% \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