* Copyright (c) 1983 Regents of the University of California.
* %sccs.include.redist.c%
#if defined(LIBC_SCCS) && !defined(lint)
static char sccsid
[] = "@(#)random.c 5.9 (Berkeley) %G%";
#endif /* LIBC_SCCS and not lint */
* An improved random number generation package. In addition to the standard
* rand()/srand() like interface, this package also has a special state info
* interface. The initstate() routine is called with a seed, an array of
* bytes, and a count of how many bytes are being passed in; this array is
* then initialized to contain information for random number generation with
* that much state information. Good sizes for the amount of state
* information are 32, 64, 128, and 256 bytes. The state can be switched by
* calling the setstate() routine with the same array as was initiallized
* with initstate(). By default, the package runs with 128 bytes of state
* information and generates far better random numbers than a linear
* congruential generator. If the amount of state information is less than
* 32 bytes, a simple linear congruential R.N.G. is used.
* Internally, the state information is treated as an array of longs; the
* zeroeth element of the array is the type of R.N.G. being used (small
* integer); the remainder of the array is the state information for the
* R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
* state information, which will allow a degree seven polynomial. (Note:
* the zeroeth word of state information also has some other information
* stored in it -- see setstate() for details).
* The random number generation technique is a linear feedback shift register
* approach, employing trinomials (since there are fewer terms to sum up that
* way). In this approach, the least significant bit of all the numbers in
* the state table will act as a linear feedback shift register, and will
* have period 2^deg - 1 (where deg is the degree of the polynomial being
* used, assuming that the polynomial is irreducible and primitive). The
* higher order bits will have longer periods, since their values are also
* influenced by pseudo-random carries out of the lower bits. The total
* period of the generator is approximately deg*(2**deg - 1); thus doubling
* the amount of state information has a vast influence on the period of the
* generator. Note: the deg*(2**deg - 1) is an approximation only good for
* large deg, when the period of the shift register is the dominant factor.
* With deg equal to seven, the period is actually much longer than the
* 7*(2**7 - 1) predicted by this formula.
* For each of the currently supported random number generators, we have a
* break value on the amount of state information (you need at least this
* many bytes of state info to support this random number generator), a degree
* for the polynomial (actually a trinomial) that the R.N.G. is based on, and
* the separation between the two lower order coefficients of the trinomial.
#define TYPE_0 0 /* linear congruential */
#define TYPE_1 1 /* x**7 + x**3 + 1 */
#define TYPE_2 2 /* x**15 + x + 1 */
#define TYPE_3 3 /* x**31 + x**3 + 1 */
#define TYPE_4 4 /* x**63 + x + 1 */
* Array versions of the above information to make code run faster --
* relies on fact that TYPE_i == i.
#define MAX_TYPES 5 /* max number of types above */
static int degrees
[MAX_TYPES
] = { DEG_0
, DEG_1
, DEG_2
, DEG_3
, DEG_4
};
static int seps
[MAX_TYPES
] = { SEP_0
, SEP_1
, SEP_2
, SEP_3
, SEP_4
};
* Initially, everything is set up as if from:
* initstate(1, &randtbl, 128);
* Note that this initialization takes advantage of the fact that srandom()
* advances the front and rear pointers 10*rand_deg times, and hence the
* rear pointer which starts at 0 will also end up at zero; thus the zeroeth
* element of the state information, which contains info about the current
* position of the rear pointer is just
* MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
static long randtbl
[DEG_3
+ 1] = {
0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
* fptr and rptr are two pointers into the state info, a front and a rear
* pointer. These two pointers are always rand_sep places aparts, as they
* cycle cyclically through the state information. (Yes, this does mean we
* could get away with just one pointer, but the code for random() is more
* efficient this way). The pointers are left positioned as they would be
* initstate(1, randtbl, 128);
* (The position of the rear pointer, rptr, is really 0 (as explained above
* in the initialization of randtbl) because the state table pointer is set
* to point to randtbl[1] (as explained below).
static long *fptr
= &randtbl
[SEP_3
+ 1];
static long *rptr
= &randtbl
[1];
* The following things are the pointer to the state information table, the
* type of the current generator, the degree of the current polynomial being
* used, and the separation between the two pointers. Note that for efficiency
* of random(), we remember the first location of the state information, not
* the zeroeth. Hence it is valid to access state[-1], which is used to
* store the type of the R.N.G. Also, we remember the last location, since
* this is more efficient than indexing every time to find the address of
* the last element to see if the front and rear pointers have wrapped.
static long *state
= &randtbl
[1];
static int rand_type
= TYPE_3
;
static int rand_deg
= DEG_3
;
static int rand_sep
= SEP_3
;
static long *end_ptr
= &randtbl
[DEG_3
+ 1];
* Initialize the random number generator based on the given seed. If the
* type is the trivial no-state-information type, just remember the seed.
