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
34#if defined(LIBC_SCCS) && !defined(lint)
35static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95";
36#endif /* LIBC_SCCS and not lint */
37#include <sys/cdefs.h>
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39
40#include "namespace.h"
41#include <sys/time.h> /* for srandomdev() */
42#include <fcntl.h> /* for srandomdev() */
43#include <stdio.h>
44#include <stdlib.h>
45#include <unistd.h> /* for srandomdev() */
46#include "un-namespace.h"
47
48/*
49 * random.c:
50 *
51 * An improved random number generation package. In addition to the standard
52 * rand()/srand() like interface, this package also has a special state info
53 * interface. The initstate() routine is called with a seed, an array of
54 * bytes, and a count of how many bytes are being passed in; this array is
55 * then initialized to contain information for random number generation with
56 * that much state information. Good sizes for the amount of state
57 * information are 32, 64, 128, and 256 bytes. The state can be switched by
58 * calling the setstate() routine with the same array as was initiallized
59 * with initstate(). By default, the package runs with 128 bytes of state
60 * information and generates far better random numbers than a linear
61 * congruential generator. If the amount of state information is less than
62 * 32 bytes, a simple linear congruential R.N.G. is used.
63 *
64 * Internally, the state information is treated as an array of longs; the
65 * zeroeth element of the array is the type of R.N.G. being used (small
66 * integer); the remainder of the array is the state information for the
67 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
68 * state information, which will allow a degree seven polynomial. (Note:
69 * the zeroeth word of state information also has some other information
70 * stored in it -- see setstate() for details).
71 *
72 * The random number generation technique is a linear feedback shift register
73 * approach, employing trinomials (since there are fewer terms to sum up that
74 * way). In this approach, the least significant bit of all the numbers in
75 * the state table will act as a linear feedback shift register, and will
76 * have period 2^deg - 1 (where deg is the degree of the polynomial being
77 * used, assuming that the polynomial is irreducible and primitive). The
78 * higher order bits will have longer periods, since their values are also
79 * influenced by pseudo-random carries out of the lower bits. The total
80 * period of the generator is approximately deg*(2**deg - 1); thus doubling
81 * the amount of state information has a vast influence on the period of the
82 * generator. Note: the deg*(2**deg - 1) is an approximation only good for
83 * large deg, when the period of the shift is the dominant factor.
84 * With deg equal to seven, the period is actually much longer than the
85 * 7*(2**7 - 1) predicted by this formula.
86 *
87 * Modified 28 December 1994 by Jacob S. Rosenberg.
88 * The following changes have been made:
89 * All references to the type u_int have been changed to unsigned long.
90 * All references to type int have been changed to type long. Other
91 * cleanups have been made as well. A warning for both initstate and
92 * setstate has been inserted to the effect that on Sparc platforms
93 * the 'arg_state' variable must be forced to begin on word boundaries.
94 * This can be easily done by casting a long integer array to char *.
95 * The overall logic has been left STRICTLY alone. This software was
96 * tested on both a VAX and Sun SpacsStation with exactly the same
97 * results. The new version and the original give IDENTICAL results.
98 * The new version is somewhat faster than the original. As the
99 * documentation says: "By default, the package runs with 128 bytes of
100 * state information and generates far better random numbers than a linear
101 * congruential generator. If the amount of state information is less than
102 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of
103 * 128 bytes, this new version runs about 19 percent faster and for a 16
104 * byte buffer it is about 5 percent faster.
105 */
106
107/*
108 * For each of the currently supported random number generators, we have a
109 * break value on the amount of state information (you need at least this
110 * many bytes of state info to support this random number generator), a degree
111 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
112 * the separation between the two lower order coefficients of the trinomial.
113 */
114#define TYPE_0 0 /* linear congruential */
115#define BREAK_0 8
116#define DEG_0 0
117#define SEP_0 0
118
119#define TYPE_1 1 /* x**7 + x**3 + 1 */
120#define BREAK_1 32
121#define DEG_1 7
122#define SEP_1 3
123
124#define TYPE_2 2 /* x**15 + x + 1 */
125#define BREAK_2 64
126#define DEG_2 15
127#define SEP_2 1
128
129#define TYPE_3 3 /* x**31 + x**3 + 1 */
130#define BREAK_3 128
131#define DEG_3 31
132#define SEP_3 3
133
134#define TYPE_4 4 /* x**63 + x + 1 */
135#define BREAK_4 256
136#define DEG_4 63
137#define SEP_4 1
138
139/*
140 * Array versions of the above information to make code run faster --
141 * relies on fact that TYPE_i == i.
