COIN-OR::LEMON - Graph Library

source: lemon-main/lemon/random.h

Last change on this file was 1185:c8d0179a32a2, checked in by Alpar Juttner <alpar@…>, 13 months ago

Merge bugfixes #610,#611,#612,#614

File size: 33.2 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      static Word tempering(Word rnd) {
115        rnd ^= (rnd >> 11);
116        rnd ^= (rnd << 7) & 0x9D2C5680u;
117        rnd ^= (rnd << 15) & 0xEFC60000u;
118        rnd ^= (rnd >> 18);
119        return rnd;
120      }
121
122    };
123
124    template <typename _Word>
125    struct RandomTraits<_Word, 64> {
126
127      typedef _Word Word;
128      static const int bits = 64;
129
130      static const int length = 312;
131      static const int shift = 156;
132
133      static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
134      static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
135      static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
136      static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
137
138      static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
139      static const Word loMask = (Word(1u) << 31) - 1;
140      static const Word hiMask = ~loMask;
141
142      static Word tempering(Word rnd) {
143        rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
144        rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
145        rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
146        rnd ^= (rnd >> 43);
147        return rnd;
148      }
149
150    };
151
152    template <typename _Word>
153    class RandomCore {
154    public:
155
156      typedef _Word Word;
157
158    private:
159
160      static const int bits = RandomTraits<Word>::bits;
161
162      static const int length = RandomTraits<Word>::length;
163      static const int shift = RandomTraits<Word>::shift;
164
165    public:
166
167      void initState() {
168        static const Word seedArray[4] = {
169          0x12345u, 0x23456u, 0x34567u, 0x45678u
170        };
171
172        initState(seedArray, seedArray + 4);
173      }
174
175      void initState(Word seed) {
176
177        static const Word mul = RandomTraits<Word>::mul;
178
179        current = state;
180
181        Word *curr = state + length - 1;
182        curr[0] = seed; --curr;
183        for (int i = 1; i < length; ++i) {
184          curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
185          --curr;
186        }
187      }
188
189      template <typename Iterator>
190      void initState(Iterator begin, Iterator end) {
191
192        static const Word init = RandomTraits<Word>::arrayInit;
193        static const Word mul1 = RandomTraits<Word>::arrayMul1;
194        static const Word mul2 = RandomTraits<Word>::arrayMul2;
195
196
197        Word *curr = state + length - 1; --curr;
198        Iterator it = begin; int cnt = 0;
199        int num;
200
201        initState(init);
202
203        num = static_cast<int>(length > end - begin ? length : end - begin);
204        while (num--) {
205          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
206            + *it + cnt;
207          ++it; ++cnt;
208          if (it == end) {
209            it = begin; cnt = 0;
210          }
211          if (curr == state) {
212            curr = state + length - 1; curr[0] = state[0];
213          }
214          --curr;
215        }
216
217        num = length - 1; cnt = static_cast<int>(length - (curr - state) - 1);
218        while (num--) {
219          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
220            - cnt;
221          --curr; ++cnt;
222          if (curr == state) {
223            curr = state + length - 1; curr[0] = state[0]; --curr;
224            cnt = 1;
225          }
226        }
227
228        state[length - 1] = Word(1) << (bits - 1);
229      }
230
231      void copyState(const RandomCore& other) {
232        std::copy(other.state, other.state + length, state);
233        current = state + (other.current - other.state);
234      }
235
236      Word operator()() {
237        if (current == state) fillState();
238        --current;
239        Word rnd = *current;
240        return RandomTraits<Word>::tempering(rnd);
241      }
242
243    private:
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        Word *curr = state + length - 1;
253        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      Word *current;
