<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% \iffalse meta-comment/*%    \end{macrocode}*/
%
% Copyright (C) 2021 by Sigitas Tolu\v{s}is &lt;sigitas@vtex.lt&gt;
% ---------------------------------------------------------------------------
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
%   http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% This work has the LPPL maintenance status `maintained'.
%
% The Current Maintainer of this work is Sigitas Tolu\v{s}is.
%
% This work consists of the files flushend.dtx and flushend.ins
% and the derived filebase flushend.sty.
%
% \fi
%
% \iffalse
%&lt;*internal&gt;
\begingroup
%&lt;/internal&gt;
%&lt;*batchfile&gt;
\input docstrip.tex
\keepsilent\askforoverwritefalse
\preamble
%%
%% This is file `flushend.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% flushend.dtx  (with options: `package')
%% 
\endpreamble
\generate{\file{flushend.sty}{\from{flushend.dtx}{package}}}
%&lt;/batchfile&gt;
%&lt;batchfile&gt;\endbatchfile
%&lt;*internal&gt;
\generate{\file{flushend.ins}{\from{flushend.dtx}{batchfile}}}
\endgroup
%&lt;/internal&gt;
%&lt;*driver&gt;
\ProvidesFile{flushend.dtx}
%&lt;/driver&gt;
%&lt;*package&gt;
%% Copyright (C) 1997-2021 by Sigitas Tolu\v{s}is &lt;sigitas@vtex.lt&gt;
%% UAB VTeX, MokslininkÅ³ 2A, LT-08412 Vilnius, Lithuania
%% --------------------------------------------------------------------------
%% This work may be distributed and/or modified under the
%% conditions of the LaTeX Project Public License, either version 1.3
%% of this license or (at your option) any later version.
%% The latest version of this license is in
%%   http://www.latex-project.org/lppl.txt
%% and version 1.3 or later is part of all distributions of LaTeX
%% version 2005/12/01 or later.
%%
%% PURPOSE:   Balanced columns on last page in twocolumn mode.
%%
%&lt;/package&gt;
%&lt;package&gt;\NeedsTeXFormat{LaTeX2e}[1999/12/01]
%&lt;package&gt;\ProvidesPackage{flushend}
%&lt;*package&gt;
    [2021/10/04 v4.0 Balancing columns in twocolumn mode]
%&lt;/package&gt;
%
%&lt;*driver&gt;
\documentclass{ltxdoc}
\usepackage{flushend}[2021/10/04]
\usepackage{geometry}
\geometry{a4paper}
\setlength\marginparwidth{5pc}
\EnableCrossrefs
\CodelineIndex
%%\RecordChanges
\OnlyDescription
\begin{document}
  \DocInput{flushend.dtx}
  %%\PrintChanges
  %%\PrintIndex
\end{document}
%&lt;/driver&gt;
% \fi
%
% \CheckSum{2020}
%
% \CharacterTable
%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%   Digits        \0\1\2\3\4\5\6\7\8\9
%   Exclamation   \!     Double quote  \"     Hash (number) \#
%   Dollar        \$     Percent       \%     Ampersand     \&amp;
%   Acute accent  \'     Left paren    \(     Right paren   \)
%   Asterisk      \*     Plus          \+     Comma         \,
%   Minus         \-     Point         \.     Solidus       \/
%   Colon         \:     Semicolon     \;     Less than     \&lt;
%   Equals        \=     Greater than  \&gt;     Question mark \?
%   Commercial at \@     Left bracket  \[     Backslash     \\
%   Right bracket \]     Circumflex    \^     Underscore    \_
%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%   Right brace   \}     Tilde         \~}
%
%
% \changes{v0.1}{1997/05/16}{first version}
% \changes{v0.2}{1997/09/09}{support for compatibility with cuted.sty}
% \changes{v1.0}{1997/10/01}{\string\vipersep changed to \string\stripsep for compatibility with cuted.sty}
% \changes{v1.1}{2012/05/29}{Converted to DTX file}
% \changes{v2.0}{2014/03/03}{rewritten with new balance algorithm}
% \changes{v2.1}{2014/03/18}{Switched debug option off}
% \changes{v2.2}{2014/04/24}{bugfix version: removing empty box at the right column end}
% \changes{v3.0}{2015/04/08}{bugfix version and extra options:
%                            ancient/modern,
%                            spread/nospread,
%                            removelastbox/keeplastbox}
% \changes{v3.1}{2015/04/14}{set debug option off by default; keeplastbox modified;}
% \changes{v3.2}{2016/06/21}{bugfix compatibility with luatexja}
% \changes{v3.3}{2017/03/27}{bugfix for get@@footnoterule@@box; options for some checks on/off}
% \changes{v3.4}{2020/10/14}{bugfix development and test}
% \changes{v3.5}{2020/10/16}{bugfix version: modern with noautobase}
% \changes{v4.0}{2021/10/04}{another rewrite with new balance algorithm and options}
%
% \DoNotIndex{\newcommand,\newenvironment}
%
% \providecommand*{\url}{\texttt}
% \GetFileInfo{flushend.dtx}
% \title{The \textsf{flushend} package}
% \author{Sigitas Tolu\v{s}is \\ \url{sigitas@vtex.lt}}
% \date{\fileversion~from \filedate}
%
% \maketitle
%
% \section{Introduction}
%
% The package is used to balance columns on any page in twocolumn
% mode. By default it is switched on at the end of document. It is
% expected to work with leftcolumn footnotes (option checkfootnote)
% and rightcolumn top floats (option checkfloat).
%
% To compare with the previous version the package is completely rewritten
% with new balancing algorithm and new options, removed dependency on other packages.
%
% \section{Usage}
%
% Just load the package to balance the last page: that's all.
% To balance some page in middle of document use command
% \cs{flushcolsend} at that page.
%
% \medskip
% \leftline{\textbf{\textit{Available commands}}:}
%
% \begin{description}
%
% \item[\cs{flushend}]
% This macro switches on column balancing on the last page. It is used
% by default.
%
% \item[\cs{raggedend}]
% This macro switches off column balancing on the last page.
%
% \item[\cs{flushcolsend}]
% This macro switches on column balancing on the current page.
%
% \item[\cs{raggedcolsend}]
% This macro switches off column balancing on the current page.
%
% \item[\cs{atColsBreak}\meta{tokens}]
% Adds \meta{tokens} in place of the original column break (made without balancing).
%
% \medskip
% \textit{Example}: |\atColsBreak{\vskip-2pt}|
%
% \item[\cs{atColsEnd}\meta{tokens}]
% Adds \meta{tokens} at the end of right column.
%
% \item[\cs{showcolsendrule}]
% It can be used just for debugging: adds rule to the bottom of columns.
%
% \end{description}
%
% \subsection{Package options}
%
% \begin{description}
% 
% \item[\meta{|spread|}]
%   \texttt{[default]} It enables columns spreading trying to balance.
%
% \item[\meta{|nospread|}]
%   It disables columns spreading trying to balance.
%
% \item[\meta{|shrink|}]
%   \texttt{[default]} It enables columns shrinking trying to balance.
%
% \item[\meta{|noshrink|}]
%   It disables columns shrinking trying to balance.
%
% \medskip
%   \textit{Similiar options exist for single column separatly}: 
%
%   |lspread|, |nolspread|, |lshrink|, |nolshrink| -- for left column  
%
%   |rspread|, |norspread|, |rshrink|, |norshrink| -- for right column  
%
% \item[\meta{|checkfootnote|}]
%   \texttt{[default]} Adds guess and checking for possible footnote on left column.
%
% \item[\meta{|nocheckfootnote|}]
%   Skips guess for possible footnote and ignores any existing one.
%
% \item[\meta{|checkfloat|}]
%   Adds guess for top float on right column. Any box with height bigger then 5|\topskip|
%   is considered as float. There are no user interface to change this limit except 
%   internal macro definition: |\gdef\top@@floatbox@min@default{5\topskip}|
%
%   As guess is too brutal, not accurate, and somehow dangerous in case for text misplacement
%   it is switched off by default.
%
% \item[\meta{|nocheckfloat|}]
%   \texttt{[default]} Skips guess for top float on right column.
%
% \item[\meta{|debug|}]
%   Adds rules to the bottom of columns (just for debugging) and leftcolumn break place.
%   Adds some additional log info.
%
% \item[\meta{|nodebug|}]
%   \texttt{[default]} Skips putting debuging lines and additional info.
%
% \end{description}
%
% \section{Implementation}
%
% Improved balancing (at least it is expected so) is based on using possible spread and shrink
% in both columns checking constructed columns badness.
% Hard coded limit for badness is |101|. Available only as internal macro: |\def\flushend@@column@badness{101}|.
% |\pagediscards| material dimensions are used to restore original vertical skip at original columns break.  
%
% \bigskip
% \leftline{\textbf{\textit{Expected usecase}} \texttt{(with options [checkfootnote,checkfloat])}:}
%
% \begin{verbatim}
%
% --------------------------            --------------------------
% |xxxxxxxxxx    ++++++++++|            |xxxxxxxxxx    ++++++++++|                       
% |xxxxxxxxxx    +        +|            |xxxxxxxxxx    +        +| 
% |xxxxxxxxxx    +        +|            |xxxxxxxxxx    +        +|
% |xxxxxxxxxx    ++++++++++|            |xxxxxxxxxx    ++++++++++|                          
% |xxxxxxxxxx    figure    |            |xxxxxxxxxx    figure    |
% |                        |            |                        |
% |section       xxxxxxxxxx|            |section       yyyyyyyyyy|
% |              xxxxxxxxxx|   -----&gt;   |              yyyyyyyyyy|
% |xxxxxxxxxx    xxxxxxxxxx|            |xxxxxxxxxx    xxxxxxxxxx|
% |xxxxxxxxxx    xxxxxxxxxx|            |xxxxxxxxxx    xxxxxxxxxx|
% |yyyyyyyyyy    xxxxxxxxxx|            |              xxxxxxxxxx|
% |yyyyyyyyyy              |            |---           xxxxxxxxxx|
% |                        |            |footnote      xxxxxxxxxx|
% |---                     |            |                        |
% |footnote                |            |                        |
% --------------------------            --------------------------
%
% \end{verbatim}
% \StopEventually{}
%
% \iffalse
%&lt;*package&gt;
% \fi
%
%/*%    \begin{macrocode}*/
%    \begin{macrocode}

