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

: Jézéquel, Fabienne; Graillat, Stef; Mukunoki, Daichi; Imamura, Toshiyuki; Iakymchuk, Roman

Volltext ()

Online im WWW, 2020, Paper hal-02486753, 15 S.
European Commission EC
H2020; 842528; Robust
Robust and Energy-Efficient Numerical Solvers Towards Reliable and Sustainable Scientific Computations
Japan Society for the Promotion of Science JSPS
Bericht, Elektronische Publikation
Fraunhofer ITWM ()

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.