| /* 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; |
| } |