to note:

1) arttype is numeric. I thought this was the best way of allowing
arbitarily large factorials, even though factorial(2^63) is a large
number. Happy to change to integers if this is overkill.
2) since we're accepting numeric arguments, the patch tests for floats.
If a numeric is passed with non-zero decimal portion, an error is raised
since (from memory) they are undefined.

Gavin Sherry