1 /* $NetBSD: random.c,v 1.1 2005/12/20 19:28:52 christos Exp $ */ 2 3 /* 4 * Copyright (c) 1983, 1993 5 * The Regents of the University of California. All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice, this list of conditions and the following disclaimer. 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in the 14 * documentation and/or other materials provided with the distribution. 15 * 3. Neither the name of the University nor the names of its contributors 16 * may be used to endorse or promote products derived from this software 17 * without specific prior written permission. 18 * 19 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 20 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 21 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 22 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 23 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 24 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 25 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 26 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 27 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 28 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 29 * SUCH DAMAGE. 30 */ 31 32 #include <sys/cdefs.h> 33 #if defined(LIBC_SCCS) && !defined(lint) 34 #if 0 35 static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95"; 36 #else 37 __RCSID("$NetBSD: random.c,v 1.1 2005/12/20 19:28:52 christos Exp $"); 38 #endif 39 #endif /* LIBC_SCCS and not lint */ 40 41 #include "namespace.h" 42 43 #include <assert.h> 44 #include <errno.h> 45 #include <stdlib.h> 46 #include "reentrant.h" 47 48 #ifdef __weak_alias 49 __weak_alias(initstate,_initstate) 50 __weak_alias(random,_random) 51 __weak_alias(setstate,_setstate) 52 __weak_alias(srandom,_srandom) 53 #endif 54 55 static void srandom_unlocked __P((unsigned int)); 56 static long random_unlocked __P((void)); 57 58 #ifdef _REENTRANT 59 static mutex_t random_mutex = MUTEX_INITIALIZER; 60 #endif 61 62 #define USE_BETTER_RANDOM 63 64 /* 65 * random.c: 66 * 67 * An improved random number generation package. In addition to the standard 68 * rand()/srand() like interface, this package also has a special state info 69 * interface. The initstate() routine is called with a seed, an array of 70 * bytes, and a count of how many bytes are being passed in; this array is 71 * then initialized to contain information for random number generation with 72 * that much state information. Good sizes for the amount of state 73 * information are 32, 64, 128, and 256 bytes. The state can be switched by 74 * calling the setstate() routine with the same array as was initiallized 75 * with initstate(). By default, the package runs with 128 bytes of state 76 * information and generates far better random numbers than a linear 77 * congruential generator. If the amount of state information is less than 78 * 32 bytes, a simple linear congruential R.N.G. is used. 79 * 80 * Internally, the state information is treated as an array of ints; the 81 * zeroeth element of the array is the type of R.N.G. being used (small 82 * integer); the remainder of the array is the state information for the 83 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 84 * state information, which will allow a degree seven polynomial. (Note: 85 * the zeroeth word of state information also has some other information 86 * stored in it -- see setstate() for details). 87 * 88 * The random number generation technique is a linear feedback shift register 89 * approach, employing trinomials (since there are fewer terms to sum up that 90 * way). In this approach, the least significant bit of all the numbers in 91 * the state table will act as a linear feedback shift register, and will 92 * have period 2^deg - 1 (where deg is the degree of the polynomial being 93 * used, assuming that the polynomial is irreducible and primitive). The 94 * higher order bits will have longer periods, since their values are also 95 * influenced by pseudo-random carries out of the lower bits. The total 96 * period of the generator is approximately deg*(2**deg - 1); thus doubling 97 * the amount of state information has a vast influence on the period of the 98 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 99 * large deg, when the period of the shift register is the dominant factor. 100 * With deg equal to seven, the period is actually much longer than the 101 * 7*(2**7 - 1) predicted by this formula. 102 * 103 * Modified 28 December 1994 by Jacob S. Rosenberg. 