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-rw-r--r--src/fftw3/reodft/redft00e-r2hc-pad.c201
-rw-r--r--src/fftw3/reodft/redft00e-r2hc.c216
-rw-r--r--src/fftw3/reodft/reoconf.c42
-rw-r--r--src/fftw3/reodft/reodft.h41
-rw-r--r--src/fftw3/reodft/reodft010e-r2hc.c409
-rw-r--r--src/fftw3/reodft/reodft11e-r2hc-odd.c304
-rw-r--r--src/fftw3/reodft/reodft11e-r2hc.c295
-rw-r--r--src/fftw3/reodft/reodft11e-radix2.c515
-rw-r--r--src/fftw3/reodft/rodft00e-r2hc-pad.c200
-rw-r--r--src/fftw3/reodft/rodft00e-r2hc.c212
10 files changed, 2435 insertions, 0 deletions
diff --git a/src/fftw3/reodft/redft00e-r2hc-pad.c b/src/fftw3/reodft/redft00e-r2hc-pad.c
new file mode 100644
index 0000000..ec3fa35
--- /dev/null
+++ b/src/fftw3/reodft/redft00e-r2hc-pad.c
@@ -0,0 +1,201 @@
+/*
+ * 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: redft00e-r2hc-pad.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
+
+/* Do a REDFT00 problem via an R2HC problem, padded symmetrically to
+ twice the size. This is asymptotically a factor of ~2 worse than
+ redft00e-r2hc.c (the algorithm used in e.g. FFTPACK and Numerical
+ Recipes), but we abandoned the latter after we discovered that it
+ has intrinsic accuracy problems. */
+
+#include "reodft.h"
+
+typedef struct {
+ solver super;
+} S;
+
+typedef struct {
+ plan_rdft super;
+ plan *cld, *cldcpy;
+ int is;
+ 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;
+ int i, n = ego->n;
+ int iv, vl = ego->vl;
+ int ivs = ego->ivs, ovs = ego->ovs;
+ R *buf;
+
+ buf = (R *) MALLOC(sizeof(R) * (2*n), BUFFERS);
+
+ for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+ buf[0] = I[0];
+ for (i = 1; i < n; ++i) {
+ R a = I[i * is];
+ buf[i] = a;
+ buf[2*n - i] = a;
+ }
+ buf[i] = I[i * is]; /* i == n, Nyquist */
+
+ /* r2hc transform of size 2*n */
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, buf, buf);
+ }
+
+ /* copy n+1 real numbers (real parts of hc array) from buf to O */
+ {
+ plan_rdft *cldcpy = (plan_rdft *) ego->cldcpy;
+ cldcpy->apply((plan *) cldcpy, buf, O);
+ }
+ }
+
+ X(ifree)(buf);
+}
+
+static void awake(plan *ego_, int flg)
+{
+ P *ego = (P *) ego_;
+ AWAKE(ego->cld, flg);
+ AWAKE(ego->cldcpy, flg);
+}
+
+static void destroy(plan *ego_)
+{
+ P *ego = (P *) ego_;
+ X(plan_destroy_internal)(ego->cldcpy);
+ 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-pad-%d%v%(%p%)%(%p%))",
+ ego->n + 1, ego->vl, ego->cld, ego->cldcpy);
+}
+
+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->kind[0] == REDFT00
+ && p->sz->dims[0].n > 1 /* n == 1 is not well-defined */
+ );
+ }
+
+ 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 = (plan *) 0, *cldcpy;
+ R *buf = (R *) 0;
+ int n;
+ int vl, ivs, ovs;
+ opcnt ops;
+
+ static const plan_adt padt = {
+ X(rdft_solve), awake, print, destroy
+ };
+
+ if (!applicable(ego_, p_, plnr))
+ goto nada;
+
+ p = (const problem_rdft *) p_;
+
+ n = p->sz->dims[0].n - 1;
+ A(n > 0);
+ buf = (R *) MALLOC(sizeof(R) * (2*n), BUFFERS);
+
+ cld = X(mkplan_d)(plnr,X(mkproblem_rdft_1_d)(X(mktensor_1d)(2*n,1,1),
+ X(mktensor_0d)(),
+ buf, buf, R2HC));
+ if (!cld)
+ goto nada;
+
+ X(tensor_tornk1)(p->vecsz, &vl, &ivs, &ovs);
