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Issue No. 08 - Aug. (2017 vol. 66)
ISSN: 0018-9340
pp: 1281-1292
Fredrik Johansson , Inria Bordeaux-Sud-Ouest and the University of Bordeaux, Talence, France
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.
INDEX TERMS
Instruction sets, Libraries, Computer bugs, Computers, Algebra, Testing,Arbitrary-precision arithmetic, interval arithmetic, floating-point arithmetic, polynomial arithmetic
CITATION
Fredrik Johansson, "Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic", IEEE Transactions on Computers, vol. 66, no. , pp. 1281-1292, Aug. 2017, doi:10.1109/TC.2017.2690633
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