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
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
|
/* fft/factorize.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.
*/
#include <config.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_fft_complex.h>
#include "factorize.h"
static int
fft_complex_factorize (const size_t n,
size_t *nf,
size_t factors[])
{
const size_t complex_subtransforms[] =
{7, 6, 5, 4, 3, 2, 0};
/* other factors can be added here if their transform modules are
implemented. The end of the list is marked by 0. */
int status = fft_factorize (n, complex_subtransforms, nf, factors);
return status;
}
static int
fft_halfcomplex_factorize (const size_t n,
size_t *nf,
size_t factors[])
{
const size_t halfcomplex_subtransforms[] =
{5, 4, 3, 2, 0};
int status = fft_factorize (n, halfcomplex_subtransforms, nf, factors);
return status;
}
static int
fft_real_factorize (const size_t n,
size_t *nf,
size_t factors[])
{
const size_t real_subtransforms[] =
{5, 4, 3, 2, 0};
int status = fft_factorize (n, real_subtransforms, nf, factors);
return status;
}
static int
fft_factorize (const size_t n,
const size_t implemented_subtransforms[],
size_t *n_factors,
size_t factors[])
{
size_t nf = 0;
size_t ntest = n;
size_t factor;
size_t i = 0;
if (n == 0)
{
GSL_ERROR ("length n must be positive integer", GSL_EDOM);
}
if (n == 1)
{
factors[0] = 1;
*n_factors = 1;
return 0;
}
/* deal with the implemented factors first */
while (implemented_subtransforms[i] && ntest != 1)
{
factor = implemented_subtransforms[i];
while ((ntest % factor) == 0)
{
ntest = ntest / factor;
factors[nf] = factor;
nf++;
}
i++;
}
/* deal with any other even prime factors (there is only one) */
factor = 2;
while ((ntest % factor) == 0 && (ntest != 1))
{
ntest = ntest / factor;
factors[nf] = factor;
nf++;
}
/* deal with any other odd prime factors */
factor = 3;
while (ntest != 1)
{
while ((ntest % factor) != 0)
{
factor += 2;
}
ntest = ntest / factor;
factors[nf] = factor;
nf++;
}
/* check that the factorization is correct */
{
size_t product = 1;
for (i = 0; i < nf; i++)
{
product *= factors[i];
}
if (product != n)
{
GSL_ERROR ("factorization failed", GSL_ESANITY);
}
}
*n_factors = nf;
return 0;
}
static int
fft_binary_logn (const size_t n)
{
size_t ntest ;
size_t binary_logn = 0 ;
size_t k = 1;
while (k < n)
{
k *= 2;
binary_logn++;
}
ntest = (1 << binary_logn) ;
if (n != ntest )
{
return -1 ; /* n is not a power of 2 */
}
return binary_logn;
}
|
