CORDIC-Based Computation of ArcCos

Abstract

CORDIC-based algorithms to compute cos$\cos ^{ - 1} (t),\sin ^{ - 1} (t)$ and $\sqrt {1 - t^2 }$ are proposed. The implementation requires a standard CORDIC module plus a module to compute the direction of rotation, this being the same hardware required for the extended CORDIC vectoring, recently proposed by the authors [T. Lang and E. Antelo, IEEE Transactions on Computers, vol. 47, no. 7, 1998, pp. 736–749.]. Although these functions can be obtained as a special case of this extended vectoring, the specific algorithm we propose here presents two significant improvements: (1) it uses the same datapath width as the standard CORDIC, even when t has 2n bits (to achieve a granularity of 2⁻ⁿ for the whole range). In contrast, the extended vectoring unit requires about 2n bits. (2) no repetitions of iterations are needed (the extended vectoring needs some repetitions). The proposed algorithm is compatible with the extended vectoring and, in contrast with previous implementations, the number of iterations and the delay of each iteration are the same as for the conventional CORDIC algorithm.