\newif\if@footnote@check \@footnote@checktrue
\newif\if@right@column@spread \@right@column@spreadtrue
\newif\if@right@column@shrink \@right@column@shrinktrue
\newif\if@left@column@spread \@left@column@spreadtrue
\newif\if@left@column@shrink \@left@column@shrinktrue
\newif\if@balance@debug \@balance@debugfalse

\DeclareOption{spread}{%
    \global\@left@column@spreadtrue
    \global\@right@column@spreadtrue
    }
\DeclareOption{nospread}{%
    \global\@left@column@spreadfalse
    \global\@right@column@spreadfalse
    }
\DeclareOption{lspread}{\global\@left@column@spreadtrue}
\DeclareOption{nolspread}{\global\@left@column@spreadfalse}
\DeclareOption{rspread}{\global\@right@column@spreadtrue}
\DeclareOption{norspread}{\global\@right@column@spreadfalse}
\DeclareOption{shrink}{%
    \global\@left@column@shrinktrue
    \global\@right@column@shrinktrue
    }
\DeclareOption{noshrink}{%
    \global\@left@column@shrinkfalse
    \global\@right@column@shrinkfalse
    }
\DeclareOption{lshrink}{\global\@left@column@shrinktrue}
\DeclareOption{nolshrink}{\global\@left@column@shrinkfalse}
\DeclareOption{rshrink}{\global\@right@column@shrinktrue}
\DeclareOption{norshrink}{\global\@right@column@shrinkfalse}
\DeclareOption{checkfootnote}{%
    \AtEndOfPackage{%
        \let\check@@footnoterule@@box\initial@check@@footnoterule@@box
        \@footnote@checktrue
        }%
    }
\DeclareOption{nocheckfootnote}{%
    \AtEndOfPackage{%
        \let\check@@footnoterule@@box\@gobblethree
        \@footnote@checkfalse
        }%
    }
\DeclareOption{checkfloat}{%
    \AtEndOfPackage{%
        \let\top@@floatbox@min\top@@floatbox@min@default
        }%
    }
\DeclareOption{nocheckfloat}{%
    \AtEndOfPackage{%
        \let\top@@floatbox@min\maxdimen
        }%
    }
\DeclareOption{debug}{\global\@balance@debugtrue}
\DeclareOption{nodebug}{\global\@balance@debugfalse}

\ProcessOptions

\newskip\flushend@@lastskip@a
\newskip\flushend@@lastskip@b
\newcount\flushend@@lastnode
\newcount\var@@loop@iter
\newdimen\var@@temp@spread
\newdimen\var@@temp@a
\newdimen\var@@temp@loop
\newdimen\flushend@@page@rule \flushend@@page@rule\z@
\def\showcolsendrule{\global\flushend@@page@rule=.4\p@}
\gdef\top@@floatbox@min@default{5\topskip}
\let\top@@floatbox@min\maxdimen
\def\flushend@@column@badness{101}
\newbox\flushend@@varbox@lastpage
\newbox\flushend@@varbox@a
\newbox\flushend@@varbox@c
\newbox\flushend@@tempbox@a
\newbox\flushend@@tempbox@c
\newbox\flushend@@floatbox
\@ifundefined{@viper}{\newbox\@viper}{}
\@ifundefined{hold@viper}{\newbox\hold@viper}{}
\newtoks\atColsBreak \atColsBreak={}
\newtoks\atColsEnd   \atColsEnd={}
\@ifundefined{fmt@box@adds}{\def\fmt@box@adds#1{#1}}{}
\@ifundefined{fmt@vbox@adds}{\def\fmt@vbox@adds[#1]#2{#2}}{}
\def\wlog@balance@debug#1{\if@balance@debug \wlog{#1}\fi}
\def\log@box@info#1{&lt;box\the#1&gt;(\the\ht#1+\the\dp#1)x\the\wd#1}

\def\unskip@three@kern@penalty{%
    \unskip\unkern\unpenalty
    \unskip\unkern\unpenalty
    \unskip\unkern\unpenalty
    }

\gdef\remove@empty@lastbox@at@balancing#1{%
    %%
    %% Removes lastbox without dimensions.
    %% Removes latest skip, kern, penalty.
    %% Cuts the lastbox's depth bigger then strutbox's depth.
    %%
    \var@@temp@a=\z@
    \setbox\flushend@@tempbox@a\vbox{%
        \unvcopy#1%
        \unskip@three@kern@penalty
        \global\flushend@@lastnode=\lastnodetype
        }%
    \setbox#1\vbox{%
        \unvcopy\flushend@@tempbox@a
        \setbox\z@\lastbox
        \ifdim\dimexpr\ht\z@+\dp\z@+\wd\z@\relax&gt;\z@
            %% not empty lastbox - store depth of the lastbox
            \global\var@@temp@a=\dp\z@
        \else
            %% empty lastbox
            \setbox\z@\box\flushend@@tempbox@a
            \expandafter\unskip@three@kern@penalty
        \fi
        }%
    \ifvoid\flushend@@tempbox@a\else
        %% not empty lastbox - restore original
        \setbox#1\box\flushend@@tempbox@a
    \fi
    \ifdim\var@@temp@a&gt;\z@
        %% cut the depth of the lastbox with the negative skip
        \ifdim\var@@temp@a&gt;\dp\strutbox
        %% it is something more than single line depth
        \else
            \setbox#1\vbox{\unvbox#1\vskip-\var@@temp@a}%
        \fi
    \fi
    }

