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-rw-r--r--numpy/fft/fftpack.c1536
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diff --git a/numpy/fft/fftpack.c b/numpy/fft/fftpack.c
deleted file mode 100644
index 07fa2bf4c..000000000
--- a/numpy/fft/fftpack.c
+++ /dev/null
@@ -1,1536 +0,0 @@
-/*
- * fftpack.c : A set of FFT routines in C.
- * Algorithmically based on Fortran-77 FFTPACK by Paul N. Swarztrauber (Version 4, 1985).
-*/
-#define NPY_NO_DEPRECATED_API NPY_API_VERSION
-
-#include <Python.h>
-#include <math.h>
-#include <stdio.h>
-#include <numpy/ndarraytypes.h>
-
-#define DOUBLE
-#ifdef DOUBLE
-#define Treal double
-#else
-#define Treal float
-#endif
-
-#define ref(u,a) u[a]
-
-/* Macros for accurate calculation of the twiddle factors. */
-#define TWOPI 6.283185307179586476925286766559005768391
-#define cos2pi(m, n) cos((TWOPI * (m)) / (n))
-#define sin2pi(m, n) sin((TWOPI * (m)) / (n))
-
-#define MAXFAC 13 /* maximum number of factors in factorization of n */
-#define NSPECIAL 4 /* number of factors for which we have special-case routines */
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-static void sincos2pi(int m, int n, Treal* si, Treal* co)
-/* Calculates sin(2pi * m/n) and cos(2pi * m/n). It is more accurate
- * than the naive calculation as the fraction m/n is reduced to [0, 1/8) first.
- * Due to the symmetry of sin(x) and cos(x) the values for all x can be
- * determined from the function values of the reduced argument in the first
- * octant.
- */
- {
- int n8, m8, octant;
- n8 = 8 * n;
- m8 = (8 * m) % n8;
- octant = m8 / n;
- m8 = m8 % n;
- switch(octant) {
- case 0:
- *co = cos2pi(m8, n8);
- *si = sin2pi(m8, n8);
- break;
- case 1:
- *co = sin2pi(n-m8, n8);
- *si = cos2pi(n-m8, n8);
- break;
- case 2:
- *co = -sin2pi(m8, n8);
- *si = cos2pi(m8, n8);
- break;
- case 3:
- *co = -cos2pi(n-m8, n8);
- *si = sin2pi(n-m8, n8);
- break;
- case 4:
- *co = -cos2pi(m8, n8);
- *si = -sin2pi(m8, n8);
- break;
- case 5:
- *co = -sin2pi(n-m8, n8);
- *si = -cos2pi(n-m8, n8);
- break;
- case 6:
- *co = sin2pi(m8, n8);
- *si = -cos2pi(m8, n8);
- break;
- case 7:
- *co = cos2pi(n-m8, n8);
- *si = -sin2pi(n-m8, n8);
- break;
- }
- }
-
-/* ----------------------------------------------------------------------
- passf2, passf3, passf4, passf5, passf. Complex FFT passes fwd and bwd.
------------------------------------------------------------------------ */
-
-static void passf2(int ido, int l1, const Treal cc[], Treal ch[], const Treal wa1[], int isign)
- /* isign==+1 for backward transform */
- {
- int i, k, ah, ac;
- Treal ti2, tr2;
- if (ido <= 2) {
- for (k=0; k<l1; k++) {
- ah = k*ido;
- ac = 2*k*ido;
- ch[ah] = ref(cc,ac) + ref(cc,ac + ido);
- ch[ah + ido*l1] = ref(cc,ac) - ref(cc,ac + ido);
- ch[ah+1] = ref(cc,ac+1) + ref(cc,ac + ido + 1);
- ch[ah + ido*l1 + 1] = ref(cc,ac+1) - ref(cc,ac + ido + 1);
- }
- } else {
- for (k=0; k<l1; k++) {
- for (i=0; i<ido-1; i+=2) {
- ah = i + k*ido;
- ac = i + 2*k*ido;
- ch[ah] = ref(cc,ac) + ref(cc,ac + ido);
- tr2 = ref(cc,ac) - ref(cc,ac + ido);
- ch[ah+1] = ref(cc,ac+1) + ref(cc,ac + 1 + ido);
- ti2 = ref(cc,ac+1) - ref(cc,ac + 1 + ido);
- ch[ah+l1*ido+1] = wa1[i]*ti2 + isign*wa1[i+1]*tr2;
- ch[ah+l1*ido] = wa1[i]*tr2 - isign*wa1[i+1]*ti2;
- }
- }
- }
- } /* passf2 */
-
-
-static void passf3(int ido, int l1, const Treal cc[], Treal ch[],
- const Treal wa1[], const Treal wa2[], int isign)
- /* isign==+1 for backward transform */
- {
- static const Treal taur = -0.5;
- static const Treal taui = 0.86602540378443864676;
- int i, k, ac, ah;
- Treal ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;
- if (ido == 2) {
- for (k=1; k<=l1; k++) {
- ac = (3*k - 2)*ido;
- tr2 = ref(cc,ac) + ref(cc,ac + ido);
- cr2 = ref(cc,ac - ido) + taur*tr2;
- ah = (k - 1)*ido;
- ch[ah] = ref(cc,ac - ido) + tr2;
-
- ti2 = ref(cc,ac + 1) + ref(cc,ac + ido + 1);
- ci2 = ref(cc,ac - ido + 1) + taur*ti2;
- ch[ah + 1] = ref(cc,ac - ido + 1) + ti2;
-
- cr3 = isign*taui*(ref(cc,ac) - ref(cc,ac + ido));
- ci3 = isign*taui*(ref(cc,ac + 1) - ref(cc,ac + ido + 1));
- ch[ah + l1*ido] = cr2 - ci3;
- ch[ah + 2*l1*ido] = cr2 + ci3;
- ch[ah + l1*ido + 1] = ci2 + cr3;
- ch[ah + 2*l1*ido + 1] = ci2 - cr3;
- }
- } else {
- for (k=1; k<=l1; k++) {
- for (i=0; i<ido-1; i+=2) {
- ac = i + (3*k - 2)*ido;
- tr2 = ref(cc,ac) + ref(cc,ac + ido);
- cr2 = ref(cc,ac - ido) + taur*tr2;
- ah = i + (k-1)*ido;
- ch[ah] = ref(cc,ac - ido) + tr2;
- ti2 = ref(cc,ac + 1) + ref(cc,ac + ido + 1);
- ci2 = ref(cc,ac - ido + 1) + taur*ti2;
- ch[ah + 1] = ref(cc,ac - ido + 1) + ti2;
- cr3 = isign*taui*(ref(cc,ac) - ref(cc,ac + ido));
- ci3 = isign*taui*(ref(cc,ac + 1) - ref(cc,ac + ido + 1));
- dr2 = cr2 - ci3;
- dr3 = cr2 + ci3;
- di2 = ci2 + cr3;
- di3 = ci2 - cr3;
- ch[ah + l1*ido + 1] = wa1[i]*di2 + isign*wa1[i+1]*dr2;
- ch[ah + l1*ido] = wa1[i]*dr2 - isign*wa1[i+1]*di2;
- ch[ah + 2*l1*ido + 1] = wa2[i]*di3 + isign*wa2[i+1]*dr3;
- ch[ah + 2*l1*ido] = wa2[i]*dr3 - isign*wa2[i+1]*di3;
- }
- }
- }
- } /* passf3 */
-
-
-static void passf4(int ido, int l1, const Treal cc[], Treal ch[],
- const Treal wa1[], const Treal wa2[], const Treal wa3[], int isign)
- /* isign == -1 for forward transform and +1 for backward transform */
- {
- int i, k, ac, ah;
- Treal ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
- if (ido == 2) {
- for (k=0; k<l1; k++) {
- ac = 4*k*ido + 1;
- ti1 = ref(cc,ac) - ref(cc,ac + 2*ido);
- ti2 = ref(cc,ac) + ref(cc,ac + 2*ido);
