[R] logical inconsistency

[Peter Dalgaard]

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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