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-rw-r--r--src/fftw3/rdft/dht-rader.c344
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diff --git a/src/fftw3/rdft/dht-rader.c b/src/fftw3/rdft/dht-rader.c
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+++ b/src/fftw3/rdft/dht-rader.c
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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
+ *
+ */
+
+#include "rdft.h"
+
+/*
+ * Compute DHTs of prime sizes using Rader's trick: turn them
+ * into convolutions of size n - 1, which we then perform via a pair
+ * of FFTs. (We can then do prime real FFTs via rdft-dht.c.)
+ */
+
+typedef struct {
+ solver super;
+} S;
+
+typedef struct {
+ plan_rdft super;
+
+ plan *cld1, *cld2;
+ R *omega;
+ int n, g, ginv;
+ int is, os;
+ plan *cld_omega;
+} P;
+
+static rader_tl *omegas = 0;
+
+/***************************************************************************/
+
+/* If R2HC_ONLY_CONV is 1, we use a trick to perform the convolution
+ purely in terms of R2HC transforms, as opposed to R2HC followed by H2RC.
+ This requires a few more operations, but allows us to share the same
+ plan/codelets for both Rader children. */
+#define R2HC_ONLY_CONV 1
+
+static void apply(const plan *ego_, R *I, R *O)
+{
+ const P *ego = (const P *) ego_;
+ int r = ego->n;
+ int is = ego->is, os;
+ int k, gpower, g;
+ R *buf, *omega;
+ R r0;
+
+ buf = (R *) MALLOC(sizeof(R) * (r - 1), BUFFERS);
+
+ /* First, permute the input, storing in buf: */
+ g = ego->g;
+ for (gpower = 1, k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
+ buf[k] = I[gpower * is];
+ }
+ /* gpower == g^(r-1) mod r == 1 */;
+
+ os = ego->os;
+
+ /* compute RDFT of buf, storing in output (except DC): */
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld1;
+ cld->apply((plan *) cld, buf, O + os);
+ }
+
+ /* set output DC component: */
+ O[0] = (r0 = I[0]) + O[os];
+
+ /* now, multiply by omega: */
+ omega = ego->omega;
+
+ O[(0 + 1) * os] *= omega[0];
+#if R2HC_ONLY_CONV
+ for (k = 1; k < (r - 1)/2; ++k) {
+ E rB, iB, rW, iW, a, b;
+ rW = omega[k];
+ iW = omega[(r-1) - k];
+ rB = O[(k + 1) * os];
+ iB = O[((r-1) - k + 1) * os];
+ a = rW * rB - iW * iB;
+ b = rW * iB + iW * rB;
+ O[(k + 1) * os] = a + b;
+ O[((r-1) - k + 1) * os] = a - b;
+ }
+#else
+ for (k = 1; k < (r - 1)/2; ++k) {
+ E rB, iB, rW, iW;
+ rW = omega[k];
+ iW = omega[(r-1) - k];
+ rB = O[(k + 1) * os];
+ iB = O[((r-1) - k + 1) * os];
+ O[(k + 1) * os] = rW * rB - iW * iB;
+ O[((r-1) - k + 1) * os] = rW * iB + iW * rB;
+ }
+#endif
+ /* Nyquist component: */
+ O[(k + 1) * os] *= omega[k]; /* k == (r-1)/2, since r-1 is even */
+
+ /* this will add input[0] to all of the outputs after the ifft */
+ O[os] += r0;
+
+ /* inverse FFT: */
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld2;
+ cld->apply((plan *) cld, O + os, buf);
+ }
+
+ /* do inverse permutation to unshuffle the output: */
+ A(gpower == 1);
+#if R2HC_ONLY_CONV
+ O[os] = buf[0];
+ gpower = g = ego->ginv;
+ for (k = 1; k < (r - 1)/2; ++k, gpower = MULMOD(gpower, g, r)) {
+ O[gpower * os] = buf[k] + buf[r - 1 - k];
+ }
+ O[gpower * os] = buf[k];
+ ++k, gpower = MULMOD(gpower, g, r);
+ for (; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
+ O[gpower * os] = buf[r - 1 - k] - buf[k];
+ }
+#else
+ g = ego->ginv;
+ for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
+ O[gpower * os] = buf[k];
+ }
+#endif
+ A(gpower == 1);
+
+ X(ifree)(buf);
+}
+
+static R *mkomega(plan *p_, int n, int ginv)
+{
+ plan_rdft *p = (plan_rdft *) p_;
+ R *omega;
+ int i, gpower;
+ trigreal scale;
+
+ if ((omega = X(rader_tl_find)(n, n, ginv, omegas)))
+ return omega;
+
+ omega = (R *)MALLOC(sizeof(R) * (n - 1), TWIDDLES);
+
+ scale = n - 1.0; /* normalization for convolution */
+
+ for (i = 0, gpower = 1; i < n-1; ++i, gpower = MULMOD(gpower, ginv, n)) {
+ omega[i] = (X(cos2pi)(gpower, n) + X(sin2pi)(gpower, n)) / scale;
+ }
+ A(gpower == 1);
+
+ AWAKE(p_, 1);
+ p->apply(p_, omega, omega);
