float equality

[Kevin Bealer]

== Quote from Walter Bright (newshound2 at digitalmars.com)'s article
...
> I do understand that if you have a full symbolic representation, you can do so
> with zero losses. But Kevin's proposal was not that, it was for a ratio
> representation.
>
> All it represents symbolically is division. There are plenty of other operations.

I'm just answering the original poster's question.  You're right though -- it's not
a complete numerical system, (and I don't propose it for inclusion in the language
or even necessarily the library.)

I had two goals:

1. To solve the basic problem the original poster was asking -- if you are working
with simple decimals and arithmetic you can get completely accurate representations
this way.  For some cases like simple financial work this might work really well.
e.g. where float would not be because of the slow leak of information with each
operation.  (I assume real professional financial work is already done using a
(better) representation.)

2. To explain why the 'simple' task of representing something like .1 wasn't as easy
as it looks.  In other words, why the people who designed float weren't just brain
dead.  I think they really knew what they were doing but it shocks most people at
first that a modern computer can't do what they see as grade school arithmetic.

I think for some purposes though, lossless domain specific representations can
be a good tool -- if you can represent a problem in a way that is lossless you can
maybe do better calculations over long series than working with 'double' and taking
the accuracy hit.  This is necessarily an application specific technique though.

Kevin