| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: lcrand.c,v 1.2 2000/07/02 15:21:20 mdw Exp $ |
| 4 | * |
| 5 | * Simple linear congruential generator |
| 6 | * |
| 7 | * (c) 1999 Straylight/Edgeware |
| 8 | * (c) 2000 Mark Wooding |
| 9 | */ |
| 10 | |
| 11 | /*----- Licensing notice --------------------------------------------------* |
| 12 | * |
| 13 | * Copyright (c) 2000 Mark Wooding |
| 14 | * All rights reserved. |
| 15 | * |
| 16 | * Redistribution and use in source and binary forms, with or without |
| 17 | * modification, are permitted provided that the following conditions are |
| 18 | * met: |
| 19 | * |
| 20 | * 1. Redistributions of source code must retain the above copyright |
| 21 | * notice, this list of conditions and the following disclaimer. |
| 22 | * |
| 23 | * 2, Redistributions in binary form must reproduce the above copyright |
| 24 | * notice, this list of conditions and the following disclaimer in the |
| 25 | * documentation and/or other materials provided with the distribution. |
| 26 | * |
| 27 | * 3. The name of the authors may not be used to endorse or promote |
| 28 | * products derived from this software without specific prior written |
| 29 | * permission. |
| 30 | * |
| 31 | * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED |
| 32 | * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF |
| 33 | * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN |
| 34 | * NO EVENT SHALL THE AUTHORS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, |
| 35 | * INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| 36 | * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR |
| 37 | * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 38 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| 39 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN |
| 40 | * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| 41 | * POSSIBILITY OF SUCH DAMAGE. |
| 42 | * |
| 43 | * Instead of accepting the above terms, you may redistribute and/or modify |
| 44 | * this software under the terms of either the GNU General Public License, |
| 45 | * or the GNU Library General Public License, published by the Free |
| 46 | * Software Foundation; either version 2 of the License, or (at your |
| 47 | * option) any later version. |
| 48 | */ |
| 49 | |
| 50 | /*----- Revision history --------------------------------------------------* |
| 51 | * |
| 52 | * $Log: lcrand.c,v $ |
| 53 | * Revision 1.2 2000/07/02 15:21:20 mdw |
| 54 | * Fix licence text. |
| 55 | * |
| 56 | * Revision 1.1 2000/05/21 11:28:30 mdw |
| 57 | * Initial check-in. |
| 58 | * |
| 59 | * --- Past lives (Catacomb) --- * |
| 60 | * |
| 61 | * Revision 1.2 1999/12/13 15:34:01 mdw |
| 62 | * Add support for seeding from a generic pseudorandom source. |
| 63 | * |
| 64 | * Revision 1.1 1999/12/10 23:15:27 mdw |
| 65 | * Noncryptographic random number generator. |
| 66 | * |
| 67 | */ |
| 68 | |
| 69 | /*----- Header files ------------------------------------------------------*/ |
| 70 | |
| 71 | #include <stdio.h> |
| 72 | #include <stdlib.h> |
| 73 | #include <string.h> |
| 74 | |
| 75 | #include "bits.h" |
| 76 | #include "lcrand.h" |
| 77 | |
| 78 | /*----- Magic numbers -----------------------------------------------------*/ |
| 79 | |
| 80 | /* --- The generator parameters --- */ |
| 81 | |
| 82 | #define P LCRAND_P /* Modulus */ |
