COIN-OR::LEMON - Graph Library

source: lemon/lemon/random.h @ 1369:9fd86ec2cb81

Last change on this file since 1369:9fd86ec2cb81 was 1343:20f95cd51aba, checked in by Alpar Juttner <alpar@…>, 4 years ago

Merge bugfix #595

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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 <lemon/config.h>
66
67#include <algorithm>
68#include <iterator>
69#include <vector>
70#include <limits>
71#include <fstream>
72
73#include <lemon/math.h>
74#include <lemon/dim2.h>
75
76#ifndef LEMON_WIN32
77#include <sys/time.h>
78#include <ctime>
79#include <sys/types.h>
80#include <unistd.h>
81#else
82#include <lemon/bits/windows.h>
83#endif
84
85///\ingroup misc
86///\file
87///\brief Mersenne Twister random number generator
88
89namespace lemon {
90
91  namespace _random_bits {
92
93    template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
94    struct RandomTraits {};
95
96    template <typename _Word>
97    struct RandomTraits<_Word, 32> {
98
99      typedef _Word Word;
100      static const int bits = 32;
101
102      static const int length = 624;
103      static const int shift = 397;
104
105      static const Word mul = 0x6c078965u;
106      static const Word arrayInit = 0x012BD6AAu;
107      static const Word arrayMul1 = 0x0019660Du;
108      static const Word arrayMul2 = 0x5D588B65u;
109
110      static const Word mask = 0x9908B0DFu;
111      static const Word loMask = (1u << 31) - 1;
112      static const Word hiMask = ~loMask;
113
114
115      static Word tempering(Word rnd) {
116        rnd ^= (rnd >> 11);
117        rnd ^= (rnd << 7) & 0x9D2C5680u;
118        rnd ^= (rnd << 15) & 0xEFC60000u;
119        rnd ^= (rnd >> 18);
120        return rnd;
121      }
122
123    };
124
125    template <typename _Word>
126    struct RandomTraits<_Word, 64> {
127
128      typedef _Word Word;
129      static const int bits = 64;
130
131      static const int length = 312;
132      static const int shift = 156;
133
134      static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
135      static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
136      static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
137      static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
138
139      static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
140      static const Word loMask = (Word(1u) << 31) - 1;
141      static const Word hiMask = ~loMask;
142
143      static Word tempering(Word rnd) {
144        rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
145        rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
146        rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
147        rnd ^= (rnd >> 43);
148        return rnd;
149      }
150
151    };
152
153    template <typename _Word>
154    class RandomCore {
155    public:
156
157      typedef _Word Word;
158
159    private:
160
161      static const int bits = RandomTraits<Word>::bits;
162
163      static const int length = RandomTraits<Word>::length;
164      static const int shift = RandomTraits<Word>::shift;
165
166    public:
167
168      void initState() {
169        static const Word seedArray[4] = {
170          0x12345u, 0x23456u, 0x34567u, 0x45678u
171        };
172
173        initState(seedArray, seedArray + 4);
174      }
175
176      void initState(Word seed) {
177
178        static const Word mul = RandomTraits<Word>::mul;
179
180        current = state;
181
182        Word *curr = state + length - 1;
183        curr[0] = seed; --curr;
184        for (int i = 1; i < length; ++i) {
185          curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
186          --curr;
187        }
188      }
189
190      template <typename Iterator>
191      void initState(Iterator begin, Iterator end) {
192
193        static const Word init = RandomTraits<Word>::arrayInit;
194        static const Word mul1 = RandomTraits<Word>::arrayMul1;
195        static const Word mul2 = RandomTraits<Word>::arrayMul2;
196
197
198        Word *curr = state + length - 1; --curr;
199        Iterator it = begin; int cnt = 0;
200        int num;
201
202        initState(init);
203
204        num = static_cast<int>(length > end - begin ? length : end - begin);
205        while (num--) {
206          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
207            + *it + cnt;
208          ++it; ++cnt;
209          if (it == end) {
210            it = begin; cnt = 0;
