comparison src/fftw-3.3.3/dft/rader.c @ 10:37bf6b4a2645

Add FFTW3

+/*
+ * Copyright (c) 2003, 2007-11 Matteo Frigo
+ * Copyright (c) 2003, 2007-11 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  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.
+ */
+
+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;
+
+static rader_tl *omegas = 0;
+
+static R *mkomega(enum wakefulness wakefulness, plan *p_, INT n, INT ginv)
+{
+     plan_dft *p = (plan_dft *) p_;
+     R *omega;
+     INT i, gpower;
+     trigreal scale;
+     triggen *t;
+
+     if ((omega = X(rader_tl_find)(n, n, ginv, omegas)))
+	  return omega;
+
+     omega = (R *)MALLOC(sizeof(R) * (n - 1) * 2, TWIDDLES);
+
+     scale = n - 1.0; /* normalization for convolution */
+
+     t = X(mktriggen)(wakefulness, n);
+     for (i = 0, gpower = 1; i < n-1; ++i, gpower = MULMOD(gpower, ginv, n)) {
+	  trigreal w[2];
+	  t->cexpl(t, gpower, w);
+	  omega[2*i] = w[0] / scale;
+	  omega[2*i+1] = FFT_SIGN * w[1] / scale;
+     }
+     X(triggen_destroy)(t);
+     A(gpower == 1);
+
+     p->apply(p_, omega, omega + 1, omega, omega + 1);
+
+     X(rader_tl_insert)(n, n, ginv, omega, &omegas);
+     return omega;
+}
+
+static void free_omega(R *omega)
+{
+     X(rader_tl_delete)(omega, &omegas);
+}
+
+
+/***************************************************************************/
+
+/* 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(const plan *ego_, R *ri, R *ii, R *ro, R *io)
+{
+     const P *ego = (const P *) ego_;
+     INT is, os;
+     INT k, gpower, g, r;
+     R *buf;
+     R r0 = ri[0], i0 = ii[0];
+
+     r = ego->n; is = ego->is; os = ego->os; 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 */;
+
+
+     /* compute DFT of buf, storing in output (except DC): */
+     {
+	    plan_dft *cld = (plan_dft *) ego->cld1;
+	    cld->apply(ego->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: */
+     {
+	  const R *omega = ego->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 *) ego->cld2;
+	    cld->apply(ego->cld2, ro+os, io+os, buf, buf+1);
+     }
+     
+     /* finally, do inverse permutation to unshuffle the output: */
+     {
+	  INT ginv = ego->ginv;
+	  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);
+     }
+
+
+     X(ifree)(buf);
+}
+
+/***************************************************************************/
+
+static void awake(plan *ego_, enum wakefulness wakefulness)
+{
+     P *ego = (P *) ego_;
+
+     X(plan_awake)(ego->cld1, wakefulness);
+     X(plan_awake)(ego->cld2, wakefulness);
+     X(plan_awake)(ego->cld_omega, wakefulness);
+
+     switch (wakefulness) {
+	 case SLEEPY:
+	      free_omega(ego->omega);
+	      ego->omega = 0;
+	      break;
+	 default:
+	      ego->g = X(find_generator)(ego->n);
+	      ego->ginv = X(power_mod)(ego->g, ego->n - 2, ego->n);
+	      A(MULMOD(ego->g, ego->ginv, ego->n) == 1);
+
+	      ego->omega = mkomega(wakefulness,
+				   ego->cld_omega, ego->n, ego->ginv);
+	      break;
+     }
+}
+
+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, "(dft-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 applicable(const solver *ego_, const problem *p_,
+		      const planner *plnr)
+{
+     const problem_dft *p = (const problem_dft *) p_;
+     UNUSED(ego_);
+     return (1
+	     && p->sz->rnk == 1
+	     && p->vecsz->rnk == 0
+	     && CIMPLIES(NO_SLOWP(plnr), p->sz->dims[0].n > RADER_MAX_SLOW)
+	     && X(is_prime)(p->sz->dims[0].n)
+
+	     /* proclaim the solver SLOW if p-1 is not easily factorizable.
+		Bluestein should take care of this case. */
+	     && CIMPLIES(NO_SLOWP(plnr), X(factors_into_small_primes)(p->sz->dims[0].n - 1))
+	  );
+}
+
+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_f_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),
+			  NO_SLOW, 0, 0);
+     if (!cld1) goto nada;
+
+     cld2 = X(mkplan_f_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),
+			  NO_SLOW, 0, 0);
+
+     if (!cld2) goto nada;
+
+     /* plan for omega array */
+     cld_omega = X(mkplan_f_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),
+			       NO_SLOW, ESTIMATE, 0);
+     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;
+
+     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 solver *mksolver(void)
+{
+     static const solver_adt sadt = { PROBLEM_DFT, mkplan, 0 };
+     S *slv = MKSOLVER(S, &sadt);
+     return &(slv->super);
+}
+
+void X(dft_rader_register)(planner *p)
+{
+     REGISTER_SOLVER(p, mksolver());
+}