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Improving the Numerical Accuracy of Parallel Programs.

Farah Benmouhoub le

Lieu: bât 862, pièce 1073

Abstract

In high performance computing, nearly all the implementations and published experiments use floating-point arithmetic. However, since floating-point numbers are a finite approximation of real numbers, they are therefore prone to accuracy problems due to the accumulated round-off errors. These round-off errors may cause damage whose gravity varies depending on the critical level of the application. Parallelism introduces new numerical accuracy problems due to the order of operations between several computation units.

In the first part of this talk, I will describe a new technique that relies on static analysis by abstract interpretation, and which aims at improving the numerical accuracy of computations by dividing the problem, between computation units, according to the order of magnitude of data. Then, I will present two efficient parallel algorithms for accurately summing n floating-point numbers and without increasing the linear complexity of the recursive summation algorithm.