514 lines
13 KiB
C
514 lines
13 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 of *even* size by a pair of R2HC problems
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of half the size, plus some pre/post-processing. Use a trick from:
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Zhongde Wang, "On computing the discrete Fourier and cosine transforms,"
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IEEE Trans. Acoust. Speech Sig. Proc. ASSP-33 (4), 1341--1344 (1985).
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to re-express as a pair of half-size REDFT01 (DCT-III) problems. Our
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implementation looks quite a bit different from the algorithm described
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in the paper because we combined the paper's pre/post-processing with
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the pre/post-processing used to turn REDFT01 into R2HC. (Also, the
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paper uses a DCT/DST pair, but we turn the DST into a DCT via the
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usual reordering/sign-flip trick. We additionally combined a couple
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of the matrices/transformations of the paper into a single pass.)
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NOTE: We originally used a simpler method by S. C. Chan and K. L. Ho
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that turned out to have numerical problems; see reodft11e-r2hc.c.
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(For odd sizes, see reodft11e-r2hc-odd.c.)
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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, n2 = n/2;
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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 = ego->td->W;
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R *W2;
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R *buf;
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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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buf[0] = K(2.0) * I[0];
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buf[n2] = K(2.0) * I[is * (n - 1)];
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for (i = 1; i + i < n2; ++i) {
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INT k = i + i;
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E a, b, a2, b2;
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{
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E u, v;
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u = I[is * (k - 1)];
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v = I[is * k];
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a = u + v;
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b2 = u - v;
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}
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{
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E u, v;
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u = I[is * (n - k - 1)];
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v = I[is * (n - k)];
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b = u + v;
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a2 = u - v;
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}
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{
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E wa, wb;
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wa = W[2*i];
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wb = W[2*i + 1];
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{
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E apb, amb;
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apb = a + b;
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amb = a - b;
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buf[i] = wa * amb + wb * apb;
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buf[n2 - i] = wa * apb - wb * amb;
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}
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{
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E apb, amb;
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apb = a2 + b2;
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amb = a2 - b2;
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buf[n2 + i] = wa * amb + wb * apb;
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buf[n - i] = wa * apb - wb * amb;
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}
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}
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}
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if (i + i == n2) {
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E u, v;
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u = I[is * (n2 - 1)];
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v = I[is * n2];
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buf[i] = (u + v) * (W[2*i] * K(2.0));
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buf[n - i] = (u - v) * (W[2*i] * K(2.0));
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}
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/* child plan: two r2hc's of size n/2 */
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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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W2 = ego->td2->W;
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{ /* i == 0 case */
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E wa, wb;
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E a, b;
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wa = W2[0]; /* cos */
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wb = W2[1]; /* sin */
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a = buf[0];
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b = buf[n2];
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O[0] = wa * a + wb * b;
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O[os * (n - 1)] = wb * a - wa * b;
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}
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W2 += 2;
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for (i = 1; i + i < n2; ++i, W2 += 2) {
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INT k;
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E u, v, u2, v2;
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u = buf[i];
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v = buf[n2 - i];
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u2 = buf[n2 + i];
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v2 = buf[n - i];
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k = (i + i) - 1;
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{
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E wa, wb;
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E a, b;
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wa = W2[0]; /* cos */
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wb = W2[1]; /* sin */
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a = u - v;
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b = v2 - u2;
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O[os * k] = wa * a + wb * b;
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O[os * (n - 1 - k)] = wb * a - wa * b;
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}
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++k;
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W2 += 2;
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{
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E wa, wb;
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E a, b;
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wa = W2[0]; /* cos */
