---
title: Functions to Support Input and Output of Intervals
url: https://www.emergentmind.com/papers/0703003
type: paper
arxiv_id: '0703003'
arxiv_url: https://arxiv.org/abs/0703003
published: '2007-02-28'
categories:
- cs.NA
---

# Functions to Support Input and Output of Intervals

## Abstract

Interval arithmetic is hardly feasible without directed rounding as provided, for example, by the IEEE floating-point standard. Equally essential for interval methods is directed rounding for conversion between the external decimal and internal binary numerals. This is not provided by the standard I/O libraries. Conversion algorithms exist that guarantee identity upon conversion followed by its inverse. Although it may be possible to adapt these algorithms for use in decimal interval I/O, we argue that outward rounding in radix conversion is computationally a simpler problem than guaranteeing identity. Hence it is preferable to develop decimal interval I/O ab initio, which is what we do in this paper.