% \iffalse
%<pfnote>%% Style file `pfnote'.
%<fnpos>%% Style file `fnpos'.
%<dblfnote>%% Style file `dblfnote'.
%% Copyright (C) 1999-2018
%%   Hiroshi Nakashima <h.nakashima@DOMAIN;  DOMAIN=media.kyoto-u.ac.jp>
%%   (Kyoto University)
%% 
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License distributed from CTAN
%% archives in directory macros/latex/base/lppl.txt; either
%% version 1 of the License, or any later version.
%% 
% \fi
%
% \CheckSum{802}
%% \CharacterTable
%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%%   Digits        \0\1\2\3\4\5\6\7\8\9
%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
%%
% \iffalse
%%
%<*dtx>
\ProvidesFile{yafoot.dtx}
%</dtx>
%<pfnote|fnpos|dblfnote>\def\next{LaTeX2e}
%<pfnote|fnpos|dblfnote>\ifx\fmtname\next
%<pfnote|fnpos|dblfnote>\def\next{
%<pfnote|fnpos|dblfnote>\NeedsTeXFormat{LaTeX2e}[1994/12/01]
%<pfnote>\ProvidesPackage{pfnote}}
%<fnpos>\ProvidesPackage{fnpos}}
%<dblfnote>\ProvidesPackage{dblfnote}}
%<pfnote|fnpos|dblfnote>\else\def\next[#1]{}\fi
%<pfnote|fnpos|dblfnote>\next
%<driver>\ProvidesFile{yafoot-man.tex}
% \fi
% \ProvidesFile{yafoot.dtx}
[2018/09/03 v1.1 ]
% \iffalse
%<*driver>
\documentclass{ltxdoc}
\usepackage{pfnote}
\usepackage{fnpos}
\usepackage{dblfnote}
\DisableCrossrefs
\PageIndex
\CodelineNumbered
\RecordChanges
%</driver>
%<driver>\OnlyDescription
%<driver>\def\ONLYDESCRIPTION{}
%<*driver>
\advance\textwidth4em
\DFNcolumnsep1.5\columnsep
\begin{document}
\DocInput{yafoot.dtx}
\end{document}
%</driver>
% \fi
% 
% \makeatletter
% 
% \newcount\ChangeCount \ChangeCount10000
% \def\changes@#1#2#3{%
%   \global\advance\ChangeCount\@ne
%   \protected@edef\@tempa{\noexpand\glossary{#1\levelchar
%                                  \number\ChangeCount
%                                  \actualchar
%                                  \ifx\saved@macroname\@empty
%                                    \generalname
%                                  \else
%                                    \string\verb\quotechar*
%                                    \verbatimchar\saved@macroname
%                                    \verbatimchar
%                                  \fi
%                                  :\levelchar #3}}%
%   \@tempa\endgroup\@esphack}
% 
% \def\theglossary{\onecolumn \glossary@prologue
%	\GlossaryParms \let\item\@idxitem
%       \rightskip 1em plus 1fil
%       \parfillskip-1em
%       \ignorespaces}
% \def\endtheglossary{\relax}
% 
% \changes{v0.1}{1991/10/29}
%	{The style pfnote is born.}
% \changes{v0.2}{1993/05/20}
%	{Footnote pushing function is posted to comp.text.tex.}
% \changes{v0.3}{1993/08/17}
%	{Exchanging footnotes and bottom floats in fnpos is posted to
%	 fj.comp.texhax.}
% \changes{v0.4}{1995/06/21}
%	{First version of dblfnote is posted to comp.text.tex.}
% \changes{v1.0}{1999/07/14}
%	{Three styles are merged into yafoot.dtx and rewritten.}
% \changes{v1.1-1}{2018/09/03}
%	{Fix a footnote coloring problem in \string\textsf{fnpos}. (2018/09/03)}
%
% \errorcontextlines10000
% \GetFileInfo{yafoot.dtx}
% \setcounter{IndexColumns}{2}
% 
% \def\bottomfraction{.9}
% \def\cs#1{\hbox{\tt\char\escapechar#1}}
% \def\Item{\vskip-\itemsep\vskip-\parsep\vskip0pt\item}
%
% \makeatletter
% \def\nosv{\catcode`\|12}
% 
% \def\eqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
% \global\@eqnswtrue
% \global\@eqcnt\z@\tabskip\@centering\let\\=\@eqncr
% $$\halign to \displaywidth\bgroup\hskip\@centering
%   $\displaystyle\tabskip\z@{##}$\@eqnsel&\global\@eqcnt\@ne
%   \hfil$\;{##}\;$\hfil
%   &\global\@eqcnt\tw@ $\displaystyle\tabskip\z@{##}$\hfil
%    \tabskip\@centering&\llap{##}\tabskip\z@\cr}
%
% \def\Meta#1{\penalty\@highpenalty
%	\hbox{{\tt\char`\{}{\it\meta{#1}}{\tt\char`\}}}}
% \def\opt#1{{\tt[}{\it\meta{#1}}{\tt]}}
% \def\optn#1{{\tt[#1]}}
% \def\arg#1{{\tt\char`\{#1\char`\}}}
%
% \let\latex@addmarginpar\@addmarginpar
% \let\latex@latex@warning@no@line\@latex@warning@no@line
% \def\@addmarginpar{\let\@latex@warning@no@line\@gobble
%	\latex@addmarginpar
%	\let\@latex@warning@no@line\latex@latex@warning@no@line}
% \let\@font@warning\@gobble
%
% \long\def\m@cro@#1#2{\endgroup \topsep\MacroTopsep \trivlist
%    \edef\saved@macroname{\string#2}
%   \def\makelabel##1{\llap{##1\hskip\@totalleftmargin}}
%   \if@inlabel
%     \let\@tempa\@empty \count@\macro@cnt
%     \loop \ifnum\count@>\z@
%       \edef\@tempa{\@tempa\hbox{\strut}}\advance\count@\m@ne \repeat
%     \edef\makelabel##1{\llap{\vtop to\baselineskip
%                                {\@tempa\hbox{##1}\vss}
%			       \hskip\@totalleftmargin}}
%     \advance \macro@cnt \@ne
%   \else  \macro@cnt\@ne  \fi
%   \edef\@tempa{\noexpand\item[
%      #1
%        \noexpand\PrintMacroName
%      \else
%        \noexpand\PrintEnvName
%      \fi
%      {\string#2}]}
%   \@tempa
%   \global\advance\c@CodelineNo\@ne
%    #1
%       \SpecialMainIndex{#2}\nobreak
%       \DoNotIndex{#2}
%    \else
%       \SpecialMainEnvIndex{#2}\nobreak
%    \fi
%   \global\advance\c@CodelineNo\m@ne
%   \ignorespaces}
% 
% \def\dummymacro{\topsep\MacroTopsep \trivlist \item[]}
% \let\enddummymacro\endtrivlist
% 
% \def\DescribeOpt{\leavevmode\@bsphack\begingroup\MakePrivateLetters
%   \Describe@Opt}
% \def\Describe@Opt#1{\endgroup \Describe@pt{#1}}
% \def\Describe@pt#1#2{
%               \marginpar{\raggedleft\PrintDescribeMacro{#1}}
% 		\SpecialOptUsageIndex{#1}{#2}}
% \def\SpecialOptUsageIndex#1#2{
% 	\index{#1\actualchar{\protect\ttfamily#1} (#2)\encapchar usage}
%	\index{#2s:\levelchar{\protect\ttfamily#1}\encapchar usage}
%	\@esphack\ignorespaces}
% \def\SpecialOptMainIndex#1#2{
% 	\index{#1\actualchar{\protect\ttfamily#1} (#2)\encapchar main}
%	\index{#2s:\levelchar{\protect\ttfamily#1}\encapchar main}
%	\@esphack\ignorespaces}
% \def\SpecialOptIndex#1#2{
% 	\index{#1\actualchar{\protect\ttfamily#1} (#2)}
%	\index{#2s:\levelchar{\protect\ttfamily#1}}
%	\@esphack\ignorespaces}
% \def\SpecialOptIndexS#1#2{
% 	\index{#1\actualchar{\protect\ttfamily#1} (#2)}
%	\index{#2es:\levelchar{\protect\ttfamily#1}}
%	\@esphack\ignorespaces}
%
% \begingroup
% \gdef\@sverbcat{\catcode`\@\active\catcode`\#\active}
% \catcode`\@\active \gdef@{\char`\@\penalty\exhyphenpenalty}
% \catcode`\#\active \gdef#{\penalty\exhyphenpenalty}
% \endgroup
% \let\latex@sverb\@sverb
% \def\@sverb{\@sverbcat\latex@sverb}
%
% \def\theglossary{\onecolumn \glossary@prologue
%	\GlossaryParms \let\item\@idxitem \ignorespaces}
% \def\endtheglossary{\relax}
% 
% 
%
% \def\bracepair{`{\tt\char`\{\char`\}'}}
%
% \ifx\ONLYDESCRIPTION\undefined\else
% \let\SpecialUsageIndex\SpecialMainIndex
% \let\SpecialOptUsageIndex\SpecialOptMainIndex
% \fi
% 
% 
%
% \title{\textsf{pfnote}, \textsf{fnpos} and \textsf{dblfnote}\\
%	Packages for Footnotes\thanks{
%	This file has version number \fileversion, last revised \filedate.}}
% \author{Hiroshi Nakashima\\(Kyoto University)}
% \date{\filedate}
% \maketitle
% 
% \begin{abstract}
% This file provides three style files; \textsf{pfnote} to enclose footnote
% numbering in a page;  \textsf{fnpos} to control the vertical position of
% footnotes;  \textsf{dblfnote} to make footnote double-columned.
% \end{abstract}
%
% \tableofcontents
% \newpage
%
% 
% \section{Introduction}
% \label{sec:intro}
%
% \LaTeX{} users often bother about fine points of footnote.  How can I
% reset |footnote| counter when a page is produced in order to keep the
% counter from having too large, say 30, in a document with many footnotes?
% How can I place footnotes at more appropriate position?  How can I make
% footnotes double-columned while main text is single-columned?
%
% The style files distributed with this document will solve these problems.
% You will have the following three style files by processing
% \textsf{yafoot.dtx}\footnote{
%
% It stands for ``Yet Another FOOTnote.''}
%
% with \textsf{docstrip}.
%
% \begin{description}
% \item[\textsf{pfnote}]
% \DescribeOpt{pfnote}{style file}
% provides a new version of |\footnote| to make footnote numbering enclosed 
% in a page.  That is, the counter |footnote| is reset whenever a page is
% produced and thus the first footnote in a page is numbered 1 no matter how 
% it stands in the sequence of footnotes in a document.  Since this document 
% itself uses \textsf{pfnote}, you will see how footnotes are numbered.
%
% \item[\textsf{fnpos}]
% \DescribeOpt{fnpos}{style file}
% provides following commands to control the vertical position of footnotes.
%
% \begin{itemize}
% \item
% \DescribeMacro{\makeFNbottom}
% \DescribeMacro{\makeFNmid}
% |\makeFNbottom| makes footnotes always placed at the bottom of a
% |\ragged#bottom| page, while |\makeFNmid| allows footnotes directly follow
% the main text of a page as standard \LaTeX{} does.
%
% \item
% \DescribeMacro{\makeFNbelow}
% \DescribeMacro{\makeFNabove}
% |\makeFNbelow| places footnotes below bottom floats (i.e. figures and
% tables), while |\makeFNabove| is to place footnotes above bottom floats as
% standard \LaTeX{} does.
% \end{itemize}
%
% This document also uses \textsf{fnpos} to make footnotes {\em bottom} and
% {\em below}\footnote{
%
% But the effect will be hardly seen except in the right column of
% page~\pageref{pag:shfnp-2} where we show the effect explicitly.}.
%
% The first version of these commands are posted by the author to news
% groups |comp.text.tex| and |fj.comp.texhax| as the answers to the posts by
% Martin Boyer and Nobuaki Minematsu.
%
% \item[\textsf{dblfnote}]
% \DescribeOpt{dblfnote}{style file}
% makes footnotes double-columned.  It also provides a few commands to
% control column breaking.  The first version of the style file is created
% for Tim Armstrong's post to |comp.text.tex|.  Since this document uses
% \textsf{dblfnote}, you will find that the footnotes\footnote{
%.
% This document has many footnotes, some of which are just to show how our
% footnote mechanisms work.}
%
% in this page are double-columned.
% \end{description}
%
% Note that these style files may be used either solely, or combined each
% other as done in this document.
%
% 
%
% \section{Usage}
% \label{sec:usage}
% \subsection{Loading Style Files}
% \label{sec:usage-load}
%
% All the three style files are usable to both \LaTeXe{} and \LaTeX-2.09
% users with their standard package loading declaration.  If you use
% \LaTeXe{} and wish to load, for example, \textsf{pfnote} and
% \textsf{fnpos}, simply do the following.
%
