Rounding

Abstract

Computer number systems are one of the most fundamental interfaces between software and hardware, but despite recent interest they are rarely studied. We present a suite of tools and techniques to make it easier for both application-level software developers and hardware architects to study number systems and design new ones. Our key theoretical contribution is the use of rounding as an abstraction to describe the behavior of a wide variety of number systems in terms of real arithmetic. By leveraging this abstraction, we can build tools that simulate the behavior of many different number systems, efficiently track error through large computations, and automatically search for number system configurations that are optimized for a particular application.