xref: /openbsd-src/lib/libc/stdlib/random.c (revision e5157e49389faebcb42b7237d55fbf096d9c2523)
1 /*	$OpenBSD: random.c,v 1.24 2014/10/13 20:54:13 chl Exp $ */
2 /*
3  * Copyright (c) 1983 Regents of the University of California.
4  * All rights reserved.
5  *
6  * Redistribution and use in source and binary forms, with or without
7  * modification, are permitted provided that the following conditions
8  * are met:
9  * 1. Redistributions of source code must retain the above copyright
10  *    notice, this list of conditions and the following disclaimer.
11  * 2. Redistributions in binary form must reproduce the above copyright
12  *    notice, this list of conditions and the following disclaimer in the
13  *    documentation and/or other materials provided with the distribution.
14  * 3. Neither the name of the University nor the names of its contributors
15  *    may be used to endorse or promote products derived from this software
16  *    without specific prior written permission.
17  *
18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28  * SUCH DAMAGE.
29  */
30 
31 #include <sys/param.h>
32 #include <sys/sysctl.h>
33 #include <sys/time.h>
34 #include <fcntl.h>
35 #include <stdio.h>
36 #include <stdlib.h>
37 #include <unistd.h>
38 
39 #include "thread_private.h"
40 
41 /*
42  * random.c:
43  *
44  * An improved random number generation package.  In addition to the standard
45  * rand()/srand() like interface, this package also has a special state info
46  * interface.  The initstate() routine is called with a seed, an array of
47  * bytes, and a count of how many bytes are being passed in; this array is
48  * then initialized to contain information for random number generation with
49  * that much state information.  Good sizes for the amount of state
50  * information are 32, 64, 128, and 256 bytes.  The state can be switched by
51  * calling the setstate() routine with the same array as was initiallized
52  * with initstate().  By default, the package runs with 128 bytes of state
53  * information and generates far better random numbers than a linear
54  * congruential generator.  If the amount of state information is less than
55  * 32 bytes, a simple linear congruential R.N.G. is used.
56  *
57  * Internally, the state information is treated as an array of int32_t; the
58  * zeroeth element of the array is the type of R.N.G. being used (small
59  * integer); the remainder of the array is the state information for the
60  * R.N.G.  Thus, 32 bytes of state information will give 7 int32_ts worth of
61  * state information, which will allow a degree seven polynomial.  (Note:
62  * the zeroeth word of state information also has some other information
63  * stored in it -- see setstate() for details).
64  *
65  * The random number generation technique is a linear feedback shift register
66  * approach, employing trinomials (since there are fewer terms to sum up that
67  * way).  In this approach, the least significant bit of all the numbers in
68  * the state table will act as a linear feedback shift register, and will
69  * have period 2^deg - 1 (where deg is the degree of the polynomial being
70  * used, assuming that the polynomial is irreducible and primitive).  The
71  * higher order bits will have longer periods, since their values are also
72  * influenced by pseudo-random carries out of the lower bits.  The total
73  * period of the generator is approximately deg*(2**deg - 1); thus doubling
74  * the amount of state information has a vast influence on the period of the
75  * generator.  Note: the deg*(2**deg - 1) is an approximation only good for
76  * large deg, when the period of the shift register is the dominant factor.
77  * With deg equal to seven, the period is actually much longer than the
78  * 7*(2**7 - 1) predicted by this formula.
79  */
80 
81 /*
82  * For each of the currently supported random number generators, we have a
83  * break value on the amount of state information (you need at least this
84  * many bytes of state info to support this random number generator), a degree
85  * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
86  * the separation between the two lower order coefficients of the trinomial.
