// 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