2 * Copyright (c) 1983 Regents of the University of California.
5 * Redistribution and use in source and binary forms are permitted
6 * provided that the above copyright notice and this paragraph are
7 * duplicated in all such forms and that any documentation,
8 * advertising materials, and other materials related to such
9 * distribution and use acknowledge that the software was developed
10 * by the University of California, Berkeley. The name of the
11 * University may not be used to endorse or promote products derived
12 * from this software without specific prior written permission.
13 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
14 * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
15 * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
19 * This is derived from the Berkeley source:
20 * @(#)random.c 5.5 (Berkeley) 7/6/88
21 * It was reworked for the GNU C Library by Roland McGrath.
31 /* An improved random number generation package. In addition to the standard
32 rand()/srand() like interface, this package also has a special state info
33 interface. The initstate() routine is called with a seed, an array of
34 bytes, and a count of how many bytes are being passed in; this array is
35 then initialized to contain information for random number generation with
36 that much state information. Good sizes for the amount of state
37 information are 32, 64, 128, and 256 bytes. The state can be switched by
38 calling the setstate() function with the same array as was initiallized
39 with initstate(). By default, the package runs with 128 bytes of state
40 information and generates far better random numbers than a linear
41 congruential generator. If the amount of state information is less than
42 32 bytes, a simple linear congruential R.N.G. is used. Internally, the
43 state information is treated as an array of longs; the zeroeth element of
44 the array is the type of R.N.G. being used (small integer); the remainder
45 of the array is the state information for the R.N.G. Thus, 32 bytes of
46 state information will give 7 longs worth of state information, which will
47 allow a degree seven polynomial. (Note: The zeroeth word of state
48 information also has some other information stored in it; see setstate
49 for details). The random number generation technique is a linear feedback
50 shift register approach, employing trinomials (since there are fewer terms
51 to sum up that way). In this approach, the least significant bit of all
52 the numbers in the state table will act as a linear feedback shift register,
53 and will have period 2^deg - 1 (where deg is the degree of the polynomial
54 being used, assuming that the polynomial is irreducible and primitive).
55 The higher order bits will have longer periods, since their values are
56 also influenced by pseudo-random carries out of the lower bits. The
57 total period of the generator is approximately deg*(2**deg - 1); thus
58 doubling the amount of state information has a vast influence on the
59 period of the generator. Note: The deg*(2**deg - 1) is an approximation
60 only good for large deg, when the period of the shift register is the
61 dominant factor. With deg equal to seven, the period is actually much
62 longer than the 7*(2**7 - 1) predicted by this formula. */
66 /* For each of the currently supported random number generators, we have a
67 break value on the amount of state information (you need at least thi
68 bytes of state info to support this random number generator), a degree for
69 the polynomial (actually a trinomial) that the R.N.G. is based on, and
70 separation between the two lower order coefficients of the trinomial. */
72 /* Linear congruential. */
78 /* x**7 + x**3 + 1. */
90 /* x**31 + x**3 + 1. */
103 /* Array versions of the above information to make code run faster.
104 Relies on fact that TYPE_i == i. */
106 #define MAX_TYPES 5 /* Max number of types above. */
108 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
109 static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
113 /* Initially, everything is set up as if from:
114 initstate(1, randtbl, 128);
115 Note that this initialization takes advantage of the fact that srandom
116 advances the front and rear pointers 10*rand_deg times, and hence the
117 rear pointer which starts at 0 will also end up at zero; thus the zeroeth
118 element of the state information, which contains info about the current
119 position of the rear pointer is just
120 (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3. */
122 static long int randtbl[DEG_3 + 1] =
125 -851904987, -43806228, -2029755270, 1390239686, -1912102820,
126 -485608943, 1969813258, -1590463333, -1944053249, 455935928, 508023712,
127 -1714531963, 1800685987, -2015299881, 654595283, -1149023258,
128 -1470005550, -1143256056, -1325577603, -1568001885, 1275120390,
129 -607508183, -205999574, -1696891592, 1492211999, -1528267240,
130 -952028296, -189082757, 362343714, 1424981831, 2039449641,
133 /* FPTR and RPTR are two pointers into the state info, a front and a rear
134 pointer. These two pointers are always rand_sep places aparts, as they
135 cycle through the state information. (Yes, this does mean we could get
136 away with just one pointer, but the code for random is more efficient
137 this way). The pointers are left positioned as they would be from the call:
138 initstate(1, randtbl, 128);
139 (The position of the rear pointer, rptr, is really 0 (as explained above
140 in the initialization of randtbl) because the state table pointer is set
141 to point to randtbl[1] (as explained below).) */
143 static long int *fptr = &randtbl[SEP_3 + 1];
144 static long int *rptr = &randtbl[1];
148 /* The following things are the pointer to the state information table,
149 the type of the current generator, the degree of the current polynomial
150 being used, and the separation between the two pointers.
