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+/*
+ * Copyright (c) 1999 Apple Computer, Inc. All rights reserved.
+ *
+ * @APPLE_LICENSE_HEADER_START@
+ *
+ * Copyright (c) 1999-2003 Apple Computer, Inc. All Rights Reserved.
+ *
+ * This file contains Original Code and/or Modifications of Original Code
+ * as defined in and that are subject to the Apple Public Source License
+ * Version 2.0 (the 'License'). You may not use this file except in
+ * compliance with the License. Please obtain a copy of the License at
+ * http://www.opensource.apple.com/apsl/ and read it before using this
+ * file.
+ *
+ * The Original Code and all software distributed under the License are
+ * distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER
+ * EXPRESS OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES,
+ * INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT.
+ * Please see the License for the specific language governing rights and
+ * limitations under the License.
+ *
+ * @APPLE_LICENSE_HEADER_END@
+ */
+/*
+ * 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.
+ * 3. All advertising materials mentioning features or use of this software
+ * must display the following acknowledgement:
+ * This product includes software developed by the University of
+ * California, Berkeley and its contributors.
+ * 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.
+ */
+
+
+#include <stdio.h>
+#include <stdlib.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 long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
+static long 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 long rand_type = TYPE_3;
+static long rand_deg = DEG_3;
+static long 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.
+ */
+void
+srandom(x)
+ unsigned long x;
+{
+ register long i;
+
+ 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++)
+ (void)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.
+ *
+ * Note: The Sparc platform requires that arg_state begin on a long
+ * word boundary; otherwise a bus error will occur. Even so, lint will
+ * complain about mis-alignment, but you should disregard these messages.
+ */
+char *
+initstate(seed, arg_state, n)
+ unsigned long seed; /* seed for R.N.G. */
+ char *arg_state; /* pointer to state array */
+ long n; /* # bytes of state info */
+{
+ register char *ostate = (char *)(&state[-1]);
+ register long *long_arg_state = (long *) 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 = (long *) (long_arg_state + 1); /* first location */
+ end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
+ srandom(seed);
+ if (rand_type == TYPE_0)
+ long_arg_state[0] = rand_type;
+ else
+ long_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 a long
+ * word boundary; otherwise a bus error will occur. Even so, lint will
+ * complain about mis-alignment, but you should disregard these messages.
+ */
+char *
+setstate(arg_state)
+ char *arg_state; /* pointer to state array */
+{
+ register long *new_state = (long *) arg_state;
+ register long type = new_state[0] % MAX_TYPES;
+ register long 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 = (long *) (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()
+{
+ register long i;
+ register long *f, *r;
+
+ if (rand_type == TYPE_0) {
+ i = state[0];
+ state[0] = i = (i * 1103515245 + 12345) & 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(i);
+}