/*
* Copyright (c) 1983, 1993
* The Regents of the University of California. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* This product includes software developed by the University of
* California, Berkeley and its contributors.
* 4. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* $FreeBSD: src/lib/libc/stdlib/random.c,v 1.4.2.2 1999/09/05 11:16:45 peter Exp $
*
*/
#if defined(LIBC_SCCS) && !defined(lint)
static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95";
#endif /* LIBC_SCCS and not lint */
/*
* random.c:
*
* 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.
*
* Modified 28 December 1994 by Jacob S. Rosenberg.
* The following changes have been made:
* All references to the type u_int have been changed to unsigned long.
* All references to type int have been changed to type long. Other
* cleanups have been made as well. A warning for both initstate and
* setstate has been inserted to the effect that on Sparc platforms
* the 'arg_state' variable must be forced to begin on word boundaries.
* This can be easily done by casting a long integer array to char *.
* The overall logic has been left STRICTLY alone. This software was
* tested on both a VAX and Sun SpacsStation with exactly the same
* results. The new version and the original give IDENTICAL results.
* The new version is somewhat faster than the original. As the
* documentation says: "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." For a buffer of
* 128 bytes, this new version runs about 19 percent faster and for a 16
* byte buffer it is about 5 percent faster.
*/
/*
* 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 BREAK_0 8
#define DEG_0 0
#define SEP_0 0
#define MAX_TYPES 5 /* max number of types above */
/*
* 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.
*/
/*
* 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
* from the call
*
* 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 unsigned long *fptr = &randtbl[SEP_3 + 1];
static unsigned 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 unsigned long *state = &randtbl[1];
static long rand_type = TYPE_3;
static long rand_deg = DEG_3;
static long rand_sep = SEP_3;
static unsigned long *end_ptr = &randtbl[DEG_3 + 1];
static inline long good_rand (long);
static inline long
good_rand (
register long x
)
{
#ifdef USE_WEAK_SEEDING
/*
* Historic implementation compatibility.
* The random sequences do not vary much with the seed,
* even with overflowing.
*/
return (1103515245 * x + 12345);
#else /* !USE_WEAK_SEEDING */
/*
* Compute x = (7^5 * x) mod (2^31 - 1)
* wihout overflowing 31 bits:
* (2^31 - 1) = 127773 * (7^5) + 2836
* From "Random number generators: good ones are hard to find",
* Park and Miller, Communications of the ACM, vol. 31, no. 10,
* October 1988, p. 1195.
*/
register long hi, lo;
hi = x / 127773;
lo = x % 127773;
x = 16807 * lo - 2836 * hi;
if (x <= 0)
x += 0x7fffffff;
return (x);
#endif /* !USE_WEAK_SEEDING */
}
/*
* srandom:
*
* 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.
*/
void
ntp_srandom(
unsigned long x
)
{
long i;
if (rand_type == TYPE_0) {
state[0] = x;
} else {
state[0] = x;
for (i = 1; i < rand_deg; i++)
state[i] = good_rand(state[i - 1]);
fptr = &state[rand_sep];
rptr = &state[0];
for (i = 0; i < 10 * rand_deg; i++)
x = ntp_random();
}
/* seed the likely faster (and poorer) rand() as well */
srand((u_int)x);
}
/*
* srandomdev:
*
* Many programs choose the seed value in a totally predictable manner.
* This often causes problems. We seed the generator using the much more
* secure urandom(4) interface. Note that this particular seeding
* procedure can generate states which are impossible to reproduce by
* calling srandom() with any value, since the succeeding terms in the
* state buffer are no longer derived from the LC algorithm applied to
* a fixed seed.
*/
#ifdef NEED_SRANDOMDEV
void
ntp_srandomdev( void )
{
struct timeval tv;
unsigned long junk; /* Purposely used uninitialized */
/*
* ntp_initstate() and ntp_setstate() are unused in our codebase and
* trigger warnings due to casting to a more-strictly-aligned pointer
* on alignment-sensitive platforms. #ifdef them away to save noise,
* build time, and binary space, but retain the code in case we find a
* use.
