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. Neither the name of the University nor the names of its contributors 14 * may be used to endorse or promote products derived from this software 15 * without specific prior written permission. 16 * 17 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 18 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 21 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 22 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 23 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 24 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 25 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 26 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 27 * SUCH DAMAGE. 28 */ 29 30 #if defined(LIBC_SCCS) && !defined(lint) 31 static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95"; 32 #endif /* LIBC_SCCS and not lint */ 33 #include <sys/cdefs.h> 34 __FBSDID("$FreeBSD$"); 35 36 #include "namespace.h" 37 #include <sys/param.h> 38 #include <sys/sysctl.h> 39 #include <stdint.h> 40 #include <stdio.h> 41 #include <stdlib.h> 42 #include "un-namespace.h" 43 44 /* 45 * random.c: 46 * 47 * An improved random number generation package. In addition to the standard 48 * rand()/srand() like interface, this package also has a special state info 49 * interface. The initstate() routine is called with a seed, an array of 50 * bytes, and a count of how many bytes are being passed in; this array is 51 * then initialized to contain information for random number generation with 52 * that much state information. Good sizes for the amount of state 53 * information are 32, 64, 128, and 256 bytes. The state can be switched by 54 * calling the setstate() routine with the same array as was initiallized 55 * with initstate(). By default, the package runs with 128 bytes of state 56 * information and generates far better random numbers than a linear 57 * congruential generator. If the amount of state information is less than 58 * 32 bytes, a simple linear congruential R.N.G. is used. 59 * 60 * Internally, the state information is treated as an array of uint32_t's; the 61 * zeroeth element of the array is the type of R.N.G. being used (small 62 * integer); the remainder of the array is the state information for the 63 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 64 * state information, which will allow a degree seven polynomial. (Note: 65 * the zeroeth word of state information also has some other information 66 * stored in it -- see setstate() for details). 67 * 68 * The random number generation technique is a linear feedback shift register 69 * approach, employing trinomials (since there are fewer terms to sum up that 70 * way). In this approach, the least significant bit of all the numbers in 71 * the state table will act as a linear feedback shift register, and will 72 * have period 2^deg - 1 (where deg is the degree of the polynomial being 73 * used, assuming that the polynomial is irreducible and primitive). The 74 * higher order bits will have longer periods, since their values are also 75 * influenced by pseudo-random carries out of the lower bits. The total 76 * period of the generator is approximately deg*(2**deg - 1); thus doubling 77 * the amount of state information has a vast influence on the period of the 78 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 79 * large deg, when the period of the shift is the dominant factor. 80 * With deg equal to seven, the period is actually much longer than the 81 * 7*(2**7 - 1) predicted by this formula. 82 * 83 * Modified 28 December 1994 by Jacob S. Rosenberg. 84 * The following changes have been made: 85 * All references to the type u_int have been changed to unsigned long. 86 * All references to type int have been changed to type long. Other 87 * cleanups have been made as well. A warning for both initstate and 88 * setstate has been inserted to the effect that on Sparc platforms 89 * the 'arg_state' variable must be forced to begin on word boundaries. 90 * This can be easily done by casting a long integer array to char *. 91 * The overall logic has been left STRICTLY alone. This software was 92 * tested on both a VAX and Sun SpacsStation with exactly the same 93 * results. The new version and the original give IDENTICAL results. 94 * The new version is somewhat faster than the original. As the 95 * documentation says: "By default, the package runs with 128 bytes of 96 * state information and generates far better random numbers than a linear 97 * congruential generator. If the amount of state information is less than 98 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 99 * 128 bytes, this new version runs about 19 percent faster and for a 16 100 * byte buffer it is about 5 percent faster. 101 */ 102 103 /* 104 * For each of the currently supported random number generators, we have a 105 * break value on the amount of state information (you need at least this 106 * many bytes of state info to support this random number generator), a degree 107 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 108 * the separation between the two lower order coefficients of the trinomial. 