As far as I know this library doesn't exist. We have thought about log and sqrt before, and we may implement them in the future:
Even if they don't exist yet, we can think about their feasibility.
The first question we should be asking is what is the time complexity of calculating these functions. Anything that runs in linear time or more is probably not a good fit for the blockchain. N(x) does not look promising in that sense, but I'm not really familiar with algorithms for this kind of function.
In your case N(x) seems like the "critical path" that you should have a good look at before proceding. If you do some research about it please share with us!