lemon/random.h
author Alpar Juttner <alpar@cs.elte.hu>
Mon, 16 Feb 2009 18:15:52 +0000
changeset 562 b9b3473327e3
parent 463 88ed40ad0d4f
parent 511 879c55700cd4
child 564 2b6d5d22bb23
permissions -rw-r--r--
Merge
     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 = 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 = 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         register Word *curr = state + length - 1;
   253         register 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, bool pos = (exp >= 0)>
   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>(2.0);
   353         return res;
   354       }
   355     };
   356 
   357     template <typename Result, int exp>
   358     struct ShiftMultiplier<Result, exp, false> {
   359       static const Result multiplier() {
   360         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   361         res *= res;
   362         if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
   363         return res;
   364       }
   365     };
   366 
   367     template <typename Result>
   368     struct ShiftMultiplier<Result, 0, true> {
   369       static const Result multiplier() {
   370         return static_cast<Result>(1.0);
   371       }
   372     };
   373 
   374     template <typename Result>
   375     struct ShiftMultiplier<Result, -20, true> {
   376       static const Result multiplier() {
   377         return static_cast<Result>(1.0/1048576.0);
   378       }
   379     };
   380 
   381     template <typename Result>
   382     struct ShiftMultiplier<Result, -32, true> {
   383       static const Result multiplier() {
   384         return static_cast<Result>(1.0/424967296.0);
   385       }
   386     };
   387 
   388     template <typename Result>
   389     struct ShiftMultiplier<Result, -53, true> {
   390       static const Result multiplier() {
   391         return static_cast<Result>(1.0/9007199254740992.0);
   392       }
   393     };
   394 
   395     template <typename Result>
   396     struct ShiftMultiplier<Result, -64, true> {
   397       static const Result multiplier() {
   398         return static_cast<Result>(1.0/18446744073709551616.0);
   399       }
   400     };
   401 
   402     template <typename Result, int exp>
   403     struct Shifting {
   404       static Result shift(const Result& result) {
   405         return result * ShiftMultiplier<Result, exp>::multiplier();
   406       }
   407     };
   408 
   409     template <typename Result, typename Word,
   410               int rest = std::numeric_limits<Result>::digits, int shift = 0,
   411               bool last = rest <= std::numeric_limits<Word>::digits>
   412     struct RealConversion{
   413       static const int bits = std::numeric_limits<Word>::digits;
   414 
   415       static Result convert(RandomCore<Word>& rnd) {
   416         return Shifting<Result, - shift - rest>::
   417           shift(static_cast<Result>(rnd() >> (bits - rest)));
   418       }
   419     };
   420 
   421     template <typename Result, typename Word, int rest, int shift>
   422     struct RealConversion<Result, Word, rest, shift, false> {
   423       static const int bits = std::numeric_limits<Word>::digits;
   424 
   425       static Result convert(RandomCore<Word>& rnd) {
   426         return Shifting<Result, - shift - bits>::
   427           shift(static_cast<Result>(rnd())) +
   428           RealConversion<Result, Word, rest-bits, shift + bits>::
   429           convert(rnd);
   430       }
   431     };
   432 
   433     template <typename Result, typename Word>
   434     struct Initializer {
   435 
   436       template <typename Iterator>
   437       static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
   438         std::vector<Word> ws;
   439         for (Iterator it = begin; it != end; ++it) {
   440           ws.push_back(Word(*it));
   441         }
   442         rnd.initState(ws.begin(), ws.end());
   443       }
   444 
   445       static void init(RandomCore<Word>& rnd, Result seed) {
   446         rnd.initState(seed);
   447       }
   448     };
   449 
   450     template <typename Word>
   451     struct BoolConversion {
   452       static bool convert(RandomCore<Word>& rnd) {
   453         return (rnd() & 1) == 1;
   454       }
   455     };
   456 
   457     template <typename Word>
   458     struct BoolProducer {
   459       Word buffer;
   460       int num;
   461 
   462       BoolProducer() : num(0) {}
   463 
   464       bool convert(RandomCore<Word>& rnd) {
   465         if (num == 0) {
   466           buffer = rnd();
   467           num = RandomTraits<Word>::bits;
   468         }
   469         bool r = (buffer & 1);
   470         buffer >>= 1;
   471         --num;
   472         return r;
   473       }
   474     };
   475 
   476   }
   477 
   478   /// \ingroup misc
   479   ///
   480   /// \brief Mersenne Twister random number generator
   481   ///
   482   /// The Mersenne Twister is a twisted generalized feedback
   483   /// shift-register generator of Matsumoto and Nishimura. The period
   484   /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
   485   /// equi-distributed in 623 dimensions for 32-bit numbers. The time
   486   /// performance of this generator is comparable to the commonly used
   487   /// generators.
