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. 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 * @(#)random.c 8.2 (Berkeley) 5/19/95
30 * $FreeBSD: src/lib/libc/stdlib/random.c,v 1.25 2007/01/09 00:28:10 imp Exp $
31 */
32
33 #include "namespace.h"
34 #include <sys/time.h> /* for srandomdev() */
35 #include <sys/sysctl.h>
36 #include <fcntl.h> /* for srandomdev() */
37 #include <stdint.h>
38 #include <stdio.h>
39 #include <stdlib.h>
40 #include <unistd.h> /* for srandomdev() */
41 #include "un-namespace.h"
42
43 /*
44 * random.c:
45 *
46 * An improved random number generation package. In addition to the standard
47 * rand()/srand() like interface, this package also has a special state info
48 * interface. The initstate() routine is called with a seed, an array of
49 * bytes, and a count of how many bytes are being passed in; this array is
50 * then initialized to contain information for random number generation with
51 * that much state information. Good sizes for the amount of state
52 * information are 32, 64, 128, and 256 bytes. The state can be switched by
53 * calling the setstate() routine with the same array as was initiallized
54 * with initstate(). By default, the package runs with 128 bytes of state
55 * information and generates far better random numbers than a linear
56 * congruential generator. If the amount of state information is less than
57 * 32 bytes, a simple linear congruential R.N.G. is used.
58 *
59 * Internally, the state information is treated as an array of uint32_t's; the
60 * zeroeth element of the array is the type of R.N.G. being used (small
61 * integer); the remainder of the array is the state information for the
62 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of
63 * state information, which will allow a degree seven polynomial. (Note:
64 * the zeroeth word of state information also has some other information
65 * stored in it -- see setstate() for details).
66 *
67 * The random number generation technique is a linear feedback shift register
68 * approach, employing trinomials (since there are fewer terms to sum up that
69 * way). In this approach, the least significant bit of all the numbers in
70 * the state table will act as a linear feedback shift register, and will
71 * have period 2^deg - 1 (where deg is the degree of the polynomial being
72 * used, assuming that the polynomial is irreducible and primitive). The
73 * higher order bits will have longer periods, since their values are also
74 * influenced by pseudo-random carries out of the lower bits. The total
75 * period of the generator is approximately deg*(2**deg - 1); thus doubling
76 * the amount of state information has a vast influence on the period of the
77 * generator. Note: the deg*(2**deg - 1) is an approximation only good for
78 * large deg, when the period of the shift is the dominant factor.
79 * With deg equal to seven, the period is actually much longer than the
80 * 7*(2**7 - 1) predicted by this formula.
81 *
82 * Modified 28 December 1994 by Jacob S. Rosenberg.
83 * The following changes have been made:
84 * All references to the type u_int have been changed to unsigned long.
85 * All references to type int have been changed to type long. Other
86 * cleanups have been made as well. A warning for both initstate and
87 * setstate has been inserted to the effect that on Sparc platforms
88 * the 'arg_state' variable must be forced to begin on word boundaries.
89 * This can be easily done by casting a long integer array to char *.
90 * The overall logic has been left STRICTLY alone. This software was
91 * tested on both a VAX and Sun SpacsStation with exactly the same
92 * results. The new version and the original give IDENTICAL results.
93 * The new version is somewhat faster than the original. As the
94 * documentation says: "By default, the package runs with 128 bytes of
95 * state information and generates far better random numbers than a linear
96 * congruential generator. If the amount of state information is less than
97 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of
98 * 128 bytes, this new version runs about 19 percent faster and for a 16
99 * byte buffer it is about 5 percent faster.
100 */
101
102 /*
103 * For each of the currently supported random number generators, we have a
104 * break value on the amount of state information (you need at least this
105 * many bytes of state info to support this random number generator), a degree
106 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
107 * the separation between the two lower order coefficients of the trinomial.
108 */
109 #define TYPE_0 0 /* linear congruential */
110 #define BREAK_0 8
111 #define DEG_0 0
112 #define SEP_0 0
113
114 #define TYPE_1 1 /* x**7 + x**3 + 1 */
115 #define BREAK_1 32
116 #define DEG_1 7
117 #define SEP_1 3
118
119 #define TYPE_2 2 /* x**15 + x + 1 */
120 #define BREAK_2 64
121 #define DEG_2 15
122 #define SEP_2 1
123
124 #define TYPE_3 3 /* x**31 + x**3 + 1 */
125 #define BREAK_3 128
126 #define DEG_3 31
127 #define SEP_3 3
128
129 #define TYPE_4 4 /* x**63 + x + 1 */
130 #define BREAK_4 256
131 #define DEG_4 63
132 #define SEP_4 1
133
134 /*
135 * Array versions of the above information to make code run faster --
136 * relies on fact that TYPE_i == i.
