COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/random.h @ 2254:50cb2b90daa9

Last change on this file since 2254:50cb2b90daa9 was 2245:f09b1ea5c249, checked in by Balazs Dezso, 13 years ago

Little modification on interface and documentation

File size: 19.1 KB
Line 
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#include <cmath>
29
30///\ingroup misc
31///\file
32///\brief Mersenne Twister random number generator
33///
34///\author Balazs Dezso
35
36namespace lemon {
37
38  namespace _random_bits {
39   
40    template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
41    struct RandomTraits {};
42
43    template <typename _Word>
44    struct RandomTraits<_Word, 32> {
45
46      typedef _Word Word;
47      static const int bits = 32;
48
49      static const int length = 624;
50      static const int shift = 397;
51     
52      static const Word mul = 0x6c078965u;
53      static const Word arrayInit = 0x012BD6AAu;
54      static const Word arrayMul1 = 0x0019660Du;
55      static const Word arrayMul2 = 0x5D588B65u;
56
57      static const Word mask = 0x9908B0DFu;
58      static const Word loMask = (1u << 31) - 1;
59      static const Word hiMask = ~loMask;
60
61
62      static Word tempering(Word rnd) {
63        rnd ^= (rnd >> 11);
64        rnd ^= (rnd << 7) & 0x9D2C5680u;
65        rnd ^= (rnd << 15) & 0xEFC60000u;
66        rnd ^= (rnd >> 18);
67        return rnd;
68      }
69
70    };
71
72    template <typename _Word>
73    struct RandomTraits<_Word, 64> {
74
75      typedef _Word Word;
76      static const int bits = 64;
77
78      static const int length = 312;
79      static const int shift = 156;
80
81      static const Word mul = (Word)0x5851F42Du << 32 | (Word)0x4C957F2Du;
82      static const Word arrayInit = (Word)0x00000000u << 32 |(Word)0x012BD6AAu;
83      static const Word arrayMul1 = (Word)0x369DEA0Fu << 32 |(Word)0x31A53F85u;
84      static const Word arrayMul2 = (Word)0x27BB2EE6u << 32 |(Word)0x87B0B0FDu;
85
86      static const Word mask = (Word)0xB5026F5Au << 32 | (Word)0xA96619E9u;
87      static const Word loMask = ((Word)1u << 31) - 1;
88      static const Word hiMask = ~loMask;
89
90      static Word tempering(Word rnd) {
91        rnd ^= (rnd >> 29) & ((Word)0x55555555u << 32 | (Word)0x55555555u);
92        rnd ^= (rnd << 17) & ((Word)0x71D67FFFu << 32 | (Word)0xEDA60000u);
93        rnd ^= (rnd << 37) & ((Word)0xFFF7EEE0u << 32 | (Word)0x00000000u);
94        rnd ^= (rnd >> 43);
95        return rnd;
96      }
97
98    };
99
100    template <typename _Word>
101    class RandomCore {
102    public:
103
104      typedef _Word Word;
105
106    private:
107
108      static const int bits = RandomTraits<Word>::bits;
109
110      static const int length = RandomTraits<Word>::length;
111      static const int shift = RandomTraits<Word>::shift;
112
113    public:
114
115      void initState() {
116        static const Word seedArray[4] = {
117          0x12345u, 0x23456u, 0x34567u, 0x45678u
118        };
119   
120        initState(seedArray, seedArray + 4);
121      }
122
123      void initState(Word seed) {
124
125        static const Word mul = RandomTraits<Word>::mul;
126
127        current = state;
128
129        Word *curr = state + length - 1;
130        curr[0] = seed; --curr;
131        for (int i = 1; i < length; ++i) {
132          curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
133          --curr;
134        }
135      }
136
137      template <typename Iterator>
138      void initState(Iterator begin, Iterator end) {
139
140        static const Word init = RandomTraits<Word>::arrayInit;
141        static const Word mul1 = RandomTraits<Word>::arrayMul1;
142        static const Word mul2 = RandomTraits<Word>::arrayMul2;
143
144
145        Word *curr = state + length - 1; --curr;
146        Iterator it = begin; int cnt = 0;
147        int num;
148
149        initState(init);
150
151        num = length > end - begin ? length : end - begin;
152        while (num--) {
153          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
154            + *it + cnt;
155          ++it; ++cnt;
156          if (it == end) {
157            it = begin; cnt = 0;
158          }
159          if (curr == state) {
160            curr = state + length - 1; curr[0] = state[0];
161          }
162          --curr;
163        }
164
165        num = length - 1; cnt = length - (curr - state) - 1;
166        while (num--) {
167          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
168            - cnt;
169          --curr; ++cnt;
170          if (curr == state) {
171            curr = state + length - 1; curr[0] = state[0]; --curr;
172            cnt = 1;
173          }
174        }
175       
176        state[length - 1] = (Word)1 << (bits - 1);
177      }
178     
179      void copyState(const RandomCore& other) {
180        std::copy(other.state, other.state + length, state);
181        current = state + (other.current - other.state);
182      }
183
184      Word operator()() {
185        if (current == state) fillState();
186        --current;
