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. 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 sccsid[] = "@(#)random.c 8.1 (Berkeley) 6/4/93"; 36 #endif /* LIBC_SCCS and not lint */ 37 38 #ifdef COMPAT_WEAK_SEEDING 39 #define USE_WEAK_SEEDING 40 #define random orandom 41 #define srandom osrandom 42 #define initstate oinitstate 43 #define setstate osetstate 44 #endif 45 46 #include <stdio.h> 47 #include <stdlib.h> 48 49 /* 50 * random.c: 51 * 52 * An improved random number generation package. In addition to the standard 53 * rand()/srand() like interface, this package also has a special state info 54 * interface. The initstate() routine is called with a seed, an array of 55 * bytes, and a count of how many bytes are being passed in; this array is 56 * then initialized to contain information for random number generation with 57 * that much state information. Good sizes for the amount of state 58 * information are 32, 64, 128, and 256 bytes. The state can be switched by 59 * calling the setstate() routine with the same array as was initiallized 60 * with initstate(). By default, the package runs with 128 bytes of state 61 * information and generates far better random numbers than a linear 62 * congruential generator. If the amount of state information is less than 63 * 32 bytes, a simple linear congruential R.N.G. is used. 64 * 65 * Internally, the state information is treated as an array of longs; the 66 * zeroeth element of the array is the type of R.N.G. being used (small 67 * integer); the remainder of the array is the state information for the 68 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of 69 * state information, which will allow a degree seven polynomial. (Note: 70 * the zeroeth word of state information also has some other information 71 * stored in it -- see setstate() for details). 72 * 73 * The random number generation technique is a linear feedback shift register 74 * approach, employing trinomials (since there are fewer terms to sum up that 75 * way). In this approach, the least significant bit of all the numbers in 76 * the state table will act as a linear feedback shift register, and will 77 * have period 2^deg - 1 (where deg is the degree of the polynomial being 78 * used, assuming that the polynomial is irreducible and primitive). The 79 * higher order bits will have longer periods, since their values are also 80 * influenced by pseudo-random carries out of the lower bits. The total 81 * period of the generator is approximately deg*(2**deg - 1); thus doubling 82 * the amount of state information has a vast influence on the period of the 83 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 84 * large deg, when the period of the shift register is the dominant factor. 85 * With deg equal to seven, the period is actually much longer than the 86 * 7*(2**7 - 1) predicted by this formula. 87 */ 88 89 /* 90 * For each of the currently supported random number generators, we have a 91 * break value on the amount of state information (you need at least this 92 * many bytes of state info to support this random number generator), a degree 93 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 94 * the separation between the two lower order coefficients of the trinomial. 95 */ 96 #define TYPE_0 0 /* linear congruential */ 97 #define BREAK_0 8 98 #define DEG_0 0 99 #define SEP_0 0 100 101 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 102 #define BREAK_1 32 103 #define DEG_1 7 104 #define SEP_1 3 105 106 #define TYPE_2 2 /* x**15 + x + 1 */ 107 #define BREAK_2 64 108 #define DEG_2 15 109 #define SEP_2 1 110 111 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 112 #define BREAK_3 128 113 #define DEG_3 31 114 #define SEP_3 3 115 116 #define TYPE_4 4 /* x**63 + x + 1 */ 117 #define BREAK_4 256 118 #define DEG_4 63 119 #define SEP_4 1 120 121 /* 122 * Array versions of the above information to make code run faster -- 123 * relies on fact that TYPE_i == i. 124 */ 125 #define MAX_TYPES 5 /* max number of types above */ 126 127 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 128 static int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 129 130 /* 131 * Initially, everything is set up as if from: 132 * 133 * initstate(1, randtbl, 128); 134 * 135 * Note that this initialization takes advantage of the fact that srandom() 136 * advances the front and rear pointers 10*rand_deg times, and hence the 137 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 138 * element of the state information, which contains info about the current 139 * position