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TERATEC 2017 Forum
Workshop 8 - Wednesday, June 28 from 14:00 to 17:30

Numerical precision and stability in HPC simulation

Code analyses for numerical accuracy with affine forms: from diagnosis to the origin of the numerical errors
Franck VEDRINE, research engineer, CEA LIST

Abstract :  Since several years, CEA LIST has developed code analyses dedicated to the accuracy of floating-point computations; the main objective was to cover all the execution paths with a fine diagnosis for the numerical errors [Fluctuat]. From the user's point of view, the analyses with domains and errors modeled with affine forms often provide more exploitable results than other kinds of analyses. If exhaustiveness is reachable for numeric components and libraries, we have needed to relax this property for industrial codes that implement complex physical systems. Nevertheless, we have obtained good results on some codes by introducing small formal perturbations as noise on the code's inputs. The conservative propagation of such perturbations on more than twenty thousand lines of code provides bounded errors on a majority of simulation cycles. The ratio between the formal conservative propagation of the rounding errors and the effective relative error observed on concrete simulations seems very reasonable for such lengths of code. The direct application of such techniques on complete HPC codes of millions of lines is not reasonable for scaling and precision reasons. They nevertheless could highlight the instructions that contribute the most to an observed unstable result. For that, we are trying to trigger such analyses on some delimited portions of code during a simulation. The objective is to provide a diagnosis for the developer that could locally add more precision for the computations that need it.

Bio : Franck VĂ©drine works as research engineer at CEA LIST since the 2000s. His Phd Thesis was on the static analysis of C++ codes by Abstract Interpretation. Since 2009, he has worked on the problems of numerical accuracy as developer and maintainer of the Fluctuat tool. Recently he has extracted from Fluctuat a library of affine forms "float_diagnosis" to propose accuracy analyses inside simulations of numerical systems.

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