1 /* 2 * Copyright (c) 1983, 1993 3 * The Regents of the University of California. 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 * $FreeBSD: src/lib/libc/stdlib/random.c,v 1.4.2.2 1999/09/05 11:16:45 peter Exp $ 34 * 35 */ 36 37 #if defined(LIBC_SCCS) && !defined(lint) 38 static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95"; 39 #endif /* LIBC_SCCS and not lint */ 40 41 #include "config.h" 42 #ifdef HAVE_SYS_TYPES_H 43 # include <sys/types.h> 44 #endif 45 #ifdef HAVE_UNISTD_H 46 # include <unistd.h> 47 #endif 48 #include <stdio.h> 49 50 #include <ntp_types.h> 51 #include <ntp_random.h> 52 #include <ntp_unixtime.h> 53 54 /* 55 * random.c: 56 * 57 * An improved random number generation package. In addition to the standard 58 * rand()/srand() like interface, this package also has a special state info 59 * interface. The initstate() routine is called with a seed, an array of 60 * bytes, and a count of how many bytes are being passed in; this array is 61 * then initialized to contain information for random number generation with 62 * that much state information. Good sizes for the amount of state 63 * information are 32, 64, 128, and 256 bytes. The state can be switched by 64 * calling the setstate() routine with the same array as was initiallized 65 * with initstate(). By default, the package runs with 128 bytes of state 66 * information and generates far better random numbers than a linear 67 * congruential generator. If the amount of state information is less than 68 * 32 bytes, a simple linear congruential R.N.G. is used. 69 * 70 * Internally, the state information is treated as an array of longs; the 71 * zeroeth element of the array is the type of R.N.G. being used (small 72 * integer); the remainder of the array is the state information for the 73 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of 74 * state information, which will allow a degree seven polynomial. (Note: 75 * the zeroeth word of state information also has some other information 76 * stored in it -- see setstate() for details). 77 * 78 * The random number generation technique is a linear feedback shift register 79 * approach, employing trinomials (since there are fewer terms to sum up that 80 * way). In this approach, the least significant bit of all the numbers in 81 * the state table will act as a linear feedback shift register, and will 82 * have period 2^deg - 1 (where deg is the degree of the polynomial being 83 * used, assuming that the polynomial is irreducible and primitive). The 84 * higher order bits will have longer periods, since their values are also 85 * influenced by pseudo-random carries out of the lower bits. The total 86 * period of the generator is approximately deg*(2**deg - 1); thus doubling 87 * the amount of state information has a vast influence on the period of the 88 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 89 * large deg, when the period of the shift register is the dominant factor. 90 * With deg equal to seven, the period is actually much longer than the 91 * 7*(2**7 - 1) predicted by this formula. 92 * 93 * Modified 28 December 1994 by Jacob S. Rosenberg. 94 * The following changes have been made: 95 * All references to the type u_int have been changed to unsigned long. 96 * All references to type int have been changed to type long. Other 97 * cleanups have been made as well. A warning for both initstate and 98 * setstate has been inserted to the effect that on Sparc platforms 99 * the 'arg_state' variable must be forced to begin on word boundaries. 100 * This can be easily done by casting a long integer array to char *. 101 * The overall logic has been left STRICTLY alone. This software was 102 * tested on both a VAX and Sun SpacsStation with exactly the same 103 * results. The new version and the original give IDENTICAL results. 104 * The new version is somewhat faster than the original. As the 105 * documentation says: "By default, the package runs with 128 bytes of 106 * state information and generates far better random numbers than a linear 107 * congruential generator. If the amount of state information is less than 108 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 109 * 128 bytes, this new version runs about 19 percent faster and for a 16 110 * byte buffer it is about 5 percent faster. 