[jaclaz]

JFYI, I find it simpler to use this method, (same method of halving and doubling) used often for Roman numerals multiplication, but in the version that uses two colums only, crossing out the lines not needed (more similar to the "sieve" approach BTW):

http://rbutterworth.nfshost.com/Tables/romanmult

and making a final sum (as opposed to partial sums as in the given "Russian Peasant" reference).