From 99baacb1f33acaea45b00e6661c29302b01562a6 Mon Sep 17 00:00:00 2001
From: ottjk <joshott16@gmail.com>
Date: Sun, 31 Dec 2023 15:01:25 -0500
Subject: sway and tex

---
 texmf/source/latex/revtex/ltxgrid.dtx | 6849 +++++++++++++++++++++++++++++++++
 1 file changed, 6849 insertions(+)
 create mode 100644 texmf/source/latex/revtex/ltxgrid.dtx

(limited to 'texmf/source/latex/revtex/ltxgrid.dtx')

diff --git a/texmf/source/latex/revtex/ltxgrid.dtx b/texmf/source/latex/revtex/ltxgrid.dtx
new file mode 100644
index 0000000..6d0c659
--- /dev/null
+++ b/texmf/source/latex/revtex/ltxgrid.dtx
@@ -0,0 +1,6849 @@
+% \iffalse meta-comment balanced on line 109
+% ltxgrid.dtx: package to change page grid, MVL.
+% Copyright (c) 2009 Arthur Ogawa
+%
+% Disclaimer
+%   This file is distributed WITHOUT ANY WARRANTY;
+%   without even the implied warranty of
+%   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+% License
+%   You may distribute this file under the conditions of the 
+%   LaTeX Project Public License 1.3c or later 
+%   (http://www.latex-project.org/lppl.txt).
+% ReadMe
+%   For the documentation and more detailed instructions for
+%   installation, typeset this document with \LaTeX.
+% Maintenance Status
+%   This work has the LPPL maintenance status "maintained";
+%   Current Maintainer of this work is Arthur Ogawa
+%   changes for version 4.2d and 4.2e by Phelype Oleinik.
+%
+% This work consists of the main source file ltxgrid.dtx
+% and the derived files
+%    ltxgrid.sty, ltxgrid.pdf
+% Distribution:
+%    CTAN:macros/latex/contrib/revtex/
+%
+% Unpacking:
+%    tex ltxgrid.dtx
+%
+% Documentation:
+%    latex ltxgrid.dtx; ...
+%
+%    Programm calls to get the documentation (example):
+%       pdflatex ltxgrid.dtx
+%       makeindex -s gind.ist ltxgrid
+%       makeindex -s gglo.ist -o ltxgrid.gls ltxgrid.glo
+%       pdflatex ltxgrid.dtx
+%       makeindex -s gind.ist ltxgrid.idx
+%       pdflatex ltxgrid.dtx
+%
+% Installation:
+%    TDS:doc/latex/revtex/
+%    TDS:tex/latex/revtex/
+%    TDS:source/latex/revtex/
+%
+% Thanks, Heiko!
+%    This method of letting a single .dtx file serve as both
+%    documentation (via latex) and installer (via tex) follows
+%    the example of Heiko Oberdiek. Thanks!
+%<*ignore>
+\begingroup
+  \def\x{LaTeX2e}%
+\expandafter\endgroup
+\ifcase
+ 0\expandafter\ifx\csname processbatchFile\endcsname\relax\else1\fi\ifx\fmtname\x\else 1\fi
+ \relax
+\else
+ \csname fi\endcsname
+%</ignore>
+%<*install>
+%% This file will generate documentation and runtime files
+%% from ltxgrid.dtx when run through LaTeX or TeX.
+\input docstrip
+\preamble
+
+This is a generated file;
+altering it directly is inadvisable;
+instead, modify the original source file.
+See the URL in the file README-LTXGRID.tex.
+
+License
+   You may distribute this file under the conditions of the 
+   LaTeX Project Public License 1.3c or later 
+   (http://www.latex-project.org/lppl.txt).
+   
+   This file is distributed WITHOUT ANY WARRANTY; 
+   without even the implied warranty of MERCHANTABILITY 
+   or FITNESS FOR A PARTICULAR PURPOSE.
+
+\endpreamble
+\askforoverwritefalse
+\keepsilent
+ \generate{%
+  %{ignore}
+% \usedir{tex/latex/revtex}%
+  \file{ltxgrid.sty}{%
+   \from{ltxgrid.dtx}{package,kernel}%
+  }%
+ }%
+\ifToplevel{
+\Msg{***********************************************************}
+\Msg{*}
+\Msg{* To finish the installation, please move}
+\Msg{*    ltxgrid.sty}
+\Msg{* into a directory searched by TeX;}
+\Msg{* in a TDS-compliant installation:}
+\Msg{* texmf/tex/macros/latex/revtex/.}
+\Msg{*}
+\Msg{* To produce the documentation,
+       run ltxgrid.dtx through LaTeX.}
+\Msg{*}
+\Msg{* Happy TeXing}
+\Msg{***********************************************************}
+}
+\endbatchfile
+%</install>
+%<*ignore>
+\fi
+%</ignore>
+% \fi
+%
+% \GetFileInfo{ltxgrid.dtx}
+%
+% \iffalse ltxdoc klootch
+%<*package>
+%%%  @LaTeX-file{
+%%%     filename        = "ltxgrid.dtx",
+%%%     version         = "4.2e",
+%%%     date            = "2020/10/03",
+%%%     author          = "Arthur Ogawa (mailto:arthur_ogawa at sbcglobal.net),
+%%%                        Phelype Oleinik (mailto:phelype.oleinik at latex-project.org),
+%%%                        commissioned by the American Physical Society.
+%%%                        ",
+%%%     copyright       = "Copyright (C) 1999, 2009 Arthur Ogawa,
+%%%                        distributed under the terms of the 
+%%%                        LaTeX Project Public License 1.3c, see
+%%%                        ftp://ctan.tug.org/macros/latex/base/lppl.txt
+%%%                        ",
+%%%     address         = "Arthur Ogawa,
+%%%                        USA",
+%%%     telephone       = "",
+%%%     FAX             = "",
+%%%     email           = "mailto colon arthur_ogawa at sbcglobal.net",
+%%%     codetable       = "ISO/ASCII",
+%%%     keywords        = "latex, page grid, main vertical list",
+%%%     supported       = "yes",
+%%%     abstract        = "package to change page grid, MVL",
+%%%  }
+%</package>
+% \fi
+%
+% \iffalse ltxdoc klootch
+% The following references the \file{README-LTXGRID} file,
+% which contains basic information about this package.
+% The contents of this file are generated when
+% you typeset the programmer's documentation.
+% Search on "{filecontents*}{README-LTXGRID}" to locate it.
+% \fi\input{README-LTXGRID}%
+%
+% \subsection{Bill of Materials}
+%
+% Following is a list of the files in this distribution arranged
+% according to provenance.
+%
+% \subsubsection{Primary Source}%
+% One single file generates all.
+%\begin{verbatim}
+%ltxgrid.dtx
+%\end{verbatim}
+%
+% \subsubsection{Generated by \texttt{latex ltxgrid.dtx}}%
+% Typesetting the source file under \LaTeX\
+% generates the readme and the installer.
+%\begin{verbatim}
+%README-LTXGRID   ltxgrid.ins
+%\end{verbatim}
+%
+% \subsubsection{Generated by \texttt{tex ltxgrid.ins}}%
+% Typesetting the installer generates
+% the package files.
+%\begin{verbatim}
+%ltxgrid.sty
+%\end{verbatim}
+%
+% \subsubsection{Documentation}%
+% The following are the online documentation:
+% \begin{verbatim}
+%ltxgrid.pdf
+% \end{verbatim}
+%
+% \subsubsection{Auxiliary}%
+% The following are auxiliary files generated
+% in the course of running \LaTeX:
+% \begin{verbatim}
+%ltxgrid.aux ltxgrid.idx ltxgrid.ind ltxgrid.log ltxgrid.toc
+% \end{verbatim}
+%
+% \section{Code common to all modules}%
+%
+% The following may look a bit klootchy, but we
+% want to require only one place in this file
+% where the version number is stated,
+% and we also want to ensure that the version
+% number is embedded into every generated file.
+%
+% Now we declare that
+% these files can only be used with \LaTeXe.
+% An appropriate message is displayed if
+% a different \TeX{} format is used.
+%    \begin{macrocode}
+%<*driver|package>
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]%
+%</driver|package>
+%    \end{macrocode}
+% As desired, the following modules all
+% take common version information:
+%    \begin{macrocode}
+%<kernel&!package&!doc>\typeout{%
+%<*package|doc>
+\ProvidesFile{%
+%</package|doc>
+%<*kernel|package|doc>
+ltxgrid%
+%</kernel|package|doc>
+%<*doc>
+.dtx%
+%</doc>
+%<package>.sty%
+%<*package|doc>
+}%
+%</package|doc>
+%    \end{macrocode}
+%
+% The following line contains, for once and for all,
+% the version and date information.
+% By various means, this information is reproduced
+% consistently in all generated files and in the
+% typeset documentation.
+% Give credit where due. 
+%    \begin{macrocode}
+%<*doc|package|kernel>
+%<version>
+ [2020/10/03 4.2e page grid package (portions licensed from W. E. Baxter web at superscript.com)]% \fileversion
+%</doc|package|kernel>
+%<kernel&!package&!doc>}%
+%    \end{macrocode}
+%
+%
+% \section{The driver module \texttt{doc}}
+%
+% This module, consisting of the present section,
+% typesets the programmer's documentation,
+% generating the \file{.ins} installer and \file{README-LTXGRID} as required.
+%
+% Because the only uncommented-out lines of code at the beginning of
+% this file constitute the \file{doc} module itself,
+% we can simply typeset the \file{.dtx} file directly,
+% and there is thus rarely any need to
+% generate the ``doc'' {\sc docstrip} module.
+% Module delimiters are nonetheless required so that
+% this code does not find its way into the other modules.
+%
+% The \enve{document} command concludes the typesetting run.
+%
+%    \begin{macrocode}
+%<*driver>
+%    \end{macrocode}
+%
+% \subsection{The Preamble}
+% The programmers documentation is formatted
+% with the \classname{ltxdoc} class with local customizations,
+% and with the usual code line indexing.
+%    \begin{macrocode}
+\documentclass{ltxdoc}
+\RequirePackage{ltxdocext}%
+\RequirePackage[colorlinks=true,linkcolor=blue]{hyperref}%
+%\ifx\package@font\@undefined\else
+% \expandafter\expandafter
+% \expandafter\RequirePackage
+% \expandafter\expandafter
+% \expandafter{%
+%              \csname package@font\endcsname
+%             }%
+%\fi
+\CodelineIndex\EnableCrossrefs % makeindex -s gind.ist ltxgrid
+\RecordChanges % makeindex -s gglo.ist -o ltxgrid.gls ltxgrid.glo
+%    \end{macrocode}
+%
+% \subsubsection{Docstrip and info directives}
+%    We use so many {\sc docstrip} modules that we set the
+%    \texttt{StandardModuleDepth} counter to 1.
+%    \begin{macrocode}
+\setcounter{StandardModuleDepth}{1}
+%    \end{macrocode}
+%    The following command retrieves the date and version information
+%    from this file.
+%    \begin{macrocode}
+\expandafter\GetFileInfo\expandafter{\jobname.dtx}%
+%    \end{macrocode}
+%
+% \subsection{The ``Read Me'' File}
+% As promised above, here is the contents of the
+% ``Read Me'' file. That file serves a double purpose,
+% since it also constitutes the beginining of the
+% programmer's documentation. What better thing, after
+% all, to have appear at the beginning of the
+% typeset documentation?
+%
+% A good discussion of how to write a ReadMe file can be found in
+% Engst, Tonya, ``Writing a ReadMe File? Read This''
+% \emph{MacTech} October 1998, p. 58.
+%
+% Note the appearance of the
+% \cmd\StopEventually\ command, which marks the
+% dividing line between the user documentation
+% and the programmer documentation.
+%
+% The usual user will not be asked to
+% do a full build, not to speak
+% of the bootstrap.
+% Instructions for carrying these processes
+% begin the programmer's manual.
+%
+%    \begin{macrocode}
+\begin{filecontents*}{README-LTXGRID}
+\title{%
+ A \LaTeX\ Package for changing the page grid and MVL%
+ \thanks{%
+  This file has version number \fileversion,
+  last revised \filedate.%
+ }%
+ \thanks{%
+  Version \fileversion\ \copyright\ 2019--2020 American Physical Society
+ }%
+}%
+\author{%
+ Arthur Ogawa%
+  \thanks{\texttt{mailto:arthur\_ogawa at sbcglobal.net}}%
+}%
+%\iffalse
+% For version number and date,
+% search on "\fileversion" in the .dtx file,
+% or see the end of the README-LTXGRID file.
+%\fi
+\maketitle
+
+This file embodies the \classname{ltxgrid} package,
+the implementation and its user documentation.
+
+The distribution point for this work is
+\url{journals.aps.org/revtex},
+which contains the REV\TeX\ package, and includes source and documentation for this package.
+
+The \classname{ltxgrid} package was commissioned by the American Physical Society
+and is distributed under the terms of the \LaTeX\ Project Public License 1.3c,
+the same license under which all the portions of \LaTeX\ itself is distributed.
+Please see \url{http://ctan.tug.org/macros/latex/base/lppl.txt} for details.
+
+To use this document class, you must have a working
+\TeX\ installation equipped with \LaTeXe\ 
+and possibly pdftex and Adobe Acrobat Reader or equivalent.
+
+To install, retrieve the distribution,
+unpack it into a directory on the target computer,
+into a location in your filesystem where it will be found by \LaTeX;
+in a TDS-compliant installation this would be:
+\file{texmf/tex/macros/latex/revtex/.}
+
+To use, read the user documentation \file{src/ltxgrid.pdf}.
+
+\tableofcontents
+
+\section{Processing Instructions}
+
+The package file \file{ltxgrid.sty}
+is generated from this file, \file{ltxgrid.dtx},
+using the {\sc docstrip} facility of \LaTeX
+via |tex ltxgrid.dtx|.
+The typeset documentation that you are now reading is generated from
+this same file by typesetting it with \LaTeX\ or pdftex
+via |latex ltxgrid.dtx| or |pdflatex ltxgrid.dtx|.
+
+\subsection{Build Instructions}
+
+You may bootstrap this suite of files solely from \file{ltxgrid.dtx}.
+Prepare by installing \LaTeXe\ (and either tex or pdftex) on your computer,
+then carry out the following steps:
+\begin{enumerate}
+\item
+Within an otherwise empty directory,
+typeset \file{ltxgrid.dtx} with \TeX\ or pdftex;
+thereby generating the package file \file{ltxgrid.sty}.
+
+\item
+Now typeset \file{ltxgrid.dtx} with \LaTeX\ or pdflatex;
+you will obtain the typeset documentation you are now reading,
+along with the file \file{README-LTXGRID}.
+
+Note: you will have to run \LaTeX\ twice, then \file{makeindex}, then
+\LaTeX\ again in order to obtain a valid index and table of contents.
+
+\item
+Install the following files into indicated locations within your 
+TDS-compliant \texttt{texmf} tree (you may need root access):
+\begin{itemize}
+\item
+\file{$TEXMF/}\file{tex/}\file{latex/}\file{revtex/}\classname{ltxgrid.sty}
+\item
+\file{$TEXMF/}\file{source/}\file{latex/}\file{revtex/}\classname{ltxgrid.dtx}
+\item
+\file{$TEXMF/}\file{doc/}\file{latex/}\file{revtex/}\classname{ltxgrid.pdf}
+\end{itemize}
+where \file{TEXMF/} stands for \file{texmf-local/}, or some other \texttt{texmf} tree in your installation.
+\item
+Run \texttt{mktexlsr} on directory \file{$TEXMF/} (you may need root access).
+\item
+Build and installation are now complete; 
+now put a \cmd\usepackage\texttt{\{ltxgrid\}} in your document preamble!
+(Note: \texttt{ltxgrid} requires package \texttt{ltxutil}.)
+\end{enumerate}
+
+\subsection{Change Log}
+\changes{4.0a}{2001/06/18}{Introduce \cs{marry@height} }
+\changes{4.0a}{2001/06/18}{Introduce \cs{set@marry@height} }
+\changes{4.0a}{2008/06/26 }{\cs{@yfloat}: de-fang \cs{set@footnotewidth} (see ltxutil.dtx): we have already done its job. }
+\changes{4.1a}{2008/06/29}{Change \cs{LT@array@new}: restore \cs{@tabularcr} and \cs{@xtabularcr}}
+\changes{4.1a}{2008/06/29}{Change \cs{LT@array@new}: set \cs{LT@LL@FM@cr} to \cs{@arraycr@array} instead of \cs{@arraycr}}
+\changes{4.1a}{2008/06/29}{Repair error in \cs{endlongtable@new} involving \cs{@ifx}: argument not delimited.}
+\changes{4.1b}{2008/08/04}{Get rid of the \cs{reserved@a} idiom}
+\changes{4.1b}{2008/08/04}{Turn off the \cs{set@footnotewidth} mechanism; a float `knows' its proper typesetting context}
+\changes{4.1b}{2008/08/04}{(AO, 452) Support length checking: show size of shipped out text.}
+\changes{4.1b}{2008/08/04}{(AO, 456) Compatibility with other packages that override the output routine, following suggestion by David Kastrup.}
+\changes{4.1b}{2008/08/04}{}
+\changes{4.1b}{2008/08/04}{Box \cs{footbox} changed to box \cs{footsofar}}
+\changes{4.1b}{2008/08/04}{Change \cs{@combinepage} to \cs{@combinepage} with argument}
+\changes{4.1b}{2008/08/04}{Change \cs{@makecol} to \cs{@makecolumn} with argument}
+\changes{4.1b}{2008/08/04}{Change \cs{set@colroom} to \cs{set@colht}}
+\changes{4.1b}{2008/08/04}{New procedure \cs{@iffpsbit} replaces \cs{@getfpsbit}}
+\changes{4.1b}{2008/08/04}{New procedure \cs{@output@combined@page}}
+\changes{4.1b}{2008/08/04}{New procedure for showing a box contents, \cs{trace@box}}
+\changes{4.1b}{2008/08/04}{Procedure \cs{@outputpage@head} headpatches \cs{@outputpage}}%
+\changes{4.1b}{2008/08/04}{Procedure \cs{@outputpage@tail} tailpatches \cs{@outputpage}}%
+\changes{4.1b}{2008/08/04}{Procedure \cs{balance@2} defined more transparently}%
+\changes{4.1b}{2008/08/04}{Tally the height of the float}
+\changes{4.1b}{2008/08/04}{Use \cs{document@inithook} instead of \cs{AtBeginDocument}}
+\changes{4.1b}{2008/08/04}{Use \cs{trace@box} instead of \cs{showbox}}
+\changes{4.1f}{2009/07/07}{(AO, 515) Prevent line numbering within a footnote}
+\changes{4.1f}{2009/07/10}{(AO, 518) Tally register overflow when locument is long}
+\changes{4.1f}{2009/07/14}{(AO, 519) \cs{footins} content must be preserved and reintegrated}
+\changes{4.1f}{2009/07/15}{(AO, 519) Preserve footnotes that are in \cs{footsofar} across a page grid change}
+\changes{4.1g}{2009/10/06}{(AO, 531) Fix package \classname{float} }
+\changes{4.1n}{2009/12/02}{Restore the \cs{lastbox} if it is not a footnote}
+\changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+\changes{4.1n}{2009/12/18}{(AO, 571) Deconstruct balanced footnotes when needed}
+\changes{4.1n}{2010/01/02}{(AO, 571) Interface \cs{set@footnotewidth} for determining the set width of footnotes}%
+\changes{4.1n}{2010/01/02}{(AO, 571) Footnotes, when columns are balanced or when they are composed with their column}%
+\changes{4.1n}{2010/01/02}{(AO, 571) Abandon \cs{recover@footins} in favor of \cs{recover@column}}%
+\changes{4.1n}{2010/01/02}{(AO, 571) Use procedures \cs{output@do@prep} and \cs{output@column@do} as dispatchers}
+\changes{4.1n}{2010/01/02}{(AO, 571) coding convention: use \cs{bgroup}, \cs{egroup} (instead of braces) when a box is being built}%
+\changes{4.1n}{2010/01/02}{(AO, 571) calling sequence of \cs{combine@foot@inserts} and \cs{grid@column} to expose box registers; that of \cs{append@column@} its column counters}%
+\changes{4.1n}{2010/01/02}{(AO, 571) footnote rule is leaders, so that it may be removed by \cs{vsplit}; mechanism of \cs{kern} signals to indicate footnote height}%
+\changes{4.1o}{2010/02/02}{(AO, 576) Allow \classname{lscape} to act on \cs{@outputbox} at the right time}%
+\changes{4.1p}{2010/02/24}{(AO, 583) Provide setup code also for footnotes in a one-column document}%
+\changes{4.2a}{2018/12/12}{(MD) Updated name of README file and use standard fonts when typesetting}%
+\changes{4.2d}{2020/09/19}{(PHO) Adapt \cs{document} and \cs{enddocument} hooks to the 2020-10-01 \LaTeX{} release.}%
+\changes{4.2d}{2020/09/30}{(PHO) Correct \cs{@normalcr} patch for \LaTeX{} 2020-02-02 and later.}%
+\end{filecontents*}
+%    \end{macrocode}
+%
+% \subsection{The Document Body}
+%
+% Here is the document body, containing only a
+% \cmd\DocInput\ directive---referring to this very file.
+% This very cute self-reference is a common \classname{ltxdoc} idiom.
+%    \begin{macrocode}
+\begin{document}%
+\def\revtex{REV\TeX}%
+\expandafter\DocInput\expandafter{\jobname.dtx}%
+\end{document}
+%</driver>
+%    \end{macrocode}
+%
+% \section{Using this package}
+% Once this package is installed on your filesystem, you can employ it in
+% adding functionality to \LaTeX\ by invoking it in your document or document class.
+%
+% \subsection{Invoking the package}
+% In your document, you can simply call it up in your preamble:
+% \begin{verbatim}
+%\documentclass{book}%
+%\usepackage{ltxgrid}%
+%\begin{document}
+%<your document here>
+%\end{document}
+% \end{verbatim}
+% However, the preferred way is to invoke this package from within your
+% customized document class:
+% \begin{verbatim}
+%\NeedsTeXFormat{LaTeX2e}[1995/12/01]%
+%\ProvidesClass{myclass}%
+%\LoadClass{book}%
+%\RequirePackage{ltxgrid}%
+%<class customization commands>
+%\endinput
+% \end{verbatim}
+%
+% Note that this package requires the features of the \classname{ltxutil} package,
+% available at
+% \url{publish.aps.org/revtex}.
+%
+% Once loaded, the package gives you acccess to certain procedures,
+% usually to be invoked by a \LaTeX\ command or environment, but not at the document level.
+% 
+% \subsection{Changing the page grid}%
+% This package provides two procedures, \cmd\onecolumngrid, \cmd\twocolumngrid,
+% that change the page grid (it can be extended to more columns and to other page grids).
+%
+% They differ from standard \LaTeX's \cmd\onecolumn\ and \cmd\twocolumn\ commands in that
+% they do not force a page break. Also, upon leaving a multiple-column grid, the columns are balanced.
+% In other respects they work same.
+%
+% They differ from the grid-changing commands of Frank Mittelbach's \classname{multicol} package
+% in that they allow floats of all types (single- and double column floats, that is) and
+% preserve compatability with the \classname{longtable} package.
+% 
+% These commands must be issued in vertical mode (conceivably via a \cmd\vadjust) such that
+% they are ultimately present in the MVL, where they can do their work.
+% Because they do not work in \LaTeX's left-right mode, they are unsuitable at the 
+% document level.
+% Furthermore, packaging a grid command in a \cmd\vadjust, although possible, will probably 
+% not acheive satisfactory page layout.
+%
+% Page grid commands are not intended to be issued unnecessarily: only the first of
+% two successive \cmd\onecolumngrid\ commands is effective; the second will be silently ignored.
+%
+% \DescribeMacro\onecolumngrid
+% You command \LaTeX\ to return to the one-column grid with the
+% \cmd\onecolumngrid\ command. If you are already in the one-column grid, this
+% is a no-op. The one-column grid is considered special of all page grids, in that
+% no portion of the page is held back (in \cmd\pagesofar); all items that might go
+% on the current page (with the exception of floats and footnotes) are on the MVL.
+%
+% \DescribeMacro\twocolumngrid
+% You command \LaTeX\ to return to the two-column grid with the
+% \cmd\twocolumngrid\ command. If you are already in the two-column grid, this
+% is a no-op.
+% 
+% These two commands should be issued by a macro procedure that can ensure that 
+% \TeX\ is in outer vertical mode. 
+% 
+% \subsection{Changing the MVL}%
+%
+% This package also provides commands to modify the main vertical list (MVL) in a safe way.
+% The scheme here is to structure, insofar possible, \TeX's MVL as follows:
+%\begin{quotation}
+%box or boxes\\
+%penalty\\
+%glue
+%\end{quotation}
+% This should be a familiar sequence. It is the prototype sequence for a vertical list,
+% and is followed when \TeX\ breaks paragraphs into lines, and when \TeX\ generates 
+% a display math equation.
+%
+% If you (as a macro programmer) wish to modify the value of the penalty or glue item, 
+% you can use one of the MVL-altering commands to do so. Certain operations are implemented
+% here; you can make up your own.
+% 
+% Note that these commands must be issued in vertical mode, perhaps via a \cmd\vadjust\ or a \cmd\noalign.
+% They can work directly if you are in inner mode (say within a parbox or a minipage).
+%
+% \DescribeMacro\removestuff
+% You instruct \LaTeX\ to remove both the penalty and the glue item with this command.
+%
+% \DescribeMacro\addstuff
+% You issue the \cmd\addstuff\arg{penalty}\arg{glue} command to add a penalty, glue, or both.
+% If you do not wish to add one or the other, the corresponding argument should be nil.
+% Note that the effect of \cmd\addstuff\ is to stack the penalties and glue items.
+% Therefore, the lesser of the two penalties takes effect,
+% and the two glue items add together. 
+%
+% \cmd\addstuff\ is limited because once applied, it cannot be applied again with correct results.
+%
+% \DescribeMacro\replacestuff
+% The \cmd\replacestuff\ command is syntactically the same as \cmd\addstuff, but works
+% differently: the existing penalty and glue are replaced or modified.
+%
+% The specified penalty is not inserted if the existing penalty is greater than 10000
+% (that is, in case of a \cmd\nobreak), otherwise, the lower (non-zero) of the two penalties is inserted.
+% 
+% If the specified glue has a larger natural component than the existing glue, we replace the glue.
+% However, if the specified glue's natural component is negative, then the existing glue's natural component is 
+% changed by that amount.
+%
+% \cmd\replacestuff\ can be applied mutiple times bceause it retains the list structure in the canonical form.
+%
+% Note that we treat two penalties specially (as does \TeX): a penalty of 10000 is considered 
+% a garbage value, to be replaced if found. This is the signal value that \TeX\ inserts on
+% the MVL replacing the penalty that caused the page break (if the page break occurred at a penalty).
+% Also, a penalty of zero is indistinguishable from no penalty at all, so it will always 
+% be replaced by the given value.
+%
+% Therefore, it is highly recommended to never set any of \TeX's penalty parameters to 
+% zero (a value of, say, 1, is practically the same), nor should a skip parameter be set to zero
+% (instead, use, say, 1sp). Also, to prevent a pagebreak, do not use a penalty of 10000, use, say
+% 10001 instead.
+%
+% You can define your own construct that modifies the MVL:
+% Define a command, say, \cmd\myadjust, as follows:
+%\begin{verbatim}
+%\def\myadjust#1{\noexpand\do@main@vlist{\noexpand\@myadjust{#1}}\@tempa}%
+%\end{verbatim}
+% that is, \cmd\myadjust\ invokes \cmd\do@main@vlist, passing it the procedure name
+% \cmd\@myadjust\ along with the arguments thereof pre-expanded.
+% Next,  define the procedure \cmd\@myadjust:
+%\begin{verbatim}
+%\def\@myadjust#1{<meddle with the MVL>}%
+%\end{verbatim}
+% when \cmd\@myadjust\ executes, you will be in the output routine (in inner vertical mode)
+% and the MVL will be that very vertical list.
+%
+%
+%
+%
+% \section{Compatability with \LaTeX's Required Packages}
+% Certain packages, usually ones written by members of the 
+% \LaTeX\ Project itself, have been designated ``required'' and
+% are distributed as part of standard \LaTeX.
+% These packages have been placed in a priviledged position
+% vis \'a vis the \LaTeX\ kernel in that they override the definitions of certain kernel macros.
+%
+% Compatability between \classname{ltxgrid} and these packages is complicated
+% by a number of factors. First is that \classname{ltxgrid} alters the meaning of some of the same
+% kernel macros as certain of the ``required'' packages.
+% Second is that fact that certain of the ``required'' packages of \LaTeX\ are incompatible with 
+% each other.
+%
+% Examples of the first kind are the \classname{ftnright}, \classname{multicol}, and \classname{longtable} 
+% packages.
+% The \classname{ltxgrid} package is not compatible with \classname{multicol},
+% but if you are using \classname{ltxgrid}, you do not need to use \classname{ftnright} or \classname{multicol}
+% anyway. The \classname{ltxgrid} package does however attempt to be compatible with \classname{longtable}.
+%
+% Among the ``required'' packages that are mutually incompatible are \classname{multicol} and \classname{longtable},
+% the incompatibility arising because both packages replace \LaTeX's output routine:
+% if one package is active, the other must not be so.
+% This state of affairs has remained essentially unchanged since the introduction of the two as \LaTeX2.09 packages in the late 1980s.
+%
+% The reason that \classname{ltxgrid} can remain compatible with \classname{longtable} is due to the
+% introduction of a more modern architecture, the ``output routine dispatcher'', which allows all macro packages access to the
+% safe processing environment of the output routine, on an equal footing.
+% The relevant portions of the \classname{longtable} package are reimplemented in \classname{ltxgrid}
+% to take advantage of this mechanism.
+%
+% Timing is critical:
+% the \classname{ltxgrid} package will be incompatible with any package that
+% redefines any of the kernel macros that \classname{ltxgrid} patches---if that
+% package is loaded \emph{after} \classname{ltxgrid}.
+%
+% Hereinafter follows some notes on specific \LaTeX\ packages.
+%
+% \subsection{ftnright}
+% Frank Mittelbach's \classname{ftnright} package effects a change to \LaTeX's
+% \cmd\twocolumn\ mode such that footnotes are set at the bottom of the right-hand
+% column instead of at the foot of each of the two columns.
+%
+% Note that it overwrites three \LaTeX\ kernel macros: \cmd\@outputdblcol, \cmd\@startcolumn, and \cmd\@makecolumn.
+% Fortunately none of the three are patched by \classname{ltxgrid}, so that compatability
+% is not excluded on this basis.
+%
+% At the same time, it changes the meaning of \cmd\footnotesize, the macro that is automatically 
+% invoked when setting a document's footnote into type.
+% One might well argue that it is an error for the meaning of \cmd\footnotesize\ to be determined by 
+% a package such as \classname{ftnright}, that indeed such a choice should be made in the 
+% document class, or in a file such as \file{bk10.clo}.
+%
+% To avoid being tripped up by this misfeature in \classname{ftnright}, it is only necessary to 
+% reassert our meaning for \cmd\footnotesize\ later on, after \classname{ftnright} has been loaded.
+%
+% Note that \classname{ftnright} inserts code that demands that \LaTeX's flag \cmd\if@twocolumn\
+% is true, that is, it will complain if deployed in a \cmd\onecolumn\ document.
+% It is therefore necessary for any other multicolumn package to assert that flag in order to
+% avoid this package's complaint. It is an interesting question exactly why this package has
+% this limitation. After all, a one-column page grid is just a degenerate case of the
+% two column.
+%
+% \subsection{longtable}
+% David Carlisle's \classname{longtable} package sets tables that can be so long as to break over pages.
+% According to its author, it uses the same override of \LaTeX's output routine as
+% Frank Mittelbach's \classname{multicol} package. By implication, then, it has a hard
+% incompatability with the latter.
+% 
+% The \classname{longtable} package also performs a check of whether the document is in 
+% \cmd\twocolumn\ mode, and declines to work if this is the case. It is not clear, however,
+% that there is any true incompatability present if so. It's just that David did not see any reason
+% anyone would want to set such long tables in a multicolumn document, hence the check.
+%
+% There does not appear to be any indication that \classname{longtable} would work less 
+% well under \classname{ltxgrid} than under standard \LaTeX's \cmd\twocolumn\ mode.
+% Therefore, this \classname{ltxgrid} patches \classname{longtable} (if loaded) so as to provide
+% compatability. In the course of which, \classname{longtable} becomes more robust
+% (\classname{longtable} has mumerous bugs and incompatabilities of long standing,
+% some of which are repaired by \classname{ltxgrid}).
+%
+% One problem remains, namely that, if a \env{longtable} environment breaks over columns
+% and thereby inserts its special headers and footers at that break, and those columms are then
+% balanced (due to a return to the one-column page grid), then those inserted rows
+% will remain, and may no longer fall at the column break. This will, of course look
+% wrong.
+%
+% The only way to fix this problem is to avoid doing column balancing in the way 
+% I have implemented here; such an enhancement to this package is possible.
+%
+% \subsection{multicol}
+% Frank Mittelbach's \classname{multicol} package provides a page grid with many columns,
+% albeit denies the placement of floats in individual columns.
+%
+% It establishes its own \cmd\output\ routine, which is the reason it runs afoul of 
+% the \classname{longtable} package. On the other hand, \classname{ltxgrid} specifically
+% allows for the case where a package installs its own \cmd\output\ routine, so 
+% there is no incompatability on that basis.
+%
+% Still, it is pointless to use \classname{multicol} if you are using \classname{ltxgrid},
+% since both packages provide multicolumn page layouts.
+% Therefore, \classname{multicol} is not supported by \classname{ltxgrid}.
+%
+% \subsection{ltxgrid}
+% It has been pointed out that one of the disadvantages of adopting the \classname{ltxgrid} package is that 
+% it does alter the \LaTeX\ kernel. 
+% Any package that itself alters the \LaTeX\ kernel may be incompatible with \classname{ltxgrid}, and new packages
+% (destined perhaps to become part of the successor to \LaTeXe) may break \classname{ltxgrid}.
+%
+% The consequence is that packages introduced in future, and future changes to \LaTeX\ may be incompatible 
+% with \classname{ltxgrid}. 
+% This is, of course, true.
+% The development plan for \classname{ltxgrid} is that when such packages and \LaTeX\ kernel changes come about,
+% the burden will be on \classname{ltxgrid} to change in a way that provides for continued compatability with
+% those packages and \LaTeX\ kernel changes.
+% 
+%
+% \section{How \classname{ltxgrid} places footnotes}
+%
+% In conventional multicolumn layouts, a footnote will appear at the bottom of the column in which it is called out. 
+% The \classname{ltxgrid} package implements this conventional layout choice by default.
+% However, other choices are possible (a la \classname{ftnright}, whose compatability with \classname{ltxgrid} has not been tested).
+%
+% One unusual feature of \classname{ltxgrid}'s default implementation must be mentioned, though,
+% namely the case in a two-column page grid, where a footnote is followed by a temporary change to the one-column page grid
+% (e.g., for a wide equation).
+% In such a case, the material above the wide material is split into two columns, and a footnote whose callout 
+% appears in the right-hand column will nonetheless be set at the base of the left column.
+%
+% This arrangement was chosen because it ensures that the footnotes at the bottom of any page will appear in 
+% numerical order. It can be argued that this choice is ``incorrect'', but be that as it may,
+% the \classname{ltxgrid} package does not foreclose on other arrangements for the footnotes.
+% The package can be adapted to accomodate any page design desired.
+%
+% \section{Limitations in \classname{ltxgrid}'s default column balancing method}%
+%
+% In a multicolumn page grid, when encountering a page that is not completely full,
+% it is customary to set the material in balanced columns (typically with the last column no longer than any of the others).
+% Such a case also crops up when temporarily interrupting the multicolumn grid to set material on the full width of the page:
+% the material on the page above the break is customarily set in balanced columns.
+%
+% An awkward case arises when we have already set one or more complete columns of type before encountering the need to 
+% balance columns. In this subset of cases, the default in \classname{ltxgrid} is to 
+% do an operation I call ``re-balancing'':
+% the material on the page so far is pasted back together into a single column, and new, balanced column breaks are
+% calculated.
+%
+% This scheme typically works fine, but it has a significant vulnerability:
+% any discardable items trimmed at the original column break are lost, never to be retrieved.
+% Consequently, after re-balancing, an element like, say, a section head can fail to have the correct amount of whitespace above.
+%
+% This problem is due to an unfortunate optimization in \TeX, wherein a certain class of nodes is trimmed from the 
+% top of main vertical list upon returning from the output routine:
+% any penalty, glue, or leader node falls in to this class of discardable nodes,
+% and trimming proceeds until a non-discardable node (such as a box, or rule) is encountered.
+% It gets better: a third class of nodes is transparent to this trimming process;
+% they are neither discarded nor do they halt the process of trimming:
+% mark nodes and all whatsits fall into this class of transparent nodes;
+% they are quietly passed over during trimming.
+%
+% An alternative approach for \TeX\ to take would have been, 
+% rather than discarding the node entirely, to simply \emph{mark} it as discarded.
+% (Implementors of extended \TeX, please note!)
+% Then, upon shipping out, such nodes would not make it into the DVI.
