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1 // MersenneTwister.h
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2 // Mersenne Twister random number generator -- a C++ class MTRand
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3 // Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
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4 // Richard J. Wagner v1.0 15 May 2003 rjwagner@writeme.com
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5
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6 // The Mersenne Twister is an algorithm for generating random numbers. It
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7 // was designed with consideration of the flaws in various other generators.
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8 // The period, 2^19937-1, and the order of equidistribution, 623 dimensions,
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9 // are far greater. The generator is also fast; it avoids multiplication and
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10 // division, and it benefits from caches and pipelines. For more information
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11 // see the inventors' web page at http://www.math.keio.ac.jp/~matumoto/emt.html
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12
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13 // Reference
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14 // M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally
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15 // Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on
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16 // Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.
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17
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18 // Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
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19 // Copyright (C) 2000 - 2003, Richard J. Wagner
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20 // All rights reserved.
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21 //
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22 // Redistribution and use in source and binary forms, with or without
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23 // modification, are permitted provided that the following conditions
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24 // are met:
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25 //
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26 // 1. Redistributions of source code must retain the above copyright
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27 // notice, this list of conditions and the following disclaimer.
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28 //
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29 // 2. Redistributions in binary form must reproduce the above copyright
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30 // notice, this list of conditions and the following disclaimer in the
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31 // documentation and/or other materials provided with the distribution.
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32 //
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33 // 3. The names of its contributors may not be used to endorse or promote
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34 // products derived from this software without specific prior written
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35 // permission.
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36 //
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37 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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38 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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39 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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40 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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41 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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42 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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43 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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44 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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45 // LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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46 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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47 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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48
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49 // The original code included the following notice:
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50 //
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51 // When you use this, send an email to: matumoto@math.keio.ac.jp
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52 // with an appropriate reference to your work.
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53 //
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54 // It would be nice to CC: rjwagner@writeme.com and Cokus@math.washington.edu
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55 // when you write.
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56
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57 #ifndef MERSENNETWISTER_H
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58 #define MERSENNETWISTER_H
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59
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60 // Not thread safe (unless auto-initialization is avoided and each thread has
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61 // its own MTRand object)
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62
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63 #include <iostream>
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64 #include <limits.h>
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65 #include <stdio.h>
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66 #include <time.h>
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67 #include <math.h>
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68
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69 class MTRand {
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70 // Data
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71 public:
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72 typedef unsigned long uint32; // unsigned integer type, at least 32 bits
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73
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74 enum { N = 624 }; // length of state vector
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75 enum { SAVE = N + 1 }; // length of array for save()
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76
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77 protected:
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78 enum { M = 397 }; // period parameter
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79
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80 uint32 state[N]; // internal state
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81 uint32 *pNext; // next value to get from state
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82 int left; // number of values left before reload needed
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83
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84
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85 //Methods
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86 public:
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87 MTRand( const uint32& oneSeed ); // initialize with a simple uint32
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88 MTRand( uint32 *const bigSeed, uint32 const seedLength = N ); // or an array
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89 MTRand(); // auto-initialize with /dev/urandom or time() and clock()
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90
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91 // Do NOT use for CRYPTOGRAPHY without securely hashing several returned
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92 // values together, otherwise the generator state can be learned after
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93 // reading 624 consecutive values.
