random.c revision 24151
1/* 2 * Copyright (c) 1983, 1993 3 * The Regents of the University of California. All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright 9 * notice, this list of conditions and the following disclaimer. 10 * 2. Redistributions in binary form must reproduce the above copyright 11 * notice, this list of conditions and the following disclaimer in the 12 * documentation and/or other materials provided with the distribution. 13 * 3. All advertising materials mentioning features or use of this software 14 * must display the following acknowledgement: 15 * This product includes software developed by the University of 16 * California, Berkeley and its contributors. 17 * 4. Neither the name of the University nor the names of its contributors 18 * may be used to endorse or promote products derived from this software 19 * without specific prior written permission. 20 * 21 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 22 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 23 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 24 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 25 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 26 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 27 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 28 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 29 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 30 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 31 * SUCH DAMAGE. 32 */ 33 34#if defined(LIBC_SCCS) && !defined(lint) 35static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95"; 36#endif /* LIBC_SCCS and not lint */ 37 38#ifdef COMPAT_WEAK_SEEDING 39#define USE_WEAK_SEEDING 40#define random orandom 41#define srandom osrandom 42#define initstate oinitstate 43#define setstate osetstate 44#endif 45 46#include <fcntl.h> /* for srandomdev() */ 47#include <stdio.h> 48#include <stdlib.h> 49#include <unistd.h> /* for srandomdev() */ 50 51/* 52 * random.c: 53 * 54 * An improved random number generation package. In addition to the standard 55 * rand()/srand() like interface, this package also has a special state info 56 * interface. The initstate() routine is called with a seed, an array of 57 * bytes, and a count of how many bytes are being passed in; this array is 58 * then initialized to contain information for random number generation with 59 * that much state information. Good sizes for the amount of state 60 * information are 32, 64, 128, and 256 bytes. The state can be switched by 61 * calling the setstate() routine with the same array as was initiallized 62 * with initstate(). By default, the package runs with 128 bytes of state 63 * information and generates far better random numbers than a linear 64 * congruential generator. If the amount of state information is less than 65 * 32 bytes, a simple linear congruential R.N.G. is used. 66 * 67 * Internally, the state information is treated as an array of longs; the 68 * zeroeth element of the array is the type of R.N.G. being used (small 69 * integer); the remainder of the array is the state information for the 70 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of 71 * state information, which will allow a degree seven polynomial. (Note: 72 * the zeroeth word of state information also has some other information 73 * stored in it -- see setstate() for details). 74 * 75 * The random number generation technique is a linear feedback shift register 76 * approach, employing trinomials (since there are fewer terms to sum up that 77 * way). In this approach, the least significant bit of all the numbers in 78 * the state table will act as a linear feedback shift register, and will 79 * have period 2^deg - 1 (where deg is the degree of the polynomial being 80 * used, assuming that the polynomial is irreducible and primitive). The 81 * higher order bits will have longer periods, since their values are also 82 * influenced by pseudo-random carries out of the lower bits. The total 83 * period of the generator is approximately deg*(2**deg - 1); thus doubling 84 * the amount of state information has a vast influence on the period of the 85 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 86 * large deg, when the period of the shift register is the dominant factor. 87 * With deg equal to seven, the period is actually much longer than the 88 * 7*(2**7 - 1) predicted by this formula. 89 * 90 * Modified 28 December 1994 by Jacob S. Rosenberg. 