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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 1.5 2003/09/06 08:19:16 asmodai Exp $
36 * @(#)random.c 8.2 (Berkeley) 5/19/95
39 #include <sys/time.h> /* for srandomdev() */
40 #include <fcntl.h> /* for srandomdev() */
43 #include <unistd.h> /* for srandomdev() */
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.
61 * Internally, the state information is treated as an array of ints; 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 ints 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).
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.
84 * Modified 28 December 1994 by Jacob S. Rosenberg.
85 * The following changes have been made:
86 * All references to the type u_int have been changed to unsigned long.
87 * All references to type int have been changed to type long. Other
88 * cleanups have been made as well. A warning for both initstate and
89 * setstate has been inserted to the effect that on Sparc platforms
90 * the 'arg_state' variable must be forced to begin on word boundaries.
91 * This can be easily done by casting a long integer array to char *.
92 * The overall logic has been left STRICTLY alone. This software was
93 * tested on both a VAX and Sun SpacsStation with exactly the same
94 * results. The new version and the original give IDENTICAL results.
95 * The new version is somewhat faster than the original. As the
96 * documentation says: "By default, the package runs with 128 bytes of
97 * state information and generates far better random numbers than a linear
98 * congruential generator. If the amount of state information is less than
99 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of
100 * 128 bytes, this new version runs about 19 percent faster and for a 16
101 * byte buffer it is about 5 percent faster.
105 * For each of the currently supported random number generators, we have a
106 * break value on the amount of state information (you need at least this
107 * many bytes of state info to support this random number generator), a degree
108 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
109 * the separation between the two lower order coefficients of the trinomial.
111 #define TYPE_0 0 /* linear congruential */
116 #define TYPE_1 1 /* x**7 + x**3 + 1 */
121 #define TYPE_2 2 /* x**15 + x + 1 */
126 #define TYPE_3 3 /* x**31 + x**3 + 1 */
131 #define TYPE_4 4 /* x**63 + x + 1 */
137 * Array versions of the above information to make code run faster --
138 * relies on fact that TYPE_i == i.
140 #define MAX_TYPES 5 /* max number of types above */
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 #ifdef USE_WEAK_SEEDING
162 /* Historic implementation compatibility */
163 /* The random sequences do not vary much with the seed */
164 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
165 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
166 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
167 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
168 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
170 #else /* !USE_WEAK_SEEDING */
171 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
172 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
173 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
174 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
175 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
177 #endif /* !USE_WEAK_SEEDING */
181 * fptr and rptr are two pointers into the state info, a front and a rear
182 * pointer. These two pointers are always rand_sep places aparts, as they
183 * cycle cyclically through the state information. (Yes, this does mean we
184 * could get away with just one pointer, but the code for random() is more
185 * efficient this way). The pointers are left positioned as they would be
188 * initstate(1, randtbl, 128);
190 * (The position of the rear pointer, rptr, is really 0 (as explained above
191 * in the initialization of randtbl) because the state table pointer is set
192 * to point to randtbl[1] (as explained below).
194 static uint32_t *fptr = &randtbl[SEP_3 + 1];
195 static uint32_t *rptr = &randtbl[1];
198 * The following things are the pointer to the state information table, the
199 * type of the current generator, the degree of the current polynomial being
200 * used, and the separation between the two pointers. Note that for efficiency
201 * of random(), we remember the first location of the state information, not
202 * the zeroeth. Hence it is valid to access state[-1], which is used to
203 * store the type of the R.N.G. Also, we remember the last location, since
204 * this is more efficient than indexing every time to find the address of
205 * the last element to see if the front and rear pointers have wrapped.
207 static uint32_t *state = &randtbl[1];
208 static int rand_type = TYPE_3;
209 static int rand_deg = DEG_3;
210 static int rand_sep = SEP_3;
211 static uint32_t *end_ptr = &randtbl[DEG_3 + 1];
213 static inline long good_rand (long);
215 static inline long good_rand (x)
218 #ifdef USE_WEAK_SEEDING
220 * Historic implementation compatibility.
221 * The random sequences do not vary much with the seed,
222 * even with overflowing.
224 return (1103515245 * x + 12345);
225 #else /* !USE_WEAK_SEEDING */
227 * Compute x = (7^5 * x) mod (2^31 - 1)
228 * wihout overflowing 31 bits:
229 * (2^31 - 1) = 127773 * (7^5) + 2836
230 * From "Random number generators: good ones are hard to find",
231 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
232 * October 1988, p. 1195.
238 x = 16807 * lo - 2836 * hi;
242 #endif /* !USE_WEAK_SEEDING */
248 * Initialize the random number generator based on the given seed. If the
249 * type is the trivial no-state-information type, just remember the seed.
250 * Otherwise, initializes state[] based on the given "seed" via a linear
251 * congruential generator. Then, the pointers are set to known locations
252 * that are exactly rand_sep places apart. Lastly, it cycles the state
253 * information a given number of times to get rid of any initial dependencies
254 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
255 * for default usage relies on values produced by this routine.
