Fast Fourier/Cosine/Sine Transform
dimension :two
data length :power of 2
decimation :frequency
radix :split-radix, row-column
data :inplace
table :use
functions
cdft2d: Complex Discrete Fourier Transform
rdft2d: Real Discrete Fourier Transform
ddct2d: Discrete Cosine Transform
ddst2d: Discrete Sine Transform
function prototypes
void cdft2d(int, int, int, double **, double *, int *, double *);
void rdft2d(int, int, int, double **, double *, int *, double *);
void rdft2dsort(int, int, int, double **);
void ddct2d(int, int, int, double **, double *, int *, double *);
void ddst2d(int, int, int, double **, double *, int *, double *);
necessary package
fftsg.c : 1D-FFT package
macro definitions
USE_FFT2D_PTHREADS : default=not defined
FFT2D_MAX_THREADS : must be 2^N, default=4
FFT2D_THREADS_BEGIN_N : default=65536
USE_FFT2D_WINTHREADS : default=not defined
FFT2D_MAX_THREADS : must be 2^N, default=4
FFT2D_THREADS_BEGIN_N : default=131072
-------- Complex DFT (Discrete Fourier Transform) --------
[definition]
<case1>
X[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 x[j1][j2] *
exp(2*pi*i*j1*k1/n1) *
exp(2*pi*i*j2*k2/n2), 0<=k1<n1, 0<=k2<n2
<case2>
X[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 x[j1][j2] *
exp(-2*pi*i*j1*k1/n1) *
exp(-2*pi*i*j2*k2/n2), 0<=k1<n1, 0<=k2<n2
(notes: sum_j=0^n-1 is a summation from j=0 to n-1)
[usage]
<case1>
ip[0] = 0; // first time only
cdft2d(n1, 2*n2, 1, a, t, ip, w);
<case2>
ip[0] = 0; // first time only
cdft2d(n1, 2*n2, -1, a, t, ip, w);
[parameters]
n1 :data length (int)
n1 >= 1, n1 = power of 2
2*n2 :data length (int)
n2 >= 1, n2 = power of 2
a[0...n1-1][0...2*n2-1]
:input/output data (double **)
input data
a[j1][2*j2] = Re(x[j1][j2]),
a[j1][2*j2+1] = Im(x[j1][j2]),
0<=j1<n1, 0<=j2<n2
output data
a[k1][2*k2] = Re(X[k1][k2]),
a[k1][2*k2+1] = Im(X[k1][k2]),
0<=k1<n1, 0<=k2<n2
t[0...*]
:work area (double *)
length of t >= 8*n1, if single thread,
length of t >= 8*n1*FFT2D_MAX_THREADS, if multi threads,
t is dynamically allocated, if t == NULL.
ip[0...*]
:work area for bit reversal (int *)
length of ip >= 2+sqrt(n)
(n = max(n1, n2))
ip[0],ip[1] are pointers of the cos/sin table.
w[0...*]
:cos/sin table (double *)
length of w >= max(n1/2, n2/2)
w[],ip[] are initialized if ip[0] == 0.
[remark]
Inverse of
cdft2d(n1, 2*n2, -1, a, t, ip, w);
is
cdft2d(n1, 2*n2, 1, a, t, ip, w);
for (j1 = 0; j1 <= n1 - 1; j1++) {
for (j2 = 0; j2 <= 2 * n2 - 1; j2++) {
a[j1][j2] *= 1.0 / n1 / n2;
}
}
.
-------- Real DFT / Inverse of Real DFT --------
[definition]
<case1> RDFT
R[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 a[j1][j2] *
cos(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2),
0<=k1<n1, 0<=k2<n2
I[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 a[j1][j2] *
sin(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2),
0<=k1<n1, 0<=k2<n2
<case2> IRDFT (excluding scale)
a[k1][k2] = (1/2) * sum_j1=0^n1-1 sum_j2=0^n2-1
(R[j1][j2] *
cos(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2) +
I[j1][j2] *
sin(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2)),
0<=k1<n1, 0<=k2<n2
(notes: R[n1-k1][n2-k2] = R[k1][k2],
I[n1-k1][n2-k2] = -I[k1][k2],
R[n1-k1][0] = R[k1][0],
I[n1-k1][0] = -I[k1][0],
R[0][n2-k2] = R[0][k2],
I[0][n2-k2] = -I[0][k2],
0<k1<n1, 0<k2<n2)
[usage]
<case1>
ip[0] = 0; // first time only
rdft2d(n1, n2, 1, a, t, ip, w);
<case2>
ip[0] = 0; // first time only
rdft2d(n1, n2, -1, a, t, ip, w);
[parameters]
n1 :data length (int)
n1 >= 2, n1 = power of 2
