lsst::geom::polynomials::SafeSum< T > Class Template Reference

A numerically stable summation algorithm for floating-point numbers. More...

#include <SafeSum.h>

Public Member Functions
	SafeSum (T initial=static_cast< T >(0)) noexcept
SafeSum &	operator= (T value) noexcept
SafeSum &	operator+= (T value) noexcept
SafeSum &	operator-= (T value) noexcept
	operator T () const noexcept

Detailed Description

template<typename T>
class lsst::geom::polynomials::SafeSum< T >

A numerically stable summation algorithm for floating-point numbers.

SafeSum implements += and -= operators that can be used to accumulate floating point numbers with very different magnitudes, with accuracy limited only by the usual floating-point inaccuracy in represented the final sum.

SafeSum is explicitly convertible to and from its underlying floating-point type and only supports in-place addition and subtraction, in order to avoid cases where a combination of implicit conversion and multiple overloaded operators could lead to accidental use of regular floating-point operations.

SafeSum uses the Kahan-Neumaier algorithm (though this should be considered an implementation detail by callers), which maintains a lower-order-bit correction that compensates for the loss of precision in the main sum. Particularly aggressive compiler optimizations that do not preserve IEEE floating point behavior (e.g. gcc's -fassociative-math) may optimize away the correction and reduce SafeSum's behavior to a standard unsafe sum.

Definition at line 62 of file SafeSum.h.

Constructor & Destructor Documentation

SafeSum()

template<typename T>

lsst::geom::polynomials::SafeSum< T >::SafeSum ( T  initial = static_cast<T>(0) )

inlineexplicitnoexcept

Definition at line 65 of file SafeSum.h.

                                                           :
        _sum(initial),
        _correction(static_cast<T>(0))
    {}

Member Function Documentation

operator T()

template<typename T>

lsst::geom::polynomials::SafeSum< T >::operator T ( ) const

inlineexplicitnoexcept

Definition at line 93 of file SafeSum.h.

                                         {
        return _sum + _correction;
    }

operator+=()

template<typename T>

SafeSum& lsst::geom::polynomials::SafeSum< T >::operator+= ( T  value )

inlinenoexcept

Definition at line 76 of file SafeSum.h.

                                           {
        T t = _sum + value;
        // update _correction to account for lost low-order bits of the
        // greater of _sum and value
        if (std::abs(_sum) >= std::abs(value)) {
            _correction += (_sum - t) + value;
        } else {
            _correction += (value - t) + _sum;
        }
        _sum = t;
        return *this;
    }

operator-=()

template<typename T>

SafeSum& lsst::geom::polynomials::SafeSum< T >::operator-= ( T  value )

inlinenoexcept

Definition at line 89 of file SafeSum.h.

                                           {
        return operator+=(-value);
    }

operator=()

template<typename T>

SafeSum& lsst::geom::polynomials::SafeSum< T >::operator= ( T  value )

inlinenoexcept

Definition at line 70 of file SafeSum.h.

                                          {
        _sum = value;
        _correction = static_cast<T>(0);
        return *this;
    }

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The documentation for this class was generated from the following file:

• /j/snowflake/release/lsstsw/stack/Linux64/geom/19.0.0-1-ge3aa853/include/lsst/geom/polynomials/SafeSum.h