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furnace/extern/fftw/libbench2/verify-lib.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 "verify.h"
#include <math.h>
#include <stdlib.h>
#include <stdio.h>
/*
* Utility functions:
*/
static double dabs(double x) { return (x < 0.0) ? -x : x; }
static double dmin(double x, double y) { return (x < y) ? x : y; }
static double norm2(double x, double y) { return dmax(dabs(x), dabs(y)); }
double dmax(double x, double y) { return (x > y) ? x : y; }
static double aerror(C *a, C *b, int n)
{
if (n > 0) {
/* compute the relative Linf error */
double e = 0.0, mag = 0.0;
int i;
for (i = 0; i < n; ++i) {
e = dmax(e, norm2(c_re(a[i]) - c_re(b[i]),
c_im(a[i]) - c_im(b[i])));
mag = dmax(mag,
dmin(norm2(c_re(a[i]), c_im(a[i])),
norm2(c_re(b[i]), c_im(b[i]))));
}
e /= mag;
#ifdef HAVE_ISNAN
BENCH_ASSERT(!isnan(e));
#endif
return e;
} else
return 0.0;
}
#ifdef HAVE_DRAND48
# if defined(HAVE_DECL_DRAND48) && !HAVE_DECL_DRAND48
extern double drand48(void);
# endif
double mydrand(void)
{
return drand48() - 0.5;
}
#else
double mydrand(void)
{
double d = rand();
return (d / (double) RAND_MAX) - 0.5;
}
#endif
void arand(C *a, int n)
{
int i;
/* generate random inputs */
for (i = 0; i < n; ++i) {
c_re(a[i]) = mydrand();
c_im(a[i]) = mydrand();
}
}
/* make array real */
void mkreal(C *A, int n)
{
int i;
for (i = 0; i < n; ++i) {
c_im(A[i]) = 0.0;
}
}
static void assign_conj(C *Ac, C *A, int rank, const bench_iodim *dim, int stride)
{
if (rank == 0) {
c_re(*Ac) = c_re(*A);
c_im(*Ac) = -c_im(*A);
}
else {
int i, n0 = dim[rank - 1].n, s = stride;
rank -= 1;
stride *= n0;
assign_conj(Ac, A, rank, dim, stride);
for (i = 1; i < n0; ++i)
assign_conj(Ac + (n0 - i) * s, A + i * s, rank, dim, stride);
}
}
/* make array hermitian */
void mkhermitian(C *A, int rank, const bench_iodim *dim, int stride)
{
if (rank == 0)
c_im(*A) = 0.0;
else {
int i, n0 = dim[rank - 1].n, s = stride;
rank -= 1;
stride *= n0;
mkhermitian(A, rank, dim, stride);
for (i = 1; 2*i < n0; ++i)
assign_conj(A + (n0 - i) * s, A + i * s, rank, dim, stride);
if (2*i == n0)
mkhermitian(A + i * s, rank, dim, stride);
}
}
void mkhermitian1(C *a, int n)
{
bench_iodim d;
d.n = n;
d.is = d.os = 1;
mkhermitian(a, 1, &d, 1);
}
/* C = A */
void acopy(C *c, C *a, int n)
{
int i;
for (i = 0; i < n; ++i) {
c_re(c[i]) = c_re(a[i]);
c_im(c[i]) = c_im(a[i]);
}
}
/* C = A + B */
void aadd(C *c, C *a, C *b, int n)
{
int i;
for (i = 0; i < n; ++i) {
c_re(c[i]) = c_re(a[i]) + c_re(b[i]);
c_im(c[i]) = c_im(a[i]) + c_im(b[i]);
}
}
/* C = A - B */
void asub(C *c, C *a, C *b, int n)
{
int i;
for (i = 0; i < n; ++i) {
c_re(c[i]) = c_re(a[i]) - c_re(b[i]);
c_im(c[i]) = c_im(a[i]) - c_im(b[i]);
}
}
/* B = rotate left A (complex) */
void arol(C *b, C *a, int n, int nb, int na)
{
int i, ib, ia;
for (ib = 0; ib < nb; ++ib) {
for (i = 0; i < n - 1; ++i)
for (ia = 0; ia < na; ++ia) {
C *pb = b + (ib * n + i) * na + ia;
C *pa = a + (ib * n + i + 1) * na + ia;
c_re(*pb) = c_re(*pa);
c_im(*pb) = c_im(*pa);
}
for (ia = 0; ia < na; ++ia) {
C *pb = b + (ib * n + n - 1) * na + ia;
C *pa = a + ib * n * na + ia;
c_re(*pb) = c_re(*pa);
c_im(*pb) = c_im(*pa);
}
}
}
void aphase_shift(C *b, C *a, int n, int nb, int na, double sign)
{
int j, jb, ja;
trigreal twopin;
twopin = K2PI / n;
for (jb = 0; jb < nb; ++jb)
for (j = 0; j < n; ++j) {
trigreal s = sign * SIN(j * twopin);
trigreal c = COS(j * twopin);
for (ja = 0; ja < na; ++ja) {
int k = (jb * n + j) * na + ja;
c_re(b[k]) = c_re(a[k]) * c - c_im(a[k]) * s;
