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Parallel experiments with RARE-BLAS

Chemseddine Chohra 1 Philippe Langlois 1 David Parello 1
1 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : Numerical reproducibility failures rise in parallel computation because of the non-associativity of floating-point summation. Optimizations on massively parallel systems dynamically modify the floating-point operation order. Hence, numerical results may change from one run to another. We propose to ensure reproducibility by extending as far as possible the IEEE-754 correct rounding property to larger operation sequences. Our RARE-BLAS (Reproducible, Accurately Rounded and Efficient BLAS) benefits from recent accurate and efficient summation algorithms. Solutions for level 1 (asum, dot and nrm2) and level 2 (gemv) routines are provided. We compare their performance to the Intel MKL library and to other existing reproducible algorithms. For both shared and distributed memory parallel systems, we exhibit an extra-cost of 2× in the worst case scenario, which is satisfying for a wide range of applications. For Intel Xeon Phi accelerator a larger extra-cost (4× to 6×) is observed, which is still helpful at least for debugging and validation.
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Submitted on : Thursday, July 28, 2016 - 1:11:57 PM
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Chemseddine Chohra, Philippe Langlois, David Parello. Parallel experiments with RARE-BLAS. SYNASC: Symbolic and Numeric Algorithms for Scientific Computing, Sep 2016, Timisoara, Romania. pp.135-138, ⟨10.1109/SYNASC.2016.032⟩. ⟨lirmm-01349698⟩



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