/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2007

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 /*

  * This file contains the reimplemented version of the Mersenne Twister

  * Generator of Matsumoto and Nishimura.

  *

  * See the appropriate copyright notice below.

  * 

  * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,

  * All rights reserved.                          

  *

  * Redistribution and use in source and binary forms, with or without

  * modification, are permitted provided that the following conditions

  * are met:

  *

  * 1. Redistributions of source code must retain the above copyright

  *    notice, this list of conditions and the following disclaimer.

  *

  * 2. Redistributions in binary form must reproduce the above copyright

  *    notice, this list of conditions and the following disclaimer in the

  *    documentation and/or other materials provided with the distribution.

  *

  * 3. The names of its contributors may not be used to endorse or promote 

  *    products derived from this software without specific prior written 

  *    permission.

  *

  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS

  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT

  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS

  * FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE

  * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,

  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES

  * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR

  * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)

  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,

  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)

  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED

  * OF THE POSSIBILITY OF SUCH DAMAGE.

  *

  *

  * 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)

  */

 #ifndef LEMON_RANDOM_H

 #define LEMON_RANDOM_H

 #include <algorithm>

 #include <iterator>

 #include <vector>

 #include <ctime>

 #include <cmath>

 #include <lemon/dim2.h>

 ///\ingroup misc

 ///\file

 ///\brief Mersenne Twister random number generator

 ///

 ///\author Balazs Dezso

 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;

       static const Word mask = 0x9908B0DFu;

       static const Word loMask = (1u << 31) - 1;

       static const Word hiMask = ~loMask;

       static Word tempering(Word rnd) {

         rnd ^= (rnd >> 11);

         rnd ^= (rnd << 7) & 0x9D2C5680u;

         rnd ^= (rnd << 15) & 0xEFC60000u;

         rnd ^= (rnd >> 18);

         return rnd;

       }

     };

     template <typename _Word>

     struct RandomTraits<_Word, 64> {

       typedef _Word Word;

       static const int bits = 64;

       static const int length = 312;

       static const int shift = 156;

       static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);

       static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);

       static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);

       static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);

       static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);

       static const Word loMask = (Word(1u) << 31) - 1;

       static const Word hiMask = ~loMask;

       static Word tempering(Word rnd) {

         rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));

         rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));

         rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));

         rnd ^= (rnd >> 43);

         return rnd;

       }

     };

     template <typename _Word>

     class RandomCore {

     public:

       typedef _Word Word;

     private:

       static const int bits = RandomTraits<Word>::bits;

       static const int length = RandomTraits<Word>::length;

       static const int shift = RandomTraits<Word>::shift;

     public:

       void initState() {

         static const Word seedArray[4] = {

           0x12345u, 0x23456u, 0x34567u, 0x45678u

         };

         initState(seedArray, seedArray + 4);

       }

       void initState(Word seed) {

         static const Word mul = RandomTraits<Word>::mul;

         current = state; 

         Word *curr = state + length - 1;

         curr[0] = seed; --curr;

         for (int i = 1; i < length; ++i) {

           curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);

           --curr;

         }

       }

       template <typename Iterator>

       void initState(Iterator begin, Iterator end) {

         static const Word init = RandomTraits<Word>::arrayInit;

         static const Word mul1 = RandomTraits<Word>::arrayMul1;

         static const Word mul2 = RandomTraits<Word>::arrayMul2;

         Word *curr = state + length - 1; --curr;

         Iterator it = begin; int cnt = 0;

         int num;

         initState(init);

         num = length > end - begin ? length : end - begin;

         while (num--) {

           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) 

             + *it + cnt;

           ++it; ++cnt;

           if (it == end) {

             it = begin; cnt = 0;

           }

           if (curr == state) {

             curr = state + length - 1; curr[0] = state[0];

           }

           --curr;

         }

         num = length - 1; cnt = length - (curr - state) - 1;

         while (num--) {

           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))

             - cnt;

           --curr; ++cnt;

           if (curr == state) {

             curr = state + length - 1; curr[0] = state[0]; --curr;

             cnt = 1;

