lemon/random.h
author Alpar Juttner <alpar@cs.elte.hu>
Thu, 20 Mar 2008 21:59:35 +0000
changeset 104 cdbba181b786
parent 92 5d4decd1b870
child 110 f2d66d810c88
permissions -rw-r--r--
Restored (and modified) StoreBoolMap (it was removed in 7ff1c348ae0c)

- also restored _maps_bits::IteratorTraits
- removes the Functor template parameter from StoreBoolMap
- doc changed a bit
     1 /* -*- C++ -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library
     4  *
     5  * Copyright (C) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 /*
    20  * This file contains the reimplemented version of the Mersenne Twister
    21  * Generator of Matsumoto and Nishimura.
    22  *
    23  * See the appropriate copyright notice below.
    24  * 
    25  * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
    26  * All rights reserved.                          
    27  *
    28  * Redistribution and use in source and binary forms, with or without
    29  * modification, are permitted provided that the following conditions
    30  * are met:
    31  *
    32  * 1. Redistributions of source code must retain the above copyright
    33  *    notice, this list of conditions and the following disclaimer.
    34  *
    35  * 2. Redistributions in binary form must reproduce the above copyright
    36  *    notice, this list of conditions and the following disclaimer in the
    37  *    documentation and/or other materials provided with the distribution.
    38  *
    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 
    41  *    permission.
    42  *
    43  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
    44  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
    45  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
    46  * FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE
    47  * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
    48  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
    49  * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
    50  * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
    51  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
    52  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
    53  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
    54  * OF THE POSSIBILITY OF SUCH DAMAGE.
    55  *
    56  *
    57  * Any feedback is very welcome.
    58  * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
    59  * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
    60  */
    61 
    62 #ifndef LEMON_RANDOM_H
    63 #define LEMON_RANDOM_H
    64 
    65 #include <algorithm>
    66 #include <iterator>
    67 #include <vector>
    68 
    69 #include <ctime>
    70 
    71 #include <lemon/math.h>
    72 #include <lemon/dim2.h>
    73 
    74 ///\ingroup misc
    75 ///\file
    76 ///\brief Mersenne Twister random number generator
    77 
    78 namespace lemon {
    79 
    80   namespace _random_bits {
    81     
    82     template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
    83     struct RandomTraits {};
    84 
    85     template <typename _Word>
    86     struct RandomTraits<_Word, 32> {
    87 
    88       typedef _Word Word;
    89       static const int bits = 32;
    90 
    91       static const int length = 624;
    92       static const int shift = 397;
    93       
    94       static const Word mul = 0x6c078965u;
    95       static const Word arrayInit = 0x012BD6AAu;
    96       static const Word arrayMul1 = 0x0019660Du;
    97       static const Word arrayMul2 = 0x5D588B65u;
    98 
    99       static const Word mask = 0x9908B0DFu;
   100       static const Word loMask = (1u << 31) - 1;
   101       static const Word hiMask = ~loMask;
   102 
   103 
   104       static Word tempering(Word rnd) {
   105         rnd ^= (rnd >> 11);
   106         rnd ^= (rnd << 7) & 0x9D2C5680u;
   107         rnd ^= (rnd << 15) & 0xEFC60000u;
   108         rnd ^= (rnd >> 18);
   109         return rnd;
   110       }
   111 
   112     };
   113 
   114     template <typename _Word>
   115     struct RandomTraits<_Word, 64> {
   116 
   117       typedef _Word Word;
   118       static const int bits = 64;
   119 
   120       static const int length = 312;
   121       static const int shift = 156;
   122 
   123       static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
   124       static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
   125       static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
   126       static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
   127 
   128       static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
   129       static const Word loMask = (Word(1u) << 31) - 1;
   130       static const Word hiMask = ~loMask;
   131 
   132       static Word tempering(Word rnd) {
   133         rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
   134         rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
