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 [rescinded 22 July 1999] 14 * 4.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 (void); 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 (unsigned int x) 231{ 232 state[0] = x; 233 if (rand_type != TYPE_0) 234 { 235 register long int i; 236 for (i = 1; i < rand_deg; ++i) 237 state[i] = (1103515145 * state[i - 1]) + 12345; 238 fptr = &state[rand_sep]; 239 rptr = &state[0]; 240 for (i = 0; i < 10 * rand_deg; ++i) 241 random(); 242 } 243} 244 245/* Initialize the state information in the given array of N bytes for 246 future random number generation. Based on the number of bytes we 247 are given, and the break values for the different R.N.G.'s, we choose 248 the best (largest) one we can and set things up for it. srandom is 249 then called to initialize the state information. Note that on return 250 from srandom, we set state[-1] to be the type multiplexed with the current 251 value of the rear pointer; this is so successive calls to initstate won't 252 lose this information and will be able to restart with setstate. 253 Note: The first thing we do is save the current state, if any, just like 254 setstate so that it doesn't matter when initstate is called. 255 Returns a pointer to the old state. */ 256PTR 257initstate (unsigned int seed, PTR arg_state, unsigned long n) 258{ 259 PTR ostate = (PTR) &state[-1]; 260 261 if (rand_type == TYPE_0) 262 state[-1] = rand_type; 263 else 264 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 265 if (n < BREAK_1) 266 { 267 if (n < BREAK_0) 268 { 269 errno = EINVAL; 270 return NULL; 271 } 272 rand_type = TYPE_0; 273 rand_deg = DEG_0; 274 rand_sep = SEP_0; 275 } 276 else if (n < BREAK_2) 277 { 278 rand_type = TYPE_1; 279 rand_deg = DEG_1; 280 rand_sep = SEP_1; 281 } 282 else if (n < BREAK_3) 283 { 284 rand_type = TYPE_2; 285 rand_deg = DEG_2; 286 rand_sep = SEP_2; 287 } 288 else if (n < BREAK_4) 289 { 290 rand_type = TYPE_3; 291 rand_deg = DEG_3; 292 rand_sep = SEP_3; 293 } 294 else 295 { 296 rand_type = TYPE_4; 297 rand_deg = DEG_4; 298 rand_sep = SEP_4; 299 } 300 301 state = &((long int *) arg_state)[1]; /* First location. */ 302 /* Must set END_PTR before srandom. */ 303 end_ptr = &state[rand_deg]; 304 srandom(seed); 305 if (rand_type == TYPE_0) 306 state[-1] = rand_type; 307 else 308 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 309 310 return ostate; 311} 312 313/* Restore the state from the given state array. 314 Note: It is important that we also remember the locations of the pointers 315 in the current state information, and restore the locations of the pointers 316 from the old state information. This is done by multiplexing the pointer 317 location into the zeroeth word of the state information. Note that due 318 to the order in which things are done, it is OK to call setstate with the 319 same state as the current state 320 Returns a pointer to the old state information. */ 321 322PTR 323setstate (PTR arg_state) 324{ 325 register long int *new_state = (long int *) arg_state; 326 register int type = new_state[0] % MAX_TYPES; 327 register int rear = new_state[0] / MAX_TYPES; 328 PTR ostate = (PTR) &state[-1]; 329 330 if (rand_type == TYPE_0) 331 state[-1] = rand_type; 332 else 333 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; 334 335 switch (type) 336 { 337 case TYPE_0: 338 case TYPE_1: 339 case TYPE_2: 340 case TYPE_3: 341 case TYPE_4: 342 rand_type = type; 343 rand_deg = degrees[type]; 344 rand_sep = seps[type]; 345 break; 346 default: 347 /* State info munged. */ 348 errno = EINVAL; 349 return NULL; 350 } 351 352 state = &new_state[1]; 353 if (rand_type != TYPE_0) 354 { 355 rptr = &state[rear]; 356 fptr = &state[(rear + rand_sep) % rand_deg]; 357 } 358 /* Set end_ptr too. */ 359 end_ptr = &state[rand_deg]; 360 361 return ostate; 362} 363 364/* If we are using the trivial TYPE_0 R.N.G., just do the old linear 365 congruential bit. Otherwise, we do our fancy trinomial stuff, which is the 366 same in all ther other cases due to all the global variables that have been 367 set up. The basic operation is to add the number at the rear pointer into 368 the one at the front pointer. Then both pointers are advanced to the next 369 location cyclically in the table. The value returned is the sum generated, 370 reduced to 31 bits by throwing away the "least random" low bit. 371 Note: The code takes advantage of the fact that both the front and 372 rear pointers can't wrap on the same call by not testing the rear 373 pointer if the front one has wrapped. Returns a 31-bit random number. */ 374 375long int 376random (void) 377{ 378 if (rand_type == TYPE_0) 379 { 380 state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX; 381 return state[0]; 382 } 383 else 384 { 385 long int i; 386 *fptr += *rptr; 387 /* Chucking least random bit. */ 388 i = (*fptr >> 1) & LONG_MAX; 389 ++fptr; 390 if (fptr >= end_ptr) 391 { 392 fptr = state; 393 ++rptr; 394 } 395 else 396 { 397 ++rptr; 398 if (rptr >= end_ptr) 399 rptr = state; 400 } 401 return i; 402 } 403} 404