lemon/random.h
author Alpar Juttner <alpar@cs.elte.hu>
Tue, 17 Jun 2008 12:47:15 +0100
changeset 176 47b69d4b0759
parent 110 f2d66d810c88
child 177 b685e12e08c0
permissions -rw-r--r--
Merge
     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 #include <limits>
    69 
    70 #include <lemon/math.h>
    71 #include <lemon/dim2.h>
    72 
    73 ///\ingroup misc
    74 ///\file
    75 ///\brief Mersenne Twister random number generator
    76 
    77 namespace lemon {
    78 
    79   namespace _random_bits {
    80     
    81     template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
    82     struct RandomTraits {};
    83 
    84     template <typename _Word>
    85     struct RandomTraits<_Word, 32> {
    86 
    87       typedef _Word Word;
    88       static const int bits = 32;
    89 
    90       static const int length = 624;
    91       static const int shift = 397;
    92       
    93       static const Word mul = 0x6c078965u;
    94       static const Word arrayInit = 0x012BD6AAu;
    95       static const Word arrayMul1 = 0x0019660Du;
    96       static const Word arrayMul2 = 0x5D588B65u;
    97 
    98       static const Word mask = 0x9908B0DFu;
    99       static const Word loMask = (1u << 31) - 1;
   100       static const Word hiMask = ~loMask;
   101 
   102 
   103       static Word tempering(Word rnd) {
   104         rnd ^= (rnd >> 11);
   105         rnd ^= (rnd << 7) & 0x9D2C5680u;
   106         rnd ^= (rnd << 15) & 0xEFC60000u;
   107         rnd ^= (rnd >> 18);
   108         return rnd;
   109       }
   110 
   111     };
   112 
   113     template <typename _Word>
   114     struct RandomTraits<_Word, 64> {
   115 
   116       typedef _Word Word;
   117       static const int bits = 64;
   118 
   119       static const int length = 312;
   120       static const int shift = 156;
   121 
   122       static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
   123       static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
   124       static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
   125       static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
   126 
   127       static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
   128       static const Word loMask = (Word(1u) << 31) - 1;
   129       static const Word hiMask = ~loMask;
   130 
   131       static Word tempering(Word rnd) {
   132         rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
   133         rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
   134         rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
   135         rnd ^= (rnd >> 43);
   136         return rnd;
   137       }
   138 
   139     };
   140 
   141     template <typename _Word>
   142     class RandomCore {
   143     public:
   144 
   145       typedef _Word Word;
   146 
   147     private:
   148 
   149       static const int bits = RandomTraits<Word>::bits;
   150 
   151       static const int length = RandomTraits<Word>::length;
   152       static const int shift = RandomTraits<Word>::shift;
   153 
   154     public:
   155 
   156       void initState() {
   157         static const Word seedArray[4] = {
   158           0x12345u, 0x23456u, 0x34567u, 0x45678u
   159         };
   160     
   161         initState(seedArray, seedArray + 4);
   162       }
   163 
   164       void initState(Word seed) {
   165 
   166         static const Word mul = RandomTraits<Word>::mul;
   167 
   168         current = state; 
   169 
   170         Word *curr = state + length - 1;
   171         curr[0] = seed; --curr;
   172         for (int i = 1; i < length; ++i) {
   173           curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
   174           --curr;
   175         }
   176       }
   177 
   178       template <typename Iterator>
   179       void initState(Iterator begin, Iterator end) {
   180 
   181         static const Word init = RandomTraits<Word>::arrayInit;
   182         static const Word mul1 = RandomTraits<Word>::arrayMul1;
   183         static const Word mul2 = RandomTraits<Word>::arrayMul2;
   184 
   185 
   186         Word *curr = state + length - 1; --curr;
   187         Iterator it = begin; int cnt = 0;
   188         int num;
   189 
   190         initState(init);
   191 
   192         num = length > end - begin ? length : end - begin;
   193         while (num--) {
   194           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) 
   195             + *it + cnt;
   196           ++it; ++cnt;
   197           if (it == end) {
   198             it = begin; cnt = 0;
   199           }
   200           if (curr == state) {
   201             curr = state + length - 1; curr[0] = state[0];
   202           }
   203           --curr;
   204         }
   205 
   206         num = length - 1; cnt = length - (curr - state) - 1;
   207         while (num--) {