% \begin{quote}
% \SpecialUsageIndex{\usepackage}
% |\usepackage{pfnote}|\\
% |\usepackage{fnpos}|
% \end{quote}
%
% If you still love \LaTeX-2.09, the following is what you have to do.
%
% \begin{quote}
% \SpecialUsageIndex{\documentstyle}
% |\documentstyle[..,pfnote,fnpos,...]|\Meta{main-style}
% \end{quote}
%
% Note that any combination of three styles are allowed and they are
% insensitive to their loading order.
%
% 
% 
% \subsection{\textsf{pfnote}: Enclose Footnote Numbers within a Page}
% \label{sec:usage-pfnote}
%
% \DescribeOpt{pfnote}{style file}
% Just loading \textsf{pfnote} is everything that you have to do to make
% footnote numbering enclosed in a page\footnote{
%
% Here you will find this fourth footnote is numbered one.}.
%
% Only one thing you have to remember is that footnote numbers will be
% adjusted after you run \LaTeX{} {\em twice}, as |\ref|-erences to
% |\label|-s are.
%
% 
%
% \subsection{\textsf{fnpos}: Control Vertical Position of Footnotes}
% \label{sec:usage-fnpos}
%
% \DescribeOpt{fnpos}{style file}
% The following four commands are available to control the vertical position
% of footnotes.
%
% \begin{description}
% \item[\cs{makeFNbottom}]
% \DescribeMacro{\makeFNbottom}
% \SpecialIndex{\raggedbottom}
% makes footnotes always placed at the bottom of a |\raggedbottom| page,
% even if the page is too short to push the footnotes to its bottom because, 
% for example, the page is broken just before a tall object such as a
% |tabular|.  This is default.
%
% \item[\cs{makeFNmid}]
% \DescribeMacro{\maekFNmid}
% cancels the effect of |\makeFNbottom| to allow footnotes directly follow
% the main text of a page as standard \LaTeX{} does.
%
% \item[\cs{makeFNbelow}]
% \DescribeMacro{\maekFNbelow}
% places footnotes {\em below} bottom floats (i.e. figures and tables).
% This is default.
%
% \item[\cs{makeFNabove}]
% \DescribeMacro{\maekFNabove}
% cancels the effect of |\makeFNbelow| to place footnotes {\em above} bottom 
% floats as standard \LaTeX{} does.
% \end{description}
%
% Note that if you are using p\LaTeX{}, a Japanese version of \LaTeX, it
% might be unnecessary to use \textsf{pfnote} because p\LaTeX{} does what
% |\makeFNbottom| and |\makeFNbelow| do\footnote{
%
% Very strictly speaking, the mechanism of p\LaTeX{} is slightly different
% from that of \textsf{fnpos} but the difference is hardly recognizable.}.
%
% However, if you wish to follow the real \LaTeX's standard, |\makeFNmid|
% and |\makeFNabove| will do for you.
%
% The following two two-columned pages show the effects of the commands.
%
% \newpage
% \twocolumn
% \def\showfnposleaders{\xleaders
%	\hbox to\hsize{\hss.\vrule height.3\baselineskip width0pt\hss}\vfil}
% \def\showfnpos#1#2#3{\par#1#2\noindent
%	This column is typeset with \texttt{\string#1} and \texttt{\string#2}
%	\footnote{#3}.\par\nobreak
%	\vbox to.4\textheight{
%		\showfnposleaders\smallskip
%		\centerline{(Main text of this column is here.)}\smallskip
%		\showfnposleaders}
%	\begin{figure}[b]
%	\fboxsep0pt
%	\hbox{\fbox{\vbox to.4\textheight{\vfil
%		\centerline{Here is a bottom float.}\vfil}}}
%	\end{figure}
%	\break}
%
% \label{pag:shfnp-1}
% \showfnpos\makeFNmid\makeFNabove{
%	Therefore, this footnote is {\em above} the bottom float leaving
%	spaces at the bottom of this column.}
%
% \showfnpos\makeFNmid\makeFNbelow{
%	Therefore, this footnote is {\em below} the bottom float still
%	leaving spaces at the bottom of this column.}
%
% \label{pag:shfnp-2}
% \showfnpos\makeFNbottom\makeFNabove{
%	Therefore, this footnote is {\em above} the bottom float that is
%	pushed to the {\em bottom} of this column together with this footnote.}
%
% \showfnpos\makeFNbottom\makeFNbelow{
%	Therefore, this footnote is {\em below} the bottom float, and at the 
%	{\em bottom} of this column alone.}
%
% 
% 
% \newpage
% \onecolumn\par
% \subsection{\textsf{dblfnote}: Make Footnotes Double-Columned}
%
% \DescribeOpt{dblfnote}{style file}
% Simply loading \textsf{dblfnote} will make footnotes double-columned.  For 
% fine tuning of double-columning, however, you have a few style parameters
% and commands as follows.
%
% \begin{description}
% \item[\texttt{DFNsloppiness}]
% \DescribeOpt{DFNsloppiness}{counter}%
% defines how sloppy paragrahs in footnotes are typeset.  Since lines of
% footnotes are narrow, you might wish to typeset footnotes in some
% |\sloppy| manner in order to avoid underfull.  Setting |DFNsloppiness| to
% larger value up to 9999, footnote paragraphs will be sloppier.  The
% default is 5000.
%
% \item[\cs{DFNcolumnsep}]
% \begin{DFNinhibitcbreak}%
% \DescribeMacro{\DFNcolumnsep}%
% \SpecialIndex{\columnsep}%
% is the distance of footnote columns is specified by the value of
% |\DFNcolumn#sep|.  If you don't set this parameter explicitly\footnote{
%
% Strictly speaking, unless you set a non-negative value in the document
% preamble.},
%
% the value is that of |\columnsep|.  For example, the author set
% |\DFNcolumnsep| to $1.5\times\hbox{|\columnsep|}$ in this document.
% \end{DFNinhibitcbreak}
%
% \item[\cs{DFNcolumnwidth}]
% \DescribeMacro{\DFNcolumnwidth}%
% is the width of a footnote column.  If you don't set this parameter
% explicitly, as expected, it is automatically set to
% $(|\textwidth|-|\DFNcolumnsep|)/2$.
%
% \item[\cs{DFNallowcbreak}]
% \DescribeMacro{\DFNallowcbreak}
% \DescribeMacro{\DFNinhibitcbreak}
% allows a footnote is broken into two columns, while {\bfseries
% |\DFNinhibitcbreak|} inhibits it.  In default, column breaking is allowed.
%
% \item[\cs{DFNtrysingle}]
% \DescribeMacro{\DFNtrysingle}
% \DescribeMacro{\DFNalwaysdouble}
% places footnotes only in the left column if the page containing them has
% enough space as shown in pages~1,
% \pageref{sec:usage-fnpos} and this page, while {\bfseries
% |\DFNalwaysdouble|} makes them double-columned (almost) always.  In
% default, single-columning is tried.
%
% \item[\cs{DFNruleleft}]
% \DescribeMacro{\DFNruleleft}
% \DescribeMacro{\DFNruleboth}
% draws |\footnoterule| over footnotes in left column only, while {\bfseries
% |\DFNrule#both|} draws in both columns.  In default, the rule is drawn in
% left column only.
% \end{description}
%
% \SpecialIndex{\twocolumn}
% \SpecialIndex{\onecolumn}
% Note that \textsf{dblfnote} will do nothing if |\twocolumn| is in effect,
% as shown in pages~\pageref{pag:shfnp-1} and~\pageref{pag:shfnp-2}.  That
% is, footnotes are put as in usual double-coulumned document.  If you
% change the page structure to |\onecolumn|, the mechanism of
% \textsf{dblfnote} is enabled again as shown in this page.
% 
% 
% \section{Known Problems}
% \label{sec:prob}
%
% \begin{enumerate}
% \item
% \SpecialOptIndex{minipage}{environment}
% The style \textsf{pfnote} does not enlose the number of footnotes in
% |minipage| environment.
% 
% \item
% The style \textsf{dblfnote} may mistakingly produce a little bit too
% short pages if an extremely long paragraph has footnotes.  More
% specifically, if a paragraph runs across three or more pages $p_1$,
% \ldots, $p_n$, and its first and last footnote appears in $p_i$ ($i\leq n-2$)
% and $p_j$ ($j>i$), pages $p_{i+1}$ to $p_j$ may be a little bit too short
% especially for those without footnotes.
% \end{enumerate}
% 
% 
%
% \IndexPrologue{\newpage\section*{Index}
% Underlined number refers to the page where the specification of
% corresponding entry is described.}
% \StopEventually{
% \section*{Acknowledgments}
%
% The author thanks to Martin Boyer and Nobuaki Minematsu whose posts to
% news groups triggered writing very first version of macros in
% \textsf{fnpos}, and to Tim Armstrong whose post to \texttt{comp.text.tex}
% encouraged him to make the first version of \textsf{dblfnote} that
% requires considerable hack.  He also thanks to Hironobu Yamashita who
% found a bug, hidden in \textsf{fnpos} for 19 years (!!), by which
% footnotes were colored inappropriately. 
%
% For the implementation of three style files, the author refers the base
% implementations of the macros for \cs{footnote} and for \cs{output}
% routine.  These macros are written by Leslie Lamport as a part of
% \LaTeX-2.09 and \LaTeXe{} (1997/12/01) to which Johannes Braams and other
% authors also contributed.
%
% \PrintIndex}
%
% 
%
% \newpage
% \section{Implementation}
% \label{sec:imp}
% \subsection{Tricks for Compatibility}
% \label{sec:imp-compat}
%
% At the very beginning of each style file, we checks whether it is
% loaded by \LaTeXe{} or \LaTeX-2.09, and then declares |\NeedsTeXFormat|
% and |\ProvidesPackage| if \LaTeXe{}.  This part is embedded at the
% beginning of \textsf{yafoot.dtx} in a tricky manner to let
% \textsf{docstrip} produce the following code, for example for
% \textsf{pfnote}.
% \SpecialIndex{\NeedsTeXFormat}
% \SpecialIndex{\ProvidesPackage}
%
%\begin{quote}
%\begin{verbatim}
%\def\next{LaTeX2e}
%\ifx\fmtname\next
%\def\next{
%\NeedsTeXFormat{LaTeX2e}[1994/12/01]
%\ProvidesPackage{pfnote}}
%\else\def\next[#1]{}\fi
%\next
%[1999/07/14 v1.0 ]
%\end{verbatim}
%\end{quote}
%
% 
%
% \subsection{\textsf{pfnote}}
% \label{sec:imp-pfnote}
%
% \iffalse
%<*pfnote>
% \fi
% To enclose |\c@footnote| within a page, we identify each footnote $f_i$
% by a global serial number $i$ and associate it with the {\em physical}
% page number $p_i$ where it appears.  These attributes $i$ and $p_i$ are
% written to |.aux| file in the form of |\pfn@fnote|\Meta{$i$}\Meta{$p_i$}.
% This macro is evaluated in \LaTeX's |\document| and |\def|-ines a macro
% whose name is ``|\pfn@fn|\meta{$i$}'' and body is \meta{$p_i$}.
%
% Then, when we process the footnote $f_i$, we can have $p_i$ by evaluating
% |\pfn@fn|\meta{$i$} and compare it with $p_{i-1}$.  If $p_i\neq p_{i-1}$,
% $f_i$ is the first footnote in page $p_i$ and thus its number should be
% one.  Otherwise, the number of $f_i$ should be that of $f_{i-1}$ plus one.
%
% \begin{macro}{\pfn@fnotectr}
% \begin{macro}{\pfn@page}
% \begin{macro}{\pfn@pageprev}
% To implement the algorithm shown above, we use three |\count| registers;
% |\pfn@fnotectr| for $i$ initialized to zero; |\pfn@page| for physical page
% number initialized to one; and |\pfn@pageprev| to keep $p_{i-1}$ with
% initial value zero.  Note that |\pfn@page| is not |\c@page| but has
% physical page number, and thus any $p_i$ cannot be zero that is the initial
% value of |\pfn@pageprev|.
% \end{macro}\end{macro}\end{macro}
%
%    \begin{macrocode}