187        Word rnd = *current;
188        return RandomTraits<Word>::tempering(rnd);
189      }
190
191    private:
192
193 
194      void fillState() {
195        static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
196        static const Word loMask = RandomTraits<Word>::loMask;
197        static const Word hiMask = RandomTraits<Word>::hiMask;
198
199        current = state + length;
200
201        register Word *curr = state + length - 1;
202        register long num;
203     
204        num = length - shift;
205        while (num--) {
206          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
207            curr[- shift] ^ mask[curr[-1] & 1ul];
208          --curr;
209        }
210        num = shift - 1;
211        while (num--) {
212          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
213            curr[length - shift] ^ mask[curr[-1] & 1ul];
214          --curr;
215        }
216        curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
217          curr[length - shift] ^ mask[curr[length - 1] & 1ul];
218
219      }
220
221 
222      Word *current;
223      Word state[length];
224     
225    };
226
227
228    template <typename Result,
229              int shift = (std::numeric_limits<Result>::digits + 1) / 2>
230    struct Masker {
231      static Result mask(const Result& result) {
232        return Masker<Result, (shift + 1) / 2>::
233          mask((Result)(result | (result >> shift)));
234      }
235    };
236   
237    template <typename Result>
238    struct Masker<Result, 1> {
239      static Result mask(const Result& result) {
240        return (Result)(result | (result >> 1));
241      }
242    };
243
244    template <typename Result, typename Word,
245              int rest = std::numeric_limits<Result>::digits, int shift = 0,
246              bool last = rest <= std::numeric_limits<Word>::digits>
247    struct IntConversion {
248      static const int bits = std::numeric_limits<Word>::digits;
249   
250      static Result convert(RandomCore<Word>& rnd) {
251        return (Result)(rnd() >> (bits - rest)) << shift;
252      }
253     
254    };
255
256    template <typename Result, typename Word, int rest, int shift>
257    struct IntConversion<Result, Word, rest, shift, false> {
258      static const int bits = std::numeric_limits<Word>::digits;
259
260      static Result convert(RandomCore<Word>& rnd) {
261        return ((Result)rnd() << shift) |
262          IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
263      }
264    };
265
266
267    template <typename Result, typename Word,
268              bool one_word = std::numeric_limits<Word>::digits <
269                              std::numeric_limits<Result>::digits>
270    struct Mapping {
271      static Result map(RandomCore<Word>& rnd, const Result& bound) {
272        Word max = (Word)(bound - 1);
273        Result mask = Masker<Result>::mask(bound - 1);
274        Result num;
275        do {
276          num = IntConversion<Result, Word>::convert(rnd) & mask;
277        } while (num > max);
278        return num;
279      }
280    };
281
282    template <typename Result, typename Word>
283    struct Mapping<Result, Word, false> {
284      static Result map(RandomCore<Word>& rnd, const Result& bound) {
285        Word max = (Word)(bound - 1);
286        Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
287          ::mask(max);
288        Word num;
289        do {
290          num = rnd() & mask;
291        } while (num > max);
292        return num;
293      }
294    };
295
296    template <typename Result, int exp, bool pos = (exp >= 0)>
297    struct ShiftMultiplier {
298      static const Result multiplier() {
299        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
300        res *= res;
301        if ((exp & 1) == 1) res *= (Result)2.0;
302        return res;
303      }
304    };
305
306    template <typename Result, int exp>
307    struct ShiftMultiplier<Result, exp, false> {
308      static const Result multiplier() {
309        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
310        res *= res;
311        if ((exp & 1) == 1) res *= (Result)0.5;
312        return res;
313      }
314    };
315
316    template <typename Result>
317    struct ShiftMultiplier<Result, 0, true> {
318      static const Result multiplier() {
319        return (Result)1.0;
320      }
321    };
322
323    template <typename Result>
324    struct ShiftMultiplier<Result, -20, true> {
325      static const Result multiplier() {
326        return (Result)(1.0/1048576.0);
327      }
328    };
329   
330    template <typename Result>
331    struct ShiftMultiplier<Result, -32, true> {
332      static const Result multiplier() {
333        return (Result)(1.0/424967296.0);
334      }
335    };
336
337    template <typename Result>
338    struct ShiftMultiplier<Result, -53, true> {
339      static const Result multiplier() {
340        return (Result)(1.0/9007199254740992.0);
341      }
342    };
343
344    template <typename Result>
345    struct ShiftMultiplier<Result, -64, true> {
