Testing interval arithmetic libraries, including their IEEE-1788 compliance

TL;DR

This paper discusses the challenges of testing interval arithmetic libraries, evaluates existing testing practices, and introduces two frameworks, JInterval and ITF1788, to improve test coverage and compliance verification.

Contribution

It presents a comprehensive analysis of testing aspects for interval arithmetic libraries and introduces two dedicated frameworks to facilitate testing and IEEE-1788 compliance verification.

Findings

Existing libraries vary in test coverage and compliance

JInterval and ITF1788 frameworks simplify testing processes

Additional important tests are identified beyond frameworks

Abstract

As developers of libraries implementing interval arithmetic, we faced the same difficulties when it came 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? In this paper we list the different aspects that, in our opinion, must be tested, giving indications on the choice of test cases. Then we examine how several interval arithmetic libraries actually perform tests. Next, we introduce two frameworks developed specifically to gather test cases and to incorporate easily new libraries in order to test them, namely JInterval and ITF1788. Not every important aspects of our libraries fit in these frameworks and we list extra tests that we deem important, but not easy, to perform.