91 * The following changes have been made: 92 * All references to the type u_int have been changed to unsigned long. 93 * All references to type int have been changed to type long. Other 94 * cleanups have been made as well. A warning for both initstate and 95 * setstate has been inserted to the effect that on Sparc platforms 96 * the 'arg_state' variable must be forced to begin on word boundaries. 97 * This can be easily done by casting a long integer array to char *. 98 * The overall logic has been left STRICTLY alone. This software was 99 * tested on both a VAX and Sun SpacsStation with exactly the same 100 * results. The new version and the original give IDENTICAL results. 101 * The new version is somewhat faster than the original. As the 102 * documentation says: "By default, the package runs with 128 bytes of 103 * state information and generates far better random numbers than a linear 104 * congruential generator. If the amount of state information is less than 105 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 106 * 128 bytes, this new version runs about 19 percent faster and for a 16 107 * byte buffer it is about 5 percent faster. 108 */ 109 110/* 111 * For each of the currently supported random number generators, we have a 112 * break value on the amount of state information (you need at least this 113 * many bytes of state info to support this random number generator), a degree 114 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 115 * the separation between the two lower order coefficients of the trinomial. 116 */ 117#define TYPE_0 0 /* linear congruential */ 118#define BREAK_0 8 119#define DEG_0 0 120#define SEP_0 0 121 122#define TYPE_1 1 /* x**7 + x**3 + 1 */ 123#define BREAK_1 32 124#define DEG_1 7 125#define SEP_1 3 126 127#define TYPE_2 2 /* x**15 + x + 1 */ 128#define BREAK_2 64 129#define DEG_2 15 130#define SEP_2 1 131 132#define TYPE_3 3 /* x**31 + x**3 + 1 */ 133#define BREAK_3 128 134#define DEG_3 31 135#define SEP_3 3 136 137#define TYPE_4 4 /* x**63 + x + 1 */ 138#define BREAK_4 256 139#define DEG_4 63 140#define SEP_4 1 141 142/* 143 * Array versions of the above information to make code run faster -- 144 * relies on fact that TYPE_i == i. 145 */ 146#define MAX_TYPES 5 /* max number of types above */ 147 148static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 149static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 150 151/* 152 * Initially, everything is set up as if from: 153 * 154 * initstate(1, randtbl, 128); 155 * 156 * Note that this initialization takes advantage of the fact that srandom() 157 * advances the front and rear pointers 10*rand_deg times, and hence the 158 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 159 * element of the state information, which contains info about the current 160 * position of the rear pointer is just 161 * 162 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 163 */ 164 165static long randtbl[DEG_3 + 1] = { 166 TYPE_3, 167#ifdef USE_WEAK_SEEDING 168/* Historic implementation compatibility */ 169/* The random sequences do not vary much with the seed */ 170 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 171 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 172 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, 173 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 174 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 175 0x27fb47b9, 176#else /* !USE_WEAK_SEEDING */ 177 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 178 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 179 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 180 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 181 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 182 0xf3bec5da 183#endif /* !USE_WEAK_SEEDING */ 184}; 185 186/* 187 * fptr and rptr are two pointers into the state info, a front and a rear 188 * pointer. These two pointers are always rand_sep places aparts, as they 189 * cycle cyclically through the state information. (Yes, this does mean we 190 * could get away with just one pointer, but the code for random() is more 191 * efficient this way). The pointers are left positioned as they would be 192 * from the call 193 * 194 * initstate(1, randtbl, 128); 195 * 196 * (The position of the rear pointer, rptr, is really 0 (as explained above 197 * in the initialization of randtbl) because the state table pointer is set 198 * to point to randtbl[1] (as explained below). 