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) ^ (-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;

  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::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 );
    }
    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.
  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 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;
}


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];
}


inline std::ostream& operator<<( std::ostream& os, const MTRand& mtrand ) {
  register const MTRand::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, MTRand& mtrand ) {
  register MTRand::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;
}

#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