346      static const Result multiplier() {
347        return (Result)(1.0/18446744073709551616.0);
348      }
349    };
350
351    template <typename Result, int exp>
352    struct Shifting {
353      static Result shift(const Result& result) {
354        return result * ShiftMultiplier<Result, exp>::multiplier();
355      }
356    };
357
358    template <typename Result, typename Word,
359              int rest = std::numeric_limits<Result>::digits, int shift = 0,
360              bool last = rest <= std::numeric_limits<Word>::digits>
361    struct RealConversion{
362      static const int bits = std::numeric_limits<Word>::digits;
363
364      static Result convert(RandomCore<Word>& rnd) {
365        return Shifting<Result, - shift - rest>::
366          shift((Result)(rnd() >> (bits - rest)));
367      }
368    };
369
370    template <typename Result, typename Word, int rest, int shift>
371    struct RealConversion<Result, Word, rest, shift, false> {
372      static const int bits = std::numeric_limits<Word>::digits;
373
374      static Result convert(RandomCore<Word>& rnd) {
375        return Shifting<Result, - shift - bits>::shift((Result)rnd()) +
376          RealConversion<Result, Word, rest-bits, shift + bits>::convert(rnd);
377      }
378    };
379
380    template <typename Result, typename Word>
381    struct Initializer {
382
383      template <typename Iterator>
384      static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
385        std::vector<Word> ws;
386        for (Iterator it = begin; it != end; ++it) {
387          ws.push_back((Word)*it);
388        }
389        rnd.initState(ws.begin(), ws.end());
390      }
391
392      template <typename Iterator>
393      static void init(RandomCore<Word>& rnd, Result seed) {
394        rnd.initState(seed);
395      }
396    };
397
398    template <typename Word>
399    struct BoolConversion {
400      static bool convert(RandomCore<Word>& rnd) {
401        return (rnd() & 1) == 1;
402      }
403    };
404
405  }
406
407  /// \ingroup misc
408  ///
409  /// \brief Mersenne Twister random number generator
410  ///
411  /// The Mersenne Twister is a twisted generalized feedback
412  /// shift-register generator of Matsumoto and Nishimura. The period
413  /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
414  /// equi-distributed in 623 dimensions for 32-bit numbers. The time
415  /// performance of this generator is comparable to the commonly used
416  /// generators.
417  ///
418  /// This implementation is specialized for both 32-bit and 64-bit
419  /// architectures. The generators differ sligthly in the
420  /// initialization and generation phase so they produce two
421  /// completly different sequences.
422  ///
423  /// The generator gives back random numbers of serveral types. To
424  /// get a random number from a range of a floating point type you
425  /// can use one form of the \c operator() or the \c real() member
426  /// function. If you want to get random number from the {0, 1, ...,
427  /// n-1} integer range use the \c operator[] or the \c integer()
428  /// method. And to get random number from the whole range of an
429  /// integer type you can use the argumentless \c integer() or \c
430  /// uinteger() functions. After all you can get random bool with
431  /// equal chance of true and false or given probability of true
432  /// result with the \c boolean() member functions.
433  ///
434  ///\code
435  /// // The commented code is identical to the other
436  /// double a = rnd();                     // [0.0, 1.0)
437  /// // double a = rnd.real();             // [0.0, 1.0)
438  /// double b = rnd(100.0);                // [0.0, 100.0)
439  /// // double b = rnd.real(100.0);        // [0.0, 100.0)
440  /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
441  /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
442  /// int d = rnd[100000];                  // 0..99999
443  /// // int d = rnd.integer(100000);       // 0..99999
444  /// int e = rnd[6] + 1;                   // 1..6
445  /// // int e = rnd.integer(1, 1 + 6);     // 1..6
446  /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
447  /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
448  /// bool g = rnd.boolean();               // P(g = true) = 0.5
449  /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
450  ///\endcode
451  ///
452  /// The lemon provides a global instance of the random number
453  /// generator which name is \ref lemon::rnd "rnd". Usually it is a
454  /// good programming convenience to use this global generator to get
455  /// random numbers.
456  ///
457  /// \author Balazs Dezso
458  class Random {
459  private:
460
461    // architecture word
462    typedef unsigned long Word;
463   
464    _random_bits::RandomCore<Word> core;
465
466  public:
467
468    /// \brief Constructor
469    ///
470    /// Constructor with constant seeding.
471    Random() { core.initState(); }
472
473    /// \brief Constructor
474    ///
475    /// Constructor with seed. The current number type will be converted
476    /// to the architecture word type.
