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20 Copyright (C) 1983 Regents of the University of California.
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49 * This is derived from the Berkeley source:
50 * @(#)random.c 5.5 (Berkeley) 7/6/88
51 * It was reworked for the GNU C Library by Roland McGrath.
52 * Rewritten to be reentrant by Ulrich Drepper, 1995
64 /* An improved random number generation package. In addition to the standard
65 rand()/srand() like interface, this package also has a special state info
66 interface. The initstate() routine is called with a seed, an array of
67 bytes, and a count of how many bytes are being passed in; this array is
68 then initialized to contain information for random number generation with
69 that much state information. Good sizes for the amount of state
70 information are 32, 64, 128, and 256 bytes. The state can be switched by
71 calling the setstate() function with the same array as was initialized
72 with initstate(). By default, the package runs with 128 bytes of state
73 information and generates far better random numbers than a linear
74 congruential generator. If the amount of state information is less than
75 32 bytes, a simple linear congruential R.N.G. is used. Internally, the
76 state information is treated as an array of longs; the zeroth element of
77 the array is the type of R.N.G. being used (small integer); the remainder
78 of the array is the state information for the R.N.G. Thus, 32 bytes of
79 state information will give 7 longs worth of state information, which will
80 allow a degree seven polynomial. (Note: The zeroth word of state
81 information also has some other information stored in it; see setstate
82 for details). The random number generation technique is a linear feedback
83 shift register approach, employing trinomials (since there are fewer terms
84 to sum up that way). In this approach, the least significant bit of all
85 the numbers in the state table will act as a linear feedback shift register,
86 and will have period 2^deg - 1 (where deg is the degree of the polynomial
87 being used, assuming that the polynomial is irreducible and primitive).
88 The higher order bits will have longer periods, since their values are
89 also influenced by pseudo-random carries out of the lower bits. The
90 total period of the generator is approximately deg*(2**deg - 1); thus
91 doubling the amount of state information has a vast influence on the
92 period of the generator. Note: The deg*(2**deg - 1) is an approximation
93 only good for large deg, when the period of the shift register is the
94 dominant factor. With deg equal to seven, the period is actually much
95 longer than the 7*(2**7 - 1) predicted by this formula. */
99 /* For each of the currently supported random number generators, we have a
100 break value on the amount of state information (you need at least this many
101 bytes of state info to support this random number generator), a degree for
102 the polynomial (actually a trinomial) that the R.N.G. is based on, and
103 separation between the two lower order coefficients of the trinomial. */
105 /* Linear congruential. */
111 /* x**7 + x**3 + 1. */
123 /* x**31 + x**3 + 1. */
136 /* Array versions of the above information to make code run faster.
137 Relies on fact that TYPE_i == i. */
139 #define MAX_TYPES 5 /* Max number of types above. */
141 struct random_poly_info
144 int degrees[MAX_TYPES];
147 static const struct random_poly_info random_poly_info =
149 { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 },
150 { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }
154 # define weak_alias(local, symbol)
155 # define __set_errno(e) errno = (e)
156 # define __srandom_r srandom_r
157 # define __initstate_r initstate_r
158 # define __setstate_r setstate_r
159 # define __random_r random_r
164 /* Initialize the random number generator based on the given seed. If the
165 type is the trivial no-state-information type, just remember the seed.
166 Otherwise, initializes state[] based on the given "seed" via a linear
167 congruential generator. Then, the pointers are set to known locations
168 that are exactly rand_sep places apart. Lastly, it cycles the state
169 information a given number of times to get rid of any initial dependencies
170 introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
171 for default usage relies on values produced by this routine. */
173 __srandom_r (unsigned int seed, struct random_data *buf)
184 type = buf->rand_type;
185 if ((unsigned int) type >= MAX_TYPES)
189 /* We must make sure the seed is not 0. Take arbitrarily 1 in this case. */
199 for (i = 1; i < kc; ++i)
202 state[i] = (16807 * state[i - 1]) % 2147483647;
203 but avoids overflowing 31 bits. */
204 long int hi = word / 127773;
205 long int lo = word % 127773;
206 word = 16807 * lo - 2836 * hi;
212 buf->fptr = &state[buf->rand_sep];
213 buf->rptr = &state[0];
218 (void) __random_r (buf, &discard);
228 weak_alias (__srandom_r, srandom_r)
230 /* Initialize the state information in the given array of N bytes for
231 future random number generation. Based on the number of bytes we
232 are given, and the break values for the different R.N.G.'s, we choose
233 the best (largest) one we can and set things up for it. srandom is
234 then called to initialize the state information. Note that on return
235 from srandom, we set state[-1] to be the type multiplexed with the current
236 value of the rear pointer; this is so successive calls to initstate won't
237 lose this information and will be able to restart with setstate.
