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This commit is contained in:
Sergey Lapin
2025-07-12 12:17:44 +03:00
parent c759f60ff7
commit 792e1b937a
3507 changed files with 492613 additions and 0 deletions
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fftw-3.3.10/reodft/reodft11e-r2hc.c Normal file
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/*
* 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());
}