1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2009 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | /* |
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20 | * This file contains the reimplemented version of the Mersenne Twister |
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21 | * Generator of Matsumoto and Nishimura. |
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22 | * |
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23 | * See the appropriate copyright notice below. |
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24 | * |
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25 | * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, |
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26 | * All rights reserved. |
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27 | * |
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28 | * Redistribution and use in source and binary forms, with or without |
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29 | * modification, are permitted provided that the following conditions |
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30 | * are met: |
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31 | * |
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32 | * 1. Redistributions of source code must retain the above copyright |
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33 | * notice, this list of conditions and the following disclaimer. |
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34 | * |
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35 | * 2. Redistributions in binary form must reproduce the above copyright |
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36 | * notice, this list of conditions and the following disclaimer in the |
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37 | * documentation and/or other materials provided with the distribution. |
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38 | * |
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39 | * 3. The names of its contributors may not be used to endorse or promote |
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40 | * products derived from this software without specific prior written |
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41 | * permission. |
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42 | * |
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43 | * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
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44 | * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
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45 | * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS |
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46 | * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE |
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47 | * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, |
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48 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
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49 | * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR |
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50 | * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
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51 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
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52 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
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53 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
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54 | * OF THE POSSIBILITY OF SUCH DAMAGE. |
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55 | * |
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56 | * |
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57 | * Any feedback is very welcome. |
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58 | * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html |
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59 | * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space) |
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60 | */ |
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61 | |
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62 | #ifndef LEMON_RANDOM_H |
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63 | #define LEMON_RANDOM_H |
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64 | |
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65 | #include <lemon/config.h> |
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66 | |
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67 | #include <algorithm> |
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68 | #include <iterator> |
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69 | #include <vector> |
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70 | #include <limits> |
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71 | #include <fstream> |
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72 | |
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73 | #include <lemon/math.h> |
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74 | #include <lemon/dim2.h> |
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75 | |
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76 | #ifndef LEMON_WIN32 |
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77 | #include <sys/time.h> |
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78 | #include <ctime> |
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79 | #include <sys/types.h> |
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80 | #include <unistd.h> |
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81 | #else |
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82 | #include <lemon/bits/windows.h> |
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83 | #endif |
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84 | |
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85 | ///\ingroup misc |
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86 | ///\file |
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87 | ///\brief Mersenne Twister random number generator |
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88 | |
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89 | namespace lemon { |
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90 | |
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91 | namespace _random_bits { |
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92 | |
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93 | template <typename _Word, int _bits = std::numeric_limits<_Word>::digits> |
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94 | struct RandomTraits {}; |
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95 | |
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96 | template <typename _Word> |
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97 | struct RandomTraits<_Word, 32> { |
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98 | |
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99 | typedef _Word Word; |
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100 | static const int bits = 32; |
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101 | |
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102 | static const int length = 624; |
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103 | static const int shift = 397; |
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104 | |
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105 | static const Word mul = 0x6c078965u; |
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106 | static const Word arrayInit = 0x012BD6AAu; |
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107 | static const Word arrayMul1 = 0x0019660Du; |
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108 | static const Word arrayMul2 = 0x5D588B65u; |
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109 | |
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110 | static const Word mask = 0x9908B0DFu; |