of the rear pointer is just 140 * 141 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 142 */ 143 144 static long randtbl[DEG_3 + 1] = { 145 TYPE_3, 146 #ifdef USE_WEAK_SEEDING 147 /* Historic implementation compatibility */ 148 /* The random sequences do not vary much with the seed */ 149 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 150 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 151 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, 152 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 153 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 154 0x27fb47b9, 155 #else /* !USE_WEAK_SEEDING */ 156 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 157 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 158 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 159 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 160 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 161 0xf3bec5da 162 #endif /* !USE_WEAK_SEEDING */ 163 }; 164 165 /* 166 * fptr and rptr are two pointers into the state info, a front and a rear 167 * pointer. These two pointers are always rand_sep places aparts, as they 168 * cycle cyclically through the state information. (Yes, this does mean we 169 * could get away with just one pointer, but the code for random() is more 170 * efficient this way). The pointers are left positioned as they would be 171 * from the call 172 * 173 * initstate(1, randtbl, 128); 174 * 175 * (The position of the rear pointer, rptr, is really 0 (as explained above 176 * in the initialization of randtbl) because the state table pointer is set 177 * to point to randtbl[1] (as explained below). 178 */ 179 static long *fptr = &randtbl[SEP_3 + 1]; 180 static long *rptr = &randtbl[1]; 181 182 /* 183 * The following things are the pointer to the state information table, the 184 * type of the current generator, the degree of the current polynomial being 185 * used, and the separation between the two pointers. Note that for efficiency 186 * of random(), we remember the first location of the state information, not 187 * the zeroeth. Hence it is valid to access state[-1], which is used to 188 * store the type of the R.N.G. Also, we remember the last location, since 189 * this is more efficient than indexing every time to find the address of 190 * the last element to see if the front and rear pointers have wrapped. 191 */ 192 static long *state = &randtbl[1]; 193 static int rand_type = TYPE_3; 194 static int rand_deg = DEG_3; 195 static int rand_sep = SEP_3; 196 static long *end_ptr = &randtbl[DEG_3 + 1]; 197 198 static inline long good_rand __P((long)); 199 200 static inline long good_rand (x) 201 register long x; 202 { 203 #ifdef USE_WEAK_SEEDING 204 /* 205 * Historic implementation compatibility. 206 * The random sequences do not vary much with the seed, 207 * even with overflowing. 208 */ 209 return (1103515245 * x + 12345); 210 #else /* !USE_WEAK_SEEDING */ 211 /* 212 * Compute x = (7^5 * x) mod (2^31 - 1) 213 * wihout overflowing 31 bits: 214 * (2^31 - 1) = 127773 * (7^5) + 2836 215 * From "Random number generators: good ones are hard to find", 216 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 217 * October 1988, p. 1195. 218 */ 219 register long hi, lo; 220 221 hi = x / 127773; 222 lo = x % 127773; 223 x = 16807 * lo - 2836 * hi; 224 if (x <= 0) 225 x += 0x7fffffff; 226 return (x); 227 #endif /* !USE_WEAK_SEEDING */ 228 } 229 230 /* 231 * srandom: 232 * 233 * Initialize the random number generator based on the given seed. If the 234 * type is the trivial no-state-information type, just remember the seed. 235 * Otherwise, initializes state[] based on the given "seed" via a linear 236 * congruential generator. Then, the pointers are set to known locations 237 * that are exactly rand_sep places apart. Lastly, it cycles the state 238 * information a given number of times to get rid of any initial dependencies 239 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 240 * for default usage relies on values produced by this routine. 241 */ 242 void 243 srandom(x) 244 unsigned int x; 245 { 246 register int i; 247 248 if (rand_type == TYPE_0) 249 state[0] = x; 250 else { 251 state[0] = x; 252 for (i = 1; i < rand_deg; i++) 253 state[i] = good_rand(state[i - 1]); 254 fptr = &state[rand_sep]; 255 rptr = &state[0]; 256 for (i = 0; i < 10 * rand_deg; i++) 257 (void)random(); 258 } 259 } 260 261 /* 262 * initstate: 263 * 264 * Initialize the state information in the given array of n bytes for future 265 * random number generation. Based on the number of bytes we are given, and 266 * the break values for the different R.N.G.'s, we choose the best (largest) 267 * one we can and set things up for it. srandom() is then called to 268 * initialize the state information. 