683 lines
		
	
	
		
			24 KiB
		
	
	
	
		
			Plaintext
		
	
	
	
	
	
		
		
			
		
	
	
			683 lines
		
	
	
		
			24 KiB
		
	
	
	
		
			Plaintext
		
	
	
	
	
	
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								/* boost random/mersenne_twister.hpp header file
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								 *
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								 * Copyright Jens Maurer 2000-2001
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								 * Copyright Steven Watanabe 2010
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								 * Distributed under the Boost Software License, Version 1.0. (See
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								 * accompanying file LICENSE_1_0.txt or copy at
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								 * http://www.boost.org/LICENSE_1_0.txt)
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								 *
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								 * See http://www.boost.org for most recent version including documentation.
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								 *
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								 * $Id$
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								 *
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								 * Revision history
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								 *  2013-10-14  fixed some warnings with Wshadow (mgaunard)
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								 *  2001-02-18  moved to individual header files
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								 */
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								#ifndef BOOST_RANDOM_MERSENNE_TWISTER_HPP
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								#define BOOST_RANDOM_MERSENNE_TWISTER_HPP
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								#include <iosfwd>
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								#include <istream>
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								#include <stdexcept>
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								#include <boost/config.hpp>
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								#include <boost/cstdint.hpp>
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								#include <boost/integer/integer_mask.hpp>
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								#include <boost/random/detail/config.hpp>
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								#include <boost/random/detail/ptr_helper.hpp>
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								#include <boost/random/detail/seed.hpp>
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								#include <boost/random/detail/seed_impl.hpp>
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								#include <boost/random/detail/generator_seed_seq.hpp>
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								#include <boost/random/detail/polynomial.hpp>
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								#include <boost/random/detail/disable_warnings.hpp>
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								namespace boost {
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								namespace random {
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								/**
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								 * Instantiations of class template mersenne_twister_engine model a
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								 * \pseudo_random_number_generator. It uses the algorithm described in
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								 *
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								 *  @blockquote
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								 *  "Mersenne Twister: A 623-dimensionally equidistributed uniform
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								 *  pseudo-random number generator", Makoto Matsumoto and Takuji Nishimura,
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								 *  ACM Transactions on Modeling and Computer Simulation: Special Issue on
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								 *  Uniform Random Number Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
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								 *  @endblockquote
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								 *
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								 * @xmlnote
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								 * The boost variant has been implemented from scratch and does not
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								 * derive from or use mt19937.c provided on the above WWW site. However, it
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								 * was verified that both produce identical output.
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								 * @endxmlnote
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								 *
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								 * The seeding from an integer was changed in April 2005 to address a
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								 * <a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html">weakness</a>.
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								 *
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								 * The quality of the generator crucially depends on the choice of the
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								 * parameters.  User code should employ one of the sensibly parameterized
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								 * generators such as \mt19937 instead.
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								 *
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								 * The generator requires considerable amounts of memory for the storage of
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								 * its state array. For example, \mt11213b requires about 1408 bytes and
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								 * \mt19937 requires about 2496 bytes.
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								 */
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								template<class UIntType,
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								         std::size_t w, std::size_t n, std::size_t m, std::size_t r,
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								         UIntType a, std::size_t u, UIntType d, std::size_t s,
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								         UIntType b, std::size_t t,
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								         UIntType c, std::size_t l, UIntType f>
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								class mersenne_twister_engine
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								{
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								public:
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								    typedef UIntType result_type;
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								    BOOST_STATIC_CONSTANT(std::size_t, word_size = w);
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								    BOOST_STATIC_CONSTANT(std::size_t, state_size = n);
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								    BOOST_STATIC_CONSTANT(std::size_t, shift_size = m);
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								    BOOST_STATIC_CONSTANT(std::size_t, mask_bits = r);
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								    BOOST_STATIC_CONSTANT(UIntType, xor_mask = a);
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								    BOOST_STATIC_CONSTANT(std::size_t, tempering_u = u);
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								    BOOST_STATIC_CONSTANT(UIntType, tempering_d = d);
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								    BOOST_STATIC_CONSTANT(std::size_t, tempering_s = s);
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								    BOOST_STATIC_CONSTANT(UIntType, tempering_b = b);
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								    BOOST_STATIC_CONSTANT(std::size_t, tempering_t = t);
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								    BOOST_STATIC_CONSTANT(UIntType, tempering_c = c);
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								    BOOST_STATIC_CONSTANT(std::size_t, tempering_l = l);
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								    BOOST_STATIC_CONSTANT(UIntType, initialization_multiplier = f);
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								    BOOST_STATIC_CONSTANT(UIntType, default_seed = 5489u);
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								    // backwards compatibility
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								    BOOST_STATIC_CONSTANT(UIntType, parameter_a = a);
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								    BOOST_STATIC_CONSTANT(std::size_t, output_u = u);
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								    BOOST_STATIC_CONSTANT(std::size_t, output_s = s);
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								    BOOST_STATIC_CONSTANT(UIntType, output_b = b);
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								    BOOST_STATIC_CONSTANT(std::size_t, output_t = t);
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								    BOOST_STATIC_CONSTANT(UIntType, output_c = c);
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								    BOOST_STATIC_CONSTANT(std::size_t, output_l = l);
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								    // old Boost.Random concept requirements
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								    BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
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								    /**
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								     * Constructs a @c mersenne_twister_engine and calls @c seed().
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								     */
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								    mersenne_twister_engine() { seed(); }
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								    /**
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								     * Constructs a @c mersenne_twister_engine and calls @c seed(value).
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								     */
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								    BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister_engine,
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								                                               UIntType, value)
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								    { seed(value); }
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								    template<class It> mersenne_twister_engine(It& first, It last)
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								    { seed(first,last); }
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								    /**
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								     * Constructs a mersenne_twister_engine and calls @c seed(gen).
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								     *
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								     * @xmlnote
