/* fft/c_pass_5.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 int FUNCTION(fft_complex,pass_5) (const BASE in[], const size_t istride, BASE out[], const size_t ostride, const gsl_fft_direction sign, const size_t product, const size_t n, const TYPE(gsl_complex) twiddle1[], const TYPE(gsl_complex) twiddle2[], const TYPE(gsl_complex) twiddle3[], const TYPE(gsl_complex) twiddle4[]) { size_t i = 0, j = 0; size_t k, k1; const size_t factor = 5; const size_t m = n / factor; const size_t q = n / product; const size_t p_1 = product / factor; const size_t jump = (factor - 1) * p_1; const ATOMIC sin_2pi_by_5 = sin (2.0 * M_PI / 5.0); const ATOMIC sin_2pi_by_10 = sin (2.0 * M_PI / 10.0); for (k = 0; k < q; k++) { ATOMIC w1_real, w1_imag, w2_real, w2_imag, w3_real, w3_imag, w4_real, w4_imag; if (k == 0) { w1_real = 1.0; w1_imag = 0.0; w2_real = 1.0; w2_imag = 0.0; w3_real = 1.0; w3_imag = 0.0; w4_real = 1.0; w4_imag = 0.0; } else { if (sign == gsl_fft_forward) { /* forward tranform */ w1_real = GSL_REAL(twiddle1[k - 1]); w1_imag = GSL_IMAG(twiddle1[k - 1]); w2_real = GSL_REAL(twiddle2[k - 1]); w2_imag = GSL_IMAG(twiddle2[k - 1]); w3_real = GSL_REAL(twiddle3[k - 1]); w3_imag = GSL_IMAG(twiddle3[k - 1]); w4_real = GSL_REAL(twiddle4[k - 1]); w4_imag = GSL_IMAG(twiddle4[k - 1]); } else { /* backward tranform: w -> conjugate(w) */ w1_real = GSL_REAL(twiddle1[k - 1]); w1_imag = -GSL_IMAG(twiddle1[k - 1]); w2_real = GSL_REAL(twiddle2[k - 1]); w2_imag = -GSL_IMAG(twiddle2[k - 1]); w3_real = GSL_REAL(twiddle3[k - 1]); w3_imag = -GSL_IMAG(twiddle3[k - 1]); w4_real = GSL_REAL(twiddle4[k - 1]); w4_imag = -GSL_IMAG(twiddle4[k - 1]); } } for (k1 = 0; k1 < p_1; k1++) { ATOMIC x0_real, x0_imag, x1_real, x1_imag, x2_real, x2_imag, x3_real, x3_imag, x4_real, x4_imag; const ATOMIC z0_real = REAL(in,istride,i); const ATOMIC z0_imag = IMAG(in,istride,i); const ATOMIC z1_real = REAL(in,istride,i + m); const ATOMIC z1_imag = IMAG(in,istride,i + m); const ATOMIC z2_real = REAL(in,istride,i + 2*m); const ATOMIC z2_imag = IMAG(in,istride,i + 2*m); const ATOMIC z3_real = REAL(in,istride,i + 3*m); const ATOMIC z3_imag = IMAG(in,istride,i + 3*m); const ATOMIC z4_real = REAL(in,istride,i + 4*m); const ATOMIC z4_imag = IMAG(in,istride,i + 4*m); /* compute x = W(5) z */ /* t1 = z1 + z4 */ const ATOMIC t1_real = z1_real + z4_real; const ATOMIC t1_imag = z1_imag + z4_imag; /* t2 = z2 + z3 */ const ATOMIC t2_real = z2_real + z3_real; const ATOMIC t2_imag = z2_imag + z3_imag; /* t3 = z1 - z4 */ const ATOMIC t3_real = z1_real - z4_real; const ATOMIC t3_imag = z1_imag - z4_imag; /* t4 = z2 - z3 */ const ATOMIC t4_real = z2_real - z3_real; const ATOMIC t4_imag = z2_imag - z3_imag; /* t5 = t1 + t2 */ const ATOMIC t5_real = t1_real + t2_real; const ATOMIC t5_imag = t1_imag + t2_imag; /* t6 = (sqrt(5)/4)(t1 - t2) */ const ATOMIC t6_real = (sqrt (5.0) / 4.0) * (t1_real - t2_real); const ATOMIC t6_imag = (sqrt (5.0) / 4.0) * (t1_imag - t2_imag); /* t7 = z0 - ((t5)/4) */ const ATOMIC t7_real = z0_real - t5_real / 4.0; const ATOMIC t7_imag = z0_imag - t5_imag / 4.0; /* t8 = t7 + t6 */ const ATOMIC t8_real = t7_real + t6_real; const ATOMIC t8_imag = t7_imag + t6_imag; /* t9 = t7 - t6 */ const ATOMIC t9_real = t7_real - t6_real; const ATOMIC t9_imag = t7_imag - t6_imag; /* t10 = sin(2 pi/5) t3 + sin(2 pi/10) t4 */ const ATOMIC t10_real = ((int) sign) * (sin_2pi_by_5 * t3_real + sin_2pi_by_10 * t4_real); const ATOMIC t10_imag = ((int) sign) * (sin_2pi_by_5 * t3_imag + sin_2pi_by_10 * t4_imag); /* t11 = sin(2 pi/10) t3 - sin(2 pi/5) t4 */ const ATOMIC t11_real = ((int) sign) * (sin_2pi_by_10 * t3_real - sin_2pi_by_5 * t4_real); const ATOMIC t11_imag = ((int) sign) * (sin_2pi_by_10 * t3_imag - sin_2pi_by_5 * t4_imag); /* x0 = z0 + t5 */ x0_real = z0_real + t5_real; x0_imag = z0_imag + t5_imag; /* x1 = t8 + i t10 */ x1_real = t8_real - t10_imag; x1_imag = t8_imag + t10_real; /* x2 = t9 + i t11 */ x2_real = t9_real - t11_imag; x2_imag = t9_imag + t11_real; /* x3 = t9 - i t11 */ x3_real = t9_real + t11_imag; x3_imag = t9_imag - t11_real; /* x4 = t8 - i t10 */ x4_real = t8_real + t10_imag; x4_imag = t8_imag - t10_real; /* apply twiddle factors */ /* to0 = 1 * x0 */ REAL(out,ostride,j) = x0_real; IMAG(out,ostride,j) = x0_imag; /* to1 = w1 * x1 */ REAL(out,ostride,j + p_1) = w1_real * x1_real - w1_imag * x1_imag; IMAG(out,ostride,j + p_1) = w1_real * x1_imag + w1_imag * x1_real; /* to2 = w2 * x2 */ REAL(out,ostride,j + 2*p_1) = w2_real * x2_real - w2_imag * x2_imag; IMAG(out,ostride,j+2*p_1) = w2_real * x2_imag + w2_imag * x2_real; /* to3 = w3 * x3 */ REAL(out,ostride,j+3*p_1) = w3_real * x3_real - w3_imag * x3_imag; IMAG(out,ostride,j+3*p_1) = w3_real * x3_imag + w3_imag * x3_real; /* to4 = w4 * x4 */ REAL(out,ostride,j+4*p_1) = w4_real * x4_real - w4_imag * x4_imag; IMAG(out,ostride,j+4*p_1) = w4_real * x4_imag + w4_imag * x4_real; i++; j++; } j += jump; } return 0; }