| /* fft/real_pass_5.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_5) (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[], |
| const TYPE(gsl_complex) twiddle3[], |
| const TYPE(gsl_complex) twiddle4[]) |
| { |
| size_t k, k1; |
| |
| const size_t factor = 5; |
| const size_t m = n / factor; |
| const size_t q = n / product; |
| const size_t product_1 = product / factor; |
| |
| const ATOMIC sina = sin (2.0 * M_PI / 5.0); |
| const ATOMIC sinb = sin (2.0 * M_PI / 10.0); |
| |
| 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 size_t from3 = from2 + m; |
| const size_t from4 = from3 + 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 z3_real = VECTOR(in,istride,from3); |
| const ATOMIC z4_real = VECTOR(in,istride,from4); |
| |
| /* t1 = z1 + z4 */ |
| const ATOMIC t1_real = z1_real + z4_real; |
| |
| /* t2 = z2 + z3 */ |
| const ATOMIC t2_real = z2_real + z3_real; |
| |
| /* t3 = z1 - z4 */ |
| const ATOMIC t3_real = z1_real - z4_real; |
| |
| /* t4 = z2 - z3 */ |
| const ATOMIC t4_real = z2_real - z3_real; |
| |
| /* t5 = t1 + t2 */ |
| const ATOMIC t5_real = t1_real + t2_real; |
| |
| /* t6 = (sqrt(5)/4)(t1 - t2) */ |
| const ATOMIC t6_real = (sqrt (5.0) / 4.0) * (t1_real - t2_real); |
| |
| /* t7 = z0 - ((t5)/4) */ |
| const ATOMIC t7_real = z0_real - t5_real / 4.0; |
| |
| /* t8 = t7 + t6 */ |
| const ATOMIC t8_real = t7_real + t6_real; |
| |
| /* t9 = t7 - t6 */ |
| const ATOMIC t9_real = t7_real - t6_real; |
| |
| /* t10 = -(sin(2 pi/5) t3 + sin(2 pi/10) t4 ) */ |
| const ATOMIC t10_real = -sina * t3_real - sinb * t4_real; |
| |
| /* t11 = -(sin(2 pi/10) t3 - sin(2 pi/5) t4) */ |
| const ATOMIC t11_real = -sinb * t3_real + sina * t4_real; |
| |
| /* x0 = z0 + t5 */ |
| const ATOMIC x0_real = z0_real + t5_real; |
| |
| /* x1 = t8 + i t10 */ |
| const ATOMIC x1_real = t8_real; |
| const ATOMIC x1_imag = t10_real; |
| |
| /* x2 = t9 + i t11 */ |
| const ATOMIC x2_real = t9_real; |
| const ATOMIC x2_imag = t11_real; |
| |
| const size_t to0 = product * k1; |
| const size_t to1 = to0 + 2 * product_1 - 1; |
| const size_t to2 = to1 + 2 * product_1; |
| |
| VECTOR(out,ostride,to0) = x0_real; |
| VECTOR(out,ostride,to1) = x1_real; |
| VECTOR(out,ostride,to1 + 1) = x1_imag; |
| VECTOR(out,ostride,to2) = x2_real; |
| VECTOR(out,ostride,to2 + 1) = x2_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]); |
| const ATOMIC w3_real = GSL_REAL(twiddle3[k - 1]); |
| const ATOMIC w3_imag = -GSL_IMAG(twiddle3[k - 1]); |
| const ATOMIC w4_real = GSL_REAL(twiddle4[k - 1]); |
| const ATOMIC w4_imag = -GSL_IMAG(twiddle4[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 size_t from3 = from2 + m; |
| const size_t from4 = from3 + 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 f3_real = VECTOR(in,istride,from3); |
| const ATOMIC f3_imag = VECTOR(in,istride,from3 + 1); |
| const ATOMIC f4_real = VECTOR(in,istride,from4); |