273      Word state[length];
274
275    };
276
277
278    template <typename Result,
279              int shift = (std::numeric_limits<Result>::digits + 1) / 2>
280    struct Masker {
281      static Result mask(const Result& result) {
282        return Masker<Result, (shift + 1) / 2>::
283          mask(static_cast<Result>(result | (result >> shift)));
284      }
285    };
286
287    template <typename Result>
288    struct Masker<Result, 1> {
289      static Result mask(const Result& result) {
290        return static_cast<Result>(result | (result >> 1));
291      }
292    };
293
294    template <typename Result, typename Word,
295              int rest = std::numeric_limits<Result>::digits, int shift = 0,
296              bool last = (rest <= std::numeric_limits<Word>::digits)>
297    struct IntConversion {
298      static const int bits = std::numeric_limits<Word>::digits;
299
300      static Result convert(RandomCore<Word>& rnd) {
301        return static_cast<Result>(rnd() >> (bits - rest)) << shift;
302      }
303
304    };
305
306    template <typename Result, typename Word, int rest, int shift>
307    struct IntConversion<Result, Word, rest, shift, false> {
308      static const int bits = std::numeric_limits<Word>::digits;
309
310      static Result convert(RandomCore<Word>& rnd) {
311        return (static_cast<Result>(rnd()) << shift) |
312          IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
313      }
314    };
315
316
317    template <typename Result, typename Word,
318              bool one_word = (std::numeric_limits<Word>::digits <
319                               std::numeric_limits<Result>::digits) >
320    struct Mapping {
321      static Result map(RandomCore<Word>& rnd, const Result& bound) {
322        Word max = Word(bound - 1);
323        Result mask = Masker<Result>::mask(bound - 1);
324        Result num;
325        do {
326          num = IntConversion<Result, Word>::convert(rnd) & mask;
327        } while (num > max);
328        return num;
329      }
330    };
331
332    template <typename Result, typename Word>
333    struct Mapping<Result, Word, false> {
334      static Result map(RandomCore<Word>& rnd, const Result& bound) {
335        Word max = Word(bound - 1);
336        Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
337          ::mask(max);
338        Word num;
339        do {
340          num = rnd() & mask;
341        } while (num > max);
342        return static_cast<Result>(num);
343      }
344    };
345
346    template <typename Result, int exp>
347    struct ShiftMultiplier {
348      static const Result multiplier() {
349        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
350        res *= res;
351        if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
352        return res;
353      }
354    };
355
356    template <typename Result>
357    struct ShiftMultiplier<Result, 0> {
358      static const Result multiplier() {
359        return static_cast<Result>(1.0);
360      }
361    };
362
363    template <typename Result>
364    struct ShiftMultiplier<Result, 20> {
365      static const Result multiplier() {
366        return static_cast<Result>(1.0/1048576.0);
367      }
368    };
369
370    template <typename Result>
371    struct ShiftMultiplier<Result, 32> {
372      static const Result multiplier() {
373        return static_cast<Result>(1.0/4294967296.0);
374      }
375    };
376
377    template <typename Result>
378    struct ShiftMultiplier<Result, 53> {
379      static const Result multiplier() {
380        return static_cast<Result>(1.0/9007199254740992.0);
381      }
382    };
383
384    template <typename Result>
385    struct ShiftMultiplier<Result, 64> {
386      static const Result multiplier() {
387        return static_cast<Result>(1.0/18446744073709551616.0);
388      }
389    };
390
391    template <typename Result, int exp>
392    struct Shifting {
393      static Result shift(const Result& result) {
394        return result * ShiftMultiplier<Result, exp>::multiplier();
395      }
396    };
397
398    template <typename Result, typename Word,
399              int rest = std::numeric_limits<Result>::digits, int shift = 0,
400              bool last = rest <= std::numeric_limits<Word>::digits>
401    struct RealConversion{
402      static const int bits = std::numeric_limits<Word>::digits;
403