+% \TeX's optimization, driven by the small computer architectures current when it was developed,
+% does save mem, but at the cost of revisiting page breaks in a reliable way.
+%
+% FIXME: how to fix a column break in the above case? Widetext?
+%
+%\StopEventually{}
+%
+% \section{Implementation of package}
+%
+% Special acknowledgment: this package uses concepts pioneered
+% and first realized by William Baxter (mailto:web at superscript.com)
+% in his SuperScript line of commercial typesetting tools, and
+% which are used here with his permission. His thorough understanding
+% of \TeX's output routine underpins the entire \classname{ltxgrid}
+% package.
+%
+% \subsection{Beginning of the \file{ltxgrid} {\sc docstrip} module}
+% Requires the underpinnings of the \classname{ltxkrnext} package.
+%    \begin{macrocode}
+%<*package>
+\def\package@name{ltxgrid}%
+\expandafter\PackageInfo\expandafter{\package@name}{%
+ Page grid for \protect\LaTeXe,
+ by A. Ogawa (arthur_ogawa at sbcglobal.net)%
+}%
+\RequirePackage{ltxutil}%
+%</package>
+%    \end{macrocode}
+%
+% \subsection{Banner}%
+%    \begin{macrocode}
+%<*kernel>
+%    \end{macrocode}
+%
+% \subsection{Sundry}%
+% Here are assorted macro definitions.
+% \begin{macro}{\lineloop}
+% \begin{macro}{\linefoot}
+% The (document-level) command \cmd\lineloop\ sets numbered lines until the 
+% specified count is reached. 
+% The command \cmd\linefoot\ sets a single, automatically numbered line, but with a footnote (with the specified label);
+% it automatically increments the line counter.
+% These commands are typically used to construct test documents. 
+%
+% Because the counter is globally advanced and never reset, successive 
+% calls to \cmd\lineloop\ should have an argument ever larger.
+% The formatted output will have each line labeled with its ordinal number.
+%    \begin{macrocode}
+\newcounter{linecount}
+\def\loop@line#1#2{%
+ \par
+ \hb@xt@\hsize{%
+  \global\advance#1\@ne
+  \edef\@tempa{\@ifnum{100>#1}{0}{}\@ifnum{10>#1}{0}{}\number#1}%
+  \@tempa\edef\@tempa{\special{line:\@tempa}}\@tempa
+  \vrule depth2.5\p@#2\leaders\hrule\hfil
+ }%
+}%
+\def\lineloop#1{%
+ \loopwhile{\loop@line\c@linecount{}\@ifnum{#1>\c@linecount}}%
+}%
+\def\linefoot#1{%
+ \loop@line\c@linecount{%
+  \footnote{%
+   #1\special{foot:#1}\vrule depth2.5\p@\leaders\hrule\hfill
+  }%
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{Mark Components}%
+%
+% Override LaTeX's mark macros to allow more components.
+%
+% We remain bound by the weakness of LaTeX's scheme in that
+% one cannot emulate the action of \TeX\ whereby
+% material with marks can be inserted in the middle of
+% a vertical list such that the marks are reliably calculated.
+% If we did that, \cmd\@themark\ would no longer be utilized.
+%
+% A more robust scheme involves placing all marks (component and value)
+% into a list (using global scoping, i.e., \cmd\gdef),
+% and using \cmd\@@mark to place an index on that list into the MVL.
+% Then, e.g., \cmd\@@botmark signifies the place where that list is to be cut,
+% and the \cmd\botmark\ of any component is
+% the value of the last element of the cut
+% list having the given component. The \cmd\firstmark\ and \cmd\topmark\
+% can likewise be defined relative to \cmd\@@firstmark\ and \cmd\@@topmark,
+% except in the latter case, we want the first following the cut instead of the last
+% preceding the cut.
+%
+% The limitation of this scheme is its demands upon \TeX's mem.
+% The list of marks would need to be trimmed back to, effectively,
+% \cmd\topmark\ at the beginning of every page.
+% 
+% This approach is not yet part of the extended LaTeX kernel.
+%
+% \begin{macro}{\@@mark}
+% \begin{macro}{\@@topmark}
+% \begin{macro}{\@@firstmark}
+% \begin{macro}{\@@botmark}
+% \begin{macro}{\@@splitfirstmark}
+% \begin{macro}{\@@splitbotmark}
+% Remember primitives under a new set of names.
+%    \begin{macrocode}
+\let\@@mark\mark
+\let\@@topmark\topmark
+\let\@@firstmark\firstmark
+\let\@@botmark\botmark
+\let\@@splitfirstmark\splitfirstmark
+\let\@@splitbotmark\splitbotmark
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \subsubsection{Procedures that expose the component data structure}%
+% This portion of the code exposes the internal representation of 
+% the mark components. If we wish to add more components, we will have to revise
+% these macro definitions:
+% \cmd\@themark,
+% \cmd\nul@mark,
+% \cmd\set@mark@netw@,
+% \cmd\set@marktw@,
+% \cmd\set@markthr@@,
+% \cmd\get@mark@@ne,
+% \cmd\get@mark@tw@,
+% \cmd\get@mark@thr@@,
+% \cmd\get@mark@f@ur.
+%
+% \begin{macro}{\@themark}
+%FIXME: is it safer to eliminate \cmd\@themark\ in favor of a message that evaluates \cmd\@@botmark?
+%
+% Note: these definitions expose the data structure of mark components.
+%    \begin{macrocode}
+\def\@themark{{}{}{}{}}%
+\def\nul@mark{{}{}{}{}\@@nul}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\set@mark@netw@}
+% \begin{macro}{\set@marktw@}
+% \begin{macro}{\set@markthr@@}
+% These procedures insert the new value of a particular mark component into the given argument.
+% They expose the data structure of mark components.
+% 
+%    \begin{macrocode}
+\def\set@mark@netw@#1#2#3#4#5#6#7{\gdef#1{{#6}{#7}{#4}{#5}}\do@mark}%
+\def\set@marktw@#1#2#3#4#5#6{\gdef#1{{#2}{#6}{#4}{#5}}\do@mark}%
+\def\set@markthr@@#1#2#3#4#5#6{\gdef#1{{#2}{#3}{#6}{#5}}\do@mark}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\get@mark@@ne}
+% \begin{macro}{\get@mark@tw@}
+% \begin{macro}{\get@mark@thr@@}
+% \begin{macro}{\get@mark@f@ur}
+% These procedures retreive the value of a particular mark component.
+% They expose the data structure of mark components.
+%    \begin{macrocode}
+\def\get@mark@@ne#1#2#3#4#5\@@nul{#1}%
+\def\get@mark@tw@#1#2#3#4#5\@@nul{#2}%
+\def\get@mark@thr@@#1#2#3#4#5\@@nul{#3}%
+\def\get@mark@f@ur#1#2#3#4#5\@@nul{#4}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsubsection{Procedures that do not expose the component data structure}%
+%
+% \begin{macro}{\mark@netw@}
+% \begin{macro}{\marktw@}
+% \begin{macro}{\markthr@@}
+% These procedures insert the new value of a particular mark component into \cmd\@themark,
+% then execute \cmd\do@mark. 
+% They constitute the implementation layer for mark components one, two, and three.
+% An analogous procedure for component four could be defined; call it \cmd\markf@ur.
+% 
+%    \begin{macrocode}
+\def\mark@netw@{\expandafter\set@mark@netw@\expandafter\@themark\@themark}%
+\def\marktw@{\expandafter\set@marktw@\expandafter\@themark\@themark}%
+\def\markthr@@{\expandafter\set@markthr@@\expandafter\@themark\@themark}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\do@mark}
+% \begin{macro}{\do@@mark}
+% Access procedures \cmd\mark (AKA \cmd\@@mark).
+% The \cmd\do@mark\ procedure is used when a mark is being put down into the MVL;
+% \cmd\do@@mark\ when this happens in the output routine.
+%    \begin{macrocode}
+\def\do@mark{\do@@mark\@themark\nobreak@mark}%
+\def\do@@mark#1{%
+ \begingroup
+  \let@mark
+  \@@mark{#1}%
+ \endgroup
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\let@mark}
+% \begin{macro}{\nobreak@mark}%
+% The procedure that makes \cmd\csname s robust within a mark.
+% Use \cmd\appdef\ and \cmd\robust@\ to extend the list.
+%    \begin{macrocode}
+\def\let@mark{%
+ \let\protect\@unexpandable@protect
+ \let\label\relax
+ \let\index\relax
+ \let\glossary\relax
+}%
+\def\nobreak@mark{%
+ \@if@sw\if@nobreak\fi{\@ifvmode{\nobreak}{}}{}%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsubsection{Using mark components}%
+%
+% These procedures use the component mark mechanism to implement
+% a mark component that remembers the current environment (used in page makeup)
+% and the the two mark components left over from the original \LaTeX.
+% The fourth component is presently unused.
+%
+% \begin{macro}{\mark@envir}
+% The third mark component's access procedures.
+% The \cmd\mark@envir\ and \cmd\bot@envir\ commands are a good model of how to write 
+% access procedures for a new mark component.
+%    \begin{macrocode}
+\def\mark@envir{\markthr@@}%
+\def\bot@envir{%
+ \expandafter\expandafter
+ \expandafter\get@mark@thr@@
+ \expandafter\@@botmark
+             \nul@mark
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\markboth}
+% \begin{macro}{\markright}
+% \begin{macro}{\leftmark}
+% \begin{macro}{\rightmark}
+% Set procedures for legacy components.
+%    \begin{macrocode}
+\def\markboth{\mark@netw@}%
+\def\markright{\marktw@}%
+%    \end{macrocode}
+%
+% Retrieval procedures for legacy mark components.
+% The procedure for retrieving the first component from \cmd\botmark\ 
+% and the second component from \cmd\firstmark have names in \LaTeX;
+% they are called, respectively, \cmd\leftmark\ and \cmd\rightmark.
+%
+% It is possible to retrieve the components of \cmd\topmark\
+% as well: use \cmd\saved@@topmark.
+%    \begin{macrocode}
+\def\leftmark{%
+ \expandafter\expandafter
+ \expandafter\get@mark@@ne
+ \expandafter\saved@@botmark
+             \nul@mark
+}%
+\def\rightmark{%
+ \expandafter\expandafter
+ \expandafter\get@mark@tw@
+ \expandafter\saved@@firstmark
+             \nul@mark
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+%
+% \subsection{Output Super-routine}%
+%
+% We want to change \LaTeX's output routine, but do not wish to remain vulnerable
+% to interference from such ``required'' packages as
+% \classname{multicol} (authored by Frank Mittelbach)
+% and \classname{longtable} (authored by David P. Carlisle), which 
+% swap in their own output routines when the respective package is active.
+%
+% The better mechanism, used here, is due to William Baxter (web at superscript.com),
+% who has allowed his several ideas to be used in this package.
+%
+% In what follows, we effectively wrap up the old \LaTeX\ output routine inside
+% a new, more flexible ``super routine''. When the output routine is called,
+% the ``super routine'' acts as a dispatcher. If the old routine is needed, it is called.
+%
+% If a package attempts to substitute in their own output routine, they will effectively
+% be modifying a token register by the name of \cmd\output.
+% The primitive \cmd\output\ is now known by a different name, which should no longer be
+% necessary to use.
+%
+% Usage note: to make a visit to the output routine employing the dispatcher, enter
+% with a value of \cmd\outputpenalty\ that corresponds to a macro. Defining as follows:
+%\begin{verbatim}
+%\@namedef{output@10000}{<your code here>}%
+%\end{verbatim}
+% by convention, your output routine should void out \cmd\box\cmd\@cclv.
+%
+% In rewriting \LaTeX's output dispatcher
+% in a much simpler form, we also avoid the sin of multiple \cmd\shipout s
+% within a single visit to the output routine.
+%
+% Conceptually, we divide visits to the output routine into two classes.
+% The first involves natural page breaks
+% (at a \cmd\newpage\ or when \cmd\pagetotal $>$ \cmd\pagegoal)
+% and usually resulting in \cmd\box\cmd\@cclv\ either being shipped out or
+% salted away (e.g., each column in a multicolumn layout).
+% We might call this class the ``natural output routines''; the \cmd\outputpenalty\
+% will never be less than $-10000$.
+% Furthermore, we ensure that \cmd\holdinginserts\ is cleared when 
+% calling such routines.
+%
+% The other class involves a forced visit to the output routine
+% via a large negative penalty ($< -10000$). They do not generally
+% result in a \cmd\shipout\ of \cmd\box\cmd\@cclv: they may be dead cycles.
+% We provide a mechanism (call it a ``one-off'' output routine) that allows
+% us to specify certain processing to be done when \TeX\ reaches
+% the current position on the page.
+%
+% One-off output routines themselves fall into two divisions, ones
+% that process \cmd\box\cmd\@cclv, and ones that work on the main vertical list (MVL).
+% The former are typified by changes to the page grid, perhaps
+% even column balancing.
+% The latter involve the insertion of penalties or glue and the processing of floats.
+% 
+% The natural output routine is a single procedure. We have not introduced multiple
+% natural output routines based on the \cmd\outputpenalty\ because \TeX\ does not
+% support such a thing: \TeX\ sometimes lays down a penalty whose value is the sum 
+% of other penalties. Because of this, we cannot depend on the value of \cmd\outputpenalty\
+% in such areas.
+%
+% We do introduce flexibility in the form of a mechanism for patching into the
+% natural output routine. Three hooks are offered, allowing a procedure
+% to prepare for the upcoming visit to the output routine,
+% access to \cmd\box\cmd\@cclv, and after doing \cmd\shipout\ (or otherwise 
+% committing the material to the page).
+%
+% Environments, commands, and even packages can install their
+% own procedures into these hooks.
+% For instance, if the longtable package is loaded, it will install
+% its procedures, but those procedures will punt if the page break 
+% being processed does not actually fall within a longtable environment.
+%
+% \begin{macro}{\primitive@output}
+% Here we remember the \TeX\ primitive \cmd\output\ and its value,
+% and then proceed to take over the \cmd\csname\ of \cmd\output,
+% making it a \cmd\toks\ register and installing the old value of
+% the output routine.
+%    \begin{macrocode}
+\let\primitive@output\output
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\output@latex}
+% \begin{macro}{\output}
+% Grab the tokens in \cmd\the\cmd\output\ (but without the extra set of braces).
+% The value of \cmd\toks@\ must remain untouched until loaded into the appropriate token 
+% register; this is done a few lines below.
+%    \begin{macrocode}
+\long\def\@tempa#1\@@nil{#1}%
+            \toks@
+\expandafter\expandafter
+\expandafter{%
+\expandafter \@tempa
+             \the\primitive@output
+             \@@nil
+             }%
+\newtoks\output@latex
+\output@latex\expandafter{\the\toks@}%
+\let\output\output@latex
+%    \end{macrocode}
+%
+% A comment on compatibility with other packages that co-opt the output routine.
+%
+% Somewhere on the LaTeX-L list, David Kastrup has urged macro  writers to take over 
+% the output routine in such a way that others can do likewise. How is this to be 
+% accomplished?
+%
+% Consider what the \classname{lineno} package does when it loads.
+% \begin{enumerate}
+% \item
+%  It does \cmd\let\ cmd\@tempa\ \cmd\output. 
+%  This has the effect of identifying \cmd\@tempa\ with the 
+%  \cmd\toks\ register we created above to hold the old output routine of \LaTeX.
+%  Let us say that was \cmd\toks14. 
+% \item
+%  \classname{lineno} itself effectively does \cmd\newtoks\ \cmd\@LN@output, 
+%  which assigns that \cmd\csname\ to \cmd\toks 15.
+% \item
+%  It loads \cmd\@LN@output\ with the contents of \cmd\@tempa 
+%  (that is, \cmd\toks14, our copy of \LaTeX's output routine).
+% \item
+%  Then it loads \cmd\@tempa\ with its own desired procedure, 
+%  to be executed at \cmd\output\ time, thereby taking over what it thinks is the output routine,
+%  but which is in reality the procedure \revtex\ executes when it wants to pass control
+%  to \LaTeX's original output routine.
+% \item
+%  It then does \cmd\let\ \cmd\output\ \cmd\@LN@output, 
+%  which now identifies \cmd\output\ with \cmd\toks15, the output routine of \classname{lineno}.
+% \item
+%  When the \cmd\output\ routine is triggered, 
+%  the primitive output routine \cmd\primitive@output\ is executed, and if 
+%  appropriate, control is passed to \cmd\output@latex, which \revtex\ had loaded with the old
+%  \LaTeX\ output routine, but which is presently loaded with that of \classname{lineno}.
+% \item
+%  The output routine of \classname{lineno} is executed, and if appropriate control is passed
+%  to \cmd\@LN@output, the old output routine of \LaTeX.
+% \item
+%  Furthermore, the \cmd\csname\ \cmd\output\ now points to \cmd\@LN@output\ (\cmd\toks15).
+%  This means that someone coming in after \classname{lineno} to take over the output routine
+%  will actually get executed after that of \classname{lineno}, but before \LaTeX.
+% \end{enumerate}
+% As you can see, the process of taking over the output routine may continue until all of the 
+% \cmd\toks\ registers have been allocated. 
+% If, say, \classname{newpackage} would itself like to take over the output routine,
+% and if it uses the above set of steps, then when the output routine is triggered, the order
+% of execution is \revtex, then \classname{lineno}, then \classname{newpackage}, then \LaTeX.
+% Each new package inserts itself on front of \LaTeX.
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\dispatch@output}
+% \changes{4.1b}{2008/08/04}{(AO, 456) Compatibility with other packages that override the output routine, following suggestion by David Kastrup.}
+% We now install our own output routine in place of the original 
+% output routine of \LaTeX, which is still available as \cmd\the\ \cmd\output.
+%
+% The output routine is simply the procedure \cmd\dispatch@output.
+% It either dispatches to a procedure based on a particular value of
+% \cmd\outputpenalty\ or it executes \cmd\the\cmd\output@latex\ tokens.
+%    \begin{macrocode}
+\primitive@output{\dispatch@output}%
+\def\dispatch@output{%
+ \let\par\@@par
+%    \end{macrocode}
+% Try to interpret \cmd\outputpenalty\ as a dispatcher to a message handler, 
+% its value is, e.g., \cmd\do@startpage@pen.
+%    \begin{macrocode}
+ \expandafter\let\expandafter\output@procedure\csname output@\the\outputpenalty\endcsname
+%    \end{macrocode}
+% If we have failed to find a dispatcher, then settle for \cmd\output@latex.
+%    \begin{macrocode}
+ \@ifnotrelax\output@procedure{}{%
+  \expandafter\def\expandafter\output@procedure\expandafter{\the\output@latex}%
+ }%
+%    \end{macrocode}
+% Now test if the dispatcher is the special case of \cmd\execute@message@pen, in which case execute the \cmd\@message@saved.
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+%    \begin{macrocode}
+ \expandafter\@ifx\expandafter{\csname output@-\the\execute@message@pen\endcsname\output@procedure}{%
+  \let\output@procedure\@message@saved
+ }{}%
+ \ltxgrid@info@sw{\class@info{\string\dispatch@output}\say\output@procedure\saythe\holdinginserts}{}%
+ \outputdebug@sw{\output@debug}{}%
+ \output@procedure
+}%
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\set@output@procedure#1#2{%
+ \count@\outputpenalty\advance\count@-#2%
+ \expandafter\let\expandafter#1\csname output@\the\count@\endcsname
+}%
+%    \end{macrocode}
+%
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+% The following procedure is executed at the beginning of each visit to the output routine, 
+% contingent on the level of diagnostics specified. 
+% However, it bails out when the visit is part of a tight sequence of visits to the output routine. 
+%    \begin{macrocode}
+\def\output@debug{%
+ \def\@tempa{\save@message}%
+ \@ifx{\output@procedure\@tempa}{%
+  \true@sw
+ }{%
+  \@ifnum{\outputpenalty=-\save@column@insert@pen}{%
+   \@ifnum{\holdinginserts>\z@}%
+  }{%
+   \false@sw
+  }%
+ }%
+ {}{\output@debug@}%
+}%
+\def\output@debug@{%
+%<ignore> 	\saythe\inputlineno
+ 	\saythe\outputpenalty
+ 	\saythe\interlinepenalty
+ 	\saythe\brokenpenalty
+ 	\saythe\clubpenalty
+ 	\saythe\widowpenalty
+ 	\saythe\displaywidowpenalty
+ 	\saythe\predisplaypenalty
+ 	\saythe\interdisplaylinepenalty
+ 	\saythe\postdisplaypenalty
+ 	\saythe\badness
+ 	\say\thepagegrid
+ 	\saythe\pagegrid@col
+ 	\saythe\pagegrid@cur
+%<ignore>  \say\bot@envir
+ 	\saythe\insertpenalties
+%<ignore>  \say\@@topmark
+%<ignore>  \say\saved@@topmark
+%<ignore>  \say\@@firstmark
+%<ignore>  \say\saved@@firstmark
+ 	\say\@@botmark
+%<ignore>  \say\saved@@botmark
+ 	\saythe\pagegoal
+ 	\saythe\pagetotal
+ 	\saythe{\badness\@cclv}%
+ 	\say\@toplist
+ 	\say\@botlist
+ 	\say\@dbltoplist
+ 	\say\@deferlist
+ 	\trace@scroll{%
+ 		\showbox\@cclv
+ 		\showbox\@cclv@saved
+ 		\showbox\pagesofar
+%    \end{macrocode}
+% Klootch! The following line provides only for two-column page grid; if debugging more columns, you must
+% add more statements here. 
+%    \begin{macrocode}
+ 		\showbox\csname col@1\endcsname
+ 		\showbox\footsofar
+ 		\showbox\footins
+ 		\showbox\footins@saved
+ 		\showlists
+ 	}%
+}%
+\@ifxundefined{\outputdebug@sw}{%
+ \@booleanfalse\outputdebug@sw
+}{}%
+\def\trace@scroll#1{\begingroup\showboxbreadth\maxdimen\showboxdepth\maxdimen\scrollmode#1\endgroup}%
+\def\trace@box#1{\trace@scroll{\showbox#1}}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@outputpage}
+% \begin{macro}{\@outputpage@head}
+% \begin{macro}{\@outputpage@tail}
+% \changes{4.1b}{2008/08/04}{Procedure \cs{@outputpage@tail} tailpatches \cs{@outputpage}}%
+% \changes{4.1b}{2008/08/04}{Procedure \cs{@outputpage@head} headpatches \cs{@outputpage}}%
+% The procedure \cmd\@outputpage\ of standard \LaTeX\ is the sole place where a \cmd\shipout\ is carried out.
+% The procedures that build \cmd\@outputbox\ just before a page is shipped out by \cmd\@outputpage\ are:
+% \cmd\@makecolumn,
+% \cmd\@combinepage, and
+% \cmd\@combinedblfloats.
+%
+% We need to head- and tailpatch this procedure, so we perform here
+% the only modifications to that procedure that are essential.
+% Elsewhere, we will build up the meanings of \cmd\@outputpage@head\ and \cmd\@outputpage@tail.
+%    \begin{macrocode}
+\prepdef\@outputpage{\@outputpage@head}%
+\let\@outputpage@head\@empty
+\appdef\@outputpage{\@outputpage@tail}%
+\let\@outputpage@tail\@empty
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\show@box@size}
+% \begin{macro}{\show@text@box@size}
+% \begin{macro}{\show@pagesofar@size}
+% \begin{macro}{\show@box@size@sw}
+% \begin{macro}{\total@text}
+% \changes{4.1b}{2008/08/04}{(AO, 452) Support length checking: show size of shipped out text.}
+% Procedure \cmd\show@box@size\ is a diagnostic for the sizes of boxes;
+% the boolean \cmd\show@box@size@sw\ turns it on and off.
+%    \begin{macrocode}
+\def\show@box@size#1#2{%
+ \show@box@size@sw{%
+  \begingroup
+   \setbox\z@\vbox{\unvcopy#2\hrule}%
+   \class@info{Show box size: #1^^J%
+    (\the\ht\z@\space X \the\wd\z@) 
+    \the\c@page\space\space\the\pagegrid@cur\space\the\pagegrid@col
+   }%
+  \endgroup
+ }{}%
+}%
+%    \end{macrocode}
+% Procedure \cmd\show@text@box@size\ tallies the size of the indicated column.
+% If \cmd\box\ \cmd\pagesofar\ is a factor, then its height has been memorized
+% in the depth of the tally box.
+% 
+% \changes{4.1f}{2009/07/10}{(AO, 518) Tally register overflow when locument is long}
+%    \begin{macrocode}
+\def\show@text@box@size{%
+ \show@box@size{Text column}\@outputbox
+ \tally@box@size@sw{%
+  \@ifdim{\wd\@outputbox>\z@}{%
+   \dimen@\ht\@outputbox\divide\dimen@\@twopowerfourteen
+   \advance\dimen@-\dp\csname box@size@\the\pagegrid@col\endcsname
+   \@ifdim{\dimen@>\z@}{%
+    \advance\dimen@ \ht\csname box@size@\the\pagegrid@col\endcsname
+    \global\ht\csname box@size@\the\pagegrid@col\endcsname\dimen@
+    \show@box@size@sw{%
+     \class@info{Column: \the\dimen@}%
+    }{}%
+   }{}%
+  }{}%
+  \global\dp\csname box@size@\the\pagegrid@col\endcsname\z@
+ }{}%
+}%
+%    \end{macrocode}
+% Take the height of \cmd\box\ \cmd\pagesofar\ into account.
+%    \begin{macrocode}
+\def\show@pagesofar@size{%
+ \show@box@size{Page so far}\pagesofar
+ \dimen@\ht\pagesofar\divide\dimen@\@twopowerfourteen
+ \global\dp\csname box@size@1\endcsname\dimen@
+ \show@box@size@sw{%
+  \class@info{Pagesofar: \the\dimen@}%
+ }{}%
+}%
+\@booleanfalse\tally@box@size@sw
+\@booleanfalse\show@box@size@sw
+\expandafter\newbox\csname box@size@1\endcsname
+\expandafter\setbox\csname box@size@1\endcsname\hbox{}%
+\expandafter\newbox\csname box@size@2\endcsname
+\expandafter\setbox\csname box@size@2\endcsname\hbox{}%
+\def\total@text{%
+ \@tempdima\the\ht\csname box@size@2\endcsname\divide\@tempdima\@twopowertwo\@tempcnta\@tempdima
+ \@tempdimb\the\ht\csname box@size@1\endcsname\divide\@tempdimb\@twopowertwo\@tempcntb\@tempdimb
+ \class@info{Total text: Column(\the\@tempcnta pt), Page(\the\@tempcntb pt)}%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{Further thoughts about inserts}
+%
+% The only safe way to deal with inserts is to either set \cmd\holdininserts\ or
+% to commit to using whatever insert comes your way: you cannot change your mind
+% once you see a non-void \cmd\box\cmd\footins, say.
+%
+% Therefore all output routine processing must proceed with \cmd\holdinginserts\ set
+% until you are sure of the material to be committed to the page. At that point, you
+% can clear \cmd\holdinginserts, spew \cmd\box\cmd\@cclv, put down the appropriate penalty, 
+% and exit, with the knowledge that \TeX\ will re-find the same pagebreak, this time 
+% visiting the output routine with everything, including inserts, in their proper 
+% place.
+% This technique applies to split elements (screens, longtable, index) as well as to 
+% manufactured pages (float pages and clearpage pages). 
+%
+% Therefore, the output routine must not make assumptions about whether \cmd\holdinginserts\
+% should be cleared; instead this must be left to the one-off output routines or the natural output routine.
+%
+% If we are manufacturing pages (``float page processing''), and if \cmd\pagegoal\ is not equal to
+% \cmd\vsize, then inserts are at hand, and our criterion should take into account the insert
+% material, even though we cannot measure its height based on the size of \cmd\box\cmd\footins\
+% (because \cmd\holdinginserts\ is set, you see).
+%
+% It would be better to take the complement of \cmd\floatpagefraction\ and use that
+% as a standard for the looseness of the page. Since \cmd\pagegoal\ reflects the inserted material,
+% the criterion becomes the difference of the aggregate height of the floats and the \cmd\pagegoal\
+% versus this "page looseness" standard.
+%
+% As a check, consider what happens if we bail out: \cmd\@deferlist\ has never been touched, so it 
+% requires no attention. Also, \cmd\holdinginserts\ has never been cleared, so inserts require
+% no attention. So we only have to ensure that marks are preserved, which is already taken
+% care of by the message handler mechanism.
+%
+% If we are doing ordinary page cutting, then the scheme would be to detect whether we are within
+% a screen (or longtable as may be), do the adjustment to the page height, and return, but this time
+% with \cmd\holdinginserts\ cleared. Upon reentering the output routine, we may or may not be within
+% the screen environment, but we are now sure to have a final page break, and we can commit this
+% material (by shipping out or by saving it out as a full column).
+%
+% In the above, the first of the two visits to the output routine is a dead cycle and requires
+% propagation of marks, but nothing else.
+%
+% \subsection{The difference between inserts and floats}
+%
+% While revisiting this package in 2008, I needed to clarify under what circumstances inserts
+% would be added to the \cmd\pagesofar. My conclusion is that I had been treating them
+% exactly the same as floats, but that was a mistake. 
+%
+% Floats can be committed at the top of a column, in the middle, or at the bottom. 
+% Footnotes (the only \cmd\insert\ that is used in \LaTeX) may only be committed at the bottom
+% of a column. So, it was necessary to provide two versions of \cmd\@combinepage, one 
+% that committed \cmd\insert s, and the other that did not, the former used only when 
+% a column of text was committed. Note that even after a column is committed, we could change our minds:
+% for instance if in multicolumn grid and we decide to balance the columns. 
+%
+%
+% \subsection{The natural output routine}
+%
+% Here is the portion of the output routine that fields cases not handled by
+% the dispatcher. 
+%
+% The default is to ship out a page and then look around for more material
+% that might constitute a ``float page''. However, because \cmd\holdinginserts\
+% is normally set, this output routine must first have a dead cycle and
+% come back again with \cmd\holdinginserts\ cleared.
+% Then, after shipping out, it puts down a message that 
+% will manufacture zero or more float pages, finally terminating
+% with a procedure that commits floats to a new unfinished page.
+%
+% To accomodate special processing, we execute hooks whose name is based
+% on the value of the "envir" mark component. The default is "document",
+% ensured by an initial mark of that value; the associated procedures
+% are all nil. Any unknown envir value will "\cmd\relax\ out".
+%
+% The test made by \cmd\toggle@insert\ tells whether we are on our first visit to
+% the output routine (with \cmd\holdinginserts\ still positive), or our second
+% (with \cmd\holdinginserts\ zeroed). The output routine will toggle the setting. 
+%
+% The commands \cmd\hold@insertions\ and \cmd\move@insertions\ respectively
+% clear and set \cmd\holdinginserts, so this procedure effectively
+% clears \cmd\holdinginserts\ just long enough to pick up the insertions.
+% Important: any output routine that clears \cmd\holdinginserts\
+% must guarentee that it is restored on the subsequent visit to the output routine.
+% Or, to put it another way, if an output routine detects that \cmd\holdinginserts\ 
+% is cleared, it should take it upon itself to restore it to a positive value before exiting.
+%
+% The branch with \cmd\holdinginserts\ set is executed first; the other
+% branch follows on practically immediately thereafter. In the first branch,
+% we simply execute the appropriate hook and then execute a dead cycle.
+%
+% In the branch with \cmd\holdinginserts\ cleared, the procedure
+% builds up the current column, which is now complete, with \cmd\@makecolumn, then
+% dispatches to the shipout routine associated with the current page grid, \cmd\output@column@.
+% At the end, it triggers the execution of an output routine to prepare the next column (or page).
+%
+% \subsection{Natural output routine}%
+%
+% \begin{macro}{\natural@output}
+% \begin{macro}{\output}
+% Here is the output routine that handles natural pagebreaks:
+% we now have page that needs to be shipped out or a portion of a page that is ready to be committed to the page grid.
+% Processing is of necessity divided into phases, \cmd\output@holding\ is executed upon first encountering the natural page-breaking point, while inserts are being held.
+% The second phase, \cmd\output@moving, is set in motion by the first: here the same material (in most cases) will be processed with \cmd\holdinginserts\ cleared,
+% and the insertions (e.g., footnotes) are split off into their assigned box registers. 
+%    \begin{macrocode}
+\def\natural@output{\toggle@insert{\output@holding}{\output@moving}}%
+\output@latex{\natural@output}%
+%    \end{macrocode}
+%
+% In accordance with the scheme suggested by David Kastrup for allowing another output routine
+% to slip itself into ours, we use a token register called \cmd\output. 
+% However, we reserve the ability to restore things if we so desire.
+% This we must do in the case of the \filename{lineno.sty} package, because its functionality
+% is best served by being integrated into our own dispatcher-based output routine.
+%
+% To restore our own output routine, we can repeat the above assignment,
+% \begin{verbatim}
+%\output@latex{\natural@output}%
+% \end{verbatim}
+% some time before the document begins.
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\output@holding}
+% \begin{macro}{\@if@exceed@pagegoal}
+% The procedure \cmd\output@holding\
+% is our first cycle through the output routine; \cmd\holdinginserts\ is still set.
+% We give the current environment a heads up
+% (it is through this means that \classname{longtable} sets its running header and footer),
+% then we execute a dead cycle, which should propagate marks. 
+%
+% One corner case that can crop up is the presence of a single unbreakable chunk whose size is larger
+% than \cmd\vsize.
+% Doing a dead cycle under such circumstances will not find the same breakpoint as this time
+% (remember we threw in a \cmd\mark\ node).
+% Instead, we attempt to remove the excess height of the material, so we can continue to propagate marks.
+%
+% The corner case is at hand if the natural size of \cmd\box\cmd\@cclv\ exceeds \cmd\pagegoal\ and
+% the contents cannot be shrunk to fit.
+%
+% \changes{4.1b}{2008/08/04}{New procedure for showing a box contents, \cs{trace@box}}
+%    \begin{macrocode}
+\def\output@holding{%
+ \csname output@init@\bot@envir\endcsname
+ \@if@exceed@pagegoal{\unvcopy\@cclv}{%
+  \setbox\z@\vbox{\unvcopy\@cclv}%
+  \outputdebug@sw{\trace@box\z@}{}%
+  \dimen@\ht\@cclv\advance\dimen@-\ht\z@
+  \dead@cycle@repair\dimen@
+ }{%
+  \dead@cycle
+ }%
+}%
+\def\@if@exceed@pagegoal#1{%
+ \begingroup
+  \setbox\z@\vbox{#1}%
+  \dimen@\ht\z@\advance\dimen@\dp\z@
+  \outputdebug@sw{\saythe\dimen@}{}%
+  \@ifdim{\dimen@>\pagegoal}{%
+   \setbox\z@\vbox{\@@mark{}\unvbox\z@}%
+   \splittopskip\topskip
+   \splitmaxdepth\maxdepth
+   \vbadness\@M
+   \vfuzz\maxdimen
+   \setbox\tw@\vsplit\z@ to\pagegoal
+   \outputdebug@sw{\trace@scroll{\showbox\tw@\showbox\z@}}{}%
+   \setbox\tw@\vbox{\unvbox\tw@}%
+   \@ifdim{\ht\tw@=\z@}{%
+    \ltxgrid@info{Found overly large chunk while preparing to move insertions. Attempting repairs}%
+    \aftergroup\true@sw
+   }{%
+    \aftergroup\false@sw
+   }%
+ }{%
+  \aftergroup\false@sw
+ }%
+ \endgroup
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\output@moving}
+% \begin{macro}{\@cclv@nontrivial@sw}
+% The procedure \cmd\output@moving\ 
+% is our second cycle through the output routine; \cmd\holdinginserts\ is now cleared,
+% and \cmd\insert s will have been split off into their respective box registers, like \cmd\footins.
+%
+% \begin{enumerate}
+% \item
+%  Set the values of \cmd\topmark\ and \cmd\firstmark.
+% \item
+%  If we got here because of a \cmd\clearpage\ command, remove the protection box that this mechanism has left on the MVL.
+% \item
+%  If the contents of \cmd\box\cmd\@cclv\ are non-trivial, commit it to the current page (as a column) or ship it out, as the case may call for.
+% \item
+%  If not, discard it (we are at the end of \cmd\clearpage\ processing).
+% \item
+%  Set various values, including the available space for setting type on the next column (\cmd\@colroom).
+% \end{enumerate}
+%
+% The processing for a non-trivial \cmd\box\cmd\@cclv\ are:
+% \begin{enumerate}
+% \item
+%  Execute the head procedure for the current environment.
+% \item
+%  Make up a column and ship it out (or commit it to the current page) via a procedure keyed to the current page grid.
+% \item
+%  Put down an interrupt for \cmd\do@startcolumn@pen: this will force a visit to the output routine for the 
+%  purpose of committing floats to the next column.
+% \item
+%  Possibly put down an interrupt to continue \cmd\clearpage\ proccessing.
+% \item
+%  Execute the tail procedure for the current environment.
+% \end{enumerate}
+%
+%
+% The processing for a trivial \cmd\box\cmd\@cclv\ are:
+% \begin{enumerate}
+% \item
+%  Void out \cmd\box\cmd\@cclv\ and give appropriate warning messages and diagnostics.
+% \item
+%  Put down the same interrupts as for the non-trivial case above.
