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Invertibility Conditions for Floating-Point Formulas
Conference proceeding   Open access

Invertibility Conditions for Floating-Point Formulas

Martin Brain, Aina Niemetz, Mathias Preiner, Andrew Reynolds, Clark Barrett and Cesare Tinelli
Lecture Notes in Computer Science, Vol.11562, pp.116-136
07/12/2019
DOI: 10.1007/978-3-030-25543-5_8
url
https://doi.org/10.1007/978-3-030-25543-5_8View
Published (Version of record) Open Access

Abstract

Automated reasoning procedures are essential for a number of applications that involve bit-exact floating-point computations. This paper presents conditions that characterize when a variable in a floating-point constraint has a solution, which we call invertibility conditions. We describe a novel workflow that combines human interaction and a syntax-guided synthesis (SyGuS) solver that was used for discovering these conditions. We verify our conditions for several floating-point formats. One implication of this result is that a fragment of floating-point arithmetic admits compact quantifier elimination. We implement our invertibility conditions in a prototype extension of our solver CVC4, showing their usefulness for solving quantified constraints over floating-points.

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