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 * $DragonFly: src/lib/libc/stdlib/random.c,v 1.5 2003/09/06 08:19:16 asmodai Exp $ 35 * 36 * @(#)random.c 8.2 (Berkeley) 5/19/95 37 */ 38 39 #include <sys/time.h> /* for srandomdev() */ 40 #include <fcntl.h> /* for srandomdev() */ 41 #include <stdio.h> 42 #include <stdlib.h> 43 #include <unistd.h> /* for srandomdev() */ 44 45 /* 46 * random.c: 47 * 48 * An improved random number generation package. In addition to the standard 49 * rand()/srand() like interface, this package also has a special state info 50 * interface. The initstate() routine is called with a seed, an array of 51 * bytes, and a count of how many bytes are being passed in; this array is 52 * then initialized to contain information for random number generation with 53 * that much state information. Good sizes for the amount of state 54 * information are 32, 64, 128, and 256 bytes. The state can be switched by 55 * calling the setstate() routine with the same array as was initiallized 56 * with initstate(). By default, the package runs with 128 bytes of state 57 * information and generates far better random numbers than a linear 58 * congruential generator. If the amount of state information is less than 59 * 32 bytes, a simple linear congruential R.N.G. is used. 60 * 61 * Internally, the state information is treated as an array of ints; the 62 * zeroeth element of the array is the type of R.N.G. being used (small 63 * integer); the remainder of the array is the state information for the 64 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 65 * state information, which will allow a degree seven polynomial. (Note: 66 * the zeroeth word of state information also has some other information 67 * stored in it -- see setstate() for details). 68 * 69 * The random number generation technique is a linear feedback shift register 70 * approach, employing trinomials (since there are fewer terms to sum up that 71 * way). In this approach, the least significant bit of all the numbers in 72 * the state table will act as a linear feedback shift register, and will 73 * have period 2^deg - 1 (where deg is the degree of the polynomial being 74 * used, assuming that the polynomial is irreducible and primitive). The 75 * higher order bits will have longer periods, since their values are also 76 * influenced by pseudo-random carries out of the lower bits. The total 77 * period of the generator is approximately deg*(2**deg - 1); thus doubling 78 * the amount of state information has a vast influence on the period of the 79 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 80 * large deg, when the period of the shift register is the dominant factor. 81 * With deg equal to seven, the period is actually much longer than the 82 * 7*(2**7 - 1) predicted by this formula. 83 * 84 * Modified 28 December 1994 by Jacob S. Rosenberg. 85 * The following changes have been made: 86 * All references to the type u_int have been changed to unsigned long. 87 * All references to type int have been changed to type long. Other 88 * cleanups have been made as well. A warning for both initstate and 89 * setstate has been inserted to the effect that on Sparc platforms 90 * the 'arg_state' variable must be forced to begin on word boundaries. 91 * This can be easily done by casting a long integer array to char *. 92 * The overall logic has been left STRICTLY alone. This software was 93 * tested on both a VAX and Sun SpacsStation with exactly the same 94 * results. The new version and the original give IDENTICAL results. 95 * The new version is somewhat faster than the original. As the 96 * documentation says: "By default, the package runs with 128 bytes of 97 * state information and generates far better random numbers than a linear 98 * congruential generator. If the amount of state information is less than 99 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 100 * 128 bytes, this new version runs about 19 percent faster and for a 16 101 * byte buffer it is about 5 percent faster. 