1 /* 2 * Copyright (c) 1983 Regents of the University of California. 3 * 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 *rcsid = "$OpenBSD: random.c,v 1.12 2003/06/02 20:18:38 millert Exp $"; 32 #endif /* LIBC_SCCS and not lint */ 33 34 #include <sys/param.h> 35 #include <sys/sysctl.h> 36 #include <sys/time.h> 37 #include <fcntl.h> 38 #include <stdio.h> 39 #include <stdlib.h> 40 #include <unistd.h> 41 42 /* 43 * random.c: 44 * 45 * An improved random number generation package. In addition to the standard 46 * rand()/srand() like interface, this package also has a special state info 47 * interface. The initstate() routine is called with a seed, an array of 48 * bytes, and a count of how many bytes are being passed in; this array is 49 * then initialized to contain information for random number generation with 50 * that much state information. Good sizes for the amount of state 51 * information are 32, 64, 128, and 256 bytes. The state can be switched by 52 * calling the setstate() routine with the same array as was initiallized 53 * with initstate(). By default, the package runs with 128 bytes of state 54 * information and generates far better random numbers than a linear 55 * congruential generator. If the amount of state information is less than 56 * 32 bytes, a simple linear congruential R.N.G. is used. 57 * 58 * Internally, the state information is treated as an array of int32_t; the 59 * zeroeth element of the array is the type of R.N.G. being used (small 60 * integer); the remainder of the array is the state information for the 61 * R.N.G. Thus, 32 bytes of state information will give 7 int32_ts worth of 62 * state information, which will allow a degree seven polynomial. (Note: 63 * the zeroeth word of state information also has some other information 64 * stored in it -- see setstate() for details). 65 * 66 * The random number generation technique is a linear feedback shift register 67 * approach, employing trinomials (since there are fewer terms to sum up that 68 * way). In this approach, the least significant bit of all the numbers in 69 * the state table will act as a linear feedback shift register, and will 70 * have period 2^deg - 1 (where deg is the degree of the polynomial being 71 * used, assuming that the polynomial is irreducible and primitive). The 72 * higher order bits will have longer periods, since their values are also 73 * influenced by pseudo-random carries out of the lower bits. The total 74 * period of the generator is approximately deg*(2**deg - 1); thus doubling 75 * the amount of state information has a vast influence on the period of the 76 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 77 * large deg, when the period of the shift register is the dominant factor. 78 * With deg equal to seven, the period is actually much longer than the 79 * 7*(2**7 - 1) predicted by this formula. 80 */ 81 82 /* 83 * For each of the currently supported random number generators, we have a 84 * break value on the amount of state information (you need at least this 85 * many bytes of state info to support this random number generator), a degree 86 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 87 * the separation between the two lower order coefficients of the trinomial. 88 */ 89 #define TYPE_0 0 /* linear congruential */ 90 #define BREAK_0 8 91 #define DEG_0 0 92 #define SEP_0 0 93 94 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 95 #define BREAK_1 32 96 #define DEG_1 7 97 #define SEP_1 3 98 99 #define TYPE_2 2 /* x**15 + x + 1 */ 100 #define BREAK_2 64 101 #define DEG_2 15 102 #define SEP_2 1 103 104 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 105 #define BREAK_3 128 106 #define DEG_3 31 107 #define SEP_3 3 108 109 #define TYPE_4 4 /* x**63 + x + 1 */ 110 #define BREAK_4 256 111 #define DEG_4 63 112 #define SEP_4 1 113 114 /* 115 * Array versions of the above information to make code run faster -- 116 * relies on fact that TYPE_i == i. 117 */ 118 #define MAX_TYPES 5 /* max number of types above */ 119 120 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 121 static int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 122 123 /* 124 * Initially, everything is set up as if from: 125 * 126 * initstate(1, &randtbl, 128); 127 * 128 * Note that this initialization takes advantage of the fact that srandom() 129 * advances the front and rear pointers 10*rand_deg times, and hence the 130 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 131 * element of the state information, which contains info about the current 132 * position of the rear pointer is just 133 * 134 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 135 */ 136 137 static int32_t randtbl[DEG_3 + 