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 /* 24 * Copyright 2005 Sun Microsystems, Inc. All rights reserved. 25 * Use is subject to license terms. 26 */ 27 28 /* Copyright (c) 1984, 1986, 1987, 1988, 1989 AT&T */ 29 /* All Rights Reserved */ 30 31 /* 32 * University Copyright- Copyright (c) 1982, 1986, 1988 33 * The Regents of the University of California 34 * All Rights Reserved 35 * 36 * University Acknowledgment- Portions of this document are derived from 37 * software developed by the University of California, Berkeley, and its 38 * contributors. 39 */ 40 41 #pragma ident "%Z%%M% %I% %E% SMI" 42 43 #include "synonyms.h" 44 #include <stdio.h> 45 #include <stdlib.h> 46 #include <string.h> 47 #include <sys/types.h> 48 #include <limits.h> 49 50 /* 51 * random.c: 52 * An improved random number generation package. In addition to the standard 53 * rand()/srand() like interface, this package also has a special state info 54 * interface. The initstate() routine is called with a seed, an array of 55 * bytes, and a count of how many bytes are being passed in; this array is then 56 * initialized to contain information for random number generation with that 57 * much state information. Good sizes for the amount of state information are 58 * 32, 64, 128, and 256 bytes. The state can be switched by calling the 59 * setstate() routine with the same array as was initiallized with initstate(). 60 * By default, the package runs with 128 bytes of state information and 61 * generates far better random numbers than a linear congruential generator. 62 * If the amount of state information is less than 32 bytes, a simple linear 63 * congruential R.N.G. is used. 64 * Internally, the state information is treated as an array of ints; the 65 * zeroeth element of the array is the type of R.N.G. being used (small 66 * integer); the remainder of the array is the state information for the 67 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 68 * state information, which will allow a degree seven polynomial. (Note: the 69 * zeroeth word of state information also has some other information stored 70 * in it -- see setstate() for details). 71 * The random number generation technique is a linear feedback shift register 72 * approach, employing trinomials (since there are fewer terms to sum up that 73 * way). In this approach, the least significant bit of all the numbers in 74 * the state table will act as a linear feedback shift register, and will have 75 * period 2^deg - 1 (where deg is the degree of the polynomial being used, 76 * assuming that the polynomial is irreducible and primitive). The higher 77 * order bits will have longer periods, since their values are also influenced 78 * by pseudo-random carries out of the lower bits. The total period of the 79 * generator is approximately deg*(2**deg - 1); thus doubling the amount of 80 * state information has a vast influence on the period of the generator. 81 * Note: the deg*(2**deg - 1) is an approximation only good for large deg, 82 * when the period of the shift register is the dominant factor. With deg 83 * equal to seven, the period is actually much longer than the 7*(2**7 - 1) 84 * predicted by this formula. 85 */ 86 87 88 89 /* 90 * For each of the currently supported random number generators, we have a 91 * break value on the amount of state information (you need at least this 92 * many bytes of state info to support this random number generator), a degree 93 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 94 * the separation between the two lower order coefficients of the trinomial. 95 */ 96 97 #define TYPE_0 0 /* linear congruential */ 98 #define BREAK_0 8 99 #define DEG_0 0 100 #define SEP_0 0 101 102 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 103 #define BREAK_1 32 104 #define DEG_1 7 105 #define SEP_1 3 106 107 #define TYPE_2 2 /* x**15 + x + 1 */ 108 #define BREAK_2 64 109 #define DEG_2 15 110 #define SEP_2 1 111 112 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 113 #define BREAK_3 128 114 #define DEG_3 31 115 #define SEP_3 3 116 117 #define TYPE_4 4 /* x**63 + x + 1 */ 118 #define BREAK_4 256 119 #define DEG_4 63 120 #define SEP_4 1 121 122 123 /* 124 * Array versions of the above information to make code run faster -- relies 125 * on fact that TYPE_i == i. 126 */ 127 128 #define MAX_TYPES 5 /* max number of types above */ 129 130 static struct _randomjunk { 131 unsigned int degrees[MAX_TYPES]; 132 unsigned int seps[MAX_TYPES]; 133 unsigned int randtbl[ DEG_3 + 1 ]; 134 /* 135 * fptr and rptr are two pointers into the state info, a front and a rear 136 * pointer. These two pointers are always rand_sep places aparts, as they cycle 137 * cyclically through the state information. (Yes, this does mean we could get 138 * away with just one pointer, but the code for random() is more efficient this 139 * way). The pointers are left positioned as they would be from the call 140 * initstate( 1, randtbl, 128 ) 141 * (The position of the rear pointer, rptr, is really 0 (as explained above 142 * in the initialization of randtbl) because the state table pointer is set 143 * to point to randtbl[1] (as explained below). 