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 #if defined(LIBC_SCCS) && !defined(lint) 33 static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95"; 34 #endif /* LIBC_SCCS and not lint */ 35 #include <sys/cdefs.h> 36 __FBSDID("$FreeBSD$"); 37 38 #include "namespace.h" 39 #include <sys/param.h> 40 #include <sys/sysctl.h> 41 #include <stdint.h> 42 #include <stdlib.h> 43 #include "un-namespace.h" 44 45 /* 46 * random.c: 47 * 48 * An improved random number generation package. In addition to the standard 49 * rand()/srand() like interface, this package also has a special state info 50 * interface. The initstate() routine is called with a seed, an array of 51 * bytes, and a count of how many bytes are being passed in; this array is 52 * then initialized to contain information for random number generation with 53 * that much state information. Good sizes for the amount of state 54 * information are 32, 64, 128, and 256 bytes. The state can be switched by 55 * calling the setstate() routine with the same array as was initiallized 56 * with initstate(). By default, the package runs with 128 bytes of state 57 * information and generates far better random numbers than a linear 58 * congruential generator. If the amount of state information is less than 59 * 32 bytes, a simple linear congruential R.N.G. is used. 60 * 61 * Internally, the state information is treated as an array of uint32_t's; the 62 * zeroeth element of the array is the type of R.N.G. being used (small 63 * integer); the remainder of the array is the state information for the 64 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of 65 * state information, which will allow a degree seven polynomial. (Note: 66 * the zeroeth word of state information also has some other information 67 * stored in it -- see setstate() for details). 68 * 69 * The random number generation technique is a linear feedback shift register 70 * approach, employing trinomials (since there are fewer terms to sum up that 71 * way). In this approach, the least significant bit of all the numbers in 72 * the state table will act as a linear feedback shift register, and will 73 * have period 2^deg - 1 (where deg is the degree of the polynomial being 74 * used, assuming that the polynomial is irreducible and primitive). The 75 * higher order bits will have longer periods, since their values are also 76 * influenced by pseudo-random carries out of the lower bits. The total 77 * period of the generator is approximately deg*(2**deg - 1); thus doubling 78 * the amount of state information has a vast influence on the period of the 79 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 80 * large deg, when the period of the shift is the dominant factor. 81 * With deg equal to seven, the period is actually much longer than the 82 * 7*(2**7 - 1) predicted by this formula. 83 * 84 * Modified 28 December 1994 by Jacob S. Rosenberg. 85 * The following changes have been made: 86 * All references to the type u_int have been changed to unsigned long. 87 * All references to type int have been changed to type long. Other 88 * cleanups have been made as well. A warning for both initstate and 89 * setstate has been inserted to the effect that on Sparc platforms 90 * the 'arg_state' variable must be forced to begin on word boundaries. 91 * This can be easily done by casting a long integer array to char *. 92 * The overall logic has been left STRICTLY alone. This software was 93 * tested on both a VAX and Sun SpacsStation with exactly the same 94 * results. The new version and the original give IDENTICAL results. 95 * The new version is somewhat faster than the original. As the 96 * documentation says: "By default, the package runs with 128 bytes of 97 * state information and generates far better random numbers than a linear 98 * congruential generator. If the amount of state information is less than 99 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 100 * 128 bytes, this new version runs about 19 percent faster and for a 16 101 * byte buffer it is about 5 percent faster. 