- tr4 = ref(cc,ac + 3*ido) - ref(cc,ac + ido);
- ti3 = ref(cc,ac + ido) + ref(cc,ac + 3*ido);
- tr1 = ref(cc,ac - 1) - ref(cc,ac + 2*ido - 1);
- tr2 = ref(cc,ac - 1) + ref(cc,ac + 2*ido - 1);
- ti4 = ref(cc,ac + ido - 1) - ref(cc,ac + 3*ido - 1);
- tr3 = ref(cc,ac + ido - 1) + ref(cc,ac + 3*ido - 1);
- ah = k*ido;
- ch[ah] = tr2 + tr3;
- ch[ah + 2*l1*ido] = tr2 - tr3;
- ch[ah + 1] = ti2 + ti3;
- ch[ah + 2*l1*ido + 1] = ti2 - ti3;
- ch[ah + l1*ido] = tr1 + isign*tr4;
- ch[ah + 3*l1*ido] = tr1 - isign*tr4;
- ch[ah + l1*ido + 1] = ti1 + isign*ti4;
- ch[ah + 3*l1*ido + 1] = ti1 - isign*ti4;
- }
- } else {
- for (k=0; k<l1; k++) {
- for (i=0; i<ido-1; i+=2) {
- ac = i + 1 + 4*k*ido;
- ti1 = ref(cc,ac) - ref(cc,ac + 2*ido);
- ti2 = ref(cc,ac) + ref(cc,ac + 2*ido);
- ti3 = ref(cc,ac + ido) + ref(cc,ac + 3*ido);
- tr4 = ref(cc,ac + 3*ido) - ref(cc,ac + ido);
- tr1 = ref(cc,ac - 1) - ref(cc,ac + 2*ido - 1);
- tr2 = ref(cc,ac - 1) + ref(cc,ac + 2*ido - 1);
- ti4 = ref(cc,ac + ido - 1) - ref(cc,ac + 3*ido - 1);
- tr3 = ref(cc,ac + ido - 1) + ref(cc,ac + 3*ido - 1);
- ah = i + k*ido;
- ch[ah] = tr2 + tr3;
- cr3 = tr2 - tr3;
- ch[ah + 1] = ti2 + ti3;
- ci3 = ti2 - ti3;
- cr2 = tr1 + isign*tr4;
- cr4 = tr1 - isign*tr4;
- ci2 = ti1 + isign*ti4;
- ci4 = ti1 - isign*ti4;
- ch[ah + l1*ido] = wa1[i]*cr2 - isign*wa1[i + 1]*ci2;
- ch[ah + l1*ido + 1] = wa1[i]*ci2 + isign*wa1[i + 1]*cr2;
- ch[ah + 2*l1*ido] = wa2[i]*cr3 - isign*wa2[i + 1]*ci3;
- ch[ah + 2*l1*ido + 1] = wa2[i]*ci3 + isign*wa2[i + 1]*cr3;
- ch[ah + 3*l1*ido] = wa3[i]*cr4 -isign*wa3[i + 1]*ci4;
- ch[ah + 3*l1*ido + 1] = wa3[i]*ci4 + isign*wa3[i + 1]*cr4;
- }
- }
- }
- } /* passf4 */
-
-
-static void passf5(int ido, int l1, const Treal cc[], Treal ch[],
- const Treal wa1[], const Treal wa2[], const Treal wa3[], const Treal wa4[], int isign)
- /* isign == -1 for forward transform and +1 for backward transform */
- {
- static const Treal tr11 = 0.3090169943749474241;
- static const Treal ti11 = 0.95105651629515357212;
- static const Treal tr12 = -0.8090169943749474241;
- static const Treal ti12 = 0.58778525229247312917;
- int i, k, ac, ah;
- Treal ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3,
- ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;
- if (ido == 2) {
- for (k = 1; k <= l1; ++k) {
- ac = (5*k - 4)*ido + 1;
- ti5 = ref(cc,ac) - ref(cc,ac + 3*ido);
- ti2 = ref(cc,ac) + ref(cc,ac + 3*ido);
- ti4 = ref(cc,ac + ido) - ref(cc,ac + 2*ido);
- ti3 = ref(cc,ac + ido) + ref(cc,ac + 2*ido);
- tr5 = ref(cc,ac - 1) - ref(cc,ac + 3*ido - 1);
- tr2 = ref(cc,ac - 1) + ref(cc,ac + 3*ido - 1);
- tr4 = ref(cc,ac + ido - 1) - ref(cc,ac + 2*ido - 1);
- tr3 = ref(cc,ac + ido - 1) + ref(cc,ac + 2*ido - 1);
- ah = (k - 1)*ido;
- ch[ah] = ref(cc,ac - ido - 1) + tr2 + tr3;
- ch[ah + 1] = ref(cc,ac - ido) + ti2 + ti3;
- cr2 = ref(cc,ac - ido - 1) + tr11*tr2 + tr12*tr3;
- ci2 = ref(cc,ac - ido) + tr11*ti2 + tr12*ti3;
- cr3 = ref(cc,ac - ido - 1) + tr12*tr2 + tr11*tr3;
- ci3 = ref(cc,ac - ido) + tr12*ti2 + tr11*ti3;
- cr5 = isign*(ti11*tr5 + ti12*tr4);
- ci5 = isign*(ti11*ti5 + ti12*ti4);
- cr4 = isign*(ti12*tr5 - ti11*tr4);
- ci4 = isign*(ti12*ti5 - ti11*ti4);
- ch[ah + l1*ido] = cr2 - ci5;
- ch[ah + 4*l1*ido] = cr2 + ci5;
- ch[ah + l1*ido + 1] = ci2 + cr5;
- ch[ah + 2*l1*ido + 1] = ci3 + cr4;
- ch[ah + 2*l1*ido] = cr3 - ci4;
- ch[ah + 3*l1*ido] = cr3 + ci4;
- ch[ah + 3*l1*ido + 1] = ci3 - cr4;
- ch[ah + 4*l1*ido + 1] = ci2 - cr5;
- }
- } else {
- for (k=1; k<=l1; k++) {
- for (i=0; i<ido-1; i+=2) {
- ac = i + 1 + (k*5 - 4)*ido;
- ti5 = ref(cc,ac) - ref(cc,ac + 3*ido);
- ti2 = ref(cc,ac) + ref(cc,ac + 3*ido);
- ti4 = ref(cc,ac + ido) - ref(cc,ac + 2*ido);
- ti3 = ref(cc,ac + ido) + ref(cc,ac + 2*ido);
- tr5 = ref(cc,ac - 1) - ref(cc,ac + 3*ido - 1);
- tr2 = ref(cc,ac - 1) + ref(cc,ac + 3*ido - 1);
- tr4 = ref(cc,ac + ido - 1) - ref(cc,ac + 2*ido - 1);
- tr3 = ref(cc,ac + ido - 1) + ref(cc,ac + 2*ido - 1);
- ah = i + (k - 1)*ido;
- ch[ah] = ref(cc,ac - ido - 1) + tr2 + tr3;
- ch[ah + 1] = ref(cc,ac - ido) + ti2 + ti3;
- cr2 = ref(cc,ac - ido - 1) + tr11*tr2 + tr12*tr3;
-
- ci2 = ref(cc,ac - ido) + tr11*ti2 + tr12*ti3;
- cr3 = ref(cc,ac - ido - 1) + tr12*tr2 + tr11*tr3;
-
- ci3 = ref(cc,ac - ido) + tr12*ti2 + tr11*ti3;
- cr5 = isign*(ti11*tr5 + ti12*tr4);
- ci5 = isign*(ti11*ti5 + ti12*ti4);
- cr4 = isign*(ti12*tr5 - ti11*tr4);
- ci4 = isign*(ti12*ti5 - ti11*ti4);
- dr3 = cr3 - ci4;
- dr4 = cr3 + ci4;
- di3 = ci3 + cr4;
- di4 = ci3 - cr4;
- dr5 = cr2 + ci5;
- dr2 = cr2 - ci5;
- di5 = ci2 - cr5;
- di2 = ci2 + cr5;
- ch[ah + l1*ido] = wa1[i]*dr2 - isign*wa1[i+1]*di2;
- ch[ah + l1*ido + 1] = wa1[i]*di2 + isign*wa1[i+1]*dr2;
- ch[ah + 2*l1*ido] = wa2[i]*dr3 - isign*wa2[i+1]*di3;
- ch[ah + 2*l1*ido + 1] = wa2[i]*di3 + isign*wa2[i+1]*dr3;
- ch[ah + 3*l1*ido] = wa3[i]*dr4 - isign*wa3[i+1]*di4;
- ch[ah + 3*l1*ido + 1] = wa3[i]*di4 + isign*wa3[i+1]*dr4;
- ch[ah + 4*l1*ido] = wa4[i]*dr5 - isign*wa4[i+1]*di5;
- ch[ah + 4*l1*ido + 1] = wa4[i]*di5 + isign*wa4[i+1]*dr5;
- }
- }
- }
- } /* passf5 */
-
-
-static void passf(int *nac, int ido, int ip, int l1, int idl1,
- Treal cc[], Treal ch[],
- const Treal wa[], int isign)
- /* isign is -1 for forward transform and +1 for backward transform */
- {
- int idij, idlj, idot, ipph, i, j, k, l, jc, lc, ik, idj, idl, inc,idp;
- Treal wai, war;
-
- idot = ido / 2;
- /* nt = ip*idl1;*/
- ipph = (ip + 1) / 2;
- idp = ip*ido;
- if (ido >= l1) {
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- for (k=0; k<l1; k++) {