   208           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
   209             - cnt;
   210           --curr; ++cnt;
   211           if (curr == state) {
   212             curr = state + length - 1; curr[0] = state[0]; --curr;
   213             cnt = 1;
   214           }
   215         }
   216         
   217         state[length - 1] = Word(1) << (bits - 1);
   218       }
   219       
   220       void copyState(const RandomCore& other) {
   221         std::copy(other.state, other.state + length, state);
   222         current = state + (other.current - other.state);
   223       }
   224 
   225       Word operator()() {
   226         if (current == state) fillState();
   227         --current;
   228         Word rnd = *current;
   229         return RandomTraits<Word>::tempering(rnd);
   230       }
   231 
   232     private:
   233 
   234   
   235       void fillState() {
   236         static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
   237         static const Word loMask = RandomTraits<Word>::loMask;
   238         static const Word hiMask = RandomTraits<Word>::hiMask;
   239 
   240         current = state + length; 
   241 
   242         register Word *curr = state + length - 1;
   243         register long num;
   244       
   245         num = length - shift;
   246         while (num--) {
   247           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   248             curr[- shift] ^ mask[curr[-1] & 1ul];
   249           --curr;
   250         }
   251         num = shift - 1;
   252         while (num--) {
   253           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   254             curr[length - shift] ^ mask[curr[-1] & 1ul];
   255           --curr;
   256         }
   257         state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
   258           curr[length - shift] ^ mask[curr[length - 1] & 1ul];
   259 
   260       }
   261 
   262   
   263       Word *current;
   264       Word state[length];
   265       
   266     };
   267 
   268 
   269     template <typename Result, 
   270               int shift = (std::numeric_limits<Result>::digits + 1) / 2>
   271     struct Masker {
   272       static Result mask(const Result& result) {
   273         return Masker<Result, (shift + 1) / 2>::
   274           mask(static_cast<Result>(result | (result >> shift)));
   275       }
   276     };
   277     
   278     template <typename Result>
   279     struct Masker<Result, 1> {
   280       static Result mask(const Result& result) {
   281         return static_cast<Result>(result | (result >> 1));
   282       }
   283     };
   284 
   285     template <typename Result, typename Word, 
   286               int rest = std::numeric_limits<Result>::digits, int shift = 0, 
   287               bool last = rest <= std::numeric_limits<Word>::digits>
   288     struct IntConversion {
   289       static const int bits = std::numeric_limits<Word>::digits;
   290     
   291       static Result convert(RandomCore<Word>& rnd) {
   292         return static_cast<Result>(rnd() >> (bits - rest)) << shift;
   293       }
   294       
   295     }; 
   296 
   297     template <typename Result, typename Word, int rest, int shift> 
   298     struct IntConversion<Result, Word, rest, shift, false> {
   299       static const int bits = std::numeric_limits<Word>::digits;
   300 
   301       static Result convert(RandomCore<Word>& rnd) {
   302         return (static_cast<Result>(rnd()) << shift) | 
   303           IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
   304       }
   305     };
   306 
   307 
   308     template <typename Result, typename Word,
   309               bool one_word = (std::numeric_limits<Word>::digits < 
   310 			       std::numeric_limits<Result>::digits) >
   311     struct Mapping {
   312       static Result map(RandomCore<Word>& rnd, const Result& bound) {
   313         Word max = Word(bound - 1);
   314         Result mask = Masker<Result>::mask(bound - 1);
   315         Result num;
   316         do {
   317           num = IntConversion<Result, Word>::convert(rnd) & mask; 
   318         } while (num > max);
   319         return num;
   320       }
   321     };
   322 
   323     template <typename Result, typename Word>
   324     struct Mapping<Result, Word, false> {
   325       static Result map(RandomCore<Word>& rnd, const Result& bound) {
   326         Word max = Word(bound - 1);
   327         Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
   328           ::mask(max);
   329         Word num;
   330         do {
   331           num = rnd() & mask;
   332         } while (num > max);
   333         return num;
   334       }
   335     };
   336 
   337     template <typename Result, int exp, bool pos = (exp >= 0)>
   338     struct ShiftMultiplier {
   339       static const Result multiplier() {
