path: root/Master/texmf-dist/source/latex/l3kernel/l3intarray.dtx

% \iffalse meta-comment
%
%% File: l3intarray.dtx
%
% Copyright (C) 2017-2023 The LaTeX Project
%
% It may be distributed and/or modified under the conditions of the
% LaTeX Project Public License (LPPL), either version 1.3c of this
% license or (at your option) any later version.  The latest version
% of this license is in the file
%
%    https://www.latex-project.org/lppl.txt
%
% This file is part of the "l3kernel bundle" (The Work in LPPL)
% and all files in that bundle must be distributed together.
%
% -----------------------------------------------------------------------
%
% The development version of the bundle can be found at
%
%    https://github.com/latex3/latex3
%
% for those people who are interested.
%
%<*driver>
\documentclass[full,kernel]{l3doc}
\begin{document}
  \DocInput{\jobname.dtx}
\end{document}
%</driver>
% \fi
%
%
% \title{^^A
%   The \textsf{l3intarray} package: Fast global integer arrays^^A
% }
%
% \author{^^A
%  The \LaTeX{} Project\thanks
%    {^^A
%      E-mail:
%        \href{mailto:latex-team@latex-project.org}
%          {latex-team@latex-project.org}^^A
%    }^^A
% }
%
% \date{Released 2023-02-22}
%
% \maketitle
%
% \begin{documentation}
%
% \section{\pkg{l3intarray} documentation}
%
% For applications requiring heavy use of integers, this module provides
% arrays which can be accessed in constant time (contrast \pkg{l3seq},
% where access time is linear). These arrays have several important
% features
% \begin{itemize}
%   \item The size of the array is fixed and must be given at
%     point of initialisation
%   \item The absolute value of each entry has maximum $2^{30}-1$
%     (\emph{i.e.}~one power lower than the usual \cs{c_max_int}
%     ceiling of $2^{31}-1$)
% \end{itemize}
% The use of \texttt{intarray} data is therefore recommended for cases where
% the need for fast access is of paramount importance.
%
% \begin{function}[added = 2018-03-29]{\intarray_new:Nn, \intarray_new:cn}
%   \begin{syntax}
%     \cs{intarray_new:Nn} \meta{intarray~var} \Arg{size}
%   \end{syntax}
%   Evaluates the integer expression \meta{size} and allocates an
%   \meta{integer array variable} with that number of (zero) entries.
%   The variable name should start with |\g_| because assignments are
%   always global.
% \end{function}
%
% \begin{function}[EXP, added = 2018-03-29]{\intarray_count:N, \intarray_count:c}
%   \begin{syntax}
%     \cs{intarray_count:N} \meta{intarray~var}
%   \end{syntax}
%   Expands to the number of entries in the \meta{integer array variable}.
%   Contrarily to \cs{seq_count:N} this is performed in constant time.
% \end{function}
%
% \begin{function}[added = 2018-03-29]{\intarray_gset:Nnn, \intarray_gset:cnn}
%   \begin{syntax}
%     \cs{intarray_gset:Nnn} \meta{intarray~var} \Arg{position} \Arg{value}
%   \end{syntax}
%   Stores the result of evaluating the integer expression \meta{value}
%   into the \meta{integer array variable} at the (integer expression)
%   \meta{position}.  If the \meta{position} is not between $1$ and the
%   \cs{intarray_count:N}, or the \meta{value}'s absolute value is
%   bigger than $2^{30}-1$, an error occurs.  Assignments are always
%   global.
% \end{function}
%
% \begin{function}[added = 2018-05-04]
%   {\intarray_const_from_clist:Nn, \intarray_const_from_clist:cn}
%   \begin{syntax}
%     \cs{intarray_const_from_clist:Nn} \meta{intarray~var} \meta{int expr clist}
%   \end{syntax}
%   Creates a new constant \meta{integer array variable} or raises an
%   error if the name is already taken.  The \meta{integer array
%   variable} is set (globally) to contain as its items the results of
%   evaluating each \meta{integer expression} in the \meta{comma list}.
% \end{function}
%
% \begin{function}[added = 2018-05-04]{\intarray_gzero:N, \intarray_gzero:c}
%   \begin{syntax}
%     \cs{intarray_gzero:N} \meta{intarray~var}
%   \end{syntax}
%   Sets all entries of the \meta{integer array variable} to zero.
%   Assignments are always global.
% \end{function}
%
% \begin{function}[EXP, added = 2018-03-29]{\intarray_item:Nn, \intarray_item:cn}
%   \begin{syntax}
%     \cs{intarray_item:Nn} \meta{intarray~var} \Arg{position}
%   \end{syntax}
%   Expands to the integer entry stored at the (integer expression)
%   \meta{position} in the \meta{integer array variable}.  If the
%   \meta{position} is not between $1$ and the \cs{intarray_count:N}, an
%   error occurs.
