round-mode conditional on number size

Question

I would like to give numbers with three decimals places of precision, unless they are so small that this would round them down to zero. In that case, I would like three significant figures instead.

Here is a minimal non-working example:

\documentclass{article}
\usepackage[round-mode=places,round-precision=3]{siunitx}
\begin{document}

\num{0.0437}  % gives 0.044

\num{0.00437} % gives 0.004

\num{0.000437}% I want this to give 0.000437

\end{document}

Right now I do it by overriding the settings from the preamble for any number that is small enough. So I'd replace \num with \num[round-mode=figures]. But I'd like to do it automatically if I can.

I read the source of siunitx.sty but I still don't grok LaTeX3-style programming. I'd appreciate any advice.

Answer 1

Here's a LuaLaTeX-based solution. It defines a utility macro called \mynum which, in turns, calls a Lua function to do the actual work.

% !TEX TS-program = lualatex 
\documentclass{article}
\usepackage{siunitx}
\sisetup{round-precision=3,group-digits=false,round-mode=places}

\usepackage{luacode} % for '\luaexec' macro
%% Lua-side code:
\luaexec{%
function mynum ( n )
  if n<0.001 then tex.sprint ( "\\num[round-mode=figures]{"..n.."}" )
             else tex.sprint ( "\\num{"..n.."}" )
  end
end
}
%% LaTeX-side code:
\newcommand\mynum[1]{\directlua{mynum(#1)}}
  
\begin{document}
\num{0.0437},   \mynum{0.0437}   % both give 0.044

\num{0.00437},  \mynum{0.00437}  % both give 0.004

\num{0.000437}, \mynum{0.000437} % only \mynum gives 0.000437
\end{document}

Answer 2

Using just expl3 functions, and assuming v3 of siunitx to allow us to do this using the code-level API, we might go for

\documentclass{article}
\usepackage{siunitx}
\sisetup{round-precision=3,group-digits=false}
\ExplSyntaxOn
\NewDocumentCommand \mynum { O { } m }
  {
    \mode_leave_vertical:
    \group_begin:
      \keys_set:nn { siunitx } {#1}
      \fp_compare:nNnTF {#2} < { 0.001 }
        { \keys_set:nn { siunitx } { round-mode = none } }
        { \keys_set:nn { siunitx } { round-mode = places } }
      \siunitx_number_format:nN {#2} \l___siunitx_number_tmp_tl
      \siunitx_print_number:V \l___siunitx_number_tmp_tl
    \group_end:
  }
\ExplSyntaxOff  
\begin{document}
\num{0.0437},   \mynum{0.0437}   % both give 0.044

\num{0.00437},  \mynum{0.00437}  % both give 0.004

\num{0.000437}, \mynum{0.000437} % only \mynum gives 0.000437
\end{document}

using the demo from Mico's answer.

Note that the fp function here is limited to IEEE754 range/precision (e.g. 16 digits of mantissa), which may be an issue in some cases. (The core siunitx functions can handle arbitrary precision rounding.)