\def\set@split@topskip@to#1{%
    \splittopskip=#1\relax 
    \vfuzz=\maxdimen
    \vbadness=\maxdimen
    }

\gdef\analyze@leftcolumn@box#1{%
    %%
    %% Try to find footnotes on the leftcolumn
    %%
    \set@split@topskip@to\z@
    \flushend@@lastskip@b\ht#1%
    \advance\flushend@@lastskip@b\dp#1%
    \setbox\flushend@@varbox@a\vbox{%
        \unvbox#1%
        \global\flushend@@lastskip@a\lastskip
        \unskip\unkern\unpenalty
        \global\setbox\flushend@@tempbox@a\lastbox
        }%
    \advance\flushend@@lastskip@b -\ht\flushend@@varbox@a
    \advance\flushend@@lastskip@b -\ht\flushend@@tempbox@a
    \ifvoid\flushend@@tempbox@a
        \ifdim\ht\flushend@@varbox@a&gt;\topskip
            \flushend@@lastskip@b\ht\flushend@@varbox@a
            \var@@temp@a\ht\flushend@@varbox@a
            \loop
                \setbox\flushend@@tempbox@c\vsplit\flushend@@varbox@a to\var@@temp@a
                \ifvoid\flushend@@varbox@a
                    \setbox\flushend@@varbox@a\vbox{\unvbox\flushend@@tempbox@c}%
                    \advance\var@@temp@a -3\p@
                \else
                    \var@@temp@a=-1\p@
                \fi
            \ifdim \var@@temp@a&gt;\z@
            \repeat
            \setbox\flushend@@varbox@a\vbox{\unvbox\flushend@@varbox@a}%
            \setbox\flushend@@tempbox@c\vbox{\unvbox\flushend@@tempbox@c}%
            \advance\flushend@@lastskip@b -\ht\flushend@@varbox@a
            \advance\flushend@@lastskip@b -\ht\flushend@@tempbox@c
            \check@@footnoterule@@box\flushend@@varbox@a\flushend@@lastskip@b
                \flushend@@tempbox@c
            \setbox\flushend@@varbox@a\vbox{\unvbox\flushend@@tempbox@c}%
        \else
            \global\@footnote@checkfalse
        \fi
    \else
        \check@@footnoterule@@box\flushend@@tempbox@a\flushend@@lastskip@b\flushend@@varbox@a
    \fi
    \if@footnote@check
        \ifdim\var@@temp@loop=\ht\flushend@@varbox@a\relax
            \global\advance\var@@loop@iter\@ne
        \fi
        \var@@temp@loop=\ht\flushend@@varbox@a\relax
        \ifnum\var@@loop@iter&lt;3\relax
            %% next iteration
        \else
            %% loop limit, break loop
            \ht\flushend@@varbox@a=\z@
        \fi
        \ifdim\ht\flushend@@varbox@a&gt;\topskip
            \expandafter\analyze@leftcolumn@box\expandafter\flushend@@varbox@a
        \fi
    \fi
    }

\def\get@@footnoterule@@box{%
    \set@split@topskip@to\z@
    \setbox\flushend@@varbox@a\vbox{\strut
        \vskip\z@
        \footnoterule
        \unskip@three@kern@penalty
        }%
    \setbox\flushend@@tempbox@c\vsplit\flushend@@varbox@a to\p@
    \xdef\footnoterule@@box@@ht{\the\ht\flushend@@varbox@a}%
    \xdef\footnoterule@@box@@dp{\the\dp\flushend@@varbox@a}%
    \xdef\footnoterule@@box@@wd{\the\wd\flushend@@varbox@a}%
    \wlog@balance@debug{:footnoterule: \log@box@info{\flushend@@varbox@a}}%
    \setbox\flushend@@tempbox@c\vbox{\unvbox\flushend@@varbox@a}%
    }

\long\def\@gobblethree#1#2#3{}

\def\check@@footnoterule@@box#1#2#3{%
    \ifdim\ht#1=\footnoterule@@box@@ht
        \ifdim\dp#1=\footnoterule@@box@@dp
            \ifdim\wd#1=\footnoterule@@box@@wd
                \ifdim#2=\topskip
                \else
                    \xdef\main@box@height{\the\ht#3}%
                    \xdef\main@box@depth{\the\dp#3}%
                    \xdef\main@box@skip{\the#2}%
                    \wlog@balance@debug{^^J:footnoterule found:
                                        main@box &lt;ht=\main@box@height,
                                        skip=\main@box@skip&gt;
                                       }%
                    \global\let\check@@footnoterule@@box\@gobblethree
                    \global\@footnote@checkfalse
                \fi
            \fi
        \fi
    \fi
    }