\newcount\pfn@fnotectr \pfn@fnotectr\z@
\newcount\pfn@page \pfn@page\@ne
\newcount\pfn@pageprev \pfn@pageprev\z@

%    \end{macrocode}
%
% \begin{macro}{\pfn@footnote}
% \begin{macro}{\footnote}
% \begin{macro}{\pfn@footnotemark}
% \begin{macro}{\footnotemark}
% \begin{macro}{\pfn@mpfn}
% We have to modify |\footnote| and |\footnotemark| so that they invoke
% |\pfn@adjust| to do what we described at the beginning of this section, if 
% they refer and increment |\c@footnote|.  In order to minimize
% copy-and-modify of their original codes, we simply call their original
% versions, |\pfn@footnote| and |\pfn@footnotemark|, if optional argument is 
% given accepting a little bit performance degradation by double checking of 
% the optional argument\footnote{
%
% We of course know that we can call \cs{@xfootnote} and
% \cs{@xfootnotemark}, but this implementation is safer.}.
%
% Otherwise, |\pfn@adjust| is invoked if |\@mpfn| is ``|footnote|'', the
% body of |\pfn@mpfn| in the case of |\footnote|, or always in the case of
% |\footnotemark|.  Thus |mpfootnote| is eliminated from our mechanism as
% shown in \S\ref{sec:prob}, although including it is not hard.
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
%
%    \begin{macrocode}
\let\pfn@footnote\footnote
\def\footnote{\@ifnextchar[%]
        {\pfn@footnote}%
        {\ifx\@mpfn\pfn@mpfn \pfn@adjust \fi \pfn@footnote}}
\let\pfn@footnotemark\footnotemark
\def\footnotemark{\@ifnextchar[%]
        {\pfn@footnotemark}{\pfn@adjust \pfn@footnotemark}}
\let\pfn@mpfn\@mpfn

