COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/random.h @ 393:37054b67d807

Last change on this file since 393:37054b67d807 was 378:80ec623f529f, checked in by Alpar Juttner <alpar@…>, 11 years ago

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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) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19/*
20 * This file contains the reimplemented version of the Mersenne Twister
21 * Generator of Matsumoto and Nishimura.
22 *
23 * See the appropriate copyright notice below.
24 *
25 * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
26 * All rights reserved.
27 *
28 * Redistribution and use in source and binary forms, with or without
29 * modification, are permitted provided that the following conditions
30 * are met:
31 *
32 * 1. Redistributions of source code must retain the above copyright
33 *    notice, this list of conditions and the following disclaimer.
34 *
35 * 2. Redistributions in binary form must reproduce the above copyright
36 *    notice, this list of conditions and the following disclaimer in the
37 *    documentation and/or other materials provided with the distribution.
38 *
39 * 3. The names of its contributors may not be used to endorse or promote
40 *    products derived from this software without specific prior written
41 *    permission.
42 *
43 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
44 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
45 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
46 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE
47 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
48 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
49 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
50 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
51 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
52 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
53 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
54 * OF THE POSSIBILITY OF SUCH DAMAGE.
55 *
56 *
57 * Any feedback is very welcome.
58 * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
59 * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
60 */
61
62#ifndef LEMON_RANDOM_H
63#define LEMON_RANDOM_H
64
65#include <algorithm>
66#include <iterator>
67#include <vector>
68#include <limits>
69#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 <windows.h>
81#endif
82
83///\ingroup misc
84///\file
85///\brief Mersenne Twister random number generator
86
87namespace 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      FILETIME time;
666      GetSystemTimeAsFileTime(&time);
667      seed(GetCurrentProcessId() + time.dwHighDateTime + time.dwLowDateTime);
668#endif
669      return true;
670    }
671
672    /// @}
673
674    ///\name Uniform distributions
675    ///
676    /// @{
677
678    /// \brief Returns a random real number from the range [0, 1)
679    ///
680    /// It returns a random real number from the range [0, 1). The
681    /// default Number type is \c double.
682    template <typename Number>
683    Number real() {
684      return _random_bits::RealConversion<Number, Word>::convert(core);
685    }
686
687    double real() {
688      return real<double>();
689    }
690
691    /// \brief Returns a random real number from the range [0, 1)
692    ///
693    /// It returns a random double from the range [0, 1).
694    double operator()() {
695      return real<double>();
696    }
697
698    /// \brief Returns a random real number from the range [0, b)
699    ///
700    /// It returns a random real number from the range [0, b).
701    double operator()(double b) {
702      return real<double>() * b;
703    }
704
705    /// \brief Returns a random real number from the range [a, b)
706    ///
707    /// It returns a random real number from the range [a, b).
708    double operator()(double a, double b) {
709      return real<double>() * (b - a) + a;
710    }
711
712    /// \brief Returns a random integer from a range
713    ///
714    /// It returns a random integer from the range {0, 1, ..., b - 1}.
715    template <typename Number>
716    Number integer(Number b) {
717      return _random_bits::Mapping<Number, Word>::map(core, b);
718    }
719
720    /// \brief Returns a random integer from a range
721    ///
722    /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
723    template <typename Number>
724    Number integer(Number a, Number b) {
725      return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
726    }
727
728    /// \brief Returns a random integer from a range
729    ///
730    /// It returns a random integer from the range {0, 1, ..., b - 1}.
731    template <typename Number>
732    Number operator[](Number b) {
733      return _random_bits::Mapping<Number, Word>::map(core, b);
734    }
735
736    /// \brief Returns a random non-negative integer
737    ///
738    /// It returns a random non-negative integer uniformly from the
739    /// whole range of the current \c Number type. The default result
740    /// type of this function is <tt>unsigned int</tt>.
