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// MersenneTwister.h |
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// Mersenne Twister random number generator -- a C++ class MTRand |
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// Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus |
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// Richard J. Wagner v1.0 15 May 2003 rjwagner@writeme.com |
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|
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// The Mersenne Twister is an algorithm for generating random numbers. It |
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// was designed with consideration of the flaws in various other generators. |
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// The period, 2^19937-1, and the order of equidistribution, 623 dimensions, |
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// are far greater. The generator is also fast; it avoids multiplication and |
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// division, and it benefits from caches and pipelines. For more information |
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// see the inventors' web page at http://www.math.keio.ac.jp/~matumoto/emt.html |
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|
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// Reference |
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// M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally |
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// Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on |
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// Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30. |
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|
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// Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, |
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// Copyright (C) 2000 - 2003, Richard J. Wagner |
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// All rights reserved. |
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// |
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// Redistribution and use in source and binary forms, with or without |
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// modification, are permitted provided that the following conditions |
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// are met: |
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// |
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// 1. Redistributions of source code must retain the above copyright |
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// notice, this list of conditions and the following disclaimer. |
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// |
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// 2. Redistributions in binary form must reproduce the above copyright |
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// notice, this list of conditions and the following disclaimer in the |
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// documentation and/or other materials provided with the distribution. |
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// |
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// 3. The names of its contributors may not be used to endorse or promote |
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// products derived from this software without specific prior written |
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// permission. |
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// |
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR |
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF |
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// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING |
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
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|
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// The original code included the following notice: |
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// |
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// When you use this, send an email to: matumoto@math.keio.ac.jp |
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// with an appropriate reference to your work. |
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// |
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// It would be nice to CC: rjwagner@writeme.com and Cokus@math.washington.edu |
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// when you write. |
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|
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#ifndef MERSENNETWISTER_H |
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#define MERSENNETWISTER_H |
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|
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// Not thread safe (unless auto-initialization is avoided and each thread has |
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// its own MTRand object) |
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|
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#include <cassert> |
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#include <iostream> |
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#include <limits.h> |
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#include <stdio.h> |
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#include <time.h> |
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#include <math.h> |
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#include <vector> |
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namespace OpenMD { |
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|
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class MTRand { |
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// Data |
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public: |
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typedef unsigned long uint32; // unsigned integer type, at least 32 bits |
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|
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enum { N = 624 }; // length of state vector |
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enum { SAVE = N + 1 }; // length of array for save() |
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|
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private: |
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enum { M = 397 }; // period parameter |
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|
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uint32 state[N]; // internal state |
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uint32 *pNext; // next value to get from state |
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int left; // number of values left before reload needed |
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int nstrides_; |
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int stride_; |
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|
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//Methods |
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public: |
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MTRand( const uint32& oneSeed, int nstrides, int stride); // initialize with a simple uint32 |
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MTRand( uint32 *const bigSeed, uint32 const seedLength, int nstrides, int stride); // or an array |
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MTRand(int nstrides, int stride); // auto-initialize with /dev/urandom or time() and clock() |
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|
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// Do NOT use for CRYPTOGRAPHY without securely hashing several returned |
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// values together, otherwise the generator state can be learned after |
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// reading 624 consecutive values. |
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|
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// Access to 32-bit random numbers |
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RealType rand(); // real number in [0,1] |
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RealType rand( const RealType& n ); // real number in [0,n] |
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RealType randExc(); // real number in [0,1) |
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RealType randExc( const RealType& n ); // real number in [0,n) |
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RealType randDblExc(); // real number in (0,1) |
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RealType randDblExc( const RealType& n ); // real number in (0,n) |
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uint32 randInt(); // integer in [0,2^32-1] (modified for striding) |
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uint32 rawRandInt(); // original randInt |
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uint32 randInt( const uint32& n ); // integer in [0,n] for n < 2^32 |
