support/random.c - master - niceSOFT/gawk

support/random.c
639 строк22 KB
Arnold D. Robbins
Update random.c to use prototypes.
15 окт 2020, 09:37
15 окт 2020, 09:3720fec8c
/*
 * 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.
 */

/*
 * Per the statement at http://opensource.org/licenses/bsd-license.php,
 *
 *	The advertising clause in the license appearing on BSD Unix files was
 *	officially rescinded by the Director of the Office of Technology
 *	Licensing of the University of California on July 22 1999. He states
 *	that clause 3 is "hereby deleted in its entirety."
 *
 * I removed the advertising clause in the above copyright.
 * The above web site points to
 * ftp://ftp.cs.berkeley.edu/pub/4bsd/README.Impt.License.Change.
 *
 * Arnold Robbins
 * 15 September 2007
 */

#if defined(LIBC_SCCS) && !defined(lint)
static const char sccsid[] = "@(#)random.c	8.2 (Berkeley) 5/19/95";
#endif /* LIBC_SCCS and not lint */

#ifdef HAVE_CONFIG_H		/* gawk addition */
#include <config.h>
#endif

#ifdef HAVE_FCNTL_H
#include <fcntl.h>
#endif
#include <stdio.h>
#include <stdlib.h>
#ifdef HAVE_UNISTD_H
#include <unistd.h>
#endif

#include <assert.h>

#include "random.h"		/* gawk addition */

#ifdef HAVE_SYS_TIME_H		/* gawk addition */
#include <sys/time.h>
#endif

#if 0
#include <sys/cdefs.h>
__FBSDID("$FreeBSD: /repoman/r/ncvs/src/lib/libc/stdlib/random.c,v 1.24 2004/01/20 03:02:18 das Exp $");

#include "namespace.h"
#include <sys/time.h>          /* for srandomdev() */
#include <fcntl.h>             /* for srandomdev() */
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>            /* for srandomdev() */
#include "un-namespace.h"
#endif

/*
 * 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 uint32_t's; 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 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 06 February 2016 by Nelson H. F. Beebe to interface to a
 * shuffle buffer, producing a huge period, and removing long-range
 * correlations of the basic low-level generator.  See comments and
 * literature references in random() at the end of this file.
 */

#define SHUFFLE_BITS	9			/* see comments in random() below for this choice */
#define SHUFFLE_MAX	(1 << SHUFFLE_BITS)	/* MUST be power of two */
#define SHUFFLE_MASK	(SHUFFLE_MAX - 1)	/* (k & SHUFFLE_MASK) is in [0, SHUFFLE_MAX - 1] */

static int  shuffle_init = 1;
static long shuffle_buffer[SHUFFLE_MAX];

/*
 * 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 */

#ifdef  USE_WEAK_SEEDING
#define NSHUFF 0
#else   /* !USE_WEAK_SEEDING */
#define NSHUFF 50       /* to drop some "seed -> 1st value" linearity */
#endif  /* !USE_WEAK_SEEDING */

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.
 */

static uint32_t randtbl[DEG_3 + 1] = {
	TYPE_3,
#ifdef  USE_WEAK_SEEDING
/* Historic implementation compatibility */
/* The random sequences do not vary much with the seed */
	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,
#else   /* !USE_WEAK_SEEDING */
	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
#endif  /* !USE_WEAK_SEEDING */
};

/*
 * 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 uint32_t *fptr = &randtbl[SEP_3 + 1];
static uint32_t *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 uint32_t *state = &randtbl[1];
static int rand_type = TYPE_3;
static int rand_deg = DEG_3;
static int rand_sep = SEP_3;
static uint32_t *end_ptr = &randtbl[DEG_3 + 1];

static inline uint32_t good_rand(int32_t);

static inline uint32_t good_rand (int32_t 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.
 */
	int32_t hi, lo;

	/* Can't be initialized with 0, so use another value. */
	if (x == 0)
		x = 123459876;
	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
srandom(unsigned long x)
{
	int i, lim;

	shuffle_init = 1;

	state[0] = (uint32_t)x;
	if (rand_type == TYPE_0)
		lim = NSHUFF;
	else {
		for (i = 1; i < rand_deg; i++)
			state[i] = good_rand(state[i - 1]);
		fptr = &state[rand_sep];
		rptr = &state[0];
		lim = 10 * rand_deg;
	}
	for (i = 0; i < lim; i++)
		(void)random();
}

