Editing Kahan summation algorithm (section)

==Support by libraries==
In general, built-in "sum" functions in computer languages typically provide no guarantees that a particular summation algorithm will be employed, much less Kahan summation.{{Citation needed|date=February 2010}}  The [[BLAS]] standard for [[linear algebra]] subroutines explicitly avoids mandating any particular computational order of operations for performance reasons,<ref>[http://www.netlib.org/blas/blast-forum/ BLAS Technical Forum], section 2.7 (August 21, 2001), [https://web.archive.org/web/20040410160918/http://www.netlib.org/blas/blast-forum/chapter2.pdf#page=17 Archived on Wayback Machine].</ref> and BLAS implementations typically do not use Kahan summation.
 
The standard library of the [[Python (programming language)|Python]] computer language specifies an [https://docs.python.org/library/math.html#math.fsum fsum] function for accurate summation. Starting with Python 3.12, the built-in "sum()" function uses the Neumaier summation.<ref>[https://docs.python.org/3.12/whatsnew/3.12.html#other-language-changes What's New in Python 3.12].</ref>

In the [[Julia (programming language)|Julia]] language, the default implementation of the <code>sum</code> function does [[pairwise summation]] for high accuracy with good performance,<ref>[https://github.com/JuliaLang/julia/pull/4039 RFC: use pairwise summation for sum, cumsum, and cumprod], github.com/JuliaLang/julia pull request #4039 (August 2013).</ref> but an external library provides an implementation of Neumaier's variant named <code>sum_kbn</code> for the cases when higher accuracy is needed.<ref>[https://github.com/JuliaMath/KahanSummation.jl KahanSummation library] in Julia.</ref>

In the [[C Sharp (programming language)|C#]] language, [https://www.nuget.org/packages/HPCsharp HPCsharp nuget package] implements the Neumaier variant and [[pairwise summation]]: both as scalar, data-parallel using [[SIMD]] processor instructions, and parallel multi-core.<ref>[https://github.com/DragonSpit/HPCsharp HPCsharp nuget package of high performance algorithms].</ref>