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|
/* GSL-GENFFT - Power2 FFT C Code Generator
* Copyright (C) 2001 Tim Janik
*
* 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 <gsl/gslcommon.h>
#include <gsl/gslmath.h>
#include <gsl/gslfft.h>
#include <sys/time.h>
#include <stdlib.h>
#include <string.h>
#define MAX_FFT_SIZE (65536 * 2)
#define EPSILON (4.8e-6)
/* --- prototypes --- */
static void reference_power2_fftc (unsigned int n_values,
const double *rivalues_in,
double *rivalues_out,
int esign);
static void fill_rand (guint n,
double *a);
static double diff (guint m,
guint p,
double *a1,
double *a2,
const gchar *str);
/* --- variables --- */
static double ref_fft_in[MAX_FFT_SIZE] = { 0, };
static double ref_fft_aout[MAX_FFT_SIZE] = { 0, };
static double ref_fft_sout[MAX_FFT_SIZE] = { 0, };
static double work_fft_in[MAX_FFT_SIZE] = { 0, };
static double work_fft_aout[MAX_FFT_SIZE] = { 0, };
static double work_fft_sout[MAX_FFT_SIZE] = { 0, };
/* --- functions --- */
int
main (int argc,
char *argv[])
{
struct timeval tv;
guint i;
/* initialize GSL */
if (!g_thread_supported ())
g_thread_init (NULL);
gsl_init (NULL, NULL);
/* initialize random numbers */
gettimeofday (&tv, NULL);
srand (tv.tv_sec ^ tv.tv_usec);
/* run tests */
for (i = 2; i <= MAX_FFT_SIZE >> 1; i <<= 1)
{
double d;
g_print ("Testing fft code for size %u\n", i);
/* setup reference and work fft records */
fill_rand (i << 1, ref_fft_in);
memset (ref_fft_aout, 0, MAX_FFT_SIZE * sizeof (ref_fft_aout[0]));
memset (ref_fft_sout, 0, MAX_FFT_SIZE * sizeof (ref_fft_sout[0]));
memcpy (work_fft_in, ref_fft_in, MAX_FFT_SIZE * sizeof (work_fft_in[0]));
memset (work_fft_aout, 0, MAX_FFT_SIZE * sizeof (work_fft_aout[0]));
memset (work_fft_sout, 0, MAX_FFT_SIZE * sizeof (work_fft_sout[0]));
reference_power2_fftc (i, ref_fft_in, ref_fft_aout, +1);
reference_power2_fftc (i, ref_fft_in, ref_fft_sout, -1);
/* perform fft test */
gsl_power2_fftac (i, work_fft_in, work_fft_aout);
gsl_power2_fftsc (i, work_fft_in, work_fft_sout);
/* check differences */
d = diff (MAX_FFT_SIZE, 0, ref_fft_in, work_fft_in, "Checking input record");
if (d)
g_error ("Reference record was modified");
d = diff (MAX_FFT_SIZE, 0, ref_fft_aout, work_fft_aout, "Reference analysis against GSL analysis");
if (fabs (d) > EPSILON)
g_error ("Error sum in analysis FFT exceeds epsilon: %g > %g", d, EPSILON);
d = diff (MAX_FFT_SIZE, 0, ref_fft_sout, work_fft_sout, "Reference synthesis against GSL synthesis");
if (fabs (d) > EPSILON)
g_error ("Error sum in analysis FFT exceeds epsilon: %g > %g", d, EPSILON);
}
return 0;
}
static void
fill_rand (guint n,
double *a)
{
while (n--)
a[n] = -1. + 2. * rand() / (RAND_MAX + 1.0);
}
static double
diff (guint m,
guint p,
double *a1,
double *a2,
const gchar *str)
{
double d = 0, max = 0, min = 1e+32;
guint n;
g_print ("%s\n", str);
for (n = 0; n < m; n++)
{
double a = ABS (a1[n] - a2[n]);
if (n < p)
g_print ("%3u:%.3f) % 19.9f - % 19.9f = % 19.9f (% 19.9f)\n",
n, ((float) n) / (float) m,
a1[n], a2[n],
a1[n] - a2[n],
a1[n] / a2[n]);
d += a;
max = MAX (max, a);
