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Preprints, Working Papers, ... Year : 2020

Can we avoid rounding-error estimation in HPC codes and still get trustful results?

Abstract

Numerical validation enables one to improve the reliability of numerical computations that rely upon floating-point operations through obtaining trustful results. Discrete Stochastic Arithmetic (DSA) makes it possible to validate the accuracy of floating-point computations using random rounding. However, it may bring a large performance overhead compared with the standard floating-point operations. In this article, we show that with perturbed data it is possible to use standard floating-point arithmetic instead of DSA for the purpose of numerical validation. For instance, for codes including matrix multiplications, we can directly utilize the matrix multiplication routine (GEMM) of level-3 BLAS that is performed with standard floating-point arithmetic. Consequently, we can achieve a significant performance improvement by avoiding the performance overhead of DSA operations as well as by exploiting the speed of highly-optimized BLAS implementations. Finally, we demonstrate the performance gain using Intel MKL routines compared against the DSA version of BLAS routines.
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Dates and versions

hal-02486753 , version 1 (21-02-2020)

Identifiers

  • HAL Id : hal-02486753 , version 1

Cite

Fabienne Jézéquel, Stef Graillat, Daichi Mukunoki, Toshiyuki Imamura, Roman Iakymchuk. Can we avoid rounding-error estimation in HPC codes and still get trustful results?. 2020. ⟨hal-02486753⟩
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