diff options
Diffstat (limited to 'src/sndobj/rfftw/rader.c')
| -rw-r--r-- | src/sndobj/rfftw/rader.c | 370 |
1 files changed, 0 insertions, 370 deletions
diff --git a/src/sndobj/rfftw/rader.c b/src/sndobj/rfftw/rader.c deleted file mode 100644 index 6783580..0000000 --- a/src/sndobj/rfftw/rader.c +++ /dev/null @@ -1,370 +0,0 @@ -/*
- * Copyright (c) 1997-1999 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
- *
- */
-
-/*
- * Compute transforms of prime sizes using Rader's trick: turn them
- * into convolutions of size n - 1, which you then perform via a pair
- * of FFTs.
- */
-
-#include <stdlib.h>
-#include <math.h>
-
-#include <fftw-int.h>
-
-#ifdef FFTW_USING_CILK
-#include <cilk.h>
-#include <cilk-compat.h>
-#endif
-
-#ifdef FFTW_DEBUG
-#define WHEN_DEBUG(a) a
-#else
-#define WHEN_DEBUG(a)
-#endif
-
-/* compute n^m mod p, where m >= 0 and p > 0. */
-static int power_mod(int n, int m, int p)
-{
- if (m == 0)
- return 1;
- else if (m % 2 == 0) {
- int x = power_mod(n, m / 2, p);
- return MULMOD(x, x, p);
- }
- else
- return MULMOD(n, power_mod(n, m - 1, p), p);
-}
-
-/*
- * Find the period of n in the multiplicative group mod p (p prime).
- * That is, return the smallest m such that n^m == 1 mod p.
- */
-static int period(int n, int p)
-{
- int prod = n, period = 1;
-
- while (prod != 1) {
- prod = MULMOD(prod, n, p);
- ++period;
- if (prod == 0)
- fftw_die("non-prime order in Rader\n");
- }
- return period;
-}
-
-/* find a generator for the multiplicative group mod p, where p is prime */
-static int find_generator(int p)
-{
- int g;
-
- for (g = 1; g < p; ++g)
- if (period(g, p) == p - 1)
- break;
- if (g == p)
- fftw_die("couldn't find generator for Rader\n");
- return g;
-}
-
-/***************************************************************************/
-
-static fftw_rader_data *create_rader_aux(int p, int flags)
-{
- fftw_complex *omega, *work;
- int g, ginv, gpower;
- int i;
- FFTW_TRIG_REAL twoPiOverN;
- fftw_real scale = 1.0 / (p - 1); /* for convolution */
- fftw_plan plan;
- fftw_rader_data *d;
-
- if (p < 2)
- fftw_die("non-prime order in Rader\n");
-
- flags &= ~FFTW_IN_PLACE;
-
- d = (fftw_rader_data *) fftw_malloc(sizeof(fftw_rader_data));
-
- g = find_generator(p);
- ginv = power_mod(g, p - 2, p);
-
- omega = (fftw_complex *) fftw_malloc((p - 1) * sizeof(fftw_complex));
-
- plan = fftw_create_plan(p - 1, FFTW_FORWARD,
- flags & ~FFTW_NO_VECTOR_RECURSE);
-
- work = (fftw_complex *) fftw_malloc((p - 1) * sizeof(fftw_complex));
-
- twoPiOverN = FFTW_K2PI / (FFTW_TRIG_REAL) p;
- gpower = 1;
- for (i = 0; i < p - 1; ++i) {
- c_re(work[i]) = scale * FFTW_TRIG_COS(twoPiOverN * gpower);
- c_im(work[i]) = FFTW_FORWARD * scale * FFTW_TRIG_SIN(twoPiOverN
- * gpower);
- gpower = MULMOD(gpower, ginv, p);
- }
-
- /* fft permuted roots of unity */
- fftw_executor_simple(p - 1, work, omega, plan->root, 1, 1,
- plan->recurse_kind);
-
- fftw_free(work);
-
- d->plan = plan;
- d->omega = omega;
- d->g = g;
- d->ginv = ginv;
- d->p = p;
- d->flags = flags;
- d->refcount = 1;
- d->next = NULL;
-
- d->cdesc = (fftw_codelet_desc *) fftw_malloc(sizeof(fftw_codelet_desc));
- d->cdesc->name = NULL;
- d->cdesc->codelet = NULL;
- d->cdesc->size = p;
- d->cdesc->dir = FFTW_FORWARD;
- d->cdesc->type = FFTW_RADER;
- d->cdesc->signature = g;
- d->cdesc->ntwiddle = 0;
- d->cdesc->twiddle_order = NULL;
- return d;
-}
-
-/***************************************************************************/
