itkMersenneTwisterRandomVariateGenerator.h

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/*=========================================================================

  Program:   Insight Segmentation & Registration Toolkit
  Module:    $RCSfile: itkMersenneTwisterRandomVariateGenerator.h,v $
  Language:  C++
  Date:      $Date: 2005/06/01 12:58:03 $
  Version:   $Revision: 1.12 $

  Copyright (c) Insight Software Consortium. All rights reserved.
  See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even 
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR 
     PURPOSE.  See the above copyright notices for more information.

=========================================================================*/
#ifndef __itkMersenneTwisterRandomVariateGenerator_h
#define __itkMersenneTwisterRandomVariateGenerator_h

#include "itkMacro.h"
#include "itkObjectFactory.h"
#include "itkRandomVariateGeneratorBase.h"
#include "itkIntTypes.h"
#include "vcl_ctime.h"
#include "vnl/vnl_math.h"
#include <limits.h>


namespace itk {
namespace Statistics {

class MersenneTwisterRandomVariateGenerator : 
    public RandomVariateGeneratorBase
{
public:
  
  typedef MersenneTwisterRandomVariateGenerator Self ;
  typedef RandomVariateGeneratorBase Superclass;
  typedef SmartPointer<Self>   Pointer;
  typedef SmartPointer<const Self>  ConstPointer;
  typedef ITK_UINT32 IntegerType;

  itkTypeMacro(MersenneTwisterRandomVariateGenerator, 
               RandomVariateGeneratorBase );
 
  itkNewMacro(Self);
    
  itkStaticConstMacro(StateVectorLength,IntegerType,624);
 
  // itkStaticConstMacro(SAVE,IntegerType,625);
  
  
  
  // Methods to reseed
  
  void Initialize( const IntegerType oneSeed );
  
  //void Initialize( IntegerType *const bigSeed, 
  //        IntegerType const seedLength = StateVectorLength );  
  
  /* Initialize with vcl_clock time */ 
  void Initialize();  


  
  // Methods to get various random variates ...
  
  double GetVariateWithClosedRange();

  double GetVariateWithClosedRange( const double& n );
    
  double GetVariateWithOpenUpperRange();
  
  double GetVariateWithOpenUpperRange( const double& n );
  
  double GetVariateWithOpenRange();
  
  double GetVariateWithOpenRange( const double& n );
  
  IntegerType GetIntegerVariate();
  
  IntegerType GetIntegerVariate( const IntegerType& n );      
  
  double Get53BitVariate();
  
  /* Access to a normal random number distribution 
   * TODO: Compare with vnl_sample_normal */
  double GetNormalVariate( const double& mean = 0.0, 
      const double& variance = 1.0 );
  
  /* Access to a uniform random number distribution in the range [a, b)
   * TODO: Compare with vnl_sample_uniform */
  double GetUniformVariate( const double& a, const double& b );
  
  virtual double GetVariate();
     
  double operator()(); 
   

  // Re-seeding functions with same behavior as initializers
  inline void SetSeed( const IntegerType oneSeed );
  inline void SetSeed( IntegerType * bigSeed, const IntegerType seedLength = StateVectorLength );
  inline void SetSeed();

  /*
  // Saving and loading generator state
  void save( IntegerType* saveArray ) const;  // to array of size SAVE
  void load( IntegerType *const loadArray );  // from such array
  */

 protected:
  inline MersenneTwisterRandomVariateGenerator();
  virtual ~MersenneTwisterRandomVariateGenerator() {}; 
  virtual void PrintSelf(std::ostream& os, Indent indent) const;

  // enum { M = 397 };  // period parameter
  itkStaticConstMacro ( M, unsigned int, 397 );
  
  IntegerType state[StateVectorLength];   // internal state
  IntegerType *pNext;     // next value to get from state
  int left;          // number of values left before reload needed

  /* Reload array with N new values */
  void reload();
  
