lemon/random.h
changeset 269 f5965bbf1353
parent 178 d2bac07f1742
child 280 e7f8647ce760
equal deleted inserted replaced
14:0191b7b84be9 15:c96cd362b78b
     1 /* -*- C++ -*-
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     4  *
     5  * Copyright (C) 2003-2008
     5  * Copyright (C) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     8  *
    19 /*
    19 /*
    20  * This file contains the reimplemented version of the Mersenne Twister
    20  * This file contains the reimplemented version of the Mersenne Twister
    21  * Generator of Matsumoto and Nishimura.
    21  * Generator of Matsumoto and Nishimura.
    22  *
    22  *
    23  * See the appropriate copyright notice below.
    23  * See the appropriate copyright notice below.
    24  * 
    24  *
    25  * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
    25  * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
    26  * All rights reserved.                          
    26  * All rights reserved.
    27  *
    27  *
    28  * Redistribution and use in source and binary forms, with or without
    28  * Redistribution and use in source and binary forms, with or without
    29  * modification, are permitted provided that the following conditions
    29  * modification, are permitted provided that the following conditions
    30  * are met:
    30  * are met:
    31  *
    31  *
    34  *
    34  *
    35  * 2. Redistributions in binary form must reproduce the above copyright
    35  * 2. Redistributions in binary form must reproduce the above copyright
    36  *    notice, this list of conditions and the following disclaimer in the
    36  *    notice, this list of conditions and the following disclaimer in the
    37  *    documentation and/or other materials provided with the distribution.
    37  *    documentation and/or other materials provided with the distribution.
    38  *
    38  *
    39  * 3. The names of its contributors may not be used to endorse or promote 
    39  * 3. The names of its contributors may not be used to endorse or promote
    40  *    products derived from this software without specific prior written 
    40  *    products derived from this software without specific prior written
    41  *    permission.
    41  *    permission.
    42  *
    42  *
    43  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
    43  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
    44  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
    44  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
    45  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
    45  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
    85 ///\brief Mersenne Twister random number generator
    85 ///\brief Mersenne Twister random number generator
    86 
    86 
    87 namespace lemon {
    87 namespace lemon {
    88 
    88 
    89   namespace _random_bits {
    89   namespace _random_bits {
    90     
    90 
    91     template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
    91     template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
    92     struct RandomTraits {};
    92     struct RandomTraits {};
    93 
    93 
    94     template <typename _Word>
    94     template <typename _Word>
    95     struct RandomTraits<_Word, 32> {
    95     struct RandomTraits<_Word, 32> {
    97       typedef _Word Word;
    97       typedef _Word Word;
    98       static const int bits = 32;
    98       static const int bits = 32;
    99 
    99 
   100       static const int length = 624;
   100       static const int length = 624;
   101       static const int shift = 397;
   101       static const int shift = 397;
   102       
   102 
   103       static const Word mul = 0x6c078965u;
   103       static const Word mul = 0x6c078965u;
   104       static const Word arrayInit = 0x012BD6AAu;
   104       static const Word arrayInit = 0x012BD6AAu;
   105       static const Word arrayMul1 = 0x0019660Du;
   105       static const Word arrayMul1 = 0x0019660Du;
   106       static const Word arrayMul2 = 0x5D588B65u;
   106       static const Word arrayMul2 = 0x5D588B65u;
   107 
   107 
   165 
   165 
   166       void initState() {
   166       void initState() {
   167         static const Word seedArray[4] = {
   167         static const Word seedArray[4] = {
   168           0x12345u, 0x23456u, 0x34567u, 0x45678u
   168           0x12345u, 0x23456u, 0x34567u, 0x45678u
   169         };
   169         };
   170     
   170 
   171         initState(seedArray, seedArray + 4);
   171         initState(seedArray, seedArray + 4);
   172       }
   172       }
   173 
   173 
   174       void initState(Word seed) {
   174       void initState(Word seed) {
   175 
   175 
   176         static const Word mul = RandomTraits<Word>::mul;
   176         static const Word mul = RandomTraits<Word>::mul;
   177 
   177 
   178         current = state; 
   178         current = state;
   179 
   179 
   180         Word *curr = state + length - 1;
   180         Word *curr = state + length - 1;
   181         curr[0] = seed; --curr;
   181         curr[0] = seed; --curr;
   182         for (int i = 1; i < length; ++i) {
   182         for (int i = 1; i < length; ++i) {
   183           curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
   183           curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
   199 
   199 
   200         initState(init);
   200         initState(init);
   201 
   201 
