[Numpy-discussion] Moving forward with value based casting

[Marten van Kerkwijk]

Hi Sebastian,

Tricky! It seems a balance between unexpected memory blow-up and unexpected
wrapping (the latter mostly for integers).

Some comments specifically on your message first, then some more general
related ones.

1. I'm very much against letting `a + b` do anything else than `np.add(a,
b)`.
2. For python values, an argument for casting by value is that a python int
can be arbitrarily long; the only reasonable course of action for those
seems to make them float, and once you do that one might as well cast to
whatever type can hold the value (at least approximately).
3. Not necessarily preferred, but for casting of scalars, one can get more
consistent behaviour also by extending the casting by value to any array
that has size=1.

Overall, just on the narrow question, I'd be quite happy with your
suggestion of using type information if available, i.e., only cast python
values to a minimal dtype.If one uses numpy types, those mostly will have
come from previous calculations with the same arrays, so things will work
as expected. And in most memory-limited applications, one would do
calculations in-place anyway (or, as Tyler noted, for power users one can
assume awareness of memory and thus the incentive to tell explicitly what
dtype is wanted - just `np.add(a, b, dtype=...)`, no need to create `out`).

More generally, I guess what I don't like about the casting rules generally
is that there is a presumption that if the value can be cast, the operation
will generally succeed. For `np.add` and `np.subtract`, this perhaps is
somewhat reasonable (though for unsigned a bit more dubious), but for
`np.multiply` or `np.power` it is much less so. (Indeed, we had a long
discussion about what to do with `int ** power` - now special-casing
negative integer powers.) Changing this, however, probably really is a
bridge too far!

Finally, somewhat related: I think the largest confusing actually results
from the `uint64+in64 -> float64` casting.  Should this cast to int64
instead?

All the best,

Marten
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