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111 | static const Word loMask = (1u << 31) - 1; |
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112 | static const Word hiMask = ~loMask; |
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113 | |
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114 | static Word tempering(Word rnd) { |
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115 | rnd ^= (rnd >> 11); |
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116 | rnd ^= (rnd << 7) & 0x9D2C5680u; |
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117 | rnd ^= (rnd << 15) & 0xEFC60000u; |
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118 | rnd ^= (rnd >> 18); |
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119 | return rnd; |
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120 | } |
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121 | |
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122 | }; |
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123 | |
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124 | template <typename _Word> |
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125 | struct RandomTraits<_Word, 64> { |
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126 | |
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127 | typedef _Word Word; |
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128 | static const int bits = 64; |
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129 | |
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130 | static const int length = 312; |
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131 | static const int shift = 156; |
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132 | |
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133 | static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du); |
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134 | static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu); |
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135 | static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u); |
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136 | static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu); |
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137 | |
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138 | static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u); |
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139 | static const Word loMask = (Word(1u) << 31) - 1; |
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140 | static const Word hiMask = ~loMask; |
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141 | |
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142 | static Word tempering(Word rnd) { |
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143 | rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u)); |
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144 | rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u)); |
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145 | rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u)); |
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146 | rnd ^= (rnd >> 43); |
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147 | return rnd; |
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148 | } |
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149 | |
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150 | }; |
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151 | |
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152 | template <typename _Word> |
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153 | class RandomCore { |
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154 | public: |
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155 | |
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156 | typedef _Word Word; |
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157 | |
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158 | private: |
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159 | |
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160 | static const int bits = RandomTraits<Word>::bits; |
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161 | |
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162 | static const int length = RandomTraits<Word>::length; |
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163 | static const int shift = RandomTraits<Word>::shift; |
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164 | |
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165 | public: |
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166 | |
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167 | void initState() { |
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168 | static const Word seedArray[4] = { |
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169 | 0x12345u, 0x23456u, 0x34567u, 0x45678u |
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170 | }; |
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171 | |
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172 | initState(seedArray, seedArray + 4); |
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173 | } |
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174 | |
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175 | void initState(Word seed) { |
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176 | |
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177 | static const Word mul = RandomTraits<Word>::mul; |
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178 | |
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179 | current = state; |
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180 | |
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181 | Word *curr = state + length - 1; |
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182 | curr[0] = seed; --curr; |
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183 | for (int i = 1; i < length; ++i) { |
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184 | curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i); |
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185 | --curr; |
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186 | } |
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187 | } |
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188 | |
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189 | template <typename Iterator> |
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190 | void initState(Iterator begin, Iterator end) { |
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191 | |
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192 | static const Word init = RandomTraits<Word>::arrayInit; |
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193 | static const Word mul1 = RandomTraits<Word>::arrayMul1; |
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194 | static const Word mul2 = RandomTraits<Word>::arrayMul2; |
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195 | |
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196 | |
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197 | Word *curr = state + length - 1; --curr; |
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198 | Iterator it = begin; int cnt = 0; |
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199 | int num; |
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200 | |
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201 | initState(init); |
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202 | |
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203 | num = static_cast<int>(length > end - begin ? length : end - begin); |
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204 | while (num--) { |
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205 | curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) |
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206 | + *it + cnt; |
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207 | ++it; ++cnt; |
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208 | if (it == end) { |
