File: random.c

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/*
 * Copyright (c) 1983 Regents of the University of California.
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms are permitted
 * provided that the above copyright notice and this paragraph are
 * duplicated in all such forms and that any documentation,
 * advertising materials, and other materials related to such
 * distribution and use acknowledge that the software was developed
 * by the University of California, Berkeley.  The name of the
 * University may not be used to endorse or promote products derived
 * from this software without specific prior written permission.
 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
 * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 */

#if defined(LIBC_SCCS) && !defined(lint)
static char sccsid[] = "@(#)random.c	5.5 (Berkeley) 7/6/88";
#endif /* LIBC_SCCS and not lint */

#include <stdio.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 int degrees[MAX_TYPES] =
{DEG_0, DEG_1, DEG_2,
 DEG_3, DEG_4};

static 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 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 int rand_type = TYPE_3;
static int rand_deg = DEG_3;
static int 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.
 */

srandom (x)

     unsigned x;
{
  register int i;
  long random ();

  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++)
	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.
 */

char *
initstate (seed, arg_state, n)

     unsigned seed;		/* seed for R. N. G. */
     char *arg_state;		/* pointer to state array */
     int n;			/* # bytes of state info */
{
  register char *ostate = (char *) (&state[-1]);

  if (rand_type == TYPE_0)
    state[-1] = rand_type;
  else
    state[-1] = MAX_TYPES * (rptr - state) + rand_type;
  if (n < BREAK_1)
    {
      if (n < BREAK_0)
	{
	  fprintf (stderr, "initstate: not enough state (%d bytes) with which to do jack; ignored.\n", n);
	  return 0;
	}
      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 *) arg_state)[1]);	/* first location */
  end_ptr = &state[rand_deg];	/* must set end_ptr before srandom */
  srandom (seed);
  if (rand_type == TYPE_0)
    state[-1] = rand_type;
  else
    state[-1] = 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.
 */

char *
setstate (arg_state)

     char *arg_state;
{
  register long *new_state = (long *) arg_state;
  register int type = new_state[0] % MAX_TYPES;
  register int 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:
      fprintf (stderr, "setstate: state info has been munged; 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 ther 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 ()
{
  long i;

  if (rand_type == TYPE_0)
    {
      i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff;
    }
  else
    {
      *fptr += *rptr;
      i = (*fptr >> 1) & 0x7fffffff;	/* chucking least random bit */
      if (++fptr >= end_ptr)
	{
	  fptr = state;
	  ++rptr;
	}
      else
	{
	  if (++rptr >= end_ptr)
	    rptr = state;
	}
    }
  return (i);
}