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) 31static 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 <stdlib.h> 41#include "un-namespace.h" 42 43/* 44 * random.c: 45 * 46 * An improved random number generation package. In addition to the standard 47 * rand()/srand() like interface, this package also has a special state info 48 * interface. The initstate() routine is called with a seed, an array of 49 * bytes, and a count of how many bytes are being passed in; this array is 50 * then initialized to contain information for random number generation with 51 * that much state information. Good sizes for the amount of state 52 * information are 32, 64, 128, and 256 bytes. The state can be switched by 53 * calling the setstate() routine with the same array as was initiallized 54 * with initstate(). By default, the package runs with 128 bytes of state 55 * information and generates far better random numbers than a linear 56 * congruential generator. If the amount of state information is less than 57 * 32 bytes, a simple linear congruential R.N.G. is used. 58 * 59 * Internally, the state information is treated as an array of uint32_t's; the 60 * zeroeth element of the array is the type of R.N.G. being used (small 61 * integer); the remainder of the array is the state information for the 62 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 63 * state information, which will allow a degree seven polynomial. (Note: 64 * the zeroeth word of state information also has some other information 65 * stored in it -- see setstate() for details). 66 * 67 * The random number generation technique is a linear feedback shift register 68 * approach, employing trinomials (since there are fewer terms to sum up that 69 * way). In this approach, the least significant bit of all the numbers in 70 * the state table will act as a linear feedback shift register, and will 71 * have period 2^deg - 1 (where deg is the degree of the polynomial being 72 * used, assuming that the polynomial is irreducible and primitive). The 73 * higher order bits will have longer periods, since their values are also 74 * influenced by pseudo-random carries out of the lower bits. The total 75 * period of the generator is approximately deg*(2**deg - 1); thus doubling 76 * the amount of state information has a vast influence on the period of the 77 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 78 * large deg, when the period of the shift is the dominant factor. 79 * With deg equal to seven, the period is actually much longer than the 80 * 7*(2**7 - 1) predicted by this formula. 81 * 82 * Modified 28 December 1994 by Jacob S. Rosenberg. 83 * The following changes have been made: 84 * All references to the type u_int have been changed to unsigned long. 85 * All references to type int have been changed to type long. Other 86 * cleanups have been made as well. A warning for both initstate and 87 * setstate has been inserted to the effect that on Sparc platforms 88 * the 'arg_state' variable must be forced to begin on word boundaries. 89 * This can be easily done by casting a long integer array to char *. 90 * The overall logic has been left STRICTLY alone. This software was 91 * tested on both a VAX and Sun SpacsStation with exactly the same 92 * results. The new version and the original give IDENTICAL results. 93 * The new version is somewhat faster than the original. As the 94 * documentation says: "By default, the package runs with 128 bytes of 95 * state information and generates far better random numbers than a linear 96 * congruential generator. If the amount of state information is less than 97 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 98 * 128 bytes, this new version runs about 19 percent faster and for a 16 99 * byte buffer it is about 5 percent faster. 100 */ 101 102/* 103 * For each of the currently supported random number generators, we have a 104 * break value on the amount of state information (you need at least this 105 * many bytes of state info to support this random number generator), a degree 106 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 107 * the separation between the two lower order coefficients of the trinomial. 