   202         num = length > end - begin ? length : end - begin;
   202         num = length > end - begin ? length : end - begin;
   203         while (num--) {
   203         while (num--) {
   204           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) 
   204           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
   205             + *it + cnt;
   205             + *it + cnt;
   206           ++it; ++cnt;
   206           ++it; ++cnt;
   207           if (it == end) {
   207           if (it == end) {
   208             it = begin; cnt = 0;
   208             it = begin; cnt = 0;
   209           }
   209           }
   221           if (curr == state) {
   221           if (curr == state) {
   222             curr = state + length - 1; curr[0] = state[0]; --curr;
   222             curr = state + length - 1; curr[0] = state[0]; --curr;
   223             cnt = 1;
   223             cnt = 1;
   224           }
   224           }
   225         }
   225         }
   226         
   226 
   227         state[length - 1] = Word(1) << (bits - 1);
   227         state[length - 1] = Word(1) << (bits - 1);
   228       }
   228       }
   229       
   229 
   230       void copyState(const RandomCore& other) {
   230       void copyState(const RandomCore& other) {
   231         std::copy(other.state, other.state + length, state);
   231         std::copy(other.state, other.state + length, state);
   232         current = state + (other.current - other.state);
   232         current = state + (other.current - other.state);
   233       }
   233       }
   234 
   234 
   239         return RandomTraits<Word>::tempering(rnd);
   239         return RandomTraits<Word>::tempering(rnd);
   240       }
   240       }
   241 
   241 
   242     private:
   242     private:
   243 
   243 
   244   
   244 
   245       void fillState() {
   245       void fillState() {
   246         static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
   246         static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
   247         static const Word loMask = RandomTraits<Word>::loMask;
   247         static const Word loMask = RandomTraits<Word>::loMask;
   248         static const Word hiMask = RandomTraits<Word>::hiMask;
   248         static const Word hiMask = RandomTraits<Word>::hiMask;
   249 
   249 
   250         current = state + length; 
   250         current = state + length;
   251 
   251 
   252         register Word *curr = state + length - 1;
   252         register Word *curr = state + length - 1;
   253         register long num;
   253         register long num;
   254       
   254 
   255         num = length - shift;
   255         num = length - shift;
   256         while (num--) {
   256         while (num--) {
   257           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   257           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   258             curr[- shift] ^ mask[curr[-1] & 1ul];
   258             curr[- shift] ^ mask[curr[-1] & 1ul];
   259           --curr;
   259           --curr;
   267         state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
   267         state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
   268           curr[length - shift] ^ mask[curr[length - 1] & 1ul];
   268           curr[length - shift] ^ mask[curr[length - 1] & 1ul];
   269 
   269 
   270       }
   270       }
   271 
   271 
   272   
   272 
   273       Word *current;
   273       Word *current;
   274       Word state[length];
   274       Word state[length];
   275       
   275 
   276     };
   276     };
   277 
   277 
   278 
   278 
   279     template <typename Result, 
   279     template <typename Result,
   280               int shift = (std::numeric_limits<Result>::digits + 1) / 2>
   280               int shift = (std::numeric_limits<Result>::digits + 1) / 2>
   281     struct Masker {
   281     struct Masker {
   282       static Result mask(const Result& result) {
   282       static Result mask(const Result& result) {
   283         return Masker<Result, (shift + 1) / 2>::
   283         return Masker<Result, (shift + 1) / 2>::
   284           mask(static_cast<Result>(result | (result >> shift)));
   284           mask(static_cast<Result>(result | (result >> shift)));
   285       }
   285       }
   286     };
   286     };
   287     
   287 
   288     template <typename Result>
   288     template <typename Result>
   289     struct Masker<Result, 1> {
   289     struct Masker<Result, 1> {
   290       static Result mask(const Result& result) {
   290       static Result mask(const Result& result) {
   291         return static_cast<Result>(result | (result >> 1));
   291         return static_cast<Result>(result | (result >> 1));
   292       }
   292       }
   293     };
   293     };
   294 
   294 
   295     template <typename Result, typename Word, 
   295     template <typename Result, typename Word,
   296               int rest = std::numeric_limits<Result>::digits, int shift = 0, 
   296               int rest = std::numeric_limits<Result>::digits, int shift = 0,
   297               bool last = rest <= std::numeric_limits<Word>::digits>
   297               bool last = rest <= std::numeric_limits<Word>::digits>
   298     struct IntConversion {
   298     struct IntConversion {
   299       static const int bits = std::numeric_limits<Word>::digits;
   299       static const int bits = std::numeric_limits<Word>::digits;
   300     
   300 
