Radix-16 Evaluation of Certain Elementary Functions

This paper describes a family of algorithms for evaluation of a class of elementary functions including division, logarithms, and exponentials. The main objective is to demonstrate the feasibility of higher radix implementations, in particular, radix 16, and to compare performance with radix 2. The emphasis is not on optimality of a single algorithm, but rather on the optimality of a class of algorithms. An attempt to implement a much wider class of functions than is presently done in arithmetic units is encouraged by the current level of digital technology and the existence of suitable algorithms. Besides the definitions of the algorithms, which are based on continued products and continued sums, details related to implementation are discussed.