Constructive real interpretation of numerical programs

Abstract

We explore the feasibility of providing exact real arithmetic for use in conventional numerical programs. We have built a prototype interpreter which replaces floating point operations with operations on constructive real numbers in the execution of conventional Fortran programs. Such a facility makes it unnecessary to concern oneself with issues of numerical stability in the solution of small problems. It also provides a useful tool for the development of larger numerical programs.We discuss the computability and algorithmic issues involved in the design of the interpreter, as well as some preliminary experiences and performance measurements.