Chris@16: /* boost random/mersenne_twister.hpp header file
Chris@16:  *
Chris@16:  * Copyright Jens Maurer 2000-2001
Chris@16:  * Copyright Steven Watanabe 2010
Chris@16:  * Distributed under the Boost Software License, Version 1.0. (See
Chris@16:  * accompanying file LICENSE_1_0.txt or copy at
Chris@16:  * http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  *
Chris@16:  * See http://www.boost.org for most recent version including documentation.
Chris@16:  *
Chris@101:  * $Id$
Chris@16:  *
Chris@16:  * Revision history
Chris@101:  *  2013-10-14  fixed some warnings with Wshadow (mgaunard)
Chris@16:  *  2001-02-18  moved to individual header files
Chris@16:  */
Chris@16: 
Chris@16: #ifndef BOOST_RANDOM_MERSENNE_TWISTER_HPP
Chris@16: #define BOOST_RANDOM_MERSENNE_TWISTER_HPP
Chris@16: 
Chris@16: #include <iosfwd>
Chris@16: #include <istream>
Chris@16: #include <stdexcept>
Chris@16: #include <boost/config.hpp>
Chris@16: #include <boost/cstdint.hpp>
Chris@16: #include <boost/integer/integer_mask.hpp>
Chris@16: #include <boost/random/detail/config.hpp>
Chris@16: #include <boost/random/detail/ptr_helper.hpp>
Chris@16: #include <boost/random/detail/seed.hpp>
Chris@16: #include <boost/random/detail/seed_impl.hpp>
Chris@16: #include <boost/random/detail/generator_seed_seq.hpp>
Chris@101: #include <boost/random/detail/polynomial.hpp>
Chris@101: 
Chris@101: #include <boost/random/detail/disable_warnings.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace random {
Chris@16: 
Chris@16: /**
Chris@16:  * Instantiations of class template mersenne_twister_engine model a
Chris@16:  * \pseudo_random_number_generator. It uses the algorithm described in
Chris@16:  *
Chris@16:  *  @blockquote
Chris@16:  *  "Mersenne Twister: A 623-dimensionally equidistributed uniform
Chris@16:  *  pseudo-random number generator", Makoto Matsumoto and Takuji Nishimura,
Chris@16:  *  ACM Transactions on Modeling and Computer Simulation: Special Issue on
Chris@101:  *  Uniform Random Number Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
Chris@16:  *  @endblockquote
Chris@16:  *
Chris@16:  * @xmlnote
Chris@16:  * The boost variant has been implemented from scratch and does not
Chris@16:  * derive from or use mt19937.c provided on the above WWW site. However, it
Chris@16:  * was verified that both produce identical output.
Chris@16:  * @endxmlnote
Chris@16:  *
Chris@16:  * The seeding from an integer was changed in April 2005 to address a
Chris@16:  * <a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html">weakness</a>.
Chris@101:  *
Chris@16:  * The quality of the generator crucially depends on the choice of the
Chris@16:  * parameters.  User code should employ one of the sensibly parameterized
Chris@16:  * generators such as \mt19937 instead.
Chris@16:  *
Chris@16:  * The generator requires considerable amounts of memory for the storage of
Chris@16:  * its state array. For example, \mt11213b requires about 1408 bytes and
Chris@16:  * \mt19937 requires about 2496 bytes.
