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  v1.0  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.

// changed the #ifndef for wfmath in case someone uses both the lib
// and the identical header separately

#ifndef MERSENNETWISTER_WFMATH_H
#define MERSENNETWISTER_WFMATH_H

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

#include <iosfwd>
#include <climits>
#include <cmath>

// namespace safety for inclusion in the lib

namespace WFMath {

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 );

        static MTRand instance;

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); }
};


inline MTRand::MTRand( const uint32& oneSeed ) : pNext(0), left(0)
        { seed(oneSeed); }

inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength ) : pNext(0), left(0)
        { seed(bigSeed,seedLength); }

inline MTRand::MTRand() : pNext(0), left(0)
        { 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::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 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];
}


} // namespace

#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