477    template <typename Number>
478    Random(Number seed) {
479      _random_bits::Initializer<Number, Word>::init(core, seed);
480    }
481
482    /// \brief Constructor
483    ///
484    /// Constructor with array seeding. The given range should contain
485    /// any number type and the numbers will be converted to the
486    /// architecture word type.
487    template <typename Iterator>
488    Random(Iterator begin, Iterator end) {
489      typedef typename std::iterator_traits<Iterator>::value_type Number;
490      _random_bits::Initializer<Number, Word>::init(core, begin, end);
491    }
492
493    /// \brief Copy constructor
494    ///
495    /// Copy constructor. The generated sequence will be identical to
496    /// the other sequence. It can be used to save the current state
497    /// of the generator and later use it to generate the same
498    /// sequence.
499    Random(const Random& other) {
500      core.copyState(other.core);
501    }
502
503    /// \brief Assign operator
504    ///
505    /// Assign operator. The generated sequence will be identical to
506    /// the other sequence. It can be used to save the current state
507    /// of the generator and later use it to generate the same
508    /// sequence.
509    Random& operator=(const Random& other) {
510      if (&other != this) {
511        core.copyState(other.core);
512      }
513      return *this;
514    }
515
516    /// \brief Returns a random real number
517    ///
518    /// It returns a random real number from the range [0, 1). The
519    /// default Number type is double.
520    template <typename Number>
521    Number real() {
522      return _random_bits::RealConversion<Number, Word>::convert(core);
523    }
524
525    double real() {
526      return real<double>();
527    }
528
529    /// \brief Returns a random real number
530    ///
531    /// It returns a random real number from the range [0, b).
532    template <typename Number>
533    Number real(Number b) {
534      return real<Number>() * b;
535    }
536
537    /// \brief Returns a random real number
538    ///
539    /// It returns a random real number from the range [a, b).
540    template <typename Number>
541    Number real(Number a, Number b) {
542      return real<Number>() * (b - a) + a;
543    }
544
545    /// \brief Returns a random real number
546    ///
547    /// It returns a random double from the range [0, 1).
548    double operator()() {
549      return real<double>();
550    }
551
552    /// \brief Returns a random real number
553    ///
554    /// It returns a random real number from the range [0, b).
555    template <typename Number>
556    Number operator()(Number b) {
557      return real<Number>() * b;
558    }
559
560    /// \brief Returns a random real number
561    ///
562    /// It returns a random real number from the range [a, b).
563    template <typename Number>
564    Number operator()(Number a, Number b) {
565      return real<Number>() * (b - a) + a;
566    }
567
568    /// \brief Returns a random integer from a range
569    ///
570    /// It returns a random integer from the range {0, 1, ..., b - 1}.
571    template <typename Number>
572    Number integer(Number b) {
573      return _random_bits::Mapping<Number, Word>::map(core, b);
574    }
575
576    /// \brief Returns a random integer from a range
577    ///
578    /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
579    template <typename Number>
580    Number integer(Number a, Number b) {
581      return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
582    }
583
584    /// \brief Returns a random integer from a range
585    ///
586    /// It returns a random integer from the range {0, 1, ..., b - 1}.
587    template <typename Number>
588    Number operator[](Number b) {
589      return _random_bits::Mapping<Number, Word>::map(core, b);
590    }
591
592    /// \brief Returns a random non-negative integer
593    ///
594    /// It returns a random non-negative integer uniformly from the
595    /// whole range of the current \c Number type.  The default result
596    /// type of this function is unsigned int.
597    template <typename Number>
598    Number uinteger() {
599      return _random_bits::IntConversion<Number, Word>::convert(core);
600    }
601
602    unsigned int uinteger() {
603      return uinteger<unsigned int>();
604    }
605
606    /// \brief Returns a random integer
607    ///
608    /// It returns a random integer uniformly from the whole range of
609    /// the current \c Number type. The default result type of this
610    /// function is int.
611    template <typename Number>
612    Number integer() {
613      static const int nb = std::numeric_limits<Number>::digits +
614        (std::numeric_limits<Number>::is_signed ? 1 : 0);
615      return _random_bits::IntConversion<Number, Word, nb>::convert(core);
616    }
617
618    int integer() {
619      return integer<int>();
620    }
621   
622    /// \brief Returns a random bool
623    ///
624    /// It returns a random bool
625    bool boolean() {
626      return _random_bits::BoolConversion<Word>::convert(core);
627    }
628
629    /// \brief Returns a random bool
630    ///
631    /// It returns a random bool with given probability of true result
632    bool boolean(double p) {
633      return operator()() < p;
634    }
635   
636  };
637
638
639  extern Random rnd;
640
641}
642
643#endif
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