MersenneTwister.h

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/*
 * @file MersenneTwister.h
 * @brief Header file for Mersenne Twister random number generator
 *
 * @details 
 * 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 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) ^ (-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;
 
       uint32 s1;        // dol delted leading register
       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);
       int i = 1;        // dol delted leading register
       uint32 j = 0;        // dol delted leading register
       int k = ( N > seedLength ? N : seedLength );        // dol delted leading register
       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;        // dol delted leading register
              int i = N;        // dol delted leading register
              bool success = true;        // dol delted leading register
              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.
       uint32 *s = state;        // dol delted leading register
       uint32 *r = state;        // dol delted leading register
       int i = 1;        // dol delted leading register
       *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)
       uint32 *p = state;        // dol delted leading register
       int i;        // dol delted leading register
       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 (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::save( uint32* saveArray ) const
{
       uint32 *sa = saveArray;        // dol delted leading register
       const uint32 *s = state;        // dol delted leading register
       int i = N;        // dol delted leading register
       for( ; i--; *sa++ = *s++ ) {}
       *sa = left;
}
 
 
inline void MTRand::load( uint32 *const loadArray )
{
       uint32 *s = state;        // dol delted leading register
       uint32 *la = loadArray;        // dol delted leading register
       int i = N;        // dol delted leading register
       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;        // dol delted leading register
       int i = mtrand.N;        // dol delted leading register
       for( ; i--; os << *s++ << "\t" ) {}
       return os << mtrand.left;
}
 
 
inline std::istream& operator>>( std::istream& is, MTRand& mtrand )
{
       MTRand::uint32 *s = mtrand.state;        // dol delted leading register
       int i = mtrand.N;        // dol delted leading register
       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