On Tue, Apr 12, 2011 at 11:51 AM, Mark Wiebe wrote:
<snip>
here's the rule for a set of arbitrary arrays (not necessarily just 2):

- if all the arrays are scalars, do type promotion on the types as is
- otherwise, do type promotion on min_scalar_type(a) of each array a

The function min_scalar_type returns the array type if a has >= 1 dimensions, or the smallest type of the same kind (allowing int->uint in the case of positive-valued signed integers) to which the value can be cast without overflow if a has 0 dimensions.

The promote_types function used for the type promotion is symmetric and associative, so the result won't change when shuffling the inputs. There's a bit of a wrinkle in the implementation to handle the fact that the uint type values aren't a strict subset of the same-sized int type values, but otherwise this is what happens.

https://github.com/numpy/numpy/blob/master/numpy/core/src/multiarray/convert_datatype.c#L1075

The change I'm proposing is to modify this as follows:

- if all the arrays are scalars, do type promotion on the types as is
- if the maximum kind of all the scalars is > the maximum kind of all the arrays, do type promotion on the types as is
- otherwise, do type promotion on min_scalar_type(a) of each array a

One case where this may not capture a possible desired semantics is [complex128 scalar] * [float32 array] -> [complex128]. In this case [complex64] may be desired. This is directly analogous to the original [float64 scalar] * [int8 array], however, and in the latter case it's clear a float64 should result.

I've implemented what I suggested, and improved the documentation to better explain what's going on. One thing I adjusted slightly is instead of using the existing kinds, I used three categories: boolean, integer (int/uint), and floating point (float/complex). This way, we get [float32 array] + 0j producing a [complex64 array] instead of a [complex128 array], while still fixing the original regression.