Loading [MathJax]/extensions/tex2jax.js
LSST Applications g04a91732dc+2945638123,g07dc498a13+7e3c5f68a2,g12483e3c20+e0fa9c8503,g1409bbee79+7e3c5f68a2,g1a7e361dbc+7e3c5f68a2,g1fd858c14a+9f35e23ec3,g35bb328faa+fcb1d3bbc8,g3ad4f90e5c+e0fa9c8503,g3bd4b5ce2c+36fb6ead7f,g4e0f332c67+5d362be553,g53246c7159+fcb1d3bbc8,g5477a8d5ce+db04660fe6,g60b5630c4e+e0fa9c8503,g75b6c65c88+55830bd904,g78460c75b0+2f9a1b4bcd,g786e29fd12+cf7ec2a62a,g7b71ed6315+fcb1d3bbc8,g8852436030+4639f750a5,g89139ef638+7e3c5f68a2,g8f1d76f86f+11a01f47f4,g9125e01d80+fcb1d3bbc8,g919ac25b3e+28db628500,g95236ca021+f7a31438ed,g989de1cb63+7e3c5f68a2,g9f33ca652e+d1e6496fea,ga365f290ef+26a6f9aaf0,gaaedd4e678+7e3c5f68a2,gabe3b4be73+1e0a283bba,gb1101e3267+c09b629e83,gb4a253aaf5+0122250889,gb58c049af0+f03b321e39,gbaa7868d32+e0fa9c8503,gc99c83e5f0+76d20ab76d,gcf25f946ba+4639f750a5,gd6cbbdb0b4+c8606af20c,gde0f65d7ad+021d0de224,ge278dab8ac+932305ba37,gfba249425e+fcb1d3bbc8,w.2025.08
LSST Data Management Base Package
All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Properties Friends Macros Modules Pages
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
 
SafeSumoperator= (T value) noexcept
 
SafeSumoperator+= (T value) noexcept
 
SafeSumoperator-= (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.

65 :
66 _sum(initial),
67 _correction(static_cast<T>(0))
68 {}
A numerically stable summation algorithm for floating-point numbers.
Definition SafeSum.h:62

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.

93 {
94 return _sum + _correction;
95 }

◆ operator+=()

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

Definition at line 76 of file SafeSum.h.

76 {
77 T t = _sum + value;
78 // update _correction to account for lost low-order bits of the
79 // greater of _sum and value
80 if (std::abs(_sum) >= std::abs(value)) {
81 _correction += (_sum - t) + value;
82 } else {
83 _correction += (value - t) + _sum;
84 }
85 _sum = t;
86 return *this;
87 }

◆ operator-=()

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

Definition at line 89 of file SafeSum.h.

89 {
90 return operator+=(-value);
91 }
SafeSum & operator+=(T value) noexcept
Definition SafeSum.h:76

◆ operator=()

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

Definition at line 70 of file SafeSum.h.

70 {
71 _sum = value;
72 _correction = static_cast<T>(0);
73 return *this;
74 }

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