The algorithm for logFactorial bears re-evaluation

[treeowl]

John D. Cook claims at http://www.johndcook.com/blog/2010/08/16/how-to-compute-log-factorial/ that for values of n over approximately 256, it should be sufficient to use the approximation

log(x!) ~= (x – 1/2) log(x) – x + (1/2) log(2 π) + 1/(12 x).

If this is true, it should substantially improve the efficiency of logFactorial. Even if it is not quite true for n=256, it should become true for larger values of n. Cook also recommends using a table for values of n under around 256. His sample code uses a very slightly smaller table for unstated reasons. If a 256-entry table is judged too large for some reason, it would still pay to use a small table for the values currently calculated by sum of logs, cut over to the current approximation, and then finally cut over to Cook's suggestion (or similar).

[Shimuuar]

Probably that's correct. What's really needed for switch is

1. Evaluation of approximation's precision. Is it good enough. When we cold switch.
2. Benchmarks which show that implementation is indeed faster