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								     * The copy constructor will always be preferred over
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								     * the templated constructor.
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								     * @endxmlnote
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								     */
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								    BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(mersenne_twister_engine,
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								                                             SeedSeq, seq)
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								    { seed(seq); }
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								    // compiler-generated copy ctor and assignment operator are fine
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								    /** Calls @c seed(default_seed). */
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								    void seed() { seed(default_seed); }
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								    /**
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								     * Sets the state x(0) to v mod 2w. Then, iteratively,
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								     * sets x(i) to
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								     * (i + f * (x(i-1) xor (x(i-1) rshift w-2))) mod 2<sup>w</sup>
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								     * for i = 1 .. n-1. x(n) is the first value to be returned by operator().
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								     */
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								    BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister_engine, UIntType, value)
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								    {
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								        // New seeding algorithm from
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								        // http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html
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								        // In the previous versions, MSBs of the seed affected only MSBs of the
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								        // state x[].
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								        const UIntType mask = (max)();
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								        x[0] = value & mask;
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								        for (i = 1; i < n; i++) {
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								            // See Knuth "The Art of Computer Programming"
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								            // Vol. 2, 3rd ed., page 106
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								            x[i] = (f * (x[i-1] ^ (x[i-1] >> (w-2))) + i) & mask;
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								        }
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								        normalize_state();
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								    }
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								    /**
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								     * Seeds a mersenne_twister_engine using values produced by seq.generate().
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								     */
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								    BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(mersenne_twister_engine, SeeqSeq, seq)
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								    {
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								        detail::seed_array_int<w>(seq, x);
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								        i = n;
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								        normalize_state();
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								    }
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								    /** Sets the state of the generator using values from an iterator range. */
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								    template<class It>
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								    void seed(It& first, It last)
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								    {
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								        detail::fill_array_int<w>(first, last, x);
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								        i = n;
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								        normalize_state();
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								    }
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								    /** Returns the smallest value that the generator can produce. */
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								    static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
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								    { return 0; }
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								    /** Returns the largest value that the generator can produce. */
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								    static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
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								    { return boost::low_bits_mask_t<w>::sig_bits; }
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								    /** Produces the next value of the generator. */
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								    result_type operator()();
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								    /** Fills a range with random values */
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								    template<class Iter>
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								    void generate(Iter first, Iter last)
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								    { detail::generate_from_int(*this, first, last); }
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								    /**
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								     * Advances the state of the generator by @c z steps.  Equivalent to
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								     *
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								     * @code
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								     * for(unsigned long long i = 0; i < z; ++i) {
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								     *     gen();
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								     * }
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								     * @endcode
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								     */
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								    void discard(boost::uintmax_t z)
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								    {
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								#ifndef BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD
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								#define BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD 10000000
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								#endif
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								        if(z > BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD) {
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								            discard_many(z);
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								        } else {
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								            for(boost::uintmax_t j = 0; j < z; ++j) {
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								                (*this)();
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								            }
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								        }
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								    }
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								#ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
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								    /** Writes a mersenne_twister_engine to a @c std::ostream */
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								    template<class CharT, class Traits>
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								    friend std::basic_ostream<CharT,Traits>&
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								    operator<<(std::basic_ostream<CharT,Traits>& os,
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								               const mersenne_twister_engine& mt)
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								    {
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								        mt.print(os);
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								        return os;
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								    }
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								    /** Reads a mersenne_twister_engine from a @c std::istream */
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								    template<class CharT, class Traits>
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								    friend std::basic_istream<CharT,Traits>&
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								    operator>>(std::basic_istream<CharT,Traits>& is,
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								               mersenne_twister_engine& mt)
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								    {
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								        for(std::size_t j = 0; j < mt.state_size; ++j)
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								            is >> mt.x[j] >> std::ws;
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								        // MSVC (up to 7.1) and Borland (up to 5.64) don't handle the template
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								        // value parameter "n" available from the class template scope, so use
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								        // the static constant with the same value
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								        mt.i = mt.state_size;
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								        return is;
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								    }
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								#endif
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								    /**
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								     * Returns true if the two generators are in the same state,
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								     * and will thus produce identical sequences.
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								     */
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								    friend bool operator==(const mersenne_twister_engine& x_,
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								                           const mersenne_twister_engine& y_)
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						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        if(x_.i < y_.i) return x_.equal_imp(y_);
							 | 
						||
| 
								 | 
							
