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) 2003-2006 |
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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 | #ifndef LEMON_RANDOM_H |
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20 | #define LEMON_RANDOM_H |
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21 | |
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22 | #include <algorithm> |
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23 | #include <iterator> |
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24 | #include <vector> |
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25 | |
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26 | #include <ctime> |
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27 | #include <cmath> |
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28 | |
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29 | ///\ingroup misc |
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30 | ///\file |
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31 | ///\brief Mersenne Twister random number generator |
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32 | /// |
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33 | ///\author Balazs Dezso |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | namespace _random_bits { |
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38 | |
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39 | template <typename _Word, int _bits = std::numeric_limits<_Word>::digits> |
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40 | struct RandomTraits {}; |
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41 | |
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42 | template <typename _Word> |
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43 | struct RandomTraits<_Word, 32> { |
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44 | |
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45 | typedef _Word Word; |
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46 | static const int bits = 32; |
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47 | |
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48 | static const int length = 624; |
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49 | static const int shift = 397; |
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50 | |
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51 | static const Word mul = 0x6c078965u; |
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52 | static const Word arrayInit = 0x012BD6AAu; |
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53 | static const Word arrayMul1 = 0x0019660Du; |
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54 | static const Word arrayMul2 = 0x5D588B65u; |
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55 | |
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56 | static const Word mask = 0x9908B0DFu; |
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57 | static const Word loMask = (1u << 31) - 1; |
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58 | static const Word hiMask = ~loMask; |
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59 | |
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60 | |
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61 | static Word tempering(Word rnd) { |
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62 | rnd ^= (rnd >> 11); |
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63 | rnd ^= (rnd << 7) & 0x9D2C5680u; |
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64 | rnd ^= (rnd << 15) & 0xEFC60000u; |
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65 | rnd ^= (rnd >> 18); |
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66 | return rnd; |
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67 | } |
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68 | |
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69 | }; |
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70 | |
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71 | template <typename _Word> |
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72 | struct RandomTraits<_Word, 64> { |
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73 | |
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74 | typedef _Word Word; |
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75 | static const int bits = 64; |
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76 | |
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77 | static const int length = 312; |
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78 | static const int shift = 156; |
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79 | |
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80 | static const Word mul = (Word)0x5851F42Du << 32 | (Word)0x4C957F2Du; |
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81 | static const Word arrayInit = (Word)0x00000000u << 32 |(Word)0x012BD6AAu; |
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82 | static const Word arrayMul1 = (Word)0x369DEA0Fu << 32 |(Word)0x31A53F85u; |
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83 | static const Word arrayMul2 = (Word)0x27BB2EE6u << 32 |(Word)0x87B0B0FDu; |
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84 | |
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85 | static const Word mask = (Word)0xB5026F5Au << 32 | (Word)0xA96619E9u; |
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86 | static const Word loMask = ((Word)1u << 31) - 1; |
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87 | static const Word hiMask = ~loMask; |
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88 | |
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89 | static Word tempering(Word rnd) { |
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90 | rnd ^= (rnd >> 29) & ((Word)0x55555555u << 32 | (Word)0x55555555u); |
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91 | rnd ^= (rnd << 17) & ((Word)0x71D67FFFu << 32 | (Word)0xEDA60000u); |
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92 | rnd ^= (rnd << 37) & ((Word)0xFFF7EEE0u << 32 | (Word)0x00000000u); |
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93 | rnd ^= (rnd >> 43); |
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94 | return rnd; |
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95 | } |
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96 | |
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97 | }; |
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98 | |
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99 | template <typename _Word> |
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100 | class RandomCore { |
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101 | public: |
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102 | |
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103 | typedef _Word Word; |
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104 | |
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105 | private: |
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106 | |
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107 | static const int bits = RandomTraits<Word>::bits; |
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108 | |
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109 | static const int length = RandomTraits<Word>::length; |
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110 | static const int shift = RandomTraits<Word>::shift; |
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111 | |
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112 | public: |
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113 | |
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114 | void initState() { |
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115 | static const Word seedArray[4] = { |
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116 | 0x12345u, 0x23456u, 0x34567u, 0x45678u |
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117 | }; |
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118 | |
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119 | initState(seedArray, seedArray + 4); |
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120 | } |
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121 | |
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122 | void initState(Word seed) { |
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123 | |
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124 | static const Word mul = RandomTraits<Word>::mul; |
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125 | |
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126 | current = state; |
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127 | |
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128 | Word *curr = state + length - 1; |
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129 | curr[0] = seed; --curr; |
