mersennetwister.h

/**
* High performance random generator.
* Mersenne Twister

@article{matsumoto1998mtd,
  title={{Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator}},
  author={MATSUMOTO, M. and NISHIMURA, T.},
  journal={ACM Transactions on Modeling and Computer Simulation},
  volume={8},
  number={1},
  pages={3-30},
  year={1998}
}
*/
// 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 <iostream>
#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
    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) ^ (-static_cast<long>(loBit(s1)) & 0x9908b0dfUL);
    }
    static uint32 hash( time_t t, clock_t c );
};


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

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

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

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

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

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

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

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

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

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

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);
}

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;

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

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;
}


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


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);
    int i = 1;
    uint32 j = 0;
    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();
}


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];
        uint32 *s = bigSeed;
        int i = N;
        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() ) );
}


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.
    uint32 *s = state;
    uint32 *r = state;
    int i = 1;
    *s++ = seed & 0xffffffffUL;
    for( ; i < N; ++i )
    {
        *s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL;
        r++;
    }
}


void MTRand::reload()
{
    // Generate N new values in state
    // Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
    uint32 *p = state;
    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;
}


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


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


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


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


std::istream& operator>>( std::istream& is, MTRand& mtrand )
{
    MTRand::uint32 *s = mtrand.state;
    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