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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 * 4. Neither the name of the University nor the names of its contributors
14 * may be used to endorse or promote products derived from this software
15 * without specific prior written permission.
16 *
17 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
18 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
19 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
21 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
22 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
23 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
24 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
25 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
26 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
27 * SUCH DAMAGE.
28 */
29
30#if defined(LIBC_SCCS) && !defined(lint)
31static char sccsid[] = "@(#)random.c8.2 (Berkeley) 5/19/95";
32#endif /* LIBC_SCCS and not lint */
33#include <sys/cdefs.h>
34__FBSDID("$FreeBSD: src/lib/libc/stdlib/random.c,v 1.25 2007/01/09 00:28:10 imp Exp $");
35
36/*
37 * We always compile with __DARWIN_UNIX03 set to one, relying on the fact that
38 * (for non-LP64) sizeof(int) == sizeof(long) == sizeof(size_t), so that we
39 * don't have to have two different versions of the prototypes. For LP64,
40 * we only support the POSIX-compatible prototypes.
41 */
42#undef __DARWIN_UNIX03
43#define__DARWIN_UNIX031
44#include "namespace.h"
45#include <sys/time.h> /* for srandomdev() */
46#include <fcntl.h> /* for srandomdev() */
47#include <stdint.h>
48#include <stdio.h>
49#include <stdlib.h>
50#include <unistd.h> /* for srandomdev() */
51#include "un-namespace.h"
52
53/*
54 * random.c:
55 *
56 * An improved random number generation package. In addition to the standard
57 * rand()/srand() like interface, this package also has a special state info
58 * interface. The initstate() routine is called with a seed, an array of
59 * bytes, and a count of how many bytes are being passed in; this array is
60 * then initialized to contain information for random number generation with
61 * that much state information. Good sizes for the amount of state
62 * information are 32, 64, 128, and 256 bytes. The state can be switched by
63 * calling the setstate() routine with the same array as was initiallized
64 * with initstate(). By default, the package runs with 128 bytes of state
65 * information and generates far better random numbers than a linear
66 * congruential generator. If the amount of state information is less than
67 * 32 bytes, a simple linear congruential R.N.G. is used.
68 *
69 * Internally, the state information is treated as an array of uint32_t's; the
70 * zeroeth element of the array is the type of R.N.G. being used (small
71 * integer); the remainder of the array is the state information for the
72 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of
73 * state information, which will allow a degree seven polynomial. (Note:
74 * the zeroeth word of state information also has some other information
75 * stored in it -- see setstate() for details).
76 *
77 * The random number generation technique is a linear feedback shift register
78 * approach, employing trinomials (since there are fewer terms to sum up that
79 * way). In this approach, the least significant bit of all the numbers in
80 * the state table will act as a linear feedback shift register, and will
81 * have period 2^deg - 1 (where deg is the degree of the polynomial being
82 * used, assuming that the polynomial is irreducible and primitive). The
83 * higher order bits will have longer periods, since their values are also
84 * influenced by pseudo-random carries out of the lower bits. The total
85 * period of the generator is approximately deg*(2**deg - 1); thus doubling
86 * the amount of state information has a vast influence on the period of the
87 * generator. Note: the deg*(2**deg - 1) is an approximation only good for
88 * large deg, when the period of the shift is the dominant factor.
89 * With deg equal to seven, the period is actually much longer than the
90 * 7*(2**7 - 1) predicted by this formula.
91 *
92 * Modified 28 December 1994 by Jacob S. Rosenberg.
93 * The following changes have been made:
94 * All references to the type u_int have been changed to unsigned long.
95 * All references to type int have been changed to type long. Other
96 * cleanups have been made as well. A warning for both initstate and
97 * setstate has been inserted to the effect that on Sparc platforms
98 * the 'arg_state' variable must be forced to begin on word boundaries.
99 * This can be easily done by casting a long integer array to char *.
100 * The overall logic has been left STRICTLY alone. This software was
101 * tested on both a VAX and Sun SpacsStation with exactly the same
102 * results. The new version and the original give IDENTICAL results.
103 * The new version is somewhat faster than the original. As the
104 * documentation says: "By default, the package runs with 128 bytes of
105 * state information and generates far better random numbers than a linear
106 * congruential generator. If the amount of state information is less than
107 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of
108 * 128 bytes, this new version runs about 19 percent faster and for a 16
109 * byte buffer it is about 5 percent faster.