238 Note: The first thing we do is save the current state, if any, just like
239 setstate so that it doesn't matter when initstate is called.
240 Returns a pointer to the old state. */
242 __initstate_r (unsigned int seed, char *arg_state, size_t n,
243 struct random_data *buf)
254 old_state = buf->state;
255 if (old_state != NULL)
257 int old_type = buf->rand_type;
258 if (old_type == TYPE_0)
259 old_state[-1] = TYPE_0;
261 old_state[-1] = (MAX_TYPES * (buf->rptr - old_state)) + old_type;
265 type = n < BREAK_4 ? TYPE_3 : TYPE_4;
266 else if (n < BREAK_1)
270 __set_errno (EINVAL);
276 type = n < BREAK_2 ? TYPE_1 : TYPE_2;
278 degree = random_poly_info.degrees[type];
279 separation = random_poly_info.seps[type];
281 buf->rand_type = type;
282 buf->rand_sep = separation;
283 buf->rand_deg = degree;
284 state = &((int32_t *) arg_state)[1]; /* First location. */
285 /* Must set END_PTR before srandom. */
286 buf->end_ptr = &state[degree];
290 __srandom_r (seed, buf);
294 state[-1] = (buf->rptr - state) * MAX_TYPES + type;
299 __set_errno (EINVAL);
303 weak_alias (__initstate_r, initstate_r)
305 /* Restore the state from the given state array.
306 Note: It is important that we also remember the locations of the pointers
307 in the current state information, and restore the locations of the pointers
308 from the old state information. This is done by multiplexing the pointer
309 location into the zeroth word of the state information. Note that due
310 to the order in which things are done, it is OK to call setstate with the
311 same state as the current state
312 Returns a pointer to the old state information. */
314 __setstate_r (char *arg_state, struct random_data *buf)
316 int32_t *new_state = 1 + (int32_t *) arg_state;
323 if (arg_state == NULL || buf == NULL)
326 old_type = buf->rand_type;
327 old_state = buf->state;
328 if (old_type == TYPE_0)
329 old_state[-1] = TYPE_0;
331 old_state[-1] = (MAX_TYPES * (buf->rptr - old_state)) + old_type;
333 type = new_state[-1] % MAX_TYPES;
334 if (type < TYPE_0 || type > TYPE_4)
337 buf->rand_deg = degree = random_poly_info.degrees[type];
338 buf->rand_sep = separation = random_poly_info.seps[type];
339 buf->rand_type = type;
343 int rear = new_state[-1] / MAX_TYPES;
344 buf->rptr = &new_state[rear];
345 buf->fptr = &new_state[(rear + separation) % degree];
347 buf->state = new_state;
348 /* Set end_ptr too. */
349 buf->end_ptr = &new_state[degree];
354 __set_errno (EINVAL);
358 weak_alias (__setstate_r, setstate_r)
360 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
361 congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
362 same in all the other cases due to all the global variables that have been
363 set up. The basic operation is to add the number at the rear pointer into
364 the one at the front pointer. Then both pointers are advanced to the next
365 location cyclically in the table. The value returned is the sum generated,
366 reduced to 31 bits by throwing away the "least random" low bit.
367 Note: The code takes advantage of the fact that both the front and
368 rear pointers can't wrap on the same call by not testing the rear
369 pointer if the front one has wrapped. Returns a 31-bit random number. */
372 __random_r (struct random_data *buf, int32_t *result)
376 if (buf == NULL || result == NULL)
381 if (buf->rand_type == TYPE_0)
383 int32_t val = state[0];
384 val = ((state[0] * 1103515245) + 12345) & 0x7fffffff;
390 int32_t *fptr = buf->fptr;
391 int32_t *rptr = buf->rptr;
392 int32_t *end_ptr = buf->end_ptr;
395 val = *fptr += *rptr;
396 /* Chucking least random bit. */
397 *result = (val >> 1) & 0x7fffffff;
416 __set_errno (EINVAL);
420 weak_alias (__random_r, random_r)