1 | /* -*- C++ -*- |
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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) 2003-2007 |
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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 <algorithm> |
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66 | #include <iterator> |
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67 | #include <vector> |
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68 | |
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69 | #include <ctime> |
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70 | #include <cmath> |
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71 | |
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72 | #include <lemon/dim2.h> |
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73 | ///\ingroup misc |
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74 | ///\file |
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75 | ///\brief Mersenne Twister random number generator |
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76 | /// |
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77 | ///\author Balazs Dezso |
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78 | |
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79 | namespace lemon { |
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80 | |
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81 | namespace _random_bits { |
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82 | |
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83 | template <typename _Word, int _bits = std::numeric_limits<_Word>::digits> |
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84 | struct RandomTraits {}; |
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85 | |
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86 | template <typename _Word> |
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87 | struct RandomTraits<_Word, 32> { |
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88 | |
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89 | typedef _Word Word; |
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90 | static const int bits = 32; |
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91 | |
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92 | static const int length = 624; |
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93 | static const int shift = 397; |
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94 | |
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95 | static const Word mul = 0x6c078965u; |
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96 | static const Word arrayInit = 0x012BD6AAu; |
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97 | static const Word arrayMul1 = 0x0019660Du; |
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98 | static const Word arrayMul2 = 0x5D588B65u; |
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99 | |
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100 | static const Word mask = 0x9908B0DFu; |
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101 | static const Word loMask = (1u << 31) - 1; |
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102 | static const Word hiMask = ~loMask; |
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103 | |
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104 | |
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105 | static Word tempering(Word rnd) { |
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106 | rnd ^= (rnd >> 11); |
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107 | rnd ^= (rnd << 7) & 0x9D2C5680u; |
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108 | rnd ^= (rnd << 15) & 0xEFC60000u; |
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109 | rnd ^= (rnd >> 18); |
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110 | return rnd; |
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111 | } |
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112 | |
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113 | }; |
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114 | |
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115 | template <typename _Word> |
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116 | struct RandomTraits<_Word, 64> { |
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117 | |
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118 | typedef _Word Word; |
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119 | static const int bits = 64; |
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120 | |
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121 | static const int length = 312; |
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122 | static const int shift = 156; |
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123 | |
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124 | static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du); |
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125 | static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu); |
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126 | static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u); |
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127 | static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu); |
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128 | |
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129 | static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u); |
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130 | static const Word loMask = (Word(1u) << 31) - 1; |
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131 | static const Word hiMask = ~loMask; |
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132 | |
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133 | static Word tempering(Word rnd) { |
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134 | rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u)); |
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135 | rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u)); |
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136 | rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u)); |
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137 | rnd ^= (rnd >> 43); |
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138 | return rnd; |
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139 | } |
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140 | |
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141 | }; |
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142 | |
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143 | template <typename _Word> |
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144 | class RandomCore { |
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145 | public: |
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146 | |
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147 | typedef _Word Word; |
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148 | |
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149 | private: |
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150 | |
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151 | static const int bits = RandomTraits<Word>::bits; |
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152 | |
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153 | static const int length = RandomTraits<Word>::length; |
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154 | static const int shift = RandomTraits<Word>::shift; |
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155 | |
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156 | public: |
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157 | |
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158 | void initState() { |
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159 | static const Word seedArray[4] = { |
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160 | 0x12345u, 0x23456u, 0x34567u, 0x45678u |
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161 | }; |
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162 | |
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163 | initState(seedArray, seedArray + 4); |
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164 | } |
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165 | |
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166 | void initState(Word seed) { |
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167 | |
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168 | static const Word mul = RandomTraits<Word>::mul; |