   340         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   341         res *= res;
   342         if ((exp & 1) == 1) res *= static_cast<Result>(2.0);
   343         return res; 
   344       }
   345     };
   346 
   347     template <typename Result, int exp>
   348     struct ShiftMultiplier<Result, exp, false> {
   349       static const Result multiplier() {
   350         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   351         res *= res;
   352         if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
   353         return res; 
   354       }
   355     };
   356 
   357     template <typename Result>
   358     struct ShiftMultiplier<Result, 0, true> {
   359       static const Result multiplier() {
   360         return static_cast<Result>(1.0); 
   361       }
   362     };
   363 
   364     template <typename Result>
   365     struct ShiftMultiplier<Result, -20, true> {
   366       static const Result multiplier() {
   367         return static_cast<Result>(1.0/1048576.0); 
   368       }
   369     };
   370     
   371     template <typename Result>
   372     struct ShiftMultiplier<Result, -32, true> {
   373       static const Result multiplier() {
   374         return static_cast<Result>(1.0/424967296.0); 
   375       }
   376     };
   377 
   378     template <typename Result>
   379     struct ShiftMultiplier<Result, -53, true> {
   380       static const Result multiplier() {
   381         return static_cast<Result>(1.0/9007199254740992.0); 
   382       }
   383     };
   384 
   385     template <typename Result>
   386     struct ShiftMultiplier<Result, -64, true> {
   387       static const Result multiplier() {
   388         return static_cast<Result>(1.0/18446744073709551616.0); 
   389       }
   390     };
   391 
   392     template <typename Result, int exp>
   393     struct Shifting {
   394       static Result shift(const Result& result) {
   395         return result * ShiftMultiplier<Result, exp>::multiplier();
   396       }
   397     };
   398 
   399     template <typename Result, typename Word,
   400               int rest = std::numeric_limits<Result>::digits, int shift = 0, 
   401               bool last = rest <= std::numeric_limits<Word>::digits>
   402     struct RealConversion{ 
   403       static const int bits = std::numeric_limits<Word>::digits;
   404 
   405       static Result convert(RandomCore<Word>& rnd) {
   406         return Shifting<Result, - shift - rest>::
   407           shift(static_cast<Result>(rnd() >> (bits - rest)));
   408       }
   409     };
   410 
   411     template <typename Result, typename Word, int rest, int shift>
   412     struct RealConversion<Result, Word, rest, shift, false> { 
   413       static const int bits = std::numeric_limits<Word>::digits;
   414 
   415       static Result convert(RandomCore<Word>& rnd) {
   416         return Shifting<Result, - shift - bits>::
   417           shift(static_cast<Result>(rnd())) +
   418           RealConversion<Result, Word, rest-bits, shift + bits>::
   419           convert(rnd);
   420       }
   421     };
   422 
   423     template <typename Result, typename Word>
   424     struct Initializer {
   425 
   426       template <typename Iterator>
   427       static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
   428         std::vector<Word> ws;
   429         for (Iterator it = begin; it != end; ++it) {
   430           ws.push_back(Word(*it));
   431         }
   432         rnd.initState(ws.begin(), ws.end());
   433       }
   434 
   435       static void init(RandomCore<Word>& rnd, Result seed) {
   436         rnd.initState(seed);
   437       }
   438     };
   439 
   440     template <typename Word>
   441     struct BoolConversion {
   442       static bool convert(RandomCore<Word>& rnd) {
   443         return (rnd() & 1) == 1;
   444       }
   445     };
   446 
   447     template <typename Word>
   448     struct BoolProducer {
   449       Word buffer;
   450       int num;
   451       
   452       BoolProducer() : num(0) {}
   453 
   454       bool convert(RandomCore<Word>& rnd) {
   455         if (num == 0) {
   456           buffer = rnd();
   457           num = RandomTraits<Word>::bits;
   458         }
   459         bool r = (buffer & 1);
   460         buffer >>= 1;
   461         --num;
   462         return r;
   463       }
   464     };
   465 
   466   }
   467 
   468   /// \ingroup misc
   469   ///
   470   /// \brief Mersenne Twister random number generator
   471   ///
   472   /// The Mersenne Twister is a twisted generalized feedback
   473   /// shift-register generator of Matsumoto and Nishimura. The period
   474   /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
   475   /// equi-distributed in 623 dimensions for 32-bit numbers. The time
   476   /// performance of this generator is comparable to the commonly used
   477   /// generators.