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130 | for (int i = 1; i < length; ++i) { |
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131 | curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i); |
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132 | --curr; |
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133 | } |
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134 | } |
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135 | |
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136 | template <typename Iterator> |
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137 | void initState(Iterator begin, Iterator end) { |
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138 | |
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139 | static const Word init = RandomTraits<Word>::arrayInit; |
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140 | static const Word mul1 = RandomTraits<Word>::arrayMul1; |
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141 | static const Word mul2 = RandomTraits<Word>::arrayMul2; |
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142 | |
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143 | |
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144 | Word *curr = state + length - 1; --curr; |
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145 | Iterator it = begin; int cnt = 0; |
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146 | int num; |
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147 | |
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148 | initState(init); |
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149 | |
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150 | num = length > end - begin ? length : end - begin; |
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151 | while (num--) { |
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152 | curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) |
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153 | + *it + cnt; |
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154 | ++it; ++cnt; |
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155 | if (it == end) { |
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156 | it = begin; cnt = 0; |
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157 | } |
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158 | if (curr == state) { |
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159 | curr = state + length - 1; curr[0] = state[0]; |
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160 | } |
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161 | --curr; |
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162 | } |
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163 | |
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164 | num = length - 1; cnt = length - (curr - state) - 1; |
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165 | while (num--) { |
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166 | curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2)) |
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167 | - cnt; |
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168 | --curr; ++cnt; |
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169 | if (curr == state) { |
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170 | curr = state + length - 1; curr[0] = state[0]; --curr; |
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171 | cnt = 1; |
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172 | } |
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173 | } |
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174 | |
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175 | state[length - 1] = (Word)1 << (bits - 1); |
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176 | } |
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177 | |
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178 | void copyState(const RandomCore& other) { |
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179 | std::copy(other.state, other.state + length, state); |
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180 | current = state + (other.current - other.state); |
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181 | } |
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182 | |
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183 | Word operator()() { |
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184 | if (current == state) fillState(); |
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185 | --current; |
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186 | Word rnd = *current; |
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187 | return RandomTraits<Word>::tempering(rnd); |
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188 | } |
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189 | |
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190 | private: |
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191 | |
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192 | |
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193 | void fillState() { |
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194 | static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask }; |
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195 | static const Word loMask = RandomTraits<Word>::loMask; |
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196 | static const Word hiMask = RandomTraits<Word>::hiMask; |
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197 | |
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198 | current = state + length; |
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199 | |
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200 | register Word *curr = state + length - 1; |
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201 | register long num; |
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202 | |
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203 | num = length - shift; |
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204 | while (num--) { |
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205 | curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ |
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206 | curr[- shift] ^ mask[curr[-1] & 1ul]; |
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207 | --curr; |
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208 | } |
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209 | num = shift - 1; |
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210 | while (num--) { |
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211 | curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ |
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212 | curr[length - shift] ^ mask[curr[-1] & 1ul]; |
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213 | --curr; |
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214 | } |
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215 | curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^ |
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216 | curr[length - shift] ^ mask[curr[length - 1] & 1ul]; |
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217 | |
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218 | } |
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219 | |
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220 | |
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221 | Word *current; |
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222 | Word state[length]; |
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223 | |
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224 | }; |
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225 | |
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226 | |
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227 | template <typename Result, |
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228 | int shift = (std::numeric_limits<Result>::digits + 1) / 2> |
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229 | struct Masker { |
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230 | static Result mask(const Result& result) { |
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231 | return Masker<Result, (shift + 1) / 2>:: |
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232 | mask((Result)(result | (result >> shift))); |
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233 | } |
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234 | }; |
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235 | |
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236 | template <typename Result> |
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237 | struct Masker<Result, 1> { |
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238 | static Result mask(const Result& result) { |
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239 | return (Result)(result | (result >> 1)); |