   301       static Result convert(RandomCore<Word>& rnd) {
   301       static Result convert(RandomCore<Word>& rnd) {
   302         return static_cast<Result>(rnd() >> (bits - rest)) << shift;
   302         return static_cast<Result>(rnd() >> (bits - rest)) << shift;
   303       }
   303       }
   304       
   304 
   305     }; 
   305     };
   306 
   306 
   307     template <typename Result, typename Word, int rest, int shift> 
   307     template <typename Result, typename Word, int rest, int shift>
   308     struct IntConversion<Result, Word, rest, shift, false> {
   308     struct IntConversion<Result, Word, rest, shift, false> {
   309       static const int bits = std::numeric_limits<Word>::digits;
   309       static const int bits = std::numeric_limits<Word>::digits;
   310 
   310 
   311       static Result convert(RandomCore<Word>& rnd) {
   311       static Result convert(RandomCore<Word>& rnd) {
   312         return (static_cast<Result>(rnd()) << shift) | 
   312         return (static_cast<Result>(rnd()) << shift) |
   313           IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
   313           IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
   314       }
   314       }
   315     };
   315     };
   316 
   316 
   317 
   317 
   318     template <typename Result, typename Word,
   318     template <typename Result, typename Word,
   319               bool one_word = (std::numeric_limits<Word>::digits < 
   319               bool one_word = (std::numeric_limits<Word>::digits <
   320 			       std::numeric_limits<Result>::digits) >
   320                                std::numeric_limits<Result>::digits) >
   321     struct Mapping {
   321     struct Mapping {
   322       static Result map(RandomCore<Word>& rnd, const Result& bound) {
   322       static Result map(RandomCore<Word>& rnd, const Result& bound) {
   323         Word max = Word(bound - 1);
   323         Word max = Word(bound - 1);
   324         Result mask = Masker<Result>::mask(bound - 1);
   324         Result mask = Masker<Result>::mask(bound - 1);
   325         Result num;
   325         Result num;
   326         do {
   326         do {
   327           num = IntConversion<Result, Word>::convert(rnd) & mask; 
   327           num = IntConversion<Result, Word>::convert(rnd) & mask;
   328         } while (num > max);
   328         } while (num > max);
   329         return num;
   329         return num;
   330       }
   330       }
   331     };
   331     };
   332 
   332 
   348     struct ShiftMultiplier {
   348     struct ShiftMultiplier {
   349       static const Result multiplier() {
   349       static const Result multiplier() {
   350         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   350         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   351         res *= res;
   351         res *= res;
   352         if ((exp & 1) == 1) res *= static_cast<Result>(2.0);
   352         if ((exp & 1) == 1) res *= static_cast<Result>(2.0);
   353         return res; 
   353         return res;
   354       }
   354       }
   355     };
   355     };
   356 
   356 
   357     template <typename Result, int exp>
   357     template <typename Result, int exp>
   358     struct ShiftMultiplier<Result, exp, false> {
   358     struct ShiftMultiplier<Result, exp, false> {
   359       static const Result multiplier() {
   359       static const Result multiplier() {
   360         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   360         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   361         res *= res;
   361         res *= res;
   362         if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
   362         if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
   363         return res; 
   363         return res;
   364       }
   364       }
   365     };
   365     };
   366 
   366 
   367     template <typename Result>
   367     template <typename Result>
   368     struct ShiftMultiplier<Result, 0, true> {
   368     struct ShiftMultiplier<Result, 0, true> {
   369       static const Result multiplier() {
   369       static const Result multiplier() {
   370         return static_cast<Result>(1.0); 
   370         return static_cast<Result>(1.0);
   371       }
   371       }
   372     };
   372     };
   373 
   373 
   374     template <typename Result>
   374     template <typename Result>
   375     struct ShiftMultiplier<Result, -20, true> {
   375     struct ShiftMultiplier<Result, -20, true> {
   376       static const Result multiplier() {
   376       static const Result multiplier() {
   377         return static_cast<Result>(1.0/1048576.0); 
   377         return static_cast<Result>(1.0/1048576.0);
   378       }
   378       }
   379     };
   379     };
   380     
   380 
   381     template <typename Result>
   381     template <typename Result>
   382     struct ShiftMultiplier<Result, -32, true> {
   382     struct ShiftMultiplier<Result, -32, true> {
   383       static const Result multiplier() {
   383       static const Result multiplier() {
   384         return static_cast<Result>(1.0/424967296.0); 
   384         return static_cast<Result>(1.0/424967296.0);
   385       }
   385       }
   386     };
   386     };
   387 
   387 
   388     template <typename Result>
   388     template <typename Result>
   389     struct ShiftMultiplier<Result, -53, true> {
   389     struct ShiftMultiplier<Result, -53, true> {