111 */ 112 113 /* 114 * For each of the currently supported random number generators, we have a 115 * break value on the amount of state information (you need at least this 116 * many bytes of state info to support this random number generator), a degree 117 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 118 * the separation between the two lower order coefficients of the trinomial. 119 */ 120 #define TYPE_0 0 /* linear congruential */ 121 #define BREAK_0 8 122 #define DEG_0 0 123 #define SEP_0 0 124 125 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 126 #define BREAK_1 32 127 #define DEG_1 7 128 #define SEP_1 3 129 130 #define TYPE_2 2 /* x**15 + x + 1 */ 131 #define BREAK_2 64 132 #define DEG_2 15 133 #define SEP_2 1 134 135 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 136 #define BREAK_3 128 137 #define DEG_3 31 138 #define SEP_3 3 139 140 #define TYPE_4 4 /* x**63 + x + 1 */ 141 #define BREAK_4 256 142 #define DEG_4 63 143 #define SEP_4 1 144 145 /* 146 * Array versions of the above information to make code run faster -- 147 * relies on fact that TYPE_i == i. 148 */ 149 #define MAX_TYPES 5 /* max number of types above */ 150 151 static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 152 static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 153 154 /* 155 * Initially, everything is set up as if from: 156 * 157 * initstate(1, randtbl, 128); 158 * 159 * Note that this initialization takes advantage of the fact that srandom() 160 * advances the front and rear pointers 10*rand_deg times, and hence the 161 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 162 * element of the state information, which contains info about the current 163 * position of the rear pointer is just 164 * 165 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 166 */ 167 168 static long randtbl[DEG_3 + 1] = { 169 TYPE_3, 170 #ifdef USE_WEAK_SEEDING 171 /* Historic implementation compatibility */ 172 /* The random sequences do not vary much with the seed */ 173 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 174 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 175 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, 176 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 177 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 178 0x27fb47b9, 179 #else /* !USE_WEAK_SEEDING */ 180 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 181 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 182 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 183 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 184 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 185 0xf3bec5da 186 #endif /* !USE_WEAK_SEEDING */ 187 }; 188 189 /* 190 * fptr and rptr are two pointers into the state info, a front and a rear 191 * pointer. These two pointers are always rand_sep places aparts, as they 192 * cycle cyclically through the state information. (Yes, this does mean we 193 * could get away with just one pointer, but the code for random() is more 194 * efficient this way). The pointers are left positioned as they would be 195 * from the call 196 * 197 * initstate(1, randtbl, 128); 198 * 199 * (The position of the rear pointer, rptr, is really 0 (as explained above 200 * in the initialization of randtbl) because the state table pointer is set 201 * to point to randtbl[1] (as explained below). 202 */ 203 static long *fptr = &randtbl[SEP_3 + 1]; 204 static long *rptr = &randtbl[1]; 205 206 /* 207 * The following things are the pointer to the state information table, the 208 * type of the current generator, the degree of the current polynomial being 209 * used, and the separation between the two pointers. Note that for efficiency 210 * of random(), we remember the first location of the state information, not 211 * the zeroeth. Hence it is valid to access state[-1], which is used to 212 * store the type of the R.N.G. Also, we remember the last location, since 213 * this is more efficient than indexing every time to find the address of 214 * the last element to see if the front and rear pointers have wrapped. 