etc
/
furnace
mirror of https://github.com/tildearrow/furnace.git
0
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity
furnace/extern/fftw/rdft/dht-rader.c

387 lines
10 KiB
C
Raw Permalink Blame History

/*
* 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 "rdft/rdft.h"
/*
* Compute DHTs of prime sizes using Rader's trick: turn them
* into convolutions of size n - 1, which we then perform via a pair
* of FFTs. (We can then do prime real FFTs via rdft-dht.c.)
*
* Optionally (determined by the "pad" field of the solver), we can
* perform the (cyclic) convolution by zero-padding to a size
* >= 2*(n-1) - 1. This is advantageous if n-1 has large prime factors.
*
*/
typedef struct {
solver super;
int pad;
} S;
typedef struct {
plan_rdft super;
plan *cld1, *cld2;
R *omega;
INT n, npad, g, ginv;
INT is, os;
plan *cld_omega;
} P;
static rader_tl *omegas = 0;
/***************************************************************************/
/* If R2HC_ONLY_CONV is 1, we use a trick to perform the convolution
purely in terms of R2HC transforms, as opposed to R2HC followed by H2RC.
This requires a few more operations, but allows us to share the same
plan/codelets for both Rader children. */
#define R2HC_ONLY_CONV 1
static void apply(const plan *ego_, R *I, R *O)
{
const P *ego = (const P *) ego_;
INT n = ego->n; /* prime */
INT npad = ego->npad; /* == n - 1 for unpadded Rader; always even */
INT is = ego->is, os;
INT k, gpower, g;
R *buf, *omega;
R r0;
buf = (R *) MALLOC(sizeof(R) * npad, BUFFERS);
/* First, permute the input, storing in buf: */
g = ego->g;
for (gpower = 1, k = 0; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
buf[k] = I[gpower * is];
}
/* gpower == g^(n-1) mod n == 1 */;
A(n - 1 <= npad);
for (k = n - 1; k < npad; ++k) /* optionally, zero-pad convolution */
buf[k] = 0;
os = ego->os;
/* compute RDFT of buf, storing in buf (i.e., in-place): */
{
plan_rdft *cld = (plan_rdft *) ego->cld1;
cld->apply((plan *) cld, buf, buf);
}
/* set output DC component: */
O[0] = (r0 = I[0]) + buf[0];
/* now, multiply by omega: */
omega = ego->omega;
buf[0] *= omega[0];
for (k = 1; k < npad/2; ++k) {
E rB, iB, rW, iW, a, b;
rW = omega[k];
iW = omega[npad - k];
rB = buf[k];
iB = buf[npad - k];
a = rW * rB - iW * iB;
b = rW * iB + iW * rB;
#if R2HC_ONLY_CONV
buf[k] = a + b;
buf[npad - k] = a - b;
#else
buf[k] = a;
buf[npad - k] = b;
#endif
}
/* Nyquist component: */
A(k + k == npad); /* since npad is even */
buf[k] *= omega[k];
/* this will add input[0] to all of the outputs after the ifft */
buf[0] += r0;
/* inverse FFT: */
{
plan_rdft *cld = (plan_rdft *) ego->cld2;
cld->apply((plan *) cld, buf, buf);
}
/* do inverse permutation to unshuffle the output: */
A(gpower == 1);
#if R2HC_ONLY_CONV
O[os] = buf[0];
gpower = g = ego->ginv;
A(npad == n - 1 || npad/2 >= n - 1);
if (npad == n - 1) {