-
-static fftw_rader_data *fftw_create_rader(int p, int flags)
-{
- fftw_rader_data *d = fftw_rader_top;
-
- flags &= ~FFTW_IN_PLACE;
- while (d && (d->p != p || d->flags != flags))
- d = d->next;
- if (d) {
- d->refcount++;
- return d;
- }
- d = create_rader_aux(p, flags);
- d->next = fftw_rader_top;
- fftw_rader_top = d;
- return d;
-}
-
-/***************************************************************************/
-
-/* Compute the prime FFTs, premultiplied by twiddle factors. Below, we
- * extensively use the identity that fft(x*)* = ifft(x) in order to
- * share data between forward and backward transforms and to obviate
- * the necessity of having separate forward and backward plans. */
-
-void fftw_twiddle_rader(fftw_complex *A, const fftw_complex *W,
- int m, int r, int stride,
- fftw_rader_data * d)
-{
- fftw_complex *tmp = (fftw_complex *)
- fftw_malloc((r - 1) * sizeof(fftw_complex));
- int i, k, gpower = 1, g = d->g, ginv = d->ginv;
- fftw_real a0r, a0i;
- fftw_complex *omega = d->omega;
-
- for (i = 0; i < m; ++i, A += stride, W += r - 1) {
- /*
- * Here, we fft W[k-1] * A[k*(m*stride)], using Rader.
- * (Actually, W is pre-permuted to match the permutation that we
- * will do on A.)
- */
-
- /* First, permute the input and multiply by W, storing in tmp: */
- /* gpower == g^k mod r in the following loop */
- for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
- fftw_real rA, iA, rW, iW;
- rW = c_re(W[k]);
- iW = c_im(W[k]);
- rA = c_re(A[gpower * (m * stride)]);
- iA = c_im(A[gpower * (m * stride)]);
- c_re(tmp[k]) = rW * rA - iW * iA;
- c_im(tmp[k]) = rW * iA + iW * rA;
- }
-
- WHEN_DEBUG( {
- if (gpower != 1)
- fftw_die("incorrect generator in Rader\n");
- }
- );
-
- /* FFT tmp to A: */
- fftw_executor_simple(r - 1, tmp, A + (m * stride),
- d->plan->root, 1, m * stride,
- d->plan->recurse_kind);
-
- /* set output DC component: */
- a0r = c_re(A[0]);
- a0i = c_im(A[0]);
- c_re(A[0]) += c_re(A[(m * stride)]);
- c_im(A[0]) += c_im(A[(m * stride)]);
-
- /* now, multiply by omega: */
- for (k = 0; k < r - 1; ++k) {
- fftw_real rA, iA, rW, iW;
- rW = c_re(omega[k]);
- iW = c_im(omega[k]);
- rA = c_re(A[(k + 1) * (m * stride)]);
- iA = c_im(A[(k + 1) * (m * stride)]);
- c_re(A[(k + 1) * (m * stride)]) = rW * rA - iW * iA;
- c_im(A[(k + 1) * (m * stride)]) = -(rW * iA + iW * rA);
- }
-
- /* this will add A[0] to all of the outputs after the ifft */
- c_re(A[(m * stride)]) += a0r;
- c_im(A[(m * stride)]) -= a0i;
-
- /* inverse FFT: */
- fftw_executor_simple(r - 1, A + (m * stride), tmp,
- d->plan->root, m * stride, 1,
- d->plan->recurse_kind);
-
- /* finally, do inverse permutation to unshuffle the output: */
- for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, ginv, r)) {
- c_re(A[gpower * (m * stride)]) = c_re(tmp[k]);
- c_im(A[gpower * (m * stride)]) = -c_im(tmp[k]);
- }
-
- WHEN_DEBUG( {
- if (gpower != 1)
- fftw_die("incorrect generator in Rader\n");
- }
- );
-
- }
-
- fftw_free(tmp);
-}
-
-void fftwi_twiddle_rader(fftw_complex *A, const fftw_complex *W,
- int m, int r, int stride,
- fftw_rader_data * d)
-{
- fftw_complex *tmp = (fftw_complex *)
- fftw_malloc((r - 1) * sizeof(fftw_complex));
- int i, k, gpower = 1, g = d->g, ginv = d->ginv;
- fftw_real a0r, a0i;
- fftw_complex *omega = d->omega;
-
- for (i = 0; i < m; ++i, A += stride, W += r - 1) {
- /*
- * Here, we fft W[k-1]* * A[k*(m*stride)], using Rader.