404      static Result convert(RandomCore<Word>& rnd) {
405        return Shifting<Result, shift + rest>::
406          shift(static_cast<Result>(rnd() >> (bits - rest)));
407      }
408    };
409
410    template <typename Result, typename Word, int rest, int shift>
411    struct RealConversion<Result, Word, rest, shift, false> {
412      static const int bits = std::numeric_limits<Word>::digits;
413
414      static Result convert(RandomCore<Word>& rnd) {
415        return Shifting<Result, shift + bits>::
416          shift(static_cast<Result>(rnd())) +
417          RealConversion<Result, Word, rest-bits, shift + bits>::
418          convert(rnd);
419      }
420    };
421
422    template <typename Result, typename Word>
423    struct Initializer {
424
425      template <typename Iterator>
426      static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
427        std::vector<Word> ws;
428        for (Iterator it = begin; it != end; ++it) {
429          ws.push_back(Word(*it));
430        }
431        rnd.initState(ws.begin(), ws.end());
432      }
433
434      static void init(RandomCore<Word>& rnd, Result seed) {
435        rnd.initState(seed);
436      }
437    };
438
439    template <typename Word>
440    struct BoolConversion {
441      static bool convert(RandomCore<Word>& rnd) {
442        return (rnd() & 1) == 1;
443      }
444    };
445
446    template <typename Word>
447    struct BoolProducer {
448      Word buffer;
449      int num;
450
451      BoolProducer() : num(0) {}
452
453      bool convert(RandomCore<Word>& rnd) {
454        if (num == 0) {
455          buffer = rnd();
456          num = RandomTraits<Word>::bits;
457        }
458        bool r = (buffer & 1);
459        buffer >>= 1;
460        --num;
461        return r;
462      }
463    };
464
465    /// \ingroup misc
466    ///
467    /// \brief Mersenne Twister random number generator
468    ///
469    /// The Mersenne Twister is a twisted generalized feedback
470    /// shift-register generator of Matsumoto and Nishimura. The period
471    /// of this generator is \f$ 2^{19937} - 1\f$ and it is
472    /// equi-distributed in 623 dimensions for 32-bit numbers. The time
473    /// performance of this generator is comparable to the commonly used
474    /// generators.
475    ///
476    /// This is a template implementation of both 32-bit and
477    /// 64-bit architecture optimized versions. The generators differ
478    /// sligthly in the initialization and generation phase so they
479    /// produce two completly different sequences.
480    ///
481    /// \alert Do not use this class directly, but instead one of \ref
482    /// Random, \ref Random32 or \ref Random64.
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
491    /// \c uinteger() functions. Finally, you can get random bool with
492    /// equal chance of true and false or with given probability of true
493    /// result using the \c boolean() member functions.
494    ///
495    /// Various non-uniform distributions are also supported: normal (Gauss),
496    /// exponential, gamma, Poisson, etc.; and a few two-dimensional
497    /// distributions, too.
498    ///
499    ///\code
500    /// // The commented code is identical to the other
501    /// double a = rnd();                     // [0.0, 1.0)
502    /// // double a = rnd.real();             // [0.0, 1.0)
503    /// double b = rnd(100.0);                // [0.0, 100.0)
504    /// // double b = rnd.real(100.0);        // [0.0, 100.0)
505    /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
506    /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
507    /// int d = rnd[100000];                  // 0..99999
508    /// // int d = rnd.integer(100000);       // 0..99999
509    /// int e = rnd[6] + 1;                   // 1..6
510    /// // int e = rnd.integer(1, 1 + 6);     // 1..6
511    /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
512    /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
513    /// bool g = rnd.boolean();               // P(g = true) = 0.5
514    /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
515    ///\endcode
516    ///
517    /// LEMON provides a global instance of the random number generator:
518    /// \ref lemon::rnd "rnd". In most cases, it is a good practice
519    /// to use this global generator to get random numbers.
520    ///
521    /// \sa \ref Random, \ref Random32 or \ref Random64.
