1/*	$NetBSD: random.c,v 1.4 2014/06/12 20:59:46 christos Exp $	*/
2
3/*
4 * Copyright (c) 1983, 1993
5 *	The Regents of the University of California.  All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 *    notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 *    notice, this list of conditions and the following disclaimer in the
14 *    documentation and/or other materials provided with the distribution.
15 * 3. Neither the name of the University nor the names of its contributors
16 *    may be used to endorse or promote products derived from this software
17 *    without specific prior written permission.
18 *
19 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
20 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
21 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
22 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
23 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
24 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
25 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
26 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
27 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
28 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
29 * SUCH DAMAGE.
30 */
31
32#if !defined(_KERNEL) && !defined(_STANDALONE)
33#include <sys/cdefs.h>
34#if defined(LIBC_SCCS) && !defined(lint)
35#if 0
36static char sccsid[] = "@(#)random.c	8.2 (Berkeley) 5/19/95";
37#else
38__RCSID("$NetBSD: random.c,v 1.4 2014/06/12 20:59:46 christos Exp $");
39#endif
40#endif /* LIBC_SCCS and not lint */
41
42#include "namespace.h"
43
44#include <assert.h>
45#include <errno.h>
46#include <stdlib.h>
47#include "reentrant.h"
48
49#ifdef __weak_alias
50__weak_alias(initstate,_initstate)
51__weak_alias(random,_random)
52__weak_alias(setstate,_setstate)
53__weak_alias(srandom,_srandom)
54#endif
55
56
57#ifdef _REENTRANT
58static mutex_t random_mutex = MUTEX_INITIALIZER;
59#endif
60#else
61#include <lib/libkern/libkern.h>
62#define mutex_lock(a)	(void)0
63#define mutex_unlock(a) (void)0
64#endif
65
66#ifndef SMALL_RANDOM
67static void srandom_unlocked(unsigned int);
68static long random_unlocked(void);
69
70#define USE_BETTER_RANDOM
71
72/*
73 * random.c:
74 *
75 * An improved random number generation package.  In addition to the standard
76 * rand()/srand() like interface, this package also has a special state info
77 * interface.  The initstate() routine is called with a seed, an array of
78 * bytes, and a count of how many bytes are being passed in; this array is
79 * then initialized to contain information for random number generation with
80 * that much state information.  Good sizes for the amount of state
81 * information are 32, 64, 128, and 256 bytes.  The state can be switched by
82 * calling the setstate() routine with the same array as was initiallized
83 * with initstate().  By default, the package runs with 128 bytes of state
84 * information and generates far better random numbers than a linear
85 * congruential generator.  If the amount of state information is less than
86 * 32 bytes, a simple linear congruential R.N.G. is used.
87 *
88 * Internally, the state information is treated as an array of ints; the
89 * zeroeth element of the array is the type of R.N.G. being used (small
90 * integer); the remainder of the array is the state information for the
91 * R.N.G.  Thus, 32 bytes of state information will give 7 ints worth of
92 * state information, which will allow a degree seven polynomial.  (Note:
93 * the zeroeth word of state information also has some other information
94 * stored in it -- see setstate() for details).
95 *
96 * The random number generation technique is a linear feedback shift register
97 * approach, employing trinomials (since there are fewer terms to sum up that
98 * way).  In this approach, the least significant bit of all the numbers in
99 * the state table will act as a linear feedback shift register, and will
100 * have period 2^deg - 1 (where deg is the degree of the polynomial being
101 * used, assuming that the polynomial is irreducible and primitive).  The
102 * higher order bits will have longer periods, since their values are also
103 * influenced by pseudo-random carries out of the lower bits.  The total
104 * period of the generator is approximately deg*(2**deg - 1); thus doubling
105 * the amount of state information has a vast influence on the period of the
106 * generator.  Note: the deg*(2**deg - 1) is an approximation only good for
107 * large deg, when the period of the shift register is the dominant factor.
108 * With deg equal to seven, the period is actually much longer than the
109 * 7*(2**7 - 1) predicted by this formula.
110 *
111 * Modified 28 December 1994 by Jacob S. Rosenberg.
112 * The following changes have been made:
113 * All references to the type u_int have been changed to unsigned long.
114 * All references to type int have been changed to type long.  Other
115 * cleanups have been made as well.  A warning for both initstate and
116 * setstate has been inserted to the effect that on Sparc platforms
117 * the 'arg_state' variable must be forced to begin on word boundaries.
118 * This can be easily done by casting a long integer array to char *.
119 * The overall logic has been left STRICTLY alone.  This software was
120 * tested on both a VAX and Sun SpacsStation with exactly the same
121 * results.  The new version and the original give IDENTICAL results.