+ cldcpy =
+ X(mkplan_d)(plnr,
+ X(mkproblem_rdft_1_d)(X(mktensor_0d)(),
+ X(mktensor_1d)(n+1,1,
+ p->sz->dims[0].os),
+ buf, TAINT(p->O, ovs), R2HC));
+ if (!cldcpy)
+ goto nada;
+
+ X(ifree)(buf);
+
+ pln = MKPLAN_RDFT(P, &padt, apply);
+
+ pln->n = n;
+ pln->is = p->sz->dims[0].is;
+ pln->cld = cld;
+ pln->cldcpy = cldcpy;
+ pln->vl = vl;
+ pln->ivs = ivs;
+ pln->ovs = ovs;
+
+ X(ops_zero)(&ops);
+ ops.other = n + 2*n; /* loads + stores (input -> buf) */
+
+ 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);
+ X(ops_madd2)(pln->vl, &cldcpy->ops, &pln->super.super.ops);
+
+ return &(pln->super.super);
+
+ nada:
+ X(ifree0)(buf);
+ if (cld)
+ X(plan_destroy_internal)(cld);
+ return (plan *)0;
+}
+
+/* constructor */
+static solver *mksolver(void)
+{
+ static const solver_adt sadt = { mkplan };
+ S *slv = MKSOLVER(S, &sadt);
+ return &(slv->super);
+}
+
+void X(redft00e_r2hc_pad_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver());
+}
diff --git a/src/fftw3/reodft/redft00e-r2hc.c b/src/fftw3/reodft/redft00e-r2hc.c
new file mode 100644
index 0000000..0cd742f
--- /dev/null
+++ b/src/fftw3/reodft/redft00e-r2hc.c
@@ -0,0 +1,216 @@
+/*
+ * 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: redft00e-r2hc.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
+
+/* 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. */
+
+#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_, int flg)
+{
+ P *ego = (P *) ego_;
+ static const tw_instr redft00e_tw[] = {
+ { TW_COS, 0, 1 },
+ { TW_SIN, 0, 1 },
+ { TW_NEXT, 1, 0 }
+ };
+
+ AWAKE(ego->cld, flg);
+ X(twiddle_awake)(flg, &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_)
+{
+ UNUSED(ego_);
+ if (RDFTP(p_)) {
+ const problem_rdft *p = (const problem_rdft *) p_;
+ 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 */
+ );
+ }
+
+ 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 - 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 = { mkplan };
+ S *slv = MKSOLVER(S, &sadt);
+ return &(slv->super);
+}
+
+void X(redft00e_r2hc_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver());
+}
diff --git a/src/fftw3/reodft/reoconf.c b/src/fftw3/reodft/reoconf.c
new file mode 100644
index 0000000..1cd41b6
--- /dev/null
+++ b/src/fftw3/reodft/reoconf.c
@@ -0,0 +1,42 @@
+/*
+ * 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: reoconf.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
+
+#include "reodft.h"
+
+static const solvtab s =
+{
+ /* SOLVTAB(X(redft00e_r2hc_register)),
+ SOLVTAB(X(rodft00e_r2hc_register)), */
+ SOLVTAB(X(redft00e_r2hc_pad_register)),
+ SOLVTAB(X(rodft00e_r2hc_pad_register)),
+ SOLVTAB(X(reodft010e_r2hc_register)),
+ /* SOLVTAB(X(reodft11e_r2hc_register)), */
+ SOLVTAB(X(reodft11e_radix2_r2hc_register)),
+ SOLVTAB(X(reodft11e_r2hc_odd_register)),
+
+ SOLVTAB_END
+};
+
+void X(reodft_conf_standard)(planner *p)
+{
+ X(solvtab_exec)(s, p);
+}
diff --git a/src/fftw3/reodft/reodft.h b/src/fftw3/reodft/reodft.h
new file mode 100644
index 0000000..8c67144
--- /dev/null
+++ b/src/fftw3/reodft/reodft.h
@@ -0,0 +1,41 @@
+/*
+ * 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