104 * The following changes have been made: 105 * All references to the type u_int have been changed to unsigned long. 106 * All references to type int have been changed to type long. Other 107 * cleanups have been made as well. A warning for both initstate and 108 * setstate has been inserted to the effect that on Sparc platforms 109 * the 'arg_state' variable must be forced to begin on word boundaries. 110 * This can be easily done by casting a long integer array to char *. 111 * The overall logic has been left STRICTLY alone. This software was 112 * tested on both a VAX and Sun SpacsStation with exactly the same 113 * results. The new version and the original give IDENTICAL results. 114 * The new version is somewhat faster than the original. As the 115 * documentation says: "By default, the package runs with 128 bytes of 116 * state information and generates far better random numbers than a linear 117 * congruential generator. If the amount of state information is less than 118 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 119 * 128 bytes, this new version runs about 19 percent faster and for a 16 120 * byte buffer it is about 5 percent faster. 121 * 122 * Modified 07 January 2002 by Jason R. Thorpe. 123 * The following changes have been made: 124 * All the references to "long" have been changed back to "int". This 125 * fixes memory corruption problems on LP64 platforms. 126 */ 127 128 /* 129 * For each of the currently supported random number generators, we have a 130 * break value on the amount of state information (you need at least this 131 * many bytes of state info to support this random number generator), a degree 132 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 133 * the separation between the two lower order coefficients of the trinomial. 134 */ 135 #define TYPE_0 0 /* linear congruential */ 136 #define BREAK_0 8 137 #define DEG_0 0 138 #define SEP_0 0 139 140 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 141 #define BREAK_1 32 142 #define DEG_1 7 143 #define SEP_1 3 144 145 #define TYPE_2 2 /* x**15 + x + 1 */ 146 #define BREAK_2 64 147 #define DEG_2 15 148 #define SEP_2 1 149 150 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 151 #define BREAK_3 128 152 #define DEG_3 31 153 #define SEP_3 3 154 155 #define TYPE_4 4 /* x**63 + x + 1 */ 156 #define BREAK_4 256 157 #define DEG_4 63 158 #define SEP_4 1 159 160 /* 161 * Array versions of the above information to make code run faster -- 162 * relies on fact that TYPE_i == i. 163 */ 164 #define MAX_TYPES 5 /* max number of types above */ 165 166 static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 167 static const int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 168 169 /* 170 * Initially, everything is set up as if from: 171 * 172 * initstate(1, &randtbl, 128); 173 * 174 * Note that this initialization takes advantage of the fact that srandom() 175 * advances the front and rear pointers 10*rand_deg times, and hence the 176 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 177 * element of the state information, which contains info about the current 178 * position of the rear pointer is just 179 * 180 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 181 */ 182 183 /* LINTED */ 184 static int randtbl[DEG_3 + 1] = { 185 TYPE_3, 186 #ifdef USE_BETTER_RANDOM 187 0x991539b1, 0x16a5bce3, 0x6774a4cd, 188 0x3e01511e, 0x4e508aaa, 0x61048c05, 189 0xf5500617, 0x846b7115, 0x6a19892c, 190 0x896a97af, 0xdb48f936, 0x14898454, 191 0x37ffd106, 0xb58bff9c, 0x59e17104, 192 0xcf918a49, 0x09378c83, 0x52c7a471, 193 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 194 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 195 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 196 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 197 0xf3bec5da, 198 #else 199 0x9a319039, 0x32d9c024, 0x9b663182, 200 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 201 0xf103bc02, 0x48f340fb, 0x7449e56b, 202 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 203 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 204 0x2d436b86, 0xda672e2a, 0x1588ca88, 205 0xe369735d, 0x904f35f7, 0xd7158fd6, 206 0x6fa6f051, 0x616e6b96, 0xac94efdc, 207 0x36413f93, 0xc622c298, 0xf5a42ab8, 208 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 209 0x27fb47b9, 210 #endif /* USE_BETTER_RANDOM */ 211 }; 212 213 /* 214 * fptr and rptr are two pointers into the state info, a front and a rear 215 * pointer. These two pointers are always rand_sep places aparts, as they 216 * cycle cyclically through the state information. (Yes, this does mean we 217 * could get away with just one pointer, but the code for random() is more 218 * efficient this way). The pointers are left positioned as they would be 219 * from the call 220 * 221 * initstate(1, randtbl, 128); 222 * 223 * (The position of the rear pointer, rptr, is really 0 (as explained above 224 * in the initialization of randtbl) because the state table pointer is set 225 * to point to randtbl[1] (as explained below). 