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@…