Question

I’m training my C++ and I’m trying to write a library that’ll be able to represent the following number using XOR linked lists:

999999999 * ( [i=0]Σ[999999999] 1000000000 ^ i )

For example if my number was 711381450277869054011, it’ll be represented like this:

711 * 1000000000^2 + 381450277 * 1000000000^1 + 869054011 * 1000000000^0

Or simply:

711 * X^2 + 381450277 * X^1 + 869054011 * X^0

I overloaded the * operator for my class, but I think the algorithm I used is clumsy.

I was going to go for Karatsuba algorithm, but since it’s recursive, it’ll lead to stack overflows.

Then I checked Toom-3 algorithm. I liked it, but I couldn’t apply it because I still didn’t program negative numbers yet.

My question is: What algorithm you suggest, would be best for polynomial multiplication ? Is there any good algorithms I need to see ?

Answer 1

You can use Fast Fourier transform to perform it. There also exists non-recursive implementation of it.