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 (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2008 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 #include "lint.h" 41 #include <stdio.h> 42 #include <stdlib.h> 43 #include <string.h> 44 #include <sys/types.h> 45 #include <limits.h> 46 47 /* 48 * random.c: 49 * An improved random number generation package. In addition to the standard 50 * rand()/srand() like interface, this package also has a special state info 51 * interface. The initstate() routine is called with a seed, an array of 52 * bytes, and a count of how many bytes are being passed in; this array is then 53 * initialized to contain information for random number generation with that 54 * much state information. Good sizes for the amount of state information are 55 * 32, 64, 128, and 256 bytes. The state can be switched by calling the 56 * setstate() routine with the same array as was initiallized with initstate(). 57 * By default, the package runs with 128 bytes of state information and 58 * generates far better random numbers than a linear congruential generator. 59 * If the amount of state information is less than 32 bytes, a simple linear 60 * congruential R.N.G. is used. 61 * Internally, the state information is treated as an array of ints; the 62 * zeroeth element of the array is the type of R.N.G. being used (small 63 * integer); the remainder of the array is the state information for the 64 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 65 * state information, which will allow a degree seven polynomial. (Note: the 66 * zeroeth word of state information also has some other information stored 67 * in it -- see setstate() for details). 68 * The random number generation technique is a linear feedback shift register 69 * approach, employing trinomials (since there are fewer terms to sum up that 70 * way). In this approach, the least significant bit of all the numbers in 71 * the state table will act as a linear feedback shift register, and will have 72 * period 2^deg - 1 (where deg is the degree of the polynomial being used, 73 * assuming that the polynomial is irreducible and primitive). The higher 74 * order bits will have longer periods, since their values are also influenced 75 * by pseudo-random carries out of the lower bits. The total period of the 76 * generator is approximately deg*(2**deg - 1); thus doubling the amount of 77 * state information has a vast influence on the period of the generator. 78 * Note: the deg*(2**deg - 1) is an approximation only good for large deg, 79 * when the period of the shift register is the dominant factor. With deg 80 * equal to seven, the period is actually much longer than the 7*(2**7 - 1) 81 * predicted by this formula. 82 */ 83 84 85 86 /* 87 * For each of the currently supported random number generators, we have a 88 * break value on the amount of state information (you need at least this 89 * many bytes of state info to support this random number generator), a degree 90 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 91 * the separation between the two lower order coefficients of the trinomial. 92 */ 93 94 #define TYPE_0 0 /* linear congruential */ 95 #define BREAK_0 8 96 #define DEG_0 0 97 #define SEP_0 0 98 99 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 100 #define BREAK_1 32 101 #define DEG_1 7 102 #define SEP_1 3 103 104 #define TYPE_2 2 /* x**15 + x + 1 */ 105 #define BREAK_2 64 106 #define DEG_2 15 107 #define SEP_2 1 108 109 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 110 #define BREAK_3 128 111 #define DEG_3 31 112 #define SEP_3 3 113 114 #define TYPE_4 4 /* x**63 + x + 1 */ 115 #define BREAK_4 256 116 #define DEG_4 63 117 #define SEP_4 1 118 119 120 /* 121 * Array versions of the above information to make code run faster -- relies 122 * on fact that TYPE_i == i. 123 */ 124 125 #define MAX_TYPES 5 /* max number of types above */ 126 127 static struct _randomjunk { 128 unsigned int degrees[MAX_TYPES]; 129 unsigned int seps[MAX_TYPES]; 130 unsigned int randtbl[ DEG_3 + 1 ]; 131 /* 132 * fptr and rptr are two pointers into the state info, a front and a rear 133 * pointer. These two pointers are always rand_sep places aparts, as they cycle 134 * cyclically through the state information. (Yes, this does mean we could get 135 * away with just one pointer, but the code for random() is more efficient this 136 * way). The pointers are left positioned as they would be from the call 137 * initstate( 1, randtbl, 128 ) 138 * (The position of the rear pointer, rptr, is really 0 (as explained above 139 * in the initialization of randtbl) because the state table pointer is set 140 * to point to randtbl[1] (as explained below). 