[plt-scheme] ProfessorJ, ==, and double

On Tue, 25 Jan 2005 14:34:50 -0500, Carl Eastlund
<carl.eastlund at gmail.com> wrote:
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> 
> On Tue, 25 Jan 2005 14:02:34 -0500, Don Blaheta <dblaheta at knox.edu> wrote:
> > Quoth Carl Eastlund:
> > > The == operator doesn't operate on type double in ProfessorJ: Beginner
> > 
> > Because floating point numbers shouldn't be tested for equality, due to
> > numeric error.  Consider:
> >
> >   > double x = (1.0 / 6) * 10000;
> >   > double y = 10000.0 / 6;
> >   > x
> >   1666.6666666666665
> >   > y
> >   1666.6666666666667
> 
> Fair enough.  I've seen this reasoning before, I just wasn't sure it
> was the reason in use here.
> 
> > Now, there are situations once you know what you're doing, when you know
> > that numeric error can't arise, that you can make use of ==, but Java
> > beginners really shouldn't use those.  The correct way to test equality
> > on doubles is
> >
> >   > double epsilon = 0.0001;
> >   > Math.abs (x - y) < epsilon
> >   true
> 
> I'm very wary of the claim that this is "correct".  For very very
> large values - the distance in meters between galaxies, for instance -
> this epsilon is woefully small and this might as well be the == test.
> For very very small values - the distance in meters between electrons,
> for instance - this epsilon is woefully large and this might as well
> be the constant true.  I think floating-point comparison is a trickier
> issue than this, and not one necessarily solvable by making freshman
> students declare or use a constant epsilon.
> 

You might want to use Kawa's number library:
http://www.delorie.com/gnu/docs/kawa/kawa-tour_5.html

or some other exact/fraction implementation:
http://www.merriampark.com/fractions.htm
http://cfxweb.net/civax/code/java/Fraction.html
http://gee.cs.oswego.edu/dl/classes/EDU/oswego/cs/dl/util/concurrent/misc/Fraction.html

Daniel