/*
* 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
*
*/
#include "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.)
*/
typedef struct {
solver super;
} S;
typedef struct {
plan_rdft super;
plan *cld1, *cld2;
R *omega;
int n, 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 r = ego->n;
int is = ego->is, os;
int k, gpower, g;
R *buf, *omega;
R r0;
buf = (R *) MALLOC(sizeof(R) * (r - 1), BUFFERS);
/* First, permute the input, storing in buf: */
g = ego->g;
for (gpower = 1, k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
buf[k] = I[gpower * is];
}
/* gpower == g^(r-1) mod r == 1 */;
os = ego->os;
/* compute RDFT of buf, storing in output (except DC): */
{
plan_rdft *cld = (plan_rdft *) ego->cld1;
cld->apply((plan *) cld, buf, O + os);
}
/* set output DC component: */
O[0] = (r0 = I[0]) + O[os];
/* now, multiply by omega: */
omega = ego->omega;
O[(0 + 1) * os] *= omega[0];
#if R2HC_ONLY_CONV
for (k = 1; k < (r - 1)/2; ++k) {
E rB, iB, rW, iW, a, b;
rW = omega[k];
iW = omega[(r-1) - k];
rB = O[(k + 1) * os];
iB = O[((r-1) - k + 1) * os];
a = rW * rB - iW * iB;
b = rW * iB + iW * rB;
O[(k + 1) * os] = a + b;
O[((r-1) - k + 1) * os] = a - b;
}
#else
for (k = 1; k < (r - 1)/2; ++k) {
E rB, iB, rW, iW;
rW = omega[k];
iW = omega[(r-1) - k];
rB = O[(k + 1) * os];
iB = O[((r-1) - k + 1) * os];
O[(k + 1) * os] = rW * rB - iW * iB;
O[((r-1) - k + 1) * os] = rW * iB + iW * rB;
}
#endif
/* Nyquist component: */
O[(k + 1) * os] *= omega[k]; /* k == (r-1)/2, since r-1 is even */
/* this will add input[0] to all of the outputs after the ifft */
O[os] += r0;
/* inverse FFT: */
{
plan_rdft *cld = (plan_rdft *) ego->cld2;
cld->apply((plan *) cld, O + os, buf);
}
/* do inverse permutation to unshuffle the output: */
A(gpower == 1);
#if R2HC_ONLY_CONV
O[os] = buf[0];
gpower = g = ego->ginv;
for (k = 1; k < (r - 1)/2; ++k, gpower = MULMOD(gpower, g, r)) {
O[gpower * os] = buf[k] + buf[r - 1 - k];
}
O[gpower * os] = buf[k];
++k, gpower = MULMOD(gpower, g, r);
for (; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
O[gpower * os] = buf[r - 1 - k] - buf[k];
}
#else
g = ego->ginv;
for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
O[gpower * os] = buf[k];
}
#endif
A(gpower == 1);
X(ifree)(buf);
}
static R *mkomega(plan *p_, int n, int ginv)
{
plan_rdft *p = (plan_rdft *) p_;
R *omega;
int i, gpower;
trigreal scale;
if ((omega = X(rader_tl_find)(n, n, ginv, omegas)))
return omega;
omega = (R *)MALLOC(sizeof(R) * (n - 1), TWIDDLES);
scale = n - 1.0; /* normalization for convolution */
for (i = 0, gpower = 1; i < n-1; ++i, gpower = MULMOD(gpower, ginv, n)) {
omega[i] = (X(cos2pi)(gpower, n) + X(sin2pi)(gpower, n)) / scale;
}
A(gpower == 1);
AWAKE(p_, 1);
p->apply(p_, omega, omega);
AWAKE(p_, 0);
X(rader_tl_insert)(n, n, ginv, omega, &omegas);
return omega;
}
static void free_omega(R *omega)
{
X(rader_tl_delete)(omega, &omegas);
}
/***************************************************************************/
static void awake(plan *ego_, int flg)
{
P *ego = (P *) ego_;
AWAKE(ego->cld1, flg);
AWAKE(ego->cld2, flg);
if (flg) {
if (!ego->omega)
ego->omega = mkomega(ego->cld_omega,ego->n,ego->ginv);
} else {
free_omega(ego->omega);
ego->omega = 0;
}
}
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%ois=%oos=%(%p%)",
ego->n, 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 applicable0(const problem *p_)
{
if (RDFTP(p_)) {
const problem_rdft *p = (const problem_rdft *) p_;
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
);
}
return 0;
}
static int applicable(const solver *ego, const problem *p, const planner *plnr)
{
UNUSED(ego);
return (!NO_UGLYP(plnr) && applicable0(p));
}
static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
{
const problem_rdft *p = (const problem_rdft *) p_;
P *pln;
int n;
int is, os;
plan *cld1 = (plan *) 0;
plan *cld2 = (plan *) 0;
plan *cld_omega = (plan *) 0;
R *buf = (R *) 0;
R *O;
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;
O = p->O;
/* initial allocation for the purpose of planning */
buf = (R *) MALLOC(sizeof(R) * (n - 1), BUFFERS);
cld1 = X(mkplan_d)(plnr,
X(mkproblem_rdft_1_d)(X(mktensor_1d)(n - 1, 1, os),
X(mktensor_1d)(1, 0, 0),
buf,
O + os,
R2HC));
if (!cld1) goto nada;
cldp =
X(mkproblem_rdft_1_d)(
X(mktensor_1d)(n - 1, os, 1),
X(mktensor_1d)(1, 0, 0),
O + os,
buf,
#if R2HC_ONLY_CONV
R2HC
#else
HC2R
#endif
);
if (!(cld2 = X(mkplan_d)(plnr, cldp))) goto nada;
/* plan for omega */
plnr->planner_flags |= ESTIMATE;
cld_omega = X(mkplan_d)(plnr,
X(mkproblem_rdft_1_d)(X(mktensor_1d)(n - 1, 1, 1),
X(mktensor_1d)(1, 0, 0),
buf, buf, R2HC));
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->is = is;
pln->os = os;
pln->g = X(find_generator)(n);
pln->ginv = X(power_mod)(pln->g, n - 2, n);
A(MULMOD(pln->g, pln->ginv, n) == 1);
X(ops_add)(&cld1->ops, &cld2->ops, &pln->super.super.ops);
pln->super.super.ops.other += (n - 3) * 3 + (n - 2) * 2 + 5;
pln->super.super.ops.add += (n - 3) * 1;
pln->super.super.ops.mul += (n - 3) * 2 + 2;
#if R2HC_ONLY_CONV
pln->super.super.ops.other += (n - 2) + 4;
pln->super.super.ops.add += (n - 3) * 1 + (n - 2) * 1;
#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(void)
{
static const solver_adt sadt = { mkplan };
S *slv = MKSOLVER(S, &sadt);
return &(slv->super);
}
void X(dht_rader_register)(planner *p)
{
REGISTER_SOLVER(p, mksolver());
}