- for (i=0; i<ido; i++) {
- ch[i + (k + j*l1)*ido] =
- ref(cc,i + (j + k*ip)*ido) + ref(cc,i + (jc + k*ip)*ido);
- ch[i + (k + jc*l1)*ido] =
- ref(cc,i + (j + k*ip)*ido) - ref(cc,i + (jc + k*ip)*ido);
- }
- }
- }
- for (k=0; k<l1; k++)
- for (i=0; i<ido; i++)
- ch[i + k*ido] = ref(cc,i + k*ip*ido);
- } else {
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- for (i=0; i<ido; i++) {
- for (k=0; k<l1; k++) {
- ch[i + (k + j*l1)*ido] = ref(cc,i + (j + k*ip)*ido) + ref(cc,i + (jc + k*
- ip)*ido);
- ch[i + (k + jc*l1)*ido] = ref(cc,i + (j + k*ip)*ido) - ref(cc,i + (jc + k*
- ip)*ido);
- }
- }
- }
- for (i=0; i<ido; i++)
- for (k=0; k<l1; k++)
- ch[i + k*ido] = ref(cc,i + k*ip*ido);
- }
-
- idl = 2 - ido;
- inc = 0;
- for (l=1; l<ipph; l++) {
- lc = ip - l;
- idl += ido;
- for (ik=0; ik<idl1; ik++) {
- cc[ik + l*idl1] = ch[ik] + wa[idl - 2]*ch[ik + idl1];
- cc[ik + lc*idl1] = isign*wa[idl-1]*ch[ik + (ip-1)*idl1];
- }
- idlj = idl;
- inc += ido;
- for (j=2; j<ipph; j++) {
- jc = ip - j;
- idlj += inc;
- if (idlj > idp) idlj -= idp;
- war = wa[idlj - 2];
- wai = wa[idlj-1];
- for (ik=0; ik<idl1; ik++) {
- cc[ik + l*idl1] += war*ch[ik + j*idl1];
- cc[ik + lc*idl1] += isign*wai*ch[ik + jc*idl1];
- }
- }
- }
- for (j=1; j<ipph; j++)
- for (ik=0; ik<idl1; ik++)
- ch[ik] += ch[ik + j*idl1];
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- for (ik=1; ik<idl1; ik+=2) {
- ch[ik - 1 + j*idl1] = cc[ik - 1 + j*idl1] - cc[ik + jc*idl1];
- ch[ik - 1 + jc*idl1] = cc[ik - 1 + j*idl1] + cc[ik + jc*idl1];
- ch[ik + j*idl1] = cc[ik + j*idl1] + cc[ik - 1 + jc*idl1];
- ch[ik + jc*idl1] = cc[ik + j*idl1] - cc[ik - 1 + jc*idl1];
- }
- }
- *nac = 1;
- if (ido == 2) return;
- *nac = 0;
- for (ik=0; ik<idl1; ik++)
- cc[ik] = ch[ik];
- for (j=1; j<ip; j++) {
- for (k=0; k<l1; k++) {
- cc[(k + j*l1)*ido + 0] = ch[(k + j*l1)*ido + 0];
- cc[(k + j*l1)*ido + 1] = ch[(k + j*l1)*ido + 1];
- }
- }
- if (idot <= l1) {
- idij = 0;
- for (j=1; j<ip; j++) {
- idij += 2;
- for (i=3; i<ido; i+=2) {
- idij += 2;
- for (k=0; k<l1; k++) {
- cc[i - 1 + (k + j*l1)*ido] =
- wa[idij - 2]*ch[i - 1 + (k + j*l1)*ido] -
- isign*wa[idij-1]*ch[i + (k + j*l1)*ido];
- cc[i + (k + j*l1)*ido] =
- wa[idij - 2]*ch[i + (k + j*l1)*ido] +
- isign*wa[idij-1]*ch[i - 1 + (k + j*l1)*ido];
- }
- }
- }
- } else {
- idj = 2 - ido;
- for (j=1; j<ip; j++) {
- idj += ido;
- for (k = 0; k < l1; k++) {
- idij = idj;
- for (i=3; i<ido; i+=2) {
- idij += 2;
- cc[i - 1 + (k + j*l1)*ido] =
- wa[idij - 2]*ch[i - 1 + (k + j*l1)*ido] -
- isign*wa[idij-1]*ch[i + (k + j*l1)*ido];
- cc[i + (k + j*l1)*ido] =
- wa[idij - 2]*ch[i + (k + j*l1)*ido] +
- isign*wa[idij-1]*ch[i - 1 + (k + j*l1)*ido];
- }
- }
- }
- }
- } /* passf */
-
-
- /* ----------------------------------------------------------------------
-radf2,radb2, radf3,radb3, radf4,radb4, radf5,radb5, radfg,radbg.
-Treal FFT passes fwd and bwd.
----------------------------------------------------------------------- */
-
-static void radf2(int ido, int l1, const Treal cc[], Treal ch[], const Treal wa1[])
- {
- int i, k, ic;
- Treal ti2, tr2;
- for (k=0; k<l1; k++) {
- ch[2*k*ido] =
- ref(cc,k*ido) + ref(cc,(k + l1)*ido);
- ch[(2*k+1)*ido + ido-1] =
- ref(cc,k*ido) - ref(cc,(k + l1)*ido);
- }
- if (ido < 2) return;
- if (ido != 2) {
- for (k=0; k<l1; k++) {
- for (i=2; i<ido; i+=2) {
- ic = ido - i;
- tr2 = wa1[i - 2]*ref(cc, i-1 + (k + l1)*ido) + wa1[i - 1]*ref(cc, i + (k + l1)*ido);
- ti2 = wa1[i - 2]*ref(cc, i + (k + l1)*ido) - wa1[i - 1]*ref(cc, i-1 + (k + l1)*ido);
- ch[i + 2*k*ido] = ref(cc,i + k*ido) + ti2;
- ch[ic + (2*k+1)*ido] = ti2 - ref(cc,i + k*ido);
- ch[i - 1 + 2*k*ido] = ref(cc,i - 1 + k*ido) + tr2;
- ch[ic - 1 + (2*k+1)*ido] = ref(cc,i - 1 + k*ido) - tr2;
- }
- }
- if (ido % 2 == 1) return;
- }
- for (k=0; k<l1; k++) {
- ch[(2*k+1)*ido] = -ref(cc,ido-1 + (k + l1)*ido);
- ch[ido-1 + 2*k*ido] = ref(cc,ido-1 + k*ido);
- }
- } /* radf2 */
-
-
-static void radb2(int ido, int l1, const Treal cc[], Treal ch[], const Treal wa1[])
- {
- int i, k, ic;
- Treal ti2, tr2;
- for (k=0; k<l1; k++) {
- ch[k*ido] =
- ref(cc,2*k*ido) + ref(cc,ido-1 + (2*k+1)*ido);
- ch[(k + l1)*ido] =
- ref(cc,2*k*ido) - ref(cc,ido-1 + (2*k+1)*ido);
- }
- if (ido < 2) return;
- if (ido != 2) {
- for (k = 0; k < l1; ++k) {
- for (i = 2; i < ido; i += 2) {
- ic = ido - i;
- ch[i-1 + k*ido] =
- ref(cc,i-1 + 2*k*ido) + ref(cc,ic-1 + (2*k+1)*ido);
- tr2 = ref(cc,i-1 + 2*k*ido) - ref(cc,ic-1 + (2*k+1)*ido);
- ch[i + k*ido] =
- ref(cc,i + 2*k*ido) - ref(cc,ic + (2*k+1)*ido);
- ti2 = ref(cc,i + (2*k)*ido) + ref(cc,ic + (2*k+1)*ido);
- ch[i-1 + (k + l1)*ido] =
- wa1[i - 2]*tr2 - wa1[i - 1]*ti2;
- ch[i + (k + l1)*ido] =
- wa1[i - 2]*ti2 + wa1[i - 1]*tr2;
- }
- }
- if (ido % 2 == 1) return;
- }
- for (k = 0; k < l1; k++) {
- ch[ido-1 + k*ido] = 2*ref(cc,ido-1 + 2*k*ido);
- ch[ido-1 + (k + l1)*ido] = -2*ref(cc,(2*k+1)*ido);
- }
- } /* radb2 */
-
-
-static void radf3(int ido, int l1, const Treal cc[], Treal ch[],
- const Treal wa1[], const Treal wa2[])
- {
- static const Treal taur = -0.5;
- static const Treal taui = 0.86602540378443864676;
- int i, k, ic;
- Treal ci2, di2, di3, cr2, dr2, dr3, ti2, ti3, tr2, tr3;
- for (k=0; k<l1; k++) {
- cr2 = ref(cc,(k + l1)*ido) + ref(cc,(k + 2*l1)*ido);
- ch[3*k*ido] = ref(cc,k*ido) + cr2;
- ch[(3*k+2)*ido] = taui*(ref(cc,(k + l1*2)*ido) - ref(cc,(k + l1)*ido));
- ch[ido-1 + (3*k + 1)*ido] = ref(cc,k*ido) + taur*cr2;
- }
- if (ido == 1) return;
- for (k=0; k<l1; k++) {