+% \end{enumerate}
+%
+% This instance of \cmd\@makecolumn\ is followed by \cmd\output@column@, 
+% that is, it builds a column for \cmd\shipout\ rather than for adding to \cmd\pagesofar. 
+%
+% We need to handle cases where the \cmd\output@pre@, \cmd\output@column@, or \cmd\output@post@\
+% dispatchers come up \cmd\relax ed out: the default is to execute the corresponding 
+% procedures from the \env{docuemnt} environment and the one-column grid respectively.
+%
+% One such case comes up with frequency: at the end of the document, where the \cmd\botmark\ is
+% now empty.
+% \changes{4.1b}{2008/08/04}{Change \cs{@makecol} to \cs{@makecolumn} with argument}
+% \changes{4.1b}{2008/08/04}{Change \cs{set@colroom} to \cs{set@colht}}
+% \changes{4.1n}{2010/01/02}{(AO, 571) Use procedures \cs{output@do@prep} and \cs{output@column@do} as dispatchers}
+%    \begin{macrocode}
+\def\output@moving{%
+ \set@top@firstmark
+ \@ifnum{\outputpenalty=\do@newpage@pen}{%
+  \setbox\@cclv\vbox{%
+   \unvbox\@cclv
+   \remove@lastbox
+   \@ifdim{\ht\z@=\ht\@protection@box}{\box\lastbox}{\unskip}%
+  }%
+ }{}%
+ \@cclv@nontrivial@sw{%
+  \expandafter\output@do@prep\csname output@prep@\bot@envir \endcsname
+  \@makecolumn\true@sw
+  \expandafter\output@column@do\csname output@column@\thepagegrid\endcsname
+  \protect@penalty\do@startcolumn@pen
+  \clearpage@sw{%
+   \protect@penalty\do@endpage@pen
+  }{}%
+  \expandafter\let\expandafter\output@post@\csname output@post@\bot@envir \endcsname
+  \outputdebug@sw{\say\output@post@}{}%
+  \@ifx{\output@post@\relax}{\output@post@document}{\output@post@}%
+ }{%
+  \void@cclv
+ }%
+ \set@colht
+ \global\@mparbottom\z@
+ \global\@textfloatsheight\z@
+}%
+%    \end{macrocode}
+% Procedure \cmd\output@do@prep\ dispatches to the proper procedure to prepare page.
+%    \begin{macrocode}
+\def\output@do@prep#1{%
+ \outputdebug@sw{\class@info{Prep: \string#1}}{}%
+ \@ifx{#1\relax}{\output@prep@document}{#1}%
+}%
+%    \end{macrocode}
+% Procedure \cmd\output@column@do\ dispatches to the proper procedure to output column or page.
+%    \begin{macrocode}
+\def\output@column@do#1{%
+  \outputdebug@sw{\class@info{Output column: \string#1}}{}%
+  \@ifx{#1\relax}{\output@column@one}{#1}%
+}%
+\def\void@cclv{\begingroup\setbox\z@\box\@cclv\endgroup}%
+\def\remove@lastbox{\setbox\z@\lastbox}%
+%    \end{macrocode}
+%
+% The procedure \cmd\@cclv@nontrivial@sw\ determines if this visit to \cmd\output@moving\
+% is a trivial one, which happens at the end of \cmd\clearpage\ processing and under some pathological circumstances.
+% It emits a Boolean, so it is syntactically like \cmd\true@sw, albeit does not execute solely via expansion.
+%
+% Note: the case where \cmd\box\cmd\@cclv\ is void comes up at the very beginning of the job, when 
+% typesetting a (full-page-width) title block in a two-column layout.
+%
+% Note: the code that removes the last box and skip from the output is intended to detect the case
+% where the output has whatsit nodes followed by topskip and a protection box.
+% This is what happens under normal circumstances at the end of \cmd\clearpage\ processing.
+% \changes{4.1b}{2008/08/04}{New procedure for showing a box contents, \cs{trace@box}}
+%    \begin{macrocode}
+\def\@cclv@nontrivial@sw{%
+ \@ifx@empty\@toplist{%
+  \@ifx@empty\@botlist{%
+   \@ifvoid\footins{%
+    \@ifvoid\@cclv{%
+     \false@sw
+    }{%
+     \setbox\z@\vbox{\unvcopy\@cclv}%
+     \@ifdim{\ht\z@=\topskip}{%
+      \setbox\z@\vbox\bgroup
+       \unvbox\z@
+       \remove@lastbox
+       \dimen@\lastskip\unskip
+       \@ifdim{\ht\z@=\ht\@protection@box}{%
+        \advance\dimen@\ht\z@
+        \@ifdim{\dimen@=\topskip}{%
+         \aftergroup\true@sw
+        }{%
+         \aftergroup\false@sw
+        }%
+       }{%
+        \aftergroup\false@sw
+       }%
+%    \end{macrocode}
+% End of \cmd\box\cmd\z@.
+%    \begin{macrocode}
+      \egroup
+      {%
+%    \end{macrocode}
+% Normal for \clearpage
+%    \begin{macrocode}
+       \false@sw
+      }{%
+       \true@sw
+      }%
+     }{%
+      \@ifdim{\ht\z@=\z@}{%
+       \ltxgrid@info{Found trivial column. Discarding it}%
+       \outputdebug@sw{\trace@box\@cclv}{}%
+       \false@sw
+      }{%
+       \true@sw
+      }%
+     }%
+    }%
+   }{%
+    \true@sw
+   }%
+  }{%
+   \true@sw
+  }%
+ }{%
+  \true@sw
+ }%
+}%
+%    \end{macrocode}
+%
+% 
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\protect@penalty}
+% The procedure \cmd\protect@penalty\ is the utility procedure for invoking a 
+% one-off output routine. Such a routine can expect to find the protection box
+% above it in \cmd\box\cmd\@cclv: it should remove that box.
+%
+% Note that \cmd\execute@message\ does the same thing as \cmd\protect@penalty, but
+% in a slightly different way.
+%
+% We create a specially formulated box that will be universally used when a protection box is needed.
+% In this way, we can always recognize when \cmd\box\cmd\@cclv\ is trivial:
+% it will consist of whatsits followed by \cmd\topskip\ glue and the \cmd\@protection@box.
+%    \begin{macrocode}
+\def\protect@penalty#1{\protection@box\penalty-#1\relax}%
+\newbox\@protection@box
+\setbox\@protection@box\vbox to1986sp{\vfil}%
+\def\protection@box{\nointerlineskip\copy\@protection@box}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\dead@cycle}
+% \begin{macro}{\dead@cycle@repair}
+% The procedure \cmd\dead@cycle\ is defined separately as a utility which can be used by
+% any output processing routine to emulate what takes place in the standard output routine.
+%
+% Here, we have entered the output routine with \cmd\holdinginserts\ enabled, which means that we 
+% are not yet ready to ship out material, because the \cmd\insert\ registers are being held.
+% We want to clear \cmd\holdinginserts\ and come back here with the same page break as before, whereupon
+% we may properly proceed with page makeup.
+%
+% To do this, we
+% propagate marks, then spew the contents of \cmd\box\cmd\@cclv\ followed by the 
+% original output penalty that landed us here (but only if it is not 10000,
+% the flag value for a pagebreak not at a penalty).
+%
+% However, the natural output routine should do this only if \cmd\box\cmd\@cclv\ is nontrivial.
+% A pathological case exists wherein a box of height greater than \cmd\textheight\ would cause an infinite loop involving the output routine.
+% The procedure \cmd\dead@cycle@repair, attempts to catch this case and avoid the loop.
+%
+% The test of the height of \cmd\box\cmd\@cclv\ is not the correct one, because this test will run afoul in
+% the case where \cmd\box\cmd\@cclv\ contains nothing but an \cmd\insert\ node. What to do?
+%
+% It is possible that the pathological case can be detected by looking at \cmd\pagetotal. If that quantity is
+% zero, then \cmd\box\cmd\@cclv\ really is trivial.
+%
+% In the procedure \cmd\dead@cycle@repair, if \cmd\box\cmd\@cclv\ is nontrivial, we execute \cmd\dead@cycle,
+% otherwise it contains nothing but a mark, so we dispense with propagating marks
+% and we simply spew out \cmd\box\cmd\@cclv\ without an accompanying mark.
+% This has the effect of failing to propagate marks, but this problem is preferrable to the infinite loop,
+% which in principle could crash even a robust operating system by filling up the file system.
+%
+% If a document has such a large chunk, it should be fixed, so we give a message in the log.
+%
+% You ask, ``In what way does this infinite loop come about?'' Good question!
+%
+% The setup is a chunk in the MVL that is taller than \cmd\textheight. 
+% (Yes, it's that simple.)
+% As soon as the previous page ships out, the MVL will contain a mark (propagated from the previous page) followed
+% by that large chunk (call it the `big bad box', albeit does not need to be a single box).
+% The next visit to the output routine will be a natural page break, but
+% \TeX\ will select the juncture between the mark and the big bad box as the least-cost page break.
+% Unless the test in \cmd\dead@cycle\ is done, the cycle is perpetuated when the macro 
+% reinserts the mark.
+%
+% The crux matter is achieving, in a robust way, the goal of going from a \cmd\holdinginserts\ state to one
+% where the insertions are moving.
+%
+%    \begin{macrocode}
+\def\dead@cycle@repair#1{%
+ \expandafter\do@@mark
+ \expandafter{%
+              \@@botmark
+             }%
+ \unvbox\@cclv
+ \nointerlineskip
+ \vbox to#1{\vss}%
+ \@ifnum{\outputpenalty<\@M}{\penalty\outputpenalty}{}%
+}%
+\def\dead@cycle@repair@protected#1{%
+ \expandafter\do@@mark
+ \expandafter{%
+              \@@botmark
+             }%
+ \begingroup
+  \unvbox\@cclv
+%    \end{macrocode}
+% Remove the protection box
+%    \begin{macrocode}
+  \remove@lastbox
+  \nointerlineskip
+  \advance#1-\ht\@protection@box
+  \vbox to#1{\vss}%
+  \protection@box % Reinsert protection box
+  \@ifnum{\outputpenalty<\@M}{\penalty\outputpenalty}{}%
+ \endgroup
+}%
+\def\dead@cycle{%
+ \expandafter\do@@mark
+ \expandafter{%
+              \@@botmark
+             }%
+ \unvbox\@cclv
+ \@ifnum{\outputpenalty<\@M}{\penalty\outputpenalty}{}%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\output@init@document}
+% \begin{macro}{\output@prep@document}
+% \begin{macro}{\output@post@document}
+% The default processing simply provides for insertion of held-over footnotes.
+% At a natural page break, we are either at the bottom of a column or at the bottom 
+% of a page. In either case, the \cmd\output@init@\ processing adjusts for the height
+% of the held-over footnotes and bails out.
+% Upon our return, at \cmd\output@prep@\ time, the page break will accomodate the material;
+% it is now actually inserted by concatenating it with the contents of \cmd\footins.
+% The default processing for \cmd\output@post@\ is nil.
+% \changes{4.1b}{2008/08/04}{Box \cs{footbox} changed to box \cs{footsofar}}
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+%    \begin{macrocode}
+\def\output@init@document{%
+ \ltxgrid@info@sw{\class@info{\string\output@init@document}}{}%
+ \global\vsize\vsize
+}%
+%    \end{macrocode}
+% QUERY: the following procedure is very like \cmd\combine@foot@inserts. Should it be the same?
+% Answer: no, the two differ: this procedure makes a local assignment of \cmd\footins;
+% the latter makes a global assignment of \cmd\footsofar.
+%
+% Note: In a multicolumn document, footnotes must \emph{not} be balanced at this point.
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+%    \begin{macrocode}
+\def\output@prep@document{%
+ \ltxgrid@foot@info@sw{\class@info{\string\output@prep@document}\trace@scroll{\showbox\footins\showbox\footsofar}}{}%
+ \@ifvoid\footsofar{%
+ }{%
+  \global\setbox\footins\vbox\bgroup
+   \unvbox\footsofar
+   \@ifvoid\footins{}{%
+    \marry@baselines
+    \unvbox\footins
+   }%
+  \egroup
+  \ltxgrid@foot@info@sw{\trace@box\footins}{}%
+ }%
+}%
+\def\output@post@document{}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@opcol}
+% The standard \LaTeX\ procedure \cmd\@opcol\ is now completely obsoleted.
+%    \begin{macrocode}
+\let\@opcol\@undefined
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@makecolumn}
+% \changes{4.1b}{2008/08/04}{Change \cs{@makecol} to \cs{@makecolumn} with argument}
+% The procedure \cmd\@makecolumn\ packages up a page along with all its insertions and floats.
+% Therefore it is essential that it be executed with \cmd\holdininserts\ cleared.
+%
+% Note that there is a corner case when in a multi-column grid, where the change back to 
+% one-column grid occurs just after a complete page ships out. We want to detect when
+% \cmd\@cclv\ contains nothing but a \cmd\mark, but this is a \TeX\ impossibility.
+%
+% Note on \cmd\@kludgeins: we have removed this mechanism from \LaTeX, because the implementation 
+% of \cmd\enlargethispage\ no longer requires it. 
+% Here, for consistency sake, we remove \cmd\@makespecialcolbox.
+% 
+% The argument of \cmd\@makecolumn\ is a Boolean and determines if we combine the footnote material
+% into the present column. If the procedure is building a column for shipping out, then we will
+% combine the footnote material, if not, we return with the \cmd\footins\ box unchanged.
+%
+% \changes{4.1f}{2009/07/14}{(AO, 519) \cs{footins} content must be preserved and reintegrated}
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+% \changes{4.1n}{2010/01/02}{(AO, 571) coding convention: use \cs{bgroup}, \cs{egroup} (instead of braces) when a box is being built}%
+% \changes{4.1n}{2010/01/02}{(AO, 571) change calling sequence of \cs{combine@foot@inserts} to expose box registers}%
+% I changed the behavior of this procedure in the case where the argument is \cmd\false@sw:
+% send the unused footnote material to \cmd\footsofar.
+%    \begin{macrocode}
+\def\@makecolumn#1{%
+ \ltxgrid@foot@info@sw{\class@info{\string\@makecolumn\string#1}}{}%
+ \setbox\@outputbox\vbox\bgroup
+  \boxmaxdepth\@maxdepth
+  \@tempdima\dp\@cclv
+  \unvbox\@cclv
+  \vskip-\@tempdima
+ \egroup
+ \xdef\@freelist{\@freelist\@midlist}\global\let\@midlist\@empty
+ \show@text@box@size
+ \@combinefloats
+ #1{%
+  \@combineinserts\@outputbox\footins
+ }{%
+  \combine@foot@inserts\footsofar\footins
+ }%
+ \set@adj@colht\dimen@
+ \count@\vbadness
+ \vbadness\@M
+ \setbox\@outputbox\vbox to\dimen@\bgroup
+  \@texttop
+  \dimen@\dp\@outputbox
+  \unvbox\@outputbox
+  \vskip-\dimen@
+  \@textbottom
+ \egroup
+ \vbadness\count@
+ \global\maxdepth\@maxdepth
+}%
+\let\@makespecialcolbox\@undefined
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@combineinserts}
+% The procedure to add the specified insertions to the packaged-up page. 
+% All other classes of insertions should also be dealt with at this time. 
+%
+% Note that the second argument must be a \cmd\newinsert\ register: we access the \cmd\box\ along with the \cmd\skip.
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+% \changes{4.1n}{2010/01/02}{(AO, 571) coding convention: use \cs{bgroup}, \cs{egroup} (instead of braces) when a box is being built}%
+% \changes{4.1n}{2010/01/02}{(AO, 571) footnote rule is leaders, so that it may be removed by \cs{vsplit}; mechanism of \cs{kern} signals to indicate footnote height}%
+%    \begin{macrocode}
+\def\@combineinserts#1#2{%
+ \ltxgrid@foot@info@sw{\class@info{\string\@combineinserts\string#1\string#2}\trace@box#2}{}%
+ \setbox#1\vbox\bgroup
+  \unvbox#1%
+  \@ifvoid{#2}{}{%
+   \dimen@\ht#2\advance\dimen@\dp#2\advance\dimen@\skip#2%
+   \show@box@size{Combining inserts}#2%
+   \vskip\skip#2%
+%    \end{macrocode}
+% The footnote rule is created as leaders, so that it may be removed automatically (via \cmd\vsplit) 
+% in the event the footnote is recovered from this column. 
+% Note that if \cmd\color@begingroup\ or \cmd\normalcolor\ produce marks, this technique will be confounded. 
+%    \begin{macrocode}
+   \setbox\z@\vbox{\footnoterule}\dimen@i\ht\z@
+   \color@begingroup
+   \normalcolor
+   \cleaders\box\z@\vskip\dimen@i\kern-\dimen@i
+   \csname combine@insert@\the\pagegrid@col\endcsname#2%
+   \color@endgroup
+%    \end{macrocode}
+% The following tells \cmd\recover@column\ the size of the footnotes added here, including the skip glue above. 
+%    \begin{macrocode}
+   \kern-\dimen@\kern\dimen@
+  }%
+ \egroup
+ \ltxgrid@foot@info@sw{\trace@box#1}{}%
+}%
+%    \end{macrocode}
+% We provide for a layer of abstraction for the laying down of footnotes at the bottom of this column or page. 
+% \end{macro}
+%
+% \begin{macro}{\combine@insert@tw@}
+% \begin{macro}{\combine@insert@@ne}
+% \begin{macro}{\twocolumn@grid@setup}
+% \begin{macro}{\onecolumn@grid@setup}
+% \begin{macro}{\columngrid@setup}
+% \changes{4.1p}{2010/02/24}{(AO, 583) Provide setup code also for footnotes in a one-column document}%
+% The following two definitions cover the cases of a two-column document (with footnotes set on a single-column width),
+% and a one-column document.
+% However, the case of a two-column document with footnotes set on full text width is not covered. 
+% 
+% For a document in an overall two-column page grid, execute the commands
+% \cmd\twocolumn@grid@setup\ followed by \cmd\open@twocolumn;
+% if on the full page width (one-column grid), the command \cmd\onecolumn@grid@setup. 
+%
+% The following is the way REVTeX does the initialization.
+% The procedure \cmd\select@column@grid\ is executed at \cmd\AtBeginDocument\ time;
+% the boolean \cmd\twocolumn@sw\ selects between the two alternatives.
+% \begin{verbatim}
+%\def\select@column@grid{%
+% \twocolumn@sw{%
+%  \twocolumn@grid@setup
+%  \open@twocolumn
+% }{%
+%  \onecolumn@grid@setup
+% }%
+%}%
+%\appdef\class@documenthook{%
+% \select@column@grid
+%}%
+% \end{verbatim}
+%
+%    \begin{macrocode}
+\def\combine@insert@tw@#1{%
+ \compose@footnotes@two#1\@ifvbox{#1}{\unvbox}{\box}#1%
+}%
+\def\combine@insert@@ne#1{%
+ \compose@footnotes@one#1\@ifvbox{#1}{\unvbox}{\box}#1%
+}%
+\def\twocolumn@grid@setup{%
+ \expandafter\let\csname combine@insert@1\endcsname\combine@insert@tw@
+ \expandafter\let\csname combine@insert@2\endcsname\combine@insert@@ne
+}%
+\def\onecolumn@grid@setup{%
+ \expandafter\let\csname combine@insert@1\endcsname\combine@insert@@ne
+ \expandafter\let\csname combine@insert@2\endcsname\combine@insert@@ne
+}%
+\let\columngrid@setup\onecolumn@grid@setup
+\columngrid@setup
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@floatplacement}
+% In standard \LaTeX, someone (DPC?) makes the assumption that \cmd\@fpmin\ can be assigned
+% locally. This is no longer true now that we ship no more than one page per visit to the output routine.
+% We apply a bandaid.
+%    \begin{macrocode}
+\appdef\@floatplacement{%
+ \global\@fpmin\@fpmin
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pagebreak@pen}
+% While we are in the way of registering certain penalty values,
+% let us register the smallest one that will force a visit to the output routine. 
+% However, this penalty will not have an assciated macro: we wish to execute the 
+% natural output routine instead.
+%
+% Note that this penalty is invoked by \cmd\clearpage\ and \cmd\newpage.
+%    \begin{macrocode}
+\mathchardef\pagebreak@pen=\@M
+\expandafter\let\csname output@-\the\pagebreak@pen\endcsname\relax
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Float placement}%
+%
+% \begin{macro}{\do@startcolumn@pen}
+% The procedure \cmd\do@startcolumn@pen\ is executed as a one-off output routine
+% just after a page is shipped out (or, in a multicolumn page grid, a column is salted away).
+%
+% Its job is to either generate a ``float page'' (in reality a column) for shipping out,
+% or to commit deferred floats to the fresh column, concluding with a dead cycle.
+% In the former case, we accomodate split footnotes and other insertions (by comparing \cmd\vsize\ and \cmd\pagegoal):
+% the floats are spewed onto the page, whereupon \LaTeX's output routine will place the footnotes and ship out,
+% iterating the process once again.
+%
+% Note that when this procedure is invoked, \cmd\box\cmd\@cclv\ still has within it the protection box, so we
+% start by removing it. Note also that if there was a split insertion held over from the previous page, the
+% insert node will be present in \cmd\box\cmd\@cclv, \emph{prior to} the protection box. For this reason, we cannot 
+% just throw away that box, as we might be tempted to do. 
+%
+% FIXME: where else do we possibly inappropriately discard \cmd\box\cmd\@cclv?
+%
+% Note that, because a column or page page had previously just been completed, 
+% we can assume that there is nothing of importance on the page,
+% and because no message is being passed, we can preserve marks in a simple way.
+%
+% A Note on terminology:
+% In a single-column page grid, you might expect that we would execute the procedure \cmd\do@startpage.
+% But this is not so.
+% \LaTeX\ has a confustion of long standing,
+% in which the procedures that handle full-page width floats in a two-column page grid all have in their names
+% the string `dbl', which erroneously suggests having something to do with ``double''. It does not:
+% when you see `dbl', think ``full page width''.
+% \changes{4.1b}{2008/08/04}{Change \cs{set@colroom} to \cs{set@colht}}
+%    \begin{macrocode}
+\mathchardef\do@startcolumn@pen=10005
+\@namedef{output@-\the\do@startcolumn@pen}{\do@startcolumn}%
+\def\do@startcolumn{%
+ \setbox\@cclv\vbox{\unvbox\@cclv\remove@lastbox\unskip}%
+ \clearpage@sw{\@clearfloatplacement}{\@floatplacement}%
+ \set@colht
+ \@booleanfalse\pfloat@avail@sw
+ \begingroup
+  \@colht\@colroom
+  \@booleanfalse\float@avail@sw
+  \@tryfcolumn\test@colfloat
+  \float@avail@sw{\aftergroup\@booleantrue\aftergroup\pfloat@avail@sw}{}%
+ \endgroup
+ \fcolmade@sw{%
+  \setbox\@cclv\vbox{\unvbox\@outputbox\unvbox\@cclv}%
+%    \end{macrocode}
+% Now ask for a return visit, this time with insertions and all.
+%    \begin{macrocode}
+  \outputpenalty-\pagebreak@pen
+  \dead@cycle
+ }{%
+  \begingroup
+   \let\@elt\@scolelt
+   \let\reserved@b\@deferlist\global\let\@deferlist\@empty\reserved@b
+  \endgroup
+  \clearpage@sw{%
+   \outputpenalty\@M
+  }{%
+   \outputpenalty\do@newpage@pen
+  }%
+  \dead@cycle
+ }%
+ \check@deferlist@stuck\do@startcolumn
+ \set@vsize
+}%
+\def\@scolelt#1{\def\@currbox{#1}\@addtonextcol}%
+\def\test@colfloat#1{%
+ \csname @floatselect@sw@\thepagegrid\endcsname#1{}{\@testtrue}%
+ \@if@sw\if@test\fi{}{\aftergroup\@booleantrue\aftergroup\float@avail@sw}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@addtonextcol}
+% We must adjust \cmd\@addtonextcol\ to take held-over inserts into account.
+% Now that all deferred floats are queued up together (in order), we must have a way of 
+% differentiating them; this is done by the page grid-dependent procedure \cmd\@floatselect@sw@.
+%    \begin{macrocode}
+\def\@addtonextcol{%
+ \begingroup
+  \@insertfalse
+  \@setfloattypecounts
+  \csname @floatselect@sw@\thepagegrid\endcsname\@currbox{%
+   \@ifnum{\@fpstype=8 }{}{%
+     \@ifnum{\@fpstype=24 }{}{%
+       \@flsettextmin
+       \@reqcolroom \ht\@currbox
+       \advance \@reqcolroom \@textmin
+       \advance \@reqcolroom \vsize % take into account split insertions
+       \advance \@reqcolroom -\pagegoal
+       \@ifdim{\@colroom>\@reqcolroom}{%
+         \@flsetnum \@colnum
+         \@ifnum{\@colnum>\z@}{%
+            \@bitor\@currtype\@deferlist
+            \@if@sw\if@test\fi{}{%
+              \@addtotoporbot
+            }%
+         }{}%
+       }{}%
+     }%
+   }%
+  }{}%
+  \@if@sw\if@insert\fi{}{%
+    \@cons\@deferlist\@currbox
+  }%
+ \endgroup
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\do@startpage@pen}
+% \begin{macro}{\forcefloats@sw}
+% \begin{macro}{\@output@combined@page}
+% \begin{macro}{\@sdblcolelt}
+% \begin{macro}{\test@dblfloat}
+% \begin{macro}{\@if@notdblfloat}
+% Similar to \cmd\do@startcolumn,
+% the procedure \cmd\do@startpage\ starts up a new page (not column) in a multi-column page grid. 
+% It is invoked after a page is shipped out in a multi-column page grid, and
+% it commits full-page-width floats to the fresh page, possibly resulting in a float page.
+% In implementation, it is similar to \cmd\do@startcolumn, except that
+% it commits effectively via \cmd\@addtodblcol\ instead of \cmd\@addtonextcol.
+% Note that this procedure will inevitably be followed by \cmd\do@startcolumn.
+%
+% Some details of the procedure:
+%
+% We begin by removing the protection box from \cmd\box\cmd\@cclv, then setting the values of the
+% float placement parameters appropriately, and resetting \cmd\@colht, \cmd\@colroom, and \cmd\vsize\ to base values.
+%
+% Next we attempt to compose a float page, a page consisting entirely of floats. If successful,
+% we ship out the float page and lay down an interrupt that will send us back here for another try.
+%
+% If no float page is formed, we attempt to commit full-page-width floats to the text page, and return with a dead cycle.
+% We are now ready to compose columns of text.
+%
+% Note that all floats (both column floats and full-page-width floats) move through a single queue.
+% To differentiate between the two, the width of the float is compared to \cmd\textwidth.
+% This comparison is encapsulated in the macro \cmd\@if@notdblfloat, which should be used whenever 
+% such a determination must be made. This procedure returns a Boolean.
+%
+% \changes{4.1b}{2008/08/04}{Change \cs{set@colroom} to \cs{set@colht}}
+%    \begin{macrocode}
+\mathchardef\do@startpage@pen=10006
+\@namedef{output@-\the\do@startpage@pen}{\do@startpage}%
+\def\do@startpage{%
+ \setbox\@cclv\vbox{\unvbox\@cclv\remove@lastbox\unskip}%
+ \clearpage@sw{\@clearfloatplacement}{\@dblfloatplacement}%
+ \set@colht
+ \@booleanfalse\pfloat@avail@sw
+ \begingroup
+  \@booleanfalse\float@avail@sw
+  \@tryfcolumn\test@dblfloat
+  \float@avail@sw{\aftergroup\@booleantrue\aftergroup\pfloat@avail@sw}{}%
+ \endgroup
+ \fcolmade@sw{%
+  \global\setbox\pagesofar\vbox{\unvbox\pagesofar\unvbox\@outputbox}%
+  \@output@combined@page
+ }{%
+  \begingroup
+   \@booleanfalse\float@avail@sw
+   \let\@elt\@sdblcolelt
+   \let\reserved@b\@deferlist\global\let\@deferlist\@empty\reserved@b
+  \endgroup
+  \@ifdim{\@colht=\textheight}{% No luck...
+   \pfloat@avail@sw{% ...but a float *was* available!
+    \forcefloats@sw{%
+     \ltxgrid@warn{Forced dequeueing of floats stalled}%
+    }{%
+     \ltxgrid@warn{Dequeueing of floats stalled}%
+    }%
+   }{}%
+  }{}%
+  \outputpenalty\@M
+  \dead@cycle
+ }%
+ \check@deferlist@stuck\do@startpage
+ \set@colht
+}%
+%    \end{macrocode}
+%
+% Procedure \cmd\@output@combined@page\ is a utility that ships out a page consisting of the
+% result of \cmd\@combinepage\ and \cmd\@combinedblfloats, after which it prepares for 
+% the process to repeat.
+%
+% It is coincidentally identical to what needs to happen with 
+% a float page that has been built by \cmd\@tryfcolumn, in the multi-column page grid, 
+% and also handles the case where a page needs to be shipped out when in multicolumn mode.
+% \changes{4.1b}{2008/08/04}{New procedure \cs{@output@combined@page}}
+% \changes{4.1b}{2008/08/04}{Change \cs{@combinepage} to \cs{@combinepage} with argument}
+%    \begin{macrocode}
+\def\@output@combined@page{%
+ \@combinepage\true@sw
+ \@combinedblfloats
+ \@outputpage
+ \global\pagegrid@cur\@ne
+ \protect@penalty\do@startpage@pen
+}%
+\def\@sdblcolelt#1{\def\@currbox{#1}\@addtodblcol}%
+\def\test@dblfloat#1{%
+ \@if@notdblfloat{#1}{\@testtrue}{}%
+ \@if@sw\if@test\fi{}{\aftergroup\@booleantrue\aftergroup\float@avail@sw}%
+}%
+\def\@if@notdblfloat#1{\@ifdim{\wd#1<\textwidth}}%
+\@booleanfalse\forcefloats@sw
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@addtodblcol}
+%
+% The procedure \cmd\@addtodblcol\ is called into play at the beginning of each fresh page
+% and operates on each deferred float, in the hopes of placing one or more such floats
+% at the top of the current page.
+% 
+% We alter the procedure of standard \LaTeX\ by putting failed floats into 
+% \cmd\@deferlist\ instead of \cmd\@dbldeferlist. Having done so, we must have a means
+% of differentiating full-page-width floats from column-width floats.
+% We assume that the latter will always be narrower than \cmd\textwidth.
+%
+% In aid of detecting a stalled float flushing process, we set a Boolean if we encounter
+% a qualified full-page-width float here. Any that qualify but fail the rest of the tests
+% might still pass when reconsidered on an otherwise blank page.
+%    \begin{macrocode}
+\def\@addtodblcol{%
+ \begingroup
+  \@if@notdblfloat{\@currbox}{%
+   \false@sw
+  }{%
+   \@setfloattypecounts
+   \@getfpsbit \tw@
+   \@bitor \@currtype \@deferlist
+   \@if@sw\if@test\fi{%
+    \false@sw
+   }{%
+    \@ifodd\@tempcnta{%
+     \aftergroup\@booleantrue\aftergroup\float@avail@sw
+     \@flsetnum \@dbltopnum
+     \@ifnum{\@dbltopnum>\z@}{%
+       \@ifdim{\@dbltoproom>\ht\@currbox}{%
+        \true@sw
+       }{%
+        \@ifnum{\@fpstype<\sixt@@n}{%
+         \begingroup
+          \advance \@dbltoproom \@textmin
+          \@ifdim{\@dbltoproom>\ht\@currbox}{%
+           \endgroup\true@sw
+          }{%
+           \endgroup\false@sw
+          }%
+        }{%
+         \false@sw
+        }%
+       }%
+     }{%
+      \false@sw
+     }%
+    }{%
+     \false@sw
+    }%
+   }%
+  }%
+  {%
+   \@tempdima -\ht\@currbox
+   \advance\@tempdima
+    -\@ifx{\@dbltoplist\@empty}{\dbltextfloatsep}{\dblfloatsep}%
+   \global \advance \@dbltoproom \@tempdima
+   \global \advance \@colht \@tempdima
+   \global \advance \@dbltopnum \m@ne
+   \@cons \@dbltoplist \@currbox
+  }{%
+   \@cons \@deferlist \@currbox
+  }%
+ \endgroup
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@tryfcolumn}
+% \begin{macro}{\@wtryfc}
+% \begin{macro}{\@xtryfc}
+% \begin{macro}{\@ztryfc}
+% Whenever a page is shipped out, \LaTeX\ automatically tries out a float column:
+% a page containing nothing but floats (and, as we have added here, split footnotes).
+%
+% The following four procedures employ certain macros to communicate between each other:
+%
+% \cmd\fcolmade@sw, a boolean, says whether we were successful in making a float column.
+%
+% \cmd\if@test, a \cmd\newif\ switch, says a float has failed some test.
+% 
+% \cmd\@deferlist, is the input to the process, a list, of deferred floats.
+% 
+% \cmd\@trylist, a list, stores the deferred floats to be tried out on the float column.
+%
+% \cmd\@failedlist, a list of floats that have failed the selection for the float column.
+%
+% \cmd\@flfail, a list of floats that have failed the second selection for the float column.
+%
+% \cmd\@flsucceed, a list, the floats that have been successfully placed on the float column.
+%
+% \cmd\@freelist, a list, receives any freed floats.
+%
+% \cmd\@colht, a dimen, the available space for the column, including column floats and insertions (footnotes).
+%
+% \cmd\@fpmin, a dimen, the required minimum height for the float column.
+%
+% \cmd\@outputbox, a box, the output of the process.
+%
+% \cmd\@fptop, \cmd\@fpsep, \cmd\@fpbot, glue, placed above, between, and below floats on the float column.
+%
+% \cmd\@currtype, a count, used temporarily for the float's bits.
+%
+% \cmd\@tempcnta, a count, used temporarily for the float's bits.
+%
+% In \cmd\@tryfcolumn, we alter the criterion for a float page, because if footnotes are present at this point
+% (presumably due to a split insertion) then \cmd\@fpmin is no longer the right threshold to apply.
+% 
+% Note that we have changed \cmd\@tryfcolumn, \cmd\@xtryfc, and \cmd\@ztryfc\ syntactically so that the procedure
+% to test for the float's being a column float versus a full-page-width float is passed in as an 
+% argument.
+%
+%    \begin{macrocode}
+\def\@tryfcolumn#1{%
+  \global\@booleanfalse\fcolmade@sw
+  \@ifx@empty\@deferlist{}{%
+    \global\let\@trylist\@deferlist
+    \global\let\@failedlist\@empty
+    \begingroup
+      \dimen@\vsize\advance\dimen@-\pagegoal\@ifdim{\dimen@>\z@}{%
+       \advance\@fpmin-\dimen@
+      }{}%
+      \def\@elt{\@xtryfc#1}\@trylist
+    \endgroup
+    \fcolmade@sw{%
+      \global\setbox\@outputbox\vbox{\vskip \@fptop}%
+      \let \@elt \@wtryfc \@flsucceed
+      \global\setbox\@outputbox\vbox{\unvbox\@outputbox
+        \unskip \vskip \@fpbot
+      }%
+      \let \@elt \relax
+      \xdef\@deferlist{\@failedlist\@flfail}%
+      \xdef\@freelist{\@freelist\@flsucceed}%
+    }{}%
+  }%
+}%
+\def\@wtryfc #1{%
+  \global\setbox\@outputbox\vbox{\unvbox\@outputbox
+    \box #1\vskip\@fpsep
+  }%
+}%
+\def\@xtryfc#1#2{%
+  \@next\reserved@a\@trylist{}{}% trim \@trylist. Ugly!
+  \@currtype \count #2%
+  \divide\@currtype\@xxxii\multiply\@currtype\@xxxii
+  \@bitor \@currtype \@failedlist
+  \@testfp #2%
+  #1#2%
+  \@ifdim{\ht #2>\@colht   }{\@testtrue}{}%
+  \@if@sw\if@test\fi{%
+   \@cons\@failedlist #2%
+  }{%
+   \begingroup
+     \gdef\@flsucceed{\@elt #2}%
+     \global\let\@flfail\@empty
+     \@tempdima\ht #2%
+     \def \@elt {\@ztryfc#1}\@trylist
+     \@ifdim{\@tempdima >\@fpmin}{%
+       \global\@booleantrue\fcolmade@sw
+     }{%
+       \@cons\@failedlist #2%
+     }%
+   \endgroup
+   \fcolmade@sw{%
+     \let \@elt \@gobble
+   }{}%
+  }%
+}%
+\def\@ztryfc #1#2{%
+  \@tempcnta \count#2%
+  \divide\@tempcnta\@xxxii\multiply\@tempcnta\@xxxii
+  \@bitor \@tempcnta {\@failedlist \@flfail}%
+  \@testfp #2%
+  #1#2%
+  \@tempdimb\@tempdima
+  \advance\@tempdimb \ht#2\advance\@tempdimb\@fpsep
+  \@ifdim{\@tempdimb >\@colht}{%
+    \@testtrue
+  }{}%
+  \@if@sw\if@test\fi{%
+    \@cons\@flfail #2%
+  }{%
+    \@cons\@flsucceed #2%
+    \@tempdima\@tempdimb
+  }%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{Clearing pages}%
+% 
+% Clearing the page is an elaboration of ending the page: it entails flushing all floats.
