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 8.2 (Berkeley) 5/19/95"; 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 * Modified 28 December 1994 by Jacob S. Rosenberg. 89 * The following changes have been made: 90 * All references to the type u_int have been changed to unsigned long. 91 * All references to type int have been changed to type long. Other 92 * cleanups have been made as well. A warning for both initstate and 93 * setstate has been inserted to the effect that on Sparc platforms 94 * the 'arg_state' variable must be forced to begin on word boundaries. 95 * This can be easily done by casting a long integer array to char *. 96 * The overall logic has been left STRICTLY alone. This software was 97 * tested on both a VAX and Sun SpacsStation with exactly the same 98 * results. The new version and the original give IDENTICAL results. 99 * The new version is somewhat faster than the original. As the 100 * documentation says: "By default, the package runs with 128 bytes of 101 * state information and generates far better random numbers than a linear 102 * congruential generator. If the amount of state information is less than 103 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 104 * 128 bytes, this new version runs about 19 percent faster and for a 16 105 * byte buffer it is about 5 percent faster. 106 */ 107 108 /* 109 * For each of the currently supported random number generators, we have a 110 * break value on the amount of state information (you need at least this 111 * many bytes of state info to support this random number generator), a degree 112 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 113 * the separation between the two lower order coefficients of the trinomial. 114 */ 115 #define TYPE_0 0 /* linear congruential */ 116 #define BREAK_0 8 117 #define DEG_0 0 118 #define SEP_0 0 119 120 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 121 #define BREAK_1 32 122 #define DEG_1 7 123 #define SEP_1 3 124 125 #define TYPE_2 2 /* x**15 + x + 1 */ 126 #define BREAK_2 64 127 #define DEG_2 15 128 #define SEP_2 1 129 130 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 131 #define BREAK_3 128 132 #define DEG_3 31 133 #define SEP_3 3 134 135 #define TYPE_4 4 /* x**63 + x + 1 */ 136 #define BREAK_4 256 137 #define DEG_4 63 138 #define SEP_4 1 139 140 /* 141 * Array versions of the above information to make code run faster -- 142 * relies on fact that TYPE_i == i. 143 */ 144 #define MAX_TYPES 5 /* max number of types above */ 145 146 static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 147 static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 148 149 /* 150 * Initially, everything is set up as if from: 151 * 152 * initstate(1, randtbl, 128); 153 * 154 * Note that this initialization takes advantage of the fact that srandom() 155 * advances the front and rear pointers 10*rand_deg times, and hence the 156 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 157 * element of the state information, which contains info about the current 158 * position of the rear pointer is just 159 * 160 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 161 */ 162 163 static long randtbl[DEG_3 + 1] = { 164 TYPE_3, 165 #ifdef USE_WEAK_SEEDING 166 /* Historic implementation compatibility */ 167 /* The random sequences do not vary much with the seed */ 168 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 169 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 170 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, 171 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 172 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 173 0x27fb47b9, 174 #else /* !USE_WEAK_SEEDING */ 175 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 176 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 177 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 178 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 179 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 180 0xf3bec5da 181 #endif /* !USE_WEAK_SEEDING */ 182 }; 183 184 /* 185 * fptr and rptr are two pointers into the state info, a front and a rear 186 * pointer. These two pointers are always rand_sep places aparts, as they 187 * cycle cyclically through the state information. (Yes, this does mean we 188 * could get away with just one pointer, but the code for random() is more 189 * efficient this way). The pointers are left positioned as they would be 190 * from the call 191 * 192 * initstate(1, randtbl, 128); 193 * 194 * (The position of the rear pointer, rptr, is really 0 (as explained above 195 * in the initialization of randtbl) because the state table pointer is set 196 * to point to randtbl[1] (as explained below). 