355 lines
9.9 KiB
C
355 lines
9.9 KiB
C
/*
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* Copyright (c) 2005 Matteo Frigo
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* Copyright (c) 2005 Massachusetts Institute of Technology
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*
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*/
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/* Do an R{E,O}DFT00 problem (of an odd length n) recursively via an
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R{E,O}DFT00 problem and an RDFT problem of half the length.
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This works by "logically" expanding the array to a real-even/odd DFT of
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length 2n-/+2 and then applying the split-radix algorithm.
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In this way, we can avoid having to pad to twice the length
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(ala redft00-r2hc-pad), saving a factor of ~2 for n=2^m+/-1,
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but don't incur the accuracy loss that the "ordinary" algorithm
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sacrifices (ala redft00-r2hc.c).
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*/
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#include "reodft/reodft.h"
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typedef struct {
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solver super;
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} S;
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typedef struct {
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plan_rdft super;
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plan *clde, *cldo;
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twid *td;
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INT is, os;
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INT n;
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INT vl;
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INT ivs, ovs;
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} P;
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/* redft00 */
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static void apply_e(const plan *ego_, R *I, R *O)
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{
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const P *ego = (const P *) ego_;
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INT is = ego->is, os = ego->os;
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INT i, j, n = ego->n + 1, n2 = (n-1)/2;
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INT iv, vl = ego->vl;
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INT ivs = ego->ivs, ovs = ego->ovs;
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R *W = ego->td->W - 2;
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R *buf;
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buf = (R *) MALLOC(sizeof(R) * n2, BUFFERS);
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for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
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/* do size (n-1)/2 r2hc transform of odd-indexed elements
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with stride 4, "wrapping around" end of array with even
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boundary conditions */
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for (j = 0, i = 1; i < n; i += 4)
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buf[j++] = I[is * i];
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for (i = 2*n-2-i; i > 0; i -= 4)
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buf[j++] = I[is * i];
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{
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plan_rdft *cld = (plan_rdft *) ego->cldo;
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cld->apply((plan *) cld, buf, buf);
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}
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/* do size (n+1)/2 redft00 of the even-indexed elements,
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writing to O: */
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{
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plan_rdft *cld = (plan_rdft *) ego->clde;
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cld->apply((plan *) cld, I, O);
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}
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/* combine the results with the twiddle factors to get output */
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{ /* DC element */
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E b20 = O[0], b0 = K(2.0) * buf[0];
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O[0] = b20 + b0;
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O[2*(n2*os)] = b20 - b0;
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/* O[n2*os] = O[n2*os]; */
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}
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for (i = 1; i < n2 - i; ++i) {
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E ap, am, br, bi, wr, wi, wbr, wbi;
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br = buf[i];
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bi = buf[n2 - i];
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wr = W[2*i];
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wi = W[2*i+1];
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#if FFT_SIGN == -1
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wbr = K(2.0) * (wr*br + wi*bi);
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wbi = K(2.0) * (wr*bi - wi*br);
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#else
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wbr = K(2.0) * (wr*br - wi*bi);
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wbi = K(2.0) * (wr*bi + wi*br);
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#endif
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ap = O[i*os];
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O[i*os] = ap + wbr;
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O[(2*n2 - i)*os] = ap - wbr;
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am = O[(n2 - i)*os];
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#if FFT_SIGN == -1
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O[(n2 - i)*os] = am - wbi;
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O[(n2 + i)*os] = am + wbi;
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#else
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O[(n2 - i)*os] = am + wbi;
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O[(n2 + i)*os] = am - wbi;
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#endif
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}
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if (i == n2 - i) { /* Nyquist element */
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E ap, wbr;
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wbr = K(2.0) * (W[2*i] * buf[i]);
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ap = O[i*os];
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O[i*os] = ap + wbr;
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O[(2*n2 - i)*os] = ap - wbr;
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}
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}
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X(ifree)(buf);
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}
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/* rodft00 */
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static void apply_o(const plan *ego_, R *I, R *O)
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{
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const P *ego = (const P *) ego_;