Chris@16:  */
Chris@16: template<class UIntType,
Chris@16:          std::size_t w, std::size_t n, std::size_t m, std::size_t r,
Chris@16:          UIntType a, std::size_t u, UIntType d, std::size_t s,
Chris@16:          UIntType b, std::size_t t,
Chris@16:          UIntType c, std::size_t l, UIntType f>
Chris@16: class mersenne_twister_engine
Chris@16: {
Chris@16: public:
Chris@16:     typedef UIntType result_type;
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, word_size = w);
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, state_size = n);
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, shift_size = m);
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, mask_bits = r);
Chris@16:     BOOST_STATIC_CONSTANT(UIntType, xor_mask = a);
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, tempering_u = u);
Chris@16:     BOOST_STATIC_CONSTANT(UIntType, tempering_d = d);
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, tempering_s = s);
Chris@16:     BOOST_STATIC_CONSTANT(UIntType, tempering_b = b);
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, tempering_t = t);
Chris@16:     BOOST_STATIC_CONSTANT(UIntType, tempering_c = c);
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, tempering_l = l);
Chris@16:     BOOST_STATIC_CONSTANT(UIntType, initialization_multiplier = f);
Chris@16:     BOOST_STATIC_CONSTANT(UIntType, default_seed = 5489u);
Chris@101: 
Chris@16:     // backwards compatibility
Chris@16:     BOOST_STATIC_CONSTANT(UIntType, parameter_a = a);
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, output_u = u);
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, output_s = s);
Chris@16:     BOOST_STATIC_CONSTANT(UIntType, output_b = b);
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, output_t = t);
Chris@16:     BOOST_STATIC_CONSTANT(UIntType, output_c = c);
Chris@16:     BOOST_STATIC_CONSTANT(std::size_t, output_l = l);
Chris@101: 
Chris@16:     // old Boost.Random concept requirements
Chris@16:     BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
Chris@16: 
Chris@16: 
Chris@16:     /**
Chris@16:      * Constructs a @c mersenne_twister_engine and calls @c seed().
Chris@16:      */
Chris@16:     mersenne_twister_engine() { seed(); }
Chris@16: 
Chris@16:     /**
Chris@16:      * Constructs a @c mersenne_twister_engine and calls @c seed(value).
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister_engine,
Chris@16:                                                UIntType, value)
Chris@16:     { seed(value); }
Chris@16:     template<class It> mersenne_twister_engine(It& first, It last)
Chris@16:     { seed(first,last); }
Chris@16: 
Chris@16:     /**
Chris@16:      * Constructs a mersenne_twister_engine and calls @c seed(gen).
Chris@16:      *
Chris@16:      * @xmlnote
Chris@16:      * The copy constructor will always be preferred over
Chris@16:      * the templated constructor.
Chris@16:      * @endxmlnote
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(mersenne_twister_engine,
Chris@16:                                              SeedSeq, seq)
Chris@16:     { seed(seq); }
Chris@16: 
Chris@16:     // compiler-generated copy ctor and assignment operator are fine
Chris@16: 
Chris@16:     /** Calls @c seed(default_seed). */
Chris@16:     void seed() { seed(default_seed); }
Chris@16: 
Chris@16:     /**
Chris@16:      * Sets the state x(0) to v mod 2w. Then, iteratively,
Chris@16:      * sets x(i) to
Chris@16:      * (i + f * (x(i-1) xor (x(i-1) rshift w-2))) mod 2<sup>w</sup>
Chris@16:      * for i = 1 .. n-1. x(n) is the first value to be returned by operator().
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister_engine, UIntType, value)
Chris@16:     {
Chris@101:         // New seeding algorithm from
Chris@16:         // http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html
Chris@16:         // In the previous versions, MSBs of the seed affected only MSBs of the
Chris@16:         // state x[].
Chris@16:         const UIntType mask = (max)();
Chris@16:         x[0] = value & mask;
Chris@16:         for (i = 1; i < n; i++) {
Chris@16:             // See Knuth "The Art of Computer Programming"
Chris@16:             // Vol. 2, 3rd ed., page 106
Chris@16:             x[i] = (f * (x[i-1] ^ (x[i-1] >> (w-2))) + i) & mask;
Chris@16:         }
Chris@101: 
Chris@101:         normalize_state();
Chris@16:     }
Chris@101: 
Chris@16:     /**
Chris@16:      * Seeds a mersenne_twister_engine using values produced by seq.generate().
