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. All advertising materials mentioning features or use of this software 14 * must display the following acknowledgement: 15 * This product includes software developed by the University of 16 * California, Berkeley and its contributors. 17 * 4. Neither the name of the University nor the names of its contributors 18 * may be used to endorse or promote products derived from this software 19 * without specific prior written permission. 20 * 21 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 22 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 23 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 24 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 25 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 26 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 27 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 28 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 29 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 30 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 31 * SUCH DAMAGE. 32 */ 33 34 #if defined(LIBC_SCCS) && !defined(lint) 35 static char *rcsid = "$OpenBSD: random.c,v 1.8 2000/04/04 13:38:24 millert Exp $"; 36 #endif /* LIBC_SCCS and not lint */ 37 38 #include <sys/types.h> 39 #include <sys/time.h> 40 #include <fcntl.h> 41 #include <stdio.h> 42 #include <stdlib.h> 43 #include <unistd.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 longs; 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 longs 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 register 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 85 /* 86 * For each of the currently supported random number generators, we have a 87 * break value on the amount of state information (you need at least this 88 * many bytes of state info to support this random number generator), a degree 89 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 90 * the separation between the two lower order coefficients of the trinomial. 91 */ 92 #define TYPE_0 0 /* linear congruential */ 93 #define BREAK_0 8 94 #define DEG_0 0 95 #define SEP_0 0 96 97 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 98 #define BREAK_1 32 99 #define DEG_1 7 100 #define SEP_1 3 101 102 #define TYPE_2 2 /* x**15 + x + 1 */ 103 #define BREAK_2 64 104 #define DEG_2 15 105 #define SEP_2 1 106 107 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 108 #define BREAK_3 128 109 #define DEG_3 31 110 #define SEP_3 3 111 112 #define TYPE_4 4 /* x**63 + x + 1 */ 113 #define BREAK_4 256 114 #define DEG_4 63 115 #define SEP_4 1 116 117 /* 118 * Array versions of the above information to make code run faster -- 119 * relies on fact that TYPE_i == i. 120 */ 121 #define MAX_TYPES 5 /* max number of types above */ 122 123 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 124 static int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 125 126 /* 127 * Initially, everything is set up as if from: 128 * 129 * initstate(1, &randtbl, 128); 130 * 131 * Note that this initialization takes advantage of the fact that srandom() 132 * advances the front and rear pointers 10*rand_deg times, and hence the 133 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 134 * element of the state information, which contains info about the current 135 * position of the rear pointer is just 136 * 137 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 138 */ 139 140 static long randtbl[DEG_3 + 1] = { 141 TYPE_3, 142 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 143 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 144 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 145 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 146 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 147 0xf3bec5da, 148 }; 149 150 /* 151 * fptr and rptr are two pointers into the state info, a front and a rear 152 * pointer. These two pointers are always rand_sep places aparts, as they 153 * cycle cyclically through the state information. (Yes, this does mean we 154 * could get away with just one pointer, but the code for random() is more 155 * efficient this way). The pointers are left positioned as they would be 156 * from the call 157 * 158 * initstate(1, randtbl, 128); 159 * 160 * (The position of the rear pointer, rptr, is really 0 (as explained above 161 * in the initialization of randtbl) because the state table pointer is set 162 * to point to randtbl[1] (as explained below). 163 */ 164 static long *fptr = &randtbl[SEP_3 + 1]; 165 static long *rptr = &randtbl[1]; 166 167 /* 168 * The following things are the pointer to the state information table, the 169 * type of the current generator, the degree of the current polynomial being 170 * used, and the separation between the two pointers. Note that for efficiency 171 * of random(), we remember the first location of the state information, not 172 * the zeroeth. Hence it is valid to access state[-1], which is used to 173 * store the type of the R.N.G. Also, we remember the last location, since 174 * this is more efficient than indexing every time to find the address of 175 * the last element to see if the front and rear pointers have wrapped. 176 */ 177 static long *state = &randtbl[1]; 178 static int rand_type = TYPE_3; 179 static int rand_deg = DEG_3; 180 static int rand_sep = SEP_3; 181 static long *end_ptr = &randtbl[DEG_3 + 1]; 182 183 /* 184 * srandom: 185 * 186 * Initialize the random number generator based on the given seed. If the 187 * type is the trivial no-state-information type, just remember the seed. 188 * Otherwise, initializes state[] based on the given "seed" via a linear 189 * congruential generator. Then, the pointers are set to known locations 190 * that are exactly rand_sep places apart. Lastly, it cycles the state 191 * information a given number of times to get rid of any initial dependencies 192 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 193 * for default usage relies on values produced by this routine. 