Atan2 vs fabs

The code atan2(sin(x),cos(x)) achieves the same computation as fabs(x,2*pi()). The manual warns that fabs() can induce sampling issues; would the same issues apply to the atan2 version?

Warning is due to possible discontinuity in gradient. The same applies for any function which may produce discontinuity in gradient.

Gotcha. I have nil training in calculus; presumably atan2(sin(x),cos(x)) has a discontinuous gradient?

At n*pi, the derivative is undefined because the function is discontinuous.

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Gotcha, thanks @yizhang

The gradient is a function of the function. If you put the same function in, you get the same gradient function out. There’s no way to save a discontinuous function by reformulating it, but it’s sometimes possible to destroy a well-defined function by numerical issues in the chain rule.