\def\tabstackengineversionnumber{V2.10}
%
% THIS MATERIAL IS SUBJECT TO THE LaTeX Project Public License
%
% V1.00 -Adopted beta version 0.21 as initial release version 1.0
% V1.10 -Corrected unary/binary problem for left end of tabbed cell content;
%       -Added \TABunaryLeft (\TABbinaryRight) for "   cell{} ";
%        added \TABunaryRight (\TABbinaryLeft) for " {}cell   ";
%        added \TABbinary                      for " {}cell{} ";
%        The default is \TABunaryLeft (V1.00 wrongly equivalent to \TABbinary)
%        This removes need to brace unary negatives at lead of cell.
%       -Corrected bug of trailing \frac, noted in V1.00, by adding a
%        \relax to definition of \@postTAB in \readTABrow.
% V2.00 -Incorporate listofitems package methodology for parsing, requiring
%        some package rewrite, primarily macro \@readMANYrows.
%       -Fixed bug in \ensureTABstackMath that had automatically returned to
%        \TABstackText mode.
%       -Added \Matrixstack macro (equivalent to \tabbedVectorstack)
%       -Added \TABstackTextstyle, \TABstackMathstyle, and \clearTABstyle
%        to allow things like fontsize, \displaystyle, etc. to be set inside
%        a stack, by default.
%       -Converted \newlength\maxTAB@width to a \xdef\maxTABwd.  Introduced
%        \TABwd{}, \TABht{}, and \TABdp{} for obtaining widths of columns 
%        and heights/depths of rows.
%       -\TABstrut now defined at time of parsing, rather than reconstructed after
%        the fact.  This will prevent any confusions if the math/text stack mode 
%        settings change.
%       -Employed a \toks based approach to parsing the argument, rather than the
%        previous \protected@edef approach.  The prior approach suffered problems
%        when \\ was redefined, as in, for example, \centering or \raggedright.
% V2.01 -Take advantage of listofitems revision to allow global \readlist, via 
%        \greadlist.  This allows \setsepchar to be placed inside of group, thus
%        preventing a global change in the listofitems \setsepchar.
%       -\TABcell and \TABcellBox modified to remember recent use of
%        \ensureTABstackMath, which otherwise changes temporarily the
%        prevailing mode and style of the TABstack.
% V2.10 -Introduces \TABrule and [optionally] \TABcline{}
%       -Allows tabbed nesting within other tabbed environments (achieved via 
%        replacing select \bgroup and \egroup with \ifnum brace hacks (TeXbook p.385)
\ProvidesPackage{tabstackengine}
[2018/03/05 (\tabstackengineversionnumber) tabbed stacking]
\RequirePackage{stackengine}[2016-10-04]
\RequirePackage{listofitems}[2016/11/18]
\RequirePackage{etoolbox}

\newcounter{TABrowindex@}
\newcounter{TABcolindex@}
\newcounter{TABalignmentindex@}
\newtoggle{fixed@TABwidth}
\newtoks\TABcelltoks
\newtoks\TABcoltoks
\newtoks\LstrutTABtoks
\newtoks\RstrutTABtoks
\newtoks\TAB@toks
\newlength\TABruleshift

\def\getTABcelltoks[#1,#2]{%
  \TABcelltoks=\expandafter\expandafter\expandafter{\TABcellRaw[#1,#2]}}

\def\@getstruttedTABcelltoks[#1,#2]{%
  \getTABcelltoks[#1,#2]%
  \edef\TABstack@rownum{#1}%\
  \LstrutTABtoks=\expandafter{\expandafter\TAB@strutL\expandafter{\TABstack@rownum}}%
  \RstrutTABtoks=\expandafter{\expandafter\TAB@strutR\expandafter{\TABstack@rownum}}%
  \prepend@toksto\TABcelltoks\LstrutTABtoks%
  \append@toksto\TABcelltoks\RstrutTABtoks}

\def\prepend@toksto#1#2{#1=\expandafter\expandafter\expandafter%
  {\expandafter\the\expandafter#2\the#1}}

\def\append@toksto#1#2{#1=\expandafter\expandafter\expandafter%
  {\expandafter\the\expandafter#1\the#2}}

