High Precision Arithmetic for Scientific Applications

Abstract: All but a few digital computers used for scientific computations have supported floating-point and digital arithmetic of rather limited numerical precision. The underlying assumptions were that the systems being studied were basically deterministic and of limited complexity. The ideal scientific paradigm was the orbits of the major planets, which could be observed with high precision, predicted for thousands of years into the future, and extrapolated for thousands of years into the past. Much the same technology that has made computers possible has also provided instrumentation that has vastly expanded the scope and precision of scientific analysis. Complex nonlinear systems exhibiting so-called chaotic dynamics are now fair game for scientists and engineers in every discipline. Today it seems that computers need to enhance the precision of their numerical computations to support the needs of science. However, there is no need to wait for the necessary updates in both hardware and software; it is easy enough to monitor numerical precision with a few minor modifications to existing software.