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include <math.h>
include <mach.h>
# COMPLEX.X - File containing utility routines for complex arithmetic.
# CX_ADD - Addition of complex numbers.
procedure cx_add (ar, ai, br, bi, cr, ci)
real ar, ai #I First number
real br, bi #I Second number
real cr, ci #O Computed value
begin
cr = ar + br
ci = ai + bi
end
# CX_SUB - Subtraction of complex numbers.
procedure cx_sub (ar, ai, br, bi, cr, ci)
real ar,ai #I First number
real br,bi #I Second number
real cr,ci #O Computed value
begin
cr = ar - br
ci = ai - bi
end
# CX_MUL - Multiplication of complex numbers.
procedure cx_mul (ar, ai, br, bi, cr, ci)
real ar,ai #I First number
real br,bi #I Second number
real cr,ci #O Computed value
begin
cr = ar*br - ai*bi
ci = ai*br + ar*bi
end
# CX_DIV - Division of complex numbers.
procedure cx_div (ar, ai, br, bi, cr, ci)
real ar,ai #I First number
real br,bi #I Second number
real cr,ci #O Computed value
real r, den
begin
if (br == 0.0 && bi == 0.0) { # Trap divide by zero
cr = 0.0
ci = 0.0
return
}
if (abs(br) >= abs(bi)) {
r = bi / br
den = br + r*bi
cr = (ar + r*ai) / den
ci = (ai - r*ar) / den
} else {
r = br / bi
den = bi + r*br
cr = (ar*r + ai) / den
ci = (ai*r - ar) / den
}
end
# CX_ABS - Absolute value of complex numbers.
real procedure cx_abs (ar, ai)
real ar, ai #I First number
real x, y, ans, temp
begin
x = abs (ar)
y = abs (ai)
if (x == 0.0)
ans = y
else if (y == 0.0)
ans = x
else if (x > y) {
temp = y / x
ans = x * sqrt (1.0 + temp*temp)
} else {
temp = x / y
ans = y * sqrt (1.0 + temp*temp)
}
return (ans)
end
# CX_CONJG - Complex conjugate.
procedure cx_conjg (ar, ai, br, bi)
real ar,ai #I First number
real br,bi #I Conjugate
begin
br = ar
bi = - ai
end
# CX_SQRT - Square root of complex numbers.
procedure cx_sqrt (ar, ai, br, bi)
real ar, ai #I First number
real br, bi #I Square root
real x, y, w, r
begin
if (ar == 0.0 && ai == 0.0) {
br = 0.0
bi = 0.0
} else {
x = abs (ar)
y = abs (ai)
if (x >= y) {
r = y / x
w = sqrt (x) * sqrt (0.5*(1.0+sqrt(1.0+r*r)))
} else {
r = x / y
w = sqrt (y) * sqrt (0.5*(1.0+sqrt(1.0+r*r)))
}
if (ar >= 0.0) {
br = w
bi = ai / (2.0*w)
} else {
if (ai >= 0)
bi = w
else
bi = -w
br = ai / (2.0*bi)
}
}
end
# CEXP1 - Complex exponentiation routine.
procedure cexp1 (a, b, dr, di)
real a #I Real part of argument
real b #I Complex part of argument
real dr, di #O Resultant real/imaginary components
begin
if (a > log(MAX_REAL)) {
dr = 0.0
di = 0.0
} else
call cx_div (cos(b), sin(b), exp(a), 0.0, dr, di)
end
# CX_PAK - Pack two real arrays of an FFT into one real FFT array.
# The array `fft' must be dimensioned to at least 2*fnpts elements.
procedure cx_pak (creal, cimg, fft, fnpts)
real creal[fnpts], cimg[fnpts] #I Real/Img complex components
real fft[ARB] #O Output 'real' array
int fnpts #I Npts in array
int i,j
begin
j = 1
do i = 1, fnpts {
fft[j] = creal[i]
j = j + 1
fft[j] = cimg[i]
j = j + 1
}
end
# CX_UNPAK - Unpack one real FFT array into two component real arrays.
# The array `fft' must be dimensioned to at least 2*fnpts elements.
procedure cx_unpak (fft, creal, cimg, fnpts)
real fft[ARB] #O Output 'real' array
real creal[fnpts], cimg[fnpts] #I Real/Img complex components
int fnpts #I Npts in array
int i,j
begin
j = 1
do i = 1, fnpts {
creal[i] = fft[j]
j = j + 1
cimg[i] = fft[j]
j = j + 1
}
end
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