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+/*
+ * Copyright (c) 2003 Matteo Frigo
+ * Copyright (c) 2003 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ *
+ */
+
+/* $Id: reodft11e-r2hc-odd.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
+
+/* 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.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_, int flg)
+{
+ P *ego = (P *) ego_;
+ AWAKE(ego->cld, flg);
+}
+
+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_)
+{
+ UNUSED(ego_);
+ if (RDFTP(p_)) {
+ const problem_rdft *p = (const problem_rdft *) p_;
+ 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)
+ );
+ }
+
+ return 0;
+}
+
+static int applicable(const solver *ego, const problem *p, const planner *plnr)
+{
+ return (!NO_UGLYP(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 = { mkplan };
+ S *slv = MKSOLVER(S, &sadt);
+ return &(slv->super);
+}
+
+void X(reodft11e_r2hc_odd_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver());
+}
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