Is There A Megafunction For Arctan ?

Those links effectively do not work.

If you search for the titles on the web you will find them at IEEE, so you need access rights ($$$).

Cordic is a proven approach, well documented on the web (free) and in fact a simple algorithm.

Back in 2004 I made my own specific implementation in AHDL. I recompiled it today for 10 and 16 bits precision (16 bits is the maximum I projected at the time), if I extrapolate the LC usage an 18 bit cordic would use about 1150 LC (Cyclone I) and run at about 250 MHz in pipelined mode. Making it combinatorial will use about the same amount of LCs but will be a lot slower( est. 70 ns delay). I used a Cyclone EP1C4F324C6 device for the test compilations.