lemon/random.h
author Alpar Juttner <alpar@cs.elte.hu>
Sun, 13 Jul 2008 16:46:56 +0100
changeset 208 4317d277ba21
parent 177 b685e12e08c0
child 209 765619b7cbb2
permissions -rw-r--r--
Better source unifier

- now it is called scripts/unify-sources.sh
- replaces each tab with 8 spaces
- remove trailing spaces (and tabs)
- warnings on long lines (i.e. on lines that are more than 80 characters)
- the standard file header now turns off the space-to-tab replacement in Emacs
alpar@10
     1
/* -*- C++ -*-
alpar@10
     2
 *
alpar@10
     3
 * This file is a part of LEMON, a generic C++ optimization library
alpar@10
     4
 *
alpar@39
     5
 * Copyright (C) 2003-2008
alpar@10
     6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@10
     7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@10
     8
 *
alpar@10
     9
 * Permission to use, modify and distribute this software is granted
alpar@10
    10
 * provided that this copyright notice appears in all copies. For
alpar@10
    11
 * precise terms see the accompanying LICENSE file.
alpar@10
    12
 *
alpar@10
    13
 * This software is provided "AS IS" with no warranty of any kind,
alpar@10
    14
 * express or implied, and with no claim as to its suitability for any
alpar@10
    15
 * purpose.
alpar@10
    16
 *
alpar@10
    17
 */
alpar@10
    18
alpar@10
    19
/*
alpar@10
    20
 * This file contains the reimplemented version of the Mersenne Twister
alpar@10
    21
 * Generator of Matsumoto and Nishimura.
alpar@10
    22
 *
alpar@10
    23
 * See the appropriate copyright notice below.
alpar@10
    24
 * 
alpar@10
    25
 * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
alpar@10
    26
 * All rights reserved.                          
alpar@10
    27
 *
alpar@10
    28
 * Redistribution and use in source and binary forms, with or without
alpar@10
    29
 * modification, are permitted provided that the following conditions
alpar@10
    30
 * are met:
alpar@10
    31
 *
alpar@10
    32
 * 1. Redistributions of source code must retain the above copyright
alpar@10
    33
 *    notice, this list of conditions and the following disclaimer.
alpar@10
    34
 *
alpar@10
    35
 * 2. Redistributions in binary form must reproduce the above copyright
alpar@10
    36
 *    notice, this list of conditions and the following disclaimer in the
alpar@10
    37
 *    documentation and/or other materials provided with the distribution.
alpar@10
    38
 *
alpar@10
    39
 * 3. The names of its contributors may not be used to endorse or promote 
alpar@10
    40
 *    products derived from this software without specific prior written 
alpar@10
    41
 *    permission.
alpar@10
    42
 *
alpar@10
    43
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
alpar@10
    44
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
alpar@10
    45
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
alpar@10
    46
 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE
alpar@10
    47
 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
alpar@10
    48
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
alpar@10
    49
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
alpar@10
    50
 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
alpar@10
    51
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
alpar@10
    52
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
alpar@10
    53
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
alpar@10
    54
 * OF THE POSSIBILITY OF SUCH DAMAGE.
alpar@10
    55
 *
alpar@10
    56
 *
alpar@10
    57
 * Any feedback is very welcome.
alpar@10
    58
 * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
alpar@10
    59
 * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
alpar@10
    60
 */
alpar@10
    61
alpar@10
    62
#ifndef LEMON_RANDOM_H
alpar@10
    63
#define LEMON_RANDOM_H
alpar@10
    64
alpar@10
    65
#include <algorithm>
alpar@10
    66
#include <iterator>
alpar@10
    67
#include <vector>
deba@110
    68
#include <limits>
deba@177
    69
#include <fstream>
alpar@10
    70
alpar@68
    71
#include <lemon/math.h>
alpar@10
    72
#include <lemon/dim2.h>
alpar@68
    73
deba@177
    74
#ifndef WIN32
deba@177
    75
#include <sys/time.h>
deba@177
    76
#include <ctime>
deba@177
    77
#include <sys/types.h>
deba@177
    78
#include <unistd.h>
deba@177
    79
#else
deba@177
    80
#include <windows.h>
deba@177
    81
#endif
deba@177
    82
alpar@10
    83
///\ingroup misc
alpar@10
    84
///\file
alpar@10
    85
///\brief Mersenne Twister random number generator
alpar@10
    86
alpar@10
    87
namespace lemon {
alpar@10
    88
alpar@10
    89
  namespace _random_bits {
alpar@10
    90
    
alpar@10
    91
    template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
alpar@10
    92
    struct RandomTraits {};
alpar@10
    93
alpar@10
    94
    template <typename _Word>
alpar@10
    95
    struct RandomTraits<_Word, 32> {
alpar@10
    96
alpar@10
    97
      typedef _Word Word;
alpar@10
    98
      static const int bits = 32;
alpar@10
    99
alpar@10
   100
      static const int length = 624;
alpar@10
   101
      static const int shift = 397;
alpar@10
   102
      
