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* Copyright (c) 1983, 1993
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* The Regents of the University of California. All rights reserved.
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* $FreeBSD: src/lib/libc/stdlib/random.c,v 1.4.2.2 1999/09/05 11:16:45 peter Exp $
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#if defined(LIBC_SCCS) && !defined(lint)
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static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95";
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#endif /* LIBC_SCCS and not lint */
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#ifdef HAVE_SYS_TYPES_H
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# include <sys/types.h>
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#include <ntp_types.h>
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* An improved random number generation package. In addition to the standard
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* rand()/srand() like interface, this package also has a special state info
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* interface. The initstate() routine is called with a seed, an array of
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* bytes, and a count of how many bytes are being passed in; this array is
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* then initialized to contain information for random number generation with
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* that much state information. Good sizes for the amount of state
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* information are 32, 64, 128, and 256 bytes. The state can be switched by
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* calling the setstate() routine with the same array as was initiallized
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* with initstate(). By default, the package runs with 128 bytes of state
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* information and generates far better random numbers than a linear
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* congruential generator. If the amount of state information is less than
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* 32 bytes, a simple linear congruential R.N.G. is used.
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* Internally, the state information is treated as an array of longs; the
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* zeroeth element of the array is the type of R.N.G. being used (small
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* integer); the remainder of the array is the state information for the
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* R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
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* state information, which will allow a degree seven polynomial. (Note:
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* the zeroeth word of state information also has some other information
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* stored in it -- see setstate() for details).
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* The random number generation technique is a linear feedback shift register
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* approach, employing trinomials (since there are fewer terms to sum up that
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* way). In this approach, the least significant bit of all the numbers in
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* the state table will act as a linear feedback shift register, and will
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* have period 2^deg - 1 (where deg is the degree of the polynomial being
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* used, assuming that the polynomial is irreducible and primitive). The
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* higher order bits will have longer periods, since their values are also
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* influenced by pseudo-random carries out of the lower bits. The total
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* period of the generator is approximately deg*(2**deg - 1); thus doubling
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* the amount of state information has a vast influence on the period of the
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* generator. Note: the deg*(2**deg - 1) is an approximation only good for
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* large deg, when the period of the shift register is the dominant factor.
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* With deg equal to seven, the period is actually much longer than the
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* 7*(2**7 - 1) predicted by this formula.
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* Modified 28 December 1994 by Jacob S. Rosenberg.
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* The following changes have been made:
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* All references to the type u_int have been changed to unsigned long.
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* All references to type int have been changed to type long. Other
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* cleanups have been made as well. A warning for both initstate and
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* setstate has been inserted to the effect that on Sparc platforms
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* the 'arg_state' variable must be forced to begin on word boundaries.
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* This can be easily done by casting a long integer array to char *.
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* The overall logic has been left STRICTLY alone. This software was
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* tested on both a VAX and Sun SpacsStation with exactly the same
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* results. The new version and the original give IDENTICAL results.
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* The new version is somewhat faster than the original. As the
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* documentation says: "By default, the package runs with 128 bytes of
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* state information and generates far better random numbers than a linear
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* congruential generator. If the amount of state information is less than
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* 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of
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* 128 bytes, this new version runs about 19 percent faster and for a 16
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* byte buffer it is about 5 percent faster.
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* For each of the currently supported random number generators, we have a
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* break value on the amount of state information (you need at least this
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* many bytes of state info to support this random number generator), a degree
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* for the polynomial (actually a trinomial) that the R.N.G. is based on, and
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* the separation between the two lower order coefficients of the trinomial.
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#define TYPE_0 0 /* linear congruential */
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#define TYPE_1 1 /* x**7 + x**3 + 1 */
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#define TYPE_2 2 /* x**15 + x + 1 */
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#define TYPE_3 3 /* x**31 + x**3 + 1 */
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#define TYPE_4 4 /* x**63 + x + 1 */
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* Array versions of the above information to make code run faster --
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* relies on fact that TYPE_i == i.
