Welcome to mirror list, hosted at ThFree Co, Russian Federation.

random.h « lemon « lemon-1.3.1 « 3rd « quadriflow « extern - git.blender.org/blender.git - Unnamed repository; edit this file 'description' to name the repository.
summaryrefslogtreecommitdiff
blob: f9861f3916996ba5e96d30f62e3c398944d2c8b8 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
/* -*- mode: C++; indent-tabs-mode: nil; -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library.
 *
 * Copyright (C) 2003-2009
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
 *
 * Permission to use, modify and distribute this software is granted
 * provided that this copyright notice appears in all copies. For
 * precise terms see the accompanying LICENSE file.
 *
 * This software is provided "AS IS" with no warranty of any kind,
 * express or implied, and with no claim as to its suitability for any
 * purpose.
 *
 */

/*
 * This file contains the reimplemented version of the Mersenne Twister
 * Generator of Matsumoto and Nishimura.
 *
 * See the appropriate copyright notice below.
 *
 * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * 3. The names of its contributors may not be used to endorse or promote
 *    products derived from this software without specific prior written
 *    permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE
 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 * OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 *
 * Any feedback is very welcome.
 * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
 * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
 */

#ifndef LEMON_RANDOM_H
#define LEMON_RANDOM_H

#include <algorithm>
#include <iterator>
#include <vector>
#include <limits>
#include <fstream>

#include <lemon/math.h>
#include <lemon/dim2.h>

#ifndef WIN32
#include <sys/time.h>
#include <ctime>
#include <sys/types.h>
#include <unistd.h>
#else
#include <lemon/bits/windows.h>
#endif

///\ingroup misc
///\file
///\brief Mersenne Twister random number generator

namespace lemon {

  namespace _random_bits {

    template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
    struct RandomTraits {};

    template <typename _Word>
    struct RandomTraits<_Word, 32> {

      typedef _Word Word;
      static const int bits = 32;

      static const int length = 624;
      static const int shift = 397;

      static const Word mul = 0x6c078965u;
      static const Word arrayInit = 0x012BD6AAu;
      static const Word arrayMul1 = 0x0019660Du;
      static const Word arrayMul2 = 0x5D588B65u;

      static const Word mask = 0x9908B0DFu;
      static const Word loMask = (1u << 31) - 1;
      static const Word hiMask = ~loMask;


      static Word tempering(Word rnd) {
        rnd ^= (rnd >> 11);
        rnd ^= (rnd << 7) & 0x9D2C5680u;
        rnd ^= (rnd << 15) & 0xEFC60000u;
        rnd ^= (rnd >> 18);
        return rnd;
      }

    };

    template <typename _Word>
    struct RandomTraits<_Word, 64> {

      typedef _Word Word;
      static const int bits = 64;

      static const int length = 312;
      static const int shift = 156;

      static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
      static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
      static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
      static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);

      static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
      static const Word loMask = (Word(1u) << 31) - 1;
      static const Word hiMask = ~loMask;

      static Word tempering(Word rnd) {
        rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
        rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
        rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
        rnd ^= (rnd >> 43);
        return rnd;
      }

    };

    template <typename _Word>
    class RandomCore {
    public:

      typedef _Word Word;

    private:

      static const int bits = RandomTraits<Word>::bits;

      static const int length = RandomTraits<Word>::length;
      static const int shift = RandomTraits<Word>::shift;

    public:

      void initState() {
        static const Word seedArray[4] = {
          0x12345u, 0x23456u, 0x34567u, 0x45678u
        };

        initState(seedArray, seedArray + 4);
      }

      void initState(Word seed) {

        static const Word mul = RandomTraits<Word>::mul;

        current = state;

        Word *curr = state + length - 1;
        curr[0] = seed; --curr;
        for (int i = 1; i < length; ++i) {
          curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
          --curr;
        }
      }

      template <typename Iterator>
      void initState(Iterator begin, Iterator end) {

        static const Word init = RandomTraits<Word>::arrayInit;
        static const Word mul1 = RandomTraits<Word>::arrayMul1;
        static const Word mul2 = RandomTraits<Word>::arrayMul2;


