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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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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 | |
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30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include "mp.h" |
33 | |
34 | /*----- Main code ---------------------------------------------------------*/ |
35 | |
36 | /* --- @mp_jacobi@ --- * |
37 | * |
38 | * Arguments: @mp *a@ = an integer less than @n@ |
39 | * @mp *n@ = an odd integer |
40 | * |
41 | * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%. |
42 | * |
43 | * Use: Computes the Jacobi symbol. If @n@ is prime, this is the |
44 | * Legendre symbol and is equal to 1 if and only if @a@ is a |
45 | * quadratic residue mod @n@. The result is zero if and only if |
46 | * @a@ and @n@ have a common factor greater than one. |
47 | */ |
48 | |
49 | int mp_jacobi(mp *a, mp *n) |
50 | { |
51 | int s = 1; |
52 | |
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53 | assert(MP_ODDP(n)); |
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54 | |
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55 | /* --- Take copies of the arguments --- */ |
56 | |
57 | a = MP_COPY(a); |
58 | n = MP_COPY(n); |
59 | |
60 | /* --- Main recursive mess, flattened out into something nice --- */ |
61 | |
62 | for (;;) { |
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63 | mpw nn; |
64 | size_t e; |
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65 | |
66 | /* --- Some simple special cases --- */ |
67 | |
68 | MP_SHRINK(a); |
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69 | if (MP_ZEROP(a)) { |
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70 | s = 0; |
71 | goto done; |
72 | } |
73 | |
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74 | /* --- Main case with powers of two --- */ |
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75 | |
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76 | a = mp_odd(a, a, &e); |
77 | nn = n->v[0] & 7; |
78 | if ((e & 1) && (nn == 3 || nn == 5)) |
79 | s = -s; |
80 | if (MP_LEN(a) == 1 && a->v[0] == 1) |
81 | goto done; |
82 | if ((nn & 3) == 3 && (a->v[0] & 3) == 3) |
83 | s = -s; |
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84 | |
85 | /* --- Reduce and swap --- */ |
86 | |
87 | mp_div(0, &n, n, a); |
88 | { mp *t = n; n = a; a = t; } |
89 | } |
90 | |
91 | /* --- Wrap everything up --- */ |
92 | |
93 | done: |
94 | MP_DROP(a); |
95 | MP_DROP(n); |
96 | return (s); |
97 | } |
98 | |
99 | /*----- Test rig ----------------------------------------------------------*/ |
100 | |
101 | #ifdef TEST_RIG |
102 | |
103 | #include <mLib/testrig.h> |
104 | |
105 | static int verify(dstr *v) |
106 | { |
107 | mp *a = *(mp **)v[0].buf; |
108 | mp *n = *(mp **)v[1].buf; |
109 | int s = *(int *)v[2].buf; |
110 | int j = mp_jacobi(a, n); |
111 | int ok = 1; |
112 | |
113 | if (s != j) { |
114 | fputs("\n*** fail", stderr); |
115 | fputs("a = ", stderr); mp_writefile(a, stderr, 10); fputc('\n', stderr); |
116 | fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr); |
117 | fprintf(stderr, "s = %i\n", s); |
118 | fprintf(stderr, "j = %i\n", j); |
119 | ok = 0; |
120 | } |
121 | |
122 | mp_drop(a); |
123 | mp_drop(n); |
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124 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
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125 | return (ok); |
126 | } |
127 | |
128 | static test_chunk tests[] = { |
129 | { "jacobi", verify, { &type_mp, &type_mp, &type_int, 0 } }, |
130 | { 0, 0, { 0 } } |
131 | }; |
132 | |
133 | int main(int argc, char *argv[]) |
134 | { |
135 | sub_init(); |
136 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
137 | return (0); |
138 | } |
139 | |
140 | #endif |
141 | |
142 | /*----- That's all, folks -------------------------------------------------*/ |