| /* fft/real_pass_n.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. |
| */ |
| |
| static void |
| FUNCTION(fft_real,pass_n) (const BASE in[], |
| const size_t istride, |
| BASE out[], |
| const size_t ostride, |
| const size_t factor, |
| const size_t product, |
| const size_t n, |
| const TYPE(gsl_complex) twiddle[]) |
| { |
| size_t k, k1; |
| |
| const size_t m = n / factor; |
| const size_t q = n / product; |
| const size_t product_1 = product / factor; |
| |
| size_t e1, e2; |
| |
| const double d_theta = 2.0 * M_PI / ((double) factor); |
| const ATOMIC cos_d_theta = cos (d_theta); |
| const ATOMIC sin_d_theta = sin (d_theta); |
| |
| for (k1 = 0; k1 < q; k1++) |
| { |
| /* compute x = W(factor) z, for z real */ |
| |
| ATOMIC dw_real = 1.0, dw_imag = 0.0; |
| |
| for (e1 = 0; e1 <= factor - e1; e1++) |
| { |
| ATOMIC sum_real = 0.0; |
| ATOMIC sum_imag = 0.0; |
| |
| ATOMIC w_real = 1.0, w_imag = 0.0; |
| |
| if (e1 > 0) |
| { |
| ATOMIC tmp_real = dw_real * cos_d_theta + dw_imag * sin_d_theta; |
| ATOMIC tmp_imag = -dw_real * sin_d_theta + dw_imag * cos_d_theta; |
| dw_real = tmp_real; |
| dw_imag = tmp_imag; |
| } |
| |
| for (e2 = 0; e2 < factor; e2++) |
| { |
| ATOMIC z_real = VECTOR(in,istride,k1 * product_1 + e2 * m); |
| |
| if (e2 > 0) |
| { |
| ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag; |
| ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real; |
| w_real = tmp_real; |
| w_imag = tmp_imag; |
| } |
| |
| sum_real += w_real * z_real; |
| sum_imag += w_imag * z_real; |
| |
| } |
| if (e1 == 0) |
| { |
| const size_t to0 = product * k1; |
| VECTOR(out,ostride,to0) = sum_real; |
| } |
| else if (e1 < factor - e1) |
| { |
| const size_t to0 = k1 * product + 2 * e1 * product_1 - 1; |
| VECTOR(out,ostride,to0) = sum_real; |
| VECTOR(out,ostride,to0 + 1) = sum_imag; |
| } |
| else if (e1 == factor - e1) |
| { |
| const size_t to0 = k1 * product + 2 * e1 * product_1 - 1; |
| VECTOR(out,ostride,to0) = sum_real; |
| } |
| |
| } |
| } |
| |
| if (product_1 == 1) |
| return; |
| |
| for (k = 1; k < (product_1 + 1) / 2; k++) |
| { |
| for (k1 = 0; k1 < q; k1++) |
| { |
| |
| ATOMIC dw_real = 1.0, dw_imag = 0.0; |
| |
| for (e1 = 0; e1 < factor; e1++) |
| { |
| ATOMIC sum_real = 0.0, sum_imag = 0.0; |
| |
| ATOMIC w_real = 1.0, w_imag = 0.0; |
| |
| if (e1 > 0) |
| { |
| const ATOMIC tmp_real = dw_real * cos_d_theta + dw_imag * sin_d_theta; |
| const ATOMIC tmp_imag = -dw_real * sin_d_theta + dw_imag * cos_d_theta; |
| dw_real = tmp_real; |
| dw_imag = tmp_imag; |
| } |
| |
| for (e2 = 0; e2 < factor; e2++) |
| { |
| |
| int tskip = (product_1 + 1) / 2 - 1; |
| const size_t from0 = k1 * product_1 + 2 * k + e2 * m - 1; |
| ATOMIC tw_real, tw_imag; |
| ATOMIC z_real, z_imag; |
| |
| if (e2 == 0) |
| { |
| tw_real = 1.0; |
| tw_imag = 0.0; |
| } |
| else |
| { |
| const size_t t_index = (k - 1) + (e2 - 1) * tskip; |
| tw_real = GSL_REAL(twiddle[t_index]); |
| tw_imag = -GSL_IMAG(twiddle[t_index]); |
| } |
| |
| { |
