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 * $FreeBSD: src/lib/libc/stdlib/random.c,v 1.13 2000/01/27 23:06:49 jasone Exp $ 34 * 35 */ 36 37#include <stdio.h> 38#include <stdlib.h> 39 40 41/* An improved random number generation package. In addition to the standard 42 * rand()/srand() like interface, this package also has a special state info 43 * interface. The initstate() routine is called with a seed, an array of 44 * bytes, and a count of how many bytes are being passed in; this array is 45 * then initialized to contain information for random number generation with 46 * that much state information. Good sizes for the amount of state 47 * information are 32, 64, 128, and 256 bytes. The state can be switched by 48 * calling the setstate() routine with the same array as was initiallized 49 * with initstate(). By default, the package runs with 128 bytes of state 50 * information and generates far better random numbers than a linear 51 * congruential generator. If the amount of state information is less than 52 * 32 bytes, a simple linear congruential R.N.G. is used. 53 * 54 * Internally, the state information is treated as an array of longs; the 55 * zeroeth element of the array is the type of R.N.G. being used (small 56 * integer); the remainder of the array is the state information for the 57 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of 58 * state information, which will allow a degree seven polynomial. (Note: 59 * the zeroeth word of state information also has some other information 60 * stored in it -- see setstate() for details). 61 * 62 * The random number generation technique is a linear feedback shift register 63 * approach, employing trinomials (since there are fewer terms to sum up that 64 * way). In this approach, the least significant bit of all the numbers in 65 * the state table will act as a linear feedback shift register, and will 66 * have period 2^deg - 1 (where deg is the degree of the polynomial being 67 * used, assuming that the polynomial is irreducible and primitive). The 68 * higher order bits will have longer periods, since their values are also 69 * influenced by pseudo-random carries out of the lower bits. The total 70 * period of the generator is approximately deg*(2**deg - 1); thus doubling 71 * the amount of state information has a vast influence on the period of the 72 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 73 * large deg, when the period of the shift register is the dominant factor. 74 * With deg equal to seven, the period is actually much longer than the 75 * 7*(2**7 - 1) predicted by this formula. 76 * 77 * Modified 28 December 1994 by Jacob S. Rosenberg. 78 * The following changes have been made: 79 * All references to the type u_int have been changed to unsigned long. 80 * All references to type int have been changed to type long. Other 81 * cleanups have been made as well. A warning for both initstate and 82 * setstate has been inserted to the effect that on Sparc platforms 83 * the 'arg_state' variable must be forced to begin on word boundaries. 84 * This can be easily done by casting a long integer array to char *. 85 * The overall logic has been left STRICTLY alone. This software was 86 * tested on both a VAX and Sun SpacsStation with exactly the same 87 * results. The new version and the original give IDENTICAL results. 88 * The new version is somewhat faster than the original. As the 89 * documentation says: "By default, the package runs with 128 bytes of 90 * state information and generates far better random numbers than a linear 91 * congruential generator. If the amount of state information is less than 92 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 93 * 128 bytes, this new version runs about 19 percent faster and for a 16 94 * byte buffer it is about 5 percent faster. 95 */ 96 97/* 98 * For each of the currently supported random number generators, we have a 99 * break value on the amount of state information (you need at least this 100 * many bytes of state info to support this random number generator), a degree 101 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 102 * the separation between the two lower order coefficients of the trinomial. 103 */ 104#define TYPE_0 0 /* linear congruential */ 105#define BREAK_0 8 106#define DEG_0 0 107#define SEP_0 0 108 109#define TYPE_1 1 /* x**7 + x**3 + 1 */ 110#define BREAK_1 32 111#define DEG_1 7 112#define SEP_1 3 113 114#define TYPE_2 2 /* x**15 + x + 1 */ 115#define BREAK_2 64 116#define DEG_2 15 117#define SEP_2 1 118 119#define TYPE_3 3 /* x**31 + x**3 + 1 */ 120#define BREAK_3 128 121#define DEG_3 31 122#define SEP_3 3 123 124#define TYPE_4 4 /* x**63 + x + 1 */ 125#define BREAK_4 256 126#define DEG_4 63 127#define SEP_4 1 128 129/* 130 * Array versions of the above information to make code run faster -- 131 * relies on fact that TYPE_i == i. 132 */ 133#define MAX_TYPES 5 /* max number of types above */ 134 135static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 136static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 137 138/* 139 * Initially, everything is set up as if from: 140 * 141 * initstate(1, randtbl, 128); 142 * 143 * Note that this initialization takes advantage of the fact that srandom() 144 * advances the front and rear pointers 10*rand_deg times, and hence the 145 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 146 * element of the state information, which contains info