        Word *curr = state + length - 1; --curr;
        Iterator it = begin; int cnt = 0;
        int num;

        initState(init);

        num = length > end - begin ? length : end - begin;
        while (num--) {
          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
            + *it + cnt;
          ++it; ++cnt;
          if (it == end) {
            it = begin; cnt = 0;
          }
          if (curr == state) {
            curr = state + length - 1; curr[0] = state[0];
          }
          --curr;
        }

        num = length - 1; cnt = length - (curr - state) - 1;
        while (num--) {
          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
            - cnt;
          --curr; ++cnt;
          if (curr == state) {
            curr = state + length - 1; curr[0] = state[0]; --curr;
            cnt = 1;
          }
        }

        state[length - 1] = Word(1) << (bits - 1);
      }

      void copyState(const RandomCore& other) {
        std::copy(other.state, other.state + length, state);
        current = state + (other.current - other.state);
      }

      Word operator()() {
        if (current == state) fillState();
        --current;
        Word rnd = *current;
        return RandomTraits<Word>::tempering(rnd);
      }

    private:


      void fillState() {
        static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
        static const Word loMask = RandomTraits<Word>::loMask;
        static const Word hiMask = RandomTraits<Word>::hiMask;

        current = state + length;

        Word *curr = state + length - 1;
        long num;

        num = length - shift;
        while (num--) {
          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
            curr[- shift] ^ mask[curr[-1] & 1ul];
          --curr;
        }
        num = shift - 1;
        while (num--) {
          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
            curr[length - shift] ^ mask[curr[-1] & 1ul];
          --curr;
        }
        state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
          curr[length - shift] ^ mask[curr[length - 1] & 1ul];

      }


      Word *current;
      Word state[length];

    };


    template <typename Result,
              int shift = (std::numeric_limits<Result>::digits + 1) / 2>
    struct Masker {
      static Result mask(const Result& result) {
        return Masker<Result, (shift + 1) / 2>::
          mask(static_cast<Result>(result | (result >> shift)));
      }
    };

    template <typename Result>
    struct Masker<Result, 1> {
      static Result mask(const Result& result) {
        return static_cast<Result>(result | (result >> 1));
      }
    };

    template <typename Result, typename Word,
              int rest = std::numeric_limits<Result>::digits, int shift = 0,
              bool last = rest <= std::numeric_limits<Word>::digits>
    struct IntConversion {
      static const int bits = std::numeric_limits<Word>::digits;

      static Result convert(RandomCore<Word>& rnd) {
        return static_cast<Result>(rnd() >> (bits - rest)) << shift;
      }

    };

    template <typename Result, typename Word, int rest, int shift>
    struct IntConversion<Result, Word, rest, shift, false> {
      static const int bits = std::numeric_limits<Word>::digits;

      static Result convert(RandomCore<Word>& rnd) {
        return (static_cast<Result>(rnd()) << shift) |
          IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
      }
    };


    template <typename Result, typename Word,
              bool one_word = (std::numeric_limits<Word>::digits <
                               std::numeric_limits<Result>::digits) >
    struct Mapping {
      static Result map(RandomCore<Word>& rnd, const Result& bound) {
        Word max = Word(bound - 1);
        Result mask = Masker<Result>::mask(bound - 1);
        Result num;
        do {
          num = IntConversion<Result, Word>::convert(rnd) & mask;
        } while (num > max);
        return num;
      }
    };

    template <typename Result, typename Word>
    struct Mapping<Result, Word, false> {
      static Result map(RandomCore<Word>& rnd, const Result& bound) {
        Word max = Word(bound - 1);
        Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
          ::mask(max);
        Word num;
        do {
          num = rnd() & mask;
        } while (num > max);
        return num;
      }
    };

    template <typename Result, int exp>
    struct ShiftMultiplier {
      static const Result multiplier() {
        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
        res *= res;
        if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
        return res;
      }
    };

    template <typename Result>
    struct ShiftMultiplier<Result, 0> {
      static const Result multiplier() {
        return static_cast<Result>(1.0);
      }
    };

    template <typename Result>
    struct ShiftMultiplier<Result, 20> {
      static const Result multiplier() {
        return static_cast<Result>(1.0/1048576.0);
      }
    };

    template <typename Result>
    struct ShiftMultiplier<Result, 32> {
      static const Result multiplier() {
        return static_cast<Result>(1.0/4294967296.0);
      }
    };

    template <typename Result>
    struct ShiftMultiplier<Result, 53> {
      static const Result multiplier() {
        return static_cast<Result>(1.0/9007199254740992.0);
      }
    };