110 */
111
112/*
113 * For each of the currently supported random number generators, we have a
114 * break value on the amount of state information (you need at least this
115 * many bytes of state info to support this random number generator), a degree
116 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
117 * the separation between the two lower order coefficients of the trinomial.
118 */
119#defineTYPE_00/* linear congruential */
120#defineBREAK_08
121#defineDEG_00
122#defineSEP_00
123
124#defineTYPE_11/* x**7 + x**3 + 1 */
125#defineBREAK_132
126#defineDEG_17
127#defineSEP_13
128
129#defineTYPE_22/* x**15 + x + 1 */
130#defineBREAK_264
131#defineDEG_215
132#defineSEP_21
133
134#defineTYPE_33/* x**31 + x**3 + 1 */
135#defineBREAK_3128
136#defineDEG_331
137#defineSEP_33
138
139#defineTYPE_44/* x**63 + x + 1 */
140#defineBREAK_4256
141#defineDEG_463
142#defineSEP_41
143
144/*
145 * Array versions of the above information to make code run faster --
146 * relies on fact that TYPE_i == i.
147 */
148#defineMAX_TYPES5/* max number of types above */
149
150#ifdef USE_WEAK_SEEDING
151#define NSHUFF 0
152#else /* !USE_WEAK_SEEDING */
153#define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */
154#endif /* !USE_WEAK_SEEDING */
155
156static const int degrees[MAX_TYPES] ={ DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
157static const int seps [MAX_TYPES] ={ SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
158
159/*
160 * Initially, everything is set up as if from:
161 *
162 *initstate(1, randtbl, 128);
163 *
164 * Note that this initialization takes advantage of the fact that srandom()
165 * advances the front and rear pointers 10*rand_deg times, and hence the
166 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
167 * element of the state information, which contains info about the current
168 * position of the rear pointer is just
169 *
170 *MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
171 */
172
173static uint32_t randtbl[DEG_3 + 1] = {
174TYPE_3,
175#ifdef USE_WEAK_SEEDING
176 /* Historic implementation compatibility */
177 /* The random sequences do not vary much with the seed */
1780x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
1790xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
1800x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
1810xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
1820x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
1830x27fb47b9,
184#else /* !USE_WEAK_SEEDING */
1850x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
1860xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
1870x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
1880x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
1890x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
1900xf3bec5da
191#endif /* !USE_WEAK_SEEDING */
192};
193
194/*
195 * fptr and rptr are two pointers into the state info, a front and a rear
196 * pointer. These two pointers are always rand_sep places aparts, as they
197 * cycle cyclically through the state information. (Yes, this does mean we
198 * could get away with just one pointer, but the code for random() is more
199 * efficient this way). The pointers are left positioned as they would be
200 * from the call
201 *
202 *initstate(1, randtbl, 128);
203 *
204 * (The position of the rear pointer, rptr, is really 0 (as explained above
205 * in the initialization of randtbl) because the state table pointer is set
206 * to point to randtbl[1] (as explained below).
207 */
208static uint32_t *fptr = &randtbl[SEP_3 + 1];
209static uint32_t *rptr = &randtbl[1];
210
211/*
212 * The following things are the pointer to the state information table, the
213 * type of the current generator, the degree of the current polynomial being
214 * used, and the separation between the two pointers. Note that for efficiency
215 * of random(), we remember the first location of the state information, not
216 * the zeroeth. Hence it is valid to access state[-1], which is used to
217 * store the type of the R.N.G. Also, we remember the last location, since
218 * this is more efficient than indexing every time to find the address of
219 * the last element to see if the front and rear pointers have wrapped.
220 */
221static uint32_t *state = &randtbl[1];
222static int rand_type = TYPE_3;
223static int rand_deg = DEG_3;
224static int rand_sep = SEP_3;
225static uint32_t *end_ptr = &randtbl[DEG_3 + 1];
226
227static inline uint32_t good_rand(int32_t) __attribute__((always_inline));
228
229static inline uint32_t good_rand (x)
230int32_t x;
231{
232#ifdef USE_WEAK_SEEDING
233 /*
234 * Historic implementation compatibility.
235 * The random sequences do not vary much with the seed,
236 * even with overflowing.
