[PD-cvs] SF.net SVN: pure-data:[10497] branches/pd-extended/0.41/pd/src
eighthave at users.sourceforge.net
eighthave at users.sourceforge.net
Sat Jan 10 03:20:23 CET 2009
Revision: 10497
http://pure-data.svn.sourceforge.net/pure-data/?rev=10497&view=rev
Author: eighthave
Date: 2009-01-10 02:20:22 +0000 (Sat, 10 Jan 2009)
Log Message:
-----------
svn merge wants to replace these files for whatever reason, so I am humoring it
Added Paths:
-----------
branches/pd-extended/0.41/pd/src/d_fft_fftsg.c
branches/pd-extended/0.41/pd/src/d_fft_fftw.c
branches/pd-extended/0.41/pd/src/d_fftsg_h.c
Removed Paths:
-------------
branches/pd-extended/0.41/pd/src/d_fft_fftsg.c
branches/pd-extended/0.41/pd/src/d_fft_fftw.c
branches/pd-extended/0.41/pd/src/d_fftsg_h.c
Deleted: branches/pd-extended/0.41/pd/src/d_fft_fftsg.c
===================================================================
--- branches/pd-extended/0.41/pd/src/d_fft_fftsg.c 2009-01-10 02:18:04 UTC (rev 10496)
+++ branches/pd-extended/0.41/pd/src/d_fft_fftsg.c 2009-01-10 02:20:22 UTC (rev 10497)
@@ -1,3462 +0,0 @@
-/****************** begin Pd-specific prologue ***********************/
-
-/*
-This is the file, "fftsg.c" from the OOURA FFT package. The copyright notice
-from Ooura's README is:
-
-Copyright:
- Copyright(C) 1996-2001 Takuya OOURA
- email: ooura at mmm.t.u-tokyo.ac.jp
- download: http://momonga.t.u-tokyo.ac.jp/~ooura/fft.html
- You may use, copy, modify this code for any purpose and
- without fee. You may distribute this ORIGINAL package.
-
-After the following prologue, the code is exactly Ooura's original, which I
-believe the above notice permits me to redistribute. See Ooura's website
-for another, more permissive-sounding copyright notice. -MSP
-*/
-
-/* ---------- Pd interface to OOURA FFT; imitate Mayer API ---------- */
-#include "m_pd.h"
-#ifdef MSW
-#include <malloc.h>
-#else
-#include <alloca.h>
-#endif
-
-#define FFTFLT double
-void cdft(int, int, double *, int *, double *);
-void rdft(int, int, double *, int *, double *);
-
-int ilog2(int n);
-
-static int ooura_maxn;
-static int *ooura_bitrev;
-static int ooura_bitrevsize;
-static FFTFLT *ooura_costab;
-
-static int ooura_init( int n)
-{
- n = (1 << ilog2(n));
- if (n < 64)
- return (0);
- if (n > ooura_maxn)
- {
- post("init");
- if (ooura_maxn)
- {
- t_freebytes(ooura_bitrev, ooura_bitrevsize);
- t_freebytes(ooura_costab, ooura_maxn * sizeof(FFTFLT) / 2);
- }
- ooura_bitrevsize = sizeof(int *) * (2 + (1 << (ilog2(n)/2)));
- ooura_bitrev = (int *)t_getbytes(ooura_bitrevsize);
- ooura_bitrev[0] = 0;
- if (!ooura_bitrev)
- {
- error("out of memory allocating FFT buffer");
- ooura_maxn = 0;
- return (0);
- }
- ooura_costab = (FFTFLT *)t_getbytes(n * sizeof(FFTFLT)/2);
- if (!ooura_costab)
- {
- error("out of memory allocating FFT buffer");
- t_freebytes(ooura_bitrev, ooura_bitrevsize);
- ooura_maxn = 0;
- return (0);
- }
- ooura_maxn = n;
- ooura_bitrev[0] = 0;
- }
- return (1);
-}
-
-EXTERN void mayer_fht(t_sample *fz, int n)
-{
- post("FHT: not yet implemented");
-}
-
-EXTERN void mayer_dofft(t_sample *fz1, t_sample *fz2, int n, int sgn)
-{
- FFTFLT *buf, *fp3;
- int i;
- t_sample *fp1, *fp2;
- buf = alloca(n * (2 * sizeof(FFTFLT)));
- if (!ooura_init(n))
- return;
- for (i = 0, fp1 = fz1, fp2 = fz2, fp3 = buf; i < n; i++)
- {
- fp3[0] = *fp1++;
- fp3[1] = *fp2++;
- fp3 += 2;
- }
- cdft(2*n, sgn, buf, ooura_bitrev, ooura_costab);
- for (i = 0, fp1 = fz1, fp2 = fz2, fp3 = buf; i < n; i++)
- {
- *fp1++ = fp3[0];
- *fp2++ = fp3[1];
- fp3 += 2;
- }
-}
-
-EXTERN void mayer_fft(int n, t_sample *fz1, t_sample *fz2)
-{
- mayer_dofft(fz1, fz2, n, -1);
-}
-
-EXTERN void mayer_ifft(int n, t_sample *fz1, t_sample *fz2)
-{
- mayer_dofft(fz1, fz2, n, 1);
-}
-
-EXTERN void mayer_realfft(int n, t_sample *fz)
-{
- FFTFLT *buf, *fp3;
- int i, nover2 = n/2;
- t_sample *fp1, *fp2;
- buf = alloca(n * sizeof(FFTFLT));
- if (!ooura_init(n))
- return;
- for (i = 0, fp1 = fz, fp3 = buf; i < n; i++, fp1++, fp3++)
- buf[i] = fz[i];
- rdft(n, 1, buf, ooura_bitrev, ooura_costab);
- fz[0] = buf[0];
- fz[nover2] = buf[1];
- for (i = 1, fp1 = fz+1, fp2 = fz+(n-1), fp3 = buf+2; i < nover2;
- i++, fp1++, fp2--, fp3 += 2)
- *fp1 = fp3[0], *fp2 = fp3[1];
-}
-
-EXTERN void mayer_realifft(int n, t_sample *fz)
-{
- FFTFLT *buf, *fp3;
- int i, nover2 = n/2;
- t_sample *fp1, *fp2;
- buf = alloca(n * sizeof(FFTFLT));
- if (!ooura_init(n))
- return;
- buf[0] = fz[0];
- buf[1] = fz[nover2];
- for (i = 1, fp1 = fz+1, fp2 = fz+(n-1), fp3 = buf+2; i < nover2;
- i++, fp1++, fp2--, fp3 += 2)
- fp3[0] = *fp1, fp3[1] = *fp2;
- rdft(n, -1, buf, ooura_bitrev, ooura_costab);
- for (i = 0, fp1 = fz, fp3 = buf; i < n; i++, fp1++, fp3++)
- fz[i] = 2*buf[i];
-}
-
-/****************** end Pd-specific prologue ***********************/
-/*
-Fast Fourier/Cosine/Sine Transform
- dimension :one
- data length :power of 2
- decimation :frequency
- radix :split-radix
- data :inplace
- table :use
-functions
- cdft: Complex Discrete Fourier Transform
- rdft: Real Discrete Fourier Transform
- ddct: Discrete Cosine Transform
- ddst: Discrete Sine Transform
- dfct: Cosine Transform of RDFT (Real Symmetric DFT)
- dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
-function prototypes
- void cdft(int, int, double *, int *, double *);
- void rdft(int, int, double *, int *, double *);
- void ddct(int, int, double *, int *, double *);
- void ddst(int, int, double *, int *, double *);
- void dfct(int, double *, double *, int *, double *);
- void dfst(int, double *, double *, int *, double *);
-macro definitions
- USE_CDFT_PTHREADS : default=not defined
- CDFT_THREADS_BEGIN_N : must be >= 512, default=8192
- CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536
- USE_CDFT_WINTHREADS : default=not defined
- CDFT_THREADS_BEGIN_N : must be >= 512, default=32768
- CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288
-
-
--------- Complex DFT (Discrete Fourier Transform) --------
- [definition]
- <case1>
- X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
- <case2>
- X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
- (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
- [usage]
- <case1>
- ip[0] = 0; // first time only
- cdft(2*n, 1, a, ip, w);
- <case2>
- ip[0] = 0; // first time only
- cdft(2*n, -1, a, ip, w);
- [parameters]
- 2*n :data length (int)
- n >= 1, n = power of 2
- a[0...2*n-1] :input/output data (double *)
- input data
- a[2*j] = Re(x[j]),
- a[2*j+1] = Im(x[j]), 0<=j<n
- output data
- a[2*k] = Re(X[k]),
- a[2*k+1] = Im(X[k]), 0<=k<n
- ip[0...*] :work area for bit reversal (int *)
- length of ip >= 2+sqrt(n)
- strictly,
- length of ip >=
- 2+(1<<(int)(log(n+0.5)/log(2))/2).
- ip[0],ip[1] are pointers of the cos/sin table.
- w[0...n/2-1] :cos/sin table (double *)
- w[],ip[] are initialized if ip[0] == 0.
- [remark]
- Inverse of
- cdft(2*n, -1, a, ip, w);
- is
- cdft(2*n, 1, a, ip, w);
- for (j = 0; j <= 2 * n - 1; j++) {
- a[j] *= 1.0 / n;
- }
- .
-
-
--------- Real DFT / Inverse of Real DFT --------
- [definition]
- <case1> RDFT
- R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
- I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
- <case2> IRDFT (excluding scale)
- a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
- sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
- sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
- [usage]
- <case1>
- ip[0] = 0; // first time only
- rdft(n, 1, a, ip, w);
- <case2>
- ip[0] = 0; // first time only
- rdft(n, -1, a, ip, w);
- [parameters]
- n :data length (int)
- n >= 2, n = power of 2
- a[0...n-1] :input/output data (double *)
- <case1>
- output data
- a[2*k] = R[k], 0<=k<n/2
- a[2*k+1] = I[k], 0<k<n/2
- a[1] = R[n/2]
- <case2>
- input data
- a[2*j] = R[j], 0<=j<n/2
- a[2*j+1] = I[j], 0<j<n/2
- a[1] = R[n/2]
- ip[0...*] :work area for bit reversal (int *)
- length of ip >= 2+sqrt(n/2)
- strictly,
- length of ip >=
- 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
- ip[0],ip[1] are pointers of the cos/sin table.
- w[0...n/2-1] :cos/sin table (double *)
- w[],ip[] are initialized if ip[0] == 0.
- [remark]
- Inverse of
- rdft(n, 1, a, ip, w);
- is
- rdft(n, -1, a, ip, w);
- for (j = 0; j <= n - 1; j++) {
- a[j] *= 2.0 / n;
- }
- .
-
-
--------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
- [definition]
- <case1> IDCT (excluding scale)
- C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
- <case2> DCT
- C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
- [usage]
- <case1>
- ip[0] = 0; // first time only
- ddct(n, 1, a, ip, w);
- <case2>
- ip[0] = 0; // first time only
- ddct(n, -1, a, ip, w);
- [parameters]
- n :data length (int)
- n >= 2, n = power of 2
- a[0...n-1] :input/output data (double *)
- output data
- a[k] = C[k], 0<=k<n
- ip[0...*] :work area for bit reversal (int *)
- length of ip >= 2+sqrt(n/2)
- strictly,
- length of ip >=
- 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
- ip[0],ip[1] are pointers of the cos/sin table.
- w[0...n*5/4-1] :cos/sin table (double *)
- w[],ip[] are initialized if ip[0] == 0.
- [remark]
- Inverse of
- ddct(n, -1, a, ip, w);
- is
- a[0] *= 0.5;
- ddct(n, 1, a, ip, w);
- for (j = 0; j <= n - 1; j++) {
- a[j] *= 2.0 / n;
- }
- .
-
-
--------- DST (Discrete Sine Transform) / Inverse of DST --------
- [definition]
- <case1> IDST (excluding scale)
- S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
- <case2> DST
- S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
- [usage]
- <case1>
- ip[0] = 0; // first time only
- ddst(n, 1, a, ip, w);
- <case2>
- ip[0] = 0; // first time only
- ddst(n, -1, a, ip, w);
- [parameters]
- n :data length (int)
- n >= 2, n = power of 2
- a[0...n-1] :input/output data (double *)
- <case1>
- input data
- a[j] = A[j], 0<j<n
- a[0] = A[n]
- output data
- a[k] = S[k], 0<=k<n
- <case2>
- output data
- a[k] = S[k], 0<k<n
- a[0] = S[n]
- ip[0...*] :work area for bit reversal (int *)
- length of ip >= 2+sqrt(n/2)
- strictly,
- length of ip >=
- 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
- ip[0],ip[1] are pointers of the cos/sin table.
- w[0...n*5/4-1] :cos/sin table (double *)
- w[],ip[] are initialized if ip[0] == 0.
- [remark]
- Inverse of
- ddst(n, -1, a, ip, w);
- is
- a[0] *= 0.5;
- ddst(n, 1, a, ip, w);
- for (j = 0; j <= n - 1; j++) {
- a[j] *= 2.0 / n;
- }
- .
