Robust function for n factorial

Write a routine that computes $n!$ and discuss what can go wrong.

Loop multiplying $1\cdot2\cdots n$ in $O(n)$, with guards. Reject negative input and return $1$ for $0$. Overflow is the main issue: $20!$ is the largest that fits in a 64-bit integer and $170!$ the largest finite double, so use big integers or work with $\log n!$ (e.g. lgamma) when values get large. Recursion works but adds stack depth for no gain.