  IntegerType hiBit( const IntegerType& u ) const { return u & 0x80000000UL; }
  IntegerType loBit( const IntegerType& u ) const { return u & 0x00000001UL; }
  IntegerType loBits( const IntegerType& u ) const { return u & 0x7fffffffUL; }
  IntegerType mixBits( const IntegerType& u, const IntegerType& v ) const
    { 
    return hiBit(u) | loBits(v); 
    }
  IntegerType twist( const IntegerType& m, const IntegerType& s0, const IntegerType& s1 ) const
    { 
    return m ^ (mixBits(s0,s1)>>1) ^ (-loBit(s1) & 0x9908b0dfUL); 
    }
  static IntegerType hash( vcl_time_t t, vcl_clock_t c );
} ;  // end of class
  



// Declare inlined functions.... (must be declared in the header)
// Declare then in order to keep SGI happy

inline MersenneTwisterRandomVariateGenerator::IntegerType 
  MersenneTwisterRandomVariateGenerator::hash( vcl_time_t t, vcl_clock_t c )
  {
  // Get a IntegerType from t and c
  // Better than IntegerType(x) in case x is floating point in [0,1]
  // Based on code by Lawrence Kirby: fred at genesis dot demon dot co dot uk 

  static IntegerType differ = 0;  // guarantee time-based seeds will change

  IntegerType h1 = 0;
  unsigned char *p = (unsigned char *) &t;
  for( size_t i = 0; i < sizeof(t); ++i )
    {
    h1 *= UCHAR_MAX + 2U;
    h1 += p[i];
    }
  IntegerType 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 
  MersenneTwisterRandomVariateGenerator::Initialize( const IntegerType 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 IntegerType *s = state;
  register IntegerType *r = state;
  register IntegerType i = 1;
  *s++ = seed & 0xffffffffUL;
  for( ; i < MersenneTwisterRandomVariateGenerator::StateVectorLength; ++i )
    {
    *s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL;
    r++;
    }
  }

inline void 
  MersenneTwisterRandomVariateGenerator::reload()
  {
  // Generate N new values in state
  // Made clearer and faster by Matthew Bellew 
  // matthew dot bellew at home dot com
  
  // get rid of VS warning
  register int index = static_cast< int >(
      M-MersenneTwisterRandomVariateGenerator::StateVectorLength);
    
  register IntegerType *p = state;
  register int i;
  for( i = MersenneTwisterRandomVariateGenerator::StateVectorLength - M; i--; ++p )
    *p = twist( p[M], p[0], p[1] );
  for( i = M; --i; ++p )
    *p = twist( p[index], p[0], p[1] );
  *p = twist( p[index], p[0], state[0] );

  left = MersenneTwisterRandomVariateGenerator::StateVectorLength, pNext = state;
  }



#define SVL 624
inline void 
  MersenneTwisterRandomVariateGenerator::SetSeed( 
      IntegerType * const bigSeed, const IntegerType seedLength )
  {
  // Seed the generator with an array of IntegerType'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 StateVectorLength = 624 IntegerType'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 IntegerType i = 1;
  register IntegerType j = 0;
  register int k;
  if ( StateVectorLength > seedLength )
    {
    k = StateVectorLength;
    }
  else
    {
    k = 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 >= StateVectorLength ) { state[0] = state[StateVectorLength-1];  i = 1; }
    if( j >= seedLength ) j = 0;
    }
  for( k = StateVectorLength - 1; k; --k )
    {
    state[i] =
      state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL );
    state[i] -= i;
    state[i] &= 0xffffffffUL;
    ++i;
    if( i >= SVL ) 
      { 
      state[0] = state[StateVectorLength-1];  i = 1; 
      }
    }
  state[0] = 0x80000000UL;  // MSB is 1, assuring non-zero initial array
  reload();
}


inline void
  MersenneTwisterRandomVariateGenerator::Initialize()
  { 
  SetSeed(); 
  }


inline void 
  MersenneTwisterRandomVariateGenerator::SetSeed( const IntegerType oneSeed )
  {
  // Seed the generator with a simple IntegerType
  Initialize(oneSeed);
  reload();
  }


