I've had a book for many years called Puzzles, Mazes, and Numbers which describes a method for performing multiplication as follows called "Russian peasant multiplication":
There are two columns, on the left hand side the number is halved, rounding down and on the right hand side, each successive number is doubled. In the algorithm described in the book, rows corresponding to even numbers in the left column are struck out. In this example, rows with even numbers in the left column simply have a blank entry in the right.
45 x 89 89 22 178 11 356 356 5 712 712 2 1424 1 2848 2848 ----------------------- 4005
My understanding is that this is similar to the Ancient Egyptian method of multiplication, but that the Ancient Egyptians decomposed the left argument into powers of two by repeatedly subtracting the largest power of two possible, rather than by repeatedly dividing by two and checking the parity.
I'm curious whether a doubling and mediation algorithm with the parity check as described here was ever the/an ordinary of doing multiplication anywhere in the world.
One source cited by the Wikipedia article claims that the supposed Russian origin of the algorithm is a bit murky and hard to definitively show.