141 */ 142 unsigned int *fptr, *rptr; 143 /* 144 * The following things are the pointer to the state information table, 145 * the type of the current generator, the degree of the current polynomial 146 * being used, and the separation between the two pointers. 147 * Note that for efficiency of random(), we remember the first location of 148 * the state information, not the zeroeth. Hence it is valid to access 149 * state[-1], which is used to store the type of the R.N.G. 150 * Also, we remember the last location, since this is more efficient than 151 * indexing every time to find the address of the last element to see if 152 * the front and rear pointers have wrapped. 153 */ 154 unsigned int *state; 155 unsigned int rand_type, rand_deg, rand_sep; 156 unsigned int *end_ptr; 157 } *__randomjunk, *_randomjunk(void), _randominit = { 158 /* 159 * Initially, everything is set up as if from : 160 * initstate( 1, &randtbl, 128 ); 161 * Note that this initialization takes advantage of the fact 162 * that srandom() advances the front and rear pointers 10*rand_deg 163 * times, and hence the rear pointer which starts at 0 will also 164 * end up at zero; thus the zeroeth element of the state 165 * information, which contains info about the current 166 * position of the rear pointer is just 167 * MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3. 168 */ 169 { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }, 170 { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }, 171 { TYPE_3, 172 0x9a319039U, 0x32d9c024U, 0x9b663182U, 0x5da1f342U, 173 0xde3b81e0U, 0xdf0a6fb5U, 0xf103bc02U, 0x48f340fbU, 174 0x7449e56bU, 0xbeb1dbb0U, 0xab5c5918U, 0x946554fdU, 175 0x8c2e680fU, 0xeb3d799fU, 0xb11ee0b7U, 0x2d436b86U, 176 0xda672e2aU, 0x1588ca88U, 0xe369735dU, 0x904f35f7U, 177 0xd7158fd6U, 0x6fa6f051U, 0x616e6b96U, 0xac94efdcU, 178 0x36413f93U, 0xc622c298U, 0xf5a42ab8U, 0x8a88d77bU, 179 0xf5ad9d0eU, 0x8999220bU, 0x27fb47b9U }, 180 &_randominit.randtbl[ SEP_3 + 1 ], 181 &_randominit.randtbl[ 1 ], 182 &_randominit.randtbl[ 1 ], 183 TYPE_3, DEG_3, SEP_3, 184 &_randominit.randtbl[ DEG_3 + 1] 185 }; 186 187 static struct _randomjunk * 188 _randomjunk(void) 189 { 190 struct _randomjunk *rp = __randomjunk; 191 192 if (rp == NULL) { 193 rp = (struct _randomjunk *)malloc(sizeof (*rp)); 194 if (rp == NULL) 195 return (NULL); 196 (void) memcpy(rp, &_randominit, sizeof (*rp)); 197 __randomjunk = rp; 198 } 199 return (rp); 200 } 201 202 203 /* 204 * initstate: 205 * Initialize the state information in the given array of n bytes for 206 * future random number generation. Based on the number of bytes we 207 * are given, and the break values for the different R.N.G.'s, we choose 208 * the best (largest) one we can and set things up for it. srandom() is 209 * then called to initialize the state information. 210 * Note that on return from srandom(), we set state[-1] to be the type 211 * multiplexed with the current value of the rear pointer; this is so 212 * successive calls to initstate() won't lose this information and will 213 * be able to restart with setstate(). 214 * Note: the first thing we do is save the current state, if any, just like 215 * setstate() so that it doesn't matter when initstate is called. 216 * Returns a pointer to the old state. 217 */ 218 219 char * 220 initstate( 221 unsigned int seed, /* seed for R. N. G. */ 222 char *arg_state, /* pointer to state array */ 223 size_t size) /* # bytes of state info */ 224 { 225 unsigned int n; 226 struct _randomjunk *rp = _randomjunk(); 227 char *ostate; 228 229 if (size > UINT_MAX) 230 n = UINT_MAX; 231 else 232 n = (unsigned int)size; 233 234 if (rp == NULL) 235 return (NULL); 236 ostate = (char *)(&rp->state[ -1 ]); 237 238 if (rp->rand_type == TYPE_0) rp->state[ -1 ] = rp->rand_type; 239 else rp->state[ -1 ] = 240 (unsigned int)(MAX_TYPES*(rp->rptr - rp->state) + rp->rand_type); 241 if (n < BREAK_1) { 242 if (n < BREAK_0) { 243 return (NULL); 244 } 245 rp->rand_type = TYPE_0; 246 rp->rand_deg = DEG_0; 247 rp->rand_sep = SEP_0; 248 } else { 249 if (n < BREAK_2) { 250 rp->rand_type = TYPE_1; 251 rp->rand_deg = DEG_1; 252 rp->rand_sep = SEP_1; 253 } else { 254 if (n < BREAK_3) { 255 rp->rand_type = TYPE_2; 256 rp->rand_deg = DEG_2; 257 rp->rand_sep = SEP_2; 258 } else { 259 if (n < BREAK_4) { 260 rp->rand_type = TYPE_3; 261 rp->rand_deg = DEG_3; 262 rp->rand_sep = SEP_3; 263 } else { 264 rp->rand_type = TYPE_4; 265 rp->rand_deg = DEG_4; 266 rp->rand_sep = SEP_4; 267 } 268 } 269 } 270 } 271 /* first location */ 272 rp->state = &(((unsigned int *)(uintptr_t)arg_state)[1]); 273 /* must set end_ptr before srandom */ 274 rp->end_ptr = &rp->state[rp->rand_deg]; 275 srandom(seed); 276 if (rp->rand_type == TYPE_0) rp->state[ -1 ] = rp->rand_type; 277 else 278 rp->state[-1] = (unsigned int)(MAX_TYPES* 279 (rp->rptr - rp->state) + rp->rand_type); 280 return (ostate); 281 } 282 283 284 285 /* 286 * setstate: 287 * Restore the state from the given state array. 