1/* gen-jacobi.c 2 3 Contributed to the GNU project by Niels M��ller. 4 5Copyright 2010 Free Software Foundation, Inc. 6 7This file is part of the GNU MP Library. 8 9The GNU MP Library is free software; you can redistribute it and/or modify 10it under the terms of either: 11 12 * the GNU Lesser General Public License as published by the Free 13 Software Foundation; either version 3 of the License, or (at your 14 option) any later version. 15 16or 17 18 * the GNU General Public License as published by the Free Software 19 Foundation; either version 2 of the License, or (at your option) any 20 later version. 21 22or both in parallel, as here. 23 24The GNU MP Library is distributed in the hope that it will be useful, but 25WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 26or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 27for more details. 28 29You should have received copies of the GNU General Public License and the 30GNU Lesser General Public License along with the GNU MP Library. If not, 31see https://www.gnu.org/licenses/. */ 32 33/* Generate the lookup table needed for fast left-to-right computation 34 of the Jacobi symbol. */ 35 36#include <assert.h> 37#include <stdio.h> 38#include <stdlib.h> 39 40static const struct 41{ 42 unsigned char a; 43 unsigned char b; 44} decode_table[13] = { 45 /* 0 */ { 0, 1 }, 46 /* 1 */ { 0, 3 }, 47 /* 2 */ { 1, 1 }, 48 /* 3 */ { 1, 3 }, 49 /* 4 */ { 2, 1 }, 50 /* 5 */ { 2, 3 }, 51 /* 6 */ { 3, 1 }, 52 /* 7 */ { 3, 3 }, /* d = 1 */ 53 /* 8 */ { 1, 0 }, 54 /* 9 */ { 1, 2 }, 55 /* 10 */ { 3, 0 }, 56 /* 11 */ { 3, 2 }, 57 /* 12 */ { 3, 3 }, /* d = 0 */ 58 59}; 60#define JACOBI_A(bits) (decode_table[(bits)>>1].a) 61#define JACOBI_B(bits) (decode_table[(bits)>>1].b) 62 63#define JACOBI_E(bits) ((bits) & 1) 64#define JACOBI_D(bits) (((bits)>>1) == 7) /* Gives 0 for don't care states. */ 65 66static unsigned 67encode (unsigned a, unsigned b, unsigned d) 68{ 69 unsigned i; 70 71 assert (d < 2); 72 assert (a < 4); 73 assert (b < 4); 74 assert ( (a | b ) & 1); 75 76 if (a == 3 && b == 3) 77 return d ? 7 : 12; 78 79 for (i = 0; i < 12; i++) 80 if (decode_table[i].a == a 81 && decode_table[i].b == b) 82 return i; 83 84 abort (); 85} 86 87int 88main (int argc, char **argv) 89{ 90 unsigned bits; 91 92 for (bits = 0; bits < 208; bits++) 93 { 94 unsigned e, a, b, d_old, d, q; 95 96 if (bits && !(bits & 0xf)) 97 printf("\n"); 98 99 q = bits & 3; 100 d = (bits >> 2) & 1; 101 102 e = JACOBI_E (bits >> 3); 103 a = JACOBI_A (bits >> 3); 104 b = JACOBI_B (bits >> 3); 105 d_old = JACOBI_D (bits >> 3); 106 107 if (d != d_old && a == 3 && b == 3) 108 e ^= 1; 109 110 if (d == 1) 111 { 112 if (b == 2) 113 e ^= (q & (a >> 1)) ^ (q >> 1); 114 a = (a - q * b) & 3; 115 } 116 else 117 { 118 if (a == 2) 119 e ^= (q & (b >> 1)) ^ (q >> 1); 120 b = (b - q * a) & 3; 121 } 122 123 printf("%2d,", (encode (a, b, d) << 1) | e); 124 } 125 printf("\n"); 126 127 return 0; 128} 129