///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002-2012, 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
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///////////////////////////////////////////////////////////////////////////
#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
// non-uniform distributions:
//
// class Rand32
// class Rand48
// solidSphereRand()
// hollowSphereRand()
// gaussRand()
// gaussSphereRand()
//
// Note: class Rand48() calls erand48() and nrand48(), which are not
// available on all operating systems. For compatibility we include
// our own versions of erand48() and nrand48(). Our functions have
// been reverse-engineered from the corresponding Unix/Linux man page.
//
//-----------------------------------------------------------------------------
#include "ImathNamespace.h"
#include "ImathExport.h"
#include <stdlib.h>
#include <math.h>
IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
//-----------------------------------------------
// Fast random-number generator that generates
// a uniformly distributed sequence with a period
// length of 2^32.
//-----------------------------------------------
class IMATH_EXPORT 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 erand48(), nrand48() & 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];
};
//------------------------------------------------------------
// 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);
//---------------------------------
// erand48(), nrand48() and friends
//---------------------------------
IMATH_EXPORT double erand48 (unsigned short state[3]);
IMATH_EXPORT double drand48 ();
IMATH_EXPORT long int nrand48 (unsigned short state[3]);
IMATH_EXPORT long int lrand48 ();
IMATH_EXPORT void srand48 (long int seed);
//---------------
// 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 (float rangeMin, float rangeMax)
{
float f = nextf();
return rangeMin * (1 - f) + rangeMax * f;
}
inline void
Rand48::init (unsigned long int seed)
{
seed = (seed * 0xa5a573a5L) ^ 0x5a5a5a5aL;
_state[0] = (unsigned short int) (seed & 0xFFFF);
_state[1] = (unsigned short int) ((seed >> 16) & 0xFFFF);
_state[2] = (unsigned short int) (seed & 0xFFFF);
}
inline
Rand48::Rand48 (unsigned long int seed)
{
init (seed);
}
inline bool
Rand48::nextb ()
{
return nrand48 (_state) & 1;
}
inline long int
Rand48::nexti ()
{
return nrand48 (_state);
}
inline double
Rand48::nextf ()
{
return erand48 (_state);
}
inline double
Rand48::nextf (double rangeMin, double rangeMax)
{
double f = nextf();
return rangeMin * (1 - f) + rangeMax * f;
}
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 (double (length2)) / length2);
}
template <class Vec, class Rand>
Vec
gaussSphereRand (Rand &rand)
{
return hollowSphereRand <Vec> (rand) * gaussRand (rand);
}
IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
#endif // INCLUDED_IMATHRANDOM_H