On error representation in exact-decisions number types

TL;DR

This paper reviews how error bounds are used in accuracy-driven computation within exact-decisions number types, comparing various methods and highlighting potential issues supported by experimental evidence.

Contribution

It provides a comparative overview of error bound representations in accuracy-driven computation and discusses associated caveats, supported by experimental results.

Findings

Different approaches to error bound representation are compared.

The paper identifies caveats in current error bound methods.

Experiments support the analysis and comparisons.

Abstract

Accuracy-driven computation is a strategy widely used in exact-decisions number types for robust geometric algorithms. This work provides an overview on the usage of error bounds in accuracy-driven computation, compares different approaches on the representation and computation of these error bounds and points out some caveats. The stated claims are supported by experiments.