How do you calculate %xHKO?

But you still need to calculate the array somehow, and the best and most straightforward approach seems to be to perform the convolution on each P_n in succession. Binary convolution as you mentioned near the end of your pdf still ends up being quadratic because you're working with larger and larger intervals, so it wouldn't be a significant time saving.

Regarding defense, you could use another convolution with a negative interval for that and use that as your base interval.

Hmm, sorry about the spoiler, I didn't read it. Indeed correct that both are O(HP^2).

I've implemented the discrete convolution function, and it is indeed way slower than I thought it would be. Binary convolution does apparently not seem to help enough either.

Seems like I have to do a more direct approach with convolution, which is kind of messy:
Make a real convolution-function which takes two functions in and returns the convoluted function. If done correctly, should be way faster than discrete convolution. It is not exact, however. (Though the error-margin is minimal)
Wouldn't be too difficult, I hope. As the functions are only compositions of polynomials, it shouldn't be impossible to work out something that works.

Noah