    template <typename Result>
    struct ShiftMultiplier<Result, 64> {
      static const Result multiplier() {
        return static_cast<Result>(1.0/18446744073709551616.0);
      }
    };

    template <typename Result, int exp>
    struct Shifting {
      static Result shift(const Result& result) {
        return result * ShiftMultiplier<Result, exp>::multiplier();
      }
    };

    template <typename Result, typename Word,
              int rest = std::numeric_limits<Result>::digits, int shift = 0,
              bool last = rest <= std::numeric_limits<Word>::digits>
    struct RealConversion{
      static const int bits = std::numeric_limits<Word>::digits;

      static Result convert(RandomCore<Word>& rnd) {
        return Shifting<Result, shift + rest>::
          shift(static_cast<Result>(rnd() >> (bits - rest)));
      }
    };

    template <typename Result, typename Word, int rest, int shift>
    struct RealConversion<Result, Word, rest, shift, false> {
      static const int bits = std::numeric_limits<Word>::digits;

      static Result convert(RandomCore<Word>& rnd) {
        return Shifting<Result, shift + bits>::
          shift(static_cast<Result>(rnd())) +
          RealConversion<Result, Word, rest-bits, shift + bits>::
          convert(rnd);
      }
    };

    template <typename Result, typename Word>
    struct Initializer {

      template <typename Iterator>
      static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
        std::vector<Word> ws;
        for (Iterator it = begin; it != end; ++it) {
          ws.push_back(Word(*it));
        }
        rnd.initState(ws.begin(), ws.end());
      }

      static void init(RandomCore<Word>& rnd, Result seed) {
        rnd.initState(seed);
      }
    };

    template <typename Word>
    struct BoolConversion {
      static bool convert(RandomCore<Word>& rnd) {
        return (rnd() & 1) == 1;
      }
    };

    template <typename Word>
    struct BoolProducer {
      Word buffer;
      int num;

      BoolProducer() : num(0) {}

      bool convert(RandomCore<Word>& rnd) {
        if (num == 0) {
          buffer = rnd();
          num = RandomTraits<Word>::bits;
        }
        bool r = (buffer & 1);
        buffer >>= 1;
        --num;
        return r;
      }
    };

  }

  /// \ingroup misc
  ///
  /// \brief Mersenne Twister random number generator
  ///
  /// The Mersenne Twister is a twisted generalized feedback
  /// shift-register generator of Matsumoto and Nishimura. The period
  /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
  /// equi-distributed in 623 dimensions for 32-bit numbers. The time
  /// performance of this generator is comparable to the commonly used
  /// generators.
  ///
  /// This implementation is specialized for both 32-bit and 64-bit
  /// architectures. The generators differ sligthly in the
  /// initialization and generation phase so they produce two
  /// completly different sequences.
  ///
  /// The generator gives back random numbers of serveral types. To
  /// get a random number from a range of a floating point type you
  /// can use one form of the \c operator() or the \c real() member
  /// function. If you want to get random number from the {0, 1, ...,
  /// n-1} integer range use the \c operator[] or the \c integer()
  /// method. And to get random number from the whole range of an
  /// integer type you can use the argumentless \c integer() or \c
  /// uinteger() functions. After all you can get random bool with
  /// equal chance of true and false or given probability of true
  /// result with the \c boolean() member functions.
  ///
  ///\code
  /// // The commented code is identical to the other
  /// double a = rnd();                     // [0.0, 1.0)
  /// // double a = rnd.real();             // [0.0, 1.0)
  /// double b = rnd(100.0);                // [0.0, 100.0)
  /// // double b = rnd.real(100.0);        // [0.0, 100.0)
  /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
  /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
  /// int d = rnd[100000];                  // 0..99999
  /// // int d = rnd.integer(100000);       // 0..99999
  /// int e = rnd[6] + 1;                   // 1..6
  /// // int e = rnd.integer(1, 1 + 6);     // 1..6
  /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
  /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
  /// bool g = rnd.boolean();               // P(g = true) = 0.5
  /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
  ///\endcode
  ///
  /// LEMON provides a global instance of the random number
  /// generator which name is \ref lemon::rnd "rnd". Usually it is a
  /// good programming convenience to use this global generator to get
  /// random numbers.
  class Random {
  private:

    // Architecture word
    typedef unsigned long Word;

    _random_bits::RandomCore<Word> core;
    _random_bits::BoolProducer<Word> bool_producer;


  public:

