RE: Comparing of values

[Mike Miller]

On Fri, 22 Oct 2004, Hall, Benjamin wrote:

> Searching for exact matches to floating point numbers can be troublesome 
> just due to the nature of floating point numbers in computers 
> (unfortunately, I can't really give a better answer than that!).  For 
> instance
>
> > > 3*0.05 - 0.15
>
> ans =
>
>  2.7756e-017
>
> One work-around is the following:
>
> beta = 0.05:0.05:0.95;
>
> beta( beta == 3*0.05 )
>
> or
>
> beta( abs( beta - 0.15 ) < 0.00000001 )


It seems to me that this problem has come up fairly often.  Here's a 
suggestion that might help:

Develop an additional boolean operator called "approximately equal" that 
would return 1 if terms were within, say, 10*eps, and 0 otherwise.  It 
could use "~~", and work like this:

beta( beta ~~ 0.15 )

It would have the benefit of simplifying code and drawing attention to the 
problem of rounding errors.  It would not be MATLAB compatible.  It would 
require work that I am not able to do.

Even if that can't be done, maybe the 'help' entry for "==" could be 
changed to add a bit about the way that comparisons are made -- exact 
binary matches are required.  For example, the computer's binary 
representation of .15 does not exactly match its binary representation of 
3*.05, and therefore, .15 == 3*.05 returns 0.

Mike

--
Michael B. Miller, Ph.D.
Assistant Professor
Division of Epidemiology and Community Health
and Institute of Human Genetics
University of Minnesota
http://taxa.epi.umn.edu/~mbmiller/



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