[Numpy-discussion] Value based promotion and user DTypes

[Sebastian Berg]

On Tue, 2021-01-26 at 06:11 +0100, Ralf Gommers wrote:
> On Tue, Jan 26, 2021 at 2:01 AM Sebastian Berg <  
> sebastian at sipsolutions.net>
> wrote:
> 
> > Hi all,
> > 
> > does anyone have a thought about how user DTypes (i.e. DTypes not
> > currently part of NumPy) should interact with the "value based
> > promotion" logic we currently have?
> > For now I can just do anything, and we will find out later.  And I
> > will
> > have to do something for now, basically with the hope that it all
> > turns
> > out all-right.
> > 
> > But there are multiple options for both what to offer to user
> > DTypes
> > and where we want to move (I am using `bfloat16` as a potential
> > DType
> > here).
> > 
> > 1. The "weak" dtype option (this is what JAX does), where:
> > 
> >        np.array([1], dtype=bfloat16) + 4.
> > 
> >    returns a bfloat16, because 4. is "lower" than all floating
> >    point types.
> >    In this scheme the user defined `bfloat16` knows that the input
> >    is a Python float, but it does not know its value (if an
> >    overflow occurs during conversion, it could warn or error but
> >    not upcast).  For example `np.array([1], dtype=uint4) + 2**5`
> >    will try `uint4(2**5)` assuming it works.
> >    NumPy is different `2.**300` would ensure the result is a
> > `float64`.
> > 
> >    If a DType does not make use of this, it would get the behaviour
> >    of option 2.
> > 
> > 2. The "default" DType option: np.array([1], dtype=bfloat16) + 4.
> > is
> >    always the same as `bfloat16 + float64 -> float64`.
> > 
> > 3. Use whatever NumPy considers the "smallest appropriate dtype".
> >    This will not always work correctly for unsigned integers, and
> > for
> >    floats this would be float16, which doesn't help with bfloat16.
> > 
> > 4. Try to expose the actual value. (I do not want to do this, but
> > it
> >    is probably a plausible extension with most other options, since
> >    the other options can be the "default".)
> > 
> > 
> > Within these options, there is one more difficulty. NumPy currently
> > applies the same logic for:
> > 
> >     np.array([1], dtype=bfloat16) + np.array(4., dtype=np.float64)
> > 
> > which in my opinion is wrong (the second array is typed). We do
> > have
> > the same issue with deciding what to do in the future for NumPy
> > itself.
> > Right now I feel that new (user) DTypes should live in the future
> > (whatever that future is).
> > 
> 
> I agree. And I have a preference for option 1. Option 2 is too greedy
> in
> upcasting, the value-based casting is problematic in multiple ways
> (e.g.,
> hard for Numba because output dtype cannot be predicted from input
> dtypes),
> and option 4 is hard to understand a rationale for (maybe so the user
> dtype
> itself can implement option 3?).

Yes, well, the "rational" for option 4 is that you expose everything
that NumPy currently needs (assuming we make no changes). That would be
the only way that allows a `bfloat16` to work exactly comparable to a
`float16` as currently defined in NumPy.

To be clear: It horrifies me, but defining a "better" way is much
easier than trying to keep everything as (at least for now) while also
thinking about how it should look like in the future (and making sure
that user DTypes are ready for that future).

My guess is, we can agree on aiming for Option 1 and trying to limit it
to Python operators.  Unfortunately, only time will tell how feasible
that will actually be.

> 
> 
> > I have said previously, that we could distinguish this for
> > universal
> > functions.  But calls like `np.asarray(4.)` are common, and they
> > would
> > lose the information that `4.` was originally a Python float.
> > 
> 
> Hopefully the future will have way fewer asarray calls in it.
> Rejecting
> scalar input to functions would be nice. This is what most other
> array/tensor libraries do.
> 

Well, right now NumPy has scalars (both ours and Python), and I would
expect that changing that may well be more disruptive than changing the
value based promotion (assuming we can add good FutureWarnings).

I would probabaly need a bit convincing that forbidding `np.add(array,
2)` is worth the trouble, but luckily that is probably an orthogonal
question.  (The fact that we even accept 0-D arrays as "value based" is
probably the biggest difficulty.)

> 
> > 
> > So, recently, I was considering that a better option may be to
> > limit
> > this to math Python operators: +, -, /, **, ...
> > 
> 
> +1
> 
> This discussion may be relevant:
> https://github.com/data-apis/array-api/issues/14.
> 

I have browsed through it, I guess you also were thinking of limiting
scalars to operators (although possibly even more broadly rather than
just for promotion purposes).  I am not sure I understand this:

    Non-array ("scalar") operands are not permitted to participate in
type promotion.

