% \section{Overview}
% \label{sec:imp-ovv}
% 
% \subsection{Column-Pages}
% \label{sec:imp-ovv-colpage}
% 
% In our parallel multi-column typesetting, a column may grow independently
% of other columns and may cross its page boundary asynchronously with
% others.  Therefore, we cannot throw away the contents of a column in a
% page, or a {\em\Uidx\colpage} in short, when a page break occurs in the
% column.  Instead, we have to keep \colpage{}s until all columns are
% {\em\Uidx\sync{}ed} implicitly or explicitly.
% 
% An {\em\Uidx\imsync} takes place when all columns in a page see
% page-breaks to let the page is shipped out.  In general, all columns but
% the last one which arrives the page-break have completed \colpage{}s in the
% page in question and some of them may have succeeding \colpage{}s.
% Therefore, we maintain the list of completed \colpage{}s
% $\Uidx\S_c=|\pcol@shipped|{\cdot}c$
% 
% \SpecialArrayMainIndex{c}{\pcol@shipped}
% 
% for each column $c\In0\C$, where $\Uidx\C=\!\pcol@ncol!$ is the number of
% columns given through the argument of \env{paracol} environment, and the
% set of them $\Uidx\SS=\Set{\S_c}{c\In0\C}$.
% 
% Each element $\Uidx\s_c(p)$ of a list $\S_c$ is an \!\insert! whose
% \!\vbox! contains the 
% $p$-th completed \colpage\footnote{
% 
% Other registers such as \cs{count} are not used.},
% 
% where $p=0$ for the first \colpage{} produced in \env{paracol}
% environment or that following a page flushing macro \!\flushpage!,
% \!\clearpage! or \!\cleardoublepage!.  That is, $\S_c$ is defined as
% follows, where $\Uidx\pbase=\!\pcol@basepage!$ is the zero-origin ordinal
% of the {\em\Uidx\bpage} being the oldest page not shipped out yet.
% 
% \begin{eqnarray*}
% \S_c&=&(\s_c(\pbase),\s_c(\pbase{+}1),\ldots,\s_c(\pbase{+}k{-}1))\\
% &=&\!\@elt!\,\s_c(\pbase)\;\!\@elt!\,\s_c(\pbase{+}1)\;\cdots\;
% 	\!\@elt!\,\s_c(\pbase{+}k{-}1)
% \end{eqnarray*}
% 
% Note that a list $\S_c$ can be empty and all members in $\SS$ may be empty.
% 
% The other type of \sync{}ation, {\em\Uidx\exsync}, takes place by
% \!\switchcolumn!|*| or the beginning of starred \csenv{}s, by
% \Endparacol, or by one of page flushing macros \!\flushpage!, 
% \!\clearpage! and \!\cleardoublepage!.  A flushing \exsync{} ships out the
% pages from $\pbase$ to $\Uidx\ptop=\!\pcol@toppage!$ being the ordinal of
% the {\em\Uidx\tpage} to which the most advanced {\em\Uidx\lcolumn} has
% reached.  On the other hand, other non-flushing \exsync{} keeps the page
% $\ptop$ from being shipped out because the \colpage{}s in it or the page
% itself will grow further.
% 
% 
% 
% \subsection{Current Column-Pages and Their Contexts}
% \label{sec:imp-ovv-ccol}
% \changes{v1.3-4}{2013/09/17}
%	{Remove $\mu$ for \cs{@mparbottom} from column-context because it is
%	 now in page context.}
% 
% We also have to maintain another type of \colpage{}s which are currently
% built, or {\em\Uidx\ccolpage{}s} in short, to switch from a column to
% another.  Since each column may have its own {\em context} for the
% typsetting of it, or {\em\Uidx\cctext} in short, it were perfect to save
% the context when we leave from a 
% column and to restore that when we revisit the column if we could.
% However, \TeX{} and \LaTeX{} has a tremendously large number of context
% variables and the number becomes virtualy boundless when we take variables
% defined in various styles and by users themselves into account.
% Therefore, we had to abandon to keep the whole context of the column but
% carefully chose a small subset comprising variables automatically modified
% outside of users' control.  That is, the \cctext{}
% $\Uidx\cc_c=|\pcol@col|{\cdot}c$
% 
% \SpecialArrayMainIndex{c}{\pcol@col}
% 
% of a column $c$ consists of the following elements, each of which named
% $e$ is referred to as $\cc_c(e)$ hereafter.
% 
% \begin{itemize}
% \item $\Uidx\vb$
% represents $\!\insert!{\cdot}\vb$ containing the followings.
% 
% \begin{itemize}
% \item
% $\vb^b=\!\box!{\cdot}\vb=\!\@holdpg!$ is the \!\vbox! containing the main
% vertical list which has already contributed to the \ccolpage{}.
% 
% \item
% $\vb^p=\!\count!{\cdot}\vb=\!\pcol@page!$ means the \ccolpage{} belongs to
% the page $\vb^p$.
% 
% \item
% $\vb^r=\!\dimen!{\cdot}\vb=\!\@colroom!$ is the room of the column.
% \end{itemize}
% 
% \item $\Uidx\ft=\Midx{\!\pcol@currfoot!}$
% is the \!\insert! containing the footnotes added in the \ccolpage, if
% \Mcfnote{} typesetting is in effect.  Its constituent \!\box!, \!\count!,
% \!\dimen! and \!\skip! are denoted as $\ft^b$, $\ft^c$, $\ft^d$ and
% $\ft^s$ respectively.  On the other hand, if \Scfnote{} typesetting is in
% effect, $\ft$ is always empty\footnote{
% 
% But the macro \cs{pcol@currfoot} is used to keep \Scfnote{}s temporarily.}.
% 
% \item $\Uidx\pd=\!\pcol@prevdepth!$
% is the depth of the last vertical item in $\vb^b$ obtained by
% \!\prevdepth!.
% 
% \item $\Uidx\tl=\!\@toplist!$
% is the list of top floats inserted in the \ccolpage.
% 
% \item $\Uidx\ml=\!\@midlist!$
% is the list of mid floats inserted in the \ccolpage.
% 
% \item $\Uidx\bl=\!\@botlist!$
% is the list of bottom floats inserted in the \ccolpage.
% 
% \item $\Uidx\dl=\!\@deferlist!$
% is the list of \cwise{} floats deferred to the next \colpage.
% 
% \item $\Uidx\tf=\!\pcol@textfloatsep!$
% is the vertical skip used instead of \!\textfloatsep! for top floats in the
% \ccolpage{} if it has \sync{}ation points, or $\infty$ otherwise.
% 
% \item $\Uidx\fh=\!\@textfloatsheight!$
% is the total height of mid floats and their separators in the \ccolpage.
% 
% \item $\Uidx\tn=\!\@topnum!$
% is the maximum number of top floats which the \ccolpage{} can accommodate
% further.
% 
% \item $\Uidx\tr=\!\@toproom!$
% is the room for top floats in the \ccolpage.
% 
% \item $\Uidx\bn=\!\@botnum!$
% is the maximum number of bottom floats which the \ccolpage{} can accommodate
% further.
% 
% \item $\Uidx\br=\!\@botroom!$
% is the room for bottom floats in the \ccolpage.
%
% \item $\Uidx\cn=\!\@colnum!$
% is the maximum total number of floats which the \ccolpage{} can accommodate
% further.
% 
% \item $\Uidx\sw$
% is the following encoding of \CSIndex{if@nobreak} and
% \CSIndex{if@afterindent} at the time we left from the column $c$.
% $$
% \sw=\cases{0&$\CSIndex{if@nobreak}=\false$\cr
%            1&$\CSIndex{if@nobreak}=\true\;\land\;
%               \CSIndex{if@afterindent}=\true$\cr
%            2&$\CSIndex{if@nobreak}=\true\;\land\;
%               \CSIndex{if@afterindent}=\false$}
% $$
% Note that we have only three states because \CSIndex{if@afterindent} is
% meaningful only when $\CSIndex{if@nobreak}=\true$\footnote{
% 
% If only with the standard \LaTeX{} and so far.}.
% 
% \item $\Uidx\ep=\!\everypar!$
% is the tokens stored in \!\everypar! at the time we left from the column
% $c$.
% \end{itemize}
% 
% \changes{v1.1}{2012/05/11}
% 	{Add description of $w_c\EQ\cs{pcol@columnwidth}{\cdot}c$.}
% 
% In addition, we have special context variables
% $\Uidx\w_c=|\pcol@columnwidth|{\cdot}c$
% 
% \SpecialArrayMainIndex{c}{\pcol@columnwidth}
% 
% in which we keep \!\columnwidth! for the column $c$.
% 
% Note that we could add other variables to the saved context and/or provide
% some API macro to define them by users, but abandon them because it should
% be too complicated for users\footnote{
% 
% And for the author if we include save/restore of macros, though it could
% be done with a \cs{toks} containing the \cs{def}initions of macros.}.
% 
% Also note that we provide a save/restore mechanism for \lcounter{}s as
% discussed in \secref{sec:imp-ovv-counter}.
% 
% 
% 
% \subsection{Pages and Their Contexts}
% \label{sec:imp-ovv-page}
% \changes{v1.2-2}{2013/05/11}
%	{Redesign page context and its implementation.}
% \changes{v1.3-3}{2013/09/17}
%	{Add $\pi^s(p)$ to the page context of $p$ for column-separating
%	 rule drawing and background painting.}
% \changes{v1.3-4}{2013/09/17}
%	{Add $\pi^m(p)$ to the page context of $p$ for marginal note
%	 placement.}
% 
% Besides the \colpage{}s, we have to keep track each whole page not yet
% shipped out but has some complete or incomplete (i.e., current) \colpage{}s.
% We maintain the list;
% 
% \SpecialMainIndex{\pcol@pages}
% 
% \begin{eqnarray*}
% \Uidx\PP
% &=&\!\pcol@pages!=(\Uidx\pp(\pbase),\pp(\pbase{+}1),\ldots\pp(\ptop{-}1))\\
% &=&\!\@elt!\,\pp(\pbase)\;\!\@elt!\,\pp(\pbase{+}1)\;\cdots\;
%    \!\@elt!\,\pp(\ptop{-}1)\\
% \pp(p)&=&|{|\pp^p(p)|}|\pp^i(p)\pp^f(p)|{|\pp^s(p)|}||{|\pp^m(p)|}|
% \end{eqnarray*}
% 
% where $\pp(p)$ is the {\em\Uidx\pctext} of $p$ and its elements $\pp^p(p)$,
% $\pp^i(p)$, $\pp^f(p)$, $\pp^s(p)$ and $\pp^m(p)$ have the followings.
% 
% \begin{itemize}
% \item
% $\pp^p(p)=\Uidx\page(p)$ is the value of the counter \counter{page}
% (i.e. \!\c@page!) for the page $p$.
% 
% \item
% Iff $\pp^i(p)\neq\bot$, the page $p$ has \pwise{} floats or the
% single-column {\em\Uidx\preenv} preceeding \beginparacol{} in the
% {\em\Uidx\spage} where it resides and spannig all columns.  In this case
% $\pp^i(p)=i$ represents $\!\insert!{\cdot}i$, often {\em cached}
% in the macro \!\pcol@spanning!, for such {\em\Uidx\spanning}
% whose registers have the followings.
% 
% \begin{itemize}
% \item
% $\pp^b(p)=\!\box!{\cdot}i$ contains the \spanning.
% 
% \item
% $\pp^h(p)=\!\dimen!{\cdot}i=\!\@colht!$ if positive for the height of
% columns shrunk by the \spanning.  If negative, the page is only for
% the \spanning, i.e. a {\em\Uidx\fpage}.  We use the notation $\pp^h(p)$
% for the pages $\pp^i(p)=\bot$ to mean \!\textheight!.
% 
% \item
% $\pp^t(p)=\!\skip!{\cdot}i=\!\pcol@topskip!$ being the value of
% \!\topskip! at \beginparacol{} to be inserted at the top of each column in
% each non-first page.  Otherwise, i.e., for the columns in the \spage{}
% following the \preenv{}, it has 0 to prevent the \!\topskip! insertion.
% We use the notation $\pp^t(p)$ for the pages $\pp^i(p)=\bot$ to
% mean \!\pcol@topskip!.
% \end{itemize}
% 
% \item
% Iff $\pp^f(p)\neq\bot$, \Scfnote{} typesetting, discussed in
% \secref{sec:imp-ovv-scfnote}, is in effect and the page $p$ has some
% footnotes in $\!\box!\cdot\pp^f(p)$.  This element is often {\em cached}
% in the macro \Midx{\!\pcol@footins!}.
% 
% \SpecialMainIndex{\pcol@pages}
% 
% \item
% $\pp^s(p)=(\Uidx\spt(H_1,h_1),\ldots,\spt(H_n,h_n))=
% \!\@elt!\Arg{H_1,h_1}\ldots\!\@elt!\Arg{H_n,h_n}$ is the list of \mctext{}s
% in the page $p$, where $i$-th one's top edge is at $H_i$ from the top of
% the page (excluding \spanning) and its height-plus-depth is $h_i$, where
% $H_i$ and $h_i$ are represented in the form of integers.  Therefore, it is
% emptied by \!\pcol@startpage!, and then the elements are added by
% \!\pcol@makecol! (only for the last one) and \!\pcol@output@switch!
% whenever they find a \mctext{} completes.  The element is often {\em
% cached} in the macro \!\pcol@sptextlist! and is referred to by
% \!\pcol@buildcolseprule! to draw \cseprule{} and to paint columns and
% \csepgap{} leaving spaces for \mctext{}s.  The usage of this element is
% discussed in \secref{sec:imp-ovv-cswap} a little bit more detailedly.
% 
% \item
% $\pp^m(p)=\Arg{\Uidx\mpb_L^l}\Arg{\mpb_L^r}\Arg{\mpb_R^l}\Arg{\mpb_R^r}$
% is the set of lists of marginal notes in the left ($l$) and right
% ($r$) margins and in the left ($L$) and right ($R$) \parapag{}es.  The
% words left and right of margins mean physical left and right, while left
% and right of \parapag{}es mean the logical ones, i.e., the page where the
% column-0 resides is left.  Each element $\mpb_{\{L,R\}}^{\{l,r\}}$ has a
% list $(\Uidx\mpar(t_1,b_1),\ldots,\mpar(t_n,b_n))=
% \!\@elt!\Arg{t_1}\Arg{b_1}\ldots\!\@elt!\Arg{t_n}\Arg{b_n}$ of marginal
% notes whose top and bottom are at $t_i$ and $b_i$ from the top of the
% column area, where $t_i$ and $b_i$ are represented in the form of
% integers.  Each element can be empty of course, and $\pp^m(p)$ itself can
% be so as well to mean all elements are empty\footnote{
% 
% To minimize the possibility of miscoding for emptying and save a small
% amount of memory for pages having no marginal notes.}.
% 
% Therefore, $\pp^m(p)$ is emptied by
% \!\pcol@startpage!, and then examined and modified by
% \!\pcol@addmarginpar! when it adds a marginal note through macros
% \!\pcol@getmparbottom! and \!\pcol@setmpbelt!.  Another modifier
% \!\pcol@output@start! initializes one of the element $\mpb_L^{\{l,r\}}$
% with the value representing the last marginal note in \preenv{}, while
% another examiner \!\pcol@output@end! lets the outside \!\@mparbottom! have
% a value based on $b_n$ of one of the element, according to \LaTeX's
% setting of marginal note placement.  The whole elemnt $\pp^m(p)$ is often
% {\em cached} in the macro \!\pcol@mparbottom!.  The usage of this
% element is discussed in \secref{sec:imp-ovv-cswap} a little bit more
% detailedly.
% \end{itemize}
% 
% Note that even in \parapag{}ing and in \npaired{} one in particular,
% a page $p$ consists of all columns $c\In0\C$.  Therefore, the term {\em
% left\slash right \parapag{}e} $p$ always mean the left and right component
% of a \parapag{}e (pair) $p$.
% 
% The reason why we keep track of $\page(p)$ is that page numbering is not
% necessrary to be consecutive.  If such a {\em jump} occurs randomly in any
% columns explicitly updating \counter{page}, it is very tough to give a
% consistent view of the page number of a specific page to all columns.
% Therefore we suppose jumps occur only in the leftmost column 0\footnote{
% 
% But we neither inhibit nor nullify a jump in non-leftmost column and thus
% the update can be seen referring to \texttt{page} counter explicitly.}
% 
% which controls the page numbering, while non-leftmost columns are expected
% to refer the \counter{page} passively.
%
% This page numbering is implemented as follows.  Each time a \colpage{} at
% $p$ of the leftmost column is completed to start a new \colpage{},
% $\page(p)$ is fixed to be the value of \counter{page} and
% $\page(q)=\pp^p(q)$ for all $q\in[p,\ptop]$ are let be $\page(p)+(q-p)$ in
% usual cases but $\page(p)+2(q-p)$ in \npaired{} \parapag{}ing.
% This update also takes place on \cswitch{} from the leftmost \colpage{} at
% $p$ to another column so that a jump happning before the switching is
% notified to other columns.  On the other hand, starting or \cswitch{} to a
% non-leftmost \colpage{} at $p$ lets \counter{page} have $\page(p)$
% referring to $\pp(p)$, unless the column starts the most advanced \tpage.
% In this new \tpage{} case, $\pp(\ptop{+}1)$ is added to $\PP$ with the
% temporary setting $\pp^p(\ptop+1)=\page(\ptop+1)=\page(\ptop)+1$ usually but
% $\pp^p(\ptop+1)=\page(\ptop+1)=\page(\ptop)+2$ in \npaired{}
% \parapag{}ing, and $\ptop$ is incremented.
% 
% Note that this management is imperfect because direct references of
% \counter{page} in non-leftmost columns can give inconsistent results if 
% \counter{page} is modified in a non-leftmost column or the reference occurs
% in a page $p$ after that the leftmost column modifies \counter{page} in a
% page $q$ such that $q\leq p$.  In addition to them, this mechanism in
% \npaired{} \parapag{}ing always gives incorrect page number to the
% columns in a right \parapag{}e because $\pp^p(p)$ always has $\page(p)$
% for the left \parapag{}e.  However, it is expected that the progress of
% the leftmost column usually preceeds other columns to give consistent
% \counter{page} reference even with jumps, unless the reference is made by
% a column in a right \npaired{} \parapag{}e.  More importantly, it is
% assured that indirect refereces through |.aux| records and page numbers
% recorded in |.toc|, |.idx|, and so on are always consistent because of the
% lazy evaluation of $\counter{page}=\page(p)$ at ship-out of an ordinary
% page $p$ or a left \parapag{}e $p$, while the counter is let have
% $\page(p)+1$ when a right \npaired{} \parapag{}e $p$ is shipped out.
% 
% Also note that we also keep $\pp(\ptop)$ in \Midx{\!\pcol@currpage!}
% which is initialized by \!\pcol@output@start! to let $\pp^i(\ptop)$ have
% the \preenv.  Then the macro is redefined to have the value representing
% the new page possibly with $\pp^i(\ptop)$ for \pwise{} floats in
% \!\pcol@startpage! by the macro \!\pcol@defcurrpage!.  Another
% \!\def!inition is done in \!\pcol@output@switch! also with
% \!\pcol@defcurrpage! to let $\pp^f(\ptop)$ have \Scfnote{}s built in
% \!\footins! if \scfnote{} typsetting is in effect and the \cswitch{}
% leaves the column in $\ptop$\footnote{
% 
% The \!\def!inition of \!\pcol@currpage! in \!\pcol@setpnoelt!, and
% emptying it in \!\pcol@output@start! and \!\pcol@freshpage! are for coding
% trick and thus not for giving a really new \!\def!initions.}.
% 
% We denote the concatenation of $\PP$ and $\pp(\ptop)$ as $\Uidx\PPP$ to
% represent all pages {\em on-the-fly}.
% 
% 
% 
% \subsection{Counters}
% \label{sec:imp-ovv-counter}
% 
% Besides the context variables discussed in \secref{sec:imp-ovv-ccol}, we
% need to make counters local to each column except for those declared to be
% global by \!\globalcounter!.  Let $\Uidx\CC$ be the set (list) of all
% counters declared before \beginparacol, i.e., $\CC=\!\cl@@ckpt!$, and
% $$
% \Uidx\CG=\!\pcol@gcounters!=\{\Uidx\cg_1,\ldots\}=\!\@elt!|{|\cg_1|}|\cdots
% $$
% be the set of {\em\Uidx\gcounter{}s} which have declared so by
% \!\globalcounter!|{|$\cg_i$|}|.  Then the set of {\em\Uidx\lcounter{}s}
% $\Uidx\CTL$ is defined as follows.
% 
% \SpecialMainIndex{\pcol@counters}
% $$
% \CTL=\CC-\CG=\!\pcol@counters!=\{\Uidx\cl_1,\ldots\}=\!\@elt!|{|\cl_1|}|\cdots
% $$
% 
% Since each column has its own values in \lcounter{}s, we have to keep the
% set of counter\slash value pairs
% 
% \SpecialArrayMainIndex{c}{\pcol@counters}
% $$
% \Uidx\Cc_c=\!\pcol@counters!{\cdot}c=\{\<\cl_1,\val_c(\cl_1)\>,\ldots\}
% =\!\@elt!|{|\cl_1|}||{|\val_c(\cl_1)|}|\cdots
% $$
% for each column $c$, where $\Uidx\val_c(\cl_i)$ is the value of a counter
% $\cl_i$ local to $c$.  That is, whenever we switch from a column $c$ to
% $d$, we save $\<\cl_i,\val_c(\cl_i)\>$ in $\Cc_c$ and restore $\cl_i$ for
% $d$ by letting it have $\val_d(\cl_i)$ in $\Cc_d$, for all $\cl_i\in\CTL$.
% 
% A \gcounter{} is free from these save\slash restore operations but needs
% another special operation when it is incremented by \!\stepcounter!.  That
% is, the invocation of \!\stepcounter! for a \gcounter{} $\cg_i$ may clear
% \lcounter{}s in its set of descendant counters
% $\Uidx\clist(\cg_i)=|\pcol@cl@|{\cdot}\cg_i$
% 
% \SpecialArrayMainIndex{\theta}{\pcol@cl@}
% 
% and this clearing must be performed on the all instances of
% $\cl_j\in\clist(\cg_i)$ saved in $\Cc_c$ for all $c\In0\C$.  Therefore, on
% the \!\stepcounter!, we do the followings for all $c\In0\C$; temporarily
% restore all $\cl_k\in\CTL$ from $\Cc_c$; clear all $\cl_j\in\clist(\cg_i)$;
% and then save $\<\cl_k,\val_c(\cl_k)\>$ back to $\Cc_c$.
% 
% The other item we maintain for a \lcounter{} $\cl$ is its {\em\Uidx\lrep}
% $\arg{rep}$ in a column $c$ defined by
% $\!\definethecounter!\<\cl\>\<c\>\arg{rep}$.  The \lrep{} $\arg{rep}$ is
% kept in $|\pcol@thectr@|{\cdot}\cl{\cdot}c$ and is made \!\let!-equal to
% $|\the|{\cdot}\cl$ when the column $c$ is visted.
% 
% \SpecialArrayMainIndex{\theta{\cdot}c}{\pcol@thectr@}
% \SpecialArrayIndex{\theta}{\the}
% 
% 
% 
% \subsection{Page-Wise and Merged Footnotes}
% \label{sec:imp-ovv-scfnote}
% \changes{v1.2-2}{2013/05/11}
%	{Add the subsection ``Single-Columned and Merged Footnotes''.}
% \changes{v1.3-6}{2013/09/17}
%	{Change the title from ``Single-Columned and Merged Footnotes'' to
%	 ``Page-Wise and Merged Footnotes'' according to the new naming.}
% 
% \Uidx{\Index{page-wise footnote}}{\em Page-wise footnote}
% typesetting is completely different from ordinary {\em\Mcfnote}
% typesetting.
% 
% When a \colpage{} in the \tpage{} is built, \!\footins! keeps all footnotes
% \!\insert!ed by \!\footnote! or \!\footnotetext! in {\em any} columns in
% the page.  Therefore, \!\footnote! and \!\footnotetext! in the \tpage{}
% act as usual to add the footnote to \!\footins!.  Then if a \cswitch{}
% takes place to leave the column, \!\footins! is saved into $\pp^f(\ptop)$
% by \!\pcol@output@switch!, so that $\pp^f(\ptop)$ is \!\insert!ed to
% \!\footins! again by \!\pcol@restartcolumn! when it visits a column in
% $\ptop$, or by \!\pcol@startcolumn! when it finds a column proceeds to
% $\ptop$.
% 
% Then, when a \colpage{} in the \tpage{} completes advancing $\ptop$,
% \!\footins! is kept in $\pp^f(\ptop{-}1)$ by \!\pcol@startpage!, rather
% than being combined with the \colpage{}.  This saving into
% $\pp^f(\ptop{-}1)$ {\em fixes} the footnotes in $\ptop{-}1$ so that
% $\pp^f(\ptop{-}1)$ is combined with other materials in the page by
% \!\pcol@outputelt! or \!\pcol@makeflushedpage! through \!\pcol@putfootins!
% when the page is shipped out.
% 
% Fixing $\pp^f(p)$ for $p<\ptop$ makes it impossible to add footnotes in a
% column in the page $p$ not only to $\pp^f(p)$ but also to \!\footins!
% for the page $p$ becaues we have at least one fixed \colpage{} $\s_c(p)$
% unable to shrink to have such additional footnotes in $p$\footnote{
% 
% The \colpage{} $\s_c(p)$ could have some space at its bottom produced by,
% for example, \cs{newpage}, but exploitation of such space is extremely
% hard.}.
% 
% Therefore, such a footnote addition is {\em deferred} and is thrown into
% $\pp^f(\ptop)$ through a list;
% $$
% \Uidx\df=\!\pcol@topfnotes!=
% (f_1,f_2,\ldots,f_n)=\!\vbox!|{|f_1\;f_2\;\cdots\;f_n|}|
% $$
% where $f_i$ is a \!\vbox! containing the deferred footnote preceded by
% \!\penalty!\!\interlinepenalty! to allow \TeX{} to break footnotes to place
% them in two (or more) pages.  That is, \!\footnote! or \!\footnotetext! in
% $p<\ptop$ adds an element for the footnote to $\df$, then all the elements
% 
% \footnote{More accurately, some trailing elements may be left in $\df$ if
% its total height is too large, as discussed in
% \secref{sec:imp-sout-scfnote}.}
% 
% are \!\insert!ed to \!\footins! by \!\pcol@deferredfootins! invoked in
% \!\pcol@restartcolumn! when it visits a column in $\ptop$, or in
% \!\pcol@startcolumn! when it starts a \colpage{} in $\ptop$.  The macro
% \!\pcol@output@end! also do the \!\insert!ion by itself with \Mgfnote{}
% typesetting to let deferred footnotes be a part of \postenv.
% 
% The reference to $\pp^f(p)$ for $p<\ptop$ is also made in
% \!\pcol@restartcolumn! and \!\pcol@flushcolumn!.  The former \!\insert!s
% $\pp^f(p)$ to \!\footins! so that the \colpage{} which the macro restarts
% is built as if it has the footnotes in $\pp^f(p)$ to make the \colpage{}
% broken leaving the space for the footnotes.  However, \!\footins! is never
% grown because it has been fixed and thus additional footnotes will go
% to $\df$ as discussed above.  Then \!\footins! is discarded by
% \!\pcol@makecol! when the \colpage{} completes, or by
% \!\pcol@output@switch! when it leaves the column.
% 
% The reference to $\pp^f(p)$ by the latter macro \!\pcol@flushcolumn! is to
% build the ship-out image of the \colpage{} to be flushed.  When this macro
% and other macros, namely \!\pcol@makecol! and \!\pcol@makeflushedpage!,
% build the ship-out image in a page $p$ having $\pp^f(p)$ using
% \!\@makecol!, we have to be careful of the fact that the \colpage{} has
% been build as if it has footnotes in $\pp^f(p)$ but the footnotes are not
% included in its ship-out image but that of the page.  Therefore,
% \!\@colht! referred in \!\@makecol! should be shrunk by the sum of
% height and depth of $\pp^f(p)$ and $\!\skip!\cdot\pp^f(p)$ by
% \!\pcol@shrinkcolbyfn!.  Other and more subtle adjustment is to add the
% stretch and shrink factors of $\!\skip!\cdot\pp^f(p)$ at the tail of the
% \colpage{} by \!\pcol@unvbox@cclv!.  This is necessary because \TeX{} has
% broken the \colpage{} taking account of the stretch and, more essentially,
% shrink factors, and thus without the factors the main vertical list in the
% \colpage{} could be a little bit taller than \!\@colht! causing overfull.
% 
% The feature gathering footnotes in all columns in a page brings a problem
% to \exsync{}, because a column whose contents fit the \tpage{} at the
% last visit may be too tall on the \sync{}ation because other columns have
% put some footnotes after the last visit.  That is, we cannot simply build
% the \tpage{} combining $\s_c(\ptop)$ for all $c\In0\C$ and $\pp^f(\ptop)$
% because there could be $\s_c(\ptop)$ too tall to reside in $\ptop$ with
% $\pp^f(\ptop)$.
% 
% To solve this problem, we perform the following operations prior to fix
% the contents of $\ptop$ having an \exsync{} point in it.  First one is
% {\em\Uidx\cscan} to visit all columns by \cswitch{} prior to the
% \sync{}ation so that \TeX's page builder has opportunities to break too
% tall \colpage{}s.  Since this scan could merely break footnotes rather
% than the main vertical lists in the \colpage{}s and the broken footnotes
% will be reconnected when the \!\output!-routine is invoked for the
% \sync{}ation, we then examine if all $\s_c(\ptop)$ are accommodated in
% $\ptop$ with $\pp^f(p)$.
% 
% This examination for a \sync{}ation by \!\switchcolumn!|*| or its
% relatives is done as a part of the inherent \sync{}ing procedure to see if
% the combination of the tallest {\em top} items, i.e., top floats and the
% main vertical list, and the tallest {\em bottom} items, i.e., bottom
% floats and \Mcfnote{}s, is too large causing page flushing.  As for page
% flushing and environment closing, this {\em\Uidx\pfcheck} requires a
% special kind of \sync{}ed \cswitch{} by which we flush pages up to
% $\ptop-1$ and examine if there is a too tall column.
% 
% Then if too tall columns are found, in either cases, we move to the {\em
% tallest} column to force a page break in the column so that we have a new
% page with shorter columns and shorter \Scfnote{}s as well.  In the
% \sync{}ation by \!\switchcolumn!|*| or its relatives, this forced page
% break is then applied to all other columns so that new \colpage{}s have
% top floats, if any, below which we should place the \sync{}ation point.
% This examination and forced page break is repeated until we have a page
% without any too tall columns, because a page break may bring deferred
% floats and footnotes which may result in a too tall column.
% 
% 
% 
% \subsection{Text Coloring}
% \label{sec:imp-ovv-color}
% \changes{v1.2-1}{2013/05/11}
%	{Add the subsection ``Coloring''.}
% \changes{v1.3-5}{2013/09/17}
%	{Change the subsection title from ``Coloring'' to ``Text Coloring''
%	 to distinguish it from background painting clearly.}
% 
% \subsubsection{Fundamental Mechanism}
% \label{sec:imp-ovv-color-fundamental}
% \changes{v1.34}{2018/05/07}
% 	{Revise the description of \Sec1.6.1 according to the new
%	 implementation with \cs{insert}.}
% 
% Text coloring done by \textsf{color} package and its relatives using
% \!\special! stands on the fact that the main vertical list is {\em
% printed} in the order of occurrence in the source |.tex|.  That is, a
% command such as \!\color!|{red}| puts
% \!\special!|{color push [1 0 0]}|\footnote{
% 
% If \texttt{.dvi} is processed by \texttt{dvips}, or other
% printer-dependent command corresponding to it.}
% 
% into |.dvi| to make all stuff in the main vertical list colored red until
% other coloring \!\special! inserted by other coloring macro appears in
% |.dvi|.  This simple mechanism works well even when the pair of coloring
% \!\special!s are in different pages and/or columns because, with respect
% to the main vertical list, everything between them in |.tex| is also
% surrounded by the \!\special! pair in |.dvi|.  As for other stuff such as
% header, footer, floats and footnotes, \LaTeX{} surrounds them by
% \!\color@begingroup! and \!\color@endgroup! or other similar constructs so
% that they are colored without interference with the coloring of the main
% vertical list.
% 
% In \env{paracol} environment, however, the orders of the main vertical list
% in |.tex| and |.dvi| are not always same.  When a column encounters a page
% break, in |.dvi| the other column should intervene between the stuff in
% the broken pair of \colpage{}s possibly changing the color of the second
% \colpage.  A \cswitch{} from $c_1$ to $c_2$ also makes the main vertical
% list out-of-order to cause another unexpected coloring because a coloring
% command in $c_2$ will have no effect when $c_1$ is revisited after that
% following its pre-switching stuff in |.dvi| which was put before the
% coloring.  Therefore, we have to make {\em\Uidx\colorctext{}s} in both
% |.tex| and |.dvi| coherent inserting appropriate \!\special!s into |.dvi|
% whenever an out-of-order {\em jump} occurs in |.dvi| by a page break or in
% |.tex| by a \cswitch{}.
%
% The \textsf{color} package and its relatives\footnote{
% 
% And all other coloring mechanism compliant with \LaTeXe{}, hopefully and
% believingly.}
% 
% assume that {\em printers} have a stack for coloring and thus a coloring
% \!\special! pushes the new color into the stack while it is popped by
% another \!\special! which will be inserted by \!\aftergroup!  mechanism
% when a group surrounding the coloring \!\special! is closed.  Therefore we
% have to keep track of the \colorctext{} with {\em\Uidx\colorstack}
% $$
% \Uidx\cst=
% (\Uidx\celt_1,\celt_1,\ldots,\celt_n)=
% \!\vbox!|{|\celt_1\;\celt_2\;\ldots\;\celt_n|}|
% $$
% where $\celt_i$ is a \!\vbox! of 1\,|sp| tall, 0 deep and 0 wide containing
% a coloring \!\special! which \!\set@color! puts into the main vertical
% list.  That is, when \!\set@color! is invoked we push $\celt$ to the tail
% of $\cst$, while when the corresponding \!\reset@color! appears we pop it
% from $\cst$\@.  Then when we encounter an out-of-order jump, at first we
% rewind the \colorstack{} in |.dvi| by putting \!\special!s which
% \!\reset@color! would put, and then reestablish the \colorstack{} by
% putting \!\special!s in $\celt_i$ as if \!\set@color! for it is invoked
% for all $\celt_i\in\cst$.  Therefore from the viewpoint of a {\em
% printer}, it will see stack-rewinding at the end of each \colpage{} and
% the leaving points of \cswitch{}, while the beginning of each \colpage{}
% and the entry points of \cswitch{} should have the sequence of coloring
% \!\special!s to regain the \colorstack{} which the {\em printer} must have
% at each of the points.
% 
% \SpecialArrayMainIndex{c}{\pcol@columncolor@box}
% 
% In addition, for each column $c$ we keep
% $\Uidx\Celt^c=|\pcol@columncolor@box|\cdot c$ as the {\em default} color
% of the column $c$, optionally given by the API macro \!\columncolor! or
% \!\normalcolumncolor!.  If given for $c$, it is assumed to be at the bottom
% of the \colorstack{} denoted by
% $\Uidx\CST^c=(\Celt^c,\celt_1,\ldots,\celt_n)$ which we rewind\slash
% reestablish at each out-of-order jump in the column $c$.
% 
% 
% 
% \subsubsection{Coloring in Horizontal Mode}
% \label{sec:imp-ovv-color-hmode}
% \changes{v1.22}{2013/06/30}
%	{Add the subsection ``Coloring in Horizontal Mode''.}
% \changes{v1.34}{2018/05/07}
% 	{Revise the description of \Sec1.6.2 according to the new
%	 implementation with \cs{insert}.}
% 
% We have to pay attention to the fact a coloring command can appear in
% horizontal mode of course, and thus push/pop operations in a \colpage{}
% would be done {\em before} the \colpage{} starts when \!\set@color! or
% \!\reset@color! is in the second half of a page-crossing paragraph and if
% we immediately performed push\slash pop of the \colorstack{} in these
% macros.  In addition, even in vertical mode these macros can appear before
% \TeX{} finds a page break after which they must be in effect, if they are
% preceded by a sequece of non-breakable vertical items by which \TeX{}'s
% examination of the page break is {\em delayed} as well as the invocation
% of \!\output! at the break.
% 
% In order to solve the problem of push/pop timing, we perform push\slash
% pop operations through \!\insert! to our own register set
% \!\pcol@colorins!.  That is, we \!\insert! $\celt$ to \!\pcol@colorins!
% when we encounter a \!\set@color! for $\celt$, while its corresponding
% \!\reset@color! also \!\insert!s another \!\vbox! $\Uidx\celtpop$ of
% null-height\slash depth\slash width having a \!\special! which the
% \!\reset@color! puts into the main vertical list.  Since we let
% $\!\count!\!\pcol@colorins!=0$ and $\!\skip!\!\pcol@colorins!=0$ to keep
% the \!\insert!iion from affecting the growth of \!\pagetotal!, it is
% guaranteed that an inserted $\celt$ or $\celtpop$ is given to \!\output!
% through \!\pcol@colorins! together with |\box255| containing the
% corresponding \!\special!.
% 
% When \!\output! is invoked, \!\pcol@colorins! has $\Uidx\cstraw$
% containing $\celt_i$ and possibly its corresponding $\celtpop_i$.
% Therefore, if \!\output! is for a page break or a \cswitch, we remove all
% pairs of $\celt_i$ and $\celtpop_i$ from \!\pcol@colorins! to let it have
% $\cst$ only with $\celt_j$ whose corresponding $\celt_j^-$ is not in
% $\cstraw$.  For this removal, we scan $\cstraw$ from its tail
% incrementing\slash decrementing a counter $\Uidx\npop$ which we initialize
% to 0 before scanning.  In the scan, we remove all $\celtpop$
% unconditionally incrementing $\npop$, and $\celt$ such that $\npop>0$ on
% the encounter with it decrementing $\npop$.  This scan is done by
% \!\pcol@clearcolorstack!, invoked from \!\pcol@opcol! for a page break and
% \!\pcol@output@switch! for a \cswitch{} through \!\pcol@clearcst@unvbox!,
% and is for rewinding the \colorstack{}
% $(\Celt^c,\cstraw)=\Uidx\CSTraw^c$.  Therefore, for each $\celt$ to be kept
% because of $\npop=0$ on the encoutner with it we put \!\special! for
% \!\reset@color!.  Note that on another scan for stack reestablishment,
% \!\pcol@colorins! has $\cst$ and is kept unchanged.  Also note that other
% \!\output!  invocations such as that for floats do not touch $\cstraw$ to
% allow it grows with $\celt$ and $\celtpop$ corresponding to \!\set@color!
% and \!\reset@color! in the \colpage{} in which the invocation
% happens\footnote{
% 
% Unlike \cs{footins} which becomes void by putting its contents back to the
% main vertical list to reexamine the footnote placement possibly with
% splitting.}.
% 
% The mechanism above especially for horizontal mode has subtle issues as
% follows.
% 
% \begin{itemize}
% \item
% If \!\set@color! appears in a \!\vbox!, the \!\insert!ion for pushing
% is not effective but corresponding \!\reset@color! can be outside of the
% \!\vbox! to make pushes and pops unbalanced because \!\aftergroup! for it
% inserts it just after the closing of the \!\vbox! if \!\set@color! is not
% surrounded by an inner group.
% 
% \item
% If we are in vertical mode, we can know if we are in a \!\vbox! by
% \CSIndex{ifinner}.  However, in horizontal or math mode, \CSIndex{ifinner}
% cannot help us because it is true iff we are in a \!\hbox! or in an
% in-text math.  In short, \TeX{} does not provide us with any convenient
% means to know if we are in a \!\vbox!.
% \end{itemize}
% 
% To solve the problem above, we introduced a trick with \!\everyvbox! to
% turn a switch $\CSIndex{ifpcol@inner}=\true$ at the beginning of every
% \!\vbox! in a \env{paracol} environment, by which we supress the
% \!\insert!ion for \!\set@color! because a \!\vbox! cannot cross a
% page boundary.  As for that of \!\reset@color!, we suppress it by not
% reserving our own macro \!\pcol@reset@color@pop! for the \!\insert!ion by
% \!\aftergroup!.  That is, we reserve both \!\reset@color! and
% \!\pcol@reset@color@pop! with \!\aftergroup! if we are outside of any
% \!\vbox!es, while does the former only otherwise.  By the same reason, we
% supress the \!\insert!ion if we are in restricted horizontal mode, i.e.,
% if both \CSIndex{ifhmode} and \CSIndex{ifinner} are true.  On the other
% hand, we cannot supress the \!\insert!ion when we are in an in-text math
% because it can cross a page boundary\footnote{
% 
% If an in-text math is in a \cs{hbox}, \cs{insert}ion is not
% necessary because the math cannot cross a page boundary.  Though we can
% detect it by a trick with \!\everyhbox!, we abandon this idea because the
% request is not harmful.  Another and more serious issue of coloring in
% math mode will be discussed shortly.}.
% 
% Note that the detailed implementation shown in \secref{sec:imp-startenv}
% does not interfere the use of \!\everyvbox! inside/outside of
% \env{paracol} environments or is not affected by the use.
% 
% Another attention we should pay is that \!\color! will leave \!\aftergroup! 
% tokens of \!\reset@color! and thus they are invoked just after
% \Endparacol.  However, since we have completed all \colpage{}s in the
% \lpage, the \colorstack{} in |.dvi| should be empty.  Therefore to avoid
% stack underflow, we should reestablish $\cst$ (not $\CST^c$) so that
% elements in the stack are popped by \!\reset@color! invoked with the
% \!\aftergroup! mechanism.  We also take care of our own \colorstack{}
% popper \!\pcol@reset@color@pop! which must do nothing, i.e., must not make
% an \!\insert!ion, after we completed the \lpage, i.e., if
% \CSIndex{ifpcol@output} is $\false$.
% 
% 
% 
% \subsubsection{Changing Default Column Color}
% \label{sec:imp-ovv-color-colcolor}
% \changes{v1.34}{2018/05/07}
% 	{Split the description of \cs{columncolor} from \Sec1.6.2 to have
%	 new \Sec1.6.3 ``Changing Default Column Color'' because we have
%	 serveral new issues in the new implementation with \cs{insert}.}
% 
% The implemntation of \!\columncolor! and \!\normalcolumncolor! is
% relatively easy for the cases that they appear outside
% \env{paracol} environment or they define the default color of a
% column different from the current column.  That is, for the default color
% of a column $c$ we simply \!\def!ine
% ${\Uidx\Celtshadow}^c=|pcol@columncolor|\cdot c$ to let it have what
% \!\current@color! has for the color.  Then, in \beginparacol{} in the
% former case or immediately in the latter, we let
% $\Celt^c=|pcol@coloumncolor@box|\cdot c$ have the coloring \!\special! for
% the color acquiring an \!\insert! from \!\@freelist! if the box is
% $\bot$.
% 
% \SpecialArrayMainIndex{c}{\pcol@columncolor}
% \SpecialArrayIndex{c}{\pcol@columncolor@box}
% 
% On the other hand, when the API commands are to define the default color
% of the current column $c$, we need to place the coloring at the bottom of
% \colorstack{}s in terms of |.tex| and |.dvi|.  That is, for the former we
% have to rewind and reestablish the stack which can be different from
% $\CST^c$ because the API command can follow a page break which \TeX{} does
% not yet find.  Therefore, we maintain a {\em shadow} of $\cst$ namely;
% $$
% {\Uidx\cstshadow}={\Midx{\!\pcol@colorstack@shadow!}}
% =({\Uidx\celtshadow}_1,\celtshadow_2,\ldots,\celtshadow_n)
% =\!\@elt!\Arg{\celtshadow_1}\;\!\@elt!\Arg{\celtshadow_2}\;\cdots\;
%  \!\@elt!\Arg{\celtshadow_n}
% $$
% to which our version of \!\set@color! pushes $\celtshadow_i$ being
% \!\current@color! which the original one defines, while popping is done
% automatically by \TeX's grouping mechanism because pushes are done by
% \!\edef! rather than \!\xdef!.  Then before we \!\def!ine $\Celtshadow^c$
% we rewind
% ${\Uidx\CSTshadow}^c=(\Celtshadow^c,\celtshadow_1,\ldots,\celtshadow_n)$
% putting \!\special! for pop to the main vertical list for each elements,
% and then after the \!\def!initon of $\Celtshadow^c$ we reestablish
% $\CSTshadow^c$ putting coloring \!\special! for each element.
% 
% As for placing $\Celt^c$ at the bottom of $\CST^c$, we must ensure that
% the placement is done for the \colpage{} in which the API command
% belongs to, as we did in ordinary push\slash pop of the \colorstack.
% Therefore the API command \!\insert!s $\Celt^c$ to $\cstraw$ in the form
% of a \!\vbox!, whose height and depth are 1\,|sp| and width is 0,
% containing the coloring \!\special! for $\Celt^c$.  Then when $\cstraw$ is
% scanned for rewinding in \!\output!, this \!\vbox! is found to let
% $\Celt^c$ have the \!\special! acquiring an \!\insert! from \!\@freelist!
% it was $\bot$.  Note that $\cstraw$ may have multiple \!\vbox!es to update
% $\Celt^c$ and if so the last one is effective.
% 
% 
% 
% \subsubsection{Coloring in Math Mode}
% \label{sec:imp-ovv-color-mmode}
% \changes{v1.24}{2013/07/27}
%	{Add the subsection ``Coloring in Math Mode''.}
% \changes{v1.34}{2018/05/07}
% 	{Revise the description of \Sec1.6.4 according to the new
%	 implementation with \cs{insert}.}
% 
% Unfortunately the solution above is imperfect because \TeX{} builds an
% implicit \!\hbox! for a |{|\textit{math stuff}|}| construct in math mode
% and an \!\insert! in the construct does not contribute to
% the main vertical list at all\footnote{
% 
% The contents is not thrown away but \cs{insert}ion itself is added
% to the list rather than given to \cs{output}.}.
% 
% Since the implicit \!\hbox! does not care about \!\everyhbox!, we cannot
% use the trick similar to that with \!\everyvbox!.  Another bad news is
% that built-in \cs{if}s for mode checking cannot help us because we always
% have $\CSIndex{ifvmode}=\CSIndex{ifhmode}=\false$ and
% $\CSIndex{ifmmode}=\true$ while $\CSIndex{ifinner}$ is $\true$ or $\false$
% when we are in in-text or displayed math mode respectively.  Therefore, we
% have to take care of the potential loss of \!\insert!ion for pushes and
% thus unmatched pops in $\cstraw$.
% 
% For example, we have to remember that, in the cases like
% |${|\!\color!$\Arg{c}\textit{text}$|}$| or
% |$|\!\textcolor!$\~\Arg{c}\ARg{text}$|$| expanded to the former, the
% \!\insert!ion for push is lost while its counterpart for pop survives
% making it necessary to check the existance of pushing counterpart for each
% pop in $\cstraw$\footnote{
% 
% Since a pop is always in a group one level outer from its push
% counterpart, the pop request should be presented if the push does.}.
