1/*- 2 * SPDX-License-Identifier: BSD-3-Clause 3 * 4 * Copyright (c) 1983, 1993 5 * The Regents of the University of California. All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice, this list of conditions and the following disclaimer. 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in the 14 * documentation and/or other materials provided with the distribution. 15 * 3. Neither the name of the University nor the names of its contributors 16 * may be used to endorse or promote products derived from this software 17 * without specific prior written permission. 18 * 19 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 20 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 21 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 22 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 23 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 24 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 25 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 26 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 27 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 28 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 29 * SUCH DAMAGE. 30 */ 31 32#include <stdint.h> 33#include <stdlib.h> 34 35/* 36 * random.c: 37 * 38 * An improved random number generation package. In addition to the standard 39 * rand()/srand() like interface, this package also has a special state info 40 * interface. The initstate() routine is called with a seed, an array of 41 * bytes, and a count of how many bytes are being passed in; this array is 42 * then initialized to contain information for random number generation with 43 * that much state information. Good sizes for the amount of state 44 * information are 32, 64, 128, and 256 bytes. The state can be switched by 45 * calling the setstate() routine with the same array as was initiallized 46 * with initstate(). By default, the package runs with 128 bytes of state 47 * information and generates far better random numbers than a linear 48 * congruential generator. If the amount of state information is less than 49 * 32 bytes, a simple linear congruential R.N.G. is used. 50 * 51 * Internally, the state information is treated as an array of uint32_t's; the 52 * zeroeth element of the array is the type of R.N.G. being used (small 53 * integer); the remainder of the array is the state information for the 54 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 55 * state information, which will allow a degree seven polynomial. (Note: 56 * the zeroeth word of state information also has some other information 57 * stored in it -- see setstate() for details). 58 * 59 * The random number generation technique is a linear feedback shift register 60 * approach, employing trinomials (since there are fewer terms to sum up that 61 * way). In this approach, the least significant bit of all the numbers in 62 * the state table will act as a linear feedback shift register, and will 63 * have period 2^deg - 1 (where deg is the degree of the polynomial being 64 * used, assuming that the polynomial is irreducible and primitive). The 65 * higher order bits will have longer periods, since their values are also 66 * influenced by pseudo-random carries out of the lower bits. The total 67 * period of the generator is approximately deg*(2**deg - 1); thus doubling 68 * the amount of state information has a vast influence on the period of the 69 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 70 * large deg, when the period of the shift is the dominant factor. 71 * With deg equal to seven, the period is actually much longer than the 72 * 7*(2**7 - 1) predicted by this formula. 73 * 74 * Modified 28 December 1994 by Jacob S. Rosenberg. 75 * The following changes have been made: 76 * All references to the type u_int have been changed to unsigned long. 77 * All references to type int have been changed to type long. Other 78 * cleanups have been made as well. A warning for both initstate and 79 * setstate has been inserted to the effect that on Sparc platforms 80 * the 'arg_state' variable must be forced to begin on word boundaries. 