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boost/random/mersenne_twister.hpp

/* boost random/mersenne_twister.hpp header file
 *
 * Copyright Jens Maurer 2000-2001
 * Copyright Steven Watanabe 2010
 * Distributed under the Boost Software License, Version 1.0. (See
 * accompanying file LICENSE_1_0.txt or copy at
 * http://www.boost.org/LICENSE_1_0.txt)
 *
 * See http://www.boost.org for most recent version including documentation.
 *
 * $Id: mersenne_twister.hpp 74867 2011-10-09 23:13:31Z steven_watanabe $
 *
 * Revision history
 *  2001-02-18  moved to individual header files
 */

#ifndef BOOST_RANDOM_MERSENNE_TWISTER_HPP
#define BOOST_RANDOM_MERSENNE_TWISTER_HPP

#include <iosfwd>
#include <istream>
#include <stdexcept>
#include <boost/config.hpp>
#include <boost/cstdint.hpp>
#include <boost/integer/integer_mask.hpp>
#include <boost/random/detail/config.hpp>
#include <boost/random/detail/ptr_helper.hpp>
#include <boost/random/detail/seed.hpp>
#include <boost/random/detail/seed_impl.hpp>
#include <boost/random/detail/generator_seed_seq.hpp>

namespace boost {
namespace random {

/**
 * Instantiations of class template mersenne_twister_engine model a
 * \pseudo_random_number_generator. It uses the algorithm described in
 *
 *  @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
 *
 * @xmlnote
 * The boost variant has been implemented from scratch and does not
 * derive from or use mt19937.c provided on the above WWW site. However, it
 * was verified that both produce identical output.
 * @endxmlnote
 *
 * The seeding from an integer was changed in April 2005 to address a
 * <a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html">weakness</a>.
 * 
 * The quality of the generator crucially depends on the choice of the
 * parameters.  User code should employ one of the sensibly parameterized
 * generators such as \mt19937 instead.
 *
 * The generator requires considerable amounts of memory for the storage of
 * its state array. For example, \mt11213b requires about 1408 bytes and
 * \mt19937 requires about 2496 bytes.
 */
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>
class mersenne_twister_engine
{
public:
    typedef UIntType result_type;
    BOOST_STATIC_CONSTANT(std::size_t, word_size = w);
    BOOST_STATIC_CONSTANT(std::size_t, state_size = n);
    BOOST_STATIC_CONSTANT(std::size_t, shift_size = m);
    BOOST_STATIC_CONSTANT(std::size_t, mask_bits = r);
    BOOST_STATIC_CONSTANT(UIntType, xor_mask = a);
    BOOST_STATIC_CONSTANT(std::size_t, tempering_u = u);
    BOOST_STATIC_CONSTANT(UIntType, tempering_d = d);
    BOOST_STATIC_CONSTANT(std::size_t, tempering_s = s);
    BOOST_STATIC_CONSTANT(UIntType, tempering_b = b);
    BOOST_STATIC_CONSTANT(std::size_t, tempering_t = t);
    BOOST_STATIC_CONSTANT(UIntType, tempering_c = c);
    BOOST_STATIC_CONSTANT(std::size_t, tempering_l = l);
    BOOST_STATIC_CONSTANT(UIntType, initialization_multiplier = f);
    BOOST_STATIC_CONSTANT(UIntType, default_seed = 5489u);
  
    // backwards compatibility
    BOOST_STATIC_CONSTANT(UIntType, parameter_a = a);
    BOOST_STATIC_CONSTANT(std::size_t, output_u = u);
    BOOST_STATIC_CONSTANT(std::size_t, output_s = s);
    BOOST_STATIC_CONSTANT(UIntType, output_b = b);
    BOOST_STATIC_CONSTANT(std::size_t, output_t = t);
    BOOST_STATIC_CONSTANT(UIntType, output_c = c);
    BOOST_STATIC_CONSTANT(std::size_t, output_l = l);
    
    // old Boost.Random concept requirements
    BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);


    /**
     * Constructs a @c mersenne_twister_engine and calls @c seed().
     */
    mersenne_twister_engine() { seed(); }

    /**
     * Constructs a @c mersenne_twister_engine and calls @c seed(value).
     */
    BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister_engine,
                                               UIntType, value)
    { seed(value); }
    template<class It> mersenne_twister_engine(It& first, It last)
    { seed(first,last); }