137 */
138 #define MAX_TYPES 5 /* max number of types above */
139 #define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */
140
141 static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
142 static const int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
143
144 /*
145 * Initially, everything is set up as if from:
146 *
147 * initstate(1, randtbl, 128);
148 *
149 * Note that this initialization takes advantage of the fact that srandom()
150 * advances the front and rear pointers 10*rand_deg times, and hence the
151 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
152 * element of the state information, which contains info about the current
153 * position of the rear pointer is just
154 *
155 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
156 */
157
158 static uint32_t randtbl[DEG_3 + 1] = {
159 TYPE_3,
160 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
161 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
162 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
163 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
164 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
165 0xf3bec5da
166 };
167
168 /*
169 * fptr and rptr are two pointers into the state info, a front and a rear
170 * pointer. These two pointers are always rand_sep places aparts, as they
171 * cycle cyclically through the state information. (Yes, this does mean we
172 * could get away with just one pointer, but the code for random() is more
173 * efficient this way). The pointers are left positioned as they would be
174 * from the call
175 *
176 * initstate(1, randtbl, 128);
177 *
178 * (The position of the rear pointer, rptr, is really 0 (as explained above
179 * in the initialization of randtbl) because the state table pointer is set
180 * to point to randtbl[1] (as explained below).
181 */
182 static uint32_t *fptr = &randtbl[SEP_3 + 1];
183 static uint32_t *rptr = &randtbl[1];
184
185 /*
186 * The following things are the pointer to the state information table, the
187 * type of the current generator, the degree of the current polynomial being
188 * used, and the separation between the two pointers. Note that for efficiency
189 * of random(), we remember the first location of the state information, not
190 * the zeroeth. Hence it is valid to access state[-1], which is used to
191 * store the type of the R.N.G. Also, we remember the last location, since
192 * this is more efficient than indexing every time to find the address of
193 * the last element to see if the front and rear pointers have wrapped.
194 */
195 static uint32_t *state = &randtbl[1];
196 static int rand_type = TYPE_3;
197 static int rand_deg = DEG_3;
198 static int rand_sep = SEP_3;
199 static uint32_t *end_ptr = &randtbl[DEG_3 + 1];
200
201 static inline uint32_t good_rand(int32_t);
202
203 /*
204 * Compute x = (7^5 * x) mod (2^31 - 1)
205 * wihout overflowing 31 bits:
206 * (2^31 - 1) = 127773 * (7^5) + 2836
207 * From "Random number generators: good ones are hard to find",
208 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
209 * October 1988, p. 1195.
210 */
211 static inline uint32_t
good_rand(int32_t x)212 good_rand(int32_t x)
213 {
214 int32_t hi, lo;
215
216 /* Can't be initialized with 0, so use another value. */
217 if (x == 0)
218 x = 123459876;
219 hi = x / 127773;
220 lo = x % 127773;
221 x = 16807 * lo - 2836 * hi;
222 if (x < 0)
223 x += 0x7fffffff;
224 return (x);
225 }
226
227 /*
228 * srandom:
229 *
230 * Initialize the random number generator based on the given seed. If the
231 * type is the trivial no-state-information type, just remember the seed.
232 * Otherwise, initializes state[] based on the given "seed" via a linear
233 * congruential generator. Then, the pointers are set to known locations
234 * that are exactly rand_sep places apart. Lastly, it cycles the state
235 * information a given number of times to get rid of any initial dependencies
236 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
237 * for default usage relies on values produced by this routine.
238 */
239 void
srandom(unsigned long x)240 srandom(unsigned long x)
241 {
242 int i, lim;
243
244 state[0] = (uint32_t)x;
245 if (rand_type == TYPE_0)
246 lim = NSHUFF;
247 else {
248 for (i = 1; i < rand_deg; i++)
249 state[i] = good_rand(state[i - 1]);
250 fptr = &state[rand_sep];
251 rptr = &state[0];
252 lim = 10 * rand_deg;
253 }
254 for (i = 0; i < lim; i++)
255 random();
256 }
257
258 /*
259 * srandomdev:
260 *
261 * Many programs choose the seed value in a totally predictable manner.
262 * This often causes problems. We seed the generator using the much more
263 * secure random(4) interface. Note that this particular seeding
264 * procedure can generate states which are impossible to reproduce by
265 * calling srandom() with any value, since the succeeding terms in the
266 * state buffer are no longer derived from the LC algorithm applied to
267 * a fixed seed.
268 */
269
270 void
srandomdev(void)271 srandomdev(void)
272 {
273 size_t len;
274 size_t n;
275 int fd;
276
277 if (rand_type == TYPE_0)
278 len = sizeof state[0];
279 else
280 len = rand_deg * sizeof state[0];
281
282 /*
283 * Standard
284 */
285 fd = _open("/dev/random", O_RDONLY|O_CLOEXEC, 0);
286 if (fd >= 0) {
287 n = _read(fd, (void *)state, len);
288 _close(fd);
289 if ((ssize_t)n < 0)
290 n = 0;
291 }
292
293 /*
294 * Back-off incase chroot has no access to /dev/random
295 */
296 n = n & ~15;
297 if (n < len) {
298 size_t r = len - n;
299 if (sysctlbyname("kern.random", (char *)state + n,
300 &r, NULL, 0) == 0) {
301 n += r;
302 }
303 }
304
305 /*
306 * Pray
307 *
308 * NOTE: 'random' data on the stack is not random, don't try to
309 * access it.