108 */ 109#define TYPE_0 0 /* linear congruential */ 110#define BREAK_0 8 111#define DEG_0 0 112#define SEP_0 0 113 114#define TYPE_1 1 /* x**7 + x**3 + 1 */ 115#define BREAK_1 32 116#define DEG_1 7 117#define SEP_1 3 118 119#define TYPE_2 2 /* x**15 + x + 1 */ 120#define BREAK_2 64 121#define DEG_2 15 122#define SEP_2 1 123 124#define TYPE_3 3 /* x**31 + x**3 + 1 */ 125#define BREAK_3 128 126#define DEG_3 31 127#define SEP_3 3 128 129#define TYPE_4 4 /* x**63 + x + 1 */ 130#define BREAK_4 256 131#define DEG_4 63 132#define SEP_4 1 133 134/* 135 * Array versions of the above information to make code run faster -- 136 * relies on fact that TYPE_i == i. 137 */ 138#define MAX_TYPES 5 /* max number of types above */ 139 140#define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */ 141 142static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 143static 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 159static uint32_t randtbl[DEG_3 + 1] = { 160 TYPE_3, 161 0x2cf41758, 0x27bb3711, 0x4916d4d1, 0x7b02f59f, 0x9b8e28eb, 0xc0e80269, 162 0x696f5c16, 0x878f1ff5, 0x52d9c07f, 0x916a06cd, 0xb50b3a20, 0x2776970a, 163 0xee4eb2a6, 0xe94640ec, 0xb1d65612, 0x9d1ed968, 0x1043f6b7, 0xa3432a76, 164 0x17eacbb9, 0x3c09e2eb, 0x4f8c2b3, 0x708a1f57, 0xee341814, 0x95d0e4d2, 165 0xb06f216c, 0x8bd2e72e, 0x8f7c38d7, 0xcfc6a8fc, 0x2a59495, 0xa20d2a69, 166 0xe29d12d1 167}; 168 169/* 170 * fptr and rptr are two pointers into the state info, a front and a rear 171 * pointer. These two pointers are always rand_sep places aparts, as they 172 * cycle cyclically through the state information. (Yes, this does mean we 173 * could get away with just one pointer, but the code for random() is more 174 * efficient this way). The pointers are left positioned as they would be 175 * from the call 176 * 177 * initstate(1, randtbl, 128); 178 * 179 * (The position of the rear pointer, rptr, is really 0 (as explained above 180 * in the initialization of randtbl) because the state table pointer is set 181 * to point to randtbl[1] (as explained below). 182 */ 183static uint32_t *fptr = &randtbl[SEP_3 + 1]; 184static uint32_t *rptr = &randtbl[1]; 185 186/* 187 * The following things are the pointer to the state information table, the 188 * type of the current generator, the degree of the current polynomial being 189 * used, and the separation between the two pointers. Note that for efficiency 190 * of random(), we remember the first location of the state information, not 191 * the zeroeth. Hence it is valid to access state[-1], which is used to 192 * store the type of the R.N.G. Also, we remember the last location, since 193 * this is more efficient than indexing every time to find the address of 194 * the last element to see if the front and rear pointers have wrapped. 195 */ 196static uint32_t *state = &randtbl[1]; 197static int rand_type = TYPE_3; 198static int rand_deg = DEG_3; 199static int rand_sep = SEP_3; 200static uint32_t *end_ptr = &randtbl[DEG_3 + 1]; 201 202static inline uint32_t 203good_rand(uint32_t ctx) 204{ 205/* 206 * Compute x = (7^5 * x) mod (2^31 - 1) 207 * wihout overflowing 31 bits: 208 * (2^31 - 1) = 127773 * (7^5) + 2836 209 * From "Random number generators: good ones are hard to find", 210 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 211 * October 1988, p. 1195. 212 */ 213 int32_t hi, lo, x; 214 215 /* Transform to [1, 0x7ffffffe] range. */ 216 x = (ctx % 0x7ffffffe) + 1; 217 hi = x / 127773; 218 lo = x % 127773; 219 x = 16807 * lo - 2836 * hi; 220 if (x < 0) 221 x += 0x7fffffff; 222 /* Transform to [0, 0x7ffffffd] range. */ 223 return (x - 1); 224} 225 226/* 227 * srandom: 228 * 229 * Initialize the random number generator based on the given seed. If the 230 * type is the trivial no-state-information type, just remember the seed. 231 * Otherwise, initializes state[] based on the given "seed" via a linear 232 * congruential generator. Then, the pointers are set to known locations 233 * that are exactly rand_sep places apart. Lastly, it cycles the state 234 * information a given number of times to get rid of any initial dependencies 235 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 236 * for default usage relies on values produced by this routine. 237 */ 238void 239srandom(unsigned int x) 240{ 241 int i, lim; 242 243 state[0] = (uint32_t)x; 244 if (rand_type == TYPE_0) 245 lim = NSHUFF; 246 else { 247 for (i = 1; i < rand_deg; i++) 248 state[i] = good_rand(state[i - 1]); 249 fptr = &state[rand_sep]; 250 rptr = &state[0]; 251 lim = 10 * rand_deg; 252 } 253 for (i = 0; i < lim; i++) 254 (void)random(); 255} 256 257/* 258 * srandomdev: 259 * 260 * Many programs choose the seed value in a totally predictable manner. 261 * This often causes problems. We seed the generator using pseudo-random 262 * data from the kernel. 263 * 264 * Note that this particular seeding procedure can generate states 265 * which are impossible to reproduce by calling srandom() with any 266 * value, since the succeeding terms in the state buffer are no longer 267 * derived from the LC algorithm applied to a fixed seed. 268 */ 269void 270srandomdev(void) 271{ 272 int mib[2]; 273 size_t len; 274 275 if (rand_type == TYPE_0) 276 len = sizeof(state[0]); 277 else 278 len = rand_deg * sizeof(state[0]); 279 280 mib[0] = CTL_KERN; 281 mib[1] = KERN_ARND; 282 sysctl(mib, 2, state, &len, NULL, 0); 283 284 if (rand_type != TYPE_0) { 285 fptr = &state[rand_sep]; 286 rptr = &state[0]; 287 } 288} 289 290/* 291 * initstate: 292 * 293 * Initialize the state information in the given array of n bytes for future 294 * random number generation. Based on the number of bytes we are given, and 295 * the break values for the different R.N.G.'s, we choose the best (largest) 296 * one we can and set things up for it. srandom() is then called to 297 * initialize the state information. 