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 #include <sys/types.h> 43 #ifdef HAVE_UNISTD_H 44 # include <unistd.h> 45 #endif 46 #include <stdio.h> 47 48 #include <l_stdlib.h> 49 #include <ntp_random.h> 50 #include <ntp_unixtime.h> 51 52 /* 53 * random.c: 54 * 55 * An improved random number generation package. In addition to the standard 56 * rand()/srand() like interface, this package also has a special state info 57 * interface. The initstate() routine is called with a seed, an array of 58 * bytes, and a count of how many bytes are being passed in; this array is 59 * then initialized to contain information for random number generation with 60 * that much state information. Good sizes for the amount of state 61 * information are 32, 64, 128, and 256 bytes. The state can be switched by 62 * calling the setstate() routine with the same array as was initiallized 63 * with initstate(). By default, the package runs with 128 bytes of state 64 * information and generates far better random numbers than a linear 65 * congruential generator. If the amount of state information is less than 66 * 32 bytes, a simple linear congruential R.N.G. is used. 67 * 68 * Internally, the state information is treated as an array of longs; the 69 * zeroeth element of the array is the type of R.N.G. being used (small 70 * integer); the remainder of the array is the state information for the 71 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of 72 * state information, which will allow a degree seven polynomial. (Note: 73 * the zeroeth word of state information also has some other information 74 * stored in it -- see setstate() for details). 75 * 76 * The random number generation technique is a linear feedback shift register 77 * approach, employing trinomials (since there are fewer terms to sum up that 78 * way). In this approach, the least significant bit of all the numbers in 79 * the state table will act as a linear feedback shift register, and will 80 * have period 2^deg - 1 (where deg is the degree of the polynomial being 81 * used, assuming that the polynomial is irreducible and primitive). The 82 * higher order bits will have longer periods, since their values are also 83 * influenced by pseudo-random carries out of the lower bits. The total 84 * period of the generator is approximately deg*(2**deg - 1); thus doubling 85 * the amount of state information has a vast influence on the period of the 86 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 87 * large deg, when the period of the shift register is the dominant factor. 88 * With deg equal to seven, the period is actually much longer than the 89 * 7*(2**7 - 1) predicted by this formula. 90 * 91 * Modified 28 December 1994 by Jacob S. Rosenberg. 92 * The following changes have been made: 93 * All references to the type u_int have been changed to unsigned long. 94 * All references to type int have been changed to type long. Other 95 * cleanups have been made as well. A warning for both initstate and 96 * setstate has been inserted to the effect that on Sparc platforms 97 * the 'arg_state' variable must be forced to begin on word boundaries. 98 * This can be easily done by casting a long integer array to char *. 99 * The overall logic has been left STRICTLY alone. This software was 100 * tested on both a VAX and Sun SpacsStation with exactly the same 101 * results. The new version and the original give IDENTICAL results. 102 * The new version is somewhat faster than the original. As the 103 * documentation says: "By default, the package runs with 128 bytes of 104 * state information and generates far better random numbers than a linear 105 * congruential generator. If the amount of state information is less than 106 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of 107 * 128 bytes, this new version runs about 19 percent faster and for a 16 108 * byte buffer it is about 5 percent faster. 109 */ 110 111 /* 112 * For each of the currently supported random number generators, we have a 113 * break value on the amount of state information (you need at least this 114 * many bytes of state info to support this random number generator), a degree 115 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 116 * the separation between the two lower order coefficients of the trinomial. 