diff options
author | scuri <scuri> | 2008-10-17 06:10:15 +0000 |
---|---|---|
committer | scuri <scuri> | 2008-10-17 06:10:15 +0000 |
commit | 5a422aba704c375a307a902bafe658342e209906 (patch) | |
tree | 5005011e086bb863d8fb587ad3319bbec59b2447 /src/fftw3/reodft/reodft010e-r2hc.c |
First commit - moving from LuaForge to SourceForge
Diffstat (limited to 'src/fftw3/reodft/reodft010e-r2hc.c')
-rw-r--r-- | src/fftw3/reodft/reodft010e-r2hc.c | 409 |
1 files changed, 409 insertions, 0 deletions
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()); +} |