Publishers Inc., 1960.  Section 6.7, p199.
+*
+*     2  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
+*
+*  Called:  slPVEL
+*
+*  P.T.Wallace   Starlink   18 March 1999
+*
+*  Copyright (C) 1999 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION U(13)
+      INTEGER JFORMR,JFORM
+      DOUBLE PRECISION EPOCH,ORBINC,ANODE,PERIH,AORQ,E,AORL,DM
+      INTEGER JSTAT
+
+*  Gaussian gravitational constant (exact)
+      DOUBLE PRECISION GCON
+      PARAMETER (GCON=0.01720209895D0)
+
+*  Canonical days to seconds
+      DOUBLE PRECISION CD2S
+      PARAMETER (CD2S=GCON/86400D0)
+
+      INTEGER I
+      DOUBLE PRECISION PMASS,DATE,PV(6)
+
+
+*  Unpack the universal elements.
+      PMASS = U(1)-1D0
+      DATE = U(3)
+      DO I=1,3
+         PV(I) = U(I+3)
+         PV(I+3) = U(I+6)*CD2S
+      END DO
+
+*  Convert the position and velocity etc into conventional elements.
+      CALL slPVEL(PV,DATE,PMASS,JFORMR,JFORM,EPOCH,ORBINC,ANODE,
+     :               PERIH,AORQ,E,AORL,DM,JSTAT)
+
+      END
diff --git a/math/slalib/ue2pv.f b/math/slalib/ue2pv.f
new file mode 100644
index 00000000..8024bc65
--- /dev/null
+++ b/math/slalib/ue2pv.f
@@ -0,0 +1,253 @@
+      SUBROUTINE slUEPV ( DATE, U, PV, JSTAT )
+*+
+*     - - - - - -
+*      U E P V
+*     - - - - - -
+*
+*  Heliocentric position and velocity of a planet, asteroid or comet,
+*  starting from orbital elements in the "universal variables" form.
+*
+*  Given:
+*     DATE     d       date, Modified Julian Date (JD-2400000.5)
+*
+*  Given and returned:
+*     U        d(13)   universal orbital elements (updated; Note 1)
+*
+*       given    (1)   combined mass (M+m)
+*         "      (2)   total energy of the orbit (alpha)
+*         "      (3)   reference (osculating) epoch (t0)
+*         "    (4-6)   position at reference epoch (r0)
+*         "    (7-9)   velocity at reference epoch (v0)
+*         "     (10)   heliocentric distance at reference epoch
+*         "     (11)   r0.v0
+*     returned  (12)   date (t)
+*         "     (13)   universal eccentric anomaly (psi) of date
+*
+*  Returned:
+*     PV       d(6)    position (AU) and velocity (AU/s)
+*     JSTAT    i       status:  0 = OK
+*                              -1 = radius vector zero
+*                              -2 = failed to converge
+*
+*  Notes
+*
+*  1  The "universal" elements are those which define the orbit for the
+*     purposes of the method of universal variables (see reference).
+*     They consist of the combined mass of the two bodies, an epoch,
+*     and the position and velocity vectors (arbitrary reference frame)
+*     at that epoch.  The parameter set used here includes also various
+*     quantities that can, in fact, be derived from the other
+*     information.  This approach is taken to avoiding unnecessary
+*     computation and loss of accuracy.  The supplementary quantities
+*     are (i) alpha, which is proportional to the total energy of the
+*     orbit, (ii) the heliocentric distance at epoch, (iii) the
+*     outwards component of the velocity at the given epoch, (iv) an
+*     estimate of psi, the "universal eccentric anomaly" at a given
+*     date and (v) that date.
+*
+*  2  The companion routine is slELUE.  This takes the conventional
+*     orbital elements and transforms them into the set of numbers
+*     needed by the present routine.  A single prediction requires one
+*     one call to slELUE followed by one call to the present routine;
+*     for convenience, the two calls are packaged as the routine
+*     slPLNE.  Multiple predictions may be made by again
+*     calling slELUE once, but then calling the present routine
+*     multiple times, which is faster than multiple calls to slPLNE.
+*
+*     It is not obligatory to use slELUE to obtain the parameters.
+*     However, it should be noted that because slELUE performs its
+*     own validation, no checks on the contents of the array U are made
+*     by the present routine.
+*
+*  3  DATE is the instant for which the prediction is required.  It is
+*     in the TT timescale (formerly Ephemeris Time, ET) and is a
+*     Modified Julian Date (JD-2400000.5).
+*
+*  4  The universal elements supplied in the array U are in canonical
+*     units (solar masses, AU and canonical days).  The position and
+*     velocity are not sensitive to the choice of reference frame.  The
+*     slELUE routine in fact produces coordinates with respect to the
+*     J2000 equator and equinox.
+*
+*  5  The algorithm was originally adapted from the EPHSLA program of
+*     D.H.P.Jones (private communication, 1996).  The method is based
+*     on Stumpff's Universal Variables.
+*
+*  Reference:  Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
+*
+*  P.T.Wallace   Starlink   22 October 2005
+*
+*  Copyright (C) 2005 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DATE,U(13),PV(6)
+      INTEGER JSTAT
+
+*  Gaussian gravitational constant (exact)
+      DOUBLE PRECISION GCON
+      PARAMETER (GCON=0.01720209895D0)
+
+*  Canonical days to seconds
+      DOUBLE PRECISION CD2S
+      PARAMETER (CD2S=GCON/86400D0)
+
+*  Test value for solution and maximum number of iterations
+      DOUBLE PRECISION TEST
+      INTEGER NITMAX
+      PARAMETER (TEST=1D-13,NITMAX=25)
+
+      INTEGER I,NIT,N
+
+      DOUBLE PRECISION CM,ALPHA,T0,P0(3),V0(3),R0,SIGMA0,T,PSI,DT,W,
+     :                 TOL,PSJ,PSJ2,BETA,S0,S1,S2,S3,
+     :                 FF,R,FLAST,PLAST,F,G,FD,GD
+
+
+
+*  Unpack the parameters.
+      CM = U(1)
+      ALPHA = U(2)
+      T0 = U(3)
+      DO I=1,3
+         P0(I) = U(I+3)
+         V0(I) = U(I+6)
+      END DO
+      R0 = U(10)
+      SIGMA0 = U(11)
+      T = U(12)
+      PSI = U(13)
+
+*  Approximately update the universal eccentric anomaly.
+      PSI = PSI+(DATE-T)*GCON/R0
+
+*  Time from reference epoch to date (in Canonical Days: a canonical
+*  day is 58.1324409... days, defined as 1/GCON).
+      DT = (DATE-T0)*GCON
+
+*  Refine the universal eccentric anomaly, psi.
+      NIT = 1
+      W = 1D0
+      TOL = 0D0
+      DO WHILE (ABS(W).GE.TOL)
+
+*     Form half angles until BETA small enough.
+         N = 0
+         PSJ = PSI
+         PSJ2 = PSJ*PSJ
+         BETA = ALPHA*PSJ2
+         DO WHILE (ABS(BETA).GT.0.7D0)
+            N = N+1
+            BETA = BETA/4D0
+            PSJ = PSJ/2D0
+            PSJ2 = PSJ2/4D0
+         END DO
+
+*     Calculate Universal Variables S0,S1,S2,S3 by nested series.
+         S3 = PSJ*PSJ2*((((((BETA/210D0+1D0)
+     :                      *BETA/156D0+1D0)
+     :                      *BETA/110D0+1D0)
+     :                      *BETA/72D0+1D0)
+     :                      *BETA/42D0+1D0)
+     :                      *BETA/20D0+1D0)/6D0
+         S2 = PSJ2*((((((BETA/182D0+1D0)
+     :                  *BETA/132D0+1D0)
+     :                  *BETA/90D0+1D0)
+     :                  *BETA/56D0+1D0)
+     :                  *BETA/30D0+1D0)
+     :                  *BETA/12D0+1D0)/2D0
+         S1 = PSJ+ALPHA*S3
+         S0 = 1D0+ALPHA*S2
+
+*     Undo the angle-halving.
+         TOL = TEST
+         DO WHILE (N.GT.0)
+            S3 = 2D0*(S0*S3+PSJ*S2)
+            S2 = 2D0*S1*S1
+            S1 = 2D0*S0*S1
+            S0 = 2D0*S0*S0-1D0
+            PSJ = PSJ+PSJ
+            TOL = TOL+TOL
+            N = N-1
+         END DO
+
+*     Values of F and F' corresponding to the current value of psi.
+         FF = R0*S1+SIGMA0*S2+CM*S3-DT
+         R = R0*S0+SIGMA0*S1+CM*S2
+
+*     If first iteration, create dummy "last F".
+         IF ( NIT.EQ.1) FLAST = FF
+
+*     Check for sign change.
+         IF ( FF*FLAST.LT.0D0 ) THEN
+
+*        Sign change:  get psi adjustment using secant method.
+            W = FF*(PLAST-PSI)/(FLAST-FF)
+         ELSE
+
+*        No sign change:  use Newton-Raphson method instead.
+            IF (R.EQ.0D0) GO TO 9010
+            W = FF/R
+         END IF
+
+*     Save the last psi and F values.
+         PLAST = PSI
+         FLAST = FF
+
+*     Apply the Newton-Raphson or secant adjustment to psi.
+         PSI = PSI-W
+
+*     Next iteration, unless too many already.
+         IF (NIT.GT.NITMAX) GO TO 9020
+         NIT = NIT+1
+      END DO
+
+*  Project the position and velocity vectors (scaling velocity to AU/s).
+      W = CM*S2
+      F = 1D0-W/R0
+      G = DT-CM*S3
+      FD = -CM*S1/(R0*R)
+      GD = 1D0-W/R
+      DO I=1,3
+         PV(I) = P0(I)*F+V0(I)*G
+         PV(I+3) = CD2S*(P0(I)*FD+V0(I)*GD)
+      END DO
+
+*  Update the parameters to allow speedy prediction of PSI next time.
+      U(12) = DATE
+      U(13) = PSI
+
+*  OK exit.
+      JSTAT = 0
+      GO TO 9999
+
+*  Null radius vector.
+ 9010 CONTINUE
+      JSTAT = -1
+      GO TO 9999
+
+*  Failed to converge.
+ 9020 CONTINUE
+      JSTAT = -2
+
+ 9999 CONTINUE
+      END
diff --git a/math/slalib/unpcd.f b/math/slalib/unpcd.f
new file mode 100644
index 00000000..c4de5fbb
--- /dev/null
+++ b/math/slalib/unpcd.f
@@ -0,0 +1,145 @@
+      SUBROUTINE slUPCD ( DISCO, X, Y )
+*+
+*     - - - - - -
+*      U P C D
+*     - - - - - -
+*
+*  Remove pincushion/barrel distortion from a distorted [x,y] to give
+*  tangent-plane [x,y].
+*
+*  Given:
+*     DISCO    d      pincushion/barrel distortion coefficient
+*     X,Y      d      distorted coordinates
+*
+*  Returned:
+*     X,Y      d      tangent-plane coordinates
+*
+*  Notes:
+*
+*  1)  The distortion is of the form RP = R*(1+C*R^2), where R is
+*      the radial distance from the tangent point, C is the DISCO
+*      argument, and RP is the radial distance in the presence of
+*      the distortion.
+*
+*  2)  For pincushion distortion, C is +ve;  for barrel distortion,
+*      C is -ve.
+*
+*  3)  For X,Y in "radians" - units of one projection radius,
+*      which in the case of a photograph is the focal length of
+*      the camera - the following DISCO values apply:
+*
+*          Geometry          DISCO
+*
+*          astrograph         0.0
+*          Schmidt           -0.3333
+*          AAT PF doublet  +147.069
+*          AAT PF triplet  +178.585
+*          AAT f/8          +21.20
+*          JKT f/8          +13.32
+*
+*  4)  The present routine is a rigorous inverse of the companion
+*      routine slPCD.  The expression for RP in Note 1 is rewritten
+*      in the form x^3+a*x+b=0 and solved by standard techniques.
+*
+*  5)  Cases where the cubic has multiple real roots can sometimes
+*      occur, corresponding to extreme instances of barrel distortion
+*      where up to three different undistorted [X,Y]s all produce the
+*      same distorted [X,Y].  However, only one solution is returned,
+*      the one that produces the smallest change in [X,Y].
+*
+*  P.T.Wallace   Starlink   3 September 2000
+*
+*  Copyright (C) 2000 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION DISCO,X,Y
+
+      DOUBLE PRECISION THIRD
+      PARAMETER (THIRD=1D0/3D0)
+      DOUBLE PRECISION D2PI
+      PARAMETER (D2PI=6.283185307179586476925286766559D0)
+
+      DOUBLE PRECISION RP,Q,R,D,W,S,T,F,C,T3,F1,F2,F3,W1,W2,W3
+
+
+
+*  Distance of the point from the origin.
+      RP = SQRT(X*X+Y*Y)
+
+*  If zero, or if no distortion, no action is necessary.
+      IF (RP.NE.0D0.AND.DISCO.NE.0D0) THEN
+
+*     Begin algebraic solution.
+         Q = 1D0/(3D0*DISCO)
+         R = RP/(2D0*DISCO)
+         W = Q*Q*Q+R*R
+
+*     Continue if one real root, or three of which only one is positive.
+         IF (W.GE.0D0) THEN
+            D = SQRT(W)
+            W = R+D
+            S = SIGN(ABS(W)**THIRD,W)
+            W = R-D
+            T = SIGN((ABS(W))**THIRD,W)
+            F = S+T
+         ELSE
+
+*        Three different real roots:  use geometrical method instead.
+            W = 2D0/SQRT(-3D0*DISCO)
+            C = 4D0*RP/(DISCO*W*W*W)
+            S = SQRT(1D0-MIN(C*C,1D0))
+            T3 = ATAN2(S,C)
+
+*        The three solutions.
+            F1 = W*COS((D2PI-T3)/3D0)
+            F2 = W*COS((T3)/3D0)
+            F3 = W*COS((D2PI+T3)/3D0)
+
+*        Pick the one that moves [X,Y] least.
+            W1 = ABS(F1-RP)
+            W2 = ABS(F2-RP)
+            W3 = ABS(F3-RP)
+            IF (W1.LT.W2) THEN
+               IF (W1.LT.W3) THEN
+                  F = F1
+               ELSE
+                  F = F3
+               END IF
+            ELSE
+               IF (W2.LT.W3) THEN
+                  F = F2
+               ELSE
+                  F = F3
+               END IF
+            END IF
+
+         END IF
+
+*     Remove the distortion.
+         F = F/RP
+         X = F*X
+         Y = F*Y
+
+      END IF
+
+      END
diff --git a/math/slalib/v2tp.f b/math/slalib/v2tp.f
new file mode 100644
index 00000000..bb56af7a
--- /dev/null
+++ b/math/slalib/v2tp.f
@@ -0,0 +1,96 @@
+      SUBROUTINE slV2TP (V, V0, XI, ETA, J)
+*+
+*     - - - - -
+*      V 2 T P
+*     - - - - -
+*
+*  Given the direction cosines of a star and of the tangent point,
+*  determine the star's tangent-plane coordinates.
+*
+*  (single precision)
+*
+*  Given:
+*     V         r(3)    direction cosines of star
+*     V0        r(3)    direction cosines of tangent point
+*
+*  Returned:
+*     XI,ETA    r       tangent plane coordinates of star
+*     J         i       status:   0 = OK
+*                                 1 = error, star too far from axis
+*                                 2 = error, antistar on tangent plane
+*                                 3 = error, antistar too far from axis
+*
+*  Notes:
+*
+*  1  If vector V0 is not of unit length, or if vector V is of zero
+*     length, the results will be wrong.
+*
+*  2  If V0 points at a pole, the returned XI,ETA will be based on the
+*     arbitrary assumption that the RA of the tangent point is zero.
+*
+*  3  This routine is the Cartesian equivalent of the routine slS2TP.
+*
+*  P.T.Wallace   Starlink   27 November 1996
+*
+*  Copyright (C) 1996 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL V(3),V0(3),XI,ETA
+      INTEGER J
+
+      REAL X,Y,Z,X0,Y0,Z0,R2,R,W,D
+
+      REAL TINY
+      PARAMETER (TINY=1E-6)
+
+
+      X=V(1)
+      Y=V(2)
+      Z=V(3)
+      X0=V0(1)
+      Y0=V0(2)
+      Z0=V0(3)
+      R2=X0*X0+Y0*Y0
+      R=SQRT(R2)
+      IF (R.EQ.0.0) THEN
+         R=1E-20
+         X0=R
+      END IF
+      W=X*X0+Y*Y0
+      D=W+Z*Z0
+      IF (D.GT.TINY) THEN
+         J=0
+      ELSE IF (D.GE.0.0) THEN
+         J=1
+         D=TINY
+      ELSE IF (D.GT.-TINY) THEN
+         J=2
+         D=-TINY
+      ELSE
+         J=3
+      END IF
+      D=D*R
+      XI=(Y*X0-X*Y0)/D
+      ETA=(Z*R2-Z0*W)/D
+
+      END
diff --git a/math/slalib/vdv.f b/math/slalib/vdv.f
new file mode 100644
index 00000000..fc686b9d
--- /dev/null
+++ b/math/slalib/vdv.f
@@ -0,0 +1,45 @@
+      REAL FUNCTION slVDV (VA, VB)
+*+
+*     - - - -
+*      V D V
+*     - - - -
+*
+*  Scalar product of two 3-vectors  (single precision)
+*
+*  Given:
+*      VA      real(3)     first vector
+*      VB      real(3)     second vector
+*
+*  The result is the scalar product VA.VB (single precision)
+*
+*  P.T.Wallace   Starlink   November 1984
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL VA(3),VB(3)
+
+
+      slVDV=VA(1)*VB(1)+VA(2)*VB(2)+VA(3)*VB(3)
+
+      END
diff --git a/math/slalib/veri.f.in b/math/slalib/veri.f.in
new file mode 100644
index 00000000..76eb4380
--- /dev/null
+++ b/math/slalib/veri.f.in
@@ -0,0 +1,52 @@
+      INTEGER FUNCTION sla_VERI ()
+*+
+*     - - - - -
+*      V E R I
+*     - - - - -
+*
+*  Report the SLALIB version number as an integer.
+*
+*  Given:
+*    None
+*
+*  The result is the SLALIB version number as an integer m*1e6+n*1e3+r,
+*  where m is the major version, n the minor version and r the release
+*  number.
+*
+*  Notes:
+*
+*    To obtain the version number in a printable form, see
+*    subroutine sla_vers(version).
+*
+*    The sla_veri subroutine was introduced in SLALIB version 2.5-1, so
+*    if this function is absent, one can only tell that the release
+*    predates that one.
+*
+*  Norman Gray   Starlink   8 April 2005
+*
+*  Copyright (C) 2005 Council for the Central Laboratory of the
+*  Research Councils
+*
+*  Licence:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*-
+
+      IMPLICIT NONE
+
+      sla_VERI=@PACKAGE_VERSION_INTEGER@
+
+      END
diff --git a/math/slalib/vers.f.in b/math/slalib/vers.f.in
new file mode 100644
index 00000000..b9ef9544
--- /dev/null
+++ b/math/slalib/vers.f.in
@@ -0,0 +1,58 @@
+      SUBROUTINE sla_VERS (VERSION)
+*+
+*     - - - - -
+*      V E R S
+*     - - - - -
+*
+*  Report the SLALIB version number.
+*
+*  Given:
+*    None
+*
+*  Returned:
+*    VERSION   c*(*)   Version number, in the form 'm.n-r'.
+*                      The major version is m, the minor version n, and
+*                      release r.  The string passed in should be at least
+*                      8 characters in length, to account for the (remote)
+*                      possibility that these numbers will ever go to
+*                      two digits.
+*
+*  Notes:
+*
+*    To obtain the version number in a more easily processed form, see
+*    function sla_veri().
+*
+*    The sla_vers subroutine was introduced in SLALIB version 2.5-1, so
+*    if this function is absent, one can only tell that the release
+*    predates that one.
+*
+*  Norman Gray   Starlink   8 April 2005
+*
+*  Copyright (C) 2005 Council for the Central Laboratory of the
+*  Research Councils
+*
+*  Licence:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*-
+
+      IMPLICIT NONE
+
+      CHARACTER VERSION*(*)
+
+      VERSION='@PACKAGE_VERSION@'
+
+      END
diff --git a/math/slalib/vn.f b/math/slalib/vn.f
new file mode 100644
index 00000000..8bbb33d9
--- /dev/null
+++ b/math/slalib/vn.f
@@ -0,0 +1,64 @@
+      SUBROUTINE slVN (V, UV, VM)
+*+
+*     - - -
+*      V N
+*     - - -
+*
+*  Normalizes a 3-vector also giving the modulus (single precision)
+*
+*  Given:
+*     V       real(3)      vector
+*
+*  Returned:
+*     UV      real(3)      unit vector in direction of V
+*     VM      real         modulus of V
+*
+*  If the modulus of V is zero, UV is set to zero as well
+*
+*  P.T.Wallace   Starlink   23 November 1995
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL V(3),UV(3),VM
+
+      INTEGER I
+      REAL W1,W2
+
+
+*  Modulus
+      W1=0.0
+      DO I=1,3
+         W2=V(I)
+         W1=W1+W2*W2
+      END DO
+      W1=SQRT(W1)
+      VM=W1
+
+*  Normalize the vector
+      IF (W1.LE.0.0) W1=1.0
+      DO I=1,3
+         UV(I)=V(I)/W1
+      END DO
+
+      END
diff --git a/math/slalib/vxv.f b/math/slalib/vxv.f
new file mode 100644
index 00000000..688764bd
--- /dev/null
+++ b/math/slalib/vxv.f
@@ -0,0 +1,57 @@
+      SUBROUTINE slVXV (VA, VB, VC)
+*+
+*     - - - -
+*      V X V
+*     - - - -
+*
+*  Vector product of two 3-vectors (single precision)
+*
+*  Given:
+*      VA      real(3)     first vector
+*      VB      real(3)     second vector
+*
+*  Returned:
+*      VC      real(3)     vector result
+*
+*  P.T.Wallace   Starlink   March 1986
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      REAL VA(3),VB(3),VC(3)
+
+      REAL VW(3)
+      INTEGER I
+
+
+*  Form the vector product VA cross VB
+      VW(1)=VA(2)*VB(3)-VA(3)*VB(2)
+      VW(2)=VA(3)*VB(1)-VA(1)*VB(3)
+      VW(3)=VA(1)*VB(2)-VA(2)*VB(1)
+
+*  Return the result
+      DO I=1,3
+         VC(I)=VW(I)
+      END DO
+
+      END
diff --git a/math/slalib/wait.f__vms b/math/slalib/wait.f__vms
new file mode 100644
index 00000000..5897e7e6
--- /dev/null
+++ b/math/slalib/wait.f__vms
@@ -0,0 +1,60 @@
+      SUBROUTINE sla_WAIT (DELAY)
+*+
+*     - - - - -
+*      W A I T
+*     - - - - -
+*
+*  Interval wait
+*
+*  !!! VAX/VMS specific !!!
