bool last = rest <= std::numeric_limits<Word>::digits>

               bool last = (rest <= std::numeric_limits<Word>::digits)>

   }

     /// \ingroup misc

     ///

     /// \brief Mersenne Twister random number generator

     ///

     /// The Mersenne Twister is a twisted generalized feedback

     /// shift-register generator of Matsumoto and Nishimura. The period

     /// of this generator is \f$ 2^{19937} - 1 \f$ and it is

     /// equi-distributed in 623 dimensions for 32-bit numbers. The time

     /// performance of this generator is comparable to the commonly used

     /// generators.

     ///

     /// This is a template version implementation both 32-bit and

     /// 64-bit architecture optimized versions. The generators differ

     /// sligthly in the initialization and generation phase so they

     /// produce two completly different sequences.

     ///

     /// \alert Do not use this class directly, but instead one of \ref

     /// Random, \ref Random32 or \ref Random64.

     ///

     /// The generator gives back random numbers of serveral types. To

     /// get a random number from a range of a floating point type you

     /// can use one form of the \c operator() or the \c real() member

     /// function. If you want to get random number from the {0, 1, ...,

     /// n-1} integer range use the \c operator[] or the \c integer()

     /// method. And to get random number from the whole range of an

     /// integer type you can use the argumentless \c integer() or \c

     /// uinteger() functions. After all you can get random bool with

     /// equal chance of true and false or given probability of true

     /// result with the \c boolean() member functions.

     ///

     ///\code

     /// // The commented code is identical to the other

     /// double a = rnd();                     // [0.0, 1.0)

     /// // double a = rnd.real();             // [0.0, 1.0)

     /// double b = rnd(100.0);                // [0.0, 100.0)

     /// // double b = rnd.real(100.0);        // [0.0, 100.0)

     /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)

     /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)

     /// int d = rnd[100000];                  // 0..99999

     /// // int d = rnd.integer(100000);       // 0..99999

     /// 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.

     ///

     /// \sa \ref Random, \ref Random32 or \ref Random64.

     ///

     template<class Word>

     class Random {

     private:

       _random_bits::RandomCore<Word> core;

       _random_bits::BoolProducer<Word> bool_producer;

     public:

       ///\name Initialization

       ///

       /// @{

       /// \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);

       }

       /// \brief Copy constructor

       ///

       /// Copy constructor. The generated sequence will be identical to

       /// the other sequence. It can be used to save the current state

       /// of the generator and later use it to generate the same

       /// sequence.

       Random(const Random& other) {

         core.copyState(other.core);

       }

       /// \brief Assign operator

       ///

       /// Assign operator. The generated sequence will be identical to

       /// the other sequence. It can be used to save the current state

       /// of the generator and later use it to generate the same

       /// sequence.

       Random& operator=(const Random& other) {

         if (&other != this) {

           core.copyState(other.core);

         }

         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 Seeding from file or from process id and time

       ///

       /// By default, this function calls the \c seedFromFile() member

       /// function with the <tt>/dev/urandom</tt> file. If it does not success,

       /// it uses the \c seedFromTime().

       /// \return Currently always \c true.

       bool seed() {

 #ifndef LEMON_WIN32

         if (seedFromFile("/dev/urandom", 0)) return true;

 #endif

         if (seedFromTime()) return true;

         return false;

       }

       /// \brief Seeding from file

       ///

       /// Seeding the random sequence from file. The linux kernel has two

       /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which

       /// could give good seed values for pseudo random generators (The

       /// difference between two devices is that the <tt>random</tt> may

       /// block the reading operation while the kernel can give good

       /// source of randomness, while the <tt>urandom</tt> does not

       /// block the input, but it could give back bytes with worse

       /// entropy).

       /// \param file The source file

       /// \param offset The offset, from the file read.

       /// \return \c true when the seeding successes.

 #ifndef LEMON_WIN32

       bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)

 #else

         bool seedFromFile(const std::string& file = "", int offset = 0)

 #endif

       {

         std::ifstream rs(file.c_str());

         const int size = 4;

         Word buf[size];

         if (offset != 0 && !rs.seekg(offset)) return false;

         if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;

         seed(buf, buf + size);

         return true;

       }

       /// \brief Seding from process id and time

       ///

       /// Seding from process id and time. This function uses the

       /// current process id and the current time for initialize the

       /// random sequence.

