| /* fft/hc_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_halfcomplex,radix2_backward) (BASE data[], |
| const size_t stride, |
| const size_t n) |
| { |
| int status = FUNCTION(gsl_fft_halfcomplex,radix2_transform) (data, stride, n) ; |
| return status ; |
| } |
| |
| int |
| FUNCTION(gsl_fft_halfcomplex,radix2_inverse) (BASE data[], |
| const size_t stride, |
| const size_t n) |
| { |
| int status = FUNCTION(gsl_fft_halfcomplex,radix2_transform) (data, stride, n); |
| |
| if (status) |
| { |
| return status; |
| } |
| |
| /* normalize inverse fft with 1/n */ |
| |
| { |
| const ATOMIC norm = 1.0 / n; |
| size_t i; |
| for (i = 0; i < n; i++) |
| { |
| data[stride*i] *= norm; |
| } |
| } |
| return status; |
| } |
| |
| int |
| FUNCTION(gsl_fft_halfcomplex,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 ; |
| } |
| |
| /* apply fft recursion */ |
| |
| p = n; q = 1 ; p_1 = n/2 ; |
| |
| for (i = 1; i <= logn; i++) |
| { |
| size_t a, b; |
| |
| /* a = 0 */ |
| |
| for (b = 0; b < q; b++) |
| { |
| const ATOMIC z0 = VECTOR(data,stride,b*p); |
| const ATOMIC z1 = VECTOR(data,stride,b*p + p_1); |
| |
| const ATOMIC t0_real = z0 + z1 ; |
| const ATOMIC t1_real = z0 - z1 ; |
| |
| 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 ATOMIC 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 - a) ; |
| ATOMIC z1_real = VECTOR(data,stride,b*p + p_1 - a) ; |
| ATOMIC z1_imag = -VECTOR(data,stride,b*p + p_1 + a) ; |
| |
| /* t0 = z0 + z1 */ |
| |
| ATOMIC t0_real = z0_real + z1_real; |
| ATOMIC t0_imag = z0_imag + z1_imag; |
| |
| /* t1 = (z0 - z1) */ |
| |
| ATOMIC t1_real = z0_real - z1_real; |
| ATOMIC t1_imag = z0_imag - z1_imag; |
| |
| VECTOR(data,stride,b*p + a) = t0_real ; |
| VECTOR(data,stride,b*p + p_1 - a) = t0_imag ; |
| |
| VECTOR(data,stride,b*p + p_1 + a) = (w_real * t1_real - w_imag * t1_imag) ; |
| VECTOR(data,stride,b*p + p - a) = (w_real * t1_imag + w_imag * t1_real) ; |
| } |
| } |
| } |
| |
| if (p_1 > 1) { |
| for (b = 0; b < q; b++) { |
| VECTOR(data,stride,b*p + p_1/2) *= 2 ; |
| VECTOR(data,stride,b*p + p_1 + p_1/2) *= -2 ; |
| } |
| } |
| |
| p_1 = p_1 / 2 ; |
| p = p / 2 ; |
| q = q * 2 ; |
| } |
| |
| /* bit reverse the ordering of output data for decimation in |
| frequency algorithm */ |
| |
| status = FUNCTION(fft_real,bitreverse_order)(data, stride, n, logn) ; |
| |
| return 0; |
| |
| } |