From 5a422aba704c375a307a902bafe658342e209906 Mon Sep 17 00:00:00 2001 From: scuri Date: Fri, 17 Oct 2008 06:10:15 +0000 Subject: First commit - moving from LuaForge to SourceForge --- src/fftw3/rdft/rader-hc2hc.c | 513 +++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 513 insertions(+) create mode 100644 src/fftw3/rdft/rader-hc2hc.c (limited to 'src/fftw3/rdft/rader-hc2hc.c') diff --git a/src/fftw3/rdft/rader-hc2hc.c b/src/fftw3/rdft/rader-hc2hc.c new file mode 100644 index 0000000..f1b6f34 --- /dev/null +++ b/src/fftw3/rdft/rader-hc2hc.c @@ -0,0 +1,513 @@ +/* + * 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()); +} -- cgit v1.2.3