102 */ 103 104 /* 105 * For each of the currently supported random number generators, we have a 106 * break value on the amount of state information (you need at least this 107 * many bytes of state info to support this random number generator), a degree 108 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 109 * the separation between the two lower order coefficients of the trinomial. 110 */ 111 #define TYPE_0 0 /* linear congruential */ 112 #define BREAK_0 8 113 #define DEG_0 0 114 #define SEP_0 0 115 116 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 117 #define BREAK_1 32 118 #define DEG_1 7 119 #define SEP_1 3 120 121 #define TYPE_2 2 /* x**15 + x + 1 */ 122 #define BREAK_2 64 123 #define DEG_2 15 124 #define SEP_2 1 125 126 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 127 #define BREAK_3 128 128 #define DEG_3 31 129 #define SEP_3 3 130 131 #define TYPE_4 4 /* x**63 + x + 1 */ 132 #define BREAK_4 256 133 #define DEG_4 63 134 #define SEP_4 1 135 136 /* 137 * Array versions of the above information to make code run faster -- 138 * relies on fact that TYPE_i == i. 139 */ 140 #define MAX_TYPES 5 /* max number of types above */ 141 142 static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 143 static const int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 144 145 /* 146 * Initially, everything is set up as if from: 147 * 148 * initstate(1, randtbl, 128); 149 * 150 * Note that this initialization takes advantage of the fact that srandom() 151 * advances the front and rear pointers 10*rand_deg times, and hence the 152 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 153 * element of the state information, which contains info about the current 154 * position of the rear pointer is just 155 * 156 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 157 */ 158 159 static uint32_t randtbl[DEG_3 + 1] = { 160 TYPE_3, 161 #ifdef USE_WEAK_SEEDING 162 /* Historic implementation compatibility */ 163 /* The random sequences do not vary much with the seed */ 164 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 165 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 166 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, 167 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 168 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 169 0x27fb47b9, 170 #else /* !USE_WEAK_SEEDING */ 171 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 172 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 173 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 174 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 175 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 176 0xf3bec5da 177 #endif /* !USE_WEAK_SEEDING */ 178 }; 179 180 /* 181 * fptr and rptr are two pointers into the state info, a front and a rear 182 * pointer. These two pointers are always rand_sep places aparts, as they 183 * cycle cyclically through the state information. (Yes, this does mean we 184 * could get away with just one pointer, but the code for random() is more 185 * efficient this way). The pointers are left positioned as they would be 186 * from the call 187 * 188 * initstate(1, randtbl, 128); 189 * 190 * (The position of the rear pointer, rptr, is really 0 (as explained above 191 * in the initialization of randtbl) because the state table pointer is set 192 * to point to randtbl[1] (as explained below). 193 */ 194 static uint32_t *fptr = &randtbl[SEP_3 + 1]; 195 static uint32_t *rptr = &randtbl[1]; 196 197 /* 198 * The following things are the pointer to the state information table, the 199 * type of the current generator, the degree of the current polynomial being 200 * used, and the separation between the two pointers. Note that for efficiency 201 * of random(), we remember the first location of the state information, not 202 * the zeroeth. Hence it is valid to access state[-1], which is used to 203 * store the type of the R.N.G. Also, we remember the last location, since 204 * this is more efficient than indexing every time to find the address of 205 * the last element to see if the front and rear pointers have wrapped. 206 */ 207 static uint32_t *state = &randtbl[1]; 208 static int rand_type = TYPE_3; 209 static int rand_deg = DEG_3; 210 static int rand_sep = SEP_3; 211 static uint32_t *end_ptr = &randtbl[DEG_3 + 1]; 212 213 static inline long good_rand (long); 214 215 static inline long good_rand (x) 216 long x; 217 { 218 #ifdef USE_WEAK_SEEDING 219 /* 220 * Historic implementation compatibility. 