diff src/fftw-3.3.8/reodft/reodft11e-radix2.c @ 167:bd3cc4d1df30

Add FFTW 3.3.8 source, and a Linux build

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/fftw-3.3.8/reodft/reodft11e-radix2.c	Tue Nov 19 14:52:55 2019 +0000
@@ -0,0 +1,513 @@
+/*
+ * 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 an R{E,O}DFT11 problem of *even* size by a pair of R2HC problems
+   of half the size, plus some pre/post-processing.  Use a trick from:
+
+   Zhongde Wang, "On computing the discrete Fourier and cosine transforms,"
+   IEEE Trans. Acoust. Speech Sig. Proc. ASSP-33 (4), 1341--1344 (1985).
+
+   to re-express as a pair of half-size REDFT01 (DCT-III) problems.  Our
+   implementation looks quite a bit different from the algorithm described
+   in the paper because we combined the paper's pre/post-processing with
+   the pre/post-processing used to turn REDFT01 into R2HC.  (Also, the
+   paper uses a DCT/DST pair, but we turn the DST into a DCT via the
+   usual reordering/sign-flip trick.  We additionally combined a couple
+   of the matrices/transformations of the paper into a single pass.)
+
+   NOTE: We originally used a simpler method by S. C. Chan and K. L. Ho
+   that turned out to have numerical problems; see reodft11e-r2hc.c.
+
+   (For odd sizes, see reodft11e-r2hc-odd.c.)
+*/
+
+#include "reodft/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, n2 = n/2;
+     INT iv, vl = ego->vl;
+     INT ivs = ego->ivs, ovs = ego->ovs;
+     R *W = ego->td->W;
+     R *W2;
+     R *buf;
+
+     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+	  buf[0] = K(2.0) * I[0];
+	  buf[n2] = K(2.0) * I[is * (n - 1)];
+	  for (i = 1; i + i < n2; ++i) {
+	       INT k = i + i;
+	       E a, b, a2, b2;
+	       {
+		    E u, v;
+		    u = I[is * (k - 1)];
+		    v = I[is * k];
+		    a = u + v;
+		    b2 = u - v;
+	       }
+	       {
+		    E u, v;
+		    u = I[is * (n - k - 1)];
+		    v = I[is * (n - k)];
+		    b = u + v;
+		    a2 = u - v;
+	       }
+	       {
+		    E wa, wb;
+		    wa = W[2*i];
+		    wb = W[2*i + 1];
+		    {
+			 E apb, amb;
+			 apb = a + b;
+			 amb = a - b;
+			 buf[i] = wa * amb + wb * apb; 
+			 buf[n2 - i] = wa * apb - wb * amb; 
+		    }
+		    {
+			 E apb, amb;
+			 apb = a2 + b2;
+			 amb = a2 - b2;
+			 buf[n2 + i] = wa * amb + wb * apb; 
+			 buf[n - i] = wa * apb - wb * amb; 
+		    }
+	       }
+	  }
+	  if (i + i == n2) {
+	       E u, v;
+	       u = I[is * (n2 - 1)];
+	       v = I[is * n2];
+	       buf[i] = (u + v) * (W[2*i] * K(2.0));
+	       buf[n - i] = (u - v) * (W[2*i] * K(2.0));
+	  }
+
+
+	  /* child plan: two r2hc's of size n/2 */
+	  {
+	       plan_rdft *cld = (plan_rdft *) ego->cld;
+	       cld->apply((plan *) cld, buf, buf);
+	  }
+	  
+	  W2 = ego->td2->W;
+	  { /* i == 0 case */
+	       E wa, wb;
+	       E a, b;
+	       wa = W2[0]; /* cos */
+	       wb = W2[1]; /* sin */
+	       a = buf[0];
+	       b = buf[n2];
+	       O[0] = wa * a + wb * b;
+	       O[os * (n - 1)] = wb * a - wa * b;
+	  }
+	  W2 += 2;
+	  for (i = 1; i + i < n2; ++i, W2 += 2) {
+	       INT k;
+	       E u, v, u2, v2;
+	       u = buf[i];
+	       v = buf[n2 - i];
+	       u2 = buf[n2 + i];
+	       v2 = buf[n - i];
+	       k = (i + i) - 1;
+	       {
+                    E wa, wb;
+                    E a, b;
