Propagation of roundoff errors in finite precision computations: A semantics approach

Abstract

We introduce a concrete semantics for floating-point operationswhich describes the propagation of roundoff errors throughout acomputation. This semantics is used to assert the correctness of an abstract interpretation which can be straight forwardly derived from it.In our model, every elementary operation introduces a new first order errorterm, which is later combined with other error terms, yielding higher order error terms. The semantics is parameterized by the maximal orderof 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.