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c
c-----------------------------------------------------------------------
c subroutine: fft842
c fast fourier transform for n=2**m
c complex input
c-----------------------------------------------------------------------
c
subroutine fft842 (in, n, x, y, ier)
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(*), y(*), 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
c+noao
c iw = i1mach(2)
ier = 0
c-noao
c
pi2 = 8.*atan(1.)
p7 = 1./sqrt(2.)
do 10 i=1,31
m = i
nt = 2**i
if (n.eq.nt) go to 20
10 continue
c+noao
c write (iw,9999)
c9999 format (35h n is not a power of two for fft842)
c stop
ier = 1
return
c-noao
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=1,31
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
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
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
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
|
