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) 35 static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95"; 36 #endif /* LIBC_SCCS and not lint */ 37 #include <sys/cdefs.h> 38 __FBSDID("$FreeBSD$"); 39 40 #include "namespace.h" 41 #include <sys/time.h> /* for srandomdev() */ 42 #include <fcntl.h> /* for srandomdev() */ 43 #include <stdint.h> 44 #include <stdio.h> 45 #include <stdlib.h> 46 #include <unistd.h> /* for srandomdev() */ 47 #include "un-namespace.h" 48 49 /* 50 * random.c: 51 * 52 * An improved random number generation package. In addition to the standard 53 * rand()/srand() like interface, this package also has a special state info 54 * interface. The initstate() routine is called with a seed, an array of 55 * bytes, and a count of how many bytes are being passed in; this array is 56 * then initialized to contain information for random number generation with 57 * that much state information. Good sizes for the amount of state 58 * information are 32, 64, 128, and 256 bytes. The state can be switched by 59 * calling the setstate() routine with the same array as was initiallized 60 * with initstate(). By default, the package runs with 128 bytes of state 61 * information and generates far better random numbers than a linear 62 * congruential generator. If the amount of state information is less than 63 * 32 bytes, a simple linear congruential R.N.G. is used. 64 * 65 * Internally, the state information is treated as an array of uint32_t's; the 66 * zeroeth element of the array is the type of R.N.G. being used (small 67 * integer); the remainder of the array is the state information for the 68 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 69 * state information, which will allow a degree seven polynomial. (Note: 70 * the zeroeth word of state information also has some other information 71 * stored in it -- see setstate() for details). 72 * 73 * The random number generation technique is a linear feedback shift register 74 * approach, employing trinomials (since there are fewer terms to sum up that 75 * way). In this approach, the least significant bit of all the numbers in 76 * the state table will act as a linear feedback shift register, and will 77 * have period 2^deg - 1 (where deg is the degree of the polynomial being 78 * used, assuming that the polynomial is irreducible and primitive). The 79 * higher order bits will have longer periods, since their values are also 80 * influenced by pseudo-random carries out of the lower bits. The total 81 * period of the generator is approximately deg*(2**deg - 1); thus doubling 82 * the amount of state information has a vast influence on the period of the 83 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 84 * large deg, when the period of the shift is the dominant factor. 85 * With deg equal to seven, the period is actually much longer than the 86 * 7*(2**7 - 1) predicted by this formula. 87 * 88 * Modified 28 December 1994 by Jacob S. Rosenberg. 89 * The following changes have been made: 90 * All references to the type u_int have been changed to unsigned long. 91 * All references to type int have been changed to type long. Other 92 * cleanups have been made as well. A warning for both initstate and 93 * setstate has been inserted to the effect that on Sparc platforms 94 * the 'arg_state' variable must be forced to begin on word boundaries. 95 * This can be easily done by casting a long integer array to char *. 96 * The overall logic has been left STRICTLY alone. This software was 97 * tested on both a VAX and Sun SpacsStation with exactly the same 98 * results. The new version and the original give IDENTICAL results. 99 * The new version is somewhat faster than the original. As the 100 * documentation says: "By default, the package runs with 128 bytes of 101 * state information and generates far better random numbers than a linear 102 * congruential generator. If the amount of state information is less than 103 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 104 * 128 bytes, this new version runs about 19 percent faster and for a 16 105 * byte buffer it is about 5 percent faster. 