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240 | } |
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241 | }; |
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242 | |
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243 | template <typename Result, typename Word, |
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244 | int rest = std::numeric_limits<Result>::digits, int shift = 0, |
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245 | bool last = rest <= std::numeric_limits<Word>::digits> |
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246 | struct IntConversion { |
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247 | static const int bits = std::numeric_limits<Word>::digits; |
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248 | |
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249 | static Result convert(RandomCore<Word>& rnd) { |
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250 | return (Result)(rnd() >> (bits - rest)) << shift; |
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251 | } |
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252 | |
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253 | }; |
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254 | |
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255 | template <typename Result, typename Word, int rest, int shift> |
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256 | struct IntConversion<Result, Word, rest, shift, false> { |
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257 | static const int bits = std::numeric_limits<Word>::digits; |
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258 | |
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259 | static Result convert(RandomCore<Word>& rnd) { |
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260 | return ((Result)rnd() << shift) | |
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261 | IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd); |
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262 | } |
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263 | }; |
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264 | |
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265 | |
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266 | template <typename Result, typename Word, |
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267 | bool one_word = std::numeric_limits<Word>::digits < |
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268 | std::numeric_limits<Result>::digits> |
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269 | struct Mapping { |
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270 | static Result map(RandomCore<Word>& rnd, const Result& bound) { |
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271 | Word max = (Word)(bound - 1); |
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272 | Result mask = Masker<Result>::mask(bound - 1); |
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273 | Result num; |
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274 | do { |
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275 | num = IntConversion<Result, Word>::convert(rnd) & mask; |
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276 | } while (num > max); |
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277 | return num; |
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278 | } |
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279 | }; |
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280 | |
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281 | template <typename Result, typename Word> |
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282 | struct Mapping<Result, Word, false> { |
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283 | static Result map(RandomCore<Word>& rnd, const Result& bound) { |
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284 | Word max = (Word)(bound - 1); |
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285 | Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2> |
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286 | ::mask(max); |
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287 | Word num; |
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288 | do { |
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289 | num = rnd() & mask; |
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290 | } while (num > max); |
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291 | return num; |
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292 | } |
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293 | }; |
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294 | |
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295 | template <typename Result, int exp, bool pos = (exp >= 0)> |
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296 | struct ShiftMultiplier { |
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297 | static const Result multiplier() { |
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298 | Result res = ShiftMultiplier<Result, exp / 2>::multiplier(); |
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299 | res *= res; |
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300 | if ((exp & 1) == 1) res *= (Result)2.0; |
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301 | return res; |
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302 | } |
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303 | }; |
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304 | |
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305 | template <typename Result, int exp> |
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306 | struct ShiftMultiplier<Result, exp, false> { |
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307 | static const Result multiplier() { |
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308 | Result res = ShiftMultiplier<Result, exp / 2>::multiplier(); |
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309 | res *= res; |
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310 | if ((exp & 1) == 1) res *= (Result)0.5; |
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311 | return res; |
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312 | } |
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313 | }; |
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314 | |
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315 | template <typename Result> |
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316 | struct ShiftMultiplier<Result, 0, true> { |
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317 | static const Result multiplier() { |
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318 | return (Result)1.0; |
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319 | } |
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320 | }; |
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321 | |
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322 | template <typename Result> |
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323 | struct ShiftMultiplier<Result, -20, true> { |
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324 | static const Result multiplier() { |
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325 | return (Result)(1.0/1048576.0); |
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326 | } |
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327 | }; |
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328 | |
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329 | template <typename Result> |
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330 | struct ShiftMultiplier<Result, -32, true> { |
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331 | static const Result multiplier() { |
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332 | return (Result)(1.0/424967296.0); |
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333 | } |
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334 | }; |
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335 | |
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336 | template <typename Result> |
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337 | struct ShiftMultiplier<Result, -53, true> { |
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338 | static const Result multiplier() { |
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339 | return (Result)(1.0/9007199254740992.0); |
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340 | } |
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341 | }; |
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342 | |
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343 | template <typename Result> |
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344 | struct ShiftMultiplier<Result, -64, true> { |
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345 | static const Result multiplier() { |
