COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/random.h @ 2356:57c316cb868b

Last change on this file since 2356:57c316cb868b was 2356:57c316cb868b, checked in by Alpar Juttner, 13 years ago

Further doc improvements

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2006
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#ifndef LEMON_RANDOM_H
20#define LEMON_RANDOM_H
21
22#include <algorithm>
23#include <iterator>
24#include <vector>
25
26#include <ctime>
27#include <cmath>
28
29///\ingroup misc
30///\file
31///\brief Mersenne Twister random number generator
32///
33///\author Balazs Dezso
34
35namespace lemon {
36
37  namespace _random_bits {
38   
39    template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
40    struct RandomTraits {};
41
42    template <typename _Word>
43    struct RandomTraits<_Word, 32> {
44
45      typedef _Word Word;
46      static const int bits = 32;
47
48      static const int length = 624;
49      static const int shift = 397;
50     
51      static const Word mul = 0x6c078965u;
52      static const Word arrayInit = 0x012BD6AAu;
53      static const Word arrayMul1 = 0x0019660Du;
54      static const Word arrayMul2 = 0x5D588B65u;
55
56      static const Word mask = 0x9908B0DFu;
57      static const Word loMask = (1u << 31) - 1;
58      static const Word hiMask = ~loMask;
59
60
61      static Word tempering(Word rnd) {
62        rnd ^= (rnd >> 11);
63        rnd ^= (rnd << 7) & 0x9D2C5680u;
64        rnd ^= (rnd << 15) & 0xEFC60000u;
65        rnd ^= (rnd >> 18);
66        return rnd;
67      }
68
69    };
70
71    template <typename _Word>
72    struct RandomTraits<_Word, 64> {
73
74      typedef _Word Word;
75      static const int bits = 64;
76
77      static const int length = 312;
78      static const int shift = 156;
79
80      static const Word mul = (Word)0x5851F42Du << 32 | (Word)0x4C957F2Du;
81      static const Word arrayInit = (Word)0x00000000u << 32 |(Word)0x012BD6AAu;
82      static const Word arrayMul1 = (Word)0x369DEA0Fu << 32 |(Word)0x31A53F85u;
83      static const Word arrayMul2 = (Word)0x27BB2EE6u << 32 |(Word)0x87B0B0FDu;
84
85      static const Word mask = (Word)0xB5026F5Au << 32 | (Word)0xA96619E9u;
86      static const Word loMask = ((Word)1u << 31) - 1;
87      static const Word hiMask = ~loMask;
88
89      static Word tempering(Word rnd) {
90        rnd ^= (rnd >> 29) & ((Word)0x55555555u << 32 | (Word)0x55555555u);
91        rnd ^= (rnd << 17) & ((Word)0x71D67FFFu << 32 | (Word)0xEDA60000u);
92        rnd ^= (rnd << 37) & ((Word)0xFFF7EEE0u << 32 | (Word)0x00000000u);
93        rnd ^= (rnd >> 43);
94        return rnd;
95      }
96
97    };
98
99    template <typename _Word>
100    class RandomCore {
101    public:
102
103      typedef _Word Word;
104
105    private:
106
107      static const int bits = RandomTraits<Word>::bits;
108
109      static const int length = RandomTraits<Word>::length;
110      static const int shift = RandomTraits<Word>::shift;
111
112    public:
113
114      void initState() {
115        static const Word seedArray[4] = {
116          0x12345u, 0x23456u, 0x34567u, 0x45678u
117        };
118   
119        initState(seedArray, seedArray + 4);
120      }
121
122      void initState(Word seed) {
123
124        static const Word mul = RandomTraits<Word>::mul;
125
126        current = state;
127
128        Word *curr = state + length - 1;
129        curr[0] = seed; --curr;
130        for (int i = 1; i < length; ++i) {
131          curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
132          --curr;
133        }
134      }
135
136      template <typename Iterator>
137      void initState(Iterator begin, Iterator end) {
138
139        static const Word init = RandomTraits<Word>::arrayInit;
140        static const Word mul1 = RandomTraits<Word>::arrayMul1;
141        static const Word mul2 = RandomTraits<Word>::arrayMul2;
142
143
144        Word *curr = state + length - 1; --curr;
145        Iterator it = begin; int cnt = 0;
146        int num;
147
148        initState(init);
149
150        num = length > end - begin ? length : end - begin;
151        while (num--) {
152          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
153            + *it + cnt;
154          ++it; ++cnt;
155          if (it == end) {
156            it = begin; cnt = 0;