   478   ///
   479   /// This implementation is specialized for both 32-bit and 64-bit
   480   /// architectures. The generators differ sligthly in the
   481   /// initialization and generation phase so they produce two
   482   /// completly different sequences.
   483   ///
   484   /// The generator gives back random numbers of serveral types. To
   485   /// get a random number from a range of a floating point type you
   486   /// can use one form of the \c operator() or the \c real() member
   487   /// function. If you want to get random number from the {0, 1, ...,
   488   /// n-1} integer range use the \c operator[] or the \c integer()
   489   /// method. And to get random number from the whole range of an
   490   /// integer type you can use the argumentless \c integer() or \c
   491   /// uinteger() functions. After all you can get random bool with
   492   /// equal chance of true and false or given probability of true
   493   /// result with the \c boolean() member functions.
   494   ///
   495   ///\code
   496   /// // The commented code is identical to the other
   497   /// double a = rnd();                     // [0.0, 1.0)
   498   /// // double a = rnd.real();             // [0.0, 1.0)
   499   /// double b = rnd(100.0);                // [0.0, 100.0)
   500   /// // double b = rnd.real(100.0);        // [0.0, 100.0)
   501   /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
   502   /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
   503   /// int d = rnd[100000];                  // 0..99999
   504   /// // int d = rnd.integer(100000);       // 0..99999
   505   /// int e = rnd[6] + 1;                   // 1..6
   506   /// // int e = rnd.integer(1, 1 + 6);     // 1..6
   507   /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
   508   /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
   509   /// bool g = rnd.boolean();               // P(g = true) = 0.5
   510   /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
   511   ///\endcode
   512   ///
   513   /// LEMON provides a global instance of the random number
   514   /// generator which name is \ref lemon::rnd "rnd". Usually it is a
   515   /// good programming convenience to use this global generator to get
   516   /// random numbers.
   517   class Random {
   518   private:
   519 
   520     // Architecture word
   521     typedef unsigned long Word;
   522     
   523     _random_bits::RandomCore<Word> core;
   524     _random_bits::BoolProducer<Word> bool_producer;
   525     
   526 
   527   public:
   528 
   529     /// \brief Default constructor
   530     ///
   531     /// Constructor with constant seeding.
   532     Random() { core.initState(); }
   533 
   534     /// \brief Constructor with seed
   535     ///
   536     /// Constructor with seed. The current number type will be converted
   537     /// to the architecture word type.
   538     template <typename Number>
   539     Random(Number seed) { 
   540       _random_bits::Initializer<Number, Word>::init(core, seed);
   541     }
   542 
   543     /// \brief Constructor with array seeding
   544     ///
   545     /// Constructor with array seeding. The given range should contain
   546     /// any number type and the numbers will be converted to the
   547     /// architecture word type.