\let\initial@check@@footnoterule@@box\check@@footnoterule@@box

\def\analyze@rightcolumn@box#1{%
    %%
    %% Looking for the top floats on the right column.
    %%
    %% Top box is considered as float if box's height 
    %% is larger then \top@@floatbox@min.
    %% So, it is a dangerous feature to be used carefully.
    %%
    \bgroup
        \xdef\top@@floatbox@ht{\z@}%
        \set@split@topskip@to\z@
        \setbox\flushend@@varbox@a\vbox{\strut
            \vskip\z@
            \unvcopy#1%
            }%
        \setbox\flushend@@tempbox@c\vsplit\flushend@@varbox@a to\p@
        \flushend@@lastskip@a\ht\flushend@@varbox@a
        \advance\flushend@@lastskip@a\dp\flushend@@varbox@a
        \ifdim\flushend@@lastskip@a&gt;\z@
            %% analyze non empty rightcolumn box
            \var@@temp@a=3\p@
            \loop
                \setbox\flushend@@tempbox@c\vsplit\flushend@@varbox@a to\var@@temp@a
                \flushend@@lastskip@b\ht\flushend@@varbox@a
                \advance\flushend@@lastskip@b\dp\flushend@@varbox@a
                \ifvoid\flushend@@tempbox@c
                    \advance\var@@temp@a by3\p@
                    \ifdim\var@@temp@a&gt;\flushend@@lastskip@b
                        %% reach column end, break loop
                        \var@@temp@a=-1\p@
                    \fi
                \else
                    \setbox\flushend@@tempbox@c\vbox{\unvbox\flushend@@tempbox@c}%
                    \ifdim\ht\flushend@@tempbox@c&gt;\top@@floatbox@min
                        %% found float; set height; look for the next
                        \setbox\flushend@@tempbox@a\vbox{\splitdiscards}%
                        \ifvoid\flushend@@tempbox@a
                        \else
                            \advance\flushend@@lastskip@b \ht\flushend@@tempbox@a
                            \advance\flushend@@lastskip@b \dp\flushend@@tempbox@a
                        \fi
                        \advance\flushend@@lastskip@b -\flushend@@lastskip@a
                        \flushend@@lastskip@b=-\flushend@@lastskip@b 
                        \xdef\top@@floatbox@ht{\the\flushend@@lastskip@b}%
                        \var@@temp@a=3\p@
                    \else
                        %% break loop
                        \var@@temp@a=-1\p@
                    \fi
                \fi
            \ifdim \var@@temp@a&gt;\z@
            \repeat
        \fi
    \egroup
    }

