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authorNorbert Preining <norbert@preining.info>2019-09-15 03:00:57 +0000
committerNorbert Preining <norbert@preining.info>2019-09-15 03:00:57 +0000
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tree3cae3cde89de26b178894a2e88d9ef5ba89dafcc /macros/latex-dev/required/tools/multicol.dtx
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+% \iffalse meta-comment
+%
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+%
+% \iffalse This is a METACOMMENT
+%
+%% Package `multicol' to use with LaTeX2e
+%% Copyright 1989-2019 Frank Mittelbach
+%%
+%% In addition to the terms of LPPL any distributed version
+%% (unchanged or modified) of multicol has to keep the statement
+%% about the moral obligation for using multicol. In case of major
+%% changes where this would not be appropriate the author of the
+%% changed version should contact the copyright holder.
+%%
+%%
+%% Moral obligation for using multicol:
+%% ------------------------------------
+%%
+%% Users of multicol who wish to include or use multicol or a modified
+%% version in a proprietary and commercially market product are asked
+%% under certain conditions (see below) for the payment of a license
+%% fee. The size of this fee is to be determined, in each instance,
+%% by the commercial user, depending on his/her judgment of the value of
+%% multicol for his/her product.
+%%
+%%
+%% The conditions for this are as follows:
+%%
+%% The producer of a proprietary and commercially market product
+%% that involves typesetting using multicol is asked to determine
+%% the value of a license fee for using multicol if
+%%
+%% - the product is a document and the producer has decided to
+%% include multicol to typeset (parts of) the document or has
+%% directed the author of the document to include multicol (for
+%% example, by providing a class file to be used by the author)
+%%
+%% - the product is a LaTeX class or package that includes multicol
+%%
+%%
+%% There is no moral obligation in case
+%%
+%% - the product is a document but producer has not directed
+%% the author to include multicol (in that case the moral obligation
+%% lies with the author of the document)
+%%
+%% - the product does not involve typesetting, e.g., consists, for
+%% example, of distributing multicol and its documentation.
+%%
+%% - the product is not proprietary, i.e., is made available as free
+%% software itself (which doesn't prohibit its commercial marketing)
+%%
+%% - multicol is used for non-commercial purposes
+%%
+%%
+%% Determining a license fee might result in a license fee of zero
+%% (i.e., no payment) in case a producer has determined that the use
+%% of multicol has no enhancing effect on the product. This is a
+%% plausible scenario, i.e., in the above two cases the producer is
+%% only asked to evaluate the value of multicol for the product
+%% not for the payment of a license fee per se (which might or might
+%% not follow from this evaluation).
+%%
+%% The license fee, if any, can be payed either to the LaTeX3 fund
+%% (see ltx3info.txt in the base LaTeX distribution) or to the author of
+%% the program who can be contacted at
+%%
+%% Frank.Mittelbach@latex-project.org
+%%
+%<*dtx>
+ \ProvidesFile{multicol.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}[2018-04-01]
+%<package>
+%<package>\providecommand\DeclareRelease[3]{}
+%<package>\providecommand\DeclareCurrentRelease[2]{}
+%<package>
+%<package>\DeclareRelease{}{2017-04-11}{multicol-2017-04-11.sty}
+%<package>\DeclareCurrentRelease{}{2018-04-01}
+%<package>
+%<package>\ProvidesPackage{multicol}
+%<driver> \ProvidesFile{multicol.drv}
+% \fi
+% \ProvidesFile{multicol.dtx}
+ [2019/03/01 v1.8w multicolumn formatting (FMi)]
+%
+%
+%%
+%
+% \changes{v1.5n}{1997/06/05}{Applied improvement of documentation,
+% kindly done by Robin Fairbairns.}
+% \changes{v1.4h}{1992/06/04}{Added mark tracing with
+% tracingmulticols$\ge2$}
+% \changes{v1.4a}{1992/02/11}{Added support for multicol in inner mode}
+% \changes{v1.0d}{1989/05/17}{All lines shortened to 72 or less.}
+% \changes{v1.0e}{1989/06/21}{Redefinition of description env. to use
+% \cs{descriptionmargin}\quotechar=5pt
+% in documentation.}
+% \changes{v1.0f}{1989/07/11}{Changed \cs{z@} to 0pt in redefinition of
+% description.}
+% \changes{v1.1a}{1989/09/20}{\cs{multicolssep} changed to \cs{multicolsep}.}
+%
+% \def\description{\list{}{\labelwidth 0pt \leftmargin\descriptionmargin
+% \itemindent-\leftmargin \let\makelabel\descriptionlabel}}
+% \newdimen\descriptionmargin \descriptionmargin=5pt
+%
+% \DoNotIndex{\@M,\@Mi,\@bsphack,\@cclv,\@colht,\@currlist,\@deferlist}
+% \DoNotIndex{\@elt,\@esphack,\@floatplacement}
+% \DoNotIndex{\@ifundefined,\@ifnextchar,\@makecol}
+% \DoNotIndex{\@ne,\@outputpage,\@scolelt,\@spaces,\@tempb,\@tempcnta}
+% \DoNotIndex{\@width}
+% \DoNotIndex{\addvspace,\advance,\allowbreak}
+% \DoNotIndex{\baselineskip,\begingroup,\box,\columnsep,\copy,\count}
+% \DoNotIndex{\count@,\def,\dimen@,\divide,\docdate}
+% \DoNotIndex{\edef,\eject,\egroup,\else,\endgroup,\endinput}
+% \DoNotIndex{\fi,\fileversion,\filedate}
+% \DoNotIndex{\gdef,\global}
+% \DoNotIndex{\hbox,\hfil,\hrule,\ht,\hss}
+% \DoNotIndex{\ifdim,\ifnum,\ifvoid,\ignorespaces,\insert,\immediate}
+% \DoNotIndex{\let,\loop}
+% \DoNotIndex{\maxdepth,\message,\multiply}
+% \DoNotIndex{\newbox,\newcount,\newdimen,\newskip,\number,\newpage}
+% \DoNotIndex{\outputpenalty,\p@,\penalty}
+% \DoNotIndex{\relax,\repeat,\setbox,\skip,\space,\splitmaxdepth}
+% \DoNotIndex{\splittopskip,\string,\sixt@@n}
+% \DoNotIndex{\the,\thepage,\thr@@,\topskip,\tw@,\typeout}
+% \DoNotIndex{\unvbox,\vbox,\vfill,\vsplit,\voidb@x,\vrule}
+% \DoNotIndex{\write,\wd}
+% \DoNotIndex{\z@}
+%
+% \MakeShortVerb{\|}
+% \newcommand{\mc}{\textsf{multicols}}
+% \newcommand{\TUB}{{\sl TUGboat\/}}
+% \newcommand{\TB}{{\sl\TeX book\/}}
+%
+%
+% \setcounter{StandardModuleDepth}{2}
+% \setcounter{collectmore}{3}
+%
+% \GetFileInfo{multicol.dtx}
+% \title{An environment for multicolumn output\thanks{This file
+% has version number \fileversion, last
+% revised \filedate.}%
+% \thanks{Note: This package is released under terms which affect
+% its use in commercial applications. Please see the details at
+% the top of the source file.}}
+% \author{Frank Mittelbach\\
+% {\rm Email:} see top of the source file}
+% \date{Printed \today}
+%
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+% \begin{abstract}
+% This article describes the use and the implementation of the \mc{}
+% environment. This environment allows switching between
+% one and multicolumn format on the same page. Footnotes are handled
+% correctly (for the most part), but will be placed at the bottom of
+% the page and not under each column. \LaTeX{}'s float mechanism,
+% however, is partly disabled in this implementation. At the
+% moment only page-wide floats (i.e., star-forms) can be used within
+% the scope of the environment.
+% \end{abstract}
+%
+% \begin{multicols}{3}[\section*{Preface to version 1.8}]
+% The 1.8 release improves on the balancing approach. If due to a
+% limited number of break points (e.g., due to large objects) the
+% balanced columns exceed the available vertical space, then
+% balancing is canceled and a normal page is produced first. Some
+% overflow is allowed (controlled by the parameter
+% |\maxbalancingoverflow| which defaults to 12pt). This ensures
+% that we only cut a normal page if we get enough material carried
+% over to next page.
+%
+% Also added was support for |\enlargethispage|. This means it is
+% now possible to request a page to be artificially enlarged or
+% shortened. Note that if you enlarge pages by more than one line
+% you may have to increase the \textsf{collectmore} counter value to
+% ensure that enough material is being picked up.
+%
+% This command was used on the second page of this manual to shorten
+% it by one line, in order to get rid of a number of widow lines on
+% the following pages.
+%
+% There are also some small enhancements to the balancing algorithm
+% including a ways to require a minimum number of rows in the result.
+%
+% Finally, version 1.8 adds the command |\docolaction| to help with
+% more complicated actions that depend on the current column. This
+% command expects 3 arguments: code that is executed if we are in
+% the ``first'' column, code to execute if we end up in any
+% ``middle'' column (if there are more than two) and finally code to
+% execute if we are in the ``last'' column. Thus
+%\begin{verbatim}
+% \docolaction{first}
+% {middle}{last}
+%\end{verbatim}
+% would typeset a different word depending the type of column this
+% code is executed. Using it like this is probably pointless, but
+% you can imagine applications like writing something into the
+% nearest margin, etc.
+%
+% As this feature needs at least two \LaTeX{} runs to produce correct
+% results and as it adds to the processing complexity it is only
+% made available if one add the option \texttt{colaction} when
+% loading the package.
+%
+% \end{multicols}
+%
+%
+% \begin{multicols}{3}[\section*{Preface to version 1.7
+% (right to left support)}]
+% The 1.7 release adds support for languages that are typeset
+% right-to-left. For those languages the order of the columns on the page
+% also need to be reversed---something that wasn't supported before. The next
+% paragraph demonstrates the result (as it is typeset as if we are writing
+% in a left-to-right language--- so read the rightmost column
+% first). The change is initialized via
+% |\RLmulticolcolumns| and returning to left-right (default)
+% is done via |\LRmulticolcolumns|.
+% \end{multicols}
+%
+% \RLmulticolcolumns
+%
+% \begin{multicols}{3}
+% Right-to-left typesetting will only reverse the column orders. Any
+% other support needed will have to be provided by other means,
+% e.g., using appropriate fonts and reversing the writing directions
+% within the columns. As footnotes are typeset in full measure the
+% footnote rule needs to be redefined as if they are below a single
+% column, i.e., using |\textwidth| not |\columnwidth|. For example:
+%\begin{verbatim}
+%\renewcommand \footnoterule{%
+% \kern-3pt\hbox to\textwidth
+% {\hskip .6\textwidth
+% \hrulefill }%
+% \kern2.6pt}
+%\end{verbatim}
+% \end{multicols}
+%
+% \LRmulticolcolumns
+%
+% \begin{multicols}{3}[\section*{Preface to version 1.5 + 1.6}]
+% \hbadness=10000
+% The 1.5 release contains two major changes: \mc{} will now
+% support up to 10 columns and two more tuning possibilities have
+% been added to the balancing routine. The balancing routine now
+% checks the badness
+% of the resulting columns and rejects solutions that are larger
+% than a certain threshold.
+% At the same time \mc{} has been upgraded to run under \LaTeXe{}.
+%
+% Later changes to 1.5 include |\columnbreak| and |multicols*|.
+%
+% For version 1.6 micro-spacing around the boxes produced by \mc{}
+% has been improved to allow for baseline-grid typesetting.
+% \end{multicols}
+%
+%
+% \setcounter{collectmore}{2}
+% \begin{multicols}{3}[\section{Introduction}]
+% \hbadness=10000
+% Switching between two-column and one-column layout is possible in
+% \LaTeX{}, but every use of |\twocolumn| or |\onecolumn|
+% starts a new page. Moreover, the last page of two-column output
+% isn't balanced and this often results in an empty, or nearly
+% empty, right column. When I started to write macros for
+% \textsf{doc.sty} (see ``The \texttt{doc}--Option'', \TUB\
+% volume 10~\#2, pp.~245--273) I thought that it would be nice to
+% place the index
+% on the same page as the bibliography. And balancing the last page
+% would not only look better, it also would save space; provided of
+% course that it is also possible to start the next article on the
+% same page. Rewriting the index environment was comparatively easy,
+% but the next goal, designing an environment which takes care of
+% footnotes, floats, etc., was a harder task. It took me a whole
+% weekend\footnote{I started with the algorithm given in the \TeX
+% book on page 417. Without this help a weekend would not have been
+% enough. (This remark was made in the documentation of the initial
+% release, since then several hundreds more hours went into
+% improving the original code.)} to get together the few lines of
+% code below and there is
+% still a good chance that I missed something after all.
+%
+% Try it and, hopefully, enjoy it; and {\em please\/} direct bug
+% reports and suggestions back to Mainz.
+% \end{multicols}
+%
+%
+% \setcounter{collectmore}{0}
+% \begin{multicols}{3}[\section{The User Interface}]
+% \hbadness=10000
+% To use the environment one simply says\\*[2mm]
+% \hspace*{2mm}|\begin{multicols}{|\meta{number}|}|
+% \hspace*{12mm}\meta{multicolumn text}\\
+% \hspace*{2mm}|\end{multicols}|\\[2mm]
+% where \meta{number} is the required number of columns and
+%^^A\meta{multicolumn text}
+% $\langle${\it multi\-column text\/}$\rangle$ may contain arbitrary
+% \LaTeX{} commands, except that floats and marginpars are not
+% allowed in the current implementation\footnote{This is dictated by
+% lack of time. To implement floats one has to reimplement the
+% whole \LaTeX{} output routine.}.
+%
+% \enlargethispage{-1\baselineskip}
+%
+% \DescribeMacro\premulticols
+% As its first action, the \textsf{multicols} environment measures the
+% current page to determine whether there is enough room for some
+% portion of multicolumn output. This is controlled by the
+% \meta{dimen} variable |\premulticols| which can be changed by
+% the user with ordinary \LaTeX{} commands.
+% \DescribeMacro\multicolsep
+% If the space is less than |\premulticols|, a new page is
+% started. Otherwise, a |\vskip| of |\multicolsep| is
+% added.\footnote{Actually the added space may be less because we use
+% \cs{addvspace} (see the \LaTeX{} manual for further
+% information about this command).}
+%
+% \DescribeMacro\postmulticols
+% When the end of the \mc{} environment is encountered, an
+% analogous mechanism is employed, but now we test whether there is a
+% space larger than |\postmulticols| available. Again we add
+% |\multicolsep| or start a new page.
+%
+% It is often convenient to spread some text over all columns, just
+% before the multicolumn output, without any page break in between. To
+% achieve this the \mc{} environment has an optional second
+% argument which can be used for this purpose. For example, the text
+% you are now reading was started with
+% \begin{verbatim}
+% \begin{multicols}{3}
+% [\section{The User
+% Interface}] ...
+%\end{verbatim}
+% If such text is unusually long (or short) the value of
+% |\premulticols| might need adjusting to prevent a bad page
+% break. We therefore provide a third argument which can be used to
+% overwrite the default value of |\premulticols| just for this
+% occasion. So if you want to combine some longer single column text
+% with a multicols environment you could write
+% \begin{verbatim}
+% \begin{multicols}{3}
+% [\section{Index}
+% This index contains ...]
+% [6cm]
+% ...
+%\end{verbatim}
+%
+%
+% \DescribeMacro\columnsep
+% The space between columns is controlled by the length parameter
+% |\columnsep|. The width for the individual columns is automatically
+% calculated from this parameter and the current |\linewidth|. In this
+% article a value of \textsf{\the\columnsep} was used.
+%
+%
+% \DescribeMacro\columnseprule
+% Separation of columns with vertical rules is achieved by setting the
+% parameter |\columnseprule| to some positive value. In this
+% article a value of \textsf{.4pt} was used.
+%
+% \DescribeMacro\columnseprulecolor
+% The color of the rules separating the columns can be specified through
+% |\columnseprulecolor|. The default value is |\normalcolor|.
+%
+% \DescribeMacro\multicolbaselineskip
+% Since narrow columns tend to need adjustments in interline spacing
+% we also provide a \meta{skip} parameter called
+% |\multicolbaselineskip| which is added to the
+% |\baselineskip| parameter inside the \mc{}
+% environment. Please use this parameter with care or leave it alone;
+% it is intended only for package file designers since even small
+% changes might produce totally unexpected changes to your document.
+%
+%
+% \subsection{Balancing columns}
+%
+%
+% Besides the previously mentioned parameters, some others are
+% provided to influence the layout of the columns generated.
+%
+% Paragraphing in \TeX{} is controlled by several parameters. One of
+% the most important is called |\tolerance|: this controls the
+% allowed `looseness' (i.e.\ the amount of blank space between words).
+% Its default value is 200 (the \LaTeX{} |\fussy|) which is too
+% small for narrow columns. On the other hand the |\sloppy|
+% declaration (which sets |\tolerance| to $10000=\infty$) is too
+% large, allowing really bad spacing.\footnote{Look at the next
+% paragraph, it was set with the \cs{sloppy} declaration.}
+%
+% \begin{sloppypar}
+% \DescribeMacro\multicoltolerance \DescribeMacro\multicolpretolerance
+% We therefore use a |\multicoltolerance| parameter for the
+% |\tolerance| value inside the \mc{} environment. Its default value
+% is 9999 which is less than infinity but `bad' enough for most
+% paragraphs in a multicolumn environment. Changing its value should
+% be done outside the \mc{} environment. Since |\tolerance| is set
+% to |\multicoltolerance| at the beginning of every \textsf{multicols}
+% environment one can locally overwrite this default by assigning
+% \verb*+\tolerance = +\meta{desired value}. There also exists a
+% |\multicolpretolerance| parameter holding the value for
+% |\pretolerance| within a \mc{} environment. Both parameters are
+% usually used only by package designers.
+% \end{sloppypar}
+%
+% Generation of multicolumn output can be divided into two parts. In
+% the first part we are collecting material for a page, shipping it
+% out, collecting material for the next page, and so on. As a second
+% step, balancing will be done when the end of the \mc{} environment
+% is reached.
+% In the first step \TeX{} might consider more material whilst
+% finding the final column content than it actually uses when shipping out the
+% page. This might cause a problem if a footnote is encountered in
+% the part of the input considered, but not used, on the current page.
+% In this case the footnote might show up on the current page, while the
+% footnotemark corresponding to this footnote might be set on the next
+% one.\footnote{The reason behind this behavior is the asynchronous
+% character of the \TeX{} {\it page\_builder}.
+% However, this
+% could be avoided by defining very complicated output
+% routines which don't use \TeX{} primitives like
+% \cs{insert} but do everything by hand.
+% This is clearly beyond the scope of a weekend problem.}
+% Therefore the \mc{} environment gives a warning
+% message\footnote{This message will be generated even if there are no
+% footnotes in this part of the text.} whenever it is unable to use
+% all the material considered so far.
+%
+% If you don't use footnotes too often the chances of something
+% actually going wrong are very slim, but if this happens you can help
+% \TeX{} by using a |\pagebreak| command in the final document.
+% Another way to influence the behavior of \TeX{} in this respect is
+% given by the counter variable `\textsf{collectmore}'. If you use the
+% |\setcounter| declaration to set this counter to \meta{number},
+% \TeX{} will consider \meta{number} more (or less) lines before
+% making its final decision. So a value of $-1$ may solve all your
+% problems at the cost of slightly less optimal columns.
+%
+%
+% In the second step (balancing columns) we have other bells and
+% whistles. First of all you can say |\raggedcolumns| if you
+% don't want the bottom lines to be aligned.
+% The default is |\flushcolumns|, so \TeX{} will normally try to
+% make both
+% the top and bottom baselines of all columns align.
+%
+% If there is only a small amount of material available for balancing
+% then you may end up with very few lines per column. In an extreme
+% case there may be only one line which looks distinctly odd. In that
+% case it might be better to have more material distributed to the
+% earlier columns even if that means that later columns are empty or
+% partially empty. This is controlled through the counter
+% `\textsf{minrows}' (default 1). If set to a higher value then the
+% balancing will have at least that many rows in the first column (and
+% also all further columns until it runs outs of material).
+%
+% Additionally you can set another counter, the `\textsf{unbalance}'
+% counter, to some positive \meta{number}. This will make all but the
+% right-most column \meta{number} of lines longer than they would
+% normally have been. `Lines' in this context refer to normal text
+% lines (i.e.\ one |\baselineskip| apart); thus, if your columns
+% contain displays,
+% for example, you may need a higher \meta{number}
+% to shift something from one column into another. A negative value can make sense if
+% you have set \textsf{minrows} and want to locally adjust that.
+%
+% Unlike `\textsf{collectmore},' the `\textsf{unbalance}' counter is reset
+% to zero at the end of the environment so it only applies to one
+% \mc{} environment.
+%
+% The two methods may be combined but I suggest using these features
+% only when fine tuning important publications.
+%
+% Two more general tuning possibilities were added with version~1.5.
+% \TeX{} allows to measure the badness of a column in terms of an
+% integer value, where 0 means optimal and any higher value means a
+% certain amount of extra white space. 10000 is considered to be
+% infinitely bad (\TeX{} does not distinguish any further). In addition
+% the special value 100000 means overfull (i.e., the column contains
+% more text than could possibly fit into it).
+%
+% The new release now measures every generated column and ignores
+% solutions where at least one column has a badness being larger than
+% the value of the counter \textsf{columnbadness}. The default value for
+% this counter is 10000, thus \TeX{} will accept all solutions except
+% those being overfull.
+% By setting the counter to a smaller value you can force the algorithm
+% to search for solutions that do not have columns with a lot of white
+% space.
+%
+% However, if the setting is too low, the algorithm may not find any
+% acceptable solution at all and will then finally choose the extreme
+% solution of placing all text into the first column.
+%
+% Often, when columns are balanced, it is impossible to find a solution
+% that distributes the text evenly over all columns. If that is the case
+% the last column usually has less text than the others. In the earlier
+% releases this text was stretched to produce a column with the same
+% height as all others, sometimes resulting in really ugly looking
+% columns.
