| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: lcrand.c,v 1.3 2000/06/17 11:29:03 mdw Exp $ |
| 4 | * |
| 5 | * Simple linear congruential generator |
| 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: lcrand.c,v $ |
| 33 | * Revision 1.3 2000/06/17 11:29:03 mdw |
| 34 | * Add the flags word to the generic generator. |
| 35 | * |
| 36 | * Revision 1.2 1999/12/13 15:34:01 mdw |
| 37 | * Add support for seeding from a generic pseudorandom source. |
| 38 | * |
| 39 | * Revision 1.1 1999/12/10 23:15:27 mdw |
| 40 | * Noncryptographic random number generator. |
| 41 | * |
| 42 | */ |
| 43 | |
| 44 | /*----- Header files ------------------------------------------------------*/ |
| 45 | |
| 46 | #include <stdarg.h> |
| 47 | #include <stdio.h> |
| 48 | #include <stdlib.h> |
| 49 | #include <string.h> |
| 50 | |
| 51 | #include <mLib/bits.h> |
| 52 | #include <mLib/sub.h> |
| 53 | |
| 54 | #include "grand.h" |
| 55 | #include "lcrand.h" |
| 56 | |
| 57 | /*----- Magic numbers -----------------------------------------------------*/ |
| 58 | |
| 59 | /* --- The generator parameters --- */ |
| 60 | |
| 61 | #define P LCRAND_P /* Modulus */ |
| 62 | #define A LCRAND_A /* Multiplier (primitive mod @p@) */ |
| 63 | #define C LCRAND_C /* Additive constant */ |
| 64 | |
| 65 | /* --- Precomputed values for modular reduction --- */ |
| 66 | |
| 67 | #define D 5 /* %$p = 2^{32} - d$% */ |
| 68 | |
| 69 | /* --- Other useful bits --- */ |
| 70 | |
| 71 | #define P256 4294967040u /* Highest multiple of 256 < %$p$% */ |
| 72 | |
| 73 | /*----- Main code ---------------------------------------------------------*/ |
| 74 | |
| 75 | /* --- @lcrand@ --- * |
| 76 | * |
| 77 | * Arguments: @uint32 x@ = seed value |
| 78 | * |
| 79 | * Returns: New state of the generator. |
| 80 | * |
| 81 | * Use: Steps the generator. Returns %$ax + c \bmod p$%. |
| 82 | */ |
| 83 | |
| 84 | uint32 lcrand(uint32 x) |
| 85 | { |
| 86 | uint32 a[2], xx[2]; |
| 87 | uint32 yy[2]; |
| 88 | |
| 89 | /* --- Unpack things into the arrays --- */ |
| 90 | |
| 91 | a[0] = U16(A); a[1] = U16(A >> 16); |
| 92 | xx[0] = U16(x); xx[1] = U16(x >> 16); |
| 93 | |
| 94 | /* --- Multiply everything together --- * |
| 95 | * |
| 96 | * This is plain old long multiplication, although it looks a bit strange. |
| 97 | * I set up the top and bottom partial products directly where they're |
| 98 | * supposed to be. The cross terms I add together, with the low 16 bits in |
| 99 | * @q@ and the high 32 bits in @p@. These I then add into the product. |
| 100 | */ |
| 101 | |
| 102 | { |
| 103 | uint32 p, q; |
| 104 | |
| 105 | yy[0] = a[0] * xx[0]; |
| 106 | yy[1] = a[1] * xx[1]; |
| 107 | |
| 108 | p = a[0] * xx[1]; |
| 109 | q = p + a[1] * xx[0]; |
| 110 | p = ((q < p) << 16) + (q >> 16); |
| 111 | q = U16(q) << 16; |
| 112 | |
| 113 | q += yy[0]; |
| 114 | if (q < yy[0]) |
| 115 | p++; |
| 116 | else |
| 117 | p += (q >> 16) >> 16; |
| 118 | yy[0] = q; |
| 119 | |
| 120 | yy[1] += p; |
| 121 | } |
| 122 | |
| 123 | /* --- Now reduce mod p --- * |
| 124 | * |
| 125 | * I'm using shifts and adds to do the multiply step here. This needs to |
| 126 | * be changed if @D@ ever becomes something other than 5. |
| 127 | */ |
| 128 | |
| 129 | #if D != 5 |
| 130 | # error "Change shift sequence!" |
| 131 | #endif |
| 132 | |
| 133 | { |
| 134 | uint32 q; |
| 135 | |
| 136 | q = yy[1]; |
| 137 | x = yy[0]; |
| 138 | |
| 139 | while (q) { |
| 140 | uint32 y, z; |
| 141 | y = q >> 30; |
| 142 | z = q << 2; |
| 143 | z += q; |
| 144 | if (z < q) |
| 145 | y++; |
| 146 | else |
| 147 | y += (q >> 16) >> 16; |
| 148 | q = y; |
| 149 | x += z; |
| 150 | if (x < z || x > P) |
| 151 | x -= P; |
| 152 | } |
| 153 | } |
| 154 | |
| 155 | /* --- Now add on the constant --- */ |
| 156 | |
| 157 | x += C; |
| 158 | if (x < C || x >= P) |
| 159 | x -= P; |
| 160 | |
| 161 | /* --- Done --- */ |
| 162 | |
| 163 | return (x); |
| 164 | } |
| 165 | |
| 166 | /* --- @lcrand_range@ --- * |
| 167 | * |
| 168 | * Arguments: @uint32 *x@ = pointer to seed value (updated) |