117 */ 118 #define TYPE_0 0 /* linear congruential */ 119 #define BREAK_0 8 120 #define DEG_0 0 121 #define SEP_0 0 122 123 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 124 #define BREAK_1 32 125 #define DEG_1 7 126 #define SEP_1 3 127 128 #define TYPE_2 2 /* x**15 + x + 1 */ 129 #define BREAK_2 64 130 #define DEG_2 15 131 #define SEP_2 1 132 133 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 134 #define BREAK_3 128 135 #define DEG_3 31 136 #define SEP_3 3 137 138 #define TYPE_4 4 /* x**63 + x + 1 */ 139 #define BREAK_4 256 140 #define DEG_4 63 141 #define SEP_4 1 142 143 #define MAX_TYPES 5 /* max number of types above */ 144 145 /* 146 * Initially, everything is set up as if from: 147 * 148 * initstate(1, randtbl, 128); 149 * 150 * Note that this initialization takes advantage of the fact that srandom() 151 * advances the front and rear pointers 10*rand_deg times, and hence the 152 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 153 * element of the state information, which contains info about the current 154 * position of the rear pointer is just 155 * 156 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 157 */ 158 159 static unsigned long randtbl[DEG_3 + 1] = { 160 TYPE_3, 161 #ifdef USE_WEAK_SEEDING 162 /* Historic implementation compatibility */ 163 /* The random sequences do not vary much with the seed */ 164 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5, 165 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, 166 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88, 167 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, 168 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b, 169 0x27fb47b9, 170 #else /* !USE_WEAK_SEEDING */ 171 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 172 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 173 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 174 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 175 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 176 0xf3bec5da 177 #endif /* !USE_WEAK_SEEDING */ 178 }; 179 180 /* 181 * fptr and rptr are two pointers into the state info, a front and a rear 182 * pointer. These two pointers are always rand_sep places aparts, as they 183 * cycle cyclically through the state information. (Yes, this does mean we 184 * could get away with just one pointer, but the code for random() is more 185 * efficient this way). The pointers are left positioned as they would be 186 * from the call 187 * 188 * initstate(1, randtbl, 128); 189 * 190 * (The position of the rear pointer, rptr, is really 0 (as explained above 191 * in the initialization of randtbl) because the state table pointer is set 192 * to point to randtbl[1] (as explained below). 193 */ 194 static unsigned long *fptr = &randtbl[SEP_3 + 1]; 195 static unsigned long *rptr = &randtbl[1]; 196 197 /* 198 * The following things are the pointer to the state information table, the 199 * type of the current generator, the degree of the current polynomial being 200 * used, and the separation between the two pointers. Note that for efficiency 201 * of random(), we remember the first location of the state information, not 202 * the zeroeth. Hence it is valid to access state[-1], which is used to 203 * store the type of the R.N.G. Also, we remember the last location, since 204 * this is more efficient than indexing every time to find the address of 205 * the last element to see if the front and rear pointers have wrapped. 206 */ 207 static unsigned long *state = &randtbl[1]; 208 static long rand_type = TYPE_3; 209 static long rand_deg = DEG_3; 210 static long rand_sep = SEP_3; 211 static unsigned long *end_ptr = &randtbl[DEG_3 + 1]; 212 213 static inline long good_rand (long); 214 215 static inline long 216 good_rand ( 217 register long x 218 ) 219 { 220 #ifdef USE_WEAK_SEEDING 221 /* 222 * Historic implementation compatibility. 223 * The random sequences do not vary much with the seed, 224 * even with overflowing. 225 */ 226 return (1103515245 * x + 12345); 227 #else /* !USE_WEAK_SEEDING */ 228 /* 229 * Compute x = (7^5 * x) mod (2^31 - 1) 230 * wihout overflowing 31 bits: 231 * (2^31 - 1) = 127773 * (7^5) + 2836 232 * From "Random number generators: good ones are hard to find", 233 * Park and Miller, Communications of the ACM, vol. 31, no. 10, 234 * October 1988, p. 1195. 