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169 | |
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170 | current = state; |
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171 | |
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172 | Word *curr = state + length - 1; |
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173 | curr[0] = seed; --curr; |
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174 | for (int i = 1; i < length; ++i) { |
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175 | curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i); |
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176 | --curr; |
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177 | } |
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178 | } |
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179 | |
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180 | template <typename Iterator> |
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181 | void initState(Iterator begin, Iterator end) { |
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182 | |
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183 | static const Word init = RandomTraits<Word>::arrayInit; |
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184 | static const Word mul1 = RandomTraits<Word>::arrayMul1; |
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185 | static const Word mul2 = RandomTraits<Word>::arrayMul2; |
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186 | |
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187 | |
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188 | Word *curr = state + length - 1; --curr; |
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189 | Iterator it = begin; int cnt = 0; |
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190 | int num; |
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191 | |
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192 | initState(init); |
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193 | |
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194 | num = length > end - begin ? length : end - begin; |
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195 | while (num--) { |
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196 | curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) |
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197 | + *it + cnt; |
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198 | ++it; ++cnt; |
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199 | if (it == end) { |
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200 | it = begin; cnt = 0; |
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201 | } |
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202 | if (curr == state) { |
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203 | curr = state + length - 1; curr[0] = state[0]; |
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204 | } |
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205 | --curr; |
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206 | } |
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207 | |
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208 | num = length - 1; cnt = length - (curr - state) - 1; |
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209 | while (num--) { |
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210 | curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2)) |
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211 | - cnt; |
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212 | --curr; ++cnt; |
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213 | if (curr == state) { |
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214 | curr = state + length - 1; curr[0] = state[0]; --curr; |
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215 | cnt = 1; |
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216 | } |
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217 | } |
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218 | |
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219 | state[length - 1] = Word(1) << (bits - 1); |
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220 | } |
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221 | |
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222 | void copyState(const RandomCore& other) { |
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223 | std::copy(other.state, other.state + length, state); |
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224 | current = state + (other.current - other.state); |
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225 | } |
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226 | |
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227 | Word operator()() { |
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228 | if (current == state) fillState(); |
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229 | --current; |
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230 | Word rnd = *current; |
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231 | return RandomTraits<Word>::tempering(rnd); |
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232 | } |
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233 | |
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234 | private: |
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235 | |
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236 | |
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237 | void fillState() { |
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238 | static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask }; |
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239 | static const Word loMask = RandomTraits<Word>::loMask; |
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240 | static const Word hiMask = RandomTraits<Word>::hiMask; |
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241 | |
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242 | current = state + length; |
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243 | |
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244 | register Word *curr = state + length - 1; |
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245 | register long num; |
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246 | |
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247 | num = length - shift; |
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248 | while (num--) { |
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249 | curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ |
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250 | curr[- shift] ^ mask[curr[-1] & 1ul]; |
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251 | --curr; |
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252 | } |
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253 | num = shift - 1; |
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254 | while (num--) { |
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255 | curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ |
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256 | curr[length - shift] ^ mask[curr[-1] & 1ul]; |
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257 | --curr; |
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258 | } |
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259 | curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^ |
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260 | curr[length - shift] ^ mask[curr[length - 1] & 1ul]; |
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261 | |
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262 | } |
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263 | |
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264 | |
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265 | Word *current; |
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266 | Word state[length]; |
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267 | |
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268 | }; |
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269 | |
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270 | |
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271 | template <typename Result, |
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272 | int shift = (std::numeric_limits<Result>::digits + 1) / 2> |
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273 | struct Masker { |
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274 | static Result mask(const Result& result) { |