102 */ 103 104 /* 105 * For each of the currently supported random number generators, we have a 106 * break value on the amount of state information (you need at least this 107 * many bytes of state info to support this random number generator), a degree 108 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 109 * the separation between the two lower order coefficients of the trinomial. 110 */ 111 #define TYPE_0 0 /* linear congruential */ 112 #define BREAK_0 8 113 #define DEG_0 0 114 #define SEP_0 0 115 116 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 117 #define BREAK_1 32 118 #define DEG_1 7 119 #define SEP_1 3 120 121 #define TYPE_2 2 /* x**15 + x + 1 */ 122 #define BREAK_2 64 123 #define DEG_2 15 124 #define SEP_2 1 125 126 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 127 #define BREAK_3 128 128 #define DEG_3 31 129 #define SEP_3 3 130 131 #define TYPE_4 4 /* x**63 + x + 1 */ 132 #define BREAK_4 256 133 #define DEG_4 63 134 #define SEP_4 1 135 136 /* 137 * Array versions of the above information to make code run faster -- 138 * relies on fact that TYPE_i == i. 139 */ 140 #define MAX_TYPES 5 /* max number of types above */ 141 142 #define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */ 143 144 static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 145 static const int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 146 147 /* 148 * Initially, everything is set up as if from: 149 * 150 * initstate(1, randtbl, 128); 151 * 152 * Note that this initialization takes advantage of the fact that srandom() 153 * advances the front and rear pointers 10*rand_deg times, and hence the 154 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 155 * element of the state information, which contains info about the current 156 * position of the rear pointer is just 157 * 158 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 159 */ 160 161 static uint32_t randtbl[DEG_3 + 1] = { 162 TYPE_3, 163 0x2cf41758, 0x27bb3711, 0x4916d4d1, 0x7b02f59f, 0x9b8e28eb, 0xc0e80269, 164 0x696f5c16, 0x878f1ff5, 0x52d9c07f, 0x916a06cd, 0xb50b3a20, 0x2776970a, 165 0xee4eb2a6, 0xe94640ec, 0xb1d65612, 0x9d1ed968, 0x1043f6b7, 0xa3432a76, 166 0x17eacbb9, 0x3c09e2eb, 0x4f8c2b3, 0x708a1f57, 0xee341814, 0x95d0e4d2, 167 0xb06f216c, 0x8bd2e72e, 0x8f7c38d7, 0xcfc6a8fc, 0x2a59495, 0xa20d2a69, 168 0xe29d12d1 169 }; 170 171 /* 172 * fptr and rptr are two pointers into the state info, a front and a rear 173 * pointer. These two pointers are always rand_sep places aparts, as they 174 * cycle cyclically through the state information. (Yes, this does mean we 175 * could get away with just one pointer, but the code for random() is more 176 * efficient this way). The pointers are left positioned as they would be 177 * from the call 178 * 179 * initstate(1, randtbl, 128); 180 * 181 * (The position of the rear pointer, rptr, is really 0 (as explained above 182 * in the initialization of randtbl) because the state table pointer is set 183 * to point to randtbl[1] (as explained below). 184 */ 185 static uint32_t *fptr = &randtbl[SEP_3 + 1]; 186 static uint32_t *rptr = &randtbl[1]; 187 188 /* 189 * The following things are the pointer to the state information table, the 190 * type of the current generator, the degree of the current polynomial being 191 * used, and the separation between the two pointers. Note that for efficiency 192 * of random(), we remember the first location of the state information, not 193 * the zeroeth. Hence it is valid to access state[-1], which is used to 194 * store the type of the R.N.G. Also, we remember the last location, since 195 * this is more efficient than indexing every time to find the address of 196 * the last element to see if the front and rear pointers have wrapped. 