   135         rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
   136         rnd ^= (rnd >> 43);
   137         return rnd;
   138       }
   139 
   140     };
   141 
   142     template <typename _Word>
   143     class RandomCore {
   144     public:
   145 
   146       typedef _Word Word;
   147 
   148     private:
   149 
   150       static const int bits = RandomTraits<Word>::bits;
   151 
   152       static const int length = RandomTraits<Word>::length;
   153       static const int shift = RandomTraits<Word>::shift;
   154 
   155     public:
   156 
   157       void initState() {
   158         static const Word seedArray[4] = {
   159           0x12345u, 0x23456u, 0x34567u, 0x45678u
   160         };
   161     
   162         initState(seedArray, seedArray + 4);
   163       }
   164 
   165       void initState(Word seed) {
   166 
   167         static const Word mul = RandomTraits<Word>::mul;
   168 
   169         current = state; 
   170 
   171         Word *curr = state + length - 1;
   172         curr[0] = seed; --curr;
   173         for (int i = 1; i < length; ++i) {
   174           curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
   175           --curr;
   176         }
   177       }
   178 
   179       template <typename Iterator>
   180       void initState(Iterator begin, Iterator end) {
   181 
   182         static const Word init = RandomTraits<Word>::arrayInit;
   183         static const Word mul1 = RandomTraits<Word>::arrayMul1;
   184         static const Word mul2 = RandomTraits<Word>::arrayMul2;
   185 
   186 
   187         Word *curr = state + length - 1; --curr;
   188         Iterator it = begin; int cnt = 0;
   189         int num;
   190 
   191         initState(init);
   192 
   193         num = length > end - begin ? length : end - begin;
   194         while (num--) {
   195           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) 
   196             + *it + cnt;
   197           ++it; ++cnt;
   198           if (it == end) {
   199             it = begin; cnt = 0;
   200           }
   201           if (curr == state) {
   202             curr = state + length - 1; curr[0] = state[0];
   203           }
   204           --curr;
   205         }
   206 
   207         num = length - 1; cnt = length - (curr - state) - 1;
   208         while (num--) {
   209           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
   210             - cnt;
   211           --curr; ++cnt;
   212           if (curr == state) {
   213             curr = state + length - 1; curr[0] = state[0]; --curr;
   214             cnt = 1;
   215           }
   216         }
   217         
   218         state[length - 1] = Word(1) << (bits - 1);
   219       }
   220       
   221       void copyState(const RandomCore& other) {
   222         std::copy(other.state, other.state + length, state);
   223         current = state + (other.current - other.state);
   224       }
   225 
   226       Word operator()() {
   227         if (current == state) fillState();
   228         --current;
   229         Word rnd = *current;
   230         return RandomTraits<Word>::tempering(rnd);
   231       }
   232 
   233     private:
   234 
   235   
   236       void fillState() {
   237         static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
   238         static const Word loMask = RandomTraits<Word>::loMask;
   239         static const Word hiMask = RandomTraits<Word>::hiMask;
   240 
   241         current = state + length; 
   242 
   243         register Word *curr = state + length - 1;
   244         register long num;
   245       
   246         num = length - shift;
   247         while (num--) {
   248           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   249             curr[- shift] ^ mask[curr[-1] & 1ul];
   250           --curr;
   251         }
   252         num = shift - 1;
   253         while (num--) {
   254           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   255             curr[length - shift] ^ mask[curr[-1] & 1ul];
   256           --curr;
   257         }
   258         state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
   259           curr[length - shift] ^ mask[curr[length - 1] & 1ul];
   260 
   261       }
   262 
   263   
   264       Word *current;
   265       Word state[length];
   266       
   267     };
   268 
   269 
   270     template <typename Result, 
   271               int shift = (std::numeric_limits<Result>::digits + 1) / 2>
   272     struct Masker {
   273       static Result mask(const Result& result) {
   274         return Masker<Result, (shift + 1) / 2>::
   275           mask(static_cast<Result>(result | (result >> shift)));
   276       }
   277     };
   278     
   279     template <typename Result>
   280     struct Masker<Result, 1> {
   281       static Result mask(const Result& result) {
   282         return static_cast<Result>(result | (result >> 1));
