α-CORDIC:: An adaptive CORDIC algorithm

In this work we briefly review the basic CORDIC algorithm and its drawbacks. Next, we propose an adaptive CORDIC algorithm (alpha-CORDIC) which removes all the CORDIC drawbacks: (a) the number of iterations is reduced, (b) full machine accuracy is assured, (c) the scale-factor problem is eliminated, (d) the operating range is unlimited, (e) computation noise is reduced, and (f) ability to utilize the fast multiply/accumulate instructions now prevalent in digital signal processing (DSP) chips is added. The new algorithm uses a better strategy for choosing the step size in each iteration, but requires a parallel multiplier and extra look-up tables. This condition is easily satisfied in most new microprocessor chips. Simulation results, assuming 32-bit floating-point data format, are presented which clearly show the advantages of the proposed algorithm.