2011/9/30 Mark Wiebe <[email protected]> > On Fri, Sep 23, 2011 at 1:52 PM, Olivier Delalleau <[email protected]> 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! It's re-assuring to hear that part of it is caused by a bug, and the other part has some logic behind it (even though it leads to surprising results). I appreciate you taking the time to clear it up for me :)
-=- Olivier
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