    ///\name Initialization
    ///
    /// @{

    /// \brief Default constructor
    ///
    /// Constructor with constant seeding.
    Random() { core.initState(); }

    /// \brief Constructor with seed
    ///
    /// Constructor with seed. The current number type will be converted
    /// to the architecture word type.
    template <typename Number>
    Random(Number seed) {
      _random_bits::Initializer<Number, Word>::init(core, seed);
    }

    /// \brief Constructor with array seeding
    ///
    /// Constructor with array seeding. The given range should contain
    /// any number type and the numbers will be converted to the
    /// architecture word type.
    template <typename Iterator>
    Random(Iterator begin, Iterator end) {
      typedef typename std::iterator_traits<Iterator>::value_type Number;
      _random_bits::Initializer<Number, Word>::init(core, begin, end);
    }

    /// \brief Copy constructor
    ///
    /// Copy constructor. The generated sequence will be identical to
    /// the other sequence. It can be used to save the current state
    /// of the generator and later use it to generate the same
    /// sequence.
    Random(const Random& other) {
      core.copyState(other.core);
    }

    /// \brief Assign operator
    ///
    /// Assign operator. The generated sequence will be identical to
    /// the other sequence. It can be used to save the current state
    /// of the generator and later use it to generate the same
    /// sequence.
    Random& operator=(const Random& other) {
      if (&other != this) {
        core.copyState(other.core);
      }
      return *this;
    }

    /// \brief Seeding random sequence
    ///
    /// Seeding the random sequence. The current number type will be
    /// converted to the architecture word type.
    template <typename Number>
    void seed(Number seed) {
      _random_bits::Initializer<Number, Word>::init(core, seed);
    }

    /// \brief Seeding random sequence
    ///
    /// Seeding the random sequence. The given range should contain
    /// any number type and the numbers will be converted to the
    /// architecture word type.
    template <typename Iterator>
    void seed(Iterator begin, Iterator end) {
      typedef typename std::iterator_traits<Iterator>::value_type Number;
      _random_bits::Initializer<Number, Word>::init(core, begin, end);
    }

    /// \brief Seeding from file or from process id and time
    ///
    /// By default, this function calls the \c seedFromFile() member
    /// function with the <tt>/dev/urandom</tt> file. If it does not success,
    /// it uses the \c seedFromTime().
    /// \return Currently always \c true.
    bool seed() {
#ifndef WIN32
      if (seedFromFile("/dev/urandom", 0)) return true;
#endif
      if (seedFromTime()) return true;
      return false;
    }

    /// \brief Seeding from file
    ///
    /// Seeding the random sequence from file. The linux kernel has two
    /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
    /// could give good seed values for pseudo random generators (The
    /// difference between two devices is that the <tt>random</tt> may
    /// block the reading operation while the kernel can give good
    /// source of randomness, while the <tt>urandom</tt> does not
    /// block the input, but it could give back bytes with worse
    /// entropy).
    /// \param file The source file
    /// \param offset The offset, from the file read.
    /// \return \c true when the seeding successes.
#ifndef WIN32
    bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)
#else
    bool seedFromFile(const std::string& file = "", int offset = 0)
#endif
    {
      std::ifstream rs(file.c_str());
      const int size = 4;
      Word buf[size];
      if (offset != 0 && !rs.seekg(offset)) return false;
      if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;
      seed(buf, buf + size);
      return true;
    }

    /// \brief Seding from process id and time
    ///
    /// Seding from process id and time. This function uses the
    /// current process id and the current time for initialize the
    /// random sequence.
    /// \return Currently always \c true.
    bool seedFromTime() {
#ifndef WIN32
      timeval tv;
      gettimeofday(&tv, 0);
      seed(getpid() + tv.tv_sec + tv.tv_usec);
#else
      seed(bits::getWinRndSeed());
#endif
      return true;
    }

    /// @}

    ///\name Uniform Distributions
    ///
    /// @{

    /// \brief Returns a random real number from the range [0, 1)
    ///
    /// It returns a random real number from the range [0, 1). The
    /// default Number type is \c double.
    template <typename Number>
    Number real() {
      return _random_bits::RealConversion<Number, Word>::convert(core);
    }

    double real() {
      return real<double>();
    }

    /// \brief Returns a random real number from the range [0, 1)
    ///
    /// It returns a random double from the range [0, 1).
    double operator()() {
      return real<double>();
    }