157          }
158          if (curr == state) {
159            curr = state + length - 1; curr[0] = state[0];
160          }
161          --curr;
162        }
163
164        num = length - 1; cnt = length - (curr - state) - 1;
165        while (num--) {
166          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
167            - cnt;
168          --curr; ++cnt;
169          if (curr == state) {
170            curr = state + length - 1; curr[0] = state[0]; --curr;
171            cnt = 1;
172          }
173        }
174       
175        state[length - 1] = (Word)1 << (bits - 1);
176      }
177     
178      void copyState(const RandomCore& other) {
179        std::copy(other.state, other.state + length, state);
180        current = state + (other.current - other.state);
181      }
182
183      Word operator()() {
184        if (current == state) fillState();
185        --current;
186        Word rnd = *current;
187        return RandomTraits<Word>::tempering(rnd);
188      }
189
190    private:
191
192 
193      void fillState() {
194        static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
195        static const Word loMask = RandomTraits<Word>::loMask;
196        static const Word hiMask = RandomTraits<Word>::hiMask;
197
198        current = state + length;
199
200        register Word *curr = state + length - 1;
201        register long num;
202     
203        num = length - shift;
204        while (num--) {
205          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
206            curr[- shift] ^ mask[curr[-1] & 1ul];
207          --curr;
208        }
209        num = shift - 1;
210        while (num--) {
211          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
212            curr[length - shift] ^ mask[curr[-1] & 1ul];
213          --curr;
214        }
215        curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
216          curr[length - shift] ^ mask[curr[length - 1] & 1ul];
217
218      }
219
220 
221      Word *current;
222      Word state[length];
223     
224    };
225
226
227    template <typename Result,
228              int shift = (std::numeric_limits<Result>::digits + 1) / 2>
229    struct Masker {
230      static Result mask(const Result& result) {
231        return Masker<Result, (shift + 1) / 2>::
232          mask((Result)(result | (result >> shift)));
233      }
234    };
235   
236    template <typename Result>
237    struct Masker<Result, 1> {
238      static Result mask(const Result& result) {
239        return (Result)(result | (result >> 1));
240      }
241    };
242
243    template <typename Result, typename Word,
244              int rest = std::numeric_limits<Result>::digits, int shift = 0,
245              bool last = rest <= std::numeric_limits<Word>::digits>
246    struct IntConversion {
247      static const int bits = std::numeric_limits<Word>::digits;
248   
249      static Result convert(RandomCore<Word>& rnd) {
250        return (Result)(rnd() >> (bits - rest)) << shift;
251      }
252     
253    };
254
255    template <typename Result, typename Word, int rest, int shift>
256    struct IntConversion<Result, Word, rest, shift, false> {
257      static const int bits = std::numeric_limits<Word>::digits;
258
259      static Result convert(RandomCore<Word>& rnd) {
260        return ((Result)rnd() << shift) |
261          IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
262      }
263    };
264
265
266    template <typename Result, typename Word,
267              bool one_word = std::numeric_limits<Word>::digits <
268                              std::numeric_limits<Result>::digits>
269    struct Mapping {
270      static Result map(RandomCore<Word>& rnd, const Result& bound) {
271        Word max = (Word)(bound - 1);
272        Result mask = Masker<Result>::mask(bound - 1);
273        Result num;
274        do {
275          num = IntConversion<Result, Word>::convert(rnd) & mask;
276        } while (num > max);
277        return num;
278      }
279    };
280
281    template <typename Result, typename Word>
282    struct Mapping<Result, Word, false> {
283      static Result map(RandomCore<Word>& rnd, const Result& bound) {
284        Word max = (Word)(bound - 1);
285        Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
286          ::mask(max);
287        Word num;