+*
+*  Given:
+*     DELAY     real      delay in seconds
+*
+*  A delay 100ns < DELAY < 200s is requested.
+*
+*  P.T.Wallace   Starlink   14 October 1991
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*-
+
+      IMPLICIT NONE
+
+      REAL DELAY
+
+      INTEGER JSTAT
+      INTEGER SYS$SCHDWK,SYS$HIBER
+
+      INTEGER IDT(2)
+      DATA IDT(2)/-1/
+
+
+
+*  Encode delta time
+      IDT(1)=-NINT(MAX(1.0,1E7*MIN(200.0,DELAY)))
+
+
+*  Schedule a wakeup
+      JSTAT=SYS$SCHDWK(,,IDT,)
+      IF (.NOT.JSTAT) CALL LIB$STOP(%VAL(JSTAT))
+
+*  Hibernate
+      JSTAT=SYS$HIBER()
+      IF (.NOT.JSTAT) CALL LIB$STOP(%VAL(JSTAT))
+
+      END
diff --git a/math/slalib/wait.f__win b/math/slalib/wait.f__win
new file mode 100644
index 00000000..b018650c
--- /dev/null
+++ b/math/slalib/wait.f__win
@@ -0,0 +1,83 @@
+      SUBROUTINE sla_WAIT (DELAY)
+*+
+*     - - - - -
+*      W A I T
+*     - - - - -
+*
+*  Interval wait
+*
+*  !!! PC only - Microsoft Fortran specific !!!
+*
+*  Given:
+*     DELAY     real      delay in seconds
+*
+*  A delay of up to 10000 seconds occurs.
+*
+*  Called:  GETTIM (Microsoft Fortran run-time library)
+*
+*  P.T.Wallace   Starlink   14 October 1991
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*-
+
+      IMPLICIT NONE
+
+      REAL DELAY
+
+      INTEGER IDELAY,IH,IM,IS,I,IT,IT0,IDT
+      LOGICAL FIRST,LOOP
+
+
+
+
+*  Convert requested delay to 0.01 second ticks
+      IDELAY=NINT(MAX(MIN(DELAY,1E4),0.0)*1E2)
+
+*  Set "note start time" flag
+      FIRST=.TRUE.
+
+*  Set "wait in progress" flag
+      LOOP=.TRUE.
+
+*  Main loop
+      DO WHILE (LOOP)
+
+*     Get the current time and convert to 0.01 second ticks
+         CALL GETTIM(IH,IM,IS,I)
+         IT=((IH*60+IM)*60+IS)*100+I
+
+*     First time through the loop?
+         IF (FIRST) THEN
+
+*        Yes: note the time and reset the flag
+            IT0=IT
+            FIRST=.FALSE.
+         ELSE
+
+*        No: subtract the start time, handling 0 hours wrap
+            IDT=IT-IT0
+            IF (IDT.LT.0) IDT=IDT+8640000
+
+*        If the requested delay has elapsed, stop looping
+            LOOP=IDT.LT.IDELAY
+         END IF
+      END DO
+
+      END
diff --git a/math/slalib/wait.fdefault b/math/slalib/wait.fdefault
new file mode 100644
index 00000000..75e2720f
--- /dev/null
+++ b/math/slalib/wait.fdefault
@@ -0,0 +1,49 @@
+      SUBROUTINE sla_WAIT (DELAY)
+*+
+*     - - - - -
+*      W A I T
+*     - - - - -
+*
+*  Interval wait
+*
+*  !!! Version for: SPARC/SunOS4, 
+*                   SPARC/Solaris2, 
+*                   DEC Mips/Ultrix
+*                   DEC AXP/Digital Unix
+*                   Intel/Linux
+*                   Convex
+*
+*  Given:
+*     DELAY     real      delay in seconds
+*
+*  Called:  SLEEP (a Fortran Intrinsic on all obove platforms)
+*
+*  P.T.Wallace   Starlink   22 January 1998
+*
+*  Copyright (C) 1998 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the 
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, 
+*    Boston, MA  02110-1301  USA
+*
+*-
+
+      IMPLICIT NONE
+
+      REAL DELAY
+
+      CALL SLEEP(NINT(DELAY))
+
+      END
diff --git a/math/slalib/xy2xy.f b/math/slalib/xy2xy.f
new file mode 100644
index 00000000..b9c770a3
--- /dev/null
+++ b/math/slalib/xy2xy.f
@@ -0,0 +1,67 @@
+      SUBROUTINE slXYXY (X1,Y1,COEFFS,X2,Y2)
+*+
+*     - - - - - -
+*      X Y X Y
+*     - - - - - -
+*
+*  Transform one [X,Y] into another using a linear model of the type
+*  produced by the slFTXY routine.
+*
+*  Given:
+*     X1       d        x-coordinate
+*     Y1       d        y-coordinate
+*     COEFFS  d(6)      transformation coefficients (see note)
+*
+*  Returned:
+*     X2       d        x-coordinate
+*     Y2       d        y-coordinate
+*
+*  The model relates two sets of [X,Y] coordinates as follows.
+*  Naming the elements of COEFFS:
+*
+*     COEFFS(1) = A
+*     COEFFS(2) = B
+*     COEFFS(3) = C
+*     COEFFS(4) = D
+*     COEFFS(5) = E
+*     COEFFS(6) = F
+*
+*  the present routine performs the transformation:
+*
+*     X2 = A + B*X1 + C*Y1
+*     Y2 = D + E*X1 + F*Y1
+*
+*  See also slFTXY, slPXY, slINVF, slDCMF
+*
+*  P.T.Wallace   Starlink   5 December 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION X1,Y1,COEFFS(6),X2,Y2
+
+
+      X2=COEFFS(1)+COEFFS(2)*X1+COEFFS(3)*Y1
+      Y2=COEFFS(4)+COEFFS(5)*X1+COEFFS(6)*Y1
+
+      END
diff --git a/math/slalib/zd.f b/math/slalib/zd.f
new file mode 100644
index 00000000..c7376266
--- /dev/null
+++ b/math/slalib/zd.f
@@ -0,0 +1,80 @@
+      DOUBLE PRECISION FUNCTION slZD (HA, DEC, PHI)
+*+
+*     - - -
+*      Z D
+*     - - -
+*
+*  HA, Dec to Zenith Distance (double precision)
+*
+*  Given:
+*     HA     d     Hour Angle in radians
+*     DEC    d     declination in radians
+*     PHI    d     observatory latitude in radians
+*
+*  The result is in the range 0 to pi.
+*
+*  Notes:
+*
+*  1)  The latitude must be geodetic.  In critical applications,
+*      corrections for polar motion should be applied.
+*
+*  2)  In some applications it will be important to specify the
+*      correct type of hour angle and declination in order to
+*      produce the required type of zenith distance.  In particular,
+*      it may be important to distinguish between the zenith distance
+*      as affected by refraction, which would require the "observed"
+*      HA,Dec, and the zenith distance in vacuo, which would require
+*      the "topocentric" HA,Dec.  If the effects of diurnal aberration
+*      can be neglected, the "apparent" HA,Dec may be used instead of
+*      the topocentric HA,Dec.
+*
+*  3)  No range checking of arguments is done.
+*
+*  4)  In applications which involve many zenith distance calculations,
+*      rather than calling the present routine it will be more efficient
+*      to use inline code, having previously computed fixed terms such
+*      as sine and cosine of latitude, and perhaps sine and cosine of
+*      declination.
+*
+*  P.T.Wallace   Starlink   3 April 1994
+*
+*  Copyright (C) 1995 Rutherford Appleton Laboratory
+*
+*  License:
+*    This program is free software; you can redistribute it and/or modify
+*    it under the terms of the GNU General Public License as published by
+*    the Free Software Foundation; either version 2 of the License, or
+*    (at your option) any later version.
+*
+*    This program is distributed in the hope that it will be useful,
+*    but WITHOUT ANY WARRANTY; without even the implied warranty of
+*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+*    GNU General Public License for more details.
+*
+*    You should have received a copy of the GNU General Public License
+*    along with this program (see SLA_CONDITIONS); if not, write to the
+*    Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+*    Boston, MA  02110-1301  USA
+*
+*  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+*-
+
+      IMPLICIT NONE
+
+      DOUBLE PRECISION HA,DEC,PHI
+
+      DOUBLE PRECISION SH,CH,SD,CD,SP,CP,X,Y,Z
+
+
+      SH=SIN(HA)
+      CH=COS(HA)
+      SD=SIN(DEC)
+      CD=COS(DEC)
+      SP=SIN(PHI)
+      CP=COS(PHI)
+      X=CH*CD*SP-SD*CP
+      Y=SH*CD
+      Z=CH*CD*CP+SD*SP
+      slZD=ATAN2(SQRT(X*X+Y*Y),Z)
+
+      END
diff --git a/math/surfit/doc/iscoeff.hlp b/math/surfit/doc/iscoeff.hlp
new file mode 100644
index 00000000..ea0b292c
--- /dev/null
+++ b/math/surfit/doc/iscoeff.hlp
@@ -0,0 +1,63 @@
+.help iscoeff Apr85 "Surfit Package"
+.ih
+NAME
+iscoeff - get the number and values of the surface coefficients
+.ih
+SYNOPSIS
+iscoeff (sf, coeff, ncoeff)
+
+.nf
+pointer	sf		# surface descriptor
+real	coeff[ncoeff]	# coefficient array
+int	ncoeff		# number of coefficients
+.fi
+.ih
+ARGUMENTS
+.ls sf   
+Pointer to the surface descriptor.
+.le
+.ls coeff
+Array of coefficients.
+.le
+.ls ncoeff
+The number of coefficients.
+.le
+
+.ih
+DESCRIPTION
+ISCOEFF fetches the coefficient array and the number of coefficients from
+the surface descriptor structure. A 1-D array ncoeff elements long
+is required to hold the coefficients where ncoeff is defined as follows:
+
+.nf
+	SF_LEGENDRE:		nxcoeff = xorder
+				nycoeff = yorder
+				ncoeff = xorder * yorder        xterms = yes
+				ncoeff = nycoeff + nxcoeff - 1  xterms = no
+
+	SF_CHEBYSHEV:		nxcoeff = xorder
+				nycoeff = yorder
+				ncoeff = xorder * yorder        xterms = yes
+				ncoeff = nycoeff + nxcoeff - 1  xterms = no
+
+	SF_SPLINE3:		nxcoeff = xorder + 3
+				nycoeff = yorder + 3
+				ncoeff = (xorder + 3) * (yorder + 3)
+
+	SF_SPLINE1:		nxcoeff = xorder + 1
+				nycoeff = yorder + 1
+				ncoeff = (xorder + 1) * (yorder + 1)
+
+.fi
+
+The coefficient of basis function B(i,x) * B(j,y) will be stored in
+element (i - 1) *
+nycoeff + j of the array coeff if the xterms parameter was set
+to yes by ISINIT. Otherwise the nycoeff y-term coefficients will be output
+first followed by the (nxcoeff - 1) x-term coefficients.
+
+.ih
+NOTES
+.ih
+SEE ALSO
+.endhelp
diff --git a/math/surfit/doc/iseval.hlp b/math/surfit/doc/iseval.hlp
new file mode 100644
index 00000000..53853cfe
--- /dev/null
+++ b/math/surfit/doc/iseval.hlp
@@ -0,0 +1,34 @@
+.help iseval Apr85 "Surfit Package"
+.ih
+NAME
+iseval -- evaluate the fitted surface at x and y
+.ih
+SYNOPSIS
+y = iseval (sf, x, y)
+
+.nf
+pointer	sf		# surface descriptor
+real	x		# x value, 1 <= x <= ncols
+real	y		# y value, 1 <= y <= nlines
+.fi
+.ih
+ARGUMENTS
+.ls sf      
+Pointer to the surface descriptor structure.
+.le
+.ls x, y
+X and y values at which the surface is to be evaluated.
+.le
+.ih
+DESCRIPTION
+Evaluate the surface at the specified value of x and y. ISEVAL is a real
+valued function which returns the fitted value.
+.ih
+NOTES
+ISEVAL uses the coefficient array stored in the surface descriptor structure.
+Checking for out of bounds x and y values is the responsibility of the calling
+program.
+.ih
+SEE ALSO
+isvector
+.endhelp
diff --git a/math/surfit/doc/isfree.hlp b/math/surfit/doc/isfree.hlp
new file mode 100644
index 00000000..04f52b5f
--- /dev/null
+++ b/math/surfit/doc/isfree.hlp
@@ -0,0 +1,27 @@
+.help isfree Apr85 "Surfit Package"
+.ih
+NAME
+isfree -- free the surface grid descriptor structure
+.ih
+SYNOPSIS
+isfree (sf)
+
+.nf
+pointer	sf		# surface descriptor
+.fi
+.ih
+ARGUMENTS
+.ls sf    
+Pointer to the surface descriptor structure.
+.le
+.ih
+DESCRIPTION
+Frees the surface descriptor structure and all the vectors and arrays used
+by the numerical routines.
+.ih
+NOTES
+ISFREE should be called after the surface fit is complete.
+.ih
+SEE ALSO
+isinit
+.endhelp
diff --git a/math/surfit/doc/isinit.hlp b/math/surfit/doc/isinit.hlp
new file mode 100644
index 00000000..e0f2123c
--- /dev/null
+++ b/math/surfit/doc/isinit.hlp
@@ -0,0 +1,61 @@
+.help isinit Apr85 "Surfit Package"
+.ih
+NAME
+isinit -- initialize surface grid descriptor
+.ih
+SYNOPSIS
+include <math/surfit.h>
+
+.nf
+isinit (sf, surface_type, xorder, yorder, xterms, ncols, nlines)
+.fi
+
+.nf
+pointer	sf		# surface descriptor
+int	surface_type	# surface function
+int	xorder		# order of function in x
+int	yorder		# order of function in y
+int	xterms		# include cross-terms? (YES/NO)
+int	ncols		# number of columns in the surface grid
+int	nlines		# number of lines in the surface grid
+.fi
+.ih
+ARGUMENTS
+.ls sf    
+Pointer to the surface descriptor structure.
+.le
+.ls surface_type
+Fitting function. Permitted values are SF_LEGENDRE and SF_CHEBYSHEV for
+the Legendre and Chebyshev polynomials and SF_SPLINE1 and SF_SPLINE3
+for the linear and bicubic splines.
+.le
+.ls xorder, yorder
+Order of the polynomial to be fit in x and y or the number of spline pieces to 
+be fit in x and y. The orders must be greater than or equal to 1.
+.le
+.ls xterms
+Include cross-terms? If xterms = YES coefficients are fit to terms containing
+the cross products of x and y polynomials. Xterms defaults to YES for the
+spline functions.
+.le
+.ls ncols
+The number of columns in the surface grid. The surface is assumed to lie
+on a rectangular grid such that 1 <= x <= ncols.
+.le
+.ls nlines
+The number of lines in the surface to be grid. The surface is assumed to lie
+on a rectangular grid such that 1 <= y <= nlines.
+.le
+.ih
+DESCRIPTION
+ISINIT allocates space for the surface descriptor and the arrays and vectors
+used by the numerical routines. It initializes all arrays and vectors to zero,
+calculates and stores the basis functions in x and y
+and returns the surface descriptor to the calling routine.
+.ih
+NOTES
+ISINIT must be the first SURFIT routine called.
+.ih
+SEE ALSO
+isfree
+.endhelp
diff --git a/math/surfit/doc/islaccum.hlp b/math/surfit/doc/islaccum.hlp
new file mode 100644
index 00000000..48481cf0
--- /dev/null
+++ b/math/surfit/doc/islaccum.hlp
@@ -0,0 +1,60 @@
+.help islaccum Apr85 "Surfit Package"
+.ih
+NAME
+islaccum -- accumulate a surface grid line into the fit
+.ih
+SYNOPSIS
+include <math/surfit.h>
+
+islaccum (sf, cols, lineno, z, w, npts, wtflag)
+
+.nf
+pointer	sf		# surface grid descriptor
+int	cols[npts]	# column values, 1 <= col[i] <= ncols
+int	lineno		# number of line, 1 <= lineno <= nlines 
+real	z[npts]		# surface values on lineno at cols
+real	w[npts]		# array of weights
+int	npts		# number of surface values, npts <= ncols
+int	wtflag		# type of weighting desired
+.fi
+.ih
+ARGUMENTS
+.ls sf      
+Pointer to the surface grid descriptor structure.
+.le
+.ls cols
+The column numbers of surface grid points on line lineno to be added to the
+dataset.
+.le
+.ls lineno
+The line number of the surface grid line to be added to the data set.
+.le
+.ls z      
+The data values.
+.le
+.ls w
+The array of weights for the data points.
+.le
+.ls npts
+The number of surface grid values on line number lineno to be added to the
+data set.
+.le
+.ls wtflag
+Type of weighting. The options are SF_USER and SF_UNIFORM. If wtflag
+equals SF_USER the weight for each data point is supplied by the user
+and points with zero-valued weights are not included in the fit.
+If wtflag equals SF_UNIFORM the routine sets the weights to 1.
+.le
+.ih
+DESCRIPTION
+ISLACCUM computes the contribution of each data point to the normal
+equations in x, sums that contribution into the appropriate arrays and
+vectors and stores these intermediate results for use by ISLSOLVE.
+.ih
+NOTES
+Checking for out of bounds col values and INDEF valued data points is
+the responsibility of the calling program.
+.ih
+SEE ALSO
+isinit, islfit, islrefit, islsolve, islzero, issolve, isfree
+.endhelp
diff --git a/math/surfit/doc/islfit.hlp b/math/surfit/doc/islfit.hlp
new file mode 100644
index 00000000..5adf0a59
--- /dev/null
+++ b/math/surfit/doc/islfit.hlp
@@ -0,0 +1,67 @@
+.help islfit Apr85 "Surfit Package"
+.ih
+NAME
+islfit -- fit a surface grid line
+.ih
+SYNOPSIS
+include <math/surfit.h>
+
+islfit (sf, cols, lineno, z, w, npts, wtflag, ier)
+
+.nf
+pointer	sf		# surface grid descriptor
+real	cols[npts]	# array of column numbers, 1 <= cols[i] <= ncols
+int	lineno		# number of surface grid line to be added
+real	z[npts]		# data values
+real	w[npts]		# weight array
+int	npts		# number of data points, npts <= ncols
+int	wtflag		# type of weighting
+int	ier		# error code
+.fi
+.ih
+ARGUMENTS
+.ls sf    
+Pointer to the surface grid descriptor structure.
+.le
+.ls cols
+The column numbers of surface grid points to be added to the dataset.
+.le
+.ls lineno
+The line number of the surface grid line to be added to the dataset.
+.le
+.ls z      
+Array of data values.
+.le
+.ls w
+Array of weights.
+.le
+.ls npts
+Number of data points.
+.le
+.ls wtflag
+Type of weighting. The options are SF_USER and SF_UNIFORM. If wtflag =
+SF_USER individual weights for each data point are supplied by the calling
+program and points with zero-valued weights are not included in the fit.
+If wtflag = SF_UNIFORM, all weights are assigned values of 1.
+.le
+.ls ier     
+Error code for the fit. The options are OK, SINGULAR and NO_DEG_FREEDOM.
+If ier = SINGULAR, the numerical routines will compute a solution but one
+or more of the coefficients will be zero. If ier = NO_DEG_FREEDOM there
+were too few data points to solve the matrix equations and the routine
+returns without fitting the data.
+.le
+.ih
+DESCRIPTION
+ISLFIT zeroes the appropriate arrays and vectors,
+computes the contribution of each data point to the normal equations
+in x and accumulates it into the appropriate array and vector elements.  The
+x coefficients are stored for later use by ISSOLVE.
+.ih
+NOTES
+Checking for out of bounds col values and INDEF values pixels is the
+responsibility of the user.
+.ih
+SEE ALSO
+isinit, islrefit, islaccum, islsolve, islzero, issolve, isfree
+.endhelp
diff --git a/math/surfit/doc/islrefit.hlp b/math/surfit/doc/islrefit.hlp
new file mode 100644
index 00000000..c34476d6
--- /dev/null
+++ b/math/surfit/doc/islrefit.hlp
@@ -0,0 +1,51 @@
+.help islrefit Aug85 "Gsurfit Package"
+.ih
+NAME
+islrefit -- refit surface grid line  assuming old cols, w vector
+.ih
+SYNOPSIS
+include <math/surfit.h>
+
+islrefit (sf, cols, lineno, z, w)
+
+.nf
+pointer	sf			# surface grid descriptor
+int	cols[ARB]		# columns to be fit, 1 <= cols[i] <= ncols
+int	lineno			# line number of surface grid line to be fit
+real	z[ARB]			# array of data values
+real	w[ARB]			# array of weights
+.fi
+.ih
+ARGUMENTS
+.ls sf          
+Pointer to the surface grid descriptor structure.