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RealType operator()() { return rand(); } // same as rand() |
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|
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// Access to 53-bit random numbers (capacity of IEEE RealType precision) |
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RealType rand53(); // real number in [0,1) |
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|
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// Access to nonuniform random number distributions |
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RealType randNorm( const RealType mean = 0.0, const RealType variance = 0.0 ); |
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|
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// Re-seeding functions with same behavior as initializers |
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void seed( const uint32 oneSeed ); |
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void seed( uint32 *const bigSeed, const uint32 seedLength = N ); |
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void seed(); |
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|
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std::vector<uint32>generateSeeds(); |
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|
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// Saving and loading generator state |
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void save( uint32* saveArray ) const; // to array of size SAVE |
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void load( uint32 *const loadArray ); // from such array |
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friend std::ostream& operator<<( std::ostream& os, const MTRand& mtrand ); |
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friend std::istream& operator>>( std::istream& is, MTRand& mtrand ); |
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|
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protected: |
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void initialize( const uint32 oneSeed ); |
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void reload(); |
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uint32 hiBit( const uint32& u ) const { return u & 0x80000000UL; } |
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uint32 loBit( const uint32& u ) const { return u & 0x00000001UL; } |
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uint32 loBits( const uint32& u ) const { return u & 0x7fffffffUL; } |
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uint32 mixBits( const uint32& u, const uint32& v ) const |
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{ return hiBit(u) | loBits(v); } |
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#ifdef _MSC_VER |
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#pragma warning( push ) // save current warning settings |
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#pragma warning( disable : 4146 ) // warning C4146: unary minus operator applied to unsigned type, result still unsigned |
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#endif |
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uint32 twist( const uint32& m, const uint32& s0, const uint32& s1 ) const |
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{ return m ^ (mixBits(s0,s1)>>1) ^ (-loBit(s1) & 0x9908b0dfUL); } |
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#ifdef _MSC_VER |
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#pragma warning( pop ) // return warning settings to what they were |
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#endif |
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|
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static uint32 hash( time_t t, clock_t c ); |
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}; |
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|
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|
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inline MTRand::MTRand( const uint32& oneSeed, int nstrides, int stride) : nstrides_(nstrides), stride_(stride) { |
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assert(stride_ < nstrides_ && stride_ >= 0); |
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seed(oneSeed); |
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} |
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|
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inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength, int nstrides, int stride) : nstrides_(nstrides), stride_(stride) { |
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assert(stride_ < nstrides_ && stride_ >= 0); |
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seed(bigSeed,seedLength); |
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} |
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|
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inline MTRand::MTRand(int nstrides, int stride) : nstrides_(nstrides), stride_(stride){ |
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assert(stride_ < nstrides_ && stride_ >= 0); |
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seed(); |
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} |
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|
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inline RealType MTRand::rand() |
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{ return RealType(randInt()) * (1.0/4294967295.0); } |
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|
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inline RealType MTRand::rand( const RealType& n ) |
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{ return rand() * n; } |
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|
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inline RealType MTRand::randExc() |
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{ return RealType(randInt()) * (1.0/4294967296.0); } |
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|
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inline RealType MTRand::randExc( const RealType& n ) |
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{ return randExc() * n; } |
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|
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inline RealType MTRand::randDblExc() |
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{ return ( RealType(randInt()) + 0.5 ) * (1.0/4294967296.0); } |
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|
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inline RealType MTRand::randDblExc( const RealType& n ) |
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{ return randDblExc() * n; } |
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|
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inline RealType MTRand::rand53() |
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{ |
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uint32 a = randInt() >> 5, b = randInt() >> 6; |
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return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0); // by Isaku Wada |
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} |
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|
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inline RealType MTRand::randNorm( const RealType mean, const RealType variance ) |
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{ |
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// Return a real number from a normal (Gaussian) distribution with given |
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// mean and variance by Box-Muller method |
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assert(variance > 0); |
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RealType r = sqrt( -2.0 * log( 1.0-randDblExc()) * variance); |
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RealType phi = 2.0 * 3.14159265358979323846264338328 * randExc(); |
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return mean + r * cos(phi); |
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} |
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|
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/** |
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* This function is modified from the original to allow for random |
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* streams on parallel jobs. It now takes numbers from by striding |
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* through the random stream and picking up only one of the random |
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* numbers per nstrides_. The number it picks is the stride_'th |
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* number in the stride sequence. |
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*/ |
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inline MTRand::uint32 MTRand::randInt() { |
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|
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std::vector<uint32> ranNums(nstrides_); |
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|
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for (int i = 0; i < nstrides_; ++i) { |