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(mersenne_twister_engine, SeeqSeq, seq)
Chris@16:     {
Chris@16:         detail::seed_array_int<w>(seq, x);
Chris@16:         i = n;
Chris@16: 
Chris@101:         normalize_state();
Chris@16:     }
Chris@16: 
Chris@16:     /** Sets the state of the generator using values from an iterator range. */
Chris@16:     template<class It>
Chris@16:     void seed(It& first, It last)
Chris@16:     {
Chris@16:         detail::fill_array_int<w>(first, last, x);
Chris@16:         i = n;
Chris@16: 
Chris@101:         normalize_state();
Chris@16:     }
Chris@101: 
Chris@16:     /** Returns the smallest value that the generator can produce. */
Chris@16:     static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
Chris@16:     { return 0; }
Chris@16:     /** Returns the largest value that the generator can produce. */
Chris@16:     static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
Chris@16:     { return boost::low_bits_mask_t<w>::sig_bits; }
Chris@101: 
Chris@16:     /** Produces the next value of the generator. */
Chris@16:     result_type operator()();
Chris@16: 
Chris@16:     /** Fills a range with random values */
Chris@16:     template<class Iter>
Chris@16:     void generate(Iter first, Iter last)
Chris@16:     { detail::generate_from_int(*this, first, last); }
Chris@16: 
Chris@16:     /**
Chris@16:      * Advances the state of the generator by @c z steps.  Equivalent to
Chris@16:      *
Chris@16:      * @code
Chris@16:      * for(unsigned long long i = 0; i < z; ++i) {
Chris@16:      *     gen();
Chris@16:      * }
Chris@16:      * @endcode
Chris@16:      */
Chris@16:     void discard(boost::uintmax_t z)
Chris@16:     {
Chris@101: #ifndef BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD
Chris@101: #define BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD 10000000
Chris@101: #endif
Chris@101:         if(z > BOOST_RANDOM_MERSENNE_TWISTER_DISCARD_THRESHOLD) {
Chris@101:             discard_many(z);
Chris@101:         } else {
Chris@101:             for(boost::uintmax_t j = 0; j < z; ++j) {
Chris@101:                 (*this)();
Chris@101:             }
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@16: #ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
Chris@16:     /** Writes a mersenne_twister_engine to a @c std::ostream */
Chris@16:     template<class CharT, class Traits>
Chris@16:     friend std::basic_ostream<CharT,Traits>&
Chris@16:     operator<<(std::basic_ostream<CharT,Traits>& os,
Chris@16:                const mersenne_twister_engine& mt)
Chris@16:     {
Chris@16:         mt.print(os);
Chris@16:         return os;
Chris@16:     }
Chris@101: 
Chris@16:     /** Reads a mersenne_twister_engine from a @c std::istream */
Chris@16:     template<class CharT, class Traits>
Chris@16:     friend std::basic_istream<CharT,Traits>&
Chris@16:     operator>>(std::basic_istream<CharT,Traits>& is,
Chris@16:                mersenne_twister_engine& mt)
Chris@16:     {
Chris@16:         for(std::size_t j = 0; j < mt.state_size; ++j)
Chris@16:             is >> mt.x[j] >> std::ws;
Chris@16:         // MSVC (up to 7.1) and Borland (up to 5.64) don't handle the template
Chris@16:         // value parameter "n" available from the class template scope, so use
Chris@16:         // the static constant with the same value
Chris@16:         mt.i = mt.state_size;
Chris@16:         return is;
Chris@16:     }
Chris@16: #endif
Chris@16: 
Chris@16:     /**
Chris@16:      * Returns true if the two generators are in the same state,
Chris@16:      * and will thus produce identical sequences.
Chris@16:      */
Chris@101:     friend bool operator==(const mersenne_twister_engine& x_,
Chris@101:                            const mersenne_twister_engine& y_)
Chris@16:     {
Chris@101:         if(x_.i < y_.i) return x_.equal_imp(y_);
Chris@101:         else return y_.equal_imp(x_);
Chris@16:     }
Chris@101: 
Chris@16:     /**
Chris@16:      * Returns true if the two generators are in different states.