       /// \return Currently always \c true.

       bool seedFromTime() {

 #ifndef LEMON_WIN32

         timeval tv;

         gettimeofday(&tv, 0);

         seed(getpid() + tv.tv_sec + tv.tv_usec);

 #else

         seed(bits::getWinRndSeed());

 #endif

         return true;

       }

       /// @}

       ///\name Uniform Distributions

       ///

       /// @{

       /// \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 from the range [0, 1)

       ///

       /// It returns a random double from the range [0, 1).

       double operator()() {

         return real<double>();

       }

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

       ///

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

       double operator()(double b) {

         return real<double>() * b;

       }

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

       ///

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

       double operator()(double a, double b) {

         return real<double>() * (b - a) + a;

       }

       /// \brief Returns a random integer from a range

       ///

       /// It returns a random integer from the range {0, 1, ..., b - 1}.

       template <typename Number>

       Number integer(Number b) {

         return _random_bits::Mapping<Number, Word>::map(core, b);

       }

       /// \brief Returns a random integer from a range

       ///

       /// It returns a random integer from the range {a, a + 1, ..., b - 1}.

       template <typename Number>

       Number integer(Number a, Number b) {

         return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;

       }

       /// \brief Returns a random integer from a range

       ///

       /// It returns a random integer from the range {0, 1, ..., b - 1}.

       template <typename Number>

       Number operator[](Number b) {

         return _random_bits::Mapping<Number, Word>::map(core, b);

       }

       /// \brief Returns a random non-negative integer

       ///

       /// It returns a random non-negative integer uniformly from the

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

       /// type of this function is <tt>unsigned int</tt>.

       template <typename Number>

       Number uinteger() {

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

       }

       unsigned int uinteger() {

         return uinteger<unsigned int>();

       }

       /// \brief Returns a random integer

       ///

       /// 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 with given probability of true result.

       ///

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

       bool boolean(double p) {

         return operator()() < p;

       }

       /// Standard normal (Gauss) distribution

       /// Standard normal (Gauss) distribution.

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

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

       double gauss()

       {

         double V1,V2,S;

         do {

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

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

           S=V1*V1+V2*V2;

         } while(S>=1);

         return std::sqrt(-2*std::log(S)/S)*V1;

       }

       /// Normal (Gauss) distribution with given mean and standard deviation

       /// Normal (Gauss) distribution with given mean and standard deviation.

       /// \sa gauss()

       double gauss(double mean,double std_dev)

       {

         return gauss()*std_dev+mean;

       }

       /// Lognormal distribution

       /// Lognormal distribution. The parameters are the mean and the standard

       /// deviation of <tt>exp(X)</tt>.

       ///

       double lognormal(double n_mean,double n_std_dev)

       {

         return std::exp(gauss(n_mean,n_std_dev));

       }

       /// Lognormal distribution

       /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of

       /// the mean and the standard deviation of <tt>exp(X)</tt>.

       ///

       double lognormal(const std::pair<double,double> &params)

       {

         return std::exp(gauss(params.first,params.second));

       }

       /// Compute the lognormal parameters from mean and standard deviation

       /// This function computes the lognormal parameters from mean and

       /// standard deviation. The return value can direcly be passed to

       /// lognormal().

       std::pair<double,double> lognormalParamsFromMD(double mean,

                                                      double std_dev)

       {

         double fr=std_dev/mean;

         fr*=fr;

         double lg=std::log(1+fr);

         return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg));

       }

       /// Lognormal distribution with given mean and standard deviation

       /// Lognormal distribution with given mean and standard deviation.

       ///

       double lognormalMD(double mean,double std_dev)

       {

         return lognormal(lognormalParamsFromMD(mean,std_dev));

       }

       /// Exponential distribution with given mean

       /// This function generates an exponential distribution random number

       /// with mean <tt>1/lambda</tt>.

