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
______________________________________________________________________
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