   488   ///
   489   /// This implementation is specialized for both 32-bit and 64-bit
   490   /// architectures. The generators differ sligthly in the
   491   /// initialization and generation phase so they produce two
   492   /// completly different sequences.
   493   ///
   494   /// The generator gives back random numbers of serveral types. To
   495   /// get a random number from a range of a floating point type you
   496   /// can use one form of the \c operator() or the \c real() member
   497   /// function. If you want to get random number from the {0, 1, ...,
   498   /// n-1} integer range use the \c operator[] or the \c integer()
   499   /// method. And to get random number from the whole range of an
   500   /// integer type you can use the argumentless \c integer() or \c
   501   /// uinteger() functions. After all you can get random bool with
   502   /// equal chance of true and false or given probability of true
   503   /// result with the \c boolean() member functions.
   504   ///
   505   ///\code
   506   /// // The commented code is identical to the other
   507   /// double a = rnd();                     // [0.0, 1.0)
   508   /// // double a = rnd.real();             // [0.0, 1.0)
   509   /// double b = rnd(100.0);                // [0.0, 100.0)
   510   /// // double b = rnd.real(100.0);        // [0.0, 100.0)
   511   /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
   512   /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
   513   /// int d = rnd[100000];                  // 0..99999
   514   /// // int d = rnd.integer(100000);       // 0..99999
   515   /// int e = rnd[6] + 1;                   // 1..6
   516   /// // int e = rnd.integer(1, 1 + 6);     // 1..6
   517   /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
   518   /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
   519   /// bool g = rnd.boolean();               // P(g = true) = 0.5
   520   /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
   521   ///\endcode
   522   ///
   523   /// LEMON provides a global instance of the random number
   524   /// generator which name is \ref lemon::rnd "rnd". Usually it is a
   525   /// good programming convenience to use this global generator to get
   526   /// random numbers.
   527   class Random {
   528   private:
   529 
   530     // Architecture word
   531     typedef unsigned long Word;
   532 
   533     _random_bits::RandomCore<Word> core;
   534     _random_bits::BoolProducer<Word> bool_producer;
   535 
   536 
   537   public:
   538 
   539     ///\name Initialization
   540     ///
   541     /// @{
   542 
   543     /// \brief Default constructor
   544     ///
   545     /// Constructor with constant seeding.
   546     Random() { core.initState(); }
   547 
   548     /// \brief Constructor with seed
   549     ///
   550     /// Constructor with seed. The current number type will be converted
   551     /// to the architecture word type.
   552     template <typename Number>
   553     Random(Number seed) {
   554       _random_bits::Initializer<Number, Word>::init(core, seed);
   555     }
   556 
   557     /// \brief Constructor with array seeding
   558     ///
   559     /// Constructor with array seeding. The given range should contain
   560     /// any number type and the numbers will be converted to the
   561     /// architecture word type.
   562     template <typename Iterator>
   563     Random(Iterator begin, Iterator end) {
   564       typedef typename std::iterator_traits<Iterator>::value_type Number;
   565       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   566     }
   567 
   568     /// \brief Copy constructor
   569     ///
   570     /// Copy constructor. 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(const Random& other) {
   575       core.copyState(other.core);
   576     }
   577 
   578     /// \brief Assign operator
   579     ///
   580     /// Assign operator. The generated sequence will be identical to
   581     /// the other sequence. It can be used to save the current state
   582     /// of the generator and later use it to generate the same
   583     /// sequence.
   584     Random& operator=(const Random& other) {
   585       if (&other != this) {
   586         core.copyState(other.core);
   587       }
   588       return *this;
   589     }
   590 
   591     /// \brief Seeding random sequence
   592     ///
   593     /// Seeding the random sequence. The current number type will be
   594     /// converted to the architecture word type.
   595     template <typename Number>
   596     void seed(Number seed) {
   597       _random_bits::Initializer<Number, Word>::init(core, seed);
   598     }
   599 
   600     /// \brief Seeding random sequence
   601     ///
   602     /// Seeding the random sequence. The given range should contain
   603     /// any number type and the numbers will be converted to the
   604     /// architecture word type.