   283       }
   284     };
   285 
   286     template <typename Result, typename Word, 
   287               int rest = std::numeric_limits<Result>::digits, int shift = 0, 
   288               bool last = rest <= std::numeric_limits<Word>::digits>
   289     struct IntConversion {
   290       static const int bits = std::numeric_limits<Word>::digits;
   291     
   292       static Result convert(RandomCore<Word>& rnd) {
   293         return static_cast<Result>(rnd() >> (bits - rest)) << shift;
   294       }
   295       
   296     }; 
   297 
   298     template <typename Result, typename Word, int rest, int shift> 
   299     struct IntConversion<Result, Word, rest, shift, false> {
   300       static const int bits = std::numeric_limits<Word>::digits;
   301 
   302       static Result convert(RandomCore<Word>& rnd) {
   303         return (static_cast<Result>(rnd()) << shift) | 
   304           IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
   305       }
   306     };
   307 
   308 
   309     template <typename Result, typename Word,
   310               bool one_word = (std::numeric_limits<Word>::digits < 
   311 			       std::numeric_limits<Result>::digits) >
   312     struct Mapping {
   313       static Result map(RandomCore<Word>& rnd, const Result& bound) {
   314         Word max = Word(bound - 1);
   315         Result mask = Masker<Result>::mask(bound - 1);
   316         Result num;
   317         do {
   318           num = IntConversion<Result, Word>::convert(rnd) & mask; 
   319         } while (num > max);
   320         return num;
   321       }
   322     };
   323 
   324     template <typename Result, typename Word>
   325     struct Mapping<Result, Word, false> {
   326       static Result map(RandomCore<Word>& rnd, const Result& bound) {
   327         Word max = Word(bound - 1);
   328         Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
   329           ::mask(max);
   330         Word num;
   331         do {
   332           num = rnd() & mask;
   333         } while (num > max);
   334         return num;
   335       }
   336     };
   337 
   338     template <typename Result, int exp, bool pos = (exp >= 0)>
   339     struct ShiftMultiplier {
   340       static const Result multiplier() {
   341         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   342         res *= res;
   343         if ((exp & 1) == 1) res *= static_cast<Result>(2.0);
   344         return res; 
   345       }
   346     };
   347 
   348     template <typename Result, int exp>
   349     struct ShiftMultiplier<Result, exp, false> {
   350       static const Result multiplier() {
   351         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   352         res *= res;
   353         if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
   354         return res; 
   355       }
   356     };
   357 
   358     template <typename Result>
   359     struct ShiftMultiplier<Result, 0, true> {
   360       static const Result multiplier() {
   361         return static_cast<Result>(1.0); 
   362       }
   363     };
   364 
   365     template <typename Result>
   366     struct ShiftMultiplier<Result, -20, true> {
   367       static const Result multiplier() {
   368         return static_cast<Result>(1.0/1048576.0); 
   369       }
   370     };
   371     
   372     template <typename Result>
   373     struct ShiftMultiplier<Result, -32, true> {
   374       static const Result multiplier() {
   375         return static_cast<Result>(1.0/424967296.0); 
   376       }
   377     };
   378 
   379     template <typename Result>
   380     struct ShiftMultiplier<Result, -53, true> {
   381       static const Result multiplier() {
   382         return static_cast<Result>(1.0/9007199254740992.0); 
   383       }
   384     };
   385 
   386     template <typename Result>
   387     struct ShiftMultiplier<Result, -64, true> {
   388       static const Result multiplier() {
   389         return static_cast<Result>(1.0/18446744073709551616.0); 
   390       }
   391     };
   392 
   393     template <typename Result, int exp>
   394     struct Shifting {
   395       static Result shift(const Result& result) {
   396         return result * ShiftMultiplier<Result, exp>::multiplier();
   397       }
   398     };
   399 
   400     template <typename Result, typename Word,
   401               int rest = std::numeric_limits<Result>::digits, int shift = 0, 
   402               bool last = rest <= std::numeric_limits<Word>::digits>
   403     struct RealConversion{ 
   404       static const int bits = std::numeric_limits<Word>::digits;
   405 
   406       static Result convert(RandomCore<Word>& rnd) {
   407         return Shifting<Result, - shift - rest>::
   408           shift(static_cast<Result>(rnd() >> (bits - rest)));
   409       }
   410     };
   411 
   412     template <typename Result, typename Word, int rest, int shift>