211          }
212          if (curr == state) {
213            curr = state + length - 1; curr[0] = state[0];
214          }
215          --curr;
216        }
217
218        num = length - 1; cnt = static_cast<int>(length - (curr - state) - 1);
219        while (num--) {
220          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
221            - cnt;
222          --curr; ++cnt;
223          if (curr == state) {
224            curr = state + length - 1; curr[0] = state[0]; --curr;
225            cnt = 1;
226          }
227        }
228
229        state[length - 1] = Word(1) << (bits - 1);
230      }
231
232      void copyState(const RandomCore& other) {
233        std::copy(other.state, other.state + length, state);
234        current = state + (other.current - other.state);
235      }
236
237      Word operator()() {
238        if (current == state) fillState();
239        --current;
240        Word rnd = *current;
241        return RandomTraits<Word>::tempering(rnd);
242      }
243
244    private:
245
246
247      void fillState() {
248        static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
249        static const Word loMask = RandomTraits<Word>::loMask;
250        static const Word hiMask = RandomTraits<Word>::hiMask;
251
252        current = state + length;
253
254        Word *curr = state + length - 1;
255        long num;
256
257        num = length - shift;
258        while (num--) {
259          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
260            curr[- shift] ^ mask[curr[-1] & 1ul];
261          --curr;
262        }
263        num = shift - 1;
264        while (num--) {
265          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
266            curr[length - shift] ^ mask[curr[-1] & 1ul];
267          --curr;
268        }
269        state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
270          curr[length - shift] ^ mask[curr[length - 1] & 1ul];
271
272      }
273
274
275      Word *current;
276      Word state[length];
277
278    };
279
280
281    template <typename Result,
282              int shift = (std::numeric_limits<Result>::digits + 1) / 2>
283    struct Masker {
284      static Result mask(const Result& result) {
285        return Masker<Result, (shift + 1) / 2>::
286          mask(static_cast<Result>(result | (result >> shift)));
287      }
288    };
289
290    template <typename Result>
291    struct Masker<Result, 1> {
292      static Result mask(const Result& result) {
293        return static_cast<Result>(result | (result >> 1));
294      }
295    };
296
297    template <typename Result, typename Word,
298              int rest = std::numeric_limits<Result>::digits, int shift = 0,
299              bool last = rest <= std::numeric_limits<Word>::digits>
300    struct IntConversion {
301      static const int bits = std::numeric_limits<Word>::digits;
302
303      static Result convert(RandomCore<Word>& rnd) {
304        return static_cast<Result>(rnd() >> (bits - rest)) << shift;
305      }
306
307    };
308
309    template <typename Result, typename Word, int rest, int shift>
310    struct IntConversion<Result, Word, rest, shift, false> {
311      static const int bits = std::numeric_limits<Word>::digits;
312
313      static Result convert(RandomCore<Word>& rnd) {
314        return (static_cast<Result>(rnd()) << shift) |
315          IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
316      }
317    };
318
319
320    template <typename Result, typename Word,
321              bool one_word = (std::numeric_limits<Word>::digits <
322                               std::numeric_limits<Result>::digits) >
323    struct Mapping {
324      static Result map(RandomCore<Word>& rnd, const Result& bound) {
325        Word max = Word(bound - 1);
326        Result mask = Masker<Result>::mask(bound - 1);
327        Result num;
328        do {
329          num = IntConversion<Result, Word>::convert(rnd) & mask;
330        } while (num > max);
331        return num;
332      }
333    };
334
335    template <typename Result, typename Word>
336    struct Mapping<Result, Word, false> {
337      static Result map(RandomCore<Word>& rnd, const Result& bound) {
338        Word max = Word(bound - 1);
339        Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
340          ::mask(max);
341        Word num;
342        do {
343          num = rnd() & mask;
344        } while (num > max);
