There are very efficient ways to calculate powers of integers modulo an integer, one of them is implemented by the Python pow function.
I need to calculate something of the form floor(num^k) % n where num is irrational and k, n are integers.
For example how can I calculate the exact value floor(π^k) % n without actually calculating the huge value of π^k?
Thank you all brilliant people.
The only way I know of to speed up exponentiation modulo an integer $n$ (compared to general exponentiation) is using the fact that everything is integers to reduce the intermediate results modulo $n$. As the intermediate results in your case aren't integers, you can't do that.
The only transformation I can see of your expression is: $$ \left\lfloor x^k\right\rfloor \pmod n =\left\lfloor x^k\pmod n\right\rfloor $$ and that doesn't make the computation any easier.