| 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 -------------------------------------------------*/ |