- for (i=2; i<ido; i+=2) {
- ic = ido - i;
- dr2 = wa1[i - 2]*ref(cc,i - 1 + (k + l1)*ido) +
- wa1[i - 1]*ref(cc,i + (k + l1)*ido);
- di2 = wa1[i - 2]*ref(cc,i + (k + l1)*ido) - wa1[i - 1]*ref(cc,i - 1 + (k + l1)*ido);
- dr3 = wa2[i - 2]*ref(cc,i - 1 + (k + l1*2)*ido) + wa2[i - 1]*ref(cc,i + (k + l1*2)*ido);
- di3 = wa2[i - 2]*ref(cc,i + (k + l1*2)*ido) - wa2[i - 1]*ref(cc,i - 1 + (k + l1*2)*ido);
- cr2 = dr2 + dr3;
- ci2 = di2 + di3;
- ch[i - 1 + 3*k*ido] = ref(cc,i - 1 + k*ido) + cr2;
- ch[i + 3*k*ido] = ref(cc,i + k*ido) + ci2;
- tr2 = ref(cc,i - 1 + k*ido) + taur*cr2;
- ti2 = ref(cc,i + k*ido) + taur*ci2;
- tr3 = taui*(di2 - di3);
- ti3 = taui*(dr3 - dr2);
- ch[i - 1 + (3*k + 2)*ido] = tr2 + tr3;
- ch[ic - 1 + (3*k + 1)*ido] = tr2 - tr3;
- ch[i + (3*k + 2)*ido] = ti2 + ti3;
- ch[ic + (3*k + 1)*ido] = ti3 - ti2;
- }
- }
- } /* radf3 */
-
-
-static void radb3(int ido, int l1, const Treal cc[], Treal ch[],
- const Treal wa1[], const Treal wa2[])
- {
- static const Treal taur = -0.5;
- static const Treal taui = 0.86602540378443864676;
- int i, k, ic;
- Treal ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;
- for (k=0; k<l1; k++) {
- tr2 = 2*ref(cc,ido-1 + (3*k + 1)*ido);
- cr2 = ref(cc,3*k*ido) + taur*tr2;
- ch[k*ido] = ref(cc,3*k*ido) + tr2;
- ci3 = 2*taui*ref(cc,(3*k + 2)*ido);
- ch[(k + l1)*ido] = cr2 - ci3;
- ch[(k + 2*l1)*ido] = cr2 + ci3;
- }
- if (ido == 1) return;
- for (k=0; k<l1; k++) {
- for (i=2; i<ido; i+=2) {
- ic = ido - i;
- tr2 = ref(cc,i - 1 + (3*k + 2)*ido) + ref(cc,ic - 1 + (3*k + 1)*ido);
- cr2 = ref(cc,i - 1 + 3*k*ido) + taur*tr2;
- ch[i - 1 + k*ido] = ref(cc,i - 1 + 3*k*ido) + tr2;
- ti2 = ref(cc,i + (3*k + 2)*ido) - ref(cc,ic + (3*k + 1)*ido);
- ci2 = ref(cc,i + 3*k*ido) + taur*ti2;
- ch[i + k*ido] = ref(cc,i + 3*k*ido) + ti2;
- cr3 = taui*(ref(cc,i - 1 + (3*k + 2)*ido) - ref(cc,ic - 1 + (3*k + 1)*ido));
- ci3 = taui*(ref(cc,i + (3*k + 2)*ido) + ref(cc,ic + (3*k + 1)*ido));
- dr2 = cr2 - ci3;
- dr3 = cr2 + ci3;
- di2 = ci2 + cr3;
- di3 = ci2 - cr3;
- ch[i - 1 + (k + l1)*ido] = wa1[i - 2]*dr2 - wa1[i - 1]*di2;
- ch[i + (k + l1)*ido] = wa1[i - 2]*di2 + wa1[i - 1]*dr2;
- ch[i - 1 + (k + 2*l1)*ido] = wa2[i - 2]*dr3 - wa2[i - 1]*di3;
- ch[i + (k + 2*l1)*ido] = wa2[i - 2]*di3 + wa2[i - 1]*dr3;
- }
- }
- } /* radb3 */
-
-
-static void radf4(int ido, int l1, const Treal cc[], Treal ch[],
- const Treal wa1[], const Treal wa2[], const Treal wa3[])
- {
- static const Treal hsqt2 = 0.70710678118654752440;
- int i, k, ic;
- Treal ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
- for (k=0; k<l1; k++) {
- tr1 = ref(cc,(k + l1)*ido) + ref(cc,(k + 3*l1)*ido);
- tr2 = ref(cc,k*ido) + ref(cc,(k + 2*l1)*ido);
- ch[4*k*ido] = tr1 + tr2;
- ch[ido-1 + (4*k + 3)*ido] = tr2 - tr1;
- ch[ido-1 + (4*k + 1)*ido] = ref(cc,k*ido) - ref(cc,(k + 2*l1)*ido);
- ch[(4*k + 2)*ido] = ref(cc,(k + 3*l1)*ido) - ref(cc,(k + l1)*ido);
- }
- if (ido < 2) return;
- if (ido != 2) {
- for (k=0; k<l1; k++) {
- for (i=2; i<ido; i += 2) {
- ic = ido - i;
- cr2 = wa1[i - 2]*ref(cc,i - 1 + (k + l1)*ido) + wa1[i - 1]*ref(cc,i + (k + l1)*ido);
- ci2 = wa1[i - 2]*ref(cc,i + (k + l1)*ido) - wa1[i - 1]*ref(cc,i - 1 + (k + l1)*ido);
- cr3 = wa2[i - 2]*ref(cc,i - 1 + (k + 2*l1)*ido) + wa2[i - 1]*ref(cc,i + (k + 2*l1)*
- ido);
- ci3 = wa2[i - 2]*ref(cc,i + (k + 2*l1)*ido) - wa2[i - 1]*ref(cc,i - 1 + (k + 2*l1)*
- ido);
- cr4 = wa3[i - 2]*ref(cc,i - 1 + (k + 3*l1)*ido) + wa3[i - 1]*ref(cc,i + (k + 3*l1)*
- ido);
- ci4 = wa3[i - 2]*ref(cc,i + (k + 3*l1)*ido) - wa3[i - 1]*ref(cc,i - 1 + (k + 3*l1)*
- ido);
- tr1 = cr2 + cr4;
- tr4 = cr4 - cr2;
- ti1 = ci2 + ci4;
- ti4 = ci2 - ci4;
- ti2 = ref(cc,i + k*ido) + ci3;
- ti3 = ref(cc,i + k*ido) - ci3;
- tr2 = ref(cc,i - 1 + k*ido) + cr3;
- tr3 = ref(cc,i - 1 + k*ido) - cr3;
- ch[i - 1 + 4*k*ido] = tr1 + tr2;
- ch[ic - 1 + (4*k + 3)*ido] = tr2 - tr1;
- ch[i + 4*k*ido] = ti1 + ti2;
- ch[ic + (4*k + 3)*ido] = ti1 - ti2;
- ch[i - 1 + (4*k + 2)*ido] = ti4 + tr3;
- ch[ic - 1 + (4*k + 1)*ido] = tr3 - ti4;
- ch[i + (4*k + 2)*ido] = tr4 + ti3;
- ch[ic + (4*k + 1)*ido] = tr4 - ti3;
- }
- }
- if (ido % 2 == 1) return;
- }
- for (k=0; k<l1; k++) {
- ti1 = -hsqt2*(ref(cc,ido-1 + (k + l1)*ido) + ref(cc,ido-1 + (k + 3*l1)*ido));
- tr1 = hsqt2*(ref(cc,ido-1 + (k + l1)*ido) - ref(cc,ido-1 + (k + 3*l1)*ido));
- ch[ido-1 + 4*k*ido] = tr1 + ref(cc,ido-1 + k*ido);
- ch[ido-1 + (4*k + 2)*ido] = ref(cc,ido-1 + k*ido) - tr1;
- ch[(4*k + 1)*ido] = ti1 - ref(cc,ido-1 + (k + 2*l1)*ido);
- ch[(4*k + 3)*ido] = ti1 + ref(cc,ido-1 + (k + 2*l1)*ido);
- }
- } /* radf4 */
-
-
-static void radb4(int ido, int l1, const Treal cc[], Treal ch[],
- const Treal wa1[], const Treal wa2[], const Treal wa3[])
- {
- static const Treal sqrt2 = 1.41421356237309504880;
- int i, k, ic;
- Treal ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
- for (k = 0; k < l1; k++) {
- tr1 = ref(cc,4*k*ido) - ref(cc,ido-1 + (4*k + 3)*ido);
- tr2 = ref(cc,4*k*ido) + ref(cc,ido-1 + (4*k + 3)*ido);
- tr3 = ref(cc,ido-1 + (4*k + 1)*ido) + ref(cc,ido-1 + (4*k + 1)*ido);
- tr4 = ref(cc,(4*k + 2)*ido) + ref(cc,(4*k + 2)*ido);
- ch[k*ido] = tr2 + tr3;
- ch[(k + l1)*ido] = tr1 - tr4;
- ch[(k + 2*l1)*ido] = tr2 - tr3;
- ch[(k + 3*l1)*ido] = tr1 + tr4;
- }
- if (ido < 2) return;
- if (ido != 2) {
- for (k = 0; k < l1; ++k) {
- for (i = 2; i < ido; i += 2) {
- ic = ido - i;
- ti1 = ref(cc,i + 4*k*ido) + ref(cc,ic + (4*k + 3)*ido);
- ti2 = ref(cc,i + 4*k*ido) - ref(cc,ic + (4*k + 3)*ido);
