MersenneTwister.hpp

Go to the documentation of this file.

// 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.

// Minor modifications made by Michele Bosi:
// - MTRand renamed MersenneTwister.
// - MersenneTwister derived from vl::Object.
// - MersenneTwister included in vl namespace to avoid collisions with other MersenneTwister versions.
// - prepended VL_ to MERSENNETWISTER_H to avoid collisions with other MersenneTwister headers.
// - fixed minor warnings.

#ifndef VL_MERSENNETWISTER_H
#define VL_MERSENNETWISTER_H

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

#include <iostream>
#include <climits>
#include <cstdio>
#include <ctime>
#include <cmath>
#include <vlCore/Object.hpp>

namespace vl
{
  //-------------------------------------------------------------------------
  class MersenneTwister;
  //-------------------------------------------------------------------------
  VLCORE_EXPORT MersenneTwister* defMersenneTwister();
  VLCORE_EXPORT void setDefMersenneTwister(MersenneTwister*);
  //-------------------------------------------------------------------------
  class MersenneTwister: public Object
  {
  // 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:
      MersenneTwister( const uint32 oneSeed );  // initialize with a simple uint32
      MersenneTwister( uint32 *const bigSeed, uint32 const seedLength = N );  // or array
      MersenneTwister();  // auto-initialize with /dev/urandom or time() and clock()
      MersenneTwister( const MersenneTwister& 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 MersenneTwister& mtrand );
      friend std::istream& operator>>( std::istream& is, MersenneTwister& mtrand );
      MersenneTwister& operator=( const MersenneTwister& 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 MersenneTwister::uint32 MersenneTwister::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 MersenneTwister::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 MersenneTwister::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
      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 MersenneTwister::seed( const uint32 oneSeed )
  {
      // Seed the generator with a simple uint32
      initialize(oneSeed);
      reload();
  }

  inline void MersenneTwister::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 ? (int)N : (int)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 MersenneTwister::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 ) != 0;
          fclose(urandom);
          if( success ) { seed( bigSeed, N );  return; }
      }
    
      // Was not successful, so use time() and clock() instead
      seed( hash( time(NULL), clock() ) );
  }

  inline MersenneTwister::MersenneTwister( const uint32 oneSeed )
      { seed(oneSeed); }

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

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

  inline MersenneTwister::MersenneTwister( const MersenneTwister& o ): Object(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 MersenneTwister::uint32 MersenneTwister::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 MersenneTwister::uint32 MersenneTwister::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 MersenneTwister::rand()
      { return double(randInt()) * (1.0/4294967295.0); }

  inline double MersenneTwister::rand( const double n )
      { return rand() * n; }

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

  inline double MersenneTwister::randExc( const double n )
      { return randExc() * n; }

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

  inline double MersenneTwister::randDblExc( const double n )
      { return randDblExc() * n; }

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

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

  inline void MersenneTwister::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 MersenneTwister::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 MersenneTwister& mtrand )
  {
      register const MersenneTwister::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, MersenneTwister& mtrand )
  {
      register MersenneTwister::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 MersenneTwister& MersenneTwister::operator=( const MersenneTwister& 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