alpar@10
   103
      static const Word mul = 0x6c078965u;
alpar@10
   104
      static const Word arrayInit = 0x012BD6AAu;
alpar@10
   105
      static const Word arrayMul1 = 0x0019660Du;
alpar@10
   106
      static const Word arrayMul2 = 0x5D588B65u;
alpar@10
   107
alpar@10
   108
      static const Word mask = 0x9908B0DFu;
alpar@10
   109
      static const Word loMask = (1u << 31) - 1;
alpar@10
   110
      static const Word hiMask = ~loMask;
alpar@10
   111
alpar@10
   112
alpar@10
   113
      static Word tempering(Word rnd) {
alpar@10
   114
        rnd ^= (rnd >> 11);
alpar@10
   115
        rnd ^= (rnd << 7) & 0x9D2C5680u;
alpar@10
   116
        rnd ^= (rnd << 15) & 0xEFC60000u;
alpar@10
   117
        rnd ^= (rnd >> 18);
alpar@10
   118
        return rnd;
alpar@10
   119
      }
alpar@10
   120
alpar@10
   121
    };
alpar@10
   122
alpar@10
   123
    template <typename _Word>
alpar@10
   124
    struct RandomTraits<_Word, 64> {
alpar@10
   125
alpar@10
   126
      typedef _Word Word;
alpar@10
   127
      static const int bits = 64;
alpar@10
   128
alpar@10
   129
      static const int length = 312;
alpar@10
   130
      static const int shift = 156;
alpar@10
   131
alpar@10
   132
      static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
alpar@10
   133
      static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
alpar@10
   134
      static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
alpar@10
   135
      static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
alpar@10
   136
alpar@10
   137
      static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
alpar@10
   138
      static const Word loMask = (Word(1u) << 31) - 1;
alpar@10
   139
      static const Word hiMask = ~loMask;
alpar@10
   140
alpar@10
   141
      static Word tempering(Word rnd) {
alpar@10
   142
        rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
alpar@10
   143
        rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
alpar@10
   144
        rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
alpar@10
   145
        rnd ^= (rnd >> 43);
alpar@10
   146
        return rnd;
alpar@10
   147
      }
alpar@10
   148
alpar@10
   149
    };
alpar@10
   150
alpar@10
   151
    template <typename _Word>
alpar@10
   152
    class RandomCore {
alpar@10
   153
    public:
alpar@10
   154
alpar@10
   155
      typedef _Word Word;
alpar@10
   156
alpar@10
   157
    private:
alpar@10
   158
alpar@10
   159
      static const int bits = RandomTraits<Word>::bits;
alpar@10
   160
alpar@10
   161
      static const int length = RandomTraits<Word>::length;
alpar@10
   162
      static const int shift = RandomTraits<Word>::shift;
alpar@10
   163
alpar@10
   164
    public:
alpar@10
   165
alpar@10
   166
      void initState() {
alpar@10
   167
        static const Word seedArray[4] = {
alpar@10
   168
          0x12345u, 0x23456u, 0x34567u, 0x45678u
alpar@10
   169
        };
alpar@10
   170
    
alpar@10
   171
        initState(seedArray, seedArray + 4);
alpar@10
   172
      }
alpar@10
   173
alpar@10
   174
      void initState(Word seed) {
alpar@10
   175
alpar@10
   176
        static const Word mul = RandomTraits<Word>::mul;
alpar@10
   177
alpar@10
   178
        current = state; 
alpar@10
   179
alpar@10
   180
        Word *curr = state + length - 1;
alpar@10
   181
        curr[0] = seed; --curr;
alpar@10
   182
        for (int i = 1; i < length; ++i) {
alpar@10
   183
          curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
alpar@10
   184
          --curr;
alpar@10
   185
        }
alpar@10
   186
      }
alpar@10
   187
alpar@10
   188
      template <typename Iterator>
alpar@10
   189
      void initState(Iterator begin, Iterator end) {
alpar@10
   190
alpar@10
   191
        static const Word init = RandomTraits<Word>::arrayInit;
alpar@10
   192
        static const Word mul1 = RandomTraits<Word>::arrayMul1;
alpar@10
   193
        static const Word mul2 = RandomTraits<Word>::arrayMul2;
alpar@10
   194
alpar@10
   195
alpar@10
   196
        Word *curr = state + length - 1; --curr;
alpar@10
   197
        Iterator it = begin; int cnt = 0;
alpar@10
   198
        int num;
alpar@10
   199
alpar@10
   200
        initState(init);
alpar@10
   201
alpar@10
   202
        num = length > end - begin ? length : end - begin;
alpar@10
   203
        while (num--) {
alpar@10
   204
          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) 
alpar@10
   205
            + *it + cnt;
alpar@10
   206
          ++it; ++cnt;
alpar@10
   207
          if (it == end) {
alpar@10
   208
            it = begin; cnt = 0;
alpar@10
   209
          }
alpar@10
   210
          if (curr == state) {
alpar@10
   211
            curr = state + length - 1; curr[0] = state[0];
alpar@10
   212
          }
alpar@10
   213
          --curr;
alpar@10
   214
        }
alpar@10
   215
alpar@10
   216
        num = length - 1; cnt = length - (curr - state) - 1;
alpar@10
   217
        while (num--) {
alpar@10
   218
          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
alpar@10
   219
            - cnt;
alpar@10
   220
          --curr; ++cnt;
alpar@10
   221
          if (curr == state) {
alpar@10
   222
            curr = state + length - 1; curr[0] = state[0]; --curr;
alpar@10
   223
            cnt = 1;
alpar@10
   224
          }
alpar@10
   225
        }
alpar@10
   226
        
alpar@10
   227
        state[length - 1] = Word(1) << (bits - 1);
alpar@10
   228
      }
alpar@10
   229
      
alpar@10
   230
      void copyState(const RandomCore& other) {
alpar@10
   231
        std::copy(other.state, other.state + length, state);
alpar@10
   232
        current = state + (other.current - other.state);
alpar@10
   233
      }
alpar@10
   234
alpar@10
   235
      Word operator()() {
alpar@10
   236
        if (current == state) fillState();
alpar@10
   237
        --current;
alpar@10
   238
        Word rnd = *current;
alpar@10
   239
        return RandomTraits<Word>::tempering(rnd);
alpar@10
   240
      }
alpar@10
   241
alpar@10
   242
    private:
alpar@10
   243
alpar@10
   244
  
alpar@10
   245
      void fillState() {
alpar@10
   246
        static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
alpar@10
   247
        static const Word loMask = RandomTraits<Word>::loMask;
alpar@10
   248
        static const Word hiMask = RandomTraits<Word>::hiMask;
alpar@10
   249
alpar@10
   250
        current = state + length; 
alpar@10
   251
alpar@10
   252
        register Word *curr = state + length - 1;
alpar@10
   253
        register long num;
alpar@10
   254
      
alpar@10
   255
        num = length - shift;
alpar@10
   256
        while (num--) {
alpar@10
   257
          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
alpar@10
   258
            curr[- shift] ^ mask[curr[-1] & 1ul];
alpar@10
   259
          --curr;
alpar@10
   260
        }
alpar@10
   261
        num = shift - 1;
alpar@10
   262
        while (num--) {
alpar@10
   263
          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
alpar@10
   264
            curr[length - shift] ^ mask[curr[-1] & 1ul];
alpar@10
   265
          --curr;
alpar@10
   266
        }
deba@62
   267
        state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
alpar@10
   268
          curr[length - shift] ^ mask[curr[length - 1] & 1ul];
alpar@10
   269
alpar@10
   270
      }
alpar@10
   271
alpar@10
   272
  
