G'day all.
Quoting Thorkil Naur
Finding the "machine epsilon", perhaps, that is, the smallest (floating point, surely) number for which 1.0+machine_eps==1.0 would be a candidate?
The machine epsilon is the smallest relative separation between two adjacent normalised floating point numbers. (The largest is the machine epsilon multiplied by the radix, more or less.) So as I understand it, if you're thinking relative error, this test: (fabs(x1-x2) < machine_eps * fabs(x1)) should be true if and only if x1 == x2, assuming that x1 and x2 are nonzero and normalised. I've always had the impression that using the machine epsilon for pseudo-equality testing is fairly useless, especially if you can work out a meaningful problem-specific tolerance. What seems to be more useful is using the machine epsilon to compute an estimate of how much relative error your algorithm accumulates. I've seen this in a lot of Serious Numeric Code(tm), and I've done it myself (probably inexpertly) a few times. I haven't tried this, but I imagine that a computed relative error estimate could be useful for assisting your approximate-equality tests under some circumstances. Richard might know of some circumstances where this sort of thing would be useful. Cheers, Andrew Bromage