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209 | it = begin; cnt = 0; |
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210 | } |
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211 | if (curr == state) { |
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212 | curr = state + length - 1; curr[0] = state[0]; |
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213 | } |
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214 | --curr; |
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215 | } |
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216 | |
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217 | num = length - 1; cnt = static_cast<int>(length - (curr - state) - 1); |
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218 | while (num--) { |
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219 | curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2)) |
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220 | - cnt; |
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221 | --curr; ++cnt; |
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222 | if (curr == state) { |
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223 | curr = state + length - 1; curr[0] = state[0]; --curr; |
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224 | cnt = 1; |
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225 | } |
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226 | } |
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227 | |
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228 | state[length - 1] = Word(1) << (bits - 1); |
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229 | } |
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230 | |
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231 | void copyState(const RandomCore& other) { |
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232 | std::copy(other.state, other.state + length, state); |
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233 | current = state + (other.current - other.state); |
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234 | } |
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235 | |
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236 | Word operator()() { |
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237 | if (current == state) fillState(); |
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238 | --current; |
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239 | Word rnd = *current; |
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240 | return RandomTraits<Word>::tempering(rnd); |
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241 | } |
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242 | |
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243 | private: |
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244 | |
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245 | void fillState() { |
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246 | static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask }; |
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247 | static const Word loMask = RandomTraits<Word>::loMask; |
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248 | static const Word hiMask = RandomTraits<Word>::hiMask; |
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249 | |
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250 | current = state + length; |
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251 | |
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252 | Word *curr = state + length - 1; |
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253 | long num; |
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254 | |
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255 | num = length - shift; |
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256 | while (num--) { |
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257 | curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ |
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258 | curr[- shift] ^ mask[curr[-1] & 1ul]; |
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259 | --curr; |
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260 | } |
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261 | num = shift - 1; |
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262 | while (num--) { |
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263 | curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ |
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264 | curr[length - shift] ^ mask[curr[-1] & 1ul]; |
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265 | --curr; |
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266 | } |
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267 | state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^ |
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268 | curr[length - shift] ^ mask[curr[length - 1] & 1ul]; |
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269 | |
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270 | } |
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271 | |
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272 | Word *current; |
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273 | Word state[length]; |
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274 | |
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275 | }; |
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276 | |
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277 | |
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278 | template <typename Result, |
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279 | int shift = (std::numeric_limits<Result>::digits + 1) / 2> |
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280 | struct Masker { |
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281 | static Result mask(const Result& result) { |
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282 | return Masker<Result, (shift + 1) / 2>:: |
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283 | mask(static_cast<Result>(result | (result >> shift))); |
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284 | } |
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285 | }; |
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286 | |
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287 | template <typename Result> |
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288 | struct Masker<Result, 1> { |
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289 | static Result mask(const Result& result) { |
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290 | return static_cast<Result>(result | (result >> 1)); |
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291 | } |
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292 | }; |
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293 | |
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294 | template <typename Result, typename Word, |
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295 | int rest = std::numeric_limits<Result>::digits, int shift = 0, |
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296 | bool last = (rest <= std::numeric_limits<Word>::digits)> |
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297 | struct IntConversion { |
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298 | static const int bits = std::numeric_limits<Word>::digits; |
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299 | |
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300 | static Result convert(RandomCore<Word>& rnd) { |
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301 | return static_cast<Result>(rnd() >> (bits - rest)) << shift; |
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302 | } |
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303 | |
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304 | }; |
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305 | |
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306 | template <typename Result, typename Word, int rest, int shift> |
