Implementation of the reciprocal square root in MPFR

2008/01/01 by Paul Zimmermann, Zimmermann, Paul
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #MPFR library #Model Reduction and Neural Networks #Multiple precision #Numerical Methods and Algorithms #correct rounding #floating-point #inverse square root

paper · doi:10.4230/dagsemproc.08021.12

openalex publication_date 2008/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 extscmpn layer, while guaranteeing a rigorous 1/2 ulp bound on the roundoff error.

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