High-level algorithms for correctly-rounded reciprocal square roots - INRIA - Institut National de Recherche en Informatique et en Automatique Access content directly
Conference Papers Year : 2022

High-level algorithms for correctly-rounded reciprocal square roots


We analyze two fast and accurate algorithms recently presented by Borges for computing $x^{-1/2}$ in binary floating-point arithmetic (assuming that efficient and correctly-rounded FMA and square root are available). The first algorithm is based on the Newton-Raphson iteration, and the second one uses an order-3 iteration. We give attainable relative-error bounds for these two algorithms, build counterexamples showing that in very rare cases they do not provide a correctly-rounded result, and characterize precisely when such failures happen in IEEE 754 binary32 and binary64 arithmetics. We then give a generic (i.e., precision-independent) algorithm that always returns a correctly-rounded result, and show how it can be simplified and made more efficient in the important cases of binary32 and binary64.
Fichier principal
Vignette du fichier
cr_rsqrt.pdf (331.03 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03728088 , version 1 (20-07-2022)


  • HAL Id : hal-03728088 , version 1


Carlos F. Borges, Claude-Pierre Jeannerod, Jean-Michel Muller. High-level algorithms for correctly-rounded reciprocal square roots. 29th IEEE Symposium on Computer Arithmetic (ARITH 2022), Sep 2022, Lyon (virtual meeting due to the COVID pandemic), France. ⟨hal-03728088⟩
262 View
368 Download


Gmail Facebook X LinkedIn More