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