Python -- floating point arithmetic

[David Cournapeau]

On Thu, Jul 8, 2010 at 5:41 AM, Zooko O'Whielacronx <zooko at zooko.com> wrote:
> I'm starting to think that one should use Decimals by default and
> reserve floats for special cases.
>
> This is somewhat analogous to the way that Python provides
> arbitrarily-big integers by default and Python programmers only use
> old-fashioned fixed-size integers for special cases, such as
> interoperation with external systems or highly optimized pieces (in
> numpy or in native extension modules, for example).

I don't think it is analogous at all. Arbitrary-bit integers have a
simple tradeoff: you are willing to lose performance and memory for
bigger integer. If you leave performance aside, there is no downside
that I know of for using big int instead of "machine int". Since you
are using python, you already bought this kind of tradeoff anyway.

Decimal vs float is a different matter altogether: decimal has
downsides compared to float. First, there is this irreconcilable fact
that no matter how small your range is, it is impossible to represent
exactly all (even most) numbers exactly with finite memory - float and
decimal are two different solutions to this issue, with different
tradeoffs. Decimal are more "intuitive" than float for numbers that
can be represented as decimal - but most numbers cannot be represented
as (finite) decimal.

Except for some special usecases, you cannot expect to exactly
represent real numbers. Once you accept that fact, you can make a
decision on decimal, fraction, float or whatever format you see fit.

> And most of the time (in my experience) the inputs and outputs to your
> system and the literals in your code are actually decimal, so
> converting them to float immediately introduces a lossy data
> conversion before you've even done any computation. Decimal doesn't
> have that problem.

That's not true anymore once you start doing any computation, if by
decimal you mean finite decimal. And that will be never true once you
start using non trivial computation (i.e. transcendental functions
like log, exp, etc...).

David