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ImathRandom.h

///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
// 
// All rights reserved.
// 
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
// *       Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// *       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.
// *       Neither the name of Industrial Light & Magic nor the names of
// its contributors may 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.
//
///////////////////////////////////////////////////////////////////////////


#ifndef INCLUDED_IMATHRANDOM_H
#define INCLUDED_IMATHRANDOM_H

//-----------------------------------------------------------------------------
//
//    Generators for uniformly distributed pseudo-random numbers and
//    functions that use those generators to generate numbers with
//    different distributions:
//
//    class Rand32
//    class Rand48
//    solidSphereRand()
//    hollowSphereRand()
//    gaussRand()
//    gaussSphereRand()
//
//-----------------------------------------------------------------------------

//
// Here is the copyright for the *rand48() functions implemented for
// PLATFORM_DARWIN_PPC and PLATFORM_WINDOWS
//

//
// Copyright (c) 1993 Martin Birgmeier
// All rights reserved.
//
// You may redistribute unmodified or modified versions of this source
// code provided that the above copyright notice and this and the
// following conditions are retained.
//
// This software is provided ``as is'', and comes with no warranties
// of any kind. I shall in no event be liable for anything that happens
// to anyone/anything when using this software.
//

#include <stdlib.h>
#include <math.h>

namespace Imath {


//-----------------------------------------------
// Fast random-number generator that generates
// a uniformly distributed sequence with a period
// length of 2^32.
//-----------------------------------------------

class Rand32
{
  public:

    //------------
    // Constructor
    //------------

    Rand32 (unsigned long int seed = 0);
    

    //--------------------------------
    // Re-initialize with a given seed
    //--------------------------------

    void          init (unsigned long int seed);


    //----------------------------------------------------------
    // Get the next value in the sequence (range: [false, true])
    //----------------------------------------------------------

    bool          nextb ();


    //---------------------------------------------------------------
    // Get the next value in the sequence (range: [0 ... 0xffffffff])
    //---------------------------------------------------------------

    unsigned long int   nexti ();


    //------------------------------------------------------
    // Get the next value in the sequence (range: [0 ... 1[)
    //------------------------------------------------------

    float         nextf ();


    //-------------------------------------------------------------------
    // Get the next value in the sequence (range [rangeMin ... rangeMax[)
    //-------------------------------------------------------------------

    float         nextf (float rangeMin, float rangeMax);


  private:

    void          next ();

    unsigned long int   _state;
};


//--------------------------------------------------------
// Random-number generator based on the C Standard Library
// functions drand48(), lrand48() & company; generates a
// uniformly distributed sequence.
//--------------------------------------------------------

class Rand48
{
  public:

    //------------
    // Constructor
    //------------

    Rand48 (unsigned long int seed = 0);
    

    //--------------------------------
    // Re-initialize with a given seed
    //--------------------------------

    void          init (unsigned long int seed);


    //----------------------------------------------------------
    // Get the next value in the sequence (range: [false, true])
    //----------------------------------------------------------

    bool          nextb ();


    //---------------------------------------------------------------
    // Get the next value in the sequence (range: [0 ... 0x7fffffff])
    //---------------------------------------------------------------

    long int            nexti ();


    //------------------------------------------------------
    // Get the next value in the sequence (range: [0 ... 1[)
    //------------------------------------------------------

    double        nextf ();


    //-------------------------------------------------------------------
    // Get the next value in the sequence (range [rangeMin ... rangeMax[)
    //-------------------------------------------------------------------

    double        nextf (double rangeMin, double rangeMax);


  private:

    unsigned short int  _state[3];
    
#if defined( PLATFORM_DARWIN_PPC ) || defined ( PLATFORM_WINDOWS )
    void                shiftState();
#endif
};


//------------------------------------------------------------
// Return random points uniformly distributed in a sphere with
// radius 1 around the origin (distance from origin <= 1).
//------------------------------------------------------------

template <class Vec, class Rand>
Vec         
solidSphereRand (Rand &rand);


//-------------------------------------------------------------
// Return random points uniformly distributed on the surface of
// a sphere with radius 1 around the origin.
//-------------------------------------------------------------

template <class Vec, class Rand>
Vec         
hollowSphereRand (Rand &rand);


//-----------------------------------------------
// Return random numbers with a normal (Gaussian)
// distribution with zero mean and unit variance.
//-----------------------------------------------

template <class Rand>
float
gaussRand (Rand &rand);


//----------------------------------------------------
// Return random points whose distance from the origin
// has a normal (Gaussian) distribution with zero mean
// and unit variance.
//----------------------------------------------------

template <class Vec, class Rand>
Vec
gaussSphereRand (Rand &rand);


