1502 lines
50 KiB
C
1502 lines
50 KiB
C
/*
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* fftpack.c : A set of FFT routines in C.
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* Algorithmically based on Fortran-77 FFTPACK by Paul N. Swarztrauber (Version 4, 1985).
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*/
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#define NPY_VISIBILITY_HIDDEN
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/* #define NPY_NO_DEPRECATED_API NPY_API_VERSION */
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#include <math.h>
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#include <stdio.h>
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#define DOUBLE
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#ifdef DOUBLE
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#define Treal double
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#else
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#define Treal float
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#endif
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#define ref(u,a) u[a]
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#define MAXFAC 13 /* maximum number of factors in factorization of n */
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#define NSPECIAL 4 /* number of factors for which we have special-case routines */
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#ifdef __cplusplus
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extern "C" {
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#endif
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/* ----------------------------------------------------------------------
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passf2, passf3, passf4, passf5, passf. Complex FFT passes fwd and bwd.
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----------------------------------------------------------------------- */
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static void passf2(int ido, int l1, const Treal cc[], Treal ch[], const Treal wa1[], int isign)
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/* isign==+1 for backward transform */
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{
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int i, k, ah, ac;
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Treal ti2, tr2;
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if (ido <= 2) {
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for (k=0; k<l1; k++) {
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ah = k*ido;
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ac = 2*k*ido;
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ch[ah] = ref(cc,ac) + ref(cc,ac + ido);
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ch[ah + ido*l1] = ref(cc,ac) - ref(cc,ac + ido);
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ch[ah+1] = ref(cc,ac+1) + ref(cc,ac + ido + 1);
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ch[ah + ido*l1 + 1] = ref(cc,ac+1) - ref(cc,ac + ido + 1);
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}
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} else {
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for (k=0; k<l1; k++) {
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for (i=0; i<ido-1; i+=2) {
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ah = i + k*ido;
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ac = i + 2*k*ido;
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ch[ah] = ref(cc,ac) + ref(cc,ac + ido);
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tr2 = ref(cc,ac) - ref(cc,ac + ido);
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ch[ah+1] = ref(cc,ac+1) + ref(cc,ac + 1 + ido);
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ti2 = ref(cc,ac+1) - ref(cc,ac + 1 + ido);
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ch[ah+l1*ido+1] = wa1[i]*ti2 + isign*wa1[i+1]*tr2;
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ch[ah+l1*ido] = wa1[i]*tr2 - isign*wa1[i+1]*ti2;
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}
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}
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}
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} /* passf2 */
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static void passf3(int ido, int l1, const Treal cc[], Treal ch[],
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const Treal wa1[], const Treal wa2[], int isign)
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/* isign==+1 for backward transform */
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{
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static const Treal taur = -0.5;
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static const Treal taui = 0.866025403784439;
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int i, k, ac, ah;
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Treal ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;
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if (ido == 2) {
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for (k=1; k<=l1; k++) {
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ac = (3*k - 2)*ido;
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tr2 = ref(cc,ac) + ref(cc,ac + ido);
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cr2 = ref(cc,ac - ido) + taur*tr2;
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ah = (k - 1)*ido;
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ch[ah] = ref(cc,ac - ido) + tr2;
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ti2 = ref(cc,ac + 1) + ref(cc,ac + ido + 1);
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ci2 = ref(cc,ac - ido + 1) + taur*ti2;
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ch[ah + 1] = ref(cc,ac - ido + 1) + ti2;
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cr3 = isign*taui*(ref(cc,ac) - ref(cc,ac + ido));
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ci3 = isign*taui*(ref(cc,ac + 1) - ref(cc,ac + ido + 1));