+.le
+.ls cols
+The column numbers of the surface grid line to be added to the dataset.
+.le
+.ls lineno
+The number of the surface grid line to be added to the dataset.
+.le
+.ls z    
+Array of data values.
+.le
+.ls w    
+Array of weights.
+.le
+.ih
+DESCRIPTION
+In some applications the cols, and w values remain unchanged from fit
+to fit and only the z values vary. In this case it is redundant to
+reaccumulate the matrix and perform the Cholesky factorization for each
+succeeding surface grid line. ISLREFIT
+zeros and reaccumulates the vector on the right hand side of the matrix
+equation and performs the forward and back substitution phase to fit for
+a new coefficient vector.
+.ih
+NOTES
+It is the responsibility of the calling program to check for out of bounds
+column values and INDEF valued pixels.
+.ih
+SEE ALSO
+isinit, islfit, islaccum, islsolve, islzero, issolve, isfree
+.endhelp
diff --git a/math/surfit/doc/islsolve.hlp b/math/surfit/doc/islsolve.hlp
new file mode 100644
index 00000000..752cbc19
--- /dev/null
+++ b/math/surfit/doc/islsolve.hlp
@@ -0,0 +1,45 @@
+.help islsolve Apr85 "Surfit Package"
+.ih
+NAME
+islsolve -- solve the equations for a surface grid line
+.ih
+SYNOPSIS
+include <math/surfit.h>
+
+islsolve (sf, lineno, ier)
+
+.nf
+pointer	sf		# surface grid descriptor
+int	lineno		# surface grid line number
+int	ier		# error code
+.fi
+.ih
+ARGUMENTS
+.ls sf     
+Pointer to the surface grid descriptor structure.
+.le
+.ls lineno
+The number of the surface grid line to be added to the dataset.
+.le
+.ls ier      
+Error code returned by the fitting routines. The options are OK, SINGULAR,
+and NO_DEG_FREEDOM. If ier = SINGULAR the matrix is singular, ISLSOLVE
+will compute a solution to the normal equations but one or more of the
+coefficients will be zero. If ier = NO_DEG_FREEDOM, too few data points
+exist for a reasonable solution to be computed and ISLSOLVE returns without
+fitting the data.
+.le
+.ih
+DESCRIPTION
+ISLSOLVE computes the Cholesky factorization of the data matrix and
+solves for the coefficients
+of the x fitting function by forward and back substitution.
+An error code is
+returned by ISLSOLVE if it is unable to solve the normal equations as
+formulated.
+.ih
+NOTES
+.ih
+SEE ALSO
+isinit, islfit, islrefit, islaccum, islzero, issolve, isfree
+.endhelp
diff --git a/math/surfit/doc/islzero.hlp b/math/surfit/doc/islzero.hlp
new file mode 100644
index 00000000..cbdb9515
--- /dev/null
+++ b/math/surfit/doc/islzero.hlp
@@ -0,0 +1,32 @@
+.help islzero Apr85 "Surfit Package"
+.ih
+NAME
+islzero -- set up for a new surface grid line fit
+.ih
+SYNOPSIS
+islzero (sf, lineno)
+
+.nf
+pointer	sf		# surface grid descriptor
+int	lineno		# surface grid line number
+.fi
+.ih
+ARGUMENTS
+.ls sf     
+Pointer to the surface grid descriptor structure.
+.le
+.ls lineno
+Line number of the surface grid line fit to be zeroed.
+.le
+.ih
+DESCRIPTION
+ISLZERO zeros the appropriate arrays and vectors for the surface grid line
+number line number. The line can then be refit by calls to ISLACCUM and
+ISLSOLVE. Alternatively a single call to ISLFIT can perform the combined
+functions of ISLZERO, ISLACCUM and ISLSOLVE.
+.ih
+NOTES
+.ih
+SEE ALSO
+isinit, islfit, islrefit, islaccum, islsolve, issolve
+.endhelp
diff --git a/math/surfit/doc/isreplace.hlp b/math/surfit/doc/isreplace.hlp
new file mode 100644
index 00000000..d248e5f8
--- /dev/null
+++ b/math/surfit/doc/isreplace.hlp
@@ -0,0 +1,33 @@
+.help isreplace Apr1985 "Surfit Package"
+.ih
+NAME
+isreplace -- restore a surface fit saved by issave
+.ih
+SYNOPSIS
+isreplace (sf, fit)
+
+.nf
+pointer	sf		# surface grid descriptor
+real	fit[ARB]	# fit array
+.fi
+
+.ih
+ARGUMENTS
+
+.ls sf
+The pointer to the surface grid descriptor.
+.le
+.ls fit
+The array containing the fit parameters and coefficients.
+.le
+
+.ih
+DESCRIPTION
+
+ISREPLACE restores the fit saved by ISSAVE for use by ISEVAL or ISVECTOR.
+.ih
+NOTES
+.ih
+SEE ALSO
+issave
+.endhelp
diff --git a/math/surfit/doc/isresolve.hlp b/math/surfit/doc/isresolve.hlp
new file mode 100644
index 00000000..afed8ed8
--- /dev/null
+++ b/math/surfit/doc/isresolve.hlp
@@ -0,0 +1,45 @@
+.help isresolve Aug85 "Surfit Package"
+.ih
+NAME
+isresolve -- resolve the surface, same lines array
+.ih
+SYNOPSIS
+include <math/surfit.h>
+
+isresolve (sf, lines, ier)
+
+.nf
+pointer	sf		# surface grid descriptor
+int	lines[nlines]	# surface grid line numbers, 1 <= lines[i] <= nlines
+int	ier		# error code
+.fi
+.ih
+ARGUMENTS
+.ls sf     
+Pointer to the surface grid descriptor structure.
+.le
+.ls nlines
+The number of surface grid lines to be fit.
+.le
+.ls ier      
+Error code returned by the fitting routines. The options are OK, SINGULAR,
+and NO_DEG_FREEDOM. If ier = SINGULAR the matrix is singular, ISSOLVE
+will compute a solution to the normal equations but one or more of the
+coefficients will be zero. If ier = NO_DEG_FREEDOM, too few data points
+exist for a reasonable solution to be computed. ISSOLVE returns without
+fitting the data.
+.le
+.ih
+DESCRIPTION
+In some applications it is necessary to refit the same surface several
+times with the same lines array. In this case it is inefficient to reaccumulate
+the matrices and calculate the Cholesky factorization for each fit.
+ISERESOLVE reaccumulates only the right side of the equation.
+.ih
+NOTES
+It is the responsibility of the calling program to check for out of bounds
+lines values.
+.ih
+SEE ALSO
+issolve, isinit, slzero, islfit, islrefit, islaccum, islresolve, isfree
+.endhelp
diff --git a/math/surfit/doc/issave.hlp b/math/surfit/doc/issave.hlp
new file mode 100644
index 00000000..6ec97cd6
--- /dev/null
+++ b/math/surfit/doc/issave.hlp
@@ -0,0 +1,55 @@
+.help issave Apr85 "Surfit Package"
+.ih
+NAME
+issave - save the surface fit
+.ih
+SYNOPSIS
+issave (sf, fit)
+
+.nf
+pointer	sf		# surface descriptor
+real	fit[ARB]	# fit array
+.fi
+.ih
+ARGUMENTS
+.ls sf   
+Pointer to the surface grid descriptor.
+.le
+.ls fit
+Array for storing the fit. The fit array must be at least SAVE_COEFF + ncoeff
+elements long.
+.le
+
+.ih
+DESCRIPTION
+ISSAVE stores the surface parameters and coefficient array
+in the 1-D reall array fit. Fit must be at least ncoeff + SAVE_COEFF
+elements long where ncoeff is defined as follows.
+
+.nf
+	SF_LEGENDRE:		nxcoeff = xorder
+				nycoeff = yorder
+				ncoeff = xorder * yorder        xterms = yes
+				ncoeff = nycoeff + nxcoeff - 1  xterms = no
+
+	SF_CHEBYSHEV:		nxcoeff = xorder
+				nycoeff = yorder
+				ncoeff = xorder * yorder        xterms = yes
+				ncoeff = nycoeff + nxcoeff - 1  xterms = no
+
+	SF_SPLINE3:		nxcoeff = xorder + 3
+				nycoeff = yorder + 3
+				ncoeff = (xorder + 3) * (yorder + 3)
+
+	SF_SPLINE1:		nxcoeff = xorder + 1
+				nycoeff = yorder + 1
+				ncoeff = (xorder + 1) * (yorder + 1)
+
+.fi
+
+.ih
+NOTES
+.ih
+SEE ALSO
+isreplace
+.endhelp
diff --git a/math/surfit/doc/issolve.hlp b/math/surfit/doc/issolve.hlp
new file mode 100644
index 00000000..312d69a3
--- /dev/null
+++ b/math/surfit/doc/issolve.hlp
@@ -0,0 +1,49 @@
+.help issolve Aug85 "Surfit Package"
+.ih
+NAME
+issolve -- solve the surface
+.ih
+SYNOPSIS
+include <math/surfit.h>
+
+issolve (sf, lines, nlines, ier)
+
+.nf
+pointer	sf		# surface grid descriptor
+int	lines[nlines]	# surface grid line numbers, 1 <= lines[i] <= nlines
+int	nlines		# number of lines
+int	ier		# error code
+.fi
+.ih
+ARGUMENTS
+.ls sf     
+Pointer to the surface grid descriptor structure.
+.le
+.ls lines
+The line number of surface grid lines to be included in the fit.
+.le
+.ls nlines
+The number of surface grid lines to be fit.
+.le
+.ls ier      
+Error code returned by the fitting routines. The options are OK, SINGULAR,
+and NO_DEG_FREEDOM. If ier = SINGULAR the matrix is singular, ISSOLVE
+will compute a solution to the normal equations but one or more of the
+coefficients will be zero. If ier = NO_DEG_FREEDOM, too few data points
+exist for a reasonable solution to be computed. ISSOLVE returns without
+fitting the data.
+.le
+.ih
+DESCRIPTION
+ISSOLVE solves for the surface coefficients.
+An error code is
+returned by ISSOLVE if it is unable to solve the normal equations as
+formulated.
+.ih
+NOTES
+It is the responsibility of the calling program to check for out of bounds
+lines values.
+.ih
+SEE ALSO
+isinit, slzero, islfit, islrefit, islaccum, islresolve, isfree
+.endhelp
diff --git a/math/surfit/doc/isvector.hlp b/math/surfit/doc/isvector.hlp
new file mode 100644
index 00000000..fabbdcc7
--- /dev/null
+++ b/math/surfit/doc/isvector.hlp
@@ -0,0 +1,41 @@
+.help isvector Aug85 "Surfit Package"
+.ih
+NAME
+isvector -- evaluate the fitted surface at a set of points
+.ih
+SYNOPSIS
+isvector (sf, x, y, zfit, npts)
+
+.nf
+pointer	sf		# surface grid descriptor
+real	x[npts]		# x array, 1 <= x[i] <= ncols
+real	y[npts]		# y array, 1 <= y[i] <= nlines
+real	zfit[npts]	# data values
+int	npts		# number of data points
+.fi
+.ih
+ARGUMENTS
+.ls sf    
+Pointer to the surface grid descriptor structure.
+.le
+.ls x, y
+Arrays of x and y values.
+.le
+.ls zfit
+Array of fitted values.
+.le
+.ls npts
+The number of points to be fit.
+.le
+.ih
+DESCRIPTION
+Fit the surface to an array of x and y values. ISVECTOR uses the coefficients
+stored in the surface descriptor structure.
+.ih
+NOTES
+Checking for out of bounds x and y values is the responsibility of the
+calling program.
+.ih
+SEE ALSO
+iseval
+.endhelp
diff --git a/math/surfit/doc/iszero.hlp b/math/surfit/doc/iszero.hlp
new file mode 100644
index 00000000..4c338807
--- /dev/null
+++ b/math/surfit/doc/iszero.hlp
@@ -0,0 +1,26 @@
+.help iszero Aug85 "Surfit Package"
+.ih
+NAME
+iszero -- set up for a new surface fit
+.ih
+SYNOPSIS
+iszero (sf)
+
+.nf
+pointer	sf		# surface grid descriptor
+.fi
+.ih
+ARGUMENTS
+.ls sf     
+Pointer to the surface grid descriptor structure.
+.le
+.ih
+DESCRIPTION
+ISZERO zeros all matrices and vectors used by the fitting program. It
+should be used only if one wishes to refit the surface from scratch.
+.ih
+NOTES
+.ih
+SEE ALSO
+isinit, islzero, islaccum, islfit, islrefit, islsolve, issolve, isfree
+.endhelp
diff --git a/math/surfit/doc/surfit.hd b/math/surfit/doc/surfit.hd
new file mode 100644
index 00000000..18e7ec1a
--- /dev/null
+++ b/math/surfit/doc/surfit.hd
@@ -0,0 +1,19 @@
+# HELP Directory for SURFIT package
+
+$surfit = "math$surfit/"
+
+iscoeff		hlp = iscoeff.hlp,		src = surfit$iscoeff.x
+iseval		hlp = iseval.hlp,		src = surfit$iseval.x
+isfree		hlp = isfree.hlp,		src = surfit$isfree.x
+isinit		hlp = isinit.hlp,		src = surfit$isinit.x
+islaccum	hlp = islaccum.hlp,		src = surfit$islaccum.x
+islfit		hlp = islfit.hlp,		src = surfit$islfit.x
+islrefit	hlp = islrefit.hlp,		src = surfit$islrefit.x
+islsolve	hlp = islsolve.hlp,		src = surfit$islsolve.x
+islzero		hlp = islzero.hlp,		src = surfit$islzero.x
+isreplace	hlp = isreplace.hlp,		src = surfit$isreplace.x
+isresolve	hlp = isresolve.hlp,		src = surfit$isresolve.x
+issave		hlp = issave.hlp,		src = surfit$issave.x
+issolve		hlp = issolve.hlp,		src = surfit$issolve.x
+isvector	hlp = isvector.hlp,		src = surfit$isvector.x
+iszero		hlp = iszero.hlp,		src = surfit$iszero.x
diff --git a/math/surfit/doc/surfit.hlp b/math/surfit/doc/surfit.hlp
new file mode 100644
index 00000000..a7c347cc
--- /dev/null
+++ b/math/surfit/doc/surfit.hlp
@@ -0,0 +1,157 @@
+.help surfit Aug84 "Math Package"
+
+.ih
+NAME
+surfit -- set of routines for fitting gridded surface data
+
+
+.ih
+SYNOPSIS
+
+The surface is defined in the following way. The x and y values are
+assumed to be integers and lie in the range 0 <= x <= ncols + 1 and
+0 <= y <= nlines + 1. The package prefix is for image surface fit.
+Package routines with a prefix followed by l operate on individual
+image lines only.
+
+.nf
+        isinit	(sf, surf_type, xorder, yorder, xterms, ncols, nlines)
+	iszero	(sf)
+       islzero	(sf, lineno)
+      islaccum	(sf, cols, lineno, z, w, ncols, wtflag)
+      islsolve	(sf, lineno, ier)
+        islfit	(sf, cols, lineno, z, w, ncols, wtflag, ier)
+      islrefit	(sf, cols, lineno, z, w, ier)
+       issolve	(sf, lines, nlines, ier)
+     isresolve	(sf, lines, ier)
+    z = iseval	(sf, x, y)
+      isvector	(sf, x, y, zfit, npts)
+        issave	(sf, surface)
+     isrestore	(sf, surface)
+        isfree	(sf)
+.fi
+
+.ih
+DESCRIPTION
+
+The SURFIT package provides a set of routines for fitting surfaces to functions
+linear in their coefficients using the tensor product method and least squares
+techniques. The basic numerical
+technique employed is the solution of the normal equations by the Cholesky
+method.
+
+.ih
+NOTES
+
+The following series of steps illustrates the use of the package.
+
+.ls 4
+.ls (1)
+Include an include <math/surfit.h> statement in the calling program to make the
+SURFIT package definitions available to the user program.
+.le
+.ls (2)
+Call ISINIT to initialize the surface fitting parameters.
+.le
+.ls (3)
+Call ISLACCUM to select a weighting function and accumulate data points
+for each line into the appropriate arrays and vectors. Call ISLSOLVE
+to compute the coefficients in x for each line. The coefficients are
+stored inside SURFIT. Repeat this procedure for each line. ISLACCUM
+and SFLSOLVE can be combined by a call to SFLFIT. If the x values
+and weights remain the same from line to line ISLREFIT can be called.
+.le
+.ls (4)
+Call ISSOLVE to solve for the surface coefficients.
+.le
+.ls (5)
+Call ISEVAL or ISVECTOR to evaluate the fitted surface at the x and y
+value(s) of interest.
+.le
+.ls (6)
+Call ISFREE to release the space allocated for the fit.
+.le
+.le
+
+.ih
+EXAMPLES
+
+.nf
+Example 1: Fit a 2nd order Lengendre polynomial in x and y to an image
+and output the fitted image
+
+include <imhdr.h>
+include <math/surfit.h>
+
+ 	
+	old = immap (old_image, READ_ONLY, 0)
+	new = immap (new_image, NEW_COPY, 0)
+	
+	ncols = IM_LEN(old, 1)
+	nlines = IM_LEN(old, 2)
+	
+	# initialize surface fit
+	call isinit (sf, LEGENDRE, 3, 3, YES, ncols, nlines)
+        
+	# allocate space for lines, columns and weight arrays
+	call malloc (cols, ncols, TY_INT)
+	call malloc (lines, nlines, TY_INT)
+	call malloc (weight, ncols, TY_REAL)
+
+	# initialize lines and columns arrays
+	do i = 1, ncols
+	    Memi[cols - 1 + i] = i
+	do i = 1, nlines
+	    Memi[lines - 1 + i] = i
+
+	# fit the surface in x line by line
+	call amovkl (long(1), v, IM_MAXDIM)
+	do i = 1, nlines {
+	    if (imgnlr (old, inbuf, v) == EOF)
+		call error (0, "Error reading image.")
+	    if (i == 1) {
+		call islfit (sf, Memi[cols], i, Memr[inbuf], Memr[weight],
+				ncols, SF_WTSUNIFORM, ier)
+		if (ier != OK)
+		    ...
+	    } else
+		call islrefit (sf, Memi[cols], i, Memr[inbuf], Memr[weight],
+				ier)
+	}
+
+	# solve for surface coefficients
+	call issolve (sf, Memi[lines], nlines, ier)
+
+	# free space used in fitting arrays
+	call mfree (cols, TY_INT)
+	call mfree (lines, TY_INT)
+	call mfree (weight, TY_REAL)
+
+	# allocate space for x and y arrays
+	call malloc (x, ncols, TY_REAL)
+	call malloc (y, ncols, TY_REAL)
+
+	# intialize z array
+	do i = 1, ncols
+	    Memr[x - 1 + i] = real (i)
+
+	# create fitted image
+	call amovkl (long(10, v, IM_MAXDIM)
+	do i = 1, nlines {
+	    if (impnlr (new, outbuf, v) == EOF)
+		call error (0, "Error writing image.")
+	    call amovkr (real (i), Memr[y], ncols)
+	    call isvector (sf, Memr[x], Memr[y], Memr[outbuf], ncols)
+	}
+
+	# close files and cleanup
+	call mfree (x, TY_REAL)
+	call mfree (y, TY_REAL
+
+	call isfree (sf)
+
+	call imunmap (old)
+	call imunmap (new)
+
+.fi
+.endhelp
diff --git a/math/surfit/doc/surfit.men b/math/surfit/doc/surfit.men
new file mode 100644
index 00000000..4a3b3258
--- /dev/null
+++ b/math/surfit/doc/surfit.men
@@ -0,0 +1,15 @@
+         isinit - initialize surface descriptor
+        iscoeff - get coefficients of surface
+         iseval - evaluate the surface at a point
+         isfree - free surface descriptor
+       islaccum - accumulate surface at a given line number
+         islfit - fit the surface at a given line number
+       islrefit - refit the surface at a given line number, same columns
+       islsolve - solve the surface at a given line number
+        islzero - zero the fit for a given line number
+        issolve - solve the surface
+      isreplace - restore the surface fit
+      isresolve - resolve surface, same lines
+         issave - save the surface fit
+       isvector - fit surface at a set of (x,y) values
+         iszero - zero the surface fit
diff --git a/math/surfit/doc/surfit.spc b/math/surfit/doc/surfit.spc
new file mode 100644
index 00000000..07f2b934
--- /dev/null
+++ b/math/surfit/doc/surfit.spc
@@ -0,0 +1,500 @@
+.help surfit Aug84 "Math Package"
+.CE
+Specifications for the Surface Fitting Package
+.CE
+Lindsey Davis
+.CE
+August 1984
+.CE
+First Draft
+
+.sh
+1. Introduction
+
+The SURFIT package provides a set of routines for fitting surfaces to functions
+linear in their coefficients using least squares techniques. The basic numerical
+technique employed is the solution of the normal equations by the Cholesky
+method.
+
+.sh
+2. Requirements
+
+.ls (1)
+The package shall take as input a surface or section of
+a surface.
+The data are assumed to be on a rectangular grid and to have the following
+ranges, 0 <= x <= ncols + 1 and 0 <= y <= nlines + 1.
+The package routines assume that data values equal to INDEF have
+been removed from the data set or replaced with appropriate interpolated
+values prior to entering the package routines. It is not necessary that
+all the data be present to perform the fit.
+.le
+.ls (2)
+The package shall perform the following operations:
+.ls o
+Determine the coefficients of the fitting function by solving the normal
+equations. The surface fitting function is selected at run time from the
+following list: (1) SF_LEGENDRE, Legendre polynomials in x and y,
+(2) SF_CHEBYSHEV, Chebyshev polynomials in x and y, (3) SF_SPLINE3, bicubic
+spline with break points evenly spaced in x and y. The calling sequence
+must be invariant to the form of the fitting function.