\newcommand\setstackTAB[1]{\ifstrempty{#1}{\def\TAB@char{ }}{\def\TAB@char{#1}}}

\newcommand\readTABstack@ORIG[1]{%
  \expandafter\expandafter\expandafter\setsepchar\expandafter\expandafter%
    \expandafter{\expandafter\SEP@char\expandafter/\TAB@char}%
  \greadlist*\TABcellRaw{#1}%
  \edef\TABstack@rows{\TABcellRawlen}%
  \edef\TABstack@cols{\listlen\TABcellRaw[1]}%
  \def\maxTABwd{0pt}%
  \setcounter{TABrowindex@}{0}%
  \whileboolexpr{test {\ifnumless{\theTABrowindex@}{\TABstack@rows}}}{% ROW LOOP
    \def\@accumulatedTAB{}%
    \stepcounter{TABrowindex@}%
    \setcounter{TABcolindex@}{0}%
    \whileboolexpr{test {\ifnumless{\theTABcolindex@}{\TABstack@cols}}}{% COL LOOP
      \stepcounter{TABcolindex@}%
      \ifnum\value{TABrowindex@}=1\relax\csxdef{col\theTABcolindex@ TAB@wd}{0pt}\fi%
      \getTABcelltoks[\theTABrowindex@,\theTABcolindex@]%
      \expandafter\g@addto@macro\expandafter\@accumulatedTAB\expandafter{%
        \the\TABcelltoks{}}%
      \setbox0=\hbox{\stack@delim\TAB@delim{%
        \TAB@strutL{0}\the\TABcelltoks\TAB@strutR{0}}\stack@delim}%
      \ifdim\wd0>\csuse{col\theTABcolindex@ TAB@wd}\relax%
        \csxdef{col\theTABcolindex@ TAB@wd}{\the\wd0}%
      \ifdim\wd0>\maxTABwd\relax\xdef\maxTABwd{\the\wd0}\fi\fi%
      \csxdef{col\theTABcolindex@ TAB@stackalignment}{c}% DEFAULT, LATER CHANGED
    }%
    \setbox0=\hbox{\stack@delim\TAB@delim{\@accumulatedTAB}\stack@delim}%
    \csxdef{row\theTABrowindex@ TAB@ht}{\the\ht0}%
    \csxdef{row\theTABrowindex@ TAB@dp}{\the\dp0}%
    \global\let\recent@TAB@delim\TAB@delim%
  }%
}

\newcommand\TABwd[1]{\csuse{col#1TAB@wd}}
\newcommand\TABht[1]{\csuse{row#1TAB@ht}}
\newcommand\TABdp[1]{\csuse{row#1TAB@dp}}
\newcommand\TABstrut[1]{\ifnum#1<1\relax{}\else%
  \protect\rule[-\TABdp{#1}]{0pt}{\dimexpr\TABdp{#1}+\TABht{#1}\relax}\fi}

\newcommand\TABcell[2]{%
  \setTABrulecolumn{#2}% THIS LINE ADDED TO SET COLUMN FOR POSSIBLE \TABrule
  \stack@delim\recent@TAB@delim{\TABcellRaw[#1,#2]}\stack@delim}

\newcommand\TABcellBox[3][\relax]{\ifx\relax#1\relax%
  \TABcellBox@aux{\csuse{col#3TAB@stackalignment}}{#2}{#3}\else
  \TABcellBox@aux{#1}{#2}{#3}\fi}

\newcommand\TABcellBox@aux[3]{\makebox[\TABwd{#3}][#1]{\stack@delim%
  \recent@TAB@delim{\TAB@strutL{#2}\TABcellRaw[#2,#3]\TAB@strutR{#2}}\stack@delim}}

\newcommand\TABcells[1]{\listlen\TABcellRaw[#1]}

\newcommand\TABunaryLeft{\def\TAB@strutL##1{}%
                         \def\TAB@strutR##1{\TABstrut{##1}}}
\newcommand\TABunaryRight{\def\TAB@strutL##1{\TABstrut{##1}}%
                          \def\TAB@strutR##1{}}
\newcommand\TABbinary{\def\TAB@strutL##1{{}}%
                      \def\TAB@strutR##1{\TABstrut{##1}}}
\let\TABbinaryRight\TABunaryLeft
\let\TABbinaryLeft\TABunaryRight