   390       static const Result multiplier() {
   390       static const Result multiplier() {
   391         return static_cast<Result>(1.0/9007199254740992.0); 
   391         return static_cast<Result>(1.0/9007199254740992.0);
   392       }
   392       }
   393     };
   393     };
   394 
   394 
   395     template <typename Result>
   395     template <typename Result>
   396     struct ShiftMultiplier<Result, -64, true> {
   396     struct ShiftMultiplier<Result, -64, true> {
   397       static const Result multiplier() {
   397       static const Result multiplier() {
   398         return static_cast<Result>(1.0/18446744073709551616.0); 
   398         return static_cast<Result>(1.0/18446744073709551616.0);
   399       }
   399       }
   400     };
   400     };
   401 
   401 
   402     template <typename Result, int exp>
   402     template <typename Result, int exp>
   403     struct Shifting {
   403     struct Shifting {
   405         return result * ShiftMultiplier<Result, exp>::multiplier();
   405         return result * ShiftMultiplier<Result, exp>::multiplier();
   406       }
   406       }
   407     };
   407     };
   408 
   408 
   409     template <typename Result, typename Word,
   409     template <typename Result, typename Word,
   410               int rest = std::numeric_limits<Result>::digits, int shift = 0, 
   410               int rest = std::numeric_limits<Result>::digits, int shift = 0,
   411               bool last = rest <= std::numeric_limits<Word>::digits>
   411               bool last = rest <= std::numeric_limits<Word>::digits>
   412     struct RealConversion{ 
   412     struct RealConversion{
   413       static const int bits = std::numeric_limits<Word>::digits;
   413       static const int bits = std::numeric_limits<Word>::digits;
   414 
   414 
   415       static Result convert(RandomCore<Word>& rnd) {
   415       static Result convert(RandomCore<Word>& rnd) {
   416         return Shifting<Result, - shift - rest>::
   416         return Shifting<Result, - shift - rest>::
   417           shift(static_cast<Result>(rnd() >> (bits - rest)));
   417           shift(static_cast<Result>(rnd() >> (bits - rest)));
   418       }
   418       }
   419     };
   419     };
   420 
   420 
   421     template <typename Result, typename Word, int rest, int shift>
   421     template <typename Result, typename Word, int rest, int shift>
   422     struct RealConversion<Result, Word, rest, shift, false> { 
   422     struct RealConversion<Result, Word, rest, shift, false> {
   423       static const int bits = std::numeric_limits<Word>::digits;
   423       static const int bits = std::numeric_limits<Word>::digits;
   424 
   424 
   425       static Result convert(RandomCore<Word>& rnd) {
   425       static Result convert(RandomCore<Word>& rnd) {
   426         return Shifting<Result, - shift - bits>::
   426         return Shifting<Result, - shift - bits>::
   427           shift(static_cast<Result>(rnd())) +
   427           shift(static_cast<Result>(rnd())) +
   456 
   456 
   457     template <typename Word>
   457     template <typename Word>
   458     struct BoolProducer {
   458     struct BoolProducer {
   459       Word buffer;
   459       Word buffer;
   460       int num;
   460       int num;
   461       
   461 
   462       BoolProducer() : num(0) {}
   462       BoolProducer() : num(0) {}
   463 
   463 
   464       bool convert(RandomCore<Word>& rnd) {
   464       bool convert(RandomCore<Word>& rnd) {
   465         if (num == 0) {
   465         if (num == 0) {
   466           buffer = rnd();
   466           buffer = rnd();
   527   class Random {
   527   class Random {
   528   private:
   528   private:
   529 
   529 
   530     // Architecture word
   530     // Architecture word
   531     typedef unsigned long Word;
   531     typedef unsigned long Word;
   532     
   532 
   533     _random_bits::RandomCore<Word> core;
   533     _random_bits::RandomCore<Word> core;
   534     _random_bits::BoolProducer<Word> bool_producer;
   534     _random_bits::BoolProducer<Word> bool_producer;
   535     
   535 
   536 
   536 
   537   public:
   537   public:
   538 
   538 
   539     ///\name Initialization
   539     ///\name Initialization
   540     ///
   540     ///
   552     /// \brief Constructor with seed
   552     /// \brief Constructor with seed
   553     ///
   553     ///
   554     /// Constructor with seed. The current number type will be converted
   554     /// Constructor with seed. The current number type will be converted
   555     /// to the architecture word type.
   555     /// to the architecture word type.
   556     template <typename Number>
   556     template <typename Number>
   557     Random(Number seed) { 
   557     Random(Number seed) {
   558       _random_bits::Initializer<Number, Word>::init(core, seed);
   558       _random_bits::Initializer<Number, Word>::init(core, seed);
   559     }
   559     }
   560 
   560 
   561     /// \brief Constructor with array seeding
   561     /// \brief Constructor with array seeding
   562     ///
   562     ///
   563     /// Constructor with array seeding. The given range should contain
   563     /// Constructor with array seeding. The given range should contain
   564     /// any number type and the numbers will be converted to the
   564     /// any number type and the numbers will be converted to the
   565     /// architecture word type.
   565     /// architecture word type.