142 */
143#define MAX_TYPES 5 /* max number of types above */
144
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147static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
148static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
149
150/*
151 * Initially, everything is set up as if from:
152 *
153 * initstate(1, randtbl, 128);
154 *
155 * Note that this initialization takes advantage of the fact that srandom()
156 * advances the front and rear pointers 10*rand_deg times, and hence the
157 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
158 * element of the state information, which contains info about the current
159 * position of the rear pointer is just
160 *
161 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
162 */
163
164static long randtbl[DEG_3 + 1] = {
165 TYPE_3,
166#ifdef USE_WEAK_SEEDING
167/* Historic implementation compatibility */
168/* The random sequences do not vary much with the seed */
169 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
170 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
171 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
172 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
173 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
174 0x27fb47b9,
175#else /* !USE_WEAK_SEEDING */
176 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
177 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
178 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
179 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
180 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
181 0xf3bec5da
182#endif /* !USE_WEAK_SEEDING */
183};
184
185/*
186 * fptr and rptr are two pointers into the state info, a front and a rear
187 * pointer. These two pointers are always rand_sep places aparts, as they
188 * cycle cyclically through the state information. (Yes, this does mean we
189 * could get away with just one pointer, but the code for random() is more
190 * efficient this way). The pointers are left positioned as they would be
191 * from the call
192 *
193 * initstate(1, randtbl, 128);
194 *
195 * (The position of the rear pointer, rptr, is really 0 (as explained above
196 * in the initialization of randtbl) because the state table pointer is set
197 * to point to randtbl[1] (as explained below).
198 */
199static long *fptr = &randtbl[SEP_3 + 1];
200static long *rptr = &randtbl[1];
201
202/*
203 * The following things are the pointer to the state information table, the
204 * type of the current generator, the degree of the current polynomial being
205 * used, and the separation between the two pointers. Note that for efficiency
206 * of random(), we remember the first location of the state information, not
207 * the zeroeth. Hence it is valid to access state[-1], which is used to
208 * store the type of the R.N.G. Also, we remember the last location, since
209 * this is more efficient than indexing every time to find the address of
210 * the last element to see if the front and rear pointers have wrapped.
211 */
212static long *state = &randtbl[1];
213static long rand_type = TYPE_3;
214static long rand_deg = DEG_3;
215static long rand_sep = SEP_3;
216static long *end_ptr = &randtbl[DEG_3 + 1];
217
218static inline long good_rand(long);
219
220static inline long good_rand (x)
221 long x;
222{
223#ifdef USE_WEAK_SEEDING
224/*
225 * Historic implementation compatibility.
226 * The random sequences do not vary much with the seed,
227 * even with overflowing.
228 */
229 return (1103515245 * x + 12345);
230#else /* !USE_WEAK_SEEDING */
231/*
232 * Compute x = (7^5 * x) mod (2^31 - 1)
233 * wihout overflowing 31 bits:
234 * (2^31 - 1) = 127773 * (7^5) + 2836
235 * From "Random number generators: good ones are hard to find",
236 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
237 * October 1988, p. 1195.
238 */
239 long hi, lo;
240
241 /* Can't be initialized with 0, so use another value. */
242 if (x == 0)
243 x = 123459876;
244 hi = x / 127773;
245 lo = x % 127773;
246 x = 16807 * lo - 2836 * hi;
247 if (x < 0)
248 x += 0x7fffffff;
249 return (x);
250#endif /* !USE_WEAK_SEEDING */
251}
252
253/*
254 * srandom:
255 *
256 * Initialize the random number generator based on the given seed. If the
257 * type is the trivial no-state-information type, just remember the seed.
258 * Otherwise, initializes state[] based on the given "seed" via a linear
259 * congruential generator. Then, the pointers are set to known locations
260 * that are exactly rand_sep places apart. Lastly, it cycles the state
261 * information a given number of times to get rid of any initial dependencies
262 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
263 * for default usage relies on values produced by this routine.
264 */
265void
266srandom(x)
267 unsigned long x;
268{
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283}
284
285/*
286 * srandomdev:
287 *
288 * Many programs choose the seed value in a totally predictable manner.
289 * This often causes problems. We seed the generator using the much more
290 * secure random(4) interface. Note that this particular seeding
291 * procedure can generate states which are impossible to reproduce by
292 * calling srandom() with any value, since the succeeding terms in the
293 * state buffer are no longer derived from the LC algorithm applied to
294 * a fixed seed.
295 */
296void
297srandomdev()
298{
299 int fd, done;
300 size_t len;
301
302 if (rand_type == TYPE_0)
303 len = sizeof state[0];
304 else
305 len = rand_deg * sizeof state[0];
306
307 done = 0;
308 fd = _open("/dev/random", O_RDONLY, 0);
309 if (fd >= 0) {
310 if (_read(fd, (void *) state, len) == (ssize_t) len)
311 done = 1;
312 _close(fd);
313 }
314
315 if (!done) {
316 struct timeval tv;
317 unsigned long junk;
318
319 gettimeofday(&tv, NULL);
320 srandom((getpid() << 16) ^ tv.tv_sec ^ tv.tv_usec ^ junk);
321 return;
322 }
323
324 if (rand_type != TYPE_0) {
325 fptr = &state[rand_sep];
326 rptr = &state[0];
327 }
328}
329
330/*
331 * initstate:
332 *
333 * Initialize the state information in the given array of n bytes for future
334 * random number generation. Based on the number of bytes we are given, and
335 * the break values for the different R.N.G.'s, we choose the best (largest)
336 * one we can and set things up for it. srandom() is then called to
337 * initialize the state information.
