Fast Algorithm for the Log P-value of Fisher's Exact Test or Hypergeometric Distribution

Can be applied to relatively very large numbers (Total<100000)

example: after identifying a list of 30 genes from the entire genome of
20000 genes, 5 genes are related to cycle, while there are totally 200
cell cylce gene in the genome, then the log p-value will be:
ln_p=log_hypergeometric(5,30,200,20000);
% or, in 10 based log p-value
lg_p=log_hypergeometric(5,30,200,20000)/log(10);
% or, the decimal p-value
p=exp(log_hypergeometric(5,30,200,20000));

This is to say, 5 genes are in gene list,
and related to cell cycle; 25 genes are in the gene list but not related
to cell cycle; 195 genes are related to cell cycle but not in the gene
list; 19775 genes are not in the gene list and not related to cell cycle.
then the log p-value will be:
% ln_p=log_fisher_test(5,25,195,19775)
or, in 10 based log p-value
% lg_p=log_fisher_test(5,25,195,19775)/log(10);
or, the decimal p-value
% p=exp(log_fisher_test(5,25,195,19775));

Reference:
Meng, J., Gao, S. & Huang, Y. Enrichment constrained time-dependent clustering analysis for finding meaningful temporal transcription modules. Bioinformatics 25, 1521-1527, doi:10.1093/bioinformatics/btp235 (2009)