diff src/fftw-3.3.3/rdft/dht-rader.c @ 10:37bf6b4a2645

Add FFTW3

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/fftw-3.3.3/rdft/dht-rader.c	Wed Mar 20 15:35:50 2013 +0000
@@ -0,0 +1,386 @@
+/*
+ * 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 "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.)
+ *
+ * Optionally (determined by the "pad" field of the solver), we can
+ * perform the (cyclic) convolution by zero-padding to a size
+ * >= 2*(n-1) - 1.  This is advantageous if n-1 has large prime factors.
+ *
+ */
+
+typedef struct {
+     solver super;
+     int pad;
+} S;
+
+typedef struct {
+     plan_rdft super;
+
+     plan *cld1, *cld2;
+     R *omega;
+     INT n, npad, 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 n = ego->n; /* prime */
+     INT npad = ego->npad; /* == n - 1 for unpadded Rader; always even */
+     INT is = ego->is, os;
+     INT k, gpower, g;
+     R *buf, *omega;
+     R r0;
+
+     buf = (R *) MALLOC(sizeof(R) * npad, BUFFERS);
+
+     /* First, permute the input, storing in buf: */
+     g = ego->g; 
+     for (gpower = 1, k = 0; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
+	  buf[k] = I[gpower * is];
+     }
+     /* gpower == g^(n-1) mod n == 1 */;
+
+     A(n - 1 <= npad);
+     for (k = n - 1; k < npad; ++k) /* optionally, zero-pad convolution */
+	  buf[k] = 0;
+
+     os = ego->os;
+
+     /* compute RDFT of buf, storing in buf (i.e., in-place): */
+     {
+	    plan_rdft *cld = (plan_rdft *) ego->cld1;
+	    cld->apply((plan *) cld, buf, buf);
+     }
+
+     /* set output DC component: */
+     O[0] = (r0 = I[0]) + buf[0];
+
+     /* now, multiply by omega: */
+     omega = ego->omega;
+     buf[0] *= omega[0];
+     for (k = 1; k < npad/2; ++k) {
+	  E rB, iB, rW, iW, a, b;
+	  rW = omega[k];
+	  iW = omega[npad - k];
+	  rB = buf[k];
+	  iB = buf[npad - k];
+	  a = rW * rB - iW * iB;
+	  b = rW * iB + iW * rB;
+#if R2HC_ONLY_CONV
+	  buf[k] = a + b;
+	  buf[npad - k] = a - b;
+#else
+	  buf[k] = a;
+	  buf[npad - k] = b;
+#endif
+     }
+     /* Nyquist component: */
+     A(k + k == npad); /* since npad is even */
+     buf[k] *= omega[k];
+     
+     /* this will add input[0] to all of the outputs after the ifft */
+     buf[0] += r0;
+
+     /* inverse FFT: */
+     {
+	    plan_rdft *cld = (plan_rdft *) ego->cld2;
+	    cld->apply((plan *) cld, buf, buf);
+     }
+
+     /* do inverse permutation to unshuffle the output: */
+     A(gpower == 1);
+#if R2HC_ONLY_CONV
+     O[os] = buf[0];
+     gpower = g = ego->ginv;
+     A(npad == n - 1 || npad/2 >= n - 1);
+     if (npad == n - 1) {
+	  for (k = 1; k < npad/2; ++k, gpower = MULMOD(gpower, g, n)) {
+	       O[gpower * os] = buf[k] + buf[npad - k];
+	  }
+	  O[gpower * os] = buf[k];
+	  ++k, gpower = MULMOD(gpower, g, n);
+	  for (; k < npad; ++k, gpower = MULMOD(gpower, g, n)) {
+	       O[gpower * os] = buf[npad - k] - buf[k];
+	  }
+     }
+     else {
+	  for (k = 1; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
+	       O[gpower * os] = buf[k] + buf[npad - k];
+	  }
+     }
+#else
+     g = ego->ginv;
+     for (k = 0; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
+	  O[gpower * os] = buf[k];
+     }
+#endif
+     A(gpower == 1);
+
+     X(ifree)(buf);
+}
+
+static R *mkomega(enum wakefulness wakefulness,
+		  plan *p_, INT n, INT npad, INT ginv)
+{
+     plan_rdft *p = (plan_rdft *) p_;
+     R *omega;
+     INT i, gpower;
+     trigreal scale;
+     triggen *t;
+
+     if ((omega = X(rader_tl_find)(n, npad + 1, ginv, omegas))) 
+	  return omega;
+
+     omega = (R *)MALLOC(sizeof(R) * npad, TWIDDLES);
+
+     scale = npad; /* 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[i] = (w[0] + w[1]) / scale;
+     }
+     X(triggen_destroy)(t);
+     A(gpower == 1);
+
+     A(npad == n - 1 || npad >= 2*(n - 1) - 1);