122 * The new version is somewhat faster than the original.  As the
123 * documentation says:  "By default, the package runs with 128 bytes of
124 * state information and generates far better random numbers than a linear
125 * congruential generator.  If the amount of state information is less than
126 * 32 bytes, a simple linear congruential R.N.G. is used."  For a buffer of
127 * 128 bytes, this new version runs about 19 percent faster and for a 16
128 * byte buffer it is about 5 percent faster.
129 *
130 * Modified 07 January 2002 by Jason R. Thorpe.
131 * The following changes have been made:
132 * All the references to "long" have been changed back to "int".  This
133 * fixes memory corruption problems on LP64 platforms.
134 */
135
136/*
137 * For each of the currently supported random number generators, we have a
138 * break value on the amount of state information (you need at least this
139 * many bytes of state info to support this random number generator), a degree
140 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
141 * the separation between the two lower order coefficients of the trinomial.
142 */
143#define	TYPE_0		0		/* linear congruential */
144#define	BREAK_0		8
145#define	DEG_0		0
146#define	SEP_0		0
147
148#define	TYPE_1		1		/* x**7 + x**3 + 1 */
149#define	BREAK_1		32
150#define	DEG_1		7
151#define	SEP_1		3
152
153#define	TYPE_2		2		/* x**15 + x + 1 */
154#define	BREAK_2		64
155#define	DEG_2		15
156#define	SEP_2		1
157
158#define	TYPE_3		3		/* x**31 + x**3 + 1 */
159#define	BREAK_3		128
160#define	DEG_3		31
161#define	SEP_3		3
162
163#define	TYPE_4		4		/* x**63 + x + 1 */
164#define	BREAK_4		256
165#define	DEG_4		63
166#define	SEP_4		1
167
168/*
169 * Array versions of the above information to make code run faster --
170 * relies on fact that TYPE_i == i.
171 */
172#define	MAX_TYPES	5		/* max number of types above */
173
174static const int degrees[MAX_TYPES] =	{ DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
175static const int seps[MAX_TYPES] =	{ SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
176
177/*
178 * Initially, everything is set up as if from:
179 *
180 *	initstate(1, &randtbl, 128);
181 *
182 * Note that this initialization takes advantage of the fact that srandom()
183 * advances the front and rear pointers 10*rand_deg times, and hence the
184 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
185 * element of the state information, which contains info about the current
186 * position of the rear pointer is just
187 *
188 *	MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
189 */
190
191/* LINTED */
192static int randtbl[DEG_3 + 1] = {
193	TYPE_3,
194#ifdef USE_BETTER_RANDOM
195	0x991539b1, 0x16a5bce3, 0x6774a4cd,
196	0x3e01511e, 0x4e508aaa, 0x61048c05,
197	0xf5500617, 0x846b7115, 0x6a19892c,
198	0x896a97af, 0xdb48f936, 0x14898454,
199	0x37ffd106, 0xb58bff9c, 0x59e17104,
200	0xcf918a49, 0x09378c83, 0x52c7a471,
201	0x8d293ea9, 0x1f4fc301, 0xc3db71be,
202	0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
203	0x19edc328, 0x87bf4bdd, 0xc9b240e5,
204	0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
205	0xf3bec5da,
206#else
207	0x9a319039, 0x32d9c024, 0x9b663182,
208	0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
209	0xf103bc02, 0x48f340fb, 0x7449e56b,
210	0xbeb1dbb0, 0xab5c5918, 0x946554fd,
211	0x8c2e680f, 0xeb3d799f, 0xb11ee0b7,
212	0x2d436b86, 0xda672e2a, 0x1588ca88,
213	0xe369735d, 0x904f35f7, 0xd7158fd6,
214	0x6fa6f051, 0x616e6b96, 0xac94efdc,
215	0x36413f93, 0xc622c298, 0xf5a42ab8,
216	0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
217	0x27fb47b9,
218#endif /* USE_BETTER_RANDOM */
219};
220
221/*
222 * fptr and rptr are two pointers into the state info, a front and a rear
223 * pointer.  These two pointers are always rand_sep places aparts, as they
224 * cycle cyclically through the state information.  (Yes, this does mean we
225 * could get away with just one pointer, but the code for random() is more
226 * efficient this way).  The pointers are left positioned as they would be
227 * from the call
228 *
229 *	initstate(1, randtbl, 128);
230 *
231 * (The position of the rear pointer, rptr, is really 0 (as explained above
232 * in the initialization of randtbl) because the state table pointer is set
233 * to point to randtbl[1] (as explained below).
234 */
235static int *fptr = &randtbl[SEP_3 + 1];
236static int *rptr = &randtbl[1];
237
238/*
239 * The following things are the pointer to the state information table, the
240 * type of the current generator, the degree of the current polynomial being
241 * used, and the separation between the two pointers.  Note that for efficiency
242 * of random(), we remember the first location of the state information, not
243 * the zeroeth.  Hence it is valid to access state[-1], which is used to
244 * store the type of the R.N.G.  Also, we remember the last location, since
245 * this is more efficient than indexing every time to find the address of
246 * the last element to see if the front and rear pointers have wrapped.
