[Numpy-discussion] Weird upcast behavior with 1.6.x, working as intended?

[Mark Wiebe]

On Fri, Sep 23, 2011 at 1:52 PM, Olivier Delalleau <shish at keba.be> wrote:

> NB: I opened a ticket (http://projects.scipy.org/numpy/ticket/1949) about
> this, in case it would help getting some attention on this issue.
>

A lot of what you're seeing here is due to changes I did for 1.6. I
generally made the casting mechanism symmetric (before it could give
different types depending on the order of the input arguments), and added a
little bit of value-based casting for scalars to reduce some of the overflow
that could happen. Before, it always downcast to the smallest-size type
regardless of the value in the scalar.


> Besides this, I've been experimenting with the cast mechanisms of mixed
> scalar / array operations in numpy 1.6.1 on a Linux x86_64 architecture, and
> I can't make sense out of the current behavior. Here are some experiments
> adding a two-element array to a scalar (both of integer types):
>
> (1) [0 0] (int8) + 0 (int32) -> [0 0] (int8)
> (2) [0 0] (int8) + 127 (int32) -> [127 127] (int16)
> (3) [0 0] (int8) + -128 (int32) -> [-128 -128] (int8)
> (4) [0 0] (int8) + 2147483647 (int32) -> [2147483647 2147483647] (int32)
> (5) [1 1] (int8) + 127 (int32) -> [128 128] (int16)
> (6) [1 1] (int8) + 2147483647 (int32) -> [-2147483648 -2147483648] (int32)
> (7) [127 127] (int8) + 1 (int32) -> [-128 -128] (int8)
> (8) [127 127] (int8) + 127 (int32) -> [254 254] (int16)
>
> Here are some examples of things that confuse me:
> - Output dtype in (2) is int16 while in (3) it is int8, although both
> results can be written as int8
>

Here would be the cause of it:

https://github.com/numpy/numpy/blob/master/numpy/core/src/multiarray/convert_datatype.c#L1098

It should be a <= instead of a <, to include the value 127.


> - Adding a number that would cause an overflow causes the output dtype to
> be upgraded to a dtype that can hold the result in (5), but not in (6)
>

Actually, it's upgraded because of the previous point, not because of the
overflow. With the change to <= above, this would produce int8


> - Adding a small int32 in (7) that causes an overflow makes it keep the
> base int8 dtype, but a bigger int32 (although still representable as an
> int8) in (8) makes it switch to int16 (if someone wonders, adding 126
> instead of 127 in (8) would result in [-3 -3] (int8), so 127 is special for
> some reason).
>
> My feeling is actually that the logic is to try to downcast the scalar as
> much as possible without changing its value, but with a bug that 127 is not
> downcasted to int8, and remains int16 (!).
>
> Some more behavior that puzzles me, this time comparing + vs -:
> (9) [0 0] (uint32) + -1 (int32) -> [-1 -1] (int64)
> (10) [0 0] (uint32) - 1 (int32) -> [4294967295 4294967295] (uint32)
>
> Here I would expect that adding -1 would be the same as subtracting 1, but
> that is not the case.
>

In the second case, it's equivalent to np.subtract(np.array([0, 0],
np.uint32), np.int32(1)). The scalar 1 fits into the uint32, so the result
type of the subtraction is uint32. In the first case, the scalar -1 does not
fit into the uint32, so it is upgraded to int64.


>
> Is there anyone with intimate knowledge of the numpy casting behavior for
> mixed scalar / array operations who could explain what are the rules
> governing it?
>

Hopefully my explanations help a bit. I think this situation is less than
ideal, and it would be better to do something more automatic, like doing an
up-conversion on overflow. This would more closely emulate Python's behavior
of integers never overflowing, at least until 64 bits. This kind of change
would be a fair bit of work, and would likely reduce the performance of
NumPy slightly.

Cheers,
Mark


>
> Thanks,
>
> -=- Olivier
>
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