345        return num;
346      }
347    };
348
349    template <typename Result, int exp>
350    struct ShiftMultiplier {
351      static const Result multiplier() {
352        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
353        res *= res;
354        if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
355        return res;
356      }
357    };
358
359    template <typename Result>
360    struct ShiftMultiplier<Result, 0> {
361      static const Result multiplier() {
362        return static_cast<Result>(1.0);
363      }
364    };
365
366    template <typename Result>
367    struct ShiftMultiplier<Result, 20> {
368      static const Result multiplier() {
369        return static_cast<Result>(1.0/1048576.0);
370      }
371    };
372
373    template <typename Result>
374    struct ShiftMultiplier<Result, 32> {
375      static const Result multiplier() {
376        return static_cast<Result>(1.0/4294967296.0);
377      }
378    };
379
380    template <typename Result>
381    struct ShiftMultiplier<Result, 53> {
382      static const Result multiplier() {
383        return static_cast<Result>(1.0/9007199254740992.0);
384      }
385    };
386
387    template <typename Result>
388    struct ShiftMultiplier<Result, 64> {
389      static const Result multiplier() {
390        return static_cast<Result>(1.0/18446744073709551616.0);
391      }
392    };
393
394    template <typename Result, int exp>
395    struct Shifting {
396      static Result shift(const Result& result) {
397        return result * ShiftMultiplier<Result, exp>::multiplier();
398      }
399    };
400
401    template <typename Result, typename Word,
402              int rest = std::numeric_limits<Result>::digits, int shift = 0,
403              bool last = rest <= std::numeric_limits<Word>::digits>
404    struct RealConversion{
405      static const int bits = std::numeric_limits<Word>::digits;
406
407      static Result convert(RandomCore<Word>& rnd) {
408        return Shifting<Result, shift + rest>::
409          shift(static_cast<Result>(rnd() >> (bits - rest)));
410      }
411    };
412
413    template <typename Result, typename Word, int rest, int shift>
414    struct RealConversion<Result, Word, rest, shift, false> {
415      static const int bits = std::numeric_limits<Word>::digits;
416
417      static Result convert(RandomCore<Word>& rnd) {
418        return Shifting<Result, shift + bits>::
419          shift(static_cast<Result>(rnd())) +
420          RealConversion<Result, Word, rest-bits, shift + bits>::
421          convert(rnd);
422      }
423    };
424
425    template <typename Result, typename Word>
426    struct Initializer {
427
428      template <typename Iterator>
429      static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
430        std::vector<Word> ws;
431        for (Iterator it = begin; it != end; ++it) {
432          ws.push_back(Word(*it));
433        }
434        rnd.initState(ws.begin(), ws.end());
435      }
436
437      static void init(RandomCore<Word>& rnd, Result seed) {
438        rnd.initState(seed);
439      }
440    };
441
442    template <typename Word>
443    struct BoolConversion {
444      static bool convert(RandomCore<Word>& rnd) {
445        return (rnd() & 1) == 1;
446      }
447    };
448
449    template <typename Word>
450    struct BoolProducer {
451      Word buffer;
452      int num;
453
454      BoolProducer() : num(0) {}
455
456      bool convert(RandomCore<Word>& rnd) {
457        if (num == 0) {
458          buffer = rnd();
459          num = RandomTraits<Word>::bits;
460        }
461        bool r = (buffer & 1);
462        buffer >>= 1;
463        --num;
464        return r;
465      }
466    };
467
468  }
469
470  /// \ingroup misc
471  ///
472  /// \brief Mersenne Twister random number generator
473  ///
474  /// The Mersenne Twister is a twisted generalized feedback
475  /// shift-register generator of Matsumoto and Nishimura. The period
476  /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
477  /// equi-distributed in 623 dimensions for 32-bit numbers. The time
478  /// performance of this generator is comparable to the commonly used
479  /// generators.
480  ///
481  /// This implementation is specialized for both 32-bit and 64-bit
482  /// architectures. The generators differ sligthly in the
483  /// initialization and generation phase so they produce two
484  /// completly different sequences.
