CORDIC: Elementary Function Computation Using Recursive Sequences

Many of us who teach calculus and mathematical topics that use calculus have taken for granted that hand-held calculators use Taylor series or a variant to compute transcendental functions. Thus, it was a surprise to learn that this was not the case. The CORDIC method (Coordinate Rotation Digital Computer) was developed by Jack Volder [6] in the late 1950’s. Hewlett-Packard was quick to realize the usefulness of this method; it required only the most efficient processes to compute values of the standard transcendental functions. It should be noted at the outset that, while this presentation presumes base two arithmetic, calculators use base ten arithmetic with specially designed chips that use binary coded decimal (BCD) arithmetic. This was done to reduce the need for limited storage in the early years. While storage is no longer a problem, the algorithms are very efficient and adequate for calculator use. Many of the papers on CORDIC that I have located were written for an engineering audience. These include the original paper by Volder and, subsequently, papers by Linhardt and Miller [1], Walther [7], and Schmid and Bogacki [4]. Two sources of information on CORDIC for a mathematics audience are articles by Schelin [3] and the COMAP article by Pulskamp and Delaney [2].