1/* 2 * random.c 3 * 4 * BSD random function to support the TclX random command on SysV based 5 * systems. 6 *----------------------------------------------------------------------------- 7 * $Id: random.c,v 1.1 2001/10/24 23:31:47 hobbs Exp $ 8 *----------------------------------------------------------------------------- 9 */ 10 11 12/* 13 * Copyright (c) 1983 Regents of the University of California. 14 * All rights reserved. 15 * 16 * Redistribution and use in source and binary forms, with or without 17 * modification, are permitted provided that the following conditions 18 * are met: 19 * 1. Redistributions of source code must retain the above copyright 20 * notice, this list of conditions and the following disclaimer. 21 * 2. Redistributions in binary form must reproduce the above copyright 22 * notice, this list of conditions and the following disclaimer in the 23 * documentation and/or other materials provided with the distribution. 24 * 3. All advertising materials mentioning features or use of this software 25 * must display the following acknowledgement: 26 * This product includes software developed by the University of 27 * California, Berkeley and its contributors. 28 * 4. Neither the name of the University nor the names of its contributors 29 * may be used to endorse or promote products derived from this software 30 * without specific prior written permission. 31 * 32 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 33 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 34 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 35 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 36 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 37 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 38 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 39 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 40 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 41 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 42 * SUCH DAMAGE. 43 */ 44 45/* 46 * static char sccsid[] = "@(#)random.c 5.9 (Berkeley) 2/23/91"; 47 */ 48 49 50#include <stdio.h> 51 52long random(); 53 54typedef unsigned int u_int; 55 56/* 57 * random.c: 58 * 59 * An improved random number generation package. In addition to the standard 60 * rand()/srand() like interface, this package also has a special state info 61 * interface. The initstate() routine is called with a seed, an array of 62 * bytes, and a count of how many bytes are being passed in; this array is 63 * then initialized to contain information for random number generation with 64 * that much state information. Good sizes for the amount of state 65 * information are 32, 64, 128, and 256 bytes. The state can be switched by 66 * calling the setstate() routine with the same array as was initiallized 67 * with initstate(). By default, the package runs with 128 bytes of state 68 * information and generates far better random numbers than a linear 69 * congruential generator. If the amount of state information is less than 70 * 32 bytes, a simple linear congruential R.N.G. is used. 71 * 72 * Internally, the state information is treated as an array of longs; the 73 * zeroeth element of the array is the type of R.N.G. being used (small 74 * integer); the remainder of the array is the state information for the 75 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of 76 * state information, which will allow a degree seven polynomial. (Note: 77 * the zeroeth word of state information also has some other information 78 * stored in it -- see setstate() for details). 79 * 80 * The random number generation technique is a linear feedback shift register 81 * approach, employing trinomials (since there are fewer terms to sum up that 82 * way). In this approach, the least significant bit of all the numbers in 83 * the state table will act as a linear feedback shift register, and will 84 * have period 2^deg - 1 (where deg is the degree of the polynomial being 85 * used, assuming that the polynomial is irreducible and primitive). The 86 * higher order bits will have longer periods, since their values are also 87 * influenced by pseudo-random carries out of the lower bits. The total 88 * period of the generator is approximately deg*(2**deg - 1); thus doubling 89 * the amount of state information has a vast influence on the period of the 90 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 91 * large deg, when the period of the shift register is the dominant factor. 92 * With deg equal to seven, the period is actually much longer than the 93 * 7*(2**7 - 1) predicted by this formula. 