   605     template <typename Iterator>
   606     void seed(Iterator begin, Iterator end) {
   607       typedef typename std::iterator_traits<Iterator>::value_type Number;
   608       _random_bits::Initializer<Number, Word>::init(core, begin, end);
   609     }
   610 
   611     /// \brief Seeding from file or from process id and time
   612     ///
   613     /// By default, this function calls the \c seedFromFile() member
   614     /// function with the <tt>/dev/urandom</tt> file. If it does not success,
   615     /// it uses the \c seedFromTime().
   616     /// \return Currently always true.
   617     bool seed() {
   618 #ifndef WIN32
   619       if (seedFromFile("/dev/urandom", 0)) return true;
   620 #endif
   621       if (seedFromTime()) return true;
   622       return false;
   623     }
   624 
   625     /// \brief Seeding from file
   626     ///
   627     /// Seeding the random sequence from file. The linux kernel has two
   628     /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
   629     /// could give good seed values for pseudo random generators (The
   630     /// difference between two devices is that the <tt>random</tt> may
   631     /// block the reading operation while the kernel can give good
   632     /// source of randomness, while the <tt>urandom</tt> does not
   633     /// block the input, but it could give back bytes with worse
   634     /// entropy).
   635     /// \param file The source file
   636     /// \param offset The offset, from the file read.
   637     /// \return True when the seeding successes.
   638 #ifndef WIN32
   639     bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)
   640 #else
   641     bool seedFromFile(const std::string& file = "", int offset = 0)
   642 #endif
   643     {
   644       std::ifstream rs(file.c_str());
   645       const int size = 4;
   646       Word buf[size];
   647       if (offset != 0 && !rs.seekg(offset)) return false;
   648       if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;
   649       seed(buf, buf + size);
   650       return true;
   651     }
   652 
   653     /// \brief Seding from process id and time
   654     ///
   655     /// Seding from process id and time. This function uses the
   656     /// current process id and the current time for initialize the
   657     /// random sequence.
   658     /// \return Currently always true.
   659     bool seedFromTime() {
   660 #ifndef WIN32
   661       timeval tv;
   662       gettimeofday(&tv, 0);
   663       seed(getpid() + tv.tv_sec + tv.tv_usec);
   664 #else
   665       seed(bits::getWinRndSeed());
   666 #endif
   667       return true;
   668     }
   669 
   670     /// @}
   671 
   672     ///\name Uniform distributions
   673     ///
   674     /// @{
   675 
   676     /// \brief Returns a random real number from the range [0, 1)
   677     ///
   678     /// It returns a random real number from the range [0, 1). The
   679     /// default Number type is \c double.
   680     template <typename Number>
   681     Number real() {
   682       return _random_bits::RealConversion<Number, Word>::convert(core);
   683     }
   684 
   685     double real() {
   686       return real<double>();
   687     }
   688 
   689     /// \brief Returns a random real number from the range [0, 1)
   690     ///
   691     /// It returns a random double from the range [0, 1).
   692     double operator()() {
   693       return real<double>();
   694     }
   695 
   696     /// \brief Returns a random real number from the range [0, b)
   697     ///
   698     /// It returns a random real number from the range [0, b).
   699     double operator()(double b) {
   700       return real<double>() * b;
   701     }
   702 
   703     /// \brief Returns a random real number from the range [a, b)
   704     ///
   705     /// It returns a random real number from the range [a, b).
   706     double operator()(double a, double b) {
   707       return real<double>() * (b - a) + a;
   708     }
   709 
   710     /// \brief Returns a random integer from a range
   711     ///
   712     /// It returns a random integer from the range {0, 1, ..., b - 1}.
   713     template <typename Number>
   714     Number integer(Number b) {
   715       return _random_bits::Mapping<Number, Word>::map(core, b);
   716     }
   717 
   718     /// \brief Returns a random integer from a range
   719     ///
   720     /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
   721     template <typename Number>
   722     Number integer(Number a, Number b) {
   723       return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
   724     }
   725 
   726     /// \brief Returns a random integer from a range
   727     ///
   728     /// It returns a random integer from the range {0, 1, ..., b - 1}.
   729     template <typename Number>
   730     Number operator[](Number b) {
   731       return _random_bits::Mapping<Number, Word>::map(core, b);
   732     }
   733 
   734     /// \brief Returns a random non-negative integer
   735     ///
   736     /// It returns a random non-negative integer uniformly from the
   737     /// whole range of the current \c Number type. The default result
   738     /// type of this function is <tt>unsigned int</tt>.