106 */ 107 108 /* 109 * For each of the currently supported random number generators, we have a 110 * break value on the amount of state information (you need at least this 111 * many bytes of state info to support this random number generator), a degree 112 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 113 * the separation between the two lower order coefficients of the trinomial. 114 */ 115 #define TYPE_0 0 /* linear congruential */ 116 #define BREAK_0 8 117 #define DEG_0 0 118 #define SEP_0 0 119 120 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 121 #define BREAK_1 32 122 #define DEG_1 7 123 #define SEP_1 3 124 125 #define TYPE_2 2 /* x**15 + x + 1 */ 126 #define BREAK_2 64 127 #define DEG_2 15 128 #define SEP_2 1 129 130 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 131 #define BREAK_3 128 132 #define DEG_3 31 133 #define SEP_3 3 134 135 #define TYPE_4 4 /* x**63 + x + 1 */ 136 #define BREAK_4 256 137 #define DEG_4 63 138 #define SEP_4 1 139 140 /* 141 * Array versions of the above information to make code run faster -- 142 * relies on fact that TYPE_i == i. 143 */ 144 #define MAX_TYPES 5 /* max number of types above */ 145 146 #ifdef USE_WEAK_SEEDING 147 #define NSHUFF 0 148 #else /* !USE_WEAK_SEEDING */ 149 #define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */ 150 #endif /* !USE_WEAK_SEEDING */ 151 152 static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 153 static const int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 154 155 /* 156 * Initially, everything is set up as if from: 157 * 158 * initstate(1, randtbl, 128); 159 * 160 * Note that this initialization takes advantage of the fact that srandom() 161 * advances the front and rear pointers 10*rand_deg times, and hence the 162 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 163 * element of the state information, which contains info about the current 164 * position of the rear pointer is just 165 * 166 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 167 */ 168 169 static uint32_t randtbl[DEG_3 + 1] = { 170 TYPE_3, 171 #ifdef USE_WEAK_SEEDING 172 /* Historic implementation compatibility */ 173 /* The random sequences do not vary much with the seed */ 174 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 175 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 176 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, 177 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 178 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 179 0x27fb47b9, 180 #else /* !USE_WEAK_SEEDING */ 181 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 182 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 183 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 184 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 185 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 186 0xf3bec5da 187 #endif /* !USE_WEAK_SEEDING */ 188 }; 189 190 /* 191 * fptr and rptr are two pointers into the state info, a front and a rear 192 * pointer. These two pointers are always rand_sep places aparts, as they 193 * cycle cyclically through the state information. (Yes, this does mean we 194 * could get away with just one pointer, but the code for random() is more 195 * efficient this way). The pointers are left positioned as they would be 196 * from the call 197 * 198 * initstate(1, randtbl, 128); 199 * 200 * (The position of the rear pointer, rptr, is really 0 (as explained above 201 * in the initialization of randtbl) because the state table pointer is set 202 * to point to randtbl[1] (as explained below). 203 */ 204 static uint32_t *fptr = &randtbl[SEP_3 + 1]; 205 static uint32_t *rptr = &randtbl[1]; 206 207 /* 208 * The following things are the pointer to the state information table, the 209 * type of the current generator, the degree of the current polynomial being 210 * used, and the separation between the two pointers. Note that for efficiency 211 * of random(), we remember the first location of the state information, not 212 * the zeroeth. Hence it is valid to access state[-1], which is used to 213 * store the type of the R.N.G. Also, we remember the last location, since 214 * this is more efficient than indexing every time to find the address of 215 * the last element to see if the front and rear pointers have wrapped. 