I am writing a math paper on the Karatsuba Algorithm. The algorithm is never formally given. What I have so far is
The Karatsuba Algorithm reduces the multiplication of two n-digit numbers to at most single digit multiplication. In general when n is a power of 2.
u=pr v=(q-p)(s-r) w=q*s. so
a*b=u*10^n+(u+w-v)*10^(n/2)+w
I've never seen an algorithm written formally, i tried looking some up to help me write it formally but couldn't find any. Any feedback would help.