%    \end{macrocode}
%
% \begin{macro}{\pfn@adjust}
% The main procedure of enclosing is performed by |\pfn@adjust|.  First,
% after |\global|-ly incrementing |\pfn@fnotectr| ($i$), it |\write|-s
% |\pfn@fnpage|\Meta{$i$}\Meta{$P$} by well-known technique of the
% combination of delayed evaluation of physical page number $P$ and
% immediate evaluation of other staffs.
%
% Then it obtains $p_i$ by evaluating |\pfn@fn|$i$ and compares it to
% $p_{i-1}$ in |\pfn@pageprev|.  If they are not equal, |\c@footnote| is
% reset to make $f_i$ have number one, and |\pfn@pageprev| is set to $p_i$.
% Since we also reset |\c@footnote| if |\pfn@fn|$i$ is undefined, all the
% footnotes will have number one on the first run of \LaTeX{} for a
% document.
% \end{macro}
%
%    \begin{macrocode}
\def\pfn@adjust{\global\advance\pfn@fnotectr by\@ne
        \if@filesw
                \edef\@tempa{\write\@auxout{\string\pfn@fnpage
                        {\number\pfn@fnotectr}%
                        {\noexpand\number\noexpand\pfn@page}}}\@tempa \fi
        \expandafter\ifx\csname pfn@fn\number\pfn@fnotectr\endcsname\relax
                \global\c@footnote\z@ \else
        \expandafter\@tempcnta\csname pfn@fn\number\pfn@fnotectr\endcsname
        \relax \ifnum\@tempcnta=\pfn@pageprev\else
                \global\pfn@pageprev\@tempcnta \global\c@footnote\z@ \fi \fi}

%    \end{macrocode}
%
% \begin{macro}{\pfn@fnpage}
% The macro |\pfn@fnpage|\Meta{$i$}\Meta{$p_i$} written in |.aux| and
% evaluated in |\document| simply |\def|-ines |\pfn@fn|$i$ with the body
% $p_i$.
% \end{macro}
%
%    \begin{macrocode}
\def\pfn@fnpage#1#2{\global\@namedef{pfn@fn#1}{#2}}

%    \end{macrocode}
%
% \begin{macro}{\pfn@outputpage}
% \begin{macro}{\@outputpage}
% To keep track physical page number in |\pfn@page|, we modify
% |\@outputpage| so that it increments |\pfn@page| when it does |\c@page|.
% \end{macro}\end{macro}
%
%    \begin{macrocode}
\let\pfn@outputpage\@outputpage
\def\@outputpage{\pfn@outputpage \global\advance\pfn@page\@ne}
%    \end{macrocode}
%
% \iffalse
%</pfnote>
% \fi
%
% 
%
% \subsection{\textsf{fnpos}}
% \label{sec:imp-fnpos}
%
% \iffalse
%<*fnpos>
% \fi
% \begin{macro}{\iffnp@bottom}
% \begin{macro}{\iffnp@below}
% To control the position of footnotes, we introduce two switches;
% |\iffnp@bottom| is true if |\makeFNbottom| is in effect;  |\iffnp@below|
% is true if |\makeFNbelow| is in effect.  In default, they both are true.
% \end{macro}\end{macro}
%
%    \begin{macrocode}

\newif\iffnp@bottom \fnp@bottomtrue
\newif\iffnp@below \fnp@belowtrue

%    \end{macrocode}
%
% \newpage
% \begin{macro}{\makeFNbottom}
% \begin{macro}{\makeFNmid}
% \begin{macro}{\makeFNbelow}
% \begin{macro}{\makeFNabove}
% User interface macros are trivial, i.e. they turn the switches true or false.
% \end{macro}\end{macro}\end{macro}\end{macro}
%
%    \begin{macrocode}
\def\makeFNbottom{\fnp@bottomtrue}
\def\makeFNmid{\fnp@bottomfalse}
\def\makeFNbelow{\fnp@belowtrue}
\def\makeFNabove{\fnp@belowfalse}