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ranNums[i] = rawRandInt(); |
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} |
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|
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return ranNums[stride_]; |
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} |
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|
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/** |
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* This is the original randInt function which implements the mersenne |
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* twister. |
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*/ |
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inline MTRand::uint32 MTRand::rawRandInt() |
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{ |
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// Pull a 32-bit integer from the generator state |
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// Every other access function simply transforms the numbers extracted here |
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|
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if( left == 0 ) reload(); |
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--left; |
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|
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register uint32 s1; |
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s1 = *pNext++; |
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s1 ^= (s1 >> 11); |
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s1 ^= (s1 << 7) & 0x9d2c5680UL; |
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s1 ^= (s1 << 15) & 0xefc60000UL; |
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return ( s1 ^ (s1 >> 18) ); |
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} |
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|
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inline MTRand::uint32 MTRand::randInt( const uint32& n ) |
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{ |
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// Find which bits are used in n |
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// Optimized by Magnus Jonsson (magnus@smartelectronix.com) |
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uint32 used = n; |
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used |= used >> 1; |
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used |= used >> 2; |
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used |= used >> 4; |
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used |= used >> 8; |
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used |= used >> 16; |
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|
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// Draw numbers until one is found in [0,n] |
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uint32 i; |
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do |
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i = randInt() & used; // toss unused bits to shorten search |
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while( i > n ); |
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return i; |
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} |
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|
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|
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inline void MTRand::seed( const uint32 oneSeed ) |
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{ |
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// Seed the generator with a simple uint32 |
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initialize(oneSeed); |
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reload(); |
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} |
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|
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|
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inline void MTRand::seed( uint32 *const bigSeed, const uint32 seedLength ) |
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{ |
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// Seed the generator with an array of uint32's |
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// There are 2^19937-1 possible initial states. This function allows |
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// all of those to be accessed by providing at least 19937 bits (with a |
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// default seed length of N = 624 uint32's). Any bits above the lower 32 |
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// in each element are discarded. |
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// Just call seed() if you want to get array from /dev/urandom |
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initialize(19650218UL); |
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register int i = 1; |
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register uint32 j = 0; |
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register int k = ( N > seedLength ? N : seedLength ); |
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for( ; k; --k ) |
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{ |
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state[i] = |
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state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL ); |
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state[i] += ( bigSeed[j] & 0xffffffffUL ) + j; |
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state[i] &= 0xffffffffUL; |
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++i; ++j; |
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if( i >= N ) { state[0] = state[N-1]; i = 1; } |
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if( j >= seedLength ) j = 0; |
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} |
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for( k = N - 1; k; --k ) |
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{ |
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state[i] = |
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state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL ); |
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state[i] -= i; |
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state[i] &= 0xffffffffUL; |
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++i; |
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if( i >= N ) { state[0] = state[N-1]; i = 1; } |
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} |
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state[0] = 0x80000000UL; // MSB is 1, assuring non-zero initial array |
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reload(); |
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} |
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|
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|
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inline void MTRand::seed() |
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{ |
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std::vector<uint32> seeds; |
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|
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seeds = generateSeeds(); |
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|
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if (seeds.size() == 1) { |
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seed( seeds[0] ); |
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} else { |
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seed( &seeds[0], seeds.size() ); |
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} |
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} |
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|
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|
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inline std::vector<MTRand::uint32> MTRand::generateSeeds() { |
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// Seed the generator with an array from /dev/urandom if available |
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// Otherwise use a hash of time() and clock() values |
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|
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std::vector<uint32> bigSeed; |
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|
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// First try getting an array from /dev/urandom |
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FILE* urandom = fopen( "/dev/urandom", "rb" ); |
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if( urandom ) |
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{ |
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bigSeed.resize(N); |
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register uint32 *s = &bigSeed[0]; |
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register int i = N; |
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register bool success = true; |
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while( success && i-- ) |