% 
% Note that the fact that the pop in the examples is in the in-text math
% does not help us, because the pop in
% |$|\!\begingroup!\!\color!\Arg{c}\textit{text}\!\endgroup!|$| is also in
% the in-text math while its pushing counterpart performs an effective
% \!\insert!ion, and two \!\insert!ions must be presented in $\cstraw$
% because we can have a page-break in \textit{text}.  Therefore, we have to
% find a means to examine whether a pop $\celtpop_i$ has its counterpart
% $\celt_i$ in $\cstraw$ to remove $\celt_i$ from $\cstraw$ if exists or to
% igonore $\celtpop_i$ otherwise.  That is, we have to attach an identifier
% $m$ to $\celt_i$ and $\celtpop_i$, i.e., to make them $\Uidx\mcelt_{i,m}$
% and $\Uidx\mceltpop_{i,m}$.
% 
% Since the only means we have for the communication with \!\output! routine
% is what we \!\insert! to $\cstraw$, the \!\insert!ed \!\vbox! must carry an
% identifier $m$ for a push\slash pop in math mode.  To do that, we make
% \!\vbox! $m$\,|sp| wide ($m>0$) if our version of \!\set@color! is in math
% mode to represent $\mcelt_{i,m}$ and $\mceltpop_{i,m}$, while the width is
% 0 otherwise as described in \secref{sec:imp-ovv-color-hmode}.  Then in the
% scan of $\cstraw$ for rewinding in \!\output!, we supress
% incrementing\slash decrementing $\npop$ for $\mcelt_{i,m}$ and
% $\mceltpop_{i,m}$, but remove $\mcelt_{i,m}$ if $\mceltpop_{i,m}$ is in
% $\cstraw$ as a successor while we keep it in $\cstraw$ otherwise putting a
% \!\special! of pop for it to the main vertical list.
% 
% To ensure that $\mcelt_{i,m}$ has its counterpart $\mceltpop_{i,m}$ in
% $\cstraw$ iff the push and pop are in a \colpage, we maintain the counter
% \!\pcol@mcid! incremented before (the attempt of) the \!\insert!ion of
% $\mcelt_{i,m}$ with $m=\!\pcol@mcid!$ and the \!\aftergroup! reservaion
% for that of $\mceltpop_{i,m}$.  Then the counter is zero-cleared by
% \!\output! routine in order to keep it less than
% $\!\pcol@mcpushlimit!=1000$ unless, roughly speaking, a \colpage{} has a
% unexpectedly large number of math constructs having coloring commands in
% them.  Note that this zero-clearing does not ensure that an identifier $m$
% is unique in $\cstraw$.  That is, it can happen that $\cstraw$ has
% $\mcelt_{i,m}$, $\mceltpop_{i,m}$, $\mcelt_{j,m}$ and/or $\mceltpop_{j,m}$
% in this order for $i<j$, when two math constructs with coloring for $i$
% and $j$ are in different paragraphs and \!\output! is invoked at or after
% the end of the paragraph with the math for $i$.  This potential
% duplication is, however, unharmful because of the following.
% 
% \begin{itemize}
% \item
% Since a math construct cannot have immediate \!\output! invocations in it,
% the order of the elements in $\cstraw$ must be $\mcelt_{i,m}$,
% $\mceltpop_{i,m}$, $\mcelt_{j,m}$ and $\mceltpop_{j,m}$ from its bottom to
% top, though some of them could be missing.  Therefore, if
% $\mceltpop_{i,m}$ is in $\cstraw$, $\mcelt_{j,m}$ must follow it if
% exsits not causing accidental matching with $\mceltpop_{i,m}$.
% 
% \item
% If $\mcelt_{i,m}$ is in $\cstraw$ but $\mceltpop_{i,m}$ is not, it means
% we have a page break between vertical items corresponding to
% $\mcelt_{i,m}$ and $\mceltpop_{i,m}$ to keep the \!\insert!ion of
% $\mceltpop_{i,m}$ and anything following it from appended into $\cstraw$.
% Therefore, $\cstraw$ cannot have $\mceltpop_{j,m}$ not causing accidental
% matching with $\mcelt_{i,m}$.
% \end{itemize}
% 
% 
% 
% \subsubsection{Emptiness of a Column-Page}
% \label{sec:imp-ovv-color-emptycol}
% 
% The mechanism above works well with respect to coloring, but it has a
% problem that a \colpage{} created by, for example, a forced page break may
% not be perfectly empty but can have some coloring \!\special!s for
% \colorstack{} reestablishing and rewinding.  They are of course invisible
% but affect the examination of \colpage{} emptiness for \exsync.  That is,
% we examine if a \colpage{} does not have anything by a tricky way by
% \!\pcol@ifempty! but the existence of coloring \!\special!s makes the
% examination failed even if no other ordinary stuff such as boxes and skips
% are in the \colpage.
% 
% Therefore we need to put coloring \!\special!s for \colorstack{}
% establishing and rewinding a little bit more carefully to avoid empty
% \colpage{}s just having such \!\special!s as follows.  When we start a new
% \colpage{}, we don't put \!\special!s for establishing immediately but
% save the \colorstack{} $\CST^c$ into
% $\Uidx\csts=\!\pcol@colorstack@saved!$.  Then when we leave the
% \colpage{} by switching or page breaking, we examine the emptiness of the
% \colpage{} and if so we do nothing, while otherwise we put the
% \!\special!s for reestablishing $\csts$ at the top of the \colpage{} and
% those for rewinding $\cstraw$ at the bottom.  Similary, when we revisit a
% \colpage, we examine its emptiness and if so we save $\CST^c$ into
% $\csts$, while otherwise we put \!\special!s for reestablishing $\CST^c$
% and nullify $\csts$ so that nothing will be put at the top of the
% \colpage{} when we leave it.  By these mechanisms, an empty \colpage{}
% should not have coloring \!\special!s, while non-empty ones should have a
% sequence of triples; reestablishing \!\special!s; ordinary main vertical
% list items including coloring \!\special!s inserted by \!\color! etc.; and
% then rewinding \!\special!s.
% 
% 
% 
% \subsection
% [Parallel-Paging, Column-Swapping, Column-Separating Rule
%   Drawing and Background Painting]
% {Parallel-Paging, Column-Swapping, Column-Separating\\Rule
%   Drawing and Background Painting}
% \label{sec:imp-ovv-cswap}
% \changes{v1.2-4}{2013/05/11}
%	{Add the subsection ``Column-Swapping''}
% \changes{v1.3-1}{2013/09/17}
%	{Change the section title from ``Column-Swapping'' to
%	 ``Parallel-Paging, Column-Swapping, Column-Separating Rule Drawing
%	 and Background Painting'' to discuss related issues together''.}
% \changes{v1.3-2}{2013/09/17}
%	{Add overview description of parallel-paging.}
% \changes{v1.3-3}{2013/09/17}
%	{Add overview description of column-separating rule drawing and
%	 background painting.}
% 
% We have the following four extensions, which are correlated to each other,
% from the basic parallel-columning.
% 
% \paragraph{\em Parallel-paging}\UsageIndex{parallel-paging}\hskip-.5em
% to extend the concept of parallel-columning in a page to a pair of
% adjacent pages.  A {\em left} \parapag{}e starts from column-0, has
% $\Uidx\CL$ columns where $\CL$ is given by the first optional argument of
% \beginparacol, while a {\em right} \parapag{}e starts from column-$\CL$
% and has $\C-\CL$ columns.  Since we let $\CL=\C$ when \parapag{}ing is not
% in effect, we may ship out columns $c\In0\CL$ always and then, if
% $\CL<\C$, ship out columns $c\In\CL\C$ as a right \parapag{}e.
% 
% The pair of \parapag{}es can be {\em\Uidx\paired} to comprise a virtual
% page $p$ and thus has common page number $\page(p)$, while
% {\em\Uidx\npaired} \parapag{}ing produces two individual pages from a
% internal page $p$ (i.e., set of all columns $\Set{c}{c\In0\C}$) whose
% left and right components have page numbers $\page(p)$ and $\page(p)+1$
% respectively.  Since a page $p$ is internally considered as the set of all
% columns $c\In0\C$ always, regardless of \paired{} or \npaired{}
% \parapag{}ing, the difference between them arises only in two-sided
% ship-out process in which the header, footer and left-margin are common
% for left\slash right \paired{} \parapag{}s while they have to depend on
% the parity of the number of each \npaired{} \parapag{}e.  Note that
% \textsf{paracol} does not specify the parity of a left \npaired{}
% \parapag{}e number, but the number is decided by the page from which a
% \parapag{}ed \env{paracol} environment starts.
% 
% In ship-out process, we build the ship-out image of a right \parapag{}e in
% our own \!\box! register \!\pcol@rightpage! instead of the usual
% \!\@outputbox!.  The register, however, must {\em survive} after
% \Endparacol{} to keep the columns in the last right \parapag{}e,
% 
% \Index{last page}
% 
% so that it is shipped out when the whole of last page including \postenv{}
% is shipped out, or, more complicatedly, to be passed to the next
% \env{paracol} environment as a part of its \preenv.
% 
% {\em Page-wise stuff}
% \UsageIndex{page-wise stuff}
% spanning all columns, i.e., \spanning{} being \preenv{} or \pwise{}
% floats, \mctext{}s, \scfnote{} footnotes and \postenv{} are always placed
% in a left \parapag{}e, while the corresponding regions for them in a right
% \parapag{}e are always blank\footnote{
% 
% So far.  In some future, we could implement a special setting to let
% \preenv{}, \postenv{} and \scfnote{} footnotes are split into both
% \parapag{}es, and to make it possible that a \pwise{} float or a
% \mctext{} has its counterpart placed in the corresponding right
% \parapag{}e.}
% 
% unless \preenv{} has the \lpage{} of the previous \env{paracol}
% environment.
%
% \paragraph{\em Column-swapping}\UsageIndex{column-swapping}\hskip-.5em
% to reverse the order of columns in even numbered pages from left-to-right
% to right-to-left.  It is enabled by the specifier `|c|' of
% \!\twosided!\footnote{
% 
% Or the backward compatible macro \!\swapcolumninevenpages!.}.
% 
% Though it is fundamentally simple because we just need to reverse the
% scanning order of columns from left-to-right (i.e., 0 to $\C-1$) to
% right-to-left (i.e., $\C-1$ to 0) in the ship-out process of an even
% numbered page, there are a few complications in the implementation of
% related functionalities.
% 
% First, a \paired{} \parapag{}e should also be swapped so that a
% \emph{physical} left (resp.\ right) \parapag{}e has columns $\C-1$ to
% $\CL$ (resp.\ $\CL-1$ to 0) in this order.  Note that this \parapag{}e
% swapping also swaps the page in which \pwstuff{} are placed.  That is, if
% both \paired{} \parapag{}ing and \cswap{} are in effect, \pwstuff{} are
% placed in the physical right \parapag{}e, or in other words they always
% placed in the page in which column-0 resides.  Note that since \cswap{}
% with \npaired{} \parapag{}ing is meaningless and thus \cswap{} is
% disabled.
% 
% Second, the side margin to which a marginal note goes can be swapped but
% enabling this swap is independent of \cswap{} and done by the specifier
% `|m|' of \!\twosided!, though almost all users will specify both swapping
% consistently.  Since the side margin for a marginal note is decided in
% \!\output! routine by \!\pcol@addmarginpar! being our own version of
% \LaTeX's macro for maginal notes \!\@addmarginpar!, the page in which the
% margial note resides has been fixed.  However, the number of the page and
% thus its parity may not have been fixed yet due to the possible jump in
% column-0 taking place afterward, unlike \cswap{} for which the page number
% has been fixed because it is performed in ship-out process.  Since it is
% too costly to avoid this possibly wrong placement, we have to accept the
% possibility as \LaTeX{} itself does.  Also unlike \cswap, the swapping of
% marginal notes is not disabled in \npaired{} \parapag{}ing because it is
% meaningful.
% 
% Another remark for marginal notes is that two ore more columns may {\em
% share} a margin, inevitably if a (parallel) page has three or more columns
% or intentionally with a setting of \!\marginparthreshold!.  Therefore, the
% context of marginal notes cannot be in \cctext{} but should be in \pctext,
% or cannot simply give the bottom of the last marginal note (i.e., \LaTeX's
% \!\@mparbottom!) but should show all marginal notes in margins in a
% page\footnote{
% 
% Before version 1.3, we have \!\@mparbottom! in \cctext{} because a column
% has its own area for marginal notes, which can be the gap between columns
% rather than a margin of a page.}.
% 
% Therefore, each \pctext{} has all marginal notes in the form of lists of
% their top and bottom positions in all margins as $\pp^m(p)$, so that we
% find a space for a marginal note in a column to add it to not only to the
% bottom but also into a space between two marginal notes having already
% been put by other columns.
% 
% Third and finally, we have to take care the placement of \mctext{}s.  In
% version 1.2 to which \cswap{} is introduced, we let a \mctext{} belong to
% column-$(\C-1)$ instead usual column-0 so that its left edge is aligned to
% the left edge of the leftmost column, i.e., that of the text area.
% However this simple solution has a severe problem that, if a \mctext{} is
% broken into two pages, its second half should be put in the rightmost
% column.  In addition, even when a \mctext{} does not have page break in
% it, such wrong placement may happen if the text is followed by \!\nobreak!
% and thus a page break is made above the text but {\em after} the text is
% processed.
% 
% In version 1.3, this problem is solved by capturing the first half of a
% \mctext{} in \!\output! routine for the page break in the text, and the
% second half or the whole of it in that for \sync{}ed \cswitch{} to close
% the text.  Since an invocation of \!\output! routine means that it has been
% fixed which page the \mctext{} or its part resides in, we can place the
% text much more reliably expecting the parity of the page number has also
% been fixed.  In addition, this decision making in \!\output! routine allows
% (or forces) us to let \mctext{}s always belong to column-0 preserving the
% consistency of, for example, local counter values referred to in them,
% while we need to shift a text to the left edge of the text area if it
% resides in an even numbered page.  Furhtermore, this \mctext{} capturing
% enables to measure the vertical size of the captured text together with the
% vertical position of its top edge to record them in the list $\pp^s(p)$,
% so that we draw \cseprule{}s skipping the text and painting its \bground{}
% with a specific color different from colors of columns and \csepgap{}s, as
% discussed shortly.
% 
% \paragraph{\em Column-separating rule drawing}
% \UsageIndex{column-separating rule}\hskip-.5em
% to draw a vertical rule in {\em\Uidx\csepgap} is correlated with a part of
% {\em\bgpaint} to paint each region in a page with a color specific to the
% region.  Thanks to the list of \mctext{}s $\pp^s(p)=(\spt(H_i,h_i))_i^n$, we
% can draw \cseprule{}s skipping \mctext{}s in the page $p$ as the sequence
% of;
% 
% \begingroup
% \def\RULE{\mathit{rule}}\def\GAP{\mathit{gap}}
% \begin{eqnarray*}
% &&\RULE(H'_1),\GAP(h_1),\ldots,\RULE(H'_n),\GAP(H'_n),\RULE(H'_{n+1})\\
% &&H'_i=H_i-(H_{i-1}+h_{i-1})
% \qquad H_0=h_0=0
% \qquad H_{n+1}=\pp^h(p)
% \end{eqnarray*}
% \endgroup
% 
% where $\mathit{rule}(H')$ is a vertical rule of $H'$ high and
% $\mathit{gap}(h)$ is a vertical space of $h$.  A rule may be colored with
% the color specified by \!\colseprulecolor! for each \csepgap{} or all
% of them.  Note that if \cswap{} is in effect, a column $c$ is {\em
% preceded} by $c$-th \csepgap{} which may have its own width and color for
% its rule, rather than being followed by it.
% 
% \paragraph{\em Background painting}\UsageIndex{background painting}\hskip-.5em
% also uses the list $\pp^s(p)$ to paint the \bground{} of each column-$c$
% with the color $\Uidx\bgc_c^c$, each \csepgap{} following the column-$c$
% with $\bgc_g^c$, and \mctext{}s with $\bgc_s$ and $\bgc_S$, where
% $\bgc_a^{[c]}$ is specified by the second argument of
% $\!\backgroundcolor!\Arg{\hbox{\ttfamily\itshape a}|[|c|]|}\~\Arg{color}$
% ($\hbox{\ttfamily\itshape a}\in\{|c|,|g|,|s|,|S|\}$) and kept in the macro
% $|\pcol@bg@color@|{\cdot}a[|@|{\cdot}c]$.
% 
% \SpecialArrayMainIndex{a}{\pcol@bg@color@}
% \SpecialArrayMainIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}
% 
% The region to be painted for each item is as follows where
% $[(x_0,y_0)(x_1,y_1)]$ means the region
% $\Set{(x,y)}{x\In{x_0}{x_1},\;y\In{y_0}{y_1}}$ of the top-down
% $xy$-coordinate whose origin is at the left-top corner of the leftmost
% column.
% 
% \begingroup\def\sS{{\{s,S\}}}
% \begin{eqnarray*}
% \Uidx\bgr_c^c(i)&=&[(\Uidx\W_c,\;H_{i-1}+h_{i-1})\;
%   (\W_c+w_c,\;H_i+d_{c/g})]\\
% \bgr_g^c(i)&=&[(\W_c+w_c,\;H_{i-1}+h_{i-1})\;(\W_{c+1},\;H_i+d_{c/g})]\\
% \bgr_\sS(i)&=&[(0,\;H_i)\;(\Uidx\WT,\;H_i+h_i+d_s)]\\
% \W_{c}&=&\sum_{d=c_0}^{c-1}(w_c+g_c)\qquad
%     c_0=\cases{0&$c<\CL$\cr
%		 \CL&$c\geq\CL$}\qquad
%     \WT=\!\textwidth!\\
% d_{c/g}&=&\cases{\!\maxdepth!&$i=n+1\;\land\;H'_{n+1}>0\;\land\;$non-\lpage\cr
%                0&otherwise}\\[1ex]
% d_s&=&\cases{H_{n+1}-(H_n+h_n)+\!\maxdepth!&
%                $i=n\;\land\;H'_{n+1}=0\;\land\;$non-\lpage\cr
%              0&otherwise}
% \end{eqnarray*}
% \endgroup
% 
% In the specifications above, $\w_c$ and $\Uidx\gap_c$ is the width of the
% column $c$ and that of the \csepgap{} following it, defined by
% \!\columnratio! or \!\setcolumnwidth! and stored in
% $|\pcol@columnwidth|{\cdot}c$ and $|\pcol@columnsep|{\cdot}c$
% respectively.
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% \SpecialArrayMainIndex{c}{\pcol@columnsep}
% 
% The additions of $d_{c/g}$ and $d_s$ are to extend the bottom edge of each
% region down to the bottom of text area.  In addition, for each
% $\bgr_a^{[c]}=[(x_0,y_0)(x_1,y_1)]$, {\em\Uidx\bgext}s
% $\Uidx{\bge}_a^{[c]}(\{x,y\}^\pm)$ can be specified to shift the base
% points $x_0$, $y_0$, $x_1$ and $y_1$ left ($x^-$), right ($x^+$), upward
% ($y^-$) and downward ($y^+$) respectively.  That is, a region is defined
% as;
% $$
% \bgr_a^{[c]}=[(x_0-\bge_a^{[c]}(x^-),\;y_0-\bge_a^{[c]}(y^-))\;
%               (x_1+\bge_a^{[c]}(x^+),\;y_1+\bge_a^{[c]}(y^+))]
% $$
% \begingroup\par\hfuzz0.9pt\noindent
% with the optional shifts specified by the first argument of
% \!\backgroundcolor!  as
% \Arg{\hbox{\ttfamily\itshape{a}}\oarg{c}$|(|x^\pm|,|y^\pm|)|$} (for both
% $x^-$/$y^-$ and $x^+$/$y^+$) or \Arg{\hbox{\ttfamily\itshape
% a}\oarg{c}$|(|x^-|,|y^-|)||(|x^+|,|y^+|)|$} and kept in macros
% $|\pcol@bg@ext@|{\cdot}\~d{\cdot}|@|{\cdot}a[{\cdot}|@|{\cdot}c]$
% 
% \SpecialArrayIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}
% \SpecialArrayIndex
%   {d{\cdot}\string\texttt{@}{\cdot}a{\cdot}\string\texttt{@}{\cdot}c}
%   {\pcol@bg@ext@}
% 
% where $d\in\{|l|,|r|,|t|,|b|\}$ for $x^-$ (|l|), $x^+$ (|r|), $y^-$ (|t|)
% and $y^+$ (|b|).  Note that $\bge_a^{[c]}(\{x,y\}^\pm)$ can be extremely
% large, namely greater than or equal to 9000pt, to mean the region is
% extended to a border near by the corresponding paper edge.  More
% specifically, by this {\em\Uidx\bginfext}, each $xy$ coordinate in
% $[(x_0,y_0)(x_1,y_1)]$ is defined as follows to represent a coordinate
% being $10000\PT-\bge_a^{[c]}(\{x,y\}^\pm)+\!\pagerim!$ inside from the page
% edge;
% \par\endgroup
% 
% \begingroup \def\feven{f_{\mathit{even}}}
% \begin{eqnarray*}
% x_0&=&-\WM+(10000\PT-\bge_a^{[c]}(x^-)+\WR)\\
% y_0&=&-(\HS+\HM)+(10000\PT-\bge_a^{[c]}(y^-)+\HR)\\
% x_1&=&(\WP-\WM)-(10000\PT-\bge_a^{[c]}(x^+)+\WR)\\
% y_1&=&(\HP-\HS-\HM)-(10000\PT-\bge_a^{[c]}(y^+)+\HR)\\
% \Uidx\WP&=&\!\paperwidth!\\
% \Uidx\WM&=&1|in|+\cases{\!\oddsidemargin!&$\lnot\feven$\cr
%                         \!\evensidemargin!&$\feven$}\\
% \Uidx\WR&=&\Uidx\HR=\!\pagerim!\\
% \Uidx\HP&=&\!\paperheight!\\
% \Uidx\HM&=&\!\headsep!+\!\headheight!+\!\topmargin!+1|in|\\
% \Uidx\HS&=&\mathit{height}(\pp^b(p))+\mathit{depth}(\pp^b(p))
% \end{eqnarray*}
% \endgroup
% 
% where $f_{\mathit{even}}$ is $\true$ iff we are in an even numbered page
% and two-sided typesetting is specified by the optional argument of
% \!\documentclass! or by the specifier `|p|' of \!\twosided! explicitly or
% implicitly.
% 
% Another remark is that \cswap{} affects $\bgr_c^c(i)$ and $\bgr_s^c(i)$ to
% {\em\Uidx\mirror} the region making a reflection-symmetric transformation
% on it using a vertical edge of a page as the axis.  That is,
% $[(x_0,y_0)(x_1,y_1)]$ for a region is transformed to
% $[(\WT-x_1,y_0)(\WT-x_0,y_1)]$ if $x_{\{0,1\}}$ is not extended infinitely.
% With \bginfext{} on the other hand, before this transformation $x_0$ and/or
% $x_1$ are calculated by the rule above replacing $\WM$ with
% $\WP-(\WM+\WT)$ to represent the width of the right margin rather than the
% left.
% 
% On the other hand, the \mirror{}ing of $\bgr_{\{s,S\}}$ is enabled by the
% specifier `|b|' of \!\twosided!, together with other regions being top
% margin ($t,T$), bottom margin ($b,B$), left margin ($l,L$), right margin
% ($r,R$), \pwise{} floats ($f,F$) and \scfnote{} footnotes ($n,N$).  The
% geometical specifications $\bgr_a$ for those regions are given as follows,
% but the coordinate origin is at the top-left corner of text area (rather
% than the leftmost column).
% 
% \begin{eqnarray*}
% \bgr_{\{t,T\}}&=&[(-\WM+\WR,\;-\HM+\HR),\;(\WP-\WM-\WR,\;0)]\\
% \bgr_{\{b,B\}}&=&[(-\WM+\WR,\;\HT-\HM),\;(\WP-\WM-\WR,\;\HP-\HM-\HR)]\\
% \bgr_{\{l,L\}}&=&[(-\WM+\WR,\;0),\;(0,\HT)]\\
% \bgr_{\{r,R\}}&=&[(\WT,\;0),\;(\WP-\WM-\WR,\;\HT)]\\
% \bgr_{\{f,F\}}&=&[(0.\;0),\;(\WT,\;\HS)]\\
% \bgr_{\{n,N\}}&=&[(0,\;\HT-\HN)\;(\WT,\;\HT)]\\
% \Uidx\HT&=&\!\textheight!+\!\maxdepth!\\
% \Uidx\HN&=&\!\skip!\!\footins!+\!\ht!\!\footins!+\!\dp!\!\footins!
% \end{eqnarray*}
% 
% Note that, since we use text area coordinates, in the calculation of
% \bginfext{} $\HS$ is let be 0.
% 
% We have other regions for columns and \csepgap{}s, namely $\bgr_C^c$ and
% $\bgr_G^c$, which vertically span all over text area regardless exsistance
% of any \pwstuff.  Therefore, their geometical specifications are as
% follows with text area coordinates.
% 
% \begin{eqnarray*}
% \bgr_C^c&=&[(\W_{c-1},\;0),\:(\W_{c-1}+w_c,\;\HT)]\\
% \bgr_G^c&=&[(\W_{c-1}+w_c,\:0),\;(\W_c,\;\HT)]
% \end{eqnarray*}
% 
% In addition, we have to paint \preenv{} and \postenv{} with color
% $\bgc_{\{p,P\}}$.  The region $\bgr_{\{p,P\}}$ for them is defined as
% follows with text area coordinates where $\Uidx\HB$ is the $y$-coordinate
% of the bottom of previous \env{paracol} environment if any, or 0
% otherwise.
% $$
% \bgr_{\{p,P\}}=\cases{
%	[(0,\;\HB)\;(\WT,\;\HS)]&	\preenv\cr
% 	[(0,\;\HB)\;(\WT,\;\HT)]&	\postenv}
% $$
% Note that paiting of \postenv{} is done {\em outside} \env{paracol}
% environment when the \postenv{} encounters a page break, unless another
% \env{paracol} environment starts in the page and thus the \postenv{}
% becomes \preenv{} of the second (or subsequent) environment.
% 
% Finally, we define the order of \bgpaint{} as follows, where $a$, $a(i)$,
% $a^c$ and $a^c(i)$ mean $\bgr_a$, $\bgr_a(i)$, $\bgr_a^c$ and
% $\bgr_a^c(i)$ respectively, so that a succeding region is {\em overlaid}
% on preceding regions.
% 
% \begin{eqnarray*}
% T&\to&B\to L\to R\\
% &\to&G^0\to\cdots\to G^{\C-2}\to C^0\to\cdots\to C^{\C-1}\\
% &\to&t\to b\to l\to r\to N\to n\to\{F,P\}\to\{f,p\}\footnotemark\\
% &\to&S(1)\to\cdots\to\S(n)\\
% &\to&g^0(1)\to\cdots\to g^{\C-2}(1)\to c^0(1)\to\cdots\to c^{\C-1}(1)\to
% 	s(1)\\
% &\to&\cdots\\
% &\to&g^0(n)\to\cdots\to g^{\C-2}(n)\to c^0(n)\to\cdots\to c^{\C-1}(n)\to
% 	s(n)\\
% &\to&g^0(n{+}1)\to\cdots\to g^{\C-2}(n{+}1)
%  \to c^0(n{+}1)\to\cdots\to c^{\C-1}(n{+}1)
% \end{eqnarray*}
% 
% \footnotetext{In column flushing, the order is $\{F,P\}\to\{f,p\}\to N\to
% n$ but this reversion should have no effect (almost always).}
%
% 
% 
% \subsection{Page-wise Float Placement}
% \label{sec:imp-ovv-float}
% \changes{v1.32-3}{2015/10/10}
% 	{Add the section ``Page-wise Float Placement'' to discuss the
%	 page-wise float problem.} 
% 
% In the release on 2015/01/10, \LaTeX{}'s float placement mechanism was
% drastically changed to avoid {\em out-of-order\/} appearance of \pwise{}
% floats as follows.  Since the cause of overtaking of a \pwise{} float by a
% \cwise{} float is that they are in two separated lists \!\@dbldeferlist!
% for the former and \!\@deferlist! for the latter, in the new implemenation
% the two lists are merged to let all floats go to \!\@deferlist!.  To
% distinguish \pwise{} and \cwise{} floats in the list, \!\end@dblfloat!
% lets the \pwise{} float processed by the macro have a special depth of
% |1sp|, while depth of \cwise{} floats are 0 since \!\@endfloatbox! add a
% \!\vskip! of 0 at the end of the box of floats.
% 
% Then all float placement macros invoked in \!\output!-routine examine the
% depth of floats in the list they are working on against a newly introduced
% macro \!\f@depth! by also newly introduced \!\@testwrongwidth!, so that
% they process only floats of a page/column category specified by
% \!\f@depth!, while those not matching to \!\f@depth! are let go to
% \!\@deferlist! to inhibit succeeding floats of the same type from
% overtaking them.  The \!\def!inition of \!\f@depth! is done only by
% modified \!\@dblfloatplacement!, always invoked in a group, to let it have
% |1sp| so that float placement macros usually work on \cwise{} ones with
% the default setting of $\!\f@depth!=\!\z@!$ except for special occasions
% in which the placement of \pwise{} floats is tried.
% 
% Though the mechanism should work well with {\em ordinary\/} multi-columned
% documents, it is incompatible with \Paracol{} almost inherently.  That is,
% in the first place we have to separate float-related lists into the sets
% of them corresponding to columns as we do\footnote{
% 
% If counters \counter{figure} and \counter{table} are global and we have to
% avoid inter-column overtaking with respect to, for example, the partial
% ordering rooted by the top-left corner, merging \cwise{} lists together
% with the merge of \cs{@deferlist} and \cs{@dbldeferlist} might be a
% solution to let the depth of a \cwise{} float be $c\,\texttt{sp}$ while
% that of \pwise{} is $\C$\,\texttt{sp}.  However such implementation is not
% only tough but also doubtful to be worthwhile.}.
% 
% Therefore, it is obviously nonsense to merge the list for  \pwise{} floats,
% i.e., \!\@dbldeferlist!, to \!\@deferlist! of a particular column, and
% thus we have to stick with the conventional implementation to process
% \pwise{} and \cwise{} floats separately as follows.
% 
% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
% \item
% \label{item:ovv-float-end@dblfloat}
% We \!\def!ine our own \!\end@dblfloat! namely \!\pcol@end@dblfloat!
% whose definition is exactly same as the old version of \!\end@dblfloat!,
% and replace the new version with it by \!\let!ting them equivalent in
% \!\pcol@zparacol! by which start \env{paracol} environments.  Therefore,
% \pwise{} floats composed in a \env{paracol} environment is processed in
% the traditional way, i.e., being inclueded in \!\@dbldeferlist! rather than
% \!\@deferlist! and having ordinary depth 0.
% 
% \item
% \label{item:ovv-float-@dblfloatplacement}
% Each invocation of \!\@dblfloatplacement! in our own \!\output!-routine is
% followed by a \!\let! to nullify the setting of $\!\f@depth!=|1sp|$ done
% by \!\@dblfloatplacement! by doing \!\f@depth!=\!\z@!.  By this setting,
% \!\@tryfcolumn! in \!\pcol@startpage!  and \!\@makefcolumn! in
% \!\pcol@output@clear! work on their argument \!\@dbldeferlist! in the way
% exactly same as in 2014 or before.
% 
% \item
% \label{item:ovv-float-@addtodblcol}
% Among \LaTeX's macros in its \!\output!-routine which we use in our own
% one as well, only \!\@addtodblcol! changed its target from
% \!\@dbldeferlist! to \!\@deferlist!.  That is, if the macro fails to put a
% \pwise{} float to the page we just have started by \!\pcol@startpage!,
% the float is added to \!\@deferlist! rather than \!\@dbldeferlist!.
% Therefore, when we apply \!\@sdblcolelt! to the copy of \!\@dbldeferlist!
% to invoke \!\@addtodblcol! for each of its element float, we have to save
% \!\@deferlist! somewhere, to \!\reserved@c! in reality, and clear it prior
% to the application.  Then after all elements are processed, we have to let
% \!\@dbldeferlist! have what \!\@deferlist! have, while \!\@deferlist!
% should regain its origial contents from the saved place.  A subtle issue
% is that we might work with \LaTeX{} of 2014 or older in which the floats
% are returned to \!\@dbldeferlist!.  Therefore to make \Paracol{}
% compatible with both of new and old versions, we have to {\em add}
% \!\@deferlist! to \!\@dbldeferlist! rather than replacing
% \!\@dbldeferlist! with \!\@deferlist!.  This addition should work well,
% because we clear both lists before the application of \!\@sdblcolelt!  and
% then one of them will have the still-deferred floats after the application
% while the other remains empty.
% 
% \item
% \label{item:ovv-float-@output@start}
% We convert \!\@deferlist! to \!\@dbldeferlist! in \!\pcol@output@start! to
% start a \env{paracol} environment, and perform the reverse operation in
% \!\pcol@output@end! to close the environment.  Though it is very unlikely
% (or maybe impossible) that the \!\@deferlist! {\em imported\/} in the
% former operation has \LaTeX's (i.e., not \Paracol's) double-column floats
% of |1sp| deep, we make such floats old-fashioned making their depth 0 so
% that they can be put in a page built in the \env{paracol} environment.  On
% the other hand, the latter cannot {\em export\/} a list having floats of
% |1sp| deep because they have been produced in the closing \env{paracol}
% environment or have passed our {\em custom\/} \!\pcol@output@start! when
% they were imported\footnote{
% 
% Therefore, if one try to {\em smuggle\/} a double-column float of the new
% scheme into a \env{paracol} and to pass it through the environment to
% another double-column world, the float will become a single-column one.
% Even if such guy a really exists and complains abount this transformation,
% however, we have good right to say ``don't do that''.}.
% \end{enumerate}
% 
% Note that the operations (1), (2) and (4) are fully compatible with 2014
% or older version of \LaTeX{}, because with the old version; (1) 
% \!\pcol@end@dblfloat! is equivalent to \!\end@dblfloat!; (2) modification
% of \!\f@depth! cannot be seen because it does not exist;  and (4) we
% virtually do nothing in the importation.  As for (3), we explicitly take
% care of the compatibility as shown above.
% 
% 
% 
% \section{Interaction with \TeX{} and \LaTeX{}}
% \label{sec:imp-tex}
% 
% The macros of \Paracol{} interacts with \TeX{} and \LaTeX{} through
% various registers and macros as discussed in this section.
% 
% \subsection{Registers}
% \label{sec:imp-tex-reg}
% 
% \subsubsection{Insertion Registers}
% 
% \begin{description}
% \item[\Uidx{\!\footins!}]
% is used to \!\insert! footnotes through it by \!\footnote! and
% \!\footnotetext!, and then in \!\output! routine the footnotes
% \!\insert!ed in a page is presented in the register.  The register is
% referred to by the following macros.
% 
% \begin{itemize}
% \item
% \!\pcol@makecol! examines if the register has \Scfnote{}s and, if so,
% saves it into $\pp^f(p)$ if $p=\ptop$ or discards it otherwise.
% 
% \item
% \!\pcol@startcolumn! \!\insert!s $\pp^f(p)$ into the \colpage{} to be
% created through the register.
% 
% \item
% \!\pcol@specialoutput! logs the contents of the register for debugging.
% 
% \item
% \!\pcol@output@start! examines if the register has footnotes to be merged
% with those in \env{paracol} environment, refers to its height plus depth to
% calculate effective \!\@colht!, and/or \!\insert!s its contents through
% itself to the main vertical list as the first part of \Mgfnote{}s.
% 
% \item
% \!\pcol@makenormalcol! combines footnotes in the register to other
% \preenv{} to make a \spanning, or makes save\slash restore of the register
% to/from \!\@tempboxa! to exclude footnotes from \spanning{} when
% \mgfnote{}-footnote typesetting is specified.
% 
% \item
% \!\pcol@output@switch! saves the register into $\pp^f(p)$ or $\cc_c(\ft)$,
% or discards its contents, when we leave from the column $c$ with footnotes.
% 
% \item
% \!\pcol@restartcolumn! restores $\cc_d(\ft)$ or $\pp^f(p)$ to the register
% and then \!\insert!s the contents of \!\box!\!\footins! into itself so
% that it contributes to the main vertical list to be rebuilt for the column
% $d$.
% 
% \item
% \!\pcol@getcurrfoot! for column $d$ lets the register have $\cc_d(\ft)$.
% 
% \item
% \!\pcol@savefootins! saves the register into an \!\insert! for $\pp^f(p)$
% or $\cc_c(\ft)$.
% 
% \item
% \!\pcol@deferredfootins! refers the \!\skip! component of the register to
% have the vertical skip above \Scfnote{}s and \!\insert!s deferred
% footnotes through the register.
% 
% \item
% \!\pcol@output@end! \!\insert!s $\pp^f(p)$ into the \lpage{} through the
% register.
% 
% \item
% \!\pcol@fntexttop!\marg{text} \!\insert!s the footnote $\arg{text}$ and a
% penalty through the register.
% 
% \item
% \!\pcol@fntextbody!\marg{text} refers to the \!\skip! component of the
% register to cap the height of the footnote $\arg{text}$.
% \end{itemize}
% 
% \item[\rm\Uidx{\!\bx@A!}, \ldots, \Uidx{\!\bx@R!}]
% have floats created by \!\@xfloat! in the ordinary usage of {\em
% fundamental\/} \LaTeX{} of 2014 or earlier or that without the extension
% of e-\TeX{} or its relatives.  On the other hand, in \LaTeX{} of 2015 or
% later and with e-\TeX{} or its relatives, the set is \!\bx@A!, \ldots,
% \Uidx{\!\bx@Z!}, \Uidx{\!\bx@AA!}, \ldots, \Uidx{\!\bx@ZZ!}\@.  In addtion
% to the use in \LaTeX, we use these registers for completed \colpage{}s
% $s_c(p)$ (\!\pcol@opcol!, \!\pcol@flushcolumn!), main vertical list
% $\cc_c(\vb)$ (\!\pcol@output@start!, \!\pcol@output@switch!,
% \!\pcol@flushcolumn!)  and \Mcfnote{}s $\cc_c(\ft)$
% (\!\pcol@output@switch!) in \ccolpage{}s, \spanning{} including \preenv{}
% $\pp^i(p)$ (\!\pcol@startpage!, \!\pcol@output@start!) and \Scfnote{}s
% $\pp^f(p)$ (\!\pcol@makecol!, \!\pcol@output@switch!) in pages,
% \mvlfloat{}s for main vertical lists in \sync{}ed pages
% (\!\pcol@synccolumn!), and \pwise{} floats deferred from \env{paracol} to
% \postenv{} (\!\pcol@output@end!).
% \end{description}
% 
% 
% 
% \subsubsection{Integer Registers}
% 
% \begin{description}
% \item[\Uidx{\!\deadcycles!}]
% is \TeX's primitive register to count the number of \!\output! requests
% made between two \!\shipout! operatios.  It is zero-cleared by
% \!\pcol@invokeoutput! because it can have a large number in a
% \env{paracol} environment.
% 
% \item[\Uidx{\!\outputpenalty!}]
% is \TeX's primitive register to have the page-break penalty with which
% \!\output! routine is invoked.  It is referred to by \!\pcol@output! to
% know whether it has special code less than $-10000$, and by
% \!\pcol@specialoutput! in detail for the dispatch according to the code.
% The register is also used for the communication from the latter, which lets
% it be $-10000$ for our own special \!\output! routines, to the former to
% determine \!\vsize! according to if the register has a value greater than
% $-10004$ or not.
% 
% \item[\Uidx{\!\interlinepenalty!}]
% is \TeX's primitive register to have the page-break penalty inserted
% between two lines.  The register is referred to in the following macros.
% 
% \begin{itemize}
% \item
% \!\pcol@output@start!  to make \Preenv{} \Mgfnote{}s followed by this
% \!\penalty! on the \!\insert!ion, and to insert it to start the first
% \colpage{} allowing page-break before the start unless it is inhibited
% by $\CSIndex{if@nobreak}=\true$.
% 
% \item
% \!\pcol@restartcolumn! to insert this \!\penalty! to resume a \colpage{}
% allowing page-break if $\CSIndex{if@nobreak}=\false$.
% 
% \item
% \!\pcol@deferredfootins!  to let the secnod half of split $\df$ have this
% \!\penalty! as the very first element.
% 
% \item
% \!\pcol@fntexttop!\marg{text} to make the footnote $\arg{text}$ followed
% by this \!\penalty! on the \!\insert!ion.
% 
% \item
% \!\pcol@fntextother!\marg{text} to make the footnote $\arg{text}$ preceded
% by this \!\penalty! in $\df$.
% 
% \item
% \!\pcol@fntextbody! to let the register have \!\interfootnotelinepenalty!.
% \end{itemize}
% 
% \item[\Uidx{\!\floatingpenalty!}]
% is \TeX's primitive register to have the page-break penalty added to
% \!\insertpenalties! if an \!\insert! is moved to the page next to the page
% in which the line having the \!\insert! resides.  It is let have 20000 in
% \!\pcol@fntextbody! for footnote typesetting.
% 
% \item[\Uidx{\!\vbadness!}]
% is \TeX's primitive register to have the threshold of the badness of
% \!\vbox! construction with underfull messages.  That is, if the badness
% exceeds the threshold on a \!\vbox! construction, \TeX{} will complain
% showing an underfull message. In \!\pcol@makenormalcol!  and
% \!\pcol@deferredfootins!, the register is temporarily let have 10000 to
% avoid that \!\@makecol! invoked in the former and \!\vsplit! done in the
% latter causes the message with inevitable underfull.
% 
% \item[\Uidx{\!\showboxdepth!}]
% is \TeX's primitive register to determine the maximum depth of box
% structure to be shown in logging etc.  The register is let have 10000 in
% \!\pcol@ShowBox!  for full logging.
% 
% \item[\Uidx{\!\showboxbreadth!}]
% is \TeX's primitive register to determine the maximum breadth of box
% structure to be shown in logging etc.  The register is let have 10000 in
% \!\pcol@ShowBox!  for full logging.
% 
% \item[\Uidx{\!\interfootnotelinepenalty!}]
% is an API \!\count! register to have \!\interlinepenalty! for footnotes.
% It is used in \!\pcol@fntextbody! to let \!\interlinepenalty! have it.
% 
% \item[\Uidx{\!\@ne!}]
% is a \!\chardef! register to have 1.  The register is referred to by the
% following macros mainly for incrementing another register.
% 
% \begin{quote}\raggedright
% \!\pcol@F@count!,
% \!\pcol@output!,
% \!\pcol@opcol!,
% \!\pcol@setpnoelt!,
% \!\pcol@nextpage!,
% \!\pcol@nextpelt!,
% \!\pcol@startpage!,
% \!\pcol@checkshipped!,
% \!\pcol@outputelt!,
% \!\pcol@ioutputelt!,
% \!\@outputpage!,
% \!\pcol@bg@paint@ii!,
% \!\pcol@output@start!,
% \!\pcol@makenormalcol!,
% \!\pcol@output@switch!,
% \!\pcol@setcurrcol!,
% \!\pcol@iscancst!,
% \!\pcol@addmarginpar!,
% \!\pcol@do@mpbout@i!,
% \!\pcol@sync!,
% \!\pcol@flushcolumn!,
% \!\pcol@measurecolumn!,
% \!\pcol@synccolumn!,
% \!\pcol@makeflushedpage!,
% \!\pcol@imakeflushedpage!,
% \!\pcol@iflushfloats!,
% \!\pcol@freshpage!,
% \!\pcol@output@end!,
% \!\pcol@invokeoutput!,
% \!\pcol@zparacol!,
% \!\pcol@setcolwidth@r!,
% \!\pcol@setcolwidth@s!,
% \!\pcol@setcw@scan!,
% \!\pcol@setcw@calcf!,
% \!\pcol@synccounter!,
% \!\pcol@com@syncallcounters!,
% \!\pcol@stepcounter!,
% \!\pcol@com@switchcolumn!,
% \!\pcol@sptext!,
% \!\pcol@visitallcols!,
% \!\pcol@ifootnote!,
% \!\pcol@ifootnotemark!.
% \!\pcol@swapcolumn!,
% \!\pcol@set@color@push!,
% \end{quote}
% 
% \item[\Uidx{\!\tw@!}]
% is a \!\chardef! register to have 2.  It is used in \!\pcol@setcurrcol! to
% let $\cc_c(\sw)=2$ when $\CSIndex{if@nobreak}=\true$ but
% $\CSIndex{if@afterindent}=\false$, in
% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ to calculate $x\cdot2^k$, $y/2^k$
% and $(x/y)\cdot2^k$ with various $k$, and in \!\pcol@swapcolumn! to
% calculate $\Cto-(c'-\Cfrom)-2=c-1=c^g$ for the \csepgap{} ordinal $c^g$
% physically following the column $c$ at the position $c'$.
% 
% \item[\Uidx{\!\m@ne!}]
% is a \!\count! register to have $-1$.  It is used in the following macros.
% 
% \begin{itemize}
% \item
% \!\pcol@setpnoelt!, \!\pcol@nextpelt!, \!\pcol@getpelt! and
% \!\pcol@setmpbelt! to decrement
% \!\@tempcnta! which initially has $p-\pbase$ for a page $p$.
% 
% \item
% \!\pcol@bg@paint@i! to decrement $\CBto$ by one locally to have the column
% scanning range $\LBRP\CBfrom{\CBto{-}1}$.
% 
% \item
% \!\pcol@iscancst! to decrement $\npop$ by one.
% 
% \item
% \!\pcol@do@mpbout@i! to let \!\@tempcnta! have it to indicate left margin.
% 
% \item
% \!\pcol@setcolwidth@r! to calculate $\Cto-\Cfrom-1$.
% 
% \item
% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ in \!\@whilenum! loops to
% calculate $z'/2^k$ and $z'/2{k-16}$ where $z'/2^k\approx x/y$.
% 
% \item
% \!\pcol@iadjustfnctr! to decrement \!\c@footnote!.
% \end{itemize}
% 
% \item[\Uidx{\!\sixt@@n!}]
% is a \!\chardef! register to have 16.  It is used in
% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ to calculate
% $Z=z\times1\,|pt|=z'\cdot2^{16-k}$ where $z'/2^k\approx x/y$.
% 
% \item[\Uidx{\!\@m!}]
% is a \!\mathchardef! register to have 1000.  It is used in
% \!\pcol@synccolumn! and \!\pcol@output@end! to let
% $\!\prevdepth!=1000\,|pt|$ on a \sync{}ation or the closing \env{paracol}
% environment with an empty main vertical list, and in
% \!\pcol@setcw@getspec@i! to add 1000\,|pt| to strech and shrink
% compontents of \!\@tempskipa! having a column\slash gap sepcification to
% make it sure the skip register has those components.
% 
% \item[\Uidx{\!\@M!}]
% is a \!\mathchardef! register to have 10000.  It is used in the following
% macros
% 
% \begin{itemize}
% \item
% \!\pcol@ShowBox! to let \!\showboxdepth! and \!\showboxbreadth!  have
% 10000 for full logging of a box.
% 
% \item
% \!\pcol@output! to examine if $\!\outputpenalty!<-10000$ to mean a special
% \!\output! request.
% 
% \item
% \!\pcol@specialoutput! to let $\!\outputpenalty!=-10000$ to tell
% \!\pcol@output! that the special \!\output! request is our own.
