Floating point non-exactness

[Andrew Koenig]

In article <5467 at quanta.eng.ohio-state.edu>, rob at baloo.eng.ohio-state.edu (Rob Carriere) writes:

> In other words, usually what you want is something like

> int fcmp( double a, double b, double eps )
> {
>    if (  fabs( a-b ) < eps  ) return 0;
>    if (  a > b  ) return 1;
>    return -1;
> }

Probably not.

The trouble is that if a and b are big enough, then a-b will either be
exactly 0 or will be larger than eps.  (Here, `big enough' is approximately
eps * 2^n, where n is the number of significant bits in a floating-point
freaction.)  There is also the possibility that a-b might overflow,
in which case the comparison would surely have been valid if done directly.

Floating point arithmetic is *hard*.
-- 
				--Andrew Koenig
				  ark at europa.att.com