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Verified Compilation of Floating-Point Computations

Abstract : Floating-point arithmetic is known to be tricky: roundings, formats, exceptional values. The IEEE-754 standard was a push towards straightening the field and made formal reasoning about floating-point computations easier and flourishing. Unfortunately, this is not sufficient to guarantee the final result of a program, as several other actors are involved: programming language, compiler, architecture. The CompCert formally-verified compiler provides a solution to this problem: this compiler comes with a mathematical specification of the semantics of its source language (a large subset of ISO C90) and target platforms (ARM, PowerPC, x86-SSE2), and with a proof that compilation preserves semantics. In this paper, we report on our recent success in formally specifying and proving correct CompCert's compilation of floating-point arithmetic. Since CompCert is verified using the Coq proof assistant, this effort required a suitable Coq formalization of the IEEE-754 standard; we extended the Flocq library for this purpose. As a result, we obtain the first formally verified compiler that provably preserves the semantics of floating-point programs.
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Submitted on : Friday, November 7, 2014 - 4:17:14 PM
Last modification on : Tuesday, October 25, 2022 - 4:19:15 PM
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Sylvie Boldo, Jacques-Henri Jourdan, Xavier Leroy, Guillaume Melquiond. Verified Compilation of Floating-Point Computations. Journal of Automated Reasoning, 2015, 54 (2), pp.135-163. ⟨10.1007/s10817-014-9317-x⟩. ⟨hal-00862689v3⟩



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