+%
+% This package might make number of float flushing algorithms available,
+% a very simple one that does not try to produce excellent pages,
+% another that tries to make the best use of space,
+% and a more complex one that tries to balance columns.
+% 
+% At the beginning of the page-clearing process, by definition all of the paragraph text involved is on the MVL and all floats have been encountered.
+% There may be material in \cmd\pagesofar, and (in a multi-column page grid) any number of columns of the page have been composed.
+% Also, there might be footnote material saved up in \cmd\footsofar.
+% 
+% Because we did not want to perform multiple \cmd\shipout s per visit to the output routine,
+% our multi-column page makeup will not compose multiple columns per visit.
+% This implementation detail may not require alteration, but it is not a limitation that is truly necessary:
+% it is only multiple \cmd\shipout s per visit that must be avoided.
+% 
+% The crux matter is how to continue with flushing floats even after the material in the MVL is exhausted.
+% At that point, we must, upon completion of the output routine, 
+% insert into the MVL an interrupt that triggers the next step in the processing.
+%
+% Therefore, after processing a \cmd\do@startcolumn\ interrupt, we must somehow force the completion of that column.
+% This could be done by inserting a \cmd\do@newpage@pen\ interrupt.
+% 
+% And after processing a \cmd\do@startpage@pen\ interrupt, that results in \cmd\@dbltopinsert s,
+% we must ensure that the multiple columns on the page get completed, so that the page itself finally gets shipped out.
+% This part will proceed automatically given that \cmd\do@startcolumn\ processing completes successfully.
+% 
+% The process will not be complete until all deferred floats have been placed and shipped out, and all saved-up footnotes have been inserted.
+% 
+% Full-page-width floats can get out of order of column floats. This problem can be remedied by holding them all in the same list.
+% We therefore stop using \cmd\@dbldeferlist\ entirely, and all of the procedures that formerly used it have been rewritten to
+% use \cmd\@deferlist\ instead. When traversing the list, we apply a selector on the given box that determines whether it is a column-width or page-width float.
+% This selector is different depending on the page grid.
+%
+% When the \cmd\@deferlist\ is processed (by any means), we have to take care of the case where a float of one category is passed over but we are looking for a float of the other category.
+% Here, we must terminate processing, to avoid disordering the floats. This we do by the usual means.
+% 
+% The system has a Boolean that says we are clearing pages: \cmd\clearpage@sw; if it is true,
+% then at the tail of \cmd\do@startcolumn\ processing, we should put down a (\cmd\vfil?) \cmd\do@newpage@pen\ interrupt.
+% This is because the MVL is now empty, so we have to force the columns to complete.
+% 
+% One potential very pathological case would be where there is one or more deferred floats that never successfully get placed:
+% placing floats has stalled, and we will ship out blank pages indefinitely. How to detect this case?
+% 
+% First, \cmd\do@startpage\ will evidently be stalled if the following are all true:
+% a) \cmd\@tryfcolumn\ and \cmd\@sdblcolelt\ both fail,
+% b) there are deferred floats available for page placement, and
+% c) the \cmd\@colht=\cmd\textheight, that is, the full page height is available for placement of column floats.
+% 
+% Second, \cmd\do@startcolumn\ will evidently be stalled if the following are all true:
+% a) tryfcolumn fails,
+% b) there are deferred floats available for column placement, and
+% a) the \cmd\@colroom=\cmd\textheight, that is, the full page height is available for placement of column floats.
+% 
+%
+% \begin{macro}{\cleardoublepage}
+% \begin{macro}{\clearpage}
+% \begin{macro}{\newpage}
+% \begin{macro}{\newpage@prep}
+% The function of \cmd\clearpage\ is to end the current page with \cmd\newpage\ and then
+% ship out additional pages until (\footins) inserts and (deferred) floats are exhausted.
+%
+% The method involves setting the float placement parameters to completely permissive values
+% and kicking out the current page (using a non-discardable penalty).
+% A possibly short page will be shipped out, followed
+% by any number of float pages. However these float pages, because using permissive float placement,
+% will exhaust all inserts and deferred floats.
+%
+% Bug Note: in the code for \cmd\clearpage, the first penalty we output is an unprotected \cmd\pagebreak@pen.
+% I tried using a protected \cmd\do@newpage@pen, but that gave rise to a corner case where a blank page
+% was output.
+%
+% At present, the \cmd\clearpage\ procedure does the same as \cmd\newpage,
+% except that \cmd\clearpage@sw\ is turned on,
+% and the (discardable) \cmd\newpage\ is inevitably followed by the same procedures
+% that are executed if a page is shipped out.
+%
+% FIXME: it seems that better than \cmd\pagebreak@pen\ would be an unprotected penalty of a special value that would
+% entail output routine processing consisting of the following steps:
+% 3) \cmd\unvbox\cmd\@cclv,
+% 1) set \cmd\clearpage@sw\ to \cmd\true@sw,
+% 2) put down a protected \cmd\do@startcolumn@pen,
+% 4) take a dead cycle.
+%
+% The effect would be to liberalize float placement options for the current column as well as further columns that may be output as part of \cmd\clearpage\ processing.
+% Of course, it would still be necessary to set \cmd\clearpage@sw\ again via an interrupt.
+%
+% An optimization might be to clear \cmd\clearpage@sw\ as part of the same interrupt,
+% but that would actually not work properly, because it is necessary for \cmd\do@endpage\ to
+% possibly invoke further visits to the output routine before clearpage processing ceases.
+%    \begin{macrocode}
+\def\newpage@prep{%
+  \if@noskipsec
+    \ifx \@nodocument\relax
+      \leavevmode
+      \global \@noskipsecfalse
+    \fi
+  \fi
+  \if@inlabel
+    \leavevmode
+    \global \@inlabelfalse
+  \fi
+  \if@nobreak \@nobreakfalse \everypar{}\fi
+  \par
+}%
+\def \newpage {%
+ \newpage@prep
+ \do@output@MVL{%
+  \vfil
+  \penalty-\pagebreak@pen
+ }%
+}%
+\def\clearpage{%
+ \newpage@prep
+ \do@output@MVL{%
+  \vfil
+  \penalty-\pagebreak@pen
+  \global\@booleantrue\clearpage@sw
+  \protect@penalty\do@startcolumn@pen
+  \protect@penalty\do@endpage@pen
+ }%
+ \do@output@MVL{%
+  \global\@booleanfalse\clearpage@sw
+ }%
+}%
+\def\cleardoublepage{%
+ \clearpage
+ \@if@sw\if@twoside\fi{%
+  \@ifodd\c@page{}{%
+   \null\clearpage
+  }%
+ }{}%
+}%
+\@booleanfalse\clearpage@sw
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\do@endpage@pen}
+% The penalty \cmd\do@endpage@pen\ simply dispatches to the page grid procedure that forces an end page.
+% That procedure should test whether there is anything to ship out (say committed floats), then act accordingly.
+% Note that as part of this work, it should \cmd\unvbox\cmd\@cclv, which has been left boxed up so it can be 
+% measured.
+%    \begin{macrocode}
+\mathchardef\do@endpage@pen=10007
+\@namedef{output@-\the\do@endpage@pen}{\csname end@column@\thepagegrid\endcsname}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\do@newpage@pen}
+% The penalty \cmd\do@newpage@pen\ allows a ``non-discardable \cmd\newpage'' command:
+% a \cmd\newpage\ command that will not disappear at a pagebreak.
+% This visit to the output routine will not be dispatched to an interrupt,
+% rather the natural output routine will be executed, where it
+% will remove the protection box.
+% 
+% Call this routine by executing \cmd\protect@penalty\cmd\do@newpage@pen.
+%    \begin{macrocode}
+\mathchardef\do@newpage@pen=10001
+\expandafter\let\csname output@-\the\do@newpage@pen\endcsname\relax
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@clearfloatplacement}
+% The procedure \cmd\@clearfloatplacement\ sets the float placement parameters
+% to completely permissive values (except for \cmd\@fpmin). The standard values are:
+%
+% \begin{tabular}{ll}
+%\cmd\@topnum      &\cmd\c@topnumber\\
+%\cmd\@toproom     &\cmd\topfraction\cmd\@colht\\
+%\cmd\@botnum      &\cmd\c@bottomnumber\\
+%\cmd\@botroom     &\cmd\bottomfraction\cmd\@colht\\
+%\cmd\@colnum      &\cmd\c@totalnumber\\
+%\cmd\@fpmin       &\cmd\floatpagefraction\cmd\@colht\\
+%\cmd\@dbltopnum   &\cmd\c@dbltopnumber\\
+%\cmd\@dbltoproom  &\cmd\dbltopfraction\cmd\@colht\\
+%\cmd\@textmin     &\cmd\@colht\cmd\advance\cmd\@textmin -\cmd\@dbltoproom\\
+%\cmd\@fpmin       &\cmd\dblfloatpagefraction\cmd\textheight
+% \end{tabular}
+%    \begin{macrocode}
+\def\@clearfloatplacement{%
+ \global\@topnum     \maxdimen
+ \global\@toproom    \maxdimen
+ \global\@botnum     \maxdimen
+ \global\@botroom    \maxdimen
+ \global\@colnum     \maxdimen
+ \global\@dbltopnum  \maxdimen
+ \global\@dbltoproom \maxdimen
+ \global\@textmin    \z@      
+ \global\@fpmin      \z@      
+ \let\@testfp\@gobble
+ \appdef\@setfloattypecounts{\@fpstype16\advance\@fpstype\m@ne}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@doclearpage}
+% \begin{macro}{\@makefcolumn}
+% \begin{macro}{\@makecol}
+% The \cmd\@doclearpage\ procedure is now obsoleted, as is \cmd\@makefcolumn, which it invoked.
+% We also completely avoid using \cmd\@makecol\ (in favor of \cmd\@makecolumn).
+%    \begin{macrocode}
+\let\@doclearpage\@undefined
+\let\@makefcolumn\@undefined
+\let\@makecol\@undefined
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\clr@top@firstmark}
+% \begin{macro}{\set@top@firstmark}
+% \begin{macro}{\@outputpage@tail}
+% We want accurate values of \cmd\topmark\ and \cmd\firstmark, but we must deal with 
+% the fact that there are many different ways of contributing material
+% to the page. Only upon the first contribution to the page is the value of \cmd\topmark\
+% accurate. However, with \cmd\firstmark\ we must potentially examine each contribution
+% because the first mark on the page may happen to fall in the last piece of material contributed.
+%
+% To begin, we define the procedure that initializes the macros to appropriate flag values.
+%    \begin{macrocode}
+\def\clr@top@firstmark{%
+ \global\let\saved@@topmark\@undefined
+ \global\let\saved@@firstmark\@empty
+ \global\let\saved@@botmark\@empty
+}%
+\clr@top@firstmark
+%    \end{macrocode}
+%
+% Note that the flag value for \cmd\saved@@topmark\ is \cmd\@undefined, just as one would
+% expect. But that for \cmd\saved@@firstmark\ and \cmd\saved@@botmark\ is \cmd\@empty.
+%
+% Next, we define procedure \cmd\set@top@firstmark; it will be exercised everywhere material is contributed,
+% capturing the mark values if appropriate.
+%    \begin{macrocode}
+\def\set@top@firstmark{%
+ \@ifxundefined\saved@@topmark{\expandafter\gdef\expandafter\saved@@topmark\expandafter{\@@topmark}}{}%
+ \@if@empty\saved@@firstmark{\expandafter\gdef\expandafter\saved@@firstmark\expandafter{\@@firstmark}}{}%
+ \@if@empty\@@botmark{}{\expandafter\gdef\expandafter\saved@@botmark\expandafter{\@@botmark}}%
+}%
+%    \end{macrocode}
+% When should \cmd\set@top@firstmark\ be called?
+% A good candidate for a universal procedure for handling contributed material is
+% the natural output routine; are any other calls needed?
+%
+% Yes, in \cmd\save@column\ we must execute \cmd\set@top@firstmark\ because we are about to 
+% save away \cmd\box\cmd\@cclv, and we will never see its marks again (unless it is unboxed into the MVL),
+% because \TeX\ lets one access a box's marks only within an output routine that has put that box into \cmd\box\cmd\@cclv.
+%
+% As soon as a page is shipped out, we initialize the two macros that
+% hold the values of \cmd\topmark\ and \cmd\firstmark, respectively.
+% \changes{4.1b}{2008/08/04}{Procedure \cs{@outputpage@tail} tailpatches \cs{@outputpage}}%
+%    \begin{macrocode}
+\appdef\@outputpage@tail{%
+ \clr@top@firstmark
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{Other interfaces to \LaTeX}%
+%
+% \begin{macro}{\@float}
+% \begin{macro}{\@dblfloat}
+% \begin{macro}{\@yfloat}
+% \begin{macro}{\fps@}
+% \begin{macro}{\fpsd@}
+% The \LaTeX\ kernel procedures \cmd\@float\ and \cmd\@dblfloat\ are treated on an equal footing.
+% Each now takes environment-specific float placement defaults.
+% If none are defined for the calling environment, we apply a default.
+%
+% A parameter is passed that will set the width of text within the float, normally \cmd\columnwidth,
+% and in the "dbl" version, \cmd\textwidth. However, an environment such as \env{turnpage}
+% may change the meanings of these macros to allow turnpage floats.
+%
+% \changes{4.0a}{2008/06/26 }{\cs{@yfloat}: de-fang \cs{set@footnotewidth} (see ltxutil.dtx): we have already done its job. }
+%
+% Note on \cmd\@xfloat: the optional argument must come to it fully expanded, because the macro
+% does a weird procedure on this argument, involving \cmd\@onelevel@sanitize, which I do not
+% understand, and which does not work if not so expanded. 
+% \changes{4.1b}{2008/08/04}{Get rid of the \cs{reserved@a} idiom}
+%    \begin{macrocode}
+\def\@float#1{%
+ \@ifnextchar[{%
+%    \end{macrocode}
+% \verb+}]{+Brace-matching klootch
+%    \begin{macrocode}
+  \@yfloat\width@float{#1}%
+ }{%
+  \@ifxundefined@cs{fps@#1}{}{\expandafter\let\expandafter\fps@\csname fps@#1\endcsname}%
+  \expandafter\@argswap\expandafter{\expandafter[\fps@]}{\@yfloat\width@float{#1}}%
+ }%
+}%
+\def\@dblfloat#1{%
+ \@ifnum{\pagegrid@col=\@ne}{%
+  \@float{#1}%
+ }{%
+  \@ifnextchar[{%
+%    \end{macrocode}
+% \verb+}]{+Brace-matching klootch
+%    \begin{macrocode}
+   \@yfloat\widthd@float{#1}%
+  }{%
+   \@ifxundefined@cs{fpsd@#1}{}{\expandafter\let\expandafter\fpsd@\csname fpsd@#1\endcsname}%
+   \expandafter\@argswap\expandafter{\expandafter[\fpsd@]}{\@yfloat\widthd@float{#1}}%
+  }%
+ }%
+}%
+%    \end{macrocode}
+% \changes{4.1b}{2008/08/04}{Turn off the \cs{set@footnotewidth} mechanism; a float `knows' its proper typesetting context}
+% \changes{4.1n}{2010/01/02}{(AO, 571) Interface \cs{set@footnotewidth} for determining the set width of footnotes}%
+% \cmd\@yfloat\ is the go-to procdure for creating the proper environment for the content of a float.
+% Argument \verb+#1+ is the width of the float environment (we disable \cmd\set@footnotewidth), and 
+% we establish a self-contained (minipage) environment for footnotes. 
+%    \begin{macrocode}
+\def\@yfloat#1#2[#3]{%
+ \@xfloat{#2}[#3]%
+ \hsize#1\linewidth\hsize
+ \let\set@footnotewidth\@empty
+ \minipagefootnote@init
+}%
+\def\fps@{tbp}%
+\def\fpsd@{tp}%
+\def\width@float{\columnwidth}%
+\def\widthd@float{\textwidth}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\end@float}
+% \begin{macro}{\end@dblfloat}
+% \begin{macro}{\end@@float}
+% \begin{macro}{\check@currbox@count}
+% \begin{macro}{\minipagefootnote@init}
+% \begin{macro}{\minipagefootnote@here}
+% \LaTeX\ kernel procedures \cmd\end@float\ and \cmd\end@dblfloat\
+% have been changed to work alike; in particular, floats of both classes
+% are deferred into the same queue.
+% This measure ensures that they will be placed in their original order, 
+% an aspect in which \LaTeX\ is broken.
+%
+% Note: when retrieving floats from the queues, we can differentiate those of the two categories
+% by the width of the box.
+%
+% Floats are processed via an output routine message, and are checked for 
+% sanity in re the float placement options. In the case of full-page-width floats,
+% we ensure that the h and b float placement options are never asserted, because they
+% make no sense.
+%
+% Note that if we get to the end of the float box and still have pending
+% footnotes, we put then out.
+%
+% LaTeX Bug note: if a user types \cmd\begin{table*}[h], the float will never succeed in being placed!
+% we try to catch such cases.
+%
+% Note that the macro \cmd\check@currbox@count\ tries to catch cases where the float placement options
+% are such that the float can never be placed.
+%
+% The calls to \cmd\@iffpsbit\ are part of a procedure to deny certain of the float placement
+% parameters: ``h'' and ``b'' are not possible, the former because the \cmd\marginpar\ mechanism
+% cannot place a full-page-width float within a multicolumn page grid, the latter because nobody
+% has yet written the code to do so (pretty bad reason, I know).
+% \changes{4.1b}{2008/08/04}{New procedure \cs{@iffpsbit} replaces \cs{@getfpsbit}}
+%    \begin{macrocode}
+\def\end@float{%
+ \end@@float{%
+  \check@currbox@count
+ }%
+}%
+\def\end@dblfloat{%
+ \@ifnum{\pagegrid@col=\@ne}{%
+  \end@float
+ }{%
+  \end@@float{%
+   \@iffpsbit\@ne{\global\advance\count\@currbox\m@ne}{}%
+   \@iffpsbit\f@ur{\global\advance\count\@currbox-4\relax}{}%
+   \global\wd\@currbox\textwidth % Klootch
+   \check@currbox@count
+  }%
+ }%
+}%
+\def\end@@float#1{%
+ \minipagefootnote@here
+ \@endfloatbox
+ #1%
+ \@ifnum{\@floatpenalty <\z@}{%
+  \@largefloatcheck
+  \@cons\@currlist\@currbox
+  \@ifnum{\@floatpenalty <-\@Mii}{%
+   \do@output@cclv{\@add@float}%
+  }{%
+   \vadjust{\do@output@cclv{\@add@float}}%
+   \@Esphack
+  }%
+ }{}%
+}%
+%    \end{macrocode}
+% The \classname{float} package of Anselm Lingnau fails when used under \classname{ltxgrid}, but
+% we can fix things. 
+% We also repair a bug in that package. 
+%
+% \changes{4.1g}{2009/10/06}{(AO, 531) Fix package \classname{float} }
+%    \begin{macrocode}
+\newcommand\float@end@float{%
+ \@endfloatbox
+ \global\setbox\@currbox\float@makebox\columnwidth
+ \let\@endfloatbox\relax
+ \end@float
+}%
+\newcommand\float@end@ltx{%
+ \end@@float{%
+  \global\setbox\@currbox\float@makebox\columnwidth
+  \check@currbox@count
+ }%
+}%
+\newcommand\newfloat@float[3]{%
+ \@namedef{ext@#1}{#3} %!
+ \let\float@do=\relax
+ \xdef\@tempa{\noexpand\float@exts{\the\float@exts \float@do{#3}}}%
+ \@tempa
+ \floatplacement{#1}{#2}%
+ \@ifundefined{fname@#1}{\floatname{#1}{#1}}{} %!
+ \expandafter\edef\csname ftype@#1\endcsname{\value{float@type}}%
+ \addtocounter{float@type}{\value{float@type}} %!
+ \restylefloat{#1}%
+ \expandafter\edef\csname fnum@#1\endcsname{%
+  \expandafter\noexpand\csname fname@#1\endcsname{} %!
+  \expandafter\noexpand\csname the#1\endcsname
+ }
+ \@ifnextchar[%]
+  {%
+   \float@newx{#1}%
+  }{%
+   \@ifundefined{c@#1}{\newcounter{#1}\@namedef{the#1}{\arabic{#1}}}{}%
+  }%
+}%
+\newcommand\newfloat@ltx[3]{%
+ \@namedef{ext@#1}{#3}%
+ \let\float@do=\relax
+ \xdef\@tempa{\noexpand\float@exts{\the\float@exts \float@do{#3}}}%
+ \@tempa
+ \floatplacement{#1}{#2}%
+ \@ifundefined{fname@#1}{\floatname{#1}{#1}}{}%
+ \expandafter\edef\csname ftype@#1\expandafter\endcsname\expandafter{\the\c@float@type}%
+ \addtocounter{float@type}{\value{float@type}}%
+ \restylefloat{#1}%
+ \expandafter\edef\csname fnum@#1\endcsname{%
+  \expandafter\noexpand\csname fname@#1\endcsname{}%
+  \expandafter\noexpand\csname the#1\endcsname
+ }
+ \@ifnextchar[%]
+  {%
+   \float@newx{#1}%
+  }{%
+   \@ifundefined{c@#1}{\newcounter{#1}\@namedef{the#1}{\arabic{#1}}}{}%
+  }%
+}%
+\appdef\document@inithook{%
+ \@ifxundefined\newfloat{}{%
+  \@ifx{\float@end\float@end@float}{%
+   \@ifx{\newfloat\newfloat@float}{\true@sw}{\false@sw}%
+   }{\false@sw}% 
+   {%
+    \class@warn{Repair the float package}%
+    \let\float@end\float@end@ltx
+    \let\newfloat\newfloat@ltx
+   }{%
+    \class@warn{Failed to patch the float package}%
+   }%
+ }% 
+}%
+%    \end{macrocode}
+%
+% Boolean procedure \cmd\@iffpsbit\ is similar to the \cmd\@getfpsbit\ of \LaTeX, except
+% that we do not expose the scratch count register or even change its value.
+%    \begin{macrocode}
+\def\@iffpsbit#1{%
+ \begingroup
+  \@tempcnta\count\@currbox
+  \divide\@tempcnta#1\relax
+  \@ifodd\@tempcnta{\aftergroup\true@sw}{\aftergroup\false@sw}%
+ \endgroup
+}%
+%    \end{macrocode}
+%
+% In procedure \cmd\check@currbox@count, we calculate the net float placement
+% directive (encoded into \cmd\count\ \cmd\@currbox's least significant four bits).
+% If zero, issue a warning.
+% \changes{4.1b}{2008/08/04}{Tally the height of the float}
+%    \begin{macrocode}
+\def\check@currbox@count{%
+ \@ifnum{\count\@currbox>\z@}{%
+  \count@\count\@currbox\divide\count@\sixt@@n\multiply\count@\sixt@@n
+  \@tempcnta\count\@currbox\advance\@tempcnta-\count@
+  \@ifnum{\@tempcnta=\z@}{%
+   \ltxgrid@warn{Float cannot be placed}%
+  }{}%
+  \expandafter\tally@float\expandafter{\@captype}%
+ }{%
+%    \end{macrocode}
+% In this case, the float is a \cmd\marginpar.
+%    \begin{macrocode}
+ }%
+}%
+\providecommand\minipagefootnote@init{}%
+\providecommand\minipagefootnote@here{}%
+\providecommand\tally@float[1]{}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@specialoutput}
+% The \cmd\@add@float\ procedure used to reside in standard \LaTeX's \cmd\@specialoutput,
+% which is no more.
+%
+% Historical Note: \cmd\@specialoutput\ and Lamport's method of an output routine dispatcher
+% is the genesis of our more powerful and refined way of using \TeX's output routine to 
+% safely accomplish page makeup tasks. To it and to him we owe acknowledgement and thanks.
+%    \begin{macrocode}
+\let\@specialoutput\@undefined
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@add@float}
+% In the following, we do not need to execute \cmd\@reinserts, which was wrong anyway, as you cannot
+% reliably recover insertions when they split (unless you have a way of reinserting the captured insertion
+% ahead of the split-off part).
+%
+% Now that full-page-width floats are being processed the same as column floats, we
+% have to nip in here and cause them always to be deferred.
+%
+% At the very end, the \cmd\vsize\ is adjusted for any newly committed float.
+%    \begin{macrocode}
+\def\@add@float{%
+ \@pageht\ht\@cclv\@pagedp\dp\@cclv
+ \unvbox\@cclv
+ \@next\@currbox\@currlist{%
+  \csname @floatselect@sw@\thepagegrid\endcsname\@currbox{%
+   \@ifnum{\count\@currbox>\z@}{%
+    \advance \@pageht \@pagedp
+%    \end{macrocode}
+% Do not assume \cmd\holdinginserts is cleared:
+%    \begin{macrocode}
+    \advance \@pageht \vsize \advance \@pageht -\pagegoal
+%    \end{macrocode}
+% Commit an `h' float:
+%    \begin{macrocode}
+    \@addtocurcol
+   }{%
+    \@addmarginpar
+   }%
+  }{%
+   \@resethfps
+   \@cons\@deferlist\@currbox
+  }%
+ }{\@latexbug}%
+ \@ifnum{\outputpenalty<\z@}{%
+  \@if@sw\if@nobreak\fi{%
+   \nobreak
+  }{%
+   \addpenalty \interlinepenalty
+  }%
+ }{}%
+ \set@vsize
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@reinserts}
+% The \cmd\@reinserts\ procedure of standard \LaTeX\ is now obsoleted (it had been erroneous anyway).
+%    \begin{macrocode}
+\let\@reinserts\@undefined
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@addtocurcol}
+% We modify the \cmd\@addtocurcol\ procedure of standard \LaTeX\ 
+% so that a float placed ``here'' may break over pages.
+%    \begin{macrocode}
+\def \@addtocurcol {%
+   \@insertfalse
+   \@setfloattypecounts
+   \ifnum \@fpstype=8
+   \else
+     \ifnum \@fpstype=24
+     \else
+       \@flsettextmin
+       \advance \@textmin \@textfloatsheight
+       \@reqcolroom \@pageht
+       \ifdim \@textmin>\@reqcolroom
+         \@reqcolroom \@textmin
+       \fi
+       \advance \@reqcolroom \ht\@currbox
+       \ifdim \@colroom>\@reqcolroom
+         \@flsetnum \@colnum
+         \ifnum \@colnum>\z@
+           \@bitor\@currtype\@deferlist
+           \if@test
+           \else
+             \@bitor\@currtype\@botlist
+             \if@test
+               \@addtobot
+             \else
+               \ifodd \count\@currbox
+                 \advance \@reqcolroom \intextsep
+                 \ifdim \@colroom>\@reqcolroom
+                   \global \advance \@colnum \m@ne
+                   \global \advance \@textfloatsheight \ht\@currbox
+                   \global \advance \@textfloatsheight 2\intextsep
+                   \@cons \@midlist \@currbox
+                   \if@nobreak
+                     \nobreak
+                     \@nobreakfalse
+                     \everypar{}%
+                   \else
+                     \addpenalty \interlinepenalty
+                   \fi
+                   \vskip \intextsep
+                   \unvbox\@currbox %AO
+                   \penalty\interlinepenalty
+                   \vskip\intextsep
+                   \ifnum\outputpenalty <-\@Mii \vskip -\parskip\fi
+                   \outputpenalty \z@
+                   \@inserttrue
+                 \fi
+               \fi
+               \if@insert
+               \else
+                 \@addtotoporbot
+               \fi
+             \fi
+           \fi
+         \fi
+       \fi
+     \fi
+   \fi
+   \if@insert
+   \else
+     \@resethfps
+     \@cons\@deferlist\@currbox
+   \fi
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\if@twocolumn}
+% The \cmd\newif\ switch \cmd\if@twocolumn\ is entirely unused. However its access words are invoked by
+% \LaTeX's \cmd\document\ procedure, so we de-fang it.
+%    \begin{macrocode}
+\@twocolumnfalse
+\let\@twocolumntrue\@twocolumnfalse
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@addmarginpar}
+% The procedure \cmd\@addmarginpar\ used to access \cmd\if@twocolumn, but that switch is not reliable;
+% the better way is to use \cmd\thepagegrid. We establish a convention for a page-grid-oriented
+% procedure, e.g., \cmd\@addmarginpar@one, that emits a boolean, telling this procedure
+% whether to set the marginpar on the left or right.
+%    \begin{macrocode}
+\def\@addmarginpar{%
+ \@next\@marbox\@currlist{%
+  \@cons\@freelist\@marbox\@cons\@freelist\@currbox
+ }\@latexbug
+ \setbox\@marbox\hb@xt@\columnwidth{%
+  \csname @addmarginpar@\thepagegrid\endcsname{%
+   \hskip-\marginparsep\hskip-\marginparwidth
+   \box\@currbox
+  }{%
+   \hskip\columnwidth\hskip\marginparsep
+   \box\@marbox
+  }%
+  \hss
+ }%
+ \setbox\z@\box\@currbox
+    \@tempdima\@mparbottom
+    \advance\@tempdima -\@pageht
+    \advance\@tempdima\ht\@marbox
+ \@ifdim{\@tempdima >\z@}{%
+   \@latex@warning@no@line {Marginpar on page \thepage\space moved}%
+ }{%
+   \@tempdima\z@
+ }%
+    \global\@mparbottom\@pageht
+    \global\advance\@mparbottom\@tempdima
+    \global\advance\@mparbottom\dp\@marbox
+    \global\advance\@mparbottom\marginparpush
+    \advance\@tempdima -\ht\@marbox
+    \global\setbox \@marbox
+                   \vbox {\vskip \@tempdima
+                          \box \@marbox}%
+    \global \ht\@marbox \z@
+    \global \dp\@marbox \z@
+    \kern -\@pagedp
+    \nointerlineskip
+  \box\@marbox
+    \nointerlineskip
+    \hbox{\vrule \@height\z@ \@width\z@ \@depth\@pagedp}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{environment}{turnpage}
+% Any float (viz., \env{figure} or \env{table}) within the scope of this environment
+% will be a turnpage float: It will be assumed to occupy an entire page (constitute a float page),
+% the width will be \cmd\textheight, the height \cmd\textwidth, and the entire float will be presented
+% rotated 90 degrees. 
+%
+% The implementation requires the services of the \cmd\rotatebox\ command, so we supply a dummy definition
+% that explains things to the user.
+%    \begin{macrocode}
+\newenvironment{turnpage}{%
+ \def\width@float{\textheight}%
+ \def\widthd@float{\textheight}%
+ \appdef\@endfloatbox{%
+  \@ifxundefined\@currbox{%
+   \ltxgrid@warn{Cannot rotate! Not a float}%
+  }{%
+   \setbox\@currbox\vbox to\textwidth{\vfil\unvbox\@currbox\vfil}%
+   \global\setbox\@currbox\vbox{\rotatebox{90}{\box\@currbox}}%
+  }%
+ }%
+}{%
+}%
+\def\rotatebox@dummy#1#2{%
+ \ltxgrid@warn{You must load the graphics or graphicx package in order to use the turnpage environment}%
+ #2%
+}%
+%    \end{macrocode}
+% \changes{4.1b}{2008/08/04}{Use \cs{document@inithook} instead of \cs{AtBeginDocument}}
+%    \begin{macrocode}
+\appdef\document@inithook{%
+ \@ifxundefined\rotatebox{\let\rotatebox\rotatebox@dummy}{}%
+}%
+%    \end{macrocode}
+% \end{environment}
+%
+%
+% \subsection{One-off output routines}
+%
+% These procedures are executed in lieu of \cmd\the\cmd\output\ when the output penalty has the associated flag value.
+%
+% \begin{macro}{output@-1073741824}
+% The first one-off output routine handles the end of the job, wherein
+% \LaTeX\ executes \cmd\@@end, and breaks to the output with a penalty of
+% $"40000000 = 2^{32}/4 = 1073741824$. 
+% We simply discard \cmd\box\cmd\@cclv\ and leave.
+% This means that \LaTeX\ is obligated to do \cmd\clearpage\ as part of
+% its \enve{document} processing, otherwise material will be lost.
+%    \begin{macrocode}
+\@namedef{output@-1073741824}{%
+ \deadcycles\z@
+%    \end{macrocode}
+%    \begin{verbatim}
+%\showbox\@cclv
+%    \end{verbatim}
+%    \begin{macrocode}
+ \void@cclv
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\save@column@pen}
+% The one-off output routine associated with \cmd\penalty\cmd\save@column@pen\
+% will be called within a sequence of three such routines by \cmd\execute@message
+% or its companion routine \cmd\execute@message@insert.
+% This procedure must save away any the current page and preserve marks.
+%    \begin{macrocode}
+\mathchardef\save@column@pen=10016
+\@namedef{output@-\the\save@column@pen}{\save@column}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@cclv@saved}
+% We take over the \cmd\@holdpg\ box register. Hereafter,
+% we no longer use the \cmd\@holdpg\ box register, so let the world know.
+% This should decisively break packages that assume standard \LaTeX.
+% Breaking decisively is preferred to quietly proceeding erroneously.
+%    \begin{macrocode}
+\let \@cclv@saved \@holdpg
+\let \@holdpg \@undefined
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\save@column}
+% The procedure \cmd\save@column\ does the actual work of saving away the material
+% on the page. It is invoked both by \cmd\save@column@pen\ and by \cmd\save@column@insert@pen.
+% We save \cmd\box\cmd\@cclv\ and the primitive \cmd\@@topmark.
+%    \begin{macrocode}
+\def\save@column{%
+ \@ifvoid\@cclv@saved{%
+  \set@top@firstmark
+  \global\@topmark@saved\expandafter{\@@topmark}%
+ }{}%
+ \global\setbox\@cclv@saved\vbox{%
+  \@ifvoid\@cclv@saved{}{%
+   \unvbox\@cclv@saved
+   \marry@baselines
+  }%
+  \unvbox\@cclv
+  \lose@breaks
+  \remove@lastbox
+ }%
+}%
+\newtoks\@topmark@saved
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\prep@cclv}
+% The procedure \cmd\prep@cclv\ is used by message handlers to set up their environment
+% to ape that of the usual output routine, with the boxed-up page in \cmd\box\cmd\@cclv.
+% Here, we retrieve the material from \cmd\@cclv@saved, where it was saved away by
+% the one-off output routine associated with \cmd\save@column@pen.
+%    \begin{macrocode}
+\def\prep@cclv{%
+ \void@cclv
+ \setbox\@cclv\box\@cclv@saved
+ \vbadness\@M
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\save@column@insert@pen}
+% The one-off output routine associated with \cmd\penalty\cmd\save@column@insert@pen\
+% is similar to that of \cmd\save@column@pen\ augmented with the processing of insertions.
+% It is called by \cmd\execute@message@insert\  (i.e., at a grid change)
+% and saves away the current page and preserves marks.
+% In addition, it saves away any insertions that fall on the current page.
+% As with the natural output routine, it executes in two phases,
+% first with \cmd\holdinginserts\ set, then cleared. 
+%    \begin{macrocode}
+\mathchardef\save@column@insert@pen=10017
+\@namedef{output@-\the\save@column@insert@pen}{\toggle@insert{\savecolumn@holding}{\savecolumn@moving}}%
+%    \end{macrocode}
+% The procedure \cmd\savecolumn@holding\ is the first phase of saving a column with its inserts.
+% This phase must detect and remedy the one circumstance that will confound our efforts to propagate marks.
+% It is similar to \cmd\output@holding, except that we have to deal with the protection box, which must
+% remain, because the messaging mechanism is being used.
+%
+% If it appears that we have the pathological ``Big Bad Box'' case at hand, we use the \cmd\dead@cycle@repair@protected\
+% procedure instead of \cmd\dead@cycle\ to do our dead cycle.
+% \changes{4.1b}{2008/08/04}{Use \cs{trace@box} instead of \cs{showbox}}
+%    \begin{macrocode}
+\def\savecolumn@holding{%
+ \@if@exceed@pagegoal{\unvcopy\@cclv\remove@lastbox}{%
+  \setbox\z@\vbox{\unvcopy\@cclv\remove@lastbox}%
+  \outputdebug@sw{\trace@box\z@}{}%
+  \dimen@\ht\@cclv\advance\dimen@-\ht\z@
+  \dead@cycle@repair@protected\dimen@
+ }{%
+  \dead@cycle
+ }%
+}%
+%    \end{macrocode}
+% \changes{4.1b}{2008/08/04}{New procedure for showing a box contents, \cs{trace@box}}
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+% The procedure \cmd\save@column@moving\ is the second phase of saving a column with its inserts. 
+% Now that \cmd\holdinginserts\ is cleared, we can look in the various \cmd\insert\ registers for 
+% our inserts (at present there is only one, \cmd\footins, along with \cmd\footins@saved). 
+% if anything is there, we save it away and ask for another cycle (because it may have split). 
+% 
+% Note that the message that is about to be executed had better deal properly with the contents of 
+% the \cmd\footins@saved\ box.
+%
+%    \begin{macrocode}
+\def\savecolumn@moving{%
+ \ltxgrid@info@sw{\class@info{\string\savecolumn@moving}}{}%
+ \@cclv@nontrivial@sw{%
+  \save@column
+ }{%
+  \void@cclv
+ }%
+ \@ifvoid\footins{}{%
+  \ltxgrid@foot@info@sw{\class@info{\string\savecolumn@moving}\trace@scroll{\showbox\footins@saved\showbox\footins}}{}%
+%    \end{macrocode}
+% Save all away in \cmd\footins@saved. Note that if \cmd\footins\ is void, then \cmd\footins@saved\ remains untouched. 