+.le
+.ls o
+Set an error code if the numerical routines are unable to fit the specified
+function.
+.le
+.ls o
+Optionally output the values of the coefficients. The coefficients will be
+stored internal to the SURFIT package. However in some applications it is
+the coefficients which are of primary interest. A package routine shall
+exist to extract the coefficients from the curve descriptor structure.
+.le
+.ls o
+Evaluate the surface at arbitrary value(s) of x and y. The evaluating
+routines shall use the calculated coefficients and the user supplied
+x values(s).
+.le
+.ls o
+Be capable of storing the fitted surface parameters and coefficients in a
+user supplied array and restoring the saved fit for later use by the
+evaluating routines.
+.le
+.ls o
+Input surface parameters and surface coefficients derived external to
+the surfit package into the surfit format for use by the evaluate
+routines.
+.le
+.le
+.ls (3)
+The program shall perform a weighted fit to the surface using a user
+supplied weight array and weight flag. The weighting options will be
+SF_WTSUSER and SF_WTSUNIFORM. In SF_WTSUNIFORM mode the package routines
+set all the weights to 1. In SF_WTSUSER mode the package routines apply
+user supplied weights to the individual data points.
+.le
+.ls (4)
+The input data set, output coefficients, error and fitted z arrays are
+single precision real quantities. All package arithmetic shall be performed
+in single precision.
+.le
+
+.sh
+3. Specifications
+
+.sh
+3.1. List of Routines
+
+
+The surface is defined in the following way. The x and y values are
+assumed to be integers and lie in the range 0 <= x <= ncols + 1 and
+0 <= y <= nlines + 1. The package prefix is is for image surface fit.
+Package routines with a prefix followed by l operate on individual
+image lines only.
+
+.nf
+	z = f (col, line)
+.fi
+
+.nf
+        isinit	(sf, surf_type, xorder, yorder, xterms, ncols, nlines)
+	iszero	(sf)
+       islzero	(sf, lineno)
+      islaccum	(sf, cols, lineno, z, w, ncols, wtflag)
+      islsolve	(sf, lineno, ier)
+        islfit	(sf, cols, lineno, z, w, ncols, wtflag, ier)
+      islrefit	(sf, cols, lineno, z, w, ier)
+       issolve	(sf, lines, nlines, ier)
+     isresolve	(sf, lines, ier)
+    z = iseval	(sf, x, y)
+      isvector	(sf, x, y, zfit, npts)
+        issave	(sf, surface)
+     isrestore	(sf, surface)
+        isfree	(sf)
+.fi
+
+.sh
+3.2. Algorithms
+
+.sh
+3.2.1. Polynomial Basis Functions
+
+The approximating function is assumed to be of the following form,
+
+.nf
+    f(x,y) = sum (a[i,j] * F(i,x) * F(j,y))    i = 1...nxcoeff  j = 1...nycoeff
+.fi
+
+where the F(i,x) are the polynomial basis functions containing terms of order
+x**(i-1) and the a(i,j) are the coefficients. In order to avoid a very
+ill-conditioned linear system for moderate or large i, the Legendre and
+Chebyshev polynomials were chosen for the basis functions. The Chebyshev
+and Legendre polynomials are orthogonal over -1. <= x,y <= 1. The data x and
+y values are normalized to this regime using the number of lines and columns
+supplied by the user. For each data point the basis
+functions are calculated using the following recursion relations. The
+cross terms are optional.
+
+Legendre series:
+.nf
+
+    F(1,x) = 1.
+    F(2,x) = x
+    F(i,x) = [(2*i-1)*x*F(i-1,x)-(i-2)*F(i-2,x)]/(i-1)
+    F(1,y) = 1.
+    F(2,y) = y
+    F(j,y) = [(2*j-1)*y*F(j-1,y)-(j-2)*F(j-2,y)]/(j-1)
+
+.fi
+Chebyshev series:
+.nf
+
+    F(1,x) = 1.
+    F(2,x) = x
+    F(i,x) = 2.*x*F(i-1,x)-F(i-2,x)
+    F(1,y) = 1.
+    F(2,y) = y
+    F(j,y) = 2.*y*F(j-1,y)-F(j-2,y)
+.fi
+
+
+.sh
+3.2.2. Bicubic Cardinal B-spline
+
+The approximating function is of the form
+
+.nf
+    f(x,y) =  sum (x(i,j) * F(i,x) * F(j,y))   i=1...nxcoeff j=1...nycoeff
+.fi
+
+where the basis functions, F(i,x), are the cubic cardinal B-splines
+(Prenter 1975). The user supplies the number of columns and lines and the
+number of polynomial pieces in x and y, nxpieces and nypieces, to be fit
+to the data set. The number of bicubic spline coefficients, ncoeff, will be
+
+.nf
+    nxcoeff = (nxpieces + 3)
+    nycoeff = (nypieces + 3)
+    ncoeff = nxcoeff * nycoeff
+.fi
+
+The cardinal B-spline is stored in a lookup table. For each x and y the
+appropriate break point is selected and the four non-zero B-splines are
+calculated by nearest neighbour interpolation in the lookup table.
+
+.sh
+3.2.3. Method of Solution
+
+.sh
+3.2.3.1. Full Surface Fit
+
+The normal equations are accumulated in the following form.
+
+.nf
+    c * x = b
+    c[i,j] = (B(i,x,y), B(j,x,y))
+    b[j] = (B(j,x,y), S(x,y))
+.fi
+
+B(i,x,y) is the ith basis function at x and y, S(x,y) is the surface to
+be approximated and the inner product of two functions G and H is
+given by 
+
+.nf
+    (G,H) = sum (w[i] * G(x[i],y[i]) * H(x[i],y[i]))  i = 1...npts
+.fi
+
+Since the matrix c is symmetric and positive semi-definite it may
+be solved by the Cholesky method.
+The coefficient matrix c  can be written as
+
+.nf
+    c = l * d * l-transpose
+.fi
+
+where l is a unit lower triangular matrix and d is the diagonal of c
+(de Boor 1978). Near zero pivots are handled in the following way.
+At the nth elimination step the current value of the nth diagonal
+element is compared with the original nth diagonal element. If the
+diagonal element has been reduced by one computer word length, the
+entire nth row is declared linearly dependent on the previous n-1
+rows and x(n) = 0.
+
+The triangular system
+
+.nf
+    l * w = b
+.fi
+
+is solved for w (forward substitution), the vector d  ** (-1) * w is
+computed and the triangular system
+
+.nf
+    l-transpose * x = d ** (-1) * w
+.fi
+
+solved for the coefficients, x (backward substitution).
+
+
+.sh
+3.2.3.2. Line by Line Fit
+
+Each line of the surface can be represented by the following equation.
+
+.nf
+    S(x,yo) = a[i](yo) * B[i](x)            i = 1...nxcoeff for each yo
+.fi
+
+The normal equations for each image line are formed
+
+.nf
+    c * a = b
+    c[i,j] = (B(i,x), B(j,x))
+    b[j] = (B(j,x), S(x,yo))
+.fi
+
+and solved for a as described in the previous section.
+After fitting the entire image matrix a has nxcoeff columns and
+nlines rows.
+
+For each column i in a the normal equations
+are formed and solved for the c[i,j]
+
+.nf
+    c * x  = b
+    c[j,k] = (B(j,y), B(k,x))
+    b[i,j] = (a[i](y), B(j,y))
+.fi
+
+.sh
+3.2.4. Number of Operations
+
+It is worth while to calculate the number of operations reqired to compute
+the surface fit by the full surface method versus the line by line method.
+The number of operations required to accumulate the normal equations
+and solve the set is the following
+
+.nf
+    nop = npts * order ** 2 / 2 + order ** 3 /6
+.fi
+
+where the first term is the number of operations required to accumulate the
+matrix and the second is the number required to solve the system.
+
+.nf
+Example 1: full surface, 3 by 3 polynomial no cross terms, 512 by 512 image
+
+    norder = 5
+    npts = 512 * 512
+    nops(accum) = 3,276,800
+    nops(solve) = 21
+
+Example 2: full surface, 30 by 30 spline, 512 by 512 image
+
+    norder = 900
+    npts = 512 * 512
+    nops(accum) = 1.062 * 10 ** 11
+    nops(solve) = 1.216 * 10 ** 8
+
+Example 3: line by line method, 3 by 3 polynomial, 512 by 512 image
+
+    step 1 solve for a coefficients
+    norder = 3
+    npts = 512
+    nlines = 512
+    nops(accum) = 1,179,648
+    nops(solve) = 2304
+
+    step 2 solve for c coefficients
+    norder = 3
+    npts = 512
+    nlines = 3
+    nops(accum) = 6912
+    nops(solve) = 14
+
+Example 4: line by line method, 30 by 30 spline, 512 by 512 image
+
+    step 1 solve coefficients
+    norder = 30
+    npts = 512
+    nlines = 512
+    nops(accum) = 117,964,800
+    nops(solve) = 2,304,000
+
+    step 2 solve for c coefficients
+    norder = 30
+    npts = 512
+    nlines = 30
+    nops(accum) = 6,912,000
+    nops(solve) = 135,000
+.fi
+
+The figures for the line by line method are worst case numbers. If the
+x values remain the same from line to line then the coefficient matrix
+only has to be accumulated and inverted twice.
+For the bicubic spline function the number of operations is significantly
+reduced by taking advantage of the banded nature of the matrices.
+
+.sh
+4. Usage
+
+.sh
+4.1. User Notes
+
+The following series of steps illustrates the use of the package.
+
+.ls 4
+.ls (1)
+Include an include <surfit.h> statement in the calling program to make the
+SURFIT package definitions available to the user program.
+.le
+.ls (2)
+Call SFINIT to initialize the surface fitting parameters.
+.le
+.ls (3)
+Call SFLACCUM to select a weighting function and accumulate data points
+for each line into the appropriate arrays and vectors. Call SFLSOLVE
+to compute the coefficients in x for each line. The coefficents are
+stored inside SURFIT. Repeat this procedure for each line. SFLACCUM
+and SFLSOLVE can be combined by a call to SFLFIT. If the x values
+and weights remain the same from line to line SFLREFIT can be called.
+.le
+.ls (4)
+Call SFSOLVE to solve for the surface coefficients.
+.le
+.ls (5)
+Call SFEVAL or SFVECTOR to evaluate the fitted surface at the x and y
+value(s) of interest.
+.le
+.ls (6)
+Call SFFREE to release the space allocated for the fit.
+.le
+.le
+
+.sh
+4.2. Examples
+
+.nf
+Example 1: Fit a 2nd order Lengendre polynomial in x and y to an image
+and output the fitted image
+
+include <imhdr.h>
+include <math/surfit.h>
+
+ 	
+	old = immap (old_image, READ_ONLY, 0)
+	new = immap (new_image, NEW_COPY, 0)
+	
+	ncols = IM_LEN(old, 1)
+	nlines = IM_LEN(old, 2)
+	
+	# initialize surface fit
+	call isinit (sf, LEGENDRE, 3, 3, YES, ncols, nlines)
+        
+	# allocate space for lines, columns and weight arrays
+	call malloc (cols, ncols, TY_INT)
+	call malloc (lines, nlines, TY_INT)
+	call malloc (weight, ncols, TY_REAL)
+
+	# initialize lines and columns arrays
+	do i = 1, ncols
+	    Memi[cols - 1 + i] = i
+	do i = 1, nlines
+	    Memi[lines - 1 + i] = i
+
+	# fit the surface in x line by line
+	call amovkl (long(1), v, IM_MAXDIM)
+	do i = 1, nlines {
+	    if (imgnlr (old, inbuf, v) == EOF)
+		call error (0, "Error reading image.")
+	    if (i == 1) {
+		call islfit (sf, Memi[cols], i, Memr[inbuf], Memr[weight],
+				ncols, SF_WTSUNIFORM, ier)
+		if (ier != OK)
+		    ...
+	    } else
+		call sflrefit (sf, Memi[cols], i, Memr[inbuf], Memr[weight],
+				ier)
+	}
+
+	# solve for surface coefficients
+	call issolve (sf, Memi[lines], nlines, ier)
+
+	# free space used in fitting arrays
+	call mfree (cols, TY_INT)
+	call mfree (lines, TY_INT)
+	call mfree (weight, TY_REAL)
+
+	# allocate space for x and y arrays
+	call malloc (x, ncols, TY_REAL)
+	call malloc (y, ncols, TY_REAL)
+
+	# intialize z array
+	do i = 1, ncols
+	    Memr[x - 1 + i] = real (i)
+
+	# create fitted image
+	call amovkl (long(10, v, IM_MAXDIM)
+	do i = 1, nlines {
+	    if (impnlr (new, outbuf, v) == EOF)
+		call error (0, "Error writing image.")
+	    call amovkr (real (i), Memr[y], ncols)
+	    call isvector (sf, Memr[x], Memr[y], Memr[outbuf], ncols)
+	}
+
+	# close files and cleanup
+	call mfree (x, TY_REAL)
+	call mfree (y, TY_REAL
+
+	call isfree (sf)
+
+	call imunmap (old)
+	call imunmap (new)
+
+.fi
+.sh
+5. Detailed Design
+
+.sh
+5.1. Surface Descriptor Structure
+
+To be written when specifications are finalised.
+
+.sh
+5.2. Storage Requirements
+
+The minimum storage requirements for the full surface fit method
+assuming that points are to be rejected from the fit without revaluating
+the matrix are the following.
+
+.nf
+    (nxcoeff*nycoeff) ** 2    -- coefficient array plus triangularized matrix
+    nxcoeff*nycoeff           -- right side
+    nxcoeff*nycoeff           -- solution vector
+.fi
+
+For a 30 by 30 spline roughly 811,800 storage units are required.
+For a 3 by 3 polynomial the requirements are 675 storage units. The
+requirements are roughly half when rejection is disabled.
+
+The minimum storage requirements for the line by line method are
+
+.nf
+    nx*nx*2   -- The x matrix and its factorization
+    nx*nlines -- The x coefficient matrix
+    ny*ny*2 -- The y matrix and its factorization
+    nx*ny -- The solution
+.fi
+
+
+.sh
+6. References
+
+.ls (1)
+Carl de Boor, "A Practical Guide to Splines", 1978, Springer-Verlag New York
+Inc.
+.le
+.ls (2)
+P.M. Prenter, "Splines and Variational Methods", 1975, John Wiley and Sons
+Inc.
+.le
+.endhelp
diff --git a/math/surfit/iscoeff.x b/math/surfit/iscoeff.x
new file mode 100644
index 00000000..f656e7e6
--- /dev/null
+++ b/math/surfit/iscoeff.x
@@ -0,0 +1,37 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "surfitdef.h"
+
+# ISCOEFF -- Procedure to fetch the number and magnitude of the coefficients.
+# If the surface type is a bicubic spline or polynomials with cross terms
+# then the  number of coefficients is SF_NXCOEFF(sf) * SF_NYCOEFF(sf) and
+# the coefficient of B(i,x) * B(j,y) will be stored in element
+# (i - 1) * SF_NYCOEFF(sf) + j of the array coeff. Otherwise the number
+# of coefficients will be (SF_NXCOEFF(sf) + SF_NYCOEFF(sf) - 1), and
+# the SF_NYCOEFF(sf) y coefficients will be output first followed by
+# the (SF_NXCOEFF(sf) - 1) x coefficients.
+
+procedure iscoeff (sf, coeff, ncoeff)
+
+pointer	sf		# pointer to the surface fitting descriptor
+real	coeff[ARB]	# the coefficients of the fit
+int	ncoeff		# the number of coefficients
+
+int	i
+pointer	cptr
+
+begin
+	# calculate the number of coefficients
+	if (SF_XTERMS(sf) == NO) {
+	    ncoeff = SF_NXCOEFF(sf) + SF_NYCOEFF(sf) - 1
+	    call amovr (COEFF(SF_COEFF(sf)), coeff, SF_NYCOEFF(sf))
+	    cptr = SF_COEFF(sf) + SF_NYCOEFF(sf)
+	    do i = SF_NYCOEFF(sf) + 1, ncoeff {
+		coeff[i] = COEFF(cptr)
+		cptr = cptr + SF_NYCOEFF(sf)
+	    }
+	} else {
+	    ncoeff = SF_NXCOEFF(sf) * SF_NYCOEFF(sf)
+	    call amovr (COEFF(SF_COEFF(sf)), coeff, ncoeff)
+	}
+end
diff --git a/math/surfit/iseval.x b/math/surfit/iseval.x
new file mode 100644
index 00000000..08ef5f89
--- /dev/null
+++ b/math/surfit/iseval.x
@@ -0,0 +1,92 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/surfit.h>
+include "surfitdef.h"
+
+# ISEVAL -- Procedure to evaluate the fitted surface at a single point.
+# The SF_NXCOEFF(sf) by SF_NYCOEFF(sf) coefficients are stored in the
+# SF_NYCOEFF(sf) by SF_NXCOEFF(sf) matrix COEFF. The j-th element of the ith
+# row of COEFF contains the coefficient of the i-th basis function in x and
+# the j-th basis function in y.
+
+real procedure iseval (sf, x, y)
+
+pointer	sf		# pointer to surface descriptor structure
+real	x		# x value
+real	y		# y value
+
+real	sum, accum
+int	i, k, leftx, lefty, yorder
+pointer	sp, xb, xzb, yb, yzb, czptr
+
+begin
+	# allocate space for the basis functions
+	call smark (sp)
+	call salloc (xb, SF_XORDER(sf), MEM_TYPE)
+	xzb = xb - 1
+	call salloc (yb, SF_YORDER(sf), MEM_TYPE)
+	yzb = yb - 1
+
+	# calculate the basis functions
+	switch (SF_TYPE(sf)) {
+	case SF_CHEBYSHEV:
+	    leftx = 0
+	    lefty = 0
+	    czptr = SF_COEFF(sf) - 1
+	    call sf_b1cheb (x, SF_XORDER(sf), SF_XMAXMIN(sf), SF_XRANGE(sf),
+		XBS(xb))
+	    call sf_b1cheb (y, SF_YORDER(sf), SF_YMAXMIN(sf), SF_YRANGE(sf),
+		YBS(yb))
+
+	case SF_LEGENDRE:
+	    leftx = 0
+	    lefty = 0
+	    czptr = SF_COEFF(sf) - 1
+	    call sf_b1leg (x, SF_XORDER(sf), SF_XMAXMIN(sf), SF_XRANGE(sf),
+		XBS(xb))
+	    call sf_b1leg (y, SF_YORDER(sf), SF_YMAXMIN(sf), SF_YRANGE(sf),
+		YBS(yb))
+
+	case SF_SPLINE3:
+	    call sf_b1spline3 (x, SF_NXPIECES(sf), -SF_XMIN(sf),
+	        SF_XSPACING(sf), XBS(xb), leftx)
+	    call sf_b1spline3 (y, SF_NYPIECES(sf), -SF_YMIN(sf),
+	        SF_YSPACING(sf), YBS(yb), lefty)
+	    czptr = SF_COEFF(sf) - 1 + lefty + leftx * SF_NYCOEFF(sf)
+
+	case SF_SPLINE1:
+	    call sf_b1spline1 (x, SF_NXPIECES(sf), -SF_XMIN(sf),
+	        SF_XSPACING(sf), XBS(xb), leftx)
+	    call sf_b1spline1 (y, SF_NYPIECES(sf), -SF_YMIN(sf),
+	        SF_YSPACING(sf), YBS(yb), lefty)
+	    czptr = SF_COEFF(sf) - 1 + lefty + leftx * SF_NYCOEFF(sf)
+	}
+
+	# initialize accumulator
+	# basis functions
+	sum = 0.
+
+	# loop over y basis functions
+	yorder = SF_YORDER(sf)
+	do i = 1, SF_XORDER(sf) {
+
+	    # loop over the x basis functions
+	    accum = 0.
+	    do k = 1, yorder {
+		accum = accum + COEFF(czptr+k) * YBS(yzb+k) 
+	    }
+	    accum = accum * XBS(xzb+i)
+	    sum = sum + accum
+
+	    # elements of COEFF where neither k = 1 or i = 1
+	    # are not calculated if SF_XTERMS(sf) = NO
+	    if (SF_XTERMS(sf) == NO)
+		yorder = 1
+
+	    czptr = czptr + SF_NYCOEFF(sf)
+	}
+
+	call sfree (sp)
+
+	return (sum)
+end
diff --git a/math/surfit/isfree.x b/math/surfit/isfree.x
new file mode 100644
index 00000000..2eb25891
--- /dev/null
+++ b/math/surfit/isfree.x
@@ -0,0 +1,45 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "surfitdef.h"
+
+# ISFREE -- Procedure to free the surface descriptor
+
+procedure isfree (sf)
+
+pointer	sf		# pointer to the surface descriptor
+errchk	mfree
+
+begin
+	# free arrays in memory
+
+	# first the basis functions
+	if (SF_XBASIS(sf) != NULL)
+	    call mfree (SF_XBASIS(sf), MEM_TYPE)
+	if (SF_XLEFT(sf) != NULL)
+	    call mfree (SF_XLEFT(sf), TY_INT)
+	if (SF_YBASIS(sf) != NULL)
+	    call mfree (SF_YBASIS(sf), MEM_TYPE)
+	if (SF_YLEFT(sf) != NULL)
+	    call mfree (SF_YLEFT(sf), TY_INT)
+
+	# next the x and y matrices
+	if (SF_XMATRIX(sf) != NULL)
+	    call mfree (SF_XMATRIX(sf), MEM_TYPE)
+	if (SF_YMATRIX(sf) != NULL)
+	    call mfree (SF_YMATRIX(sf), MEM_TYPE)
+
+	# last the coefficient matrices
+	if (SF_XCOEFF(sf) != NULL)
+	    call mfree (SF_XCOEFF(sf), MEM_TYPE)
+	if (SF_COEFF(sf) != NULL)
+	    call mfree (SF_COEFF(sf), MEM_TYPE)
+
+	if (SF_WZ(sf) != NULL)
+	    call mfree (SF_WZ(sf), MEM_TYPE)
+	if (SF_TLEFT(sf) != NULL)
+	    call mfree (SF_TLEFT(sf), TY_INT)
+
+	# free surface descriptor
+	if (sf != NULL)
+	    call mfree (sf, TY_STRUCT)
+end
diff --git a/math/surfit/isinit.x b/math/surfit/isinit.x
new file mode 100644
index 00000000..ade35b47
--- /dev/null
+++ b/math/surfit/isinit.x
@@ -0,0 +1,167 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/surfit.h>
+include "surfitdef.h"
+
+# ISINIT --  Procedure to set up the surface  descriptor.
