logical inconsistency
nashjc at uottawa.ca wrote:
This comment is orthogonal to most of the others. It seems that folk often
want to test for equality of "real" numbers. One important one is for
convergence tests. When writing my Compact Numerical Methods book I had to
avoid lots of logical tests, but wanted to compare two REALs. I found that
the following approach, possibly considered a trick, is to use an offset
and compare
xnew + offset
to
xold + offset
This works on the examples given to motivate the current thread with an
offset of 10, for example.
Motivation: Small xold, xnew compare offset with itself. Large xold and
xnew are compared bitwise. Essentially we change from using a tolerance to
using 1/tolerance.
Perfect? No. But usable? Yes. And I believe worth keeping in mind for
those annoying occasions where one needs to do a comparison but wants to
get round the issue of knowing the machine precision etc.
Hmm. Echos of some early battles with R's qbeta() in this. I don't think it can be recommended. The problem is that you can end up in a situation where xnew=xold-1ulp and xnewnew is xnew+1ulp. I.e. in two iterations you're back at xold. Even in cases where this provably cannot happen, modern optimizers may make it happen anyway...
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