+%
+% In the new release this stretching is only done if the badness of
+% the final column is not larger than the value of the counter
+% \textsf{finalcolumnbadness}. The default setting is 9999, thus preventing
+% the stretching for all columns that \TeX{} would consider infinitely
+% bad. In that case the final column is allowed to run short which gives
+% a much better result.
+%
+% And there are two more parameters of some experimental nature, one
+% called |\multicolovershoot| the other |\multicolundershoot|. They
+% control the amount of space a column within the \mc{} environment is
+% allowed to be ``too full'' or ``too short'' without affecting the
+% column badness. They are set to 0pt and 2pt, respectively.
+%
+% Finally, when doing the balancing at the end, columns may become
+% higher than the remaining available space. In that case the
+% algorithm aborts and instead generates a normal page. However, if the
+% amount is not too large, e.g., a line or so, then it might be better to
+% keep everything on the same page instead of starting a new page with
+% just one line after balancing. So the parameter
+% |\maxbalancingoverflow| governs this process: only when the excess
+% gets larger than its value balancing is aborted.
+%
+% \subsection{Not balancing the columns}
+%
+% Although this package was written to solve the problem of balancing
+% columns, I got repeated requests to provide a version where all
+% white space is automatically placed in the last column or
+% columns. Since version v1.5q this now exists: if you use
+% \texttt{multicols*} instead of the usual environment the columns on
+% the last page are not balanced. Of course, this environment only
+% works on top-level, e.g., inside a box one has to balance to
+% determine a column height in absence of a fixed value.
+%
+%
+% \subsection{Manually breaking columns}
+%
+% Another request often voiced was: ``How do I tell \LaTeX{} that it
+% should break the first column after this particular line?''. The
+% |\pagebreak| command (which works with the two-column option of
+% \LaTeX{}) is of no use here since it would end the collection phase
+% of \mc{} and thus all columns on that page. So with version 1.5u
+% the |\columnbreak| command was added. If used within a paragraph it
+% marks the end of the current line as the desired breakpoint. You can
+% observe its effect on
+% the previous page where three lines of text have been artificially
+% forced into the second column (resulting in some white
+% space between paragraphs in the first column).
+%
+% \subsection{Floats inside a \mc{} environment}
+%
+% Within the \mc{} environment the usual star float commands are
+% available but their function is somewhat different as in the
+% two-column mode of standard \LaTeX. Stared floats, e.g.,
+% \texttt{figure*}, denote page wide floats that are handled in a similar
+% fashion as normal floats outside the \mc{} environment. However,
+% they will never show up on the page where they are encountered. In
+% other words, one can influence their placement by specifying a
+% combination of \texttt{t}, \texttt{b}, and/or \texttt{p} in their optional
+% argument, but \texttt{h} doesn't work because the first possible place
+% is the top of the next page. One should also note, that this means
+% that their placement behavior is determined by the values of
+% |\topfraction|, etc.\ rather than by |\dbl...|.
+%
+%
+% \subsection{Support for right-to-left typesetting}
+%
+% In right-to-left typesetting the order of the columns on the page
+% also need to be reversed, i.e., the first column has to appear on the far
+% right and the last column on the left. This is supported through the
+% commands |\RLmulticolcolumns| (switching to right-to-left typesetting)
+% and |\LRmulticolcolumns| (switching to left-to-right typesetting) the
+% latter being the default.
+%
+% \subsection{Warnings}
+%
+% Under certain circumstances the use of the \mc{} environment may
+% result in some
+% warnings from \TeX{} or \LaTeX{}. Here is a list
+% of the important ones and the possible cause:
+% \begin{description}
+%
+% \item[] {\hspace*{-\labelsep}\tt Underfull \string\hbox\space
+% (badness ...)}
+%
+% As the columns are often very narrow \TeX{} wasn't able to find a
+% good way to break the paragraph. Underfull denotes a loose line but
+% as long as the badness value is below $10000$ the result is probably
+% acceptable.
+%
+% \item[]
+% {\hspace*{-\labelsep}\tt Underfull \string\vbox\space ... while
+% \string\output\space is active}
+%
+% If a column contains a character with an unusual depth, for
+% example a `(', in the bottom line then this message may show up. It
+% usually has no significance as long as the value is not more than a
+% few points.
+%
+% \item[] {\hspace*{-\labelsep}\tt LaTeX Warning: I moved some lines
+% to the next page}
+%
+% As mentioned above, \mc{} sometimes screws up the footnote
+% numbering. As a precaution, whenever there is a footnote on a
+% page where \mc{} had to leave a remainder for the following
+% page this warning appears. Check the footnote numbering on this
+% page. If it turns out that it is wrong, you have to manually break
+% the page using |\newpage| or |\pagebreak[..]|.
+%
+% \item[] {\hspace*{-\labelsep}\tt Floats and marginpars not allowed
+% inside `multicols' environment!}
+%
+% This message appears if you try to use the |\marginpar| command or
+% an unstarred version of the \textsf{figure} or \textsf{table} environment.
+% Such floats will disappear!
+%
+% \item[] {\hspace*{-\labelsep}\tt Very deep columns!
+% Grid alignment might be broken}
+%
+% This message can only appear if the option \texttt{grid} was
+% chosen. In that case it will show up if a column has a very large
+% depth so that \mc{} is unable to back up to its baseline. This
+% is only relevant if one tries to produce a document where all
+% text lines are aligned at an invisible grid, something that
+% requires careful adjustment of many parameters and macros, e.g.,
+% heading definitions.
+%
+% \end{description}
+%
+%
+% \subsection{Tracing the output}
+%
+% To understand the reasoning behind the decisions \TeX{} makes when
+% processing a \mc{} environment, a tracing mechanism is provided.
+% If you set the counter `\texttt{tracingmulticols}'
+% to a positive \meta{number} you then
+% will get some tracing information on the terminal and in the
+% transcript file:
+% \begin{description}
+% \item[$\meta{number}=1$.] \TeX{} will now tell you, whenever it
+% enters or leaves a \mc{} environment, the number of columns it
+% is working on and its decision about starting a new page before
+% or after the environment.
+% \item[$\meta{number}=2$.]
+% In this case you also get information from the balancing routine:
+% the heights tried for the left and right-most columns,
+% information about shrinking if the |\raggedcolumns|
+% declaration is in force and the value of the `\textsf{unbalance}'
+% counter if positive.
+% \item[$\meta{number}= 3$.] Setting \meta{number}\pagebreak[2] to
+% this value will additionally trace the mark handling
+% algorithm. It will show what marks are found, what marks are
+% considered, etc. To fully understand this information you will
+% probably have to read carefully trough the implementation.
+% \item[$\meta{number}\geq 4$.] Setting \meta{number}\pagebreak[2] to
+% such a high value will additionally place an |\hrule| into your
+% output, separating the part of text which had already been
+% considered on the previous page from the rest. Clearly this
+% setting should {\em not\/} be used for the final output. It will
+% also activate even more debugging code for mark handling.
+% \end{description}
+%
+%
+% \end{multicols}
+%
+% \begin{multicols}{3}[\section{Prefaces to older versions}
+% \subsection{Preface to version 1.4}]
+% \hbadness=10000
+% Beside fixing some bugs as mentioned in the \textsf{multicol.bug} file
+% this new release enhances the \mc{} environment by allowing for
+% balancing in arbitrary contexts. It is now, for example, possible
+% to balance text within a \mc{} or a \textsf{minipage} as shown in
+% \ref{tab:newcmds} where a \textsf{multicols} environment within a
+% \textsf{quote} environment was used. It is now even possible to nest
+% \mc{} environments.
+%
+% The only restriction to such inner \mc{} environments (nested, or
+% within \TeX's internal vertical mode) is that such variants will
+% produce a box with the balanced material in it, so that they can
+% not be broken across pages or columns.
+%
+% Additionally I rewrote the algorithm for balancing so that it will
+% now produce slightly better results.
+%
+% I updated the source documentation but like to apologize in
+% advance for some `left over' parts that slipped through the
+% revision.
+%
+% A note to people who like to improve the balancing algorithm of
+% \mc{}: The balancing routine is now placed into a single macro
+% which is called |\balance@columns|. This means that one can easily
+% try different balancing routines by rewriting this macro. The
+% interface for it is explained in table \ref{tab:balance}. There are
+% several improvements possible, one can think of integrating the
+% |\badness| function of \TeX3, define a faster algorithm for finding
+% the right column height, etc. If somebody thinks he/she has an
+% enhancement I would be pleased to learn about it. But please obey
+% the copyright notice and don't change \textsf{multicol.dtx} directly!
+% \begin{table*}
+% \begin{quote}
+% \begin{multicols}{2}
+% \raggedcolumns
+% The macro |\balance@columns| that contains the code for balancing
+% gathered material is a macro without parameters. It assumes that
+% the material for balancing is stored in the box |\mult@box| which
+% is a |\vbox|. It also ``knows'' about all parameters set up by the
+% \mc{} environment, like |\col@number|, etc. It can also assume
+% that |\@colroom| is the still available space on the current page.
+%
+% When it finishes it must return the individual columns in boxes
+% suitable for further processing with |\page@sofar|. This means
+% that the left column should be stored in box register
+% |\mult@gfirstbox|, the next
+% in register |\mult@firstbox|${}+2$, \ldots,
+% only the last one as an exception in
+% register |\mult@grightbox|. Furthermore it has to set up
+% the two macros
+% |\kept@firstmark| and |\kept@botmark| to hold the values for the
+% first and bottom mark as found in the individual columns. There
+% are some helper functions defined in section \ref{sec:v14} which
+% may be used for this. Getting the marks right ``by hand'' is
+% non-trivial and it may pay off to first take a look at the
+% documentation and implementation of |\balance@columns| below
+% before trying anew.
+% \end{multicols}
+% \end{quote}
+% \vspace*{-3ex}
+% \vspace*{-0ex}
+% \caption{Interface description for \cs{balance@columns}}
+% \label{tab:balance}
+% \end{table*}
+% \end{multicols}
+%
+% \begin{multicols}{3}[\subsection{Preface to version 1.2}]
+% \hbadness=10000
+% After the article about the \mc{} environment was published in
+% \TUB\ 10\#3, I got numerous requests for these macros. However, I
+% also got a changed version of my style file, together with a
+% letter asking me if I would include the changes to get better
+% paragraphing results in the case of narrow lines. The main
+% differences to my original style option were additional parameters
+% (like |\multicoladjdemerits| to be used for |\adjdemerits|, etc.)
+% which would influence the line breaking algorithm.
+%
+% But actually resetting such parameters to zero or even worse to a
+% negative value won't give better line breaks inside the \mc{}
+% environment. \TeX{}s line breaking algorithm will only look at
+% those possible line breaks which can be reached without a badness
+% higher than the current value of |\tolerance| (or |\pretolerance|
+% in the first pass). If this isn't possible, then, as a last
+% resort, \TeX{} will produce overfull boxes. All those (and only
+% those) possible break points will be considered and finally the
+% sequence which results in the fewest demerits will be chosen. This
+% means that a value of $-1000$ for |\adjdemerits| instructs \TeX{}
+% to prefer visibly incompatible lines instead of producing better
+% line breaks.
+%
+% However, with \TeX{} 3.0 it is possible to get decent line breaks
+% even in small columns by setting |\emergencystretch| to an
+% appropriate value. I implemented a version which is capable of
+% running both in the old and the new \TeX{} (actually it will
+% simply ignore the new feature if it is not available). The
+% calculation of |\emergencystretch| is probably incorrect. I
+% made a few tests but of course one has to have much more experience
+% with the new possibilities to achieve the maximum quality.
+%
+% Version 1.1a had a nice `feature': the penalty for using the
+% forbidden floats was their ultimate removal from \LaTeX{}s
+% |\@freelist| so that after a few |\marginpar|s inside the \mc{}
+% environment floats where disabled forever. (Thanks to Chris
+% Rowley for pointing this out.) I removed this misbehavior and at
+% the same time decided to allow at least floats spanning all
+% columns, e.g., generated by the |figure*| environment. You can
+% see the new functionality in table~\ref{tab:newcmds} which was
+% inserted at this very point.
+% \begin{table*}
+% \small
+% \setlength{\multicolsep}{0pt}
+% \begin{quote}
+% \begin{multicols}{2}
+% |\setemergencystretch|: This is a hook for people who like
+% to play around. It is supposed to set the
+% |\emergencystretch| \meta{dimen} register provided in the
+% new \TeX{} 3.0. The first argument is the number of columns and
+% the second one is the current |\hsize|. At the moment the
+% default definition is $4\texttt{pt} \times |#1|$, i.e.\ the
+% |\hsize| isn't used at all. But maybe there are better
+% formulae.
+%
+% \setlength{\emergencystretch}{20pt} |\set@floatcmds|: This is
+% the hook for the experts who like to implement a full float
+% mechanism for the \mc{} environment. The |@| in the name
+% should signal that this might not be easy.
+% \end{multicols}
+% \end{quote}
+% \vspace*{-1ex}
+% \vspace*{-0ex}
+% \caption[]{The new commands of \textsf{multicol.sty} version 1.2.
+% Both commands might be removed if good solutions to these
+% open problems are found. I hope that these commands will
+% prevent that nearly identical style files derived from
+% this one are floating around.}
+% \label{tab:newcmds}
+% \end{table*}
+% However single column floats are still forbidden and I don't think
+% I will have time to tackle this problem in the near future. As an
+% advice for all who want to try: wait for \TeX{} 3.0. It has a few
+% features which will make life much easier in multi-column
+% surroundings. Nevertheless we are working here at the edge of
+% \TeX{}s capabilities, really perfect solutions would need a
+% different approach than it was done in \TeX{}s page builder.
+%
+% The text below is nearly unchanged, I only added documentation at
+% places where new code was added.
+% \end{multicols}
+%
+% \changes{v1.5l}{1996/01/13}{Try hard to explain unresolved reference
+% that happens if \cs{OnlyDescription} is used}
+%
+% \StopEventually{\PrintIndex \PrintChanges
+% \ifx\Finale\relax
+% \typeout{**********************************}
+% \typeout{* Info: Typesetting this document with
+% \protect\OnlyDescription\space will}
+% \typeout{* Info: result in one unresolved
+% reference to `sec:v14'.}
+% \typeout{* Info: --- tough, it's just not there in this case!}
+% \typeout{**********************************}
+% \fi
+% }
+%
+%
+% \begin{multicols}{2}[\section{The Implementation}
+% We are now switching to two-column output to show the
+% abilities of this environment (and bad layout decisions).
+% \subsection{The documentation driver file}
+% ][10\baselineskip]
+%
+% \hbadness=10000
+%
+%
+% The next bit of code contains the documentation driver file for
+% \TeX{}, i.e., the file that will produce the documentation you are
+% currently reading. It will be extracted from this file by the \texttt{docstrip} program.
+% Since this is the first code in this file one can produce the
+% documentation
+% simply by running \LaTeX{} on the \texttt{.dtx} file.
+% \begin{macrocode}
+%<*driver>
+\documentclass{ltxdoc}
+% \end{macrocode}
+% We use the \texttt{balancingshow} option when loading \mc{} so
+% that full tracing is produced. This has to be done before the
+% \texttt{doc} package is loaded, since \texttt{doc} otherwise
+% requires \mc{} without any options.
+% \begin{macrocode}
+\usepackage{multicol}[1999/05/25]
+\usepackage{doc}
+% \end{macrocode}
+% First we set up the page layout suitable for
+% this article.
+% \begin{macrocode}
+\setlength{\textwidth}{39pc}
+\setlength{\textheight}{54pc}
+\setlength{\parindent}{1em}
+\setlength{\parskip}{0pt plus 1pt}
+\setlength{\oddsidemargin}{0pc}
+\setlength{\marginparwidth}{0pc}
+\setlength{\topmargin}{-2.5pc}
+\setlength{\headsep}{20pt}
+\setlength{\columnsep}{1.5pc}
+% \end{macrocode}
+% We want a rule between columns.
+% \begin{macrocode}
+\setlength\columnseprule{.4pt}
+% \end{macrocode}
+% We also want to ensure that a new \mc{} environment finds enough
+% space at the bottom of the page.
+% \begin{macrocode}
+\setlength\premulticols{6\baselineskip}
+% \end{macrocode}
+% When balancing columns we disregard solutions that
+% are too bad. Also, if the last column is too bad
+% we typeset it without stretch.
+% \begin{macrocode}
+\setcounter{columnbadness}{7000}
+\setcounter{finalcolumnbadness}{7000}
+% \end{macrocode}
+% The index is supposed to come out in four columns.
+% And we don't show macro names in the margin.
+% \begin{macrocode}
+\setcounter{IndexColumns}{4}
+\let\DescribeMacro\SpecialUsageIndex
+\let\DescribeEnv\SpecialEnvIndex
+\renewcommand\PrintMacroName[1]{}
+\CodelineIndex
+%\DisableCrossrefs % Partial index
+\RecordChanges % Change log
+% \end{macrocode}
+% Line numbers are very small for this article.
+% \begin{macrocode}
+\renewcommand{\theCodelineNo}
+ {\scriptsize\rm\arabic{CodelineNo}}
+\settowidth\MacroIndent{\scriptsize\rm 00\ }
+
+\begin{document}
+ \typeout
+ {****************************************
+ ^^J* Expect some Under- and overfull boxes.
+ ^^J****************************************}
+ \DocInput{multicol.dtx}
+\end{document}
+%</driver>
+% \end{macrocode}
+%
+%
+% \end{multicols}
+%
+% \begin{multicols}{2}[\subsection{Identification and
+% option processing}]
+%
+%
+% We start by identifying the package. Since it makes use of features
+% only available in \LaTeXe{} we ensure that this format is available.
+% (Now this is done earlier in the file.)
+% \begin{macrocode}
+%<*package>
+% \NeedsTeXFormat{LaTeX2e}
+% \ProvidesPackage{multicol}[..../../..
+% v... multicolumn formatting]
+% \end{macrocode}
+%
+%^^A \subsection{Option processing}
+%
+% Next we declare options supported by \mc{}. Two-column mode
+% and \mc{} do not work together so we warn about possible
+% problems. However, since you can revert to |\onecolumn|
+% in which case \mc{} does work, we don't make this an error.
+% \begin{macrocode}
+\DeclareOption{twocolumn}
+ {\PackageWarning{multicol}{May not work
+ with the twocolumn option}}
+% \end{macrocode}
+% Tracing is done using a counter. However
+% it is also possible to invoke the tracing
+% using the options declared below.
+% \begin{macrocode}
+\newcount\c@tracingmulticols
+\DeclareOption{errorshow}
+ {\c@tracingmulticols\z@}
+\DeclareOption{infoshow}
+ {\c@tracingmulticols\@ne}
+\DeclareOption{balancingshow}
+ {\c@tracingmulticols\tw@}
+\DeclareOption{markshow}
+ {\c@tracingmulticols\thr@@}
+\DeclareOption{debugshow}
+ {\c@tracingmulticols5\relax}
+% \end{macrocode}
+% The next option is intended for typesetting on a |\baselineskip|
+% grid. Right now it doesn't do anything other than warning if it
+% thinks that the grid got lost.
+% \changes{v1.6a}{2003/03/15}{New option grid}
+% \begin{macrocode}
+\let\mc@gridwarn\maxdimen
+\DeclareOption{grid}{\def\mc@gridwarn{\maxdepth}}
+% \end{macrocode}
+%
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+% Next option enables the |\docolaction| command. As this changes
+% the \texttt{.aux} file content this is not automatically enabled.
+% \begin{macrocode}
+\DeclareOption{colaction}{%
+ \def\mc@col@status@write{%
+ \protected@write\@auxout{}%
+ {\string\mc@col@status
+ {\ifmc@firstcol 1\else 2\fi}}%
+ \mc@firstcolfalse}%
+ \def\mc@lastcol@status@write{%
+ \protected@write\@auxout{}%
+ {\string\mc@col@status{3}}}%
+}
+\let\mc@col@status@write\relax
+\let\mc@lastcol@status@write\relax
+% \end{macrocode}
+%
+% \begin{macrocode}
+\ProcessOptions
+% \end{macrocode}
+%
+%
+% \end{multicols}
+%
+% \begin{multicols}{2}[\subsection{Starting and
+% Ending the \mc{} Environment}]
+%
+% \begin{macro}{\multicols}
+% As mentioned before, the \mc{} environment has one mandatory
+% argument (the number of columns) and up to two optional ones. We
+% start by reading the number of columns into the |\col@number|
+% register.
+% \begin{macrocode}
+\def\multicols#1{\col@number#1\relax
+% \end{macrocode}
+% If the user forgot the argument, \TeX{} will complain about a
+% missing number at this point. The error recovery mechanism will
+% then use zero, which isn't a good choice in this case. So we
+% should now test whether everything is okay. The minimum is two
+% columns at the moment.
+% \changes{v1.3b}{1990/10/09}{Minimum of two columns}
+% \begin{macrocode}
+ \ifnum\col@number<\tw@
+ \PackageWarning{multicol}%
+ {Using `\number\col@number'
+ columns doesn't seem a good idea.^^J
+ I therefore use two columns instead}%
+ \col@number\tw@ \fi
+% \end{macrocode}
+% We have only enough box registers for ten columns, so we need to
+% check that the user hasn't asked for more.
+% \changes{v1.4k}{1992/06/27}{Maximum of 5 columns (temp)}
+% \changes{v1.5a}{1992/11/04}{Allow 10 columns again}
+% \begin{macrocode}
+ \ifnum\col@number>10
+ \PackageError{multicol}%
+ {Too many columns}%
+ {Current implementation doesn't
+ support more than 10 columns.%
+ \MessageBreak
+ I therefore use 10 columns instead}%
+ \col@number10 \fi
+% \end{macrocode}
+% Within the environment we need a special version of the
+% kernel |\@footnotetext| command since the original sets the
+% the |\hsize| to |\columnwidth| which is not correct in the
+% multicol environment. Here |\columnwidth| refers to the width of
+% the individual column and the footnote should be in |\textwidth|.
+% Since |\@footnotetext| has a different definition inside a
+% minipage environment we do not redefine it directly. Instead we
+% locally set |\columnwidth| to |\textwidth| and call the original
+% (current) definition stored in |\orig@footnotetext|.