- ti3 = ref(cc,i + (4*k + 2)*ido) - ref(cc,ic + (4*k + 1)*ido);
- tr4 = ref(cc,i + (4*k + 2)*ido) + ref(cc,ic + (4*k + 1)*ido);
- tr1 = ref(cc,i - 1 + 4*k*ido) - ref(cc,ic - 1 + (4*k + 3)*ido);
- tr2 = ref(cc,i - 1 + 4*k*ido) + ref(cc,ic - 1 + (4*k + 3)*ido);
- ti4 = ref(cc,i - 1 + (4*k + 2)*ido) - ref(cc,ic - 1 + (4*k + 1)*ido);
- tr3 = ref(cc,i - 1 + (4*k + 2)*ido) + ref(cc,ic - 1 + (4*k + 1)*ido);
- ch[i - 1 + k*ido] = tr2 + tr3;
- cr3 = tr2 - tr3;
- ch[i + k*ido] = ti2 + ti3;
- ci3 = ti2 - ti3;
- cr2 = tr1 - tr4;
- cr4 = tr1 + tr4;
- ci2 = ti1 + ti4;
- ci4 = ti1 - ti4;
- ch[i - 1 + (k + l1)*ido] = wa1[i - 2]*cr2 - wa1[i - 1]*ci2;
- ch[i + (k + l1)*ido] = wa1[i - 2]*ci2 + wa1[i - 1]*cr2;
- ch[i - 1 + (k + 2*l1)*ido] = wa2[i - 2]*cr3 - wa2[i - 1]*ci3;
- ch[i + (k + 2*l1)*ido] = wa2[i - 2]*ci3 + wa2[i - 1]*cr3;
- ch[i - 1 + (k + 3*l1)*ido] = wa3[i - 2]*cr4 - wa3[i - 1]*ci4;
- ch[i + (k + 3*l1)*ido] = wa3[i - 2]*ci4 + wa3[i - 1]*cr4;
- }
- }
- if (ido % 2 == 1) return;
- }
- for (k = 0; k < l1; k++) {
- ti1 = ref(cc,(4*k + 1)*ido) + ref(cc,(4*k + 3)*ido);
- ti2 = ref(cc,(4*k + 3)*ido) - ref(cc,(4*k + 1)*ido);
- tr1 = ref(cc,ido-1 + 4*k*ido) - ref(cc,ido-1 + (4*k + 2)*ido);
- tr2 = ref(cc,ido-1 + 4*k*ido) + ref(cc,ido-1 + (4*k + 2)*ido);
- ch[ido-1 + k*ido] = tr2 + tr2;
- ch[ido-1 + (k + l1)*ido] = sqrt2*(tr1 - ti1);
- ch[ido-1 + (k + 2*l1)*ido] = ti2 + ti2;
- ch[ido-1 + (k + 3*l1)*ido] = -sqrt2*(tr1 + ti1);
- }
- } /* radb4 */
-
-
-static void radf5(int ido, int l1, const Treal cc[], Treal ch[],
- const Treal wa1[], const Treal wa2[], const Treal wa3[], const Treal wa4[])
- {
- static const Treal tr11 = 0.3090169943749474241;
- static const Treal ti11 = 0.95105651629515357212;
- static const Treal tr12 = -0.8090169943749474241;
- static const Treal ti12 = 0.58778525229247312917;
- int i, k, ic;
- Treal ci2, di2, ci4, ci5, di3, di4, di5, ci3, cr2, cr3, dr2, dr3, dr4, dr5,
- cr5, cr4, ti2, ti3, ti5, ti4, tr2, tr3, tr4, tr5;
- for (k = 0; k < l1; k++) {
- cr2 = ref(cc,(k + 4*l1)*ido) + ref(cc,(k + l1)*ido);
- ci5 = ref(cc,(k + 4*l1)*ido) - ref(cc,(k + l1)*ido);
- cr3 = ref(cc,(k + 3*l1)*ido) + ref(cc,(k + 2*l1)*ido);
- ci4 = ref(cc,(k + 3*l1)*ido) - ref(cc,(k + 2*l1)*ido);
- ch[5*k*ido] = ref(cc,k*ido) + cr2 + cr3;
- ch[ido-1 + (5*k + 1)*ido] = ref(cc,k*ido) + tr11*cr2 + tr12*cr3;
- ch[(5*k + 2)*ido] = ti11*ci5 + ti12*ci4;
- ch[ido-1 + (5*k + 3)*ido] = ref(cc,k*ido) + tr12*cr2 + tr11*cr3;
- ch[(5*k + 4)*ido] = ti12*ci5 - ti11*ci4;
- }
- if (ido == 1) return;
- for (k = 0; k < l1; ++k) {
- for (i = 2; i < ido; i += 2) {
- ic = ido - i;
- dr2 = wa1[i - 2]*ref(cc,i - 1 + (k + l1)*ido) + wa1[i - 1]*ref(cc,i + (k + l1)*ido);
- di2 = wa1[i - 2]*ref(cc,i + (k + l1)*ido) - wa1[i - 1]*ref(cc,i - 1 + (k + l1)*ido);
- dr3 = wa2[i - 2]*ref(cc,i - 1 + (k + 2*l1)*ido) + wa2[i - 1]*ref(cc,i + (k + 2*l1)*ido);
- di3 = wa2[i - 2]*ref(cc,i + (k + 2*l1)*ido) - wa2[i - 1]*ref(cc,i - 1 + (k + 2*l1)*ido);
- dr4 = wa3[i - 2]*ref(cc,i - 1 + (k + 3*l1)*ido) + wa3[i - 1]*ref(cc,i + (k + 3*l1)*ido);
- di4 = wa3[i - 2]*ref(cc,i + (k + 3*l1)*ido) - wa3[i - 1]*ref(cc,i - 1 + (k + 3*l1)*ido);
- dr5 = wa4[i - 2]*ref(cc,i - 1 + (k + 4*l1)*ido) + wa4[i - 1]*ref(cc,i + (k + 4*l1)*ido);
- di5 = wa4[i - 2]*ref(cc,i + (k + 4*l1)*ido) - wa4[i - 1]*ref(cc,i - 1 + (k + 4*l1)*ido);
- cr2 = dr2 + dr5;
- ci5 = dr5 - dr2;
- cr5 = di2 - di5;
- ci2 = di2 + di5;
- cr3 = dr3 + dr4;
- ci4 = dr4 - dr3;
- cr4 = di3 - di4;
- ci3 = di3 + di4;
- ch[i - 1 + 5*k*ido] = ref(cc,i - 1 + k*ido) + cr2 + cr3;
- ch[i + 5*k*ido] = ref(cc,i + k*ido) + ci2 + ci3;
- tr2 = ref(cc,i - 1 + k*ido) + tr11*cr2 + tr12*cr3;
- ti2 = ref(cc,i + k*ido) + tr11*ci2 + tr12*ci3;
- tr3 = ref(cc,i - 1 + k*ido) + tr12*cr2 + tr11*cr3;
- ti3 = ref(cc,i + k*ido) + tr12*ci2 + tr11*ci3;
- tr5 = ti11*cr5 + ti12*cr4;
- ti5 = ti11*ci5 + ti12*ci4;
- tr4 = ti12*cr5 - ti11*cr4;
- ti4 = ti12*ci5 - ti11*ci4;
- ch[i - 1 + (5*k + 2)*ido] = tr2 + tr5;
- ch[ic - 1 + (5*k + 1)*ido] = tr2 - tr5;
- ch[i + (5*k + 2)*ido] = ti2 + ti5;
- ch[ic + (5*k + 1)*ido] = ti5 - ti2;
- ch[i - 1 + (5*k + 4)*ido] = tr3 + tr4;
- ch[ic - 1 + (5*k + 3)*ido] = tr3 - tr4;
- ch[i + (5*k + 4)*ido] = ti3 + ti4;
- ch[ic + (5*k + 3)*ido] = ti4 - ti3;
- }
- }
- } /* radf5 */
-
-
-static void radb5(int ido, int l1, const Treal cc[], Treal ch[],
- const Treal wa1[], const Treal wa2[], const Treal wa3[], const Treal wa4[])
- {
- static const Treal tr11 = 0.3090169943749474241;
- static const Treal ti11 = 0.95105651629515357212;
- static const Treal tr12 = -0.8090169943749474241;
- static const Treal ti12 = 0.58778525229247312917;
- int i, k, ic;
- Treal ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3,
- ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;
- for (k = 0; k < l1; k++) {
- ti5 = 2*ref(cc,(5*k + 2)*ido);
- ti4 = 2*ref(cc,(5*k + 4)*ido);
- tr2 = 2*ref(cc,ido-1 + (5*k + 1)*ido);
- tr3 = 2*ref(cc,ido-1 + (5*k + 3)*ido);
- ch[k*ido] = ref(cc,5*k*ido) + tr2 + tr3;
- cr2 = ref(cc,5*k*ido) + tr11*tr2 + tr12*tr3;
- cr3 = ref(cc,5*k*ido) + tr12*tr2 + tr11*tr3;
- ci5 = ti11*ti5 + ti12*ti4;
- ci4 = ti12*ti5 - ti11*ti4;
- ch[(k + l1)*ido] = cr2 - ci5;
- ch[(k + 2*l1)*ido] = cr3 - ci4;
- ch[(k + 3*l1)*ido] = cr3 + ci4;
- ch[(k + 4*l1)*ido] = cr2 + ci5;
- }
- if (ido == 1) return;
- for (k = 0; k < l1; ++k) {
- for (i = 2; i < ido; i += 2) {
- ic = ido - i;
- ti5 = ref(cc,i + (5*k + 2)*ido) + ref(cc,ic + (5*k + 1)*ido);
- ti2 = ref(cc,i + (5*k + 2)*ido) - ref(cc,ic + (5*k + 1)*ido);