c_im(b[k]) = c_re(a[k]) * s + c_im(a[k]) * c;
}
}
}
/* A = alpha * A (complex, in place) */
void ascale(C *a, C alpha, int n)
{
int i;
for (i = 0; i < n; ++i) {
R xr = c_re(a[i]), xi = c_im(a[i]);
c_re(a[i]) = xr * c_re(alpha) - xi * c_im(alpha);
c_im(a[i]) = xr * c_im(alpha) + xi * c_re(alpha);
}
}
double acmp(C *a, C *b, int n, const char *test, double tol)
{
double d = aerror(a, b, n);
if (d > tol) {
ovtpvt_err("Found relative error %e (%s)\n", d, test);
{
int i, N;
N = n > 300 && verbose <= 2 ? 300 : n;
for (i = 0; i < N; ++i)
ovtpvt_err("%8d %16.12f %16.12f %16.12f %16.12f\n", i,
(double) c_re(a[i]), (double) c_im(a[i]),
(double) c_re(b[i]), (double) c_im(b[i]));
}
bench_exit(EXIT_FAILURE);
}
return d;
}
/*
* Implementation of the FFT tester described in
*
* Funda Erg<72>n. Testing multivariate linear functions: Overcoming the
* generator bottleneck. In Proceedings of the Twenty-Seventh Annual
* ACM Symposium on the Theory of Computing, pages 407-416, Las Vegas,
* Nevada, 29 May--1 June 1995.
*
* Also: F. Ergun, S. R. Kumar, and D. Sivakumar, "Self-testing without
* the generator bottleneck," SIAM J. on Computing 29 (5), 1630-51 (2000).
*/
static double impulse0(dofft_closure *k,
int n, int vecn,
C *inA, C *inB, C *inC,
C *outA, C *outB, C *outC,
C *tmp, int rounds, double tol)
{
int N = n * vecn;
double e = 0.0;
int j;
k->apply(k, inA, tmp);
e = dmax(e, acmp(tmp, outA, N, "impulse 1", tol));
for (j = 0; j < rounds; ++j) {
arand(inB, N);
asub(inC, inA, inB, N);
k->apply(k, inB, outB);
k->apply(k, inC, outC);
aadd(tmp, outB, outC, N);
e = dmax(e, acmp(tmp, outA, N, "impulse", tol));
}
return e;
}
double impulse(dofft_closure *k,
int n, int vecn,
C *inA, C *inB, C *inC,
C *outA, C *outB, C *outC,
C *tmp, int rounds, double tol)
{
int i, j;
double e = 0.0;
/* check impulsive input */
for (i = 0; i < vecn; ++i) {
R x = (sqrt(n)*(i+1)) / (double)(vecn+1);
for (j = 0; j < n; ++j) {
c_re(inA[j + i * n]) = 0;
c_im(inA[j + i * n]) = 0;
c_re(outA[j + i * n]) = x;
c_im(outA[j + i * n]) = 0;
}
c_re(inA[i * n]) = x;
c_im(inA[i * n]) = 0;
}
e = dmax(e, impulse0(k, n, vecn, inA, inB, inC, outA, outB, outC,
tmp, rounds, tol));
/* check constant input */
for (i = 0; i < vecn; ++i) {
R x = (i+1) / ((double)(vecn+1) * sqrt(n));
for (j = 0; j < n; ++j) {
c_re(inA[j + i * n]) = x;
c_im(inA[j + i * n]) = 0;
c_re(outA[j + i * n]) = 0;
c_im(outA[j + i * n]) = 0;
}
c_re(outA[i * n]) = n * x;
c_im(outA[i * n]) = 0;
}
e = dmax(e, impulse0(k, n, vecn, inA, inB, inC, outA, outB, outC,
tmp, rounds, tol));
return e;
}
double linear(dofft_closure *k, int realp,
int n, C *inA, C *inB, C *inC, C *outA,
C *outB, C *outC, C *tmp, int rounds, double tol)
{
int j;
double e = 0.0;
for (j = 0; j < rounds; ++j) {
C alpha, beta;
c_re(alpha) = mydrand();
c_im(alpha) = realp ? 0.0 : mydrand();
c_re(beta) = mydrand();
c_im(beta) = realp ? 0.0 : mydrand();
arand(inA, n);
arand(inB, n);
k->apply(k, inA, outA);
k->apply(k, inB, outB);
ascale(outA, alpha, n);
ascale(outB, beta, n);
aadd(tmp, outA, outB, n);
ascale(inA, alpha, n);
ascale(inB, beta, n);
aadd(inC, inA, inB, n);
k->apply(k, inC, outC);
e = dmax(e, acmp(outC, tmp, n, "linear", tol));
}
return e;
}
double tf_shift(dofft_closure *k,
int realp, const bench_tensor *sz,
int n, int vecn, double sign,
C *inA, C *inB, C *outA, C *outB, C *tmp,
int rounds, double tol, int which_shift)
{
int nb, na, dim, N = n * vecn;
int i, j;
double e = 0.0;
/* test 3: check the time-shift property */
