"In summary, one way to compute log factorial is to pre-compute log(n!) for n = 1, 2, 3, … 256 and store the results in an array. For values of n ≤ 256, look up the result from the table. For n > 256, return

(x – 1/2) log(x) – x + (1/2) log(2 π) + 1/(12 x)

with x = n + 1."

Nice method of trading additions for multiplications in calculating factorials.