Computer Algebra Style (Multiprecision) Interval and Complex Arithmetic

Using the approach in [2, 4, 5], interval bounds for values in R or R∪ [−∞, +∞], which is what one is interested in in most industrial applications, can be computed. These approaches, however, do not in all cases reflect all that is known about the interval valued expressions, as is required during prototyping or in a computer algebra environment. A similar remark holds for the complex arithmetic guidelines proposed in Annex G of the latest C programming language standard [1]. The approach is sufficiently correct when some additional background information is available about the evaluated expression. The lack of such information, however, may lead to the ambiguous interpretation of results. In the authors’ implementation, a more theoretical point of view on interval and complex arithmetic is proposed to tackle the above issue. It is natural, when taking a computer algebra style viewpoint, to deal not only with double precision, but also consider true higher precisions.