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/* fft/real_radix2.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
*
* 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.
*/
int
FUNCTION(gsl_fft_real,radix2_transform) (BASE data[], const size_t stride, const size_t n)
{
int result ;
size_t p, p_1, q;
size_t i;
size_t logn = 0;
int status;
if (n == 1) /* identity operation */
{
return 0 ;
}
/* make sure that n is a power of 2 */
result = fft_binary_logn(n) ;
if (result == -1)
{
GSL_ERROR ("n is not a power of 2", GSL_EINVAL);
}
else
{
logn = result ;
}
/* bit reverse the ordering of input data for decimation in time algorithm */
status = FUNCTION(fft_real,bitreverse_order)(data, stride, n, logn) ;
/* apply fft recursion */
p = 1; q = n ;
for (i = 1; i <= logn; i++)
{
size_t a, b;
p_1 = p ;
p = 2 * p ;
q = q / 2 ;
/* a = 0 */
for (b = 0; b < q; b++)
{
ATOMIC t0_real = VECTOR(data,stride,b*p) + VECTOR(data,stride,b*p + p_1) ;
ATOMIC t1_real = VECTOR(data,stride,b*p) - VECTOR(data,stride,b*p + p_1) ;
VECTOR(data,stride,b*p) = t0_real ;
VECTOR(data,stride,b*p + p_1) = t1_real ;
}
/* a = 1 ... p_{i-1}/2 - 1 */
{
ATOMIC w_real = 1.0;
ATOMIC w_imag = 0.0;
const double theta = - 2.0 * M_PI / p;
const ATOMIC s = sin (theta);
const ATOMIC t = sin (theta / 2.0);
const ATOMIC s2 = 2.0 * t * t;
for (a = 1; a < (p_1)/2; a++)
{
/* trignometric recurrence for w-> exp(i theta) w */
{
const ATOMIC tmp_real = w_real - s * w_imag - s2 * w_real;
const ATOMIC tmp_imag = w_imag + s * w_real - s2 * w_imag;
w_real = tmp_real;
w_imag = tmp_imag;
}
for (b = 0; b < q; b++)
{
ATOMIC z0_real = VECTOR(data,stride,b*p + a) ;
ATOMIC z0_imag = VECTOR(data,stride,b*p + p_1 - a) ;
ATOMIC z1_real = VECTOR(data,stride,b*p + p_1 + a) ;
ATOMIC z1_imag = VECTOR(data,stride,b*p + p - a) ;
/* t0 = z0 + w * z1 */
ATOMIC t0_real = z0_real + w_real * z1_real - w_imag * z1_imag;
ATOMIC t0_imag = z0_imag + w_real * z1_imag + w_imag * z1_real;
/* t1 = z0 - w * z1 */
ATOMIC t1_real = z0_real - w_real * z1_real + w_imag * z1_imag;
ATOMIC t1_imag = z0_imag - w_real * z1_imag - w_imag * z1_real;
VECTOR(data,stride,b*p + a) = t0_real ;
VECTOR(data,stride,b*p + p - a) = t0_imag ;
VECTOR(data,stride,b*p + p_1 - a) = t1_real ;
VECTOR(data,stride,b*p + p_1 + a) = -t1_imag ;
}
}
}
if (p_1 > 1)
{
for (b = 0; b < q; b++)
{
/* a = p_{i-1}/2 */
VECTOR(data,stride,b*p + p - p_1/2) *= -1 ;
}
}
}
return 0;
}
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