summaryrefslogtreecommitdiff
path: root/src/fftw3/dft/rader.c
diff options
context:
space:
mode:
Diffstat (limited to 'src/fftw3/dft/rader.c')
-rw-r--r--src/fftw3/dft/rader.c491
1 files changed, 491 insertions, 0 deletions
diff --git a/src/fftw3/dft/rader.c b/src/fftw3/dft/rader.c
new file mode 100644
index 0000000..f31f370
--- /dev/null
+++ b/src/fftw3/dft/rader.c
@@ -0,0 +1,491 @@
+/*
+ * 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 "dft.h"
+
+/*
+ * Compute transforms of prime sizes using Rader's trick: turn them
+ * into convolutions of size n - 1, which you then perform via a pair
+ * of FFTs. This file contains both nontwiddle (direct) and
+ * twiddle (DIT Cooley-Tukey) solvers.
+ */
+
+typedef struct {
+ solver super;
+} S;
+
+typedef struct {
+ plan_dft super;
+
+ plan *cld1, *cld2;
+ R *omega;
+ int n, g, ginv;
+ int is, os;
+ plan *cld_omega;
+} P;
+
+typedef struct {
+ P super;
+ plan *cld;
+ R *W;
+ int os;
+ int m;
+} P_dit;
+
+
+static rader_tl *twiddles = 0;
+
+/***************************************************************************/
+
+/* Below, we extensively use the identity that fft(x*)* = ifft(x) in
+ order to share data between forward and backward transforms and to
+ obviate the necessity of having separate forward and backward
+ plans. (Although we often compute separate plans these days anyway
+ due to the differing strides, etcetera.)
+
+ Of course, since the new FFTW gives us separate pointers to
+ the real and imaginary parts, we could have instead used the
+ fft(r,i) = ifft(i,r) form of this identity, but it was easier to
+ reuse the code from our old version. */
+
+static void apply_aux(int r, int ginv, plan *cld1,plan *cld2, const R *omega,
+ R *buf, R r0, R i0, R *ro, R *io, int os)
+{
+ int gpower, k;
+
+ /* compute DFT of buf, storing in output (except DC): */
+ {
+ plan_dft *cld = (plan_dft *) cld1;
+ cld->apply(cld1, buf, buf+1, ro+os, io+os);
+ }
+
+ /* set output DC component: */
+ ro[0] = r0 + ro[os];
+ io[0] = i0 + io[os];
+
+ /* now, multiply by omega: */
+ for (k = 0; k < r - 1; ++k) {
+ E rB, iB, rW, iW;
+ rW = omega[2*k];
+ iW = omega[2*k+1];
+ rB = ro[(k+1)*os];
+ iB = io[(k+1)*os];
+ ro[(k+1)*os] = rW * rB - iW * iB;
+ io[(k+1)*os] = -(rW * iB + iW * rB);
+ }
+
+ /* this will add input[0] to all of the outputs after the ifft */
+ ro[os] += r0;
+ io[os] -= i0;
+
+ /* inverse FFT: */
+ {
+ plan_dft *cld = (plan_dft *) cld2;
+ cld->apply(cld2, ro+os, io+os, buf, buf+1);
+ }
+
+ /* finally, do inverse permutation to unshuffle the output: */
+ gpower = 1;
+ for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, ginv, r)) {
+ ro[gpower * os] = buf[2*k];
+ io[gpower * os] = -buf[2*k+1];
+ }
+ A(gpower == 1);
+}
+
+static void apply(const plan *ego_, R *ri, R *ii, R *ro, R *io)
+{
+ const P *ego = (const P *) ego_;
+ int is;
+ int k, gpower, g, r;
+ R *buf;
+
+ r = ego->n; is = ego->is; g = ego->g;
+ buf = (R *) MALLOC(sizeof(R) * (r - 1) * 2, BUFFERS);
+
+ /* First, permute the input, storing in buf: */
+ for (gpower = 1, k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
+ R rA, iA;
+ rA = ri[gpower * is];
+ iA = ii[gpower * is];
+ buf[2*k] = rA; buf[2*k + 1] = iA;
+ }
+ /* gpower == g^(r-1) mod r == 1 */;
+
+ apply_aux(r, ego->ginv, ego->cld1, ego->cld2, ego->omega,
+ buf, ri[0], ii[0], ro, io, ego->os);
+
+ X(ifree)(buf);
+}
+
+static void apply_dit(const plan *ego_, R *ri, R *ii, R *ro, R *io)
+{
+ const P_dit *ego_dit = (const P_dit *) ego_;
+ const P *ego;
+ plan *cld1, *cld2;