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94
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95 // Access to 32-bit random numbers
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96 double rand(); // real number in [0,1]
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97 double rand( const double& n ); // real number in [0,n]
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98 double randExc(); // real number in [0,1)
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99 double randExc( const double& n ); // real number in [0,n)
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100 double randDblExc(); // real number in (0,1)
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101 double randDblExc( const double& n ); // real number in (0,n)
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102 uint32 randInt(); // integer in [0,2^32-1]
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103 uint32 randInt( const uint32& n ); // integer in [0,n] for n < 2^32
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104 double operator()() { return rand(); } // same as rand()
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105
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106 // Access to 53-bit random numbers (capacity of IEEE double precision)
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107 double rand53(); // real number in [0,1)
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108
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109 // Access to nonuniform random number distributions
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110 double randNorm( const double& mean = 0.0, const double& variance = 0.0 );
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111
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112 // Re-seeding functions with same behavior as initializers
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113 void seed( const uint32 oneSeed );
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114 void seed( uint32 *const bigSeed, const uint32 seedLength = N );
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115 void seed();
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116
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117 // Saving and loading generator state
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118 void save( uint32* saveArray ) const; // to array of size SAVE
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119 void load( uint32 *const loadArray ); // from such array
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120 friend std::ostream& operator<<( std::ostream& os, const MTRand& mtrand );
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121 friend std::istream& operator>>( std::istream& is, MTRand& mtrand );
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122
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123 protected:
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124 void initialize( const uint32 oneSeed );
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125 void reload();
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126 uint32 hiBit( const uint32& u ) const { return u & 0x80000000UL; }
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127 uint32 loBit( const uint32& u ) const { return u & 0x00000001UL; }
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128 uint32 loBits( const uint32& u ) const { return u & 0x7fffffffUL; }
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129 uint32 mixBits( const uint32& u, const uint32& v ) const
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130 { return hiBit(u) | loBits(v); }
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131 uint32 twist( const uint32& m, const uint32& s0, const uint32& s1 ) const
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132 { return m ^ (mixBits(s0,s1)>>1) ^ (-loBit(s1) & 0x9908b0dfUL); }
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133 static uint32 hash( time_t t, clock_t c );
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134 };
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135
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136
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137 inline MTRand::MTRand( const uint32& oneSeed )
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138 { seed(oneSeed); }
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139
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140 inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength )
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141 { seed(bigSeed,seedLength); }
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142
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143 inline MTRand::MTRand()
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144 { seed(); }
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145
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146 inline double MTRand::rand()
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147 { return double(randInt()) * (1.0/4294967295.0); }
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148
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149 inline double MTRand::rand( const double& n )
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150 { return rand() * n; }
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151
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152 inline double MTRand::randExc()
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153 { return double(randInt()) * (1.0/4294967296.0); }
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154
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155 inline double MTRand::randExc( const double& n )
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156 { return randExc() * n; }
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157
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158 inline double MTRand::randDblExc()
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159 { return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0); }
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160
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161 inline double MTRand::randDblExc( const double& n )
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162 { return randDblExc() * n; }
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163
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164 inline double MTRand::rand53()
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165 {
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166 uint32 a = randInt() >> 5, b = randInt() >> 6;
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167 return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0); // by Isaku Wada
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168 }
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169
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170 inline double MTRand::randNorm( const double& mean, const double& variance )
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171 {
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172 // Return a real number from a normal (Gaussian) distribution with given
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173 // mean and variance by Box-Muller method
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174 double r = sqrt( -2.0 * log( 1.0-randDblExc()) ) * variance;
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175 double phi = 2.0 * 3.14159265358979323846264338328 * randExc();
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176 return mean + r * cos(phi);
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177 }
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178
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179 inline MTRand::uint32 MTRand::randInt()
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180 {
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181 // Pull a 32-bit integer from the generator state
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182 // Every other access function simply transforms the numbers extracted here
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183
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184 if( left == 0 ) reload();
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185 --left;
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186
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187 register uint32 s1;
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188 s1 = *pNext++;
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189 s1 ^= (s1 >> 11);
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190 s1 ^= (s1 << 7) & 0x9d2c5680UL;
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191 s1 ^= (s1 << 15) & 0xefc60000UL;
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192 return ( s1 ^ (s1 >> 18) );
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193 }
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194
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195 inline MTRand::uint32 MTRand::randInt( const uint32& n )
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196 {
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197 // Find which bits are used in n
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198 // Optimized by Magnus Jonsson (magnus@smartelectronix.com)
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199 uint32 used = n;
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200 used |= used >> 1;
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201 used |= used >> 2;
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202 used |= used >> 4;
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203 used |= used >> 8;
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204 used |= used >> 16;
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205
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206 // Draw numbers until one is found in [0,n]
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207 uint32 i;
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208 do
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209 i = randInt() & used; // toss unused bits to shorten search
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210 while( i > n );
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211 return i;
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212 }
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213
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214
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215 inline void MTRand::seed( const uint32 oneSeed )
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216 {
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217 // Seed the generator with a simple uint32
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218 initialize(oneSeed);
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219 reload();
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220 }
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221
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222
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223 inline void MTRand::seed( uint32 *const bigSeed, const uint32 seedLength )
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224 {
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225 // Seed the generator with an array of uint32's
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226 // There are 2^19937-1 possible initial states. This function allows
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227 // all of those to be accessed by providing at least 19937 bits (with a
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228 // default seed length of N = 624 uint32's). Any bits above the lower 32
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229 // in each element are discarded.
