Mersenne Twister random number generator -- a C++ class MTRand

MersenneTwister.h

// 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  v1.1  28 September 2009  [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.sci.hiroshima-u.ac.jp/~m-mat/MT/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 - 2009, 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 <iostream>
#include <climits>
#include <cstdio>
#include <ctime>
#include <cmath>

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 array
		MTRand();  // auto-initialize with /dev/urandom or time() and clock()
		MTRand( const MTRand& o );  // copy

		// 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
		uint32 randInt();                     // integer in [0,2^32-1]
		uint32 randInt( const uint32 n );     // integer in [0,n] for n < 2^32
		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)
		double operator()();                  // 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 stddev = 1.0 );

		// 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 );
		MTRand& operator=( const MTRand& o );

	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 magic( const uint32 u ) const
		{ return loBit(u) ? 0x9908b0dfUL : 0x0UL; }
		uint32 twist( const uint32 m, const uint32 s0, const uint32 s1 ) const
		{ return m ^ (mixBits(s0,s1)>>1) ^ magic(s1); }
		static uint32 hash( time_t t, clock_t c );
};

// Functions are defined in order of usage to assist inlining

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::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])
	static const int MmN = int(M) - int(N);  // in case enums are unsigned
	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[MmN], p[0], p[1] );
	*p = twist( p[MmN], p[0], state[0] );

	left = N, pNext = state;
}

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

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

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

inline MTRand::MTRand( const MTRand& o )
{
	register const uint32 *t = o.state;
	register uint32 *s = state;
	register int i = N;
	for( ; i--; *s++ = *t++ ) {}
	left = o.left;
	pNext = &state[N-left];
}

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 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 stddev )
{
	// Return a real number from a normal (Gaussian) distribution with given
	// mean and standard deviation by polar form of Box-Muller transformation
	double x, y, r;
	do
	{
		x = 2.0 * rand() - 1.0;
		y = 2.0 * rand() - 1.0;
		r = x * x + y * y;
	}
	while ( r >= 1.0 || r == 0.0 );
	double s = sqrt( -2.0 * log(r) / r );
	return mean + x * s * stddev;
}

inline double MTRand::operator()()
{
	return rand();
}

inline void MTRand::save( uint32* saveArray ) const
{
	register const uint32 *s = state;
	register uint32 *sa = saveArray;
	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;
}

inline MTRand& MTRand::operator=( const MTRand& o )
{
	if( this == &o ) return (*this);
	register const uint32 *t = o.state;
	register uint32 *s = state;
	register int i = N;
	for( ; i--; *s++ = *t++ ) {}
	left = o.left;
	pNext = &state[N-left];
	return (*this);
}

#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
//
// v1.1 - Corrected parameter label in randNorm from "variance" to "stddev"
//      - Changed randNorm algorithm from basic to polar form for efficiency
//      - Updated includes from deprecated <xxxx.h> to standard <cxxxx> forms
//      - Cleaned declarations and definitions to please Intel compiler
//      - Revised twist() operator to work on ones'-complement machines
//      - Fixed reload() function to work when N and M are unsigned
//      - Added copy constructor and copy operator from Salvador Espana