Tests of probabilistic models for propagation of roundoff errors

Abstract

In any prolonged computation it is generally assumed that the accumulated effect of roundoff errors is in some sense statistical. The purpose of this paper is to give precise descriptions of certain probabilistic models for roundoff error, and then to describe a series of experiments for testing the validity of these models. It is concluded that the models are in general very good. Discrepancies are both rare and mild. The test techniques can also be used to experiment with various types of special arithmetic.