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furnace/extern/fftw/reodft/reodft00e-splitradix.c

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/*
* Copyright (c) 2005 Matteo Frigo
* Copyright (c) 2005 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}DFT00 problem (of an odd length n) recursively via an
R{E,O}DFT00 problem and an RDFT problem of half the length.
This works by "logically" expanding the array to a real-even/odd DFT of
length 2n-/+2 and then applying the split-radix algorithm.
In this way, we can avoid having to pad to twice the length
(ala redft00-r2hc-pad), saving a factor of ~2 for n=2^m+/-1,
but don't incur the accuracy loss that the "ordinary" algorithm
sacrifices (ala redft00-r2hc.c).
*/
#include "reodft/reodft.h"
typedef struct {
solver super;
} S;
typedef struct {
plan_rdft super;
plan *clde, *cldo;
twid *td;
INT is, os;
INT n;
INT vl;
INT ivs, ovs;
} P;
/* redft00 */
static void apply_e(const plan *ego_, R *I, R *O)
{
const P *ego = (const P *) ego_;
INT is = ego->is, os = ego->os;
INT i, j, n = ego->n + 1, n2 = (n-1)/2;
INT iv, vl = ego->vl;
INT ivs = ego->ivs, ovs = ego->ovs;
R *W = ego->td->W - 2;
R *buf;
buf = (R *) MALLOC(sizeof(R) * n2, BUFFERS);
for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
/* do size (n-1)/2 r2hc transform of odd-indexed elements
with stride 4, "wrapping around" end of array with even
boundary conditions */
for (j = 0, i = 1; i < n; i += 4)
buf[j++] = I[is * i];
for (i = 2*n-2-i; i > 0; i -= 4)
buf[j++] = I[is * i];
{
plan_rdft *cld = (plan_rdft *) ego->cldo;
cld->apply((plan *) cld, buf, buf);
}
/* do size (n+1)/2 redft00 of the even-indexed elements,
writing to O: */
{
plan_rdft *cld = (plan_rdft *) ego->clde;
cld->apply((plan *) cld, I, O);
}
/* combine the results with the twiddle factors to get output */
{ /* DC element */
E b20 = O[0], b0 = K(2.0) * buf[0];
O[0] = b20 + b0;
O[2*(n2*os)] = b20 - b0;
/* O[n2*os] = O[n2*os]; */
}
for (i = 1; i < n2 - i; ++i) {
E ap, am, br, bi, wr, wi, wbr, wbi;
br = buf[i];
bi = buf[n2 - i];
wr = W[2*i];
wi = W[2*i+1];
#if FFT_SIGN == -1
wbr = K(2.0) * (wr*br + wi*bi);
wbi = K(2.0) * (wr*bi - wi*br);
#else
wbr = K(2.0) * (wr*br - wi*bi);
wbi = K(2.0) * (wr*bi + wi*br);
#endif
ap = O[i*os];
O[i*os] = ap + wbr;
O[(2*n2 - i)*os] = ap - wbr;
am = O[(n2 - i)*os];
#if FFT_SIGN == -1
O[(n2 - i)*os] = am - wbi;
O[(n2 + i)*os] = am + wbi;
#else
O[(n2 - i)*os] = am + wbi;
O[(n2 + i)*os] = am - wbi;
#endif
}
if (i == n2 - i) { /* Nyquist element */
E ap, wbr;
wbr = K(2.0) * (W[2*i] * buf[i]);
ap = O[i*os];
O[i*os] = ap + wbr;
O[(2*n2 - i)*os] = ap - wbr;
}
}
X(ifree)(buf);
}
/* rodft00 */
static void apply_o(const plan *ego_, R *I, R *O)
{
const P *ego = (const P *) ego_;
INT is = ego->is, os = ego->os;
INT i, j, n = ego->n - 1, n2 = (n+1)/2;
INT iv, vl = ego->vl;
INT ivs = ego->ivs, ovs = ego->ovs;
R *W = ego->td->W - 2;
R *buf;
buf = (R *) MALLOC(sizeof(R) * n2, BUFFERS);
for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
/* do size (n+1)/2 r2hc transform of even-indexed elements
with stride 4, "wrapping around" end of array with odd
boundary conditions */
for (j = 0, i = 0; i < n; i += 4)
buf[j++] = I[is * i];
for (i = 2*n-i; i > 0; i -= 4)
buf[j++] = -I[is * i];
{
plan_rdft *cld = (plan_rdft *) ego->cldo;
cld->apply((plan *) cld, buf, buf);
}
/* do size (n-1)/2 rodft00 of the odd-indexed elements,
writing to O: */
{
plan_rdft *cld = (plan_rdft *) ego->clde;
if (I == O) {
/* can't use I+is and I, subplan would lose in-placeness */
cld->apply((plan *) cld, I + is, I + is);
/* we could maybe avoid this copy by modifying the
twiddle loop, but currently I can't be bothered. */
A(is >= os);
for (i = 0; i < n2-1; ++i)
O[os*i] = I[is*(i+1)];
}
else
cld->apply((plan *) cld, I + is, O);
}
/* combine the results with the twiddle factors to get output */
