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1/*
2 * Copyright (c) 1983 Regents of the University of California.
3 * 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
34#if defined(LIBC_SCCS) && !defined(lint)
35static char *rcsid = "$OpenBSD: random.c,v 1.9 2000/04/04 14:27:00 millert Exp $";
36#endif /* LIBC_SCCS and not lint */
37
38#include <sys/types.h>
39#include <sys/time.h>
40#include <fcntl.h>
41#include <stdio.h>
42#include <stdlib.h>
43#include <unistd.h>
44
45/*
46 * random.c:
47 *
48 * An improved random number generation package. In addition to the standard
49 * rand()/srand() like interface, this package also has a special state info
50 * interface. The initstate() routine is called with a seed, an array of
51 * bytes, and a count of how many bytes are being passed in; this array is
52 * then initialized to contain information for random number generation with
53 * that much state information. Good sizes for the amount of state
54 * information are 32, 64, 128, and 256 bytes. The state can be switched by
55 * calling the setstate() routine with the same array as was initiallized
56 * with initstate(). By default, the package runs with 128 bytes of state
57 * information and generates far better random numbers than a linear
58 * congruential generator. If the amount of state information is less than
59 * 32 bytes, a simple linear congruential R.N.G. is used.
60 *
61 * Internally, the state information is treated as an array of longs; the
62 * zeroeth element of the array is the type of R.N.G. being used (small
63 * integer); the remainder of the array is the state information for the
64 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
65 * state information, which will allow a degree seven polynomial. (Note:
66 * the zeroeth word of state information also has some other information
67 * stored in it -- see setstate() for details).
68 *
69 * The random number generation technique is a linear feedback shift register
70 * approach, employing trinomials (since there are fewer terms to sum up that
71 * way). In this approach, the least significant bit of all the numbers in
72 * the state table will act as a linear feedback shift register, and will
73 * have period 2^deg - 1 (where deg is the degree of the polynomial being
74 * used, assuming that the polynomial is irreducible and primitive). The
75 * higher order bits will have longer periods, since their values are also
76 * influenced by pseudo-random carries out of the lower bits. The total
77 * period of the generator is approximately deg*(2**deg - 1); thus doubling
78 * the amount of state information has a vast influence on the period of the
79 * generator. Note: the deg*(2**deg - 1) is an approximation only good for
80 * large deg, when the period of the shift register is the dominant factor.
81 * With deg equal to seven, the period is actually much longer than the
82 * 7*(2**7 - 1) predicted by this formula.
83 */
84
85/*
86 * For each of the currently supported random number generators, we have a
87 * break value on the amount of state information (you need at least this
88 * many bytes of state info to support this random number generator), a degree
89 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
90 * the separation between the two lower order coefficients of the trinomial.
91 */
92#define TYPE_0 0 /* linear congruential */
93#define BREAK_0 8
94#define DEG_0 0
95#define SEP_0 0
96
97#define TYPE_1 1 /* x**7 + x**3 + 1 */
98#define BREAK_1 32
99#define DEG_1 7
100#define SEP_1 3
101
102#define TYPE_2 2 /* x**15 + x + 1 */
103#define BREAK_2 64
104#define DEG_2 15
105#define SEP_2 1
106
107#define TYPE_3 3 /* x**31 + x**3 + 1 */
108#define BREAK_3 128
109#define DEG_3 31
110#define SEP_3 3
111
112#define TYPE_4 4 /* x**63 + x + 1 */
113#define BREAK_4 256
114#define DEG_4 63
115#define SEP_4 1
116
117/*
118 * Array versions of the above information to make code run faster --
119 * relies on fact that TYPE_i == i.
120 */
121#define MAX_TYPES 5 /* max number of types above */
122
123static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
124static int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
125
126/*
127 * Initially, everything is set up as if from:
128 *
129 * initstate(1, &randtbl, 128);
130 *
131 * Note that this initialization takes advantage of the fact that srandom()
132 * advances the front and rear pointers 10*rand_deg times, and hence the
133 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
134 * element of the state information, which contains info about the current
135 * position of the rear pointer is just
136 *
137 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
138 */
139
140static long randtbl[DEG_3 + 1] = {
141 TYPE_3,
142 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
143 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
144 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
145 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
146 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
147 0xf3bec5da,
148};
149
150/*
151 * fptr and rptr are two pointers into the state info, a front and a rear
152 * pointer. These two pointers are always rand_sep places aparts, as they
153 * cycle cyclically through the state information. (Yes, this does mean we
154 * could get away with just one pointer, but the code for random() is more
155 * efficient this way). The pointers are left positioned as they would be
156 * from the call
157 *
158 * initstate(1, randtbl, 128);
159 *
160 * (The position of the rear pointer, rptr, is really 0 (as explained above
161 * in the initialization of randtbl) because the state table pointer is set
162 * to point to randtbl[1] (as explained below).
163 */
164static long *fptr = &randtbl[SEP_3 + 1];
165static long *rptr = &randtbl[1];
166
167/*
168 * The following things are the pointer to the state information table, the
169 * type of the current generator, the degree of the current polynomial being
170 * used, and the separation between the two pointers. Note that for efficiency
171 * of random(), we remember the first location of the state information, not
172 * the zeroeth. Hence it is valid to access state[-1], which is used to
173 * store the type of the R.N.G. Also, we remember the last location, since
174 * this is more efficient than indexing every time to find the address of
175 * the last element to see if the front and rear pointers have wrapped.
176 */
177static long *state = &randtbl[1];
178static int rand_type = TYPE_3;
179static int rand_deg = DEG_3;
180static int rand_sep = SEP_3;
181static long *end_ptr = &randtbl[DEG_3 + 1];
182
183/*
184 * srandom:
185 *
186 * Initialize the random number generator based on the given seed. If the
187 * type is the trivial no-state-information type, just remember the seed.
188 * Otherwise, initializes state[] based on the given "seed" via a linear
189 * congruential generator. Then, the pointers are set to known locations
190 * that are exactly rand_sep places apart. Lastly, it cycles the state
191 * information a given number of times to get rid of any initial dependencies
192 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
193 * for default usage relies on values produced by this routine.
194 */
195void
196srandom(x)
197 u_int x;
198{
199 register long int test;
200 register int i;
201 ldiv_t val;
202
203 if (rand_type == TYPE_0)
204 state[0] = x;
205 else {
206 state[0] = x;
207 for (i = 1; i < rand_deg; i++) {
208 /*
209 * Implement the following, without overflowing 31 bits:
210 *
211 * state[i] = (16807 * state[i - 1]) % 2147483647;
212 *
213 * 2^31-1 (prime) = 2147483647 = 127773*16807+2836
214 */
215 val = ldiv(state[i-1], 127773);
216 test = 16807 * val.rem - 2836 * val.quot;
217 state[i] = test + (test < 0 ? 2147483647 : 0);
218 }
219 fptr = &state[rand_sep];
220 rptr = &state[0];
221 for (i = 0; i < 10 * rand_deg; i++)
222 (void)random();
223 }
224}
225
226/*
227 * srandomdev:
228 *
229 * Many programs choose the seed value in a totally predictable manner.
230 * This often causes problems. We seed the generator using the much more
231 * secure arandom(4) interface. Note that this particular seeding
232 * procedure can generate states which are impossible to reproduce by
233 * calling srandom() with any value, since the succeeding terms in the
234 * state buffer are no longer derived from the LC algorithm applied to
235 * a fixed seed.
236 */
237void
238srandomdev()
239{
240 int fd;
241 size_t len;
242
243 if (rand_type == TYPE_0)
244 len = sizeof(state[0]);
245 else
246 len = rand_deg * sizeof(state[0]);
247
248 if ((fd = open("/dev/arandom", O_RDONLY, 0)) != -1 &&
249 read(fd, (void *) state, len) == (ssize_t) len) {
250 close(fd);
251 } else {
252 struct timeval tv;
253 u_int junk;
254
255 /* XXX - this could be better */
256 gettimeofday(&tv, NULL);
257 srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk);
258 if (fd != -1)
259 close(fd);
260 return;
261 }
262
263 if (rand_type != TYPE_0) {
264 fptr = &state[rand_sep];
265 rptr = &state[0];
266 }
267}
268
269/*
270 * initstate:
271 *
272 * Initialize the state information in the given array of n bytes for future
273 * random number generation. Based on the number of bytes we are given, and
274 * the break values for the different R.N.G.'s, we choose the best (largest)
275 * one we can and set things up for it. srandom() is then called to
276 * initialize the state information.
