5b00a0ea |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: mp-jacobi.c,v 1.1 1999/11/22 20:50:37 mdw Exp $ |
4 | * |
5 | * Compute Jacobi symbol |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: mp-jacobi.c,v $ |
33 | * Revision 1.1 1999/11/22 20:50:37 mdw |
34 | * Add support for computing Jacobi symbols. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include "mp.h" |
41 | |
42 | /*----- Main code ---------------------------------------------------------*/ |
43 | |
44 | /* --- @mp_jacobi@ --- * |
45 | * |
46 | * Arguments: @mp *a@ = an integer less than @n@ |
47 | * @mp *n@ = an odd integer |
48 | * |
49 | * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%. |
50 | * |
51 | * Use: Computes the Jacobi symbol. If @n@ is prime, this is the |
52 | * Legendre symbol and is equal to 1 if and only if @a@ is a |
53 | * quadratic residue mod @n@. The result is zero if and only if |
54 | * @a@ and @n@ have a common factor greater than one. |
55 | */ |
56 | |
57 | int mp_jacobi(mp *a, mp *n) |
58 | { |
59 | int s = 1; |
60 | |
61 | /* --- Take copies of the arguments --- */ |
62 | |
63 | a = MP_COPY(a); |
64 | n = MP_COPY(n); |
65 | |
66 | /* --- Main recursive mess, flattened out into something nice --- */ |
67 | |
68 | for (;;) { |
69 | |
70 | /* --- Some simple special cases --- */ |
71 | |
72 | MP_SHRINK(a); |
73 | |
74 | if (MP_LEN(a) == 0) { |
75 | s = 0; |
76 | goto done; |
77 | } |
78 | |
79 | /* --- Find the power-of-two factor in @a@ --- */ |
80 | |
81 | { |
82 | mpscan sc; |
83 | mpw nn; |
84 | unsigned e; |
85 | |
86 | /* --- Scan for a set bit --- */ |
87 | |
88 | MP_SCAN(&sc, a); |
89 | e = 0; |
90 | while (MP_STEP(&sc) && !MP_BIT(&sc)) |
91 | e++; |
92 | |
93 | /* --- Do the shift --- */ |
94 | |
95 | if (e) |
96 | a = mp_lsr(a, a, e); |
97 | |
98 | /* --- Maybe adjust the sign of @s@ --- */ |
99 | |
100 | nn = n->v[0] & 7; |
101 | if ((e & 1) && (nn == 3 || nn == 5)) |
102 | s = -s; |
103 | |
104 | if (MP_LEN(a) == 1 && a->v[0] == 1) |
105 | goto done; |
106 | |
107 | if ((nn & 3) == 3 && (a->v[0] & 3) == 3) |
108 | s = -s; |
109 | } |
110 | |
111 | /* --- Reduce and swap --- */ |
112 | |
113 | mp_div(0, &n, n, a); |
114 | { mp *t = n; n = a; a = t; } |
115 | } |
116 | |
117 | /* --- Wrap everything up --- */ |
118 | |
119 | done: |
120 | MP_DROP(a); |
121 | MP_DROP(n); |
122 | return (s); |
123 | } |
124 | |
125 | /*----- Test rig ----------------------------------------------------------*/ |
126 | |
127 | #ifdef TEST_RIG |
128 | |
129 | #include <mLib/testrig.h> |
130 | |
131 | static int verify(dstr *v) |
132 | { |
133 | mp *a = *(mp **)v[0].buf; |
134 | mp *n = *(mp **)v[1].buf; |
135 | int s = *(int *)v[2].buf; |
136 | int j = mp_jacobi(a, n); |
137 | int ok = 1; |
138 | |
139 | if (s != j) { |
140 | fputs("\n*** fail", stderr); |
141 | fputs("a = ", stderr); mp_writefile(a, stderr, 10); fputc('\n', stderr); |
142 | fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr); |
143 | fprintf(stderr, "s = %i\n", s); |
144 | fprintf(stderr, "j = %i\n", j); |
145 | ok = 0; |
146 | } |
147 | |
148 | mp_drop(a); |
149 | mp_drop(n); |
150 | return (ok); |
151 | } |
152 | |
153 | static test_chunk tests[] = { |
154 | { "jacobi", verify, { &type_mp, &type_mp, &type_int, 0 } }, |
155 | { 0, 0, { 0 } } |
156 | }; |
157 | |
158 | int main(int argc, char *argv[]) |
159 | { |
160 | sub_init(); |
161 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
162 | return (0); |
163 | } |
164 | |
165 | #endif |
166 | |
167 | /*----- That's all, folks -------------------------------------------------*/ |