[Python-ideas] Python Numbers as Human Concept Decimal System

[Chris Angelico]

On Fri, Mar 7, 2014 at 11:17 AM, Mark H. Harris <harrismh777 at gmail.com> wrote:
> Well, clearly s1 is wrong.  And yet, s1 was coded by giving the system a
> normal
> human number, at a human level, and very innocently s1 is really badly
> broken
> but not immediately noticed until we try to square it...
>
> s2 on the other hand is correct, but we had to go through some hoops
> to make sure that the system received the correct type.  The system should
> be able to make this determination without the user having to determine
> types.

Once again, the problem occurs only because you're using a float
literal, and 2.01 can't perfectly round-trip.

>>> Decimal(2.01)
Decimal('2.0099999999999997868371792719699442386627197265625')

That's pretty much the value you had (I have a few more digits there,
the square rooting and squaring probably cost some accuracy), so I'd
say Decimal correctly round-tripped. The problem is the conversion
from string (source code) to float to Decimal. You think that str()ing
a float gives you a better round-trip, but that works only because
you're using relatively small numbers.

Hmm. Is the rounding done by float.__str__() an attractive nuisance?
Would it be better to show exactly what's stored, if only to remove
the temptation to treat str(f) as "more correct" than f?

ChrisA