% \end{function}
%
% \begin{function}[EXP, added = 2018-05-05]
%   {\intarray_rand_item:N, \intarray_rand_item:c}
%   \begin{syntax}
%     \cs{intarray_rand_item:N} \meta{intarray~var}
%   \end{syntax}
%   Selects a pseudo-random item of the \meta{integer array}.  If the
%   \meta{integer array} is empty, produce an error.
% \end{function}
%
% \begin{function}[added = 2018-05-04]
%   {\intarray_show:N, \intarray_show:c, \intarray_log:N, \intarray_log:c}
%   \begin{syntax}
%     \cs{intarray_show:N} \meta{intarray~var}
%     \cs{intarray_log:N} \meta{intarray~var}
%   \end{syntax}
%   Displays the items in the \meta{integer array variable} in the
%   terminal or writes them in the log file.
% \end{function}
%
% \subsection{Implementation notes}
%
% It is a wrapper around the \tn{fontdimen} primitive, used to store
% arrays of integers (with a restricted range: absolute value at most
% $2^{30}-1$).  In contrast to \pkg{l3seq} sequences the access to
% individual entries is done in constant time rather than linear time,
% but only integers can be stored.  More precisely, the primitive
% \tn{fontdimen} stores dimensions but the \pkg{l3intarray} package
% transparently converts these from/to integers.  Assignments are always
% global.
%
% While \LuaTeX{}'s memory is extensible, other engines can
% \enquote{only} deal with a bit less than $4\times 10^6$ entries in all
% \tn{fontdimen} arrays combined (with default \TeX{} Live settings).
%
% \end{documentation}
%
% \begin{implementation}
%
% \section{\pkg{l3intarray} implementation}
%
%    \begin{macrocode}
%<*package>
%    \end{macrocode}
%
%    \begin{macrocode}
%<@@=intarray>
%    \end{macrocode}
%
% There are two implementations for this module: One \cs{fontdimen} based one
% for more traditional \TeX\ engines and a Lua based one for engines with Lua support.
%
% Both versions do not allow negative array sizes.
%    \begin{macrocode}
%<*tex>
\msg_new:nnn { kernel } { negative-array-size }
  { Size~of~array~may~not~be~negative:~#1 }
%    \end{macrocode}
%
% \begin{variable}{\l_@@_loop_int}
%   A loop index.
%    \begin{macrocode}
\int_new:N \l_@@_loop_int
%    \end{macrocode}
% \end{variable}
%
% \subsection{Lua implementation}
% First, let's look at the Lua variant:
%
% We select the Lua version if the Lua helpers were defined. This can be detected by
% the presence of \cs{@@_gset_count:Nw}.
%
%    \begin{macrocode}
\cs_if_exist:NTF \@@_gset_count:Nw
  {
%    \end{macrocode}
%
% \subsubsection{Allocating arrays}
%
% \begin{variable}{\g_@@_table_int, \l_@@_bad_index_int}
%   Used to differentiate intarrays in Lua and to record an invalid index.
%    \begin{macrocode}
    \int_new:N \g_@@_table_int
    \int_new:N \l_@@_bad_index_int
%</tex>
%    \end{macrocode}
% \end{variable}
%
% \begin{macro}{\@@:w}
%   Used as marker for intarrays in Lua. Followed by an unbraced number
%   identifying the array and a single space. This format is used to make it
%   easy to scan from Lua.
%    \begin{macrocode}
%<*lua>
luacmd('@@:w', function()
  scan_int()
  tex.error'LaTeX Error: Isolated intarray ignored'
end, 'protected', 'global')
%</lua>
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\intarray_new:Nn, \intarray_new:cn}
% \begin{macro}{\@@_new:N}
%   Declare |#1| as a tokenlist with the scanmark and a unique number.
%   Pass the array's size to the Lua helper.
%   Every \texttt{intarray} must be global; it's enough to run this
%   check in \cs{intarray_new:Nn}.
%    \begin{macrocode}
%<*tex>
    \cs_new_protected:Npn \@@_new:N #1
      {
        \__kernel_chk_if_free_cs:N #1
        \int_gincr:N \g_@@_table_int
        \cs_gset_nopar:Npx #1 { \@@:w \int_use:N \g_@@_table_int \c_space_tl }
      }
    \cs_new_protected:Npn \intarray_new:Nn #1#2
      {
        \@@_new:N #1
        \@@_gset_count:Nw #1 \int_eval:n {#2} \scan_stop:
        \int_compare:nNnT { \intarray_count:N #1 } < 0
          {
            \msg_error:nnx { kernel } { negative-array-size }
              { \intarray_count:N #1 }
          }
      }
    \cs_generate_variant:Nn \intarray_new:Nn { c }
%</tex>
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% Before we get to the first command implmented in Lua, we first need some
% definitions. Since \texttt{token.create} only works correctly if \TeX{}
% has seen the tokens before, we first run a short \TeX{} sequence to ensure
% that all relevant control sequences are known.
