457 lines
15 KiB
C++
457 lines
15 KiB
C++
// 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 v1.1 28 September 2009 wagnerr@umich.edu
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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
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// http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
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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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// Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
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// Copyright (C) 2000 - 2009, 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 "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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#ifndef MERSENNETWISTER_H
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#define MERSENNETWISTER_H
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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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#include <iostream>
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#include <climits>
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#include <cstdio>
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#include <ctime>
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#include <cmath>
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class MTRand {
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// Data
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public:
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typedef long uint32; // unsigned integer type, at least 32 bits
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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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protected:
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enum { M = 397 }; // period parameter
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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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// Methods
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public:
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MTRand( const uint32 oneSeed ); // initialize with a simple uint32
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MTRand( uint32 *const bigSeed, uint32 const seedLength = N ); // or array
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MTRand(); // auto-initialize with /dev/urandom or time() and clock()
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MTRand( const MTRand& o ); // copy
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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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// Access to 32-bit random numbers
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uint32 randInt(); // integer in [0,2^32-1]
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uint32 randInt( const uint32 n ); // integer in [0,n] for n < 2^32
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double rand(); // real number in [0,1]
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double rand( const double n ); // real number in [0,n]
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double randExc(); // real number in [0,1)
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double randExc( const double n ); // real number in [0,n)
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double randDblExc(); // real number in (0,1)
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double randDblExc( const double n ); // real number in (0,n)
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double operator()(); // same as rand()
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// Access to 53-bit random numbers (capacity of IEEE double precision)
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double rand53(); // real number in [0,1)
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// Access to nonuniform random number distributions
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double randNorm( const double mean = 0.0, const double stddev = 1.0 );
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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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// 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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MTRand& operator=( const MTRand& o );
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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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uint32 magic( const uint32 u ) const
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{ return loBit(u) ? 0x9908b0dfUL : 0x0UL; }
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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) ^ magic(s1); }
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static uint32 hash( time_t t, clock_t c );
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};
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// Functions are defined in order of usage to assist inlining
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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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static uint32 differ = 0; // guarantee time-based seeds will change
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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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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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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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static const int MmN = int(M) - int(N); // in case enums are unsigned
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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[MmN], p[0], p[1] );
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*p = twist( p[MmN], p[0], state[0] );
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left = N, pNext = state;
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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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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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inline void MTRand::seed()
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{
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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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// First try getting an array from /dev/urandom
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/* // Commented out by FakeTruth because doing this 200 times a tick is SUUUUPEERRR SLOW!!~~!<21>Ne
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FILE* urandom = fopen( "/dev/urandom", "rb" );
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if( urandom )
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{
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uint32 bigSeed[N];
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register uint32 *s = bigSeed;
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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 );
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fclose(urandom);
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if( success ) { seed( bigSeed, N ); return; }
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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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seed( hash( time(NULL), clock() ) );
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}
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inline MTRand::MTRand( const uint32 oneSeed )
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{ seed(oneSeed); }
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inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength )
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{ seed(bigSeed,seedLength); }
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inline MTRand::MTRand()
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{ seed(); }
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inline MTRand::MTRand( const MTRand& o )
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{
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register const uint32 *t = o.state;
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register uint32 *s = state;
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register int i = N;
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for( ; i--; *s++ = *t++ ) {}
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left = o.left;
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pNext = &state[N-left];
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}
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inline MTRand::uint32 MTRand::randInt()
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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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if( left == 0 ) reload();
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--left;
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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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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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// 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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inline double MTRand::rand()
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{ return double(randInt()) * (1.0/4294967295.0); }
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inline double MTRand::rand( const double n )
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{ return rand() * n; }
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inline double MTRand::randExc()
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{ return double(randInt()) * (1.0/4294967296.0); }
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inline double MTRand::randExc( const double n )
