id,summary,reporter,owner,description,type,status,milestone,component,version,severity,resolution,keywords,cc
1540,Poisson distribution very slow for large mean (and may also overflow).,John Maddock,Steven Watanabe,"Joel Eidsath reports:

The poisson_distribution code will fail for any mean larger than 750
or so (on my x86_64 machine). The problem is a comparison with
exp(-_mean) which evaluates as zero right around there.

The easiest fix is to operate with logs instead of exponents. I
changed the operator() code to be something like this:

RealType product = RealType(0);
    for(result_type m = 0; ; ++m) {
      product += log(eng());
      if(product <= -_mean)
        return m;
    }

This also makes it possible to get rid of the init() function and the
_exp_mean private member variable.

A far better fix would be to use an algorithm other than Knuth's for
this. Knuth's algorithm is simple, but O(n).

References to better implementation methods include:

* Numerical Recipes
* http://statistik.wu-wien.ac.at/unuran
* ""Non-Uniform Random Variate Generation"" by Luc Devroye. Full text available for free at http://cg.scs.carleton.ca/~luc/rnbookindex.html with Poisson covered in chapt 10 at http://cg.scs.carleton.ca/~luc/chapter_ten.pdf starting p501.",Bugs,closed,Boost 1.36.0,random,Boost 1.34.1,Problem,fixed,,jeidsath@… pbristow@…