The modified CORDIC algorithm

A Modified CORDIC Algorithm (MCA) has been developed for the evaluation of elementary arithmetic functions. MCA incorporates increased parallelism over the original CORDIC algorithm, thus, resulting in an enhanced speed of computation. This has been accomplished by decoupling the CORDIC interation equations and transforming the sequential nature of these equations, n-bit fixed point data operands are assumed and the parameter k relates to the level of parallelism in the algorithm. The modified algorithm employs a [k+1]n² n-bit ROM for lookup tables that enable elementary arithmetic functions to be evluated in no more than [3n+2] and no less than 2 time steps. The two bounds correspond to a pipelined and a parallel implementation, respectively. The formulation of the MCA can be manipulated to obtain implementations with various speed/cost characteristics. This compares to n(3n+1)/2 time steps for the original CORDIC algorithm. For example, 32-bit ALU has k=12 and n=32; so, a 13,312-bit ROM is required to store the lookup tables, and the computation requires 98 time steps for a pipelined implementation.