% 
% \item
% \!\pcol@makenormalcol! and \!\pcol@deferredfootins! to let \!\vbadness!
% have 10000 temporarily to avoid underfull messages.
% 
% \item
% \!\pcol@synccolumn!  to bias \!\pcol@textfloatsep! by 10000\,|pt| to
% indicate a \colpage{} has an \mvlfloat{} and in \!\pcol@cflt! and
% \!\pcol@addflhd! to remove the bias.
% 
% \item
% \!\pcol@switchcol! and \!\pcol@flushclear! to put \!\penalty!|-10000| for
% forced page break.
% 
% \item
% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ to let $Z=z\times1\,|pt|=10000\,|pt|$
% if $x/y$ is too large.
% \end{itemize}
% 
% \item[\Uidx{\!\@Mii!}]
% is a \!\mathchardef! register to have 10002.  It is used in
% \!\pcol@end@dblfloat! to examine if $\!\@floatpenalty!=-10002$ to mean the
% float environment to be closed is given in horizontal mode.
% 
% \item[\Uidx{\!\@Miv!}]
% is a \!\mathchardef! register to have 10004.  It is used in \!\pcol@output!
% to examine if $\!\outputpenalty!=-10004$ for a dummy \!\output! request
% made by \LaTeX's float-related macros and our \!\pcol@invokeoutput! to
% ensure the real request is not eliminated when it is made at the very
% beginning of a page or a \colpage.  It is also used in
% \!\pcol@specialoutput! for footnote logging when
% $\!\outputpenalty!=-10004$.
% 
% \item[\Uidx{\!\@MM!}]
% is a \!\mathchardef! register to have 20000.  It is used in
% \!\pcol@fntextbody! to let \!\floatingpenalty! have it for footnote
% typesetting.
% 
% \item[\Uidx{\!\@beginparpenalty!}]
% is a \!\count! register to have the page-break penalty inserted before the
% first \!\item! of each \env{list}-like environment.  The penalty is
% determined in class files and is, for example, $-\!\@lowpenalty!=-51$ with
% \textsf{article.cls}.  It is referred to and inserted by \!\pcol@zparacol!
% when it finds the \env{paracol} environment to start is at the very
% beginning of a \env{list}-like environment.
% 
% \item[\Uidx{\!\@floatpenalty!}]
% is a \!\count! register to have the penalty code -10002 or -10003 given by
% \!\@xfloat! at the beginning of a float environment according to the
% environment is in horizontal or vertical mode respectively, or by
% \!\marginpar! for a marginal note in the same meaning.  It is
% referred to by \!\pcol@end@dblfloat! to insert the penalty, and by
% \!\pcol@xympar! to confirm \!\marginpar! is error free.
% 
% \item[\Uidx{\!\@topnum!}]
% is a \!\count! register to have the maximum number of top floats which the
% \ccolpage{} can accept further.  It is used in \!\pcol@setcurrcol!
% and \!\pcol@iigetcurrcol! to save\slash restore it into\slash from
% $\cc_c(\tn)$.  The macro \!\pcol@synccolumn! also lets $\!\@topnum!=0$ to
% inhibit top-float insertions in the \ccolpage{} any more after a
% \sync{}ation.
% 
% \item[\Uidx{\!\@botnum!}]
% is a \!\count! register to have the maximum number of bottom floats which
% the \ccolpage{} can accept further.  It is used in \!\pcol@setcurrcol!
% and \!\pcol@iigetcurrcol! to save\slash restore it into\slash from
% $\cc_c(\bn)$.
% 
% \item[\Uidx{\!\@colnum!}]
% is a \!\count! register to have the maximum total number of floats which
% the \ccolpage{} can accept further.  It is used in \!\pcol@setcurrcol!
% and \!\pcol@iigetcurrcol! to save\slash restore it into\slash from
% $\cc_c(\cn)$.
% 
% \item[\Uidx{\!\col@number!}]
% is a \!\count! register to have the number of columns.  It is let have 1
% by \!\pcol@zparacol! and \!\pcol@sptext! regardless the real number of
% columns $\C$ in order to keep \!\maketitle! from putting the title by
% \!\twocolumn!.
% 
% \item[\Uidx{\!\c@page!}]
% is \LaTeX's counter \Uidx{\counter{page}} being a \!\count! register to
% have the page number.  It is referred to by \!\pcol@setpnoelt!, and
% \!\pcol@output@start! to let $\pp^p(p)=\page(p)$.  The macro
% \!\pcol@startpage! reload the register from $\pp^p(\ptop{-}1)$ and then
% increment it by one usually but two in \npaired{} \parapag{}ing, and
% repeat $\pp^p(\ptop)=\page(\ptop)$ and incrementing $\page(p)$ for each
% \fpage{}s of \pwise{} floats.  Reloading $\page(p)$ to the register from
% $\pp^p(p)$ is also done by \!\pcol@getpelt! for macros using
% \!\pcol@getcurrpage!, and by \!\pcol@outputelt!, \!\pcol@sync! and
% \!\pcol@makeflushedpage! by \!\pcol@getcurrpinfo!.  Then the register is
% referred to by the following macros to exmine its parity.
% 
% \begin{itemize}
% \item
% Our own \!\@outputpage! to give $\page(p)$ or $\page(p)+1$ to
% \!\pcol@outputpage@l! and \!\pcol@outputpage@r! which finally let the
% register have the value to be referred to by \!\pcol@@outputpage! being
% \LaTeX's \!\@outputpage!.
% 
% \item
% \begin{Sloppy}{2800}%
% \!\pcol@bg@swappage! to determine the values of \!\pcol@bg@leftmargin!
% and \CSIndex{ifpcol@bg@@swap} with other factors.
% \end{Sloppy}
% 
% \item
% \!\pcol@shiftspanning! to decide the necessity of shifting \mctext{} left
% with \cswap{}, examining {\em raw} \!\c@page! at the \!\output! request to
% close the \mctext{} rather than $\pp^p(\ptop)$ which will have the correct
% value with respect to possible jump {\em after} the macro completes its
% work.
% 
% \item
% \!\pcol@addmarginpar! to determine the margin to which a marginal note
% goes.
% 
% \item
% \!\pcol@do@mpbout@i! to determine which of $\mpb_L^l$ or $\mpb_L^r$ is the
% target of the operation specified by \!\pcol@do@mpbout@elem!.
% 
% \item
% $\!\pcol@swapcolumn!\<c_1\>\<c_2\>\<\Cfrom\>\<\Cto\>$ to determine $c_2$
% for $c_1$ if \cswap{} is in effect.
% \end{itemize}
% 
% In addition, to do the parity examination in \!\pcol@bg@swappage! above
% correctly, the macros \!\pcol@ioutputelt!, \!\pcol@makeflushedpage!,
% \!\pcol@imakeflushedpage!, \!\pcol@iflushfloats! and \!\pcol@output@end!
% temporarily increment the register by one when they are working on a right
% \npaired{} \parapag{}e.
% 
% The other users are \!\localcounter!\marg{ctr} to check
% $\arg{ctr}\neq\counter{page}$, \!\pcol@remctrelt! to let
% $|\cl@|{\cdot}\theta=\!\pcol@stepcounter!\Arg{\theta}$
% 
% \SpecialArrayIndex{\theta}{\cl@}
% 
% unless $\theta=\counter{page}$, and \!\pcol@FF! to write it to a log file
% as a part the logging information of memory leak debugging.
% 
% \item[\Uidx{\!\c@footnote!}]
% is \LaTeX's counter \Uidx{\counter{footnote}} being a \!\count! register
% to have the footnote number.  It is referred to by \!\pcol@zparacol! to
% let $\bf=\!\pcol@footnotebase!$ have its value, by \!\pcol@calcfnctr! to
% calculate the footnote ordinal which the one of its invoker
% \!\pcol@iadjustfnctr! sets into the register, and by \!\endparacol! to let
% the register have $\bf+\nf=\!\pcol@footnotebase!+\!\pcol@nfootnotes!$.
% 
% \item[$\cs{c@}{\cdot}\theta$]
% \SpecialArrayUsageIndex{\theta}{\c@}
% 
% is a \!\count! register being \LaTeX's counter $\theta$.  It is referred
% to by \!\pcol@savectrelt! to let $\val_c(\theta)=\Val(\theta)$ for saving
% it in $\Cc_c$, by \!\pcol@cmpctrelt! to examine if
% $\val_0(\theta)=\Val(\theta)$ to detect a modification outside
% \env{paracol} environment, and by \!\pcol@syncctrelt! to let
% $\val_c(\theta)=\Val(\theta)$ for all $c$ for \csync{}.  It is also
% referred to by \!\pcol@remctrelt! and \!\localcounter! to examine if
% $\theta=\counter{page}$.  The macros \!\pcol@setctrelt! and
% \!\pcol@stpldelt! restore the value of the counter from $\val_c(\theta)$,
% while \!\pcol@stpclelt! lets $\Val(\theta)=0$ for zero-clearing of
% descendent counters.
% 
% \item[\Uidx{\!\count@!}]
% is a \!\count! register for temporary use.  It is used in
% \!\pcol@iscancst! to have $m$ of $\mcelt_{i,m}$,
% \!\pcol@addmarginpar! to have the physical column position of the current
% column $c$ in which \!\marginpar! is given, and in
% $\!\pcol@extract@fil@i!\<s\>\!\@nil!$ to exract the unit of the stretch
% component $s$ of a glue.
% 
% \item[\Uidx{\!\@tempcnta!}]
% is a \!\count! register for temporary use.  The usages of this register
% are as follows.
% 
% \begin{itemize}
% \item
% In \!\pcol@F@count!, it is used to measure the cardinality of
% \!\@freelist!.
% 
% \item
% In \!\pcol@makecol!, it is used to keep $\page(\ptop)$ gotten by
% \!\pcol@getcurrpinfo! until we store it back by \!\pcol@defcurrpage!.
% 
% \item\begin{Sloppy}{3700}
% In \!\pcol@setpageno!, \!\pcol@setpnoelt!, \!\pcol@nextpage!,
% \!\pcol@nextpelt!, \!\pcol@getcurrpage!, \!\pcol@getpelt!,
% \!\pcol@addmarginpar! and \!\pcol@setmpbelt!, it has $p-q$ when we scan
% $\pp(q)$ for all $q\in[\pbase,\ptop]$ and the \ccolpage{} is at $p$.
% \end{Sloppy}
% 
% \item
% In \!\pcol@checkshipped!, it has $c$ when we scan $\S_c$ for all
% $c\In0\C$ to examine if all of them are not empty and thus we have pages
% to be shipped out.
% 
% \item
% In \!\pcol@ioutputelt!, it has $c'$ when we scan $\s_c(q)$ for all
% $c\In0\CL$ or $c\In\CL\C$ to build the shipping out image of a page $q$,
% where $c=c'$ or $c=\Cto-1-(c'-\Cfrom)$ where
% $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$.
% 
% \item
% In \!\@outputpage!, it has $\page(p)$ or $\page(p)+1$ to be given to
% \!\pcol@outputpage@l! or \!\pcol@outputpage@r! as their argument when they
% are used to ship out the second (not always right) component of a
% \parapag{}e pair.
% 
% \item
% In \!\pcol@bg@columnleft!, it has a value in $\LBRP\CBfrom{c}$ to sum up
% the width of columns and \csepgap{}s in the range.
% 
% \item
% In \!\pcol@output@switch!, it is used to have $\page(p)$ obtained by
% \!\pcol@getcurrp~info! and simply to store the value in $\pp^p(p)$ by
% \!\pcol@defcurrpage!  when we use these macros to add an element to
% $\pp^s(p)$ and/or let $\pp^f(p)=\!\footins!$.
% 
% \item
% In \!\pcol@setcurrcol!, it has the code calculated from
% \CSIndex{if@nobreak} and |\if@after|\~|indent| to be saved in
% $\cc_c(\sw)$.
% 
% \SpecialIndex{\if@afterindent}
% 
% \item
% In $\!\pcol@scancst!\arg{box}$, it is let have
% $\arg{box}\in\{\!\pcol@colorins!,|\pcol@color|\~|stack@saved|\}$ and then is
% referred to in \!\pcol@iscancst!.
% \SpecialIndex{\pcol@colorstack@saved}
% 
% \item
% In \!\pcol@addmarginpar! besides the page scan shown above, it is used to
% scan all columns whose physical position is left from the current
% colum $c$ to measure the distance between the left edges of the leftmost
% column and $c$.
% 
% \item
% In \!\pcol@do@mpbout@i!, it has $\pm1$ according to the margin ($\rm
% left=-1$) which marginal notes outside \env{paracol} environments goes
% to.
% 
% \item
% In \!\pcol@flushcolumn!, it is used to throw $\page(\ptop)$ away when we
% get it by \!\pcol@getcurrpinfo! because we don't need it.
% 
% \item
% In \!\pcol@setcolwidth@r!, it has $c$ to scan fractions $r_d$ where
% $d=c-\Cfrom$ in its argument $\arg{ratio}$ specified by \!\columnratio!,
% and then to distribute the unspecifed portion of \!\textwidth! evenly to
% $\w_c$ for all $c\In{\Cfrom{+}k{+}1}\Cto$, where $k$ is the number of
% fractions and $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$.
% 
% \item
% In $\!\pcol@setcw@scan!\<\Cfrom\>\<\Cto\>\Arg{spec}$, it has $c$ for two
% loops for $c\In\Cfrom\Cto$ to add `|,|' to the tail of $\arg{spec}$ as
% many as $k=\Cto-\Cfrom$ and then to process first $k$ elements in
% $\arg{spec}$, and is referred to by \!\pcol@setcw@set! invoked in the
% second loop.
% 
% \item
% In $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$, it used to calculate and to have
% $k$ such that $z'/2^k\approx x/y$.
% 
% \item
% In \!\pcol@cmpctrelt!, it has $\Val(\theta)$ of a counter $\theta$ to be
% compared with $\val_0(\theta)$.
% 
% \item
% In \!\pcol@com@switchcolumn!, it has $(c+1)\bmod\C$ being the target of
% \cswitch{}.
% 
% \item
% In \!\pcol@sptext!, it temporarily has $d$ being the target of \cswitch{}
% during we let \!\pcol@nextcol! have 0 to visit the leftmost column
% to put a \mctext{}.
% 
% \item
% In \!\pcol@visitallcols!, it has $d\In0\C-\{c\}$ being the columns to be
% visited for \cscan{}ning.
% 
% \item
% In \!\definecolumnpreamble!\marg{c}\marg{pream}, $c$ is assigned to the
% register to ensure $c$ is a number.
% 
% \item
% In \!\pcol@calcfnctr!, it has the footnote ordinal calculated by the
% macro to be referred to by the invokers \!\pcol@iadjustfnctr! and
% \!\pcol@iifootnotetext!.
% 
% \item
% In $\!\marginparthreshold!\Arg{t_l}|[|t_r|]|$ it is let have $t_l$, while
% in the related macro $\!\pcol@marginparthreshold!|[|t_r|]|$ it is let have
% $t_r$.
% \end{itemize}
% 
% \item[\Uidx{\!\@tempcntb!}]
% is a \!\count! register for temporary use.  It is used in the following
% macros.
% 
% \begin{itemize}
% \item
% In \!\pcol@ioutputelt! it has $c$, while in \!\pcol@imakeflushedpage! and
% \!\pcol@iflushfloats! it has $c'$, to have $c=c'$ or $c=\Cto-1-(c'-\Cfrom)$
% according to \cswap{} for $c'$-th iteration of column scanning loop for
% $c'\In\Cfrom\Cto$, where $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$.
% 
% \item
% In \!\pcol@scancst! and \!\pcol@iscancst!, it has $\npop$.
% 
% \item
% In \!\pcol@addmarginpar!, it is let have the column number $d$ whose
% phisical position is left from the current colum $c$ to measure the
% distance between the left edges of the leftmost column and $c$.
% 
% \item
% In \!\pcol@sync! and \!\pcol@measurecolumn!, it has the (so-far) tallest
% column which gives $\VP$.
% 
% \item
% In \!\pcol@setcolwidth@r!, it has $\Cto-\Cfrom-1$ then $\Cto-1$ and
% finally $\Cto-\min(\Cfrom{+}k,\,\Cto{-}1)$, where $k$ is the number of
% fractions given in the argument of \!\columnratio! and
% $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$.
% 
% \item
% In $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$, at first it is used to calculate
% $z'/2^k\approx x/y$ and then to calculate
% $Z=z\times1\,|pt|=z'\cdot2^{16-k}$.
% 
% \item
% In \!\pcol@visitallcols!, it has $c=\!\pcol@currcol!$ to exclude it from
% the \cscan{} targets.
% \end{itemize}
% \end{description}
% 
% 
% 
% \subsubsection{Dimension Registers}
% 
% \begin{description}
% \item[\Uidx{\!\vsize!}]
% is \TeX's primitive register to have the height of a page or a \colpage{}
% being built.  It is let be \!\@colroom! or \!\maxdimen! by
% \!\pcol@output!.
% 
% \item[\Uidx{\!\hsize!}]
% is \TeX's primitive register to have the width of a page or a \colpage{}
% being built.  It is let be $\w_c$ by \!\pcol@invokeoutput! to restart (or
% stay in) the column $c$, be \!\textwidth! by \!\pcol@sptext! for \mctext,
% and be either of \!\textwidth! or $\w_c$ by \!\pcol@fntextbody! according
% to the footnote typesetting being \scfnote{} or \mcfnote{} resepectively.
% 
% \item[\Uidx{\!\maxdepth!}]
% is \TeX's primitive register to have the maximum depth of the page being
% built.  In \LaTeX, it is assumed that its value is fixed at
% \beginenv{document}, in which the value is saved into \!\@maxdepth!, for
% the typesetting throughout the document, unless a bottom float is added to
% a page in which the register is let have 0 until it is shipped out.  This
% temporary setting for a page with bottom floats has some reasonability but
% its implementation for \env{paracol} environments having \cswitch{}
% from/to a \colpage{} with bottom floats to/from another one without
% them is too costly\footnote{
% 
% That is, we would need to incorporate \cs{maxdepth} as a member of
% \cctext, but we don't because the idea of temporary setting itself is too
% vague to pay the effort and a precious membership in \cctext.}.
% 
% Therefore, we let the register have \!\@maxdepth! in \!\pcol@output! and
% \!\pcol@combinefloats! to cancel the temporary setting done in
% \!\@addtobot! for the references by \TeX's page builder and \!\@cflt!
% respectively.
% 
% \item[\Uidx{\!\boxmaxdepth!}]
% is \TeX's primitive register to have the maximum depth of \!\vbox!es.
% The macros \!\pcol@cflt!, \!\pcol@opcol!,
% \!\pcol@ioutputelt!, \!\pcol@combine~floats!, \!\pcol@output@flush! and
% \!\pcol@output@clear! let it be \!\@maxdepth! for the boxes having a
% completed \colpage{} or page to cap the depth of the box.  The macro
% $\!\pcol@@makecol!\<d\>$ also do that when $d=\!\@maxdepth!$ but it can be
% $d=0$ when it is invoked to build \lpage{}.
% 
% \item[\Uidx{\!\splitmaxdepth!}]
% is \TeX's primitive register to have the maximum depth of the \!\vbox!
% being the first half of a box being split.  It is used in
% \!\pcol@deferredfootins! to cap the depth of the first half of deferred
% footnotes split from $\df$, and in \!\pcol@fntextbody! to let it have the
% depth of \!\strutbox!.
% 
% \item[\Uidx{\!\prevdepth!}]
% is \TeX's primitive register to have the depth of the box which just has
% been added to a vertical list, or to be given to \TeX's vertical list
% builder for the calculation of the vertical skip inserted below the last
% box.  The macro \!\pcol@invokeoutput! refers to it to save its value in
% \!\pcol@prevdepth! before putting a dummy \!\vbox! and making a \!\output!
% request, and then let it have \!\pcol@prevdepth! which is given by
% \!\output! routine for the column that we resume.  The macro
% \!\pcol@zparacol!  also refers to it to save it in \!\pcol@firstprevdepth!
% for the \preenv.
% 
% \item[\Uidx{\!\vfuzz!}]
% is \TeX's primitive register to have the threshold height of overfull
% messaging.  It is set to 0 in $\!\pcol@ShowBox!\arg{b}$ to ensure overfull
% for any \!\box! $b$ of non-null height.
% 
% \item[\Uidx{\!\maxdimen!}]
% is a \!\dimen! register to have $16383.99999\,|pt|$ being the largest
% legal dimensional value.  The usages of this register are as follows.
% 
% \begin{itemize}
% \item
% For the \!\insert! register set $\!\pcol@colorins!=\cstraw$,
% \!\dimen!\!\pcol@colorins! is let be \!\maxdimen! for the consistency with
% our intention that a \colpage{} can have virtually infinite number of
% \!\insert!ions for text coloring.
% 
% \item
% In \!\pcol@output!, it is set into \!\vsize! when $\!\outputpenalty!=-10004$
% for the dummy \!\output! request so that no page break should occur
% between the dummy and real requests.
% 
% \item
% Our own \!\dimen! register \!\pcol@textfloatsep! has \!\maxdimen! if a
% \colpage{} does not have \sync{}ation points to let top floats are
% inserted in usual way.  Therefore, \!\pcol@floatplacement! and
% \!\pcol@zparacol!  let the register have \!\maxdimen! as the initial
% value.  Then the macros \!\pcol@makecol! and \!\pcol@combinefloats!
% examine if $\!\pcol@textfloatsep!=\!\maxdimen!$ to determine the operation
% type of top float insertion, while \!\pcol@synccolumn! does that to know
% if it is flushing a \colpage{} with a \sync{}ation point or is setting the
% first \sync{}ation point in the \colpage{}.  The macro \!\pcol@addflhd!
% also examines it for the measurement of the combined height of top and
% bottom floats, while \!\pcol@measurecolumn! gives it \!\maxdimen! as its
% third argument for bottom floats.
% 
% \item
% The \pctext{} $\pp^h(p)$ has $-\!\maxdimen!$ if the page is a \fpage{}.
% The macro \!\pcol@startpage! makes that when it creates such a page.
% 
% \item
% Our own \!\pcol@prevdepth! and that saved in $\cc_c(\pd)$ have
% \!\maxdimen! if the main vertical list is empty at a \sync{}ation.  The
% macro \!\pcol@measurecolumn! makes that when it finds an empty list.
% 
% \item
% The \cctext{} $\cc_c(\tr)$ may have \!\maxdimen! if the column $c$ has a
% \fcolumn{} in the \lpage{} of a \env{paracol} environment and the floats in
% it can be put as top floats.  The macro \!\pcol@makefcolumn! makes this
% special assignment, and \!\pcol@flushcolumn! and \!\pcol@imakeflushedpage!
% examine it.
% 
% \item
% The macro \!\pcol@makefcolelt! let the room for floats in a \fpage{} be
% $-\!\maxdimen!$ if it finds no futher floats can be added to the page.
% 
% \item
% At a \sync{}ation, we measure the maximum combined size of top floats and
% the main vertical list $\VT$, that of footnotes and bottom floats $\VB$,
% that of four items $\VP$, and $\VPP$ being $\VP$ or $\VP+\!\textfloatsep!$
% according to the existence of bottom floats.  We also let $\DT$ and $\DP$
% be the minimum depth of the \colpage{}s which gives $\VT$ and $\VPP$
% respectively.  For the measurement, the macro \!\pcol@sync! lets
% $\VT=\VB=\VP=\VPP=-\!\maxdimen!$ and $\DT=\DP=\!\maxdimen!$ as their
% initial values.  Then the macro \!\pcol@synccolumn! examines if
% $\DT=\!\maxdimen!$ to mean the \sync{}ation point is set just below the
% top floats of a column whose main vertical list is empty.  On the other
% hand, \!\pcol@makeflushedpage! and \!\pcol@output@end! examine if
% $\VPP=-\!\maxdimen!$ to mean the last \colpage{}s are empty.
% \end{itemize}
% 
% \item[\Uidx{\!\linewidth!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
% of a line possibly shorter than \!\columnwidth! in \env{list}-like
% environments.  It is let have $\w_c-\lrm$ by
% \!\pcol@invokeoutput! for the outermost paragraphs in \env{paracol}
% environment, where $\lrm=\!\pcol@lrmargin!=\!\textwidth!-l$ which
% \!\pcol@zparacol! lets have to represent the left-plus-right margin of the
% \env{list}-like environment, whose \!\linewidth! is $l$, enclosing
% \env{paracol} if any.  The macro \!\pcol@sptext! also sets the register
% temporarily for \mctext{}s but letting it have $\!\textwidth!-\lrm$.
% 
% \item[\Uidx{\!\footnotesep!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
% vertical space inserted in a footnote when it is split into two or more
% pages.  It is uesed in \!\pcol@fntextbody! to \!\splittopskip! have it,
% and to make the first line of the footnote is at least as tall as the
% amount in the register.
% 
% \item[\Uidx{\!\topmargin!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
% (height) of the top margin minus 1\,inch.  The register is used as an
% element of \!\pcol@bg@pagetop! to calculate the distance from the origin
% at the left-top corner of text area to the top edge of a page.  The
% other users are \!\pcol@ioutputelt! and \!\pcol@makeflushedpage!
% temporarily add the height-plus-depth of $\pp^b(p)$ to the register to
% make the calculation biased shifting the origin to the left-top corner of
% column area, i.e., below $\pp^b(p)$.  The macro \!\@outputpage! also
% refers to the register together with \!\headheight! and \!\headsep! to
% calculate the distance from the page top (ingoring 1\,inch shift) to the
% text area top.
% 
% \item[\Uidx{\!\oddsidemargin!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
% of the left margin minus 1\,inch for two-sided odd-numbered pages and
% all single-sided pages.  The register is used together with
% \!\evensidemargin! in \!\pcol@outputpage@l!, \!\pcol@outputpage@r! and
% \!\pcol@bg@swappage! to decide the left margin of the page they are
% working on.
% 
% \item[\Uidx{\!\evensidemargin!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
% of the left margin minus 1\,inch for two-sided even-numbered pages.  The
% register is used together with \!\oddsidemargin! in \!\pcol@outputpage@l!,
% \!\pcol@outputpage@r! and \!\pcol@bg@swappage! to decide the left margin
% of the page they are working on.
% 
% \item[\Uidx{\!\headheight!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
% height of page headers.  The register is used together with \!\topmargin!
% and \!\headsep! as an element of \!\pcol@bg@pagetop! and in \!\@outputpage!
% to calculate the distance from the real and imaginary page top to the text
% area top respectively.
% 
% \item[\Uidx{\!\headsep!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
% vertical distance from the bottom of a page header to the text area top.
% The register is used together with \!\topmargin!  and \!\headheight! as an
% element of \!\pcol@bg@pagetop! and in \!\@outputpage!  to calculate the
% distance from the real and imaginary page top to the text area top
% respectively.
% 
% \item[\Uidx{\!\textheight!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
% height of text area in a page.  The register is referred to by
% \!\pcol@output! to examine if a page is very short, by \!\pcol@getpinfo!,
% \!\pcol@startpage!, \!\pcol@flushfloats! and \!\pcol@output@end! to let
% \!\@colht! be it for a page without \spanning{} (so far), by
% \!\pcol@outputelt!, \!\@outputpage!, \!\pcol@output@flush! and
% \!\pcol@output@clear! to build a page to be shipped out, by
% \!\pcol@bg@textheight! to calculate $\HT$, and by \!\pcol@fntextbody! to
% cap the height of a footnote.
% 
% \item[\Uidx{\!\textwidth!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
% of a page, which we occasionally refer to as $\WT$.  The register is
% referred to by \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage! and
% \!\pcol@iflushfloats! to build a \!\hbox! of \!\textwidth! wide to have
% all columns (in a left or right \parapag{}e).  It also referred to by
% following macros; \!\pcol@bg@swappage! to calculate the right margin for
% \mirror{}ed \bgpaint; \!\pcol@bg@@r!, \!\pcol@bg@@f!, \!\pcol@bg@@n!,
% \!\pcol@bg@@p!  and \!\pcol@bg@@s! to specify the width of \bground{} of
% \pwstuff{} to be painted; \!\pcol@shiftspanning! to calculate the
% left-shift amount of a \mctext{} in \cswap; \!\pcol@addmarginpar! to
% measure the distance between the right edges of the rightmost and current
% columns; \!\pcol@zparacol! for the calculation of
% $\lrm=\!\pcol@lrmargin!$; \!\pcol@setcolwidth@r! for the calculation of
% $\w_c$ for all $c\In0\CL$ or $c\In\CL\C$; \!\pcol@setcw@calcfactors! for
% the calculation of $\WT/W$ and $(\WT-W)/F$; \!\pcol@sptext!,
% \!\footnoterule!  of \env{paracol}'s local and \!\endparacol!  to set it
% in \!\columnwidth!; and \!\pcol@fntextbody!  to set it in \!\hsize! if
% \Scfnote{} typesetting is in effect.
% 
% \item[\Uidx{\!\columnwidth!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
% of a column.  The register is let have $\w_c$ by \!\pcol@getcurrcol! for
% the column $c$, then is referred to by the following macros;
% \!\pcol@shiftspanning! to calculate the left-shift amount of a \mctext{} in
% \cswap; \!\pcol@addmarginpar! to measure the distance between the right
% edges of the rightmost and current columns; \!\pcol@imakeflushedpage! and
% \!\pcol@iflushfloats! to put each \colpage{} into a \!\hbox! of $\w_c$ wide
% for shipping a page out; \!\pcol@invokeoutput! to let \!\linewidth! and
% \!\hsize!  have the value of or based on it; and \!\pcol@fntextbody! to
% let \!\hsize! have it for \Mcfnote{} typesetting.  The register is also
% let have \!\textwidth! by \!\footnoterule! of \env{paracol}'s local
% defined in \!\pcol@zparacol! if \Scfnote{} typesetting is in effect, by
% \!\pcol@sptext!  for \mctext{}s, and by \!\endparacol! for \postenv.
% 
% \item[\Uidx{\!\columnsep!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
% of \csepgap{}s.  It is referred to by \!\pcol@setcolwidth@r! to
% calculate $\w_c$ for all $c\In0\CL$ or $c\In\CL\C$, and by
% \!\pcol@setcw@getspec! as the default width of \csepgap{}s.
% 
% \item[\Uidx{\!\columnseprule!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
% of the rules to be drawn in \csepgap{}s. It is referred to by
% \!\pcol@buildcolseprule! and \!\pcol@buildcselt! to draw the rule, and by
% \!\pcol@hfil! to examine if it is positive to mean the rule is really
% drawn and if so to add skips of $-\!\columnseprule!/2$ to surround the
% rule to nullify the width of the rule.
% 
% \item[\Uidx{\!\marginparwidth!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
% of a marginal note.  It is temporarily modified by \!\pcol@addmarginpar!
% so that a left marginal note is placed appropriately.
% 
% \item[\Uidx{\!\marginparsep!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
% distance between a marginal note and text area.  It is temporarily
% modified by \!\pcol@addmarginpar!  so that a right marginal note is placed
% appropriately.
% 
% \item[\Uidx{\!\marginparpush!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
% minimum vertical distance between two marginal notes.  It is referred to
% by \!\pcol@addmarginpar! to find a place for a marginal note and remember
% the place in $\pp^m(p)$.
% 
% \item[\Uidx{\!\paperheight!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the height
% of physical pages $\HP$.  It is referred to by \!\pcol@bg@paperheight!
% to calculate $\HP-2\WR$.
% 
% \item[\Uidx{\!\paperwidth!}]
% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
% of physical pages $\WP$.  It is referred to by \!\pcol@bg@swappage! to
% calculate the right margin for \mirror{}ed \bgpaint, and by
% \!\pcol@bg@paperwidth!  to calculate $\WP-2\WR$.
% 
% \item[\Uidx{\!\z@!}]
% is a \!\dimen! register to have 0\,|pt| to initialize \!\pagerim!,
% \!\belowfootnoteskip! and \!\skip!\!\pcol@colorins! at their declarations,
% and is used in the following macros.
% 
% \begin{quote}\raggedright
% \!\pcol@ShowBox!,
% \!\pcol@makecol!,
% \!\pcol@combinefloats!,
% \!\pcol@nextpelt!,
% \!\pcol@floatplacement!,
% \!\pcol@startpage!,
% \!\pcol@restartcolumn!,
% \!\pcol@outputelt!,
% \!\pcol@ioutputelt!,
% \!\pcol@buildcolseprule!,
% \!\pcol@buildcselt@S!,
% \!\pcol@buildcselt!,
% \!\@outputpage!,
% \!\pcol@startcolumn!,
% \!\pcol@bg@paint@i!,
% \!\pcol@bg@paintregion!,
% \!\pcol@output@start!,
% \!\pcol@putbackmvl!,
% \!\pcol@iscancst!,
% \!\pcol@deferredfootins!,
% \!\pcol@combinefootins!,
% \!\pcol@addmarginpar!,
% \!\pcol@getmparbottom!,
% \!\pcol@sync!,
% \!\pcol@measurecolumn!,
% \!\pcol@synccolumn!,
% \!\pcol@makeflushedpage!,
% \!\pcol@imakeflushedpage!,
% \!\pcol@output@end!,
% \!\pcol@invokeoutput!,
% \!\pcol@setcolwidth@s!,
% \!\pcol@setcw@calcfactors!,
% \!\pcol@setcw@calcf!,
% \!\pcol@extract@fil@ii!,
% \!\pcol@sptext!,
% \!\pcol@fntextbody!.
% \!\pcol@marginpar!,
% \!\pcol@icolumncolor!,
% \!\pcol@set@color@push!,
% \!\pcol@reset@color@pop!,
% \!\pcol@reset@color@mpop!,
% \!\pcol@backgroundcolor@iii!.
% \end{quote}
% 
% It is also used to give the number 0 for the initializations of
% \!\pcol@currcol!, \!\pcol@ncol!, \!\pcol@ncolleft! and
% \!\count!\!\pcol@colorins! at their declarations, and in the following
% macros.
% 
% \begin{quote}\raggedright
% \!\pcol@ShowBox!,
% \!\pcol@F@count!,
% \!\pcol@makecol!,
% \!\pcol@opcol!,
% \!\pcol@setpnoelt!,
% \!\pcol@nextpelt!,
% \!\pcol@checkshipped!,
% \!\pcol@getpelt!,
% \!\pcol@outputelt!,
% \!\pcol@ioutputelt!,
% \!\@outputpage!,
% \!\pcol@startcolumn!,
% \!\pcol@output@start!,
% \!\pcol@output@switch!,
% \!\pcol@setcurrcol!,
% \!\pcol@iscancst!,
% \!\pcol@addmarginpar!,
% \!\pcol@setmpbelt!,
% \!\pcol@do@mpbout@i!,
% \!\pcol@sync!,
% \!\pcol@synccolumn!,
% \!\pcol@makeflushedpage!,
% \!\pcol@imakeflushedpage!,
% \!\pcol@flushfloats!,
% \!\pcol@iflushfloats!,
% \!\pcol@freshpage!,
% \!\pcol@output@end!,
% \!\pcol@zparacol!,
% \!\pcol@setcolwidth@r!,
% \!\pcol@setcw@calcf!,
% \!\pcol@synccounter!,
% \!\pcol@com@syncallcounters!,
% \!\pcol@stepcounter!,
% \!\pcol@stpclelt!,
% \!\pcol@com@switchcolumn!,
% \!\pcol@switchcolumn!,
% \!\pcol@sptext!,
% \!\pcol@switchcol!,
% \!\pcol@visitallcols!,
% \!\pcol@xympar!,
% \!\endparacol!.
% \end{quote}
% 
% \item[\Uidx{\!\p@!}]
% \begin{Sloppy}{3950}%
% is a \!\dimen! register to have 1\,|pt|.  It is used in \!\pcol@ShowBox!,
% \!\pcol@cflt!, \!\pcol@addflhd!, \!\pcol@synccolumn!, \!\pcol@output@end!,
% \!\pcol@setcolwidth@s!, \!\pcol@setcw@getspec@i!, \!\pcol@setcw@fill! and
% \!\pcol@setcw@calcf!, and the top level assignment to \!\@tempskipa! for
% the invocation of \!\pcol@defkw!, as the shorthand of |pt|.
% \end{Sloppy}
% 
% \item[\Uidx{\!\@totalleftmargin!}]
% is a \!\dimen! register to have the total size of the left margins of a
% \env{list}-like environment and those surrounding it.  It is given to
% \!\parshape! by \!\pcol@invokeoutput! and \!\pcol@sptext! if \env{paracol}
% is enclosed in a \env{list}-like environment.
% 
% \item[\Uidx{\!\@themargin!}]
% is a control sequence \!\let!-equal to \!\evensidemargin! for two-sided
% even numbered pages or \!\oddsidemargin! for others.  In
% \!\pcol@outputpage@l! and \!\pcol@outputpage@r! it is bound to one of
% \!\dimen! registers for the references in \!\pcol@outputpage@ev!\footnote{
% 
% The reference in \CSIndex{pcol@@outputpage} being \LaTeX's
% \CSIndex{@outputpage} is done after the macro itself makes the assignment,
% which is of course consistent with those in our macros.}.
% 
% \item[\Uidx{\!\@maxdepth!}]
% is a \!\dimen! register to have \!\maxdepth! at \beginenv{document} to
% recover the temporary update of \!\maxdepth! with 0 by \!\@addtobot! for
% bottom float incorporation in a page.  As discussed in the explanation of
% \!\maxdepth!, in \env{paracol} environments \!\maxdepth! is let have
% \!\@maxdepth! always by the assignments in \!\pcol@output! and
% \!\pcol@combinefloats!.  Other users, \!\pcol@cflt!, \!\pcol@opcol!,
% \!\pcol@ioutputelt!, \!\pcol@combinefootins!, \!\pcol@output@flush! and
% \!\pcol@output@clear!, let \!\boxmaxdepth! have \!\@maxdepth! so as to
% limit the depth of boxes for a completed \colpage{} or page to the value
% for page typesetting, while \!\pcol@flushcolumn! and
% \!\pcol@imakeflushedpage! do that by \!\pcol@@makecol! giving the register
% to it.  The other usage of the register is to calculate \bgpaint{}
% parameter $\HT$ by \!\pcol@bg@textheight!, and to determine the bottom
% edge of the \bground{}s of columns and \csepgap{}s through the argument of
% \!\pcol@buildcolseprule! given by \!\pcol@ioutputelt!,
% \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats!.  The register is also
% referred to by \!\pcol@unvbox@cclv! to go back the last baseline of the
% main vertical list in \!\box!|255|, and by \!\pcol@deferredfootins! to let
% \!\splitmaxdepth! have its value to cap the depth of the first half of
% footnotes split from $\df$.
% 
% \item[\Uidx{\!\@colht!}]
% is a \!\dimen! register to have the height of columns in a page possibly
% shrunk from \!\textheight! by \spanning.  The usages of the register
% are as folllows.
% 
% \begin{itemize}
% \item\begin{Sloppy}{1600}
% In \!\pcol@startpage!, \!\pcol@output@start!, \!\pcol@flushfloats!  and
% \!\pcol@output@end!, it is initialized to \!\textheight!.  In first two,
% the value of the register is reduced to reflect \spanning{} if exists and
% then set into $\pp^h(p)$, while the setting by the third is referred to by
% its callee \!\pcol@iflushfloats!.
% \end{Sloppy}
% 
% \item
% In \!\pcol@getpelt!, \!\pcol@sync!, \!\pcol@flushcolumn!,
% \!\pcol@makeflushedpage! and \!\pcol@imakeflushedpage!, it is let have
% $\pp^h(p)$.  In addition \!\pcol@sync! examines if
% $\!\@colht!<\VT+\VB+v(f)$, and \!\pcol@makefcolumn! uses it to initialize
% the room of a \fcolumn{} as well as the height of $\cc_c(\vb)$ for it.
% 
% \item
% In \!\pcol@opcol!, it is used to add \!\pcol@clearcolorstack! to the
% bottom of $\cc_c(\vb)$ whose height is \!\@colht!.
% 
% \item
% In \!\pcol@startcolumn!(*), \!\pcol@flushcolumn!(*) and
% \!\pcol@freshpage!, it is used to let \!\@colroom! have it.
% 
% \item
% In \!\pcol@restartcolumn!(*), it is saved and restored for the use as the
% height cap of deferred footnote \!\insert!ion in \!\pcol@deferredfootins!
% because it can be shrunk by the non-deferred \Scfnote{}s.
% 
% \item
% In \!\pcol@output@flush! and \!\pcol@output@clear!, it is given to
% \!\pcol@make~flushedpage! as its argument.  The macro
% \!\pcol@makeflushedpage!(*) lets \!\@colht! be the argument if it is less
% than \!\@colht! and thus is given by \!\pcol@output@end!.
% \end{itemize}
% 
% In addition, in the macros with `(*)' above and \!\pcol@makecol!, the
% register is passed to \!\pcol@shrinkcolbyfn! to shrink the height in it
% temporarily to keep the space required to put \Scfnote{}s in the page they
% are working on, for the reference by starred macros themselves or
% \!\@makecol! invoked in \!\pcol@makecol!.
% 
% \item[\Uidx{\!\@colroom!}]
% is a \!\dimen! register to have the height of a column possibly shrunk
% from \!\@colht! by top and bottom floats.  The register is initialized to
% have \!\@colht! by \!\pcol@startcolumn!, \!\pcol@output@start!,
% \!\pcol@flushcolumn! and \!\pcol@freshpage!, the last three of which also
% save it into $\cc_c(\vb^r)$.  This save operation is also done by
% \!\pcol@output@switch! while restoring from it done by
% \!\pcol@restartcolumn!, but the latter macro may shrink the amount in its
% callee \!\pcol@putbackmvl! to capture a \mctext{} while the former cancel
% this shrinkage.  The macros \!\pcol@output! and \!\pcol@output@start! also
% refer to this register to let \!\vsize! have it in the former and to
% calculate the room for each \colpage{} in the \spage{} in the latter.  The
% macro \!\pcol@output@end!  lets the register have \!\textheight! for the
% \postenv{} because the \colpage{}s above it simply precedes the stuff in
% the main vertical list.  The other users \!\pcol@makefcolumn! and
% \!\pcol@makefcolelt! use this register to accumulate the total size of
% floats to be put in a \fcolumn{} temporarily.
% 
% \item[\Uidx{\!\@pageht!}]
% is a \!\dimen! register to be used in \LaTeX's \!\@specialoutput! to have
% the height of \!\@holdpg!.  It is referred to by \!\pcol@addmarginpar! to
% deteremine the position at which a marginal note is placed.
% We also use it as a scratchpad to have $\VP$ in \!\pcol@sync! and
% \!\pcol@measurecolumn!, and to save $\pp^h(\ptop)$ in \!\pcol@flushcolumn!
% for the reference in itself, and to do so in \!\pcol@makeflushedpage! for
% \!\pcol@imakeflushedpage!.
% 
% \item[\Uidx{\!\@pagedp!}]
% is a \!\dimen! register to be used in \LaTeX's \!\@specialoutput! to have
% the depth of \!\@holdpg!.  However, we use it as a scratchpad in
% \!\pcol@sync! and \!\pcol@measurecolumn! to have $\DP$, and in
% \!\pcol@output@end! to have the value to be set in \!\pcol@prevdepth!.
% 
% \item[\Uidx{\!\@toproom!}]
% is a \!\dimen! register to have the room for top floats.  The register is
% saved in $\cc_c(\tr)$ by \!\pcol@setcurrcol! and restored from it by
% \!\pcol@iigetcurrcol!.  The macro \!\pcol@makefcolumn! uses this register
% as a flag to indicate that $\cc_c(\tl)$ of the column $c$ having
% $\cc_c(\tr)=\infty$ contains floats to be put in its last \fcolumn{}
% possibly as top floats so that it is examined by \!\pcol@flushcolumn! and
% \!\pcol@imakeflushedpage!, the former of which then lets $\cc_c(\tr)=0$ to
% mean the floats are put in a \fcolumn{} in a non-\lpage{} by the macro.
% 
% \item[\Uidx{\!\@botroom!}]
% is a \!\dimen! register to have the room for bottom floats.  The register
% is saved in $\cc_c(\br)$ by \!\pcol@setcurrcol! and restored from it by
% \!\pcol@iigetcurrcol!.
% 
% \item[\Uidx{\!\@fpmin!}]
% is a \!\dimen! register to have $\!\floatpagefraction!\times\!\@colht!$
% being the minimum total size of floats for which an ordinary (not flushed)
% \fcolumn{} can be build.  It is referred to by \!\pcol@makefcolumn! as the
% threshhold below which floats in the last \fcolumn{} can be put as top
% floats.
% 
% \item[\Uidx{\!\@mparbottom!}]
% is a \!\dimen! register to have the bottom position of the last
% \!\marginpar! stuff.  Its value at \beginparacol{} is referred to by
% \!\pcol@output@start! to let $\mpb_L^l$ or $\mpb_L^r$ of $\pp^m(0)$ has an
% element based on it, while the tail of one of the lists in $\pp^m(\ptop)$
% defines the value at \Endparacol{} which \!\pcol@output@end! lets the
% register have.  The register is also updated by \!\pcol@getmparbottom! and
% \!\pcol@getmpbelt! to let \!\pcol@@addmarginpar! being \LaTeX's original
% \!\@addmarginpar! know the uppermost available position for the marginal
% note to be added.  This update is, however, just for communicatoin betwee
% these macros and thus is ineffective for typesetting posterior to that, as
% well as the update in \!\pcol@@addmarginpar!, because whole information
% for marginal note placement is kept in $\pp^m(p)$ in $\PPP$.
% 
% \item[\Uidx{\!\@textfloatsheight!}]
% is a \!\dimen! register to have the combined height of mid floats and
% their separators.  It is initialize to be 0 by \!\pcol@floatplacement!,
% saved in $\cc_c(\fh)$ by \!\pcol@setcurrcol!, and restored from it by
% \!\pcol@iigetcurrcol!.
% 
% \item[\Uidx{\!\dimen@!}]
% is a \!\dimen! register for temporary use.  It is used in the following
% macros.
% 
% \begin{itemize}
% \item
% \!\pcol@buildcolseprule!, \!\pcol@buildcselt@S! and \!\pcol@buildcselt! to
% have the argument $d\in\{\!\@maxdepth!,0\}$ of the first macro.
% 
% \item
% \!\pcol@bg@paintregion@i! to have $y_1$ of $\bgr_a^{[c]}$.
% 
% \item
% $\!\pcol@bias@mpbout@i!\Arg{y}\Arg{t}\Arg{b}$ to have $t$ and then $t+y$.
% 
% \item
% \!\pcol@output@switch! to have the height of \prespan{} in
% \!\pcol@prespan!, or 0 if it is $\bot$.
% 
% \item
% \!\pcol@sync! to have $V$ or $V-\DT+\VE$.
% 
% \item
% \!\pcol@addflhd! and \!\pcol@hdflelt! to measure the height of top and
% bottom floats, \!\pcol@makecol! and \!\pcol@output@switch! to measure
% the height of \prespan{} including the top floats, and
% \!\pcol@measurecolumn! for top and bottom floats and $\VT$, $\VB$ and
% $\VP$.
% 
% \item
% \!\pcol@setcolwidth@s! and \!\pcol@setcw@accumwd! to accumulate $W$ being
% the sum of natural widths of column\slash gap specifications, and then
% used by \!\pcol@setcw@calcfactors! to calculate $W/\WT$ and $W-\WT$.
