387 lines
10 KiB
C
387 lines
10 KiB
C
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/*
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* Copyright (c) 2003, 2007-14 Matteo Frigo
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* Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*
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*/
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#include "rdft/rdft.h"
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/*
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* Compute DHTs of prime sizes using Rader's trick: turn them
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* into convolutions of size n - 1, which we then perform via a pair
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* of FFTs. (We can then do prime real FFTs via rdft-dht.c.)
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*
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* Optionally (determined by the "pad" field of the solver), we can
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* perform the (cyclic) convolution by zero-padding to a size
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* >= 2*(n-1) - 1. This is advantageous if n-1 has large prime factors.
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*
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*/
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typedef struct {
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solver super;
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int pad;
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} S;
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typedef struct {
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plan_rdft super;
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plan *cld1, *cld2;
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R *omega;
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INT n, npad, g, ginv;
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INT is, os;
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plan *cld_omega;
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} P;
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static rader_tl *omegas = 0;
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/***************************************************************************/
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/* If R2HC_ONLY_CONV is 1, we use a trick to perform the convolution
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purely in terms of R2HC transforms, as opposed to R2HC followed by H2RC.
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This requires a few more operations, but allows us to share the same
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plan/codelets for both Rader children. */
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#define R2HC_ONLY_CONV 1
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static void apply(const plan *ego_, R *I, R *O)
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{
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const P *ego = (const P *) ego_;
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INT n = ego->n; /* prime */
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INT npad = ego->npad; /* == n - 1 for unpadded Rader; always even */
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INT is = ego->is, os;
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INT k, gpower, g;
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R *buf, *omega;
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R r0;
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buf = (R *) MALLOC(sizeof(R) * npad, BUFFERS);
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/* First, permute the input, storing in buf: */
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g = ego->g;
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for (gpower = 1, k = 0; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
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buf[k] = I[gpower * is];
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}
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/* gpower == g^(n-1) mod n == 1 */;
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A(n - 1 <= npad);
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for (k = n - 1; k < npad; ++k) /* optionally, zero-pad convolution */
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buf[k] = 0;
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os = ego->os;
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/* compute RDFT of buf, storing in buf (i.e., in-place): */
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{
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plan_rdft *cld = (plan_rdft *) ego->cld1;
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cld->apply((plan *) cld, buf, buf);
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}
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/* set output DC component: */
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O[0] = (r0 = I[0]) + buf[0];
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/* now, multiply by omega: */
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omega = ego->omega;
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buf[0] *= omega[0];
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for (k = 1; k < npad/2; ++k) {
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E rB, iB, rW, iW, a, b;
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rW = omega[k];
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iW = omega[npad - k];
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rB = buf[k];
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iB = buf[npad - k];
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a = rW * rB - iW * iB;
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b = rW * iB + iW * rB;
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#if R2HC_ONLY_CONV
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buf[k] = a + b;
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buf[npad - k] = a - b;
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#else
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buf[k] = a;
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buf[npad - k] = b;
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#endif
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}
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/* Nyquist component: */
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A(k + k == npad); /* since npad is even */
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buf[k] *= omega[k];
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/* this will add input[0] to all of the outputs after the ifft */
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buf[0] += r0;
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/* inverse FFT: */
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{
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plan_rdft *cld = (plan_rdft *) ego->cld2;
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cld->apply((plan *) cld, buf, buf);
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}
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/* do inverse permutation to unshuffle the output: */
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A(gpower == 1);
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#if R2HC_ONLY_CONV
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O[os] = buf[0];
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gpower = g = ego->ginv;
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A(npad == n - 1 || npad/2 >= n - 1);
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if (npad == n - 1) {
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for (k = 1; k < npad/2; ++k, gpower = MULMOD(gpower, g, n)) {
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O[gpower * os] = buf[k] + buf[npad - k];
