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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-radix2.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
-
-/* Do an R{E,O}DFT11 problem of *even* size by a pair of R2HC problems
- of half the size, plus some pre/post-processing. Use a trick from:
-
- Zhongde Wang, "On computing the discrete Fourier and cosine transforms,"
- IEEE Trans. Acoust. Speech Sig. Proc. ASSP-33 (4), 1341--1344 (1985).
-
- to re-express as a pair of half-size REDFT01 (DCT-III) problems. Our
- implementation looks quite a bit different from the algorithm described
- in the paper because we combined the paper's pre/post-processing with
- the pre/post-processing used to turn REDFT01 into R2HC. (Also, the
- paper uses a DCT/DST pair, but we turn the DST into a DCT via the
- usual reordering/sign-flip trick. We additionally combined a couple
- of the matrices/transformations of the paper into a single pass.)
-
- NOTE: We originally used a simpler method by S. C. Chan and K. L. Ho
- that turned out to have numerical problems; see reodft11e-r2hc.c.
-
- (For odd sizes, see reodft11e-r2hc-odd.c.)
-*/
-
-#include "reodft.h"
-
-typedef struct {
- solver super;
-} S;
-
-typedef struct {
- plan_rdft super;
- plan *cld;
- twid *td, *td2;
- int is, os;
- int n;
- int vl;
- int ivs, ovs;
- rdft_kind kind;
-} P;
-
-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 *W = ego->td->W;
- R *W2;
- R *buf;
-
- buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
-
- for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
- buf[0] = K(2.0) * I[0];
- buf[n2] = K(2.0) * I[is * (n - 1)];
- for (i = 1; i + i < n2; ++i) {
- int k = i + i;
- E a, b, a2, b2;
- {
- E u, v;
- u = I[is * (k - 1)];
- v = I[is * k];
- a = u + v;
- b2 = u - v;
- }
- {
- E u, v;
- u = I[is * (n - k - 1)];
- v = I[is * (n - k)];
- b = u + v;
- a2 = u - v;
- }
- {
- E wa, wb;
- wa = W[2*i];
- wb = W[2*i + 1];
- {
- E apb, amb;
- apb = a + b;
- amb = a - b;
- buf[i] = wa * amb + wb * apb;
- buf[n2 - i] = wa * apb - wb * amb;
- }
- {
- E apb, amb;
- apb = a2 + b2;
- amb = a2 - b2;
- buf[n2 + i] = wa * amb + wb * apb;
- buf[n - i] = wa * apb - wb * amb;
- }
- }
- }
- if (i + i == n2) {
- E u, v;
- u = I[is * (n2 - 1)];
- v = I[is * n2];
- buf[i] = K(2.0) * (u + v) * W[2*i];
- buf[n - i] = K(2.0) * (u - v) * W[2*i];
- }
-
-
- /* child plan: two r2hc's of size n/2 */
- {
- plan_rdft *cld = (plan_rdft *) ego->cld;
- cld->apply((plan *) cld, buf, buf);
- }
-
- W2 = ego->td2->W;
- { /* i == 0 case */
- E wa, wb;
- E a, b;
- wa = W2[0]; /* cos */
- wb = W2[1]; /* sin */
- a = buf[0];
- b = buf[n2];
- O[0] = wa * a + wb * b;
- O[os * (n - 1)] = wb * a - wa * b;
- }
- W2 += 2;
- for (i = 1; i + i < n2; ++i, W2 += 2) {
- int k;
- E u, v, u2, v2;
- u = buf[i];
- v = buf[n2 - i];
- u2 = buf[n2 + i];
- v2 = buf[n - i];
- k = (i + i) - 1;
- {
- E wa, wb;
- E a, b;
- wa = W2[0]; /* cos */
- wb = W2[1]; /* sin */
- a = u - v;
- b = v2 - u2;
- O[os * k] = wa * a + wb * b;
- O[os * (n - 1 - k)] = wb * a - wa * b;
- }
- ++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)] = wb * a - wa * b;
- }
- }
- 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] = wa * a - wb * b;
- O[os * (n - 1 - k)] = wb * a + wa * b;
- }
- }
-
- X(ifree)(buf);
-}
-
-#if 0
-
-/* This version of apply_re11 uses REDFT01 child plans, more similar
- to the original paper by Z. Wang. We keep it around for reference
- (it is simpler) and because it may become more efficient if we
- ever implement REDFT01 codelets. */
-
-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;