%    \begin{macrocode}
%<*lua>

local scan_token = token.scan_token
local put_next = token.put_next
local intarray_marker = token_create_safe'@@:w'
local use_none = token_create_safe'use_none:n'
local use_i = token_create_safe'use:n'
local expand_after_scan_stop = {token_create_safe'exp_after:wN',
                                token_create_safe'scan_stop:'}
local comma = token_create(string.byte',')
%    \end{macrocode}
%
% \begin{macro}{@@_table}
%   Internal helper to scan an intarray token, extract the associated
%   Lua table and return an error if the input is invalid.
%
%    \begin{macrocode}
local @@_table do
  local tables = get_luadata and get_luadata'@@' or {[0] = {}}
  function @@_table()
    local t = scan_token()
    if t ~= intarray_marker then
      put_next(t)
      tex.error'LaTeX Error: intarray expected'
      return tables[0]
    end
    local i = scan_int()
    local current_table = tables[i]
    if current_table then return current_table end
    current_table = {}
    tables[i] = current_table
    return current_table
  end
%    \end{macrocode}
% Since in \LaTeX{} this is loaded in the format, we want to preserve any intarrays
% which are created while format building for the actual run.
%
% To do this, we use the \texttt{register_luadata} mechanism from \pkg{l3luatex}:
% Directly before the format get dumped, the following function gets invoked and serializes
% all existing tables into a string. This string gets compiled and dumped into the format and
% is made available at the beginning of regular runs as \texttt{get_luadata'@@'}.
%    \begin{macrocode}
  if register_luadata then
    register_luadata('@@', function()
      local t = "{[0]={},"
      for i=1, #tables do
        t = string.format("%s{%s},", t, table.concat(tables[i], ','))
      end
      return t .. "}"
    end)
  end
end
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]{\intarray_count:N, \intarray_count:c}
% \begin{macro}[EXP]{\@@_gset_count:Nw}
%   Set and get the size of an array. ``Setting the size'' means in this context that
%   we add zeros until we reach the desired size.
%    \begin{macrocode}

local sprint = tex.sprint

luacmd('@@_gset_count:Nw', function()
  local t = @@_table()
  local n = scan_int()
  for i=#t+1, n do t[i] = 0 end
end, 'protected', 'global')

luacmd('intarray_count:N', function()
  sprint(-2, #@@_table())
end, 'global')
%</lua>
%    \end{macrocode}
%
%    \begin{macrocode}
%<*tex>
    \cs_generate_variant:Nn \intarray_count:N { c }
%</tex>
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \subsubsection{Array items}
%
% \begin{macro}{\@@_gset:wF, \@@_gset:w}
%   The setter provided by Lua. The argument order somewhat emulates the |\fontdimen|:
%   First the array index, followed by the intarray and then the new value.
%   This has been chosen over a more conventional order to provide a delimiter for the numbers.
%    \begin{macrocode}
%<*lua>
luacmd('@@_gset:wF', function()
  local i = scan_int()
  local t = @@_table()
  if t[i] then
    t[i] = scan_int()
    put_next(use_none)
  else
    tex.count.l_@@_bad_index_int = i
    scan_int()
    put_next(use_i)
  end
end, 'protected', 'global')

luacmd('@@_gset:w', function()
  local i = scan_int()
  local t = @@_table()
  t[i] = scan_int()
end, 'protected', 'global')
%</lua>
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\intarray_gset:Nnn, \intarray_gset:cnn, \__kernel_intarray_gset:Nnn}
%   The \cs{__kernel_intarray_gset:Nnn} function does not use
%   \cs{int_eval:n}, namely its arguments must be suitable for
%   \cs{int_value:w}.  The user version checks the position and value
%   are within bounds.
%    \begin{macrocode}
%<*tex>
    \cs_new_protected:Npn \__kernel_intarray_gset:Nnn #1#2#3
      { \@@_gset:w #2 #1 #3 \scan_stop: }
    \cs_new_protected:Npn \intarray_gset:Nnn #1#2#3
      {
        \@@_gset:wF \int_eval:n {#2} #1 \int_eval:n{#3}
          {
            \msg_error:nnxxx { kernel } { out-of-bounds }
              { \token_to_str:N #1 } { \int_use:N \l_@@_bad_index_int } { \intarray_count:N #1 }
          }
      }
    \cs_generate_variant:Nn \intarray_gset:Nnn { c }
%</tex>
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\intarray_gzero:N, \intarray_gzero:c}
%   Set the appropriate array entry to zero.  No bound checking
%   needed.
%    \begin{macrocode}
%<*lua>
luacmd('intarray_gzero:N', function()
  local t = @@_table()
  for i=1, #t do
    t[i] = 0
  end
end, 'global', 'protected')
%</lua>
%<*tex>
    \cs_generate_variant:Nn \intarray_gzero:N { c }
%</tex>
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]{\intarray_item:Nn, \intarray_item:cn, \__kernel_intarray_item:Nn}
% \begin{macro}{\@@_item:wF,\@@_item:w}
%   Get the appropriate entry and perform bound checks.  The
%   \cs{__kernel_intarray_item:Nn} function omits bound checks and omits
%   \cs{int_eval:n}, namely its argument must be a \TeX{} integer
%   suitable for \cs{int_value:w}.