\newcommand\TABstackMath{\renewcommand\TAB@delim[1]{\ensuremath{\TAB@mathstyle##1}}%
  \let\recent@TAB@delim\TAB@delim}
\newcommand\TABstackText{\renewcommand\TAB@delim[1]{\TAB@textstyle##1}%
  \let\recent@TAB@delim\TAB@delim}
\newcommand\TABstackMathstyle[1]{\renewcommand\TAB@mathstyle{#1}}
\newcommand\TABstackTextstyle[1]{\renewcommand\TAB@textstyle{#1}}
\newcommand\clearTABstyle{\renewcommand\TAB@textstyle{}\renewcommand\TAB@mathstyle{}}

\newcommand\tabbedShortstack[2][\stackalignment]{%
  \@TAB@stack{#1}{#2}{D}{\Shortstack}}

\newcommand\alignShortstack[1]{%
  \@TAB@stack{}{#1}{A}{\Shortstack}}

\newcommand\tabularShortstack[2]{%
  \@TAB@stack{}{#2}{#1}{\Shortstack}}

\newcommand\tabbedShortunderstack[2][\stackalignment]{%
  \@TAB@stack{#1}{#2}{D}{\Shortunderstack}}

\newcommand\alignShortunderstack[1]{%
  \@TAB@stack{}{#1}{A}{\Shortunderstack}}

\newcommand\tabularShortunderstack[2]{%
  \@TAB@stack{}{#2}{#1}{\Shortunderstack}}

\newcommand\tabbedLongstack[2][\stackalignment]{%
  \@TAB@stack{#1}{#2}{D}{\Longstack}}

\newcommand\alignLongstack[1]{%
  \@TAB@stack{}{#1}{A}{\Longstack}}

\newcommand\tabularLongstack[2]{%
  \@TAB@stack{}{#2}{#1}{\Longstack}}

\newcommand\tabbedLongunderstack[2][\stackalignment]{%
  \@TAB@stack{#1}{#2}{D}{\Longunderstack}}

\newcommand\alignLongunderstack[1]{%
  \@TAB@stack{}{#1}{A}{\Longunderstack}}

\newcommand\tabularLongunderstack[2]{%
  \@TAB@stack{}{#2}{#1}{\Longunderstack}}

\newcommand\tabbedCenterstack[2][\stackalignment]{%
  \@TAB@stack{#1}{#2}{D}{\Centerstack}}

\newcommand\alignCenterstack[1]{%
  \@TAB@stack{}{#1}{A}{\Centerstack}}

\newcommand\tabularCenterstack[2]{%
  \@TAB@stack{}{#2}{#1}{\Centerstack}}

\newcommand\tabbedVectorstack[2][\stackalignment]{%
  \ensureTABstackMath{\@TAB@stack{#1}{#2}{D}{\Vectorstack}}}

\newcommand\alignVectorstack[1]{%
  \ensureTABstackMath{\@TAB@stack{}{#1}{A}{\Vectorstack}}}

\newcommand\tabularVectorstack[2]{%
  \ensureTABstackMath{\@TAB@stack{}{#2}{#1}{\Vectorstack}}}

\let\Matrixstack\tabbedVectorstack% ADDED V2.00

\newcommand\parenMatrixstack[2][\stackalignment]{%
  \ensureTABstackMath{\left(\@TAB@stack{#1}{#2}{D}{\Vectorstack}\right)}}

\newcommand\braceMatrixstack[2][\stackalignment]{%
  \ensureTABstackMath{\left\{\@TAB@stack{#1}{#2}{D}{\Vectorstack}\right\}}}

\newcommand\bracketMatrixstack[2][\stackalignment]{%
  \ensureTABstackMath{\left[\@TAB@stack{#1}{#2}{D}{\Vectorstack}\right]}}

\newcommand\vertMatrixstack[2][\stackalignment]{%
  \ensureTABstackMath{\left|\@TAB@stack{#1}{#2}{D}{\Vectorstack}\right|}}