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}
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O[gpower * os] = buf[k];
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++k, gpower = MULMOD(gpower, g, n);
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for (; k < npad; ++k, gpower = MULMOD(gpower, g, n)) {
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O[gpower * os] = buf[npad - k] - buf[k];
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}
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}
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else {
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for (k = 1; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
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O[gpower * os] = buf[k] + buf[npad - k];
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}
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}
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#else
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g = ego->ginv;
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for (k = 0; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
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O[gpower * os] = buf[k];
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}
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#endif
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A(gpower == 1);
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X(ifree)(buf);
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}
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static R *mkomega(enum wakefulness wakefulness,
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plan *p_, INT n, INT npad, INT ginv)
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{
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plan_rdft *p = (plan_rdft *) p_;
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R *omega;
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INT i, gpower;
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trigreal scale;
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triggen *t;
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if ((omega = X(rader_tl_find)(n, npad + 1, ginv, omegas)))
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return omega;
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omega = (R *)MALLOC(sizeof(R) * npad, TWIDDLES);
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scale = npad; /* normalization for convolution */
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t = X(mktriggen)(wakefulness, n);
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for (i = 0, gpower = 1; i < n-1; ++i, gpower = MULMOD(gpower, ginv, n)) {
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trigreal w[2];
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t->cexpl(t, gpower, w);
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omega[i] = (w[0] + w[1]) / scale;
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}
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X(triggen_destroy)(t);
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A(gpower == 1);
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A(npad == n - 1 || npad >= 2*(n - 1) - 1);
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for (; i < npad; ++i)
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omega[i] = K(0.0);
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if (npad > n - 1)
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for (i = 1; i < n-1; ++i)
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omega[npad - i] = omega[n - 1 - i];
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p->apply(p_, omega, omega);
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X(rader_tl_insert)(n, npad + 1, ginv, omega, &omegas);
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return omega;
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}
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static void free_omega(R *omega)
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{
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X(rader_tl_delete)(omega, &omegas);
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}
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/***************************************************************************/
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static void awake(plan *ego_, enum wakefulness wakefulness)
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{
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P *ego = (P *) ego_;
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X(plan_awake)(ego->cld1, wakefulness);
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X(plan_awake)(ego->cld2, wakefulness);
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X(plan_awake)(ego->cld_omega, wakefulness);
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switch (wakefulness) {
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case SLEEPY:
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free_omega(ego->omega);
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ego->omega = 0;
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break;
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default:
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ego->g = X(find_generator)(ego->n);
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ego->ginv = X(power_mod)(ego->g, ego->n - 2, ego->n);
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A(MULMOD(ego->g, ego->ginv, ego->n) == 1);
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A(!ego->omega);
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ego->omega = mkomega(wakefulness,
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ego->cld_omega,ego->n,ego->npad,ego->ginv);
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break;
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}
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}
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static void destroy(plan *ego_)
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{
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P *ego = (P *) ego_;
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X(plan_destroy_internal)(ego->cld_omega);
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X(plan_destroy_internal)(ego->cld2);
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X(plan_destroy_internal)(ego->cld1);
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}
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static void print(const plan *ego_, printer *p)
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{
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const P *ego = (const P *) ego_;
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p->print(p, "(dht-rader-%D/%D%ois=%oos=%(%p%)",
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ego->n, ego->npad, ego->is, ego->os, ego->cld1);
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if (ego->cld2 != ego->cld1)
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p->print(p, "%(%p%)", ego->cld2);
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if (ego->cld_omega != ego->cld1 && ego->cld_omega != ego->cld2)
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p->print(p, "%(%p%)", ego->cld_omega);
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p->putchr(p, ')');
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}
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static int applicable(const solver *ego, const problem *p_, const planner *plnr)
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{
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const problem_rdft *p = (const problem_rdft *) p_;
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UNUSED(ego);
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return (1
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&& p->sz->rnk == 1
