Hi everyone!
Here's another collection of little tricks and general ideas that might make your life better.
Evaluating polynomial modulo $$$p$$$ in all points in $$$O(p \log p)$$$. You can Evaluate $$$P(x)$$$ in every possible $$$x$$$ modulo $$$p$$$ as $$$P(0), P(g^0), P(g^1), \dots, P(g^{p-2})$$$ with chirp Z-transform, where $$$g$$$ is a primitive root modulo $$$p$$$.