+ *
+ */
+
+#ifndef __REODFT_H__
+#define __REODFT_H__
+
+#include "ifftw.h"
+#include "rdft.h"
+
+#define REODFT_KINDP(k) ((k) >= REDFT00 && (k) <= RODFT11)
+
+void X(redft00e_r2hc_register)(planner *p);
+void X(redft00e_r2hc_pad_register)(planner *p);
+void X(rodft00e_r2hc_register)(planner *p);
+void X(rodft00e_r2hc_pad_register)(planner *p);
+void X(reodft010e_r2hc_register)(planner *p);
+void X(reodft11e_r2hc_register)(planner *p);
+void X(reodft11e_radix2_r2hc_register)(planner *p);
+void X(reodft11e_r2hc_odd_register)(planner *p);
+
+/* configurations */
+void X(reodft_conf_standard)(planner *p);
+
+#endif /* __REODFT_H__ */
diff --git a/src/fftw3/reodft/reodft010e-r2hc.c b/src/fftw3/reodft/reodft010e-r2hc.c
new file mode 100644
index 0000000..ace14de
--- /dev/null
+++ b/src/fftw3/reodft/reodft010e-r2hc.c
@@ -0,0 +1,409 @@
+/*
+ * 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: reodft010e-r2hc.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
+
+/* Do an R{E,O}DFT{01,10} problem via an R2HC problem, with some
+ pre/post-processing ala FFTPACK. */
+
+#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;
+ rdft_kind kind;
+} P;
+
+/* A real-even-01 DFT operates logically on a size-4N array:
+ I 0 -r(I*) -I 0 r(I*),
+ where r denotes reversal and * denotes deletion of the 0th element.
+ To compute the transform of this, we imagine performing a radix-4
+ (real-input) DIF step, which turns the size-4N DFT into 4 size-N
+ (contiguous) DFTs, two of which are zero and two of which are
+ conjugates. The non-redundant size-N DFT has halfcomplex input, so
+ we can do it with a size-N hc2r transform. (In order to share
+ plans with the re10 (inverse) transform, however, we use the DHT
+ trick to re-express the hc2r problem as r2hc. This has little cost
+ since we are already pre- and post-processing the data in {i,n-i}
+ order.) Finally, we have to write out the data in the correct
+ order...the two size-N redundant (conjugate) hc2r DFTs correspond
+ to the even and odd outputs in O (i.e. the usual interleaved output
+ of DIF transforms); since this data has even symmetry, we only
+ write the first half of it.
+
+ The real-even-10 DFT is just the reverse of these steps, i.e. a
+ radix-4 DIT transform. There, however, we just use the r2hc
+ transform naturally without resorting to the DHT trick.
+
+ A real-odd-01 DFT is very similar, except that the input is
+ 0 I (rI)* 0 -I -(rI)*. This format, however, can be transformed
+ into precisely the real-even-01 format above by sending I -> rI
+ and shifting the array by N. The former swap is just another
+ transformation on the input during preprocessing; the latter
+ multiplies the even/odd outputs by i/-i, which combines with
+ the factor of -i (to take the imaginary part) to simply flip
+ the sign of the odd outputs. Vice-versa for real-odd-10.
+
+ The FFTPACK source code was very helpful in working this out.
+ (They do unnecessary passes over the array, though.)
+
+ Note that Numerical Recipes suggests a different algorithm that
+ requires more operations and uses trig. functions for both the pre-
+ and post-processing passes.