n2 :data length (int)
n2 >= 2, n2 = power of 2
a[0...n1-1][0...n2-1]
:input/output data (double **)
<case1>
output data
a[k1][2*k2] = R[k1][k2] = R[n1-k1][n2-k2],
a[k1][2*k2+1] = I[k1][k2] = -I[n1-k1][n2-k2],
0<k1<n1, 0<k2<n2/2,
a[0][2*k2] = R[0][k2] = R[0][n2-k2],
a[0][2*k2+1] = I[0][k2] = -I[0][n2-k2],
0<k2<n2/2,
a[k1][0] = R[k1][0] = R[n1-k1][0],
a[k1][1] = I[k1][0] = -I[n1-k1][0],
a[n1-k1][1] = R[k1][n2/2] = R[n1-k1][n2/2],
a[n1-k1][0] = -I[k1][n2/2] = I[n1-k1][n2/2],
0<k1<n1/2,
a[0][0] = R[0][0],
a[0][1] = R[0][n2/2],
a[n1/2][0] = R[n1/2][0],
a[n1/2][1] = R[n1/2][n2/2]
<case2>
input data
a[j1][2*j2] = R[j1][j2] = R[n1-j1][n2-j2],
a[j1][2*j2+1] = I[j1][j2] = -I[n1-j1][n2-j2],
0<j1<n1, 0<j2<n2/2,
a[0][2*j2] = R[0][j2] = R[0][n2-j2],
a[0][2*j2+1] = I[0][j2] = -I[0][n2-j2],
0<j2<n2/2,
a[j1][0] = R[j1][0] = R[n1-j1][0],
a[j1][1] = I[j1][0] = -I[n1-j1][0],
a[n1-j1][1] = R[j1][n2/2] = R[n1-j1][n2/2],
a[n1-j1][0] = -I[j1][n2/2] = I[n1-j1][n2/2],
0<j1<n1/2,
a[0][0] = R[0][0],
a[0][1] = R[0][n2/2],
a[n1/2][0] = R[n1/2][0],
a[n1/2][1] = R[n1/2][n2/2]
---- output ordering ----
rdft2d(n1, n2, 1, a, t, ip, w);
rdft2dsort(n1, n2, 1, a);
// stored data is a[0...n1-1][0...n2+1]:
// a[k1][2*k2] = R[k1][k2],
// a[k1][2*k2+1] = I[k1][k2],
// 0<=k1<n1, 0<=k2<=n2/2.
// the stored data is larger than the input data!
---- input ordering ----
rdft2dsort(n1, n2, -1, a);
rdft2d(n1, n2, -1, a, t, ip, w);
t[0...*]
:work area (double *)
length of t >= 8*n1, if single thread,
length of t >= 8*n1*FFT2D_MAX_THREADS, if multi threads,
t is dynamically allocated, if t == NULL.
ip[0...*]
:work area for bit reversal (int *)
length of ip >= 2+sqrt(n)
(n = max(n1, n2/2))
ip[0],ip[1] are pointers of the cos/sin table.
w[0...*]
:cos/sin table (double *)
length of w >= max(n1/2, n2/4) + n2/4
w[],ip[] are initialized if ip[0] == 0.
[remark]
Inverse of
rdft2d(n1, n2, 1, a, t, ip, w);
is
rdft2d(n1, n2, -1, a, t, ip, w);
for (j1 = 0; j1 <= n1 - 1; j1++) {
for (j2 = 0; j2 <= n2 - 1; j2++) {
a[j1][j2] *= 2.0 / n1 / n2;
}
}
.
-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
[definition]
<case1> IDCT (excluding scale)
C[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 a[j1][j2] *
cos(pi*j1*(k1+1/2)/n1) *
cos(pi*j2*(k2+1/2)/n2),
0<=k1<n1, 0<=k2<n2
<case2> DCT
C[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 a[j1][j2] *
cos(pi*(j1+1/2)*k1/n1) *
cos(pi*(j2+1/2)*k2/n2),
0<=k1<n1, 0<=k2<n2
[usage]
<case1>
ip[0] = 0; // first time only
ddct2d(n1, n2, 1, a, t, ip, w);
<case2>
ip[0] = 0; // first time only
ddct2d(n1, n2, -1, a, t, ip, w);
[parameters]
n1 :data length (int)
n1 >= 2, n1 = power of 2
n2 :data length (int)
n2 >= 2, n2 = power of 2
a[0...n1-1][0...n2-1]
:input/output data (double **)
output data
a[k1][k2] = C[k1][k2], 0<=k1<n1, 0<=k2<n2
t[0...*]
:work area (double *)
length of t >= 4*n1, if single thread,
length of t >= 4*n1*FFT2D_MAX_THREADS, if multi threads,
t is dynamically allocated, if t == NULL.
ip[0...*]
:work area for bit reversal (int *)
length of ip >= 2+sqrt(n)
(n = max(n1/2, n2/2))
ip[0],ip[1] are pointers of the cos/sin table.
w[0...*]
:cos/sin table (double *)
length of w >= max(n1*3/2, n2*3/2)
w[],ip[] are initialized if ip[0] == 0.
[remark]
Inverse of
ddct2d(n1, n2, -1, a, t, ip, w);
is
for (j1 = 0; j1 <= n1 - 1; j1++) {
a[j1][0] *= 0.5;
}
for (j2 = 0; j2 <= n2 - 1; j2++) {
a[0][j2] *= 0.5;
}
ddct2d(n1, n2, 1, a, t, ip, w);
for (j1 = 0; j1 <= n1 - 1; j1++) {
for (j2 = 0; j2 <= n2 - 1; j2++) {
a[j1][j2] *= 4.0 / n1 / n2;
}
}
.