about the current 147 * position of the rear pointer is just 148 * 149 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 150 */ 151 152static long randtbl[DEG_3 + 1] = { 153 TYPE_3, 154#ifdef USE_WEAK_SEEDING 155/* Historic implementation compatibility */ 156/* The random sequences do not vary much with the seed */ 157 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 158 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 159 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, 160 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 161 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 162 0x27fb47b9, 163#else /* !USE_WEAK_SEEDING */ 164 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 165 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 166 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 167 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 168 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 169 0xf3bec5da 170#endif /* !USE_WEAK_SEEDING */ 171}; 172 173/* 174 * fptr and rptr are two pointers into the state info, a front and a rear 175 * pointer. These two pointers are always rand_sep places aparts, as they 176 * cycle cyclically through the state information. (Yes, this does mean we 177 * could get away with just one pointer, but the code for random() is more 178 * efficient this way). The pointers are left positioned as they would be 179 * from the call 180 * 181 * initstate(1, randtbl, 128); 182 * 183 * (The position of the rear pointer, rptr, is really 0 (as explained above 184 * in the initialization of randtbl) because the state table pointer is set 185 * to point to randtbl[1] (as explained below). 186 */ 187static long *fptr = &randtbl[SEP_3 + 1]; 188static long *rptr = &randtbl[1]; 189 190/* 191 * The following things are the pointer to the state information table, the 192 * type of the current generator, the degree of the current polynomial being 193 * used, and the separation between the two pointers. Note that for efficiency 194 * of random(), we remember the first location of the state information, not 195 * the zeroeth. Hence it is valid to access state[-1], which is used to 196 * store the type of the R.N.G. Also, we remember the last location, since 197 * this is more efficient than indexing every time to find the address of 198 * the last element to see if the front and rear pointers have wrapped. 199 */ 200static long *state = &randtbl[1]; 201static long rand_type = TYPE_3; 202static long rand_deg = DEG_3; 203static long rand_sep = SEP_3; 204static long *end_ptr = &randtbl[DEG_3 + 1]; 205 206static inline long good_rand(long); 207 208static inline long good_rand(long x) 209{ 210#ifdef USE_WEAK_SEEDING 211/* 212 * Historic implementation compatibility. 213 * The random sequences do not vary much with the seed, 214 * even with overflowing. 215 */ 216 return (1103515245 * x + 12345); 217#else /* !USE_WEAK_SEEDING */ 218/* 219 * Compute x = (7^5 * x) mod (2^31 - 1) 220 * wihout overflowing 31 bits: 221 * (2^31 - 1) = 127773 * (7^5) + 2836 222 * From "Random number generators: good ones are hard to find", 223 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 224 * October 1988, p. 1195. 225 */ 226 register long hi, lo; 227 228 hi = x / 127773; 229 lo = x % 127773; 230 x = 16807 * lo - 2836 * hi; 231 if (x <= 0) 232 x += 0x7fffffff; 233 return (x); 234#endif /* !USE_WEAK_SEEDING */ 235} 236 237/* 238 * srandom: 239 * 240 * Initialize the random number generator based on the given seed. If the 241 * type is the trivial no-state-information type, just remember the seed. 242 * Otherwise, initializes state[] based on the given "seed" via a linear 243 * congruential generator. Then, the pointers are set to known locations 244 * that are exactly rand_sep places apart. Lastly, it cycles the state 245 * information a given number of times to get rid of any initial dependencies 246 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 247 * for default usage relies on values produced by this routine. 248 */ 249void 250srandom(unsigned int x) 251{ 252 long i; 253 254 if (rand_type == TYPE_0) { 255 state[0] = x; 256 } else { 257 state[0] = x; 258 for (i = 1; i < rand_deg; i++) { 259 state[i] = good_rand(state[i - 1]); 260 } 261 fptr = &state[rand_sep]; 262 rptr = &state[0]; 263 for (i = 0; i < 10 * rand_deg; i++) { 264 (void)random(); 265 } 266 } 267} 268 269/* 270 * srandomdev: 271 * 272 * Many programs choose the seed value in a totally predictable manner. 273 * This often causes problems. We seed the generator using the much more 274 * secure urandom(4) interface. Note that this particular seeding 275 * procedure can generate states which are impossible to reproduce by 276 * calling srandom() with any value, since the succeeding terms in the 277 * state buffer are no longer derived from the LC algorithm applied to 278 * a fixed seed. 279 */ 280#if 0 281void 282srandomdev() 283{ 284 int fd, done; 285 size_t len; 286 287 if (rand_type == TYPE_0) 288 len = sizeof state[0]; 289 else 290 len = rand_deg * sizeof state[0]; 291 292 done = 0; 293 fd = _open("/dev/urandom", O_RDONLY, 0); 294 if (fd >= 0) { 295 if (_read(fd, (void *) state, len) == (ssize_t) len) 296 done = 1; 297 _close(fd); 298 } 299 300 if (!done) { 301 struct timeval tv; 302 unsigned long junk; 303 304 gettimeofday(&tv, NULL); 305 srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk); 306 return; 307 } 308 309 if (rand_type != TYPE_0) { 310 fptr = &state[rand_sep]; 311 rptr = &state[0]; 312 } 313} 314#endif 315 316/* 317 * initstate: 318 * 319 * Initialize the state information in the given array of n bytes for future 320 * random number generation. Based on the number of bytes we are given, and 321 * the break values for the different R.N.G.'s, we choose the best (largest) 322 * one we can and set things up for it. srandom() is then called to 323 * initialize the state information. 