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ch[ah + l1*ido] = cr2 - ci3;
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ch[ah + 2*l1*ido] = cr2 + ci3;
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ch[ah + l1*ido + 1] = ci2 + cr3;
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ch[ah + 2*l1*ido + 1] = ci2 - cr3;
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}
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} else {
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for (k=1; k<=l1; k++) {
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for (i=0; i<ido-1; i+=2) {
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ac = i + (3*k - 2)*ido;
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tr2 = ref(cc,ac) + ref(cc,ac + ido);
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cr2 = ref(cc,ac - ido) + taur*tr2;
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ah = i + (k-1)*ido;
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ch[ah] = ref(cc,ac - ido) + tr2;
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ti2 = ref(cc,ac + 1) + ref(cc,ac + ido + 1);
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ci2 = ref(cc,ac - ido + 1) + taur*ti2;
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ch[ah + 1] = ref(cc,ac - ido + 1) + ti2;
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cr3 = isign*taui*(ref(cc,ac) - ref(cc,ac + ido));
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ci3 = isign*taui*(ref(cc,ac + 1) - ref(cc,ac + ido + 1));
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dr2 = cr2 - ci3;
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dr3 = cr2 + ci3;
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di2 = ci2 + cr3;
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di3 = ci2 - cr3;
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ch[ah + l1*ido + 1] = wa1[i]*di2 + isign*wa1[i+1]*dr2;
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ch[ah + l1*ido] = wa1[i]*dr2 - isign*wa1[i+1]*di2;
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ch[ah + 2*l1*ido + 1] = wa2[i]*di3 + isign*wa2[i+1]*dr3;
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ch[ah + 2*l1*ido] = wa2[i]*dr3 - isign*wa2[i+1]*di3;
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}
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}
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}
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} /* passf3 */
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static void passf4(int ido, int l1, const Treal cc[], Treal ch[],
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const Treal wa1[], const Treal wa2[], const Treal wa3[], int isign)
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/* isign == -1 for forward transform and +1 for backward transform */
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{
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int i, k, ac, ah;
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Treal ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2, tr3, tr4;
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if (ido == 2) {
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for (k=0; k<l1; k++) {
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ac = 4*k*ido + 1;
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ti1 = ref(cc,ac) - ref(cc,ac + 2*ido);
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ti2 = ref(cc,ac) + ref(cc,ac + 2*ido);
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tr4 = ref(cc,ac + 3*ido) - ref(cc,ac + ido);
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ti3 = ref(cc,ac + ido) + ref(cc,ac + 3*ido);
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tr1 = ref(cc,ac - 1) - ref(cc,ac + 2*ido - 1);
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tr2 = ref(cc,ac - 1) + ref(cc,ac + 2*ido - 1);
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ti4 = ref(cc,ac + ido - 1) - ref(cc,ac + 3*ido - 1);
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tr3 = ref(cc,ac + ido - 1) + ref(cc,ac + 3*ido - 1);
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ah = k*ido;
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ch[ah] = tr2 + tr3;
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ch[ah + 2*l1*ido] = tr2 - tr3;
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ch[ah + 1] = ti2 + ti3;
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ch[ah + 2*l1*ido + 1] = ti2 - ti3;
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ch[ah + l1*ido] = tr1 + isign*tr4;
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ch[ah + 3*l1*ido] = tr1 - isign*tr4;
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ch[ah + l1*ido + 1] = ti1 + isign*ti4;
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ch[ah + 3*l1*ido + 1] = ti1 - isign*ti4;
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}
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} else {
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for (k=0; k<l1; k++) {
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for (i=0; i<ido-1; i+=2) {
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ac = i + 1 + 4*k*ido;
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ti1 = ref(cc,ac) - ref(cc,ac + 2*ido);
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ti2 = ref(cc,ac) + ref(cc,ac + 2*ido);
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ti3 = ref(cc,ac + ido) + ref(cc,ac + 3*ido);
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tr4 = ref(cc,ac + 3*ido) - ref(cc,ac + ido);
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tr1 = ref(cc,ac - 1) - ref(cc,ac + 2*ido - 1);
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tr2 = ref(cc,ac - 1) + ref(cc,ac + 2*ido - 1);
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ti4 = ref(cc,ac + ido - 1) - ref(cc,ac + 3*ido - 1);
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tr3 = ref(cc,ac + ido - 1) + ref(cc,ac + 3*ido - 1);
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ah = i + k*ido;
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ch[ah] = tr2 + tr3;
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cr3 = tr2 - tr3;
