Normalized floating-point arithmetic with an index of significance

Abstract

It has been frequently pointed out that the task of determining an error-bound for the results of a problem is usually a long difficult calculation, which is avoided as much as possible by the programmer. The introduction of floating-point arithmetic in modern computers and the ever-growing use of compilers makes the task of error analysis even more difficult and its computation even less probable. Clearly, a machine method is needed to automatically calculate a bound for the propagated and generated error, given the initial error in the input and the residual error due to approximating functions.