/* the paper performs more tests, but this code should be fine too */
nb = 1;
na = n;
/* check shifts across all SZ dimensions */
for (dim = 0; dim < sz->rnk; ++dim) {
int ncur = sz->dims[dim].n;
na /= ncur;
for (j = 0; j < rounds; ++j) {
arand(inA, N);
if (which_shift == TIME_SHIFT) {
for (i = 0; i < vecn; ++i) {
if (realp) mkreal(inA + i * n, n);
arol(inB + i * n, inA + i * n, ncur, nb, na);
}
k->apply(k, inA, outA);
k->apply(k, inB, outB);
for (i = 0; i < vecn; ++i)
aphase_shift(tmp + i * n, outB + i * n, ncur,
nb, na, sign);
e = dmax(e, acmp(tmp, outA, N, "time shift", tol));
} else {
for (i = 0; i < vecn; ++i) {
if (realp)
mkhermitian(inA + i * n, sz->rnk, sz->dims, 1);
aphase_shift(inB + i * n, inA + i * n, ncur,
nb, na, -sign);
}
k->apply(k, inA, outA);
k->apply(k, inB, outB);
for (i = 0; i < vecn; ++i)
arol(tmp + i * n, outB + i * n, ncur, nb, na);
e = dmax(e, acmp(tmp, outA, N, "freq shift", tol));
}
}
nb *= ncur;
}
return e;
}
void preserves_input(dofft_closure *k, aconstrain constrain,
int n, C *inA, C *inB, C *outB, int rounds)
{
int j;
int recopy_input = k->recopy_input;
k->recopy_input = 1;
for (j = 0; j < rounds; ++j) {
arand(inA, n);
if (constrain)
constrain(inA, n);
acopy(inB, inA, n);
k->apply(k, inB, outB);
acmp(inB, inA, n, "preserves_input", 0.0);
}
k->recopy_input = recopy_input;
}
/* Make a copy of the size tensor, with the same dimensions, but with
the strides corresponding to a "packed" row-major array with the
given stride. */
bench_tensor *verify_pack(const bench_tensor *sz, int s)
{
bench_tensor *x = tensor_copy(sz);
if (BENCH_FINITE_RNK(x->rnk) && x->rnk > 0) {
int i;
x->dims[x->rnk - 1].is = s;
x->dims[x->rnk - 1].os = s;
for (i = x->rnk - 1; i > 0; --i) {
x->dims[i - 1].is = x->dims[i].is * x->dims[i].n;
x->dims[i - 1].os = x->dims[i].os * x->dims[i].n;
}
}
return x;
}
static int all_zero(C *a, int n)
{
int i;
for (i = 0; i < n; ++i)
if (c_re(a[i]) != 0.0 || c_im(a[i]) != 0.0)
return 0;
return 1;
}
static int one_accuracy_test(dofft_closure *k, aconstrain constrain,
int sign, int n, C *a, C *b,
double t[6])
{
double err[6];
if (constrain)
constrain(a, n);
if (all_zero(a, n))
return 0;
k->apply(k, a, b);
fftaccuracy(n, a, b, sign, err);
t[0] += err[0];
t[1] += err[1] * err[1];
t[2] = dmax(t[2], err[2]);
t[3] += err[3];
t[4] += err[4] * err[4];
t[5] = dmax(t[5], err[5]);
return 1;
}
void accuracy_test(dofft_closure *k, aconstrain constrain,
int sign, int n, C *a, C *b, int rounds, int impulse_rounds,
double t[6])
{
int r, i;
int ntests = 0;
bench_complex czero = {0, 0};
for (i = 0; i < 6; ++i) t[i] = 0.0;
for (r = 0; r < rounds; ++r) {
arand(a, n);
if (one_accuracy_test(k, constrain, sign, n, a, b, t))
++ntests;
}
/* impulses at beginning of array */
for (r = 0; r < impulse_rounds; ++r) {
if (r > n - r - 1)
continue;
caset(a, n, czero);
c_re(a[r]) = c_im(a[r]) = 1.0;
if (one_accuracy_test(k, constrain, sign, n, a, b, t))
++ntests;
}
/* impulses at end of array */
for (r = 0; r < impulse_rounds; ++r) {
if (r <= n - r - 1)
continue;
caset(a, n, czero);
c_re(a[n - r - 1]) = c_im(a[n - r - 1]) = 1.0;
if (one_accuracy_test(k, constrain, sign, n, a, b, t))
++ntests;
}
/* randomly-located impulses */
for (r = 0; r < impulse_rounds; ++r) {
caset(a, n, czero);
i = rand() % n;
c_re(a[i]) = c_im(a[i]) = 1.0;
if (one_accuracy_test(k, constrain, sign, n, a, b, t))
++ntests;
}
t[0] /= ntests;
t[1] = sqrt(t[1] / ntests);
t[3] /= ntests;
t[4] = sqrt(t[4] / ntests);
fftaccuracy_done();
}
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