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275 | return Masker<Result, (shift + 1) / 2>:: |
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276 | mask(static_cast<Result>(result | (result >> shift))); |
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277 | } |
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278 | }; |
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279 | |
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280 | template <typename Result> |
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281 | struct Masker<Result, 1> { |
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282 | static Result mask(const Result& result) { |
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283 | return static_cast<Result>(result | (result >> 1)); |
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284 | } |
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285 | }; |
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286 | |
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287 | template <typename Result, typename Word, |
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288 | int rest = std::numeric_limits<Result>::digits, int shift = 0, |
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289 | bool last = rest <= std::numeric_limits<Word>::digits> |
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290 | struct IntConversion { |
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291 | static const int bits = std::numeric_limits<Word>::digits; |
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292 | |
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293 | static Result convert(RandomCore<Word>& rnd) { |
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294 | return static_cast<Result>(rnd() >> (bits - rest)) << shift; |
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295 | } |
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296 | |
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297 | }; |
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298 | |
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299 | template <typename Result, typename Word, int rest, int shift> |
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300 | struct IntConversion<Result, Word, rest, shift, false> { |
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301 | static const int bits = std::numeric_limits<Word>::digits; |
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302 | |
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303 | static Result convert(RandomCore<Word>& rnd) { |
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304 | return (static_cast<Result>(rnd()) << shift) | |
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305 | IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd); |
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306 | } |
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307 | }; |
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308 | |
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309 | |
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310 | template <typename Result, typename Word, |
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311 | bool one_word = (std::numeric_limits<Word>::digits < |
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312 | std::numeric_limits<Result>::digits) > |
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313 | struct Mapping { |
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314 | static Result map(RandomCore<Word>& rnd, const Result& bound) { |
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315 | Word max = Word(bound - 1); |
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316 | Result mask = Masker<Result>::mask(bound - 1); |
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317 | Result num; |
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318 | do { |
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319 | num = IntConversion<Result, Word>::convert(rnd) & mask; |
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320 | } while (num > max); |
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321 | return num; |
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322 | } |
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323 | }; |
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324 | |
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325 | template <typename Result, typename Word> |
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326 | struct Mapping<Result, Word, false> { |
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327 | static Result map(RandomCore<Word>& rnd, const Result& bound) { |
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328 | Word max = Word(bound - 1); |
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329 | Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2> |
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330 | ::mask(max); |
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331 | Word num; |
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332 | do { |
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333 | num = rnd() & mask; |
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334 | } while (num > max); |
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335 | return num; |
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336 | } |
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337 | }; |
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338 | |
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339 | template <typename Result, int exp, bool pos = (exp >= 0)> |
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340 | struct ShiftMultiplier { |
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341 | static const Result multiplier() { |
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342 | Result res = ShiftMultiplier<Result, exp / 2>::multiplier(); |
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343 | res *= res; |
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344 | if ((exp & 1) == 1) res *= static_cast<Result>(2.0); |
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345 | return res; |
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346 | } |
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347 | }; |
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348 | |
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349 | template <typename Result, int exp> |
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350 | struct ShiftMultiplier<Result, exp, false> { |
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351 | static const Result multiplier() { |
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352 | Result res = ShiftMultiplier<Result, exp / 2>::multiplier(); |
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353 | res *= res; |
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354 | if ((exp & 1) == 1) res *= static_cast<Result>(0.5); |
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355 | return res; |
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356 | } |
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357 | }; |
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358 | |
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359 | template <typename Result> |
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360 | struct ShiftMultiplier<Result, 0, true> { |
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361 | static const Result multiplier() { |
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362 | return static_cast<Result>(1.0); |
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363 | } |
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364 | }; |
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365 | |
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366 | template <typename Result> |
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367 | struct ShiftMultiplier<Result, -20, true> { |
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368 | static const Result multiplier() { |
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369 | return static_cast<Result>(1.0/1048576.0); |
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370 | } |
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371 | }; |
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372 | |
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373 | template <typename Result> |
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374 | struct ShiftMultiplier<Result, -32, true> { |
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375 | static const Result multiplier() { |
