COIN-OR::LEMON - Graph Library

source: lemon/lemon/random.h @ 1379:db1d342a1087

Last change on this file since 1379:db1d342a1087 was 1379:db1d342a1087, checked in by Alpar Juttner <alpar@…>, 6 years ago

Platform independent Random generators (#602)

File size: 33.0 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) 2003-2009
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    /// \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 is a template version implementation both 32-bit and
480    /// 64-bit architecture optimized versions. The generators differ
481    /// sligthly in the initialization and generation phase so they
482    /// produce two completly different sequences.
483    ///
484    /// \alert Do not use this class directly, but instead one of \ref
485    /// Random, \ref Random32 or \ref Random64.
486    ///
487    /// The generator gives back random numbers of serveral types. To
488    /// get a random number from a range of a floating point type you
489    /// can use one form of the \c operator() or the \c real() member
490    /// function. If you want to get random number from the {0, 1, ...,
491    /// n-1} integer range use the \c operator[] or the \c integer()
492    /// method. And to get random number from the whole range of an
493    /// integer type you can use the argumentless \c integer() or \c
494    /// uinteger() functions. After all you can get random bool with
495    /// equal chance of true and false or given probability of true
496    /// result with the \c boolean() member functions.
497    ///
498    ///\code
499    /// // The commented code is identical to the other
500    /// double a = rnd();                     // [0.0, 1.0)
501    /// // double a = rnd.real();             // [0.0, 1.0)
502    /// double b = rnd(100.0);                // [0.0, 100.0)
503    /// // double b = rnd.real(100.0);        // [0.0, 100.0)
504    /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
505    /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
506    /// int d = rnd[100000];                  // 0..99999
507    /// // int d = rnd.integer(100000);       // 0..99999
508    /// int e = rnd[6] + 1;                   // 1..6
509    /// // int e = rnd.integer(1, 1 + 6);     // 1..6
510    /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
511    /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
512    /// bool g = rnd.boolean();               // P(g = true) = 0.5
513    /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
514    ///\endcode
515    ///
516    /// LEMON provides a global instance of the random number
517    /// generator which name is \ref lemon::rnd "rnd". Usually it is a
518    /// good programming convenience to use this global generator to get
519    /// random numbers.
520    ///
521    /// \sa \ref Random, \ref Random32 or \ref Random64.
522    ///
523    template<class Word>
524    class Random {
525    private:
526
527      _random_bits::RandomCore<Word> core;
528      _random_bits::BoolProducer<Word> bool_producer;
529
530
531    public:
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 \c true.
611      bool seed() {
612#ifndef LEMON_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 \c true when the seeding successes.
632#ifndef LEMON_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 \c true.
653      bool seedFromTime() {
654#ifndef LEMON_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      /// \brief Returns a random real number from the range [0, 1)
684      ///
685      /// It returns a random double from the range [0, 1).
686      double operator()() {
687        return real<double>();
688      }
689
690      /// \brief Returns a random real number from the range [0, b)
691      ///
692      /// It returns a random real number from the range [0, b).
693      double operator()(double b) {
694        return real<double>() * b;
695      }
696
697      /// \brief Returns a random real number from the range [a, b)
698      ///
699      /// It returns a random real number from the range [a, b).
700      double operator()(double a, double b) {
701        return real<double>() * (b - a) + a;
702      }
703
704      /// \brief Returns a random integer from a range
705      ///
706      /// It returns a random integer from the range {0, 1, ..., b - 1}.
707      template <typename Number>
708      Number integer(Number b) {
709        return _random_bits::Mapping<Number, Word>::map(core, b);
710      }
711
712      /// \brief Returns a random integer from a range
713      ///
714      /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
715      template <typename Number>
716      Number integer(Number a, Number b) {
717        return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
718      }
719
720      /// \brief Returns a random integer from a range
721      ///
722      /// It returns a random integer from the range {0, 1, ..., b - 1}.
723      template <typename Number>
724      Number operator[](Number b) {
725        return _random_bits::Mapping<Number, Word>::map(core, b);
726      }
727
728      /// \brief Returns a random non-negative integer
729      ///
730      /// It returns a random non-negative integer uniformly from the
731      /// whole range of the current \c Number type. The default result
732      /// type of this function is <tt>unsigned int</tt>.
733      template <typename Number>
734      Number uinteger() {
735        return _random_bits::IntConversion<Number, Word>::convert(core);
736      }
737
738      unsigned int uinteger() {
739        return uinteger<unsigned int>();
740      }
741
742      /// \brief Returns a random integer
743      ///
744      /// It returns a random integer uniformly from the whole range of
745      /// the current \c Number type. The default result type of this
746      /// function is \c int.
