Abstract
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.
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Acknowledgements
This research was partially supported by the European Union’s Horizon 2020 research, innovation programme under the Marie Skłodowska-Curie grant agreement via the Robust project No. 842528 and the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant No. 19K20286.
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Jézéquel, F., Graillat, S., Mukunoki, D., Imamura, T., Iakymchuk, R. (2020). Can We Avoid Rounding-Error Estimation in HPC Codes and Still Get Trustworthy Results?. In: Christakis, M., Polikarpova, N., Duggirala, P.S., Schrammel, P. (eds) Software Verification. NSV VSTTE 2020 2020. Lecture Notes in Computer Science(), vol 12549. Springer, Cham. https://doi.org/10.1007/978-3-030-63618-0_10
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