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376 | return static_cast<Result>(1.0/424967296.0); |
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377 | } |
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378 | }; |
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379 | |
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380 | template <typename Result> |
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381 | struct ShiftMultiplier<Result, -53, true> { |
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382 | static const Result multiplier() { |
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383 | return static_cast<Result>(1.0/9007199254740992.0); |
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384 | } |
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385 | }; |
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386 | |
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387 | template <typename Result> |
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388 | struct ShiftMultiplier<Result, -64, true> { |
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389 | static const Result multiplier() { |
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390 | return static_cast<Result>(1.0/18446744073709551616.0); |
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391 | } |
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392 | }; |
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393 | |
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394 | template <typename Result, int exp> |
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395 | struct Shifting { |
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396 | static Result shift(const Result& result) { |
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397 | return result * ShiftMultiplier<Result, exp>::multiplier(); |
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398 | } |
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399 | }; |
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400 | |
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401 | template <typename Result, typename Word, |
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402 | int rest = std::numeric_limits<Result>::digits, int shift = 0, |
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403 | bool last = rest <= std::numeric_limits<Word>::digits> |
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404 | struct RealConversion{ |
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405 | static const int bits = std::numeric_limits<Word>::digits; |
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406 | |
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407 | static Result convert(RandomCore<Word>& rnd) { |
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408 | return Shifting<Result, - shift - rest>:: |
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409 | shift(static_cast<Result>(rnd() >> (bits - rest))); |
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410 | } |
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411 | }; |
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412 | |
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413 | template <typename Result, typename Word, int rest, int shift> |
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414 | struct RealConversion<Result, Word, rest, shift, false> { |
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415 | static const int bits = std::numeric_limits<Word>::digits; |
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416 | |
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417 | static Result convert(RandomCore<Word>& rnd) { |
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418 | return Shifting<Result, - shift - bits>:: |
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419 | shift(static_cast<Result>(rnd())) + |
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420 | RealConversion<Result, Word, rest-bits, shift + bits>:: |
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421 | convert(rnd); |
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422 | } |
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423 | }; |
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424 | |
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425 | template <typename Result, typename Word> |
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426 | struct Initializer { |
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427 | |
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428 | template <typename Iterator> |
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429 | static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) { |
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430 | std::vector<Word> ws; |
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431 | for (Iterator it = begin; it != end; ++it) { |
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432 | ws.push_back(Word(*it)); |
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433 | } |
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434 | rnd.initState(ws.begin(), ws.end()); |
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435 | } |
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436 | |
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437 | static void init(RandomCore<Word>& rnd, Result seed) { |
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438 | rnd.initState(seed); |
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439 | } |
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440 | }; |
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441 | |
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442 | template <typename Word> |
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443 | struct BoolConversion { |
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444 | static bool convert(RandomCore<Word>& rnd) { |
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445 | return (rnd() & 1) == 1; |
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446 | } |
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447 | }; |
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448 | |
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449 | template <typename Word> |
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450 | struct BoolProducer { |
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451 | Word buffer; |
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452 | int num; |
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453 | |
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454 | BoolProducer() : num(0) {} |
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455 | |
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456 | bool convert(RandomCore<Word>& rnd) { |
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457 | if (num == 0) { |
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458 | buffer = rnd(); |
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459 | num = RandomTraits<Word>::bits; |
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460 | } |
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461 | bool r = (buffer & 1); |
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462 | buffer >>= 1; |
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463 | --num; |
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464 | return r; |
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465 | } |
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466 | }; |
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467 | |
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468 | } |
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469 | |
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470 | /// \ingroup misc |
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471 | /// |
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472 | /// \brief Mersenne Twister random number generator |
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473 | /// |
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474 | /// The Mersenne Twister is a twisted generalized feedback |
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475 | /// shift-register generator of Matsumoto and Nishimura. The period |
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476 | /// of this generator is \f$ 2^{19937} - 1 \f$ and it is |
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477 | /// equi-distributed in 623 dimensions for 32-bit numbers. The time |
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478 | /// performance of this generator is comparable to the commonly used |