+*/
+
+static void apply_re01(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;
+
+ buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+ for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+ buf[0] = I[0];
+ for (i = 1; i < n - i; ++i) {
+ E a, b, apb, amb, wa, wb;
+ a = I[is * i];
+ b = I[is * (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) * I[is * i] * W[2*i];
+ }
+
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, buf, buf);
+ }
+
+ O[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)] = a - b;
+ O[os * k] = a + b;
+ }
+ if (i == n - i) {
+ O[os * (n - 1)] = buf[i];
+ }
+ }
+
+ X(ifree)(buf);
+}
+
+/* ro01 is same as re01, but with i <-> n - 1 - i in the input and
+ the sign of the odd output elements flipped. */
+static void apply_ro01(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;
+
+ buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+ for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+ buf[0] = I[is * (n - 1)];
+ for (i = 1; i < n - i; ++i) {
+ E a, b, apb, amb, wa, wb;
+ a = I[is * (n - 1 - i)];
+ b = I[is * (i - 1)];
+ 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) * I[is * (i - 1)] * W[2*i];
+ }
+
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, buf, buf);
+ }
+
+ O[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)] = b - a;
+ O[os * k] = a + b;
+ }
+ if (i == n - i) {
+ O[os * (n - 1)] = -buf[i];
+ }
+ }
+
+ X(ifree)(buf);
+}
+
+static void apply_re10(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;
+
+ buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+ for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+ buf[0] = I[0];
+ for (i = 1; i < n - i; ++i) {
+ E u, v;
+ int k = i + i;
+ u = I[is * (k - 1)];
+ v = I[is * k];
+ buf[n - i] = u;
+ buf[i] = v;
+ }
+ if (i == n - i) {
+ buf[i] = I[is * (n - 1)];
+ }
+
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, buf, buf);
+ }
+
+ O[0] = K(2.0) * buf[0];
+ for (i = 1; i < n - i; ++i) {
+ E a, b, wa, wb;
+ a = K(2.0) * buf[i];
+ b = K(2.0) * buf[n - i];
+ wa = W[2*i];
+ wb = W[2*i + 1];
+ O[os * i] = wa * a + wb * b;
+ O[os * (n - i)] = wb * a - wa * b;
+ }
+ if (i == n - i) {
+ O[os * i] = K(2.0) * buf[i] * W[2*i];
+ }
+ }
+
+ X(ifree)(buf);
+}
+
+/* ro10 is same as re10, but with i <-> n - 1 - i in the output and
+ the sign of the odd input elements flipped. */
+static void apply_ro10(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;
+
+ buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+ for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+ buf[0] = I[0];
+ for (i = 1; i < n - i; ++i) {
+ E u, v;
+ int k = i + i;
+ u = -I[is * (k - 1)];
+ v = I[is * k];
+ buf[n - i] = u;
+ buf[i] = v;
+ }
+ if (i == n - i) {
+ buf[i] = -I[is * (n - 1)];
+ }
+
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, buf, buf);
+ }
+
+ O[os * (n - 1)] = K(2.0) * buf[0];
+ for (i = 1; i < n - i; ++i) {
+ E a, b, wa, wb;
+ a = K(2.0) * buf[i];
+ b = K(2.0) * buf[n - i];
+ wa = W[2*i];
+ wb = W[2*i + 1];
+ O[os * (n - 1 - i)] = wa * a + wb * b;
+ O[os * (i - 1)] = wb * a - wa * b;
+ }
+ if (i == n - i) {
+ O[os * (i - 1)] = K(2.0) * buf[i] * W[2*i];
+ }
+ }
+
+ X(ifree)(buf);
+}
+
+static void awake(plan *ego_, int flg)
+{
+ P *ego = (P *) ego_;
+ static const tw_instr reodft010e_tw[] = {
+ { TW_COS, 0, 1 },
+ { TW_SIN, 0, 1 },
+ { TW_NEXT, 1, 0 }
+ };