% \end{itemize}
% 
% \item[\Uidx{\!\dimen@ii!}]
% is a \!\dimen! register for temporary use.  It is used in the following
% macros.
% 
% \begin{itemize}
% \item
% \!\pcol@makecol! to measure the total height of top floats by
% \!\pcol@addflhd!.
% 
% \item
% \!\pcol@bg@addext! to have
% $e=|pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}\{a{\cdot}|@|{\cdot}c,a\}$
% 
% \SpecialArrayIndex{d{\cdot}\string\texttt{@}
%     {\cdot}a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@ext@}
% \SpecialArrayIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}
% 
% and then $10000\PT-e$ to calculate an \bgext{} of \bgpaint.
% 
% \item
% $\!\pcol@bias@mpbout@i!\Arg{y}\Arg{t}\Arg{b}$ to have $b$ and then $b+y$.
% 
% \item
% \!\pcol@measurecolumn! to measure $\VT$, $\VP$ and $\DP$.
% 
% \item
% \!\pcol@setcolwidth@s! and \!\pcol@setcw@accumwd! to accumulate $F$ being
% the sum of infinite stretch factors in column\slash gap specifications with
% the unit of pt, and then used by \!\pcol@setcw@calcfactors! to calculate
% $(W-\WT)/F$, where $W$ is the sum of natural widths.
% 
% \item
% \!\pcol@setcw@calcfactors! to have $(W-\WT)/F$ above or 0 to be used in
% \!\pcol@def@extract@fil@iii!  through \!\pcol@setcw@filunit!  made
% \!\let!-equal to the register by \!\pcol@setcolwidth@s!.
% \end{itemize}
% 
% \item[\Uidx{\!\@tempdima!}]
% is a \!\dimen! register for temporary use.  The usages of this register
% are as follows.
% 
% \begin{itemize}
% \item
% In \!\pcol@makecol! and \!\pcol@startpage!, it is used to throw
% $\pp^h(\ptop)$ away when we get it by \!\pcol@getcurrpinfo! because we
% don't need it.
% 
% \item
% In \!\pcol@outputelt!, it has $\pp^h(p)$ to examine if $p$ is a \fpage.
% 
% \item
% In \!\pcol@ioutputelt!, it has $\pp^h(p)$ possibly shrunk by \Scfnote{}s
% to know the \bground{}s to be painted for columns etc.  After that it has
% $\w_c$ being the width of each \!\hbox! into which the \colpage{} of each
% column $c$ is put.
% 
% \item
% In \!\pcol@buildcolseprule! and its callees \!\pcol@buildcselt@S! and
% \!\pcol@buildcselt!, the register has the first argment $H=\pp^h(p)$ of
% the caller macro.
% 
% \item
% In \!\pcol@hfil!$\<c\>$, it has $\gap_c=|\pcol@columnsep|{\cdot}c$.
% 
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
% \item
% In \!\@outputpage!, it has the sum of \!\topmargin!, \!\headheight! and
% \!\headsep! being the distance between tops of imaginary page and its text
% area.
% 
% \item
% In \!\pcol@startcolumn!, it is used to save \!\@colht! which can be shrunk
% temporarily by \Scfnote{}s.
% 
% \item
% In \!\pcol@bg@paintregion@i!, it is let have $x_0$ of $\bgr_a^{[c]}$.
% 
% \item
% In \!\pcol@output@start!, it is used to have the room for each \colpage{}
% in the \spage, and then the height-plus-depth of the \preenv.
% 
% \item
% In \!\pcol@output@switch!, it is used to throw $\pp^h(p)$ away when
% we get it by \!\pcol@getcurrpinfo! because we don't need it.
% 
% \item
% In \!\pcol@shiftspanning!, it is let have the left-shift amount of a
% \mctext{} in \cswap.
% 
% \item
% In \!\pcol@restartcolumn!, it is used to save \!\@colht! which can be
% shrunk temporarily by \Scfnote{}s.
% 
% \item
% In \!\pcol@unvbox@cclv!$\arg{ins}$, it has the depth of \!\box!|255| for
% going back to the baseline of the box, and then has the natural component
% of $\!\skip!\arg{ins}$ to add its stretch and shrink components only.
% 
% \item
% In \!\pcol@addmarginpar!, at first it has the distance between left edges
% of the leftmost and current columns.  Then it is let have the distance
% between top edges of the column and the marginal text to be put.
% 
% \item
% In $\!\pcol@getmparbottom!\<t\>\<h\>$ and
% $\!\pcol@getmpbelt!\<t_i\>\<b_i\>$, it at first has $t$ and then is
% let have $b_i$ when the marginal note cannot be put at $t$.
% 
% \item
% In \!\pcol@sync!, \!\pcol@measurecolumn! and \!\pcol@synccolumn!, it has
% $\VT$ being the maximum combined height of top floats and the main
% vertical list.
% 
% \item
% In \!\pcol@makefcolumn! and \!\pcol@makefcolelt!, it has the room for
% floats to be put in a \fcolumn{}.
% 
% \item
% In \!\pcol@makeflushedpage!, it has the height-plus-depth of \spanning in
% $\pp^i(\ptop)$.
% 
% \item
% In \!\pcol@output@end!, at first it is let have $\VPP-H$, where $H$ is the
% height(-plus-depth) of \!\@outputbox! having the ship-out image of the
% \lpage, being the negative counterpart of the height-plus-depth of
% \spanning{} in the \lpage{} for setting $\mpbout$, and then have $H$ to be
% set in \!\pcol@bg@preposttop! for the \bgpaint{} of \postenv.
% 
% \item
% In \!\pcol@setcolwidth@r!, it has
% $\!\textwidth!-(\Cto-\Cfrom-1)\!\columnsep!$ being the base of $\w_c$.
% 
% \item
% In \!\pcol@setcw@getspec@i!, it is let have the natural width of a
% column\slash gap specification, to be used in \!\pcol@setcolwidth@s!,
% \!\pcol@setcw@accumwd! and \!\pcol@setcw@set!, while in the last of them
% it finally has $\w_c$ or $\gap_c$.
% 
% \item
% In $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$, at first it has $y$, then
% $y/2^{k_2}$, and then $\lceil y/2^{k_2+k_3}\rceil$, where $k_2$ and $k_3$
% are scaling parameters for good approximation.
% 
% \item
% In \!\pcol@switchcol!, it is let have what \!\pcol@ensurevspace! has so
% that the dimensional expression in it is evaluated in the macro and the
% evaluateion result is assigned to $\VE=\!\pcol@@ensurevspace!$.
% 
% \item
% In $\!\ensurevspace!\ARg{space}$, it is let have $\arg{space}$ to ensure
% the argument is a dimension including forced one.
% 
% \item
% In \!\pcol@fntextbody!, it has the height-plus-depth of the \!\vbox! in
% which the footnote is encapsulated.
% 
% \item
% In \!\pcol@set@color@push!, it has the width of the \!\vbox! to be
% \!\insert!ed, which is $m$\,|sp| for a math-mode push of $\mcelt_{i,m}$ or
% 0 for a non-math one $\celt_i$.
% 
% \item
% In $\!\pcol@bg@defext!\Arg{d}\Arg{e}$, it is let have $e$ to confirm $e$
% is a proper dimension.
% \end{itemize}
% 
% \item[\Uidx{\!\@tempdimb!}]
% is a \!\dimen! register for temporary use.  The usages of this register
% are as follows.
% 
% \begin{itemize}
% \item
% In \!\pcol@makecol!, it is used to measure the height-plus-depth $h_i$ of
% decapsulated \!\box!|255| and its original form to add an element
% $\spt(H_i,h_i)$ to $\pp^s(\ptop)$ for a \mctext{} captured in the box.
% 
% \item
% In \!\pcol@ioutputelt!, if has the height-plus-depth of \spanning{}
% $\pp^b(q)$ to be temporarily added to \!\topmargin!.
% 
% \item
% In \!\pcol@buildcolseprule! it has $H_0+h_0$, while in its callee
% $\!\pcol@buildcselt!\<H_i\>\~\<h_i\>$ it has $H_{i-1}+h_{i-1}$ and then
% $H_i+h_i$ where $\spt(H_i,h_i)\in\pp^s(p)$.
% 
% \item
% In \!\pcol@bg@paintregion@i!, it is let have $y_0$ of $\bgr_a^{[c]}$.
% 
% \item
% In \!\pcol@output@switch!, it is let have the height-plus-depth $h_i$ of
% \!\@holdpg! having a \mctext{} to add an element $\spt(H_i,h_i)$ to
% $\pp^s(\ptop)$.
% 
% \item
% In \!\pcol@shrinkcolbyfn!, it is let have the inverse of the \!\skip!
% component of the argument \!\insert! register of the macro, so that in
% \!\pcol@startcolumn! and \!\pcol@restartcolumn! it has that of $\pp^f(p)$
% if $p$ has \Scfnote{}s, or 0 otherwise, and then is referred to by
% \!\pcol@deferredfootins! which then lets the register have the height cap
% of $\df$ splitting.
% 
% \item
% In \!\pcol@addmarginpar!, \!\pcol@getmparbottom! and \!\pcol@getmpbelt!,
% it is let have the vertical space to be occupied
% by the marginal text to be put, being the second argument of
% \!\pcol@getmparbottom!.
% 
% \item
% In \!\pcol@sync! and \!\pcol@measurecolumn!, it has $\VB$ and then, in the
% former, it has $\VP+v(f)$, $\VT$ or $\VT+\VB+v(f)$ according to the
% contents of the page to be \sync{}ed.
% 
% \item
% In \!\pcol@makefcolelt!, it has the size of vertical space consumed by a
% float.
% 
% \item
% In \!\pcol@synccolumn!, it has $\VT-\vc(t)$ being the vertical space from
% the bottom of $\cc_c(\vb^b)$ to the \sync{}ation point.  If the
% \sync{}ation point is defined by a column without main vertical list but
% with top floats, then the register is let have
% $\VT-\vc(t)+\!\textfloatsep!-\!\floatsep!+10000\,|pt|$ to be set in
% $\cc_c(\tf)=\!\pcol@textfloatsep!$ as the space below the \mvlfloat{}
% biased by 10000\,|pt| to indicate the last float is the \mvlfloat{}.
% 
% \item
% In \!\pcol@setcolwidth@r!, it has
% $\!\textwidth!-(\Cto-\Cfrom-1)\!\columnsep!-\sum_{d=0}^{k-1}w_d$ being the
% base of $\w_c$ for $c\In{\Cfrom{+}k}{\,\Cto}$ where $k$ is the number of
% fractions given in the argument of \!\columnratio!.
% 
% \item
% In $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$, at first it is let have $x$,
% then $x\cdot2^{k_1}$, then
% $z'=\break\lfloor(x\cdot2^{k_1})/\lceil{}y/2^{k_2+k_3}\rceil\rfloor$, and
% finally
% $Z=z\times1\,|pt|=z'\cdot2^{16-k}$ referred to by
% \!\pcol@setcw@calcfactors! as $\phi_f=(\WT-W)/F$, where $k_1$, $k_2$ and
% $k_3$ are scaling parameters for good approximation and $k=k_1+k_2+k_3$.
% 
% \item
% In \!\pcol@extract@fil@ii! and \!\pcol@extract@fil@iii!, it is let have
% the infinite stretch factor of a column\slash gap specification
% represented with the unit \!\pcol@setcw@filunit!, to be used in
% \!\pcol@setcolwidth@s!, \!\pcol@setcw@accumwd!, and \!\pcol@setcw@set!.
% 
% \item
% In \!\pcol@fntextbody!, it has $\!\textheight!-\!\skip!\!\footins!$ as the
% cap of the footnote.
% \end{itemize}
% 
% 
% \item[\Uidx{\!\@tempdimc!}]
% is a \!\dimen! register for temporary use.  It is let have values as
% follows.
% 
% \begin{itemize}
% \item
% $H_i-(H_{i-1}+h_{i-1})$ in $\!\pcol@buildcselt!\<H_i\>\<h_i\>$.
% 
% \item
% $x_1$ of $\bgr_a^{[c]}$ in \!\pcol@bg@paintregion@i!.
% 
% \item
% $t+h$ in $\!\pcol@getmparbottom!\<t\>\<h\>$.
% 
% \item
% $\max(t,b_{i-1})+h$ in $\!\pcol@getmpbelt!\<t_i\>\<b_i\>$ invoked from
% $\!\pcol@getmparbottom!\<t\>\~\<h\>$.
% 
% \item
% $\DT$ in \!\pcol@sync!, \!\pcol@measurecolumn! and \!\pcol@synccolumn!.
% 
% \item
% \!\floatsep! or \!\@fpsep! in \!\pcol@makefcolumn! and
% \!\pcol@makefcolelt!.
% 
% \item
% $\w_c$ being the width of column $c$ in \!\pcol@setcolwidth@r!.
% 
% \item
% $\WT-W$ in \!\pcol@setcw@calcfactors!.
% 
% \item
% At first for calculation of $y/2^{k_2}$ and then $z'/2^k\approx x/y$
% in $\!\pcol@setcw@calcf!\<x\>\<y\>\~\<z\>$ where $k_2$ and $k$ are scaling
% parameters for good approximation.
% \end{itemize}
% \end{description}
% 
% 
% 
% \subsubsection{Skip Registers}
% 
% \begin{description}
% \item[\Uidx{\!\baselineskip!}]
% is \TeX's primitive register to have the vertical skip to separate
% adjacent baselines.  It is referred to by \!\pcol@output! and
% \!\pcol@output@start! to examine if \!\@colroom! is unexpectedly small,
% and by \!\pcol@switchcol! to give it to \!\ensurevspace! to let
% \!\pcol@ensurevspace! have the default value.
% 
% \item[\Uidx{\!\topskip!}]
% is \TeX's primitive register to have the vertical skip from the top edge
% of a page to the baseline of its first vertical item.  It is let be 0 by
% \!\pcol@output@start! if we have \preenv{} and is saved in $\pp^t(0)$,
% while \!\pcol@startpage! lets it be \!\pcol@topskip!, into which
% \!\pcol@zparacol! saves the value outside \env{paracol} environment,
% saving the value in $\pp^t(p)$.  Then the register is restored from
% $\pp^t(p)$ by \!\pcol@getpelt! and \!\pcol@sync!, while
% \!\pcol@synccolumn! refers to the value restored by the latter to adjust a
% \sync{}ation point.  The macro \!\pcol@putbackmvl! lets the register have
% 0 when it starts a \mctext{} because it originally follows \prespan{} in
% the \colpage{} to be restarted rather than at the page top.  The macro
% \!\pcol@output@end!  temporarily lets the register have 0 if we have
% non-empty columns in the last page, while \!\endparacol! restores it from
% \!\pcol@topskip! for the pages outside \env{paracol} environmnet.
% 
% \item[\Uidx{\!\splittopskip!}]
% is \TeX's primitive register to have the vertical skip inserted at the
% beginning of the second half of the box split by \!\vsplit! or \TeX's
% internal operation for splitting an \!\insert! at a page break.  The
% register is temporarily let have 0 by \!\pcol@deferredfootins! when it
% splits $\df$ so that the second half does not have any skip at the top.
% The register is also let have \!\footnotesep! in \!\pcol@fntextbody! for
% footnote typesetting.
% 
% \item[\Uidx{\!\parskip!}]
% is \TeX's primitive register to have the vertical skip inserted above each
% paragraph.  It is referred to by \!\pcol@zparacol! to nullify the
% insertion going to be made by the first \!\item! of a \env{list}-like
% environment, when the macro finds the \env{paracol} environment to start
% is at the very beginning of a \env{list}-like environment.
% 
% \item[\Uidx{\!\fill!}]
% is an API \!\skip! register to have a skip 0\,|pt| |plus| 1\,|fill|.  In
% our macros, however, it is used as a keyword in \!\pcol@setcw@getspec!,
% \!\pcol@setcw@getspec@i! and \!\pcol@setcw@fill! to extract the infinite
% stretch factor $f$ given as $f\!\fill!$ in the specification.
% 
% \item[\Uidx{\!\itemsep!}]
% is an API \!\skip! register to have the vertical skip inserted above each
% non-first \!\item! in \env{list}-like environments.  It is referred to by
% \!\pcol@zparacol! to nullify the insertion going to be made by the first
% \!\item! of a \env{list}-like environment, when the macro finds the
% \env{paracol} environment to start is at the very beginning of a
% \env{list}-like environment.
% 
% \item[\Uidx{\!\floatsep!}]
% is an API \!\skip! register to have the vertical skip between adjacent floats.
% It is referred to by \!\pcol@cflt! to cancel the skip following the last
% float, by \!\pcol@makefcolumn! to let \!\pcol@makefcolelt! examine the
% capacity of a \fcolumn{} in the \lpage, by \!\pcol@addflhd! and
% \!\pcol@hdflelt!  to measure the total height of top and bottom floats,
% and by \!\pcol@sync! to calculate the space below the \mvlfloat.
% 
% \item[\Uidx{\!\textfloatsep!}]
% is an API \!\skip! register to have the vertical skip between the main
% vertical list and top\slash bottom floats.  It is referred to by
% \!\pcol@output@start! to calculate the room for each \colpage{} in the
% \spage{} with bottom floats in the \preenv{}, by \!\pcol@combinefloats! to
% insert a skip below the bottom floats in the \preenv{} and \lpage{},
% by \!\pcol@measurecolumn! to take this skip into account in the
% calculation of $\VPP$, by \!\pcol@addflhd!  to measure the vertical space
% for top and bottom floats, and by \!\pcol@synccolumn! to calculate the
% \sync{}ation point for columns with top floats.
% 
% \item[\Uidx{\!\dblfloatsep!}]
% is an API \!\skip! register to have the vertical skip between adjacent
% \pwise{} floats, and is used in \!\pcol@startpage! to cancel the skip
% below the last float.
% 
% \item[\Uidx{\!\dbltextfloatsep!}]
% is an API \!\skip! register to have the vertical skip between the last
% \pwise{} float and the top of columns, and is used in
% \!\pcol@startpage! to put the skip.
% 
% \item[\Uidx{\!\@topsep!}]
% is a \!\skip! register to have the vertical skip inserted above the first
% \!\item! of a \env{list}-like environment.  The actual value is determined
% by \!\@trivlist! from API parameters \!\topsep!, \!\partopsep! and
% \!\parskip! depending on how the environment appears.  The skip in the
% register is inserted by \!\pcol@zparacol! when it finds the \env{paracol}
% environment to start is at the very beginning of a \env{list}-like
% environment.
% 
% \item[\Uidx{\!\@fptop!}]
% is a \!\skip! register to have the vertical skip inserted at the top of
% a \fcolumn, and is used in \!\pcol@makefcolpage!.
% 
% \item[\Uidx{\!\@fpsep!}]
% is a \!\skip! register to have the vertical skip between adjacent floats
% in a \fcolumn, and is used in \!\pcol@makefcolpage!.
% 
% \item[\Uidx{\!\@fpbot!}]
% is a \!\skip! register to have the vertical skip inserted at the bottom of
% a \fcolumn, and is used in \!\pcol@makefcolpage!.
% 
% \item[\Uidx{\!\@tempskipa!}]
% is a \!\skip! register for temporary use.  It is used in the following
% macros.
% 
% \begin{itemize}
% \item
% \begin{Sloppy}{2400}%
% \!\pcol@makecol!, \!\pcol@startpage!, \!\pcol@outputelt!,
% \!\pcol@output@switch!, \!\pcol@flushcolumn! and \!\pcol@makeflushedpage!
% to throw $\pp^t(p)$ away because we don't need it.
% \end{Sloppy}
% 
% \item
% \!\pcol@output@start! to determine \!\topskip! for the \spage.
% 
% \item
% \!\pcol@setcw@getspec@i! and \!\pcol@setcw@fill! to have the width
% specification of a column or gap.
% \end{itemize}
% It is also used in the top level invocation of \!\pcol@defkw! with a glue
% of $0\,|pt|\ |plus|\ 1\,|fil|\~\ |minus|\ 1\,|fil|$.
% \end{description}
% 
% 
% 
% \subsubsection{Box Registers}
% 
% \begin{description}
% \item[\Uidx{\!\strutbox!}]
% is an API \!\box! register to have the strut for the current font size.
% It is used in \!\pcol@fntextbody!\marg{text} to let \!\splitmaxdepth! have
% its depth, and to let the last line of the footnote $\arg{text}$ have its
% depth at shallowest.
% 
% \item[\Uidx{\!\@cclv!}] 
% is a \!\box! register but \TeX{} defines that it has the main vertical
% list when \!\output! routine is invoked.  It is referred to by
% \!\pcol@makecol! when it has a broken \mctext{} to measure its
% height-plus-depth for the element to be added to $\pp^s(\ptop)$ and to
% update it combining its contents with \prespan{} optionally shifting it
% left by passing the register to \!\pcol@shiftspanning!.  The macro also
% uses the register together with its callee \!\pcol@unvbox@cclv! to add
% stretch\slash shrink factor of \!\skip!\!\footins! at its bottom for a
% \colpage{} in a page having \Scfnote{}s.  The macro \!\pcol@specialoutput!
% examines the register to discard the dummy \!\vbox! inserted in it by
% \!\pcol@invokeoutput!.  The other users \!\pcol@output@start!,
% \!\pcol@makenormalcol!, \!\pcol@flushcolumn! and \!\pcol@imakeflushedpage!
% let the register have the main vertical list of \preenv{} or a column to
% be passed to \!\@makecol!, and \!\pcol@flushcolumn! also takes care the
% skip above \Scfnote{}s.
% 
% \item[\Uidx{\!\voidb@x!}]
% is a \!\box! register to be void ($\bot$) always.  It is used to
% initialize \!\pcol@prespan! and \!\pcol@rightpage! at their declaration,
% and is referred to by the following macros.
% 
% \begin{itemize}
% \item
% \!\pcol@makecol! to make \!\pcol@currfoot! void unless \Scfnote{}s in
% \!\foot~ins! is saved into $\pp^f(p)$.
% 
% \item
% \!\pcol@startpage! to let
% $\pp^i(\ptop)=\bot$ if the new \tpage{} does not have \spanning{} and
% $\pp^f(\ptop)=\bot$ for all \fpage{}s and the new \tpage.
% 
% \item
% \!\pcol@outputelt! to initialize \!\@outputbox!.
% 
% \item
% \!\pcol@ioutputelt! to examine if $\S_c$ is empty.
% 
% \item
% \!\pcol@output@start! to let $\pp^f(0)=\bot$, and $\Celt^c=\bot$ if
% $\Celtshadow^c$ is undefined.
% 
% \item
% \!\pcol@output@switch! to let $\cc_c(\ft^b)=\bot$ if the column does
% not have \Mcfnote{}s.
% 
% \item
% \!\pcol@getcurrfoot! to let \!\footins! be void if so.
% 
% \item
% \!\pcol@setcurrcolnf! to let $\cc_c(\ft^b)=\bot$ because the column $c$
% does not have \Mcfnote{}s.
% 
% \item
% \!\pcol@putbackmvl! to let $\!\pcol@prespan!=\bot$ if a \mctext{} really
% starts from the top of a \colpage, and $\csts=\bot$ if the \colpage{}
% $\cc_c(\vb)$ to be restarted is non-empty.
% 
% \item
% \!\pcol@savecolorstack! to let $\csts=\bot$ or its first item be $\bot$ if
% $\CST^c$ or $\Celt^c$ is $\bot$, resepectively.
% 
% \item
% \!\pcol@savefootins! to let its argument macro have a void box if
% \!\@freelist! is exhausted.
% 
% \item
% \!\pcol@makeflushedpage! to initialize \!\@outputbox! and
% \!\pcol@rightpage! to be $\bot$ if the flushed page does not have
% \spanning{}, and to let $\pp^f(\ptop)=\bot$ after putting it in the
% \lpage{} so that \!\pcol@output@end! will be unaware of the \scfnote{} and
% non-\Mgfnote{}s.
% 
% \item
% \!\pcol@flushfloats! to let $\!\pcol@rightpage!=\bot$ if \parapag{}ing is
% not in effect.
% 
% \item
% \!\pcol@output@end! to let $\!\pcol@rightpage!=\bot$ if
% the last page has nothing other than \spanning{} being \pwise{} floats
% and thus we don't have the right \parapag{}e.  The macro also lets
% $\Celt^c=\bot$ for all $c$ and $\cst=\bot$.
%
% \item
% \!\pcol@com@flushpage! and \!\pcol@com@clearpage! gives the void box to
% \!\pcol@flushclear! as its argument to mean these macros are only aware
% of \CSIndex{ifpcol@flush} as the result of \pfcheck.  The macro
% \!\endparacol! also does that if the footnote typesetting is \mgfnote.
% \end{itemize}
% 
% \item[\Uidx{\!\@holdpg!}]
% is a \!\box! register to have the main vertical list when \!\output! is
% invoked with a special \!\penalty! code.  It is let have that by
% \!\pcol@specialoutput!, and is referred to by \!\pcol@output@start!  and
% \!\pcol@makenormalcol! for \preenv{}, and by \!\pcol@output@switch! for the
% column from which we are leaving.
% 
% \item[\Uidx{\!\@outputbox!}]
% is a \!\box! register to have a partial or the complete ship-out image
% of a column or a page.  The usages of the register are as follows.
% 
% \begin{itemize}
% \item
% In \!\pcol@@makecol!, it has a \colpage{} made by \!\@makecol! for
% \!\pcol@flush~column! and \!\pcol@imakeflushedpage!.
% 
% \item
% In \!\pcol@combinefloats!, it has a \colpage{} to which top and bottom
% floats are combined.
% 
% \item
% In \!\pcol@cflt!, it has a \colpage{} to which top floats are combined.
% 
% \item
% In \!\pcol@opcol!, it has the complete \colpage{} built by \!\@makecol!.
% 
% \item
% In \!\pcol@startpage!, it has the complete \fpage{} built by \!\@tryfcolumn!.
% 
% \item
% In \!\pcol@outputelt!, it has the complete (left parallel-) page to be
% shipped out by \!\@outputpage!.
% \Index{parallel-paging}
% 
% \item
% In \!\pcol@outputpage@r!, it is temporarily made \!\let!-equal to
% \!\pcol@rightpage! so that the box is shipped out by \!\pcol@@outputpage!
% being \LaTeX's \!\@outputpage! instead of the real \!\@outputbox!.
% 
% \item\begin{Sloppy}{1700}
% In \!\pcol@output@start!, it has the \preenv{} built by
% \!\pcol@makenormalcol!.
% \end{Sloppy}
% 
% \item
% In \!\pcol@combinefootins!, it is let have the \preenv{} with footnotes.
% 
% \item
% In \!\pcol@flushcolumn!, it has a flushed \colpage{} built by \!\@makecol!
% or a \fcolumn{} built by \!\@makefcolumn!.
% 
% \item
% In \!\pcol@output@flush! and \!\pcol@output@clear!, it has a flushed page
% built by \!\pcol@makeflushedpage! and \!\pcol@imakeflushedpage! in which
% it has each of flushed \colpage{} built by \!\@makecol!.
% 
% \item
% In \!\pcol@flushfloats!, it has the complete (left parallel) page for
% flushed \fcolumn{}s.
% 
% \Index{parallel-paging}
% 
% \item
% In \!\pcol@iflushfloats!, it has a \fcolumn{} built by
% \!\pcol@makefcolumn!.
% 
% \item
% In \!\pcol@output@end!, it has the ship-out image of the \lpage{} of a
% \env{paracol} environment built by \!\pcol@makeflushedpage! and
% \!\pcol@imakeflushedpage!.
% \end{itemize}
% 
% \item[\Uidx{\!\@tempboxa!}]
% is a \!\box! register for temporary use.  The usages of the register are
% as follows.
% 
% \begin{itemize}
% \item
% In \!\pcol@makecol!, it is used to decapsulate \!\box!|255| containing a
% broken \mctext{}.  In the macro and \!\pcol@output@switch!, it is also
% used as a waste bascket to make \!\footins! void when it contains
% \Scfnote{}s in a non-\tpage.
% 
% \item\begin{Sloppy}{2100}
% In \!\pcol@cflt! and \!\pcol@startpage!, it has top column-\slash
% \pwise{} floats combined by the application of
% \!\@comflelt!\slash\!\@comdblflelt! to \!\@toplist!\slash\!\@dbltoplist!
% respectively.
% \end{Sloppy}
% 
% \item
% In \!\pcol@phantom!$\<b\>$, it has an empty box whose height and depth are
% equal to those of the argument box $b$.
% 
% \item
% By \!\pcol@buildcolseprule! and its callees \!\pcol@buildcselt@S! and
% \!\pcol@buildcselt!, it is let have the painted \bground{}s for columns,
% \csepgap{}s and \mctext{}s in a page, and then is put into the ship-out
% image of the page by \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage! or
% \!\pcol@iflushfloats!.
% 
% \item
% In \!\@outputpage!, it is let have the painted \bground{} of the right
% page referred to by its callee \!\pcol@outputpage@r!.
% 
% \item
% In $\!\pcol@bg@paint@i!\Arg{body}$, it is let have painted \bground{}s
% built by $\arg{body}$.
% 
% \item
% In $\!\pcol@bg@paintregion!\arg{a}\arg{c}$, it is let have painted
% \bground{} of the region $\bgr_a^{[c]}$.
% 
% \item
% In \!\pcol@specialoutput!, it is used to discard the dummy \!\vbox! put by
% \!\pcol@invokeoutput!.
% 
% \item
% In \!\pcol@makenormalcol!, it is used to save \!\footins! into it and make
% it $\bot$ temporarily to exclude \mgfnote{} footnotes from \spanning{} for
% \preenv.
% 
% \item
% In \!\pcol@ifempty!$\arg{box}\arg{then}\arg{else}$, it is used to examine
% if $\arg{box}$ is empty.
% 
% \item
% In $\!\pcol@scancst!\arg{box}$ and \!\pcol@iscancst!, it is used to have
% what $\cst$ or $\csts$ has after the scan of $\arg{box}\in\{\cst,\csts\}$.
% 
% \item
% In \!\pcol@savecolorstack!, it is used to have the \!\vbox! for $\Celt^c$
% to be placed at the top of $\csts$.
% 
% \item
% In \!\pcol@deferredfootins!, it is used to have the first half split from
% $\df$ being the deferred footnotes to be \!\insert!ed.
% 
% \item
% In \!\pcol@fntextbody!\marg{text}, it is used to encapsulate $\arg{text}$
% in it.
% 
% \item
% In \!\pcol@icolumncolor!, it is used to have a \!\vbox! to be \!\insert!ed
% for the update of $\Celt^c$.
% 
% \item
% In \!\pcol@set@color@push!, it is used to have a \!\vbox! to be \!\insert!ed
% to push $\celt_i$ or $\mcelt_{i,m}$ to $\cstraw$.
% 
% \item
% In \!\pcol@reset@color@pop! and \!\pcol@reset@color@mpop!, it is used to
% have a \!\vbox! to be \!\insert!ed to add $\celtpop_i$ or
% $\mceltpop_{i,m}$ to $\cstraw$.
% \end{itemize}
% \end{description}
% 
% 
% 
% \subsubsection{Token Registers}
% 
% \begin{description}
% \item[\Uidx{\!\output!}]
% is \TeX's primitive to have \!\output! routine.  It is let have
% \!\pcol@output! as its sole token by \!\pcol@zparacol!.
% 
% \item[\Uidx{\!\everypar!}]
% is \TeX's primitive to have tokens inserted at the beginning of each
% paragarph.  In \!\pcol@sptext! and \!\pcol@com@endcolumn!, it is
% \!\global!ized to keep its contents after the end of a group.  In
% \!\pcol@output@switch!, its contents are broadcasted to $\cc_c(\ep)$ for
% all $c\In0\C$ if columns are \sync{}ed with a \mctext.  Then these values
% or that simply given in a column are saved into $\cc_c(\ep)$ by
% \!\pcol@setcurrcol!, and then restored from it by \!\pcol@iigetcurrcol!.
% 
% \item[\Uidx{\!\everyvbox!}]
% is \TeX's primitive to have tokens inserted at the beginning of each
% \!\vbox!.  In \!\pcol@zparacol!, after tokens in it are saved into
% \!\pcol@everyvbox!, it is let have a \!\the!-reference to
% \!\pcol@everyvbox! and |\pcol@innertrue| to turn
% $\CSIndex{ifpcol@inner}=\true$, and then the register itself is made
% \!\let!-equal to \!\pcol@everyvbox!.  In addition, it is let have tokens
% in \!\pcol@everyvbox! if a \!\global! assignment to the register is made
% in the \env{paracol} just having been closed.  Another usage of this
% register is to insert a painted page \bground{} to the \!\vbox! to be
% \!\shipout! by \!\pcol@@outputpage! being \LaTeX's \!\@outputpage!, and is
% used for this purpose by \!\pcol@outputpage@l! and \!\pcol@outputpage@r!,
% and by \!\pcol@outputpage@ev! to nullify this special function for other
% inside \!\vbox!es.
% 
% \item[\Uidx{\!\@temptokena!}]
% is a \!\toks! register for temporary use.  It is used in
% \!\pcol@output@switch! to broadcast \!\everypar! to $\cc_c(\ep)$ for all
% $c\In0\C$.
% 
% \end{description}
% 
% 
% 
% \subsubsection{Switches}
% 
% \begin{description}
% \item[\Uidx{\CSIndex{if@twocolumn}}]
% is a switch to be $\true$ iff multi-column pages are being typeset.  It is
% turned $\true$ by \!\pcol@zparacol!, and then turned $\false$ by
% \!\endparacol!.  In addition, it is turned $\false$ when \!\pcol@output!
% finds that the \!\output! request for a page break outside \env{paracol}
% is sneaked into our own \!\output! routine, in order to avoid that
% \LaTeX's original \!\output! routine misunderstands it is working on a
% two-columned document.  The switch is examined by \LaTeX's own macros
% including old \!\end@dblfloat! kept in our own \!\pcol@end@dblfloat!.  It
% is also examined by \!\pcol@zparacol! before being turned $\true$ to
% ensure it is $\false$ or to complain about the inappropriateness otherwise.
% 
% \item[\Uidx{\CSIndex{if@firstcolumn}}]
% is a switch to be $\true$ iff the first column is being typeset.  Its
% truth value is determined by \!\pcol@addmarginpar! to tell
% \!\pcol@@addmarginpar!, \!\pcol@getmparbottom@i! and \!\pcol@setmpbelt@i!
% the margin which a marginal note goes to.
% 
% \item[\Uidx{\CSIndex{if@twoside}}]
% is a switch to be $\true$ iff two-sided page typesetting is in effect and
% thus even numbered page may have their own left margins, headers and
% footers different from those for odd numbered pages.  Besides the
% initialization by the main class file such as \textsf{article.cls}
% according to the class option |twoside|, the switch is \!\global!ly turned
% $\false$ by \!\pcol@twosided! for the case in which API macro \!\twosided!
% does not have `|p|' in its optional argument, and then \!\global!ly turned
% $\true$ by \!\pcol@twosided@p! which is invoked when the argument contains
% `|p|', or the API macro does not have the argument at all.  Then the
% switch is referred to by \!\pcol@outputpage@l!, \!\pcol@outputpage@r! and
% \!\pcol@bg@swappage! to decide the left margin of even numbered pages,
% i.e., \!\evensidemargin! if the switch is $\true$ or \!\oddsidemargin!
% otherwise.  The switch is also referred to by \!\pcol@com@cleardoublepage!
% to have a blank page if the switch is $\true$ and the command
% \!\cleardoublepage! is used in an odd-numbered page.
% 
% \item[\Uidx{\CSIndex{if@reversemargin}}]
% is a switch to be $\true$ iff \!\reversemarginpar! is specified to reverse
% the side which marginal notes go to.  It is examined by
% \!\pcol@addmarginpar! as a factor to decide the margin which a marginal
% note goes to, and by \!\pcol@do@mpbout@i! for the same purpose but for
% marginal notes in pre-environment or \postenv.
% 
% \Index{pre-environment stuff}
% 
% \item[\Uidx{\CSIndex{if@mparswitch}}]
% is a switch to be $\true$ iff it is specified by, for example,
% \texttt{twoside} option of a class such as \textsf{article}, that marginal
% notes in even numbered pages go to thier left margin.  It is examined by
% \!\pcol@do@mpbout@i! as a factor to decide the margin which a maginal note
% goes to in pre-environment or \postenv{}.
% 
% \Index{pre-environment stuff}
% 
% \item[\Uidx{\CSIndex{if@nobreak}}]
% is a switch to be $\true$ iff the last paragraph is for a sectioning
% command.  The switch is saved into $\cc_c(\sw)$ together with
% \CSIndex{if@afterindent} by \!\pcol@setcurrcol!, and then restored from
% it by \!\pcol@iigetcurrcol!.  The macro \!\pcol@output@switch! refers to
% it to broadcast its value set by a \mctext{} to $\cc_c(\sw)$ for all
% $c\In0\C$, while \!\pcol@output@start! and \!\pcol@restartcolumn! insert
% $\!\penalty!=10000$ by \!\nobreak! if the switch is $\true$.  This
% conditional \!\nobreak!  is also done by \!\pcol@icolumncolor!,
% \!\pcol@set@color@push!, \!\pcol@reset@color@pop! and
% \!\pcol@reset@color@mpop! to avoid a break after an \!\insert!.  The macro
% \!\pcol@zparacol! also exmaines the switch, but with the truth value in it
% given outside \env{paracol} environment, to invoke \!\@nbitem! if $\true$
% when the macro finds the \env{paracol} environment to start is at the very
% beginning of a \env{list}-like environment.
% 
% \item[\Uidx{\CSIndex{if@newlist}}]
% is a switch to be $\true$ in the duration after a \env{list}-like
% environment starts and until its first \!\item! appears.  The switch is
% examined by \!\pcol@zparacol! to know if the \env{paracol} environment to
% start is at the very beginning of a \env{list}-like environment and, if
% so, is turned $\false$ by the macro after it inserts vertical skips
% pretending the first \!\item! is given.
% 
% \item[\Uidx{\CSIndex{if@inlabel}}]
% is a switch to be $\true$ in the duration after an \!\item! appears and
% until its first paragraph is given.  The switch is examined by
% \!\pcol@zparacol! together with \CSIndex{if@newlist} to know if the
% \env{paracol} environment to start is at the very beginning of a
% \env{list}-like environment ($\false$) and not \env{trivlist}-like one
% ($\true$).
% 
% \item[\Uidx{\CSIndex{if@afterindent}}]
% is a switch to be $\true$ iff a sectioning commmand tells that the fisrt
% paragraph following it is to be indented.  The switch is saved into
% $\cc_c(\sw)$ together with \CSIndex{if@nobreak} by \!\pcol@setcurrcol!,
% and then restored from it by \!\pcol@iigetcurrcol!.  The macro
% \!\pcol@output@switch! refers to it to broadcast its value set by a
% \mctext{} to $\cc_c(\sw)$ for all $c\In0\C$.
% 
% \item[\Uidx{\CSIndex{if@fcolmade}}]
% is a switch to be $\true$ iff a \fcolumn{} or \fpage{} is built by
% \!\@tryfcolumn! or \!\@makefcolumn!.  The value is set by \!\@tryfcolumn!
% for $\cc_c(\dl)$ is referred to by \!\pcol@output!, \!\pcol@startcolumn!
% and \!\pcol@freshpage!, while that for \!\@dbldeferlist! is referred to by
% \!\pcol@startpage!.  The value set by \!\@makefcolumn! for $\cc_c(\dl)$ is
% referred to by \!\pcol@flushcolumn!, while that for \!\@dbldeferlist! is
% referred to by \!\pcol@output@clear!.  The macros \!\pcol@flushfloats! and
% \!\pcol@iflushfloats! also refer to the switch to build pages having only
% \fcolumn{}s and turn the switch $\true$ or $\false$ by themselves to know
% such paegs are still to be built or not.  The macro \!\pcol@output@end!
% also turns the switch $\true$ if a \lpage{} will be followed by page(s)
% having \fcolumn{}s to tell that to \!\pcol@flushfloats!.
% 
% \item[\Uidx{\CSIndex{if@tempswa}}]
% is a switch for temporary use.  The usages of the switch are as follows.
% 
% \begin{itemize}
% \item
% In \!\pcol@checkshipped!, it is turned $\true$ iff $\S_c$ for all
% $c\In0\C$ have \colpage{}s to be shipped out, and then it is examined by 
% \!\pcol@opcol!.
% 
% \item
% In \!\pcol@nextpage! and \!\pcol@nextpelt!, it is $\true$ until
% \!\pcol@nextpelt! finds the first $q$ such that $q>p$ and
% $\pp^h(q)\geq0$ to mean $q$ is not for a \fpage{}, so that we let $p=q$
% to skip \fpage{}s following to the old $p$ if any.
% 
% \item
% In \!\pcol@outputcolumns! and \!\pcol@outputelt!, it is $\true$ until
% \!\pcol@outputelt! finds the first $q$ such that $q\geq\pbase$ and
% $\pp^h(q)\geq0$ to mean $q$ is not for a \fpage{}, and the arguemnt of
% \!\pcol@outputcolumns! is 0 to mean that it is not for page flushing, so that
% we ship out $q$ and all \fpage{}s following it if any.
% 
% \item
% In \!\@outputpage! it is let have the value of \CSIndex{ifpcol@bg@painted}
% indicating if \bgpaint{} for the left page is done, and then it is
% examined by \!\pcol@outputpage@l! to determine whether the \bground{} is
% put into the final ship-out image.
% 
% \item
% In \!\pcol@makenormalcol!, it is $\true$ iff the footnotes in \preenv{} is
% included in \!\@outputbox! which the macro builds.
% 
% \item
% In \!\pcol@output@switch!, at first it holds \CSIndex{if@nobreak} of the
% \mctext{} if columns are \sync{}ed with it to broadcast
% \CSIndex{if@nobreak} to all $\cc_c(\sw)$.  Then it is turned $\true$ iff
% $\CSIndex{ifpcol@sync}=\true$ for \sync{}ation or
% $\CSIndex{ifpcol@clear}={\true}$ for flushing, so as to invoke
% \!\pcol@sync!.  And finally, it is turned $\true$ iff
% $\CSIndex{ifpcol@clear}={\false}$ or $\CSIndex{ifpcol@sync}=\true$, so as
% to invoke \!\pcol@restartcolumn!.
% 
% \item
% In \!\pcol@restartcolumn!, it is turned $\true$ iff footnote typesetting
% is \scfnote{} and $p<\ptop$.
% 
% \item
% In \!\pcol@scancst!, it is initialized to be $\true$.  Then it is referred
% to by \!\pcol@iscancst! for each $\celt\in\cstraw$ to update $\Celt^c$ and
% then turned $\false$ when the first one is found.
% 
% \item
% In \!\pcol@savecolorstack!, it is $\true$ iff either $\cst\neq\bot$ or
% $\Celt^c\neq\bot$, i.e., $\CST^c$ to be saved is not $\bot$.
% 
% \item
% In \!\pcol@getmparbottom!, it is intialized to be $\false$ and then may be
% turned $\true$ by \!\pcol@getmpbelt! if it finds a gap between two marginal
% notes to accommodate that to be added, and then examined by
% \!\pcol@getmparbottom! to know the fact.
% 
% \item
% In \!\pcol@sync!, it is turned $\true$ iff the \sync{}ed or flushed page
% can be built by \!\pcol@synccolumn!.
% 
% \item
% In \!\pcol@makefcolumn! having non-empty $\cc_c(\tl)$, it is turned
% $\false$ iff the macro is acting on a column in the \lpage{}, $\cc_c(\dl)$
% is emptied by the macro itself, and the total size of the floats to be put
% in the \fcolumn{} being built by the macro is less than \!\@fpmin!, to
% mean it is possible that the floats in $\cc_c(\tl)$ is put in the
% \fcolumn{} as top floats.
% 
% \item
% In \!\pcol@measurecolumn! and \!\pcol@addflhd!, it is set to be $\false$
% iff both top floats and the main vertical list are empty, so that
% \!\pcol@measureupdate! examines it for the update of $\VT$ and $\DT$.
% Then it is kept $\false$ iff both of footnotes and bottom floats are
% empty, so that \!\pcol@measurecolumn! examines it for the update of $\VP$
% and \!\pcol@measureupdate! does for $\VPP$ and $\DP$.
% 
% \item
% In \!\pcol@makeflushedpage!, it is made $\false$ iff $\ptop$ is the
% \lpage{}, $\VPP=-\infty$ to mean all columns are empty and
% $\pp^f(\ptop)=\bot$, so as to make the \spanning{} in $\pp^i(\ptop)$ a
% float in \postenv{} if \CSIndex{ifpcol@dfloats} also $\false$.  Then it is
% kept $\false$ if $\CSIndex{ifpcol@dfloats}=\false$ or $\pp^i(\ptop)=\bot$
% to mean nothing is shipped out for \lpage{}.  Then it is made $\false$ iff
% $\ptop$ is the \lpage{} without deferred floats and \Mgfnote{}
% typesetting is in effect, i.e., the switch is $\true$ iff \Scfnote{}s are
% put in the page to be flushed.
% 
% \item
% In \!\pcol@imakeflushedpage!, it is turned $\true$ iff $\cc_c(\tr)=\infty$
% and $\VPP=\pp^h(\ptop)$ to mean the floats in $\cc_c(\tl)$ should be put in
% a \fcolumn{} in the \lpage{} as usual.
% 
% \item
% In \!\pcol@iflushfloats!, it is turned $\true$ iff one or more columns have
% non-empty $\cc_c(\dl)$ after shipping a page for \fcolumn{}s out, so that
% \CSIndex{if@fcolmade} is let have its value after scanning all columns.
% 
% \item
% In \!\pcol@output@end!, it is turned $\true$ iff we built \fcolumn{}s, or
% the main vertical list in the \lpage{} is empty and the page is not the
% \spage, so that we create a new page for the \postenv.
% 
% \item
% In \!\globalcounter!\marg{ctr}, it is turned $\true$ iff $\arg{ctr}\in\CG$
% already.
% 
% \item
% In $\!\pcol@cmpctrelt!\arg{\theta}$, it is turned $\true$ iff $\theta$ is
% not in $\Cc_0$ or $\Val(\theta)\neq\val_0(\theta)$, so that $\theta$ is
% added to \!\@gtempa! being the list of \lcounter{}s to be synchronized.
% 
% \item
% In \!\pcol@switchcolumn!$|[|d|]|$, it is turned $\false$ iff $0\leq d<\C$
% so that we complain $c$ is invalid if the switch is $\true$.
% 
% \item
% In $\!\pcol@ac@caption@def!\arg{s}\arg{t}$, \CSIndex{@tempswatrue} or
% \CSIndex{@tempswafalse} is given as its first argument $s$ by
% $\!\pcol@ac@caption@enable!$ or $\!\pcol@ac@caption@disable!$ respectively,
% so that $|\if@ac@caption@if@|{\cdot}t$ is made \!\let!-equal to $s$ and
% \!\pcol@ac@caption! examines it for enabling\slash disabling
% \!\addcontentsline! respectively.  The macros \!\pcol@ac@caption@if@lof!
% and \!\pcol@ac@caption@if@lot! are initialized to be \!\let!-equal to
% \!\@tempswatrue! as the default.
% 
% \item
% In \!\pcol@icolumncolor!, it is turned $\true$ iff we are in a \!\vbox! or
% in restricted horizontal or math mode.
