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 1999 Sun Microsystems, Inc. All rights reserved. 24 * Use is subject to license terms. 25 */ 26 27 #pragma ident "%Z%%M% %I% %E% SMI" 28 29 #include <stdio.h> 30 #include <stdlib.h> 31 32 /* 33 * random.c: 34 * An improved random number generation package. In addition to the standard 35 * rand()/srand() like interface, this package also has a special state info 36 * interface. The initstate() routine is called with a seed, an array of 37 * bytes, and a count of how many bytes are being passed in; this array is then 38 * initialized to contain information for random number generation with that 39 * much state information. Good sizes for the amount of state information are 40 * 32, 64, 128, and 256 bytes. The state can be switched by calling the 41 * setstate() routine with the same array as was initiallized with initstate(). 42 * By default, the package runs with 128 bytes of state information and 43 * generates far better random numbers than a linear congruential generator. 44 * If the amount of state information is less than 32 bytes, a simple linear 45 * congruential R.N.G. is used. 46 * Internally, the state information is treated as an array of longs; the 47 * zeroeth element of the array is the type of R.N.G. being used (small 48 * integer); the remainder of the array is the state information for the 49 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of 50 * state information, which will allow a degree seven polynomial. (Note: the 51 * zeroeth word of state information also has some other information stored 52 * in it -- see setstate() for details). 53 * The random number generation technique is a linear feedback shift register 54 * approach, employing trinomials (since there are fewer terms to sum up that 55 * way). In this approach, the least significant bit of all the numbers in 56 * the state table will act as a linear feedback shift register, and will have 57 * period 2^deg - 1 (where deg is the degree of the polynomial being used, 58 * assuming that the polynomial is irreducible and primitive). The higher 59 * order bits will have longer periods, since their values are also influenced 60 * by pseudo-random carries out of the lower bits. The total period of the 61 * generator is approximately deg*(2**deg - 1); thus doubling the amount of 62 * state information has a vast influence on the period of the generator. 63 * Note: the deg*(2**deg - 1) is an approximation only good for large deg, 64 * when the period of the shift register is the dominant factor. With deg 65 * equal to seven, the period is actually much longer than the 7*(2**7 - 1) 66 * predicted by this formula. 67 */ 68 69 70 71 /* 72 * For each of the currently supported random number generators, we have a 73 * break value on the amount of state information (you need at least this 74 * many bytes of state info to support this random number generator), a degree 75 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 76 * the separation between the two lower order coefficients of the trinomial. 77 */ 78 79 #define TYPE_0 0 /* linear congruential */ 80 #define BREAK_0 8 81 #define DEG_0 0 82 #define SEP_0 0 83 84 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 85 #define BREAK_1 32 86 #define DEG_1 7 87 #define SEP_1 3 88 89 #define TYPE_2 2 /* x**15 + x + 1 */ 90 #define BREAK_2 64 91 #define DEG_2 15 92 #define SEP_2 1 93 94 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 95 #define BREAK_3 128 96 #define DEG_3 31 97 #define SEP_3 3 98 99 #define TYPE_4 4 /* x**63 + x + 1 */ 100 #define BREAK_4 256 101 #define DEG_4 63 102 #define SEP_4 1 103 104 105 /* 106 * Array versions of the above information to make code run faster -- relies 107 * on fact that TYPE_i == i. 108 */ 109 110 #define MAX_TYPES 5 /* max number of types above */ 111 112 static struct _randomjunk { 113 int degrees[MAX_TYPES]; 114 int seps[MAX_TYPES]; 115 long randtbl[ DEG_3 + 1 ]; 116 /* 117 * fptr and rptr are two pointers into the state info, a front and a rear 118 * pointer. These two pointers are always rand_sep places aparts, as they cycle 119 * cyclically through the state information. (Yes, this does mean we could get 120 * away with just one pointer, but the code for random() is more efficient this 121 * way). The pointers are left positioned as they would be from the call 122 * initstate(1, randtbl, 128) 123 * (The position of the rear pointer, rptr, is really 0 (as explained above 124 * in the initialization of randtbl) because the state table pointer is set 125 * to point to randtbl[1] (as explained below). 