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