lemon/random.h
author Alpar Juttner <alpar@cs.elte.hu>
Tue, 14 Apr 2015 16:14:32 +0200
changeset 1338 0998f70d0b2d
parent 1328 d51126dc39fa
child 1343 20f95cd51aba
permissions -rw-r--r--
Clang -std=c++11 related fixes (#325)
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     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 #include <fstream>
    70 
    71 #include <lemon/math.h>
    72 #include <lemon/dim2.h>
    73 
    74 #ifndef WIN32
    75 #include <sys/time.h>
    76 #include <ctime>
    77 #include <sys/types.h>
    78 #include <unistd.h>
    79 #else
    80 #include <lemon/bits/windows.h>
    81 #endif
    82 
    83 ///\ingroup misc
    84 ///\file
    85 ///\brief Mersenne Twister random number generator
    86 
    87 namespace lemon {
    88 
    89   namespace _random_bits {
    90 
    91     template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
    92     struct RandomTraits {};
    93 
    94     template <typename _Word>
    95     struct RandomTraits<_Word, 32> {
    96 
    97       typedef _Word Word;
    98       static const int bits = 32;
    99 
   100       static const int length = 624;
   101       static const int shift = 397;
   102 
   103       static const Word mul = 0x6c078965u;
   104       static const Word arrayInit = 0x012BD6AAu;
   105       static const Word arrayMul1 = 0x0019660Du;
   106       static const Word arrayMul2 = 0x5D588B65u;
   107 
   108       static const Word mask = 0x9908B0DFu;
   109       static const Word loMask = (1u << 31) - 1;
   110       static const Word hiMask = ~loMask;
   111 
   112 
   113       static Word tempering(Word rnd) {
   114         rnd ^= (rnd >> 11);
   115         rnd ^= (rnd << 7) & 0x9D2C5680u;
   116         rnd ^= (rnd << 15) & 0xEFC60000u;
   117         rnd ^= (rnd >> 18);
   118         return rnd;
   119       }
   120 
   121     };
   122 
   123     template <typename _Word>
   124     struct RandomTraits<_Word, 64> {
   125 
   126       typedef _Word Word;
   127       static const int bits = 64;
   128 
   129       static const int length = 312;
   130       static const int shift = 156;
   131 
   132       static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
   133       static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
   134       static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
   135       static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
   136 
   137       static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
   138       static const Word loMask = (Word(1u) << 31) - 1;
   139       static const Word hiMask = ~loMask;
   140 
   141       static Word tempering(Word rnd) {
   142         rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
   143         rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
   144         rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
   145         rnd ^= (rnd >> 43);
   146         return rnd;
   147       }
   148 
   149     };
   150 
   151     template <typename _Word>
   152     class RandomCore {
   153     public:
   154 
   155       typedef _Word Word;
   156 
   157     private:
   158 
   159       static const int bits = RandomTraits<Word>::bits;
   160 
   161       static const int length = RandomTraits<Word>::length;
   162       static const int shift = RandomTraits<Word>::shift;
   163 
   164     public:
   165 
   166       void initState() {
   167         static const Word seedArray[4] = {
   168           0x12345u, 0x23456u, 0x34567u, 0x45678u
   169         };
   170 
   171         initState(seedArray, seedArray + 4);
   172       }
   173 
   174       void initState(Word seed) {
   175 
   176         static const Word mul = RandomTraits<Word>::mul;
   177 
   178         current = state;
   179 
   180         Word *curr = state + length - 1;
   181         curr[0] = seed; --curr;
   182         for (int i = 1; i < length; ++i) {
   183           curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
   184           --curr;
   185         }
   186       }
   187 
   188       template <typename Iterator>
   189       void initState(Iterator begin, Iterator end) {
   190 
   191         static const Word init = RandomTraits<Word>::arrayInit;
   192         static const Word mul1 = RandomTraits<Word>::arrayMul1;
   193         static const Word mul2 = RandomTraits<Word>::arrayMul2;
   194 
   195 
   196         Word *curr = state + length - 1; --curr;
   197         Iterator it = begin; int cnt = 0;
   198         int num;
   199 
   200         initState(init);
   201 
   202         num = static_cast<int>(length > end - begin ? length : end - begin);