- int iv, vl = ego->vl;
- int ivs = ego->ivs, ovs = ego->ovs;
- R *W;
- R *buf;
-
- buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
-
- for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
- buf[0] = K(2.0) * I[0];
- buf[n/2] = K(2.0) * I[is * (n - 1)];
- for (i = 1; i + i < n; ++i) {
- int k = i + i;
- E a, b;
- a = I[is * (k - 1)];
- b = I[is * k];
- buf[i] = a + b;
- buf[n - i] = a - b;
- }
-
- /* child plan: two redft01's (DCT-III) */
- {
- plan_rdft *cld = (plan_rdft *) ego->cld;
- cld->apply((plan *) cld, buf, buf);
- }
-
- W = ego->td2->W;
- for (i = 0; i + 1 < n/2; ++i, W += 2) {
- {
- E wa, wb;
- E a, b;
- wa = W[0]; /* cos */
- wb = W[1]; /* sin */
- a = buf[i];
- b = buf[n/2 + i];
- O[os * i] = wa * a + wb * b;
- O[os * (n - 1 - i)] = wb * a - wa * b;
- }
- ++i;
- W += 2;
- {
- E wa, wb;
- E a, b;
- wa = W[0]; /* cos */
- wb = W[1]; /* sin */
- a = buf[i];
- b = buf[n/2 + i];
- O[os * i] = wa * a - wb * b;
- O[os * (n - 1 - i)] = wb * a + wa * b;
- }
- }
- if (i < n/2) {
- E wa, wb;
- E a, b;
- wa = W[0]; /* cos */
- wb = W[1]; /* sin */
- a = buf[i];
- b = buf[n/2 + i];
- O[os * i] = wa * a + wb * b;
- O[os * (n - 1 - i)] = wb * a - wa * b;
- }
- }
-
- X(ifree)(buf);
-}
-
-#endif /* 0 */
-
-/* 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 *W = ego->td->W;
- R *W2;
- R *buf;
-
- buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
-
- for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
- buf[0] = K(2.0) * I[is * (n - 1)];
- buf[n2] = K(2.0) * I[0];
- for (i = 1; i + i < n2; ++i) {
- int k = i + i;
- E a, b, a2, b2;
- {
- E u, v;
- u = I[is * (n - k)];
- v = I[is * (n - 1 - k)];
- a = u + v;
- b2 = u - v;
- }
- {
- E u, v;
- u = I[is * (k)];
- v = I[is * (k - 1)];
- b = u + v;
- a2 = u - v;
- }
- {
- E wa, wb;
- wa = W[2*i];
- wb = W[2*i + 1];
- {
- E apb, amb;
- apb = a + b;
- amb = a - b;
- buf[i] = wa * amb + wb * apb;
- buf[n2 - i] = wa * apb - wb * amb;
- }
- {
- E apb, amb;
- apb = a2 + b2;
- amb = a2 - b2;
- buf[n2 + i] = wa * amb + wb * apb;
- buf[n - i] = wa * apb - wb * amb;
- }
- }
- }
- if (i + i == n2) {
- E u, v;
- u = I[is * n2];
- v = I[is * (n2 - 1)];
- buf[i] = K(2.0) * (u + v) * W[2*i];
- buf[n - i] = K(2.0) * (u - v) * W[2*i];
- }
-
-
- /* child plan: two r2hc's of size n/2 */
- {
- plan_rdft *cld = (plan_rdft *) ego->cld;
- cld->apply((plan *) cld, buf, buf);
- }
-
- W2 = ego->td2->W;
- { /* i == 0 case */
- E wa, wb;
- E a, b;
- wa = W2[0]; /* cos */
- wb = W2[1]; /* sin */
- a = buf[0];
- b = buf[n2];
- O[0] = wa * a + wb * b;
- O[os * (n - 1)] = wa * b - wb * a;
- }
- W2 += 2;
- for (i = 1; i + i < n2; ++i, W2 += 2) {
- int k;
- E u, v, u2, v2;
- u = buf[i];
- v = buf[n2 - i];
- u2 = buf[n2 + i];
- v2 = buf[n - i];
- k = (i + i) - 1;
- {
- E wa, wb;
- E a, b;
- wa = W2[0]; /* cos */
- wb = W2[1]; /* sin */
- a = v - u;
- b = u2 - v2;
- O[os * k] = wa * a + wb * b;
- O[os * (n - 1 - k)] = wa * b - wb * a;
- }
- ++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_, int flg)
-{
- 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 }
- };
-
- AWAKE(ego->cld, flg);
-
- X(twiddle_awake)(flg, &ego->td, reodft010e_tw, 2*ego->n, 1, ego->n/4+1);
- X(twiddle_awake)(flg, &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_)
-{
- 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 == 0
- && (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/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 = { mkplan };
- S *slv = MKSOLVER(S, &sadt);
- return &(slv->super);
-}
-
-void X(reodft11e_radix2_r2hc_register)(planner *p)
-{
- REGISTER_SOLVER(p, mksolver());
-}