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
34#if defined(LIBC_SCCS) && !defined(lint)
35static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95";
36#endif /* LIBC_SCCS and not lint */
37#include <sys/cdefs.h>
38__FBSDID("$FreeBSD: head/lib/libc/stdlib/random.c 110280 2003-02-03 10:22:12Z ache $");
39
40#include "namespace.h"
41#include <sys/time.h> /* for srandomdev() */
42#include <fcntl.h> /* for srandomdev() */
43#include <stdio.h>
44#include <stdlib.h>
45#include <unistd.h> /* for srandomdev() */
46#include "un-namespace.h"
47
48/*
49 * random.c:
50 *
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
55 * then initialized to contain information for random number generation with
56 * that much state information. Good sizes for the amount of state
57 * information are 32, 64, 128, and 256 bytes. The state can be switched by
58 * calling the setstate() routine with the same array as was initiallized
59 * with initstate(). By default, the package runs with 128 bytes of state
60 * information and generates far better random numbers than a linear
61 * congruential generator. If the amount of state information is less than
62 * 32 bytes, a simple linear congruential R.N.G. is used.
63 *
64 * Internally, the state information is treated as an array of longs; the
65 * zeroeth element of the array is the type of R.N.G. being used (small
66 * integer); the remainder of the array is the state information for the
67 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
68 * state information, which will allow a degree seven polynomial. (Note:
69 * the zeroeth word of state information also has some other information
70 * stored in it -- see setstate() for details).
71 *
72 * The random number generation technique is a linear feedback shift register
73 * approach, employing trinomials (since there are fewer terms to sum up that
74 * way). In this approach, the least significant bit of all the numbers in
75 * the state table will act as a linear feedback shift register, and will
76 * have period 2^deg - 1 (where deg is the degree of the polynomial being
77 * used, assuming that the polynomial is irreducible and primitive). The
78 * higher order bits will have longer periods, since their values are also
79 * influenced by pseudo-random carries out of the lower bits. The total
80 * period of the generator is approximately deg*(2**deg - 1); thus doubling
81 * the amount of state information has a vast influence on the period of the
82 * generator. Note: the deg*(2**deg - 1) is an approximation only good for
83 * large deg, when the period of the shift is the dominant factor.
84 * With deg equal to seven, the period is actually much longer than the
85 * 7*(2**7 - 1) predicted by this formula.
86 *
87 * Modified 28 December 1994 by Jacob S. Rosenberg.
88 * The following changes have been made:
89 * All references to the type u_int have been changed to unsigned long.
90 * All references to type int have been changed to type long. Other
91 * cleanups have been made as well. A warning for both initstate and
92 * setstate has been inserted to the effect that on Sparc platforms
93 * the 'arg_state' variable must be forced to begin on word boundaries.
94 * This can be easily done by casting a long integer array to char *.
95 * The overall logic has been left STRICTLY alone. This software was
96 * tested on both a VAX and Sun SpacsStation with exactly the same
97 * results. The new version and the original give IDENTICAL results.
98 * The new version is somewhat faster than the original. As the
99 * documentation says: "By default, the package runs with 128 bytes of
100 * state information and generates far better random numbers than a linear
101 * congruential generator. If the amount of state information is less than
102 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of
103 * 128 bytes, this new version runs about 19 percent faster and for a 16
104 * byte buffer it is about 5 percent faster.
105 */
106
107/*
108 * For each of the currently supported random number generators, we have a
109 * break value on the amount of state information (you need at least this
110 * many bytes of state info to support this random number generator), a degree
111 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
112 * the separation between the two lower order coefficients of the trinomial.
113 */
114#define TYPE_0 0 /* linear congruential */
115#define BREAK_0 8
116#define DEG_0 0
117#define SEP_0 0
118
119#define TYPE_1 1 /* x**7 + x**3 + 1 */
120#define BREAK_1 32
121#define DEG_1 7
122#define SEP_1 3
123
124#define TYPE_2 2 /* x**15 + x + 1 */
125#define BREAK_2 64
126#define DEG_2 15
127#define SEP_2 1
128
129#define TYPE_3 3 /* x**31 + x**3 + 1 */
130#define BREAK_3 128
131#define DEG_3 31
132#define SEP_3 3
133
134#define TYPE_4 4 /* x**63 + x + 1 */
135#define BREAK_4 256
136#define DEG_4 63
137#define SEP_4 1
138
139/*
140 * Array versions of the above information to make code run faster --
141 * relies on fact that TYPE_i == i.