+
+ AWAKE(ego->cld, flg);
+
+ X(twiddle_awake)(flg, &ego->td, reodft010e_tw, 4*ego->n, 1, ego->n/2+1);
+}
+
+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_)
+{
+ UNUSED(ego_);
+ if (RDFTP(p_)) {
+ const problem_rdft *p = (const problem_rdft *) p_;
+ return (1
+ && p->sz->rnk == 1
+ && p->vecsz->rnk <= 1
+ && (p->kind[0] == REDFT01 || p->kind[0] == REDFT10
+ || p->kind[0] == RODFT01 || p->kind[0] == RODFT10)
+ );
+ }
+
+ 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;
+
+ switch (p->kind[0]) {
+ case REDFT01: pln = MKPLAN_RDFT(P, &padt, apply_re01); break;
+ case REDFT10: pln = MKPLAN_RDFT(P, &padt, apply_re10); break;
+ case RODFT01: pln = MKPLAN_RDFT(P, &padt, apply_ro01); break;
+ case RODFT10: pln = MKPLAN_RDFT(P, &padt, apply_ro10); break;
+ default: A(0); return (plan*)0;
+ }
+
+ pln->n = n;
+ pln->is = p->sz->dims[0].is;
+ pln->os = p->sz->dims[0].os;
+ pln->cld = cld;
+ pln->td = 0;
+ pln->kind = p->kind[0];
+
+ X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
+
+ X(ops_zero)(&ops);
+ ops.other = 4 + (n-1)/2 * 10 + (1 - n % 2) * 5;
+ if (p->kind[0] == REDFT01 || p->kind[0] == RODFT01) {
+ ops.add = (n-1)/2 * 6;
+ ops.mul = (n-1)/2 * 4 + (1 - n % 2) * 2;
+ }
+ else { /* 10 transforms */
+ ops.add = (n-1)/2 * 2;
+ ops.mul = 1 + (n-1)/2 * 6 + (1 - n % 2) * 2;
+ }
+
+ 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(reodft010e_r2hc_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver());
+}
diff --git a/src/fftw3/reodft/reodft11e-r2hc-odd.c b/src/fftw3/reodft/reodft11e-r2hc-odd.c
new file mode 100644
index 0000000..471f7ca
--- /dev/null
+++ b/src/fftw3/reodft/reodft11e-r2hc-odd.c
@@ -0,0 +1,304 @@
+/*
+ * 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());
+}
diff --git a/src/fftw3/reodft/reodft11e-r2hc.c b/src/fftw3/reodft/reodft11e-r2hc.c
new file mode 100644
index 0000000..d4366e3
--- /dev/null
+++ b/src/fftw3/reodft/reodft11e-r2hc.c
@@ -0,0 +1,295 @@
+/*
+ * 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.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
+
+/* 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_, int flg)
+{
+ 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 }
+ };
+
+ AWAKE(ego->cld, flg);
+
+ X(twiddle_awake)(flg, &ego->td, reodft010e_tw, 4*ego->n, 1, ego->n/2+1);
+ X(twiddle_awake)(flg, &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_)
+{
+ UNUSED(ego_);
+ if (RDFTP(p_)) {
+ const problem_rdft *p = (const problem_rdft *) p_;
+ return (1
+ && p->sz->rnk == 1
+ && p->vecsz->rnk <= 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->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 = { mkplan };
+ S *slv = MKSOLVER(S, &sadt);
+ return &(slv->super);
+}
+
+void X(reodft11e_r2hc_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver());
+}
diff --git a/src/fftw3/reodft/reodft11e-radix2.c b/src/fftw3/reodft/reodft11e-radix2.c
new file mode 100644
index 0000000..674f7b4
--- /dev/null
+++ b/src/fftw3/reodft/reodft11e-radix2.c
@@ -0,0 +1,515 @@
+/*
+ * 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-radix2.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
+
+/* 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.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] = K(2.0) * (u + v) * W[2*i];
+ buf[n - i] = K(2.0) * (u - v) * W[2*i];
+ }
+
+