* Otherwise, initializes state[] based on the given "seed" via a linear
* congruential generator. Then, the pointers are set to known locations
* that are exactly rand_sep places apart. Lastly, it cycles the state
* information a given number of times to get rid of any initial dependencies
* introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
* for default usage relies on values produced by this routine.
for (i
= 1; i
< rand_deg
; i
++)
state
[i
] = 1103515245 * state
[i
- 1] + 12345;
for (i
= 0; i
< 10 * rand_deg
; i
++)
* Initialize the state information in the given array of n bytes for future
* random number generation. Based on the number of bytes we are given, and
* the break values for the different R.N.G.'s, we choose the best (largest)
* one we can and set things up for it. srandom() is then called to
* initialize the state information.
* Note that on return from srandom(), we set state[-1] to be the type
* multiplexed with the current value of the rear pointer; this is so
* successive calls to initstate() won't lose this information and will be
* able to restart with setstate().
* Note: the first thing we do is save the current state, if any, just like
* setstate() so that it doesn't matter when initstate is called.
* Returns a pointer to the old state.
initstate(seed
, arg_state
, n
)
u_int seed
; /* seed for R.N.G. */
char *arg_state
; /* pointer to state array */
int n
; /* # bytes of state info */
register char *ostate
= (char *)(&state
[-1]);
state
[-1] = MAX_TYPES
* (rptr
- state
) + rand_type
;
"random: not enough state (%d bytes); ignored.\n", n
);
} else if (n
< BREAK_2
) {
} else if (n
< BREAK_3
) {
} else if (n
< BREAK_4
) {
state
= &(((long *)arg_state
)[1]); /* first location */
end_ptr
= &state
[rand_deg
]; /* must set end_ptr before srandom */
state
[-1] = MAX_TYPES
*(rptr
- state
) + rand_type
;
* Restore the state from the given state array.
* Note: it is important that we also remember the locations of the pointers
* in the current state information, and restore the locations of the pointers
* from the old state information. This is done by multiplexing the pointer
* location into the zeroeth word of the state information.
* Note that due to the order in which things are done, it is OK to call
* setstate() with the same state as the current state.
* Returns a pointer to the old state information.
register long *new_state
= (long *)arg_state
;
register int type
= new_state
[0] % MAX_TYPES
;
register int rear
= new_state
[0] / MAX_TYPES
;
char *ostate
= (char *)(&state
[-1]);
state
[-1] = MAX_TYPES
* (rptr
- state
) + rand_type
;
rand_deg
= degrees
[type
];
"random: state info corrupted; not changed.\n");
if (rand_type
!= TYPE_0
) {
fptr
= &state
[(rear
+ rand_sep
) % rand_deg
];
end_ptr
= &state
[rand_deg
]; /* set end_ptr too */
* If we are using the trivial TYPE_0 R.N.G., just do the old linear
* congruential bit. Otherwise, we do our fancy trinomial stuff, which is
* the same in all the other cases due to all the global variables that have
* been set up. The basic operation is to add the number at the rear pointer
* into the one at the front pointer. Then both pointers are advanced to
* the next location cyclically in the table. The value returned is the sum
* generated, reduced to 31 bits by throwing away the "least random" low bit.
* Note: the code takes advantage of the fact that both the front and
* rear pointers can't wrap on the same call by not testing the rear
* pointer if the front one has wrapped.
* Returns a 31-bit random number.
i
= state
[0] = (state
[0] * 1103515245 + 12345) & 0x7fffffff;
i
= (*fptr
>> 1) & 0x7fffffff; /* chucking least random bit */
} else if (++rptr
>= end_ptr
)