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. All advertising materials mentioning features or use of this software 14 * must display the following acknowledgement: 15 * This product includes software developed by the University of 16 * California, Berkeley and its contributors. 17 * 4. Neither the name of the University nor the names of its contributors 18 * may be used to endorse or promote products derived from this software 19 * without specific prior written permission. 20 * 21 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 22 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 23 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 24 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 25 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 26 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 27 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 28 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 29 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 30 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 31 * SUCH DAMAGE. 32 */ 33 34 #if defined(LIBC_SCCS) && !defined(lint) 35 static char *rcsid = "$OpenBSD: random.c,v 1.6 1998/02/07 02:16:25 millert Exp $"; 36 #endif /* LIBC_SCCS and not lint */ 37 38 #include <stdio.h> 39 #include <stdlib.h> 40 41 /* 42 * random.c: 43 * 44 * An improved random number generation package. In addition to the standard 45 * rand()/srand() like interface, this package also has a special state info 46 * interface. The initstate() routine is called with a seed, an array of 47 * bytes, and a count of how many bytes are being passed in; this array is 48 * then initialized to contain information for random number generation with 49 * that much state information. Good sizes for the amount of state 50 * information are 32, 64, 128, and 256 bytes. The state can be switched by 51 * calling the setstate() routine with the same array as was initiallized 52 * with initstate(). By default, the package runs with 128 bytes of state 53 * information and generates far better random numbers than a linear 54 * congruential generator. If the amount of state information is less than 55 * 32 bytes, a simple linear congruential R.N.G. is used. 56 * 57 * Internally, the state information is treated as an array of longs; the 58 * zeroeth element of the array is the type of R.N.G. being used (small 59 * integer); the remainder of the array is the state information for the 60 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of 61 * state information, which will allow a degree seven polynomial. (Note: 62 * the zeroeth word of state information also has some other information 63 * stored in it -- see setstate() for details). 64 * 65 * The random number generation technique is a linear feedback shift register 66 * approach, employing trinomials (since there are fewer terms to sum up that 67 * way). In this approach, the least significant bit of all the numbers in 68 * the state table will act as a linear feedback shift register, and will 69 * have period 2^deg - 1 (where deg is the degree of the polynomial being 70 * used, assuming that the polynomial is irreducible and primitive). The 71 * higher order bits will have longer periods, since their values are also 72 * influenced by pseudo-random carries out of the lower bits. The total 73 * period of the generator is approximately deg*(2**deg - 1); thus doubling 74 * the amount of state information has a vast influence on the period of the 75 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 76 * large deg, when the period of the shift register is the dominant factor. 77 * With deg equal to seven, the period is actually much longer than the 78 * 7*(2**7 - 1) predicted by this formula. 79 */ 80 81 /* 82 * For each of the currently supported random number generators, we have a 83 * break value on the amount of state information (you need at least this 84 * many bytes of state info to support this random number generator), a degree 85 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 86 * the separation between the two lower order coefficients of the trinomial. 