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/* Copyright (C) 1995 DJ Delorie, see COPYING.DJ for details */

/* This is file RANDOM.C */

/* This file may have been modified by DJ Delorie (Jan 1995).  If so,

** these modifications are Coyright (C) 1993 DJ Delorie, 24 Kirsten Ave,

** Rochester NH, 03867-2954, USA.

*/

/*

 * Copyright (c) 1983 Regents of the University of California.

 * All rights reserved.

 *

 * Redistribution and use in source and binary forms are permitted

 * provided that: (1) source distributions retain this entire copyright

 * notice and comment, and (2) distributions including binaries display

 * the following acknowledgement:  ``This product includes software

 * developed by the University of California, Berkeley and its contributors''

 * in the documentation or other materials provided with the distribution

 * and in all advertising materials mentioning features or use of this

 * software. 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 ``AS IS'' AND WITHOUT ANY EXPRESS OR

 * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED

 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.

 */

#include 

/*

 * 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 unsigned long randtbl[DEG_3 + 1] = { TYPE_3,

			    0x9a319039U, 0x32d9c024U, 0x9b663182U, 0x5da1f342U,

			    0xde3b81e0U, 0xdf0a6fb5U, 0xf103bc02U, 0x48f340fbU,

			    0x7449e56bU, 0xbeb1dbb0U, 0xab5c5918U, 0x946554fdU,

			    0x8c2e680fU, 0xeb3d799fU, 0xb11ee0b7U, 0x2d436b86U,

			    0xda672e2aU, 0x1588ca88U, 0xe369735dU, 0x904f35f7U,

			    0xd7158fd6U, 0x6fa6f051U, 0x616e6b96U, 0xac94efdcU,

			    0x36413f93U, 0xc622c298U, 0xf5a42ab8U, 0x8a88d77bU,

					 0xf5ad9d0eU, 0x8999220bU, 0x27fb47b9U };

/*

 * 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.

 */

int

srandom(int x)

{

  int i, j;

  if (rand_type == TYPE_0)

  {

    state[ 0 ] = x;

  }

  else

  {

    j = 1;

    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();

  }

  return 0;

}

/*

 * 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 (unsigned seed, char *arg_state, int n)

{

  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)

      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(char *arg_state)

{

  long *new_state = (long *)arg_state;

  int type = new_state[0]%MAX_TYPES;

  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;

  }

  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(void)

{

  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;

}