    // MersenneTwister.h
    // Mersenne Twister random number generator -- a C++ class MTRand
    // Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
    // Richard J. Wagner  v1.0  15 May 2003  rjwagner@writeme.com

    // The Mersenne Twister is an algorithm for generating random numbers.  It
    // was designed with consideration of the flaws in various other generators.
    // The period, 2^19937-1, and the order of equidistribution, 623 dimensions,
    // are far greater.  The generator is also fast; it avoids multiplication and
    // division, and it benefits from caches and pipelines.  For more information
    // see the inventors' web page at http://www.math.keio.ac.jp/~matumoto/emt.html

    // Reference
    // M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally
    // Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on
    // Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.

    // Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
    // Copyright (C) 2000 - 2003, Richard J. Wagner
    // All rights reserved.
    //
    // Redistribution and use in source and binary forms, with or without
    // modification, are permitted provided that the following conditions
    // are met:
    //
    //   1. Redistributions of source code must retain the above copyright
    //      notice, this list of conditions and the following disclaimer.
    //
    //   2. Redistributions in binary form must reproduce the above copyright
    //      notice, this list of conditions and the following disclaimer in the
    //      documentation and/or other materials provided with the distribution.
    //
    //   3. The names of its contributors may not be used to endorse or promote
    //      products derived from this software without specific prior written
    //      permission.
    //
    // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
    // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
    // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
    // A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
    // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
    // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
    // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
    // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
    // LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
    // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
    // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

    // The original code included the following notice:
    //
    //     When you use this, send an email to: matumoto@math.keio.ac.jp
    //     with an appropriate reference to your work.
    //
    // It would be nice to CC: rjwagner@writeme.com and Cokus@math.washington.edu
    // when you write.

    #ifndef MERSENNETWISTER_H
    #define MERSENNETWISTER_H

    // Not thread safe (unless auto-initialization is avoided and each thread has
    // its own MTRand object)

    #include
    #include
    #include
    #include
    #include

    class MTRand {
    // Data
    public:
    	typedef unsigned long uint32;  // unsigned integer type, at least 32 bits

    	enum { N = 624 };       // length of state vector
    	enum { SAVE = N + 1 };  // length of array for save()

    protected:
    	enum { M = 397 };  // period parameter

    	uint32 state[N];   // internal state
    	uint32 *pNext;     // next value to get from state
    	int left;          // number of values left before reload needed

    //Methods
    public:
    	MTRand( const uint32& oneSeed );  // initialize with a simple uint32
    	MTRand( uint32 *const bigSeed, uint32 const seedLength = N );  // or an array
    	MTRand();  // auto-initialize with /dev/urandom or time() and clock()

    	// Do NOT use for CRYPTOGRAPHY without securely hashing several returned
    	// values together, otherwise the generator state can be learned after
    	// reading 624 consecutive values.

    	// Access to 32-bit random numbers
    	double rand();                          // real number in [0,1]
    	double rand( const double& n );         // real number in [0,n]
    	double randExc();                       // real number in [0,1)
    	double randExc( const double& n );      // real number in [0,n)
    	double randDblExc();                    // real number in (0,1)
    	double randDblExc( const double& n );   // real number in (0,n)
    	uint32 randInt();                       // integer in [0,2^32-1]
    	uint32 randInt( const uint32& n );      // integer in [0,n] for n < 2^32
    	double operator()() { return rand(); }  // same as rand()

    	// Access to 53-bit random numbers (capacity of IEEE double precision)
    	double rand53();  // real number in [0,1)

    	// Access to nonuniform random number distributions
    	double randNorm( const double& mean = 0.0, const double& variance = 0.0 );

    	// Re-seeding functions with same behavior as initializers
    	void seed( const uint32 oneSeed );
    	void seed( uint32 *const bigSeed, const uint32 seedLength = N );
    	void seed();

    	// Saving and loading generator state
    	void save( uint32* saveArray ) const;  // to array of size SAVE
    	void load( uint32 *const loadArray );  // from such array
    	friend std::ostream& operator<<( std::ostream& os, const MTRand& mtrand );
    	friend std::istream& operator>>( std::istream& is, MTRand& mtrand );

    protected:
    	void initialize( const uint32 oneSeed );
    	void reload();
    	uint32 hiBit( const uint32& u ) const { return u & 0x80000000UL; }
    	uint32 loBit( const uint32& u ) const { return u & 0x00000001UL; }
    	uint32 loBits( const uint32& u ) const { return u & 0x7fffffffUL; }
    	uint32 mixBits( const uint32& u, const uint32& v ) const
    		{ return hiBit(u) | loBits(v); }
    	uint32 twist( const uint32& m, const uint32& s0, const uint32& s1 ) const
    		{ return m ^ (mixBits(s0,s1)>>1) ^ (-loBit(s1) & 0x9908b0dfUL); }
    	static uint32 hash( time_t t, clock_t c );
    };