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307 | struct IntConversion<Result, Word, rest, shift, false> { |
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308 | static const int bits = std::numeric_limits<Word>::digits; |
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309 | |
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310 | static Result convert(RandomCore<Word>& rnd) { |
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311 | return (static_cast<Result>(rnd()) << shift) | |
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312 | IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd); |
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313 | } |
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314 | }; |
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315 | |
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316 | |
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317 | template <typename Result, typename Word, |
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318 | bool one_word = (std::numeric_limits<Word>::digits < |
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319 | std::numeric_limits<Result>::digits) > |
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320 | struct Mapping { |
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321 | static Result map(RandomCore<Word>& rnd, const Result& bound) { |
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322 | Word max = Word(bound - 1); |
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323 | Result mask = Masker<Result>::mask(bound - 1); |
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324 | Result num; |
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325 | do { |
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326 | num = IntConversion<Result, Word>::convert(rnd) & mask; |
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327 | } while (num > max); |
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328 | return num; |
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329 | } |
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330 | }; |
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331 | |
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332 | template <typename Result, typename Word> |
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333 | struct Mapping<Result, Word, false> { |
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334 | static Result map(RandomCore<Word>& rnd, const Result& bound) { |
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335 | Word max = Word(bound - 1); |
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336 | Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2> |
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337 | ::mask(max); |
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338 | Word num; |
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339 | do { |
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340 | num = rnd() & mask; |
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341 | } while (num > max); |
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342 | return static_cast<Result>(num); |
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343 | } |
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344 | }; |
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345 | |
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346 | template <typename Result, int exp> |
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347 | struct ShiftMultiplier { |
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348 | static const Result multiplier() { |
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349 | Result res = ShiftMultiplier<Result, exp / 2>::multiplier(); |
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350 | res *= res; |
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351 | if ((exp & 1) == 1) res *= static_cast<Result>(0.5); |
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352 | return res; |
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353 | } |
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354 | }; |
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355 | |
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356 | template <typename Result> |
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357 | struct ShiftMultiplier<Result, 0> { |
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358 | static const Result multiplier() { |
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359 | return static_cast<Result>(1.0); |
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360 | } |
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361 | }; |
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362 | |
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363 | template <typename Result> |
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364 | struct ShiftMultiplier<Result, 20> { |
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365 | static const Result multiplier() { |
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366 | return static_cast<Result>(1.0/1048576.0); |
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367 | } |
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368 | }; |
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369 | |
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370 | template <typename Result> |
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371 | struct ShiftMultiplier<Result, 32> { |
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372 | static const Result multiplier() { |
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373 | return static_cast<Result>(1.0/4294967296.0); |
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374 | } |
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375 | }; |
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376 | |
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377 | template <typename Result> |
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378 | struct ShiftMultiplier<Result, 53> { |
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379 | static const Result multiplier() { |
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380 | return static_cast<Result>(1.0/9007199254740992.0); |
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381 | } |
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382 | }; |
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383 | |
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384 | template <typename Result> |
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385 | struct ShiftMultiplier<Result, 64> { |
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386 | static const Result multiplier() { |
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387 | return static_cast<Result>(1.0/18446744073709551616.0); |
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388 | } |
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389 | }; |
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390 | |
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391 | template <typename Result, int exp> |
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392 | struct Shifting { |
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393 | static Result shift(const Result& result) { |
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394 | return result * ShiftMultiplier<Result, exp>::multiplier(); |
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395 | } |
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396 | }; |
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397 | |
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398 | template <typename Result, typename Word, |
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399 | int rest = std::numeric_limits<Result>::digits, int shift = 0, |
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400 | bool last = rest <= std::numeric_limits<Word>::digits> |
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401 | struct RealConversion{ |