197 */ 198 static long *fptr = &randtbl[SEP_3 + 1]; 199 static long *rptr = &randtbl[1]; 200 201 /* 202 * The following things are the pointer to the state information table, the 203 * type of the current generator, the degree of the current polynomial being 204 * used, and the separation between the two pointers. Note that for efficiency 205 * of random(), we remember the first location of the state information, not 206 * the zeroeth. Hence it is valid to access state[-1], which is used to 207 * store the type of the R.N.G. Also, we remember the last location, since 208 * this is more efficient than indexing every time to find the address of 209 * the last element to see if the front and rear pointers have wrapped. 210 */ 211 static long *state = &randtbl[1]; 212 static long rand_type = TYPE_3; 213 static long rand_deg = DEG_3; 214 static long rand_sep = SEP_3; 215 static long *end_ptr = &randtbl[DEG_3 + 1]; 216 217 static inline long good_rand __P((long)); 218 219 static inline long good_rand (x) 220 register long x; 221 { 222 #ifdef USE_WEAK_SEEDING 223 /* 224 * Historic implementation compatibility. 225 * The random sequences do not vary much with the seed, 226 * even with overflowing. 227 */ 228 return (1103515245 * x + 12345); 229 #else /* !USE_WEAK_SEEDING */ 230 /* 231 * Compute x = (7^5 * x) mod (2^31 - 1) 232 * wihout overflowing 31 bits: 233 * (2^31 - 1) = 127773 * (7^5) + 2836 234 * From "Random number generators: good ones are hard to find", 235 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 236 * October 1988, p. 1195. 237 */ 238 register long hi, lo; 239 240 hi = x / 127773; 241 lo = x % 127773; 242 x = 16807 * lo - 2836 * hi; 243 if (x <= 0) 244 x += 0x7fffffff; 245 return (x); 246 #endif /* !USE_WEAK_SEEDING */ 247 } 248 249 /* 250 * srandom: 251 * 252 * Initialize the random number generator based on the given seed. If the 253 * type is the trivial no-state-information type, just remember the seed. 254 * Otherwise, initializes state[] based on the given "seed" via a linear 255 * congruential generator. Then, the pointers are set to known locations 256 * that are exactly rand_sep places apart. Lastly, it cycles the state 257 * information a given number of times to get rid of any initial dependencies 258 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 259 * for default usage relies on values produced by this routine. 260 */ 261 void 262 srandom(x) 263 unsigned long x; 264 { 265 register long i; 266 267 if (rand_type == TYPE_0) 268 state[0] = x; 269 else { 270 state[0] = x; 271 for (i = 1; i < rand_deg; i++) 272 state[i] = good_rand(state[i - 1]); 273 fptr = &state[rand_sep]; 274 rptr = &state[0]; 275 for (i = 0; i < 10 * rand_deg; i++) 276 (void)random(); 277 } 278 } 279 280 /* 281 * initstate: 282 * 283 * Initialize the state information in the given array of n bytes for future 284 * random number generation. Based on the number of bytes we are given, and 285 * the break values for the different R.N.G.'s, we choose the best (largest) 286 * one we can and set things up for it. srandom() is then called to 287 * initialize the state information. 288 * 289 * Note that on return from srandom(), we set state[-1] to be the type 290 * multiplexed with the current value of the rear pointer; this is so 291 * successive calls to initstate() won't lose this information and will be 292 * able to restart with setstate(). 293 * 294 * Note: the first thing we do is save the current state, if any, just like 295 * setstate() so that it doesn't matter when initstate is called. 296 * 297 * Returns a pointer to the old state. 298 * 299 * Note: The Sparc platform requires that arg_state begin on a long 300 * word boundary; otherwise a bus error will occur. Even so, lint will 301 * complain about mis-alignment, but you should disregard these messages. 