3 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
21 FUNCTION(fft_complex,pass_5) (const BASE in[],
25 const gsl_fft_direction sign,
28 const TYPE(gsl_complex) twiddle1[],
29 const TYPE(gsl_complex) twiddle2[],
30 const TYPE(gsl_complex) twiddle3[],
31 const TYPE(gsl_complex) twiddle4[])
36 const size_t factor = 5;
37 const size_t m = n / factor;
38 const size_t q = n / product;
39 const size_t p_1 = product / factor;
40 const size_t jump = (factor - 1) * p_1;
42 const ATOMIC sin_2pi_by_5 = sin (2.0 * M_PI / 5.0);
43 const ATOMIC sin_2pi_by_10 = sin (2.0 * M_PI / 10.0);
45 for (k = 0; k < q; k++)
48 ATOMIC w1_real, w1_imag, w2_real, w2_imag, w3_real, w3_imag, w4_real,
64 if (sign == gsl_fft_forward)
66 /* forward tranform */
67 w1_real = GSL_REAL(twiddle1[k - 1]);
68 w1_imag = GSL_IMAG(twiddle1[k - 1]);
69 w2_real = GSL_REAL(twiddle2[k - 1]);
70 w2_imag = GSL_IMAG(twiddle2[k - 1]);
71 w3_real = GSL_REAL(twiddle3[k - 1]);
72 w3_imag = GSL_IMAG(twiddle3[k - 1]);
73 w4_real = GSL_REAL(twiddle4[k - 1]);
74 w4_imag = GSL_IMAG(twiddle4[k - 1]);
78 /* backward tranform: w -> conjugate(w) */
79 w1_real = GSL_REAL(twiddle1[k - 1]);
80 w1_imag = -GSL_IMAG(twiddle1[k - 1]);
81 w2_real = GSL_REAL(twiddle2[k - 1]);
82 w2_imag = -GSL_IMAG(twiddle2[k - 1]);
83 w3_real = GSL_REAL(twiddle3[k - 1]);
84 w3_imag = -GSL_IMAG(twiddle3[k - 1]);
85 w4_real = GSL_REAL(twiddle4[k - 1]);
86 w4_imag = -GSL_IMAG(twiddle4[k - 1]);
90 for (k1 = 0; k1 < p_1; k1++)
93 ATOMIC x0_real, x0_imag, x1_real, x1_imag, x2_real, x2_imag,
94 x3_real, x3_imag, x4_real, x4_imag;
96 const ATOMIC z0_real = REAL(in,istride,i);
97 const ATOMIC z0_imag = IMAG(in,istride,i);
98 const ATOMIC z1_real = REAL(in,istride,i + m);
99 const ATOMIC z1_imag = IMAG(in,istride,i + m);
100 const ATOMIC z2_real = REAL(in,istride,i + 2*m);
101 const ATOMIC z2_imag = IMAG(in,istride,i + 2*m);
102 const ATOMIC z3_real = REAL(in,istride,i + 3*m);
103 const ATOMIC z3_imag = IMAG(in,istride,i + 3*m);
104 const ATOMIC z4_real = REAL(in,istride,i + 4*m);
105 const ATOMIC z4_imag = IMAG(in,istride,i + 4*m);
107 /* compute x = W(5) z */
110 const ATOMIC t1_real = z1_real + z4_real;
111 const ATOMIC t1_imag = z1_imag + z4_imag;
114 const ATOMIC t2_real = z2_real + z3_real;
115 const ATOMIC t2_imag = z2_imag + z3_imag;
118 const ATOMIC t3_real = z1_real - z4_real;
119 const ATOMIC t3_imag = z1_imag - z4_imag;
122 const ATOMIC t4_real = z2_real - z3_real;
123 const ATOMIC t4_imag = z2_imag - z3_imag;
126 const ATOMIC t5_real = t1_real + t2_real;
127 const ATOMIC t5_imag = t1_imag + t2_imag;
129 /* t6 = (sqrt(5)/4)(t1 - t2) */
130 const ATOMIC t6_real = (sqrt (5.0) / 4.0) * (t1_real - t2_real);
131 const ATOMIC t6_imag = (sqrt (5.0) / 4.0) * (t1_imag - t2_imag);
133 /* t7 = z0 - ((t5)/4) */
134 const ATOMIC t7_real = z0_real - t5_real / 4.0;
135 const ATOMIC t7_imag = z0_imag - t5_imag / 4.0;
138 const ATOMIC t8_real = t7_real + t6_real;
139 const ATOMIC t8_imag = t7_imag + t6_imag;
142 const ATOMIC t9_real = t7_real - t6_real;
143 const ATOMIC t9_imag = t7_imag - t6_imag;
145 /* t10 = sin(2 pi/5) t3 + sin(2 pi/10) t4 */
146 const ATOMIC t10_real = ((int) sign) * (sin_2pi_by_5 * t3_real +
147 sin_2pi_by_10 * t4_real);
148 const ATOMIC t10_imag = ((int) sign) * (sin_2pi_by_5 * t3_imag +
149 sin_2pi_by_10 * t4_imag);
151 /* t11 = sin(2 pi/10) t3 - sin(2 pi/5) t4 */
152 const ATOMIC t11_real = ((int) sign) * (sin_2pi_by_10 * t3_real -
153 sin_2pi_by_5 * t4_real);
154 const ATOMIC t11_imag = ((int) sign) * (sin_2pi_by_10 * t3_imag -
155 sin_2pi_by_5 * t4_imag);
158 x0_real = z0_real + t5_real;
159 x0_imag = z0_imag + t5_imag;
161 /* x1 = t8 + i t10 */
162 x1_real = t8_real - t10_imag;
163 x1_imag = t8_imag + t10_real;
165 /* x2 = t9 + i t11 */
166 x2_real = t9_real - t11_imag;
167 x2_imag = t9_imag + t11_real;
169 /* x3 = t9 - i t11 */
170 x3_real = t9_real + t11_imag;
171 x3_imag = t9_imag - t11_real;
173 /* x4 = t8 - i t10 */
174 x4_real = t8_real + t10_imag;
175 x4_imag = t8_imag - t10_real;
177 /* apply twiddle factors */
180 REAL(out,ostride,j) = x0_real;
181 IMAG(out,ostride,j) = x0_imag;
184 REAL(out,ostride,j + p_1) = w1_real * x1_real - w1_imag * x1_imag;
185 IMAG(out,ostride,j + p_1) = w1_real * x1_imag + w1_imag * x1_real;
188 REAL(out,ostride,j + 2*p_1) = w2_real * x2_real - w2_imag * x2_imag;
189 IMAG(out,ostride,j+2*p_1) = w2_real * x2_imag + w2_imag * x2_real;
192 REAL(out,ostride,j+3*p_1) = w3_real * x3_real - w3_imag * x3_imag;
193 IMAG(out,ostride,j+3*p_1) = w3_real * x3_imag + w3_imag * x3_real;
196 REAL(out,ostride,j+4*p_1) = w4_real * x4_real - w4_imag * x4_imag;
197 IMAG(out,ostride,j+4*p_1) = w4_real * x4_imag + w4_imag * x4_real;