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230 // Just call seed() if you want to get array from /dev/urandom
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231 initialize(19650218UL);
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232 register int i = 1;
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233 register uint32 j = 0;
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234 register int k = ( N > seedLength ? N : seedLength );
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235 for( ; k; --k )
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236 {
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237 state[i] =
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238 state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL );
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239 state[i] += ( bigSeed[j] & 0xffffffffUL ) + j;
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240 state[i] &= 0xffffffffUL;
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241 ++i; ++j;
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242 if( i >= N ) { state[0] = state[N-1]; i = 1; }
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243 if( j >= seedLength ) j = 0;
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244 }
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245 for( k = N - 1; k; --k )
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246 {
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247 state[i] =
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248 state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL );
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249 state[i] -= i;
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250 state[i] &= 0xffffffffUL;
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251 ++i;
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252 if( i >= N ) { state[0] = state[N-1]; i = 1; }
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253 }
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254 state[0] = 0x80000000UL; // MSB is 1, assuring non-zero initial array
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255 reload();
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256 }
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257
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258
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259 inline void MTRand::seed()
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260 {
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261 // Seed the generator with an array from /dev/urandom if available
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262 // Otherwise use a hash of time() and clock() values
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263
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264 // First try getting an array from /dev/urandom
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265 FILE* urandom = fopen( "/dev/urandom", "rb" );
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266 if( urandom )
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267 {
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268 uint32 bigSeed[N];
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269 register uint32 *s = bigSeed;
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270 register int i = N;
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271 register bool success = true;
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272 while( success && i-- )
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273 success = fread( s++, sizeof(uint32), 1, urandom );
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274 fclose(urandom);
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275 if( success ) { seed( bigSeed, N ); return; }
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276 }
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277
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278 // Was not successful, so use time() and clock() instead
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279 seed( hash( time(NULL), clock() ) );
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280 }
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281
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282
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283 inline void MTRand::initialize( const uint32 seed )
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284 {
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285 // Initialize generator state with seed
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286 // See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
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287 // In previous versions, most significant bits (MSBs) of the seed affect
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288 // only MSBs of the state array. Modified 9 Jan 2002 by Makoto Matsumoto.
