Re: floating point comparison

[schlafly@bbs.cruzio.com]

In article <Pine.SOL.3.91.970808104726.13390B-100000@mpqgrav1.mpq.mpg.de>, Gerhard Heinzel <ghh@mpq.mpg.de> writes:
> On 7 Aug 1997 schlafly@bbs.cruzio.com wrote:
> Second, if you want to compare two numbers that come from some algorithm
> (i.e. is an eigenvalue zero? is a pivot zero? is a correlation coefficient
> unity?) In these cases one must NEVER test for exact equality, but always
> take into account rounding errors and devise some test such as
> 
> fabs(x-y)<EPSILON
> 
> or fabs((x-y)/y)<EPSILON
> 
> or something similar, depending on the situation.

I don't agree.  A program might have to only test for 0 pivots
because it already has an error estimation piece that measures
the effect of small pivots.  Or it might have a lot of
correlation coefficients which are exactly 1, and only want to
compute some auxillary numbers when the coefficient is not 1.

You seem to be presuming that if someone does not do error
analysis in the style that you usually do it, then no error
analysis is being done.  On the contrary, if someone does a
careful error analysis elsewhere in the program, then a floating
point equality test can be quite harmless.

Roger