151 Note that for efficiency of random, we remember the first location of
152 the state information, not the zeroeth. Hence it is valid to access
153 state[-1], which is used to store the type of the R.N.G.
154 Also, we remember the last location, since this is more efficient than
155 indexing every time to find the address of the last element to see if
156 the front and rear pointers have wrapped. */
158 static long int *state = &randtbl[1];
160 static int rand_type = TYPE_3;
161 static int rand_deg = DEG_3;
162 static int rand_sep = SEP_3;
164 static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])];
166 /* Initialize the random number generator based on the given seed. If the
167 type is the trivial no-state-information type, just remember the seed.
168 Otherwise, initializes state[] based on the given "seed" via a linear
169 congruential generator. Then, the pointers are set to known locations
170 that are exactly rand_sep places apart. Lastly, it cycles the state
171 information a given number of times to get rid of any initial dependencies
172 introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
173 for default usage relies on values produced by this routine. */
175 DEFUN(__srandom, (x), unsigned int x)
178 if (rand_type != TYPE_0)
181 for (i = 1; i < rand_deg; ++i)
182 state[i] = (1103515145 * state[i - 1]) + 12345;
183 fptr = &state[rand_sep];
185 for (i = 0; i < 10 * rand_deg; ++i)
190 weak_alias (__srandom, srandom)
191 weak_alias (__srandom, srand)
193 /* Initialize the state information in the given array of N bytes for
194 future random number generation. Based on the number of bytes we
195 are given, and the break values for the different R.N.G.'s, we choose
196 the best (largest) one we can and set things up for it. srandom is
197 then called to initialize the state information. Note that on return
198 from srandom, we set state[-1] to be the type multiplexed with the current
199 value of the rear pointer; this is so successive calls to initstate won't
200 lose this information and will be able to restart with setstate.
201 Note: The first thing we do is save the current state, if any, just like
202 setstate so that it doesn't matter when initstate is called.
203 Returns a pointer to the old state. */
205 DEFUN(__initstate, (seed, arg_state, n),
206 unsigned int seed AND PTR arg_state AND size_t n)
208 PTR ostate = (PTR) &state[-1];
210 if (rand_type == TYPE_0)
211 state[-1] = rand_type;
213 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
225 else if (n < BREAK_2)
231 else if (n < BREAK_3)
237 else if (n < BREAK_4)
250 state = &((long int *) arg_state)[1]; /* First location. */
251 /* Must set END_PTR before srandom. */
252 end_ptr = &state[rand_deg];
254 if (rand_type == TYPE_0)
255 state[-1] = rand_type;
257 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
262 weak_alias (__initstate, initstate)
264 /* Restore the state from the given state array.
265 Note: It is important that we also remember the locations of the pointers
266 in the current state information, and restore the locations of the pointers
267 from the old state information. This is done by multiplexing the pointer
268 location into the zeroeth word of the state information. Note that due
269 to the order in which things are done, it is OK to call setstate with the
270 same state as the current state
271 Returns a pointer to the old state information. */
273 DEFUN(__setstate, (arg_state), PTR arg_state)
275 register long int *new_state = (long int *) arg_state;
276 register int type = new_state[0] % MAX_TYPES;
277 register int rear = new_state[0] / MAX_TYPES;
278 PTR ostate = (PTR) &state[-1];
280 if (rand_type == TYPE_0)
281 state[-1] = rand_type;
283 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
293 rand_deg = degrees[type];
294 rand_sep = seps[type];
297 /* State info munged. */
302 state = &new_state[1];
303 if (rand_type != TYPE_0)
306 fptr = &state[(rear + rand_sep) % rand_deg];
308 /* Set end_ptr too. */
309 end_ptr = &state[rand_deg];
314 weak_alias (__setstate, setstate)
316 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
317 congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
318 same in all ther other cases due to all the global variables that have been
319 set up. The basic operation is to add the number at the rear pointer into
320 the one at the front pointer. Then both pointers are advanced to the next
321 location cyclically in the table. The value returned is the sum generated,
322 reduced to 31 bits by throwing away the "least random" low bit.
323 Note: The code takes advantage of the fact that both the front and
324 rear pointers can't wrap on the same call by not testing the rear
325 pointer if the front one has wrapped. Returns a 31-bit random number. */
330 if (rand_type == TYPE_0)
332 state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX;
339 /* Chucking least random bit. */
340 i = (*fptr >> 1) & LONG_MAX;
357 weak_alias (__random, random)