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authorscuri <scuri>2009-08-20 12:35:06 +0000
committerscuri <scuri>2009-08-20 12:35:06 +0000
commit5d735255ddd3cb2f547abd3d03969af3fb7eb04e (patch)
tree8fb66510bc625bb1b08ccb41f1b83fb0f7cb8f19 /src/fftw3/reodft/reodft11e-r2hc-odd.c
parent35733b87eed86e5228f12fa10c98a3d9d22a6073 (diff)
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-/*
- * Copyright (c) 2003 Matteo Frigo
- * Copyright (c) 2003 Massachusetts Institute of Technology
- *
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation; either version 2 of the License, or
- * (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
- *
- */
-
-/* $Id: reodft11e-r2hc-odd.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
-
-/* Do an R{E,O}DFT11 problem via an R2HC problem of the same *odd* size,
- with some permutations and post-processing, as described in:
-
- S. C. Chan and K. L. Ho, "Fast algorithms for computing the
- discrete cosine transform," IEEE Trans. Circuits Systems II:
- Analog & Digital Sig. Proc. 39 (3), 185--190 (1992).
-
- (For even sizes, see reodft11e-radix2.c.)
-
- This algorithm is related to the 8 x n prime-factor-algorithm (PFA)
- decomposition of the size 8n "logical" DFT corresponding to the
- R{EO}DFT11.
-
- Aside from very confusing notation (several symbols are redefined
- from one line to the next), be aware that this paper has some
- errors. In particular, the signs are wrong in Eqs. (34-35). Also,
- Eqs. (36-37) should be simply C(k) = C(2k + 1 mod N), and similarly
- for S (or, equivalently, the second cases should have 2*N - 2*k - 1
- instead of N - k - 1). Note also that in their definition of the
- DFT, similarly to FFTW's, the exponent's sign is -1, but they
- forgot to correspondingly multiply S (the sine terms) by -1.
-*/
-
-#include "reodft.h"
-
-typedef struct {
- solver super;
-} S;
-
-typedef struct {
- plan_rdft super;
- plan *cld;
- int is, os;
- int n;
- int vl;
- int ivs, ovs;
- rdft_kind kind;
-} P;
-
-static DK(SQRT2, +1.4142135623730950488016887242096980785696718753769);
-
-#define SGN_SET(x, i) ((i) % 2 ? -(x) : (x))
-
-static void apply_re11(const plan *ego_, R *I, R *O)
-{
- const P *ego = (const P *) ego_;
- int is = ego->is, os = ego->os;
- int i, n = ego->n, n2 = n/2;
- int iv, vl = ego->vl;
- int ivs = ego->ivs, ovs = ego->ovs;
- R *buf;
-
- buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
-
- for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
- {
- int m;
- for (i = 0, m = n2; m < n; ++i, m += 4)
- buf[i] = I[is * m];
- for (; m < 2 * n; ++i, m += 4)
- buf[i] = -I[is * (2*n - m - 1)];
- for (; m < 3 * n; ++i, m += 4)
- buf[i] = -I[is * (m - 2*n)];
- for (; m < 4 * n; ++i, m += 4)
- buf[i] = I[is * (4*n - m - 1)];
- m -= 4 * n;
- for (; i < n; ++i, m += 4)
- buf[i] = I[is * m];
- }
-
- { /* child plan: R2HC of size n */
- plan_rdft *cld = (plan_rdft *) ego->cld;
- cld->apply((plan *) cld, buf, buf);
- }
-
- /* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */
- for (i = 0; i + i + 1 < n2; ++i) {
- int k = i + i + 1;
- E c1, s1;
- E c2, s2;
- c1 = buf[k];
- c2 = buf[k + 1];
- s2 = buf[n - (k + 1)];
- s1 = buf[n - k];
-
- O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2) +
- SGN_SET(s1, i/2));
- O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2) -
- SGN_SET(s1, (n-(i+1))/2));
-
- O[os * (n2 - (i+1))] = SQRT2 * (SGN_SET(c2, (n2-i)/2) -
- SGN_SET(s2, (n2-(i+1))/2));
- O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2) +