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402 | static const int bits = std::numeric_limits<Word>::digits; |
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403 | |
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404 | static Result convert(RandomCore<Word>& rnd) { |
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405 | return Shifting<Result, shift + rest>:: |
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406 | shift(static_cast<Result>(rnd() >> (bits - rest))); |
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407 | } |
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408 | }; |
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409 | |
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410 | template <typename Result, typename Word, int rest, int shift> |
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411 | struct RealConversion<Result, Word, rest, shift, false> { |
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412 | static const int bits = std::numeric_limits<Word>::digits; |
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413 | |
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414 | static Result convert(RandomCore<Word>& rnd) { |
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415 | return Shifting<Result, shift + bits>:: |
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416 | shift(static_cast<Result>(rnd())) + |
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417 | RealConversion<Result, Word, rest-bits, shift + bits>:: |
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418 | convert(rnd); |
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419 | } |
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420 | }; |
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421 | |
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422 | template <typename Result, typename Word> |
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423 | struct Initializer { |
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424 | |
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425 | template <typename Iterator> |
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426 | static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) { |
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427 | std::vector<Word> ws; |
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428 | for (Iterator it = begin; it != end; ++it) { |
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429 | ws.push_back(Word(*it)); |
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430 | } |
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431 | rnd.initState(ws.begin(), ws.end()); |
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432 | } |
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433 | |
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434 | static void init(RandomCore<Word>& rnd, Result seed) { |
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435 | rnd.initState(seed); |
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436 | } |
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437 | }; |
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438 | |
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439 | template <typename Word> |
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440 | struct BoolConversion { |
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441 | static bool convert(RandomCore<Word>& rnd) { |
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442 | return (rnd() & 1) == 1; |
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443 | } |
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444 | }; |
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445 | |
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446 | template <typename Word> |
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447 | struct BoolProducer { |
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448 | Word buffer; |
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449 | int num; |
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450 | |
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451 | BoolProducer() : num(0) {} |
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452 | |
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453 | bool convert(RandomCore<Word>& rnd) { |
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454 | if (num == 0) { |
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455 | buffer = rnd(); |
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456 | num = RandomTraits<Word>::bits; |
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457 | } |
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458 | bool r = (buffer & 1); |
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459 | buffer >>= 1; |
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460 | --num; |
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461 | return r; |
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462 | } |
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463 | }; |
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464 | |
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465 | /// \ingroup misc |
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466 | /// |
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467 | /// \brief Mersenne Twister random number generator |
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468 | /// |
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469 | /// The Mersenne Twister is a twisted generalized feedback |
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470 | /// shift-register generator of Matsumoto and Nishimura. The period |
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471 | /// of this generator is \f$ 2^{19937} - 1\f$ and it is |
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472 | /// equi-distributed in 623 dimensions for 32-bit numbers. The time |
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473 | /// performance of this generator is comparable to the commonly used |
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474 | /// generators. |
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475 | /// |
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476 | /// This is a template implementation of both 32-bit and |
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477 | /// 64-bit architecture optimized versions. The generators differ |
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478 | /// sligthly in the initialization and generation phase so they |
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479 | /// produce two completly different sequences. |
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480 | /// |
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481 | /// \alert Do not use this class directly, but instead one of \ref |
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482 | /// Random, \ref Random32 or \ref Random64. |
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483 | /// |
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484 | /// The generator gives back random numbers of serveral types. To |
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485 | /// get a random number from a range of a floating point type, you |
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486 | /// can use one form of the \c operator() or the \c real() member |
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487 | /// function. If you want to get random number from the {0, 1, ..., |
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488 | /// n-1} integer range, use the \c operator[] or the \c integer() |
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489 | /// method. And to get random number from the whole range of an |
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490 | /// integer type, you can use the argumentless \c integer() or |
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491 | /// \c uinteger() functions. Finally, you can get random bool with |
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492 | /// equal chance of true and false or with given probability of true |
