Environment parameters and basic functions for floating-point computation

Abstract

This paper presents a language-independent proposal for environment parameters and basic functions for floating-point computation, and suggests a specific representation in terms of generic functions for Fortran 77. The environment parameters were originally introduced in 1967 by Forsythe and Moler [1], who attributed the essentials of their theory to Wilkinson [2]. These parameters are also used in the PORT mathematical subroutine library [3], with precise definitions in terms of a more recent model of floating-point computation [4], and a similar set has been proposed by the IFIP Working on Numerical Software [5]. Three of the basic functions are taken from a proposal by Ford, Reid, and Smith [6], but redefined in terms of the parameters and the model to provide a firm theoretical foundation. The other three basic functions can be expressed in terms of these, but we feel they should be provided separately for convenience. The stated purpose of the model is to capture the fundamental concepts of floating-point computation in a small set of parameters and a small set of axioms. In this paper we extend the earlier work by proposing basic functions to analyze, synthesize, and scale floating-point numbers, and to provide sharp measures of roundoff error.