%    \end{macrocode}
%
% \begin{macro}{\@makecol}
% \changes{v1.1-1}{2018/09/03}
%	{Remove inappropriate spaces preceeding three \cs{endcsname}.}
% \begin{macro}{\fnp@textbottom}
% The essential part of \textsf{fnpos} is a modified version of |\@makecol|.
% If |\iffnp@below| is true, we reverse the order of |\@combinefloats| and
% the insertion of |\footins|.  At the insertion of |\footins|, we insert
% |\@textbottom| prior to |\footins| to push it to the bottom if
% |\iffnp@bottom| is true.  We also temporarily nullify |\@textbottom|,
% whose definition is saved into |\fnp@textbottom|, if it has been inserted
% with |\footins| in order to keep the following |\@outputbox| construction
% in |\@makecol| or |\@makespecialcolbox| from inserting it again.
%
% Here we discuss a few compatibility issues.  In \LaTeXe, |\footins|
% inserted in the construct of |\color@begroup| and |\color@endgroup| which
% \LaTeX-2.09 does not have.  Thus we call them and |\normalcolor| by
% |\csname|\slash |\endcsname| construct to allow they are undefined.
%
% The |\insert|-ion object |\@kludgeins| and the macro |\@makespecialcolbox|
% are also \LaTeXe's new comers for |\enlargethispage|.  For \LaTeX-2.09, we
% make |\@klugeins| |\let|-equal to |\voidb@x| that will never be a |\vbox|,
% and thus |\@makespecialcolbox| will never be expanded.
%
% We also have to take care of p\LaTeX{} whose |\@makespecialcolbox| inserts
% |\footins| and |\@texbottom| as we do for |\makeFNbottom| and
% |\makeFNbelow|.  However, since |\footins| is set to void by our insertion
% and |\@textbottom| is nullified if |\iffnp@bottom| is true, these
% insertions will have no effect as have to be.
% \end{macro}\end{macro}
%
%    \begin{macrocode}
\def\@makecol{\setbox\@outputbox\box\@cclv
        \xdef\@freelist{\@freelist\@midlist}\global\let\@midlist\@empty
        \iffnp@below \@combinefloats \fi
        \let\fnp@textbottom\@textbottom
        \ifvoid\footins\else
                \setbox\@outputbox\vbox{\boxmaxdepth\maxdepth
                        \unvbox\@outputbox
                        \iffnp@bottom \@textbottom \fi
                        \vskip\skip\footins
                        \csname color@begingroup\endcsname
                        \csname normalcolor\endcsname
                        \footnoterule \unvbox\footins
                        \csname color@endgroup\endcsname}%
                \iffnp@bottom \let\@textbottom\relax \fi \fi
        \iffnp@below\else \@combinefloats \fi
        \ifvbox\@kludgeins \@makespecialcolbox
        \else \setbox\@outputbox\vbox to\@colht{\@texttop
                \dimen@\dp\@outputbox \unvbox\@outputbox
                \vskip-\dimen@ \@textbottom}\fi
        \let\@textbottom\fnp@textbottom
        \global \maxdepth \@maxdepth}
\ifx\@kludgeins\undefined \let\@kludgeins\voidb@x \fi
%    \end{macrocode}
%
% \iffalse
%</fnpos>
% \fi
% 
%
% \subsection{\textsf{dblfnote}}
% \label{sec:imp-dblfnote}
%
% \iffalse
%<*dblfnote>
% \fi
% 
% \subsubsection{Problems and Solutions}
% \label{sec:imp-dfn-ovv}
%
% \def\DH{{\mit\Delta}H}
% 
% \LaTeX's |\footnote| utilizes \TeX's mechanism |\insert| that is perfectly 
% fit to the purpose.  Roughly speaking, |\footnote|\Meta{text} invokes
% |\insert\footins|\Meta{text$'$} to do the following.
%
% \begin{enumerate}
% \item
% \meta{text$'$} is kept in a special place, properly contributing to
% \TeX's page breaking mechanism with their height and depth.
%
% \item
% When the |\output| routine is invoked with the contents of a page
% including {\em footnoted} text, it is also given \meta{text$'$}, together 
% with other |\footnote| texts which should appear in the page, through the
% box |\footins|.  The page breaking mechanism will never, well hardly
% ever\footnote{
%
% See Exercise 15.13 of \TeX{}book for the possibility of placing a footnote
% text in a page other than that its reference appears.},
%
% miss to couple \meta{text$'$} and its reference in main text.
%
% \item
% The |\output| routine put |\footins| at the bottom of the page.
% \end{enumerate}
%
% This simple mechanism, however, cannot be straightforwardly applied to our 
% double-columned footnotes.  The major difficulty lies in the fact that
% when |\footnote| is processed we cannot know how \meta{text$'$}
% contributes to the page in which it and its reference appear after it is
% double-columned with other footnote texts.  For example, \TeX{}book shows
% a simple estimation method setting |\count\footnote| to 500 so that a half 
% (500/1000) of the height plus depth of \meta{text$'$} contributes to the
% page.  This method, however, will underestimate the contribution of
% \meta{text$'$} having three lines, which will be broken into two and one
% lines and thus finally has two line height, by assuming the contribution
% is one and a half lines.  Thus we have to have a better estimation method.
% 
% Another problem is that, even if we estimate the contribution better, we
% cannot directly |\insert| \meta{text$'$} because its {\em natural} height
% plus depth may be different from the estimated contribution.  Note that
% changing the magnification factor in |\count\footins| dynamically is not
% good idea because its value is referred by the page breaking mechanism not
% at the time when we do |\insert| but when the paragraph including
% |\footnote| is completed possibly after other |\footnote|-s change the
% factor again.  Also note that we cannot give up using |\insert| and adopt
% a method similar to that for floats\footnote{
%
% As the buggy implementation of earlier version of \textsf{dblfnote}.},
%
% because a float may be decoupled from its reference and {\em float} to
% another page.  Thus we have to |\insert| something other than
% \meta{text$'$} while keeping it in some other place.
% 
% To solve these problems, the following algorithm is devised for
% \textsf{dblfnote}.  Let $f_1$, \ldots, $f_{i-1}$ be footnote texts which
% have not yet been |\output|, and $f_i$ be that which we now process.  Let
% $H_i$ be the height plus depth of double-columned typesetting result of
% $f_1$, \ldots, $f_i$, which can be obtained by tentatively doing that.  We
% estimate the contribution of $f_i$ to the page as $\DH_i=H_i-H_{i-1}$,
% which will be exact if $f_1$, \ldots, $f_i$ is put in a page\footnote{
%
% As discussed later, this condition does not always hold and thus we will
% have an error.}.
%
% Then we |\insert| an empty box whose height is $\DH_i$ through |\footins|,
% while appending $f_i$ to the tail of |\vbox| $F$, which has contained
% $f_1$, \ldots, $f_{i-1}$, so that the |\output| routine and following
% |\footnote|-s refer it.
%
% When the |\output| routine is invoked, we have $f_1$, \ldots, $f_n$ in
% $F$, and \TeX{} moved $m$ ($m\leq n$) |\insert|-ed empty |\vbox|-es into
% the box |\footins|.  Thus we have to know $m$ and have to pick $f_1$,
% \ldots, $f_m$ from $F$.  Since $m$ is the number of |\vbox|-es in
% |\footins|, we can count them by a well-known technique of iterative
% |\unvbox| and |\lastbox|\footnote{
%
% Since \cs{footins} contains only a sequence of empty \cs{vbox}-es, i.e. no
% glues, penalties nor other troublesome stuffs, we can count \cs{vbox}-es
% exactly.}.
%
% In order to pick $f_1$, \ldots, $f_m$, we maintain a list
% $L=\{h_1,\ldots,h_n\}$ where $h_i$ is the height plus depth of $f_i$ and
% calculate $s_m=\sum_{i=1}^m h_i$.  With this $s_m$, we can |\vsplit| the
% box $F$ to obtain a |\vbox| $F'$ containing $f_1$, \ldots, $f_m$ and to
% leave $f_{m+1}, \ldots, f_n$ in $F$.  We also remove $h_1$, \ldots, $h_m$
% from $L$.  Then we |\vsplit| $F'$ into two columns to have what we finally
% put at the bottom of the page.
%
% If $m=n$, that is, if all the |\footnote|-s that have occurred are combined 
% with the page, we have no problem to finish the |\output| routine and to
% continue the process.  If $m<n$, that is, if there are |\footnote|-s that
% have occurred but are left for the next (or farther) page, however, we have 
% a problem.   Remember that we estimate the contribution of $f_i$, $\DH_i$, 
% assuming that $f_1$, \ldots, $f_i$ are put in a page.  Since $f_{m+1}$,
% \ldots, $f_n$ are {\em not} put in the page where $f_1$, \ldots, $f_m$ are 
% put, our estimation could have some error.  In fact, for example, if all
% $f_i$ has one line and $m$ is odd, $H_m=H_{m+1}$ and thus $\DH_{m+1}$ is
% zero while its real contribution should be the height of one line.  In
% general, $\DH_i$ for $m<i\leq n$ were underestimated and thus somehow we
% have to compensate the underestimation that would cause overfull in the
% |\output| process for the next page.
%
% For the compensation, the element of $L$ is not just $h_i$ but the pair
% $(h_i,\DH_i)$ to remember the estimated contribution.  After we put $f_1$, 
% \ldots, $f_m$, we estimate the contribution of $f_{m+1}$, \ldots, $f_n$
% again by tentatively building double-columned output to have $H'_{m+1}$,
% \ldots, $H'_n$ where $H'_i$ is the height plus depth of the double-columned 
% box of $f_{m+1}$, \ldots, $f_i$.  Then we calculate
% 
% \begin{equation}\label{eq:eta}
% \eta=\max_{m<i\leq n}(H'_i-\sum_{\llap{$\scriptstyle j=m+1$\hss}}^i\DH_i)
% \end{equation}
% 
% and |\insert| an empty |\vbox| of $\eta$ high which is conceptually placed 
% at the top of next page.  We also add an element $(0,\eta)$ at the head of 
% $L$.  Remember that this compensation makes $\DH_i$ overestimated and thus
% the next page will be too short if a part of $f_{m+1}$, \ldots, $f_n$ are
% still deferred on the next page building as noted in \S\ref{sec:prob}.
% However, this overestimation is unlikely revealed because we also
% |\insert| an empty |\vbox| whose negative height $\eta'$ is;
% 
% \begin{equation}\label{eq:eta'}
% \eta'=H'_n-(\sum_{\llap{$\scriptstyle j=m+1$\hss}}^n\DH_i+\eta)
% \end{equation}
% 
% at the tail of the main vertical list which is not yet |\output|, add an
% element $(0,\eta')$ to the tail of $L$, and set $H_n$ to $H'_n$.  That is, 
% if the next page has a |\par|, the overestimation is reset.
%
% 
%
% \subsubsection{Register Declaration}
% \label{sec:imp-dfn-decl}
% 
% First of all, we declare the following three switches, together with user
% interface commands to turn them.
%
% \begin{itemize}
% \item
% \begin{macro}{\ifdfn@allowcbreak}
% \begin{macro}{\DFNallowcbreak}
% \begin{macro}{\DFNinhibitcbreak}
% |\ifdfn@allowcbreak| is true (default) if |\DFNallowcbreak| is in effect
% to allow a footnote is broken into two columns.  It is false if
% |\DFNinhibitcbreak| is in effect to enclose a footnote by a |\vbox| to
% inhibit the breaking.
% \end{macro}\end{macro}\end{macro}
%
% \item
% \begin{macro}{\ifdfn@trysingle}
% \begin{macro}{\DFNtrysingle}
% \begin{macro}{\DFNalwaysdouble}
% |\ifdnf@trysingle| is true (default) if |\DFNtrysingle| is in effect to
% place footnotes only in the left column if possible.  It is false if
% |\DFNalwaysdouble| is in effect not to try single-columning.
% \end{macro}\end{macro}\end{macro}
% 
% \item
% \begin{macro}{\ifdfn@ruleboth}
% \begin{macro}{\DFNruleboth}
% \begin{macro}{\DFNruleleft}
% |\ifdfn@ruleboth| is true if |\DFNruleboth| is in effect to draw
% |\footnoterule| over both columns.  It is false (default) if
% |\DFNruleleft| is in effect to draw it over the left column only.
% \end{macro}\end{macro}\end{macro}
% \end{itemize}
%
% We also use a working switch |\@tempswa|.
%
%    \begin{macrocode}