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346 | return (Result)(1.0/18446744073709551616.0); |
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347 | } |
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348 | }; |
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349 | |
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350 | template <typename Result, int exp> |
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351 | struct Shifting { |
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352 | static Result shift(const Result& result) { |
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353 | return result * ShiftMultiplier<Result, exp>::multiplier(); |
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354 | } |
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355 | }; |
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356 | |
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357 | template <typename Result, typename Word, |
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358 | int rest = std::numeric_limits<Result>::digits, int shift = 0, |
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359 | bool last = rest <= std::numeric_limits<Word>::digits> |
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360 | struct RealConversion{ |
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361 | static const int bits = std::numeric_limits<Word>::digits; |
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362 | |
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363 | static Result convert(RandomCore<Word>& rnd) { |
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364 | return Shifting<Result, - shift - rest>:: |
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365 | shift((Result)(rnd() >> (bits - rest))); |
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366 | } |
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367 | }; |
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368 | |
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369 | template <typename Result, typename Word, int rest, int shift> |
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370 | struct RealConversion<Result, Word, rest, shift, false> { |
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371 | static const int bits = std::numeric_limits<Word>::digits; |
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372 | |
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373 | static Result convert(RandomCore<Word>& rnd) { |
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374 | return Shifting<Result, - shift - bits>::shift((Result)rnd()) + |
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375 | RealConversion<Result, Word, rest-bits, shift + bits>::convert(rnd); |
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376 | } |
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377 | }; |
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378 | |
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379 | template <typename Result, typename Word> |
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380 | struct Initializer { |
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381 | |
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382 | template <typename Iterator> |
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383 | static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) { |
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384 | std::vector<Word> ws; |
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385 | for (Iterator it = begin; it != end; ++it) { |
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386 | ws.push_back((Word)*it); |
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387 | } |
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388 | rnd.initState(ws.begin(), ws.end()); |
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389 | } |
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390 | |
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391 | static void init(RandomCore<Word>& rnd, Result seed) { |
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392 | rnd.initState(seed); |
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393 | } |
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394 | }; |
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395 | |
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396 | template <typename Word> |
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397 | struct BoolConversion { |
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398 | static bool convert(RandomCore<Word>& rnd) { |
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399 | return (rnd() & 1) == 1; |
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400 | } |
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401 | }; |
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402 | |
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403 | } |
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404 | |
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405 | /// \ingroup misc |
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406 | /// |
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407 | /// \brief Mersenne Twister random number generator |
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408 | /// |
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409 | /// The Mersenne Twister is a twisted generalized feedback |
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410 | /// shift-register generator of Matsumoto and Nishimura. The period |
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411 | /// of this generator is \f$ 2^{19937} - 1 \f$ and it is |
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412 | /// equi-distributed in 623 dimensions for 32-bit numbers. The time |
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413 | /// performance of this generator is comparable to the commonly used |
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414 | /// generators. |
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415 | /// |
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416 | /// This implementation is specialized for both 32-bit and 64-bit |
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417 | /// architectures. The generators differ sligthly in the |
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418 | /// initialization and generation phase so they produce two |
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419 | /// completly different sequences. |
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420 | /// |
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421 | /// The generator gives back random numbers of serveral types. To |
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422 | /// get a random number from a range of a floating point type you |
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423 | /// can use one form of the \c operator() or the \c real() member |
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424 | /// function. If you want to get random number from the {0, 1, ..., |
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425 | /// n-1} integer range use the \c operator[] or the \c integer() |
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426 | /// method. And to get random number from the whole range of an |
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427 | /// integer type you can use the argumentless \c integer() or \c |
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428 | /// uinteger() functions. After all you can get random bool with |
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429 | /// equal chance of true and false or given probability of true |
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430 | /// result with the \c boolean() member functions. |
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431 | /// |
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432 | ///\code |
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433 | /// // The commented code is identical to the other |
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434 | /// double a = rnd(); // [0.0, 1.0) |
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435 | /// // double a = rnd.real(); // [0.0, 1.0) |
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436 | /// double b = rnd(100.0); // [0.0, 100.0) |
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437 | /// // double b = rnd.real(100.0); // [0.0, 100.0) |
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438 | /// double c = rnd(1.0, 2.0); // [1.0, 2.0) |
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439 | /// // double c = rnd.real(1.0, 2.0); // [1.0, 2.0) |
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440 | /// int d = rnd[100000]; // 0..99999 |
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441 | /// // int d = rnd.integer(100000); // 0..99999 |
