A framework to test interval arithmetic libraries and their IEEE 1788-2015 compliance

TL;DR

This paper presents a framework and initial test suite for evaluating interval arithmetic libraries' correctness and compliance with the IEEE 1788-2015 standard, focusing on test case exchange and coverage.

Contribution

It introduces a standardized test case format and provides initial tests for interval arithmetic libraries, aiding developers in verifying correctness and standard compliance.

Findings

Initial test suite for interval arithmetic libraries

Julia's IntervalArithmetic.jl performance on tests analyzed

Additional important tests identified for future work

Abstract

As developers of libraries implementing interval arithmetic, we faced the same difficulties when it comes to testing our libraries. What must be tested? How can we devise relevant test cases for unit testing? How can we ensure a high (and possibly 100%) test coverage? Before considering these questions, we briefly recall the main features of interval arithmetic and of the IEEE 1788-2015 standard for interval arithmetic. After listing the different aspects that, in our opinion, must be tested, we contribute a first step towards offering a test suite for an interval arithmetic library. First we define a format that enables the exchange of test cases, so that they can be read and tried easily. Then we offer a first set of test cases, for a selected set of mathematical functions. Next, we examine how the Julia interval arithmetic library, IntervalArithmetic.jl, actually performs to these tests. As this is an ongoing work, we list extra tests that we deem important to perform.