   548     template <typename Iterator>
   549     Random(Iterator begin, Iterator end) { 
   550       typedef typename std::iterator_traits<Iterator>::value_type Number;
   551       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   552     }
   553 
   554     /// \brief Copy constructor
   555     ///
   556     /// Copy constructor. The generated sequence will be identical to
   557     /// the other sequence. It can be used to save the current state
   558     /// of the generator and later use it to generate the same
   559     /// sequence.
   560     Random(const Random& other) {
   561       core.copyState(other.core);
   562     }
   563 
   564     /// \brief Assign operator
   565     ///
   566     /// Assign operator. The generated sequence will be identical to
   567     /// the other sequence. It can be used to save the current state
   568     /// of the generator and later use it to generate the same
   569     /// sequence.
   570     Random& operator=(const Random& other) {
   571       if (&other != this) {
   572         core.copyState(other.core);
   573       }
   574       return *this;
   575     }
   576 
   577     /// \brief Seeding random sequence
   578     ///
   579     /// Seeding the random sequence. The current number type will be
   580     /// converted to the architecture word type.
   581     template <typename Number>
   582     void seed(Number seed) { 
   583       _random_bits::Initializer<Number, Word>::init(core, seed);
   584     }
   585 
   586     /// \brief Seeding random sequence
   587     ///
   588     /// Seeding the random sequence. The given range should contain
   589     /// any number type and the numbers will be converted to the
   590     /// architecture word type.
   591     template <typename Iterator>
   592     void seed(Iterator begin, Iterator end) { 
   593       typedef typename std::iterator_traits<Iterator>::value_type Number;
   594       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   595     }
   596 
   597     /// \brief Returns a random real number from the range [0, 1)
   598     ///
   599     /// It returns a random real number from the range [0, 1). The
   600     /// default Number type is \c double.
   601     template <typename Number>
   602     Number real() {
   603       return _random_bits::RealConversion<Number, Word>::convert(core);
   604     }
   605 
   606     double real() {
   607       return real<double>();
   608     }
   609 
   610     /// \brief Returns a random real number the range [0, b)
   611     ///
   612     /// It returns a random real number from the range [0, b).
   613     template <typename Number>
   614     Number real(Number b) { 
   615       return real<Number>() * b; 
   616     }
   617 
   618     /// \brief Returns a random real number from the range [a, b)
   619     ///
   620     /// It returns a random real number from the range [a, b).
   621     template <typename Number>
   622     Number real(Number a, Number b) { 
   623       return real<Number>() * (b - a) + a; 
   624     }
   625 
   626     /// \brief Returns a random real number from the range [0, 1)
   627     ///
   628     /// It returns a random double from the range [0, 1).
   629     double operator()() {
   630       return real<double>();
   631     }
   632 
   633     /// \brief Returns a random real number from the range [0, b)
   634     ///
   635     /// It returns a random real number from the range [0, b).
   636     template <typename Number>
   637     Number operator()(Number b) { 
   638       return real<Number>() * b; 
   639     }
   640 
   641     /// \brief Returns a random real number from the range [a, b)
   642     ///
   643     /// It returns a random real number from the range [a, b).
   644     template <typename Number>
   645     Number operator()(Number a, Number b) { 
   646       return real<Number>() * (b - a) + a; 
   647     }
   648 
   649     /// \brief Returns a random integer from a range
   650     ///
   651     /// It returns a random integer from the range {0, 1, ..., b - 1}.
   652     template <typename Number>
   653     Number integer(Number b) {
   654       return _random_bits::Mapping<Number, Word>::map(core, b);
   655     }
   656 
   657     /// \brief Returns a random integer from a range
   658     ///
   659     /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
   660     template <typename Number>
   661     Number integer(Number a, Number b) {
   662       return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
   663     }
   664 
   665     /// \brief Returns a random integer from a range
   666     ///
   667     /// It returns a random integer from the range {0, 1, ..., b - 1}.
