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 are permitted 6 * provided that the above copyright notice and this paragraph are 7 * duplicated in all such forms and that any documentation, 8 * advertising materials, and other materials related to such 9 * distribution and use acknowledge that the software was developed 10 * by the University of California, Berkeley. The name of the 11 * University may not be used to endorse or promote products derived 12 * from this software without specific prior written permission. 13 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR 14 * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED 15 * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE. 16 */ 17 18 #if defined(LIBC_SCCS) && !defined(lint) 19 static char sccsid[] = "@(#)random.c 5.6 (Berkeley) 01/02/90"; 20 #endif /* LIBC_SCCS and not lint */ 21 22 #include <stdio.h> 23 24 /* 25 * random.c: 26 * An improved random number generation package. In addition to the standard 27 * rand()/srand() like interface, this package also has a special state info 28 * interface. The initstate() routine is called with a seed, an array of 29 * bytes, and a count of how many bytes are being passed in; this array is then 30 * initialized to contain information for random number generation with that 31 * much state information. Good sizes for the amount of state information are 32 * 32, 64, 128, and 256 bytes. The state can be switched by calling the 33 * setstate() routine with the same array as was initiallized with initstate(). 34 * By default, the package runs with 128 bytes of state information and 35 * generates far better random numbers than a linear congruential generator. 36 * If the amount of state information is less than 32 bytes, a simple linear 37 * congruential R.N.G. is used. 38 * Internally, the state information is treated as an array of longs; the 39 * zeroeth element of the array is the type of R.N.G. being used (small 40 * integer); the remainder of the array is the state information for the 41 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of 42 * state information, which will allow a degree seven polynomial. (Note: the 43 * zeroeth word of state information also has some other information stored 44 * in it -- see setstate() for details). 45 * The random number generation technique is a linear feedback shift register 46 * approach, employing trinomials (since there are fewer terms to sum up that 47 * way). In this approach, the least significant bit of all the numbers in 48 * the state table will act as a linear feedback shift register, and will have 49 * period 2^deg - 1 (where deg is the degree of the polynomial being used, 50 * assuming that the polynomial is irreducible and primitive). The higher 51 * order bits will have longer periods, since their values are also influenced 52 * by pseudo-random carries out of the lower bits. The total period of the 53 * generator is approximately deg*(2**deg - 1); thus doubling the amount of 54 * state information has a vast influence on the period of the generator. 55 * Note: the deg*(2**deg - 1) is an approximation only good for large deg, 56 * when the period of the shift register is the dominant factor. With deg 57 * equal to seven, the period is actually much longer than the 7*(2**7 - 1) 58 * predicted by this formula. 59 */ 60 61 62 63 /* 64 * For each of the currently supported random number generators, we have a 65 * break value on the amount of state information (you need at least this 66 * many bytes of state info to support this random number generator), a degree 67 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 68 * the separation between the two lower order coefficients of the trinomial. 69 */ 70 71 #define TYPE_0 0 /* linear congruential */ 72 #define BREAK_0 8 73 #define DEG_0 0 74 #define SEP_0 0 75 76 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 77 #define BREAK_1 32 78 #define DEG_1 7 79 #define SEP_1 3 80 81 #define TYPE_2 2 /* x**15 + x + 1 */ 82 #define BREAK_2 64 83 #define DEG_2 15 84 #define SEP_2 1 85 86 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 87 #define BREAK_3 128 88 #define DEG_3 31 89 #define SEP_3 3 90 91 #define TYPE_4 4 /* x**63 + x + 1 */ 92 #define BREAK_4 256 93 #define DEG_4 63 94 #define SEP_4 1 95 96 97 /* 98 * Array versions of the above information to make code run faster -- relies 99 * on fact