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 [rescinded 22 July 1999] 14 * 4.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}, void *@var{arg_state}, unsigned long @var{n}) 42@deftypefnx Supplement void* setstate (void *@var{arg_state}) 43 44Random number functions. @code{random} returns a random number in the 45range 0 to @code{LONG_MAX}. @code{srandom} initializes the random 46number generator to some starting point determined by @var{seed} 47(else, the values returned by @code{random} are always the same for each 48run of the program). @code{initstate} and @code{setstate} allow fine-grained 49control over the state of the random number generator. 50 51@end deftypefn 52 53*/ 54 55#include <errno.h> 56 57#if 0 58 59#include <ansidecl.h> 60#include <limits.h> 61#include <stddef.h> 62#include <stdlib.h> 63 64#else 65 66#define ULONG_MAX ((unsigned long)(~0L)) /* 0xFFFFFFFF for 32-bits */ 67#define LONG_MAX ((long)(ULONG_MAX >> 1)) /* 0x7FFFFFFF for 32-bits*/ 68 69#ifdef __STDC__ 70# define PTR void * 71# ifndef NULL 72# define NULL (void *) 0 73# endif 74#else 75# define PTR char * 76# ifndef NULL 77# define NULL (void *) 0 78# endif 79#endif 80 81#endif 82 83long int random (); 84 85/* An improved random number generation package. In addition to the standard 86 rand()/srand() like interface, this package also has a special state info 87 interface. The initstate() routine is called with a seed, an array of 88 bytes, and a count of how many bytes are being passed in; this array is 89 then initialized to contain information for random number generation with 90 that much state information. Good sizes for the amount of state 91 information are 32, 64, 128, and 256 bytes. The state can be switched by 92 calling the setstate() function with the same array as was initiallized 93 with initstate(). By default, the package runs with 128 bytes of state 94 information and generates far better random numbers than a linear 95 congruential generator. If the amount of state information is less than 96 32 bytes, a simple linear congruential R.N.G. is used. Internally, the 97 state information is treated as an array of longs; the zeroeth element of 98 the array is the type of R.N.G. being used (small integer); the remainder 99 of the array is the state information for the R.N.G. Thus, 32 bytes of 100 state information will give 7 longs worth of state information, which will 101 allow a degree seven polynomial. (Note: The zeroeth word of state 102 information also has some other information stored in it; see setstate 103 for details). The random number generation technique is a linear feedback 104 shift register approach, employing trinomials (since there are fewer terms 105 to sum up that way). In this approach, the least significant bit of all 106 the numbers in the state table will act as a linear feedback shift register, 107 and will have period 2^deg - 1 (where deg is the degree of the polynomial 108 being used, assuming that the polynomial is irreducible and primitive). 109 The higher order bits will have longer periods, since their values are 110 also influenced by pseudo-random carries out of the lower bits. The 111 total period of the generator is approximately deg*(2**deg - 1); thus 112 doubling the amount of state information has a vast influence on the 113 period of the generator. Note: The deg*(2**deg - 1) is an approximation 114 only good for large deg, when the period of the shift register is the 115 dominant factor. With deg equal to seven, the period is actually much 116 longer than the 7*(2**7 - 1) predicted by this formula. */ 117 118 119 120/* For each of the currently supported random number generators, we have a 121 break value on the amount of state information (you need at least thi 122 bytes of state info to support this random number generator), a degree for 123 the polynomial (actually a trinomial) that the R.N.G. is based on, and 124 separation between the two lower order coefficients of the trinomial. */ 125 126/* Linear congruential. */ 127#define TYPE_0 0 128#define BREAK_0 8 129#define DEG_0 0 130#define SEP_0 0 131 132/* x**7 + x**3 + 1. */ 133#define TYPE_1 1 134#define BREAK_1 32 135#define DEG_1 7 136#define SEP_1 3 137 138/* x**15 + x + 1. */ 139#define TYPE_2 2 140#define BREAK_2 64 141#define DEG_2 15 142#define SEP_2 1 143 144/* x**31 + x**3 + 1. */ 145#define TYPE_3 3 146#define BREAK_3 128 147#define DEG_3 31 148#define SEP_3 3 149 150/* x**63 + x + 1. */ 151#define TYPE_4 4 152#define BREAK_4 256 153#define DEG_4 63 154#define SEP_4 1 155 156 157/* Array versions of the above information to make code run faster. 