221 * The random sequences do not vary much with the seed, 222 * even with overflowing. 223 */ 224 return (1103515245 * x + 12345); 225 #else /* !USE_WEAK_SEEDING */ 226 /* 227 * Compute x = (7^5 * x) mod (2^31 - 1) 228 * wihout overflowing 31 bits: 229 * (2^31 - 1) = 127773 * (7^5) + 2836 230 * From "Random number generators: good ones are hard to find", 231 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 232 * October 1988, p. 1195. 233 */ 234 long hi, lo; 235 236 hi = x / 127773; 237 lo = x % 127773; 238 x = 16807 * lo - 2836 * hi; 239 if (x <= 0) 240 x += 0x7fffffff; 241 return (x); 242 #endif /* !USE_WEAK_SEEDING */ 243 } 244 245 /* 246 * srandom: 247 * 248 * Initialize the random number generator based on the given seed. If the 249 * type is the trivial no-state-information type, just remember the seed. 250 * Otherwise, initializes state[] based on the given "seed" via a linear 251 * congruential generator. Then, the pointers are set to known locations 252 * that are exactly rand_sep places apart. Lastly, it cycles the state 253 * information a given number of times to get rid of any initial dependencies 254 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 255 * for default usage relies on values produced by this routine. 256 */ 257 void 258 srandom(x) 259 unsigned long x; 260 { 261 int i; 262 263 if (rand_type == TYPE_0) 264 state[0] = (uint32_t)x; 265 else { 266 state[0] = (uint32_t)x; 267 for (i = 1; i < rand_deg; i++) 268 state[i] = (uint32_t)good_rand(state[i - 1]); 269 fptr = &state[rand_sep]; 270 rptr = &state[0]; 271 for (i = 0; i < 10 * rand_deg; i++) 272 (void)random(); 273 } 274 } 275 276 /* 277 * srandomdev: 278 * 279 * Many programs choose the seed value in a totally predictable manner. 280 * This often causes problems. We seed the generator using the much more 281 * secure urandom(4) interface. Note that this particular seeding 282 * procedure can generate states which are impossible to reproduce by 283 * calling srandom() with any value, since the succeeding terms in the 284 * state buffer are no longer derived from the LC algorithm applied to 285 * a fixed seed. 286 */ 287 void 288 srandomdev() 289 { 290 int fd, done; 291 size_t len; 292 293 if (rand_type == TYPE_0) 294 len = sizeof state[0]; 295 else 296 len = rand_deg * sizeof state[0]; 297 298 done = 0; 299 fd = _open("/dev/urandom", O_RDONLY, 0); 300 if (fd >= 0) { 301 if (_read(fd, (void *) state, len) == (ssize_t) len) 302 done = 1; 303 _close(fd); 304 } 305 306 if (!done) { 307 struct timeval tv; 308 unsigned long junk; 309 310 gettimeofday(&tv, NULL); 311 srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk); 312 return; 313 } 314 315 if (rand_type != TYPE_0) { 316 fptr = &state[rand_sep]; 317 rptr = &state[0]; 318 } 319 } 320 321 /* 322 * initstate: 323 * 324 * Initialize the state information in the given array of n bytes for future 325 * random number generation. Based on the number of bytes we are given, and 326 * the break values for the different R.N.G.'s, we choose the best (largest) 327 * one we can and set things up for it. srandom() is then called to 328 * initialize the state information. 329 * 330 * Note that on return from srandom(), we set state[-1] to be the type 331 * multiplexed with the current value of the rear pointer; this is so 332 * successive calls to initstate() won't lose this information and will be 333 * able to restart with setstate(). 334 * 335 * Note: the first thing we do is save the current state, if any, just like 336 * setstate() so that it doesn't matter when initstate is called. 337 * 338 * Returns a pointer to the old state. 339 * 340 * Note: The Sparc platform requires that arg_state begin on an int 341 * word boundary; otherwise a bus error will occur. Even so, lint will 342 * complain about mis-alignment, but you should disregard these messages. 