87 */ 88 #define TYPE_0 0 /* linear congruential */ 89 #define BREAK_0 8 90 #define DEG_0 0 91 #define SEP_0 0 92 93 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 94 #define BREAK_1 32 95 #define DEG_1 7 96 #define SEP_1 3 97 98 #define TYPE_2 2 /* x**15 + x + 1 */ 99 #define BREAK_2 64 100 #define DEG_2 15 101 #define SEP_2 1 102 103 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 104 #define BREAK_3 128 105 #define DEG_3 31 106 #define SEP_3 3 107 108 #define TYPE_4 4 /* x**63 + x + 1 */ 109 #define BREAK_4 256 110 #define DEG_4 63 111 #define SEP_4 1 112 113 /* 114 * Array versions of the above information to make code run faster -- 115 * relies on fact that TYPE_i == i. 116 */ 117 #define MAX_TYPES 5 /* max number of types above */ 118 119 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 120 static int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 121 122 /* 123 * Initially, everything is set up as if from: 124 * 125 * initstate(1, &randtbl, 128); 126 * 127 * Note that this initialization takes advantage of the fact that srandom() 128 * advances the front and rear pointers 10*rand_deg times, and hence the 129 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 130 * element of the state information, which contains info about the current 131 * position of the rear pointer is just 132 * 133 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 134 */ 135 136 static long randtbl[DEG_3 + 1] = { 137 TYPE_3, 138 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 139 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 140 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 141 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 142 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 143 0xf3bec5da, 144 }; 145 146 /* 147 * fptr and rptr are two pointers into the state info, a front and a rear 148 * pointer. These two pointers are always rand_sep places aparts, as they 149 * cycle cyclically through the state information. (Yes, this does mean we 150 * could get away with just one pointer, but the code for random() is more 151 * efficient this way). The pointers are left positioned as they would be 152 * from the call 153 * 154 * initstate(1, randtbl, 128); 155 * 156 * (The position of the rear pointer, rptr, is really 0 (as explained above 157 * in the initialization of randtbl) because the state table pointer is set 158 * to point to randtbl[1] (as explained below). 159 */ 160 static long *fptr = &randtbl[SEP_3 + 1]; 161 static long *rptr = &randtbl[1]; 162 163 /* 164 * The following things are the pointer to the state information table, the 165 * type of the current generator, the degree of the current polynomial being 166 * used, and the separation between the two pointers. Note that for efficiency 167 * of random(), we remember the first location of the state information, not 168 * the zeroeth. Hence it is valid to access state[-1], which is used to 169 * store the type of the R.N.G. Also, we remember the last location, since 170 * this is more efficient than indexing every time to find the address of 171 * the last element to see if the front and rear pointers have wrapped. 172 */ 173 static long *state = &randtbl[1]; 174 static int rand_type = TYPE_3; 175 static int rand_deg = DEG_3; 176 static int rand_sep = SEP_3; 177 static long *end_ptr = &randtbl[DEG_3 + 1]; 178 179 /* 180 * srandom: 181 * 182 * Initialize the random number generator based on the given seed. If the 183 * type is the trivial no-state-information type, just remember the seed. 184 * Otherwise, initializes state[] based on the given "seed" via a linear 185 * congruential generator. Then, the pointers are set to known locations 186 * that are exactly rand_sep places apart. Lastly, it cycles the state 187 * information a given number of times to get rid of any initial dependencies 188 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 189 * for default usage relies on values produced by this routine. 190 */ 191 void 192 srandom(x) 193 u_int x; 194 { 195 register long int test; 196 register int i; 197 ldiv_t val; 198 199 if (rand_type == TYPE_0) 200 state[0] = x; 201 else { 202 state[0] = x; 203 for (i = 1; i < rand_deg; i++) { 204 /* 205 * Implement the following, without overflowing 31 bits: 206 * 207 * state[i] = (16807 * state[i - 1]) % 2147483647; 208 * 209 * 2^31-1 (prime) = 2147483647 = 127773*16807+2836 210 */ 211 val = ldiv(state[i-1], 127773); 212 test = 16807 * val.rem - 2836 * val.quot; 213 state[i] = test + (test < 0 ? 2147483647 : 0); 214 } 215 fptr = &state[rand_sep]; 216 rptr = &state[0]; 217 for (i = 0; i < 10 * rand_deg; i++) 218 (void)random(); 219 } 220 } 221 222 /* 223 * initstate: 224 * 225 * Initialize the state information in the given array of n bytes for future 226 * random number generation. Based on the number of bytes we are given, and 227 * the break values for the different R.N.G.'s, we choose the best (largest) 228 * one we can and set things up for it. srandom() is then called to 229 * initialize the state information. 