								        else return y_.equal_imp(x_);
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    /**
							 | 
						||
| 
								 | 
							
								     * Returns true if the two generators are in different states.
							 | 
						||
| 
								 | 
							
								     */
							 | 
						||
| 
								 | 
							
								    friend bool operator!=(const mersenne_twister_engine& x_,
							 | 
						||
| 
								 | 
							
								                           const mersenne_twister_engine& y_)
							 | 
						||
| 
								 | 
							
								    { return !(x_ == y_); }
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								private:
							 | 
						||
| 
								 | 
							
								    /// \cond show_private
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    void twist();
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    /**
							 | 
						||
| 
								 | 
							
								     * Does the work of operator==.  This is in a member function
							 | 
						||
| 
								 | 
							
								     * for portability.  Some compilers, such as msvc 7.1 and
							 | 
						||
| 
								 | 
							
								     * Sun CC 5.10 can't access template parameters or static
							 | 
						||
| 
								 | 
							
								     * members of the class from inline friend functions.
							 | 
						||
| 
								 | 
							
								     *
							 | 
						||
| 
								 | 
							
								     * requires i <= other.i
							 | 
						||
| 
								 | 
							
								     */
							 | 
						||
| 
								 | 
							
								    bool equal_imp(const mersenne_twister_engine& other) const
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        UIntType back[n];
							 | 
						||
| 
								 | 
							
								        std::size_t offset = other.i - i;
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = 0; j + offset < n; ++j)
							 | 
						||
| 
								 | 
							
								            if(x[j] != other.x[j+offset])
							 | 
						||
| 
								 | 
							
								                return false;
							 | 
						||
| 
								 | 
							
								        rewind(&back[n-1], offset);
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = 0; j < offset; ++j)
							 | 
						||
| 
								 | 
							
								            if(back[j + n - offset] != other.x[j])
							 | 
						||
| 
								 | 
							
								                return false;
							 | 
						||
| 
								 | 
							
								        return true;
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    /**
							 | 
						||
| 
								 | 
							
								     * Does the work of operator<<.  This is in a member function
							 | 
						||
| 
								 | 
							
								     * for portability.
							 | 
						||
| 
								 | 
							
								     */
							 | 
						||
| 
								 | 
							
								    template<class CharT, class Traits>
							 | 
						||
| 
								 | 
							
								    void print(std::basic_ostream<CharT, Traits>& os) const
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        UIntType data[n];
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = 0; j < i; ++j) {
							 | 
						||
| 
								 | 
							
								            data[j + n - i] = x[j];
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								        if(i != n) {
							 | 
						||
| 
								 | 
							
								            rewind(&data[n - i - 1], n - i);
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								        os << data[0];
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = 1; j < n; ++j) {
							 | 
						||
| 
								 | 
							
								            os << ' ' << data[j];
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    /**
							 | 
						||
| 
								 | 
							
								     * Copies z elements of the state preceding x[0] into
							 | 
						||
| 
								 | 
							
								     * the array whose last element is last.
							 | 
						||
| 
								 | 
							
								     */
							 | 
						||
| 
								 | 
							
								    void rewind(UIntType* last, std::size_t z) const
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
							 | 
						||
| 
								 | 
							
								        const UIntType lower_mask = ~upper_mask;
							 | 
						||
| 
								 | 
							
								        UIntType y0 = x[m-1] ^ x[n-1];
							 | 
						||
| 
								 | 
							
								        if(y0 & (static_cast<UIntType>(1) << (w-1))) {
							 | 
						||
| 
								 | 
							
								            y0 = ((y0 ^ a) << 1) | 1;
							 | 
						||
| 
								 | 
							
								        } else {
							 | 
						||
| 
								 | 
							
								            y0 = y0 << 1;
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								        for(std::size_t sz = 0; sz < z; ++sz) {
							 | 
						||
| 
								 | 
							