81 * This can be easily done by casting a long integer array to char *. 82 * The overall logic has been left STRICTLY alone. This software was 83 * tested on both a VAX and Sun SpacsStation with exactly the same 84 * results. The new version and the original give IDENTICAL results. 85 * The new version is somewhat faster than the original. As the 86 * documentation says: "By default, the package runs with 128 bytes of 87 * state information and generates far better random numbers than a linear 88 * congruential generator. If the amount of state information is less than 89 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 90 * 128 bytes, this new version runs about 19 percent faster and for a 16 91 * byte buffer it is about 5 percent faster. 92 */ 93 94/* 95 * For each of the currently supported random number generators, we have a 96 * break value on the amount of state information (you need at least this 97 * many bytes of state info to support this random number generator), a degree 98 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 99 * the separation between the two lower order coefficients of the trinomial. 100 */ 101#define TYPE_0 0 /* linear congruential */ 102#define BREAK_0 8 103#define DEG_0 0 104#define SEP_0 0 105 106#define TYPE_1 1 /* x**7 + x**3 + 1 */ 107#define BREAK_1 32 108#define DEG_1 7 109#define SEP_1 3 110 111#define TYPE_2 2 /* x**15 + x + 1 */ 112#define BREAK_2 64 113#define DEG_2 15 114#define SEP_2 1 115 116#define TYPE_3 3 /* x**31 + x**3 + 1 */ 117#define BREAK_3 128 118#define DEG_3 31 119#define SEP_3 3 120 121#define TYPE_4 4 /* x**63 + x + 1 */ 122#define BREAK_4 256 123#define DEG_4 63 124#define SEP_4 1 125 126/* 127 * Array versions of the above information to make code run faster -- 128 * relies on fact that TYPE_i == i. 129 */ 130#define MAX_TYPES 5 /* max number of types above */ 131 132#define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */ 133 134static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 135static const int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 136 137/* 138 * Initially, everything is set up as if from: 139 * 140 * initstate(1, randtbl, 128); 141 * 142 * Note that this initialization takes advantage of the fact that srandom() 143 * advances the front and rear pointers 10*rand_deg times, and hence the 144 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 145 * element of the state information, which contains info about the current 146 * position of the rear pointer is just 147 * 148 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 149 */ 150 151static uint32_t randtbl[DEG_3 + 1] = { 152 TYPE_3, 153 0x2cf41758, 0x27bb3711, 0x4916d4d1, 0x7b02f59f, 0x9b8e28eb, 0xc0e80269, 154 0x696f5c16, 0x878f1ff5, 0x52d9c07f, 0x916a06cd, 0xb50b3a20, 0x2776970a, 155 0xee4eb2a6, 0xe94640ec, 0xb1d65612, 0x9d1ed968, 0x1043f6b7, 0xa3432a76, 156 0x17eacbb9, 0x3c09e2eb, 0x4f8c2b3, 0x708a1f57, 0xee341814, 0x95d0e4d2, 157 0xb06f216c, 0x8bd2e72e, 0x8f7c38d7, 0xcfc6a8fc, 0x2a59495, 0xa20d2a69, 158 0xe29d12d1 159}; 160 161/* 162 * fptr and rptr are two pointers into the state info, a front and a rear 163 * pointer. These two pointers are always rand_sep places aparts, as they 164 * cycle cyclically through the state information. (Yes, this does mean we 165 * could get away with just one pointer, but the code for random() is more 166 * efficient this way). The pointers are left positioned as they would be 167 * from the call 168 * 169 * initstate(1, randtbl, 128); 170 * 171 * (The position of the rear pointer, rptr, is really 0 (as explained above 172 * in the initialization of randtbl) because the state table pointer is set 173 * to point to randtbl[1] (as explained below). 174 */ 175static uint32_t *fptr = &randtbl[SEP_3 + 1]; 176static uint32_t *rptr = &randtbl[1]; 177 178/* 179 * The following things are the pointer to the state information table, the 180 * type of the current generator, the degree of the current polynomial being 181 * used, and the separation between the two pointers. Note that for efficiency 182 * of random(), we remember the first location of the state information, not 183 * the zeroeth. Hence it is valid to access state[-1], which is used to 184 * store the type of the R.N.G. Also, we remember the last location, since 185 * this is more efficient than indexing every time to find the address of 186 * the last element to see if the front and rear pointers have wrapped. 