237 */
238return (1103515245 * x + 12345);
239#else /* !USE_WEAK_SEEDING */
240 /*
241 * Compute x = (7^5 * x) mod (2^31 - 1)
242 * wihout overflowing 31 bits:
243 * (2^31 - 1) = 127773 * (7^5) + 2836
244 * From "Random number generators: good ones are hard to find",
245 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
246 * October 1988, p. 1195.
247 */
248int32_t hi, lo;
249
250/* Can't be initialized with 0, so use another value. */
251if (x == 0)
252x = 123459876;
253hi = x / 127773;
254lo = x % 127773;
255x = 16807 * lo - 2836 * hi;
256if (x < 0)
257x += 0x7fffffff;
258return (x);
259#endif /* !USE_WEAK_SEEDING */
260}
261
262/*
263 * srandom:
264 *
265 * Initialize the random number generator based on the given seed. If the
266 * type is the trivial no-state-information type, just remember the seed.
267 * Otherwise, initializes state[] based on the given "seed" via a linear
268 * congruential generator. Then, the pointers are set to known locations
269 * that are exactly rand_sep places apart. Lastly, it cycles the state
270 * information a given number of times to get rid of any initial dependencies
271 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
272 * for default usage relies on values produced by this routine.
273 */
274void
275srandom(x)
276unsigned x;
277{
278int i, lim;
279
280state[0] = (uint32_t)x;
281if (rand_type == TYPE_0)
282lim = NSHUFF;
283else {
284for (i = 1; i < rand_deg; i++)
285state[i] = good_rand(state[i - 1]);
286fptr = &state[rand_sep];
287rptr = &state[0];
288lim = 10 * rand_deg;
289}
290for (i = 0; i < lim; i++)
291(void)random();
292}
293
294/*
295 * srandomdev:
296 *
297 * Many programs choose the seed value in a totally predictable manner.
298 * This often causes problems. We seed the generator using the much more
299 * secure random(4) interface. Note that this particular seeding
300 * procedure can generate states which are impossible to reproduce by
301 * calling srandom() with any value, since the succeeding terms in the
302 * state buffer are no longer derived from the LC algorithm applied to
303 * a fixed seed.
304 */
305void
306srandomdev()
307{
308int fd, done;
309size_t len;
310
311if (rand_type == TYPE_0)
312len = sizeof state[0];
313else
314len = rand_deg * sizeof state[0];
315
316done = 0;
317fd = _open("/dev/random", O_RDONLY, 0);
318if (fd >= 0) {
319if (_read(fd, (void *) state, len) == (ssize_t) len)
320done = 1;
321_close(fd);
322}
323
324if (!done) {
325struct timeval tv;
326unsigned long junk;
327
328gettimeofday(&tv, NULL);
329srandom((getpid() << 16) ^ tv.tv_sec ^ tv.tv_usec ^ junk);
330return;
331}
332
333if (rand_type != TYPE_0) {
334fptr = &state[rand_sep];
335rptr = &state[0];
336}
337}
338
339/*
340 * initstate:
341 *
342 * Initialize the state information in the given array of n bytes for future
343 * random number generation. Based on the number of bytes we are given, and
344 * the break values for the different R.N.G.'s, we choose the best (largest)
345 * one we can and set things up for it. srandom() is then called to
346 * initialize the state information.
347 *
348 * Note that on return from srandom(), we set state[-1] to be the type
349 * multiplexed with the current value of the rear pointer; this is so
350 * successive calls to initstate() won't lose this information and will be
351 * able to restart with setstate().
352 *
353 * Note: the first thing we do is save the current state, if any, just like
354 * setstate() so that it doesn't matter when initstate is called.
355 *
356 * Returns a pointer to the old state.
357 *
358 * Note: The Sparc platform requires that arg_state begin on an int
359 * word boundary; otherwise a bus error will occur. Even so, lint will
360 * complain about mis-alignment, but you should disregard these messages.
