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