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

Charles R Harris charlesr.harris at gmail.com
Wed Oct 26 15:57:29 EDT 2016


On Wed, Oct 26, 2016 at 1:39 PM, <josef.pktd at gmail.com> wrote:

>
>
> 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.)
>

Current master is different. I'm not too worried in the array cases as the
results for negative exponents were zero except then raising -1 to a power.
Since that result is incorrect raising an error  falls on the fine line
between bug fix and compatibility break. If the pre-releases cause too much
trouble.

Chuck
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