288        do {
289          num = rnd() & mask;
290        } while (num > max);
291        return num;
292      }
293    };
294
295    template <typename Result, int exp, bool pos = (exp >= 0)>
296    struct ShiftMultiplier {
297      static const Result multiplier() {
298        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
299        res *= res;
300        if ((exp & 1) == 1) res *= (Result)2.0;
301        return res;
302      }
303    };
304
305    template <typename Result, int exp>
306    struct ShiftMultiplier<Result, exp, false> {
307      static const Result multiplier() {
308        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
309        res *= res;
310        if ((exp & 1) == 1) res *= (Result)0.5;
311        return res;
312      }
313    };
314
315    template <typename Result>
316    struct ShiftMultiplier<Result, 0, true> {
317      static const Result multiplier() {
318        return (Result)1.0;
319      }
320    };
321
322    template <typename Result>
323    struct ShiftMultiplier<Result, -20, true> {
324      static const Result multiplier() {
325        return (Result)(1.0/1048576.0);
326      }
327    };
328   
329    template <typename Result>
330    struct ShiftMultiplier<Result, -32, true> {
331      static const Result multiplier() {
332        return (Result)(1.0/424967296.0);
333      }
334    };
335
336    template <typename Result>
337    struct ShiftMultiplier<Result, -53, true> {
338      static const Result multiplier() {
339        return (Result)(1.0/9007199254740992.0);
340      }
341    };
342
343    template <typename Result>
344    struct ShiftMultiplier<Result, -64, true> {
345      static const Result multiplier() {
346        return (Result)(1.0/18446744073709551616.0);
347      }
348    };
349
350    template <typename Result, int exp>
351    struct Shifting {
352      static Result shift(const Result& result) {
353        return result * ShiftMultiplier<Result, exp>::multiplier();
354      }
355    };
356
357    template <typename Result, typename Word,
358              int rest = std::numeric_limits<Result>::digits, int shift = 0,
359              bool last = rest <= std::numeric_limits<Word>::digits>
360    struct RealConversion{
361      static const int bits = std::numeric_limits<Word>::digits;
362
363      static Result convert(RandomCore<Word>& rnd) {
364        return Shifting<Result, - shift - rest>::
365          shift((Result)(rnd() >> (bits - rest)));
366      }
367    };
368
369    template <typename Result, typename Word, int rest, int shift>
370    struct RealConversion<Result, Word, rest, shift, false> {
371      static const int bits = std::numeric_limits<Word>::digits;
372
373      static Result convert(RandomCore<Word>& rnd) {
374        return Shifting<Result, - shift - bits>::shift((Result)rnd()) +
375          RealConversion<Result, Word, rest-bits, shift + bits>::convert(rnd);
376      }
377    };
378
379    template <typename Result, typename Word>
380    struct Initializer {
381
382      template <typename Iterator>
383      static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
384        std::vector<Word> ws;
385        for (Iterator it = begin; it != end; ++it) {
386          ws.push_back((Word)*it);
387        }
388        rnd.initState(ws.begin(), ws.end());
389      }
390
391      static void init(RandomCore<Word>& rnd, Result seed) {
392        rnd.initState(seed);
393      }
394    };
395
396    template <typename Word>
397    struct BoolConversion {
398      static bool convert(RandomCore<Word>& rnd) {
399        return (rnd() & 1) == 1;
400      }
401    };
402
403  }
404
405  /// \ingroup misc
406  ///
407  /// \brief Mersenne Twister random number generator
408  ///
409  /// The Mersenne Twister is a twisted generalized feedback
410  /// shift-register generator of Matsumoto and Nishimura. The period
411  /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
412  /// equi-distributed in 623 dimensions for 32-bit numbers. The time
413  /// performance of this generator is comparable to the commonly used
414  /// generators.
415  ///
416  /// This implementation is specialized for both 32-bit and 64-bit
417  /// architectures. The generators differ sligthly in the
418  /// initialization and generation phase so they produce two
419  /// completly different sequences.