   566     template <typename Iterator>
   566     template <typename Iterator>
   567     Random(Iterator begin, Iterator end) { 
   567     Random(Iterator begin, Iterator end) {
   568       typedef typename std::iterator_traits<Iterator>::value_type Number;
   568       typedef typename std::iterator_traits<Iterator>::value_type Number;
   569       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   569       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   570     }
   570     }
   571 
   571 
   572     /// \brief Copy constructor
   572     /// \brief Copy constructor
   595     /// \brief Seeding random sequence
   595     /// \brief Seeding random sequence
   596     ///
   596     ///
   597     /// Seeding the random sequence. The current number type will be
   597     /// Seeding the random sequence. The current number type will be
   598     /// converted to the architecture word type.
   598     /// converted to the architecture word type.
   599     template <typename Number>
   599     template <typename Number>
   600     void seed(Number seed) { 
   600     void seed(Number seed) {
   601       _random_bits::Initializer<Number, Word>::init(core, seed);
   601       _random_bits::Initializer<Number, Word>::init(core, seed);
   602     }
   602     }
   603 
   603 
   604     /// \brief Seeding random sequence
   604     /// \brief Seeding random sequence
   605     ///
   605     ///
   606     /// Seeding the random sequence. The given range should contain
   606     /// Seeding the random sequence. The given range should contain
   607     /// any number type and the numbers will be converted to the
   607     /// any number type and the numbers will be converted to the
   608     /// architecture word type.
   608     /// architecture word type.
   609     template <typename Iterator>
   609     template <typename Iterator>
   610     void seed(Iterator begin, Iterator end) { 
   610     void seed(Iterator begin, Iterator end) {
   611       typedef typename std::iterator_traits<Iterator>::value_type Number;
   611       typedef typename std::iterator_traits<Iterator>::value_type Number;
   612       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   612       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   613     }
   613     }
   614 
   614 
   615     /// \brief Seeding from file or from process id and time
   615     /// \brief Seeding from file or from process id and time
   623       if (seedFromFile("/dev/urandom", 0)) return true;
   623       if (seedFromFile("/dev/urandom", 0)) return true;
   624 #endif
   624 #endif
   625       if (seedFromTime()) return true;
   625       if (seedFromTime()) return true;
   626       return false;
   626       return false;
   627     }
   627     }
   628     
   628 
   629     /// \brief Seeding from file
   629     /// \brief Seeding from file
   630     ///
   630     ///
   631     /// Seeding the random sequence from file. The linux kernel has two
   631     /// Seeding the random sequence from file. The linux kernel has two
   632     /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
   632     /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
   633     /// could give good seed values for pseudo random generators (The
   633     /// could give good seed values for pseudo random generators (The
   638     /// entropy).
   638     /// entropy).
   639     /// \param file The source file
   639     /// \param file The source file
   640     /// \param offset The offset, from the file read.
   640     /// \param offset The offset, from the file read.
   641     /// \return True when the seeding successes.
   641     /// \return True when the seeding successes.
   642 #ifndef WIN32
   642 #ifndef WIN32
   643     bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0) 
   643     bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)
   644 #else
   644 #else
   645     bool seedFromFile(const std::string& file = "", int offset = 0) 
   645     bool seedFromFile(const std::string& file = "", int offset = 0)
   646 #endif
   646 #endif
   647     {
   647     {
   648       std::ifstream rs(file.c_str());
   648       std::ifstream rs(file.c_str());
   649       const int size = 4;
   649       const int size = 4;
   650       Word buf[size];
   650       Word buf[size];
   658     ///
   658     ///
   659     /// Seding from process id and time. This function uses the
   659     /// Seding from process id and time. This function uses the
   660     /// current process id and the current time for initialize the
   660     /// current process id and the current time for initialize the
   661     /// random sequence.
   661     /// random sequence.
   662     /// \return Currently always true.
   662     /// \return Currently always true.
   663     bool seedFromTime() { 	
   663     bool seedFromTime() {
   664 #ifndef WIN32
   664 #ifndef WIN32
   665       timeval tv;
   665       timeval tv;
   666       gettimeofday(&tv, 0);
   666       gettimeofday(&tv, 0);
   667       seed(getpid() + tv.tv_sec + tv.tv_usec);
   667       seed(getpid() + tv.tv_sec + tv.tv_usec);
   668 #else
   668 #else
   694 
   694 
   695     /// \brief Returns a random real number the range [0, b)
   695     /// \brief Returns a random real number the range [0, b)
   696     ///
   696     ///
   697     /// It returns a random real number from the range [0, b).
   697     /// It returns a random real number from the range [0, b).
   698     template <typename Number>
   698     template <typename Number>
   699     Number real(Number b) { 
   699     Number real(Number b) {
   700       return real<Number>() * b; 
   700       return real<Number>() * b;
   701     }
   701     }
   702 
   702 
   703     /// \brief Returns a random real number from the range [a, b)
   703     /// \brief Returns a random real number from the range [a, b)
   704     ///
   704     ///
   705     /// It returns a random real number from the range [a, b).
   705     /// It returns a random real number from the range [a, b).
