295 lines
7.7 KiB
C
295 lines
7.7 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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/* Do an R{E,O}DFT11 problem via an R2HC problem, with some
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pre/post-processing ala FFTPACK. Use a trick from:
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S. C. Chan and K. L. Ho, "Direct methods for computing discrete
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sinusoidal transforms," IEE Proceedings F 137 (6), 433--442 (1990).
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to re-express as an REDFT01 (DCT-III) problem.
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NOTE: We no longer use this algorithm, because it turns out to suffer
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a catastrophic loss of accuracy for certain inputs, apparently because
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its post-processing multiplies the output by a cosine. Near the zero
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of the cosine, the REDFT01 must produce a near-singular output.
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*/
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#include "reodft/reodft.h"
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typedef struct {
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solver super;
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} S;
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typedef struct {
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plan_rdft super;
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plan *cld;
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twid *td, *td2;
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INT is, os;
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INT n;
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INT vl;
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INT ivs, ovs;
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rdft_kind kind;
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} P;
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static void apply_re11(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 is = ego->is, os = ego->os;
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INT i, n = ego->n;
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INT iv, vl = ego->vl;
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INT ivs = ego->ivs, ovs = ego->ovs;
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R *W;
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R *buf;
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E cur;
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buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
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for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
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/* I wish that this didn't require an extra pass. */
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/* FIXME: use recursive/cascade summation for better stability? */
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buf[n - 1] = cur = K(2.0) * I[is * (n - 1)];
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for (i = n - 1; i > 0; --i) {
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E curnew;
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buf[(i - 1)] = curnew = K(2.0) * I[is * (i - 1)] - cur;
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cur = curnew;
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}
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W = ego->td->W;
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for (i = 1; i < n - i; ++i) {
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E a, b, apb, amb, wa, wb;
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a = buf[i];
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b = buf[n - i];
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apb = a + b;
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amb = a - b;
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wa = W[2*i];
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wb = W[2*i + 1];
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buf[i] = wa * amb + wb * apb;
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buf[n - i] = wa * apb - wb * amb;
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}
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if (i == n - i) {
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buf[i] = K(2.0) * buf[i] * W[2*i];
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}
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{
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plan_rdft *cld = (plan_rdft *) ego->cld;
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cld->apply((plan *) cld, buf, buf);
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}
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W = ego->td2->W;
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O[0] = W[0] * buf[0];
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for (i = 1; i < n - i; ++i) {
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E a, b;
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INT k;
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a = buf[i];
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b = buf[n - i];
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k = i + i;
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O[os * (k - 1)] = W[k - 1] * (a - b);
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O[os * k] = W[k] * (a + b);
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}
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if (i == n - i) {
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O[os * (n - 1)] = W[n - 1] * buf[i];
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}
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}
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X(ifree)(buf);
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}
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/* like for rodft01, rodft11 is obtained from redft11 by
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reversing the input and flipping the sign of every other output. */
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static void apply_ro11(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 is = ego->is, os = ego->os;
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INT i, n = ego->n;
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INT iv, vl = ego->vl;
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INT ivs = ego->ivs, ovs = ego->ovs;
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R *W;
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R *buf;
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E cur;
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buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
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for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
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/* I wish that this didn't require an extra pass. */
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/* FIXME: use recursive/cascade summation for better stability? */
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buf[n - 1] = cur = K(2.0) * I[0];
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for (i = n - 1; i > 0; --i) {
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E curnew;
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buf[(i - 1)] = curnew = K(2.0) * I[is * (n - i)] - cur;
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cur = curnew;
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}
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W = ego->td->W;
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for (i = 1; i < n - i; ++i) {
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E a, b, apb, amb, wa, wb;
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a = buf[i];
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b = buf[n - i];
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apb = a + b;
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amb = a - b;
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wa = W[2*i];
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wb = W[2*i + 1];
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buf[i] = wa * amb + wb * apb;
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buf[n - i] = wa * apb - wb * amb;
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}
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if (i == n - i) {
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buf[i] = K(2.0) * buf[i] * W[2*i];
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}
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{
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plan_rdft *cld = (plan_rdft *) ego->cld;
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cld->apply((plan *) cld, buf, buf);
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}
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W = ego->td2->W;
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O[0] = W[0] * buf[0];
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for (i = 1; i < n - i; ++i) {
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E a, b;
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INT k;
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a = buf[i];
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b = buf[n - i];
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k = i + i;
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O[os * (k - 1)] = W[k - 1] * (b - a);
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O[os * k] = W[k] * (a + b);
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}
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if (i == n - i) {
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O[os * (n - 1)] = -W[n - 1] * buf[i];
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}
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}
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X(ifree)(buf);
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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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static const tw_instr reodft010e_tw[] = {
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{ TW_COS, 0, 1 },
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{ TW_SIN, 0, 1 },
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{ TW_NEXT, 1, 0 }
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};
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static const tw_instr reodft11e_tw[] = {
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{ TW_COS, 1, 1 },
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{ TW_NEXT, 2, 0 }
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};
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X(plan_awake)(ego->cld, wakefulness);
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X(twiddle_awake)(wakefulness,
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&ego->td, reodft010e_tw, 4*ego->n, 1, ego->n/2+1);
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X(twiddle_awake)(wakefulness,
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&ego->td2, reodft11e_tw, 8*ego->n, 1, ego->n * 2);
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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);
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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, "(%se-r2hc-%D%v%(%p%))",
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X(rdft_kind_str)(ego->kind), ego->n, ego->vl, ego->cld);
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}
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static int applicable0(const solver *ego_, const problem *p_)
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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 <= 1
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&& (p->kind[0] == REDFT11 || p->kind[0] == RODFT11)
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);
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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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return (!NO_SLOWP(plnr) && applicable0(ego, p));
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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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P *pln;
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const problem_rdft *p;
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plan *cld;
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R *buf;
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INT n;
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opcnt ops;
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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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p = (const problem_rdft *) p_;
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n = p->sz->dims[0].n;
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buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
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cld = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(X(mktensor_1d)(n, 1, 1),
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X(mktensor_0d)(),
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buf, buf, R2HC));
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X(ifree)(buf);
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if (!cld)
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return (plan *)0;
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pln = MKPLAN_RDFT(P, &padt, p->kind[0]==REDFT11 ? apply_re11:apply_ro11);
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pln->n = n;
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pln->is = p->sz->dims[0].is;
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pln->os = p->sz->dims[0].os;
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pln->cld = cld;
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pln->td = pln->td2 = 0;
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pln->kind = p->kind[0];
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X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
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X(ops_zero)(&ops);
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ops.other = 5 + (n-1) * 2 + (n-1)/2 * 12 + (1 - n % 2) * 6;
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ops.add = (n - 1) * 1 + (n-1)/2 * 6;
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ops.mul = 2 + (n-1) * 1 + (n-1)/2 * 6 + (1 - n % 2) * 3;
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X(ops_zero)(&pln->super.super.ops);
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X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops);
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X(ops_madd2)(pln->vl, &cld->ops, &pln->super.super.ops);
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return &(pln->super.super);
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}
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/* constructor */
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static solver *mksolver(void)
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{
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static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
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S *slv = MKSOLVER(S, &sadt);
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return &(slv->super);
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}
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void X(reodft11e_r2hc_register)(planner *p)
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{
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REGISTER_SOLVER(p, mksolver());
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}
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