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diff --git a/src/fftw3/rdft/rader-hc2hc.c b/src/fftw3/rdft/rader-hc2hc.c
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+++ b/src/fftw3/rdft/rader-hc2hc.c
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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
+ *
+ */
+
+#include "rdft.h"
+#include "dft.h"
+
+/*
+ * Compute transforms with large prime factors using Rader's trick:
+ * turn the factors into convolutions of size n - 1, which you then
+ * perform via a pair of FFTs. This file contains only twiddle hc2hc
+ * transforms, which are actually ordinary complex transforms in a
+ * slightly funny order.
+ */
+
+typedef struct {
+ solver super;
+ rdft_kind kind;
+} S;
+
+typedef struct {
+ plan_rdft super;
+
+ plan *cldr, *cldr0;
+ plan *cld;
+ R *W;
+ R *omega;
+ int m, r, g, ginv;
+ int os, ios;
+ rdft_kind kind;
+} P;
+
+static rader_tl *twiddles = 0;
+
+/***************************************************************************/
+
+/* Below, we extensively use the identity that fft(x*)* = ifft(x) in
+ order to share data between forward and backward transforms and to
+ obviate the necessity of having separate forward and backward
+ plans. */
+
+static void apply_aux(int r, plan_dft *cldr, const R *omega,
+ R *buf, R *ro, R i0, R *io)
+{
+ R r0;
+ int k;
+
+ /* compute DFT of buf, operating in-place */
+ cldr->apply((plan *) cldr, buf, buf+1, buf, buf+1);
+
+ /* set output DC component: */
+ ro[0] = (r0 = ro[0]) + buf[0];
+ io[0] = i0 + buf[1];
+
+ /* now, multiply by omega: */
+ for (k = 0; k < r - 1; ++k) {
+ R rB, iB, rW, iW;
+ rW = omega[2*k];
+ iW = omega[2*k+1];
+ rB = buf[2*k];
+ iB = buf[2*k+1];
+ buf[2*k] = rW * rB - iW * iB;
+ buf[2*k+1] = -(rW * iB + iW * rB);
+ }
+
+ /* this will add input[0] to all of the outputs after the ifft */
+ buf[0] += r0;
+ buf[1] -= i0;
+
+ /* inverse FFT: */
+ cldr->apply((plan *) cldr, buf, buf+1, buf, buf+1);
+}
+
+static void apply_dit(const plan *ego_, R *I, R *O)
+{
+ const P *ego = (const P *) ego_;
+ plan_dft *cldr;
+ int os, ios;
+ int j, k, gpower, g, ginv, r, m;
+ R *buf, *rio, *ii, *io;
+ const R *omega, *W;
+
+ /* size-m child transforms: */
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, I, O);
+ }
+
+ /* 0th twiddle transform is just size-r (prime) R2HC: */
+ {
+ plan_rdft *cldr0 = (plan_rdft *) ego->cldr0;
+ cldr0->apply((plan *) cldr0, O, O);
+ }
+
+ cldr = (plan_dft *) ego->cldr;
+ r = ego->r;
+ m = ego->m;
+ g = ego->g;
+ ginv = ego->ginv;
+ omega = ego->omega;
+ W = ego->W;
+ os = ego->os;
+ ios = ego->ios;
+ gpower = 1;
+ rio = O + os;
+ ii = O + (m - 1) * os;
+ io = O + (r * m - 1) * os;
+
+ buf = (R *) MALLOC(sizeof(R) * (r - 1) * 2, BUFFERS);
+
+ for (j = 2; j < m; j += 2, rio += os, ii -= os, io -= os, W += 2*(r-1)) {
+ /* First, permute the input and multiply by W, storing in buf: */
+ A(gpower == 1);
+ for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
+ R rA, iA, rW, iW;
+ rA = rio[gpower * ios];
+ iA = ii[gpower * ios];