   706     template <typename Number>
   706     template <typename Number>
   707     Number real(Number a, Number b) { 
   707     Number real(Number a, Number b) {
   708       return real<Number>() * (b - a) + a; 
   708       return real<Number>() * (b - a) + a;
   709     }
   709     }
   710 
   710 
   711     /// @}
   711     /// @}
   712 
   712 
   713     ///\name Uniform distributions
   713     ///\name Uniform distributions
   723 
   723 
   724     /// \brief Returns a random real number from the range [0, b)
   724     /// \brief Returns a random real number from the range [0, b)
   725     ///
   725     ///
   726     /// It returns a random real number from the range [0, b).
   726     /// It returns a random real number from the range [0, b).
   727     template <typename Number>
   727     template <typename Number>
   728     Number operator()(Number b) { 
   728     Number operator()(Number b) {
   729       return real<Number>() * b; 
   729       return real<Number>() * b;
   730     }
   730     }
   731 
   731 
   732     /// \brief Returns a random real number from the range [a, b)
   732     /// \brief Returns a random real number from the range [a, b)
   733     ///
   733     ///
   734     /// It returns a random real number from the range [a, b).
   734     /// It returns a random real number from the range [a, b).
   735     template <typename Number>
   735     template <typename Number>
   736     Number operator()(Number a, Number b) { 
   736     Number operator()(Number a, Number b) {
   737       return real<Number>() * (b - a) + a; 
   737       return real<Number>() * (b - a) + a;
   738     }
   738     }
   739 
   739 
   740     /// \brief Returns a random integer from a range
   740     /// \brief Returns a random integer from a range
   741     ///
   741     ///
   742     /// It returns a random integer from the range {0, 1, ..., b - 1}.
   742     /// It returns a random integer from the range {0, 1, ..., b - 1}.
   782     /// It returns a random integer uniformly from the whole range of
   782     /// It returns a random integer uniformly from the whole range of
   783     /// the current \c Number type. The default result type of this
   783     /// the current \c Number type. The default result type of this
   784     /// function is \c int.
   784     /// function is \c int.
   785     template <typename Number>
   785     template <typename Number>
   786     Number integer() {
   786     Number integer() {
   787       static const int nb = std::numeric_limits<Number>::digits + 
   787       static const int nb = std::numeric_limits<Number>::digits +
   788         (std::numeric_limits<Number>::is_signed ? 1 : 0);
   788         (std::numeric_limits<Number>::is_signed ? 1 : 0);
   789       return _random_bits::IntConversion<Number, Word, nb>::convert(core);
   789       return _random_bits::IntConversion<Number, Word, nb>::convert(core);
   790     }
   790     }
   791 
   791 
   792     int integer() {
   792     int integer() {
   793       return integer<int>();
   793       return integer<int>();
   794     }
   794     }
   795     
   795 
   796     /// \brief Returns a random bool
   796     /// \brief Returns a random bool
   797     ///
   797     ///
   798     /// It returns a random bool. The generator holds a buffer for
   798     /// It returns a random bool. The generator holds a buffer for
   799     /// random bits. Every time when it become empty the generator makes
   799     /// random bits. Every time when it become empty the generator makes
   800     /// a new random word and fill the buffer up.
   800     /// a new random word and fill the buffer up.
   804 
   804 
   805     /// @}
   805     /// @}
   806 
   806 
   807     ///\name Non-uniform distributions
   807     ///\name Non-uniform distributions
   808     ///
   808     ///
   809     
   809 
   810     ///@{
   810     ///@{
   811     
   811 
   812     /// \brief Returns a random bool
   812     /// \brief Returns a random bool
   813     ///
   813     ///
   814     /// It returns a random bool with given probability of true result.
   814     /// It returns a random bool with given probability of true result.
   815     bool boolean(double p) {
   815     bool boolean(double p) {
   816       return operator()() < p;
   816       return operator()() < p;
   820 
   820 
   821     /// Standard Gauss distribution.
   821     /// Standard Gauss distribution.
   822     /// \note The Cartesian form of the Box-Muller
   822     /// \note The Cartesian form of the Box-Muller
   823     /// transformation is used to generate a random normal distribution.
   823     /// transformation is used to generate a random normal distribution.
   824     /// \todo Consider using the "ziggurat" method instead.
   824     /// \todo Consider using the "ziggurat" method instead.
   825     double gauss() 
   825     double gauss()
   826     {
   826     {
   827       double V1,V2,S;
   827       double V1,V2,S;
   828       do {
   828       do {
   829 	V1=2*real<double>()-1;
   829         V1=2*real<double>()-1;
   830 	V2=2*real<double>()-1;
   830         V2=2*real<double>()-1;
   831 	S=V1*V1+V2*V2;
   831         S=V1*V1+V2*V2;
   832       } while(S>=1);
   832       } while(S>=1);
   833       return std::sqrt(-2*std::log(S)/S)*V1;
   833       return std::sqrt(-2*std::log(S)/S)*V1;
   834     }
   834     }
   835     /// Gauss distribution with given mean and standard deviation
   835     /// Gauss distribution with given mean and standard deviation
   836 
   836 
   852     }
   852     }
   853 
   853 
   854     /// Gamma distribution with given integer shape
   854     /// Gamma distribution with given integer shape
   855 
   855 
   856     /// This function generates a gamma distribution random number.