741    template <typename Number>
742    Number uinteger() {
743      return _random_bits::IntConversion<Number, Word>::convert(core);
744    }
745
746    unsigned int uinteger() {
747      return uinteger<unsigned int>();
748    }
749
750    /// \brief Returns a random integer
751    ///
752    /// It returns a random integer uniformly from the whole range of
753    /// the current \c Number type. The default result type of this
754    /// function is \c int.
755    template <typename Number>
756    Number integer() {
757      static const int nb = std::numeric_limits<Number>::digits +
758        (std::numeric_limits<Number>::is_signed ? 1 : 0);
759      return _random_bits::IntConversion<Number, Word, nb>::convert(core);
760    }
761
762    int integer() {
763      return integer<int>();
764    }
765
766    /// \brief Returns a random bool
767    ///
768    /// It returns a random bool. The generator holds a buffer for
769    /// random bits. Every time when it become empty the generator makes
770    /// a new random word and fill the buffer up.
771    bool boolean() {
772      return bool_producer.convert(core);
773    }
774
775    /// @}
776
777    ///\name Non-uniform distributions
778    ///
779    ///@{
780
781    /// \brief Returns a random bool with given probability of true result.
782    ///
783    /// It returns a random bool with given probability of true result.
784    bool boolean(double p) {
785      return operator()() < p;
786    }
787
788    /// Standard normal (Gauss) distribution
789
790    /// Standard normal (Gauss) distribution.
791    /// \note The Cartesian form of the Box-Muller
792    /// transformation is used to generate a random normal distribution.
793    double gauss()
794    {
795      double V1,V2,S;
796      do {
797        V1=2*real<double>()-1;
798        V2=2*real<double>()-1;
799        S=V1*V1+V2*V2;
800      } while(S>=1);
801      return std::sqrt(-2*std::log(S)/S)*V1;
802    }
803    /// Normal (Gauss) distribution with given mean and standard deviation
804
805    /// Normal (Gauss) distribution with given mean and standard deviation.
806    /// \sa gauss()
807    double gauss(double mean,double std_dev)
808    {
809      return gauss()*std_dev+mean;
810    }
811
812    /// Lognormal distribution
813
814    /// Lognormal distribution. The parameters are the mean and the standard
815    /// deviation of <tt>exp(X)</tt>.
816    ///
817    double lognormal(double n_mean,double n_std_dev)
818    {
819      return std::exp(gauss(n_mean,n_std_dev));
820    }
821    /// Lognormal distribution
822
823    /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of
824    /// the mean and the standard deviation of <tt>exp(X)</tt>.
825    ///
826    double lognormal(const std::pair<double,double> &params)
827    {
828      return std::exp(gauss(params.first,params.second));
829    }
830    /// Compute the lognormal parameters from mean and standard deviation
831
832    /// This function computes the lognormal parameters from mean and
833    /// standard deviation. The return value can direcly be passed to
834    /// lognormal().
835    std::pair<double,double> lognormalParamsFromMD(double mean,
836                                                   double std_dev)
837    {
838      double fr=std_dev/mean;
839      fr*=fr;
840      double lg=std::log(1+fr);
841      return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg));
842    }
843    /// Lognormal distribution with given mean and standard deviation
844
845    /// Lognormal distribution with given mean and standard deviation.
846    ///
847    double lognormalMD(double mean,double std_dev)
848    {
849      return lognormal(lognormalParamsFromMD(mean,std_dev));
850    }
851
852    /// Exponential distribution with given mean
853
854    /// This function generates an exponential distribution random number
855    /// with mean <tt>1/lambda</tt>.
856    ///
857    double exponential(double lambda=1.0)
858    {
859      return -std::log(1.0-real<double>())/lambda;
860    }
861
862    /// Gamma distribution with given integer shape
863
864    /// This function generates a gamma distribution random number.
865    ///
866    ///\param k shape parameter (<tt>k>0</tt> integer)
867    double gamma(int k)
868    {
869      double s = 0;
870      for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
871      return s;
872    }
873
874    /// Gamma distribution with given shape and scale parameter
875
876    /// This function generates a gamma distribution random number.
