diff options
author | scuri <scuri> | 2008-10-17 06:10:15 +0000 |
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committer | scuri <scuri> | 2008-10-17 06:10:15 +0000 |
commit | 5a422aba704c375a307a902bafe658342e209906 (patch) | |
tree | 5005011e086bb863d8fb587ad3319bbec59b2447 /src/fftw3/reodft/reodft11e-radix2.c |
First commit - moving from LuaForge to SourceForge
Diffstat (limited to 'src/fftw3/reodft/reodft11e-radix2.c')
-rw-r--r-- | src/fftw3/reodft/reodft11e-radix2.c | 515 |
1 files changed, 515 insertions, 0 deletions
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()); +} |