       ///

       double exponential(double lambda=1.0)

       {

         return -std::log(1.0-real<double>())/lambda;

       }

       /// Gamma distribution with given integer shape

       /// This function generates a gamma distribution random number.

       ///

       ///\param k shape parameter (<tt>k>0</tt> integer)

       double gamma(int k)

       {

         double s = 0;

         for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());

         return s;

       }

       /// Gamma distribution with given shape and scale parameter

       /// This function generates a gamma distribution random number.

       ///

       ///\param k shape parameter (<tt>k>0</tt>)

       ///\param theta scale parameter

       ///

       double gamma(double k,double theta=1.0)

       {

         double xi,nu;

         const double delta = k-std::floor(k);

         const double v0=E/(E-delta);

         do {

           double V0=1.0-real<double>();

           double V1=1.0-real<double>();

           double V2=1.0-real<double>();

           if(V2<=v0)

             {

               xi=std::pow(V1,1.0/delta);

               nu=V0*std::pow(xi,delta-1.0);

             }

           else

             {

               xi=1.0-std::log(V1);

               nu=V0*std::exp(-xi);

             }

         } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));

         return theta*(xi+gamma(int(std::floor(k))));

       }

       /// Weibull distribution

       /// This function generates a Weibull distribution random number.

       ///

       ///\param k shape parameter (<tt>k>0</tt>)

       ///\param lambda scale parameter (<tt>lambda>0</tt>)

       ///

       double weibull(double k,double lambda)

       {

         return lambda*pow(-std::log(1.0-real<double>()),1.0/k);

       }

       /// Pareto distribution

       /// This function generates a Pareto distribution random number.

       ///

       ///\param k shape parameter (<tt>k>0</tt>)

       ///\param x_min location parameter (<tt>x_min>0</tt>)

       ///

       double pareto(double k,double x_min)

       {

         return exponential(gamma(k,1.0/x_min))+x_min;

       }

       /// Poisson distribution

       /// This function generates a Poisson distribution random number with

       /// parameter \c lambda.

       ///

       /// The probability mass function of this distribusion is

       /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]

       /// \note The algorithm is taken from the book of Donald E. Knuth titled

       /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the

       /// return value.

       int poisson(double lambda)

       {

         const double l = std::exp(-lambda);

         int k=0;

         double p = 1.0;

         do {

           k++;

           p*=real<double>();

         } while (p>=l);

         return k-1;

       }

       ///@}

       ///\name Two Dimensional Distributions

       ///

       ///@{

       /// Uniform distribution on the full unit circle

       /// Uniform distribution on the full unit circle.

       ///

       dim2::Point<double> disc()

       {

         double V1,V2;

         do {

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

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

         } while(V1*V1+V2*V2>=1);

         return dim2::Point<double>(V1,V2);

       }

       /// A kind of two dimensional normal (Gauss) distribution

       /// This function provides a turning symmetric two-dimensional distribution.

       /// Both coordinates are of standard normal distribution, but they are not

       /// independent.

       ///

       /// \note The coordinates are the two random variables provided by

       /// the Box-Muller method.

       dim2::Point<double> gauss2()

       {

         double V1,V2,S;

         do {

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

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

           S=V1*V1+V2*V2;

         } while(S>=1);

         double W=std::sqrt(-2*std::log(S)/S);

         return dim2::Point<double>(W*V1,W*V2);

       }

       /// A kind of two dimensional exponential distribution

       /// This function provides a turning symmetric two-dimensional distribution.

       /// The x-coordinate is of conditionally exponential distribution

       /// with the condition that x is positive and y=0. If x is negative and

       /// y=0 then, -x is of exponential distribution. The same is true for the

       /// y-coordinate.

       dim2::Point<double> exponential2()

       {

         double V1,V2,S;

         do {

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

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

           S=V1*V1+V2*V2;

         } while(S>=1);

         double W=-std::log(S)/S;

         return dim2::Point<double>(W*V1,W*V2);

       }

       ///@}

     };

   };

   /// The Mersenne Twister is a twisted generalized feedback

   /// This class implements either the 32 bit or the 64 bit version of

   /// shift-register generator of Matsumoto and Nishimura. The period

   /// the Mersenne Twister random number generator algorithm

   /// of this generator is \f$ 2^{19937} - 1 \f$ and it is

   /// depending the the system architecture.