-
-
--------- Cosine Transform of RDFT (Real Symmetric DFT) --------
- [definition]
- C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
- [usage]
- ip[0] = 0; // first time only
- dfct(n, a, t, ip, w);
- [parameters]
- n :data length - 1 (int)
- n >= 2, n = power of 2
- a[0...n] :input/output data (double *)
- output data
- a[k] = C[k], 0<=k<=n
- t[0...n/2] :work area (double *)
- ip[0...*] :work area for bit reversal (int *)
- length of ip >= 2+sqrt(n/4)
- strictly,
- length of ip >=
- 2+(1<<(int)(log(n/4+0.5)/log(2))/2).
- ip[0],ip[1] are pointers of the cos/sin table.
- w[0...n*5/8-1] :cos/sin table (double *)
- w[],ip[] are initialized if ip[0] == 0.
- [remark]
- Inverse of
- a[0] *= 0.5;
- a[n] *= 0.5;
- dfct(n, a, t, ip, w);
- is
- a[0] *= 0.5;
- a[n] *= 0.5;
- dfct(n, a, t, ip, w);
- for (j = 0; j <= n; j++) {
- a[j] *= 2.0 / n;
- }
- .
-
-
--------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
- [definition]
- S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
- [usage]
- ip[0] = 0; // first time only
- dfst(n, a, t, ip, w);
- [parameters]
- n :data length + 1 (int)
- n >= 2, n = power of 2
- a[0...n-1] :input/output data (double *)
- output data
- a[k] = S[k], 0<k<n
- (a[0] is used for work area)
- t[0...n/2-1] :work area (double *)
- ip[0...*] :work area for bit reversal (int *)
- length of ip >= 2+sqrt(n/4)
- strictly,
- length of ip >=
- 2+(1<<(int)(log(n/4+0.5)/log(2))/2).
- ip[0],ip[1] are pointers of the cos/sin table.
- w[0...n*5/8-1] :cos/sin table (double *)
- w[],ip[] are initialized if ip[0] == 0.
- [remark]
- Inverse of
- dfst(n, a, t, ip, w);
- is
- dfst(n, a, t, ip, w);
- for (j = 1; j <= n - 1; j++) {
- a[j] *= 2.0 / n;
- }
- .
-
-
-Appendix :
- The cos/sin table is recalculated when the larger table required.
- w[] and ip[] are compatible with all routines.
-*/
-
-
-void cdft(int n, int isgn, double *a, int *ip, double *w)
-{
- void makewt(int nw, int *ip, double *w);
- void cftfsub(int n, double *a, int *ip, int nw, double *w);
- void cftbsub(int n, double *a, int *ip, int nw, double *w);
- int nw;
-
- nw = ip[0];
- if (n > (nw << 2)) {
- nw = n >> 2;
- makewt(nw, ip, w);
- }
- if (isgn >= 0) {
- cftfsub(n, a, ip, nw, w);
- } else {
- cftbsub(n, a, ip, nw, w);
- }
-}
-
-
-void rdft(int n, int isgn, double *a, int *ip, double *w)
-{
- void makewt(int nw, int *ip, double *w);
- void makect(int nc, int *ip, double *c);
- void cftfsub(int n, double *a, int *ip, int nw, double *w);
- void cftbsub(int n, double *a, int *ip, int nw, double *w);
- void rftfsub(int n, double *a, int nc, double *c);
- void rftbsub(int n, double *a, int nc, double *c);
- int nw, nc;
- double xi;
-
- nw = ip[0];
- if (n > (nw << 2)) {
- nw = n >> 2;
- makewt(nw, ip, w);
- }
- nc = ip[1];
- if (n > (nc << 2)) {
- nc = n >> 2;
- makect(nc, ip, w + nw);
- }
- if (isgn >= 0) {
- if (n > 4) {
- cftfsub(n, a, ip, nw, w);
- rftfsub(n, a, nc, w + nw);
- } else if (n == 4) {
- cftfsub(n, a, ip, nw, w);
- }
- xi = a[0] - a[1];
- a[0] += a[1];
- a[1] = xi;
- } else {
- a[1] = 0.5 * (a[0] - a[1]);
- a[0] -= a[1];
- if (n > 4) {
- rftbsub(n, a, nc, w + nw);
- cftbsub(n, a, ip, nw, w);
- } else if (n == 4) {
- cftbsub(n, a, ip, nw, w);
- }
- }
-}
-
-
-void ddct(int n, int isgn, double *a, int *ip, double *w)
-{
- void makewt(int nw, int *ip, double *w);
- void makect(int nc, int *ip, double *c);
- void cftfsub(int n, double *a, int *ip, int nw, double *w);
- void cftbsub(int n, double *a, int *ip, int nw, double *w);
- void rftfsub(int n, double *a, int nc, double *c);
- void rftbsub(int n, double *a, int nc, double *c);
- void dctsub(int n, double *a, int nc, double *c);
- int j, nw, nc;
- double xr;
-
- nw = ip[0];
- if (n > (nw << 2)) {
- nw = n >> 2;
- makewt(nw, ip, w);
- }
- nc = ip[1];
- if (n > nc) {
- nc = n;
- makect(nc, ip, w + nw);
- }
- if (isgn < 0) {
- xr = a[n - 1];
- for (j = n - 2; j >= 2; j -= 2) {
- a[j + 1] = a[j] - a[j - 1];
- a[j] += a[j - 1];
- }
- a[1] = a[0] - xr;
- a[0] += xr;
- if (n > 4) {
- rftbsub(n, a, nc, w + nw);
- cftbsub(n, a, ip, nw, w);
- } else if (n == 4) {
- cftbsub(n, a, ip, nw, w);
- }
- }
- dctsub(n, a, nc, w + nw);
- if (isgn >= 0) {
- if (n > 4) {
- cftfsub(n, a, ip, nw, w);
- rftfsub(n, a, nc, w + nw);
- } else if (n == 4) {
- cftfsub(n, a, ip, nw, w);
- }
- xr = a[0] - a[1];
- a[0] += a[1];
- for (j = 2; j < n; j += 2) {
- a[j - 1] = a[j] - a[j + 1];
- a[j] += a[j + 1];
- }
- a[n - 1] = xr;
- }
-}
-
-
-void ddst(int n, int isgn, double *a, int *ip, double *w)
-{
- void makewt(int nw, int *ip, double *w);
- void makect(int nc, int *ip, double *c);
- void cftfsub(int n, double *a, int *ip, int nw, double *w);
- void cftbsub(int n, double *a, int *ip, int nw, double *w);
- void rftfsub(int n, double *a, int nc, double *c);
- void rftbsub(int n, double *a, int nc, double *c);
- void dstsub(int n, double *a, int nc, double *c);
- int j, nw, nc;
- double xr;
-
- nw = ip[0];
- if (n > (nw << 2)) {
- nw = n >> 2;
- makewt(nw, ip, w);
- }
- nc = ip[1];
- if (n > nc) {
- nc = n;
- makect(nc, ip, w + nw);
- }
- if (isgn < 0) {
- xr = a[n - 1];
- for (j = n - 2; j >= 2; j -= 2) {
- a[j + 1] = -a[j] - a[j - 1];
- a[j] -= a[j - 1];
- }
- a[1] = a[0] + xr;
- a[0] -= xr;
- if (n > 4) {
- rftbsub(n, a, nc, w + nw);
- cftbsub(n, a, ip, nw, w);
- } else if (n == 4) {
- cftbsub(n, a, ip, nw, w);
- }
- }
- dstsub(n, a, nc, w + nw);
- if (isgn >= 0) {
- if (n > 4) {
- cftfsub(n, a, ip, nw, w);
- rftfsub(n, a, nc, w + nw);
- } else if (n == 4) {
- cftfsub(n, a, ip, nw, w);
- }
- xr = a[0] - a[1];
- a[0] += a[1];
- for (j = 2; j < n; j += 2) {
- a[j - 1] = -a[j] - a[j + 1];
- a[j] -= a[j + 1];
- }
- a[n - 1] = -xr;
- }
-}
-
-
-void dfct(int n, double *a, double *t, int *ip, double *w)
-{
- void makewt(int nw, int *ip, double *w);
- void makect(int nc, int *ip, double *c);
- void cftfsub(int n, double *a, int *ip, int nw, double *w);
- void rftfsub(int n, double *a, int nc, double *c);
- void dctsub(int n, double *a, int nc, double *c);
- int j, k, l, m, mh, nw, nc;
- double xr, xi, yr, yi;
-
- nw = ip[0];
- if (n > (nw << 3)) {
- nw = n >> 3;
- makewt(nw, ip, w);
- }
- nc = ip[1];
- if (n > (nc << 1)) {
- nc = n >> 1;
- makect(nc, ip, w + nw);
- }
- m = n >> 1;
- yi = a[m];
- xi = a[0] + a[n];
- a[0] -= a[n];
- t[0] = xi - yi;
- t[m] = xi + yi;
- if (n > 2) {
- mh = m >> 1;
- for (j = 1; j < mh; j++) {
- k = m - j;
- xr = a[j] - a[n - j];
- xi = a[j] + a[n - j];
- yr = a[k] - a[n - k];
- yi = a[k] + a[n - k];
- a[j] = xr;
- a[k] = yr;
- t[j] = xi - yi;
- t[k] = xi + yi;
- }
- t[mh] = a[mh] + a[n - mh];
- a[mh] -= a[n - mh];
- dctsub(m, a, nc, w + nw);
- if (m > 4) {
- cftfsub(m, a, ip, nw, w);
- rftfsub(m, a, nc, w + nw);
- } else if (m == 4) {
- cftfsub(m, a, ip, nw, w);
- }
- a[n - 1] = a[0] - a[1];
- a[1] = a[0] + a[1];
- for (j = m - 2; j >= 2; j -= 2) {
- a[2 * j + 1] = a[j] + a[j + 1];
- a[2 * j - 1] = a[j] - a[j + 1];
- }
- l = 2;
- m = mh;
- while (m >= 2) {
- dctsub(m, t, nc, w + nw);
- if (m > 4) {
- cftfsub(m, t, ip, nw, w);
- rftfsub(m, t, nc, w + nw);
- } else if (m == 4) {
- cftfsub(m, t, ip, nw, w);
- }
- a[n - l] = t[0] - t[1];
- a[l] = t[0] + t[1];
- k = 0;
- for (j = 2; j < m; j += 2) {
- k += l << 2;
- a[k - l] = t[j] - t[j + 1];
- a[k + l] = t[j] + t[j + 1];
- }
- l <<= 1;
- mh = m >> 1;
- for (j = 0; j < mh; j++) {
- k = m - j;
- t[j] = t[m + k] - t[m + j];
- t[k] = t[m + k] + t[m + j];
- }
- t[mh] = t[m + mh];
- m = mh;
- }
- a[l] = t[0];
- a[n] = t[2] - t[1];
- a[0] = t[2] + t[1];
- } else {
- a[1] = a[0];
- a[2] = t[0];
- a[0] = t[1];
- }
-}
-
-
-void dfst(int n, double *a, double *t, int *ip, double *w)
-{
- void makewt(int nw, int *ip, double *w);
- void makect(int nc, int *ip, double *c);
- void cftfsub(int n, double *a, int *ip, int nw, double *w);
- void rftfsub(int n, double *a, int nc, double *c);
- void dstsub(int n, double *a, int nc, double *c);
- int j, k, l, m, mh, nw, nc;
- double xr, xi, yr, yi;
-
- nw = ip[0];
- if (n > (nw << 3)) {
- nw = n >> 3;
- makewt(nw, ip, w);
- }
- nc = ip[1];
- if (n > (nc << 1)) {
- nc = n >> 1;
- makect(nc, ip, w + nw);
- }
- if (n > 2) {
- m = n >> 1;
- mh = m >> 1;
- for (j = 1; j < mh; j++) {
- k = m - j;
- xr = a[j] + a[n - j];
- xi = a[j] - a[n - j];
- yr = a[k] + a[n - k];
- yi = a[k] - a[n - k];
- a[j] = xr;
- a[k] = yr;
- t[j] = xi + yi;
- t[k] = xi - yi;
- }
- t[0] = a[mh] - a[n - mh];
- a[mh] += a[n - mh];
- a[0] = a[m];
- dstsub(m, a, nc, w + nw);
- if (m > 4) {
- cftfsub(m, a, ip, nw, w);
- rftfsub(m, a, nc, w + nw);
- } else if (m == 4) {
- cftfsub(m, a, ip, nw, w);
- }
- a[n - 1] = a[1] - a[0];
- a[1] = a[0] + a[1];
- for (j = m - 2; j >= 2; j -= 2) {
- a[2 * j + 1] = a[j] - a[j + 1];
- a[2 * j - 1] = -a[j] - a[j + 1];
- }
- l = 2;
- m = mh;
- while (m >= 2) {
- dstsub(m, t, nc, w + nw);
- if (m > 4) {
- cftfsub(m, t, ip, nw, w);
- rftfsub(m, t, nc, w + nw);
- } else if (m == 4) {
- cftfsub(m, t, ip, nw, w);
- }
- a[n - l] = t[1] - t[0];
- a[l] = t[0] + t[1];
- k = 0;
- for (j = 2; j < m; j += 2) {
- k += l << 2;
- a[k - l] = -t[j] - t[j + 1];
- a[k + l] = t[j] - t[j + 1];
- }
- l <<= 1;
- mh = m >> 1;
- for (j = 1; j < mh; j++) {
- k = m - j;
- t[j] = t[m + k] + t[m + j];