+
+procedure isinit (sf, surf_type, xorder, yorder, xterms, ncols, nlines)
+
+pointer	sf		# pointer to surface descriptor structure
+int	surf_type	# type of surface to be fitted
+int	xorder		# x order of surface to be fit, or in the case of the
+			# spline the number of polynomial pieces in x to be fit
+int	yorder		# y order of surface to be fit, or in the case of the
+			# spline the number of polynomial pieces in y to be fit
+int	xterms		# cross terms for polynomials?
+int	ncols		# number of columns in the surface
+int	nlines		# number of lines in the surface
+
+int	i
+pointer	x, y
+pointer	sp
+errchk	malloc, calloc
+
+begin
+	# allocate space for the surface descriptor
+	call malloc (sf, LEN_SFSTRUCT, TY_STRUCT)
+
+	if (xorder < 1 || yorder < 1)
+	    call error (0, "SFLINIT: Illegal order.")
+
+	if (ncols < 1)
+	    call error (0, "SFLINIT: x data range is 0.")
+	if (nlines < 1)
+	    call error (0, "SFLINIT: y data range is 0.")
+
+	switch (surf_type) {
+
+	case SF_CHEBYSHEV, SF_LEGENDRE:
+	    SF_NXCOEFF(sf) = xorder
+	    SF_XORDER(sf) = xorder
+	    SF_XRANGE(sf) = 2. / real (ncols + 1)
+	    SF_XMAXMIN(sf) = - real (ncols + 1) / 2.
+	    SF_XMIN(sf) = 0.
+	    SF_XMAX(sf) = real (ncols + 1)
+	    SF_NYCOEFF(sf) = yorder
+	    SF_YORDER(sf) = yorder
+	    SF_YRANGE(sf) = 2. / real (nlines + 1)
+	    SF_YMAXMIN(sf) = - real (nlines + 1) / 2.
+	    SF_YMIN(sf) = 0.
+	    SF_YMAX(sf) = real (nlines + 1)
+	    SF_XTERMS(sf) = xterms
+
+	case SF_SPLINE3:
+	    SF_NXCOEFF(sf) = (xorder + SPLINE3_ORDER - 1)
+	    SF_XORDER(sf) = SPLINE3_ORDER
+	    SF_NXPIECES(sf) = xorder - 1
+	    SF_XSPACING(sf) = xorder / real (ncols + 1)
+	    SF_NYCOEFF(sf) = (yorder + SPLINE3_ORDER - 1)
+	    SF_YORDER(sf) = SPLINE3_ORDER
+	    SF_NYPIECES(sf) = yorder - 1
+	    SF_YSPACING(sf) = yorder / real (nlines + 1)
+	    SF_XMIN(sf) = 0.
+	    SF_XMAX(sf) = real (ncols + 1)
+	    SF_YMIN(sf) = 0.
+	    SF_YMAX(sf) = real (nlines + 1)
+	    SF_XTERMS(sf) = YES
+
+	case SF_SPLINE1:
+	    SF_NXCOEFF(sf) = (xorder + SPLINE1_ORDER - 1)
+	    SF_XORDER(sf) = SPLINE1_ORDER
+	    SF_NXPIECES(sf) = xorder - 1
+	    SF_XSPACING(sf) = xorder / real (ncols + 1)
+	    SF_NYCOEFF(sf) = (yorder + SPLINE1_ORDER - 1)
+	    SF_YORDER(sf) = SPLINE1_ORDER
+	    SF_NYPIECES(sf) = yorder - 1
+	    SF_YSPACING(sf) = yorder / real (nlines + 1)
+	    SF_XMIN(sf) = 0.
+	    SF_XMAX(sf) = real (ncols + 1)
+	    SF_YMIN(sf) = 0.
+	    SF_YMAX(sf) = real (nlines + 1)
+	    SF_XTERMS(sf) = YES
+
+	default:
+	    call error (0, "SFINIT: Unknown surface type.")
+	}
+
+	SF_TYPE(sf) = surf_type
+	SF_NLINES(sf) = nlines
+	SF_NCOLS(sf) = ncols
+
+	# allocate space for the matrix and vectors
+	call calloc (SF_XBASIS(sf), SF_XORDER(sf) * SF_NCOLS(sf),
+		    MEM_TYPE)
+	call calloc (SF_YBASIS(sf), SF_YORDER(sf) * SF_NLINES(sf),
+		    MEM_TYPE)
+	call calloc (SF_XMATRIX(sf), SF_XORDER(sf) * SF_NXCOEFF(sf), MEM_TYPE)
+	call calloc (SF_XCOEFF(sf), SF_NLINES(sf) * SF_NXCOEFF(sf), MEM_TYPE)
+	call calloc (SF_YMATRIX(sf), SF_YORDER(sf) * SF_NYCOEFF(sf), MEM_TYPE)
+	call calloc (SF_COEFF(sf), SF_NXCOEFF(sf) * SF_NYCOEFF(sf), MEM_TYPE)
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (x, SF_NCOLS(sf), MEM_TYPE)
+	call salloc (y, SF_NLINES(sf), MEM_TYPE)
+
+	# calculate all possible x basis functions and store
+	do i = 1, SF_NCOLS(sf)
+	    Memr[x+i-1] = i
+
+	switch (SF_TYPE(sf)) {
+	case SF_LEGENDRE:
+	    SF_XLEFT(sf) = NULL
+	    call sf_bleg (Memr[x], SF_NCOLS(sf), SF_XORDER(sf), SF_XMAXMIN(sf),
+		SF_XRANGE(sf), XBASIS(SF_XBASIS(sf)))
+
+	case SF_CHEBYSHEV:
+	    SF_XLEFT(sf) = NULL
+	    call sf_bcheb (Memr[x], SF_NCOLS(sf), SF_XORDER(sf), SF_XMAXMIN(sf),
+		SF_XRANGE(sf), XBASIS(SF_XBASIS(sf)))
+
+	case SF_SPLINE3:
+	    call calloc (SF_XLEFT(sf), SF_NCOLS(sf), TY_INT)
+	    call sf_bspline3 (Memr[x], SF_NCOLS(sf), SF_NXPIECES(sf),
+	        -SF_XMIN(sf), SF_XSPACING(sf), XBASIS(SF_XBASIS(sf)),
+	        XLEFT(SF_XLEFT(sf)))
+
+	case SF_SPLINE1:
+	    call calloc (SF_XLEFT(sf), SF_NCOLS(sf), TY_INT)
+	    call sf_bspline1 (Memr[x], SF_NCOLS(sf), SF_NXPIECES(sf),
+	        -SF_XMIN(sf), SF_XSPACING(sf), XBASIS(SF_XBASIS(sf)),
+	        XLEFT(SF_XLEFT(sf)))
+	}
+
+	# calculate all possible y basis functions and store
+	do i = 1, SF_NLINES(sf)
+	    Memr[y+i-1] = i
+
+	switch (SF_TYPE(sf)) {
+	case SF_LEGENDRE:
+	    SF_YLEFT(sf) = NULL
+	    call sf_bleg (Memr[y], SF_NLINES(sf), SF_YORDER(sf),
+	        SF_YMAXMIN(sf), SF_YRANGE(sf), YBASIS(SF_YBASIS(sf)))
+
+	case SF_CHEBYSHEV:
+	    SF_YLEFT(sf) = NULL
+	    call sf_bcheb (Memr[y], SF_NLINES(sf), SF_YORDER(sf),
+	        SF_YMAXMIN(sf), SF_YRANGE(sf), YBASIS(SF_YBASIS(sf)))
+
+	case SF_SPLINE3:
+	    call calloc (SF_YLEFT(sf), SF_NLINES(sf), TY_INT)
+	    call sf_bspline3 (Memr[y], SF_NLINES(sf), SF_NYPIECES(sf),
+	        -SF_YMIN(sf), SF_YSPACING(sf), YBASIS(SF_YBASIS(sf)),
+	        YLEFT(SF_YLEFT(sf)))
+
+	case SF_SPLINE1:
+	    call calloc (SF_YLEFT(sf), SF_NLINES(sf), TY_INT)
+	    call sf_bspline1 (Memr[y], SF_NLINES(sf), SF_NYPIECES(sf),
+	        -SF_YMIN(sf), SF_YSPACING(sf), YBASIS(SF_YBASIS(sf)),
+	        YLEFT(SF_YLEFT(sf)))
+	}
+
+	SF_WZ(sf) = NULL
+	SF_TLEFT(sf) = NULL
+
+	call sfree (sp)
+end
diff --git a/math/surfit/islaccum.x b/math/surfit/islaccum.x
new file mode 100644
index 00000000..cc69323a
--- /dev/null
+++ b/math/surfit/islaccum.x
@@ -0,0 +1,117 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/surfit.h>
+include "surfitdef.h"
+
+# ISLACCUM -- Procedure to add points on a line to the data set.
+# The inner products of the non-zero x basis functions are stored
+# in the SF_XORDER(sf) by SF_NXCOEFF(sf) matrix XMATRIX. The
+# main diagonal is stored in the first row of XMATRIX. Successive
+# non-zero diagonals are stored in the succeeding rows. This method
+# of storage is particularly efficient for the large symmetric
+# banded matrices produced during spline fits. The inner products
+# of the data ordinates and the non-zero x basis functions are
+# caculated and stored in the lineno-th row of the SF_NXCOEFF(sf)
+# by SF_NLINES(sf) matrix XCOEFF.
+
+procedure islaccum (sf, cols, lineno, z, w, ncols, wtflag)
+
+pointer	sf		# pointer to surface descriptor
+int	cols[ncols]	# column values
+int	lineno		# lineno of data being accumulated
+real	z[ncols]	# surface values on lineno at cols
+real	w[ncols]	# weight of the data points
+int	ncols		# number of data points
+int	wtflag		# type of weighting desired
+
+int	i, ii, j, k
+pointer	xbzptr, xbptr
+pointer	xlzptr
+pointer	xmzptr, xmindex
+pointer	xczptr, xcindex
+pointer	bw, rows, left
+pointer sp
+
+begin
+	# count the number of points
+	SF_NXPTS(sf) = SF_NXPTS(sf) + ncols
+
+	# calculate the weights, default is uniform weighting
+	switch (wtflag) {
+	case SF_UNIFORM:
+	    call amovkr (1.0, w, ncols)
+	case SF_USER:
+	    # do not alter weights
+	default:
+	    call amovkr (1.0, w, ncols)
+	}
+
+	# set up temporary storage
+	call smark (sp)
+	call salloc (bw, ncols, TY_REAL)
+	call salloc (left, ncols, TY_INT)
+	call salloc (rows, ncols, TY_INT)
+
+	# set up the pointers
+	xbzptr = SF_XBASIS(sf) - 1
+	xmzptr = SF_XMATRIX(sf)
+	xczptr = SF_XCOEFF(sf) + (lineno - 1) * SF_NXCOEFF(sf) - 1
+
+	# accumulate the line
+	switch (SF_TYPE(sf)) {
+	case SF_LEGENDRE, SF_CHEBYSHEV:
+
+	    do i = 1, SF_XORDER(sf) {
+		do j = 1, ncols
+		    Memr[bw+j-1] = w[j] * XBASIS(xbzptr+cols[j]) 
+		xcindex = xczptr + i
+		do j = 1, ncols
+		    XCOEFF(xcindex) = XCOEFF(xcindex) + Memr[bw+j-1] * z[j]
+		xbptr  = xbzptr
+		ii = 0
+		do k = i, SF_XORDER(sf) {
+		    xmindex = xmzptr + ii
+		    do j = 1, ncols
+			XMATRIX(xmindex) = XMATRIX(xmindex) + Memr[bw+j-1] *
+			    XBASIS(xbptr+cols[j])
+		    ii = ii + 1
+		    xbptr = xbptr + SF_NCOLS(sf)
+		}
+		xbzptr = xbzptr + SF_NCOLS(sf)
+		xmzptr = xmzptr + SF_XORDER(sf)
+	    }
+
+	case SF_SPLINE3, SF_SPLINE1:
+
+	    xlzptr = SF_XLEFT(sf) - 1
+	    do j = 1, ncols
+	        Memi[left+j-1] = XLEFT(xlzptr+cols[j])
+	    call amulki (Memi[left], SF_XORDER(sf), Memi[rows], ncols)
+	    call aaddki (Memi[rows], SF_XMATRIX(sf), Memi[rows], ncols)
+	    call aaddki (Memi[left], xczptr, Memi[left], ncols) 
+
+	    do i = 1, SF_XORDER(sf) {
+		do j = 1, ncols {
+		    Memr[bw+j-1] = w[j] * XBASIS(xbzptr+cols[j])
+		    xcindex = Memi[left+j-1] + i
+		    XCOEFF(xcindex) = XCOEFF(xcindex) + Memr[bw+j-1] * z[j]
+		}
+		xbptr = xbzptr
+		ii = 0
+		do k = i, SF_XORDER(sf) {
+		    do j = 1, ncols {
+			xmindex = Memi[rows+j-1] + ii
+			XMATRIX(xmindex) = XMATRIX(xmindex) + Memr[bw+j-1] *
+			    XBASIS(xbptr+cols[j])
+		    }
+		    ii = ii + 1
+		    xbptr = xbptr + SF_NCOLS(sf)
+		}
+		xbzptr = xbzptr + SF_NCOLS(sf)
+		call aaddki (Memi[rows], SF_XORDER(sf), Memi[rows], ncols)
+	    }
+	}
+
+	# release space
+	call sfree (sp)
+end
diff --git a/math/surfit/islfit.x b/math/surfit/islfit.x
new file mode 100644
index 00000000..7b60c361
--- /dev/null
+++ b/math/surfit/islfit.x
@@ -0,0 +1,150 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/surfit.h>
+include "surfitdef.h"
+
+# ISLFIT -- Procedure to fit a single line of a surface. The inner products
+# of the x basis functions are calculated and accumulated into the
+# SF_XORDER(sf) by SF_NXCOEFF(sf) matrix XMATRIX. The main diagonal is stored
+# in the first row of XMATRIX followed by the non-zero lower diagonals. This
+# method of storage is very efficient for the large symmetric banded matrices
+# generated by spline fits. The Cholesky factorization of XMATRIX is calculated
+# and stored in XMATRIX destroying the original data. The inner products
+# of the x basis functions and the data ordinates are stored in the lineno-th
+# row of the SF_NXCOEFF(sf) by SF_NLINES(sf) matrix XCOEFF. The x coefficients
+# for each line are calculated by forward and back substitution and
+# stored in the lineno-th line of XCOEFF destroying the original data.
+
+procedure islfit (sf, cols, lineno, z, w, ncols, wtflag, ier)
+
+pointer	sf		# pointer to the surface descriptor
+int	cols[ncols]	# array of columns
+int	lineno    	# lineno
+real	z[ncols]	# the surface values
+real	w[ncols]	# array of weights
+int	ncols		# the number of columns
+int	wtflag		# type of weighting
+int	ier		# error codes
+
+int	i, ii, j, k
+pointer	xbzptr, xbptr
+pointer	xmzptr, xmindex
+pointer	xczptr, xcindex
+pointer	xlzptr
+pointer	left, rows, bw
+pointer	sp
+real	adotr()
+
+begin
+	# index the pointers
+	xbzptr = SF_XBASIS(sf) - 1
+	xmzptr = SF_XMATRIX(sf)
+	xczptr = SF_XCOEFF(sf) + (lineno - 1) * SF_NXCOEFF(sf) - 1
+
+	# zero the accumulators
+	call aclrr (XMATRIX(SF_XMATRIX(sf)), SF_NXCOEFF(sf) * SF_XORDER(sf))
+	call aclrr (XCOEFF(xczptr + 1), SF_NXCOEFF(sf))
+
+	# free space used by previous islrefit calls
+	if (SF_WZ(sf) != NULL)
+	    call mfree (SF_WZ(sf), MEM_TYPE)
+	if (SF_TLEFT(sf) != NULL)
+	    call mfree (SF_TLEFT(sf), TY_INT)
+
+	# reset number of points
+	SF_NXPTS(sf) = ncols
+
+	# calculate the weights, default is uniform weighting
+	switch (wtflag) {
+	case SF_UNIFORM:
+	    call amovkr (1.0, w, ncols)
+	case SF_USER:
+	    # do not alter weights
+	default:
+	    call amovkr (1.0, w, ncols)
+	}
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (bw, ncols, TY_REAL)
+
+	switch (SF_TYPE(sf)) {
+	case SF_LEGENDRE, SF_CHEBYSHEV:
+
+	    do i = 1, SF_XORDER(sf) {
+		do j = 1, ncols
+		    Memr[bw+j-1] = w[j] * XBASIS(xbzptr+cols[j])
+
+		xcindex = xczptr + i
+		XCOEFF(xcindex) = XCOEFF(xcindex) + adotr (Memr[bw], z, ncols)
+
+		xbptr = xbzptr
+		ii = 0
+		do k = i, SF_XORDER(sf) {
+		    xmindex = xmzptr + ii
+		    do j = 1, ncols
+		        XMATRIX(xmindex) = XMATRIX(xmindex) + Memr[bw+j-1] *
+			    XBASIS(xbptr+cols[j])
+		    ii = ii + 1
+		    xbptr = xbptr + SF_NCOLS(sf)
+		}
+
+		xbzptr = xbzptr + SF_NCOLS(sf)
+		xmzptr = xmzptr + SF_XORDER(sf)
+	    }
+
+	case SF_SPLINE3, SF_SPLINE1:
+	    xlzptr = SF_XLEFT(sf) - 1
+
+	    call salloc (left, ncols, TY_INT)
+	    call salloc (rows, ncols, TY_INT)
+
+	    do j = 1, ncols
+		Memi[left+j-1] = XLEFT(xlzptr+cols[j])
+	    call amulki (Memi[left], SF_XORDER(sf), Memi[rows], ncols)
+	    call aaddki (Memi[rows], SF_XMATRIX(sf), Memi[rows], ncols)
+	    call aaddki (Memi[left], xczptr, Memi[left], ncols)
+
+	    do i = 1, SF_XORDER(sf) {
+		do j = 1, ncols {
+		    Memr[bw+j-1] = w[j] * XBASIS(xbzptr+cols[j])
+		    xcindex = Memi[left+j-1] + i
+		    XCOEFF(xcindex) = XCOEFF(xcindex) + Memr[bw+j-1] * z[j]
+		}
+
+		xbptr = xbzptr
+		ii = 0
+		do k = i, SF_XORDER(sf) {
+		    do j = 1, ncols {
+			xmindex = Memi[rows+j-1] + ii
+			XMATRIX(xmindex) = XMATRIX(xmindex) + Memr[bw+j-1] *
+			    XBASIS(xbptr+cols[j])
+		    }
+		    ii = ii + 1
+		    xbptr = xbptr + SF_NCOLS(sf)
+		}
+
+		xbzptr = xbzptr + SF_NCOLS(sf)
+		call aaddki (Memi[rows], SF_XORDER(sf), Memi[rows], ncols)
+	    }
+	}
+
+	# release space
+	call sfree (sp)
+
+	# return if not enough data points
+	ier = OK
+	if ((SF_NXPTS(sf) - SF_NXCOEFF(sf)) < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# calculate the Cholesky factorization of XMATRIX
+	call sfchofac (XMATRIX(SF_XMATRIX(sf)), SF_XORDER(sf), SF_NXCOEFF(sf),
+	    XMATRIX(SF_XMATRIX(sf)), ier)
+
+	# calculate the x coefficients for lineno-th image line and place in the
+	# lineno-th row of XCOEFF
+	call sfchoslv (XMATRIX(SF_XMATRIX(sf)), SF_XORDER(sf), SF_NXCOEFF(sf),
+	    XCOEFF(xczptr + 1), XCOEFF(xczptr + 1))
+end
diff --git a/math/surfit/islrefit.x b/math/surfit/islrefit.x
new file mode 100644
index 00000000..b0430e5b
--- /dev/null
+++ b/math/surfit/islrefit.x
@@ -0,0 +1,74 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/surfit.h>
+include "surfitdef.h"
+
+# ISLREFIT -- Procedure to refit the data assuming that the cols and w
+# arrays do not change. SIFLREFIT assumes that the Cholesky factorization
+# of XMATRIX is stored in XMATRIX. The inner products of the x basis
+# functions and the data ordinates are accumulated into the lineno-th
+# row of the SF_NXCOEFF(sf) by SF_NLINES(sf) matrix XCOEFF. The coefficients
+# for line number lineno are calculated by forward and back
+# substitution and placed in the lineno-th row of XCOEFF replacing the
+# original data.
