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Conference papers
Reproducible, Accurately Rounded and Efficient BLAS
Abstract : Numerical reproducibility failures rise in parallel computation because floating-point summation is non-associative. Massively parallel and optimized executions 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. We introduce our RARE-BLAS (Reproducible, Accurately Rounded and Efficient BLAS) that benefits from recent accurate and efficient summation algorithms. Solutions for level 1 (asum, dot and nrm2) and level 2 (gemv) routines are presented. Their performance is studied compared to Intel MKL library and 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 steps.
Cited literature [15 references]
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01280324
Contributor : Philippe Langlois Connect in order to contact the contributor
Submitted on : Thursday, July 28, 2016 - 1:22:03 PM
Last modification on : Wednesday, November 3, 2021 - 7:45:20 AM
Contributor : Philippe Langlois Connect in order to contact the contributor
Submitted on : Thursday, July 28, 2016 - 1:22:03 PM
Last modification on : Wednesday, November 3, 2021 - 7:45:20 AM
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REPPAR16.pdf
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