2 * Copyright (c) 1983 Regents of the University of California.
5 * Redistribution and use in source and binary forms are permitted
6 * provided that: (1) source distributions retain this entire copyright
7 * notice and comment, and (2) distributions including binaries display
8 * the following acknowledgement: ``This product includes software
9 * developed by the University of California, Berkeley and its contributors''
10 * in the documentation or other materials provided with the distribution
11 * and in all advertising materials mentioning features or use of this
12 * software. Neither the name of the University nor the names of its
13 * contributors may be used to endorse or promote products derived
14 * from this software without specific prior written permission.
15 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
16 * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
17 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
20 /* ATTENTION: there are quite a few static variables in here that will
21 * during execution. But since this is a random-number generator,
22 * this can only make for better random-results ;-)) */
26 * An improved random number generation package. In addition to the standard
27 * rand()/srand() like interface, this package also has a special state info
28 * interface. The initstate() routine is called with a seed, an array of
29 * bytes, and a count of how many bytes are being passed in; this array is then
30 * initialized to contain information for random number generation with that
31 * much state information. Good sizes for the amount of state information are
32 * 32, 64, 128, and 256 bytes. The state can be switched by calling the
33 * setstate() routine with the same array as was initiallized with initstate().
34 * By default, the package runs with 128 bytes of state information and
35 * generates far better random numbers than a linear congruential generator.
36 * If the amount of state information is less than 32 bytes, a simple linear
37 * congruential R.N.G. is used.
38 * Internally, the state information is treated as an array of longs; the
39 * zeroeth element of the array is the type of R.N.G. being used (small
40 * integer); the remainder of the array is the state information for the
41 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
42 * state information, which will allow a degree seven polynomial. (Note: the
43 * zeroeth word of state information also has some other information stored
44 * in it -- see setstate() for details).
45 * The random number generation technique is a linear feedback shift register
46 * approach, employing trinomials (since there are fewer terms to sum up that
47 * way). In this approach, the least significant bit of all the numbers in
48 * the state table will act as a linear feedback shift register, and will have
49 * period 2^deg - 1 (where deg is the degree of the polynomial being used,
50 * assuming that the polynomial is irreducible and primitive). The higher
51 * order bits will have longer periods, since their values are also influenced
52 * by pseudo-random carries out of the lower bits. The total period of the
53 * generator is approximately deg*(2**deg - 1); thus doubling the amount of
54 * state information has a vast influence on the period of the generator.
55 * Note: the deg*(2**deg - 1) is an approximation only good for large deg,
56 * when the period of the shift register is the dominant factor. With deg
57 * equal to seven, the period is actually much longer than the 7*(2**7 - 1)
58 * predicted by this formula.
62 * For each of the currently supported random number generators, we have a
63 * break value on the amount of state information (you need at least this
64 * many bytes of state info to support this random number generator), a degree
65 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
66 * the separation between the two lower order coefficients of the trinomial.
69 #define TYPE_0 0 /* linear congruential */
74 #define TYPE_1 1 /* x**7 + x**3 + 1 */
79 #define TYPE_2 2 /* x**15 + x + 1 */
84 #define TYPE_3 3 /* x**31 + x**3 + 1 */
89 #define TYPE_4 4 /* x**63 + x + 1 */
96 * Array versions of the above information to make code run faster -- relies
97 * on fact that TYPE_i == i.
100 #define MAX_TYPES 5 /* max number of types above */
102 static int degrees
[ MAX_TYPES
] = { DEG_0
, DEG_1
, DEG_2
,
105 static int seps
[ MAX_TYPES
] = { SEP_0
, SEP_1
, SEP_2
,
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.
121 static long randtbl
[ DEG_3
+ 1 ] = { TYPE_3
,
122 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
123 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
124 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
125 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
126 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
127 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
128 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
129 0xf5ad9d0e, 0x8999220b, 0x27fb47b9 };
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 cycle
134 * cyclically 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 this
136 * 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).
143 static long *fptr
= &randtbl
[ SEP_3
+ 1 ];
144 static long *rptr
= &randtbl
[ 1 ];
149 * The following things are the pointer to the state information table,
150 * the type of the current generator, the degree of the current polynomial
151 * being used, and the separation between the two pointers.
152 * Note that for efficiency of random(), we remember the first location of
153 * the state information, not the zeroeth. Hence it is valid to access
154 * state[-1], which is used to store the type of the R.N.G.
155 * Also, we remember the last location, since this is more efficient than
156 * indexing every time to find the address of the last element to see if
157 * the front and rear pointers have wrapped.