| 169 | * @uint32 m@ = limit allowable |
| 170 | * |
| 171 | * Returns: A uniformly distributed pseudorandom integer in the interval |
| 172 | * %$[0, m)$%. |
| 173 | */ |
| 174 | |
| 175 | uint32 lcrand_range(uint32 *x, uint32 m) |
| 176 | { |
| 177 | uint32 xx = *x; |
| 178 | uint32 r = P - P % m; |
| 179 | do xx = lcrand(xx); while (xx >= r); |
| 180 | *x = xx; |
| 181 | return (xx / (r / m)); |
| 182 | } |
| 183 | |
| 184 | /*----- Generic interface -------------------------------------------------*/ |
| 185 | |
| 186 | typedef struct gctx { |
| 187 | grand r; |
| 188 | uint32 x; |
| 189 | } gctx; |
| 190 | |
| 191 | static void gdestroy(grand *r) |
| 192 | { |
| 193 | gctx *g = (gctx *)r; |
| 194 | DESTROY(g); |
| 195 | } |
| 196 | |
| 197 | static int gmisc(grand *r, unsigned op, ...) |
| 198 | { |
| 199 | gctx *g = (gctx *)r; |
| 200 | va_list ap; |
| 201 | int rc = 0; |
| 202 | va_start(ap, op); |
| 203 | |
| 204 | switch (op) { |
| 205 | case GRAND_CHECK: |
| 206 | switch (va_arg(ap, unsigned)) { |
| 207 | case GRAND_CHECK: |
| 208 | case GRAND_SEEDINT: |
| 209 | case GRAND_SEEDUINT32: |
| 210 | case GRAND_SEEDRAND: |
| 211 | rc = 1; |
| 212 | break; |
| 213 | default: |
| 214 | rc = 0; |
| 215 | break; |
| 216 | } |
| 217 | break; |
| 218 | case GRAND_SEEDINT: |
| 219 | g->x = va_arg(ap, unsigned); |
| 220 | break; |
| 221 | case GRAND_SEEDUINT32: |
| 222 | g->x = va_arg(ap, uint32); |
| 223 | break; |
| 224 | case GRAND_SEEDRAND: { |
| 225 | grand *rr = va_arg(ap, grand *); |
| 226 | uint32 x; |
| 227 | do x = rr->ops->word(rr); while (x >= P || x == LCRAND_FIXEDPT); |
| 228 | g->x = x; |
| 229 | } break; |
| 230 | default: |
| 231 | GRAND_BADOP; |
| 232 | break; |
| 233 | } |
| 234 | |
| 235 | va_end(ap); |
| 236 | return (rc); |
| 237 | } |
| 238 | |
| 239 | static uint32 graw(grand *r) |
| 240 | { |
| 241 | gctx *g = (gctx *)r; |
| 242 | g->x = lcrand(g->x); |
| 243 | return (g->x); |
| 244 | } |
| 245 | |
| 246 | static octet gbyte(grand *r) |
| 247 | { |
| 248 | gctx *g = (gctx *)r; |
| 249 | uint32 x = g->x; |
| 250 | do x = lcrand(x); while (x >= P256); |
| 251 | g->x = x; |
| 252 | return (x / (P256 / 256)); |
| 253 | } |
| 254 | |
| 255 | static uint32 grange(grand *r, uint32 l) |
| 256 | { |
| 257 | gctx *g = (gctx *)r; |
| 258 | return (lcrand_range(&g->x, l)); |
| 259 | } |
| 260 | |
| 261 | static const grand_ops gops = { |
| 262 | "lcrand", |
| 263 | LCRAND_P, 0, |
| 264 | gmisc, gdestroy, |
| 265 | graw, gbyte, grand_word, grange, grand_fill |
| 266 | }; |
| 267 | |
| 268 | /* --- @lcrand_create@ --- * |
| 269 | * |
| 270 | * Arguments: @uint32 x@ = initial seed |
| 271 | * |
| 272 | * Returns: Pointer to a generic generator. |
| 273 | * |
| 274 | * Use: Constructs a generic generator interface over a linear |
| 275 | * congruential generator. |
| 276 | */ |
| 277 | |
| 278 | grand *lcrand_create(uint32 x) |
| 279 | { |
| 280 | gctx *g = CREATE(gctx); |
| 281 | g->r.ops = &gops; |
| 282 | g->x = x; |
| 283 | return (&g->r); |
| 284 | } |
| 285 | |
| 286 | /*----- Test rig ----------------------------------------------------------*/ |
| 287 | |
| 288 | #ifdef TEST_RIG |
| 289 | |
| 290 | #include <mLib/testrig.h> |
| 291 | |
| 292 | static int verify(dstr *v) |
| 293 | { |
| 294 | uint32 x = *(uint32 *)v[0].buf; |
| 295 | uint32 y = *(uint32 *)v[1].buf; |
| 296 | uint32 z = lcrand(x); |
| 297 | int ok = 1; |
| 298 | if (y != z) { |
| 299 | fprintf(stderr, |
| 300 | "\n*** lcrand failed. lcrand(%lu) = %lu, expected %lu\n", |
| 301 | (unsigned long)x, (unsigned long)z, (unsigned long)y); |
| 302 | ok = 0; |
| 303 | } |
| 304 | return (ok); |
| 305 | } |
| 306 | |
| 307 | static test_chunk tests[] = { |
| 308 | { "lcrand", verify, { &type_uint32, &type_uint32, 0 } }, |
| 309 | { 0, 0, { 0 } } |
| 310 | }; |
| 311 | |
| 312 | int main(int argc, char *argv[]) |
| 313 | { |
| 314 | test_run(argc, argv, tests, SRCDIR"/tests/lcrand"); |
| 315 | return (0); |
| 316 | } |
| 317 | |
| 318 | #endif |
| 319 | |
| 320 | /*----- That's all, folks -------------------------------------------------*/ |