+ int os, osm;
+ int j, k, gpower, g, ginv, r, m;
+ R *buf;
+ const R *omega, *W;
+
+ {
+ plan *cld0 = ego_dit->cld;
+ plan_dft *cld = (plan_dft *) cld0;
+ cld->apply(cld0, ri, ii, ro, io);
+ }
+
+ ego = (const P *) ego_;
+ cld1 = ego->cld1;
+ cld2 = ego->cld2;
+ r = ego->n;
+ m = ego_dit->m;
+ g = ego->g;
+ ginv = ego->ginv;
+ omega = ego->omega;
+ W = ego_dit->W;
+ os = ego_dit->os;
+ osm = ego->os;
+ gpower = 1;
+
+ buf = (R *) MALLOC(sizeof(R) * (r - 1) * 2, BUFFERS);
+
+ for (j = 0; j < m; ++j, ro += os, io += os, W += 2*(r - 1)) {
+ /* First, permute the input and multiply by W, storing in buf: */
+ A(gpower == 1);
+ for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
+ E rA, iA, rW, iW;
+ rA = ro[gpower * osm];
+ iA = io[gpower * osm];
+ rW = W[2*k];
+ iW = W[2*k+1];
+ buf[2*k] = rW * rA - iW * iA;
+ buf[2*k + 1] = rW * iA + iW * rA;
+ }
+ /* gpower == g^(r-1) mod r == 1 */;
+
+ apply_aux(r, ginv, cld1, cld2, omega,
+ buf, ro[0], io[0], ro, io, osm);
+ }
+
+ X(ifree)(buf);
+}
+
+static R *mktwiddle(int m, int r, int g)
+{
+ int i, j, gpower;
+ int n = r * m;
+ R *W;
+
+ if ((W = X(rader_tl_find)(m, r, g, twiddles)))
+ return W;
+
+ W = (R *)MALLOC(sizeof(R) * (r - 1) * m * 2, TWIDDLES);
+ for (i = 0; i < m; ++i) {
+ for (gpower = 1, j = 0; j < r - 1;
+ ++j, gpower = MULMOD(gpower, g, r)) {
+ int k = i * (r - 1) + j;
+ W[2*k] = X(cos2pi)(i * gpower, n);
+ W[2*k+1] = FFT_SIGN * X(sin2pi)(i * gpower, n);
+ }
+ A(gpower == 1);
+ }
+
+ X(rader_tl_insert)(m, r, g, W, &twiddles);
+ return W;
+}
+
+static void free_twiddle(R *twiddle)
+{
+ X(rader_tl_delete)(twiddle, &twiddles);
+}
+
+/***************************************************************************/
+
+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 =
+ X(dft_rader_mkomega)(ego->cld_omega, ego->n, ego->ginv);
+ } else {
+ X(dft_rader_free_omega)(&ego->omega);
+ }
+}
+
+static void awake_dit(plan *ego_, int flg)
+{
+ P_dit *ego = (P_dit *) ego_;
+
+ AWAKE(ego->cld, flg);
+ if (flg)
+ ego->W = mktwiddle(ego->m, ego->super.n, ego->super.g);
+ else {
+ free_twiddle(ego->W);
+ ego->W = 0;
+ }
+
+ awake(ego_, flg);
+}
+
+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 destroy_dit(plan *ego_)
+{
+ P_dit *ego = (P_dit *) ego_;
+ X(plan_destroy_internal)(ego->cld);
+ destroy(ego_);
+}
+
+static void print_aux(const char *name, const P *ego, printer *p)
+{
+ p->print(p, "(%s-%d%ois=%oos=%(%p%)",
+ name, 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);
+}
+
+static void print(const plan *ego_, printer *p)
+{
+ print_aux("dft-rader", (const P *) ego_, p);
+ p->putchr(p, ')');
+}
+
+static void print_dit(const plan *ego_, printer *p)
+{
+ const P_dit *ego_dit = (const P_dit *) ego_;
+
+ print_aux("dft-rader-dit", (const P *) ego_, p);
+ p->print(p, "%(%p%))", ego_dit->cld);
+}
+
+static int applicable0(const solver *ego_, const problem *p_)
+{
+ UNUSED(ego_);
+ if (DFTP(p_)) {
+ const problem_dft *p = (const problem_dft *) p_;
+ return (1
+ && p->sz->rnk == 1
+ && p->vecsz->rnk == 0
+ && X(is_prime)(p->sz->dims[0].n)
+ );
+ }
+
+ return 0;
+}
+
+static int applicable0_dit(const solver *ego_, const problem *p_)
+{
+ UNUSED(ego_);
+ if (DFTP(p_)) {
+ const problem_dft *p = (const problem_dft *) p_;
+ return (1
+ && p->sz->rnk == 1
+ && p->vecsz->rnk == 0
+ && p->sz->dims[0].n > 1
+ );
+ }
+
+ return 0;
+}
+
+static int applicable(const solver *ego_, const problem *p_,
+ const planner *plnr)
+{
+ return (!NO_UGLYP(plnr) && applicable0(ego_, p_));
+}
+
