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Numerical validation in quadruple precision using stochastic arithmetic

16 pagesPublished: October 11, 2018


Discrete Stochastic Arithmetic (DSA) enables one to estimate rounding errors and to detect numerical instabilities in simulation programs. DSA is implemented in the CADNA library that can analyze the numerical quality of single and double precision programs. In this article, we show how the CADNA library has been improved to enable the estimation of rounding errors in programs using quadruple precision floating-point variables, i.e. having 113-bit mantissa length. Although an implementation of DSA called SAM exists for arbitrary precision programs, a significant performance improvement has been obtained with CADNA compared to SAM for the numerical validation of programs with 113-bit mantissa length variables. This new version of CADNA has been successfully used for the control of accuracy in quadruple precision applications, such as a chaotic sequence and the computation of multiple roots of polynomials. We also describe a new version of the PROMISE tool, based on CADNA, that aimed at reducing in numerical programs the number of double precision variable declarations in favor of single precision ones, taking into account a requested accuracy of the results. The new version of PROMISE can now provide type declarations mixing single, double and quadruple precision.

Keyphrases: Accuracy, floating-point arithmetic, IEEE 754-2008 standard, numerical validation, Quadruple precision, rounding errors, Stochastic arithmetic

In: Matthieu Martel, Nasrine Damouche and Julien Alexandre Dit Sandretto (editors). TNC'18. Trusted Numerical Computations, vol 8, pages 38--53

BibTeX entry
  author    = {Stef Graillat and Fabienne J\textbackslash{}'ez\textbackslash{}'equel and Romain Picot and Fran\textbackslash{}c\{c\}ois F\textbackslash{}'evotte and Bruno Lathuili\textbackslash{}`ere},
  title     = {Numerical validation in quadruple precision using stochastic arithmetic},
  booktitle = {TNC'18. Trusted Numerical Computations},
  editor    = {Matthieu Martel and Nasrine Damouche and Julien Alexandre Dit Sandretto},
  series    = {Kalpa Publications in Computing},
  volume    = {8},
  pages     = {38--53},
  year      = {2018},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2515-1762},
  url       = {},
  doi       = {10.29007/5c91}}
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