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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());
+}
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