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INT is = ego->is, os = ego->os;
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INT i, j, n = ego->n - 1, n2 = (n+1)/2;
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INT iv, vl = ego->vl;
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INT ivs = ego->ivs, ovs = ego->ovs;
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R *W = ego->td->W - 2;
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R *buf;
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buf = (R *) MALLOC(sizeof(R) * n2, BUFFERS);
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for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
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/* do size (n+1)/2 r2hc transform of even-indexed elements
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with stride 4, "wrapping around" end of array with odd
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boundary conditions */
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for (j = 0, i = 0; i < n; i += 4)
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buf[j++] = I[is * i];
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for (i = 2*n-i; i > 0; i -= 4)
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buf[j++] = -I[is * i];
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{
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plan_rdft *cld = (plan_rdft *) ego->cldo;
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cld->apply((plan *) cld, buf, buf);
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}
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/* do size (n-1)/2 rodft00 of the odd-indexed elements,
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writing to O: */
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{
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plan_rdft *cld = (plan_rdft *) ego->clde;
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if (I == O) {
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/* can't use I+is and I, subplan would lose in-placeness */
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cld->apply((plan *) cld, I + is, I + is);
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/* we could maybe avoid this copy by modifying the
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twiddle loop, but currently I can't be bothered. */
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A(is >= os);
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for (i = 0; i < n2-1; ++i)
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O[os*i] = I[is*(i+1)];
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}
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else
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cld->apply((plan *) cld, I + is, O);
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}
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/* combine the results with the twiddle factors to get output */
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O[(n2-1)*os] = K(2.0) * buf[0];
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for (i = 1; i < n2 - i; ++i) {
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E ap, am, br, bi, wr, wi, wbr, wbi;
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br = buf[i];
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bi = buf[n2 - i];
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wr = W[2*i];
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wi = W[2*i+1];
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#if FFT_SIGN == -1
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wbr = K(2.0) * (wr*br + wi*bi);
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wbi = K(2.0) * (wi*br - wr*bi);
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#else
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wbr = K(2.0) * (wr*br - wi*bi);
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wbi = K(2.0) * (wr*bi + wi*br);
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#endif
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ap = O[(i-1)*os];
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O[(i-1)*os] = wbi + ap;
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O[(2*n2-1 - i)*os] = wbi - ap;
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am = O[(n2-1 - i)*os];
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#if FFT_SIGN == -1
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O[(n2-1 - i)*os] = wbr + am;
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O[(n2-1 + i)*os] = wbr - am;
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#else
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O[(n2-1 - i)*os] = wbr + am;
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O[(n2-1 + i)*os] = wbr - am;
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#endif
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}
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if (i == n2 - i) { /* Nyquist element */
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E ap, wbi;
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wbi = K(2.0) * (W[2*i+1] * buf[i]);
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ap = O[(i-1)*os];
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O[(i-1)*os] = wbi + ap;
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O[(2*n2-1 - i)*os] = wbi - ap;
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}
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}
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X(ifree)(buf);
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}
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static void awake(plan *ego_, enum wakefulness wakefulness)
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{
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P *ego = (P *) ego_;
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static const tw_instr reodft00e_tw[] = {
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{ TW_COS, 1, 1 },
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{ TW_SIN, 1, 1 },
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{ TW_NEXT, 1, 0 }
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};
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X(plan_awake)(ego->clde, wakefulness);
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X(plan_awake)(ego->cldo, wakefulness);
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X(twiddle_awake)(wakefulness, &ego->td, reodft00e_tw,
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2*ego->n, 1, ego->n/4);
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}
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static void destroy(plan *ego_)
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{
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P *ego = (P *) ego_;
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X(plan_destroy_internal)(ego->cldo);
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X(plan_destroy_internal)(ego->clde);
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}
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static void print(const plan *ego_, printer *p)
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{
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const P *ego = (const P *) ego_;
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if (ego->super.apply == apply_e)
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p->print(p, "(redft00e-splitradix-%D%v%(%p%)%(%p%))",
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ego->n + 1, ego->vl, ego->clde, ego->cldo);
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else
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p->print(p, "(rodft00e-splitradix-%D%v%(%p%)%(%p%))",
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ego->n - 1, ego->vl, ego->clde, ego->cldo);
