1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
|
/* fft/real_pass_2.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_2) (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) twiddle[])
{
size_t k, k1;
const size_t factor = 2;
const size_t m = n / factor;
const size_t q = n / product;
const size_t product_1 = product / factor;
for (k1 = 0; k1 < q; k1++)
{
const size_t from0 = k1 * product_1;
const size_t from1 = from0 + m;
const ATOMIC r0 = VECTOR(in,istride,from0);
const ATOMIC r1 = VECTOR(in,istride,from1);
const ATOMIC s0 = r0 + r1;
const ATOMIC s1 = r0 - r1;
const size_t to0 = product * k1;
const size_t to1 = to0 + product - 1;
VECTOR(out,ostride,to0) = s0;
VECTOR(out,ostride,to1) = s1;
}
if (product_1 == 1)
return;
for (k = 1; k < (product_1 + 1) / 2; k++)
{
/* forward real transform: w -> conjugate(w) */
const ATOMIC w_real = GSL_REAL(twiddle[k - 1]);
const ATOMIC w_imag = -GSL_IMAG(twiddle[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 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 z0_real = f0_real;
const ATOMIC z0_imag = f0_imag;
const ATOMIC z1_real = w_real * f1_real - w_imag * f1_imag;
const ATOMIC z1_imag = w_real * f1_imag + w_imag * f1_real;
/* compute x = W(2) z */
/* x0 = z0 + z1 */
const ATOMIC x0_real = z0_real + z1_real;
const ATOMIC x0_imag = z0_imag + z1_imag;
/* x1 = z0 - z1 */
const ATOMIC x1_real = z0_real - z1_real;
const ATOMIC x1_imag = z0_imag - z1_imag;
const size_t to0 = k1 * product + 2 * k - 1;
const size_t to1 = k1 * product + product - 2 * k - 1;
VECTOR(out,ostride,to0) = x0_real;
VECTOR(out,ostride,to0 + 1) = x0_imag;
/* stored in conjugate location */
VECTOR(out,ostride,to1) = x1_real;
VECTOR(out,ostride,to1 + 1) = -x1_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 to0 = k1 * product + product_1 - 1;
VECTOR(out,ostride,to0) = VECTOR(in,istride,from0);
VECTOR(out,ostride,to0 + 1) = -VECTOR(in,istride,from1);
}
return;
}
|
