diff -r 40d6f625e549 -r 45f8b617339e lemon/random.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/random.h	Thu Jan 03 11:13:29 2008 +0100
@@ -0,0 +1,872 @@
+/* -*- 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
+
+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.
+  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
+
+    /// 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 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));
+    }  
+      
+    ///@}
+    
+    ///\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 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