// 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  [email protected]

// 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: [email protected]

//     with an appropriate reference to your work.

//

// It would be nice to CC: [email protected] and [email protected]

// 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 <limits.h>

#include <stdio.h>

#include <time.h>

#include <math.h>

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

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 ([email protected])

	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 );

		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 ([email protected])

	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 ([email protected])

	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];

}

#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