Floating point problems

[Jon Fairbairn]

This is more of a haskell-café than a ghc users question,
but I'll put some thoughts here:

On 2006-08-30 at 19:38BST Jamie Brandon wrote:
> I recently defied my supervisor and used Haskell to write my coursework
> instead of C.

If the object of the course is to teach you (more about) C,
that might not go down too well :-)

> All went well until I needed floating point and
> started having odd results.

My first experience with floating point numbers (some time
in the middle of the last half of the last century...) was
so discouraging that I decided to avoid them as much as
possible.  They really are very badly behaved.

> As far as I can tell it isn't
> substantially affecting my results but it is rather embarrassing after
> slagging off C so much. Here are some examples:
>         
>         *Main> 0.2 + 0.1
>         0.30000000000000004
>         *Main> 0.200000000000000 + 0.100000000000000000
>         0.30000000000000004
>         *Main> 0.3 + 0.1
>         0.4
>         *Main> 0.2 + 0.1
>         0.30000000000000004
>         *Main> it + 0.1
>         0.4
>         
> I assume this is a result of the discrepancy between
> binary and decimal representations of the numbers.

That and the finiteness of the representations.

> Is there any way around? For a start, it would be nice to
> have a simple way to get 0.1 + 0.2 == 0.3 = True

You can have that, like this:

   *MyIdiom>  0.1 + 0.2 == 0.3
   False
   *MyIdiom> :m + Ratio
   *MyIdiom Ratio> 0.1 + 0.2 == (0.3::Rational)
   True

but doing something like that is really the only reliable
way.  If you are working with floating point, equality is
something you should never test for; you should check to see
if the difference between the numbers is smaller than some
acceptable epsilon.

Incidentally, if I run 


   #include <stdio.h>
   #include <stdlib.h>
   main () 
   {
     printf ("%d",0.2 + 0.1 == 0.3);
   }

the output is 0...
-- 
Jón Fairbairn                              Jon.Fairbairn at cl.cam.ac.uk