87  */
88 #define	TYPE_0		0		/* linear congruential */
89 #define	BREAK_0		8
90 #define	DEG_0		0
91 #define	SEP_0		0
92 
93 #define	TYPE_1		1		/* x**7 + x**3 + 1 */
94 #define	BREAK_1		32
95 #define	DEG_1		7
96 #define	SEP_1		3
97 
98 #define	TYPE_2		2		/* x**15 + x + 1 */
99 #define	BREAK_2		64
100 #define	DEG_2		15
101 #define	SEP_2		1
102 
103 #define	TYPE_3		3		/* x**31 + x**3 + 1 */
104 #define	BREAK_3		128
105 #define	DEG_3		31
106 #define	SEP_3		3
107 
108 #define	TYPE_4		4		/* x**63 + x + 1 */
109 #define	BREAK_4		256
110 #define	DEG_4		63
111 #define	SEP_4		1
112 
113 /*
114  * Array versions of the above information to make code run faster --
115  * relies on fact that TYPE_i == i.
116  */
117 #define	MAX_TYPES	5		/* max number of types above */
118 
119 static int degrees[MAX_TYPES] =	{ DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
120 static int seps [MAX_TYPES] =	{ SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
121 
122 /*
123  * Initially, everything is set up as if from:
124  *
125  *	initstate(1, &randtbl, 128);
126  *
127  * Note that this initialization takes advantage of the fact that srandom()
128  * advances the front and rear pointers 10*rand_deg times, and hence the
129  * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
130  * element of the state information, which contains info about the current
131  * position of the rear pointer is just
132  *
133  *	MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
134  */
135 
136 static int32_t randtbl[DEG_3 + 1] = {
137 	TYPE_3,
138 	0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
139 	0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
140 	0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
141 	0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
142 	0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
143 	0xf3bec5da,
144 };
145 
146 /*
147  * fptr and rptr are two pointers into the state info, a front and a rear
148  * pointer.  These two pointers are always rand_sep places aparts, as they
149  * cycle cyclically through the state information.  (Yes, this does mean we
150  * could get away with just one pointer, but the code for random() is more
151  * efficient this way).  The pointers are left positioned as they would be
152  * from the call
153  *
154  *	initstate(1, randtbl, 128);
155  *
156  * (The position of the rear pointer, rptr, is really 0 (as explained above
157  * in the initialization of randtbl) because the state table pointer is set
158  * to point to randtbl[1] (as explained below).
159  */
160 static int32_t *fptr = &randtbl[SEP_3 + 1];
161 static int32_t *rptr = &randtbl[1];
162 
163 /*
164  * The following things are the pointer to the state information table, the
165  * type of the current generator, the degree of the current polynomial being
166  * used, and the separation between the two pointers.  Note that for efficiency
167  * of random(), we remember the first location of the state information, not
168  * the zeroeth.  Hence it is valid to access state[-1], which is used to
169  * store the type of the R.N.G.  Also, we remember the last location, since
170  * this is more efficient than indexing every time to find the address of
171  * the last element to see if the front and rear pointers have wrapped.
172  */
173 static int32_t *state = &randtbl[1];
174 static int32_t *end_ptr = &randtbl[DEG_3 + 1];
175 static int rand_type = TYPE_3;
176 static int rand_deg = DEG_3;
177 static int rand_sep = SEP_3;
178 
179 static int use_arc4random;
180 
181 _THREAD_PRIVATE_MUTEX(random);
182 static long random_l(void);
183 
184 #define LOCK() _THREAD_PRIVATE_MUTEX_LOCK(random)
185 #define UNLOCK() _THREAD_PRIVATE_MUTEX_UNLOCK(random)
186 
187 /*
188  * srandom:
189  *
190  * Initialize the random number generator based on the given seed.  If the
191  * type is the trivial no-state-information type, just remember the seed.
192  * Otherwise, initializes state[] based on the given "seed" via a linear
193  * congruential generator.  Then, the pointers are set to known locations
194  * that are exactly rand_sep places apart.  Lastly, it cycles the state
195  * information a given number of times to get rid of any initial dependencies
196  * introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
197  * for default usage relies on values produced by this routine.
