Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic
This work provides a versatile and efficient arbitrary-precision interval arithmetic library for numerical computing, enabling rigorous error bounds in a range of applications.
Arb is a C library for arbitrary-precision interval arithmetic using midpoint-radius representation, achieving performance competitive with non-interval types like MPFR and MPC while supporting real and complex numbers, polynomials, power series, matrices, and special functions.
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.