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#define MAX_TYPES 5 /* max number of types above */
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static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
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static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
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* Initially, everything is set up as if from:
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* initstate(1, randtbl, 128);
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* Note that this initialization takes advantage of the fact that srandom()
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* advances the front and rear pointers 10*rand_deg times, and hence the
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* rear pointer which starts at 0 will also end up at zero; thus the zeroeth
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* element of the state information, which contains info about the current
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* position of the rear pointer is just
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* MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
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static long randtbl[DEG_3 + 1] = {
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#ifdef USE_WEAK_SEEDING
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/* Historic implementation compatibility */
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/* The random sequences do not vary much with the seed */
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0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
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0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
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0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
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0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
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0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
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#else /* !USE_WEAK_SEEDING */
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0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
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0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
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0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
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0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
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0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
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#endif /* !USE_WEAK_SEEDING */
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* fptr and rptr are two pointers into the state info, a front and a rear
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* pointer. These two pointers are always rand_sep places aparts, as they
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* cycle cyclically through the state information. (Yes, this does mean we
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* could get away with just one pointer, but the code for random() is more
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* efficient this way). The pointers are left positioned as they would be
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* initstate(1, randtbl, 128);
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* (The position of the rear pointer, rptr, is really 0 (as explained above
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* in the initialization of randtbl) because the state table pointer is set
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* to point to randtbl[1] (as explained below).
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static long *fptr = &randtbl[SEP_3 + 1];
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static long *rptr = &randtbl[1];
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* The following things are the pointer to the state information table, the
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* type of the current generator, the degree of the current polynomial being
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* used, and the separation between the two pointers. Note that for efficiency
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* of random(), we remember the first location of the state information, not
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* the zeroeth. Hence it is valid to access state[-1], which is used to
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* store the type of the R.N.G. Also, we remember the last location, since
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* this is more efficient than indexing every time to find the address of
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* the last element to see if the front and rear pointers have wrapped.
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static long *state = &randtbl[1];
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static long rand_type = TYPE_3;
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static long rand_deg = DEG_3;
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static long rand_sep = SEP_3;
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static long *end_ptr = &randtbl[DEG_3 + 1];
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static inline long good_rand P((long));
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long random P((void));
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#ifdef USE_WEAK_SEEDING
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* Historic implementation compatibility.
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* The random sequences do not vary much with the seed,
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* even with overflowing.
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return (1103515245 * x + 12345);
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#else /* !USE_WEAK_SEEDING */
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* Compute x = (7^5 * x) mod (2^31 - 1)
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* wihout overflowing 31 bits:
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* (2^31 - 1) = 127773 * (7^5) + 2836
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* From "Random number generators: good ones are hard to find",
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* Park and Miller, Communications of the ACM, vol. 31, no. 10,
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* October 1988, p. 1195.
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register long hi, lo;
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x = 16807 * lo - 2836 * hi;
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#endif /* !USE_WEAK_SEEDING */
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* Initialize the random number generator based on the given seed. If the
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* type is the trivial no-state-information type, just remember the seed.
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* Otherwise, initializes state[] based on the given "seed" via a linear
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* congruential generator. Then, the pointers are set to known locations
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* that are exactly rand_sep places apart. Lastly, it cycles the state
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* information a given number of times to get rid of any initial dependencies
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* introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
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* for default usage relies on values produced by this routine.
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if (rand_type == TYPE_0)
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for (i = 1; i < rand_deg; i++)
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state[i] = good_rand(state[i - 1]);
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fptr = &state[rand_sep];
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for (i = 0; i < 10 * rand_deg; i++)
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* Many programs choose the seed value in a totally predictable manner.
