I haven't looked at the code, but I like the concept!

Note to self: if we do this, u.mag should almost certainly refer to units.function.mag rather than units.astrophys.mag -- the latter would just be used internally in the function units (or in composite units).

Set the 1.10 milestone, since I think with this merged, the preferred API for function units changes: one would do u.dex(u.cm/u.s**2) instead of u.DexUnit(u.cm/u.s**2). And if this is still done in the same milestone, we don't have to make any explicit notices about preferred API.

@mdboom - here's an update on the callable units. It now makes mag, dex, and dB be subclass instances of their normal classes which have an additional __call__ method. Can you have a look that you think the implementation is OK? In principle, one could also add a __call__ method to UnitBase (which normally would raise a TypeError), but I thought it was better to keep the changes completely separate. It does mean that mag, dex and dB are now defined in function.units instead of in astrophys, but that seems, if anything, a more logical place (and in practice one would just get them from the top level anyway).

I'll try to update the documentation later today.

Looks good other than my one minor comment.

@mdboom - OK, changed those names. I now also updated the documentation, including giving a little teaser in the "getting started" section of units.

@mdboom - I think this is now all done (I now use the callable units in the parser and resolved a small issue found while testing with __numpy_ufunc__); if you want to check anything, perhaps the revised documentation?

@mdboom - would you want/have a chance to have a last look at this PR? (And the follow-up in #3851...)