uu.seUppsala University Publications

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Exploring Approximations for Floating-Point Arithmetic using UppSATPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); (English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### Keyword [en]

SAT, SMT, approximations, model construction, floating-point arithmetic
##### National Category

Computer Sciences
##### Research subject

Computer Science
##### Identifiers

URN: urn:nbn:se:uu:diva-334564OAI: oai:DiVA.org:uu-334564DiVA: diva2:1159879
#####

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Available from: 2017-11-24 Created: 2017-11-24 Last updated: 2018-01-13
##### In thesis

We consider the problem of solving floating-point constraints obtained from software verification. We present UppSAT --- a new implementation of a systematic approximation refinement framework [ZWR17] as an abstract SMT solver. Provided with an approximation and a decision procedure (implemented in an off-the-shelf SMT solver), UppSAT yields an approximating SMT solver. Additionally, UppSAT includes a library of predefined approximation components which can be combined and extended to define new encodings, orderings and solving strategies. We propose that UppSAT can be used as a sandbox for easy and flexible exploration of new approximations. To substantiate this, we explore several approximations of floating-point arithmetic. Approximations can be viewed as a composition of an encoding into a target theory, a precision ordering, and a number of strategies for model reconstruction and precision (or approximation) refinement. We present encodings of floating-point arithmetic into reduced precision floating-point arithmetic, real-arithmetic, and fixed-point arithmetic (encoded into the theory of bit-vectors in practice). In an experimental evaluation, we compare the advantages and disadvantages of approximating solvers obtained by combining various encodings and decision procedures (based on existing, state-of-the-art SMT solvers for floating-point, real, and bit-vector arithmetic).

1. From Machine Arithmetic to Approximations and back again: Improved SMT Methods for Numeric Data Types$(function(){PrimeFaces.cw("OverlayPanel","overlay1159882",{id:"formSmash:j_idt707:0:j_idt711",widgetVar:"overlay1159882",target:"formSmash:j_idt707:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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