1 /* 2 * CDDL HEADER START 3 * 4 * The contents of this file are subject to the terms of the 5 * Common Development and Distribution License, Version 1.0 only 6 * (the "License"). You may not use this file except in compliance 7 * with the License. 8 * 9 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 10 * or http://www.opensolaris.org/os/licensing. 11 * See the License for the specific language governing permissions 12 * and limitations under the License. 13 * 14 * When distributing Covered Code, include this CDDL HEADER in each 15 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 16 * If applicable, add the following below this CDDL HEADER, with the 17 * fields enclosed by brackets "[]" replaced with your own identifying 18 * information: Portions Copyright [yyyy] [name of copyright owner] 19 * 20 * CDDL HEADER END 21 */ 22 /* 23 * Copyright 2004 Sun Microsystems, Inc. All rights reserved. 24 * Use is subject to license terms. 25 */ 26 27 /* Copyright (c) 1984, 1986, 1987, 1988, 1989 AT&T */ 28 /* All Rights Reserved */ 29 30 /* 31 * University Copyright- Copyright (c) 1982, 1986, 1988 32 * The Regents of the University of California 33 * All Rights Reserved 34 * 35 * University Acknowledgment- Portions of this document are derived from 36 * software developed by the University of California, Berkeley, and its 37 * contributors. 38 */ 39 40 #pragma ident "%Z%%M% %I% %E% SMI" 41 42 #include "synonyms.h" 43 #include <stdio.h> 44 #include <stdlib.h> 45 #include <sys/types.h> 46 #include <limits.h> 47 48 /* 49 * random.c: 50 * An improved random number generation package. In addition to the standard 51 * rand()/srand() like interface, this package also has a special state info 52 * interface. The initstate() routine is called with a seed, an array of 53 * bytes, and a count of how many bytes are being passed in; this array is then 54 * initialized to contain information for random number generation with that 55 * much state information. Good sizes for the amount of state information are 56 * 32, 64, 128, and 256 bytes. The state can be switched by calling the 57 * setstate() routine with the same array as was initiallized with initstate(). 58 * By default, the package runs with 128 bytes of state information and 59 * generates far better random numbers than a linear congruential generator. 60 * If the amount of state information is less than 32 bytes, a simple linear 61 * congruential R.N.G. is used. 62 * Internally, the state information is treated as an array of ints; the 63 * zeroeth element of the array is the type of R.N.G. being used (small 64 * integer); the remainder of the array is the state information for the 65 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 66 * state information, which will allow a degree seven polynomial. (Note: the 67 * zeroeth word of state information also has some other information stored 68 * in it -- see setstate() for details). 69 * The random number generation technique is a linear feedback shift register 70 * approach, employing trinomials (since there are fewer terms to sum up that 71 * way). In this approach, the least significant bit of all the numbers in 72 * the state table will act as a linear feedback shift register, and will have 73 * period 2^deg - 1 (where deg is the degree of the polynomial being used, 74 * assuming that the polynomial is irreducible and primitive). The higher 75 * order bits will have longer periods, since their values are also influenced 76 * by pseudo-random carries out of the lower bits. The total period of the 77 * generator is approximately deg*(2**deg - 1); thus doubling the amount of 78 * state information has a vast influence on the period of the generator. 