alpar@10
   273
      Word *current;
alpar@10
   274
      Word state[length];
alpar@10
   275
      
alpar@10
   276
    };
alpar@10
   277
alpar@10
   278
alpar@10
   279
    template <typename Result, 
alpar@10
   280
              int shift = (std::numeric_limits<Result>::digits + 1) / 2>
alpar@10
   281
    struct Masker {
alpar@10
   282
      static Result mask(const Result& result) {
alpar@10
   283
        return Masker<Result, (shift + 1) / 2>::
alpar@10
   284
          mask(static_cast<Result>(result | (result >> shift)));
alpar@10
   285
      }
alpar@10
   286
    };
alpar@10
   287
    
alpar@10
   288
    template <typename Result>
alpar@10
   289
    struct Masker<Result, 1> {
alpar@10
   290
      static Result mask(const Result& result) {
alpar@10
   291
        return static_cast<Result>(result | (result >> 1));
alpar@10
   292
      }
alpar@10
   293
    };
alpar@10
   294
alpar@10
   295
    template <typename Result, typename Word, 
alpar@10
   296
              int rest = std::numeric_limits<Result>::digits, int shift = 0, 
alpar@10
   297
              bool last = rest <= std::numeric_limits<Word>::digits>
alpar@10
   298
    struct IntConversion {
alpar@10
   299
      static const int bits = std::numeric_limits<Word>::digits;
alpar@10
   300
    
alpar@10
   301
      static Result convert(RandomCore<Word>& rnd) {
alpar@10
   302
        return static_cast<Result>(rnd() >> (bits - rest)) << shift;
alpar@10
   303
      }
alpar@10
   304
      
alpar@10
   305
    }; 
alpar@10
   306
alpar@10
   307
    template <typename Result, typename Word, int rest, int shift> 
alpar@10
   308
    struct IntConversion<Result, Word, rest, shift, false> {
alpar@10
   309
      static const int bits = std::numeric_limits<Word>::digits;
alpar@10
   310
alpar@10
   311
      static Result convert(RandomCore<Word>& rnd) {
alpar@10
   312
        return (static_cast<Result>(rnd()) << shift) | 
alpar@10
   313
          IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
alpar@10
   314
      }
alpar@10
   315
    };
alpar@10
   316
alpar@10
   317
alpar@10
   318
    template <typename Result, typename Word,
alpar@10
   319
              bool one_word = (std::numeric_limits<Word>::digits < 
alpar@10
   320
			       std::numeric_limits<Result>::digits) >
alpar@10
   321
    struct Mapping {
alpar@10
   322
      static Result map(RandomCore<Word>& rnd, const Result& bound) {
alpar@10
   323
        Word max = Word(bound - 1);
alpar@10
   324
        Result mask = Masker<Result>::mask(bound - 1);
alpar@10
   325
        Result num;
alpar@10
   326
        do {
alpar@10
   327
          num = IntConversion<Result, Word>::convert(rnd) & mask; 
alpar@10
   328
        } while (num > max);
alpar@10
   329
        return num;
alpar@10
   330
      }
alpar@10
   331
    };
alpar@10
   332
alpar@10
   333
    template <typename Result, typename Word>
alpar@10
   334
    struct Mapping<Result, Word, false> {
alpar@10
   335
      static Result map(RandomCore<Word>& rnd, const Result& bound) {
alpar@10
   336
        Word max = Word(bound - 1);
alpar@10
   337
        Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
alpar@10
   338
          ::mask(max);
alpar@10
   339
        Word num;
alpar@10
   340
        do {
alpar@10
   341
          num = rnd() & mask;
alpar@10
   342
        } while (num > max);
alpar@10
   343
        return num;
alpar@10
   344
      }
alpar@10
   345
    };
alpar@10
   346
alpar@10
   347
    template <typename Result, int exp, bool pos = (exp >= 0)>
alpar@10
   348
    struct ShiftMultiplier {
alpar@10
   349
      static const Result multiplier() {
alpar@10
   350
        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
alpar@10
   351
        res *= res;
alpar@10
   352
        if ((exp & 1) == 1) res *= static_cast<Result>(2.0);
alpar@10
   353
        return res; 
alpar@10
   354
      }
alpar@10
   355
    };
alpar@10
   356
alpar@10
   357
    template <typename Result, int exp>
alpar@10
   358
    struct ShiftMultiplier<Result, exp, false> {
alpar@10
   359
      static const Result multiplier() {
alpar@10
   360
        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
alpar@10
   361
        res *= res;
alpar@10
   362
        if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
alpar@10
   363
        return res; 
alpar@10
   364
      }
alpar@10
   365
    };
alpar@10
   366
alpar@10
   367
    template <typename Result>
alpar@10
   368
    struct ShiftMultiplier<Result, 0, true> {
alpar@10
   369
      static const Result multiplier() {
alpar@10
   370
        return static_cast<Result>(1.0); 
alpar@10
   371
      }
alpar@10
   372
    };
alpar@10
   373
alpar@10
   374
    template <typename Result>
alpar@10
   375
    struct ShiftMultiplier<Result, -20, true> {
alpar@10
   376
      static const Result multiplier() {
alpar@10
   377
        return static_cast<Result>(1.0/1048576.0); 
alpar@10
   378
      }
alpar@10
   379
    };
alpar@10
   380
    
