[apple/libc.git] / stdlib / random.c

/*
 * Copyright (c) 1999 Apple Computer, Inc. All rights reserved.
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 * Copyright (c) 1999-2003 Apple Computer, Inc.  All Rights Reserved.
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/*
 * Copyright (c) 1983, 1993
 *      The Regents of the University of California.  All rights reserved.
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 * modification, are permitted provided that the following conditions
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 *      This product includes software developed by the University of
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#include <stdio.h>
#include <stdlib.h>

/*
 * 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.
 */

/*
 * 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 TYPE_1          1               /* x**7 + x**3 + 1 */
#define BREAK_1         32
#define DEG_1           7
#define SEP_1           3

#define TYPE_2          2               /* x**15 + x + 1 */
#define BREAK_2         64
#define DEG_2           15
#define SEP_2           1

#define TYPE_3          3               /* x**31 + x**3 + 1 */
#define BREAK_3         128
#define DEG_3           31
#define SEP_3           3

#define TYPE_4          4               /* x**63 + x + 1 */
#define BREAK_4         256
#define DEG_4           63
#define SEP_4           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 long degrees[MAX_TYPES] =        { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
static long 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] = {
        TYPE_3,
        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,
        0x27fb47b9,
};

/*
 * 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 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 long rand_type = TYPE_3;
static long rand_deg = DEG_3;
static long rand_sep = SEP_3;
static long *end_ptr = &randtbl[DEG_3 + 1];

/*
 * 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
srandom(x)
        unsigned long x;
{
        register long i;

        if (rand_type == TYPE_0)
                state[0] = x;
        else {
                state[0] = x;
                for (i = 1; i < rand_deg; i++)
                        state[i] = 1103515245 * state[i - 1] + 12345;
                fptr = &state[rand_sep];
                rptr = &state[0];
                for (i = 0; i < 10 * rand_deg; i++)
                        (void)random();
        }
}

/*
 * 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 *
initstate(seed, arg_state, n)
        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 = (long *) (long_arg_state + 1); /* first location */
        end_ptr = &state[rand_deg];     /* must set end_ptr before srandom */
        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 *
setstate(arg_state)
        char *arg_state;                /* pointer to state array */
{
        register long *new_state = (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 = (long *) (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);
}

/*
 * 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
random()
{
        register long i;
        register long *f, *r;

        if (rand_type == TYPE_0) {
                i = state[0];
                state[0] = i = (i * 1103515245 + 12345) & 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);
}