Determine if negative axis argument is equivalent to zero

[douglasdavis]

Determining if axis is equivalent to zero if it's negative...

Given this array,

>>> array = ak.Array([[{"x": 1.1, "y": [1]}], [], [{"x": 2.2, "y": [1, 2]}]])
>>> array.type.show()
3 * var * {
    x: float64,
    y: var * int64
}

For x, axis=-2 is equivalent to axis=0:

>>> ak.sum(array.x, axis=0), ak.sum(array.x, axis=-2)
(<Array [3.3] type='1 * float64'>, <Array [3.3] type='1 * float64'>)

For y, axis=-3 is equivalent to axis=0:

>>> ak.sum(array.y, axis=0), ak.sum(array.y, axis=-3)
(<Array [[2, 2]] type='1 * var * int64'>, <Array [[2, 2]] type='1 * var * int64'>)

We could derive that from the minmax_depth:

>>> array.layout.minmax_depth
(2, 3)

which doesn't say which has depth 2 and which has depth 3, just that something does. If a given axis is negative and

• -axis > min(array.layout.minmax_depth), then it will be an index out of range error for some part of the array
• min(array.layout.minmax_depth) <= -axis <= max(array.layout.minmax_depth), then it will be axis == 0 for some part of the array
• -axis < min(array.layout.minmax_depth), then it will be axis != 0 for all parts of the array.

This last case is one that you can always offload to Awkward. If

• -axis == min(array.layout.minmax_depth) == max(array.layout.minmax_depth), then it's a valid request, equivalent to axis == 0, but not handled by dask-awkward (NotImplementedError).

The only other case, -axis > min(array.layout.minmax_depth) would even be an Awkward axis out of range error (np.AxisError, but maybe ValueError?).

>>> ak.sum(array.y, axis=-4)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/jpivarski/irishep/awkward/src/awkward/operations/ak_sum.py", line 218, in sum
    return _impl(array, axis, keepdims, mask_identity, highlevel, behavior)
  File "/home/jpivarski/irishep/awkward/src/awkward/operations/ak_sum.py", line 292, in _impl
    out = ak._do.reduce(
  File "/home/jpivarski/irishep/awkward/src/awkward/_do.py", line 383, in reduce
    raise ak._errors.wrap_error(
ValueError: while calling

    ak.sum(
        array = <Array [[[1]], [], [[1, 2]]] type='3 * var * var * int64'>
        axis = -4
        keepdims = False
        mask_identity = False
        highlevel = True
        behavior = None
    )

Error details: axis=-4 exceeds the depth of the nested list structure (which is 3)

I expected that to be an np.AxisError, not a ValueError...

Originally posted by @jpivarski in #151 (comment)