- * (Actually, W is pre-permuted to match the permutation that
- * we will do on A.)
- */
-
- /* First, permute the input and multiply by W*, storing in tmp: */
- /* gpower == g^k mod r in the following loop */
- for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
- fftw_real rA, iA, rW, iW;
- rW = c_re(W[k]);
- iW = c_im(W[k]);
- rA = c_re(A[gpower * (m * stride)]);
- iA = c_im(A[gpower * (m * stride)]);
- c_re(tmp[k]) = rW * rA + iW * iA;
- c_im(tmp[k]) = iW * rA - rW * iA;
- }
-
- WHEN_DEBUG( {
- if (gpower != 1)
- fftw_die("incorrect generator in Rader\n");
- }
- );
-
- /* FFT tmp to A: */
- fftw_executor_simple(r - 1, tmp, A + (m * stride),
- d->plan->root, 1, m * stride,
- d->plan->recurse_kind);
-
- /* set output DC component: */
- a0r = c_re(A[0]);
- a0i = c_im(A[0]);
- c_re(A[0]) += c_re(A[(m * stride)]);
- c_im(A[0]) -= c_im(A[(m * stride)]);
-
- /* now, multiply by omega: */
- for (k = 0; k < r - 1; ++k) {
- fftw_real rA, iA, rW, iW;
- rW = c_re(omega[k]);
- iW = c_im(omega[k]);
- rA = c_re(A[(k + 1) * (m * stride)]);
- iA = c_im(A[(k + 1) * (m * stride)]);
- c_re(A[(k + 1) * (m * stride)]) = rW * rA - iW * iA;
- c_im(A[(k + 1) * (m * stride)]) = -(rW * iA + iW * rA);
- }
-
- /* this will add A[0] to all of the outputs after the ifft */
- c_re(A[(m * stride)]) += a0r;
- c_im(A[(m * stride)]) += a0i;
-
- /* inverse FFT: */
- fftw_executor_simple(r - 1, A + (m * stride), tmp,
- d->plan->root, m * stride, 1,
- d->plan->recurse_kind);
-
- /* finally, do inverse permutation to unshuffle the output: */
- for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, ginv, r)) {
- A[gpower * (m * stride)] = tmp[k];
- }
-
- WHEN_DEBUG( {
- if (gpower != 1)
- fftw_die("incorrect generator in Rader\n");
- }
- );
- }
-
- fftw_free(tmp);
-}
-
-/***************************************************************************/
-
-/*
- * Make an FFTW_RADER plan node. Note that this function must go
- * here, rather than in putils.c, because it indirectly calls the
- * fftw_planner. If we included it in putils.c, which is also used
- * by rfftw, then any program using rfftw would be linked with all
- * of the FFTW codelets, even if they were not needed. I wish that the
- * darn linkers operated on a function rather than a file granularity.
- */
-fftw_plan_node *fftw_make_node_rader(int n, int size, fftw_direction dir,
- fftw_plan_node *recurse,
- int flags)
-{
- fftw_plan_node *p = fftw_make_node();
-
- p->type = FFTW_RADER;
- p->nodeu.rader.size = size;
- p->nodeu.rader.codelet = dir == FFTW_FORWARD ?
- fftw_twiddle_rader : fftwi_twiddle_rader;
- p->nodeu.rader.rader_data = fftw_create_rader(size, flags);
- p->nodeu.rader.recurse = recurse;
- fftw_use_node(recurse);
-
- if (flags & FFTW_MEASURE)
- p->nodeu.rader.tw =
- fftw_create_twiddle(n, p->nodeu.rader.rader_data->cdesc);
- else
- p->nodeu.rader.tw = 0;
- return p;
-}
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