+ rW = W[2*k];
+ iW = W[2*k+1];
+ buf[2*k] = rW * rA - iW * iA;
+ buf[2*k+1] = rW * iA + iW * rA;
+ }
+ /* gpower == g^(r-1) mod r == 1 */;
+
+ apply_aux(r, cldr, omega, buf, rio, ii[0], io);
+
+ /* finally, do inverse permutation to unshuffle the output: */
+ A(gpower == 1);
+ for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, ginv, r)) {
+ rio[gpower * ios] = buf[2*k];
+ io[-gpower * ios] = -buf[2*k+1];
+ }
+ A(gpower == 1);
+
+ /* second half of array must be fiddled to get real/imag
+ parts in correct spots: */
+ for (k = (r+1)/2; k < r; ++k) {
+ R t;
+ t = rio[k * ios];
+ rio[k * ios] = -io[-k * ios];
+ io[-k * ios] = t;
+ }
+ }
+
+ /* Avoid funny m/2-th iter by requiring m odd. This always
+ happens anyway because all the factors of 2 get divided out
+ first by codelets (Rader is UGLY for small factors). */
+
+ X(ifree)(buf);
+}
+
+static void apply_dif(const plan *ego_, R *I, R *O)
+{
+ const P *ego = (const P *) ego_;
+ plan_dft *cldr;
+ int is, ios;
+ int j, k, gpower, g, ginv, r, m;
+ R *buf, *rio, *ii, *io;
+ const R *omega, *W;
+
+ /* 0th twiddle transform is just size-r (prime) HC2R: */
+ {
+ plan_rdft *cldr0 = (plan_rdft *) ego->cldr0;
+ cldr0->apply((plan *) cldr0, I, I);
+ }
+
+ cldr = (plan_dft *) ego->cldr;
+ r = ego->r;
+ m = ego->m;
+ g = ego->g;
+ ginv = ego->ginv;
+ omega = ego->omega;
+ W = ego->W + 2*(r-1); /* simplify reverse indexing of W */
+ is = ego->os;
+ ios = ego->ios;
+ gpower = 1;
+ rio = I + is;
+ io = I + (m - 1) * is;
+ ii = I + (r * m - 1) * is;
+
+ buf = (R *) MALLOC(sizeof(R) * (r - 1) * 2, BUFFERS);
+
+ for (j = 2; j < m; j += 2, rio += is, ii -= is, io -= is, W += 2*(r-1)) {
+ /* second half of array must be unfiddled to get real/imag
+ parts from correct spots: */
+ for (k = (r+1)/2; k < r; ++k) {
+ R t;
+ t = rio[k * ios];
+ rio[k * ios] = ii[-k * ios];
+ ii[-k * ios] = -t;
+ }
+
+ /* First, permute the input, storing in buf: */
+ A(gpower == 1);
+ for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
+ buf[2*k] = rio[gpower * ios];
+ buf[2*k+1] = -ii[-gpower * ios];
+ }
+ /* gpower == g^(r-1) mod r == 1 */;
+ A(gpower == 1);
+
+ apply_aux(r, cldr, omega, buf, rio, -ii[0], io);
+ io[0] = -io[0];
+
+ /* finally, do inverse permutation to unshuffle the output,
+ also multiplying by the inverse twiddle factors W*.
+ The twiddle factors are accessed in reverse order W[-k],
+ because here we exponentiating ginv and not g as in
+ mktwiddle. */
+ { /* W[-0] = W[0] case must be handled specially */
+ R rA, iA, rW, iW;
+ rA = buf[0]; iA = buf[1];
+ rW = W[-2*(r-1)]; iW = W[-2*(r-1) + 1];
+ rio[ios] = rA * rW + iA * iW;
+ io[ios] = iA * rW - rA * iW;
+ }
+ gpower = ginv;
+ for (k = 1; k < r - 1; ++k, gpower = MULMOD(gpower, ginv, r)) {
+ R rA, iA, rW, iW;
+ rA = buf[2*k]; iA = buf[2*k+1];
+ rW = W[-2*k]; iW = W[-2*k+1];
+ rio[gpower * ios] = rA * rW + iA * iW;
+ io[gpower * ios] = iA * rW - rA * iW;
+ }
+ A(gpower == 1);
+ }
+
+ /* Avoid funny m/2-th iter by requiring m odd. This always
+ happens anyway because all the factors of 2 get divided out