+%    \begin{macrocode}
+  \@ifvoid\footins@saved{%
+   \global\setbox\footins@saved\box\footins
+  }{%
+   \global\setbox\footins@saved\vbox\bgroup
+    \unvbox\footins@saved
+    \marry@baselines
+    \unvbox\footins
+   \egroup
+  }%
+  \ltxgrid@foot@info@sw{\trace@box\footins@saved}{}%
+  \protect@penalty\save@column@insert@pen
+ }%
+}%
+\newbox\footins@saved
+\newbox\footins@recovered
+\newbox\column@recovered
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\save@message@pen}
+% The one-off output routine associated with \cmd\penalty\cmd\save@message@pen\
+% saves away the message that has been passed.
+% This procedure is penultimate in a sequence of one-off output routine calls;
+% earlier ones have saved away the MVL and preserved marks, the last executes the message.
+%
+% Note that we are passing tokens to \TeX's primitive \cmd\mark\ mechanism, so we must ensure
+% that they are not inappropriately expanded. We use the same mechanism for all such cases,
+% namely \cmd\let@mark.
+%
+% Note: we expect that \cmd\box\cmd\@cclv's contents are well known:
+% \cmd\topskip, protection box, and a \cmd\mark, the latter containing the message.
+% But if we came here via \cmd\penalty 10017, there might be an \cmd\insert\ node present as well, 
+% because a footnote may have split. 
+% Because this procedure simply voids out \cmd\box\cmd\@cclv, such material would be lost.
+% Perhaps we can repair things by manipulating the \cmd\insert \ mechanism temporarily.
+%    \begin{macrocode}
+\mathchardef\save@message@pen=10018
+\@namedef{output@-\the\save@message@pen}{\save@message}%
+\def\save@message{%
+ \void@cclv 
+%    \end{macrocode}
+%FIXME: what if \cmd\box\cmd\@cclv is not empty?
+%    \begin{macrocode}
+ \toks@\expandafter{\@@firstmark}%
+ \expandafter\gdef\expandafter\@message@saved\expandafter{\the\toks@}%
+ \expandafter\do@@mark\expandafter{\the\@topmark@saved}%
+}%
+\gdef\@message@saved{}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\execute@message@pen}
+% The one-off output routine associated with \cmd\execute@message@pen\ 
+% simply executes the given message. It is last in a sequence of one-off output routine calls;
+% earlier ones have saved all that require saving.
+%    \begin{macrocode}
+\mathchardef\execute@message@pen=10019
+\@namedef{output@-\the\execute@message@pen}{\@message@saved}%
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Output messages}
+%
+% Message handlers are procedures that execute output messages, tokens that are passed to
+% the output routine for execution in an environment appropriate to page makeup.
+%
+% How it works. We put down three large negative penalties, each of which will be handled by
+% the output dispatcher (\emph{not} the natural output routine), each penalty being protected by
+% a removable, non-discardable item (i.e., a box).
+% Either three or four invocations of one-off output routines are involved per message.
+%
+% We make the last of the three protection boxes have a depth equal to the value of \cmd\prevdepth\
+% that was current when the procedure is called. This effectively restores \cmd\prevdepth.
+%
+% In each case, the one-off output routine will remove the extraneous box we have inserted.
+% And the second and third one-off routines will simply void \cmd\box\cmd\@cclv, because its contents
+% are entirely artificial.
+%
+% FIXME: not so! If \cmd\holdinginserts\ is cleared, that box may have an insert node; it must be preserved, too.
+%
+% The first routine saves away the current column contents and remembers the \cmd\topmark\ for later
+% use. There is a variant routine that first clears \cmd\holdinginserts, so that the message can
+% handle any inserts present in the boxed-up page; this of course entails yet another
+% visit to the output routine.
+%
+% The penultimate routine saves away the tokens transmitted in via the \cmd\@@mark: the argument of
+% the macro. These tokens are of course the very thing we wish to execute within the safety
+% of the output routine. It also puts down a mark containing the \cmd\topmark\ tokens saved
+% by the first routine. By this means, the mark, which we have clobbered, is restored.
+%
+% The last routine simply executes the given tokens.
+% In the course of doing this, it must take care of \cmd\box\cmd\@cclv, either by shipping it out,
+% or by \cmd\unvbox ing it onto the MVL.
+%
+% \begin{macro}{\execute@message}
+% The procedure \cmd\execute@message\ simply calls the utility procedure \cmd\@execute@message\
+% with a penalty value for the standard treatment.
+%    \begin{macrocode}
+\def\execute@message{%
+ \@execute@message\save@column@pen
+%    \end{macrocode}
+% Implicit second argument
+%    \begin{macrocode}
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\execute@message@insert}
+% The procedure \cmd\execute@message@insert\ is like \cmd\execute@message\ in all respects
+% except that the penalty value is \cmd\save@column@insert@pen, which arranges for the 
+% message handler involved to deal with the page's insertions.
+% At the same time, we prepare the \cmd\footins\ box so that these insertions can be dealt with.
+%
+% Note:
+% If more insertions are added to \LaTeX\ (presumably via \cmd\newinsert), then they
+% must be dealt with in a way entirely analogous to \cmd\footins.
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+%    \begin{macrocode}
+\def\execute@message@insert#1{%
+ \@execute@message\save@column@insert@pen{%
+  \setbox \footins \box \footins@saved
+  \ltxgrid@foot@info@sw{\class@info{\string\execute@message@insert}\trace@box\footins}{}%
+  #1%
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@execute@message}
+% The utility procedure \cmd\@execute@message\ is called by \cmd\execute@message\ and \cmd\execute@message@insert.
+% We prepare by creating a \cmd\vbox\ containing all the needed nodes and proceed by simply
+% \cmd\unvbox ing that box onto the MVL.
+% We ensure that \cmd\box\cmd\@cclv\ is properly set up for the output message handler
+% by always inserting \cmd\prep@cclv\ in advance of the argument.
+%
+% Note that each one-off output routine is invoked effectively the same as
+% \cmd\protect@penalty, except that the second invocation involves an additional
+% \cmd\mark\ node, and the third a specially prepared protection box.
+%
+% Note also that \TeX's primitive \cmd\mark\ is called here without any expansion protection.
+% This is the only place where it is called that way, but it's OK because those tokens
+% have have been pre-expanded by procedures that call \cmd\execute@message.
+% FIXME: all procedures calling \cmd\execute@message\ must pre-expand their tokens!
+%    \begin{macrocode}
+\long\def\@execute@message#1#2{%
+ \begingroup
+  \dimen@\prevdepth\@ifdim{\dimen@<\z@}{\dimen@\z@}{}%
+  \setbox\z@\vbox{%
+   \protect@penalty#1%
+   \protection@box
+   \toks@{\prep@cclv#2}%
+   \@@mark{\the\toks@}%
+   \penalty-\save@message@pen
+%    \end{macrocode}
+%\begin{verbatim}
+%  \hbox{\vrule\@height\z@\@width\z@\@depth\dimen@}%
+%\end{verbatim}
+%    \begin{macrocode}
+   \setbox\z@\null\dp\z@\dimen@\ht\z@-\dimen@
+   \nointerlineskip\box\z@
+   \penalty-\execute@message@pen
+  }\unvbox\z@
+ \endgroup
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\do@output@cclv}
+% The procedure \cmd\do@output@cclv\ provides access to message handlers at their simplest.
+% The message will execute in the usual environment of the output routine, with
+% the boxed-up page in \cmd\box\cmd\@cclv, and we assume that \cmd\holdinginserts\ remains set.
+% This procedure must be invoked within main vertical mode;
+% it is the obligation of the macro writer to ensure that this is the case.
+%    \begin{macrocode}
+\def\do@output@cclv{\execute@message}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\do@output@MVL}
+% The procedure \cmd\do@output@MVL, like \cmd\do@output@cclv, is an interface for messages,
+% but provides two additional services: the command may also be invoked in horizontal mode, and
+% the message handler will execute with the MVL unboxed. 
+%    \begin{macrocode}
+\def\do@output@MVL#1{%
+ \@ifvmode{%
+  \begingroup\execute@message{\unvbox\@cclv#1}\endgroup
+ }{%
+  \@ifhmode{%
+   \vadjust{\execute@message{\unvbox\@cclv#1}}%
+  }{%
+   \@latexerr{\string\do@output@MVL\space cannot be executed in this mode!}\@eha
+  }%
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\lose@breaks}
+% The purpose of this procedure is to get rid of all the extraneous
+% \cmd\penalty\cmd\@M\ nodes that tend to build up in the MVL.
+%    \begin{macrocode}
+\def\lose@breaks{%
+ \loopwhile{%
+  \count@\lastpenalty
+  \@ifnum{\count@=\@M}{%
+%    \end{macrocode}
+% Note: 10000 is a TeX magic number!
+%    \begin{macrocode}
+   \unpenalty\true@sw
+  }{%
+   \false@sw
+  }%
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\removestuff}
+% \cmd\removestuff\ is a document-level command that removes the bottom skip glue item
+% from the MVL.
+%    \begin{macrocode}
+\def\removestuff{\do@output@MVL{\unskip\unpenalty}}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\removephantombox}
+% The procedure \cmd\removephantombox\ is a special-purpose message handler exclusively for 
+% preventing incorrect spacing above display math. It must be issued in
+% horizontal mode within the phantom paragraph generated when display math starts up in
+% vertical mode.
+%    \begin{macrocode}
+\def\removephantombox{%
+ \vadjust{%
+  \execute@message{%
+   \unvbox\@cclv
+   \remove@lastbox
+   \unskip
+   \unskip
+   \unpenalty
+   \penalty\predisplaypenalty
+   \vskip\abovedisplayskip
+  }%
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\addstuff}
+% \cmd\addstuff\ is a document-level command that adds penalty, glue, or both to the 
+% MVL. The penalty and glue items are rearranged so that all penalties nodes precede all the glue nodes,
+% which is the canonical arrangement.
+%    \begin{macrocode}
+\def\addstuff#1#2{\edef\@tempa{\noexpand\do@output@MVL{\noexpand\@addstuff{#1}{#2}}}\@tempa}%
+\def\@addstuff#1#2{%
+ \skip@\lastskip\unskip
+ \count@\lastpenalty\unpenalty
+ \@if@empty{#1}{}{\penalty#1\relax}%
+ \@ifnum{\count@=\z@}{}{\penalty\count@}%
+ \vskip\skip@
+ \@if@empty{#2}{}{\vskip#2\relax}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\replacestuff}
+% \cmd\replacestuff\ is a document-level command similar to \cmd\addstuff;
+% but it replaces penalty, glue, or both in the MVL.
+% The penalty and glue items are rearranged so that all penalties nodes precede all the glue nodes,
+% which is the canonical arrangement.
+%    \begin{macrocode}
+\def\replacestuff#1#2{\edef\@tempa{\noexpand\do@output@MVL{\noexpand\@replacestuff{#1}{#2}}}\@tempa}%
+\def\@replacestuff#1#2{%
+ \skip@\lastskip\unskip
+ \count@\lastpenalty\unpenalty
+ \@if@empty{#1}{}{%
+ \@ifnum{\count@>\@M}{}{%
+   \@ifnum{\count@=\z@}{\count@=#1\relax}{%
+    \@ifnum{\count@<#1\relax}{}{%
+     \count@=#1\relax
+    }%
+   }%
+ }%
+ }%
+ \@ifnum{\count@=\z@}{}{\penalty\count@}%
+ \@if@empty{#2}{}{%
+  \@tempskipa#2\relax
+  \@ifdim{\z@>\@tempskipa}{%
+   \advance\skip@-\@tempskipa
+  }{%
+   \@ifdim{\skip@>\@tempskipa}{}{%
+    \skip@\@tempskipa
+   }%
+  }%
+ }%
+ \vskip\skip@
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\move@insertions}
+% \begin{macro}{\hold@insertions}
+% In order to avoid bolluxing up \cmd\insert\ registers by our one-off 
+% output routines, we set \cmd\holdinginserts\ to zero by default and only 
+% clear it (briefly) while we handle cases where we want inserts to show up.
+%    \begin{macrocode}
+\def\move@insertions{\global\holdinginserts\z@}%
+\def\hold@insertions{\global\holdinginserts\@ne}%
+\hold@insertions
+\def\toggle@insert#1#2{%
+ \@ifnum{\holdinginserts>\z@}{\move@insertions#1}{\hold@insertions#2}%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{Messages to alter the page grid}%
+%
+% Here is the implementation of the grid-switching procedures.
+% We perform two checks when changing the page grid; first to ensure that 
+% the target page grid is known (defensive programming), second to ensure that
+% the switch is a non-trivial one. The latter check must be performed within
+% the safety of the output routine, so requires using an output message.
+% Thus, a grid change requires two messages, for a total of six visits to the output routine.
+%
+% \begin{macro}{\do@columngrid}
+% Utility procedure \cmd\do@columngrid\ changes the page grid.
+% Note that this command forces an end to the current paragraph. This is necessary, because
+% a page grid change makes no sense unless we can alter the \cmd\hsize\ before commencing to
+% typeset the following paragraph. So the command should never be executed in horizontal mode
+% anyway.
+%    \begin{macrocode}
+\def\do@columngrid#1#2{%
+ \par
+ \expandafter\let\expandafter\@tempa\csname open@column@#1\endcsname
+ \@ifx{\relax\@tempa}{%
+  \ltxgrid@warn{Unknown page grid #1. No action taken}%
+ }{%
+  \do@output@MVL{\start@column{#1}{#2}}%
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\start@column}
+% Procedure \cmd\start@column\ lays down the interrupts to switch the page grid.
+% If the change to the page grid would have been trivial, it bails out.
+% It seems a reasonable tradeoff of processing versus security: once we commit
+% to changing the page grid, we clear \cmd\holdinginserts, so there is no turning back.
+% 
+% Note that the second argument to the macro allows us to pass an argument to the 
+% page grid that is starting up. This can be handy, because a single procedure can 
+% handle multiple page grids, differing only by the value of a parameter.
+%
+% FIXME: this means that you cannot switch between mlt page grids in a single step.
+% But do we want to do this, at all, at all?
+%    \begin{macrocode}
+\def\start@column#1#2{%
+ \def\@tempa{#1}\@ifx{\@tempa\thepagegrid}{%
+  \ltxgrid@info{Already in page grid \thepagegrid. No action taken}%
+ }{%
+  \expandafter\execute@message@insert
+  \expandafter{%
+               \csname shut@column@\thepagegrid\expandafter\endcsname
+               \csname open@column@#1\endcsname{#2}%
+               \set@vsize
+             }%
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\thepagegrid}
+% The macro \cmd\thepagegrid\ tracks what kind of page grid we are in.
+%
+% Note: Access \cmd\thepagegrid\ only within the safety of the output routine.
+%
+% Warning: The page grid should be changed only within the safety of the output routine.
+% People who write multicol page grid mechanisms appear not to understand the matter, so they
+% should particularly heed this warning. Think about it: obviously Lamport did so, which is why
+% his \cmd\twocolumn\ command forced a pagebreak, which is limiting, but safe.
+%    \begin{macrocode}
+\def\thepagegrid{one}%
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Application Note: implementing a page grid}
+%
+% If you want to create a new page grid for \LaTeX,
+% you must define five procedures with specific names:
+% \cmd\open@column@ name, \cmd\shut@column@ name, \cmd\end@column@ name,
+% \cmd\output@column@ name, and \cmd\@addmarginpar@ name, where ``name'' is the 
+% name of your page grid.
+%
+% The procedure \cmd\open@column@ name starts the new page grid. It should define \cmd\thepagegrid,
+% deal with \cmd\box\cmd\pagesofar\ and \cmd\box\cmd\footsofar\ (perhaps by leaving them alone),
+% and it should set the values of \LaTeX's page layout parameters for the column size and height.
+%
+% The procedure \cmd\shut@column@ name should expect to be called with \cmd\holdinginserts\
+% cleared (it can assume that \cmd\holdinginserts\ will automatically be restored).
+% It should properly deal with insertions (like footnotes); calling \cmd\@makecolumn\
+% with an argument of \cmd\false@sw\ will do this.
+% It should know that the page grid is being terminated
+% in the middle of a page, so it should make arrangements to carry the footnotes down to the 
+% bottom of the column or page, and it should possibly salt away the material for later
+% incorporation into the page. The box registers \cmd\footsofar\ and \cmd\pagesofar\ are customarily used 
+% for this purpose.
+%
+% The procedure \cmd\end@column@ name should kick out a possibly short page containing all the 
+% floats committed to the page. It will be invoked during \cmd\clearpage\ processing.
+% After that, it should \cmd\unvbox\cmd\@cclv.
+%
+% The procedure \cmd\output@column@ name should ship out or commit the current \cmd\@outputbox.
+% In a one-column layout, you ship out; in a multicolumn layout, you commit the box as the contents
+% of a particular column, and if that column is the last, you ship out.
+%
+% The procedure \cmd\@addmarginpar@ name should return a boolean (either \cmd\true@sw\ or \cmd\false@sw\ or an equivalent)
+% to tell the marginpar mechanism to place the marginal material to the right or left, respectively.
+%
+% You can use the existing page grids ``one'' and ``mlt'' as a point of departure for creating others.
+% The former can be the basis for, say, a single-column page grid with a side column.
+%
+% \begin{macro}{\pagesofar}
+% \begin{macro}{\footsofar}
+% The box register \cmd\pagesofar\ holds the portion of the (full-width) page that is already composed into columns. 
+% This, plus the finished columns, each with its floats, plus \cmd\box255 constitute the full galley.
+%
+% The box register \cmd\footsofar\ holds all of the footnotes associated with \cmd\pagesofar.
+%    \begin{macrocode}
+\newbox\pagesofar
+\newbox\footsofar
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\combine@foot@inserts}
+% \changes{4.1n}{2010/01/02}{(AO, 571) calling sequence of \cs{combine@foot@inserts} and \cs{grid@column} to expose box registers; that of \cs{append@column@} its column counters}%
+% \changes{4.1n}{2010/01/02}{(AO, 571) coding convention: use \cs{bgroup}, \cs{egroup} (instead of braces) when a box is being built}%
+% The procedure \cmd\combine@foot@inserts\ is for the purpose of merging 
+% the recently contributed footnotes (usually \cmd\box\cmd\footins)
+% with those saved from earlier on the page (usually \cmd\box\cmd\footsofar). 
+%
+% It is employed in a number of circumstances. 
+%
+% \cmd\@makecolumn (when its argument is \cmd\false@sw): 
+% we are not shipping out, so we need to salt away any footnotes there may be. 
+% 
+% \cmd\shut@column@one: we are leaving the one-column page grid, so recover the footnotes from that material
+% and combine them with those of \cmd\pagesofar. 
+%
+% \expandafter\cmd\csname balance@2\endcsname: two columns of type have been balanced, so now balance the footnotes. 
+% The \cmd\combine@foot@inserts\ procedure is first used to gather footnotes from the columns balanced with those of \cmd\pagesofar. 
+%
+% Bug 571 note: if balancing a two-column page grid, and there had been footnotes in the \cmd\pagesofar, 
+% those footnotes will have been balanced into a page-width box, \cmd\box\cmd\footsofar. 
+% We need to now re-cast them into a single, column-width galley, and only then 
+% combine them with those in \cmd\box\cmd\footins. 
+% 
+%    \begin{macrocode}
+\def\combine@foot@inserts#1#2{%
+  \ltxgrid@info@sw{\class@info{\string\combine@foot@inserts\string#1\string#2}}{}%
+  \@ifvoid#1{%
+    \ltxgrid@foot@info@sw{\trace@box#2}{}\global\setbox#1\box#2%
+  }{%
+   \global\setbox#1\vbox\bgroup
+    \ltxgrid@foot@info@sw{\trace@box#1}{}\unvbox#1%
+    \@ifvoid#2{}{%
+     \marry@baselines
+     \ltxgrid@foot@info@sw{\trace@box#2}{}\unvbox#2%
+    }%
+   \egroup
+  }%
+  \ltxgrid@foot@info@sw{\trace@scroll{\showbox#1\showbox#2}}{}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsubsection{One-column page grid}
+%
+% \begin{macro}{\onecolumngrid}
+% \begin{macro}{\open@column@one}
+% \begin{macro}{\shut@column@one}
+% \begin{macro}{\float@column@one}
+% \begin{macro}{\end@column@one}
+% \begin{macro}{\output@column@one}
+% \begin{macro}{\@addmarginpar@one}
+% Here are all the procedures necessary for the standard page grid named ``one'':
+% a single column layout. It is, of course, \LaTeX's familiar \cmd\onecolumn\ layout.
+% We begin with the procedure exposed to the style writer.
+% This is, however, not a \LaTeX\ command; users should not change the page grid.
+%    \begin{macrocode}
+\newcommand\onecolumngrid{\do@columngrid{one}{\@ne}}%
+%    \end{macrocode}
+%
+% Note that a document class that issues the command \cmd\onecolumn\ will break. This includes
+% \LaTeX's standard classes.dtx-based classes: if your class descends from one of these, you
+% must expunge it of all such commands.
+%    \begin{macrocode}
+\let\onecolumn\@undefined
+%    \end{macrocode}
+%
+% The procedure \cmd\open@column@one\ takes advantage of the special nature of the one-column
+% page grid to deal with \cmd\box\cmd\pagesofar, therefore it must also reset \cmd\@colroom.
+% \changes{4.1b}{2008/08/04}{Change \cs{set@colroom} to \cs{set@colht}}
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+%    \begin{macrocode}
+\def\open@column@one#1{%
+ \ltxgrid@info@sw{\class@info{\string\open@column@one\string#1}}{}%
+%    \end{macrocode}
+% Throw the \cmd\pagesofar\ back onto the Main Vertical List. 
+% At this point, we must also \cmd\insert\ the footnotes back into the MVL. 
+% \changes{4.1n}{2010/01/02}{(AO, 571) coding convention: use \cs{bgroup}, \cs{egroup} (instead of braces) when a box is being built}%
+%    \begin{macrocode}
+ \unvbox\pagesofar
+ \@ifvoid{\footsofar}{}{%
+  \insert\footins\bgroup\unvbox\footsofar\egroup
+  \penalty\z@
+ }%
+%    \end{macrocode}
+% Record which page grid we are using. Then calculate the set width (\cmd\hsize) and the goal height (\cmd\vsize).
+%
+% Klootch: we set the \cmd\count\cmd\footins\ to a magic number. This is only correct in the case of a two-column document.
+%    \begin{macrocode}
+ \gdef\thepagegrid{one}%
+ \global\pagegrid@col#1%
+ \global\pagegrid@cur\@ne
+ \global\count\footins\@m
+ \global\divide\count\footins\tw@
+ \set@column@hsize\pagegrid@col
+ \set@colht
+}%
+%    \end{macrocode}
+%
+% The procedure \cmd\shut@column@one\ saves away the one-column material into the box register \cmd\pagesofar.
+% Because it is called from a message handler, we are assured that marks are properly taken care of.
+%
+% This instance of \cmd\@makecolumn\ is building a column for saving into \cmd\pagesofar.
+% \changes{4.1b}{2008/08/04}{Change \cs{@makecol} to \cs{@makecolumn} with argument}
+% \changes{4.1b}{2008/08/04}{Change \cs{set@colroom} to \cs{set@colht}}
+% \changes{4.1f}{2009/07/15}{(AO, 519) Preserve footnotes that are in \cs{footsofar} across a page grid change}
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+% \changes{4.1n}{2010/01/02}{(AO, 571) calling sequence of \cs{combine@foot@inserts} and \cs{grid@column} to expose box registers; that of \cs{append@column@} its column counters}%
+% We recover the footnotes into \cmd\footsofar\ (globally) and the column into \cmd\pagesofar\ (also globally), voiding \cmd\@outputbox\ by side effect. 
+%    \begin{macrocode}
+\def\shut@column@one{%
+ \ltxgrid@info@sw{\class@info{\string\shut@column@one}}{}%
+ \@makecolumn\false@sw
+%    \end{macrocode}
+% Split text portion of \cmd\@outputbox\ into \cmd\pagesofar,
+% and add its footnote portion to \cmd\footsofar.
+% Then void out \cmd\@outputbox.
+%    \begin{macrocode}
+ \global\setbox\pagesofar\vbox\bgroup
+  \recover@column\@outputbox\footsofar\column@recovered\footins@recovered
+ \egroup
+ \begingroup\setbox\z@\box\@outputbox\endgroup
+%    \end{macrocode}
+% FIXME: is \cmd\combine@foot@inserts\ needed?
+% Also: if this procedure is immediately followed by \cmd\open@column@ \texttt{grid}, then \cmd\set@colht\ will be unneeded.
+%    \begin{macrocode}
+ \combine@foot@inserts\footsofar\footins
+ \set@colht
+}%
+%    \end{macrocode}
+%
+%FIXME: the first line of a footnote should have an up-strut, and the last line a down-strut, so that they can marry baselines.
+% The latter is the case; how about the former?
+%
+% The procedure \cmd\float@column@one\ takes care of a float column that has been built by 
+% \cmd\@tryfcolumn, in the single-column page grid.
+%
+% This instance of \cmd\@makecolumn\ is followed by \cmd\@outputpage: it is building 
+% a column for \cmd\shipout, rather than for saving into \cmd\pagesofar.
+% \changes{4.1b}{2008/08/04}{Change \cs{@makecol} to \cs{@makecolumn} with argument}
+%    \begin{macrocode}
+\def\float@column@one{%
+ \@makecolumn\true@sw
+ \@outputpage
+}%
+%    \end{macrocode}
+%
+% The procedure \cmd\end@column@one\ is executed at the end of \cmd\clearpage\ processing,
+% if we were in a one-column page grid, once all permissive float pages have been shipped out.
+% At this point, one could perhaps
+% assume that nothing more need be done, but let us anyway test for committed floats and force a shipout.
+%
+% FIXME: this procedure does the same as \cmd\end@column@mlt 
+% (except for the test of \cmd\@ifx@empty\cmd\@dbltoplist):
+% the two could almost be the same procedure.
+%
+% I have changed this procedure to avoid the testing it once did: it simply puts down interrupts,
+% upon which it relies to correctly do what \cmd\clearpage\ requires.
+%    \begin{macrocode}
+\def\end@column@one{%
+ \unvbox\@cclv\remove@lastbox
+ \protect@penalty\do@newpage@pen
+}%
+%    \end{macrocode}
+%
+% The procedure \cmd\output@column@one\ is dispatched from the output routine when
+% we have completed a page (that is, a column in a one-column page grid);
+% it ships out the page using the \cmd\@outputpage.
+% It will be followed up with an output routine message to prepare a new column.
+%
+% Query: by what mechanism do the footnotes get placed onto such a page?
+%    \begin{macrocode}
+\def\output@column@one{%
+ \@outputpage
+}%
+%    \end{macrocode}
+%
+% The following procedure determines which side of the page a marginpar will appear.
+% It reproduces the behavior of standard \LaTeX.
+%    \begin{macrocode}
+\def\@addmarginpar@one{%
+ \@if@sw\if@mparswitch\fi{%
+  \@ifodd\c@page{\false@sw}{\true@sw}%
+ }{\false@sw}{%
+  \@if@sw\if@reversemargin\fi{\false@sw}{\true@sw}%
+ }{%
+  \@if@sw\if@reversemargin\fi{\true@sw}{\false@sw}%
+ }%
+}%
+%    \end{macrocode}
+%
+% The following procedure yields a Boolean value; it determines whether a float in the deferred queue
+% is appropriate for placing. In the one-column grid, all floats are so.
+%    \begin{macrocode}
+\def\@floatselect@sw@one#1{\true@sw}%
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\onecolumngrid@push{%
+ \do@output@MVL{%
+  \@ifnum{\pagegrid@col=\@ne}{%
+   \global\let\restorecolumngrid\@empty
+  }{%
+   \xdef\restorecolumngrid{%
+    \noexpand\start@column{\thepagegrid}{\the\pagegrid@col}%
+   }%
+   \start@column{one}{\@ne}%
+  }%
+ }%
+}%
+\def\onecolumngrid@pop{%
+ \do@output@MVL{\restorecolumngrid}%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsubsection{Two-column page grid}
+%
+% \begin{macro}{\twocolumngrid}
+% \begin{macro}{\open@column@mlt}
+% \begin{macro}{\shut@column@mlt}
+% \begin{macro}{\end@column@mlt}
+% \begin{macro}{\output@column@mlt}
+% \begin{macro}{\@addmarginpar@mlt}
+% \begin{macro}{\set@footnotewidth@mlt}
+% \begin{macro}{\set@footnotewidth@two}
+% \begin{macro}{\compose@footnotes@two}
+% Here are all the procedures necessary for the standard page grid named ``mlt'':
+% the multi-column page grid. With an argument of "2", it is,
+% of course, \LaTeX's familiar \cmd\twocolumn\ layout.
+%
+% We start with the procedure to switch to the two-column page grid.
+%    \begin{macrocode}
+\newcommand\twocolumngrid{\do@columngrid{mlt}{\tw@}}%
+%    \end{macrocode}
+%
+% The corresponding command of \LaTeX\ is obsolete.
+%    \begin{macrocode}
+\let\twocolumn\@undefined
+%    \end{macrocode}
+%
+% Of course, \cmd\@topnewpage\ is also obsolete. Just do 
+%\begin{quote}
+% \cmd\clearpage\cmd\onecolumngrid<vertical mode material>\cmd\twocolumngrid.
+%\end{quote}
+%    \begin{macrocode}
+\let\@topnewpage\@undefined
+%    \end{macrocode}
+%
+% If your document class descends from one of \LaTeX's standard classes.dtx-derived
+% classes, it will break. You must expunge from it all such commands.
+% 
+% \changes{4.1b}{2008/08/04}{Change \cs{set@colroom} to \cs{set@colht}}
+%
+% Bug 571 note: it is not enough to have the \cmd\pagesofar, we must also deal with the \cmd\footsofar.
+% At this juncture, we should treat the case where the document has an essentially two-column page grid, 
+% with occasional excursions into the one-column grid. 
+% If a footnote is set within the latter grid, its set width should be that of the two-column grid. 
+%
+% When a page is shipped out, if we are currently in a one-column grid, we will compose the footnotes onto the page
+% in the form of balanced columns. This is only one way to handle footnotes: \classname{multicol}
+% appears to set footnotes on the full text width.
+%    \begin{macrocode}
+\def\open@column@mlt#1{%
+ \ltxgrid@info@sw{\class@info{\string\open@column@mlt\string#1}}{}%
+%    \end{macrocode}
+% At this point, we must \cmd\insert\ the footnotes back into the Main Vertical List.
+% \changes{4.1n}{2010/01/02}{(AO, 571) coding convention: use \cs{bgroup}, \cs{egroup} (instead of braces) when a box is being built}%
+%    \begin{macrocode}
+ \@ifvoid{\footsofar}{}{%
+  \insert\footins\bgroup\unvbox\footsofar\egroup
+ }%
+%    \end{macrocode}
+% Record which page grid we are using. Then calculate the set width (\cmd\hsize) and the goal height (\cmd\vsize).
+%
+% Klootch: we set the \cmd\count\cmd\footins\ to a magic number. This value is valid whether footnotes are being
+% set on the column width or the full text width. 
+%    \begin{macrocode}
+ \gdef\thepagegrid{mlt}%
+ \global\pagegrid@col#1%
+ \global\pagegrid@cur\@ne
+ \global\count\footins\@m
+ \set@column@hsize\pagegrid@col
+ \set@colht
+}%
+%    \end{macrocode}
+%
+% The procedure \cmd\shut@column@mlt\ ends the current column, balances the columns, and
+% salts away all in \cmd\pagesofar. Because it is called in a message handler,
+% we are assured that marks are handled properly.
+% Attention: because this procedure balances columns, all footnotes are
+% held aside in \cmd\footsofar\ for placement at the bottom of the page.
+%
+% Bug note: the last macro executed by this procedure is \cmd\set@colht, 
+% but had been erroneously \cmd\set@colroom.
+% I now believe that the latter should be changed pretty much everywhere to the former.
+%
+% This instance of \cmd\@makecolumn\ is building material for \cmd\pagesofar, rather than 
+% for \cmd\shipout.
+% \changes{4.1b}{2008/08/04}{Change \cs{@makecol} to \cs{@makecolumn} with argument}
+% \changes{4.1b}{2008/08/04}{Change \cs{@combinepage} to \cs{@combinepage} with argument}
+% \changes{4.1b}{2008/08/04}{Change \cs{set@colroom} to \cs{set@colht}}
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+% \changes{4.1n}{2010/01/02}{(AO, 571) calling sequence of \cs{combine@foot@inserts} and \cs{grid@column} to expose box registers; that of \cs{append@column@} its column counters}%
+%    \begin{macrocode}
+\def\shut@column@mlt{%
+ \ltxgrid@info@sw{\class@info{\string\shut@column@mlt}}{}%
+ \@cclv@nontrivial@sw{%
+  \@makecolumn\false@sw
+  \@ifnum{\pagegrid@cur<\pagegrid@col}{%
+   \expandafter\global\expandafter\setbox\csname col@\the\pagegrid@cur\endcsname\box\@outputbox
+   \global\advance\pagegrid@cur\@ne
+  }{}%
+ }{%
+  \void@cclv
+ }%
+ \@ifnum{\pagegrid@cur>\@ne}{%
+  \csname balance@\the\pagegrid@col\endcsname
+  \grid@column\@outputbox{}%
+  \@combinepage\false@sw
+  \@combinedblfloats
+  \global\setbox\pagesofar\box\@outputbox
+  \show@pagesofar@size
+ }{}%
+ \set@colht
+}%
+%    \end{macrocode}
+%
+% The procedure \cmd\float@column@mlt\ takes care of a float page that has been built by \cmd\@tryfcolumn,
+% in the multi-column page grid. It is coincidentally identical to what happens in 
+% \cmd\do@startpage\ when a page needs to be shipped out.
+% \changes{4.1b}{2008/08/04}{New procedure \cs{@output@combined@page}}
+%    \begin{macrocode}
+\def\float@column@mlt{%
+  \@output@combined@page
+}%
+%    \end{macrocode}
+%
+% The procedure \cmd\end@column@mlt\ is executed at the end of \cmd\clearpage\ processing,
+% if we were in a multi-column page grid, once all permissive float pages have been shipped out.
+% If no floats are committed and if no columns are yet filled, we have nothing to do.
+% Otherwise, we kick out a column and try again.
+%
+% Note that in our code to kick out a column, we must deal properly with the case where the column
+% is trivial: it will have nothing but \cmd\topskip\ glue plus a protection box. We substitute an ordinary
+% \cmd\null\ for the protection box.
+% 
+%    \begin{macrocode}
+\def\end@column@mlt{%
+ \@ifx@empty\@toplist{%
+  \@ifx@empty\@botlist{%
+   \@ifx@empty\@dbltoplist{%
+    \@ifx@empty\@deferlist{%
+     \@ifnum{\pagegrid@cur=\@ne}{%
+      \false@sw
+     }{%
+      \true@sw
+     }%
+    }{%
+     \true@sw
+    }%
+   }{%
+    \true@sw
+   }%
+  }{%
+   \true@sw
+  }%
+ }{%
+  \true@sw
+ }%
+ % true = kick out a column and try again
+ {%
+  \@cclv@nontrivial@sw{%
+   \unvbox\@cclv\remove@lastbox
+  }{%
+   \unvbox\@cclv\remove@lastbox\unskip\null
+  }%
+  \protect@penalty\do@newpage@pen
+  \protect@penalty\do@endpage@pen
+ }{%
+  \unvbox\@cclv\remove@lastbox
+ }%
+}%
+%    \end{macrocode}
+%
+% The procedure \cmd\output@column@mlt (cf. \cmd\output@column@one)
+% is dispatched from the output routine when
+% we have completed a column in a multi-column page grid).
+% (It replaces the \cmd\@outputdblcol\ of standard \LaTeX.)
+% If a complete set of columns is at hand, it ships out the page and 
+% lays down an interrupt for \cmd\do@startpage@pen, which will commit the 
+% full-page-width floats to the next page.
+% Like \cmd\output@column@mlt, this is followed by
+% an output routine message to prepare a new column.
+%
+% If a page needs to be shipped out, it uses the same mechanism as \cmd\do@startpage.
+% \changes{4.1b}{2008/08/04}{New procedure \cs{@output@combined@page}}
+% \changes{4.1n}{2010/01/02}{(AO, 571) calling sequence of \cs{combine@foot@inserts} and \cs{grid@column} to expose box registers; that of \cs{append@column@} its column counters}%
+%    \begin{macrocode}
+\def\output@column@mlt{%
+ \@ifnum{\pagegrid@cur<\pagegrid@col}{%
+  \expandafter\global\expandafter\setbox\csname col@\the\pagegrid@cur\endcsname\box\@outputbox
+  \global\advance\pagegrid@cur\@ne
+ }{%
+  \set@adj@colht\dimen@
+  \grid@column\@outputbox{}%
+  \@output@combined@page
+ }%
+}%
+%    \end{macrocode}
+% The procedure \cmd\output@column@mlt\ obsoletes \LaTeX's \cmd\@outputdblcol
+%    \begin{macrocode}
+\let\@outputdblcol\@undefined
+%    \end{macrocode}
+%
+% The following procedure yields a Boolean value; it determines whether a float in the deferred queue
+% is appropriate for placement in the column. In the multi-column grid, only those narrower than \cmd\textwidth\ are so.
