Fast calculation of inverse square root with the use of magic constant - analytical approach

2016/03/14 by Leonid V. Moroz, Leonid Moroz, Cezary J. Walczyk +8 · 1 voice
Computer Science · #Digital Filter Design and Implementation #FOS: Computer and information sciences #G.1.2 #G.4 #Mathematical Software (cs.MS) #Numerical Methods and Algorithms #cs.MS

paper · pdf · doi:10.48550/arxiv.1603.04483

17 pages, 8 figures

arxiv created 2016/03/14 · openalex publication_date 2016/03/14 · arxiv published 2016/03/14 · arxiv updated 2016/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a mathematical analysis of transformations used in fast calculation of inverse square root for single-precision floating-point numbers. Optimal values of the so called magic constants are derived in a systematic way, minimizing either absolute or relative errors at subsequent stages of the discussed algorithm.

Discussions

• While I have you all reading math papers, I've been seeing that Quake III inverse square root code floating around YouTube. Here's a paper on it and how to do a few other tricks using the IEEE 754 sta [bsky, 2 points, 0 comments]

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