comparison src/fftw-3.3.5/reodft/redft00e-r2hc.c @ 42:2cd0e3b3e1fd

Current fftw source

+/*
+ * Copyright (c) 2003, 2007-14 Matteo Frigo
+ * Copyright (c) 2003, 2007-14 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 a REDFT00 problem via an R2HC problem, with some pre/post-processing.
+
+   This code uses the trick from FFTPACK, also documented in a similar
+   form by Numerical Recipes.  Unfortunately, this algorithm seems to
+   have intrinsic numerical problems (similar to those in
+   reodft11e-r2hc.c), possibly due to the fact that it multiplies its
+   input by a cosine, causing a loss of precision near the zero.  For
+   transforms of 16k points, it has already lost three or four decimal
+   places of accuracy, which we deem unacceptable.
+
+   So, we have abandoned this algorithm in favor of the one in
+   redft00-r2hc-pad.c, which unfortunately sacrifices 30-50% in speed.
+   The only other alternative in the literature that does not have
+   similar numerical difficulties seems to be the direct adaptation of
+   the Cooley-Tukey decomposition for symmetric data, but this would
+   require a whole new set of codelets and it's not clear that it's
+   worth it at this point.  However, we did implement the latter
+   algorithm for the specific case of odd n (logically adapting the
+   split-radix algorithm); see reodft00e-splitradix.c. */
+
+#include "reodft.h"
+
+typedef struct {
+     solver super;
+} S;
+
+typedef struct {
+     plan_rdft super;
+     plan *cld;
+     twid *td;
+     INT is, os;
+     INT n;
+     INT vl;
+     INT ivs, ovs;
+} P;
+
+static void apply(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 = ego->td->W;
+     R *buf;
+     E csum;
+
+     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+	  buf[0] = I[0] + I[is * n];
+	  csum = I[0] - I[is * n];
+	  for (i = 1; i < n - i; ++i) {
+	       E a, b, apb, amb;
+	       a = I[is * i];
+	       b = I[is * (n - i)];
+	       csum += W[2*i] * (amb = K(2.0)*(a - b));
+	       amb = W[2*i+1] * amb;
+	       apb = (a + b);
+	       buf[i] = apb - amb;
+	       buf[n - i] = apb + amb;
+	  }
+	  if (i == n - i) {
+	       buf[i] = K(2.0) * I[is * i];
+	  }
+	  
+	  {
+	       plan_rdft *cld = (plan_rdft *) ego->cld;
+	       cld->apply((plan *) cld, buf, buf);
+	  }
+	  
+	  /* FIXME: use recursive/cascade summation for better stability? */
+	  O[0] = buf[0];
+	  O[os] = csum;
+	  for (i = 1; i + i < n; ++i) {
+	       INT k = i + i;
+	       O[os * k] = buf[i];
+	       O[os * (k + 1)] = O[os * (k - 1)] - buf[n - i];
+	  }
+	  if (i + i == n) {
+	       O[os * n] = buf[i];
+	  }
+     }
+
+     X(ifree)(buf);
+}
+
+static void awake(plan *ego_, enum wakefulness wakefulness)
+{
+     P *ego = (P *) ego_;
+     static const tw_instr redft00e_tw[] = {
+          { TW_COS, 0, 1 },
+          { TW_SIN, 0, 1 },
+          { TW_NEXT, 1, 0 }
+     };
+
+     X(plan_awake)(ego->cld, wakefulness);
+     X(twiddle_awake)(wakefulness,
+		      &ego->td, redft00e_tw, 2*ego->n, 1, (ego->n+1)/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, "(redft00e-r2hc-%D%v%(%p%))", ego->n + 1, 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] == REDFT00
+	     && p->sz->dims[0].n > 1  /* n == 1 is not well-defined */
+	  );
+}
+
+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 - 1;
+     A(n > 0);
+     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, apply);
+
+     pln->n = n;
+     pln->is = p->sz->dims[0].is;
+     pln->os = p->sz->dims[0].os;
+     pln->cld = cld;
+     pln->td = 0;
+
+     X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
+     
+     X(ops_zero)(&ops);
+     ops.other = 8 + (n-1)/2 * 11 + (1 - n % 2) * 5;
+     ops.add = 2 + (n-1)/2 * 5;
+     ops.mul = (n-1)/2 * 3 + (1 - n % 2) * 1;
+
+     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(redft00e_r2hc_register)(planner *p)
+{
+     REGISTER_SOLVER(p, mksolver());
+}