-------- DST (Discrete Sine Transform) / Inverse of DST --------
[definition]
<case1> IDST (excluding scale)
S[k1][k2] = sum_j1=1^n1 sum_j2=1^n2 A[j1][j2] *
sin(pi*j1*(k1+1/2)/n1) *
sin(pi*j2*(k2+1/2)/n2),
0<=k1<n1, 0<=k2<n2
<case2> DST
S[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 a[j1][j2] *
sin(pi*(j1+1/2)*k1/n1) *
sin(pi*(j2+1/2)*k2/n2),
0<k1<=n1, 0<k2<=n2
[usage]
<case1>
ip[0] = 0; // first time only
ddst2d(n1, n2, 1, a, t, ip, w);
<case2>
ip[0] = 0; // first time only
ddst2d(n1, n2, -1, a, t, ip, w);
[parameters]
n1 :data length (int)
n1 >= 2, n1 = power of 2
n2 :data length (int)
n2 >= 2, n2 = power of 2
a[0...n1-1][0...n2-1]
:input/output data (double **)
<case1>
input data
a[j1][j2] = A[j1][j2], 0<j1<n1, 0<j2<n2,
a[j1][0] = A[j1][n2], 0<j1<n1,
a[0][j2] = A[n1][j2], 0<j2<n2,
a[0][0] = A[n1][n2]
(i.e. A[j1][j2] = a[j1 % n1][j2 % n2])
output data
a[k1][k2] = S[k1][k2], 0<=k1<n1, 0<=k2<n2
<case2>
output data
a[k1][k2] = S[k1][k2], 0<k1<n1, 0<k2<n2,
a[k1][0] = S[k1][n2], 0<k1<n1,
a[0][k2] = S[n1][k2], 0<k2<n2,
a[0][0] = S[n1][n2]
(i.e. S[k1][k2] = a[k1 % n1][k2 % n2])
t[0...*]
:work area (double *)
length of t >= 4*n1, if single thread,
length of t >= 4*n1*FFT2D_MAX_THREADS, if multi threads,
t is dynamically allocated, if t == NULL.
ip[0...*]
:work area for bit reversal (int *)
length of ip >= 2+sqrt(n)
(n = max(n1/2, n2/2))
ip[0],ip[1] are pointers of the cos/sin table.
w[0...*]
:cos/sin table (double *)
length of w >= max(n1*3/2, n2*3/2)
w[],ip[] are initialized if ip[0] == 0.
[remark]
Inverse of
ddst2d(n1, n2, -1, a, t, ip, w);
is
for (j1 = 0; j1 <= n1 - 1; j1++) {
a[j1][0] *= 0.5;
}
for (j2 = 0; j2 <= n2 - 1; j2++) {
a[0][j2] *= 0.5;
}
ddst2d(n1, n2, 1, a, t, ip, w);
for (j1 = 0; j1 <= n1 - 1; j1++) {
for (j2 = 0; j2 <= n2 - 1; j2++) {
a[j1][j2] *= 4.0 / n1 / n2;
}
}
.
*/
#include <stdio.h>
#include <stdlib.h>
#define fft2d_alloc_error_check(p) { \
if ((p) == NULL) { \
fprintf(stderr, "fft2d memory allocation error\n"); \
exit(1); \
} \
}
#ifdef USE_FFT2D_PTHREADS
#define USE_FFT2D_THREADS
#ifndef FFT2D_MAX_THREADS
#define FFT2D_MAX_THREADS 4
#endif
#ifndef FFT2D_THREADS_BEGIN_N
#define FFT2D_THREADS_BEGIN_N 65536
#endif
#include <pthread.h>
#define fft2d_thread_t pthread_t
#define fft2d_thread_create(thp,func,argp) { \
if (pthread_create(thp, NULL, func, (void *) (argp)) != 0) { \
fprintf(stderr, "fft2d thread error\n"); \
exit(1); \
} \
}
#define fft2d_thread_wait(th) { \
if (pthread_join(th, NULL) != 0) { \
fprintf(stderr, "fft2d thread error\n"); \
exit(1); \
} \
}
#endif
#ifdef USE_FFT2D_WINTHREADS
#define USE_FFT2D_THREADS
#ifndef FFT2D_MAX_THREADS
#define FFT2D_MAX_THREADS 4
#endif
#ifndef FFT2D_THREADS_BEGIN_N
#define FFT2D_THREADS_BEGIN_N 131072
#endif
#include <windows.h>
#define fft2d_thread_t HANDLE
#define fft2d_thread_create(thp,func,argp) { \
DWORD thid; \
*(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) (func), (LPVOID) (argp), 0, &thid); \
if (*(thp) == 0) { \
fprintf(stderr, "fft2d thread error\n"); \
exit(1); \
} \
}
#define fft2d_thread_wait(th) { \
WaitForSingleObject(th, INFINITE); \
CloseHandle(th); \
}
#endif
void cdft2d(int n1, int n2, int isgn, double **a, double *t,
int *ip, double *w)
{
void makewt(int nw, int *ip, double *w);
