" long int fac(unsigned long int n) { return lround(exp(lgamma(n+1))); } "

Sounds great! What's the factorial of 40? Let's use some python:

>>> int(math.exp(math.lgamma(41)))

815915283247882431423526575245034982027017846784L

Huh, weird. I would've thought the factorial of 40 would be divisible by ten. Let's try it another way:

Prelude> let fac n = foldr1 (*) [1..n]

Prelude> fac 40

815915283247897734345611269596115894272000000000

The author's disdain for the lambda calculus, as if it is somehow not real math (because it doesn't involve numbers in the familiar sense?), is bizarre.