Is it safe to assume that atan2(0,0) returns 0?

Question

It seems thatatan2(0,0) in C is defined this way. Python just delegates the common trigonometric functions to the underlying C implementation, right?

Answer 1

The Python docs don't explicitly specify atan2(0, 0), but the CPython implementation goes to specific effort to ensure special cases follow C99 even if the underlying C library doesn't. This includes a code path that handles making atan2(0, 0) return 0.0:

if (Py_IS_INFINITY(x) || y == 0.) {
    if (copysign(1., x) == 1.)
        /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
        return copysign(0., y);
    ...

In general, functions provided in the math module that correspond to C standard library functions are expected to match the C standard behavior. There are a few blanket statements to this effect, such as this one near the top of the docs:

This module is always available. It provides access to the mathematical functions defined by the C standard.

and this one near the bottom:

Behavior in exceptional cases follows Annex F of the C99 standard where appropriate.

although Annex F isn't the part of the standard that defines atan2.

Answer 2

As @user2357112 said, docs do not specify this. If you need something well documented - use numpy.arctan2 - see Notes section in https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.arctan2.html