    /**
     * Constructs a mersenne_twister_engine and calls @c seed(gen).
     *
     * @xmlnote
     * The copy constructor will always be preferred over
     * the templated constructor.
     * @endxmlnote
     */
    BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(mersenne_twister_engine,
                                             SeedSeq, seq)
    { seed(seq); }

    // compiler-generated copy ctor and assignment operator are fine

    /** Calls @c seed(default_seed). */
    void seed() { seed(default_seed); }

    /**
     * Sets the state x(0) to v mod 2w. Then, iteratively,
     * sets x(i) to
     * (i + f * (x(i-1) xor (x(i-1) rshift w-2))) mod 2<sup>w</sup>
     * for i = 1 .. n-1. x(n) is the first value to be returned by operator().
     */
    BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister_engine, UIntType, value)
    {
        // New seeding algorithm from 
        // http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html
        // In the previous versions, MSBs of the seed affected only MSBs of the
        // state x[].
        const UIntType mask = (max)();
        x[0] = value & mask;
        for (i = 1; i < n; i++) {
            // See Knuth "The Art of Computer Programming"
            // Vol. 2, 3rd ed., page 106
            x[i] = (f * (x[i-1] ^ (x[i-1] >> (w-2))) + i) & mask;
        }
    }
    
    /**
     * Seeds a mersenne_twister_engine using values produced by seq.generate().
     */
    BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(mersenne_twister_engine, SeeqSeq, seq)
    {
        detail::seed_array_int<w>(seq, x);
        i = n;

        // fix up the state if it's all zeroes.
        if((x[0] & (~static_cast<UIntType>(0) << r)) == 0) {
            for(std::size_t j = 1; j < n; ++j) {
                if(x[j] != 0) return;
            }
            x[0] = static_cast<UIntType>(1) << (w-1);
        }
    }

    /** Sets the state of the generator using values from an iterator range. */
    template<class It>
    void seed(It& first, It last)
    {
        detail::fill_array_int<w>(first, last, x);
        i = n;

        // fix up the state if it's all zeroes.
        if((x[0] & (~static_cast<UIntType>(0) << r)) == 0) {
            for(std::size_t j = 1; j < n; ++j) {
                if(x[j] != 0) return;
            }
            x[0] = static_cast<UIntType>(1) << (w-1);
        }
    }
  
    /** Returns the smallest value that the generator can produce. */
    static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
    { return 0; }
    /** Returns the largest value that the generator can produce. */
    static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
    { return boost::low_bits_mask_t<w>::sig_bits; }
    
    /** Produces the next value of the generator. */
    result_type operator()();

    /** Fills a range with random values */
    template<class Iter>
    void generate(Iter first, Iter last)
    { detail::generate_from_int(*this, first, last); }

    /**
     * Advances the state of the generator by @c z steps.  Equivalent to
     *
     * @code
     * for(unsigned long long i = 0; i < z; ++i) {
     *     gen();
     * }
     * @endcode
     */
    void discard(boost::uintmax_t z)
    {
        for(boost::uintmax_t j = 0; j < z; ++j) {
            (*this)();
        }
    }

#ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
    /** Writes a mersenne_twister_engine to a @c std::ostream */
    template<class CharT, class Traits>
    friend std::basic_ostream<CharT,Traits>&
    operator<<(std::basic_ostream<CharT,Traits>& os,
               const mersenne_twister_engine& mt)
    {
        mt.print(os);
        return os;
    }
    
    /** Reads a mersenne_twister_engine from a @c std::istream */
    template<class CharT, class Traits>
    friend std::basic_istream<CharT,Traits>&
    operator>>(std::basic_istream<CharT,Traits>& is,
               mersenne_twister_engine& mt)
    {
        for(std::size_t j = 0; j < mt.state_size; ++j)
            is >> mt.x[j] >> std::ws;
        // MSVC (up to 7.1) and Borland (up to 5.64) don't handle the template
        // value parameter "n" available from the class template scope, so use
        // the static constant with the same value
        mt.i = mt.state_size;
        return is;
    }
#endif

    /**
     * Returns true if the two generators are in the same state,
     * and will thus produce identical sequences.
     */
    friend bool operator==(const mersenne_twister_engine& x,
                           const mersenne_twister_engine& y)
    {
        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;
        }
    }

    /**
     * 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));
        }
    }

    /// \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)

#endif // BOOST_RANDOM_MERSENNE_TWISTER_HPP