\newcommand\@TAB@stack[4]{{\ifnum`}=\z@\fi%
  \set@TABrule@gap{#3}%
  \readTABstack{#2}%
  \edef\stackalignment{#1}%
  \setcounter{TABcolindex@}{0}%
  \whileboolexpr{test {\ifnumless{\theTABcolindex@}{\TABstack@cols}}}{% COL LOOP
    \stepcounter{TABcolindex@}%
    \@getstruttedTABcelltoks[1,\theTABcolindex@]%
    \TABcoltoks=\expandafter{\expandafter\TAB@delim\expandafter{\the\TABcelltoks}}%
    \@getTABalignment{#3}{\theTABcolindex@}%
    \ifboolexpr{test {\ifnumgreater{\theTABcolindex@}{1}}}%
      {\add@TAB@gap{#3}{\theTABcolindex@}}{}%
    \setcounter{TABrowindex@}{1}%
    \whileboolexpr{test {\ifnumless{\theTABrowindex@}{\TABstack@rows}}}{% ROW LOOP
      \stepcounter{TABrowindex@}%
      \@getstruttedTABcelltoks[\theTABrowindex@,\theTABcolindex@]%
      \TABcoltoks=\expandafter\expandafter\expandafter\expandafter\expandafter%
        \expandafter\expandafter{\expandafter\expandafter\expandafter%
        \the\expandafter\expandafter\expandafter\TABcoltoks\expandafter%
        \SEP@char\expandafter\TAB@delim\expandafter{\the\TABcelltoks}}%
    }%
    \iftoggle{fixed@TABwidth}%
      {\makebox[\maxTABwd][\stackalignment]{%
        \expandafter#4\expandafter{\the\TABcoltoks}}}%
      {\expandafter#4\expandafter{\the\TABcoltoks}}%
  }%
\ifnum`{=\z@\fi}}

\newcommand\tabbedstackon[3][\stackgap]{%
  \@TABstackonunder{#1}{#2}{#3}{D}{\stackon}}

\newcommand\alignstackon[3][\stackgap]{%
  \@TABstackonunder{#1}{#2}{#3}{A}{\stackon}}

\newcommand\tabularstackon[4][\stackgap]{%
  \@TABstackonunder{#1}{#3}{#4}{#2}{\stackon}}

\newcommand\tabbedstackunder[3][\stackgap]{%
  \@TABstackonunder{#1}{#2}{#3}{D}{\stackunder}}

\newcommand\alignstackunder[3][\stackgap]{%
  \@TABstackonunder{#1}{#2}{#3}{A}{\stackunder}}

\newcommand\tabularstackunder[4][\stackgap]{%
  \@TABstackonunder{#1}{#3}{#4}{#2}{\stackunder}}

\newcommand\tabbedstackanchor[3][\stackgap]{%
  \@TABstackonunder{#1}{#2}{#3}{D}{\stackanchor}}

\newcommand\alignstackanchor[3][\stackgap]{%
  \@TABstackonunder{#1}{#2}{#3}{A}{\stackanchor}}

\newcommand\tabularstackanchor[4][\stackgap]{%
  \@TABstackonunder{#1}{#3}{#4}{#2}{\stackanchor}}

\newcommand\@TABstackonunder[5]{{\ifnum`}=\z@\fi%
  \set@TABrule@gap{#4}%
  \def\TAB@tmp{#2}%
  \ifnum\TAB@testcline#2\relax=0\relax
    \expandafter\g@addto@macro\expandafter\TAB@tmp\expandafter{\SEP@char}%
  \fi%
  \g@addto@macro\TAB@tmp{#3}%
  \expandafter\readTABstack\expandafter{\TAB@tmp}%
  \setcounter{TABcolindex@}{0}%
  \whileboolexpr{test {\ifnumless{\theTABcolindex@}{\TABstack@cols}}}{% COL LOOP
    \stepcounter{TABcolindex@}%
    \@getTABalignment{#4}{\theTABcolindex@}%
    \ifboolexpr{test {\ifnumgreater{\theTABcolindex@}{1}}%
    }{\add@TAB@gap{#4}{\theTABcolindex@}}{}%
    \iftoggle{fixed@TABwidth}%
      {\makebox[\maxTABwd][\stackalignment]{%
       #5[#1]%
         {\TAB@delim{\TAB@strutL{1}\TABcellRaw[1,\theTABcolindex@]\TAB@strutR{1}}}%
         {\TAB@delim{\TAB@strutL{2}\TABcellRaw[2,\theTABcolindex@]\TAB@strutR{2}}}}}%
      {#5[#1]%
         {\TAB@delim{\TAB@strutL{1}\TABcellRaw[1,\theTABcolindex@]\TAB@strutR{1}}}%
         {\TAB@delim{\TAB@strutL{1}\TABcellRaw[2,\theTABcolindex@]\TAB@strutR{2}}}}%
  }%
\ifnum`{=\z@\fi}}

