Guido van Rossum wrote:
Also, why do you consider a float to be a "larger" value type than decimal? Do you mean that a float is less precise?
(Warning: I think the following is a sound model, but I'm still practicing how to explain it right.)
I have this ordering of the types in mind:
int/long < decimal < rational < float < complex \---------------------------/ \-------------/ exact inexact
This is different from the Scheme numeric "tower" -- I no longer agree with the Scheme model any more.
The ordering is only to determine what happens on mixed arithmetic: the result has the rightmost type in the diagram (or a type further on the right in some cases).
Interesting. Here's what I use in mxNumber: mx.Number.Float ^ | --------> Python float | ^ | | | mx.Number.Rational | ^ | | Python long --> mx.Number.Integer ^ ^ | | -------- Python integer
The ints are a subset of the decimal numbers, and the decimal numbers (in this view) are a subset of the rational numbers. Ints and decimals aren't closed under division -- the result of division on these (in general) is a rational. While the exact values of floats are a subset of the rationals, the inexactness property (which I give all floats) makes that each float stands for an infinite set of numbers *including* the exact value. When a binary operation involves an exact and an inexact operand, the result is inexact.
Tim's "numeric context" contains a bunch of flags controlling detailed behavior of numeric operations. It could specify that mixing exact and inexact numbers is illegal, and that would be Michael's pedantic mode. It could also specify warnings. (I would never call a mode that issues warnings "safe" :-)
Could you perhaps write this coercion scheme up as informational PEP ? I think it would help a lot as reference to what Python should do and serve well for numeric extension writers as basis for their coercion decisions. -- Marc-Andre Lemburg CEO eGenix.com Software GmbH ______________________________________________________________________ Consulting & Company: http://www.egenix.com/ Python Software: http://www.lemburg.com/python/