522    template<class Word>
523    class Random {
524    private:
525
526      _random_bits::RandomCore<Word> core;
527      _random_bits::BoolProducer<Word> bool_producer;
528
529
530    public:
531
532      ///\name Initialization
533      ///
534      /// @{
535
536      /// \brief Default constructor
537      ///
538      /// Constructor with constant seeding.
539      Random() { core.initState(); }
540
541      /// \brief Constructor with seed
542      ///
543      /// Constructor with seed. The current number type will be converted
544      /// to the architecture word type.
545      template <typename Number>
546      Random(Number seed) {
547        _random_bits::Initializer<Number, Word>::init(core, seed);
548      }
549
550      /// \brief Constructor with array seeding
551      ///
552      /// Constructor with array seeding. The given range should contain
553      /// any number type and the numbers will be converted to the
554      /// architecture word type.
555      template <typename Iterator>
556      Random(Iterator begin, Iterator end) {
557        typedef typename std::iterator_traits<Iterator>::value_type Number;
558        _random_bits::Initializer<Number, Word>::init(core, begin, end);
559      }
560
561      /// \brief Copy constructor
562      ///
563      /// Copy constructor. The generated sequence will be identical to
564      /// the other sequence. It can be used to save the current state
565      /// of the generator and later use it to generate the same
566      /// sequence.
567      Random(const Random& other) {
568        core.copyState(other.core);
569      }
570
571      /// \brief Assign operator
572      ///
573      /// Assign operator. The generated sequence will be identical to
574      /// the other sequence. It can be used to save the current state
575      /// of the generator and later use it to generate the same
576      /// sequence.
577      Random& operator=(const Random& other) {
578        if (&other != this) {
579          core.copyState(other.core);
580        }
581        return *this;
582      }
583
584      /// \brief Seeding random sequence
585      ///
586      /// Seeding the random sequence. The current number type will be
587      /// converted to the architecture word type.
588      template <typename Number>
589      void seed(Number seed) {
590        _random_bits::Initializer<Number, Word>::init(core, seed);
591      }
592
593      /// \brief Seeding random sequence
594      ///
595      /// Seeding the random sequence. The given range should contain
596      /// any number type and the numbers will be converted to the
597      /// architecture word type.
598      template <typename Iterator>
599      void seed(Iterator begin, Iterator end) {
600        typedef typename std::iterator_traits<Iterator>::value_type Number;
601        _random_bits::Initializer<Number, Word>::init(core, begin, end);
602      }
603
604      /// \brief Seeding from file or from process id and time
605      ///
606      /// By default, this function calls the \c seedFromFile() member
607      /// function with the <tt>/dev/urandom</tt> file. If it does not success,
608      /// it uses the \c seedFromTime().
609      /// \return Currently always \c true.
610      bool seed() {
611#ifndef LEMON_WIN32
612        if (seedFromFile("/dev/urandom", 0)) return true;
613#endif
614        if (seedFromTime()) return true;
615        return false;
616      }
617
618      /// \brief Seeding from file
619      ///
620      /// Seeding the random sequence from file. The linux kernel has two
621      /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
622      /// could give good seed values for pseudo random generators (The
623      /// difference between two devices is that the <tt>random</tt> may
624      /// block the reading operation while the kernel can give good
625      /// source of randomness, while the <tt>urandom</tt> does not
626      /// block the input, but it could give back bytes with worse
627      /// entropy).
628      /// \param file The source file
629      /// \param offset The offset, from the file read.
630      /// \return \c true when the seeding successes.
631#ifndef LEMON_WIN32
632      bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)
633#else
634        bool seedFromFile(const std::string& file = "", int offset = 0)
635#endif
636      {
637        std::ifstream rs(file.c_str());
638        const int size = 4;
639        Word buf[size];
640        if (offset != 0 && !rs.seekg(offset)) return false;
641        if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;
642        seed(buf, buf + size);
643        return true;
644      }
645
646      /// \brief Seeding from process id and time
647      ///
648      /// Seeding from process id and time. This function uses the
649      /// current process id and the current time for initialize the
650      /// random sequence.