288 * Note: it is important that we also remember the locations of the pointers 289 * in the current state information, and restore the locations of the pointers 290 * from the old state information. This is done by multiplexing the pointer 291 * location into the zeroeth word of the state information. 292 * Note that due to the order in which things are done, it is OK to call 293 * setstate() with the same state as the current state. 294 * Returns a pointer to the old state information. 295 */ 296 297 char * 298 setstate(const char *arg_state) 299 { 300 struct _randomjunk *rp = _randomjunk(); 301 unsigned int *new_state; 302 unsigned int type; 303 unsigned int rear; 304 char *ostate; 305 306 if (rp == NULL) 307 return (NULL); 308 new_state = (unsigned int *)(uintptr_t)arg_state; 309 type = new_state[0]%MAX_TYPES; 310 rear = new_state[0]/MAX_TYPES; 311 ostate = (char *)(&rp->state[ -1 ]); 312 313 if (rp->rand_type == TYPE_0) rp->state[ -1 ] = rp->rand_type; 314 else 315 rp->state[-1] = (unsigned int)(MAX_TYPES* 316 (rp->rptr - rp->state) + rp->rand_type); 317 switch (type) { 318 case TYPE_0: 319 case TYPE_1: 320 case TYPE_2: 321 case TYPE_3: 322 case TYPE_4: 323 rp->rand_type = type; 324 rp->rand_deg = rp->degrees[ type ]; 325 rp->rand_sep = rp->seps[ type ]; 326 break; 327 328 default: 329 return (NULL); 330 } 331 rp->state = &new_state[ 1 ]; 332 if (rp->rand_type != TYPE_0) { 333 rp->rptr = &rp->state[ rear ]; 334 rp->fptr = &rp->state[ (rear + rp->rand_sep)%rp->rand_deg ]; 335 } 336 rp->end_ptr = &rp->state[ rp->rand_deg ]; /* set end_ptr too */ 337 return (ostate); 338 } 339 340 341 342 /* 343 * random: 344 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 345 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is the 346 * same in all ther other cases due to all the global variables that have been 347 * set up. The basic operation is to add the number at the rear pointer into 348 * the one at the front pointer. Then both pointers are advanced to the next 349 * location cyclically in the table. The value returned is the sum generated, 350 * reduced to 31 bits by throwing away the "least random" low bit. 351 * Note: the code takes advantage of the fact that both the front and 352 * rear pointers can't wrap on the same call by not testing the rear 353 * pointer if the front one has wrapped. 354 * Returns a 31-bit random number. 355 */ 356 357 long 358 random(void) 359 { 360 struct _randomjunk *rp = _randomjunk(); 361 unsigned int i; 362 363 if (rp == NULL) 364 return (0L); 365 if (rp->rand_type == TYPE_0) { 366 i = rp->state[0] = (rp->state[0]*1103515245 + 12345)&0x7fffffff; 367 } else { 368 *rp->fptr += *rp->rptr; 369 i = (*rp->fptr >> 1)&0x7fffffff; /* chucking least random bit */ 370 if (++rp->fptr >= rp->end_ptr) { 371 rp->fptr = rp->state; 372 ++rp->rptr; 373 } else { 374 if (++rp->rptr >= rp->end_ptr) rp->rptr = rp->state; 375 } 376 } 377 return ((long)i); 378 } 379 380 /* 381 * srandom: 382 * Initialize the random number generator based on the given seed. If the 383 * type is the trivial no-state-information type, just remember the seed. 384 * Otherwise, initializes state[] based on the given "seed" via a linear 385 * congruential generator. Then, the pointers are set to known locations 386 * that are exactly rand_sep places apart. Lastly, it cycles the state 387 * information a given number of times to get rid of any initial dependencies 388 * introduced by the L.C.R.N.G. 389 * Note that the initialization of randtbl[] for default usage relies on 390 * values produced by this routine. 391 */ 392 393 void 394 srandom(unsigned int x) 395 { 396 struct _randomjunk *rp = _randomjunk(); 397 unsigned int i; 398 399 if (rp == NULL) 400 return; 401 if (rp->rand_type == TYPE_0) { 402 rp->state[ 0 ] = x; 403 } else { 404 rp->state[ 0 ] = x; 405 for (i = 1; i < rp->rand_deg; i++) { 406 rp->state[i] = 1103515245*rp->state[i - 1] + 12345; 407 } 408 rp->fptr = &rp->state[ rp->rand_sep ]; 409 rp->rptr = &rp->state[ 0 ]; 410 for (i = 0; i < 10*rp->rand_deg; i++) (void)random(); 411 } 412 } 413