diff src/fftw-3.3.8/reodft/reodft11e-r2hc-odd.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-r2hc-odd.c	Tue Nov 19 14:52:55 2019 +0000
@@ -0,0 +1,300 @@
+/*
+ * 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 via an R2HC problem of the same *odd* size,
+   with some permutations and post-processing, as described in:
+
+     S. C. Chan and K. L. Ho, "Fast algorithms for computing the
+     discrete cosine transform," IEEE Trans. Circuits Systems II:
+     Analog & Digital Sig. Proc. 39 (3), 185--190 (1992).
+
+   (For even sizes, see reodft11e-radix2.c.)  
+
+   This algorithm is related to the 8 x n prime-factor-algorithm (PFA)
+   decomposition of the size 8n "logical" DFT corresponding to the
+   R{EO}DFT11.
+
+   Aside from very confusing notation (several symbols are redefined
+   from one line to the next), be aware that this paper has some
+   errors.  In particular, the signs are wrong in Eqs. (34-35).  Also,
+   Eqs. (36-37) should be simply C(k) = C(2k + 1 mod N), and similarly
+   for S (or, equivalently, the second cases should have 2*N - 2*k - 1
+   instead of N - k - 1).  Note also that in their definition of the
+   DFT, similarly to FFTW's, the exponent's sign is -1, but they
+   forgot to correspondingly multiply S (the sine terms) by -1.
+*/
+
+#include "reodft/reodft.h"
+
+typedef struct {
+     solver super;
+} S;
+
+typedef struct {
+     plan_rdft super;
+     plan *cld;
+     INT is, os;
+     INT n;
+     INT vl;
+     INT ivs, ovs;
+     rdft_kind kind;
+} P;
+
+static DK(SQRT2, +1.4142135623730950488016887242096980785696718753769);
+
+#define SGN_SET(x, i) ((i) % 2 ? -(x) : (x))
+
+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 *buf;
+
+     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+	  {
+	       INT m;
+	       for (i = 0, m = n2; m < n; ++i, m += 4)
+		    buf[i] = I[is * m];
+	       for (; m < 2 * n; ++i, m += 4)
+		    buf[i] = -I[is * (2*n - m - 1)];
+	       for (; m < 3 * n; ++i, m += 4)
+		    buf[i] = -I[is * (m - 2*n)];
+	       for (; m < 4 * n; ++i, m += 4)
+		    buf[i] = I[is * (4*n - m - 1)];
+	       m -= 4 * n;
+	       for (; i < n; ++i, m += 4)
+		    buf[i] = I[is * m];
+	  }
+
+	  { /* child plan: R2HC of size n */
+	       plan_rdft *cld = (plan_rdft *) ego->cld;
+	       cld->apply((plan *) cld, buf, buf);
+	  }
+	  
+	  /* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */
+	  for (i = 0; i + i + 1 < n2; ++i) {
+	       INT k = i + i + 1;
+	       E c1, s1;
+	       E c2, s2;
+	       c1 = buf[k];
+	       c2 = buf[k + 1];
+	       s2 = buf[n - (k + 1)];
+	       s1 = buf[n - k];
+	       
+	       O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2) +
+				    SGN_SET(s1, i/2));
+	       O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2) -
+					      SGN_SET(s1, (n-(i+1))/2));
+	       
+	       O[os * (n2 - (i+1))] = SQRT2 * (SGN_SET(c2, (n2-i)/2) -
+					       SGN_SET(s2, (n2-(i+1))/2));
+	       O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2) +
+					       SGN_SET(s2, (n2+(i+1))/2));
+	  }
+	  if (i + i + 1 == n2) {
+	       E c, s;
+	       c = buf[n2];
+	       s = buf[n - n2];
+	       O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2) +
+				    SGN_SET(s, i/2));
+	       O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2) +
+					      SGN_SET(s, (i+1)/2));
+	  }
+	  O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2);
+     }
+
+     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, n2 = n/2;
+     INT iv, vl = ego->vl;
+     INT ivs = ego->ivs, ovs = ego->ovs;
+     R *buf;
+
+     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+	  {
+	       INT m;
+	       for (i = 0, m = n2; m < n; ++i, m += 4)
+		    buf[i] = I[is * (n - 1 - m)];
+	       for (; m < 2 * n; ++i, m += 4)
+		    buf[i] = -I[is * (m - n)];
+	       for (; m < 3 * n; ++i, m += 4)
+		    buf[i] = -I[is * (3*n - 1 - m)];
+	       for (; m < 4 * n; ++i, m += 4)
+		    buf[i] = I[is * (m - 3*n)];
+	       m -= 4 * n;
+	       for (; i < n; ++i, m += 4)
+		    buf[i] = I[is * (n - 1 - m)];
+	  }
+
+	  { /* child plan: R2HC of size n */
+	       plan_rdft *cld = (plan_rdft *) ego->cld;
+	       cld->apply((plan *) cld, buf, buf);
+	  }
+	  
+	  /* FIXME: strength-reduce loop by 4 to eliminate ugly sgn_set? */
+	  for (i = 0; i + i + 1 < n2; ++i) {
+	       INT k = i + i + 1;
+	       INT j;
+	       E c1, s1;
+	       E c2, s2;
+	       c1 = buf[k];
+	       c2 = buf[k + 1];
+	       s2 = buf[n - (k + 1)];
+	       s1 = buf[n - k];
+	       
+	       O[os * i] = SQRT2 * (SGN_SET(c1, (i+1)/2 + i) +
+				    SGN_SET(s1, i/2 + i));
+	       O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c1, (n-i)/2 + i) -
+					      SGN_SET(s1, (n-(i+1))/2 + i));
+	       
+	       j = n2 - (i+1);
+	       O[os * j] = SQRT2 * (SGN_SET(c2, (n2-i)/2 + j) -
+				    SGN_SET(s2, (n2-(i+1))/2 + j));
+	       O[os * (n2 + (i+1))] = SQRT2 * (SGN_SET(c2, (n2+i+2)/2 + j) +
+					       SGN_SET(s2, (n2+(i+1))/2 + j));
+	  }
+	  if (i + i + 1 == n2) {
+	       E c, s;
+	       c = buf[n2];
+	       s = buf[n - n2];
+	       O[os * i] = SQRT2 * (SGN_SET(c, (i+1)/2 + i) +
+				    SGN_SET(s, i/2 + i));
+	       O[os * (n - (i+1))] = SQRT2 * (SGN_SET(c, (i+2)/2 + i) +
+					      SGN_SET(s, (i+1)/2 + i));
+	  }
+	  O[os * n2] = SQRT2 * SGN_SET(buf[0], (n2+1)/2 + n2);
+     }
+
+     X(ifree)(buf);
+}
+
+static void awake(plan *ego_, enum wakefulness wakefulness)
+{
+     P *ego = (P *) ego_;
+     X(plan_awake)(ego->cld, wakefulness);
+}
+
+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-odd-%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 == 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->kind = p->kind[0];
+     
+     X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
+     
+     X(ops_zero)(&ops);
+     ops.add = n - 1;
+     ops.mul = n;
+     ops.other = 4*n;
+
+     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_odd_register)(planner *p)
+{
+     REGISTER_SOLVER(p, mksolver());
+}