- ti4 = ref(cc,i + (5*k + 4)*ido) + ref(cc,ic + (5*k + 3)*ido);
- ti3 = ref(cc,i + (5*k + 4)*ido) - ref(cc,ic + (5*k + 3)*ido);
- tr5 = ref(cc,i - 1 + (5*k + 2)*ido) - ref(cc,ic - 1 + (5*k + 1)*ido);
- tr2 = ref(cc,i - 1 + (5*k + 2)*ido) + ref(cc,ic - 1 + (5*k + 1)*ido);
- tr4 = ref(cc,i - 1 + (5*k + 4)*ido) - ref(cc,ic - 1 + (5*k + 3)*ido);
- tr3 = ref(cc,i - 1 + (5*k + 4)*ido) + ref(cc,ic - 1 + (5*k + 3)*ido);
- ch[i - 1 + k*ido] = ref(cc,i - 1 + 5*k*ido) + tr2 + tr3;
- ch[i + k*ido] = ref(cc,i + 5*k*ido) + ti2 + ti3;
- cr2 = ref(cc,i - 1 + 5*k*ido) + tr11*tr2 + tr12*tr3;
-
- ci2 = ref(cc,i + 5*k*ido) + tr11*ti2 + tr12*ti3;
- cr3 = ref(cc,i - 1 + 5*k*ido) + tr12*tr2 + tr11*tr3;
-
- ci3 = ref(cc,i + 5*k*ido) + tr12*ti2 + tr11*ti3;
- cr5 = ti11*tr5 + ti12*tr4;
- ci5 = ti11*ti5 + ti12*ti4;
- cr4 = ti12*tr5 - ti11*tr4;
- ci4 = ti12*ti5 - ti11*ti4;
- dr3 = cr3 - ci4;
- dr4 = cr3 + ci4;
- di3 = ci3 + cr4;
- di4 = ci3 - cr4;
- dr5 = cr2 + ci5;
- dr2 = cr2 - ci5;
- di5 = ci2 - cr5;
- di2 = ci2 + cr5;
- ch[i - 1 + (k + l1)*ido] = wa1[i - 2]*dr2 - wa1[i - 1]*di2;
- ch[i + (k + l1)*ido] = wa1[i - 2]*di2 + wa1[i - 1]*dr2;
- ch[i - 1 + (k + 2*l1)*ido] = wa2[i - 2]*dr3 - wa2[i - 1]*di3;
- ch[i + (k + 2*l1)*ido] = wa2[i - 2]*di3 + wa2[i - 1]*dr3;
- ch[i - 1 + (k + 3*l1)*ido] = wa3[i - 2]*dr4 - wa3[i - 1]*di4;
- ch[i + (k + 3*l1)*ido] = wa3[i - 2]*di4 + wa3[i - 1]*dr4;
- ch[i - 1 + (k + 4*l1)*ido] = wa4[i - 2]*dr5 - wa4[i - 1]*di5;
- ch[i + (k + 4*l1)*ido] = wa4[i - 2]*di5 + wa4[i - 1]*dr5;
- }
- }
- } /* radb5 */
-
-
-static void radfg(int ido, int ip, int l1, int idl1,
- Treal cc[], Treal ch[], const Treal wa[])
- {
- int idij, ipph, i, j, k, l, j2, ic, jc, lc, ik, is, nbd;
- Treal dc2, ai1, ai2, ar1, ar2, ds2, dcp, dsp, ar1h, ar2h;
- sincos2pi(1, ip, &dsp, &dcp);
- ipph = (ip + 1) / 2;
- nbd = (ido - 1) / 2;
- if (ido != 1) {
- for (ik=0; ik<idl1; ik++) ch[ik] = cc[ik];
- for (j=1; j<ip; j++)
- for (k=0; k<l1; k++)
- ch[(k + j*l1)*ido] = cc[(k + j*l1)*ido];
- if (nbd <= l1) {
- is = -ido;
- for (j=1; j<ip; j++) {
- is += ido;
- idij = is-1;
- for (i=2; i<ido; i+=2) {
- idij += 2;
- for (k=0; k<l1; k++) {
- ch[i - 1 + (k + j*l1)*ido] =
- wa[idij - 1]*cc[i - 1 + (k + j*l1)*ido] + wa[idij]*cc[i + (k + j*l1)*ido];
- ch[i + (k + j*l1)*ido] =
- wa[idij - 1]*cc[i + (k + j*l1)*ido] - wa[idij]*cc[i - 1 + (k + j*l1)*ido];
- }
- }
- }
- } else {
- is = -ido;
- for (j=1; j<ip; j++) {
- is += ido;
- for (k=0; k<l1; k++) {
- idij = is-1;
- for (i=2; i<ido; i+=2) {
- idij += 2;
- ch[i - 1 + (k + j*l1)*ido] =
- wa[idij - 1]*cc[i - 1 + (k + j*l1)*ido] + wa[idij]*cc[i + (k + j*l1)*ido];
- ch[i + (k + j*l1)*ido] =
- wa[idij - 1]*cc[i + (k + j*l1)*ido] - wa[idij]*cc[i - 1 + (k + j*l1)*ido];
- }
- }
- }
- }
- if (nbd >= l1) {
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- for (k=0; k<l1; k++) {
- for (i=2; i<ido; i+=2) {
- cc[i - 1 + (k + j*l1)*ido] = ch[i - 1 + (k + j*l1)*ido] + ch[i - 1 + (k + jc*l1)*ido];
- cc[i - 1 + (k + jc*l1)*ido] = ch[i + (k + j*l1)*ido] - ch[i + (k + jc*l1)*ido];
- cc[i + (k + j*l1)*ido] = ch[i + (k + j*l1)*ido] + ch[i + (k + jc*l1)*ido];
- cc[i + (k + jc*l1)*ido] = ch[i - 1 + (k + jc*l1)*ido] - ch[i - 1 + (k + j*l1)*ido];
- }
- }
- }
- } else {
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- for (i=2; i<ido; i+=2) {
- for (k=0; k<l1; k++) {
- cc[i - 1 + (k + j*l1)*ido] =
- ch[i - 1 + (k + j*l1)*ido] + ch[i - 1 + (k + jc*l1)*ido];
- cc[i - 1 + (k + jc*l1)*ido] = ch[i + (k + j*l1)*ido] - ch[i + (k + jc*l1)*ido];
- cc[i + (k + j*l1)*ido] = ch[i + (k + j*l1)*ido] + ch[i + (k + jc*l1)*ido];
- cc[i + (k + jc*l1)*ido] = ch[i - 1 + (k + jc*l1)*ido] - ch[i - 1 + (k + j*l1)*ido];
- }
- }
- }
- }
- } else { /* now ido == 1 */
- for (ik=0; ik<idl1; ik++) cc[ik] = ch[ik];
- }
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- for (k=0; k<l1; k++) {
- cc[(k + j*l1)*ido] = ch[(k + j*l1)*ido] + ch[(k + jc*l1)*ido];
- cc[(k + jc*l1)*ido] = ch[(k + jc*l1)*ido] - ch[(k + j*l1)*ido];
- }
- }
-
- ar1 = 1;
- ai1 = 0;
- for (l=1; l<ipph; l++) {
- lc = ip - l;
- ar1h = dcp*ar1 - dsp*ai1;
- ai1 = dcp*ai1 + dsp*ar1;
- ar1 = ar1h;
- for (ik=0; ik<idl1; ik++) {
- ch[ik + l*idl1] = cc[ik] + ar1*cc[ik + idl1];
- ch[ik + lc*idl1] = ai1*cc[ik + (ip-1)*idl1];
- }
- dc2 = ar1;
- ds2 = ai1;
- ar2 = ar1;
- ai2 = ai1;
- for (j=2; j<ipph; j++) {
- jc = ip - j;
- ar2h = dc2*ar2 - ds2*ai2;
- ai2 = dc2*ai2 + ds2*ar2;
- ar2 = ar2h;
- for (ik=0; ik<idl1; ik++) {
- ch[ik + l*idl1] += ar2*cc[ik + j*idl1];
- ch[ik + lc*idl1] += ai2*cc[ik + jc*idl1];
- }
- }
- }
-
- for (j=1; j<ipph; j++)
- for (ik=0; ik<idl1; ik++)
- ch[ik] += cc[ik + j*idl1];
-
- if (ido >= l1) {
- for (k=0; k<l1; k++) {
- for (i=0; i<ido; i++) {
- ref(cc,i + k*ip*ido) = ch[i + k*ido];
- }
- }
- } else {
- for (i=0; i<ido; i++) {
- for (k=0; k<l1; k++) {
- ref(cc,i + k*ip*ido) = ch[i + k*ido];
- }
- }
- }
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- j2 = 2*j;
- for (k=0; k<l1; k++) {
- ref(cc,ido-1 + (j2 - 1 + k*ip)*ido) =
- ch[(k + j*l1)*ido];
- ref(cc,(j2 + k*ip)*ido) =
- ch[(k + jc*l1)*ido];
- }
- }
- if (ido == 1) return;
- if (nbd >= l1) {
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- j2 = 2*j;
- for (k=0; k<l1; k++) {
- for (i=2; i<ido; i+=2) {
- ic = ido - i;
- ref(cc,i - 1 + (j2 + k*ip)*ido) = ch[i - 1 + (k + j*l1)*ido] + ch[i - 1 + (k + jc*l1)*ido];
- ref(cc,ic - 1 + (j2 - 1 + k*ip)*ido) = ch[i - 1 + (k + j*l1)*ido] - ch[i - 1 + (k + jc*l1)*ido];
- ref(cc,i + (j2 + k*ip)*ido) = ch[i + (k + j*l1)*ido] + ch[i + (k + jc*l1)*ido];
