Can We Avoid Rounding-Error Estimation in HPC Codes and Still Get Trustworthy Results?
| Autor: | Stef Graillat, Roman Iakymchuk, Fabienne Jézéquel, Daichi Mukunoki, Toshiyuki Imamura |
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| Přispěvatelé: | Performance et Qualité des Algorithmes Numériques (PEQUAN), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Panthéon-Assas (UP2), RIKEN Center for Computational Science [Kobe] (RIKEN CCS), RIKEN - Institute of Physical and Chemical Research [Japon] (RIKEN), Fraunhofer Institute of Industrial Mathematics (Fraunhofer ITWM), Fraunhofer (Fraunhofer-Gesellschaft), Marie Curie grant, Robust project No. 842528Japan Society for the Promotion of Science (JSPS) KAKENHI Grant No. 19K20286, JEZEQUEL, Fabienne |
| Rok vydání: | 2020 |
| Předmět: |
Floating point
floating-point arithmetic Computer science Computation Reliability (computer networking) 010103 numerical & computational mathematics 02 engineering and technology Parallel computing [INFO] Computer Science [cs] 01 natural sciences [INFO.INFO-PF] Computer Science [cs]/Performance [cs.PF] [INFO.INFO-DC] Computer Science [cs]/Distributed Parallel and Cluster Computing [cs.DC] rounding errors 0202 electrical engineering electronic engineering information engineering Overhead (computing) numerical validation [INFO]Computer Science [cs] 0101 mathematics [INFO.INFO-AO]Computer Science [cs]/Computer Arithmetic Rounding 020207 software engineering Discrete Stochastic Arithmetic (DSA) Matrix multiplication [INFO.INFO-PF]Computer Science [cs]/Performance [cs.PF] BLAS [INFO.INFO-AO] Computer Science [cs]/Computer Arithmetic [INFO.INFO-DC]Computer Science [cs]/Distributed Parallel and Cluster Computing [cs.DC] Round-off error Performance improvement |
| Zdroj: | Lecture Notes in Computer Science ISBN: 9783030636173 VSTTE Lecture Notes in Computer Science Lecture Notes in Computer Science-Software Verification NSV'20, 13th International Workshop on Numerical Software Verification NSV'20, 13th International Workshop on Numerical Software Verification, Jul 2020, Los Angeles, CA, United States |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/978-3-030-63618-0_10 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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