94 */ 95 96/* 97 * For each of the currently supported random number generators, we have a 98 * break value on the amount of state information (you need at least this 99 * many bytes of state info to support this random number generator), a degree 100 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 101 * the separation between the two lower order coefficients of the trinomial. 102 */ 103#define TYPE_0 0 /* linear congruential */ 104#define BREAK_0 8 105#define DEG_0 0 106#define SEP_0 0 107 108#define TYPE_1 1 /* x**7 + x**3 + 1 */ 109#define BREAK_1 32 110#define DEG_1 7 111#define SEP_1 3 112 113#define TYPE_2 2 /* x**15 + x + 1 */ 114#define BREAK_2 64 115#define DEG_2 15 116#define SEP_2 1 117 118#define TYPE_3 3 /* x**31 + x**3 + 1 */ 119#define BREAK_3 128 120#define DEG_3 31 121#define SEP_3 3 122 123#define TYPE_4 4 /* x**63 + x + 1 */ 124#define BREAK_4 256 125#define DEG_4 63 126#define SEP_4 1 127 128/* 129 * Array versions of the above information to make code run faster -- 130 * relies on fact that TYPE_i == i. 131 */ 132#define MAX_TYPES 5 /* max number of types above */ 133 134static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 135static int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 136 137/* 138 * Initially, everything is set up as if from: 139 * 140 * initstate(1, &randtbl, 128); 141 * 142 * Note that this initialization takes advantage of the fact that srandom() 143 * advances the front and rear pointers 10*rand_deg times, and hence the 144 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 145 * element of the state information, which contains info about the current 146 * position of the rear pointer is just 147 * 148 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 149 */ 150 151static long randtbl[DEG_3 + 1] = { 152 TYPE_3, 153 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 154 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 155 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, 156 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 157 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 158 0x27fb47b9, 159}; 160 161/* 162 * fptr and rptr are two pointers into the state info, a front and a rear 163 * pointer. These two pointers are always rand_sep places aparts, as they 164 * cycle cyclically through the state information. (Yes, this does mean we 165 * could get away with just one pointer, but the code for random() is more 166 * efficient this way). The pointers are left positioned as they would be 167 * from the call 168 * 169 * initstate(1, randtbl, 128); 170 * 171 * (The position of the rear pointer, rptr, is really 0 (as explained above 172 * in the initialization of randtbl) because the state table pointer is set 173 * to point to randtbl[1] (as explained below). 174 */ 175static long *fptr = &randtbl[SEP_3 + 1]; 176static long *rptr = &randtbl[1]; 177 178/* 179 * The following things are the pointer to the state information table, the 180 * type of the current generator, the degree of the current polynomial being 181 * used, and the separation between the two pointers. Note that for efficiency 182 * of random(), we remember the first location of the state information, not 183 * the zeroeth. Hence it is valid to access state[-1], which is used to 184 * store the type of the R.N.G. Also, we remember the last location, since 185 * this is more efficient than indexing every time to find the address of 186 * the last element to see if the front and rear pointers have wrapped. 187 */ 188static long *state = &randtbl[1]; 189static int rand_type = TYPE_3; 190static int rand_deg = DEG_3; 191static int rand_sep = SEP_3; 192static long *end_ptr = &randtbl[DEG_3 + 1]; 193 194/* 195 * srandom: 196 * 197 * Initialize the random number generator based on the given seed. If the 198 * type is the trivial no-state-information type, just remember the seed. 199 * Otherwise, initializes state[] based on the given "seed" via a linear 200 * congruential generator. Then, the pointers are set to known locations 201 * that are exactly rand_sep places apart. Lastly, it cycles the state 202 * information a given number of times to get rid of any initial dependencies 203 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 204 * for default usage relies on values produced by this routine. 205 */ 206void 207srandom(x) 208 u_int x; 209{ 210 register int i, j; 211 212 if (rand_type == TYPE_0) 213 state[0] = x; 214 else { 215 j = 1; 216 state[0] = x; 217 for (i = 1; i < rand_deg; i++) 218 state[i] = 1103515245 * state[i - 1] + 12345; 219 fptr = &state[rand_sep]; 220 rptr = &state[0]; 221 for (i = 0; i < 10 * rand_deg; i++) 222 (void)random(); 223 } 224} 225 226/* 227 * initstate: 228 * 229 * Initialize the state information in the given array of n bytes for future 230 * random number generation. Based on the number of bytes we are given, and 231 * the break values for the different R.N.G.'s, we choose the best (largest) 232 * one we can and set things up for it. srandom() is then called to 233 * initialize the state information. 