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wb = W2[1]; /* sin */
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a = u + v;
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b = u2 + v2;
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O[os * k] = wa * a + wb * b;
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O[os * (n - 1 - k)] = wb * a - wa * b;
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}
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}
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if (i + i == n2) {
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INT k = (i + i) - 1;
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E wa, wb;
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E a, b;
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wa = W2[0]; /* cos */
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wb = W2[1]; /* sin */
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a = buf[i];
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b = buf[n2 + i];
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O[os * k] = wa * a - wb * b;
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O[os * (n - 1 - k)] = wb * a + wa * b;
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}
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}
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X(ifree)(buf);
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}
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#if 0
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/* This version of apply_re11 uses REDFT01 child plans, more similar
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to the original paper by Z. Wang. We keep it around for reference
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(it is simpler) and because it may become more efficient if we
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ever implement REDFT01 codelets. */
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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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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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buf[0] = K(2.0) * I[0];
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buf[n/2] = K(2.0) * I[is * (n - 1)];
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for (i = 1; i + i < n; ++i) {
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INT k = i + i;
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E a, b;
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a = I[is * (k - 1)];
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b = I[is * k];
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buf[i] = a + b;
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buf[n - i] = a - b;
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}
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/* child plan: two redft01's (DCT-III) */
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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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for (i = 0; i + 1 < n/2; ++i, W += 2) {
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{
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E wa, wb;
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E a, b;
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wa = W[0]; /* cos */
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wb = W[1]; /* sin */
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a = buf[i];
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b = buf[n/2 + i];
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O[os * i] = wa * a + wb * b;
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O[os * (n - 1 - i)] = wb * a - wa * b;
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}
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++i;
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W += 2;
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{
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E wa, wb;
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E a, b;
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wa = W[0]; /* cos */
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wb = W[1]; /* sin */
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a = buf[i];
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b = buf[n/2 + i];
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O[os * i] = wa * a - wb * b;
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O[os * (n - 1 - i)] = wb * a + wa * b;
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}
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}
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if (i < n/2) {
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E wa, wb;
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E a, b;
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wa = W[0]; /* cos */
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wb = W[1]; /* sin */
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a = buf[i];
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b = buf[n/2 + i];
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O[os * i] = wa * a + wb * b;
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O[os * (n - 1 - i)] = wb * a - wa * b;
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}
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}
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X(ifree)(buf);
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}
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#endif /* 0 */
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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, n2 = n/2;
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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 = ego->td->W;
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R *W2;
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R *buf;
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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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buf[0] = K(2.0) * I[is * (n - 1)];
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buf[n2] = K(2.0) * I[0];
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for (i = 1; i + i < n2; ++i) {
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INT k = i + i;
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E a, b, a2, b2;
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{
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E u, v;
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u = I[is * (n - k)];
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v = I[is * (n - 1 - k)];
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a = u + v;
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b2 = u - v;
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}
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{
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E u, v;
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u = I[is * (k)];
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v = I[is * (k - 1)];
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b = u + v;
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a2 = u - v;
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}
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{
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E wa, wb;
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wa = W[2*i];
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wb = W[2*i + 1];
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{
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E apb, amb;
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apb = a + b;
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amb = a - b;
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buf[i] = wa * amb + wb * apb;
