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. [rescinded 22 July 1999] 14 * 4. 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/* 32 * This is derived from the Berkeley source: 33 * @(#)random.c 5.5 (Berkeley) 7/6/88 34 * It was reworked for the GNU C Library by Roland McGrath. 35 */ 36 37/* 38 39@deftypefn Supplement {long int} random (void) 40@deftypefnx Supplement void srandom (unsigned int @var{seed}) 41@deftypefnx Supplement void* initstate (unsigned int @var{seed}, @ 42 void *@var{arg_state}, unsigned long @var{n}) 43@deftypefnx Supplement void* setstate (void *@var{arg_state}) 44 45Random number functions. @code{random} returns a random number in the 46range 0 to @code{LONG_MAX}. @code{srandom} initializes the random 47number generator to some starting point determined by @var{seed} 48(else, the values returned by @code{random} are always the same for each 49run of the program). @code{initstate} and @code{setstate} allow fine-grained 50control over the state of the random number generator. 51 52@end deftypefn 53 54*/ 55 56#include <errno.h> 57 58#if 0 59 60#include <ansidecl.h> 61#include <limits.h> 62#include <stddef.h> 63#include <stdlib.h> 64 65#else 66 67#define ULONG_MAX ((unsigned long)(~0L)) /* 0xFFFFFFFF for 32-bits */ 68#define LONG_MAX ((long)(ULONG_MAX >> 1)) /* 0x7FFFFFFF for 32-bits*/ 69 70#ifdef __STDC__ 71# ifndef NULL 72# define NULL (void *) 0 73# endif 74#else 75# ifndef NULL 76# define NULL (void *) 0 77# endif 78#endif 79 80#endif 81 82long int random (void); 83 84/* An improved random number generation package. In addition to the standard 85 rand()/srand() like interface, this package also has a special state info 86 interface. The initstate() routine is called with a seed, an array of 87 bytes, and a count of how many bytes are being passed in; this array is 88 then initialized to contain information for random number generation with 89 that much state information. Good sizes for the amount of state 90 information are 32, 64, 128, and 256 bytes. The state can be switched by 91 calling the setstate() function with the same array as was initiallized 92 with initstate(). By default, the package runs with 128 bytes of state 93 information and generates far better random numbers than a linear 94 congruential generator. If the amount of state information is less than 95 32 bytes, a simple linear congruential R.N.G. is used. Internally, the 96 state information is treated as an array of longs; the zeroeth element of 97 the array is the type of R.N.G. being used (small integer); the remainder 98 of the array is the state information for the R.N.G. Thus, 32 bytes of 99 state information will give 7 longs worth of state information, which will 100 allow a degree seven polynomial. (Note: The zeroeth word of state 101 information also has some other information stored in it; see setstate 102 for details). The random number generation technique is a linear feedback 103 shift register approach, employing trinomials (since there are fewer terms 104 to sum up that way). In this approach, the least significant bit of all 105 the numbers in the state table will act as a linear feedback shift register, 106 and will have period 2^deg - 1 (where deg is the degree of the polynomial 107 being used, assuming that the polynomial is irreducible and primitive). 108 The higher order bits will have longer periods, since their values are 109 also influenced by pseudo-random carries out of the lower bits. The 110 total period of the generator is approximately deg*(2**deg - 1); thus 111 doubling the amount of state information has a vast influence on the 112 period of the generator. Note: The deg*(2**deg - 1) is an approximation 113 only good for large deg, when the period of the shift register is the 114 dominant factor. With deg equal to seven, the period is actually much 115 longer than the 7*(2**7 - 1) predicted by this formula. */ 116 117 118 119/* For each of the currently supported random number generators, we have a 120 break value on the amount of state information (you need at least thi 121 bytes of state info to support this random number generator), a degree for 122 the polynomial (actually a trinomial) that the R.N.G. is based on, and 123 separation between the two lower order coefficients of the trinomial. */ 124 125/* Linear congruential. */ 126#define TYPE_0 0 127#define BREAK_0 8 128#define DEG_0 0 129#define SEP_0 0 130 131/* x**7 + x**3 + 1. */ 132#define TYPE_1 1 133#define BREAK_1 32 134#define DEG_1 7 135#define SEP_1 3 136 137/* x**15 + x + 1. */ 138#define TYPE_2 2 139#define BREAK_2 64 140#define DEG_2 15 141#define SEP_2 1 142 143/* x**31 + x**3 + 1. */ 144#define TYPE_3 3 145#define BREAK_3 128 146#define DEG_3 31 147#define SEP_3 3 148 149/* x**63 + x + 1. */ 150#define TYPE_4 4 151#define BREAK_4 256 152#define DEG_4 63 153#define SEP_4 1 154 155 156/* Array versions of the above information to make code run faster. 