199 */ 200static long *fptr = &randtbl[SEP_3 + 1]; 201static long *rptr = &randtbl[1]; 202 203/* 204 * The following things are the pointer to the state information table, the 205 * type of the current generator, the degree of the current polynomial being 206 * used, and the separation between the two pointers. Note that for efficiency 207 * of random(), we remember the first location of the state information, not 208 * the zeroeth. Hence it is valid to access state[-1], which is used to 209 * store the type of the R.N.G. Also, we remember the last location, since 210 * this is more efficient than indexing every time to find the address of 211 * the last element to see if the front and rear pointers have wrapped. 212 */ 213static long *state = &randtbl[1]; 214static long rand_type = TYPE_3; 215static long rand_deg = DEG_3; 216static long rand_sep = SEP_3; 217static long *end_ptr = &randtbl[DEG_3 + 1]; 218 219static inline long good_rand __P((long)); 220 221static inline long good_rand (x) 222 register long x; 223{ 224#ifdef USE_WEAK_SEEDING 225/* 226 * Historic implementation compatibility. 227 * The random sequences do not vary much with the seed, 228 * even with overflowing. 229 */ 230 return (1103515245 * x + 12345); 231#else /* !USE_WEAK_SEEDING */ 232/* 233 * Compute x = (7^5 * x) mod (2^31 - 1) 234 * wihout overflowing 31 bits: 235 * (2^31 - 1) = 127773 * (7^5) + 2836 236 * From "Random number generators: good ones are hard to find", 237 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 238 * October 1988, p. 1195. 239 */ 240 register long hi, lo; 241 242 hi = x / 127773; 243 lo = x % 127773; 244 x = 16807 * lo - 2836 * hi; 245 if (x <= 0) 246 x += 0x7fffffff; 247 return (x); 248#endif /* !USE_WEAK_SEEDING */ 249} 250 251/* 252 * srandom: 253 * 254 * Initialize the random number generator based on the given seed. If the 255 * type is the trivial no-state-information type, just remember the seed. 256 * Otherwise, initializes state[] based on the given "seed" via a linear 257 * congruential generator. Then, the pointers are set to known locations 258 * that are exactly rand_sep places apart. Lastly, it cycles the state 259 * information a given number of times to get rid of any initial dependencies 260 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 261 * for default usage relies on values produced by this routine. 262 */ 263void 264srandom(x) 265 unsigned long x; 266{ 267 register long i; 268 269 if (rand_type == TYPE_0) 270 state[0] = x; 271 else { 272 state[0] = x; 273 for (i = 1; i < rand_deg; i++) 274 state[i] = good_rand(state[i - 1]); 275 fptr = &state[rand_sep]; 276 rptr = &state[0]; 277 for (i = 0; i < 10 * rand_deg; i++) 278 (void)random(); 279 } 280} 281 282/* 283 * srandomdev: 284 * 285 * Many programs choose the seed value in a totally predictable manner. 286 * This often causes problems. We seed the generator using the much more 287 * secure `/dev/random' interface. Note that this particular seeding 288 * procedure can generate states which are impossible to reproduce by 289 * calling srandom() with any value, since the succeeding terms in the 290 * state buffer are no longer derived from the LC algorithm applied to 291 * a fixed seed. 292 */ 293int 294srandomdev() 295{ 296 int fd; 297 size_t len; 298 299 if (rand_type == TYPE_0) 300 len = sizeof state[0]; 301 else 302 len = rand_deg * sizeof state[0]; 303 304 fd = open("/dev/urandom", O_RDONLY, 0); 305 if (fd < 0) 306 return -1; 307 if (read(fd, (void *) state, len) < (ssize_t) len) { 308 close(fd); 309 return -1; 310 } 311 close(fd); 312 313 if (rand_type != TYPE_0) { 314 fptr = &state[rand_sep]; 315 rptr = &state[0]; 316 } 317 return 0; 318} 319 320/* 321 * initstate: 322 * 323 * Initialize the state information in the given array of n bytes for future 324 * random number generation. Based on the number of bytes we are given, and 325 * the break values for the different R.N.G.'s, we choose the best (largest) 326 * one we can and set things up for it. srandom() is then called to 327 * initialize the state information. 328 * 329 * Note that on return from srandom(), we set state[-1] to be the type 330 * multiplexed with the current value of the rear pointer; this is so 331 * successive calls to initstate() won't lose this information and will be 332 * able to restart with setstate(). 333 * 334 * Note: the first thing we do is save the current state, if any, just like 335 * setstate() so that it doesn't matter when initstate is called. 336 * 337 * Returns a pointer to the old state. 