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:
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