Chris@16:      */
Chris@101:     friend bool operator!=(const mersenne_twister_engine& x_,
Chris@101:                            const mersenne_twister_engine& y_)
Chris@101:     { return !(x_ == y_); }
Chris@16: 
Chris@16: private:
Chris@16:     /// \cond show_private
Chris@16: 
Chris@16:     void twist();
Chris@16: 
Chris@16:     /**
Chris@16:      * Does the work of operator==.  This is in a member function
Chris@16:      * for portability.  Some compilers, such as msvc 7.1 and
Chris@16:      * Sun CC 5.10 can't access template parameters or static
Chris@16:      * members of the class from inline friend functions.
Chris@16:      *
Chris@16:      * requires i <= other.i
Chris@16:      */
Chris@16:     bool equal_imp(const mersenne_twister_engine& other) const
Chris@16:     {
Chris@16:         UIntType back[n];
Chris@16:         std::size_t offset = other.i - i;
Chris@16:         for(std::size_t j = 0; j + offset < n; ++j)
Chris@16:             if(x[j] != other.x[j+offset])
Chris@16:                 return false;
Chris@16:         rewind(&back[n-1], offset);
Chris@16:         for(std::size_t j = 0; j < offset; ++j)
Chris@16:             if(back[j + n - offset] != other.x[j])
Chris@16:                 return false;
Chris@16:         return true;
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Does the work of operator<<.  This is in a member function
Chris@16:      * for portability.
Chris@16:      */
Chris@16:     template<class CharT, class Traits>
Chris@16:     void print(std::basic_ostream<CharT, Traits>& os) const
Chris@16:     {
Chris@16:         UIntType data[n];
Chris@16:         for(std::size_t j = 0; j < i; ++j) {
Chris@16:             data[j + n - i] = x[j];
Chris@16:         }
Chris@16:         if(i != n) {
Chris@16:             rewind(&data[n - i - 1], n - i);
Chris@16:         }
Chris@16:         os << data[0];
Chris@16:         for(std::size_t j = 1; j < n; ++j) {
Chris@16:             os << ' ' << data[j];
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Copies z elements of the state preceding x[0] into
Chris@16:      * the array whose last element is last.
Chris@16:      */
Chris@16:     void rewind(UIntType* last, std::size_t z) const
Chris@16:     {
Chris@16:         const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
Chris@16:         const UIntType lower_mask = ~upper_mask;
Chris@16:         UIntType y0 = x[m-1] ^ x[n-1];
Chris@16:         if(y0 & (static_cast<UIntType>(1) << (w-1))) {
Chris@16:             y0 = ((y0 ^ a) << 1) | 1;
Chris@16:         } else {
Chris@16:             y0 = y0 << 1;
Chris@16:         }
Chris@16:         for(std::size_t sz = 0; sz < z; ++sz) {
Chris@16:             UIntType y1 =
Chris@16:                 rewind_find(last, sz, m-1) ^ rewind_find(last, sz, n-1);
Chris@16:             if(y1 & (static_cast<UIntType>(1) << (w-1))) {
Chris@16:                 y1 = ((y1 ^ a) << 1) | 1;
Chris@16:             } else {
Chris@16:                 y1 = y1 << 1;
Chris@16:             }
Chris@16:             *(last - sz) = (y0 & upper_mask) | (y1 & lower_mask);
Chris@16:             y0 = y1;
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@101:      * Converts an arbitrary array into a valid generator state.
Chris@101:      * First we normalize x[0], so that it contains the same
Chris@101:      * value we would get by running the generator forwards
Chris@101:      * and then in reverse.  (The low order r bits are redundant).
Chris@101:      * Then, if the state consists of all zeros, we set the
Chris@101:      * high order bit of x[0] to 1.  This function only needs to
Chris@101:      * be called by seed, since the state transform preserves
Chris@101:      * this relationship.
Chris@101:      */
Chris@101:     void normalize_state()
Chris@101:     {
Chris@101:         const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
Chris@101:         const UIntType lower_mask = ~upper_mask;
Chris@101:         UIntType y0 = x[m-1] ^ x[n-1];
Chris@101:         if(y0 & (static_cast<UIntType>(1) << (w-1))) {
Chris@101:             y0 = ((y0 ^ a) << 1) | 1;
Chris@101:         } else {
Chris@101:             y0 = y0 << 1;
Chris@101:         }
Chris@101:         x[0] = (x[0] & upper_mask) | (y0 & lower_mask);
Chris@101: 
Chris@101:         // fix up the state if it's all zeroes.