+                    wa = W2[0]; /* cos */
+                    wb = W2[1]; /* sin */
+                    a = u - v;
+                    b = v2 - u2;
+                    O[os * k] = wa * a + wb * b;
+                    O[os * (n - 1 - k)] = wb * a - wa * b;
+               }
+	       ++k;
+	       W2 += 2;
+	       {
+		    E wa, wb;
+		    E a, b;
+		    wa = W2[0]; /* cos */
+		    wb = W2[1]; /* sin */
+		    a = u + v;
+		    b = u2 + v2;
+		    O[os * k] = wa * a + wb * b;
+		    O[os * (n - 1 - k)] = wb * a - wa * b;
+	       }
+	  }
+	  if (i + i == n2) {
+	       INT k = (i + i) - 1;
+	       E wa, wb;
+	       E a, b;
+	       wa = W2[0]; /* cos */
+	       wb = W2[1]; /* sin */
+	       a = buf[i];
+	       b = buf[n2 + i];
+	       O[os * k] = wa * a - wb * b;
+	       O[os * (n - 1 - k)] = wb * a + wa * b;
+	  }
+     }
+
+     X(ifree)(buf);
+}
+
+#if 0
+
+/* This version of apply_re11 uses REDFT01 child plans, more similar
+   to the original paper by Z. Wang.  We keep it around for reference
+   (it is simpler) and because it may become more efficient if we
+   ever implement REDFT01 codelets. */
+
+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;
+
+     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+	  buf[0] = K(2.0) * I[0];
+	  buf[n/2] = K(2.0) * I[is * (n - 1)];
+	  for (i = 1; i + i < n; ++i) {
+	       INT k = i + i;
+	       E a, b;
+	       a = I[is * (k - 1)];
+	       b = I[is * k];
+	       buf[i] = a + b;
+	       buf[n - i] = a - b;
+	  }
+
+	  /* child plan: two redft01's (DCT-III) */
+	  {
+	       plan_rdft *cld = (plan_rdft *) ego->cld;
+	       cld->apply((plan *) cld, buf, buf);
+	  }
+	  
+	  W = ego->td2->W;
+	  for (i = 0; i + 1 < n/2; ++i, W += 2) {
+	       {
+		    E wa, wb;
+		    E a, b;
+		    wa = W[0]; /* cos */
+		    wb = W[1]; /* sin */
+		    a = buf[i];
+		    b = buf[n/2 + i];
+		    O[os * i] = wa * a + wb * b;
+		    O[os * (n - 1 - i)] = wb * a - wa * b;
+	       }
+	       ++i;
+	       W += 2;
+	       {
+                    E wa, wb;
+                    E a, b;
+                    wa = W[0]; /* cos */
+                    wb = W[1]; /* sin */
+                    a = buf[i];
+                    b = buf[n/2 + i];
+                    O[os * i] = wa * a - wb * b;
+                    O[os * (n - 1 - i)] = wb * a + wa * b;
+               }
+	  }
+	  if (i < n/2) {
+	       E wa, wb;
+	       E a, b;
+	       wa = W[0]; /* cos */
+	       wb = W[1]; /* sin */
+	       a = buf[i];
+	       b = buf[n/2 + i];
+	       O[os * i] = wa * a + wb * b;
+	       O[os * (n - 1 - i)] = wb * a - wa * b;
+	  }
+     }
+
+     X(ifree)(buf);
+}
+
+#endif /* 0 */
+
+/* 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, n2 = n/2;
+     INT iv, vl = ego->vl;
+     INT ivs = ego->ivs, ovs = ego->ovs;
+     R *W = ego->td->W;
+     R *W2;
+     R *buf;
+
+     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+	  buf[0] = K(2.0) * I[is * (n - 1)];
+	  buf[n2] = K(2.0) * I[0];
+	  for (i = 1; i + i < n2; ++i) {
+	       INT k = i + i;
+	       E a, b, a2, b2;
+	       {
+		    E u, v;
+		    u = I[is * (n - k)];
+		    v = I[is * (n - 1 - k)];
+		    a = u + v;
+		    b2 = u - v;
+	       }
+	       {
+		    E u, v;
+		    u = I[is * (k)];
+		    v = I[is * (k - 1)];
+		    b = u + v;
