The Mainstreaming of Interval Arithmetic

Abstract

Interval arithmetic and validated arithmetic methods are almost unknown in the United States, and are absent in the federally funded High Performance Computing efforts of the last twenty years. The focus has been on ßoatingpoint operations per second (FLOPS) to the exclusion of any concern for the correctness of the result. However, the treaty-mandated need to validate nuclear weapons without physical experiments (the ASCI program) may prove to be the key to changing this. Radiation transport provides an example where bounded intervals can provide much more useful answers than existing point methods, whether they are used for modeling nuclear reactions or for computer-generated graphics. This example, and others, can be used to illustrate a general strategy that will allow us to move interval arithmetic into the mainstream of high-speed computing.