   739     template <typename Number>
   740     Number uinteger() {
   741       return _random_bits::IntConversion<Number, Word>::convert(core);
   742     }
   743 
   744     unsigned int uinteger() {
   745       return uinteger<unsigned int>();
   746     }
   747 
   748     /// \brief Returns a random integer
   749     ///
   750     /// It returns a random integer uniformly from the whole range of
   751     /// the current \c Number type. The default result type of this
   752     /// function is \c int.
   753     template <typename Number>
   754     Number integer() {
   755       static const int nb = std::numeric_limits<Number>::digits +
   756         (std::numeric_limits<Number>::is_signed ? 1 : 0);
   757       return _random_bits::IntConversion<Number, Word, nb>::convert(core);
   758     }
   759 
   760     int integer() {
   761       return integer<int>();
   762     }
   763 
   764     /// \brief Returns a random bool
   765     ///
   766     /// It returns a random bool. The generator holds a buffer for
   767     /// random bits. Every time when it become empty the generator makes
   768     /// a new random word and fill the buffer up.
   769     bool boolean() {
   770       return bool_producer.convert(core);
   771     }
   772 
   773     /// @}
   774 
   775     ///\name Non-uniform distributions
   776     ///
   777     ///@{
   778 
   779     /// \brief Returns a random bool with given probability of true result.
   780     ///
   781     /// It returns a random bool with given probability of true result.
   782     bool boolean(double p) {
   783       return operator()() < p;
   784     }
   785 
   786     /// Standard normal (Gauss) distribution
   787 
   788     /// Standard normal (Gauss) distribution.
   789     /// \note The Cartesian form of the Box-Muller
   790     /// transformation is used to generate a random normal distribution.
   791     double gauss()
   792     {
   793       double V1,V2,S;
   794       do {
   795         V1=2*real<double>()-1;
   796         V2=2*real<double>()-1;
   797         S=V1*V1+V2*V2;
   798       } while(S>=1);
   799       return std::sqrt(-2*std::log(S)/S)*V1;
   800     }
   801     /// Normal (Gauss) distribution with given mean and standard deviation
   802 
   803     /// Normal (Gauss) distribution with given mean and standard deviation.
   804     /// \sa gauss()
   805     double gauss(double mean,double std_dev)
   806     {
   807       return gauss()*std_dev+mean;
   808     }
   809 
   810     /// Lognormal distribution
   811 
   812     /// Lognormal distribution. The parameters are the mean and the standard
   813     /// deviation of <tt>exp(X)</tt>.
   814     ///
   815     double lognormal(double n_mean,double n_std_dev)
   816     {
   817       return std::exp(gauss(n_mean,n_std_dev));
   818     }
   819     /// Lognormal distribution
   820 
   821     /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of
   822     /// the mean and the standard deviation of <tt>exp(X)</tt>.
   823     ///
   824     double lognormal(const std::pair<double,double> &params)
   825     {
   826       return std::exp(gauss(params.first,params.second));
   827     }
   828     /// Compute the lognormal parameters from mean and standard deviation
   829 
   830     /// This function computes the lognormal parameters from mean and
   831     /// standard deviation. The return value can direcly be passed to
   832     /// lognormal().
   833     std::pair<double,double> lognormalParamsFromMD(double mean,
   834                                                    double std_dev)
   835     {
   836       double fr=std_dev/mean;
   837       fr*=fr;
   838       double lg=std::log(1+fr);
   839       return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg));
   840     }
   841     /// Lognormal distribution with given mean and standard deviation
   842 
   843     /// Lognormal distribution with given mean and standard deviation.
   844     ///
   845     double lognormalMD(double mean,double std_dev)
   846     {
   847       return lognormal(lognormalParamsFromMD(mean,std_dev));
   848     }
   849 
   850     /// Exponential distribution with given mean
   851 
   852     /// This function generates an exponential distribution random number
   853     /// with mean <tt>1/lambda</tt>.
   854     ///
   855     double exponential(double lambda=1.0)
   856     {
   857       return -std::log(1.0-real<double>())/lambda;
   858     }
   859 
   860     /// Gamma distribution with given integer shape
   861 
   862     /// This function generates a gamma distribution random number.
   863     ///
   864     ///\param k shape parameter (<tt>k>0</tt> integer)
   865     double gamma(int k)
   866     {
   867       double s = 0;
   868       for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
   869       return s;
   870     }
   871 
   872     /// Gamma distribution with given shape and scale parameter
   873 
   874     /// This function generates a gamma distribution random number.