+% \changes{v1.5p}{1997/12/14}{Redefinition of \cs{@footnotetext}
+% only within env pr/2689.}
+% \changes{v1.5r}{1998/08/17}{Use \cs{@footnotetext} but with
+% local change to \cs{columnwidth}.}
+% \changes{v1.5w}{1999/10/21}{Make \cs{@footnotetext} long to allow
+% multi-paragraph footnotes.}
+% If the \mc{} environment is nested inside another \mc{}
+% environment then the redefinition has already happened. So be
+% better test for this situation. Otherwise, we will get a \TeX{}
+% stack overflow as this would generate a self-referencing definition.
+% \changes{v1.6e}{2004/02/14}{Avoid self-referencing definition of
+% \cs{@footnotetext} (pr/3618)}.
+% \begin{macrocode}
+ \ifx\@footnotetext\mult@footnotetext\else
+ \let\orig@footnotetext\@footnotetext
+ \let\@footnotetext\mult@footnotetext
+ \fi
+% \end{macrocode}
+% Now we can safely look for the optional arguments.
+% \begin{macrocode}
+ \@ifnextchar[\mult@cols{\mult@cols[]}}
+% \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\mult@footnotetext}
+%
+% \begin{macrocode}
+\long\def\mult@footnotetext#1{\begingroup
+ \columnwidth\textwidth
+ \orig@footnotetext{#1}\endgroup}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\mult@cols}
+% The |\mult@cols| macro grabs the first optional argument
+% (if any) and looks for the second one.
+% \begin{macrocode}
+\def\mult@cols[#1]{\@ifnextchar[%
+% \end{macrocode}
+% This argument should be a \meta{dimen} denoting the minimum free
+% space needed on the current page to start the environment. If the
+% user didn't supply one, we use |\premulticols| as a
+% default.
+% \begin{macrocode}
+ {\mult@@cols{#1}}%
+ {\mult@@cols{#1}[\premulticols]}}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\mult@@cols}
+% After removing all arguments from the input we are able
+% to start with |\mult@@cols|.
+% \begin{macrocode}
+\def\mult@@cols#1[#2]{%
+% \end{macrocode}
+% First thing we do is to decide whether or not this is an
+% unbounded multicols environment, i.e. one that may split across
+% pages, or one that has to be typeset into a box. If we are in
+% \TeX's ``inner'' mode (e.g., inside a box already) then we have a
+% boxed version of multicols therefore we set the |@boxedmulticols|
+% switch to true. The \mc{} should start in vertical mode. If we
+% are not already there we now force it with |\par| since otherwise
+% the test for ``inner'' mode wouldn't show if we are in a box.
+% \changes{v1.4f}{1992/04/28}{\cs{par} added to allow for correct inner test}
+% \begin{macrocode}
+ \par
+ \ifinner \@boxedmulticolstrue
+% \end{macrocode}
+% Otherwise we check |\doublecol@number|. This counter is zero
+% outside a multicols environment but positive inside (this happens
+% a little later on). In the second case we need to process the
+% current multicols also in ``boxed mode'' and so change the switch
+% accordingly.
+% \begin{macrocode}
+ \else
+ \ifnum \doublecol@number>\z@
+ \@boxedmulticolstrue
+ \fi
+ \fi
+% \end{macrocode}
+% Then we look to see if statistics are requested:
+% \begin{macrocode}
+ \mult@info\z@
+ {Starting environment with
+ \the\col@number\space columns%
+% \end{macrocode}
+% In boxed mode we add some more info.
+% \changes{v1.4f}{1992/04/28}{\cs{on@line} added to tracing info}
+% \begin{macrocode}
+ \if@boxedmulticols\MessageBreak
+ (boxed mode)\fi
+ }%
+% \end{macrocode}
+% Then we measure the current page to see whether a useful portion
+% of the multicolumn environment can be typeset. This routine
+% might start a new page.
+% \changes{v1.4a}{1992/02/14}{Forgotten braces added}
+% \begin{macrocode}
+ \enough@room{#2}%
+% \end{macrocode}
+% Now we output the first argument and produce vertical space
+% above the columns. (Note that this argument corresponds to the
+% first optional argument of the \textsf{multicols} environment.)
+% For many releases this argument was typeset in a group to get
+% a similar effect as |\twocolumn[..]| where the argument is
+% also implicitly surrounded by braces. However, this conflicts
+% with local changes done by things like sectioning commands (which
+% account for the majority of commands used in that argument)
+% messing up vertical spacing etc.\ later in the document so that
+% from version v1.5q on this argument is again typeset at the outer
+% level.
+% \changes{v1.4e}{1992/03/16}{Typeset optional arg inside group}
+% \changes{v1.5q}{1998/01/19}{And removed the group again six years later}
+% \begin{macrocode}
+ #1\par\addvspace\multicolsep
+% \end{macrocode}
+% When the last line of a paragraph had a positive depth then this
+% depth normally taken into account by the baselineskip calculation
+% for the next line. However, the columns produced by a following
+% \texttt{multicol} are rigid and thus the distance from the
+% baseline of a previous text line to the first line in a
+% \texttt{multicol} would differ depending on the depth of the
+% previous line. To account for this we add a negative space unless
+% the depth is \texttt{-1000pt} which signals something special to
+% \TeX and is not supposed to be a real depth.
+% \changes{v1.5z1}{2003/02/17}{Add a kern to cancel potential depth of
+% previous line}
+% \begin{macrocode}
+ \ifdim \prevdepth = -\@m\p@
+ \else
+% \end{macrocode}
+% The actual generation of this corrective space is a little bit
+% more complicated as it doesn't make sense to always back up to
+% the previous baseline (in case an object with a very large depth
+% was placed there, e.g., a centered tabular). So we only back up
+% to the extend that we are within the |\baselineskip| grid. We
+% know that the box produced by \mc{} has |\topskip| at its top so
+% that also needs to be taken into account.
+% \changes{v1.6a}{2003/03/15}{Adjust spacing}
+% \begin{macrocode}
+ \@tempcnta\prevdepth
+ \@tempcntb\baselineskip
+ \divide\@tempcnta\@tempcntb
+ \advance\@tempcnta\@ne
+ \dimen@\prevdepth
+ \advance\dimen@ -\@tempcnta\baselineskip
+ \advance\dimen@ \topskip
+ \kern-\dimen@
+ \fi
+% \end{macrocode}
+% We start a new grouping level to hide all subsequent changes
+% (done in |\prepare@multicols| for example).
+% \begin{macrocode}
+ \begingroup
+ \prepare@multicols
+% \end{macrocode}
+% If we are in boxed mode we now open a box to typeset all material
+% from the multicols body into it, otherwise we simply go ahead.
+% \changes{v1.4g}{1992/05/07}{\cs{global} was probably wrong but at least
+% unnecessary}
+% \begin{macrocode}
+ \if@boxedmulticols
+ \setbox\mult@box\vbox\bgroup
+% \end{macrocode}
+%
+% \changes{v1.8c}{2013/11/03}{Add \cs{color@setgroup} to prevent color leak}
+% \begin{macrocode}
+ \color@setgroup
+% \end{macrocode}
+% \changes{v1.5?}{1994/?/?}{Penalty moved to later point}
+% We may have to reset some parameters at this point,
+% perhaps |\@parboxrestore|
+% would be the right action but I leave it for the moment.
+% \changes{v1.4l}{1992/08/17}{\cs{@totalleftmargin} now in
+% \cs{prepare@multicols}}
+% \begin{macrocode}
+ \fi
+% \end{macrocode}
+% We finish by suppressing initial spaces.
+% \begin{macrocode}
+ \ignorespaces}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\if@boxedmulticols}
+% Here is the switch and the box for ``boxed'' multicols code.
+% \begin{macrocode}
+\newif\if@boxedmulticols
+\@boxedmulticolsfalse
+\newbox\mult@box
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\enough@room}
+% \changes{v1.0c}{1989/05/12}{Penalty 0 added to empty the contribution
+% list.}
+% The |\enough@room| macro used
+% above isn't perfect but works reasonably well in this context. We
+% measure the free space on the current page by subtracting
+% |\pagetotal| from |\pagegoal|. This isn't entirely
+% correct since it doesn't take the `shrinking' (i.e.\
+% |\pageshrink|) into account. The `recent contribution list'
+% might be nonempty so we start with |\par| and an explicit
+% |\penalty|.\footnote{See the documentation of
+% \cs{endmulticols} for further details.}
+% Actually, we use |\addpenalty| to ensure that a following
+% |\addvspace| will `see' the vertical space that might be
+% present.
+% The use of |\addpenalty| will have the effect that all items from
+% the recent contributions will be moved to the main vertical list
+% and the |\pagetotal| value will be updated correctly. However,
+% the penalty will be placed in front of any dangling glue item
+% with the result that the main vertical list may already be
+% overfull even if \TeX{} is not invoking the output routine.
+% \changes{v1.3b}{1990/10/09}{Do \cs{penalty} with \cs{addpenalty}}
+% \changes{v1.4e}{1992/03/16}{But ignore \cs{@nobreak} in \cs{addpenalty}}
+% \begin{macrocode}
+\def\enough@room#1{%
+% \end{macrocode}
+% Measuring makes only sense when we are not in ``boxed mode'' so
+% the routine does nothing if the switch is true.
+% \begin{macrocode}
+ \if@boxedmulticols\else
+ \par
+% \end{macrocode}
+% \label{mac:enoughroom}
+% To empty the contribution list the first release contained a
+% penalty zero but this had the result that |\addvspace| couldn't
+% detect preceding glue. So this was changed to |\addpenalty|. But
+% this turned out to be not enough as |\addpenalty| will not add a
+% penalty when |@nobreak| is true. Therefore we force this switch
+% locally to false. As a result there may be a break between
+% preceding text and the start of a multicols environment, but this
+% seems acceptable since there is the optional argument for exactly
+% this reason.
+% \begin{macrocode}
+ \bgroup\@nobreakfalse\addpenalty\z@\egroup
+ \page@free \pagegoal
+ \advance \page@free -\pagetotal
+% \end{macrocode}
+% To be able to output the value we need to assign it to a register
+% first since it might be a register (default) in which case we
+% need to use |\the| or it might be a plain value in which case
+% |\the| would be wrong.
+% \changes{v1.5e}{1994/05/26}{Assign arg to skip register to be able
+% to output value}
+% \begin{macrocode}
+ \@tempskipa#1\relax
+% \end{macrocode}
+% Now we test whether tracing information is required:
+% \begin{macrocode}
+ \mult@info\z@
+ {Current page:\MessageBreak
+ height=%
+ \the\pagegoal: used \the\pagetotal
+ \space -> free=\the\page@free
+ \MessageBreak
+ needed \the\@tempskipa
+ \space(for #1)}%
+% \end{macrocode}
+% Our last action is to force a page break if there isn't enough
+% room left.
+% \begin{macrocode}
+ \ifdim \page@free <#1\newpage \fi
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\prepare@multicols}
+% When preparing for multicolumn output several things must
+% be done.
+% \begin{macrocode}
+\def\prepare@multicols{%
+% \end{macrocode}
+% We start saving the current |\@totalleftmargin| and then
+% resetting the |\parshape| in case we are inside some list
+% environment. The correct indentation for the \mc{} environment in
+% such a case will be produced by moving the result to the right by
+% |\multicol@leftmargin| later on. If we would use the value of of
+% |\@totalleftmargin| directly then lists inside the \mc{}
+% environment could cause a shift of the output.
+% \changes{v1.4l}{1992/08/17}{saved \cs{@totalleftmargin}}
+% \begin{macrocode}
+ \multicol@leftmargin\@totalleftmargin
+ \@totalleftmargin\z@
+ \parshape\z@
+% \end{macrocode}
+% We also set the register |\doublecol@number| for later use. This
+% register should contain $2\times |\col@number|$. This is also an
+% indicator that we are within a \mc{} environment as mentioned
+% above.
+% \changes{v1.5a}{1992/11/04}{Add offset to \cs{doublecolnumber}}
+% \begin{macrocode}
+ \doublecol@number\col@number
+ \multiply\doublecol@number\tw@
+ \advance\doublecol@number\mult@rightbox
+% \end{macrocode}
+%
+% \begin{macrocode}
+ \if@boxedmulticols
+ \let\l@kept@firstmark\kept@firstmark
+ \let\l@kept@botmark\kept@botmark
+ \global\let\kept@firstmark\@empty
+ \global\let\kept@botmark\@empty
+ \else
+% \end{macrocode}
+% We add an empty box to the main vertical list to ensure that we
+% catch any insertions (held over or inserted at the top of the
+% page). Otherwise it might happen that the |\eject| is discarded
+% without calling the output routine. Inside the output routine we
+% remove this box again. Again this code applies only if we are on
+% the main vertical list and not within a box.
+% However, it is not enough to turn off interline spacing, we also
+% have to clear |\topskip| before adding this box, since |\topskip|
+% is always inserted before the first box on a page which would
+% leave us with an extra space of |\topskip| if \mc{} start on a
+% fresh sheet.
+% \changes{v1.3c}{1991/03/03}{\cs{null} inserted and removed in output}
+% \changes{v1.4a}{1992/02/11}{Conditional code for boxed mode added.}
+% \changes{v1.4o}{1992/11/22}{\cs{topskip} locally zeroed.}
+% \begin{macrocode}
+ \nointerlineskip {\topskip\z@\null}%
+ \output{%
+ \global\setbox\partial@page\vbox
+ {%
+% \end{macrocode}
+% Now we have to make sure that we catch one special situation which
+% may result in loss of text! If the user has a huge amount of
+% vertical material within the first optional argument that is larger
+% then |\premulticols| and we are near the bottom of the page then it
+% can happen that not the |\eject| is triggering this special output
+% routine but rather the overfull main vertical list. In that case
+% we get another breakpoint through the |\eject| penalty. As a result
+% this special output routine would be called twice and the contents
+% of |\partial@page|, i.e.\ the material before the \mc{}
+% environment gets lost. There are several solutions to avoid this
+% problem, but for now we will simply detect this and inform the user
+% that he/she has to enlarge the |\premulticols| by using a suitable
+% value for the second argument.
+% \changes{v1.4a}{1992/02/11}{Checking for text losses.}
+% \begin{macrocode}
+%<*check>
+ \ifvoid\partial@page\else
+ \PackageError{multicol}%
+ {Error saving partial page}%
+ {The part of the page before
+ the multicols environment was
+ nearly full with^^Jthe result
+ that starting the environment
+ will produce an overfull
+ page. Some^^Jtext may be lost!
+ Please increase \premulticols
+ either generally or for this%
+ ^^Jenvironment by specifying a
+ suitable value in the second
+ optional argument to^^Jthe
+ multicols environment.}
+ \unvbox\partial@page
+ \box\last@line
+ \fi
+%</check>
+ \unvbox\@cclv
+ \global\setbox\last@line\lastbox
+ }%
+% \end{macrocode}
+% Finally we need to record the marks that are present within the
+% |\partial@page| so that we can construct correct first and bottom
+% marks later on. This is done by the following code.
+% \changes{v1.4a}{1992/02/14}{kept marks initiated}
+% \begin{macrocode}
+ \prep@keptmarks
+% \end{macrocode}
+% Finally we have to initialize |\kept@topmark| which should
+% ideally be initialized with the mark that is current on ``top''
+% of this page. Unfortunately we can't use |\topmark| because this
+% register will not always contain what its name promises because
+% \LaTeX{} sometimes calls the output routine for float
+% management.\footnote{During such a call the \cs{botmark}
+% gets globally copied to \cs{topmark} by the \TeX{}
+% program.} Therefore we use the second best solution by
+% initializing it with |\firstmark|. In fact, for our purpose this
+% doesn't matter as we use |\kept@topmark| only to initialize
+% |\firstmark| and |\botmark| of a following page if we don't find
+% any marks on the current one.
+% \changes{v1.4i}{1992/06/18}{\cs{kept@topmark} initialized.}
+% \begin{macrocode}
+ \global\let\kept@topmark\firstmark
+ }\eject
+% \end{macrocode}
+% The next thing to do is to assign a new value to |\vsize|.
+% \LaTeX{} maintains the free room on the page (i.e.\ the page
+% height without the space for already contributed floats) in the
+% register |\@colroom|. We must subtract the height of
+% |\partial@page| to put the actual free room into this
+% variable.
+% \begin{macrocode}
+ \advance\@colroom-\ht\partial@page
+% \end{macrocode}
+% Then we have to calculate the |\vsize| value to use during column
+% assembly. |\set@mult@vsize| takes an argument which allows to
+% make the setting local (|\relax|) or global (|\global|). The
+% latter variant is used inside the output routine below. At this
+% point here we have to make a local change to |\vsize| because we
+% want to get the original value for |\vsize| restored in case
+% this \mc{} environment ends on the same page where it has started.
+% \changes{v1.4p}{1992/11/26}{Use different \cs{vsize} setting}
+% \changes{v1.4p}{1992/11/26}{Code moved to \cs{set@mult@vsize}}
+% \begin{macrocode}
+ \set@mult@vsize\relax
+% \end{macrocode}
+% Now we switch to a new |\output| routine which will be used
+% to put the gathered column material together.
+% \begin{macrocode}
+ \output{\multi@column@out}%
+% \end{macrocode}
+% Finally we handle the footnote insertions. We have to multiply
+% the magnification factor and the extra skip by the number of
+% columns since each footnote reduces the space for every column
+% (remember that we have page-wide footnotes). If, on the other
+% hand, footnotes are typeset at the very end of the document, our
+% scheme still works since |\count\footins| is zero then, so it
+% will not change.
+% To allow even further customization the setting of the |\footins|
+% parameters is done in a separate macro.
+% \changes{v1.5?}{1994/?/?}{Use \cs{init@mult@footins}}
+% \begin{macrocode}
+ \init@mult@footins
+% \end{macrocode}
+% For the same reason (page-wide footnotes), the \meta{dimen}
+% register controlling the maximum space used for footnotes isn't
+% changed. Having done this, we must reinsert all the footnotes
+% which are already present (i.e.\ those encountered when the
+% material saved in |\partial@page| was first processed). This
+% will reduce the free space (i.e.\ |\pagetotal|) by the
+% appropriate amount since we have changed the magnification
+% factor, etc.\ above.
+% \begin{macrocode}
+ \reinsert@footnotes
+% \end{macrocode}
+% Inside \mc{} a |\clearpage| is fairly useless as we aren't supporting
+% floats. In fact, it can cause harm as it doesn't know about the
+% |\partial@page| and may therefore result in making columns too long.
+% So we change that to behave like |\newpage| but also check if there
+% are any deferred floats. If so, perhaps the user tried to place them through
+% that |\clearpage| (but that needs to be done before starting the \mc{}
+% environment.
+% \changes{v1.8q}{2017/04/11}{Make \cs{clearpage} behave like \cs{newpage} (pr/4511)}
+% \begin{macrocode}
+ \def\clearpage{%
+ \ifx\@deferlist\@empty\else
+ \PackageError{multicol}%
+ {Deferred floats not cleared}%
+ {A \string\clearpage\space inside multicols acts like
+ \string\newpage\space and doesn't clear floats.\MessageBreak
+ Move it before the multicols environment if you need it.}%
+ \fi
+ \newpage}%
+% \end{macrocode}
+% All the code above was only necessary for the unrestricted \mc{}
+% version, i.e.\ the one that allows page breaks. If we are within
+% a box there is no point in setting up special output routines or
+% |\vsize|, etc.
+% \begin{macrocode}
+ \fi
+% \end{macrocode}
+% But now we are coming to code that is necessary in all cases. We
+% assign new values to |\vbadness|, |\hbadness| and |\tolerance|
+% since it's rather hard for \TeX{} to produce `good' paragraphs
+% within narrow columns.
+% \changes{v1.2a}{1990/02/05}{\cs{vbadness} 10001 now.}
+% \begin{macrocode}
+ \vbadness\@Mi \hbadness5000
+ \tolerance\multicoltolerance
+% \end{macrocode}
+% Since nearly always the first pass will fail we ignore it
+% completely telling \TeX{} to hyphenate directly. In fact, we now
+% use another register to keep the value for the multicol
+% pre-tolerance, so that a designer may allow to use
+% |\pretolerance|.
+% \changes{v1.2a}{1990/02/05}{\cs{pretolerance} -1 because it nearly never
+% succeeds.}
+% \changes{v1.4e}{1992/03/20}{Using}
+% \begin{macrocode}
+ \pretolerance\multicolpretolerance
+% \end{macrocode}
+% For use with the new \TeX{} we set |\emergencystretch| to
+% $|\col@number| \times 4pt$. However this is only a guess
+% so at the moment this is done in a macro
+% |\setemergencystretch| which gets the current |\hsize|
+% and the number of columns as arguments. Therefore users are able
+% to figure out their own formula.
+% \changes{v1.2a}{1990/02/05}{\cs{setemergencystretch} added.}
+% \begin{macrocode}
+ \setemergencystretch\col@number\hsize
+% \end{macrocode}
+% Another hook to allow people adding their own extensions without
+% making a new package is |\set@floatcmds| which handles any
+% redefinitions of \LaTeX{}s internal float commands to work with
+% the \mc{} environment. At the moment it is only used to redefine
+% |\@dblfloat| and |\end@dblfloat|.
+% \changes{v1.2a}{1990/02/05}{\cs{set@floatcmds} added.}
+% \begin{macrocode}
+ \set@floatcmds
+% \end{macrocode}
+% Additionally, we advance |\baselineskip| by
+% |\multicolbaselineskip| to allow corrections for narrow
+% columns.
+% \begin{macrocode}
+ \advance\baselineskip\multicolbaselineskip
+% \end{macrocode}
+% \changes{v1.0e}{1989/06/21}{\cs{textwidth} changed to \cs{linewidth}.}
+% \changes{v1.0e}{1989/06/21}{So this file will
+% work with the `twocolumn' command.}
+% The |\hsize| of the columns is given by the formula:
+% \[
+% { |\linewidth| - (|\col@number|-1)
+% \times
+% |\columnsep|
+% \over
+% |\col@number|}
+% \]
+% The formula above has changed from release to release. We now
+% start with the current value of |\linewidth| so that the column
+% width is properly calculated when we are inside a minipage or a
+% list or some other environment.