								            UIntType y1 =
							 | 
						||
| 
								 | 
							
								                rewind_find(last, sz, m-1) ^ rewind_find(last, sz, n-1);
							 | 
						||
| 
								 | 
							
								            if(y1 & (static_cast<UIntType>(1) << (w-1))) {
							 | 
						||
| 
								 | 
							
								                y1 = ((y1 ^ a) << 1) | 1;
							 | 
						||
| 
								 | 
							
								            } else {
							 | 
						||
| 
								 | 
							
								                y1 = y1 << 1;
							 | 
						||
| 
								 | 
							
								            }
							 | 
						||
| 
								 | 
							
								            *(last - sz) = (y0 & upper_mask) | (y1 & lower_mask);
							 | 
						||
| 
								 | 
							
								            y0 = y1;
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    /**
							 | 
						||
| 
								 | 
							
								     * Converts an arbitrary array into a valid generator state.
							 | 
						||
| 
								 | 
							
								     * First we normalize x[0], so that it contains the same
							 | 
						||
| 
								 | 
							
								     * value we would get by running the generator forwards
							 | 
						||
| 
								 | 
							
								     * and then in reverse.  (The low order r bits are redundant).
							 | 
						||
| 
								 | 
							
								     * Then, if the state consists of all zeros, we set the
							 | 
						||
| 
								 | 
							
								     * high order bit of x[0] to 1.  This function only needs to
							 | 
						||
| 
								 | 
							
								     * be called by seed, since the state transform preserves
							 | 
						||
| 
								 | 
							
								     * this relationship.
							 | 
						||
| 
								 | 
							
								     */
							 | 
						||
| 
								 | 
							
								    void normalize_state()
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
							 | 
						||
| 
								 | 
							
								        const UIntType lower_mask = ~upper_mask;
							 | 
						||
| 
								 | 
							
								        UIntType y0 = x[m-1] ^ x[n-1];
							 | 
						||
| 
								 | 
							
								        if(y0 & (static_cast<UIntType>(1) << (w-1))) {
							 | 
						||
| 
								 | 
							
								            y0 = ((y0 ^ a) << 1) | 1;
							 | 
						||
| 
								 | 
							
								        } else {
							 | 
						||
| 
								 | 
							
								            y0 = y0 << 1;
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								        x[0] = (x[0] & upper_mask) | (y0 & lower_mask);
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								        // fix up the state if it's all zeroes.
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = 0; j < n; ++j) {
							 | 
						||
| 
								 | 
							
								            if(x[j] != 0) return;
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								        x[0] = static_cast<UIntType>(1) << (w-1);
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    /**
							 | 
						||
| 
								 | 
							
								     * Given a pointer to the last element of the rewind array,
							 | 
						||
| 
								 | 
							
								     * and the current size of the rewind array, finds an element
							 | 
						||
| 
								 | 
							
								     * relative to the next available slot in the rewind array.
							 | 
						||
| 
								 | 
							
								     */
							 | 
						||
| 
								 | 
							
								    UIntType
							 | 
						||
| 
								 | 
							
								    rewind_find(UIntType* last, std::size_t size, std::size_t j) const
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        std::size_t index = (j + n - size + n - 1) % n;
							 | 
						||
| 
								 | 
							
								        if(index < n - size) {
							 | 
						||
| 
								 | 
							
								            return x[index];
							 | 
						||
| 
								 | 
							
								        } else {
							 | 
						||
| 
								 | 
							
								            return *(last - (n - 1 - index));
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    /**
							 | 
						||
| 
								 | 
							
								     * Optimized algorithm for large jumps.
							 | 
						||
| 
								 | 
							
								     *
							 | 
						||
| 
								 | 
							
								     * Hiroshi Haramoto, Makoto Matsumoto, and Pierre L'Ecuyer. 2008.
							 | 
						||
| 
								 | 
							
								     * A Fast Jump Ahead Algorithm for Linear Recurrences in a Polynomial
							 | 
						||
| 
								 | 
							
								     * Space. In Proceedings of the 5th international conference on
							 | 
						||
| 
								 | 
							
								     * Sequences and Their Applications (SETA '08).
							 | 
						||
| 
								 | 
							
								     * DOI=10.1007/978-3-540-85912-3_26
							 | 
						||
| 
								 | 
							
								     */
							 | 
						||
| 
								 | 
							
								    void discard_many(boost::uintmax_t z)
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        // Compute the minimal polynomial, phi(t)
							 | 
						||
| 
								 | 
							
