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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: reodft010e-r2hc.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
+
+/* Do an R{E,O}DFT{01,10} problem via an R2HC problem, with some
+ pre/post-processing ala FFTPACK. */
+
+#include "reodft.h"
+
+typedef struct {
+ solver super;
+} S;
+
+typedef struct {
+ plan_rdft super;
+ plan *cld;
+ twid *td;
+ int is, os;
+ int n;
+ int vl;
+ int ivs, ovs;
+ rdft_kind kind;
+} P;
+
+/* A real-even-01 DFT operates logically on a size-4N array:
+ I 0 -r(I*) -I 0 r(I*),
+ where r denotes reversal and * denotes deletion of the 0th element.
+ To compute the transform of this, we imagine performing a radix-4
+ (real-input) DIF step, which turns the size-4N DFT into 4 size-N
+ (contiguous) DFTs, two of which are zero and two of which are
+ conjugates. The non-redundant size-N DFT has halfcomplex input, so
+ we can do it with a size-N hc2r transform. (In order to share
+ plans with the re10 (inverse) transform, however, we use the DHT
+ trick to re-express the hc2r problem as r2hc. This has little cost
+ since we are already pre- and post-processing the data in {i,n-i}
+ order.) Finally, we have to write out the data in the correct
+ order...the two size-N redundant (conjugate) hc2r DFTs correspond
+ to the even and odd outputs in O (i.e. the usual interleaved output
+ of DIF transforms); since this data has even symmetry, we only
+ write the first half of it.
+
+ The real-even-10 DFT is just the reverse of these steps, i.e. a
+ radix-4 DIT transform. There, however, we just use the r2hc
+ transform naturally without resorting to the DHT trick.
+
+ A real-odd-01 DFT is very similar, except that the input is
+ 0 I (rI)* 0 -I -(rI)*. This format, however, can be transformed
+ into precisely the real-even-01 format above by sending I -> rI
+ and shifting the array by N. The former swap is just another
+ transformation on the input during preprocessing; the latter
+ multiplies the even/odd outputs by i/-i, which combines with
+ the factor of -i (to take the imaginary part) to simply flip
+ the sign of the odd outputs. Vice-versa for real-odd-10.
+
+ The FFTPACK source code was very helpful in working this out.
+ (They do unnecessary passes over the array, though.)
+
+ Note that Numerical Recipes suggests a different algorithm that
+ requires more operations and uses trig. functions for both the pre-
+ and post-processing passes.
+*/
+
+static void apply_re01(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 = ego->td->W;
+ R *buf;
+
+ buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+ for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+ buf[0] = I[0];
+ for (i = 1; i < n - i; ++i) {
+ E a, b, apb, amb, wa, wb;
+ a = I[is * i];
+ b = I[is * (n - i)];
+ apb = a + b;
+ amb = a - b;
+ wa = W[2*i];
+ wb = W[2*i + 1];
+ buf[i] = wa * amb + wb * apb;
+ buf[n - i] = wa * apb - wb * amb;
+ }
+ if (i == n - i) {
+ buf[i] = K(2.0) * I[is * i] * W[2*i];
+ }
+
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, buf, buf);
+ }
+
+ O[0] = buf[0];
+ for (i = 1; i < n - i; ++i) {
+ E a, b;
+ int k;
+ a = buf[i];
+ b = buf[n - i];
+ k = i + i;
+ O[os * (k - 1)] = a - b;
+ O[os * k] = a + b;
+ }
+ if (i == n - i) {
+ O[os * (n - 1)] = buf[i];
+ }
+ }
+
+ X(ifree)(buf);
+}
+
+/* ro01 is same as re01, but with i <-> n - 1 - i in the input and
+ the sign of the odd output elements flipped. */
+static void apply_ro01(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 = ego->td->W;
+ R *buf;
+
+ buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+ for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+ buf[0] = I[is * (n - 1)];
+ for (i = 1; i < n - i; ++i) {
+ E a, b, apb, amb, wa, wb;
+ a = I[is * (n - 1 - i)];
