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
|
/*
* Copyright (c) 2008-2012 Stefan Krah. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include "mpdecimal.h"
#include <stdio.h>
#include <assert.h>
#include "bits.h"
#include "numbertheory.h"
#include "umodarith.h"
#include "difradix2.h"
/* Bignum: The actual transform routine (decimation in frequency). */
/*
* Generate index pairs (x, bitreverse(x)) and carry out the permutation.
* n must be a power of two.
* Algorithm due to Brent/Lehmann, see Joerg Arndt, "Matters Computational",
* Chapter 1.14.4. [http://www.jjj.de/fxt/]
*/
static inline void
bitreverse_permute(mpd_uint_t a[], mpd_size_t n)
{
mpd_size_t x = 0;
mpd_size_t r = 0;
mpd_uint_t t;
do { /* Invariant: r = bitreverse(x) */
if (r > x) {
t = a[x];
a[x] = a[r];
a[r] = t;
}
/* Flip trailing consecutive 1 bits and the first zero bit
* that absorbs a possible carry. */
x += 1;
/* Mirror the operation on r: Flip n_trailing_zeros(x)+1
high bits of r. */
r ^= (n - (n >> (mpd_bsf(x)+1)));
/* The loop invariant is preserved. */
} while (x < n);
}
/* Fast Number Theoretic Transform, decimation in frequency. */
void
fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams)
{
mpd_uint_t *wtable = tparams->wtable;
mpd_uint_t umod;
#ifdef PPRO
double dmod;
uint32_t dinvmod[3];
#endif
mpd_uint_t u0, u1, v0, v1;
mpd_uint_t w, w0, w1, wstep;
mpd_size_t m, mhalf;
mpd_size_t j, r;
assert(ispower2(n));
assert(n >= 4);
SETMODULUS(tparams->modnum);
/* m == n */
mhalf = n / 2;
for (j = 0; j < mhalf; j += 2) {
w0 = wtable[j];
w1 = wtable[j+1];
u0 = a[j];
v0 = a[j+mhalf];
u1 = a[j+1];
v1 = a[j+1+mhalf];
a[j] = addmod(u0, v0, umod);
v0 = submod(u0, v0, umod);
a[j+1] = addmod(u1, v1, umod);
v1 = submod(u1, v1, umod);
MULMOD2(&v0, w0, &v1, w1);
a[j+mhalf] = v0;
a[j+1+mhalf] = v1;
}
wstep = 2;
for (m = n/2; m >= 2; m>>=1, wstep<<=1) {
mhalf = m / 2;
/* j == 0 */
for (r = 0; r < n; r += 2*m) {
u0 = a[r];
v0 = a[r+mhalf];
u1 = a[m+r];
v1 = a[m+r+mhalf];
a[r] = addmod(u0, v0, umod);
v0 = submod(u0, v0, umod);
a[m+r] = addmod(u1, v1, umod);
v1 = submod(u1, v1, umod);
a[r+mhalf] = v0;
a[m+r+mhalf] = v1;
}
for (j = 1; j < mhalf; j++) {
w = wtable[j*wstep];
for (r = 0; r < n; r += 2*m) {
u0 = a[r+j];
v0 = a[r+j+mhalf];
u1 = a[m+r+j];
v1 = a[m+r+j+mhalf];
a[r+j] = addmod(u0, v0, umod);
v0 = submod(u0, v0, umod);
a[m+r+j] = addmod(u1, v1, umod);
v1 = submod(u1, v1, umod);
MULMOD2C(&v0, &v1, w);
a[r+j+mhalf] = v0;
a[m+r+j+mhalf] = v1;
}
}
}
bitreverse_permute(a, n);
}
|