								        // This depends only on the transition function,
							 | 
						||
| 
								 | 
							
								        // which is constant.  The characteristic
							 | 
						||
| 
								 | 
							
								        // polynomial is the same as the minimal
							 | 
						||
| 
								 | 
							
								        // polynomial for a maximum period generator
							 | 
						||
| 
								 | 
							
								        // (which should be all specializations of
							 | 
						||
| 
								 | 
							
								        // mersenne_twister.)  Even if it weren't,
							 | 
						||
| 
								 | 
							
								        // the characteristic polynomial is guaranteed
							 | 
						||
| 
								 | 
							
								        // to be a multiple of the minimal polynomial,
							 | 
						||
| 
								 | 
							
								        // which is good enough.
							 | 
						||
| 
								 | 
							
								        detail::polynomial phi = get_characteristic_polynomial();
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								        // calculate g(t) = t^z % phi(t)
							 | 
						||
| 
								 | 
							
								        detail::polynomial g = mod_pow_x(z, phi);
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								        // h(s_0, t) = \sum_{i=0}^{2k-1}o(s_i)t^{2k-i-1}
							 | 
						||
| 
								 | 
							
								        detail::polynomial h;
							 | 
						||
| 
								 | 
							
								        const std::size_t num_bits = w*n - r;
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = 0; j < num_bits * 2; ++j) {
							 | 
						||
| 
								 | 
							
								            // Yes, we're advancing the generator state
							 | 
						||
| 
								 | 
							
								            // here, but it doesn't matter because
							 | 
						||
| 
								 | 
							
								            // we're going to overwrite it completely
							 | 
						||
| 
								 | 
							
								            // in reconstruct_state.
							 | 
						||
| 
								 | 
							
								            if(i >= n) twist();
							 | 
						||
| 
								 | 
							
								            h[2*num_bits - j - 1] = x[i++] & UIntType(1);
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								        // g(t)h(s_0, t)
							 | 
						||
| 
								 | 
							
								        detail::polynomial gh = g * h;
							 | 
						||
| 
								 | 
							
								        detail::polynomial result;
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = 0; j <= num_bits; ++j) {
							 | 
						||
| 
								 | 
							
								            result[j] = gh[2*num_bits - j - 1];
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								        reconstruct_state(result);
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								    static detail::polynomial get_characteristic_polynomial()
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        const std::size_t num_bits = w*n - r;
							 | 
						||
| 
								 | 
							
								        detail::polynomial helper;
							 | 
						||
| 
								 | 
							
								        helper[num_bits - 1] = 1;
							 | 
						||
| 
								 | 
							
								        mersenne_twister_engine tmp;
							 | 
						||
| 
								 | 
							
								        tmp.reconstruct_state(helper);
							 | 
						||
| 
								 | 
							
								        // Skip the first num_bits elements, since we
							 | 
						||
| 
								 | 
							
								        // already know what they are.
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = 0; j < num_bits; ++j) {
							 | 
						||
| 
								 | 
							
								            if(tmp.i >= n) tmp.twist();
							 | 
						||
| 
								 | 
							
								            if(j == num_bits - 1)
							 | 
						||
| 
								 | 
							
								                assert((tmp.x[tmp.i] & 1) == 1);
							 | 
						||
| 
								 | 
							
								            else
							 | 
						||
| 
								 | 
							
								                assert((tmp.x[tmp.i] & 1) == 0);
							 | 
						||
| 
								 | 
							
								            ++tmp.i;
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								        detail::polynomial phi;
							 | 
						||
| 
								 | 
							
								        phi[num_bits] = 1;
							 | 
						||
| 
								 | 
							
								        detail::polynomial next_bits = tmp.as_polynomial(num_bits);
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = 0; j < num_bits; ++j) {
							 | 
						||
| 
								 | 
							
								            int val = next_bits[j] ^ phi[num_bits-j-1];
							 | 
						||
| 
								 | 
							
								            phi[num_bits-j-1] = val;
							 | 
						||
| 
								 | 
							
								            if(val) {
							 | 
						||
| 
								 | 
							
								                for(std::size_t k = j + 1; k < num_bits; ++k) {
							 | 
						||
| 
								 | 
							