#if 0 /* gawk doesn't use this */
/*
 * 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 random(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.
 */
void
srandomdev()
{
	int fd, done;
	size_t len;

	if (rand_type == TYPE_0)
		len = sizeof state[0];
	else
		len = rand_deg * sizeof state[0];

	done = 0;
	fd = open("/dev/random", O_RDONLY, 0);
	if (fd >= 0) {
		if (read(fd, (void *) state, len) == (ssize_t) len)
			done = 1;
		close(fd);
	}

	if (!done) {
		struct timeval tv;
		unsigned long junk;

		gettimeofday(&tv, NULL);
		srandom((getpid() << 16) ^ tv.tv_sec ^ tv.tv_usec ^ junk);
		return;
	}

	if (rand_type != TYPE_0) {
		fptr = &state[rand_sep];
		rptr = &state[0];
	}
}
#endif

/*
 * 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 long seed,		/* seed for R.N.G. */
	char *arg_state,		/* pointer to state array */
	long n)				/* # bytes of state info */
{
	char *ostate = (char *)(&state[-1]);
	uint32_t *int_arg_state = (uint32_t *)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 = int_arg_state + 1; /* first location */
	end_ptr = &state[rand_deg];	/* must set end_ptr before srandom */
	srandom(seed);
	if (rand_type == TYPE_0)
		int_arg_state[0] = rand_type;
	else
		int_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 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 *
setstate(char *arg_state)		/* pointer to state array */
{
	uint32_t *new_state = (uint32_t *)arg_state;
	uint32_t type = new_state[0] % MAX_TYPES;
	uint32_t 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);
}

/*
 * 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_old()
{
	uint32_t i;
	uint32_t *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((long)i);
}

long
random()
{
	/*
	 * This function is a wrapper to the original random(), now renamed
	 * random_old(), to interpose a shuffle buffer to dramatically extend
	 * the generator period at nearly zero additional execution cost,
	 * and an additional storage cost set by the size of the
	 * shuffle buffer (default: 512 longs, or 2K or 4K bytes).
	 * The algorithm was first described in
	 *
	 *     Carter Bays and S. D. Durham
	 *     Improving a Poor Random Number Generator
	 *     ACM Transactions on Mathematical Software (TOMS) 2(1) 59--64 (March 1976)
	 *     http://dx.doi.org/10.1145/355666.355670
	 * 
	 * and later revisited in
	 * 
	 *     Carter Bays
	 *     C364. Improving a random number generator: a comparison between two shuffling methods
	 *     Journal of Statistical Computation and Simulation 36(1) 57--59 (May 1990)
	 *     http://dx.doi.org/10.1080/00949659008811264
	 *
	 * The second paper is critically important because it
	 * emphasizes how an apparently trivial change to the final
	 * element selection can destroy the period-lengthening
	 * feature of the original shuffle algorithm.
	 * 
	 * Here is a table of the increase in period size for a
	 * shuffle generator using 32-bit and 64-bit unsigned integer
	 * linear congruential generators, which are known to have
	 * significant correlations, and are thus inadvisable for
	 * serious work with random numbers:
	 *
	 * hocd128> for (n = 32; n < 4096; n *= 2) \
	 *              printf("%7d\t%12.3.4e\t%12.3.4e\n",
	 *              n, \
	 *              sqrt(PI * gamma(n + 1)/(2**32 - 1)) / (2**32 - 1), \\
	 *              sqrt(PI * gamma(n + 1)/(2**64 - 1)) / (2**64 - 1))
	 * 
	 *      32    3.230e+03       1.148e-11
	 *      64    2.243e+30       7.969e+15
	 *     128    3.910e+93       1.389e+79
	 *     256   1.844e+239      6.552e+224
	 *     512   1.174e+569      4.172e+554
	 *    1024  4.635e+1305     1.647e+1291
	 *    2048  8.144e+2932     2.893e+2918
	 *
	 * A generator giving one result per nanosecond would produce
	 * about 3.16e16 random numbers per year, so even for
	 * massively parallel operations with, say, one million CPU
	 * cores, it could not produce more than 10**23 values per
	 * year.  The main benefit of an enormous period is that it
	 * makes long-range correlations vanishingly unlikely, even
	 * when starting seeds are similar (e.g., seeds of 0, 1, 2,
	 * ...), and therefore makes possible families of generators
	 * (needed in parallel computations) where the probability of
	 * sequence overlap between family members is essentially
	 * zero.
	 */

	int k;
	long r;
	static long s = 0xcafefeedL;

	if (shuffle_init) {	/* first time, or seed changed by srand() */
		for (k = 0; k < SHUFFLE_MAX; k++)
			shuffle_buffer[k] = random_old();

		s = random_old();
		shuffle_init = 0;
	}

	r = random_old();
	k = s & SHUFFLE_MASK;		/* random index into shuffle_buffer[] */

	assert(0L <= k && k < SHUFFLE_MAX);

	s = shuffle_buffer[k];
	shuffle_buffer[k] = r;

	return (s);
}