Fast exact summation using small and large superaccumulators · HackerPapers discussions

Fast exact summation using small and large superaccumulators — mentioned by lifthrasiir

Mon, 04 Nov 2024 00:14:16 GMT

Indeed, this approach is known as a superaccumulator [1] and faster overall than the Kahan summation for a large amount of numbers. I don't exactly know the currently accepted threshold but 10,000 numbers should be conservative enough for that. [1] https://arxiv.org/abs/1505.05571

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Fast exact summation using small and large superaccumulators — mentioned by radford-neal

Sun, 26 May 2024 16:13:03 GMT

Exact addition using accumulators has progressed since the work of Zhu and Hayes in 2010. See my paper at https://arxiv.org/abs/1505.05571 (repository at https://gitlab.com/radfordneal/xsum), which is used in the Julia xsum package (https://docs.juliahub.com/General/Xsum/stable/). There's also recent work by Marko Lange at https://web.archive.org/web/20220616031105id_/https://dl.acm... I think these methods are probably faster than the exact methods you benchmark.

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Fast exact summation using small and large superaccumulators — mentioned by radford-neal

Fri, 29 May 2020 23:26:03 GMT

While Kahan summation is more accurate than naive summation, it still does not produce the precise result (the true sum rounded to the final precision). It is not too costly to do the summation exactly. Several algorithms for this have been developed. You can read about mine at https://arxiv.org/abs/1505.05571 and get the code for them at https://gitlab.com/radfordneal/xsum

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Fast exact summation using small and large superaccumulators — mentioned by StefanKarpinski

Mon, 25 Mar 2019 16:46:09 GMT

It's an interesting connection. Any finite collection of real values (represented in floating-point or otherwise) has a definite correct sum. If you're constrained to the floating-point to represent that value, you should ideally round the true value to the closest float and return that. Computing this true sum of a sequence of floating-point values is surprisingly hard though. The state of the art seems to be Radford Neal's paper on superaccumulators from 2015: https://arxiv.org/abs/1505.05571 Fortunately pairwise summation (Julia's default) is fast and fairly hard to trip up, although it…

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Fast exact summation using small and large superaccumulators — HN submission

Thu, 19 Jan 2017 15:32:23 GMT

Fast exact summation using small and large superaccumulators

31 points; 7 discussion replies on HN. Paper and source history. A submission is not an endorsement.