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ch[ah + 1] = ti2 + ti3;
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ci3 = ti2 - ti3;
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cr2 = tr1 + isign*tr4;
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cr4 = tr1 - isign*tr4;
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ci2 = ti1 + isign*ti4;
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ci4 = ti1 - isign*ti4;
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ch[ah + l1*ido] = wa1[i]*cr2 - isign*wa1[i + 1]*ci2;
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ch[ah + l1*ido + 1] = wa1[i]*ci2 + isign*wa1[i + 1]*cr2;
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ch[ah + 2*l1*ido] = wa2[i]*cr3 - isign*wa2[i + 1]*ci3;
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ch[ah + 2*l1*ido + 1] = wa2[i]*ci3 + isign*wa2[i + 1]*cr3;
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ch[ah + 3*l1*ido] = wa3[i]*cr4 -isign*wa3[i + 1]*ci4;
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ch[ah + 3*l1*ido + 1] = wa3[i]*ci4 + isign*wa3[i + 1]*cr4;
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}
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}
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}
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} /* passf4 */
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static void passf5(int ido, int l1, const Treal cc[], Treal ch[],
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const Treal wa1[], const Treal wa2[], const Treal wa3[], const Treal wa4[], int isign)
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/* isign == -1 for forward transform and +1 for backward transform */
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{
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static const Treal tr11 = 0.309016994374947;
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static const Treal ti11 = 0.951056516295154;
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static const Treal tr12 = -0.809016994374947;
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static const Treal ti12 = 0.587785252292473;
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int i, k, ac, ah;
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Treal ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4, ti2, ti3,
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ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;
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if (ido == 2) {
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for (k = 1; k <= l1; ++k) {
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ac = (5*k - 4)*ido + 1;
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ti5 = ref(cc,ac) - ref(cc,ac + 3*ido);
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ti2 = ref(cc,ac) + ref(cc,ac + 3*ido);
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ti4 = ref(cc,ac + ido) - ref(cc,ac + 2*ido);
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ti3 = ref(cc,ac + ido) + ref(cc,ac + 2*ido);
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tr5 = ref(cc,ac - 1) - ref(cc,ac + 3*ido - 1);
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tr2 = ref(cc,ac - 1) + ref(cc,ac + 3*ido - 1);
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tr4 = ref(cc,ac + ido - 1) - ref(cc,ac + 2*ido - 1);
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tr3 = ref(cc,ac + ido - 1) + ref(cc,ac + 2*ido - 1);
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ah = (k - 1)*ido;
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ch[ah] = ref(cc,ac - ido - 1) + tr2 + tr3;
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ch[ah + 1] = ref(cc,ac - ido) + ti2 + ti3;
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cr2 = ref(cc,ac - ido - 1) + tr11*tr2 + tr12*tr3;
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ci2 = ref(cc,ac - ido) + tr11*ti2 + tr12*ti3;
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cr3 = ref(cc,ac - ido - 1) + tr12*tr2 + tr11*tr3;
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ci3 = ref(cc,ac - ido) + tr12*ti2 + tr11*ti3;
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cr5 = isign*(ti11*tr5 + ti12*tr4);
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ci5 = isign*(ti11*ti5 + ti12*ti4);
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cr4 = isign*(ti12*tr5 - ti11*tr4);
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ci4 = isign*(ti12*ti5 - ti11*ti4);
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ch[ah + l1*ido] = cr2 - ci5;
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ch[ah + 4*l1*ido] = cr2 + ci5;
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ch[ah + l1*ido + 1] = ci2 + cr5;
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ch[ah + 2*l1*ido + 1] = ci3 + cr4;
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ch[ah + 2*l1*ido] = cr3 - ci4;
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ch[ah + 3*l1*ido] = cr3 + ci4;
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ch[ah + 3*l1*ido + 1] = ci3 - cr4;
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ch[ah + 4*l1*ido + 1] = ci2 - cr5;
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}
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} else {
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for (k=1; k<=l1; k++) {
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for (i=0; i<ido-1; i+=2) {
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ac = i + 1 + (k*5 - 4)*ido;
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ti5 = ref(cc,ac) - ref(cc,ac + 3*ido);
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ti2 = ref(cc,ac) + ref(cc,ac + 3*ido);
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ti4 = ref(cc,ac + ido) - ref(cc,ac + 2*ido);
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ti3 = ref(cc,ac + ido) + ref(cc,ac + 2*ido);
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tr5 = ref(cc,ac - 1) - ref(cc,ac + 3*ido - 1);
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tr2 = ref(cc,ac - 1) + ref(cc,ac + 3*ido - 1);