for (k = 1; k < npad/2; ++k, gpower = MULMOD(gpower, g, n)) {
O[gpower * os] = buf[k] + buf[npad - k];
}
O[gpower * os] = buf[k];
++k, gpower = MULMOD(gpower, g, n);
for (; k < npad; ++k, gpower = MULMOD(gpower, g, n)) {
O[gpower * os] = buf[npad - k] - buf[k];
}
}
else {
for (k = 1; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
O[gpower * os] = buf[k] + buf[npad - k];
}
}
#else
g = ego->ginv;
for (k = 0; k < n - 1; ++k, gpower = MULMOD(gpower, g, n)) {
O[gpower * os] = buf[k];
}
#endif
A(gpower == 1);
X(ifree)(buf);
}
static R *mkomega(enum wakefulness wakefulness,
plan *p_, INT n, INT npad, INT ginv)
{
plan_rdft *p = (plan_rdft *) p_;
R *omega;
INT i, gpower;
trigreal scale;
triggen *t;
if ((omega = X(rader_tl_find)(n, npad + 1, ginv, omegas)))
return omega;
omega = (R *)MALLOC(sizeof(R) * npad, TWIDDLES);
scale = npad; /* normalization for convolution */
t = X(mktriggen)(wakefulness, n);
for (i = 0, gpower = 1; i < n-1; ++i, gpower = MULMOD(gpower, ginv, n)) {
trigreal w[2];
t->cexpl(t, gpower, w);
omega[i] = (w[0] + w[1]) / scale;
}
X(triggen_destroy)(t);
A(gpower == 1);
A(npad == n - 1 || npad >= 2*(n - 1) - 1);
for (; i < npad; ++i)
omega[i] = K(0.0);
if (npad > n - 1)
for (i = 1; i < n-1; ++i)
omega[npad - i] = omega[n - 1 - i];
p->apply(p_, omega, omega);
X(rader_tl_insert)(n, npad + 1, ginv, omega, &omegas);
return omega;
}
static void free_omega(R *omega)
{
X(rader_tl_delete)(omega, &omegas);
}
/***************************************************************************/
static void awake(plan *ego_, enum wakefulness wakefulness)
{
P *ego = (P *) ego_;
X(plan_awake)(ego->cld1, wakefulness);
X(plan_awake)(ego->cld2, wakefulness);
X(plan_awake)(ego->cld_omega, wakefulness);
switch (wakefulness) {
case SLEEPY:
free_omega(ego->omega);
ego->omega = 0;
break;
default:
ego->g = X(find_generator)(ego->n);
ego->ginv = X(power_mod)(ego->g, ego->n - 2, ego->n);
A(MULMOD(ego->g, ego->ginv, ego->n) == 1);
A(!ego->omega);
ego->omega = mkomega(wakefulness,
ego->cld_omega,ego->n,ego->npad,ego->ginv);
break;
}
}
static void destroy(plan *ego_)
{
P *ego = (P *) ego_;
X(plan_destroy_internal)(ego->cld_omega);
X(plan_destroy_internal)(ego->cld2);
X(plan_destroy_internal)(ego->cld1);
}
static void print(const plan *ego_, printer *p)
{
const P *ego = (const P *) ego_;
p->print(p, "(dht-rader-%D/%D%ois=%oos=%(%p%)",
ego->n, ego->npad, ego->is, ego->os, ego->cld1);
if (ego->cld2 != ego->cld1)
p->print(p, "%(%p%)", ego->cld2);
if (ego->cld_omega != ego->cld1 && ego->cld_omega != ego->cld2)
p->print(p, "%(%p%)", ego->cld_omega);
p->putchr(p, ')');
}
static int applicable(const solver *ego, const problem *p_, const planner *plnr)
{
const problem_rdft *p = (const problem_rdft *) p_;
UNUSED(ego);
return (1
&& p->sz->rnk == 1
&& p->vecsz->rnk == 0
&& p->kind[0] == DHT
&& X(is_prime)(p->sz->dims[0].n)
&& p->sz->dims[0].n > 2
