xref: /illumos-gate/usr/src/lib/libc/port/gen/random.c (revision 7257d1b4)
1 /*
2  * CDDL HEADER START
3  *
4  * The contents of this file are subject to the terms of the
5  * Common Development and Distribution License (the "License").
6  * You may not use this file except in compliance with the License.
7  *
8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9  * or http://www.opensolaris.org/os/licensing.
10  * See the License for the specific language governing permissions
11  * and limitations under the License.
12  *
13  * When distributing Covered Code, include this CDDL HEADER in each
14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15  * If applicable, add the following below this CDDL HEADER, with the
16  * fields enclosed by brackets "[]" replaced with your own identifying
17  * information: Portions Copyright [yyyy] [name of copyright owner]
18  *
19  * CDDL HEADER END
20  */
21 
22 /*
23  * Copyright 2008 Sun Microsystems, Inc.  All rights reserved.
24  * Use is subject to license terms.
25  */
26 
27 /*	Copyright (c) 1984, 1986, 1987, 1988, 1989 AT&T	*/
28 /*	  All Rights Reserved  	*/
29 
30 /*
31  * University Copyright- Copyright (c) 1982, 1986, 1988
32  * The Regents of the University of California
33  * All Rights Reserved
34  *
35  * University Acknowledgment- Portions of this document are derived from
36  * software developed by the University of California, Berkeley, and its
37  * contributors.
38  */
39 
40 #pragma ident	"%Z%%M%	%I%	%E% SMI"
41 
42 #include "lint.h"
43 #include <stdio.h>
44 #include <stdlib.h>
45 #include <string.h>
46 #include <sys/types.h>
47 #include <limits.h>
48 
49 /*
50  * random.c:
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 then
55  * initialized to contain information for random number generation with that
56  * much state information.  Good sizes for the amount of state information are
57  * 32, 64, 128, and 256 bytes.  The state can be switched by calling the
58  * setstate() routine with the same array as was initiallized with initstate().
59  * By default, the package runs with 128 bytes of state information and
60  * generates far better random numbers than a linear congruential generator.
61  * If the amount of state information is less than 32 bytes, a simple linear
62  * congruential R.N.G. is used.
63  * Internally, the state information is treated as an array of ints; the
64  * zeroeth element of the array is the type of R.N.G. being used (small
65  * integer); the remainder of the array is the state information for the
66  * R.N.G.  Thus, 32 bytes of state information will give 7 ints worth of
67  * state information, which will allow a degree seven polynomial.  (Note: the
68  * zeroeth word of state information also has some other information stored
69  * in it -- see setstate() for details).
70  * The random number generation technique is a linear feedback shift register
71  * approach, employing trinomials (since there are fewer terms to sum up that
72  * way).  In this approach, the least significant bit of all the numbers in
73  * the state table will act as a linear feedback shift register, and will have
74  * period 2^deg - 1 (where deg is the degree of the polynomial being used,
75  * assuming that the polynomial is irreducible and primitive).  The higher
76  * order bits will have longer periods, since their values are also influenced
77  * by pseudo-random carries out of the lower bits.  The total period of the
78  * generator is approximately deg*(2**deg - 1); thus doubling the amount of
79  * state information has a vast influence on the period of the generator.
80  * Note: the deg*(2**deg - 1) is an approximation only good for large deg,
81  * when the period of the shift register is the dominant factor.  With deg
82  * equal to seven, the period is actually much longer than the 7*(2**7 - 1)
83  * predicted by this formula.
84  */
85 
86 
87 
88 /*
89  * For each of the currently supported random number generators, we have a
90  * break value on the amount of state information (you need at least this
91  * many bytes of state info to support this random number generator), a degree
92  * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
93  * the separation between the two lower order coefficients of the trinomial.
94  */
95 
96 #define		TYPE_0		0		/* linear congruential */
97 #define		BREAK_0		8
98 #define		DEG_0		0
99 #define		SEP_0		0
100 
101 #define		TYPE_1		1		/* x**7 + x**3 + 1 */
102 #define		BREAK_1		32
103 #define		DEG_1		7
104 #define		SEP_1		3
105 
106 #define		TYPE_2		2		/* x**15 + x + 1 */
107 #define		BREAK_2		64
108 #define		DEG_2		15
109 #define		SEP_2		1
110 
111 #define		TYPE_3		3		/* x**31 + x**3 + 1 */
112 #define		BREAK_3		128
113 #define		DEG_3		31
114 #define		SEP_3		3
115 
116 #define		TYPE_4		4		/* x**63 + x + 1 */
117 #define		BREAK_4		256
118 #define		DEG_4		63
119 #define		SEP_4		1
120 
121 
122 /*
123  * Array versions of the above information to make code run faster -- relies
124  * on fact that TYPE_i == i.