O[(n2-1)*os] = K(2.0) * buf[0];
for (i = 1; i < n2 - i; ++i) {
E ap, am, br, bi, wr, wi, wbr, wbi;
br = buf[i];
bi = buf[n2 - i];
wr = W[2*i];
wi = W[2*i+1];
#if FFT_SIGN == -1
wbr = K(2.0) * (wr*br + wi*bi);
wbi = K(2.0) * (wi*br - wr*bi);
#else
wbr = K(2.0) * (wr*br - wi*bi);
wbi = K(2.0) * (wr*bi + wi*br);
#endif
ap = O[(i-1)*os];
O[(i-1)*os] = wbi + ap;
O[(2*n2-1 - i)*os] = wbi - ap;
am = O[(n2-1 - i)*os];
#if FFT_SIGN == -1
O[(n2-1 - i)*os] = wbr + am;
O[(n2-1 + i)*os] = wbr - am;
#else
O[(n2-1 - i)*os] = wbr + am;
O[(n2-1 + i)*os] = wbr - am;
#endif
}
if (i == n2 - i) { /* Nyquist element */
E ap, wbi;
wbi = K(2.0) * (W[2*i+1] * buf[i]);
ap = O[(i-1)*os];
O[(i-1)*os] = wbi + ap;
O[(2*n2-1 - i)*os] = wbi - ap;
}
}
X(ifree)(buf);
}
static void awake(plan *ego_, enum wakefulness wakefulness)
{
P *ego = (P *) ego_;
static const tw_instr reodft00e_tw[] = {
{ TW_COS, 1, 1 },
{ TW_SIN, 1, 1 },
{ TW_NEXT, 1, 0 }
};
X(plan_awake)(ego->clde, wakefulness);
X(plan_awake)(ego->cldo, wakefulness);
X(twiddle_awake)(wakefulness, &ego->td, reodft00e_tw,
2*ego->n, 1, ego->n/4);
}
static void destroy(plan *ego_)
{
P *ego = (P *) ego_;
X(plan_destroy_internal)(ego->cldo);
X(plan_destroy_internal)(ego->clde);
}
static void print(const plan *ego_, printer *p)
{
const P *ego = (const P *) ego_;
if (ego->super.apply == apply_e)
p->print(p, "(redft00e-splitradix-%D%v%(%p%)%(%p%))",
ego->n + 1, ego->vl, ego->clde, ego->cldo);
else
p->print(p, "(rodft00e-splitradix-%D%v%(%p%)%(%p%))",
ego->n - 1, ego->vl, ego->clde, ego->cldo);
}
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] == REDFT00 || p->kind[0] == RODFT00)
&& p->sz->dims[0].n > 1 /* don't create size-0 sub-plans */
&& p->sz->dims[0].n % 2 /* odd: 4 divides "logical" DFT */
&& (p->I != p->O || p->vecsz->rnk == 0
|| p->vecsz->dims[0].is == p->vecsz->dims[0].os)
&& (p->kind[0] != RODFT00 || p->I != p->O ||
p->sz->dims[0].is >= p->sz->dims[0].os) /* laziness */
);
}
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 *clde, *cldo;
R *buf;
INT n, n0;
opcnt ops;
int inplace_odd;
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 = (n0 = p->sz->dims[0].n) + (p->kind[0] == REDFT00 ? (INT)-1 : (INT)1);
A(n > 0 && n % 2 == 0);
buf = (R *) MALLOC(sizeof(R) * (n/2), BUFFERS);
inplace_odd = p->kind[0]==RODFT00 && p->I == p->O;
clde = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(
X(mktensor_1d)(n0-n/2, 2*p->sz->dims[0].is,
inplace_odd ? p->sz->dims[0].is
: p->sz->dims[0].os),
X(mktensor_0d)(),
TAINT(p->I
+ p->sz->dims[0].is * (p->kind[0]==RODFT00),
p->vecsz->rnk ? p->vecsz->dims[0].is : 0),
TAINT(p->O
+ p->sz->dims[0].is * inplace_odd,
p->vecsz->rnk ? p->vecsz->dims[0].os : 0),
p->kind[0]));
if (!clde) {
X(ifree)(buf);
return (plan *)0;
}
cldo = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(
X(mktensor_1d)(n/2, 1, 1),
X(mktensor_0d)(),
buf, buf, R2HC));
X(ifree)(buf);
if (!cldo)
return (plan *)0;
pln = MKPLAN_RDFT(P, &padt, p->kind[0] == REDFT00 ? apply_e : apply_o);
pln->n = n;
pln->is = p->sz->dims[0].is;
pln->os = p->sz->dims[0].os;
pln->clde = clde;
pln->cldo = cldo;
pln->td = 0;
X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
X(ops_zero)(&ops);
ops.other = n/2;
ops.add = (p->kind[0]==REDFT00 ? (INT)2 : (INT)0) +
(n/2-1)/2 * 6 + ((n/2)%2==0) * 2;
ops.mul = 1 + (n/2-1)/2 * 6 + ((n/2)%2==0) * 2;
/* tweak ops.other so that r2hc-pad is used for small sizes, which
seems to be a lot faster on my machine: */
ops.other += 256;
X(ops_zero)(&pln->super.super.ops);
X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops);
X(ops_madd2)(pln->vl, &clde->ops, &pln->super.super.ops);
X(ops_madd2)(pln->vl, &cldo->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(reodft00e_splitradix_register)(planner *p)
{
REGISTER_SOLVER(p, mksolver());
}
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