343 */ 344 char * 345 initstate(seed, arg_state, n) 346 unsigned long seed; /* seed for R.N.G. */ 347 char *arg_state; /* pointer to state array */ 348 long n; /* # bytes of state info */ 349 { 350 char *ostate = (char *)(&state[-1]); 351 uint32_t *int_arg_state = (uint32_t *)(void *)arg_state; 352 353 if (rand_type == TYPE_0) 354 state[-1] = rand_type; 355 else 356 state[-1] = MAX_TYPES * (uint32_t)(rptr - state) + rand_type; 357 if (n < BREAK_0) { 358 (void)fprintf(stderr, 359 "random: not enough state (%ld bytes); ignored.\n", n); 360 return(0); 361 } 362 if (n < BREAK_1) { 363 rand_type = TYPE_0; 364 rand_deg = DEG_0; 365 rand_sep = SEP_0; 366 } else if (n < BREAK_2) { 367 rand_type = TYPE_1; 368 rand_deg = DEG_1; 369 rand_sep = SEP_1; 370 } else if (n < BREAK_3) { 371 rand_type = TYPE_2; 372 rand_deg = DEG_2; 373 rand_sep = SEP_2; 374 } else if (n < BREAK_4) { 375 rand_type = TYPE_3; 376 rand_deg = DEG_3; 377 rand_sep = SEP_3; 378 } else { 379 rand_type = TYPE_4; 380 rand_deg = DEG_4; 381 rand_sep = SEP_4; 382 } 383 state = (uint32_t *) (int_arg_state + 1); /* first location */ 384 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 385 srandom((uint32_t)seed); 386 if (rand_type == TYPE_0) 387 int_arg_state[0] = rand_type; 388 else 389 int_arg_state[0] = MAX_TYPES * (uint32_t)(rptr - state) + rand_type; 390 return(ostate); 391 } 392 393 /* 394 * setstate: 395 * 396 * Restore the state from the given state array. 397 * 398 * Note: it is important that we also remember the locations of the pointers 399 * in the current state information, and restore the locations of the pointers 400 * from the old state information. This is done by multiplexing the pointer 401 * location into the zeroeth word of the state information. 402 * 403 * Note that due to the order in which things are done, it is OK to call 404 * setstate() with the same state as the current state. 405 * 406 * Returns a pointer to the old state information. 407 * 408 * Note: The Sparc platform requires that arg_state begin on a long 409 * word boundary; otherwise a bus error will occur. Even so, lint will 410 * complain about mis-alignment, but you should disregard these messages. 411 */ 412 char * 413 setstate(arg_state) 414 char *arg_state; /* pointer to state array */ 415 { 416 uint32_t *new_state = (uint32_t *)(void *)arg_state; 417 uint32_t type = new_state[0] % MAX_TYPES; 418 uint32_t rear = new_state[0] / MAX_TYPES; 419 char *ostate = (char *)(&state[-1]); 420 421 if (rand_type == TYPE_0) 422 state[-1] = rand_type; 423 else 424 state[-1] = MAX_TYPES * (uint32_t)(rptr - state) + rand_type; 425 switch(type) { 426 case TYPE_0: 427 case TYPE_1: 428 case TYPE_2: 429 case TYPE_3: 430 case TYPE_4: 431 rand_type = type; 432 rand_deg = degrees[type]; 433 rand_sep = seps[type]; 434 break; 435 default: 436 (void)fprintf(stderr, 437 "random: state info corrupted; not changed.\n"); 438 } 439 state = (uint32_t *) (new_state + 1); 440 if (rand_type != TYPE_0) { 441 rptr = &state[rear]; 442 fptr = &state[(rear + rand_sep) % rand_deg]; 443 } 444 end_ptr = &state[rand_deg]; /* set end_ptr too */ 445 return(ostate); 446 } 447 448 /* 449 * random: 450 * 451 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 452 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 453 * the same in all the other cases due to all the global variables that have 454 * been set up. The basic operation is to add the number at the rear pointer 455 * into the one at the front pointer. Then both pointers are advanced to 456 * the next location cyclically in the table. The value returned is the sum 457 * generated, reduced to 31 bits by throwing away the "least random" low bit. 458 * 459 * Note: the code takes advantage of the fact that both the front and 460 * rear pointers can't wrap on the same call by not testing the rear 461 * pointer if the front one has wrapped. 462 * 463 * Returns a 31-bit random number. 464 */ 465 long 466 random() 467 { 468 uint32_t i; 469 uint32_t *f, *r; 470 471 if (rand_type == TYPE_0) { 472 i = state[0]; 473 state[0] = i = (good_rand(i)) & 0x7fffffff; 474 } else { 475 /* 476 * Use local variables rather than static variables for speed. 477 */ 478 f = fptr; r = rptr; 479 *f += *r; 480 /* chucking least random bit */ 481 i = (*f >> 1) & 0x7fffffff; 482 if (++f >= end_ptr) { 483 f = state; 484 ++r; 485 } 486 else if (++r >= end_ptr) { 487 r = state; 488 } 489 490 fptr = f; rptr = r; 491 } 492 return((long)i); 493 } 494