/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

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

 *

 * Copyright (C) 2003-2009

 * 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 <lemon/config.h>

#include <algorithm>

#include <iterator>

#include <vector>

#include <limits>

#include <fstream>

#include <lemon/math.h>

#include <lemon/dim2.h>

#ifndef LEMON_WIN32

#include <sys/time.h>

#include <ctime>

#include <sys/types.h>

#include <unistd.h>

#else

#include <lemon/bits/windows.h>

#endif

///\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 = static_cast<int>(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 = static_cast<int>(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;

        Word *curr = state + length - 1;

        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;

        }

        state[0] = (((state[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>

    struct ShiftMultiplier {

      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> {

      static const Result multiplier() {

        return static_cast<Result>(1.0);

      }

    };

    template <typename Result>

    struct ShiftMultiplier<Result, 20> {

      static const Result multiplier() {

        return static_cast<Result>(1.0/1048576.0);

      }

    };

    template <typename Result>

    struct ShiftMultiplier<Result, 32> {

      static const Result multiplier() {

        return static_cast<Result>(1.0/4294967296.0);

      }

    };

    template <typename Result>

    struct ShiftMultiplier<Result, 53> {

      static const Result multiplier() {

        return static_cast<Result>(1.0/9007199254740992.0);

      }

    };

    template <typename Result>

    struct ShiftMultiplier<Result, 64> {

      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 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;