235 */ 236 register long hi, lo; 237 238 hi = x / 127773; 239 lo = x % 127773; 240 x = 16807 * lo - 2836 * hi; 241 if (x <= 0) 242 x += 0x7fffffff; 243 return (x); 244 #endif /* !USE_WEAK_SEEDING */ 245 } 246 247 /* 248 * srandom: 249 * 250 * Initialize the random number generator based on the given seed. If the 251 * type is the trivial no-state-information type, just remember the seed. 252 * Otherwise, initializes state[] based on the given "seed" via a linear 253 * congruential generator. Then, the pointers are set to known locations 254 * that are exactly rand_sep places apart. Lastly, it cycles the state 255 * information a given number of times to get rid of any initial dependencies 256 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 257 * for default usage relies on values produced by this routine. 258 */ 259 void 260 ntp_srandom( 261 unsigned long x 262 ) 263 { 264 long i; 265 266 if (rand_type == TYPE_0) { 267 state[0] = x; 268 } else { 269 state[0] = x; 270 for (i = 1; i < rand_deg; i++) 271 state[i] = good_rand(state[i - 1]); 272 fptr = &state[rand_sep]; 273 rptr = &state[0]; 274 for (i = 0; i < 10 * rand_deg; i++) 275 x = ntp_random(); 276 } 277 278 /* seed the likely faster (and poorer) rand() as well */ 279 srand((u_int)x); 280 } 281 282 /* 283 * srandomdev: 284 * 285 * Many programs choose the seed value in a totally predictable manner. 286 * This often causes problems. We seed the generator using the much more 287 * secure urandom(4) interface. Note that this particular seeding 288 * procedure can generate states which are impossible to reproduce by 289 * calling srandom() with any value, since the succeeding terms in the 290 * state buffer are no longer derived from the LC algorithm applied to 291 * a fixed seed. 292 */ 293 #ifdef NEED_SRANDOMDEV 294 void 295 ntp_srandomdev( void ) 296 { 297 struct timeval tv; 298 unsigned long junk; /* Purposely used uninitialized */ 299 300 GETTIMEOFDAY(&tv, NULL); 301 ntp_srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk); 302 return; 303 } 304 #endif 305 306 307 /* 308 * ntp_initstate() and ntp_setstate() are unused in our codebase and 309 * trigger warnings due to casting to a more-strictly-aligned pointer 310 * on alignment-sensitive platforms. #ifdef them away to save noise, 311 * build time, and binary space, but retain the code in case we find a 312 * use. 313 */ 314 #ifdef COMPILE_UNUSED_FUNCTIONS 315 /* 316 * Array versions of the above information to make code run faster -- 317 * relies on fact that TYPE_i == i. 318 */ 319 #define MAX_TYPES 5 /* max number of types above */ 320 321 static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 322 static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 323 324 /* 325 * initstate: 326 * 327 * Initialize the state information in the given array of n bytes for future 328 * random number generation. Based on the number of bytes we are given, and 329 * the break values for the different R.N.G.'s, we choose the best (largest) 330 * one we can and set things up for it. srandom() is then called to 331 * initialize the state information. 332 * 333 * Note that on return from srandom(), we set state[-1] to be the type 334 * multiplexed with the current value of the rear pointer; this is so 335 * successive calls to initstate() won't lose this information and will be 336 * able to restart with setstate(). 337 * 338 * Note: the first thing we do is save the current state, if any, just like 339 * setstate() so that it doesn't matter when initstate is called. 340 * 341 * Returns a pointer to the old state. 342 * 343 * Note: The Sparc platform requires that arg_state begin on a long 344 * word boundary; otherwise a bus error will occur. Even so, lint will 345 * complain about mis-alignment, but you should disregard these messages. 346 */ 347 char * 348 ntp_initstate( 349 unsigned long seed, /* seed for R.N.G. */ 350 char *arg_state, /* pointer to state array */ 351 long n /* # bytes of state info */ 352 ) 353 { 354 register char *ostate = (char *)(&state[-1]); 355 register long *long_arg_state = (long *) arg_state; 356 357 if (rand_type == TYPE_0) 358 state[-1] = rand_type; 359 else 360 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 361 if (n < BREAK_0) { 362 (void)fprintf(stderr, 363 "random: not enough state (%ld bytes); ignored.