Design and Implementation of a High Precision Arithmetic with Rigorous Error Bounds

In this paper we present the design of a rigorous, high precision floating point arithmetic. The algorithms presented are implementation in FORTRAN, and are made available through the COSY INFINITY rigorous computation package. The three design objectives for these high precision intervals are high speed, particularly for the elementary operations, absolutely rigorous treatment of roundoff errors, and scalability to arbitrary precision. The main focus of these algorithms lies on relatively low precision of up to 100 significant digits. Unlike many available high precision packages, we do not rely on large integer arithmetic to emulate floating point numbers with arbitrary mantissa length. Instead, we utilize unevaluated series of double precision floating point numbers. Combined with algorithms for exact operations on floating point numbers, this allows us to implement operations very efficiently.