- t[k] = t[m + k] - t[m + j];
- }
- t[0] = t[m + mh];
- m = mh;
- }
- a[l] = t[0];
- }
- a[0] = 0;
-}
-
-
-/* -------- initializing routines -------- */
-
-
-#include <math.h>
-
-void makewt(int nw, int *ip, double *w)
-{
- void makeipt(int nw, int *ip);
- int j, nwh, nw0, nw1;
- double delta, wn4r, wk1r, wk1i, wk3r, wk3i;
-
- ip[0] = nw;
- ip[1] = 1;
- if (nw > 2) {
- nwh = nw >> 1;
- delta = atan(1.0) / nwh;
- wn4r = cos(delta * nwh);
- w[0] = 1;
- w[1] = wn4r;
- if (nwh == 4) {
- w[2] = cos(delta * 2);
- w[3] = sin(delta * 2);
- } else if (nwh > 4) {
- makeipt(nw, ip);
- w[2] = 0.5 / cos(delta * 2);
- w[3] = 0.5 / cos(delta * 6);
- for (j = 4; j < nwh; j += 4) {
- w[j] = cos(delta * j);
- w[j + 1] = sin(delta * j);
- w[j + 2] = cos(3 * delta * j);
- w[j + 3] = -sin(3 * delta * j);
- }
- }
- nw0 = 0;
- while (nwh > 2) {
- nw1 = nw0 + nwh;
- nwh >>= 1;
- w[nw1] = 1;
- w[nw1 + 1] = wn4r;
- if (nwh == 4) {
- wk1r = w[nw0 + 4];
- wk1i = w[nw0 + 5];
- w[nw1 + 2] = wk1r;
- w[nw1 + 3] = wk1i;
- } else if (nwh > 4) {
- wk1r = w[nw0 + 4];
- wk3r = w[nw0 + 6];
- w[nw1 + 2] = 0.5 / wk1r;
- w[nw1 + 3] = 0.5 / wk3r;
- for (j = 4; j < nwh; j += 4) {
- wk1r = w[nw0 + 2 * j];
- wk1i = w[nw0 + 2 * j + 1];
- wk3r = w[nw0 + 2 * j + 2];
- wk3i = w[nw0 + 2 * j + 3];
- w[nw1 + j] = wk1r;
- w[nw1 + j + 1] = wk1i;
- w[nw1 + j + 2] = wk3r;
- w[nw1 + j + 3] = wk3i;
- }
- }
- nw0 = nw1;
- }
- }
-}
-
-
-void makeipt(int nw, int *ip)
-{
- int j, l, m, m2, p, q;
-
- ip[2] = 0;
- ip[3] = 16;
- m = 2;
- for (l = nw; l > 32; l >>= 2) {
- m2 = m << 1;
- q = m2 << 3;
- for (j = m; j < m2; j++) {
- p = ip[j] << 2;
- ip[m + j] = p;
- ip[m2 + j] = p + q;
- }
- m = m2;
- }
-}
-
-
-void makect(int nc, int *ip, double *c)
-{
- int j, nch;
- double delta;
-
- ip[1] = nc;
- if (nc > 1) {
- nch = nc >> 1;
- delta = atan(1.0) / nch;
- c[0] = cos(delta * nch);
- c[nch] = 0.5 * c[0];
- for (j = 1; j < nch; j++) {
- c[j] = 0.5 * cos(delta * j);
- c[nc - j] = 0.5 * sin(delta * j);
- }
- }
-}
-
-
-/* -------- child routines -------- */
-
-
-#ifdef USE_CDFT_PTHREADS
-#define USE_CDFT_THREADS
-#ifndef CDFT_THREADS_BEGIN_N
-#define CDFT_THREADS_BEGIN_N 8192
-#endif
-#ifndef CDFT_4THREADS_BEGIN_N
-#define CDFT_4THREADS_BEGIN_N 65536
-#endif
-#include <pthread.h>
-#include <stdio.h>
-#include <stdlib.h>
-#define cdft_thread_t pthread_t
-#define cdft_thread_create(thp,func,argp) { \
- if (pthread_create(thp, NULL, func, (void *) argp) != 0) { \
- fprintf(stderr, "cdft thread error\n"); \
- exit(1); \
- } \
-}
-#define cdft_thread_wait(th) { \
- if (pthread_join(th, NULL) != 0) { \
- fprintf(stderr, "cdft thread error\n"); \
- exit(1); \
- } \
-}
-#endif /* USE_CDFT_PTHREADS */
-
-
-#ifdef USE_CDFT_WINTHREADS
-#define USE_CDFT_THREADS
-#ifndef CDFT_THREADS_BEGIN_N
-#define CDFT_THREADS_BEGIN_N 32768
-#endif
-#ifndef CDFT_4THREADS_BEGIN_N
-#define CDFT_4THREADS_BEGIN_N 524288
-#endif
-#include <windows.h>
-#include <stdio.h>
-#include <stdlib.h>
-#define cdft_thread_t HANDLE
-#define cdft_thread_create(thp,func,argp) { \
- DWORD thid; \
- *(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, (LPVOID) argp, 0, &thid); \
- if (*(thp) == 0) { \
- fprintf(stderr, "cdft thread error\n"); \
- exit(1); \
- } \
-}
-#define cdft_thread_wait(th) { \
- WaitForSingleObject(th, INFINITE); \
- CloseHandle(th); \
-}
-#endif /* USE_CDFT_WINTHREADS */
-
-
-void cftfsub(int n, double *a, int *ip, int nw, double *w)
-{
- void bitrv2(int n, int *ip, double *a);
- void bitrv216(double *a);
- void bitrv208(double *a);
- void cftf1st(int n, double *a, double *w);
- void cftrec4(int n, double *a, int nw, double *w);
- void cftleaf(int n, int isplt, double *a, int nw, double *w);
- void cftfx41(int n, double *a, int nw, double *w);
- void cftf161(double *a, double *w);
- void cftf081(double *a, double *w);
- void cftf040(double *a);
- void cftx020(double *a);
-#ifdef USE_CDFT_THREADS
- void cftrec4_th(int n, double *a, int nw, double *w);
-#endif /* USE_CDFT_THREADS */
-
- if (n > 8) {
- if (n > 32) {
- cftf1st(n, a, &w[nw - (n >> 2)]);
-#ifdef USE_CDFT_THREADS
- if (n > CDFT_THREADS_BEGIN_N) {
- cftrec4_th(n, a, nw, w);
- } else
-#endif /* USE_CDFT_THREADS */
- if (n > 512) {
- cftrec4(n, a, nw, w);
- } else if (n > 128) {
- cftleaf(n, 1, a, nw, w);
- } else {
- cftfx41(n, a, nw, w);
- }
- bitrv2(n, ip, a);
- } else if (n == 32) {
- cftf161(a, &w[nw - 8]);
- bitrv216(a);
- } else {
- cftf081(a, w);
- bitrv208(a);
- }
- } else if (n == 8) {
- cftf040(a);
- } else if (n == 4) {
- cftx020(a);
- }
-}
-
-
-void cftbsub(int n, double *a, int *ip, int nw, double *w)
-{
- void bitrv2conj(int n, int *ip, double *a);
- void bitrv216neg(double *a);
- void bitrv208neg(double *a);
- void cftb1st(int n, double *a, double *w);
- void cftrec4(int n, double *a, int nw, double *w);
- void cftleaf(int n, int isplt, double *a, int nw, double *w);
- void cftfx41(int n, double *a, int nw, double *w);
- void cftf161(double *a, double *w);
- void cftf081(double *a, double *w);
- void cftb040(double *a);
- void cftx020(double *a);
-#ifdef USE_CDFT_THREADS
- void cftrec4_th(int n, double *a, int nw, double *w);
-#endif /* USE_CDFT_THREADS */
-
- if (n > 8) {
- if (n > 32) {
- cftb1st(n, a, &w[nw - (n >> 2)]);
-#ifdef USE_CDFT_THREADS
- if (n > CDFT_THREADS_BEGIN_N) {
- cftrec4_th(n, a, nw, w);
- } else
-#endif /* USE_CDFT_THREADS */
- if (n > 512) {
- cftrec4(n, a, nw, w);
- } else if (n > 128) {
- cftleaf(n, 1, a, nw, w);
- } else {
- cftfx41(n, a, nw, w);
- }
- bitrv2conj(n, ip, a);
- } else if (n == 32) {
- cftf161(a, &w[nw - 8]);
- bitrv216neg(a);
- } else {
- cftf081(a, w);
- bitrv208neg(a);
- }
- } else if (n == 8) {
- cftb040(a);
- } else if (n == 4) {
- cftx020(a);
- }
-}
-
-
-void bitrv2(int n, int *ip, double *a)
-{
- int j, j1, k, k1, l, m, nh, nm;
- double xr, xi, yr, yi;
-
- m = 1;
- for (l = n >> 2; l > 8; l >>= 2) {
- m <<= 1;
- }
- nh = n >> 1;
- nm = 4 * m;
- if (l == 8) {
- for (k = 0; k < m; k++) {
- for (j = 0; j < k; j++) {
- j1 = 4 * j + 2 * ip[m + k];
- k1 = 4 * k + 2 * ip[m + j];
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += 2 * nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 -= nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += 2 * nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nh;
- k1 += 2;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= 2 * nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 += nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= 2 * nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += 2;
- k1 += nh;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += 2 * nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 -= nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += 2 * nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nh;
- k1 -= 2;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= 2 * nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 += nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= 2 * nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- }
- k1 = 4 * k + 2 * ip[m + k];
- j1 = k1 + 2;
- k1 += nh;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += 2 * nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 -= nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= 2;
- k1 -= nh;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nh + 2;
- k1 += nh + 2;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nh - nm;
- k1 += 2 * nm - 2;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- }
- } else {
- for (k = 0; k < m; k++) {
- for (j = 0; j < k; j++) {
- j1 = 4 * j + ip[m + k];
- k1 = 4 * k + ip[m + j];
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nh;
- k1 += 2;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += 2;
- k1 += nh;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nh;
- k1 -= 2;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- }
- k1 = 4 * k + ip[m + k];
- j1 = k1 + 2;
- k1 += nh;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += nm;
- xr = a[j1];
- xi = a[j1 + 1];
- yr = a[k1];
- yi = a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- }
- }
-}
-
-
-void bitrv2conj(int n, int *ip, double *a)
-{
- int j, j1, k, k1, l, m, nh, nm;
- double xr, xi, yr, yi;
-
- m = 1;
- for (l = n >> 2; l > 8; l >>= 2) {
- m <<= 1;
- }
- nh = n >> 1;
- nm = 4 * m;
- if (l == 8) {
- for (k = 0; k < m; k++) {
- for (j = 0; j < k; j++) {
- j1 = 4 * j + 2 * ip[m + k];
- k1 = 4 * k + 2 * ip[m + j];
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += 2 * nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 -= nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += 2 * nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nh;
- k1 += 2;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= 2 * nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 += nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= 2 * nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += 2;
- k1 += nh;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += 2 * nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 -= nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += 2 * nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nh;
