+/* Copyright (c) 1982 Regents of the University of California */
+
+static char sccsid[] = "@(#)random.c 4.1 (Berkeley) 82/11/22";
+
+#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.
+ */
+
+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 );
+}
+
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