+		    a2 = u - v;
+	       }
+	       {
+		    E wa, wb;
+		    wa = W[2*i];
+		    wb = W[2*i + 1];
+		    {
+			 E apb, amb;
+			 apb = a + b;
+			 amb = a - b;
+			 buf[i] = wa * amb + wb * apb; 
+			 buf[n2 - i] = wa * apb - wb * amb; 
+		    }
+		    {
+			 E apb, amb;
+			 apb = a2 + b2;
+			 amb = a2 - b2;
+			 buf[n2 + i] = wa * amb + wb * apb; 
+			 buf[n - i] = wa * apb - wb * amb; 
+		    }
+	       }
+	  }
+	  if (i + i == n2) {
+	       E u, v;
+	       u = I[is * n2];
+	       v = I[is * (n2 - 1)];
+	       buf[i] = (u + v) * (W[2*i] * K(2.0));
+	       buf[n - i] = (u - v) * (W[2*i] * K(2.0));
+	  }
+
+
+	  /* child plan: two r2hc's of size n/2 */
+	  {
+	       plan_rdft *cld = (plan_rdft *) ego->cld;
+	       cld->apply((plan *) cld, buf, buf);
+	  }
+	  
+	  W2 = ego->td2->W;
+	  { /* i == 0 case */
+	       E wa, wb;
+	       E a, b;
+	       wa = W2[0]; /* cos */
+	       wb = W2[1]; /* sin */
+	       a = buf[0];
+	       b = buf[n2];
+	       O[0] = wa * a + wb * b;
+	       O[os * (n - 1)] = wa * b - wb * a;
+	  }
+	  W2 += 2;
+	  for (i = 1; i + i < n2; ++i, W2 += 2) {
+	       INT k;
+	       E u, v, u2, v2;
+	       u = buf[i];
+	       v = buf[n2 - i];
+	       u2 = buf[n2 + i];
+	       v2 = buf[n - i];
+	       k = (i + i) - 1;
+	       {
+                    E wa, wb;
+                    E a, b;
+                    wa = W2[0]; /* cos */
+                    wb = W2[1]; /* sin */
+                    a = v - u;
+                    b = u2 - v2;
+                    O[os * k] = wa * a + wb * b;
+                    O[os * (n - 1 - k)] = wa * b - wb * a;
+               }
+	       ++k;
+	       W2 += 2;
+	       {
+		    E wa, wb;
+		    E a, b;
+		    wa = W2[0]; /* cos */
+		    wb = W2[1]; /* sin */
+		    a = u + v;
+		    b = u2 + v2;
+		    O[os * k] = wa * a + wb * b;
+		    O[os * (n - 1 - k)] = wa * b - wb * a;
+	       }
+	  }
+	  if (i + i == n2) {
+	       INT k = (i + i) - 1;
+	       E wa, wb;
+	       E a, b;
+	       wa = W2[0]; /* cos */
+	       wb = W2[1]; /* sin */
+	       a = buf[i];
+	       b = buf[n2 + i];
+	       O[os * k] = wb * b - wa * a;
+	       O[os * (n - 1 - k)] = wa * b + wb * a;
+	  }
+     }
+
+     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_SIN, 1, 1 },
+          { TW_NEXT, 2, 0 }
+     };
+
+     X(plan_awake)(ego->cld, wakefulness);
+
+     X(twiddle_awake)(wakefulness, &ego->td, reodft010e_tw, 
+		      2*ego->n, 1, ego->n/4+1);
+     X(twiddle_awake)(wakefulness, &ego->td2, reodft11e_tw, 
+		      8*ego->n, 1, ego->n);
+}
+
+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-radix2-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->sz->dims[0].n % 2 == 0
+	     && (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/2, 1, 1),
+                                                   X(mktensor_1d)(2, n/2, n/2),
+                                                   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.add = 2 + (n/2 - 1)/2 * 20;
+     ops.mul = 6 + (n/2 - 1)/2 * 16;
+     ops.other = 4*n + 2 + (n/2 - 1)/2 * 6;
+     if ((n/2) % 2 == 0) {
+	  ops.add += 4;
+	  ops.mul += 8;
+	  ops.other += 4;
+     }
+
+     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_radix2_r2hc_register)(planner *p)
+{
+     REGISTER_SOLVER(p, mksolver());
+}