Best possible accuracy for single precision floating point division

Question

Is it possible to perform division and obtain IEEE-754 single-precision correct values if one is using single-precision add/sub and multiplication hardware only (no FMA)?

Specifically if the Newton-Raphson method for carrying out floating-point division is carried out on single-precision hardware, is it possible to achieve a result that is IEEE-754 correct?

Answer 1

Is it possible to perform division and obtain IEEE-754 single-precision correct values if one is using single-precision add/sub and multiplication hardware only (no FMA)?

Yes.

It is always possible to emulate higher precision by representing numbers as the sum of several single-precision floats, either two, three, or four (see the QD library on this page). You should only need the precision brought by two single-precision numbers for a correctly-rounded single-precision division, and the necessary operations for this representation can be implemented with only single-precision addition, subtraction and multiplication.