alpar@10
   381
    template <typename Result>
alpar@10
   382
    struct ShiftMultiplier<Result, -32, true> {
alpar@10
   383
      static const Result multiplier() {
alpar@10
   384
        return static_cast<Result>(1.0/424967296.0); 
alpar@10
   385
      }
alpar@10
   386
    };
alpar@10
   387
alpar@10
   388
    template <typename Result>
alpar@10
   389
    struct ShiftMultiplier<Result, -53, true> {
alpar@10
   390
      static const Result multiplier() {
alpar@10
   391
        return static_cast<Result>(1.0/9007199254740992.0); 
alpar@10
   392
      }
alpar@10
   393
    };
alpar@10
   394
alpar@10
   395
    template <typename Result>
alpar@10
   396
    struct ShiftMultiplier<Result, -64, true> {
alpar@10
   397
      static const Result multiplier() {
alpar@10
   398
        return static_cast<Result>(1.0/18446744073709551616.0); 
alpar@10
   399
      }
alpar@10
   400
    };
alpar@10
   401
alpar@10
   402
    template <typename Result, int exp>
alpar@10
   403
    struct Shifting {
alpar@10
   404
      static Result shift(const Result& result) {
alpar@10
   405
        return result * ShiftMultiplier<Result, exp>::multiplier();
alpar@10
   406
      }
alpar@10
   407
    };
alpar@10
   408
alpar@10
   409
    template <typename Result, typename Word,
alpar@10
   410
              int rest = std::numeric_limits<Result>::digits, int shift = 0, 
alpar@10
   411
              bool last = rest <= std::numeric_limits<Word>::digits>
alpar@10
   412
    struct RealConversion{ 
alpar@10
   413
      static const int bits = std::numeric_limits<Word>::digits;
alpar@10
   414
alpar@10
   415
      static Result convert(RandomCore<Word>& rnd) {
alpar@10
   416
        return Shifting<Result, - shift - rest>::
alpar@10
   417
          shift(static_cast<Result>(rnd() >> (bits - rest)));
alpar@10
   418
      }
alpar@10
   419
    };
alpar@10
   420
alpar@10
   421
    template <typename Result, typename Word, int rest, int shift>
alpar@10
   422
    struct RealConversion<Result, Word, rest, shift, false> { 
alpar@10
   423
      static const int bits = std::numeric_limits<Word>::digits;
alpar@10
   424
alpar@10
   425
      static Result convert(RandomCore<Word>& rnd) {
alpar@10
   426
        return Shifting<Result, - shift - bits>::
alpar@10
   427
          shift(static_cast<Result>(rnd())) +
alpar@10
   428
          RealConversion<Result, Word, rest-bits, shift + bits>::
alpar@10
   429
          convert(rnd);
alpar@10
   430
      }
alpar@10
   431
    };
alpar@10
   432
alpar@10
   433
    template <typename Result, typename Word>
alpar@10
   434
    struct Initializer {
alpar@10
   435
alpar@10
   436
      template <typename Iterator>
alpar@10
   437
      static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
alpar@10
   438
        std::vector<Word> ws;
alpar@10
   439
        for (Iterator it = begin; it != end; ++it) {
alpar@10
   440
          ws.push_back(Word(*it));
alpar@10
   441
        }
alpar@10
   442
        rnd.initState(ws.begin(), ws.end());
alpar@10
   443
      }
alpar@10
   444
alpar@10
   445
      static void init(RandomCore<Word>& rnd, Result seed) {
alpar@10
   446
        rnd.initState(seed);
alpar@10
   447
      }
alpar@10
   448
    };
alpar@10
   449
alpar@10
   450
    template <typename Word>
alpar@10
   451
    struct BoolConversion {
alpar@10
   452
      static bool convert(RandomCore<Word>& rnd) {
alpar@10
   453
        return (rnd() & 1) == 1;
alpar@10
   454
      }
alpar@10
   455
    };
alpar@10
   456
alpar@10
   457
    template <typename Word>
alpar@10
   458
    struct BoolProducer {
alpar@10
   459
      Word buffer;
alpar@10
   460
      int num;
alpar@10
   461
      
alpar@10
   462
      BoolProducer() : num(0) {}
alpar@10
   463
alpar@10
   464
      bool convert(RandomCore<Word>& rnd) {
alpar@10
   465
        if (num == 0) {
alpar@10
   466
          buffer = rnd();
alpar@10
   467
          num = RandomTraits<Word>::bits;
alpar@10
   468
        }
alpar@10
   469
        bool r = (buffer & 1);
alpar@10
   470
        buffer >>= 1;
alpar@10
   471
        --num;
alpar@10
   472
        return r;
alpar@10
   473
      }
alpar@10
   474
    };
alpar@10
   475
alpar@10
   476
  }
alpar@10
   477
alpar@10
   478
  /// \ingroup misc
alpar@10
   479
  ///
alpar@10
   480
  /// \brief Mersenne Twister random number generator
alpar@10
   481
  ///
alpar@10
   482
  /// The Mersenne Twister is a twisted generalized feedback
alpar@10
   483
  /// shift-register generator of Matsumoto and Nishimura. The period
alpar@10
   484
  /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
alpar@10
   485
  /// equi-distributed in 623 dimensions for 32-bit numbers. The time
alpar@10
   486
  /// performance of this generator is comparable to the commonly used
alpar@10
   487
  /// generators.
alpar@10
   488
  ///
alpar@10
   489
  /// This implementation is specialized for both 32-bit and 64-bit
alpar@10
   490
  /// architectures. The generators differ sligthly in the
alpar@10
   491
  /// initialization and generation phase so they produce two
alpar@10
   492
  /// completly different sequences.
alpar@10
   493
  ///
alpar@10
   494
  /// The generator gives back random numbers of serveral types. To
alpar@10
   495
  /// get a random number from a range of a floating point type you
alpar@10
   496
  /// can use one form of the \c operator() or the \c real() member
alpar@10
   497
  /// function. If you want to get random number from the {0, 1, ...,
alpar@10
   498
  /// n-1} integer range use the \c operator[] or the \c integer()
alpar@10
   499
  /// method. And to get random number from the whole range of an
alpar@10
   500
  /// integer type you can use the argumentless \c integer() or \c
alpar@10
   501
  /// uinteger() functions. After all you can get random bool with
alpar@10
   502
  /// equal chance of true and false or given probability of true
alpar@10
   503
  /// result with the \c boolean() member functions.
alpar@10
   504
  ///
alpar@10
   505
  ///\code
alpar@10
   506
  /// // The commented code is identical to the other
alpar@10
   507
  /// double a = rnd();                     // [0.0, 1.0)
alpar@10
   508
  /// // double a = rnd.real();             // [0.0, 1.0)
alpar@10
   509
  /// double b = rnd(100.0);                // [0.0, 100.0)
alpar@10
   510
  /// // double b = rnd.real(100.0);        // [0.0, 100.0)
alpar@10
   511
  /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
alpar@10
   512
  /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
alpar@10
   513
  /// int d = rnd[100000];                  // 0..99999
alpar@10
   514
  /// // int d = rnd.integer(100000);       // 0..99999
alpar@10
   515
  /// int e = rnd[6] + 1;                   // 1..6
alpar@10
   516
  /// // int e = rnd.integer(1, 1 + 6);     // 1..6
alpar@10
   517
  /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
alpar@10
   518
  /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
alpar@10
   519
  /// bool g = rnd.boolean();               // P(g = true) = 0.5
alpar@10
   520
  /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
alpar@10
   521
  ///\endcode
alpar@10
   522
  ///
kpeter@49
   523
  /// LEMON provides a global instance of the random number
alpar@10
   524
  /// generator which name is \ref lemon::rnd "rnd". Usually it is a
alpar@10
   525
  /// good programming convenience to use this global generator to get
alpar@10
   526
  /// random numbers.
alpar@10
   527
  class Random {
alpar@10
   528
  private:
alpar@10
   529
kpeter@16
   530
    // Architecture word
alpar@10
   531
    typedef unsigned long Word;
alpar@10
   532
    
