Three Dimensional CORDIC with reduced iterations

This paper describes a modification to the three dimensional CORDIC algorithm using an approximation of the Taylor series. The modification has the potential to reduce the number of iterations required for a three dimensional CORDIC operation by at least 25%. The approach used is based upon a modification of the two dimensional CORDIC algorithm originally suggested by H.M Ahmed[1]. Introduction The COordinate Rotation DIgital Computer or CORDIC was first suggested in 1959 by J. E. Volder [2]. The motivation was a need for accurate calculations for on board an aircraft navigation. The system was capable of rapidly computing vector rotations, and performing Cartesian to circular co-ordinate conversions. The same hardware was also able to multiply, divide, and convert between binary and mixed-radix number systems. The CORDIC algorithm is now widely used for trigonometric evaluation [3, 4]. The basic CORDIC iteration can be described as a rotation and extension of a vector. Ignoring the vector extension, the relationship between the two vectors is: Xi+1 = Xi ± 2 − i Yi and Yi+1 = Yi m 2 − i Xi