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
|
/*
* 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 <stdlib.h>
#include <assert.h>
#include "bits.h"
#include "umodarith.h"
#include "numbertheory.h"
/* Bignum: Initialize the Number Theoretic Transform. */
/*
* Return the nth root of unity in F(p). This corresponds to e**((2*pi*i)/n)
* in the Fourier transform. We have w**n == 1 (mod p).
* n := transform length.
* sign := -1 for forward transform, 1 for backward transform.
* modnum := one of {P1, P2, P3}.
*/
mpd_uint_t
_mpd_getkernel(mpd_uint_t n, int sign, int modnum)
{
mpd_uint_t umod, p, r, xi;
#ifdef PPRO
double dmod;
uint32_t dinvmod[3];
#endif
SETMODULUS(modnum);
r = mpd_roots[modnum]; /* primitive root of F(p) */
p = umod;
xi = (p-1) / n;
if (sign == -1)
return POWMOD(r, (p-1-xi));
else
return POWMOD(r, xi);
}
/*
* Initialize and return transform parameters.
* n := transform length.
* sign := -1 for forward transform, 1 for backward transform.
* modnum := one of {P1, P2, P3}.
*/
struct fnt_params *
_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum)
{
struct fnt_params *tparams;
mpd_uint_t umod;
#ifdef PPRO
double dmod;
uint32_t dinvmod[3];
#endif
mpd_uint_t kernel, w;
mpd_uint_t i;
mpd_size_t nhalf;
assert(ispower2(n));
assert(sign == -1 || sign == 1);
assert(P1 <= modnum && modnum <= P3);
nhalf = n/2;
tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t));
if (tparams == NULL) {
return NULL;
}
SETMODULUS(modnum);
kernel = _mpd_getkernel(n, sign, modnum);
tparams->modnum = modnum;
tparams->modulus = umod;
tparams->kernel = kernel;
/* wtable[] := w**0, w**1, ..., w**(nhalf-1) */
w = 1;
for (i = 0; i < nhalf; i++) {
tparams->wtable[i] = w;
w = MULMOD(w, kernel);
}
return tparams;
}
/* Initialize wtable of size three. */
void
_mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum)
{
mpd_uint_t umod;
#ifdef PPRO
double dmod;
uint32_t dinvmod[3];
#endif
mpd_uint_t kernel;
SETMODULUS(modnum);
kernel = _mpd_getkernel(3, sign, modnum);
w3table[0] = 1;
w3table[1] = kernel;
w3table[2] = POWMOD(kernel, 2);
}
|