void cdft(int n, int isgn, double *a, int *ip, double *w);
void cdft2d_sub(int n1, int n2, int isgn, double **a, double *t,
int *ip, double *w);
#ifdef USE_FFT2D_THREADS
void xdft2d0_subth(int n1, int n2, int icr, int isgn, double **a,
int *ip, double *w);
void cdft2d_subth(int n1, int n2, int isgn, double **a, double *t,
int *ip, double *w);
#endif
int n, itnull, nthread, nt, i;
n = n1 << 1;
if (n < n2) {
n = n2;
}
if (n > (ip[0] << 2)) {
makewt(n >> 2, ip, w);
}
itnull = 0;
if (t == NULL) {
itnull = 1;
nthread = 1;
#ifdef USE_FFT2D_THREADS
nthread = FFT2D_MAX_THREADS;
#endif
nt = 8 * nthread * n1;
if (n2 == 4 * nthread) {
nt >>= 1;
} else if (n2 < 4 * nthread) {
nt >>= 2;
}
t = (double *) malloc(sizeof(double) * nt);
fft2d_alloc_error_check(t);
}
#ifdef USE_FFT2D_THREADS
if ((double) n1 * n2 >= (double) FFT2D_THREADS_BEGIN_N) {
xdft2d0_subth(n1, n2, 0, isgn, a, ip, w);
cdft2d_subth(n1, n2, isgn, a, t, ip, w);
} else
#endif
{
for (i = 0; i < n1; i++) {
cdft(n2, isgn, a[i], ip, w);
}
cdft2d_sub(n1, n2, isgn, a, t, ip, w);
}
if (itnull != 0) {
free(t);
}
}
void rdft2d(int n1, int n2, int isgn, 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 rdft(int n, int isgn, double *a, int *ip, double *w);
void cdft2d_sub(int n1, int n2, int isgn, double **a, double *t,
int *ip, double *w);
void rdft2d_sub(int n1, int n2, int isgn, double **a);
#ifdef USE_FFT2D_THREADS
void xdft2d0_subth(int n1, int n2, int icr, int isgn, double **a,
int *ip, double *w);
void cdft2d_subth(int n1, int n2, int isgn, double **a, double *t,
int *ip, double *w);
#endif
int n, nw, nc, itnull, nthread, nt, i;
n = n1 << 1;
if (n < n2) {
n = n2;
}
nw = ip[0];
if (n > (nw << 2)) {
nw = n >> 2;
makewt(nw, ip, w);
}
nc = ip[1];
if (n2 > (nc << 2)) {
nc = n2 >> 2;
makect(nc, ip, w + nw);
}
itnull = 0;
if (t == NULL) {
itnull = 1;
nthread = 1;
#ifdef USE_FFT2D_THREADS
nthread = FFT2D_MAX_THREADS;
#endif
nt = 8 * nthread * n1;
if (n2 == 4 * nthread) {
nt >>= 1;
} else if (n2 < 4 * nthread) {
nt >>= 2;
}
t = (double *) malloc(sizeof(double) * nt);
fft2d_alloc_error_check(t);
}
#ifdef USE_FFT2D_THREADS
if ((double) n1 * n2 >= (double) FFT2D_THREADS_BEGIN_N) {
if (isgn < 0) {
rdft2d_sub(n1, n2, isgn, a);
cdft2d_subth(n1, n2, isgn, a, t, ip, w);
}
xdft2d0_subth(n1, n2, 1, isgn, a, ip, w);
if (isgn >= 0) {
cdft2d_subth(n1, n2, isgn, a, t, ip, w);
rdft2d_sub(n1, n2, isgn, a);
}
} else
#endif
{
if (isgn < 0) {
rdft2d_sub(n1, n2, isgn, a);
cdft2d_sub(n1, n2, isgn, a, t, ip, w);
}
for (i = 0; i < n1; i++) {
rdft(n2, isgn, a[i], ip, w);
}
if (isgn >= 0) {
cdft2d_sub(n1, n2, isgn, a, t, ip, w);
rdft2d_sub(n1, n2, isgn, a);
}
}
if (itnull != 0) {
free(t);
}
}
void rdft2dsort(int n1, int n2, int isgn, double **a)
{
int n1h, i;
double x, y;
n1h = n1 >> 1;
if (isgn < 0) {
for (i = n1h + 1; i < n1; i++) {
a[i][0] = a[i][n2 + 1];
a[i][1] = a[i][n2];
}
a[0][1] = a[0][n2];
a[n1h][1] = a[n1h][n2];
} else {
for (i = n1h + 1; i < n1; i++) {
y = a[i][0];
x = a[i][1];
a[i][n2] = x;
a[i][n2 + 1] = y;
a[n1 - i][n2] = x;
a[n1 - i][n2 + 1] = -y;
a[i][0] = a[n1 - i][0];
a[i][1] = -a[n1 - i][1];
}
a[0][n2] = a[0][1];
a[0][n2 + 1] = 0;
a[0][1] = 0;
a[n1h][n2] = a[n1h][1];
a[n1h][n2 + 1] = 0;
a[n1h][1] = 0;
}
}
