| /* fft/real_pass_2.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_2) (const BASE in[], |
| const size_t istride, |
| BASE out[], |
| const size_t ostride, |
| const size_t product, |
| const size_t n, |
| const TYPE(gsl_complex) twiddle[]) |
| { |
| size_t k, k1; |
| |
| const size_t factor = 2; |
| const size_t m = n / factor; |
| const size_t q = n / product; |
| const size_t product_1 = product / factor; |
| |
| for (k1 = 0; k1 < q; k1++) |
| { |
| const size_t from0 = k1 * product_1; |
| const size_t from1 = from0 + m; |
| |
| const ATOMIC r0 = VECTOR(in,istride,from0); |
| const ATOMIC r1 = VECTOR(in,istride,from1); |
| |
| const ATOMIC s0 = r0 + r1; |
| const ATOMIC s1 = r0 - r1; |
| |
| const size_t to0 = product * k1; |
| const size_t to1 = to0 + product - 1; |
| |
| VECTOR(out,ostride,to0) = s0; |
| VECTOR(out,ostride,to1) = s1; |
| } |
| |
| if (product_1 == 1) |
| return; |
| |
| for (k = 1; k < (product_1 + 1) / 2; k++) |
| { |
| |
| /* forward real transform: w -> conjugate(w) */ |
| const ATOMIC w_real = GSL_REAL(twiddle[k - 1]); |
| const ATOMIC w_imag = -GSL_IMAG(twiddle[k - 1]); |
| |
| for (k1 = 0; k1 < q; k1++) |
| { |
| const size_t from0 = k1 * product_1 + 2 * k - 1; |
| const size_t from1 = from0 + m; |
| |
| const ATOMIC f0_real = VECTOR(in,istride,from0); |
| const ATOMIC f0_imag = VECTOR(in,istride,from0 + 1); |
| |
| const ATOMIC f1_real = VECTOR(in,istride,from1); |
| const ATOMIC f1_imag = VECTOR(in,istride,from1 + 1); |
| |
| const ATOMIC z0_real = f0_real; |
| const ATOMIC z0_imag = f0_imag; |
| |
| const ATOMIC z1_real = w_real * f1_real - w_imag * f1_imag; |
| const ATOMIC z1_imag = w_real * f1_imag + w_imag * f1_real; |
| |
| /* compute x = W(2) z */ |
| |
| /* x0 = z0 + z1 */ |
| const ATOMIC x0_real = z0_real + z1_real; |
| const ATOMIC x0_imag = z0_imag + z1_imag; |
| |
| /* x1 = z0 - z1 */ |
| const ATOMIC x1_real = z0_real - z1_real; |
| const ATOMIC x1_imag = z0_imag - z1_imag; |
| |
| const size_t to0 = k1 * product + 2 * k - 1; |
| const size_t to1 = k1 * product + product - 2 * k - 1; |
| |
| VECTOR(out,ostride,to0) = x0_real; |
| VECTOR(out,ostride,to0 + 1) = x0_imag; |
| |
| /* stored in conjugate location */ |
| VECTOR(out,ostride,to1) = x1_real; |
| VECTOR(out,ostride,to1 + 1) = -x1_imag; |
| } |
| } |
| |
| if (product_1 % 2 == 1) |
| return; |
| |
| for (k1 = 0; k1 < q; k1++) |
| { |
| const size_t from0 = k1 * product_1 + product_1 - 1; |
| const size_t from1 = from0 + m; |
| const size_t to0 = k1 * product + product_1 - 1; |
| |
| VECTOR(out,ostride,to0) = VECTOR(in,istride,from0); |
| VECTOR(out,ostride,to0 + 1) = -VECTOR(in,istride,from1); |
| } |
| return; |
| } |