301 lines
8.6 KiB
C
301 lines
8.6 KiB
C
/*
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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 of the same *odd* size,
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with some permutations and post-processing, as described in:
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S. C. Chan and K. L. Ho, "Fast algorithms for computing the
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discrete cosine transform," IEEE Trans. Circuits Systems II:
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Analog & Digital Sig. Proc. 39 (3), 185--190 (1992).
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(For even sizes, see reodft11e-radix2.c.)
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This algorithm is related to the 8 x n prime-factor-algorithm (PFA)
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decomposition of the size 8n "logical" DFT corresponding to the
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R{EO}DFT11.
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Aside from very confusing notation (several symbols are redefined
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from one line to the next), be aware that this paper has some
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errors. In particular, the signs are wrong in Eqs. (34-35). Also,
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Eqs. (36-37) should be simply C(k) = C(2k + 1 mod N), and similarly
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for S (or, equivalently, the second cases should have 2*N - 2*k - 1
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instead of N - k - 1). Note also that in their definition of the
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DFT, similarly to FFTW's, the exponent's sign is -1, but they
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forgot to correspondingly multiply S (the sine terms) by -1.
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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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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 DK(SQRT2, +1.4142135623730950488016887242096980785696718753769);
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#define SGN_SET(x, i) ((i) % 2 ? -(x) : (x))
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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 *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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{
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INT m;
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for (i = 0, m = n2; m < n; ++i, m += 4)
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buf[i] = I[is * m];
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for (; m < 2 * n; ++i, m += 4)
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buf[i] = -I[is * (2*n - m - 1)];
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for (; m < 3 * n; ++i, m += 4)
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buf[i] = -I[is * (m - 2*n)];
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for (; m < 4 * n; ++i, m += 4)
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buf[i] = I[is * (4*n - m - 1)];
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m -= 4 * n;
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for (; i < n; ++i, m += 4)
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buf[i] = I[is * m];
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}
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{ /* child plan: R2HC of size n */
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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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/* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */
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for (i = 0; i + i + 1 < n2; ++i) {
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INT k = i + i + 1;
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E c1, s1;
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E c2, s2;
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c1 = buf[k];
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c2 = buf[k + 1];
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s2 = buf[n - (k + 1)];
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s1 = buf[n - k];
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O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2) +
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SGN_SET(s1, i/2));
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O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2) -
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SGN_SET(s1, (n-(i+1))/2));
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O[os * (n2 - (i+1))] = SQRT2 * (SGN_SET(c2, (n2-i)/2) -
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SGN_SET(s2, (n2-(i+1))/2));
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O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2) +
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SGN_SET(s2, (n2+(i+1))/2));
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}
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if (i + i + 1 == n2) {
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E c, s;
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c = buf[n2];
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s = buf[n - n2];
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O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2) +
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SGN_SET(s, i/2));
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O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2) +
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SGN_SET(s, (i+1)/2));
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}
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O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2);
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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, 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 *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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{
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INT m;
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for (i = 0, m = n2; m < n; ++i, m += 4)
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buf[i] = I[is * (n - 1 - m)];
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for (; m < 2 * n; ++i, m += 4)
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buf[i] = -I[is * (m - n)];
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for (; m < 3 * n; ++i, m += 4)
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buf[i] = -I[is * (3*n - 1 - m)];
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for (; m < 4 * n; ++i, m += 4)
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buf[i] = I[is * (m - 3*n)];
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m -= 4 * n;
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for (; i < n; ++i, m += 4)
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buf[i] = I[is * (n - 1 - m)];
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}
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{ /* child plan: R2HC of size n */
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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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/* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */
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for (i = 0; i + i + 1 < n2; ++i) {
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INT k = i + i + 1;
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INT j;
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E c1, s1;
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E c2, s2;
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c1 = buf[k];
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c2 = buf[k + 1];
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s2 = buf[n - (k + 1)];
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s1 = buf[n - k];
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O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2 + i) +
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SGN_SET(s1, i/2 + i));
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O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2 + i) -
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SGN_SET(s1, (n-(i+1))/2 + i));
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j = n2 - (i+1);
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O[os * j] = SQRT2 * (SGN_SET(c2, (n2-i)/2 + j) -
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SGN_SET(s2, (n2-(i+1))/2 + j));
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O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2 + j) +
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SGN_SET(s2, (n2+(i+1))/2 + j));
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}
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if (i + i + 1 == n2) {
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E c, s;
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c = buf[n2];
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s = buf[n - n2];
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O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2 + i) +
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SGN_SET(s, i/2 + i));
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O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2 + i) +
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SGN_SET(s, (i+1)/2 + i));
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}
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O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2 + n2);
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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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X(plan_awake)(ego->cld, wakefulness);
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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-odd-%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->sz->dims[0].n % 2 == 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->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.add = n - 1;
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ops.mul = n;
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ops.other = 4*n;
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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_odd_register)(planner *p)
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{
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REGISTER_SOLVER(p, mksolver());
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}
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