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 * Any feedback is very welcome.

 * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html

 * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)

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#ifndef LEMON_RANDOM_H

#define LEMON_RANDOM_H

#include <algorithm>

#include <iterator>

#include <vector>

#include <limits>

#include <lemon/math.h>

#include <lemon/dim2.h>

///\ingroup misc

///\file

///\brief Mersenne Twister random number generator

namespace lemon {

  namespace _random_bits {

    template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>

    struct RandomTraits {};

    template <typename _Word>

    struct RandomTraits<_Word, 32> {

      typedef _Word Word;

      static const int bits = 32;

      static const int length = 624;

      static const int shift = 397;

      static const Word mul = 0x6c078965u;

      static const Word arrayInit = 0x012BD6AAu;

      static const Word arrayMul1 = 0x0019660Du;

      static const Word arrayMul2 = 0x5D588B65u;

  /// int e = rnd[6] + 1;                   // 1..6

  /// // int e = rnd.integer(1, 1 + 6);     // 1..6

  /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1

  /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1

  /// bool g = rnd.boolean();               // P(g = true) = 0.5

  /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8

  ///\endcode

  ///

  /// LEMON provides a global instance of the random number

  /// generator which name is \ref lemon::rnd "rnd". Usually it is a

  /// good programming convenience to use this global generator to get

  /// random numbers.

  class Random {

  private:

    // Architecture word

    typedef unsigned long Word;

    _random_bits::RandomCore<Word> core;

    _random_bits::BoolProducer<Word> bool_producer;

  public:

    /// \brief Default constructor

    ///

    /// Constructor with constant seeding.

    Random() { core.initState(); }

    /// \brief Constructor with seed

    ///

    /// Constructor with seed. The current number type will be converted

    /// to the architecture word type.

    template <typename Number>

    Random(Number seed) { 

      _random_bits::Initializer<Number, Word>::init(core, seed);

    }

    /// \brief Constructor with array seeding

    ///

    /// Constructor with array seeding. The given range should contain

    /// any number type and the numbers will be converted to the

    /// architecture word type.

    template <typename Iterator>

    Random(Iterator begin, Iterator end) { 

      typedef typename std::iterator_traits<Iterator>::value_type Number;

      _random_bits::Initializer<Number, Word>::init(core, begin, end);

    }

      }

      return *this;

    }

    /// \brief Seeding random sequence

    ///

    /// Seeding the random sequence. The current number type will be

    /// converted to the architecture word type.

    template <typename Number>

    void seed(Number seed) { 

      _random_bits::Initializer<Number, Word>::init(core, seed);

    }

    /// \brief Seeding random sequence

    ///

    /// Seeding the random sequence. The given range should contain

    /// any number type and the numbers will be converted to the

    /// architecture word type.

    template <typename Iterator>

    void seed(Iterator begin, Iterator end) { 

      typedef typename std::iterator_traits<Iterator>::value_type Number;

      _random_bits::Initializer<Number, Word>::init(core, begin, end);

    }

    /// \brief Returns a random real number from the range [0, 1)

    ///

    /// It returns a random real number from the range [0, 1). The

    /// default Number type is \c double.

    template <typename Number>

    Number real() {

      return _random_bits::RealConversion<Number, Word>::convert(core);

    }

    double real() {

      return real<double>();

    }

    /// \brief Returns a random real number the range [0, b)

    ///

    /// It returns a random real number from the range [0, b).

    template <typename Number>

    Number real(Number b) { 

      return real<Number>() * b; 

    }

    /// \brief Returns a random real number from the range [a, b)

    ///

    /// It returns a random real number from the range [a, b).

    ///

    /// It returns a random integer uniformly from the whole range of

    /// the current \c Number type. The default result type of this

    /// function is \c int.

    template <typename Number>

    Number integer() {

      static const int nb = std::numeric_limits<Number>::digits + 

        (std::numeric_limits<Number>::is_signed ? 1 : 0);

      return _random_bits::IntConversion<Number, Word, nb>::convert(core);

    }

    int integer() {

      return integer<int>();

    }

    /// \brief Returns a random bool

    ///

    /// It returns a random bool. The generator holds a buffer for

    /// random bits. Every time when it become empty the generator makes

    /// a new random word and fill the buffer up.

    bool boolean() {

      return bool_producer.convert(core);

    }

    ///\name Non-uniform distributions

    ///

    ///@{

    /// \brief Returns a random bool

    ///

    /// It returns a random bool with given probability of true result.

    bool boolean(double p) {

      return operator()() < p;

    }

    /// Standard Gauss distribution

    /// Standard Gauss distribution.

    /// \note The Cartesian form of the Box-Muller

    /// transformation is used to generate a random normal distribution.

    /// \todo Consider using the "ziggurat" method instead.

    double gauss() 

    {

      double V1,V2,S;

      do {

	V1=2*real<double>()-1;

	V2=2*real<double>()-1;