230 * 231 * Note that on return from srandom(), we set state[-1] to be the type 232 * multiplexed with the current value of the rear pointer; this is so 233 * successive calls to initstate() won't lose this information and will be 234 * able to restart with setstate(). 235 * 236 * Note: the first thing we do is save the current state, if any, just like 237 * setstate() so that it doesn't matter when initstate is called. 238 * 239 * Returns a pointer to the old state. 240 */ 241 char * 242 initstate(seed, arg_state, n) 243 u_int seed; /* seed for R.N.G. */ 244 char *arg_state; /* pointer to state array */ 245 size_t n; /* # bytes of state info */ 246 { 247 register char *ostate = (char *)(&state[-1]); 248 249 if (rand_type == TYPE_0) 250 state[-1] = rand_type; 251 else 252 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 253 if (n < BREAK_0) 254 return(NULL); 255 if (n < BREAK_1) { 256 rand_type = TYPE_0; 257 rand_deg = DEG_0; 258 rand_sep = SEP_0; 259 } else if (n < BREAK_2) { 260 rand_type = TYPE_1; 261 rand_deg = DEG_1; 262 rand_sep = SEP_1; 263 } else if (n < BREAK_3) { 264 rand_type = TYPE_2; 265 rand_deg = DEG_2; 266 rand_sep = SEP_2; 267 } else if (n < BREAK_4) { 268 rand_type = TYPE_3; 269 rand_deg = DEG_3; 270 rand_sep = SEP_3; 271 } else { 272 rand_type = TYPE_4; 273 rand_deg = DEG_4; 274 rand_sep = SEP_4; 275 } 276 state = &(((long *)arg_state)[1]); /* first location */ 277 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 278 srandom(seed); 279 if (rand_type == TYPE_0) 280 state[-1] = rand_type; 281 else 282 state[-1] = MAX_TYPES*(rptr - state) + rand_type; 283 return(ostate); 284 } 285 286 /* 287 * setstate: 288 * 289 * Restore the state from the given state array. 290 * 291 * Note: it is important that we also remember the locations of the pointers 292 * in the current state information, and restore the locations of the pointers 293 * from the old state information. This is done by multiplexing the pointer 294 * location into the zeroeth word of the state information. 295 * 296 * Note that due to the order in which things are done, it is OK to call 297 * setstate() with the same state as the current state. 298 * 299 * Returns a pointer to the old state information. 300 */ 301 char * 302 setstate(arg_state) 303 const char *arg_state; 304 { 305 register long *new_state = (long *)arg_state; 306 register int type = new_state[0] % MAX_TYPES; 307 register int rear = new_state[0] / MAX_TYPES; 308 char *ostate = (char *)(&state[-1]); 309 310 if (rand_type == TYPE_0) 311 state[-1] = rand_type; 312 else 313 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 314 switch(type) { 315 case TYPE_0: 316 case TYPE_1: 317 case TYPE_2: 318 case TYPE_3: 319 case TYPE_4: 320 rand_type = type; 321 rand_deg = degrees[type]; 322 rand_sep = seps[type]; 323 break; 324 default: 325 return(NULL); 326 } 327 state = &new_state[1]; 328 if (rand_type != TYPE_0) { 329 rptr = &state[rear]; 330 fptr = &state[(rear + rand_sep) % rand_deg]; 331 } 332 end_ptr = &state[rand_deg]; /* set end_ptr too */ 333 return(ostate); 334 } 335 336 /* 337 * random: 338 * 339 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 340 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 341 * the same in all the other cases due to all the global variables that have 342 * been set up. The basic operation is to add the number at the rear pointer 343 * into the one at the front pointer. Then both pointers are advanced to 344 * the next location cyclically in the table. The value returned is the sum 345 * generated, reduced to 31 bits by throwing away the "least random" low bit. 346 * 347 * Note: the code takes advantage of the fact that both the front and 348 * rear pointers can't wrap on the same call by not testing the rear 349 * pointer if the front one has wrapped. 350 * 351 * Returns a 31-bit random number. 352 */ 353 long 354 random() 355 { 356 long i; 357 358 if (rand_type == TYPE_0) 359 i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff; 360 else { 361 *fptr += *rptr; 362 i = (*fptr >> 1) & 0x7fffffff; /* chucking least random bit */ 363 if (++fptr >= end_ptr) { 364 fptr = state; 365 ++rptr; 366 } else if (++rptr >= end_ptr) 367 rptr = state; 368 } 369 return(i); 370 } 371