%    \begin{macrocode}
%<*lua>
luacmd('@@_item:wF', function()
  local i = scan_int()
  local t = @@_table()
  local item = t[i]
  if item then
    put_next(use_none)
  else
    tex.l_@@_bad_index_int = i
    put_next(use_i)
  end
  put_next(expand_after_scan_stop)
  scan_token()
  if item then
    sprint(-2, item)
  end
end, 'global')

luacmd('@@_item:w', function()
  local i = scan_int()
  local t = @@_table()
  sprint(-2, t[i])
end, 'global')
%</lua>
%    \end{macrocode}
%
%    \begin{macrocode}
%<*tex>
    \cs_new:Npn \__kernel_intarray_item:Nn #1#2
      { \@@_item:w #2 #1 }
    \cs_new:Npn \intarray_item:Nn #1#2
      {
        \@@_item:wF \int_eval:n {#2} #1
          {
            \msg_expandable_error:nnfff { kernel } { out-of-bounds }
              { \token_to_str:N #1 } { \int_use:N \l_@@_bad_index_int } { \intarray_count:N #1 }
            0
          }
      }
    \cs_generate_variant:Nn \intarray_item:Nn { c }
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\intarray_rand_item:N, \intarray_rand_item:c}
%   Importantly, \cs{intarray_item:Nn} only evaluates its argument once.
%    \begin{macrocode}
    \cs_new:Npn \intarray_rand_item:N #1
      { \intarray_item:Nn #1 { \int_rand:n { \intarray_count:N #1 } } }
    \cs_generate_variant:Nn \intarray_rand_item:N { c }
%    \end{macrocode}
% \end{macro}
%
% \subsubsection{Working with contents of integer arrays}
%
% \begin{macro}{\intarray_const_from_clist:Nn, \intarray_const_from_clist:cn}
%   We use the \cs{__kernel_intarray_gset:Nnn} which does not do bounds checking
%   and instead automatically resizes the array.
%   This is not implemented in Lua to ensure that the clist parsing is consistent
%   with the clist module.
%    \begin{macrocode}
    \cs_new_protected:Npn \intarray_const_from_clist:Nn #1#2
      {
        \@@_new:N #1
        \int_zero:N \l_@@_loop_int
        \clist_map_inline:nn {#2}
          {
            \int_incr:N \l_@@_loop_int
            \__kernel_intarray_gset:Nnn #1 \l_@@_loop_int { \int_eval:n {##1} } }
      }
    \cs_generate_variant:Nn \intarray_const_from_clist:Nn { c }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}[rEXP]{\intarray_to_clist:N, \intarray_to_clist:c}
% \begin{macro}[rEXP]{\@@_to_clist:Nn, \@@_to_clist:w}
%   The \cs{@@_to_clist:Nn} auxiliary allows to choose the delimiter and
%   is also used in \cs{intarray_show:N}. Here we just pass the information
%   to Lua and let \texttt{table.concat} do the actual work.
%   We discard the category codes of the passed delimiter but this is not
%   an issue since the delimiter is always just a comma or a comma and a space.
%   In both cases \texttt{sprint(2, ...)} provides the right catcodes.
%    \begin{macrocode}
    \cs_new:Npn \intarray_to_clist:N #1 { \@@_to_clist:Nn #1 { , } }
    \cs_generate_variant:Nn \intarray_to_clist:N { c }
%</tex>
%<*lua>
local concat = table.concat
luacmd('@@_to_clist:Nn', function()
  local t = @@_table()
  local sep = token.scan_string()
  sprint(-2, concat(t, sep))
end, 'global')
%</lua>
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}[rEXP]{\__kernel_intarray_range_to_clist:Nnn, \@@_range_to_clist:w}
%   Loop through part of the array.
%    \begin{macrocode}
%<*tex>
    \cs_new:Npn \__kernel_intarray_range_to_clist:Nnn #1#2#3
      {
        \@@_range_to_clist:w #1
        \int_eval:n {#2} ~ \int_eval:n {#3} ~
      }
%</tex>
%<*lua>
luacmd('@@_range_to_clist:w', function()
  local t = @@_table()
  local from = scan_int()
  local to = scan_int()
  sprint(-2, concat(t, ',', from, to))
end, 'global')
%</lua>
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\__kernel_intarray_gset_range_from_clist:Nnn, \@@_gset_range:nNw}
%   Loop through part of the array. We allow additional commas at the end.
%    \begin{macrocode}
%<*tex>
    \cs_new_protected:Npn \__kernel_intarray_gset_range_from_clist:Nnn #1#2#3
      {
        \@@_gset_range:w \int_eval:w #2 #1 #3 , , \scan_stop:
      }
%</tex>
%<*lua>
luacmd('@@_gset_range:w', function()
  local from = scan_int()
  local t = @@_table()
  while true do
    local tok = scan_token()
    if tok == comma then
      repeat
        tok = scan_token()
      until tok ~= comma
      break
    else
      put_next(tok)
    end
    t[from] = scan_int()
    scan_token()
    from = from + 1
  end
  end, 'global', 'protected')
%</lua>
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@@_gset_overflow_test:nw}
%   In order to allow some code sharing later we provide the
%   \cs{@@_gset_overflow_test:nw} name here. It doesn't actually test anything
%   since the Lua implementation accepts all integers which could be tested with
%   \cs{tex_ifabsnum:D}.