485  ///
486  /// The generator gives back random numbers of serveral types. To
487  /// get a random number from a range of a floating point type you
488  /// can use one form of the \c operator() or the \c real() member
489  /// function. If you want to get random number from the {0, 1, ...,
490  /// n-1} integer range use the \c operator[] or the \c integer()
491  /// method. And to get random number from the whole range of an
492  /// integer type you can use the argumentless \c integer() or \c
493  /// uinteger() functions. After all you can get random bool with
494  /// equal chance of true and false or given probability of true
495  /// result with the \c boolean() member functions.
496  ///
497  ///\code
498  /// // The commented code is identical to the other
499  /// double a = rnd();                     // [0.0, 1.0)
500  /// // double a = rnd.real();             // [0.0, 1.0)
501  /// double b = rnd(100.0);                // [0.0, 100.0)
502  /// // double b = rnd.real(100.0);        // [0.0, 100.0)
503  /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
504  /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
505  /// int d = rnd[100000];                  // 0..99999
506  /// // int d = rnd.integer(100000);       // 0..99999
507  /// int e = rnd[6] + 1;                   // 1..6
508  /// // int e = rnd.integer(1, 1 + 6);     // 1..6
509  /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
510  /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
511  /// bool g = rnd.boolean();               // P(g = true) = 0.5
512  /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
513  ///\endcode
514  ///
515  /// LEMON provides a global instance of the random number
516  /// generator which name is \ref lemon::rnd "rnd". Usually it is a
517  /// good programming convenience to use this global generator to get
518  /// random numbers.
519  class Random {
520  private:
521
522    // Architecture word
523    typedef unsigned long Word;
524
525    _random_bits::RandomCore<Word> core;
526    _random_bits::BoolProducer<Word> bool_producer;
527
528
529  public:
530
531    ///\name Initialization
532    ///
533    /// @{
534
535    /// \brief Default constructor
536    ///
537    /// Constructor with constant seeding.
538    Random() { core.initState(); }
539
540    /// \brief Constructor with seed
541    ///
542    /// Constructor with seed. The current number type will be converted
543    /// to the architecture word type.
544    template <typename Number>
545    Random(Number seed) {
546      _random_bits::Initializer<Number, Word>::init(core, seed);
547    }
548
549    /// \brief Constructor with array seeding
550    ///
551    /// Constructor with array seeding. The given range should contain
552    /// any number type and the numbers will be converted to the
553    /// architecture word type.
554    template <typename Iterator>
555    Random(Iterator begin, Iterator end) {
556      typedef typename std::iterator_traits<Iterator>::value_type Number;
557      _random_bits::Initializer<Number, Word>::init(core, begin, end);
558    }
559
560    /// \brief Copy constructor
561    ///
562    /// Copy constructor. The generated sequence will be identical to
563    /// the other sequence. It can be used to save the current state
564    /// of the generator and later use it to generate the same
565    /// sequence.
566    Random(const Random& other) {
567      core.copyState(other.core);
568    }
569
570    /// \brief Assign operator
571    ///
572    /// Assign operator. The generated sequence will be identical to
573    /// the other sequence. It can be used to save the current state
574    /// of the generator and later use it to generate the same
575    /// sequence.
576    Random& operator=(const Random& other) {
577      if (&other != this) {
578        core.copyState(other.core);
579      }
580      return *this;
581    }
582
583    /// \brief Seeding random sequence
584    ///
585    /// Seeding the random sequence. The current number type will be
586    /// converted to the architecture word type.
587    template <typename Number>
588    void seed(Number seed) {
589      _random_bits::Initializer<Number, Word>::init(core, seed);
590    }
591
592    /// \brief Seeding random sequence
593    ///
594    /// Seeding the random sequence. The given range should contain
595    /// any number type and the numbers will be converted to the
596    /// architecture word type.
597    template <typename Iterator>
598    void seed(Iterator begin, Iterator end) {
599      typedef typename std::iterator_traits<Iterator>::value_type Number;
600      _random_bits::Initializer<Number, Word>::init(core, begin, end);
601    }
602
603    /// \brief Seeding from file or from process id and time
604    ///
605    /// By default, this function calls the \c seedFromFile() member
606    /// function with the <tt>/dev/urandom</tt> file. If it does not success,
607    /// it uses the \c seedFromTime().