142 */
143#define MAX_TYPES 5 /* max number of types above */
144
145static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
146static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
147
148/*
149 * Initially, everything is set up as if from:
150 *
151 * initstate(1, randtbl, 128);
152 *
153 * Note that this initialization takes advantage of the fact that srandom()
154 * advances the front and rear pointers 10*rand_deg times, and hence the
155 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
156 * element of the state information, which contains info about the current
157 * position of the rear pointer is just
158 *
159 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
160 */
161
162static long randtbl[DEG_3 + 1] = {
163 TYPE_3,
164#ifdef USE_WEAK_SEEDING
165/* Historic implementation compatibility */
166/* The random sequences do not vary much with the seed */
167 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
168 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
169 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
170 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
171 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
172 0x27fb47b9,
173#else /* !USE_WEAK_SEEDING */
174 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
175 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
176 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
177 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
178 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
179 0xf3bec5da
180#endif /* !USE_WEAK_SEEDING */
181};
182
183/*
184 * fptr and rptr are two pointers into the state info, a front and a rear
185 * pointer. These two pointers are always rand_sep places aparts, as they
186 * cycle cyclically through the state information. (Yes, this does mean we
187 * could get away with just one pointer, but the code for random() is more
188 * efficient this way). The pointers are left positioned as they would be
189 * from the call
190 *
191 * initstate(1, randtbl, 128);
192 *
193 * (The position of the rear pointer, rptr, is really 0 (as explained above
194 * in the initialization of randtbl) because the state table pointer is set
195 * to point to randtbl[1] (as explained below).
196 */
197static long *fptr = &randtbl[SEP_3 + 1];
198static long *rptr = &randtbl[1];
199
200/*
201 * The following things are the pointer to the state information table, the
202 * type of the current generator, the degree of the current polynomial being
203 * used, and the separation between the two pointers. Note that for efficiency
204 * of random(), we remember the first location of the state information, not
205 * the zeroeth. Hence it is valid to access state[-1], which is used to
206 * store the type of the R.N.G. Also, we remember the last location, since
207 * this is more efficient than indexing every time to find the address of
208 * the last element to see if the front and rear pointers have wrapped.
209 */
210static long *state = &randtbl[1];
211static long rand_type = TYPE_3;
212static long rand_deg = DEG_3;
213static long rand_sep = SEP_3;
214static long *end_ptr = &randtbl[DEG_3 + 1];
215
216static inline long good_rand(long);
217
218static inline long good_rand (x)
219 long x;
220{
221#ifdef USE_WEAK_SEEDING
222/*
223 * Historic implementation compatibility.
224 * The random sequences do not vary much with the seed,
225 * even with overflowing.
226 */
227 return (1103515245 * x + 12345);
228#else /* !USE_WEAK_SEEDING */
229/*
230 * Compute x = (7^5 * x) mod (2^31 - 1)
231 * wihout overflowing 31 bits:
232 * (2^31 - 1) = 127773 * (7^5) + 2836
233 * From "Random number generators: good ones are hard to find",
234 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
235 * October 1988, p. 1195.
236 */
237 long hi, lo;
238
239 /* Can't be initialized with 0, so use another value. */
240 if (x == 0)
241 x = 123459876;
242 hi = x / 127773;
243 lo = x % 127773;
244 x = 16807 * lo - 2836 * hi;
245 if (x < 0)
246 x += 0x7fffffff;
247 return (x);
248#endif /* !USE_WEAK_SEEDING */
249}
250
251/*
252 * srandom:
253 *
254 * Initialize the random number generator based on the given seed. If the
255 * type is the trivial no-state-information type, just remember the seed.
256 * Otherwise, initializes state[] based on the given "seed" via a linear
257 * congruential generator. Then, the pointers are set to known locations
258 * that are exactly rand_sep places apart. Lastly, it cycles the state
259 * information a given number of times to get rid of any initial dependencies
260 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
261 * for default usage relies on values produced by this routine.
262 */
263void
264srandom(x)
265 unsigned long x;
266{
267 long i;
268
269 if (rand_type == TYPE_0)
270 state[0] = x;
271 else {
272 state[0] = x;
273 for (i = 1; i < rand_deg; i++)
274 state[i] = good_rand(state[i - 1]);
275 fptr = &state[rand_sep];
276 rptr = &state[0];
277 for (i = 0; i < 10 * rand_deg; i++)
278 (void)random();
279 }
280}
281
282/*
283 * srandomdev:
284 *
285 * Many programs choose the seed value in a totally predictable manner.
286 * This often causes problems. We seed the generator using the much more
287 * secure random(4) interface. Note that this particular seeding
288 * procedure can generate states which are impossible to reproduce by
289 * calling srandom() with any value, since the succeeding terms in the
290 * state buffer are no longer derived from the LC algorithm applied to
291 * a fixed seed.
292 */
293void
294srandomdev()
295{
296 int fd, done;
297 size_t len;
298
299 if (rand_type == TYPE_0)
300 len = sizeof state[0];
301 else
302 len = rand_deg * sizeof state[0];
303
304 done = 0;
305 fd = _open("/dev/random", O_RDONLY, 0);
306 if (fd >= 0) {
307 if (_read(fd, (void *) state, len) == (ssize_t) len)
308 done = 1;
309 _close(fd);
310 }
311
312 if (!done) {
313 struct timeval tv;
314 unsigned long junk;
315
316 gettimeofday(&tv, NULL);
317 srandom((getpid() << 16) ^ tv.tv_sec ^ tv.tv_usec ^ junk);
318 return;
319 }
320
321 if (rand_type != TYPE_0) {
322 fptr = &state[rand_sep];
323 rptr = &state[0];
324 }
325}
326
327/*
328 * initstate:
329 *
330 * Initialize the state information in the given array of n bytes for future
331 * random number generation. Based on the number of bytes we are given, and
332 * the break values for the different R.N.G.'s, we choose the best (largest)
333 * one we can and set things up for it. srandom() is then called to
334 * initialize the state information.
335 *
336 * Note that on return from srandom(), we set state[-1] to be the type
337 * multiplexed with the current value of the rear pointer; this is so
338 * successive calls to initstate() won't lose this information and will be
339 * able to restart with setstate().
340 *
341 * Note: the first thing we do is save the current state, if any, just like
342 * setstate() so that it doesn't matter when initstate is called.
343 *
344 * Returns a pointer to the old state.
345 *
346 * Note: The Sparc platform requires that arg_state begin on a long
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 */
350char *
351initstate(seed, arg_state, n)
352 unsigned long seed; /* seed for R.N.G. */
353 char *arg_state; /* pointer to state array */
354 long n; /* # bytes of state info */
355{
356 char *ostate = (char *)(&state[-1]);
357 long *long_arg_state = (long *) arg_state;
358
359 if (rand_type == TYPE_0)
360 state[-1] = rand_type;
361 else
362 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
363 if (n < BREAK_0) {
364 (void)fprintf(stderr,
365 "random: not enough state (%ld bytes); ignored.\n", n);
366 return(0);
367 }
368 if (n < BREAK_1) {
369 rand_type = TYPE_0;
370 rand_deg = DEG_0;
371 rand_sep = SEP_0;
372 } else if (n < BREAK_2) {
373 rand_type = TYPE_1;
374 rand_deg = DEG_1;
375 rand_sep = SEP_1;
376 } else if (n < BREAK_3) {
377 rand_type = TYPE_2;
378 rand_deg = DEG_2;
379 rand_sep = SEP_2;
380 } else if (n < BREAK_4) {
381 rand_type = TYPE_3;
382 rand_deg = DEG_3;
383 rand_sep = SEP_3;
384 } else {
385 rand_type = TYPE_4;
386 rand_deg = DEG_4;
387 rand_sep = SEP_4;
388 }
389 state = (long *) (long_arg_state + 1); /* first location */
390 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
391 srandom(seed);
392 if (rand_type == TYPE_0)
393 long_arg_state[0] = rand_type;
394 else
395 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
396 return(ostate);
397}
398
399/*
400 * setstate:
401 *
402 * Restore the state from the given state array.
403 *
404 * Note: it is important that we also remember the locations of the pointers
405 * in the current state information, and restore the locations of the pointers
406 * from the old state information. This is done by multiplexing the pointer
407 * location into the zeroeth word of the state information.
408 *
409 * Note that due to the order in which things are done, it is OK to call
410 * setstate() with the same state as the current state.
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 */
418char *
419setstate(arg_state)
420 char *arg_state; /* pointer to state array */
421{
422 long *new_state = (long *) arg_state;
423 long type = new_state[0] % MAX_TYPES;
424 long rear = new_state[0] / MAX_TYPES;
425 char *ostate = (char *)(&state[-1]);
426
427 if (rand_type == TYPE_0)
428 state[-1] = rand_type;
429 else
430 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
431 switch(type) {
432 case TYPE_0:
433 case TYPE_1:
434 case TYPE_2:
435 case TYPE_3:
436 case TYPE_4:
437 rand_type = type;
438 rand_deg = degrees[type];
439 rand_sep = seps[type];
440 break;
441 default:
442 (void)fprintf(stderr,
443 "random: state info corrupted; not changed.\n");
444 }
445 state = (long *) (new_state + 1);
446 if (rand_type != TYPE_0) {
447 rptr = &state[rear];
448 fptr = &state[(rear + rand_sep) % rand_deg];
449 }
450 end_ptr = &state[rand_deg]; /* set end_ptr too */
451 return(ostate);
452}
453
454/*
455 * random:
456 *
457 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
458 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
459 * the same in all the other cases due to all the global variables that have
460 * been set up. The basic operation is to add the number at the rear pointer
461 * into the one at the front pointer. Then both pointers are advanced to
462 * the next location cyclically in the table. The value returned is the sum
463 * generated, reduced to 31 bits by throwing away the "least random" low bit.
464 *
465 * Note: the code takes advantage of the fact that both the front and
466 * rear pointers can't wrap on the same call by not testing the rear
467 * pointer if the front one has wrapped.
468 *
469 * Returns a 31-bit random number.
470 */
471long
472random()
473{
474 long i;
475 long *f, *r;
476
477 if (rand_type == TYPE_0) {
478 i = state[0];
479 state[0] = i = (good_rand(i)) & 0x7fffffff;
480 } else {
481 /*
482 * Use local variables rather than static variables for speed.
483 */
484 f = fptr; r = rptr;
485 *f += *r;
486 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */
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(i);
498}
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
34#if defined(LIBC_SCCS) && !defined(lint)
35static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95";
36#endif /* LIBC_SCCS and not lint */
37#include <sys/cdefs.h>
38__FBSDID("$FreeBSD: head/lib/libc/stdlib/random.c 110280 2003-02-03 10:22:12Z ache $");
39
40#include "namespace.h"
41#include <sys/time.h> /* for srandomdev() */
42#include <fcntl.h> /* for srandomdev() */
43#include <stdio.h>
44#include <stdlib.h>
45#include <unistd.h> /* for srandomdev() */
46#include "un-namespace.h"
47
48/*
49 * random.c:
50 *
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
55 * then initialized to contain information for random number generation with
56 * that much state information. Good sizes for the amount of state
57 * information are 32, 64, 128, and 256 bytes. The state can be switched by
58 * calling the setstate() routine with the same array as was initiallized
59 * with initstate(). By default, the package runs with 128 bytes of state
60 * information and generates far better random numbers than a linear
61 * congruential generator. If the amount of state information is less than
62 * 32 bytes, a simple linear congruential R.N.G. is used.
63 *
64 * Internally, the state information is treated as an array of longs; the
65 * zeroeth element of the array is the type of R.N.G. being used (small
66 * integer); the remainder of the array is the state information for the
67 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
68 * state information, which will allow a degree seven polynomial. (Note:
69 * the zeroeth word of state information also has some other information
70 * stored in it -- see setstate() for details).
71 *
72 * The random number generation technique is a linear feedback shift register
73 * approach, employing trinomials (since there are fewer terms to sum up that
74 * way). In this approach, the least significant bit of all the numbers in
75 * the state table will act as a linear feedback shift register, and will
76 * have period 2^deg - 1 (where deg is the degree of the polynomial being
77 * used, assuming that the polynomial is irreducible and primitive). The
78 * higher order bits will have longer periods, since their values are also
79 * influenced by pseudo-random carries out of the lower bits. The total
80 * period of the generator is approximately deg*(2**deg - 1); thus doubling
81 * the amount of state information has a vast influence on the period of the
82 * generator. Note: the deg*(2**deg - 1) is an approximation only good for
83 * large deg, when the period of the shift is the dominant factor.
