/* -*- 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 static_cast<Result>(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 implementation of 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. Finally, you can get random bool with

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

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

     ///

     /// Various non-uniform distributions are also supported: normal (Gauss),

     /// exponential, gamma, Poisson, etc.; and a few two-dimensional

     /// distributions, too.

     ///

     ///\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:

     /// \ref lemon::rnd "rnd". In most cases, it is a good practice

     /// 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 Seeding from process id and time

       ///

       /// Seeding 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);

       }

       ///@}

     };

   };

   /// \ingroup misc

   ///

   /// \brief Mersenne Twister random number generator

   ///

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

   /// the Mersenne Twister random number generator algorithm

   /// depending on the system architecture.

   /// 

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

   /// \ref _random_bits::Random.

   ///

   /// \sa \ref _random_bits::Random

   typedef _random_bits::Random<unsigned long> Random;

   /// \ingroup misc

   ///

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

   ///

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

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

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

   /// sequence will be generated on every platfrom.

   ///

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

   /// \ref _random_bits::Random.

   ///

   /// \sa \ref _random_bits::Random

   typedef _random_bits::Random<unsigned int> Random32;

   /// \ingroup misc

   ///

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

   ///

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

   /// random number generator algorithm. (Even though it runs

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

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

   /// will be generated on every platfrom.

   ///

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

   /// \ref _random_bits::Random.

   ///

   /// \sa \ref _random_bits::Random

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

   extern Random rnd;

 }

 #endif