Computing accurate Horner form approximations to special functions in finite precision arithmetic

TL;DR

This paper introduces a heuristic method for automatically designing finite-precision implementations of special functions like exp and arctan, optimizing for accuracy by considering roundoff errors.

Contribution

It presents a new heuristic approach that automates the creation of Horner form approximations with explicit error control in finite precision arithmetic.

Findings

Effective in producing accurate approximations

Accounts for roundoff errors explicitly

Automates the design process for special functions

Abstract

In various applications, computers are required to compute approximations to univariate elementary and special functions such as $\exp$ and $\arctan$ to modest accuracy. This paper proposes a new heuristic for automating the design of such implementations. This heuristic takes a certain restricted specification of program structure and the desired error properties as input and takes explicit account of roundoff error during evaluation.