   203         while (num--) {
   204           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
   205             + *it + cnt;
   206           ++it; ++cnt;
   207           if (it == end) {
   208             it = begin; cnt = 0;
   209           }
   210           if (curr == state) {
   211             curr = state + length - 1; curr[0] = state[0];
   212           }
   213           --curr;
   214         }
   215 
   216         num = length - 1; cnt = static_cast<int>(length - (curr - state) - 1);
   217         while (num--) {
   218           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
   219             - cnt;
   220           --curr; ++cnt;
   221           if (curr == state) {
   222             curr = state + length - 1; curr[0] = state[0]; --curr;
   223             cnt = 1;
   224           }
   225         }
   226 
   227         state[length - 1] = Word(1) << (bits - 1);
   228       }
   229 
   230       void copyState(const RandomCore& other) {
   231         std::copy(other.state, other.state + length, state);
   232         current = state + (other.current - other.state);
   233       }
   234 
   235       Word operator()() {
   236         if (current == state) fillState();
   237         --current;
   238         Word rnd = *current;
   239         return RandomTraits<Word>::tempering(rnd);
   240       }
   241 
   242     private:
   243 
   244 
   245       void fillState() {
   246         static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
   247         static const Word loMask = RandomTraits<Word>::loMask;
   248         static const Word hiMask = RandomTraits<Word>::hiMask;
   249 
   250         current = state + length;
   251 
   252         Word *curr = state + length - 1;
   253         long num;
   254 
   255         num = length - shift;
   256         while (num--) {
   257           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   258             curr[- shift] ^ mask[curr[-1] & 1ul];
   259           --curr;
   260         }
   261         num = shift - 1;
   262         while (num--) {
   263           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   264             curr[length - shift] ^ mask[curr[-1] & 1ul];
   265           --curr;
   266         }
   267         state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
   268           curr[length - shift] ^ mask[curr[length - 1] & 1ul];
   269 
   270       }
   271 
   272 
   273       Word *current;
   274       Word state[length];
   275 
   276     };
   277 
   278 
   279     template <typename Result,
   280               int shift = (std::numeric_limits<Result>::digits + 1) / 2>
   281     struct Masker {
   282       static Result mask(const Result& result) {
   283         return Masker<Result, (shift + 1) / 2>::
   284           mask(static_cast<Result>(result | (result >> shift)));
   285       }
   286     };
   287 
   288     template <typename Result>
   289     struct Masker<Result, 1> {
   290       static Result mask(const Result& result) {
   291         return static_cast<Result>(result | (result >> 1));
   292       }
   293     };
   294 
   295     template <typename Result, typename Word,
   296               int rest = std::numeric_limits<Result>::digits, int shift = 0,
   297               bool last = rest <= std::numeric_limits<Word>::digits>
   298     struct IntConversion {
   299       static const int bits = std::numeric_limits<Word>::digits;
   300 
   301       static Result convert(RandomCore<Word>& rnd) {
   302         return static_cast<Result>(rnd() >> (bits - rest)) << shift;
   303       }
   304 
   305     };
   306 
   307     template <typename Result, typename Word, int rest, int shift>
   308     struct IntConversion<Result, Word, rest, shift, false> {
   309       static const int bits = std::numeric_limits<Word>::digits;
   310 
   311       static Result convert(RandomCore<Word>& rnd) {
   312         return (static_cast<Result>(rnd()) << shift) |
   313           IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
   314       }
   315     };
   316 
   317 
   318     template <typename Result, typename Word,
   319               bool one_word = (std::numeric_limits<Word>::digits <
   320                                std::numeric_limits<Result>::digits) >
   321     struct Mapping {
   322       static Result map(RandomCore<Word>& rnd, const Result& bound) {
   323         Word max = Word(bound - 1);
   324         Result mask = Masker<Result>::mask(bound - 1);
   325         Result num;
   326         do {
   327           num = IntConversion<Result, Word>::convert(rnd) & mask;
   328         } while (num > max);
