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better atan function?

Greetings all,

I have found that the phase I get from the FFT has
a precision of only ~10e-8, and that the precision depends
on what value phase has.

I think I've traced this to the atan function, or perhaps the
division that takes place in the atan function.

Does anyone have a better atan function (more precise)?

Or is this merely the way it is when one is bumping up against
precision errors?

By comparison, my  "simulation" does get the amplitudes
of the spectral components to a precision of ~10e-14 or so.
(as expected for double precision variables, and no noise)

stockwell (at) co-ra (dot) com