1] = { 138 TYPE_3, 139 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 140 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 141 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 142 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 143 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 144 0xf3bec5da, 145 }; 146 147 /* 148 * fptr and rptr are two pointers into the state info, a front and a rear 149 * pointer. These two pointers are always rand_sep places aparts, as they 150 * cycle cyclically through the state information. (Yes, this does mean we 151 * could get away with just one pointer, but the code for random() is more 152 * efficient this way). The pointers are left positioned as they would be 153 * from the call 154 * 155 * initstate(1, randtbl, 128); 156 * 157 * (The position of the rear pointer, rptr, is really 0 (as explained above 158 * in the initialization of randtbl) because the state table pointer is set 159 * to point to randtbl[1] (as explained below). 160 */ 161 static int32_t *fptr = &randtbl[SEP_3 + 1]; 162 static int32_t *rptr = &randtbl[1]; 163 164 /* 165 * The following things are the pointer to the state information table, the 166 * type of the current generator, the degree of the current polynomial being 167 * used, and the separation between the two pointers. Note that for efficiency 168 * of random(), we remember the first location of the state information, not 169 * the zeroeth. Hence it is valid to access state[-1], which is used to 170 * store the type of the R.N.G. Also, we remember the last location, since 171 * this is more efficient than indexing every time to find the address of 172 * the last element to see if the front and rear pointers have wrapped. 173 */ 174 static int32_t *state = &randtbl[1]; 175 static int32_t *end_ptr = &randtbl[DEG_3 + 1]; 176 static int rand_type = TYPE_3; 177 static int rand_deg = DEG_3; 178 static int rand_sep = SEP_3; 179 180 /* 181 * srandom: 182 * 183 * Initialize the random number generator based on the given seed. If the 184 * type is the trivial no-state-information type, just remember the seed. 185 * Otherwise, initializes state[] based on the given "seed" via a linear 186 * congruential generator. Then, the pointers are set to known locations 187 * that are exactly rand_sep places apart. Lastly, it cycles the state 188 * information a given number of times to get rid of any initial dependencies 189 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 190 * for default usage relies on values produced by this routine. 191 */ 192 void 193 srandom(x) 194 unsigned int x; 195 { 196 int i; 197 int32_t test; 198 div_t val; 199 200 if (rand_type == TYPE_0) 201 state[0] = x; 202 else { 203 state[0] = x; 204 for (i = 1; i < rand_deg; i++) { 205 /* 206 * Implement the following, without overflowing 31 bits: 207 * 208 * state[i] = (16807 * state[i - 1]) % 2147483647; 209 * 210 * 2^31-1 (prime) = 2147483647 = 127773*16807+2836 211 */ 212 val = div(state[i-1], 127773); 213 test = 16807 * val.rem - 2836 * val.quot; 214 state[i] = test + (test < 0 ? 2147483647 : 0); 215 } 216 fptr = &state[rand_sep]; 217 rptr = &state[0]; 218 for (i = 0; i < 10 * rand_deg; i++) 219 (void)random(); 220 } 221 } 222 223 /* 224 * srandomdev: 225 * 226 * Many programs choose the seed value in a totally predictable manner. 227 * This often causes problems. We seed the generator using the much more 228 * secure arandom(4) interface. Note that this particular seeding 229 * procedure can generate states which are impossible to reproduce by 230 * calling srandom() with any value, since the succeeding terms in the 231 * state buffer are no longer derived from the LC algorithm applied to 232 * a fixed seed. 233 */ 234 void 235 srandomdev() 236 { 237 int fd, i, mib[2], n; 238 size_t len; 239 240 if (rand_type == TYPE_0) 241 len = sizeof(state[0]); 242 else 243 len = rand_deg * sizeof(state[0]); 244 245 /* 246 * To get seed data, first try reading from /dev/arandom. 247 * If that fails, try the KERN_ARND sysctl() (one int at a time). 248 * As a last resort, call srandom(). 249 */ 250 if ((fd = open("/dev/arandom", O_RDONLY, 0)) != -1 && 251 read(fd, (void *) state, len) == (ssize_t) len) { 252 close(fd); 253 } else { 254 if (fd != -1) 255 close(fd); 256 mib[0] = CTL_KERN; 257 mib[1] = KERN_ARND; 258 n = len / sizeof(int); 259 len = sizeof(int); 260 for (i = 0; i < n; i++) { 261 if (sysctl(mib, 2, (char *)((int *)state + i), &len, 262 NULL, 0) == -1) 263 break; 264 } 265 if (i != n) { 266 struct timeval tv; 267 u_int junk; 268 269 /* XXX - this could be better */ 270 gettimeofday(&tv, NULL); 271 srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk); 272 return; 273 } 274 } 275 276 if (rand_type != TYPE_0) { 277 fptr = &state[rand_sep]; 278 rptr = &state[0]; 279 } 280 } 281 282 /* 283 * initstate: 284 * 285 * Initialize the state information in the given array of n bytes for future 286 * random number generation. Based on the number of bytes we are given, and 287 * the break values for the different R.N.G.'s, we choose the best (largest) 288 * one we can and set things up for it. srandom() is then called to 289 * initialize the state information. 