+%    \begin{macrocode}
+\def\@floatselect@sw@mlt#1{\@if@notdblfloat{#1}}%
+%    \end{macrocode}
+%
+% The following procedure determines which side of the page a marginpar will appear.
+% It reproduces the behavior of standard \LaTeX.
+%    \begin{macrocode}
+\def\@addmarginpar@mlt{% emits a boolean
+ \@ifnum{\pagegrid@cur=\@ne}%
+}%
+%    \end{macrocode}
+%
+% \cmd\set@footnotewidth@one\ sets the width of type within footnotes to span the full text width; 
+% \cmd\set@footnotewidth@two\ to span a single column of the two-column grid, and 
+% more generally \cmd\set@footnotewidth@mlt\ for a multi-column page grid. 
+%    \begin{macrocode}
+\def\set@footnotewidth@one{%
+ \hsize\columnwidth
+ \linewidth\hsize
+}%
+\def\set@footnotewidth@two{\set@footnotewidth@mlt\tw@}%
+\def\set@footnotewidth@mlt#1{%
+ \hsize\textwidth
+ \advance\hsize\columnsep
+ \divide\hsize#1%
+ \advance\hsize-\columnsep
+ \linewidth\hsize
+}%
+%    \end{macrocode}
+%
+% \cmd\compose@footnotes\ is the procedure for arranging the footnotes for
+% placement at the bottom of the page or column. 
+% In the former case, the material will be shipped out; in the latter, we must allow
+% the column to possibly be balanced later on. 
+%
+% \cmd\compose@footnotes@one\ is a no-op, because the footnotes require no rearrangement. 
+% In a scheme where footnotes are set on the full text width, this would be the procedure called. 
+%
+% \cmd\compose@footnotes@two\ implements the case where a two-column document has been interrupted
+% with full-page-width text (e.g., the widetext environment or the end of the document), 
+% and a natural page break appears. 
+%
+% In either case, we assume that argument \verb+#1+ is an \cmd\insert\  register and must be assigned globally,
+% so that when it is accessed with \cmd\box\ or \cmd\unvbox, it will be voided globally as well. 
+% 
+% To extend this scheme to a three-column page grid \cmd\compose@footnotes@thr@@\ would be created:
+% it would balance the saved up footnotes into three columns. 
+%
+%    \begin{macrocode}
+\def\compose@footnotes@one#1{%
+ \ltxgrid@foot@info@sw{\class@info{\string\compose@footnotes@one\string#1}\trace@box#1}{}%
+}%
+\let\compose@footnotes\compose@footnotes@one
+\def\compose@footnotes@two#1{%
+ \ltxgrid@foot@info@sw{\class@info{\string\compose@footnotes@two\string#1}\trace@box#1}{}%
+ \setbox\z@\box\@tempboxa
+ \let\recover@column\recover@column@null
+ \let\marry@baselines\@empty
+ \balance@two#1\@tempboxa
+ \global\setbox#1\hbox to\textwidth{\box#1\hfil\box\@tempboxa}%
+ \ltxgrid@foot@info@sw{\trace@box#1}{}%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsubsection{Page grid utility procedures}
+%
+% \begin{macro}{\pagegrid@cur}
+% \begin{macro}{\pagegrid@col}
+% \begin{macro}{\pagegrid@init}
+% We take over \LaTeX's \cmd\col@number, and \cmd\@leftcolumn, which are obsolete (\cmd\@holdpg\ could also be taken over). 
+% We create two counters to hold the columns in the page grid and the current column within.
+% We also create the first of a set of box registers to hold the committted columns.
+%    \begin{macrocode}
+\let\pagegrid@cur\col@number
+\let\col@number\@undefined
+\newcount\pagegrid@col
+\pagegrid@cur\@ne
+\expandafter\let\csname col@\the\pagegrid@cur\endcsname\@leftcolumn
+\let\@leftcolumn\@undefined
+%    \end{macrocode}
+%
+% The default is for maximum two columns.
+% If your class will require more columns, assign that number to \cmd\pagegrid@col\
+% before \envb{document} time.
+%    \begin{macrocode}
+\pagegrid@col\tw@
+%    \end{macrocode}
+%
+% The procedure \cmd\pagegrid@init\ is a loop, exercising \cmd\newbox\ sufficiently to create the 
+% boxes for holding the columns in the page grid; these have names like \expandafter\cmd\csname col@1\endcsname, etc. 
+%    \begin{macrocode}
+\def\pagegrid@init{%
+ \advance\pagegrid@cur\@ne
+ \@ifnum{\pagegrid@cur<\pagegrid@col}{%
+  \csname newbox\expandafter\endcsname\csname  col@\the\pagegrid@cur\endcsname
+  \pagegrid@init
+ }{%
+ }%
+}%
+\appdef\class@documenthook{%
+ \pagegrid@init
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\grid@column}
+% \changes{4.1n}{2010/01/02}{(AO, 571) calling sequence of \cs{combine@foot@inserts} and \cs{grid@column} to expose box registers; that of \cs{append@column@} its column counters}%
+% The procedure \cmd\grid@column\ knows how to lay up the columns in a multi-column page grid.
+% It uses utility procedures \cmd\append@column@\ and \cmd\box@column.
+%
+% The first argument is the box register to create, usually \cmd\@outputbox, and provides both input and output. 
+% The second argument a dimension, allowing us to strut down the depth of the box we create. 
+%
+%    \begin{macrocode}
+\def\grid@column#1#2{%
+ \ltxgrid@info@sw{\class@info{\string\grid@column\string#1}}{}%
+ \global\setbox#1\vbox\bgroup
+  \hb@xt@\textwidth\bgroup
+   \vrule\@height\z@\@width\z@\@if@empty{#2}{}{\@depth#2}%
+   \pagegrid@cur\@ne
+   \@ifnum{\pagegrid@cur<\pagegrid@col}{\loopwhile{\append@column@\pagegrid@cur\pagegrid@col}}{}%
+   \box@column#1%
+  \egroup
+%    \end{macrocode}
+% FIXME: page depth!
+%    \begin{macrocode}
+  \vskip\z@skip
+ \egroup
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\append@column@}
+% \begin{macro}{\box@column}
+% \begin{macro}{\marry@baselines}
+% The procedure \cmd\append@column@\ appends columns for \cmd\grid@column,
+% \cmd\box@column\ builds the columns for \cmd\append@column@,
+% and \cmd\marry@baselines\ pastes vertical things back together.
+% \changes{4.0a}{2001/06/18}{Introduce \cs{marry@height} }
+%
+% Note that \cmd\box@column\ makes an attempt to prevent excessive \cmd\topskip\
+% or \cmd\baselineskip\ glue
+% from being applied by \TeX\ when \cmd\@outputbox\ is contributed to the MVL.
+% If this is not done, it is possible to get into an infinite loop in the corner case,
+% wherein the page grid is changed to one column and the balanced-up columns are
+% already sufficient to fill the page.
+%
+% Note (AO 0920):  I have changed the dimension involved with \cmd\box@column\ from
+% \cmd\vsize\ to \cmd\textheight, because the former is certainly not the correct value
+% to use: it will change if floats have been placed in the last column of the page.
+% I believe \cmd\textheight\ is the correct parameter to use here.
+%
+% A REVTeX4 user, Sergey Strelkov (strelkov@maik.rssi.ru), wants the option
+% of ragged-bottom columns. Implementing this feature properly means reboxing the 
+% columns to their natural height only if \cmd\raggedcolumn@sw\ is true.
+% Otherwise, they get reboxed to their common height (\cmd\@colht?).
+%
+% Note that the default has hereby changed from ragged to flush. 
+% It's not clear that anyone but Sergey will notice.
+%
+% The macro \cmd\marry@skip\  addresses (in a limited way)
+% the fact that neither the value of \cmd\baselineskip\ nor that of \cmd\topskip\
+% can be relied upon for the purpose of marrying the baselines of two split columns.
+% (Because there might have been a local change to their values at the point where
+% the output routine got triggered.)
+%
+% For best results, your document class should call for grid changes only when in basal text
+% settings. The \cmd\marry@baselines\ procedure will use the values appropriate to that point
+% when attempting to put the columns back together.
+%
+% In any case, we are not attempting to solve the more general problem of how to marry baselines
+% where the leading can change arbitrarily within the galley or where glue could have been trimmed
+% at a page top.
+%
+% \changes{4.1n}{2010/01/02}{(AO, 571) calling sequence of \cs{combine@foot@inserts} and \cs{grid@column} to expose box registers; that of \cs{append@column@} its column counters}%
+% Procedure \cmd\append@column@\ composes a column onto the horizontal list along with its \cmd\columnseprule. 
+% Its arguments are: \verb+#1+---\cmd\pagegrid@cur, and \verb+#2+---\cmd\pagegrid@col
+%    \begin{macrocode}
+\def\append@column@#1#2{%
+ \expandafter\box@column\csname col@\the#1\endcsname
+ \hfil\vrule\@width\columnseprule\hfil
+ \advance#1\@ne
+%    \end{macrocode}
+% This procedure is the argument of \cmd\loopwhile, so it must leave a Boolean (e.g., \cmd\true@sw) in \TeX's scanner. 
+%    \begin{macrocode}
+ \@ifnum{#1<#2}%
+}%
+%    \end{macrocode}
+% \changes{4.1n}{2010/01/02}{(AO, 571) calling sequence of \cs{combine@foot@inserts} and \cs{grid@column} to expose box registers; that of \cs{append@column@} its column counters}%
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+% \changes{4.1n}{2010/01/02}{(AO, 571) coding convention: use \cs{bgroup}, \cs{egroup} (instead of braces) when a box is being built}%
+% Procdure \cmd\box@column, used by \cmd\append@column@, puts down a box containing the specified column.
+% Its height is adjusted down to \cmd\@colht, if needed; likewise, the width is set to \cmd\columnwidth. 
+% The rag at the bottom is controlled by \cmd\raggedcolumn@skip. 
+%    \begin{macrocode}
+\def\box@column#1{%
+ \ltxgrid@info@sw{\class@info{\string\box@column\string#1}}{}%
+ \raise\topskip
+ \hb@xt@\columnwidth\bgroup
+  \dimen@\ht#1\@ifdim{\dimen@>\@colht}{\dimen@\@colht}{}%
+  \count@\vbadness\vbadness\@M
+  \dimen@ii\vfuzz\vfuzz\maxdimen
+  \ltxgrid@info@sw{\saythe\@colht\saythe\dimen@}{}%
+  \vtop to\dimen@\bgroup
+   \hrule\@height\z@
+   \unvbox#1%
+   \raggedcolumn@skip
+  \egroup
+  \vfuzz\dimen@ii
+  \vbadness\count@
+  \hss
+ \egroup
+}%
+%    \end{macrocode}
+% The purpose of procedure \cmd\marry@baselines\ is to ensure that the baseline spacing is correct; 
+% it does this by making adjustments to the previous line, compensating for its depth, and by adding in 
+% skip glue in an amount that assumes the added material has \cmd\topskip\ glue above. 
+%    \begin{macrocode}
+\def\marry@baselines{%
+ \begingroup
+  \setbox\z@\lastbox
+  \@ifvoid{\z@}{%
+   \endgroup
+  }{%
+   \aftergroup\kern
+   \aftergroup-%
+   \expandafter\box\expandafter\z@\expandafter\endgroup\the\dp\z@\relax
+  }%
+ \vskip\marry@skip\relax
+}%
+\gdef\marry@skip{\z@skip}%
+\def\set@marry@skip{%
+ \begingroup
+  \skip@\baselineskip\advance\skip@-\topskip
+  \@ifdim{\skip@>\z@}{%
+   \xdef\marry@skip{\the\skip@}%
+  }{}%
+ \endgroup
+}%
+%    \end{macrocode}
+% \changes{4.1b}{2008/08/04}{Use \cs{document@inithook} instead of \cs{AtBeginDocument}}
+%    \begin{macrocode}
+\appdef\document@inithook{%
+ \@ifxundefined\raggedcolumn@sw{\@booleanfalse\raggedcolumn@sw}{}%
+}%
+\def\raggedcolumn@skip{%
+ \vskip\z@\raggedcolumn@sw{\@plus.0001fil\@minus.0001fil}{}\relax
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@combinepage}
+% The procedure \cmd\@combinepage\ prepends the stored page (\cmd\pagesofar) to \cmd\@outputbox\ and
+% employs \cmd\@combineinserts\ to lay down the footnotes. 
+% The next event will usually be shipping out the made-up page, but not always. 
+% Therefore the argument of \cmd\@combinepage, which must be a Boolean, determines
+% if the footnotes are to be combined into this page.
+% 
+% \changes{4.1b}{2008/08/04}{Change \cs{@combinepage} to \cs{@combinepage} with argument}
+% \changes{4.1b}{2008/08/04}{(AO, 452) Support length checking: show size of shipped out text.}
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+%
+% QUERY: In the following, if \cmd\box\cmd\footins\ is not void, its contents are lost. Can this ever happen?
+%    \begin{macrocode}
+\def\@combinepage#1{%
+ \ltxgrid@foot@info@sw{\class@info{\string\@combinepage\string#1}}{}%
+ \@ifvoid\pagesofar{}{%
+  \setbox\@outputbox\vbox{%
+   \unvbox\pagesofar
+   \marry@baselines
+   \unvbox\@outputbox
+  }%
+ }%
+ #1{%
+  \@ifvoid\footsofar{}{%
+%    \end{macrocode}
+% At this point, \cmd\footins\ is empty; all of the footnotes have been combined into \cmd\footsofar.
+%    \begin{macrocode}
+   \show@box@size{Combining page footnotes}\footsofar
+   \setbox\footins\box\footsofar
+%    \end{macrocode}
+% Depending on the page grid, we compose the footnotes for placement on the page. 
+%    \begin{macrocode}
+   \compose@footnotes
+   \@combineinserts\@outputbox\footins
+  }%
+ }{%
+%    \end{macrocode}
+%QUERY: The following line was removed, probably to fix a bug. When was this done?
+%    \begin{verbatim}
+% \global\setbox\footins\box\footsofar
+%    \end{verbatim}
+%    \begin{macrocode}
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@cflt}
+% \begin{macro}{\@cflb}
+% \changes{4.1b}{2008/08/04}{}
+% We modify \LaTeX's \cmd\@cflt\ and \cmd\@cflb\ to remove the unwanted glue with \cmd\unskip.
+%    \begin{macrocode}
+\def \@cflt{%
+ \let \@elt \@comflelt
+ \setbox\@tempboxa \vbox{}%
+ \@toplist
+ \setbox\@outputbox \vbox{%
+  \boxmaxdepth \maxdepth
+  \unvbox\@tempboxa\unskip
+  \topfigrule\vskip \textfloatsep
+  \unvbox\@outputbox
+ }%
+ \let\@elt\relax
+ \xdef\@freelist{\@freelist\@toplist}%
+ \global\let\@toplist\@empty
+}%
+\def \@cflb {%
+ \let\@elt\@comflelt
+ \setbox\@tempboxa \vbox{}%
+ \@botlist
+ \setbox\@outputbox \vbox{%
+  \unvbox\@outputbox
+  \vskip \textfloatsep\botfigrule
+  \unvbox\@tempboxa\unskip
+ }%
+ \let\@elt\relax
+ \xdef\@freelist{\@freelist\@botlist}%
+ \global \let \@botlist\@empty
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@combinedblfloats}
+% We modify \LaTeX's \cmd\@combinedblfloats\ to be more appropriate for incremental page building:
+% we \cmd\unvbox\ the \cmd\@outputbox.
+%    \begin{macrocode}
+\def\@combinedblfloats{%
+ \@ifx@empty\@dbltoplist{}{%
+  \setbox\@tempboxa\vbox{}%
+  \let\@elt\@comdblflelt\@dbltoplist
+  \let\@elt\relax\xdef\@freelist{\@freelist\@dbltoplist}%
+  \global\let\@dbltoplist\@empty
+  \setbox\@outputbox\vbox{%
+   %\boxmaxdepth\maxdepth   %% probably not needed, CAR
+   \unvbox\@tempboxa\unskip
+   \@ifnum{\@dbltopnum>\m@ne}{\dblfigrule}{}%FIXME: how is \@dbltopnum maintained?
+   \vskip\dbltextfloatsep
+   \unvbox\@outputbox
+  }%
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\set@column@hsize}%
+% The procedure \cmd\set@column@hsize\ takes care of setting up the horizontal dimensions
+% for the current page grid. The present routine will certainly not be adequate for more
+% complex page layouts (e.g., with a side column), but works for the common ones.
+% \changes{4.0a}{2001/06/18}{Introduce \cs{set@marry@height} }
+%    \begin{macrocode}
+\def\set@column@hsize#1{%
+ \pagegrid@col#1%
+ \global\columnwidth\textwidth
+ \global\advance\columnwidth\columnsep
+ \global\divide\columnwidth\pagegrid@col
+ \global\advance\columnwidth-\columnsep
+ \global\hsize\columnwidth
+ \global\linewidth\columnwidth
+ \skip@\baselineskip\advance\skip@-\topskip
+ \@ifnum{\pagegrid@col>\@ne}{\set@marry@skip}{}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\set@colht}%
+% \begin{macro}{\set@colroom}%
+% \begin{macro}{\set@vsize}%
+% \begin{macro}{\set@adj@colht}%
+% The story of \cmd\textheight, \cmd\@colht, \cmd\@colroom, and \cmd\vsize.
+%
+% \cmd\textheight---height of the text column. Not a running parameter, however, each time a page is 
+% shipped out, the \cmd\textheight\ could in principle be altered. This must be done before
+%
+% \cmd\@colht---\cmd\textheight\ minus the height of any full-page-width floats. The latter are committed
+% only just after shipping out, and only if we are in a multicolumn page grid.
+% Therefore, \cmd\@colht\ should be set after a \cmd\shipout\ (by \cmd\@outputpage) and
+% will be adjusted when full-page-width floats are committed to the fresh page by \cmd\do@startpage.
+%
+% \cmd\@colroom---\cmd\@colht\ (adjusted by \cmd\pagesofar) minus the height of any column-width floats.
+% The latter are committed anywhere on the page, at which point \cmd\@colroom\ must be adjusted.
+% Therefore, \cmd\@colroom\ should be set (by \cmd\set@colroom) whenever a column is prepared (by ).
+%FIXME: committed (by \cmd\output@column@) and
+% will be adjusted (by \cmd\@add@float\ or \cmd\do@startcolumn) whenever a float is committted to the column.
+%
+% \cmd\vsize---\cmd\@colroom.
+% Therefore, \cmd\vsize\ should be set (by \cmd\set@vsize) whenever
+% the \cmd\@colroom\ is set (by \cmd\set@colroom) or adjusted (by \cmd\@add@float\ or \cmd\do@startcolumn)
+%FIXME: or when the \cmd\pagesofar\ box is changed (after invoking \cmd\open@column@).
+%
+% Question: what if there are committed floats? Footnotes?
+% Answer: full-page-width floats are only committed at top, and they are already reckoned with in \cmd\@colht.
+% Column-width committed floats are incorporated by \cmd\@makecolumn.
+%
+% As to footnotes, our scheme is to keep the \cmd\footins\ insert register up to date, and to use the insert mechanism 
+% to ensure room for footnotes. 
+% When a change is made to the page grid, the footnotes will need to be propagated back into the MVL. 
+%
+% Note: FIXME: adjusting for \cmd\pagesofar\ is done at not quite the right time. I need to reexamine \cmd\set@colht,
+% because \cmd\@dbltoplist\ and \cmd\pagesofar\ really should be on the same footing.
+% Perhaps \cmd\@colht\ and \cmd\@colroom\ should both deal with their respective ``lists'' in the same way?
+%
+% These concerns will be particularly germane if we ever extend this package to deal with full-page-width floats
+% placed at the bottom of the page, or committed on the same page as called out.
+%
+% It occurs to me that we should ditch \cmd\set@colroom\ and only ever execute \cmd\set@colht, 
+% which sets \cmd\@colroom\ as a side effect.
+% If so, we can make \cmd\@colht\ take \cmd\pagesofar\ into account, as it should. Then \cmd\@colht\ will return to its 
+% original significance as the value that \cmd\@colroom\ is set to after a column is committed.
+%
+% On the other hand, why not simply forget all this caching and (re-)calculate \cmd\vsize\ as late as possible?
+% Particularly, \cmd\@colht\ is an artifact of the old way of doing things, where once it was set, it would never change.
+% 
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+%    \begin{macrocode}
+\def\set@colht{%
+ \set@adj@textheight\@colht
+ \global\let\enlarge@colroom\@empty
+ \set@colroom
+}%
+\def\set@adj@textheight#1{%
+ \ltxgrid@info@sw{\class@info{\string\set@adj@textheight\string#1}\saythe\textheight}{}%
+ #1\textheight
+ \def\@elt{\adj@page#1}%
+ \@booleantrue\firsttime@sw\@dbltoplist
+ \let\@elt\relax
+ \global#1#1\relax
+ \ltxgrid@info@sw{\saythe#1}{}%
+}%
+\def\set@colroom{%
+ \ltxgrid@info@sw{\class@info{\string\set@colroom}}{}%
+ \set@adj@colht\@colroom
+ \@if@empty\enlarge@colroom{}{%
+  \global\advance\@colroom\enlarge@colroom\relax
+  \ltxgrid@info@sw{\saythe\@colroom}{}%
+ }%
+ \@ifdim{\@colroom>\topskip}{}{%
+  \ltxgrid@info{Not enough room: \string\@colroom=\the\@colroom; increasing to \the\topskip}%
+  \@colroom\topskip
+ }%
+ \global\@colroom\@colroom
+%<ignore> \ltxgrid@info@sw{\class@info{\string\set@colroom\string\vsize=\string\colroom}\saythe\vsize}{}%
+ \set@vsize
+}%
+%
+\def\set@vsize{%
+ \global\vsize\@colroom
+ \ltxgrid@info@sw{\class@info{\string\set@vsize\string\vsize=\string\colroom}\saythe\vsize}{}%
+}%
+%    \end{macrocode}
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+%    \begin{macrocode}
+\def\set@adj@colht#1{%
+ #1\@colht
+ \ltxgrid@info@sw{\class@info{\string\set@adj@colht\string#1-\string\pagesofar}\saythe#1}{}%
+ \@ifvoid\pagesofar{}{%
+  \advance#1-\ht\pagesofar\advance#1-\dp\pagesofar
+  \ltxgrid@info@sw{\class@info{\string\pagesofar}\saythe#1}{}%
+ }%
+ \def\@elt{\adj@column#1}%
+ \@booleantrue\firsttime@sw\@toplist
+ \@booleantrue\firsttime@sw\@botlist
+ \let\@elt\relax
+}%
+\def\adj@column#1#2{%
+ \advance#1-\ht#2%
+ \advance#1-\firsttime@sw{\textfloatsep\@booleanfalse\firsttime@sw}{\floatsep}%
+ \ltxgrid@info@sw{\class@info{\string\adj@column\string#1-\string#2}\saythe#1}{}%
+}%
+\def\adj@page#1#2{%
+ \advance#1-\ht#2%
+ \advance#1-\firsttime@sw{\dbltextfloatsep\@booleanfalse\firsttime@sw}{\dblfloatsep}%
+ \ltxgrid@info@sw{\class@info{\string\adj@page\string#1-\string#2}\saythe#1}{}%
+}%
+\def\set@adj@box#1#2{%
+ \@ifvoid#2{}{%
+  \advance#1-\ht#2\advance#1-\dp#2%
+  \@booleantrue\temp@sw
+  \ltxgrid@foot@info@sw{\class@info{\string\set@adj@box\string#2}\saythe#1}{}%
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@outputpage@tail}%
+% \changes{4.1b}{2008/08/04}{Procedure \cs{@outputpage@tail} tailpatches \cs{@outputpage}}%
+% In \cmd\@outputpage@tail, we set \cmd\@colht\ and the float placement parameters
+% (this is the one point where it is appropriate to set \cmd\@colht).
+% At \cmd\do@startpage\ time, we adjust \cmd\@colht's value to reflect committed 
+% full-page-width floats.
+%
+% Note: with a correctly written output routine, a call to \cmd\@outputpage\ will inevitably be 
+% followed by a call to \cmd\do@startpage, so these procedure calls would be unneeded.
+%    \begin{macrocode}
+\appdef\@outputpage@tail{%
+ \set@colht          % FIXME: needed?
+ \@floatplacement    % FIXME: needed?
+ \@dblfloatplacement % FIXME: needed?
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{balance@2}
+% \changes{4.1b}{2008/08/04}{Procedure \cs{balance@2} defined more transparently}%
+% We define procedures for balancing columns in a multicolumn layout.
+% For now, we define only one: a procedure for the two-column grid.
+% All others will simply \cmd\relax\ out.
+%
+% The following code defines \verb+\balance@2+ without all the clunky \cmd\csname\ commands
+% in the replacement part,
+% which appears on the right-hand side of the assignment to \cmd\toks@.
+%
+% The method is straightforward: balance the two columns of text, and balance the footnotes.
+% Later on, \cmd\@combineinserts\ will be called to place the footnotes after the now-balanced columns.
+%
+% \changes{4.1f}{2009/07/14}{(AO, 519) \cs{footins} content must be preserved and reintegrated}
+% It was necessary to deal with the case where \cmd\box\cmd\footsofar\ was not empty
+% upon execution of this balancing code. We store it away in \cmd\box\cmd\footins\ and
+% add it back in afterwards.
+%
+% Here is a conundrum: if we switch between single-, two-, and three-column page grids:
+% On what measure should the footnotes be set?
+%    \begin{macrocode}
+\begingroup
+ \catcode`\1=\cat@letter
+ \catcode`\2=\cat@letter
+%    \end{macrocode}
+% \cmd\toks@\ contains the repacement part for an effective \cmd\def\cs{balance@2}.
+%    \begin{macrocode}
+ \toks@{%
+%    \end{macrocode}
+% \cmd\balance@two, by side effect, strips footnotes into \cmd\box\cmd\footins. 
+%    \begin{macrocode}
+  \setbox\footins\box\footsofar
+  \balance@two\col@1\@outputbox
+%    \end{macrocode}
+% We ensure that the box assignments are global. 
+%    \begin{macrocode}
+  \global\setbox\col@1\box\col@1
+  \global\setbox\@outputbox\box\@outputbox
+%    \end{macrocode}
+% The following line puts all footnotes into the footnote galley, \cmd\footsofar.
+%    \begin{macrocode}
+  \combine@foot@inserts\footsofar\footins
+ }%
+ \aftergroup\def\aftergroup\balance@2\expandafter
+\endgroup\expandafter{\the\toks@}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\balance@two}
+% The procedure \cmd\balance@two\ takes two columns and balances them; in the process it removes
+% any footnotes that may be present to a place of safety \cmd\footsofar, 
+% for later placement at the foot of the shipped-out page. 
+% The box register \cmd\box\cmd\@ne\ is the aggregate of all columns.
+% The box register \cmd\box\cmd \z@\ is the last column.
+% The box register \cmd\box\cmd\tw@\ is the first column.
+% The \cmd\dimen\ register \cmd\dimen@\  is the trial value to \cmd\vsplit\ to, 
+% initially half the height of \cmd\box\cmd\@ne.
+% The \cmd\dimen\ register \cmd\dimen@i\ is the increment for the next trial;
+% its initial value is equal to the initial value of \cmd\dimen@.
+% The \cmd\dimen\ register \cmd\dimen@ii\ is the difference of the heights of the two columns.
+%
+% The procedure uses a binary search for that value of \cmd\dimen@\ which is stable to within .5\cmd\p@\ and which
+% makes the last column be shorter than the others.
+%
+% This procedure can be extended to multiple columns simply by changing it to execute \cmd\vsplit\ multiple
+% times (one less than the total number of columns in the page layout) and to calculating \cmd\dimen@ii\
+% to be the difference of the heights of last column and the \cmd\dimen@.
+% Upon termination of the search, one would excute the \cmd\vsplit s once again, this time 
+% using the actual \cmd\col@\ box registers to store the 
+% balanced columns, thereby clobbering their former contents.
+%
+% Bug Note:
+% as originally written, this macro had a bug, which is well worth avoiding under similar circumstances anywhere.
+% So, learn from the mistakes of others, as they say.
+% In trying to remove the depth of the boxes created via \cmd\vsplit\ within the \cmd\loopwhile\ control,
+% I originally coded
+% \cmd\unvbox
+% \cmd\z@\
+% \cmd\setbox
+% \cmd\z@
+% \cmd\lastbox\
+% \cmd\dimen@
+% \cmd\dp
+% \cmd\z@\
+% \cmd\box
+% \cmd\z@\
+% \cmd\vskip-%
+% \cmd\dimen@.
+% The error here is that the (horizontal) shift of the last box in the vertical list will be lost in the process.
+% Simply put, \cmd\setbox\cmd\z@\cmd\lastbox\ fails to retain the shift of the box node in the vertical list,
+% and when it is put down again via \cmd\box\cmd\z@, it will no longer have the correct shift.
+%
+% This bug affected things placed in the MVL with \cmd\moveleft, \cmd\moveright, \cmd\parshape, and 
+% \cmd\hangindent, as well as things shifted by \TeX's primitive mechanisms.
+%
+% A superior strategy for removing the depth of the last line of the list is more expensive, but safer:
+% make a separate copy of the list, measure the depth of the last box as above, but then discard
+% the list, retaining only the value of the dimension.
+% 
+% Note that this procedure will not work if the material within is excessively chunky.
+% A particular failure mode exists where none of the material is allocated to the last (right) column.
+% We detect this case and revert to unbalanced columns.
+%
+% Another failure mode is where a large chunk occurs at the beginning of the composite box.
+% In this case, the left column may fill up even when \cmd\dimen@\ is very small.
+% If this configuration leaves the left column longer than the right, then we are done,
+% but \cmd\dimen@\ by  no means represents the height of either finished box.
+%
+% Therefore the last step in the process is to rebox the two columns to a common height determined
+% independently of the balancing process.
+%
+% The dimension involved is checked against the current \cmd\@colroom\ to guard against the case where
+% excessive material happens to fall in either column.
+% \changes{4.1b}{2008/08/04}{Change \cs{set@colroom} to \cs{set@colht}}
+% \changes{4.1n}{2009/12/02}{More diagnostics of column balancing}
+% \changes{4.1n}{2010/01/02}{(AO, 571) coding convention: use \cs{bgroup}, \cs{egroup} (instead of braces) when a box is being built}%
+% \changes{4.1n}{2010/01/02}{(AO, 571) Footnotes, when columns are balanced or when they are composed with their column}%
+% \changes{4.1n}{2010/01/02}{(AO, 571) Change \cs{balance@two}'s balancing algorithm to more successfully balance extremely short columns.}
+%    \begin{macrocode}
+\def\balance@two#1#2{%
+ \ltxgrid@info@sw{\class@info{\string\balance@two\string#1\string#2}}{}%
+ \outputdebug@sw{\trace@scroll{\showbox#1\showbox#2}}{}%
+%    \end{macrocode}
+% The first step is to recover the footnotes from the bottoms of the two columns (globally, into \cmd\footsofar)
+% and to combine the text into \cmd\box\cmd\@ne, but without voiding either of the argument boxes. 
+%    \begin{macrocode}
+ \setbox\thr@@\copy\footsofar
+ \setbox\@ne\vbox\bgroup
+  \@ifvoid{#1}{}{%
+   \recover@column#1\footsofar\column@recovered\footins@recovered
+   \@ifvoid{#2}{}{\marry@baselines}%
+  }%
+  \@ifvoid{#2}{}{%
+   \recover@column#2\footsofar\column@recovered\footins@recovered
+  }%
+ \egroup
+ \outputdebug@sw{\trace@scroll{\showbox\@ne}}{}%
+ \ltxgrid@foot@info@sw{\trace@scroll{\showbox\footsofar}}{}%
+%    \end{macrocode}
+% Hereunder, \cmd\dimen@\ is the split value. We adjust it until the step size is small enough, while the split is acceptable. 
+% Also, \cmd\dimen@i\ is the step size. Once this value is greater than a half point, we must iterate. 
+%    \begin{macrocode}
+ \dimen@\ht\@ne\divide\dimen@\tw@
+ \dimen@i\dimen@
+ \vbadness\@M
+ \vfuzz\maxdimen
+ \splittopskip\topskip
+ \loopwhile{%
+  \setbox\z@\copy\@ne\setbox\tw@\vsplit\z@ to\dimen@
+  \remove@depth\z@\remove@depth\tw@
+%    \end{macrocode}
+% The following line would provide a diagnostic of the iterations of column balancing, were we to use it.
+%    \begin{verbatim}
+%  \outputdebug@sw{\trace@scroll{\showbox\tw@\showbox\z@}}{}%
+%    \end{verbatim}
+% Hereunder, \cmd\dimen@ii\ is used to reckon the difference in height between the left box and the right. 
+%    \begin{macrocode}
+  \dimen@ii\ht\tw@\advance\dimen@ii-\ht\z@
+  \dimen@i=.5\dimen@i
+  \ltxgrid@info@sw{\saythe\dimen@\saythe\dimen@i\saythe\dimen@ii}{}%
+%    \end{macrocode}
+% If the columns are within a half-point of each other, 
+%    \begin{macrocode}
+  \@ifdim{\dimen@ii<.5\p@}{%
+   \@ifdim{\dimen@ii>-.5\p@}%
+  }{%
+   \false@sw
+  }%
+%    \end{macrocode}
+% The above results in a Boolean, which now chooses between the following two brace-delimited clauses.
+% If the step size is less than a half-point, then terminate the loop. 
+%    \begin{macrocode}
+  {%
+   \true@sw
+  }{%
+   \@ifdim{\dimen@i<.5\p@}%
+  }%
+%    \end{macrocode}
+% The above results in a Boolean, which now chooses between the following two brace-delimited clauses.
+% The true-part terminates the loop, otherwise iterate. 
+%    \begin{macrocode}
+  {%
+   \false@sw
+  }%
+  {%
+%    \end{macrocode}
+% For the next iteration, the candidate split dimension \cmd\dimen@\ will be one step larger 
+% if the height of the left box is less than that of the right box. 
+% Otherwise it will be one step smaller. 
+%    \begin{macrocode}
+   \advance\dimen@\@ifdim{\dimen@ii<\z@}{}{-}\dimen@i
+   \true@sw
+  }%
+ }%
+%    \end{macrocode}
+% The loop has terminated.
+%    \begin{macrocode}
+ \ltxgrid@info@sw{\saythe\dimen@\saythe\dimen@i\saythe\dimen@ii}{}%
+%    \end{macrocode}
+% The algorithm has failed to find a satisfactory result if
+% the left column is of non-zero height and the right column is of zero height. 
+%    \begin{macrocode}
+ \@ifdim{\ht\z@=\z@}{%
+  \@ifdim{\ht\tw@=\z@}%
+ }{%
+  \true@sw
+ }%
+%    \end{macrocode}
+% The \cmd\false@sw\ branch is executed if the algorithm has failed. 
+% We restore the original boxes. 
+%    \begin{macrocode}
+ {%
+ }{%
+  \ltxgrid@info{Unsatifactorily balanced columns: giving up}%
+  \setbox\tw@\box#1%
+  \setbox\z@ \box#2%
+  \global\setbox\footsofar\box\thr@@
+ }%
+ \setbox\tw@\vbox{\unvbox\tw@\vskip\z@skip}%
+ \setbox\z@ \vbox{\unvbox\z@ \vskip\z@skip}%
+ \set@colht
+ \dimen@\ht\z@\@ifdim{\dimen@<\ht\tw@}{\dimen@\ht\tw@}{}%
+ \@ifdim{\dimen@>\@colroom}{\dimen@\@colroom}{}%
+ \ltxgrid@info@sw{\saythe{\ht\z@}\saythe{\ht\tw@}\saythe\@colroom\saythe\dimen@}{}%
+ \setbox#1\vbox to\dimen@{\unvbox\tw@\unskip\raggedcolumn@skip}%
+ \setbox#2\vbox to\dimen@{\unvbox\z@ \unskip\raggedcolumn@skip}%
+ \outputdebug@sw{\trace@scroll{\showbox#1\showbox#2}}{}%
+}%
+%    \end{macrocode}
+% Procedure \cmd\remove@depth\ rearranges the given (vertical) box register so that it has zero depth. 
+%    \begin{macrocode}
+\def\remove@depth#1{%
+  \setbox#1\vbox\bgroup
+   \unvcopy#1%
+   \setbox\z@\vbox\bgroup
+    \unvbox#1%
+    \setbox\z@\lastbox
+    \aftergroup\kern\aftergroup-\expandafter
+   \egroup
+   \the\dp\z@\relax
+  \egroup
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \changes{4.1n}{2010/01/02}{(AO, 571) Abandon \cs{recover@footins} in favor of \cs{recover@column}}%
+% Procedure \cmd\recover@column\ is a utility to separate a column box into text and footnotes;
+% the former being contributed to the current (vertical) list, the latter appended to the given register, usually \cmd\footsofar. 
