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29 * @(#)random.c 8.2 (Berkeley) 5/19/95
30 * $FreeBSD: src/lib/libc/stdlib/random.c,v 1.25 2007/01/09 00:28:10 imp Exp $
31 * $DragonFly: src/lib/libc/stdlib/random.c,v 1.9 2005/11/24 17:18:30 swildner Exp $
34 #include "namespace.h"
35 #include <sys/time.h> /* for srandomdev() */
36 #include <fcntl.h> /* for srandomdev() */
40 #include <unistd.h> /* for srandomdev() */
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 #ifdef USE_WEAK_SEEDING
142 #else /* !USE_WEAK_SEEDING */
143 #define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */
144 #endif /* !USE_WEAK_SEEDING */
146 static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
147 static const int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
150 * Initially, everything is set up as if from:
152 * initstate(1, randtbl, 128);
154 * Note that this initialization takes advantage of the fact that srandom()
155 * advances the front and rear pointers 10*rand_deg times, and hence the
156 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
157 * element of the state information, which contains info about the current
158 * position of the rear pointer is just
160 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
163 static uint32_t randtbl[DEG_3 + 1] = {
165 #ifdef USE_WEAK_SEEDING
166 /* Historic implementation compatibility */
167 /* The random sequences do not vary much with the seed */
168 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
169 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
170 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
171 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
172 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
174 #else /* !USE_WEAK_SEEDING */
175 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
176 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
177 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
178 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
179 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
181 #endif /* !USE_WEAK_SEEDING */
185 * fptr and rptr are two pointers into the state info, a front and a rear
186 * pointer. These two pointers are always rand_sep places aparts, as they
187 * cycle cyclically through the state information. (Yes, this does mean we
188 * could get away with just one pointer, but the code for random() is more
189 * efficient this way). The pointers are left positioned as they would be
192 * initstate(1, randtbl, 128);
194 * (The position of the rear pointer, rptr, is really 0 (as explained above
195 * in the initialization of randtbl) because the state table pointer is set
196 * to point to randtbl[1] (as explained below).
198 static uint32_t *fptr = &randtbl[SEP_3 + 1];
199 static uint32_t *rptr = &randtbl[1];
202 * The following things are the pointer to the state information table, the
203 * type of the current generator, the degree of the current polynomial being
204 * used, and the separation between the two pointers. Note that for efficiency
205 * of random(), we remember the first location of the state information, not
206 * the zeroeth. Hence it is valid to access state[-1], which is used to
207 * store the type of the R.N.G. Also, we remember the last location, since
208 * this is more efficient than indexing every time to find the address of
209 * the last element to see if the front and rear pointers have wrapped.
211 static uint32_t *state = &randtbl[1];
212 static int rand_type = TYPE_3;
213 static int rand_deg = DEG_3;
214 static int rand_sep = SEP_3;
215 static uint32_t *end_ptr = &randtbl[DEG_3 + 1];
217 static inline uint32_t good_rand(int32_t);
219 static inline uint32_t
222 #ifdef USE_WEAK_SEEDING
224 * Historic implementation compatibility.
225 * The random sequences do not vary much with the seed,
226 * even with overflowing.
228 return (1103515245 * x + 12345);
229 #else /* !USE_WEAK_SEEDING */
231 * Compute x = (7^5 * x) mod (2^31 - 1)
232 * wihout overflowing 31 bits:
233 * (2^31 - 1) = 127773 * (7^5) + 2836
234 * From "Random number generators: good ones are hard to find",
235 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
236 * October 1988, p. 1195.
240 /* Can't be initialized with 0, so use another value. */
245 x = 16807 * lo - 2836 * hi;
249 #endif /* !USE_WEAK_SEEDING */
255 * Initialize the random number generator based on the given seed. If the
256 * type is the trivial no-state-information type, just remember the seed.
257 * Otherwise, initializes state[] based on the given "seed" via a linear
258 * congruential generator. Then, the pointers are set to known locations
259 * that are exactly rand_sep places apart. Lastly, it cycles the state
260 * information a given number of times to get rid of any initial dependencies
261 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
262 * for default usage relies on values produced by this routine.
265 srandom(unsigned long x)
269 state[0] = (uint32_t)x;
270 if (rand_type == TYPE_0)
273 for (i = 1; i < rand_deg; i++)
274 state[i] = good_rand(state[i - 1]);
275 fptr = &state[rand_sep];
279 for (i = 0; i < lim; i++)
286 * Many programs choose the seed value in a totally predictable manner.