+ /* 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] = K(2.0) * (u + v) * W[2*i];
+ buf[n - i] = K(2.0) * (u - v) * W[2*i];
+ }
+
+
+ /* 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_, int flg)
+{
+ 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 }
+ };
+
+ AWAKE(ego->cld, flg);
+
+ X(twiddle_awake)(flg, &ego->td, reodft010e_tw, 2*ego->n, 1, ego->n/4+1);
+ X(twiddle_awake)(flg, &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_)
+{
+ 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 == 0
+ && (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/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 = { mkplan };
+ S *slv = MKSOLVER(S, &sadt);
+ return &(slv->super);
+}
+
+void X(reodft11e_radix2_r2hc_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver());
+}
diff --git a/src/fftw3/reodft/rodft00e-r2hc-pad.c b/src/fftw3/reodft/rodft00e-r2hc-pad.c
new file mode 100644
index 0000000..0b48585
--- /dev/null
+++ b/src/fftw3/reodft/rodft00e-r2hc-pad.c
@@ -0,0 +1,200 @@
+/*
+ * 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: rodft00e-r2hc-pad.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
+
+/* Do a RODFT00 problem via an R2HC problem, padded antisymmetrically to
+ twice the size. This is asymptotically a factor of ~2 worse than
+ rodft00e-r2hc.c (the algorithm used in e.g. FFTPACK and Numerical
+ Recipes), but we abandoned the latter after we discovered that it
+ has intrinsic accuracy problems. */
+
+#include "reodft.h"
+
+typedef struct {
+ solver super;
+} S;
+
+typedef struct {
+ plan_rdft super;
+ plan *cld, *cldcpy;
+ int is;
+ 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;
+ int i, n = ego->n;
+ int iv, vl = ego->vl;
+ int ivs = ego->ivs, ovs = ego->ovs;
+ R *buf;
+
+ buf = (R *) MALLOC(sizeof(R) * (2*n), BUFFERS);
+
+ for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+ buf[0] = 0.0;
+ for (i = 1; i < n; ++i) {
+ R a = I[(i-1) * is];
+ buf[i] = -a;
+ buf[2*n - i] = a;
+ }
+ buf[i] = 0.0; /* i == n, Nyquist */
+
+ /* r2hc transform of size 2*n */
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, buf, buf);
+ }
+
+ /* copy n-1 real numbers (imag. parts of hc array) from buf to O */
+ {
+ plan_rdft *cldcpy = (plan_rdft *) ego->cldcpy;
+ cldcpy->apply((plan *) cldcpy, buf+2*n-1, O);
+ }
+ }
+
+ X(ifree)(buf);
+}
+
+static void awake(plan *ego_, int flg)
+{
+ P *ego = (P *) ego_;
+ AWAKE(ego->cld, flg);
+ AWAKE(ego->cldcpy, flg);
+}
+
+static void destroy(plan *ego_)
+{
+ P *ego = (P *) ego_;
+ X(plan_destroy_internal)(ego->cldcpy);
+ X(plan_destroy_internal)(ego->cld);
+}
+
+static void print(const plan *ego_, printer *p)
+{
+ const P *ego = (const P *) ego_;
+ p->print(p, "(rodft00e-r2hc-pad-%d%v%(%p%)%(%p%))",
+ ego->n - 1, ego->vl, ego->cld, ego->cldcpy);
+}
+
+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->kind[0] == RODFT00
+ );
+ }
+
+ 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 = (plan *) 0, *cldcpy;
+ R *buf = (R *) 0;
+ int n;
+ int vl, ivs, ovs;
+ opcnt ops;
+
+ static const plan_adt padt = {
+ X(rdft_solve), awake, print, destroy
+ };
+
+ if (!applicable(ego_, p_, plnr))
+ goto nada;
+
+ p = (const problem_rdft *) p_;
+
+ n = p->sz->dims[0].n + 1;
+ A(n > 0);
+ buf = (R *) MALLOC(sizeof(R) * (2*n), BUFFERS);
+
+ cld = X(mkplan_d)(plnr,X(mkproblem_rdft_1_d)(X(mktensor_1d)(2*n,1,1),
+ X(mktensor_0d)(),
+ buf, buf, R2HC));
+ if (!cld)