+
+procedure islrefit (sf, cols, lineno, z, w)
+
+pointer	sf		# pointer to surface descriptor
+int	cols[ARB]	# columns to be fit 
+int	lineno		# line number
+real	z[ARB]		# surface values
+real	w[ARB]		# weight values
+
+int	i, j
+pointer	xbzptr, xczptr, xcindex, xlzptr
+
+begin
+	# set pointers
+	xbzptr = SF_XBASIS(sf) - 1
+	xczptr = SF_XCOEFF(sf) + (lineno - 1) * SF_NXCOEFF(sf) - 1
+	xlzptr = SF_XLEFT(sf) - 1
+
+	# reset lineno-th row of the x coefficient matrix
+	call aclrr (XCOEFF(xczptr+1), SF_NXCOEFF(sf))
+
+	if (SF_WZ(sf) == NULL)
+	    call malloc (SF_WZ(sf), SF_NXPTS(sf), MEM_TYPE)
+
+	# calculate new right sides
+	call amulr (w, z, Memr[SF_WZ(sf)], SF_NXPTS(sf))
+
+	switch (SF_TYPE(sf)) {
+	case SF_LEGENDRE, SF_CHEBYSHEV:
+
+	    do i = 1, SF_XORDER(sf) {
+		xcindex = xczptr + i
+		do j = 1, SF_NXPTS(sf)
+		    XCOEFF(xcindex) = XCOEFF(xcindex) + Memr[SF_WZ(sf)+j-1] *
+			XBASIS(xbzptr+cols[j])
+		xbzptr = xbzptr + SF_NCOLS(sf)
+	    }
+
+	case SF_SPLINE3, SF_SPLINE1:
+
+	    if (SF_TLEFT(sf) == NULL)
+	        call malloc (SF_TLEFT(sf), SF_NXPTS(sf), TY_INT)
+
+	    do i = 1, SF_NXPTS(sf)
+		Memi[SF_TLEFT(sf)+i-1] = XLEFT(xlzptr+cols[i]) + xczptr
+
+	    do i = 1, SF_XORDER(sf) {
+		do j = 1, SF_NXPTS(sf) {
+		    xcindex = Memi[SF_TLEFT(sf)+j-1] + i
+		    XCOEFF(xcindex) = XCOEFF(xcindex) + Memr[SF_WZ(sf)+j-1] *
+			XBASIS(xbzptr+cols[j])
+		}
+		xbzptr = xbzptr + SF_NCOLS(sf)
+	    }
+
+	}
+
+	# solve for the new x coefficients for line number lineno
+	call sfchoslv (XMATRIX(SF_XMATRIX(sf)), SF_XORDER(sf), SF_NXCOEFF(sf),
+	    XCOEFF(xczptr+1), XCOEFF(xczptr+1))
+end
diff --git a/math/surfit/islsolve.x b/math/surfit/islsolve.x
new file mode 100644
index 00000000..11d0d313
--- /dev/null
+++ b/math/surfit/islsolve.x
@@ -0,0 +1,48 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/surfit.h>
+include "surfitdef.h"
+
+# ISLSOLVE -- Procedure to  solve for the x coefficients of image line
+# number lineno. The inner products of the x basis functions are assumed
+# to be in the SF_XORDER(sf) by SF_NXCOEFF(sf) array XMATRIX,
+# while the inner products of the basis functions and
+# the data ordinated for line number lineno are assumed to be in the
+# lineno-th row of the SF_NXCOEFF(sf) by SF_NLINES(sf) matrix XCOEFF.
+# The Cholesky factorization of XMATRIX is calculated and placed
+# in XMATRIX overwriting the original data. The x coefficients for
+# line number lineno are calculated and placed in the lineno-th row
+# of XCOEFF replacing the original data.
+
+procedure islsolve (sf, lineno, ier)
+
+pointer	sf 		# pointer to the surface descriptor structure
+int	lineno		# line being fitted in x
+int	ier		# ier = 0, everything OK
+			# ier = 1, matrix is singular
+			# ier = 2, no degree of freedom
+
+pointer	xcptr
+
+begin
+	# return if there are insuffucient points to solve the matrix
+	ier = OK
+	if ((SF_NXPTS(sf) - SF_NXCOEFF(sf)) < 0 ) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# calculate the Cholesky factorization of the x matrix and store
+	# separately for possible use by SFLREFIT
+
+	call sfchofac (XMATRIX(SF_XMATRIX(sf)), SF_XORDER(sf), SF_NXCOEFF(sf),
+	    XMATRIX(SF_XMATRIX(sf)), ier)
+
+	# solve for the x coefficients for line lineno assuming the
+	# data are in row lineno of xcoeff, the solution is placed
+	# on top of the data
+
+	xcptr = SF_XCOEFF(sf) + (lineno - 1) * SF_NXCOEFF(sf)
+	call sfchoslv (XMATRIX(SF_XMATRIX(sf)), SF_XORDER(sf), SF_NXCOEFF(sf),
+	    XCOEFF(xcptr), XCOEFF(xcptr))
+end
diff --git a/math/surfit/islzero.x b/math/surfit/islzero.x
new file mode 100644
index 00000000..03034f01
--- /dev/null
+++ b/math/surfit/islzero.x
@@ -0,0 +1,25 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "surfitdef.h"
+
+# ISLZERO -- Procedure to zero the accumulators for line number lineno.
+
+procedure islzero (sf, lineno)
+
+pointer	sf	# pointer to the surface descriptor
+int	lineno	# line number
+pointer	xcptr
+
+begin
+	SF_NXPTS(sf) = 0
+
+	call aclrr (XMATRIX(SF_XMATRIX(sf)),
+		     SF_XORDER(sf) * SF_NXCOEFF(sf))
+	xcptr = SF_XCOEFF(sf) + (lineno - 1) * SF_NXCOEFF(sf)
+	call aclrr (XCOEFF(xcptr), SF_NXCOEFF(sf))
+
+	if (SF_WZ(sf) != NULL)
+	    call mfree (SF_WZ(sf), MEM_TYPE)
+	if (SF_TLEFT(sf) != NULL)
+	    call mfree (SF_TLEFT(sf), TY_INT)
+end
diff --git a/math/surfit/isreplace.x b/math/surfit/isreplace.x
new file mode 100644
index 00000000..1ba69479
--- /dev/null
+++ b/math/surfit/isreplace.x
@@ -0,0 +1,114 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/surfit.h>
+include "surfitdef.h"
+
+# ISREPLACE -- Procedure to restore the surface fit stored by SIFSAVE
+# to the surface descriptor for use by the evaluating routines. The
+# surface parameters, surface type, xorder (or number of polynomial
+# pieces in x), yorder (or number of polynomial pieces in y), xterms,
+# number of columns and number of lines, are stored in the first
+# six elements of the real array fit, followed by the SF_NYCOEFF(sf) *
+# SF_NYCOEFF(sf) surface coefficients. The coefficient of B(i,x) * B(j,y)
+# is stored in element number 6 + (i - 1) * SF_NYCOEFF(sf) + j of the
+# array fit.
+
+procedure isreplace (sf, fit)
+
+pointer	sf		# surface descriptor
+real	fit[ARB]	# array containing the surface parameters and
+			# coefficients
+
+int	surface_type, xorder, yorder, ncols, nlines
+
+begin
+	# allocate space for the surface descriptor
+	call calloc (sf, LEN_SFSTRUCT, TY_STRUCT)
+
+	xorder = nint (SF_SAVEXORDER(fit))
+	if (xorder < 1)
+	    call error (0, "SFRESTORE: Illegal x order.")
+	yorder = nint (SF_SAVEYORDER(fit))
+	if (yorder < 1)
+	    call error (0, "SFRESTORE: Illegal y order.")
+
+	ncols = nint (SF_SAVENCOLS(fit))
+	if (ncols < 1)
+	    call error (0, "SFRESTORE: Illegal x range.")
+	nlines = nint (SF_SAVENLINES(fit))
+	if (nlines < 1)
+	    call error (0, "SFRESTORE: Illegal y range.")
+
+	# set surface type dependent surface descriptor parameters
+	surface_type = nint (SF_SAVETYPE(fit))
+
+	switch (surface_type) {
+	case SF_LEGENDRE, SF_CHEBYSHEV:
+	    SF_NXCOEFF(sf) = xorder
+	    SF_XORDER(sf) = xorder
+	    SF_XRANGE(sf) = 2. / real (ncols + 1)
+	    SF_XMAXMIN(sf) =  - real (ncols + 1) / 2.
+	    SF_XMIN(sf) = 0.
+	    SF_XMAX(sf) = real (ncols + 1)
+	    SF_NYCOEFF(sf) = yorder
+	    SF_YORDER(sf) = yorder
+	    SF_YRANGE(sf) = 2. / real (nlines + 1)
+	    SF_YMAXMIN(sf) =  - real (nlines + 1) / 2.
+	    SF_YMIN(sf) = 0.
+	    SF_YMAX(sf) = real (nlines + 1)
+	    SF_XTERMS(sf) = SF_SAVEXTERMS(fit)
+
+	case SF_SPLINE3:
+	    SF_NXCOEFF(sf) = (xorder + SPLINE3_ORDER - 1)
+	    SF_XORDER(sf) = SPLINE3_ORDER
+	    SF_NXPIECES(sf) = xorder - 1
+	    SF_XSPACING(sf) = xorder / real (ncols + 1)
+	    SF_XMIN(sf) = 0.
+	    SF_XMAX(sf) = real (ncols + 1)
+	    SF_NYCOEFF(sf) = (yorder + SPLINE3_ORDER - 1)
+	    SF_YORDER(sf) = SPLINE3_ORDER
+	    SF_NYPIECES(sf) = yorder - 1
+	    SF_YSPACING(sf) = yorder / real (nlines + 1)
+	    SF_YMIN(sf) = 0.
+	    SF_YMAX(sf) = real (nlines + 1)
+	    SF_XTERMS(sf) = YES
+
+	case SF_SPLINE1:
+	    SF_NXCOEFF(sf) = (xorder + SPLINE1_ORDER - 1)
+	    SF_XORDER(sf) = SPLINE1_ORDER
+	    SF_NXPIECES(sf) = xorder - 1
+	    SF_XSPACING(sf) = xorder / real (ncols + 1)
+	    SF_XMIN(sf) = 0.
+	    SF_XMAX(sf) = real (ncols + 1)
+	    SF_NYCOEFF(sf) = (yorder + SPLINE1_ORDER - 1)
+	    SF_YORDER(sf) = SPLINE1_ORDER
+	    SF_NYPIECES(sf) = yorder - 1
+	    SF_YSPACING(sf) = yorder / real (nlines + 1)
+	    SF_YMIN(sf) = 0.
+	    SF_YMAX(sf) = real (nlines + 1)
+	    SF_XTERMS(sf) = YES
+
+	default:
+	    call error (0, "SFRESTORE: Unknown surface type.")
+	}
+
+	# set remaining curve parameters
+	SF_TYPE(sf) = surface_type
+	SF_NLINES(sf) = nlines
+	SF_NCOLS(sf) = ncols
+
+	# allocate space for the coefficient array
+	SF_XBASIS(sf) = NULL
+	SF_YBASIS(sf) = NULL
+	SF_XMATRIX(sf) = NULL
+	SF_YMATRIX(sf) = NULL
+	SF_XCOEFF(sf) = NULL
+	SF_WZ(sf) = NULL
+	SF_TLEFT(sf) = NULL
+
+	call calloc (SF_COEFF(sf), SF_NXCOEFF(sf) * SF_NYCOEFF(sf), MEM_TYPE)
+
+	# restore coefficient array
+	call amovr (fit[SF_SAVECOEFF+1], COEFF(SF_COEFF(sf)), SF_NYCOEFF(sf) *
+	    SF_NXCOEFF(sf))
+end
diff --git a/math/surfit/isresolve.x b/math/surfit/isresolve.x
new file mode 100644
index 00000000..7af6a8da
--- /dev/null
+++ b/math/surfit/isresolve.x
@@ -0,0 +1,127 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/surfit.h>
+include "surfitdef.h"
+
+# ISRESOLVE -- Procedure to solve the x coefficient matrix for the surface
+# coefficients assuming that the lines array is unchanged since the last
+# call to SIFSOLVE. The Cholesky factorization of YMATRIX is assumed to be
+# stored in YMATRIX. The inner product of the y basis functions and i-th
+# column of XCOEFF containing the i-th x coefficients for each line are
+# calculated and stored in the i-th row of the SF_NYCOEFF(sf) by
+# SF_NXCOEFF(sf) array COEFF. Each of the SF_NXCOEFF(sf) rows of COEFF
+# is solved to determine the SF_NYCOEFF(sf) by SF_NXCOEFF(sf) surface
+# coefficients. After a call to SIFSOLVE the coefficient for the i-th
+# y basis function and the j-th x coefficient is found in the j-th row
+# and i-th column of COEFF.
+
+procedure isresolve (sf, lines, ier)
+
+pointer	sf		# pointer to the surface descriptor structure
+int	lines[ARB]	# line numbers included in the fit
+int	ier		# error code
+
+int	i, j, k, nxcoeff
+pointer	ybzptr
+pointer	ylzptr
+pointer	xczptr, xcptr, xcindex
+pointer	czptr, cptr
+pointer	left, tleft
+pointer	sp
+
+begin
+	# define pointers
+	ybzptr = SF_YBASIS(sf) - 1
+	xczptr = SF_XCOEFF(sf) - SF_NXCOEFF(sf) - 1
+	czptr = SF_COEFF(sf) - 1
+
+	# zero out coefficient matrix
+	call aclrr (COEFF(SF_COEFF(sf)), SF_NXCOEFF(sf) * SF_NYCOEFF(sf))
+
+	switch (SF_TYPE(sf)) {
+	case SF_LEGENDRE, SF_CHEBYSHEV:
+
+	    # loop over the y basis functions
+	    nxcoeff = SF_NXCOEFF(sf)
+	    do i = 1, SF_YORDER(sf) {
+		cptr = czptr + i
+		do k = 1, nxcoeff {
+		    xcptr = xczptr + k
+		    do j = 1, SF_NYPTS(sf) {
+			xcindex = xcptr + lines[j] * SF_NXCOEFF(sf)
+		        COEFF(cptr) = COEFF(cptr) +
+		    		  YBASIS(ybzptr+lines[j]) * XCOEFF(xcindex)
+		    }
+		    cptr = cptr + SF_NYCOEFF(sf)
+		}
+
+		ybzptr = ybzptr + SF_NYPTS(sf)
+
+		# if SF_XTERMS(sf) = NO do not accumulate elements
+		# of COEFF where i != 1 and k != 1
+		if (SF_XTERMS(sf) == NO)
+		    nxcoeff = 1
+	    }
+
+	case SF_SPLINE3, SF_SPLINE1:
+	    call smark (sp)
+	    call salloc (left, SF_NYPTS(sf), TY_INT)
+	    call salloc (tleft, SF_NYPTS(sf), TY_INT)
+
+	    ylzptr = SF_YLEFT(sf) - 1
+	    do j = 1, SF_NYPTS(sf)
+		Memi[left+j-1] = YLEFT(ylzptr+lines[j])
+	    call aaddki (Memi[left], czptr, Memi[left], SF_NYPTS(sf))
+
+	    nxcoeff = SF_NXCOEFF(sf)
+	    do i = 1, SF_YORDER(sf) {
+		call aaddki (Memi[left], i, Memi[tleft], SF_NYPTS(sf))
+		do k = 1, nxcoeff {
+		    xcptr = xczptr + k
+		    do j = 1, SF_NYPTS(sf) {
+			cptr = Memi[tleft+j-1]
+			xcindex = xcptr + lines[j] * SF_NXCOEFF(sf)
+			COEFF(cptr) = COEFF(cptr) + YBASIS(ybzptr+lines[j]) *
+			    XCOEFF(xcindex)
+		    }
+		    call aaddki (Memi[tleft], SF_NYCOEFF(sf), Memi[tleft],
+			SF_NYPTS(sf))
+		}
+
+		ybzptr = ybzptr + SF_NYPTS(sf)
+	    }
+
+	    call sfree (sp)
+	}
+
+	# return if not enough points
+	ier = OK
+	if ((SF_NYPTS(sf) - SF_NYCOEFF(sf)) < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	if (SF_XTERMS(sf) == YES) {
+
+	    # solve for the nxcoeff right sides
+	    cptr = SF_COEFF(sf)
+	    do i = 1, SF_NXCOEFF(sf) {
+	        call sfchoslv (YMATRIX(SF_YMATRIX(sf)), SF_YORDER(sf),
+	    		       SF_NYCOEFF(sf), COEFF(cptr), COEFF(cptr))
+	        cptr = cptr + SF_NYCOEFF(sf)
+	    }
+
+	} else {
+
+	    # solve for the y coefficients
+	    cptr = SF_NYCOEFF(sf)
+	    call sfchoslv (YMATRIX(SF_YMATRIX(sf)), SF_YORDER(sf),
+			      SF_NYCOEFF(sf), COEFF(cptr), COEFF(cptr))
+
+	    # solve for the x coefficients
+	    do i = 2, SF_NXCOEFF(sf) {
+		cptr = czptr + SF_NYCOEFF(sf)
+		COEFF(cptr) = COEFF(cptr) / SF_NYPTS(sf)
+	    }
+	}
+end
diff --git a/math/surfit/issave.x b/math/surfit/issave.x
new file mode 100644
index 00000000..5a3ecab8
--- /dev/null
+++ b/math/surfit/issave.x
@@ -0,0 +1,44 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include	<math/surfit.h>
+include	"surfitdef.h"
+
+# ISSAVE -- Procedure to save the surface fit for later use by the
+# evaluate routines. After a call to SIFSAVE the first six elements
+# of fit contain the surface type, xorder (or number of polynomial pieces
+# in x), yorder (or the number of polynomial pieces in y), xterms, ncols
+# and nlines. The remaining spaces are filled by the SF_NYCOEFF(sf) *
+# SF_NXCOEFF(sf) surface coefficients. The coefficient of B(i,x) * B(j,y)
+# is located in element number 6 + (i - 1) * SF_NYCOEFF(sf) + j of the
+# array fit where i <= SF_NXCOEFF(sf) and j <= SF_NYCOEFF(sf).
+
+procedure issave (sf, fit)
+
+pointer	sf		# pointer to the surface descriptor
+real	fit[ARB]	# array for storing fit
+
+begin
+	# get the surface parameters
+
+	# order is surface type dependent
+	switch (SF_TYPE(sf)) {
+	case SF_LEGENDRE, SF_CHEBYSHEV:
+	    SF_SAVEXORDER(fit) = SF_XORDER(sf)
+	    SF_SAVEYORDER(fit) = SF_YORDER(sf)
+	case SF_SPLINE3, SF_SPLINE1:
+	    SF_SAVEXORDER(fit) = SF_NXPIECES(sf) + 1
+	    SF_SAVEYORDER(fit) = SF_NYPIECES(sf) + 1
+	default:
+	    call error (0, "SIFSAVE: Unknown surface type.")
+	}
+
+	# save remaining parameters
+	SF_SAVETYPE(fit) = SF_TYPE(sf)
+	SF_SAVENLINES(fit) = SF_NLINES(sf)
+	SF_SAVENCOLS(fit) = SF_NCOLS(sf)
+	SF_SAVEXTERMS(fit) = SF_XTERMS(sf)
+
+	# save the coefficients
+	call amovr (COEFF(SF_COEFF(sf)), fit[SF_SAVECOEFF+1], SF_NXCOEFF(sf) *
+	    SF_NYCOEFF(sf))
+end
diff --git a/math/surfit/issolve.x b/math/surfit/issolve.x
new file mode 100644
index 00000000..7790ef60
--- /dev/null
+++ b/math/surfit/issolve.x
@@ -0,0 +1,169 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/surfit.h>
+include "surfitdef.h"
+
+# ISSOLVE -- Procedure to solve the x coefficient matrix for the surface
+# coefficients. The inner products of the y basis functions are accumulated
+# and stored in the SF_YORDER(sf) by SF_NYCOEFF(sf) array YMATRIX. The
+# main diagonal of YMATRIX is stored in the first row of YMATRIX followed
+# by the remaining non-zero lower diagonals. The Cholesky factorization
+# of YMATRIX is calculated and stored on top of YMATRIX destroying the
+# original data. The inner products of the y basis functions and 
+# and the i-th column of the SF_NXCOEFF(sf) by SF_NLINES(sf) matrix XCOEFF
+# containing the i-th x coefficients for each line are calculated and
+# placed in the i-th row of the SF_NYCOEFF(sf) by SF_NXCOEFF(sf) matrix
+# COEFF. Each of the SF_NXCOEFF(sf) rows of COEFF is solved to determine
+# the SF_NXCOEFF(sf) by SF_NYCOEFF(sf) surface coefficients. After a
+# call to SIFSOLVE the coefficient of the i-th x basis function and the
+# j-th y basis function will be found in the j-th column and i-th row
+# of COEFF.
