Order of signed zeros when computing the minimum and maximum

[kgryte]

Currently, the specifications for computing the min and max do not state what should happen in the event of signed zeros. E.g.,

> x = xp.asarray([0.0, -0.0])
> xp.min(x)
???

NumPy returns -0.0 for the above, which is likely the desired behavior.

In [1]: np.min([0.0, -0.0])
Out[1]: -0.0

In [2]: np.min([-0.0, 0.0] )
Out[2]: -0.0

The ordering of signed zeros does not appear to have been discussed in https://github.com/data-apis/array-api/issues/10 or in https://github.com/data-apis/array-api/pull/17 which were opened during initial development of the Array API Standard.

This issue has relevance for https://github.com/data-apis/array-api/issues/667, as, if signed zeros are ordered when computing the minimum and maximum, xp.where is not a simple replacement for element-wise minimum and maximum APIs.

[rgommers]

Implementations don't sort signed zeros:

>>> import numpy as np
>>> x = np.asarray([-0.0, 0.0])
>>> x
array([-0.,  0.])
>>> np.min(x)
0.0
>>> np.signbit(x)
array([ True, False])
>>> np.signbit(np.min(x))
False
>>> np.min([-0.0, 0.0])
0.0
>>> np.min([0.0, -0.0])
-0.0

>>> import cupy as cp
>>> cp.signbit(cp.min(cp.asarray([-0.0, 0.0])))
array(False)
>>> cp.signbit(cp.min(cp.asarray([0.0, -0.0])))
array(True)

>>> import torch
>>> torch.signbit(torch.min(torch.asarray([0.0, -0.0])))
tensor(True)
>>> torch.signbit(torch.min(torch.asarray([-0.0, 0.0])))
tensor(False)

>>> np.sort([0.0, -0.0])
array([ 0., -0.])
>>> np.sort([-0.0, 0.0])
array([-0.,  0.])

So -1 for requiring that. I'm not sure it's useful to even mention that, since sorting properties are used in multiple APIs and the semantics are already given by how == behaves.

[leofang]

-1 on this too. IEEE-754 says +0 and -0 compares equal (https://en.wikipedia.org/wiki/IEEE_754#Comparison_predicates), and often when computing max/min we just call std::less or other comparison operators in the reduction algorithm, so this is likely hard to implement.

[kgryte]

@rgommers Odd. I am not able to recreate your results for NumPy. For me, NumPy consistently returns -0. Looking at my NumPy version, I have v1.23.5. Did this behavior change in more recent NumPy versions?

[rgommers]

Perhaps, not sure. May be version and platform-dependent, because min/max have SIMD implementations.

[kgryte]

During the previous workgroup meeting (2023-11-16), this issue was discussed, and consensus was that the order of signed zeros when computing the minimum and maximum should not be specified. Hence, the return value of xp.min(xp.array([0.0, -0.0])) should be implementation-defined.

As a follow-up, we should explicitly add a note to min and max indicating that users should not expect consistent behavior across array libraries for this specific edge case.