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tr4 = ref(cc,ac + ido - 1) - ref(cc,ac + 2*ido - 1);
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tr3 = ref(cc,ac + ido - 1) + ref(cc,ac + 2*ido - 1);
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ah = i + (k - 1)*ido;
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ch[ah] = ref(cc,ac - ido - 1) + tr2 + tr3;
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ch[ah + 1] = ref(cc,ac - ido) + ti2 + ti3;
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cr2 = ref(cc,ac - ido - 1) + tr11*tr2 + tr12*tr3;
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ci2 = ref(cc,ac - ido) + tr11*ti2 + tr12*ti3;
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cr3 = ref(cc,ac - ido - 1) + tr12*tr2 + tr11*tr3;
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ci3 = ref(cc,ac - ido) + tr12*ti2 + tr11*ti3;
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cr5 = isign*(ti11*tr5 + ti12*tr4);
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ci5 = isign*(ti11*ti5 + ti12*ti4);
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cr4 = isign*(ti12*tr5 - ti11*tr4);
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ci4 = isign*(ti12*ti5 - ti11*ti4);
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dr3 = cr3 - ci4;
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dr4 = cr3 + ci4;
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di3 = ci3 + cr4;
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di4 = ci3 - cr4;
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dr5 = cr2 + ci5;
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dr2 = cr2 - ci5;
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di5 = ci2 - cr5;
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di2 = ci2 + cr5;
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ch[ah + l1*ido] = wa1[i]*dr2 - isign*wa1[i+1]*di2;
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ch[ah + l1*ido + 1] = wa1[i]*di2 + isign*wa1[i+1]*dr2;
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ch[ah + 2*l1*ido] = wa2[i]*dr3 - isign*wa2[i+1]*di3;
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ch[ah + 2*l1*ido + 1] = wa2[i]*di3 + isign*wa2[i+1]*dr3;
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ch[ah + 3*l1*ido] = wa3[i]*dr4 - isign*wa3[i+1]*di4;
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ch[ah + 3*l1*ido + 1] = wa3[i]*di4 + isign*wa3[i+1]*dr4;
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ch[ah + 4*l1*ido] = wa4[i]*dr5 - isign*wa4[i+1]*di5;
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ch[ah + 4*l1*ido + 1] = wa4[i]*di5 + isign*wa4[i+1]*dr5;
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}
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}
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}
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} /* passf5 */
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static void passf(int *nac, int ido, int ip, int l1, int idl1,
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Treal cc[], Treal ch[],
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const Treal wa[], int isign)
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/* isign is -1 for forward transform and +1 for backward transform */
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{
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int idij, idlj, idot, ipph, i, j, k, l, jc, lc, ik, idj, idl, inc,idp;
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Treal wai, war;
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idot = ido / 2;
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/* nt = ip*idl1;*/
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ipph = (ip + 1) / 2;
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idp = ip*ido;
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if (ido >= l1) {
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for (j=1; j<ipph; j++) {
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jc = ip - j;
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for (k=0; k<l1; k++) {
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for (i=0; i<ido; i++) {
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ch[i + (k + j*l1)*ido] =
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ref(cc,i + (j + k*ip)*ido) + ref(cc,i + (jc + k*ip)*ido);
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ch[i + (k + jc*l1)*ido] =
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ref(cc,i + (j + k*ip)*ido) - ref(cc,i + (jc + k*ip)*ido);
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}
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}
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}
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for (k=0; k<l1; k++)
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for (i=0; i<ido; i++)
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ch[i + k*ido] = ref(cc,i + k*ip*ido);
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} else {
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for (j=1; j<ipph; j++) {
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jc = ip - j;
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for (i=0; i<ido; i++) {
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for (k=0; k<l1; k++) {
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ch[i + (k + j*l1)*ido] = ref(cc,i + (j + k*ip)*ido) + ref(cc,i + (jc + k*
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ip)*ido);
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ch[i + (k + jc*l1)*ido] = ref(cc,i + (j + k*ip)*ido) - ref(cc,i + (jc + k*
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ip)*ido);
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}
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}
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}
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for (i=0; i<ido; i++)
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for (k=0; k<l1; k++)
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ch[i + k*ido] = ref(cc,i + k*ip*ido);
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}