           }

         }

         state[length - 1] = Word(1) << (bits - 1);

       }

       void copyState(const RandomCore& other) {

         std::copy(other.state, other.state + length, state);

         current = state + (other.current - other.state);

       }

       Word operator()() {

         if (current == state) fillState();

         --current;

         Word rnd = *current;

         return RandomTraits<Word>::tempering(rnd);

       }

     private:

       void fillState() {

         static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };

         static const Word loMask = RandomTraits<Word>::loMask;

         static const Word hiMask = RandomTraits<Word>::hiMask;

         current = state + length; 

         register Word *curr = state + length - 1;

         register long num;

         num = length - shift;

         while (num--) {

           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^

             curr[- shift] ^ mask[curr[-1] & 1ul];

           --curr;

         }

         num = shift - 1;

         while (num--) {

           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^

             curr[length - shift] ^ mask[curr[-1] & 1ul];

           --curr;

         }

         curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^

           curr[length - shift] ^ mask[curr[length - 1] & 1ul];

       }

       Word *current;

       Word state[length];

     };

     template <typename Result, 

               int shift = (std::numeric_limits<Result>::digits + 1) / 2>

     struct Masker {

       static Result mask(const Result& result) {

         return Masker<Result, (shift + 1) / 2>::

           mask(static_cast<Result>(result | (result >> shift)));

       }

     };

     template <typename Result>

     struct Masker<Result, 1> {

       static Result mask(const Result& result) {

         return static_cast<Result>(result | (result >> 1));

       }

     };

     template <typename Result, typename Word, 

               int rest = std::numeric_limits<Result>::digits, int shift = 0, 

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

     struct IntConversion {

       static const int bits = std::numeric_limits<Word>::digits;

       static Result convert(RandomCore<Word>& rnd) {

         return static_cast<Result>(rnd() >> (bits - rest)) << shift;

       }

     }; 

     template <typename Result, typename Word, int rest, int shift> 

     struct IntConversion<Result, Word, rest, shift, false> {

       static const int bits = std::numeric_limits<Word>::digits;

       static Result convert(RandomCore<Word>& rnd) {

         return (static_cast<Result>(rnd()) << shift) | 

           IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);

       }

     };

     template <typename Result, typename Word,

               bool one_word = (std::numeric_limits<Word>::digits < 

 			       std::numeric_limits<Result>::digits) >

     struct Mapping {

       static Result map(RandomCore<Word>& rnd, const Result& bound) {

         Word max = Word(bound - 1);

         Result mask = Masker<Result>::mask(bound - 1);

         Result num;

         do {

           num = IntConversion<Result, Word>::convert(rnd) & mask; 

         } while (num > max);

         return num;

       }

     };

     template <typename Result, typename Word>

     struct Mapping<Result, Word, false> {

       static Result map(RandomCore<Word>& rnd, const Result& bound) {

         Word max = Word(bound - 1);

         Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>

           ::mask(max);

         Word num;

         do {

           num = rnd() & mask;

         } while (num > max);

         return num;

       }

     };

     template <typename Result, int exp, bool pos = (exp >= 0)>

     struct ShiftMultiplier {

       static const Result multiplier() {

         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();

         res *= res;

         if ((exp & 1) == 1) res *= static_cast<Result>(2.0);

         return res; 

       }

     };

     template <typename Result, int exp>

     struct ShiftMultiplier<Result, exp, false> {

       static const Result multiplier() {

         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();

         res *= res;

         if ((exp & 1) == 1) res *= static_cast<Result>(0.5);

         return res; 

       }

     };

     template <typename Result>

     struct ShiftMultiplier<Result, 0, true> {

       static const Result multiplier() {

         return static_cast<Result>(1.0); 

       }

     };

     template <typename Result>

     struct ShiftMultiplier<Result, -20, true> {

       static const Result multiplier() {

         return static_cast<Result>(1.0/1048576.0); 

       }

     };

     template <typename Result>

     struct ShiftMultiplier<Result, -32, true> {

       static const Result multiplier() {

         return static_cast<Result>(1.0/424967296.0); 