   413     struct RealConversion<Result, Word, rest, shift, false> { 
   414       static const int bits = std::numeric_limits<Word>::digits;
   415 
   416       static Result convert(RandomCore<Word>& rnd) {
   417         return Shifting<Result, - shift - bits>::
   418           shift(static_cast<Result>(rnd())) +
   419           RealConversion<Result, Word, rest-bits, shift + bits>::
   420           convert(rnd);
   421       }
   422     };
   423 
   424     template <typename Result, typename Word>
   425     struct Initializer {
   426 
   427       template <typename Iterator>
   428       static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
   429         std::vector<Word> ws;
   430         for (Iterator it = begin; it != end; ++it) {
   431           ws.push_back(Word(*it));
   432         }
   433         rnd.initState(ws.begin(), ws.end());
   434       }
   435 
   436       static void init(RandomCore<Word>& rnd, Result seed) {
   437         rnd.initState(seed);
   438       }
   439     };
   440 
   441     template <typename Word>
   442     struct BoolConversion {
   443       static bool convert(RandomCore<Word>& rnd) {
   444         return (rnd() & 1) == 1;
   445       }
   446     };
   447 
   448     template <typename Word>
   449     struct BoolProducer {
   450       Word buffer;
   451       int num;
   452       
   453       BoolProducer() : num(0) {}
   454 
   455       bool convert(RandomCore<Word>& rnd) {
   456         if (num == 0) {
   457           buffer = rnd();
   458           num = RandomTraits<Word>::bits;
   459         }
   460         bool r = (buffer & 1);
   461         buffer >>= 1;
   462         --num;
   463         return r;
   464       }
   465     };
   466 
   467   }
   468 
   469   /// \ingroup misc
   470   ///
   471   /// \brief Mersenne Twister random number generator
   472   ///
   473   /// The Mersenne Twister is a twisted generalized feedback
   474   /// shift-register generator of Matsumoto and Nishimura. The period
   475   /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
   476   /// equi-distributed in 623 dimensions for 32-bit numbers. The time
   477   /// performance of this generator is comparable to the commonly used
   478   /// generators.
   479   ///
   480   /// This implementation is specialized for both 32-bit and 64-bit
   481   /// architectures. The generators differ sligthly in the
   482   /// initialization and generation phase so they produce two
   483   /// completly different sequences.
   484   ///
   485   /// The generator gives back random numbers of serveral types. To
   486   /// get a random number from a range of a floating point type you
   487   /// can use one form of the \c operator() or the \c real() member
   488   /// function. If you want to get random number from the {0, 1, ...,
   489   /// n-1} integer range use the \c operator[] or the \c integer()
   490   /// method. And to get random number from the whole range of an
   491   /// integer type you can use the argumentless \c integer() or \c
   492   /// uinteger() functions. After all you can get random bool with
   493   /// equal chance of true and false or given probability of true
   494   /// result with the \c boolean() member functions.
   495   ///
   496   ///\code
   497   /// // The commented code is identical to the other
   498   /// double a = rnd();                     // [0.0, 1.0)
   499   /// // double a = rnd.real();             // [0.0, 1.0)
   500   /// double b = rnd(100.0);                // [0.0, 100.0)
   501   /// // double b = rnd.real(100.0);        // [0.0, 100.0)
   502   /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
   503   /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
   504   /// int d = rnd[100000];                  // 0..99999
   505   /// // int d = rnd.integer(100000);       // 0..99999
   506   /// int e = rnd[6] + 1;                   // 1..6
   507   /// // int e = rnd.integer(1, 1 + 6);     // 1..6
   508   /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
   509   /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
   510   /// bool g = rnd.boolean();               // P(g = true) = 0.5
   511   /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
   512   ///\endcode
   513   ///
   514   /// LEMON provides a global instance of the random number
   515   /// generator which name is \ref lemon::rnd "rnd". Usually it is a
   516   /// good programming convenience to use this global generator to get
   517   /// random numbers.
   518   class Random {
   519   private:
   520 
   521     // Architecture word
   522     typedef unsigned long Word;
   523     
   524     _random_bits::RandomCore<Word> core;
   525     _random_bits::BoolProducer<Word> bool_producer;
   526     
   527 
   528   public:
   529 
   530     /// \brief Default constructor
   531     ///
   532     /// Constructor with constant seeding.