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&& p->vecsz->rnk == 0
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&& p->kind[0] == DHT
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&& X(is_prime)(p->sz->dims[0].n)
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&& p->sz->dims[0].n > 2
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&& CIMPLIES(NO_SLOWP(plnr), p->sz->dims[0].n > RADER_MAX_SLOW)
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/* proclaim the solver SLOW if p-1 is not easily
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factorizable. Unlike in the complex case where
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Bluestein can solve the problem, in the DHT case we
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may have no other choice */
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&& CIMPLIES(NO_SLOWP(plnr), X(factors_into_small_primes)(p->sz->dims[0].n - 1))
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);
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}
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static INT choose_transform_size(INT minsz)
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{
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static const INT primes[] = { 2, 3, 5, 0 };
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while (!X(factors_into)(minsz, primes) || minsz % 2)
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++minsz;
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return minsz;
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}
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static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
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{
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const S *ego = (const S *) ego_;
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const problem_rdft *p = (const problem_rdft *) p_;
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P *pln;
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INT n, npad;
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INT is, os;
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plan *cld1 = (plan *) 0;
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plan *cld2 = (plan *) 0;
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plan *cld_omega = (plan *) 0;
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R *buf = (R *) 0;
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problem *cldp;
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static const plan_adt padt = {
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X(rdft_solve), awake, print, destroy
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};
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if (!applicable(ego_, p_, plnr))
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return (plan *) 0;
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n = p->sz->dims[0].n;
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is = p->sz->dims[0].is;
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os = p->sz->dims[0].os;
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if (ego->pad)
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npad = choose_transform_size(2 * (n - 1) - 1);
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else
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npad = n - 1;
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/* initial allocation for the purpose of planning */
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buf = (R *) MALLOC(sizeof(R) * npad, BUFFERS);
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cld1 = X(mkplan_f_d)(plnr,
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X(mkproblem_rdft_1_d)(X(mktensor_1d)(npad, 1, 1),
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X(mktensor_1d)(1, 0, 0),
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buf, buf,
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R2HC),
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NO_SLOW, 0, 0);
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if (!cld1) goto nada;
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cldp =
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X(mkproblem_rdft_1_d)(
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X(mktensor_1d)(npad, 1, 1),
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X(mktensor_1d)(1, 0, 0),
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buf, buf,
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#if R2HC_ONLY_CONV
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R2HC
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#else
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HC2R
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#endif
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);
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if (!(cld2 = X(mkplan_f_d)(plnr, cldp, NO_SLOW, 0, 0)))
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goto nada;
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/* plan for omega */
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cld_omega = X(mkplan_f_d)(plnr,
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X(mkproblem_rdft_1_d)(
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X(mktensor_1d)(npad, 1, 1),
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X(mktensor_1d)(1, 0, 0),
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buf, buf, R2HC),
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NO_SLOW, ESTIMATE, 0);
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if (!cld_omega) goto nada;
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/* deallocate buffers; let awake() or apply() allocate them for real */
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X(ifree)(buf);
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buf = 0;
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pln = MKPLAN_RDFT(P, &padt, apply);
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pln->cld1 = cld1;
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pln->cld2 = cld2;
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pln->cld_omega = cld_omega;
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pln->omega = 0;
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pln->n = n;
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pln->npad = npad;
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pln->is = is;
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pln->os = os;
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X(ops_add)(&cld1->ops, &cld2->ops, &pln->super.super.ops);
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pln->super.super.ops.other += (npad/2-1)*6 + npad + n + (n-1) * ego->pad;
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pln->super.super.ops.add += (npad/2-1)*2 + 2 + (n-1) * ego->pad;
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pln->super.super.ops.mul += (npad/2-1)*4 + 2 + ego->pad;
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#if R2HC_ONLY_CONV
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|
pln->super.super.ops.other += n-2 - ego->pad;
|
||
|
|
pln->super.super.ops.add += (npad/2-1)*2 + (n-2) - ego->pad;
|
||
|
|
#endif
|
||
|
|
|
||
|
|
return &(pln->super.super);
|
||
|
|
|
||
|
|
nada:
|
||
|
|
X(ifree0)(buf);
|
||
|
|
X(plan_destroy_internal)(cld_omega);
|
||
|
|
X(plan_destroy_internal)(cld2);
|
||
|
|
X(plan_destroy_internal)(cld1);
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* constructors */
|
||
|
|
|
||
|
|
static solver *mksolver(int pad)
|
||
|
|
{
|
||
|
|
static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
|
||
|
|
S *slv = MKSOLVER(S, &sadt);
|
||
|
|
slv->pad = pad;
|
||
|
|
return &(slv->super);
|
||
|
|
}
|
||
|
|
|
||
|
|
void X(dht_rader_register)(planner *p)
|
||
|
|
{
|
||
|
|
REGISTER_SOLVER(p, mksolver(0));
|
||
|
|
REGISTER_SOLVER(p, mksolver(1));
|
||
|
|
}
|