79 * Note: the deg*(2**deg - 1) is an approximation only good for large deg, 80 * when the period of the shift register is the dominant factor. With deg 81 * equal to seven, the period is actually much longer than the 7*(2**7 - 1) 82 * predicted by this formula. 83 */ 84 85 86 87 /* 88 * For each of the currently supported random number generators, we have a 89 * break value on the amount of state information (you need at least this 90 * many bytes of state info to support this random number generator), a degree 91 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 92 * the separation between the two lower order coefficients of the trinomial. 93 */ 94 95 #define TYPE_0 0 /* linear congruential */ 96 #define BREAK_0 8 97 #define DEG_0 0 98 #define SEP_0 0 99 100 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 101 #define BREAK_1 32 102 #define DEG_1 7 103 #define SEP_1 3 104 105 #define TYPE_2 2 /* x**15 + x + 1 */ 106 #define BREAK_2 64 107 #define DEG_2 15 108 #define SEP_2 1 109 110 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 111 #define BREAK_3 128 112 #define DEG_3 31 113 #define SEP_3 3 114 115 #define TYPE_4 4 /* x**63 + x + 1 */ 116 #define BREAK_4 256 117 #define DEG_4 63 118 #define SEP_4 1 119 120 121 /* 122 * Array versions of the above information to make code run faster -- relies 123 * on fact that TYPE_i == i. 124 */ 125 126 #define MAX_TYPES 5 /* max number of types above */ 127 128 static struct _randomjunk { 129 unsigned int degrees[MAX_TYPES]; 130 unsigned int seps[MAX_TYPES]; 131 unsigned int randtbl[ DEG_3 + 1 ]; 132 /* 133 * fptr and rptr are two pointers into the state info, a front and a rear 134 * pointer. These two pointers are always rand_sep places aparts, as they cycle 135 * cyclically through the state information. (Yes, this does mean we could get 136 * away with just one pointer, but the code for random() is more efficient this 137 * way). The pointers are left positioned as they would be from the call 138 * initstate( 1, randtbl, 128 ) 139 * (The position of the rear pointer, rptr, is really 0 (as explained above 140 * in the initialization of randtbl) because the state table pointer is set 141 * to point to randtbl[1] (as explained below). 142 */ 143 unsigned int *fptr, *rptr; 144 /* 145 * The following things are the pointer to the state information table, 146 * the type of the current generator, the degree of the current polynomial 147 * being used, and the separation between the two pointers. 148 * Note that for efficiency of random(), we remember the first location of 149 * the state information, not the zeroeth. Hence it is valid to access 150 * state[-1], which is used to store the type of the R.N.G. 151 * Also, we remember the last location, since this is more efficient than 152 * indexing every time to find the address of the last element to see if 153 * the front and rear pointers have wrapped. 154 */ 155 unsigned int *state; 156 unsigned int rand_type, rand_deg, rand_sep; 157 unsigned int *end_ptr; 158 } *__randomjunk, *_randomjunk(void), _randominit = { 159 /* 160 * Initially, everything is set up as if from : 161 * initstate( 1, &randtbl, 128 ); 162 * Note that this initialization takes advantage of the fact 163 * that srandom() advances the front and rear pointers 10*rand_deg 164 * times, and hence the rear pointer which starts at 0 will also 165 * end up at zero; thus the zeroeth element of the state 166 * information, which contains info about the current 167 * position of the rear pointer is just 168 * MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3. 