234 * 235 * Note that on return from srandom(), we set state[-1] to be the type 236 * multiplexed with the current value of the rear pointer; this is so 237 * successive calls to initstate() won't lose this information and will be 238 * able to restart with setstate(). 239 * 240 * Note: the first thing we do is save the current state, if any, just like 241 * setstate() so that it doesn't matter when initstate is called. 242 * 243 * Returns a pointer to the old state. 244 */ 245char * 246initstate(seed, arg_state, n) 247 u_int seed; /* seed for R.N.G. */ 248 char *arg_state; /* pointer to state array */ 249 int n; /* # bytes of state info */ 250{ 251 register char *ostate = (char *)(&state[-1]); 252 253 if (rand_type == TYPE_0) 254 state[-1] = rand_type; 255 else 256 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 257 if (n < BREAK_0) { 258 (void)fprintf(stderr, 259 "random: not enough state (%d bytes); ignored.\n", n); 260 return(0); 261 } 262 if (n < BREAK_1) { 263 rand_type = TYPE_0; 264 rand_deg = DEG_0; 265 rand_sep = SEP_0; 266 } else if (n < BREAK_2) { 267 rand_type = TYPE_1; 268 rand_deg = DEG_1; 269 rand_sep = SEP_1; 270 } else if (n < BREAK_3) { 271 rand_type = TYPE_2; 272 rand_deg = DEG_2; 273 rand_sep = SEP_2; 274 } else if (n < BREAK_4) { 275 rand_type = TYPE_3; 276 rand_deg = DEG_3; 277 rand_sep = SEP_3; 278 } else { 279 rand_type = TYPE_4; 280 rand_deg = DEG_4; 281 rand_sep = SEP_4; 282 } 283 state = &(((long *)arg_state)[1]); /* first location */ 284 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 285 srandom(seed); 286 if (rand_type == TYPE_0) 287 state[-1] = rand_type; 288 else 289 state[-1] = MAX_TYPES*(rptr - state) + rand_type; 290 return(ostate); 291} 292 293/* 294 * setstate: 295 * 296 * Restore the state from the given state array. 297 * 298 * Note: it is important that we also remember the locations of the pointers 299 * in the current state information, and restore the locations of the pointers 300 * from the old state information. This is done by multiplexing the pointer 301 * location into the zeroeth word of the state information. 302 * 303 * Note that due to the order in which things are done, it is OK to call 304 * setstate() with the same state as the current state. 305 * 306 * Returns a pointer to the old state information. 307 */ 308char * 309setstate(arg_state) 310 char *arg_state; 311{ 312 register long *new_state = (long *)arg_state; 313 register int type = new_state[0] % MAX_TYPES; 314 register int rear = new_state[0] / MAX_TYPES; 315 char *ostate = (char *)(&state[-1]); 316 317 if (rand_type == TYPE_0) 318 state[-1] = rand_type; 319 else 320 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 321 switch(type) { 322 case TYPE_0: 323 case TYPE_1: 324 case TYPE_2: 325 case TYPE_3: 326 case TYPE_4: 327 rand_type = type; 328 rand_deg = degrees[type]; 329 rand_sep = seps[type]; 330 break; 331 default: 332 (void)fprintf(stderr, 333 "random: state info corrupted; not changed.\n"); 334 } 335 state = &new_state[1]; 336 if (rand_type != TYPE_0) { 337 rptr = &state[rear]; 338 fptr = &state[(rear + rand_sep) % rand_deg]; 339 } 340 end_ptr = &state[rand_deg]; /* set end_ptr too */ 341 return(ostate); 342} 343 344/* 345 * random: 346 * 347 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 348 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 349 * the same in all the other cases due to all the global variables that have 350 * been set up. The basic operation is to add the number at the rear pointer 351 * into the one at the front pointer. Then both pointers are advanced to 352 * the next location cyclically in the table. The value returned is the sum 353 * generated, reduced to 31 bits by throwing away the "least random" low bit. 354 * 355 * Note: the code takes advantage of the fact that both the front and 356 * rear pointers can't wrap on the same call by not testing the rear 357 * pointer if the front one has wrapped. 358 * 359 * Returns a 31-bit random number. 360 */ 361long 362random() 363{ 364 long i; 365 366 if (rand_type == TYPE_0) 367 i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff; 368 else { 369 *fptr += *rptr; 370 i = (*fptr >> 1) & 0x7fffffff; /* chucking least random bit */ 371 if (++fptr >= end_ptr) { 372 fptr = state; 373 ++rptr; 374 } else if (++rptr >= end_ptr) 375 rptr = state; 376 } 377 return(i); 378} 379 380 381