   533     Random() { core.initState(); }
   534 
   535     /// \brief Constructor with seed
   536     ///
   537     /// Constructor with seed. The current number type will be converted
   538     /// to the architecture word type.
   539     template <typename Number>
   540     Random(Number seed) { 
   541       _random_bits::Initializer<Number, Word>::init(core, seed);
   542     }
   543 
   544     /// \brief Constructor with array seeding
   545     ///
   546     /// Constructor with array seeding. The given range should contain
   547     /// any number type and the numbers will be converted to the
   548     /// architecture word type.
   549     template <typename Iterator>
   550     Random(Iterator begin, Iterator end) { 
   551       typedef typename std::iterator_traits<Iterator>::value_type Number;
   552       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   553     }
   554 
   555     /// \brief Copy constructor
   556     ///
   557     /// Copy constructor. The generated sequence will be identical to
   558     /// the other sequence. It can be used to save the current state
   559     /// of the generator and later use it to generate the same
   560     /// sequence.
   561     Random(const Random& other) {
   562       core.copyState(other.core);
   563     }
   564 
   565     /// \brief Assign operator
   566     ///
   567     /// Assign operator. The generated sequence will be identical to
   568     /// the other sequence. It can be used to save the current state
   569     /// of the generator and later use it to generate the same
   570     /// sequence.
   571     Random& operator=(const Random& other) {
   572       if (&other != this) {
   573         core.copyState(other.core);
   574       }
   575       return *this;
   576     }
   577 
   578     /// \brief Seeding random sequence
   579     ///
   580     /// Seeding the random sequence. The current number type will be
   581     /// converted to the architecture word type.
   582     template <typename Number>
   583     void seed(Number seed) { 
   584       _random_bits::Initializer<Number, Word>::init(core, seed);
   585     }
   586 
   587     /// \brief Seeding random sequence
   588     ///
   589     /// Seeding the random sequence. The given range should contain
   590     /// any number type and the numbers will be converted to the
   591     /// architecture word type.
   592     template <typename Iterator>
   593     void seed(Iterator begin, Iterator end) { 
   594       typedef typename std::iterator_traits<Iterator>::value_type Number;
   595       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   596     }
   597 
   598     /// \brief Returns a random real number from the range [0, 1)
   599     ///
   600     /// It returns a random real number from the range [0, 1). The
   601     /// default Number type is \c double.
   602     template <typename Number>
   603     Number real() {
   604       return _random_bits::RealConversion<Number, Word>::convert(core);
   605     }
   606 
   607     double real() {
   608       return real<double>();
   609     }
   610 
   611     /// \brief Returns a random real number the range [0, b)
   612     ///
   613     /// It returns a random real number from the range [0, b).
   614     template <typename Number>
   615     Number real(Number b) { 
   616       return real<Number>() * b; 
   617     }
   618 
   619     /// \brief Returns a random real number from the range [a, b)
   620     ///
   621     /// It returns a random real number from the range [a, b).
   622     template <typename Number>
   623     Number real(Number a, Number b) { 
   624       return real<Number>() * (b - a) + a; 
   625     }
   626 
   627     /// \brief Returns a random real number from the range [0, 1)
   628     ///
   629     /// It returns a random double from the range [0, 1).
   630     double operator()() {
   631       return real<double>();
   632     }
   633 
   634     /// \brief Returns a random real number from the range [0, b)
   635     ///
   636     /// It returns a random real number from the range [0, b).
   637     template <typename Number>
   638     Number operator()(Number b) { 
   639       return real<Number>() * b; 
   640     }
   641 
   642     /// \brief Returns a random real number from the range [a, b)
   643     ///
   644     /// It returns a random real number from the range [a, b).
   645     template <typename Number>
   646     Number operator()(Number a, Number b) { 
   647       return real<Number>() * (b - a) + a; 
   648     }
   649 
   650     /// \brief Returns a random integer from a range
   651     ///
   652     /// It returns a random integer from the range {0, 1, ..., b - 1}.