- ref(cc,ic + (j2 - 1 + k*ip)*ido) = ch[i + (k + jc*l1)*ido] - ch[i + (k + j*l1)*ido];
- }
- }
- }
- } else {
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- j2 = 2*j;
- for (i=2; i<ido; i+=2) {
- ic = ido - i;
- for (k=0; k<l1; k++) {
- ref(cc,i - 1 + (j2 + k*ip)*ido) = ch[i - 1 + (k + j*l1)*ido] + ch[i - 1 + (k + jc*l1)*ido];
- ref(cc,ic - 1 + (j2 - 1 + k*ip)*ido) = ch[i - 1 + (k + j*l1)*ido] - ch[i - 1 + (k + jc*l1)*ido];
- ref(cc,i + (j2 + k*ip)*ido) = ch[i + (k + j*l1)*ido] + ch[i + (k + jc*l1)*ido];
- ref(cc,ic + (j2 - 1 + k*ip)*ido) = ch[i + (k + jc*l1)*ido] - ch[i + (k + j*l1)*ido];
- }
- }
- }
- }
- } /* radfg */
-
-
-static void radbg(int ido, int ip, int l1, int idl1,
- Treal cc[], Treal ch[], const Treal wa[])
- {
- int idij, ipph, i, j, k, l, j2, ic, jc, lc, ik, is;
- Treal dc2, ai1, ai2, ar1, ar2, ds2;
- int nbd;
- Treal dcp, dsp, ar1h, ar2h;
- sincos2pi(1, ip, &dsp, &dcp);
- nbd = (ido - 1) / 2;
- ipph = (ip + 1) / 2;
- if (ido >= l1) {
- for (k=0; k<l1; k++) {
- for (i=0; i<ido; i++) {
- ch[i + k*ido] = ref(cc,i + k*ip*ido);
- }
- }
- } else {
- for (i=0; i<ido; i++) {
- for (k=0; k<l1; k++) {
- ch[i + k*ido] = ref(cc,i + k*ip*ido);
- }
- }
- }
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- j2 = 2*j;
- for (k=0; k<l1; k++) {
- ch[(k + j*l1)*ido] = ref(cc,ido-1 + (j2 - 1 + k*ip)*ido) + ref(cc,ido-1 + (j2 - 1 + k*ip)*
- ido);
- ch[(k + jc*l1)*ido] = ref(cc,(j2 + k*ip)*ido) + ref(cc,(j2 + k*ip)*ido);
- }
- }
-
- if (ido != 1) {
- if (nbd >= l1) {
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- for (k=0; k<l1; k++) {
- for (i=2; i<ido; i+=2) {
- ic = ido - i;
- ch[i - 1 + (k + j*l1)*ido] = ref(cc,i - 1 + (2*j + k*ip)*ido) + ref(cc,
- ic - 1 + (2*j - 1 + k*ip)*ido);
- ch[i - 1 + (k + jc*l1)*ido] = ref(cc,i - 1 + (2*j + k*ip)*ido) -
- ref(cc,ic - 1 + (2*j - 1 + k*ip)*ido);
- ch[i + (k + j*l1)*ido] = ref(cc,i + (2*j + k*ip)*ido) - ref(cc,ic
- + (2*j - 1 + k*ip)*ido);
- ch[i + (k + jc*l1)*ido] = ref(cc,i + (2*j + k*ip)*ido) + ref(cc,ic
- + (2*j - 1 + k*ip)*ido);
- }
- }
- }
- } else {
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- for (i=2; i<ido; i+=2) {
- ic = ido - i;
- for (k=0; k<l1; k++) {
- ch[i - 1 + (k + j*l1)*ido] = ref(cc,i - 1 + (2*j + k*ip)*ido) + ref(cc,
- ic - 1 + (2*j - 1 + k*ip)*ido);
- ch[i - 1 + (k + jc*l1)*ido] = ref(cc,i - 1 + (2*j + k*ip)*ido) -
- ref(cc,ic - 1 + (2*j - 1 + k*ip)*ido);
- ch[i + (k + j*l1)*ido] = ref(cc,i + (2*j + k*ip)*ido) - ref(cc,ic
- + (2*j - 1 + k*ip)*ido);
- ch[i + (k + jc*l1)*ido] = ref(cc,i + (2*j + k*ip)*ido) + ref(cc,ic
- + (2*j - 1 + k*ip)*ido);
- }
- }
- }
- }
- }
-
- ar1 = 1;
- ai1 = 0;
- for (l=1; l<ipph; l++) {
- lc = ip - l;
- ar1h = dcp*ar1 - dsp*ai1;
- ai1 = dcp*ai1 + dsp*ar1;
- ar1 = ar1h;
- for (ik=0; ik<idl1; ik++) {
- cc[ik + l*idl1] = ch[ik] + ar1*ch[ik + idl1];
- cc[ik + lc*idl1] = ai1*ch[ik + (ip-1)*idl1];
- }
- dc2 = ar1;
- ds2 = ai1;
- ar2 = ar1;
- ai2 = ai1;
- for (j=2; j<ipph; j++) {
- jc = ip - j;
- ar2h = dc2*ar2 - ds2*ai2;
- ai2 = dc2*ai2 + ds2*ar2;
- ar2 = ar2h;
- for (ik=0; ik<idl1; ik++) {
- cc[ik + l*idl1] += ar2*ch[ik + j*idl1];
- cc[ik + lc*idl1] += ai2*ch[ik + jc*idl1];
- }
- }
- }
- for (j=1; j<ipph; j++) {
- for (ik=0; ik<idl1; ik++) {
- ch[ik] += ch[ik + j*idl1];
- }
- }
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- for (k=0; k<l1; k++) {
- ch[(k + j*l1)*ido] = cc[(k + j*l1)*ido] - cc[(k + jc*l1)*ido];
- ch[(k + jc*l1)*ido] = cc[(k + j*l1)*ido] + cc[(k + jc*l1)*ido];
- }
- }
-
- if (ido == 1) return;
- if (nbd >= l1) {
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- for (k=0; k<l1; k++) {
- for (i=2; i<ido; i+=2) {
- ch[i - 1 + (k + j*l1)*ido] = cc[i - 1 + (k + j*l1)*ido] - cc[i + (k + jc*l1)*ido];
- ch[i - 1 + (k + jc*l1)*ido] = cc[i - 1 + (k + j*l1)*ido] + cc[i + (k + jc*l1)*ido];
- ch[i + (k + j*l1)*ido] = cc[i + (k + j*l1)*ido] + cc[i - 1 + (k + jc*l1)*ido];
- ch[i + (k + jc*l1)*ido] = cc[i + (k + j*l1)*ido] - cc[i - 1 + (k + jc*l1)*ido];
- }
- }
- }
- } else {
- for (j=1; j<ipph; j++) {
- jc = ip - j;
- for (i=2; i<ido; i+=2) {
- for (k=0; k<l1; k++) {
- ch[i - 1 + (k + j*l1)*ido] = cc[i - 1 + (k + j*l1)*ido] - cc[i + (k + jc*l1)*ido];
- ch[i - 1 + (k + jc*l1)*ido] = cc[i - 1 + (k + j *l1)*ido] + cc[i + (k + jc*l1)*ido];
- ch[i + (k + j*l1)*ido] = cc[i + (k + j*l1)*ido] + cc[i - 1 + (k + jc*l1)*ido];
- ch[i + (k + jc*l1)*ido] = cc[i + (k + j*l1)*ido] - cc[i - 1 + (k + jc*l1)*ido];
- }
- }
- }
- }
- for (ik=0; ik<idl1; ik++) cc[ik] = ch[ik];
- for (j=1; j<ip; j++)
- for (k=0; k<l1; k++)
- cc[(k + j*l1)*ido] = ch[(k + j*l1)*ido];
- if (nbd <= l1) {
- is = -ido;
- for (j=1; j<ip; j++) {
- is += ido;
- idij = is-1;
- for (i=2; i<ido; i+=2) {
- idij += 2;
- for (k=0; k<l1; k++) {
- cc[i - 1 + (k + j*l1)*ido] = wa[idij - 1]*ch[i - 1 + (k + j*l1)*ido] - wa[idij]*
- ch[i + (k + j*l1)*ido];
- cc[i + (k + j*l1)*ido] = wa[idij - 1]*ch[i + (k + j*l1)*ido] + wa[idij]*ch[i - 1 + (k + j*l1)*ido];
- }
- }
- }
- } else {
- is = -ido;
- for (j=1; j<ip; j++) {
- is += ido;
- for (k=0; k<l1; k++) {
- idij = is - 1;
- for (i=2; i<ido; i+=2) {
- idij += 2;
- cc[i - 1 + (k + j*l1)*ido] = wa[idij-1]*ch[i - 1 + (k + j*l1)*ido] - wa[idij]*
- ch[i + (k + j*l1)*ido];
- cc[i + (k + j*l1)*ido] = wa[idij-1]*ch[i + (k + j*l1)*ido] + wa[idij]*ch[i - 1 + (k + j*l1)*ido];
- }
- }
- }
- }
- } /* radbg */
-
- /* ------------------------------------------------------------
-cfftf1, npy_cfftf, npy_cfftb, cffti1, npy_cffti. Complex FFTs.