min = MIN (min, a);
}
g_print ("Diff sum: %.9f, ", d);
g_print ("min/av/max: %.9f %.9f %.9f, ", min, d / (double) m, max);
g_print ("noise: %u %u %u\n",
g_bit_storage (1. / min),
g_bit_storage (m / d),
g_bit_storage (1. / max));
return d;
}
/* --- fft implementation --- */
#define BUTTERFLY_XY(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,Wre,Wim) { \
register double T1re, T1im, T2re, T2im; \
T1re = X2re * Wre; \
T1im = X2im * Wre; \
T2re = X2im * Wim; \
T2im = X2re * Wim; \
T1re -= T2re; \
T1im += T2im; \
T2re = X1re - T1re; \
T2im = X1im - T1im; \
Y1re = X1re + T1re; \
Y1im = X1im + T1im; \
Y2re = T2re; \
Y2im = T2im; \
}
#define BUTTERFLY_10(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,_1,_2) { \
register double T2re, T2im; \
T2re = X1re - X2re; \
T2im = X1im - X2im; \
Y1re = X1re + X2re; \
Y1im = X1im + X2im; \
Y2re = T2re; \
Y2im = T2im; \
}
#define BUTTERFLY_01(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,_1,_2) { \
register double T2re, T2im; \
T2re = X1re + X2im; \
T2im = X1im - X2re; \
Y1re = X1re - X2im; \
Y1im = X1im + X2re; \
Y2re = T2re; \
Y2im = T2im; \
}
#define BUTTERFLY_0m(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,_1,_2) { \
register double T2re, T2im; \
T2re = X1re - X2im; \
T2im = X1im + X2re; \
Y1re = X1re + X2im; \
Y1im = X1im - X2re; \
Y2re = T2re; \
Y2im = T2im; \
}
#define BUTTERFLY_10scale(X1re,X1im,X2re,X2im,Y1re,Y1im,Y2re,Y2im,S) { \
register double T2re, T2im; \
T2re = X1re - X2re; \
T2im = X1im - X2im; \
Y1re = X1re + X2re; \
Y1im = X1im + X2im; \
Y2re = T2re * S; \
Y2im = T2im * S; \
Y1re *= S; \
Y1im *= S; \
}
#define WMULTIPLY(Wre,Wim,Dre,Dim) { \
register double T1re, T1im, T2re, T2im; \
T1re = Wre * Dre; \
T1im = Wim * Dre; \
T2re = Wim * Dim; \
T2im = Wre * Dim; \
T1re -= T2re; \
T1im += T2im; \
Wre += T1re; \
Wim += T1im; \
}
static inline void
reference_bitreverse_fft2analysis (const unsigned int n,
const double *X,
double *Y)
{
const unsigned int n2 = n >> 1, n1 = n + n2, max = n >> 2;
unsigned int i, r;
BUTTERFLY_10 (X[0], X[1],
X[n], X[n + 1],
Y[0], Y[1],
Y[2], Y[3],
__1, __0);
if (n < 4)
return;
BUTTERFLY_10 (X[n2], X[n2 + 1],
X[n1], X[n1 + 1],
Y[4], Y[5],
Y[6], Y[7],
__1, __0);
if (n < 8)
return;
for (i = 1, r = 0; i < max; i++)
{
unsigned int k, j = n >> 1;
while (r >= j)
{
r -= j;
j >>= 1;
}
r |= j;
k = r >> 1;
j = i << 3;
BUTTERFLY_10 (X[k], X[k + 1],
X[k + n], X[k + n + 1],
Y[j], Y[j + 1],
Y[j + 2], Y[j + 3],
__1, __0);
k += n2;
j += 4;
BUTTERFLY_10 (X[k], X[k + 1],
X[k + n], X[k + n + 1],
Y[j], Y[j + 1],
Y[j + 2], Y[j + 3],
__1, __0);
}
}
static inline void
reference_bitreverse_fft2synthesis (const unsigned int n,
const double *X,
double *Y)
{
const unsigned int n2 = n >> 1, n1 = n + n2, max = n >> 2;
unsigned int i, r;
double scale = n;
scale = 1.0 / scale;
BUTTERFLY_10scale (X[0], X[1],
X[n], X[n + 1],
Y[0], Y[1],
Y[2], Y[3],
scale);
if (n < 4)
return;
BUTTERFLY_10scale (X[n2], X[n2 + 1],
X[n1], X[n1 + 1],
Y[4], Y[5],
Y[6], Y[7],
scale);
if (n < 8)
return;
for (i = 1, r = 0; i < max; i++)
{
unsigned int k, j = n >> 1;
while (r >= j)
{
r -= j;