alpar@10
   533
    _random_bits::RandomCore<Word> core;
alpar@10
   534
    _random_bits::BoolProducer<Word> bool_producer;
alpar@10
   535
    
alpar@10
   536
alpar@10
   537
  public:
alpar@10
   538
deba@177
   539
    ///\name Initialization
deba@177
   540
    ///
deba@177
   541
    /// @{
deba@177
   542
alpar@178
   543
    ///\name Initialization
alpar@178
   544
    ///
alpar@178
   545
    /// @{
alpar@178
   546
kpeter@49
   547
    /// \brief Default constructor
alpar@10
   548
    ///
alpar@10
   549
    /// Constructor with constant seeding.
alpar@10
   550
    Random() { core.initState(); }
alpar@10
   551
kpeter@49
   552
    /// \brief Constructor with seed
alpar@10
   553
    ///
alpar@10
   554
    /// Constructor with seed. The current number type will be converted
alpar@10
   555
    /// to the architecture word type.
alpar@10
   556
    template <typename Number>
alpar@10
   557
    Random(Number seed) { 
alpar@10
   558
      _random_bits::Initializer<Number, Word>::init(core, seed);
alpar@10
   559
    }
alpar@10
   560
kpeter@49
   561
    /// \brief Constructor with array seeding
alpar@10
   562
    ///
alpar@10
   563
    /// Constructor with array seeding. The given range should contain
alpar@10
   564
    /// any number type and the numbers will be converted to the
alpar@10
   565
    /// architecture word type.
alpar@10
   566
    template <typename Iterator>
alpar@10
   567
    Random(Iterator begin, Iterator end) { 
alpar@10
   568
      typedef typename std::iterator_traits<Iterator>::value_type Number;
alpar@10
   569
      _random_bits::Initializer<Number, Word>::init(core, begin, end);
alpar@10
   570
    }
alpar@10
   571
alpar@10
   572
    /// \brief Copy constructor
alpar@10
   573
    ///
alpar@10
   574
    /// Copy constructor. The generated sequence will be identical to
alpar@10
   575
    /// the other sequence. It can be used to save the current state
alpar@10
   576
    /// of the generator and later use it to generate the same
alpar@10
   577
    /// sequence.
alpar@10
   578
    Random(const Random& other) {
alpar@10
   579
      core.copyState(other.core);
alpar@10
   580
    }
alpar@10
   581
alpar@10
   582
    /// \brief Assign operator
alpar@10
   583
    ///
alpar@10
   584
    /// Assign operator. The generated sequence will be identical to
alpar@10
   585
    /// the other sequence. It can be used to save the current state
alpar@10
   586
    /// of the generator and later use it to generate the same
alpar@10
   587
    /// sequence.
alpar@10
   588
    Random& operator=(const Random& other) {
alpar@10
   589
      if (&other != this) {
alpar@10
   590
        core.copyState(other.core);
alpar@10
   591
      }
alpar@10
   592
      return *this;
alpar@10
   593
    }
alpar@10
   594
deba@102
   595
    /// \brief Seeding random sequence
deba@102
   596
    ///
deba@102
   597
    /// Seeding the random sequence. The current number type will be
deba@102
   598
    /// converted to the architecture word type.
deba@102
   599
    template <typename Number>
deba@102
   600
    void seed(Number seed) { 
deba@102
   601
      _random_bits::Initializer<Number, Word>::init(core, seed);
deba@102
   602
    }
deba@102
   603
deba@102
   604
    /// \brief Seeding random sequence
deba@102
   605
    ///
deba@102
   606
    /// Seeding the random sequence. The given range should contain
deba@102
   607
    /// any number type and the numbers will be converted to the
deba@102
   608
    /// architecture word type.
deba@102
   609
    template <typename Iterator>
deba@102
   610
    void seed(Iterator begin, Iterator end) { 
deba@102
   611
      typedef typename std::iterator_traits<Iterator>::value_type Number;
deba@102
   612
      _random_bits::Initializer<Number, Word>::init(core, begin, end);
deba@102
   613
    }
deba@102
   614
deba@177
   615
    /// \brief Seeding from file or from process id and time
deba@177
   616
    ///
deba@177
   617
    /// By default, this function calls the \c seedFromFile() member
alpar@178
   618
    /// function with the <tt>/dev/urandom</tt> file. If it does not success,
deba@177
   619
    /// it uses the \c seedFromTime().
deba@177
   620
    /// \return Currently always true.
deba@177
   621
    bool seed() {
deba@177
   622
#ifndef WIN32
deba@177
   623
      if (seedFromFile("/dev/urandom", 0)) return true;
deba@177
   624
#endif
deba@177
   625
      if (seedFromTime()) return true;
deba@177
   626
      return false;
deba@177
   627
    }
deba@177
   628
    