144 */ 145 unsigned int *fptr, *rptr; 146 /* 147 * The following things are the pointer to the state information table, 148 * the type of the current generator, the degree of the current polynomial 149 * being used, and the separation between the two pointers. 150 * Note that for efficiency of random(), we remember the first location of 151 * the state information, not the zeroeth. Hence it is valid to access 152 * state[-1], which is used to store the type of the R.N.G. 153 * Also, we remember the last location, since this is more efficient than 154 * indexing every time to find the address of the last element to see if 155 * the front and rear pointers have wrapped. 156 */ 157 unsigned int *state; 158 unsigned int rand_type, rand_deg, rand_sep; 159 unsigned int *end_ptr; 160 } *__randomjunk, *_randomjunk(void), _randominit = { 161 /* 162 * Initially, everything is set up as if from : 163 * initstate( 1, &randtbl, 128 ); 164 * Note that this initialization takes advantage of the fact 165 * that srandom() advances the front and rear pointers 10*rand_deg 166 * times, and hence the rear pointer which starts at 0 will also 167 * end up at zero; thus the zeroeth element of the state 168 * information, which contains info about the current 169 * position of the rear pointer is just 170 * MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3. 171 */ 172 { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }, 173 { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }, 174 { TYPE_3, 175 0x9a319039U, 0x32d9c024U, 0x9b663182U, 0x5da1f342U, 176 0xde3b81e0U, 0xdf0a6fb5U, 0xf103bc02U, 0x48f340fbU, 177 0x7449e56bU, 0xbeb1dbb0U, 0xab5c5918U, 0x946554fdU, 178 0x8c2e680fU, 0xeb3d799fU, 0xb11ee0b7U, 0x2d436b86U, 179 0xda672e2aU, 0x1588ca88U, 0xe369735dU, 0x904f35f7U, 180 0xd7158fd6U, 0x6fa6f051U, 0x616e6b96U, 0xac94efdcU, 181 0x36413f93U, 0xc622c298U, 0xf5a42ab8U, 0x8a88d77bU, 182 0xf5ad9d0eU, 0x8999220bU, 0x27fb47b9U }, 183 &_randominit.randtbl[ SEP_3 + 1 ], 184 &_randominit.randtbl[ 1 ], 185 &_randominit.randtbl[ 1 ], 186 TYPE_3, DEG_3, SEP_3, 187 &_randominit.randtbl[ DEG_3 + 1] 188 }; 189 190 static struct _randomjunk * 191 _randomjunk(void) 192 { 193 struct _randomjunk *rp = __randomjunk; 194 195 if (rp == NULL) { 196 rp = (struct _randomjunk *)malloc(sizeof (*rp)); 197 if (rp == NULL) 198 return (NULL); 199 (void) memcpy(rp, &_randominit, sizeof (*rp)); 200 __randomjunk = rp; 201 } 202 return (rp); 203 } 204 205 206 /* 207 * initstate: 208 * Initialize the state information in the given array of n bytes for 209 * future random number generation. Based on the number of bytes we 210 * are given, and the break values for the different R.N.G.'s, we choose 211 * the best (largest) one we can and set things up for it. srandom() is 212 * then called to initialize the state information. 213 * Note that on return from srandom(), we set state[-1] to be the type 214 * multiplexed with the current value of the rear pointer; this is so 215 * successive calls to initstate() won't lose this information and will 216 * be able to restart with setstate(). 217 * Note: the first thing we do is save the current state, if any, just like 218 * setstate() so that it doesn't matter when initstate is called. 219 * Returns a pointer to the old state. 220 */ 221 222 char * 223 initstate( 224 unsigned int seed, /* seed for R. N. G. */ 225 char *arg_state, /* pointer to state array */ 226 size_t size) /* # bytes of state info */ 227 { 228 unsigned int n; 229 struct _randomjunk *rp = _randomjunk(); 230 char *ostate; 231 232 if (size > UINT_MAX) 233 n = UINT_MAX; 234 else 235 n = (unsigned int)size; 236 237 if (rp == NULL) 238 return (NULL); 239 ostate = (char *)(&rp->state[ -1 ]); 240 241 if (rp->rand_type == TYPE_0) rp->state[ -1 ] = rp->rand_type; 242 else rp->state[ -1 ] = 243 (unsigned int)(MAX_TYPES*(rp->rptr - rp->state) + rp->rand_type); 244 if (n < BREAK_1) { 245 if (n < BREAK_0) { 246 return (NULL); 247 } 248 rp->rand_type = TYPE_0; 249 rp->rand_deg = DEG_0; 250 rp->rand_sep = SEP_0; 251 } else { 252 if (n < BREAK_2) { 253 rp->rand_type = TYPE_1; 254 rp->rand_deg = DEG_1; 255 rp->rand_sep = SEP_1; 256 } else { 257 if (n < BREAK_3) { 258 rp->rand_type = TYPE_2; 259 rp->rand_deg = DEG_2; 260 rp->rand_sep = SEP_2; 261 } else { 262 if (n < BREAK_4) { 263 rp->rand_type = TYPE_3; 264 rp->rand_deg = DEG_3; 265 rp->rand_sep = SEP_3; 266 } else { 267 rp->rand_type = TYPE_4; 268 rp->rand_deg = DEG_4; 269 rp->rand_sep = SEP_4; 270 } 271 } 272 } 273 } 274 /* first location */ 275 rp->state = &(((unsigned int *)(uintptr_t)arg_state)[1]); 276 /* must set end_ptr before srandom */ 277 rp->end_ptr = &rp->state[rp->rand_deg]; 278 srandom(seed); 279 if (rp->rand_type == TYPE_0) rp->state[ -1 ] = rp->rand_type; 280 else 281 rp->state[-1] = (unsigned int)(MAX_TYPES* 282 (rp->rptr - rp->state) + rp->rand_type); 283 return (ostate); 284 } 285 286 287 288 /* 289 * setstate: 290 * Restore the state from the given state array. 