% 
% \item
% In \!\pcol@backgroundcolor@i!, it is exmained if the root of the
% invocation chain is \!\backgroundcolor! which turns the switch $\true$, or
% \!\nobackgroundcolor! which turns it $\false$, to determine whether the
% \bground{} of a region is painted or not.
% \end{itemize}
% \end{description}
% 
% 
% 
% \subsection{Macros}
% \label{sec:imp-tex-macro}
% 
% \subsubsection{Procedural Macros}
% 
% \begin{description}
% \item[\Uidx{\CSIndex{par}}]
% is \TeX's primitive to end\slash start paragraphs, but may be modified by
% \LaTeX{} to have some special functionality occasionally.  The macro
% \!\pcol@output! makes it \!\let!-equal to \hbox{\!\@@par!} in which the
% \TeX's orinigal definition is kept, while \!\pcol@zparacol! and
% \!\pcol@par! use it as is.
% 
% \item[\Uidx{\!\space!}]
% is an API macro to have a space token.  It is used in \!\pcol@output!,
% \!\pcol@icolumncolor!, \!\pcol@defcseprulecolor@i! and
% \!\pcol@backgroundcolor@ii! for warning messages, and in
% \!\pcol@def@extract@fil! to \!\def!ine the macro \!\pcol@extract@fil!
% having spaces in its argument specification.
% 
% \item[\Uidx{\!\nointerlineskip!}]
% is an API macro to let $\!\prevdepth!=-1000$\,pt to inhibit \TeX's
% baseline progress mechanism.  It is used in \!\pcol@ioutputelt!,
% \!\pcol@makeflushedpage! and \!\pcol@imakeflushedpage! to joint boxes
% without \!\baselineskip! between them, in \!\pcol@outputpage@ev! to
% suppress the \!\baselineskip! insertion after the first box of painted
% \bground{} in the final ship-out image, and in \!\pcol@bg@paint@i!
% for the same purpose for the box having painted \bground{}s.
% 
% \item[\Uidx{\!\offinterlineskip!}]
% is an API macro to let $\!\baselineskip!=-1000$\,pt, $\!\lineskip!=0$ and
% $\!\lineskiplimit!=\!\maxdimen!$ to supress \!\baselineskip! insertion for
% all boxes following this macro.  It is used in \!\pcol@bg@paint@i! to do
% that in the box in which painted \bground{}s are built.
% 
% \item[\Uidx{\!\thepage!}]
% is an API macro to have the representation of the counter \counter{page}.
% It is used in \!\pcol@output! for a warning message.
% 
% \item[\Uidx{$\cs{the}{\cdot}\theta$}]
% \SpecialArrayIndex{\theta}{\the}
% 
% is an API macro to have the representation of the counter $\theta$.  The
% macro is kept in $|\pcol@thectr@|{\cdot}\theta$
% 
% \SpecialArrayIndex{\theta}{\pcol@thectr@}
% 
% by \!\pcol@thectrelt! which also makes the macro \!\let!-equal to
% $|\pcol@thectr@|{\cdot}\theta{\cdot}0$
% 
% \SpecialArrayIndex{\theta{\cdot}c}{\pcol@thectr@}
% 
% if the \lrep{} of $\theta$ in the column 0 is defined by
% \!\definethecounter!.  The macro \!\pcol@setctrelt! also makes this
% overriding for the column $c$ to which the macro belongs if
% $|\pcol@thectr@|{\cdot}\theta{\cdot}c$
% 
% \SpecialArrayIndex{\theta{\cdot}c}{\pcol@thectr@}
% 
% being the \lrep{} for $c$ is defined, while it makes $|\the|{\cdot}\theta$
% 
% \SpecialArrayIndex{\theta}{\the}
% 
% \!\let!-equal to $|\pcol@thectr@|{\cdot}\theta$
% 
% \SpecialArrayIndex{\theta}{\pcol@thectr@}
% 
% otherwise to give it its original definition.
% 
% \item[\Uidx{$\!\stepcounter!\<\theta\>$}]
% is an API macro to increment the counter $\theta$ and zero-clear its
% descendant counters.  It is used in \!\pcol@startpage! for the counter
% \counter{page}, and in \!\pcol@iifootnotetext! for \counter{footnote}.
% 
% \item[\Uidx{\!\nobreak!}]
% is an API macro to insert $\!\penalty!=10000$ to inhibit line or page
% breaks.  It is used in \!\pcol@output@start!, \!\pcol@restartcolumn!,
% \!\pcol@icolumncolor!, \!\pcol@set@color@push!, \!\pcol@reset@color@pop!
% and \!\pcol@reset@color@mpop!  to meet the page-break inhibition request
% made by $\CSIndex{if@nobreak}=\true$.
% 
% \item[\Uidx{$\!\addvspace!$\marg{skip}}]
% is an API macro to insert a vertical $\arg{skip}$ if
% $\!\lastskip!<\arg{skip}$, or a skip of $\arg{skip}+\!\lastskip!$
% otherwise.  The macro is used in \!\pcol@zparacol!  when it finds the
% \env{paracol} environment to start is at the very beginning of a
% \env{list}-like environment, to insert \!\@topsep! instead of
% $\!\parskip!+\!\itemsep!$ going to be inserted by the first \!\item!.
% 
% \item[\Uidx{$\!\addpenalty!\arg{pen}$}]
% is an API macro to insert a page break $\!\penalty!=\arg{pen}$ if
% $\CSIndex{if@nobreak}={\false}$.  The \!\penalty! is inserted removing the
% last vertical skip which is reinserted after the \!\penalty!.  The macro
% is used in \!\pcol@output@start! and \!\pcol@restartcolumn! to insert
% \!\interlinepenalty! if $\CSIndex{if@nobreak}=\false$, while
% \!\pcol@zparacol! uses it to insert \!\@beginparpenalty! when it finds the
% \env{paracol} environment to start is at the very beginning of a
% \env{list}-like environment.
% 
% \item[\Uidx{\!\footnotesize!}]
% is an API macro to set the font size for footnotes.  It is used in
% \!\pcol@fntextbody! for footnote typesetting.
% 
% \item[\Uidx{\!\rule!\oarg{\mbox{$r$}}$\Arg{w}\Arg{h}$}]
% is an API macro to draw a vertical rule of $w$ width and $h$ tall,
% optionally raised by $r$.  It is used in \!\pcol@fntextbody! to have the
% rule of $w=r=0$ and $h=\!\footnotesep!$ to make the first line of the
% footnote is at least as tall as \!\footnotesep!.
% 
% \item[\Uidx{$\!\addcontentsline!\arg{file}\arg{sec}\arg{entry}$}]
% is an API macro to put \!\addtocontents! for the arguments to |.aux| file.
% The orignial definition of the macro is kept in
% \!\pcol@addcontentsline! so that \!\pcol@ac@disable@toc! and
% \!\pcol@ac@caption! make the macro regain its original definition after
% temporarily disabling its function by making it \!\let!-equal to
% \!\pcol@gobblethree!.
% 
% \item[\Uidx{\!\marginpar!}\oarg{left}\marg{right}]
% is an API macro to put merginal note $\arg{left}$ or $\arg{right}$ to the
% left or right margin.  In \!\pcol@zparacol! it is made \!\let!-equal to
% \!\pcol@marginpar! for the emulation of \!\marginnote!, while its original
% version is kept in \!\pcol@@marginpar!.
% 
% \item[\Uidx{\!\footnote!}\oarg{num}\marg{text}]
% is an API macro to give a footnote $\arg{text}$ optionally with its number
% $\arg{num}$.  In \!\pcol@zparacol! it is made \!\let!-equal to
% \!\pcol@footnote!  to implement its starred version and the adjustment of
% \counter{footnote} at \Endparacol, while its original version is kept in
% \!\pcol@@footnote!.
% 
% \item[\Uidx{\!\footnotemark!}\oarg{num}]
% is an API macro to give a footnote mark optionally with the number
% $\arg{num}$ which the mark represents.  In \!\pcol@zparacol! it is made
% \!\let!-equal to \!\pcol@footnotemark! to implement its starred version
% and the adjustment of \counter{footnote} at \Endparacol, while its
% original version is kept in \!\pcol@@footnotemark!.
% 
% \item[\Uidx{\!\footnotetext!}\oarg{num}\marg{text}]
% is an API macro to give a footnote $\arg{text}$ optionally with its number
% $\arg{num}$ but without putting the mark in the footnoted text.  In
% \!\pcol@zparacol!  it is made \!\let!-equal to \!\pcol@footnotetext! to
% implement its starred version, while its original version is kept in
% \!\pcol@@footnotetext!.
% 
% \item[\Uidx{\!\footnoterule!}]
% is an API macro to draw a horizontal line above footnotes, or to insert
% whatever it has above them.  With \Scfnote{} typesetting, it is redefined
% in \!\pcol@zparacol! so that it refers to \!\textwidth! instead of
% \!\columnwidth! for drawing the horizontal line or whatever defined, while
% the original version is kept in \!\pcol@footnoterule!.  Then it is used in
% \!\pcol@putfootins! to separate footnotes from the stuff above them, with
% the original or modified definition.
% 
% \item[\Uidx{\!\newpage!}]
% is an API macro to break a page.  It is used in \!\pcol@switchcol! as the
% argument of \!\pcol@visitallcols! to break the \colpage{}s visited in the
% \cscan{} when the \sync{}ed \cswitch{} requires explicit page breaks.
% 
% \item[\Uidx{\!\dblfigrule!}]
% is an API macro to draw a horizontal line between the last \pwise{}
% floats and the main vertical list, or to insert whatever it has between
% them.  The macro is used in \!\pcol@startpage! to build \spanning{} in
% the page $p$ in $\pp^b(p)$.
% 
% \item[\Uidx{\!\topfigrule!}]
% is an API macro to draw a horizontal line between the last \cwise{}
% top float and the main vertical list, or to insert whatever it has between
% them.  The macro is used in \!\pcol@cflt! and \!\pcol@synccolumn! to
% insert it below the last (real) top float.  It is also made \!\let!-equal
% to \!\relax! temporarily by \!\pcol@imakeflushedpage! when it put floats in
% a \fcolumn{} as top floats.  Note that the macro and its bottom
% counterpart \!\botfigrule! should produce a vertical list whose total
% height and depth is 0, because \LaTeX's float mechanism and thus our
% macros believe so.
% 
% \item[\Uidx{\!\normalcolor!}]
% is an API macro to have color specification stuff for normal coloring.
% The macro is used in \!\pcol@putfootins! to specify the color of footnotes
% to be put in \!\@outputbox!, in \!\normalcolumncolor!\oarg{c} to
% define that the default color of the column $c$ is the normal color,
% in \!\normalcolseprulecolor! to specify that the color for \cseprule{}s is
% \!\normalcolor!, and in the initial definition of \!\pcol@colseprulecolor!
% to give the default color for \cseprule{}s.
% 
% \item[\Uidx{\!\color!}\oarg{mode}\marg{color}]
% is an API macro defined in coloring pacakges to start text coloring with
% $\arg{color}$ optionally with $\arg{mode}$.  The macro is used in
% \!\pcol@xcolumncolor!\oarg{mode}\~\marg{color}\oarg{c} and
% \!\pcol@ycolumncolor!\marg{color}\oarg{c} to define the default color of
% the column $c$ is $\arg{color}$ optionally with $\arg{mode}$, in
% \!\pcol@defcseprulecolor@x! and \!\pcol@defcseprulecolor@y! to define the
% color of \cseprule{}s, and in \!\pcol@backgroundcolor@x! to define the
% color for \bgpaint{} of a region.
% 
% \item[\Uidx{\!\pfmtname!}]
% is an API macro defined in p\LaTeX{} to have its format name |pLaTeX2e|
% (so far).  It is used in the top level assignment of the constant switch
% \CSIndex{ifpcol@bfbottom}.
% 
% \item[\Uidx{$\!\PackageError!\arg{pkg}\arg{msg}\arg{hlp}$}]
% is a developer's API macro to stop the exectution showing the error
% message $\arg{msg}$ with the package identification $\arg{pkg}$ and the
% help mssage $\arg{hlp}$.  The macro is used in the following macros;
% \!\pcol@ovf! on \!\@freelist! shortage; \!\pcol@set@color@push! on too
% many math-mode colorings; in \!\pcol@zparacol! on two-column
% typesetting outside \env{paracol} and illegal nesting of \env{paracol};
% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ on too large $x/y$;
% \!\pcol@switchcolumn! on invalid target column; \!\pcol@switchenv! on
% illegal \cswitch{} commands\slash environments in a \csenv;
% \!\addcontentsonly! on unknown contents type; \!\footnotelayout! on
% unknown layout;  \!\pcol@twosided! on unknown two-sided typesetting
% feature;  \!\pcol@backgroundcolor! on unknown region of \bgpaint;  and in 
% \!\pcol@backgroundcolor@i! on a region not being a column or \csepgap{}
% but its ordinal being specified.
% 
% \item[\Uidx{$\!\PackageWarning!\arg{pkg}\arg{msg}$}]
% is a developer's API macro to report a warning message $\arg{msg}$ with
% the package identification $\arg{pkg}$.  The macro is used in
% \!\pcol@ignore! to complain an API macro appears in \env{paracol}
% inappropriately, in \!\pcol@fntextbody!  if the footnote is taller than
% $\!\textheight!-\!\skip!\!\footins!$, in \!\pcol@mn@warning! to show
% \!\marginnote! is emulated, and in \!\pcol@icolumncolor!,
% \!\pcol@defcseprulecolor@i! and \!\pcol@backgroundcolor@ii! to complain
% \!\columncolor!\slash\!\normalcolumncolor!,
% \!\colseprulecolor!\slash\!\normalcolseprulecolor! or \!\background~color!
% is used without coloring packages respectively.
% 
% \item[\Uidx{\!\@@par!}]
% is an internal macro to keep \TeX's original primitive \CSIndex{par} in it.
% The macro is used in \!\pcol@output! to let \CSIndex{par} act with its
% original definition, and in \!\pcol@switchcol! and \!\pcol@flushclear! as
% the argument given to \!\pcol@visitallcols! to give \TeX's page builder
% the chance of page break in \cscan{}ning.
% 
% \item[\Uidx{\!\@height!}]
% is an internal macro having the keyword |height|.  It is used in
% \!\pcol@buildcolsep~rule!, \!\pcol@buildcselt!, \!\pcol@bg@paintregion@i!,
% \!\pcol@output@start!, and \!\pcol@putbackmvl! to draw a \!\hrule! for
% \cseprule{} in the first two, a \!\vrule! to be painted in the third, and
% an invisible \!\hrule! in the fourth and last.
% 
% \item[\Uidx{\!\@width!}]
% is an internal macro having the keyword |width|.  It is used in
% \!\pcol@buildcolsep~rule!, \!\pcol@buildcselt!, \!\pcol@bg@paintregion@i!,
% \!\pcol@output@start!, and \!\pcol@putbackmvl! to draw a \!\hrule! for
% \cseprule{} in the first two, a \!\vrule! to be painted in the third, and
% an invisible \!\hrule! in the fourth and last.
% 
% \item[\Uidx{\!\@plus!}]
% is an internal macro having the keyword |plus|.  It is used in the
% following macros.
% 
% \begin{itemize}
% \item
% \!\pcol@makecol! to \!\def!ine \!\@textbottom! with the body of a vertical
% skip with small infinite stretch and shrink.
% 
% \item
% \!\pcol@combinefloats! for a skip of the same amount in \!\@textbottom!
% above and that of negative amount to {\em move} the effect.
% 
% \item
% \!\pcol@hfil! for skips having 1\,|fil| infinite stretch with $\gap_c$ or
% $\gap_c/2$ to make it sure the series of columns and \csepgap{}s does not
% cause underfull.
% 
% \item
% \!\pcol@synccolumn! to put a $1\,|fil|$ infinte stretch below the
% main vertical list together with a small infinte shrink in the \colpage{}
% being flushed and having a \sync{}ation point, and a vertical skip with a
% small infinite stretch to push up the main vertical list above a
% \sync{}ation point.
% 
% \item
% \!\pcol@setcw@getspec@i! to add $0\,|pt|\ |plus|\ 1000\,|pt|\ |minus|\
% 1000\,|pt|$ to \!\@tempskipa! to ensure the register have stretch and
% shrink components.
% 
% \item
% \!\pcol@setcw@fill! to let $\!\@tempskipa!=0\,|pt|\ |plus|\ f\,|fil|$ as
% the infinite stretch factor of $f$.
% \end{itemize}
% 
% It is also used in the top level assignment of $0\,|pt|\ |plus|\ 1\,|fil|\
% |minus|\ 1\,|fil|$ to \!\@tempskipa! for the invocatoin of \!\pcol@defkw!.
% 
% \item[\Uidx{\!\@minus!}]
% is an internal macro having the keyword |minus|.  It is used in the
% following macros.
% 
% \begin{itemize}
% \item
% \!\pcol@makecol! to \!\def!ine \!\@textbottom! with the body of a vertical
% skip with small infinite stretch and shrink.
% 
% \item
% \!\pcol@combinefloats!  for a skip of the same amount and that of negative
% amount.
% 
% \item
% \!\pcol@synccolumn! to put a small infinite shrink together with a
% stretch of $1\,|fil|$ at the bottom of the main vertical list in a
% \colpage{} being flused and having a \sync{}ation point.
%
% \item
% \!\pcol@setcw@getspec@i! to add $0\,|pt|\ |plus|\ 1000\,|pt|\ |minus|\
% 1000\,|pt|$ to \!\@tempskipa! to ensure the register have stretch and
% shrink components.
% \end{itemize}
% 
% It is also used in the top level assignment of $0\,|pt|\ |plus|\ 1\,|fil|\
% |minus|\ 1\,|fil|$ to \!\@tempskipa! for the invocatoin of \!\pcol@defkw!.
% 
% \item[\Uidx{\!\hb@xt@!}]
% is an internal macro having the sequence ``\!\hbox!| to|''.  It is used in 
% \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats! to
% put each \colpage{} in a \!\hbox! of \!\columnwidth! wide and to enclose
% all of them in a \!\hbox! of \!\textwidth! wide.
% 
% \item[\Uidx{$\!\@namedef!\arg{cs}\arg{body}$}]
% is an internal macro to do $\!\def!|\|\arg{cs}\Arg{body}$.  It is used in
% the following macros.
% 
% \begin{itemize}
% \item
% \!\pcol@zparacol! for \!\column*! and \!\pcol@com@column*!.
% 
% \item
% $\!\pcol@remctrelt!\<\theta\>$ for $|\cl@|{\cdot}\theta$.
% 
% \SpecialArrayIndex{\theta}{\cl@}
% 
% \item
% $\!\definethecounter!\<\theta\>\<c\>\arg{rep}$ for
% $|\pcol@thectr@|{\cdot}\theta{\cdot}c$,
% 
% \SpecialArrayIndex{\theta{\cdot}c}{\pcol@thectr@}
% 
% \item
% $\!\pcol@loadctrelt!\<\theta\>\<\val_c(\theta)\>$ for
% $|\pcol@ctr@|{\cdot}\theta$.
% 
% \SpecialArrayIndex{\theta}{\pcol@ctr@}
% 
% \item
% \!\pcol@defcolumn! for \!\pcol@com@column*!.
% 
% \item
% \!\pcol@defcseprulecolor@i! for $\!\pcol@colseprulecolor![{\cdot}c]$.
% 
% \SpecialArrayIndex{c}{\pcol@colseprulecolor}
% 
% \end{itemize}
% 
% We also use this macro in top level \!\def!initions of
% \!\pcol@com@nthcolumn*!, \!\pcol@com@leftcolumn*! and
% \!\pcol@com@rightcolumn*! for the starter of the environments
% \env{nthcolumn*}, \env{leftcolumn*} and \env{rightcolumn*}.
% 
% \item[\Uidx{$\!\@nameuse!\arg{cs}$}]
% is an internal macro to do $|\|\arg{cs}$.  It is used in the following
% macros.
% 
% \begin{itemize}
% \item
% $\!\pcol@bg@addext!\arg{z}\Arg{s}\Arg{d}$ for
% $|\pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}\{a{\cdot}|@|{\cdot}c,a\}$.
% 
% \SpecialArrayIndex{d{\cdot}\string\texttt{@}
%     {\cdot}a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@ext@}
% \SpecialArrayIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}
% 
% \item
% \!\pcol@bg@columnleft! for $|\pcol@columnwidth|{\cdot}c$ and
% $|\pcol@columnsep|{\cdot}c$.
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
% \item
% \!\pcol@bg@columnwidth! for $|\pcol@columnwidth|{\cdot}c$.
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% 
% \item
% \!\pcol@bg@columnsep! for $|\pcol@columnsep|{\cdot}c$.
% 
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
% \item
% \!\pcol@ccuse! for
% $\Celt^c=|\pcol@columncolor@box|{\cdot}c$ or
% $\Celtshadow^c=|\pcol@columncolor|{\cdot}c$.
% 
% \SpecialArrayIndex{c}{\pcol@columncolor}
% \SpecialArrayIndex{c}{\pcol@columncolor@box}
% 
% \item
% \!\column*! for \!\pcol@com@column*!.
% 
% \item
% \!\pcol@zparacol! for $|\pcol@colpream|{\cdot}0$.
% 
% \SpecialArrayIndex{c}{\pcol@colpream}
% 
% \item
% $\!\pcol@storectrelt!\<\theta\>$ for $|\pcol@ctr@|{\cdot}\theta$.
% 
% \SpecialArrayIndex{\theta}{\pcol@ctr@}
% 
% \item
% $\!\pcol@cmpctrelt!\<\theta\>$ for $|\c@|{\cdot}\theta$
% 
% \SpecialArrayIndex{\theta}{\c@}
% 
% and $|\pcol@ctr@|{\cdot}\theta$.
% 
% \SpecialArrayIndex{\theta}{\pcol@ctr@}
% 
% \item
% \!\pcol@synccounter! for $|\pcol@counters|{\cdot}c$ for the column $c$.
% 
% \SpecialArrayIndex{c}{\pcol@counters}
% 
% \item
% $\!\pcol@syncctrelt!\<\theta\>$ for $|\c@|{\cdot}\theta$.
% 
% \SpecialArrayIndex{\theta}{\c@}
% 
% \item
% $\!\pcol@stepcounter!\<\theta\>$ for $|\pcol@counters|{\cdot}c$ for the
% column $c$,
% 
% \SpecialArrayIndex{c}{\pcol@counters}
% 
% and for $|\cl@|{\cdot}\theta$.
% 
% \SpecialArrayIndex{\theta}{\cl@}
% 
% \item
% \!\pcol@switchcol! to the column $c$ for $|\pcol@colpream|{\cdot}c$.
% 
% \SpecialArrayIndex{c}{\pcol@colpream}
% 
% \item
% $\!\pcol@aconlyelt!\<t\>\<c\>$ for $|\pcol@ac@def@|{\cdot}t$.
% 
% \SpecialIndex{\pcol@ac@def@lof}\SpecialIndex{\pcol@ac@def@lot}
% 
% \item
% $\!\pcol@ac@def@lof!\arg{eord}$ and $\!\pcol@ac@def@lot!\arg{eord}$
% for $|\pcol@ac@caption@|{\cdot}\~\arg{eord}$.
% 
% \SpecialIndex{\pcol@ac@caption@enable}
% \SpecialIndex{\pcol@ac@caption@disable}
% 
% \item
% $\!\pcol@ac@caption!\arg{type}|[|\arg{lcap}|]|\arg{cap}$ for
% $|\pcol@ac@caption@if@|{\cdot}t$
% 
% \SpecialIndex{\pcol@ac@caption@if@lof}
% \SpecialIndex{\pcol@ac@caption@if@lot}
% 
% and for $|\ext@|{\cdot}\~\arg{type}$.
% 
% \SpecialIndex{\ext@figure}\SpecialIndex{\ext@table}
% 
% \item
% $\!\footnotelayout!\Arg{l}$ for $|pcol@fnlayout@|{\cdot}l$.
% 
% \SpecialArrayIndex{l}{\pcol@fnlayout@}
% \SpecialIndex{\pcol@fnlayout@c}
% \SpecialIndex{\pcol@fnlayout@p}
% \SpecialIndex{\pcol@fnlayout@m}
% 
% \item
% $\!\pcol@twosided!|[|T|]|$ for $|pcol@twosided@|{\cdot}t$ where $t\in T$.
% 
% \SpecialArrayIndex{t}{\pcol@twosided@}
% \SpecialIndex{\pcol@twosided@p}
% \SpecialIndex{\pcol@twosided@c}
% \SpecialIndex{\pcol@twosided@m}
% \SpecialIndex{\pcol@twosided@b}
% \end{itemize}
% 
% \item[\Uidx{$\!\@gobble!\arg{arg}$}]
% discards its argument $\arg{arg}$.  It is used in \!\pcol@output@start!,
% \!\pcol@icolumncolor! and \!\pcol@set@color@push! for temporarily letting
% \!\aftergroup! be \!\@gobble! to nullify \!\aftergroup! with
% \!\reset@color! invoked in \!\pcol@set@color!, being the original version
% of \!\set@color!, and in \!\pcol@zparacol! to make \!\pcol@bg@paintbox!
% \!\let!-equal to \!\@gobble! to nullify it if any coloring packages have
% not been loaded.  In addition, the macros \!\pcol@F! and \!\pcol@Fe! for
% logging are made \!\let!-equial to \!\@gobble! at the top level to nullify
% them.
% 
% \item[\Uidx{$\!\@ifundefined!\arg{cs}\arg{then}\arg{else}$}]
% \begin{Hfuzz}{0.8pt}%
% is an internal macro to do $\arg{then}$ or $\arg{else}$ if $\arg{cs}$ is
% undefined or defined respectively.
% It is used in the following macros;
% $\!\pcol@bg@paintregion!\arg{a}\arg{c}$ to examine if either
% $|\pcol@bg@color@|{\cdot}a{\cdot}|@|{\cdot}c$ or
% $|\pcol@bg@color@|{\cdot}a$ is defined;
% 
% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}
% \SpecialArrayIndex{a}{\pcol@bg@color@}
% 
% \!\add~contentsonly!$\<t\>\<c\>$ to stop the execution if
% $|\pcol@ac@def@|{\cdot}t$ is not defined;
% 
% \SpecialArrayIndex{t}{\pcol@ac@def@}
% 
% \!\footnote~layout!$\Arg{l}$ to stop the execution if
% $|\pcol@fnlayout@|{\cdot}l$ is not defined;
% 
% \SpecialArrayIndex{l}{\pcol@fnlayout@}
% 
% $\!\pcol@twosided!|[|T|]|$ to stop the execution if $T$ has $t$
% such that $|\pcol@twosided@|{\cdot}t$ is not defined;
% 
% \SpecialArrayIndex{t}{\pcol@twosided@}
% 
% \!\pcol@backgroundcolor! to stop the execution if $|\pcol@bg@@|{\cdot}a$
% is not defined for a region $a$;
% 
% \SpecialArrayIndex{a}{\pcol@bg@@}
% 
% and \!\pcol@backgroundcolor@i! to stop the execution if
% $|\pcol@bg@mayhavecol|{\cdot}a$ is not defined for a region $a$.
% \end{Hfuzz}
% 
% \item[\Uidx{$\!\@ifnextchar!\arg{char}\arg{then}\arg{else}$}]
% is an internal macro to do $\arg{then}$ or $\arg{else}$ if the character
% following to the macro is $\arg{char}$ or not respectively.  It is used in
% the following macros to examine if they are followed by a `\texttt{\LB}'.
% 
% \begin{quote}\raggedright
% \!\paracol!,
% \!\pcol@zparacol!,
% \!\columnratio!,
% \!\pcol@com@column*!\hbox{ (initial definition)},
% \!\pcol@com@switchcolumn!,
% \!\pcol@iswitchcolumn!,
% \!\pcol@adjustfnctr!,
% \!\pcol@ifootnotetext!,
% \!\twosided!,
% \!\marginparthreshold!,
% \!\columncolor!,
% \!\pcol@columncolor!,
% \!\normalcolumncolor!.
% \!\colseprulecolor!,
% \!\pcol@defcseprulecolor!,
% \!\normalcolseprulecolor!,
% \!\pcol@backgroundcolor!,
% \!\pcol@backgroundcolor@w!.
% \end{quote}
% It is also used in \!\pcol@backgroundcolor@iii! and
% \!\pcol@backgroundcolor@iv! if they are followed by a `\texttt{\LP}'.
% 
% \item[\Uidx{$\!\@ifstar!\arg{then}\arg{else}$}]
% is an internal macro to do $\arg{then}$ or $\arg{else}$ if the character
% following to the macro is `|*|'.  It is used in \!\pcol@yparacol!,
% \!\globalcounter!, \!\pcol@switchcolumn!, \!\pcol@footnote!,
% \!\pcol@footnotemark! and \!\pcol@footnotetext! to examine if the optional
% `|*|' is specified.
% 
% \item[\Uidx{$\!\@whilesw!\arg{sw}\cs{fi}\arg{body}$}]
% is an internal macro to iterate $\arg{body}$ while the switch $\arg{sw}$
% is $\true$.  It is used in \!\pcol@output!, \!\pcol@startpage!,
% \!\pcol@output@clear!, \!\pcol@flushfloats!, \!\pcol@freshpage! and
% \!\pcol@output@end! to iterate building process of \fcolumn{}s or
% \fpage{}s while $\CSIndex{if@fcolmade}=\true$, and in \!\pcol@switchcol!
% and \!\pcol@flushclear! to iterate the height check of \sync{}ed or
% flushed pages while $\CSIndex{ifpcol@flush}=\true$.
% 
% \item[\Uidx{$\!\@whilenum!\arg{ifnum}\cs{do}\arg{body}$}]
% is an internal macro to interate $\arg{body}$ while the integer comparison
% expression $\arg{ifnum}$ is $\true$.  The macro is used in the following
% macros to iterate their own procedures for all columns $c\In0\C$.
% 
% \begin{quote}\raggedright
% \!\pcol@checkshipped!,
% \!\pcol@output@start!,
% \!\pcol@output@switch!,
% \!\pcol@sync!,
% \!\pcol@makeflushedpage!,
% \!\pcol@freshpage!,
% \!\pcol@output@end!,
% \!\pcol@synccounter!,
% \!\pcol@com@syncallcounters!,
% \!\pcol@stepcounter!,
% \!\pcol@visitallcols!.
% \end{quote}
% 
% The macro is also used in the following macros for the ranges following
% macro name, where $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$ and $c$ is the
% column they are working on.
% 
% \begin{quote}
% \!\pcol@ioutputelt! $\LBRP\Cfrom\Cto$\\
% \!\pcol@bg@paint@ii! $\LBRP\CBfrom{\Cto{-}1}$\\
% \!\pcol@bg@columnleft! $\LBRP\CBfrom{c}$\\
% \!\pcol@addmarginpar! $\LBRP\Cfrom{c'}$ ($c'\in\{c,\;\Cto-(c-\Cfrom)-1\}$)\\
% \!\pcol@imakeflushedpage! $\LBRP\Cfrom\Cto$\\
% \!\pcol@iflushfloats! $\LBRP\Cfrom\Cto$\\
% \!\pcol@setcw@scan! $\LBRP\Cfrom\Cto$
% \end{quote}
% 
% The other users have a little bit more complicated range as follows.
% \begin{itemize}
% \item
% \!\pcol@flushcolumn! to iterate \fcolumn{} building for a column $c$ in
% pages $q$ such that $q\in(\cc_c(\vb^p),\ptop)$.
% 
% \item
% \!\pcol@setcolwidth@r! to make assignment of $\w_c$ for
% $c\In{\min(\Cfrom{+}k,\Cto{-}1)}{\,\Cto}$ where $k$ is the number of
% fractions given as the first or second argument of
% \!\columnratio! and kept in \!\pcol@columnratioleft! or
% \!\pcol@columnratioright!, respectively.
% 
% \item
% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ to calculate
% $\lceil{y/2^{k_2+k_3}}\rceil$ finding $k_3$ by iterating $y/2$ until the
% result becomes less than $2^{15}$, to calculate $z'/2^k$ with the range
% $\LBRP0k$, to calculate $z'/2^{k-16}$ with the range $\LBRP0{\,k{-}16}$,
% and to calculate $z'\cdot2^{16-k}$ with the range $\LBRP0{\,16{-}k}$,
% where $z'\cdot2^{16-k}=Z=z\times1\,|pt|$ and $k_2$, $k_3$ and $k$ are
% scaling parameters for good approximation.
% \end{itemize}
% 
% \item[\Uidx{$\!\@whiledim!\arg{ifdim}\cs{do}\arg{body}$}]
% is an internal macro to interate $\arg{body}$ while the dimensional
% comparison expression $\arg{ifdim}$ is $\true$.  The macro is used in
% $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ twice, at first to find
% $k_1=\min\Set{k}{x\cdot2^k\geq2^{13}\,|pt|}$ and to have $x\cdot2^{k_1}$,
% and then to find $k_2=\max\Set{k}{y\bmod2^k=0}$ and to have $y/2^{k_2}$.
% 
% \item[$\Uidx{\!\@for!}\arg{cs}\texttt{:=}\arg{list}\cs{do}\arg{body}$]
% is an internal macro to iterate $\arg{body}$ for each element of the
% comma-separated $\arg{list}$ letting $\arg{cs}$ have the element.  The
% macro is used in \!\pcol@setcolwidth@r! to scan its argument
% $\arg{ratio}$ defined by \!\columnratio!, and in \!\pcol@setcw@scan! to
% scan its argment $\arg{spec}$ defined by \!\setcolumnwidth!.
% 
% \item[$\Uidx{\!\@tfor!}\arg{cs}|:=|\arg{list}\cs{do}\arg{body}$]
% is an internal macro to iterate $\arg{body}$ for each non-space token in
% $\arg{list}$ letting $\arg{cs}$ have the token.  The macro is used in
% \!\pcol@bg@paint@ii!, \!\pcol@setcw@getspec! and \!\pcol@twosided! to scan
% their arguments, in \!\pcol@setcw@getspec@i! to scan a column\slash
% gap specification to remove spaces from it, and in
% $\!\pcol@twosided!|[|T|]|$ to scan all tokens being two-sided typesetting
% features in $T$.
% 
% \item[\Uidx{$\!\@next!\arg{elm}\arg{lst}\arg{suc}\arg{fail}$}]
% is an internal macro to remove the first element from $\arg{lst}$,
% \!\def!ine $\arg{elm}$ to have the first element, and then do $\arg{suc}$,
% if $\arg{lst}$ is not empty.  Otherwise, it performs $\arg{fail}$.  The
% macro is used in the following macros to obtain an \!\insert! from
% \!\@freelist!.
% 
% \begin{itemize}
% \item
% \!\pcol@opcol! for the completed \colpage{}.
% 
% \item
% \!\pcol@startpage! for \fpage{}s and \spanning{} for \pwise{} top
% floats.
% 
% \item
% \!\pcol@output@start! for the \preenv{}, and \colpage{}s and $\Celt^c$ of
% all columns.
% 
% \item
% \!\pcol@output@switch! for the \colpage{} from which we are leaving.
% 
% \item
% \!\pcol@iscancst! for $\Celt^c$.
% 
% \item
% \!\pcol@savefootins! for footnotes.
% 
% \item
% \!\pcol@flushcolumn! for \fcolumn{}s and the empty \colpage{} in $\ptop$.
% 
% \item
% \!\pcol@synccolumn! for an \mvlfloat{} on a \sync{}ation if its point
% defined by a column whose main vertical list is empty.
% 
% \item
% \!\pcol@output@end! for the \pwise{} floats in the \lpage{} if the
% main vertical list of the page is empty.
% 
% \item
% \!\pcol@icolumncolor! for $\Celt^c$.
% \end{itemize}
% 
% The macro is also used in \!\pcol@ioutputelt! to obtain completed
% \colpage{}s from $\S_c$.
% 
% \item[\Uidx{%
%	$\!\@xnext!\cs{@elt}\arg{car}\arg{cdr}\cs{@@}\arg{first}\arg{rest}$}]
% is an internal macro to remove the first element $|\@elt|\arg{car}$ from a
% list in the form of $|\@elt|\,e_1\,\cdots\,|\@elt|\,e_n$ where
% $\arg{cdr}=|\@elt|\,e_2\,\cdots\~\,|\@elt|\,e_n$ and |\def|ine
% $\arg{first}$ as $\arg{car}$ and globally |\def|ine $\arg{rest}$ as
% $\arg{cdr}$.  It is used in \!\pcol@addmarginpar! to get the first element
% of \!\@currlist! being a \!\insert! for a right marginal note without
% modifying \!\@currlist!.
% 
% \item[\Uidx{$\!\@cons!\arg{lst}\arg{elm}$}]
% is an internal macro to add $\!\@elt!\arg{elm}$ to the tail of $\arg{lst}$.
% 
% \begin{itemize}
% \item
% \!\pcol@makecol! to add $\spt(H,h)$ to the tail of $\pp^s(\ptop)$.
% 
% \item
% \!\pcol@opcol! to add the completed \ccolpage{} $\cc_c(\vb)$ to $\S_c$.
% 
% \item
% \!\pcol@startpage! to add $\pp(\ptop-1)$ and \fpage{}s to $\PP$.
% 
% \item
% \!\pcol@outputelt! to return \spanning{} $\pp^i(q)$ in a shipped-out \fpage{}
% $q$ to \!\@freelist!, or to add $\pp(q)$ to $\PP$ if the page $q$ is kept.
% 
% \item
% \!\pcol@ioutputelt! to return \spanning{} $\pp^i(q)$, \Scfnote{}s
% $\pp^f(q)$ and/or \colpage{}s $\s_c(q)$ for all $c\In0C$ in a shipped-out
% page $q$ to \!\@freelist!.
% 
% \item
% \!\pcol@output@start! to return the \ccolpage{} $\cc_0(\vb)$ to
% \!\@freelist!.
% 
% \item
% \!\pcol@output@switch! to add $\spt(H,h)$ to the tail of $\pp^s(\ptop)$.
% 
% \item
% \!\pcol@restartcolumn! to return the \ccolpage{} $\cc_c(\vb)$ to be resumed,
% and its footnotes $\cc_c(\ft)$ if any, to \!\@freelist!.
% 
% \item
% $\!\pcol@getmparbottom!\<t\>\<h\>$ to add
% $\mpar(\max(t,b_n),\max(t,b_n){+}h)$ to the tail of the list
% $\mpb_{\{L,R\}}^{\{l,r\}}$, and its callee
% $\!\pcol@getmpbelt!\<t_i\>\<b_i\>$ to add $\mpar(t_i,b_i)$ or
% $\mpar(\max(t,b_{i-1}),\max(t,b_{i-1}){+}h)$ to the so-far tail of the
% list in rebuilding.
% 
% \item
% \!\pcol@flushcolumn! to return footnotes $\cc_c(\ft)$ in the \ccolpage{}
% of $c$ to be flushed to \!\@freelist! if any, and to add the flushed
% \colpage{} and \fcolumn{}s to $\S_c$.
% 
% \item
% \!\pcol@makefcolelt! to add a float to \!\@toplist! or $\cc_c(\dl)$.
% 
% \item
% \!\pcol@synccolumn! to add an \mvlfloat{} for \sync{}ation to
% $\cc_c(\tl)$.
% 
% \item
% \!\pcol@makeflushedpage! to return \spanning{} $\pp^i(\ptop)$ and/or
% \Scfnote{}s $\pp^f(\ptop)$ in the top page to be flushed to \!\@freelist!
% if any.
% 
% \item
% \!\pcol@imakeflushedpage! to return \Mcfnote{}s in $\cc_c(\ft)$ s.t.\
% $\cc_c(\vb^p)=\ptop$ to \!\@freelist! if any.
% 
% \item
% \!\pcol@output@end! to return $\pp^f(\ptop)$, all \ccolpage{}s
% $\cc_c(\vb)$, and all $\Celt^c\neq\bot$ to \!\@freelist!.
% 
% \item
% \!\pcol@end@dblfloat! to add a \pwise{} float in \!\@currbox! to
% \!\@dbldeferlist!.
% 
% \item
% $\!\globalcounter!\<\theta\>$ to add a \gcounter{} $\theta$ to $\CG$.
% 
% \item
% $\!\pcol@iremctrelt!\<\theta\>$ to add a \lcounter{} $\theta$ to $\CTL$.
% 
% \item
% $\!\pcol@storectrelt!\<\theta\>$ to add a pair $\<\theta,\val_c(\theta)\>$
% to $\Cc_c$ for a column $c$.
% 
% \item
% $\!\pcol@savectrelt!\<\theta\>$ to add a pair $\<\theta,\val(\theta)\>$ to
% $\Cc_c$ for a column $c$.
% 
% \item
% $\!\pcol@cmpctrelt!\<\theta\>$ to add a counter $\theta$ to the list of
% \lcounter{}s to be synchronized.
% 
% \item
% $\!\addcontentsonly!\<t\>\<c\>$ to add a pair $\<t,c\>$ to $\T$.
% 
% \item
% \!\pcol@backgroundcolor@ii! to add a region whose \bground{} is painted to
% \!\pcol@bg@defined!.
% \end{itemize}
% 
% \item[\Uidx{$\!\@cdr!\<a_1\>\<a_2\>\cdots\<a_n\>\cs{@nil}$}]
% is an internal macro to be expanded to $\<a_2\>\cdots\<a_n\>$. It is used
% in $\!\pcol@getcurrpinfo!\arg{cs}$ to extract $\pp(\ptop)$ from
% $\!\pcol@currpage!=\!\@elt!\arg{\pp(\ptop)}$ and to \!\def!ine $\arg{cs}$
% letting it have $\pp(\ptop)$.
% 
% \item[\Uidx{$\!\protected@edef!\arg{macro}$\marg{body}}]
% is an internal macro to do \!\edef!$\arg{macro}$\marg{body} with the
% \!\protect!ion so that \!\protect!$\arg{cs}$ is kept in the expansion.  It
% is used in \!\pcol@fntextbody! to \!\edef!ine \!\@currentlabel!.
% 
% \item[\Uidx{$\!\@latex@warning@no@line!\arg{msg}$}]
% is an internal macro to report a warning message $\arg{msg}$ without the
% line number in which the cause lies.  It is used in \!\pcol@output! if
% a page with floats and very short main vertical list is built.
% 
% \item[\Uidx{\!\@eha!}]
% is an internal macro having a help message saying the command causing an
% error is ignored.  It is used in \!\pcol@zparacol!, \!\pcol@setcw@calcf!,
% \!\pcol@switchcolumn!, \!\pcol@switchenv!, and \!\addcontentsonly! as the
% argument of \!\PackageError!.
% 
% \item[\Uidx{\!\@ehb!}]
% is an internal macro having a help message saying the error causes a
% serious problem.  It is used in \!\pcol@ovf!, \!\pcol@zparacol! and
% \!\pcol@set@color@push! as the argument of \!\PackageError!.
% 
% \item[\Uidx{\!\@parmoderr!}]
% is an internal macro to complain about misplacement of a macro or
% environment which is expected to appear in ``outer par mode''.
% It is used in \!\pcol@zparacol! if it finds $\CSIndex{ifinner}=\true$.
% 
% \item[\Uidx{\!\@Esphack!}]
% is an internal macro to put back the horizontal skip and space factor
% saved by \!\@bsphack! at the end of an environment.  It is used in
% \!\pcol@end@dblfloat!.
% 
% \item[\Uidx{\!\reset@font!}]
% is an internal macro \!\let!-equal to \!\normalfont! to use a starndard
% font.  It is used in \!\pcol@fntextbody! for footnote typesetting.
% 
% \item[\Uidx{\!\set@color!}]
% is an internal macro to start coloring of texts following it.  By default
% it is \!\relax! but may have a definition to put a \!\special! for
% coloring with the color in \!\current@color!.  In the following macros, it
% is examined if $\!\set@color!=\!\relax!$ and/or some local definition is
% given to \!\set@color!.
% 
% \begin{itemize}
% \item
% \!\pcol@output! lets $\!\set@color!=\!\pcol@set@color!$ i.e., lets it
% regain its original definition because we don't need any special
% operations in \!\output! routine.
% 
% \item
% \!\@outputpage! performs \bgpaint{} if $\!\set@color!\neq\!\relax!$.
% 
% \item
% \!\pcol@zparacol! performs set-up operations for text coloring, including
% making \!\set@color! \!\let!-equal to \!\pcol@set@color@push! saving
% its original definition into \!\pcol@set@color!, and enabling \bgpaint{}
% macros if $\!\set@color!\neq\!\relax!$, while these \bgpaint{} macros are
% nullified otherwise.
% 
% \item
% \!\pcol@icolumncolor! complains that no color packages have been loaded if
% \!\set@color!${}={}$\!\relax!, and then otherwise temporarily lets it be
% the original saved in \!\pcol@set@color! to \!\insert! a \!\vbox! to
% update $\Celt^c$ or to do the update immediately.
% 
% \item
% \!\pcol@iicolumncolor! temporarily lets $\!\set@color!=\!\relax!$ so that
% \!\color! or \!\normalcolor! invoked in the macro just defines
% \!\current@color! to be set into $\Celtshadow^c$ without doing any other
% coloring operations.
% 
% \item
% \!\pcol@defcseprulecolor@i! complains that no color packages have been
% loaded if $\!\set@color!=\!\relax!$, while otherwise the macro temporarily
% lets $\!\set@color!=\!\relax!$ to invoke \!\color! (or \!\normalcolor!) to
% check if its arguments are properly given.
% 
% \item
% \!\pcol@backgroundcolor@ii! complains that no color packages have been
% loaded if $\!\set@color!=\!\relax!$, while otherwise its descendent 
% \!\pcol@backgroundcolor@x! temporarily lets
% $\!\set@color!=\!\pcol@backgroundcolor@y!$ to \!\def!ine
% $|\pcol@bg@|\~|color@|a[|@|{\cdot}c]$ to be \!\current@color!.
% 
% \SpecialArrayIndex{a}{\pcol@bg@color@}
% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}
% \end{itemize}
% 
% \item[\Uidx{\!\reset@color!}]
% is an internal macro to finish text coloring started by \!\set@color!.  By
% default it is undefined but may have some definition to put a \!\special!
% to finish coloring.  It is used in \!\pcol@clearcolorstack! so as to apply
% it to all elements in $\CST^c$, in \!\pcol@iscancst! to put it to the
% main vertical list in the case that $\Celt^c$ was $\bot$ and then updated,
% in \!\pcol@icolumncolor! to apply it to all elements in $\CSTshadow^c$,
% and in \!\pcol@reset@color@pop! and \!\pcol@reset@color@mpop! to have an
% uncoloring \!\special! in the \!\vbox! for $\celt_i$ and $\mcelt_{i,m}$.
% 
% \item[\Uidx{\!\color@begingroup!}]
% is an internal macro to open a group in which a color is specified.  It is
% used in \!\pcol@putfootins! to enclose footnotes with \!\normalcolor!, and
% in \!\pcol@fntextbody!\marg{text} to enclose the coloring in the footnote
% $\arg{text}$.
% 
% \item[\Uidx{\!\color@endgroup!}]
% is an internal macro to close a group in which a color is specified.  It is
% used in \!\pcol@putfootins! to enclose footnotes with \!\normalcolor!, and
% in \!\pcol@fntextbody!\marg{text} to enclose the coloring in the footnote
% $\arg{text}$.
