text: /*
   * 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.
   * 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.
   */
  
  #if defined(LIBC_SCCS) && !defined(lint)
  static char sccsid[] = "@(#)random.c	8.2 (Berkeley) 5/19/95";
  #endif /* LIBC_SCCS and not lint */
  #include <sys/cdefs.h>
  __FBSDID("$FreeBSD$");
  
  /* #include "namespace.h" */
  /* #include <sys/time.h>          /\* for srandomdev() *\/ */
  /* #include <fcntl.h>             /\* for srandomdev() *\/ */
  #include <stdint.h>
  #include <stdio.h>
  #include <stdlib.h>
  #include "posixcompat.h"
  /* #include <unistd.h>            /\* for srandomdev() *\/ */
  /* #include "un-namespace.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 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.
   */
  
  /*
   * 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 int x)
  {
  	int i, lim;
  
  	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
  /*
   * 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(void)
  {
  	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 int seed, char *arg_state, size_t n)
  	/* 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)
  	/* 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.
   */
  long random(void)
  {
  	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);
  }
  