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 <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 */ 141 142 static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 143 static 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 */ 158 159 static 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 */ 183 static uint32_t *fptr = &randtbl[SEP_3 + 1]; 184 static 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 */ 196 static uint32_t *state = &randtbl[1]; 197 static int rand_type = TYPE_3; 198 static int rand_deg = DEG_3; 199 static int rand_sep = SEP_3; 200 static uint32_t *end_ptr = &randtbl[DEG_3 + 1]; 201 202 static inline uint32_t 203 good_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 */ 238 void 239 srandom(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 */ 269 void 270 srandomdev(void) 271 { 272 int mib[2]; 273 size_t expected, len; 274 275 if (rand_type == TYPE_0) 276 expected = len = sizeof(state[0]); 277 else 278 expected = len = rand_deg * sizeof(state[0]); 279 280 mib[0] = CTL_KERN; 281 mib[1] = KERN_ARND; 282 if (sysctl(mib, 2, state, &len, NULL, 0) == -1 || len != expected) 283 abort(); 284 285 if (rand_type != TYPE_0) { 286 fptr = &state[rand_sep]; 287 rptr = &state[0]; 288 } 289 } 290 291 /* 292 * initstate: 293 * 294 * Initialize the state information in the given array of n bytes for future 295 * random number generation. Based on the number of bytes we are given, and 296 * the break values for the different R.N.G.'s, we choose the best (largest) 297 * one we can and set things up for it. srandom() is then called to 298 * initialize the state information. 299 * 300 * Note that on return from srandom(), we set state[-1] to be the type 301 * multiplexed with the current value of the rear pointer; this is so 302 * successive calls to initstate() won't lose this information and will be 303 * able to restart with setstate(). 304 * 305 * Note: the first thing we do is save the current state, if any, just like 306 * setstate() so that it doesn't matter when initstate is called. 307 * 308 * Returns a pointer to the old state. 309 * 310 * Note: The Sparc platform requires that arg_state begin on an int 311 * word boundary; otherwise a bus error will occur. Even so, lint will 312 * complain about mis-alignment, but you should disregard these messages. 313 */ 314 char * 315 initstate(unsigned int seed, char *arg_state, size_t n) 316 { 317 char *ostate = (char *)(&state[-1]); 318 uint32_t *int_arg_state = (uint32_t *)arg_state; 319 320 if (n < BREAK_0) 321 return (NULL); 322 if (rand_type == TYPE_0) 323 state[-1] = rand_type; 324 else 325 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 326 if (n < BREAK_1) { 327 rand_type = TYPE_0; 328 rand_deg = DEG_0; 329 rand_sep = SEP_0; 330 } else if (n < BREAK_2) { 331 rand_type = TYPE_1; 332 rand_deg = DEG_1; 333 rand_sep = SEP_1; 334 } else if (n < BREAK_3) { 335 rand_type = TYPE_2; 336 rand_deg = DEG_2; 337 rand_sep = SEP_2; 338 } else if (n < BREAK_4) { 339 rand_type = TYPE_3; 340 rand_deg = DEG_3; 341 rand_sep = SEP_3; 342 } else { 343 rand_type = TYPE_4; 344 rand_deg = DEG_4; 345 rand_sep = SEP_4; 346 } 347 state = int_arg_state + 1; /* first location */ 348 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 349 srandom(seed); 350 if (rand_type == TYPE_0) 351 int_arg_state[0] = rand_type; 352 else 353 int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 354 return (ostate); 355 } 356 357 /* 358 * setstate: 359 * 360 * Restore the state from the given state array. 361 * 362 * Note: it is important that we also remember the locations of the pointers 363 * in the current state information, and restore the locations of the pointers 364 * from the old state information. This is done by multiplexing the pointer 365 * location into the zeroeth word of the state information. 366 * 367 * Note that due to the order in which things are done, it is OK to call 368 * setstate() with the same state as the current state. 369 * 370 * Returns a pointer to the old state information. 371 * 372 * Note: The Sparc platform requires that arg_state begin on an int 373 * word boundary; otherwise a bus error will occur. Even so, lint will 374 * complain about mis-alignment, but you should disregard these messages. 375 */ 376 char * 377 setstate(char *arg_state) 378 { 379 uint32_t *new_state = (uint32_t *)arg_state; 380 uint32_t type = new_state[0] % MAX_TYPES; 381 uint32_t rear = new_state[0] / MAX_TYPES; 382 char *ostate = (char *)(&state[-1]); 383 384 if (type != TYPE_0 && rear >= degrees[type]) 385 return (NULL); 386 if (rand_type == TYPE_0) 387 state[-1] = rand_type; 388 else 389 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 390 rand_type = type; 391 rand_deg = degrees[type]; 392 rand_sep = seps[type]; 393 state = new_state + 1; 394 if (rand_type != TYPE_0) { 395 rptr = &state[rear]; 396 fptr = &state[(rear + rand_sep) % rand_deg]; 397 } 398 end_ptr = &state[rand_deg]; /* set end_ptr too */ 399 return (ostate); 400 } 401 402 /* 403 * random: 404 * 405 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 406 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 407 * the same in all the other cases due to all the global variables that have 408 * been set up. The basic operation is to add the number at the rear pointer 409 * into the one at the front pointer. Then both pointers are advanced to 410 * the next location cyclically in the table. The value returned is the sum 411 * generated, reduced to 31 bits by throwing away the "least random" low bit. 412 * 413 * Note: the code takes advantage of the fact that both the front and 414 * rear pointers can't wrap on the same call by not testing the rear 415 * pointer if the front one has wrapped. 416 * 417 * Returns a 31-bit random number. 418 */ 419 long 420 random(void) 421 { 422 uint32_t i; 423 uint32_t *f, *r; 424 425 if (rand_type == TYPE_0) { 426 i = state[0]; 427 state[0] = i = good_rand(i); 428 } else { 429 /* 430 * Use local variables rather than static variables for speed. 431 */ 432 f = fptr; r = rptr; 433 *f += *r; 434 i = *f >> 1; /* chucking least random bit */ 435 if (++f >= end_ptr) { 436 f = state; 437 ++r; 438 } 439 else if (++r >= end_ptr) { 440 r = state; 441 } 442 443 fptr = f; rptr = r; 444 } 445 return ((long)i); 446 } 447