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493 | /// result using the \c boolean() member functions. |
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494 | /// |
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495 | /// Various non-uniform distributions are also supported: normal (Gauss), |
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496 | /// exponential, gamma, Poisson, etc.; and a few two-dimensional |
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497 | /// distributions, too. |
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498 | /// |
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499 | ///\code |
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500 | /// // The commented code is identical to the other |
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501 | /// double a = rnd(); // [0.0, 1.0) |
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502 | /// // double a = rnd.real(); // [0.0, 1.0) |
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503 | /// double b = rnd(100.0); // [0.0, 100.0) |
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504 | /// // double b = rnd.real(100.0); // [0.0, 100.0) |
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505 | /// double c = rnd(1.0, 2.0); // [1.0, 2.0) |
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506 | /// // double c = rnd.real(1.0, 2.0); // [1.0, 2.0) |
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507 | /// int d = rnd[100000]; // 0..99999 |
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508 | /// // int d = rnd.integer(100000); // 0..99999 |
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509 | /// int e = rnd[6] + 1; // 1..6 |
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510 | /// // int e = rnd.integer(1, 1 + 6); // 1..6 |
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511 | /// int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1 |
---|
512 | /// int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1 |
---|
513 | /// bool g = rnd.boolean(); // P(g = true) = 0.5 |
---|
514 | /// bool h = rnd.boolean(0.8); // P(h = true) = 0.8 |
---|
515 | ///\endcode |
---|
516 | /// |
---|
517 | /// LEMON provides a global instance of the random number generator: |
---|
518 | /// \ref lemon::rnd "rnd". In most cases, it is a good practice |
---|
519 | /// to use this global generator to get random numbers. |
---|
520 | /// |
---|
521 | /// \sa \ref Random, \ref Random32 or \ref Random64. |
---|
522 | template<class Word> |
---|
523 | class Random { |
---|
524 | private: |
---|
525 | |
---|
526 | _random_bits::RandomCore<Word> core; |
---|
527 | _random_bits::BoolProducer<Word> bool_producer; |
---|
528 | |
---|
529 | |
---|
530 | public: |
---|
531 | |
---|
532 | ///\name Initialization |
---|
533 | /// |
---|
534 | /// @{ |
---|
535 | |
---|
536 | /// \brief Default constructor |
---|
537 | /// |
---|
538 | /// Constructor with constant seeding. |
---|
539 | Random() { core.initState(); } |
---|
540 | |
---|
541 | /// \brief Constructor with seed |
---|
542 | /// |
---|
543 | /// Constructor with seed. The current number type will be converted |
---|
544 | /// to the architecture word type. |
---|
545 | template <typename Number> |
---|
546 | Random(Number seed) { |
---|
547 | _random_bits::Initializer<Number, Word>::init(core, seed); |
---|
548 | } |
---|
549 | |
---|
550 | /// \brief Constructor with array seeding |
---|
551 | /// |
---|
552 | /// Constructor with array seeding. The given range should contain |
---|
553 | /// any number type and the numbers will be converted to the |
---|
554 | /// architecture word type. |
---|
555 | template <typename Iterator> |
---|
556 | Random(Iterator begin, Iterator end) { |
---|
557 | typedef typename std::iterator_traits<Iterator>::value_type Number; |
---|
558 | _random_bits::Initializer<Number, Word>::init(core, begin, end); |
---|
559 | } |
---|
560 | |
---|
561 | /// \brief Copy constructor |
---|
562 | /// |
---|
563 | /// Copy constructor. The generated sequence will be identical to |
---|
564 | /// the other sequence. It can be used to save the current state |
---|
565 | /// of the generator and later use it to generate the same |
---|
566 | /// sequence. |
---|
567 | Random(const Random& other) { |
---|
568 | core.copyState(other.core); |
---|
569 | } |
---|
570 | |
---|
571 | /// \brief Assign operator |
---|
572 | /// |
---|
573 | /// Assign operator. The generated sequence will be identical to |
---|
574 | /// the other sequence. It can be used to save the current state |
---|
575 | /// of the generator and later use it to generate the same |
---|
576 | /// sequence. |
---|
577 | Random& operator=(const Random& other) { |
---|
578 | if (&other != this) { |
---|
579 | core.copyState(other.core); |
---|
580 | } |
---|
581 | return *this; |
---|
582 | } |
---|
583 | |
---|
584 | /// \brief Seeding random sequence |
---|
585 | /// |
---|
586 | /// Seeding the random sequence. The current number type will be |
---|
587 | /// converted to the architecture word type. |
---|
588 | template <typename Number> |
---|
589 | void seed(Number seed) { |
---|
590 | _random_bits::Initializer<Number, Word>::init(core, seed); |
---|
591 | } |
---|
592 | |
---|
593 | /// \brief Seeding random sequence |
---|
594 | /// |
---|
595 | /// Seeding the random sequence. The given range should contain |
---|
596 | /// any number type and the numbers will be converted to the |
---|
597 | /// architecture word type. |
---|
598 | template <typename Iterator> |
---|
599 | void seed(Iterator begin, Iterator end) { |
---|
600 | typedef typename std::iterator_traits<Iterator>::value_type Number; |
---|
601 | _random_bits::Initializer<Number, Word>::init(core, begin, end); |
---|
602 | } |
---|
603 | |
---|
604 | /// \brief Seeding from file or from process id and time |
---|
605 | /// |
---|
606 | /// By default, this function calls the \c seedFromFile() member |
---|
607 | /// function with the <tt>/dev/urandom</tt> file. If it does not success, |
---|
608 | /// it uses the \c seedFromTime(). |
---|
609 | /// \return Currently always \c true. |
---|
610 | bool seed() { |
---|
611 | #ifndef LEMON_WIN32 |
---|
612 | if (seedFromFile("/dev/urandom", 0)) return true; |
---|
613 | #endif |
---|
614 | if (seedFromTime()) return true; |
---|
615 | return false; |
---|
616 | } |
---|
617 | |
---|
618 | /// \brief Seeding from file |
---|
619 | /// |
---|
620 | /// Seeding the random sequence from file. The linux kernel has two |
---|
621 | /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which |
---|
622 | /// could give good seed values for pseudo random generators (The |
---|
623 | /// difference between two devices is that the <tt>random</tt> may |
---|
624 | /// block the reading operation while the kernel can give good |
---|
625 | /// source of randomness, while the <tt>urandom</tt> does not |
---|
626 | /// block the input, but it could give back bytes with worse |
---|
627 | /// entropy). |
---|
628 | /// \param file The source file |
---|
629 | /// \param offset The offset, from the file read. |
---|
630 | /// \return \c true when the seeding successes. |
---|
631 | #ifndef LEMON_WIN32 |
---|
632 | bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0) |
---|
633 | #else |
---|
634 | bool seedFromFile(const std::string& file = "", int offset = 0) |
---|
635 | #endif |
---|
636 | { |
---|
637 | std::ifstream rs(file.c_str()); |
---|
638 | const int size = 4; |
---|
639 | Word buf[size]; |
---|
640 | if (offset != 0 && !rs.seekg(offset)) return false; |
---|
641 | if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false; |
---|
642 | seed(buf, buf + size); |
---|
643 | return true; |
---|
644 | } |
---|
645 | |
---|
646 | /// \brief Seeding from process id and time |
---|
647 | /// |
---|
648 | /// Seeding from process id and time. This function uses the |
---|
649 | /// current process id and the current time for initialize the |
---|
650 | /// random sequence. |
---|
651 | /// \return Currently always \c true. |
---|
652 | bool seedFromTime() { |
---|
653 | #ifndef LEMON_WIN32 |
---|
654 | timeval tv; |
