API/BUG: Behaviour of NA in BooleanArray pow operation

[jorisvandenbossche]

For IntegerArray, we have some special-case behaviour for NAs in pow operation. For example, 1 ** NA == 1 and not NA as normal NA-propagation would be.

For BooleanArray, we don't have that, but maybe we should do the same? So that the boolean power of boolean-cast-to-int8 power operations for the same?

Right now this is different:

>>> a = pd.array([True] * 3 + [False] * 3 + [None] * 3, dtype="boolean")
>>> b = pd.array([True, False, None] * 3, dtype="boolean")  
>>> a 
<BooleanArray>
[True, True, True, False, False, False, <NA>, <NA>, <NA>]
Length: 9, dtype: boolean
>>> b
<BooleanArray>
[True, False, <NA>, True, False, <NA>, True, False, <NA>]
Length: 9, dtype: boolean

>>> a ** b
<IntegerArray>
[1, 1, <NA>, 0, 1, <NA>, <NA>, <NA>, <NA>]
Length: 9, dtype: Int8

>>> a.astype("Int8") ** b.astype("Int8") 
<IntegerArray>
[1, 1, 1, 0, 1, <NA>, <NA>, 1, <NA>]
Length: 9, dtype: Int8

[jbrockmendel]

I'd be fine with this.