    inline MTRand::MTRand( const uint32& oneSeed )
    	{ seed(oneSeed); }

    inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength )
    	{ seed(bigSeed,seedLength); }

    inline MTRand::MTRand()
    	{ seed(); }

    inline double MTRand::rand()
    	{ return double(randInt()) * (1.0/4294967295.0); }

    inline double MTRand::rand( const double& n )
    	{ return rand() * n; }

    inline double MTRand::randExc()
    	{ return double(randInt()) * (1.0/4294967296.0); }

    inline double MTRand::randExc( const double& n )
    	{ return randExc() * n; }

    inline double MTRand::randDblExc()
    	{ return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0); }

    inline double MTRand::randDblExc( const double& n )
    	{ return randDblExc() * n; }

    inline double MTRand::rand53()
    {
    	uint32 a = randInt() >> 5, b = randInt() >> 6;
    	return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0);  // by Isaku Wada
    }

    inline double MTRand::randNorm( const double& mean, const double& variance )
    {
    	// Return a real number from a normal (Gaussian) distribution with given
    	// mean and variance by Box-Muller method
    	double r = sqrt( -2.0 * log( 1.0-randDblExc()) ) * variance;
    	double phi = 2.0 * 3.14159265358979323846264338328 * randExc();
    	return mean + r * cos(phi);
    }

    inline MTRand::uint32 MTRand::randInt()
    {
    	// Pull a 32-bit integer from the generator state
    	// Every other access function simply transforms the numbers extracted here

    	if( left == 0 ) reload();
    	--left;

    	register uint32 s1;
    	s1 = *pNext++;
    	s1 ^= (s1 >> 11);
    	s1 ^= (s1 <<  7) & 0x9d2c5680UL;
    	s1 ^= (s1 << 15) & 0xefc60000UL;
    	return ( s1 ^ (s1 >> 18) );
    }

    inline MTRand::uint32 MTRand::randInt( const uint32& n )
    {
    	// Find which bits are used in n
    	// Optimized by Magnus Jonsson (magnus@smartelectronix.com)
    	uint32 used = n;
    	used |= used >> 1;
    	used |= used >> 2;
    	used |= used >> 4;
    	used |= used >> 8;
    	used |= used >> 16;

    	// Draw numbers until one is found in [0,n]
    	uint32 i;
    	do
    		i = randInt() & used;  // toss unused bits to shorten search
    	while( i > n );
    	return i;
    }

    inline void MTRand::seed( const uint32 oneSeed )
    {
    	// Seed the generator with a simple uint32
    	initialize(oneSeed);
    	reload();
    }

    inline void MTRand::seed( uint32 *const bigSeed, const uint32 seedLength )
    {
    	// Seed the generator with an array of uint32's
    	// There are 2^19937-1 possible initial states.  This function allows
    	// all of those to be accessed by providing at least 19937 bits (with a
    	// default seed length of N = 624 uint32's).  Any bits above the lower 32
    	// in each element are discarded.
    	// Just call seed() if you want to get array from /dev/urandom
    	initialize(19650218UL);
    	register int i = 1;
    	register uint32 j = 0;
    	register int k = ( N > seedLength ? N : seedLength );
    	for( ; k; --k )
    	{
    		state[i] =
    			state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL );
    		state[i] += ( bigSeed[j] & 0xffffffffUL ) + j;
    		state[i] &= 0xffffffffUL;
    		++i;  ++j;
    		if( i >= N ) { state[0] = state[N-1];  i = 1; }
    		if( j >= seedLength ) j = 0;
    	}
    	for( k = N - 1; k; --k )
    	{
    		state[i] =
    			state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL );
    		state[i] -= i;
    		state[i] &= 0xffffffffUL;
    		++i;
    		if( i >= N ) { state[0] = state[N-1];  i = 1; }
    	}
    	state[0] = 0x80000000UL;  // MSB is 1, assuring non-zero initial array
    	reload();
    }

    inline void MTRand::seed()
    {
    	// Seed the generator with an array from /dev/urandom if available
    	// Otherwise use a hash of time() and clock() values

    	// First try getting an array from /dev/urandom
    	FILE* urandom = fopen( "/dev/urandom", "rb" );
    	if( urandom )
    	{
    		uint32 bigSeed[N];
    		register uint32 *s = bigSeed;
    		register int i = N;
    		register bool success = true;
    		while( success && i-- )
    			success = fread( s++, sizeof(uint32), 1, urandom ) != 0;
    		fclose(urandom);
    		if( success ) { seed( bigSeed, N );  return; }
    	}