651      /// \return Currently always \c true.
652      bool seedFromTime() {
653#ifndef LEMON_WIN32
654        timeval tv;
655        gettimeofday(&tv, 0);
656        seed(getpid() + tv.tv_sec + tv.tv_usec);
657#else
658        seed(bits::getWinRndSeed());
659#endif
660        return true;
661      }
662
663      /// @}
664
665      ///\name Uniform Distributions
666      ///
667      /// @{
668
669      /// \brief Returns a random real number from the range [0, 1)
670      ///
671      /// It returns a random real number from the range [0, 1). The
672      /// default Number type is \c double.
673      template <typename Number>
674      Number real() {
675        return _random_bits::RealConversion<Number, Word>::convert(core);
676      }
677
678      double real() {
679        return real<double>();
680      }
681
682      /// \brief Returns a random real number from the range [0, 1)
683      ///
684      /// It returns a random double from the range [0, 1).
685      double operator()() {
686        return real<double>();
687      }
688
689      /// \brief Returns a random real number from the range [0, b)
690      ///
691      /// It returns a random real number from the range [0, b).
692      double operator()(double b) {
693        return real<double>() * b;
694      }
695
696      /// \brief Returns a random real number from the range [a, b)
697      ///
698      /// It returns a random real number from the range [a, b).
699      double operator()(double a, double b) {
700        return real<double>() * (b - a) + a;
701      }
702
703      /// \brief Returns a random integer from a range
704      ///
705      /// It returns a random integer from the range {0, 1, ..., b - 1}.
706      template <typename Number>
707      Number integer(Number b) {
708        return _random_bits::Mapping<Number, Word>::map(core, b);
709      }
710
711      /// \brief Returns a random integer from a range
712      ///
713      /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
714      template <typename Number>
715      Number integer(Number a, Number b) {
716        return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
717      }
718
719      /// \brief Returns a random integer from a range
720      ///
721      /// It returns a random integer from the range {0, 1, ..., b - 1}.
722      template <typename Number>
723      Number operator[](Number b) {
724        return _random_bits::Mapping<Number, Word>::map(core, b);
725      }
726
727      /// \brief Returns a random non-negative integer
728      ///
729      /// It returns a random non-negative integer uniformly from the
730      /// whole range of the current \c Number type. The default result
731      /// type of this function is <tt>unsigned int</tt>.
732      template <typename Number>
733      Number uinteger() {
734        return _random_bits::IntConversion<Number, Word>::convert(core);
735      }
736
737      unsigned int uinteger() {
738        return uinteger<unsigned int>();
739      }
740
741      /// \brief Returns a random integer
742      ///
743      /// It returns a random integer uniformly from the whole range of
744      /// the current \c Number type. The default result type of this
745      /// function is \c int.
746      template <typename Number>
747      Number integer() {
748        static const int nb = std::numeric_limits<Number>::digits +
749          (std::numeric_limits<Number>::is_signed ? 1 : 0);
750        return _random_bits::IntConversion<Number, Word, nb>::convert(core);
751      }
752
753      int integer() {
754        return integer<int>();
755      }
756
757      /// \brief Returns a random bool
758      ///
759      /// It returns a random bool. The generator holds a buffer for
760      /// random bits. Every time when it become empty the generator makes
761      /// a new random word and fill the buffer up.
762      bool boolean() {
763        return bool_producer.convert(core);
764      }
765
766      /// @}
767
768      ///\name Non-uniform Distributions
769      ///
770      ///@{
771
772      /// \brief Returns a random bool with given probability of true result.
773      ///
774      /// It returns a random bool with given probability of true result.
775      bool boolean(double p) {
776        return operator()() < p;
777      }
778
779      /// Standard normal (Gauss) distribution
780
781      /// Standard normal (Gauss) distribution.
