xref: /netbsd-src/common/lib/libc/stdlib/random.c (revision f16aa4743c0ce42bb2139b97e4aa7dde46b58422)

/*	$NetBSD: random.c,v 1.4 2014/06/12 20:59:46 christos Exp $	*/

/*
 * 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. 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.
 */

#if !defined(_KERNEL) && !defined(_STANDALONE)
#include <sys/cdefs.h>
#if defined(LIBC_SCCS) && !defined(lint)
#if 0
static char sccsid[] = "@(#)random.c	8.2 (Berkeley) 5/19/95";
#else
__RCSID("$NetBSD: random.c,v 1.4 2014/06/12 20:59:46 christos Exp $");
#endif
#endif /* LIBC_SCCS and not lint */

#include "namespace.h"

#include <assert.h>
#include <errno.h>
#include <stdlib.h>
#include "reentrant.h"

#ifdef __weak_alias
__weak_alias(initstate,_initstate)
__weak_alias(random,_random)
__weak_alias(setstate,_setstate)
__weak_alias(srandom,_srandom)
#endif


#ifdef _REENTRANT
static mutex_t random_mutex = MUTEX_INITIALIZER;
#endif
#else
#include <lib/libkern/libkern.h>
#define mutex_lock(a)	(void)0
#define mutex_unlock(a) (void)0
#endif

#ifndef SMALL_RANDOM
static void srandom_unlocked(unsigned int);
static long random_unlocked(void);

#define USE_BETTER_RANDOM

/*
 * 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 ints; 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 ints 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.
 *
 * Modified 07 January 2002 by Jason R. Thorpe.
 * The following changes have been made:
 * All the references to "long" have been changed back to "int".  This
 * fixes memory corruption problems on LP64 platforms.
 */

/*
 * 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 const int degrees[MAX_TYPES] =	{ DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
static const 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.
 */

/* LINTED */
static int randtbl[DEG_3 + 1] = {
	TYPE_3,
#ifdef USE_BETTER_RANDOM
	0x991539b1, 0x16a5bce3, 0x6774a4cd,
	0x3e01511e, 0x4e508aaa, 0x61048c05,
	0xf5500617, 0x846b7115, 0x6a19892c,
	0x896a97af, 0xdb48f936, 0x14898454,
	0x37ffd106, 0xb58bff9c, 0x59e17104,
	0xcf918a49, 0x09378c83, 0x52c7a471,
	0x8d293ea9, 0x1f4fc301, 0xc3db71be,
	0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
	0x19edc328, 0x87bf4bdd, 0xc9b240e5,
	0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
	0xf3bec5da,
#else
	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,
#endif /* USE_BETTER_RANDOM */
};

/*
 * 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 int *fptr = &randtbl[SEP_3 + 1];
static int *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 int *state = &randtbl[1];
static int rand_type = TYPE_3;
static int rand_deg = DEG_3;
static int rand_sep = SEP_3;
static int *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.
 */
static void
srandom_unlocked(unsigned int x)
{
	int i;

	if (rand_type == TYPE_0)
		state[0] = x;
	else {
		state[0] = x;
		for (i = 1; i < rand_deg; i++) {
#ifdef USE_BETTER_RANDOM
			int x1, hi, lo, t;

			/*
			 * Compute x[n + 1] = (7^5 * x[n]) mod (2^31 - 1).
			 * 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.
			 */
			x1 = state[i - 1];
			hi = x1 / 127773;
			lo = x1 % 127773;
			t = 16807 * lo - 2836 * hi;
			if (t <= 0)
				t += 0x7fffffff;
			state[i] = t;
#else
			state[i] = 1103515245 * state[i - 1] + 12345;
#endif /* USE_BETTER_RANDOM */
		}
		fptr = &state[rand_sep];
		rptr = &state[0];
		for (i = 0; i < 10 * rand_deg; i++)
			(void)random_unlocked();
	}
}

void
srandom(unsigned int x)
{

	mutex_lock(&random_mutex);
	srandom_unlocked(x);
	mutex_unlock(&random_mutex);
}

/*
 * 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 an int
 * word boundary; otherwise a bus error will occur. Even so, lint will
 * complain about mis-alignment, but you should disregard these messages.
 */
char *
initstate(
	unsigned int seed,		/* seed for R.N.G. */
	char *arg_state,		/* pointer to state array */
	size_t n)			/* # bytes of state info */
{
	void *ostate = (void *)(&state[-1]);
	int *int_arg_state;

	_DIAGASSERT(arg_state != NULL);

	int_arg_state = (int *)(void *)arg_state;

	mutex_lock(&random_mutex);
	if (rand_type == TYPE_0)
		state[-1] = rand_type;
	else
		state[-1] = MAX_TYPES * (int)(rptr - state) + rand_type;
	if (n < BREAK_0) {
		mutex_unlock(&random_mutex);
		return (NULL);
	} else 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 = (int *) (int_arg_state + 1); /* first location */
	end_ptr = &state[rand_deg];	/* must set end_ptr before srandom */
	srandom_unlocked(seed);
	if (rand_type == TYPE_0)
		int_arg_state[0] = rand_type;
	else
		int_arg_state[0] = MAX_TYPES * (int)(rptr - state) + rand_type;
	mutex_unlock(&random_mutex);
	return((char *)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(char *arg_state)		/* pointer to state array */
{
	int *new_state;
	int type;
	int rear;
	void *ostate = (void *)(&state[-1]);

	_DIAGASSERT(arg_state != NULL);

	new_state = (int *)(void *)arg_state;
	type = (int)(new_state[0] % MAX_TYPES);
	rear = (int)(new_state[0] / MAX_TYPES);

	mutex_lock(&random_mutex);
	if (rand_type == TYPE_0)
		state[-1] = rand_type;
	else
		state[-1] = MAX_TYPES * (int)(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:
		mutex_unlock(&random_mutex);
		return (NULL);
	}
	state = (int *) (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 */
	mutex_unlock(&random_mutex);
	return((char *)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.
 */
static long
random_unlocked(void)
{
	int i;
	int *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;
		/* chucking least random bit */
		i = ((unsigned int)*f >> 1) & 0x7fffffff;
		if (++f >= end_ptr) {
			f = state;
			++r;
		}
		else if (++r >= end_ptr) {
			r = state;
		}

		fptr = f; rptr = r;
	}
	return(i);
}

long
random(void)
{
	long r;

	mutex_lock(&random_mutex);
	r = random_unlocked();
	mutex_unlock(&random_mutex);
	return (r);
}
#else
long
random(void)
{
	static u_long randseed = 1;
	long x, hi, lo, t;

	/*
	 * Compute x[n + 1] = (7^5 * x[n]) mod (2^31 - 1).
	 * 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.
	 */
	x = randseed;
	hi = x / 127773;
	lo = x % 127773;
	t = 16807 * lo - 2836 * hi;
	if (t <= 0)
		t += 0x7fffffff;
	randseed = t;
	return (t);
}
#endif /* SMALL_RANDOM */