287 * This often causes problems. We seed the generator using the much more
288 * secure random(4) interface. Note that this particular seeding
289 * procedure can generate states which are impossible to reproduce by
290 * calling srandom() with any value, since the succeeding terms in the
291 * state buffer are no longer derived from the LC algorithm applied to
300 if (rand_type == TYPE_0)
301 len = sizeof state[0];
303 len = rand_deg * sizeof state[0];
306 fd = _open("/dev/random", O_RDONLY, 0);
308 if (_read(fd, (void *) state, len) == (ssize_t) len)
315 unsigned long junk; /* XXX left uninitialized on purpose */
317 gettimeofday(&tv, NULL);
318 srandom((getpid() << 16) ^ tv.tv_sec ^ tv.tv_usec ^ junk);
322 if (rand_type != TYPE_0) {
323 fptr = &state[rand_sep];
331 * Initialize the state information in the given array of n bytes for future
332 * random number generation. Based on the number of bytes we are given, and
333 * the break values for the different R.N.G.'s, we choose the best (largest)
334 * one we can and set things up for it. srandom() is then called to
335 * initialize the state information.
337 * Note that on return from srandom(), we set state[-1] to be the type
338 * multiplexed with the current value of the rear pointer; this is so
339 * successive calls to initstate() won't lose this information and will be
340 * able to restart with setstate().
342 * Note: the first thing we do is save the current state, if any, just like
343 * setstate() so that it doesn't matter when initstate is called.
346 * seed: seed for R.N.G.
347 * arg_state: pointer to state array
348 * n: # bytes of state info
350 * Returns a pointer to the old state.
352 * Note: The Sparc platform requires that arg_state begin on an int
353 * word boundary; otherwise a bus error will occur. Even so, lint will
354 * complain about mis-alignment, but you should disregard these messages.
357 initstate(unsigned long seed, char *arg_state, long n)
359 char *ostate = (char *)(&state[-1]);
360 uint32_t *int_arg_state = (uint32_t *)arg_state;
362 if (rand_type == TYPE_0)
363 state[-1] = rand_type;
365 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
368 "random: not enough state (%ld bytes); ignored.\n", n);
375 } else if (n < BREAK_2) {
379 } else if (n < BREAK_3) {
383 } else if (n < BREAK_4) {
392 state = int_arg_state + 1; /* first location */
393 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
395 if (rand_type == TYPE_0)
396 int_arg_state[0] = rand_type;
398 int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
405 * Restore the state from the given state array.
407 * Note: it is important that we also remember the locations of the pointers
408 * in the current state information, and restore the locations of the pointers
409 * from the old state information. This is done by multiplexing the pointer
410 * location into the zeroeth word of the state information.
412 * Note that due to the order in which things are done, it is OK to call
413 * setstate() with the same state as the current state.
416 * arg_state: pointer to state array
418 * Returns a pointer to the old state information.
420 * Note: The Sparc platform requires that arg_state begin on an int
421 * word boundary; otherwise a bus error will occur. Even so, lint will
422 * complain about mis-alignment, but you should disregard these messages.
425 setstate(char *arg_state)
427 uint32_t *new_state = (uint32_t *)arg_state;
428 uint32_t type = new_state[0] % MAX_TYPES;
429 uint32_t rear = new_state[0] / MAX_TYPES;
430 char *ostate = (char *)(&state[-1]);
432 if (rand_type == TYPE_0)
433 state[-1] = rand_type;
435 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
443 rand_deg = degrees[type];
444 rand_sep = seps[type];
448 "random: state info corrupted; not changed.\n");
450 state = new_state + 1;
451 if (rand_type != TYPE_0) {
453 fptr = &state[(rear + rand_sep) % rand_deg];
455 end_ptr = &state[rand_deg]; /* set end_ptr too */
462 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
463 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
464 * the same in all the other cases due to all the global variables that have
465 * been set up. The basic operation is to add the number at the rear pointer
466 * into the one at the front pointer. Then both pointers are advanced to
467 * the next location cyclically in the table. The value returned is the sum
468 * generated, reduced to 31 bits by throwing away the "least random" low bit.
470 * Note: the code takes advantage of the fact that both the front and
471 * rear pointers can't wrap on the same call by not testing the rear
472 * pointer if the front one has wrapped.
474 * Returns a 31-bit random number.
482 if (rand_type == TYPE_0) {
484 state[0] = i = (good_rand(i)) & 0x7fffffff;
487 * Use local variables rather than static variables for speed.
491 /* chucking least random bit */
492 i = (*f >> 1) & 0x7fffffff;
493 if (++f >= end_ptr) {
497 else if (++r >= end_ptr) {