xref: /dragonfly/lib/libc/stdlib/random.c (revision 6fb88001)
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. All advertising materials mentioning features or use of this software
14  *    must display the following acknowledgement:
15  *	This product includes software developed by the University of
16  *	California, Berkeley and its contributors.
17  * 4. Neither the name of the University nor the names of its contributors
18  *    may be used to endorse or promote products derived from this software
19  *    without specific prior written permission.
20  *
21  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
22  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
23  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
24  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
25  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
26  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
27  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
28  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
29  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
30  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
31  * SUCH DAMAGE.
32  *
33  * $FreeBSD: src/lib/libc/stdlib/random.c,v 1.13 2000/01/27 23:06:49 jasone Exp $
34  * $DragonFly: src/lib/libc/stdlib/random.c,v 1.9 2005/11/24 17:18:30 swildner Exp $
35  *
36  * @(#)random.c	8.2 (Berkeley) 5/19/95
37  */
38 
39 #include "namespace.h"
40 #include <sys/time.h>          /* for srandomdev() */
41 #include <fcntl.h>             /* for srandomdev() */
42 #include <stdio.h>
43 #include <stdlib.h>
44 #include <unistd.h>            /* for srandomdev() */
45 #include "un-namespace.h"
46 
47 /*
48  * random.c:
49  *
50  * An improved random number generation package.  In addition to the standard
51  * rand()/srand() like interface, this package also has a special state info
52  * interface.  The initstate() routine is called with a seed, an array of
53  * bytes, and a count of how many bytes are being passed in; this array is
54  * then initialized to contain information for random number generation with
55  * that much state information.  Good sizes for the amount of state
56  * information are 32, 64, 128, and 256 bytes.  The state can be switched by
57  * calling the setstate() routine with the same array as was initiallized
58  * with initstate().  By default, the package runs with 128 bytes of state
59  * information and generates far better random numbers than a linear
60  * congruential generator.  If the amount of state information is less than
61  * 32 bytes, a simple linear congruential R.N.G. is used.
62  *
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:
68  * the zeroeth word of state information also has some other information
69  * stored in it -- see setstate() for details).
70  *
71  * The random number generation technique is a linear feedback shift register
72  * approach, employing trinomials (since there are fewer terms to sum up that
73  * way).  In this approach, the least significant bit of all the numbers in
74  * the state table will act as a linear feedback shift register, and will
75  * have period 2^deg - 1 (where deg is the degree of the polynomial being
76  * used, assuming that the polynomial is irreducible and primitive).  The
77  * higher order bits will have longer periods, since their values are also
78  * influenced by pseudo-random carries out of the lower bits.  The total
79  * period of the generator is approximately deg*(2**deg - 1); thus doubling
80  * the amount of state information has a vast influence on the period of the
81  * generator.  Note: the deg*(2**deg - 1) is an approximation only good for
82  * large deg, when the period of the shift register is the dominant factor.
83  * With deg equal to seven, the period is actually much longer than the
84  * 7*(2**7 - 1) predicted by this formula.
85  *
86  * Modified 28 December 1994 by Jacob S. Rosenberg.
87  * The following changes have been made:
88  * All references to the type u_int have been changed to unsigned long.
89  * All references to type int have been changed to type long.  Other
90  * cleanups have been made as well.  A warning for both initstate and
91  * setstate has been inserted to the effect that on Sparc platforms
92  * the 'arg_state' variable must be forced to begin on word boundaries.
93  * This can be easily done by casting a long integer array to char *.
94  * The overall logic has been left STRICTLY alone.  This software was
95  * tested on both a VAX and Sun SpacsStation with exactly the same
96  * results.  The new version and the original give IDENTICAL results.
97  * The new version is somewhat faster than the original.  As the
98  * documentation says:  "By default, the package runs with 128 bytes of
99  * state information and generates far better random numbers than a linear
100  * congruential generator.  If the amount of state information is less than
101  * 32 bytes, a simple linear congruential R.N.G. is used."  For a buffer of
102  * 128 bytes, this new version runs about 19 percent faster and for a 16
103  * byte buffer it is about 5 percent faster.
104  */
105 
106 /*
107  * For each of the currently supported random number generators, we have a
108  * break value on the amount of state information (you need at least this
109  * many bytes of state info to support this random number generator), a degree
110  * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
111  * the separation between the two lower order coefficients of the trinomial.
