| /* fft/real_pass_3.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_3) (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) twiddle1[], |
| const TYPE(gsl_complex) twiddle2[]) |
| { |
| size_t k, k1; |
| |
| const size_t factor = 3; |
| const size_t m = n / factor; |
| const size_t q = n / product; |
| const size_t product_1 = product / factor; |
| |
| const ATOMIC tau = sqrt (3.0) / 2.0; |
| |
| for (k1 = 0; k1 < q; k1++) |
| { |
| const size_t from0 = k1 * product_1; |
| const size_t from1 = from0 + m; |
| const size_t from2 = from1 + m; |
| |
| const ATOMIC z0_real = VECTOR(in,istride,from0); |
| const ATOMIC z1_real = VECTOR(in,istride,from1); |
| const ATOMIC z2_real = VECTOR(in,istride,from2); |
| |
| const ATOMIC t1 = z1_real + z2_real; |
| |
| const ATOMIC x0_real = z0_real + t1; |
| const ATOMIC x1_real = z0_real - t1 / 2.0; |
| const ATOMIC x1_imag = -tau * (z1_real - z2_real); |
| |
| const size_t to0 = product * k1; |
| const size_t to1 = to0 + 2 * product_1 - 1; |
| |
| VECTOR(out,ostride,to0) = x0_real; |
| VECTOR(out,ostride,to1) = x1_real; |
| VECTOR(out,ostride,to1 + 1) = x1_imag; |
| } |
| |
| if (product_1 == 1) |
| return; |
| |
| for (k = 1; k < (product_1 + 1) / 2; k++) |
| { |
| const ATOMIC w1_real = GSL_REAL(twiddle1[k - 1]); |
| const ATOMIC w1_imag = -GSL_IMAG(twiddle1[k - 1]); |
| const ATOMIC w2_real = GSL_REAL(twiddle2[k - 1]); |
| const ATOMIC w2_imag = -GSL_IMAG(twiddle2[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 size_t from2 = from1 + 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 f2_real = VECTOR(in,istride,from2); |
| const ATOMIC f2_imag = VECTOR(in,istride,from2 + 1); |
| |
| const ATOMIC z0_real = f0_real; |
| const ATOMIC z0_imag = f0_imag; |
| const ATOMIC z1_real = w1_real * f1_real - w1_imag * f1_imag; |
| const ATOMIC z1_imag = w1_real * f1_imag + w1_imag * f1_real; |
| const ATOMIC z2_real = w2_real * f2_real - w2_imag * f2_imag; |
| const ATOMIC z2_imag = w2_real * f2_imag + w2_imag * f2_real; |
| |
| /* compute x = W(3) z */ |
| |
| /* t1 = z1 + z2 */ |
| const ATOMIC t1_real = z1_real + z2_real; |
| const ATOMIC t1_imag = z1_imag + z2_imag; |
| |
| /* t2 = z0 - t1/2 */ |
| const ATOMIC t2_real = z0_real - t1_real / 2; |
| const ATOMIC t2_imag = z0_imag - t1_imag / 2; |
| |
| /* t3 = (+/-) sin(pi/3)*(z1 - z2) */ |
| const ATOMIC t3_real = -tau * (z1_real - z2_real); |
| const ATOMIC t3_imag = -tau * (z1_imag - z2_imag); |
| |
| /* x0 = z0 + t1 */ |
| const ATOMIC x0_real = z0_real + t1_real; |
| const ATOMIC x0_imag = z0_imag + t1_imag; |
| |
| /* x1 = t2 + i t3 */ |
| const ATOMIC x1_real = t2_real - t3_imag; |
| const ATOMIC x1_imag = t2_imag + t3_real; |
| |
| /* x2 = t2 - i t3 */ |
| const ATOMIC x2_real = t2_real + t3_imag; |
| const ATOMIC x2_imag = t2_imag - t3_real; |
| |
| /* apply twiddle factors */ |
| |
| const size_t to0 = k1 * product + 2 * k - 1; |
| const size_t to1 = to0 + 2 * product_1; |
| const size_t to2 = 2 * product_1 - 2 * k + k1 * product - 1; |
| |
| /* to0 = 1 * x0 */ |
| VECTOR(out,ostride,to0) = x0_real; |
| VECTOR(out,ostride,to0 + 1) = x0_imag; |
| |
| /* to1 = 1 * x1 */ |
| VECTOR(out,ostride,to1) = x1_real; |
| VECTOR(out,ostride,to1 + 1) = x1_imag; |
| |
| /* to2 = 1 * x2 */ |
| VECTOR(out,ostride,to2) = x2_real; |
| VECTOR(out,ostride,to2 + 1) = -x2_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 from2 = from1 + m; |
| |
| const ATOMIC z0_real = VECTOR(in,istride,from0); |
| const ATOMIC z1_real = VECTOR(in,istride,from1); |
| const ATOMIC z2_real = VECTOR(in,istride,from2); |
| |
| const ATOMIC t1 = z1_real - z2_real; |
| const ATOMIC x0_real = z0_real + t1 / 2.0; |
| const ATOMIC x0_imag = -tau * (z1_real + z2_real); |
| const ATOMIC x1_real = z0_real - t1; |
| |
| const size_t to0 = k1 * product + product_1 - 1; |
| const size_t to1 = to0 + 2 * product_1; |
| |
| VECTOR(out,ostride,to0) = x0_real; |
| VECTOR(out,ostride,to0 + 1) = x0_imag; |
| VECTOR(out,ostride,to1) = x1_real; |
| } |
| |
| return; |
| } |