+ b = I[is * (i - 1)];
+ apb = a + b;
+ amb = a - b;
+ wa = W[2*i];
+ wb = W[2*i+1];
+ buf[i] = wa * amb + wb * apb;
+ buf[n - i] = wa * apb - wb * amb;
+ }
+ if (i == n - i) {
+ buf[i] = K(2.0) * I[is * (i - 1)] * W[2*i];
+ }
+
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, buf, buf);
+ }
+
+ O[0] = buf[0];
+ for (i = 1; i < n - i; ++i) {
+ E a, b;
+ int k;
+ a = buf[i];
+ b = buf[n - i];
+ k = i + i;
+ O[os * (k - 1)] = b - a;
+ O[os * k] = a + b;
+ }
+ if (i == n - i) {
+ O[os * (n - 1)] = -buf[i];
+ }
+ }
+
+ X(ifree)(buf);
+}
+
+static void apply_re10(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 = ego->td->W;
+ R *buf;
+
+ buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+ for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+ buf[0] = I[0];
+ for (i = 1; i < n - i; ++i) {
+ E u, v;
+ int k = i + i;
+ u = I[is * (k - 1)];
+ v = I[is * k];
+ buf[n - i] = u;
+ buf[i] = v;
+ }
+ if (i == n - i) {
+ buf[i] = I[is * (n - 1)];
+ }
+
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, buf, buf);
+ }
+
+ O[0] = K(2.0) * buf[0];
+ for (i = 1; i < n - i; ++i) {
+ E a, b, wa, wb;
+ a = K(2.0) * buf[i];
+ b = K(2.0) * buf[n - i];
+ wa = W[2*i];
+ wb = W[2*i + 1];
+ O[os * i] = wa * a + wb * b;
+ O[os * (n - i)] = wb * a - wa * b;
+ }
+ if (i == n - i) {
+ O[os * i] = K(2.0) * buf[i] * W[2*i];
+ }
+ }
+
+ X(ifree)(buf);
+}
+
+/* ro10 is same as re10, but with i <-> n - 1 - i in the output and
+ the sign of the odd input elements flipped. */
+static void apply_ro10(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 = ego->td->W;
+ R *buf;
+
+ buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+ for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+ buf[0] = I[0];
+ for (i = 1; i < n - i; ++i) {
+ E u, v;
+ int k = i + i;
+ u = -I[is * (k - 1)];
+ v = I[is * k];
+ buf[n - i] = u;
+ buf[i] = v;
+ }
+ if (i == n - i) {
+ buf[i] = -I[is * (n - 1)];
+ }
+
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, buf, buf);
+ }
+
+ O[os * (n - 1)] = K(2.0) * buf[0];
+ for (i = 1; i < n - i; ++i) {
+ E a, b, wa, wb;
+ a = K(2.0) * buf[i];
+ b = K(2.0) * buf[n - i];
+ wa = W[2*i];
+ wb = W[2*i + 1];
+ O[os * (n - 1 - i)] = wa * a + wb * b;
+ O[os * (i - 1)] = wb * a - wa * b;
+ }
+ if (i == n - i) {
+ O[os * (i - 1)] = K(2.0) * buf[i] * W[2*i];
+ }
+ }
+
+ 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 }
+ };
+
+ AWAKE(ego->cld, flg);
+
+ X(twiddle_awake)(flg, &ego->td, reodft010e_tw, 4*ego->n, 1, ego->n/2+1);
+}
+
+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-%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->kind[0] == REDFT01 || p->kind[0] == REDFT10
+ || p->kind[0] == RODFT01 || p->kind[0] == RODFT10)
+ );
+ }
+
+ 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;
+
+ switch (p->kind[0]) {
+ case REDFT01: pln = MKPLAN_RDFT(P, &padt, apply_re01); break;
+ case REDFT10: pln = MKPLAN_RDFT(P, &padt, apply_re10); break;
+ case RODFT01: pln = MKPLAN_RDFT(P, &padt, apply_ro01); break;
+ case RODFT10: pln = MKPLAN_RDFT(P, &padt, apply_ro10); break;
+ default: A(0); return (plan*)0;
+ }
+
+ pln->n = n;
+ pln->is = p->sz->dims[0].is;
+ pln->os = p->sz->dims[0].os;
+ pln->cld = cld;
+ pln->td = 0;
+ pln->kind = p->kind[0];
+
+ X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
+
+ X(ops_zero)(&ops);
+ ops.other = 4 + (n-1)/2 * 10 + (1 - n % 2) * 5;
+ if (p->kind[0] == REDFT01 || p->kind[0] == RODFT01) {
+ ops.add = (n-1)/2 * 6;
+ ops.mul = (n-1)/2 * 4 + (1 - n % 2) * 2;
+ }
+ else { /* 10 transforms */
+ ops.add = (n-1)/2 * 2;
+ ops.mul = 1 + (n-1)/2 * 6 + (1 - n % 2) * 2;
+ }
+
+ 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(reodft010e_r2hc_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver());
+}
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