j >>= 1;
}
r |= j;
k = r >> 1;
j = i << 3;
BUTTERFLY_10scale (X[k], X[k + 1],
X[k + n], X[k + n + 1],
Y[j], Y[j + 1],
Y[j + 2], Y[j + 3],
scale);
k += n2;
j += 4;
BUTTERFLY_10scale (X[k], X[k + 1],
X[k + n], X[k + n + 1],
Y[j], Y[j + 1],
Y[j + 2], Y[j + 3],
scale);
}
}
static void
reference_power2_fftc (unsigned int n_values,
const double *rivalues_in,
double *rivalues,
int esign)
{
const unsigned int n_values2 = n_values << 1;
double theta = esign < 0 ? -3.1415926535897932384626433832795029 : 3.1415926535897932384626433832795029;
unsigned int block_size = 2 << 1;
double last_sin;
if (esign > 0)
reference_bitreverse_fft2analysis (n_values, rivalues_in, rivalues);
else
reference_bitreverse_fft2synthesis (n_values, rivalues_in, rivalues);
theta *= (double) 1.0 / 2.;
last_sin = sin (theta);
if (n_values < 4)
return;
do
{
double Dre, Dim, Wre, Wim;
unsigned int k, i, half_block = block_size >> 1;
unsigned int block_size2 = block_size << 1;
theta *= 0.5;
Dim = last_sin;
last_sin = sin (theta);
Dre = last_sin * last_sin * -2.;
/* loop over first coefficient in each block ==> w == {1,0} */
for (i = 0; i < n_values2; i += block_size2)
{
unsigned int v1 = i, v2 = i + block_size;
BUTTERFLY_10 (rivalues[v1], rivalues[v1 + 1],
rivalues[v2], rivalues[v2 + 1],
rivalues[v1], rivalues[v1 + 1],
rivalues[v2], rivalues[v2 + 1],
__1, __0);
}
Wre = Dre + 1.0; /* update Wk */
Wim = Dim; /* update Wk */
/* loop for every Wk in the first half of each subblock */
for (k = 2; k < half_block; k += 2)
{
/* loop over kth coefficient in each block */
for (i = k; i < n_values2; i += block_size2)
{
unsigned int v1 = i, v2 = i + block_size;
BUTTERFLY_XY (rivalues[v1], rivalues[v1 + 1],
rivalues[v2], rivalues[v2 + 1],
rivalues[v1], rivalues[v1 + 1],
rivalues[v2], rivalues[v2 + 1],
Wre, Wim);
}
WMULTIPLY (Wre, Wim, Dre, Dim); /* update Wk */
}
/* handle middle coefficient ==> w == {0,+-1} */
if (k < block_size)
{
/* loop over kth coefficient in each block */
if (esign > 0)
for (i = k; i < n_values2; i += block_size2)
{
unsigned int v1 = i, v2 = i + block_size;
BUTTERFLY_01 (rivalues[v1], rivalues[v1 + 1],
rivalues[v2], rivalues[v2 + 1],
rivalues[v1], rivalues[v1 + 1],
rivalues[v2], rivalues[v2 + 1],
__0, __1);
}
else
for (i = k; i < n_values2; i += block_size2)
{
unsigned int v1 = i, v2 = i + block_size;
BUTTERFLY_0m (rivalues[v1], rivalues[v1 + 1],
rivalues[v2], rivalues[v2 + 1],
rivalues[v1], rivalues[v1 + 1],
rivalues[v2], rivalues[v2 + 1],
__0, __1);
}
/* update Wk */
if (esign > 0)
{
Wre = -Dim;
Wim = Dre + 1.0;
}
else
{
Wre = Dim;
Wim = -Dre - 1.0;
}
k += 2;
}
/* loop for every Wk in the second half of each subblock */
for (; k < block_size; k += 2)
{
/* loop over kth coefficient in each block */
for (i = k; i < n_values2; i += block_size2)
{
unsigned int v1 = i, v2 = i + block_size;
BUTTERFLY_XY (rivalues[v1], rivalues[v1 + 1],
rivalues[v2], rivalues[v2 + 1],
rivalues[v1], rivalues[v1 + 1],
rivalues[v2], rivalues[v2 + 1],
Wre, Wim);
}
WMULTIPLY (Wre, Wim, Dre, Dim); /* update Wk */
}
block_size = block_size2;
}
while (block_size <= n_values);
}
|