%% Register Declaration

\newif\ifdfn@allowcbreak \dfn@allowcbreaktrue
\def\DFNallowcbreak{\dfn@allowcbreaktrue}
\def\DFNinhibitcbreak{\dfn@allowcbreakfalse}

\newif\ifdfn@trysingle \dfn@trysingletrue
\def\DFNtrysingle{\dfn@trysingletrue}
\def\DFNalwaysdouble{\dfn@trysinglefalse}

\newif\ifdfn@ruleboth \dfn@rulebothfalse
\def\DFNruleboth{\dfn@rulebothtrue}
\def\DFNruleleft{\dfn@rulebothfalse}

%    \end{macrocode}
%
% \begin{macro}{\c@DFNsloppiness}
% Then we declare a \LaTeX{} counter |DFNsloppiness| that is the value of
% |\hbadness| of the footnote paragraphs, and set it to the default value
% 5000.
% \end{macro}
% We also use a working |\count| register, |\@tempcnta|.
%
%    \begin{macrocode}
\newcounter{DFNsloppiness}\c@DFNsloppiness5000

%    \end{macrocode}
%
% \begin{dummymacro}
% Next come the declarations of the following six |\dimen| registers.
%
% \begin{itemize}
% \item
% \begin{macro}{\DFNcolumnsep}
% \begin{macro}{\DFNcolumnwidth}
% |\DFNcolumnsep| and |\DFNcolumnwidth| are the counterparts of |\columnsep| 
% and |\columnwidth|.  Their defaults are both $-|\maxdimen|$ to indicate
% that they are set to the default values in |\document|.
% \end{macro}\end{macro}
%
% \item
% \begin{macro}{\dfn@fnht}
% |\dfn@fnht| is $H_i$ shown in \S\ref{sec:imp-dfn-ovv}.
% \end{macro}
%
% \item
% \begin{macro}{\dfn@fnmaxdp}
% |\dfn@fnmaxdp| has the depth of |\strutbox| in |\footnotesize| and is used 
% to set |\boxmaxdepth| and |\splitmaxdepth| for footnote boxes.
% \end{macro}
%
% \item
% \begin{macro}{\dfn@dima}
% \begin{macro}{\dfn@dimb}
% \begin{DFNinhibitcbreak}%
% |\dfn@dima| and |\dfn@dimb| are our own scratch-pads.  We also use
% \LaTeX's scratch-pads |\@tempdima| and |\@tempdimb|\footnote{
%
% \cs{@tempdimc} is not used because it is unavailable in \LaTeX-2.09.}.
% \end{DFNinhibitcbreak}%
% \end{macro}\end{macro}
% \end{itemize}
% \end{dummymacro}
%
%    \begin{macrocode}
\newdimen\DFNcolumnsep \DFNcolumnsep-\maxdimen
\newdimen\DFNcolumnwidth \DFNcolumnwidth-\maxdimen
\newdimen\dfn@fnht
\newdimen\dfn@fnmaxdp {\footnotesize \global\dfn@fnmaxdp\dp\strutbox}
\newdimen\dfn@dima \newdimen\dfn@dimb

%    \end{macrocode}
%
% \begin{macro}{\dfn@ins}
% \begin{macro}{\dfn@boxa}
% \begin{macro}{\dfn@boxb}
% Next declarations are for boxes, |\dfn@ins| for $F$ shown in
% \S\ref{sec:imp-dfn-ovv}, and two working registers |\dfn@boxa| and
% |\dfn@boxb|.
% \end{macro}\end{macro}\end{macro}
%
%    \begin{macrocode}
\newbox\dfn@ins
\newbox\dfn@boxa \newbox\dfn@boxb

%    \end{macrocode}
%
% \begin{macro}{\dfn@output}
% Finally, we declare a |\toks| register |\dfn@output| that contains
% original token list for |\output| that is refered in our own version of
% it.
% \end{macro}
%
%    \begin{macrocode}
\newtoks\dfn@output \dfn@output\output

%%^L
%    \end{macrocode}
% 
% 
%
% \subsubsection{Make a Footnote}
% \label{sec:imp-dfn-fntext}
%
% \begin{macro}{\dfn@footnotetext}
% \begin{macro}{\dfn@latex@footnotetext}
% \begin{macro}{\@footnotetext}
% \begin{macro}{\dfn@gobble}
% To implement a part of our algorithm described in \S\ref{sec:imp-dfn-ovv},
% we have to modify the part of |\footnote|, |\@footnotext|\Meta{text}, in
% which \LaTeX{} does |\insert\footins|\Meta{text$'$}.  Our own
% |\@footnotext|, named |\dfn@footnotetext|, first typesets \meta{text$'$}
% in a box |\dfn@boxa| ($f_i$) by calling \LaTeX's \hbox{|\@footnotetext|}
% that is renamed |\dfn@latex@footnotetext|.  Before calling it, we make
% |\insert| |\let|-equal to |\dfn@gobble| that simply returns the body to be
% |\insert|-ed, and set |\columnwidth| and |\hbadness| to appropriate values
% to make double-columned paragraphs.
% \end{macro}\end{macro}\end{macro}\end{macro}
%
% \begin{macro}{\@makefnmark}
% \begin{macro}{\dfn@makefnmark}
% \begin{DFNinhibitcbreak}%
% The other operation performed prior to calling |\dfn@latex@footnotetext|
% is redefinition of |\@makefnmark| so that it |\smash|-es the footnote
% mark produced by its original version |\dfn@makefnmark|.  This prevents
% the first line of footnote being too tall\footnote{
%
% The superscripted footnote number is sometimes taller than \cs{strut} of
% \cs{footnotesize}.}
%
% and makes columns well-balanced.
% \end{DFNinhibitcbreak}%
% \end{macro}\end{macro}
%
% \begin{dummymacro}
% Then we calculate $h_i$ (|\dfn@dima|) and append $f_i$ to the tail of $F$
% (|\dfn@ins|).  Since we need that $h_i$ is positive to get $f_i$ from $F$
% afterward, we enclose $f_i$ with a |\vbox| of 1\,|sp| high if $h_i$ is
% unexpectedly non-positive.  The appendix is done by |\unvbox| of $f_i$ if
% |\ifdfn@allowcbreak| is true, while the |\vbox| envelope is kept otherwise
% to inhibit column break in $f_i$.  In both cases, $f_i$ is preceded by
% |\allowbreak| and |\nointerlinepenalty| to allow column break and to
% prevent glue for |\baslineskip| inserted.
% \end{dummymacro}
%
% \begin{macro}{\dfn@split}
% Next we evaluate $H_i$ by tentatively building double-columned typesetting
% result from $F$.  This is done by the macro;
%
% \begin{quote}
% |\dfn@split|\meta{height}\meta{src}\meta{dst}\meta{maxdepth}\meta{topskip}
% \end{quote}
%
% which |\vsplit|-s the box \meta{src} at \meta{height} to set the first
% half to \meta{dst} while leaving the second half in \meta{src}.  The
% parameters for |\vsplit|, |\splitmaxdepth| and |\splittopskip|, are given
% by \meta{maxdepth} and \meta{topskip}.  After |\vsplit|, it sets
% conceptual height and depth of double-columned result, $h_D$
% (|\@tempdima|) and $d_D$ (|\@tempdimb|) as follows.
%
% \begin{eqnarray*}
% h_D&=&\max({\it ht}(\meta{src}),\;{\it ht}(\meta{dst}))\\
% d_D&=&\max({\it ht}(\meta{src})+{\it dp}(\meta{src}),\;
%	   {\it ht}(\meta{dst})+{\it dp}(\meta{dst}))-h_D
% \end{eqnarray*}
%
% Thus we have $H_i=h_D+d_D$ (|\dfn@fnht|) and $\DH_i=H_i-H_{i-1}$
% (|\@tempdima|).
% \end{macro}
%
% \begin{macro}{\dfn@list}
% Finally we |\insert| an empty |\vbox| of $\DH_i$ high, and append
% |\@elt|\meta{$h_i$}\meta{$\DH_i$} at the tail of $L$ (|\dfn@list|).  Note
% that $h_i$ and $\DH_i$ are represented with the unit |sp| rather than |pt| 
% to avoid conversion error.
% \end{macro}
%
%    \begin{macrocode}

