An implementation of user-oriented floating point arithmetic

Abstract

The results of arithmetic operations performed on digital computers are seldom exactly correct. There are two reasons for this. First, input data are often only approximations to true values. Secondly, the finite length of computer storage will only allow the performance of approximations to arithmetic operations as they are normally defined. The inherent inaccuracy of computer arithmetic can cause serious problems for computer users. These problems are further intensified if the user is given no indication as to the degree of accuracy of computer output. In the research reported here a system has been devised which provides a variable length floating point arithmetic that can extend the precision of computer operations. It also gives an indication of the significance of the results which are obtained. This arithmetic system has been implemented in a high level computer language which allows user control of the base of the number system used and of the roundoff method employed.