diff src/fftw-3.3.3/reodft/reodft11e-r2hc.c @ 10:37bf6b4a2645

Add FFTW3

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/fftw-3.3.3/reodft/reodft11e-r2hc.c	Wed Mar 20 15:35:50 2013 +0000
@@ -0,0 +1,294 @@
+/*
+ * 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
+ *
+ */
+
+
+/* Do an R{E,O}DFT11 problem via an R2HC problem, with some
+   pre/post-processing ala FFTPACK.  Use a trick from: 
+
+     S. C. Chan and K. L. Ho, "Direct methods for computing discrete
+     sinusoidal transforms," IEE Proceedings F 137 (6), 433--442 (1990).
+
+   to re-express as an REDFT01 (DCT-III) problem.
+
+   NOTE: We no longer use this algorithm, because it turns out to suffer
+   a catastrophic loss of accuracy for certain inputs, apparently because
+   its post-processing multiplies the output by a cosine.  Near the zero
+   of the cosine, the REDFT01 must produce a near-singular output.
+*/
+
+#include "reodft.h"
+
+typedef struct {
+     solver super;
+} S;
+
+typedef struct {
+     plan_rdft super;
+     plan *cld;
+     twid *td, *td2;
+     INT is, os;
+     INT n;
+     INT vl;
+     INT ivs, ovs;
+     rdft_kind kind;
+} P;
+
+static void apply_re11(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;
+     R *buf;
+     E cur;
+
+     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+	  /* I wish that this didn't require an extra pass. */
+	  /* FIXME: use recursive/cascade summation for better stability? */
+	  buf[n - 1] = cur = K(2.0) * I[is * (n - 1)];
+	  for (i = n - 1; i > 0; --i) {
+	       E curnew;
+	       buf[(i - 1)] = curnew = K(2.0) * I[is * (i - 1)] - cur;
+	       cur = curnew;
+	  }
+	  
+	  W = ego->td->W;
+	  for (i = 1; i < n - i; ++i) {
+	       E a, b, apb, amb, wa, wb;
+	       a = buf[i];
+	       b = buf[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) * buf[i] * W[2*i];
+	  }
+	  
+	  {
+	       plan_rdft *cld = (plan_rdft *) ego->cld;
+	       cld->apply((plan *) cld, buf, buf);
+	  }
+	  
+	  W = ego->td2->W;
+	  O[0] = W[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)] = W[k - 1] * (a - b);
+	       O[os * k] = W[k] * (a + b);
+	  }
+	  if (i == n - i) {
+	       O[os * (n - 1)] = W[n - 1] * buf[i];
+	  }
+     }
+
+     X(ifree)(buf);
+}
+
+/* like for rodft01, rodft11 is obtained from redft11 by
+   reversing the input and flipping the sign of every other output. */
+static void apply_ro11(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;
+     R *buf;
+     E cur;
+
+     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+	  /* I wish that this didn't require an extra pass. */
+	  /* FIXME: use recursive/cascade summation for better stability? */
+	  buf[n - 1] = cur = K(2.0) * I[0];
+	  for (i = n - 1; i > 0; --i) {
+	       E curnew;
+	       buf[(i - 1)] = curnew = K(2.0) * I[is * (n - i)] - cur;
+	       cur = curnew;
+	  }
+	  
+	  W = ego->td->W;
+	  for (i = 1; i < n - i; ++i) {
+	       E a, b, apb, amb, wa, wb;
+	       a = buf[i];
+	       b = buf[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) * buf[i] * W[2*i];
+	  }
+	  
+	  {
+	       plan_rdft *cld = (plan_rdft *) ego->cld;
+	       cld->apply((plan *) cld, buf, buf);
+	  }
+	  
+	  W = ego->td2->W;
+	  O[0] = W[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)] = W[k - 1] * (b - a);
+	       O[os * k] = W[k] * (a + b);
+	  }
+	  if (i == n - i) {
+	       O[os * (n - 1)] = -W[n - 1] * buf[i];
+	  }
+     }
+
+     X(ifree)(buf);
+}
+
+static void awake(plan *ego_, enum wakefulness wakefulness)
+{
+     P *ego = (P *) ego_;
+     static const tw_instr reodft010e_tw[] = {
+          { TW_COS, 0, 1 },
+          { TW_SIN, 0, 1 },
+          { TW_NEXT, 1, 0 }
+     };
+     static const tw_instr reodft11e_tw[] = {
+          { TW_COS, 1, 1 },
+          { TW_NEXT, 2, 0 }
+     };
+
+     X(plan_awake)(ego->cld, wakefulness);
+
+     X(twiddle_awake)(wakefulness,
+		      &ego->td, reodft010e_tw, 4*ego->n, 1, ego->n/2+1);
+     X(twiddle_awake)(wakefulness,
+		      &ego->td2, reodft11e_tw, 8*ego->n, 1, ego->n * 2);
+}
+
+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_)
+{
+     const problem_rdft *p = (const problem_rdft *) p_;
+
+     UNUSED(ego_);
+
+     return (1
+	     && p->sz->rnk == 1
+	     && p->vecsz->rnk <= 1
+	     && (p->kind[0] == REDFT11 || p->kind[0] == RODFT11)
+	  );
+}
+
+static int applicable(const solver *ego, const problem *p, const planner *plnr)
+{
+     return (!NO_SLOWP(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;
+
+     pln = MKPLAN_RDFT(P, &padt, p->kind[0]==REDFT11 ? apply_re11:apply_ro11);
+     pln->n = n;
+     pln->is = p->sz->dims[0].is;
+     pln->os = p->sz->dims[0].os;
+     pln->cld = cld;
+     pln->td = pln->td2 = 0;
+     pln->kind = p->kind[0];
+     
+     X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
+     
+     X(ops_zero)(&ops);
+     ops.other = 5 + (n-1) * 2 + (n-1)/2 * 12 + (1 - n % 2) * 6;
+     ops.add = (n - 1) * 1 + (n-1)/2 * 6;
+     ops.mul = 2 + (n-1) * 1 + (n-1)/2 * 6 + (1 - n % 2) * 3;
+
+     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 = { PROBLEM_RDFT, mkplan, 0 };
+     S *slv = MKSOLVER(S, &sadt);
+     return &(slv->super);
+}
+
+void X(reodft11e_r2hc_register)(planner *p)
+{
+     REGISTER_SOLVER(p, mksolver());
+}