%% Make a Footnote

\long\def\dfn@footnotetext#1{{\setbox\dfn@boxa\vbox{
        \let\insert\dfn@gobble
        \columnwidth\DFNcolumnwidth \hbadness\c@DFNsloppiness
        \def\@makefnmark{\smash{\dfn@makefnmark}}
        \dfn@latex@footnotetext{#1}\par \boxmaxdepth\dfn@fnmaxdp}%
        \dfn@dima\ht\dfn@boxa \advance\dfn@dima\dp\dfn@boxa
        \ifdim\dfn@dima>\z@\else
                \dfn@dima1sp\relax
                \setbox\dfn@boxa\vbox{\vbox to1sp{\unvbox\dfn@boxa\vfil}}\fi
        \global\setbox\dfn@ins\vbox{\boxmaxdepth\dfn@fnmaxdp
                \ifvoid\dfn@ins\else
                        \unvbox\dfn@ins \allowbreak \nointerlineskip \fi
                \ifdfn@allowcbreak \unvbox \else \box \fi \dfn@boxa}%
        \setbox\dfn@boxa\copy\dfn@ins
        \dfn@split{.5\ht\dfn@boxa}\dfn@boxa\dfn@boxb\dfn@fnmaxdp\footnotesep
        \advance\@tempdima\@tempdimb \@tempdimb\@tempdima
        \advance\@tempdima-\dfn@fnht \global\dfn@fnht\@tempdimb
        \insert\footins{\floatingpenalty\@MM \vbox to\@tempdima{}}%
        \xdef\dfn@list{\dfn@list\@elt{\number\dfn@dima}{\number\@tempdima}}}}
\let\dfn@latex@footnotetext\@footnotetext
\let\@footnotetext\dfn@footnotetext
\long\def\dfn@gobble#1#2{#2}
\let\dfn@makefnmark\@makefnmark
\def\dfn@list{}

\def\dfn@split#1#2#3#4#5{\@tempdima#1\relax
        \vbadness\@M \vfuzz\maxdimen \splitmaxdepth#4\splittopskip#5\relax
        \setbox#3\vsplit#2to\@tempdima
        \setbox#3\vbox{\boxmaxdepth#4\unvbox#3}%
        \@tempdima\ht#3\advance\@tempdima\dp#3\relax
        \@tempdimb\ht#2\advance\@tempdimb\dp#2\relax
        \ifdim\@tempdimb<\@tempdima \@tempdimb\@tempdima \fi
        \@tempdima\ht#3\ifdim\@tempdima<\ht#2\@tempdima\ht#2\fi
        \advance\@tempdimb-\@tempdima}

%%^L
%    \end{macrocode}
%
% 
%
% \subsubsection{Output Footnotes}
% \label{sec:imp-dfn-makecol}
%
% \begin{macro}{\dfn@makecol}
% The other part of our algorithm described in \S\ref{sec:imp-dfn-ovv} is
% implemented as our own version of |\@makecol|, named |\dfn@makecol|.
% First we check if |\footins| has |\insert|-ed empty boxes for $f_1$,
% \ldots, $f_m$, and do (almost) nothing if none.  Then we get $H_m$
% (|\dfn@dima|) that is the height of |\footins|.
% \end{macro}
%
% \begin{macro}{\dfn@countins}
% Next we count the boxes in |\footins| to get $m$ (|\@tempcnta|) by
% |\dfn@countins|.  It repeatedly removes the |\lastbox| of |\footins|
% counting up $m$ until no box is obtained.
% \end{macro}
%
% \begin{macro}{\dfn@elt@getht}
% \begin{macro}{\dfn@endgetht}
% Then we {\em execute} $L$ (|\dfn@list|) making |\@elt| |\let|-equal to
% |\dfn@elt@getht| to calculate $s_m=\sum_{i=1}^m h_i$ (|\@tempdima|).  This
% execution also removes $(h_1,\DH_1)$, \ldots, $(h_m,\DH_m)$ from $L$ by
% |\dfn@endgetht|.
% \end{macro}\end{macro}
%
% \begin{dummymacro}
% Note that $s_m$ could be zero if |\footins| only has |\vbox|-es for error
% compensation, i.e.\ $(0,\eta)$ and/or $(0,\eta')$.  In this case, we don't 
% have any footnotes to be output.  This decision is correct because we
% enclosed footnotes having non-positive height by a |\vbox| of 1\,|sp| high
% as described in \S\ref{sec:imp-dfn-fntext}.  Thus we can safely pick $f_1$,
% \ldots, $f_m$ from $F$ by |\vsplit|-ting it at $s_m$ by |\dfn@split|
% \footnote{
%
% Unfortunately, this is not perfectly safe because $f_i$ may have
% stretchable and/or shrinkable glues together with negative penalties which
% could make the break point between $f_m$ and $f_{m+1}$ not least costly.
% Although we could have a perfect solution to cope with this unsafeness, we 
% ignore such an unusual case because of the simplicity of implementation.},
%
% and store them in |\dfn@boxa|.
% \end{dummymacro}
%
% \begin{dummymacro}
% Then if |\dfn@trysingle| is true, we check whether the page has enough
% space to put $f_1$, \ldots, $f_m$ in one column by examining the following 
% inequality;
% $$
% r\geq h_p+h_d+\sigma+s_m
% $$
% where $r$ is |\@colroom|, $h_p$ and $h_d$ are height and depth of the body 
% of the page given through |\box\@cclv|, and $\sigma$ is natural space of
% |\skip\footins|\footnote{
%
% Thus we ignore the shrinkability of the page body and \cs{skip}\cs{footins},
% because the former is hardly obtained.  Remember \cs{pageshrink} is not the
% total shrinkability at the break point but at somewhere \cs{output} routine
% is invoked.}.
%
% Note that $h_p$ and $h_d$ are {\em not} height and depth of |\box\@cclv|,
% which are |\pagegoal| and depth of the last item (or |\maxdepth|), but
% those of the |\vbox| containing |\unvbox\@cclv|\footnote{
%
% \TeX{} does not provide any other more convenient way to get them.}.
%
% If the inequality is satisfied, $f_1$, \ldots, $f_m$ are simply put into
% the box |\footins| together with |\footnoterule| preceding them.
% \end{dummymacro}
%
% \begin{dummymacro}
% Otherwise, we split $f_1$, \ldots, $f_m$ at $H_m$ by |\dfn@split| to
% obtain both columns to output.  Then each column, preceded by
% |\footnoterule| and follwed by |\vss|, is put into a |\vbox| whose height
% is {\em conceptual} one calculated by |\dfn@split| so that first baselines
% of both column are adjusted.  This also adjusts the last baseline of taller
% column with those of footnotes in other pages if |\makeFNbottom| of
% \textsf{fnpos} is in effect.  Note that |\footnoterule| of the right
% column will not be put if |\ifdfn@ruleboth| is false, but a vertical space
% to compensate the height and depth of |\footnoterule| is although it is
% usually zero.  For the completeness, we don't forget to set |\prevdepth|
% to the depth of |\footnoterule| though it has also no effect.
% \end{dummymacro}
%
% \begin{dummymacro}
% Then two boxes are put into |\hbox|-es of |\DFNcolumnwidth| wide separated 
% by a space of |\DFNcolumnsep| surrounded by another |\hbox|.  This outmost 
% |\hbox| is redundantly enclosed by a |\vbox| to which |\footins| is set,
% because it will be unsealed by |\unvbox| afterward.
% \end{dummymacro}
%
% \begin{macro}{\dfn@elt@adjust}
% Now we finished the job for footnotes to be output to the current page,
% and start to take care of those left in $L$ and defered to the next (or
% farther) page.  First, we {\em execute} $L$ (|\dfn@list|) making |\@elt|
% |\let|-equal to |\dfn@elt@adjust| to calculate $\eta$ (|\dfn@dimb|) of the
% equation (\ref{eq:eta}) in \S\ref{sec:imp-dfn-ovv}.  It also calculate
% $H'_n$ (|\@tempdima|) and $\sum_{j=m+1}^n H_i$ (|\dfn@fnht|) for $\eta'$
% of the equation (\ref{eq:eta'}) in \S\ref{sec:imp-dfn-ovv}.
% \end{macro}
%
% \begin{dummymacro}
% Then if $\eta$ is positive, we add $(0,\eta)$ to the head of $L$ and
% |\insert| an empty box of $\eta$ high to compensate the underestimation.
% Since \TeX{} places the vertical list constructed in |\output| routine
% at the page break point, the |\insert|-ion for $\eta$ is followed by those 
% for $f_{m+1}$, \ldots, $f_n$.
% \end{dummymacro}
% 
% \begin{macro}{\output}
% \begin{macro}{\dfn@afteroutput}
% We also add $(0,\eta')$ to the tail of $L$ and |\insert| an empty box of
% $\eta'$ high to compenstate the overestimation caused by $\eta$, if
% $\eta'$ is negative.  This |\insert|-ion, however, should follow
% $f_{m+1}$, \ldots, $f_n$.  To do this delayed |\insert|-ion, we modify
% |\output| so that it invoke |\dfn@afteroutput| through |\aftergroup|.
% Since \TeX{} closes the implicit group for |\output| {\em after} it
% reconstructs main vertical list\footnote{
%
% This fact is not described in \TeX{}book but \texttt{tex.web} does so.},
%
% |\dfn@afteroutput| will |\insert| the box where we wish to place and
% then nullify itself.
% \end{macro}\end{macro}
%
% \begin{macro}{\dfn@footnoterule}
% Now we finished everything for doulbe-columned footnotes.  So, we call
% \LaTeX's \hbox{|\@make|}\allowbreak\hbox{|col|}, |\dfn@latex@makecol|, to
% make a page with |\footins|.  Since the macro calls |\footnoterule| before
% |\footins| is put and we have already done it, we temporarily nullify
% |\footnoterule| and reactivate it after the macro with its original
% definition saved in |\dfn@footnoterule|.
% \end{macro}
%
%    \begin{macrocode}

