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