`torch.result_type` results are order-dependent when default dtype is `float64`

[mdhaber]

torch.result_type results are order-dependent when default dtype is float64.

from array_api_compat import torch as xp
xp.set_default_dtype(xp.float64)

dtypes = ['float32', 'float64', 'int32', 'int64', 'complex64', 'complex128']
for dtype_a in dtypes:
    for dtype_b in dtypes:
        a = xp.asarray([2, 1], dtype=getattr(xp, dtype_a))
        b = xp.asarray([1, -1], dtype=getattr(xp, dtype_b))
        dtype_1 = xp.result_type(a, b, 1.0)
        dtype_2 = xp.result_type(b, a, 1.0)
        if dtype_1 != dtype_2:
            print('dtype_1 != dtype_2:', dtype_1, dtype_2)

# dtype_1 != dtype_2: torch.float64 torch.float32
# dtype_1 != dtype_2: torch.float64 torch.float32
# dtype_1 != dtype_2: torch.float32 torch.float64
# dtype_1 != dtype_2: torch.complex64 torch.complex128
# dtype_1 != dtype_2: torch.float32 torch.float64
# dtype_1 != dtype_2: torch.complex64 torch.complex128
# dtype_1 != dtype_2: torch.complex128 torch.complex64
# dtype_1 != dtype_2: torch.complex128 torch.complex64

Thanks @ev-br for figuring out that it was dependent on the default dtype!

[ev-br]

The root cause seems to be this:

In [1]: import torch

In [2]: torch.set_default_dtype(torch.float64)

In [3]: dt_a, dt_b = torch.float32, torch.int32

In [4]: a, b = torch.empty(1, dtype=dt_a), torch.empty(1, dtype=dt_b)

In [5]: torch.result_type(a, 1.0)
Out[5]: torch.float32

In [6]: torch.result_type(b, 1.0)
Out[6]: torch.float64

This is, strictly speaking, unspecified by the Array API spec because it combines a python float and an integer array.
This is still something we should fix in array-api-compat, and relatively quickly.
I think we'll release array-api-compat==1.11.2 once data-apis/array-api-tests#349 and #277 land.