/* fft/real_pass_n.c * * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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; }