lemon/random.h
author ladanyi
Sat, 13 Oct 2007 08:48:07 +0000
changeset 2495 e4f8367beb41
parent 2391 14a343be7a5a
child 2545 2bed3e806e1e
permissions -rw-r--r--
Added the function isFinite(), and replaced the calls to finite() with it.
This was necessary because finite() is not a standard function. Neither can
we use its standard counterpart isfinite(), because it was introduced only
in C99, and therefore it is not supplied by all C++ implementations.
     1 /* -*- C++ -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library
     4  *
     5  * Copyright (C) 2003-2007
     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 #include <cmath>
    71 
    72 #include <lemon/dim2.h>
    73 ///\ingroup misc
    74 ///\file
    75 ///\brief Mersenne Twister random number generator
    76 ///
    77 ///\author Balazs Dezso
    78 
    79 namespace lemon {
    80 
    81   namespace _random_bits {
    82     
    83     template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
    84     struct RandomTraits {};
    85 
    86     template <typename _Word>
    87     struct RandomTraits<_Word, 32> {
    88 
    89       typedef _Word Word;
    90       static const int bits = 32;
    91 
    92       static const int length = 624;
    93       static const int shift = 397;
    94       
    95       static const Word mul = 0x6c078965u;
    96       static const Word arrayInit = 0x012BD6AAu;
    97       static const Word arrayMul1 = 0x0019660Du;
    98       static const Word arrayMul2 = 0x5D588B65u;
    99 
   100       static const Word mask = 0x9908B0DFu;
   101       static const Word loMask = (1u << 31) - 1;
   102       static const Word hiMask = ~loMask;
   103 
   104 
   105       static Word tempering(Word rnd) {
   106         rnd ^= (rnd >> 11);
   107         rnd ^= (rnd << 7) & 0x9D2C5680u;
   108         rnd ^= (rnd << 15) & 0xEFC60000u;
   109         rnd ^= (rnd >> 18);
   110         return rnd;
   111       }
   112 
   113     };
   114 
   115     template <typename _Word>
   116     struct RandomTraits<_Word, 64> {
   117 
   118       typedef _Word Word;
   119       static const int bits = 64;
   120 
   121       static const int length = 312;
   122       static const int shift = 156;
   123 
   124       static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
   125       static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
   126       static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
   127       static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
   128 
   129       static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
   130       static const Word loMask = (Word(1u) << 31) - 1;
   131       static const Word hiMask = ~loMask;
   132 
   133       static Word tempering(Word rnd) {
   134         rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
   135         rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
   136         rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
   137         rnd ^= (rnd >> 43);
   138         return rnd;
   139       }
   140 
   141     };
   142 
   143     template <typename _Word>
   144     class RandomCore {
   145     public:
   146 
   147       typedef _Word Word;
   148 
   149     private:
   150 
   151       static const int bits = RandomTraits<Word>::bits;
   152 
   153       static const int length = RandomTraits<Word>::length;
   154       static const int shift = RandomTraits<Word>::shift;
   155 
   156     public:
   157 
   158       void initState() {
   159         static const Word seedArray[4] = {
   160           0x12345u, 0x23456u, 0x34567u, 0x45678u
   161         };
   162     
   163         initState(seedArray, seedArray + 4);
   164       }
   165 
   166       void initState(Word seed) {
   167 
   168         static const Word mul = RandomTraits<Word>::mul;
   169 
   170         current = state; 
   171 
   172         Word *curr = state + length - 1;
   173         curr[0] = seed; --curr;
   174         for (int i = 1; i < length; ++i) {
   175           curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
   176           --curr;
   177         }
   178       }
   179 
   180       template <typename Iterator>
   181       void initState(Iterator begin, Iterator end) {
   182 
   183         static const Word init = RandomTraits<Word>::arrayInit;
   184         static const Word mul1 = RandomTraits<Word>::arrayMul1;
   185         static const Word mul2 = RandomTraits<Word>::arrayMul2;
   186 
   187 
   188         Word *curr = state + length - 1; --curr;
   189         Iterator it = begin; int cnt = 0;
   190         int num;
   191 
   192         initState(init);
   193 
   194         num = length > end - begin ? length : end - begin;
   195         while (num--) {
   196           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) 
   197             + *it + cnt;
   198           ++it; ++cnt;
   199           if (it == end) {
   200             it = begin; cnt = 0;
   201           }
   202           if (curr == state) {