338 *
339 * Note that on return from srandom(), we set state[-1] to be the type
340 * multiplexed with the current value of the rear pointer; this is so
341 * successive calls to initstate() won't lose this information and will be
342 * able to restart with setstate().
343 *
344 * Note: the first thing we do is save the current state, if any, just like
345 * setstate() so that it doesn't matter when initstate is called.
346 *
347 * Returns a pointer to the old state.
348 *
349 * Note: The Sparc platform requires that arg_state begin on a long
350 * word boundary; otherwise a bus error will occur. Even so, lint will
351 * complain about mis-alignment, but you should disregard these messages.
352 */
353char *
354initstate(seed, arg_state, n)
355 unsigned long seed; /* seed for R.N.G. */
356 char *arg_state; /* pointer to state array */
357 long n; /* # bytes of state info */
358{
359 char *ostate = (char *)(&state[-1]);
360 long *long_arg_state = (long *) arg_state;
361
362 if (rand_type == TYPE_0)
363 state[-1] = rand_type;
364 else
365 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
366 if (n < BREAK_0) {
367 (void)fprintf(stderr,
368 "random: not enough state (%ld bytes); ignored.\n", n);
369 return(0);
370 }
371 if (n < BREAK_1) {
372 rand_type = TYPE_0;
373 rand_deg = DEG_0;
374 rand_sep = SEP_0;
375 } else if (n < BREAK_2) {
376 rand_type = TYPE_1;
377 rand_deg = DEG_1;
378 rand_sep = SEP_1;
379 } else if (n < BREAK_3) {
380 rand_type = TYPE_2;
381 rand_deg = DEG_2;
382 rand_sep = SEP_2;
383 } else if (n < BREAK_4) {
384 rand_type = TYPE_3;
385 rand_deg = DEG_3;
386 rand_sep = SEP_3;
387 } else {
388 rand_type = TYPE_4;
389 rand_deg = DEG_4;
390 rand_sep = SEP_4;
391 }
392 state = (long *) (long_arg_state + 1); /* first location */
393 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
394 srandom(seed);
395 if (rand_type == TYPE_0)
396 long_arg_state[0] = rand_type;
397 else
398 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
399 return(ostate);
400}
401
402/*
403 * setstate:
404 *
405 * Restore the state from the given state array.
406 *
407 * Note: it is important that we also remember the locations of the pointers
408 * in the current state information, and restore the locations of the pointers
409 * from the old state information. This is done by multiplexing the pointer
410 * location into the zeroeth word of the state information.
411 *
412 * Note that due to the order in which things are done, it is OK to call
413 * setstate() with the same state as the current state.
414 *
415 * Returns a pointer to the old state information.
416 *
417 * Note: The Sparc platform requires that arg_state begin on a long
418 * word boundary; otherwise a bus error will occur. Even so, lint will
419 * complain about mis-alignment, but you should disregard these messages.
420 */
421char *
422setstate(arg_state)
423 char *arg_state; /* pointer to state array */
424{
425 long *new_state = (long *) arg_state;
426 long type = new_state[0] % MAX_TYPES;
427 long rear = new_state[0] / MAX_TYPES;
428 char *ostate = (char *)(&state[-1]);
429
430 if (rand_type == TYPE_0)
431 state[-1] = rand_type;
432 else
433 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
434 switch(type) {
435 case TYPE_0:
436 case TYPE_1:
437 case TYPE_2:
438 case TYPE_3:
439 case TYPE_4:
440 rand_type = type;
441 rand_deg = degrees[type];
442 rand_sep = seps[type];
443 break;
444 default:
445 (void)fprintf(stderr,
446 "random: state info corrupted; not changed.\n");
447 }
448 state = (long *) (new_state + 1);
449 if (rand_type != TYPE_0) {
450 rptr = &state[rear];
451 fptr = &state[(rear + rand_sep) % rand_deg];
452 }
453 end_ptr = &state[rand_deg]; /* set end_ptr too */
454 return(ostate);
455}
456
457/*
458 * random:
459 *
460 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
461 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
462 * the same in all the other cases due to all the global variables that have
463 * been set up. The basic operation is to add the number at the rear pointer
464 * into the one at the front pointer. Then both pointers are advanced to
465 * the next location cyclically in the table. The value returned is the sum
466 * generated, reduced to 31 bits by throwing away the "least random" low bit.
467 *
468 * Note: the code takes advantage of the fact that both the front and
469 * rear pointers can't wrap on the same call by not testing the rear
470 * pointer if the front one has wrapped.
471 *
472 * Returns a 31-bit random number.
473 */
474long
475random()
476{
477 long i;
478 long *f, *r;
479
480 if (rand_type == TYPE_0) {
481 i = state[0];
482 state[0] = i = (good_rand(i)) & 0x7fffffff;
483 } else {
484 /*
485 * Use local variables rather than static variables for speed.
486 */
487 f = fptr; r = rptr;
488 *f += *r;
489 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */
490 if (++f >= end_ptr) {
491 f = state;
492 ++r;
493 }
494 else if (++r >= end_ptr) {
495 r = state;
496 }
497
498 fptr = f; rptr = r;
499 }
500 return(i);
501}
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