290 * 291 * Note that on return from srandom(), we set state[-1] to be the type 292 * multiplexed with the current value of the rear pointer; this is so 293 * successive calls to initstate() won't lose this information and will be 294 * able to restart with setstate(). 295 * 296 * Note: the first thing we do is save the current state, if any, just like 297 * setstate() so that it doesn't matter when initstate is called. 298 * 299 * Returns a pointer to the old state. 300 */ 301 char * 302 initstate(seed, arg_state, n) 303 u_int seed; /* seed for R.N.G. */ 304 char *arg_state; /* pointer to state array */ 305 size_t n; /* # bytes of state info */ 306 { 307 char *ostate = (char *)(&state[-1]); 308 309 if (rand_type == TYPE_0) 310 state[-1] = rand_type; 311 else 312 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 313 if (n < BREAK_0) 314 return(NULL); 315 if (n < BREAK_1) { 316 rand_type = TYPE_0; 317 rand_deg = DEG_0; 318 rand_sep = SEP_0; 319 } else if (n < BREAK_2) { 320 rand_type = TYPE_1; 321 rand_deg = DEG_1; 322 rand_sep = SEP_1; 323 } else if (n < BREAK_3) { 324 rand_type = TYPE_2; 325 rand_deg = DEG_2; 326 rand_sep = SEP_2; 327 } else if (n < BREAK_4) { 328 rand_type = TYPE_3; 329 rand_deg = DEG_3; 330 rand_sep = SEP_3; 331 } else { 332 rand_type = TYPE_4; 333 rand_deg = DEG_4; 334 rand_sep = SEP_4; 335 } 336 state = &(((int32_t *)arg_state)[1]); /* first location */ 337 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 338 srandom(seed); 339 if (rand_type == TYPE_0) 340 state[-1] = rand_type; 341 else 342 state[-1] = MAX_TYPES*(rptr - state) + rand_type; 343 return(ostate); 344 } 345 346 /* 347 * setstate: 348 * 349 * Restore the state from the given state array. 350 * 351 * Note: it is important that we also remember the locations of the pointers 352 * in the current state information, and restore the locations of the pointers 353 * from the old state information. This is done by multiplexing the pointer 354 * location into the zeroeth word of the state information. 355 * 356 * Note that due to the order in which things are done, it is OK to call 357 * setstate() with the same state as the current state. 358 * 359 * Returns a pointer to the old state information. 360 */ 361 char * 362 setstate(arg_state) 363 const char *arg_state; 364 { 365 int32_t *new_state = (int32_t *)arg_state; 366 int32_t type = new_state[0] % MAX_TYPES; 367 int32_t rear = new_state[0] / MAX_TYPES; 368 char *ostate = (char *)(&state[-1]); 369 370 if (rand_type == TYPE_0) 371 state[-1] = rand_type; 372 else 373 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 374 switch(type) { 375 case TYPE_0: 376 case TYPE_1: 377 case TYPE_2: 378 case TYPE_3: 379 case TYPE_4: 380 rand_type = type; 381 rand_deg = degrees[type]; 382 rand_sep = seps[type]; 383 break; 384 default: 385 return(NULL); 386 } 387 state = &new_state[1]; 388 if (rand_type != TYPE_0) { 389 rptr = &state[rear]; 390 fptr = &state[(rear + rand_sep) % rand_deg]; 391 } 392 end_ptr = &state[rand_deg]; /* set end_ptr too */ 393 return(ostate); 394 } 395 396 /* 397 * random: 398 * 399 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 400 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 401 * the same in all the other cases due to all the global variables that have 402 * been set up. The basic operation is to add the number at the rear pointer 403 * into the one at the front pointer. Then both pointers are advanced to 404 * the next location cyclically in the table. The value returned is the sum 405 * generated, reduced to 31 bits by throwing away the "least random" low bit. 406 * 407 * Note: the code takes advantage of the fact that both the front and 408 * rear pointers can't wrap on the same call by not testing the rear 409 * pointer if the front one has wrapped. 410 * 411 * Returns a 31-bit random number. 412 */ 413 long 414 random() 415 { 416 int32_t i; 417 418 if (rand_type == TYPE_0) 419 i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff; 420 else { 421 *fptr += *rptr; 422 i = (*fptr >> 1) & 0x7fffffff; /* chucking least random bit */ 423 if (++fptr >= end_ptr) { 424 fptr = state; 425 ++rptr; 426 } else if (++rptr >= end_ptr) 427 rptr = state; 428 } 429 return((long)i); 430 } 431