420  ///
421  /// The generator gives back random numbers of serveral types. To
422  /// get a random number from a range of a floating point type you
423  /// can use one form of the \c operator() or the \c real() member
424  /// function. If you want to get random number from the {0, 1, ...,
425  /// n-1} integer range use the \c operator[] or the \c integer()
426  /// method. And to get random number from the whole range of an
427  /// integer type you can use the argumentless \c integer() or \c
428  /// uinteger() functions. After all you can get random bool with
429  /// equal chance of true and false or given probability of true
430  /// result with the \c boolean() member functions.
431  ///
432  ///\code
433  /// // The commented code is identical to the other
434  /// double a = rnd();                     // [0.0, 1.0)
435  /// // double a = rnd.real();             // [0.0, 1.0)
436  /// double b = rnd(100.0);                // [0.0, 100.0)
437  /// // double b = rnd.real(100.0);        // [0.0, 100.0)
438  /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
439  /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
440  /// int d = rnd[100000];                  // 0..99999
441  /// // int d = rnd.integer(100000);       // 0..99999
442  /// int e = rnd[6] + 1;                   // 1..6
443  /// // int e = rnd.integer(1, 1 + 6);     // 1..6
444  /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
445  /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
446  /// bool g = rnd.boolean();               // P(g = true) = 0.5
447  /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
448  ///\endcode
449  ///
450  /// The lemon provides a global instance of the random number
451  /// generator which name is \ref lemon::rnd "rnd". Usually it is a
452  /// good programming convenience to use this global generator to get
453  /// random numbers.
454  ///
455  /// \author Balazs Dezso
456  class Random {
457  private:
458
459    // architecture word
460    typedef unsigned long Word;
461   
462    _random_bits::RandomCore<Word> core;
463
464  public:
465
466    /// \brief Constructor
467    ///
468    /// Constructor with constant seeding.
469    Random() { core.initState(); }
470
471    /// \brief Constructor
472    ///
473    /// Constructor with seed. The current number type will be converted
474    /// to the architecture word type.
475    template <typename Number>
476    Random(Number seed) {
477      _random_bits::Initializer<Number, Word>::init(core, seed);
478    }
479
480    /// \brief Constructor
481    ///
482    /// Constructor with array seeding. The given range should contain
483    /// any number type and the numbers will be converted to the
484    /// architecture word type.
485    template <typename Iterator>
486    Random(Iterator begin, Iterator end) {
487      typedef typename std::iterator_traits<Iterator>::value_type Number;
488      _random_bits::Initializer<Number, Word>::init(core, begin, end);
489    }
490
491    /// \brief Copy constructor
492    ///
493    /// Copy constructor. The generated sequence will be identical to
494    /// the other sequence. It can be used to save the current state
495    /// of the generator and later use it to generate the same
496    /// sequence.
497    Random(const Random& other) {
498      core.copyState(other.core);
499    }
500
501    /// \brief Assign operator
502    ///
503    /// Assign operator. The generated sequence will be identical to
504    /// the other sequence. It can be used to save the current state
505    /// of the generator and later use it to generate the same
506    /// sequence.
507    Random& operator=(const Random& other) {
508      if (&other != this) {
509        core.copyState(other.core);
510      }
511      return *this;
512    }
513
514    /// \brief Returns a random real number from the range [0, 1)
515    ///
516    /// It returns a random real number from the range [0, 1). The
517    /// default Number type is double.
518    template <typename Number>
519    Number real() {
520      return _random_bits::RealConversion<Number, Word>::convert(core);
521    }
522
523    double real() {
524      return real<double>();
525    }
526
527    /// \brief Returns a random real number the range [0, b)
528    ///
529    /// It returns a random real number from the range [0, b).
530    template <typename Number>
531    Number real(Number b) {
532      return real<Number>() * b;
533    }
534
535    /// \brief Returns a random real number from the range [a, b)
536    ///
537    /// It returns a random real number from the range [a, b).
538    template <typename Number>
539    Number real(Number a, Number b) {
540      return real<Number>() * (b - a) + a;
541    }
542
543    /// \brief Returns a random real number from the range [0, 1)
544    ///
545    /// It returns a random double from the range [0, 1).