   329         return num;
   330       }
   331     };
   332 
   333     template <typename Result, typename Word>
   334     struct Mapping<Result, Word, false> {
   335       static Result map(RandomCore<Word>& rnd, const Result& bound) {
   336         Word max = Word(bound - 1);
   337         Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
   338           ::mask(max);
   339         Word num;
   340         do {
   341           num = rnd() & mask;
   342         } while (num > max);
   343         return num;
   344       }
   345     };
   346 
   347     template <typename Result, int exp>
   348     struct ShiftMultiplier {
   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> {
   359       static const Result multiplier() {
   360         return static_cast<Result>(1.0);
   361       }
   362     };
   363 
   364     template <typename Result>
   365     struct ShiftMultiplier<Result, 20> {
   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> {
   373       static const Result multiplier() {
   374         return static_cast<Result>(1.0/4294967296.0);
   375       }
   376     };
   377 
   378     template <typename Result>
   379     struct ShiftMultiplier<Result, 53> {
   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> {
   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     ///\name Initialization
   530     ///
   531     /// @{
   532 
   533     /// \brief Default constructor
   534     ///
   535     /// Constructor with constant seeding.
   536     Random() { core.initState(); }
   537 
   538     /// \brief Constructor with seed
   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 with array seeding
   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 Seeding random sequence
   582     ///
   583     /// Seeding the random sequence. The current number type will be
   584     /// converted to the architecture word type.
   585     template <typename Number>
   586     void seed(Number seed) {
   587       _random_bits::Initializer<Number, Word>::init(core, seed);
   588     }
   589 
   590     /// \brief Seeding random sequence
   591     ///
   592     /// Seeding the random sequence. The given range should contain
   593     /// any number type and the numbers will be converted to the
   594     /// architecture word type.
   595     template <typename Iterator>
   596     void seed(Iterator begin, Iterator end) {
   597       typedef typename std::iterator_traits<Iterator>::value_type Number;
   598       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   599     }
   600 
   601     /// \brief Seeding from file or from process id and time
   602     ///
   603     /// By default, this function calls the \c seedFromFile() member
   604     /// function with the <tt>/dev/urandom</tt> file. If it does not success,
   605     /// it uses the \c seedFromTime().
   606     /// \return Currently always \c true.
   607     bool seed() {
   608 #ifndef WIN32
   609       if (seedFromFile("/dev/urandom", 0)) return true;
   610 #endif
   611       if (seedFromTime()) return true;
   612       return false;
   613     }
   614 
   615     /// \brief Seeding from file
   616     ///
   617     /// Seeding the random sequence from file. The linux kernel has two
   618     /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
   619     /// could give good seed values for pseudo random generators (The
   620     /// difference between two devices is that the <tt>random</tt> may
   621     /// block the reading operation while the kernel can give good
   622     /// source of randomness, while the <tt>urandom</tt> does not
   623     /// block the input, but it could give back bytes with worse
   624     /// entropy).
   625     /// \param file The source file
   626     /// \param offset The offset, from the file read.
   627     /// \return \c true when the seeding successes.
   628 #ifndef WIN32
   629     bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)
   630 #else
   631     bool seedFromFile(const std::string& file = "", int offset = 0)
   632 #endif
   633     {
   634       std::ifstream rs(file.c_str());
   635       const int size = 4;
   636       Word buf[size];
   637       if (offset != 0 && !rs.seekg(offset)) return false;
   638       if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;
   639       seed(buf, buf + size);
   640       return true;
   641     }
   642 
   643     /// \brief Seding from process id and time
   644     ///
   645     /// Seding from process id and time. This function uses the
   646     /// current process id and the current time for initialize the
   647     /// random sequence.