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442 | /// int e = rnd[6] + 1; // 1..6 |
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443 | /// // int e = rnd.integer(1, 1 + 6); // 1..6 |
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444 | /// int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1 |
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445 | /// int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1 |
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446 | /// bool g = rnd.boolean(); // P(g = true) = 0.5 |
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447 | /// bool h = rnd.boolean(0.8); // P(h = true) = 0.8 |
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448 | ///\endcode |
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449 | /// |
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450 | /// The lemon provides a global instance of the random number |
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451 | /// generator which name is \ref lemon::rnd "rnd". Usually it is a |
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452 | /// good programming convenience to use this global generator to get |
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453 | /// random numbers. |
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454 | /// |
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455 | /// \author Balazs Dezso |
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456 | class Random { |
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457 | private: |
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458 | |
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459 | // architecture word |
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460 | typedef unsigned long Word; |
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461 | |
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462 | _random_bits::RandomCore<Word> core; |
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463 | |
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464 | public: |
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465 | |
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466 | /// \brief Constructor |
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467 | /// |
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468 | /// Constructor with constant seeding. |
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469 | Random() { core.initState(); } |
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470 | |
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471 | /// \brief Constructor |
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472 | /// |
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473 | /// Constructor with seed. The current number type will be converted |
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474 | /// to the architecture word type. |
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475 | template <typename Number> |
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476 | Random(Number seed) { |
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477 | _random_bits::Initializer<Number, Word>::init(core, seed); |
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478 | } |
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479 | |
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480 | /// \brief Constructor |
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481 | /// |
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482 | /// Constructor with array seeding. The given range should contain |
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483 | /// any number type and the numbers will be converted to the |
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484 | /// architecture word type. |
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485 | template <typename Iterator> |
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486 | Random(Iterator begin, Iterator end) { |
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487 | typedef typename std::iterator_traits<Iterator>::value_type Number; |
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488 | _random_bits::Initializer<Number, Word>::init(core, begin, end); |
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489 | } |
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490 | |
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491 | /// \brief Copy constructor |
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492 | /// |
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493 | /// Copy constructor. The generated sequence will be identical to |
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494 | /// the other sequence. It can be used to save the current state |
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495 | /// of the generator and later use it to generate the same |
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496 | /// sequence. |
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497 | Random(const Random& other) { |
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498 | core.copyState(other.core); |
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499 | } |
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500 | |
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501 | /// \brief Assign operator |
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502 | /// |
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503 | /// Assign operator. The generated sequence will be identical to |
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504 | /// the other sequence. It can be used to save the current state |
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505 | /// of the generator and later use it to generate the same |
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506 | /// sequence. |
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507 | Random& operator=(const Random& other) { |
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508 | if (&other != this) { |
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509 | core.copyState(other.core); |
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510 | } |
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511 | return *this; |
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512 | } |
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513 | |
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514 | /// \brief Returns a random real number from the range [0, 1) |
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515 | /// |
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516 | /// It returns a random real number from the range [0, 1). The |
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517 | /// default Number type is double. |
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518 | template <typename Number> |
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519 | Number real() { |
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520 | return _random_bits::RealConversion<Number, Word>::convert(core); |
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521 | } |
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522 | |
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523 | double real() { |
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524 | return real<double>(); |
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525 | } |
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526 | |
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527 | /// \brief Returns a random real number the range [0, b) |
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528 | /// |
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529 | /// It returns a random real number from the range [0, b). |
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530 | template <typename Number> |
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531 | Number real(Number b) { |
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532 | return real<Number>() * b; |
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533 | } |
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534 | |
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535 | /// \brief Returns a random real number from the range [a, b) |
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536 | /// |
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537 | /// It returns a random real number from the range [a, b). |
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538 | template <typename Number> |
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539 | Number real(Number a, Number b) { |
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540 | return real<Number>() * (b - a) + a; |
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541 | } |
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542 | |
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543 | /// \brief Returns a random real number from the range [0, 1) |