338 * 339 * Note: The Sparc platform requires that arg_state begin on a long 340 * word boundary; otherwise a bus error will occur. Even so, lint will 341 * complain about mis-alignment, but you should disregard these messages. 342 */ 343char * 344initstate(seed, arg_state, n) 345 unsigned long seed; /* seed for R.N.G. */ 346 char *arg_state; /* pointer to state array */ 347 long n; /* # bytes of state info */ 348{ 349 register char *ostate = (char *)(&state[-1]); 350 register long *long_arg_state = (long *) arg_state; 351 352 if (rand_type == TYPE_0) 353 state[-1] = rand_type; 354 else 355 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 356 if (n < BREAK_0) { 357 (void)fprintf(stderr, 358 "random: not enough state (%ld bytes); ignored.\n", n); 359 return(0); 360 } 361 if (n < BREAK_1) { 362 rand_type = TYPE_0; 363 rand_deg = DEG_0; 364 rand_sep = SEP_0; 365 } else if (n < BREAK_2) { 366 rand_type = TYPE_1; 367 rand_deg = DEG_1; 368 rand_sep = SEP_1; 369 } else if (n < BREAK_3) { 370 rand_type = TYPE_2; 371 rand_deg = DEG_2; 372 rand_sep = SEP_2; 373 } else if (n < BREAK_4) { 374 rand_type = TYPE_3; 375 rand_deg = DEG_3; 376 rand_sep = SEP_3; 377 } else { 378 rand_type = TYPE_4; 379 rand_deg = DEG_4; 380 rand_sep = SEP_4; 381 } 382 state = (long *) (long_arg_state + 1); /* first location */ 383 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 384 srandom(seed); 385 if (rand_type == TYPE_0) 386 long_arg_state[0] = rand_type; 387 else 388 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 389 return(ostate); 390} 391 392/* 393 * setstate: 394 * 395 * Restore the state from the given state array. 396 * 397 * Note: it is important that we also remember the locations of the pointers 398 * in the current state information, and restore the locations of the pointers 399 * from the old state information. This is done by multiplexing the pointer 400 * location into the zeroeth word of the state information. 401 * 402 * Note that due to the order in which things are done, it is OK to call 403 * setstate() with the same state as the current state. 404 * 405 * Returns a pointer to the old state information. 406 * 407 * Note: The Sparc platform requires that arg_state begin on a long 408 * word boundary; otherwise a bus error will occur. Even so, lint will 409 * complain about mis-alignment, but you should disregard these messages. 410 */ 411char * 412setstate(arg_state) 413 char *arg_state; /* pointer to state array */ 414{ 415 register long *new_state = (long *) arg_state; 416 register long type = new_state[0] % MAX_TYPES; 417 register long rear = new_state[0] / MAX_TYPES; 418 char *ostate = (char *)(&state[-1]); 419 420 if (rand_type == TYPE_0) 421 state[-1] = rand_type; 422 else 423 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 424 switch(type) { 425 case TYPE_0: 426 case TYPE_1: 427 case TYPE_2: 428 case TYPE_3: 429 case TYPE_4: 430 rand_type = type; 431 rand_deg = degrees[type]; 432 rand_sep = seps[type]; 433 break; 434 default: 435 (void)fprintf(stderr, 436 "random: state info corrupted; not changed.\n"); 437 } 438 state = (long *) (new_state + 1); 439 if (rand_type != TYPE_0) { 440 rptr = &state[rear]; 441 fptr = &state[(rear + rand_sep) % rand_deg]; 442 } 443 end_ptr = &state[rand_deg]; /* set end_ptr too */ 444 return(ostate); 445} 446 447/* 448 * random: 449 * 450 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 451 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 452 * the same in all the other cases due to all the global variables that have 453 * been set up. The basic operation is to add the number at the rear pointer 454 * into the one at the front pointer. Then both pointers are advanced to 455 * the next location cyclically in the table. The value returned is the sum 456 * generated, reduced to 31 bits by throwing away the "least random" low bit. 457 * 458 * Note: the code takes advantage of the fact that both the front and 459 * rear pointers can't wrap on the same call by not testing the rear 460 * pointer if the front one has wrapped. 461 * 462 * Returns a 31-bit random number. 463 */ 464long 465random() 466{ 467 register long i; 468 register long *f, *r; 469 470 if (rand_type == TYPE_0) { 471 i = state[0]; 472 state[0] = i = (good_rand(i)) & 0x7fffffff; 473 } else { 474 /* 475 * Use local variables rather than static variables for speed. 476 */ 477 f = fptr; r = rptr; 478 *f += *r; 479 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */ 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