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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
- *
- */
-
-/* $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());
-}
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