% 
% \item[\Uidx{$\!\@stpelt!\<\theta\>$}]
% is an internal macro to zero-clear the counter $\theta$ for the
% implementation of \!\stepcounter!.  It is used in \!\pcol@stepcounter! to
% clear the descendent counters of a \gcounter{} $\cg$ listed in
% $|\pcol@cl@|{\cdot}\cg$.
% 
% \SpecialArrayIndex{\theta}{\pcol@cl@}
% 
% \item[\Uidx{\!\@nbitem!}]
% is an internal macro to insert a vertical skip of
% $\!\@outerparskip!-\!\parskip!$ above the first \!\item! of a
% \env{list}-like environment when $\CSIndex{if@nobreak}=\true$.  It is used
% by \!\pcol@zparacol! when it finds the \env{paracol} environment to start
% is at the very beginning of a \env{list}-like environment and
% $\CSIndex{if@nobreak}=\true$.
% 
% \item[\Uidx{\!\@parboxrestore!}]
% is an internal macro to set up typesetting paramenters for paragraphs
% encapsulated in a box.  It is used in \!\pcol@fntextbody! for paragraphs
% in a footnonte.
% 
% \item[\Uidx{\!\@finalstrut!}$\arg{box}$]
% is an internal macro to add an invisible vertical rule whose depth is that
% of a $\arg{box}$.  It is used in \!\pcol@fntextbody! to make the last line
% of the footnotes is as deep as \!\strutbox! at shallowest.
% 
% \item[\Uidx{\!\@sect!}]
% is an internal macro to implement sectioning commands.  The original
% definition of the macro is kept in \!\pcol@ac@enable@toc!, while
% \!\pcol@ac@def@toc! makes it \!\let!-equal to \!\pcol@ac@enable@toc! or
% \!\pcol@ac@disable@toc!, the latter of which uses the original version
% temporarily disabling \!\addcontentsline!.
% 
% \item[\Uidx{\!\@svsechd!}]
% is an internal macro (locally) \!\def!ined in \!\@sect! and \!\@ssect! to
% keep the section header of a sectioning command such as \!\paragraph!
% which puts the header as the leading text of the paragraph following the
% command rather than putting it as an individual paragraph.  The macro is
% \!\global!ized in \!\pcol@sptext! so that it is properly referred to in
% \!\everypar! for the paragraph led by the text in case that a \mctext{}
% has the sectioning command only and thus the \!\def!inition of the macro
% must survive after we close the group in which the \mctext{} is put.
% 
% \item[\Uidx{\!\@svsec!}]
% is an internal macro (locally) \!\def!ined in \!\@sect! to keep
% \!\thesection!  etc.\ to be displayed as the leading part of the section
% header.  The macro is \!\global!ized in \!\pcol@sptext! together with
% \!\@svsechd!  because it is in the body of \!\@svsechd!.
% 
% \item[\Uidx{\!\@caption!}]
% is an internal macro to implement \!\caption!.  The original definition of
% the macro is kept in \!\pcol@ac@caption@latex!, while
% \!\pcol@ac@caption@def! makes it \!\let!-equal to \!\pcol@ac@caption!
% which uses the original version temporarily disabling \!\addcontentsline!
% if necessary.
% 
% \item[\Uidx{\!\end@float!}]
% is an internal macro to close a \cwise{} float environment.  It is used in
% \!\pcol@end@dblfloat! (but never invoked because we havd \cs{if@twocolumn}
% true always).
% 
% \item[\Uidx{\!\end@dblfloat!}]
% is an internal macro to close a \pwise{} float environment.  It is replaced
% with our own \!\pcol@end@dblfloat!.
% 
% \item[\Uidx{\!\@endfloatbox!}]
% is an internal macro to close a \!\vbox! for a float.  It is used in
% \!\pcol@end@dblfloat!.
% 
% \item[\Uidx{\!\@largefloatcheck!}]
% is an internal macro to examine if a float is too large.  It is used in
% \!\pcol@end@dblfloat!.
% 
% \item[\Uidx{\!\@floatplacement!}]
% is an internal macro for \!\output! routine to reinitialize \cwise{}
% float placement parameters.  It is used in our own version of it,
% \!\pcol@floatplacement!.
% 
% \item[\Uidx{\!\@dblfloatplacement!}]
% is an internal macro for \!\output! routine to reinitialize \pwise{}
% float placement paramenters.  It is used in \!\pcol@startpage! and
% \!\pcol@output@clear! prior to processing \pwise{} floats in
% \!\@dbldeferlist!.  As discussed in
% item-(\ref{item:ovv-float-@dblfloatplacement}) of
% \secref{sec:imp-ovv-float}, this macro in 2015 or later version of
% \LaTeX{} lets $\!\f@depth!=|1sp|$.
% 
% \item[\Uidx{\!\@xympar!}]
% is an interal macro to perform the last operations for \!\marginpar!.  In
% \!\pcol@zparacol! it is made \!\let!-equal to \!\pcol@xympar! for the
% emulation of \!\marginnote!, while its original version is kept in
% \!\pcol@@xympar!.
% 
% \item[\Uidx{\!\p@footnote!}]
% is an internal macro to have the prefix to \!\thefootnote! in the printed
% reference of the counter \counter{footnote}.  It is used in
% \!\pcol@fntextbody! to produce \!\@currentlabel!.
% 
% \item[\Uidx{\!\@thefnmark!}]
% is an internal macro to have \!\thefootnote!\footnote{
% 
% Or \cs{thempfootnote} in \env{minipage} environment.}.
% 
% It is used in \!\pcol@fntextbody! to produce \!\@currentlabel!.
% 
% \item[\Uidx{\!\@footnotetext!}\marg{text}]
% is an internal macro to implement \!\footnote! and \!\footnotetext! for
% $\arg{text}$.  In \!\pcol@zparacol!, it is made \!\let!-equal to
% \!\pcol@fntext!.
% 
% \item[\Uidx{\!\@makefntext!}\marg{fn}]
% is an internal macro to typeset the footnote $\arg{fn}$.  It is used in
% \!\pcol@fntextbody!\marg{text} to typeset the footnote $\arg{text}$ with
% some other stuff.
% 
% \item[\Uidx{\!\@emptycol!}]
% is an internal macro for \!\output! routine to put back an empty page to
% the main vertical list.  It is used \!\pcol@output! if a page with floats
% and very short main vertical list is built.
% 
% \item[\Uidx{\!\@specialoutput!}]
% is an internal macro for \!\output! routine to process an \!\output!
% request made by \LaTeX's original \!\clearpage!, $\!\end!\Arg{float}$ and
% \!\marginpar!.  It is used in \!\pcol@specialoutput! to process the
% request for floats or marginal notes.
% 
% \item[\Uidx{\!\@opcol!}]
% is an internal macro for \!\output! routine to output a page or to keep
% the first column until the second one is completed.  This macro is used in
% \!\pcol@output! to process a sneaked \!\output! request from outside of
% \env{paracol}, and in \!\pcol@output@end! for the case \pwise{} floats
% are left at \Endparacol{} and they are put in \fpage{}s.
% 
% \item[\Uidx{\!\@makecol!}]
% is an internal macro for \!\output! routine to build the ship-out
% image of a column in \!\@outputbox! consisting of top floats, main
% vertical list in \!\box!|255|, footnotes in \!\footins!, and bottom
% floats\footnote{
% 
% In p\LaTeX, the order of footnotes and bottom floats are reversed.}.
% 
% It is used in \!\pcol@output! to process a sneaked \!\output!  request
% from outside of \env{paracol}, in \!\pcol@@makecol! for a \colpage{} to be
% flushed by \!\pcol@flushcolumn! and \!\pcol@makeflushedpage!, in
% \!\pcol@makecol! for an ordinary \colpage{}, and in \!\pcol@output@start!
% and \!\pcol@makenormalcol! for \preenv{}.
% 
% \item[\Uidx{\!\@textbottom!}]
% is an internal macro for \!\output! routine to be put at the bottom of
% \!\@outputbox! in which a \colpage{} is stored, by \!\@makecol!.  This
% macro is temporarily re\!\def!ined by \!\pcol@makecol! for a \colpage{}
% having \sync{}ation points so that it has a vertical skip of inifinite
% stretch and shrink to push up/down the stuff below the last \sync{}ation
% point in order to adjust its top to the point.  After that, its original
% definition kept in \!\pcol@textbottom! is restored.  Another modifiers of
% the macro are as follows; \!\pcol@makenormalcol! to make the macro
% \!\let!-equal to \!\relax! temporarily to avoid the insertion of whatever
% the macro has in \!\@makecol!; and \!\pcol@makeflushedpage! to let the
% macro have \!\vfil! temporarily so that empty columns in a \lpage{} are
% made {\em full size} without underfull.
% 
% \item[\Uidx{\!\@outputpage!}]
% is an internal macro for \!\output! routine to output a page kept in
% \!\@outputbox! together with the header and footer.  The original
% definition of this macro is saved in \!\pcol@@outputpage! to be used in
% \!\pcol@outputpage@l! and \!\pcol@outputpage@r! being callees of our own
% revised version of \!\@outputpage!.  Therefore, any \!\output! request to
% result in page ship-out reaches our own \!\@outputpage! and then \LaTeX's
% one after we perform operations for \parapag{}ing and \bgpaint{} onto the
% ship-out image.
% 
% \item[\Uidx{\!\@combinefloats!}]
% is an internal macro for \!\output! routine to combine top and bottom
% floats in \!\@toplist! and \!\@botlist! respectively with \!\@outputbox!
% in which the main vertical list and footnotes\footnote{
% 
% In p\LaTeX, footnotes are not in \cs{@outputbox} because of the reversal of
% footnotes and bottom floats.}
% 
% have been put by \!\@makecol!, and to have the result in \!\@outputbox!
% again.  In \!\pcol@zparacol!, it is made \!\let!-equal to our own
% \!\pcol@combinefloats!  so that \!\@makecol! and \!\pcol@makenormalcol!
% uses it instead of the original one.  However, if \!\pcol@output! finds
% that the \!\output!  request for a page break outside \env{paracol} is
% sneaked into our own \!\output! routine, it makes this macro \!\let!-equal
% to \!\pcol@@combinefloats! in which \LaTeX's version is kept so that
% \LaTeX's original \!\output! routine works perfectly as original.
% 
% \item[\Uidx{\!\@cflt!}]
% is an internal macro for \!\output! routine to put all top floats in
% \!\@toplist! and related stuff such as the vertical skip of
% \!\textfloatsep! into \!\@outputbox!  together with its old contents being
% the main vertical list and footnotes
% 
% \addtocounter{footnote}{-1}\footnotemark.
% 
% It is used in \!\pcol@combinefloats! if the \colpage{} being processed
% does not have \sync{}ation points.
% 
% \item[\Uidx{\!\@cflb!}]
% is an internal macro for \!\output! routine to put all bottom floats in
% \!\@botlist! and related stuff such as the vertical skip of
% \!\textfloatsep! into \!\@outputbox!  together with its old contents being
% top floats, the main vertical list and footnotes
% 
% \addtocounter{footnote}{-1}\footnotemark.
% 
% It is used in \!\pcol@combinefloats!.
% 
% \item[\Uidx{$\!\@comflelt!\arg{flt}$}]
% is an internal macro for \!\output! routine to put $\arg{flt}$ being a
% \cwise{} top or bottom float to the tail of \!\@tempboxa! which
% finally has all top\slash bottom floats in a column.  It is used in
% \!\pcol@cflt! to apply it to each element of \!\@toplist!.
% 
% \item[\Uidx{$\!\@comdblflelt!\arg{flt}$}]
% is an internal macro for \!\output! routine to put $\arg{flt}$ being a
% \pwise{} float to the tail of \!\@tempboxa! which finally has the
% \spanning{} for \pwise{} floats.  It is used in \!\pcol@startpage! to
% apply to each element of \!\@dbltoplist! to have the \spanning.
% 
% \item[\Uidx{\!\@startcolumn!}]
% is an internal macro for \!\output! routine which tries to build a
% \fcolumn{} for the floats in \!\@deferlist! and, if the column
% is not built, tries to move floats to \!\@toplist! and \!\@botlist!.  This
% macro is used in \!\pcol@output! to process a sneaked \!\output! request
% from outside of \env{paracol}, and in \!\pcol@output@end! for the case
% \pwise{} floats are left at \Endparacol{} after which they become
% \cwise{} ones.
% 
% \item[\Uidx{$\!\@tryfcolumn!\arg{lst}$}]
% is an internal macro for \!\output! routine which examines if a \fcolumn{}
% or a \fpage{} can be built with some floats in $\arg{lst}$ and, if so,
% builds the page in \!\@outputbox! removing floats put in the page from
% $\arg{lst}$.  It is used in \!\pcol@startpage! for \pwise{} floats in
% \!\@dbldeferlist!, and in \!\pcol@startcolumn! for \cwise{} floats in
% $\cc_c(\dl)$.
% 
% \item[\Uidx{$\!\@scolelt!\arg{flt}$}]
% is an internal macro for \!\output! routine which examines if a
% \cwise{} float $\arg{flt}$ can be added to \!\@toplist! or
% \!\@botlist! being the list of the floats to be put at the top or bottom
% of a page respectively.  Then, if the examination succeeds, $\arg{flt}$ is
% added to \!\@toplist! or \!\@botlist!, while it is added to
% \!\@deferlist! otherwise.  It is used in \!\pcol@trynextcolumn! to
% apply to each element of (the copy of) $\cc_c(\dl)$.
% 
% \item[\Uidx{$\!\@sdblcolelt!\arg{flt}$}]
% is an internal macro for \!\output! routine which examines if a
% \pwise{} float $\arg{flt}$ can be added to \!\@dbltoplist! being the
% list of the floats to be put at the top of a page, and if so, adds
% $\arg{flt}$ to \!\@dbltoplist!, while it is added to \!\@dbldeferlist! or
% \!\@deferlist! depending on \LaTeX's version otherwise as discussed in
% item-(\ref{item:ovv-float-@addtodblcol}) of \secref{sec:imp-ovv-float}.
% It is used in \!\pcol@startpage! to apply to each element of (the copy of)
% \!\@dbldeferlist!.
% 
% \item[\Uidx{\!\@addmarginpar!}]
% is an internal macro for \!\output! routine to add a marginal note.  Its
% original definition is kept in \!\pcol@@addmarginpar! and used in
% \!\pcol@addmarginpar! being our own \!\@addmarginpar!.
% 
% \item[\Uidx{$\!\@makefcolumn!\arg{lst}$}]
% is an internal macro for \!\output! routine to build a \fcolumn{} with
% some floats at the head of a float list $\arg{lst}$ and to remove the
% floats from the list.  It is used in \!\pcol@flushcolumn! and
% \!\pcol@iflushfloats! for $\cc_c(\dl)$ of \cwise{} floats, and in
% \!\pcol@output@clear! for \!\@dbldeferlist! of \pwise{} floats.
% \end{description}
%
% 
% 
% \subsubsection{Structural Macros}
% 
% \begin{description}
% \item[\Uidx{$\!\@elt!\<a_1\>\cdots\<a_n\>$}]
% is an internal control sequence to represent a list element having $n$
% subelements.  The sequence is often made \!\let!-equal to a macro which
% processes $\<a_1\>\cdots\<a_n\>$ and is applied to all members in a list.
% It is also made \!\let!-equal to \!\relax! on a manipulation of a list,
% such as element addition and concatenation, by \!\edef! or \!\xdef!.  The
% usages of the sequence are as follows.
% 
% \begin{itemize}
% \item
% \!\pcol@F@count! \!\def!ines \!\@elt! as a macro to increment
% \!\@tempcnta! by one to measure the cardinality of \!\@freelist!.
% 
% \item
% \!\pcol@cflt! lets $\!\@elt!=\!\@comflelt!$ for $\cc_c(\tl)$, and then
% $\!\@elt!=\!\relax!$ to concatenate \!\@freelist! and $\cc_c(\tl)$.
% 
% \item
% \!\pcol@setpageno! lets $\!\@elt!=\!\pcol@setpnoelt!$ for $\PP$.
% 
% \item
% \!\pcol@setpnoelt! and \!\pcol@setmpbelt! let $\!\@elt!=\!\relax!$ to add
% $\pp(q)$ to $\PP$.  It also uses \!\@elt! to \!\def!ine \!\pcol@currpage!
% with $\!\@elt!
% \Arg{\pp^p(q)}\<\pp^i(q)\>\<\pp^f(q)\>\~\Arg{\pp^s(p)}\Arg{\pp^m(p)}$.
% 
% \item
% \!\pcol@defcurrpage! lets $\!\@elt!=\!\relax!$ to \!\xdef!ine
% \!\pcol@currpage! with
% $\!\@elt!\Arg{\pp^p(q)}\<\pp^i(q)\>\<\pp^f(q)\>\Arg{\pp^s(p)}\Arg{\pp^m(p)}$.
% 
% \item
% \!\pcol@nextpage! lets $\!\@elt!=\!\pcol@nextpelt!$ for $\PP$.
% 
% \item
% \!\pcol@getcurrpage! lets $\!\@elt!=\!\pcol@getpelt!$ for $\PPP$.
% 
% \item
% \!\pcol@startpage! lets $\!\@elt!=\!\@sdblcolelt!$ for (the copy of)
% \!\@dbldeferlist!, and $\!\@elt!=\!\@comdblflelt!$ for \!\@dbltoplist!.  It
% also lets $\!\@elt!=\!\relax!$ for the concatenation of \!\@dbldeferlist!
% and \!\@deferlist!, and that of \!\@freelist! and \!\@dbltoplist!.
% 
% \item
% \!\pcol@outputcolumns! lets $\!\@elt!=\!\pcol@outputelt!$ with two arguments
% for (the copy of) $\PP$.
% 
% \item
% \begin{Sloppy}{2400}%
% \!\pcol@ioutputelt! \!\def!ines \!\pcol@bg@footnoteheight! and
% \!\pcol@bg@float~height! with \!\@elt! to let painting macros add elements
% in them to have the height of the \bground{} regions $\bgr_{\{n,N\}}$ and
% $\bgr_{\{f,F\}}$ to be painted.
% \end{Sloppy}
% 
% \item
% \!\pcol@buildcolseprule! lets $\!\@elt!=\!\pcol@buildcselt@S!$ and then
% $\!\@elt!=\!\pcol@buildcselt!$ for $\pp^s(p)$, and then \!\def!ines
% \!\pcol@bg@columnheight! with \!\@elt! to add $H'_n$ and $\!\@maxdepth!$
% or 0 for the \bground{} region $\bgr_{\{c,g\}}^c(n+1)$ where
% $n=\Abs{\pp^s(p)}$.
% 
% \item
% \!\pcol@buildcselt@S! \!\def!ines \!\pcol@bg@spanningtop! and
% \!\pcol@bg@spanning~height! with \!\@elt! to define the region
% $\bgr_S(i)$.
% 
% \item
% \begin{Hfuzz}{0.55pt}
% \!\pcol@buildcselt! \!\def!ines \!\pcol@bg@columnheight!,
% \!\pcol@bg@spanningtop! and \!\pcol@bg@spanningheight! with \!\@elt! to
% define regions $\bgr_{\{c,g\}}^c(i)$ and $\bgr_s(i)$.
% \end{Hfuzz}
% 
% \item
% $\!\pcol@bg@calculate!\arg{z}\arg{z_0}\Arg{F}$ lets
% $\!\@elt!=\!\pcol@bg@advance!$ to let $\!\@elt!\arg{f}$ in $F$ do
% $z\gets z+f$.
% 
% \item
% $\!\pcol@bg@negative!\Arg{F^-}$ lets $\!\@elt!=\!\pcol@bg@nadvance!$ to
% let $\!\@elt!\arg{f}$ in $F^-$ do $z\gets z-f$, and then lets
% $\!\@elt!=\!\pcol@bg@advance!$ to go back to addition.
% 
% \item
% \!\pcol@output@start! lets all floats $f$ imported in \!\@dbldeferlist!
% have depth 0 by \!\def!ining $\!\@elt!\arg{f}$ to do it, \!\edef!ines
% \!\pcol@bg@textheight! with \!\@elt!  having height-plus-depth of
% \preenv{} for \bgpaint{} of it, and \!\def!ines $\pp^m(0)$ having one
% element in $\mpb_L^l$ or $\mpb_L^r$ for \!\@mparbottom! in \preenv{}.
% 
% \item
% \!\pcol@makenormalcol! lets $\!\@elt!=\!\relax!$ to concatenate
% \!\@freelist! and \!\@midlist!.
% 
% \item
% \!\pcol@trynextcolumn! lets $\!\@elt!=\!\@scolelt!$ for (the copy of)
% $\cc_c(\dl)$.
% 
% \item
% \!\pcol@setcurrcol! lets $\!\@elt!=\!\relax!$ to \!\xdef!ine $\cc_c$ with
% $\cc_c(\tl)=\!\@toplist!$, $\cc_c(\ml)=\!\@midlist!$,
% $\cc_c(\bl)=\!\@botlist!$  and $\cc_c(\dl)=\!\@deferlist!$.
% 
% \item
% \!\pcol@scancst! and \!\pcol@iscancst! let $\!\@elt!=\!\relax!$ to
% \!\edef!ine the list $M=(m\,\Bar\,\mceltpop_{j,m}\in\cstraw,\;j\geq i)$ for
% $\mceltpop_{i,*}$, and then the latter \!\def!ines \!\@elt! as a macro with
% an argument $m$ to examine $m\in M$ for $\mcelt_{i,m}$.
% 
% \item
% \!\pcol@addmarginpar! lets $\!\@elt!=\!\pcol@setmpbelt!$ for $\PPP$.
% 
% \item
% \!\pcol@getmparbottom! lets $\!\@elt!=\!\pcol@getmpbelt!$ for the list
% $\mpb_{\{L,R\}}^{\{l,r\}}$.  It also lets $\!\@elt!=\!\relax!$ for the
% addition of $\mpar(h_i,t_i)$ to the list by itself and
% \!\pcol@getmpbelt!.
% 
% \item
% \!\pcol@mparbottom@zero! has \!\@elt! in its body to have $\mpar(0,0)$ for
% each $M\in\Set{\mpb_X^x}{X\in\{L,R\},x\in\{l,r\}}$ the macro has.
% 
% \item
% $\!\pcol@bias@mpbout@i!\Arg{y}\!\@elt!\Arg{t}\Arg{b}\!\@nil!$ has \!\@elt!
% in its argument specification, and \!\def!ines \!\reserved@b! with
% \!\@elt! for $\mpar(t+y,b+y)$.
% 
% \item
% \begingroup\def\,{\mskip0mu plus2mu\relax}
% $\!\pcol@getmparbottom@last@i!\,
% \Arg{y}\,\mpar(t_1,b_1)\,\cdots\,\mpar(t_n,b_n)\,\!\@nil!$ at first
% \!\def!\-ines \!\reserved@b! with \!\@elt! for $\mpar(y,y)$ and then
% \!\def!ines \!\@elt!  to do it for $\mpar(t_i,b_i)$ for all $i\in[1,n]$.
% \endgroup
% 
% \item
% \!\pcol@makefcolumn! lets $\!\@elt!=\!\pcol@makefcolelt!$ for (the copy
% of) $\cc_c(\dl)$ to examine if each float in it can be put in a \fcolumn{}
% to be built, and then \!\def!ine it to put floats in $\cc_c(\tl)$ into
% $\cc_c(\vb^b)$.
% 
% \item
% \!\pcol@addflhd! lets $\!\@elt!=\!\pcol@hdflelt!$ for its argument
% $\cc_c(\tl)$ or $\cc_c(\bl)$, and then $\!\@elt!=\!\relax!$ to give the
% default.
% 
% \item
% \!\pcol@makeflushedpage! \!\edef!ines \!\pcol@bg@floatheight! with
% \!\@elt! letting it be \!\relax!.
% 
% \item
% \!\pcol@imakeflushedpage! \!\def!ines \!\pcol@bg@footnoteheight! with
% \!\@elt!.
% 
% \item
% \!\pcol@output@end! uses \!\@elt! in the argument specification of the
% \!\def!inition of \!\pcol@do@mpbout@elem!, lets $\!\@elt!=\!\relax!$ to
% add the \spanning{} of the last page to the head of \!\@dbldeferlist!, and
% uses it in the body of \!\pcol@bg@textheight! and
% \!\pcol@bg@footnoteheight! to be \!\def!ined for \bgpaint{} of
% \Scfnote{}s.
% 
% \item
% \begin{Hfuzz}{0.14pt}%
% \!\pcol@zparacol! lets $\!\@elt!=\!\pcol@remctrelt!$ for $\CG$,
% $\!\@elt!=\!\pcol@thectrelt!$ for $\CTL$, $\!\@elt!=\!\pcol@loadctrelt!$
% for $\Cc_0$, $\!\@elt!=\!\pcol@cmpctrelt!$ for $\CTL$,
% $\!\@elt!=\!\pcol@defcomelt!$ for \!\pcol@localcommands!, and then
% $\!\@elt!=\!\relax!$ to give the default.
% \end{Hfuzz}
% 
% \item
% \!\globalcounter!\marg{ctr} defeines \!\@elt!\marg{\theta} for $\CG$ to
% check if there is $\theta\in\CG$ such that $\theta=\arg{ctr}$.
% 
% \item
% \!\pcol@localcommands! has the sequence of $\!\@elt!\ARg{com}$ for all
% \lcommand{}s $|\|\arg{com}$.
% 
% \item
% \!\pcol@gcounters! has \!\@elt!|{page}| as its initial definition.
% 
% \item
% $\!\pcol@removecounter!\arg{\Theta'}\arg{\theta}$ lets
% $\!\@elt!=\!\pcol@iremctrelt!$ for (the copy of) its argument
% $\mathit{\Theta}'$ to remove $\theta$ from it.
% 
% \item
% $\!\pcol@sscounters!\arg{elt}$ lets $\!\@elt!=\arg{elt}$, where
% $\arg{elt}=\!\pcol@storectrelt!$ or $\arg{elt}=\!\pcol@savectrelt!$, for
% $\CTL$, and then $\!\@elt!=\!\relax!$ to \!\xdef!ine $\Cc_c$.
% 
% \item \begingroup\hfuzz1.4pt
% $\!\pcol@com@synccounter!\<\theta\>$ gives $\!\@elt!\Arg{\theta}$ as the
% argument of |\pcol@synccounter|.
% 
% \SpecialIndex{\pcol@synccounter}
% \par\endgroup
% 
% \item \begingroup\hfuzz0.51pt
% $\!\pcol@synccounter!\arg{lst}$ lets $\!\@elt!=\!\relax!$ to have the list
% $\arg{lst}$ in \!\reserved@a! by \!\edef!, $\!\@elt!=\!\pcol@loadctrelt!$
% for $\CC_c$, and then $\!\@elt!=\!\pcol@syncctrelt!$ for $\arg{lst}$.
% \par\endgroup
% 
% \item
% $\!\pcol@stepcounter!\<\theta\>$ lets $\!\@elt!=\!\pcol@stpldelt!$ for
% $\CTL$, $\!\@elt!=|\pcol@|\~|stpclelt|$
% 
% \SpecialIndex{\pcol@stpclelt}
% 
% for $\clist(\theta)$, and then $\!\@elt!=\!\@stpelt!$ for
% $\clist(\theta)$.
% 
% \item
% \!\pcol@switchcol! lets $\!\@elt!=\!\pcol@setctrelt!$ for $\CC_c$,
% $\!\@elt!=|\pcol@|\~|aconlyelt|$
% 
% \SpecialIndex{\pcol@aconlyelt}
% 
% for $\T$, and then $\!\@elt!=\!\relax!$ to give the default.
% 
% \item
% \!\pcol@icolumncolor! \!\def!ines $\!\@elt!\arg{\celtshadow_i}$ to apply
% \!\reset@color! for rewinding and \!\pcol@set@color! for reestablishing
% to each $\celtshadow_i\in\CSTshadow^c=(\Celtshadow^c,\cstshadow)$
% by \!\pcol@scancst@shadow!, in which \!\@elt! is explicitly applied to
% $\Celtshadow^c$ if it is defined and then implicitly done to
% $\cstshadow=\!\pcol@colorstack@shadow!$.
% 
% \item
% \!\pcol@set@color@push! lets $\!\@elt!=\!\relax!$ to push a color
% information into $\cstshadow$, with save\slash restore of its original
% value.
% 
% \item
% \!\resetbackgroundcolor! lets $\!\@elt!=\!\pcol@resetbackgroundcolor!$ to
% scan \!\pcol@bg@defined! containing $\!\@elt!\Arg{a'_i}$ to let
% $|\pcol@bg@color|{\cdot}a'_i$ for each of $i$.
% 
% \SpecialArrayIndex{a}{\pcol@bg@color@}
% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}
% \end{itemize}
% 
% \item[\Uidx{\!\@empty!}]
% is a macro always having nothing.  Its major usages are to examine if a
% macro often having a list is empty, and to make such a macro empty.  The
% following macros use \!\@empty! to examine the emptiness of the objects in
% parentheses.
% 
% \begin{quote}
% \!\pcol@combinefloats! ($\cc_c(\tl)$, $\cc_c(\bl)$)\\
% \!\pcol@checkshipped! ($S_c$)\\
% \!\pcol@startpage! ($\pp(\ptop)$, \!\@dbltoplist!)\\
% \!\pcol@makenormalcol! (\!\@botlist! in \preenv)\\
% \!\pcol@getmparbottom! ($\pp^m(p)$)\\
% \!\pcol@getmparbottom@last! ($\pp^m(\ptop)$)\\
% \!\pcol@setmpbelt! ($\pp^m(p)$)\\
% \!\pcol@flushcolumn! ($\cc_c(\dl)$)\\
% \!\pcol@makefcolumn! ($\cc_c(\tl)$, $\cc_c(\dl)$)\\
% \!\pcol@measurecolumn! ($\cc_c(\bl),\cc_c(\dl)$)\\
% \!\pcol@addflhd! ($\cc_c(\tl)$, $\cc_c(\bl)$)\\
% \!\pcol@synccolumn! ($\cc_c(\tl)$)\\
% \!\pcol@makeflushedpage! ($\cc_c(\dl)$)\\
% \!\pcol@imakeflushedpage! ($\cc_c(\dl)$)\\
% \!\pcol@iflushfloats! ($\cc_c(\dl)$)\\
% $\!\pcol@setcw@getspec@i!\arg{default}\<x'_d\>$ ($x'_d$)\\
% $\!\pcol@setcw@fill!\<f\>\!\fill!$ ($f$)
% \end{quote}
% 
% The following macros use \!\@empty! to empty the objects in parentheses.
% 
% \begin{quote}
% \!\pcol@cflt! ($\cc_c(\tl)$)\\
% \!\pcol@setpageno! ($\PP$, $\pp(\ptop)$)\\
% \!\pcol@startpage! ($\cc_c(\dl)$, \!\@dbldeferlist!, \!\@deferlist!,
% 	\!\@dbltoplist!)\\
% \!\pcol@trynextcolumn! ($\cc_c(\dl)$)\\
% \!\pcol@output@start! ($\PP$, $\pp(\ptop)$, $\cc_c(\dl)$)\\
% \!\pcol@makenormalcol! (\!\@midlist! in \preenv)\\
% \!\pcol@addmarginpar! ($\PP$, $\pp(\ptop)$)\\
% \!\pcol@getmparbottom! ($\mpb_{\{L,R\}}^{\{l,r\}}$)\\
% \!\pcol@makefcolumn! ($\cc_c(\dl)$, $\cc_c(\tl)$)\\
% \!\pcol@makeflushedpage! ($\cc_c(\tl)$)\\
% \!\pcol@freshpage! ($\PP$, $\pp(\ptop)$)\\
% \!\pcol@zparacol! (\!\@gtempa!)\\
% \!\pcol@removecounter!$\<\mathit{\Theta}'\>\Arg{\theta}$
% ($\mathit{\Theta}'\in\{\CG,\CL\}$)\\
% \!\pcol@sscounters! ($\Cc_c$)
% \end{quote}
% 
% \item[\Uidx{\!\@currentlabel!}]
% is an internal macro to have the reference to be associated with the
% \!\label! following it.  It is defined in \!\pcol@fntextbody! to have the
% reference to the footnote with \!\@thefnmark!.
% 
% \item[\Uidx{\!\ext@figure!}]
% is an internal macro having ``|lof|'' being the extention of the file for
% list of figures.  It is used in
% $\!\pcol@ac@caption!\arg{type}|[|\arg{lcap}|]|\<cap\>$ to have ``|lof|''
% when $\arg{type}=|figure|$.
% 
% \item[\Uidx{\!\ext@table!}]
% is an internal macro having ``|lot|'' being the extention of the file for
% list of tables.  It is used in
% $\!\pcol@ac@caption!\arg{type}|[|\arg{lcap}|]|\<cap\>$ to have ``|lot|''
% when $\arg{type}=|table|$.
% 
% \item[\Uidx{\!\@currbox!}]
% is an internal macro which conventionally has an \!\insert! for floats,
% etc.  The follwing macros use \!\@currbox! having the objects in
% parentheses.
% 
% \begin{quote}
% \!\pcol@opcol! ($\cc_c(\vb)$)\\
% \!\pcol@startpage! ($\pp^i(\ptop)$)\\
% \!\pcol@ioutputelt! ($\s_c(q)$)\\
% \!\pcol@output@start! ($\pp^i(0)$, $\cc_c(\vb)$, $\Celt^c$)\\
% \!\pcol@output@switch! ($\cc_c(\vb)$)\\
% \!\pcol@restartcolumn! ($\cc_c(\vb)$)\\
% \!\pcol@igetcurrcol! ($\cc_c(\vb)$)\\
% \!\pcol@setcurrcol! ($\cc_c(\vb)$)\\
% \!\pcol@putbackmvl! ($\cc_c(\vb)$)\\
% \!\pcol@iscancst! ($\Celt^c$)\\
% \!\pcol@addmarginpar! (left marginal note)\\
% \!\pcol@flushcolumn! ($\cc_c(\vb), \s_c(q)$)\\
% \!\pcol@makefcolumn! ($\cc_c(\vb)$)\\
% \!\pcol@measurecolumn! ($\cc_c(\vb)$)\\
% \!\pcol@synccolumn! ($\cc_c(\vb)$)\\
% \!\pcol@imakeflushedpage! ($\cc_c(\vb)$)\\
% \!\pcol@freshpage! ($\cc_c(\vb)$)\\
% \!\pcol@output@end! (top float, $\cc_c(\vb)$)\\
% \!\pcol@end@dblfloat! (\pwise{} float)\\
% \!\pcol@icolumncolor! ($\Celt^c$)
% \end{quote}
% 
% \item[\Uidx{\!\@marbox!}]
% is an internal macro which has an \!\insert! for left marginal notes.  It
% is used in \!\pcol@xympar!.
% 
% \item[\Uidx{\!\@currlist!}]
% is an internal macro which has an list of \!\insert!s for floats and
% marginal notes given to \!output!.  It is used in \!\pcol@addmarginpar! to
% get the right marginal note from its head.
% 
% \item[\Uidx{\!\@freelist!}]
% is an internal macro having available \!\insert!s for floats originially,
% but also \colpage{}s, \spanning{}, footnotes and default column-color in
% our usage.  Besides the acquisition of an \!\insert! from it shown in the
% description of \!\@next!, it is used by the following macros to return the
% the objects in parentheses to \!\@freelist!.
% 
% \begin{quote}
% \!\pcol@cflt! ($\cc_c(\tl)$)\\
% \!\pcol@startpage! (\!\@dbltoplist!)\\
% \!\pcol@outputelt! ($\pp^i(q)$)\\
% \!\pcol@ioutputelt! ($\pp^i(q)$, $\pp^f(q)$, $\s_c(q)$)\\
% \!\pcol@startcolumn! ($\pp^f(\ptop)$)\\
% \!\pcol@output@start! ($\cc_0(\vb)$)\\
% \!\pcol@makenormalcol! (\!\@midlist! in \preenv)\\
% \!\pcol@restartcolumn! ($\cc_c(\vb)$, $\pp^f(p)$ or $\cc_c(\ft)$)\\
% \!\pcol@savefootins! ($\pp^f(p)$ or $\cc_c(\ft)$)\\
% \!\pcol@flushcolumn! ($\cc_c(\ft)$)\\
% \!\pcol@makefcolpage! ($\cc_c(\tl)$)\\
% \!\pcol@makeflushedpage! ($\pp^i(\ptop)$, $\pp^f(\ptop)$)\\
% \!\pcol@imakeflushedpage! ($\cc_c(\ft)$)\\
% \!\pcol@output@end! ($\pp^f(\ptop)$, $\cc_c(\vb)$, $\Celt^c$)
% \end{quote}
% 
% In addition \!\pcol@F@count! scans its element to have its cardinality.
% 
% \item[\Uidx{\!\@nil!}]
% is an internal control sequence which is conventionally used to terminate
% a variable length argument.  It is used in the following macros.
% 
% \begin{itemize}
% \item
% \!\pcol@getcurrpinfo! for the invocation of \!\@cdr!.
% 
% \item
% $\!\pcol@bias@mpbout@i!\Arg{y}\!\@elt!\Arg{t}\Arg{b}\!\@nil!$ to capture
% $t$ and $b$ following the convention in \!\pcol@do@mpb@all@ii!.
% 
% \item
% \begingroup\def\,{\mskip0mu plus2mu\relax}
% $\!\pcol@getmparbottom@last@i!\,
% \Arg{y}\,\mpar(t_1,b_1)\,\cdots\,\mpar(t_n,b_n)\,\!\@nil!$ to capture
% $\mpar(t_i,b_i)$ for all $i\in[1,n]$.
% \endgroup
% 
% \item
% $\!\pcol@do@mpb@all@i!
% \Arg{\mpb_L^l}\Arg{\mpb_L^r}\Arg{\mpb_R^l}\Arg{\mpb_R^r}$ to terminate the
% list $M\in\Set{\mpb_X^x}{X\in\{L,R\},x\in\{l,r\}}$ in the invocation of
% \!\pcol@do@mpb@all@ii!.
% 
% \item
% $\!\pcol@do@mpb@all@ii!
% \Arg{y}\mpar(t_1,b_1)\cdots\mpar(t_n,b_n)\!\@nil!$ to capture
% $\mpar(t_i,b_i)$ for all $i\in[1,n]$, and then to terminate them
% passed to \!\pcol@bias@mpbout@i! or \!\pcol@getmparbottom@last!.
% 
% \item
% \!\pcol@setcw@scan! for the invocation of\\\mbox{}\qquad
% $\!\pcol@setcw@getspec!\<w'_d\>|/|\<g'_d\>|/|\arg{garbage}\~\!\@nil!$.
% 
% \item
% \!\pcol@setcw@getspec@i! for the invocation of\\\mbox{}\qquad
% $\!\pcol@extract@fil!\<n\>| plus |\<f\>| minus|\arg{garbage}\!\@nil!$\\
% and thus in the \!\def!inition of it in \!\pcol@def@extract@fil!.
% 
% \item
% \!\pcol@defkw! has \!\@nil! in its argument specification to terminate the
% argument $0\,|pt|\ |plus|\ 1\,|fil|\ |minus|\ 1\,|fil|$.
% 
% \item
% \!\pcol@extract@fil@i!, \!\pcol@extract@fil@ii! and
% \!\pcol@extract@fil@iii! have \!\@nil! in their argument specifications as
% the terminator, and thus \!\@nil! appears in their invocations in
% \!\pcol@extract@fil!, \!\pcol@extract@fil@i! and \!\pcol@extract@fil@ii!
% respectively, and in the \!\def!inition of \!\pcol@extract@fil@iii! in
% \!\pcol@def@extract@fil@iii!.
% 
% \item
% \!\pcol@iadjustfnctr! and \!\pcol@iifootnotetext! to terminate their
% argument |[|$[|+-|]\meta{disp}$|]| passed to \!\pcol@calcfnctr!.
% 
% \item
% \!\backgroundcolor! and \!\nobackgroundcolor! to terminate their first
% argument given to \!\pcol@backgroundcolor! so that its descendants
% \!\pcol@backgroundcolor@x! and \!\pcol@backgroundcolor@z! finally capture
% everything not processed by their ancestors.
% \end{itemize}
% 
% \item[\Uidx{\!\current@color!}]
% is an internal macro having color information to be put into |.dvi| as a
% part of the argument of coloring \!\special!.  It is referred to by
% \!\pcol@bg@paintregion@i!,
% \!\pcol@output@start!,
% \!\pcol@icolumncolor!,
% \!\pcol@iicolumncolor!, and
% \!\pcol@set@color@push!,
% \!\pcol@backgroundcolor@y!.
% 
% \item[\Uidx{\!\@dbldeferlist!}]
% is an internal macro having the list of \pwise{} floats whose page
% appearance are not yet fixed.  It is scanned and then updated in
% \!\pcol@startpage! and \!\pcol@output@clear!, while \!\pcol@output@start!
% lets it have \!\@deferlist! made before \beginparacol, and
% \!\pcol@output@end! adds \pwise{} floats to be put in the empty
% \lpage{} to it and then move the whole of the list to \!\@deferlist!.
% As discussed in \secref{sec:imp-ovv-float}, 2015 or later version of
% \LaTeX{} no longer uses this list, but we stick with it for \pwise{}
% floats produced in \env{paracol} environments and thus have its top level
% definition with empty body in \Paracol.
% 
% \item[\Uidx{\!\@dbltoplist!}]
% is an internal macro having the list of \pwise{} floats which
% \!\@sdblcolelt! decided to be put in the new page.  The macro
% \!\pcol@startpage! scans it to put all floats into the page $\ptop$ as its
% \spanning{} $\pp^i(\ptop)$, and then empties it after returning all floats
% to \!\@freelist!.
% 
% \item[\Uidx{\!\@deferlist!}]
% is an internal macro having the list of \cwise{} floats whose page
% appearance are not yet fixed.  It is scanned and then updated in
% \!\pcol@startcolumn!, \!\pcol@trynextcolumn!, \!\pcol@flushcolumn!,
% \!\pcol@makefcolumn! and \!\pcol@iflushfloats!, while the following macros
% also act on it.
% 
% \begin{itemize}
% \item
% \!\pcol@output@start! moves it to \!\@dbldeferlist! because it is created
% before \beginparacol.
% 
% \item
% \!\pcol@startpage! uses it as the interface with \!\@addtodblcol! of 2015
% or later version of \LaTeX{} as discussed in
% item-(\ref{item:ovv-float-@addtodblcol}) of
% \secref{sec:imp-ovv-float}.
% 
% \item
% \!\pcol@setcurrcol! and \!\pcol@igetcurrcol! saves\slash restores it
% into/from $\cc_c(\dl)$, respectively.
% 
% \item
% \!\pcol@makefcolelt!$\arg{flt}$ returns $\arg{flt}$ to the list if
% $\arg{flt}$ cannot be put in the \fcolumn{} which the macro is working on.
% 
% \item
% \!\pcol@measurecolumn! examines its emptiness to let
% $\CSIndex{ifpcol@dfloats}=\true$ iff not empty.
% 
% \item
% \!\pcol@output@end! lets it have \!\@dbldeferlist! so that it processed as
% \cwise{} floats after \Endparacol.
% \end{itemize}
% 
% \item[\Uidx{\!\@toplist!}]
% is an internal macro having the list of \cwise{} floats which is
% decided to be put at the top of the \ccolpage{} by float environments or by
% \!\pcol@trynextcolumn!.  This list is scanned by \!\pcol@cflt! if its
% invoker \!\pcol@combinefloats! finds the macro is not empty.  The list is
% also scanned by \!\pcol@makecol!, \!\pcol@output@switch! and
% \!\pcol@measurecolumn! using \!\pcol@addflhd! for the measurement of the
% combined size of top floats, while \!\pcol@setcurrcol! and
% \!\pcol@igetcurrcol!  saves\slash restores the list into/from $\cc_c(\tl)$
% respectively.  In addition our macros may add an element or build the
% entire list in the following two cases.  One case is for a \sync{}ation
% for which \!\pcol@synccolumn! lets the main vertical list in
% $\cc_c(\vb^b)$ be a float, namely {\em\mvlfloat} to be added to this list.
% Another case is for a \fcolumn{} in the \lpage{} for which
% \!\pcol@makefcolumn! and \!\pcol@makefcolelt! build this list for deferred
% floats.  In the latter case, the list is scanned by \!\pcol@makefcolpage!
% invoked from \!\pcol@makefcolumn! itself, \!\pcol@flushcolumn! and
% \!\pcol@makeflushedpage!.
% 
% \item[\Uidx{\!\@botlist!}]
% is an internal macro having the list of \cwise{} floats which is
% decided to be put at the bottom of the \ccolpage{} by float environments or
% by \!\pcol@trynextcolumn!.  The emptiness of this list examined by
% \!\pcol@combinefloats! to invoke the scanner \!\@cflb! unless empty,
% by \!\pcol@output@start! to calculate the room for each \colpage{} in the
% \spage, and by \!\pcol@makenormalcol! to decide whether \!\@makecol! is
% used or not for building \preenv.  The list is also scanned by
% \!\pcol@measurecolumn! for the measurement of the combined size of bottom
% floats, while \!\pcol@setcurrcol! and \!\pcol@igetcurrcol! saves\slash
% restores the list into/from $\cc_c(\bl)$ respectively.
% 
% \item[\Uidx{\!\@midlist!}]
% is an internal macro having the list of in-text floats which has already
% been put in the \ccolpage{} but is kept to check the ordering of the
% succeeding floats.  The list is emptied by \!\pcol@makenormalcol! after
% returning all elements in it to \!\@freelist!, while \!\pcol@setcurrcol!
% and \!\pcol@igetcurrcol! saves\slash restores the list into/from
% $\cc_c(\ml)$ respectively.
% 
% \item[\Uidx{\!\f@depth!}]
% is an internal macro having |1sp| or being \!\let!-equal to \!\z@! to
% specify the float category, \pwise{} or \cwise{} respectively, which
% float-related macros work on.  As discussed in
% item-(\ref{item:ovv-float-@dblfloatplacement}) of
% \secref{sec:imp-ovv-float}, this feature introduced in 2015 version
% of \LaTeX{} is nullified in \env{paracol} environments and thus the
% setting with |1sp| done by \!\@dblfloatplacement! is overriden by
% \!\pcol@startpage! and \!\pcol@output@clear! when they invoke the macro.
% 
% \item[\Uidx{\!\cl@@ckpt!}]
% is an internal macro having the list of all counters defined by
% \!\newcounter! and the counter \counter{page}.  The original usage of this
% macro is to log the values of all counters into |.aux| by \!\include!, but
% we use it to obatin all counters in \!\pcol@zparacol! and
% \!\pcol@globalcounter@s!.
% 
% \item[$\cs{cl@}{\cdot}\theta$]
% is an internal macro having the list $\clist(\theta)$ of descendant
% counters of the counter $\theta$ whose increment by \!\stepcounter! lets
% them 0.  The macro \!\pcol@remctrelt! moves it to
% $|\pcol@cl@|{\cdot}\theta$
% 
% \Uidx{\SpecialArrayIndex{\theta}{\cl@}}
% 
% and re\!\def!ines it to have $\!\pcol@stepcounter!\Arg{\theta}$.
% 
% \item[\Uidx{\!\reserved@a!}]
% is an internal macro for temporary use.  Its usages are as follows.
% 
% \begin{itemize}
% \item
% In \!\pcol@Fe!, it is used to keep the cardinality of \!\@freelist! in
% \!\pcol@F@n! to log it by \!\pcol@FF! after \!\pcol@F@n! is let have
% another measurement result.
