1 /* $NetBSD: random.c,v 1.4 2014/06/12 20:59:46 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 #if !defined(_KERNEL) && !defined(_STANDALONE) 33 #include <sys/cdefs.h> 34 #if defined(LIBC_SCCS) && !defined(lint) 35 #if 0 36 static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95"; 37 #else 38 __RCSID("$NetBSD: random.c,v 1.4 2014/06/12 20:59:46 christos Exp $"); 39 #endif 40 #endif /* LIBC_SCCS and not lint */ 41 42 #include "namespace.h" 43 44 #include <assert.h> 45 #include <errno.h> 46 #include <stdlib.h> 47 #include "reentrant.h" 48 49 #ifdef __weak_alias 50 __weak_alias(initstate,_initstate) 51 __weak_alias(random,_random) 52 __weak_alias(setstate,_setstate) 53 __weak_alias(srandom,_srandom) 54 #endif 55 56 57 #ifdef _REENTRANT 58 static mutex_t random_mutex = MUTEX_INITIALIZER; 59 #endif 60 #else 61 #include <lib/libkern/libkern.h> 62 #define mutex_lock(a) (void)0 63 #define mutex_unlock(a) (void)0 64 #endif 65 66 #ifndef SMALL_RANDOM 67 static void srandom_unlocked(unsigned int); 68 static long random_unlocked(void); 69 70 #define USE_BETTER_RANDOM 71 72 /* 73 * random.c: 74 * 75 * An improved random number generation package. In addition to the standard 76 * rand()/srand() like interface, this package also has a special state info 77 * interface. The initstate() routine is called with a seed, an array of 78 * bytes, and a count of how many bytes are being passed in; this array is 79 * then initialized to contain information for random number generation with 80 * that much state information. Good sizes for the amount of state 81 * information are 32, 64, 128, and 256 bytes. The state can be switched by 82 * calling the setstate() routine with the same array as was initiallized 83 * with initstate(). By default, the package runs with 128 bytes of state 84 * information and generates far better random numbers than a linear 85 * congruential generator. If the amount of state information is less than 86 * 32 bytes, a simple linear congruential R.N.G. is used. 87 * 88 * Internally, the state information is treated as an array of ints; the 89 * zeroeth element of the array is the type of R.N.G. being used (small 90 * integer); the remainder of the array is the state information for the 91 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 92 * state information, which will allow a degree seven polynomial. (Note: 93 * the zeroeth word of state information also has some other information 94 * stored in it -- see setstate() for details). 95 * 96 * The random number generation technique is a linear feedback shift register 97 * approach, employing trinomials (since there are fewer terms to sum up that 98 * way). In this approach, the least significant bit of all the numbers in 99 * the state table will act as a linear feedback shift register, and will 100 * have period 2^deg - 1 (where deg is the degree of the polynomial being 101 * used, assuming that the polynomial is irreducible and primitive). The 102 * higher order bits will have longer periods, since their values are also 103 * influenced by pseudo-random carries out of the lower bits. The total 104 * period of the generator is approximately deg*(2**deg - 1); thus doubling 105 * the amount of state information has a vast influence on the period of the 106 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 107 * large deg, when the period of the shift register is the dominant factor. 108 * With deg equal to seven, the period is actually much longer than the 109 * 7*(2**7 - 1) predicted by this formula. 110 * 111 * Modified 28 December 1994 by Jacob S. Rosenberg. 112 * The following changes have been made: 113 * All references to the type u_int have been changed to unsigned long. 114 * All references to type int have been changed to type long. Other 115 * cleanups have been made as well. A warning for both initstate and 116 * setstate has been inserted to the effect that on Sparc platforms 117 * the 'arg_state' variable must be forced to begin on word boundaries. 118 * This can be easily done by casting a long integer array to char *. 119 * The overall logic has been left STRICTLY alone. This software was 120 * tested on both a VAX and Sun SpacsStation with exactly the same 121 * results. The new version and the original give IDENTICAL results. 