&& CIMPLIES(NO_SLOWP(plnr), p->sz->dims[0].n > RADER_MAX_SLOW)
/* proclaim the solver SLOW if p-1 is not easily
factorizable. Unlike in the complex case where
Bluestein can solve the problem, in the DHT case we
may have no other choice */
&& CIMPLIES(NO_SLOWP(plnr), X(factors_into_small_primes)(p->sz->dims[0].n - 1))
);
}
static INT choose_transform_size(INT minsz)
{
static const INT primes[] = { 2, 3, 5, 0 };
while (!X(factors_into)(minsz, primes) || minsz % 2)
++minsz;
return minsz;
}
static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
{
const S *ego = (const S *) ego_;
const problem_rdft *p = (const problem_rdft *) p_;
P *pln;
INT n, npad;
INT is, os;
plan *cld1 = (plan *) 0;
plan *cld2 = (plan *) 0;
plan *cld_omega = (plan *) 0;
R *buf = (R *) 0;
problem *cldp;
static const plan_adt padt = {
X(rdft_solve), awake, print, destroy
};
if (!applicable(ego_, p_, plnr))
return (plan *) 0;
n = p->sz->dims[0].n;
is = p->sz->dims[0].is;
os = p->sz->dims[0].os;
if (ego->pad)
npad = choose_transform_size(2 * (n - 1) - 1);
else
npad = n - 1;
/* initial allocation for the purpose of planning */
buf = (R *) MALLOC(sizeof(R) * npad, BUFFERS);
cld1 = X(mkplan_f_d)(plnr,
X(mkproblem_rdft_1_d)(X(mktensor_1d)(npad, 1, 1),
X(mktensor_1d)(1, 0, 0),
buf, buf,
R2HC),
NO_SLOW, 0, 0);
if (!cld1) goto nada;
cldp =
X(mkproblem_rdft_1_d)(
X(mktensor_1d)(npad, 1, 1),
X(mktensor_1d)(1, 0, 0),
buf, buf,
#if R2HC_ONLY_CONV
R2HC
#else
HC2R
#endif
);
if (!(cld2 = X(mkplan_f_d)(plnr, cldp, NO_SLOW, 0, 0)))
goto nada;
/* plan for omega */
cld_omega = X(mkplan_f_d)(plnr,
X(mkproblem_rdft_1_d)(
X(mktensor_1d)(npad, 1, 1),
X(mktensor_1d)(1, 0, 0),
buf, buf, R2HC),
NO_SLOW, ESTIMATE, 0);
if (!cld_omega) goto nada;
/* deallocate buffers; let awake() or apply() allocate them for real */
X(ifree)(buf);
buf = 0;
pln = MKPLAN_RDFT(P, &padt, apply);
pln->cld1 = cld1;
pln->cld2 = cld2;
pln->cld_omega = cld_omega;
pln->omega = 0;
pln->n = n;
pln->npad = npad;
pln->is = is;
pln->os = os;
X(ops_add)(&cld1->ops, &cld2->ops, &pln->super.super.ops);
pln->super.super.ops.other += (npad/2-1)*6 + npad + n + (n-1) * ego->pad;
pln->super.super.ops.add += (npad/2-1)*2 + 2 + (n-1) * ego->pad;
pln->super.super.ops.mul += (npad/2-1)*4 + 2 + ego->pad;
#if R2HC_ONLY_CONV
pln->super.super.ops.other += n-2 - ego->pad;
pln->super.super.ops.add += (npad/2-1)*2 + (n-2) - ego->pad;
#endif
return &(pln->super.super);
nada:
X(ifree0)(buf);
X(plan_destroy_internal)(cld_omega);
X(plan_destroy_internal)(cld2);
X(plan_destroy_internal)(cld1);
return 0;
}
/* constructors */
static solver *mksolver(int pad)
{
static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
S *slv = MKSOLVER(S, &sadt);
slv->pad = pad;
return &(slv->super);
}
void X(dht_rader_register)(planner *p)
{
REGISTER_SOLVER(p, mksolver(0));
REGISTER_SOLVER(p, mksolver(1));
}
Reference in New Issue View Git Blame Copy Permalink