    	// Was not successful, so use time() and clock() instead
    	seed( hash( time(NULL), clock() ) );
    }

    inline void MTRand::initialize( const uint32 seed )
    {
    	// Initialize generator state with seed
    	// See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
    	// In previous versions, most significant bits (MSBs) of the seed affect
    	// only MSBs of the state array.  Modified 9 Jan 2002 by Makoto Matsumoto.
    	register uint32 *s = state;
    	register uint32 *r = state;
    	register int i = 1;
    	*s++ = seed & 0xffffffffUL;
    	for( ; i < N; ++i )
    	{
    		*s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL;
    		r++;
    	}
    }

    inline void MTRand::reload()
    {
    	// Generate N new values in state
    	// Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
    	register uint32 *p = state;
    	register int i;
    	for( i = N - M; i--; ++p )
    		*p = twist( p[M], p[0], p[1] );
    	for( i = M; --i; ++p )
    		*p = twist( p[M-N], p[0], p[1] );
    	*p = twist( p[M-N], p[0], state[0] );

    	left = N, pNext = state;
    }

    inline MTRand::uint32 MTRand::hash( time_t t, clock_t c )
    {
    	// Get a uint32 from t and c
    	// Better than uint32(x) in case x is floating point in [0,1]
    	// Based on code by Lawrence Kirby (fred@genesis.demon.co.uk)

    	static uint32 differ = 0;  // guarantee time-based seeds will change

    	uint32 h1 = 0;
    	unsigned char *p = (unsigned char *) &t;
    	for( size_t i = 0; i < sizeof(t); ++i )
    	{
    		h1 *= UCHAR_MAX + 2U;
    		h1 += p[i];
    	}
    	uint32 h2 = 0;
    	p = (unsigned char *) &c;
    	for( size_t j = 0; j < sizeof(c); ++j )
    	{
    		h2 *= UCHAR_MAX + 2U;
    		h2 += p[j];
    	}
    	return ( h1 + differ++ ) ^ h2;
    }

    inline void MTRand::save( uint32* saveArray ) const
    {
    	register uint32 *sa = saveArray;
    	register const uint32 *s = state;
    	register int i = N;
    	for( ; i--; *sa++ = *s++ ) {}
    	*sa = left;
    }

    inline void MTRand::load( uint32 *const loadArray )
    {
    	register uint32 *s = state;
    	register uint32 *la = loadArray;
    	register int i = N;
    	for( ; i--; *s++ = *la++ ) {}
    	left = *la;
    	pNext = &state[N-left];
    }

    inline std::ostream& operator<<( std::ostream& os, const MTRand& mtrand )
    {
    	register const MTRand::uint32 *s = mtrand.state;
    	register int i = mtrand.N;
    	for( ; i--; os << *s++ << "\t" ) {}
    	return os << mtrand.left;
    }

    inline std::istream& operator>>( std::istream& is, MTRand& mtrand )
    {
    	register MTRand::uint32 *s = mtrand.state;
    	register int i = mtrand.N;
    	for( ; i--; is >> *s++ ) {}
    	is >> mtrand.left;
    	mtrand.pNext = &mtrand.state[mtrand.N-mtrand.left];
    	return is;
    }

    #endif  // MERSENNETWISTER_H

    // Change log:
    //
    // v0.1 - First release on 15 May 2000
    //      - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
    //      - Translated from C to C++
    //      - Made completely ANSI compliant
    //      - Designed convenient interface for initialization, seeding, and
    //        obtaining numbers in default or user-defined ranges
    //      - Added automatic seeding from /dev/urandom or time() and clock()
    //      - Provided functions for saving and loading generator state
    //
    // v0.2 - Fixed bug which reloaded generator one step too late
    //
    // v0.3 - Switched to clearer, faster reload() code from Matthew Bellew
    //
    // v0.4 - Removed trailing newline in saved generator format to be consistent
    //        with output format of built-in types
    //
    // v0.5 - Improved portability by replacing static const int's with enum's and
    //        clarifying return values in seed(); suggested by Eric Heimburg
    //      - Removed MAXINT constant; use 0xffffffffUL instead
    //
    // v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits
    //      - Changed integer [0,n] generator to give better uniformity
    //
    // v0.7 - Fixed operator precedence ambiguity in reload()
    //      - Added access for real numbers in (0,1) and (0,n)
    //
    // v0.8 - Included time.h header to properly support time_t and clock_t
    //
    // v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto
    //      - Allowed for seeding with arrays of any length
    //      - Added access for real numbers in [0,1) with 53-bit resolution
    //      - Added access for real numbers from normal (Gaussian) distributions
    //      - Increased overall speed by optimizing twist()
    //      - Doubled speed of integer [0,n] generation
    //      - Fixed out-of-range number generation on 64-bit machines
    //      - Improved portability by substituting literal constants for long enum's
    //      - Changed license from GNU LGPL to BSD