310 */
311 n = n & ~15;
312 if (n < len) {
313 struct timeval tv;
314
315 gettimeofday(&tv, NULL);
316 srandom((getpid() << 16) ^ tv.tv_sec ^ tv.tv_usec);
317 return;
318 }
319
320 if (rand_type != TYPE_0) {
321 fptr = &state[rand_sep];
322 rptr = &state[0];
323 }
324 }
325
326 /*
327 * initstate:
328 *
329 * Initialize the state information in the given array of n bytes for future
330 * random number generation. Based on the number of bytes we are given, and
331 * the break values for the different R.N.G.'s, we choose the best (largest)
332 * one we can and set things up for it. srandom() is then called to
333 * initialize the state information.
334 *
335 * Note that on return from srandom(), we set state[-1] to be the type
336 * multiplexed with the current value of the rear pointer; this is so
337 * successive calls to initstate() won't lose this information and will be
338 * able to restart with setstate().
339 *
340 * Note: the first thing we do is save the current state, if any, just like
341 * setstate() so that it doesn't matter when initstate is called.
342 *
343 * Parameters:
344 * seed: seed for R.N.G.
345 * arg_state: pointer to state array
346 * n: # bytes of state info
347 *
348 * Returns a pointer to the old state.
349 *
350 * Note: The Sparc platform requires that arg_state begin on an int
351 * word boundary; otherwise a bus error will occur. Even so, lint will
352 * complain about mis-alignment, but you should disregard these messages.
353 */
354 char *
initstate(unsigned long seed,char * arg_state,long n)355 initstate(unsigned long seed, char *arg_state, long n)
356 {
357 char *ostate = (char *)(&state[-1]);
358 uint32_t *int_arg_state = (uint32_t *)arg_state;
359
360 if (rand_type == TYPE_0)
361 state[-1] = rand_type;
362 else
363 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
364 if (n < BREAK_0) {
365 fprintf(stderr,
366 "random: not enough state (%ld bytes); ignored.\n", n);
367 return(0);
368 }
369 if (n < BREAK_1) {
370 rand_type = TYPE_0;
371 rand_deg = DEG_0;
372 rand_sep = SEP_0;
373 } else if (n < BREAK_2) {
374 rand_type = TYPE_1;
375 rand_deg = DEG_1;
376 rand_sep = SEP_1;
377 } else if (n < BREAK_3) {
378 rand_type = TYPE_2;
379 rand_deg = DEG_2;
380 rand_sep = SEP_2;
381 } else if (n < BREAK_4) {
382 rand_type = TYPE_3;
383 rand_deg = DEG_3;
384 rand_sep = SEP_3;
385 } else {
386 rand_type = TYPE_4;
387 rand_deg = DEG_4;
388 rand_sep = SEP_4;
389 }
390 state = int_arg_state + 1; /* first location */
391 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
392 srandom(seed);
393 if (rand_type == TYPE_0)
394 int_arg_state[0] = rand_type;
395 else
396 int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
397 return(ostate);
398 }
399
400 /*
401 * setstate:
402 *
403 * Restore the state from the given state array.
404 *
405 * Note: it is important that we also remember the locations of the pointers
406 * in the current state information, and restore the locations of the pointers
407 * from the old state information. This is done by multiplexing the pointer
408 * location into the zeroeth word of the state information.
409 *
410 * Note that due to the order in which things are done, it is OK to call
411 * setstate() with the same state as the current state.
412 *
413 * Parameters:
414 * arg_state: pointer to state array
415 *
416 * Returns a pointer to the old state information.
417 *
418 * Note: The Sparc platform requires that arg_state begin on an int
419 * word boundary; otherwise a bus error will occur. Even so, lint will
420 * complain about mis-alignment, but you should disregard these messages.
421 */
422 char *
setstate(char * arg_state)423 setstate(char *arg_state)
424 {
425 uint32_t *new_state = (uint32_t *)arg_state;
426 uint32_t type = new_state[0] % MAX_TYPES;
427 uint32_t 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 fprintf(stderr,
446 "random: state info corrupted; not changed.\n");
447 }
448 state = 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 */
474 long
random(void)475 random(void)
476 {
477 uint32_t i;
478 uint32_t *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 /* chucking least random bit */
490 i = (*f >> 1) & 0x7fffffff;
491 if (++f >= end_ptr) {
492 f = state;
493 ++r;
494 }
495 else if (++r >= end_ptr) {
496 r = state;
497 }
498
499 fptr = f; rptr = r;
500 }
501 return((long)i);
502 }
503