apparatus and method for performing ieee - rounded floating - point division utilizing goldschmidt &# 39 ; s algorithm . the use of newton &# 39 ; s method in computing quotients requires two multiplication operations , which must be performed sequentially , and therefore incurs waiting delays and decreases throughput . goldschmidt &# 39 ; s algorithm uses two multiplication operations which are independent and therefore may be performed simultaneously via pipelining . unfortunately , current error estimates for goldschmidt &# 39 ; s algorithm are imprecise , requiring high - precision multiplication operations for stability , thereby reducing the advantages of the pipelining . a new error analysis provides improved methods for estimating the error in the goldschmidt algorithm iterations , resulting in reductions in the hardware , improved pipeline organization , reducing the number and length of clock cycles , reducing latency , and increasing throughput .