---------------------------------------------------------------- */
-
-static void cfftf1(int n, Treal c[], Treal ch[], const Treal wa[], const int ifac[MAXFAC+2], int isign)
- {
- int idot, i;
- int k1, l1, l2;
- int na, nf, ip, iw, ix2, ix3, ix4, nac, ido, idl1;
- Treal *cinput, *coutput;
- nf = ifac[1];
- na = 0;
- l1 = 1;
- iw = 0;
- for (k1=2; k1<=nf+1; k1++) {
- ip = ifac[k1];
- l2 = ip*l1;
- ido = n / l2;
- idot = ido + ido;
- idl1 = idot*l1;
- if (na) {
- cinput = ch;
- coutput = c;
- } else {
- cinput = c;
- coutput = ch;
- }
- switch (ip) {
- case 4:
- ix2 = iw + idot;
- ix3 = ix2 + idot;
- passf4(idot, l1, cinput, coutput, &wa[iw], &wa[ix2], &wa[ix3], isign);
- na = !na;
- break;
- case 2:
- passf2(idot, l1, cinput, coutput, &wa[iw], isign);
- na = !na;
- break;
- case 3:
- ix2 = iw + idot;
- passf3(idot, l1, cinput, coutput, &wa[iw], &wa[ix2], isign);
- na = !na;
- break;
- case 5:
- ix2 = iw + idot;
- ix3 = ix2 + idot;
- ix4 = ix3 + idot;
- passf5(idot, l1, cinput, coutput, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4], isign);
- na = !na;
- break;
- default:
- passf(&nac, idot, ip, l1, idl1, cinput, coutput, &wa[iw], isign);
- if (nac != 0) na = !na;
- }
- l1 = l2;
- iw += (ip - 1)*idot;
- }
- if (na == 0) return;
- for (i=0; i<2*n; i++) c[i] = ch[i];
- } /* cfftf1 */
-
-
-NPY_VISIBILITY_HIDDEN void npy_cfftf(int n, Treal c[], Treal wsave[])
- {
- int iw1, iw2;
- if (n == 1) return;
- iw1 = 2*n;
- iw2 = iw1 + 2*n;
- cfftf1(n, c, wsave, wsave+iw1, (int*)(wsave+iw2), -1);
- } /* npy_cfftf */
-
-
-NPY_VISIBILITY_HIDDEN void npy_cfftb(int n, Treal c[], Treal wsave[])
- {
- int iw1, iw2;
- if (n == 1) return;
- iw1 = 2*n;
- iw2 = iw1 + 2*n;
- cfftf1(n, c, wsave, wsave+iw1, (int*)(wsave+iw2), +1);
- } /* npy_cfftb */
-
-
-static void factorize(int n, int ifac[MAXFAC+2], const int ntryh[NSPECIAL])
- /* Factorize n in factors in ntryh and rest. On exit,
-ifac[0] contains n and ifac[1] contains number of factors,
-the factors start from ifac[2]. */
- {
- int ntry=3, i, j=0, ib, nf=0, nl=n, nq, nr;
-startloop:
- if (j < NSPECIAL)
- ntry = ntryh[j];
- else
- ntry+= 2;
- j++;
- do {
- nq = nl / ntry;
- nr = nl - ntry*nq;
- if (nr != 0) goto startloop;
- nf++;
- ifac[nf + 1] = ntry;
- nl = nq;
- if (ntry == 2 && nf != 1) {
- for (i=2; i<=nf; i++) {
- ib = nf - i + 2;
- ifac[ib + 1] = ifac[ib];
- }
- ifac[2] = 2;
- }
- } while (nl != 1);
- ifac[0] = n;
- ifac[1] = nf;
- }
-
-
-static void cffti1(int n, Treal wa[], int ifac[MAXFAC+2])
- {
- int fi, idot, i, j;
- int i1, k1, l1, l2;
- int ld, ii, nf, ip;
- int ido, ipm;
-
- static const int ntryh[NSPECIAL] = {
- 3,4,2,5 }; /* Do not change the order of these. */
-
- factorize(n,ifac,ntryh);
- nf = ifac[1];
- i = 1;
- l1 = 1;
- for (k1=1; k1<=nf; k1++) {
- ip = ifac[k1+1];
- ld = 0;
- l2 = l1*ip;
- ido = n / l2;
- idot = ido + ido + 2;
- ipm = ip - 1;
- for (j=1; j<=ipm; j++) {
- i1 = i;
- wa[i-1] = 1;
- wa[i] = 0;
- ld += l1;
- fi = 0;
- for (ii=4; ii<=idot; ii+=2) {
- i+= 2;
- fi+= 1;
- sincos2pi(fi*ld, n, wa+i, wa+i-1);
- }
- if (ip > 5) {
- wa[i1-1] = wa[i-1];
- wa[i1] = wa[i];
- }
- }
- l1 = l2;
- }
- } /* cffti1 */
-
-
-NPY_VISIBILITY_HIDDEN void npy_cffti(int n, Treal wsave[])
- {
- int iw1, iw2;
- if (n == 1) return;
- iw1 = 2*n;
- iw2 = iw1 + 2*n;
- cffti1(n, wsave+iw1, (int*)(wsave+iw2));
- } /* npy_cffti */
-
- /* -------------------------------------------------------------------
-rfftf1, rfftb1, npy_rfftf, npy_rfftb, rffti1, npy_rffti. Treal FFTs.
----------------------------------------------------------------------- */
-
-static void rfftf1(int n, Treal c[], Treal ch[], const Treal wa[], const int ifac[MAXFAC+2])
- {
- int i;
- int k1, l1, l2, na, kh, nf, ip, iw, ix2, ix3, ix4, ido, idl1;
- Treal *cinput, *coutput;
- nf = ifac[1];
- na = 1;
- l2 = n;
- iw = n-1;
- for (k1 = 1; k1 <= nf; ++k1) {
- kh = nf - k1;
- ip = ifac[kh + 2];
- l1 = l2 / ip;
- ido = n / l2;
- idl1 = ido*l1;
- iw -= (ip - 1)*ido;
- na = !na;
- if (na) {
- cinput = ch;
- coutput = c;
- } else {
- cinput = c;
- coutput = ch;
- }
- switch (ip) {
- case 4:
- ix2 = iw + ido;
- ix3 = ix2 + ido;
- radf4(ido, l1, cinput, coutput, &wa[iw], &wa[ix2], &wa[ix3]);
- break;
- case 2:
- radf2(ido, l1, cinput, coutput, &wa[iw]);
- break;
- case 3:
- ix2 = iw + ido;
- radf3(ido, l1, cinput, coutput, &wa[iw], &wa[ix2]);
- break;
- case 5:
- ix2 = iw + ido;
- ix3 = ix2 + ido;
- ix4 = ix3 + ido;
- radf5(ido, l1, cinput, coutput, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);
- break;
- default:
- if (ido == 1)
- na = !na;
- if (na == 0) {
- radfg(ido, ip, l1, idl1, c, ch, &wa[iw]);
- na = 1;
- } else {
- radfg(ido, ip, l1, idl1, ch, c, &wa[iw]);
- na = 0;
- }
- }
- l2 = l1;
- }
- if (na == 1) return;
- for (i = 0; i < n; i++) c[i] = ch[i];
- } /* rfftf1 */
-
-
-static void rfftb1(int n, Treal c[], Treal ch[], const Treal wa[], const int ifac[MAXFAC+2])
- {
- int i;
- int k1, l1, l2, na, nf, ip, iw, ix2, ix3, ix4, ido, idl1;
- Treal *cinput, *coutput;
- nf = ifac[1];
- na = 0;
- l1 = 1;
- iw = 0;
- for (k1=1; k1<=nf; k1++) {
- ip = ifac[k1 + 1];
- l2 = ip*l1;
- ido = n / l2;
- idl1 = ido*l1;
- if (na) {
- cinput = ch;
- coutput = c;
- } else {
- cinput = c;
- coutput = ch;
- }
- switch (ip) {
- case 4:
- ix2 = iw + ido;
- ix3 = ix2 + ido;
- radb4(ido, l1, cinput, coutput, &wa[iw], &wa[ix2], &wa[ix3]);
- na = !na;
- break;
- case 2:
- radb2(ido, l1, cinput, coutput, &wa[iw]);
- na = !na;
- break;
- case 3:
- ix2 = iw + ido;
- radb3(ido, l1, cinput, coutput, &wa[iw], &wa[ix2]);
- na = !na;
- break;
- case 5:
- ix2 = iw + ido;
- ix3 = ix2 + ido;
- ix4 = ix3 + ido;
- radb5(ido, l1, cinput, coutput, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4]);
- na = !na;
- break;
- default:
- radbg(ido, ip, l1, idl1, cinput, coutput, &wa[iw]);
- if (ido == 1) na = !na;
- }
- l1 = l2;
- iw += (ip - 1)*ido;
- }
- if (na == 0) return;
- for (i=0; i<n; i++) c[i] = ch[i];
- } /* rfftb1 */
-
-
-NPY_VISIBILITY_HIDDEN void npy_rfftf(int n, Treal r[], Treal wsave[])
- {
- if (n == 1) return;
- rfftf1(n, r, wsave, wsave+n, (int*)(wsave+2*n));
- } /* npy_rfftf */
-
-
-NPY_VISIBILITY_HIDDEN void npy_rfftb(int n, Treal r[], Treal wsave[])
- {
- if (n == 1) return;
- rfftb1(n, r, wsave, wsave+n, (int*)(wsave+2*n));
- } /* npy_rfftb */
-
-
-static void rffti1(int n, Treal wa[], int ifac[MAXFAC+2])
- {
- int fi, i, j;
- int k1, l1, l2;
- int ld, ii, nf, ip, is;
- int ido, ipm, nfm1;
- static const int ntryh[NSPECIAL] = {
- 4,2,3,5 }; /* Do not change the order of these. */
- factorize(n,ifac,ntryh);
- nf = ifac[1];
- is = 0;
- nfm1 = nf - 1;
- l1 = 1;
- if (nfm1 == 0) return;
- for (k1 = 1; k1 <= nfm1; k1++) {
- ip = ifac[k1 + 1];
- ld = 0;
- l2 = l1*ip;
- ido = n / l2;
- ipm = ip - 1;
- for (j = 1; j <= ipm; ++j) {
- ld += l1;
- i = is;
- fi = 0;
- for (ii = 3; ii <= ido; ii += 2) {
- i += 2;
- fi += 1;
- sincos2pi(fi*ld, n, wa+i-1, wa+i-2);
- }
- is += ido;
- }
- l1 = l2;
- }
- } /* rffti1 */
-
-
-NPY_VISIBILITY_HIDDEN void npy_rffti(int n, Treal wsave[])
- {
- if (n == 1) return;
- rffti1(n, wsave+n, (int*)(wsave+2*n));
- } /* npy_rffti */
-
-#ifdef __cplusplus
-}
-#endif
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