169 */ 170 { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }, 171 { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }, 172 { TYPE_3, 173 0x9a319039U, 0x32d9c024U, 0x9b663182U, 0x5da1f342U, 174 0xde3b81e0U, 0xdf0a6fb5U, 0xf103bc02U, 0x48f340fbU, 175 0x7449e56bU, 0xbeb1dbb0U, 0xab5c5918U, 0x946554fdU, 176 0x8c2e680fU, 0xeb3d799fU, 0xb11ee0b7U, 0x2d436b86U, 177 0xda672e2aU, 0x1588ca88U, 0xe369735dU, 0x904f35f7U, 178 0xd7158fd6U, 0x6fa6f051U, 0x616e6b96U, 0xac94efdcU, 179 0x36413f93U, 0xc622c298U, 0xf5a42ab8U, 0x8a88d77bU, 180 0xf5ad9d0eU, 0x8999220bU, 0x27fb47b9U }, 181 &_randominit.randtbl[ SEP_3 + 1 ], 182 &_randominit.randtbl[ 1 ], 183 &_randominit.randtbl[ 1 ], 184 TYPE_3, DEG_3, SEP_3, 185 &_randominit.randtbl[ DEG_3 + 1] 186 }; 187 188 static struct _randomjunk * 189 _randomjunk(void) 190 { 191 struct _randomjunk *rp = __randomjunk; 192 193 if (rp == NULL) { 194 rp = (struct _randomjunk *)malloc(sizeof (*rp)); 195 if (rp == NULL) 196 return (NULL); 197 *rp = _randominit; 198 __randomjunk = rp; 199 } 200 return (rp); 201 } 202 203 204 /* 205 * initstate: 206 * Initialize the state information in the given array of n bytes for 207 * future random number generation. Based on the number of bytes we 208 * are given, and the break values for the different R.N.G.'s, we choose 209 * the best (largest) one we can and set things up for it. srandom() is 210 * then called to initialize the state information. 211 * Note that on return from srandom(), we set state[-1] to be the type 212 * multiplexed with the current value of the rear pointer; this is so 213 * successive calls to initstate() won't lose this information and will 214 * be able to restart with setstate(). 215 * Note: the first thing we do is save the current state, if any, just like 216 * setstate() so that it doesn't matter when initstate is called. 217 * Returns a pointer to the old state. 218 */ 219 220 char * 221 initstate( 222 unsigned int seed, /* seed for R. N. G. */ 223 char *arg_state, /* pointer to state array */ 224 size_t size) /* # bytes of state info */ 225 { 226 unsigned int n; 227 struct _randomjunk *rp = _randomjunk(); 228 char *ostate; 229 230 if (size > UINT_MAX) 231 n = UINT_MAX; 232 else 233 n = (unsigned int)size; 234 235 if (rp == NULL) 236 return (NULL); 237 ostate = (char *)(&rp->state[ -1 ]); 238 239 if (rp->rand_type == TYPE_0) rp->state[ -1 ] = rp->rand_type; 240 else rp->state[ -1 ] = 241 (unsigned int)(MAX_TYPES*(rp->rptr - rp->state) + rp->rand_type); 242 if (n < BREAK_1) { 243 if (n < BREAK_0) { 244 return (NULL); 245 } 246 rp->rand_type = TYPE_0; 247 rp->rand_deg = DEG_0; 248 rp->rand_sep = SEP_0; 249 } else { 250 if (n < BREAK_2) { 251 rp->rand_type = TYPE_1; 252 rp->rand_deg = DEG_1; 253 rp->rand_sep = SEP_1; 254 } else { 255 if (n < BREAK_3) { 256 rp->rand_type = TYPE_2; 257 rp->rand_deg = DEG_2; 258 rp->rand_sep = SEP_2; 259 } else { 260 if (n < BREAK_4) { 261 rp->rand_type = TYPE_3; 262 rp->rand_deg = DEG_3; 263 rp->rand_sep = SEP_3; 264 } else { 265 rp->rand_type = TYPE_4; 266 rp->rand_deg = DEG_4; 267 rp->rand_sep = SEP_4; 268 } 269 } 270 } 271 } 272 /* first location */ 273 rp->state = &(((unsigned int *)(uintptr_t)arg_state)[1]); 274 /* must set end_ptr before srandom */ 275 rp->end_ptr = &rp->state[rp->rand_deg]; 276 srandom(seed); 277 if (rp->rand_type == TYPE_0) rp->state[ -1 ] = rp->rand_type; 278 else 279 rp->state[-1] = (unsigned int)(MAX_TYPES* 280 (rp->rptr - rp->state) + rp->rand_type); 281 return (ostate); 282 } 283 284 285 286 /* 287 * setstate: 288 * Restore the state from the given state array. 289 * Note: it is important that we also remember the locations of the pointers 290 * in the current state information, and restore the locations of the pointers 291 * from the old state information. This is done by multiplexing the pointer 292 * location into the zeroeth word of the state information. 