%% Output Footnotes

\def\dfn@makecol{{\ifvoid\footins\else
        \dfn@dima\ht\footins
        \@tempcnta\z@ \dfn@countins
        \@tempdima\z@ \let\@elt\dfn@elt@getht
        \dfn@list\@nil
        \ifdim\@tempdima=\z@\else
        \dfn@split\@tempdima\dfn@ins\dfn@boxa\z@\z@
        \global\setbox\dfn@ins\box\dfn@ins
        \@tempswatrue
        \ifdfn@trysingle
                \setbox\dfn@boxb\vbox{\unvcopy\@cclv}\@tempdima\@colroom
                \advance\@tempdima-\ht\dfn@boxb \advance\@tempdima-\dp\dfn@boxb
                \advance\@tempdima-\skip\footins
                \advance\@tempdima-\ht\dfn@boxa
                \ifdim\@tempdima<\z@\else \@tempswafalse
                        \global\setbox\footins\vbox{\boxmaxdepth\dfn@fnmaxdp
                                \footnoterule \unvbox\dfn@boxa}\fi\fi
        \if@tempswa
        \dfn@split{\dfn@dima}\dfn@boxa\dfn@boxb\dfn@fnmaxdp\footnotesep
        \global\setbox\footins\vbox{\hbox{%
                \hbox to\DFNcolumnwidth{\vbox to\@tempdima{\footnoterule
                        \unvbox\dfn@boxb\vss}\hss}\hskip\DFNcolumnsep
                \hbox to\DFNcolumnwidth{\ifvoid\dfn@boxa\else
                        \vbox to\@tempdima{
                                \setbox\@tempboxa\vbox{\footnoterule}
                                \ifdfn@ruleboth \unvbox\@tempboxa
                                \else \@tempdima\ht\@tempboxa
                                        \advance\@tempdima\dp\@tempboxa
                                        \vskip\@tempdima
                                        \prevdepth\dp\@tempboxa \fi
                                \unvbox\dfn@boxa\vss}\fi\hss}}}\fi\fi
        \global\dfn@fnht\z@
        \ifx\dfn@list\@empty\else
                \let\@elt\dfn@elt@adjust \dfn@dima\z@ \dfn@dimb\z@
                \dfn@list \global\advance\dfn@fnht\dfn@dimb
                \let\@elt\relax
                \ifdim\dfn@dimb>\z@
                        \xdef\dfn@list{\@elt{0}{\number\dfn@dimb}\dfn@list}%
                        \insert\footins{\floatingpenalty\@MM
                                \vbox to\dfn@dimb{}}\fi
                \ifdim\dfn@fnht>\@tempdima
                        \@tempdimb\@tempdima \advance\@tempdimb-\dfn@fnht
                        \global\dfn@fnht\@tempdima
                        \xdef\dfn@list{\dfn@list\@elt{0}{\number\@tempdimb}}%
                        \xdef\dfn@afteroutput{\insert\footins{
                                        \floatingpenalty\@MM
                                        \vbox to\number\@tempdimb sp{}}%
                                \global\let\noexpand\dfn@afteroutput\relax}%
                \fi\fi
        \fi}%
        \let\footnoterule\relax \dfn@latex@makecol
        \let\footnoterule\dfn@footnoterule}
\let\dfn@footnoterule\footnoterule

\def\dfn@countins{\setbox\footins\vbox{\unvbox\footins
                \global\setbox\dfn@boxa\lastbox}%
        \ifvoid\dfn@boxa \let\next\relax
        \else \advance\@tempcnta\@ne \let\next\dfn@countins \fi \next}

\def\dfn@elt@getht#1#2{\advance\@tempdima#1sp\relax \advance\@tempcnta\m@ne
        \ifnum\@tempcnta>\z@ \let\next\relax
        \else\let\next\dfn@endgetht \fi \next}
\def\dfn@endgetht#1\@nil{\gdef\dfn@list{#1}}

\def\dfn@elt@adjust#1#2{\advance\dfn@dima#1sp\advance\dfn@fnht#2sp\relax
        \ifvoid\dfn@ins \@tempdima\z@ \@tempdimb\z@
        \else \setbox\dfn@boxa\copy\dfn@ins
                \dfn@split\dfn@dima\dfn@boxa\dfn@boxb\z@\z@
                \dfn@split{.5\ht\dfn@boxb}\dfn@boxb\dfn@boxa
                        \dfn@fnmaxdp\footnotesep
                \advance\@tempdimb\@tempdima \@tempdima\@tempdimb \fi
        \advance\@tempdimb-\dfn@fnht\relax
        \ifdim\@tempdimb>\dfn@dimb \dfn@dimb\@tempdimb \fi}

\let\dfn@afteroutput\relax
\output{\the\dfn@output \aftergroup\dfn@afteroutput}

%%^L
%    \end{macrocode}
%
% 
%
% \subsubsection{Initialization, etc.}
% \label{sec:imp-dfn-init}
%
% \begin{macro}{\dfn@document}
% \begin{macro}{\document}
% Since the default value of |\DFNcolumnsep| is that of |\columnsep| that
% may be set in other styles and/or preamble, we have to modify |\document|
% to set |\DFNcolumnsep| to the value of |\columnsep| if it is negative
% after the invocation of the original version of |\document|,
% |\dfn@document|.  We also set |\DFNcolumnwidth| to its default value
% calculated from |\DFNcolumnsep| and |\textwidth| if it is negative.
% \end{macro}\end{macro}
%
% \begin{macro}{\dfn@latex@makecol}
% \begin{macro}{\@makecol}
% Another reason why we modify |\document| is the modification of
% |\@makecol|.  In order to allow our footnote styles (and others hopefully) 
% to be loaded in any order, we capture possibly-modified definition of
% |\@makecol| in |\document| to save it in |\dfn@latex@makecol| as the
% original version, and make |\@makecol| |\let|-equal to our own version
% |\dfn@makecol|.
% \end{macro}\end{macro}
%
%    \begin{macrocode}

%% Initialization, etc.

\let\dfn@document\document
\def\document{\dfn@document
        \ifdim\DFNcolumnsep<\z@ \DFNcolumnsep\columnsep \fi
        \ifdim\DFNcolumnwidth<\z@
                \DFNcolumnwidth\textwidth
                \advance\DFNcolumnwidth-\DFNcolumnsep
                \divide\DFNcolumnwidth\tw@ \fi
        \dfn@fnht\z@
        \let\dfn@latex@makecol\@makecol
        \let\@makecol\dfn@makecol}

%    \end{macrocode}
%
% \begin{macro}{\dfn@twocolumn}
% \begin{macro}{\twocolumn}
% \begin{macro}{\dfn@onecolumn}
% \begin{macro}{\onecolumn}
% We also switch |\@makecol| to original\slash own version in modified
% |\twocolumn|\slash |\onecolumn| because double-columned footnotes are
% available only in single column documents.  In those macros, prior to
% the invocation of their original versions, |\dfn@twocolumn| and
% |\dfn@onecolumn|, |\@footnotetext| is also set to corresponding macros that
% are original |\dfn@latex@footnotetext| or our own |\dfn@footnotetext|.
% \end{macro}\end{macro}\end{macro}\end{macro}
%
%    \begin{macrocode}
\let\dfn@twocolumn\twocolumn
\def\twocolumn{\clearpage
        \let\@footnotetext\dfn@latex@footnotetext
        \let\@makecol\dfn@latex@makecol
        \dfn@twocolumn}
\let\dfn@onecolumn\onecolumn
\def\onecolumn{\clearpage
        \let\@footnotetext\dfn@footnotetext
        \let\@makecol\dfn@makecol
        \dfn@onecolumn}
%    \end{macrocode}
% 
% \iffalse
%</dblfnote>
% \fi
% 
% 
%
% \IndexPrologue{\newpage\section*{Index}
% Italicized number refers to the page where the specification and usage of
% corresponding entry is described, while underlined is for the
% implementation of the entry.}
% \Finale
% \GlossaryPrologue{\newpage\section*{Revision History}}
% \PrintChanges
\endinput
