Semantics of roundoff error propagation in finite precision calculations
Higher-Order and Symbolic Computation
Improved bound for stochastic formal correctness of numerical algorithms
Innovations in Systems and Software Engineering
An overview of semantics for the validation of numerical programs
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Semantics-based transformation of arithmetic expressions
SAS'07 Proceedings of the 14th international conference on Static Analysis
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Studying floating point arithmetic, authors have shown that the implemented operations (addition, subtraction, multiplication, division and square root) can compute a result and an exact correcting term using the same format as the inputs. Following a path initiated in 1965, many authors supposed that neither underflow nor overflow occurred in the process. Overflow is not critical as this kind of exception creates persisting non numeric quantities. Underflow may be fatal to the process as it returns wrong numeric values with little warning. Our new conditions guarantee that the correcting term is exact when the result is a number. We have validated our proofs against Coq automatic proof checker. Our development has raised manyquestions, some of them were expected while other ones were surprising.