302 */ 303 char * 304 initstate(seed, arg_state, n) 305 unsigned long seed; /* seed for R.N.G. */ 306 char *arg_state; /* pointer to state array */ 307 long n; /* # bytes of state info */ 308 { 309 register char *ostate = (char *)(&state[-1]); 310 register long *long_arg_state = (long *) arg_state; 311 312 if (rand_type == TYPE_0) 313 state[-1] = rand_type; 314 else 315 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 316 if (n < BREAK_0) { 317 (void)fprintf(stderr, 318 "random: not enough state (%ld bytes); ignored.\n", n); 319 return(0); 320 } 321 if (n < BREAK_1) { 322 rand_type = TYPE_0; 323 rand_deg = DEG_0; 324 rand_sep = SEP_0; 325 } else if (n < BREAK_2) { 326 rand_type = TYPE_1; 327 rand_deg = DEG_1; 328 rand_sep = SEP_1; 329 } else if (n < BREAK_3) { 330 rand_type = TYPE_2; 331 rand_deg = DEG_2; 332 rand_sep = SEP_2; 333 } else if (n < BREAK_4) { 334 rand_type = TYPE_3; 335 rand_deg = DEG_3; 336 rand_sep = SEP_3; 337 } else { 338 rand_type = TYPE_4; 339 rand_deg = DEG_4; 340 rand_sep = SEP_4; 341 } 342 state = (long *) (long_arg_state + 1); /* first location */ 343 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 344 srandom(seed); 345 if (rand_type == TYPE_0) 346 long_arg_state[0] = rand_type; 347 else 348 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 349 return(ostate); 350 } 351 352 /* 353 * setstate: 354 * 355 * Restore the state from the given state array. 356 * 357 * Note: it is important that we also remember the locations of the pointers 358 * in the current state information, and restore the locations of the pointers 359 * from the old state information. This is done by multiplexing the pointer 360 * location into the zeroeth word of the state information. 361 * 362 * Note that due to the order in which things are done, it is OK to call 363 * setstate() with the same state as the current state. 364 * 365 * Returns a pointer to the old state information. 366 * 367 * Note: The Sparc platform requires that arg_state begin on a long 368 * word boundary; otherwise a bus error will occur. Even so, lint will 369 * complain about mis-alignment, but you should disregard these messages. 370 */ 371 char * 372 setstate(arg_state) 373 char *arg_state; /* pointer to state array */ 374 { 375 register long *new_state = (long *) arg_state; 376 register long type = new_state[0] % MAX_TYPES; 377 register long rear = new_state[0] / MAX_TYPES; 378 char *ostate = (char *)(&state[-1]); 379 380 if (rand_type == TYPE_0) 381 state[-1] = rand_type; 382 else 383 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 384 switch(type) { 385 case TYPE_0: 386 case TYPE_1: 387 case TYPE_2: 388 case TYPE_3: 389 case TYPE_4: 390 rand_type = type; 391 rand_deg = degrees[type]; 392 rand_sep = seps[type]; 393 break; 394 default: 395 (void)fprintf(stderr, 396 "random: state info corrupted; not changed.\n"); 397 } 398 state = (long *) (new_state + 1); 399 if (rand_type != TYPE_0) { 400 rptr = &state[rear]; 401 fptr = &state[(rear + rand_sep) % rand_deg]; 402 } 403 end_ptr = &state[rand_deg]; /* set end_ptr too */ 404 return(ostate); 405 } 406 407 /* 408 * random: 409 * 410 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 411 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 412 * the same in all the other cases due to all the global variables that have 413 * been set up. The basic operation is to add the number at the rear pointer 414 * into the one at the front pointer. Then both pointers are advanced to 415 * the next location cyclically in the table. The value returned is the sum 416 * generated, reduced to 31 bits by throwing away the "least random" low bit. 417 * 418 * Note: the code takes advantage of the fact that both the front and 419 * rear pointers can't wrap on the same call by not testing the rear 420 * pointer if the front one has wrapped. 421 * 422 * Returns a 31-bit random number. 423 */ 424 long 425 random() 426 { 427 register long i; 428 register long *f, *r; 429 430 if (rand_type == TYPE_0) { 431 i = state[0]; 432 state[0] = i = (good_rand(i)) & 0x7fffffff; 433 } else { 434 /* 435 * Use local variables rather than static variables for speed. 436 */ 437 f = fptr; r = rptr; 438 *f += *r; 439 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */ 440 if (++f >= end_ptr) { 441 f = state; 442 ++r; 443 } 444 else if (++r >= end_ptr) { 445 r = state; 446 } 447 448 fptr = f; rptr = r; 449 } 450 return(i); 451 } 452