COIN-OR::LEMON - Graph Library

source: lemon/lemon/random.h @ 517:afd134142111

Last change on this file since 517:afd134142111 was 517:afd134142111, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Various fixes for compiling on AIX (#211, #212)

File size: 28.9 KB
Line 
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 <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    ///\name Initialization
534    ///
535    /// @{
536
537    /// \brief Default constructor
538    ///
539    /// Constructor with constant seeding.
540    Random() { core.initState(); }
541
542    /// \brief Constructor with seed
543    ///
544    /// Constructor with seed. The current number type will be converted
545    /// to the architecture word type.
546    template <typename Number>
547    Random(Number seed) {
548      _random_bits::Initializer<Number, Word>::init(core, seed);
549    }
550
551    /// \brief Constructor with array seeding
552    ///
553    /// Constructor with array seeding. The given range should contain
554    /// any number type and the numbers will be converted to the
555    /// architecture word type.
556    template <typename Iterator>
557    Random(Iterator begin, Iterator end) {
558      typedef typename std::iterator_traits<Iterator>::value_type Number;
559      _random_bits::Initializer<Number, Word>::init(core, begin, end);
560    }
561
562    /// \brief Copy constructor
563    ///
564    /// Copy constructor. The generated sequence will be identical to
565    /// the other sequence. It can be used to save the current state
566    /// of the generator and later use it to generate the same
567    /// sequence.
568    Random(const Random& other) {
569      core.copyState(other.core);
570    }
571
572    /// \brief Assign operator
573    ///
574    /// Assign operator. The generated sequence will be identical to
575    /// the other sequence. It can be used to save the current state
576    /// of the generator and later use it to generate the same
577    /// sequence.
578    Random& operator=(const Random& other) {
579      if (&other != this) {
580        core.copyState(other.core);
581      }
582      return *this;
583    }
584
585    /// \brief Seeding random sequence
586    ///
587    /// Seeding the random sequence. The current number type will be
588    /// converted to the architecture word type.
589    template <typename Number>
590    void seed(Number seed) {
591      _random_bits::Initializer<Number, Word>::init(core, seed);
592    }
593
594    /// \brief Seeding random sequence
595    ///
596    /// Seeding the random sequence. The given range should contain
597    /// any number type and the numbers will be converted to the
598    /// architecture word type.
599    template <typename Iterator>
600    void seed(Iterator begin, Iterator end) {
601      typedef typename std::iterator_traits<Iterator>::value_type Number;
602      _random_bits::Initializer<Number, Word>::init(core, begin, end);
603    }
604
605    /// \brief Seeding from file or from process id and time
606    ///
607    /// By default, this function calls the \c seedFromFile() member
608    /// function with the <tt>/dev/urandom</tt> file. If it does not success,
609    /// it uses the \c seedFromTime().
610    /// \return Currently always true.
611    bool seed() {
612#ifndef WIN32
613      if (seedFromFile("/dev/urandom", 0)) return true;
614#endif
615      if (seedFromTime()) return true;
616      return false;
617    }
618
619    /// \brief Seeding from file
620    ///
621    /// Seeding the random sequence from file. The linux kernel has two
622    /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
623    /// could give good seed values for pseudo random generators (The
624    /// difference between two devices is that the <tt>random</tt> may
625    /// block the reading operation while the kernel can give good
626    /// source of randomness, while the <tt>urandom</tt> does not
627    /// block the input, but it could give back bytes with worse
628    /// entropy).
629    /// \param file The source file
630    /// \param offset The offset, from the file read.
631    /// \return True when the seeding successes.
632#ifndef WIN32
633    bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)
634#else
635    bool seedFromFile(const std::string& file = "", int offset = 0)
636#endif
637    {
638      std::ifstream rs(file.c_str());
639      const int size = 4;
640      Word buf[size];
641      if (offset != 0 && !rs.seekg(offset)) return false;
642      if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;
643      seed(buf, buf + size);
644      return true;
645    }
646
647    /// \brief Seding from process id and time
648    ///
649    /// Seding from process id and time. This function uses the
650    /// current process id and the current time for initialize the
651    /// random sequence.
