An angle recoding method for CORDIC algorithm implementation

The coordinate rotation digital computer (CORDIC), an iterative arithmetic algorithm for computing generalized vector rotations without performing multiplications, is discussed. For applications where the angle of rotation is known in advance, a method to speed up the execution of the CORDIC algorithm by reducing the total number of iterations is presented. This is accomplished by using a technique called angle recoding, which encodes the desired rotation angle as a linear combination of very few elementary rotation angles. Each of these elementary rotation angles takes one CORDIC iteration to compute. The fewer the number of elementary rotation angles, the fewer the number of iterations are required. A greedy algorithm which takes only O(n/sup 2/) operations is developed to perform CORDIC angle recoding. It is proven that this algorithm is able to reduce the total number of required elementary rotation angles by at least 50% without affecting the computational accuracy.<>