+% This will be achieved with:
+% \begin{macrocode}
+ \hsize\linewidth \advance\hsize\columnsep
+ \advance\hsize-\col@number\columnsep
+ \divide\hsize\col@number
+% \end{macrocode}
+% We also set |\linewidth| and |\columnwidth| to |\hsize| In the past
+% |\columnwidth| was left unchanged. This is inconsistent,
+% but |\columnwidth| is used only by floats (which
+% aren't allowed in their current implementation) and by the
+% |\footnote| macro. Since we want page-wide
+% footnotes\footnote{I'm not sure that I really want page-wide
+% footnotes. But balancing of the last page can
+% only be achieved with this approach or with a
+% multi-path algorithm which is complicated and
+% slow. But it's a challenge to everybody to
+% prove me wrong! Another possibility is to
+% reimplement a small part of the {\it
+% fire\_up\/} procedure in \TeX{} (the program).
+% I think that this is the best solution if you
+% are interested in complex page makeup, but it
+% has the disadvantage that the resulting
+% program cannot be called \TeX{} thereafter.}
+% this simple trick saved us from rewriting the |\footnote|
+% macros. However, some applications referred to |\columnwidth| as
+% the ``width of the current column'' to typeset displays
+% (the \texttt{amsmath} package, for example) and to allow the use
+% of such applications together with \texttt{multicol} this is now
+% changed.
+%
+% Before we change |\linewidth| to the new value we record its old
+% value in some register called |\full@width|. This value is
+% used later on when we package all columns together.
+% \changes{v1.0e}{1989/06/21}{Setting of \cs{columnwidth} removed.}
+% \changes{v1.5o}{1997/11/16}{Setting of \cs{columnwidth} added again
+% pr/2664.}
+% \begin{macrocode}
+ \full@width\linewidth
+ \linewidth\hsize
+ \columnwidth\hsize
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\init@mult@footins}
+% This macro is used to set up the parameters associated
+% with footnote floats. It can be redefined by applications that
+% require different amount of spaces when typesetting footnotes.
+% \begin{macrocode}
+\def\init@mult@footins{%
+ \multiply\count\footins\col@number
+ \multiply\skip \footins\col@number
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\set@mult@vsize}
+%
+% Since we have to set |\col@umber| columns on one page,
+% each with a height of |\@colroom|, we have to assign
+% $
+% |\vsize| = |\col@number| \times |\@colroom|
+% $
+% in order to collect enough material before entering the
+% |\output| routine again. In fact we have to add another
+% $
+% (|\col@number|-1) \times (|\baselineskip|-|\topskip|)
+% $
+% if you think about it.
+% \changes{v1.4p}{1992/11/26}{Macro added.}
+% \begin{macrocode}
+\def\set@mult@vsize#1{%
+ \vsize\@colroom
+ \@tempdima\baselineskip
+ \advance\@tempdima-\topskip
+ \advance\vsize\@tempdima
+ \vsize\col@number\vsize
+ \advance\vsize-\@tempdima
+% \end{macrocode}
+% But this might not be enough since we use |\vsplit| later to
+% extract the columns from the gathered material. Therefore we add
+% some `extra lines,' one for each column plus a corrective action
+% depending on the value of the `\texttt{collectmore}' counter.
+% The final value is assigned globally if |#1| is |\global| because
+% we want to use this macro later inside the output routine too.
+% \changes{v1.6c}{2003/04/08}{Collect one line per column more}
+% \begin{macrocode}
+ \advance\vsize\col@number\baselineskip
+ #1\advance\vsize
+ \c@collectmore\baselineskip}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\multicol@leftmargin}
+% Here is the dimen register we need for saving away the outer
+% value of |\@totalleftmargin|.
+% \begin{macrocode}
+\newdimen\multicol@leftmargin
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@Mvi}
+% In versions prior to 1.8r the balancing at the end of the
+% environment was done by changing the output routine from
+% |\multi@column@out| to |\balance@column@out|. As it turned out
+% that this has a couple of issues when the last columns should not
+% be balanced after all (for example because they contained several
+% |\columnbreak| commands we now stay with one output routine for
+% the environment and only signal that we reached the end of the
+% environment by marking it with a special penalty that we can check
+% for later.
+% \changes{v1.8r}{2018/01/28}{Macro added}
+% \begin{macrocode}
+\mathchardef\@Mvi=10006 % 10005 is \columnbreak
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\endmulticols}
+% When the end of the \mc{} environment is sensed we have to
+% balance the gathered material. Depending on whether or not we are
+% inside a boxed multicol different things must happen. But first
+% we end the current paragraph with a |\par| command.
+% \begin{macrocode}
+\def\endmulticols{\par
+ \if@boxedmulticols
+% \end{macrocode}
+% In boxed mode we have to close the box in which we have gathered
+% all material for the columns. But before we do this we need to
+% remove any space at the end of the box as we don't want to use
+% this in balancing. Because of the |\color@endgroup| this can't be
+% done later in |\balance@columns| as the color command will hide
+% it.
+% \changes{v1.8c}{2013/11/03}{Add \cs{color@endgroup} to prevent color leak}
+% \changes{v1.8f}{2014/06/19}{Discard spaces before adding \cs{color@endgroup}}
+% \begin{macrocode}
+ \remove@discardable@items\color@endgroup\egroup
+% \end{macrocode}
+% Now we call |\balance@columns| the routine that balances material
+% stored in the box |\mult@box|.
+% \changes{v1.5?}{1994/?/?}{Splitting off zero box moved to
+% \cs{balance@columns}}
+% \begin{macrocode}
+ \balance@columns
+% \end{macrocode}
+% After balancing the result has to be returned by the command
+% |\page@sofar|. But before we do this we reinsert any marks found
+% in box |\mult@box|.
+% \begin{macrocode}
+ \return@nonemptymark{first}%
+ \kept@firstmark
+ \return@nonemptymark{bot}%
+ \kept@botmark
+ \page@sofar
+% \end{macrocode}
+%
+% \begin{macrocode}
+ \global\let\kept@firstmark
+ \l@kept@firstmark
+ \global\let\kept@botmark
+ \l@kept@botmark
+%<*marktrace>
+ \mult@info\tw@
+ {Restore kept marks to\MessageBreak
+ first: \meaning\kept@firstmark
+ \MessageBreak bot\space\space:
+ \meaning\kept@botmark }%
+%</marktrace>
+% \end{macrocode}
+% This finishes the code for the ``boxed'' case.
+% \begin{macrocode}
+ \else
+% \end{macrocode}
+% If there was a |\columnbreak| on the very last line all material
+% will have been moved to the |\colbreak@box|. Thus the the galley
+% will be empty and no output routine gets called so that the text
+% is lost. To avoid this problem (though unlikely) we check if the
+% current galley is empty and the |\colbreak@box| contains text and
+% if so return that to the galley. If the galley is non-empty any
+% material in |\colbreak@box| is added in the output routine since
+% it needs to be put in front.
+% \changes{v1.6d}{2003/04/17}{Catch problem with \cs{columnbreak} in
+% last line}
+% \begin{macrocode}
+ \ifdim\pagegoal=\maxdimen
+ \ifvoid\colbreak@box\else
+ \mult@info\@ne{Re-adding forced
+ break(s) for splitting}%
+ \unvbox\colbreak@box\fi
+ \fi
+% \end{macrocode}
+% If we are in an unrestricted \mc{} environment we end the current
+% paragraph above with |\par| but this isn't sufficient since \TeX{}s
+% {\it page\_builder} will not totally empty the contribution
+% list.\footnote{This once caused a puzzling bug where some of the
+% material was balanced twice, resulting in some overprints. The
+% reason was the \cs{eject} which was placed at the end of
+% the contribution list. Then the {\it page\_builder} was called
+% (an explicit \cs{penalty} will empty the contribution
+% list), but the line with the \cs{eject} didn't fit onto
+% the current page. It was then reconsidered after the output
+% routine had ended, causing a second break after one line.}
+% Therefore we must also add an explicit |\penalty|. Now the
+% contribution list will be emptied and, if its material doesn't
+% all fit onto the current page then the output routine will be
+% called before we change it.
+% \changes{v1.3b}{1990/10/09}{Do \cs{penalty} with \cs{addpenalty}}
+% \changes{v1.4e}{1992/03/16}{But ignore \cs{@nobreak} in \cs{addpenalty}}
+% \changes{v1.5c}{1993/04/18}{Again use \cs{penalty}}
+% At this point we need to use |\penalty| not |\addpenalty| to
+% ensure that a) the recent contributions are emptied and b) that
+% the very last item on the main vertical list is a valid break
+% point so that \TeX{} breaks the page in case it is overfull.
+% \begin{macrocode}
+ \penalty\z@
+% \end{macrocode}
+% Now it's safe to call the output routine in order to balance
+% the columns. We do this by calling it with a special penalty.
+% \changes{v1.8r}{2018/01/28}{Use special penalty to signal end of environment}
+% \begin{macrocode}
+ \penalty-\@Mvi
+% \end{macrocode}
+% If the \mc{} environment body was completely empty or if a
+% multi-page \mc{} just ends at a page boundary we have the unusual
+% case that the |\eject| will have no effect (since the main
+% vertical list is empty)---thus no output routine is called at
+% all. As a result the material preceding the \mc{} (stored in
+% |\partial@page| will get lost if we don't put this back by hand.
+% \changes{v1.4m}{1992/09/04}{Check \cs{partial@page} being emptied}
+% \begin{macrocode}
+ \ifvbox\partial@page
+ \unvbox\partial@page\fi
+% \end{macrocode}
+% After the output routine has acted we restore
+% the kept marks to their initial value.
+% \begin{macrocode}
+ \global\let\kept@firstmark\@empty
+ \global\let\kept@botmark\@empty
+%<*marktrace>
+ \mult@info\tw@
+ {Make kept marks empty}%
+%</marktrace>
+ \fi
+% \end{macrocode}
+% The output routine above will take care of the |\vsize| and
+% reinsert the balanced columns, etc. But it can't reinsert the
+% |\footnotes| because we first have to restore the
+% |\footins| parameter since we are returning to one column
+% mode. This will be done in the next line of code; we simply close
+% the group started in |\multicols|.
+%
+% To fix an obscure bug which is the result of the current
+% definition of the |\begin| \ldots\ |\end| macros, we check that
+% we are still (logically speaking) in the \mc{} environment. If,
+% for example, we forget to close some environment inside the
+% \mc{} environment, the following |\endgroup| would be
+% incorrectly considered to be the closing of this environment.
+% \changes{v1.3c}{1991/03/14}{Check closing env.}
+% \begin{macrocode}
+ \@checkend{multicols}%
+ \endgroup
+% \end{macrocode}
+% We also set the `\textsf{unbalance}' counter to its default. This is
+% done globally since \LaTeX{} counters are always changed this
+% way.\footnote{Actually, we are still in a group started by the
+% \cs{begin} macro, so \cs{global} must be used
+% anyway.}
+% \begin{macrocode}
+ \global\c@unbalance\z@
+% \end{macrocode}
+% Now it's time to return any footnotes if we are in unrestricted
+% mode. In boxed mode footnotes are kept inside, but in that case
+% we have to write another column status into the \texttt{.aux}
+% file to support \cs{docolaction} in case we have nested
+% environments.
+% \changes{v1.8s}{2018/04/20}{Support for \cs{docolaction} (issue/39)}
+% \begin{macrocode}
+ \if@boxedmulticols
+ \mc@col@status@write
+ \else
+ \reinsert@footnotes
+% \end{macrocode}
+% We also take a look at the amount of free space on the current
+% page to see if it's time for a page break. The vertical space
+% added thereafter will vanish if |\enough@room| starts a new
+% page.
+%
+% But there is one catch. If the |\end{multicols}| is at the top of
+% which can happen if there is a break point just before it (such
+% as end ending environment) which was chosen. In that case we
+% would do the next page using the internal |\vsize| for multicol
+% collection which is a disaster. So we better catch this
+% case. Fortunately we can detect it by looking at |\pagegoal|.
+% \changes{v1.5x}{2000/05/05}{Detect and fix problem if a multicols
+% ends at the top of a page}
+% \begin{macrocode}
+ \ifdim \pagegoal=\maxdimen
+ \global\vsize\@colroom
+ \else
+ \enough@room\postmulticols
+ \fi
+ \fi
+ \addvspace\multicolsep
+% \end{macrocode}
+% There is one more thing to do: the balanced result of the
+% environment is supposed to have a |\prevdepth| of zero as we
+% backed up by its real prevdepth within |\page@sofar|. However if
+% the balancing happened in the output routine then \TeX{} reverts
+% to the |\prevdepth| that was current before the OR once the OR has
+% finished. In short |\prevdepth| is something you can't set
+% globally it is alway local to the current list being built. Thus
+% we need to set it back to zero here to avoid incorrect spacing.
+% \changes{v1.8h}{2014/09/12}{Set \cs{prevdepdth} for current vlist
+% when returning from multicols environment}
+% \begin{macrocode}
+ \prevdepth\z@
+% \end{macrocode}
+% If statistics are required we finally report that we have
+% finished everything.
+% \begin{macrocode}
+ \mult@info\z@
+ {Ending environment
+ \if@boxedmulticols
+ \space(boxed mode)\fi
+ }}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\c@unbalance}
+% \SpecialMainIndex{\c@collectmore}
+% \SpecialMainIndex{\col@number}
+% \SpecialMainIndex{\doublecol@number}
+% \SpecialMainIndex{\premulticols}
+% \SpecialMainIndex{\multicoltolerance}
+% \SpecialMainIndex{\multicolpretolerance}
+% \SpecialMainIndex{\page@free}
+% \SpecialMainIndex{\premulticols}
+% \SpecialMainIndex{\postmulticols}
+% \SpecialMainIndex{\multicolsep}
+% \SpecialMainIndex{\multicolbaselineskip}
+% \SpecialMainIndex{\partial@page}
+% Let us end this section by allocating all the registers used so
+% far.
+% \begin{macrocode}
+\newcount\c@unbalance
+\newcount\c@collectmore
+% \end{macrocode}
+% In the new \LaTeX{} release |\col@number| is already allocated by
+% the kernel, so we don't allocate it again.
+% \begin{macrocode}
+%\newcount\col@number
+\newcount\doublecol@number
+\newcount\multicoltolerance
+\newcount\multicolpretolerance
+\newdimen\full@width
+\newdimen\page@free
+\newdimen\premulticols
+\newdimen\postmulticols
+\newskip\multicolsep
+\newskip\multicolbaselineskip
+\newbox\partial@page
+\newbox\last@line
+% \end{macrocode}
+% And here are their default values:
+% \begin{macrocode}
+\c@unbalance = 0
+\c@collectmore = 0
+% \end{macrocode}
+% To allow checking whether some macro is used within the \mc{}
+% environment the counter |\col@number| gets a default of |1|
+% outside the the environment.
+% \changes{v1.3d}{1991/10/23}{\cs{col@number} set to one}
+% \changes{v1.8o}{2016/02/08}{\cs{col@number} already initialized in the
+% kernel, so not initializing it in the package
+% in case the document is in two-column (pr/4435)}
+% \begin{macrocode}
+%\col@number = 1
+\multicoltolerance = 9999
+\multicolpretolerance = -1
+\premulticols = 50pt
+\postmulticols= 20pt
+\multicolsep = 12pt plus 4pt minus 3pt
+\multicolbaselineskip=0pt
+% \end{macrocode}
+% \end{macro}
+%
+% \end{multicols}
+%
+% \begin{multicols}{2}[\subsection{The output routines}]
+%
+% We first start with some simple macros. When typesetting the page we
+% save the columns either in the box registers 0, 2, 4,\ldots\
+% (locally) or 1, 3, 5,\ldots\ (globally). This is \PlainTeX{} policy
+% to avoid an overflow of the save stack.
+%
+% \begin{macro}{\process@cols}
+% Therefore we define a |\process@cols| macro to help us in
+% using these registers in the output routines below. It has two
+% arguments: the first one is a number; the second one is the
+% processing information. It loops starting with |\count@=#1|
+% (|\count@| is a scratch register defined in \PlainTeX),
+% processes argument |#2|, adds two to |\count@|,
+% processes argument |#2| again, etc.\ until |\count@| is
+% higher than |\doublecol@number|. It might be easier to
+% understand it through an example, so we define it now and
+% explain its usage afterwards.
+% \begin{macrocode}
+\def\process@cols#1#2{\count@#1\relax
+ \loop
+%<*debug>
+ \typeout{Looking at box \the\count@}
+%</debug>
+ #2%
+ \advance\count@\tw@
+ \ifnum\count@<\doublecol@number
+ \repeat}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\page@sofar}
+% We now define |\page@sofar| to give an example of the
+% |\process@cols| macro. |\page@sofar| should output everything
+% prepared by the balancing routine |\balance@columns|.
+% \begin{macrocode}
+\def\page@sofar{%
+% \end{macrocode}
+% |\balance@columns| prepares its output in the even numbered
+% scratch box registers.
+% Now we output the columns gathered assuming that they are saved
+% in the box registers 2 (left column), 4 (second column), \ldots\
+% However, the last column (i.e.\ the right-most) should be saved in
+% box register 0.\footnote{You will see the reason for this numbering
+% when we look at the output routines
+% \cs{multi@column@out} and
+% \cs{balance@columns@out}.}
+% First we ensure that the columns have equal width. We use
+% |\process@cols| for this purpose, starting with
+% $|\count@|=|\mult@rightbox|$. Therefore |\count@| loops through
+% |\mult@rightbox|, $|\mult@rightbox| + 2$,\ldots
+% (to |\doublecol@number|).
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+% \begin{macrocode}
+ \process@cols\mult@rightbox
+% \end{macrocode}
+% We have to check if the box in question is void, because the
+% operation |\wd|\meta{number} on a void box will \emph{not} change
+% its dimension (sigh).
+% \changes{v1.5h}{1994/08/26}{Check for void boxes}
+% \changes{v1.5i}{1994/10/02}{But don't remove original code.}
+% \begin{macrocode}
+ {\ifvoid\count@
+ \setbox\count@\hbox to\hsize{}%
+ \else
+ \wd\count@\hsize
+ \fi}%
+% \end{macrocode}
+% Now we give some tracing information.
+% \changes{v1.4l}{1992/08/17}{use \cs{multicol@leftmargin} instead of
+% \cs{@totalleftmargin}}
+% \changes{v1.6b}{2003/03/15}{Different info display}
+% \begin{macrocode}
+ \count@\col@number \advance\count@\m@ne
+ \mult@info\z@
+ {Column spec: \the\full@width\space = indent
+ + columns + sep =\MessageBreak
+ \the\multicol@leftmargin\space
+ + \the\col@number\space
+ x \the\hsize\space
+ + \the\count@\space
+ x \the\columnsep
+ }%
+% \end{macrocode}
+% At this point we should always be in vertical mode.
+% \begin{macrocode}
+\ifvmode\else\errmessage{Multicol Error}\fi
+% \end{macrocode}
+% Now we put all columns together in an |\hbox| of width
+% |\full@width| (shifting it by |\multicol@leftmargin| to the right
+% so that it will be placed correctly if we are within a list
+% environment)
+% and separating the columns with a rule if desired.
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+% \changes{v1.5z}{2000/07/10}{Ensure that column rule has always
+% \cs{normalcolor}}
+% \changes{v1.6f}{2006/09/19}{Make the color of the rule a hook}
+% \changes{v1.4l}{1992/08/17}{use \cs{multicol@leftmargin} instead of
+% \cs{@totalleftmargin}}
+%
+% The box containing the columns has a large height and thus will
+% always result in using |\lineskip| if the normal |\baselineskip|
+% calculations are used. We therefore better cancel that process.
+% \changes{v1.5z1}{2003/02/17}{Suppress interline glue at this point}
+% \begin{macrocode}
+ \nointerlineskip
+% \end{macrocode}
+% As mentioned earlier we want to have the reference point of the
+% box we put on the page being at the baseline of the last line of
+% the columns but we also want to ensure that the box has no depth
+% so that any following skip is automatically starting from that
+% baseline.
+% We achieve this by recording the depths of all columns and then
+% finally backing up by the maximum. (perhaps a simpler method
+% would be to assemble the box in a register and set the depth of
+% that box to zero (not checked).
+%
+% We need a global scratch register for this; using standard \TeX{}
+% conventions we choose |\dimen2| and initialize it with the depth
+% of the character ``p'' since that is one of the depths that
+% compete for the maximum.
+% \changes{v1.6a}{2003/03/15}{Preparing for adjusting \cs{prevdepth}}
+% \begin{macrocode}
+ \setbox\z@\hbox{p}\global\dimen\tw@\dp\z@
+ \moveright\multicol@leftmargin
+ \hbox to\full@width{%
+% \end{macrocode}
+% If the document is written in a language that is typeset right-to-left
+% then, of course, the multicol columns should be also typeset
+% right-to-left. To support this we call |\mc@align@columns| which
+% with execute different code depending on the typesetting direction.
+% \changes{v1.7b}{2011/12/18}{RL language support fixed}
+% \begin{macrocode}
+ \mc@align@columns
+% \end{macrocode}
+% The depths of the columns depend on their last lines. To ensure
+% that we will always get a similar look as far as the rules are
+% concerned we force the depth to be at least the depth of a
+% letter~`p' (which is what we set |\dimen2| to above).
+% \begin{macrocode}
+ \rlap{\phantom p}%
+ }%
+% \end{macrocode}
+% The processed material might consist of a last line with a
+% descender in which case the |\prevdepth| will be
+% non-zero. However, this material is getting reformatted now so
+% that this value is likely to be wrong. We therefore normalize the
+% situation by pretending that the depth is zero. However, if |\page@sofar|
+% is being called inside the OR then setting |\prevdepth| here has
+% no long-lasting effect, we therefore have to repeat this once we
+% return to the main vertical list. Here we set it only for those
+% cases where the command is used within a list and then followed by
+% something else.