291 * Note: it is important that we also remember the locations of the pointers 292 * in the current state information, and restore the locations of the pointers 293 * from the old state information. This is done by multiplexing the pointer 294 * location into the zeroeth word of the state information. 295 * Note that due to the order in which things are done, it is OK to call 296 * setstate() with the same state as the current state. 297 * Returns a pointer to the old state information. 298 */ 299 300 char * 301 setstate(const char *arg_state) 302 { 303 struct _randomjunk *rp = _randomjunk(); 304 unsigned int *new_state; 305 unsigned int type; 306 unsigned int rear; 307 char *ostate; 308 309 if (rp == NULL) 310 return (NULL); 311 new_state = (unsigned int *)(uintptr_t)arg_state; 312 type = new_state[0]%MAX_TYPES; 313 rear = new_state[0]/MAX_TYPES; 314 ostate = (char *)(&rp->state[ -1 ]); 315 316 if (rp->rand_type == TYPE_0) rp->state[ -1 ] = rp->rand_type; 317 else 318 rp->state[-1] = (unsigned int)(MAX_TYPES* 319 (rp->rptr - rp->state) + rp->rand_type); 320 switch (type) { 321 case TYPE_0: 322 case TYPE_1: 323 case TYPE_2: 324 case TYPE_3: 325 case TYPE_4: 326 rp->rand_type = type; 327 rp->rand_deg = rp->degrees[ type ]; 328 rp->rand_sep = rp->seps[ type ]; 329 break; 330 331 default: 332 return (NULL); 333 } 334 rp->state = &new_state[ 1 ]; 335 if (rp->rand_type != TYPE_0) { 336 rp->rptr = &rp->state[ rear ]; 337 rp->fptr = &rp->state[ (rear + rp->rand_sep)%rp->rand_deg ]; 338 } 339 rp->end_ptr = &rp->state[ rp->rand_deg ]; /* set end_ptr too */ 340 return (ostate); 341 } 342 343 344 345 /* 346 * random: 347 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 348 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is the 349 * same in all ther other cases due to all the global variables that have been 350 * set up. The basic operation is to add the number at the rear pointer into 351 * the one at the front pointer. Then both pointers are advanced to the next 352 * location cyclically in the table. The value returned is the sum generated, 353 * reduced to 31 bits by throwing away the "least random" low bit. 354 * Note: the code takes advantage of the fact that both the front and 355 * rear pointers can't wrap on the same call by not testing the rear 356 * pointer if the front one has wrapped. 357 * Returns a 31-bit random number. 358 */ 359 360 long 361 random(void) 362 { 363 struct _randomjunk *rp = _randomjunk(); 364 unsigned int i; 365 366 if (rp == NULL) 367 return (0L); 368 if (rp->rand_type == TYPE_0) { 369 i = rp->state[0] = (rp->state[0]*1103515245 + 12345)&0x7fffffff; 370 } else { 371 *rp->fptr += *rp->rptr; 372 i = (*rp->fptr >> 1)&0x7fffffff; /* chucking least random bit */ 373 if (++rp->fptr >= rp->end_ptr) { 374 rp->fptr = rp->state; 375 ++rp->rptr; 376 } else { 377 if (++rp->rptr >= rp->end_ptr) rp->rptr = rp->state; 378 } 379 } 380 return ((long)i); 381 } 382 383 /* 384 * srandom: 385 * Initialize the random number generator based on the given seed. If the 386 * type is the trivial no-state-information type, just remember the seed. 387 * Otherwise, initializes state[] based on the given "seed" via a linear 388 * congruential generator. Then, the pointers are set to known locations 389 * that are exactly rand_sep places apart. Lastly, it cycles the state 390 * information a given number of times to get rid of any initial dependencies 391 * introduced by the L.C.R.N.G. 392 * Note that the initialization of randtbl[] for default usage relies on 393 * values produced by this routine. 394 */ 395 396 void 397 srandom(unsigned int x) 398 { 399 struct _randomjunk *rp = _randomjunk(); 400 unsigned int i; 401 402 if (rp == NULL) 403 return; 404 if (rp->rand_type == TYPE_0) { 405 rp->state[ 0 ] = x; 406 } else { 407 rp->state[ 0 ] = x; 408 for (i = 1; i < rp->rand_deg; i++) { 409 rp->state[i] = 1103515245*rp->state[i - 1] + 12345; 410 } 411 rp->fptr = &rp->state[ rp->rand_sep ]; 412 rp->rptr = &rp->state[ 0 ]; 413 for (i = 0; i < 10*rp->rand_deg; i++) (void)random(); 414 } 415 } 416