\def\set@outputbox@with@footnote@and@float{%
    %%
    %% The main unit formatting balanced columns. 
    %%
    %% \flushend@@tempbox@a - left column
    %% \flushend@@tempbox@c - left column with natural dimensions
    %% \flushend@@varbox@a  - right column
    %% \flushend@@varbox@c  - right column with natural dimensions
    %% \flushend@@floatbox  - rightcolumn top float
    %% \@leftcolumn         - void or leftcolumn footnote
    %%
    \@tempdimb\ht\flushend@@varbox@lastpage
    \ifdim\top@@floatbox@ht&gt;\z@
        \advance\@tempdimb \textfloatsep
        \advance\@tempdimb \top@@floatbox@ht
    \fi
    \ifdim\main@box@skip&gt;\z@
        \advance\@tempdimb \main@box@skip
        \advance\@tempdimb \ht\@leftcolumn
    \fi
    \@tempdimb=.5\@tempdimb
    \ifdim\@tempdimb&gt;\@colht
        \@tempdimb=\@colht
    \fi
    \ifdim\main@box@skip&gt;\z@
        \advance\@tempdimb -\main@box@skip
        \advance\@tempdimb -\ht\@leftcolumn
    \fi
    \set@split@topskip@to\topskip
    \loop
        \xdef\saved@tempdimb{\the\@tempdimb}%
        \setbox\flushend@@varbox@a\copy\flushend@@varbox@lastpage
        \setbox\flushend@@tempbox@a\vsplit\flushend@@varbox@a to\@tempdimb
        \ifdim\main@box@skip&gt;\z@
            \setbox\flushend@@tempbox@c\vbox{%
                \unvbox\flushend@@tempbox@a
                \vskip\main@box@skip
                \vskip\z@ plus\p@
                \unvcopy\@leftcolumn
                }%
        \else
            \setbox\flushend@@tempbox@c\vbox{\unvbox\flushend@@tempbox@a}%
        \fi
        \setbox\flushend@@tempbox@a\vbox to\@tempdimb{\unvcopy\flushend@@tempbox@c}%
        \xdef\var@@leftcolumn@badness{\the\badness}%
        \ifdim\top@@floatbox@ht&gt;\z@
            \setbox\flushend@@varbox@c\vbox{%
                \unvcopy\flushend@@floatbox
                \vskip\textfloatsep
                \vskip\z@ plus\p@ minus\p@
                \unvbox\flushend@@varbox@a
                }%
        \else
            \setbox\flushend@@varbox@c\vbox{\unvbox\flushend@@varbox@a}%
        \fi
        \setbox\flushend@@varbox@a\vbox to\@tempdimb{\unvcopy\flushend@@varbox@c}%
        \xdef\var@@rightcolumn@badness{\the\badness}%
        \var@@temp@spread=\ht\flushend@@tempbox@c
        \advance\var@@temp@spread by\dp\flushend@@tempbox@c
        \advance\var@@temp@spread by-\ht\flushend@@varbox@c
        \advance\var@@temp@spread by-\dp\flushend@@varbox@c
        \wlog@balance@debug{-----
                            ^^JLeft: \the\ht\flushend@@tempbox@c
                            +\the\dp\flushend@@tempbox@c\space / \var@@leftcolumn@badness
                            ^^JRight: \the\ht\flushend@@varbox@c
                            +\the\dp\flushend@@varbox@c\space / \var@@rightcolumn@badness
                            ^^JSplit: \the\@tempdimb
                            ^^JExtra height: \the\var@@temp@spread
                           }%
        \ifdim\main@box@skip&gt;\z@
            \wlog@balance@debug{Footnote: \the\dimexpr\main@box@skip + \the\ht\@leftcolumn\relax}%
        \fi
        \ifdim\top@@floatbox@ht&gt;\z@
            \wlog@balance@debug{Float: \the\dimexpr\the\ht\flushend@@floatbox + \textfloatsep\relax}%
        \fi
        \ifnum\var@@leftcolumn@badness&lt;\flushend@@column@badness
            \ifnum\var@@rightcolumn@badness&lt;\flushend@@column@badness
                \ifdim\main@box@skip&gt;\z@
                    \advance\@tempdimb -\main@box@skip
                    \advance\@tempdimb -\ht\@leftcolumn
                \fi
                \var@@temp@spread=\z@
            \fi
        \fi
        \ifdim\var@@temp@spread&lt;\z@
            \if@left@column@spread
                \if@right@column@shrink
                    \ifdim\dimexpr\var@@temp@spread+\pageshrink&gt;\z@
                        \var@@temp@a=\dimexpr\ht\flushend@@tempbox@c-0.5\var@@temp@spread\relax
                    \else
                        \var@@temp@a=-\dimexpr\var@@temp@spread+.5\pageshrink\relax
                    \fi
                    \setbox\flushend@@varbox@a\vbox to\var@@temp@a{\unvcopy\flushend@@tempbox@c}%
                    \ifnum\badness&lt;\flushend@@column@badness
                        \@tempdimb=\var@@temp@a
                        \ifdim\main@box@skip&gt;\z@
                            \advance\@tempdimb -\main@box@skip
                            \advance\@tempdimb -\ht\@leftcolumn
                        \fi
                        \var@@temp@spread=\z@
                    \fi
                    \wlog{[leftcolumn badness]: \number\badness\space on \the\var@@temp@a}%
                    \setbox\flushend@@varbox@a\vbox to\var@@temp@a{\unvcopy\flushend@@varbox@c}%
                    \wlog{[rightcolumn badness]: \number\badness\space on \the\var@@temp@a}%
                \else
                    \setbox\flushend@@varbox@a\vbox to\ht\flushend@@varbox@c{%
                        \unvcopy\flushend@@tempbox@c
                        }%
                    \ifnum\badness&lt;\flushend@@column@badness
                        \@tempdimb=\ht\flushend@@varbox@c
                        \ifdim\main@box@skip&gt;\z@
                            \advance\@tempdimb -\main@box@skip
                            \advance\@tempdimb -\ht\@leftcolumn
                        \fi
                        \var@@temp@spread=\z@
                    \fi
                    \wlog{[leftcolumn badness]: \number\badness on \the\ht\flushend@@varbox@c}%
                    \setbox\flushend@@varbox@a\vbox to\ht\flushend@@varbox@c{%