608    /// \return Currently always \c true.
609    bool seed() {
610#ifndef LEMON_WIN32
611      if (seedFromFile("/dev/urandom", 0)) return true;
612#endif
613      if (seedFromTime()) return true;
614      return false;
615    }
616
617    /// \brief Seeding from file
618    ///
619    /// Seeding the random sequence from file. The linux kernel has two
620    /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
621    /// could give good seed values for pseudo random generators (The
622    /// difference between two devices is that the <tt>random</tt> may
623    /// block the reading operation while the kernel can give good
624    /// source of randomness, while the <tt>urandom</tt> does not
625    /// block the input, but it could give back bytes with worse
626    /// entropy).
627    /// \param file The source file
628    /// \param offset The offset, from the file read.
629    /// \return \c true when the seeding successes.
630#ifndef LEMON_WIN32
631    bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)
632#else
633    bool seedFromFile(const std::string& file = "", int offset = 0)
634#endif
635    {
636      std::ifstream rs(file.c_str());
637      const int size = 4;
638      Word buf[size];
639      if (offset != 0 && !rs.seekg(offset)) return false;
640      if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;
641      seed(buf, buf + size);
642      return true;
643    }
644
645    /// \brief Seding from process id and time
646    ///
647    /// Seding from process id and time. This function uses the
648    /// current process id and the current time for initialize the
649    /// random sequence.
650    /// \return Currently always \c true.
651    bool seedFromTime() {
652#ifndef LEMON_WIN32
653      timeval tv;
654      gettimeofday(&tv, 0);
655      seed(getpid() + tv.tv_sec + tv.tv_usec);
656#else
657      seed(bits::getWinRndSeed());
658#endif
659      return true;
660    }
661
662    /// @}
663
664    ///\name Uniform Distributions
665    ///
666    /// @{
667
668    /// \brief Returns a random real number from the range [0, 1)
669    ///
670    /// It returns a random real number from the range [0, 1). The
671    /// default Number type is \c double.
672    template <typename Number>
673    Number real() {
674      return _random_bits::RealConversion<Number, Word>::convert(core);
675    }
676
677    double real() {
678      return real<double>();
679    }
680
681    /// \brief Returns a random real number from the range [0, 1)
682    ///
683    /// It returns a random double from the range [0, 1).
684    double operator()() {
685      return real<double>();
686    }
687
688    /// \brief Returns a random real number from the range [0, b)
689    ///
690    /// It returns a random real number from the range [0, b).
691    double operator()(double b) {
692      return real<double>() * b;
693    }
694
695    /// \brief Returns a random real number from the range [a, b)
696    ///
697    /// It returns a random real number from the range [a, b).
698    double operator()(double a, double b) {
699      return real<double>() * (b - a) + a;
700    }
701
702    /// \brief Returns a random integer from a range
703    ///
704    /// It returns a random integer from the range {0, 1, ..., b - 1}.
705    template <typename Number>
706    Number integer(Number b) {
707      return _random_bits::Mapping<Number, Word>::map(core, b);
708    }
709
710    /// \brief Returns a random integer from a range
711    ///
712    /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
713    template <typename Number>
714    Number integer(Number a, Number b) {
715      return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
716    }
717
718    /// \brief Returns a random integer from a range
719    ///
720    /// It returns a random integer from the range {0, 1, ..., b - 1}.
721    template <typename Number>
722    Number operator[](Number b) {
723      return _random_bits::Mapping<Number, Word>::map(core, b);
724    }
725
726    /// \brief Returns a random non-negative integer
727    ///
728    /// It returns a random non-negative integer uniformly from the
729    /// whole range of the current \c Number type. The default result
730    /// type of this function is <tt>unsigned int</tt>.