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479 | /// generators. |
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480 | /// |
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481 | /// This implementation is specialized for both 32-bit and 64-bit |
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482 | /// architectures. The generators differ sligthly in the |
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483 | /// initialization and generation phase so they produce two |
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484 | /// completly different sequences. |
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485 | /// |
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486 | /// The generator gives back random numbers of serveral types. To |
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487 | /// get a random number from a range of a floating point type you |
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488 | /// can use one form of the \c operator() or the \c real() member |
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489 | /// function. If you want to get random number from the {0, 1, ..., |
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490 | /// n-1} integer range use the \c operator[] or the \c integer() |
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491 | /// method. And to get random number from the whole range of an |
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492 | /// integer type you can use the argumentless \c integer() or \c |
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493 | /// uinteger() functions. After all you can get random bool with |
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494 | /// equal chance of true and false or given probability of true |
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495 | /// result with the \c boolean() member functions. |
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496 | /// |
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497 | ///\code |
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498 | /// // The commented code is identical to the other |
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499 | /// double a = rnd(); // [0.0, 1.0) |
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500 | /// // double a = rnd.real(); // [0.0, 1.0) |
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501 | /// double b = rnd(100.0); // [0.0, 100.0) |
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502 | /// // double b = rnd.real(100.0); // [0.0, 100.0) |
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503 | /// double c = rnd(1.0, 2.0); // [1.0, 2.0) |
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504 | /// // double c = rnd.real(1.0, 2.0); // [1.0, 2.0) |
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505 | /// int d = rnd[100000]; // 0..99999 |
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506 | /// // int d = rnd.integer(100000); // 0..99999 |
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507 | /// int e = rnd[6] + 1; // 1..6 |
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508 | /// // int e = rnd.integer(1, 1 + 6); // 1..6 |
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509 | /// int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1 |
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510 | /// int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1 |
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511 | /// bool g = rnd.boolean(); // P(g = true) = 0.5 |
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512 | /// bool h = rnd.boolean(0.8); // P(h = true) = 0.8 |
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513 | ///\endcode |
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514 | /// |
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515 | /// The lemon provides a global instance of the random number |
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516 | /// generator which name is \ref lemon::rnd "rnd". Usually it is a |
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517 | /// good programming convenience to use this global generator to get |
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518 | /// random numbers. |
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519 | /// |
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520 | /// \author Balazs Dezso |
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521 | class Random { |
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522 | private: |
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523 | |
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524 | // architecture word |
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525 | typedef unsigned long Word; |
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526 | |
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527 | _random_bits::RandomCore<Word> core; |
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528 | _random_bits::BoolProducer<Word> bool_producer; |
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529 | |
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530 | |
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531 | public: |
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532 | |
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533 | /// \brief Constructor |
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534 | /// |
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535 | /// Constructor with constant seeding. |
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536 | Random() { core.initState(); } |
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537 | |
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538 | /// \brief Constructor |
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539 | /// |
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540 | /// Constructor with seed. The current number type will be converted |
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541 | /// to the architecture word type. |
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542 | template <typename Number> |
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543 | Random(Number seed) { |
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544 | _random_bits::Initializer<Number, Word>::init(core, seed); |
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545 | } |
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546 | |
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547 | /// \brief Constructor |
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548 | /// |
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549 | /// Constructor with array seeding. The given range should contain |
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550 | /// any number type and the numbers will be converted to the |
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551 | /// architecture word type. |
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552 | template <typename Iterator> |
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553 | Random(Iterator begin, Iterator end) { |
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554 | typedef typename std::iterator_traits<Iterator>::value_type Number; |
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555 | _random_bits::Initializer<Number, Word>::init(core, begin, end); |
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556 | } |
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557 | |
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558 | /// \brief Copy constructor |
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559 | /// |
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560 | /// Copy constructor. The generated sequence will be identical to |
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561 | /// the other sequence. It can be used to save the current state |
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562 | /// of the generator and later use it to generate the same |
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563 | /// sequence. |
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564 | Random(const Random& other) { |
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565 | core.copyState(other.core); |
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566 | } |
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567 | |
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568 | /// \brief Assign operator |
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569 | /// |
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570 | /// Assign operator. The generated sequence will be identical to |