                        \unvcopy\flushend@@varbox@c
                        }%
                    \wlog{[rightcolumn badness]: \number\badness on \the\ht\flushend@@varbox@c}%
                \fi
            \else
                \if@right@column@shrink
                    \ifdim\dimexpr\var@@temp@spread+\pageshrink&lt;\z@
                    \else
                        \@tempdimb=\ht\flushend@@tempbox@c
                        \ifdim\main@box@skip&gt;\z@
                            \advance\@tempdimb -\main@box@skip
                            \advance\@tempdimb -\ht\@leftcolumn
                        \fi
                        \var@@temp@spread=\z@
                    \fi
                \fi 
            \fi
        \else
            \ifdim\var@@temp@spread&gt;\z@
                \ifdim\dimexpr\@tempdimb+\p@\relax&gt;\@colht
                    \@tempdimb=\@colht
                    \ifdim\main@box@skip&gt;\z@
                        \advance\@tempdimb -\main@box@skip
                        \advance\@tempdimb -\ht\@leftcolumn
                    \fi
                    \var@@temp@spread=\z@
                \fi
            \fi
        \fi
    \ifdim\var@@temp@spread&lt;\z@
        \advance\@tempdimb 1\p@
    \repeat
    %% final construction of the lastpage
    \wlog{- LAST -%
          ^^JExtra skip:\the\var@@temp@spread
          ^^JLeft:\the\ht\flushend@@tempbox@c/\the\dp\flushend@@tempbox@c
          ^^JRight:\the\ht\flushend@@varbox@c/\the\dp\flushend@@varbox@c
          ^^JSplit: \saved@tempdimb
          ^^JOutput:\the\@tempdimb
          ^^JPageshrink: \the\pageshrink
          ^^JPagestretch: \the\pagestretch
          ^^J@colht:\the\@colht
          }%
    \setbox\flushend@@tempbox@c\vsplit\flushend@@varbox@lastpage to\saved@tempdimb
    \ifdim\main@box@skip&gt;\z@
        \@tempdimb=\dimexpr\@tempdimb+\main@box@skip+\ht\@leftcolumn\relax
        \setbox\@leftcolumn\vbox to\@tempdimb{%
            \flushend@@lastskip@a=\dimexpr
                \@tempdimb
                -\ht\flushend@@tempbox@c
                -\main@box@skip
                -\ht\@leftcolumn
                \relax
            \unvbox\flushend@@tempbox@c
            \vskip\main@box@skip
            \vskip\z@ plus\p@
            \unvbox\@leftcolumn
            \prevdepth\z@
            \hrule\@height\flushend@@page@rule width\textwidth
            \vskip-\flushend@@page@rule
            \ifdim\flushend@@lastskip@a&gt;\z@
                \if@left@column@spread
                \else
                    \vss
                \fi
            \else
                \ifdim\flushend@@lastskip@a&lt;\z@
                    \if@left@column@shrink
                    \else
                        \vss
                    \fi
                \fi 
            \fi
            }%
    \else
        \setbox\@leftcolumn\vbox to\@tempdimb{%
            \flushend@@lastskip@a=\dimexpr
                \@tempdimb-\ht\flushend@@tempbox@c
                \relax
            \var@@temp@spread=\dp\flushend@@tempbox@c
            \unvbox\flushend@@tempbox@c
            \ifdim\var@@temp@spread&gt;\dp\strutbox
            \else
                \vskip-\var@@temp@spread
            \fi
            \prevdepth\z@
            \hrule\@height\flushend@@page@rule width\textwidth
            \vskip-\flushend@@page@rule
            \ifdim\flushend@@lastskip@a&gt;\z@
                \if@left@column@spread
                \else
                    \vss
                \fi
            \else
                \ifdim\flushend@@lastskip@a&lt;\z@
                    \if@left@column@shrink
                    \else
                        \vss
                    \fi
                \fi 
            \fi
            }%
    \fi
    \wlog{FLUSHEND [output]: \the\@tempdimb
          ^^JFLUSHEND [leftcolumn badness]: \number\badness
         }%
    \global\ht\@leftcolumn=\the\@tempdima
    \ifdim\top@@floatbox@ht&gt;\z@
        \setbox\@outputbox\vbox to\@tempdimb{%
            \flushend@@lastskip@a=\dimexpr
                \@tempdimb
                -\ht\flushend@@floatbox
                -\textfloatsep
                -\ht\flushend@@varbox@lastpage
                \relax
            \unvbox\flushend@@floatbox
            \vskip\textfloatsep
            \vskip\z@ plus\p@ minus\p@
            \unvbox\flushend@@varbox@lastpage
            \ifdim\flushend@@lastskip@a&gt;\z@
                \if@right@column@spread
                \else
                    \vss
                \fi
            \else
                \ifdim\flushend@@lastskip@a&lt;\z@
                    \if@right@column@shrink
                    \else
                        \vss
                    \fi
                \fi 
            \fi
            }%
    \else
        \setbox\@outputbox\vbox to\@tempdimb{%
            \flushend@@lastskip@a=\dimexpr
                \@tempdimb-\ht\flushend@@varbox@lastpage
                \relax
            \unvbox\flushend@@varbox@lastpage
            \ifdim\flushend@@lastskip@a&gt;\z@
                \if@right@column@spread
                \else
                    \vss
                \fi
            \else
                \ifdim\flushend@@lastskip@a&lt;\z@
                    \if@right@column@shrink
                    \else
                        \vss
                    \fi
                \fi 
            \fi
            }%
    \fi
    \wlog{FUSHEND [rightcolumn badness]: \number\badness}%
    \global\ht\@outputbox=\the\@tempdima
    }

