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authorRoland McGrath <roland@gnu.org>1995-02-18 01:27:10 +0000
committerRoland McGrath <roland@gnu.org>1995-02-18 01:27:10 +0000
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initial import
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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.
+ */
+
+/*
+ * This is derived from the Berkeley source:
+ * @(#)random.c 5.5 (Berkeley) 7/6/88
+ * It was reworked for the GNU C Library by Roland McGrath.
+ */
+
+#include <ansidecl.h>
+#include <errno.h>
+#include <limits.h>
+#include <stddef.h>
+#include <stdlib.h>
+
+
+/* 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() function 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 thi
+ 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
+ separation between the two lower order coefficients of the trinomial. */
+
+/* Linear congruential. */
+#define TYPE_0 0
+#define BREAK_0 8
+#define DEG_0 0
+#define SEP_0 0
+
+/* x**7 + x**3 + 1. */
+#define TYPE_1 1
+#define BREAK_1 32
+#define DEG_1 7
+#define SEP_1 3
+
+/* x**15 + x + 1. */
+#define TYPE_2 2
+#define BREAK_2 64
+#define DEG_2 15
+#define SEP_2 1
+
+/* x**31 + x**3 + 1. */
+#define TYPE_3 3
+#define BREAK_3 128
+#define DEG_3 31
+#define SEP_3 3
+
+/* x**63 + x + 1. */
+#define TYPE_4 4
+#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 int randtbl[DEG_3 + 1] =
+ {
+ TYPE_3,
+ -851904987, -43806228, -2029755270, 1390239686, -1912102820,
+ -485608943, 1969813258, -1590463333, -1944053249, 455935928, 508023712,
+ -1714531963, 1800685987, -2015299881, 654595283, -1149023258,
+ -1470005550, -1143256056, -1325577603, -1568001885, 1275120390,
+ -607508183, -205999574, -1696891592, 1492211999, -1528267240,
+ -952028296, -189082757, 362343714, 1424981831, 2039449641,
+ };
+
+/* 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 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 int *fptr = &randtbl[SEP_3 + 1];
+static long int *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 int *state = &randtbl[1];
+
+static int rand_type = TYPE_3;
+static int rand_deg = DEG_3;
+static int rand_sep = SEP_3;
+
+static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])];
+
+/* 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
+DEFUN(__srandom, (x), unsigned int x)
+{
+ state[0] = x;
+ if (rand_type != TYPE_0)
+ {
+ register long int i;
+ for (i = 1; i < rand_deg; ++i)
+ state[i] = (1103515145 * state[i - 1]) + 12345;
+ fptr = &state[rand_sep];
+ rptr = &state[0];
+ for (i = 0; i < 10 * rand_deg; ++i)
+ (void) __random();
+ }
+}
+
+weak_alias (__srandom, srandom)
+weak_alias (__srandom, srand)
+
+/* 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. */
+PTR
+DEFUN(__initstate, (seed, arg_state, n),
+ unsigned int seed AND PTR arg_state AND size_t n)
+{
+ PTR ostate = (PTR) &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)
+ {
+ errno = EINVAL;
+ return NULL;
+ }
+ 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 int *) arg_state)[1]; /* First location. */
+ /* Must set END_PTR before srandom. */
+ end_ptr = &state[rand_deg];
+ __srandom(seed);
+ if (rand_type == TYPE_0)
+ state[-1] = rand_type;
+ else
+ state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
+
+ return ostate;
+}
+
+weak_alias (__initstate, initstate)
+
+/* 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. */
+PTR
+DEFUN(__setstate, (arg_state), PTR arg_state)
+{
+ register long int *new_state = (long int *) arg_state;
+ register int type = new_state[0] % MAX_TYPES;
+ register int rear = new_state[0] / MAX_TYPES;
+ PTR ostate = (PTR) &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:
+ /* State info munged. */
+ errno = EINVAL;
+ return NULL;
+ }
+
+ state = &new_state[1];
+ if (rand_type != TYPE_0)
+ {
+ rptr = &state[rear];
+ fptr = &state[(rear + rand_sep) % rand_deg];
+ }
+ /* Set end_ptr too. */
+ end_ptr = &state[rand_deg];
+
+ return ostate;
+}
+
+weak_alias (__setstate, setstate)
+
+/* 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 int
+DEFUN_VOID(__random)
+{
+ if (rand_type == TYPE_0)
+ {
+ state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX;
+ return state[0];
+ }
+ else
+ {
+ long int i;
+ *fptr += *rptr;
+ /* Chucking least random bit. */
+ i = (*fptr >> 1) & LONG_MAX;
+ ++fptr;
+ if (fptr >= end_ptr)
+ {
+ fptr = state;
+ ++rptr;
+ }
+ else
+ {
+ ++rptr;
+ if (rptr >= end_ptr)
+ rptr = state;
+ }
+ return i;
+ }
+}
+
+weak_alias (__random, random)