Customize grouping of digits using siunitx

Question

Consider this simple example.

\documentclass[12pt]{standalone}
\usepackage{siunitx}
\begin{document}
\begin{tabular}{S[group-separator={,}]}
  123456789
\end{tabular}

This is displayed as

123,456,789

In the Indian numerical system, digits are grouped somewhat differently. To quote the Wikipedia article on Decimal separator:

The Indian numbering system is somewhat more complex: it groups the rightmost three digits together (until the hundreds place) and thereafter groups by sets of two digits. For example, one trillion [10^{12}] would thus be written as 10,00,00,00,00,000 or 10 kharab.

In this particular example, I would like to group the number as

12,34,56,789

More generally, support for grouping numbers together in groups of arbitrary length could be useful. In the absence of such support, a workaround/hack might be helpful.

See the related GitHub issue, Feature request: group separators a variable number of digits apart.

Answer 1

The following solution formats large numbers -- positive integers, to be precise -- in "Indian style" (for lack of a better term). The solution, which provides a user macro called \indnum, relies on Lua's string library and hence must be compiled under LuaLaTeX.

This formatting method is compatible with the siunitx package in the sense that the solution actually relies on the \num macro to format numbers smaller than 100,000 -- oops, 1,00,000. However, the numbers cannot be employed directly in a column of type S. On the other hand, the argument of \indnum needn't be an explicit integer; it's fine to input something such as 2e8*4+20/4, as long as the argument evaluates to a number according to Lua's rules of syntax.

A side-remark: You claimed in a comment that "part of siunitx's functionality is number formatting". Speaking for myself, I actually strongly disagree with your claim -- and I'd immediately change it to "part of siunitx's functionality is number formatting according to recognized SI principles" [emphasis added]. The only such principle I know of is grouping in multiplicative increments of 1000. In my opinion, all other grouping methods -- including multiplicative increments of 100 for numbers greater than 999 -- are therefore not in the scope of what the siunitx package should be concerned with. Naturally, I will happily let Joseph Wright (the author and maintainer of the siunitx package) weigh in with his own opinion on this topic.

At any rate, I can't see why one couldn't use the r column type to typeset numbers formatted in the "Indian style". See the table below for an application.

% !TEX TS-program = lualatex
\documentclass{article} % or some other suitable document class
\usepackage[group-separator={,},
            group-minimum-digits=4,
            input-decimal-markers={.}]{siunitx}
\usepackage{luacode} % for "luacode" environment
\begin{luacode}

function indnum ( n )
   local s, t
   n = math.floor ( n ) -- retain integer part
   if n<1e5 then -- invoke "\num" macro to format and print
      tex.sprint ( "\\num{" .. n .. "}" )
   else
      s = string.reverse ( "" .. n ) -- convert to string & reverse
      t = s:sub(1,3) .. "," .. s:sub(4,5) .. ","
      s = s:sub(6) -- discard first 5 digits of 's' string
      while #s > 2 do
         t = t .. s:sub(1,2) .. ","
         s = s:sub(3) -- discard first 2 digits of 's' string
      end
      t = t .. s -- last step: 's' contains 0, 1, or 2 digits
      tex.sprint ( string.reverse ( t ) ) -- reverse order and print
   end
end

\end{luacode}
\newcommand\indnum[1]{\directlua{ indnum(#1) }}

\begin{document}
\begin{tabular}{r l}
  \indnum{500}\\
  \indnum{5e4}\\
  \indnum{1e5} & 1 lakh\\
  \indnum{1e7} & 1 crore\\
  \indnum{2e8*4+20/4}\\
  \indnum{123456789e1}\\
  \indnum{123456789e2}\\
  \indnum{123456789e3}\\
  \indnum{123456789e4}
\end{tabular}
\end{document}

Answer 2

One possible: not efficient and using internals, but at present that's the only way:

\documentclass{article}
\usepackage{siunitx}
\ExplSyntaxOn
\cs_gset:Npn \__siunitx_number_output_integer_aux:n #1
  {
    \int_compare:nNnTF { \tl_count:n {#1} } > 3
      {
        \exp_args:Ne \__siunitx_number_output_integer_auxii:n
          { \tl_reverse:n {#1} }
      }
      { \exp_not:n {#1} }
  }
\cs_new:Npn \__siunitx_number_output_integer_auxii:n #1
  {
    \__siunitx_number_output_integer_auxiii:w #1
      \q_recursion_tail \q_recursion_tail \q_recursion_stop
    \__siunitx_number_output_integer_end:n { }
  }
\cs_new:Npn \__siunitx_number_output_integer_auxiii:w #1#2#3
  {
    \__siunitx_number_output_integer_store:nw {#3#2#1}
    \__siunitx_number_output_integer_auxiv:w
  }
\cs_new:Npn \__siunitx_number_output_integer_auxiv:w #1#2
  {
    \quark_if_recursion_tail_stop:N #1
    \quark_if_recursion_tail_stop_do:Nn #2
      { \__siunitx_number_output_integer_store:nw {#1} }
    \__siunitx_number_output_integer_store:nw
      {
        #2#1
        \str_if_eq:VnTF \l__siunitx_number_group_separator_tl { , }
          { \exp_not:N \mathord }
          { \use:n }
            { \exp_not:V \l__siunitx_number_group_separator_tl }
      }
    \__siunitx_number_output_integer_auxiv:w
  }
\cs_new:Npn \__siunitx_number_output_integer_end:n #1
  { \exp_not:n {#1} }
\cs_new:Npn \__siunitx_number_output_integer_store:nw
  #1#2 \__siunitx_number_output_integer_end:n #3
  {
    #2
    \__siunitx_number_output_integer_end:n {#1#3}
  }
\ExplSyntaxOff
\begin{document}
\begin{tabular}{S[group-separator={,}]}
  123456789
\end{tabular}
\end{document}

Answer 3

You can use the options to specify the size of the first group and the subsequent groups:

    digit-group-first-size=3,
    digit-group-other-size=2,
    group-separator={,},

Below, I define the \numI macro which uses the above options and produces the result on the second line:

Code:

\documentclass{article}
\usepackage{siunitx}
\sisetup{group-minimum-digits=4}
\newcommand{\numI}[1]{%
    \num[
        digit-group-first-size=3,
        digit-group-other-size=2,
        group-separator={,},
    ]{#1}%
}
\begin{document}
Default: $\num{123456789}$
Indian: $\numI{123456789}$
\end{document}