Fast computation of arctangent functions for embedded applications: A comparative analysis

Inverse tangent or arctangent function has many applications, for example, in estimating the phase angle of complex number utilized in electrical ac circuit analysis, power systems analysis, etc. Therefore, fast and accurate computation of the arctangent function is of great importance. Implementation of the arctan or atan2 using series expansions is accurate when computational cost is not an issue. However, for embedded applications such implementations cannot be used. As alternative, different approximations are proposed. In this paper, we present an efficient implementation using look-up table with 101-points. The accuracy is then increased by linear interpolation. The arctangent computation is extended to four quadrant operation using particular properties of arctan. The proposed scheme is implemented in a 60MHz microcontroller platform, typical for embedded applications. Comparative evaluations show that the accuracy of the proposed method is better than the reported approximation techniques. The time consumption of the proposed method is significantly less than that of the library function of the same microcontroller platform.