Original ticket http://projects.scipy.org/numpy/ticket/1798 on 2011-04-11 by @mwiebe, assigned to @mwiebe.

[scalar float64]*[array int8] should produce [array float64], but when the value of the scalar float64 is small, it may produce [array float16] or [array float32]. Here is the current behavior:

>>> 3.1*np.ones(2,dtype=np.int8)
array([ 3.09960938,  3.09960938], dtype=float16)
>>> 1e10*np.ones(2,dtype=np.int8)
array([  1.00000000e+10,   1.00000000e+10], dtype=float32)
>>> 1e40*np.ones(2,dtype=np.int8)
array([  1.00000000e+40,   1.00000000e+40])

I propose a fix in two parts.

1. Fix this in the PyArray_ResultType/numpy.result_type function of the type promotion API. In particular, the algorithm should track the promoted array and scalar types separately, then if the kind of the promoted scalar type is greater than the kind of the promoted array type, continue the promotion of the promoted array type with the scalars without using minscalartype.
2. Change the ufunc to detect binary operators during creation, and set a flag for it. Then, during evaluation, use PyArray_ResultType to do the type promotion for binary operators instead of the existing slow linear search. The ufunc doesn't have a flags field, but it does have a field called 'check_return' which is unused, and could be repurposed as a flags field without changing the size of the python type.