   648     /// \return Currently always \c true.
   649     bool seedFromTime() {
   650 #ifndef WIN32
   651       timeval tv;
   652       gettimeofday(&tv, 0);
   653       seed(getpid() + tv.tv_sec + tv.tv_usec);
   654 #else
   655       seed(bits::getWinRndSeed());
   656 #endif
   657       return true;
   658     }
   659 
   660     /// @}
   661 
   662     ///\name Uniform Distributions
   663     ///
   664     /// @{
   665 
   666     /// \brief Returns a random real number from the range [0, 1)
   667     ///
   668     /// It returns a random real number from the range [0, 1). The
   669     /// default Number type is \c double.
   670     template <typename Number>
   671     Number real() {
   672       return _random_bits::RealConversion<Number, Word>::convert(core);
   673     }
   674 
   675     double real() {
   676       return real<double>();
   677     }
   678 
   679     /// \brief Returns a random real number from the range [0, 1)
   680     ///
   681     /// It returns a random double from the range [0, 1).
   682     double operator()() {
   683       return real<double>();
   684     }
   685 
   686     /// \brief Returns a random real number from the range [0, b)
   687     ///
   688     /// It returns a random real number from the range [0, b).
   689     double operator()(double b) {
   690       return real<double>() * b;
   691     }
   692 
   693     /// \brief Returns a random real number from the range [a, b)
   694     ///
   695     /// It returns a random real number from the range [a, b).
   696     double operator()(double a, double b) {
   697       return real<double>() * (b - a) + a;
   698     }
   699 
   700     /// \brief Returns a random integer from a range
   701     ///
   702     /// It returns a random integer from the range {0, 1, ..., b - 1}.
   703     template <typename Number>
   704     Number integer(Number b) {
   705       return _random_bits::Mapping<Number, Word>::map(core, b);
   706     }
   707 
   708     /// \brief Returns a random integer from a range
   709     ///
   710     /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
   711     template <typename Number>
   712     Number integer(Number a, Number b) {
   713       return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
   714     }
   715 
   716     /// \brief Returns a random integer from a range
   717     ///
   718     /// It returns a random integer from the range {0, 1, ..., b - 1}.
   719     template <typename Number>
   720     Number operator[](Number b) {
   721       return _random_bits::Mapping<Number, Word>::map(core, b);
   722     }
   723 
   724     /// \brief Returns a random non-negative integer
   725     ///
   726     /// It returns a random non-negative integer uniformly from the
   727     /// whole range of the current \c Number type. The default result
   728     /// type of this function is <tt>unsigned int</tt>.
   729     template <typename Number>
   730     Number uinteger() {
   731       return _random_bits::IntConversion<Number, Word>::convert(core);
   732     }
   733 
   734     unsigned int uinteger() {
   735       return uinteger<unsigned int>();
   736     }
   737 
   738     /// \brief Returns a random integer
   739     ///
   740     /// It returns a random integer uniformly from the whole range of
   741     /// the current \c Number type. The default result type of this
   742     /// function is \c int.
   743     template <typename Number>
   744     Number integer() {
   745       static const int nb = std::numeric_limits<Number>::digits +
   746         (std::numeric_limits<Number>::is_signed ? 1 : 0);
   747       return _random_bits::IntConversion<Number, Word, nb>::convert(core);
   748     }
   749 
   750     int integer() {
   751       return integer<int>();
   752     }
   753 
   754     /// \brief Returns a random bool
   755     ///
   756     /// It returns a random bool. The generator holds a buffer for
   757     /// random bits. Every time when it become empty the generator makes
   758     /// a new random word and fill the buffer up.
   759     bool boolean() {
   760       return bool_producer.convert(core);
   761     }
   762 
   763     /// @}
   764 
   765     ///\name Non-uniform Distributions
   766     ///
   767     ///@{
   768 
   769     /// \brief Returns a random bool with given probability of true result.