731    template <typename Number>
732    Number uinteger() {
733      return _random_bits::IntConversion<Number, Word>::convert(core);
734    }
735
736    unsigned int uinteger() {
737      return uinteger<unsigned int>();
738    }
739
740    /// \brief Returns a random integer
741    ///
742    /// It returns a random integer uniformly from the whole range of
743    /// the current \c Number type. The default result type of this
744    /// function is \c int.
745    template <typename Number>
746    Number integer() {
747      static const int nb = std::numeric_limits<Number>::digits +
748        (std::numeric_limits<Number>::is_signed ? 1 : 0);
749      return _random_bits::IntConversion<Number, Word, nb>::convert(core);
750    }
751
752    int integer() {
753      return integer<int>();
754    }
755
756    /// \brief Returns a random bool
757    ///
758    /// It returns a random bool. The generator holds a buffer for
759    /// random bits. Every time when it become empty the generator makes
760    /// a new random word and fill the buffer up.
761    bool boolean() {
762      return bool_producer.convert(core);
763    }
764
765    /// @}
766
767    ///\name Non-uniform Distributions
768    ///
769    ///@{
770
771    /// \brief Returns a random bool with given probability of true result.
772    ///
773    /// It returns a random bool with given probability of true result.
774    bool boolean(double p) {
775      return operator()() < p;
776    }
777
778    /// Standard normal (Gauss) distribution
779
780    /// Standard normal (Gauss) distribution.
781    /// \note The Cartesian form of the Box-Muller
782    /// transformation is used to generate a random normal distribution.
783    double gauss()
784    {
785      double V1,V2,S;
786      do {
787        V1=2*real<double>()-1;
788        V2=2*real<double>()-1;
789        S=V1*V1+V2*V2;
790      } while(S>=1);
791      return std::sqrt(-2*std::log(S)/S)*V1;
792    }
793    /// Normal (Gauss) distribution with given mean and standard deviation
794
795    /// Normal (Gauss) distribution with given mean and standard deviation.
796    /// \sa gauss()
797    double gauss(double mean,double std_dev)
798    {
799      return gauss()*std_dev+mean;
800    }
801
802    /// Lognormal distribution
803
804    /// Lognormal distribution. The parameters are the mean and the standard
805    /// deviation of <tt>exp(X)</tt>.
806    ///
807    double lognormal(double n_mean,double n_std_dev)
808    {
809      return std::exp(gauss(n_mean,n_std_dev));
810    }
811    /// Lognormal distribution
812
813    /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of
814    /// the mean and the standard deviation of <tt>exp(X)</tt>.
815    ///
816    double lognormal(const std::pair<double,double> &params)
817    {
818      return std::exp(gauss(params.first,params.second));
819    }
820    /// Compute the lognormal parameters from mean and standard deviation
821
822    /// This function computes the lognormal parameters from mean and
823    /// standard deviation. The return value can direcly be passed to
824    /// lognormal().
825    std::pair<double,double> lognormalParamsFromMD(double mean,
826                                                   double std_dev)
827    {
828      double fr=std_dev/mean;
829      fr*=fr;
830      double lg=std::log(1+fr);
831      return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg));
832    }
833    /// Lognormal distribution with given mean and standard deviation
834
835    /// Lognormal distribution with given mean and standard deviation.
836    ///
837    double lognormalMD(double mean,double std_dev)
838    {
839      return lognormal(lognormalParamsFromMD(mean,std_dev));
840    }
841
842    /// Exponential distribution with given mean
843
844    /// This function generates an exponential distribution random number
845    /// with mean <tt>1/lambda</tt>.
846    ///
847    double exponential(double lambda=1.0)
848    {
849      return -std::log(1.0-real<double>())/lambda;
850    }
851
852    /// Gamma distribution with given integer shape
853
854    /// This function generates a gamma distribution random number.
855    ///
856    ///\param k shape parameter (<tt>k>0</tt> integer)
857    double gamma(int k)
858    {
859      double s = 0;
860      for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
861      return s;
862    }
863
864    /// Gamma distribution with given shape and scale parameter
865
866    /// This function generates a gamma distribution random number.