\def\TAB@testcline#1#2\relax{\ifx\TABcline#1 1\else0\fi}

\newcommand\@getTABalignment[2]{%
  \ifstrequal{#1}{D}{}{%                     T, DO NOTHING (USE \stackalignment)
    \ifstrequal{#1}{A}{%
      \ifnumequal{1}{#2}{%
        \def\stackalignment{r}}{%            A, 1st ELEMENT, SET TO r
        \if l\stackalignment%
          \def\stackalignment{r}\else%       A, SWITCH l TO r
          \def\stackalignment{l}\fi}}{%      A, SWITCH r TO l
          \set@tabularcellalignment{#1}{#2}% tabular, READ #2 location
      }%
  }%
  \csxdef{col\theTABcolindex@ TAB@stackalignment}{\stackalignment}%
}

\newcommand\setstacktabbedgap[1]{\def\tabbed@gap{#1}}
\newcommand\setstackaligngap[1]{\def\align@gap{#1}}
\newcommand\setstacktabulargap[1]{\def\tabular@gap{#1}}

\newcommand\add@TAB@gap[2]{%
  \ifstrequal{#1}{D}{\hspace{\tabbed@gap}}{%
    \ifstrequal{#1}{A}%
      {\if r\stackalignment\hspace{\align@gap}\fi}{\hspace{\tabular@gap}}%
  }%
}

\newcommand\set@tabularcellalignment[2]{%
  \setcounter{TABalignmentindex@}{1}%
  \edef\tabular@settings{#1.}%
  \whileboolexpr{test {\ifnumless{\theTABalignmentindex@}{#2}}}{%
    \stepcounter{TABalignmentindex@}%
    \edef\tabular@settings{\expandafter\@gobble\tabular@settings.}%
  }%
  \expandafter\@getnextTABchar\tabular@settings\\% GET NEXT TAB ALIGNMENT
  \if l\@nextTABchar\edef\stackalignment{l}\else%
    \if r\@nextTABchar\edef\stackalignment{r}\else%
      \if c\@nextTABchar\edef\stackalignment{c}\fi%
    \fi%                                        IGNORE IF NOT l, c, OR r
  \fi%
}

\def\@getnextTABchar#1#2\\{\gdef\@nextTABchar{#1}}

\newcommand\fixTABwidth[1]{%
  \if T#1\toggletrue{fixed@TABwidth}\else\togglefalse{fixed@TABwidth}\fi}

\newcommand\ensureTABstackMath[1]{%
  \let\sv@TABmode\TAB@delim\TABstackMath#1\let\TAB@delim\sv@TABmode}

%%% \TABrule

\newcommand\TABrule[1][\TABruleshift]{%
  \ifnum1=\value{TABcolindex@}\relax%
    \makebox[\TABwd{\theTABcolindex@}][l]{%
      \rule[\TABruleshift]{%
        \dimexpr\TABwd{\theTABcolindex@}+.5\dimexpr\TAB@gap\relax}{\fboxrule}}%
  \else%
    \ifnum\TABcells{1}=\value{TABcolindex@}\relax%
      \makebox[\TABwd{\theTABcolindex@}][r]{%
        \rule[\TABruleshift]{%
          \dimexpr\TABwd{\theTABcolindex@}+.5\dimexpr\TAB@gap\relax}{\fboxrule}}%
    \else%
      \makebox[\TABwd{\theTABcolindex@}][c]{%
        \rule[\TABruleshift]{%
          \dimexpr\TABwd{\theTABcolindex@}+1.\dimexpr\TAB@gap\relax}{\fboxrule}}%
    \fi%
  \fi%
}

\newcommand\set@TABrule@gap[1]{%
  \ifstrequal{#1}{D}{\gdef\TAB@gap{\tabbed@gap}}{%
      \ifstrequal{#1}{A}{\gdef\TAB@gap{0pt}}{\gdef\TAB@gap{\tabular@gap}}%
  }%
}