\newdimen\oldbreak@skip

\def\combine@columns@for@balance{%
    %%
    %% Combines lastpage columns for balancing.
    %%
    \setbox\flushend@@tempbox@a\vbox{\pagediscards}%
    \oldbreak@skip=\ht\flushend@@tempbox@a
    \advance\oldbreak@skip by\dp\flushend@@tempbox@a
    \setbox\@outputbox\vbox{\strut
        \vskip\z@
        \unvbox\@outputbox
        }%
    \set@split@topskip@to\z@
    %% Removes topskip
    \setbox\flushend@@tempbox@c\vsplit\@outputbox to\p@
    \ifdim\top@@floatbox@ht&gt;\z@
        %% removes top float from right column (if option enabled)
        \setbox\flushend@@floatbox\vsplit\@outputbox to\top@@floatbox@ht
        \setbox\flushend@@floatbox\vbox{\unvbox\flushend@@floatbox}%
    \fi
    \setbox\flushend@@varbox@lastpage\vbox{%
        \remove@empty@lastbox@at@balancing\flushend@@varbox@a
        \unvbox\flushend@@varbox@a
        \hrule\@height\flushend@@page@rule width\columnwidth
        \vskip-\flushend@@page@rule
        \hrule\@height\z@ width\columnwidth
        \penalty\z@
        \ifdim\var@@temp@a&gt;\z@
            \ifdim\var@@temp@a&gt;\dp\strutbox
            \else
                \vskip\var@@temp@a
            \fi
        \fi
        \vskip\oldbreak@skip
        \the\atColsBreak
        \remove@empty@lastbox@at@balancing\@outputbox
        \unvbox\@outputbox
        \the\atColsEnd
        }%
    }