+% 
+% Argument \verb+#1+ is the input: it should be a \cmd\vbox, and it remains unaltered. 
+% Argument \verb+#2+ is the box into which to (globally) add the footnotes, usually \cmd\footsofar.
+% Arguments \verb+#3+ and \verb+#4+ are scratch box registers to use in this calculation.
+% As a side effect, \verb+#3+ will be unboxed into whatever vertical mode we are in at the moment (should be a \cmd\vbox). 
+%    \begin{macrocode}
+\def\recover@column#1#2#3#4{%
+ \ltxgrid@info@sw{\class@info{\string\recover@column\string#1\string#2\string#3\string#4}}{}%
+ \setbox#4\vbox{\unvcopy#1}%
+ \ltxgrid@foot@info@sw{\trace@scroll{\showbox#4}}{}%
+ \dimen@\ht#4%
+ \ltxgrid@foot@info@sw{\saythe\dimen@}{}%
+ \setbox#4\vbox\bgroup
+  \unvbox#4\unskip
+%    \end{macrocode}
+% We now strip the footnotes from the bottom of this box, adding them to \cmd\footsofar.
+% The method relies on a signal, consisting of a complementary pair of kerns, placed at the bottom of the box by \cmd\@combineinserts. 
+%    \begin{macrocode}
+  \dimen@i\lastkern\unkern\advance\dimen@i\lastkern
+  \@ifdim{\dimen@i=\z@}{%
+   \dimen@i\lastkern\unkern
+   \ltxgrid@foot@info@sw{\saythe\dimen@i}{}%
+   \aftergroup\dimen@i
+   \expandafter\egroup\the\dimen@i\relax
+  }{%
+   \egroup
+  }%
+%    \end{macrocode}
+% Split the column into \verb+#3+ and the footnote into \verb+#4+.
+% Append the footnote to \verb+#2+.
+%    \begin{macrocode}
+ \@ifdim{\dimen@i<\z@}{%
+  \advance\dimen@\dimen@i
+  \ltxgrid@foot@info@sw{\saythe\dimen@i\saythe\dimen@}{}%
+  \splittopskip\z@skip
+  \global\setbox#3\vsplit#4 to\dimen@
+  \global\setbox#4\vbox{\unvbox#4}%
+  \ltxgrid@foot@info@sw{\trace@scroll{\showbox#1\showbox#2\showbox#3\showbox#4}}{}%
+  \global\setbox#2\vbox\bgroup\unvbox#2\vskip\z@skip\unvbox#4\egroup
+ }{%
+%    \end{macrocode}
+% What if \cmd\dimen@i\ is zero? 
+% In that case, \cmd\setbox\#3\cmd\box\#4, and do not touch \cmd\box\#2.
+%    \begin{macrocode}
+  \setbox#3\box#4%
+  \ltxgrid@foot@info@sw{\trace@scroll{\showbox#1\showbox#2\showbox#3\showbox#4}}{}%
+ }%
+ \unvbox#3%
+ \loopwhile{\dimen@\lastskip\@ifdim{\dimen@>\z@}{\unskip\true@sw}{\false@sw}}%
+}%
+\def\recover@column@null#1#2#3#4{%
+ \unvcopy#1%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@begindocumenthook}
+% Initialization:
+% we initialize to the page grid named ``one''.
+% If the class decides to initially set type in a different grid, it
+% should execute these same commands, but changing the first to the appropriate procedure.
+%
+% Note that the point where this sequence is executed would be an excellent place to arrange for 
+% floats to be committed to the first page of a document. 
+% That is, we execute \cmd\do@startpage, which triggers \cmd\do@startcolumn.
+%
+% FIXME: it should be the job of the page grid to determine the procedure to execute at 
+% the start of the job. Make this a hook.
+%    \begin{macrocode}
+\rvtx@ifformat@geq{2020-10-01}%
+  {%
+    \AddToHook{begindocument}{%
+      \open@column@one\@ne
+      \set@colht
+      \@floatplacement
+      \@dblfloatplacement
+    }%
+  }{%
+    \prepdef\@begindocumenthook{%
+     \open@column@one\@ne
+     \set@colht
+     \@floatplacement
+     \@dblfloatplacement
+    }%
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% Comment: our technique of balancing columns is severely limited, because it cannot properly work
+% with \env{longtable}, which places material at the bottom and top of the column break.
+%
+% The proper way to handle a grid change in the middle of the page is to accumulate all the material for
+% an entire article (or chapter) and then assemble finished pages therefrom. This approach is fundamentally
+% superior for complex layouts: it corresponds to real-world workflows.
+% Such a scheme is an excellent subject for another \LaTeX\ package.
+%
+%
+% \subsection{Patches for the longtable package}%
+%
+% \LaTeX's ``required'' package \classname{longtable} (written by David P. Carlilsle),
+% which is part of /latex/required/tools, is incmpatible with both
+% \LaTeX's ``required'' package \classname{multicol} and with
+% \LaTeX's native \cmd\twocolumn\ capability. There is no essential reason
+% for this incompatability, aside from implementation details, and the
+% \classname{ltxgrid} package gives us the ability to lift them.
+%
+% Only four of \classname{longtable}'s procedures require rewriting:
+% \cmd\longtable,
+% \cmd\endlongtable,
+% \cmd\LT@start, and
+% \cmd\LT@end@hd@ft. 
+% The procedure \cmd\switch@longtable\ checks against their expected meanings
+% and, if all is as expected, applies the patches.
+% In the process, we simplify things considerably and also make them more
+% secure.
+%
+% Why does \classname{longtable} need to access the output routine, anyway?
+% What it comes down to, is what happens when a pagebreak falls within a
+% long table. If this happens, we would like to append a row at the bottom of
+% the broken table and add a row at the top of the next page.
+%
+% These things can be accomodated easily by the \classname{ltxgrid} output
+% routine hooks.
+%
+% \begin{macro}{\longtable}
+%    \begin{macrocode}
+\def\longtable@longtable{%
+ \par
+ \ifx\multicols\@undefined\else\ifnum\col@number>\@ne\@twocolumntrue\fi\fi
+ \if@twocolumn\LT@err{longtable not in 1-column mode}\@ehc\fi
+ \begingroup
+ \@ifnextchar[\LT@array{\LT@array[x]}%
+}%
+\def\longtable@new{%
+ \par
+  \@ifnextchar[\LT@array{\LT@array[x]}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\endlongtable}
+%    \begin{macrocode}
+\def\endlongtable@longtable{%
+  \crcr
+  \noalign{%
+    \let\LT@entry\LT@entry@chop
+    \xdef\LT@save@row{\LT@save@row}}%
+  \LT@echunk
+  \LT@start
+  \unvbox\z@
+  \LT@get@widths
+  \if@filesw
+    {\let\LT@entry\LT@entry@write\immediate\write\@auxout{%
+      \gdef\expandafter\noexpand
+        \csname LT@\romannumeral\c@LT@tables\endcsname
+          {\LT@save@row}}}%
+  \fi
+  \ifx\LT@save@row\LT@@save@row
+  \else
+    \LT@warn{Column \@width s have changed\MessageBreak
+             in table \thetable}%
+    \LT@final@warn
+  \fi
+  \endgraf\penalty -\LT@end@pen
+  \endgroup
+  \global\@mparbottom\z@
+  \pagegoal\vsize
+  \endgraf\penalty\z@\addvspace\LTpost
+  \ifvoid\footins\else\insert\footins{}\fi
+}%
+%    \end{macrocode}
+% \changes{4.1a}{2008/06/29}{Repair error in \cs{endlongtable@new} involving \cs{@ifx}: argument not delimited.}
+%    \begin{macrocode}
+\def\endlongtable@new{%
+  \crcr
+  \noalign{%
+   \let\LT@entry\LT@entry@chop
+   \xdef\LT@save@row{\LT@save@row}%
+  }%
+  \LT@echunk
+  \LT@start
+  \unvbox\z@
+  \LT@get@widths
+  \@if@sw\if@filesw\fi{%
+   {%
+    \let\LT@entry\LT@entry@write
+    \immediate\write\@auxout{%
+     \gdef\expandafter\noexpand\csname LT@\romannumeral\c@LT@tables\endcsname
+     {\LT@save@row}%
+    }%
+   }%
+  }{}%
+  \@ifx{\LT@save@row\LT@@save@row}{}{%
+   \LT@warn{%
+    Column \@width s have changed\MessageBreak in table \thetable
+   }\LT@final@warn
+  }%
+  \endgraf
+  \nobreak
+  \box\@ifvoid\LT@lastfoot{\LT@foot}{\LT@lastfoot}%
+ \global\@mparbottom\z@
+ \endgraf
+ \LT@post
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@start}
+%    \begin{macrocode}
+\def\LT@start@longtable{%
+  \let\LT@start\endgraf
+  \endgraf\penalty\z@\vskip\LTpre
+  \dimen@\pagetotal
+  \advance\dimen@ \ht\ifvoid\LT@firsthead\LT@head\else\LT@firsthead\fi
+  \advance\dimen@ \dp\ifvoid\LT@firsthead\LT@head\else\LT@firsthead\fi
+  \advance\dimen@ \ht\LT@foot
+  \dimen@ii\vfuzz
+  \vfuzz\maxdimen
+    \setbox\tw@\copy\z@
+    \setbox\tw@\vsplit\tw@ to \ht\@arstrutbox
+    \setbox\tw@\vbox{\unvbox\tw@}%
+  \vfuzz\dimen@ii
+  \advance\dimen@ \ht
+        \ifdim\ht\@arstrutbox>\ht\tw@\@arstrutbox\else\tw@\fi
+  \advance\dimen@\dp
+        \ifdim\dp\@arstrutbox>\dp\tw@\@arstrutbox\else\tw@\fi
+  \advance\dimen@ -\pagegoal
+  \ifdim \dimen@>\z@\vfil\break\fi
+      \global\@colroom\@colht
+  \ifvoid\LT@foot\else
+    \advance\vsize-\ht\LT@foot
+    \global\advance\@colroom-\ht\LT@foot
+    \dimen@\pagegoal\advance\dimen@-\ht\LT@foot\pagegoal\dimen@
+    \maxdepth\z@
+  \fi
+  \ifvoid\LT@firsthead\copy\LT@head\else\box\LT@firsthead\fi
+%    \end{macrocode}
+% At some point before version 4.11, the \cmd\nobreak\ was added. 
+%    \begin{macrocode}
+\nobreak
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+  \output{\LT@output}%
+}%
+\def\LT@start@new{%
+ \let\LT@start\endgraf
+ \endgraf
+ \markthr@@{}%
+ \LT@pre
+ \@ifvoid\LT@firsthead{\LT@top}{\box\LT@firsthead\nobreak}%
+ \mark@envir{longtable}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@end}
+%    \begin{macrocode}
+\def\LT@end@hd@ft@longtable#1{%
+ \LT@echunk
+ \ifx\LT@start\endgraf
+  \LT@err{Longtable head or foot not at start of table}{Increase LTchunksize}%
+ \fi
+ \setbox#1\box\z@
+ \LT@get@widths\LT@bchunk
+}%
+\def\LT@end@hd@ft@new#1{%
+ \LT@echunk
+ \@ifx{\LT@start\endgraf}{%
+  \LT@err{Longtable head or foot not at start of table}{Increase LTchunksize}%
+ }%
+ \global\setbox#1\box\z@
+ \LT@get@widths
+ \LT@bchunk
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@array}
+%
+% 
+%    \begin{macrocode}
+\def\LT@array@longtable[#1]#2{%
+  \refstepcounter{table}\stepcounter{LT@tables}%
+  \if l#1%
+    \LTleft\z@ \LTright\fill
+  \else\if r#1%
+    \LTleft\fill \LTright\z@
+  \else\if c#1%
+    \LTleft\fill \LTright\fill
+  \fi\fi\fi
+  \let\LT@mcol\multicolumn
+  \let\LT@@tabarray\@tabarray
+  \let\LT@@hl\hline
+  \def\@tabarray{%
+    \let\hline\LT@@hl
+    \LT@@tabarray}%
+  \let\\\LT@tabularcr\let\tabularnewline\\%
+  \def\newpage{\noalign{\break}}%
+  \def\pagebreak{\noalign{\ifnum`}=0\fi\@testopt{\LT@no@pgbk-}4}%
+  \def\nopagebreak{\noalign{\ifnum`}=0\fi\@testopt\LT@no@pgbk4}%
+  \let\hline\LT@hline \let\kill\LT@kill\let\caption\LT@caption
+  \@tempdima\ht\strutbox
+  \let\@endpbox\LT@endpbox
+  \ifx\extrarowheight\@undefined
+    \let\@acol\@tabacol
+    \let\@classz\@tabclassz \let\@classiv\@tabclassiv
+    \def\@startpbox{\vtop\LT@startpbox}%
+    \let\@@startpbox\@startpbox
+    \let\@@endpbox\@endpbox
+    \let\LT@LL@FM@cr\@tabularcr
+  \else
+    \advance\@tempdima\extrarowheight
+    \col@sep\tabcolsep
+    \let\@startpbox\LT@startpbox\let\LT@LL@FM@cr\@arraycr
+  \fi
+  \setbox\@arstrutbox\hbox{\vrule
+    \@height \arraystretch \@tempdima
+    \@depth \arraystretch \dp \strutbox
+    \@width \z@}%
+  \let\@sharp##\let\protect\relax
+   \begingroup
+    \@mkpream{#2}%
+    \xdef\LT@bchunk{%
+       \global\advance\c@LT@chunks\@ne
+       \global\LT@rows\z@\setbox\z@\vbox\bgroup
+       \LT@setprevdepth
+%    \end{macrocode}
+% At some point before version 4.11, the \cmd\noexpand\ was added. 
+% We need not change our own version, because we did it right, back in 1998 (using \cmd\appdef). 
+%    \begin{macrocode}
+       \tabskip\LTleft \noexpand\halign to\hsize\bgroup
+      \tabskip\z@ \@arstrut \@preamble \tabskip\LTright \cr}%
+  \endgroup
+  \expandafter\LT@nofcols\LT@bchunk&\LT@nofcols
+  \LT@make@row
+  \m@th\let\par\@empty
+  \everycr{}\lineskip\z@\baselineskip\z@
+  \LT@bchunk}%
+\def\LT@LR@l{\LTleft\z@   \LTright\fill}%
+\def\LT@LR@r{\LTleft\fill \LTright\z@  }%
+\def\LT@LR@c{\LTleft\fill \LTright\fill}%
+\def\LT@array@new[#1]#2{%
+ \refstepcounter{table}\stepcounter{LT@tables}%
+ \table@hook
+ \LTleft\fill \LTright\fill
+ \csname LT@LR@#1\endcsname
+ \let\LT@mcol\multicolumn
+ \let\LT@@hl\hline
+ \prepdef\@tabarray{\let\hline\LT@@hl}%
+ \let\\\LT@tabularcr
+ \let\tabularnewline\\%
+ \def\newpage{\noalign{\break}}%
+ \def\pagebreak{\noalign{\ifnum`}=0\fi\@testopt{\LT@no@pgbk-}4}%
+ \def\nopagebreak{\noalign{\ifnum`}=0\fi\@testopt\LT@no@pgbk4}%
+ \let\hline\LT@hline
+ \let\kill\LT@kill
+ \let\caption\LT@caption
+ \@tempdima\ht\strutbox
+ \let\@endpbox\LT@endpbox
+ \@ifxundefined\extrarowheight{%
+  \let\@acol\@tabacol
+  \let\@classz\@tabclassz
+  \let\@classiv\@tabclassiv
+  \def\@startpbox{\vtop\LT@startpbox}%
+  \let\@@startpbox\@startpbox
+  \let\@@endpbox\@endpbox
+%    \end{macrocode}
+% Because \classname{ltxutil} patches \LaTeX's \cmd\@tabularcr and \cmd\@xtabularcr,
+% we must restore these procedures in the scope of \env{longtable}.
+% Ironically, the patches in \classname{ltxutil} were for the purpose of extending
+% the \env{tabular} environment to prevent pagebreaks with the *-form of \cmd\\,
+% just the same as is being done here. But the two mechanisms conflict. 
+% \changes{4.1a}{2008/06/29}{Change \cs{LT@array@new}: restore \cs{@tabularcr} and \cs{@xtabularcr}}
+%    \begin{macrocode}
+  \let\LT@LL@FM@cr\@tabularcr@LaTeX
+  \let\@xtabularcr\@xtabularcr@LaTeX
+ }{%
+  \advance\@tempdima\extrarowheight
+  \col@sep\tabcolsep
+  \let\@startpbox\LT@startpbox
+%    \end{macrocode}
+% \changes{4.1a}{2008/06/29}{Change \cs{LT@array@new}: set \cs{LT@LL@FM@cr} to \cs{@arraycr@array} instead of \cs{@arraycr}}
+%    \begin{macrocode}
+  \let\LT@LL@FM@cr\@arraycr@array
+ }%
+%
+ \let\@acoll\@tabacoll
+ \let\@acolr\@tabacolr
+ \let\@acol\@tabacol
+%
+ \setbox\@arstrutbox\hbox{%
+  \vrule
+  \@height \arraystretch \@tempdima
+  \@depth \arraystretch \dp \strutbox
+  \@width \z@
+ }%
+ \let\@sharp##%
+ \let\protect\relax
+ \begingroup
+  \@mkpream{#2}%
+  \@mkpream@relax
+  \edef\@preamble{\@preamble}%
+  \prepdef\@preamble{%
+   \global\advance\c@LT@chunks\@ne
+   \global\LT@rows\z@
+   \setbox\z@\vbox\bgroup
+    \LT@setprevdepth
+    \tabskip\LTleft
+    \halign to\hsize\bgroup
+     \tabskip\z@
+     \@arstrut
+  }%
+  \appdef\@preamble{%
+     \tabskip\LTright
+     \cr
+  }%
+  \global\let\LT@bchunk\@preamble
+ \endgroup
+ \expandafter\LT@nofcols\LT@bchunk&\LT@nofcols
+ \LT@make@row
+ \m@th
+ \let\par\@empty
+ \everycr{}%
+ \lineskip\z@
+ \baselineskip\z@
+ \LT@bchunk
+}%
+\appdef\table@hook{}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\switch@longtable}
+%
+% Here is the switch from standard \classname{longtable} to the new, \classname{ltxgrid}-compatible values.
+%
+% At this point, we extend \env{longtable} with a \env{longtable*} form, which signifies that we want to 
+% use the full page width for setting the table.
+% You can think this way: \env{longtable*} is to \env{longtable} as \env{table*} is to \env{table}.
+%
+%    \begin{macrocode}
+\def\switch@longtable{%
+ \@ifpackageloaded{longtable}{%
+  \@ifx{\longtable\longtable@longtable}{%
+   \@ifx{\endlongtable\endlongtable@longtable}{%
+    \@ifx{\LT@start\LT@start@longtable}{%
+     \@ifx{\LT@end@hd@ft\LT@end@hd@ft@longtable}{%
+      \@ifx{\LT@array\LT@array@longtable}{%
+       \true@sw
+      }{\false@sw}%
+     }{\false@sw}%
+    }{\false@sw}%
+   }{\false@sw}%
+  }{\false@sw}%
+  {%
+   \class@info{Patching longtable package}%
+  }{%
+   \class@info{Patching unrecognized longtable package. (Proceeding with fingers crossed)}%
+  }%
+  \let\longtable\longtable@new
+  \let\endlongtable\endlongtable@new
+  \let\LT@start\LT@start@new
+  \let\LT@end@hd@ft\LT@end@hd@ft@new
+  \let\LT@array\LT@array@new
+  \newenvironment{longtable*}{%
+   \onecolumngrid@push
+   \longtable
+  }{%
+   \endlongtable
+   \onecolumngrid@pop
+  }%
+%    \end{macrocode}
+% Removed obsolete code.
+%    \begin{macrocode}
+ }{}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@pre}
+% \begin{macro}{\LT@bot}
+% \begin{macro}{\LT@top}
+% \begin{macro}{\LT@post}
+% \begin{macro}{\LT@adj}
+% Note that at the end of the longtable environment, we reestablish the \cmd\mark@envir\ of the
+% containing environment. We have left \cmd\curr@envir\ alone, so this will work.
+%    \begin{macrocode}
+\def\LT@pre{\penalty\z@\vskip\LTpre}%
+\def\LT@bot{\nobreak\copy\LT@foot\vfil}%
+\def\LT@top{\copy\LT@head\nobreak}%
+\def\LT@post{\penalty\z@\addvspace\LTpost\mark@envir{\curr@envir}}%
+\def\LT@adj{%
+ \setbox\z@\vbox{\null}\dimen@-\ht\z@
+ \setbox\z@\vbox{\unvbox\z@\LT@bot}\advance\dimen@\ht\z@
+ \global\advance\vsize-\dimen@
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{output@init}
+% \begin{macro}{output@prep}
+% \begin{macro}{output@post}
+%    \begin{macrocode}
+\def\output@init@longtable{\LT@adj}%
+\def\output@prep@longtable{\setbox\@cclv\vbox{\unvbox\@cclv\LT@bot}}%
+\def\output@post@longtable{\LT@top}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{Patches for index processing}%
+%
+% Another feature that uses the output routine hooks occurs within
+% an index, where one wishes to apply a ``continue head'' when a
+% column breaks within a primary index entry. 
+% Some book designs call for the continue head to only be applied
+% at a turnpage break.
+%
+% In any case, it is easy enough for \cmd\output@post@theindex\ 
+% to do this in conjunction with component marks.
+% Only the bare outlines are shown here.
+%
+% \begin{macro}{\output@init}
+% \begin{macro}{\output@prep}
+% \begin{macro}{\output@post}
+%    \begin{macrocode}
+\let\output@init@theindex\@empty
+\let\output@prep@theindex\@empty
+\def\output@post@theindex{%
+ \@ifodd\c@page{}{%
+  \@ifnum{\pagegrid@cur=\@ne}{%
+%    \end{macrocode}
+% We have the leftmost column of a verso page:
+% Insert the current top-level continued head.
+%    \begin{macrocode}
+  }%
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{Checking the auxiliary file}%
+%
+% We relegate the checking of the auxiliary file to the output routine.
+% This task must wait until the last page is shipped out, because otherwise
+% the stream might get closed before the last page is shipped out.
+% Obviously, we must use \cmd\do@output@MVL\ for the job.
+%
+% \begin{macro}{\check@aux}
+%    \begin{macrocode}
+\def\check@aux{\do@output@MVL{\do@check@aux}}%
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \subsection{Dealing with stuck floats and stalled float dequeueing}%
+%
+% \LaTeX's float placement mechanism is fundamentally flawed, as evidenced by 
+% its warning message ``too many unprocessed floats'', which users understandably find frustrating.
+% The \classname{ltxgrid} package provides tools for ameliorating the situation somewhat.
+%
+% Two cases require detection and rectification:
+% \begin{enumerate}
+% \item
+%  A float is ``stuck'' in the \cmd\@deferlist: for whatever reason, the float fails to be committed,
+%  even at the start of a fresh page.
+%  Once this condition prevails, following floats can never be committed, subsequently all of \LaTeX's 
+%  float registers are used up.
+%
+%  If this condition is detected, we reconsider float dequeueing under permissive (\cmd\clearpage-style) processing.
+%  
+% \item
+%  The \cmd\@freelist\ is exhausted:
+%  a large concentration of floats, say, uses up all of \LaTeX's float registers all at once.
+%  This condition commonly occurs when the user collects floats at the end of the document, for some reason.
+%
+%  When a float is encountered, \LaTeX\ uses a float register (allocated from a pool of free registers) to contain it until it can be placed.
+%  However, no further action is taken until the pagebuilder is visited, so floats can accumulate.
+%  Also, even after the pagebuilder is visited, deferred floats can accumulate, and these are not committed
+%  until a column (or page) of text is completed.
+%
+%  Once the last free float register is used, action should be taken that will commit some of the deferred floats,
+%  even if this might require ending the page right where we are (resulting in a short page).
+%
+%  Perhaps, committed floats should be stored using some mechanism other than a list, as is currently done.
+%  A feasible alternative storage method would be to use a \cmd\box\ register in place of 
+%  \cmd\@toplist,
+%  \cmd\@botlist, and
+%  \cmd\@dbltoplist.
+%  This is probably just fine, since such committed floats are not reconsidered (I think).
+%  
+% \end{enumerate}
+%
+% The  emergency processing implemented here immediately ends the current page and begins to output float pages under (\cmd\clearpage-style) rules.
+% It proceeds until all deferred floats have been flushed.
+%
+% Users should expect non-optimal page makeup under these circumstances.
+%
+% Note that there is a weakness in our approach that we have not attempted to repair: if floats are being
+% added as part of a paragraph, we will not be able to take these remedial steps until the paragraph ends.
+% This means that the approach implemented here cannot fix all \LaTeX\ documents. Users can still construct
+% documents that exhaust \LaTeX's pool of float registers!
+%
+% \begin{macro}{\check@deferlist@stuck}
+% \begin{macro}{\@outputpage@tail}
+% \changes{4.1b}{2008/08/04}{Procedure \cs{@outputpage@tail} tailpatches \cs{@outputpage}}%
+% We detect the case where, at the start of a fresh page, there are deferred floats, but none are
+% committed. We memorize the \cmd\@deferlist\ at \cmd\shipout\ time, then examine it at the point where
+% our efforts to commit floats to the new page are complete.
+% If it has not changed, the first float must be stuck, and we
+% attempt to fix things via \cmd\force@deferlist@stuck.
+%
+% This simple approach is comp[letely effective in for typical documents.
+%
+% Note that we try to avoid an infinite loop by examining the value of \cmd\clearpage@sw:
+% if we come here with that boolean true, we are in a loop.
+%    \begin{macrocode}
+\def\check@deferlist@stuck#1{%
+ \@ifx{\@deferlist@postshipout\@empty}{}{%
+  \@ifx{\@deferlist@postshipout\@deferlist}{%
+   \@fltstk
+   \clearpage@sw{%
+    \ltxgrid@warn{Deferred float stuck during \string\clearpage\space processing}%
+   }{%
+    \force@deferlist@stuck#1%
+   }%
+  }{%
+%    \end{macrocode}
+% We have successfully committed float(s)
+%    \begin{macrocode}
+  }%
+  \global\let\@deferlist@postshipout\@empty
+ }%
+}%
+\def\@fltstk{%
+ \@latex@warning{A float is stuck (cannot be placed without \string\clearpage)}%
+}%
+\appdef\@outputpage@tail{%
+ \global\let\@deferlist@postshipout\@deferlist
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@next}
+% \begin{macro}{\@xnext}
+% We rewrite the \LaTeX\ kernel macros that dequeue float registers from, e.g., \cmd\@deferlist,
+% providing a test for the condition where the pool of free registers is about to underflow.
+%
+% In this case, we attempt to fix things via \cmd\force@deferlist@empty.
+%    \begin{macrocode}
+\def\@next#1#2{%
+ \@ifx{#2\@empty}{\false@sw}{%
+  \expandafter\@xnext#2\@@#1#2%
+  \true@sw
+ }%
+}%
+\def\@xnext\@elt#1#2\@@#3#4{%
+ \def#3{#1}%
+ \gdef#4{#2}%
+ \def\@tempa{#4}\def\@tempb{\@freelist}%
+ \@ifx{\@tempa\@tempb}{%
+  \@ifx{#4\@empty}{%
+   \force@deferlist@empty%{Float register pool exhausted}%
+  }{}%
+ }{}%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\force@deferlist@stuck}
+% \begin{macro}{\force@deferlist@empty}
+% \begin{macro}{\force@deferlist@sw}
+% \begin{macro}{\do@forcecolumn@pen}
+% \begin{macro}{\do@forcecolumn}
+% The procedure \cmd\force@deferlist@empty\ is an attempt to rectify a situation where \LaTeX's float placement mechanism
+% may fail (``too many unprocessed floats'').
+%
+% We put down interrupts that call for the float placement to be redone, but under permissive conditions,
+% just the same as if \cmd\clearpage\ had been invoked.
+%
+% Note that the attempt to rectify the error is contingent on the setting of \cmd\force@deferlist@sw,
+% default false. A document class using this package that wishes to enable this error recovery mechanism should
+% set this boolean to true.
+%
+% The interrupt \cmd\do@forcecolumn@pen, which invokes the procedure \cmd\do@forcecolumn,
+% does the same as \cmd\do@startcolumn, except under permissive conditions:
+% we are trying to empty out the float registers completely.
+%
+% In order to properly with the case where there is material in \cmd\box\cmd\@cclv, 
+% \cmd\@toplist, \cmd\@botlist, \cmd\@dbltoplist, etc,
+% we do what amounts to \cmd\newpage\ to get things rolling.
+%
+% In \cmd\force@deferlist@stuck, we take advantage of already being in the output routine:
+% simply reinvoke \cmd\do@startcolumn\ under permissive conditions.
+%
+%    \begin{macrocode}
+\def\force@deferlist@stuck#1{%
+ \force@deferlist@sw{%
+  \@booleantrue\clearpage@sw
+  \@booleantrue\forcefloats@sw
+  #1%
+ }{%
+ }%
+}%
+\def\force@deferlist@empty{%
+ \force@deferlist@sw{%
+  \penalty-\pagebreak@pen
+  \protect@penalty\do@forcecolumn@pen
+ }{%
+ }%
+}%
+\@booleanfalse\force@deferlist@sw
+\mathchardef\do@forcecolumn@pen=10009
+\@namedef{output@-\the\do@forcecolumn@pen}{\do@forcecolumn}%
+\def\do@forcecolumn{%
+ \@booleantrue\clearpage@sw
+ \@booleantrue\forcefloats@sw
+%    \end{macrocode}
+%    \begin{verbatim}
+%\unvbox\@cclv
+%\vfil
+%\penalty-\pagebreak@pen
+%    \end{verbatim}
+%    \begin{macrocode}
+ \do@startcolumn
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% A more thorough revision of \LaTeX's float placement mechanism would involve substituting a single \cmd\box\
+% register for the \cmd\@deferlist. This way, \LaTeX's ability to have latent floats would be limited by
+% box memory alone. 
+%
+% Because only the \cmd\box\ and \cmd\count\ components of the float box register are actually used by \LaTeX,
+% our scheme can be accomplished if we can find a way to encode the information held in the \cmd\count\ component.
+%
+% A first-in, first-out mechanism exists, wherein a box-penalty pair is dequeued by \cmd\lastbox\cmd\lastpenalty\cmd\unpenalty\ and enqueued
+% by \cmd\setbox\cmd\foo=\cmd\hbox\cmd\bgroup\cmd\penalty\cmd\floatpenalty\cmd\box\cmd\floatbox\cmd\unhbox\cmd\foo\cmd\egroup.
+%
+% Note that this scheme is made possible by our change to \LaTeX's float placement mechanism,
+% wherein we consolidated the two \cmd\@deferlist s into one.
+%
+% \section{Support for legacy \LaTeX\ commands}
+%
+% We provide support for the \cmd\enlargethispage\ command.
+%
+% Note: using a command of this sort does not automatically enlarge both pages of a spread, which would be the convention in page composition.
+%
+% Timing Note: In a multicolumn page grid, the user should issue the \cmd\enlargethispage\ command 
+% while the first column of the page is being typeset. 
+% We provide a helpful message if the timing is wrong.
+%
+% This code can serve as a model for introducing commands that need to execute within the safety of the output routine.
+% We ensure that the arguments are fully expanded, then execute \cmd\do@output@MVL\ to cause an output procedure,
+% \cmd\@@enlargethispage, to execute. When it does execute, the MVL will be exposed.
+%
+% The \cmd\@@enlargethispage\ procedure simply adjusts the vertical dimensions of the page.
+% The adjustment will persist until the column is committed, at which point the page dimension
+% will revert to its standard value.
+%    \begin{macrocode}
+\def\enlargethispage{%
+ \@ifstar{%
+  \@enlargethispage{}%
+ }{%
+  \@enlargethispage{}%
+ }%
+}%
+\def\@enlargethispage#1#2{%
+ \begingroup
+  \dimen@#2\relax
+  \edef\@tempa{#1}%
+  \edef\@tempa{\noexpand\@@enlargethispage{\@tempa}{\the\dimen@}}%
+  \expandafter\do@output@MVL\expandafter{\@tempa}%
+ \endgroup
+}%
+\def\@@enlargethispage#1#2{%
+ \def\@tempa{one}%
+ \@ifx{\thepagegrid\@tempa}{%
+  \true@sw
+ }{%
+  \def\@tempa{mlt}%
+  \@ifx{\thepagegrid\@tempa}{%
+   \@ifnum{\pagegrid@cur=\@ne}{% 
+%    \end{macrocode}
+%   OK to adjust this page
+%    \begin{macrocode}
+    \gdef\enlarge@colroom{#2}%
+    \true@sw
+   }{% 
+%    \end{macrocode}
+%   Can only adjust this column; give up
+%    \begin{macrocode}
+    \ltxgrid@warn{Too late to enlarge this page; move the command to the first column.}%
+    \false@sw
+   }%
+  }{% 
+%    \end{macrocode}
+%  Unknown page grid
+%    \begin{macrocode}
+   \ltxgrid@warn{Unable to enlarge a page of this kind.}%
+   \false@sw
+  }%
+ }%
+ {%
+  \class@info{Enlarging page \thepage\space by #2}%
+  \global\advance\@colroom#2\relax
+  \set@vsize
+ }{%
+%    \end{macrocode}
+% Could not adjust this page
+%    \begin{macrocode}
+ }%
+}%
+\let\enlarge@colroom\@empty
+%    \end{macrocode}
+% The \cmd\@kludgeins\ insert register is now unneeded.
+% Ensure that packages using this mechanism break (preferrable to subtle bugs).
+%    \begin{macrocode}
+\let\@kludgeins\@undefined
+%    \end{macrocode}
+%
+% \subsubsection{Building the page for shipout}
+%
+% \begin{macro}{\@outputpage@head}
+% We set \cmd\@outputpage@head\ to make the \cmd\@outputbox\ be of fixed height.
+% \changes{4.1b}{2008/08/04}{Procedure \cs{@outputpage@head} headpatches \cs{@outputpage}}%
+%    \begin{macrocode}
+\@booleantrue\textheight@sw
+\prepdef\@outputpage@head{%
+ \textheight@sw{%
+  \count@\vbadness\vbadness\@M
+  \dimen@\vfuzz\vfuzz\maxdimen
+  \setbox\@outputbox\vbox to\textheight{\unvbox\@outputbox}%
+  \vfuzz\dimen@
+  \vbadness\count@
+ }{}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@outputpage@head}
+% For compatibility with David Carlisle's \classname{lscape} package, we need to allow the 
+% \cmd\LS@rot\ procedure to mung \cmd\@outputbox. 
+%
+% Implementation note: the \classname{lscape} package effectively tailpatches two \LaTeX\ internals to accomplish its purpose,
+% an approach that is not robust. It is more robust to headpatch \cmd\@outputpage, which is what we do here. 
+% \changes{4.1o}{2010/02/02}{(AO, 576) Allow \classname{lscape} to act on \cs{@outputbox} at the right time}%
+%    \begin{macrocode}
+\appdef\@outputpage@head{%
+ \@ifx{\LS@rot\@undefined}{}{\LS@rot}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Warning message}
+%
+% \begin{macro}{\ltxgrid@info}
+% \begin{macro}{\ltxgrid@warn}
+% Something has happened that the user might be interested in.
+% Print a message to the log, but only if the user selected the verbose option.
+%    \begin{macrocode}
+\def\ltxgrid@info{%
+ \ltxgrid@info@sw{\class@info}{\@gobble}%
+}%
+\@booleanfalse\ltxgrid@info@sw
+\def\ltxgrid@warn{%
+ \ltxgrid@warn@sw{\class@warn}{\@gobble}%
+}%
+\@booleantrue\ltxgrid@warn@sw
+\@booleanfalse\ltxgrid@foot@info@sw
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \section{Line-wise processing}%
+% Sometimes we wish to process each line of type that will be placed into the galley,
+% for example, applying line numbering to a document.
+% To accomplish the task, we have to force a visit to the output routine after each such line, whereupon
+% we can process it accordingly (in the case of line numbering, we could do as \filename{lineno.sty} and
+% append an appropriately formed box to the MVL).
+%
+% In implementing such a scheme, we will have to instantiate interrupts for the following cases:
+% \begin{description}
+%
+% \item[\cmd\interlinepenalty\ and friends] These include \cmd\clubpenalty, \cmd\widowpenalty, \cmd\displaywidowpenalty, and \cmd\brokenpenalty.
+%
+%
+% \item[Display math penalties] Includes \cmd\predisplaypenalty, \cmd\postdisplaypenalty, and \cmd\interdisplaylinepenalty.
+%
+%
+% \item[\cs{par}] The penalty following the last line of the paragraph.
+%
+%
+% \item[\cmd\vadjust] A trap for any \cmd\vadjust\ command that falls in the paragraph.
+%
+% \end{description}
+%
+% \begin{macro}{\def@next@handler}
+% \begin{macro}{\def@line@handler}
+% Utility procedures \cmd\def@next@handler\ and \cmd\def@line@handler\ help in the creation of 
+% interrupt handlers. 
+%
+% \cmd\def@next@handler\ increments the scratch count register (argument 1), 
+% using this value to \cmd\mathchardef\ its second argument
+% as the negative of the flag value to be used as a penalty for exciting the interrupt (argument 3).