\newcommand\setTABrulecolumn[1]{\setcounter{TABcolindex@}{#1}}

%% \TABcline

\newcommand\readTABstack@cline[1]{%
  \expandafter\expandafter\expandafter\setsepchar\expandafter\expandafter%
    \expandafter{\expandafter\SEP@char\expandafter/\TAB@char}%
% REMEMBER # COLUMNS IN ADVANCE
  \greadlist*\TABcellRaw{#1}%
  \edef\TABstack@cols{\listlen\TABcellRaw[1]}%[\TABstack@cols]%
  \TAB@toks={}%
  \setcounter{TABrowindex@}{0}%
  \TAB@preread#1\relax\TABcline\relax\TAB@end%
  \expandafter\expandafter\expandafter\setsepchar\expandafter\expandafter%
    \expandafter{\expandafter\SEP@char\expandafter/\TAB@char}%
% THE FOLLOWING WILL FIX LINES ENDING IN EOL SEPARATOR (SHOULDN'T DO THAT!)
  \pad@cols%
%%
  \expandafter\greadlist\expandafter*\expandafter\TABcellRaw\expandafter{\the\TAB@toks}%
  \edef\TABstack@rows{\TABcellRawlen}%
  \def\maxTABwd{0pt}%
  \setcounter{TABrowindex@}{0}%
  \whileboolexpr{test {\ifnumless{\theTABrowindex@}{\TABstack@rows}}}{% ROW LOOP
    \def\@accumulatedTAB{}%
    \stepcounter{TABrowindex@}%
    \setcounter{TABcolindex@}{0}%
    \whileboolexpr{test {\ifnumless{\theTABcolindex@}{\TABstack@cols}}}{% COL LOOP
      \stepcounter{TABcolindex@}%
      \ifnum\value{TABrowindex@}=1\relax\csxdef{col\theTABcolindex@ TAB@wd}{0pt}\fi%
      \getTABcelltoks[\theTABrowindex@,\theTABcolindex@]%
      \expandafter\g@addto@macro\expandafter\@accumulatedTAB\expandafter{%
        \the\TABcelltoks{}}%
      \setbox0=\hbox{\stack@delim\TAB@delim{%
        \TAB@strutL{0}\the\TABcelltoks\TAB@strutR{0}}\stack@delim}%
      \ifdim\wd0>\csuse{col\theTABcolindex@ TAB@wd}\relax%
        \csxdef{col\theTABcolindex@ TAB@wd}{\the\wd0}%
      \ifdim\wd0>\maxTABwd\relax\xdef\maxTABwd{\the\wd0}\fi\fi%
      \csxdef{col\theTABcolindex@ TAB@stackalignment}{c}% DEFAULT, LATER CHANGED
    }%
    \setbox0=\hbox{\stack@delim\TAB@delim{\@accumulatedTAB}\stack@delim}%
    \csxdef{row\theTABrowindex@ TAB@ht}{\the\ht0}%
    \csxdef{row\theTABrowindex@ TAB@dp}{\the\dp0}%
    \global\let\recent@TAB@delim\TAB@delim%
  }%
}

\def\TAB@preread#1\TABcline#2#3\TAB@end{\TAB@toks=\expandafter{\the\TAB@toks#1}%
  \stepcounter{TABrowindex@}%
  \ifx\relax#2\relax%
    \TAB@toks=\expandafter{\the\TAB@toks\unskip}%
    \let\next\relax%
  \else%
    \discern@TABlines{#2}%
    \setcounter{TABcolindex@}{0}%
    \whileboolexpr{test {\ifnumless{\theTABcolindex@}{\TABline@colcount}}}{% COLUMN LOOP
      \stepcounter{TABcolindex@}%
      \ifnum\theTABcolindex@=1\relax\else%
        \TAB@toks=\expandafter\expandafter\expandafter{%
          \expandafter\the\expandafter\TAB@toks\TAB@char}%
      \fi
      \TAB@toks=\expandafter\expandafter\expandafter\expandafter\expandafter%
        \expandafter\expandafter{\expandafter\expandafter\expandafter%
        \the\expandafter\expandafter\expandafter\TAB@toks%
          \csname TABline@[\theTABcolindex@]\endcsname}%
    }%
    \ifnum0=\TAB@testend#3\relax\relax%
      \TAB@toks=\expandafter\expandafter\expandafter{%
        \expandafter\the\expandafter\TAB@toks\SEP@char}%
    \fi%
    \def\next{\TAB@preread#3\TAB@end}%
  \fi%
  \next%
}

