Because of the hacky way I use the warnings.catch_warnings context manager, I think (as previously noted) a luckily timed ctrl+c could lead to strange behavior...but the worst that could happen is these warnings won't appear.

I should also say that an alternate to this is to add an issue to Known Issues and wait for numpy 1.12

This look OK, though I'm slightly wary about about adding execution time. Could you do a few quick timing checks (on single values or small arrays, where it would matter most, and for simple ufuncs like addition). If speed is an issue, we could make a specific list of ufuncs for which this problem might occur.

A propos ensuring it only gets done when needed: the very simplest optimization is to turn on the warnings filter only inside the if any(converters): clause. But my sense is that we should be a little more conservative, and only do it for functions where it actually matters.

@mhvk For this type of warning, I think this can only happen in inverse trig functions: arcsin, arccos, arccosh, arctanh -- so how about:

if any(converters):
    ...

    if function in [np.arcsin, np.arccos, np.arcosh, np.arctanh]:
        # filter warning

Yes, I like the explicitness. In order to make it even faster it would be good to define the list of functions at the top as a set, i.e., something like

_UNIT_NOT_INITIALISED = "(Unit not initialised)"
_UFUNCS_FILTER_WARNINGS = {np.arcsin, np.arccos, np.arccosh, np.arctanh}

...
    if any(converters):
       ...
        if function in _UFUNCS_FILTER_WARNINGS:

@mhvk OK, good idea!

This looks good modulo the small movement requested above. Also, a changelog entry... I think this is properly classified as a bug, so it would be in the 1.2.2 section. And we might as well have a test case to ensure this doesn't come back: maybe simply the one from #3240 (maybe after test_arcsin_invalid_units in test_quantity_ufuncs.py).

@mhvk Thanks for the comments!

Looks good, merging! Thanks, @adrn!