MersenneTwister.h

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// 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  wagnerr@umich.edu
 
// 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: m-mat@math.sci.hiroshima-u.ac.jp
//     with an appropriate reference to your work.
// 
// It would be nice to CC: wagnerr@umich.edu 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 <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 (fred@genesis.demon.co.uk)
    
    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.
    uint32 *s = state;
    uint32 *r = state;
    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)
    static const int MmN = int(M) - int(N);  // in case enums are unsigned
    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[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);
    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();
}
 
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];
        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() ) );
}
 
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 )
{
    const uint32 *t = o.state;
    uint32 *s = state;
    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;
    
    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 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
{
    const uint32 *s = state;
    uint32 *sa = saveArray;
    int i = N;
    for( ; i--; *sa++ = *s++ ) {}
    *sa = left;
}
 
inline 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];
}
 
inline 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;
}
 
inline 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;
}
 
inline MTRand& MTRand::operator=( const MTRand& o )
{
    if( this == &o ) return (*this);
    const uint32 *t = o.state;
    uint32 *s = state;
    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