293 * Note that due to the order in which things are done, it is OK to call 294 * setstate() with the same state as the current state. 295 * Returns a pointer to the old state information. 296 */ 297 298 char * 299 setstate(const char *arg_state) 300 { 301 struct _randomjunk *rp = _randomjunk(); 302 unsigned int *new_state; 303 unsigned int type; 304 unsigned int rear; 305 char *ostate; 306 307 if (rp == NULL) 308 return (NULL); 309 new_state = (unsigned int *)(uintptr_t)arg_state; 310 type = new_state[0]%MAX_TYPES; 311 rear = new_state[0]/MAX_TYPES; 312 ostate = (char *)(&rp->state[ -1 ]); 313 314 if (rp->rand_type == TYPE_0) rp->state[ -1 ] = rp->rand_type; 315 else 316 rp->state[-1] = (unsigned int)(MAX_TYPES* 317 (rp->rptr - rp->state) + rp->rand_type); 318 switch (type) { 319 case TYPE_0: 320 case TYPE_1: 321 case TYPE_2: 322 case TYPE_3: 323 case TYPE_4: 324 rp->rand_type = type; 325 rp->rand_deg = rp->degrees[ type ]; 326 rp->rand_sep = rp->seps[ type ]; 327 break; 328 329 default: 330 return (NULL); 331 } 332 rp->state = &new_state[ 1 ]; 333 if (rp->rand_type != TYPE_0) { 334 rp->rptr = &rp->state[ rear ]; 335 rp->fptr = &rp->state[ (rear + rp->rand_sep)%rp->rand_deg ]; 336 } 337 rp->end_ptr = &rp->state[ rp->rand_deg ]; /* set end_ptr too */ 338 return (ostate); 339 } 340 341 342 343 /* 344 * random: 345 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 346 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is the 347 * same in all ther other cases due to all the global variables that have been 348 * set up. The basic operation is to add the number at the rear pointer into 349 * the one at the front pointer. Then both pointers are advanced to the next 350 * location cyclically in the table. The value returned is the sum generated, 351 * reduced to 31 bits by throwing away the "least random" low bit. 352 * Note: the code takes advantage of the fact that both the front and 353 * rear pointers can't wrap on the same call by not testing the rear 354 * pointer if the front one has wrapped. 355 * Returns a 31-bit random number. 356 */ 357 358 long 359 random(void) 360 { 361 struct _randomjunk *rp = _randomjunk(); 362 unsigned int i; 363 364 if (rp == NULL) 365 return (0L); 366 if (rp->rand_type == TYPE_0) { 367 i = rp->state[0] = (rp->state[0]*1103515245 + 12345)&0x7fffffff; 368 } else { 369 *rp->fptr += *rp->rptr; 370 i = (*rp->fptr >> 1)&0x7fffffff; /* chucking least random bit */ 371 if (++rp->fptr >= rp->end_ptr) { 372 rp->fptr = rp->state; 373 ++rp->rptr; 374 } else { 375 if (++rp->rptr >= rp->end_ptr) rp->rptr = rp->state; 376 } 377 } 378 return ((long)i); 379 } 380 381 /* 382 * srandom: 383 * Initialize the random number generator based on the given seed. If the 384 * type is the trivial no-state-information type, just remember the seed. 385 * Otherwise, initializes state[] based on the given "seed" via a linear 386 * congruential generator. Then, the pointers are set to known locations 387 * that are exactly rand_sep places apart. Lastly, it cycles the state 388 * information a given number of times to get rid of any initial dependencies 389 * introduced by the L.C.R.N.G. 390 * Note that the initialization of randtbl[] for default usage relies on 391 * values produced by this routine. 392 */ 393 394 void 395 srandom(unsigned int x) 396 { 397 struct _randomjunk *rp = _randomjunk(); 398 unsigned int i; 399 400 if (rp == NULL) 401 return; 402 if (rp->rand_type == TYPE_0) { 403 rp->state[ 0 ] = x; 404 } else { 405 rp->state[ 0 ] = x; 406 for (i = 1; i < rp->rand_deg; i++) { 407 rp->state[i] = 1103515245*rp->state[i - 1] + 12345; 408 } 409 rp->fptr = &rp->state[ rp->rand_sep ]; 410 rp->rptr = &rp->state[ 0 ]; 411 for (i = 0; i < 10*rp->rand_deg; i++) (void)random(); 412 } 413 } 414