High-precision computation: Applications and challenges [Keynote I]

Abstract

Summary form only given, as follows. High-precision floating-point arithmetic software, ranging from "double-double" or "quad" precision to arbitrarily high-precision (hundreds or thousands of digits), has been available for years. Such facilities are standard features of Mathematica and Maple, and software packages such as MPFR, QD and ARPREC are available on the Internet. Some of these packages include high-level language interface modules that make conversion of standard-precision programs a relatively simple task. However, until recently such facilities were widely considered as novelty items - why would anyone need such exalted levels of numeric precision in "practical" research or engineering? In fact, during the past decade or two, numerous applications have arisen for high-precision floatingpoint arithmetic. This presentation will briefly describe some of these applications, which mostly arise in mathematical physics, applied physics and mathematics. Many heretofore unknown identities and relationships have been discovered, and features have been identified in computed data that were not "visible" with ordinary 64-bit precision. Applications of double-double (31 digits) or quad-double precision (62 digits) are particularly common, but there are also some interesting applications for as high as 50,000 digits. The speaker will also outline what is needed in improved facilities for high-precision computation to address challenges that lie ahead.