109 */ 110 #define TYPE_0 0 /* linear congruential */ 111 #define BREAK_0 8 112 #define DEG_0 0 113 #define SEP_0 0 114 115 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 116 #define BREAK_1 32 117 #define DEG_1 7 118 #define SEP_1 3 119 120 #define TYPE_2 2 /* x**15 + x + 1 */ 121 #define BREAK_2 64 122 #define DEG_2 15 123 #define SEP_2 1 124 125 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 126 #define BREAK_3 128 127 #define DEG_3 31 128 #define SEP_3 3 129 130 #define TYPE_4 4 /* x**63 + x + 1 */ 131 #define BREAK_4 256 132 #define DEG_4 63 133 #define SEP_4 1 134 135 /* 136 * Array versions of the above information to make code run faster -- 137 * relies on fact that TYPE_i == i. 138 */ 139 #define MAX_TYPES 5 /* max number of types above */ 140 141 #ifdef USE_WEAK_SEEDING 142 #define NSHUFF 0 143 #else /* !USE_WEAK_SEEDING */ 144 #define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */ 145 #endif /* !USE_WEAK_SEEDING */ 146 147 static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 148 static const int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 149 150 /* 151 * Initially, everything is set up as if from: 152 * 153 * initstate(1, randtbl, 128); 154 * 155 * Note that this initialization takes advantage of the fact that srandom() 156 * advances the front and rear pointers 10*rand_deg times, and hence the 157 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 158 * element of the state information, which contains info about the current 159 * position of the rear pointer is just 160 * 161 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 162 */ 163 164 static uint32_t randtbl[DEG_3 + 1] = { 165 TYPE_3, 166 #ifdef USE_WEAK_SEEDING 167 /* Historic implementation compatibility */ 168 /* The random sequences do not vary much with the seed */ 169 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 170 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 171 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, 172 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 173 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 174 0x27fb47b9, 175 #else /* !USE_WEAK_SEEDING */ 176 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 177 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 178 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 179 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 180 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 181 0xf3bec5da 182 #endif /* !USE_WEAK_SEEDING */ 183 }; 184 185 /* 186 * fptr and rptr are two pointers into the state info, a front and a rear 187 * pointer. These two pointers are always rand_sep places aparts, as they 188 * cycle cyclically through the state information. (Yes, this does mean we 189 * could get away with just one pointer, but the code for random() is more 190 * efficient this way). The pointers are left positioned as they would be 191 * from the call 192 * 193 * initstate(1, randtbl, 128); 194 * 195 * (The position of the rear pointer, rptr, is really 0 (as explained above 196 * in the initialization of randtbl) because the state table pointer is set 197 * to point to randtbl[1] (as explained below). 198 */ 199 static uint32_t *fptr = &randtbl[SEP_3 + 1]; 200 static uint32_t *rptr = &randtbl[1]; 201 202 /* 203 * The following things are the pointer to the state information table, the 204 * type of the current generator, the degree of the current polynomial being 205 * used, and the separation between the two pointers. Note that for efficiency 206 * of random(), we remember the first location of the state information, not 207 * the zeroeth. Hence it is valid to access state[-1], which is used to 208 * store the type of the R.N.G. Also, we remember the last location, since 209 * this is more efficient than indexing every time to find the address of 210 * the last element to see if the front and rear pointers have wrapped. 211 */ 212 static uint32_t *state = &randtbl[1]; 213 static int rand_type = TYPE_3; 214 static int rand_deg = DEG_3; 215 static int rand_sep = SEP_3; 216 static uint32_t *end_ptr = &randtbl[DEG_3 + 1]; 217 218 static inline uint32_t 219 good_rand(int32_t x) 220 { 221 #ifdef USE_WEAK_SEEDING 222 /* 223 * Historic implementation compatibility. 224 * The random sequences do not vary much with the seed, 225 * even with overflowing. 226 */ 227 return (1103515245 * x + 12345); 228 #else /* !USE_WEAK_SEEDING */ 229 /* 230 * Compute x = (7^5 * x) mod (2^31 - 1) 231 * wihout overflowing 31 bits: 232 * (2^31 - 1) = 127773 * (7^5) + 2836 233 * From "Random number generators: good ones are hard to find", 234 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 235 * October 1988, p. 1195. 236 */ 237 int32_t hi, lo; 238 239 /* Can't be initialized with 0, so use another value. */ 240 if (x == 0) 241 x = 123459876; 242 hi = x / 127773; 243 lo = x % 127773; 244 x = 16807 * lo - 2836 * hi; 245 if (x < 0) 246 x += 0x7fffffff; 247 return (x); 248 #endif /* !USE_WEAK_SEEDING */ 249 } 250 251 /* 252 * srandom: 253 * 254 * Initialize the random number generator based on the given seed. If the 255 * type is the trivial no-state-information type, just remember the seed. 256 * Otherwise, initializes state[] based on the given "seed" via a linear 257 * congruential generator. Then, the pointers are set to known locations 258 * that are exactly rand_sep places apart. Lastly, it cycles the state 259 * information a given number of times to get rid of any initial dependencies 260 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 261 * for default usage relies on values produced by this routine. 