Review geometric distribution sampler

[szhorvat]

igraph's geometric sampler, igraph_rng_get_geom() is currently implemented as follows:

igraph_rng_get_pois(rng, igraph_i_exp_rand(rng) * ((1 - p) / p))

Given how complex igraph_rng_get_pois() is, this is likely quite inefficient. Another method that is likely more efficient is floor(log(1-r) / log(1-p)) where r is uniform variate from $[0,1)$. I am not sure why we're not using this, but I suspect that there must be good reasons. The current implementation is lifted from R's source code, which I am inclined to trust.

https://github.com/wch/r-source/blob/trunk/src/nmath/rgeom.c

There may be precision issues with the naive implementation, especially when $p \ll 1$.

The reference they give is:

 *  NOTES
 *
 *    We generate lambda as exponential with scale parameter
 *    p / (1 - p).  Return a Poisson deviate with mean lambda.
 *    See Example 1.5 in Devroye (1986), Chapter 10, pages 488f.
 *
 *  REFERENCE
 *
 *    Devroye, L. (1986).
 *    Non-Uniform Random Variate Generation.
 *    New York: Springer-Verlag.
 *    Pages 488f.

This is a very old reference. There is a much more recent one we should review and possible adopt the ideas from,

https://link.springer.com/chapter/10.1007/978-3-642-39206-1_23

Karl Bringmann & Tobias Friedrich: Exact and Efficient Generation of Geometric Random Variates and Random Graphs https://doi.org/10.1007/978-3-642-39206-1_23

Also useful: https://peteroupc.github.io/randmisc.html#On_Geometric_Samplers

Why is this important? It is critical to efficient sampling fro the $G(n,p)$ model, which is also the motivation for the Bringmann and Friedrich paper. Good precision with very small $p$ is critical for this use case.