+
+procedure issolve (sf, lines, nlines, ier)
+
+pointer	sf		# pointer to the curve descriptor structure
+int	lines[ARB]	# line numbers included in the fit
+int	nlines		# number of lines fit
+int	ier		# error code
+
+int	i, ii, j, k, nxcoeff
+pointer	ybzptr, ybptr
+pointer	ylzptr
+pointer	ymzptr, ymindex
+pointer	xczptr, xcptr, xcindex
+pointer	czptr, cptr
+pointer	left, tleft, rows
+pointer	sp
+
+begin
+	# define pointers
+	ybzptr = SF_YBASIS(sf) - 1
+	ymzptr = SF_YMATRIX(sf)
+	xczptr = SF_XCOEFF(sf) - SF_NXCOEFF(sf) - 1
+	czptr = SF_COEFF(sf) - 1
+
+	# zero out coefficient matrix and the y coefficient matrix
+	call aclrr (YMATRIX(SF_YMATRIX(sf)), SF_YORDER(sf) * SF_NYCOEFF(sf))
+	call aclrr (COEFF(SF_COEFF(sf)), SF_NXCOEFF(sf) * SF_NYCOEFF(sf))
+
+	# increment the number of points
+	SF_NYPTS(sf) =  nlines
+
+	switch (SF_TYPE(sf)) {
+	case SF_LEGENDRE, SF_CHEBYSHEV:
+
+	    # accumulate the y value in the y matrix 
+	    nxcoeff = SF_NXCOEFF(sf)
+	    do i = 1, SF_YORDER(sf) {
+		cptr = czptr + i
+		do k = 1, nxcoeff {
+		    xcptr = xczptr + k
+		    do j = 1, nlines {
+		        xcindex = xcptr + lines[j] * SF_NXCOEFF(sf)
+		        COEFF(cptr) = COEFF(cptr) +
+			    YBASIS(ybzptr+lines[j]) * XCOEFF(xcindex)
+		    }
+		    cptr = cptr + SF_NYCOEFF(sf)
+		}
+		ii = 0
+		ybptr = ybzptr
+		do k = i, SF_YORDER(sf) {
+		    ymindex = ymzptr + ii
+		    do j = 1, nlines  
+		        YMATRIX(ymindex) = YMATRIX(ymindex) +
+				     YBASIS(ybzptr+lines[j]) *
+				     YBASIS(ybptr+lines[j])
+		    ii = ii + 1
+		    ybptr = ybptr + SF_NLINES(sf)
+		}
+
+		if (SF_XTERMS(sf) == NO)
+		    nxcoeff = 1
+
+		ybzptr = ybzptr + SF_NLINES(sf)
+		ymzptr = ymzptr + SF_YORDER(sf)
+	    }
+
+	case SF_SPLINE3, SF_SPLINE1:
+
+	    call smark (sp)
+	    call salloc (left, nlines, TY_INT)
+	    call salloc (tleft, nlines, TY_INT)
+	    call salloc (rows, nlines, TY_INT)
+
+	    ylzptr = SF_YLEFT(sf) - 1
+	    do j = 1, nlines
+		Memi[left+j-1] = YLEFT(ylzptr+lines[j])
+	    call amulki (Memi[left], SF_YORDER(sf), Memi[rows], nlines)
+	    call aaddki (Memi[rows], SF_YMATRIX(sf), Memi[rows], nlines)
+	    call aaddki (Memi[left], czptr, Memi[left], nlines)
+
+	    # accumulate the y value in the y matrix 
+	    nxcoeff = SF_NXCOEFF(sf)
+	    do i = 1, SF_YORDER(sf) {
+		call aaddki (Memi[left], i, Memi[tleft], nlines)
+		do k = 1, nxcoeff {
+		    xcptr = xczptr + k
+		    do j = 1, nlines {
+			cptr = Memi[tleft+j-1]
+			xcindex = xcptr + lines[j] * SF_NXCOEFF(sf)
+		        COEFF(cptr) = COEFF(cptr) + YBASIS(ybzptr+lines[j]) *
+			    XCOEFF(xcindex)
+		    }
+		    call aaddki (Memi[tleft], SF_NYCOEFF(sf), Memi[tleft],
+		        nlines)
+		}
+		ii = 0
+		ybptr = ybzptr
+		do k = i, SF_YORDER(sf) {
+		    do j = 1, nlines {  
+		        ymindex = Memi[rows+j-1] + ii
+		        YMATRIX(ymindex) = YMATRIX(ymindex) +
+				     YBASIS(ybzptr+lines[j]) *
+				     YBASIS(ybptr+lines[j])
+		    }
+		    ii = ii + 1
+		    ybptr = ybptr + SF_NLINES(sf)
+		}
+
+		ybzptr = ybzptr + SF_NLINES(sf)
+		call aaddki (Memi[rows], SF_YORDER(sf), Memi[rows], nlines)
+	    }
+
+	    call sfree (sp)
+
+	}
+
+	# return if not enough points
+	ier = OK
+	if ((SF_NYPTS(sf) - SF_NYCOEFF(sf)) < 0) {
+	    ier = NO_DEG_FREEDOM
+	    return
+	}
+
+	# calculate the Cholesky factorization of the y matrix
+	call sfchofac (YMATRIX(SF_YMATRIX(sf)), SF_YORDER(sf), SF_NYCOEFF(sf),
+		       YMATRIX(SF_YMATRIX(sf)), ier)
+
+	if (SF_XTERMS(sf) == YES) {
+
+	    # solve for the nxcoeff right sides
+	    cptr = SF_COEFF(sf)
+	    do i = 1, SF_NXCOEFF(sf) {
+	        call sfchoslv (YMATRIX(SF_YMATRIX(sf)), SF_YORDER(sf),
+	    		       SF_NYCOEFF(sf), COEFF(cptr), COEFF(cptr))
+		cptr = cptr + SF_NYCOEFF(sf)
+	    }
+
+	} else {
+
+	    cptr = SF_COEFF(sf)
+	    call sfchoslv (YMATRIX(SF_YMATRIX(sf)), SF_YORDER(sf),
+			      SF_NYCOEFF(sf), COEFF(cptr), COEFF(cptr))
+
+	    do i = 2, SF_NXCOEFF(sf) {
+		cptr = cptr + SF_NYCOEFF(sf)
+		COEFF(cptr) = COEFF(cptr) / SF_NYPTS(sf)
+	    }
+	}
+end
diff --git a/math/surfit/isvector.x b/math/surfit/isvector.x
new file mode 100644
index 00000000..023d3f4d
--- /dev/null
+++ b/math/surfit/isvector.x
@@ -0,0 +1,76 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/surfit.h>
+include "surfitdef.h"
+
+# ISVECTOR -- Procedure to evaluate the fitted surface at an array of points.
+# The SF_NXCOEFF(sf) by SF_NYCOEFF(sf) coefficients are stored in the
+# SF_NYCOEFF(sf) by SF_NXCOEFF(sf) matrix COEFF. The j-th element of the ith
+# row of COEFF contains the coefficient of the i-th basis function in x and
+# the j-th basis function in y.
+
+procedure isvector (sf, x, y, zfit, npts)
+
+pointer	sf		# pointer to surface descriptor structure
+real	x[ARB]		# x value
+real	y[ARB]		# y value
+real	zfit[ARB]	# fits surface values
+int	npts		# number of data points
+
+int	i
+pointer	xcoeff, cptr, sp
+
+begin
+	# evaluate the surface along the vector
+	switch (SF_TYPE(sf)) {
+	case SF_CHEBYSHEV:
+	    if (SF_XORDER(sf) == 1) {
+		call cv_evcheb (COEFF(SF_COEFF(sf)), y, zfit, npts,
+		    SF_YORDER(sf), SF_YMAXMIN(sf), SF_YRANGE(sf))
+	    } else if (SF_YORDER(sf) == 1) {
+		call smark (sp)
+		call salloc (xcoeff, SF_NXCOEFF(sf), MEM_TYPE)
+		cptr = SF_COEFF(sf)
+		do i = 1, SF_NXCOEFF(sf) {
+		    Memr[xcoeff+i-1] = COEFF(cptr)
+		    cptr = cptr + SF_NYCOEFF(sf)
+		}
+		call cv_evcheb (Memr[xcoeff], x, zfit, npts,
+		    SF_XORDER(sf), SF_XMAXMIN(sf), SF_XRANGE(sf))
+		call sfree (sp)
+	    } else
+	        call sf_evcheb (COEFF(SF_COEFF(sf)), x, y, zfit, npts,
+	            SF_XTERMS(sf), SF_XORDER(sf), SF_YORDER(sf), SF_XMAXMIN(sf),
+		    SF_XRANGE(sf), SF_YMAXMIN(sf), SF_YRANGE(sf))
+
+	case SF_LEGENDRE:
+	    if (SF_XORDER(sf) == 1) {
+		call cv_evleg (COEFF(SF_COEFF(sf)), y, zfit, npts,
+		    SF_YORDER(sf), SF_YMAXMIN(sf), SF_YRANGE(sf))
+	    } else if (SF_YORDER(sf) == 1) {
+		call smark (sp)
+		call salloc (xcoeff, SF_NXCOEFF(sf), MEM_TYPE)
+		cptr = SF_COEFF(sf)
+		do i = 1, SF_NXCOEFF(sf) {
+		    Memr[xcoeff+i-1] = COEFF(cptr)
+		    cptr = cptr + SF_NYCOEFF(sf)
+		}
+		call cv_evcheb (Memr[xcoeff], x, zfit, npts,
+		    SF_XORDER(sf), SF_XMAXMIN(sf), SF_XRANGE(sf))
+		call sfree (sp)
+	    } else
+	        call sf_evleg (COEFF(SF_COEFF(sf)), x, y, zfit, npts,
+		    SF_XTERMS(sf), SF_XORDER(sf), SF_YORDER(sf), SF_XMAXMIN(sf),
+		    SF_XRANGE(sf), SF_YMAXMIN(sf), SF_YRANGE(sf))
+
+	case SF_SPLINE3:
+	    call sf_evspline3 (COEFF(SF_COEFF(sf)), x, y, zfit, npts,
+	        SF_NXPIECES(sf), SF_NYPIECES(sf), -SF_XMIN(sf), SF_XSPACING(sf),
+		-SF_YMIN(sf), SF_YSPACING(sf))
+
+	case SF_SPLINE1:
+	    call sf_evspline1 (COEFF(SF_COEFF(sf)), x, y, zfit, npts,
+	        SF_NXPIECES(sf), SF_NYPIECES(sf), -SF_XMIN(sf), SF_XSPACING(sf),
+		-SF_YMIN(sf), SF_YSPACING(sf))
+	}
+end
diff --git a/math/surfit/iszero.x b/math/surfit/iszero.x
new file mode 100644
index 00000000..d453d1fd
--- /dev/null
+++ b/math/surfit/iszero.x
@@ -0,0 +1,26 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include "surfitdef.h"
+
+# ISZERO -- Procedure to zero the accumulators for line number lineno.
+
+procedure iszero (sf)
+
+pointer	sf	# pointer to the surface descriptor
+
+begin
+	SF_NXPTS(sf) = 0
+	SF_NYPTS(sf) = 0
+
+	call aclrr (XMATRIX(SF_XMATRIX(sf)),
+		     SF_XORDER(sf) * SF_NXCOEFF(sf))
+	call aclrr (YMATRIX(SF_YMATRIX(sf)),
+		    SF_YORDER(sf) * SF_NYCOEFF(sf))
+	call aclrr (XCOEFF(SF_XCOEFF(sf)), SF_NXCOEFF(sf) * SF_NLINES(sf))
+	call aclrr (COEFF(SF_COEFF(sf)), SF_NXCOEFF(sf) * SF_NYCOEFF(sf))
+
+	if (SF_WZ(sf) != NULL)
+	    call mfree (SF_WZ(sf), MEM_TYPE)
+	if (SF_TLEFT(sf) != NULL)
+	    call mfree (SF_TLEFT(sf), TY_INT)
+end
diff --git a/math/surfit/mkpkg b/math/surfit/mkpkg
new file mode 100644
index 00000000..58948e29
--- /dev/null
+++ b/math/surfit/mkpkg
@@ -0,0 +1,29 @@
+# Surface fitting tools library.
+
+$checkout libsurfit.a lib$
+$update   libsurfit.a
+$checkin  libsurfit.a lib$
+$exit
+
+libsurfit.a:
+	iscoeff.x	surfitdef.h
+	iseval.x	surfitdef.h <math/surfit.h>
+	isfree.x	surfitdef.h
+	isinit.x	surfitdef.h <math/surfit.h>
+	islaccum.x	surfitdef.h <math/surfit.h>
+	islfit.x	surfitdef.h <math/surfit.h>
+	islrefit.x	surfitdef.h <math/surfit.h>
+	islsolve.x	surfitdef.h <math/surfit.h>
+	islzero.x	surfitdef.h
+	isreplace.x	surfitdef.h <math/surfit.h>
+	isresolve.x	surfitdef.h <math/surfit.h>
+	issave.x	surfitdef.h <math/surfit.h>
+	issolve.x	surfitdef.h <math/surfit.h>
+	isvector.x	surfitdef.h <math/surfit.h>
+	iszero.x	surfitdef.h
+	sf_b1eval.x	
+	sf_beval.x	
+	sf_f1deval.x	
+	sf_feval.x	
+	sfchomat.x	surfitdef.h <mach.h> <math/surfit.h>
+	;
diff --git a/math/surfit/sf_b1eval.x b/math/surfit/sf_b1eval.x
new file mode 100644
index 00000000..d07006fc
--- /dev/null
+++ b/math/surfit/sf_b1eval.x
@@ -0,0 +1,108 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# SF_B1LEG -- Procedure to evaluate all the non-zero Legendrefunctions for
+# a single point and given order.
+
+procedure sf_b1leg (x, order, k1, k2, basis)
+
+real	x		# array of data points
+int	order		# order of polynomial, order = 1, constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+
+int	i
+real	ri, xnorm
+
+begin
+	basis[1] = 1.
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2 
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order {
+	    ri = i
+	    basis[i] = ((2. * ri - 3.) * xnorm * basis[i-1] -
+		       (ri - 2.) * basis[i-2]) / (ri - 1.)	
+	}
+end
+
+
+# SF_B1CHEB -- Procedure to evaluate all the non zero Chebyshev function
+# for a given x and order.
+
+procedure sf_b1cheb (x, order, k1, k2, basis)
+
+real	x		# number of data points
+int	order		# order of polynomial, 1 is a constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# array of basis functions
+
+int	i
+real	xnorm
+
+begin
+	basis[1] = 1.
+	if (order == 1)
+	    return
+
+	xnorm = (x + k1) * k2
+	basis[2] = xnorm
+	if (order == 2)
+	    return
+
+	do i = 3, order
+	    basis[i] = 2. * xnorm * basis[i-1] - basis[i-2]
+end
+
+
+# SF_B1SPLINE1 -- Evaluate all the non-zero spline1 functions for a
+# single point.
+
+procedure sf_b1spline1 (x, npieces, k1, k2, basis, left)
+
+real	x		# set of data points
+int	npieces		# number of polynomial pieces minus 1
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+int	left		# index of the appropriate spline functions
+
+real	xnorm
+
+begin
+	xnorm = (x + k1) * k2
+	left = min (int (xnorm), npieces)
+
+	basis[2] = xnorm - left
+	basis[1] = 1. - basis[2]
+end
+
+
+# SF_B1SPLINE3 --  Procedure to evaluate all the non-zero basis functions
+# for a cubic spline.
+
+procedure sf_b1spline3 (x, npieces, k1, k2, basis, left)
+
+real	x		# array of data points
+int	npieces		# number of polynomial pieces
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# array of basis functions
+int	left		# array of indices for first non-zero spline
+
+real	sx, tx
+
+begin
+	sx = (x + k1) * k2
+	left = min (int (sx), npieces)
+
+	sx = sx - left
+	tx = 1. - sx
+
+	basis[1] = tx * tx * tx
+	basis[2] = 1. + tx * (3. + tx * (3. - 3. * tx))
+	basis[3] = 1. + sx * (3. + sx * (3. - 3. * sx))
+	basis[4] = sx * sx * sx
+end
diff --git a/math/surfit/sf_beval.x b/math/surfit/sf_beval.x
new file mode 100644
index 00000000..301967f9
--- /dev/null
+++ b/math/surfit/sf_beval.x
@@ -0,0 +1,143 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# SF_BCHEB -- Procedure to evaluate all the non-zero Chebyshev functions for
+# a set of points and given order.
+
+procedure sf_bcheb (x, npts, order, k1, k2, basis)
+
+real	x[npts]		# array of data points
+int	npts		# number of points
+int	order		# order of polynomial, order = 1, constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+
+int	k, bptr
+
+begin
+	bptr = 1
+	do k = 1, order {
+
+	    if (k == 1)
+	        call amovkr (1., basis, npts)
+	    else if (k == 2)
+		call altar (x, basis[bptr], npts, k1, k2)
+	    else {
+		call amulr (basis[1+npts], basis[bptr-npts], basis[bptr],
+				npts)
+		call amulkr (basis[bptr], 2., basis[bptr], npts)
+		call asubr (basis[bptr], basis[bptr-2*npts], basis[bptr], npts)
+	    }
+		
+	    bptr = bptr + npts
+	}
+end
+
+
+# SF_BLEG -- Procedure to evaluate all the non zero Legendre function
+# for a given order and set of points.
+
+procedure sf_bleg (x, npts, order, k1, k2, basis)
+
+real	x[npts]		# number of data points
+int	npts		# number of points
+int	order		# order of polynomial, 1 is a constant
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# array of basis functions
+
+int	k, bptr
+real	ri, ri1, ri2
+
+begin
+	bptr = 1
+
+	do k = 1, order {
+	    if (k == 1)
+		call amovkr (1., basis, npts)
+	    else if (k == 2)
+		call altar (x, basis[bptr], npts, k1, k2)
+	    else {
+		ri = k
+		ri1 = (2. * ri - 3.) / (ri - 1.)
+		ri2 = - (ri - 2.) / (ri - 1.)
+		call amulr (basis[1+npts], basis[bptr-npts], basis[bptr],
+				npts)
+		call awsur (basis[bptr], basis[bptr-2*npts],
+			basis[bptr], npts, ri1, ri2)
+	    }
+			
+	    bptr = bptr + npts
+	}
+end
+
+
+# SF_BSPLINE1 -- Evaluate all the non-zero spline1 functions for a set
+# of points.
+
+procedure sf_bspline1 (x, npts, npieces, k1, k2, basis, left)
+
+real	x[npts]		# set of data points
+int	npts		# number of points
+int	npieces		# number of polynomial pieces minus 1
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# basis functions
+int	left[ARB]	# indices of the appropriate spline functions
+
+int	k
+
+begin
+	call altar (x, basis[1+npts], npts, k1, k2)
+	call achtri (basis[1+npts], left, npts)
+	call aminki (left, npieces, left, npts)
+
+	do k = 1, npts {
+	    basis[npts+k] = basis[npts+k] - left[k]
+	    basis[k] = 1. - basis[npts+k]
+	}
+end
+
+
+# SF_BSPLINE3 --  Procedure to evaluate all the non-zero basis functions
+# for a cubic spline.
+
+procedure sf_bspline3 (x, npts, npieces, k1, k2, basis, left)
+
+real	x[npts]		# array of data points
+int	npts		# number of data points
+int	npieces		# number of polynomial pieces minus 1
+real	k1, k2		# normalizing constants
+real	basis[ARB]	# array of basis functions
+int	left[ARB]	# array of indices for first non-zero spline
+
+int	i
+pointer	sp, sx, tx
+
+begin
+	# allocate space
+	call smark (sp)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (tx, npts, TY_REAL)
+
+	# calculate the index of the first non-zero coeff
+	call altar (x, Memr[sx], npts, k1, k2)
+	call achtri (Memr[sx], left, npts)
+	call aminki (left, npieces, left, npts)
+
+	# normalize x to 0 to 1
+	do i = 1, npts {
+	    Memr[sx+i-1] = Memr[sx+i-1] - left[i]
+	    Memr[tx+i-1] = 1. - Memr[sx+i-1]
+	}
+
+	# calculate the basis function
+	call apowkr (Memr[tx], 3, basis, npts)
+	do i = 1, npts {
+	    basis[npts+i] = 1. + Memr[tx+i-1] * (3. + Memr[tx+i-1] * (3. -
+		3. * Memr[tx+i-1]))
+	    basis[2*npts+i] = 1. + Memr[sx+i-1] * (3. + Memr[sx+i-1] * (3. -
+		3. * Memr[sx+i-1]))
+	}
+	call apowkr (Memr[sx], 3, basis[1+3*npts], npts)
+
+	# release space
+	call sfree (sp)
+end
diff --git a/math/surfit/sf_f1deval.x b/math/surfit/sf_f1deval.x
new file mode 100644
index 00000000..01cb98d0
--- /dev/null
+++ b/math/surfit/sf_f1deval.x
@@ -0,0 +1,233 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# CV_EVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure cv_evcheb (coeff, x, yfit, npts, order, k1, k2)
+
+real	coeff[ARB]		# EV array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	yfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	order			# order of the polynomial, 1 = constant
+real	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer sp
+real	c1, c2
+
+begin
+	# fit a constant
+	call amovkr (coeff[1], yfit, npts)
+	if (order == 1)
+	    return
+
+	# fit a linear function
+	c1 = k2 * coeff[2]
+	c2 = c1 * k1 + coeff[1]
+	call altmr (x, yfit, npts, c1, c2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (pn, npts, TY_REAL)
+	call salloc (pnm1, npts, TY_REAL)
+	call salloc (pnm2, npts, TY_REAL)
+
+	# a higher order polynomial
+	call amovkr (1., Memr[pnm2], npts)
+	call altar (x, Memr[sx], npts, k1, k2)
+	call amovr (Memr[sx], Memr[pnm1], npts)
+	call amulkr (Memr[sx], 2., Memr[sx], npts)
+	do i = 3, order {
+	    call amulr (Memr[sx], Memr[pnm1], Memr[pn], npts)
+	    call asubr (Memr[pn], Memr[pnm2], Memr[pn], npts)
+	    if (i < order) {
+	        call amovr (Memr[pnm1], Memr[pnm2], npts)
+	        call amovr (Memr[pn], Memr[pnm1], npts)
+	    }
+	    call amulkr (Memr[pn], coeff[i], Memr[pn], npts)
+	    call aaddr (yfit, Memr[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
+
+
+# CV_EVLEG -- Procedure to evaluate a Legendre polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure cv_evleg (coeff, x, yfit, npts, order, k1, k2)
+
+real	coeff[ARB]		# EV array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	yfit[npts]		# the fitted points
+int	npts			# number of data points
+int	order			# order of the polynomial, 1 = constant
+real	k1, k2			# normalizing constants
+
+int	i
+pointer	sx, pn, pnm1, pnm2
+pointer	sp
+real	ri, ri1, ri2
+
+begin
+	# fit a constant
+	call amovkr (coeff[1], yfit, npts)
+	if (order == 1)
+	    return
+
+	# fit a linear function
+	ri1 = k2 * coeff[2]
+	ri2 = ri1 * k1 + coeff[1]
+	call altmr (x, yfit, npts, ri1, ri2)
+	if (order == 2)
+	    return
+
+	# allocate temporary space
+	call smark (sp)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (pn, npts, TY_REAL)
+	call salloc (pnm1, npts, TY_REAL)
+	call salloc (pnm2, npts, TY_REAL)
+
+	# a higher order polynomial
+	call amovkr (1., Memr[pnm2], npts)
+	call altar (x, Memr[sx], npts, k1, k2)
+	call amovr (Memr[sx], Memr[pnm1], npts)
+	do i = 3, order {
+	    ri = i
+	    ri1 = (2. * ri - 3.) / (ri - 1.)
