Assisted verification of elementary functions using Gappa

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 hand. 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 co...

• Type: Journal
• Year: 2006
• Where: SAC
• Authors: Florent de Dinechin, Christoph Quirin Lauter, Guillaume Melquiond
• Keywords: Applied Computing, Code, Interval Elementary Function, Proof Assistant, SAC 2006