160 static long *state
= &randtbl
[ 1 ];
162 static int rand_type
= TYPE_3
;
163 static int rand_deg
= DEG_3
;
164 static int rand_sep
= SEP_3
;
166 static long *end_ptr
= &randtbl
[ DEG_3
+ 1 ];
172 * Initialize the random number generator based on the given seed. If the
173 * type is the trivial no-state-information type, just remember the seed.
174 * Otherwise, initializes state[] based on the given "seed" via a linear
175 * congruential generator. Then, the pointers are set to known locations
176 * that are exactly rand_sep places apart. Lastly, it cycles the state
177 * information a given number of times to get rid of any initial dependencies
178 * introduced by the L.C.R.N.G.
179 * Note that the initialization of randtbl[] for default usage relies on
180 * values produced by this routine.
187 void srandom(unsigned x
)
192 if( rand_type
== TYPE_0
) {
198 for( i
= 1; i
< rand_deg
; i
++ ) {
199 state
[i
] = 1103515245*state
[i
- 1] + 12345;
201 fptr
= &state
[ rand_sep
];
203 for( i
= 0; i
< 10*rand_deg
; i
++ ) random();
211 * Initialize the state information in the given array of n bytes for
212 * future random number generation. Based on the number of bytes we
213 * are given, and the break values for the different R.N.G.'s, we choose
214 * the best (largest) one we can and set things up for it. srandom() is
215 * then called to initialize the state information.
216 * Note that on return from srandom(), we set state[-1] to be the type
217 * multiplexed with the current value of the rear pointer; this is so
218 * successive calls to initstate() won't lose this information and will
219 * be able to restart with setstate().
220 * Note: the first thing we do is save the current state, if any, just like
221 * setstate() so that it doesn't matter when initstate is called.
222 * Returns a pointer to the old state.
226 initstate( seed
, arg_state
, n
)
228 unsigned seed
; /* seed for R. N. G. */
229 char *arg_state
; /* pointer to state array */
230 int n
; /* # bytes of state info */
232 register char *ostate
= (char *)( &state
[ -1 ] );
234 if( rand_type
== TYPE_0
) state
[ -1 ] = rand_type
;
235 else state
[ -1 ] = MAX_TYPES
*(rptr
- state
) + rand_type
;
270 state
= &( ( (long *)arg_state
)[1] ); /* first location */
271 end_ptr
= &state
[ rand_deg
]; /* must set end_ptr before srandom */
273 if( rand_type
== TYPE_0
) state
[ -1 ] = rand_type
;
274 else state
[ -1 ] = MAX_TYPES
*(rptr
- state
) + rand_type
;
282 * Restore the state from the given state array.
283 * Note: it is important that we also remember the locations of the pointers
284 * in the current state information, and restore the locations of the pointers
285 * from the old state information. This is done by multiplexing the pointer
286 * location into the zeroeth word of the state information.
287 * Note that due to the order in which things are done, it is OK to call
288 * setstate() with the same state as the current state.
289 * Returns a pointer to the old state information.
292 char *setstate(char *arg_state
)
294 register long *new_state
= (long *)arg_state
;
295 register int type
= new_state
[0]%MAX_TYPES
;
296 register int rear
= new_state
[0]/MAX_TYPES
;
297 char *ostate
= (char *)(&state
[-1]);
299 if (rand_type
== TYPE_0
) state
[-1] = rand_type
;
300 else state
[ -1 ] = MAX_TYPES
*(rptr
- state
) + rand_type
;
310 rand_deg
= degrees
[type
];
311 rand_sep
= seps
[type
];
314 state
= &new_state
[1];
315 if (rand_type
!= TYPE_0
)
318 fptr
= &state
[(rear
+ rand_sep
)%rand_deg
];
320 end_ptr
= &state
[rand_deg
]; /* set end_ptr too */
329 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
330 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
331 * same in all ther other cases due to all the global variables that have been
332 * set up. The basic operation is to add the number at the rear pointer into
333 * the one at the front pointer. Then both pointers are advanced to the next
334 * location cyclically in the table. The value returned is the sum generated,
335 * reduced to 31 bits by throwing away the "least random" low bit.
336 * Note: the code takes advantage of the fact that both the front and
337 * rear pointers can't wrap on the same call by not testing the rear
338 * pointer if the front one has wrapped.
339 * Returns a 31-bit random number.
346 if (rand_type
== TYPE_0
)
348 i
= state
[0] = (state
[0]*1103515245 + 12345)&0x7fffffff;
353 i
= (*fptr
>> 1)&0x7fffffff; /* chucking least random bit */
354 if (++fptr
>= end_ptr
)
361 if (++rptr
>= end_ptr
) rptr
= state
;