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Methods for High-Throughput Computation of Elementary Functions

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Parallel Processing and Applied Mathematics (PPAM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8384))

Abstract

Computing elementary functions on large arrays is an essential part of many machine learning and signal processing algorithms. Since the introduction of floating-point computations in mainstream processors, table lookups, division, square root, and piecewise approximations were essential components of elementary functions implementations. However, we suggest that these operations can not deliver high throughput on modern processors, and argue that algorithms which rely only on multiplication, addition, and integer operations would achieve higher performance. We propose 4 design principles for high-throughput elementary functions and suggest how to apply them to implementation of log, exp, sin, and tan functions. We evaluate the performance and accuracy of the new algorithms on three recent x86 microarchitectures and demonstrate that they compare favorably to previously published research and vendor-optimized libraries.

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Notes

  1. 1.

    Repository is hosted on bitbucket.org/MDukhan/hysteria.

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Acknowledgements

This work was supported in part by the National Science Foundation (NSF) under NSF CAREER award number 0953100 and the U.S. Dept. of Energy (DOE), Office of Science, Advanced Scientific Computing Research under award DE-FC02-10ER26006/DE-SC0004915. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of NSF or DOE.

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Authors and Affiliations

  1. School of Computational Science and Engineering, College of Computing, Georgia Institute of Technology, 266 Ferst Drive NW, Atlanta, GA, 30332, USA

    Marat Dukhan & Richard Vuduc

Authors
  1. Marat Dukhan
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  2. Richard Vuduc
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Correspondence to Marat Dukhan .

Editor information

Editors and Affiliations

  1. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Department of Computer Science, Knoxville, Tennessee, USA

    Jack Dongarra

  3. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

  4. Technical University of Denmark Informatics and Mathematical Modelling, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Dukhan, M., Vuduc, R. (2014). Methods for High-Throughput Computation of Elementary Functions. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2013. Lecture Notes in Computer Science(), vol 8384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55224-3_9

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  • DOI: https://doi.org/10.1007/978-3-642-55224-3_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55223-6

  • Online ISBN: 978-3-642-55224-3

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