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* This often causes problems. We seed the generator using the much more
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* secure urandom(4) interface. Note that this particular seeding
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* procedure can generate states which are impossible to reproduce by
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* calling srandom() with any value, since the succeeding terms in the
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* state buffer are no longer derived from the LC algorithm applied to
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unsigned long junk; /* Purposely used uninitialized */
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gettimeofday(&tv, NULL);
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srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk);
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* Initialize the state information in the given array of n bytes for future
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* random number generation. Based on the number of bytes we are given, and
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* the break values for the different R.N.G.'s, we choose the best (largest)
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* one we can and set things up for it. srandom() is then called to
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* initialize the state information.
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* Note that on return from srandom(), we set state[-1] to be the type
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* multiplexed with the current value of the rear pointer; this is so
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* successive calls to initstate() won't lose this information and will be
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* able to restart with setstate().
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* Note: the first thing we do is save the current state, if any, just like
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* setstate() so that it doesn't matter when initstate is called.
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* Returns a pointer to the old state.
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* Note: The Sparc platform requires that arg_state begin on a long
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* word boundary; otherwise a bus error will occur. Even so, lint will
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* complain about mis-alignment, but you should disregard these messages.
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unsigned long seed, /* seed for R.N.G. */
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char *arg_state, /* pointer to state array */
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long n /* # bytes of state info */
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register char *ostate = (char *)(&state[-1]);
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register long *long_arg_state = (long *) arg_state;
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if (rand_type == TYPE_0)
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state[-1] = rand_type;
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state[-1] = MAX_TYPES * (rptr - state) + rand_type;
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(void)fprintf(stderr,
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"random: not enough state (%ld bytes); ignored.\n", n);
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} else if (n < BREAK_2) {
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} else if (n < BREAK_3) {
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} else if (n < BREAK_4) {
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state = (long *) (long_arg_state + 1); /* first location */
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end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
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if (rand_type == TYPE_0)
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long_arg_state[0] = rand_type;
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long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
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* Restore the state from the given state array.
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* Note: it is important that we also remember the locations of the pointers
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* in the current state information, and restore the locations of the pointers
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* from the old state information. This is done by multiplexing the pointer
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* location into the zeroeth word of the state information.
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* Note that due to the order in which things are done, it is OK to call
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* setstate() with the same state as the current state.
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* Returns a pointer to the old state information.
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* Note: The Sparc platform requires that arg_state begin on a long
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* word boundary; otherwise a bus error will occur. Even so, lint will
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* complain about mis-alignment, but you should disregard these messages.
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char *arg_state /* pointer to state array */
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register long *new_state = (long *) arg_state;
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register long type = new_state[0] % MAX_TYPES;
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register long rear = new_state[0] / MAX_TYPES;
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char *ostate = (char *)(&state[-1]);
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if (rand_type == TYPE_0)
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state[-1] = rand_type;
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state[-1] = MAX_TYPES * (rptr - state) + rand_type;
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rand_deg = degrees[type];
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rand_sep = seps[type];
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(void)fprintf(stderr,
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"random: state info corrupted; not changed.\n");
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state = (long *) (new_state + 1);
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if (rand_type != TYPE_0) {
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fptr = &state[(rear + rand_sep) % rand_deg];
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end_ptr = &state[rand_deg]; /* set end_ptr too */
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* If we are using the trivial TYPE_0 R.N.G., just do the old linear
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* congruential bit. Otherwise, we do our fancy trinomial stuff, which is
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* the same in all the other cases due to all the global variables that have
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* been set up. The basic operation is to add the number at the rear pointer
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* into the one at the front pointer. Then both pointers are advanced to
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* the next location cyclically in the table. The value returned is the sum
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* generated, reduced to 31 bits by throwing away the "least random" low bit.
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* Note: the code takes advantage of the fact that both the front and
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* rear pointers can't wrap on the same call by not testing the rear
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* pointer if the front one has wrapped.
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* Returns a 31-bit random number.
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register long *f, *r;
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if (rand_type == TYPE_0) {
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state[0] = i = (good_rand(i)) & 0x7fffffff;
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* Use local variables rather than static variables for speed.
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i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */
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if (++f >= end_ptr) {
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else if (++r >= end_ptr) {
added
removed
libntp/random.c