158 Relies on fact that TYPE_i == i. */ 159 160#define MAX_TYPES 5 /* Max number of types above. */ 161 162static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 163static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 164 165 166 167/* Initially, everything is set up as if from: 168 initstate(1, randtbl, 128); 169 Note that this initialization takes advantage of the fact that srandom 170 advances the front and rear pointers 10*rand_deg times, and hence the 171 rear pointer which starts at 0 will also end up at zero; thus the zeroeth 172 element of the state information, which contains info about the current 173 position of the rear pointer is just 174 (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3. */ 175 176static long int randtbl[DEG_3 + 1] = 177 { TYPE_3, 178 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 179 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb, 180 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 181 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 182 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7, 183 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 184 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 185 0xf5ad9d0e, 0x8999220b, 0x27fb47b9 186 }; 187 188/* FPTR and RPTR are two pointers into the state info, a front and a rear 189 pointer. These two pointers are always rand_sep places aparts, as they 190 cycle through the state information. (Yes, this does mean we could get 191 away with just one pointer, but the code for random is more efficient 192 this way). The pointers are left positioned as they would be from the call: 193 initstate(1, randtbl, 128); 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 198static long int *fptr = &randtbl[SEP_3 + 1]; 199static long int *rptr = &randtbl[1]; 200 201 202 203/* The following things are the pointer to the state information table, 204 the type of the current generator, the degree of the current polynomial 205 being used, and the separation between the two pointers. 206 Note that for efficiency of random, we remember the first location of 207 the state information, not the zeroeth. Hence it is valid to access 208 state[-1], which is used to store the type of the R.N.G. 209 Also, we remember the last location, since this is more efficient than 210 indexing every time to find the address of the last element to see if 211 the front and rear pointers have wrapped. */ 212 213static long int *state = &randtbl[1]; 214 215static int rand_type = TYPE_3; 216static int rand_deg = DEG_3; 217static int rand_sep = SEP_3; 218 219static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])]; 220 221/* Initialize the random number generator based on the given seed. If the 222 type is the trivial no-state-information type, just remember the seed. 223 Otherwise, initializes state[] based on the given "seed" via a linear 224 congruential generator. Then, the pointers are set to known locations 225 that are exactly rand_sep places apart. Lastly, it cycles the state 226 information a given number of times to get rid of any initial dependencies 227 introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 228 for default usage relies on values produced by this routine. */ 229void 230srandom (x) 231 unsigned int x; 232{ 233 state[0] = x; 234 if (rand_type != TYPE_0) 235 { 236 register long int i; 237 for (i = 1; i < rand_deg; ++i) 238 state[i] = (1103515145 * state[i - 1]) + 12345; 239 fptr = &state[rand_sep]; 240 rptr = &state[0]; 241 for (i = 0; i < 10 * rand_deg; ++i) 242 random(); 243 } 244} 245 246/* Initialize the state information in the given array of N bytes for 247 future random number generation. Based on the number of bytes we 248 are given, and the break values for the different R.N.G.'s, we choose 249 the best (largest) one we can and set things up for it. srandom is 250 then called to initialize the state information. Note that on return 251 from srandom, we set state[-1] to be the type multiplexed with the current 252 value of the rear pointer; this is so successive calls to initstate won't 253 lose this information and will be able to restart with setstate. 