+	    ri2 = - (ri - 2.) / (ri - 1.)
+	    call amulr (Memr[sx], Memr[pnm1], Memr[pn], npts)
+	    call awsur (Memr[pn], Memr[pnm2], Memr[pn], npts, ri1, ri2)
+	    if (i < order) {
+	        call amovr (Memr[pnm1], Memr[pnm2], npts)
+	        call amovr (Memr[pn], Memr[pnm1], npts)
+	    }
+	    call amulkr (Memr[pn], coeff[i], Memr[pn], npts)
+	    call aaddr (yfit, Memr[pn], yfit, npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+
+end
+
+
+# CV_EVSPLINE1 -- Procedure to evaluate a piecewise linear spline function
+# assuming that the coefficients have been calculated.
+
+procedure cv_evspline1 (coeff, x, yfit, npts, npieces, k1, k2)
+
+real	coeff[ARB]		# array of coefficients
+real	x[npts]			# array of x values
+real	yfit[npts]		# array of fitted values
+int	npts			# number of data points
+int	npieces			# number of fitted points minus 1
+real	k1, k2			# normalizing constants
+
+int	j
+pointer sx, tx, index
+pointer	sp
+
+begin
+	# allocate the required space
+	call smark (sp)
+	call salloc (sx, npts, TY_REAL)
+	call salloc (tx, npts, TY_REAL)
+	call salloc (index, npts, TY_INT)
+
+	# calculate the index of the first non-zero coefficient
+	# for each point
+	call altar (x, Memr[sx], npts, k1, k2)
+	call achtri (Memr[sx], Memi[index], npts)
+	call aminki (Memi[index], npieces, Memi[index], npts)
+
+	# transform sx to range 0 to 1
+	do j = 1, npts {
+	    Memr[sx+j-1] = Memr[sx+j-1] - Memi[index+j-1]
+	    Memr[tx+j-1] = 1. - Memr[sx+j-1]
+	}
+
+    	# calculate yfit using the two non-zero basis function
+	call aclrr (yfit, npts)
+	do j = 1, npts
+	    yfit[j] = Memr[tx+j-1] * coeff[1+Memi[index+j-1]] +
+		      Memr[sx+j-1] * coeff[2+Memi[index+j-1]]
+
+        # free space
+	call sfree (sp)
+
+end
+
+
+# CV_EVSPLINE3 -- Procedure to evaluate the cubic spline assuming that
+# the coefficients of the fit are known.
+
+procedure cv_evspline3 (coeff, x, yfit, npts, npieces, k1, k2)
+
+real	coeff[ARB]	# array of coeffcients
+real	x[npts]		# array of x values
+real	yfit[npts]	# array of fitted values
+int	npts		# number of data points
+int	npieces		# number of polynomial pieces
+real	k1, k2		# normalizing constants
+
+int	i, j
+pointer	sx, tx, temp, index, sp
+
+begin
+
+	# allocate the required space
+	call smark (sp)
+        call salloc (sx, npts, TY_REAL)
+	call salloc (tx, npts, TY_REAL)
+	call salloc (temp, npts, TY_REAL)
+	call salloc (index, npts, TY_INT)
+
+	# calculate to which coefficients the x values contribute to
+        call altar (x, Memr[sx], npts, k1, k2)
+        call achtri (Memr[sx], Memi[index], npts)
+        call aminki (Memi[index], npieces, Memi[index], npts)
+
+        # transform sx to range 0 to 1
+	do j = 1, npts {
+	    Memr[sx+j-1] = Memr[sx+j-1] - Memi[index+j-1]
+	    Memr[tx+j-1] = 1. - Memr[sx+j-1]
+	}
+
+        # calculate yfit using the four non-zero basis function
+	call aclrr (yfit, npts)
+        do i = 1, 4 {
+
+	    switch (i) {
+	    case 1:
+		call apowkr (Memr[tx], 3, Memr[temp], npts)
+	    case 2:
+		do j = 1, npts {
+		    Memr[temp+j-1] = 1. + Memr[tx+j-1] * (3. + Memr[tx+j-1] *
+			(3. - 3. * Memr[tx+j-1]))
+		}
+	    case 3:
+		do j = 1, npts {
+		    Memr[temp+j-1] = 1. + Memr[sx+j-1] * (3. + Memr[sx+j-1] *
+			(3. - 3. * Memr[sx+j-1]))
+		}
+	    case 4:
+		call apowkr (Memr[sx], 3, Memr[temp], npts)
+	    }
+
+	    do j = 1, npts
+		Memr[temp+j-1] = Memr[temp+j-1] * coeff[i+Memi[index+j-1]]
+	    call aaddr (yfit, Memr[temp], yfit, npts)
+	}
+
+	# free space
+	call sfree (sp)
+end
diff --git a/math/surfit/sf_feval.x b/math/surfit/sf_feval.x
new file mode 100644
index 00000000..58b2f765
--- /dev/null
+++ b/math/surfit/sf_feval.x
@@ -0,0 +1,280 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+# SF_EVCHEB -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure sf_evcheb (coeff, x, y, zfit, npts, xterms, xorder, yorder, k1x, k2x,
+	k1y, k2y)
+
+real	coeff[ARB]		# 1D array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	y[npts]
+real	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+real	k1x, k2x		# normalizing constants
+real	k1y, k2y
+
+int	i, k, j
+int	ytorder, cptr
+pointer	sp
+pointer	xb, yb, accum
+pointer ybzptr, ybptr, xbzptr
+
+begin
+	# fit a constant
+	if (xorder == 1 && yorder == 1) {
+	    call amovkr (coeff[1], zfit, npts)
+	    return
+	}
+
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+
+	# calculate basis functions
+	call sf_bcheb (x, npts, xorder, k1x, k2x, Memr[xb])
+	call sf_bcheb (y, npts, yorder, k1y, k2y, Memr[yb])
+
+	# clear the accumulator
+	call aclrr (zfit, npts)
+
+	# accumulate the values
+	cptr = 0
+	ybzptr = yb - 1
+	xbzptr = xb - 1
+	ytorder = yorder
+
+	do i = 1, xorder {
+	    call aclrr (Memr[accum], npts)
+	    ybptr = ybzptr
+	    do k = 1, ytorder {
+		do j = 1, npts
+		    Memr[accum+j-1] = Memr[accum+j-1] + coeff[cptr+k] *
+		        Memr[ybptr+j]
+		ybptr = ybptr + npts
+	    }
+	    do j = 1, npts
+		zfit[j] = zfit[j] + Memr[accum+j-1] * Memr[xbzptr+j]
+
+	    if (xterms == NO)
+		ytorder = 1
+
+	    cptr = cptr + yorder
+	    xbzptr = xbzptr + npts
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+
+# SF_EVLEG -- Procedure to evaluate a Chebyshev polynomial assuming that
+# the coefficients have been calculated. 
+
+procedure sf_evleg (coeff, x, y, zfit, npts, xterms, xorder, yorder, k1x, k2x,
+	k1y, k2y)
+
+real	coeff[ARB]		# 1D array of coefficients
+real	x[npts]			# x values of points to be evaluated
+real	y[npts]
+real	zfit[npts]		# the fitted points
+int	npts			# number of points to be evaluated
+int	xterms			# cross terms ?
+int	xorder,yorder		# order of the polynomials in x and y
+real	k1x, k2x		# normalizing constants
+real	k1y, k2y
+
+int	i, k, j
+int	ytorder, cptr
+pointer	sp
+pointer	xb, yb, accum
+pointer ybzptr, ybptr, xbzptr
+
+begin
+	# fit a constant
+	if (xorder == 1 && yorder == 1) {
+	    call amovkr (coeff[1], zfit, npts)
+	    return
+	}
+
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, xorder * npts, TY_REAL)
+	call salloc (yb, yorder * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+
+	# calculate basis functions
+	call sf_bleg (x, npts, xorder, k1x, k2x, Memr[xb])
+	call sf_bleg (y, npts, yorder, k1y, k2y, Memr[yb])
+
+	# clear the accumulator
+	call aclrr (zfit, npts)
+
+	# accumulate the values
+	cptr = 0
+	ybzptr = yb - 1
+	xbzptr = xb - 1
+	ytorder = yorder
+
+	do i = 1, xorder {
+	    call aclrr (Memr[accum], npts)
+	    ybptr = ybzptr
+	    do k = 1, ytorder {
+		do j = 1, npts
+		    Memr[accum+j-1] = Memr[accum+j-1] + coeff[cptr+k] *
+		        Memr[ybptr+j]
+		ybptr = ybptr + npts
+	    }
+	    do j = 1, npts
+		zfit[j] = zfit[j] + Memr[accum+j-1] * Memr[xbzptr+j]
+
+	    if (xterms == NO)
+		ytorder = 1
+
+	    cptr = cptr + yorder
+	    xbzptr = xbzptr + npts
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+
+# SF_EVSPLINE3 -- Procedure to evaluate a piecewise linear spline function
+# assuming that the coefficients have been calculated.
+
+procedure sf_evspline3 (coeff, x, y, zfit, npts, nxpieces, nypieces, k1x, k2x,
+	k1y, k2y)
+
+real	coeff[ARB]		# array of coefficients
+real	x[npts]			# array of x values
+real	y[npts]			# array of y values
+real	zfit[npts]		# array of fitted values
+int	npts			# number of data points
+int	nxpieces, nypieces	# number of fitted points minus 1
+real	k1x, k2x		# normalizing constants
+real	k1y, k2y
+
+int	i, j, k, cindex
+pointer	xb, xbzptr, yb, ybzptr, ybptr
+pointer	accum, leftx, lefty
+pointer	sp
+
+begin
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, 4 * npts, TY_REAL)
+	call salloc (yb, 4 * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+	call salloc (leftx, npts, TY_INT)
+	call salloc (lefty, npts, TY_INT)
+
+	# calculate basis functions
+	call sf_bspline3 (x, npts, nxpieces, k1x, k2x, Memr[xb], Memi[leftx])
+	call sf_bspline3 (y, npts, nypieces, k1y, k2y, Memr[yb], Memi[lefty])
+
+	# set up the indexing
+	call amulki (Memi[leftx], (nypieces+4), Memi[leftx], npts)
+	call aaddi (Memi[leftx], Memi[lefty], Memi[lefty], npts)
+
+	# clear the accumulator
+	call aclrr (zfit, npts)
+
+	# accumulate the values
+
+	ybzptr = yb - 1
+	xbzptr = xb - 1
+
+	do i = 1, 4 {
+	    call aclrr (Memr[accum], npts)
+	    ybptr = ybzptr
+	    do k = 1, 4 {
+		do j = 1, npts {
+		    cindex = k + Memi[lefty+j-1]
+		    Memr[accum+j-1] = Memr[accum+j-1] + coeff[cindex] *
+		        Memr[ybptr+j]
+		}
+		ybptr = ybptr + npts
+	    }
+	    do j = 1, npts
+		zfit[j] = zfit[j] + Memr[accum+j-1] * Memr[xbzptr+j]
+
+	    xbzptr = xbzptr + npts
+	    call aaddki (Memi[lefty], (nypieces+4), Memi[lefty], npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
+
+
+# SF_EVSPLINE1 -- Procedure to evaluate a piecewise linear spline function
+# assuming that the coefficients have been calculated.
+
+procedure sf_evspline1 (coeff, x, y, zfit, npts, nxpieces, nypieces, k1x, k2x,
+	k1y, k2y)
+
+real	coeff[ARB]		# array of coefficients
+real	x[npts]			# array of x values
+real	y[npts]			# array of y values
+real	zfit[npts]		# array of fitted values
+int	npts			# number of data points
+int	nxpieces, nypieces	# number of fitted points minus 1
+real	k1x, k2x		# normalizing constants
+real	k1y, k2y
+
+int	i, j, k, cindex
+pointer	xb, xbzptr, yb, ybzptr, ybptr
+pointer	accum, leftx, lefty
+pointer	sp
+
+begin
+	# allocate temporary space for the basis functions
+	call smark (sp)
+	call salloc (xb, 2 * npts, TY_REAL)
+	call salloc (yb, 2 * npts, TY_REAL)
+	call salloc (accum, npts, TY_REAL)
+	call salloc (leftx, npts, TY_INT)
+	call salloc (lefty, npts, TY_INT)
+
+	# calculate basis functions
+	call sf_bspline1 (x, npts, nxpieces, k1x, k2x, Memr[xb], Memi[leftx])
+	call sf_bspline1 (y, npts, nypieces, k1y, k2y, Memr[yb], Memi[lefty])
+
+	# set up the indexing
+	call amulki (Memi[leftx], (nypieces+2), Memi[leftx], npts)
+	call aaddi (Memi[leftx], Memi[lefty], Memi[lefty], npts)
+
+	# clear the accumulator
+	call aclrr (zfit, npts)
+
+	# accumulate the values
+
+	ybzptr = yb - 1
+	xbzptr = xb - 1
+
+	do i = 1, 2 {
+	    call aclrr (Memr[accum], npts)
+	    ybptr = ybzptr
+	    do k = 1, 2 {
+		do j = 1, npts {
+		    cindex = k + Memi[lefty+j-1]
+		    Memr[accum+j-1] = Memr[accum+j-1] + coeff[cindex] *
+		        Memr[ybptr+j]
+		}
+		ybptr = ybptr + npts
+	    }
+	    do j = 1, npts
+		zfit[j] = zfit[j] + Memr[accum+j-1] * Memr[xbzptr+j]
+
+	    xbzptr = xbzptr + npts
+	    call aaddki (Memi[lefty], (nypieces+2), Memi[lefty], npts)
+	}
+
+	# free temporary space
+	call sfree (sp)
+end
diff --git a/math/surfit/sfchomat.x b/math/surfit/sfchomat.x
new file mode 100644
index 00000000..419fe777
--- /dev/null
+++ b/math/surfit/sfchomat.x
@@ -0,0 +1,105 @@
+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+include <math/surfit.h>
+include "surfitdef.h"
+include <mach.h>
+
+# SFCHOFAC -- Routine to calculate the Cholesky factorization of a
+# symmetric, positive semi-definite banded matrix. This routines was
+# adapted from the bchfac.f routine described in "A Practical Guide
+# to Splines", Carl de Boor (1978).
+
+procedure sfchofac (matrix, nbands, nrows, matfac, ier)
+
+VAR_TYPE matrix[nbands, nrows]	# data matrix
+int	nbands			# number of bands
+int	nrows			# number of rows
+VAR_TYPE matfac[nbands, nrows]	# Cholesky factorization
+int	ier			# error code
+
+int	i, n, j, imax, jmax
+VAR_TYPE ratio
+
+begin
+	if (nrows == 1) {
+	    if (matrix[1,1] > 0.)
+	        matfac[1,1] = 1. / matrix[1,1]
+	    return
+	}
+		
+	# copy matrix into matfac
+	do n = 1, nrows {
+	    do j = 1, nbands
+		matfac[j,n] = matrix[j,n]
+	}
+
+	do n = 1, nrows {
+	    # test to see if matrix is singular
+	    if (((matfac[1,n] + matrix[1,n]) - matrix[1,n]) <= DELTA) {
+		do j = 1, nbands
+		    matfac[j,n] = 0.
+		ier = SINGULAR
+		next
+	    }
+
+	    matfac[1,n] = 1. / matfac[1,n]
+	    imax = min (nbands - 1, nrows - n)
+	    if (imax < 1)
+		next
+
+	    jmax = imax
+	    do i = 1, imax {
+		ratio = matfac[i+1,n] * matfac[1,n]
+		do j = 1, jmax
+		    matfac[j,n+i] = matfac[j,n+i] - matfac[j+i,n] * ratio
+		jmax = jmax - 1
+		matfac[i+1,n] = ratio
+	    }
+	}
+end
+
+
+# SFCHOSLV -- Solve the matrix whose Cholesky factorization was calculated in
+# SFCHOFAC for the coefficients. This routine was adapted from bchslv.f
+# described in "A Practical Guide to Splines", by Carl de Boor (1978).
+
+procedure sfchoslv (matfac, nbands, nrows, vector, coeff)
+
+VAR_TYPE matfac[nbands,nrows] 		# Cholesky factorization
+int	nbands				# number of bands
+int	nrows				# number of rows
+VAR_TYPE vector[nrows]			# right side of matrix equation
+VAR_TYPE coeff[nrows]			# coefficients
+
+int	i, n, j, jmax, nbndm1
+
+begin
+	if (nrows == 1) {
+	    coeff[1] = vector[1] * matfac[1,1]
+	    return
+	}
+
+	# copy vector to coefficients
+	do i = 1, nrows
+	    coeff[i] = vector[i]
+
+	# forward substitution
+	nbndm1 = nbands - 1
+	do n = 1, nrows {
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+	        do j = 1, jmax
+		    coeff[j+n] = coeff[j+n] - matfac[j+1,n] * coeff[n]
+	    }
+	}
+
+	# back substitution
+	for (n = nrows; n >= 1; n = n - 1) {
+	    coeff[n] = coeff[n] * matfac[1,n]
+	    jmax = min (nbndm1, nrows - n)
+	    if (jmax >= 1) {
+		do j = 1, jmax
+		    coeff[n] = coeff[n] - matfac[j+1,n] * coeff[j+n]
+	    }
+	}
+end
diff --git a/math/surfit/surfitdef.h b/math/surfit/surfitdef.h
new file mode 100644
index 00000000..846109ea
--- /dev/null
+++ b/math/surfit/surfitdef.h
@@ -0,0 +1,74 @@
+# set up the curve fitting structure
+
+define	LEN_SFSTRUCT	 35
+
+define	SF_TYPE		Memi[$1]	# Type of curve to be fitted
+define	SF_NXCOEFF	Memi[$1+1]	# Number of coefficients
+define	SF_XORDER	Memi[$1+2]	# Order of the fit in x
+define	SF_NXPIECES	Memi[$1+3]	# Number of x polynomial pieces - 1
+define	SF_NCOLS	Memi[$1+4]	# Maximum x value
+define	SF_NXPTS	Memi[$1+5]	# Number of points in x
+define	SF_NYCOEFF	Memi[$1+6]	# Number of y coefficients
+define	SF_YORDER	Memi[$1+7]	# Order of the fit in y
+define	SF_NYPIECES	Memi[$1+8]	# Number of y polynomial pieces - 1
+define	SF_NLINES	Memi[$1+9]	# Minimum x value
+define	SF_NYPTS	Memi[$1+10]	# Number of y points
+define	SF_XTERMS	Memi[$1+11]	# cross terms?
+
+define	SF_XBASIS	Memi[$1+12]	# Pointer to the x basis functions
+define	SF_XLEFT	Memi[$1+13]	# Indices to x basis functions, spline
+define	SF_YBASIS	Memi[$1+14]	# Pointer to the y basis functions
+define	SF_YLEFT	Memi[$1+15]	# Indices to y basis functions, spline
+define	SF_XMATRIX	Memi[$1+16]	# Pointer to x data matrix
+define	SF_YMATRIX	Memi[$1+17]	# Pointer to y data matrix
+define	SF_XCOEFF	Memi[$1+18]	# X coefficient matrix
+define	SF_COEFF	Memi[$1+19]	# Pointer to coefficient vector
+
+define	SF_XMIN		Memr[P2R($1+20)] # Min x value
+define	SF_XMAX		Memr[P2R($1+21)] # Max x value
+define	SF_XRANGE	Memr[P2R($1+22)] # 2. / (xmax - xmin), polynomials
+define	SF_XMAXMIN	Memr[P2R($1+23)] # - (xmax + xmin) / 2., polynomials
+define	SF_XSPACING	Memr[P2R($1+24)] # order / (xmax - xmin), splines
+define	SF_YMIN		Memr[P2R($1+25)] # Min y value
+define	SF_YMAX		Memr[P2R($1+26)] # Max y value
+define	SF_YRANGE	Memr[P2R($1+27)] # 2. / (ymax - ymin), polynomials
+define	SF_YMAXMIN	Memr[P2R($1+28)] # - (ymax + ymin) / 2., polynomials
+define	SF_YSPACING	Memr[P2R($1+29)] # order / (ymax - ymin), splines
+
+define	SF_WZ		Memi[$1+30]
+define	SF_TLEFT	Memi[$1+31]
+
+# matrix and vector element definitions
+
+define	XBASIS		Memr[P2P($1)]	#
+define	XBS		Memr[P2P($1)]	#
+define	YBASIS		Memr[P2P($1)]	#
+define	YBS		Memr[P2P($1)]	#
+define	XMATRIX		Memr[P2P($1)]	#
+define	XCHOFAC		Memr[P2P($1)]	# 
+define	YMATRIX		Memr[P2P($1)]	#
+define	XCOEFF		Memr[P2P($1)]	#
+define	COEFF		Memr[P2P($1)]	#
+define	XLEFT		Memi[$1]	#
+define	YLEFT		Memi[$1]	#
+
+# structure definitions for the save restore functions
+
+define	SF_SAVETYPE	$1[1]
+define	SF_SAVEXORDER	$1[2]
+define	SF_SAVEYORDER	$1[3]
+define	SF_SAVEXTERMS	$1[4]
+define	SF_SAVENCOLS	$1[5]
+define	SF_SAVENLINES	$1[6]
+define	SF_SAVECOEFF	6
+
+# miscellaneous
+
+define	SPLINE3_ORDER	4
+define	SPLINE1_ORDER	2
+
+# data type
+
+define	MEM_TYPE	TY_REAL
+define	VAR_TYPE	real
+define	DELTA		EPSILON