Ulrich W. Kulisch
University of Karlsruhe
Karlsruhe, Germany
email: ulrich.kulisch@math.uni-karlsruhe.de
Abstract: The way arithmetic is used in scientific computing (floating-point arithmetic) can be traced back to the early 1940s when the technology was poor. Many real life and expensive accidents have been attributed to the loss of numeric accuracy in a floating-point calculation or to other arithmetic failures. Examples are: bursting of a large turbine under test due to wrongly predicted eigenvalues; failure of early space shuttle retriever arm under space conditions; disastrous failure on ground to air missile missions (the Dharan accident); failure in the Ariane guidance program, and so on.
Advances in computer technology are now so profound that the arithmetic capability and repertoire of computers can and should be expanded. With steadily increasing speed the arithmetic must be put on a broader base. Advanced computer arithmetic requires that all computer approximations of arithmetic operations - in particular those in the usual product spaces - differ from the correct result by at most one rounding. The implementation of advanced computer arithmetic by fast hardware will be examined in the talk. The new expanded computational capability is gained at modest cost. It increases both the speed of a computation and the accuracy of the computed result. With it fast multiple precision arithmetic can be easily provided. All this strongly supports the case for implementing this advanced arithmetic on every CPU.
At processor speeds of gigaflops and teraflops future computers also must be furnished with the capability to control the accuracy of the computed result at least to a certain extent. The amount of numbers produced at these speeds is too large to be judged by hand.
The talk will give an overview of the speaker's new book which is entitled:
Advanced Arithmetic for the Digital Computer - Design of Arithmetic Units,
Springer-Verlag, Nov. 2002.