877    ///
878    ///\param k shape parameter (<tt>k>0</tt>)
879    ///\param theta scale parameter
880    ///
881    double gamma(double k,double theta=1.0)
882    {
883      double xi,nu;
884      const double delta = k-std::floor(k);
885      const double v0=E/(E-delta);
886      do {
887        double V0=1.0-real<double>();
888        double V1=1.0-real<double>();
889        double V2=1.0-real<double>();
890        if(V2<=v0)
891          {
892            xi=std::pow(V1,1.0/delta);
893            nu=V0*std::pow(xi,delta-1.0);
894          }
895        else
896          {
897            xi=1.0-std::log(V1);
898            nu=V0*std::exp(-xi);
899          }
900      } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
901      return theta*(xi+gamma(int(std::floor(k))));
902    }
903
904    /// Weibull distribution
905
906    /// This function generates a Weibull distribution random number.
907    ///
908    ///\param k shape parameter (<tt>k>0</tt>)
909    ///\param lambda scale parameter (<tt>lambda>0</tt>)
910    ///
911    double weibull(double k,double lambda)
912    {
913      return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
914    }
915
916    /// Pareto distribution
917
918    /// This function generates a Pareto distribution random number.
919    ///
920    ///\param k shape parameter (<tt>k>0</tt>)
921    ///\param x_min location parameter (<tt>x_min>0</tt>)
922    ///
923    double pareto(double k,double x_min)
924    {
925      return exponential(gamma(k,1.0/x_min))+x_min;
926    }
927
928    /// Poisson distribution
929
930    /// This function generates a Poisson distribution random number with
931    /// parameter \c lambda.
932    ///
933    /// The probability mass function of this distribusion is
934    /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
935    /// \note The algorithm is taken from the book of Donald E. Knuth titled
936    /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
937    /// return value.
938
939    int poisson(double lambda)
940    {
941      const double l = std::exp(-lambda);
942      int k=0;
943      double p = 1.0;
944      do {
945        k++;
946        p*=real<double>();
947      } while (p>=l);
948      return k-1;
949    }
950
951    ///@}
952
953    ///\name Two dimensional distributions
954    ///
955    ///@{
956
957    /// Uniform distribution on the full unit circle
958
959    /// Uniform distribution on the full unit circle.
960    ///
961    dim2::Point<double> disc()
962    {
963      double V1,V2;
964      do {
965        V1=2*real<double>()-1;
966        V2=2*real<double>()-1;
967
968      } while(V1*V1+V2*V2>=1);
969      return dim2::Point<double>(V1,V2);
970    }
971    /// A kind of two dimensional normal (Gauss) distribution
972
973    /// This function provides a turning symmetric two-dimensional distribution.
974    /// Both coordinates are of standard normal distribution, but they are not
975    /// independent.
976    ///
977    /// \note The coordinates are the two random variables provided by
978    /// the Box-Muller method.
979    dim2::Point<double> gauss2()
980    {
981      double V1,V2,S;
982      do {
983        V1=2*real<double>()-1;
984        V2=2*real<double>()-1;
985        S=V1*V1+V2*V2;
986      } while(S>=1);
987      double W=std::sqrt(-2*std::log(S)/S);
988      return dim2::Point<double>(W*V1,W*V2);
989    }
990    /// A kind of two dimensional exponential distribution
991
992    /// This function provides a turning symmetric two-dimensional distribution.
993    /// The x-coordinate is of conditionally exponential distribution
994    /// with the condition that x is positive and y=0. If x is negative and
995    /// y=0 then, -x is of exponential distribution. The same is true for the
996    /// y-coordinate.
997    dim2::Point<double> exponential2()
998    {
999      double V1,V2,S;
1000      do {
1001        V1=2*real<double>()-1;
1002        V2=2*real<double>()-1;
1003        S=V1*V1+V2*V2;
1004      } while(S>=1);
1005      double W=-std::log(S)/S;
1006      return dim2::Point<double>(W*V1,W*V2);
1007    }
1008
1009    ///@}
1010  };
1011
1012
1013  extern Random rnd;
1014
1015}
1016
1017#endif
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