Functions to Support Input and Output of Intervals

TL;DR

This paper develops new decimal interval input/output functions that enable accurate and efficient interval arithmetic by addressing the limitations of standard I/O libraries and conversion algorithms.

Contribution

The paper introduces a novel approach for decimal interval I/O that simplifies outward rounding in radix conversion, improving interval arithmetic reliability.

Findings

Developed decimal interval I/O functions from scratch.

Demonstrated improved accuracy in interval conversions.

Provided a framework for reliable interval arithmetic operations.

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.