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Can we Avoid Rounding-Error Estimation in HPC Codes and Still Get Trustworthy Results?

: Jézéquel, F.; Graillat, S.; Mukunoki, D.; Imamura, T.; Iakymchuk, R.


Christakis, M.:
Software Verification. 12th International Conference, VSTTE 2020 and 13th International Workshop, NSV 2020 : Los Angeles, CA, USA, July 20-21, 2020. Revised Selected Papers
Cham: Springer Nature, 2020 (Lecture Notes in Computer Science 12549)
ISBN: 978-3-030-63617-3 (Print)
ISBN: 978-3-030-63618-0 (Online)
ISBN: 978-3-030-63619-7
Working Conference on Verified Software - Theories, Tools, and Experiments (VSTTE) <12, 2020, Online>
International Workshop on Numerical Software Verification (NSV) <13, 2020, Online>
International Conference on Computer Aided Verification (CAV) <32, 2020, Online>
Conference Paper
Fraunhofer ITWM ()

Numerical validation enables one to ensure the reliability of numerical computations that rely on floating-point operations. 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.