#ifndef lintstatic char sccsid[] = "@(#)random.c	4.3	(Berkeley)	84/04/16";#endif#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, 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();	}}/* * 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" );		return;	    }	    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. */longrandom(){	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 );}