198  */
199 static void
200 srandom_l(unsigned int x)
201 {
202 	int i;
203 	int32_t test;
204 	div_t val;
205 
206 	use_arc4random = 0;
207 	if (rand_type == TYPE_0)
208 		state[0] = x;
209 	else {
210 		/* A seed of 0 would result in state[] always being zero. */
211 		state[0] = x ? x : 1;
212 		for (i = 1; i < rand_deg; i++) {
213 			/*
214 			 * Implement the following, without overflowing 31 bits:
215 			 *
216 			 *	state[i] = (16807 * state[i - 1]) % 2147483647;
217 			 *
218 			 *	2^31-1 (prime) = 2147483647 = 127773*16807+2836
219 			 */
220 			val = div(state[i-1], 127773);
221 			test = 16807 * val.rem - 2836 * val.quot;
222 			state[i] = test + (test < 0 ? 2147483647 : 0);
223 		}
224 		fptr = &state[rand_sep];
225 		rptr = &state[0];
226 		for (i = 0; i < 10 * rand_deg; i++)
227 			(void)random_l();
228 	}
229 }
230 
231 void
232 srandom(unsigned int x)
233 {
234 	LOCK();
235 	srandom_l(x);
236 	UNLOCK();
237 }
238 
239 #if defined(APIWARN)
240 __warn_references(srandom,
241     "warning: srandom() seed choices are invariably poor");
242 #endif
243 
244 /*
245  * srandomdev:
246  *
247  * Many programs choose the seed value in a totally predictable manner.
248  * This often causes problems.  We seed the generator using random data.
249  * Note that this particular seeding procedure can generate states
250  * which are impossible to reproduce by calling srandom() with any
251  * value, since the succeeding terms in the state buffer are no longer
252  * derived from the LC algorithm applied to a fixed seed.
253  */
254 void
255 srandomdev(void)
256 {
257 	LOCK();
258 	use_arc4random = 1;
259 	UNLOCK();
260 }
261 
262 #if defined(APIWARN)
263 __warn_references(srandomdev,
264     "warning: srandomdev() usage; consider switching to arc4random()");
265 #endif
266 
267 /*
268  * initstate:
269  *
270  * Initialize the state information in the given array of n bytes for future
271  * random number generation.  Based on the number of bytes we are given, and
272  * the break values for the different R.N.G.'s, we choose the best (largest)
273  * one we can and set things up for it.  srandom() is then called to
274  * initialize the state information.
275  *
276  * Note that on return from srandom(), we set state[-1] to be the type
277  * multiplexed with the current value of the rear pointer; this is so
278  * successive calls to initstate() won't lose this information and will be
279  * able to restart with setstate().
280  *
281  * Note: the first thing we do is save the current state, if any, just like
282  * setstate() so that it doesn't matter when initstate is called.
283  *
284  * Returns a pointer to the old state.
285  */
286 char *
287 initstate(u_int seed, char *arg_state, size_t n)
288 {
289 	char *ostate = (char *)(&state[-1]);
290 
291 	LOCK();
292 	use_arc4random = 0;
293 	if (rand_type == TYPE_0)
294 		state[-1] = rand_type;
295 	else
296 		state[-1] = MAX_TYPES * (rptr - state) + rand_type;
297 	if (n < BREAK_0) {
298 		UNLOCK();
299 		return(NULL);
300 	}
301 	if (n < BREAK_1) {
302 		rand_type = TYPE_0;
303 		rand_deg = DEG_0;
304 		rand_sep = SEP_0;
305 	} else if (n < BREAK_2) {
306 		rand_type = TYPE_1;
307 		rand_deg = DEG_1;
308 		rand_sep = SEP_1;
309 	} else if (n < BREAK_3) {
310 		rand_type = TYPE_2;
311 		rand_deg = DEG_2;
312 		rand_sep = SEP_2;
313 	} else if (n < BREAK_4) {
314 		rand_type = TYPE_3;
315 		rand_deg = DEG_3;
316 		rand_sep = SEP_3;
317 	} else {
318 		rand_type = TYPE_4;
319 		rand_deg = DEG_4;
320 		rand_sep = SEP_4;
321 	}
322 	state = &(((int32_t *)arg_state)[1]);	/* first location */
323 	end_ptr = &state[rand_deg];	/* must set end_ptr before srandom */
324 	srandom_l(seed);
325 	if (rand_type == TYPE_0)
326 		state[-1] = rand_type;
327 	else
328 		state[-1] = MAX_TYPES*(rptr - state) + rand_type;
329 	UNLOCK();
330 	return(ostate);
331 }
332 
333 /*
334  * setstate:
335  *
336  * Restore the state from the given state array.