125  */
126 
127 #define		MAX_TYPES	5		/* max number of types above */
128 
129 static struct _randomjunk {
130 	unsigned int	degrees[MAX_TYPES];
131 	unsigned int	seps[MAX_TYPES];
132 	unsigned int	randtbl[ DEG_3 + 1 ];
133 /*
134  * fptr and rptr are two pointers into the state info, a front and a rear
135  * pointer.  These two pointers are always rand_sep places aparts, as they cycle
136  * cyclically through the state information.  (Yes, this does mean we could get
137  * away with just one pointer, but the code for random() is more efficient this
138  * way).  The pointers are left positioned as they would be from the call
139  *			initstate( 1, randtbl, 128 )
140  * (The position of the rear pointer, rptr, is really 0 (as explained above
141  * in the initialization of randtbl) because the state table pointer is set
142  * to point to randtbl[1] (as explained below).
143  */
144 	unsigned int	*fptr, *rptr;
145 /*
146  * The following things are the pointer to the state information table,
147  * the type of the current generator, the degree of the current polynomial
148  * being used, and the separation between the two pointers.
149  * Note that for efficiency of random(), we remember the first location of
150  * the state information, not the zeroeth.  Hence it is valid to access
151  * state[-1], which is used to store the type of the R.N.G.
152  * Also, we remember the last location, since this is more efficient than
153  * indexing every time to find the address of the last element to see if
154  * the front and rear pointers have wrapped.
155  */
156 	unsigned int	*state;
157 	unsigned int	rand_type, rand_deg, rand_sep;
158 	unsigned int	*end_ptr;
159 } *__randomjunk, *_randomjunk(void), _randominit = {
160 	/*
161 	 * Initially, everything is set up as if from :
162 	 *		initstate( 1, &randtbl, 128 );
163 	 * Note that this initialization takes advantage of the fact
164 	 * that srandom() advances the front and rear pointers 10*rand_deg
165 	 * times, and hence the rear pointer which starts at 0 will also
166 	 * end up at zero; thus the zeroeth element of the state
167 	 * information, which contains info about the current
168 	 * position of the rear pointer is just
169 	 *	MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3.
170 	 */
171 	{ DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 },
172 	{ SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 },
173 	{ TYPE_3,
174 	    0x9a319039U, 0x32d9c024U, 0x9b663182U, 0x5da1f342U,
175 	    0xde3b81e0U, 0xdf0a6fb5U, 0xf103bc02U, 0x48f340fbU,
176 	    0x7449e56bU, 0xbeb1dbb0U, 0xab5c5918U, 0x946554fdU,
177 	    0x8c2e680fU, 0xeb3d799fU, 0xb11ee0b7U, 0x2d436b86U,
178 	    0xda672e2aU, 0x1588ca88U, 0xe369735dU, 0x904f35f7U,
179 	    0xd7158fd6U, 0x6fa6f051U, 0x616e6b96U, 0xac94efdcU,
180 	    0x36413f93U, 0xc622c298U, 0xf5a42ab8U, 0x8a88d77bU,
181 			0xf5ad9d0eU, 0x8999220bU, 0x27fb47b9U },
182 	&_randominit.randtbl[ SEP_3 + 1 ],
183 	&_randominit.randtbl[ 1 ],
184 	&_randominit.randtbl[ 1 ],
185 	TYPE_3, DEG_3, SEP_3,
186 	&_randominit.randtbl[ DEG_3 + 1]
187 };
188 
189 static struct _randomjunk *
_randomjunk(void)190 _randomjunk(void)
191 {
192 	struct _randomjunk *rp = __randomjunk;
193 
194 	if (rp == NULL) {
195 		rp = (struct _randomjunk *)malloc(sizeof (*rp));
196 		if (rp == NULL)
197 			return (NULL);
198 		(void) memcpy(rp, &_randominit, sizeof (*rp));
199 		__randomjunk = rp;
200 	}
201 	return (rp);
202 }
203 
204 
205 /*
206  * initstate:
207  * Initialize the state information in the given array of n bytes for
208  * future random number generation.  Based on the number of bytes we
209  * are given, and the break values for the different R.N.G.'s, we choose
210  * the best (largest) one we can and set things up for it.  srandom() is
211  * then called to initialize the state information.
