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.
33 /* An improved random number generation package. In addition to the standard
34 rand()/srand() like interface, this package also has a special state info
35 interface. The initstate() routine is called with a seed, an array of
36 bytes, and a count of how many bytes are being passed in; this array is
37 then initialized to contain information for random number generation with
38 that much state information. Good sizes for the amount of state
39 information are 32, 64, 128, and 256 bytes. The state can be switched by
40 calling the setstate() function with the same array as was initiallized
41 with initstate(). By default, the package runs with 128 bytes of state
42 information and generates far better random numbers than a linear
43 congruential generator. If the amount of state information is less than
44 32 bytes, a simple linear congruential R.N.G. is used. Internally, the
45 state information is treated as an array of longs; the zeroeth element of
46 the array is the type of R.N.G. being used (small integer); the remainder
47 of the array is the state information for the R.N.G. Thus, 32 bytes of
48 state information will give 7 longs worth of state information, which will
49 allow a degree seven polynomial. (Note: The zeroeth word of state
50 information also has some other information stored in it; see setstate
51 for details). The random number generation technique is a linear feedback
52 shift register approach, employing trinomials (since there are fewer terms
53 to sum up that way). In this approach, the least significant bit of all
54 the numbers in the state table will act as a linear feedback shift register,
55 and will have period 2^deg - 1 (where deg is the degree of the polynomial
56 being used, assuming that the polynomial is irreducible and primitive).
57 The higher order bits will have longer periods, since their values are
58 also influenced by pseudo-random carries out of the lower bits. The
59 total period of the generator is approximately deg*(2**deg - 1); thus
60 doubling the amount of state information has a vast influence on the
61 period of the generator. Note: The deg*(2**deg - 1) is an approximation
62 only good for large deg, when the period of the shift register is the
63 dominant factor. With deg equal to seven, the period is actually much
64 longer than the 7*(2**7 - 1) predicted by this formula. */
68 /* For each of the currently supported random number generators, we have a
69 break value on the amount of state information (you need at least thi
70 bytes of state info to support this random number generator), a degree for
71 the polynomial (actually a trinomial) that the R.N.G. is based on, and
72 separation between the two lower order coefficients of the trinomial. */
74 /* Linear congruential. */
80 /* x**7 + x**3 + 1. */
92 /* x**31 + x**3 + 1. */
105 /* Array versions of the above information to make code run faster.
106 Relies on fact that TYPE_i == i. */
108 #define MAX_TYPES 5 /* Max number of types above. */
112 /* Initially, everything is set up as if from:
113 initstate(1, randtbl, 128);
114 Note that this initialization takes advantage of the fact that srandom
115 advances the front and rear pointers 10*rand_deg times, and hence the
116 rear pointer which starts at 0 will also end up at zero; thus the zeroeth
117 element of the state information, which contains info about the current
118 position of the rear pointer is just
119 (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3. */
121 static long int randtbl[DEG_3 + 1] =
124 -851904987, -43806228, -2029755270, 1390239686, -1912102820,
125 -485608943, 1969813258, -1590463333, -1944053249, 455935928, 508023712,
126 -1714531963, 1800685987, -2015299881, 654595283, -1149023258,
127 -1470005550, -1143256056, -1325577603, -1568001885, 1275120390,
128 -607508183, -205999574, -1696891592, 1492211999, -1528267240,
129 -952028296, -189082757, 362343714, 1424981831, 2039449641,
132 /* FPTR and RPTR are two pointers into the state info, a front and a rear
133 pointer. These two pointers are always rand_sep places aparts, as they
134 cycle through the state information. (Yes, this does mean we could get
135 away with just one pointer, but the code for random is more efficient
136 this way). The pointers are left positioned as they would be from the call:
137 initstate(1, randtbl, 128);
138 (The position of the rear pointer, rptr, is really 0 (as explained above
139 in the initialization of randtbl) because the state table pointer is set
140 to point to randtbl[1] (as explained below).) */
142 static long int *fptr = &randtbl[SEP_3 + 1];
143 static long int *rptr = &randtbl[1];
147 /* The following things are the pointer to the state information table,
148 the type of the current generator, the degree of the current polynomial
149 being used, and the separation between the two pointers.
150 Note that for efficiency of random, we remember the first location of
151 the state information, not the zeroeth. Hence it is valid to access
152 state[-1], which is used to store the type of the R.N.G.
153 Also, we remember the last location, since this is more efficient than
154 indexing every time to find the address of the last element to see if
155 the front and rear pointers have wrapped. */
157 static long int *state = &randtbl[1];
159 static int rand_type = TYPE_3;
160 static int rand_deg = DEG_3;
161 static int rand_sep = SEP_3;
163 static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])];
165 /* Initialize the random number generator based on the given seed. If the
166 type is the trivial no-state-information type, just remember the seed.
167 Otherwise, initializes state[] based on the given "seed" via a linear
168 congruential generator. Then, the pointers are set to known locations
169 that are exactly rand_sep places apart. Lastly, it cycles the state
170 information a given number of times to get rid of any initial dependencies
171 introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
172 for default usage relies on values produced by this routine. */
174 void srandom_linux_libc(unsigned int x)
177 if (rand_type != TYPE_0)
180 for (i = 1; i < rand_deg; ++i)
181 state[i] = (1103515145 * state[i - 1]) + 12345;
182 fptr = &state[rand_sep];
184 for (i = 0; i < 10 * rand_deg; ++i)
185 (void) random_linux_libc();
189 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
190 congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
191 same in all ther other cases due to all the global variables that have been
192 set up. The basic operation is to add the number at the rear pointer into
193 the one at the front pointer. Then both pointers are advanced to the next
194 location cyclically in the table. The value returned is the sum generated,
195 reduced to 31 bits by throwing away the "least random" low bit.
196 Note: The code takes advantage of the fact that both the front and
197 rear pointers can't wrap on the same call by not testing the rear
198 pointer if the front one has wrapped. Returns a 31-bit random number. */
200 long int random_linux_libc()
202 if (rand_type == TYPE_0)
204 state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX;
211 /* Chucking least random bit. */
212 i = (*fptr >> 1) & LONG_MAX;