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success = (fread( s++, sizeof(uint32), 1, urandom ) == 0); |
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fclose(urandom); |
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if( success ) { return bigSeed; } |
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} |
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|
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// Was not successful, so use time() and clock() instead |
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|
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bigSeed.push_back(hash( time(NULL), clock())); |
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return bigSeed; |
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} |
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|
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|
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inline void MTRand::initialize( const uint32 seed ) |
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{ |
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// Initialize generator state with seed |
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// See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier. |
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// In previous versions, most significant bits (MSBs) of the seed affect |
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// only MSBs of the state array. Modified 9 Jan 2002 by Makoto Matsumoto. |
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register uint32 *s = state; |
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register uint32 *r = state; |
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register int i = 1; |
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*s++ = seed & 0xffffffffUL; |
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for( ; i < N; ++i ) |
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{ |
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*s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL; |
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r++; |
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} |
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} |
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|
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|
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inline void MTRand::reload() |
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{ |
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// Generate N new values in state |
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// Made clearer and faster by Matthew Bellew (matthew.bellew@home.com) |
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register uint32 *p = state; |
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register int i; |
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for( i = N - M; i--; ++p ) |
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*p = twist( p[M], p[0], p[1] ); |
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for( i = M; --i; ++p ) |
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*p = twist( p[M-N], p[0], p[1] ); |
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*p = twist( p[M-N], p[0], state[0] ); |
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|
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left = N, pNext = state; |
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} |
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|
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|
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inline MTRand::uint32 MTRand::hash( time_t t, clock_t c ) |
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{ |
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// Get a uint32 from t and c |
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// Better than uint32(x) in case x is floating point in [0,1] |
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// Based on code by Lawrence Kirby (fred@genesis.demon.co.uk) |
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|
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static uint32 differ = 0; // guarantee time-based seeds will change |
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|
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uint32 h1 = 0; |
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unsigned char *p = (unsigned char *) &t; |
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for( size_t i = 0; i < sizeof(t); ++i ) |
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{ |
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h1 *= UCHAR_MAX + 2U; |
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h1 += p[i]; |
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} |
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uint32 h2 = 0; |
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p = (unsigned char *) &c; |
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for( size_t j = 0; j < sizeof(c); ++j ) |
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{ |
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h2 *= UCHAR_MAX + 2U; |
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h2 += p[j]; |
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} |
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return ( h1 + differ++ ) ^ h2; |
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} |
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|
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|
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inline void MTRand::save( uint32* saveArray ) const |
| 405 |
{ |
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register uint32 *sa = saveArray; |
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register const uint32 *s = state; |
| 408 |
register int i = N; |
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for( ; i--; *sa++ = *s++ ) {} |
| 410 |
*sa = left; |
| 411 |
} |
| 412 |
|
| 413 |
|
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inline void MTRand::load( uint32 *const loadArray ) |
| 415 |
{ |
| 416 |
register uint32 *s = state; |
| 417 |
register uint32 *la = loadArray; |
| 418 |
register int i = N; |
| 419 |
for( ; i--; *s++ = *la++ ) {} |
| 420 |
left = *la; |
| 421 |
pNext = &state[N-left]; |
| 422 |
} |
| 423 |
|
| 424 |
|
| 425 |
inline std::ostream& operator<<( std::ostream& os, const MTRand& mtrand ) |
| 426 |
{ |
| 427 |
register const MTRand::uint32 *s = mtrand.state; |
| 428 |
register int i = mtrand.N; |
| 429 |
for( ; i--; os << *s++ << "\t" ) {} |
| 430 |
return os << mtrand.left; |
| 431 |
} |
| 432 |
|
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|
| 434 |
inline std::istream& operator>>( std::istream& is, MTRand& mtrand ) |
| 435 |
{ |
| 436 |
register MTRand::uint32 *s = mtrand.state; |
| 437 |
register int i = mtrand.N; |
| 438 |
for( ; i--; is >> *s++ ) {} |
| 439 |
is >> mtrand.left; |
| 440 |
mtrand.pNext = &mtrand.state[mtrand.N-mtrand.left]; |
| 441 |
return is; |
| 442 |
} |
| 443 |
|
| 444 |
} |
| 445 |
#endif // MERSENNETWISTER_H |
| 446 |
|
| 447 |
// Change log: |
| 448 |
// |
| 449 |
// v0.1 - First release on 15 May 2000 |
| 450 |
// - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus |
| 451 |
// - Translated from C to C++ |
| 452 |
// - Made completely ANSI compliant |
| 453 |
// - Designed convenient interface for initialization, seeding, and |
| 454 |
// obtaining numbers in default or user-defined ranges |
| 455 |
// - Added automatic seeding from /dev/urandom or time() and clock() |
| 456 |
// - Provided functions for saving and loading generator state |
| 457 |
// |
| 458 |
// v0.2 - Fixed bug which reloaded generator one step too late |
| 459 |
// |
| 460 |
// v0.3 - Switched to clearer, faster reload() code from Matthew Bellew |
| 461 |
// |
| 462 |
// v0.4 - Removed trailing newline in saved generator format to be consistent |
| 463 |
// with output format of built-in types |
| 464 |
// |
| 465 |
// v0.5 - Improved portability by replacing static const int's with enum's and |
| 466 |
// clarifying return values in seed(); suggested by Eric Heimburg |
| 467 |
// - Removed MAXINT constant; use 0xffffffffUL instead |
| 468 |
// |
| 469 |
// v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits |
| 470 |
// - Changed integer [0,n] generator to give better uniformity |
| 471 |
// |
| 472 |
// v0.7 - Fixed operator precedence ambiguity in reload() |
| 473 |
// - Added access for real numbers in (0,1) and (0,n) |
| 474 |
// |
| 475 |
// v0.8 - Included time.h header to properly support time_t and clock_t |
| 476 |
// |
| 477 |
// v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto |
| 478 |
// - Allowed for seeding with arrays of any length |
| 479 |
// - Added access for real numbers in [0,1) with 53-bit resolution |
| 480 |
// - Added access for real numbers from normal (Gaussian) distributions |
| 481 |
// - Increased overall speed by optimizing twist() |
| 482 |
// - Doubled speed of integer [0,n] generation |
| 483 |
// - Fixed out-of-range number generation on 64-bit machines |
| 484 |
// - Improved portability by substituting literal constants for long enum's |
| 485 |
// - Changed license from GNU LGPL to BSD |
