random.cpp

Bubble Oscillation Algorithm. It is used to implement balancing load traffic, which is similar to wh

/*
 * 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.
 */

#ifdef COMPAT_WEAK_SEEDING
#define USE_WEAK_SEEDING
#define random orandom
#define srandom osrandom
#define initstate oinitstate
#define setstate osetstate
#endif

#include "random.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.
 *
 * 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	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,
#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 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];

static long good_rand (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.