194 */ 195 void 196 srandom(x) 197 u_int x; 198 { 199 register long int test; 200 register int i; 201 ldiv_t val; 202 203 if (rand_type == TYPE_0) 204 state[0] = x; 205 else { 206 state[0] = x; 207 for (i = 1; i < rand_deg; i++) { 208 /* 209 * Implement the following, without overflowing 31 bits: 210 * 211 * state[i] = (16807 * state[i - 1]) % 2147483647; 212 * 213 * 2^31-1 (prime) = 2147483647 = 127773*16807+2836 214 */ 215 val = ldiv(state[i-1], 127773); 216 test = 16807 * val.rem - 2836 * val.quot; 217 state[i] = test + (test < 0 ? 2147483647 : 0); 218 } 219 fptr = &state[rand_sep]; 220 rptr = &state[0]; 221 for (i = 0; i < 10 * rand_deg; i++) 222 (void)random(); 223 } 224 } 225 226 /* 227 * srandomdev: 228 * 229 * Many programs choose the seed value in a totally predictable manner. 230 * This often causes problems. We seed the generator using the much more 231 * secure arandom(4) interface. Note that this particular seeding 232 * procedure can generate states which are impossible to reproduce by 233 * calling srandom() with any value, since the succeeding terms in the 234 * state buffer are no longer derived from the LC algorithm applied to 235 * a fixed seed. 236 */ 237 void 238 srandomdev() 239 { 240 int fd; 241 size_t len; 242 243 if (rand_type == TYPE_0) 244 len = sizeof(state[0]); 245 else 246 len = rand_deg * sizeof(state[0]); 247 248 if ((fd = open("/dev/arandom", O_RDONLY, 0)) == -1 || 249 read(fd, (void *) state, len) != (ssize_t) len) { 250 struct timeval tv; 251 u_int junk; 252 253 /* XXX - this could be better */ 254 gettimeofday(&tv, NULL); 255 srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk); 256 return; 257 } 258 if (fd != -1) 259 close(fd); 260 261 if (rand_type != TYPE_0) { 262 fptr = &state[rand_sep]; 263 rptr = &state[0]; 264 } 265 } 266 267 /* 268 * initstate: 269 * 270 * Initialize the state information in the given array of n bytes for future 271 * random number generation. Based on the number of bytes we are given, and 272 * the break values for the different R.N.G.'s, we choose the best (largest) 273 * one we can and set things up for it. srandom() is then called to 274 * initialize the state information. 275 * 276 * Note that on return from srandom(), we set state[-1] to be the type 277 * multiplexed with the current value of the rear pointer; this is so 278 * successive calls to initstate() won't lose this information and will be 279 * able to restart with setstate(). 280 * 281 * Note: the first thing we do is save the current state, if any, just like 282 * setstate() so that it doesn't matter when initstate is called. 283 * 284 * Returns a pointer to the old state. 285 */ 286 char * 287 initstate(seed, arg_state, n) 288 u_int seed; /* seed for R.N.G. */ 289 char *arg_state; /* pointer to state array */ 290 size_t n; /* # bytes of state info */ 291 { 292 register char *ostate = (char *)(&state[-1]); 293 294 if (rand_type == TYPE_0) 295 state[-1] = rand_type; 296 else 297 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 298 if (n < BREAK_0) 299 return(NULL); 300 if (n < BREAK_1) { 301 rand_type = TYPE_0; 302 rand_deg = DEG_0; 303 rand_sep = SEP_0; 304 } else if (n < BREAK_2) { 305 rand_type = TYPE_1; 306 rand_deg = DEG_1; 307 rand_sep = SEP_1; 308 } else if (n < BREAK_3) { 309 rand_type = TYPE_2; 310 rand_deg = DEG_2; 311 rand_sep = SEP_2; 312 } else if (n < BREAK_4) { 313 rand_type = TYPE_3; 314 rand_deg = DEG_3; 315 rand_sep = SEP_3; 316 } else { 317 rand_type = TYPE_4; 318 rand_deg = DEG_4; 319 rand_sep = SEP_4; 320 } 321 state = &(((long *)arg_state)[1]); /* first location */ 322 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 323 srandom(seed); 324 if (rand_type == TYPE_0) 325 state[-1] = rand_type; 326 else 327 state[-1] = MAX_TYPES*(rptr - state) + rand_type; 328 return(ostate); 329 } 330 331 /* 332 * setstate: 333 * 334 * Restore the state from the given state array. 335 * 336 * Note: it is important that we also remember the locations of the pointers 337 * in the current state information, and restore the locations of the pointers 338 * from the old state information. This is done by multiplexing the pointer 339 * location into the zeroeth word of the state information. 340 * 341 * Note that due to the order in which things are done, it is OK to call 342 * setstate() with the same state as the current state. 343 * 344 * Returns a pointer to the old state information. 345 */ 346 char * 347 setstate(arg_state) 348 const char *arg_state; 349 { 350 register long *new_state = (long *)arg_state; 351 register int type = new_state[0] % MAX_TYPES; 352 register int rear = new_state[0] / MAX_TYPES; 353 char *ostate = (char *)(&state[-1]); 354 355 if (rand_type == TYPE_0) 356 state[-1] = rand_type; 357 else 358 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 359 switch(type) { 360 case TYPE_0: 361 case TYPE_1: 362 case TYPE_2: 363 case TYPE_3: 364 case TYPE_4: 365 rand_type = type; 366 rand_deg = degrees[type]; 367 rand_sep = seps[type]; 368 break; 369 default: 370 return(NULL); 371 } 372 state = &new_state[1]; 373 if (rand_type != TYPE_0) { 374 rptr = &state[rear]; 375 fptr = &state[(rear + rand_sep) % rand_deg]; 376 } 377 end_ptr = &state[rand_deg]; /* set end_ptr too */ 378 return(ostate); 379 } 380 381 /* 382 * random: 383 * 384 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 385 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 386 * the same in all the other cases due to all the global variables that have 387 * been set up. The basic operation is to add the number at the rear pointer 388 * into the one at the front pointer. Then both pointers are advanced to 389 * the next location cyclically in the table. The value returned is the sum 390 * generated, reduced to 31 bits by throwing away the "least random" low bit. 391 * 392 * Note: the code takes advantage of the fact that both the front and 393 * rear pointers can't wrap on the same call by not testing the rear 394 * pointer if the front one has wrapped. 395 * 396 * Returns a 31-bit random number. 397 */ 398 long 399 random() 400 { 401 long i; 402 403 if (rand_type == TYPE_0) 404 i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff; 405 else { 406 *fptr += *rptr; 407 i = (*fptr >> 1) & 0x7fffffff; /* chucking least random bit */ 408 if (++fptr >= end_ptr) { 409 fptr = state; 410 ++rptr; 411 } else if (++rptr >= end_ptr) 412 rptr = state; 413 } 414 return(i); 415 } 416