122 * The new version is somewhat faster than the original. As the 123 * documentation says: "By default, the package runs with 128 bytes of 124 * state information and generates far better random numbers than a linear 125 * congruential generator. If the amount of state information is less than 126 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 127 * 128 bytes, this new version runs about 19 percent faster and for a 16 128 * byte buffer it is about 5 percent faster. 129 * 130 * Modified 07 January 2002 by Jason R. Thorpe. 131 * The following changes have been made: 132 * All the references to "long" have been changed back to "int". This 133 * fixes memory corruption problems on LP64 platforms. 134 */ 135 136 /* 137 * For each of the currently supported random number generators, we have a 138 * break value on the amount of state information (you need at least this 139 * many bytes of state info to support this random number generator), a degree 140 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 141 * the separation between the two lower order coefficients of the trinomial. 142 */ 143 #define TYPE_0 0 /* linear congruential */ 144 #define BREAK_0 8 145 #define DEG_0 0 146 #define SEP_0 0 147 148 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 149 #define BREAK_1 32 150 #define DEG_1 7 151 #define SEP_1 3 152 153 #define TYPE_2 2 /* x**15 + x + 1 */ 154 #define BREAK_2 64 155 #define DEG_2 15 156 #define SEP_2 1 157 158 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 159 #define BREAK_3 128 160 #define DEG_3 31 161 #define SEP_3 3 162 163 #define TYPE_4 4 /* x**63 + x + 1 */ 164 #define BREAK_4 256 165 #define DEG_4 63 166 #define SEP_4 1 167 168 /* 169 * Array versions of the above information to make code run faster -- 170 * relies on fact that TYPE_i == i. 171 */ 172 #define MAX_TYPES 5 /* max number of types above */ 173 174 static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 175 static const int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 176 177 /* 178 * Initially, everything is set up as if from: 179 * 180 * initstate(1, &randtbl, 128); 181 * 182 * Note that this initialization takes advantage of the fact that srandom() 183 * advances the front and rear pointers 10*rand_deg times, and hence the 184 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 185 * element of the state information, which contains info about the current 186 * position of the rear pointer is just 187 * 188 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 189 */ 190 191 /* LINTED */ 192 static int randtbl[DEG_3 + 1] = { 193 TYPE_3, 194 #ifdef USE_BETTER_RANDOM 195 0x991539b1, 0x16a5bce3, 0x6774a4cd, 196 0x3e01511e, 0x4e508aaa, 0x61048c05, 197 0xf5500617, 0x846b7115, 0x6a19892c, 198 0x896a97af, 0xdb48f936, 0x14898454, 199 0x37ffd106, 0xb58bff9c, 0x59e17104, 200 0xcf918a49, 0x09378c83, 0x52c7a471, 201 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 202 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 203 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 204 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 205 0xf3bec5da, 206 #else 207 0x9a319039, 0x32d9c024, 0x9b663182, 208 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 209 0xf103bc02, 0x48f340fb, 0x7449e56b, 210 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 211 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 212 0x2d436b86, 0xda672e2a, 0x1588ca88, 213 0xe369735d, 0x904f35f7, 0xd7158fd6, 214 0x6fa6f051, 0x616e6b96, 0xac94efdc, 215 0x36413f93, 0xc622c298, 0xf5a42ab8, 216 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 217 0x27fb47b9, 218 #endif /* USE_BETTER_RANDOM */ 219 }; 220 221 /* 222 * fptr and rptr are two pointers into the state info, a front and a rear 223 * pointer. These two pointers are always rand_sep places aparts, as they 224 * cycle cyclically through the state information. (Yes, this does mean we 225 * could get away with just one pointer, but the code for random() is more 226 * efficient this way). The pointers are left positioned as they would be 227 * from the call 228 * 229 * initstate(1, randtbl, 128); 230 * 231 * (The position of the rear pointer, rptr, is really 0 (as explained above 232 * in the initialization of randtbl) because the state table pointer is set 233 * to point to randtbl[1] (as explained below). 