157 Relies on fact that TYPE_i == i. */ 158 159#define MAX_TYPES 5 /* Max number of types above. */ 160 161static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 162static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 163 164 165 166/* Initially, everything is set up as if from: 167 initstate(1, randtbl, 128); 168 Note that this initialization takes advantage of the fact that srandom 169 advances the front and rear pointers 10*rand_deg times, and hence the 170 rear pointer which starts at 0 will also end up at zero; thus the zeroeth 171 element of the state information, which contains info about the current 172 position of the rear pointer is just 173 (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3. */ 174 175static long int randtbl[DEG_3 + 1] = 176 { TYPE_3, 177 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 178 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb, 179 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 180 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 181 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7, 182 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 183 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 184 0xf5ad9d0e, 0x8999220b, 0x27fb47b9 185 }; 186 187/* FPTR and RPTR are two pointers into the state info, a front and a rear 188 pointer. These two pointers are always rand_sep places aparts, as they 189 cycle through the state information. (Yes, this does mean we could get 190 away with just one pointer, but the code for random is more efficient 191 this way). The pointers are left positioned as they would be from the call: 192 initstate(1, randtbl, 128); 193 (The position of the rear pointer, rptr, is really 0 (as explained above 194 in the initialization of randtbl) because the state table pointer is set 195 to point to randtbl[1] (as explained below).) */ 196 197static long int *fptr = &randtbl[SEP_3 + 1]; 198static long int *rptr = &randtbl[1]; 199 200 201 202/* The following things are the pointer to the state information table, 203 the type of the current generator, the degree of the current polynomial 204 being used, and the separation between the two pointers. 205 Note that for efficiency of random, we remember the first location of 206 the state information, not the zeroeth. Hence it is valid to access 207 state[-1], which is used to store the type of the R.N.G. 208 Also, we remember the last location, since this is more efficient than 209 indexing every time to find the address of the last element to see if 210 the front and rear pointers have wrapped. */ 211 212static long int *state = &randtbl[1]; 213 214static int rand_type = TYPE_3; 215static int rand_deg = DEG_3; 216static int rand_sep = SEP_3; 217 218static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])]; 219 220/* Initialize the random number generator based on the given seed. If the 221 type is the trivial no-state-information type, just remember the seed. 222 Otherwise, initializes state[] based on the given "seed" via a linear 223 congruential generator. Then, the pointers are set to known locations 224 that are exactly rand_sep places apart. Lastly, it cycles the state 225 information a given number of times to get rid of any initial dependencies 226 introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 227 for default usage relies on values produced by this routine. */ 228void 229srandom (unsigned int x) 230{ 231 state[0] = x; 232 if (rand_type != TYPE_0) 233 { 234 register long int i; 235 for (i = 1; i < rand_deg; ++i) 236 state[i] = (1103515145 * state[i - 1]) + 12345; 237 fptr = &state[rand_sep]; 238 rptr = &state[0]; 239 for (i = 0; i < 10 * rand_deg; ++i) 240 random(); 241 } 242} 243 244/* Initialize the state information in the given array of N bytes for 245 future random number generation. Based on the number of bytes we 246 are given, and the break values for the different R.N.G.'s, we choose 247 the best (largest) one we can and set things up for it. srandom is 248 then called to initialize the state information. Note that on return 249 from srandom, we set state[-1] to be the type multiplexed with the current 250 value of the rear pointer; this is so successive calls to initstate won't 251 lose this information and will be able to restart with setstate. 