Multiprecision division: Expanded Version

This paper presents a study of multiprecision division on processors containing word-by-word multipliers. It compares several algorithms by first optimizing each for the software environment, and then comparing their performances on simple machine models. While the study was originally motivated by floating-point division in the small-word environment, the results are extended to multiprecision floatingpoint and integer division in general to the extent possible without extensive architecture-specific analysis. Two algorithms are found to be best for multiprecision division. For many floating-point division problems, and especially for any division by a small divisor, a hybrid of the Newton-Raphson and Byte Division algorithms is optimal, where significant reciprocal refinement is performed before beginning very high radix Byte Division iterations. Low-precision arithmetic and a method of inexpensively boosting accuracy during Newton-Raphson reciprocal refinement improve algorithm efficiency. For other division problems, Restoring Division is best, and is easy to implement. The asymptotic costs for floating-point division of each of these algorithms is the same as that of multiprecision multiplication.