   203             curr = state + length - 1; curr[0] = state[0];
   204           }
   205           --curr;
   206         }
   207 
   208         num = length - 1; cnt = length - (curr - state) - 1;
   209         while (num--) {
   210           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
   211             - cnt;
   212           --curr; ++cnt;
   213           if (curr == state) {
   214             curr = state + length - 1; curr[0] = state[0]; --curr;
   215             cnt = 1;
   216           }
   217         }
   218         
   219         state[length - 1] = Word(1) << (bits - 1);
   220       }
   221       
   222       void copyState(const RandomCore& other) {
   223         std::copy(other.state, other.state + length, state);
   224         current = state + (other.current - other.state);
   225       }
   226 
   227       Word operator()() {
   228         if (current == state) fillState();
   229         --current;
   230         Word rnd = *current;
   231         return RandomTraits<Word>::tempering(rnd);
   232       }
   233 
   234     private:
   235 
   236   
   237       void fillState() {
   238         static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
   239         static const Word loMask = RandomTraits<Word>::loMask;
   240         static const Word hiMask = RandomTraits<Word>::hiMask;
   241 
   242         current = state + length; 
   243 
   244         register Word *curr = state + length - 1;
   245         register long num;
   246       
   247         num = length - shift;
   248         while (num--) {
   249           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   250             curr[- shift] ^ mask[curr[-1] & 1ul];
   251           --curr;
   252         }
   253         num = shift - 1;
   254         while (num--) {
   255           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   256             curr[length - shift] ^ mask[curr[-1] & 1ul];
   257           --curr;
   258         }
   259         curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
   260           curr[length - shift] ^ mask[curr[length - 1] & 1ul];
   261 
   262       }
   263 
   264   
   265       Word *current;
   266       Word state[length];
   267       
   268     };
   269 
   270 
   271     template <typename Result, 
   272               int shift = (std::numeric_limits<Result>::digits + 1) / 2>
   273     struct Masker {
   274       static Result mask(const Result& result) {
   275         return Masker<Result, (shift + 1) / 2>::
   276           mask(static_cast<Result>(result | (result >> shift)));
   277       }
   278     };
   279     
   280     template <typename Result>
   281     struct Masker<Result, 1> {
   282       static Result mask(const Result& result) {
   283         return static_cast<Result>(result | (result >> 1));
   284       }
   285     };
   286 
   287     template <typename Result, typename Word, 
   288               int rest = std::numeric_limits<Result>::digits, int shift = 0, 
   289               bool last = rest <= std::numeric_limits<Word>::digits>
   290     struct IntConversion {
   291       static const int bits = std::numeric_limits<Word>::digits;
   292     
   293       static Result convert(RandomCore<Word>& rnd) {
   294         return static_cast<Result>(rnd() >> (bits - rest)) << shift;
   295       }
   296       
   297     }; 
   298 
   299     template <typename Result, typename Word, int rest, int shift> 
   300     struct IntConversion<Result, Word, rest, shift, false> {
   301       static const int bits = std::numeric_limits<Word>::digits;
   302 
   303       static Result convert(RandomCore<Word>& rnd) {
   304         return (static_cast<Result>(rnd()) << shift) | 
   305           IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
   306       }
   307     };
   308 
   309 
   310     template <typename Result, typename Word,
   311               bool one_word = (std::numeric_limits<Word>::digits < 
   312 			       std::numeric_limits<Result>::digits) >
   313     struct Mapping {
   314       static Result map(RandomCore<Word>& rnd, const Result& bound) {
   315         Word max = Word(bound - 1);
   316         Result mask = Masker<Result>::mask(bound - 1);
   317         Result num;
   318         do {
   319           num = IntConversion<Result, Word>::convert(rnd) & mask; 
   320         } while (num > max);
   321         return num;
   322       }
   323     };
   324 
   325     template <typename Result, typename Word>
   326     struct Mapping<Result, Word, false> {
   327       static Result map(RandomCore<Word>& rnd, const Result& bound) {
   328         Word max = Word(bound - 1);
   329         Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
   330           ::mask(max);
   331         Word num;
   332         do {
   333           num = rnd() & mask;
   334         } while (num > max);
   335         return num;
   336       }
   337     };
   338 
   339     template <typename Result, int exp, bool pos = (exp >= 0)>