void ddct2d(int n1, int n2, int isgn, 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 ddct(int n, int isgn, double *a, int *ip, double *w);
void ddxt2d_sub(int n1, int n2, int ics, int isgn, double **a,
double *t, int *ip, double *w);
#ifdef USE_FFT2D_THREADS
void ddxt2d0_subth(int n1, int n2, int ics, int isgn, double **a,
int *ip, double *w);
void ddxt2d_subth(int n1, int n2, int ics, int isgn, double **a,
double *t, int *ip, double *w);
#endif
int n, nw, nc, itnull, nthread, nt, i;
n = n1;
if (n < n2) {
n = n2;
}
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);
}
itnull = 0;
if (t == NULL) {
itnull = 1;
nthread = 1;
#ifdef USE_FFT2D_THREADS
nthread = FFT2D_MAX_THREADS;
#endif
nt = 4 * nthread * n1;
if (n2 == 2 * nthread) {
nt >>= 1;
} else if (n2 < 2 * nthread) {
nt >>= 2;
}
t = (double *) malloc(sizeof(double) * nt);
fft2d_alloc_error_check(t);
}
#ifdef USE_FFT2D_THREADS
if ((double) n1 * n2 >= (double) FFT2D_THREADS_BEGIN_N) {
ddxt2d0_subth(n1, n2, 0, isgn, a, ip, w);
ddxt2d_subth(n1, n2, 0, isgn, a, t, ip, w);
} else
#endif
{
for (i = 0; i < n1; i++) {
ddct(n2, isgn, a[i], ip, w);
}
ddxt2d_sub(n1, n2, 0, isgn, a, t, ip, w);
}
if (itnull != 0) {
free(t);
}
}
void ddst2d(int n1, int n2, int isgn, 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 ddst(int n, int isgn, double *a, int *ip, double *w);
void ddxt2d_sub(int n1, int n2, int ics, int isgn, double **a,
double *t, int *ip, double *w);
#ifdef USE_FFT2D_THREADS
void ddxt2d0_subth(int n1, int n2, int ics, int isgn, double **a,
int *ip, double *w);
void ddxt2d_subth(int n1, int n2, int ics, int isgn, double **a,
double *t, int *ip, double *w);
#endif
int n, nw, nc, itnull, nthread, nt, i;
n = n1;
if (n < n2) {
n = n2;
}
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);
}
itnull = 0;
if (t == NULL) {
itnull = 1;
nthread = 1;
#ifdef USE_FFT2D_THREADS
nthread = FFT2D_MAX_THREADS;
#endif
nt = 4 * nthread * n1;
if (n2 == 2 * nthread) {
nt >>= 1;
} else if (n2 < 2 * nthread) {
nt >>= 2;
}
t = (double *) malloc(sizeof(double) * nt);
fft2d_alloc_error_check(t);
}
#ifdef USE_FFT2D_THREADS
if ((double) n1 * n2 >= (double) FFT2D_THREADS_BEGIN_N) {
ddxt2d0_subth(n1, n2, 1, isgn, a, ip, w);
ddxt2d_subth(n1, n2, 1, isgn, a, t, ip, w);
} else
#endif
{
for (i = 0; i < n1; i++) {
ddst(n2, isgn, a[i], ip, w);
}
ddxt2d_sub(n1, n2, 1, isgn, a, t, ip, w);
}
if (itnull != 0) {
free(t);
}
}
void cdft2d_sub(int n1, int n2, int isgn, double **a, double *t,
int *ip, double *w)
{
void cdft(int n, int isgn, double *a, int *ip, double *w);
int i, j;
if (n2 > 4) {
for (j = 0; j < n2; j += 8) {
for (i = 0; i < n1; i++) {
t[2 * i] = a[i][j];
t[2 * i + 1] = a[i][j + 1];
t[2 * n1 + 2 * i] = a[i][j + 2];
t[2 * n1 + 2 * i + 1] = a[i][j + 3];
t[4 * n1 + 2 * i] = a[i][j + 4];
t[4 * n1 + 2 * i + 1] = a[i][j + 5];
t[6 * n1 + 2 * i] = a[i][j + 6];
t[6 * n1 + 2 * i + 1] = a[i][j + 7];
}
cdft(2 * n1, isgn, t, ip, w);
cdft(2 * n1, isgn, &t[2 * n1], ip, w);
cdft(2 * n1, isgn, &t[4 * n1], ip, w);
cdft(2 * n1, isgn, &t[6 * n1], ip, w);
for (i = 0; i < n1; i++) {
a[i][j] = t[2 * i];
a[i][j + 1] = t[2 * i + 1];
a[i][j + 2] = t[2 * n1 + 2 * i];
a[i][j + 3] = t[2 * n1 + 2 * i + 1];
a[i][j + 4] = t[4 * n1 + 2 * i];
a[i][j + 5] = t[4 * n1 + 2 * i + 1];
a[i][j + 6] = t[6 * n1 + 2 * i];