%    \begin{macrocode}
%<*tex>
    \cs_new_protected:Npn \@@_gset_overflow_test:nw #1
    {
    }
%    \end{macrocode}
% \end{macro}
%
% \subsection{Font dimension based implementation}
%
% Go to the false branch of the conditional above.
%    \begin{macrocode}
  }
  {
%    \end{macrocode}
%
% \subsubsection{Allocating arrays}
%
% \begin{macro}{\@@_entry:w, \@@_count:w}
%   We use these primitives quite a lot in this module.
%    \begin{macrocode}
    \cs_new_eq:NN \@@_entry:w \tex_fontdimen:D
    \cs_new_eq:NN \@@_count:w \tex_hyphenchar:D
%    \end{macrocode}
% \end{macro}
%
% \begin{variable}{\c_@@_sp_dim}
%   Used to convert integers to dimensions fast.
%    \begin{macrocode}
    \dim_const:Nn \c_@@_sp_dim { 1 sp }
%    \end{macrocode}
% \end{variable}
%
% \begin{variable}{\g_@@_font_int}
%   Used to assign one font per array.
%    \begin{macrocode}
    \int_new:N \g_@@_font_int
%    \end{macrocode}
% \end{variable}
%
% \begin{macro}{\intarray_new:Nn, \intarray_new:cn}
% \begin{macro}{\@@_new:N}
%   Declare |#1| to be a font (arbitrarily |cmr10| at a never-used
%   size).  Store the array's size as the \tn{hyphenchar} of that font
%   and make sure enough \tn{fontdimen} are allocated, by setting the
%   last one.  Then clear any \tn{fontdimen} that |cmr10| starts with.
%   It seems \LuaTeX{}'s |cmr10| has an extra \tn{fontdimen} parameter
%   number $8$ compared to other engines (for a math font we would
%   replace $8$ by $22$ or some such).
%   Every \texttt{intarray} must be global; it's enough to run this
%   check in \cs{intarray_new:Nn}.
%    \begin{macrocode}
    \cs_new_protected:Npn \@@_new:N #1
      {
        \__kernel_chk_if_free_cs:N #1
        \int_gincr:N \g_@@_font_int
        \tex_global:D \tex_font:D #1
          = cmr10~at~ \g_@@_font_int \c_@@_sp_dim \scan_stop:
        \int_step_inline:nn { 8 }
          { \__kernel_intarray_gset:Nnn #1 {##1} \c_zero_int }
      }
    \cs_new_protected:Npn \intarray_new:Nn #1#2
      {
        \@@_new:N #1
        \@@_count:w #1 = \int_eval:n {#2} \scan_stop:
        \int_compare:nNnT { \intarray_count:N #1 } < 0
          {
            \msg_error:nnx { kernel } { negative-array-size }
              { \intarray_count:N #1 }
          }
        \int_compare:nNnT { \intarray_count:N #1 } > 0
          { \__kernel_intarray_gset:Nnn #1 { \intarray_count:N #1 } { 0 } }
      }
    \cs_generate_variant:Nn \intarray_new:Nn { c }
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}[EXP]{\intarray_count:N, \intarray_count:c}
%   Size of an array.
%    \begin{macrocode}
    \cs_new:Npn \intarray_count:N #1 { \int_value:w \@@_count:w #1 }
    \cs_generate_variant:Nn \intarray_count:N { c }
%    \end{macrocode}
% \end{macro}
%
% \subsubsection{Array items}
%
% \begin{macro}[EXP]{\@@_signed_max_dim:n}
%   Used when an item to be stored is larger than \cs{c_max_dim} in
%   absolute value; it is replaced by $\pm\cs{c_max_dim}$.
%    \begin{macrocode}
    \cs_new:Npn \@@_signed_max_dim:n #1
      { \int_value:w \int_compare:nNnT {#1} < 0 { - } \c_max_dim }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]{\@@_bounds:NNnTF, \@@_bounds_error:NNnw}
%   The functions \cs{intarray_gset:Nnn} and \cs{intarray_item:Nn} share
%   bounds checking.  The |T| branch is used if |#3| is within bounds of
%   the array |#2|.
