Italian Folk Multiplication Algorithm Is Indeed Better: It Is More Parallelizable

Traditionally, many ethnic groups had their own versions of arithmetic algorithms. Nowadays, most of these algorithms are studied mostly as pedagogical curiosities, as an interesting way to make arithmetic more exciting to the kids: by applying to their patriotic feelings – if they are studying the algorithms traditionally used by their ethic group – or simply to their sense of curiosity. Somewhat surprisingly, we show that one of these algorithms – a traditional Italian multiplication algorithm – is actually in some reasonable sense better than the algorithm that we all normally use – namely, it is easier to parallelize. 1 Formulation of the Problem How we learn to multiply numbers. How students learn multiplication is school? – First, they memorize the multiplication table – which enables them to multiply 1-digit numbers. – Then, they learn how to multiply a multi-digit number by a digit. – Finally, they learn how to multiply two multi-digit numbers. Let us recall how this is taught in school. To multiply a multi-digit number by a digit, e.g., multiply 23 by 4, 23 X 4 --? we start with the lowest digit – in this case, with 3, and multiply it by 4. From the multiplication table, we know that the result is 12, so we place 2 in the corresponding digit of a product, and remember 1 as a carry, to be added to the next digit: 23 X 4 --?2 2 M. Ceberio, O. Kosheleva, and V. Kreinovich Then, we multiply the next digit (in this case, 2) by 4, getting 8, and add the carry (in this case, 1) to this product, getting 9: