Error reduction technique for four-quadrant arctangent approximations

A general technique of error reduction to improve the accuracy of four-quadrant arctangent approximations through the Mobius transformation is proposed. Simple identities connecting the regular arctangent function and the four-quadrant arctangent function are derived and used to obtain novel four- quadrant arctangent approximations. The new approximations can provide improved accuracy at the expense of a moderate increase in computational cost.