Abstract
BNCpack is a multiple precision numerical computation library built on the functions provided by MPFR/GMP which is currently fastest and the most reliable multiple precision floating-point arithmetic library. It can handle complex arithmetic, basic linear computation, polynomial computation, root finding, numerical integration, and initial value problem of ordinary differential equation in double precision and in multiple and mixed precision. Parts of these functions such as basic linear computation, the Durand-Kerner method and numerical integration are parallelized by using a message-passing interface (MPI) to obtain higher performance using parallelized programs provided by BNCpack on MPI PC clusters. In this paper, we first introduce MPFR/GMP and its functions. Second, we explain the numerical algorithms implemented in BNCpack and the method for parallelizing numerical computation using MPFR/GMP. Third, we describe benchmark tests performed using BNCpack to demonstrate its effectiveness. Finally, we discuss future works on BNCpack.
