mirror of
https://github.com/tildearrow/furnace.git
synced 2024-11-24 13:35:11 +00:00
294 lines
7.7 KiB
C
294 lines
7.7 KiB
C
/*
|
|
* Copyright (c) 2003, 2007-14 Matteo Frigo
|
|
* Copyright (c) 2003, 2007-14 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
|
|
*
|
|
*/
|
|
|
|
|
|
/* Do an R{E,O}DFT11 problem via an R2HC problem, with some
|
|
pre/post-processing ala FFTPACK. Use a trick from:
|
|
|
|
S. C. Chan and K. L. Ho, "Direct methods for computing discrete
|
|
sinusoidal transforms," IEE Proceedings F 137 (6), 433--442 (1990).
|
|
|
|
to re-express as an REDFT01 (DCT-III) problem.
|
|
|
|
NOTE: We no longer use this algorithm, because it turns out to suffer
|
|
a catastrophic loss of accuracy for certain inputs, apparently because
|
|
its post-processing multiplies the output by a cosine. Near the zero
|
|
of the cosine, the REDFT01 must produce a near-singular output.
|
|
*/
|
|
|
|
#include "reodft/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;
|
|
INT iv, vl = ego->vl;
|
|
INT ivs = ego->ivs, ovs = ego->ovs;
|
|
R *W;
|
|
R *buf;
|
|
E cur;
|
|
|
|
buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
|
|
|
|
for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
|
|
/* I wish that this didn't require an extra pass. */
|
|
/* FIXME: use recursive/cascade summation for better stability? */
|
|
buf[n - 1] = cur = K(2.0) * I[is * (n - 1)];
|
|
for (i = n - 1; i > 0; --i) {
|
|
E curnew;
|
|
buf[(i - 1)] = curnew = K(2.0) * I[is * (i - 1)] - cur;
|
|
cur = curnew;
|
|
}
|
|
|
|
W = ego->td->W;
|
|
for (i = 1; i < n - i; ++i) {
|
|
E a, b, apb, amb, wa, wb;
|
|
a = buf[i];
|
|
b = buf[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) * buf[i] * W[2*i];
|
|
}
|
|
|
|
{
|
|
plan_rdft *cld = (plan_rdft *) ego->cld;
|
|
cld->apply((plan *) cld, buf, buf);
|
|
}
|
|
|
|
W = ego->td2->W;
|
|
O[0] = W[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)] = W[k - 1] * (a - b);
|
|
O[os * k] = W[k] * (a + b);
|
|
}
|
|
if (i == n - i) {
|
|
O[os * (n - 1)] = W[n - 1] * buf[i];
|
|
}
|
|
}
|
|
|
|
X(ifree)(buf);
|
|
}
|
|
|
|
/* 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;
|
|
INT iv, vl = ego->vl;
|
|
INT ivs = ego->ivs, ovs = ego->ovs;
|
|
R *W;
|
|
R *buf;
|
|
E cur;
|
|
|
|
buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);
|
|
|
|
for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
|
|
/* I wish that this didn't require an extra pass. */
|
|
/* FIXME: use recursive/cascade summation for better stability? */
|
|
buf[n - 1] = cur = K(2.0) * I[0];
|
|
for (i = n - 1; i > 0; --i) {
|
|
E curnew;
|
|
buf[(i - 1)] = curnew = K(2.0) * I[is * (n - i)] - cur;
|
|
cur = curnew;
|
|
}
|
|
|
|
W = ego->td->W;
|
|
for (i = 1; i < n - i; ++i) {
|
|
E a, b, apb, amb, wa, wb;
|
|
a = buf[i];
|
|
b = buf[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) * buf[i] * W[2*i];
|
|
}
|
|
|
|
{
|
|
plan_rdft *cld = (plan_rdft *) ego->cld;
|
|
cld->apply((plan *) cld, buf, buf);
|
|
}
|
|
|
|
W = ego->td2->W;
|
|
O[0] = W[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)] = W[k - 1] * (b - a);
|
|
O[os * k] = W[k] * (a + b);
|
|
}
|
|
if (i == n - i) {
|
|
O[os * (n - 1)] = -W[n - 1] * buf[i];
|
|
}
|
|
}
|
|
|
|
X(ifree)(buf);
|
|
}
|
|
|
|
static void awake(plan *ego_, enum wakefulness wakefulness)
|
|
{
|
|
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_NEXT, 2, 0 }
|
|
};
|
|
|
|
X(plan_awake)(ego->cld, wakefulness);
|
|
|
|
X(twiddle_awake)(wakefulness,
|
|
&ego->td, reodft010e_tw, 4*ego->n, 1, ego->n/2+1);
|
|
X(twiddle_awake)(wakefulness,
|
|
&ego->td2, reodft11e_tw, 8*ego->n, 1, ego->n * 2);
|
|
}
|
|
|
|
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_)
|
|
{
|
|
const problem_rdft *p = (const problem_rdft *) p_;
|
|
|
|
UNUSED(ego_);
|
|
|
|
return (1
|
|
&& p->sz->rnk == 1
|
|
&& p->vecsz->rnk <= 1
|
|
&& (p->kind[0] == REDFT11 || p->kind[0] == RODFT11)
|
|
);
|
|
}
|
|
|
|
static int applicable(const solver *ego, const problem *p, const planner *plnr)
|
|
{
|
|
return (!NO_SLOWP(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;
|
|
|
|
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.other = 5 + (n-1) * 2 + (n-1)/2 * 12 + (1 - n % 2) * 6;
|
|
ops.add = (n - 1) * 1 + (n-1)/2 * 6;
|
|
ops.mul = 2 + (n-1) * 1 + (n-1)/2 * 6 + (1 - n % 2) * 3;
|
|
|
|
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 = { PROBLEM_RDFT, mkplan, 0 };
|
|
S *slv = MKSOLVER(S, &sadt);
|
|
return &(slv->super);
|
|
}
|
|
|
|
void X(reodft11e_r2hc_register)(planner *p)
|
|
{
|
|
REGISTER_SOLVER(p, mksolver());
|
|
}
|