   653     template <typename Number>
   654     Number integer(Number b) {
   655       return _random_bits::Mapping<Number, Word>::map(core, b);
   656     }
   657 
   658     /// \brief Returns a random integer from a range
   659     ///
   660     /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
   661     template <typename Number>
   662     Number integer(Number a, Number b) {
   663       return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
   664     }
   665 
   666     /// \brief Returns a random integer from a range
   667     ///
   668     /// It returns a random integer from the range {0, 1, ..., b - 1}.
   669     template <typename Number>
   670     Number operator[](Number b) {
   671       return _random_bits::Mapping<Number, Word>::map(core, b);
   672     }
   673 
   674     /// \brief Returns a random non-negative integer
   675     ///
   676     /// It returns a random non-negative integer uniformly from the
   677     /// whole range of the current \c Number type. The default result
   678     /// type of this function is <tt>unsigned int</tt>.
   679     template <typename Number>
   680     Number uinteger() {
   681       return _random_bits::IntConversion<Number, Word>::convert(core);
   682     }
   683 
   684     unsigned int uinteger() {
   685       return uinteger<unsigned int>();
   686     }
   687 
   688     /// \brief Returns a random integer
   689     ///
   690     /// It returns a random integer uniformly from the whole range of
   691     /// the current \c Number type. The default result type of this
   692     /// function is \c int.
   693     template <typename Number>
   694     Number integer() {
   695       static const int nb = std::numeric_limits<Number>::digits + 
   696         (std::numeric_limits<Number>::is_signed ? 1 : 0);
   697       return _random_bits::IntConversion<Number, Word, nb>::convert(core);
   698     }
   699 
   700     int integer() {
   701       return integer<int>();
   702     }
   703     
   704     /// \brief Returns a random bool
   705     ///
   706     /// It returns a random bool. The generator holds a buffer for
   707     /// random bits. Every time when it become empty the generator makes
   708     /// a new random word and fill the buffer up.
   709     bool boolean() {
   710       return bool_producer.convert(core);
   711     }
   712 
   713     ///\name Non-uniform distributions
   714     ///
   715     
   716     ///@{
   717     
   718     /// \brief Returns a random bool
   719     ///
   720     /// It returns a random bool with given probability of true result.
   721     bool boolean(double p) {
   722       return operator()() < p;
   723     }
   724 
   725     /// Standard Gauss distribution
   726 
   727     /// Standard Gauss distribution.
   728     /// \note The Cartesian form of the Box-Muller
   729     /// transformation is used to generate a random normal distribution.
   730     /// \todo Consider using the "ziggurat" method instead.
   731     double gauss() 
   732     {
   733       double V1,V2,S;
   734       do {
   735 	V1=2*real<double>()-1;
   736 	V2=2*real<double>()-1;
   737 	S=V1*V1+V2*V2;
   738       } while(S>=1);
   739       return std::sqrt(-2*std::log(S)/S)*V1;
   740     }
   741     /// Gauss distribution with given mean and standard deviation
   742 
   743     /// Gauss distribution with given mean and standard deviation.
   744     /// \sa gauss()
   745     double gauss(double mean,double std_dev)
   746     {
   747       return gauss()*std_dev+mean;
   748     }
   749 
   750     /// Exponential distribution with given mean
   751 
   752     /// This function generates an exponential distribution random number
   753     /// with mean <tt>1/lambda</tt>.
   754     ///
   755     double exponential(double lambda=1.0)
   756     {
   757       return -std::log(1.0-real<double>())/lambda;
   758     }
   759 
   760     /// Gamma distribution with given integer shape
   761 
   762     /// This function generates a gamma distribution random number.
   763     /// 
   764     ///\param k shape parameter (<tt>k>0</tt> integer)
   765     double gamma(int k) 
   766     {
   767       double s = 0;
   768       for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
   769       return s;
   770     }
   771     
   772     /// Gamma distribution with given shape and scale parameter
   773 
   774     /// This function generates a gamma distribution random number.