   770     ///
   771     /// It returns a random bool with given probability of true result.
   772     bool boolean(double p) {
   773       return operator()() < p;
   774     }
   775 
   776     /// Standard normal (Gauss) distribution
   777 
   778     /// Standard normal (Gauss) distribution.
   779     /// \note The Cartesian form of the Box-Muller
   780     /// transformation is used to generate a random normal distribution.
   781     double gauss()
   782     {
   783       double V1,V2,S;
   784       do {
   785         V1=2*real<double>()-1;
   786         V2=2*real<double>()-1;
   787         S=V1*V1+V2*V2;
   788       } while(S>=1);
   789       return std::sqrt(-2*std::log(S)/S)*V1;
   790     }
   791     /// Normal (Gauss) distribution with given mean and standard deviation
   792 
   793     /// Normal (Gauss) distribution with given mean and standard deviation.
   794     /// \sa gauss()
   795     double gauss(double mean,double std_dev)
   796     {
   797       return gauss()*std_dev+mean;
   798     }
   799 
   800     /// Lognormal distribution
   801 
   802     /// Lognormal distribution. The parameters are the mean and the standard
   803     /// deviation of <tt>exp(X)</tt>.
   804     ///
   805     double lognormal(double n_mean,double n_std_dev)
   806     {
   807       return std::exp(gauss(n_mean,n_std_dev));
   808     }
   809     /// Lognormal distribution
   810 
   811     /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of
   812     /// the mean and the standard deviation of <tt>exp(X)</tt>.
   813     ///
   814     double lognormal(const std::pair<double,double> &params)
   815     {
   816       return std::exp(gauss(params.first,params.second));
   817     }
   818     /// Compute the lognormal parameters from mean and standard deviation
   819 
   820     /// This function computes the lognormal parameters from mean and
   821     /// standard deviation. The return value can direcly be passed to
   822     /// lognormal().
   823     std::pair<double,double> lognormalParamsFromMD(double mean,
   824                                                    double std_dev)
   825     {
   826       double fr=std_dev/mean;
   827       fr*=fr;
   828       double lg=std::log(1+fr);
   829       return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg));
   830     }
   831     /// Lognormal distribution with given mean and standard deviation
   832 
   833     /// Lognormal distribution with given mean and standard deviation.
   834     ///
   835     double lognormalMD(double mean,double std_dev)
   836     {
   837       return lognormal(lognormalParamsFromMD(mean,std_dev));
   838     }
   839 
   840     /// Exponential distribution with given mean
   841 
   842     /// This function generates an exponential distribution random number
   843     /// with mean <tt>1/lambda</tt>.
   844     ///
   845     double exponential(double lambda=1.0)
   846     {
   847       return -std::log(1.0-real<double>())/lambda;
   848     }
   849 
   850     /// Gamma distribution with given integer shape
   851 
   852     /// This function generates a gamma distribution random number.
   853     ///
   854     ///\param k shape parameter (<tt>k>0</tt> integer)
   855     double gamma(int k)
   856     {
   857       double s = 0;
   858       for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
   859       return s;
   860     }
   861 
   862     /// Gamma distribution with given shape and scale parameter
   863 
   864     /// This function generates a gamma distribution random number.
   865     ///
   866     ///\param k shape parameter (<tt>k>0</tt>)
   867     ///\param theta scale parameter
   868     ///
   869     double gamma(double k,double theta=1.0)
   870     {
   871       double xi,nu;
   872       const double delta = k-std::floor(k);
   873       const double v0=E/(E-delta);
   874       do {
   875         double V0=1.0-real<double>();
   876         double V1=1.0-real<double>();
   877         double V2=1.0-real<double>();
   878         if(V2<=v0)
   879           {
   880             xi=std::pow(V1,1.0/delta);
   881             nu=V0*std::pow(xi,delta-1.0);
   882           }
   883         else
   884           {
   885             xi=1.0-std::log(V1);
   886             nu=V0*std::exp(-xi);
   887           }
   888       } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
   889       return theta*(xi+gamma(int(std::floor(k))));
   890     }
   891 
   892     /// Weibull distribution
   893 
   894     /// This function generates a Weibull distribution random number.
