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The Design of Fast and Energy-Efficient Linear Solvers: On the Potential of Half-Precision Arithmetic and Iterative Refinement Techniques

  • Azzam Haidar
  • Ahmad Abdelfattah
  • Mawussi Zounon
  • Panruo Wu
  • Srikara Pranesh
  • Stanimire Tomov
  • Jack Dongarra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10860)

Abstract

As parallel computers approach exascale, power efficiency in high-performance computing (HPC) systems is of increasing concern. Exploiting both the hardware features and algorithms is an effective solution to achieve power efficiency, and to address the energy constraints in modern and future HPC systems. In this work, we present a novel design and implementation of an energy-efficient solution for dense linear systems of equations, which are at the heart of large-scale HPC applications. The proposed energy-efficient linear system solvers are based on two main components: (1) iterative refinement techniques, and (2) reduced-precision computing features in modern accelerators and coprocessors. While most of the energy efficiency approaches aim to reduce the consumption with a minimal performance penalty, our method improves both the performance and the energy efficiency. Compared to highly-optimized linear system solvers, our kernels deliver the same accuracy solution up to \(2\times \) faster and reduce the energy consumption up to half on Intel Knights Landing (KNL) architectures. By efficiently using the Tensor Cores available in the NVIDIA V100 PCIe GPUs, the speedups can be up to \(4\times \), with more than 80% reduction in the energy consumption.

Keywords

FP16 Tensor cores Mixed-precision HPC Solvers 

Notes

Acknowledgments

This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. The work was also partially supported by NVIDIA and NSF grant No. OAC-1740250.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Azzam Haidar
    • 1
  • Ahmad Abdelfattah
    • 1
  • Mawussi Zounon
    • 4
  • Panruo Wu
    • 2
  • Srikara Pranesh
    • 4
  • Stanimire Tomov
    • 1
  • Jack Dongarra
    • 1
    • 3
    • 4
  1. 1.Innovative Computing LaboratoryUniversity of TennesseeKnoxvilleUSA
  2. 2.University of HoustonHoustonUSA
  3. 3.Oak Ridge National LaboratoryOak RidgeUSA
  4. 4.University of ManchesterManchesterUK

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