Software division and square root using Goldschmidt’s algorithms

Goldschmidt’s Algorithms for division and square root are often characterized as being useful for hardware implementation, and lacking self-correction. A reexamination of these algorithms show that there are good software counterparts that retain the speed advantage of Goldschmidt’s Algorithm over the Newton-Raphson iteration. A final step is needed, however, to get the last bit rounded correctly. Key words: division, square root, Goldschmidt, floating-point