%    \begin{macrocode}
    \cs_new:Npn \@@_bounds:NNnTF #1#2#3
      {
        \if_int_compare:w 1 > #3 \exp_stop_f:
          \@@_bounds_error:NNnw #1 #2 {#3}
        \else:
          \if_int_compare:w #3 > \intarray_count:N #2 \exp_stop_f:
            \@@_bounds_error:NNnw #1 #2 {#3}
          \fi:
        \fi:
        \use_i:nn
      }
    \cs_new:Npn \@@_bounds_error:NNnw #1#2#3#4 \use_i:nn #5#6
      {
        #4
        #1 { kernel } { out-of-bounds }
          { \token_to_str:N #2 } {#3} { \intarray_count:N #2 }
        #6
      }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\intarray_gset:Nnn, \intarray_gset:cnn, \__kernel_intarray_gset:Nnn}
% \begin{macro}{\@@_gset:Nnn, \@@_gset_overflow:Nnn}
%   Set the appropriate \tn{fontdimen}.  The
%   \cs{__kernel_intarray_gset:Nnn} function does not use
%   \cs{int_eval:n}, namely its arguments must be suitable for
%   \cs{int_value:w}.  The user version checks the position and value
%   are within bounds.
%    \begin{macrocode}
    \cs_new_protected:Npn \__kernel_intarray_gset:Nnn #1#2#3
      { \@@_entry:w #2 #1 #3 \c_@@_sp_dim }
    \cs_new_protected:Npn \intarray_gset:Nnn #1#2#3
      {
        \exp_after:wN \@@_gset:Nww
        \exp_after:wN #1
        \int_value:w \int_eval:n {#2} \exp_after:wN ;
        \int_value:w \int_eval:n {#3} ;
      }
    \cs_generate_variant:Nn \intarray_gset:Nnn { c }
    \cs_new_protected:Npn \@@_gset:Nww #1#2 ; #3 ;
      {
        \@@_bounds:NNnTF \msg_error:nnxxx #1 {#2}
          {
            \@@_gset_overflow_test:nw {#3}
            \__kernel_intarray_gset:Nnn #1 {#2} {#3}
          }
          { }
      }
    \cs_if_exist:NTF \tex_ifabsnum:D
      {
        \cs_new_protected:Npn \@@_gset_overflow_test:nw #1
          {
            \tex_ifabsnum:D #1 > \c_max_dim
              \exp_after:wN \@@_gset_overflow:NNnn
            \fi:
          }
      }
      {
        \cs_new_protected:Npn \@@_gset_overflow_test:nw #1
          {
            \if_int_compare:w \int_abs:n {#1} > \c_max_dim
              \exp_after:wN \@@_gset_overflow:NNnn
            \fi:
          }
      }
    \cs_new_protected:Npn \@@_gset_overflow:NNnn #1#2#3#4
      {
        \msg_error:nnxxxx { kernel } { overflow }
          { \token_to_str:N #2 } {#3} {#4} {  \@@_signed_max_dim:n {#4} }
        #1 #2 {#3} { \@@_signed_max_dim:n {#4} }
      }
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\intarray_gzero:N, \intarray_gzero:c}
%   Set the appropriate \tn{fontdimen} to zero.  No bound checking
%   needed.  The \cs{prg_replicate:nn} possibly uses quite a lot of
%   memory, but this is somewhat comparable to the size of the array,
%   and it is much faster than an \cs{int_step_inline:nn} loop.
%    \begin{macrocode}
    \cs_new_protected:Npn \intarray_gzero:N #1
      {
        \int_zero:N \l_@@_loop_int
        \prg_replicate:nn { \intarray_count:N #1 }
          {
            \int_incr:N \l_@@_loop_int
            \@@_entry:w \l_@@_loop_int #1 \c_zero_dim
          }
      }
    \cs_generate_variant:Nn \intarray_gzero:N { c }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}[EXP]{\intarray_item:Nn, \intarray_item:cn, \__kernel_intarray_item:Nn}
% \begin{macro}{\@@_item:Nn}
%   Get the appropriate \tn{fontdimen} and perform bound checks.  The
%   \cs{__kernel_intarray_item:Nn} function omits bound checks and omits
%   \cs{int_eval:n}, namely its argument must be a \TeX{} integer
%   suitable for \cs{int_value:w}.
%    \begin{macrocode}
    \cs_new:Npn \__kernel_intarray_item:Nn #1#2
      { \int_value:w \@@_entry:w #2 #1 }
    \cs_new:Npn \intarray_item:Nn #1#2
      {
        \exp_after:wN \@@_item:Nw
        \exp_after:wN #1
        \int_value:w \int_eval:n {#2} ;
      }
    \cs_generate_variant:Nn \intarray_item:Nn { c }
    \cs_new:Npn \@@_item:Nw #1#2 ;
      {
        \@@_bounds:NNnTF \msg_expandable_error:nnfff #1 {#2}
          { \__kernel_intarray_item:Nn #1 {#2} }
          { 0 }
      }
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\intarray_rand_item:N, \intarray_rand_item:c}
%   Importantly, \cs{intarray_item:Nn} only evaluates its argument once.