								                    phi[num_bits-k-1] ^= next_bits[k-j-1];
							 | 
						||
| 
								 | 
							
								                }
							 | 
						||
| 
								 | 
							
								            }
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								        return phi;
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								    detail::polynomial as_polynomial(std::size_t size) {
							 | 
						||
| 
								 | 
							
								        detail::polynomial result;
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = 0; j < size; ++j) {
							 | 
						||
| 
								 | 
							
								            if(i >= n) twist();
							 | 
						||
| 
								 | 
							
								            result[j] = x[i++] & UIntType(1);
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								        return result;
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								    void reconstruct_state(const detail::polynomial& p)
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
							 | 
						||
| 
								 | 
							
								        const UIntType lower_mask = ~upper_mask;
							 | 
						||
| 
								 | 
							
								        const std::size_t num_bits = w*n - r;
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = num_bits - n + 1; j <= num_bits; ++j)
							 | 
						||
| 
								 | 
							
								            x[j % n] = p[j];
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								        UIntType y0 = 0;
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = num_bits + 1; j >= n - 1; --j) {
							 | 
						||
| 
								 | 
							
								            UIntType y1 = x[j % n] ^ x[(j + m) % n];
							 | 
						||
| 
								 | 
							
								            if(p[j - n + 1])
							 | 
						||
| 
								 | 
							
								                y1 = (y1 ^ a) << UIntType(1) | UIntType(1);
							 | 
						||
| 
								 | 
							
								            else
							 | 
						||
| 
								 | 
							
								                y1 = y1 << UIntType(1);
							 | 
						||
| 
								 | 
							
								            x[(j + 1) % n] = (y0 & upper_mask) | (y1 & lower_mask);
							 | 
						||
| 
								 | 
							
								            y0 = y1;
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								        i = 0;
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    /// \endcond
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    // state representation: next output is o(x(i))
							 | 
						||
| 
								 | 
							
								    //   x[0]  ... x[k] x[k+1] ... x[n-1]   represents
							 | 
						||
| 
								 | 
							
								    //  x(i-k) ... x(i) x(i+1) ... x(i-k+n-1)
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    UIntType x[n];
							 | 
						||
| 
								 | 
							
								    std::size_t i;
							 | 
						||
| 
								 | 
							
								};
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								/// \cond show_private
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
							 | 
						||
| 
								 | 
							
								//  A definition is required even for integral static constants
							 | 
						||
| 
								 | 
							
								#define BOOST_RANDOM_MT_DEFINE_CONSTANT(type, name)                         \
							 | 
						||
| 
								 | 
							
								template<class UIntType, std::size_t w, std::size_t n, std::size_t m,       \
							 | 
						||
| 
								 | 
							
								    std::size_t r, UIntType a, std::size_t u, UIntType d, std::size_t s,    \
							 | 
						||
| 
								 | 
							
								    UIntType b, std::size_t t, UIntType c, std::size_t l, UIntType f>       \
							 | 
						||
| 
								 | 
							
								const type mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::name
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, word_size);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, state_size);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, shift_size);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, mask_bits);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, xor_mask);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_u);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_d);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_s);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_b);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_t);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_c);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_l);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, initialization_multiplier);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, default_seed);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, parameter_a);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_u );
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_s);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, output_b);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_t);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, output_c);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_l);
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_MT_DEFINE_CONSTANT(bool, has_fixed_range);
							 | 
						||
| 
								 | 
							
								#undef BOOST_RANDOM_MT_DEFINE_CONSTANT
							 | 
						||
| 
								 | 
							
								#endif
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								template<class UIntType,
							 | 
						||
| 
								 | 
							
								         std::size_t w, std::size_t n, std::size_t m, std::size_t r,
							 | 
						||
| 
								 | 
							
								         UIntType a, std::size_t u, UIntType d, std::size_t s,
							 | 
						||
| 
								 | 
							
								         UIntType b, std::size_t t,
							 | 
						||
| 
								 | 
							
								         UIntType c, std::size_t l, UIntType f>
							 | 
						||
| 
								 | 
							
								void
							 | 
						||
| 
								 | 
							
								mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::twist()
							 | 
						||
| 
								 | 
							
								{
							 | 
						||
| 
								 | 
							
								    const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
							 | 
						||
| 
								 | 
							
								    const UIntType lower_mask = ~upper_mask;
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    const std::size_t unroll_factor = 6;
							 | 
						||
| 
								 | 
							
								    const std::size_t unroll_extra1 = (n-m) % unroll_factor;
							 | 
						||
| 
								 | 
							
								    const std::size_t unroll_extra2 = (m-1) % unroll_factor;
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								    // split loop to avoid costly modulo operations
							 | 
						||
| 
								 | 
							
								    {  // extra scope for MSVC brokenness w.r.t. for scope
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = 0; j < n-m-unroll_extra1; j++) {
							 | 
						||
| 
								 | 
							
