Implement two-digit-rounding (with uncertainty) in LaTeX using siunitx

Question

I would like to implement the following recommendation for rounding values in tables:

• in general two-digit-uncertainty rounding should be used in tables: the uncertainty is always rounded to two significant digits
• the central value should have a precision that matches the uncertainty

The siunitx package provides options for rounding to a fixed number of significant digits but here we need to do this in dependence on the uncertainty. How can this be achieved?

Answer 1

With version 3 of siunitx you can use round-mode = uncertainty, for example

\documentclass{article}
\usepackage{booktabs}
\usepackage{siunitx}
\begin{document}
  \sisetup{uncertainty-mode = separate, round-mode = uncertainty}
  \begin{tabular}{
    l
    S[table-format=3.2(2)]
    S[table-format=3.3(2)]
  }
  \toprule
    2 tight $\tau$s     & 72.293(269)     &    80.839(51) \\
    2 medium $\tau$s    & 212.383(461)    &   231.155(125) \\
  \bottomrule
  \end{tabular}
\end{document}

or

\documentclass{article}
\usepackage{booktabs}
\usepackage{siunitx}
\begin{document}
  \sisetup{uncertainty-mode = separate, round-mode = uncertainty}
  \begin{tabular}{
    l
    S[table-format=6(2)]
    S[table-format=6(2)]
  }
  \toprule
    2 tight $\tau$s     & 72293(269)     &    80839(51) \\
    2 medium $\tau$s    & 212383(461)    &   231155(125) \\
  \bottomrule
  \end{tabular}
\end{document}

Answer 2

Based on my very limited knowledge of TeX (and searching the Internet) I came up with the following solution which I will provide here as a start for others to improve on this:

\documentclass{minimal}

\usepackage{siunitx}
\usepackage{stringstrings}

\newcommand*{\numRF}[2]{\num[round-mode=figures,round-precision=#2]{#1}}

\begin{document}

  \newcommand{\matchroundtabular}[2]{% only works for integer values
    {%
    \aftergroup\round
    \stringlength[q]{#1}
    \newcount\numlen
    \numlen=\theresult
    \stringlength[q]{#2}
    \newcount\errorlen
    \errorlen=\theresult
    \newcount\round
    \round=\numlen
    \advance\round by -\errorlen
    \advance\round by 1
    \expandafter
    }
    \the\round
    {\numRF{#1}{\round}} & {\numRF{#2}{2}}%
  }

  % Problem 1: alignment off  
  \sisetup{round-mode = figures,round-precision = 2, table-number-alignment = right}%
  \begin{tabular}{
    l
    S[table-format=6.0]@{$\,\pm\,$}S[table-format=3.0]@{~}
    S[table-format=6.0]@{$\,\pm\,$}S[table-format=3.0]@{~}
  }
    2 tight $\tau$s     & \matchroundtabular{72293}{269}     &    80839 &   51 \\
    2 medium $\tau$s    & \matchroundtabular{212383}{461}    &   231155 &  125 \\
  \end{tabular}

  % Problem 2: not working here
  \begin{tabular}{c@{$\,\pm\,$}c}
    Aaaaa & Bbbbb \\
    \matchroundtabular{343454}{455}
  \end{tabular}

\end{document}

Output:

So this works but has two problems:

1. The alignment is off. (Compare with the column with 81000+-51, which is correctly aligned but not rounded correctly.)
2. It does not work outside the S column definition. (See second table. My code is bad.)

It currently also only works for integers. (Doing the same for floats is certainly much more complicated -- and I don't need it right now.)