---|
655 | gettimeofday(&tv, 0); |
---|
656 | seed(getpid() + tv.tv_sec + tv.tv_usec); |
---|
657 | #else |
---|
658 | seed(bits::getWinRndSeed()); |
---|
659 | #endif |
---|
660 | return true; |
---|
661 | } |
---|
662 | |
---|
663 | /// @} |
---|
664 | |
---|
665 | ///\name Uniform Distributions |
---|
666 | /// |
---|
667 | /// @{ |
---|
668 | |
---|
669 | /// \brief Returns a random real number from the range [0, 1) |
---|
670 | /// |
---|
671 | /// It returns a random real number from the range [0, 1). The |
---|
672 | /// default Number type is \c double. |
---|
673 | template <typename Number> |
---|
674 | Number real() { |
---|
675 | return _random_bits::RealConversion<Number, Word>::convert(core); |
---|
676 | } |
---|
677 | |
---|
678 | double real() { |
---|
679 | return real<double>(); |
---|
680 | } |
---|
681 | |
---|
682 | /// \brief Returns a random real number from the range [0, 1) |
---|
683 | /// |
---|
684 | /// It returns a random double from the range [0, 1). |
---|
685 | double operator()() { |
---|
686 | return real<double>(); |
---|
687 | } |
---|
688 | |
---|
689 | /// \brief Returns a random real number from the range [0, b) |
---|
690 | /// |
---|
691 | /// It returns a random real number from the range [0, b). |
---|
692 | double operator()(double b) { |
---|
693 | return real<double>() * b; |
---|
694 | } |
---|
695 | |
---|
696 | /// \brief Returns a random real number from the range [a, b) |
---|
697 | /// |
---|
698 | /// It returns a random real number from the range [a, b). |
---|
699 | double operator()(double a, double b) { |
---|
700 | return real<double>() * (b - a) + a; |
---|
701 | } |
---|
702 | |
---|
703 | /// \brief Returns a random integer from a range |
---|
704 | /// |
---|
705 | /// It returns a random integer from the range {0, 1, ..., b - 1}. |
---|
706 | template <typename Number> |
---|
707 | Number integer(Number b) { |
---|
708 | return _random_bits::Mapping<Number, Word>::map(core, b); |
---|
709 | } |
---|
710 | |
---|
711 | /// \brief Returns a random integer from a range |
---|
712 | /// |
---|
713 | /// It returns a random integer from the range {a, a + 1, ..., b - 1}. |
---|
714 | template <typename Number> |
---|
715 | Number integer(Number a, Number b) { |
---|
716 | return _random_bits::Mapping<Number, Word>::map(core, b - a) + a; |
---|
717 | } |
---|
718 | |
---|
719 | /// \brief Returns a random integer from a range |
---|
720 | /// |
---|
721 | /// It returns a random integer from the range {0, 1, ..., b - 1}. |
---|
722 | template <typename Number> |
---|
723 | Number operator[](Number b) { |
---|
724 | return _random_bits::Mapping<Number, Word>::map(core, b); |
---|
725 | } |
---|
726 | |
---|
727 | /// \brief Returns a random non-negative integer |
---|
728 | /// |
---|
729 | /// It returns a random non-negative integer uniformly from the |
---|
730 | /// whole range of the current \c Number type. The default result |
---|
731 | /// type of this function is <tt>unsigned int</tt>. |
---|
732 | template <typename Number> |
---|
733 | Number uinteger() { |
---|
734 | return _random_bits::IntConversion<Number, Word>::convert(core); |
---|
735 | } |
---|
736 | |
---|
737 | unsigned int uinteger() { |
---|
738 | return uinteger<unsigned int>(); |
---|
739 | } |
---|
740 | |
---|
741 | /// \brief Returns a random integer |
---|
742 | /// |
---|
743 | /// It returns a random integer uniformly from the whole range of |
---|
744 | /// the current \c Number type. The default result type of this |
---|
745 | /// function is \c int. |
---|
746 | template <typename Number> |
---|
747 | Number integer() { |
---|
748 | static const int nb = std::numeric_limits<Number>::digits + |
---|
749 | (std::numeric_limits<Number>::is_signed ? 1 : 0); |
---|
750 | return _random_bits::IntConversion<Number, Word, nb>::convert(core); |
---|
751 | } |
---|
752 | |
---|
753 | int integer() { |
---|
754 | return integer<int>(); |
---|
755 | } |
---|
756 | |
---|
757 | /// \brief Returns a random bool |
---|
758 | /// |
---|
759 | /// It returns a random bool. The generator holds a buffer for |
---|
760 | /// random bits. Every time when it become empty the generator makes |
---|
761 | /// a new random word and fill the buffer up. |
---|
762 | bool boolean() { |
---|
763 | return bool_producer.convert(core); |
---|
764 | } |
---|
765 | |
---|
766 | /// @} |
---|
767 | |
---|
768 | ///\name Non-uniform Distributions |
---|
769 | /// |
---|
770 | ///@{ |
---|
771 | |
---|
772 | /// \brief Returns a random bool with given probability of true result. |
---|
773 | /// |
---|
774 | /// It returns a random bool with given probability of true result. |
---|
775 | bool boolean(double p) { |
---|
776 | return operator()() < p; |
---|
777 | } |
---|
778 | |
---|
779 | /// Standard normal (Gauss) distribution |
---|
780 | |
---|
781 | /// Standard normal (Gauss) distribution. |
---|
782 | /// \note The Cartesian form of the Box-Muller |
---|
783 | /// transformation is used to generate a random normal distribution. |
---|
784 | double gauss() |
---|
785 | { |
---|
786 | double V1,V2,S; |
---|
787 | do { |
---|
788 | V1=2*real<double>()-1; |
---|
789 | V2=2*real<double>()-1; |
---|
790 | S=V1*V1+V2*V2; |
---|
791 | } while(S>=1); |
---|
792 | return std::sqrt(-2*std::log(S)/S)*V1; |
---|
793 | } |
---|
794 | /// Normal (Gauss) distribution with given mean and standard deviation |
---|
795 | |
---|
796 | /// Normal (Gauss) distribution with given mean and standard deviation. |
---|
797 | /// \sa gauss() |
---|
798 | double gauss(double mean,double std_dev) |
---|
799 | { |
---|
800 | return gauss()*std_dev+mean; |
---|
801 | } |
---|
802 | |
---|
803 | /// Lognormal distribution |
---|
804 | |
---|
805 | /// Lognormal distribution. The parameters are the mean and the standard |
---|
806 | /// deviation of <tt>exp(X)</tt>. |
---|
807 | /// |
---|
808 | double lognormal(double n_mean,double n_std_dev) |
---|
809 | { |
---|
810 | return std::exp(gauss(n_mean,n_std_dev)); |
---|
811 | } |
---|
812 | /// Lognormal distribution |
---|
813 | |
---|
814 | /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of |
---|
815 | /// the mean and the standard deviation of <tt>exp(X)</tt>. |
---|
816 | /// |
---|
817 | double lognormal(const std::pair<double,double> ¶ms) |
---|
818 | { |
---|
819 | return std::exp(gauss(params.first,params.second)); |
---|
820 | } |
---|
821 | /// Compute the lognormal parameters from mean and standard deviation |
---|
822 | |
---|
823 | /// This function computes the lognormal parameters from mean and |
---|
824 | /// standard deviation. The return value can direcly be passed to |
---|
825 | /// lognormal(). |
---|
826 | std::pair<double,double> lognormalParamsFromMD(double mean, |
---|
827 | double std_dev) |
---|
828 | { |
---|
829 | double fr=std_dev/mean; |
---|
830 | fr*=fr; |
---|
831 | double lg=std::log(1+fr); |
---|
832 | return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg)); |
---|
833 | } |
---|
834 | /// Lognormal distribution with given mean and standard deviation |
---|
835 | |
---|
836 | /// Lognormal distribution with given mean and standard deviation. |
---|
837 | /// |
---|
838 | double lognormalMD(double mean,double std_dev) |
---|
839 | { |
---|
840 | return lognormal(lognormalParamsFromMD(mean,std_dev)); |
---|
841 | } |
---|
842 | |
---|
843 | /// Exponential distribution with given mean |
---|
844 | |
---|
845 | /// This function generates an exponential distribution random number |
---|
846 | /// with mean <tt>1/lambda</tt>. |
---|
847 | /// |
---|
848 | double exponential(double lambda=1.0) |
---|
849 | { |
---|
850 | return -std::log(1.0-real<double>())/lambda; |
---|
851 | } |
---|
852 | |
---|
853 | /// Gamma distribution with given integer shape |
---|
854 | |
---|
855 | /// This function generates a gamma distribution random number. |
---|
856 | /// |
---|
857 | ///\param k shape parameter (<tt>k>0</tt> integer) |
---|
858 | double gamma(int k) |
---|
859 | { |
---|
860 | double s = 0; |
---|
861 | for(int i=0;i<k;i++) s-=std::log(1.0-real<double>()); |
---|
862 | return s; |
---|
863 | } |
---|
864 | |
---|
865 | /// Gamma distribution with given shape and scale parameter |