%    \begin{macrocode}
    \cs_new:Npn \intarray_rand_item:N #1
      { \intarray_item:Nn #1 { \int_rand:n { \intarray_count:N #1 } } }
    \cs_generate_variant:Nn \intarray_rand_item:N { c }
%    \end{macrocode}
% \end{macro}
%
% \subsubsection{Working with contents of integer arrays}
%
% \begin{macro}{\intarray_const_from_clist:Nn, \intarray_const_from_clist:cn}
% \begin{macro}{\@@_const_from_clist:nN}
%   Similar to \cs{intarray_new:Nn} (which we don't use because when
%   debugging is enabled that function checks the variable name starts
%   with |g_|).  We make use of the fact that \TeX{} allows allocation
%   of successive \tn{fontdimen} as long as no other font has been
%   declared: no need to count the comma list items first.  We need the
%   code in \cs{intarray_gset:Nnn} that checks the item value is not too
%   big, namely \cs{@@_gset_overflow_test:nw}, but not the code that
%   checks bounds.  At the end, set the size of the intarray.
%    \begin{macrocode}
    \cs_new_protected:Npn \intarray_const_from_clist:Nn #1#2
      {
        \@@_new:N #1
        \int_zero:N \l_@@_loop_int
        \clist_map_inline:nn {#2}
          { \exp_args:Nf \@@_const_from_clist:nN { \int_eval:n {##1} } #1 }
        \@@_count:w #1 \l_@@_loop_int
      }
    \cs_generate_variant:Nn \intarray_const_from_clist:Nn { c }
    \cs_new_protected:Npn \@@_const_from_clist:nN #1#2
      {
        \int_incr:N \l_@@_loop_int
        \@@_gset_overflow_test:nw {#1}
        \__kernel_intarray_gset:Nnn #2 \l_@@_loop_int {#1}
      }
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}[rEXP]{\intarray_to_clist:N, \intarray_to_clist:c}
% \begin{macro}[rEXP]{\@@_to_clist:Nn, \@@_to_clist:w}
%   Loop through the array, putting a comma before each item.  Remove
%   the leading comma with |f|-expansion.  We also use the auxiliary in
%   \cs{intarray_show:N} with argument comma, space.
%    \begin{macrocode}
    \cs_new:Npn \intarray_to_clist:N #1 { \@@_to_clist:Nn #1 { , } }
    \cs_generate_variant:Nn \intarray_to_clist:N { c }
    \cs_new:Npn \@@_to_clist:Nn #1#2
      {
        \int_compare:nNnF { \intarray_count:N #1 } = \c_zero_int
          {
            \exp_last_unbraced:Nf \use_none:n
              { \@@_to_clist:w 1 ; #1 {#2} \prg_break_point: }
          }
      }
    \cs_new:Npn \@@_to_clist:w #1 ; #2#3
      {
        \if_int_compare:w #1 > \@@_count:w #2
          \prg_break:n
        \fi:
        #3 \__kernel_intarray_item:Nn #2 {#1}
        \exp_after:wN \@@_to_clist:w
        \int_value:w \int_eval:w #1 + \c_one_int ; #2 {#3}
      }
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}[rEXP]{\__kernel_intarray_range_to_clist:Nnn, \@@_range_to_clist:ww}
%   Loop through part of the array.
%    \begin{macrocode}
    \cs_new:Npn \__kernel_intarray_range_to_clist:Nnn #1#2#3
      {
        \exp_last_unbraced:Nf \use_none:n
          {
            \exp_after:wN \@@_range_to_clist:ww
            \int_value:w \int_eval:w #2 \exp_after:wN ;
            \int_value:w \int_eval:w #3 ;
            #1 \prg_break_point:
          }
      }
    \cs_new:Npn \@@_range_to_clist:ww #1 ; #2 ; #3
      {
        \if_int_compare:w #1 > #2 \exp_stop_f:
          \prg_break:n
        \fi:
        , \__kernel_intarray_item:Nn #3 {#1}
        \exp_after:wN \@@_range_to_clist:ww
        \int_value:w \int_eval:w #1 + \c_one_int ; #2 ; #3
      }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\__kernel_intarray_gset_range_from_clist:Nnn, \@@_gset_range:Nw}
%   Loop through part of the array.