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571 | /// the other sequence. It can be used to save the current state |
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572 | /// of the generator and later use it to generate the same |
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573 | /// sequence. |
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574 | Random& operator=(const Random& other) { |
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575 | if (&other != this) { |
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576 | core.copyState(other.core); |
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577 | } |
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578 | return *this; |
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579 | } |
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580 | |
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581 | /// \brief Returns a random real number from the range [0, 1) |
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582 | /// |
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583 | /// It returns a random real number from the range [0, 1). The |
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584 | /// default Number type is double. |
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585 | template <typename Number> |
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586 | Number real() { |
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587 | return _random_bits::RealConversion<Number, Word>::convert(core); |
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588 | } |
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589 | |
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590 | double real() { |
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591 | return real<double>(); |
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592 | } |
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593 | |
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594 | /// \brief Returns a random real number the range [0, b) |
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595 | /// |
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596 | /// It returns a random real number from the range [0, b). |
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597 | template <typename Number> |
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598 | Number real(Number b) { |
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599 | return real<Number>() * b; |
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600 | } |
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601 | |
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602 | /// \brief Returns a random real number from the range [a, b) |
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603 | /// |
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604 | /// It returns a random real number from the range [a, b). |
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605 | template <typename Number> |
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606 | Number real(Number a, Number b) { |
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607 | return real<Number>() * (b - a) + a; |
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608 | } |
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609 | |
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610 | /// \brief Returns a random real number from the range [0, 1) |
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611 | /// |
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612 | /// It returns a random double from the range [0, 1). |
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613 | double operator()() { |
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614 | return real<double>(); |
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615 | } |
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616 | |
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617 | /// \brief Returns a random real number from the range [0, b) |
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618 | /// |
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619 | /// It returns a random real number from the range [0, b). |
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620 | template <typename Number> |
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621 | Number operator()(Number b) { |
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622 | return real<Number>() * b; |
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623 | } |
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624 | |
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625 | /// \brief Returns a random real number from the range [a, b) |
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626 | /// |
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627 | /// It returns a random real number from the range [a, b). |
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628 | template <typename Number> |
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629 | Number operator()(Number a, Number b) { |
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630 | return real<Number>() * (b - a) + a; |
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631 | } |
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632 | |
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633 | /// \brief Returns a random integer from a range |
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634 | /// |
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635 | /// It returns a random integer from the range {0, 1, ..., b - 1}. |
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636 | template <typename Number> |
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637 | Number integer(Number b) { |
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638 | return _random_bits::Mapping<Number, Word>::map(core, b); |
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639 | } |
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640 | |
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641 | /// \brief Returns a random integer from a range |
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642 | /// |
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643 | /// It returns a random integer from the range {a, a + 1, ..., b - 1}. |
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644 | template <typename Number> |
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645 | Number integer(Number a, Number b) { |
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646 | return _random_bits::Mapping<Number, Word>::map(core, b - a) + a; |
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647 | } |
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648 | |
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649 | /// \brief Returns a random integer from a range |
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650 | /// |
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651 | /// It returns a random integer from the range {0, 1, ..., b - 1}. |
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652 | template <typename Number> |
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653 | Number operator[](Number b) { |
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654 | return _random_bits::Mapping<Number, Word>::map(core, b); |
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655 | } |
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656 | |
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657 | /// \brief Returns a random non-negative integer |
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658 | /// |
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659 | /// It returns a random non-negative integer uniformly from the |
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660 | /// whole range of the current \c Number type. The default result |
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661 | /// type of this function is unsigned int. |
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662 | template <typename Number> |
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663 | Number uinteger() { |
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664 | return _random_bits::IntConversion<Number, Word>::convert(core); |
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665 | } |
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666 | |
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667 | unsigned int uinteger() { |
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668 | return uinteger<unsigned int>(); |