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289 register uint32 *s = state;
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290 register uint32 *r = state;
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291 register int i = 1;
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292 *s++ = seed & 0xffffffffUL;
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293 for( ; i < N; ++i )
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294 {
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295 *s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL;
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296 r++;
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297 }
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298 }
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299
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300
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301 inline void MTRand::reload()
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302 {
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303 // Generate N new values in state
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304 // Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
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305 register uint32 *p = state;
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306 register int i;
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307 for( i = N - M; i--; ++p )
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308 *p = twist( p[M], p[0], p[1] );
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309 for( i = M; --i; ++p )
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310 *p = twist( p[M-N], p[0], p[1] );
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311 *p = twist( p[M-N], p[0], state[0] );
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312
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313 left = N, pNext = state;
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314 }
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315
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316
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317 inline MTRand::uint32 MTRand::hash( time_t t, clock_t c )
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318 {
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319 // Get a uint32 from t and c
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320 // Better than uint32(x) in case x is floating point in [0,1]
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321 // Based on code by Lawrence Kirby (fred@genesis.demon.co.uk)
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322
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323 static uint32 differ = 0; // guarantee time-based seeds will change
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324
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325 uint32 h1 = 0;
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326 unsigned char *p = (unsigned char *) &t;
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327 for( size_t i = 0; i < sizeof(t); ++i )
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328 {
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329 h1 *= UCHAR_MAX + 2U;
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330 h1 += p[i];
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331 }
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332 uint32 h2 = 0;
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333 p = (unsigned char *) &c;
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334 for( size_t j = 0; j < sizeof(c); ++j )
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335 {
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336 h2 *= UCHAR_MAX + 2U;
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337 h2 += p[j];
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338 }
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339 return ( h1 + differ++ ) ^ h2;
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340 }
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341
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342
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343 inline void MTRand::save( uint32* saveArray ) const
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344 {
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345 register uint32 *sa = saveArray;
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346 register const uint32 *s = state;
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347 register int i = N;
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348 for( ; i--; *sa++ = *s++ ) {}
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349 *sa = left;
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350 }
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351
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352
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353 inline void MTRand::load( uint32 *const loadArray )
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354 {
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355 register uint32 *s = state;
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356 register uint32 *la = loadArray;
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357 register int i = N;
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358 for( ; i--; *s++ = *la++ ) {}
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359 left = *la;
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360 pNext = &state[N-left];
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361 }
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362
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363
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364 inline std::ostream& operator<<( std::ostream& os, const MTRand& mtrand )
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365 {
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366 register const MTRand::uint32 *s = mtrand.state;
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367 register int i = mtrand.N;
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368 for( ; i--; os << *s++ << "\t" ) {}
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369 return os << mtrand.left;
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370 }
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371
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372
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373 inline std::istream& operator>>( std::istream& is, MTRand& mtrand )
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374 {
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375 register MTRand::uint32 *s = mtrand.state;
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376 register int i = mtrand.N;
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377 for( ; i--; is >> *s++ ) {}
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378 is >> mtrand.left;
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379 mtrand.pNext = &mtrand.state[mtrand.N-mtrand.left];
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380 return is;
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381 }
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382
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383 #endif // MERSENNETWISTER_H
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384
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385 // Change log:
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386 //
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387 // v0.1 - First release on 15 May 2000
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388 // - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
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389 // - Translated from C to C++
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390 // - Made completely ANSI compliant
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391 // - Designed convenient interface for initialization, seeding, and
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392 // obtaining numbers in default or user-defined ranges
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393 // - Added automatic seeding from /dev/urandom or time() and clock()
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394 // - Provided functions for saving and loading generator state
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395 //
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396 // v0.2 - Fixed bug which reloaded generator one step too late
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397 //
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398 // v0.3 - Switched to clearer, faster reload() code from Matthew Bellew
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399 //
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400 // v0.4 - Removed trailing newline in saved generator format to be consistent
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401 // with output format of built-in types
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402 //
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403 // v0.5 - Improved portability by replacing static const int's with enum's and
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404 // clarifying return values in seed(); suggested by Eric Heimburg
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405 // - Removed MAXINT constant; use 0xffffffffUL instead
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406 //
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407 // v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits
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408 // - Changed integer [0,n] generator to give better uniformity
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409 //
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410 // v0.7 - Fixed operator precedence ambiguity in reload()
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411 // - Added access for real numbers in (0,1) and (0,n)
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412 //
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413 // v0.8 - Included time.h header to properly support time_t and clock_t
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414 //
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415 // v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto
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416 // - Allowed for seeding with arrays of any length
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417 // - Added access for real numbers in [0,1) with 53-bit resolution
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418 // - Added access for real numbers from normal (Gaussian) distributions
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419 // - Increased overall speed by optimizing twist()
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420 // - Doubled speed of integer [0,n] generation
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421 // - Fixed out-of-range number generation on 64-bit machines
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422 // - Improved portability by substituting literal constants for long enum's
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423 // - Changed license from GNU LGPL to BSD
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