215 */ 216 static long *state = &randtbl[1]; 217 static long rand_type = TYPE_3; 218 static long rand_deg = DEG_3; 219 static long rand_sep = SEP_3; 220 static long *end_ptr = &randtbl[DEG_3 + 1]; 221 222 static inline long good_rand P((long)); 223 224 static inline long 225 good_rand ( 226 register long x 227 ) 228 { 229 #ifdef USE_WEAK_SEEDING 230 /* 231 * Historic implementation compatibility. 232 * The random sequences do not vary much with the seed, 233 * even with overflowing. 234 */ 235 return (1103515245 * x + 12345); 236 #else /* !USE_WEAK_SEEDING */ 237 /* 238 * Compute x = (7^5 * x) mod (2^31 - 1) 239 * wihout overflowing 31 bits: 240 * (2^31 - 1) = 127773 * (7^5) + 2836 241 * From "Random number generators: good ones are hard to find", 242 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 243 * October 1988, p. 1195. 244 */ 245 register long hi, lo; 246 247 hi = x / 127773; 248 lo = x % 127773; 249 x = 16807 * lo - 2836 * hi; 250 if (x <= 0) 251 x += 0x7fffffff; 252 return (x); 253 #endif /* !USE_WEAK_SEEDING */ 254 } 255 256 /* 257 * srandom: 258 * 259 * Initialize the random number generator based on the given seed. If the 260 * type is the trivial no-state-information type, just remember the seed. 261 * Otherwise, initializes state[] based on the given "seed" via a linear 262 * congruential generator. Then, the pointers are set to known locations 263 * that are exactly rand_sep places apart. Lastly, it cycles the state 264 * information a given number of times to get rid of any initial dependencies 265 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 266 * for default usage relies on values produced by this routine. 267 */ 268 void 269 ntp_srandom( 270 unsigned long x 271 ) 272 { 273 register long i; 274 275 if (rand_type == TYPE_0) 276 state[0] = x; 277 else { 278 state[0] = x; 279 for (i = 1; i < rand_deg; i++) 280 state[i] = good_rand(state[i - 1]); 281 fptr = &state[rand_sep]; 282 rptr = &state[0]; 283 for (i = 0; i < 10 * rand_deg; i++) 284 (void)ntp_random(); 285 } 286 } 287 288 /* 289 * srandomdev: 290 * 291 * Many programs choose the seed value in a totally predictable manner. 292 * This often causes problems. We seed the generator using the much more 293 * secure urandom(4) interface. Note that this particular seeding 294 * procedure can generate states which are impossible to reproduce by 295 * calling srandom() with any value, since the succeeding terms in the 296 * state buffer are no longer derived from the LC algorithm applied to 297 * a fixed seed. 298 */ 299 #ifdef NEED_SRANDOMDEV 300 void 301 ntp_srandomdev( void ) 302 { 303 struct timeval tv; 304 unsigned long junk; /* Purposely used uninitialized */ 305 306 GETTIMEOFDAY(&tv, NULL); 307 ntp_srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk); 308 return; 309 } 310 #endif 311 312 /* 313 * initstate: 314 * 315 * Initialize the state information in the given array of n bytes for future 316 * random number generation. Based on the number of bytes we are given, and 317 * the break values for the different R.N.G.'s, we choose the best (largest) 318 * one we can and set things up for it. srandom() is then called to 319 * initialize the state information. 320 * 321 * Note that on return from srandom(), we set state[-1] to be the type 322 * multiplexed with the current value of the rear pointer; this is so 323 * successive calls to initstate() won't lose this information and will be 324 * able to restart with setstate(). 325 * 326 * Note: the first thing we do is save the current state, if any, just like 327 * setstate() so that it doesn't matter when initstate is called. 328 * 329 * Returns a pointer to the old state. 330 * 331 * Note: The Sparc platform requires that arg_state begin on a long 332 * word boundary; otherwise a bus error will occur. Even so, lint will 333 * complain about mis-alignment, but you should disregard these messages. 