Chris@101:         for(std::size_t j = 0; j < n; ++j) {
Chris@101:             if(x[j] != 0) return;
Chris@101:         }
Chris@101:         x[0] = static_cast<UIntType>(1) << (w-1);
Chris@101:     }
Chris@101: 
Chris@101:     /**
Chris@16:      * Given a pointer to the last element of the rewind array,
Chris@16:      * and the current size of the rewind array, finds an element
Chris@16:      * relative to the next available slot in the rewind array.
Chris@16:      */
Chris@16:     UIntType
Chris@16:     rewind_find(UIntType* last, std::size_t size, std::size_t j) const
Chris@16:     {
Chris@16:         std::size_t index = (j + n - size + n - 1) % n;
Chris@16:         if(index < n - size) {
Chris@16:             return x[index];
Chris@16:         } else {
Chris@16:             return *(last - (n - 1 - index));
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@101:     /**
Chris@101:      * Optimized algorithm for large jumps.
Chris@101:      *
Chris@101:      * Hiroshi Haramoto, Makoto Matsumoto, and Pierre L'Ecuyer. 2008.
Chris@101:      * A Fast Jump Ahead Algorithm for Linear Recurrences in a Polynomial
Chris@101:      * Space. In Proceedings of the 5th international conference on
Chris@101:      * Sequences and Their Applications (SETA '08).
Chris@101:      * DOI=10.1007/978-3-540-85912-3_26
Chris@101:      */
Chris@101:     void discard_many(boost::uintmax_t z)
Chris@101:     {
Chris@101:         // Compute the minimal polynomial, phi(t)
Chris@101:         // This depends only on the transition function,
Chris@101:         // which is constant.  The characteristic
Chris@101:         // polynomial is the same as the minimal
Chris@101:         // polynomial for a maximum period generator
Chris@101:         // (which should be all specializations of
Chris@101:         // mersenne_twister.)  Even if it weren't,
Chris@101:         // the characteristic polynomial is guaranteed
Chris@101:         // to be a multiple of the minimal polynomial,
Chris@101:         // which is good enough.
Chris@101:         detail::polynomial phi = get_characteristic_polynomial();
Chris@101: 
Chris@101:         // calculate g(t) = t^z % phi(t)
Chris@101:         detail::polynomial g = mod_pow_x(z, phi);
Chris@101: 
Chris@101:         // h(s_0, t) = \sum_{i=0}^{2k-1}o(s_i)t^{2k-i-1}
Chris@101:         detail::polynomial h;
Chris@101:         const std::size_t num_bits = w*n - r;
Chris@101:         for(std::size_t j = 0; j < num_bits * 2; ++j) {
Chris@101:             // Yes, we're advancing the generator state
Chris@101:             // here, but it doesn't matter because
Chris@101:             // we're going to overwrite it completely
Chris@101:             // in reconstruct_state.
Chris@101:             if(i >= n) twist();
Chris@101:             h[2*num_bits - j - 1] = x[i++] & UIntType(1);
Chris@101:         }
Chris@101:         // g(t)h(s_0, t)
Chris@101:         detail::polynomial gh = g * h;
Chris@101:         detail::polynomial result;
Chris@101:         for(std::size_t j = 0; j <= num_bits; ++j) {
Chris@101:             result[j] = gh[2*num_bits - j - 1];
Chris@101:         }
Chris@101:         reconstruct_state(result);
Chris@101:     }
Chris@101:     static detail::polynomial get_characteristic_polynomial()
Chris@101:     {
Chris@101:         const std::size_t num_bits = w*n - r;
Chris@101:         detail::polynomial helper;
Chris@101:         helper[num_bits - 1] = 1;
Chris@101:         mersenne_twister_engine tmp;
Chris@101:         tmp.reconstruct_state(helper);
Chris@101:         // Skip the first num_bits elements, since we
Chris@101:         // already know what they are.
