Composite Arithmetic: Proposal for a New Standard

Abstract

Frustrated by the limitations of integer arithmetic, scientists and engineers developed a floating-point number representation. The subsequent adoption of a binary floating-point standard greatly enhanced scientific computing. But floating-point is too specialized for spreadsheets and inadequate for computer graphics. It also complicates programming. Finally, it does not even yield exact results: One very popular calculator gives the answer -0.000000001 to the calculation ((1 \divide 3) x 3)-1! These circumstances, coupled with developments in circuit technology and computation, have encouraged and made possible a more general arithmetic. In this article I propose what I call composite arithmetic, which combines aspects of traditional integer and floating-point arithmetics with less familiar aspects of rational and logarithmic arithmetics. Composite arithmetic complements the binary floating-point standard and satisfies more diverse computational needs. Successful development of a composite arithmetic standard would be most timely, given the burgeoning ability to manufacture complex processors and the interest in extended forms of arithmetic being shown in the research literature. It would also be highly beneficial in support of better electronic calculator arithmetic and standard operation of generic software packages such as those including spreadsheet capabilities.