- k1 -= 2;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= 2 * nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 += nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= 2 * nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- }
- k1 = 4 * k + 2 * ip[m + k];
- j1 = k1 + 2;
- k1 += nh;
- a[j1 - 1] = -a[j1 - 1];
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- a[k1 + 3] = -a[k1 + 3];
- j1 += nm;
- k1 += 2 * nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 -= nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= 2;
- k1 -= nh;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nh + 2;
- k1 += nh + 2;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nh - nm;
- k1 += 2 * nm - 2;
- a[j1 - 1] = -a[j1 - 1];
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- a[k1 + 3] = -a[k1 + 3];
- }
- } else {
- for (k = 0; k < m; k++) {
- for (j = 0; j < k; j++) {
- j1 = 4 * j + ip[m + k];
- k1 = 4 * k + ip[m + j];
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nh;
- k1 += 2;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += 2;
- k1 += nh;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 += nm;
- k1 += nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nh;
- k1 -= 2;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- j1 -= nm;
- k1 -= nm;
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- }
- k1 = 4 * k + ip[m + k];
- j1 = k1 + 2;
- k1 += nh;
- a[j1 - 1] = -a[j1 - 1];
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- a[k1 + 3] = -a[k1 + 3];
- j1 += nm;
- k1 += nm;
- a[j1 - 1] = -a[j1 - 1];
- xr = a[j1];
- xi = -a[j1 + 1];
- yr = a[k1];
- yi = -a[k1 + 1];
- a[j1] = yr;
- a[j1 + 1] = yi;
- a[k1] = xr;
- a[k1 + 1] = xi;
- a[k1 + 3] = -a[k1 + 3];
- }
- }
-}
-
-
-void bitrv216(double *a)
-{
- double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
- x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i,
- x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i;
-
- x1r = a[2];
- x1i = a[3];
- x2r = a[4];
- x2i = a[5];
- x3r = a[6];
- x3i = a[7];
- x4r = a[8];
- x4i = a[9];
- x5r = a[10];
- x5i = a[11];
- x7r = a[14];
- x7i = a[15];
- x8r = a[16];
- x8i = a[17];
- x10r = a[20];
- x10i = a[21];
- x11r = a[22];
- x11i = a[23];
- x12r = a[24];
- x12i = a[25];
- x13r = a[26];
- x13i = a[27];
- x14r = a[28];
- x14i = a[29];
- a[2] = x8r;
- a[3] = x8i;
- a[4] = x4r;
- a[5] = x4i;
- a[6] = x12r;
- a[7] = x12i;
- a[8] = x2r;
- a[9] = x2i;
- a[10] = x10r;
- a[11] = x10i;
- a[14] = x14r;
- a[15] = x14i;
- a[16] = x1r;
- a[17] = x1i;
- a[20] = x5r;
- a[21] = x5i;
- a[22] = x13r;
- a[23] = x13i;
- a[24] = x3r;
- a[25] = x3i;
- a[26] = x11r;
- a[27] = x11i;
- a[28] = x7r;
- a[29] = x7i;
-}
-
-
-void bitrv216neg(double *a)
-{
- double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
- x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i,
- x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i,
- x13r, x13i, x14r, x14i, x15r, x15i;
-
- x1r = a[2];
- x1i = a[3];
- x2r = a[4];
- x2i = a[5];
- x3r = a[6];
- x3i = a[7];
- x4r = a[8];
- x4i = a[9];
- x5r = a[10];
- x5i = a[11];
- x6r = a[12];
- x6i = a[13];
- x7r = a[14];
- x7i = a[15];
- x8r = a[16];
- x8i = a[17];
- x9r = a[18];
- x9i = a[19];
- x10r = a[20];
- x10i = a[21];
- x11r = a[22];
- x11i = a[23];
- x12r = a[24];
- x12i = a[25];
- x13r = a[26];
- x13i = a[27];
- x14r = a[28];
- x14i = a[29];
- x15r = a[30];
- x15i = a[31];
- a[2] = x15r;
- a[3] = x15i;
- a[4] = x7r;
- a[5] = x7i;
- a[6] = x11r;
- a[7] = x11i;
- a[8] = x3r;
- a[9] = x3i;
- a[10] = x13r;
- a[11] = x13i;
- a[12] = x5r;
- a[13] = x5i;
- a[14] = x9r;
- a[15] = x9i;
- a[16] = x1r;
- a[17] = x1i;
- a[18] = x14r;
- a[19] = x14i;
- a[20] = x6r;
- a[21] = x6i;
- a[22] = x10r;
- a[23] = x10i;
- a[24] = x2r;
- a[25] = x2i;
- a[26] = x12r;
- a[27] = x12i;
- a[28] = x4r;
- a[29] = x4i;
- a[30] = x8r;
- a[31] = x8i;
-}
-
-
-void bitrv208(double *a)
-{
- double x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i;
-
- x1r = a[2];
- x1i = a[3];
- x3r = a[6];
- x3i = a[7];
- x4r = a[8];
- x4i = a[9];
- x6r = a[12];
- x6i = a[13];
- a[2] = x4r;
- a[3] = x4i;
- a[6] = x6r;
- a[7] = x6i;
- a[8] = x1r;
- a[9] = x1i;
- a[12] = x3r;
- a[13] = x3i;
-}
-
-
-void bitrv208neg(double *a)
-{
- double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
- x5r, x5i, x6r, x6i, x7r, x7i;
-
- x1r = a[2];
- x1i = a[3];
- x2r = a[4];
- x2i = a[5];
- x3r = a[6];
- x3i = a[7];
- x4r = a[8];
- x4i = a[9];
- x5r = a[10];
- x5i = a[11];
- x6r = a[12];
- x6i = a[13];
- x7r = a[14];
- x7i = a[15];
- a[2] = x7r;
- a[3] = x7i;
- a[4] = x3r;
- a[5] = x3i;
- a[6] = x5r;
- a[7] = x5i;
- a[8] = x1r;
- a[9] = x1i;
- a[10] = x6r;
- a[11] = x6i;
- a[12] = x2r;
- a[13] = x2i;
- a[14] = x4r;
- a[15] = x4i;
-}
-
-
-void cftf1st(int n, double *a, double *w)
-{
- int j, j0, j1, j2, j3, k, m, mh;
- double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
- wd1r, wd1i, wd3r, wd3i;
- double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
- y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
-
- mh = n >> 3;
- m = 2 * mh;
- j1 = m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[0] + a[j2];
- x0i = a[1] + a[j2 + 1];
- x1r = a[0] - a[j2];
- x1i = a[1] - a[j2 + 1];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- a[0] = x0r + x2r;
- a[1] = x0i + x2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i - x2i;
- a[j2] = x1r - x3i;
- a[j2 + 1] = x1i + x3r;
- a[j3] = x1r + x3i;
- a[j3 + 1] = x1i - x3r;
- wn4r = w[1];
- csc1 = w[2];
- csc3 = w[3];
- wd1r = 1;
- wd1i = 0;
- wd3r = 1;
- wd3i = 0;
- k = 0;
- for (j = 2; j < mh - 2; j += 4) {
- k += 4;
- wk1r = csc1 * (wd1r + w[k]);
- wk1i = csc1 * (wd1i + w[k + 1]);
- wk3r = csc3 * (wd3r + w[k + 2]);
- wk3i = csc3 * (wd3i + w[k + 3]);
- wd1r = w[k];
- wd1i = w[k + 1];
- wd3r = w[k + 2];
- wd3i = w[k + 3];
- j1 = j + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j] + a[j2];
- x0i = a[j + 1] + a[j2 + 1];
- x1r = a[j] - a[j2];
- x1i = a[j + 1] - a[j2 + 1];
- y0r = a[j + 2] + a[j2 + 2];
- y0i = a[j + 3] + a[j2 + 3];
- y1r = a[j + 2] - a[j2 + 2];
- y1i = a[j + 3] - a[j2 + 3];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- y2r = a[j1 + 2] + a[j3 + 2];
- y2i = a[j1 + 3] + a[j3 + 3];
- y3r = a[j1 + 2] - a[j3 + 2];
- y3i = a[j1 + 3] - a[j3 + 3];
- a[j] = x0r + x2r;
- a[j + 1] = x0i + x2i;
- a[j + 2] = y0r + y2r;
- a[j + 3] = y0i + y2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i - x2i;
- a[j1 + 2] = y0r - y2r;
- a[j1 + 3] = y0i - y2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- a[j2] = wk1r * x0r - wk1i * x0i;
- a[j2 + 1] = wk1r * x0i + wk1i * x0r;
- x0r = y1r - y3i;
- x0i = y1i + y3r;
- a[j2 + 2] = wd1r * x0r - wd1i * x0i;
- a[j2 + 3] = wd1r * x0i + wd1i * x0r;
- x0r = x1r + x3i;
- x0i = x1i - x3r;
- a[j3] = wk3r * x0r + wk3i * x0i;
- a[j3 + 1] = wk3r * x0i - wk3i * x0r;
- x0r = y1r + y3i;
- x0i = y1i - y3r;
- a[j3 + 2] = wd3r * x0r + wd3i * x0i;
- a[j3 + 3] = wd3r * x0i - wd3i * x0r;
- j0 = m - j;
- j1 = j0 + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j0] + a[j2];
- x0i = a[j0 + 1] + a[j2 + 1];
- x1r = a[j0] - a[j2];
- x1i = a[j0 + 1] - a[j2 + 1];
- y0r = a[j0 - 2] + a[j2 - 2];
- y0i = a[j0 - 1] + a[j2 - 1];
- y1r = a[j0 - 2] - a[j2 - 2];
- y1i = a[j0 - 1] - a[j2 - 1];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- y2r = a[j1 - 2] + a[j3 - 2];
- y2i = a[j1 - 1] + a[j3 - 1];
- y3r = a[j1 - 2] - a[j3 - 2];
- y3i = a[j1 - 1] - a[j3 - 1];
- a[j0] = x0r + x2r;
- a[j0 + 1] = x0i + x2i;
- a[j0 - 2] = y0r + y2r;
- a[j0 - 1] = y0i + y2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i - x2i;
- a[j1 - 2] = y0r - y2r;
- a[j1 - 1] = y0i - y2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- a[j2] = wk1i * x0r - wk1r * x0i;
- a[j2 + 1] = wk1i * x0i + wk1r * x0r;
- x0r = y1r - y3i;
- x0i = y1i + y3r;
- a[j2 - 2] = wd1i * x0r - wd1r * x0i;
- a[j2 - 1] = wd1i * x0i + wd1r * x0r;
- x0r = x1r + x3i;
- x0i = x1i - x3r;
- a[j3] = wk3i * x0r + wk3r * x0i;
- a[j3 + 1] = wk3i * x0i - wk3r * x0r;
- x0r = y1r + y3i;
- x0i = y1i - y3r;
- a[j3 - 2] = wd3i * x0r + wd3r * x0i;
- a[j3 - 1] = wd3i * x0i - wd3r * x0r;
- }
- wk1r = csc1 * (wd1r + wn4r);
- wk1i = csc1 * (wd1i + wn4r);
- wk3r = csc3 * (wd3r - wn4r);
- wk3i = csc3 * (wd3i - wn4r);
- j0 = mh;
- j1 = j0 + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j0 - 2] + a[j2 - 2];
- x0i = a[j0 - 1] + a[j2 - 1];
- x1r = a[j0 - 2] - a[j2 - 2];
- x1i = a[j0 - 1] - a[j2 - 1];
- x2r = a[j1 - 2] + a[j3 - 2];
- x2i = a[j1 - 1] + a[j3 - 1];
- x3r = a[j1 - 2] - a[j3 - 2];
- x3i = a[j1 - 1] - a[j3 - 1];
- a[j0 - 2] = x0r + x2r;
- a[j0 - 1] = x0i + x2i;
- a[j1 - 2] = x0r - x2r;
- a[j1 - 1] = x0i - x2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- a[j2 - 2] = wk1r * x0r - wk1i * x0i;
- a[j2 - 1] = wk1r * x0i + wk1i * x0r;
- x0r = x1r + x3i;
- x0i = x1i - x3r;
- a[j3 - 2] = wk3r * x0r + wk3i * x0i;
- a[j3 - 1] = wk3r * x0i - wk3i * x0r;
- x0r = a[j0] + a[j2];
- x0i = a[j0 + 1] + a[j2 + 1];
- x1r = a[j0] - a[j2];
- x1i = a[j0 + 1] - a[j2 + 1];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- a[j0] = x0r + x2r;
- a[j0 + 1] = x0i + x2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i - x2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- a[j2] = wn4r * (x0r - x0i);