								            UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
							 | 
						||
| 
								 | 
							
								            x[j] = x[j+m] ^ (y >> 1) ^ ((x[j+1]&1) * a);
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = n-m-unroll_extra1; j < n-m; j++) {
							 | 
						||
| 
								 | 
							
								            UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
							 | 
						||
| 
								 | 
							
								            x[j] = x[j+m] ^ (y >> 1) ^ ((x[j+1]&1) * a);
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = n-m; j < n-1-unroll_extra2; j++) {
							 | 
						||
| 
								 | 
							
								            UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
							 | 
						||
| 
								 | 
							
								            x[j] = x[j-(n-m)] ^ (y >> 1) ^ ((x[j+1]&1) * a);
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        for(std::size_t j = n-1-unroll_extra2; j < n-1; j++) {
							 | 
						||
| 
								 | 
							
								            UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
							 | 
						||
| 
								 | 
							
								            x[j] = x[j-(n-m)] ^ (y >> 1) ^ ((x[j+1]&1) * a);
							 | 
						||
| 
								 | 
							
								        }
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								    // last iteration
							 | 
						||
| 
								 | 
							
								    UIntType y = (x[n-1] & upper_mask) | (x[0] & lower_mask);
							 | 
						||
| 
								 | 
							
								    x[n-1] = x[m-1] ^ (y >> 1) ^ ((x[0]&1) * a);
							 | 
						||
| 
								 | 
							
								    i = 0;
							 | 
						||
| 
								 | 
							
								}
							 | 
						||
| 
								 | 
							
								/// \endcond
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								template<class UIntType,
							 | 
						||
| 
								 | 
							
								         std::size_t w, std::size_t n, std::size_t m, std::size_t r,
							 | 
						||
| 
								 | 
							
								         UIntType a, std::size_t u, UIntType d, std::size_t s,
							 | 
						||
| 
								 | 
							
								         UIntType b, std::size_t t,
							 | 
						||
| 
								 | 
							
								         UIntType c, std::size_t l, UIntType f>
							 | 
						||
| 
								 | 
							
								inline typename
							 | 
						||
| 
								 | 
							
								mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::result_type
							 | 
						||
| 
								 | 
							
								mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::operator()()
							 | 
						||
| 
								 | 
							
								{
							 | 
						||
| 
								 | 
							
								    if(i == n)
							 | 
						||
| 
								 | 
							
								        twist();
							 | 
						||
| 
								 | 
							
								    // Step 4
							 | 
						||
| 
								 | 
							
								    UIntType z = x[i];
							 | 
						||
| 
								 | 
							
								    ++i;
							 | 
						||
| 
								 | 
							
								    z ^= ((z >> u) & d);
							 | 
						||
| 
								 | 
							
								    z ^= ((z << s) & b);
							 | 
						||
| 
								 | 
							
								    z ^= ((z << t) & c);
							 | 
						||
| 
								 | 
							
								    z ^= (z >> l);
							 | 
						||
| 
								 | 
							
								    return z;
							 | 
						||
| 
								 | 
							
								}
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								/**
							 | 
						||
| 
								 | 
							
								 * The specializations \mt11213b and \mt19937 are from
							 | 
						||
| 
								 | 
							
								 *
							 | 
						||
| 
								 | 
							
								 *  @blockquote
							 | 
						||
| 
								 | 
							
								 *  "Mersenne Twister: A 623-dimensionally equidistributed
							 | 
						||
| 
								 | 
							
								 *  uniform pseudo-random number generator", Makoto Matsumoto
							 | 
						||
| 
								 | 
							
								 *  and Takuji Nishimura, ACM Transactions on Modeling and
							 | 
						||
| 
								 | 
							
								 *  Computer Simulation: Special Issue on Uniform Random Number
							 | 
						||
| 
								 | 
							
								 *  Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
							 | 
						||
| 
								 | 
							
								 *  @endblockquote
							 | 
						||
| 
								 | 
							
								 */
							 | 
						||
| 
								 | 
							
								typedef mersenne_twister_engine<uint32_t,32,351,175,19,0xccab8ee7,
							 | 
						||
| 
								 | 
							
								    11,0xffffffff,7,0x31b6ab00,15,0xffe50000,17,1812433253> mt11213b;
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								/**
							 | 
						||
| 
								 | 
							
								 * The specializations \mt11213b and \mt19937 are from
							 | 
						||
| 
								 | 
							
								 *
							 | 
						||
| 
								 | 
							
								 *  @blockquote
							 | 
						||
| 
								 | 
							
								 *  "Mersenne Twister: A 623-dimensionally equidistributed
							 | 
						||
| 
								 | 
							
								 *  uniform pseudo-random number generator", Makoto Matsumoto
							 | 
						||
| 
								 | 
							