+static int applicable_dit(const solver *ego_, const problem *p_,
+ const planner *plnr)
+{
+ return (!NO_UGLYP(plnr) && applicable0_dit(ego_, p_));
+}
+
+static int mkP(P *pln, int n, int is, int os, R *ro, R *io,
+ planner *plnr)
+{
+ plan *cld1 = (plan *) 0;
+ plan *cld2 = (plan *) 0;
+ plan *cld_omega = (plan *) 0;
+ R *buf = (R *) 0;
+
+ /* initial allocation for the purpose of planning */
+ buf = (R *) MALLOC(sizeof(R) * (n - 1) * 2, BUFFERS);
+
+ cld1 = X(mkplan_d)(plnr,
+ X(mkproblem_dft_d)(X(mktensor_1d)(n - 1, 2, os),
+ X(mktensor_1d)(1, 0, 0),
+ buf, buf + 1, ro + os, io + os));
+ if (!cld1) goto nada;
+
+ cld2 = X(mkplan_d)(plnr,
+ X(mkproblem_dft_d)(X(mktensor_1d)(n - 1, os, 2),
+ X(mktensor_1d)(1, 0, 0),
+ ro + os, io + os, buf, buf + 1));
+
+ if (!cld2) goto nada;
+
+ /* plan for omega array */
+ plnr->planner_flags |= ESTIMATE;
+ cld_omega = X(mkplan_d)(plnr,
+ X(mkproblem_dft_d)(X(mktensor_1d)(n - 1, 2, 2),
+ X(mktensor_1d)(1, 0, 0),
+ buf, buf + 1, buf, buf + 1));
+ if (!cld_omega) goto nada;
+
+ /* deallocate buffers; let awake() or apply() allocate them for real */
+ X(ifree)(buf);
+ buf = 0;
+
+ 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 - 1) * (4 * 2 + 6) + 6;
+ pln->super.super.ops.add += (n - 1) * 2 + 4;
+ pln->super.super.ops.mul += (n - 1) * 4;
+
+ return 1;
+
+ nada:
+ X(ifree0)(buf);
+ X(plan_destroy_internal)(cld_omega);
+ X(plan_destroy_internal)(cld2);
+ X(plan_destroy_internal)(cld1);
+ return 0;
+}
+
+static plan *mkplan(const solver *ego, const problem *p_, planner *plnr)
+{
+ const problem_dft *p = (const problem_dft *) p_;
+ P *pln;
+ int n;
+ int is, os;
+
+ static const plan_adt padt = {
+ X(dft_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;
+
+ pln = MKPLAN_DFT(P, &padt, apply);
+ if (!mkP(pln, n, is, os, p->ro, p->io, plnr)) {
+ X(ifree)(pln);
+ return (plan *) 0;
+ }
+ return &(pln->super.super);
+}
+
+static plan *mkplan_dit(const solver *ego, const problem *p_, planner *plnr)
+{
+ const problem_dft *p = (const problem_dft *) p_;
+ P_dit *pln = 0;
+ int n, r, m;
+ int is, os;
+ plan *cld = (plan *) 0;
+
+ static const plan_adt padt = {
+ X(dft_solve), awake_dit, print_dit, destroy_dit
+ };
+
+ if (!applicable_dit(ego, p_, plnr))
+ goto nada;
+
+ n = p->sz->dims[0].n;
+ is = p->sz->dims[0].is;
+ os = p->sz->dims[0].os;
+
+ r = X(first_divisor)(n);
+ m = n / r;
+
+ cld = X(mkplan_d)(plnr,
+ X(mkproblem_dft_d)(X(mktensor_1d)(m, r * is, os),
+ X(mktensor_1d)(r, is, m * os),
+ p->ri, p->ii, p->ro, p->io));
+ if (!cld) goto nada;
+
+ pln = MKPLAN_DFT(P_dit, &padt, apply_dit);
+ if (!mkP(&pln->super, r, os*m, os*m, p->ro, p->io, plnr))
+ goto nada;
+
+ pln->os = os;
+ pln->m = m;
+ pln->cld = cld;
+ pln->W = 0;
+
+ pln->super.super.super.ops.add += 2 * (r-1);
+ pln->super.super.super.ops.mul += 4 * (r-1);
+ X(ops_madd)(m, &pln->super.super.super.ops, &cld->ops,
+ &pln->super.super.super.ops);
+
+ return &(pln->super.super.super);
+
+ nada:
+ X(plan_destroy_internal)(cld);
+ X(ifree0)(pln);
+ return (plan *) 0;
+}
+
+/* constructors */
+
+static solver *mksolver(void)
+{
+ static const solver_adt sadt = { mkplan };
+ S *slv = MKSOLVER(S, &sadt);
+ return &(slv->super);
+}
+
+static solver *mksolver_dit(void)
+{
+ static const solver_adt sadt = { mkplan_dit };
+ S *slv = MKSOLVER(S, &sadt);
+ return &(slv->super);
+}
+
+void X(dft_rader_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver());
+ REGISTER_SOLVER(p, mksolver_dit());
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-21 22:00:40 +0000