334 */ 335 char * 336 ntp_initstate( 337 unsigned long seed, /* seed for R.N.G. */ 338 char *arg_state, /* pointer to state array */ 339 long n /* # bytes of state info */ 340 ) 341 { 342 register char *ostate = (char *)(&state[-1]); 343 register long *long_arg_state = (long *) arg_state; 344 345 if (rand_type == TYPE_0) 346 state[-1] = rand_type; 347 else 348 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 349 if (n < BREAK_0) { 350 (void)fprintf(stderr, 351 "random: not enough state (%ld bytes); ignored.\n", n); 352 return(0); 353 } 354 if (n < BREAK_1) { 355 rand_type = TYPE_0; 356 rand_deg = DEG_0; 357 rand_sep = SEP_0; 358 } else if (n < BREAK_2) { 359 rand_type = TYPE_1; 360 rand_deg = DEG_1; 361 rand_sep = SEP_1; 362 } else if (n < BREAK_3) { 363 rand_type = TYPE_2; 364 rand_deg = DEG_2; 365 rand_sep = SEP_2; 366 } else if (n < BREAK_4) { 367 rand_type = TYPE_3; 368 rand_deg = DEG_3; 369 rand_sep = SEP_3; 370 } else { 371 rand_type = TYPE_4; 372 rand_deg = DEG_4; 373 rand_sep = SEP_4; 374 } 375 state = (long *) (long_arg_state + 1); /* first location */ 376 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 377 ntp_srandom(seed); 378 if (rand_type == TYPE_0) 379 long_arg_state[0] = rand_type; 380 else 381 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 382 return(ostate); 383 } 384 385 /* 386 * setstate: 387 * 388 * Restore the state from the given state array. 389 * 390 * Note: it is important that we also remember the locations of the pointers 391 * in the current state information, and restore the locations of the pointers 392 * from the old state information. This is done by multiplexing the pointer 393 * location into the zeroeth word of the state information. 394 * 395 * Note that due to the order in which things are done, it is OK to call 396 * setstate() with the same state as the current state. 397 * 398 * Returns a pointer to the old state information. 399 * 400 * Note: The Sparc platform requires that arg_state begin on a long 401 * word boundary; otherwise a bus error will occur. Even so, lint will 402 * complain about mis-alignment, but you should disregard these messages. 403 */ 404 char * 405 ntp_setstate( 406 char *arg_state /* pointer to state array */ 407 ) 408 { 409 register long *new_state = (long *) arg_state; 410 register long type = new_state[0] % MAX_TYPES; 411 register long rear = new_state[0] / MAX_TYPES; 412 char *ostate = (char *)(&state[-1]); 413 414 if (rand_type == TYPE_0) 415 state[-1] = rand_type; 416 else 417 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 418 switch(type) { 419 case TYPE_0: 420 case TYPE_1: 421 case TYPE_2: 422 case TYPE_3: 423 case TYPE_4: 424 rand_type = type; 425 rand_deg = degrees[type]; 426 rand_sep = seps[type]; 427 break; 428 default: 429 (void)fprintf(stderr, 430 "random: state info corrupted; not changed.\n"); 431 } 432 state = (long *) (new_state + 1); 433 if (rand_type != TYPE_0) { 434 rptr = &state[rear]; 435 fptr = &state[(rear + rand_sep) % rand_deg]; 436 } 437 end_ptr = &state[rand_deg]; /* set end_ptr too */ 438 return(ostate); 439 } 440 441 /* 442 * random: 443 * 444 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 445 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 446 * the same in all the other cases due to all the global variables that have 447 * been set up. The basic operation is to add the number at the rear pointer 448 * into the one at the front pointer. Then both pointers are advanced to 449 * the next location cyclically in the table. The value returned is the sum 450 * generated, reduced to 31 bits by throwing away the "least random" low bit. 451 * 452 * Note: the code takes advantage of the fact that both the front and 453 * rear pointers can't wrap on the same call by not testing the rear 454 * pointer if the front one has wrapped. 455 * 456 * Returns a 31-bit random number. 457 */ 458 long 459 ntp_random( void ) 460 { 461 register long i; 462 register long *f, *r; 463 464 if (rand_type == TYPE_0) { 465 i = state[0]; 466 state[0] = i = (good_rand(i)) & 0x7fffffff; 467 } else { 468 /* 469 * Use local variables rather than static variables for speed. 470 */ 471 f = fptr; r = rptr; 472 *f += *r; 473 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */ 474 if (++f >= end_ptr) { 475 f = state; 476 ++r; 477 } 478 else if (++r >= end_ptr) { 479 r = state; 480 } 481 482 fptr = f; rptr = r; 483 } 484 return(i); 485 } 486