Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY

摘要

The goal of this paper is to prove that the implementation of Taylor models in COSY, based on floating-point arithmetic, Computes results satisfying the "containment property", i.e. guaranteed results.First, Taylor models are defined and their implementation in the COSY software by Makino and Berz is detailed. Afterwards IEEE-754 floating-point arithmetic is introduced. Then the core of this paper is given: the algorithms implemented in COSY for multiplying a Taylor model by a scalar, for adding or multiplying two Taylor models are given and are proven to return Taylor models satisfying the containment property. (c) 2004 Elsevier Inc. All rights reserved.