- SGN_SET(s2, (n2+(i+1))/2));
- }
- if (i + i + 1 == n2) {
- E c, s;
- c = buf[n2];
- s = buf[n - n2];
- O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2) +
- SGN_SET(s, i/2));
- O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2) +
- SGN_SET(s, (i+1)/2));
- }
- O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2);
- }
-
- X(ifree)(buf);
-}
-
-/* like for rodft01, rodft11 is obtained from redft11 by
- reversing the input and flipping the sign of every other output. */
-static void apply_ro11(const plan *ego_, R *I, R *O)
-{
- const P *ego = (const P *) ego_;
- int is = ego->is, os = ego->os;
- int i, n = ego->n, n2 = n/2;
- int iv, vl = ego->vl;
- int ivs = ego->ivs, ovs = ego->ovs;
- R *buf;
-
- buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
-
- for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
- {
- int m;
- for (i = 0, m = n2; m < n; ++i, m += 4)
- buf[i] = I[is * (n - 1 - m)];
- for (; m < 2 * n; ++i, m += 4)
- buf[i] = -I[is * (m - n)];
- for (; m < 3 * n; ++i, m += 4)
- buf[i] = -I[is * (3*n - 1 - m)];
- for (; m < 4 * n; ++i, m += 4)
- buf[i] = I[is * (m - 3*n)];
- m -= 4 * n;
- for (; i < n; ++i, m += 4)
- buf[i] = I[is * (n - 1 - m)];
- }
-
- { /* child plan: R2HC of size n */
- plan_rdft *cld = (plan_rdft *) ego->cld;
- cld->apply((plan *) cld, buf, buf);
- }
-
- /* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */
- for (i = 0; i + i + 1 < n2; ++i) {
- int k = i + i + 1;
- int j;
- E c1, s1;
- E c2, s2;
- c1 = buf[k];
- c2 = buf[k + 1];
- s2 = buf[n - (k + 1)];
- s1 = buf[n - k];
-
- O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2 + i) +
- SGN_SET(s1, i/2 + i));
- O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2 + i) -
- SGN_SET(s1, (n-(i+1))/2 + i));
-
- j = n2 - (i+1);
- O[os * j] = SQRT2 * (SGN_SET(c2, (n2-i)/2 + j) -
- SGN_SET(s2, (n2-(i+1))/2 + j));
- O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2 + j) +
- SGN_SET(s2, (n2+(i+1))/2 + j));
- }
- if (i + i + 1 == n2) {
- E c, s;
- c = buf[n2];
- s = buf[n - n2];
- O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2 + i) +
- SGN_SET(s, i/2 + i));
- O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2 + i) +
- SGN_SET(s, (i+1)/2 + i));
- }
- O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2 + n2);
- }
-
- X(ifree)(buf);
-}
-
-static void awake(plan *ego_, int flg)
-{
- P *ego = (P *) ego_;
- AWAKE(ego->cld, flg);
-}
-
-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-r2hc-odd-%d%v%(%p%))",
- X(rdft_kind_str)(ego->kind), ego->n, ego->vl, ego->cld);
-}
-
-static int applicable0(const solver *ego_, const problem *p_)
-{
- UNUSED(ego_);
- if (RDFTP(p_)) {
- const problem_rdft *p = (const problem_rdft *) p_;
- return (1
- && p->sz->rnk == 1
- && p->vecsz->rnk <= 1
- && p->sz->dims[0].n % 2 == 1
- && (p->kind[0] == REDFT11 || p->kind[0] == RODFT11)
- );
- }
-
- return 0;
-}
-
-static int applicable(const solver *ego, const problem *p, const planner *plnr)
-{
- return (!NO_UGLYP(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, 1, 1),
- X(mktensor_0d)(),
- 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->kind = p->kind[0];
-
- X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
-
- X(ops_zero)(&ops);
- ops.add = n - 1;
- ops.mul = n;
- ops.other = 4*n;
-
- 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 = { mkplan };
- S *slv = MKSOLVER(S, &sadt);
- return &(slv->super);
-}
-
-void X(reodft11e_r2hc_odd_register)(planner *p)
-{
- REGISTER_SOLVER(p, mksolver());
-}