+ goto nada;
+
+ X(tensor_tornk1)(p->vecsz, &vl, &ivs, &ovs);
+ cldcpy =
+ X(mkplan_d)(plnr,
+ X(mkproblem_rdft_1_d)(X(mktensor_0d)(),
+ X(mktensor_1d)(n-1,-1,
+ p->sz->dims[0].os),
+ buf+2*n-1,TAINT(p->O, ovs), R2HC));
+ if (!cldcpy)
+ goto nada;
+
+ X(ifree)(buf);
+
+ pln = MKPLAN_RDFT(P, &padt, apply);
+
+ pln->n = n;
+ pln->is = p->sz->dims[0].is;
+ pln->cld = cld;
+ pln->cldcpy = cldcpy;
+ pln->vl = vl;
+ pln->ivs = ivs;
+ pln->ovs = ovs;
+
+ X(ops_zero)(&ops);
+ ops.other = n-1 + 2*n; /* loads + stores (input -> buf) */
+
+ 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);
+ X(ops_madd2)(pln->vl, &cldcpy->ops, &pln->super.super.ops);
+
+ return &(pln->super.super);
+
+ nada:
+ X(ifree0)(buf);
+ if (cld)
+ X(plan_destroy_internal)(cld);
+ return (plan *)0;
+}
+
+/* constructor */
+static solver *mksolver(void)
+{
+ static const solver_adt sadt = { mkplan };
+ S *slv = MKSOLVER(S, &sadt);
+ return &(slv->super);
+}
+
+void X(rodft00e_r2hc_pad_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver());
+}
diff --git a/src/fftw3/reodft/rodft00e-r2hc.c b/src/fftw3/reodft/rodft00e-r2hc.c
new file mode 100644
index 0000000..46bb299
--- /dev/null
+++ b/src/fftw3/reodft/rodft00e-r2hc.c
@@ -0,0 +1,212 @@
+/*
+ * 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: rodft00e-r2hc.c,v 1.1 2008/10/17 06:13:18 scuri Exp $ */
+
+/* Do a RODFT00 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 sine, 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
+ rodft00-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 antisymmetric data, but this
+ would require a whole new set of codelets and it's not clear that
+ it's worth it at this point. */
+
+#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;
+
+ buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
+
+ for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
+ buf[0] = 0;
+ for (i = 1; i < n - i; ++i) {
+ E a, b, apb, amb;
+ a = I[is * (i - 1)];
+ b = I[is * ((n - i) - 1)];
+ apb = K(2.0) * W[i] * (a + b);
+ amb = (a - b);
+ buf[i] = apb + amb;
+ buf[n - i] = apb - amb;
+ }
+ if (i == n - i) {
+ buf[i] = K(4.0) * I[is * (i - 1)];
+ }
+
+ {
+ 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] * 0.5;
+ for (i = 1; i + i < n - 1; ++i) {
+ int k = i + i;
+ O[os * (k - 1)] = -buf[n - i];
+ O[os * k] = O[os * (k - 2)] + buf[i];
+ }
+ if (i + i == n - 1) {
+ O[os * (n - 2)] = -buf[n - i];
+ }
+ }
+
+ X(ifree)(buf);
+}
+
+static void awake(plan *ego_, int flg)
+{
+ P *ego = (P *) ego_;
+ static const tw_instr rodft00e_tw[] = {
+ { TW_SIN, 0, 1 },
+ { TW_NEXT, 1, 0 }
+ };
+
+ AWAKE(ego->cld, flg);
+
+ X(twiddle_awake)(flg, &ego->td, rodft00e_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, "(rodft00e-r2hc-%d%v%(%p%))", ego->n - 1, 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->kind[0] == RODFT00
+ );
+ }
+
+ 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 + 1;
+ 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 = 4 + (n-1)/2 * 5 + (n-2)/2 * 5;
+ ops.add = (n-1)/2 * 4 + (n-2)/2 * 1;
+ ops.mul = 1 + (n-1)/2 * 2;
+ if (n % 2 == 0)
+ ops.mul += 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 = { mkplan };
+ S *slv = MKSOLVER(S, &sadt);
+ return &(slv->super);
+}
+
+void X(rodft00e_r2hc_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver());
+}
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