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Invertibility Conditions for Floating-Point Formulae

Brain, M. ORCID: 0000-0003-4216-7151, Niemetz, A., Preiner, M. , Reynolds, A., Barrett, C. & Tinelli, C. (2019). Invertibility Conditions for Floating-Point Formulae. In: Dillig, I. & Tasiran, S. (Eds.), Computer Aided Verification. CAV 2019.


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.

Publication Type: Conference or Workshop Item (Paper)
Additional Information: © The Author(s) 2019. This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Science & Technology > Computer Science
School of Science & Technology > Computer Science > Software Reliability
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