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669 | } |
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670 | |
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671 | /// \brief Returns a random integer |
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672 | /// |
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673 | /// It returns a random integer uniformly from the whole range of |
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674 | /// the current \c Number type. The default result type of this |
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675 | /// function is int. |
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676 | template <typename Number> |
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677 | Number integer() { |
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678 | static const int nb = std::numeric_limits<Number>::digits + |
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679 | (std::numeric_limits<Number>::is_signed ? 1 : 0); |
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680 | return _random_bits::IntConversion<Number, Word, nb>::convert(core); |
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681 | } |
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682 | |
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683 | int integer() { |
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684 | return integer<int>(); |
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685 | } |
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686 | |
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687 | /// \brief Returns a random bool |
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688 | /// |
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689 | /// It returns a random bool. The generator holds a buffer for |
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690 | /// random bits. Every time when it become empty the generator makes |
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691 | /// a new random word and fill the buffer up. |
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692 | bool boolean() { |
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693 | return bool_producer.convert(core); |
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694 | } |
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695 | |
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696 | ///\name Nonuniform distributions |
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697 | /// |
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698 | |
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699 | ///@{ |
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700 | |
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701 | /// \brief Returns a random bool |
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702 | /// |
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703 | /// It returns a random bool with given probability of true result |
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704 | bool boolean(double p) { |
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705 | return operator()() < p; |
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706 | } |
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707 | |
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708 | /// Standard Gauss distribution |
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709 | |
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710 | /// Standard Gauss distribution. |
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711 | /// \note The Cartesian form of the Box-Muller |
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712 | /// transformation is used to generate a random normal distribution. |
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713 | /// \todo Consider using the "ziggurat" method instead. |
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714 | double gauss() |
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715 | { |
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716 | double V1,V2,S; |
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717 | do { |
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718 | V1=2*real<double>()-1; |
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719 | V2=2*real<double>()-1; |
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720 | S=V1*V1+V2*V2; |
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721 | } while(S>=1); |
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722 | return std::sqrt(-2*std::log(S)/S)*V1; |
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723 | } |
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724 | /// Gauss distribution with given mean and standard deviation |
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725 | |
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726 | /// \sa gauss() |
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727 | /// |
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728 | double gauss(double mean,double std_dev) |
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729 | { |
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730 | return gauss()*std_dev+mean; |
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731 | } |
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732 | |
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733 | /// Exponential distribution with given mean |
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734 | |
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735 | /// This function generates an exponential distribution random number |
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736 | /// with mean <tt>1/lambda</tt>. |
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737 | /// |
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738 | double exponential(double lambda=1.0) |
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739 | { |
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740 | return -std::log(1.0-real<double>())/lambda; |
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741 | } |
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742 | |
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743 | /// Gamma distribution with given integer shape |
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744 | |
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745 | /// This function generates a gamma distribution random number. |
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746 | /// |
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747 | ///\param k shape parameter (<tt>k>0</tt> integer) |
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748 | double gamma(int k) |
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749 | { |
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750 | double s = 0; |
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751 | for(int i=0;i<k;i++) s-=std::log(1.0-real<double>()); |
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752 | return s; |
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753 | } |
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754 | |
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755 | /// Gamma distribution with given shape and scale parameter |
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756 | |
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757 | /// This function generates a gamma distribution random number. |
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758 | /// |
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759 | ///\param k shape parameter (<tt>k>0</tt>) |
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760 | ///\param theta scale parameter |
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761 | /// |
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762 | double gamma(double k,double theta=1.0) |
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763 | { |
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764 | double xi,nu; |
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765 | const double delta = k-std::floor(k); |
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766 | const double v0=M_E/(M_E-delta); |
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767 | do { |
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768 | double V0=1.0-real<double>(); |
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769 | double V1=1.0-real<double>(); |
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770 | double V2=1.0-real<double>(); |
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771 | if(V2<=v0) |