747      template <typename Number>
748      Number integer() {
749        static const int nb = std::numeric_limits<Number>::digits +
750          (std::numeric_limits<Number>::is_signed ? 1 : 0);
751        return _random_bits::IntConversion<Number, Word, nb>::convert(core);
752      }
753
754      int integer() {
755        return integer<int>();
756      }
757
758      /// \brief Returns a random bool
759      ///
760      /// It returns a random bool. The generator holds a buffer for
761      /// random bits. Every time when it become empty the generator makes
762      /// a new random word and fill the buffer up.
763      bool boolean() {
764        return bool_producer.convert(core);
765      }
766
767      /// @}
768
769      ///\name Non-uniform Distributions
770      ///
771      ///@{
772
773      /// \brief Returns a random bool with given probability of true result.
774      ///
775      /// It returns a random bool with given probability of true result.
776      bool boolean(double p) {
777        return operator()() < p;
778      }
779
780      /// Standard normal (Gauss) distribution
781
782      /// Standard normal (Gauss) distribution.
783      /// \note The Cartesian form of the Box-Muller
784      /// transformation is used to generate a random normal distribution.
785      double gauss()
786      {
787        double V1,V2,S;
788        do {
789          V1=2*real<double>()-1;
790          V2=2*real<double>()-1;
791          S=V1*V1+V2*V2;
792        } while(S>=1);
793        return std::sqrt(-2*std::log(S)/S)*V1;
794      }
795      /// Normal (Gauss) distribution with given mean and standard deviation
796
797      /// Normal (Gauss) distribution with given mean and standard deviation.
798      /// \sa gauss()
799      double gauss(double mean,double std_dev)
800      {
801        return gauss()*std_dev+mean;
802      }
803
804      /// Lognormal distribution
805
806      /// Lognormal distribution. The parameters are the mean and the standard
807      /// deviation of <tt>exp(X)</tt>.
808      ///
809      double lognormal(double n_mean,double n_std_dev)
810      {
811        return std::exp(gauss(n_mean,n_std_dev));
812      }
813      /// Lognormal distribution
814
815      /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of
816      /// the mean and the standard deviation of <tt>exp(X)</tt>.
817      ///
818      double lognormal(const std::pair<double,double> &params)
819      {
820        return std::exp(gauss(params.first,params.second));
821      }
822      /// Compute the lognormal parameters from mean and standard deviation
823
824      /// This function computes the lognormal parameters from mean and
825      /// standard deviation. The return value can direcly be passed to
826      /// lognormal().
827      std::pair<double,double> lognormalParamsFromMD(double mean,
828                                                     double std_dev)
829      {
830        double fr=std_dev/mean;
831        fr*=fr;
832        double lg=std::log(1+fr);
833        return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg));
834      }
835      /// Lognormal distribution with given mean and standard deviation
836
837      /// Lognormal distribution with given mean and standard deviation.
838      ///
839      double lognormalMD(double mean,double std_dev)
840      {
841        return lognormal(lognormalParamsFromMD(mean,std_dev));
842      }
843
844      /// Exponential distribution with given mean
845
846      /// This function generates an exponential distribution random number
847      /// with mean <tt>1/lambda</tt>.
848      ///
849      double exponential(double lambda=1.0)
850      {
851        return -std::log(1.0-real<double>())/lambda;
852      }
853
854      /// Gamma distribution with given integer shape
855
856      /// This function generates a gamma distribution random number.
857      ///
858      ///\param k shape parameter (<tt>k>0</tt> integer)
859      double gamma(int k)
860      {
861        double s = 0;
862        for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
863        return s;
864      }
865
866      /// Gamma distribution with given shape and scale parameter
867
868      /// This function generates a gamma distribution random number.
869      ///
870      ///\param k shape parameter (<tt>k>0</tt>)
871      ///\param theta scale parameter
872      ///
873      double gamma(double k,double theta=1.0)
874      {
875        double xi,nu;
876        const double delta = k-std::floor(k);
877        const double v0=E/(E-delta);
878        do {
879          double V0=1.0-real<double>();
880          double V1=1.0-real<double>();
881          double V2=1.0-real<double>();
882          if(V2<=v0)
883            {
884              xi=std::pow(V1,1.0/delta);
885              nu=V0*std::pow(xi,delta-1.0);
886            }
887          else
888            {
889              xi=1.0-std::log(V1);
890              nu=V0*std::exp(-xi);
891            }
892        } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
893        return theta*(xi+gamma(int(std::floor(k))));
894      }
895
896      /// Weibull distribution
897
898      /// This function generates a Weibull distribution random number.
899      ///
900      ///\param k shape parameter (<tt>k>0</tt>)
901      ///\param lambda scale parameter (<tt>lambda>0</tt>)
902      ///
903      double weibull(double k,double lambda)
904      {
905        return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
906      }
907
908      /// Pareto distribution
909
910      /// This function generates a Pareto distribution random number.
