1 /* $OpenBSD: random.c,v 1.23 2014/07/13 14:21:14 tedu 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 size_t len; 258 259 LOCK(); 260 use_arc4random = 1; 261 UNLOCK(); 262 } 263 264 #if defined(APIWARN) 265 __warn_references(srandomdev, 266 "warning: srandomdev() usage; consider switching to arc4random()"); 267 #endif 268 269 /* 270 * initstate: 271 * 272 * Initialize the state information in the given array of n bytes for future 273 * random number generation. Based on the number of bytes we are given, and 274 * the break values for the different R.N.G.'s, we choose the best (largest) 275 * one we can and set things up for it. srandom() is then called to 276 * initialize the state information. 277 * 278 * Note that on return from srandom(), we set state[-1] to be the type 279 * multiplexed with the current value of the rear pointer; this is so 280 * successive calls to initstate() won't lose this information and will be 281 * able to restart with setstate(). 282 * 283 * Note: the first thing we do is save the current state, if any, just like 284 * setstate() so that it doesn't matter when initstate is called. 285 * 286 * Returns a pointer to the old state. 287 */ 288 char * 289 initstate(u_int seed, char *arg_state, size_t n) 290 { 291 char *ostate = (char *)(&state[-1]); 292 293 LOCK(); 294 use_arc4random = 0; 295 if (rand_type == TYPE_0) 296 state[-1] = rand_type; 297 else 298 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 299 if (n < BREAK_0) { 300 UNLOCK(); 301 return(NULL); 302 } 303 if (n < BREAK_1) { 304 rand_type = TYPE_0; 305 rand_deg = DEG_0; 306 rand_sep = SEP_0; 307 } else if (n < BREAK_2) { 308 rand_type = TYPE_1; 309 rand_deg = DEG_1; 310 rand_sep = SEP_1; 311 } else if (n < BREAK_3) { 312 rand_type = TYPE_2; 313 rand_deg = DEG_2; 314 rand_sep = SEP_2; 315 } else if (n < BREAK_4) { 316 rand_type = TYPE_3; 317 rand_deg = DEG_3; 318 rand_sep = SEP_3; 319 } else { 320 rand_type = TYPE_4; 321 rand_deg = DEG_4; 322 rand_sep = SEP_4; 323 } 324 state = &(((int32_t *)arg_state)[1]); /* first location */ 325 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 326 srandom_l(seed); 327 if (rand_type == TYPE_0) 328 state[-1] = rand_type; 329 else 330 state[-1] = MAX_TYPES*(rptr - state) + rand_type; 331 UNLOCK(); 332 return(ostate); 333 } 334 335 /* 336 * setstate: 337 * 338 * Restore the state from the given state array. 339 * 340 * Note: it is important that we also remember the locations of the pointers 341 * in the current state information, and restore the locations of the pointers 342 * from the old state information. This is done by multiplexing the pointer 343 * location into the zeroeth word of the state information. 344 * 345 * Note that due to the order in which things are done, it is OK to call 346 * setstate() with the same state as the current state. 347 * 348 * Returns a pointer to the old state information. 349 */ 350 char * 351 setstate(char *arg_state) 352 { 353 int32_t *new_state = (int32_t *)arg_state; 354 int32_t type = new_state[0] % MAX_TYPES; 355 int32_t rear = new_state[0] / MAX_TYPES; 356 char *ostate = (char *)(&state[-1]); 357 358 LOCK(); 359 use_arc4random = 0; 360 if (rand_type == TYPE_0) 361 state[-1] = rand_type; 362 else 363 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 364 switch(type) { 365 case TYPE_0: 366 case TYPE_1: 367 case TYPE_2: 368 case TYPE_3: 369 case TYPE_4: 370 rand_type = type; 371 rand_deg = degrees[type]; 372 rand_sep = seps[type]; 373 break; 374 default: 375 UNLOCK(); 376 return(NULL); 377 } 378 state = &new_state[1]; 379 if (rand_type != TYPE_0) { 380 rptr = &state[rear]; 381 fptr = &state[(rear + rand_sep) % rand_deg]; 382 } 383 end_ptr = &state[rand_deg]; /* set end_ptr too */ 384 UNLOCK(); 385 return(ostate); 386 } 387 388 /* 389 * random: 390 * 391 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 392 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 393 * the same in all the other cases due to all the global variables that have 394 * been set up. The basic operation is to add the number at the rear pointer 395 * into the one at the front pointer. Then both pointers are advanced to 396 * the next location cyclically in the table. The value returned is the sum 397 * generated, reduced to 31 bits by throwing away the "least random" low bit. 398 * 399 * Note: the code takes advantage of the fact that both the front and 400 * rear pointers can't wrap on the same call by not testing the rear 401 * pointer if the front one has wrapped. 402 * 403 * Returns a 31-bit random number. 404 */ 405 static long 406 random_l(void) 407 { 408 int32_t i; 409 410 if (use_arc4random) 411 return arc4random() & 0x7fffffff; 412 413 if (rand_type == TYPE_0) 414 i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff; 415 else { 416 *fptr += *rptr; 417 i = (*fptr >> 1) & 0x7fffffff; /* chucking least random bit */ 418 if (++fptr >= end_ptr) { 419 fptr = state; 420 ++rptr; 421 } else if (++rptr >= end_ptr) 422 rptr = state; 423 } 424 return((long)i); 425 } 426 427 long 428 random(void) 429 { 430 long r; 431 LOCK(); 432 r = random_l(); 433 UNLOCK(); 434 return r; 435 } 436 437 #if defined(APIWARN) 438 __warn_references(random, 439 "warning: random() isn't random; consider using arc4random()"); 440 #endif 441