[Python-Dev] Unifying Long Integers and Integers: baseint

[Gareth McCaughan]

On Tuesday 2004-08-10 14:35, Skip Montanaro wrote:
> 
>     >> I think it would be worth considering all the numeric types at once
>     >> and come up with a reasonable hierarchy that includes float, complex
>     >> and decimal types as well.  (It's clear there is no "best" way to do
>     >> that.)
> 
>     Dmitry> Something like following?
> 
>     Dmitry> object
>     Dmitry>      numeric
>     Dmitry>          integer
>     Dmitry>              int
>     Dmitry>              long
>     Dmitry>          float
>     Dmitry>          complex
> 
> At some level it seems that float is a specialization of complex (w/ imag
> field == 0).  Also, it's not clear that float or complex don't have
> something other than a sibling relationship to integers.

Start by thinking about the mathematical types, which have
nice clear subset relationships between them:

    number
      complex
        real
          integer

Python doesn't have anything between "number" and "complex" and
there's no particular reason to think it ever will, so let's
simplify:

    number
      real
        integer

Now consider the different implementation types and fit them
in:

    number
      complex
      real
        (Decimal)
        float
        integer
          int
          long

I've reintroduced "complex" here as a name for the implementation
type, which in some sense should really be called complex_float
or something like that.

By way of clarification of the principles here, this is what
would happen to the hierarchy if Python were to acquire a
type for ratios of integers. I'll call that type "fraction"
and the underlying mathematical type "rational". Then we'd
get:

    number
      complex
      real
        (Decimal)
        float
        rational
          fraction
          integer
            int
            long

(You could argue that floats are rationals really, but that's
misleading even though it's true. The *structure* of arithmetic
operations on floats isn't the same as that on rationals.)

-- 
g