a[i][j + 7] = t[6 * n1 + 2 * i + 1];
}
}
} else if (n2 == 4) {
for (i = 0; i < n1; i++) {
t[2 * i] = a[i][0];
t[2 * i + 1] = a[i][1];
t[2 * n1 + 2 * i] = a[i][2];
t[2 * n1 + 2 * i + 1] = a[i][3];
}
cdft(2 * n1, isgn, t, ip, w);
cdft(2 * n1, isgn, &t[2 * n1], ip, w);
for (i = 0; i < n1; i++) {
a[i][0] = t[2 * i];
a[i][1] = t[2 * i + 1];
a[i][2] = t[2 * n1 + 2 * i];
a[i][3] = t[2 * n1 + 2 * i + 1];
}
} else if (n2 == 2) {
for (i = 0; i < n1; i++) {
t[2 * i] = a[i][0];
t[2 * i + 1] = a[i][1];
}
cdft(2 * n1, isgn, t, ip, w);
for (i = 0; i < n1; i++) {
a[i][0] = t[2 * i];
a[i][1] = t[2 * i + 1];
}
}
}
void rdft2d_sub(int n1, int n2, int isgn, double **a)
{
int n1h, i, j;
double xi;
n1h = n1 >> 1;
if (isgn < 0) {
for (i = 1; i < n1h; i++) {
j = n1 - i;
xi = a[i][0] - a[j][0];
a[i][0] += a[j][0];
a[j][0] = xi;
xi = a[j][1] - a[i][1];
a[i][1] += a[j][1];
a[j][1] = xi;
}
} else {
for (i = 1; i < n1h; i++) {
j = n1 - i;
a[j][0] = 0.5 * (a[i][0] - a[j][0]);
a[i][0] -= a[j][0];
a[j][1] = 0.5 * (a[i][1] + a[j][1]);
a[i][1] -= a[j][1];
}
}
}
void ddxt2d_sub(int n1, int n2, int ics, int isgn, double **a,
double *t, int *ip, double *w)
{
void ddct(int n, int isgn, double *a, int *ip, double *w);
void ddst(int n, int isgn, double *a, int *ip, double *w);
int i, j;
if (n2 > 2) {
for (j = 0; j < n2; j += 4) {
for (i = 0; i < n1; i++) {
t[i] = a[i][j];
t[n1 + i] = a[i][j + 1];
t[2 * n1 + i] = a[i][j + 2];
t[3 * n1 + i] = a[i][j + 3];
}
if (ics == 0) {
ddct(n1, isgn, t, ip, w);
ddct(n1, isgn, &t[n1], ip, w);
ddct(n1, isgn, &t[2 * n1], ip, w);
ddct(n1, isgn, &t[3 * n1], ip, w);
} else {
ddst(n1, isgn, t, ip, w);
ddst(n1, isgn, &t[n1], ip, w);
ddst(n1, isgn, &t[2 * n1], ip, w);
ddst(n1, isgn, &t[3 * n1], ip, w);
}
for (i = 0; i < n1; i++) {
a[i][j] = t[i];
a[i][j + 1] = t[n1 + i];
a[i][j + 2] = t[2 * n1 + i];
a[i][j + 3] = t[3 * n1 + i];
}
}
} else if (n2 == 2) {
for (i = 0; i < n1; i++) {
t[i] = a[i][0];
t[n1 + i] = a[i][1];
}
if (ics == 0) {
ddct(n1, isgn, t, ip, w);
ddct(n1, isgn, &t[n1], ip, w);
} else {
ddst(n1, isgn, t, ip, w);
ddst(n1, isgn, &t[n1], ip, w);
}
for (i = 0; i < n1; i++) {
a[i][0] = t[i];
a[i][1] = t[n1 + i];
}
}
}
#ifdef USE_FFT2D_THREADS
struct fft2d_arg_st {
int nthread;
int n0;
int n1;
int n2;
int ic;
int isgn;
double **a;
double *t;
int *ip;
double *w;
};
typedef struct fft2d_arg_st fft2d_arg_t;
void xdft2d0_subth(int n1, int n2, int icr, int isgn, double **a,
int *ip, double *w)
{
void *xdft2d0_th(void *p);
fft2d_thread_t th[FFT2D_MAX_THREADS];
fft2d_arg_t ag[FFT2D_MAX_THREADS];
int nthread, i;
nthread = FFT2D_MAX_THREADS;
if (nthread > n1) {
nthread = n1;
}
for (i = 0; i < nthread; i++) {
ag[i].nthread = nthread;
ag[i].n0 = i;
ag[i].n1 = n1;
ag[i].n2 = n2;
ag[i].ic = icr;
ag[i].isgn = isgn;
ag[i].a = a;
ag[i].ip = ip;
ag[i].w = w;
fft2d_thread_create(&th[i], xdft2d0_th, &ag[i]);
}
for (i = 0; i < nthread; i++) {
fft2d_thread_wait(th[i]);
}
}
void cdft2d_subth(int n1, int n2, int isgn, double **a, double *t,
int *ip, double *w)
{
void *cdft2d_th(void *p);
fft2d_thread_t th[FFT2D_MAX_THREADS];
fft2d_arg_t ag[FFT2D_MAX_THREADS];
int nthread, nt, i;
nthread = FFT2D_MAX_THREADS;
nt = 8 * n1;
if (n2 == 4 * FFT2D_MAX_THREADS) {
nt >>= 1;
} else if (n2 < 4 * FFT2D_MAX_THREADS) {
nthread = n2 >> 1;
nt >>= 2;