+
+     for (; i < npad; ++i)
+	  omega[i] = K(0.0);
+     if (npad > n - 1)
+	  for (i = 1; i < n-1; ++i)
+	       omega[npad - i] = omega[n - 1 - i];
+
+     p->apply(p_, omega, omega);
+
+     X(rader_tl_insert)(n, npad + 1, ginv, omega, &omegas);
+     return omega;
+}
+
+static void free_omega(R *omega)
+{
+     X(rader_tl_delete)(omega, &omegas);
+}
+
+/***************************************************************************/
+
+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);
+
+	      A(!ego->omega);
+	      ego->omega = mkomega(wakefulness, 
+				   ego->cld_omega,ego->n,ego->npad,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, "(dht-rader-%D/%D%ois=%oos=%(%p%)",
+              ego->n, ego->npad, 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_rdft *p = (const problem_rdft *) p_;
+     UNUSED(ego);
+     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
+	     && CIMPLIES(NO_SLOWP(plnr), p->sz->dims[0].n > RADER_MAX_SLOW)
+	     /* proclaim the solver SLOW if p-1 is not easily
+		factorizable.  Unlike in the complex case where
+		Bluestein can solve the problem, in the DHT case we
+		may have no other choice */
+	     && CIMPLIES(NO_SLOWP(plnr), X(factors_into_small_primes)(p->sz->dims[0].n - 1))
+	  );
+}
+
+static INT choose_transform_size(INT minsz)
+{
+     static const INT primes[] = { 2, 3, 5, 0 };
+     while (!X(factors_into)(minsz, primes) || minsz % 2)
+	  ++minsz;
+     return minsz;
+}
+
+static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
+{
+     const S *ego = (const S *) ego_;
+     const problem_rdft *p = (const problem_rdft *) p_;
+     P *pln;
+     INT n, npad;
+     INT is, os;
+     plan *cld1 = (plan *) 0;
+     plan *cld2 = (plan *) 0;
+     plan *cld_omega = (plan *) 0;
+     R *buf = (R *) 0;
+     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;
+
+     if (ego->pad)
+	  npad = choose_transform_size(2 * (n - 1) - 1);
+     else
+	  npad = n - 1;
+
+     /* initial allocation for the purpose of planning */
+     buf = (R *) MALLOC(sizeof(R) * npad, BUFFERS);
+
+     cld1 = X(mkplan_f_d)(plnr, 
+			  X(mkproblem_rdft_1_d)(X(mktensor_1d)(npad, 1, 1),
+						X(mktensor_1d)(1, 0, 0),
+						buf, buf,
+						R2HC),
+			  NO_SLOW, 0, 0);
+     if (!cld1) goto nada;
+
+     cldp =
+          X(mkproblem_rdft_1_d)(
+               X(mktensor_1d)(npad, 1, 1),
+               X(mktensor_1d)(1, 0, 0),
+	       buf, buf, 
+#if R2HC_ONLY_CONV
+	       R2HC
+#else
+	       HC2R
+#endif
+	       );
+     if (!(cld2 = X(mkplan_f_d)(plnr, cldp, NO_SLOW, 0, 0)))
+	  goto nada;
+
+     /* plan for omega */
+     cld_omega = X(mkplan_f_d)(plnr, 
+			       X(mkproblem_rdft_1_d)(
+				    X(mktensor_1d)(npad, 1, 1),
+				    X(mktensor_1d)(1, 0, 0),
+				    buf, buf, R2HC),
+			       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 = MKPLAN_RDFT(P, &padt, apply);
+     pln->cld1 = cld1;
+     pln->cld2 = cld2;
+     pln->cld_omega = cld_omega;
+     pln->omega = 0;
+     pln->n = n;
+     pln->npad = npad;
+     pln->is = is;
+     pln->os = os;
+
+     X(ops_add)(&cld1->ops, &cld2->ops, &pln->super.super.ops);
+     pln->super.super.ops.other += (npad/2-1)*6 + npad + n + (n-1) * ego->pad;
+     pln->super.super.ops.add += (npad/2-1)*2 + 2 + (n-1) * ego->pad;
+     pln->super.super.ops.mul += (npad/2-1)*4 + 2 + ego->pad;
+#if R2HC_ONLY_CONV
+     pln->super.super.ops.other += n-2 - ego->pad;
+     pln->super.super.ops.add += (npad/2-1)*2 + (n-2) - ego->pad;
+#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(int pad)
+{
+     static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
+     S *slv = MKSOLVER(S, &sadt);
+     slv->pad = pad;
+     return &(slv->super);
+}
+
+void X(dht_rader_register)(planner *p)
+{
+     REGISTER_SOLVER(p, mksolver(0));
+     REGISTER_SOLVER(p, mksolver(1));
+}