234 */ 235 static int *fptr = &randtbl[SEP_3 + 1]; 236 static int *rptr = &randtbl[1]; 237 238 /* 239 * The following things are the pointer to the state information table, the 240 * type of the current generator, the degree of the current polynomial being 241 * used, and the separation between the two pointers. Note that for efficiency 242 * of random(), we remember the first location of the state information, not 243 * the zeroeth. Hence it is valid to access state[-1], which is used to 244 * store the type of the R.N.G. Also, we remember the last location, since 245 * this is more efficient than indexing every time to find the address of 246 * the last element to see if the front and rear pointers have wrapped. 247 */ 248 static int *state = &randtbl[1]; 249 static int rand_type = TYPE_3; 250 static int rand_deg = DEG_3; 251 static int rand_sep = SEP_3; 252 static int *end_ptr = &randtbl[DEG_3 + 1]; 253 254 /* 255 * srandom: 256 * 257 * Initialize the random number generator based on the given seed. If the 258 * type is the trivial no-state-information type, just remember the seed. 259 * Otherwise, initializes state[] based on the given "seed" via a linear 260 * congruential generator. Then, the pointers are set to known locations 261 * that are exactly rand_sep places apart. Lastly, it cycles the state 262 * information a given number of times to get rid of any initial dependencies 263 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 264 * for default usage relies on values produced by this routine. 265 */ 266 static void 267 srandom_unlocked(unsigned int x) 268 { 269 int i; 270 271 if (rand_type == TYPE_0) 272 state[0] = x; 273 else { 274 state[0] = x; 275 for (i = 1; i < rand_deg; i++) { 276 #ifdef USE_BETTER_RANDOM 277 int x1, hi, lo, t; 278 279 /* 280 * Compute x[n + 1] = (7^5 * x[n]) mod (2^31 - 1). 281 * From "Random number generators: good ones are hard 282 * to find", Park and Miller, Communications of the ACM, 283 * vol. 31, no. 10, 284 * October 1988, p. 1195. 285 */ 286 x1 = state[i - 1]; 287 hi = x1 / 127773; 288 lo = x1 % 127773; 289 t = 16807 * lo - 2836 * hi; 290 if (t <= 0) 291 t += 0x7fffffff; 292 state[i] = t; 293 #else 294 state[i] = 1103515245 * state[i - 1] + 12345; 295 #endif /* USE_BETTER_RANDOM */ 296 } 297 fptr = &state[rand_sep]; 298 rptr = &state[0]; 299 for (i = 0; i < 10 * rand_deg; i++) 300 (void)random_unlocked(); 301 } 302 } 303 304 void 305 srandom(unsigned int x) 306 { 307 308 mutex_lock(&random_mutex); 309 srandom_unlocked(x); 310 mutex_unlock(&random_mutex); 311 } 312 313 /* 314 * initstate: 315 * 316 * Initialize the state information in the given array of n bytes for future 317 * random number generation. Based on the number of bytes we are given, and 318 * the break values for the different R.N.G.'s, we choose the best (largest) 319 * one we can and set things up for it. srandom() is then called to 320 * initialize the state information. 321 * 322 * Note that on return from srandom(), we set state[-1] to be the type 323 * multiplexed with the current value of the rear pointer; this is so 324 * successive calls to initstate() won't lose this information and will be 325 * able to restart with setstate(). 326 * 327 * Note: the first thing we do is save the current state, if any, just like 328 * setstate() so that it doesn't matter when initstate is called. 329 * 330 * Returns a pointer to the old state. 331 * 332 * Note: The Sparc platform requires that arg_state begin on an int 333 * word boundary; otherwise a bus error will occur. Even so, lint will 334 * complain about mis-alignment, but you should disregard these messages. 335 */ 336 char * 337 initstate( 338 unsigned int seed, /* seed for R.N.G. */ 339 char *arg_state, /* pointer to state array */ 340 size_t n) /* # bytes of state info */ 341 { 342 void *ostate = (void *)(&state[-1]); 343 int *int_arg_state; 344 345 _DIAGASSERT(arg_state != NULL); 346 347 int_arg_state = (int *)(void *)arg_state; 348 349 mutex_lock(&random_mutex); 350 if (rand_type == TYPE_0) 351 state[-1] = rand_type; 352 else 353 state[-1] = MAX_TYPES * (int)(rptr - state) + rand_type; 354 if (n < BREAK_0) { 355 mutex_unlock(&random_mutex); 356 return (NULL); 357 } else if (n < BREAK_1) { 358 rand_type = TYPE_0; 359 rand_deg = DEG_0; 360 rand_sep = SEP_0; 361 } else if (n < BREAK_2) { 362 rand_type = TYPE_1; 363 rand_deg = DEG_1; 364 rand_sep = SEP_1; 365 } else if (n < BREAK_3) { 366 rand_type = TYPE_2; 367 rand_deg = DEG_2; 368 rand_sep = SEP_2; 369 } else if (n < BREAK_4) { 370 rand_type = TYPE_3; 371 rand_deg = DEG_3; 372 rand_sep = SEP_3; 373 } else { 374 rand_type = TYPE_4; 375 rand_deg = DEG_4; 376 rand_sep = SEP_4; 377 } 378 state = (int *) (int_arg_state + 1); /* first location */ 379 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 380 srandom_unlocked(seed); 381 if (rand_type == TYPE_0) 382 int_arg_state[0] = rand_type; 383 else 384 int_arg_state[0] = MAX_TYPES * (int)(rptr - state) + rand_type; 385 mutex_unlock(&random_mutex); 386 return((char *)ostate); 387 } 388 389 /* 390 * setstate: 391 * 392 * Restore the state from the given state array. 