- a[j2 + 1] = wn4r * (x0i + x0r);
- x0r = x1r + x3i;
- x0i = x1i - x3r;
- a[j3] = -wn4r * (x0r + x0i);
- a[j3 + 1] = -wn4r * (x0i - x0r);
- x0r = a[j0 + 2] + a[j2 + 2];
- x0i = a[j0 + 3] + a[j2 + 3];
- x1r = a[j0 + 2] - a[j2 + 2];
- x1i = a[j0 + 3] - a[j2 + 3];
- x2r = a[j1 + 2] + a[j3 + 2];
- x2i = a[j1 + 3] + a[j3 + 3];
- x3r = a[j1 + 2] - a[j3 + 2];
- x3i = a[j1 + 3] - a[j3 + 3];
- a[j0 + 2] = x0r + x2r;
- a[j0 + 3] = x0i + x2i;
- a[j1 + 2] = x0r - x2r;
- a[j1 + 3] = x0i - x2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- a[j2 + 2] = wk1i * x0r - wk1r * x0i;
- a[j2 + 3] = wk1i * x0i + wk1r * x0r;
- x0r = x1r + x3i;
- x0i = x1i - x3r;
- a[j3 + 2] = wk3i * x0r + wk3r * x0i;
- a[j3 + 3] = wk3i * x0i - wk3r * x0r;
-}
-
-
-void cftb1st(int n, double *a, double *w)
-{
- int j, j0, j1, j2, j3, k, m, mh;
- double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
- wd1r, wd1i, wd3r, wd3i;
- double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
- y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
-
- mh = n >> 3;
- m = 2 * mh;
- j1 = m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[0] + a[j2];
- x0i = -a[1] - a[j2 + 1];
- x1r = a[0] - a[j2];
- x1i = -a[1] + a[j2 + 1];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- a[0] = x0r + x2r;
- a[1] = x0i - x2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i + x2i;
- a[j2] = x1r + x3i;
- a[j2 + 1] = x1i + x3r;
- a[j3] = x1r - x3i;
- a[j3 + 1] = x1i - x3r;
- wn4r = w[1];
- csc1 = w[2];
- csc3 = w[3];
- wd1r = 1;
- wd1i = 0;
- wd3r = 1;
- wd3i = 0;
- k = 0;
- for (j = 2; j < mh - 2; j += 4) {
- k += 4;
- wk1r = csc1 * (wd1r + w[k]);
- wk1i = csc1 * (wd1i + w[k + 1]);
- wk3r = csc3 * (wd3r + w[k + 2]);
- wk3i = csc3 * (wd3i + w[k + 3]);
- wd1r = w[k];
- wd1i = w[k + 1];
- wd3r = w[k + 2];
- wd3i = w[k + 3];
- j1 = j + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j] + a[j2];
- x0i = -a[j + 1] - a[j2 + 1];
- x1r = a[j] - a[j2];
- x1i = -a[j + 1] + a[j2 + 1];
- y0r = a[j + 2] + a[j2 + 2];
- y0i = -a[j + 3] - a[j2 + 3];
- y1r = a[j + 2] - a[j2 + 2];
- y1i = -a[j + 3] + a[j2 + 3];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- y2r = a[j1 + 2] + a[j3 + 2];
- y2i = a[j1 + 3] + a[j3 + 3];
- y3r = a[j1 + 2] - a[j3 + 2];
- y3i = a[j1 + 3] - a[j3 + 3];
- a[j] = x0r + x2r;
- a[j + 1] = x0i - x2i;
- a[j + 2] = y0r + y2r;
- a[j + 3] = y0i - y2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i + x2i;
- a[j1 + 2] = y0r - y2r;
- a[j1 + 3] = y0i + y2i;
- x0r = x1r + x3i;
- x0i = x1i + x3r;
- a[j2] = wk1r * x0r - wk1i * x0i;
- a[j2 + 1] = wk1r * x0i + wk1i * x0r;
- x0r = y1r + y3i;
- x0i = y1i + y3r;
- a[j2 + 2] = wd1r * x0r - wd1i * x0i;
- a[j2 + 3] = wd1r * x0i + wd1i * x0r;
- x0r = x1r - x3i;
- x0i = x1i - x3r;
- a[j3] = wk3r * x0r + wk3i * x0i;
- a[j3 + 1] = wk3r * x0i - wk3i * x0r;
- x0r = y1r - y3i;
- x0i = y1i - y3r;
- a[j3 + 2] = wd3r * x0r + wd3i * x0i;
- a[j3 + 3] = wd3r * x0i - wd3i * x0r;
- j0 = m - j;
- j1 = j0 + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j0] + a[j2];
- x0i = -a[j0 + 1] - a[j2 + 1];
- x1r = a[j0] - a[j2];
- x1i = -a[j0 + 1] + a[j2 + 1];
- y0r = a[j0 - 2] + a[j2 - 2];
- y0i = -a[j0 - 1] - a[j2 - 1];
- y1r = a[j0 - 2] - a[j2 - 2];
- y1i = -a[j0 - 1] + a[j2 - 1];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- y2r = a[j1 - 2] + a[j3 - 2];
- y2i = a[j1 - 1] + a[j3 - 1];
- y3r = a[j1 - 2] - a[j3 - 2];
- y3i = a[j1 - 1] - a[j3 - 1];
- a[j0] = x0r + x2r;
- a[j0 + 1] = x0i - x2i;
- a[j0 - 2] = y0r + y2r;
- a[j0 - 1] = y0i - y2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i + x2i;
- a[j1 - 2] = y0r - y2r;
- a[j1 - 1] = y0i + y2i;
- x0r = x1r + x3i;
- x0i = x1i + x3r;
- a[j2] = wk1i * x0r - wk1r * x0i;
- a[j2 + 1] = wk1i * x0i + wk1r * x0r;
- x0r = y1r + y3i;
- x0i = y1i + y3r;
- a[j2 - 2] = wd1i * x0r - wd1r * x0i;
- a[j2 - 1] = wd1i * x0i + wd1r * x0r;
- x0r = x1r - x3i;
- x0i = x1i - x3r;
- a[j3] = wk3i * x0r + wk3r * x0i;
- a[j3 + 1] = wk3i * x0i - wk3r * x0r;
- x0r = y1r - y3i;
- x0i = y1i - y3r;
- a[j3 - 2] = wd3i * x0r + wd3r * x0i;
- a[j3 - 1] = wd3i * x0i - wd3r * x0r;
- }
- wk1r = csc1 * (wd1r + wn4r);
- wk1i = csc1 * (wd1i + wn4r);
- wk3r = csc3 * (wd3r - wn4r);
- wk3i = csc3 * (wd3i - wn4r);
- j0 = mh;
- j1 = j0 + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j0 - 2] + a[j2 - 2];
- x0i = -a[j0 - 1] - a[j2 - 1];
- x1r = a[j0 - 2] - a[j2 - 2];
- x1i = -a[j0 - 1] + a[j2 - 1];
- x2r = a[j1 - 2] + a[j3 - 2];
- x2i = a[j1 - 1] + a[j3 - 1];
- x3r = a[j1 - 2] - a[j3 - 2];
- x3i = a[j1 - 1] - a[j3 - 1];
- a[j0 - 2] = x0r + x2r;
- a[j0 - 1] = x0i - x2i;
- a[j1 - 2] = x0r - x2r;
- a[j1 - 1] = x0i + x2i;
- x0r = x1r + x3i;
- x0i = x1i + x3r;
- a[j2 - 2] = wk1r * x0r - wk1i * x0i;
- a[j2 - 1] = wk1r * x0i + wk1i * x0r;
- x0r = x1r - x3i;
- x0i = x1i - x3r;
- a[j3 - 2] = wk3r * x0r + wk3i * x0i;
- a[j3 - 1] = wk3r * x0i - wk3i * x0r;
- x0r = a[j0] + a[j2];
- x0i = -a[j0 + 1] - a[j2 + 1];
- x1r = a[j0] - a[j2];
- x1i = -a[j0 + 1] + a[j2 + 1];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- a[j0] = x0r + x2r;
- a[j0 + 1] = x0i - x2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i + x2i;
- x0r = x1r + x3i;
- x0i = x1i + x3r;
- a[j2] = wn4r * (x0r - x0i);
- a[j2 + 1] = wn4r * (x0i + x0r);
- x0r = x1r - x3i;
- x0i = x1i - x3r;
- a[j3] = -wn4r * (x0r + x0i);
- a[j3 + 1] = -wn4r * (x0i - x0r);
- x0r = a[j0 + 2] + a[j2 + 2];
- x0i = -a[j0 + 3] - a[j2 + 3];
- x1r = a[j0 + 2] - a[j2 + 2];
- x1i = -a[j0 + 3] + a[j2 + 3];
- x2r = a[j1 + 2] + a[j3 + 2];
- x2i = a[j1 + 3] + a[j3 + 3];
- x3r = a[j1 + 2] - a[j3 + 2];
- x3i = a[j1 + 3] - a[j3 + 3];
- a[j0 + 2] = x0r + x2r;
- a[j0 + 3] = x0i - x2i;
- a[j1 + 2] = x0r - x2r;
- a[j1 + 3] = x0i + x2i;
- x0r = x1r + x3i;
- x0i = x1i + x3r;
- a[j2 + 2] = wk1i * x0r - wk1r * x0i;
- a[j2 + 3] = wk1i * x0i + wk1r * x0r;
- x0r = x1r - x3i;
- x0i = x1i - x3r;
- a[j3 + 2] = wk3i * x0r + wk3r * x0i;
- a[j3 + 3] = wk3i * x0i - wk3r * x0r;
-}
-
-
-#ifdef USE_CDFT_THREADS
-struct cdft_arg_st {
- int n0;
- int n;
- double *a;
- int nw;
- double *w;
-};
-typedef struct cdft_arg_st cdft_arg_t;
-
-
-void cftrec4_th(int n, double *a, int nw, double *w)
-{
- void *cftrec1_th(void *p);
- void *cftrec2_th(void *p);
- int i, idiv4, m, nthread;
- cdft_thread_t th[4];
- cdft_arg_t ag[4];
-
- nthread = 2;
- idiv4 = 0;
- m = n >> 1;
- if (n > CDFT_4THREADS_BEGIN_N) {
- nthread = 4;
- idiv4 = 1;
- m >>= 1;
- }
- for (i = 0; i < nthread; i++) {
- ag[i].n0 = n;
- ag[i].n = m;
- ag[i].a = &a[i * m];
- ag[i].nw = nw;
- ag[i].w = w;
- if (i != idiv4) {
- cdft_thread_create(&th[i], cftrec1_th, &ag[i]);
- } else {
- cdft_thread_create(&th[i], cftrec2_th, &ag[i]);
- }
- }
- for (i = 0; i < nthread; i++) {
- cdft_thread_wait(th[i]);
- }
-}
-
-
-void *cftrec1_th(void *p)
-{
- int cfttree(int n, int j, int k, double *a, int nw, double *w);
- void cftleaf(int n, int isplt, double *a, int nw, double *w);
- void cftmdl1(int n, double *a, double *w);
- int isplt, j, k, m, n, n0, nw;
- double *a, *w;
-
- n0 = ((cdft_arg_t *) p)->n0;
- n = ((cdft_arg_t *) p)->n;
- a = ((cdft_arg_t *) p)->a;
- nw = ((cdft_arg_t *) p)->nw;
- w = ((cdft_arg_t *) p)->w;
- m = n0;
- while (m > 512) {
- m >>= 2;
- cftmdl1(m, &a[n - m], &w[nw - (m >> 1)]);
- }
- cftleaf(m, 1, &a[n - m], nw, w);
- k = 0;
- for (j = n - m; j > 0; j -= m) {
- k++;
- isplt = cfttree(m, j, k, a, nw, w);
- cftleaf(m, isplt, &a[j - m], nw, w);
- }
- return (void *) 0;
-}
-
-
-void *cftrec2_th(void *p)
-{
- int cfttree(int n, int j, int k, double *a, int nw, double *w);
- void cftleaf(int n, int isplt, double *a, int nw, double *w);
- void cftmdl2(int n, double *a, double *w);
- int isplt, j, k, m, n, n0, nw;
- double *a, *w;
-
- n0 = ((cdft_arg_t *) p)->n0;
- n = ((cdft_arg_t *) p)->n;
- a = ((cdft_arg_t *) p)->a;
- nw = ((cdft_arg_t *) p)->nw;
- w = ((cdft_arg_t *) p)->w;
- k = 1;
- m = n0;
- while (m > 512) {
- m >>= 2;
- k <<= 2;
- cftmdl2(m, &a[n - m], &w[nw - m]);
- }
- cftleaf(m, 0, &a[n - m], nw, w);
- k >>= 1;
- for (j = n - m; j > 0; j -= m) {
- k++;
- isplt = cfttree(m, j, k, a, nw, w);
- cftleaf(m, isplt, &a[j - m], nw, w);
- }
- return (void *) 0;
-}
-#endif /* USE_CDFT_THREADS */
-
-
-void cftrec4(int n, double *a, int nw, double *w)
-{
- int cfttree(int n, int j, int k, double *a, int nw, double *w);
- void cftleaf(int n, int isplt, double *a, int nw, double *w);
- void cftmdl1(int n, double *a, double *w);
- int isplt, j, k, m;
-
- m = n;
- while (m > 512) {
- m >>= 2;
- cftmdl1(m, &a[n - m], &w[nw - (m >> 1)]);
- }
- cftleaf(m, 1, &a[n - m], nw, w);
- k = 0;
- for (j = n - m; j > 0; j -= m) {
- k++;
- isplt = cfttree(m, j, k, a, nw, w);
- cftleaf(m, isplt, &a[j - m], nw, w);
- }
-}
-
-
-int cfttree(int n, int j, int k, double *a, int nw, double *w)
-{
- void cftmdl1(int n, double *a, double *w);
- void cftmdl2(int n, double *a, double *w);
- int i, isplt, m;
-
- if ((k & 3) != 0) {
- isplt = k & 1;
- if (isplt != 0) {
- cftmdl1(n, &a[j - n], &w[nw - (n >> 1)]);
- } else {
- cftmdl2(n, &a[j - n], &w[nw - n]);
- }
- } else {
- m = n;
- for (i = k; (i & 3) == 0; i >>= 2) {
- m <<= 2;
- }
- isplt = i & 1;
- if (isplt != 0) {
- while (m > 128) {
- cftmdl1(m, &a[j - m], &w[nw - (m >> 1)]);
