1 /* $OpenBSD: random.c,v 1.24 2014/10/13 20:54:13 chl Exp $ */ 2 /* 3 * Copyright (c) 1983 Regents of the University of California. 4 * All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 3. Neither the name of the University nor the names of its contributors 15 * may be used to endorse or promote products derived from this software 16 * without specific prior written permission. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 28 * SUCH DAMAGE. 29 */ 30 31 #include <sys/param.h> 32 #include <sys/sysctl.h> 33 #include <sys/time.h> 34 #include <fcntl.h> 35 #include <stdio.h> 36 #include <stdlib.h> 37 #include <unistd.h> 38 39 #include "thread_private.h" 40 41 /* 42 * random.c: 43 * 44 * An improved random number generation package. In addition to the standard 45 * rand()/srand() like interface, this package also has a special state info 46 * interface. The initstate() routine is called with a seed, an array of 47 * bytes, and a count of how many bytes are being passed in; this array is 48 * then initialized to contain information for random number generation with 49 * that much state information. Good sizes for the amount of state 50 * information are 32, 64, 128, and 256 bytes. The state can be switched by 51 * calling the setstate() routine with the same array as was initiallized 52 * with initstate(). By default, the package runs with 128 bytes of state 53 * information and generates far better random numbers than a linear 54 * congruential generator. If the amount of state information is less than 55 * 32 bytes, a simple linear congruential R.N.G. is used. 56 * 57 * Internally, the state information is treated as an array of int32_t; the 58 * zeroeth element of the array is the type of R.N.G. being used (small 59 * integer); the remainder of the array is the state information for the 60 * R.N.G. Thus, 32 bytes of state information will give 7 int32_ts worth of 61 * state information, which will allow a degree seven polynomial. (Note: 62 * the zeroeth word of state information also has some other information 63 * stored in it -- see setstate() for details). 64 * 65 * The random number generation technique is a linear feedback shift register 66 * approach, employing trinomials (since there are fewer terms to sum up that 67 * way). In this approach, the least significant bit of all the numbers in 68 * the state table will act as a linear feedback shift register, and will 69 * have period 2^deg - 1 (where deg is the degree of the polynomial being 70 * used, assuming that the polynomial is irreducible and primitive). The 71 * higher order bits will have longer periods, since their values are also 72 * influenced by pseudo-random carries out of the lower bits. The total 73 * period of the generator is approximately deg*(2**deg - 1); thus doubling 74 * the amount of state information has a vast influence on the period of the 75 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 76 * large deg, when the period of the shift register is the dominant factor. 77 * With deg equal to seven, the period is actually much longer than the 78 * 7*(2**7 - 1) predicted by this formula. 79 */ 80 81 /* 82 * For each of the currently supported random number generators, we have a 83 * break value on the amount of state information (you need at least this 84 * many bytes of state info to support this random number generator), a degree 85 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 86 * the separation between the two lower order coefficients of the trinomial. 87 */ 88 #define TYPE_0 0 /* linear congruential */ 89 #define BREAK_0 8 90 #define DEG_0 0 91 #define SEP_0 0 92 93 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 94 #define BREAK_1 32 95 #define DEG_1 7 96 #define SEP_1 3 97 98 #define TYPE_2 2 /* x**15 + x + 1 */ 99 #define BREAK_2 64 100 #define DEG_2 15 101 #define SEP_2 1 102 103 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 104 #define BREAK_3 128 105 #define DEG_3 31 106 #define SEP_3 3 107 108 #define TYPE_4 4 /* x**63 + x + 1 */ 109 #define BREAK_4 256 110 #define DEG_4 63 111 #define SEP_4 1 112 113 /* 114 * Array versions of the above information to make code run faster -- 115 * relies on fact that TYPE_i == i. 116 */ 117 #define MAX_TYPES 5 /* max number of types above */ 118 119 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 120 static int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 121 122 /* 123 * Initially, everything is set up as if from: 124 * 125 * initstate(1, &randtbl, 128); 126 * 127 * Note that this initialization takes advantage of the fact that srandom() 128 * advances the front and rear pointers 10*rand_deg times, and hence the 129 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 130 * element of the state information, which contains info about the current 131 * position of the rear pointer is just 132 * 133 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 134 */ 135 136 static int32_t randtbl[DEG_3 + 1] = { 137 TYPE_3, 138 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 139 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 140 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 141 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 142 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 143 0xf3bec5da, 144 }; 145 146 /* 147 * fptr and rptr are two pointers into the state info, a front and a rear 148 * pointer. These two pointers are always rand_sep places aparts, as they 149 * cycle cyclically through the state information. (Yes, this does mean we 150 * could get away with just one pointer, but the code for random() is more 151 * efficient this way). The pointers are left positioned as they would be 152 * from the call 153 * 154 * initstate(1, randtbl, 128); 155 * 156 * (The position of the rear pointer, rptr, is really 0 (as explained above 157 * in the initialization of randtbl) because the state table pointer is set 158 * to point to randtbl[1] (as explained below). 159 */ 160 static int32_t *fptr = &randtbl[SEP_3 + 1]; 161 static int32_t *rptr = &randtbl[1]; 162 163 /* 164 * The following things are the pointer to the state information table, the 165 * type of the current generator, the degree of the current polynomial being 166 * used, and the separation between the two pointers. Note that for efficiency 167 * of random(), we remember the first location of the state information, not 168 * the zeroeth. Hence it is valid to access state[-1], which is used to 169 * store the type of the R.N.G. Also, we remember the last location, since 170 * this is more efficient than indexing every time to find the address of 171 * the last element to see if the front and rear pointers have wrapped. 172 */ 173 static int32_t *state = &randtbl[1]; 174 static int32_t *end_ptr = &randtbl[DEG_3 + 1]; 175 static int rand_type = TYPE_3; 176 static int rand_deg = DEG_3; 177 static int rand_sep = SEP_3; 178 179 static int use_arc4random; 180 181 _THREAD_PRIVATE_MUTEX(random); 182 static long random_l(void); 183 184 #define LOCK() _THREAD_PRIVATE_MUTEX_LOCK(random) 185 #define UNLOCK() _THREAD_PRIVATE_MUTEX_UNLOCK(random) 186 187 /* 188 * srandom: 189 * 190 * Initialize the random number generator based on the given seed. If the 191 * type is the trivial no-state-information type, just remember the seed. 192 * Otherwise, initializes state[] based on the given "seed" via a linear 193 * congruential generator. Then, the pointers are set to known locations 194 * that are exactly rand_sep places apart. Lastly, it cycles the state 195 * information a given number of times to get rid of any initial dependencies 196 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 197 * for default usage relies on values produced by this routine. 198 */ 199 static void 200 srandom_l(unsigned int x) 201 { 202 int i; 203 int32_t test; 204 div_t val; 205 206 use_arc4random = 0; 207 if (rand_type == TYPE_0) 208 state[0] = x; 209 else { 210 /* A seed of 0 would result in state[] always being zero. */ 211 state[0] = x ? x : 1; 212 for (i = 1; i < rand_deg; i++) { 213 /* 214 * Implement the following, without overflowing 31 bits: 215 * 216 * state[i] = (16807 * state[i - 1]) % 2147483647; 217 * 218 * 2^31-1 (prime) = 2147483647 = 127773*16807+2836 219 */ 220 val = div(state[i-1], 127773); 221 test = 16807 * val.rem - 2836 * val.quot; 222 state[i] = test + (test < 0 ? 2147483647 : 0); 223 } 224 fptr = &state[rand_sep]; 225 rptr = &state[0]; 226 for (i = 0; i < 10 * rand_deg; i++) 227 (void)random_l(); 228 } 229 } 230 231 void 232 srandom(unsigned int x) 233 { 234 LOCK(); 235 srandom_l(x); 236 UNLOCK(); 237 } 238 239 #if defined(APIWARN) 240 __warn_references(srandom, 241 "warning: srandom() seed choices are invariably poor"); 242 #endif 243 244 /* 245 * srandomdev: 246 * 247 * Many programs choose the seed value in a totally predictable manner. 