Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic

2016/11/09 by Fredrik Johansson, Johansson, Fredrik · 1 voice · 19 citations
Computer Science · Mathematics · #Algorithm #Arbitrary-precision arithmetic #Arithmetic #Ball (mathematics) #Combinatorics #Cryptography and Residue Arithmetic #Digital Filter Design and Implementation #Discrete mathematics #Double-precision floating-point format #Floating point #Geometry #Interval (graph theory) #Interval arithmetic #Machine epsilon #Mathematical analysis #Mathematics #Midpoint #Numerical Methods and Algorithms #Polynomial #Power series #Range (aeronautics) #Real number #Representation (politics)

paper · pdf · doi:10.48550/arxiv.1611.02831

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2016/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Arb is a C library for arbitrary-precision interval arithmetic using the midpoint-radius representation, also known as ball arithmetic. It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many special functions. The core number types are designed for versatility and speed in a range of scenarios, allowing performance that is competitive with non-interval arbitrary-precision types such as MPFR and MPC floating-point numbers. We discuss the low-level number representation, strategies for precision and error bounds, and the implementation of efficient polynomial arithmetic with interval coefficients.

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Discussions

• Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic (2016) [hn, 78 points, 42 comments]

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