[Numpy-discussion] Integers to integer powers

[josef.pktd at gmail.com]

On Thu, May 19, 2016 at 10:16 PM, <josef.pktd at gmail.com> wrote:

>
>
> On Thu, May 19, 2016 at 5:37 PM, Charles R Harris <
> charlesr.harris at gmail.com> wrote:
>
>> Hi All,
>>
>> There are currently several pull requests apropos integer arrays/scalars
>> to integer powers and, because the area is messy and involves tradeoffs,
>> I'd like to see some discussion here on the list before proceeding.
>>
>> *Scalars in 1.10*
>>
>> In [1]: 1 ** -1
>> Out[1]: 1.0
>>
>> In [2]: int16(1) ** -1
>> Out[2]: 1
>>
>> In [3]: int32(1) ** -1
>> Out[3]: 1
>>
>> In [4]: int64(1) ** -1
>> Out[4]: 1.0
>>
>> In [5]: 2 ** -1
>> Out[5]: 0.5
>>
>> In [6]: int16(2) ** -1
>> Out[6]: 0
>>
>> In [7]: int32(2) ** -1
>> Out[7]: 0
>>
>> In [8]: int64(2) ** -1
>> Out[8]: 0.5
>>
>> In [9]: 0 ** -1
>>
>> ---------------------------------------------------------------------------
>> ZeroDivisionError                         Traceback (most recent call
>> last)
>> <ipython-input-9-fd405d6cf4bc> in <module>()
>> ----> 1 0 ** -1
>>
>> ZeroDivisionError: 0.0 cannot be raised to a negative power
>>
>> In [10]: int16(0) ** -1
>> /home/charris/.local/bin/ipython:1: RuntimeWarning: divide by zero
>> encountered in power
>>   #!/usr/bin/python
>> /home/charris/.local/bin/ipython:1: RuntimeWarning: invalid value
>> encountered in power
>>   #!/usr/bin/python
>> Out[10]: -9223372036854775808
>>
>> In [11]: int32(0) ** -1
>> Out[11]: -9223372036854775808
>>
>> In [12]: int64(0) ** -1
>> /home/charris/.local/bin/ipython:1: RuntimeWarning: divide by zero
>> encountered in long_scalars
>>   #!/usr/bin/python
>> Out[12]: inf
>>
>> Proposed
>>
>>    - for non-zero numbers the return type should be float.
>>    - for zero numbers a zero division error should be raised.
>>
>>
>>
>>
>> *Scalar Arrays in 1.10*
>> In [1]: array(1, dtype=int16) ** -1
>> Out[1]: 1
>>
>> In [2]: array(1, dtype=int32) ** -1
>> Out[2]: 1
>>
>> In [3]: array(1, dtype=int64) ** -1
>> Out[3]: 1
>>
>> In [4]: array(2, dtype=int16) ** -1
>> Out[4]: 0
>>
>> In [5]: array(2, dtype=int32) ** -1
>> Out[5]: 0
>>
>> In [6]: array(2, dtype=int64) ** -1
>> Out[6]: 0
>>
>> In [7]: array(0, dtype=int16) ** -1
>> /home/charris/.local/bin/ipython:1: RuntimeWarning: divide by zero
>> encountered in power
>>   #!/usr/bin/python
>> /home/charris/.local/bin/ipython:1: RuntimeWarning: invalid value
>> encountered in power
>>   #!/usr/bin/python
>> Out[7]: -9223372036854775808
>>
>> In [8]: array(0, dtype=int32) ** -1
>> Out[8]: -9223372036854775808
>>
>> In [9]: array(0, dtype=int64) ** -1
>> Out[9]: -9223372036854775808
>>
>> In [10]: type(array(1, dtype=int64) ** -1)
>> Out[10]: numpy.int64
>>
>> In [11]: type(array(1, dtype=int32) ** -1)
>> Out[11]: numpy.int64
>>
>> In [12]: type(array(1, dtype=int16) ** -1)
>> Out[12]: numpy.int64
>>
>> Note that the return type is always int64 in all these cases. However,
>> type is preserved in non-scalar arrays, although the value of int16 is not
>> compatible with int32 and int64 for zero division.
>>
>> In [22]: array([0]*2, dtype=int16) ** -1
>> Out[22]: array([0, 0], dtype=int16)
>>
>> In [23]: array([0]*2, dtype=int32) ** -1
>> Out[23]: array([-2147483648, -2147483648], dtype=int32)
>>
>> In [24]: array([0]*2, dtype=int64) ** -1
>> Out[24]: array([-9223372036854775808, -9223372036854775808])
>>
>> Proposed:
>>
>>    - Raise an ZeroDivisionError for zero division, that is, in the ufunc.
>>    - Scalar arrays to return scalar arrays
>>
>>
>> Thoughts?
>>
> Why does negative exponent not upcast to float like division?
> sounds like python 2 to me
>

from __future__ import negative_power

Josef


>
> Josef
>
>
>
>> Chuck
>>
>>
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>>
>>
>
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