| const ATOMIC f0_real = VECTOR(in,istride,from0); |
| const ATOMIC f0_imag = VECTOR(in,istride,from0 + 1); |
| |
| z_real = tw_real * f0_real - tw_imag * f0_imag; |
| z_imag = tw_real * f0_imag + tw_imag * f0_real; |
| } |
| |
| if (e2 > 0) |
| { |
| const ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag; |
| const ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real; |
| w_real = tmp_real; |
| w_imag = tmp_imag; |
| } |
| |
| sum_real += w_real * z_real - w_imag * z_imag; |
| sum_imag += w_real * z_imag + w_imag * z_real; |
| } |
| |
| if (e1 < factor - e1) |
| { |
| const size_t to0 = k1 * product - 1 + 2 * e1 * product_1 + 2 * k; |
| VECTOR(out,ostride,to0) = sum_real; |
| VECTOR(out,ostride,to0 + 1) = sum_imag; |
| } |
| else |
| { |
| const size_t to0 = k1 * product - 1 + 2 * (factor - e1) * product_1 - 2 * k; |
| VECTOR(out,ostride,to0) = sum_real; |
| VECTOR(out,ostride,to0 + 1) = -sum_imag; |
| } |
| |
| } |
| } |
| } |
| |
| |
| if (product_1 % 2 == 1) |
| return; |
| |
| { |
| double tw_arg = M_PI / ((double) factor); |
| ATOMIC cos_tw_arg = cos (tw_arg); |
| ATOMIC sin_tw_arg = -sin (tw_arg); |
| |
| for (k1 = 0; k1 < q; k1++) |
| { |
| ATOMIC dw_real = 1.0, dw_imag = 0.0; |
| |
| for (e1 = 0; e1 < factor; e1++) |
| { |
| ATOMIC z_real, z_imag; |
| |
| ATOMIC sum_real = 0.0; |
| ATOMIC sum_imag = 0.0; |
| |
| ATOMIC w_real = 1.0, w_imag = 0.0; |
| ATOMIC tw_real = 1.0, tw_imag = 0.0; |
| |
| if (e1 > 0) |
| { |
| ATOMIC t_real = dw_real * cos_d_theta + dw_imag * sin_d_theta; |
| ATOMIC t_imag = -dw_real * sin_d_theta + dw_imag * cos_d_theta; |
| dw_real = t_real; |
| dw_imag = t_imag; |
| } |
| |
| for (e2 = 0; e2 < factor; e2++) |
| { |
| |
| if (e2 > 0) |
| { |
| ATOMIC tmp_real = tw_real * cos_tw_arg - tw_imag * sin_tw_arg; |
| ATOMIC tmp_imag = tw_real * sin_tw_arg + tw_imag * cos_tw_arg; |
| tw_real = tmp_real; |
| tw_imag = tmp_imag; |
| } |
| |
| if (e2 > 0) |
| { |
| ATOMIC tmp_real = dw_real * w_real - dw_imag * w_imag; |
| ATOMIC tmp_imag = dw_real * w_imag + dw_imag * w_real; |
| w_real = tmp_real; |
| w_imag = tmp_imag; |
| } |
| |
| |
| { |
| const size_t from0 = k1 * product_1 + 2 * k + e2 * m - 1; |
| const ATOMIC f0_real = VECTOR(in,istride,from0); |
| z_real = tw_real * f0_real; |
| z_imag = tw_imag * f0_real; |
| } |
| |
| sum_real += w_real * z_real - w_imag * z_imag; |
| sum_imag += w_real * z_imag + w_imag * z_real; |
| } |
| |
| if (e1 + 1 < factor - e1) |
| { |
| const size_t to0 = k1 * product - 1 + 2 * e1 * product_1 + 2 * k; |
| VECTOR(out,ostride,to0) = sum_real; |
| VECTOR(out,ostride,to0 + 1) = sum_imag; |
| } |
| else if (e1 + 1 == factor - e1) |
| { |
| const size_t to0 = k1 * product - 1 + 2 * e1 * product_1 + 2 * k; |
| VECTOR(out,ostride,to0) = sum_real; |
| } |
| else |
| { |
| const size_t to0 = k1 * product - 1 + 2 * (factor - e1) * product_1 - 2 * k; |
| VECTOR(out,ostride,to0) = sum_real; |
| VECTOR(out,ostride,to0 + 1) = -sum_imag; |
| } |
| |
| } |
| } |
| } |
| return; |
| } |