   340     struct ShiftMultiplier {
   341       static const Result multiplier() {
   342         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   343         res *= res;
   344         if ((exp & 1) == 1) res *= static_cast<Result>(2.0);
   345         return res; 
   346       }
   347     };
   348 
   349     template <typename Result, int exp>
   350     struct ShiftMultiplier<Result, exp, false> {
   351       static const Result multiplier() {
   352         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   353         res *= res;
   354         if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
   355         return res; 
   356       }
   357     };
   358 
   359     template <typename Result>
   360     struct ShiftMultiplier<Result, 0, true> {
   361       static const Result multiplier() {
   362         return static_cast<Result>(1.0); 
   363       }
   364     };
   365 
   366     template <typename Result>
   367     struct ShiftMultiplier<Result, -20, true> {
   368       static const Result multiplier() {
   369         return static_cast<Result>(1.0/1048576.0); 
   370       }
   371     };
   372     
   373     template <typename Result>
   374     struct ShiftMultiplier<Result, -32, true> {
   375       static const Result multiplier() {
   376         return static_cast<Result>(1.0/424967296.0); 
   377       }
   378     };
   379 
   380     template <typename Result>
   381     struct ShiftMultiplier<Result, -53, true> {
   382       static const Result multiplier() {
   383         return static_cast<Result>(1.0/9007199254740992.0); 
   384       }
   385     };
   386 
   387     template <typename Result>
   388     struct ShiftMultiplier<Result, -64, true> {
   389       static const Result multiplier() {
   390         return static_cast<Result>(1.0/18446744073709551616.0); 
   391       }
   392     };
   393 
   394     template <typename Result, int exp>
   395     struct Shifting {
   396       static Result shift(const Result& result) {
   397         return result * ShiftMultiplier<Result, exp>::multiplier();
   398       }
   399     };
   400 
   401     template <typename Result, typename Word,
   402               int rest = std::numeric_limits<Result>::digits, int shift = 0, 
   403               bool last = rest <= std::numeric_limits<Word>::digits>
   404     struct RealConversion{ 
   405       static const int bits = std::numeric_limits<Word>::digits;
   406 
   407       static Result convert(RandomCore<Word>& rnd) {
   408         return Shifting<Result, - shift - rest>::
   409           shift(static_cast<Result>(rnd() >> (bits - rest)));
   410       }
   411     };
   412 
   413     template <typename Result, typename Word, int rest, int shift>
   414     struct RealConversion<Result, Word, rest, shift, false> { 
   415       static const int bits = std::numeric_limits<Word>::digits;
   416 
   417       static Result convert(RandomCore<Word>& rnd) {
   418         return Shifting<Result, - shift - bits>::
   419           shift(static_cast<Result>(rnd())) +
   420           RealConversion<Result, Word, rest-bits, shift + bits>::
   421           convert(rnd);
   422       }
   423     };
   424 
   425     template <typename Result, typename Word>
   426     struct Initializer {
   427 
   428       template <typename Iterator>
   429       static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
   430         std::vector<Word> ws;
   431         for (Iterator it = begin; it != end; ++it) {
   432           ws.push_back(Word(*it));
   433         }
   434         rnd.initState(ws.begin(), ws.end());
   435       }
   436 
   437       static void init(RandomCore<Word>& rnd, Result seed) {
   438         rnd.initState(seed);
   439       }
   440     };
   441 
   442     template <typename Word>
   443     struct BoolConversion {
   444       static bool convert(RandomCore<Word>& rnd) {
   445         return (rnd() & 1) == 1;
   446       }
   447     };
   448 
   449     template <typename Word>
   450     struct BoolProducer {
   451       Word buffer;
   452       int num;
   453       
   454       BoolProducer() : num(0) {}
   455 
   456       bool convert(RandomCore<Word>& rnd) {
   457         if (num == 0) {
   458           buffer = rnd();
   459           num = RandomTraits<Word>::bits;
   460         }
   461         bool r = (buffer & 1);
   462         buffer >>= 1;
   463         --num;
   464         return r;
   465       }
   466     };
   467 
   468   }
   469 
   470   /// \ingroup misc
   471   ///
   472   /// \brief Mersenne Twister random number generator
   473   ///
   474   /// The Mersenne Twister is a twisted generalized feedback
   475   /// shift-register generator of Matsumoto and Nishimura. The period
   476   /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
   477   /// equi-distributed in 623 dimensions for 32-bit numbers. The time
   478   /// performance of this generator is comparable to the commonly used
   479   /// generators.
