COIN-OR::LEMON - Graph Library

source: lemon/lemon/random.h @ 753:9314d9339475

Last change on this file since 753:9314d9339475 was 631:33c6b6e755cd, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Small doc improvements (#263)

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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) 2003-2009
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
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>
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
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