Chris@101:         for(std::size_t j = 0; j < num_bits; ++j) {
Chris@101:             if(tmp.i >= n) tmp.twist();
Chris@101:             if(j == num_bits - 1)
Chris@101:                 assert((tmp.x[tmp.i] & 1) == 1);
Chris@101:             else
Chris@101:                 assert((tmp.x[tmp.i] & 1) == 0);
Chris@101:             ++tmp.i;
Chris@101:         }
Chris@101:         detail::polynomial phi;
Chris@101:         phi[num_bits] = 1;
Chris@101:         detail::polynomial next_bits = tmp.as_polynomial(num_bits);
Chris@101:         for(std::size_t j = 0; j < num_bits; ++j) {
Chris@101:             int val = next_bits[j] ^ phi[num_bits-j-1];
Chris@101:             phi[num_bits-j-1] = val;
Chris@101:             if(val) {
Chris@101:                 for(std::size_t k = j + 1; k < num_bits; ++k) {
Chris@101:                     phi[num_bits-k-1] ^= next_bits[k-j-1];
Chris@101:                 }
Chris@101:             }
Chris@101:         }
Chris@101:         return phi;
Chris@101:     }
Chris@101:     detail::polynomial as_polynomial(std::size_t size) {
Chris@101:         detail::polynomial result;
Chris@101:         for(std::size_t j = 0; j < size; ++j) {
Chris@101:             if(i >= n) twist();
Chris@101:             result[j] = x[i++] & UIntType(1);
Chris@101:         }
Chris@101:         return result;
Chris@101:     }
Chris@101:     void reconstruct_state(const detail::polynomial& p)
Chris@101:     {
Chris@101:         const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
Chris@101:         const UIntType lower_mask = ~upper_mask;
Chris@101:         const std::size_t num_bits = w*n - r;
Chris@101:         for(std::size_t j = num_bits - n + 1; j <= num_bits; ++j)
Chris@101:             x[j % n] = p[j];
Chris@101: 
Chris@101:         UIntType y0 = 0;
Chris@101:         for(std::size_t j = num_bits + 1; j >= n - 1; --j) {
Chris@101:             UIntType y1 = x[j % n] ^ x[(j + m) % n];
Chris@101:             if(p[j - n + 1])
Chris@101:                 y1 = (y1 ^ a) << UIntType(1) | UIntType(1);
Chris@101:             else
Chris@101:                 y1 = y1 << UIntType(1);
Chris@101:             x[(j + 1) % n] = (y0 & upper_mask) | (y1 & lower_mask);
Chris@101:             y0 = y1;
Chris@101:         }
Chris@101:         i = 0;
Chris@101:     }
Chris@101: 
Chris@16:     /// \endcond
Chris@16: 
Chris@16:     // state representation: next output is o(x(i))
Chris@16:     //   x[0]  ... x[k] x[k+1] ... x[n-1]   represents
Chris@16:     //  x(i-k) ... x(i) x(i+1) ... x(i-k+n-1)
Chris@16: 
Chris@101:     UIntType x[n];
Chris@16:     std::size_t i;
Chris@16: };
Chris@16: 
Chris@16: /// \cond show_private
Chris@16: 
Chris@16: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
Chris@16: //  A definition is required even for integral static constants
Chris@16: #define BOOST_RANDOM_MT_DEFINE_CONSTANT(type, name)                         \
Chris@16: template<class UIntType, std::size_t w, std::size_t n, std::size_t m,       \
Chris@16:     std::size_t r, UIntType a, std::size_t u, UIntType d, std::size_t s,    \
Chris@16:     UIntType b, std::size_t t, UIntType c, std::size_t l, UIntType f>       \
Chris@16: const type mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::name
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, word_size);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, state_size);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, shift_size);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, mask_bits);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, xor_mask);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_u);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_d);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_s);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_b);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_t);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_c);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_l);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, initialization_multiplier);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, default_seed);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, parameter_a);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_u );
