Line data Source code
1 : /*
2 : * Copyright (c) 2008-2012 Stefan Krah. All rights reserved.
3 : *
4 : * Redistribution and use in source and binary forms, with or without
5 : * modification, are permitted provided that the following conditions
6 : * are met:
7 : *
8 : * 1. Redistributions of source code must retain the above copyright
9 : * notice, this list of conditions and the following disclaimer.
10 : *
11 : * 2. Redistributions in binary form must reproduce the above copyright
12 : * notice, this list of conditions and the following disclaimer in the
13 : * documentation and/or other materials provided with the distribution.
14 : *
15 : * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
16 : * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 : * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 : * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 : * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 : * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 : * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 : * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 : * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 : * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 : * SUCH DAMAGE.
26 : */
27 :
28 :
29 : #include "mpdecimal.h"
30 : #include <stdlib.h>
31 : #include <assert.h>
32 : #include "bits.h"
33 : #include "umodarith.h"
34 : #include "numbertheory.h"
35 :
36 :
37 : /* Bignum: Initialize the Number Theoretic Transform. */
38 :
39 :
40 : /*
41 : * Return the nth root of unity in F(p). This corresponds to e**((2*pi*i)/n)
42 : * in the Fourier transform. We have w**n == 1 (mod p).
43 : * n := transform length.
44 : * sign := -1 for forward transform, 1 for backward transform.
45 : * modnum := one of {P1, P2, P3}.
46 : */
47 : mpd_uint_t
48 0 : _mpd_getkernel(mpd_uint_t n, int sign, int modnum)
49 : {
50 : mpd_uint_t umod, p, r, xi;
51 : #ifdef PPRO
52 : double dmod;
53 : uint32_t dinvmod[3];
54 : #endif
55 :
56 0 : SETMODULUS(modnum);
57 0 : r = mpd_roots[modnum]; /* primitive root of F(p) */
58 0 : p = umod;
59 0 : xi = (p-1) / n;
60 :
61 0 : if (sign == -1)
62 0 : return POWMOD(r, (p-1-xi));
63 : else
64 0 : return POWMOD(r, xi);
65 : }
66 :
67 : /*
68 : * Initialize and return transform parameters.
69 : * n := transform length.
70 : * sign := -1 for forward transform, 1 for backward transform.
71 : * modnum := one of {P1, P2, P3}.
72 : */
73 : struct fnt_params *
74 0 : _mpd_init_fnt_params(mpd_size_t n, int sign, int modnum)
75 : {
76 : struct fnt_params *tparams;
77 : mpd_uint_t umod;
78 : #ifdef PPRO
79 : double dmod;
80 : uint32_t dinvmod[3];
81 : #endif
82 : mpd_uint_t kernel, w;
83 : mpd_uint_t i;
84 : mpd_size_t nhalf;
85 :
86 : assert(ispower2(n));
87 : assert(sign == -1 || sign == 1);
88 : assert(P1 <= modnum && modnum <= P3);
89 :
90 0 : nhalf = n/2;
91 0 : tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t));
92 0 : if (tparams == NULL) {
93 0 : return NULL;
94 : }
95 :
96 0 : SETMODULUS(modnum);
97 0 : kernel = _mpd_getkernel(n, sign, modnum);
98 :
99 0 : tparams->modnum = modnum;
100 0 : tparams->modulus = umod;
101 0 : tparams->kernel = kernel;
102 :
103 : /* wtable[] := w**0, w**1, ..., w**(nhalf-1) */
104 0 : w = 1;
105 0 : for (i = 0; i < nhalf; i++) {
106 0 : tparams->wtable[i] = w;
107 0 : w = MULMOD(w, kernel);
108 : }
109 :
110 0 : return tparams;
111 : }
112 :
113 : /* Initialize wtable of size three. */
114 : void
115 0 : _mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum)
116 : {
117 : mpd_uint_t umod;
118 : #ifdef PPRO
119 : double dmod;
120 : uint32_t dinvmod[3];
121 : #endif
122 : mpd_uint_t kernel;
123 :
124 0 : SETMODULUS(modnum);
125 0 : kernel = _mpd_getkernel(3, sign, modnum);
126 :
127 0 : w3table[0] = 1;
128 0 : w3table[1] = kernel;
129 0 : w3table[2] = POWMOD(kernel, 2);
130 0 : }
131 :
132 :
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