262 */ 263 void 264 srandom(unsigned long x) 265 { 266 int i, lim; 267 268 state[0] = (uint32_t)x; 269 if (rand_type == TYPE_0) 270 lim = NSHUFF; 271 else { 272 for (i = 1; i < rand_deg; i++) 273 state[i] = good_rand(state[i - 1]); 274 fptr = &state[rand_sep]; 275 rptr = &state[0]; 276 lim = 10 * rand_deg; 277 } 278 for (i = 0; i < lim; i++) 279 (void)random(); 280 } 281 282 /* 283 * srandomdev: 284 * 285 * Many programs choose the seed value in a totally predictable manner. 286 * This often causes problems. We seed the generator using pseudo-random 287 * data from the kernel. 288 * 289 * Note that this particular seeding procedure can generate states 290 * which are impossible to reproduce by calling srandom() with any 291 * value, since the succeeding terms in the state buffer are no longer 292 * derived from the LC algorithm applied to a fixed seed. 293 */ 294 void 295 srandomdev(void) 296 { 297 int mib[2]; 298 size_t len; 299 300 if (rand_type == TYPE_0) 301 len = sizeof(state[0]); 302 else 303 len = rand_deg * sizeof(state[0]); 304 305 mib[0] = CTL_KERN; 306 mib[1] = KERN_ARND; 307 sysctl(mib, 2, state, &len, NULL, 0); 308 309 if (rand_type != TYPE_0) { 310 fptr = &state[rand_sep]; 311 rptr = &state[0]; 312 } 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 an int 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(unsigned long seed, char *arg_state, long n) 340 { 341 char *ostate = (char *)(&state[-1]); 342 uint32_t *int_arg_state = (uint32_t *)arg_state; 343 344 if (rand_type == TYPE_0) 345 state[-1] = rand_type; 346 else 347 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 348 if (n < BREAK_0) { 349 (void)fprintf(stderr, 350 "random: not enough state (%ld bytes); ignored.\n", n); 351 return (0); 352 } 353 if (n < BREAK_1) { 354 rand_type = TYPE_0; 355 rand_deg = DEG_0; 356 rand_sep = SEP_0; 357 } else if (n < BREAK_2) { 358 rand_type = TYPE_1; 359 rand_deg = DEG_1; 360 rand_sep = SEP_1; 361 } else if (n < BREAK_3) { 362 rand_type = TYPE_2; 363 rand_deg = DEG_2; 364 rand_sep = SEP_2; 365 } else if (n < BREAK_4) { 366 rand_type = TYPE_3; 367 rand_deg = DEG_3; 368 rand_sep = SEP_3; 369 } else { 370 rand_type = TYPE_4; 371 rand_deg = DEG_4; 372 rand_sep = SEP_4; 373 } 374 state = int_arg_state + 1; /* first location */ 375 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 376 srandom(seed); 377 if (rand_type == TYPE_0) 378 int_arg_state[0] = rand_type; 379 else 380 int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 381 return (ostate); 382 } 383 384 /* 385 * setstate: 386 * 387 * Restore the state from the given state array. 388 * 389 * Note: it is important that we also remember the locations of the pointers 390 * in the current state information, and restore the locations of the pointers 391 * from the old state information. This is done by multiplexing the pointer 392 * location into the zeroeth word of the state information. 393 * 394 * Note that due to the order in which things are done, it is OK to call 395 * setstate() with the same state as the current state. 396 * 397 * Returns a pointer to the old state information. 398 * 399 * Note: The Sparc platform requires that arg_state begin on an int 400 * word boundary; otherwise a bus error will occur. Even so, lint will 401 * complain about mis-alignment, but you should disregard these messages. 402 */ 403 char * 404 setstate(char *arg_state) 405 { 406 uint32_t *new_state = (uint32_t *)arg_state; 407 uint32_t type = new_state[0] % MAX_TYPES; 408 uint32_t rear = new_state[0] / MAX_TYPES; 409 char *ostate = (char *)(&state[-1]); 410 411 if (rand_type == TYPE_0) 412 state[-1] = rand_type; 413 else 414 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 415 switch(type) { 416 case TYPE_0: 417 case TYPE_1: 418 case TYPE_2: 419 case TYPE_3: 420 case TYPE_4: 421 rand_type = type; 422 rand_deg = degrees[type]; 423 rand_sep = seps[type]; 424 break; 425 default: 426 (void)fprintf(stderr, 427 "random: state info corrupted; not changed.\n"); 428 } 429 state = new_state + 1; 430 if (rand_type != TYPE_0) { 431 rptr = &state[rear]; 432 fptr = &state[(rear + rand_sep) % rand_deg]; 433 } 434 end_ptr = &state[rand_deg]; /* set end_ptr too */ 435 return (ostate); 436 } 437 438 /* 439 * random: 440 * 441 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 442 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 443 * the same in all the other cases due to all the global variables that have 444 * been set up. The basic operation is to add the number at the rear pointer 445 * into the one at the front pointer. Then both pointers are advanced to 446 * the next location cyclically in the table. The value returned is the sum 447 * generated, reduced to 31 bits by throwing away the "least random" low bit. 448 * 449 * Note: the code takes advantage of the fact that both the front and 450 * rear pointers can't wrap on the same call by not testing the rear 451 * pointer if the front one has wrapped. 452 * 453 * Returns a 31-bit random number. 454 */ 455 long 456 random(void) 457 { 458 uint32_t i; 459 uint32_t *f, *r; 460 461 if (rand_type == TYPE_0) { 462 i = state[0]; 463 state[0] = i = (good_rand(i)) & 0x7fffffff; 464 } else { 465 /* 466 * Use local variables rather than static variables for speed. 467 */ 468 f = fptr; r = rptr; 469 *f += *r; 470 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */ 471 if (++f >= end_ptr) { 472 f = state; 473 ++r; 474 } 475 else if (++r >= end_ptr) { 476 r = state; 477 } 478 479 fptr = f; rptr = r; 480 } 481 return ((long)i); 482 } 483