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_s);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, output_b);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_t);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, output_c);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_l);
Chris@16: BOOST_RANDOM_MT_DEFINE_CONSTANT(bool, has_fixed_range);
Chris@16: #undef BOOST_RANDOM_MT_DEFINE_CONSTANT
Chris@16: #endif
Chris@16: 
Chris@16: template<class UIntType,
Chris@16:          std::size_t w, std::size_t n, std::size_t m, std::size_t r,
Chris@16:          UIntType a, std::size_t u, UIntType d, std::size_t s,
Chris@16:          UIntType b, std::size_t t,
Chris@16:          UIntType c, std::size_t l, UIntType f>
Chris@16: void
Chris@16: mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::twist()
Chris@16: {
Chris@16:     const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
Chris@16:     const UIntType lower_mask = ~upper_mask;
Chris@16: 
Chris@16:     const std::size_t unroll_factor = 6;
Chris@16:     const std::size_t unroll_extra1 = (n-m) % unroll_factor;
Chris@16:     const std::size_t unroll_extra2 = (m-1) % unroll_factor;
Chris@16: 
Chris@16:     // split loop to avoid costly modulo operations
Chris@16:     {  // extra scope for MSVC brokenness w.r.t. for scope
Chris@16:         for(std::size_t j = 0; j < n-m-unroll_extra1; j++) {
Chris@16:             UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
Chris@16:             x[j] = x[j+m] ^ (y >> 1) ^ ((x[j+1]&1) * a);
Chris@16:         }
Chris@16:     }
Chris@16:     {
Chris@16:         for(std::size_t j = n-m-unroll_extra1; j < n-m; j++) {
Chris@16:             UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
Chris@16:             x[j] = x[j+m] ^ (y >> 1) ^ ((x[j+1]&1) * a);
Chris@16:         }
Chris@16:     }
Chris@16:     {
Chris@16:         for(std::size_t j = n-m; j < n-1-unroll_extra2; j++) {
Chris@16:             UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
Chris@16:             x[j] = x[j-(n-m)] ^ (y >> 1) ^ ((x[j+1]&1) * a);
Chris@16:         }
Chris@16:     }
Chris@16:     {
Chris@16:         for(std::size_t j = n-1-unroll_extra2; j < n-1; j++) {
Chris@16:             UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
Chris@16:             x[j] = x[j-(n-m)] ^ (y >> 1) ^ ((x[j+1]&1) * a);
Chris@16:         }
Chris@16:     }
Chris@16:     // last iteration
Chris@16:     UIntType y = (x[n-1] & upper_mask) | (x[0] & lower_mask);
Chris@16:     x[n-1] = x[m-1] ^ (y >> 1) ^ ((x[0]&1) * a);
Chris@16:     i = 0;
Chris@16: }
Chris@16: /// \endcond
Chris@16: 
Chris@16: template<class UIntType,
Chris@16:          std::size_t w, std::size_t n, std::size_t m, std::size_t r,
Chris@16:          UIntType a, std::size_t u, UIntType d, std::size_t s,
Chris@16:          UIntType b, std::size_t t,
Chris@16:          UIntType c, std::size_t l, UIntType f>
Chris@16: inline typename
Chris@16: mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::result_type
Chris@16: mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::operator()()
Chris@16: {
Chris@16:     if(i == n)
Chris@16:         twist();
Chris@16:     // Step 4
Chris@16:     UIntType z = x[i];
Chris@16:     ++i;
Chris@16:     z ^= ((z >> u) & d);
Chris@16:     z ^= ((z << s) & b);
Chris@16:     z ^= ((z << t) & c);
Chris@16:     z ^= (z >> l);
Chris@16:     return z;
Chris@16: }
Chris@16: 
Chris@16: /**