324 * 325 * Note that on return from srandom(), we set state[-1] to be the type 326 * multiplexed with the current value of the rear pointer; this is so 327 * successive calls to initstate() won't lose this information and will be 328 * able to restart with setstate(). 329 * 330 * Note: the first thing we do is save the current state, if any, just like 331 * setstate() so that it doesn't matter when initstate is called. 332 * 333 * Returns a pointer to the old state. 334 * 335 * Note: The Sparc platform requires that arg_state begin on a long 336 * word boundary; otherwise a bus error will occur. Even so, lint will 337 * complain about mis-alignment, but you should disregard these messages. 338 */ 339char * 340initstate(unsigned int seed, char *arg_state, size_t n) 341{ 342 register char *ostate = (char *)(&state[-1]); 343 register long *long_arg_state = (long *) arg_state; 344 345 if (rand_type == TYPE_0) 346 state[-1] = rand_type; 347 else 348 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 349 if (n < BREAK_0) { 350 (void)fprintf(stderr, 351 "random: not enough state (%ld bytes); ignored.\n", n); 352 return(0); 353 } 354 if (n < BREAK_1) { 355 rand_type = TYPE_0; 356 rand_deg = DEG_0; 357 rand_sep = SEP_0; 358 } else if (n < BREAK_2) { 359 rand_type = TYPE_1; 360 rand_deg = DEG_1; 361 rand_sep = SEP_1; 362 } else if (n < BREAK_3) { 363 rand_type = TYPE_2; 364 rand_deg = DEG_2; 365 rand_sep = SEP_2; 366 } else if (n < BREAK_4) { 367 rand_type = TYPE_3; 368 rand_deg = DEG_3; 369 rand_sep = SEP_3; 370 } else { 371 rand_type = TYPE_4; 372 rand_deg = DEG_4; 373 rand_sep = SEP_4; 374 } 375 state = (long *) (long_arg_state + 1); /* first location */ 376 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 377 srandom(seed); 378 if (rand_type == TYPE_0) 379 long_arg_state[0] = rand_type; 380 else 381 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 382 return(ostate); 383} 384 385/* 386 * setstate: 387 * 388 * Restore the state from the given state array. 389 * 390 * Note: it is important that we also remember the locations of the pointers 391 * in the current state information, and restore the locations of the pointers 392 * from the old state information. This is done by multiplexing the pointer 393 * location into the zeroeth word of the state information. 394 * 395 * Note that due to the order in which things are done, it is OK to call 396 * setstate() with the same state as the current state. 397 * 398 * Returns a pointer to the old state information. 399 * 400 * Note: The Sparc platform requires that arg_state begin on a long 401 * word boundary; otherwise a bus error will occur. Even so, lint will 402 * complain about mis-alignment, but you should disregard these messages. 403 */ 404char * 405setstate(arg_state) 406 char *arg_state; /* pointer to state array */ 407{ 408 register long *new_state = (long *) arg_state; 409 register long type = new_state[0] % MAX_TYPES; 410 register long rear = new_state[0] / MAX_TYPES; 411 char *ostate = (char *)(&state[-1]); 412 413 if (rand_type == TYPE_0) 414 state[-1] = rand_type; 415 else 416 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 417 switch(type) { 418 case TYPE_0: 419 case TYPE_1: 420 case TYPE_2: 421 case TYPE_3: 422 case TYPE_4: 423 rand_type = type; 424 rand_deg = degrees[type]; 425 rand_sep = seps[type]; 426 break; 427 default: 428 (void)fprintf(stderr, 429 "random: state info corrupted; not changed.\n"); 430 } 431 state = (long *) (new_state + 1); 432 if (rand_type != TYPE_0) { 433 rptr = &state[rear]; 434 fptr = &state[(rear + rand_sep) % rand_deg]; 435 } 436 end_ptr = &state[rand_deg]; /* set end_ptr too */ 437 return(ostate); 438} 439 440 441/* 442 * random: 443 * 444 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 445 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 446 * the same in all the other cases due to all the global variables that have 447 * been set up. The basic operation is to add the number at the rear pointer 448 * into the one at the front pointer. Then both pointers are advanced to 449 * the next location cyclically in the table. The value returned is the sum 450 * generated, reduced to 31 bits by throwing away the "least random" low bit. 451 * 452 * Note: the code takes advantage of the fact that both the front and 453 * rear pointers can't wrap on the same call by not testing the rear 454 * pointer if the front one has wrapped. 455 * 456 * Returns a 31-bit random number. 457 */ 458int 459random(void) 460{ 461 long i; 462 long *f; 463 long *r; 464 465 if (rand_type == TYPE_0) { 466 i = state[0]; 467 state[0] = i = (good_rand(i)) & 0x7fffffff; 468 } else { 469 /* 470 * Use local variables rather than static variables for speed. 471 */ 472 f = fptr; r = rptr; 473 *f += *r; 474 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */ 475 if (++f >= end_ptr) { 476 f = state; 477 ++r; 478 } 479 else if (++r >= end_ptr) { 480 r = state; 481 } 482 483 fptr = f; rptr = r; 484 } 485 return(i); 486} 487