197 */ 198 static uint32_t *state = &randtbl[1]; 199 static int rand_type = TYPE_3; 200 static int rand_deg = DEG_3; 201 static int rand_sep = SEP_3; 202 static uint32_t *end_ptr = &randtbl[DEG_3 + 1]; 203 204 static inline uint32_t 205 good_rand(uint32_t ctx) 206 { 207 /* 208 * Compute x = (7^5 * x) mod (2^31 - 1) 209 * wihout overflowing 31 bits: 210 * (2^31 - 1) = 127773 * (7^5) + 2836 211 * From "Random number generators: good ones are hard to find", 212 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 213 * October 1988, p. 1195. 214 */ 215 int32_t hi, lo, x; 216 217 /* Transform to [1, 0x7ffffffe] range. */ 218 x = (ctx % 0x7ffffffe) + 1; 219 hi = x / 127773; 220 lo = x % 127773; 221 x = 16807 * lo - 2836 * hi; 222 if (x < 0) 223 x += 0x7fffffff; 224 /* Transform to [0, 0x7ffffffd] range. */ 225 return (x - 1); 226 } 227 228 /* 229 * srandom: 230 * 231 * Initialize the random number generator based on the given seed. If the 232 * type is the trivial no-state-information type, just remember the seed. 233 * Otherwise, initializes state[] based on the given "seed" via a linear 234 * congruential generator. Then, the pointers are set to known locations 235 * that are exactly rand_sep places apart. Lastly, it cycles the state 236 * information a given number of times to get rid of any initial dependencies 237 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 238 * for default usage relies on values produced by this routine. 239 */ 240 void 241 srandom(unsigned int x) 242 { 243 int i, lim; 244 245 state[0] = (uint32_t)x; 246 if (rand_type == TYPE_0) 247 lim = NSHUFF; 248 else { 249 for (i = 1; i < rand_deg; i++) 250 state[i] = good_rand(state[i - 1]); 251 fptr = &state[rand_sep]; 252 rptr = &state[0]; 253 lim = 10 * rand_deg; 254 } 255 for (i = 0; i < lim; i++) 256 (void)random(); 257 } 258 259 /* 260 * srandomdev: 261 * 262 * Many programs choose the seed value in a totally predictable manner. 263 * This often causes problems. We seed the generator using pseudo-random 264 * data from the kernel. 265 * 266 * Note that this particular seeding procedure can generate states 267 * which are impossible to reproduce by calling srandom() with any 268 * value, since the succeeding terms in the state buffer are no longer 269 * derived from the LC algorithm applied to a fixed seed. 270 */ 271 void 272 srandomdev(void) 273 { 274 int mib[2]; 275 size_t expected, len; 276 277 if (rand_type == TYPE_0) 278 expected = len = sizeof(state[0]); 279 else 280 expected = len = rand_deg * sizeof(state[0]); 281 282 mib[0] = CTL_KERN; 283 mib[1] = KERN_ARND; 284 if (sysctl(mib, 2, state, &len, NULL, 0) == -1 || len != expected) { 285 /* 286 * The sysctl cannot fail. If it does fail on some FreeBSD 287 * derivative or after some future change, just abort so that 288 * the problem will be found and fixed. abort is not normally 289 * suitable for a library but makes sense here. 290 */ 291 abort(); 292 } 293 294 if (rand_type != TYPE_0) { 295 fptr = &state[rand_sep]; 296 rptr = &state[0]; 297 } 298 } 299 300 /* 301 * initstate: 302 * 303 * Initialize the state information in the given array of n bytes for future 304 * random number generation. Based on the number of bytes we are given, and 305 * the break values for the different R.N.G.'s, we choose the best (largest) 306 * one we can and set things up for it. srandom() is then called to 307 * initialize the state information. 308 * 309 * Note that on return from srandom(), we set state[-1] to be the type 310 * multiplexed with the current value of the rear pointer; this is so 311 * successive calls to initstate() won't lose this information and will be 312 * able to restart with setstate(). 313 * 314 * Note: the first thing we do is save the current state, if any, just like 315 * setstate() so that it doesn't matter when initstate is called. 316 * 317 * Returns a pointer to the old state. 318 * 319 * Note: The Sparc platform requires that arg_state begin on an int 320 * word boundary; otherwise a bus error will occur. Even so, lint will 321 * complain about mis-alignment, but you should disregard these messages. 