867    ///
868    ///\param k shape parameter (<tt>k>0</tt>)
869    ///\param theta scale parameter
870    ///
871    double gamma(double k,double theta=1.0)
872    {
873      double xi,nu;
874      const double delta = k-std::floor(k);
875      const double v0=E/(E-delta);
876      do {
877        double V0=1.0-real<double>();
878        double V1=1.0-real<double>();
879        double V2=1.0-real<double>();
880        if(V2<=v0)
881          {
882            xi=std::pow(V1,1.0/delta);
883            nu=V0*std::pow(xi,delta-1.0);
884          }
885        else
886          {
887            xi=1.0-std::log(V1);
888            nu=V0*std::exp(-xi);
889          }
890      } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
891      return theta*(xi+gamma(int(std::floor(k))));
892    }
893
894    /// Weibull distribution
895
896    /// This function generates a Weibull distribution random number.
897    ///
898    ///\param k shape parameter (<tt>k>0</tt>)
899    ///\param lambda scale parameter (<tt>lambda>0</tt>)
900    ///
901    double weibull(double k,double lambda)
902    {
903      return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
904    }
905
906    /// Pareto distribution
907
908    /// This function generates a Pareto distribution random number.
909    ///
910    ///\param k shape parameter (<tt>k>0</tt>)
911    ///\param x_min location parameter (<tt>x_min>0</tt>)
912    ///
913    double pareto(double k,double x_min)
914    {
915      return exponential(gamma(k,1.0/x_min))+x_min;
916    }
917
918    /// Poisson distribution
919
920    /// This function generates a Poisson distribution random number with
921    /// parameter \c lambda.
922    ///
923    /// The probability mass function of this distribusion is
924    /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
925    /// \note The algorithm is taken from the book of Donald E. Knuth titled
926    /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
927    /// return value.
928
929    int poisson(double lambda)
930    {
931      const double l = std::exp(-lambda);
932      int k=0;
933      double p = 1.0;
934      do {
935        k++;
936        p*=real<double>();
937      } while (p>=l);
938      return k-1;
939    }
940
941    ///@}
942
943    ///\name Two Dimensional Distributions
944    ///
945    ///@{
946
947    /// Uniform distribution on the full unit circle
948
949    /// Uniform distribution on the full unit circle.
950    ///
951    dim2::Point<double> disc()
952    {
953      double V1,V2;
954      do {
955        V1=2*real<double>()-1;
956        V2=2*real<double>()-1;
957
958      } while(V1*V1+V2*V2>=1);
959      return dim2::Point<double>(V1,V2);
960    }
961    /// A kind of two dimensional normal (Gauss) distribution
962
963    /// This function provides a turning symmetric two-dimensional distribution.
964    /// Both coordinates are of standard normal distribution, but they are not
965    /// independent.
966    ///
967    /// \note The coordinates are the two random variables provided by
968    /// the Box-Muller method.
969    dim2::Point<double> gauss2()
970    {
971      double V1,V2,S;
972      do {
973        V1=2*real<double>()-1;
974        V2=2*real<double>()-1;
975        S=V1*V1+V2*V2;
976      } while(S>=1);
977      double W=std::sqrt(-2*std::log(S)/S);
978      return dim2::Point<double>(W*V1,W*V2);
979    }
980    /// A kind of two dimensional exponential distribution
981
982    /// This function provides a turning symmetric two-dimensional distribution.
983    /// The x-coordinate is of conditionally exponential distribution
984    /// with the condition that x is positive and y=0. If x is negative and
985    /// y=0 then, -x is of exponential distribution. The same is true for the
986    /// y-coordinate.
987    dim2::Point<double> exponential2()
988    {
989      double V1,V2,S;
990      do {
991        V1=2*real<double>()-1;
992        V2=2*real<double>()-1;
993        S=V1*V1+V2*V2;
994      } while(S>=1);
995      double W=-std::log(S)/S;
996      return dim2::Point<double>(W*V1,W*V2);
997    }
998
999    ///@}
1000  };
1001
1002
1003  extern Random rnd;
1004
1005}
1006
1007#endif
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