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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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https://hal.archives-ouvertes.fr/hal-02486753
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Submitted on : Friday, February 21, 2020 - 10:52:01 AM
Last modification on : Thursday, May 26, 2022 - 3:57:21 AM
Long-term archiving on: : Friday, May 22, 2020 - 2:38:27 PM

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  • HAL Id : hal-02486753, version 1

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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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