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772 | { |
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773 | xi=std::pow(V1,1.0/delta); |
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774 | nu=V0*std::pow(xi,delta-1.0); |
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775 | } |
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776 | else |
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777 | { |
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778 | xi=1.0-std::log(V1); |
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779 | nu=V0*std::exp(-xi); |
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780 | } |
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781 | } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi)); |
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782 | return theta*(xi-gamma(int(std::floor(k)))); |
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783 | } |
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784 | |
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785 | /// Weibull distribution |
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786 | |
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787 | /// This function generates a Weibull distribution random number. |
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788 | /// |
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789 | ///\param k shape parameter (<tt>k>0</tt>) |
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790 | ///\param lambda scale parameter (<tt>lambda>0</tt>) |
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791 | /// |
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792 | double weibull(double k,double lambda) |
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793 | { |
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794 | return lambda*pow(-std::log(1.0-real<double>()),1.0/k); |
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795 | } |
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796 | |
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797 | /// Pareto distribution |
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798 | |
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799 | /// This function generates a Pareto distribution random number. |
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800 | /// |
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801 | ///\param x_min location parameter (<tt>x_min>0</tt>) |
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802 | ///\param k shape parameter (<tt>k>0</tt>) |
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803 | /// |
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804 | ///\warning This function used inverse transform sampling, therefore may |
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805 | ///suffer from numerical unstability. |
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806 | /// |
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807 | ///\todo Implement a numerically stable method |
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808 | double pareto(double x_min,double k) |
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809 | { |
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810 | return x_min*pow(1.0-real<double>(),1.0/k); |
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811 | } |
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812 | |
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813 | ///@} |
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814 | |
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815 | ///\name Two dimensional distributions |
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816 | /// |
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817 | |
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818 | ///@{ |
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819 | |
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820 | /// Uniform distribution on the full unit circle. |
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821 | dim2::Point<double> disc() |
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822 | { |
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823 | double V1,V2; |
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824 | do { |
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825 | V1=2*real<double>()-1; |
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826 | V2=2*real<double>()-1; |
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827 | |
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828 | } while(V1*V1+V2*V2>=1); |
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829 | return dim2::Point<double>(V1,V2); |
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830 | } |
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831 | /// A kind of two dimensional Gauss distribution |
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832 | |
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833 | /// This function provides a turning symmetric two-dimensional distribution. |
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834 | /// Both coordinates are of standard normal distribution, but they are not |
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835 | /// independent. |
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836 | /// |
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837 | /// \note The coordinates are the two random variables provided by |
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838 | /// the Box-Muller method. |
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839 | dim2::Point<double> gauss2() |
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840 | { |
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841 | double V1,V2,S; |
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842 | do { |
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843 | V1=2*real<double>()-1; |
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844 | V2=2*real<double>()-1; |
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845 | S=V1*V1+V2*V2; |
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846 | } while(S>=1); |
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847 | double W=std::sqrt(-2*std::log(S)/S); |
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848 | return dim2::Point<double>(W*V1,W*V2); |
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849 | } |
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850 | /// A kind of two dimensional exponential distribution |
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851 | |
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852 | /// This function provides a turning symmetric two-dimensional distribution. |
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853 | /// The x-coordinate is of conditionally exponential distribution |
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854 | /// with the condition that x is positive and y=0. If x is negative and |
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855 | /// y=0 then, -x is of exponential distribution. The same is true for the |
---|
856 | /// y-coordinate. |
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857 | dim2::Point<double> exponential2() |
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858 | { |
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859 | double V1,V2,S; |
---|
860 | do { |
---|
861 | V1=2*real<double>()-1; |
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862 | V2=2*real<double>()-1; |
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863 | S=V1*V1+V2*V2; |
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864 | } while(S>=1); |
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865 | double W=-std::log(S)/S; |
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866 | return dim2::Point<double>(W*V1,W*V2); |
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867 | } |
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868 | |
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869 | ///@} |
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870 | }; |
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871 | |
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872 | |
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873 | extern Random rnd; |
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874 | |
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875 | } |
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876 | |
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877 | #endif |
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