+% As a byproduct, it leaves the given scratch counter incremented. 
+%    \begin{macrocode}
+\def\def@next@handler#1#2#3{%
+ \advance#1\@ne\mathchardef#2\the#1%
+ \expandafter\def\csname output@-\the#1\endcsname{#3}%
+%    \end{macrocode}
+% The following line is for diagnostic purposes.
+%    \begin{verbatim}
+% \typeout{\string#2(\expandafter\string\csname output@\the#1\endcsname:\expandafter\meaning\csname output@\the#1\endcsname)}%
+%    \end{verbatim}
+%    \begin{macrocode}
+}%
+%    \end{macrocode}
+% \cmd\def@line@handler\ uses \cmd\int@parpenalty\ as a base.
+% The interrupt is the sum of that base with the first argument, 
+% and the handler is the second argument.
+%    \begin{macrocode}
+\def\def@line@handler#1#2{%
+ \begingroup
+  \@tempcnta\int@parpenalty
+  \advance\@tempcnta-#1%
+%    \end{macrocode}
+% The following line is for diagnostic purposes.
+%    \begin{verbatim}
+%  \typeout{Defining: \expandafter\string\csname output@\the\linenopenalty\endcsname}%
+%    \end{verbatim}
+%    \begin{macrocode}
+  \aftergroup\def
+  \expandafter\aftergroup\csname output@-\the\@tempcnta\endcsname
+ \endgroup{#2}%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\int@parpenalty}
+% \begin{macro}{\@handle@line@ltx}
+% \begin{macro}{\@@handle@line@ltx}
+% We first set \cmd\int@parpenalty\ to our chosen base value${}\le -11012$. 
+% We then define all the handlers for lines within a paragraph, of which there are 12 different cases.
+%    \begin{macrocode}
+\mathchardef\int@parpenalty11012
+\def@line@handler\z@{\@handle@line@ltx{}{}{}}%
+\def@line@handler\@ne{\@handle@line@ltx{}{}{\brokenpenalty@ltx}}%
+\def@line@handler\tw@{\@handle@line@ltx{}{\clubpenalty@ltx}{}}%
+\def@line@handler\thr@@{\@handle@line@ltx{\clubpenalty@ltx}{}{\brokenpenalty@ltx}}%
+\def@line@handler\f@ur{\@handle@line@ltx{\widowpenalty@ltx}{}{}}%
+\def@line@handler{5}{\@handle@line@ltx{\widowpenalty@ltx}{}{\brokenpenalty@ltx}}%
+\def@line@handler{6}{\@handle@line@ltx{\widowpenalty@ltx}{\clubpenalty@ltx}{}}%
+\def@line@handler{7}{\@handle@line@ltx{\widowpenalty@ltx}{\clubpenalty@ltx}{\brokenpenalty@ltx}}%
+\def@line@handler{8}{\@handle@line@ltx{\displaywidowpenalty@ltx}{}{}}%
+\def@line@handler{9}{\@handle@line@ltx{\displaywidowpenalty@ltx}{}{\brokenpenalty@ltx}}%
+\def@line@handler{10}{\@handle@line@ltx{\displaywidowpenalty@ltx}{\clubpenalty@ltx}{}}%
+\def@line@handler{11}{\@handle@line@ltx{\displaywidowpenalty@ltx}{\clubpenalty@ltx}{\brokenpenalty@ltx}}%
+%    \end{macrocode}
+%
+% The default handler for lines within a paragraph simply 
+% restores the value of the \cmd\penalty\ to the normal value.
+% If something more useful needs to be done, we can change the definition of \cmd\@@handle@line@ltx.
+%    \begin{macrocode}
+\def\@handle@line@ltx#1#2#3{%
+ \@@handle@line@ltx
+ \@tempcnta\lastpenalty
+ \@tempcntb\interlinepenalty@ltx\relax
+ \@if@empty{#1}{}{\advance\@tempcntb#1\relax}%
+ \@if@empty{#2}{}{\advance\@tempcntb#2\relax}%
+ \@if@empty{#3}{}{\advance\@tempcntb#3\relax}%
+ \penalty\@ifnum{\@tempcnta<\@tempcntb}{\@tempcntb}{\@tempcnta}%
+}%
+\let\@@handle@line@ltx\@empty
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\int@postparpenalty}
+% \begin{macro}{\int@vadjustpenalty}
+% \begin{macro}{\int@whatsitpenalty}
+% \begin{macro}{\int@predisplaypenalty}
+% \begin{macro}{\int@interdisplaylinepenalty}
+% \begin{macro}{\int@postdisplaypenalty}
+% \begin{macro}{\@handle@display@ltx}
+% \begin{macro}{\@@handle@display@ltx}
+% \begin{macro}{\handle@par@ltx}
+% We herewith define all the handlers for cases relating to display math:
+% last line before a display math,
+% last line of a display math, and a line within a display math.
+% We also handle the last line of a paragraph, a whatsit node, and a \cmd\vadjust.
+%    \begin{macrocode}
+\@tempcnta\int@parpenalty
+\def@next@handler\@tempcnta\int@postparpenalty{\reset@queues@ltx\handle@par@ltx}%
+\def@next@handler\@tempcnta\int@vadjustpenalty{\handle@vadjust@ltx}%
+\def@next@handler\@tempcnta\int@whatsitpenalty{\handle@whatsit@ltx}%
+\def@next@handler\@tempcnta\int@predisplaypenalty{\reset@queues@ltx\@handle@display@ltx{\predisplaypenalty@ltx}}%
+\def@next@handler\@tempcnta\int@interdisplaylinepenalty{\@handle@display@ltx{\interdisplaylinepenalty@ltx}}%
+\def@next@handler\@tempcnta\int@postdisplaypenalty{\@handle@display@ltx{\postdisplaypenalty@ltx}}%
+%    \end{macrocode}
+% The default handler for display math lines simply 
+% restores the value of the \cmd\penalty\ to the normal value.
+% If something more useful needs to be done, we can change the definition of \cmd\@@handle@display@ltx. 
+%    \begin{macrocode}
+\def\@handle@display@ltx#1{%
+ \@@handle@display@ltx
+ \@tempcnta\lastpenalty
+ \@tempcntb#1%
+ \penalty\@ifnum{\@tempcnta<\@tempcntb}{\@tempcntb}{\@tempcnta}%
+}%
+\let\@@handle@display@ltx\@empty
+%    \end{macrocode}
+%
+% We provide stub definitions for the handlers for the last line of a paragraph, a \cmd\vadjust, and a whatsit node (e.g., \cmd\write, \cmd\special). 
+% There is no canonical penalty for such cases.
+%    \begin{macrocode}
+\def\handle@par@ltx{}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% Note that a whatsit needs to be handled differently from a \cmd\vadjust:
+% a whatsit node does not affect the (crucial) depth of \cmd\box\cmd\@cclv, while the more
+% general \cmd\vadjust\ may cause any kind of vertical mode material to be interposed just below the line
+% we are trying to trap, in particular \cmd\vskip s and \cmd\penalty s.
+%
+% \begin{macro}{\set@linepenalties}
+% \begin{macro}{\restore@linepenalties}
+% \begin{macro}{\set@displaypenalties}
+% Now we define utility procedures that set up for a paragraph to be broken into lines, 
+% restoring the penalties afterwards.
+% 
+% Utility procedure \cmd\set@linepenalties\ systematically sets the penalties of paragraph breaking
+% to flag values, meanwhile storing away the normal values for access by the output routine. 
+%    \begin{macrocode}
+\def\set@linepenalties{%
+ \expandafter\def\expandafter\interlinepenalty@ltx\expandafter{\the\interlinepenalty}%
+ \interlinepenalty-\int@parpenalty
+ \expandafter\def\expandafter\brokenpenalty@ltx\expandafter{\the\brokenpenalty}%
+ \brokenpenalty\@ne
+ \expandafter\def\expandafter\clubpenalty@ltx\expandafter{\the\clubpenalty}%
+ \clubpenalty\tw@
+ \expandafter\def\expandafter\widowpenalty@ltx\expandafter{\the\widowpenalty}%
+ \widowpenalty\f@ur
+ \expandafter\def\expandafter\displaywidowpenalty@ltx\expandafter{\the\displaywidowpenalty}%
+ \displaywidowpenalty8\relax
+}%
+%    \end{macrocode}
+%
+% Utility procedure \cmd\restore@linepenalties\ restores the values of the penalty parameters that were
+% modified by \cmd\set@linepenalties.
+%    \begin{macrocode}
+\def\restore@linepenalties{%
+ \interlinepenalty\interlinepenalty@ltx
+ \brokenpenalty\brokenpenalty@ltx
+ \clubpenalty\clubpenalty@ltx
+ \widowpenalty\widowpenalty@ltx
+ \displaywidowpenalty\displaywidowpenalty@ltx
+ \relax
+}%
+%    \end{macrocode}
+%
+% In the following, the first argument should be a boolean (either \cmd\true@sw\ or \cmd\false@sw).
+%    \begin{macrocode}
+\def\set@displaypenalties#1{%
+ \expandafter\def\expandafter\predisplaypenalty@ltx\expandafter{\the\predisplaypenalty}%
+ \expandafter\def\expandafter\interdisplaylinepenalty@ltx\expandafter{\the\interdisplaylinepenalty}%
+ \expandafter\def\expandafter\postdisplaypenalty@ltx\expandafter{\the\postdisplaypenalty}%
+ \@ifhmode{\predisplaypenalty-\int@predisplaypenalty\relax}{}%
+ #1{\interdisplaylinepenalty-\int@interdisplaylinepenalty\relax}{}%
+ #1{\postdisplaypenalty-\int@postdisplaypenalty\relax}{}%
+}%
+%    \end{macrocode}
+% We provide no procedure to restore the respective penalties, because they are altered within a group:
+% \TeX 's context stack will automatically restore things.
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\enqueue@whatsit@ltx}%
+% \begin{macro}{\handle@whatsit@ltx}%
+% \begin{macro}{\do@whatsit}%
+% \begin{macro}{\@g@pop@ltx}%
+% Here is a facility for dealing with whatsit nodes while we are trapping paragraph lines. 
+% We simply enqueue a macro that will create the desired whatsit node, dequeueing it in the output routine.
+%    \begin{macrocode}
+\def\enqueue@whatsit@ltx#1{%
+ \gappdef\g@whatsit@queue{{#1}}%
+ \vadjust{\penalty-\int@whatsitpenalty}%
+}%
+\def\handle@whatsit@ltx{%
+ \unvbox\@cclv
+ \g@pop@ltx\g@whatsit@queue\@tempa
+ \expandafter\do@whatsit\expandafter{\@tempa}%
+}%
+\def\do@whatsit#1{}%
+\def\g@pop@ltx#1#2{%
+ \expandafter\@g@pop@ltx#1{}{}\@@#1#2%
+}%
+\def\@g@pop@ltx#1#2\@@#3#4{%
+ \gdef#3{#2}%
+ \def#4{#1}%
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\vspace}%
+% \begin{macro}{\pagebreak}%
+% \begin{macro}{\nopagebreak}%
+% \begin{macro}{\\}%
+% \begin{macro}{\@arrayparboxrestore}%
+% We wish to prevent \filename{lineno.sty} from patching \cmd\vspace\ and \cmd\pagebreak, 
+% because that package does it through global assignments, which is prone to failure. 
+%
+% We also wish to prevent that package from patching \cmd\@arrayparboxrestore, because
+% it prevents us from \cmd\unvbox ing vertical mode material into the MVL and numbering those
+% lines.
+% 
+% We start by retaining the original definitions of these commands, so we can restore them
+% if \filename{lineno.sty} does get loaded. 
+%    \begin{macrocode}
+\let\vspace@ltx\vspace
+\let\pagebreak@ltx\pagebreak
+\let\nopagebreak@ltx\nopagebreak
+\let\endline@ltx\\
+\let\@arrayparboxrestore@ltx\@arrayparboxrestore
+%    \end{macrocode}
+%
+% Next, we provide for line-wise processing by patching the procedures associated with these same three commands.
+%
+% Depending on the running version of \LaTeX, these commands use \cs{vskip} (before 2020-10-01), or
+% \cs{@vspace@calcify} to add \textsf{calc}-like support in the kernel.  To avoid duplicating the tests,
+% define a macro \cs{@tempa} that takes the right form of the primitive spacing command and defines \LaTeX's
+% spacing macros accordingly.
+%    \begin{macrocode}
+\def\@tempa#1{%
+%    \end{macrocode}
+%
+% There are exactly four core \LaTeX\ procedures that use \cmd\vadjust\ to insert vertical mode material 
+% into the main vertical list: \cmd\vspace, \cmd\pagebreak, \cmd\nopagebreak, and \cmd\\. 
+% Other commands may use \cmd\vadjust, but they are inserting an interrupt (via a penalty${}<10000$), 
+% and such a thing does not mask the depth of \cmd\box\cmd\@cclv, hence is permissible.
+%
+% In each case, we replace the core \LaTeX\ procedure with one that itself replaces \cmd\vadjust\ with
+% \cmd\ex@vadjust@ltx. The meaning of this procedure can be left as \cmd\vadjust, or it can be changed to
+% one that accomplishes the equivalent without masking the depth of \cmd\box\cmd\@cclv.
+% 
+% The first procedure is \cmd\@vspace, here shown in original form and in the patched alternative form. 
+% This procedure and \cmd\@vspacer\ implement the \cmd\vspace\ command.
+%
+%    \begin{macrocode}
+\def\@vspace@org ##1{%
+  \ifvmode
+    #1% \vskip #1
+    \vskip\z@skip
+   \else
+     \@bsphack
+     \vadjust{\@restorepar
+              #1% \vskip #1
+              \vskip\z@skip
+              }%
+     \@esphack
+   \fi
+}%
+\def\@vspace@ltx##1{%
+ \@ifvmode{%
+  #1% \vskip #1
+  \vskip\z@skip
+ }{%
+  \@bsphack
+  \ex@vadjust@ltx{%
+   \@restorepar
+   \nobreak
+   #1% \vskip #1
+   \vskip\z@skip
+  }%
+  \@esphack
+ }%
+}%
+%    \end{macrocode}
+% 
+% The second procedure is \cmd\@vspacer.
+%    \begin{macrocode}
+\def\@vspacer@org##1{%
+  \ifvmode
+    \dimen@\prevdepth
+    \hrule \@height\z@
+    \nobreak
+    #1%\vskip #1
+    \vskip\z@skip
+    \prevdepth\dimen@
+  \else
+    \@bsphack
+    \vadjust{\@restorepar
+             \hrule \@height\z@
+             \nobreak
+             #1%\vskip #1
+             \vskip\z@skip}%
+    \@esphack
+\fi
+}%
+\def\@vspacer@ltx##1{%
+ \@ifvmode{%
+  \dimen@\prevdepth
+  \hrule\@height\z@
+  \nobreak
+  #1%\vskip#1
+  \vskip\z@skip
+  \prevdepth\dimen@
+ }{%
+  \@bsphack
+  \ex@vadjust@ltx{%
+   \@restorepar
+   \hrule\@height\z@
+   \nobreak
+   #1%\vskip#1
+   \vskip\z@skip
+  }%
+  \@esphack
+ }%
+}%
+%    \end{macrocode}
+%
+% Now define the macros above conditionally depending on the \LaTeX version.
+%    \begin{macrocode}
+}
+\rvtx@ifformat@geq{2020/10/01}%
+  {\@tempa{\@vspace@calcify{#1}}}%
+  {\@tempa{\vskip #1 }}%
+%    \end{macrocode}
+%
+% The procedure \cmd\@no@pgbk\ implements both \cmd\pagebreak\ and \cmd\nopagebreak.
+%    \begin{macrocode}
+\def\@no@pgbk@org #1[#2]{%
+  \ifvmode
+    \penalty #1\@getpen{#2}%
+  \else
+    \@bsphack
+    \vadjust{\penalty #1\@getpen{#2}}%
+    \@esphack
+  \fi
+}%
+\def\@no@pgbk@ltx#1[#2]{%
+ \@ifvmode{%
+  \penalty#1\@getpen{#2}%
+ }{%
+  \@bsphack
+  \ex@vadjust@ltx{%
+   \penalty#1\@getpen{#2}%
+  }%
+  \@esphack
+ }%
+}%
+%    \end{macrocode}
+%
+% The command to end a line of type, \cmd\\, is defined via \cmd\DeclareRobustCommand,
+% so we must proceed carefully: 
+% A procedure is defined whose \cmd\long\cmd\csname\ is contructed via the incantation:
+% \cmd\csname\cmd\expandafter\cmd\@gobble\cmd\string\cmd\\ \cmd\endcsname.
+% Note the non-trivial space character after the \cmd\\: it is incorporated into 
+% the \cmd\csname.
+%
+% Here is the original core \LaTeX\ definition for 
+% the procedure involved, along with our revised version. 
+% \changes{2020/09/30}{4.2d}{Conditionally use \cs{protected} or \cs{long} to track \LaTeX{} changes.}
+%    \begin{macrocode}
+\rvtx@ifformat@geq{2020/02/02}%
+{\protected}{\long}\def\end@line@org{%
+ \let\reserved@e\relax
+ \let\reserved@f\relax
+ \@ifstar{%
+  \let\reserved@e\vadjust
+  \let\reserved@f\nobreak
+  \@xnewline
+ }%
+ \@xnewline
+}%
+\rvtx@ifformat@geq{2020/02/02}%
+{\protected}{\long}\def\end@line@ltx{%
+ \let\reserved@e\relax
+ \let\reserved@f\relax
+ \@ifstar{%
+  \let\reserved@e\ex@vadjust@ltx
+  \let\reserved@f\nobreak
+  \@xnewline
+ }{%
+  \@xnewline
+ }%
+}%
+%    \end{macrocode}
+% An additional procedure requiring patching has the following original core \LaTeX\
+% definition; we modify it correspondingly.
+%    \begin{macrocode}
+\def\@tempa#1{%
+  \def\@newline@org[##1]{%
+   \let\reserved@e\vadjust
+   \@gnewline{#1}% \vskip#1
+  }%
+  \def\@newline@ltx[##1]{%
+   \let\reserved@e\ex@vadjust@ltx
+   \@gnewline{#1}% \vskip#1
+  }%
+}
+\rvtx@ifformat@geq{2020/10/01}%
+  {\@tempa{\@vspace@calcify{#1}}}%
+  {\@tempa{\vskip #1}}%
+%    \end{macrocode}
+% We now install our patches. 
+% If some package overrides these macros, we will detect and complain.
+% 
+%    \begin{macrocode}
+ \@ifx{\@vspace\@vspace@org}{%
+  \@ifx{\@vspacer\@vspacer@org}{%
+   \@ifx{\@no@pgbk\@no@pgbk@org}{%
+    \@ifx{\@newline\@newline@org}{%
+     \expandafter\@ifx\expandafter{%
+       \csname\rvtx@ifformat@geq{2020/02/02}%
+         {\expandafter\@gobble\string\\}%
+         {\expandafter\@gobble\string\\ }\endcsname
+       \end@line@org
+     }{%
+       \true@sw
+     }{\false@sw}%
+    }{\false@sw}%
+   }{\false@sw}%
+  }{\false@sw}%
+ }{\false@sw}%
+ {%
+  \class@info{Overriding \string\@vspace, \string\@vspacer, \string\@no@pgbk, \string\@newline, and \string\\ }%
+  \let\@normalcr\end@line@ltx
+  \expandafter\let
+    \csname\rvtx@ifformat@geq{2020/02/02}%
+      {\expandafter\@gobble\string\\}%
+      {\expandafter\@gobble\string\\ }\endcsname\@normalcr
+  \let\@newline\@newline@ltx
+  \let\@vspace\@vspace@ltx
+  \let\@vspacer\@vspacer@ltx
+  \let\@no@pgbk\@no@pgbk@ltx
+ }{%
+  \class@warn{%
+   Failed to recognize \string\@vspace, \string\@vspacer, \string\@no@pgbk, \string\@newline, and \string\\; 
+   no patches applied. Please get a more up-to-date class,
+  }%
+ }%
+%    \end{macrocode}
+% Note that we have assigned the same meaning to \cmd\@normalcr, which is necessary to \LaTeX.
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% 
+% \begin{macro}{\ex@vadjust@ltx}
+% \begin{macro}{\enqueue@vadjust@ltx}
+% \begin{macro}{\handle@vadjust@ltx}
+% \begin{macro}{\g@vadjust@line}
+% \begin{macro}{\reset@queues@ltx}
+% Here we give the default definition for \cmd\ex@vadjust@ltx\ along with
+% the definitions for the alternative version and its the associated handler. 
+%    \begin{macrocode}
+\let\ex@vadjust@ltx\vadjust
+\def\enqueue@vadjust@ltx#1{%
+ \gappdef\g@vadjust@queue{{#1}}%
+ \vadjust{\penalty-\int@vadjustpenalty}%
+}%
+\def\handle@vadjust@ltx{%
+ \unvbox\@cclv
+ \g@pop@ltx\g@vadjust@queue\@tempa
+ \expandafter\gappdef\expandafter\g@vadjust@line\expandafter{\@tempa}%
+}%
+\let\g@vadjust@line\@empty
+%    \end{macrocode}
+% Procedure \cmd\reset@queues@ltx\ resets the whatsit queue and the \cmd\vadjust\ queues 
+% to their empty state. This should be done whenever we leave horizontal mode and
+% complete the processing of these queues: upon executing, effectively, primitive \cmd\par\
+% or interrupting a paragraph with display math. 
+%    \begin{macrocode}
+\def\reset@queues@ltx{%
+ \global\let\g@whatsit@queue\@empty
+ \global\let\g@vadjust@queue\@empty
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \section{Patching the lineno.sty package}
+%
+% \filename{lineno.sty} is a \LaTeX\ package that applies line numbering to a document.
+% The basic method is to give \cmd\interlinepenalty\ and like penalties such a value as 
+% to force a visit to the output routine, where the line of type is given its number. 
+% In order to properly measure the depth of \cmd\box\cmd\@cclv, it defers \cmd\vadjust\ 
+% commands that may insert \cmd\vskip\ or \cmd\penalty\ nodes.
+%
+% The implementation of that package, however, manipulates \cmd\holdinginserts\ in a dangerous
+% way: outside the safety of the output routine. It also alters the meaning of \cmd\vadjust\
+% using global assignments. We patch its code to avoid these problems. The \filename{ltxgrid}
+% package already has the needed mechanisms in place to do these jobs correctly.
+%
+% The methods we use can accomodate any values of penalties like \cmd\clubpenalty, etc:
+% we do not make assumptions about the range of values these penalty parameters could take.
+%
+%
+% \begin{macro}{\linenomathWithnumbers}
+% \begin{macro}{\linenomathNonumbers}
+% \begin{macro}{\endlinenomath}
+% \begin{macro}{\linenumberpar}
+% Here are the definitions of procedures in \filename{lineno.sty}
+% that alter \cmd\holdinginserts. They are current as of version v4.41, 2005/11/02.
+% We patch them to avoid doing this: in ltxgrid-based classes like REVTeX, the output routine properly manages \cmd\holdinginserts, so packages should not attempt to do so.
+% Also, we will want \cmd\linenumberpar\ to set \cmd\interlinepenaly\ to dispatch to \cmd\MakeLineNo. 
+%
+%    \begin{macrocode}
+\newcommand\linenomathWithnumbers@LN{%
+  \ifLineNumbers 
+    \ifnum\interlinepenalty>-\linenopenaltypar
+      \global\holdinginserts\thr@@ 
+      \advance\interlinepenalty \linenopenalty
+     \ifhmode
+      \advance\predisplaypenalty \linenopenalty
+     \fi 
+      \advance\postdisplaypenalty \linenopenalty
+      \advance\interdisplaylinepenalty \linenopenalty
+    \fi
+  \fi
+  \ignorespaces
+}%
+\newcommand\linenomathNonumbers@LN{%
+  \ifLineNumbers 
+    \ifnum\interlinepenalty>-\linenopenaltypar
+      \global\holdinginserts\thr@@ 
+      \advance\interlinepenalty \linenopenalty
+     \ifhmode
+      \advance\predisplaypenalty \linenopenalty
+     \fi 
+    \fi
+  \fi
+  \ignorespaces
+}%
+\def\endlinenomath@LN{% 
+  \ifLineNumbers
+   \global\holdinginserts\@LN@outer@holdins
+  \fi 
+  \global\@ignoretrue
+}
+\def\linenumberpar@LN{%
+  \ifvmode \@@@par \else 
+    \ifinner \@@@par \else
+      \xdef\@LN@outer@holdins{\the\holdinginserts}%
+      \advance \interlinepenalty \linenopenalty
+      \linenoprevgraf \prevgraf
+      \global \holdinginserts \thr@@ 
+      \@@@par
+      \ifnum\prevgraf>\linenoprevgraf
+        \penalty-\linenopenaltypar
+      \fi
+      \@LN@parpgbrk 
+      \global\holdinginserts\@LN@outer@holdins
+      \advance\interlinepenalty -\linenopenalty
+    \fi
+  \fi
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\class@documenthook}
+% We patch only if we recognize the definitions of all the procedures we are to patch. 
+%    \begin{macrocode}
+\appdef\class@documenthook{%
+ \@ifpackageloaded{lineno}{%
+  \@ifx{\linenomathWithnumbers\linenomathWithnumbers@LN}{%
+   \@ifx{\linenomathNonumbers\linenomathNonumbers@LN}{%
+    \@ifx{\endlinenomath\endlinenomath@LN}{%
+     \@ifx{\linenumberpar\linenumberpar@LN}{%
+      \true@sw
+     }{\false@sw}%
+    }{\false@sw}%
+   }{\false@sw}%
+  }{\false@sw}%
+  {%
+   \class@info{Overriding lineo.sty, restoring output routine,}%
+%    \end{macrocode}
+% We commence overriding the procedures of \filename{lineno.sty}.
+%    \begin{macrocode}
+   \let\linenumberpar\linenumberpar@ltx
+   \let\endlinenomath\endlinenomath@ltx
+   \expandafter\let\csname endlinenomath*\endcsname\endlinenomath@ltx
+   \let\linenomathWithnumbers\linenomathWithnumbers@ltx
+   \let\linenomathNonumbers\linenomathNonumbers@ltx
+%    \end{macrocode}
+% Override \filename{lineno.sty}'s equipment for \cmd\vadjust\ and \cmd\linelabel:
+% we have existing interrupts and handlers for these purposes. 
+%    \begin{macrocode}
+   \let\ex@vadjust@ltx\ex@vadjust@line
+   \let\@LN@postlabel\enqueue@whatsit@ltx
+   \let\do@whatsit\write@linelabel
+%    \end{macrocode}
+% Redirect handlers to those provided by \filename{lineno.sty}, and
+% give an appropriate meaning to the respective headpatch within the handlers.
+%    \begin{macrocode}
+   \let\handle@par@ltx\handle@par@LN
+   \let\@@handle@line@ltx\Make@LineNo@ltx
+   \let\@@handle@display@ltx\Make@LineNo@ltx
+%    \end{macrocode}
+% Next, we undo the action taken by \filename{lineno.sty} wherein it
+% took over the output routine. Instead, we service \filename{lineno.sty}
+% existing equipment of \filename{ltxgrid}.
+% We also revert the core \LaTeX\ definitions of 
+% \cmd\vspace, \cmd\pagebreak, \cmd\nopagebreak, and \cmd\\,
+% which that package takes over (we have our own ways of doing these things). 
+%    \begin{macrocode}
+   \output@latex{\natural@output}%
+   \let\vspace\vspace@ltx
+   \let\pagebreak\pagebreak@ltx
+   \let\nopagebreak\nopagebreak@ltx
+   \let\@arrayparboxrestore\@arrayparboxrestore@ltx
+   \let\\\endline@ltx
+%    \end{macrocode}
+% \changes{4.1f}{2009/07/07}{(AO, 515) Prevent line numbering within a footnote}
+% When line numbering  is in effect, we must avoid any attempt to number the lines of a footnote.
+%    \begin{macrocode}
+   \appdef\set@footnotefont{%
+    \let\par\@@@par
+    \let\@@par\@@@par
+   }%
+%    \end{macrocode}
+% At last, we detect if the \cmd\linenumbers\ command has already been given; 
+% if so, we do its assignments again, because we have changed the meaning of \cmd\linenumberpar. 
+%    \begin{macrocode}
+   \@if@sw\ifLineNumbers\fi{%
+    \class@info{Reinvoke \string\linenumbers}%
+    \let\@@par\linenumberpar
+    \@ifx{\@par\linenumberpar@LN}{\let\@par\linenumberpar}{}%
+    \@ifx{\par\linenumberpar@LN}{\let\par\linenumberpar}{}%
+   }{%
+    \class@info{Line numbering not turned on yet}%
+   }%
+%    \end{macrocode}
+% Here ends the ``true branch'' of the patch code.
+%    \begin{macrocode}
+  }{%
+%    \end{macrocode}
+% If the \filename{lineno.sty} package is loaded, but we fail to patch it, notify the user.
+%    \begin{macrocode}
+   \class@warn{Failed to recognize lineno.sty procedures; no patches applied. Please get a more up-to-date class.}%
+  }%
+ }{%
+%    \end{macrocode}
+% \filename{lineno.sty} is not loaded, so no patches are needed. 
+%    \begin{macrocode}
+ }%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\linenumberpar}
+% \begin{macro}{\@linenumberpar}
+% Procedure \cmd\linenumberpar\ takes the place of \cmd\par\ when line numbering is in effect; 
+% It executes the \cmd\par\ primitive if we are in vertical mode.
+% Otherwise we are in horizontal mode in the MVL and wish to end the current paragraph,
+% or we have \cmd\unvbox ed material onto the MVL. 
+% 
+%    \begin{macrocode}
+\def\linenumberpar@ltx{\@ifvmode{\@@@par}{\@linenumberpar}}%
+%    \end{macrocode}
+%
+% Procedure \cmd\@linenumberpar
+%    \begin{macrocode}
+\def\@linenumberpar{%
+%    \end{macrocode}
+% Prepare for our trip into the output routine by 
+% saving away the current value of \cmd\prevgraf. 
+%    \begin{macrocode}
+   \linenoprevgraf\prevgraf
+%    \end{macrocode}
+% The following will be used in the output routine dispatcher
+% to sense that we came from here. 
+%    \begin{macrocode}
+   \set@linepenalties
+%    \end{macrocode}
+% Finally, call primitive \cmd\par\ with the signal value of \cmd\interlinepenalty\ and friends. 
+%    \begin{macrocode}
+   \@@@par
+%    \end{macrocode}
+% We are now in vertical mode. 
+% If lines of type were contributed to the MVL (non-trivial paragraph),
+% we must force another trip into the output routine to apply
+% line numbering to the last line of the paragraph.
+%    \begin{macrocode}
+   \@ifnum{\prevgraf>\linenoprevgraf}{
+    \penalty-\int@postparpenalty
+   }{}%
+%    \end{macrocode}
+% Execute procedure \cmd\@LN@parpgbrk, which has been set up in the 
+% output routine for us to invoke here.
+% 
+%    \begin{macrocode}
+   \@LN@parpgbrk
+%    \end{macrocode}
+% To wrap things up, we restore the original value of \cmd\interlinepenalty\ and friends.
+%
+% Query: why not employ \TeX's context stack to do the restore?
+% Would there be something wrong with executing primitive \cmd\par\ within a group?
+%    \begin{macrocode}
+   \restore@linepenalties
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\linenomathWithnumbers}
+% \begin{macro}{\linenomathNonumbers}
+% Here are the patched definitions for the commands enabling 
+% line numbering in display math. 
+%    \begin{macrocode}
+\newcommand\linenomathWithnumbers@ltx{\@linenomathnumbers@ltx\true@sw}%
+\newcommand\linenomathNonumbers@ltx{\@linenomathnumbers@ltx\false@sw}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@linenomathnumbers}
+% \begin{macro}{\endlinenomath}
+% We have just begun a display math, and any paragraph we are setting will now end.
+% We set all relevant penalties to interrupt values; in the visit to the output routine, 
+% we will replace the penalty with its normal value. 
+%    \begin{macrocode}
+\def\@linenomathnumbers@ltx#1{%
+ \@if@sw\ifLineNumbers\fi{%
+   \set@linepenalties
+   \set@displaypenalties#1%
+ }{}%
+ \ignorespaces
+}%
+\def\endlinenomath@ltx{%
+ \global\@ignoretrue
+}%
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% We provide a handler for the last line of a paragraph.
+%    \begin{macrocode}
+\def\handle@par@LN{%
+ \Make@LineNo@ltx
+%    \end{macrocode}
+% After setting the line number, we arrange for an appropriate penalty to 
+% be laid down after this visit to the output routine ends.
+%
+% Query: why not contribute the penalty right here in the visit to the output routine?
+%    \begin{macrocode}
+ \@tempcnta\lastpenalty 
+ \@ifnum{\@tempcnta=\z@}{}{%
+  \expandafter\gdef
+  \expandafter\@LN@parpgbrk
+  \expandafter{% 
+   \expandafter\penalty
+               \the\@tempcnta
+%    \end{macrocode}
+% When \cmd\@LN@parpgbrk\ is executed, it resets itself to the default value,
+% \cmd\@LN@screenoff@pen. 
+%
+% Query: \cmd\@LN@screenoff@pen\ appears to try to restore the depth of the last box:
+% why is this being done outside the safety of the output routine?
+%    \begin{macrocode}
+   \global\let\@LN@parpgbrk\@LN@screenoff@pen
+  }%
+ }%
+}%
+%    \end{macrocode}
+%
+% \begin{macro}{\Make@LineNo}
+% The procedure \cmd\Make@LineNo\ sets the box containing the line number itself.
+%    \begin{macrocode}
+\def\Make@LineNo@ltx{%
+ \@LN@maybe@normalLineNumber
+%    \end{macrocode}
+% We measure the depth of \cmd\box\cmd\@cclv\ and unbox it.
+% At this point, it is crucial that that box have the same depth as that of the last 
+% box within it. 
+%
+% In the simple case, \cmd\box\cmd\@cclv\ is
+% a \cmd\vbox\ containing as its last box the \cmd\hbox\ of the paragraph we are processing.
+%
+% Query: under what circumstances will this \emph{not} be the case?
+%    \begin{macrocode}
+ \boxmaxdepth\maxdimen\setbox\z@\vbox{\unvbox\@cclv}%
+ \@tempdima\dp\z@
+ \unvbox\z@
+%    \end{macrocode}
+% Then we create the box with the line number, setting its height to zero.
+%    \begin{macrocode}
+ \sbox\@tempboxa{\hb@xt@\z@{\makeLineNumber}}%
+ \ht\@tempboxa\z@
+%    \end{macrocode}
+% With these preparations, we invoke \cmd\@LN@depthbox, which
+% lays that box down (with its depth appropriately set):
+% this procedure depends on our having set \cmd\@tempdima\ and \cmd\@tempboxa
+% (kinda kludgy way of passing arguments, really).
+%    \begin{macrocode}
+ \@LN@depthbox
+%    \end{macrocode}
+% Now increment the line number. I have relocated this token past \cmd\@LN@depthbox: 
+% this may induce a bug, but I am going to hereby force the issue: 
+% why split up the procedure that lays down boxes with a procedure that sets a register value?
+%    \begin{macrocode}
+ \stepLineNumber
+%    \end{macrocode}
+% Finally, execute the \cmd\vadjust s that fell within the line that we just handled. 
+%
+% Note that \cmd\enqueue@vadjust@ltx\ had queued up all the \cmd\vadjust\ commands for the paragraph
+% into \cmd\g@vadjust@queue, laying down an (\cmd\int@vadjustpenalty) interrupt in each ones' place.
+% The interrupts associated with this line of the paragraph have now moved the tokens to \cmd\g@vadjust@line,
+% which we now expand and execute.
+%    \begin{macrocode}
+ \g@vadjust@line
+ \global\let\g@vadjust@line\@empty
+}%
+%    \end{macrocode}
+% 
+%    \begin{macrocode}
+\def\write@linelabel#1{% 
+ \protected@write\@auxout{}{%
+  \string\newlabel{#1}{{\theLineNumber}{\thepage}{}{}{}}%
+ }% 
+}%
+%    \end{macrocode}
+% 
+%    \begin{macrocode}
+\def\ex@vadjust@line{%
+ \@if@sw\ifLineNumbers\fi{\enqueue@vadjust@ltx}{\vadjust}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% Note that the \cmd\linelabel\ commands use a mechanism different from \cmd\vadjust, 
+% embodied in the procedure \cmd\enqueue@vadjust@ltx, wherein the 
+% \cmd\write\ primitives are enqueued while the paragraph is being processed, each replaced with
+% an interrupt, then dequeued and executed by the interrupt handler, leaving a \cmd\write\ node
+% in place of the interrupt (just where the \cmd\vadjust 's vertical mode material would had been) 
+% just below the box containing the line of type. This \cmd\write, like all whatsits,
+% does not affect the depth of \cmd\box\cmd\@cclv, unlike the case of general vertical mode material,
+% which could have interfered.
+%
+% \section{End of the \file{ltxgrid} {\sc docstrip} module}
+% Here ends the module.
+%    \begin{macrocode}
+%</kernel>
+%    \end{macrocode}
+%
+% \Finale
+% %Here ends the programmer's documentation.
+% \endinput
+%
+\endinput
+%%EOF
-- 
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