| const ATOMIC f4_imag = VECTOR(in,istride,from4 + 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; |
| const ATOMIC z3_real = w3_real * f3_real - w3_imag * f3_imag; |
| const ATOMIC z3_imag = w3_real * f3_imag + w3_imag * f3_real; |
| const ATOMIC z4_real = w4_real * f4_real - w4_imag * f4_imag; |
| const ATOMIC z4_imag = w4_real * f4_imag + w4_imag * f4_real; |
| |
| /* 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 = -sina * t3_real - sinb * t4_real; |
| const ATOMIC t10_imag = -sina * t3_imag - sinb * t4_imag; |
| |
| /* t11 = -(sin(2 pi/10) t3 - sin(2 pi/5) t4) */ |
| const ATOMIC t11_real = -sinb * t3_real + sina * t4_real; |
| const ATOMIC t11_imag = -sinb * t3_imag + sina * t4_imag; |
| |
| /* x0 = z0 + t5 */ |
| const ATOMIC x0_real = z0_real + t5_real; |
| const ATOMIC x0_imag = z0_imag + t5_imag; |
| |
| /* x1 = t8 + i t10 */ |
| const ATOMIC x1_real = t8_real - t10_imag; |
| const ATOMIC x1_imag = t8_imag + t10_real; |
| |
| /* x2 = t9 + i t11 */ |
| const ATOMIC x2_real = t9_real - t11_imag; |
| const ATOMIC x2_imag = t9_imag + t11_real; |
| |
| /* x3 = t9 - i t11 */ |
| const ATOMIC x3_real = t9_real + t11_imag; |
| const ATOMIC x3_imag = t9_imag - t11_real; |
| |
| /* x4 = t8 - i t10 */ |
| const ATOMIC x4_real = t8_real + t10_imag; |
| const ATOMIC x4_imag = t8_imag - t10_real; |
| |
| const size_t to0 = k1 * product + 2 * k - 1; |
| const size_t to1 = to0 + 2 * product_1; |
| const size_t to2 = to1 + 2 * product_1; |
| const size_t to3 = 2 * product_1 - 2 * k + k1 * product - 1; |
| const size_t to4 = to3 + 2 * product_1; |
| |
| VECTOR(out,ostride,to0) = x0_real; |
| VECTOR(out,ostride,to0 + 1) = x0_imag; |
| |
| VECTOR(out,ostride,to1) = x1_real; |
| VECTOR(out,ostride,to1 + 1) = x1_imag; |
| |
| VECTOR(out,ostride,to2) = x2_real; |
| VECTOR(out,ostride,to2 + 1) = x2_imag; |
| |
| VECTOR(out,ostride,to3) = x4_real; |
| VECTOR(out,ostride,to3 + 1) = -x4_imag; |
| |
| VECTOR(out,ostride,to4) = x3_real; |
| VECTOR(out,ostride,to4 + 1) = -x3_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 size_t from3 = from2 + m; |
| const size_t from4 = from3 + 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 z3_real = VECTOR(in,istride,from3); |
| const ATOMIC z4_real = VECTOR(in,istride,from4); |
| |
| const ATOMIC t1 = z1_real - z4_real; |
| const ATOMIC t2 = z1_real + z4_real; |
| const ATOMIC t3 = z2_real - z3_real; |
| const ATOMIC t4 = z2_real + z3_real; |
| const ATOMIC t5 = t1 - t3; |
| const ATOMIC t6 = z0_real + t5 / 4.0; |
| const ATOMIC t7 = (sqrt (5.0) / 4.0) * (t1 + t3); |
| |
| const size_t to0 = k1 * product + product_1 - 1; |
| const size_t to1 = to0 + 2 * product_1; |
| const size_t to2 = to1 + 2 * product_1; |
| |
| VECTOR(out,ostride,to0) = t6 + t7; |
| VECTOR(out,ostride,to0 + 1) = -sinb * t2 - sina * t4; |
| |
| VECTOR(out,ostride,to1) = t6 - t7; |
| VECTOR(out,ostride,to1 + 1) = -sina * t2 + sinb * t4; |
| |
| VECTOR(out,ostride,to2) = z0_real - t5; |
| } |
| |
| return; |
| } |