% 
% \item
% In $\!\pcol@iLogLevel!\<l\>\arg{name}$, it is used to implement
% $\!\let!|\|\arg{name}=|\|\arg{name}{\cdot}l'$ where $l'$ is the roman
% representation of the level $l$.
% 
% \item
% In \!\pcol@setpageno!, it has $\PPP$ so that we update $\PP$ and
% $\pp(\ptop)$ scanning their original contents.
% 
% \item
% In \!\pcol@getcurrpinfo!, it has $\pp(\ptop)$ so that we give its five
% components to \!\pcol@getpinfo! as its first five arguments.
% 
% \item
% In \!\@outputpage!, it has a sequence of \bgpaint{} for both left and
% right \parapag{}es to be shipped out outside \env{paracol} environment.
% 
% \item
% In \!\pcol@outputpage@ev!, it has the expansion result of
% \!\meaning!\!\yoko! to be compared with \!\reserved@b! having
% \!\string!\!\yoko! for examining if \!\yoko! is a primitive of underlying
% \TeX{}.
% 
% \item
% In $\!\pcol@bg@paintregion!\arg{a}\arg{c}$, it is let have
% $a'=a{\cdot}|@|{\cdot}c$ or $a'=a$, and then referred to by
% \!\pcol@bg@paintregion@i! to use $|\pcol@bg@color|{\cdot}a'$, and by
% $\!\pcol@bg@addext!\arg{z}\Arg{s}\Arg{d}$ to use
% $|\pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}a'$.
% 
% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}
% \SpecialArrayIndex{a}{\pcol@bg@color@}
% \SpecialArrayIndex{d{\cdot}\string\texttt{@}
%     {\cdot}a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@ext@}
% \SpecialArrayIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}
% 
% \item
% In \!\pcol@specialoutput!, it is \!\let!-equal to $|\pcol@output@|{\cdot}f$
% corresponding to $\!\outputpenalty!=|\pcol@op@|{\cdot}f$, or
% \!\@specialoutput!.
% 
% \item
% In \!\pcol@output@start!, it is let have a \bgpaint{} macro
% \!\pcol@bg@paintbox! and the definition of a parameter
% \!\pcol@bg@textheight! for it.
% 
% \item
% In \!\pcol@output@switch!, it is \!\let!-equal to \!\@nobreaktrue! or
% \!\@nobreakfalse! according to \CSIndex{if@nobreak} in the leaving column
% to broadcast it to other columns.
% 
% \item
% In \!\pcol@ifempty!$\arg{box}\arg{then}\arg{else}$, it has $\arg{then}$ or
% $\arg{else}$ according to the emptiness of $\arg{box}$.
% 
% \item
% In \!\pcol@clearcolorstack!, it is \!\def!ined to put an uncoloring
% \!\special! by \!\reset@color! for its argument $\celt_i$ in
% \!\pcol@iscancst!.
% 
% \item
% In \!\pcol@restorecst!, it is \!\def!ined to put a coloring \!\special! in
% its argument $\celt_i$ by \!\unvbox! done in \!\pcol@iscancst!.
% 
% \item
% In \!\pcol@addmarginpar!, at first it is made let equal to 0 or $\CL$
% according to $c<\CL$ or not.  Then it is let have $\PPP$ to be scanned to
% find $\pp^m(p)$.
% 
% \item
% In \!\pcol@getmparbottom@i!, it is let have one of
% $\mpb_{\{L,R\}}^{\{l,r\}}$ according to the side margin which the marginal
% note to be added goes to, and then it is referred to by
% \!\pcol@getmparbottom!.
% 
% \item
% In \!\pcol@setmpbelt@i!, it is let have what $\pp^m(p)$ should have after
% the update of a list of marginal notes in it, and then \!\pcol@setmpbelt!
% updates $\pp(p)$ with the new $\pp^m(p)$ in the macro.
% 
% \item
% In $\!\pcol@bias@mpbout!\Arg{y}$ and $\!\pcol@getmparbottom@last!\Arg{y}$,
% it is let have $\!\pcol@bias@mpbout@i!\Arg{y}$ and
% $\!\pcol@getmparbottom@last@i!\Arg{y}$ respectively, so that they are
% invoked in \!\pcol@do@mpb@all@ii!.
% 
% \item
% In \!\pcol@makeflushedpage!, it is let have an invocation of
% \!\pcol@bg@paintbox! for \pwise{} floats in $\pp^i(\ptop)$ together with
% the condition of the \bgpaint.
% 
% \item
% In \!\pcol@output@end!, it is let have the invocation of
% \!\pcol@bg@paintbox!  for \bgpaint{} of \Scfnote{}s with the condition to
% do it and a \!\def!inition of \!\pcol@bg@footnoteheight!.
% 
% \item
% In $\!\pcol@defcomelt!\arg{com}$, it is used to implement
% $\!\let!|\|\arg{com}=|\pcol@com@|{\cdot}\~\arg{com}$.
% 
% \item
% In \!\pcol@setcolumnwidth!, it is made \!\let!-equal to
% \!\pcol@setcolwidth@s! or \!\pcol@setcolwidth@r! according to
% $\!\pcol@columnratioleft!=\!\relax!$ or not.
% 
% \item
% In \!\pcol@setcolwidth@r!, it is used to have the fraction $r_d$ being a
% comma-seperated list element in its argument $\arg{ratio}$ defined by
% \!\columnratio! and scanned by a \!\@for! loop.
% 
% \item
% In $\!\pcol@setcw@scan!\<\Cfrom\>\<\Cto\>\Arg{spec}$, at first it is let
% have $\arg{spec}$, then the result of adding `|,|' as many as
% $\Cto-\Cfrom$ to the tail, and finally each element in the extended
% $\arg{spec}$ in a \!\@for! loop.
% 
% \item
% In $\!\pcol@setcw@getspec@i!\arg{default}\<x'_d\>$, it is let have
% $\<x'_d\>$ from which all space tokens are removed.
% 
% \item
% In \!\pcol@setcw@calcfactors!, it is used as a waste bascket to throw away
% $(\WT-W)/(F\times1\,|pt|)$ calculated by \!\pcol@setcw@calcf!.
% 
% \item
% In $\!\pcol@extract@fil@i!\<n\>|.|\<m{\cdot}\mathit{unit}\>\!\@nil!$, it has
% $\<n\>|.|\<m{\cdot}\mathit{unit}\>$, and is referred to by
% \!\pcol@extract@fil@ii!.
% 
% \item
% In \!\globalcounter!\marg{ctr}, it is used to have $\arg{ctr}$ for the
% \CSIndex{ifx}-comparison with each $\theta\in\CG$.
% 
% \item
% In $\!\pcol@remctrelt!\<\theta\>$, it is used to implement
% $\!\let!|\pcol@cl@|{\cdot}\theta=|\cl@|{\cdot}\theta$,
% 
% \SpecialArrayIndex{\theta}{\pcol@cl@}\SpecialArrayIndex{\theta}{\cl@}
% 
% \item
% In $\!\pcol@removecounter!\<\mathit{\Theta}'\>\Arg{\theta}$, it is used to
% have $\theta$ for the \CSIndex{ifx}-comparison in \!\pcol@iremctrelt!.
% 
% \item
% In $\!\pcol@thectrelt!\<\theta\>$, it is used to implement
% $\!\let!|\pcol@thectr@|{\cdot}\theta=|\the|{\cdot}\theta$,
% 
% \SpecialArrayIndex{\theta}{\pcol@thectr@}\SpecialArrayIndex{\theta}{\the}
% 
% and then is made \!\let!-equal to $|\pcol@thectr@|{\cdot}\theta{\cdot}0$.
% 
% \SpecialArrayIndex{\theta{\cdot}c}{\pcol@thectr@}
% 
% \item
% In $\!\pcol@synccounter!\arg{lst}$, it has $\arg{lst}$.
% 
% \item
% In $\!\pcol@setctrelt!\<\theta\>\<\val_c(\theta)\>$, it is made
% \!\let!-equal to $|\pcol@thectr@|{\cdot}\theta$
% 
% \SpecialArrayIndex{\theta}{\pcol@thectr@}
% 
% or
% $|\pcol@thectr@|{\cdot}\theta{\cdot}c$.
% 
% \SpecialArrayIndex{\theta{\cdot}c}{\pcol@thectr@}
% 
% \item
% In \!\pcol@switchenv!, it is used to save \!\switchcolumn! which is
% redefined in the macro, and then to invoke \!\switchcolumn! with the
% original definition.
% 
% \item
% In \!\pcol@fntext!\marg{text}, it is \!\let!-equal to \!\pcol@fntextother!
% or \!\pcol@fntext~top! according to the footnote $\arg{text}$ is deferred
% or not.
% 
% \item
% \begin{Hfuzz}{0.6pt}%
% In \!\pcol@calcfnctr!$\arg{num}$\!\@nil!, it has the first token of
% $\arg{num}$ for \CSIndex{ifx}-comparison with `|+|' and `|-|'.
% \end{Hfuzz}
% 
% \item
% In $\!\pcol@twosided!|[|T|]|$, it is let have each non-space token in $T$
% given by a \!\@tfor! loop.
% \end{itemize}
% 
% \item[\Uidx{\!\reserved@b!}]
% is an internal macro for temporary use.  It is used in the following
% macros to keep a list shown in paraentheses so that we update the list in
% the scan of list elements. 
% 
% \begin{quote}
% \!\pcol@startpage! (\!\@dbldeferlist!)\\
% \!\pcol@outputcolumns! ($\PP$)\\
% \!\pcol@trynextcolumn! ($\cc_c(\dl)$)\\
% \!\pcol@makefcolumn! ($\cc_c(\dl)$)\\
% \!\pcol@removecounter!$\<\mathit{\Theta}'\>\Arg{\theta}$
% ($\mathit{\Theta}'\in\{\CG,\CC\}$)
% \end{quote}
% 
% In addition, it is used in the following macros.
% 
% \begin{itemize}
% \item
% In \!\pcol@outputpage@ev!, it has the expansion result of
% \!\string!\!\yoko! to be compared with \!\reserved@a! having
% \!\meaning!\!\yoko! for examining if \!\yoko! is a primitive of underlying
% \TeX{}.
% 
% \item
% In \!\pcol@bg@paint@ii!, it has a token in the arguments $K_b$, $K_g$ and
% $K_c$ of the macro scanned by \!\@tfor!.
% 
% \item
% In \!\pcol@output@switch!, it is \!\let!-equal to |\@afterindenttrue| or
% |\@after|\~|indentfalse| according to \CSIndex{if@afterindent} in the
% leaving column to broadcast it to other columns.
% 
% \item
% In \!\pcol@clearcolorstack!, it is \!\def!ined to put an uncoloring
% \!\special! by \!\reset@color! for its argument $\Celt^c$ in
% \!\pcol@scancst!.
% 
% \item
% In \!\pcol@restorecst!, it is \!\def!ined to put a coloring \!\special! in
% its argument $\Celt^c$ by \!\unvcopy! done in \!\pcol@scancst!.
% 
% \item
% In \!\pcol@scancst! and \!\pcol@iscancst!, after the reference for the
% purposes shown in the two items above, it has
% $M=(m\,\Bar\,\mceltpop_{j,m}\in\cstraw,\;j\geq i)$ for $\mceltpop_{i,*}$
% and in the latter is scanned to find $m$ for $\mcelt_{i,m}$ in $M$.
% 
% \item
% In \!\pcol@addmarginpar!, it is made let equal to $\CL$ or $\C$
% according to $c<\CL$ or not.
% 
% \item
% In $\!\pcol@bias@mpbout@i!\Arg{y}\!\@elt!\Arg{t}\Arg{b}\!\@nil!$, it is
% let have $\mpar(t+y,b+y)$, and in $\!\pcol@getmparbottom@last@i!
% \Arg{y}\mpar(t_1,b_1)\cdots\mpar(t_n,b_n)\!\@nil!$ it is let have
% $\mpar(y,y)$ or $\mpar(t_n,b_n)$, so that they are let be a
% $\mpb_{\{L,R\}}^{\{l,r\}}$ by \!\pcol@do@mpb@all@ii!.
% 
% \item
% In $\!\pcol@setcw@getspec@i!\arg{default}\<x'_d\>$, it is let have each
% non-space token in $\<x'_d\>$ to remove space tokens from it.
% 
% \item
% In $\!\pcol@setcw@fill!\<f\>\!\fill!$, it is let have $f$.
% 
% \item
% In $\!\pcol@extract@fil@ii!\arg{unit}\!\@nil!$, it is let have
% $\arg{unit}$.
% 
% \item
% In \!\globalcounter!$\Arg{\theta}$, it has $\cg_i\in\CG$ for
% \CSIndex{ifx}-comparison with $\theta$.
% 
% \item
% In $\!\pcol@iremctrelt!\<\mathit{\Theta}'\>\Arg\theta$, it has $\theta$ for
% \CSIndex{ifx}-comparison with $\theta'$ to be removed from $\CG$ or $\CC$.
% 
% \item
% In \!\pcol@calcfnctr!$\arg{num}$\!\@nil!, it has `|+|' and then `|-|' for
% \CSIndex{ifx}-comparison with the first token of $\arg{num}$.
% 
% \item
% In \!\pcol@backgroundcolor@ii!, it has \!\pcol@backgroundcolor@x! or
% \!\pcol@back~groundcolor@z! according that the region of \bgpaint{} and its
% color is defined or undefined.
% \end{itemize}
% 
% \item[\Uidx{\!\reserved@c!}]
% is an internal macro for temporary use.  It is used in \!\pcol@startpage!
% to save \!\@deferlist! in it and then to restore the list from it, and in
% \!\pcol@iscancst! to have \!\relax! or the macro itself to iterate the
% macro recursively.
% 
% \item[\Uidx{\!\reserved@d!}]
% is an internal macro for temporary use.  It is used in
% \!\pcol@iscancst! as a \!\chardef! register to have 0 if $m$ for
% $\mcelt_{i,m}$ is not in the list
% $M=(n\,\Bar\,\mceltpop_{j,n}\in\cstraw,\;j\geq i)$, or 1 if found.
% 
% \item[\Uidx{\!\@gtempa!}]
% is an internal macro used as a \!\global!ly modifiable scratchpad.  Its
% usages are as follows.
% 
% \begin{itemize}
% \item
% In \!\pcol@ifempty!$\arg{box}\arg{then}\arg{else}$, it has \!\lastpenalty!
% in a \!\vbox! whose value is examined outside the \!\vbox! for the
% emptiness check of $\arg{box}$.
% 
% \item
% In \!\pcol@addmarginpar!, it is given to \!\@xnext! as the target to have
% the second and successive elements of \!\@currlist! which we cannot modify.
% 
% \item
% In \!\pcol@zparacol! and \!\pcol@cmpctrelt!, it has the list of counters
% to be synchronized.
% 
% \item
% In $\!\pcol@setcw@getspec@i!\arg{default}\<x'_d\>$, it is made
% \!\@empty! or \!\relax! according to $x'_d$ has \!\fill! or not.
% 
% \item
% In \!\pcol@storectrelt!, \!\pcol@savectrelt! and \!\pcol@sscounters!, it
% has the new version of $\CC_c$.
% \end{itemize}
% \end{description}
% 
% 
% 
%\iffalse
%<*paracol>
%\fi
% 
% \section{Register Declaration}
% \label{sec:imp-decl}
% 
% \subsection{\cs{count} Registers}
% 
% Here we declare registers and switches.  The first group is for \!\count!
% registers.
% 
% \begin{macro}{\pcol@currcol}
% \changes{v1.2-1}{2013/05/11}
%	{Add initialization to 0 after the declaration.}
% 
% The register \!\pcol@currcol! has the zero-origin ordinal $c$ of the
% column which we were in when \!\output! is invoked.  Therefore, for
% example, in the process of \!\switchcolumn!, the register has $c$ from
% which we are switching to another column.  The register is initialized to
% be 0 by \!\pcol@output@start!, and then set to $\!\pcol@nextcol!=d$ by
% \!\pcol@restartcolumn! to switch to (or stay in) $d$.  Note that these two
% assignments are \!\global! while other macros may {\em locally} use the
% register to, for example, scan all columns $c\In0\C$.  Besides two macros
% above, the following macros refer to the register to know which column we
% are in (or which column is processed by their invokers).
% 
% \begin{quote}\raggedright
% \!\pcol@Log@iii!,
% \!\pcol@Log@ii!,
% \!\pcol@FF!,
% \!\pcol@makecol!,
% \!\pcol@opcol!,
% \!\pcol@bg@columnleft!,
% \!\pcol@bg@columnwidth!,
% \!\pcol@bg@columnsep!,
% \!\pcol@output@switch!,
% \!\pcol@getcurrcol!,
% \!\pcol@setcurrcol!,
% \!\pcol@clearcolorstack!,
% \!\pcol@restorecolorstack!,
% \!\pcol@addmarginpar!,
% \!\pcol@getmparbottom@i!,
% \!\pcol@setmpbelt@i!,
% \!\pcol@invokeoutput!\footnote{
% 
% Only for logging.},
% 
% \!\thecolumn!,
% \!\pcol@sscounters!,
% \!\pcol@setctrelt!,
% \!\pcol@com@switchcolumn!,
% \!\pcol@switchcol!,
% \!\pcol@visitallcols!,
% \!\pcol@aconlyelt!,
% \!\pcol@flushclear!.
% \!\pcol@columncolor!,
% \!\normalcolumncolor!,
% \!\pcol@icolumncolor!,
% \end{quote}
% 
% Among the macros above, \!\columncolor! and \!\normalcolumncolor! could
% refer to the register outside \env{paracol} environment and thus before
% the initialization by \!\pcol@output@start!.  Therefore, the register is
% also initialized to be 0 after its declaration to assure safe reference.
% 
% The following macros use the register for the scan of all $c\In0\C$ by
% themselves or their invokers.
% 
% \begin{quote}\raggedright
% \!\pcol@output@start!,
% \!\pcol@output@switch!,
% \!\pcol@sync!,
% \!\pcol@flushcolumn!,
% \!\pcol@measurecolumn!,
% \!\pcol@synccolumn!,
% \!\pcol@makeflushedpage!,
% \!\pcol@flushfloats!,
% \!\pcol@freshpage!,
% \!\pcol@output@end!,
% \!\pcol@synccounter!,
% \!\pcol@com@syncallcounters!,
% \!\pcol@stepcounter!.
% \end{quote}
% 
% The macros \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats! also use
% the register for scanning but for $\LBRP\Cfrom\Cto$ given by their
% arguments.
% 
% In addition \!\pcol@ccuse!, \!\pcol@ifccdefined! and \!\pcol@ccxdef!
% refer to the register to have the control sequence
% $|\pcol@columncolor|\cdot c=\Celtshadow^c$ or
% $|\pcol@columncolor@box|\cdot c=\Celt^c$ where $c$ is for the current
% column or for all columns depending on their invokers.
% 
% \SpecialArrayIndex{c}{\pcol@columncolor}
% \SpecialArrayIndex{c}{\pcol@columncolor@box}
% \end{macro}
% 
% \begin{macro}{\pcol@nextcol}
% The register \!\pcol@nextcol! has the zero-origin ordinal $d$ of the
% column to which we are switching, or in which we are staying, to be set
% into \!\pcol@currcol! by \!\pcol@restartcolumn!.  The main usage of the
% register is to set the switching target in \!\pcol@switchcolumn!, but
% other macros use it to specify the (temporary) target of
% \!\pcol@switchcol!; the tallest column in \!\pcol@sync!; 0 in
% \!\pcol@zparacol!, \!\pcol@sptext! and \!\endparacol!; all in $\LBRP0\C$
% but $c=\!\pcol@currcol!$ in \!\pcol@visitallcols!; and $c$ in
% \!\pcol@flushclear! to stay in the current column $c$.  The other user of
% this register is \!\pcol@invokeoutput! but only for logging.
% \end{macro}
% 
% \begin{macro}{\pcol@ncol}
% \changes{v1.3-3}{2013/09/17}
%	{Add initial zero-clearing for safe reference in \cs{@outputpage}
%	 invokded prior to the first \string\texttt{paracol}.}
% \begin{macro}{\pcol@ncolleft}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced to specify the number of columns in left
%	 parallel-pages.}
% 
% The register \!\pcol@ncol! has the number of columns $\C$ given as the
% argument of \!\paracol!, whose callee \!\pcol@zparacol! being the sole
% modifier of the register \!\global!ly assigns $C$ to the register to give
% safe reference to \!\@outputbox! invoked after a \env{paracol} is closed.
% In addition for the reference in \!\@outputbox! before the first
% \env{paracol}, the register is initialized with zero after the declaration.
% 
% The following macros refer to the register to scan all columns $c\In0\C$.
% 
% \begin{quote}\raggedright
% \!\pcol@checkshipped!,
% \!\pcol@output@start!,
% \!\pcol@output@switch!,
% \!\pcol@sync!,
% \!\pcol@makeflushedpage!,
% \!\pcol@freshpage!,
% \!\pcol@output@end!,
% \!\pcol@synccounter!,
% \!\pcol@com@syncallcounters!,
% \!\pcol@stepcounter!,
% \!\pcol@visitallcols!.
% \end{quote}
% 
% The register \!\pcol@ncolleft! has $\Uidx\CL$ being the number of columns
% in the left {\em\Uidx\parapag{}e} if \parapag{}ing is in effect, or have
% $\C$ otherwise.  Similar to $\C$, the number $\CL$ is given as the
% optional argument of \!\pcol@zparacol! and is \!\global!ly assigned to the
% register by the sole modifier \!\pcol@zparacol!, unless the optional
% arugment is not less than $\C$ which is assigned to $\CL$ if this
% exception is found.  The reason of the \!\global! assignment and the
% initial zero-clearing after the declaration is same as that for $C$, i.e.,
% for the reference in \!\@outputpage! outside \env{paracol}.
% 
% The following macros examines if $\Uidx\CL<\C$, i.e., if \parapag{}ing is
% in effect.
% 
% \begin{quote}\raggedright
% \!\pcol@outputelt!,
% \!\@outputpage!,
% \!\pcol@output@start!,
% \!\pcol@output@flush!,
% \!\pcol@output@clear!,
% \!\pcol@makeflushedpage!,
% \!\pcol@flushfloats!,
% \!\pcol@output@end!,
% \!\pcol@zparacol!,
% \end{quote}
% 
% \begin{Sloppy}{2350}
% In the macros listed above, \!\pcol@outputelt!, \!\pcol@makeflushedpage!
% and \!\pcol@flushfloats! passes $\LBRP0\CL$ and $\LBRP\CL\C$ to their
% respective callees \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage!  and
% \!\pcol@iflushfloats! as their argument pair
% $\LBRP{\Uidx\Cfrom}{\Uidx\Cto}$ to let them work on the left and right
% \parapag{}es repsectively.  The callees above also pass the pair to
% \!\pcol@swapcolumn! to swap the scanning order of columns if \cswap{} is
% in efect.
% 
% They also pass the pair to \!\pcol@buildcolseprule! which then passes it
% to \!\pcol@bg@paintcolumns!  and \!\pcol@bg@paintbox! by binding it to
% $\LBRP\CBfrom\CBto=\LBRP{\!\pcol@bg@from!}{\~\!\pcol@bg@to!}$ referred to
% by \!\pcol@bg@paint@i! and its callee \!\pcol@bg@paint@ii! to define the
% range of columns to be painted is $\LBRP\CBfrom\CBto$.  Similar passing is
% done by (our own version of) \!\@outputpage!, but it directly uses
% $\LBRP0\CL$ and $\LBRP\CL\C$ as the sources and the target painting macros
% are \!\pcol@bg@paintpage!, \!\pcol@bg@@paintpage! and
% \!\pcol@bg@paintbox!.  Note that $\CBto$ is initialized to be
% \!\let!-equal to $\C$ because it may be referred to without
% binding\footnote{
% 
% This meaningless reference has no harmful side effects.}.
% \end{Sloppy}
% 
% The macro \!\pcol@addmarginpar! also referes to $\CL$ to know if the
% column $c$ on which it is working on is in the left or right \parapag{}e,
% i.e., $c<\CL$ or not, to decide the margin to which a marginal note is put,
% and to pass $\LBRP0\CL$ or $\LBRP\CL\C$ to \!\pcol@swapcolumn! to
% calculate the distance to the left or right margin from the column.  The
% examination of $c<\CL$ is also done in related macros
% \!\pcol@getmparbottom@i! and \!\pcol@setmpbelt@i!.
% 
% Similar column-range specification is done for the argument pair
% $\LBRP\Cfrom\Cto$ of \!\pcol@setcolumnwidth!  invoked from
% \!\pcol@zparacol!.  Then the arguments are passed to the callees
% \!\pcol@setcolwidth@r! or \!\pcol@setcolwidth@s!, the latter of
% which also passes them to its callee \!\pcol@setcw@scan!, to define the
% width of columns in $\LBRP\Cfrom\Cto$ and thier separators.
% 
% The other references to $\C$ are made by \!\pcol@com@switchcolumn! and
% \!\pcol@switchcolumn! to examine $c<\C$, to wraparound $\C-1$ to 0 for the
% former and to complain if $c\geq\C$ for the latter.
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@page}
% The register \!\pcol@page! has the zero-orgin ordinal $p$ of the page
% which we are in.  The register is initialized to be 0 not only by
% \!\pcol@output@start! to give the obvious starting point, but also by
% \!\pcol@freshpage! for page flushing which clears $\PP=\!\pcol@pages!$ to
% give us another type of starting point.  Then the register is incremented
% by \!\pcol@nextpage! to advance one page, by \!\pcol@nextpelt! to skip a
% \fpage, and by \!\pcol@startpage! for a \fpage{} to be created.  The other
% type of updates of the register is done by \!\pcol@restartcolumn! which
% lets $p$ be $\cc_c(\vb^p)$ when we revisit the column $c$ belonging to the
% page $p$.  Note that, besides these \!\global!  updates,
% \!\pcol@flushcolumn! locally updates the register to scan
% $\PP=\!\pcol@pages!$, and \!\pcol@freshpage! also performs local updates
% but in more weird manner.  Besides the updates discussed above, the
% macros \!\pcol@Log@iii!, \!\pcol@Log@ii!, \!\pcol@FF!, \!\pcol@makecol!,
% \!\pcol@opcol!, \!\pcol@setpageno!, \!\pcol@getcurrpage!,
% \!\pcol@startcolumn!, \!\pcol@output@switch!, \!\pcol@addmarginpar! and
% \!\pcol@fntext! refer to the register to know which page they are
% operating on.
% \end{macro}
% 
% \begin{macro}{\pcol@basepage}
% The register \!\pcol@basepage! has the ordinal $\pbase$ of the \bpage{}
% being the oldest page not shipped out yet.  The register is initialized to
% be 0 by \!\pcol@output@start! and \!\pcol@freshpage! together with
% \!\pcol@page!, and then incremented by \!\pcol@outputelt! when it ships
% the page $\pbase$ out.  The macros \!\pcol@setpageno!, \!\pcol@nextpage!,
% \!\pcol@getcurrpage! and \!\pcol@addmarginpar! refer to the register in
% their scans of $\PP$ or $\PPP$ to know the zero-origin ordinal of the
% element for the current page $p$ is $p-\pbase$.
% \end{macro}
% 
% \begin{macro}{\pcol@toppage}
% \changes{v1.0}{2011/10/10}
%	{Renamed from \cs{pcol@maxpage}.}
% 
% The register \!\pcol@toppage! has the ordinal $\ptop$ of the \tpage{}
% having the most advanced \colpage{}s, or {\em\Uidx\lcolpage{}s} in short.
% The register is initialized to be 0 by \!\pcol@output@start! and
% \!\pcol@freshpage! together with \!\pcol@page!, and then let be
% $p=\!\pcol@page!$ by \!\pcol@startpage! to start a new page $p$.  The
% macros \!\pcol@makecol!, \!\pcol@opcol!, \!\pcol@startcolumn!,
% \!\pcol@output@switch! and \!\pcol@restartcolumn!  refer to the register
% to examine if they are working on a \colpage{} in the \tpage, while
% \!\pcol@flushcolumn! and \!\pcol@fntext! examines if the \ccolpage{} is
% behind the \tpage.  The register is also referred to by \!\pcol@Log@iii!,
% \!\pcol@Log@ii! and \!\pcol@FF! for logging.
% \end{macro}
% 
% \begin{macro}{\pcol@footnotebase}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for page-wise footnotes.}
% 
% The register \!\pcol@footnotebase! is let have the value of \!\c@footnote!
% at the start of a \env{paracol} environment by \!\pcol@zparacol! to give
% the base value $\Uidx\bf$ for relative numbering of \counter{footnote}
% done in \!\pcol@calcfnctr! for the starred versions of \!\footnote!,
% \!\footnotemark! and \!\footnotetext!.  The register is also referred to
% by \!\endparacol!  to let \!\c@footnote! have $\bf+\nf$ where
% $\nf=\!\pcol@nfootnotes!$ shown below is the number of footnotes in the
% \env{paracol} environment to be closed.
% \end{macro}
% 
% \begin{macro}{\pcol@nfootnotes}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for page-wise footnotes.}
% 
% The register \!\pcol@nfootnotes! is to accumulate the number of footnotes
% $\Uidx\nf$ in a \env{paracol} environment.  Therefore, it is zero-cleared
% by \!\pcol@zparacol!, then incremented by \!\pcol@ifootnote! and
% \!\pcol@ifootnotemark! for \!\footnote! and \!\footnotemark!, and finally
% referred to by \!\endparacol! to let $\!\c@footnote!=\bf+\nf$.
% \end{macro}
% 
% \begin{macro}{\pcol@mcid}
% \changes{v1.24}{2013/07/27}
%	{Introduced for coloring specified in math mode.}
% \changes{v1.34}{2018/05/07}
% 	{Change its meaning and operations with it a little bit according to
%	 the new text coloring with \cs{insert}.}
% 
% The register \!\pcol@mcid! has the number of pushes of
% \colorstack{} by coloring commands in math mode between two consecutive
% invocations of \!\output!.  The register is
% zero-cleared by \!\pcol@output! because we are definitely in the main
% vertical mode and thus all pops corresponding to pushes in math mode must
% have been applied to |.tex|'s \colorstack.  Then the register
% is referred to by \!\pcol@set@color@push! when it is invoked in math mode,
% to increment it and then examine if it does not exceed the limit
% \!\pcol@mcpushlimit! to mean the math-mode coloring still can be made.  The
% macro then uses the value of the register as the identifier of the push
% operation given to \!\output! through an \!\insert!ion.
% \end{macro}
%    \begin{macrocode}

%% Register Declaration

\newcount\pcol@currcol \global\pcol@currcol\z@
\newcount\pcol@nextcol
\newcount\pcol@ncol \global\pcol@ncol\z@
\newcount\pcol@ncolleft \global\pcol@ncolleft\z@
\newcount\pcol@page
\newcount\pcol@basepage
\newcount\pcol@toppage
\newcount\pcol@footnotebase
\newcount\pcol@nfootnotes
\newcount\pcol@mcid
%    \end{macrocode}
% 
% 
% 
% \subsection{Switches}
% 
% The second declaration group is for switches.
% 
% \begin{macro}{\ifpcol@output}
% \changes{v1.2-7}{2013/05/11}
% 	{Introduced to solve the \cs{output} request sneaking.}
% \changes{v1.22}{2013/06/30}
%	{Add a user \cs{pcol@reset@color@pop} to inhibit uncoloring if
%	 $\mathit{false}$.}
% \changes{v1.3-2}{2013/09/17}
%	{Add a user \cs{@outputpage} for parallel-paging.}
% \changes{v1.3-3}{2013/09/17}
%	{Add a user \cs{@outputpage} for background-painting.}
% 
% The switch \CSIndex{ifpcol@output} is $\true$ iff \!\pcol@output@start!
% which turns the switch $\true$ has been invoked but \!\pcol@output@end!
% which does $\false$ has not yet.  Then the switch is examined by
% \!\pcol@output! to detect an \!\output! request sneaked from outside of
% the \env{paracol} environment.  The other users \!\@outputpage! and
% \!\pcol@reset@color@pop! examine this switch to know if the macro is
% invoked inside or outside of \env{paracol} environment, while the macro
% \!\pcol@output@start!  temporarily turns the switch $\false$ when it ships
% out a page having \preenv{} only.
% \end{macro}
% 
% \begin{macro}{\ifpcol@nospan}
% \changes{v1.0}{2011/10/10}
%	{Renamed from \cs{pcol@textonly}.}
% 
% The switch |\ifpcol@nospan| is $\true$ iff a page $p$ does not have
% \spanning, i.e., $\pp^i(p)=\bot$.  It is set by by
% \!\pcol@getpinfo! for the examination in \!\pcol@ioutputelt!,
% \!\pcol@makeflushedpage! and \!\pcol@output@end!.
% \end{macro}
% 
% \begin{macro}{\ifpcol@sync}
% \changes{v1.0}{2011/10/10}
%	{Add initialization to be $\string\mathit{false}$.}
% \changes{v1.2-2}{2013/05/11}
%	{Add \cs{pcol@switchcol} and \cs{pcol@flushclear} to the macros
%	 turning the switch $\string\mathit{true}$ due to column scanning
%	 and pre-flushing column height check.}
% 
% The switch |\ifpcol@sync| is $\true$ iff \!\pcol@output@switch! is invoked
% for \sync{}ed \cswitch{} by \!\switchcolumn!|*| or its relative
% enviroment openers, or \pfcheck{} prior to page flushing or environment
% closing.  Therefore, the switch is \!\global!ly turned $\true$ by
% \!\pcol@iswitchcolumn! and \!\pcol@sptext! for the \sync{}ing
% \cswitch{}ing but then temporarily turned $\false$ by \!\pcol@switchcol!
% invoked by them for \cscan{}ning and then turned $\true$ again by the
% macro.  For \pfcheck{}, the macro \!\pcol@flushclear! turns the switch
% $\true$.  The other macro turns this switch is \!\pcol@output@switch! at
% the end of which the switch is turned $\false$ to go back to the default
% state.  The macros examining this switch are \!\pcol@output@switch!,
% \!\pcol@putbackmvl!, \!\pcol@sync!, \!\pcol@invokeoutput! (for logging) and
% \!\pcol@switchcol!.
% \end{macro}
% 
% \begin{macro}{\ifpcol@sptextstart}
% \changes{v1.3-1}{2013/09/17}
%	{Introduced to capture the starting point of a spanning text so that
%	 the text is split from other main vertical list stuff.}
% \begin{macro}{\ifpcol@sptext}
% \changes{v1.0}{2011/10/10}
%	{Introduced to restrict the broadcast of \cs{if@nobreak} and
%	 \cs{everypar} only when a column-switching is accompanied with
%	 spanning text.}
% \changes{v1.3-1}{2013/09/17}
%	{Renamed from \cs{ifpcol@mctext} following the naming convention, and
%	 move the timing of turning $\string\mathit{true}$ from the end
%	 of a spanning text to its beginning.}
% 
% The switch |\ifpcol@sptextstart| is $\true$ iff \!\pcol@output@switch! is
% invoked from \!\pcol@sptext! prior to a \mctext.  That is, the switch is
% \!\global!ly\footnote{
% 
% Not necessary to be \cs{global}ly turned but we dare to do that to clearly
% distinguish that from the local turning in \cs{pcol@putbackmvl}.}
% 
% let $\true$ and then $\false$ by \!\pcol@sptext! before and
% after the invocation of \sync{}ed \!\pcol@switchcol! prior to the
% \mctext.  Then the switch is examined by \!\pcol@putbackmvl! after
% the \sync{}ation to save the {\em\Uidx\prespan}, being all stuff in main
% vertical list prior to the \sync{}ation, so that the \mctext{} is split
% from the stuff and is captured afterward by \!\pcol@makecol! and/or
% \!\pcol@output@switch!.  The macro also locally turns the switch
% $\false$ if it does not follow the \sync{}ation, i.e., its invocation is
% for \cscan{}ning or is caused by pre-\sync{}ation page break, to do the
% saving only when it follows the \sync{}ation.  The switch is also examined
% in \!\pcol@output! to inhibit the warning and forced page break even when
% $\cc_0(\vb^r)=\!\@colroom!<1.5\!\baselineskip!$, because we may let it have
% a small value when the \mctext{} starts near the page bottom to capture
% the text portion in the page by \!\pcol@makecol!.  In addition, it is
% examined by \!\pcol@switchcol! to invoke $|\pcol@colpream|{\cdot}c$,
% where $c=-1$ if $\true$ or $c=\!\pcol@currcol!$ otherwise.
% 
% \SpecialArrayIndex{c}{\pcol@colpream}
% 
% The macro \!\pcol@sptext! then \!\global!ly turns another switch
% \CSIndex{ifpcol@sptext} $\true$ before putting the \mctext{} into the main
% vertical list so that \!\pcol@makecol! for the page break in the text and
% \!\pcol@output@switch! for closing capture the text to place it
% appropriately especially when \cswap{} is in effect.  Then the switch 
% is \!\global!ly turned $\false$ by \!\pcol@output@switch! to give the
% default state after it {\em broadcasts} \CSIndex{if@nobreak},
% \CSIndex{if@afterindent} and \!\everypar! to all columns.
% \end{macro}\end{macro}
% 
% \begin{macro}{\ifpcol@clear}
% \changes{v1.0}{2011/10/10}
%	{Add initialization to be $\string\mathit{false}$.}
% \changes{v1.2-2}{2013/05/11}
%	{Add \cs{pcol@flushclear} to the macros turning the switch
%	 $\string\mathit{true}$ due to the pre-flushing column height
%	 check.}
% 
% The switch |\ifpcol@clear| is $\true$ iff \!\pcol@output@switch! is
% invoked for \pfcheck{}, page flushing or environment closing.  Therefore,
% the switch is turned $\true$ by \!\pcol@flushclear! in the first case, and
% by \!\pcol@makeflushedpage! in the latter two.  These two macros also
% turned the switch $\false$ after the direct\slash indirect invocation of
% \!\pcol@output@switch! to give the default state.  The switch is examined
% by \!\pcol@output@switch! and its descendants \!\pcol@sync!,
% \!\pcol@flushcolumn! and \!\pcol@synccolumn!  for \sync{}ation, and by
% \!\pcol@invokeoutput!  for logging.
% \end{macro}
% 
% \begin{macro}{\ifpcol@flush}
% \changes{v1.2-3}{2013/05/11}
%	{Introduced to fix the problem with a too-tall page at
%	 synchronization.}
% \changes{v1.2-2}{2013/05/11}
%	{Add uses for page-wise footnote functions.}
% 
% The switch |\ifpcol@flush| is turned $\true$ by \!\pcol@sync! iff it finds
% that the page to be \sync{}ed or to be flushed is too tall because the
% sum of the total height of top floats and main text in a column and that
% of bottom floats and footnotes in another column is larger than
% $\pp^h(\ptop)-v^f-\VE$, where $v^f$ is the total heigth-plus-depth of the
% \Scfnote{}s if $\ptop$ has them or 0 otherwise, and $\VE$ is the amount
% given by \!\ensurevspace! in \sync{}ation or 0 in flushing.  Then the
% switch is examined in \!\pcol@sync! itself to restart the tallest column
% if $\true$, in \!\pcol@putbackmvl! to check if a \mctext{} is really to
% start, in \!\pcol@switchcol! to have a explicit page break in each column
% if $\true$, and in \!\pcol@flushclear! also to have a page break if
% $\true$.  The last examiner \!\pcol@flushclear!  may turn the switch
% $\true$ when it is invoked from \!\endparacol! if the last page leaves
% deferred and non-merged \Scfnote{}s for which an explicit page break is
% also required.
% \end{macro}
% 
% \begin{macro}{\ifpcol@outputflt}
% \changes{v1.0}{2011/10/10}
%	{Renamed from \cs{ifpcol@stopoutput} with the reversal.}
% 
% The switch |\ifpcol@outputflt| is used in \!\pcol@outputelt! to know
% whether a \fpage{} is to be shipped out ($\true$) or not.  The switch is
% initialized to be $\true$ by \!\pcol@outputcolumns! which invokes
% \!\pcol@outputelt! for all $\pp(p)\in\PP$.  Then if \!\pcol@outputcolumns! is
% invoked from \!\pcol@opcol! to ship the oldest page $\pbase$ out, the
% switch is turned $\false$ when we visit the second non-\fpage.  That is,
% all \fpage{}s following the first (oldest) page are shipped out but others
% are not.  On the other hand, if \!\pcol@outputcolumns! is invoked from
% \!\pcol@sync! to ship out all pages including \fpage{}s in $\PP$, the
% switch is kept $\true$ throughout all invocations of \!\pcol@outputelt!.
% \end{macro}
% 
% \begin{macro}{\ifpcol@lastpage}
% \changes{v1.0}{2011/10/10}
%	{Introduced for special operations in the last page.}
% \begin{macro}{\ifpcol@lastpagesave}
% \changes{v1.2-7}{2013/05/11}
%	{Introduced to fix the bug that \cs{@makecol} and
%	 \cs{pcol@makefcolumn} in \cs{pcol@flushcolumn} misunderstand that
%	 non-last pages are last.}
% 
% The switch |\ifpcol@lastpage| is used to know whether the following macros
% work on the {\em\Uidx\lpage} of a \env{paracol} environment to do special
% operations if so.
% 
% \begin{itemize}
% \item
% \!\pcol@combinefloats! adds \!\textfloatsep! below bottom floats of each
% column if any so that the floats are well sepearated from the \postenv.
% 
% \item
% \!\pcol@sync! examines $\VPP$ instead of $\VP$ for the \pfcheck.
% 
% \item
% \!\pcol@makefcolumn! trys to make deferred floats as top floats.
% 
% \item
% \!\pcol@makeflushedpage! builds a short page of $\VPP$ tall, leaves
% \spanning{} from ship-out if $\VPP=\!\pcol@colht!=-\infty$ so that it
% becomes a float in \postenv, and leaves \Scfnote{}s untouched if
% \Mgfnote{} typesetting is in effect.  This macro itself turns this switch
% $\false$ if $\CSIndex{ifpcol@dfloats}=\true$ to mean one or more columns
% in the \lpage{} have deferred \cwise{} floats and thus the \lpage{}
% must be {\em full size}.
% 
% \item
% \!\pcol@imakeflushedpage! leaves the \bground{} of \Scfnote{}s unpainted,
% and lets the depth of the \lpage{} be 0 in \bgpaint{} and packing of
% \colpage{}s.
% \end{itemize}
% 
% The switch is initialized to be $\false$ by \!\pcol@zparacol!, then turned
% $\true$ by \!\endparacol!, and then finally turned $\false$ by
% \!\pcol@output@end! again for
% \fpage{}s following the \lpage{} if any.  The macro \!\pcol@flushcolumn!
% saves the switch into \CSIndex{ifpcol@lastpagesave} then turning it
% $\false$ during it works on \colpage{}s in non-top and thus non-\lpage{}s
% to keep \!\@makecol! and \!\pcol@makefcolumn! from misunderstanding the
% pages are last, and then restore the switch when the macro reaches to the
% \tpage.  This saving and temporary turning $\false$ is also done in
% \!\pcol@flushclear! when it forces a page break so that the \!\output!
% routine working on the broken non-\lpage{} correctly recognizes that.
% Another temporary turning is made by \!\pcol@makenormalcol! but in reverse
% to let the switch be $\true$ so that its indirect callee
% \!\pcol@combinefloats!  puts a vertical skip of \!\textfloatsep! below the
% bottom floats in \preenv.
% \end{macro}\end{macro}
% 
% \begin{macro}{\ifpcol@scfnote}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for page-wise footnote functions.}
% 
% The switch \!\ifpcol@scfnote! is turned $\true$ by \!\pcol@fnlayout@p!
% and \!\pcol@fnlayout@m! (through \!\pcol@fnlayout@p!) to indicate
% footnotes in all columns are merged and \scfnote, while
% \!\pcol@fnlayout@c! turns it $\false$ to make footnote typesetting
% \mcfnote{}, being default as well.  The switch is examined by the
% following macros to do special operations for \Scfnote{}s if
% it is $\true$.
% 
% \begin{itemize}
% \item
% \!\pcol@makecol! shrinks \!\@colht! and put the stretch\slash shrink
% factor of \!\skip!\!\footins! at the bottom of the \colpage{} to be built
% by the macro if the page has footnotes.  If the \colpage{} is in the
% \tpage{} $\ptop$, the macro also saves \!\footins! into \!\pcol@currfoot!
% which then will be saved into $\pp^f(\ptop)$ by \!\pcol@startpage!, or
% \!\footins! is discarded otherwise.
% 
% \item
% \!\pcol@startcolumn!, if it is invoked from \!\pcol@output! to start a
% \colpage{} in a page $p$, \!\insert!s $\pp^f(p)$ through \!\footins!, and
% also the deferred footnotes in $\df$ by \!\pcol@deferredfootins!, if
% $p=\ptop$.
% 
% \item
% \!\pcol@output@switch! saves \!\footins! into $\pp^f(\ptop)$ if the macro
% is to leave a \colpage{} in the \tpage, or discards it otherwise.
% 
% \item
% \!\pcol@restartcolumn! to restart a \colpage{} in a page $p$ \!\insert!s
% $\pp^f(p)$ through \!\footins!, and also the deferred footnotes in $\df$
% by \!\pcol@deferredfootins!, if $p=\ptop$.
% 
% \item
% \!\pcol@sync! examines whether the total height of \Scfnote{}s is too
% large to let them reside in the page to be synchronized or flushed as a
% whole.
% 
% \item
% \!\pcol@zparacol! redefines \!\footnoterule! so that it refers to
% \!\textwidth!  rather than \!\column~width! to determine the width of the
% rule above footnotes.
% 
% \item
% \!\pcol@fntext! invokes \!\pcol@fntextother! to add the footnote given to
% it to $\df$ as a deferred footnote if $p<\ptop$.
% 
% \item
% \!\pcol@fntextbody! lets \!\hsize! be \!\textwidth! rather than
% \!\columnwidth! to typeset the footnote given to it.
% \end{itemize}
% \end{macro}
% 
% \begin{macro}{\ifpcol@mgfnote}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for page-wise footnote functions.}
% 
% The switch \!\ifpcol@mgfnote! is turned $\true$ by \!\pcol@fnlayout@m!
% to indicate footnotes in the \spage{} and \lpage{} of a \env{paracol}
% environment are merged with those in pre- and \postenv{}, while
% \!\pcol@fnlayout@p! and \!\pcol@fnlayout@c! turn it $\false$ to
% put them above\slash below the columns in the starting\slash\lpage{}
% respectively, being default as well.  The switch is examined by the
% following macros to do special operations for \mgfnote{} \Scfnote{}s
% if it is $\true$.
% 
% \Index{pre-environment stuff}
% \Index{starting page}
% 
% \begin{itemize}
% \item
% \!\pcol@makenormalcol! leaves \!\footins! untouched rather than putting it
% as a part of \preenv.
% 
% \item
% \!\pcol@makeflushedpage! leaves \!\footins! untouched rather than putting it
% as a part of the \lpage{} of \env{paracol} if it works on the page.
% 
% \item
% \!\endparacol! does not let \!\pcol@flushclear! examine the existence of
% deferred footnotes in \pfcheck{} for the \lpage.