   480   ///
   481   /// This implementation is specialized for both 32-bit and 64-bit
   482   /// architectures. The generators differ sligthly in the
   483   /// initialization and generation phase so they produce two
   484   /// completly different sequences.
   485   ///
   486   /// The generator gives back random numbers of serveral types. To
   487   /// get a random number from a range of a floating point type you
   488   /// can use one form of the \c operator() or the \c real() member
   489   /// function. If you want to get random number from the {0, 1, ...,
   490   /// n-1} integer range use the \c operator[] or the \c integer()
   491   /// method. And to get random number from the whole range of an
   492   /// integer type you can use the argumentless \c integer() or \c
   493   /// uinteger() functions. After all you can get random bool with
   494   /// equal chance of true and false or given probability of true
   495   /// result with the \c boolean() member functions.
   496   ///
   497   ///\code
   498   /// // The commented code is identical to the other
   499   /// double a = rnd();                     // [0.0, 1.0)
   500   /// // double a = rnd.real();             // [0.0, 1.0)
   501   /// double b = rnd(100.0);                // [0.0, 100.0)
   502   /// // double b = rnd.real(100.0);        // [0.0, 100.0)
   503   /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
   504   /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
   505   /// int d = rnd[100000];                  // 0..99999
   506   /// // int d = rnd.integer(100000);       // 0..99999
   507   /// int e = rnd[6] + 1;                   // 1..6
   508   /// // int e = rnd.integer(1, 1 + 6);     // 1..6
   509   /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
   510   /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
   511   /// bool g = rnd.boolean();               // P(g = true) = 0.5
   512   /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
   513   ///\endcode
   514   ///
   515   /// The lemon provides a global instance of the random number
   516   /// generator which name is \ref lemon::rnd "rnd". Usually it is a
   517   /// good programming convenience to use this global generator to get
   518   /// random numbers.
   519   ///
   520   /// \author Balazs Dezso
   521   class Random {
   522   private:
   523 
   524     // architecture word
   525     typedef unsigned long Word;
   526     
   527     _random_bits::RandomCore<Word> core;
   528     _random_bits::BoolProducer<Word> bool_producer;
   529     
   530 
   531   public:
   532 
   533     /// \brief Constructor
   534     ///
   535     /// Constructor with constant seeding.
   536     Random() { core.initState(); }
   537 
   538     /// \brief Constructor
   539     ///
   540     /// Constructor with seed. The current number type will be converted
   541     /// to the architecture word type.
   542     template <typename Number>
   543     Random(Number seed) { 
   544       _random_bits::Initializer<Number, Word>::init(core, seed);
   545     }
   546 
   547     /// \brief Constructor
   548     ///
   549     /// Constructor with array seeding. The given range should contain
   550     /// any number type and the numbers will be converted to the
   551     /// architecture word type.
   552     template <typename Iterator>
   553     Random(Iterator begin, Iterator end) { 
   554       typedef typename std::iterator_traits<Iterator>::value_type Number;
   555       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   556     }
   557 
   558     /// \brief Copy constructor
   559     ///
   560     /// Copy constructor. The generated sequence will be identical to
   561     /// the other sequence. It can be used to save the current state
   562     /// of the generator and later use it to generate the same
   563     /// sequence.
   564     Random(const Random& other) {
   565       core.copyState(other.core);
   566     }
   567 
   568     /// \brief Assign operator
   569     ///
   570     /// Assign operator. The generated sequence will be identical to
   571     /// the other sequence. It can be used to save the current state
   572     /// of the generator and later use it to generate the same
   573     /// sequence.
   574     Random& operator=(const Random& other) {
   575       if (&other != this) {
   576         core.copyState(other.core);
   577       }
   578       return *this;
   579     }
   580 
   581     /// \brief Returns a random real number from the range [0, 1)
   582     ///
   583     /// It returns a random real number from the range [0, 1). The
   584     /// default Number type is double.