that TYPE_i == i. 100 */ 101 102 #define MAX_TYPES 5 /* max number of types above */ 103 104 static int degrees[ MAX_TYPES ] = { DEG_0, DEG_1, DEG_2, 105 DEG_3, DEG_4 }; 106 107 static int seps[ MAX_TYPES ] = { SEP_0, SEP_1, SEP_2, 108 SEP_3, SEP_4 }; 109 110 111 112 /* 113 * Initially, everything is set up as if from : 114 * initstate( 1, &randtbl, 128 ); 115 * Note that this initialization takes advantage of the fact that srandom() 116 * advances the front and rear pointers 10*rand_deg times, and hence the 117 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 118 * element of the state information, which contains info about the current 119 * position of the rear pointer is just 120 * MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3. 121 */ 122 123 static long randtbl[ DEG_3 + 1 ] = { TYPE_3, 124 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 125 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb, 126 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 127 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 128 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7, 129 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 130 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 131 0xf5ad9d0e, 0x8999220b, 0x27fb47b9 }; 132 133 /* 134 * fptr and rptr are two pointers into the state info, a front and a rear 135 * pointer. These two pointers are always rand_sep places aparts, as they cycle 136 * cyclically through the state information. (Yes, this does mean we could get 137 * away with just one pointer, but the code for random() is more efficient this 138 * way). The pointers are left positioned as they would be from the call 139 * initstate( 1, randtbl, 128 ) 140 * (The position of the rear pointer, rptr, is really 0 (as explained above 141 * in the initialization of randtbl) because the state table pointer is set 142 * to point to randtbl[1] (as explained below). 143 */ 144 145 static long *fptr = &randtbl[ SEP_3 + 1 ]; 146 static long *rptr = &randtbl[ 1 ]; 147 148 149 150 /* 151 * The following things are the pointer to the state information table, 152 * the type of the current generator, the degree of the current polynomial 153 * being used, and the separation between the two pointers. 154 * Note that for efficiency of random(), we remember the first location of 155 * the state information, not the zeroeth. Hence it is valid to access 156 * state[-1], which is used to store the type of the R.N.G. 157 * Also, we remember the last location, since this is more efficient than 158 * indexing every time to find the address of the last element to see if 159 * the front and rear pointers have wrapped. 160 */ 161 162 static long *state = &randtbl[ 1 ]; 163 164 static int rand_type = TYPE_3; 165 static int rand_deg = DEG_3; 166 static int rand_sep = SEP_3; 167 168 static long *end_ptr = &randtbl[ DEG_3 + 1 ]; 169 170 171 172 /* 173 * srandom: 174 * Initialize the random number generator based on the given seed. If the 175 * type is the trivial no-state-information type, just remember the seed. 176 * Otherwise, initializes state[] based on the given "seed" via a linear 177 * congruential generator. Then, the pointers are set to known locations 178 * that are exactly rand_sep places apart. Lastly, it cycles the state 179 * information a given number of times to get rid of any initial dependencies 180 * introduced by the L.C.R.N.G. 181 * Note that the initialization of randtbl[] for default usage relies on 182 * values produced by this routine. 183 */ 184 185 srandom( x ) 186 187 unsigned x; 188 { 189 register int i, j; 190 long random(); 191 192 if( rand_type == TYPE_0 ) { 193 state[ 0 ] = x; 194 } 195 else { 196 j = 1; 197 state[ 0 ] = x; 198 for( i = 1; i < rand_deg; i++ ) { 199 state[i] = 1103515245*state[i - 1] + 12345; 200 } 201 fptr = &state[ rand_sep ]; 202 rptr = &state[ 0 ]; 203 for( i = 0; i < 10*rand_deg; i++ ) random(); 204 } 205 } 206 207 208 209 /* 210 * initstate: 211 * Initialize the state information in the given array of n bytes for 212 * future random number generation. Based on the number of bytes we 213 * are given, and the break values for the different R.N.G.'s, we choose 214 * the best (largest) one we can and set things up for it. srandom() is 215 * then called to initialize the state information. 