Since they do participate also in JAX and in what I wrote here. They
just participate in an abstract way. I.e. as `Floating` or `Integer`,
but not like a specific float or integer.

> 
> > Those are the places where it may make a difference to write:
> > 
> >     arr + 4.         vs.    arr + bfloat16(4.)
> >     int8_arr + 1     vs.    int8_arr + np.int8(1)
> >     arr += 4.      (in-place may be the most significant use-case)
> > 
> > while:
> > 
> >     np.add(int8_arr, 1)    vs.   np.add(int8_arr, np.int8(1))
> > 
> > is maybe less significant. On the other hand, it would add a subtle
> > difference between operators vs. direct ufunc calls...
> > 
> > 
> > In general, it may not matter: We can choose option 1 (which the
> > bfloat16 does not have to use), and modify it if we ever change the
> > logic in NumPy itself.  Basically, I will probably pick option 1
> > for
> > now and press on, and we can reconsider later.  And hope that it
> > does
> > not make things even more complicated than it is now.
> > 
> > Or maybe better just limit it completely to always use the default
> > for
> > user DTypes?
> > 
> 
> I'm not sure I understand why you like option 1 but want to give
> user-defined dtypes the choice of opting out of it. Upcasting will
> rarely
> make sense for user-defined dtypes anyway.
> 

I never meant this as an opt-out, the question is what you do if the
user DType does not opt-in/define the operation.

Basically, the we would promote with `Floating` here (or `PyFloating`,
but there should be no difference; for now I will do PyFloating, but it
should probably be changed later). I was hinting at provide a default
fallback, so that if:

    UserDtype + Floating -> Undefined/Error

we automatically try the "default", e.g.:

    UserDType + Float64 -> Something

That would mean users don't have to worry about `Floating` itself.

But I am not opinionated here, a user DType author should be able to
quickly deal with either issue (that Float64 is undesired or that the
Error is undesired if no "default" exists).  Maybe the error is more
conservative/constructive though.

> 
> > 
> > But I would be interested if the "limit to Python operators" is
> > something we should aim for here.  This does make a small
> > difference,
> > because user DTypes could "live" in the future if we have an idea
> > of
> > how that future may look like.
> > 
> 
> A future with:
> - no array scalars
> - 0-D arrays have the same casting rules as >=1-D arrays
> - no value-based casting
> would be quite nice. For "same kind" casting like
> 

I don't think array-scalars really matter here, since they are typed
and behave identical to 0-D arrays anyway.  We can have long opinion
pieces on whether they should exist :).

>   
> https://data-apis.github.io/array-api/latest/API_specification/type_promotion.html
> .
> Mixed-kind casting isn't specified there, because it's too different
> between libraries. The JAX design (
> https://jax.readthedocs.io/en/latest/type_promotion.html)  seems
> sensible
> there.

The JAX design is the "weak DType" design (when it comes to Python
numbers). Although, the fact that a "weak" `complex` is sorted above
all floats, means that `bfloat16_arr + 1j` will go to the default
complex dtype as well.
But yes, I like the "weak" approach, just think also JAX has some
wrinkles to smoothen.


There is a good deal more to this if you get user DTypes and I add one
more important constraint that:

    from my_extension_module import uint24

must not change any existing code that does not explicitly use
`uint24`.

Then my current approach guarantees:

    np.result_type(uint24, int48, int64) -> Error

If `uint24` and `int48` do not know each other (`int64` is obviously
right here, but it is tricky to be quite certain).

The other tricky example I have was:

  The following becomes problematic (order does not matter):
          uint24 +      int16  +           uint32  -> int64
     <==      (uint24 + int16) + (uint24 + uint32) -> int64
     <==                int32  +           uint32  -> int64

With the addition that `uint24 + int32 -> int48` is defined the first
could be expected to return `int48`, but actually getting there is
tricky (and my current code will not).

If promotion result of a user DType with a builtin one, can be a
builtin one, then "ammending" the promotion with things like `uint24 +
int32 -> int48` can lead to slightly surprising promotion results. 
This happens if the result of a promotion with another "category"
(builtin) can be both a larger category or a lower one.

- Sebastian


> 
> Cheers,
> Ralf
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> NumPy-Discussion at python.org
> https://mail.python.org/mailman/listinfo/numpy-discussion

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