248 * This often causes problems. We seed the generator using random data. 249 * Note that this particular seeding procedure can generate states 250 * which are impossible to reproduce by calling srandom() with any 251 * value, since the succeeding terms in the state buffer are no longer 252 * derived from the LC algorithm applied to a fixed seed. 253 */ 254 void 255 srandomdev(void) 256 { 257 LOCK(); 258 use_arc4random = 1; 259 UNLOCK(); 260 } 261 262 #if defined(APIWARN) 263 __warn_references(srandomdev, 264 "warning: srandomdev() usage; consider switching to arc4random()"); 265 #endif 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(u_int seed, char *arg_state, size_t n) 288 { 289 char *ostate = (char *)(&state[-1]); 290 291 LOCK(); 292 use_arc4random = 0; 293 if (rand_type == TYPE_0) 294 state[-1] = rand_type; 295 else 296 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 297 if (n < BREAK_0) { 298 UNLOCK(); 299 return(NULL); 300 } 301 if (n < BREAK_1) { 302 rand_type = TYPE_0; 303 rand_deg = DEG_0; 304 rand_sep = SEP_0; 305 } else if (n < BREAK_2) { 306 rand_type = TYPE_1; 307 rand_deg = DEG_1; 308 rand_sep = SEP_1; 309 } else if (n < BREAK_3) { 310 rand_type = TYPE_2; 311 rand_deg = DEG_2; 312 rand_sep = SEP_2; 313 } else if (n < BREAK_4) { 314 rand_type = TYPE_3; 315 rand_deg = DEG_3; 316 rand_sep = SEP_3; 317 } else { 318 rand_type = TYPE_4; 319 rand_deg = DEG_4; 320 rand_sep = SEP_4; 321 } 322 state = &(((int32_t *)arg_state)[1]); /* first location */ 323 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 324 srandom_l(seed); 325 if (rand_type == TYPE_0) 326 state[-1] = rand_type; 327 else 328 state[-1] = MAX_TYPES*(rptr - state) + rand_type; 329 UNLOCK(); 330 return(ostate); 331 } 332 333 /* 334 * setstate: 335 * 336 * Restore the state from the given state array. 337 * 338 * Note: it is important that we also remember the locations of the pointers 339 * in the current state information, and restore the locations of the pointers 340 * from the old state information. This is done by multiplexing the pointer 341 * location into the zeroeth word of the state information. 342 * 343 * Note that due to the order in which things are done, it is OK to call 344 * setstate() with the same state as the current state. 345 * 346 * Returns a pointer to the old state information. 347 */ 348 char * 349 setstate(char *arg_state) 350 { 351 int32_t *new_state = (int32_t *)arg_state; 352 int32_t type = new_state[0] % MAX_TYPES; 353 int32_t rear = new_state[0] / MAX_TYPES; 354 char *ostate = (char *)(&state[-1]); 355 356 LOCK(); 357 use_arc4random = 0; 358 if (rand_type == TYPE_0) 359 state[-1] = rand_type; 360 else 361 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 362 switch(type) { 363 case TYPE_0: 364 case TYPE_1: 365 case TYPE_2: 366 case TYPE_3: 367 case TYPE_4: 368 rand_type = type; 369 rand_deg = degrees[type]; 370 rand_sep = seps[type]; 371 break; 372 default: 373 UNLOCK(); 374 return(NULL); 375 } 376 state = &new_state[1]; 377 if (rand_type != TYPE_0) { 378 rptr = &state[rear]; 379 fptr = &state[(rear + rand_sep) % rand_deg]; 380 } 381 end_ptr = &state[rand_deg]; /* set end_ptr too */ 382 UNLOCK(); 383 return(ostate); 384 } 385 386 /* 387 * random: 388 * 389 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 390 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 391 * the same in all the other cases due to all the global variables that have 392 * been set up. The basic operation is to add the number at the rear pointer 393 * into the one at the front pointer. Then both pointers are advanced to 394 * the next location cyclically in the table. The value returned is the sum 395 * generated, reduced to 31 bits by throwing away the "least random" low bit. 396 * 397 * Note: the code takes advantage of the fact that both the front and 398 * rear pointers can't wrap on the same call by not testing the rear 399 * pointer if the front one has wrapped. 400 * 401 * Returns a 31-bit random number. 402 */ 403 static long 404 random_l(void) 405 { 406 int32_t i; 407 408 if (use_arc4random) 409 return arc4random() & 0x7fffffff; 410 411 if (rand_type == TYPE_0) 412 i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff; 413 else { 414 *fptr += *rptr; 415 i = (*fptr >> 1) & 0x7fffffff; /* chucking least random bit */ 416 if (++fptr >= end_ptr) { 417 fptr = state; 418 ++rptr; 419 } else if (++rptr >= end_ptr) 420 rptr = state; 421 } 422 return((long)i); 423 } 424 425 long 426 random(void) 427 { 428 long r; 429 LOCK(); 430 r = random_l(); 431 UNLOCK(); 432 return r; 433 } 434 435 #if defined(APIWARN) 436 __warn_references(random, 437 "warning: random() isn't random; consider using arc4random()"); 438 #endif 439