\def\last@outputdblcol{%
    %%
    %% Redefined \@outputdblcol with columns balancing.
    %%
    \if@firstcolumn
        \global \@firstcolumnfalse
        \global\setbox\@leftcolumn\copy\@outputbox
        \splitmaxdepth\maxdimen
        \vbadness\maxdimen
        \setbox\@outputbox\vbox{\unvbox\@outputbox\unskip}%
        \setbox\@outputbox\vsplit\@outputbox to\maxdimen
        \toks@\expandafter{\topmark}%
        \xdef\@firstcoltopmark{\the\toks@}%
        \toks@\expandafter{\splitfirstmark}%
        \xdef\@firstcolfirstmark{\the\toks@}%
        \ifx\@firstcolfirstmark\@empty
            \global\let\@setmarks\relax
        \else
            \gdef\@setmarks{%
                \let\firstmark\@firstcolfirstmark
                \let\topmark\@firstcoltopmark
                }%
        \fi
    \else
        \global \@firstcolumntrue
        \@tempdima\ht\@leftcolumn
        \advance\@tempdima by\dp\@leftcolumn
        \set@split@topskip@to\topskip
        \var@@temp@spread=\wd\@outputbox
        \xdef\top@@floatbox@ht{\z@}%
        \xdef\main@box@skip{\z@}%
        \ifdim\var@@temp@spread&gt;\z@
            %% rightcolumn non empty
            \setbox\flushend@@varbox@a\vbox{\unvcopy\@outputbox}%
            \ifdim\dimexpr\@colht-\ht\flushend@@varbox@a&gt;\z@\relax
                \if@footnote@check
                    \get@@footnoterule@@box
                    \xdef\main@box@height{\the\ht\@leftcolumn}%
                    \setbox\flushend@@varbox@a\vbox{\unvcopy\@leftcolumn}%
                    \var@@loop@iter\z@ \var@@temp@loop\z@
                    \analyze@leftcolumn@box\flushend@@varbox@a
                \fi
                \ifdim\top@@floatbox@min&lt;\maxdimen
                    \setbox\flushend@@varbox@a\vbox{\unvcopy\@outputbox}%
                    \var@@loop@iter\z@ \var@@temp@loop\z@
                    \analyze@rightcolumn@box\flushend@@varbox@a
                \fi
                \ifdim\main@box@skip&gt;\z@
                    %% footnote in left column
                    \set@split@topskip@to\z@
                    \setbox\flushend@@varbox@a\vsplit\@leftcolumn to\main@box@height
                \else
                    %% no footnote in left column
                    \setbox\flushend@@varbox@a\box\@leftcolumn
                \fi
                \combine@columns@for@balance
            \else
                \xdef\main@box@skip{\maxdimen}%
            \fi
        \else
                %% rightcolumn empty
                \setbox\flushend@@varbox@a\box\@leftcolumn
                \setbox\flushend@@varbox@lastpage\vbox{%
                    \remove@empty@lastbox@at@balancing\flushend@@varbox@a
                    \unvbox\flushend@@varbox@a
                    \the\atColsEnd
                    }%
        \fi
        \ifdim\main@box@skip&lt;\maxdimen
            \set@outputbox@with@footnote@and@float
        \fi
        \setbox\@outputbox\vbox{%
            \hb@xt@\textwidth{%
                \hb@xt@\columnwidth{%
                    \fmt@box@adds{\box\@leftcolumn}\hss}%
                \hfil
                \vrule \@width\columnseprule
                \hfil
                \hb@xt@\columnwidth{%
                    \fmt@box@adds{\box\@outputbox}\hss}%
                }%
            }%
        \global\let\@outputdblcol\saved@orig@@outputdblcol
        \global\atColsEnd{}%
        \ifvoid\hold@viper
        \else
            \setbox\@outputbox\vbox{\box\hold@viper\box\@outputbox}%
        \fi
        \@combinedblfloats
        \csname @setmarks\endcsname
        \@outputpage
        \begingroup
            \@dblfloatplacement
            \@startdblcolumn
            \@whilesw\if@fcolmade\fi
                {\@outputpage\@startdblcolumn}%
            \ifvoid\@viper
            \else
                \global\setbox\@viper\vbox{%
                    \vskip-\stripsep
                    \unvbox\@viper
                    }%
                \csname @viperoutput\endcsname
            \fi
        \endgroup
    \fi
    }

\def\initialize@flushend{%
    %%
    %%  Activates flushend package functionality.
    %%
    \global\let\saved@orig@@outputdblcol\@outputdblcol
    \global\let\balanced@@outputdblcol\last@outputdblcol
    \edef\enddocument{%
        \unexpanded{\let\@outputdblcol\balanced@@outputdblcol}%
        \unexpanded\expandafter{\enddocument}%
        }%
    \g@addto@macro\footnoterule{\vskip\z@}%
    \savingvdiscards=\@ne
    }

\def\flushcolsend{\global\let\@outputdblcol\last@outputdblcol}
\def\raggedcolsend{\global\let\@outputdblcol\saved@orig@@outputdblcol}
\def\flushend{\global\let\balanced@@outputdblcol\last@outputdblcol}
\def\raggedend{\global\let\balanced@@outputdblcol\saved@orig@@outputdblcol}
\if@balance@debug
    \showcolsendrule
\fi
\AtBeginDocument{\initialize@flushend}
%    \end{macrocode}
%
% \iffalse
%&lt;/package&gt;
% \fi
%
% \Finale
</pre></body></html>