---|
866 | |
---|
867 | /// This function generates a gamma distribution random number. |
---|
868 | /// |
---|
869 | ///\param k shape parameter (<tt>k>0</tt>) |
---|
870 | ///\param theta scale parameter |
---|
871 | /// |
---|
872 | double gamma(double k,double theta=1.0) |
---|
873 | { |
---|
874 | double xi,nu; |
---|
875 | const double delta = k-std::floor(k); |
---|
876 | const double v0=E/(E-delta); |
---|
877 | do { |
---|
878 | double V0=1.0-real<double>(); |
---|
879 | double V1=1.0-real<double>(); |
---|
880 | double V2=1.0-real<double>(); |
---|
881 | if(V2<=v0) |
---|
882 | { |
---|
883 | xi=std::pow(V1,1.0/delta); |
---|
884 | nu=V0*std::pow(xi,delta-1.0); |
---|
885 | } |
---|
886 | else |
---|
887 | { |
---|
888 | xi=1.0-std::log(V1); |
---|
889 | nu=V0*std::exp(-xi); |
---|
890 | } |
---|
891 | } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi)); |
---|
892 | return theta*(xi+gamma(int(std::floor(k)))); |
---|
893 | } |
---|
894 | |
---|
895 | /// Weibull distribution |
---|
896 | |
---|
897 | /// This function generates a Weibull distribution random number. |
---|
898 | /// |
---|
899 | ///\param k shape parameter (<tt>k>0</tt>) |
---|
900 | ///\param lambda scale parameter (<tt>lambda>0</tt>) |
---|
901 | /// |
---|
902 | double weibull(double k,double lambda) |
---|
903 | { |
---|
904 | return lambda*pow(-std::log(1.0-real<double>()),1.0/k); |
---|
905 | } |
---|
906 | |
---|
907 | /// Pareto distribution |
---|
908 | |
---|
909 | /// This function generates a Pareto distribution random number. |
---|
910 | /// |
---|
911 | ///\param k shape parameter (<tt>k>0</tt>) |
---|
912 | ///\param x_min location parameter (<tt>x_min>0</tt>) |
---|
913 | /// |
---|
914 | double pareto(double k,double x_min) |
---|
915 | { |
---|
916 | return exponential(gamma(k,1.0/x_min))+x_min; |
---|
917 | } |
---|
918 | |
---|
919 | /// Poisson distribution |
---|
920 | |
---|
921 | /// This function generates a Poisson distribution random number with |
---|
922 | /// parameter \c lambda. |
---|
923 | /// |
---|
924 | /// The probability mass function of this distribusion is |
---|
925 | /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f] |
---|
926 | /// \note The algorithm is taken from the book of Donald E. Knuth titled |
---|
927 | /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the |
---|
928 | /// return value. |
---|
929 | |
---|
930 | int poisson(double lambda) |
---|
931 | { |
---|
932 | const double l = std::exp(-lambda); |
---|
933 | int k=0; |
---|
934 | double p = 1.0; |
---|
935 | do { |
---|
936 | k++; |
---|
937 | p*=real<double>(); |
---|
938 | } while (p>=l); |
---|
939 | return k-1; |
---|
940 | } |
---|
941 | |
---|
942 | ///@} |
---|
943 | |
---|
944 | ///\name Two-Dimensional Distributions |
---|
945 | /// |
---|
946 | ///@{ |
---|
947 | |
---|
948 | /// Uniform distribution on the full unit circle |
---|
949 | |
---|
950 | /// Uniform distribution on the full unit circle. |
---|
951 | /// |
---|
952 | dim2::Point<double> disc() |
---|
953 | { |
---|
954 | double V1,V2; |
---|
955 | do { |
---|
956 | V1=2*real<double>()-1; |
---|
957 | V2=2*real<double>()-1; |
---|
958 | |
---|
959 | } while(V1*V1+V2*V2>=1); |
---|
960 | return dim2::Point<double>(V1,V2); |
---|
961 | } |
---|
962 | /// A kind of two-dimensional normal (Gauss) distribution |
---|
963 | |
---|
964 | /// This function provides a turning symmetric two-dimensional distribution. |
---|
965 | /// Both coordinates are of standard normal distribution, but they are not |
---|
966 | /// independent. |
---|
967 | /// |
---|
968 | /// \note The coordinates are the two random variables provided by |
---|
969 | /// the Box-Muller method. |
---|
970 | dim2::Point<double> gauss2() |
---|
971 | { |
---|
972 | double V1,V2,S; |
---|
973 | do { |
---|
974 | V1=2*real<double>()-1; |
---|
975 | V2=2*real<double>()-1; |
---|
976 | S=V1*V1+V2*V2; |
---|
977 | } while(S>=1); |
---|
978 | double W=std::sqrt(-2*std::log(S)/S); |
---|
979 | return dim2::Point<double>(W*V1,W*V2); |
---|
980 | } |
---|
981 | /// A kind of two-dimensional exponential distribution |
---|
982 | |
---|
983 | /// This function provides a turning symmetric two-dimensional distribution. |
---|
984 | /// The x-coordinate is of conditionally exponential distribution |
---|
985 | /// with the condition that x is positive and y=0. If x is negative and |
---|
986 | /// y=0 then, -x is of exponential distribution. The same is true for the |
---|
987 | /// y-coordinate. |
---|
988 | dim2::Point<double> exponential2() |
---|
989 | { |
---|
990 | double V1,V2,S; |
---|
991 | do { |
---|
992 | V1=2*real<double>()-1; |
---|
993 | V2=2*real<double>()-1; |
---|
994 | S=V1*V1+V2*V2; |
---|
995 | } while(S>=1); |
---|
996 | double W=-std::log(S)/S; |
---|
997 | return dim2::Point<double>(W*V1,W*V2); |
---|
998 | } |
---|
999 | |
---|
1000 | ///@} |
---|
1001 | }; |
---|
1002 | |
---|
1003 | |
---|
1004 | }; |
---|
1005 | |
---|
1006 | /// \ingroup misc |
---|
1007 | /// |
---|
1008 | /// \brief Mersenne Twister random number generator |
---|
1009 | /// |
---|
1010 | /// This class implements either the 32-bit or the 64-bit version of |
---|
1011 | /// the Mersenne Twister random number generator algorithm |
---|
1012 | /// depending on the system architecture. |
---|
1013 | /// |
---|
1014 | /// For the API description, see its base class |
---|
1015 | /// \ref _random_bits::Random. |
---|
1016 | /// |
---|
1017 | /// \sa \ref _random_bits::Random |
---|
1018 | typedef _random_bits::Random<unsigned long> Random; |
---|
1019 | |
---|
1020 | /// \ingroup misc |
---|
1021 | /// |
---|
1022 | /// \brief Mersenne Twister random number generator (32-bit version) |
---|
1023 | /// |
---|
1024 | /// This class implements the 32-bit version of the Mersenne Twister |
---|
1025 | /// random number generator algorithm. It is recommended to be used |
---|
1026 | /// when someone wants to make sure that the \e same pseudo random |
---|
1027 | /// sequence will be generated on every platfrom. |
---|
1028 | /// |
---|
1029 | /// For the API description, see its base class |
---|
1030 | /// \ref _random_bits::Random. |
---|
1031 | /// |
---|
1032 | /// \sa \ref _random_bits::Random |
---|
1033 | typedef _random_bits::Random<unsigned int> Random32; |
---|
1034 | |
---|
1035 | /// \ingroup misc |
---|
1036 | /// |
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1037 | /// \brief Mersenne Twister random number generator (64-bit version) |
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1038 | /// |
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1039 | /// This class implements the 64-bit version of the Mersenne Twister |
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1040 | /// random number generator algorithm. (Even though it runs |
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1041 | /// on 32-bit architectures, too.) It is recommended to be used when |
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1042 | /// someone wants to make sure that the \e same pseudo random sequence |
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1043 | /// will be generated on every platfrom. |
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1044 | /// |
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1045 | /// For the API description, see its base class |
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1046 | /// \ref _random_bits::Random. |
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1047 | /// |
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1048 | /// \sa \ref _random_bits::Random |
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1049 | typedef _random_bits::Random<unsigned long long> Random64; |
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1050 | |
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1051 | extern Random rnd; |
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1052 | |
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1053 | } |
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1054 | |
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1055 | #endif |
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