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Error Estimation and Correction Using the Forward CENA Method

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Computational Science – ICCS 2021 (ICCS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12742))

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Abstract

The increasing use of heterogeneous and more energy-efficient computing systems has led to a renewed demand for reduced- or mixed-precision floating-point arithmetic. In light of this, we present the forward CENA method as an efficient roundoff error estimator and corrector. Unlike the previously published CENA method, our forward variant can be easily used in parallel high-performance computing applications. Just like the original variant, its error estimation capabilities can point out code regions where reduced or mixed precision still achieves sufficient accuracy, while the error correction capabilities can increase precision over what is natively supported on a given hardware platform, whenever higher accuracy is needed. CENA methods can also be used to increase the reproducibility of parallel sum reductions.

The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (‘Argonne’). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. http://energy.gov/downloads/doe-public-access-plan.

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Acknowledgments

We thank Vincent Baudoui for introducing us to the CENA method and constructive conversations about roundoff error. This work was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under contract number DE-AC02-06CH11357. We gratefully acknowledge the computing resources provided and operated by the Joint Laboratory for System Evaluation (JLSE) at Argonne National Laboratory.

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Authors and Affiliations

  1. Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL, USA

    Paul D. Hovland & Jan Hückelheim

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  1. Paul D. Hovland
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  2. Jan Hückelheim
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Correspondence to Jan Hückelheim .

Editor information

Editors and Affiliations

  1. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  2. Ludwig-Maximilians-Universität München, Munich, Germany

    Dieter Kranzlmüller

  3. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  4. University of Tennessee at Knoxville, Knoxville, TN, USA

    Jack J. Dongarra

  5. University of Amsterdam, Amsterdam, The Netherlands

    Peter M. A. Sloot

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Hovland, P.D., Hückelheim, J. (2021). Error Estimation and Correction Using the Forward CENA Method. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12742. Springer, Cham. https://doi.org/10.1007/978-3-030-77961-0_61

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  • DOI: https://doi.org/10.1007/978-3-030-77961-0_61

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-77960-3

  • Online ISBN: 978-3-030-77961-0

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