112  */
113 #define	TYPE_0		0		/* linear congruential */
114 #define	BREAK_0		8
115 #define	DEG_0		0
116 #define	SEP_0		0
117 
118 #define	TYPE_1		1		/* x**7 + x**3 + 1 */
119 #define	BREAK_1		32
120 #define	DEG_1		7
121 #define	SEP_1		3
122 
123 #define	TYPE_2		2		/* x**15 + x + 1 */
124 #define	BREAK_2		64
125 #define	DEG_2		15
126 #define	SEP_2		1
127 
128 #define	TYPE_3		3		/* x**31 + x**3 + 1 */
129 #define	BREAK_3		128
130 #define	DEG_3		31
131 #define	SEP_3		3
132 
133 #define	TYPE_4		4		/* x**63 + x + 1 */
134 #define	BREAK_4		256
135 #define	DEG_4		63
136 #define	SEP_4		1
137 
138 /*
139  * Array versions of the above information to make code run faster --
140  * relies on fact that TYPE_i == i.
141  */
142 #define	MAX_TYPES	5		/* max number of types above */
143 
144 static const int degrees[MAX_TYPES] =	{ DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
145 static const int seps [MAX_TYPES] =	{ SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
146 
147 /*
148  * Initially, everything is set up as if from:
149  *
150  *	initstate(1, randtbl, 128);
151  *
152  * Note that this initialization takes advantage of the fact that srandom()
153  * advances the front and rear pointers 10*rand_deg times, and hence the
154  * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
155  * element of the state information, which contains info about the current
156  * position of the rear pointer is just
157  *
158  *	MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
159  */
160 
161 static uint32_t randtbl[DEG_3 + 1] = {
162 	TYPE_3,
163 #ifdef  USE_WEAK_SEEDING
164 /* Historic implementation compatibility */
165 /* The random sequences do not vary much with the seed */
166 	0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
167 	0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
168 	0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
169 	0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
170 	0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
171 	0x27fb47b9,
172 #else   /* !USE_WEAK_SEEDING */
173 	0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
174 	0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
175 	0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
176 	0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
177 	0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
178 	0xf3bec5da
179 #endif  /* !USE_WEAK_SEEDING */
180 };
181 
182 /*
183  * fptr and rptr are two pointers into the state info, a front and a rear
184  * pointer.  These two pointers are always rand_sep places aparts, as they
185  * cycle cyclically through the state information.  (Yes, this does mean we
186  * could get away with just one pointer, but the code for random() is more
187  * efficient this way).  The pointers are left positioned as they would be
188  * from the call
189  *
190  *	initstate(1, randtbl, 128);
191  *
192  * (The position of the rear pointer, rptr, is really 0 (as explained above
193  * in the initialization of randtbl) because the state table pointer is set
194  * to point to randtbl[1] (as explained below).
195  */
196 static uint32_t *fptr = &randtbl[SEP_3 + 1];
197 static uint32_t *rptr = &randtbl[1];
198 
199 /*
200  * The following things are the pointer to the state information table, the
201  * type of the current generator, the degree of the current polynomial being
202  * used, and the separation between the two pointers.  Note that for efficiency
203  * of random(), we remember the first location of the state information, not
204  * the zeroeth.  Hence it is valid to access state[-1], which is used to
205  * store the type of the R.N.G.  Also, we remember the last location, since
206  * this is more efficient than indexing every time to find the address of
207  * the last element to see if the front and rear pointers have wrapped.
208  */
209 static uint32_t *state = &randtbl[1];
210 static int rand_type = TYPE_3;
211 static int rand_deg = DEG_3;
212 static int rand_sep = SEP_3;
213 static uint32_t *end_ptr = &randtbl[DEG_3 + 1];
214 
215 static inline long good_rand(long);
216 
217 static inline long
218 good_rand(long x)
219 {
220 #ifdef  USE_WEAK_SEEDING
221 /*
222  * Historic implementation compatibility.
223  * The random sequences do not vary much with the seed,
224  * even with overflowing.
225  */
226 	return (1103515245 * x + 12345);
227 #else   /* !USE_WEAK_SEEDING */
228 /*
229  * Compute x = (7^5 * x) mod (2^31 - 1)
230  * wihout overflowing 31 bits:
231  *      (2^31 - 1) = 127773 * (7^5) + 2836
232  * From "Random number generators: good ones are hard to find",
233  * Park and Miller, Communications of the ACM, vol. 31, no. 10,
234  * October 1988, p. 1195.
235  */
236 	long hi, lo;
237 
238 	hi = x / 127773;
239 	lo = x % 127773;
240 	x = 16807 * lo - 2836 * hi;
241 	if (x <= 0)
242 		x += 0x7fffffff;
243 	return (x);
244 #endif  /* !USE_WEAK_SEEDING */
245 }
246 
247 /*
248  * srandom:
249  *
250  * Initialize the random number generator based on the given seed.  If the
251  * type is the trivial no-state-information type, just remember the seed.