+% \changes{v1.8g}{2014/08/24}{Resetting \cs{prevdepth} in the right place}
+% \begin{macrocode}
+ \prevdepth\z@
+% \end{macrocode}
+% Now after typesetting the box we back up to its baseline by using
+% the value stored in |\dimen2| (which will hold the largest depth
+% found on any column).
+% \changes{v1.8g}{2003/03/15}{Now adjusting \cs{prevdepth}}
+% \begin{macrocode}
+ \kern-\dimen\tw@
+% \end{macrocode}
+% However, in case one of the columns was unusually deep \TeX{} may
+% have tried some corrective actions in which case backing up by
+% the saved value will not bring us back to the baseline. A good
+% indication for this is a depth of |\maxdepth| though it is not an
+% absolute proof. If the option \texttt{grid} is used
+% |\mc@gridwarn| will expand to this, otherwise to |\maxdimen| in
+% which case this warning will not show up.
+% \changes{v1.8g}{2014/08/24}{Warn if value is exceeded not when equal}
+% \begin{macrocode}
+ \ifdim\dimen\tw@ > \mc@gridwarn
+ \PackageWarning{multicol}%
+ {Very deep columns!\MessageBreak
+ Grid alignment might be broken}%
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\columnseprulecolor}
+% \changes{v1.6f}{2006/09/19}{Make the color of the rule a hook}
+% By default the vertical rule between columns will be in |\normalcolor|.
+% \begin{macrocode}
+\def\columnseprulecolor{\normalcolor}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\reinsert@footnotes}
+% Before we tackle the bigger output routines we define just one
+% more macro which will help us to find our way through the
+% mysteries later. |\reinsert@footnotes| will do what its name
+% indicates: it reinserts the footnotes present in
+% |\footinbox| so that they will be reprocessed by \TeX{}'s
+% {\it page\_builder}.
+%
+% Instead of actually reinserting the footnotes we insert an empty
+% footnote. This will trigger insertion mechanism as well and since
+% the old footnotes are still in their box and we are on a fresh page
+% |\skip| |footins| should be correctly taken into account.
+% \changes{v1.3c}{1990/03/03}{\cs{unbox}ing avoided.}
+% \begin{macrocode}
+\def\reinsert@footnotes{\ifvoid\footins\else
+ \insert\footins{}\fi}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\vfilmaxdepth}
+% This curious definition is used as the space at the bottom of a
+% column if we implement |\raggedcolumns|. Normally one only appends
+% |\vfill| in that case but this is actually wrong for columns that
+% are more or less full: by adding a glue at the bottom such a
+% column doesn't have any depth any more but without it the material
+% would be allowed a depth of |\maxdepth|. So we allow shrinking by
+% that amount. This only makes a difference if the box would
+% otherwise become overfull and shrinking never exceeds the
+% specified value, so we should be fine.
+% \changes{v1.8h}{2014/09/12}{Macro added (pr/4395)}
+% \changes{v1.8j}{2015/03/07}{Use only `0.0001fil' for stretching}
+% \begin{macrocode}
+\def\vfilmaxdepth{\vskip \z@ \@plus .0001fil
+ \@minus \maxdepth}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\multi@column@out}
+% Now we can't postpone the difficulties any longer. The
+% |\multi@column@out| routine will be called in two situations.
+% Either the page is full (i.e., we have collected enough material
+% to generate all the required columns) or a float or marginpar or
+% a |\clearpage| is
+% sensed. In the latter case the |\outputpenalty| is less
+% than $-10000$, otherwise the penalty which triggered the output
+% routine is higher. Therefore it's easy to distinguish both
+% cases: we simply test this register.
+% \changes{v1.5c}{1993/04/18}{Support \cs{clearpage}}
+% \begin{macrocode}
+\def\multi@column@out{%
+ \ifnum\outputpenalty <-\@M
+% \end{macrocode}
+% If this was a |\clearpage|, a float or a marginpar we call
+% |\speci@ls|
+% \begin{macrocode}
+ \speci@ls \else
+% \end{macrocode}
+% otherwise we construct the final page.
+% \changes{v1.5u}{1999/05/25}{Support \cs{columnbreak}}
+% \changes{v1.5v}{1999/07/18}{Added debug statements for
+% column break support}
+% For the next block of code see comments in section~\ref{sec:colbreak}.
+% \begin{macrocode}
+ \ifvoid\colbreak@box\else
+ \mult@info\@ne{Re-adding forced
+ break(s) for splitting}%
+ \setbox\@cclv\vbox{%
+ \unvbox\colbreak@box
+ \penalty-\@Mv
+ \unvbox\@cclv}%
+ \fi
+% \end{macrocode}
+% Let us now consider the
+% normal case. We have to |\vsplit| the columns from the
+% accumulated material in box 255. Therefore we first assign
+% appropriate values to |\splittopskip| and |\splitmaxdepth|.
+% \begin{macrocode}
+ \splittopskip\topskip
+ \splitmaxdepth\maxdepth
+% \end{macrocode}
+% We also need to restrict |\boxmaxdepth| so that re-boxing is not
+% generating boxes with arbitrary depth.
+% \changes{v1.8j}{2015/03/07}{Set \cs{boxmaxdepth}}
+% \begin{macrocode}
+ \boxmaxdepth\maxdepth
+% \end{macrocode}
+% Then we calculate the current column height (in |\dimen@|).
+% Note that the height of |\partial@page| is already
+% subtracted from |\@colroom| so we can use its value as a
+% starter.
+% \begin{macrocode}
+ \dimen@\@colroom
+% \end{macrocode}
+% But we must also subtract the space occupied by footnotes on the
+% current page. Note that we first have to reset the skip register
+% to its normal value.
+% Again, the actual action is carried out in a utility macro, so that
+% other applications can modify it.
+% \changes{v1.5?}{1994/?/?}{Use \cs{leave@mult@footins}}
+% \begin{macrocode}
+ \divide\skip\footins\col@number
+ \ifvoid\footins \else
+ \leave@mult@footins
+ \fi
+% \end{macrocode}
+% And there is one more adjustment that we have to make: if the
+% user has issue a |\enlargethispage| command then the height the
+% |\@kludgeins| box will be the negation of the size by which the
+% page should be enlarged. If the star form of this command has
+% been used then we also need to shrink the resulting column.
+
+% That local change will be reverted at the end of the output
+% routine So for the next page the original state will be
+% reestablished. However, in theory there is a possibility to sneak
+% in a whole multicols environment into the running header
+% definition. If that happens then it will also be affected by this
+% change---too bad I think.
+% \changes{v1.8a}{2011/12/20}{Support for \cs{enlargethispage}}
+% \changes{v1.8v}{2018/12/27}{Removed dead code, the case where this
+% can go wrong is too obscure to worry about it (gh/101)}
+% \begin{macrocode}
+ \ifvbox \@kludgeins
+ \advance \dimen@ -\ht\@kludgeins
+% \end{macrocode}
+% The star form of |\enlargethispage| makes the width of the box
+% greater than zero (sneaky isn't it?).
+% \begin{macrocode}
+ \ifdim \wd\@kludgeins>\z@
+ \shr@nkingtrue
+ \fi
+ \fi
+% \end{macrocode}
+% Now we are able to |\vsplit| off all but the last column.
+% Recall that these columns should be saved in the box registers 2,
+% 4,\ldots\ (plus offset).
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+% \begin{macrocode}
+ \process@cols\mult@gfirstbox{%
+ \setbox\count@
+ \vsplit\@cclv to\dimen@
+% \end{macrocode}
+% After splitting we update the kept marks.
+% \begin{macrocode}
+ \set@keptmarks
+% \end{macrocode}
+% If |\raggedcolumns| is in force we add a |vfill| at the bottom by
+% unboxing the split box.
+% But we need to unbox anyway to ensure that at the end of the box
+% we do not have unwanted space. This can sneak in in certain
+% situations, for example, if two lists follow each other and we
+% break between them. While such space is usually zero it still has
+% an effect because it hides depth of the last line in the column
+% and that will result in incorrect placement.
+% \changes{v1.3c}{1990/03/03}{\cs{unbox}ing avoided.}
+% \changes{v1.8b}{2013/08/28}{And 20odd years later conclude that
+% this was wrong and unboxing is always needed.}
+% \changes{v1.8b}{2013/08/28}{Remove discardable items at the
+% end of split boxes}
+% \changes{v1.8h}{2014/09/12}{Use \cs{vfilmaxdepth}}
+% \changes{v1.8k}{2015/03/22}{\cs{remove@discardable@items} removed}
+% \begin{macrocode}
+ \setbox\count@
+ \vbox to\dimen@
+ {\unvbox\count@
+ \ifshr@nking\vfilmaxdepth\fi}%
+ }%
+% \end{macrocode}
+% Then the last column follows.
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+% \changes{v1.8b}{2013/08/28}{Remove discardable items at the
+% end of split boxes}
+% \changes{v1.8h}{2014/09/12}{Use \cs{vfilmaxdepth}}
+% \changes{v1.8k}{2015/03/22}{\cs{remove@discardable@items} removed}
+% \begin{macrocode}
+ \setbox\mult@rightbox
+ \vsplit\@cclv to\dimen@
+ \set@keptmarks
+ \setbox\mult@rightbox\vbox to\dimen@
+ {\unvbox\mult@rightbox
+ \ifshr@nking\vfilmaxdepth\fi}%
+% \end{macrocode}
+% Having done this we hope that box 255 is emptied. If not, we
+% reinsert its contents.
+% \changes{v1.8a}{2011/12/20}{Only re-add output penalty if it was
+% explicitly set}
+% \begin{macrocode}
+ \ifvoid\@cclv \else
+ \unvbox\@cclv
+ \ifnum\outputpenalty=\@M
+ \else
+ \penalty\outputpenalty
+ \fi
+% \end{macrocode}
+% In this case a footnote that happens to fall into the leftover
+% bit will be typeset on the wrong page. Therefore we warn the user
+% if the current page contains footnotes. The older versions of
+% \mc{} produced this warning regardless of whether or not
+% footnotes were present, resulting in many unnecessary warnings.
+% \changes{v1.3c}{1991/02/17}{Check if footnotes are actually present
+% before issuing a warning.}
+% \begin{macrocode}
+ \ifvoid\footins\else
+ \PackageWarning{multicol}%
+ {I moved some lines to
+ the next page.\MessageBreak
+ Footnotes on page
+ \thepage\space might be wrong}%
+ \fi
+% \end{macrocode}
+% If the `\textsf{tracingmulticols}' counter is 4 or higher we also
+% add a rule.
+% \begin{macrocode}
+ \ifnum \c@tracingmulticols>\thr@@
+ \hrule\allowbreak \fi
+ \fi
+% \end{macrocode}
+% To get a correct marks for the current page we have to (locally)
+% redefine |\firstmark| and |\botmark|.
+% If |\kept@firstmark| is non-empty then |\kept@botmark| must be
+% non-empty too so we can use their values. Otherwise we use the
+% value of |\kept@topmark| which was first initialized when we
+% gathered the |\partical@page| and later on was updated to the
+% |\botmark| for the preceding page.
+%
+% \changes{v1.4a}{1992/02/14}{\cs{botmark} set to \cs{splitbotmark}}
+% \begin{macrocode}
+ \ifx\@empty\kept@firstmark
+ \let\firstmark\kept@topmark
+ \let\botmark\kept@topmark
+ \else
+ \let\firstmark\kept@firstmark
+ \let\botmark\kept@botmark
+ \fi
+% \end{macrocode}
+% We also initialize |\topmark| with |\kept@topmark|. This will make
+% this mark okay for all middle pages of the \mc{} environment.
+% \changes{v1.5d}{1993/09/15}{reinit \cs{topmark}}
+% \begin{macrocode}
+ \let\topmark\kept@topmark
+%<*marktrace>
+ \mult@info\tw@
+ {Use kept top mark:\MessageBreak
+ \meaning\kept@topmark
+ \MessageBreak
+ Use kept first mark:\MessageBreak
+ \meaning\kept@firstmark
+ \MessageBreak
+ Use kept bot mark:\MessageBreak
+ \meaning\kept@botmark
+ \MessageBreak
+ Produce first mark:\MessageBreak
+ \meaning\firstmark
+ \MessageBreak
+ Produce bot mark:\MessageBreak
+ \meaning\botmark
+ \@gobbletwo}%
+%</marktrace>
+% \end{macrocode}
+% With a little more effort we could have done better. If we had,
+% for example, recorded the shrinkage of the material in
+% |\partial@page| it would be now possible to try higher
+% values for |\dimen@| (i.e.\ the column height) to overcome
+% the problem with the nonempty box 255. But this would make the
+% code even more complex so I skipped it in the current
+% implementation.
+%
+% Now we use \LaTeX{}'s standard output
+% mechanism.\footnote{This will produce a lot of overhead since both
+% output routines are held in memory. The correct
+% solution would be to redesign the whole output
+% routine used in \LaTeX.}
+% Admittedly this is a funny way to do it.
+%
+% Within the OR |\boxmaxdepth| needs to be unrestricted so we set it back
+% now as it was changed above.
+% \changes{v1.8p}{2016/04/07}{Reset \cs{boxmaxdepth}}
+% \begin{macrocode}
+ \boxmaxdepth\maxdimen
+ \setbox\@cclv\vbox{\unvbox\partial@page
+ \page@sofar}%
+% \end{macrocode}
+% The macro |\@makecol| adds all floats assigned for the current
+% page to this page. |\@outputpage| ships out the resulting box.
+% Note that it is just possible that such floats are present even
+% if we do not allow any inside a \mc{} environment.
+% \begin{macrocode}
+ \@makecol\@outputpage
+% \end{macrocode}
+% After the page is shipped out we have to prepare the kept marks
+% for the following page. |\kept@firstmark| and |\kept@botmark|
+% reinitialized by setting them to |\@empty|. The value of
+% |\botmark| is then assigned to |\kept@topmark|.
+% \changes{v1.4g}{1992/06/03}{Only change \cs{kept@topmark} if
+% \cs{kept@botmark} non-empty}
+% \changes{v1.4i}{1992/06/18}{Set \cs{kept@topmark} to \cs{botmark}}
+% \begin{macrocode}
+ \global\let\kept@topmark\botmark
+ \global\let\kept@firstmark\@empty
+ \global\let\kept@botmark\@empty
+%<*marktrace>
+ \mult@info\tw@
+ {(Re)Init top mark:\MessageBreak
+ \meaning\kept@topmark
+ \@gobbletwo}%
+%</marktrace>
+% \end{macrocode}
+% Now we reset |\@colroom| to |\@colht| which is \LaTeX's
+% saved value of |\textheight|.
+% We also have to reset the recorded position of the last
+% |\marginpar| as well as the recorded size of in-text floats
+% as we are now on a new page.
+% \changes{v1.8d}{2014/04/23}{Reset \cs{@mparbottom} after page finishes}
+% \changes{v1.8n}{2015/08/19}{Reset \cs{@textfloatsheight} after page finishes}
+% \begin{macrocode}
+ \global\@colroom\@colht
+ \global \@mparbottom \z@
+ \global \@textfloatsheight \z@
+% \end{macrocode}
+% Then we process deferred floats waiting for their chance to be
+% placed on the next page.
+% \begin{macrocode}
+ \process@deferreds
+ \@whilesw\if@fcolmade\fi{\@outputpage
+ \global\@colroom\@colht
+ \process@deferreds}%
+% \end{macrocode}
+% If the user is interested in statistics we inform him about the
+% amount of space reserved for floats.
+% \begin{macrocode}
+ \mult@info\@ne
+ {Colroom:\MessageBreak
+ \the\@colht\space
+ after float space removed
+ = \the\@colroom \@gobble}%
+% \end{macrocode}
+% Having done all this we must prepare to tackle the next page.
+% Therefore we assign a new value to |\vsize|. New, because
+% |\partial@page| is now empty and |\@colroom| might be
+% reduced by the space reserved for floats.
+% \changes{v1.4p}{1992/11/26}{Use different \cs{vsize} setting}
+% \begin{macrocode}
+ \set@mult@vsize \global
+% \end{macrocode}
+% The |\footins| skip register will be adjusted when the output
+% group is closed.
+% \changes{v1.3c}{1991/03/03}{Unnecessary code removed}
+% \begin{macrocode}
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\leave@mult@footins}
+% This macro is used to subtract the amount of space
+% occupied by footnotes for the current space from the
+% space available for the current column. The space current column
+% is stored in |\dimen@|. See above for the description of the default
+% action.
+% \changes{v1.5?}{1994/?/?}{Macro added}
+% \begin{macrocode}
+\def\leave@mult@footins{%
+ \advance\dimen@-\skip\footins
+ \advance\dimen@-\ht\footins
+}
+% \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\speci@ls}
+% We left out two macros: |\process@deferreds| and
+% |\speci@ls|.
+% \changes{v1.5c}{1993/04/18}{Support \cs{clearpage}}
+% \begin{macrocode}
+\def\speci@ls{%
+ \ifnum\outputpenalty <-\@Mi
+% \end{macrocode}
+% If the document ends in the middle of a multicols environment, e.g.,
+% if the user forgot the |\end{multicols}|, \TeX{} adds a very
+% negative penalty to the end of the galley which is intended to signal
+% the output routine that it is time to prepare for shipping out
+% everything remaining. Since inside multicols the output routine of
+% \LaTeX{} is disabled sometimes we better check for this case: if we
+% find a very negative penalty we produce an error message and run
+% the default output routine for this case.
+% \changes{v1.5s}{1998/09/10}{check for \cs{stop} penalty pr/2873}
+% \begin{macrocode}
+ \ifnum \outputpenalty<-\@MM
+ \PackageError{multicol}{Document end
+ inside multicols environment}\@ehd
+ \@specialoutput
+ \else
+% \end{macrocode}
+% \changes{v1.5u}{1999/05/25}{Support \cs{columnbreak}}
+% \changes{v1.5v}{1999/07/18}{Added debug statements for
+% column break support}
+% For the next block of code see comments in section~\ref{sec:colbreak}.
+% \begin{macrocode}
+ \ifnum\outputpenalty = -\@Mv
+ \mult@info\@ne{Forced column
+ break seen}%
+ \global\advance\vsize-\pagetotal
+ \global\setbox\colbreak@box
+ \vbox{%
+ \ifvoid\colbreak@box
+ \else
+ \unvbox\colbreak@box
+ \penalty-\@Mv
+ \fi
+% \end{macrocode}
+% As this is the place of a forced break we now remove vertical
+% white space just in front of it (or some of it at least) as it is
+% quite likely that the break is not exactly in the right place,
+% e.g., after a display environment (if LaTeX would break here by
+% its own it would break before the space following the display).
+%
+% Thus we rebox box 255 once (using |\maxdepth| and calling
+% |\remove@discardable@items| inside). The depth of 255 will then
+% give us the depth the box would have had if it would have been a
+% natural break. We then unbox 255 to get it into the
+% |\colbreak@box| and then back up by this depth. This will position
+% the bottom of the box at its natural baseline which is useful for
+% balancing later on.
+% \changes{v1.8k}{2015/03/21}{Remove discardable items just before a
+% forced break}
+% \begin{macrocode}
+ \boxmaxdepth\maxdepth
+ \setbox\@cclv\vbox{%
+ \unvbox\@cclv
+ \remove@discardable@items}%
+ \dimen@\dp\@cclv
+ \unvbox\@cclv
+ \kern-\dimen@
+ }%
+ \reinsert@footnotes
+ \else
+% \end{macrocode}
+% Another special case is reaching the end of the \mc{}
+% environment which is signaled by |-\@Mvi|.
+% \changes{v1.8r}{2018/01/28}{Handling end of env through special penalty}
+% \begin{macrocode}
+ \ifnum\outputpenalty = -\@Mvi
+ \mult@info\@ne{End penalty of multicols seen}%
+% \end{macrocode}
+% If we are at this point then have have to run the balancing code
+% (which was previously its own output routine). First we pretend
+% that we had a normal forced breakpoint and then call
+% |\balance@column@out|. The latter may be let to |\multi@column@out|
+% if we are inside \texttt{multicols*} in which case we would get a loop
+% if the |\outputpenalty| is not changed---this could be cleaned up
+% in a better way; basically it is like this, because of the older
+% code was using different ORs and I simply reused most of it.
+% \begin{macrocode}
+ \outputpenalty\@M % pretend we had a natural forced break
+ \balance@columns@out
+ \else
+% \end{macrocode}
+% If we encounter a float or a marginpar in the current
+% implementation we simply warn the user that this is not allowed.
+% Then we reinsert the page and its footnotes.
+% \begin{macrocode}
+ \PackageWarningNoLine{multicol}%
+ {Floats and marginpars not
+ allowed inside `multicols'
+ environment!}%
+ \unvbox\@cclv\reinsert@footnotes
+% \end{macrocode}
+% Additionally we empty the |\@currlist| to avoid later error
+% messages when the \LaTeX{} output routine is again in force.
+% But first we have to place the boxes back onto the
+% |\@freelist|. (|\@elt|s default is |\relax| so
+% this is possible with |\xdef|.)
+% \changes{v1.2a}{1990/02/05}{Float boxes freed.}
+% \begin{macrocode}
+ \xdef\@freelist{\@freelist\@currlist}%
+ \gdef\@currlist{}%
+ \fi
+ \fi
+ \fi
+% \end{macrocode}
+% If the penalty is $-10001$ it will come from a |\clearpage| and
+% we will execute |\@doclearpage| to get rid of any deferred
+% floats.
+% \begin{macrocode}
+ \else \@doclearpage \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\process@deferreds}
+% |\process@deferreds| is a simplified version of \LaTeX{}'s
+% |\@startpage|. We first call the macro
+% |\@floatplacement| to save the current user parameters in
+% internal registers. Then we start a new group and save the
+% |\@deferlist| temporarily in the macro |\@tempb|.
+% \begin{macrocode}
+\def\process@deferreds{%
+ \@floatplacement
+ \@tryfcolumn\@deferlist
+ \if@fcolmade\else
+ \begingroup
+ \let\@tempb\@deferlist
+% \end{macrocode}
+% Our next action is to (globally) empty |\@deferlist| and
+% assign a new meaning to |\@elt|. Here |\@scolelt| is a
+% macro that looks at the boxes in a list to decide whether they
+% should be placed on the next page (i.e.\ on |\@toplist| or
+% |\@botlist|) or should wait for further processing.