\newcommand\discern@TABlines[1]{%
  \setcounter{TABcolindex@}{0}%
  \whileboolexpr{test {\ifnumless{\theTABcolindex@}{\TABstack@cols}}}{% COLUMN LOOP
    \stepcounter{TABcolindex@}%
    \expandafter\def\csname TABline@[\theTABcolindex@]\endcsname{\relax}%
  }%
  \setsepchar{,/-}%
  \readlist\TABline@cols{#1}%
  \def\TAB@endindex{0}%
  \foreachitem\@TABindex\in\TABline@cols{%
    \edef\TAB@startindex{\TABline@cols[\@TABindexcnt,1]}%
    \ifnum\listlen\TABline@cols[\@TABindexcnt]=2\relax%
      \edef\TAB@endindex{\TABline@cols[\@TABindexcnt,2]}%
    \else
      \edef\TAB@endindex{\TABline@cols[\@TABindexcnt,1]}%
    \fi
    \setcounter{TABcolindex@}{\numexpr\TAB@startindex-1\relax}%
    \whileboolexpr{test {\ifnumless{\theTABcolindex@}{\TAB@endindex}}}{% COLUMN LOOP
      \stepcounter{TABcolindex@}%
      \expandafter\def\csname TABline@[\theTABcolindex@]\endcsname{%
        \TABrule}%
    }%
  }%
  \edef\TABline@colcount{\TABstack@cols}%
}


\def\TAB@testend#1#2\relax{\ifx\relax#1 1\else0\fi}

\newcommand\relaxTABsyntax{%
  \def\pad@cols{%
    \setcounter{TABcolindex@}{1}%
    \whileboolexpr{test {\ifnumless{\theTABcolindex@}{\TABstack@cols}}}{% COLUMN LOOP
      \stepcounter{TABcolindex@}%
      \TAB@toks=\expandafter\expandafter\expandafter{%
        \expandafter\the\expandafter\TAB@toks\TAB@char}%
    }%
  }%
}

\newcommand\@strictTABsyntax{\let\pad@cols\relax}

\newcommand\TABcline@off{%
  \def\TABcline##1{\ignorespaces}%
  \let\readTABstack\readTABstack@ORIG%
}

\newcommand\TABcline@on{%
  \def\TABcline{}%
  \let\readTABstack\readTABstack@cline%
}

%% INITIALIZATIONS

\setstackEOL{\\}%              DEFAULT ROW SEP
\setstackTAB{&}%               DEFAULT COL SEP
\def\TAB@mathstyle{}%          NOTHING ADDED TO DEFAULT TAB MATH STYLE
\def\TAB@textstyle{}%          NOTHING ADDED TO DEFAULT TAB TEXT STYLE
\def\TAB@delim{}\TABstackText% INITIALIZE DEFAULT TO TEXT TABSTACKING
\TABunaryLeft%                 NO DEFAULT EMPTY {} GROUP AT LEFT END OF EACH CELL
\def\tabbed@gap{0pt}%          DEFAULT TABBED COL GAP
\def\align@gap{1em}%           DEFAULT ALIGN COL GAP
\def\tabular@gap{\tabcolsep}%  DEFAULT TABULAR COL GAP
\fixTABwidth{F}%               DEFAULT NON-FIXED WIDTH COLUMNS
\setlength\TABruleshift{-0pt}% RELATIVE VERTICAL SHIFT OF \TABrule
\@strictTABsyntax%             WITH \relaxTABsyntax, ADDS NCOL-1 COLUMN SEPARATORS TO END
%                              OF INPUT TOKEN LIST, TO AVOID ERROR ENDING INPUT WITH EOL.
%                              BASICALLY, ALLOWS BAD CODING STYLE WITH NEW \readTABstack

% PROCESS PACKAGE OPTIONS
\newif\iftabstackengine@TABcline
\DeclareOption{TABcline}{\tabstackengine@TABclinetrue}
\ProcessOptions\relax
\iftabstackengine@TABcline%
  \TABcline@on% ALLOW USE OF \TABcline
\else
  \TABcline@off% DISALLOW USE OF \TABcline
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\endinput