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2006

Semantics of roundoff error propagation in finite precision calculations

10 years 4 months ago
Semantics of roundoff error propagation in finite precision calculations
We introduce a concrete semantics for floating-point operations which describes the propagation of roundoff errors throughout a calculation. This semantics is used to assert the correctness of a static analysis which can be straightforwardly derived from it. In our model, every elementary operation introduces a new first order error term, which is later propagated and combined with other error terms, yielding higher order error terms. The semantics is parameterized by the maximal order of error to be examined and verifies whether higher order errors actually are negligible. We consider also coarser semantics computing the contribution, to the final error, of the errors due to some intermediate computations. As a result, we obtain a family of s and we show that the less precise ones are abstractions of the more precise ones.
Matthieu Martel
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2006
Where LISP
Authors Matthieu Martel
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