Arb

C library for arbitrary-precision interval arithmetic

Arb is an implementation of ball arithmetic, also known as mid-rad interval arithmetic. Ball arithmetic is an extension of floating-point arithmetic in which an error bound is attached to each variable. This allows computing rigorously with real and complex numbers.

With plain floating-point arithmetic, the user must do an error analysis to guarantee that results are correct. Manual error analysis is time-consuming and bug-prone. Ball arithmetic effectively makes error analysis automatic.

Arb is designed for computer algebra and computational number theory, but may be useful in any area demanding reliable or precise numerical computing. Arb scales seamlessly from tens of digits up to billions of digits. Efficiency is achieved by low level optimizations and use of asymptotically fast algorithms.