+ AWAKE(p_, 0);
+
+ X(rader_tl_insert)(n, n, ginv, omega, &omegas);
+ return omega;
+}
+
+static void free_omega(R *omega)
+{
+ X(rader_tl_delete)(omega, &omegas);
+}
+
+/***************************************************************************/
+
+static void awake(plan *ego_, int flg)
+{
+ P *ego = (P *) ego_;
+
+ AWAKE(ego->cld1, flg);
+ AWAKE(ego->cld2, flg);
+
+ if (flg) {
+ if (!ego->omega)
+ ego->omega = mkomega(ego->cld_omega,ego->n,ego->ginv);
+ } else {
+ free_omega(ego->omega);
+ ego->omega = 0;
+ }
+}
+
+static void destroy(plan *ego_)
+{
+ P *ego = (P *) ego_;
+ X(plan_destroy_internal)(ego->cld_omega);
+ X(plan_destroy_internal)(ego->cld2);
+ X(plan_destroy_internal)(ego->cld1);
+}
+
+static void print(const plan *ego_, printer *p)
+{
+ const P *ego = (const P *) ego_;
+
+ p->print(p, "(dht-rader-%d%ois=%oos=%(%p%)",
+ ego->n, ego->is, ego->os, ego->cld1);
+ if (ego->cld2 != ego->cld1)
+ p->print(p, "%(%p%)", ego->cld2);
+ if (ego->cld_omega != ego->cld1 && ego->cld_omega != ego->cld2)
+ p->print(p, "%(%p%)", ego->cld_omega);
+ p->putchr(p, ')');
+}
+
+static int applicable0(const problem *p_)
+{
+ if (RDFTP(p_)) {
+ const problem_rdft *p = (const problem_rdft *) p_;
+ return (1
+ && p->sz->rnk == 1
+ && p->vecsz->rnk == 0
+ && p->kind[0] == DHT
+ && X(is_prime)(p->sz->dims[0].n)
+ && p->sz->dims[0].n > 2
+ );
+ }
+
+ return 0;
+}
+
+static int applicable(const solver *ego, const problem *p, const planner *plnr)
+{
+ UNUSED(ego);
+ return (!NO_UGLYP(plnr) && applicable0(p));
+}
+
+static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
+{
+ const problem_rdft *p = (const problem_rdft *) p_;
+ P *pln;
+ int n;
+ int is, os;
+ plan *cld1 = (plan *) 0;
+ plan *cld2 = (plan *) 0;
+ plan *cld_omega = (plan *) 0;
+ R *buf = (R *) 0;
+ R *O;
+ problem *cldp;
+
+ static const plan_adt padt = {
+ X(rdft_solve), awake, print, destroy
+ };
+
+ if (!applicable(ego_, p_, plnr))
+ return (plan *) 0;
+
+ n = p->sz->dims[0].n;
+ is = p->sz->dims[0].is;
+ os = p->sz->dims[0].os;
+ O = p->O;
+
+ /* initial allocation for the purpose of planning */
+ buf = (R *) MALLOC(sizeof(R) * (n - 1), BUFFERS);
+
+ cld1 = X(mkplan_d)(plnr,
+ X(mkproblem_rdft_1_d)(X(mktensor_1d)(n - 1, 1, os),
+ X(mktensor_1d)(1, 0, 0),
+ buf,
+ O + os,
+ R2HC));
+ if (!cld1) goto nada;
+
+ cldp =
+ X(mkproblem_rdft_1_d)(
+ X(mktensor_1d)(n - 1, os, 1),
+ X(mktensor_1d)(1, 0, 0),
+ O + os,
+ buf,
+#if R2HC_ONLY_CONV
+ R2HC
+#else
+ HC2R
+#endif
+ );
+ if (!(cld2 = X(mkplan_d)(plnr, cldp))) goto nada;
+
+
+ /* plan for omega */
+ plnr->planner_flags |= ESTIMATE;
+ cld_omega = X(mkplan_d)(plnr,
+ X(mkproblem_rdft_1_d)(X(mktensor_1d)(n - 1, 1, 1),
+ X(mktensor_1d)(1, 0, 0),
+ buf, buf, R2HC));
+ if (!cld_omega) goto nada;
+
+ /* deallocate buffers; let awake() or apply() allocate them for real */
+ X(ifree)(buf);
+ buf = 0;
+
+ pln = MKPLAN_RDFT(P, &padt, apply);
+ pln->cld1 = cld1;
+ pln->cld2 = cld2;
+ pln->cld_omega = cld_omega;
+ pln->omega = 0;
+ pln->n = n;
+ pln->is = is;
+ pln->os = os;
+ pln->g = X(find_generator)(n);
+ pln->ginv = X(power_mod)(pln->g, n - 2, n);
+ A(MULMOD(pln->g, pln->ginv, n) == 1);
+
+ X(ops_add)(&cld1->ops, &cld2->ops, &pln->super.super.ops);
+ pln->super.super.ops.other += (n - 3) * 3 + (n - 2) * 2 + 5;
+ pln->super.super.ops.add += (n - 3) * 1;
+ pln->super.super.ops.mul += (n - 3) * 2 + 2;
+#if R2HC_ONLY_CONV
+ pln->super.super.ops.other += (n - 2) + 4;
+ pln->super.super.ops.add += (n - 3) * 1 + (n - 2) * 1;
+#endif
+
+ return &(pln->super.super);
+
+ nada:
+ X(ifree0)(buf);
+ X(plan_destroy_internal)(cld_omega);
+ X(plan_destroy_internal)(cld2);
+ X(plan_destroy_internal)(cld1);
+ return 0;
+}
+
+/* constructors */
+
+static solver *mksolver(void)
+{
+ static const solver_adt sadt = { mkplan };
+ S *slv = MKSOLVER(S, &sadt);
+ return &(slv->super);
+}
+
+void X(dht_rader_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver());
+}
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