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Implementation of the reciprocal square root in MPFR

Author Paul Zimmermann



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DagSemProc.08021.12.pdf
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Paul Zimmermann

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Paul Zimmermann. Implementation of the reciprocal square root in MPFR. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/DagSemProc.08021.12

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 extsc{mpn} layer, while guaranteeing a rigorous $1/2$ ulp bound on the roundoff error.
Keywords
  • Multiple precision
  • floating-point
  • inverse square root
  • correct rounding
  • MPFR library

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