Automatic Generation of Fast and Certified Code for Polynomial Evaluation

Christophe Mouilleron 1, * Guillaume Revy 2, *
* Corresponding author
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
2 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : Designing an efficient floating-point implementation of a function based on polynomial evaluation requires being able to find an accurate enough evaluation program, exploiting at most the target architecture features. This article introduces CGPE, a tool dealing with the generation of fast and certified codes for the evaluation of bivariate polynomials. First we discuss the issue underlying the evaluation scheme combinatorics before giving an overview of the CGPE tool. The approach we propose consists in two steps: the generation of evaluation schemes by using some heuristics so as to quickly find some of low latency; and the selection that mainly consists in automatically checking their scheduling on the given target and validating their accuracy. Then, we present on-going development and ideas for possible improvements of the whole process. Finally, we illustrate the use of CGPE on some examples, and show how it allows us to generate fast and certified codes in a few seconds and thus to reduce the development time of libms like FLIP.
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Conference papers
ARITH: Computer Arithmetic, Jul 2011, Tübingen, Germany. IEEE, Computer Arithmetic (ARITH), 2011 20th IEEE Symposium on, pp.233-242, 2011, 〈http://www.ac.usc.es/arith20/〉. 〈10.1109/ARITH.2011.39〉
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Christophe Mouilleron, Guillaume Revy. Automatic Generation of Fast and Certified Code for Polynomial Evaluation. ARITH: Computer Arithmetic, Jul 2011, Tübingen, Germany. IEEE, Computer Arithmetic (ARITH), 2011 20th IEEE Symposium on, pp.233-242, 2011, 〈http://www.ac.usc.es/arith20/〉. 〈10.1109/ARITH.2011.39〉. 〈ensl-00531721〉

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