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/*=========================================================================
Program: Visualization Toolkit
Module: vtkMathUtilities.h
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
All rights reserved.
See Copyright.txt or http://www.kitware.com/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 notice for more information.
=========================================================================*/
/**
* @class vtkMathUtilities
* @brief templated utility math functions intended for
* internal use in tests etc.
*
*
* Provide a set of inline, lightweight templated math utility functions.
* The initial motivation is to provide a few lightweight functions to help in
* testing and internal implementation files.
*/
#ifndef vtkMathUtilities_h
#define vtkMathUtilities_h
#include <cmath>
#include <limits>
namespace vtkMathUtilities
{
/**
* Perform a fuzzy compare of floats/doubles.
*/
template<class A>
bool FuzzyCompare(A a, A b)
{
return fabs(a - b) < std::numeric_limits<A>::epsilon();
}
/**
* Perform a fuzzy compare of floats/doubles, specify the allowed tolerance
*/
template<class A>
bool FuzzyCompare(A a, A b, A epsilon)
{
return fabs(a - b) < epsilon;
}
/**
* Performs safe division that catches overflow and underflow.
*/
template<class A>
A SafeDivision(A a, A b)
{
// Avoid overflow
if( (b < static_cast<A>(1)) && (a > b*std::numeric_limits<A>::max()) )
{
return std::numeric_limits<A>::max();
}
// Avoid underflow
if( (a == static_cast<A>(0)) ||
((b > static_cast<A>(1)) && (a < b*std::numeric_limits<A>::min())) )
{
return static_cast<A>(0);
}
// safe to do the division
return( a/b );
}
//@{
/**
* A slightly different fuzzy comparator that checks if two values are
* "nearly" equal based on Knuth, "The Art of Computer Programming (vol II)"
*/
template<class A>
bool NearlyEqual(A a, A b, A tol=std::numeric_limits<A>::epsilon())
{
A absdiff = fabs(a-b);
A d1 = vtkMathUtilities::SafeDivision<A>(absdiff,fabs(a));
A d2 = vtkMathUtilities::SafeDivision<A>(absdiff,fabs(b));
//@}
if( (d1 <= tol) || (d2 <= tol) )
{
return true;
}
return false;
}
} // End vtkMathUtilities namespace.
#endif // vtkMathUtilities_h
// VTK-HeaderTest-Exclude: vtkMathUtilities.h
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