   668     template <typename Number>
   669     Number operator[](Number b) {
   670       return _random_bits::Mapping<Number, Word>::map(core, b);
   671     }
   672 
   673     /// \brief Returns a random non-negative integer
   674     ///
   675     /// It returns a random non-negative integer uniformly from the
   676     /// whole range of the current \c Number type. The default result
   677     /// type of this function is <tt>unsigned int</tt>.
   678     template <typename Number>
   679     Number uinteger() {
   680       return _random_bits::IntConversion<Number, Word>::convert(core);
   681     }
   682 
   683     unsigned int uinteger() {
   684       return uinteger<unsigned int>();
   685     }
   686 
   687     /// \brief Returns a random integer
   688     ///
   689     /// It returns a random integer uniformly from the whole range of
   690     /// the current \c Number type. The default result type of this
   691     /// function is \c int.
   692     template <typename Number>
   693     Number integer() {
   694       static const int nb = std::numeric_limits<Number>::digits + 
   695         (std::numeric_limits<Number>::is_signed ? 1 : 0);
   696       return _random_bits::IntConversion<Number, Word, nb>::convert(core);
   697     }
   698 
   699     int integer() {
   700       return integer<int>();
   701     }
   702     
   703     /// \brief Returns a random bool
   704     ///
   705     /// It returns a random bool. The generator holds a buffer for
   706     /// random bits. Every time when it become empty the generator makes
   707     /// a new random word and fill the buffer up.
   708     bool boolean() {
   709       return bool_producer.convert(core);
   710     }
   711 
   712     ///\name Non-uniform distributions
   713     ///
   714     
   715     ///@{
   716     
   717     /// \brief Returns a random bool
   718     ///
   719     /// It returns a random bool with given probability of true result.
   720     bool boolean(double p) {
   721       return operator()() < p;
   722     }
   723 
   724     /// Standard Gauss distribution
   725 
   726     /// Standard Gauss distribution.
   727     /// \note The Cartesian form of the Box-Muller
   728     /// transformation is used to generate a random normal distribution.
   729     /// \todo Consider using the "ziggurat" method instead.
   730     double gauss() 
   731     {
   732       double V1,V2,S;
   733       do {
   734 	V1=2*real<double>()-1;
   735 	V2=2*real<double>()-1;
   736 	S=V1*V1+V2*V2;
   737       } while(S>=1);
   738       return std::sqrt(-2*std::log(S)/S)*V1;
   739     }
   740     /// Gauss distribution with given mean and standard deviation
   741 
   742     /// Gauss distribution with given mean and standard deviation.
   743     /// \sa gauss()
   744     double gauss(double mean,double std_dev)
   745     {
   746       return gauss()*std_dev+mean;
   747     }
   748 
   749     /// Exponential distribution with given mean
   750 
   751     /// This function generates an exponential distribution random number
   752     /// with mean <tt>1/lambda</tt>.
   753     ///
   754     double exponential(double lambda=1.0)
   755     {
   756       return -std::log(1.0-real<double>())/lambda;
   757     }
   758 
   759     /// Gamma distribution with given integer shape
   760 
   761     /// This function generates a gamma distribution random number.
   762     /// 
   763     ///\param k shape parameter (<tt>k>0</tt> integer)
   764     double gamma(int k) 
   765     {
   766       double s = 0;
   767       for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
   768       return s;
   769     }
   770     
   771     /// Gamma distribution with given shape and scale parameter
   772 
   773     /// This function generates a gamma distribution random number.
   774     /// 
   775     ///\param k shape parameter (<tt>k>0</tt>)
   776     ///\param theta scale parameter
   777     ///
   778     double gamma(double k,double theta=1.0)
   779     {
   780       double xi,nu;
   781       const double delta = k-std::floor(k);
   782       const double v0=E/(E-delta);
   783       do {
   784 	double V0=1.0-real<double>();
   785 	double V1=1.0-real<double>();
   786 	double V2=1.0-real<double>();
   787 	if(V2<=v0) 
   788 	  {
   789 	    xi=std::pow(V1,1.0/delta);
   790 	    nu=V0*std::pow(xi,delta-1.0);
   791 	  }
   792 	else 
   793 	  {
   794 	    xi=1.0-std::log(V1);
   795 	    nu=V0*std::exp(-xi);
   796 	  }
   797       } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
   798       return theta*(xi+gamma(int(std::floor(k))));
   799     }
   800     
   801     /// Weibull distribution
   802 
   803     /// This function generates a Weibull distribution random number.
