High-Precision Arithmetic in Mathematical Physics

Abstract

For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. This article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture.

Keywords

• high-precision arithmetic
• numerical integration
• PSLQ algorithm
• Ising integrals
• Poisson equation