187 */ 188static uint32_t *state = &randtbl[1]; 189static int rand_type = TYPE_3; 190static int rand_deg = DEG_3; 191static int rand_sep = SEP_3; 192static uint32_t *end_ptr = &randtbl[DEG_3 + 1]; 193 194static inline uint32_t 195good_rand(uint32_t ctx) 196{ 197/* 198 * Compute x = (7^5 * x) mod (2^31 - 1) 199 * wihout overflowing 31 bits: 200 * (2^31 - 1) = 127773 * (7^5) + 2836 201 * From "Random number generators: good ones are hard to find", 202 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 203 * October 1988, p. 1195. 204 */ 205 int32_t hi, lo, x; 206 207 /* Transform to [1, 0x7ffffffe] range. */ 208 x = (ctx % 0x7ffffffe) + 1; 209 hi = x / 127773; 210 lo = x % 127773; 211 x = 16807 * lo - 2836 * hi; 212 if (x < 0) 213 x += 0x7fffffff; 214 /* Transform to [0, 0x7ffffffd] range. */ 215 return (x - 1); 216} 217 218/* 219 * srandom: 220 * 221 * Initialize the random number generator based on the given seed. If the 222 * type is the trivial no-state-information type, just remember the seed. 223 * Otherwise, initializes state[] based on the given "seed" via a linear 224 * congruential generator. Then, the pointers are set to known locations 225 * that are exactly rand_sep places apart. Lastly, it cycles the state 226 * information a given number of times to get rid of any initial dependencies 227 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 228 * for default usage relies on values produced by this routine. 229 */ 230void 231srandom(unsigned int x) 232{ 233 int i, lim; 234 235 state[0] = (uint32_t)x; 236 if (rand_type == TYPE_0) 237 lim = NSHUFF; 238 else { 239 for (i = 1; i < rand_deg; i++) 240 state[i] = good_rand(state[i - 1]); 241 fptr = &state[rand_sep]; 242 rptr = &state[0]; 243 lim = 10 * rand_deg; 244 } 245 for (i = 0; i < lim; i++) 246 (void)random(); 247} 248 249/* 250 * srandomdev: 251 * 252 * Many programs choose the seed value in a totally predictable manner. 253 * This often causes problems. We seed the generator using pseudo-random 254 * data from the kernel. 255 * 256 * Note that this particular seeding procedure can generate states 257 * which are impossible to reproduce by calling srandom() with any 258 * value, since the succeeding terms in the state buffer are no longer 259 * derived from the LC algorithm applied to a fixed seed. 260 */ 261#if 0 262void 263srandomdev(void) 264{ 265 int mib[2]; 266 size_t expected, len; 267 268 if (rand_type == TYPE_0) 269 expected = len = sizeof(state[0]); 270 else 271 expected = len = rand_deg * sizeof(state[0]); 272 273 mib[0] = CTL_KERN; 274 mib[1] = KERN_ARND; 275 if (sysctl(mib, 2, state, &len, NULL, 0) == -1 || len != expected) { 276 /* 277 * The sysctl cannot fail. If it does fail on some FreeBSD 278 * derivative or after some future change, just abort so that 279 * the problem will be found and fixed. abort is not normally 280 * suitable for a library but makes sense here. 281 */ 282 abort(); 283 } 284 285 if (rand_type != TYPE_0) { 286 fptr = &state[rand_sep]; 287 rptr = &state[0]; 288 } 289} 290#endif 291 292/* 293 * initstate: 294 * 295 * Initialize the state information in the given array of n bytes for future 296 * random number generation. Based on the number of bytes we are given, and 297 * the break values for the different R.N.G.'s, we choose the best (largest) 298 * one we can and set things up for it. srandom() is then called to 299 * initialize the state information. 300 * 301 * Note that on return from srandom(), we set state[-1] to be the type 302 * multiplexed with the current value of the rear pointer; this is so 303 * successive calls to initstate() won't lose this information and will be 304 * able to restart with setstate(). 305 * 306 * Note: the first thing we do is save the current state, if any, just like 307 * setstate() so that it doesn't matter when initstate is called. 308 * 309 * Returns a pointer to the old state. 