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buf[n2 - i] = wa * apb - wb * amb;
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}
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{
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E apb, amb;
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apb = a2 + b2;
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amb = a2 - b2;
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buf[n2 + i] = wa * amb + wb * apb;
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buf[n - i] = wa * apb - wb * amb;
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}
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}
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}
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if (i + i == n2) {
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E u, v;
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u = I[is * n2];
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v = I[is * (n2 - 1)];
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buf[i] = (u + v) * (W[2*i] * K(2.0));
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buf[n - i] = (u - v) * (W[2*i] * K(2.0));
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}
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/* child plan: two r2hc's of size n/2 */
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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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W2 = ego->td2->W;
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{ /* i == 0 case */
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E wa, wb;
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E a, b;
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wa = W2[0]; /* cos */
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wb = W2[1]; /* sin */
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a = buf[0];
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b = buf[n2];
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O[0] = wa * a + wb * b;
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O[os * (n - 1)] = wa * b - wb * a;
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}
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W2 += 2;
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for (i = 1; i + i < n2; ++i, W2 += 2) {
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INT k;
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E u, v, u2, v2;
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u = buf[i];
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v = buf[n2 - i];
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u2 = buf[n2 + i];
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v2 = buf[n - i];
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k = (i + i) - 1;
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{
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E wa, wb;
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E a, b;
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wa = W2[0]; /* cos */
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wb = W2[1]; /* sin */
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a = v - u;
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b = u2 - v2;
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O[os * k] = wa * a + wb * b;
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O[os * (n - 1 - k)] = wa * b - wb * a;
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}
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++k;
|
||
|
|
W2 += 2;
|
||
|
|
{
|
||
|
|
E wa, wb;
|
||
|
|
E a, b;
|
||
|
|
wa = W2[0]; /* cos */
|
||
|
|
wb = W2[1]; /* sin */
|
||
|
|
a = u + v;
|
||
|
|
b = u2 + v2;
|
||
|
|
O[os * k] = wa * a + wb * b;
|
||
|
|
O[os * (n - 1 - k)] = wa * b - wb * a;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (i + i == n2) {
|
||
|
|
INT k = (i + i) - 1;
|
||
|
|
E wa, wb;
|
||
|
|
E a, b;
|
||
|
|
wa = W2[0]; /* cos */
|
||
|
|
wb = W2[1]; /* sin */
|
||
|
|
a = buf[i];
|
||
|
|
b = buf[n2 + i];
|
||
|
|
O[os * k] = wb * b - wa * a;
|
||
|
|
O[os * (n - 1 - k)] = wa * b + wb * a;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
X(ifree)(buf);
|
||
|
|
}
|
||
|
|
|
||
|
|
static void awake(plan *ego_, enum wakefulness wakefulness)
|
||
|
|
{
|
||
|
|
P *ego = (P *) ego_;
|
||
|
|
static const tw_instr reodft010e_tw[] = {
|
||
|
|
{ TW_COS, 0, 1 },
|
||
|
|
{ TW_SIN, 0, 1 },
|
||
|
|
{ TW_NEXT, 1, 0 }
|
||
|
|
};
|
||
|
|
static const tw_instr reodft11e_tw[] = {
|
||
|
|
{ TW_COS, 1, 1 },
|
||
|
|
{ TW_SIN, 1, 1 },
|
||
|
|
{ TW_NEXT, 2, 0 }
|
||
|
|
};
|
||
|
|
|
||
|
|
X(plan_awake)(ego->cld, wakefulness);
|
||
|
|
|
||
|
|
X(twiddle_awake)(wakefulness, &ego->td, reodft010e_tw,
|
||
|
|
2*ego->n, 1, ego->n/4+1);
|
||
|
|
X(twiddle_awake)(wakefulness, &ego->td2, reodft11e_tw,
|
||
|
|
8*ego->n, 1, ego->n);
|
||
|
|
}
|
||
|
|
|
||
|
|
static void destroy(plan *ego_)
|
||
|
|
{
|
||
|
|
P *ego = (P *) ego_;
|
||
|
|
X(plan_destroy_internal)(ego->cld);
|
||
|
|
}
|
||
|
|
|
||
|
|
static void print(const plan *ego_, printer *p)
|
||
|
|
{
|
||
|
|
const P *ego = (const P *) ego_;
|
||
|
|
p->print(p, "(%se-radix2-r2hc-%D%v%(%p%))",
|
||
|
|
X(rdft_kind_str)(ego->kind), ego->n, ego->vl, ego->cld);
|
||
|
|
}
|
||
|
|
|
||
|
|
static int applicable0(const solver *ego_, const problem *p_)
|
||
|
|
{
|
||
|
|
const problem_rdft *p = (const problem_rdft *) p_;
|
||
|
|
UNUSED(ego_);
|
||
|
|
|
||
|
|
return (1
|
||
|
|
&& p->sz->rnk == 1
|
||
|
|
&& p->vecsz->rnk <= 1
|
||
|
|
&& p->sz->dims[0].n % 2 == 0
|
||
|
|
&& (p->kind[0] == REDFT11 || p->kind[0] == RODFT11)
|
||
|
|
);
|
||
|
|
}
|
||
|
|
|
||
|
|
static int applicable(const solver *ego, const problem *p, const planner *plnr)
|
||
|
|
{
|
||
|
|
return (!NO_SLOWP(plnr) && applicable0(ego, p));
|
||
|
|
}
|
||
|
|
|
||
|
|
static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
|
||
|
|
{
|
||
|
|
P *pln;
|
||
|
|
const problem_rdft *p;
|
||
|
|
plan *cld;
|
||
|
|
R *buf;
|
||
|
|
INT n;
|
||
|
|
opcnt ops;
|
||
|
|
|
||
|
|
static const plan_adt padt = {
|
||
|
|
X(rdft_solve), awake, print, destroy
|
||
|
|
};
|
||
|
|
|
||
|
|
if (!applicable(ego_, p_, plnr))
|
||
|
|
return (plan *)0;
|
||
|
|
|
||
|
|
p = (const problem_rdft *) p_;
|
||
|
|
|
||
|
|
n = p->sz->dims[0].n;
|
||
|
|
buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
|
||
|
|
|
||
|
|
cld = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(X(mktensor_1d)(n/2, 1, 1),
|
||
|
|
X(mktensor_1d)(2, n/2, n/2),
|
||
|
|
buf, buf, R2HC));
|
||
|
|
X(ifree)(buf);
|
||
|
|
if (!cld)
|
||
|
|
return (plan *)0;
|
||
|
|
|
||
|
|
pln = MKPLAN_RDFT(P, &padt, p->kind[0]==REDFT11 ? apply_re11:apply_ro11);
|
||
|
|
pln->n = n;
|
||
|
|
pln->is = p->sz->dims[0].is;
|
||
|
|
pln->os = p->sz->dims[0].os;
|
||
|
|
pln->cld = cld;
|
||
|
|
pln->td = pln->td2 = 0;
|
||
|
|
pln->kind = p->kind[0];
|
||
|
|
|
||
|
|
X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
|
||
|
|
|
||
|
|
X(ops_zero)(&ops);
|
||
|
|
ops.add = 2 + (n/2 - 1)/2 * 20;
|
||
|
|
ops.mul = 6 + (n/2 - 1)/2 * 16;
|
||
|
|
ops.other = 4*n + 2 + (n/2 - 1)/2 * 6;
|
||
|
|
if ((n/2) % 2 == 0) {
|
||
|
|
ops.add += 4;
|
||
|
|
ops.mul += 8;
|
||
|
|
ops.other += 4;
|
||
|
|
}
|
||
|
|
|
||
|
|
X(ops_zero)(&pln->super.super.ops);
|
||
|
|
X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops);
|
||
|
|
X(ops_madd2)(pln->vl, &cld->ops, &pln->super.super.ops);
|
||
|
|
|
||
|
|
return &(pln->super.super);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* constructor */
|
||
|
|
static solver *mksolver(void)
|
||
|
|
{
|
||
|
|
static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
|
||
|
|
S *slv = MKSOLVER(S, &sadt);
|
||
|
|
return &(slv->super);
|
||
|
|
}
|
||
|
|
|
||
|
|
void X(reodft11e_radix2_r2hc_register)(planner *p)
|
||
|
|
{
|
||
|
|
REGISTER_SOLVER(p, mksolver());
|
||
|
|
}
|