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544 | /// |
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545 | /// It returns a random double from the range [0, 1). |
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546 | double operator()() { |
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547 | return real<double>(); |
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548 | } |
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549 | |
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550 | /// \brief Returns a random real number from the range [0, b) |
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551 | /// |
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552 | /// It returns a random real number from the range [0, b). |
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553 | template <typename Number> |
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554 | Number operator()(Number b) { |
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555 | return real<Number>() * b; |
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556 | } |
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557 | |
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558 | /// \brief Returns a random real number from the range [a, b) |
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559 | /// |
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560 | /// It returns a random real number from the range [a, b). |
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561 | template <typename Number> |
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562 | Number operator()(Number a, Number b) { |
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563 | return real<Number>() * (b - a) + a; |
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564 | } |
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565 | |
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566 | /// \brief Returns a random integer from a range |
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567 | /// |
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568 | /// It returns a random integer from the range {0, 1, ..., b - 1}. |
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569 | template <typename Number> |
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570 | Number integer(Number b) { |
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571 | return _random_bits::Mapping<Number, Word>::map(core, b); |
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572 | } |
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573 | |
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574 | /// \brief Returns a random integer from a range |
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575 | /// |
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576 | /// It returns a random integer from the range {a, a + 1, ..., b - 1}. |
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577 | template <typename Number> |
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578 | Number integer(Number a, Number b) { |
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579 | return _random_bits::Mapping<Number, Word>::map(core, b - a) + a; |
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580 | } |
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581 | |
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582 | /// \brief Returns a random integer from a range |
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583 | /// |
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584 | /// It returns a random integer from the range {0, 1, ..., b - 1}. |
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585 | template <typename Number> |
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586 | Number operator[](Number b) { |
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587 | return _random_bits::Mapping<Number, Word>::map(core, b); |
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588 | } |
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589 | |
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590 | /// \brief Returns a random non-negative integer |
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591 | /// |
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592 | /// It returns a random non-negative integer uniformly from the |
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593 | /// whole range of the current \c Number type. The default result |
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594 | /// type of this function is unsigned int. |
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595 | template <typename Number> |
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596 | Number uinteger() { |
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597 | return _random_bits::IntConversion<Number, Word>::convert(core); |
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598 | } |
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599 | |
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600 | unsigned int uinteger() { |
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601 | return uinteger<unsigned int>(); |
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602 | } |
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603 | |
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604 | /// \brief Returns a random integer |
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605 | /// |
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606 | /// It returns a random integer uniformly from the whole range of |
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607 | /// the current \c Number type. The default result type of this |
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608 | /// function is int. |
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609 | template <typename Number> |
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610 | Number integer() { |
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611 | static const int nb = std::numeric_limits<Number>::digits + |
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612 | (std::numeric_limits<Number>::is_signed ? 1 : 0); |
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613 | return _random_bits::IntConversion<Number, Word, nb>::convert(core); |
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614 | } |
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615 | |
---|
616 | int integer() { |
---|
617 | return integer<int>(); |
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618 | } |
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619 | |
---|
620 | /// \brief Returns a random bool |
---|
621 | /// |
---|
622 | /// It returns a random bool |
---|
623 | bool boolean() { |
---|
624 | return _random_bits::BoolConversion<Word>::convert(core); |
---|
625 | } |
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626 | |
---|
627 | ///\name Nonuniform distributions |
---|
628 | /// |
---|
629 | |
---|
630 | ///@{ |
---|
631 | |
---|
632 | /// \brief Returns a random bool |
---|
633 | /// |
---|
634 | /// It returns a random bool with given probability of true result |
---|
635 | bool boolean(double p) { |
---|
636 | return operator()() < p; |
---|
637 | } |
---|
638 | |
---|
639 | /// Standard Gauss distribution |
---|
640 | |
---|
641 | /// Standard Gauss distribution. |
---|
642 | /// \note The Cartesian form of the Box-Muller |
---|
643 | /// transformation is used to generate a random normal distribution. |
---|
644 | /// \todo Consider using the "ziggurat" method instead. |
---|
645 | double gauss() |
---|
646 | { |
---|
647 | double V1,V2,S; |
---|
648 | do { |
---|
649 | V1=2*real<double>()-1; |
---|
650 | V2=2*real<double>()-1; |
---|
651 | S=V1*V1+V2*V2; |
---|
652 | } while(S>=1); |
---|
653 | return std::sqrt(-2*std::log(S)/S)*V1; |
---|
654 | } |
---|
655 | /// Gauss distribution with given standard deviation and mean 0 |
---|
656 | |
---|
657 | /// \sa gauss() |
---|
658 | /// |
---|
659 | double gauss(double std_dev) |
---|
660 | { |
---|
661 | return gauss()*std_dev; |
---|
662 | } |
---|
663 | /// Gauss distribution with given mean and standard deviation |
---|
664 | |
---|
665 | /// \sa gauss() |
---|
666 | /// |
---|
667 | double gauss(double mean,double std_dev) |
---|
668 | { |
---|
669 | return gauss()*std_dev+mean; |
---|
670 | } |
---|
671 | |
---|
672 | /// Exponential distribution with given mean |
---|
673 | |
---|
674 | /// This function generates an exponential distribution random number |
---|
675 | /// with mean <tt>1/lambda</tt>. |
---|
676 | /// |
---|
677 | double exponential(double lambda=1.0) |
---|
678 | { |
---|
679 | return -log(real<double>())/lambda; |
---|
680 | } |
---|
681 | |
---|
682 | ///@} |
---|
683 | |
---|
684 | }; |
---|
685 | |
---|
686 | |
---|
687 | extern Random rnd; |
---|
688 | |
---|
689 | } |
---|
690 | |
---|
691 | #endif |
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