Indeed, all of us over-riders have to start to return NotImplemented if we don't know what the other class is - and I write this having recently realized that in astropy's Quantity I have caused similar problems by trying to make a guess (despite being admonished to refuse to do that). Of course, numpy's ndarray is the worst culprit here, just coercing everything to array.

See https://github.com/numpy/numpy/pull/12630 for a numpy enhancement proposal that would end up making dtype more easily subclassable.

Just as a heads-up, there is indeed the realisation within numpy that subclassable dtype would be great -- see https://github.com/numpy/numpy/issues/2899. If you have something like a design, I would certainly be interested (as maintainer of astropy's Quantity -- physical units should really be supported everywhere!), and I'd suggest to send a note to numpy-dev to get possible feedback/help.

@burnpanck - thanks for the very well-posed description of why units are so useful not as some meta-data, but as an integral property. Of course, this is also why making them part of a new dtype is a great idea! But failing that, I'd agree that it has to be part of something like an ndarray subclass; this is indeed what we do in astropy.units.Quantity (and concatenate does not work for us either...).

Now, off-topic but still: what is a little less wonderful is that there seem to be quite a few independent units implementations around (even just in astronomy, there is that of amuse; ours is based on things initially developped by pynbody). It may well be hard to merge them at this stage, but it would be good to think how we could at least interoperate...

@hgrecco - for astropy's Quantity, we currently also rely on __array_prepare__ and __array_wrap__. The main annoyances are (1) one cannot change the input before a numpy ufunc is called, and therefore often has no choice but to let a wrong calculation proceed; (2) proper recognition in non-ufunc functions is sparse (e.g., np.dot, etc.; see http://docs.astropy.org/en/latest/known_issues.html#quantity-issues)

Aside: at some point I'd hope to get the various implementations of units to talk together: it would be good to have an API that works such that units are inter-operable.

p.s. For concatenate, you need unit conversion as well, so sadly Quantity does need to override that too (and currently cannot, which is rather annoying).

@shoyer - fair enough, and sad we don't have __numpy_ufunc__ yet... I agree that with Quantity inside, one would end up duplicating work for every chunk, which makes it less than ideal even though it would probably be the easier approach to implement.

For the outside method, from the dask perspective, it would indeed be easiest if units were done as a dtype, since then you can punt all the decisions to helper routines. My guess, though, is that it will be a while before numpy will include what is required to tell, e.g., that if I add something in m to something in cm, the second argument has to be multiplied by 0.01. But astropy does provide something just like that: quantity_helpers exposes a dict keyed by operation, which holds functions that return the required converters given the units. E.g., in the above example, internally what happens is

``` converters, result_unit = UFUNC_HELPERSnp.add result_unit

Unit("m")

converters[0]

None

converters[1]

<function astropy.units.quantity_helper.get_converter.\<locals>.\<lambda>>

converters1

0.01

```

In dask, you could run the converters on your individual chunks, though obviously I don't know how easy it is to add an extra step like this without slowing down other aspects too much.

@shoyer - as one who thinks unit support is probably the single best thing astropy has (and is co-maintainer of astropy.units), I thought I'd pipe in: why would it be a problem that astropy's Quantity is an ndarray subclass? I must admit not having used dask arrays, but since they use ndarray internally for the pieces, shouldn't the fact that Quantity has the same interface/methods, make it relatively easy to swap ndarray for Quantity internally? I'd be quite happy to help think about this (surely it cannot be as bad as it is for MaskedArray ;-).

Alternatively, maybe it is easier to tag on the outside rather than the inside. This would also not seem to be that hard, given that astropy's Quantity is really just a wrapper around ndarray that carries a Unit instance. I think the parts that truly wrap might be separated from those that override ndarray methods, and would be willing to implement that if there is a good reason (like making dask quantities possible...). It may be that in this case one would not use Quantity proper, but rather just the parts of units where the real magic happens: in the Unit class (which does the unit conversion) and in quantity_helpers.py (which tells what unit conversion is necessary for a given operation/function).