   875     ///
   876     ///\param k shape parameter (<tt>k>0</tt>)
   877     ///\param theta scale parameter
   878     ///
   879     double gamma(double k,double theta=1.0)
   880     {
   881       double xi,nu;
   882       const double delta = k-std::floor(k);
   883       const double v0=E/(E-delta);
   884       do {
   885         double V0=1.0-real<double>();
   886         double V1=1.0-real<double>();
   887         double V2=1.0-real<double>();
   888         if(V2<=v0)
   889           {
   890             xi=std::pow(V1,1.0/delta);
   891             nu=V0*std::pow(xi,delta-1.0);
   892           }
   893         else
   894           {
   895             xi=1.0-std::log(V1);
   896             nu=V0*std::exp(-xi);
   897           }
   898       } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
   899       return theta*(xi+gamma(int(std::floor(k))));
   900     }
   901 
   902     /// Weibull distribution
   903 
   904     /// This function generates a Weibull distribution random number.
   905     ///
   906     ///\param k shape parameter (<tt>k>0</tt>)
   907     ///\param lambda scale parameter (<tt>lambda>0</tt>)
   908     ///
   909     double weibull(double k,double lambda)
   910     {
   911       return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
   912     }
   913 
   914     /// Pareto distribution
   915 
   916     /// This function generates a Pareto distribution random number.
   917     ///
   918     ///\param k shape parameter (<tt>k>0</tt>)
   919     ///\param x_min location parameter (<tt>x_min>0</tt>)
   920     ///
   921     double pareto(double k,double x_min)
   922     {
   923       return exponential(gamma(k,1.0/x_min))+x_min;
   924     }
   925 
   926     /// Poisson distribution
   927 
   928     /// This function generates a Poisson distribution random number with
   929     /// parameter \c lambda.
   930     ///
   931     /// The probability mass function of this distribusion is
   932     /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
   933     /// \note The algorithm is taken from the book of Donald E. Knuth titled
   934     /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
   935     /// return value.
   936 
   937     int poisson(double lambda)
   938     {
   939       const double l = std::exp(-lambda);
   940       int k=0;
   941       double p = 1.0;
   942       do {
   943         k++;
   944         p*=real<double>();
   945       } while (p>=l);
   946       return k-1;
   947     }
   948 
   949     ///@}
   950 
   951     ///\name Two dimensional distributions
   952     ///
   953     ///@{
   954 
   955     /// Uniform distribution on the full unit circle
   956 
   957     /// Uniform distribution on the full unit circle.
   958     ///
   959     dim2::Point<double> disc()
   960     {
   961       double V1,V2;
   962       do {
   963         V1=2*real<double>()-1;
   964         V2=2*real<double>()-1;
   965 
   966       } while(V1*V1+V2*V2>=1);
   967       return dim2::Point<double>(V1,V2);
   968     }
   969     /// A kind of two dimensional normal (Gauss) distribution
   970 
   971     /// This function provides a turning symmetric two-dimensional distribution.
   972     /// Both coordinates are of standard normal distribution, but they are not
   973     /// independent.
   974     ///
   975     /// \note The coordinates are the two random variables provided by
   976     /// the Box-Muller method.
   977     dim2::Point<double> gauss2()
   978     {
   979       double V1,V2,S;
   980       do {
   981         V1=2*real<double>()-1;
   982         V2=2*real<double>()-1;
   983         S=V1*V1+V2*V2;
   984       } while(S>=1);
   985       double W=std::sqrt(-2*std::log(S)/S);
   986       return dim2::Point<double>(W*V1,W*V2);
   987     }
   988     /// A kind of two dimensional exponential distribution
   989 
   990     /// This function provides a turning symmetric two-dimensional distribution.
   991     /// The x-coordinate is of conditionally exponential distribution
   992     /// with the condition that x is positive and y=0. If x is negative and
   993     /// y=0 then, -x is of exponential distribution. The same is true for the
   994     /// y-coordinate.
   995     dim2::Point<double> exponential2()
   996     {
   997       double V1,V2,S;
   998       do {
   999         V1=2*real<double>()-1;
  1000         V2=2*real<double>()-1;
  1001         S=V1*V1+V2*V2;
  1002       } while(S>=1);
  1003       double W=-std::log(S)/S;
  1004       return dim2::Point<double>(W*V1,W*V2);
  1005     }
  1006 
  1007     ///@}
  1008   };
  1009 
  1010 
  1011   extern Random rnd;
  1012 
  1013 }
  1014 
  1015 #endif