/*
* 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]
#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
/* ----------------------------------------------------------------------
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 = 0.866025403784439;
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 = 0.309016994374947;
static const Treal ti11 = 0.951056516295154;
static const Treal tr12 = -0.809016994374947;
static const Treal ti12 = 0.587785252292473;
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 = 0.866025403784439;
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