226 */ 227 static int *fptr = &randtbl[SEP_3 + 1]; 228 static int *rptr = &randtbl[1]; 229 230 /* 231 * The following things are the pointer to the state information table, the 232 * type of the current generator, the degree of the current polynomial being 233 * used, and the separation between the two pointers. Note that for efficiency 234 * of random(), we remember the first location of the state information, not 235 * the zeroeth. Hence it is valid to access state[-1], which is used to 236 * store the type of the R.N.G. Also, we remember the last location, since 237 * this is more efficient than indexing every time to find the address of 238 * the last element to see if the front and rear pointers have wrapped. 239 */ 240 static int *state = &randtbl[1]; 241 static int rand_type = TYPE_3; 242 static int rand_deg = DEG_3; 243 static int rand_sep = SEP_3; 244 static int *end_ptr = &randtbl[DEG_3 + 1]; 245 246 /* 247 * srandom: 248 * 249 * Initialize the random number generator based on the given seed. If the 250 * type is the trivial no-state-information type, just remember the seed. 251 * Otherwise, initializes state[] based on the given "seed" via a linear 252 * congruential generator. Then, the pointers are set to known locations 253 * that are exactly rand_sep places apart. Lastly, it cycles the state 254 * information a given number of times to get rid of any initial dependencies 255 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 256 * for default usage relies on values produced by this routine. 257 */ 258 static void 259 srandom_unlocked(x) 260 unsigned int x; 261 { 262 int i; 263 264 if (rand_type == TYPE_0) 265 state[0] = x; 266 else { 267 state[0] = x; 268 for (i = 1; i < rand_deg; i++) { 269 #ifdef USE_BETTER_RANDOM 270 int x1, hi, lo, t; 271 272 /* 273 * Compute x[n + 1] = (7^5 * x[n]) mod (2^31 - 1). 274 * From "Random number generators: good ones are hard 275 * to find", Park and Miller, Communications of the ACM, 276 * vol. 31, no. 10, 277 * October 1988, p. 1195. 278 */ 279 x1 = state[i - 1]; 280 hi = x1 / 127773; 281 lo = x1 % 127773; 282 t = 16807 * lo - 2836 * hi; 283 if (t <= 0) 284 t += 0x7fffffff; 285 state[i] = t; 286 #else 287 state[i] = 1103515245 * state[i - 1] + 12345; 288 #endif /* USE_BETTER_RANDOM */ 289 } 290 fptr = &state[rand_sep]; 291 rptr = &state[0]; 292 for (i = 0; i < 10 * rand_deg; i++) 293 (void)random_unlocked(); 294 } 295 } 296 297 void 298 srandom(x) 299 unsigned long x; 300 { 301 302 mutex_lock(&random_mutex); 303 srandom_unlocked((unsigned int) x); 304 mutex_unlock(&random_mutex); 305 } 306 307 /* 308 * initstate: 309 * 310 * Initialize the state information in the given array of n bytes for future 311 * random number generation. Based on the number of bytes we are given, and 312 * the break values for the different R.N.G.'s, we choose the best (largest) 313 * one we can and set things up for it. srandom() is then called to 314 * initialize the state information. 315 * 316 * Note that on return from srandom(), we set state[-1] to be the type 317 * multiplexed with the current value of the rear pointer; this is so 318 * successive calls to initstate() won't lose this information and will be 319 * able to restart with setstate(). 320 * 321 * Note: the first thing we do is save the current state, if any, just like 322 * setstate() so that it doesn't matter when initstate is called. 323 * 324 * Returns a pointer to the old state. 325 * 326 * Note: The Sparc platform requires that arg_state begin on an int 327 * word boundary; otherwise a bus error will occur. Even so, lint will 328 * complain about mis-alignment, but you should disregard these messages. 