[Numpy-discussion] Numpy integers to integer powers again again

[josef.pktd at gmail.com]

On Wed, Oct 26, 2016 at 3:23 PM, Charles R Harris <charlesr.harris at gmail.com
> wrote:

>
>
> On Tue, Oct 25, 2016 at 10:14 AM, Stephan Hoyer <shoyer at gmail.com> wrote:
>
>> I am also concerned about adding more special cases for NumPy scalars vs
>> arrays. These cases are already confusing (e.g., making no distinction
>> between 0d arrays and scalars) and poorly documented.
>>
>> On Mon, Oct 24, 2016 at 4:30 PM, Nathaniel Smith <njs at pobox.com> wrote:
>>
>>> On Mon, Oct 24, 2016 at 3:41 PM, Charles R Harris
>>> <charlesr.harris at gmail.com> wrote:
>>> > Hi All,
>>> >
>>> > I've been thinking about this some (a lot) more and have an alternate
>>> > proposal for the behavior of the `**` operator
>>> >
>>> > if both base and power are numpy/python scalar integers, convert to
>>> python
>>> > integers and call the `**` operator. That would solve both the
>>> precision and
>>> > compatibility problems and I think is the option of least surprise. For
>>> > those who need type preservation and modular arithmetic, the np.power
>>> > function remains, although the type conversions can be surpirising as
>>> it
>>> > seems that the base and power should  play different roles in
>>> determining
>>> > the type, at least to me.
>>> > Array, 0-d or not, are treated differently from scalars and integers
>>> raised
>>> > to negative integer powers always raise an error.
>>> >
>>> > I think this solves most problems and would not be difficult to
>>> implement.
>>> >
>>> > Thoughts?
>>>
>>> My main concern about this is that it adds more special cases to numpy
>>> scalars, and a new behavioral deviation between 0d arrays and scalars,
>>> when ideally we should be trying to reduce the
>>> duplication/discrepancies between these. It's also inconsistent with
>>> how other operations on integer scalars work, e.g. regular addition
>>> overflows rather than promoting to Python int:
>>>
>>> In [8]: np.int64(2 ** 63 - 1) + 1
>>> /home/njs/.user-python3.5-64bit/bin/ipython:1: RuntimeWarning:
>>> overflow encountered in long_scalars
>>>   #!/home/njs/.user-python3.5-64bit/bin/python3.5
>>> Out[8]: -9223372036854775808
>>>
>>> So I'm inclined to try and keep it simple, like in your previous
>>> proposal... theoretically of course it would be nice to have the
>>> perfect solution here, but at this point it feels like we might be
>>> overthinking this trying to get that last 1% of improvement. The thing
>>> where 2 ** -1 returns 0 is just broken and bites people so we should
>>> definitely fix it, but beyond that I'm not sure it really matters
>>> *that* much what we do, and "special cases aren't special enough to
>>> break the rules" and all that.
>>>
>>>
> What I have been concerned about are the follow combinations that
> currently return floats
>
> num: <type 'numpy.int8'>, exp: <type 'numpy.int8'>, res: <type
> 'numpy.float32'>
> num: <type 'numpy.int16'>, exp: <type 'numpy.int8'>, res: <type
> 'numpy.float32'>
> num: <type 'numpy.int16'>, exp: <type 'numpy.int16'>, res: <type
> 'numpy.float32'>
> num: <type 'numpy.int32'>, exp: <type 'numpy.int8'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.int32'>, exp: <type 'numpy.int16'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.int32'>, exp: <type 'numpy.int32'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.int64'>, exp: <type 'numpy.int8'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.int64'>, exp: <type 'numpy.int16'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.int64'>, exp: <type 'numpy.int32'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.int64'>, exp: <type 'numpy.int64'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.int64'>, exp: <type 'numpy.int64'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.uint64'>, exp: <type 'numpy.int8'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.uint64'>, exp: <type 'numpy.int16'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.uint64'>, exp: <type 'numpy.int32'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.uint64'>, exp: <type 'numpy.int64'>, res: <type
> 'numpy.float64'>
> num: <type 'numpy.uint64'>, exp: <type 'numpy.int64'>, res: <type
> 'numpy.float64'>
>
> The other combinations of signed and unsigned integers to signed powers
> currently raise ValueError due to the change to the power ufunc. The
> exceptions that aren't covered by uint64 + signed (which won't change) seem
> to occur when the exponent can be safely cast to the base type. I suspect
> that people have already come to depend on that, especially as python
> integers on 64 bit linux convert to int64. So in those cases we should
> perhaps raise a FutureWarning instead of an error.
>


>>> np.int64(2)**np.array(-1, np.int64)
0.5
>>> np.__version__
'1.10.4'
>>> np.int64(2)**np.array([-1, 2], np.int64)
array([0, 4], dtype=int64)
>>> np.array(2, np.uint64)**np.array([-1, 2], np.int64)
array([0, 4], dtype=int64)
>>> np.array([2], np.uint64)**np.array([-1, 2], np.int64)
array([ 0.5,  4. ])
>>> np.array([2], np.uint64).squeeze()**np.array([-1, 2], np.int64)
array([0, 4], dtype=int64)


(IMO: If you have to break backwards compatibility, break forwards not
backwards.)


Josef
http://www.stanlaurelandoliverhardy.com/nicemess.htm



>
> Chuck
>
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