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- /* fft/real_radix2.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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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