652    /// \return Currently always true.
653    bool seedFromTime() {
654#ifndef WIN32
655      timeval tv;
656      gettimeofday(&tv, 0);
657      seed(getpid() + tv.tv_sec + tv.tv_usec);
658#else
659      seed(bits::getWinRndSeed());
660#endif
661      return true;
662    }
663
664    /// @}
665
666    ///\name Uniform distributions
667    ///
668    /// @{
669
670    /// \brief Returns a random real number from the range [0, 1)
671    ///
672    /// It returns a random real number from the range [0, 1). The
673    /// default Number type is \c double.
674    template <typename Number>
675    Number real() {
676      return _random_bits::RealConversion<Number, Word>::convert(core);
677    }
678
679    double real() {
680      return real<double>();
681    }
682
683    /// @}
684
685    ///\name Uniform distributions
686    ///
687    /// @{
688
689    /// \brief Returns a random real number from the range [0, 1)
690    ///
691    /// It returns a random double from the range [0, 1).
692    double operator()() {
693      return real<double>();
694    }
695
696    /// \brief Returns a random real number from the range [0, b)
697    ///
698    /// It returns a random real number from the range [0, b).
699    double operator()(double b) {
700      return real<double>() * b;
701    }
702
703    /// \brief Returns a random real number from the range [a, b)
704    ///
705    /// It returns a random real number from the range [a, b).
706    double operator()(double a, double b) {
707      return real<double>() * (b - a) + a;
708    }
709
710    /// \brief Returns a random integer from a range
711    ///
712    /// It returns a random integer from the range {0, 1, ..., b - 1}.
713    template <typename Number>
714    Number integer(Number b) {
715      return _random_bits::Mapping<Number, Word>::map(core, b);
716    }
717
718    /// \brief Returns a random integer from a range
719    ///
720    /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
721    template <typename Number>
722    Number integer(Number a, Number b) {
723      return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
724    }
725
726    /// \brief Returns a random integer from a range
727    ///
728    /// It returns a random integer from the range {0, 1, ..., b - 1}.
729    template <typename Number>
730    Number operator[](Number b) {
731      return _random_bits::Mapping<Number, Word>::map(core, b);
732    }
733
734    /// \brief Returns a random non-negative integer
735    ///
736    /// It returns a random non-negative integer uniformly from the
737    /// whole range of the current \c Number type. The default result
738    /// type of this function is <tt>unsigned int</tt>.
739    template <typename Number>
740    Number uinteger() {
741      return _random_bits::IntConversion<Number, Word>::convert(core);
742    }
743
744    /// @}
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
782    /// \brief Returns a random bool
783    ///
784    /// It returns a random bool with given probability of true result.
785    bool boolean(double p) {
786      return operator()() < p;
787    }
788
789    /// Standard Gauss distribution
790
791    /// Standard Gauss distribution.
792    /// \note The Cartesian form of the Box-Muller
793    /// transformation is used to generate a random normal distribution.
794    double gauss()
795    {
796      double V1,V2,S;
797      do {
798        V1=2*real<double>()-1;
799        V2=2*real<double>()-1;
800        S=V1*V1+V2*V2;
801      } while(S>=1);
802      return std::sqrt(-2*std::log(S)/S)*V1;
803    }
804    /// Gauss distribution with given mean and standard deviation
805
806    /// Gauss distribution with given mean and standard deviation.
807    /// \sa gauss()
808    double gauss(double mean,double std_dev)
809    {
810      return gauss()*std_dev+mean;
811    }
812
813    /// Exponential distribution with given mean
814
815    /// This function generates an exponential distribution random number
816    /// with mean <tt>1/lambda</tt>.
817    ///
818    double exponential(double lambda=1.0)
819    {
820      return -std::log(1.0-real<double>())/lambda;
821    }
822
823    /// Gamma distribution with given integer shape
824
825    /// This function generates a gamma distribution random number.
826    ///
827    ///\param k shape parameter (<tt>k>0</tt> integer)
828    double gamma(int k)
829    {
830      double s = 0;
831      for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
832      return s;
833    }
834
835    /// Gamma distribution with given shape and scale parameter
836
837    /// This function generates a gamma distribution random number.