126 */ 127 long *fptr, *rptr; 128 /* 129 * The following things are the pointer to the state information table, 130 * the type of the current generator, the degree of the current polynomial 131 * being used, and the separation between the two pointers. 132 * Note that for efficiency of random(), we remember the first location of 133 * the state information, not the zeroeth. Hence it is valid to access 134 * state[-1], which is used to store the type of the R.N.G. 135 * Also, we remember the last location, since this is more efficient than 136 * indexing every time to find the address of the last element to see if 137 * the front and rear pointers have wrapped. 138 */ 139 long *state; 140 int rand_type, rand_deg, rand_sep; 141 long *end_ptr; 142 } *__randomjunk, *_randomjunk(void), _randominit = { 143 /* 144 * Initially, everything is set up as if from : 145 * initstate(1, &randtbl, 128); 146 * Note that this initialization takes advantage of the fact 147 * that srandom() advances the front and rear pointers 10*rand_deg 148 * times, and hence the rear pointer which starts at 0 will also 149 * end up at zero; thus the zeroeth element of the state 150 * information, which contains info about the current 151 * position of the rear pointer is just 152 * MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3. 153 */ 154 { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }, 155 { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }, 156 { TYPE_3, 157 (long)0x9a319039, (long)0x32d9c024, (long)0x9b663182, (long)0x5da1f342, 158 (long)0xde3b81e0, (long)0xdf0a6fb5, (long)0xf103bc02, (long)0x48f340fb, 159 (long)0x7449e56b, (long)0xbeb1dbb0, (long)0xab5c5918, (long)0x946554fd, 160 (long)0x8c2e680f, (long)0xeb3d799f, (long)0xb11ee0b7, (long)0x2d436b86, 161 (long)0xda672e2a, (long)0x1588ca88, (long)0xe369735d, (long)0x904f35f7, 162 (long)0xd7158fd6, (long)0x6fa6f051, (long)0x616e6b96, (long)0xac94efdc, 163 (long)0x36413f93, (long)0xc622c298, (long)0xf5a42ab8, (long)0x8a88d77b, 164 (long)0xf5ad9d0e, (long)0x8999220b, (long)0x27fb47b9 }, 165 &_randominit.randtbl[ SEP_3 + 1 ], 166 &_randominit.randtbl[1], 167 &_randominit.randtbl[1], 168 TYPE_3, DEG_3, SEP_3, 169 &_randominit.randtbl[ DEG_3 + 1] 170 }; 171 172 long random(void); 173 174 static struct _randomjunk * 175 _randomjunk(void) 176 { 177 struct _randomjunk *rp = __randomjunk; 178 179 if (rp == 0) { 180 rp = (struct _randomjunk *)malloc(sizeof (*rp)); 181 if (rp == 0) 182 return (0); 183 *rp = _randominit; 184 __randomjunk = rp; 185 } 186 return (rp); 187 } 188 189 /* 190 * srandom: 191 * Initialize the random number generator based on the given seed. If the 192 * type is the trivial no-state-information type, just remember the seed. 193 * Otherwise, initializes state[] based on the given "seed" via a linear 194 * congruential generator. Then, the pointers are set to known locations 195 * that are exactly rand_sep places apart. Lastly, it cycles the state 196 * information a given number of times to get rid of any initial dependencies 197 * introduced by the L.C.R.N.G. 198 * Note that the initialization of randtbl[] for default usage relies on 199 * values produced by this routine. 200 */ 201 202 void 203 srandom(unsigned x) 204 { 205 struct _randomjunk *rp = _randomjunk(); 206 int i; 207 208 if (rp == 0) 209 return; 210 if (rp->rand_type == TYPE_0) { 211 rp->state[0] = x; 212 } else { 213 rp->state[0] = x; 214 for (i = 1; i < rp->rand_deg; i++) { 215 rp->state[i] = 1103515245*rp->state[i - 1] + 12345; 216 } 217 rp->fptr = &rp->state[rp->rand_sep]; 218 rp->rptr = &rp->state[0]; 219 for (i = 0; i < 10 * rp->rand_deg; i++) 220 random(); 221 } 222 } 223 224 225 226 /* 227 * initstate: 228 * Initialize the state information in the given array of n bytes for 229 * future random number generation. Based on the number of bytes we 230 * are given, and the break values for the different R.N.G.'s, we choose 231 * the best (largest) one we can and set things up for it. srandom() is 232 * then called to initialize the state information. 233 * Note that on return from srandom(), we set state[-1] to be the type 234 * multiplexed with the current value of the rear pointer; this is so 235 * successive calls to initstate() won't lose this information and will 236 * be able to restart with setstate(). 237 * Note: the first thing we do is save the current state, if any, just like 238 * setstate() so that it doesn't matter when initstate is called. 