269 * 270 * Note that on return from srandom(), we set state[-1] to be the type 271 * multiplexed with the current value of the rear pointer; this is so 272 * successive calls to initstate() won't lose this information and will be 273 * able to restart with setstate(). 274 * 275 * Note: the first thing we do is save the current state, if any, just like 276 * setstate() so that it doesn't matter when initstate is called. 277 * 278 * Returns a pointer to the old state. 279 */ 280 char * 281 initstate(seed, arg_state, n) 282 unsigned int seed; /* seed for R.N.G. */ 283 char *arg_state; /* pointer to state array */ 284 int n; /* # bytes of state info */ 285 { 286 register char *ostate = (char *)(&state[-1]); 287 288 if (rand_type == TYPE_0) 289 state[-1] = rand_type; 290 else 291 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 292 if (n < BREAK_0) { 293 (void)fprintf(stderr, 294 "random: not enough state (%d bytes); ignored.\n", n); 295 return(0); 296 } 297 if (n < BREAK_1) { 298 rand_type = TYPE_0; 299 rand_deg = DEG_0; 300 rand_sep = SEP_0; 301 } else if (n < BREAK_2) { 302 rand_type = TYPE_1; 303 rand_deg = DEG_1; 304 rand_sep = SEP_1; 305 } else if (n < BREAK_3) { 306 rand_type = TYPE_2; 307 rand_deg = DEG_2; 308 rand_sep = SEP_2; 309 } else if (n < BREAK_4) { 310 rand_type = TYPE_3; 311 rand_deg = DEG_3; 312 rand_sep = SEP_3; 313 } else { 314 rand_type = TYPE_4; 315 rand_deg = DEG_4; 316 rand_sep = SEP_4; 317 } 318 state = &(((long *)arg_state)[1]); /* first location */ 319 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 320 srandom(seed); 321 if (rand_type == TYPE_0) 322 state[-1] = rand_type; 323 else 324 state[-1] = MAX_TYPES*(rptr - state) + rand_type; 325 return(ostate); 326 } 327 328 /* 329 * setstate: 330 * 331 * Restore the state from the given state array. 332 * 333 * Note: it is important that we also remember the locations of the pointers 334 * in the current state information, and restore the locations of the pointers 335 * from the old state information. This is done by multiplexing the pointer 336 * location into the zeroeth word of the state information. 337 * 338 * Note that due to the order in which things are done, it is OK to call 339 * setstate() with the same state as the current state. 340 * 341 * Returns a pointer to the old state information. 342 */ 343 char * 344 setstate(arg_state) 345 char *arg_state; 346 { 347 register long *new_state = (long *)arg_state; 348 register int type = new_state[0] % MAX_TYPES; 349 register int rear = new_state[0] / MAX_TYPES; 350 char *ostate = (char *)(&state[-1]); 351 352 if (rand_type == TYPE_0) 353 state[-1] = rand_type; 354 else 355 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 356 switch(type) { 357 case TYPE_0: 358 case TYPE_1: 359 case TYPE_2: 360 case TYPE_3: 361 case TYPE_4: 362 rand_type = type; 363 rand_deg = degrees[type]; 364 rand_sep = seps[type]; 365 break; 366 default: 367 (void)fprintf(stderr, 368 "random: state info corrupted; not changed.\n"); 369 } 370 state = &new_state[1]; 371 if (rand_type != TYPE_0) { 372 rptr = &state[rear]; 373 fptr = &state[(rear + rand_sep) % rand_deg]; 374 } 375 end_ptr = &state[rand_deg]; /* set end_ptr too */ 376 return(ostate); 377 } 378 379 /* 380 * random: 381 * 382 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 383 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 384 * the same in all the other cases due to all the global variables that have 385 * been set up. The basic operation is to add the number at the rear pointer 386 * into the one at the front pointer. Then both pointers are advanced to 387 * the next location cyclically in the table. The value returned is the sum 388 * generated, reduced to 31 bits by throwing away the "least random" low bit. 389 * 390 * Note: the code takes advantage of the fact that both the front and 391 * rear pointers can't wrap on the same call by not testing the rear 392 * pointer if the front one has wrapped. 393 * 394 * Returns a 31-bit random number. 395 */ 396 long 397 random() 398 { 399 long i; 400 401 if (rand_type == TYPE_0) 402 i = state[0] = good_rand(state[0]) & 0x7fffffff; 403 else { 404 *fptr += *rptr; 405 i = (*fptr >> 1) & 0x7fffffff; /* chucking least random bit */ 406 if (++fptr >= end_ptr) { 407 fptr = state; 408 ++rptr; 409 } else if (++rptr >= end_ptr) 410 rptr = state; 411 } 412 return(i); 413 } 414