546    double operator()() {
547      return real<double>();
548    }
549
550    /// \brief Returns a random real number from the range [0, b)
551    ///
552    /// It returns a random real number from the range [0, b).
553    template <typename Number>
554    Number operator()(Number b) {
555      return real<Number>() * b;
556    }
557
558    /// \brief Returns a random real number from the range [a, b)
559    ///
560    /// It returns a random real number from the range [a, b).
561    template <typename Number>
562    Number operator()(Number a, Number b) {
563      return real<Number>() * (b - a) + a;
564    }
565
566    /// \brief Returns a random integer from a range
567    ///
568    /// It returns a random integer from the range {0, 1, ..., b - 1}.
569    template <typename Number>
570    Number integer(Number b) {
571      return _random_bits::Mapping<Number, Word>::map(core, b);
572    }
573
574    /// \brief Returns a random integer from a range
575    ///
576    /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
577    template <typename Number>
578    Number integer(Number a, Number b) {
579      return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
580    }
581
582    /// \brief Returns a random integer from a range
583    ///
584    /// It returns a random integer from the range {0, 1, ..., b - 1}.
585    template <typename Number>
586    Number operator[](Number b) {
587      return _random_bits::Mapping<Number, Word>::map(core, b);
588    }
589
590    /// \brief Returns a random non-negative integer
591    ///
592    /// It returns a random non-negative integer uniformly from the
593    /// whole range of the current \c Number type.  The default result
594    /// type of this function is unsigned int.
595    template <typename Number>
596    Number uinteger() {
597      return _random_bits::IntConversion<Number, Word>::convert(core);
598    }
599
600    unsigned int uinteger() {
601      return uinteger<unsigned int>();
602    }
603
604    /// \brief Returns a random integer
605    ///
606    /// It returns a random integer uniformly from the whole range of
607    /// the current \c Number type. The default result type of this
608    /// function is int.
609    template <typename Number>
610    Number integer() {
611      static const int nb = std::numeric_limits<Number>::digits +
612        (std::numeric_limits<Number>::is_signed ? 1 : 0);
613      return _random_bits::IntConversion<Number, Word, nb>::convert(core);
614    }
615
616    int integer() {
617      return integer<int>();
618    }
619   
620    /// \brief Returns a random bool
621    ///
622    /// It returns a random bool
623    bool boolean() {
624      return _random_bits::BoolConversion<Word>::convert(core);
625    }
626
627    ///\name Nonuniform distributions
628    ///
629   
630    ///@{
631   
632    /// \brief Returns a random bool
633    ///
634    /// It returns a random bool with given probability of true result
635    bool boolean(double p) {
636      return operator()() < p;
637    }
638
639    /// Standard Gauss distribution
640
641    /// Standard Gauss distribution.
642    /// \note The Cartesian form of the Box-Muller
643    /// transformation is used to generate a random normal distribution.
644    /// \todo Consider using the "ziggurat" method instead.
645    double gauss()
646    {
647      double V1,V2,S;
648      do {
649        V1=2*real<double>()-1;
650        V2=2*real<double>()-1;
651        S=V1*V1+V2*V2;
652      } while(S>=1);
653      return std::sqrt(-2*std::log(S)/S)*V1;
654    }
655    /// Gauss distribution with given standard deviation and mean 0
656
657    /// \sa gauss()
658    ///
659    double gauss(double std_dev)
660    {
661      return gauss()*std_dev;
662    }
663    /// Gauss distribution with given mean and standard deviation
664
665    /// \sa gauss()
666    ///
667    double gauss(double mean,double std_dev)
668    {
669      return gauss()*std_dev+mean;
670    }
671
672    /// Exponential distribution with given mean
673
674    /// This function generates an exponential distribution random number
675    /// with mean <tt>1/lambda</tt>.
676    ///
677    double exponential(double lambda=1.0)
678    {
679      return -log(real<double>())/lambda;
680    }
681
682    ///@}
683   
684  };
685
686
687  extern Random rnd;
688
689}
690
691#endif
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