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A comparison of floating point summation methods

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James GregoryAuthors Info & Claims

Communications of the ACM, Volume 15, Issue 9

Page 838

https://doi.org/10.1145/361573.361584

Published: 01 September 1972 Publication History

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Abstract

In the June 1970 issue of Communications, Linz [1] proposed a method of pairwise summing of numbers to reduce accumulated roundoff error. Linz compared his method with only a simple recursive summation. The Linz method should have also been compared with a method published in the January 1965 issue by Kahan [2], which is more accurate.

This note compares the schemes by Linz and Kahan with the straight recursive summation. Comparisons of accuracy, speed and storage were carried out on an IBM 360/75 with various compiler optimization levels. (Linz' restriction to a binary exponent is not essential to his method.)

References

[1]

Linz, P. Accurate floating-point summation. Comm. ACM13, 6 (June 1970), 361-362.

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[2]

Kahan, W. Further remarks on reducing truncation errors. Comm. ACM 8, 1 (Jan. 1965), 40.

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He KBarrio RChen LJiang HLiu JGu TQi J(2021)A Class of Fast and Accurate Multi-layer Block Summation and Dot Product AlgorithmsNetwork and Parallel Computing10.1007/978-3-030-93571-9_6(64-75)Online publication date: 3-Nov-2021
https://dl.acm.org/doi/10.1007/978-3-030-93571-9_6
Hofmann JFey DRiedmann MEitzinger JHager GWellein G(2016)Performance Analysis of the Kahan-Enhanced Scalar Product on Current Multicore ProcessorsParallel Processing and Applied Mathematics10.1007/978-3-319-32149-3_7(63-73)Online publication date: 2-Apr-2016
https://doi.org/10.1007/978-3-319-32149-3_7
Hofmann JFey DRiedmann MEitzinger JHager GWellein G(2016)Performance analysis of the Kahan‐enhanced scalar product on current multi‐core and many‐core processorsConcurrency and Computation: Practice and Experience10.1002/cpe.392129:9Online publication date: 3-Aug-2016
https://doi.org/10.1002/cpe.3921
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Published In

Communications of the ACM Volume 15, Issue 9

Sept. 1972

59 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/361573

Editor:
M. Stuart Lynn
Rice Univ., Houston, TX

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 01 September 1972

Published in CACM Volume 15, Issue 9

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Cited By

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He KBarrio RChen LJiang HLiu JGu TQi J(2021)A Class of Fast and Accurate Multi-layer Block Summation and Dot Product AlgorithmsNetwork and Parallel Computing10.1007/978-3-030-93571-9_6(64-75)Online publication date: 3-Nov-2021
https://dl.acm.org/doi/10.1007/978-3-030-93571-9_6
Hofmann JFey DRiedmann MEitzinger JHager GWellein G(2016)Performance Analysis of the Kahan-Enhanced Scalar Product on Current Multicore ProcessorsParallel Processing and Applied Mathematics10.1007/978-3-319-32149-3_7(63-73)Online publication date: 2-Apr-2016
https://doi.org/10.1007/978-3-319-32149-3_7
Hofmann JFey DRiedmann MEitzinger JHager GWellein G(2016)Performance analysis of the Kahan‐enhanced scalar product on current multi‐core and many‐core processorsConcurrency and Computation: Practice and Experience10.1002/cpe.392129:9Online publication date: 3-Aug-2016
https://doi.org/10.1002/cpe.3921
Nagar KBakos J(2013)Accuracy, cost, and performance tradeoffs for floating-point accumulation2013 International Conference on Reconfigurable Computing and FPGAs (ReConFig)10.1109/ReConFig.2013.6732268(1-4)Online publication date: Dec-2013
https://doi.org/10.1109/ReConFig.2013.6732268
Fu B(2013)On the Complexity of Approximate Sum of Sorted ListFrontiers in Algorithmics and Algorithmic Aspects in Information and Management10.1007/978-3-642-38756-2_29(284-293)Online publication date: 2013
https://doi.org/10.1007/978-3-642-38756-2_29
Castaldo AWhaley RChronopoulos A(2008)Reducing Floating Point Error in Dot Product Using the Superblock Family of AlgorithmsSIAM Journal on Scientific Computing10.1137/07067994631:2(1156-1174)Online publication date: 1-Dec-2008
https://dl.acm.org/doi/10.1137/070679946
Zhu YYong JZheng G(2005)A New Distillation Algorithm for Floating-Point SummationSIAM Journal on Scientific Computing10.1137/03060200926:6(2066-2078)Online publication date: 1-Jan-2005
https://dl.acm.org/doi/10.1137/030602009
Anderson I(1999)A Distillation Algorithm for Floating-Point SummationSIAM Journal on Scientific Computing10.1137/S106482759631420020:5(1797-1806)Online publication date: 1-Jan-1999
https://dl.acm.org/doi/10.1137/S1064827596314200
Pollock D(1999)Classical Regression AnalysisHandbook of Time Series Analysis, Signal Processing, and Dynamics10.1016/B978-012560990-6/50010-5(201-225)Online publication date: 1999
https://doi.org/10.1016/B978-012560990-6/50010-5
Higham N(1993)The Accuracy of Floating Point SummationSIAM Journal on Scientific Computing10.1137/091405014:4(783-799)Online publication date: 1-Jul-1993
https://dl.acm.org/doi/10.1137/0914050
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Accurate floating-point summation

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