    /// \brief Returns a random real number from the range [0, b)
    ///
    /// It returns a random real number from the range [0, b).
    double operator()(double b) {
      return real<double>() * b;
    }

    /// \brief Returns a random real number from the range [a, b)
    ///
    /// It returns a random real number from the range [a, b).
    double operator()(double a, double b) {
      return real<double>() * (b - a) + a;
    }

    /// \brief Returns a random integer from a range
    ///
    /// It returns a random integer from the range {0, 1, ..., b - 1}.
    template <typename Number>
    Number integer(Number b) {
      return _random_bits::Mapping<Number, Word>::map(core, b);
    }

    /// \brief Returns a random integer from a range
    ///
    /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
    template <typename Number>
    Number integer(Number a, Number b) {
      return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
    }

    /// \brief Returns a random integer from a range
    ///
    /// It returns a random integer from the range {0, 1, ..., b - 1}.
    template <typename Number>
    Number operator[](Number b) {
      return _random_bits::Mapping<Number, Word>::map(core, b);
    }

    /// \brief Returns a random non-negative integer
    ///
    /// It returns a random non-negative integer uniformly from the
    /// whole range of the current \c Number type. The default result
    /// type of this function is <tt>unsigned int</tt>.
    template <typename Number>
    Number uinteger() {
      return _random_bits::IntConversion<Number, Word>::convert(core);
    }

    unsigned int uinteger() {
      return uinteger<unsigned int>();
    }

    /// \brief Returns a random integer
    ///
    /// It returns a random integer uniformly from the whole range of
    /// the current \c Number type. The default result type of this
    /// function is \c int.
    template <typename Number>
    Number integer() {
      static const int nb = std::numeric_limits<Number>::digits +
        (std::numeric_limits<Number>::is_signed ? 1 : 0);
      return _random_bits::IntConversion<Number, Word, nb>::convert(core);
    }

    int integer() {
      return integer<int>();
    }

    /// \brief Returns a random bool
    ///
    /// It returns a random bool. The generator holds a buffer for
    /// random bits. Every time when it become empty the generator makes
    /// a new random word and fill the buffer up.
    bool boolean() {
      return bool_producer.convert(core);
    }

    /// @}

    ///\name Non-uniform Distributions
    ///
    ///@{

    /// \brief Returns a random bool with given probability of true result.
    ///
    /// It returns a random bool with given probability of true result.
    bool boolean(double p) {
      return operator()() < p;
    }

    /// Standard normal (Gauss) distribution

    /// Standard normal (Gauss) distribution.
    /// \note The Cartesian form of the Box-Muller
    /// transformation is used to generate a random normal distribution.
    double gauss()
    {
      double V1,V2,S;
      do {
        V1=2*real<double>()-1;
        V2=2*real<double>()-1;
        S=V1*V1+V2*V2;
      } while(S>=1);
      return std::sqrt(-2*std::log(S)/S)*V1;
    }
    /// Normal (Gauss) distribution with given mean and standard deviation

    /// Normal (Gauss) distribution with given mean and standard deviation.
    /// \sa gauss()
    double gauss(double mean,double std_dev)
    {
      return gauss()*std_dev+mean;
    }

    /// Lognormal distribution

    /// Lognormal distribution. The parameters are the mean and the standard
    /// deviation of <tt>exp(X)</tt>.
    ///
    double lognormal(double n_mean,double n_std_dev)
    {
      return std::exp(gauss(n_mean,n_std_dev));
    }
    /// Lognormal distribution

    /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of
    /// the mean and the standard deviation of <tt>exp(X)</tt>.
    ///
    double lognormal(const std::pair<double,double> &params)
    {
      return std::exp(gauss(params.first,params.second));
    }
    /// Compute the lognormal parameters from mean and standard deviation

    /// This function computes the lognormal parameters from mean and
    /// standard deviation. The return value can direcly be passed to
    /// lognormal().
    std::pair<double,double> lognormalParamsFromMD(double mean,
                                                   double std_dev)
    {
      double fr=std_dev/mean;
      fr*=fr;
      double lg=std::log(1+fr);
      return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg));
    }
    /// Lognormal distribution with given mean and standard deviation

    /// Lognormal distribution with given mean and standard deviation.
    ///
    double lognormalMD(double mean,double std_dev)
    {
      return lognormal(lognormalParamsFromMD(mean,std_dev));
    }

