Hacker's Delight

8-1. Multiword Multiplication

This may be done with, basically, the traditional grade-school method. Rather than develop an array of partial products, however, it is more efficient to add each new row, as it is being computed, into a row that will become the product.

If the multiplicand is m words, and the multiplier is n words, then the product occupies m + n words (or fewer), whether signed or unsigned.

In applying the grade-school scheme, we would like to treat each 32-bit word as a single digit. This works out well if an instruction that gives the 64-bit product of two 32-bit integers is available. Unfortunately, even if the machine has such an instruction, it is not readily accessible from most high-level languages. In fact, many modern ...