263 if (rand_type == TYPE_0)
264 state[0] = (uint32_t)x;
266 state[0] = (uint32_t)x;
267 for (i = 1; i < rand_deg; i++)
268 state[i] = (uint32_t)good_rand(state[i - 1]);
269 fptr = &state[rand_sep];
271 for (i = 0; i < 10 * rand_deg; i++)
279 * Many programs choose the seed value in a totally predictable manner.
280 * This often causes problems. We seed the generator using the much more
281 * secure urandom(4) interface. Note that this particular seeding
282 * procedure can generate states which are impossible to reproduce by
283 * calling srandom() with any value, since the succeeding terms in the
284 * state buffer are no longer derived from the LC algorithm applied to
293 if (rand_type == TYPE_0)
294 len = sizeof state[0];
296 len = rand_deg * sizeof state[0];
299 fd = _open("/dev/urandom", O_RDONLY, 0);
301 if (_read(fd, (void *) state, len) == (ssize_t) len)
310 gettimeofday(&tv, NULL);
311 srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk);
315 if (rand_type != TYPE_0) {
316 fptr = &state[rand_sep];
324 * Initialize the state information in the given array of n bytes for future
325 * random number generation. Based on the number of bytes we are given, and
326 * the break values for the different R.N.G.'s, we choose the best (largest)
327 * one we can and set things up for it. srandom() is then called to
328 * initialize the state information.
330 * Note that on return from srandom(), we set state[-1] to be the type
331 * multiplexed with the current value of the rear pointer; this is so
332 * successive calls to initstate() won't lose this information and will be
333 * able to restart with setstate().
335 * Note: the first thing we do is save the current state, if any, just like
336 * setstate() so that it doesn't matter when initstate is called.
338 * Returns a pointer to the old state.
340 * Note: The Sparc platform requires that arg_state begin on an int
341 * word boundary; otherwise a bus error will occur. Even so, lint will
342 * complain about mis-alignment, but you should disregard these messages.
345 initstate(seed, arg_state, n)
346 unsigned long seed; /* seed for R.N.G. */
347 char *arg_state; /* pointer to state array */
348 long n; /* # bytes of state info */
350 char *ostate = (char *)(&state[-1]);
351 uint32_t *int_arg_state = (uint32_t *)(void *)arg_state;
353 if (rand_type == TYPE_0)
354 state[-1] = rand_type;
356 state[-1] = MAX_TYPES * (uint32_t)(rptr - state) + rand_type;
358 (void)fprintf(stderr,
359 "random: not enough state (%ld bytes); ignored.\n", n);
366 } else if (n < BREAK_2) {
370 } else if (n < BREAK_3) {
374 } else if (n < BREAK_4) {
383 state = (uint32_t *) (int_arg_state + 1); /* first location */
384 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
385 srandom((uint32_t)seed);
386 if (rand_type == TYPE_0)
387 int_arg_state[0] = rand_type;
389 int_arg_state[0] = MAX_TYPES * (uint32_t)(rptr - state) + rand_type;
396 * Restore the state from the given state array.
398 * Note: it is important that we also remember the locations of the pointers
399 * in the current state information, and restore the locations of the pointers
400 * from the old state information. This is done by multiplexing the pointer
401 * location into the zeroeth word of the state information.
403 * Note that due to the order in which things are done, it is OK to call
404 * setstate() with the same state as the current state.
406 * Returns a pointer to the old state information.
408 * Note: The Sparc platform requires that arg_state begin on a long
409 * word boundary; otherwise a bus error will occur. Even so, lint will
410 * complain about mis-alignment, but you should disregard these messages.
414 char *arg_state; /* pointer to state array */
416 uint32_t *new_state = (uint32_t *)(void *)arg_state;
417 uint32_t type = new_state[0] % MAX_TYPES;
418 uint32_t rear = new_state[0] / MAX_TYPES;
419 char *ostate = (char *)(&state[-1]);
421 if (rand_type == TYPE_0)
422 state[-1] = rand_type;
424 state[-1] = MAX_TYPES * (uint32_t)(rptr - state) + rand_type;
432 rand_deg = degrees[type];
433 rand_sep = seps[type];
436 (void)fprintf(stderr,
437 "random: state info corrupted; not changed.\n");
439 state = (uint32_t *) (new_state + 1);
440 if (rand_type != TYPE_0) {
442 fptr = &state[(rear + rand_sep) % rand_deg];
444 end_ptr = &state[rand_deg]; /* set end_ptr too */
451 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
452 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
453 * the same in all the other cases due to all the global variables that have
454 * been set up. The basic operation is to add the number at the rear pointer
455 * into the one at the front pointer. Then both pointers are advanced to
456 * the next location cyclically in the table. The value returned is the sum
457 * generated, reduced to 31 bits by throwing away the "least random" low bit.
459 * Note: the code takes advantage of the fact that both the front and
460 * rear pointers can't wrap on the same call by not testing the rear
461 * pointer if the front one has wrapped.
463 * Returns a 31-bit random number.
471 if (rand_type == TYPE_0) {
473 state[0] = i = (good_rand(i)) & 0x7fffffff;
476 * Use local variables rather than static variables for speed.
480 /* chucking least random bit */
481 i = (*f >> 1) & 0x7fffffff;
482 if (++f >= end_ptr) {
486 else if (++r >= end_ptr) {