   856     /// This function generates a gamma distribution random number.
   857     /// 
   857     ///
   858     ///\param k shape parameter (<tt>k>0</tt> integer)
   858     ///\param k shape parameter (<tt>k>0</tt> integer)
   859     double gamma(int k) 
   859     double gamma(int k)
   860     {
   860     {
   861       double s = 0;
   861       double s = 0;
   862       for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
   862       for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
   863       return s;
   863       return s;
   864     }
   864     }
   865     
   865 
   866     /// Gamma distribution with given shape and scale parameter
   866     /// Gamma distribution with given shape and scale parameter
   867 
   867 
   868     /// This function generates a gamma distribution random number.
   868     /// This function generates a gamma distribution random number.
   869     /// 
   869     ///
   870     ///\param k shape parameter (<tt>k>0</tt>)
   870     ///\param k shape parameter (<tt>k>0</tt>)
   871     ///\param theta scale parameter
   871     ///\param theta scale parameter
   872     ///
   872     ///
   873     double gamma(double k,double theta=1.0)
   873     double gamma(double k,double theta=1.0)
   874     {
   874     {
   875       double xi,nu;
   875       double xi,nu;
   876       const double delta = k-std::floor(k);
   876       const double delta = k-std::floor(k);
   877       const double v0=E/(E-delta);
   877       const double v0=E/(E-delta);
   878       do {
   878       do {
   879 	double V0=1.0-real<double>();
   879         double V0=1.0-real<double>();
   880 	double V1=1.0-real<double>();
   880         double V1=1.0-real<double>();
   881 	double V2=1.0-real<double>();
   881         double V2=1.0-real<double>();
   882 	if(V2<=v0) 
   882         if(V2<=v0)
   883 	  {
   883           {
   884 	    xi=std::pow(V1,1.0/delta);
   884             xi=std::pow(V1,1.0/delta);
   885 	    nu=V0*std::pow(xi,delta-1.0);
   885             nu=V0*std::pow(xi,delta-1.0);
   886 	  }
   886           }
   887 	else 
   887         else
   888 	  {
   888           {
   889 	    xi=1.0-std::log(V1);
   889             xi=1.0-std::log(V1);
   890 	    nu=V0*std::exp(-xi);
   890             nu=V0*std::exp(-xi);
   891 	  }
   891           }
   892       } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
   892       } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
   893       return theta*(xi+gamma(int(std::floor(k))));
   893       return theta*(xi+gamma(int(std::floor(k))));
   894     }
   894     }
   895     
   895 
   896     /// Weibull distribution
   896     /// Weibull distribution
   897 
   897 
   898     /// This function generates a Weibull distribution random number.
   898     /// This function generates a Weibull distribution random number.
   899     /// 
   899     ///
   900     ///\param k shape parameter (<tt>k>0</tt>)
   900     ///\param k shape parameter (<tt>k>0</tt>)
   901     ///\param lambda scale parameter (<tt>lambda>0</tt>)
   901     ///\param lambda scale parameter (<tt>lambda>0</tt>)
   902     ///
   902     ///
   903     double weibull(double k,double lambda)
   903     double weibull(double k,double lambda)
   904     {
   904     {
   905       return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
   905       return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
   906     }  
   906     }
   907       
   907 
   908     /// Pareto distribution
   908     /// Pareto distribution
   909 
   909 
   910     /// This function generates a Pareto distribution random number.
   910     /// This function generates a Pareto distribution random number.
   911     /// 
   911     ///
   912     ///\param k shape parameter (<tt>k>0</tt>)
   912     ///\param k shape parameter (<tt>k>0</tt>)
   913     ///\param x_min location parameter (<tt>x_min>0</tt>)
   913     ///\param x_min location parameter (<tt>x_min>0</tt>)
   914     ///
   914     ///
   915     double pareto(double k,double x_min)
   915     double pareto(double k,double x_min)
   916     {
   916     {
   917       return exponential(gamma(k,1.0/x_min))+x_min;
   917       return exponential(gamma(k,1.0/x_min))+x_min;
   918     }  
   918     }
   919       
   919 
   920     /// Poisson distribution
   920     /// Poisson distribution
   921 
   921 
   922     /// This function generates a Poisson distribution random number with
   922     /// This function generates a Poisson distribution random number with
   923     /// parameter \c lambda.
   923     /// parameter \c lambda.