Chris@16:  * The specializations \mt11213b and \mt19937 are from
Chris@16:  *
Chris@16:  *  @blockquote
Chris@16:  *  "Mersenne Twister: A 623-dimensionally equidistributed
Chris@16:  *  uniform pseudo-random number generator", Makoto Matsumoto
Chris@16:  *  and Takuji Nishimura, ACM Transactions on Modeling and
Chris@16:  *  Computer Simulation: Special Issue on Uniform Random Number
Chris@101:  *  Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
Chris@16:  *  @endblockquote
Chris@16:  */
Chris@16: typedef mersenne_twister_engine<uint32_t,32,351,175,19,0xccab8ee7,
Chris@16:     11,0xffffffff,7,0x31b6ab00,15,0xffe50000,17,1812433253> mt11213b;
Chris@16: 
Chris@16: /**
Chris@16:  * The specializations \mt11213b and \mt19937 are from
Chris@16:  *
Chris@16:  *  @blockquote
Chris@16:  *  "Mersenne Twister: A 623-dimensionally equidistributed
Chris@16:  *  uniform pseudo-random number generator", Makoto Matsumoto
Chris@16:  *  and Takuji Nishimura, ACM Transactions on Modeling and
Chris@16:  *  Computer Simulation: Special Issue on Uniform Random Number
Chris@101:  *  Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
Chris@16:  *  @endblockquote
Chris@16:  */
Chris@16: typedef mersenne_twister_engine<uint32_t,32,624,397,31,0x9908b0df,
Chris@16:     11,0xffffffff,7,0x9d2c5680,15,0xefc60000,18,1812433253> mt19937;
Chris@16: 
Chris@16: #if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T)
Chris@16: typedef mersenne_twister_engine<uint64_t,64,312,156,31,
Chris@16:     UINT64_C(0xb5026f5aa96619e9),29,UINT64_C(0x5555555555555555),17,
Chris@16:     UINT64_C(0x71d67fffeda60000),37,UINT64_C(0xfff7eee000000000),43,
Chris@16:     UINT64_C(6364136223846793005)> mt19937_64;
Chris@16: #endif
Chris@16: 
Chris@16: /// \cond show_deprecated
Chris@16: 
Chris@16: template<class UIntType,
Chris@16:          int w, int n, int m, int r,
Chris@16:          UIntType a, int u, std::size_t s,
Chris@16:          UIntType b, int t,
Chris@16:          UIntType c, int l, UIntType v>
Chris@16: class mersenne_twister :
Chris@16:     public mersenne_twister_engine<UIntType,
Chris@16:         w, n, m, r, a, u, ~(UIntType)0, s, b, t, c, l, 1812433253>
Chris@16: {
Chris@16:     typedef mersenne_twister_engine<UIntType,
Chris@16:         w, n, m, r, a, u, ~(UIntType)0, s, b, t, c, l, 1812433253> base_type;
Chris@16: public:
Chris@16:     mersenne_twister() {}
Chris@16:     BOOST_RANDOM_DETAIL_GENERATOR_CONSTRUCTOR(mersenne_twister, Gen, gen)
Chris@16:     { seed(gen); }
Chris@16:     BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister, UIntType, val)
Chris@16:     { seed(val); }
Chris@16:     template<class It>
Chris@16:     mersenne_twister(It& first, It last) : base_type(first, last) {}
Chris@16:     void seed() { base_type::seed(); }
Chris@16:     BOOST_RANDOM_DETAIL_GENERATOR_SEED(mersenne_twister, Gen, gen)
Chris@16:     {
Chris@16:         detail::generator_seed_seq<Gen> seq(gen);
Chris@16:         base_type::seed(seq);
Chris@16:     }
Chris@16:     BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister, UIntType, val)
Chris@16:     { base_type::seed(val); }
Chris@16:     template<class It>
Chris@16:     void seed(It& first, It last) { base_type::seed(first, last); }
Chris@16: };
Chris@16: 
Chris@16: /// \endcond
Chris@16: 
Chris@16: } // namespace random
Chris@16: 
Chris@16: using random::mt11213b;
Chris@16: using random::mt19937;
Chris@16: using random::mt19937_64;
Chris@16: 
Chris@16: } // namespace boost
Chris@16: 
Chris@16: BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt11213b)
Chris@16: BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937)
Chris@16: BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937_64)
Chris@16: 
Chris@101: #include <boost/random/detail/enable_warnings.hpp>
Chris@101: 
Chris@16: #endif // BOOST_RANDOM_MERSENNE_TWISTER_HPP