Is There A Megafunction For Arctan ?

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I suggest to use a look up table that store coarse values (as a an example 2^10 values that are the exact values when the 6 LSB of your input are zero). To get the final value interpolate between two adjacent points. Note that your function is quite linear around zero and almost flat far from zero. it should be easy to approximate.

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Right. If youa also utilize the symmetry between x and y in arctan(x/y), you need a table over 45 degree only. An interpolated table with 256 points can achieve about 16 bit accuracy.