| 83 | #define A LCRAND_A /* Multiplier (primitive mod @p@) */ |
| 84 | #define C LCRAND_C /* Additive constant */ |
| 85 | |
| 86 | /* --- Precomputed values for modular reduction --- */ |
| 87 | |
| 88 | #define D 5 /* %$p = 2^{32} - d$% */ |
| 89 | |
| 90 | /* --- Other useful bits --- */ |
| 91 | |
| 92 | #define P256 4294967040u /* Highest multiple of 256 < %$p$% */ |
| 93 | |
| 94 | /*----- Main code ---------------------------------------------------------*/ |
| 95 | |
| 96 | /* --- @lcrand@ --- * |
| 97 | * |
| 98 | * Arguments: @uint32 x@ = seed value |
| 99 | * |
| 100 | * Returns: New state of the generator. |
| 101 | * |
| 102 | * Use: Steps the generator. Returns %$ax + c \bmod p$%. |
| 103 | */ |
| 104 | |
| 105 | uint32 lcrand(uint32 x) |
| 106 | { |
| 107 | uint32 a[2], xx[2]; |
| 108 | uint32 yy[2]; |
| 109 | |
| 110 | /* --- Unpack things into the arrays --- */ |
| 111 | |
| 112 | a[0] = U16(A); a[1] = U16(A >> 16); |
| 113 | xx[0] = U16(x); xx[1] = U16(x >> 16); |
| 114 | |
| 115 | /* --- Multiply everything together --- * |
| 116 | * |
| 117 | * This is plain old long multiplication, although it looks a bit strange. |
| 118 | * I set up the top and bottom partial products directly where they're |
| 119 | * supposed to be. The cross terms I add together, with the low 16 bits in |
| 120 | * @q@ and the high 32 bits in @p@. These I then add into the product. |
| 121 | */ |
| 122 | |
| 123 | { |
| 124 | uint32 p, q; |
| 125 | |
| 126 | yy[0] = a[0] * xx[0]; |
| 127 | yy[1] = a[1] * xx[1]; |
| 128 | |
| 129 | p = a[0] * xx[1]; |
| 130 | q = p + a[1] * xx[0]; |
| 131 | p = ((q < p) << 16) + (q >> 16); |
| 132 | q = U16(q) << 16; |
| 133 | |
| 134 | q += yy[0]; |
| 135 | if (q < yy[0]) |
| 136 | p++; |
| 137 | else |
| 138 | p += (q >> 16) >> 16; |
| 139 | yy[0] = q; |
| 140 | |
| 141 | yy[1] += p; |
| 142 | } |
| 143 | |
| 144 | /* --- Now reduce mod p --- * |
| 145 | * |
| 146 | * I'm using shifts and adds to do the multiply step here. This needs to |
| 147 | * be changed if @D@ ever becomes something other than 5. |
| 148 | */ |
| 149 | |
| 150 | #if D != 5 |
| 151 | # error "Change shift sequence!" |
| 152 | #endif |
| 153 | |
| 154 | { |
| 155 | uint32 q; |
| 156 | |
| 157 | q = yy[1]; |
| 158 | x = yy[0]; |
| 159 | |
| 160 | while (q) { |
| 161 | uint32 y, z; |
| 162 | y = q >> 30; |
| 163 | z = q << 2; |
| 164 | z += q; |
| 165 | if (z < q) |
| 166 | y++; |
| 167 | else |
| 168 | y += (q >> 16) >> 16; |
| 169 | q = y; |
| 170 | x += z; |
| 171 | if (x < z || x > P) |
| 172 | x -= P; |
| 173 | } |
| 174 | } |
| 175 | |
| 176 | /* --- Now add on the constant --- */ |
| 177 | |
| 178 | x += C; |
| 179 | if (x < C || x >= P) |
| 180 | x -= P; |
| 181 | |
| 182 | /* --- Done --- */ |
| 183 | |
| 184 | return (x); |
| 185 | } |
| 186 | |
| 187 | /* --- @lcrand_range@ --- * |
| 188 | * |
| 189 | * Arguments: @uint32 *x@ = pointer to seed value (updated) |
| 190 | * @uint32 m@ = limit allowable |
| 191 | * |
| 192 | * Returns: A uniformly distributed pseudorandom integer in the interval |
| 193 | * %$[0, m)$%. |
| 194 | */ |
| 195 | |
| 196 | uint32 lcrand_range(uint32 *x, uint32 m) |
| 197 | { |
| 198 | uint32 xx = *x; |
| 199 | uint32 r = P - P % m; |
| 200 | do xx = lcrand(xx); while (xx >= r); |
| 201 | *x = xx; |
| 202 | return (xx / (r / m)); |
| 203 | } |
| 204 | |
| 205 | /*----- That's all, folks -------------------------------------------------*/ |