High-Precision Computation: Mathematical Physics and Dynamics
High-Precision Computation: Mathematical Physics and Dynamics D. H. Bailey ∗ R. Barrio † April 1, 2010 J. M. Borwein ‡ Abstract At the present time, IEEE 64-bit ﬂoating-point arithmetic is suﬃciently accurate for most scientiﬁc applications. However, for a rapidly growing body of important scientiﬁc computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion eﬀort. This pa- per presents a survey of recent applications of these techniques and provides some analysis of their numerical requirements. These applications include supernova sim- ulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, studies of the ﬁne structure constant, scattering amplitudes of quarks, glu- ons and bosons, nonlinear oscillator theory, experimental mathematics, evaluation of orthogonal polynomials, numerical integration of ODEs, computation of periodic orbits, studies of the splitting of separatrices, detection of strange nonchaotic at- tractors, Ising theory, quantum ﬁeld theory, and discrete dynamical systems. We conclude that high-precision arithmetic facilities are now an indispensable compo- nent of a modern large-scale scientiﬁc computing environment. Lawrence Berkeley National Laboratory, Berkeley, CA 94720, dhbailey@lbl.gov. Supported in part by the Director, Oﬃce of Computational and Technology Research, Division of Mathematical, Informa- tion, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC02- 05CH11231. GME, Depto. Matem´ tica Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza, Spain a rbarrio@unizar.es. Supported in part by the Spanish research project MTM2009-10767. School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Aus- tralia, jonathan.borwein@newcastle.edu.au jborwein@cs.dal.ca. Supported in part by the Aus- tralian Research Council and the Canada Research Chair Programme.