+ first by codelets (Rader is UGLY for small factors). */
+
+ X(ifree)(buf);
+
+ /* size-m child transforms: */
+ {
+ plan_rdft *cld = (plan_rdft *) ego->cld;
+ cld->apply((plan *) cld, I, O);
+ }
+}
+
+static R *mktwiddle(int m, int r, int g)
+{
+ int i, j, gpower;
+ int n = r * m;
+ R *W;
+
+ if ((W = X(rader_tl_find)(m, r, g, twiddles)))
+ return W;
+
+ W = (R *)MALLOC(sizeof(R) * (r - 1) * ((m-1)/2) * 2, TWIDDLES);
+ for (i = 1; i < (m+1)/2; ++i) {
+ for (gpower = 1, j = 0; j < r - 1;
+ ++j, gpower = MULMOD(gpower, g, r)) {
+ int k = (i - 1) * (r - 1) + j;
+ W[2*k] = X(cos2pi)(i * gpower, n);
+ W[2*k+1] = FFT_SIGN * X(sin2pi)(i * gpower, n);
+ }
+ A(gpower == 1);
+ }
+
+ X(rader_tl_insert)(m, r, g, W, &twiddles);
+ return W;
+}
+
+static void free_twiddle(R *twiddle)
+{
+ X(rader_tl_delete)(twiddle, &twiddles);
+}
+
+/***************************************************************************/
+
+static void awake(plan *ego_, int flg)
+{
+ P *ego = (P *) ego_;
+
+ AWAKE(ego->cldr0, flg);
+ AWAKE(ego->cldr, flg);
+ AWAKE(ego->cld, flg);
+
+ if (flg) {
+ if (!ego->omega)
+ ego->omega =
+ X(dft_rader_mkomega)(ego->cldr, ego->r, ego->ginv);
+ if (!ego->W)
+ ego->W = mktwiddle(ego->m, ego->r, ego->g);
+ } else {
+ X(dft_rader_free_omega)(&ego->omega);
+ free_twiddle(ego->W);
+ ego->W = 0;
+ }
+}
+
+static void destroy(plan *ego_)
+{
+ P *ego = (P *) ego_;
+ X(plan_destroy_internal)(ego->cld);
+ X(plan_destroy_internal)(ego->cldr);
+ X(plan_destroy_internal)(ego->cldr0);
+}
+
+static void print(const plan *ego_, printer *p)
+{
+ const P *ego = (const P *) ego_;
+
+ p->print(p, "(rdft-rader-%s-%d%(%p%)%(%p%)%(%p%))",
+ ego->kind == R2HC ? "r2hc-dit" : "hc2r-dif",
+ ego->r, ego->cldr0, ego->cldr, ego->cld);
+}
+
+static int applicable0(const solver *ego_, const problem *p_)
+{
+ if (RDFTP(p_)) {
+ const S *ego = (const S *) ego_;
+ const problem_rdft *p = (const problem_rdft *) p_;
+ return (1
+ && p->sz->rnk == 1
+ && p->vecsz->rnk == 0
+ && p->sz->dims[0].n > 1
+ && p->sz->dims[0].n % 4 /* make sure n / r = m is odd */
+ && p->kind[0] == ego->kind
+ && !X(is_prime)(p->sz->dims[0].n) /* avoid inf. loops planning cldr0 */
+ );
+ }
+
+ return 0;
+}
+
+static int applicable(const solver *ego_, const problem *p_,
+ const planner *plnr)
+{
+ return (!NO_UGLYP(plnr) && applicable0(ego_, p_));
+}
+
+static int mkP(P *pln, int r, R *O, int ios, rdft_kind kind, planner *plnr)
+{
+ plan *cldr = (plan *) 0;
+ plan *cldr0 = (plan *) 0;
+ R *buf = (R *) 0;
+
+ cldr0 = X(mkplan_d)(plnr,
+ X(mkproblem_rdft_1_d)(X(mktensor_1d)(r, ios, ios),
+ X(mktensor_1d)(1, 0, 0),
+ O, O, kind));
+ if (!cldr0) goto nada;
+
+ /* initial allocation for the purpose of planning */
+ buf = (R *) MALLOC(sizeof(R) * (r - 1) * 2, BUFFERS);
+
+ cldr = X(mkplan_d)(plnr, X(mkproblem_dft_d)(X(mktensor_1d)(r - 1, 2, 2),
+ X(mktensor_1d)(1, 0, 0),
+ buf, buf + 1, buf, buf + 1));
+ if (!cldr) goto nada;
+
+ X(ifree)(buf);
+
+ pln->cldr = cldr;
+ pln->cldr0 = cldr0;
+ pln->omega = 0;
+ pln->r = r;