247 */
248static int *state = &randtbl[1];
249static int rand_type = TYPE_3;
250static int rand_deg = DEG_3;
251static int rand_sep = SEP_3;
252static int *end_ptr = &randtbl[DEG_3 + 1];
253
254/*
255 * srandom:
256 *
257 * Initialize the random number generator based on the given seed.  If the
258 * type is the trivial no-state-information type, just remember the seed.
259 * Otherwise, initializes state[] based on the given "seed" via a linear
260 * congruential generator.  Then, the pointers are set to known locations
261 * that are exactly rand_sep places apart.  Lastly, it cycles the state
262 * information a given number of times to get rid of any initial dependencies
263 * introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
264 * for default usage relies on values produced by this routine.
265 */
266static void
267srandom_unlocked(unsigned int x)
268{
269	int i;
270
271	if (rand_type == TYPE_0)
272		state[0] = x;
273	else {
274		state[0] = x;
275		for (i = 1; i < rand_deg; i++) {
276#ifdef USE_BETTER_RANDOM
277			int x1, hi, lo, t;
278
279			/*
280			 * Compute x[n + 1] = (7^5 * x[n]) mod (2^31 - 1).
281			 * From "Random number generators: good ones are hard
282			 * to find", Park and Miller, Communications of the ACM,
283			 * vol. 31, no. 10,
284			 * October 1988, p. 1195.
285			 */
286			x1 = state[i - 1];
287			hi = x1 / 127773;
288			lo = x1 % 127773;
289			t = 16807 * lo - 2836 * hi;
290			if (t <= 0)
291				t += 0x7fffffff;
292			state[i] = t;
293#else
294			state[i] = 1103515245 * state[i - 1] + 12345;
295#endif /* USE_BETTER_RANDOM */
296		}
297		fptr = &state[rand_sep];
298		rptr = &state[0];
299		for (i = 0; i < 10 * rand_deg; i++)
300			(void)random_unlocked();
301	}
302}
303
304void
305srandom(unsigned int x)
306{
307
308	mutex_lock(&random_mutex);
309	srandom_unlocked(x);
310	mutex_unlock(&random_mutex);
311}
312
313/*
314 * initstate:
315 *
316 * Initialize the state information in the given array of n bytes for future
317 * random number generation.  Based on the number of bytes we are given, and
318 * the break values for the different R.N.G.'s, we choose the best (largest)
319 * one we can and set things up for it.  srandom() is then called to
320 * initialize the state information.
321 *
322 * Note that on return from srandom(), we set state[-1] to be the type
323 * multiplexed with the current value of the rear pointer; this is so
324 * successive calls to initstate() won't lose this information and will be
325 * able to restart with setstate().
326 *
327 * Note: the first thing we do is save the current state, if any, just like
328 * setstate() so that it doesn't matter when initstate is called.
329 *
330 * Returns a pointer to the old state.
331 *
332 * Note: The Sparc platform requires that arg_state begin on an int
333 * word boundary; otherwise a bus error will occur. Even so, lint will
334 * complain about mis-alignment, but you should disregard these messages.
335 */
336char *
337initstate(
338	unsigned int seed,		/* seed for R.N.G. */
339	char *arg_state,		/* pointer to state array */
340	size_t n)			/* # bytes of state info */
341{
342	void *ostate = (void *)(&state[-1]);
343	int *int_arg_state;
344
345	_DIAGASSERT(arg_state != NULL);
346
347	int_arg_state = (int *)(void *)arg_state;
348
349	mutex_lock(&random_mutex);
350	if (rand_type == TYPE_0)
351		state[-1] = rand_type;
352	else
353		state[-1] = MAX_TYPES * (int)(rptr - state) + rand_type;
354	if (n < BREAK_0) {
355		mutex_unlock(&random_mutex);
356		return (NULL);
357	} else if (n < BREAK_1) {
358		rand_type = TYPE_0;
359		rand_deg = DEG_0;
360		rand_sep = SEP_0;
361	} else if (n < BREAK_2) {
362		rand_type = TYPE_1;
363		rand_deg = DEG_1;
364		rand_sep = SEP_1;
365	} else if (n < BREAK_3) {
366		rand_type = TYPE_2;
367		rand_deg = DEG_2;
368		rand_sep = SEP_2;
369	} else if (n < BREAK_4) {
370		rand_type = TYPE_3;
371		rand_deg = DEG_3;
372		rand_sep = SEP_3;
373	} else {
374		rand_type = TYPE_4;
375		rand_deg = DEG_4;
376		rand_sep = SEP_4;
377	}
378	state = (int *) (int_arg_state + 1); /* first location */
379	end_ptr = &state[rand_deg];	/* must set end_ptr before srandom */
380	srandom_unlocked(seed);
381	if (rand_type == TYPE_0)
382		int_arg_state[0] = rand_type;
383	else
384		int_arg_state[0] = MAX_TYPES * (int)(rptr - state) + rand_type;
385	mutex_unlock(&random_mutex);
386	return((char *)ostate);
387}
388
389/*
390 * setstate:
391 *
392 * Restore the state from the given state array.