- m >>= 2;
- }
- } else {
- while (m > 128) {
- cftmdl2(m, &a[j - m], &w[nw - m]);
- m >>= 2;
- }
- }
- }
- return isplt;
-}
-
-
-void cftleaf(int n, int isplt, double *a, int nw, double *w)
-{
- void cftmdl1(int n, double *a, double *w);
- void cftmdl2(int n, double *a, double *w);
- void cftf161(double *a, double *w);
- void cftf162(double *a, double *w);
- void cftf081(double *a, double *w);
- void cftf082(double *a, double *w);
-
- if (n == 512) {
- cftmdl1(128, a, &w[nw - 64]);
- cftf161(a, &w[nw - 8]);
- cftf162(&a[32], &w[nw - 32]);
- cftf161(&a[64], &w[nw - 8]);
- cftf161(&a[96], &w[nw - 8]);
- cftmdl2(128, &a[128], &w[nw - 128]);
- cftf161(&a[128], &w[nw - 8]);
- cftf162(&a[160], &w[nw - 32]);
- cftf161(&a[192], &w[nw - 8]);
- cftf162(&a[224], &w[nw - 32]);
- cftmdl1(128, &a[256], &w[nw - 64]);
- cftf161(&a[256], &w[nw - 8]);
- cftf162(&a[288], &w[nw - 32]);
- cftf161(&a[320], &w[nw - 8]);
- cftf161(&a[352], &w[nw - 8]);
- if (isplt != 0) {
- cftmdl1(128, &a[384], &w[nw - 64]);
- cftf161(&a[480], &w[nw - 8]);
- } else {
- cftmdl2(128, &a[384], &w[nw - 128]);
- cftf162(&a[480], &w[nw - 32]);
- }
- cftf161(&a[384], &w[nw - 8]);
- cftf162(&a[416], &w[nw - 32]);
- cftf161(&a[448], &w[nw - 8]);
- } else {
- cftmdl1(64, a, &w[nw - 32]);
- cftf081(a, &w[nw - 8]);
- cftf082(&a[16], &w[nw - 8]);
- cftf081(&a[32], &w[nw - 8]);
- cftf081(&a[48], &w[nw - 8]);
- cftmdl2(64, &a[64], &w[nw - 64]);
- cftf081(&a[64], &w[nw - 8]);
- cftf082(&a[80], &w[nw - 8]);
- cftf081(&a[96], &w[nw - 8]);
- cftf082(&a[112], &w[nw - 8]);
- cftmdl1(64, &a[128], &w[nw - 32]);
- cftf081(&a[128], &w[nw - 8]);
- cftf082(&a[144], &w[nw - 8]);
- cftf081(&a[160], &w[nw - 8]);
- cftf081(&a[176], &w[nw - 8]);
- if (isplt != 0) {
- cftmdl1(64, &a[192], &w[nw - 32]);
- cftf081(&a[240], &w[nw - 8]);
- } else {
- cftmdl2(64, &a[192], &w[nw - 64]);
- cftf082(&a[240], &w[nw - 8]);
- }
- cftf081(&a[192], &w[nw - 8]);
- cftf082(&a[208], &w[nw - 8]);
- cftf081(&a[224], &w[nw - 8]);
- }
-}
-
-
-void cftmdl1(int n, double *a, double *w)
-{
- int j, j0, j1, j2, j3, k, m, mh;
- double wn4r, wk1r, wk1i, wk3r, wk3i;
- double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
-
- mh = n >> 3;
- m = 2 * mh;
- j1 = m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[0] + a[j2];
- x0i = a[1] + a[j2 + 1];
- x1r = a[0] - a[j2];
- x1i = a[1] - a[j2 + 1];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- a[0] = x0r + x2r;
- a[1] = x0i + x2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i - x2i;
- a[j2] = x1r - x3i;
- a[j2 + 1] = x1i + x3r;
- a[j3] = x1r + x3i;
- a[j3 + 1] = x1i - x3r;
- wn4r = w[1];
- k = 0;
- for (j = 2; j < mh; j += 2) {
- k += 4;
- wk1r = w[k];
- wk1i = w[k + 1];
- wk3r = w[k + 2];
- wk3i = w[k + 3];
- j1 = j + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j] + a[j2];
- x0i = a[j + 1] + a[j2 + 1];
- x1r = a[j] - a[j2];
- x1i = a[j + 1] - a[j2 + 1];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- a[j] = x0r + x2r;
- a[j + 1] = x0i + x2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i - x2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- a[j2] = wk1r * x0r - wk1i * x0i;
- a[j2 + 1] = wk1r * x0i + wk1i * x0r;
- x0r = x1r + x3i;
- x0i = x1i - x3r;
- a[j3] = wk3r * x0r + wk3i * x0i;
- a[j3 + 1] = wk3r * x0i - wk3i * x0r;
- j0 = m - j;
- j1 = j0 + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j0] + a[j2];
- x0i = a[j0 + 1] + a[j2 + 1];
- x1r = a[j0] - a[j2];
- x1i = a[j0 + 1] - a[j2 + 1];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- a[j0] = x0r + x2r;
- a[j0 + 1] = x0i + x2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i - x2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- a[j2] = wk1i * x0r - wk1r * x0i;
- a[j2 + 1] = wk1i * x0i + wk1r * x0r;
- x0r = x1r + x3i;
- x0i = x1i - x3r;
- a[j3] = wk3i * x0r + wk3r * x0i;
- a[j3 + 1] = wk3i * x0i - wk3r * x0r;
- }
- j0 = mh;
- j1 = j0 + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j0] + a[j2];
- x0i = a[j0 + 1] + a[j2 + 1];
- x1r = a[j0] - a[j2];
- x1i = a[j0 + 1] - a[j2 + 1];
- x2r = a[j1] + a[j3];
- x2i = a[j1 + 1] + a[j3 + 1];
- x3r = a[j1] - a[j3];
- x3i = a[j1 + 1] - a[j3 + 1];
- a[j0] = x0r + x2r;
- a[j0 + 1] = x0i + x2i;
- a[j1] = x0r - x2r;
- a[j1 + 1] = x0i - x2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- a[j2] = wn4r * (x0r - x0i);
- a[j2 + 1] = wn4r * (x0i + x0r);
- x0r = x1r + x3i;
- x0i = x1i - x3r;
- a[j3] = -wn4r * (x0r + x0i);
- a[j3 + 1] = -wn4r * (x0i - x0r);
-}
-
-
-void cftmdl2(int n, double *a, double *w)
-{
- int j, j0, j1, j2, j3, k, kr, m, mh;
- double wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
- double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;
-
- mh = n >> 3;
- m = 2 * mh;
- wn4r = w[1];
- j1 = m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[0] - a[j2 + 1];
- x0i = a[1] + a[j2];
- x1r = a[0] + a[j2 + 1];
- x1i = a[1] - a[j2];
- x2r = a[j1] - a[j3 + 1];
- x2i = a[j1 + 1] + a[j3];
- x3r = a[j1] + a[j3 + 1];
- x3i = a[j1 + 1] - a[j3];
- y0r = wn4r * (x2r - x2i);
- y0i = wn4r * (x2i + x2r);
- a[0] = x0r + y0r;
- a[1] = x0i + y0i;
- a[j1] = x0r - y0r;
- a[j1 + 1] = x0i - y0i;
- y0r = wn4r * (x3r - x3i);
- y0i = wn4r * (x3i + x3r);
- a[j2] = x1r - y0i;
- a[j2 + 1] = x1i + y0r;
- a[j3] = x1r + y0i;
- a[j3 + 1] = x1i - y0r;
- k = 0;
- kr = 2 * m;
- for (j = 2; j < mh; j += 2) {
- k += 4;
- wk1r = w[k];
- wk1i = w[k + 1];
- wk3r = w[k + 2];
- wk3i = w[k + 3];
- kr -= 4;
- wd1i = w[kr];
- wd1r = w[kr + 1];
- wd3i = w[kr + 2];
- wd3r = w[kr + 3];
- j1 = j + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j] - a[j2 + 1];
- x0i = a[j + 1] + a[j2];
- x1r = a[j] + a[j2 + 1];
- x1i = a[j + 1] - a[j2];
- x2r = a[j1] - a[j3 + 1];
- x2i = a[j1 + 1] + a[j3];
- x3r = a[j1] + a[j3 + 1];
- x3i = a[j1 + 1] - a[j3];
- y0r = wk1r * x0r - wk1i * x0i;
- y0i = wk1r * x0i + wk1i * x0r;
- y2r = wd1r * x2r - wd1i * x2i;
- y2i = wd1r * x2i + wd1i * x2r;
- a[j] = y0r + y2r;
- a[j + 1] = y0i + y2i;
- a[j1] = y0r - y2r;
- a[j1 + 1] = y0i - y2i;
- y0r = wk3r * x1r + wk3i * x1i;
- y0i = wk3r * x1i - wk3i * x1r;
- y2r = wd3r * x3r + wd3i * x3i;
- y2i = wd3r * x3i - wd3i * x3r;
- a[j2] = y0r + y2r;
- a[j2 + 1] = y0i + y2i;
- a[j3] = y0r - y2r;
- a[j3 + 1] = y0i - y2i;
- j0 = m - j;
- j1 = j0 + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j0] - a[j2 + 1];
- x0i = a[j0 + 1] + a[j2];
- x1r = a[j0] + a[j2 + 1];
- x1i = a[j0 + 1] - a[j2];
- x2r = a[j1] - a[j3 + 1];
- x2i = a[j1 + 1] + a[j3];
- x3r = a[j1] + a[j3 + 1];
- x3i = a[j1 + 1] - a[j3];
- y0r = wd1i * x0r - wd1r * x0i;
- y0i = wd1i * x0i + wd1r * x0r;
- y2r = wk1i * x2r - wk1r * x2i;
- y2i = wk1i * x2i + wk1r * x2r;
- a[j0] = y0r + y2r;
- a[j0 + 1] = y0i + y2i;
- a[j1] = y0r - y2r;
- a[j1 + 1] = y0i - y2i;
- y0r = wd3i * x1r + wd3r * x1i;
- y0i = wd3i * x1i - wd3r * x1r;
- y2r = wk3i * x3r + wk3r * x3i;
- y2i = wk3i * x3i - wk3r * x3r;
- a[j2] = y0r + y2r;
- a[j2 + 1] = y0i + y2i;
- a[j3] = y0r - y2r;
- a[j3 + 1] = y0i - y2i;
- }
- wk1r = w[m];
- wk1i = w[m + 1];
- j0 = mh;
- j1 = j0 + m;
- j2 = j1 + m;
- j3 = j2 + m;
- x0r = a[j0] - a[j2 + 1];
- x0i = a[j0 + 1] + a[j2];
- x1r = a[j0] + a[j2 + 1];
- x1i = a[j0 + 1] - a[j2];
- x2r = a[j1] - a[j3 + 1];
- x2i = a[j1 + 1] + a[j3];
- x3r = a[j1] + a[j3 + 1];
- x3i = a[j1 + 1] - a[j3];
- y0r = wk1r * x0r - wk1i * x0i;
- y0i = wk1r * x0i + wk1i * x0r;
- y2r = wk1i * x2r - wk1r * x2i;
- y2i = wk1i * x2i + wk1r * x2r;
- a[j0] = y0r + y2r;
- a[j0 + 1] = y0i + y2i;
- a[j1] = y0r - y2r;
- a[j1 + 1] = y0i - y2i;
- y0r = wk1i * x1r - wk1r * x1i;
- y0i = wk1i * x1i + wk1r * x1r;
- y2r = wk1r * x3r - wk1i * x3i;
- y2i = wk1r * x3i + wk1i * x3r;
- a[j2] = y0r - y2r;
- a[j2 + 1] = y0i - y2i;
- a[j3] = y0r + y2r;
- a[j3 + 1] = y0i + y2i;
-}
-
-
-void cftfx41(int n, double *a, int nw, double *w)
-{
- void cftf161(double *a, double *w);
- void cftf162(double *a, double *w);
- void cftf081(double *a, double *w);
- void cftf082(double *a, double *w);
-
- if (n == 128) {
- cftf161(a, &w[nw - 8]);
- cftf162(&a[32], &w[nw - 32]);
- cftf161(&a[64], &w[nw - 8]);
- cftf161(&a[96], &w[nw - 8]);
- } else {
- cftf081(a, &w[nw - 8]);
- cftf082(&a[16], &w[nw - 8]);
- cftf081(&a[32], &w[nw - 8]);
- cftf081(&a[48], &w[nw - 8]);
- }
-}
-
-
-void cftf161(double *a, double *w)
-{
- double wn4r, wk1r, wk1i,
- x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
- y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
- y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i,
- y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i,
- y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
-
- wn4r = w[1];
- wk1r = w[2];
- wk1i = w[3];
- x0r = a[0] + a[16];
- x0i = a[1] + a[17];
- x1r = a[0] - a[16];
- x1i = a[1] - a[17];
- x2r = a[8] + a[24];
- x2i = a[9] + a[25];
- x3r = a[8] - a[24];
- x3i = a[9] - a[25];
- y0r = x0r + x2r;
- y0i = x0i + x2i;
- y4r = x0r - x2r;
- y4i = x0i - x2i;
- y8r = x1r - x3i;
- y8i = x1i + x3r;
- y12r = x1r + x3i;
- y12i = x1i - x3r;
- x0r = a[2] + a[18];
- x0i = a[3] + a[19];
- x1r = a[2] - a[18];
- x1i = a[3] - a[19];
- x2r = a[10] + a[26];
- x2i = a[11] + a[27];
- x3r = a[10] - a[26];
- x3i = a[11] - a[27];
- y1r = x0r + x2r;
- y1i = x0i + x2i;
- y5r = x0r - x2r;