+% \begin{macrocode}
+ \gdef\@deferlist{}%
+ \let\@elt\@scolelt
+% \end{macrocode}
+% Now we call |\@tempb| which has the form
+% \begin{center}
+% |\@elt|\meta{box register}|\@elt|^^A
+% \meta{box register}\ldots{}
+% \end{center}
+% So |\@elt| (i.e.\ |\@scolelt|) will distribute the
+% boxes to the three lists.
+% \begin{macrocode}
+ \@tempb \endgroup
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{ifshr@nking}
+% \begin{macro}{\raggedcolumns}
+% \begin{macro}{\flushcolumns}
+% \changes{v1.1a}{1989/09/20}{\cs{flushedcolumns} renamed to \cs{flushcolumns}.}
+% The |\raggedcolumns| and |\flushcolumns|
+% declarations are defined with the help of a new |\if...|
+% macro.
+% \begin{macrocode}
+\newif\ifshr@nking
+% \end{macrocode}
+% The actual definitions are simple: we just switch to \textsf{true}
+% or \textsf{false} depending on the desired action. To avoid extra
+% spaces in the output we enclose these changes in
+% |\@bsphack|\ldots{}\allowbreak|\@esphack|.
+% \begin{macrocode}
+\def\raggedcolumns{%
+ \@bsphack\shr@nkingtrue\@esphack}
+\def\flushcolumns{%
+ \@bsphack\shr@nkingfalse\@esphack}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\balance@columns@out}
+% Now for the last part of the show: the column balancing output
+% routine. Since this code is called with an explicit penalty
+% (|\eject|) there is no need to check for something special (eg
+% floats). We start by balancing the material gathered.
+% \begin{macrocode}
+\def\balance@columns@out{%
+% \end{macrocode}
+% For this we need to put the contents of box 255 into |\mult@box|.
+% \changes{v1.5u}{1999/05/25}{Support \cs{columnbreak}}
+% \changes{v1.5v}{1999/07/18}{Added debug statements for column break
+% support} For the next block of code see also comments in
+% section~\ref{sec:colbreak}. All forced breaks except the last are
+% inside |\colbreak@box| so all we have to do is to concatenate this
+% box with box |\@cclv| and put a penalty in between. Here we test if
+% |\colbreak@box| is void so that the message is only generated if
+% we really add forced breaks and the penalty.
+% \changes{v1.8k}{2015/03/21}{Use \cs{@Mv} and not \cs{break} in case
+% this forced break is not used on this page}
+% \begin{macrocode}
+ \setbox\mult@box\vbox{%
+ \ifvoid\colbreak@box\else
+ \unvbox\colbreak@box
+ \penalty-\@Mv
+ \mult@info\@ne{Re-adding
+ forced break(s) in balancing}%
+ \fi
+ \unvbox\@cclv
+% \end{macrocode}
+% The last column again is a forced break, so here we discard white
+% space as well as that is normally unwanted.
+% \changes{v1.8k}{2015/03/21}{Add \cs{remove@discardable@items} at the
+% end of the last column when balancing.}
+% \begin{macrocode}
+ \remove@discardable@items
+ }%
+ \balance@columns
+% \end{macrocode}
+% If during balancing the columns got too long the flag
+% |\iftoo@bad| is set to true.
+% \changes{v1.8a}{2011/12/20}{Balancing concept improved}
+% \begin{macrocode}
+ \iftoo@bad
+ \mult@info\@ne
+ {Balancing failed ...
+ cut a normal page}%
+% \end{macrocode}
+% In that case we put the material back in box 255 so that we can
+% cut a normal page. The curious set of
+% |\vskip|s we add is necessary to cancel out the |\splittopskip|
+% that got added for balancing.
+% \begin{macrocode}
+ \setbox\@cclv\vbox
+ {\vskip\topskip
+ \vskip-\splittopskip
+ \unvbox\mult@box
+% \end{macrocode}
+% We also have to re-add the end of environment penalty since after
+% this page we may want balance the remaining material.
+% \changes{v1.8r}{2018/01/28}{Re-add the final penalty}
+% \begin{macrocode}
+ \penalty-\@Mvi
+ }%
+% \end{macrocode}
+% We then call the standard multicol output routine which will
+% produce a normal page for us (remember we are still within the
+% OR so some part of the code in |\multi@column@out| is actually not
+% doing anything---perhaps this should be cleaned up at some point).
+% This also means that if there was an |\enlargethispage| present
+% it will apply to this page as |\multi@column@out| will look at
+% the status of |\@kludgeins|.
+% \begin{macrocode}
+ \multi@column@out
+% \end{macrocode}
+% Because balancing made the columns too long we are sure that there
+% will be some material remaining which was put back onto the main
+% vertical list by |\multi@column@out|. This will also put the
+% explicit |\eject| penalty back so the current
+% |\balance@columns@out| output routine will be called again (so we
+% better do not add another penalty or else the OR will be called
+% twice and we may get scrambled results).
+% \changes{v1.8k}{2015/03/21}{No additional penalty here}
+% \begin{macrocode}
+ \else
+% \end{macrocode}
+% If the balancing went ok, we are in the position
+% to apply |\page@sofar|. But first we have to set |\vsize| to a
+% value suitable for one column output.
+% \begin{macrocode}
+ \global\vsize\@colroom
+ \global\advance\vsize\ht\partial@page
+% \end{macrocode}
+% We also have to look at |\@kludgeins| and generate a new
+% |\insert| in case there was one present due to an
+% |\enlargethispage| command.
+% \changes{v1.8a}{2011/12/20}{Support for \cs{enlargethispage}}
+% \begin{macrocode}
+ \ifvbox\@kludgeins\insert\@kludgeins
+ {\unvbox\@kludgeins}\fi
+% \end{macrocode}
+% Then we |\unvbox| the |\partial@page| (which may be void if we
+% are not processing the first page of this \mc{} environment.
+% \begin{macrocode}
+ \unvbox\partial@page
+% \end{macrocode}
+% Then we return the first and bottom mark and the gathered
+% material to the main vertical list.
+% \begin{macrocode}
+ \return@nonemptymark{first}\kept@firstmark
+ \return@nonemptymark{bot}\kept@botmark
+ \page@sofar
+% \end{macrocode}
+% We need to add a penalty at this point which allows to break at
+% this point since calling the output routine may have removed the
+% only permissible break point thereby ``glueing'' any following
+% skip to the balanced box. In case there are any weird settings
+% for |\multicolsep| etc. this could produce funny results.
+% \changes{v1.5c}{1993/04/18}{added penalty at output routine exit}
+% \begin{macrocode}
+ \penalty\z@
+ \fi
+}
+% \end{macrocode}
+% As we already know, reinserting of footnotes will be done in the
+% macro |\endmulticols|.
+% \end{macro}
+%
+%
+% \begin{macro}{\balance@columns}
+% This macro now does the actual balancing.
+% \begin{macrocode}
+\def\balance@columns{%
+% \end{macrocode}
+% We start by setting the kept marks by updating them with any
+% marks from this box. This has to be done \emph{before} we add a
+% penalty of $-10000$ to the top of the box, otherwise only an
+% empty box will be considered.
+% \changes{v1.5h}{1994/08/26}{Get kept marks first}
+% \begin{macrocode}
+ \get@keptmarks\mult@box
+% \end{macrocode}
+% We then continue by resetting trying to remove any discardable
+% stuff at the end of |\mult@box|. This is rather experimental. We
+% also add a forced break point at the very beginning, so that we
+% can split the box to height zero later on, thereby adding a known
+% |\splittopskip| glue at the beginning.
+% \changes{v1.8k}{2015/03/21}{\cs{remove@discardable@items} removed}
+% \begin{macrocode}
+ \setbox\mult@box\vbox{%
+ \penalty-\@M
+ \unvbox\mult@box
+ }%
+% \end{macrocode}
+% Then follow values assignments to get the |\vsplit|ting right.
+% We use the natural part of |\topskip| as the natural part for
+% |\splittopskip| and allow for a bit of undershoot and overshoot
+% by adding some stretch and shrink.
+% \changes{v1.5?}{1994/?/?}{Allow columns to come out a bit long or short}
+% \begin{macrocode}
+ \@tempdima\topskip
+ \splittopskip\@tempdima
+ \@plus\multicolundershoot
+ \@minus\multicolovershoot
+ \splitmaxdepth\maxdepth
+% \end{macrocode}
+% We also have to set |\boxmaxdepth| which normally allows to
+% build boxes with arbitrary depth, but as we are building text
+% columns we really want to restrict the depth. This is necessary as
+% we sometimes rebox the boxes generated by |\vsplit| and then the
+% restriction posed by |\splitmaxdepth| gets lost.
+% \changes{v1.8h}{2014/09/12}{All column boxes should obey
+% \cs{maxdepth} (pr/4395)}
+% \begin{macrocode}
+ \boxmaxdepth\maxdepth
+% \end{macrocode}
+% The next step is a bit tricky: when \TeX{} assembles material in
+% a box, the first line isn't preceded by interline glue, i.e.
+% there is no parameter like |\boxtopskip| in \TeX{}. This means
+% that the baseline of the first line in our box is at some
+% unpredictable point depending on the height of the largest
+% character in this line. But of course we want all columns to
+% align properly at the baselines of their first lines. For this
+% reason we have opened |\mult@box| with a |\penalty| \textsf{-10000}.
+% This will now allow us to split off from |\mult@box| a tiny bit
+% (in fact nothing since the first possible break-point is the
+% first item in the box). The result is that |\splittopskip| is
+% inserted at the top of |\mult@box| which is exactly what we like
+% to achieve.
+% \changes{v1.5?}{1994/?/?}{Do splitting to zero here}
+% \begin{macrocode}
+ \setbox\@tempboxa\vsplit\mult@box to\z@
+% \end{macrocode}
+% Next we try to find a suitable starting point for the calculation
+% of the column height. It should be less than the height finally
+% chosen, but large enough to reach this final value in only a few
+% iterations. The formula which is now implemented will try to
+% start with the nearest value which is a multiple of
+% |\baselineskip|. The coding is slightly tricky in \TeX{} and
+% there are perhaps better ways \ldots
+% \changes{v1.4d}{1992/03/04}{New algorithm for start height}
+% \begin{macrocode}
+ \@tempdima\ht\mult@box
+ \advance\@tempdima\dp\mult@box
+ \divide\@tempdima\col@number
+% \end{macrocode}
+% The code above sets |\@tempdima| to the length of a column if we
+% simply divide the whole box into equal pieces. To get to the next
+% lower multiple of |\baselineskip| we convert this dimen to a
+% number (the number of scaled points) then divide this by
+% |\baselineskip| (also in scaled points) and then multiply this
+% result with |\baselineskip| assigning the result to |\dimen@|.
+% This makes |\dimen@| $\leq$ to |\@tempdimena|.
+% \begin{macrocode}
+ \count@\@tempdima
+ \divide\count@\baselineskip
+ \dimen@\count@\baselineskip
+% \end{macrocode}
+% Next step is to correct our result by taking into account the
+% difference between |\topskip| and |\baselineskip|. We start by
+% adding |\topskip|; if this makes the result too large then we
+% have to subtract one |\baselineskip|.
+% \begin{macrocode}
+ \advance\dimen@\topskip
+ \ifdim \dimen@ >\@tempdima
+ \advance\dimen@-\baselineskip
+ \fi
+% \end{macrocode}
+% As a further restriction we want to see a minimum number of
+% rows in the balanced result based on the setting of the counter
+% |minrows|. If the starting value is lower we adjust.
+% \changes{v1.8w}{2019/03/01}{Provide minrows counter for balancing}
+% \begin{macrocode}
+ \@tempdima\dimexpr
+ \topskip +\c@minrows\baselineskip-\baselineskip\relax
+ \ifnum\dimen@<\@tempdima
+ \mult@info\@ne
+ {Start value
+ \the\dimen@ \space ->
+ \the\@tempdima \space (corrected for minrows)}%
+ \dimen@\@tempdima
+ \fi
+% \end{macrocode}
+% At the user's request we start with a higher value (or lower, but
+% this usually only increases the number of tries).
+% \begin{macrocode}
+ \advance\dimen@\c@unbalance\baselineskip
+% \end{macrocode}
+% We type out statistics if we were asked to do so.
+% \changes{v1.4f}{1992/04/28}{\cs{on@line} added to tracing info}
+% \begin{macrocode}
+ \mult@info\@ne
+ {Balance columns\on@line:
+ \ifnum\c@unbalance=\z@\else
+ (off balance=\number\c@unbalance)\fi
+ \@gobbletwo}%
+% \end{macrocode}
+% But we don't allow nonsense values for a start.
+% \begin{macrocode}
+ \ifnum\dimen@<\topskip
+ \mult@info\@ne
+ {Start value
+ \the\dimen@ \space ->
+ \the\topskip \space (corrected)}%
+ \dimen@\topskip
+ \fi
+% \end{macrocode}
+% Now we try to find the final column height. We start by setting
+% |\vbadness| to infinity (i.e.\ $10000$) to suppress
+% underfull box reports while we are trying to find an acceptable
+% solution. We do not need to do it in a group since at the end of
+% the output routine everything will be restored. The setting of
+% the final columns will nearly always produce underfull boxes with
+% badness $10000$ so there is no point in warning the user about
+% it.
+% \changes{v1.2a}{1990/02/05}{Group around main loop removed.}
+% \begin{macrocode}
+ \vbadness\@M
+% \end{macrocode}
+% We also allow for overfull boxes while we trying to split the
+% columns. They can easily happen if we have objects with unusual depth.
+% \changes{v1.8h}{2014/09/12}{Do not report overfull}
+% \begin{macrocode}
+ \vfuzz \maxdimen
+% \end{macrocode}
+% The variable |\last@try| will hold the dimension used in the
+% previous trial splitting. We initialize it with a negative value.
+% \changes{v1.5?}{1994/?/?}{Initialize \cs{last@try}}
+% \begin{macrocode}
+ \last@try-\p@
+ \loop
+% \end{macrocode}
+% In order not to clutter up \TeX{}'s valuable main memory with
+% things that are no longer needed, we empty all globally used box
+% registers. This is necessary if we return to this point after an
+% unsuccessful trial. We use |\process@cols| for this purpose,
+% starting with |\mult@grightbox|. Note the extra braces around
+% this macro call. They are needed since \PlainTeX{}'s
+% |\loop|\ldots{}\allowbreak|\repeat| mechanism cannot be nested on
+% the same level of grouping.
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+% \begin{macrocode}
+ {\process@cols\mult@grightbox
+ {\global\setbox\count@
+ \box\voidb@x}}%
+% \end{macrocode}
+% The contents of box |\mult@box| are now copied globally to
+% box~|\mult@grightbox|. (This will be the right-most column, as
+% we shall see later.)
+% \begin{macrocode}
+ \global\setbox\mult@grightbox
+ \copy\mult@box
+% \end{macrocode}
+% We start with the assumption that the trial will be successful.
+% If we end up with a solution that is too bad we set
+% |too@bad| to \texttt{true}. We also assume that all forced breaks
+% (if any) will be used during balancing. If this is not the case
+% we record this in |forcedbreak@leftover|.
+% \changes{v1.5b}{1992/11/05}{New badness mechanism}
+% \changes{v1.8k}{2015/03/21}{Init \cs{ifforcedbreak@leftover}}
+% \begin{macrocode}
+%<*badness>
+ \too@badfalse
+ \forcedbreak@leftoverfalse
+%</badness>
+% \end{macrocode}
+% Using |\vsplit| we extract the other columns from box register
+% |\mult@grightbox|. This leaves box register |\mult@box|
+% untouched so that we can start over again if this trial was
+% unsuccessful.
+% \begin{macrocode}
+ {\process@cols\mult@firstbox{%
+ \global\setbox\count@
+ \vsplit\mult@grightbox to\dimen@
+% \end{macrocode}
+% After splitting we need to ensure that there isn't any space at
+% the bottom, so we rebox once more.
+% \changes{v1.8b}{2013/08/28}{Remove discardable items at the
+% end of split boxes}
+% \changes{v1.8k}{2015/03/21}{Do not use \cs{remove@discardable@items}
+% here}
+% \begin{macrocode}
+ \global\setbox\count@
+ \vbox to\dimen@
+ {\unvbox\count@}%
+% \end{macrocode}
+% After every split we check the badness of the resulting column,
+% normally the amount of extra white in the column.
+% \begin{macrocode}
+%<*badness>
+ \ifnum\c@tracingmulticols>\@ne
+ \@tempcnta\count@
+ \advance\@tempcnta-\mult@grightbox
+ \divide\@tempcnta \tw@
+ \message{^^JColumn
+ \number\@tempcnta\space
+ badness: \the\badness\space}%
+ \fi
+% \end{macrocode}
+% If this badness is larger than the allowed column badness
+% we reject this solution by setting |too@bad| to \texttt{true}.
+% \begin{macrocode}
+ \ifnum\badness>\c@columnbadness
+ \ifnum\c@tracingmulticols>\@ne
+ \message{too bad
+ (>\the\c@columnbadness)}%
+ \fi
+ \too@badtrue
+ \fi
+%</badness>
+ }}%
+% \end{macrocode}
+% There is one subtle point here: while all other constructed boxes
+% have a depth that is determined by |\splitmaxdepth| and/or
+% |\boxmaxdepth| the last box
+% will get a natural depth disregarding the original setting and
+% the value of |\splitmaxdepth| or |\boxmaxdepth|. This means that
+% we may end up with a very large depth in box |\mult@grightbox|
+% which would
+% make the result of the testing incorrect. So we change the value
+% by unboxing the box into itself.
+% \begin{macrocode}
+ \global\setbox\mult@grightbox
+ \vbox{\unvbox\mult@grightbox}%
+% \end{macrocode}
+% We also save a copy |\mult@firstbox| at its ``natural'' size
+% for later use.
+% \begin{macrocode}
+ \setbox\mult@nat@firstbox
+ \vbox{\unvcopy\mult@firstbox}%
+% \end{macrocode}
+% After |\process@cols| has done its job we have the following
+% situation:
+% \begin{center}
+% \begin{tabular}{r@{$\:\:\longleftarrow\:\:$}l}
+% box |\mult@rightbox| & all material \\
+% box |\mult@gfirstbox| & first column \\
+% box |\mult@gfirstbox|${}+2$ & second column \\
+% \multicolumn{1}{c}{$\vdots$} &
+% \multicolumn{1}{c}{$\vdots$} \\
+% box |\mult@grightbox| & last column
+% \end{tabular}
+% \end{center}
+% We report the height of the first column, in brackets
+% the natural size is given.
+% \changes{v1.5?}{1994/?/?}{Show natural size}
+% \begin{macrocode}
+ \ifnum\c@tracingmulticols>\@ne
+ \message{^^JFirst column
+ = \the\dimen@\space
+ (\the\ht\mult@nat@firstbox)}\fi
+% \end{macrocode}
+% If |\raggedcolumns| is in force older releases of this file also
+% shrank the first column to its natural height at this point.
+% This was done so that the first column doesn't run short compared
+% to later columns but it is actually producing incorrect results
+% (overprinting of text) in boundary cases, so since version v1.5q
+% |\raggedcolumns| means allows for all columns to run slightly short.
+% \changes{v1.5q}{1998/01/19}{Do not reset \cs{mult@firstbox} (pr2739)}
+% \begin{macrocode}
+% \ifshr@nking
+% \global\setbox\mult@firstbox
+% \copy\mult@nat@firstbox
+% \fi
+% \end{macrocode}
+% Then we give information about the last column.\footnote{With
+% \TeX{} version 3.141 it is now possible to use \LaTeX's
+% \cs{newlinechar} in the \cs{message} command, but
+% people with older \TeX{} versions will now get
+% \texttt{\string^\string^J} instead of a new line on the screen.}
+% \changes{v1.4a}{1992/02/12}{Changed to proper \cs{endlinechar} in\cs{message}}
+% \begin{macrocode}
+ \ifnum\c@tracingmulticols>\@ne
+ \message{<> last column =
+ \the\ht\mult@grightbox^^J}%
+% \end{macrocode}
+% Some tracing code that we don't compile into the production version
+% unless asked for. It will produce huge listings of the boxes
+% involved in balancing in the transcript file.
+% \changes{v1.6f}{2004/07/03}{need to use \cs{mult@grightbox} in the loop}
+% \begin{macrocode}
+%<*debug>
+ \ifnum\c@tracingmulticols>4
+ {\showoutput
+ \batchmode
+ \process@cols\mult@grightbox
+ {\showbox\count@}}%
+ \errorstopmode
+ \fi
+%</debug>
+ \fi
+% \end{macrocode}
+% We check whether our trial was successful. The test used is very
+% simple: we merely compare the first and the last column. Thus
+% the intermediate columns may be longer than the first if
+% |\raggedcolumns| is used. If the right-most column is
+% longer than the first then we start over with a larger value for
+% |\dimen@|.
+% \changes{v1.3c}{1991/03/03}{\cs{global}\cs{advance} left over from older code}
+% \begin{macrocode}
+ \ifdim\ht\mult@grightbox >\dimen@
+% \end{macrocode}
+% If the height of the last box is too large we mark this trial as
+% unsuccessful.
+% \changes{v1.5v}{1999/07/18}{Added tracing statements for
+% trial unsuccessful}
+% \begin{macrocode}
+%<*badness>
+ \too@badtrue
+ \ifnum\c@tracingmulticols>\@ne
+ \typeout{Rejected: last
+ column too large!}%
+ \fi
+ \else
+% \end{macrocode}
+% \changes{v1.5v}{1999/07/18}{Check last column if it contains forced
+% break and reject trial if that is the case}
+%
+% To ensure that there isn't a forced break in the last column we
+% try to split off a box of size |\maxdimen| from |\mult@grightbox|
+% (or rather from a copy of it). This should result in a void box
+% after the split, unless there was a forced break somewhere within
+% the column in which case the material after the break would have
+% stayed in the box.