%    \begin{macrocode}
    \cs_new_protected:Npn \__kernel_intarray_gset_range_from_clist:Nnn #1#2#3
      {
        \int_set:Nn \l_@@_loop_int {#2}
        \@@_gset_range:Nw #1 #3 , , \prg_break_point:
      }
    \cs_new_protected:Npn \@@_gset_range:Nw #1 #2 ,
      {
        \if_catcode:w \scan_stop: \tl_to_str:n {#2} \scan_stop:
          \prg_break:n
        \fi:
        \__kernel_intarray_gset:Nnn #1 \l_@@_loop_int {#2}
        \int_incr:N \l_@@_loop_int
        \@@_gset_range:Nw #1
      }
%    \end{macrocode}
% \end{macro}
%
%    \begin{macrocode}
  }
%    \end{macrocode}
%
% \subsection{Common parts}
%
% \begin{macro}{\intarray_show:N, \intarray_show:c, \intarray_log:N, \intarray_log:c}
%   Convert the list to a comma list (with spaces after each comma)
%    \begin{macrocode}
\cs_new_protected:Npn \intarray_show:N { \@@_show:NN \msg_show:nnxxxx }
\cs_generate_variant:Nn \intarray_show:N { c }
\cs_new_protected:Npn \intarray_log:N { \@@_show:NN \msg_log:nnxxxx }
\cs_generate_variant:Nn \intarray_log:N { c }
\cs_new_protected:Npn \@@_show:NN #1#2
  {
    \__kernel_chk_defined:NT #2
      {
        #1 { intarray } { show }
          { \token_to_str:N #2 }
          { \intarray_count:N #2 }
          { >~ \@@_to_clist:Nn #2 { , ~ } }
          { }
      }
  }
%    \end{macrocode}
% \end{macro}
%
% \subsubsection{Random arrays}
%
% \begin{macro}{\intarray_gset_rand:Nn, \intarray_gset_rand:cn}
% \begin{macro}{\intarray_gset_rand:Nnn, \intarray_gset_rand:cnn}
% \begin{macro}
%   {
%     \@@_gset_rand:Nnn,
%     \@@_gset_rand:Nff,
%     \@@_gset_rand_auxi:Nnnn,
%     \@@_gset_rand_auxii:Nnnn,
%     \@@_gset_rand_auxiii:Nnnn,
%     \@@_gset_all_same:Nn,
%   }
%   We only perform the bounds checks once.  This is done by two
%   \cs{@@_gset_overflow_test:nw}, with an appropriate empty argument to
%   avoid a spurious \enquote{at position \texttt{\#1}} part in the
%   error message.  Then calculate the number of choices: this is at
%   most $(2^{30}-1)-(-(2^{30}-1))+1=2^{31}-1$, which just barely does
%   not overflow.  For small ranges use \cs{__kernel_randint:n} (making
%   sure to subtract~$1$ \emph{before} adding the random number to the
%   \meta{min}, to avoid overflow when \meta{min} or \meta{max} are
%   $\pm\cs{c_max_int}$), otherwise \cs{__kernel_randint:nn}.  Finally,
%   if there are no random numbers do not define any of the auxiliaries.
%    \begin{macrocode}
\cs_new_protected:Npn \intarray_gset_rand:Nn #1
  { \intarray_gset_rand:Nnn #1 { 1 } }
\cs_generate_variant:Nn \intarray_gset_rand:Nn { c }
\sys_if_rand_exist:TF
  {
    \cs_new_protected:Npn \intarray_gset_rand:Nnn #1#2#3
      {
        \@@_gset_rand:Nff #1
          { \int_eval:n {#2} } { \int_eval:n {#3} }
      }
    \cs_new_protected:Npn \@@_gset_rand:Nnn #1#2#3
      {
        \int_compare:nNnTF {#2} > {#3}
          {
            \msg_expandable_error:nnnn
              { kernel } { randint-backward-range } {#2} {#3}
            \@@_gset_rand:Nnn #1 {#3} {#2}
          }
          {
            \@@_gset_overflow_test:nw {#2}
            \@@_gset_rand_auxi:Nnnn #1 { } {#2} {#3}
          }
      }
    \cs_generate_variant:Nn \@@_gset_rand:Nnn { Nff }
    \cs_new_protected:Npn \@@_gset_rand_auxi:Nnnn #1#2#3#4
      {
        \@@_gset_overflow_test:nw {#4}
        \@@_gset_rand_auxii:Nnnn #1 { } {#4} {#3}
      }
    \cs_new_protected:Npn \@@_gset_rand_auxii:Nnnn #1#2#3#4
      {
        \exp_args:NNf \@@_gset_rand_auxiii:Nnnn #1
          { \int_eval:n { #3 - #4 + 1 } } {#4} {#3}
      }
    \cs_new_protected:Npn \@@_gset_rand_auxiii:Nnnn #1#2#3#4
      {
        \exp_args:NNf \@@_gset_all_same:Nn #1
          {
            \int_compare:nNnTF {#2} > \c__kernel_randint_max_int
              {
                \exp_stop_f:
                \int_eval:n { \__kernel_randint:nn {#3} {#4} }
              }
              {
                \exp_stop_f:
                \int_eval:n { \__kernel_randint:n {#2} - 1 + #3 }
              }
          }
      }
    \cs_new_protected:Npn \@@_gset_all_same:Nn #1#2
      {
        \int_zero:N \l_@@_loop_int
        \prg_replicate:nn { \intarray_count:N #1 }
          {
            \int_incr:N \l_@@_loop_int
            \__kernel_intarray_gset:Nnn #1 \l_@@_loop_int {#2}
          }
      }
  }
  {
    \cs_new_protected:Npn \intarray_gset_rand:Nnn #1#2#3
      {
        \msg_error:nnn { kernel } { fp-no-random }
          { \intarray_gset_rand:Nnn #1 {#2} {#3} }
      }
  }
\cs_generate_variant:Nn \intarray_gset_rand:Nnn { c }
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
%    \begin{macrocode}
%</tex>
%</package>
%    \end{macrocode}
%
% \end{implementation}
%
% \PrintIndex