239 * Returns a pointer to the old state. 240 * 241 * Arguments: 242 * seed: seed for R. N. G. 243 * arg_state: pointer to state array 244 * n: # bytes of state info 245 */ 246 247 char * 248 initstate(unsigned seed, char *arg_state, int n) 249 { 250 struct _randomjunk *rp = _randomjunk(); 251 char *ostate; 252 253 if (rp == 0) 254 return (0); 255 ostate = (char *)(&rp->state[-1]); 256 257 if (rp->rand_type == TYPE_0) rp->state[-1] = rp->rand_type; 258 else rp->state[-1] = 259 MAX_TYPES*(rp->rptr - rp->state) + rp->rand_type; 260 if (n < BREAK_0) { 261 fprintf(stderr, 262 "initstate: state array too small, ignored; minimum size is %d bytes\n", 263 BREAK_0); 264 return (0); 265 } else if (n < BREAK_1) { 266 rp->rand_type = TYPE_0; 267 rp->rand_deg = DEG_0; 268 rp->rand_sep = SEP_0; 269 } else if (n < BREAK_2) { 270 rp->rand_type = TYPE_1; 271 rp->rand_deg = DEG_1; 272 rp->rand_sep = SEP_1; 273 } else if (n < BREAK_3) { 274 rp->rand_type = TYPE_2; 275 rp->rand_deg = DEG_2; 276 rp->rand_sep = SEP_2; 277 } else if (n < BREAK_4) { 278 rp->rand_type = TYPE_3; 279 rp->rand_deg = DEG_3; 280 rp->rand_sep = SEP_3; 281 } else { 282 rp->rand_type = TYPE_4; 283 rp->rand_deg = DEG_4; 284 rp->rand_sep = SEP_4; 285 } 286 rp->state = &((long *)arg_state)[1]; /* first location */ 287 rp->end_ptr = &rp->state[rp->rand_deg]; /* set end_ptr before srandom */ 288 srandom(seed); 289 rp->state[-1] = (rp->rand_type == TYPE_0) ? rp->rand_type 290 : MAX_TYPES * (rp->rptr - rp->state) + rp->rand_type; 291 return (ostate); 292 } 293 294 295 /* 296 * setstate: 297 * Restore the state from the given state array. 298 * Note: it is important that we also remember the locations of the pointers 299 * in the current state information, and restore the locations of the pointers 300 * from the old state information. This is done by multiplexing the pointer 301 * location into the zeroeth word of the state information. 302 * Note that due to the order in which things are done, it is OK to call 303 * setstate() with the same state as the current state. 304 * Returns a pointer to the old state information. 305 */ 306 307 char * 308 setstate(char *arg_state) 309 { 310 struct _randomjunk *rp = _randomjunk(); 311 long *new_state; 312 int type; 313 int rear; 314 char *ostate; 315 316 if (rp == 0) 317 return (0); 318 new_state = (long *)arg_state; 319 type = new_state[0] % MAX_TYPES; 320 rear = new_state[0] / MAX_TYPES; 321 ostate = (char *)(&rp->state[-1]); 322 323 rp->state[-1] = (rp->rand_type == TYPE_0) ? rp->rand_type 324 : MAX_TYPES*(rp->rptr - rp->state) + rp->rand_type; 325 switch (type) { 326 case TYPE_0: 327 case TYPE_1: 328 case TYPE_2: 329 case TYPE_3: 330 case TYPE_4: 331 rp->rand_type = type; 332 rp->rand_deg = rp->degrees[type]; 333 rp->rand_sep = rp->seps[type]; 334 break; 335 336 default: 337 fprintf(stderr, "setstate: invalid state info; not changed.\n"); 338 } 339 rp->state = &new_state[1]; 340 if (rp->rand_type != TYPE_0) { 341 rp->rptr = &rp->state[rear]; 342 rp->fptr = &rp->state[(rear + rp->rand_sep) % rp->rand_deg]; 343 } 344 rp->end_ptr = &rp->state[rp->rand_deg]; /* set end_ptr too */ 345 return (ostate); 346 } 347 348 349 /* 350 * random: 351 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 352 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is the 353 * same in all ther other cases due to all the global variables that have been 354 * set up. The basic operation is to add the number at the rear pointer into 355 * the one at the front pointer. Then both pointers are advanced to the next 356 * location cyclically in the table. The value returned is the sum generated, 357 * reduced to 31 bits by throwing away the "least random" low bit. 358 * Note: the code takes advantage of the fact that both the front and 359 * rear pointers can't wrap on the same call by not testing the rear 360 * pointer if the front one has wrapped. 361 * Returns a 31-bit random number. 362 */ 363 364 long 365 random(void) 366 { 367 struct _randomjunk *rp = _randomjunk(); 368 long i; 369 370 if (rp == 0) 371 return (0); 372 if (rp->rand_type == TYPE_0) { 373 i = rp->state[0] = (rp->state[0]*1103515245 + 12345)&0x7fffffff; 374 } else { 375 *rp->fptr += *rp->rptr; 376 i = (*rp->fptr >> 1)&0x7fffffff; /* chucking least random bit */ 377 if (++rp->fptr >= rp->end_ptr) { 378 rp->fptr = rp->state; 379 ++rp->rptr; 380 } else if (++rp->rptr >= rp->end_ptr) 381 rp->rptr = rp->state; 382 } 383 return (i); 384 } 385