Conference Proceedings

Optimal Bounds for Floating-Point Addition in Constant Time

Mak Andrlon, Peter Schachte, Harald Sondergaard, Peter J Stuckey

Proceedings of the 2019 IEEE 26th Symposium on Computer Arithmetic (ARITH) | IEEE | Published : 2019

Abstract

Reasoning about floating-point numbers is notoriously difficult, owing to the lack of convenient algebraic properties such as associativity. This poses a substantial challenge for program analysis and verification tools which rely on precise floating-point constraint solving. Currently, interval methods in this domain often exhibit slow convergence even on simple examples. We present a new theorem supporting efficient computation of exact bounds of the intersection of a rectangle with the preimage of an interval under floating-point addition, in any radix or rounding mode. We thus give an efficient method of deducing optimal bounds on the components of an addition, solving the convergence pr..

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