337  *
338  * Note: it is important that we also remember the locations of the pointers
339  * in the current state information, and restore the locations of the pointers
340  * from the old state information.  This is done by multiplexing the pointer
341  * location into the zeroeth word of the state information.
342  *
343  * Note that due to the order in which things are done, it is OK to call
344  * setstate() with the same state as the current state.
345  *
346  * Returns a pointer to the old state information.
347  */
348 char *
349 setstate(char *arg_state)
350 {
351 	int32_t *new_state = (int32_t *)arg_state;
352 	int32_t type = new_state[0] % MAX_TYPES;
353 	int32_t rear = new_state[0] / MAX_TYPES;
354 	char *ostate = (char *)(&state[-1]);
355 
356 	LOCK();
357 	use_arc4random = 0;
358 	if (rand_type == TYPE_0)
359 		state[-1] = rand_type;
360 	else
361 		state[-1] = MAX_TYPES * (rptr - state) + rand_type;
362 	switch(type) {
363 	case TYPE_0:
364 	case TYPE_1:
365 	case TYPE_2:
366 	case TYPE_3:
367 	case TYPE_4:
368 		rand_type = type;
369 		rand_deg = degrees[type];
370 		rand_sep = seps[type];
371 		break;
372 	default:
373 		UNLOCK();
374 		return(NULL);
375 	}
376 	state = &new_state[1];
377 	if (rand_type != TYPE_0) {
378 		rptr = &state[rear];
379 		fptr = &state[(rear + rand_sep) % rand_deg];
380 	}
381 	end_ptr = &state[rand_deg];		/* set end_ptr too */
382 	UNLOCK();
383 	return(ostate);
384 }
385 
386 /*
387  * random:
388  *
389  * If we are using the trivial TYPE_0 R.N.G., just do the old linear
390  * congruential bit.  Otherwise, we do our fancy trinomial stuff, which is
391  * the same in all the other cases due to all the global variables that have
392  * been set up.  The basic operation is to add the number at the rear pointer
393  * into the one at the front pointer.  Then both pointers are advanced to
394  * the next location cyclically in the table.  The value returned is the sum
395  * generated, reduced to 31 bits by throwing away the "least random" low bit.
396  *
397  * Note: the code takes advantage of the fact that both the front and
398  * rear pointers can't wrap on the same call by not testing the rear
399  * pointer if the front one has wrapped.
400  *
401  * Returns a 31-bit random number.
402  */
403 static long
404 random_l(void)
405 {
406 	int32_t i;
407 
408 	if (use_arc4random)
409 		return arc4random() & 0x7fffffff;
410 
411 	if (rand_type == TYPE_0)
412 		i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff;
413 	else {
414 		*fptr += *rptr;
415 		i = (*fptr >> 1) & 0x7fffffff;	/* chucking least random bit */
416 		if (++fptr >= end_ptr) {
417 			fptr = state;
418 			++rptr;
419 		} else if (++rptr >= end_ptr)
420 			rptr = state;
421 	}
422 	return((long)i);
423 }
424 
425 long
426 random(void)
427 {
428 	long r;
429 	LOCK();
430 	r = random_l();
431 	UNLOCK();
432 	return r;
433 }
434 
435 #if defined(APIWARN)
436 __warn_references(random,
437     "warning: random() isn't random; consider using arc4random()");
438 #endif
439