322 */ 323 char * 324 initstate(unsigned int seed, char *arg_state, size_t n) 325 { 326 char *ostate = (char *)(&state[-1]); 327 uint32_t *int_arg_state = (uint32_t *)arg_state; 328 329 if (n < BREAK_0) 330 return (NULL); 331 if (rand_type == TYPE_0) 332 state[-1] = rand_type; 333 else 334 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 335 if (n < BREAK_1) { 336 rand_type = TYPE_0; 337 rand_deg = DEG_0; 338 rand_sep = SEP_0; 339 } else if (n < BREAK_2) { 340 rand_type = TYPE_1; 341 rand_deg = DEG_1; 342 rand_sep = SEP_1; 343 } else if (n < BREAK_3) { 344 rand_type = TYPE_2; 345 rand_deg = DEG_2; 346 rand_sep = SEP_2; 347 } else if (n < BREAK_4) { 348 rand_type = TYPE_3; 349 rand_deg = DEG_3; 350 rand_sep = SEP_3; 351 } else { 352 rand_type = TYPE_4; 353 rand_deg = DEG_4; 354 rand_sep = SEP_4; 355 } 356 state = int_arg_state + 1; /* first location */ 357 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 358 srandom(seed); 359 if (rand_type == TYPE_0) 360 int_arg_state[0] = rand_type; 361 else 362 int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 363 return (ostate); 364 } 365 366 /* 367 * setstate: 368 * 369 * Restore the state from the given state array. 370 * 371 * Note: it is important that we also remember the locations of the pointers 372 * in the current state information, and restore the locations of the pointers 373 * from the old state information. This is done by multiplexing the pointer 374 * location into the zeroeth word of the state information. 375 * 376 * Note that due to the order in which things are done, it is OK to call 377 * setstate() with the same state as the current state. 378 * 379 * Returns a pointer to the old state information. 380 * 381 * Note: The Sparc platform requires that arg_state begin on an int 382 * word boundary; otherwise a bus error will occur. Even so, lint will 383 * complain about mis-alignment, but you should disregard these messages. 384 */ 385 char * 386 setstate(char *arg_state) 387 { 388 uint32_t *new_state = (uint32_t *)arg_state; 389 uint32_t type = new_state[0] % MAX_TYPES; 390 uint32_t rear = new_state[0] / MAX_TYPES; 391 char *ostate = (char *)(&state[-1]); 392 393 if (type != TYPE_0 && rear >= degrees[type]) 394 return (NULL); 395 if (rand_type == TYPE_0) 396 state[-1] = rand_type; 397 else 398 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 399 rand_type = type; 400 rand_deg = degrees[type]; 401 rand_sep = seps[type]; 402 state = new_state + 1; 403 if (rand_type != TYPE_0) { 404 rptr = &state[rear]; 405 fptr = &state[(rear + rand_sep) % rand_deg]; 406 } 407 end_ptr = &state[rand_deg]; /* set end_ptr too */ 408 return (ostate); 409 } 410 411 /* 412 * random: 413 * 414 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 415 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 416 * the same in all the other cases due to all the global variables that have 417 * been set up. The basic operation is to add the number at the rear pointer 418 * into the one at the front pointer. Then both pointers are advanced to 419 * the next location cyclically in the table. The value returned is the sum 420 * generated, reduced to 31 bits by throwing away the "least random" low bit. 421 * 422 * Note: the code takes advantage of the fact that both the front and 423 * rear pointers can't wrap on the same call by not testing the rear 424 * pointer if the front one has wrapped. 425 * 426 * Returns a 31-bit random number. 427 */ 428 long 429 random(void) 430 { 431 uint32_t i; 432 uint32_t *f, *r; 433 434 if (rand_type == TYPE_0) { 435 i = state[0]; 436 state[0] = i = good_rand(i); 437 } else { 438 /* 439 * Use local variables rather than static variables for speed. 440 */ 441 f = fptr; r = rptr; 442 *f += *r; 443 i = *f >> 1; /* chucking least random bit */ 444 if (++f >= end_ptr) { 445 f = state; 446 ++r; 447 } 448 else if (++r >= end_ptr) { 449 r = state; 450 } 451 452 fptr = f; rptr = r; 453 } 454 return ((long)i); 455 } 456