252 Note: The first thing we do is save the current state, if any, just like 253 setstate so that it doesn't matter when initstate is called. 254 Returns a pointer to the old state. */ 255void * 256initstate (unsigned int seed, void *arg_state, unsigned long n) 257{ 258 void *ostate = (void *) &state[-1]; 259 260 if (rand_type == TYPE_0) 261 state[-1] = rand_type; 262 else 263 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 264 if (n < BREAK_1) 265 { 266 if (n < BREAK_0) 267 { 268 errno = EINVAL; 269 return NULL; 270 } 271 rand_type = TYPE_0; 272 rand_deg = DEG_0; 273 rand_sep = SEP_0; 274 } 275 else if (n < BREAK_2) 276 { 277 rand_type = TYPE_1; 278 rand_deg = DEG_1; 279 rand_sep = SEP_1; 280 } 281 else if (n < BREAK_3) 282 { 283 rand_type = TYPE_2; 284 rand_deg = DEG_2; 285 rand_sep = SEP_2; 286 } 287 else if (n < BREAK_4) 288 { 289 rand_type = TYPE_3; 290 rand_deg = DEG_3; 291 rand_sep = SEP_3; 292 } 293 else 294 { 295 rand_type = TYPE_4; 296 rand_deg = DEG_4; 297 rand_sep = SEP_4; 298 } 299 300 state = &((long int *) arg_state)[1]; /* First location. */ 301 /* Must set END_PTR before srandom. */ 302 end_ptr = &state[rand_deg]; 303 srandom(seed); 304 if (rand_type == TYPE_0) 305 state[-1] = rand_type; 306 else 307 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 308 309 return ostate; 310} 311 312/* Restore the state from the given state array. 313 Note: It is important that we also remember the locations of the pointers 314 in the current state information, and restore the locations of the pointers 315 from the old state information. This is done by multiplexing the pointer 316 location into the zeroeth word of the state information. Note that due 317 to the order in which things are done, it is OK to call setstate with the 318 same state as the current state 319 Returns a pointer to the old state information. */ 320 321void * 322setstate (void *arg_state) 323{ 324 register long int *new_state = (long int *) arg_state; 325 register int type = new_state[0] % MAX_TYPES; 326 register int rear = new_state[0] / MAX_TYPES; 327 void *ostate = (void *) &state[-1]; 328 329 if (rand_type == TYPE_0) 330 state[-1] = rand_type; 331 else 332 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 333 334 switch (type) 335 { 336 case TYPE_0: 337 case TYPE_1: 338 case TYPE_2: 339 case TYPE_3: 340 case TYPE_4: 341 rand_type = type; 342 rand_deg = degrees[type]; 343 rand_sep = seps[type]; 344 break; 345 default: 346 /* State info munged. */ 347 errno = EINVAL; 348 return NULL; 349 } 350 351 state = &new_state[1]; 352 if (rand_type != TYPE_0) 353 { 354 rptr = &state[rear]; 355 fptr = &state[(rear + rand_sep) % rand_deg]; 356 } 357 /* Set end_ptr too. */ 358 end_ptr = &state[rand_deg]; 359 360 return ostate; 361} 362 363/* If we are using the trivial TYPE_0 R.N.G., just do the old linear 364 congruential bit. Otherwise, we do our fancy trinomial stuff, which is the 365 same in all ther other cases due to all the global variables that have been 366 set up. The basic operation is to add the number at the rear pointer into 367 the one at the front pointer. Then both pointers are advanced to the next 368 location cyclically in the table. The value returned is the sum generated, 369 reduced to 31 bits by throwing away the "least random" low bit. 370 Note: The code takes advantage of the fact that both the front and 371 rear pointers can't wrap on the same call by not testing the rear 372 pointer if the front one has wrapped. Returns a 31-bit random number. */ 373 374long int 375random (void) 376{ 377 if (rand_type == TYPE_0) 378 { 379 state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX; 380 return state[0]; 381 } 382 else 383 { 384 long int i; 385 *fptr += *rptr; 386 /* Chucking least random bit. */ 387 i = (*fptr >> 1) & LONG_MAX; 388 ++fptr; 389 if (fptr >= end_ptr) 390 { 391 fptr = state; 392 ++rptr; 393 } 394 else 395 { 396 ++rptr; 397 if (rptr >= end_ptr) 398 rptr = state; 399 } 400 return i; 401 } 402} 403