+% \begin{macrocode}
+ \setbox\@tempboxa
+ \copy\mult@grightbox
+ \setbox\z@\vsplit\@tempboxa to\maxdimen
+ \ifvoid\@tempboxa
+% \end{macrocode}
+% Thus if |\@tempboxa| is void we have a valid solution.
+% In this case we take a closer
+% look at the last column to decide if this column should be made
+% as long as all other columns or if it should be allowed to be
+% shorter.
+% For this we first have to rebox the column into a box of the
+% appropriate height. If tracing is enabled we then display the
+% badness for this box.
+% \begin{macrocode}
+ \global\setbox\mult@grightbox
+ \vbox to\dimen@
+ {\unvbox\mult@grightbox}%
+ \ifnum\c@tracingmulticols>\@ne
+ \message{Final badness:
+ \the\badness}%
+ \fi
+% \end{macrocode}
+% We then compare this badness with the allowed badness for the final
+% column. If it does not exceed this value we use the box, otherwise
+% we rebox it once more and add some glue at the bottom.
+% \changes{v1.8h}{2014/09/12}{Use \cs{vfilmaxdepth}}
+% \changes{v1.8j}{2015/03/07}{Use \cs{vfil} in this case}
+% \begin{macrocode}
+ \ifnum\badness>\c@finalcolumnbadness
+ \global\setbox\mult@grightbox
+ \vbox to\dimen@
+ {\unvbox\mult@grightbox\vfil}%
+ \ifnum\c@tracingmulticols>\@ne
+ \message{ setting natural
+ (> \the\c@finalcolumnbadness)}%
+ \fi
+ \fi
+% \end{macrocode}
+% If |\@tempboxa| above was not void our trial was unsuccessful and
+% we report this fact and try again.
+% \changes{v1.6f}{2004/07/03}{\texttt{/colbreak} guard in the wrong position}
+% \begin{macrocode}
+ \else
+% \end{macrocode}
+% If we have unprocessed forced breaks we normally reiterate with a
+% larger column size to fit them in eventually. However, if there
+% are simply too many of them (e.g., 3 forced breaks but only 2
+% columns to balance) then this will never succeed and and we would
+% continue growing the columns until we hit the largest possible
+% column size. So in addition we check how big the column size is
+% compared to available room and if we exceed this by
+% |\maxbalancingoverflow| we give up and instead of balancing cut
+% another normal page. To be indicate this case we set
+% |forcedbreak@leftover| to true.
+% \changes{v1.8k}{2015/03/21}{Watch out for columns growing too far in
+% case of forced breaks}
+% \changes{v1.8l}{2015/03/25}{Added additional tracing if column overflows}
+% \begin{macrocode}
+ \@tempdima\@colroom
+ \advance\@tempdima \maxbalancingoverflow
+ \ifdim \dimen@ < \@tempdima
+ \too@badtrue
+ \ifnum\c@tracingmulticols>\@ne
+ \typeout{Rejected: unprocessed
+ forced break(s) in last column!}%
+ \fi
+ \else
+ \forcedbreak@leftovertrue
+ \ifnum\c@tracingmulticols>\@ne
+ \typeout{Failed: columns too large
+ with unprocessed forced break(s)!}%
+ \fi
+ \fi
+ \fi
+ \fi
+% \end{macrocode}
+% If the natural height of the first box is smaller than the
+% current trial size but is larger than the previous trial size it
+% is likely that we have missed a potentially better
+% solution. (This could have happened if for some reason our first
+% trial size was too high.) In that case we dismiss this trial and
+% restart using the natural height for the next trial.
+% \begin{macrocode}
+ \ifdim\ht\mult@nat@firstbox<\dimen@
+ \ifdim\ht\mult@nat@firstbox>\last@try
+ \too@badtrue
+ \ifnum\c@tracingmulticols>\@ne
+ \typeout{Retry: using natural
+ height of first column!}%
+ \fi
+ \dimen@\ht\mult@nat@firstbox
+ \last@try\dimen@
+ \advance\dimen@-\p@
+ \fi
+ \fi
+% \end{macrocode}
+% Finally the switch |too@bad| is tested. If it was made true
+% either earlier on or due to a rightmost column being too large
+% we try again with a slightly larger value for |\dimen@|.
+% \begin{macrocode}
+ \iftoo@bad
+%</badness>
+ \advance\dimen@\p@
+ \repeat
+% \end{macrocode}
+% If we come out of the loop with the switch |forcedbreak@leftover|
+% set to true then balancing has failed and we should cut a normal
+% page. We indicate this below with |\too@badtrue| when any of the
+% columns get too high, so we set this flag here too in order to
+% get the same processing logic.\footnote{Should get cleaned up as
+% we now have two different routes to reach this part of the
+% processing.}
+% \changes{v1.8k}{2015/03/21}{}
+% \begin{macrocode}
+ \ifforcedbreak@leftover
+ \too@badtrue
+ \else
+% \end{macrocode}
+% At that point |\dimen@| holds the height that was determined by
+% the balancing loop.
+% If that height for the columns turns out to be larger
+% than the available space (which is |\@colroom|) we squeeze the
+% columns into the space assuming that they will have enough
+% shrinkability to allow this.\footnote{This might be wrong, since
+% the shrinkability that accounts for the amount of material might
+% be present only in some columns. But it is better to try then to
+% give up directly.}
+% However, this squeezing should only be done if we are balancing
+% columns on the main galley and \emph{not} if we are building a
+% boxed multicol (in the latter case the current |\@colroom| is
+% irrelevant since the produced box might be moved anywhere at a
+% later stage).
+% \changes{v1.3c}{1991/03/03}{Limit column height to \cs{@colroom}}
+% \changes{v1.5q}{1998/01/19}{Removed setting \cs{dimen@} (pr2739)}
+% \changes{v1.5y}{2000/06/10}{Limit column height only in unrestricted
+% mode (pr/3212)}
+% \begin{macrocode}
+ \if@boxedmulticols\else
+ \ifdim\dimen@>\@colroom
+ \dimen@\@colroom
+ \fi
+ \fi
+% \end{macrocode}
+% Then we move the contents of the odd-numbered box registers to
+% the even-numbered ones, shrinking them if requested.
+% We have to use |\vbox| not |\vtop| (as it was done in
+% the first versions) since otherwise the resulting boxes will have
+% no height (\TB\/ page 81). This would mean that extra
+% |\topskip| is added when the boxes are returned to the
+% page-builder via |\page@sofar|.
+% \changes{v1.3a}{1990/05/20}{Changed \cs{vtop} to \cs{vbox}.}
+% \begin{macrocode}
+ \process@cols\mult@rightbox
+ {\@tempcnta\count@
+ \advance\@tempcnta\@ne
+% \end{macrocode}
+% when putting the final column together we want overfull
+% information:
+% \begin{macrocode}
+ \vfuzz\z@
+ \setbox\count@\vbox to\dimen@
+ {%
+% \end{macrocode}
+%
+% \changes{v1.8h}{2014/09/12}{Use \cs{vfilmaxdepth}}
+% \begin{macrocode}
+ \vskip \z@
+ \@plus-\multicolundershoot
+ \@minus-\multicolovershoot
+ \unvbox\@tempcnta
+ \ifshr@nking\vfilmaxdepth\fi
+ }%
+% \end{macrocode}
+% If the resulting box is overfull there was too much material to
+% fit into the available space. The question though is how much? If
+% it wasn't more than |\maxbalancingoverflow| we accept it still to
+% avoid getting very little material for the next page (which we
+% would then have difficulties to balance).
+% \changes{v1.8a}{2011/12/20}{Balancing concept improved}
+% \begin{macrocode}
+ \ifnum\badness>\@M
+ \vfuzz\maxdimen % no overfull warning
+ \setbox\@tempboxa \vbox to\dimen@
+ {\vskip-\maxbalancingoverflow
+ \unvcopy\count@}%
+ \ifnum\badness>\@M
+ \mult@info\@ne
+ {Balanced column more than
+ \the\maxbalancingoverflow\space
+ too large}%
+% \end{macrocode}
+% Fail the balancing attempt:
+% \begin{macrocode}
+ \too@badtrue
+ \else
+% \end{macrocode}
+% Otherwise report that there is a problem but within the accepted
+% boundary.
+% \begin{macrocode}
+ \mult@info\@ne
+ {Balanced column
+ too large, but less than
+ \the\maxbalancingoverflow}%
+ \fi
+ \fi
+ }%
+% \end{macrocode}
+% Finally end the |\ifforcedbreak@leftover| conditional.
+% \changes{v1.8k}{2015/03/21}{Finish the new conditional}
+% \begin{macrocode}
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\maxbalancingoverflow}
+% Amount that balancing is allowed to overflow the available column
+% space. We default to 12pt which means about one line in most
+% layouts.
+% \changes{v1.8a}{2011/12/20}{\cs{maxbalancingoverflow} parameter added}
+% \begin{macrocode}
+\newdimen\maxbalancingoverflow
+\maxbalancingoverflow=12pt
+% \end{macrocode}
+% \end{macro}
+
+% \end{multicols}
+%
+% \begin{multicols}{2}[\subsection{The box allocations}]
+%
+% \begin{macro}{\mult@rightbox}
+% \begin{macro}{\mult@grightbox}
+% \begin{macro}{\mult@firstbox}
+% \begin{macro}{\mult@gfirstbox}
+% Early releases of these macros used the first box registers
+% 0, 2, 4,\ldots\ for global boxes and 1, 3, 5,\ldots\ for the
+% corresponding local boxes. (You might still find some traces
+% of this setup in the documentation, sigh.) This produced a problem
+% at the moment we had more than 5 columns because then officially
+% allocated boxes were overwritten by the algorithm.
+% The new release now uses private box registers
+% \begin{macrocode}
+\newbox\mult@rightbox
+\newbox\mult@grightbox
+\newbox\mult@gfirstbox
+\newbox\mult@firstbox
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa
+\let\@tempa\relax
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \end{multicols}
+%
+%
+% \begin{multicols}{2}[\section{New macros and hacks for version 1.2}]
+%
+% \begin{macro}{\emergencystretch}
+% \begin{macro}{\setemergencystretch}
+% If we don't use \TeX{} 3.0 |\emergencystretch| is undefined
+% so in this case we simply add it as an unused \meta{dimen}
+% register.
+% \changes{v1.4j}{1992/06/25}{Setting of \cs{emergencystretch} on top
+% removed.}
+% \begin{macrocode}
+\@ifundefined{emergencystretch}
+ {\newdimen\emergencystretch}{}
+% \end{macrocode}
+% \changes{v1.2a}{1990/02/05}{Macro added.}
+% My tests showed that the following formula worked pretty well.
+% Nevertheless the |\setemergencystretch| macro also gets
+% |\hsize| as second argument to enable the user to try
+% different formulae.
+% \begin{macrocode}
+\def\setemergencystretch#1#2{%
+ \emergencystretch 4pt
+ \multiply\emergencystretch#1}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+
+
+% \begin{macro}{\set@floatcmds}
+% \changes{v1.2a}{1990/02/05}{Macro added.}
+% \changes{v1.5g}{1994/06/07}{Updated since floats have changed}
+% \changes{v1.5j}{1994/06/07}{Updated since floats have changed again}
+% \changes{v1.5l}{1995/10/19}{Added \cs{@largefloatcheck}}
+% \changes{v1.6g}{2006/02/23}{Added \cs{@minipagefalse}}
+% \changes{v1.6h}{2008/12/05}{Use \cs{@endfloatbox} to better support
+% the modifications done by the float package}
+% Even if this should be used as a hook we use a |@| in the
+% name since it is more for experts.
+% \begin{macrocode}
+\def\set@floatcmds{%
+ \let\@dblfloat\@dbflt
+ \def\end@dblfloat{\@endfloatbox
+ \@largefloatcheck
+ \outer@nobreak
+% \end{macrocode}
+% This is cheap (deferring the floats until after the current page)
+% but any other solution would go deep into \LaTeX's output
+% routine and I don't like to work on it until I know which parts
+% of the output routine have to be reimplemented anyway for
+% \LaTeX3.
+% \begin{macrocode}
+ \ifnum\@floatpenalty<\z@
+% \end{macrocode}
+% We have to add the float to the |\@deferlist| because we assume
+% that outside the \mc{} environment we are in one column mode.
+% This is not entirely correct, I already used the \mc{}
+% environment inside of \LaTeX{}s |\twocolumn| declaration but it
+% will do for most applications.
+% \begin{macrocode}
+ \@cons\@deferlist\@currbox
+ \fi
+ \ifnum\@floatpenalty=-\@Mii
+ \@Esphack
+ \fi}}
+% \end{macrocode}
+% \end{macro}
+%
+% \end{multicols}
+%
+% \begin{multicols}{2}[\subsection{Maintaining the mark registers}]
+% \label{sec:v14}
+%
+% This section contains the routines that set the marks so that they
+% will be handled correctly. They have been introduced with version~1.4.
+%
+% \begin{macro}{\kept@topmark}
+% \changes{v1.4h}{1992/06/04}{Init to double brace pair}
+% \begin{macro}{\kept@firstmark}
+% \begin{macro}{\kept@botmark}
+% First thing we do is to reserve three macro names to hold the
+% replacement text for \TeX's primitives |\firstmark|, |\botmark| and
+% |\topmark|. We initialize the first two to be empty and
+% |\kept@topmark| to contain two empty pair of braces. This is
+% necessary since |\kept@topmark| is supposed to contain the last
+% mark from a preceding page and in \LaTeX{} any ``real'' mark must
+% contain two parts representing left and right mark information.
+% \begin{macrocode}
+\def\kept@topmark{{}{}}
+\let\kept@firstmark\@empty
+\let\kept@botmark\@empty
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\return@nonemptymark}
+% Sometimes we want to return the value of a ``kept'' mark into a
+% |\mark| node on the main vertical list. This is done by the
+% function |\return@nonemptymark|. As the name suggests it only acts
+% if the replacement text of the kept mark is non-empty. This is done
+% to avoid adding an empty mark when no mark was actually present. If
+% we would nevertheless add such a mark it would be regarded as a
+% valid |\firstmark| later on.
+% \begin{macrocode}
+\def\return@nonemptymark#1#2{%
+ \ifx#2\@empty
+ \else
+% \end{macrocode}
+% For debugging purposes we take a look at the value of the kept mark
+% that we are about to return. This code will get stripped out for
+% production.
+% \begin{macrocode}
+%<*marktrace>
+ \mult@info\tw@
+ {Returned #1 mark:\MessageBreak
+ \meaning#2}%
+% \nobreak
+% \fi
+%</marktrace>
+% \end{macrocode}
+% Since the contents of the mark may be arbitrary \LaTeX{} code we
+% better make sure that it doesn't get expanded any further. (Some
+% expansion have been done already during the execution of
+% |\markright| or |\markboth|.) We therefore use the usual mechanism
+% of a toks register to prohibit expansion.\footnote{Due to the
+% current definition of \cs{markright} etc.\ it wouldn't
+% help to define the \cs{protect} command to prohibit
+% expansion as any \cs{protect} has already vanished due to
+% earlier expansions.}
+% \changes{v1.4n}{1992/09/10}{Make marks robust}
+% \changes{v1.5t}{1999/03/22}{re-add \cs{mark} command which was commented out
+% by mistake at some point in 1998 (pr/2978)}
+% \begin{macrocode}
+ \toks@\expandafter{#2}%
+ \mark{\the\toks@}%
+% \end{macrocode}
+% We don't want any breakpoint between such a returned mark and the
+% following material (which is usually just the box where the mark
+% came from).
+% \begin{macrocode}
+ \nobreak
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\get@keptmarks}
+% If we have some material in a box register we may want to get the
+% first and the last mark out of this box. This can be done with
+% |\get@keptmarks| which takes one argument: the box register number
+% or its nick name defined by |\newbox|.
+% \begin{macrocode}
+\def\get@keptmarks#1{%
+% \end{macrocode}
+% For debugging purposes we take a look at the current dimensions
+% of the box since in earlier versions of the code I made some
+% mistakes in this area.
+% \begin{macrocode}
+%<*debug>
+ \typeout{Mark box #1 before:
+ ht \the\ht#1, dp \the\dp#1}%
+%</debug>
+% \end{macrocode}
+% Now we open a new group and locally copy the box to itself. As a
+% result any operation, i.e.\ |\vsplit|, will only have a local
+% effect. Without this trick the box content would get lost up to
+% the level where the last assignment to the box register was done.
+% \begin{macrocode}
+ \begingroup
+ \vbadness\@M
+ \setbox#1\copy#1%
+% \end{macrocode}
+% Now we split the box to the maximal possible dimension. This
+% should split off the full contents of the box so that effectively
+% everything is split off. As a result |\splitfirstmark| and
+% |\splitbotmark| will contain the first and last mark in the box
+% respectively.
+% \begin{macrocode}
+ \setbox#1\vsplit#1to\maxdimen
+% \end{macrocode}
+% Therefore we can now set the kept marks which is a global
+% operation and afterwards close the group. This will restore the
+% original box contents.
+% \begin{macrocode}
+ \set@keptmarks
+ \endgroup
+% \end{macrocode}
+% For debugging we take again a look at the box dimension which
+% shouldn't have changed.
+% \begin{macrocode}
+%<*debug>
+ \typeout{Mark box #1 \space after:
+ ht \the\ht#1, dp \the\dp#1}%
+%</debug>
+}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\set@keptmarks}
+% The macro |\set@keptmarks| is responsible for setting
+% |\kept@firstmark| and |\kept@botmark|, by checking the current
+% values for |\splitfirstmark| and |\splitbotmark|.
+% \begin{macrocode}
+\def\set@keptmarks{%
+% \end{macrocode}
+% If |\kept@firstmark| is empty we assume that it isn't set. This
+% is strictly speaking not correct as we loose the ability to have
+% marks that are explicitly empty, but for standard \LaTeX{}
+% application it is sufficient. If it is non-empty we don't change
+% the value---within the output routines it will then be restored
+% to |\@empty|.
+% \begin{macrocode}
+ \ifx\kept@firstmark\@empty
+% \end{macrocode}
+% We now put the contents of |\splitfirstmark| into
+% |\kept@firstmark|. In the case that there wasn't any mark at all
+% |\kept@firstmark| will not change by that operation.
+% \begin{macrocode}
+ \expandafter\gdef\expandafter
+ \kept@firstmark
+ \expandafter{\splitfirstmark}%
+% \end{macrocode}
+% When debugging we show the assignment but only when something
+% actually happened.
+% \begin{macrocode}
+%<*marktrace>
+ \ifx\kept@firstmark\@empty\else
+ \mult@info\tw@
+ {Set kept first mark:\MessageBreak
+ \meaning\kept@firstmark%
+ \@gobbletwo}%
+ \fi
+%</marktrace>
+ \fi
+% \end{macrocode}
+% We always try to set the bottom mark to the |\splitbotmark| but
+% of course only when there has been a |\splitbotmark| at all.
+% Again, we assume that an empty |\splitbotmark| means that the
+% split off box part didn't contain any marks at all.
+% \begin{macrocode}
+ \expandafter\def\expandafter\@tempa
+ \expandafter{\splitbotmark}%
+ \ifx\@tempa\@empty\else
+ \global\let\kept@botmark\@tempa
+%<*marktrace>
+ \mult@info\tw@
+ {Set kept bot mark:\MessageBreak
+ \meaning\kept@botmark%
+ \@gobbletwo}%
+%</marktrace>
+ \fi}%
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\prep@keptmarks}
+% The |\prep@keptmarks| function is used to initialize the kept
+% marks from the contents of |\partial@page|, i.e.\ the box that
+% holds everything from the top of the current page prior to
+% starting the \mc{} environment. However, such a box is only
+% available if we are not producing a boxed \mc{}.
+% \begin{macrocode}
+\def\prep@keptmarks{%
+ \if@boxedmulticols \else
+ \get@keptmarks\partial@page
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\remove@discardable@items}
+% There are situations when we may have some space at the end of a
+% column and this macro here will attempt to get rid of it. The
+% typical \LaTeX{} sequence is a series of self-canceling glues so
+% if we remove them recursively we are usually fine.
+%
+% Special care is needed with handling |\vspace*| as that
+% corresponds to |\penalty10000|, |\vskip <skip>|, followed by
+% |\vskip 0pt|. If we see this sequence going backwards in the the
+% vertical list we assume that this is a ``desired'' space. We
+% therefore stop the recursion and reinsert the spaces.
+%
+% As the multicol code sometimes add an explicit penalty at the end
+% of a column we first attempt to remove it in case it is there.
+% \changes{v1.8m}{2015/03/31}{Another rewrite of
+% \cs{remove@discardable@items} hopefully okay now}
+% \begin{macrocode}
+\skip0=0pt
+\edef\the@zero@skip{\the\skip0}
+\def\remove@discardable@items{%
+ \unpenalty
+% \end{macrocode}
+% Save a previous skip (if there) and then remove it, we can't
+% really tell the difference between no skip an a skip of zero but
+% that's life.
+% \begin{macrocode}
+ \edef\@tempa{\the\lastskip}%
+%\typeout{s1=\@tempa}%
+ \unskip
+% \end{macrocode}
+% If it was a zero skip (or none) we save the next previous skip
+% (if any).
+% \begin{macrocode}
+ \ifx\@tempa\the@zero@skip
+ \edef\@tempb{\the\lastskip}%
+%\typeout{s2=\@tempb}%
+% \end{macrocode}
+% If this one again was zero (or more likely not there in the first
+% place) we stop.
+% \begin{macrocode}
+ \ifx\@tempb\the@zero@skip
+ \else
+% \end{macrocode}
+% Otherwise we remove this ``real'' skip. Then we look if it was
+% preceded by a penalty of 10000 (i.e., a |\nobreak|)
+% \begin{macrocode}
+ \unskip
+%\typeout{p=\lastpenalty}%
+ \ifnum \lastpenalty=\@M
+% \end{macrocode}
+% If so this was a |\vspace*| or something equivalent to
+% it. Therefore we reintroduce the skips and stop. Otherwise we
+% recurse.
+% \begin{macrocode}
+ \vskip\@tempb\vskip\@tempa\relax
+ \else
+ \remove@discardable@items
+ \fi
+ \fi
+ \else
+% \end{macrocode}
+% If the first skip was a non-zero skip we recurse as well.