   804     /// 
   805     ///\param k shape parameter (<tt>k>0</tt>)
   806     ///\param lambda scale parameter (<tt>lambda>0</tt>)
   807     ///
   808     double weibull(double k,double lambda)
   809     {
   810       return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
   811     }  
   812       
   813     /// Pareto distribution
   814 
   815     /// This function generates a Pareto distribution random number.
   816     /// 
   817     ///\param k shape parameter (<tt>k>0</tt>)
   818     ///\param x_min location parameter (<tt>x_min>0</tt>)
   819     ///
   820     double pareto(double k,double x_min)
   821     {
   822       return exponential(gamma(k,1.0/x_min))+x_min;
   823     }  
   824       
   825     /// Poisson distribution
   826 
   827     /// This function generates a Poisson distribution random number with
   828     /// parameter \c lambda.
   829     /// 
   830     /// The probability mass function of this distribusion is
   831     /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
   832     /// \note The algorithm is taken from the book of Donald E. Knuth titled
   833     /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
   834     /// return value.
   835     
   836     int poisson(double lambda)
   837     {
   838       const double l = std::exp(-lambda);
   839       int k=0;
   840       double p = 1.0;
   841       do {
   842 	k++;
   843 	p*=real<double>();
   844       } while (p>=l);
   845       return k-1;
   846     }  
   847       
   848     ///@}
   849     
   850     ///\name Two dimensional distributions
   851     ///
   852 
   853     ///@{
   854     
   855     /// Uniform distribution on the full unit circle
   856 
   857     /// Uniform distribution on the full unit circle.
   858     ///
   859     dim2::Point<double> disc() 
   860     {
   861       double V1,V2;
   862       do {
   863 	V1=2*real<double>()-1;
   864 	V2=2*real<double>()-1;
   865 	
   866       } while(V1*V1+V2*V2>=1);
   867       return dim2::Point<double>(V1,V2);
   868     }
   869     /// A kind of two dimensional Gauss distribution
   870 
   871     /// This function provides a turning symmetric two-dimensional distribution.
   872     /// Both coordinates are of standard normal distribution, but they are not
   873     /// independent.
   874     ///
   875     /// \note The coordinates are the two random variables provided by
   876     /// the Box-Muller method.
   877     dim2::Point<double> gauss2()
   878     {
   879       double V1,V2,S;
   880       do {
   881 	V1=2*real<double>()-1;
   882 	V2=2*real<double>()-1;
   883 	S=V1*V1+V2*V2;
   884       } while(S>=1);
   885       double W=std::sqrt(-2*std::log(S)/S);
   886       return dim2::Point<double>(W*V1,W*V2);
   887     }
   888     /// A kind of two dimensional exponential distribution
   889 
   890     /// This function provides a turning symmetric two-dimensional distribution.
   891     /// The x-coordinate is of conditionally exponential distribution
   892     /// with the condition that x is positive and y=0. If x is negative and 
   893     /// y=0 then, -x is of exponential distribution. The same is true for the
   894     /// y-coordinate.
   895     dim2::Point<double> exponential2() 
   896     {
   897       double V1,V2,S;
   898       do {
   899 	V1=2*real<double>()-1;
   900 	V2=2*real<double>()-1;
   901 	S=V1*V1+V2*V2;
   902       } while(S>=1);
   903       double W=-std::log(S)/S;
   904       return dim2::Point<double>(W*V1,W*V2);
   905     }
   906 
   907     ///@}    
   908   };
   909 
   910 
   911   extern Random rnd;
   912 
   913 }
   914 
   915 #endif