277 *
278 * Note that on return from srandom(), we set state[-1] to be the type
279 * multiplexed with the current value of the rear pointer; this is so
280 * successive calls to initstate() won't lose this information and will be
281 * able to restart with setstate().
282 *
283 * Note: the first thing we do is save the current state, if any, just like
284 * setstate() so that it doesn't matter when initstate is called.
285 *
286 * Returns a pointer to the old state.
287 */
288char *
289initstate(seed, arg_state, n)
290 u_int seed; /* seed for R.N.G. */
291 char *arg_state; /* pointer to state array */
292 size_t n; /* # bytes of state info */
293{
294 register char *ostate = (char *)(&state[-1]);
295
296 if (rand_type == TYPE_0)
297 state[-1] = rand_type;
298 else
299 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
300 if (n < BREAK_0)
301 return(NULL);
302 if (n < BREAK_1) {
303 rand_type = TYPE_0;
304 rand_deg = DEG_0;
305 rand_sep = SEP_0;
306 } else if (n < BREAK_2) {
307 rand_type = TYPE_1;
308 rand_deg = DEG_1;
309 rand_sep = SEP_1;
310 } else if (n < BREAK_3) {
311 rand_type = TYPE_2;
312 rand_deg = DEG_2;
313 rand_sep = SEP_2;
314 } else if (n < BREAK_4) {
315 rand_type = TYPE_3;
316 rand_deg = DEG_3;
317 rand_sep = SEP_3;
318 } else {
319 rand_type = TYPE_4;
320 rand_deg = DEG_4;
321 rand_sep = SEP_4;
322 }
323 state = &(((long *)arg_state)[1]); /* first location */
324 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
325 srandom(seed);
326 if (rand_type == TYPE_0)
327 state[-1] = rand_type;
328 else
329 state[-1] = MAX_TYPES*(rptr - state) + rand_type;
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 */
348char *
349setstate(arg_state)
350 const char *arg_state;
351{
352 register long *new_state = (long *)arg_state;
353 register int type = new_state[0] % MAX_TYPES;
354 register int rear = new_state[0] / MAX_TYPES;
355 char *ostate = (char *)(&state[-1]);
356
357 if (rand_type == TYPE_0)
358 state[-1] = rand_type;
359 else
360 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
361 switch(type) {
362 case TYPE_0:
363 case TYPE_1:
364 case TYPE_2:
365 case TYPE_3:
366 case TYPE_4:
367 rand_type = type;
368 rand_deg = degrees[type];
369 rand_sep = seps[type];
370 break;
371 default:
372 return(NULL);
373 }
374 state = &new_state[1];
375 if (rand_type != TYPE_0) {
376 rptr = &state[rear];
377 fptr = &state[(rear + rand_sep) % rand_deg];
378 }
379 end_ptr = &state[rand_deg]; /* set end_ptr too */
380 return(ostate);
381}
382
383/*
384 * random:
385 *
386 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
387 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
388 * the same in all the other cases due to all the global variables that have
389 * been set up. The basic operation is to add the number at the rear pointer
390 * into the one at the front pointer. Then both pointers are advanced to
391 * the next location cyclically in the table. The value returned is the sum
392 * generated, reduced to 31 bits by throwing away the "least random" low bit.
393 *
394 * Note: the code takes advantage of the fact that both the front and
395 * rear pointers can't wrap on the same call by not testing the rear
396 * pointer if the front one has wrapped.
397 *
398 * Returns a 31-bit random number.
399 */
400long
401random()
402{
403 long i;
404
405 if (rand_type == TYPE_0)
406 i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff;
407 else {
408 *fptr += *rptr;
409 i = (*fptr >> 1) & 0x7fffffff; /* chucking least random bit */
410 if (++fptr >= end_ptr) {
411 fptr = state;
412 ++rptr;
413 } else if (++rptr >= end_ptr)
414 rptr = state;
415 }
416 return(i);
417}