782      /// \note The Cartesian form of the Box-Muller
783      /// transformation is used to generate a random normal distribution.
784      double gauss()
785      {
786        double V1,V2,S;
787        do {
788          V1=2*real<double>()-1;
789          V2=2*real<double>()-1;
790          S=V1*V1+V2*V2;
791        } while(S>=1);
792        return std::sqrt(-2*std::log(S)/S)*V1;
793      }
794      /// Normal (Gauss) distribution with given mean and standard deviation
795
796      /// Normal (Gauss) distribution with given mean and standard deviation.
797      /// \sa gauss()
798      double gauss(double mean,double std_dev)
799      {
800        return gauss()*std_dev+mean;
801      }
802
803      /// Lognormal distribution
804
805      /// Lognormal distribution. The parameters are the mean and the standard
806      /// deviation of <tt>exp(X)</tt>.
807      ///
808      double lognormal(double n_mean,double n_std_dev)
809      {
810        return std::exp(gauss(n_mean,n_std_dev));
811      }
812      /// Lognormal distribution
813
814      /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of
815      /// the mean and the standard deviation of <tt>exp(X)</tt>.
816      ///
817      double lognormal(const std::pair<double,double> &params)
818      {
819        return std::exp(gauss(params.first,params.second));
820      }
821      /// Compute the lognormal parameters from mean and standard deviation
822
823      /// This function computes the lognormal parameters from mean and
824      /// standard deviation. The return value can direcly be passed to
825      /// lognormal().
826      std::pair<double,double> lognormalParamsFromMD(double mean,
827                                                     double std_dev)
828      {
829        double fr=std_dev/mean;
830        fr*=fr;
831        double lg=std::log(1+fr);
832        return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg));
833      }
834      /// Lognormal distribution with given mean and standard deviation
835
836      /// Lognormal distribution with given mean and standard deviation.
837      ///
838      double lognormalMD(double mean,double std_dev)
839      {
840        return lognormal(lognormalParamsFromMD(mean,std_dev));
841      }
842
843      /// Exponential distribution with given mean
844
845      /// This function generates an exponential distribution random number
846      /// with mean <tt>1/lambda</tt>.
847      ///
848      double exponential(double lambda=1.0)
849      {
850        return -std::log(1.0-real<double>())/lambda;
851      }
852
853      /// Gamma distribution with given integer shape
854
855      /// This function generates a gamma distribution random number.
856      ///
857      ///\param k shape parameter (<tt>k>0</tt> integer)
858      double gamma(int k)
859      {
860        double s = 0;
861        for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
862        return s;
863      }
864
865      /// Gamma distribution with given shape and scale parameter
866
867      /// This function generates a gamma distribution random number.
868      ///
869      ///\param k shape parameter (<tt>k>0</tt>)
870      ///\param theta scale parameter
871      ///
872      double gamma(double k,double theta=1.0)
873      {
874        double xi,nu;
875        const double delta = k-std::floor(k);
876        const double v0=E/(E-delta);
877        do {
878          double V0=1.0-real<double>();
879          double V1=1.0-real<double>();
880          double V2=1.0-real<double>();
881          if(V2<=v0)
882            {
883              xi=std::pow(V1,1.0/delta);
884              nu=V0*std::pow(xi,delta-1.0);
885            }
886          else
887            {
888              xi=1.0-std::log(V1);
889              nu=V0*std::exp(-xi);
890            }
891        } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
892        return theta*(xi+gamma(int(std::floor(k))));
893      }
894
895      /// Weibull distribution
896
897      /// This function generates a Weibull distribution random number.
898      ///
899      ///\param k shape parameter (<tt>k>0</tt>)
900      ///\param lambda scale parameter (<tt>lambda>0</tt>)
901      ///
902      double weibull(double k,double lambda)
903      {
904        return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
905      }
906
907      /// Pareto distribution
908
909      /// This function generates a Pareto distribution random number.
