2 * Copyright (c) 1983, 1993
3 * The Regents of the University of California. All rights reserved.
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
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.
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
30 #if defined(LIBC_SCCS) && !defined(lint)
31 static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95";
32 #endif /* LIBC_SCCS and not lint */
33 #include <sys/cdefs.h>
34 __FBSDID("$FreeBSD$");
36 #include "namespace.h"
37 #include <sys/param.h>
38 #include <sys/sysctl.h>
41 #include "un-namespace.h"
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.
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).
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.
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.
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.
109 #define TYPE_0 0 /* linear congruential */
114 #define TYPE_1 1 /* x**7 + x**3 + 1 */
119 #define TYPE_2 2 /* x**15 + x + 1 */
124 #define TYPE_3 3 /* x**31 + x**3 + 1 */
129 #define TYPE_4 4 /* x**63 + x + 1 */
135 * Array versions of the above information to make code run faster --
136 * relies on fact that TYPE_i == i.
138 #define MAX_TYPES 5 /* max number of types above */
140 #define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */
142 static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
143 static const int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
146 * Initially, everything is set up as if from:
148 * initstate(1, randtbl, 128);
150 * Note that this initialization takes advantage of the fact that srandom()
151 * advances the front and rear pointers 10*rand_deg times, and hence the
152 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
153 * element of the state information, which contains info about the current
154 * position of the rear pointer is just
156 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
159 static uint32_t randtbl[DEG_3 + 1] = {
161 0x2cf41758, 0x27bb3711, 0x4916d4d1, 0x7b02f59f, 0x9b8e28eb, 0xc0e80269,
162 0x696f5c16, 0x878f1ff5, 0x52d9c07f, 0x916a06cd, 0xb50b3a20, 0x2776970a,
163 0xee4eb2a6, 0xe94640ec, 0xb1d65612, 0x9d1ed968, 0x1043f6b7, 0xa3432a76,
164 0x17eacbb9, 0x3c09e2eb, 0x4f8c2b3, 0x708a1f57, 0xee341814, 0x95d0e4d2,
165 0xb06f216c, 0x8bd2e72e, 0x8f7c38d7, 0xcfc6a8fc, 0x2a59495, 0xa20d2a69,
170 * fptr and rptr are two pointers into the state info, a front and a rear
171 * pointer. These two pointers are always rand_sep places aparts, as they
172 * cycle cyclically through the state information. (Yes, this does mean we
173 * could get away with just one pointer, but the code for random() is more
174 * efficient this way). The pointers are left positioned as they would be
177 * initstate(1, randtbl, 128);
179 * (The position of the rear pointer, rptr, is really 0 (as explained above
180 * in the initialization of randtbl) because the state table pointer is set
181 * to point to randtbl[1] (as explained below).
183 static uint32_t *fptr = &randtbl[SEP_3 + 1];
184 static uint32_t *rptr = &randtbl[1];
187 * The following things are the pointer to the state information table, the
188 * type of the current generator, the degree of the current polynomial being
189 * used, and the separation between the two pointers. Note that for efficiency
190 * of random(), we remember the first location of the state information, not
191 * the zeroeth. Hence it is valid to access state[-1], which is used to
192 * store the type of the R.N.G. Also, we remember the last location, since
193 * this is more efficient than indexing every time to find the address of
194 * the last element to see if the front and rear pointers have wrapped.
196 static uint32_t *state = &randtbl[1];
197 static int rand_type = TYPE_3;
198 static int rand_deg = DEG_3;
199 static int rand_sep = SEP_3;
200 static uint32_t *end_ptr = &randtbl[DEG_3 + 1];
202 static inline uint32_t
203 good_rand(uint32_t ctx)
206 * Compute x = (7^5 * x) mod (2^31 - 1)
207 * wihout overflowing 31 bits:
208 * (2^31 - 1) = 127773 * (7^5) + 2836
209 * From "Random number generators: good ones are hard to find",
210 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
211 * October 1988, p. 1195.
215 /* Transform to [1, 0x7ffffffe] range. */
216 x = (ctx % 0x7ffffffe) + 1;
219 x = 16807 * lo - 2836 * hi;
222 /* Transform to [0, 0x7ffffffd] range. */
229 * Initialize the random number generator based on the given seed. If the
230 * type is the trivial no-state-information type, just remember the seed.
231 * Otherwise, initializes state[] based on the given "seed" via a linear
232 * congruential generator. Then, the pointers are set to known locations
233 * that are exactly rand_sep places apart. Lastly, it cycles the state
234 * information a given number of times to get rid of any initial dependencies
235 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
236 * for default usage relies on values produced by this routine.
239 srandom(unsigned int x)
243 state[0] = (uint32_t)x;
244 if (rand_type == TYPE_0)
247 for (i = 1; i < rand_deg; i++)
248 state[i] = good_rand(state[i - 1]);
249 fptr = &state[rand_sep];
253 for (i = 0; i < lim; i++)
260 * Many programs choose the seed value in a totally predictable manner.
261 * This often causes problems. We seed the generator using pseudo-random
262 * data from the kernel.
264 * Note that this particular seeding procedure can generate states
265 * which are impossible to reproduce by calling srandom() with any
266 * value, since the succeeding terms in the state buffer are no longer
267 * derived from the LC algorithm applied to a fixed seed.
273 size_t expected, len;
275 if (rand_type == TYPE_0)
276 expected = len = sizeof(state[0]);
278 expected = len = rand_deg * sizeof(state[0]);
282 if (sysctl(mib, 2, state, &len, NULL, 0) == -1 || len != expected) {
284 * The sysctl cannot fail. If it does fail on some FreeBSD
285 * derivative or after some future change, just abort so that
286 * the problem will be found and fixed. abort is not normally
287 * suitable for a library but makes sense here.
292 if (rand_type != TYPE_0) {
293 fptr = &state[rand_sep];
301 * Initialize the state information in the given array of n bytes for future
302 * random number generation. Based on the number of bytes we are given, and
303 * the break values for the different R.N.G.'s, we choose the best (largest)
304 * one we can and set things up for it. srandom() is then called to
305 * initialize the state information.
307 * Note that on return from srandom(), we set state[-1] to be the type
308 * multiplexed with the current value of the rear pointer; this is so
309 * successive calls to initstate() won't lose this information and will be
310 * able to restart with setstate().
312 * Note: the first thing we do is save the current state, if any, just like
313 * setstate() so that it doesn't matter when initstate is called.
315 * Returns a pointer to the old state.
317 * Note: The Sparc platform requires that arg_state begin on an int
318 * word boundary; otherwise a bus error will occur. Even so, lint will
319 * complain about mis-alignment, but you should disregard these messages.
322 initstate(unsigned int seed, char *arg_state, size_t n)
324 char *ostate = (char *)(&state[-1]);
325 uint32_t *int_arg_state = (uint32_t *)arg_state;
329 if (rand_type == TYPE_0)
330 state[-1] = rand_type;
332 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
337 } else if (n < BREAK_2) {
341 } else if (n < BREAK_3) {
345 } else if (n < BREAK_4) {
354 state = int_arg_state + 1; /* first location */
355 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
357 if (rand_type == TYPE_0)
358 int_arg_state[0] = rand_type;
360 int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
367 * Restore the state from the given state array.
369 * Note: it is important that we also remember the locations of the pointers
370 * in the current state information, and restore the locations of the pointers
371 * from the old state information. This is done by multiplexing the pointer
372 * location into the zeroeth word of the state information.
374 * Note that due to the order in which things are done, it is OK to call
375 * setstate() with the same state as the current state.
377 * Returns a pointer to the old state information.
379 * Note: The Sparc platform requires that arg_state begin on an int
380 * word boundary; otherwise a bus error will occur. Even so, lint will
381 * complain about mis-alignment, but you should disregard these messages.
384 setstate(char *arg_state)
386 uint32_t *new_state = (uint32_t *)arg_state;
387 uint32_t type = new_state[0] % MAX_TYPES;
388 uint32_t rear = new_state[0] / MAX_TYPES;
389 char *ostate = (char *)(&state[-1]);
391 if (type != TYPE_0 && rear >= degrees[type])
393 if (rand_type == TYPE_0)
394 state[-1] = rand_type;
396 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
398 rand_deg = degrees[type];
399 rand_sep = seps[type];
400 state = new_state + 1;
401 if (rand_type != TYPE_0) {
403 fptr = &state[(rear + rand_sep) % rand_deg];
405 end_ptr = &state[rand_deg]; /* set end_ptr too */
412 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
413 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
414 * the same in all the other cases due to all the global variables that have
415 * been set up. The basic operation is to add the number at the rear pointer
416 * into the one at the front pointer. Then both pointers are advanced to
417 * the next location cyclically in the table. The value returned is the sum
418 * generated, reduced to 31 bits by throwing away the "least random" low bit.
420 * Note: the code takes advantage of the fact that both the front and
421 * rear pointers can't wrap on the same call by not testing the rear
422 * pointer if the front one has wrapped.
424 * Returns a 31-bit random number.
432 if (rand_type == TYPE_0) {
434 state[0] = i = good_rand(i);
437 * Use local variables rather than static variables for speed.
441 i = *f >> 1; /* chucking least random bit */
442 if (++f >= end_ptr) {
446 else if (++r >= end_ptr) {