252  * Otherwise, initializes state[] based on the given "seed" via a linear
253  * congruential generator.  Then, the pointers are set to known locations
254  * that are exactly rand_sep places apart.  Lastly, it cycles the state
255  * information a given number of times to get rid of any initial dependencies
256  * introduced by the L.C.R.N.G.  Note that the initialization of randtbl[]
257  * for default usage relies on values produced by this routine.
258  */
259 void
260 srandom(unsigned long x)
261 {
262 	int i;
263 
264 	if (rand_type == TYPE_0)
265 		state[0] = (uint32_t)x;
266 	else {
267 		state[0] = (uint32_t)x;
268 		for (i = 1; i < rand_deg; i++)
269 			state[i] = (uint32_t)good_rand(state[i - 1]);
270 		fptr = &state[rand_sep];
271 		rptr = &state[0];
272 		for (i = 0; i < 10 * rand_deg; i++)
273 			random();
274 	}
275 }
276 
277 /*
278  * srandomdev:
279  *
280  * Many programs choose the seed value in a totally predictable manner.
281  * This often causes problems.  We seed the generator using the much more
282  * secure urandom(4) interface.  Note that this particular seeding
283  * procedure can generate states which are impossible to reproduce by
284  * calling srandom() with any value, since the succeeding terms in the
285  * state buffer are no longer derived from the LC algorithm applied to
286  * a fixed seed.
287  */
288 void
289 srandomdev(void)
290 {
291 	int fd, done;
292 	size_t len;
293 
294 	if (rand_type == TYPE_0)
295 		len = sizeof state[0];
296 	else
297 		len = rand_deg * sizeof state[0];
298 
299 	done = 0;
300 	fd = _open("/dev/urandom", O_RDONLY, 0);
301 	if (fd >= 0) {
302 		if (_read(fd, (void *) state, len) == (ssize_t) len)
303 			done = 1;
304 		_close(fd);
305 	}
306 
307 	if (!done) {
308 		struct timeval tv;
309 		unsigned long junk;	/* XXX left uninitialized on purpose */
310 
311 		gettimeofday(&tv, NULL);
312 		srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk);
313 		return;
314 	}
315 
316 	if (rand_type != TYPE_0) {
317 		fptr = &state[rand_sep];
318 		rptr = &state[0];
319 	}
320 }
321 
322 /*
323  * initstate:
324  *
325  * Initialize the state information in the given array of n bytes for future
326  * random number generation.  Based on the number of bytes we are given, and
327  * the break values for the different R.N.G.'s, we choose the best (largest)
328  * one we can and set things up for it.  srandom() is then called to
329  * initialize the state information.
330  *
331  * Note that on return from srandom(), we set state[-1] to be the type
332  * multiplexed with the current value of the rear pointer; this is so
333  * successive calls to initstate() won't lose this information and will be
334  * able to restart with setstate().
335  *
336  * Note: the first thing we do is save the current state, if any, just like
337  * setstate() so that it doesn't matter when initstate is called.
338  *
339  * Parameters:
340  *	seed:		seed for R.N.G.
341  *	arg_state:	pointer to state array
342  *	n:		# bytes of state info
343  *
344  * Returns a pointer to the old state.
345  *
346  * Note: The Sparc platform requires that arg_state begin on an int
347  * word boundary; otherwise a bus error will occur. Even so, lint will
348  * complain about mis-alignment, but you should disregard these messages.