361 */
362char *
363initstate(seed, arg_state, n)
364unsigned seed;/* seed for R.N.G. */
365char *arg_state;/* pointer to state array */
366size_t n;/* # bytes of state info */
367{
368char *ostate = (char *)(&state[-1]);
369uint32_t *int_arg_state = (uint32_t *)arg_state;
370
371if (rand_type == TYPE_0)
372state[-1] = rand_type;
373else
374state[-1] = MAX_TYPES * (rptr - state) + rand_type;
375if (n < BREAK_0) {
376(void)fprintf(stderr,
377 "random: not enough state (%ld bytes); ignored.\n", n);
378return(0);
379}
380if (n < BREAK_1) {
381rand_type = TYPE_0;
382rand_deg = DEG_0;
383rand_sep = SEP_0;
384} else if (n < BREAK_2) {
385rand_type = TYPE_1;
386rand_deg = DEG_1;
387rand_sep = SEP_1;
388} else if (n < BREAK_3) {
389rand_type = TYPE_2;
390rand_deg = DEG_2;
391rand_sep = SEP_2;
392} else if (n < BREAK_4) {
393rand_type = TYPE_3;
394rand_deg = DEG_3;
395rand_sep = SEP_3;
396} else {
397rand_type = TYPE_4;
398rand_deg = DEG_4;
399rand_sep = SEP_4;
400}
401state = int_arg_state + 1; /* first location */
402end_ptr = &state[rand_deg];/* must set end_ptr before srandom */
403srandom(seed);
404if (rand_type == TYPE_0)
405int_arg_state[0] = rand_type;
406else
407int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
408return(ostate);
409}
410
411/*
412 * setstate:
413 *
414 * Restore the state from the given state array.
415 *
416 * Note: it is important that we also remember the locations of the pointers
417 * in the current state information, and restore the locations of the pointers
418 * from the old state information. This is done by multiplexing the pointer
419 * location into the zeroeth word of the state information.
420 *
421 * Note that due to the order in which things are done, it is OK to call
422 * setstate() with the same state as the current state.
423 *
424 * Returns a pointer to the old state information.
425 *
426 * Note: The Sparc platform requires that arg_state begin on an int
427 * word boundary; otherwise a bus error will occur. Even so, lint will
428 * complain about mis-alignment, but you should disregard these messages.
429 */
430char *
431setstate(arg_state)
432const char *arg_state;/* pointer to state array */
433{
434uint32_t *new_state = (uint32_t *)arg_state;
435uint32_t type = new_state[0] % MAX_TYPES;
436uint32_t rear = new_state[0] / MAX_TYPES;
437char *ostate = (char *)(&state[-1]);
438
439if (rand_type == TYPE_0)
440state[-1] = rand_type;
441else
442state[-1] = MAX_TYPES * (rptr - state) + rand_type;
443switch(type) {
444 case TYPE_0:
445 case TYPE_1:
446 case TYPE_2:
447 case TYPE_3:
448 case TYPE_4:
449 rand_type = type;
450 rand_deg = degrees[type];
451 rand_sep = seps[type];
452 break;
453 default:
454 (void)fprintf(stderr,
455 "random: state info corrupted; not changed.\n");
456}
457state = new_state + 1;
458if (rand_type != TYPE_0) {
459rptr = &state[rear];
460fptr = &state[(rear + rand_sep) % rand_deg];
461}
462end_ptr = &state[rand_deg];/* set end_ptr too */
463return(ostate);
464}
465
466/*
467 * random:
468 *
469 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
470 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
471 * the same in all the other cases due to all the global variables that have
472 * been set up. The basic operation is to add the number at the rear pointer
473 * into the one at the front pointer. Then both pointers are advanced to
474 * the next location cyclically in the table. The value returned is the sum
475 * generated, reduced to 31 bits by throwing away the "least random" low bit.
476 *
477 * Note: the code takes advantage of the fact that both the front and
478 * rear pointers can't wrap on the same call by not testing the rear
479 * pointer if the front one has wrapped.
480 *
481 * Returns a 31-bit random number.
482 */
483long
484random()
485{
486uint32_t i;
487uint32_t *f, *r;
488
489if (rand_type == TYPE_0) {
490i = state[0];
491state[0] = i = (good_rand(i)) & 0x7fffffff;
492} else {
493/*
494 * Use local variables rather than static variables for speed.
495 */
496f = fptr; r = rptr;
497*f += *r;
498i = (*f >> 1) & 0x7fffffff;/* chucking least random bit */
499if (++f >= end_ptr) {
500f = state;
501++r;
502}
503else if (++r >= end_ptr) {
504r = state;
505}
506
507fptr = f; rptr = r;
508}
509return((long)i);
510}
511

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