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/*=========================================================================
*
* Copyright Insight Software Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0.txt
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*=========================================================================*/
#ifndef itkCompensatedSummation_h
#define itkCompensatedSummation_h
#include "itkNumericTraits.h"
#include "itkConceptChecking.h"
namespace itk
{
/** \class CompensatedSummation
* \brief Perform more precise accumulation of floating point numbers.
*
* The \c float and \c double datatypes only have finite precision. When
* performing a running sum of floats, the accumulated errors get progressively
* worse as the magnitude of the sum gets large relative to new elements.
*
* From Wikipedia, http://en.wikipedia.org/wiki/Kahan_summation_algorithm
*
* "In numerical analysis, the Kahan summation algorithm (also known as
* compensated summation) significantly reduces the numerical error in the total
* obtained by adding a sequence of finite precision floating point numbers,
* compared to the obvious approach. This is done by keeping a separate running
* compensation (a variable to accumulate small errors)."
*
* For example, instead of
* \code
* double sum = 0.0;
* for( unsigned int i = 0; i < array.Size(); ++i )
* {
* sum += array.GetElement(i);
* }
* \endcode
*
* do
*
* \code
* typedef CompensatedSummation<double> CompensatedSummationType;
* CompensatedSummationType compensatedSummation;
* for( unsigned int i = 0; i < array.Size(); ++i )
* {
* compensatedSummation += array.GetElement(i);
* }
* double sum = compensatedSummation.GetSum();
* \endcode
*
* \ingroup ITKCommon
*/
template < typename TFloat >
class ITK_TEMPLATE_EXPORT CompensatedSummation
{
public:
/** Type of the input elements. */
typedef TFloat FloatType;
/** Type used for the sum and compensation. */
typedef typename NumericTraits< FloatType >::AccumulateType AccumulateType;
/** Standard class typedefs. */
typedef CompensatedSummation Self;
/** Constructor. */
CompensatedSummation();
/** Copy constructor. */
CompensatedSummation( const Self & rhs );
/** Assignment operator. */
Self & operator=( const Self & rhs );
/** Add an element to the sum. */
void AddElement( const FloatType & element );
Self & operator+=( const FloatType & rhs );
/** Subtract an element from the sum. */
Self & operator-=( const FloatType & rhs );
/** Division and multiplication. These do not provide any numerical advantages
* relative to vanilla division and multiplication. */
Self & operator*=( const FloatType & rhs );
Self & operator/=( const FloatType & rhs );
/** Reset the sum and compensation to zero. */
void ResetToZero();
/** Reset the sum to the given value and the compensation to zero. */
Self & operator=( const FloatType & rhs );
/** Get the sum. */
const AccumulateType & GetSum() const;
private:
AccumulateType m_Sum;
AccumulateType m_Compensation;
// Maybe support more types in the future with template specialization.
#ifdef ITK_USE_CONCEPT_CHECKING
itkConceptMacro( OnlyDefinedForFloatingPointTypes, ( itk::Concept::IsFloatingPoint< TFloat > ) );
#endif // ITK_USE_CONCEPT_CHECKING
};
void ITKCommon_EXPORT CompensatedSummationAddElement( float& compensation, float& sum, const float& element );
void ITKCommon_EXPORT CompensatedSummationAddElement( double& compensation, double& sum, const double& element );
} // end namespace itk
#ifndef ITK_MANUAL_INSTANTIATION
#include "itkCompensatedSummation.hxx"
#endif
#endif
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