254 Note: The first thing we do is save the current state, if any, just like 255 setstate so that it doesn't matter when initstate is called. 256 Returns a pointer to the old state. */ 257PTR 258initstate (seed, arg_state, n) 259 unsigned int seed; 260 PTR arg_state; 261 unsigned long n; 262{ 263 PTR ostate = (PTR) &state[-1]; 264 265 if (rand_type == TYPE_0) 266 state[-1] = rand_type; 267 else 268 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 269 if (n < BREAK_1) 270 { 271 if (n < BREAK_0) 272 { 273 errno = EINVAL; 274 return NULL; 275 } 276 rand_type = TYPE_0; 277 rand_deg = DEG_0; 278 rand_sep = SEP_0; 279 } 280 else if (n < BREAK_2) 281 { 282 rand_type = TYPE_1; 283 rand_deg = DEG_1; 284 rand_sep = SEP_1; 285 } 286 else if (n < BREAK_3) 287 { 288 rand_type = TYPE_2; 289 rand_deg = DEG_2; 290 rand_sep = SEP_2; 291 } 292 else if (n < BREAK_4) 293 { 294 rand_type = TYPE_3; 295 rand_deg = DEG_3; 296 rand_sep = SEP_3; 297 } 298 else 299 { 300 rand_type = TYPE_4; 301 rand_deg = DEG_4; 302 rand_sep = SEP_4; 303 } 304 305 state = &((long int *) arg_state)[1]; /* First location. */ 306 /* Must set END_PTR before srandom. */ 307 end_ptr = &state[rand_deg]; 308 srandom(seed); 309 if (rand_type == TYPE_0) 310 state[-1] = rand_type; 311 else 312 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 313 314 return ostate; 315} 316 317/* Restore the state from the given state array. 318 Note: It is important that we also remember the locations of the pointers 319 in the current state information, and restore the locations of the pointers 320 from the old state information. This is done by multiplexing the pointer 321 location into the zeroeth word of the state information. Note that due 322 to the order in which things are done, it is OK to call setstate with the 323 same state as the current state 324 Returns a pointer to the old state information. */ 325 326PTR 327setstate (arg_state) 328 PTR arg_state; 329{ 330 register long int *new_state = (long int *) arg_state; 331 register int type = new_state[0] % MAX_TYPES; 332 register int rear = new_state[0] / MAX_TYPES; 333 PTR ostate = (PTR) &state[-1]; 334 335 if (rand_type == TYPE_0) 336 state[-1] = rand_type; 337 else 338 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 339 340 switch (type) 341 { 342 case TYPE_0: 343 case TYPE_1: 344 case TYPE_2: 345 case TYPE_3: 346 case TYPE_4: 347 rand_type = type; 348 rand_deg = degrees[type]; 349 rand_sep = seps[type]; 350 break; 351 default: 352 /* State info munged. */ 353 errno = EINVAL; 354 return NULL; 355 } 356 357 state = &new_state[1]; 358 if (rand_type != TYPE_0) 359 { 360 rptr = &state[rear]; 361 fptr = &state[(rear + rand_sep) % rand_deg]; 362 } 363 /* Set end_ptr too. */ 364 end_ptr = &state[rand_deg]; 365 366 return ostate; 367} 368 369/* If we are using the trivial TYPE_0 R.N.G., just do the old linear 370 congruential bit. Otherwise, we do our fancy trinomial stuff, which is the 371 same in all ther other cases due to all the global variables that have been 372 set up. The basic operation is to add the number at the rear pointer into 373 the one at the front pointer. Then both pointers are advanced to the next 374 location cyclically in the table. The value returned is the sum generated, 375 reduced to 31 bits by throwing away the "least random" low bit. 376 Note: The code takes advantage of the fact that both the front and 377 rear pointers can't wrap on the same call by not testing the rear 378 pointer if the front one has wrapped. Returns a 31-bit random number. */ 379 380long int 381random () 382{ 383 if (rand_type == TYPE_0) 384 { 385 state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX; 386 return state[0]; 387 } 388 else 389 { 390 long int i; 391 *fptr += *rptr; 392 /* Chucking least random bit. */ 393 i = (*fptr >> 1) & LONG_MAX; 394 ++fptr; 395 if (fptr >= end_ptr) 396 { 397 fptr = state; 398 ++rptr; 399 } 400 else 401 { 402 ++rptr; 403 if (rptr >= end_ptr) 404 rptr = state; 405 } 406 return i; 407 } 408} 409