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/*
* Copyright (c) 1997-1999, 2003 Massachusetts Institute of Technology
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
/*
* twiddle.c -- compute twiddle factors
* These are the twiddle factors for *direct* fft. Flip sign to get
* the inverse
*/
/* $Id: twiddle.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
#include "fftw-int.h"
#include <math.h>
#include <stdlib.h>
#include <limits.h>
#ifndef TRUE
#define TRUE (1 == 1)
#endif
#ifndef FALSE
#define FALSE (1 == 0)
#endif
#ifdef USE_FFTW_SAFE_MULMOD
/* compute (x * y) mod p, but watch out for integer overflows; we must
have x, y >= 0, p > 0. This routine is slow. */
int fftw_safe_mulmod(int x, int y, int p)
{
if (y == 0 || x <= INT_MAX / y)
return((x * y) % p);
else {
int y2 = y/2;
return((fftw_safe_mulmod(x, y2, p) +
fftw_safe_mulmod(x, y - y2, p)) % p);
}
}
#endif /* USE_FFTW_SAFE_MULMOD */
static fftw_complex *fftw_compute_rader_twiddle(int n, int r, int g)
{
FFTW_TRIG_REAL twoPiOverN;
int m = n / r;
int i, j, gpower;
fftw_complex *W;
twoPiOverN = FFTW_K2PI / (FFTW_TRIG_REAL) n;
W = (fftw_complex *) fftw_malloc((r - 1) * m * sizeof(fftw_complex));
for (i = 0; i < m; ++i)
for (gpower = 1, j = 0; j < r - 1; ++j,
gpower = MULMOD(gpower, g, r)) {
int k = i * (r - 1) + j;
FFTW_TRIG_REAL
ij = (FFTW_TRIG_REAL) (i * gpower);
c_re(W[k]) = FFTW_TRIG_COS(twoPiOverN * ij);
c_im(W[k]) = FFTW_FORWARD * FFTW_TRIG_SIN(twoPiOverN * ij);
}
return W;
}
/*
* compute the W coefficients (that is, powers of the root of 1)
* and store them into an array.
*/
static fftw_complex *fftw_compute_twiddle(int n, const fftw_codelet_desc *d)
{
FFTW_TRIG_REAL twoPiOverN;
int i, j;
fftw_complex *W;
twoPiOverN = FFTW_K2PI / (FFTW_TRIG_REAL) n;
if (!d) {
/* generic codelet, needs all twiddles in order */
W = (fftw_complex *) fftw_malloc(n * sizeof(fftw_complex));
for (i = 0; i < n; ++i) {
c_re(W[i]) = FFTW_TRIG_COS(twoPiOverN * (FFTW_TRIG_REAL) i);
c_im(W[i]) = FFTW_FORWARD * FFTW_TRIG_SIN(twoPiOverN * (FFTW_TRIG_REAL) i);
}
} else if (d->type == FFTW_RADER)
W = fftw_compute_rader_twiddle(n, d->size, d->signature);
else {
int r = d->size;
int m = n / r, m_alloc;
int r1 = d->ntwiddle;
int istart;
if (d->type == FFTW_TWIDDLE) {
istart = 0;
m_alloc = m;
} else if (d->type == FFTW_HC2HC) {
/*
* This is tricky, do not change lightly.
*/
m = (m + 1) / 2;
m_alloc = m - 1;
istart = 1;
} else {
fftw_die("compute_twiddle: invalid argument\n");
/* paranoia for gcc */
m_alloc = 0;
istart = 0;
}
W = (fftw_complex *) fftw_malloc(r1 * m_alloc * sizeof(fftw_complex));
for (i = istart; i < m; ++i)
for (j = 0; j < r1; ++j) {
int k = (i - istart) * r1 + j;
FFTW_TRIG_REAL
ij = (FFTW_TRIG_REAL) (i * d->twiddle_order[j]);
c_re(W[k]) = FFTW_TRIG_COS(twoPiOverN * ij);
c_im(W[k]) = FFTW_FORWARD * FFTW_TRIG_SIN(twoPiOverN * ij);
}
}
return W;
}
/*
* these routines implement a simple reference-count-based
* management of twiddle structures
*/
static fftw_twiddle *twlist = (fftw_twiddle *) 0;
int fftw_twiddle_size = 0; /* total allocated size, for debugging */
/* true if the two codelets can share the same twiddle factors */
static int compatible(const fftw_codelet_desc *d1, const fftw_codelet_desc *d2)
{
int i;
/* true if they are the same codelet */
if (d1 == d2)
return TRUE;
/* false if one is null and the other is not */
if (!d1 || !d2)
return FALSE;
/* false if size is different */
if (d1->size != d2->size)
return FALSE;
/* false if different types (FFTW_TWIDDLE/FFTW_HC2HC/FFTW_RADER) */
if (d1->type != d2->type)
return FALSE;
/* false if they need different # of twiddles */
if (d1->ntwiddle != d2->ntwiddle)
return FALSE;
/* false if the twiddle orders are different */
for (i = 0; i < d1->ntwiddle; ++i)
if (d1->twiddle_order[i] != d2->twiddle_order[i])
return FALSE;
return TRUE;
}
fftw_twiddle *fftw_create_twiddle(int n, const fftw_codelet_desc *d)
{
fftw_twiddle *tw;
/* lookup this n in the twiddle list */
for (tw = twlist; tw; tw = tw->next)
if (n == tw->n && compatible(d, tw->cdesc)) {
++tw->refcnt;
return tw;
}
/* not found --- allocate a new struct twiddle */
tw = (fftw_twiddle *) fftw_malloc(sizeof(fftw_twiddle));
fftw_twiddle_size += n;
tw->n = n;
tw->cdesc = d;
tw->twarray = fftw_compute_twiddle(n, d);
tw->refcnt = 1;
/* enqueue the new struct */
tw->next = twlist;
twlist = tw;
return tw;
}
void fftw_destroy_twiddle(fftw_twiddle * tw)
{
fftw_twiddle **p;
--tw->refcnt;
if (tw->refcnt == 0) {
/* remove from the list of known twiddle factors */
for (p = &twlist; p; p = &((*p)->next))
if (*p == tw) {
*p = tw->next;
fftw_twiddle_size -= tw->n;
fftw_free(tw->twarray);
fftw_free(tw);
return;
}
fftw_die("BUG in fftw_destroy_twiddle\n");
}
}
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