*/
#ifdef COMPILE_UNUSED_FUNCTIONS
/*
* 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 */
/*
* initstate:
*
* 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.
*
* Note: The Sparc platform requires that arg_state begin on a long
* word boundary; otherwise a bus error will occur. Even so, lint will
* complain about mis-alignment, but you should disregard these messages.
*/
char *
ntp_initstate(
unsigned long seed, /* seed for R.N.G. */
char *arg_state, /* pointer to state array */
long n /* # bytes of state info */
)
{
register char *ostate = (char *)(&state[-1]);
register long *long_arg_state = (long *) arg_state;
if (rand_type == TYPE_0)
state[-1] = rand_type;
else
state[-1] = MAX_TYPES * (rptr - state) + rand_type;
if (n < BREAK_0) {
(void)fprintf(stderr,
"random: not enough state (%ld bytes); ignored.\n", n);
return(0);
}
if (n < BREAK_1) {
rand_type = TYPE_0;
rand_deg = DEG_0;
rand_sep = SEP_0;
} else if (n < BREAK_2) {
rand_type = TYPE_1;
rand_deg = DEG_1;
rand_sep = SEP_1;
} else if (n < BREAK_3) {
rand_type = TYPE_2;
rand_deg = DEG_2;
rand_sep = SEP_2;
} else if (n < BREAK_4) {
rand_type = TYPE_3;
rand_deg = DEG_3;
rand_sep = SEP_3;
} else {
rand_type = TYPE_4;
rand_deg = DEG_4;
rand_sep = SEP_4;
}
state = (unsigned long *) (long_arg_state + 1); /* first location */
end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
ntp_srandom(seed);
if (rand_type == TYPE_0)
long_arg_state[0] = rand_type;
else
long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
return(ostate);
}
/*
* setstate:
*
* 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.
*
* Note: The Sparc platform requires that arg_state begin on a long
* word boundary; otherwise a bus error will occur. Even so, lint will
* complain about mis-alignment, but you should disregard these messages.
*/
char *
ntp_setstate(
char *arg_state /* pointer to state array */
)
{
register unsigned long *new_state = (unsigned long *) arg_state;
register long type = new_state[0] % MAX_TYPES;
register long rear = new_state[0] / MAX_TYPES;
char *ostate = (char *)(&state[-1]);
if (rand_type == TYPE_0)
state[-1] = rand_type;
else
state[-1] = MAX_TYPES * (rptr - state) + rand_type;
switch(type) {
case TYPE_0:
case TYPE_1:
case TYPE_2:
case TYPE_3:
case TYPE_4:
rand_type = type;
rand_deg = degrees[type];
rand_sep = seps[type];
break;
default:
(void)fprintf(stderr,
"random: state info corrupted; not changed.\n");
}
state = (new_state + 1);
if (rand_type != TYPE_0) {
rptr = &state[rear];
fptr = &state[(rear + rand_sep) % rand_deg];
}
end_ptr = &state[rand_deg]; /* set end_ptr too */
return(ostate);
}
#endif /* COMPILE_UNUSED_FUNCTIONS */
/*
* random:
*
* 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.
*/
long
ntp_random( void )
{
register long i;
register unsigned long *f, *r;
if (rand_type == TYPE_0) {
i = state[0];
state[0] = i = (good_rand(i)) & 0x7fffffff;
} else {
/*
* Use local variables rather than static variables for speed.
*/
f = fptr; r = rptr;
*f += *r;
i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */
if (++f >= end_ptr) {
f = state;
++r;
}
else if (++r >= end_ptr) {
r = state;
}
fptr = f; rptr = r;
}
return(i);
}
/*
* ntp_uurandom()
*
* Generate a Uniform-distributed Unity based random number. Replaces a
* few locations where the transformation was made in an ad-hoc style
* (and in one instance, wrong...)
*
* returns a number in [0.0 .. 1.0], both ends inclusive
*/
double
ntp_uurandom( void )
{
return (double)ntp_random() / 0x7FFFFFFFu;
}