910      ///
911      ///\param k shape parameter (<tt>k>0</tt>)
912      ///\param x_min location parameter (<tt>x_min>0</tt>)
913      ///
914      double pareto(double k,double x_min)
915      {
916        return exponential(gamma(k,1.0/x_min))+x_min;
917      }
918
919      /// Poisson distribution
920
921      /// This function generates a Poisson distribution random number with
922      /// parameter \c lambda.
923      ///
924      /// The probability mass function of this distribusion is
925      /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
926      /// \note The algorithm is taken from the book of Donald E. Knuth titled
927      /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
928      /// return value.
929
930      int poisson(double lambda)
931      {
932        const double l = std::exp(-lambda);
933        int k=0;
934        double p = 1.0;
935        do {
936          k++;
937          p*=real<double>();
938        } while (p>=l);
939        return k-1;
940      }
941
942      ///@}
943
944      ///\name Two-Dimensional Distributions
945      ///
946      ///@{
947
948      /// Uniform distribution on the full unit circle
949
950      /// Uniform distribution on the full unit circle.
951      ///
952      dim2::Point<double> disc()
953      {
954        double V1,V2;
955        do {
956          V1=2*real<double>()-1;
957          V2=2*real<double>()-1;
958
959        } while(V1*V1+V2*V2>=1);
960        return dim2::Point<double>(V1,V2);
961      }
962      /// A kind of two-dimensional normal (Gauss) distribution
963
964      /// This function provides a turning symmetric two-dimensional distribution.
965      /// Both coordinates are of standard normal distribution, but they are not
966      /// independent.
967      ///
968      /// \note The coordinates are the two random variables provided by
969      /// the Box-Muller method.
970      dim2::Point<double> gauss2()
971      {
972        double V1,V2,S;
973        do {
974          V1=2*real<double>()-1;
975          V2=2*real<double>()-1;
976          S=V1*V1+V2*V2;
977        } while(S>=1);
978        double W=std::sqrt(-2*std::log(S)/S);
979        return dim2::Point<double>(W*V1,W*V2);
980      }
981      /// A kind of two-dimensional exponential distribution
982
983      /// This function provides a turning symmetric two-dimensional distribution.
984      /// The x-coordinate is of conditionally exponential distribution
985      /// with the condition that x is positive and y=0. If x is negative and
986      /// y=0 then, -x is of exponential distribution. The same is true for the
987      /// y-coordinate.
988      dim2::Point<double> exponential2()
989      {
990        double V1,V2,S;
991        do {
992          V1=2*real<double>()-1;
993          V2=2*real<double>()-1;
994          S=V1*V1+V2*V2;
995        } while(S>=1);
996        double W=-std::log(S)/S;
997        return dim2::Point<double>(W*V1,W*V2);
998      }
999
1000      ///@}
1001    };
1002
1003
1004  };
1005
1006  /// \ingroup misc
1007  ///
1008  /// \brief Mersenne Twister random number generator
1009  ///
1010  /// This class implements either the 32-bit or the 64-bit version of
1011  /// the Mersenne Twister random number generator algorithm
1012  /// depending on the system architecture.
1013  ///
1014  /// For the API description, see its base class
1015  /// \ref _random_bits::Random.
1016  ///
1017  /// \sa \ref _random_bits::Random
1018  typedef _random_bits::Random<unsigned long> Random;
1019
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
1030  /// \ref _random_bits::Random.
1031  ///
1032  /// \sa \ref _random_bits::Random
1033  typedef _random_bits::Random<unsigned int> Random32;
1034
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 runs
1041  /// on 32-bit architectures, too.) It is recommended to be 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
1046  /// \ref _random_bits::Random.
1047  ///
1048  /// \sa \ref _random_bits::Random
1049  typedef _random_bits::Random<unsigned long long> Random64;
1050
1051  extern Random rnd;
1052 
1053}
1054
1055#endif
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