A fast and accurate approximation of atan by look-up mothod with three variants inside in c++. For more comparison to other polynomial approximation you can refer these two papers:
[1] Abhisek Ukil, Vishal H Shah, Bernhard Deck, "Fast Computation of arctangent Functions for Embedded Applications: A Comparative Analysis" IEEE International Symposium on Industrial Electronics, Pages: 1206 - 1211, DOI: 10.1109/ISIE.2011.5984330, 2011
[2] Sreeraman Rajan, Sichun Wang, Robert Inkol, and Alain Joyal "Efficient Approximations for the Arctangent Function" IEEE SIGNAL PROCESSING MAGAZINE [108] MAY 2006
Any advice or suggestion towards this simple function please contact me.