   895     ///
   896     ///\param k shape parameter (<tt>k>0</tt>)
   897     ///\param lambda scale parameter (<tt>lambda>0</tt>)
   898     ///
   899     double weibull(double k,double lambda)
   900     {
   901       return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
   902     }
   903 
   904     /// Pareto distribution
   905 
   906     /// This function generates a Pareto distribution random number.
   907     ///
   908     ///\param k shape parameter (<tt>k>0</tt>)
   909     ///\param x_min location parameter (<tt>x_min>0</tt>)
   910     ///
   911     double pareto(double k,double x_min)
   912     {
   913       return exponential(gamma(k,1.0/x_min))+x_min;
   914     }
   915 
   916     /// Poisson distribution
   917 
   918     /// This function generates a Poisson distribution random number with
   919     /// parameter \c lambda.
   920     ///
   921     /// The probability mass function of this distribusion is
   922     /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
   923     /// \note The algorithm is taken from the book of Donald E. Knuth titled
   924     /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
   925     /// return value.
   926 
   927     int poisson(double lambda)
   928     {
   929       const double l = std::exp(-lambda);
   930       int k=0;
   931       double p = 1.0;
   932       do {
   933         k++;
   934         p*=real<double>();
   935       } while (p>=l);
   936       return k-1;
   937     }
   938 
   939     ///@}
   940 
   941     ///\name Two Dimensional Distributions
   942     ///
   943     ///@{
   944 
   945     /// Uniform distribution on the full unit circle
   946 
   947     /// Uniform distribution on the full unit circle.
   948     ///
   949     dim2::Point<double> disc()
   950     {
   951       double V1,V2;
   952       do {
   953         V1=2*real<double>()-1;
   954         V2=2*real<double>()-1;
   955 
   956       } while(V1*V1+V2*V2>=1);
   957       return dim2::Point<double>(V1,V2);
   958     }
   959     /// A kind of two dimensional normal (Gauss) distribution
   960 
   961     /// This function provides a turning symmetric two-dimensional distribution.
   962     /// Both coordinates are of standard normal distribution, but they are not
   963     /// independent.
   964     ///
   965     /// \note The coordinates are the two random variables provided by
   966     /// the Box-Muller method.
   967     dim2::Point<double> gauss2()
   968     {
   969       double V1,V2,S;
   970       do {
   971         V1=2*real<double>()-1;
   972         V2=2*real<double>()-1;
   973         S=V1*V1+V2*V2;
   974       } while(S>=1);
   975       double W=std::sqrt(-2*std::log(S)/S);
   976       return dim2::Point<double>(W*V1,W*V2);
   977     }
   978     /// A kind of two dimensional exponential distribution
   979 
   980     /// This function provides a turning symmetric two-dimensional distribution.
   981     /// The x-coordinate is of conditionally exponential distribution
   982     /// with the condition that x is positive and y=0. If x is negative and
   983     /// y=0 then, -x is of exponential distribution. The same is true for the
   984     /// y-coordinate.
   985     dim2::Point<double> exponential2()
   986     {
   987       double V1,V2,S;
   988       do {
   989         V1=2*real<double>()-1;
   990         V2=2*real<double>()-1;
   991         S=V1*V1+V2*V2;
   992       } while(S>=1);
   993       double W=-std::log(S)/S;
   994       return dim2::Point<double>(W*V1,W*V2);
   995     }
   996 
   997     ///@}
   998   };
   999 
  1000 
  1001   extern Random rnd;
  1002 
  1003 }
  1004 
  1005 #endif