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idl = 2 - ido;
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inc = 0;
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for (l=1; l<ipph; l++) {
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lc = ip - l;
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idl += ido;
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for (ik=0; ik<idl1; ik++) {
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cc[ik + l*idl1] = ch[ik] + wa[idl - 2]*ch[ik + idl1];
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cc[ik + lc*idl1] = isign*wa[idl-1]*ch[ik + (ip-1)*idl1];
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}
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idlj = idl;
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inc += ido;
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for (j=2; j<ipph; j++) {
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jc = ip - j;
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idlj += inc;
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if (idlj > idp) idlj -= idp;
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war = wa[idlj - 2];
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wai = wa[idlj-1];
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for (ik=0; ik<idl1; ik++) {
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cc[ik + l*idl1] += war*ch[ik + j*idl1];
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cc[ik + lc*idl1] += isign*wai*ch[ik + jc*idl1];
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}
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}
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}
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for (j=1; j<ipph; j++)
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for (ik=0; ik<idl1; ik++)
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ch[ik] += ch[ik + j*idl1];
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for (j=1; j<ipph; j++) {
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jc = ip - j;
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for (ik=1; ik<idl1; ik+=2) {
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ch[ik - 1 + j*idl1] = cc[ik - 1 + j*idl1] - cc[ik + jc*idl1];
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ch[ik - 1 + jc*idl1] = cc[ik - 1 + j*idl1] + cc[ik + jc*idl1];
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ch[ik + j*idl1] = cc[ik + j*idl1] + cc[ik - 1 + jc*idl1];
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ch[ik + jc*idl1] = cc[ik + j*idl1] - cc[ik - 1 + jc*idl1];
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}
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}
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*nac = 1;
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if (ido == 2) return;
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*nac = 0;
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for (ik=0; ik<idl1; ik++)
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cc[ik] = ch[ik];
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for (j=1; j<ip; j++) {
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for (k=0; k<l1; k++) {
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cc[(k + j*l1)*ido + 0] = ch[(k + j*l1)*ido + 0];
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cc[(k + j*l1)*ido + 1] = ch[(k + j*l1)*ido + 1];
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}
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}
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if (idot <= l1) {
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idij = 0;
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for (j=1; j<ip; j++) {
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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 = 0.866025403784439;
|
|
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 = 0.866025403784439;
|
|
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 = 0.7071067811865475;
|
|
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 = 1.414213562373095;
|
|
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 = 0.309016994374947;
|
|
static const Treal ti11 = 0.951056516295154;
|
|
static const Treal tr12 = -0.809016994374947;
|
|
static const Treal ti12 = 0.587785252292473;
|
|
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 = 0.309016994374947;
|
|
static const Treal ti11 = 0.951056516295154;
|
|
static const Treal tr12 = -0.809016994374947;
|
|
static const Treal ti12 = 0.587785252292473;
|
|
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[])
|
|
{
|
|
static const Treal twopi = 6.28318530717959;
|
|
int idij, ipph, i, j, k, l, j2, ic, jc, lc, ik, is, nbd;
|
|
Treal dc2, ai1, ai2, ar1, ar2, ds2, dcp, arg, dsp, ar1h, ar2h;
|
|
arg = twopi / ip;
|
|
dcp = cos(arg);
|
|
dsp = sin(arg);
|
|
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[])
|
|
{
|
|
static const Treal twopi = 6.28318530717959;
|
|
int idij, ipph, i, j, k, l, j2, ic, jc, lc, ik, is;
|
|
Treal dc2, ai1, ai2, ar1, ar2, ds2;
|
|
int nbd;
|
|
Treal dcp, arg, dsp, ar1h, ar2h;
|
|
arg = twopi / ip;
|
|
dcp = cos(arg);
|
|
dsp = sin(arg);
|
|
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])
|
|
{
|
|
static const Treal twopi = 6.28318530717959;
|
|
Treal arg, argh, argld, fi;
|
|
int 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];
|
|
argh = twopi/(Treal)n;
|
|
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;
|
|
argld = ld*argh;
|
|
for (ii=4; ii<=idot; ii+=2) {
|
|
i+= 2;
|
|
fi+= 1;
|
|
arg = fi*argld;
|
|
wa[i-1] = cos(arg);
|
|
wa[i] = sin(arg);
|
|
}
|
|
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])
|
|
{
|
|
static const Treal twopi = 6.28318530717959;
|
|
Treal arg, argh, argld, fi;
|
|
int 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];
|
|
argh = twopi / n;
|
|
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;
|
|
argld = (Treal) ld*argh;
|
|
fi = 0;
|
|
for (ii = 3; ii <= ido; ii += 2) {
|
|
i += 2;
|
|
fi += 1;
|
|
arg = fi*argld;
|
|
wa[i - 2] = cos(arg);
|
|
wa[i - 1] = sin(arg);
|
|
}
|
|
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
|