216 * Note that on return from srandom(), we set state[-1] to be the type 217 * multiplexed with the current value of the rear pointer; this is so 218 * successive calls to initstate() won't lose this information and will 219 * be able to restart with setstate(). 220 * Note: the first thing we do is save the current state, if any, just like 221 * setstate() so that it doesn't matter when initstate is called. 222 * Returns a pointer to the old state. 223 */ 224 225 char * 226 initstate( seed, arg_state, n ) 227 228 unsigned seed; /* seed for R. N. G. */ 229 char *arg_state; /* pointer to state array */ 230 int n; /* # bytes of state info */ 231 { 232 register char *ostate = (char *)( &state[ -1 ] ); 233 234 if( rand_type == TYPE_0 ) state[ -1 ] = rand_type; 235 else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type; 236 if( n < BREAK_1 ) { 237 if( n < BREAK_0 ) { 238 fprintf( stderr, "initstate: not enough state (%d bytes); ignored.\n", n ); 239 return 0; 240 } 241 rand_type = TYPE_0; 242 rand_deg = DEG_0; 243 rand_sep = SEP_0; 244 } 245 else { 246 if( n < BREAK_2 ) { 247 rand_type = TYPE_1; 248 rand_deg = DEG_1; 249 rand_sep = SEP_1; 250 } 251 else { 252 if( n < BREAK_3 ) { 253 rand_type = TYPE_2; 254 rand_deg = DEG_2; 255 rand_sep = SEP_2; 256 } 257 else { 258 if( n < BREAK_4 ) { 259 rand_type = TYPE_3; 260 rand_deg = DEG_3; 261 rand_sep = SEP_3; 262 } 263 else { 264 rand_type = TYPE_4; 265 rand_deg = DEG_4; 266 rand_sep = SEP_4; 267 } 268 } 269 } 270 } 271 state = &( ( (long *)arg_state )[1] ); /* first location */ 272 end_ptr = &state[ rand_deg ]; /* must set end_ptr before srandom */ 273 srandom( seed ); 274 if( rand_type == TYPE_0 ) state[ -1 ] = rand_type; 275 else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type; 276 return( ostate ); 277 } 278 279 280 281 /* 282 * setstate: 283 * Restore the state from the given state array. 284 * Note: it is important that we also remember the locations of the pointers 285 * in the current state information, and restore the locations of the pointers 286 * from the old state information. This is done by multiplexing the pointer 287 * location into the zeroeth word of the state information. 288 * Note that due to the order in which things are done, it is OK to call 289 * setstate() with the same state as the current state. 290 * Returns a pointer to the old state information. 291 */ 292 293 char * 294 setstate( arg_state ) 295 296 char *arg_state; 297 { 298 register long *new_state = (long *)arg_state; 299 register int type = new_state[0]%MAX_TYPES; 300 register int rear = new_state[0]/MAX_TYPES; 301 char *ostate = (char *)( &state[ -1 ] ); 302 303 if( rand_type == TYPE_0 ) state[ -1 ] = rand_type; 304 else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type; 305 switch( type ) { 306 case TYPE_0: 307 case TYPE_1: 308 case TYPE_2: 309 case TYPE_3: 310 case TYPE_4: 311 rand_type = type; 312 rand_deg = degrees[ type ]; 313 rand_sep = seps[ type ]; 314 break; 315 316 default: 317 fprintf( stderr, "setstate: state info has been munged; not changed.\n" ); 318 } 319 state = &new_state[ 1 ]; 320 if( rand_type != TYPE_0 ) { 321 rptr = &state[ rear ]; 322 fptr = &state[ (rear + rand_sep)%rand_deg ]; 323 } 324 end_ptr = &state[ rand_deg ]; /* set end_ptr too */ 325 return( ostate ); 326 } 327 328 329 330 /* 331 * random: 332 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 333 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is the 334 * same in all ther other cases due to all the global variables that have been 335 * set up. The basic operation is to add the number at the rear pointer into 336 * the one at the front pointer. Then both pointers are advanced to the next 337 * location cyclically in the table. The value returned is the sum generated, 338 * reduced to 31 bits by throwing away the "least random" low bit. 339 * Note: the code takes advantage of the fact that both the front and 340 * rear pointers can't wrap on the same call by not testing the rear 341 * pointer if the front one has wrapped. 342 * Returns a 31-bit random number. 343 */ 344 345 long 346 random() 347 { 348 long i; 349 350 if( rand_type == TYPE_0 ) { 351 i = state[0] = ( state[0]*1103515245 + 12345 )&0x7fffffff; 352 } 353 else { 354 *fptr += *rptr; 355 i = (*fptr >> 1)&0x7fffffff; /* chucking least random bit */ 356 if( ++fptr >= end_ptr ) { 357 fptr = state; 358 ++rptr; 359 } 360 else { 361 if( ++rptr >= end_ptr ) rptr = state; 362 } 363 } 364 return( i ); 365 } 366 367