Implementation of the reciprocal square root in MPFR

Abstract. We describe the implementation of the reciprocal square root — also called inverse square root — as a native function in the MPFR library. The difficulty is to implement Newton’s iteration for the reciprocal square root on top’s of GNU MP’s mpn layer, while guaranteeing a rigorous 1/2 ulp bound on the roundoff error. The reciprocal square root is an important function in 3D graphics, for the normalization of 3D vectors, and as such has received much attention in the literature [5]. Indeed, given (x, y, z)