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{ return randExc() * n; }
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inline double MTRand::randDblExc()
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{ return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0); }
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inline double MTRand::randDblExc( const double n )
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{ return randDblExc() * n; }
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inline double 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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inline double MTRand::randNorm( const double mean, const double stddev )
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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 standard deviation by polar form of Box-Muller transformation
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double x, y, r;
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do
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{
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x = 2.0 * rand() - 1.0;
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y = 2.0 * rand() - 1.0;
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r = x * x + y * y;
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}
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while ( r >= 1.0 || r == 0.0 );
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double s = sqrt( -2.0 * log(r) / r );
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return mean + x * s * stddev;
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}
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inline double MTRand::operator()()
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{
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return rand();
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}
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inline void MTRand::save( uint32* saveArray ) const
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{
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register const uint32 *s = state;
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register uint32 *sa = saveArray;
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register int i = N;
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for( ; i--; *sa++ = *s++ ) {}
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*sa = left;
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}
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inline void MTRand::load( uint32 *const loadArray )
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{
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register uint32 *s = state;
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register uint32 *la = loadArray;
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register int i = N;
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for( ; i--; *s++ = *la++ ) {}
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left = *la;
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pNext = &state[N-left];
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}
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inline std::ostream& operator<<( std::ostream& os, const MTRand& mtrand )
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{
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register const MTRand::uint32 *s = mtrand.state;
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register int i = mtrand.N;
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for( ; i--; os << *s++ << "\t" ) {}
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return os << mtrand.left;
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}
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inline std::istream& operator>>( std::istream& is, MTRand& mtrand )
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{
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register MTRand::uint32 *s = mtrand.state;
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register int i = mtrand.N;
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for( ; i--; is >> *s++ ) {}
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is >> mtrand.left;
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mtrand.pNext = &mtrand.state[mtrand.N-mtrand.left];
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return is;
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}
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inline MTRand& MTRand::operator=( const MTRand& o )
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{
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if( this == &o ) return (*this);
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register const uint32 *t = o.state;
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register uint32 *s = state;
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register int i = N;
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for( ; i--; *s++ = *t++ ) {}
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left = o.left;
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pNext = &state[N-left];
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return (*this);
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}
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#endif // MERSENNETWISTER_H
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// Change log:
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//
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// v0.1 - First release on 15 May 2000
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// - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
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// - Translated from C to C++
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// - Made completely ANSI compliant
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// - Designed convenient interface for initialization, seeding, and
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// obtaining numbers in default or user-defined ranges
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// - Added automatic seeding from /dev/urandom or time() and clock()
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// - Provided functions for saving and loading generator state
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//
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// v0.2 - Fixed bug which reloaded generator one step too late
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//
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// v0.3 - Switched to clearer, faster reload() code from Matthew Bellew
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//
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// v0.4 - Removed trailing newline in saved generator format to be consistent
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// with output format of built-in types
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//
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// v0.5 - Improved portability by replacing static const int's with enum's and
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// clarifying return values in seed(); suggested by Eric Heimburg
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// - Removed MAXINT constant; use 0xffffffffUL instead
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//
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// v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits
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// - Changed integer [0,n] generator to give better uniformity
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//
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// v0.7 - Fixed operator precedence ambiguity in reload()
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// - Added access for real numbers in (0,1) and (0,n)
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//
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// v0.8 - Included time.h header to properly support time_t and clock_t
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//
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// v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto
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// - Allowed for seeding with arrays of any length
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// - Added access for real numbers in [0,1) with 53-bit resolution
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// - Added access for real numbers from normal (Gaussian) distributions
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// - Increased overall speed by optimizing twist()
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// - Doubled speed of integer [0,n] generation
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// - Fixed out-of-range number generation on 64-bit machines
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// - Improved portability by substituting literal constants for long enum's
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// - Changed license from GNU LGPL to BSD
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//
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// v1.1 - Corrected parameter label in randNorm from "variance" to "stddev"
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// - Changed randNorm algorithm from basic to polar form for efficiency
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// - Updated includes from deprecated <xxxx.h> to standard <cxxxx> forms
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// - Cleaned declarations and definitions to please Intel compiler
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// - Revised twist() operator to work on ones'-complement machines
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// - Fixed reload() function to work when N and M are unsigned
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// - Added copy constructor and copy operator from Salvador Espana
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