   585     template <typename Number>
   586     Number real() {
   587       return _random_bits::RealConversion<Number, Word>::convert(core);
   588     }
   589 
   590     double real() {
   591       return real<double>();
   592     }
   593 
   594     /// \brief Returns a random real number the range [0, b)
   595     ///
   596     /// It returns a random real number from the range [0, b).
   597     template <typename Number>
   598     Number real(Number b) { 
   599       return real<Number>() * b; 
   600     }
   601 
   602     /// \brief Returns a random real number from the range [a, b)
   603     ///
   604     /// It returns a random real number from the range [a, b).
   605     template <typename Number>
   606     Number real(Number a, Number b) { 
   607       return real<Number>() * (b - a) + a; 
   608     }
   609 
   610     /// \brief Returns a random real number from the range [0, 1)
   611     ///
   612     /// It returns a random double from the range [0, 1).
   613     double operator()() {
   614       return real<double>();
   615     }
   616 
   617     /// \brief Returns a random real number from the range [0, b)
   618     ///
   619     /// It returns a random real number from the range [0, b).
   620     template <typename Number>
   621     Number operator()(Number b) { 
   622       return real<Number>() * b; 
   623     }
   624 
   625     /// \brief Returns a random real number from the range [a, b)
   626     ///
   627     /// It returns a random real number from the range [a, b).
   628     template <typename Number>
   629     Number operator()(Number a, Number b) { 
   630       return real<Number>() * (b - a) + a; 
   631     }
   632 
   633     /// \brief Returns a random integer from a range
   634     ///
   635     /// It returns a random integer from the range {0, 1, ..., b - 1}.
   636     template <typename Number>
   637     Number integer(Number b) {
   638       return _random_bits::Mapping<Number, Word>::map(core, b);
   639     }
   640 
   641     /// \brief Returns a random integer from a range
   642     ///
   643     /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
   644     template <typename Number>
   645     Number integer(Number a, Number b) {
   646       return _random_bits::Mapping<Number, Word>::map(core, 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 operator[](Number b) {
   654       return _random_bits::Mapping<Number, Word>::map(core, b);
   655     }
   656 
   657     /// \brief Returns a random non-negative integer
   658     ///
   659     /// It returns a random non-negative integer uniformly from the
   660     /// whole range of the current \c Number type.  The default result
   661     /// type of this function is unsigned int.
   662     template <typename Number>
   663     Number uinteger() {
   664       return _random_bits::IntConversion<Number, Word>::convert(core);
   665     }
   666 
   667     unsigned int uinteger() {
   668       return uinteger<unsigned int>();
   669     }
   670 
   671     /// \brief Returns a random integer
   672     ///
   673     /// It returns a random integer uniformly from the whole range of
   674     /// the current \c Number type. The default result type of this
   675     /// function is int.
   676     template <typename Number>
   677     Number integer() {
   678       static const int nb = std::numeric_limits<Number>::digits + 
   679         (std::numeric_limits<Number>::is_signed ? 1 : 0);
   680       return _random_bits::IntConversion<Number, Word, nb>::convert(core);
   681     }
   682 
   683     int integer() {
   684       return integer<int>();
   685     }
   686     
   687     /// \brief Returns a random bool
   688     ///
   689     /// It returns a random bool. The generator holds a buffer for
   690     /// random bits. Every time when it become empty the generator makes
   691     /// a new random word and fill the buffer up.
   692     bool boolean() {
   693       return bool_producer.convert(core);
   694     }
   695 
   696     ///\name Nonuniform distributions
   697     ///
   698     
   699     ///@{
   700     
   701     /// \brief Returns a random bool
   702     ///
   703     /// It returns a random bool with given probability of true result
   704     bool boolean(double p) {
   705       return operator()() < p;
   706     }
   707 
   708     /// Standard Gauss distribution
   709 
   710     /// Standard Gauss distribution.
   711     /// \note The Cartesian form of the Box-Muller
   712     /// transformation is used to generate a random normal distribution.
   713     /// \todo Consider using the "ziggurat" method instead.