inline void 
  MersenneTwisterRandomVariateGenerator::SetSeed()
  {
  /*
  // 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 )
    {
    IntegerType bigSeed[MersenneTwisterRandomVariateGenerator::StateVectorLength];
    register IntegerType *s = bigSeed;
    register IntegerType i = MersenneTwisterRandomVariateGenerator::StateVectorLength;
    register bool success = true;
    while( success && i-- )
      success = fread( s++, sizeof(IntegerType), 1, urandom );
    fclose(urandom);
    if( success ) { seed( bigSeed, MersenneTwisterRandomVariateGenerator::StateVectorLength );  return; }
    }
   */
   // Was not successful, so use time() and clock() instead
   // /dev/urandom is not portable, just use the clock
  SetSeed( hash( vcl_time(0), vcl_clock() ) );
  }



inline MersenneTwisterRandomVariateGenerator::IntegerType 
  MersenneTwisterRandomVariateGenerator::GetIntegerVariate()
  {
  if( left == 0 ) reload();
  --left;

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


inline double 
  MersenneTwisterRandomVariateGenerator::GetVariateWithClosedRange()
  { 
  return double(GetIntegerVariate()) * (1.0/4294967295.0); 
  }

inline double 
  MersenneTwisterRandomVariateGenerator::GetVariateWithClosedRange( 
                                                    const double& n )
  { 
  return rand() * n; 
  }

inline double 
  MersenneTwisterRandomVariateGenerator::GetVariateWithOpenUpperRange()
  { 
  return double(GetIntegerVariate()) * (1.0/4294967296.0); 
  }

inline double 
  MersenneTwisterRandomVariateGenerator::GetVariateWithOpenUpperRange( 
                                                      const double& n )
  { 
  return GetVariateWithOpenUpperRange() * n; 
  }
  
inline double 
  MersenneTwisterRandomVariateGenerator::GetVariateWithOpenRange()
  {
  return ( double(GetIntegerVariate()) + 0.5 ) * (1.0/4294967296.0); 
  }


inline double 
  MersenneTwisterRandomVariateGenerator::GetVariateWithOpenRange( 
                                                  const double& n )
  { 
  return GetVariateWithOpenRange() * n; 
  }


inline MersenneTwisterRandomVariateGenerator::IntegerType 
  MersenneTwisterRandomVariateGenerator::GetIntegerVariate( 
                                        const IntegerType& n )
  {
  // Find which bits are used in n
  // Optimized by Magnus Jonsson magnus at smartelectronix dot com
  IntegerType 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]
  IntegerType i;
  do
    {
    i = GetIntegerVariate() & used;  // toss unused bits to shorten search
    }  while( i > n );
  
  return i;
  }



inline double 
  MersenneTwisterRandomVariateGenerator::Get53BitVariate()  
  {
  IntegerType a = GetIntegerVariate() >> 5, b = GetIntegerVariate() >> 6;
  return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0);  // by Isaku Wada
  }
  

/* Access to a normal randon number distribution */
// TODO: Compare with vnl_sample_normal
inline double 
  MersenneTwisterRandomVariateGenerator::GetNormalVariate( 
      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 = vcl_sqrt( -2.0 * vcl_log( 1.0-GetVariateWithOpenRange()) ) * variance;
  double phi = 2.0 * 3.14159265358979323846264338328 
                          * GetVariateWithOpenUpperRange();
  return mean + r * vcl_cos(phi);
  }



/* Access to a uniform random number distribution */
// TODO: Compare with vnl_sample_uniform
inline double 
  MersenneTwisterRandomVariateGenerator::GetUniformVariate( 
                            const double& a, const double& b )
  {
  double u = GetVariateWithOpenUpperRange();
  return ((1.0 -u) * a + u * b); 
  }


inline double 
  MersenneTwisterRandomVariateGenerator::GetVariate() 
  {
  return GetVariateWithClosedRange();
  }


inline double 
  MersenneTwisterRandomVariateGenerator::operator()()
  { 
  return GetVariate(); 
  }  
 

inline 
  MersenneTwisterRandomVariateGenerator::MersenneTwisterRandomVariateGenerator()
  {
  Initialize();
  }
  

/* Change log from MTRand.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

} // end of namespace Statistics
} // end of namespace itk

#endif

---