deba@177
   629
    /// \brief Seeding from file
deba@177
   630
    ///
deba@177
   631
    /// Seeding the random sequence from file. The linux kernel has two
deba@177
   632
    /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
deba@177
   633
    /// could give good seed values for pseudo random generators (The
deba@177
   634
    /// difference between two devices is that the <tt>random</tt> may
deba@177
   635
    /// block the reading operation while the kernel can give good
deba@177
   636
    /// source of randomness, while the <tt>urandom</tt> does not
deba@177
   637
    /// block the input, but it could give back bytes with worse
deba@177
   638
    /// entropy).
deba@177
   639
    /// \param file The source file
deba@177
   640
    /// \param offset The offset, from the file read.
alpar@178
   641
    /// \return True when the seeding successes.
deba@177
   642
#ifndef WIN32
deba@177
   643
    bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0) 
deba@177
   644
#else
deba@177
   645
    bool seedFromFile(const std::string& file = "", int offset = 0) 
deba@177
   646
#endif
deba@177
   647
    {
deba@177
   648
      std::ifstream rs(file.c_str());
deba@177
   649
      const int size = 4;
deba@177
   650
      Word buf[size];
deba@177
   651
      if (offset != 0 && !rs.seekg(offset)) return false;
deba@177
   652
      if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;
deba@177
   653
      seed(buf, buf + size);
deba@177
   654
      return true;
deba@177
   655
    }
deba@177
   656
deba@177
   657
    /// \brief Seding from process id and time
deba@177
   658
    ///
deba@177
   659
    /// Seding from process id and time. This function uses the
deba@177
   660
    /// current process id and the current time for initialize the
deba@177
   661
    /// random sequence.
deba@177
   662
    /// \return Currently always true.
deba@177
   663
    bool seedFromTime() { 	
deba@177
   664
#ifndef WIN32
deba@177
   665
      timeval tv;
deba@177
   666
      gettimeofday(&tv, 0);
deba@177
   667
      seed(getpid() + tv.tv_sec + tv.tv_usec);
deba@177
   668
#else
deba@177
   669
      FILETIME time;
deba@177
   670
      GetSystemTimeAsFileTime(&time);
deba@177
   671
      seed(GetCurrentProcessId() + time.dwHighDateTime + time.dwLowDateTime);
deba@177
   672
#endif
deba@177
   673
      return true;
deba@177
   674
    }
deba@177
   675
deba@177
   676
    /// @}
deba@177
   677
deba@177
   678
    ///\name Uniform distributions
deba@177
   679
    ///
deba@177
   680
    /// @{
deba@177
   681
alpar@10
   682
    /// \brief Returns a random real number from the range [0, 1)
alpar@10
   683
    ///
alpar@10
   684
    /// It returns a random real number from the range [0, 1). The
kpeter@49
   685
    /// default Number type is \c double.
alpar@10
   686
    template <typename Number>
alpar@10
   687
    Number real() {
alpar@10
   688
      return _random_bits::RealConversion<Number, Word>::convert(core);
alpar@10
   689
    }
alpar@10
   690
alpar@10
   691
    double real() {
alpar@10
   692
      return real<double>();
alpar@10
   693
    }
alpar@10
   694
alpar@10
   695
    /// \brief Returns a random real number the range [0, b)
alpar@10
   696
    ///
alpar@10
   697
    /// It returns a random real number from the range [0, b).
alpar@10
   698
    template <typename Number>
alpar@10
   699
    Number real(Number b) { 
alpar@10
   700
      return real<Number>() * b; 
alpar@10
   701
    }
alpar@10
   702
alpar@10
   703
    /// \brief Returns a random real number from the range [a, b)
alpar@10
   704
    ///
alpar@10
   705
    /// It returns a random real number from the range [a, b).
alpar@10
   706
    template <typename Number>
alpar@10
   707
    Number real(Number a, Number b) { 
alpar@10
   708
      return real<Number>() * (b - a) + a; 
alpar@10
   709
    }
alpar@10
   710
alpar@178
   711
    /// @}
alpar@178
   712
alpar@178
   713
    ///\name Uniform distributions
alpar@178
   714
    ///
alpar@178
   715
    /// @{
alpar@178
   716
alpar@10
   717
    /// \brief Returns a random real number from the range [0, 1)
alpar@10
   718
    ///
alpar@10
   719
    /// It returns a random double from the range [0, 1).
alpar@10
   720
    double operator()() {
alpar@10
   721
      return real<double>();
alpar@10
   722
    }
alpar@10
   723
alpar@10
   724
    /// \brief Returns a random real number from the range [0, b)
alpar@10
   725
    ///
alpar@10
   726
    /// It returns a random real number from the range [0, b).
alpar@10
   727
    template <typename Number>
alpar@10
   728
    Number operator()(Number b) { 
alpar@10
   729
      return real<Number>() * b; 
alpar@10
   730
    }
alpar@10
   731
alpar@10
   732
    /// \brief Returns a random real number from the range [a, b)
alpar@10
   733
    ///
alpar@10
   734
    /// It returns a random real number from the range [a, b).
alpar@10
   735
    template <typename Number>
alpar@10
   736
    Number operator()(Number a, Number b) { 
alpar@10
   737
      return real<Number>() * (b - a) + a; 
alpar@10
   738
    }
alpar@10
   739
alpar@10
   740
    /// \brief Returns a random integer from a range
alpar@10
   741
    ///
alpar@10
   742
    /// It returns a random integer from the range {0, 1, ..., b - 1}.
alpar@10
   743
    template <typename Number>
alpar@10
   744
    Number integer(Number b) {
alpar@10
   745
      return _random_bits::Mapping<Number, Word>::map(core, b);
alpar@10
   746
    }
alpar@10
   747
alpar@10
   748
    /// \brief Returns a random integer from a range
alpar@10
   749
    ///
alpar@10
   750
    /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
alpar@10
   751
    template <typename Number>
alpar@10
   752
    Number integer(Number a, Number b) {
alpar@10
   753
      return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
alpar@10
   754
    }
alpar@10
   755
alpar@10
   756
    /// \brief Returns a random integer from a range
alpar@10
   757
    ///
alpar@10
   758
    /// It returns a random integer from the range {0, 1, ..., b - 1}.
alpar@10
   759
    template <typename Number>
alpar@10
   760
    Number operator[](Number b) {
alpar@10
   761
      return _random_bits::Mapping<Number, Word>::map(core, b);
alpar@10
   762
    }
alpar@10
   763
alpar@10
   764
    /// \brief Returns a random non-negative integer
alpar@10
   765
    ///
alpar@10
   766
    /// It returns a random non-negative integer uniformly from the
kpeter@49
   767
    /// whole range of the current \c Number type. The default result
kpeter@49
   768
    /// type of this function is <tt>unsigned int</tt>.
alpar@10
   769
    template <typename Number>
alpar@10
   770
    Number uinteger() {
alpar@10
   771
      return _random_bits::IntConversion<Number, Word>::convert(core);
alpar@10
   772
    }
alpar@10
   773
alpar@178
   774
    /// @}
alpar@178
   775
alpar@10
   776
    unsigned int uinteger() {
alpar@10
   777
      return uinteger<unsigned int>();
alpar@10
   778
    }
alpar@10
   779
alpar@10
   780
    /// \brief Returns a random integer
alpar@10
   781
    ///
alpar@10
   782
    /// It returns a random integer uniformly from the whole range of
alpar@10
   783
    /// the current \c Number type. The default result type of this
kpeter@49
   784
    /// function is \c int.
alpar@10
   785
    template <typename Number>
alpar@10
   786
    Number integer() {
alpar@10
   787
      static const int nb = std::numeric_limits<Number>::digits + 
alpar@10
   788
        (std::numeric_limits<Number>::is_signed ? 1 : 0);
alpar@10
   789
      return _random_bits::IntConversion<Number, Word, nb>::convert(core);
alpar@10
   790
    }
alpar@10
   791
alpar@10
   792
    int integer() {
alpar@10
   793
      return integer<int>();
alpar@10
   794
    }
alpar@10
   795
    
