Assisted verification of elementary functions using Gappa

Florent de Dinechin, Christoph Quirin Lauter, Guillaume Melquiond
2006 Proceedings of the 2006 ACM symposium on Applied computing - SAC '06  
The implementation of a correctly rounded or interval elementary function needs to be proven carefully in the very last details. The proof requires a tight bound on the overall error of the implementation with respect to the mathematical function. Such work is function specific, concerns tens of lines of code for each function, and will usually be broken by the smallest change to the code (e.g. for maintenance or optimization purpose). Therefore, it is very tedious and error-prone if done by
more » ... d. This article discusses the use of the Gappa proof assistant in this context. Gappa has two main advantages over previous approaches: Its input format is very close to the actual C code to validate, and it automates error evaluation and propagation using interval arithmetic. Besides, it can be used to incrementally prove complex mathematical properties pertaining to the C code. Yet it does not require any specific knowledge about automatic theorem proving, and thus is accessible to a wider community. Moreover, Gappa may generate a formal proof of the results that can be checked independently by a lowerlevel proof assistant like Coq, hence providing an even higher confidence in the certification of the numerical code.
doi:10.1145/1141277.1141584 dblp:conf/sac/DinechinLM06 fatcat:524qrelltfe7zh7mkcnusggxbm