212  * Note that on return from srandom(), we set state[-1] to be the type
213  * multiplexed with the current value of the rear pointer; this is so
214  * successive calls to initstate() won't lose this information and will
215  * be able to restart with setstate().
216  * Note: the first thing we do is save the current state, if any, just like
217  * setstate() so that it doesn't matter when initstate is called.
218  * Returns a pointer to the old state.
219  */
220 
221 char  *
initstate(unsigned int seed,char * arg_state,size_t size)222 initstate(
223 	unsigned int seed,	/* seed for R. N. G. */
224 	char *arg_state,	/* pointer to state array */
225 	size_t size)		/* # bytes of state info */
226 {
227 	unsigned int n;
228 	struct _randomjunk *rp = _randomjunk();
229 	char		*ostate;
230 
231 	if (size > UINT_MAX)
232 		n = UINT_MAX;
233 	else
234 		n = (unsigned int)size;
235 
236 	if (rp == NULL)
237 		return (NULL);
238 	ostate = (char *)(&rp->state[ -1 ]);
239 
240 	if (rp->rand_type  ==  TYPE_0)  rp->state[ -1 ] = rp->rand_type;
241 	else  rp->state[ -1 ] =
242 	    (unsigned int)(MAX_TYPES*(rp->rptr - rp->state) + rp->rand_type);
243 	if (n  <  BREAK_1)  {
244 	    if (n  <  BREAK_0)  {
245 		return (NULL);
246 	    }
247 	    rp->rand_type = TYPE_0;
248 	    rp->rand_deg = DEG_0;
249 	    rp->rand_sep = SEP_0;
250 	} else  {
251 	    if (n  <  BREAK_2)  {
252 		rp->rand_type = TYPE_1;
253 		rp->rand_deg = DEG_1;
254 		rp->rand_sep = SEP_1;
255 	    } else  {
256 		if (n  <  BREAK_3)  {
257 		    rp->rand_type = TYPE_2;
258 		    rp->rand_deg = DEG_2;
259 		    rp->rand_sep = SEP_2;
260 		} else  {
261 		    if (n  <  BREAK_4)  {
262 			rp->rand_type = TYPE_3;
263 			rp->rand_deg = DEG_3;
264 			rp->rand_sep = SEP_3;
265 		    } else  {
266 			rp->rand_type = TYPE_4;
267 			rp->rand_deg = DEG_4;
268 			rp->rand_sep = SEP_4;
269 		    }
270 		}
271 	    }
272 	}
273 	/* first location */
274 	rp->state = &(((unsigned int *)(uintptr_t)arg_state)[1]);
275 	/* must set end_ptr before srandom */
276 	rp->end_ptr = &rp->state[rp->rand_deg];
277 	srandom(seed);
278 	if (rp->rand_type  ==  TYPE_0)  rp->state[ -1 ] = rp->rand_type;
279 	else
280 		rp->state[-1] = (unsigned int)(MAX_TYPES*
281 		    (rp->rptr - rp->state) + rp->rand_type);
282 	return (ostate);
283 }
284 
285 
286 
287 /*
288  * setstate:
289  * Restore the state from the given state array.
290  * Note: it is important that we also remember the locations of the pointers
291  * in the current state information, and restore the locations of the pointers
292  * from the old state information.  This is done by multiplexing the pointer
293  * location into the zeroeth word of the state information.
294  * Note that due to the order in which things are done, it is OK to call
295  * setstate() with the same state as the current state.
296  * Returns a pointer to the old state information.