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}
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static int applicable0(const solver *ego_, const problem *p_)
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{
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const problem_rdft *p = (const problem_rdft *) p_;
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UNUSED(ego_);
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return (1
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&& p->sz->rnk == 1
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&& p->vecsz->rnk <= 1
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&& (p->kind[0] == REDFT00 || p->kind[0] == RODFT00)
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&& p->sz->dims[0].n > 1 /* don't create size-0 sub-plans */
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&& p->sz->dims[0].n % 2 /* odd: 4 divides "logical" DFT */
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&& (p->I != p->O || p->vecsz->rnk == 0
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|| p->vecsz->dims[0].is == p->vecsz->dims[0].os)
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&& (p->kind[0] != RODFT00 || p->I != p->O ||
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p->sz->dims[0].is >= p->sz->dims[0].os) /* laziness */
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);
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}
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static int applicable(const solver *ego, const problem *p, const planner *plnr)
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{
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return (!NO_SLOWP(plnr) && applicable0(ego, p));
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}
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static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
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{
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P *pln;
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const problem_rdft *p;
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plan *clde, *cldo;
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R *buf;
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INT n, n0;
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opcnt ops;
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int inplace_odd;
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static const plan_adt padt = {
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X(rdft_solve), awake, print, destroy
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};
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if (!applicable(ego_, p_, plnr))
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return (plan *)0;
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p = (const problem_rdft *) p_;
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n = (n0 = p->sz->dims[0].n) + (p->kind[0] == REDFT00 ? (INT)-1 : (INT)1);
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A(n > 0 && n % 2 == 0);
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buf = (R *) MALLOC(sizeof(R) * (n/2), BUFFERS);
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inplace_odd = p->kind[0]==RODFT00 && p->I == p->O;
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clde = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(
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X(mktensor_1d)(n0-n/2, 2*p->sz->dims[0].is,
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inplace_odd ? p->sz->dims[0].is
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: p->sz->dims[0].os),
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X(mktensor_0d)(),
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TAINT(p->I
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+ p->sz->dims[0].is * (p->kind[0]==RODFT00),
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p->vecsz->rnk ? p->vecsz->dims[0].is : 0),
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TAINT(p->O
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+ p->sz->dims[0].is * inplace_odd,
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p->vecsz->rnk ? p->vecsz->dims[0].os : 0),
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p->kind[0]));
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if (!clde) {
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X(ifree)(buf);
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return (plan *)0;
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}
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cldo = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(
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X(mktensor_1d)(n/2, 1, 1),
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X(mktensor_0d)(),
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buf, buf, R2HC));
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X(ifree)(buf);
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if (!cldo)
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return (plan *)0;
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pln = MKPLAN_RDFT(P, &padt, p->kind[0] == REDFT00 ? apply_e : apply_o);
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pln->n = n;
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pln->is = p->sz->dims[0].is;
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pln->os = p->sz->dims[0].os;
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pln->clde = clde;
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pln->cldo = cldo;
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pln->td = 0;
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X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
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X(ops_zero)(&ops);
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ops.other = n/2;
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ops.add = (p->kind[0]==REDFT00 ? (INT)2 : (INT)0) +
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(n/2-1)/2 * 6 + ((n/2)%2==0) * 2;
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ops.mul = 1 + (n/2-1)/2 * 6 + ((n/2)%2==0) * 2;
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/* tweak ops.other so that r2hc-pad is used for small sizes, which
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seems to be a lot faster on my machine: */
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ops.other += 256;
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X(ops_zero)(&pln->super.super.ops);
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X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops);
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X(ops_madd2)(pln->vl, &clde->ops, &pln->super.super.ops);
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X(ops_madd2)(pln->vl, &cldo->ops, &pln->super.super.ops);
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return &(pln->super.super);
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}
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/* constructor */
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static solver *mksolver(void)
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{
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static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
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S *slv = MKSOLVER(S, &sadt);
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return &(slv->super);
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}
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void X(reodft00e_splitradix_register)(planner *p)
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{
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REGISTER_SOLVER(p, mksolver());
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}
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