Sichetti, FedericoAttene, MarcoPuppo, EnricoComino Trinidad, MarcMancinelli, ClaudioMaggioli, FilippoRomanengo, ChiaraCabiddu, DanielaGiorgi, Daniela2025-11-212025-11-212025978-3-03868-296-72617-4855https://doi.org/10.2312/stag.20251319https://diglib.eg.org/handle/10.2312/stag20251319Interval arithmetic is a practical method for robust computation, bridging the gap between fast, but inexact, floating-point arithmetic and slow, exact arithmetic, such as rational or arbitrary-precision. In this system, numbers are represented as intervals bounded by floating-point numbers, and operations are performed conservatively, guaranteeing that the resulting interval contains the exact mathematical result. We extend a fast C++ library for interval arithmetic by adding support for several transcendental functions. A key feature of our library is that all operations are correctly rounded, ensuring the resulting interval is the smallest floating-point interval that contains the true result. We demonstrate the library's effectiveness by applying it to complex non-polynomial problems, including surface-surface intersection and continuous collision detection for geometric primitives undergoing roto-translational motion.Attribution 4.0 International LicenseCCS Concepts: Mathematics of computing → Interval arithmetic; Mathematical software performance; Theory of computation → Rounding techniquesMathematics of computing → Interval arithmeticMathematical software performanceTheory of computation → Rounding techniques10.2312/stag.202513199 pages