Array Processing Using Alternate Arithmetic - A 20 Year Legacy

20 years ago, the first Systolic Array Workshop was held at the University of Oxford. This became an annual event with the name being changed to the Application Specific Array Processor (ASAP) Conference at the Princeton Workshop in 1990. Under either name, the conference highlights the implementation of special purpose computational processors, a basic feature of which is performing large numbers of arithmetic computations per second. In this paper we discuss representations of numbers and, in particular, the properties and advantages of arithmetic processors using these representations. In a retrospective, this paper looks at our own attempts, over the past 2 decades, to find new ways of representing, and computing with, numbers in order to achieve some advantages at the implementation level.