//---------------
// Implementation
//---------------


inline void
Rand32::init (unsigned long int seed)
{
    _state = (seed * 0xa5a573a5L) ^ 0x5a5a5a5aL;
}


inline
Rand32::Rand32 (unsigned long int seed)
{
    init (seed);
}


inline void
Rand32::next ()
{
    _state = 1664525L * _state + 1013904223L;
}


inline bool
Rand32::nextb ()
{
    next ();
    // Return the 31st (most significant) bit, by and-ing with 2 ^ 31.
    return !!(_state & 2147483648UL);
}


inline unsigned long int
Rand32::nexti ()
{
    next ();
    return _state & 0xffffffff;
}


inline float
Rand32::nextf ()
{
    next ();
    return ((int) (_state & 0xffffff)) * ((float) (1.0F / 0x1000000));
}


inline float
Rand32::nextf (float rangeMin, float rangeMax)
{
    return rangeMin + nextf() * (rangeMax - rangeMin);
}


inline void
Rand48::init (unsigned long int seed)
{
    seed = (seed * 0xa5a573a5L) ^ 0x5a5a5a5aL;

    _state[0] = (unsigned short int) (seed);
    _state[1] = (unsigned short int) (seed >> 16);
    _state[2] = (unsigned short int) (seed);
}


inline 
Rand48::Rand48 (unsigned long int seed)
{
    init (seed);
}


#if defined( PLATFORM_DARWIN_PPC ) || defined ( PLATFORM_WINDOWS )

inline void
Rand48::shiftState()
{
    unsigned long   accu;
    unsigned short  temp[2];

    accu = 0xe66dUL * ( unsigned long )_state[0] + 0x000bUL;

    temp[0] = ( unsigned short )accu;     /* lower 16 bits */
    accu >>= sizeof( unsigned short ) * 8;

    accu += 0xe66dUL * ( unsigned long )_state[1] +
          0xdeecUL * ( unsigned long )_state[0];

    temp[1] = ( unsigned short )accu;     /* middle 16 bits */
    accu >>= sizeof( unsigned short ) * 8;

    accu += 0xe66dUL * _state[2] +
          0xdeecUL * _state[1] +
          0x0005UL * _state[0];

    _state[0] = temp[0];
    _state[1] = temp[1];
    _state[2] = ( unsigned short )accu;
}

#endif

inline bool
Rand48::nextb ()
{
#if defined( PLATFORM_DARWIN_PPC ) || defined ( PLATFORM_WINDOWS )
    shiftState();
    return ( ( long( _state[2] ) << 15 ) + ( long( _state[1] ) >> 1 ) ) & 0x1;
#else
    return nrand48 (_state) & 1;
#endif
}


inline long int
Rand48::nexti ()
{
#if defined( PLATFORM_DARWIN_PPC ) || defined ( PLATFORM_WINDOWS )
    shiftState();
    return ( long( _state[2] ) << 15 ) + ( long( _state[1] ) >> 1 );
#else
    return nrand48 (_state);
#endif
}


inline double
Rand48::nextf ()
{
#if defined( PLATFORM_DARWIN_PPC ) || defined ( PLATFORM_WINDOWS )
    shiftState();
    return ldexp( double( _state[0] ), -48 ) +
         ldexp( double( _state[1] ), -32 ) +
         ldexp( double( _state[2] ), -16 );
#else
    return erand48 (_state);
#endif
}


inline double
Rand48::nextf (double rangeMin, double rangeMax)
{
    return rangeMin + nextf() * (rangeMax - rangeMin);
}


template <class Vec, class Rand>
Vec
solidSphereRand (Rand &rand)
{
    Vec v;

    do
    {
      for (unsigned int i = 0; i < Vec::dimensions(); i++)
          v[i] = (typename Vec::BaseType) rand.nextf (-1, 1);
    }
    while (v.length2() > 1);

    return v;
}


template <class Vec, class Rand>
Vec
hollowSphereRand (Rand &rand)
{
    Vec v;
    typename Vec::BaseType length;

    do
    {
      for (unsigned int i = 0; i < Vec::dimensions(); i++)
          v[i] = (typename Vec::BaseType) rand.nextf (-1, 1);

      length = v.length();
    }
    while (length > 1 || length == 0);

    return v / length;
}


template <class Rand>
float
gaussRand (Rand &rand)
{
    float x;            // Note: to avoid numerical problems with very small
    float y;            // numbers, we make these variables singe-precision
    float length2;      // floats, but later we call the double-precision log()
                  // and sqrt() functions instead of logf() and sqrtf().
    do
    {
      x = float (rand.nextf (-1, 1));
      y = float (rand.nextf (-1, 1));
      length2 = x * x + y * y;
    }
    while (length2 >= 1 || length2 == 0);

    return x * sqrt (-2 * log (length2) / length2);
}


template <class Vec, class Rand>
Vec
gaussSphereRand (Rand &rand)
{
    return hollowSphereRand <Vec> (rand) * gaussRand (rand);
}

double drand48();
long int lrand48();

} // namespace Imath

#endif

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