   714     double gauss() 
   715     {
   716       double V1,V2,S;
   717       do {
   718 	V1=2*real<double>()-1;
   719 	V2=2*real<double>()-1;
   720 	S=V1*V1+V2*V2;
   721       } while(S>=1);
   722       return std::sqrt(-2*std::log(S)/S)*V1;
   723     }
   724     /// Gauss distribution with given standard deviation and mean 0
   725 
   726     /// \sa gauss()
   727     ///
   728     double gauss(double std_dev) 
   729     {
   730       return gauss()*std_dev;
   731     }
   732     /// Gauss distribution with given mean and standard deviation
   733 
   734     /// \sa gauss()
   735     ///
   736     double gauss(double mean,double std_dev)
   737     {
   738       return gauss()*std_dev+mean;
   739     }
   740 
   741     /// Exponential distribution with given mean
   742 
   743     /// This function generates an exponential distribution random number
   744     /// with mean <tt>1/lambda</tt>.
   745     ///
   746     double exponential(double lambda=1.0)
   747     {
   748       return -std::log(real<double>())/lambda;
   749     }
   750 
   751     double gamma(int k) 
   752     {
   753       double s = 0;
   754       for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
   755       return s;
   756     }
   757     
   758     /// Gamma distribution with given shape and scale parameter
   759 
   760     /// This function generates a gamma distribution random number.
   761     /// 
   762     ///\param k shape parameter (<tt>k>0</tt>)
   763     ///\param theta scale parameter
   764     ///
   765     double gamma(double k,double theta=1.0)
   766     {
   767       double xi,nu;
   768       const double delta = k-std::floor(k);
   769       const double v0=M_E/(M_E-delta);
   770       do {
   771 	double V0=1.0-real<double>();
   772 	double V1=1.0-real<double>();
   773 	double V2=1.0-real<double>();
   774 	if(V2<=v0) 
   775 	  {
   776 	    xi=std::pow(V1,1.0/delta);
   777 	    nu=V0*std::pow(xi,delta-1.0);
   778 	  }
   779 	else 
   780 	  {
   781 	    xi=1.0-std::log(V1);
   782 	    nu=V0*std::exp(-xi);
   783 	  }
   784       } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
   785       return theta*(xi-gamma(int(std::floor(k))));
   786     }
   787     
   788       
   789     ///@}
   790     
   791     ///\name Two dimensional distributions
   792     ///
   793 
   794     ///@{
   795     
   796     /// Uniform distribution on the full unit circle.
   797     dim2::Point<double> disc() 
   798     {
   799       double V1,V2;
   800       do {
   801 	V1=2*real<double>()-1;
   802 	V2=2*real<double>()-1;
   803 	
   804       } while(V1*V1+V2*V2>=1);
   805       return dim2::Point<double>(V1,V2);
   806     }
   807     /// A kind of two dimensional Gauss distribution
   808 
   809     /// This function provides a turning symmetric two-dimensional distribution.
   810     /// Both coordinates are of standard normal distribution, but they are not
   811     /// independent.
   812     ///
   813     /// \note The coordinates are the two random variables provided by
   814     /// the Box-Muller method.
   815     dim2::Point<double> gauss2()
   816     {
   817       double V1,V2,S;
   818       do {
   819 	V1=2*real<double>()-1;
   820 	V2=2*real<double>()-1;
   821 	S=V1*V1+V2*V2;
   822       } while(S>=1);
   823       double W=std::sqrt(-2*std::log(S)/S);
   824       return dim2::Point<double>(W*V1,W*V2);
   825     }
   826     /// A kind of two dimensional exponential distribution
   827 
   828     /// This function provides a turning symmetric two-dimensional distribution.
   829     /// The x-coordinate is of conditionally exponential distribution
   830     /// with the condition that x is positive and y=0. If x is negative and 
   831     /// y=0 then, -x is of exponential distribution. The same is true for the
   832     /// y-coordinate.
   833     dim2::Point<double> exponential2() 
   834     {
   835       double V1,V2,S;
   836       do {
   837 	V1=2*real<double>()-1;
   838 	V2=2*real<double>()-1;
   839 	S=V1*V1+V2*V2;
   840       } while(S>=1);
   841       double W=-std::log(S)/S;
   842       return dim2::Point<double>(W*V1,W*V2);
   843     }
   844 
   845     ///@}    
   846   };
   847 
   848 
   849   extern Random rnd;
   850 
   851 }
   852 
   853 #endif