\n", n); 364 return(0); 365 } 366 if (n < BREAK_1) { 367 rand_type = TYPE_0; 368 rand_deg = DEG_0; 369 rand_sep = SEP_0; 370 } else if (n < BREAK_2) { 371 rand_type = TYPE_1; 372 rand_deg = DEG_1; 373 rand_sep = SEP_1; 374 } else if (n < BREAK_3) { 375 rand_type = TYPE_2; 376 rand_deg = DEG_2; 377 rand_sep = SEP_2; 378 } else if (n < BREAK_4) { 379 rand_type = TYPE_3; 380 rand_deg = DEG_3; 381 rand_sep = SEP_3; 382 } else { 383 rand_type = TYPE_4; 384 rand_deg = DEG_4; 385 rand_sep = SEP_4; 386 } 387 state = (unsigned long *) (long_arg_state + 1); /* first location */ 388 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 389 ntp_srandom(seed); 390 if (rand_type == TYPE_0) 391 long_arg_state[0] = rand_type; 392 else 393 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type; 394 return(ostate); 395 } 396 397 /* 398 * setstate: 399 * 400 * Restore the state from the given state array. 401 * 402 * Note: it is important that we also remember the locations of the pointers 403 * in the current state information, and restore the locations of the pointers 404 * from the old state information. This is done by multiplexing the pointer 405 * location into the zeroeth word of the state information. 406 * 407 * Note that due to the order in which things are done, it is OK to call 408 * setstate() with the same state as the current state. 409 * 410 * Returns a pointer to the old state information. 411 * 412 * Note: The Sparc platform requires that arg_state begin on a long 413 * word boundary; otherwise a bus error will occur. Even so, lint will 414 * complain about mis-alignment, but you should disregard these messages. 415 */ 416 char * 417 ntp_setstate( 418 char *arg_state /* pointer to state array */ 419 ) 420 { 421 register unsigned long *new_state = (unsigned long *) arg_state; 422 register long type = new_state[0] % MAX_TYPES; 423 register long rear = new_state[0] / MAX_TYPES; 424 char *ostate = (char *)(&state[-1]); 425 426 if (rand_type == TYPE_0) 427 state[-1] = rand_type; 428 else 429 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 430 switch(type) { 431 case TYPE_0: 432 case TYPE_1: 433 case TYPE_2: 434 case TYPE_3: 435 case TYPE_4: 436 rand_type = type; 437 rand_deg = degrees[type]; 438 rand_sep = seps[type]; 439 break; 440 default: 441 (void)fprintf(stderr, 442 "random: state info corrupted; not changed.\n"); 443 } 444 state = (new_state + 1); 445 if (rand_type != TYPE_0) { 446 rptr = &state[rear]; 447 fptr = &state[(rear + rand_sep) % rand_deg]; 448 } 449 end_ptr = &state[rand_deg]; /* set end_ptr too */ 450 return(ostate); 451 } 452 #endif /* COMPILE_UNUSED_FUNCTIONS */ 453 454 455 /* 456 * random: 457 * 458 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 459 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 460 * the same in all the other cases due to all the global variables that have 461 * been set up. The basic operation is to add the number at the rear pointer 462 * into the one at the front pointer. Then both pointers are advanced to 463 * the next location cyclically in the table. The value returned is the sum 464 * generated, reduced to 31 bits by throwing away the "least random" low bit. 465 * 466 * Note: the code takes advantage of the fact that both the front and 467 * rear pointers can't wrap on the same call by not testing the rear 468 * pointer if the front one has wrapped. 469 * 470 * Returns a 31-bit random number. 471 */ 472 long 473 ntp_random( void ) 474 { 475 register long i; 476 register unsigned long *f, *r; 477 478 if (rand_type == TYPE_0) { 479 i = state[0]; 480 state[0] = i = (good_rand(i)) & 0x7fffffff; 481 } else { 482 /* 483 * Use local variables rather than static variables for speed. 484 */ 485 f = fptr; r = rptr; 486 *f += *r; 487 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */ 488 if (++f >= end_ptr) { 489 f = state; 490 ++r; 491 } 492 else if (++r >= end_ptr) { 493 r = state; 494 } 495 496 fptr = f; rptr = r; 497 } 498 return(i); 499 } 500 501 /* 502 * ntp_uurandom() 503 * 504 * Generate a Uniform-distributed Unity based random number. Replaces a 505 * few locations where the transformation was made in an ad-hoc style 506 * (and in one instance, wrong...) 507 * 508 * returns a number in [0.0 .. 1.0], both ends inclusive 509 */ 510 double 511 ntp_uurandom( void ) 512 { 513 return (double)ntp_random() / 0x7FFFFFFFu; 514 } 515