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?
Chuck