VLSI architectures for Dirichlet arithmetic

Abstract

A new system of arithmetic is presented called Dirichlet arithmetic which models the arithmetic on the coefficients of a Dirichlet series. This approach has the property that output digits depend on very few of the input digits for the basic operations of addition, multiplication, and division. What is perhaps more interesting is that Dirichlet arithmetic has the same near parallelism for all the elementary transcendental functions (log, exp, sin, cos, sinh, cosh, sin/sup -1/, cos/sup -1/, etc.) as well. Furthermore, this property follows from the fact that the values of the elementary transcendental functions are represented naturally by their Dirichlet digits and can be computed by operations on the input digits as simple as those for multiplication or division.<>