911      ///
912      ///\param k shape parameter (<tt>k>0</tt>)
913      ///\param x_min location parameter (<tt>x_min>0</tt>)
914      ///
915      double pareto(double k,double x_min)
916      {
917        return exponential(gamma(k,1.0/x_min))+x_min;
918      }
919
920      /// Poisson distribution
921
922      /// This function generates a Poisson distribution random number with
923      /// parameter \c lambda.
924      ///
925      /// The probability mass function of this distribusion is
926      /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
927      /// \note The algorithm is taken from the book of Donald E. Knuth titled
928      /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
929      /// return value.
930
931      int poisson(double lambda)
932      {
933        const double l = std::exp(-lambda);
934        int k=0;
935        double p = 1.0;
936        do {
937          k++;
938          p*=real<double>();
939        } while (p>=l);
940        return k-1;
941      }
942
943      ///@}
944
945      ///\name Two Dimensional Distributions
946      ///
947      ///@{
948
949      /// Uniform distribution on the full unit circle
950
951      /// Uniform distribution on the full unit circle.
952      ///
953      dim2::Point<double> disc()
954      {
955        double V1,V2;
956        do {
957          V1=2*real<double>()-1;
958          V2=2*real<double>()-1;
959
960        } while(V1*V1+V2*V2>=1);
961        return dim2::Point<double>(V1,V2);
962      }
963      /// A kind of two dimensional normal (Gauss) distribution
964
965      /// This function provides a turning symmetric two-dimensional distribution.
966      /// Both coordinates are of standard normal distribution, but they are not
967      /// independent.
968      ///
969      /// \note The coordinates are the two random variables provided by
970      /// the Box-Muller method.
971      dim2::Point<double> gauss2()
972      {
973        double V1,V2,S;
974        do {
975          V1=2*real<double>()-1;
976          V2=2*real<double>()-1;
977          S=V1*V1+V2*V2;
978        } while(S>=1);
979        double W=std::sqrt(-2*std::log(S)/S);
980        return dim2::Point<double>(W*V1,W*V2);
981      }
982      /// A kind of two dimensional exponential distribution
983
984      /// This function provides a turning symmetric two-dimensional distribution.
985      /// The x-coordinate is of conditionally exponential distribution
986      /// with the condition that x is positive and y=0. If x is negative and
987      /// y=0 then, -x is of exponential distribution. The same is true for the
988      /// y-coordinate.
989      dim2::Point<double> exponential2()
990      {
991        double V1,V2,S;
992        do {
993          V1=2*real<double>()-1;
994          V2=2*real<double>()-1;
995          S=V1*V1+V2*V2;
996        } while(S>=1);
997        double W=-std::log(S)/S;
998        return dim2::Point<double>(W*V1,W*V2);
999      }
1000
1001      ///@}
1002    };
1003
1004
1005  };
1006
1007  /// \ingroup misc
1008  ///
1009  /// \brief Mersenne Twister random number generator
1010  ///
1011  /// This class implements either the 32 bit or the 64 bit version of
1012  /// the Mersenne Twister random number generator algorithm
1013  /// depending the the system architecture.
1014  ///
1015  /// For the API description, see its base class \ref
1016  /// _random_bits::Random
1017  ///
1018  /// \sa \ref _random_bits::Random
1019  typedef _random_bits::Random<unsigned long> Random;
1020  /// \ingroup misc
1021  ///
1022  /// \brief Mersenne Twister random number generator (32 bit version)
1023  ///
1024  /// This class implements the 32 bit version of the Mersenne Twister
1025  /// random number generator algorithm. It is recommended to be used
1026  /// when someone wants to make sure that the \e same pseudo random
1027  /// sequence will be generated on every platfrom.
1028  ///
1029  /// For the API description, see its base class \ref
1030  /// _random_bits::Random
1031  ///
1032  /// \sa \ref _random_bits::Random
1033
1034  typedef _random_bits::Random<unsigned int> Random32;
1035  /// \ingroup misc
1036  ///
1037  /// \brief Mersenne Twister random number generator (64 bit version)
1038  ///
1039  /// This class implements the 64 bit version of the Mersenne Twister
1040  /// random number generator algorithm. (Even though it will run
1041  /// on 32 bit architectures, too.) It is recommended to ber used when
1042  /// someone wants to make sure that the \e same pseudo random sequence
1043  /// will be generated on every platfrom.
1044  ///
1045  /// For the API description, see its base class \ref
1046  /// _random_bits::Random
1047  ///
1048  /// \sa \ref _random_bits::Random
1049  typedef _random_bits::Random<unsigned long long> Random64;
1050
1051
1052  extern Random rnd;
1053
1054 
1055}
1056
1057#endif
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