393 *
394 * Note: it is important that we also remember the locations of the pointers
395 * in the current state information, and restore the locations of the pointers
396 * from the old state information.  This is done by multiplexing the pointer
397 * location into the zeroeth word of the state information.
398 *
399 * Note that due to the order in which things are done, it is OK to call
400 * setstate() with the same state as the current state.
401 *
402 * Returns a pointer to the old state information.
403 *
404 * Note: The Sparc platform requires that arg_state begin on a long
405 * word boundary; otherwise a bus error will occur. Even so, lint will
406 * complain about mis-alignment, but you should disregard these messages.
407 */
408char *
409setstate(char *arg_state)		/* pointer to state array */
410{
411	int *new_state;
412	int type;
413	int rear;
414	void *ostate = (void *)(&state[-1]);
415
416	_DIAGASSERT(arg_state != NULL);
417
418	new_state = (int *)(void *)arg_state;
419	type = (int)(new_state[0] % MAX_TYPES);
420	rear = (int)(new_state[0] / MAX_TYPES);
421
422	mutex_lock(&random_mutex);
423	if (rand_type == TYPE_0)
424		state[-1] = rand_type;
425	else
426		state[-1] = MAX_TYPES * (int)(rptr - state) + rand_type;
427	switch(type) {
428	case TYPE_0:
429	case TYPE_1:
430	case TYPE_2:
431	case TYPE_3:
432	case TYPE_4:
433		rand_type = type;
434		rand_deg = degrees[type];
435		rand_sep = seps[type];
436		break;
437	default:
438		mutex_unlock(&random_mutex);
439		return (NULL);
440	}
441	state = (int *) (new_state + 1);
442	if (rand_type != TYPE_0) {
443		rptr = &state[rear];
444		fptr = &state[(rear + rand_sep) % rand_deg];
445	}
446	end_ptr = &state[rand_deg];		/* set end_ptr too */
447	mutex_unlock(&random_mutex);
448	return((char *)ostate);
449}
450
451/*
452 * random:
453 *
454 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
455 * congruential bit.  Otherwise, we do our fancy trinomial stuff, which is
456 * the same in all the other cases due to all the global variables that have
457 * been set up.  The basic operation is to add the number at the rear pointer
458 * into the one at the front pointer.  Then both pointers are advanced to
459 * the next location cyclically in the table.  The value returned is the sum
460 * generated, reduced to 31 bits by throwing away the "least random" low bit.
461 *
462 * Note: the code takes advantage of the fact that both the front and
463 * rear pointers can't wrap on the same call by not testing the rear
464 * pointer if the front one has wrapped.
465 *
466 * Returns a 31-bit random number.
467 */
468static long
469random_unlocked(void)
470{
471	int i;
472	int *f, *r;
473
474	if (rand_type == TYPE_0) {
475		i = state[0];
476		state[0] = i = (i * 1103515245 + 12345) & 0x7fffffff;
477	} else {
478		/*
479		 * Use local variables rather than static variables for speed.
480		 */
481		f = fptr; r = rptr;
482		*f += *r;
483		/* chucking least random bit */
484		i = ((unsigned int)*f >> 1) & 0x7fffffff;
485		if (++f >= end_ptr) {
486			f = state;
487			++r;
488		}
489		else if (++r >= end_ptr) {
490			r = state;
491		}
492
493		fptr = f; rptr = r;
494	}
495	return(i);
496}
497
498long
499random(void)
500{
501	long r;
502
503	mutex_lock(&random_mutex);
504	r = random_unlocked();
505	mutex_unlock(&random_mutex);
506	return (r);
507}
508#else
509long
510random(void)
511{
512	static u_long randseed = 1;
513	long x, hi, lo, t;
514
515	/*
516	 * Compute x[n + 1] = (7^5 * x[n]) mod (2^31 - 1).
517	 * From "Random number generators: good ones are hard to find",
518	 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
519	 * October 1988, p. 1195.
520	 */
521	x = randseed;
522	hi = x / 127773;
523	lo = x % 127773;
524	t = 16807 * lo - 2836 * hi;
525	if (t <= 0)
526		t += 0x7fffffff;
527	randseed = t;
528	return (t);
529}
530#endif /* SMALL_RANDOM */
531