84 * With deg equal to seven, the period is actually much longer than the
85 * 7*(2**7 - 1) predicted by this formula.
86 *
87 * Modified 28 December 1994 by Jacob S. Rosenberg.
88 * The following changes have been made:
89 * All references to the type u_int have been changed to unsigned long.
90 * All references to type int have been changed to type long. Other
91 * cleanups have been made as well. A warning for both initstate and
92 * setstate has been inserted to the effect that on Sparc platforms
93 * the 'arg_state' variable must be forced to begin on word boundaries.
94 * This can be easily done by casting a long integer array to char *.
95 * The overall logic has been left STRICTLY alone. This software was
96 * tested on both a VAX and Sun SpacsStation with exactly the same
97 * results. The new version and the original give IDENTICAL results.
98 * The new version is somewhat faster than the original. As the
99 * documentation says: "By default, the package runs with 128 bytes of
100 * state information and generates far better random numbers than a linear
101 * congruential generator. If the amount of state information is less than
102 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of
103 * 128 bytes, this new version runs about 19 percent faster and for a 16
104 * byte buffer it is about 5 percent faster.
105 */
106
107/*
108 * For each of the currently supported random number generators, we have a
109 * break value on the amount of state information (you need at least this
110 * many bytes of state info to support this random number generator), a degree
111 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
112 * the separation between the two lower order coefficients of the trinomial.
113 */
114#define TYPE_0 0 /* linear congruential */
115#define BREAK_0 8
116#define DEG_0 0
117#define SEP_0 0
118
119#define TYPE_1 1 /* x**7 + x**3 + 1 */
120#define BREAK_1 32
121#define DEG_1 7
122#define SEP_1 3
123
124#define TYPE_2 2 /* x**15 + x + 1 */
125#define BREAK_2 64
126#define DEG_2 15
127#define SEP_2 1
128
129#define TYPE_3 3 /* x**31 + x**3 + 1 */
130#define BREAK_3 128
131#define DEG_3 31
132#define SEP_3 3
133
134#define TYPE_4 4 /* x**63 + x + 1 */
135#define BREAK_4 256
136#define DEG_4 63
137#define SEP_4 1
138
139/*
140 * Array versions of the above information to make code run faster --
141 * relies on fact that TYPE_i == i.
142 */
143#define MAX_TYPES 5 /* max number of types above */
144
145static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
146static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
147
148/*
149 * Initially, everything is set up as if from:
150 *
151 * initstate(1, randtbl, 128);
152 *
153 * Note that this initialization takes advantage of the fact that srandom()
154 * advances the front and rear pointers 10*rand_deg times, and hence the
155 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
156 * element of the state information, which contains info about the current
157 * position of the rear pointer is just
158 *
159 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
160 */
161
162static long randtbl[DEG_3 + 1] = {
163 TYPE_3,
164#ifdef USE_WEAK_SEEDING
165/* Historic implementation compatibility */
166/* The random sequences do not vary much with the seed */
167 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
168 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
169 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
170 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
171 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
172 0x27fb47b9,
173#else /* !USE_WEAK_SEEDING */
174 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
175 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
176 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
177 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
178 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
179 0xf3bec5da
180#endif /* !USE_WEAK_SEEDING */
181};
182
183/*
184 * fptr and rptr are two pointers into the state info, a front and a rear
185 * pointer. These two pointers are always rand_sep places aparts, as they
186 * cycle cyclically through the state information. (Yes, this does mean we
187 * could get away with just one pointer, but the code for random() is more
188 * efficient this way). The pointers are left positioned as they would be
189 * from the call
190 *
191 * initstate(1, randtbl, 128);
192 *
193 * (The position of the rear pointer, rptr, is really 0 (as explained above
194 * in the initialization of randtbl) because the state table pointer is set
195 * to point to randtbl[1] (as explained below).
196 */
197static long *fptr = &randtbl[SEP_3 + 1];
198static long *rptr = &randtbl[1];
199
200/*
201 * The following things are the pointer to the state information table, the
202 * type of the current generator, the degree of the current polynomial being
203 * used, and the separation between the two pointers. Note that for efficiency
204 * of random(), we remember the first location of the state information, not
205 * the zeroeth. Hence it is valid to access state[-1], which is used to
206 * store the type of the R.N.G. Also, we remember the last location, since
207 * this is more efficient than indexing every time to find the address of
208 * the last element to see if the front and rear pointers have wrapped.
209 */
210static long *state = &randtbl[1];
211static long rand_type = TYPE_3;
212static long rand_deg = DEG_3;
213static long rand_sep = SEP_3;
214static long *end_ptr = &randtbl[DEG_3 + 1];
215
216static inline long good_rand(long);
217
218static inline long good_rand (x)
219 long x;
220{
221#ifdef USE_WEAK_SEEDING
222/*
223 * Historic implementation compatibility.
224 * The random sequences do not vary much with the seed,
225 * even with overflowing.
226 */
227 return (1103515245 * x + 12345);
228#else /* !USE_WEAK_SEEDING */
229/*
230 * Compute x = (7^5 * x) mod (2^31 - 1)
231 * wihout overflowing 31 bits:
232 * (2^31 - 1) = 127773 * (7^5) + 2836
233 * From "Random number generators: good ones are hard to find",
234 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
235 * October 1988, p. 1195.
236 */
237 long hi, lo;
238
239 /* Can't be initialized with 0, so use another value. */
240 if (x == 0)
241 x = 123459876;
242 hi = x / 127773;
243 lo = x % 127773;
244 x = 16807 * lo - 2836 * hi;
245 if (x < 0)
246 x += 0x7fffffff;
247 return (x);
248#endif /* !USE_WEAK_SEEDING */
249}
250
251/*
252 * srandom:
253 *
254 * Initialize the random number generator based on the given seed. If the
255 * type is the trivial no-state-information type, just remember the seed.
256 * Otherwise, initializes state[] based on the given "seed" via a linear
257 * congruential generator. Then, the pointers are set to known locations
258 * that are exactly rand_sep places apart. Lastly, it cycles the state
259 * information a given number of times to get rid of any initial dependencies
260 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
261 * for default usage relies on values produced by this routine.
262 */
263void
264srandom(x)
265 unsigned long x;
266{
267 long i;
268
269 if (rand_type == TYPE_0)
270 state[0] = x;
271 else {
272 state[0] = x;
273 for (i = 1; i < rand_deg; i++)
274 state[i] = good_rand(state[i - 1]);
275 fptr = &state[rand_sep];
276 rptr = &state[0];
277 for (i = 0; i < 10 * rand_deg; i++)
278 (void)random();
279 }
280}
281
282/*
283 * srandomdev:
284 *
285 * Many programs choose the seed value in a totally predictable manner.
286 * This often causes problems. We seed the generator using the much more
287 * secure random(4) interface. Note that this particular seeding
288 * procedure can generate states which are impossible to reproduce by
289 * calling srandom() with any value, since the succeeding terms in the
290 * state buffer are no longer derived from the LC algorithm applied to
291 * a fixed seed.
292 */
293void
294srandomdev()
295{
296 int fd, done;
297 size_t len;
298
299 if (rand_type == TYPE_0)
300 len = sizeof state[0];
301 else
302 len = rand_deg * sizeof state[0];
303
304 done = 0;
305 fd = _open("/dev/random", O_RDONLY, 0);
306 if (fd >= 0) {
307 if (_read(fd, (void *) state, len) == (ssize_t) len)
308 done = 1;
309 _close(fd);
310 }
311
312 if (!done) {
313 struct timeval tv;
314 unsigned long junk;
315
316 gettimeofday(&tv, NULL);
317 srandom((getpid() << 16) ^ tv.tv_sec ^ tv.tv_usec ^ junk);
318 return;
319 }
320
321 if (rand_type != TYPE_0) {
322 fptr = &state[rand_sep];
323 rptr = &state[0];
324 }
325}
326
327/*
328 * initstate:
329 *
330 * Initialize the state information in the given array of n bytes for future
331 * random number generation. Based on the number of bytes we are given, and
332 * the break values for the different R.N.G.'s, we choose the best (largest)
333 * one we can and set things up for it. srandom() is then called to
334 * initialize the state information.
335 *
336 * Note that on return from srandom(), we set state[-1] to be the type
337 * multiplexed with the current value of the rear pointer; this is so
338 * successive calls to initstate() won't lose this information and will be
339 * able to restart with setstate().
340 *
341 * Note: the first thing we do is save the current state, if any, just like
342 * setstate() so that it doesn't matter when initstate is called.
343 *
344 * Returns a pointer to the old state.
345 *
346 * Note: The Sparc platform requires that arg_state begin on a long
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 */
350char *
351initstate(seed, arg_state, n)
352 unsigned long seed; /* seed for R.N.G. */
353 char *arg_state; /* pointer to state array */
354 long n; /* # bytes of state info */
355{
356 char *ostate = (char *)(&state[-1]);
357 long *long_arg_state = (long *) arg_state;
358
359 if (rand_type == TYPE_0)
360 state[-1] = rand_type;
361 else
362 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
363 if (n < BREAK_0) {
364 (void)fprintf(stderr,
365 "random: not enough state (%ld bytes); ignored.\n", n);
366 return(0);
367 }
368 if (n < BREAK_1) {
369 rand_type = TYPE_0;
370 rand_deg = DEG_0;
371 rand_sep = SEP_0;
372 } else if (n < BREAK_2) {
373 rand_type = TYPE_1;
374 rand_deg = DEG_1;
375 rand_sep = SEP_1;
376 } else if (n < BREAK_3) {
377 rand_type = TYPE_2;
378 rand_deg = DEG_2;
379 rand_sep = SEP_2;
380 } else if (n < BREAK_4) {
381 rand_type = TYPE_3;
382 rand_deg = DEG_3;
383 rand_sep = SEP_3;
384 } else {
385 rand_type = TYPE_4;
386 rand_deg = DEG_4;
387 rand_sep = SEP_4;
388 }
389 state = (long *) (long_arg_state + 1); /* first location */
390 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
391 srandom(seed);
392 if (rand_type == TYPE_0)
393 long_arg_state[0] = rand_type;
394 else
395 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
396 return(ostate);
397}
398
399/*
400 * setstate:
401 *
402 * Restore the state from the given state array.
403 *
404 * Note: it is important that we also remember the locations of the pointers
405 * in the current state information, and restore the locations of the pointers
406 * from the old state information. This is done by multiplexing the pointer
407 * location into the zeroeth word of the state information.
408 *
409 * Note that due to the order in which things are done, it is OK to call
410 * setstate() with the same state as the current state.
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 */
418char *
419setstate(arg_state)
420 char *arg_state; /* pointer to state array */
421{
422 long *new_state = (long *) arg_state;
423 long type = new_state[0] % MAX_TYPES;
424 long rear = new_state[0] / MAX_TYPES;
425 char *ostate = (char *)(&state[-1]);
426
427 if (rand_type == TYPE_0)
428 state[-1] = rand_type;
429 else
430 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
431 switch(type) {
432 case TYPE_0:
433 case TYPE_1:
434 case TYPE_2:
435 case TYPE_3:
436 case TYPE_4:
437 rand_type = type;
438 rand_deg = degrees[type];
439 rand_sep = seps[type];
440 break;
441 default:
442 (void)fprintf(stderr,
443 "random: state info corrupted; not changed.\n");
444 }
445 state = (long *) (new_state + 1);
446 if (rand_type != TYPE_0) {
447 rptr = &state[rear];
448 fptr = &state[(rear + rand_sep) % rand_deg];
449 }
450 end_ptr = &state[rand_deg]; /* set end_ptr too */
451 return(ostate);
452}
453
454/*
455 * random:
456 *
457 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
458 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
459 * the same in all the other cases due to all the global variables that have
460 * been set up. The basic operation is to add the number at the rear pointer
461 * into the one at the front pointer. Then both pointers are advanced to
462 * the next location cyclically in the table. The value returned is the sum
463 * generated, reduced to 31 bits by throwing away the "least random" low bit.
464 *
465 * Note: the code takes advantage of the fact that both the front and
466 * rear pointers can't wrap on the same call by not testing the rear
467 * pointer if the front one has wrapped.
468 *
469 * Returns a 31-bit random number.
470 */
471long
472random()
473{
474 long i;
475 long *f, *r;
476
477 if (rand_type == TYPE_0) {
478 i = state[0];
479 state[0] = i = (good_rand(i)) & 0x7fffffff;
480 } else {
481 /*
482 * Use local variables rather than static variables for speed.
483 */
484 f = fptr; r = rptr;
485 *f += *r;
486 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */
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(i);
498}