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Numerical reproducibility in HPC: the interval point of view

Nathalie Revol 1, * Philippe Théveny 1, 2, *
* Corresponding author
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : What is called numerical reproducibility is the problem of getting the same result, when the scientific computation is run several times, either on the same machine (and this is called repeatability) or on different machines, with different numbers of processing units, types, execution environments, computational loads etc. This problem is especially stringent for HPC results. For interval computations, numerical reproducibility is of course an issue for testing and debugging purposes. However, as long as the computed result encloses the exact and unknown result, the inclusion property, which is the main property of interval arithmetic, is satisfied and getting bit for bit identical results may not be crucial. However, implementation issues may invalidate the inclusion property, in particular if the rounding modes set by the user are modified during the execution. We will present several ways to circumvent these issues, on the example of the product of matrices with interval coefficients.
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https://hal.inria.fr/hal-00922117
Contributor : Nathalie Revol Connect in order to contact the contributor
Submitted on : Monday, December 23, 2013 - 6:22:21 PM
Last modification on : Saturday, September 11, 2021 - 3:17:00 AM

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  • HAL Id : hal-00922117, version 1

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Nathalie Revol, Philippe Théveny. Numerical reproducibility in HPC: the interval point of view. PPAM'2013: 10th International Conference on Parallel Processing and Applied Mathematics, Sep 2013, Warsaw, Poland. ⟨hal-00922117⟩

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