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furnace/extern/fftw/dft/bluestein.c

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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
*
*/
#include "dft/dft.h"
typedef struct {
solver super;
} S;
typedef struct {
plan_dft super;
INT n; /* problem size */
INT nb; /* size of convolution */
R *w; /* lambda k . exp(2*pi*i*k^2/(2*n)) */
R *W; /* DFT(w) */
plan *cldf;
INT is, os;
} P;
static void bluestein_sequence(enum wakefulness wakefulness, INT n, R *w)
{
INT k, ksq, n2 = 2 * n;
triggen *t = X(mktriggen)(wakefulness, n2);
ksq = 0;
for (k = 0; k < n; ++k) {
t->cexp(t, ksq, w+2*k);
/* careful with overflow */
ksq += 2*k + 1; while (ksq > n2) ksq -= n2;
}
X(triggen_destroy)(t);
}
static void mktwiddle(enum wakefulness wakefulness, P *p)
{
INT i;
INT n = p->n, nb = p->nb;
R *w, *W;
E nbf = (E)nb;
p->w = w = (R *) MALLOC(2 * n * sizeof(R), TWIDDLES);
p->W = W = (R *) MALLOC(2 * nb * sizeof(R), TWIDDLES);
bluestein_sequence(wakefulness, n, w);
for (i = 0; i < nb; ++i)
W[2*i] = W[2*i+1] = K(0.0);
W[0] = w[0] / nbf;
W[1] = w[1] / nbf;
for (i = 1; i < n; ++i) {
W[2*i] = W[2*(nb-i)] = w[2*i] / nbf;
W[2*i+1] = W[2*(nb-i)+1] = w[2*i+1] / nbf;
}
{
plan_dft *cldf = (plan_dft *)p->cldf;
/* cldf must be awake */
cldf->apply(p->cldf, W, W+1, W, W+1);
}
}
static void apply(const plan *ego_, R *ri, R *ii, R *ro, R *io)
{
const P *ego = (const P *) ego_;
INT i, n = ego->n, nb = ego->nb, is = ego->is, os = ego->os;
R *w = ego->w, *W = ego->W;
R *b = (R *) MALLOC(2 * nb * sizeof(R), BUFFERS);
/* multiply input by conjugate bluestein sequence */
for (i = 0; i < n; ++i) {
E xr = ri[i*is], xi = ii[i*is];
E wr = w[2*i], wi = w[2*i+1];
b[2*i] = xr * wr + xi * wi;
b[2*i+1] = xi * wr - xr * wi;
}
for (; i < nb; ++i) b[2*i] = b[2*i+1] = K(0.0);
/* convolution: FFT */
{
plan_dft *cldf = (plan_dft *)ego->cldf;
cldf->apply(ego->cldf, b, b+1, b, b+1);
}
/* convolution: pointwise multiplication */
for (i = 0; i < nb; ++i) {
E xr = b[2*i], xi = b[2*i+1];
E wr = W[2*i], wi = W[2*i+1];
b[2*i] = xi * wr + xr * wi;
b[2*i+1] = xr * wr - xi * wi;
}
/* convolution: IFFT by FFT with real/imag input/output swapped */
{
plan_dft *cldf = (plan_dft *)ego->cldf;
cldf->apply(ego->cldf, b, b+1, b, b+1);
}
/* multiply output by conjugate bluestein sequence */
for (i = 0; i < n; ++i) {
E xi = b[2*i], xr = b[2*i+1];
E wr = w[2*i], wi = w[2*i+1];
ro[i*os] = xr * wr + xi * wi;
io[i*os] = xi * wr - xr * wi;
}
X(ifree)(b);
}
static void awake(plan *ego_, enum wakefulness wakefulness)
{
P *ego = (P *) ego_;
X(plan_awake)(ego->cldf, wakefulness);
switch (wakefulness) {
case SLEEPY:
X(ifree0)(ego->w); ego->w = 0;
X(ifree0)(ego->W); ego->W = 0;
break;
default:
A(!ego->w);
mktwiddle(wakefulness, ego);
break;
}
}
static int applicable(const solver *ego, const problem *p_,
const planner *plnr)
{
const problem_dft *p = (const problem_dft *) p_;
UNUSED(ego);
return (1
&& p->sz->rnk == 1
&& p->vecsz->rnk == 0
/* FIXME: allow other sizes */
&& X(is_prime)(p->sz->dims[0].n)
/* FIXME: avoid infinite recursion of bluestein with itself.
This works because all factors in child problems are 2, 3, 5 */
&& p->sz->dims[0].n > 16
&& CIMPLIES(NO_SLOWP(plnr), p->sz->dims[0].n > BLUESTEIN_MAX_SLOW)
);
}
static void destroy(plan *ego_)
{
P *ego = (P *) ego_;
X(plan_destroy_internal)(ego->cldf);
}
static void print(const plan *ego_, printer *p)
{
const P *ego = (const P *)ego_;
p->print(p, "(dft-bluestein-%D/%D%(%p%))",
ego->n, ego->nb, ego->cldf);
}
static INT choose_transform_size(INT minsz)
{
while (!X(factors_into_small_primes)(minsz))
++minsz;
return minsz;
}
static plan *mkplan(const solver *ego, const problem *p_, planner *plnr)
{
const problem_dft *p = (const problem_dft *) p_;
P *pln;
INT n, nb;
plan *cldf = 0;
R *buf = (R *) 0;
static const plan_adt padt = {
X(dft_solve), awake, print, destroy
};
if (!applicable(ego, p_, plnr))
return (plan *) 0;
n = p->sz->dims[0].n;
nb = choose_transform_size(2 * n - 1);
buf = (R *) MALLOC(2 * nb * sizeof(R), BUFFERS);
cldf = X(mkplan_f_d)(plnr,
X(mkproblem_dft_d)(X(mktensor_1d)(nb, 2, 2),
X(mktensor_1d)(1, 0, 0),
buf, buf+1,
buf, buf+1),
NO_SLOW, 0, 0);
if (!cldf) goto nada;
X(ifree)(buf);
pln = MKPLAN_DFT(P, &padt, apply);
pln->n = n;
pln->nb = nb;
pln->w = 0;
pln->W = 0;
pln->cldf = cldf;
pln->is = p->sz->dims[0].is;
pln->os = p->sz->dims[0].os;
X(ops_add)(&cldf->ops, &cldf->ops, &pln->super.super.ops);
pln->super.super.ops.add += 4 * n + 2 * nb;
pln->super.super.ops.mul += 8 * n + 4 * nb;
pln->super.super.ops.other += 6 * (n + nb);
return &(pln->super.super);
nada:
X(ifree0)(buf);
X(plan_destroy_internal)(cldf);
return (plan *)0;
}
static solver *mksolver(void)
{
static const solver_adt sadt = { PROBLEM_DFT, mkplan, 0 };
S *slv = MKSOLVER(S, &sadt);
return &(slv->super);
}
void X(dft_bluestein_register)(planner *p)
{
REGISTER_SOLVER(p, mksolver());
}
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