An efficient mathematically correct scale free CORDIC

In order to approximate transandental functions, several algorithms were proposed. Historically, polynomial interpolation, infinite series, · · · and other +,×,− and / based algorithms were studied for this purpose. The CORDIC (COordinate Rotation DIgital Computer) introduced by Jack E. Volder in 1959, and generalized by J. S. Walther a few years later, is a hardware based algorithm for the approximation of trigonometric, hyperbolic and logarithmic functions. As a consequence, CORDIC is used for applications in diverse areas such as signal and image processing. For these reasons, several modified versions were proposed. In this article, we present an overview of the CORDIC algorithm for the computation of the circular functions, essentially the scaling free version, and we will give a substential improvement to the commonly used one.