+% \begin{macrocode}
+ \remove@discardable@items
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macrocode}
+%<*badness>
+\newif\iftoo@bad
+\def\too@badtrue{\global\let\iftoo@bad\iftrue}
+\def\too@badfalse{\global\let\iftoo@bad\iffalse}
+% \end{macrocode}
+%
+% \changes{v1.8k}{2015/03/21}{The new switch}
+% \begin{macrocode}
+\newif\ifforcedbreak@leftover
+% \end{macrocode}
+%
+% \begin{macro}{\c@minrows}
+% \changes{v1.8w}{2019/03/01}{Provide minrows counter for balancing}
+% \begin{macrocode}
+\newcount\c@minrows
+\c@minrows=1
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\c@columnbadness}
+% \begin{macro}{\c@finalcolumnbadness}
+% \begin{macrocode}
+\newcount\c@columnbadness
+\c@columnbadness=10000
+\newcount\c@finalcolumnbadness
+\c@finalcolumnbadness=9999
+
+\newdimen\last@try
+
+% \end{macrocode}
+%
+% \changes{v1.5z1}{2003/02/17}{Change wrong default for
+% \cs{multicolovershoot} to zero (pr/3465).}
+% \begin{macrocode}
+\newdimen\multicolovershoot
+\newdimen\multicolundershoot
+\multicolovershoot=0pt
+\multicolundershoot=2pt
+\newbox\mult@nat@firstbox
+%</badness>
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\mult@info}
+% A helper for producing info messages
+% \begin{macrocode}
+\def\mult@info#1#2{%
+ \ifnum\c@tracingmulticols>#1%
+ \GenericWarning
+ {(multicol)\@spaces\@spaces}%
+ {Package multicol: #2}%
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \end{multicols}
+%
+%
+% \begin{multicols}{2}[\section{Fixing the
+% \cs{columnwidth}}]
+%
+% \begin{macro}{\@footnotetext}
+% \changes{v1.5o}{1997/11/16}{Redefinition added pr/2664.}
+% \changes{v1.5r}{1998/08/17}{Use \cs{@footnotetext} but with
+% local change to \cs{columnwidth}.}
+% \begin{macro}{\mult@footnotetext}
+% \changes{v1.5r}{1998/08/17}{Macro removed again.}
+% If we store the current column width in |\columnwidth| we have
+% to redefine the internal |\@footnotetext| macro to use |\textwidth|
+% for the width of the footnotes rather than using the original
+% definition.
+%
+% Starting with version v1.5r this is now done in a way that the original
+% definition is still used, except that locally |\columnwidth| is set to
+% |\textwidth|.
+%
+% This solves two problems: first redefinitions of |\@footnotetext|
+% done by a class will correctly survive and second if multicols is
+% used inside a minipage environment the special definition of
+% |\@footnotetext| in that environment will be picked up and not the
+% one for the main galley (the latter would result in all footnotes
+% getting lost in that case).
+%
+% See the definition of the |\multicols| command further up for the exact
+% code.
+% \end{macro}
+% \end{macro}
+% \end{multicols}
+%
+%
+% \begin{multicols*}{2}[\section{Further extensions}]
+%
+% This section does contain code for extensions added to this package
+% over time. Not all of them may be active, some might sit dormant and
+% wait for being activated in some later release.
+%
+% \subsection{Not balancing the columns}
+%
+% This is fairly trivial to implement. we just have to disable the
+% balancing output routine and replace it by the one that ships out
+% the other pages.
+%
+% \begin{macro}{\multicols*}
+% \changes{v1.5q}{1998/01/19}{Macro added}
+% The code for this environment was suggested by Matthias Clasen.
+% \begin{macrocode}
+%<*nobalance>
+ \@namedef{multicols*}{%
+% \end{macrocode}
+% If we are not on the main galley, i.e., inside a box of some
+% sort, that approach will not work since we don't have a vertical
+% size for the box so we better warn that we balance anyway.
+% \begin{macrocode}
+ \ifinner
+ \PackageWarning{multicol}%
+ {multicols* inside a box does
+ not make sense.\MessageBreak
+ Going to balance anyway}%
+ \else
+% \end{macrocode}
+% If we aren't balancing we change the |\balance@columns@out| to
+% work like the normal output routine that cuts normal
+% pages. However, there is a catch: In case the last page we cut
+% (after seeing the end of the environment) is actually larger than
+% a page (for example, if it contains more |\columnbreak| commands
+% than columns) we end up with some leftover material that is
+% returned to the main galley, but now the environment end penalty
+% is missing. So we add another one here too. Of course that
+% shouldn't be done if there is really only a single final page,
+% but fortunately in that case we have just finished a page and any
+% penalty on the recent contributions will be discarded, thus the
+% extra one is harmless---puh.
+% \changes{v1.8t}{2018/06/26}{Re-add end penalty for
+% \texttt{multicols*} environment to guard against leftovers (git/53)}
+% \begin{macrocode}
+ \def\balance@columns@out
+ {\multi@column@out \penalty-\@Mvi }%
+ \fi
+ \begin{multicols}
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\endmulticols*}
+% When ending the environment we simply end the inner
+% \texttt{multicols} environment, except that we better also stick
+% in some stretchable vertical glue so that the last column still
+% containing text is not vertically stretched out.
+%
+% We do this as follows: first we ensure that we are back in vertical mode
+% and then we cancel out |\lastskip| if it was
+% positive (in case of a negative glue we assume that it was
+% deliberate, for a deliberate positive glue one needs to use
+% |\vspace*|). We can't simply use |\remove@discardable@items| here
+% as this only works inside boxes but we are here on the main
+% vertical list.
+%
+% Then we back up by |\prevdepth| but not more than |\boxmaxdepth|
+% so that a baseline of the last box is now at the bottom. This way
+% the material will align properly in case something like |\vfill|
+% spreads it out after all.
+% Finally we append |\vfil| to put white space at the bottom of the
+% column, but we only do this if we aren't anyway doing |\raggedcolumns|.
+% \changes{v1.5q}{1998/01/19}{Macro added}
+% \changes{v1.8h}{2014/09/12}{Use \cs{vfilmaxdepth}}
+% \changes{v1.8i}{2014/10/28}{Add \cs{null} to hide the final fill and only add
+% vertical space if not doing \cs{raggedcolumns}}
+% \changes{v1.8j}{2015/03/07}{Redesign the whole approach.}
+% \changes{v1.8k}{2015/03/21}{And a bit more redesign because of the
+% change in \cs{remove@discardable@items}}
+% \changes{v1.8o}{2016/02/08}{Ensure we are back in vmode before using
+% \cs{prevdepth} (pr/4448)}
+% \begin{macrocode}
+\@namedef{endmulticols*}{%
+ \par
+ \ifdim\lastskip>\z@ \vskip-\lastskip \fi
+ \ifdim \prevdepth>\z@
+ \vskip-\ifdim\prevdepth>\boxmaxdepth
+ \boxmaxdepth
+ \else \prevdepth \fi
+ \fi
+ \ifshr@nking\else
+ \vfil
+ \fi
+ \end{multicols}}
+%</nobalance>
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Manual column breaking} \label{sec:colbreak}
+%
+% The problem with manual page breaks within \mc{} is the fact that
+% during collection of material for all columns a page-forcing penalty
+% (i.e. -10000 or higher) would stop the collecting pass which is not
+% quite what is desired. On the other hand, using a penalty like -9999
+% would mean that there would be occasions where the |\vsplit|ing
+% operations within \mc{} would ignore that penalty and still choose a
+% different break point.
+%
+% For this reason the current implementation
+% uses a completely different approach. In a nutshell it extends the \LaTeX{}
+% output routine handling by introducing an additional penalty flag
+% (i.e., a penalty which is forcing but higher than -10000 so that the
+% output routine can look at this value and thus knows why it has been
+% called).
+%
+% Inside the output routine we test for this value and if it appears
+% we do two things: save the galley up to this point in a special box
+% for later use and reduce the |\vsize| by the height of the material
+% seen. This way the forcing penalty is now hidden in that box and we
+% can restart the collection process for the remaining
+% columns. (This is done in |\speci@ls| above.)
+%
+% In the output routines that do the |\vsplit|ting either for
+% balancing or for a full page we simply combine box~255 with the
+% saved box thus getting a single box for splitting which now
+% contains forcing breaks in the right positions.
+%
+%
+% \begin{macro}{\columnbreak}
+% \changes{v1.5u}{1999/05/25}{Macro added}
+% |\columnbreak| is modeled after |\pagebreak| except that we
+% generate a penalty -10005.
+% \begin{macrocode}
+\mathchardef\@Mv=10005
+\def\columnbreak{%
+% \end{macrocode}
+% We have to ensure that it is only used within a \mc{}
+% environment since if that penalty would be seen by the unmodified
+% \LaTeX{} output routine strange things would happen.
+% \begin{macrocode}
+ \ifnum\col@number<\tw@
+ \PackageError{multicol}%
+ {\noexpand\columnbreak outside multicols}%
+ {This command can only be used within
+ a multicols or multicols* environment.}%
+ \else
+ \ifvmode
+ \penalty -\@Mv\relax
+ \else
+ \@bsphack
+ \vadjust{\penalty -\@Mv\relax}%
+ \@esphack
+ \fi
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\colbreak@box}
+% \changes{v1.5u}{1999/05/25}{Macro added}
+% Need a box to collect the galley up to the column break.
+% \begin{macrocode}
+\newbox\colbreak@box
+%</package>
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Supporting right-to-left languages} \label{sec:RL}
+%
+%
+% \changes{v1.7a}{2010/10/24}{RL language support added}
+% \changes{v1.7b}{2011/12/18}{RL language support fixed}
+%
+% \begin{macro}{\LR@column@boxes}
+% |\LR@column@boxes| is called when we are assembling the columns for left
+% to right typesetting. When we start we are inside an |\hbox| of
+% full width.
+% Left to right typesetting is fairly easy, we basically output
+% each column box intermixed with vertical rules and proper
+% spacing. As this happens inside a box of a defined width the
+% rules and the columns automatically get into the right positions.
+% \begin{macrocode}
+\def\LR@column@boxes{%
+% \end{macrocode}
+% We loop through the columns with |\process@cols|
+% \begin{macrocode}
+ \process@cols\mult@gfirstbox{%
+% \end{macrocode}
+% If the depth of the current box is larger than the maximum found
+% so far in |\dimen2| we update that register for later use.
+% \changes{v1.6a}{2003/03/15}{Preparing for adjusting \cs{prevdepth}}
+% \begin{macrocode}
+ \ifdim\dp\count@>\dimen\tw@
+ \global\dimen\tw@\dp\count@ \fi
+% \end{macrocode}
+% If the \texttt{colaction} option is given we write out status
+% information about the current column, otherwise the next command
+% does nothing.
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+% \begin{macrocode}
+ \mc@col@status@write
+% \end{macrocode}
+% The typeset box followed by the column rule material
+% \begin{macrocode}
+ \box\count@
+ \hss{\columnseprulecolor\vrule
+ \@width\columnseprule}\hss}%
+% \end{macrocode}
+% As you will have noticed, we started with box register
+% |\mult@gfirstbox| (i.e.\
+% the left column). So this time |\count@| looped through 2,
+% 4,\ldots\ (plus the appropriate offset).
+% Finally we add box |\mult@rightbox| and we are done.
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+% \changes{v1.6a}{2003/03/15}{Preparing for adjusting \cs{prevdepth}}
+% Again we may have to update |\dimen\tw@|.
+% \begin{macrocode}
+ \ifdim\dp\mult@rightbox>\dimen\tw@
+ \global\dimen\tw@\dp\mult@rightbox \fi
+% \end{macrocode}
+% If the \texttt{colaction} option is given we write out status
+% information about the last column, otherwise the next command
+% does nothing.
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+% \begin{macrocode}
+ \mc@lastcol@status@write
+ \box\mult@rightbox
+}
+% \end{macrocode}
+% \end{macro}
+
+% \begin{macro}{\RL@column@boxes}
+% Assembling the boxes for right to left typesetting is far more
+% complicated. When I first tried to build a solution for this my
+% thinking was that all that is necessary to do is to reverse the
+% order of the columns. But such an approach produces a subtle bug:
+% If we work this way then the first column put on the page will be
+% the last column of the text to read. and this means that the
+% order in which \TeX{} executes write statements or assembles mark
+% material will not happen in the order of the textual flow. So if,
+% for example each column contains a section command then these
+% sections will appear in reverse order in the table of content.
+%
+% For this reason some amount of gymnastics is needed to add the
+% columns in their natural flow.
+% \begin{macrocode}
+\def\RL@column@boxes{%
+% \end{macrocode}
+% First step is to put all rules in the right place (without adding
+% the comes which are instead represented by a space of |\hsize|.
+% \begin{macrocode}
+ \process@cols\mult@gfirstbox{%
+ \hskip\hsize
+ \hss{\columnseprulecolor\vrule
+ \@width\columnseprule}\hss
+ }%
+ \hskip\hsize
+% \end{macrocode}
+% At this point in the code our typesetting reference point is at
+% the right end of the rightmost column (or rather where that column
+% should appear).
+%
+% We are now typesetting all columns by first backing up by their
+% width (which is |\hsize|) then typesetting the box and then
+% backing up again, but this time further, i.e., also across the
+% column separation. That will then enable us to typeset the next
+% column using the same approach until we are done with all but the
+% final column.
+% \begin{macrocode}
+ \process@cols\mult@gfirstbox{%
+ \ifdim\dp\count@>\dimen\tw@
+ \global\dimen\tw@\dp\count@ \fi
+ \hskip-\hsize
+% \end{macrocode}
+%
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+% \begin{macrocode}
+ \mc@col@status@write
+ \box\count@
+ \hskip-\hsize
+ \hskip-\columnsep
+ }%
+% \end{macrocode}
+% The approach for the final column is similar only that we do not
+% have to back up over any column gap.
+% \begin{macrocode}
+ \ifdim\dp\mult@rightbox>\dimen\tw@
+ \global\dimen\tw@\dp\mult@rightbox \fi
+ \hskip-\hsize
+% \end{macrocode}
+%
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+% \begin{macrocode}
+ \mc@lastcol@status@write
+ \box\mult@rightbox
+ \hskip-\hsize
+% \end{macrocode}
+% However we do have to move the reference point to its right
+% place: to make the rules appear at the expected places, we should
+% get the typesetting position to the far right again. As we at the
+% moment at the far left we skip to the far right like this:
+% \begin{macrocode}
+ \hskip\full@width
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\RLmulticolcolumns}
+% \begin{macro}{\LRmulticolcolumns}
+% \begin{macro}{\mc@align@columns}
+% Macros to switch between left-right and right-left typesetting. In LR
+% typesetting the |\LR@column@boxes| is used to combine
+% the columns. When typesetting right to left the |\RL@column@boxes|
+% is used instead.
+% \begin{macrocode}
+\newcommand\RLmulticolcolumns
+ {\let\mc@align@columns
+ \RL@column@boxes}
+\newcommand\LRmulticolcolumns
+ {\let\mc@align@columns
+ \LR@column@boxes}
+% \end{macrocode}
+% The default is left-to-right:
+% \begin{macrocode}
+\LRmulticolcolumns
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{Supporting \texttt{\textbackslash docolaction}}
+%
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+%
+% Whenever we want to do something that depends on the current
+% column we execute \verb=\docolaction=. This command takes one
+% optional and three mandatory arguments. The mandatory ones denote
+% what to do if this is a ``left'', ``middle'', or ``right'' column
+% and the optional one is simply there to say what to do if we don't
+% know (default is to use the ``left'' column action in that case).
+%
+% \begin{macro}{\mc@col@check@num}
+% We use one counter \verb=\mc@col@check@num= to generate us unique
+% label names. Each time we execute \verb=\docolaction= we increment
+% this counter to get a new name.
+% \begin{macrocode}
+\newcount\mc@col@check@num
+% \end{macrocode}
+% \end{macro}
+%
+% The generated ``labels'' are named
+%\begin{verbatim}
+%\mc@col-\the\mc@col@check@num
+%\end{verbatim}
+% and they hold as values the
+% numbers 1, 2, or 3 denoting the current column type.
+
+% \begin{macro}{\docolaction}
+%
+% The \verb=\docolaction= scans for a star and optional argument
+% and 3 mandatory ones, but we do this in chunks (not having xparse
+% available).
+%
+% \changes{v1.8u}{2018/11/09}{Support star with \cs{docolaction}}
+% \begin{macrocode}
+\newcommand\docolaction{%
+% \end{macrocode}
+% First check is the support is enabled.
+% \begin{macrocode}
+ \ifx\mc@col@status@write\relax
+ \PackageError{multicol}%
+ {Option 'colaction' not selected}%
+ {\string\docolaction\space
+ requires the use of the 'colaction'
+ option on the package}%
+ \fi
+% \end{macrocode}
+% Then prepare \verb=\mc@col@type=.
+% \begin{macrocode}
+ \global\advance\mc@col@check@num\@ne
+ \edef\mc@col@type{\expandafter\ifx
+ \csname mc@col-\the\mc@col@check@num
+ \endcsname\relax
+ 0\else
+ \csname mc@col-\the\mc@col@check@num
+ \endcsname
+ \fi}%
+% \end{macrocode}
+% Finally check for a star, record this information and then call
+% \verb=\@docolaction= to do the rest.
+% \begin{macrocode}
+ \@ifstar
+ {\@docolactionstartrue \@docolaction}%
+ {\@docolactionstarfalse\@docolaction}%
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\newcommand\@docolaction[4][1]{%
+% \end{macrocode}
+%
+% How does the column number get associated with our label? We
+% do do this by writing another line into the aux file. Here are the
+% preparations.
+% \begin{macrocode}
+ \edef\@docolactioncheck{\write\@auxout
+ {\string\mc@set@col@status
+ {mc@col-\the\mc@col@check@num}%
+ {\mc@col@type}}}%
+% \end{macrocode}
+% Where we do the actual \verb=\write= depends on the whether or
+% not we gave seen a \texttt{*}. If yes, we do it first and then
+% execute the code argument, otherwise we execute that code first
+% and check at the point after that.
+% \begin{macrocode}
+ \if@docolactionstar \@docolactioncheck \fi
+% \end{macrocode}
+% We prefix with 0 so that an unknown label (that returns
+% \verb=\relax=) will result in case 0
+% \begin{macrocode}
+ \ifcase \mc@col@type\relax
+% \end{macrocode}
+% If column is unknown we use the default action or the action
+% denoted by the optional argument (so that arg can take the value
+% 1, 2, 3).
+% \begin{macrocode}
+ \ifcase #1\or #2\or#3\or#4\fi
+ \or
+% \end{macrocode}
+% Otherwise we know (or think we know) that this is a first, middle,
+% or last column:
+% \begin{macrocode}
+ #2% % 1 First col
+ \or
+ #3% % 2 any middle col
+ \or
+ #4% % 3 last col
+ \else
+ \ERRORwrongdefaultgiven
+ \fi
+% \end{macrocode}
+% \begin{macrocode}
+ \if@docolactionstar \else \@docolactioncheck \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% Here is the if used above:
+% \begin{macrocode}
+\newif\if@docolactionstar
+% \end{macrocode}
+%
+% Because of extra data writing to the aux file the aux file will
+% now contain something like the following after the document is
+% processed the first time:
+%\begin{verbatim}
+%\relax
+%\mc@col@status{1}
+%\mc@set@col@status{lcol-1}{0}
+%\mc@col@status{2}
+%\mc@set@col@status{lcol-2}{0}
+%\mc@col@status{3}
+%\mc@set@col@status{lcol-3}{0}
+%\mc@col@status{1}
+%\mc@col@status{2}
+%\mc@col@status{3}
+%\mc@set@col@status{lcol-4}{0}
+%\end{verbatim}
+% The \verb=\mc@col@status= line denotes the column type and has been
+% written out just before corresponding the column box was placed
+% onto the page.
+% The\verb=\mc@set@col@status= lines have been written out as part
+% of shipping the column boxes out, e.g.,
+% \verb=\mc@set@col@status{lcol-1}{0}= was therefore somewhere within
+% the first column as it appears between \verb=\mc@col@status{1}=
+% and \verb=\mc@col@status{2}=
+% The second argument in that line is the value used in the previous
+% run (or zero if there was no previous run. We can use this to
+% determine if a rerun is necessary.
+%
+% Thus with this knowledge we can set things up to get the labels
+% working.
+%
+%
+% \begin{macro}{\mc@col@status}
+%
+% When the aux file is read in \verb=\mc@col@status= is used to set
+% \verb=\mc@curr@col@status=:
+% \begin{macrocode}
+\def\mc@col@status#1{%
+ \gdef\mc@curr@col@status{#1}}
+% \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\mc@set@col@status}
+%
+% And when \verb=\mc@set@col@status= is executed we can simply set
+% up the label by associating it with the \verb=\mc@curr@col@status=
+% and ignore the second argument:
+% \begin{macrocode}
+\def\mc@set@col@status#1#2{%
+ \global\expandafter\let\csname #1\endcsname
+ \mc@curr@col@status}
+% \end{macrocode}
+% The above definition is being used when the \texttt{.aux} file is
+% read in at the beginning. At the end we need a different
+% definition to test if another typesetting run is needed. There we
+% compare the value used in the current run (stored in the second
+% argument) with the value used on the next run. If those two values
+% differ we set \verb=@tempswa= to false which will trigger the
+% ``Label(s) may have changed'' warning.
+% \begin{macrocode}
+\AtEndDocument{\def\mc@set@col@status#1#2{%
+ \ifnum #2=\mc@curr@col@status\else
+ \@tempswatrue
+ \fi}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{mc@firstcol}
+% Finally, as part of determining in which column we are, we used a
+% switch inside |\mc@col@status@write| to determine if we are in the
+% first column or not.
+% \begin{macrocode}
+\newif\ifmc@firstcol
+\mc@firstcoltrue
+% \end{macrocode}
+% \end{macro}
+% \end{multicols*}
+%
+% \Finale
+%
+\endinput
+
+