310 * 311 * Note: The Sparc platform requires that arg_state begin on an int 312 * word boundary; otherwise a bus error will occur. Even so, lint will 313 * complain about mis-alignment, but you should disregard these messages. 314 */ 315char * 316initstate(unsigned int seed, char *arg_state, size_t n) 317{ 318 char *ostate = (char *)(&state[-1]); 319 uint32_t *int_arg_state = (uint32_t *)arg_state; 320 321 if (n < BREAK_0) 322 return (NULL); 323 if (rand_type == TYPE_0) 324 state[-1] = rand_type; 325 else 326 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 327 if (n < BREAK_1) { 328 rand_type = TYPE_0; 329 rand_deg = DEG_0; 330 rand_sep = SEP_0; 331 } else if (n < BREAK_2) { 332 rand_type = TYPE_1; 333 rand_deg = DEG_1; 334 rand_sep = SEP_1; 335 } else if (n < BREAK_3) { 336 rand_type = TYPE_2; 337 rand_deg = DEG_2; 338 rand_sep = SEP_2; 339 } else if (n < BREAK_4) { 340 rand_type = TYPE_3; 341 rand_deg = DEG_3; 342 rand_sep = SEP_3; 343 } else { 344 rand_type = TYPE_4; 345 rand_deg = DEG_4; 346 rand_sep = SEP_4; 347 } 348 state = int_arg_state + 1; /* first location */ 349 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 350 srandom(seed); 351 if (rand_type == TYPE_0) 352 int_arg_state[0] = rand_type; 353 else 354 int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 355 return (ostate); 356} 357 358/* 359 * setstate: 360 * 361 * Restore the state from the given state array. 362 * 363 * Note: it is important that we also remember the locations of the pointers 364 * in the current state information, and restore the locations of the pointers 365 * from the old state information. This is done by multiplexing the pointer 366 * location into the zeroeth word of the state information. 367 * 368 * Note that due to the order in which things are done, it is OK to call 369 * setstate() with the same state as the current state. 370 * 371 * Returns a pointer to the old state information. 372 * 373 * Note: The Sparc platform requires that arg_state begin on an int 374 * word boundary; otherwise a bus error will occur. Even so, lint will 375 * complain about mis-alignment, but you should disregard these messages. 376 */ 377char * 378setstate(char *arg_state) 379{ 380 uint32_t *new_state = (uint32_t *)arg_state; 381 uint32_t type = new_state[0] % MAX_TYPES; 382 uint32_t rear = new_state[0] / MAX_TYPES; 383 char *ostate = (char *)(&state[-1]); 384 385 if (type != TYPE_0 && rear >= (uint32_t)degrees[type]) 386 return (NULL); 387 if (rand_type == TYPE_0) 388 state[-1] = rand_type; 389 else 390 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 391 rand_type = type; 392 rand_deg = degrees[type]; 393 rand_sep = seps[type]; 394 state = new_state + 1; 395 if (rand_type != TYPE_0) { 396 rptr = &state[rear]; 397 fptr = &state[(rear + rand_sep) % rand_deg]; 398 } 399 end_ptr = &state[rand_deg]; /* set end_ptr too */ 400 return (ostate); 401} 402 403/* 404 * random: 405 * 406 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 407 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 408 * the same in all the other cases due to all the global variables that have 409 * been set up. The basic operation is to add the number at the rear pointer 410 * into the one at the front pointer. Then both pointers are advanced to 411 * the next location cyclically in the table. The value returned is the sum 412 * generated, reduced to 31 bits by throwing away the "least random" low bit. 413 * 414 * Note: the code takes advantage of the fact that both the front and 415 * rear pointers can't wrap on the same call by not testing the rear 416 * pointer if the front one has wrapped. 417 * 418 * Returns a 31-bit random number. 419 */ 420int 421random(void) 422{ 423 uint32_t i; 424 uint32_t *f, *r; 425 426 if (rand_type == TYPE_0) { 427 i = state[0]; 428 state[0] = i = good_rand(i); 429 } else { 430 /* 431 * Use local variables rather than static variables for speed. 432 */ 433 f = fptr; r = rptr; 434 *f += *r; 435 i = *f >> 1; /* chucking least random bit */ 436 if (++f >= end_ptr) { 437 f = state; 438 ++r; 439 } 440 else if (++r >= end_ptr) { 441 r = state; 442 } 443 444 fptr = f; rptr = r; 445 } 446 return ((long)i); 447} 448