}
for (i = 0; i < nthread; i++) {
ag[i].nthread = nthread;
ag[i].n0 = i;
ag[i].n1 = n1;
ag[i].n2 = n2;
ag[i].isgn = isgn;
ag[i].a = a;
ag[i].t = &t[nt * i];
ag[i].ip = ip;
ag[i].w = w;
fft2d_thread_create(&th[i], cdft2d_th, &ag[i]);
}
for (i = 0; i < nthread; i++) {
fft2d_thread_wait(th[i]);
}
}
void ddxt2d0_subth(int n1, int n2, int ics, int isgn, double **a,
int *ip, double *w)
{
void *ddxt2d0_th(void *p);
fft2d_thread_t th[FFT2D_MAX_THREADS];
fft2d_arg_t ag[FFT2D_MAX_THREADS];
int nthread, i;
nthread = FFT2D_MAX_THREADS;
if (nthread > n1) {
nthread = n1;
}
for (i = 0; i < nthread; i++) {
ag[i].nthread = nthread;
ag[i].n0 = i;
ag[i].n1 = n1;
ag[i].n2 = n2;
ag[i].ic = ics;
ag[i].isgn = isgn;
ag[i].a = a;
ag[i].ip = ip;
ag[i].w = w;
fft2d_thread_create(&th[i], ddxt2d0_th, &ag[i]);
}
for (i = 0; i < nthread; i++) {
fft2d_thread_wait(th[i]);
}
}
void ddxt2d_subth(int n1, int n2, int ics, int isgn, double **a,
double *t, int *ip, double *w)
{
void *ddxt2d_th(void *p);
fft2d_thread_t th[FFT2D_MAX_THREADS];
fft2d_arg_t ag[FFT2D_MAX_THREADS];
int nthread, nt, i;
nthread = FFT2D_MAX_THREADS;
nt = 4 * n1;
if (n2 == 2 * FFT2D_MAX_THREADS) {
nt >>= 1;
} else if (n2 < 2 * FFT2D_MAX_THREADS) {
nthread = n2;
nt >>= 2;
}
for (i = 0; i < nthread; i++) {
ag[i].nthread = nthread;
ag[i].n0 = i;
ag[i].n1 = n1;
ag[i].n2 = n2;
ag[i].ic = ics;
ag[i].isgn = isgn;
ag[i].a = a;
ag[i].t = &t[nt * i];
ag[i].ip = ip;
ag[i].w = w;
fft2d_thread_create(&th[i], ddxt2d_th, &ag[i]);
}
for (i = 0; i < nthread; i++) {
fft2d_thread_wait(th[i]);
}
}
void *xdft2d0_th(void *p)
{
void cdft(int n, int isgn, double *a, int *ip, double *w);
void rdft(int n, int isgn, double *a, int *ip, double *w);
int nthread, n0, n1, n2, icr, isgn, *ip, i;
double **a, *w;
nthread = ((fft2d_arg_t *) p)->nthread;
n0 = ((fft2d_arg_t *) p)->n0;
n1 = ((fft2d_arg_t *) p)->n1;
n2 = ((fft2d_arg_t *) p)->n2;
icr = ((fft2d_arg_t *) p)->ic;
isgn = ((fft2d_arg_t *) p)->isgn;
a = ((fft2d_arg_t *) p)->a;
ip = ((fft2d_arg_t *) p)->ip;
w = ((fft2d_arg_t *) p)->w;
if (icr == 0) {
for (i = n0; i < n1; i += nthread) {
cdft(n2, isgn, a[i], ip, w);
}
} else {
for (i = n0; i < n1; i += nthread) {
rdft(n2, isgn, a[i], ip, w);
}
}
return (void *) 0;
}
void *cdft2d_th(void *p)
{
void cdft(int n, int isgn, double *a, int *ip, double *w);
int nthread, n0, n1, n2, isgn, *ip, i, j;
double **a, *t, *w;
nthread = ((fft2d_arg_t *) p)->nthread;
n0 = ((fft2d_arg_t *) p)->n0;
n1 = ((fft2d_arg_t *) p)->n1;
n2 = ((fft2d_arg_t *) p)->n2;
isgn = ((fft2d_arg_t *) p)->isgn;
a = ((fft2d_arg_t *) p)->a;
t = ((fft2d_arg_t *) p)->t;
ip = ((fft2d_arg_t *) p)->ip;
w = ((fft2d_arg_t *) p)->w;
if (n2 > 4 * nthread) {
for (j = 8 * n0; j < n2; j += 8 * nthread) {
for (i = 0; i < n1; i++) {
t[2 * i] = a[i][j];
t[2 * i + 1] = a[i][j + 1];
t[2 * n1 + 2 * i] = a[i][j + 2];
t[2 * n1 + 2 * i + 1] = a[i][j + 3];
t[4 * n1 + 2 * i] = a[i][j + 4];
t[4 * n1 + 2 * i + 1] = a[i][j + 5];
t[6 * n1 + 2 * i] = a[i][j + 6];
t[6 * n1 + 2 * i + 1] = a[i][j + 7];
}
cdft(2 * n1, isgn, t, ip, w);
cdft(2 * n1, isgn, &t[2 * n1], ip, w);
cdft(2 * n1, isgn, &t[4 * n1], ip, w);
cdft(2 * n1, isgn, &t[6 * n1], ip, w);
for (i = 0; i < n1; i++) {
a[i][j] = t[2 * i];
a[i][j + 1] = t[2 * i + 1];
a[i][j + 2] = t[2 * n1 + 2 * i];