alpar@10
   796
    /// \brief Returns a random bool
alpar@10
   797
    ///
alpar@10
   798
    /// It returns a random bool. The generator holds a buffer for
alpar@10
   799
    /// random bits. Every time when it become empty the generator makes
alpar@10
   800
    /// a new random word and fill the buffer up.
alpar@10
   801
    bool boolean() {
alpar@10
   802
      return bool_producer.convert(core);
alpar@10
   803
    }
alpar@10
   804
deba@177
   805
    /// @}
deba@177
   806
kpeter@49
   807
    ///\name Non-uniform distributions
alpar@10
   808
    ///
alpar@10
   809
    
alpar@10
   810
    ///@{
alpar@10
   811
    
alpar@10
   812
    /// \brief Returns a random bool
alpar@10
   813
    ///
kpeter@23
   814
    /// It returns a random bool with given probability of true result.
alpar@10
   815
    bool boolean(double p) {
alpar@10
   816
      return operator()() < p;
alpar@10
   817
    }
alpar@10
   818
alpar@10
   819
    /// Standard Gauss distribution
alpar@10
   820
alpar@10
   821
    /// Standard Gauss distribution.
alpar@10
   822
    /// \note The Cartesian form of the Box-Muller
alpar@10
   823
    /// transformation is used to generate a random normal distribution.
alpar@10
   824
    /// \todo Consider using the "ziggurat" method instead.
alpar@10
   825
    double gauss() 
alpar@10
   826
    {
alpar@10
   827
      double V1,V2,S;
alpar@10
   828
      do {
alpar@10
   829
	V1=2*real<double>()-1;
alpar@10
   830
	V2=2*real<double>()-1;
alpar@10
   831
	S=V1*V1+V2*V2;
alpar@10
   832
      } while(S>=1);
alpar@10
   833
      return std::sqrt(-2*std::log(S)/S)*V1;
alpar@10
   834
    }
alpar@10
   835
    /// Gauss distribution with given mean and standard deviation
alpar@10
   836
kpeter@23
   837
    /// Gauss distribution with given mean and standard deviation.
alpar@10
   838
    /// \sa gauss()
alpar@10
   839
    double gauss(double mean,double std_dev)
alpar@10
   840
    {
alpar@10
   841
      return gauss()*std_dev+mean;
alpar@10
   842
    }
alpar@10
   843
alpar@10
   844
    /// Exponential distribution with given mean
alpar@10
   845
alpar@10
   846
    /// This function generates an exponential distribution random number
alpar@10
   847
    /// with mean <tt>1/lambda</tt>.
alpar@10
   848
    ///
alpar@10
   849
    double exponential(double lambda=1.0)
alpar@10
   850
    {
alpar@11
   851
      return -std::log(1.0-real<double>())/lambda;
alpar@10
   852
    }
alpar@10
   853
alpar@10
   854
    /// Gamma distribution with given integer shape
alpar@10
   855
alpar@10
   856
    /// This function generates a gamma distribution random number.
alpar@10
   857
    /// 
alpar@10
   858
    ///\param k shape parameter (<tt>k>0</tt> integer)
alpar@10
   859
    double gamma(int k) 
alpar@10
   860
    {
alpar@10
   861
      double s = 0;
alpar@10
   862
      for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
alpar@10
   863
      return s;
alpar@10
   864
    }
alpar@10
   865
    
alpar@10
   866
    /// Gamma distribution with given shape and scale parameter
alpar@10
   867
alpar@10
   868
    /// This function generates a gamma distribution random number.
alpar@10
   869
    /// 
alpar@10
   870
    ///\param k shape parameter (<tt>k>0</tt>)
alpar@10
   871
    ///\param theta scale parameter
alpar@10
   872
    ///
alpar@10
   873
    double gamma(double k,double theta=1.0)
alpar@10
   874
    {
alpar@10
   875
      double xi,nu;
alpar@10
   876
      const double delta = k-std::floor(k);
alpar@68
   877
      const double v0=E/(E-delta);
alpar@10
   878
      do {
alpar@10
   879
	double V0=1.0-real<double>();
alpar@10
   880
	double V1=1.0-real<double>();
alpar@10
   881
	double V2=1.0-real<double>();
alpar@10
   882
	if(V2<=v0) 
alpar@10
   883
	  {
alpar@10
   884
	    xi=std::pow(V1,1.0/delta);
alpar@10
   885
	    nu=V0*std::pow(xi,delta-1.0);
alpar@10
   886
	  }
alpar@10
   887
	else 
alpar@10
   888
	  {
alpar@10
   889
	    xi=1.0-std::log(V1);
alpar@10
   890
	    nu=V0*std::exp(-xi);
alpar@10
   891
	  }
alpar@10
   892
      } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
alpar@116
   893
      return theta*(xi+gamma(int(std::floor(k))));
alpar@10
   894
    }
alpar@10
   895
    
