Numerical Validation of Compensated Summation Algorithms with Stochastic Arithmetic

Stef Graillat 1, * Fabienne Jézéquel 2, 1, * Romain Picot 1, *
* Corresponding author
1 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : Compensated summation algorithms are designed to improve the accuracy of ill-conditioned sums. They are based on algorithms, such as FastTwoSum, which are proved to provide, with rounding to nearest, the sum of two floating-point numbers and the associated rounding error. Discrete stochastic arithmetic enables one to estimate rounding error propagation in numerical codes. It requires a random rounding mode which consists in rounding each computed result toward −∞ or +∞ with the same probability. In this paper we analyse the impact of this random rounding mode on compensated summations based on the FastTwoSum algorithm. We show the accuracy improvement obtained using such compensated summations in numerical simulations controlled with discrete stochastic arithmetic.
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Stef Graillat, Fabienne Jézéquel, Romain Picot. Numerical Validation of Compensated Summation Algorithms with Stochastic Arithmetic. 8th International Workshop on Numerical Software Verification, NSV 2015, Apr 2015, Seattle, United States. pp.55-69, ⟨10.1016/j.entcs.2015.10.007⟩. ⟨hal-01230860⟩

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