Error analysis and reduction for angle calculation using the CORDIC algorithm

In this paper, we consider the errors appearing in angle computations with the CORDIC algorithm (circular and hyperbolic coordinate systems) using fixed-point arithmetic. We include errors arising not only from the finite number of iterations and the finite width of the data path, but also from the finite number of bits of the input. We show that this last contribution is significant when both operands are small and that the error is acceptable only if an input normalization stage is included, making unsatisfactory other previous proposals to reduce the error. We propose a method based on the prescaling of the input operands and a modified CORDIC recurrence and show that it is a suitable alternative to the input normalization with a smaller hardware cost. This solution can also be used in pipelined architectures with redundant carry-save arithmetic.