   924     /// 
   924     ///
   925     /// The probability mass function of this distribusion is
   925     /// The probability mass function of this distribusion is
   926     /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
   926     /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
   927     /// \note The algorithm is taken from the book of Donald E. Knuth titled
   927     /// \note The algorithm is taken from the book of Donald E. Knuth titled
   928     /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
   928     /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
   929     /// return value.
   929     /// return value.
   930     
   930 
   931     int poisson(double lambda)
   931     int poisson(double lambda)
   932     {
   932     {
   933       const double l = std::exp(-lambda);
   933       const double l = std::exp(-lambda);
   934       int k=0;
   934       int k=0;
   935       double p = 1.0;
   935       double p = 1.0;
   936       do {
   936       do {
   937 	k++;
   937         k++;
   938 	p*=real<double>();
   938         p*=real<double>();
   939       } while (p>=l);
   939       } while (p>=l);
   940       return k-1;
   940       return k-1;
   941     }  
   941     }
   942       
   942 
   943     ///@}
   943     ///@}
   944     
   944 
   945     ///\name Two dimensional distributions
   945     ///\name Two dimensional distributions
   946     ///
   946     ///
   947 
   947 
   948     ///@{
   948     ///@{
   949     
   949 
   950     /// Uniform distribution on the full unit circle
   950     /// Uniform distribution on the full unit circle
   951 
   951 
   952     /// Uniform distribution on the full unit circle.
   952     /// Uniform distribution on the full unit circle.
   953     ///
   953     ///
   954     dim2::Point<double> disc() 
   954     dim2::Point<double> disc()
   955     {
   955     {
   956       double V1,V2;
   956       double V1,V2;
   957       do {
   957       do {
   958 	V1=2*real<double>()-1;
   958         V1=2*real<double>()-1;
   959 	V2=2*real<double>()-1;
   959         V2=2*real<double>()-1;
   960 	
   960 
   961       } while(V1*V1+V2*V2>=1);
   961       } while(V1*V1+V2*V2>=1);
   962       return dim2::Point<double>(V1,V2);
   962       return dim2::Point<double>(V1,V2);
   963     }
   963     }
   964     /// A kind of two dimensional Gauss distribution
   964     /// A kind of two dimensional Gauss distribution
   965 
   965 
   971     /// the Box-Muller method.
   971     /// the Box-Muller method.
   972     dim2::Point<double> gauss2()
   972     dim2::Point<double> gauss2()
   973     {
   973     {
   974       double V1,V2,S;
   974       double V1,V2,S;
   975       do {
   975       do {
   976 	V1=2*real<double>()-1;
   976         V1=2*real<double>()-1;
   977 	V2=2*real<double>()-1;
   977         V2=2*real<double>()-1;
   978 	S=V1*V1+V2*V2;
   978         S=V1*V1+V2*V2;
   979       } while(S>=1);
   979       } while(S>=1);
   980       double W=std::sqrt(-2*std::log(S)/S);
   980       double W=std::sqrt(-2*std::log(S)/S);
   981       return dim2::Point<double>(W*V1,W*V2);
   981       return dim2::Point<double>(W*V1,W*V2);
   982     }
   982     }
   983     /// A kind of two dimensional exponential distribution
   983     /// A kind of two dimensional exponential distribution
   984 
   984 
   985     /// This function provides a turning symmetric two-dimensional distribution.
   985     /// This function provides a turning symmetric two-dimensional distribution.
   986     /// The x-coordinate is of conditionally exponential distribution
   986     /// The x-coordinate is of conditionally exponential distribution
   987     /// with the condition that x is positive and y=0. If x is negative and 
   987     /// with the condition that x is positive and y=0. If x is negative and
   988     /// y=0 then, -x is of exponential distribution. The same is true for the
   988     /// y=0 then, -x is of exponential distribution. The same is true for the
   989     /// y-coordinate.
   989     /// y-coordinate.
   990     dim2::Point<double> exponential2() 
   990     dim2::Point<double> exponential2()
   991     {
   991     {
   992       double V1,V2,S;
   992       double V1,V2,S;
   993       do {
   993       do {
   994 	V1=2*real<double>()-1;
   994         V1=2*real<double>()-1;
   995 	V2=2*real<double>()-1;
   995         V2=2*real<double>()-1;
   996 	S=V1*V1+V2*V2;
   996         S=V1*V1+V2*V2;
   997       } while(S>=1);
   997       } while(S>=1);
   998       double W=-std::log(S)/S;
   998       double W=-std::log(S)/S;
   999       return dim2::Point<double>(W*V1,W*V2);
   999       return dim2::Point<double>(W*V1,W*V2);
  1000     }
  1000     }
  1001 
  1001 
  1002     ///@}    
  1002     ///@}
  1003   };
  1003   };
  1004 
  1004 
  1005 
  1005 
  1006   extern Random rnd;
  1006   extern Random rnd;
  1007 
  1007