								 *  and Takuji Nishimura, ACM Transactions on Modeling and
							 | 
						||
| 
								 | 
							
								 *  Computer Simulation: Special Issue on Uniform Random Number
							 | 
						||
| 
								 | 
							
								 *  Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
							 | 
						||
| 
								 | 
							
								 *  @endblockquote
							 | 
						||
| 
								 | 
							
								 */
							 | 
						||
| 
								 | 
							
								typedef mersenne_twister_engine<uint32_t,32,624,397,31,0x9908b0df,
							 | 
						||
| 
								 | 
							
								    11,0xffffffff,7,0x9d2c5680,15,0xefc60000,18,1812433253> mt19937;
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								#if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T)
							 | 
						||
| 
								 | 
							
								typedef mersenne_twister_engine<uint64_t,64,312,156,31,
							 | 
						||
| 
								 | 
							
								    UINT64_C(0xb5026f5aa96619e9),29,UINT64_C(0x5555555555555555),17,
							 | 
						||
| 
								 | 
							
								    UINT64_C(0x71d67fffeda60000),37,UINT64_C(0xfff7eee000000000),43,
							 | 
						||
| 
								 | 
							
								    UINT64_C(6364136223846793005)> mt19937_64;
							 | 
						||
| 
								 | 
							
								#endif
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								/// \cond show_deprecated
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								template<class UIntType,
							 | 
						||
| 
								 | 
							
								         int w, int n, int m, int r,
							 | 
						||
| 
								 | 
							
								         UIntType a, int u, std::size_t s,
							 | 
						||
| 
								 | 
							
								         UIntType b, int t,
							 | 
						||
| 
								 | 
							
								         UIntType c, int l, UIntType v>
							 | 
						||
| 
								 | 
							
								class mersenne_twister :
							 | 
						||
| 
								 | 
							
								    public mersenne_twister_engine<UIntType,
							 | 
						||
| 
								 | 
							
								        w, n, m, r, a, u, ~(UIntType)0, s, b, t, c, l, 1812433253>
							 | 
						||
| 
								 | 
							
								{
							 | 
						||
| 
								 | 
							
								    typedef mersenne_twister_engine<UIntType,
							 | 
						||
| 
								 | 
							
								        w, n, m, r, a, u, ~(UIntType)0, s, b, t, c, l, 1812433253> base_type;
							 | 
						||
| 
								 | 
							
								public:
							 | 
						||
| 
								 | 
							
								    mersenne_twister() {}
							 | 
						||
| 
								 | 
							
								    BOOST_RANDOM_DETAIL_GENERATOR_CONSTRUCTOR(mersenne_twister, Gen, gen)
							 | 
						||
| 
								 | 
							
								    { seed(gen); }
							 | 
						||
| 
								 | 
							
								    BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister, UIntType, val)
							 | 
						||
| 
								 | 
							
								    { seed(val); }
							 | 
						||
| 
								 | 
							
								    template<class It>
							 | 
						||
| 
								 | 
							
								    mersenne_twister(It& first, It last) : base_type(first, last) {}
							 | 
						||
| 
								 | 
							
								    void seed() { base_type::seed(); }
							 | 
						||
| 
								 | 
							
								    BOOST_RANDOM_DETAIL_GENERATOR_SEED(mersenne_twister, Gen, gen)
							 | 
						||
| 
								 | 
							
								    {
							 | 
						||
| 
								 | 
							
								        detail::generator_seed_seq<Gen> seq(gen);
							 | 
						||
| 
								 | 
							
								        base_type::seed(seq);
							 | 
						||
| 
								 | 
							
								    }
							 | 
						||
| 
								 | 
							
								    BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister, UIntType, val)
							 | 
						||
| 
								 | 
							
								    { base_type::seed(val); }
							 | 
						||
| 
								 | 
							
								    template<class It>
							 | 
						||
| 
								 | 
							
								    void seed(It& first, It last) { base_type::seed(first, last); }
							 | 
						||
| 
								 | 
							
								};
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								/// \endcond
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								} // namespace random
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								using random::mt11213b;
							 | 
						||
| 
								 | 
							
								using random::mt19937;
							 | 
						||
| 
								 | 
							
								using random::mt19937_64;
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								} // namespace boost
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt11213b)
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937)
							 | 
						||
| 
								 | 
							
								BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937_64)
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								#include <boost/random/detail/enable_warnings.hpp>
							 | 
						||
| 
								 | 
							
								
							 | 
						||
| 
								 | 
							
								#endif // BOOST_RANDOM_MERSENNE_TWISTER_HPP
							 |