838    ///
839    ///\param k shape parameter (<tt>k>0</tt>)
840    ///\param theta scale parameter
841    ///
842    double gamma(double k,double theta=1.0)
843    {
844      double xi,nu;
845      const double delta = k-std::floor(k);
846      const double v0=E/(E-delta);
847      do {
848        double V0=1.0-real<double>();
849        double V1=1.0-real<double>();
850        double V2=1.0-real<double>();
851        if(V2<=v0)
852          {
853            xi=std::pow(V1,1.0/delta);
854            nu=V0*std::pow(xi,delta-1.0);
855          }
856        else
857          {
858            xi=1.0-std::log(V1);
859            nu=V0*std::exp(-xi);
860          }
861      } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
862      return theta*(xi+gamma(int(std::floor(k))));
863    }
864
865    /// Weibull distribution
866
867    /// This function generates a Weibull distribution random number.
868    ///
869    ///\param k shape parameter (<tt>k>0</tt>)
870    ///\param lambda scale parameter (<tt>lambda>0</tt>)
871    ///
872    double weibull(double k,double lambda)
873    {
874      return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
875    }
876
877    /// Pareto distribution
878
879    /// This function generates a Pareto distribution random number.
880    ///
881    ///\param k shape parameter (<tt>k>0</tt>)
882    ///\param x_min location parameter (<tt>x_min>0</tt>)
883    ///
884    double pareto(double k,double x_min)
885    {
886      return exponential(gamma(k,1.0/x_min))+x_min;
887    }
888
889    /// Poisson distribution
890
891    /// This function generates a Poisson distribution random number with
892    /// parameter \c lambda.
893    ///
894    /// The probability mass function of this distribusion is
895    /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
896    /// \note The algorithm is taken from the book of Donald E. Knuth titled
897    /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
898    /// return value.
899
900    int poisson(double lambda)
901    {
902      const double l = std::exp(-lambda);
903      int k=0;
904      double p = 1.0;
905      do {
906        k++;
907        p*=real<double>();
908      } while (p>=l);
909      return k-1;
910    }
911
912    ///@}
913
914    ///\name Two dimensional distributions
915    ///
916
917    ///@{
918
919    /// Uniform distribution on the full unit circle
920
921    /// Uniform distribution on the full unit circle.
922    ///
923    dim2::Point<double> disc()
924    {
925      double V1,V2;
926      do {
927        V1=2*real<double>()-1;
928        V2=2*real<double>()-1;
929
930      } while(V1*V1+V2*V2>=1);
931      return dim2::Point<double>(V1,V2);
932    }
933    /// A kind of two dimensional Gauss distribution
934
935    /// This function provides a turning symmetric two-dimensional distribution.
936    /// Both coordinates are of standard normal distribution, but they are not
937    /// independent.
938    ///
939    /// \note The coordinates are the two random variables provided by
940    /// the Box-Muller method.
941    dim2::Point<double> gauss2()
942    {
943      double V1,V2,S;
944      do {
945        V1=2*real<double>()-1;
946        V2=2*real<double>()-1;
947        S=V1*V1+V2*V2;
948      } while(S>=1);
949      double W=std::sqrt(-2*std::log(S)/S);
950      return dim2::Point<double>(W*V1,W*V2);
951    }
952    /// A kind of two dimensional exponential distribution
953
954    /// This function provides a turning symmetric two-dimensional distribution.
955    /// The x-coordinate is of conditionally exponential distribution
956    /// with the condition that x is positive and y=0. If x is negative and
957    /// y=0 then, -x is of exponential distribution. The same is true for the
958    /// y-coordinate.
959    dim2::Point<double> exponential2()
960    {
961      double V1,V2,S;
962      do {
963        V1=2*real<double>()-1;
964        V2=2*real<double>()-1;
965        S=V1*V1+V2*V2;
966      } while(S>=1);
967      double W=-std::log(S)/S;
968      return dim2::Point<double>(W*V1,W*V2);
969    }
970
971    ///@}
972  };
973
974
975  extern Random rnd;
976
977}
978
979#endif
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