+ pln->g = X(find_generator)(r);
+ pln->ginv = X(power_mod)(pln->g, r - 2, r);
+ pln->kind = kind;
+ A(MULMOD(pln->g, pln->ginv, r) == 1);
+
+ X(ops_add)(&cldr->ops, &cldr->ops, &pln->super.super.ops);
+ pln->super.super.ops.other += (r - 1) * (4 * 2 + 6) + 6;
+ pln->super.super.ops.add += 2 * (r - 1) * 2 + 4;
+ pln->super.super.ops.mul += 2 * (r - 1) * 4;
+
+ return 1;
+
+ nada:
+ X(ifree0)(buf);
+ X(plan_destroy_internal)(cldr);
+ X(plan_destroy_internal)(cldr0);
+ return 0;
+}
+
+static plan *mkplan_dit(const solver *ego, const problem *p_, planner *plnr)
+{
+ const problem_rdft *p = (const problem_rdft *) p_;
+ P *pln = 0;
+ int n, is, os, r, m;
+ plan *cld = (plan *) 0;
+
+ static const plan_adt padt = {
+ X(rdft_solve), awake, print, destroy
+ };
+
+ if (!applicable(ego, p_, plnr))
+ goto nada;
+
+ n = p->sz->dims[0].n;
+ is = p->sz->dims[0].is;
+ os = p->sz->dims[0].os;
+
+ r = X(first_divisor)(n);
+ m = n / r;
+
+
+ cld = X(mkplan_d)(plnr,
+ X(mkproblem_rdft_d)(X(mktensor_1d)(m, r * is, os),
+ X(mktensor_1d)(r, is, m * os),
+ p->I, p->O, p->kind));
+ if (!cld) goto nada;
+
+ pln = MKPLAN_RDFT(P, &padt, apply_dit);
+ if (!mkP(pln, r, p->O, os*m, p->kind[0], plnr))
+ goto nada;
+
+ pln->ios = os*m;
+ pln->os = os;
+ pln->m = m;
+ pln->cld = cld;
+ pln->W = 0;
+
+ X(ops_madd)((m - 1)/2, &pln->super.super.ops, &cld->ops,
+ &pln->super.super.ops);
+
+ return &(pln->super.super);
+
+ nada:
+ X(plan_destroy_internal)(cld);
+ X(ifree0)(pln);
+ return (plan *) 0;
+}
+
+static plan *mkplan_dif(const solver *ego, const problem *p_, planner *plnr)
+{
+ const problem_rdft *p = (const problem_rdft *) p_;
+ P *pln = 0;
+ int n, is, os, r, m;
+ plan *cld = (plan *) 0;
+
+ static const plan_adt padt = {
+ X(rdft_solve), awake, print, destroy
+ };
+
+ if (!applicable(ego, p_, plnr))
+ goto nada;
+
+ n = p->sz->dims[0].n;
+ is = p->sz->dims[0].is;
+ os = p->sz->dims[0].os;
+
+ r = X(first_divisor)(n);
+ m = n / r;
+
+ cld = X(mkplan_d)(plnr,
+ X(mkproblem_rdft_d)(X(mktensor_1d)(m, is, r * os),
+ X(mktensor_1d)(r, m * is, os),
+ p->I, p->O, p->kind));
+ if (!cld) goto nada;
+
+ pln = MKPLAN_RDFT(P, &padt, apply_dif);
+ if (!mkP(pln, r, p->I, is*m, p->kind[0], plnr)) goto nada;
+
+ pln->ios = is*m;
+ pln->os = is;
+ pln->m = m;
+ pln->cld = cld;
+ pln->W = 0;
+
+ X(ops_madd)((m - 1)/2, &pln->super.super.ops, &cld->ops,
+ &pln->super.super.ops);
+
+ return &(pln->super.super);
+
+ nada:
+ X(plan_destroy_internal)(cld);
+ X(ifree0)(pln);
+ return (plan *) 0;
+}
+
+/* constructors */
+
+static solver *mksolver_dit(void)
+{
+ static const solver_adt sadt = { mkplan_dit };
+ S *slv = MKSOLVER(S, &sadt);
+ slv->kind = R2HC;
+ return &(slv->super);
+}
+
+static solver *mksolver_dif(void)
+{
+ static const solver_adt sadt = { mkplan_dif };
+ S *slv = MKSOLVER(S, &sadt);
+ slv->kind = HC2R;
+ return &(slv->super);
+}
+
+void X(rdft_rader_hc2hc_register)(planner *p)
+{
+ REGISTER_SOLVER(p, mksolver_dit());
+ REGISTER_SOLVER(p, mksolver_dif());
+}
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