    /// Exponential distribution with given mean

    /// This function generates an exponential distribution random number
    /// with mean <tt>1/lambda</tt>.
    ///
    double exponential(double lambda=1.0)
    {
      return -std::log(1.0-real<double>())/lambda;
    }

    /// Gamma distribution with given integer shape

    /// This function generates a gamma distribution random number.
    ///
    ///\param k shape parameter (<tt>k>0</tt> integer)
    double gamma(int k)
    {
      double s = 0;
      for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
      return s;
    }

    /// Gamma distribution with given shape and scale parameter

    /// This function generates a gamma distribution random number.
    ///
    ///\param k shape parameter (<tt>k>0</tt>)
    ///\param theta scale parameter
    ///
    double gamma(double k,double theta=1.0)
    {
      double xi,nu;
      const double delta = k-std::floor(k);
      const double v0=E/(E-delta);
      do {
        double V0=1.0-real<double>();
        double V1=1.0-real<double>();
        double V2=1.0-real<double>();
        if(V2<=v0)
          {
            xi=std::pow(V1,1.0/delta);
            nu=V0*std::pow(xi,delta-1.0);
          }
        else
          {
            xi=1.0-std::log(V1);
            nu=V0*std::exp(-xi);
          }
      } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
      return theta*(xi+gamma(int(std::floor(k))));
    }

    /// Weibull distribution

    /// This function generates a Weibull distribution random number.
    ///
    ///\param k shape parameter (<tt>k>0</tt>)
    ///\param lambda scale parameter (<tt>lambda>0</tt>)
    ///
    double weibull(double k,double lambda)
    {
      return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
    }

    /// Pareto distribution

    /// This function generates a Pareto distribution random number.
    ///
    ///\param k shape parameter (<tt>k>0</tt>)
    ///\param x_min location parameter (<tt>x_min>0</tt>)
    ///
    double pareto(double k,double x_min)
    {
      return exponential(gamma(k,1.0/x_min))+x_min;
    }

    /// Poisson distribution

    /// This function generates a Poisson distribution random number with
    /// parameter \c lambda.
    ///
    /// The probability mass function of this distribusion is
    /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
    /// \note The algorithm is taken from the book of Donald E. Knuth titled
    /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
    /// return value.

    int poisson(double lambda)
    {
      const double l = std::exp(-lambda);
      int k=0;
      double p = 1.0;
      do {
        k++;
        p*=real<double>();
      } while (p>=l);
      return k-1;
    }

    ///@}

    ///\name Two Dimensional Distributions
    ///
    ///@{

    /// Uniform distribution on the full unit circle

    /// Uniform distribution on the full unit circle.
    ///
    dim2::Point<double> disc()
    {
      double V1,V2;
      do {
        V1=2*real<double>()-1;
        V2=2*real<double>()-1;

      } while(V1*V1+V2*V2>=1);
      return dim2::Point<double>(V1,V2);
    }
    /// A kind of two dimensional normal (Gauss) distribution

    /// This function provides a turning symmetric two-dimensional distribution.
    /// Both coordinates are of standard normal distribution, but they are not
    /// independent.
    ///
    /// \note The coordinates are the two random variables provided by
    /// the Box-Muller method.
    dim2::Point<double> gauss2()
    {
      double V1,V2,S;
      do {
        V1=2*real<double>()-1;
        V2=2*real<double>()-1;
        S=V1*V1+V2*V2;
      } while(S>=1);
      double W=std::sqrt(-2*std::log(S)/S);
      return dim2::Point<double>(W*V1,W*V2);
    }
    /// A kind of two dimensional exponential distribution

    /// This function provides a turning symmetric two-dimensional distribution.
    /// The x-coordinate is of conditionally exponential distribution
    /// with the condition that x is positive and y=0. If x is negative and
    /// y=0 then, -x is of exponential distribution. The same is true for the
    /// y-coordinate.
    dim2::Point<double> exponential2()
    {
      double V1,V2,S;
      do {
        V1=2*real<double>()-1;
        V2=2*real<double>()-1;
        S=V1*V1+V2*V2;
      } while(S>=1);
      double W=-std::log(S)/S;
      return dim2::Point<double>(W*V1,W*V2);
    }

    ///@}
  };


  extern Random rnd;

}

#endif