1 /*
2 * Copyright (c) 2008-2016 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
_mpd_getkernel(mpd_uint_t n,int sign,int modnum)48 _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 SETMODULUS(modnum);
57 r = mpd_roots[modnum]; /* primitive root of F(p) */
58 p = umod;
59 xi = (p-1) / n;
60
61 if (sign == -1)
62 return POWMOD(r, (p-1-xi));
63 else
64 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 *
_mpd_init_fnt_params(mpd_size_t n,int sign,int modnum)74 _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 nhalf = n/2;
91 tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t));
92 if (tparams == NULL) {
93 return NULL;
94 }
95
96 SETMODULUS(modnum);
97 kernel = _mpd_getkernel(n, sign, modnum);
98
99 tparams->modnum = modnum;
100 tparams->modulus = umod;
101 tparams->kernel = kernel;
102
103 /* wtable[] := w**0, w**1, ..., w**(nhalf-1) */
104 w = 1;
105 for (i = 0; i < nhalf; i++) {
106 tparams->wtable[i] = w;
107 w = MULMOD(w, kernel);
108 }
109
110 return tparams;
111 }
112
113 /* Initialize wtable of size three. */
114 void
_mpd_init_w3table(mpd_uint_t w3table[3],int sign,int modnum)115 _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 SETMODULUS(modnum);
125 kernel = _mpd_getkernel(3, sign, modnum);
126
127 w3table[0] = 1;
128 w3table[1] = kernel;
129 w3table[2] = POWMOD(kernel, 2);
130 }
131
132
133