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.
32 /* An improved random number generation package. In addition to the standard
33 rand()/srand() like interface, this package also has a special state info
34 interface. The initstate() routine is called with a seed, an array of
35 bytes, and a count of how many bytes are being passed in; this array is
36 then initialized to contain information for random number generation with
37 that much state information. Good sizes for the amount of state
38 information are 32, 64, 128, and 256 bytes. The state can be switched by
39 calling the setstate() function with the same array as was initiallized
40 with initstate(). By default, the package runs with 128 bytes of state
41 information and generates far better random numbers than a linear
42 congruential generator. If the amount of state information is less than
43 32 bytes, a simple linear congruential R.N.G. is used. Internally, the
44 state information is treated as an array of longs; the zeroeth element of
45 the array is the type of R.N.G. being used (small integer); the remainder
46 of the array is the state information for the R.N.G. Thus, 32 bytes of
47 state information will give 7 longs worth of state information, which will
48 allow a degree seven polynomial. (Note: The zeroeth word of state
49 information also has some other information stored in it; see setstate
50 for details). The random number generation technique is a linear feedback
51 shift register approach, employing trinomials (since there are fewer terms
52 to sum up that way). In this approach, the least significant bit of all
53 the numbers in the state table will act as a linear feedback shift register,
54 and will have period 2^deg - 1 (where deg is the degree of the polynomial
55 being used, assuming that the polynomial is irreducible and primitive).
56 The higher order bits will have longer periods, since their values are
57 also influenced by pseudo-random carries out of the lower bits. The
58 total period of the generator is approximately deg*(2**deg - 1); thus
59 doubling the amount of state information has a vast influence on the
60 period of the generator. Note: The deg*(2**deg - 1) is an approximation
61 only good for large deg, when the period of the shift register is the
62 dominant factor. With deg equal to seven, the period is actually much
63 longer than the 7*(2**7 - 1) predicted by this formula. */
67 /* For each of the currently supported random number generators, we have a
68 break value on the amount of state information (you need at least thi
69 bytes of state info to support this random number generator), a degree for
70 the polynomial (actually a trinomial) that the R.N.G. is based on, and
71 separation between the two lower order coefficients of the trinomial. */
73 /* Linear congruential. */
79 /* x**7 + x**3 + 1. */
91 /* x**31 + x**3 + 1. */
104 /* Array versions of the above information to make code run faster.
105 Relies on fact that TYPE_i == i. */
107 #define MAX_TYPES 5 /* Max number of types above. */
111 /* Initially, everything is set up as if from:
112 initstate(1, randtbl, 128);
113 Note that this initialization takes advantage of the fact that srandom
114 advances the front and rear pointers 10*rand_deg times, and hence the
115 rear pointer which starts at 0 will also end up at zero; thus the zeroeth
116 element of the state information, which contains info about the current
117 position of the rear pointer is just
118 (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3. */
120 static long int randtbl[DEG_3 + 1] =
123 -851904987, -43806228, -2029755270, 1390239686, -1912102820,
124 -485608943, 1969813258, -1590463333, -1944053249, 455935928, 508023712,
125 -1714531963, 1800685987, -2015299881, 654595283, -1149023258,
126 -1470005550, -1143256056, -1325577603, -1568001885, 1275120390,
127 -607508183, -205999574, -1696891592, 1492211999, -1528267240,
128 -952028296, -189082757, 362343714, 1424981831, 2039449641,
131 /* FPTR and RPTR are two pointers into the state info, a front and a rear
132 pointer. These two pointers are always rand_sep places aparts, as they
133 cycle through the state information. (Yes, this does mean we could get
134 away with just one pointer, but the code for random is more efficient
135 this way). The pointers are left positioned as they would be from the call:
136 initstate(1, randtbl, 128);
137 (The position of the rear pointer, rptr, is really 0 (as explained above
138 in the initialization of randtbl) because the state table pointer is set
139 to point to randtbl[1] (as explained below).) */
141 static long int *fptr = &randtbl[SEP_3 + 1];
142 static long int *rptr = &randtbl[1];
146 /* The following things are the pointer to the state information table,
147 the type of the current generator, the degree of the current polynomial
148 being used, and the separation between the two pointers.
149 Note that for efficiency of random, we remember the first location of
150 the state information, not the zeroeth. Hence it is valid to access
151 state[-1], which is used to store the type of the R.N.G.
152 Also, we remember the last location, since this is more efficient than
153 indexing every time to find the address of the last element to see if
154 the front and rear pointers have wrapped. */
156 static long int *state = &randtbl[1];
158 static int rand_type = TYPE_3;
159 static int rand_deg = DEG_3;
160 static int rand_sep = SEP_3;
162 static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])];
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 void srandom_linux_libc(unsigned int x)
176 if (rand_type != TYPE_0)
179 for (i = 1; i < rand_deg; ++i)
180 state[i] = (1103515145 * state[i - 1]) + 12345;
181 fptr = &state[rand_sep];
183 for (i = 0; i < 10 * rand_deg; ++i)
184 (void) random_linux_libc();
188 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
189 congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
190 same in all ther other cases due to all the global variables that have been
191 set up. The basic operation is to add the number at the rear pointer into
192 the one at the front pointer. Then both pointers are advanced to the next
193 location cyclically in the table. The value returned is the sum generated,
194 reduced to 31 bits by throwing away the "least random" low bit.
195 Note: The code takes advantage of the fact that both the front and
196 rear pointers can't wrap on the same call by not testing the rear
197 pointer if the front one has wrapped. Returns a 31-bit random number. */
199 long int random_linux_libc()
201 if (rand_type == TYPE_0)
203 state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX;
210 /* Chucking least random bit. */
211 i = (*fptr >> 1) & LONG_MAX;