298 * 299 * Note that on return from srandom(), we set state[-1] to be the type 300 * multiplexed with the current value of the rear pointer; this is so 301 * successive calls to initstate() won't lose this information and will be 302 * able to restart with setstate(). 303 * 304 * Note: the first thing we do is save the current state, if any, just like 305 * setstate() so that it doesn't matter when initstate is called. 306 * 307 * Returns a pointer to the old state. 308 * 309 * Note: The Sparc platform requires that arg_state begin on an int 310 * word boundary; otherwise a bus error will occur. Even so, lint will 311 * complain about mis-alignment, but you should disregard these messages. 312 */ 313char * 314initstate(unsigned int seed, char *arg_state, size_t n) 315{ 316 char *ostate = (char *)(&state[-1]); 317 uint32_t *int_arg_state = (uint32_t *)arg_state; 318 319 if (n < BREAK_0) 320 return (NULL); 321 if (rand_type == TYPE_0) 322 state[-1] = rand_type; 323 else 324 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 325 if (n < BREAK_1) { 326 rand_type = TYPE_0; 327 rand_deg = DEG_0; 328 rand_sep = SEP_0; 329 } else if (n < BREAK_2) { 330 rand_type = TYPE_1; 331 rand_deg = DEG_1; 332 rand_sep = SEP_1; 333 } else if (n < BREAK_3) { 334 rand_type = TYPE_2; 335 rand_deg = DEG_2; 336 rand_sep = SEP_2; 337 } else if (n < BREAK_4) { 338 rand_type = TYPE_3; 339 rand_deg = DEG_3; 340 rand_sep = SEP_3; 341 } else { 342 rand_type = TYPE_4; 343 rand_deg = DEG_4; 344 rand_sep = SEP_4; 345 } 346 state = int_arg_state + 1; /* first location */ 347 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 348 srandom(seed); 349 if (rand_type == TYPE_0) 350 int_arg_state[0] = rand_type; 351 else 352 int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 353 return (ostate); 354} 355 356/* 357 * setstate: 358 * 359 * Restore the state from the given state array. 360 * 361 * Note: it is important that we also remember the locations of the pointers 362 * in the current state information, and restore the locations of the pointers 363 * from the old state information. This is done by multiplexing the pointer 364 * location into the zeroeth word of the state information. 365 * 366 * Note that due to the order in which things are done, it is OK to call 367 * setstate() with the same state as the current state. 368 * 369 * Returns a pointer to the old state information. 370 * 371 * Note: The Sparc platform requires that arg_state begin on an int 372 * word boundary; otherwise a bus error will occur. Even so, lint will 373 * complain about mis-alignment, but you should disregard these messages. 374 */ 375char * 376setstate(char *arg_state) 377{ 378 uint32_t *new_state = (uint32_t *)arg_state; 379 uint32_t type = new_state[0] % MAX_TYPES; 380 uint32_t rear = new_state[0] / MAX_TYPES; 381 char *ostate = (char *)(&state[-1]); 382 383 if (type != TYPE_0 && rear >= degrees[type]) 384 return (NULL); 385 if (rand_type == TYPE_0) 386 state[-1] = rand_type; 387 else 388 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 389 rand_type = type; 390 rand_deg = degrees[type]; 391 rand_sep = seps[type]; 392 state = new_state + 1; 393 if (rand_type != TYPE_0) { 394 rptr = &state[rear]; 395 fptr = &state[(rear + rand_sep) % rand_deg]; 396 } 397 end_ptr = &state[rand_deg]; /* set end_ptr too */ 398 return (ostate); 399} 400 401/* 402 * random: 403 * 404 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 405 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 406 * the same in all the other cases due to all the global variables that have 407 * been set up. The basic operation is to add the number at the rear pointer 408 * into the one at the front pointer. Then both pointers are advanced to 409 * the next location cyclically in the table. The value returned is the sum 410 * generated, reduced to 31 bits by throwing away the "least random" low bit. 411 * 412 * Note: the code takes advantage of the fact that both the front and 413 * rear pointers can't wrap on the same call by not testing the rear 414 * pointer if the front one has wrapped. 415 * 416 * Returns a 31-bit random number. 417 */ 418long 419random(void) 420{ 421 uint32_t i; 422 uint32_t *f, *r; 423 424 if (rand_type == TYPE_0) { 425 i = state[0]; 426 state[0] = i = good_rand(i); 427 } else { 428 /* 429 * Use local variables rather than static variables for speed. 430 */ 431 f = fptr; r = rptr; 432 *f += *r; 433 i = *f >> 1; /* chucking least random bit */ 434 if (++f >= end_ptr) { 435 f = state; 436 ++r; 437 } 438 else if (++r >= end_ptr) { 439 r = state; 440 } 441 442 fptr = f; rptr = r; 443 } 444 return ((long)i); 445} 446