       }

     };

     template <typename Result>

     struct ShiftMultiplier<Result, -53, true> {

       static const Result multiplier() {

         return static_cast<Result>(1.0/9007199254740992.0); 

       }

     };

     template <typename Result>

     struct ShiftMultiplier<Result, -64, true> {

       static const Result multiplier() {

         return static_cast<Result>(1.0/18446744073709551616.0); 

       }

     };

     template <typename Result, int exp>

     struct Shifting {

       static Result shift(const Result& result) {

         return result * ShiftMultiplier<Result, exp>::multiplier();

       }

     };

     template <typename Result, typename Word,

               int rest = std::numeric_limits<Result>::digits, int shift = 0, 

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

     struct RealConversion{ 

       static const int bits = std::numeric_limits<Word>::digits;

       static Result convert(RandomCore<Word>& rnd) {

         return Shifting<Result, - shift - rest>::

           shift(static_cast<Result>(rnd() >> (bits - rest)));

       }

     };

     template <typename Result, typename Word, int rest, int shift>

     struct RealConversion<Result, Word, rest, shift, false> { 

       static const int bits = std::numeric_limits<Word>::digits;

       static Result convert(RandomCore<Word>& rnd) {

         return Shifting<Result, - shift - bits>::

           shift(static_cast<Result>(rnd())) +

           RealConversion<Result, Word, rest-bits, shift + bits>::

           convert(rnd);

       }

     };

     template <typename Result, typename Word>

     struct Initializer {

       template <typename Iterator>

       static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {

         std::vector<Word> ws;

         for (Iterator it = begin; it != end; ++it) {

           ws.push_back(Word(*it));

         }

         rnd.initState(ws.begin(), ws.end());

       }

       static void init(RandomCore<Word>& rnd, Result seed) {

         rnd.initState(seed);

       }

     };

     template <typename Word>

     struct BoolConversion {

       static bool convert(RandomCore<Word>& rnd) {

         return (rnd() & 1) == 1;

       }

     };

     template <typename Word>

     struct BoolProducer {

       Word buffer;

       int num;

       BoolProducer() : num(0) {}

       bool convert(RandomCore<Word>& rnd) {

         if (num == 0) {

           buffer = rnd();

           num = RandomTraits<Word>::bits;

         }

         bool r = (buffer & 1);

         buffer >>= 1;

         --num;

         return r;

       }

     };

   }

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

   /// architectures. The generators differ sligthly in the

   /// initialization and generation phase so they produce two

   /// completly different sequences.

   ///

   /// 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

   ///

   /// The 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.

   ///

   /// \author Balazs Dezso

   class Random {

   private:

     // architecture word

     typedef unsigned long Word;

     _random_bits::RandomCore<Word> core;

     _random_bits::BoolProducer<Word> bool_producer;

   public:

     /// \brief Constructor

     ///

     /// Constructor with constant seeding.

     Random() { core.initState(); }

     /// \brief Constructor

     ///

     /// 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

     ///

     /// 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 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 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).

     template <typename Number>

     Number real(Number a, Number b) { 

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

     }

     /// \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).

     template <typename Number>

     Number operator()(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).

     template <typename Number>

     Number operator()(Number a, Number b) { 

       return real<Number>() * (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 unsigned int.

     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 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 Nonuniform 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;

 	S=V1*V1+V2*V2;

       } while(S>=1);

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

     }

     /// Gauss distribution with given mean and standard deviation

     /// \sa gauss()

     ///

     double gauss(double mean,double std_dev)

     {

       return gauss()*std_dev+mean;

     }

     /// 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=M_E/(M_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 x_min location parameter (<tt>x_min>0</tt>)

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

     ///

     ///\warning This function used inverse transform sampling, therefore may

     ///suffer from numerical unstability.

     ///

     ///\todo Implement a numerically stable method

     double pareto(double x_min,double k)

     {

       return x_min*pow(1.0-real<double>(),1.0/k);

     }  

     ///@}

     ///\name Two dimensional distributions

     ///

     ///@{

     /// 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 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);

     }

     ///@}    

   };

   extern Random rnd;

 }

 #endif