329 */ 330 char * 331 initstate(seed, arg_state, n) 332 unsigned long seed; /* seed for R.N.G. */ 333 char *arg_state; /* pointer to state array */ 334 size_t n; /* # bytes of state info */ 335 { 336 void *ostate = (void *)(&state[-1]); 337 int *int_arg_state; 338 339 _DIAGASSERT(arg_state != NULL); 340 341 int_arg_state = (int *)(void *)arg_state; 342 343 mutex_lock(&random_mutex); 344 if (rand_type == TYPE_0) 345 state[-1] = rand_type; 346 else 347 state[-1] = MAX_TYPES * (int)(rptr - state) + rand_type; 348 if (n < BREAK_0) { 349 mutex_unlock(&random_mutex); 350 return (NULL); 351 } else if (n < BREAK_1) { 352 rand_type = TYPE_0; 353 rand_deg = DEG_0; 354 rand_sep = SEP_0; 355 } else if (n < BREAK_2) { 356 rand_type = TYPE_1; 357 rand_deg = DEG_1; 358 rand_sep = SEP_1; 359 } else if (n < BREAK_3) { 360 rand_type = TYPE_2; 361 rand_deg = DEG_2; 362 rand_sep = SEP_2; 363 } else if (n < BREAK_4) { 364 rand_type = TYPE_3; 365 rand_deg = DEG_3; 366 rand_sep = SEP_3; 367 } else { 368 rand_type = TYPE_4; 369 rand_deg = DEG_4; 370 rand_sep = SEP_4; 371 } 372 state = (int *) (int_arg_state + 1); /* first location */ 373 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 374 srandom_unlocked((unsigned int) seed); 375 if (rand_type == TYPE_0) 376 int_arg_state[0] = rand_type; 377 else 378 int_arg_state[0] = MAX_TYPES * (int)(rptr - state) + rand_type; 379 mutex_unlock(&random_mutex); 380 return((char *)ostate); 381 } 382 383 /* 384 * setstate: 385 * 386 * Restore the state from the given state array. 387 * 388 * Note: it is important that we also remember the locations of the pointers 389 * in the current state information, and restore the locations of the pointers 390 * from the old state information. This is done by multiplexing the pointer 391 * location into the zeroeth word of the state information. 392 * 393 * Note that due to the order in which things are done, it is OK to call 394 * setstate() with the same state as the current state. 395 * 396 * Returns a pointer to the old state information. 397 * 398 * Note: The Sparc platform requires that arg_state begin on a long 399 * word boundary; otherwise a bus error will occur. Even so, lint will 400 * complain about mis-alignment, but you should disregard these messages. 401 */ 402 char * 403 setstate(arg_state) 404 char *arg_state; /* pointer to state array */ 405 { 406 int *new_state; 407 int type; 408 int rear; 409 void *ostate = (void *)(&state[-1]); 410 411 _DIAGASSERT(arg_state != NULL); 412 413 new_state = (int *)(void *)arg_state; 414 type = (int)(new_state[0] % MAX_TYPES); 415 rear = (int)(new_state[0] / MAX_TYPES); 416 417 mutex_lock(&random_mutex); 418 if (rand_type == TYPE_0) 419 state[-1] = rand_type; 420 else 421 state[-1] = MAX_TYPES * (int)(rptr - state) + rand_type; 422 switch(type) { 423 case TYPE_0: 424 case TYPE_1: 425 case TYPE_2: 426 case TYPE_3: 427 case TYPE_4: 428 rand_type = type; 429 rand_deg = degrees[type]; 430 rand_sep = seps[type]; 431 break; 432 default: 433 mutex_unlock(&random_mutex); 434 return (NULL); 435 } 436 state = (int *) (new_state + 1); 437 if (rand_type != TYPE_0) { 438 rptr = &state[rear]; 439 fptr = &state[(rear + rand_sep) % rand_deg]; 440 } 441 end_ptr = &state[rand_deg]; /* set end_ptr too */ 442 mutex_unlock(&random_mutex); 443 return((char *)ostate); 444 } 445 446 /* 447 * random: 448 * 449 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 450 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 451 * the same in all the other cases due to all the global variables that have 452 * been set up. The basic operation is to add the number at the rear pointer 453 * into the one at the front pointer. Then both pointers are advanced to 454 * the next location cyclically in the table. The value returned is the sum 455 * generated, reduced to 31 bits by throwing away the "least random" low bit. 456 * 457 * Note: the code takes advantage of the fact that both the front and 458 * rear pointers can't wrap on the same call by not testing the rear 459 * pointer if the front one has wrapped. 460 * 461 * Returns a 31-bit random number. 462 */ 463 static long 464 random_unlocked() 465 { 466 int i; 467 int *f, *r; 468 469 if (rand_type == TYPE_0) { 470 i = state[0]; 471 state[0] = i = (i * 1103515245 + 12345) & 0x7fffffff; 472 } else { 473 /* 474 * Use local variables rather than static variables for speed. 475 */ 476 f = fptr; r = rptr; 477 *f += *r; 478 /* chucking least random bit */ 479 i = ((unsigned int)*f >> 1) & 0x7fffffff; 480 if (++f >= end_ptr) { 481 f = state; 482 ++r; 483 } 484 else if (++r >= end_ptr) { 485 r = state; 486 } 487 488 fptr = f; rptr = r; 489 } 490 return(i); 491 } 492 493 long 494 random() 495 { 496 long r; 497 498 mutex_lock(&random_mutex); 499 r = random_unlocked(); 500 mutex_unlock(&random_mutex); 501 return (r); 502 } 503