1 /* 2 * Copyright (c) 1983 Regents of the University of California. 3 * All rights reserved. 4 * 5 * %sccs.include.redist.c% 6 */ 7 8 #if defined(LIBC_SCCS) && !defined(lint) 9 static char sccsid[] = "@(#)random.c 5.9 (Berkeley) 02/23/91"; 10 #endif /* LIBC_SCCS and not lint */ 11 12 #include <stdio.h> 13 #include <stdlib.h> 14 15 /* 16 * random.c: 17 * 18 * An improved random number generation package. In addition to the standard 19 * rand()/srand() like interface, this package also has a special state info 20 * interface. The initstate() routine is called with a seed, an array of 21 * bytes, and a count of how many bytes are being passed in; this array is 22 * then initialized to contain information for random number generation with 23 * that much state information. Good sizes for the amount of state 24 * information are 32, 64, 128, and 256 bytes. The state can be switched by 25 * calling the setstate() routine with the same array as was initiallized 26 * with initstate(). By default, the package runs with 128 bytes of state 27 * information and generates far better random numbers than a linear 28 * congruential generator. If the amount of state information is less than 29 * 32 bytes, a simple linear congruential R.N.G. is used. 30 * 31 * Internally, the state information is treated as an array of longs; the 32 * zeroeth element of the array is the type of R.N.G. being used (small 33 * integer); the remainder of the array is the state information for the 34 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of 35 * state information, which will allow a degree seven polynomial. (Note: 36 * the zeroeth word of state information also has some other information 37 * stored in it -- see setstate() for details). 38 * 39 * The random number generation technique is a linear feedback shift register 40 * approach, employing trinomials (since there are fewer terms to sum up that 41 * way). In this approach, the least significant bit of all the numbers in 42 * the state table will act as a linear feedback shift register, and will 43 * have period 2^deg - 1 (where deg is the degree of the polynomial being 44 * used, assuming that the polynomial is irreducible and primitive). The 45 * higher order bits will have longer periods, since their values are also 46 * influenced by pseudo-random carries out of the lower bits. The total 47 * period of the generator is approximately deg*(2**deg - 1); thus doubling 48 * the amount of state information has a vast influence on the period of the 49 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 50 * large deg, when the period of the shift register is the dominant factor. 51 * With deg equal to seven, the period is actually much longer than the 52 * 7*(2**7 - 1) predicted by this formula. 53 */ 54 55 /* 56 * For each of the currently supported random number generators, we have a 57 * break value on the amount of state information (you need at least this 58 * many bytes of state info to support this random number generator), a degree 59 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 60 * the separation between the two lower order coefficients of the trinomial. 61 */ 62 #define TYPE_0 0 /* linear congruential */ 63 #define BREAK_0 8 64 #define DEG_0 0 65 #define SEP_0 0 66 67 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 68 #define BREAK_1 32 69 #define DEG_1 7 70 #define SEP_1 3 71 72 #define TYPE_2 2 /* x**15 + x + 1 */ 73 #define BREAK_2 64 74 #define DEG_2 15 75 #define SEP_2 1 76 77 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 78 #define BREAK_3 128 79 #define DEG_3 31 80 #define SEP_3 3 81 82 #define TYPE_4 4 /* x**63 + x + 1 */ 83 #define BREAK_4 256 84 #define DEG_4 63 85 #define SEP_4 1 86 87 /* 88 * Array versions of the above information to make code run faster -- 89 * relies on fact that TYPE_i == i. 90 */ 91 #define MAX_TYPES 5 /* max number of types above */ 92 93 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 94 static int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 95 96 /* 97 * Initially, everything is set up as if from: 98 * 99 * initstate(1, &randtbl, 128); 100 * 101 * Note that this initialization takes advantage of the fact that srandom() 102 * advances the front and rear pointers 10*rand_deg times, and hence the 103 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 104 * element of the state information, which contains info about the current 105 * position of the rear pointer is just 106 * 107 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 108 */ 109 110 static long randtbl[DEG_3 + 1] = { 111 TYPE_3, 112 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 113 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 114 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, 115 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 116 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 117 0x27fb47b9, 118 }; 119 120 /* 121 * fptr and rptr are two pointers into the state info, a front and a rear 122 * pointer. These two pointers are always rand_sep places aparts, as they 123 * cycle cyclically through the state information. (Yes, this does mean we 124 * could get away with just one pointer, but the code for random() is more 125 * efficient this way). The pointers are left positioned as they would be 126 * from the call 127 * 128 * initstate(1, randtbl, 128); 129 * 130 * (The position of the rear pointer, rptr, is really 0 (as explained above 131 * in the initialization of randtbl) because the state table pointer is set 132 * to point to randtbl[1] (as explained below). 133 */ 134 static long *fptr = &randtbl[SEP_3 + 1]; 135 static long *rptr = &randtbl[1]; 136 137 /* 138 * The following things are the pointer to the state information table, the 139 * type of the current generator, the degree of the current polynomial being 140 * used, and the separation between the two pointers. Note that for efficiency 141 * of random(), we remember the first location of the state information, not 142 * the zeroeth. Hence it is valid to access state[-1], which is used to 143 * store the type of the R.N.G. Also, we remember the last location, since 144 * this is more efficient than indexing every time to find the address of 145 * the last element to see if the front and rear pointers have wrapped. 