297  */
298 
299 char  *
setstate(const char * arg_state)300 setstate(const char *arg_state)
301 {
302 	struct _randomjunk *rp = _randomjunk();
303 	unsigned int	*new_state;
304 	unsigned int	type;
305 	unsigned int	rear;
306 	char		*ostate;
307 
308 	if (rp == NULL)
309 		return (NULL);
310 	new_state = (unsigned int *)(uintptr_t)arg_state;
311 	type = new_state[0]%MAX_TYPES;
312 	rear = new_state[0]/MAX_TYPES;
313 	ostate = (char *)(&rp->state[ -1 ]);
314 
315 	if (rp->rand_type  ==  TYPE_0) rp->state[ -1 ] = rp->rand_type;
316 	else
317 		rp->state[-1] = (unsigned int)(MAX_TYPES*
318 		    (rp->rptr - rp->state) + rp->rand_type);
319 	switch (type)  {
320 	    case  TYPE_0:
321 	    case  TYPE_1:
322 	    case  TYPE_2:
323 	    case  TYPE_3:
324 	    case  TYPE_4:
325 		rp->rand_type = type;
326 		rp->rand_deg = rp->degrees[ type ];
327 		rp->rand_sep = rp->seps[ type ];
328 		break;
329 
330 	    default:
331 		return (NULL);
332 	}
333 	rp->state = &new_state[ 1 ];
334 	if (rp->rand_type  !=  TYPE_0)  {
335 	    rp->rptr = &rp->state[ rear ];
336 	    rp->fptr = &rp->state[ (rear + rp->rand_sep)%rp->rand_deg ];
337 	}
338 	rp->end_ptr = &rp->state[ rp->rand_deg ];	/* set end_ptr too */
339 	return (ostate);
340 }
341 
342 
343 
344 /*
345  * random:
346  * If we are using the trivial TYPE_0 R.N.G., just do the old linear
347  * congruential bit.  Otherwise, we do our fancy trinomial stuff, which is the
348  * same in all ther other cases due to all the global variables that have been
349  * set up.  The basic operation is to add the number at the rear pointer into
350  * the one at the front pointer.  Then both pointers are advanced to the next
351  * location cyclically in the table.  The value returned is the sum generated,
352  * reduced to 31 bits by throwing away the "least random" low bit.
353  * Note: the code takes advantage of the fact that both the front and
354  * rear pointers can't wrap on the same call by not testing the rear
355  * pointer if the front one has wrapped.
356  * Returns a 31-bit random number.
357  */
358 
359 long
random(void)360 random(void)
361 {
362 	struct _randomjunk *rp = _randomjunk();
363 	unsigned int	i;
364 
365 	if (rp == NULL)
366 		return (0L);
367 	if (rp->rand_type  ==  TYPE_0)  {
368 	    i = rp->state[0] = (rp->state[0]*1103515245 + 12345)&0x7fffffff;
369 	} else  {
370 	    *rp->fptr += *rp->rptr;
371 	    i = (*rp->fptr >> 1)&0x7fffffff;	/* chucking least random bit */
372 	    if (++rp->fptr  >=  rp->end_ptr)  {
373 		rp->fptr = rp->state;
374 		++rp->rptr;
375 	    } else  {
376 		if (++rp->rptr  >=  rp->end_ptr)  rp->rptr = rp->state;
377 	    }
378 	}
379 	return ((long)i);
380 }
381 
382 /*
383  * srandom:
384  * Initialize the random number generator based on the given seed.  If the
385  * type is the trivial no-state-information type, just remember the seed.
386  * Otherwise, initializes state[] based on the given "seed" via a linear
387  * congruential generator.  Then, the pointers are set to known locations
388  * that are exactly rand_sep places apart.  Lastly, it cycles the state
389  * information a given number of times to get rid of any initial dependencies
390  * introduced by the L.C.R.N.G.
391  * Note that the initialization of randtbl[] for default usage relies on
392  * values produced by this routine.
393  */
394 
395 void
srandom(unsigned int x)396 srandom(unsigned int x)
397 {
398 	struct _randomjunk *rp = _randomjunk();
399 	unsigned int	i;
400 
401 	if (rp == NULL)
402 		return;
403 	if (rp->rand_type  ==  TYPE_0)  {
404 	    rp->state[ 0 ] = x;
405 	} else  {
406 	    rp->state[ 0 ] = x;
407 	    for (i = 1; i < rp->rand_deg; i++)  {
408 		rp->state[i] = 1103515245*rp->state[i - 1] + 12345;
409 	    }
410 	    rp->fptr = &rp->state[ rp->rand_sep ];
411 	    rp->rptr = &rp->state[ 0 ];
412 	    for (i = 0; i < 10*rp->rand_deg; i++)  (void)random();
413 	}
414 }
415