- y5i = x0i - x2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- y9r = wk1r * x0r - wk1i * x0i;
- y9i = wk1r * x0i + wk1i * x0r;
- x0r = x1r + x3i;
- x0i = x1i - x3r;
- y13r = wk1i * x0r - wk1r * x0i;
- y13i = wk1i * x0i + wk1r * x0r;
- x0r = a[4] + a[20];
- x0i = a[5] + a[21];
- x1r = a[4] - a[20];
- x1i = a[5] - a[21];
- x2r = a[12] + a[28];
- x2i = a[13] + a[29];
- x3r = a[12] - a[28];
- x3i = a[13] - a[29];
- y2r = x0r + x2r;
- y2i = x0i + x2i;
- y6r = x0r - x2r;
- y6i = x0i - x2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- y10r = wn4r * (x0r - x0i);
- y10i = wn4r * (x0i + x0r);
- x0r = x1r + x3i;
- x0i = x1i - x3r;
- y14r = wn4r * (x0r + x0i);
- y14i = wn4r * (x0i - x0r);
- x0r = a[6] + a[22];
- x0i = a[7] + a[23];
- x1r = a[6] - a[22];
- x1i = a[7] - a[23];
- x2r = a[14] + a[30];
- x2i = a[15] + a[31];
- x3r = a[14] - a[30];
- x3i = a[15] - a[31];
- y3r = x0r + x2r;
- y3i = x0i + x2i;
- y7r = x0r - x2r;
- y7i = x0i - x2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- y11r = wk1i * x0r - wk1r * x0i;
- y11i = wk1i * x0i + wk1r * x0r;
- x0r = x1r + x3i;
- x0i = x1i - x3r;
- y15r = wk1r * x0r - wk1i * x0i;
- y15i = wk1r * x0i + wk1i * x0r;
- x0r = y12r - y14r;
- x0i = y12i - y14i;
- x1r = y12r + y14r;
- x1i = y12i + y14i;
- x2r = y13r - y15r;
- x2i = y13i - y15i;
- x3r = y13r + y15r;
- x3i = y13i + y15i;
- a[24] = x0r + x2r;
- a[25] = x0i + x2i;
- a[26] = x0r - x2r;
- a[27] = x0i - x2i;
- a[28] = x1r - x3i;
- a[29] = x1i + x3r;
- a[30] = x1r + x3i;
- a[31] = x1i - x3r;
- x0r = y8r + y10r;
- x0i = y8i + y10i;
- x1r = y8r - y10r;
- x1i = y8i - y10i;
- x2r = y9r + y11r;
- x2i = y9i + y11i;
- x3r = y9r - y11r;
- x3i = y9i - y11i;
- a[16] = x0r + x2r;
- a[17] = x0i + x2i;
- a[18] = x0r - x2r;
- a[19] = x0i - x2i;
- a[20] = x1r - x3i;
- a[21] = x1i + x3r;
- a[22] = x1r + x3i;
- a[23] = x1i - x3r;
- x0r = y5r - y7i;
- x0i = y5i + y7r;
- x2r = wn4r * (x0r - x0i);
- x2i = wn4r * (x0i + x0r);
- x0r = y5r + y7i;
- x0i = y5i - y7r;
- x3r = wn4r * (x0r - x0i);
- x3i = wn4r * (x0i + x0r);
- x0r = y4r - y6i;
- x0i = y4i + y6r;
- x1r = y4r + y6i;
- x1i = y4i - y6r;
- a[8] = x0r + x2r;
- a[9] = x0i + x2i;
- a[10] = x0r - x2r;
- a[11] = x0i - x2i;
- a[12] = x1r - x3i;
- a[13] = x1i + x3r;
- a[14] = x1r + x3i;
- a[15] = x1i - x3r;
- x0r = y0r + y2r;
- x0i = y0i + y2i;
- x1r = y0r - y2r;
- x1i = y0i - y2i;
- x2r = y1r + y3r;
- x2i = y1i + y3i;
- x3r = y1r - y3r;
- x3i = y1i - y3i;
- a[0] = x0r + x2r;
- a[1] = x0i + x2i;
- a[2] = x0r - x2r;
- a[3] = x0i - x2i;
- a[4] = x1r - x3i;
- a[5] = x1i + x3r;
- a[6] = x1r + x3i;
- a[7] = x1i - x3r;
-}
-
-
-void cftf162(double *a, double *w)
-{
- double wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i,
- x0r, x0i, x1r, x1i, x2r, x2i,
- y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
- y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i,
- y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i,
- y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
-
- wn4r = w[1];
- wk1r = w[4];
- wk1i = w[5];
- wk3r = w[6];
- wk3i = -w[7];
- wk2r = w[8];
- wk2i = w[9];
- x1r = a[0] - a[17];
- x1i = a[1] + a[16];
- x0r = a[8] - a[25];
- x0i = a[9] + a[24];
- x2r = wn4r * (x0r - x0i);
- x2i = wn4r * (x0i + x0r);
- y0r = x1r + x2r;
- y0i = x1i + x2i;
- y4r = x1r - x2r;
- y4i = x1i - x2i;
- x1r = a[0] + a[17];
- x1i = a[1] - a[16];
- x0r = a[8] + a[25];
- x0i = a[9] - a[24];
- x2r = wn4r * (x0r - x0i);
- x2i = wn4r * (x0i + x0r);
- y8r = x1r - x2i;
- y8i = x1i + x2r;
- y12r = x1r + x2i;
- y12i = x1i - x2r;
- x0r = a[2] - a[19];
- x0i = a[3] + a[18];
- x1r = wk1r * x0r - wk1i * x0i;
- x1i = wk1r * x0i + wk1i * x0r;
- x0r = a[10] - a[27];
- x0i = a[11] + a[26];
- x2r = wk3i * x0r - wk3r * x0i;
- x2i = wk3i * x0i + wk3r * x0r;
- y1r = x1r + x2r;
- y1i = x1i + x2i;
- y5r = x1r - x2r;
- y5i = x1i - x2i;
- x0r = a[2] + a[19];
- x0i = a[3] - a[18];
- x1r = wk3r * x0r - wk3i * x0i;
- x1i = wk3r * x0i + wk3i * x0r;
- x0r = a[10] + a[27];
- x0i = a[11] - a[26];
- x2r = wk1r * x0r + wk1i * x0i;
- x2i = wk1r * x0i - wk1i * x0r;
- y9r = x1r - x2r;
- y9i = x1i - x2i;
- y13r = x1r + x2r;
- y13i = x1i + x2i;
- x0r = a[4] - a[21];
- x0i = a[5] + a[20];
- x1r = wk2r * x0r - wk2i * x0i;
- x1i = wk2r * x0i + wk2i * x0r;
- x0r = a[12] - a[29];
- x0i = a[13] + a[28];
- x2r = wk2i * x0r - wk2r * x0i;
- x2i = wk2i * x0i + wk2r * x0r;
- y2r = x1r + x2r;
- y2i = x1i + x2i;
- y6r = x1r - x2r;
- y6i = x1i - x2i;
- x0r = a[4] + a[21];
- x0i = a[5] - a[20];
- x1r = wk2i * x0r - wk2r * x0i;
- x1i = wk2i * x0i + wk2r * x0r;
- x0r = a[12] + a[29];
- x0i = a[13] - a[28];
- x2r = wk2r * x0r - wk2i * x0i;
- x2i = wk2r * x0i + wk2i * x0r;
- y10r = x1r - x2r;
- y10i = x1i - x2i;
- y14r = x1r + x2r;
- y14i = x1i + x2i;
- x0r = a[6] - a[23];
- x0i = a[7] + a[22];
- x1r = wk3r * x0r - wk3i * x0i;
- x1i = wk3r * x0i + wk3i * x0r;
- x0r = a[14] - a[31];
- x0i = a[15] + a[30];
- x2r = wk1i * x0r - wk1r * x0i;
- x2i = wk1i * x0i + wk1r * x0r;
- y3r = x1r + x2r;
- y3i = x1i + x2i;
- y7r = x1r - x2r;
- y7i = x1i - x2i;
- x0r = a[6] + a[23];
- x0i = a[7] - a[22];
- x1r = wk1i * x0r + wk1r * x0i;
- x1i = wk1i * x0i - wk1r * x0r;
- x0r = a[14] + a[31];
- x0i = a[15] - a[30];
- x2r = wk3i * x0r - wk3r * x0i;
- x2i = wk3i * x0i + wk3r * x0r;
- y11r = x1r + x2r;
- y11i = x1i + x2i;
- y15r = x1r - x2r;
- y15i = x1i - x2i;
- x1r = y0r + y2r;
- x1i = y0i + y2i;
- x2r = y1r + y3r;
- x2i = y1i + y3i;
- a[0] = x1r + x2r;
- a[1] = x1i + x2i;
- a[2] = x1r - x2r;
- a[3] = x1i - x2i;
- x1r = y0r - y2r;
- x1i = y0i - y2i;
- x2r = y1r - y3r;
- x2i = y1i - y3i;
- a[4] = x1r - x2i;
- a[5] = x1i + x2r;
- a[6] = x1r + x2i;
- a[7] = x1i - x2r;
- x1r = y4r - y6i;
- x1i = y4i + y6r;
- x0r = y5r - y7i;
- x0i = y5i + y7r;
- x2r = wn4r * (x0r - x0i);
- x2i = wn4r * (x0i + x0r);
- a[8] = x1r + x2r;
- a[9] = x1i + x2i;
- a[10] = x1r - x2r;
- a[11] = x1i - x2i;
- x1r = y4r + y6i;
- x1i = y4i - y6r;
- x0r = y5r + y7i;
- x0i = y5i - y7r;
- x2r = wn4r * (x0r - x0i);
- x2i = wn4r * (x0i + x0r);
- a[12] = x1r - x2i;
- a[13] = x1i + x2r;
- a[14] = x1r + x2i;
- a[15] = x1i - x2r;
- x1r = y8r + y10r;
- x1i = y8i + y10i;
- x2r = y9r - y11r;
- x2i = y9i - y11i;
- a[16] = x1r + x2r;
- a[17] = x1i + x2i;
- a[18] = x1r - x2r;
- a[19] = x1i - x2i;
- x1r = y8r - y10r;
- x1i = y8i - y10i;
- x2r = y9r + y11r;
- x2i = y9i + y11i;
- a[20] = x1r - x2i;
- a[21] = x1i + x2r;
- a[22] = x1r + x2i;
- a[23] = x1i - x2r;
- x1r = y12r - y14i;
- x1i = y12i + y14r;
- x0r = y13r + y15i;
- x0i = y13i - y15r;
- x2r = wn4r * (x0r - x0i);
- x2i = wn4r * (x0i + x0r);
- a[24] = x1r + x2r;
- a[25] = x1i + x2i;
- a[26] = x1r - x2r;
- a[27] = x1i - x2i;
- x1r = y12r + y14i;
- x1i = y12i - y14r;
- x0r = y13r - y15i;
- x0i = y13i + y15r;
- x2r = wn4r * (x0r - x0i);
- x2i = wn4r * (x0i + x0r);
- a[28] = x1r - x2i;
- a[29] = x1i + x2r;
- a[30] = x1r + x2i;
- a[31] = x1i - x2r;
-}
-
-
-void cftf081(double *a, double *w)
-{
- double wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
- y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
- y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
-
- wn4r = w[1];
- x0r = a[0] + a[8];
- x0i = a[1] + a[9];
- x1r = a[0] - a[8];
- x1i = a[1] - a[9];
- x2r = a[4] + a[12];
- x2i = a[5] + a[13];
- x3r = a[4] - a[12];
- x3i = a[5] - a[13];
- y0r = x0r + x2r;
- y0i = x0i + x2i;
- y2r = x0r - x2r;
- y2i = x0i - x2i;
- y1r = x1r - x3i;
- y1i = x1i + x3r;
- y3r = x1r + x3i;
- y3i = x1i - x3r;
- x0r = a[2] + a[10];
- x0i = a[3] + a[11];
- x1r = a[2] - a[10];
- x1i = a[3] - a[11];
- x2r = a[6] + a[14];
- x2i = a[7] + a[15];
- x3r = a[6] - a[14];
- x3i = a[7] - a[15];
- y4r = x0r + x2r;
- y4i = x0i + x2i;
- y6r = x0r - x2r;
- y6i = x0i - x2i;
- x0r = x1r - x3i;
- x0i = x1i + x3r;
- x2r = x1r + x3i;
- x2i = x1i - x3r;
- y5r = wn4r * (x0r - x0i);
- y5i = wn4r * (x0r + x0i);
- y7r = wn4r * (x2r - x2i);
- y7i = wn4r * (x2r + x2i);
- a[8] = y1r + y5r;
- a[9] = y1i + y5i;
- a[10] = y1r - y5r;
- a[11] = y1i - y5i;
- a[12] = y3r - y7i;
- a[13] = y3i + y7r;
- a[14] = y3r + y7i;
- a[15] = y3i - y7r;
- a[0] = y0r + y4r;
- a[1] = y0i + y4i;
- a[2] = y0r - y4r;
- a[3] = y0i - y4i;
- a[4] = y2r - y6i;
- a[5] = y2i + y6r;
- a[6] = y2r + y6i;
- a[7] = y2i - y6r;
-}
-
-
-void cftf082(double *a, double *w)
-{
- double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i,
- y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
- y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
-
- wn4r = w[1];
- wk1r = w[2];
- wk1i = w[3];
- y0r = a[0] - a[9];
- y0i = a[1] + a[8];
- y1r = a[0] + a[9];
- y1i = a[1] - a[8];
- x0r = a[4] - a[13];
- x0i = a[5] + a[12];
- y2r = wn4r * (x0r - x0i);
- y2i = wn4r * (x0i + x0r);
- x0r = a[4] + a[13];
- x0i = a[5] - a[12];
- y3r = wn4r * (x0r - x0i);
- y3i = wn4r * (x0i + x0r);
- x0r = a[2] - a[11];
- x0i = a[3] + a[10];
- y4r = wk1r * x0r - wk1i * x0i;
- y4i = wk1r * x0i + wk1i * x0r;
- x0r = a[2] + a[11];
- x0i = a[3] - a[10];
- y5r = wk1i * x0r - wk1r * x0i;
- y5i = wk1i * x0i + wk1r * x0r;
- x0r = a[6] - a[15];
- x0i = a[7] + a[14];
- y6r = wk1i * x0r - wk1r * x0i;
- y6i = wk1i * x0i + wk1r * x0r;
- x0r = a[6] + a[15];
- x0i = a[7] - a[14];
- y7r = wk1r * x0r - wk1i * x0i;