a[i][j + 3] = t[2 * n1 + 2 * i + 1];
a[i][j + 4] = t[4 * n1 + 2 * i];
a[i][j + 5] = t[4 * n1 + 2 * i + 1];
a[i][j + 6] = t[6 * n1 + 2 * i];
a[i][j + 7] = t[6 * n1 + 2 * i + 1];
}
}
} else if (n2 == 4 * nthread) {
for (i = 0; i < n1; i++) {
t[2 * i] = a[i][4 * n0];
t[2 * i + 1] = a[i][4 * n0 + 1];
t[2 * n1 + 2 * i] = a[i][4 * n0 + 2];
t[2 * n1 + 2 * i + 1] = a[i][4 * n0 + 3];
}
cdft(2 * n1, isgn, t, ip, w);
cdft(2 * n1, isgn, &t[2 * n1], ip, w);
for (i = 0; i < n1; i++) {
a[i][4 * n0] = t[2 * i];
a[i][4 * n0 + 1] = t[2 * i + 1];
a[i][4 * n0 + 2] = t[2 * n1 + 2 * i];
a[i][4 * n0 + 3] = t[2 * n1 + 2 * i + 1];
}
} else if (n2 == 2 * nthread) {
for (i = 0; i < n1; i++) {
t[2 * i] = a[i][2 * n0];
t[2 * i + 1] = a[i][2 * n0 + 1];
}
cdft(2 * n1, isgn, t, ip, w);
for (i = 0; i < n1; i++) {
a[i][2 * n0] = t[2 * i];
a[i][2 * n0 + 1] = t[2 * i + 1];
}
}
return (void *) 0;
}
void *ddxt2d0_th(void *p)
{
void ddct(int n, int isgn, double *a, int *ip, double *w);
void ddst(int n, int isgn, double *a, int *ip, double *w);
int nthread, n0, n1, n2, ics, isgn, *ip, i;
double **a, *w;
nthread = ((fft2d_arg_t *) p)->nthread;
n0 = ((fft2d_arg_t *) p)->n0;
n1 = ((fft2d_arg_t *) p)->n1;
n2 = ((fft2d_arg_t *) p)->n2;
ics = ((fft2d_arg_t *) p)->ic;
isgn = ((fft2d_arg_t *) p)->isgn;
a = ((fft2d_arg_t *) p)->a;
ip = ((fft2d_arg_t *) p)->ip;
w = ((fft2d_arg_t *) p)->w;
if (ics == 0) {
for (i = n0; i < n1; i += nthread) {
ddct(n2, isgn, a[i], ip, w);
}
} else {
for (i = n0; i < n1; i += nthread) {
ddst(n2, isgn, a[i], ip, w);
}
}
return (void *) 0;
}
void *ddxt2d_th(void *p)
{
void ddct(int n, int isgn, double *a, int *ip, double *w);
void ddst(int n, int isgn, double *a, int *ip, double *w);
int nthread, n0, n1, n2, ics, isgn, *ip, i, j;
double **a, *t, *w;
nthread = ((fft2d_arg_t *) p)->nthread;
n0 = ((fft2d_arg_t *) p)->n0;
n1 = ((fft2d_arg_t *) p)->n1;
n2 = ((fft2d_arg_t *) p)->n2;
ics = ((fft2d_arg_t *) p)->ic;
isgn = ((fft2d_arg_t *) p)->isgn;
a = ((fft2d_arg_t *) p)->a;
t = ((fft2d_arg_t *) p)->t;
ip = ((fft2d_arg_t *) p)->ip;
w = ((fft2d_arg_t *) p)->w;
if (n2 > 2 * nthread) {
for (j = 4 * n0; j < n2; j += 4 * nthread) {
for (i = 0; i < n1; i++) {
t[i] = a[i][j];
t[n1 + i] = a[i][j + 1];
t[2 * n1 + i] = a[i][j + 2];
t[3 * n1 + i] = a[i][j + 3];
}
if (ics == 0) {
ddct(n1, isgn, t, ip, w);
ddct(n1, isgn, &t[n1], ip, w);
ddct(n1, isgn, &t[2 * n1], ip, w);
ddct(n1, isgn, &t[3 * n1], ip, w);
} else {
ddst(n1, isgn, t, ip, w);
ddst(n1, isgn, &t[n1], ip, w);
ddst(n1, isgn, &t[2 * n1], ip, w);
ddst(n1, isgn, &t[3 * n1], ip, w);
}
for (i = 0; i < n1; i++) {
a[i][j] = t[i];
a[i][j + 1] = t[n1 + i];
a[i][j + 2] = t[2 * n1 + i];
a[i][j + 3] = t[3 * n1 + i];
}
}
} else if (n2 == 2 * nthread) {
for (i = 0; i < n1; i++) {
t[i] = a[i][2 * n0];
t[n1 + i] = a[i][2 * n0 + 1];
}
if (ics == 0) {
ddct(n1, isgn, t, ip, w);
ddct(n1, isgn, &t[n1], ip, w);
} else {
ddst(n1, isgn, t, ip, w);
ddst(n1, isgn, &t[n1], ip, w);
}
for (i = 0; i < n1; i++) {
a[i][2 * n0] = t[i];
a[i][2 * n0 + 1] = t[n1 + i];
}
} else if (n2 == nthread) {
for (i = 0; i < n1; i++) {
t[i] = a[i][n0];
}
if (ics == 0) {
ddct(n1, isgn, t, ip, w);
} else {
ddst(n1, isgn, t, ip, w);
}
for (i = 0; i < n1; i++) {
a[i][n0] = t[i];
}
}
return (void *) 0;
}
#endif
