Finding normal binary floating-point factors efficiently

Abstract

Solving the floating-point equation $x \otimes y = z$, where $x$, $y$ and $z$ belong to floating-point intervals, is a common task in automated reasoning for which no efficient algorithm is known in general. We show that it can be solved by computing a constant number of floating-point factors, and give a fast algorithm for computing successive normal floating-point factors of normal floating-point numbers in radix 2. This leads to an efficient procedure for solving the given equation, running in time of the same order as floating-point multiplication.