216 */ 217 static uint32_t *state = &randtbl[1]; 218 static int rand_type = TYPE_3; 219 static int rand_deg = DEG_3; 220 static int rand_sep = SEP_3; 221 static uint32_t *end_ptr = &randtbl[DEG_3 + 1]; 222 223 static inline uint32_t good_rand(int32_t); 224 225 static inline uint32_t good_rand (x) 226 int32_t x; 227 { 228 #ifdef USE_WEAK_SEEDING 229 /* 230 * Historic implementation compatibility. 231 * The random sequences do not vary much with the seed, 232 * even with overflowing. 233 */ 234 return (1103515245 * x + 12345); 235 #else /* !USE_WEAK_SEEDING */ 236 /* 237 * Compute x = (7^5 * x) mod (2^31 - 1) 238 * wihout overflowing 31 bits: 239 * (2^31 - 1) = 127773 * (7^5) + 2836 240 * From "Random number generators: good ones are hard to find", 241 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 242 * October 1988, p. 1195. 243 */ 244 int32_t hi, lo; 245 246 /* Can't be initialized with 0, so use another value. */ 247 if (x == 0) 248 x = 123459876; 249 hi = x / 127773; 250 lo = x % 127773; 251 x = 16807 * lo - 2836 * hi; 252 if (x < 0) 253 x += 0x7fffffff; 254 return (x); 255 #endif /* !USE_WEAK_SEEDING */ 256 } 257 258 /* 259 * srandom: 260 * 261 * Initialize the random number generator based on the given seed. If the 262 * type is the trivial no-state-information type, just remember the seed. 263 * Otherwise, initializes state[] based on the given "seed" via a linear 264 * congruential generator. Then, the pointers are set to known locations 265 * that are exactly rand_sep places apart. Lastly, it cycles the state 266 * information a given number of times to get rid of any initial dependencies 267 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 268 * for default usage relies on values produced by this routine. 269 */ 270 void 271 srandom(x) 272 unsigned long x; 273 { 274 int i, lim; 275 276 state[0] = (uint32_t)x; 277 if (rand_type == TYPE_0) 278 lim = NSHUFF; 279 else { 280 for (i = 1; i < rand_deg; i++) 281 state[i] = good_rand(state[i - 1]); 282 fptr = &state[rand_sep]; 283 rptr = &state[0]; 284 lim = 10 * rand_deg; 285 } 286 for (i = 0; i < lim; i++) 287 (void)random(); 288 } 289 290 /* 291 * srandomdev: 292 * 293 * Many programs choose the seed value in a totally predictable manner. 294 * This often causes problems. We seed the generator using the much more 295 * secure random(4) interface. Note that this particular seeding 296 * procedure can generate states which are impossible to reproduce by 297 * calling srandom() with any value, since the succeeding terms in the 298 * state buffer are no longer derived from the LC algorithm applied to 299 * a fixed seed. 300 */ 301 void 302 srandomdev() 303 { 304 int fd, done; 305 size_t len; 306 307 if (rand_type == TYPE_0) 308 len = sizeof state[0]; 309 else 310 len = rand_deg * sizeof state[0]; 311 312 done = 0; 313 fd = _open("/dev/random", O_RDONLY, 0); 314 if (fd >= 0) { 315 if (_read(fd, (void *) state, len) == (ssize_t) len) 316 done = 1; 317 _close(fd); 318 } 319 320 if (!done) { 321 struct timeval tv; 322 unsigned long junk; 323 324 gettimeofday(&tv, NULL); 325 srandom((getpid() << 16) ^ tv.tv_sec ^ tv.tv_usec ^ junk); 326 return; 327 } 328 329 if (rand_type != TYPE_0) { 330 fptr = &state[rand_sep]; 331 rptr = &state[0]; 332 } 333 } 334 335 /* 336 * initstate: 337 * 338 * Initialize the state information in the given array of n bytes for future 339 * random number generation. Based on the number of bytes we are given, and 340 * the break values for the different R.N.G.'s, we choose the best (largest) 341 * one we can and set things up for it. srandom() is then called to 342 * initialize the state information. 343 * 344 * Note that on return from srandom(), we set state[-1] to be the type 345 * multiplexed with the current value of the rear pointer; this is so 346 * successive calls to initstate() won't lose this information and will be 347 * able to restart with setstate(). 348 * 349 * Note: the first thing we do is save the current state, if any, just like 350 * setstate() so that it doesn't matter when initstate is called. 351 * 352 * Returns a pointer to the old state. 353 * 354 * Note: The Sparc platform requires that arg_state begin on an int 355 * word boundary; otherwise a bus error will occur. Even so, lint will 356 * complain about mis-alignment, but you should disregard these messages. 357 */ 358 char * 359 initstate(seed, arg_state, n) 360 unsigned long seed; /* seed for R.N.G. */ 361 char *arg_state; /* pointer to state array */ 362 long n; /* # bytes of state info */ 363 { 364 char *ostate = (char *)(&state[-1]); 365 uint32_t *int_arg_state = (uint32_t *)arg_state; 366 367 if (rand_type == TYPE_0) 368 state[-1] = rand_type; 369 else 370 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 371 if (n < BREAK_0) { 372 (void)fprintf(stderr, 373 "random: not enough state (%ld bytes); ignored.\n", n); 374 return(0); 375 } 376 if (n < BREAK_1) { 377 rand_type = TYPE_0; 378 rand_deg = DEG_0; 379 rand_sep = SEP_0; 380 } else if (n < BREAK_2) { 381 rand_type = TYPE_1; 382 rand_deg = DEG_1; 383 rand_sep = SEP_1; 384 } else if (n < BREAK_3) { 385 rand_type = TYPE_2; 386 rand_deg = DEG_2; 387 rand_sep = SEP_2; 388 } else if (n < BREAK_4) { 389 rand_type = TYPE_3; 390 rand_deg = DEG_3; 391 rand_sep = SEP_3; 392 } else { 393 rand_type = TYPE_4; 394 rand_deg = DEG_4; 395 rand_sep = SEP_4; 396 } 397 state = int_arg_state + 1; /* first location */ 398 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 399 srandom(seed); 400 if (rand_type == TYPE_0) 401 int_arg_state[0] = rand_type; 402 else 403 int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 404 return(ostate); 405 } 406 407 /* 408 * setstate: 409 * 410 * Restore the state from the given state array. 411 * 412 * Note: it is important that we also remember the locations of the pointers 413 * in the current state information, and restore the locations of the pointers 414 * from the old state information. This is done by multiplexing the pointer 415 * location into the zeroeth word of the state information. 416 * 417 * Note that due to the order in which things are done, it is OK to call 418 * setstate() with the same state as the current state. 419 * 420 * Returns a pointer to the old state information. 421 * 422 * Note: The Sparc platform requires that arg_state begin on an int 423 * word boundary; otherwise a bus error will occur. Even so, lint will 424 * complain about mis-alignment, but you should disregard these messages. 425 */ 426 char * 427 setstate(arg_state) 428 char *arg_state; /* pointer to state array */ 429 { 430 uint32_t *new_state = (uint32_t *)arg_state; 431 uint32_t type = new_state[0] % MAX_TYPES; 432 uint32_t rear = new_state[0] / MAX_TYPES; 433 char *ostate = (char *)(&state[-1]); 434 435 if (rand_type == TYPE_0) 436 state[-1] = rand_type; 437 else 438 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 439 switch(type) { 440 case TYPE_0: 441 case TYPE_1: 442 case TYPE_2: 443 case TYPE_3: 444 case TYPE_4: 445 rand_type = type; 446 rand_deg = degrees[type]; 447 rand_sep = seps[type]; 448 break; 449 default: 450 (void)fprintf(stderr, 451 "random: state info corrupted; not changed.\n"); 452 } 453 state = new_state + 1; 454 if (rand_type != TYPE_0) { 455 rptr = &state[rear]; 456 fptr = &state[(rear + rand_sep) % rand_deg]; 457 } 458 end_ptr = &state[rand_deg]; /* set end_ptr too */ 459 return(ostate); 460 } 461 462 /* 463 * random: 464 * 465 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 466 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 467 * the same in all the other cases due to all the global variables that have 468 * been set up. The basic operation is to add the number at the rear pointer 469 * into the one at the front pointer. Then both pointers are advanced to 470 * the next location cyclically in the table. The value returned is the sum 471 * generated, reduced to 31 bits by throwing away the "least random" low bit. 472 * 473 * Note: the code takes advantage of the fact that both the front and 474 * rear pointers can't wrap on the same call by not testing the rear 475 * pointer if the front one has wrapped. 476 * 477 * Returns a 31-bit random number. 478 */ 479 long 480 random() 481 { 482 uint32_t i; 483 uint32_t *f, *r; 484 485 if (rand_type == TYPE_0) { 486 i = state[0]; 487 state[0] = i = (good_rand(i)) & 0x7fffffff; 488 } else { 489 /* 490 * Use local variables rather than static variables for speed. 491 */ 492 f = fptr; r = rptr; 493 *f += *r; 494 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */ 495 if (++f >= end_ptr) { 496 f = state; 497 ++r; 498 } 499 else if (++r >= end_ptr) { 500 r = state; 501 } 502 503 fptr = f; rptr = r; 504 } 505 return((long)i); 506 } 507