Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic

Fredrik Johansson 1
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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 noninterval 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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Fredrik Johansson. Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2017, 66 (8), pp.1281 - 1292. ⟨10.1109/TC.2017.2690633⟩. ⟨hal-01394258v2⟩

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