146 */ 147 static long *state = &randtbl[1]; 148 static int rand_type = TYPE_3; 149 static int rand_deg = DEG_3; 150 static int rand_sep = SEP_3; 151 static long *end_ptr = &randtbl[DEG_3 + 1]; 152 153 /* 154 * srandom: 155 * 156 * Initialize the random number generator based on the given seed. If the 157 * type is the trivial no-state-information type, just remember the seed. 158 * Otherwise, initializes state[] based on the given "seed" via a linear 159 * congruential generator. Then, the pointers are set to known locations 160 * that are exactly rand_sep places apart. Lastly, it cycles the state 161 * information a given number of times to get rid of any initial dependencies 162 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 163 * for default usage relies on values produced by this routine. 164 */ 165 void 166 srandom(x) 167 u_int x; 168 { 169 register int i, j; 170 171 if (rand_type == TYPE_0) 172 state[0] = x; 173 else { 174 j = 1; 175 state[0] = x; 176 for (i = 1; i < rand_deg; i++) 177 state[i] = 1103515245 * state[i - 1] + 12345; 178 fptr = &state[rand_sep]; 179 rptr = &state[0]; 180 for (i = 0; i < 10 * rand_deg; i++) 181 (void)random(); 182 } 183 } 184 185 /* 186 * initstate: 187 * 188 * Initialize the state information in the given array of n bytes for future 189 * random number generation. Based on the number of bytes we are given, and 190 * the break values for the different R.N.G.'s, we choose the best (largest) 191 * one we can and set things up for it. srandom() is then called to 192 * initialize the state information. 193 * 194 * Note that on return from srandom(), we set state[-1] to be the type 195 * multiplexed with the current value of the rear pointer; this is so 196 * successive calls to initstate() won't lose this information and will be 197 * able to restart with setstate(). 198 * 199 * Note: the first thing we do is save the current state, if any, just like 200 * setstate() so that it doesn't matter when initstate is called. 201 * 202 * Returns a pointer to the old state. 203 */ 204 char * 205 initstate(seed, arg_state, n) 206 u_int seed; /* seed for R.N.G. */ 207 char *arg_state; /* pointer to state array */ 208 int n; /* # bytes of state info */ 209 { 210 register char *ostate = (char *)(&state[-1]); 211 212 if (rand_type == TYPE_0) 213 state[-1] = rand_type; 214 else 215 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 216 if (n < BREAK_0) { 217 (void)fprintf(stderr, 218 "random: not enough state (%d bytes); ignored.\n", n); 219 return(0); 220 } 221 if (n < BREAK_1) { 222 rand_type = TYPE_0; 223 rand_deg = DEG_0; 224 rand_sep = SEP_0; 225 } else if (n < BREAK_2) { 226 rand_type = TYPE_1; 227 rand_deg = DEG_1; 228 rand_sep = SEP_1; 229 } else if (n < BREAK_3) { 230 rand_type = TYPE_2; 231 rand_deg = DEG_2; 232 rand_sep = SEP_2; 233 } else if (n < BREAK_4) { 234 rand_type = TYPE_3; 235 rand_deg = DEG_3; 236 rand_sep = SEP_3; 237 } else { 238 rand_type = TYPE_4; 239 rand_deg = DEG_4; 240 rand_sep = SEP_4; 241 } 242 state = &(((long *)arg_state)[1]); /* first location */ 243 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 244 srandom(seed); 245 if (rand_type == TYPE_0) 246 state[-1] = rand_type; 247 else 248 state[-1] = MAX_TYPES*(rptr - state) + rand_type; 249 return(ostate); 250 } 251 252 /* 253 * setstate: 254 * 255 * Restore the state from the given state array. 256 * 257 * Note: it is important that we also remember the locations of the pointers 258 * in the current state information, and restore the locations of the pointers 259 * from the old state information. This is done by multiplexing the pointer 260 * location into the zeroeth word of the state information. 261 * 262 * Note that due to the order in which things are done, it is OK to call 263 * setstate() with the same state as the current state. 264 * 265 * Returns a pointer to the old state information. 266 */ 267 char * 268 setstate(arg_state) 269 char *arg_state; 270 { 271 register long *new_state = (long *)arg_state; 272 register int type = new_state[0] % MAX_TYPES; 273 register int rear = new_state[0] / MAX_TYPES; 274 char *ostate = (char *)(&state[-1]); 275 276 if (rand_type == TYPE_0) 277 state[-1] = rand_type; 278 else 279 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 280 switch(type) { 281 case TYPE_0: 282 case TYPE_1: 283 case TYPE_2: 284 case TYPE_3: 285 case TYPE_4: 286 rand_type = type; 287 rand_deg = degrees[type]; 288 rand_sep = seps[type]; 289 break; 290 default: 291 (void)fprintf(stderr, 292 "random: state info corrupted; not changed.\n"); 293 } 294 state = &new_state[1]; 295 if (rand_type != TYPE_0) { 296 rptr = &state[rear]; 297 fptr = &state[(rear + rand_sep) % rand_deg]; 298 } 299 end_ptr = &state[rand_deg]; /* set end_ptr too */ 300 return(ostate); 301 } 302 303 /* 304 * random: 305 * 306 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 307 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 308 * the same in all the other cases due to all the global variables that have 309 * been set up. The basic operation is to add the number at the rear pointer 310 * into the one at the front pointer. Then both pointers are advanced to 311 * the next location cyclically in the table. The value returned is the sum 312 * generated, reduced to 31 bits by throwing away the "least random" low bit. 313 * 314 * Note: the code takes advantage of the fact that both the front and 315 * rear pointers can't wrap on the same call by not testing the rear 316 * pointer if the front one has wrapped. 317 * 318 * Returns a 31-bit random number. 319 */ 320 long 321 random() 322 { 323 long i; 324 325 if (rand_type == TYPE_0) 326 i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff; 327 else { 328 *fptr += *rptr; 329 i = (*fptr >> 1) & 0x7fffffff; /* chucking least random bit */ 330 if (++fptr >= end_ptr) { 331 fptr = state; 332 ++rptr; 333 } else if (++rptr >= end_ptr) 334 rptr = state; 335 } 336 return(i); 337 } 338