>Looking things up in a multiplication table is harder because it is two-dimensional.

But T2 is pretty large, why not just make T2 have 100 elements and index it by a*10+b (i.e., just concatenate the digits together)? This is faster because you don't have to add or lookup anything in T1.

If the numbers are represented by the length of rods then this concatenation is not so easy, but neither is it in this algorithm:

> you have some thingy that slides up by T1(a) units, and then by T1(b) more, and then wherever it ends up is used to index into T2 to get the answer

So I would replace this with:

you have some thingy that slides up by a large units and then by b small units (where one large unit is 10 times longer than one small unit), and then wherever it ends up is used to index into to get the answer