393 * 394 * Note: it is important that we also remember the locations of the pointers 395 * in the current state information, and restore the locations of the pointers 396 * from the old state information. This is done by multiplexing the pointer 397 * location into the zeroeth word of the state information. 398 * 399 * Note that due to the order in which things are done, it is OK to call 400 * setstate() with the same state as the current state. 401 * 402 * Returns a pointer to the old state information. 403 * 404 * Note: The Sparc platform requires that arg_state begin on a long 405 * word boundary; otherwise a bus error will occur. Even so, lint will 406 * complain about mis-alignment, but you should disregard these messages. 407 */ 408 char * 409 setstate(char *arg_state) /* pointer to state array */ 410 { 411 int *new_state; 412 int type; 413 int rear; 414 void *ostate = (void *)(&state[-1]); 415 416 _DIAGASSERT(arg_state != NULL); 417 418 new_state = (int *)(void *)arg_state; 419 type = (int)(new_state[0] % MAX_TYPES); 420 rear = (int)(new_state[0] / MAX_TYPES); 421 422 mutex_lock(&random_mutex); 423 if (rand_type == TYPE_0) 424 state[-1] = rand_type; 425 else 426 state[-1] = MAX_TYPES * (int)(rptr - state) + rand_type; 427 switch(type) { 428 case TYPE_0: 429 case TYPE_1: 430 case TYPE_2: 431 case TYPE_3: 432 case TYPE_4: 433 rand_type = type; 434 rand_deg = degrees[type]; 435 rand_sep = seps[type]; 436 break; 437 default: 438 mutex_unlock(&random_mutex); 439 return (NULL); 440 } 441 state = (int *) (new_state + 1); 442 if (rand_type != TYPE_0) { 443 rptr = &state[rear]; 444 fptr = &state[(rear + rand_sep) % rand_deg]; 445 } 446 end_ptr = &state[rand_deg]; /* set end_ptr too */ 447 mutex_unlock(&random_mutex); 448 return((char *)ostate); 449 } 450 451 /* 452 * random: 453 * 454 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 455 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 456 * the same in all the other cases due to all the global variables that have 457 * been set up. The basic operation is to add the number at the rear pointer 458 * into the one at the front pointer. Then both pointers are advanced to 459 * the next location cyclically in the table. The value returned is the sum 460 * generated, reduced to 31 bits by throwing away the "least random" low bit. 461 * 462 * Note: the code takes advantage of the fact that both the front and 463 * rear pointers can't wrap on the same call by not testing the rear 464 * pointer if the front one has wrapped. 465 * 466 * Returns a 31-bit random number. 467 */ 468 static long 469 random_unlocked(void) 470 { 471 int i; 472 int *f, *r; 473 474 if (rand_type == TYPE_0) { 475 i = state[0]; 476 state[0] = i = (i * 1103515245 + 12345) & 0x7fffffff; 477 } else { 478 /* 479 * Use local variables rather than static variables for speed. 480 */ 481 f = fptr; r = rptr; 482 *f += *r; 483 /* chucking least random bit */ 484 i = ((unsigned int)*f >> 1) & 0x7fffffff; 485 if (++f >= end_ptr) { 486 f = state; 487 ++r; 488 } 489 else if (++r >= end_ptr) { 490 r = state; 491 } 492 493 fptr = f; rptr = r; 494 } 495 return(i); 496 } 497 498 long 499 random(void) 500 { 501 long r; 502 503 mutex_lock(&random_mutex); 504 r = random_unlocked(); 505 mutex_unlock(&random_mutex); 506 return (r); 507 } 508 #else 509 long 510 random(void) 511 { 512 static u_long randseed = 1; 513 long x, hi, lo, t; 514 515 /* 516 * Compute x[n + 1] = (7^5 * x[n]) mod (2^31 - 1). 517 * From "Random number generators: good ones are hard to find", 518 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 519 * October 1988, p. 1195. 520 */ 521 x = randseed; 522 hi = x / 127773; 523 lo = x % 127773; 524 t = 16807 * lo - 2836 * hi; 525 if (t <= 0) 526 t += 0x7fffffff; 527 randseed = t; 528 return (t); 529 } 530 #endif /* SMALL_RANDOM */ 531