349  */
350 char *
351 initstate(unsigned long seed, char *arg_state, long n)
352 {
353 	char *ostate = (char *)(&state[-1]);
354 	uint32_t *int_arg_state = (uint32_t *)(void *)arg_state;
355 
356 	if (rand_type == TYPE_0)
357 		state[-1] = rand_type;
358 	else
359 		state[-1] = MAX_TYPES * (uint32_t)(rptr - state) + rand_type;
360 	if (n < BREAK_0) {
361 		fprintf(stderr,
362 		    "random: not enough state (%ld bytes); ignored.\n", n);
363 		return(0);
364 	}
365 	if (n < BREAK_1) {
366 		rand_type = TYPE_0;
367 		rand_deg = DEG_0;
368 		rand_sep = SEP_0;
369 	} else if (n < BREAK_2) {
370 		rand_type = TYPE_1;
371 		rand_deg = DEG_1;
372 		rand_sep = SEP_1;
373 	} else if (n < BREAK_3) {
374 		rand_type = TYPE_2;
375 		rand_deg = DEG_2;
376 		rand_sep = SEP_2;
377 	} else if (n < BREAK_4) {
378 		rand_type = TYPE_3;
379 		rand_deg = DEG_3;
380 		rand_sep = SEP_3;
381 	} else {
382 		rand_type = TYPE_4;
383 		rand_deg = DEG_4;
384 		rand_sep = SEP_4;
385 	}
386 	state = (uint32_t *) (int_arg_state + 1); /* first location */
387 	end_ptr = &state[rand_deg];	/* must set end_ptr before srandom */
388 	srandom((uint32_t)seed);
389 	if (rand_type == TYPE_0)
390 		int_arg_state[0] = rand_type;
391 	else
392 		int_arg_state[0] = MAX_TYPES * (uint32_t)(rptr - state) + rand_type;
393 	return(ostate);
394 }
395 
396 /*
397  * setstate:
398  *
399  * Restore the state from the given state array.
400  *
401  * Note: it is important that we also remember the locations of the pointers
402  * in the current state information, and restore the locations of the pointers
403  * from the old state information.  This is done by multiplexing the pointer
404  * location into the zeroeth word of the state information.
405  *
406  * Note that due to the order in which things are done, it is OK to call
407  * setstate() with the same state as the current state.
408  *
409  * Parameters:
410  *	arg_state:	pointer to state array
411  *
412  * Returns a pointer to the old state information.
413  *
414  * Note: The Sparc platform requires that arg_state begin on a long
415  * word boundary; otherwise a bus error will occur. Even so, lint will
416  * complain about mis-alignment, but you should disregard these messages.
417  */
418 char *
419 setstate(char *arg_state)
420 {
421 	uint32_t *new_state = (uint32_t *)(void *)arg_state;
422 	uint32_t type = new_state[0] % MAX_TYPES;
423 	uint32_t rear = new_state[0] / MAX_TYPES;
424 	char *ostate = (char *)(&state[-1]);
425 
426 	if (rand_type == TYPE_0)
427 		state[-1] = rand_type;
428 	else
429 		state[-1] = MAX_TYPES * (uint32_t)(rptr - state) + rand_type;
430 	switch(type) {
431 	case TYPE_0:
432 	case TYPE_1:
433 	case TYPE_2:
434 	case TYPE_3:
435 	case TYPE_4:
436 		rand_type = type;
437 		rand_deg = degrees[type];
438 		rand_sep = seps[type];
439 		break;
440 	default:
441 		fprintf(stderr,
442 		    "random: state info corrupted; not changed.\n");
443 	}
444 	state = (uint32_t *) (new_state + 1);
445 	if (rand_type != TYPE_0) {
446 		rptr = &state[rear];
447 		fptr = &state[(rear + rand_sep) % rand_deg];
448 	}
449 	end_ptr = &state[rand_deg];		/* set end_ptr too */
450 	return(ostate);
451 }
452 
453 /*
454  * random:
455  *
456  * If we are using the trivial TYPE_0 R.N.G., just do the old linear
457  * congruential bit.  Otherwise, we do our fancy trinomial stuff, which is
458  * the same in all the other cases due to all the global variables that have
459  * been set up.  The basic operation is to add the number at the rear pointer
460  * into the one at the front pointer.  Then both pointers are advanced to
461  * the next location cyclically in the table.  The value returned is the sum
462  * generated, reduced to 31 bits by throwing away the "least random" low bit.
463  *
464  * Note: the code takes advantage of the fact that both the front and
465  * rear pointers can't wrap on the same call by not testing the rear
466  * pointer if the front one has wrapped.
467  *
468  * Returns a 31-bit random number.
469  */
470 long
471 random(void)
472 {
473 	uint32_t i;
474 	uint32_t *f, *r;
475 
476 	if (rand_type == TYPE_0) {
477 		i = state[0];
478 		state[0] = i = (good_rand(i)) & 0x7fffffff;
479 	} else {
480 		/*
481 		 * Use local variables rather than static variables for speed.
482 		 */
483 		f = fptr; r = rptr;
484 		*f += *r;
485 		/* chucking least random bit */
486 		i = (*f >> 1) & 0x7fffffff;
487 		if (++f >= end_ptr) {
488 			f = state;
489 			++r;
490 		}
491 		else if (++r >= end_ptr) {
492 			r = state;
493 		}
494 
495 		fptr = f; rptr = r;
496 	}
497 	return((long)i);
498 }
499