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Reproducible Triangular Solvers for High-Performance Computing

Roman Iakymchuk, David Defour, Sylvain Collange, Stef Graillat
Sorbonne Universites, UPMC Univ Paris 06, UMR 7606, LIP6, F-75005 Paris, France
hal-01116588 (14 February 2015)

@article{iakymchuk2015reproducible,

   title={Reproducible Triangular Solvers for High-Performance Computing},

   author={Iakymchuk, Roman and Defour, David and Collange, Sylvain and Graillat, Stef},

   year={2015}

}

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On modern parallel architectures, floating-point computations may become non-deterministic and, therefore, non-reproducible mainly due to non-associativity of floating-point operations. We propose an algorithm to solve dense triangular systems by leveraging the standard parallel triangular solver and our, recently introduced, multi-level exact summation approach. Finally, we present implementations of the proposed fast reproducible triangular solver and results on recent NVIDIA GPUs.
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