alpar@11
   896
    /// Weibull distribution
alpar@11
   897
alpar@11
   898
    /// This function generates a Weibull distribution random number.
alpar@11
   899
    /// 
alpar@11
   900
    ///\param k shape parameter (<tt>k>0</tt>)
alpar@11
   901
    ///\param lambda scale parameter (<tt>lambda>0</tt>)
alpar@11
   902
    ///
alpar@11
   903
    double weibull(double k,double lambda)
alpar@11
   904
    {
alpar@11
   905
      return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
alpar@11
   906
    }  
alpar@11
   907
      
alpar@11
   908
    /// Pareto distribution
alpar@11
   909
alpar@11
   910
    /// This function generates a Pareto distribution random number.
alpar@11
   911
    /// 
alpar@12
   912
    ///\param k shape parameter (<tt>k>0</tt>)
alpar@11
   913
    ///\param x_min location parameter (<tt>x_min>0</tt>)
alpar@11
   914
    ///
alpar@12
   915
    double pareto(double k,double x_min)
alpar@11
   916
    {
alpar@116
   917
      return exponential(gamma(k,1.0/x_min))+x_min;
alpar@11
   918
    }  
alpar@10
   919
      
alpar@92
   920
    /// Poisson distribution
alpar@92
   921
alpar@92
   922
    /// This function generates a Poisson distribution random number with
alpar@92
   923
    /// parameter \c lambda.
alpar@92
   924
    /// 
alpar@92
   925
    /// The probability mass function of this distribusion is
alpar@92
   926
    /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
alpar@92
   927
    /// \note The algorithm is taken from the book of Donald E. Knuth titled
alpar@92
   928
    /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
alpar@92
   929
    /// return value.
alpar@92
   930
    
alpar@92
   931
    int poisson(double lambda)
alpar@92
   932
    {
alpar@92
   933
      const double l = std::exp(-lambda);
alpar@92
   934
      int k=0;
alpar@92
   935
      double p = 1.0;
alpar@92
   936
      do {
alpar@92
   937
	k++;
alpar@92
   938
	p*=real<double>();
alpar@92
   939
      } while (p>=l);
alpar@92
   940
      return k-1;
alpar@92
   941
    }  
alpar@92
   942
      
alpar@10
   943
    ///@}
alpar@10
   944
    
alpar@10
   945
    ///\name Two dimensional distributions
alpar@10
   946
    ///
alpar@10
   947
alpar@10
   948
    ///@{
alpar@10
   949
    
kpeter@23
   950
    /// Uniform distribution on the full unit circle
kpeter@16
   951
kpeter@16
   952
    /// Uniform distribution on the full unit circle.
kpeter@16
   953
    ///
alpar@10
   954
    dim2::Point<double> disc() 
alpar@10
   955
    {
alpar@10
   956
      double V1,V2;
alpar@10
   957
      do {
alpar@10
   958
	V1=2*real<double>()-1;
alpar@10
   959
	V2=2*real<double>()-1;
alpar@10
   960
	
alpar@10
   961
      } while(V1*V1+V2*V2>=1);
alpar@10
   962
      return dim2::Point<double>(V1,V2);
alpar@10
   963
    }
alpar@10
   964
    /// A kind of two dimensional Gauss distribution
alpar@10
   965
alpar@10
   966
    /// This function provides a turning symmetric two-dimensional distribution.
alpar@10
   967
    /// Both coordinates are of standard normal distribution, but they are not
alpar@10
   968
    /// independent.
alpar@10
   969
    ///
alpar@10
   970
    /// \note The coordinates are the two random variables provided by
alpar@10
   971
    /// the Box-Muller method.
alpar@10
   972
    dim2::Point<double> gauss2()
alpar@10
   973
    {
alpar@10
   974
      double V1,V2,S;
alpar@10
   975
      do {
alpar@10
   976
	V1=2*real<double>()-1;
alpar@10
   977
	V2=2*real<double>()-1;
alpar@10
   978
	S=V1*V1+V2*V2;
alpar@10
   979
      } while(S>=1);
alpar@10
   980
      double W=std::sqrt(-2*std::log(S)/S);
alpar@10
   981
      return dim2::Point<double>(W*V1,W*V2);
alpar@10
   982
    }
alpar@10
   983
    /// A kind of two dimensional exponential distribution
alpar@10
   984
alpar@10
   985
    /// This function provides a turning symmetric two-dimensional distribution.
alpar@10
   986
    /// The x-coordinate is of conditionally exponential distribution
alpar@10
   987
    /// with the condition that x is positive and y=0. If x is negative and 
alpar@10
   988
    /// y=0 then, -x is of exponential distribution. The same is true for the
alpar@10
   989
    /// y-coordinate.
alpar@10
   990
    dim2::Point<double> exponential2() 
alpar@10
   991
    {
alpar@10
   992
      double V1,V2,S;
alpar@10
   993
      do {
alpar@10
   994
	V1=2*real<double>()-1;
alpar@10
   995
	V2=2*real<double>()-1;
alpar@10
   996
	S=V1*V1+V2*V2;
alpar@10
   997
      } while(S>=1);
alpar@10
   998
      double W=-std::log(S)/S;
alpar@10
   999
      return dim2::Point<double>(W*V1,W*V2);
alpar@10
  1000
    }
alpar@10
  1001
alpar@10
  1002
    ///@}    
alpar@10
  1003
  };
alpar@10
  1004
alpar@10
  1005
alpar@10
  1006
  extern Random rnd;
alpar@10
  1007
alpar@10
  1008
}
alpar@10
  1009
alpar@10
  1010
#endif