   /// equi-distributed in 623 dimensions for 32-bit numbers. The time

   /// 

   /// performance of this generator is comparable to the commonly used

   /// For the API description, see its base class \ref

   /// generators.

   /// _random_bits::Random

   /// This implementation is specialized for both 32-bit and 64-bit

   /// \sa \ref _random_bits::Random

   /// architectures. The generators differ sligthly in the

   typedef _random_bits::Random<unsigned long> Random;

   /// initialization and generation phase so they produce two

   /// \ingroup misc

   /// completly different sequences.

   /// The generator gives back random numbers of serveral types. To

   /// \brief Mersenne Twister random number generator (32 bit version)

   /// get a random number from a range of a floating point type you

   /// can use one form of the \c operator() or the \c real() member

   /// function. If you want to get random number from the {0, 1, ...,

   /// n-1} integer range use the \c operator[] or the \c integer()

   /// method. And to get random number from the whole range of an

   /// integer type you can use the argumentless \c integer() or \c

   /// uinteger() functions. After all you can get random bool with

   /// equal chance of true and false or given probability of true

   /// result with the \c boolean() member functions.

   ///\code

   /// This class implements the 32 bit version of the Mersenne Twister

   /// // The commented code is identical to the other

   /// random number generator algorithm. It is recommended to be used

   /// double a = rnd();                     // [0.0, 1.0)

   /// when someone wants to make sure that the \e same pseudo random

   /// // double a = rnd.real();             // [0.0, 1.0)

   /// sequence will be generated on every platfrom.

   /// double b = rnd(100.0);                // [0.0, 100.0)

   /// // double b = rnd.real(100.0);        // [0.0, 100.0)

   /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)

   /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)

   /// int d = rnd[100000];                  // 0..99999

   /// // int d = rnd.integer(100000);       // 0..99999

   /// 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

   /// For the API description, see its base class \ref

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

   /// _random_bits::Random

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

   ///

   /// random numbers.

   /// \sa \ref _random_bits::Random

   class Random {

   private:

   typedef _random_bits::Random<unsigned int> Random32;

   /// \ingroup misc

     // Architecture word

   ///

     typedef unsigned long Word;

   /// \brief Mersenne Twister random number generator (64 bit version)

   ///

     _random_bits::RandomCore<Word> core;

   /// This class implements the 64 bit version of the Mersenne Twister

     _random_bits::BoolProducer<Word> bool_producer;

   /// random number generator algorithm. (Even though it will run

   /// on 32 bit architectures, too.) It is recommended to ber used when

   /// someone wants to make sure that the \e same pseudo random sequence

   public:

   /// will be generated on every platfrom.

   ///

     ///\name Initialization

   /// For the API description, see its base class \ref

     ///

   /// _random_bits::Random

     /// @{

   ///

   /// \sa \ref _random_bits::Random

     /// \brief Default constructor

   typedef _random_bits::Random<unsigned long long> Random64;

     ///

     /// Constructor with constant seeding.

     Random() { core.initState(); }

   extern Random rnd;

     /// \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);

     }

     /// \brief Copy constructor

     ///

     /// Copy constructor. The generated sequence will be identical to

     /// the other sequence. It can be used to save the current state

     /// of the generator and later use it to generate the same

     /// sequence.

     Random(const Random& other) {

       core.copyState(other.core);

     }

     /// \brief Assign operator

     ///

     /// Assign operator. The generated sequence will be identical to

     /// the other sequence. It can be used to save the current state

     /// of the generator and later use it to generate the same

     /// sequence.

     Random& operator=(const Random& other) {

       if (&other != this) {

         core.copyState(other.core);

       }

       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 Seeding from file or from process id and time

     ///

     /// By default, this function calls the \c seedFromFile() member

     /// function with the <tt>/dev/urandom</tt> file. If it does not success,

     /// it uses the \c seedFromTime().

     /// \return Currently always \c true.

     bool seed() {

 #ifndef LEMON_WIN32

       if (seedFromFile("/dev/urandom", 0)) return true;