- y7i = wk1r * x0i + wk1i * x0r;
- x0r = y0r + y2r;
- x0i = y0i + y2i;
- x1r = y4r + y6r;
- x1i = y4i + y6i;
- a[0] = x0r + x1r;
- a[1] = x0i + x1i;
- a[2] = x0r - x1r;
- a[3] = x0i - x1i;
- x0r = y0r - y2r;
- x0i = y0i - y2i;
- x1r = y4r - y6r;
- x1i = y4i - y6i;
- a[4] = x0r - x1i;
- a[5] = x0i + x1r;
- a[6] = x0r + x1i;
- a[7] = x0i - x1r;
- x0r = y1r - y3i;
- x0i = y1i + y3r;
- x1r = y5r - y7r;
- x1i = y5i - y7i;
- a[8] = x0r + x1r;
- a[9] = x0i + x1i;
- a[10] = x0r - x1r;
- a[11] = x0i - x1i;
- x0r = y1r + y3i;
- x0i = y1i - y3r;
- x1r = y5r + y7r;
- x1i = y5i + y7i;
- a[12] = x0r - x1i;
- a[13] = x0i + x1r;
- a[14] = x0r + x1i;
- a[15] = x0i - x1r;
-}
-
-
-void cftf040(double *a)
-{
- double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
-
- x0r = a[0] + a[4];
- x0i = a[1] + a[5];
- x1r = a[0] - a[4];
- x1i = a[1] - a[5];
- x2r = a[2] + a[6];
- x2i = a[3] + a[7];
- x3r = a[2] - a[6];
- x3i = a[3] - a[7];
- a[0] = x0r + x2r;
- a[1] = x0i + x2i;
- a[2] = x1r - x3i;
- a[3] = x1i + x3r;
- a[4] = x0r - x2r;
- a[5] = x0i - x2i;
- a[6] = x1r + x3i;
- a[7] = x1i - x3r;
-}
-
-
-void cftb040(double *a)
-{
- double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
-
- x0r = a[0] + a[4];
- x0i = a[1] + a[5];
- x1r = a[0] - a[4];
- x1i = a[1] - a[5];
- x2r = a[2] + a[6];
- x2i = a[3] + a[7];
- x3r = a[2] - a[6];
- x3i = a[3] - a[7];
- a[0] = x0r + x2r;
- a[1] = x0i + x2i;
- a[2] = x1r + x3i;
- a[3] = x1i - x3r;
- a[4] = x0r - x2r;
- a[5] = x0i - x2i;
- a[6] = x1r - x3i;
- a[7] = x1i + x3r;
-}
-
-
-void cftx020(double *a)
-{
- double x0r, x0i;
-
- x0r = a[0] - a[2];
- x0i = a[1] - a[3];
- a[0] += a[2];
- a[1] += a[3];
- a[2] = x0r;
- a[3] = x0i;
-}
-
-
-void rftfsub(int n, double *a, int nc, double *c)
-{
- int j, k, kk, ks, m;
- double wkr, wki, xr, xi, yr, yi;
-
- m = n >> 1;
- ks = 2 * nc / m;
- kk = 0;
- for (j = 2; j < m; j += 2) {
- k = n - j;
- kk += ks;
- wkr = 0.5 - c[nc - kk];
- wki = c[kk];
- xr = a[j] - a[k];
- xi = a[j + 1] + a[k + 1];
- yr = wkr * xr - wki * xi;
- yi = wkr * xi + wki * xr;
- a[j] -= yr;
- a[j + 1] -= yi;
- a[k] += yr;
- a[k + 1] -= yi;
- }
-}
-
-
-void rftbsub(int n, double *a, int nc, double *c)
-{
- int j, k, kk, ks, m;
- double wkr, wki, xr, xi, yr, yi;
-
- m = n >> 1;
- ks = 2 * nc / m;
- kk = 0;
- for (j = 2; j < m; j += 2) {
- k = n - j;
- kk += ks;
- wkr = 0.5 - c[nc - kk];
- wki = c[kk];
- xr = a[j] - a[k];
- xi = a[j + 1] + a[k + 1];
- yr = wkr * xr + wki * xi;
- yi = wkr * xi - wki * xr;
- a[j] -= yr;
- a[j + 1] -= yi;
- a[k] += yr;
- a[k + 1] -= yi;
- }
-}
-
-
-void dctsub(int n, double *a, int nc, double *c)
-{
- int j, k, kk, ks, m;
- double wkr, wki, xr;
-
- m = n >> 1;
- ks = nc / n;
- kk = 0;
- for (j = 1; j < m; j++) {
- k = n - j;
- kk += ks;
- wkr = c[kk] - c[nc - kk];
- wki = c[kk] + c[nc - kk];
- xr = wki * a[j] - wkr * a[k];
- a[j] = wkr * a[j] + wki * a[k];
- a[k] = xr;
- }
- a[m] *= c[0];
-}
-
-
-void dstsub(int n, double *a, int nc, double *c)
-{
- int j, k, kk, ks, m;
- double wkr, wki, xr;
-
- m = n >> 1;
- ks = nc / n;
- kk = 0;
- for (j = 1; j < m; j++) {
- k = n - j;
- kk += ks;
- wkr = c[kk] - c[nc - kk];
- wki = c[kk] + c[nc - kk];
- xr = wki * a[k] - wkr * a[j];
- a[k] = wkr * a[k] + wki * a[j];
- a[j] = xr;
- }
- a[m] *= c[0];
-}
-
Copied: branches/pd-extended/0.41/pd/src/d_fft_fftsg.c (from rev 10495, tags/pd/0.41-4/src/d_fft_fftsg.c)
===================================================================
--- branches/pd-extended/0.41/pd/src/d_fft_fftsg.c (rev 0)
+++ branches/pd-extended/0.41/pd/src/d_fft_fftsg.c 2009-01-10 02:20:22 UTC (rev 10497)
@@ -0,0 +1,3462 @@
+/****************** begin Pd-specific prologue ***********************/
+
+/*
+This is the file, "fftsg.c" from the OOURA FFT package. The copyright notice
+from Ooura's README is:
+
+Copyright:
+ Copyright(C) 1996-2001 Takuya OOURA
+ email: ooura at mmm.t.u-tokyo.ac.jp
+ download: http://momonga.t.u-tokyo.ac.jp/~ooura/fft.html
+ You may use, copy, modify this code for any purpose and
+ without fee. You may distribute this ORIGINAL package.
+
+After the following prologue, the code is exactly Ooura's original, which I
+believe the above notice permits me to redistribute. See Ooura's website
+for another, more permissive-sounding copyright notice. -MSP
+*/
+
+/* ---------- Pd interface to OOURA FFT; imitate Mayer API ---------- */
+#include "m_pd.h"
+#ifdef MSW
+#include <malloc.h>
+#else
+#include <alloca.h>
+#endif
+
+#define FFTFLT double
+void cdft(int, int, double *, int *, double *);
+void rdft(int, int, double *, int *, double *);
+
+int ilog2(int n);
+
+static int ooura_maxn;
+static int *ooura_bitrev;
+static int ooura_bitrevsize;
+static FFTFLT *ooura_costab;
+
+static int ooura_init( int n)
+{
+ n = (1 << ilog2(n));
+ if (n < 64)
+ return (0);
+ if (n > ooura_maxn)
+ {
+ post("init");
+ if (ooura_maxn)
+ {
+ t_freebytes(ooura_bitrev, ooura_bitrevsize);
+ t_freebytes(ooura_costab, ooura_maxn * sizeof(FFTFLT) / 2);
+ }
+ ooura_bitrevsize = sizeof(int *) * (2 + (1 << (ilog2(n)/2)));
+ ooura_bitrev = (int *)t_getbytes(ooura_bitrevsize);
+ ooura_bitrev[0] = 0;
+ if (!ooura_bitrev)
+ {
+ error("out of memory allocating FFT buffer");
+ ooura_maxn = 0;
+ return (0);
+ }
+ ooura_costab = (FFTFLT *)t_getbytes(n * sizeof(FFTFLT)/2);
+ if (!ooura_costab)
+ {
+ error("out of memory allocating FFT buffer");
+ t_freebytes(ooura_bitrev, ooura_bitrevsize);
+ ooura_maxn = 0;
+ return (0);
+ }
+ ooura_maxn = n;
+ ooura_bitrev[0] = 0;
+ }
+ return (1);
+}
+
+EXTERN void mayer_fht(t_sample *fz, int n)
+{
+ post("FHT: not yet implemented");
+}
+
+EXTERN void mayer_dofft(t_sample *fz1, t_sample *fz2, int n, int sgn)
+{
+ FFTFLT *buf, *fp3;
+ int i;
+ t_sample *fp1, *fp2;
+ buf = alloca(n * (2 * sizeof(FFTFLT)));
+ if (!ooura_init(n))
+ return;
+ for (i = 0, fp1 = fz1, fp2 = fz2, fp3 = buf; i < n; i++)
+ {
+ fp3[0] = *fp1++;
+ fp3[1] = *fp2++;
+ fp3 += 2;
+ }
+ cdft(2*n, sgn, buf, ooura_bitrev, ooura_costab);
+ for (i = 0, fp1 = fz1, fp2 = fz2, fp3 = buf; i < n; i++)
+ {
+ *fp1++ = fp3[0];
+ *fp2++ = fp3[1];
+ fp3 += 2;
+ }
+}
+
+EXTERN void mayer_fft(int n, t_sample *fz1, t_sample *fz2)
+{
+ mayer_dofft(fz1, fz2, n, -1);
+}
+
+EXTERN void mayer_ifft(int n, t_sample *fz1, t_sample *fz2)
+{
+ mayer_dofft(fz1, fz2, n, 1);
+}
+
+EXTERN void mayer_realfft(int n, t_sample *fz)
+{
+ FFTFLT *buf, *fp3;
+ int i, nover2 = n/2;
+ t_sample *fp1, *fp2;
+ buf = alloca(n * sizeof(FFTFLT));
+ if (!ooura_init(n))
+ return;
+ for (i = 0, fp1 = fz, fp3 = buf; i < n; i++, fp1++, fp3++)
+ buf[i] = fz[i];
+ rdft(n, 1, buf, ooura_bitrev, ooura_costab);
+ fz[0] = buf[0];
+ fz[nover2] = buf[1];
+ for (i = 1, fp1 = fz+1, fp2 = fz+(n-1), fp3 = buf+2; i < nover2;
+ i++, fp1++, fp2--, fp3 += 2)
+ *fp1 = fp3[0], *fp2 = fp3[1];
+}
+
+EXTERN void mayer_realifft(int n, t_sample *fz)
+{
+ FFTFLT *buf, *fp3;
+ int i, nover2 = n/2;
+ t_sample *fp1, *fp2;
+ buf = alloca(n * sizeof(FFTFLT));
+ if (!ooura_init(n))
+ return;
+ buf[0] = fz[0];
+ buf[1] = fz[nover2];
+ for (i = 1, fp1 = fz+1, fp2 = fz+(n-1), fp3 = buf+2; i < nover2;
+ i++, fp1++, fp2--, fp3 += 2)
+ fp3[0] = *fp1, fp3[1] = *fp2;
+ rdft(n, -1, buf, ooura_bitrev, ooura_costab);
+ for (i = 0, fp1 = fz, fp3 = buf; i < n; i++, fp1++, fp3++)
+ fz[i] = 2*buf[i];
+}
+
+/****************** end Pd-specific prologue ***********************/
+/*
+Fast Fourier/Cosine/Sine Transform
+ dimension :one
+ data length :power of 2
+ decimation :frequency
+ radix :split-radix
+ data :inplace
+ table :use
+functions
+ cdft: Complex Discrete Fourier Transform
+ rdft: Real Discrete Fourier Transform
+ ddct: Discrete Cosine Transform
+ ddst: Discrete Sine Transform
+ dfct: Cosine Transform of RDFT (Real Symmetric DFT)
+ dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
+function prototypes
+ void cdft(int, int, double *, int *, double *);
+ void rdft(int, int, double *, int *, double *);
+ void ddct(int, int, double *, int *, double *);
+ void ddst(int, int, double *, int *, double *);
+ void dfct(int, double *, double *, int *, double *);
+ void dfst(int, double *, double *, int *, double *);
+macro definitions
+ USE_CDFT_PTHREADS : default=not defined
+ CDFT_THREADS_BEGIN_N : must be >= 512, default=8192
+ CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536
+ USE_CDFT_WINTHREADS : default=not defined
+ CDFT_THREADS_BEGIN_N : must be >= 512, default=32768
+ CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288
+
+
+-------- Complex DFT (Discrete Fourier Transform) --------
+ [definition]
+ <case1>
+ X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
+ <case2>
+ X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
+ (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
+ [usage]
+ <case1>
+ ip[0] = 0; // first time only
+ cdft(2*n, 1, a, ip, w);
+ <case2>
+ ip[0] = 0; // first time only
+ cdft(2*n, -1, a, ip, w);
+ [parameters]
+ 2*n :data length (int)
+ n >= 1, n = power of 2
+ a[0...2*n-1] :input/output data (double *)
+ input data
+ a[2*j] = Re(x[j]),
+ a[2*j+1] = Im(x[j]), 0<=j<n
+ output data
+ a[2*k] = Re(X[k]),
+ a[2*k+1] = Im(X[k]), 0<=k<n
@@ Diff output truncated at 100000 characters. @@
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