   775     /// 
   776     ///\param k shape parameter (<tt>k>0</tt>)
   777     ///\param theta scale parameter
   778     ///
   779     double gamma(double k,double theta=1.0)
   780     {
   781       double xi,nu;
   782       const double delta = k-std::floor(k);
   783       const double v0=E/(E-delta);
   784       do {
   785 	double V0=1.0-real<double>();
   786 	double V1=1.0-real<double>();
   787 	double V2=1.0-real<double>();
   788 	if(V2<=v0) 
   789 	  {
   790 	    xi=std::pow(V1,1.0/delta);
   791 	    nu=V0*std::pow(xi,delta-1.0);
   792 	  }
   793 	else 
   794 	  {
   795 	    xi=1.0-std::log(V1);
   796 	    nu=V0*std::exp(-xi);
   797 	  }
   798       } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
   799       return theta*(xi-gamma(int(std::floor(k))));
   800     }
   801     
   802     /// Weibull distribution
   803 
   804     /// This function generates a Weibull distribution random number.
   805     /// 
   806     ///\param k shape parameter (<tt>k>0</tt>)
   807     ///\param lambda scale parameter (<tt>lambda>0</tt>)
   808     ///
   809     double weibull(double k,double lambda)
   810     {
   811       return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
   812     }  
   813       
   814     /// Pareto distribution
   815 
   816     /// This function generates a Pareto distribution random number.
   817     /// 
   818     ///\param k shape parameter (<tt>k>0</tt>)
   819     ///\param x_min location parameter (<tt>x_min>0</tt>)
   820     ///
   821     double pareto(double k,double x_min)
   822     {
   823       return exponential(gamma(k,1.0/x_min));
   824     }  
   825       
   826     /// Poisson distribution
   827 
   828     /// This function generates a Poisson distribution random number with
   829     /// parameter \c lambda.
   830     /// 
   831     /// The probability mass function of this distribusion is
   832     /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
   833     /// \note The algorithm is taken from the book of Donald E. Knuth titled
   834     /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
   835     /// return value.
   836     
   837     int poisson(double lambda)
   838     {
   839       const double l = std::exp(-lambda);
   840       int k=0;
   841       double p = 1.0;
   842       do {
   843 	k++;
   844 	p*=real<double>();
   845       } while (p>=l);
   846       return k-1;
   847     }  
   848       
   849     ///@}
   850     
   851     ///\name Two dimensional distributions
   852     ///
   853 
   854     ///@{
   855     
   856     /// Uniform distribution on the full unit circle
   857 
   858     /// Uniform distribution on the full unit circle.
   859     ///
   860     dim2::Point<double> disc() 
   861     {
   862       double V1,V2;
   863       do {
   864 	V1=2*real<double>()-1;
   865 	V2=2*real<double>()-1;
   866 	
   867       } while(V1*V1+V2*V2>=1);
   868       return dim2::Point<double>(V1,V2);
   869     }
   870     /// A kind of two dimensional Gauss distribution
   871 
   872     /// This function provides a turning symmetric two-dimensional distribution.
   873     /// Both coordinates are of standard normal distribution, but they are not
   874     /// independent.
   875     ///
   876     /// \note The coordinates are the two random variables provided by
   877     /// the Box-Muller method.
   878     dim2::Point<double> gauss2()
   879     {
   880       double V1,V2,S;
   881       do {
   882 	V1=2*real<double>()-1;
   883 	V2=2*real<double>()-1;
   884 	S=V1*V1+V2*V2;
   885       } while(S>=1);
   886       double W=std::sqrt(-2*std::log(S)/S);
   887       return dim2::Point<double>(W*V1,W*V2);
   888     }
   889     /// A kind of two dimensional exponential distribution
   890 
   891     /// This function provides a turning symmetric two-dimensional distribution.
   892     /// The x-coordinate is of conditionally exponential distribution
   893     /// with the condition that x is positive and y=0. If x is negative and 
   894     /// y=0 then, -x is of exponential distribution. The same is true for the
   895     /// y-coordinate.
   896     dim2::Point<double> exponential2() 
   897     {
   898       double V1,V2,S;
   899       do {
   900 	V1=2*real<double>()-1;
   901 	V2=2*real<double>()-1;
   902 	S=V1*V1+V2*V2;
   903       } while(S>=1);
   904       double W=-std::log(S)/S;
   905       return dim2::Point<double>(W*V1,W*V2);
   906     }
   907 
   908     ///@}    
   909   };
   910 
   911 
   912   extern Random rnd;
   913 
   914 }
   915 
   916 #endif