% \end{itemize}
% \end{macro}
% 
% \begingroup\let\small\footnotesize
% \begin{macro}{\ifpcol@fncounteradjustment}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for page-wise footnote functions.}
% 
% The switch \!\ifpcol@fncounteradjustment! is turned $\true$ by the API
% macro \!\fncounter~adjustment!, which is also invoked from
% \!\pcol@fnlayout@p! and \!\pcol@fnlayout@m! (through \!\pcol@fnlayout@p!),
% to let $\!\c@footnote!=\bf+\nf$ by \!\endparacol!.  The macro
% \!\nofncounter~adjustment! turns the switch $\false$ to give the default
% state.
% \end{macro}
% \endgroup
% 
% \begin{macro}{\ifpcol@inner}
% \changes{v1.22}{2013/06/30}
%	{Introduced to know if we are in a \cs{vbox}.}
% 
% The switch \cs{ifpcol@inner} is turned $\false$ by \!\pcol@zparacol! to
% mean we are outside any \!\vbox!es, while the macro also lets
% \!\everyvbox! in the \env{paracol} environment has the operation to turn
% the switch $\true$ so that it is true whenever we are in a \!\vbox!.  The
% switch is examined by \!\pcol@set@color@push! and \!\pcol@icolumncolor!,
% the former of which also turns it $\true$ if we are in restricted
% horizontal mode, to make an \!\output! request for \colorstack{}
% manipuratoin and, in the former, to reserve the stack popper by
% \!\aftergroup!, iff the switch is $\false$.
% \end{macro}
% 
% \begin{macro}{\ifpcol@firstpage}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to know if a spanning stuff is pre-environment one.}
% 
% The switch \cs{ifpcol@firstpage} is \!\global!ly turned $\true$ or
% $\false$ by \!\pcol@output@start! if it captures \preenv{} as a
% \spanning{} or not because it is too large, respectively.  Then the switch
% is examined by \!\pcol@ioutputelt! or \!\pcol@makeflushedpage! when they
% finds a \spanning{} to be combined to the page to be printed so as to
% paint the \bground{} for the color of \pwise{} floats unless the switch is
% $\true$ to mean the stuff is pre-environment one rather than floats.  Then
% \!\pcol@outputelt! or \!\pcol@makeflushedpage! itself \!\global!ly turns
% the switch $\false$ after printing a page because we no longer have
% \preenv{} in the \env{paracol} environment we are in.
% \end{macro}
% 
% \begin{macro}{\ifpcol@havelastpage}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to know if a page to be put has the last page of a
%	 \string\texttt{paracol} environment.}
% 
% The switch \cs{ifpcol@havelastpage} is, after intiailized $\false$,
% \!\global!ly turned $\true$ by \!\pcol@output@end! if it finds the
% \lpage{} of the \env{paracol} environment is connected to the \postenv, or
% $\false$ otherwise.  Then the switch is examined by (our own version of)
% \!\@outputpage! which paints the \bground{} of the page to be printed iff
% the switch is $\true$ because a part of the page was prodcued by a
% \env{paracol} environment.  Then the macro \!\global!ly turns the switch
% $\false$ because so far \bgpaint{} should be disabled.
% \end{macro}
% 
% \begin{macro}{\ifpcol@paired}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced for parallel-paging which has paired and non-paired mode.}
% 
% The switch \cs{ifpcol@paired} is $\true$ if the \parapag{}ed typesetting
% should be done in {\em\paired} mode in which the pair of left and right
% \parapag{}es comprises a virtual page, while it is $false$ if
% \npaired{} to treat the left and right pages as individual ones.
% Therefore, the switch is \!\global!ly turned $\false$ by \!\pcol@yparacol!
% when \beginparacol{} has the optional argument for the number of columns
% in the left \parapag{}e followed by |*|, or turned $\true$
% otherwise by \!\paracol! for giving default or by \!\pcol@zparacol! if it
% finds $\CL\geq\C$ to mean \parapag{}ing is not in effect
% in reality\footnote{
% 
% The initialization to let the switch $\false$ is not necessary because it
% is examined only after the first \cs{paracol} even in the
% \cs{@outputpage} outside \texttt{paracol} environment, but we dare to do
% this for the sake of clearity.}.
% 
% Then the switch is examined by \!\pcol@setpnoelt! and \!\pcol@startpage!
% so that, if the switch is $\false$, they let $\page(q)=\page(q-1)+2$ where
% $\cc_0(\vb^p)<q\leq\ptop$ in the former and $q=\ptop$ in the latter,
% instead of $\page(q)=\page(q-1)+1$ in the usual $\true$ case, because the
% left\slash right pair of \parapag{}es is treated as two pages rather than
% one.
% 
% The other macros \!\pcol@ioutputelt!, (our own version of) \!\@outputpage!,
% \!\pcol@output@start!, \!\pcol@imakeflushedpage!, \!\pcol@iflushfloats! and
% \!\pcol@output@end! also refer to the switch so that, if $\false$, they
% temporarily let $\!\c@page!=\page(p)+1$ in building the shipout image of
% the right component of the \parapag{}e pair of the page $p$ in order to
% have the appropriate page number parity for the right component.  Among
% them, \!\@outputpage! has another mode dependant operation, if the switch
% is $\true$, to decrement \!\c@page! by one before shipping out the right
% component to cancel the increment in the ship-out process of the left
% component.  The macro \!\pcol@addmarginpar! also examines the switch to
% decide the margin for marginal notes in \npaired{} \parapag{}es.  Another
% examiner \!\pcol@zparacol! lets $\CSIndex{ifpcol@swapcolumn}=\false$
% only in the \env{paracol} environment to start if the switch is $\true$
% because \cswap{} is meaningless in \npaired{} \parapag{}ing.
% \end{macro}
% 
% \begin{macro}{\ifpcol@swapcolumn}
% \changes{v1.2-4}{2013/05/11}
%	{Introduced for column-swapping in even pages.}
% \begin{macro}{\ifpcol@swapmarginpar}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced for marginal-note-swapping in even pages.}
% \begin{macro}{\ifpcol@bg@swap}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for mirrored backgournd painting for even numbered
%	 pages.}
% \begin{macro}{\ifpcol@bg@@swap}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for mirrored backgournd painting for even numbered
%	 pages.} 
% 
% The switch \cs{ifpcol@swapcolumn}, \cs{ifpcol@swapmarginpar} and
% \cs{ifpcol@bg@swap} specify that, if $\true$, columns, marginal notes,
% and \bgpaint{} in even numbered pages are swapped, respectively.
% That is, \cs{ifpcol@swapcolumn} lets columns be put from right to left,
% \cs{ifpcol@swapmarginpar} lets marginal notes go to the opposite side from
% that in odd numbered pages, and \cs{ifpcol@bg@swap} makes \bgpaint{}
% \mirror{}ed.
% 
% Besides the initial setting to let them $\false$ \!\global!ly after the
% declaration, the switches are \!\global!ly turned $\false$ by
% \!\pcol@twosided! for the cases in which API macro \!\twosided! does not
% have `|c|', `|m|' or `|b|' in its optional argument respectively, and then
% \!\global!ly turned $\true$ by $|\pcol@twosided@|{\cdot}k$
% ($k\in\{|c|,|m|,|b|\}$ )
% 
% \SpecialIndex{\pcol@twosided@c}
% \SpecialIndex{\pcol@twosided@m}
% \SpecialIndex{\pcol@twosided@b}
% 
% which is invoked when the argument contains `|c|', `|m|' or `|b|'
% respectively, or the API macro does not have the argument at
% all\footnote{
% 
% \cs{ifpcol@swapcolumn} is also turned $\true$ and $\false$ by backward
% compatible API macros \cs{swapcolumn}\~\texttt{inevenpages} and
% \cs{noswapcolumninevenpages} respectively.}.
% 
% \SpecialIndex{\swapcolumninevenpages}
% \SpecialIndex{\noswapcolumninevenpages}
% 
% The switch \CSIndex{ifpcol@swapcolumn} is also turned $\false$ by
% \!\pcol@zparacol! but locally if \npaired{} \parapag{}ing is specified
% because \cswap{} is meaningless in the environment.  Another modifier is (our
% own version of) \!\@outputpage!, but setting and examining the switch in
% this macro is also local and is to decide the ship-out order of left and
% right \parapag{}es.
% 
% Besides the local use by \!\@outputpage!, \CSIndex{ifpcol@swapcolumn} is
% then examined by the following macros to do special operations if it is
% $\true$ and we are in an even numbered page.
% 
% \begin{itemize}
% \item
% \!\pcol@swapcolumn! to reverse the order of column visiting in
% \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats!.
% 
% \item
% \!\pcol@shiftspanning! to shift a \mctext{} to the left edge of text area.
% 
% \item
% \!\pcol@bg@paint@ii! to \mirror{} the \bgpaint{} of columns and \csepgap{}s.
% \end{itemize}
% 
% On the other hand, examiners of \CSIndex{ifpcol@swapmarginpar} and
% \CSIndex{ifpcol@bg@swap} are sole for each, namely \!\pcol@addmarginpar!
% and \!\pcol@bg@paint@i! respectively.  If each switch is $\true$ and we
% are in an even numbered page, the former reverses \CSIndex{if@firstcolumn}
% from the value having been set for non-swapping case, while the latter
% \mirror{}s the \bgpaint{} of the regions excepting columns and
% \csepgap{}s.
% 
% A related switch \CSIndex{ifpcol@bg@@swap} is let be $\true$ if
% \CSIndex{ifpcol@swapcolumn} or \cs{ifpcol@bg@}\~\texttt{swap}
% 
% \CSINDEX{ifpcol@bg@swap}
% 
% is $\true$ and we are working on a even numbered page by
% \!\pcol@bg@swappage! for \mirror{}ed \bgpaint{} of columns and
% \csepgap{}s, or other regions respectively, and then examined by
% \!\pcol@bg@paintregion@i! for \mirror{}ing.
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\ifpcol@bg@painted}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to examine if a set of regions are painted.}
% 
% The switch \cs{ifpcol@bg@painted} is \!\global!ly turned $\false$ at the
% beginning of \!\pcol@bg@paint@i!, and then \!\global!ly turned $\true$ by
% \!\pcol@bg@paintregion! if it paint the region specified by its argument,
% i.e., \!\backgroundcolor! for the region is declared.  Then the switch is
% examined by \!\pcol@bg@paint@i! to combine the painted region with others,
% by (our own version of) \!\@outputpage! and \!\pcol@outputpage@r! to
% incorporate painted regions into ship-out image.
% \end{macro}
% 
% \begin{macro}{\ifpcol@bfbottom}
% \changes{v1.3-6}{2013/09/17}
%	{Introduced to know which column-wise footnotes or bottom floats
%	 are put at the bottom of a column.}
% 
% The switch \cs{ifpcol@bfbottom} is $\true$ if \!\@makecol! puts bottom
% floats at the bottom of a column as done by the macro in \LaTeX's standard
% implementation, or $\false$ otherwise and thus bottom floats can be
% followed by footnotes as done in p\LaTeX.  Since we know only p\LaTeX{} is 
% exceptional, we let the switch $\false$ iff \!\pfmtname! is defined and
% has |pLaTeX2e| in its body.  The switch is examined by
% \!\pcol@measurecolumn! to determine which footnotes or bottom floats
% determine $\DP$ if both of them exist.
% \end{macro}
% 
% \begin{macro}{\ifpcol@dfloats}
% \changes{v1.3-6}{2013/09/17}
%	{Introduced to know if the last page has deferred column-wise floats.}
% 
% The switch \cs{ifpcol@dfloats} is $\true$ iff one or more columns (in a
% \lpage) have deferred \cwise{} floats.  Therefore, it is turned
% $\false$ by \!\pcol@sync! before it invokes \!\pcol@measurecolumn! which
% turns it $\true$ when it finds a column $c$ such that
% $\cc_c(\dl)\neq\emptyset$.  Then the switch is examined by
% \!\pcol@makeflushedpage! to make a \lpage{} {\em full size}, and by
% \!\pcol@output@end! to flush these floats.
% \end{macro}
%    \begin{macrocode}
\newif\ifpcol@output \global\pcol@outputfalse
\newif\ifpcol@nospan
\newif\ifpcol@sync \pcol@syncfalse
\newif\ifpcol@sptextstart \pcol@sptextstartfalse
\newif\ifpcol@sptext \pcol@sptextfalse
\newif\ifpcol@clear \pcol@clearfalse
\newif\ifpcol@flush
\newif\ifpcol@outputflt
\newif\ifpcol@lastpage
\newif\ifpcol@lastpagesave
\newif\ifpcol@scfnote \pcol@scfnotefalse
\newif\ifpcol@mgfnote \pcol@mgfnotefalse
\newif\ifpcol@fncounteradjustment \pcol@fncounteradjustmentfalse
\newif\ifpcol@inner
\newif\ifpcol@firstpage
\newif\ifpcol@havelastpage \global\pcol@havelastpagefalse
\newif\ifpcol@paired \global\pcol@pairedtrue
\newif\ifpcol@swapcolumn \global\pcol@swapcolumnfalse
\newif\ifpcol@swapmarginpar \global\pcol@swapmarginparfalse
\newif\ifpcol@bg@swap \global\pcol@bg@swapfalse
\newif\ifpcol@bg@@swap
\newif\ifpcol@bg@painted
\newif\ifpcol@bfbottom
\def\reserved@a{pLaTeX2e}
\ifx\reserved@a\pfmtname \pcol@bfbottomfalse \else \pcol@bfbottomtrue \fi
\newif\ifpcol@dfloats
%    \end{macrocode}
% 
% 
% 
% \subsection{\cs{dimen} and \cs{skip} Registers}
% 
% The next declaration group is for six \!\dimen! and one \!\skip!
% registers.
% 
% \begin{macro}{\pcol@prevdepth}
% The \!\dimen! register \!\pcol@prevdepth! is set to the depth of the last
% item added to the main vertical list of column $c$ from which we switch to
% another column $d$, i.e., \!\prevdepth! seen in \!\pcol@invokeoutput!
% before \!\output! request.  The value of the register is then  set into
% \!\prevdepth! also by \!\pcol@invokeoutput! after \!\output! for the
% column $d$.  The value of the register is stored in $\cc_c(\pd)$ by
% \!\pcol@setcurrcol! and then restored into the register by
% \!\pcol@igetcurrcol! for the use in \!\pcol@invokeoutput! above and in
% \!\pcol@measurecolumn!, which may let the register and $\cc_c(\pd)$ have
% $\infty$ if the \colpage{} $c$ is empty.  The register is also updated by
% \!\pcol@synccolumn! for empty main vertical list case, and by
% \!\pcol@output@end!  to be set into \!\prevdepth! for the first vertical
% item of \postenv.
% \end{macro}
% 
% \begin{macro}{\pcol@colht}
% The \!\dimen! register \!\pcol@colht! has $\VPP$ being the height of the
% tallest column in the \lpage{} taking \!\textfloatsep! below bottom floats
% into account if any.  The register is initialized to be $-\!\maxdimen!$ by
% \!\pcol@sync! and then is examined and updated in \!\pcol@measurecolumn!
% to find the tallest column.  Besides the internal use of this exploration,
% its result is referred to by \!\pcol@sync! as the threshold of \pfcheck,
% and by \!\pcol@makeflushedpage! through its argument given by
% \!\pcol@output@end! to know the height of multi-column stuff in the
% \lpage{}.  The macro \!\pcol@makeflushedpage! also lets the register have
% 0 if the \lpage{} has nothing but non-\mgfnote{} \Scfnote{}.  The other
% usage of this register is in \!\pcol@freshpage! to keep the value of
% \!\@colht! of the page made by \!\flushpage! or \!\clearpage! so that it
% is given to $\!\@colroom!=\cc_c(\vb^r)$ of each column $c$ in case a
% column $c'$ s.t.\ $c'<c$ made another page for \fcolumn{}s updating
% \!\@colht!.
% \end{macro}
% 
% \begin{macro}{\pcol@textfloatsep}
% \changes{v1.0}{2011/10/10}
%	{Introduced for the bug fix of float space enlargement.}
% 
% The \!\dimen! (not \!\skip!) register \!\pcol@textfloatsep! has
% \!\maxdimen! if a \colpage{} does not have \sync{}ation points, to let top
% floats are inserted in usual way.  If it has, the register may hold the
% vertical space amount inserted after top floats in a \colpage{} instead of
% \!\textfloatsep! so that, if a column only with top floats defines the
% first \sync{}ation point, the space for floats are extended to the
% \sync{}ation point.  In this extension case, the register has the amount
% above biased by 10000\,|pt| to distinguish the case from another case with
% ordinary top floats in which the register has non-biased \!\textfloatsep!.
% In addition, if the register is less than \!\maxdimen! including a value
% equal to \!\textfloatsep!, top floats are packed in a \!\vbox! so that
% stretch\slash shrink factor of \!\floatsep!  cannot move \sync{}ation
% points.  After the default setting to be \!\maxdimen! by \!\pcol@zparacol!
% and \!\pcol@floatplacement!, the value of the register is stored in
% $\cc_c(\tf)$ by \!\pcol@setcurrcol! and then restored into the register by
% \!\pcol@igetcurrcol! for the use in \!\pcol@makecol!,
% \!\pcol@combinefloats!, \!\pcol@cflt!, \!\pcol@output@switch!,
% \!\pcol@measurecolumn!, \!\pcol@addflhd! and \!\pcol@synccolumn!.
% \end{macro}
% 
% \begin{macro}{\pcol@lrmargin}
% \changes{v1.2-5}{2013/05/11}
%	{Introduced to let \cs{linewidth} for each column has the value
%	 according to $w_c$ and the list-like environment surrounding
%	 \string\texttt{paracol} envrionment.}
% \begin{macro}{\pcol@bg@leftmargin}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% The \!\dimen! register \!\pcol@lrmargin! is let have
% $\Uidx\lrm=\!\textwidth!-\!\linewidth!$ by \!\pcol@zparacol!, so that
% \!\linewidth! for column $c$ is let have $\w_c-\lrm$ by
% \!\pcol@invokeoutput!, which also sets \!\parshape! if $\lrm>0$.
% 
% The other usage of this register is to have the left or right margin for
% \bgpaint{} in the alias \!\pcol@bg@leftmargin! for strict local use in
% \!\pcol@bg@paint@i! and its descendent macros for \bgpaint.  That is, the
% register is aliased as \!\pcol@bg@leftmargin! by \!\pcol@bg@paint@i!, let
% have left or right margin by \!\pcol@bg@swappage!, and then referred to by
% \!\pcol@bg@pageleft!.
% \end{macro}\end{macro}
% 
% \begin{macro}{\pagerim}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to specify the page rim size for backgournd coloring.}
% 
% The API \!\dimen! register \!\pagerim! has the size of {\em\Uidx\prim{}s}
% specified by users.  Since the rims are the area for which \bgpaint{}
% is inhibited, the register is used in area specification macros
% \!\pcol@bg@paperwidth!, \!\pcol@bg@paperheight!, \!\pcol@bg@pageleft!  and
% \!\pcol@bg@pagetop!, in which the register has the negative counterpart of
% the specified value set by \!\pcol@bg@paint@i!.
% \end{macro}
% 
% \begin{macro}{\pcol@topskip}
% The \!\skip! register \!\pcol@topskip! keeps the value of \!\topskip! at
% \beginparacol{} for the ordinary usage of \!\topskip! which may have 0 in
% the starting and \lpage{} temporarily.  After the initialization by
% \!\pcol@zparacol!, it is referred to by \!\pcol@getpinfo! for pages without
% \spanning{} and thus \preenv, by \!\pcol@startpage! to let \!\topskip! and
% $\pp^t(p)$ has it for non-\spage{} $p$, by \!\pcol@output@start! for the
% second page if it finds \preenv{} is too large to combine with the
% multi-column stuff, and by \!\endparacol! to recover \!\topskip! for the
% pages following the \lpage.
% \end{macro}
% 
% \begin{macro}{\belowfootnoteskip}
% \changes{v1.35-4}{2018/12/31}
% 	{Introduced to specify the additional space below the non-merged
%	 pre-environment footnotes.}
% 
% The API \!\skip! register \!\belowfootnoteskip! has the amount of the space
% added below non-merged \Preenv{} footnotes.  The register is initialized
% with the default 0\,pt, and then used in \!\pcol@output@start! to measure
% the room in the first page, and in \!\pcol@combinefootins! to add the
% space.
% \end{macro}
% 
%    \begin{macrocode}
\newdimen\pcol@prevdepth
\newdimen\pcol@colht
\newdimen\pcol@textfloatsep
\newdimen\pcol@lrmargin
\newdimen\pagerim \pagerim\z@
\newskip\pcol@topskip
\newskip\belowfootnoteskip \belowfootnoteskip\z@
%    \end{macrocode}
% 
% 
% 
% \subsection{\cs{box} Registers}
% 
% The next declaration group is for the following \!\box! registers.
% 
% \begin{macro}{\pcol@topfnotes}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for page-wise footnote functions.}
% 
% The \!\box! register \!\pcol@topfnotes! is the implementation of $\df$ to
% have the list of deferred footnotes.  The register is made void by
% \!\pcol@output@start! and then is made grown by \!\pcol@fntextother!  with
% a deferred footnote added by the macro.  The macro
% \!\pcol@deferredfootins! invoked from \!\pcol@startcolumn! and
% \!\pcol@restartcolumn!  tries to \!\insert! the contents of the register
% through \!\footins! but may keep some of trailing ones in it if the total
% height of the footnotes is too large, while \!\pcol@output@end! does the
% \!\insert!ion without height capping.  The macro \!\endparacol! with
% non-\mgfnote{} \Scfnote{} typesetting also refers to the register to pass
% it to \!\pcol@flushclear! as its argument so as to make an explicit page
% break if the register has some deferred footnotes.
% \end{macro}
% 
% \begin{macro}{\pcol@prespan}
% \changes{v1.3-1}{2013/09/17}
%	{Introduced to save pre-spanning-text stuff.}
% 
% The \!\box! register \!\pcol@prespan! keeps the \prespan{} during a
% \mctext{} is processed by \TeX{} and our own \!\output! routine.  That is, 
% the macro \!\pcol@putbackmvl! saves the contents $\cc_0(\vb^b)$ of
% the column 0 to be restarted into the register instead of putting it back
% to the main vertical list, or makes the register $\bot$ if the column has
% nothing, when the restart follows the \sync{}ation with
% $\CSIndex{ifpcol@sptextstart}=\true$.  Then the contents of the register
% is put back to the main vertical list together with the box having
% \mctext{} after its vertical size is registered in the list $\pp^s(p)$ of
% \mctext{} postions and heights, by \!\pcol@makecol! when the text sees a
% page break, or by \!\pcol@output@switch! when the text is completed.
% \end{macro}
% 
% \begin{macro}{\pcol@rightpage}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced to have the ship-out image of a right parallel-page.}
% 
% The \!\box! register \!\pcol@rightpage! is used to build (a part of) the
% ship-out image of a right \parapag{}e in it.  The macros;
% 
% \begin{quote}\raggedright
% \!\pcol@outputelt!,
% \!\pcol@ioutputelt!,
% \!\pcol@makeflushedpage!,
% \!\pcol@flushfloats!,
% \!\pcol@output@flush!, and
% \!\pcol@output@clear!
% \end{quote}
% 
% work on the register together with \!\@outputbox! for
% the left \parapag{}e to pass both of them to (our of version of)
% \!\@outputpage!.  The macro \!\pcol@output@end! also uses the register to
% paint the \bground{} of the empty counterpart of non-merged \Scfnote{}s in
% it, or to make the register $\bot$ when it have an empty \lpage{} but with
% \spanning{} of \pwise{} floats.  After closing a \env{paracol}
% environment, the contents of the register 
% will be shiped out by
% \!\@outputpage! invoked outside \env{paracol} environment when the
% \postenv{} sees a page break, or referred to by \!\pcol@output@start! as
% the \preenv{} in the right \parapag{}e.  This right \preenv{} then will be
% combined with \colpage{}s in the right \parapag{}e by \!\pcol@ioutputelt!
% or \!\pcol@imakeflushedpage! for shipping-out, or by
% the latter indirectly invoked from \!\pcol@output@end!  as the
% last\Index{last page}{} right \parapag{}e again.  Therefore the \!\setbox!
% of the register in \!\pcol@output@start!, \!\pcol@makeflushedpage!,
% \!\pcol@imakeflushedpage! and \!\pcol@output@end!  must be done
% \!\global!ly\footnote{
% 
% The \!\global! setting in \!\pcol@makeflushedpage! and
% \!\pcol@imakeflushedpage!, together with \!\@outputbox! which does not
% need \!\global! assignment, is also required by the sake of simplicity in
% its implementation, incidentally.}.
% \end{macro}
% 
% \begin{macro}{\pcol@colorstack@saved}
% \changes{v1.34}{2018/05/07}
%	{Introduced as $\mathit{\Gamma}_s$ to keep the color stack
%	 $\mathit{\Gamma}^c$ until a column-page of $c$ becomes non-empty.}
% 
% The \!\box! register \!\pcol@colorstack@saved! is $\csts$ to keep the
% \colorctext{} $\CST^c$ of column $c$ until its \ccolpage{} becomes non-empty
% to avoid that the \colpage{} only has coloring \!\special!s for
% \colorstack{} establishing and rewinding to let \!\pcol@ifempty! misjudge
% the \colpage{} is non-empty.  It is let have $\Celt^c$, if defined,
% and $\cst$ by \!\pcol@savecolorstack! invoked from \!\pcol@startcolumn!
% and \!\pcol@output@start!, and from \!\pcol@restartcolumn! through
% \!\pcol@putbackmvl! when we know or find the (re)starting \colpage{} is
% empty.  The macro \!\pcol@putbackmvl! also makes the \!\box! register
% $\bot$ when the restarting \colpage{} is not empty and thus the \colpage{}
% has had coloring \!\special!s for establishing \colorctext{} at its
% beginning.  Then the register is given to \!\pcol@restorecst! by
% \!\pcol@clearcst@unvbox! to put leading coloring \!\special!s for
% establishing of the \colpage{} when we complete it by \!\pcol@opcol!  or
% leave from it by \!\pcol@output@switch!.
% \end{macro}
% 
% \begin{macro}{\pcol@tempboxa}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to have materials temporarily for column-separatig rule
%	 drawing or background painting.}
% \changes{v1.34}{2018/05/07}
%	{Renamed from \cs{pcol@tempbox} because its relative
%	 \cs{pcol@tempboxb} is introduced.}
% \changes{v1.34}{2018/05/07}
%	{Add ussage in \cs{pcol@scancst} and \cs{pcol@iscancst}.}
% 
% The \!\box! register \!\pcol@tempboxa! is used to have stuff temporarily as
% follows.
% 
% \begin{itemize}
% \item
% The macro \!\pcol@buildcolseprule! and its callee \!\pcol@buildcselt!
% builds the \cseprule{} in the register for a page to be shipped out, while
% its contents is put into each \csepgap{} by \!\pcol@hfil!.
% 
% \item
% In (our own version of) \!\@outputpage!, the register has the \bgpaint{}
% of the (left parallel-) page,
% 
% \Index{parallel-paging}
% 
% which is inserted into the ship-out image by its callee
% \!\pcol@outputpage@l! through \!\everyvbox! and its contents
% \!\pcol@outputpage@ev!.
% 
% \item
% In \!\pcol@scancst! and its callee \!\pcol@iscancst! to scan $\CSTraw^c$,
% $\CST^c$ or $\csts$, the sequence of (un)coloring \!\special!s to be put
% into the main vertical list is build in it.
% \end{itemize}
% \end{macro}
% 
% \begin{macro}{\pcol@tempboxb}
% \changes{v1.34}{2018/05/07}
%	{Introduced to extract the top of color stack $\mathit{\Gamma}$,
%	 $\mathit{\Gamma}_r$ or $\mathit{\Gamma}_s$.}
% 
% The \!\box! register \!\pcol@tempboxb! is used in \!\pcol@iscancst!
% to extract the top (last) element of $\cst$, $\cstraw$ or $\csts$.
% \end{macro}
% 
%    \begin{macrocode}
\newbox\pcol@topfnotes
\newbox\pcol@prespan \setbox\pcol@prespan\box\voidb@x
\newbox\pcol@rightpage \global\setbox\pcol@rightpage\box\voidb@x
\newbox\pcol@colorstack@saved
\newbox\pcol@tempboxa
\newbox\pcol@tempboxb
%    \end{macrocode}
% 
% 
% 
% \subsection{\cs{insert} Register Set}
% \changes{v1.34}{2018/05/07}
%	{Add \Sec3.6 ``\cs{insert} Register Set'' for \cs{pcol@colorins}.}
% 
% The next declaration is for the following \!\insert! register set.
% 
% \begin{macro}{\pcol@colorins}
% \changes{v1.34}{2018/05/07}
%	{Introduced to present text-coloring operations to \cs{output}
%	 synchronously with column-pages.}
% 
% The register set \!\pcol@colorins! is to \!\insert! a \!\vbox! containing a
% (un)coloring \!\special! for color pushing or popping, or the definition
% of a new default color of the current column.  In order to make it sure
% that an \!\insert!ion does not affect \!\pagetotal! and is given to
% \!\output!  with |\box255| containing the corresponding coloring
% \!\special! put in the main vertical list, \!\count!\!\pcol@colorins! and
% \!\skip!\!\pcol@colorins! are let be 0, while \!\dimen!\!\pcol@colorins! is
% let be \!\maxdimen! to allow a \colpage{} to have vitually infinite number
% of \!\insert!ions.
% 
% The \!\insert!ion is done by \!\pcol@icolumncolor! for a default color
% definition, \!\pcol@set@color@push! for color pushing, and
% \!\pcol@reset@color@pop! and \!\pcol@reset@color@mpop! for color popping
% in non-math and math mode respectrively.  Then \!\insert!ed \!\vbox!es are
% packed into \!\box!\!\pcol@colorins! and is given to \!\output! as
% $\cstraw$ to be scanned by \!\pcol@clearcolorstack! to reform it as
% $\cst$, and then scanned by \!\pcol@restorecolorstack! or saved into
% $\csts=\!\pcol@colorstack@saved!$ by \!\pcol@savecolorstack!.  The
% register is also referred to by $\!\pcol@scancst!\arg{box}$ to examine if
% $\arg{box}$ is this register or \!\pcol@colorstack@saved!, and is made
% $\bot$ by \!\pcol@output@end! after the final reestablishment of the
% \colorstack.
% 
%    \begin{macrocode}
\newinsert\pcol@colorins
\count\pcol@colorins\z@ \skip\pcol@colorins\z@ \dimen\pcol@colorins\maxdimen
%    \end{macrocode}
% \end{macro}
% 
% 
% 
% \subsection{\cs{toks} Register}
% 
% The last declaration is for the following \!\toks! register.
% 
% \begin{macro}{\pcol@everyvbox}
% \changes{v1.22}{2013/06/30}
%	{Introduced to keep \cs{everyvbox} work as usual while having
%	 \cs{pcol@innertrue} in it always.}
% 
% The register \!\pcol@everyvbox! acts as \!\everyvbox! in \env{paracol}
% environments.  That is, by \!\pcol@zparacol!, \!\everyvbox! is made
% \!\let!-equal to this register so that updates and references of
% \!\everyvbox! is made to this register, while the real \!\everyvbox! is
% let have the reference to the register and |\pcol@innertrue| to make
% $\CSIndex{ifpcol@inner}=\true$ in every \!\vbox!.  Besides
% \!\pcol@zparacol!, the register is reffered to by
% \!\pcol@restoreeveryvbox! to examine if it has been \!\global!ly updated,
% i.e., its contents is not \!\pcol@dummytoken!.
% \end{macro}
% 
%    \begin{macrocode}
\newtoks\pcol@everyvbox

%    \end{macrocode}
% 
% 
% 
% \section{Logging Tools}
% \label{sec:imp-logging}
% 
% Prior to the \!\def!initions of macros to implement \textsf{paracol}'s
% functions, we define a few macros for debug logging.
% 
% \begin{macro}{\pcol@ShowBox}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \changes{v1.3-6}{2013/09/17}
%	{Change \cs{unvcopy} to \cs{copy} to make sure the argument box
%	 causes overfull if its height is positive and even if it has
%	 nothing.}
% \changes{v1.34}{2018/05/07}
%	{Add messaging {\tt (VOID)} if $\langle b\rangle\EQ\bot$,
%	 $\cs{vfuzz}\gets0$ to ensure overfull, and \cs{vskip} of 1\,{\tt
%	 pt} if $\langle b\rangle$'s height is 0 to ensure overfull too.}
% 
% The macro $\!\pcol@ShowBox!\arg{b}$ puts a logging \!\message! showing the
% height, depth and width of the \!\box! (or \!\insert!) register $b$, or
% ``|(VOID)|'' if $b=\bot$.  Then, if $b\neq\bot$, $b$'s contents is dumped
% into |.log| file making overfull intentionally by putting $b$ into
% \!\box!|0| of null height, together with \!\vskip! of 1\,|pt| if $b$'s
% height is 0, with setting $\!\vfuzz!=0$.
% \end{macro}
% 
% \KeepSpace{13}
% \begin{macro}{\pcol@LogLevel}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@iLogLevel}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Log}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Log@iii}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Log@ii}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Log@i}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Logstart}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Logstart@ii}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Logstart@i}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Logend}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Logend@ii}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Logend@i}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Logfn}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Logfn@ii}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% \begin{macro}{\pcol@Logfn@i}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for debugging page-wise footnote functions.}
% 
% The macro $\!\pcol@LogLevel!\arg{l_1}\arg{l_2}\arg{l_3}$ defines the
% detailedness of logging done by logging macros.  It invokes
% $\!\pcol@iLogLevel!\Arg{l_i}\Arg{cs}$ to let the following $|\|\arg{cs}$
% be $|\|\arg{cs}|@|\arg{l'_i}$ where $l'_i$ is the \!\romannumeral!
% representation of $l_i$.
% 
% \begin{itemize}
% \item
% $\!\pcol@Log!\arg{cs}\Arg{m}\arg{f}$ is to log the contents of the \!\insert!
% register $f$ containing footnotes which is referred to by the macro
% $\arg{cs}$ in a context shown by $m$.  The macro \!\pcol@Log@iii!
% ($l_1=3$) logs the detailed contents of $f$ by \!\pcol@ShowBox!, while
% \!\pcol@Log@ii! ($l_1=2$) just shows the height of $f$ and \!\pcol@Log@i!
% ($l_1=1$) does nothing.
% 
% \item
% $\!\pcol@Logstart!\Arg{m}$ and $\!\pcol@Logend!\Arg{m}$ put logging
% \!\message!s `$|S:|m$' and `$|E:|m$' respectively to show the beginning
% and end of a procedure in the macro whose name is at the head of $m$, if
% $l_2=2$ and thus they are \!\let!-equal to \!\pcol@Logstart@ii! and
% \!\pcol@Logend@ii!.  If $l_2=1$, \!\pcol@Logstart@i! and \!\pcol@Logend@i!
% do nothing.
% 
% \item
% $\!\pcol@Logfn!\Arg{m}$ puts a logging \!\message! $m$ whose head is the
% macro name for footnotes whose information such as the ordinal number of
% the footnote processed by the macro may be shown in $m$ as well, if
% $l_3=2$ and thus it is \!\let!-equal to \!\pcol@Logfn@ii!.  If $l_3=1$,
% \!\pcol@Logfn@i! does nothing.
% \end{itemize}
% \end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}
% 
%    \begin{macrocode}
%% Logging Tools

\def\pcol@ShowBox#1{%
  \ifvoid#1\message{(VOID)}%
  \else
    \message{(\the\ht#1+\the\dp#1)x(\the\wd#1)}%
    {\vfuzz\z@ \showboxdepth\@M \showboxbreadth\@M
     \setbox\z@\vbox to\z@{\ifdim\ht#1=\z@ \vskip1\p@\fi \copy#1}}%
  \fi}
\def\pcol@LogLevel#1#2#3{%
  \pcol@iLogLevel{#1}{pcol@Log}%
  \pcol@iLogLevel{#2}{pcol@Logstart}%
  \pcol@iLogLevel{#2}{pcol@Logend}%
  \pcol@iLogLevel{#3}{pcol@Logfn}}
\def\pcol@iLogLevel#1#2{%
  \expandafter\let\expandafter\reserved@a
    \csname #2@\romannumeral#1\endcsname
  \expandafter\let\csname #2\endcsname\reserved@a}
\def\pcol@Log@iii#1#2#3{\message{\string#1{#2%
    (\number\pcol@page:\number\pcol@currcol/\number\pcol@toppage)}}%
  \pcol@ShowBox#3\message{end\string#1}}
\def\pcol@Log@ii#1#2#3{\message{\string#1{#2%
    (\number\pcol@page:\number\pcol@currcol/\number\pcol@toppage)}=\the\ht#3}}
\def\pcol@Log@i#1#2#3{}
\def\pcol@Logstart@ii#1{\message{S\string#1}}
\def\pcol@Logend@ii#1{\message{E\string#1}}
\def\pcol@Logstart@i#1{}
\def\pcol@Logend@i#1{}
\def\pcol@Logfn@ii#1{\message{\string#1}}
\def\pcol@Logfn@i#1{}
\pcol@LogLevel111

%    \end{macrocode}
% 
% \begin{macro}{\pcol@F@write}
% \changes{v1.32-2}{2015/10/10}
%	{Introduced for debugging memory leak problems.}
% \begin{macro}{\pcol@F}
% \changes{v1.32-2}{2015/10/10}
%	{Introduced for debugging memory leak problems.}
% \begin{macro}{\pcol@FF}
% \changes{v1.32-2}{2015/10/10}
%	{Introduced for debugging memory leak problems.}
% \begin{macro}{\pcol@F@count}
% \changes{v1.32-2}{2015/10/10}
%	{Introduced for debugging memory leak problems.}
% \begin{macro}{\pcol@F@n}
% \changes{v1.32-2}{2015/10/10}
%	{Introduced for debugging memory leak problems.}
% \begin{macro}{\pcol@Fb}
% \changes{v1.32-2}{2015/10/10}
%	{Introduced for debugging memory leak problems.}
% \begin{macro}{\pcol@Fe}
% \changes{v1.32-2}{2015/10/10}
%	{Introduced for debugging memory leak problems.}
% Another debugging tool is for investigating memory leak problems.  Since
% \Paracol{} uses \!\insert! registers for various purposes, management
% operations of them especially that for proper release of them are crusial
% for the correctness of the implmentation.  A source of toughness in
% debugging {\em memory leak} caused by missing a release of a register back
% to \!\@freelist! is that the resulting shortage is revealed long after the
% leakage to make it hard to find the point of the leakage.
% 
% The set of macros is to help such debugging by logging the aquire and
% release of \!\insert! registers into a file named $\arg{job}|.fls|$
% associated with \!\pcol@F@write! where $\arg{job}$ is given by
% \!\jobname!.  After opened when \Paracol{} is loaded, the file is written by
% $\!\pcol@FF!\Arg{m_a}\Arg{m_b}$ with a line of the following form with
% text messages $m_a$ and $m_b$, where $p=\!\pcol@page!$,
% $c=\!\pcol@currcol!$, $\ptop=\!\pcol@toppage!$, $\pi=\page(p)=\!\c@page!$,
% and $n_b=\!\pcol@F@n!$ is the cardinality of \!\@deferlist! counted by
% \!\pcol@F@count!.
% 
% \begin{itemize}\item[]
% $\arg{m_a}|(|\arg{p}|:|\arg{c}|/|\arg{\ptop}|:|\arg{\pi}|)=|
% \arg{n_b}\arg{m_b}$
% \end{itemize}
% 
% The argument $\arg{m_b}$ is empty when $\!\pcol@FF!$ is invoked from
% $\!\pcol@F!\arg{m_a}$ for snapshot, while
% $\arg{m_b}=\hbox{`|<=|$\arg{n_b}$'}$ when invoked from
% $\!\pcol@Fe!\arg{m_a}$ paired by $\!\pcol@Fb!=\!\pcol@F@count!$ by which
% the cardinality of \!\@freelist! is given to $\arg{n_b}$ through
% \!\pcol@F@n! and then \!\reserved@a!.  Therefore, by the pair of
% \!\pcol@Fb! and \!\pcol@Fe!, the consumption or restitution in a series of
% operations surrounded by the pair is logged in the file.
% 
% In the production version, the logging is disabled of course by \!\let!ting
% \!\pcol@F! and \!\pcol@Fe! be \!\@gobble! and \!\pcol@F! be \!\relax!,
% while the open of \!\pcol@F@write! is disabled as well by a pair of
% \cs{iffalse} and \cs{fi}.
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
%    \begin{macrocode}
\iffalse
\newwrite\pcol@F@write
\immediate\openout\pcol@F@write\jobname.fls
\fi
\def\pcol@F#1{\pcol@FF{#1}{}}
\def\pcol@FF#1#2{\pcol@F@count
  \immediate\write\pcol@F@write{#1(\number\pcol@page:\number\pcol@currcol/%
    \number\pcol@toppage:\number\c@page)=\pcol@F@n #2}}
\def\pcol@F@count{{\@tempcnta\z@
    \def\@elt##1{\advance\@tempcnta\@ne}\@freelist
    \xdef\pcol@F@n{\number\@tempcnta}}}
\let\pcol@Fb\pcol@F@count
\def\pcol@Fe#1{{\let\reserved@a\pcol@F@n \pcol@FF{#1}{<=\reserved@a}}}
\let\pcol@F\@gobble
\let\pcol@Fb\relax
\let\pcol@Fe\@gobble

%    \end{macrocode}
% 
% 
% 
% \section{\cs{output} Routine}
% \label{sec:imp-output}
% 
% \begin{macro}{\pcol@ovf}
% Before giving the definitions of macros in \!\output! routine, we define
% the macro \!\pcol@ovf! invoked if \!\@freelist! is empty on an acquision
% of an \!\insert! by \!\@next! and thus we have to abort the execution by
% \!\PackageError! with a message notifying the shortage.  The additional
% help message is \!\@ehb! as in \!\@fltovf!.  This macro is used in
% \!\pcol@opcol!, \!\pcol@startpage!, \!\pcol@output@start!,
% \!\pcol@output@switch!, \!\pcol@iscancst!, \!\pcol@savefootins!,
% \!\pcol@flushcolumn!, \!\pcol@synccolumn!, \!\pcol@output@end! and
% \!\pcol@icolumncolor!.
% \end{macro}
% 
%    \begin{macrocode}
%% \output Routine

\def\pcol@ovf{%
  \PackageError{paracol}{Too many unprocessed columns/floats}\@ehb}

%    \end{macrocode}
% 
% \begin{macro}{\pcol@output}
% \changes{v1.2-2}{2013/05/11}
%	{Add \cs{pcol@Logstart} and \cs{pcol@Logend}.}
% \changes{v1.2-7}{2013/05/11}
%	{Add the examination of \cs{ifpcol@output} and \protect\LaTeX's
%	 original sequence for \cs{output} request sneaked from outside of
%	 \texttt{paracol} environment.}
% \changes{v1.2-7}{2013/05/11}
%	{Add the assignment of \cs{@maxdepth} to \cs{maxdepth} to nullify
%	 the temproary setting done by \cs{@addtobot}.}
% \changes{v1.33-2}{2016/11/19}
% 	{Add a space after \cs{@opcol} to obey the coding convention.}
% 
% The macro \!\pcol@output! is the \Paracol's version of \!\output! which
% is let have this macro as its sole token by \!\pcol@zparacol!.  The
% structure of this macro is same as that of \LaTeX's \!\output! but the
% following replacements are made\footnote{.
% 
% Besides the logging with \cs{pcol@Logstart} and \cs{pcol@Logend}.}.
% 
% \begin{itemize}
% \item
% $\!\@specialoutput!\to\!\pcol@specialoutput!$ to process \LaTeX's genuine
% functions including the customized marginal note placement, and \Paracol's
% own special output functions; starting first page, \colorctext{} management,
% \cswitch, page flushing with\slash without float flusing, and building the
% multi-column part of the \lpage.
% 
% \item
% \changes{v1.0}{2011/10/10}
%	{Replace \cs{@makecol} with \cs{pcol@makecol} for a special care for
% 	 column-pages with synchronization points.}
% 
% $\!\@makecol!\to\!\pcol@makecol!$ for a special care for \ccolpage{} having
% \sync{}ation point and/or \Scfnote{}s.
% 
% \item
% $\!\@opcol!\to\!\pcol@opcol!$ to hold the \ccolpage{} which just has
% completed.
% 
% \item
% \changes{v1.2-2}{2013/05/11}
%	{Add an argument \cs{@ne} to \cs{pcol@startcolumn} to distinguish it
%	 from the invocation in \cs{pcol@freshpage}.}
% 
% $\!\@startcolumn!\to\!\pcol@startcolumn!$ to creat a new \colpage{}.  The
% argument \!\@ne! is to distinguish the invocation in this macro from
% that in \!\pcol@freshpage! so that the \!\insert!ions of $\pp^f(p)$ and
% $\df$ are done only when a new \colpage{} is created with ordinary page
% break.
% \end{itemize}
% 
% \changes{v1.22}{2013/06/30}
%	{Add reset of \cs{set@color}.}
% \changes{v1.24}{2013/07/27}
%	{Add zero-clear of \cs{pcol@mcid}.}
% \changes{v1.3-1}{2013/09/17}
%	{Add $\cs{ifpcol@sptextstart}\EQ\string\mathit{false}$ to the
%	 condition for the warning of too small \cs{vsize}.}
% 
% In addition, before we start the main body of \!\output! routine, we add
% two operations for coloring.  One is to make
% \!\set@color! \!\let!-equal to \!\pcol@set@color!, i.e, to let it regain
% its original definition throughout \!\output! routine, because
% no manipulation of \colorstack{} is necessary\footnote{
% 
% Though this operation is not necessary because \cs{everyvbox} should work
% for any \cs{set@color} because they should be in a \cs{vbox}, we dare to
% do it for clearity.}.
% 
% The other is to zero-clear the counter \!\pcol@mcid! because we are
% definitely in the main (non-internal) vertical mode and thus all push/pop
% pairs of the coloring in math mode have been processed.
% 
% Further, before we start the sequence for non-special \!\output!  request
% on page breaks, we examine if $\CSIndex{ifpcol@output}=\true$ to mean
% \!\pcol@output@start! has already been invoked in order to cope with
% \!\output! request {\em sneaking}.  This sneaking happens when
% \beginparacol{} is at a crtical position of page breaking at which the
% \preenv{} has already exceeds \!\vsize! but \TeX{} cannot make the
% \!\output! request for the page break at \CSIndex{par} at the beginning of
% \!\pcol@zparacol! because it sees $\!\penalty!=10000$ due to, e.g., a
% sectioning command just preceding \beginparacol.  In this case, the
% request is postponed until \TeX{} see a \!\penalty! less than 10000 and
% thus it is made with some non-special \!\outputpenalty! greather than
% $-10000$ when \TeX{} sees the dummy request of $\!\penalty!=-10004$ in
% \!\pcol@invokeoutput! for \!\pcol@output@start!.  At this timing,
% \!\pcol@zparacol! has already let \!\output! have \!\pcol@output! of
% course but the request must be processed by original \!\output! because it
% is made {\em outside} of the \env{paracol} environment which has just
% started.  Therefore, if $\CSIndex{ifpcol@output}=\false$, we have to
% perform the operation sequence as the original \!\output! does.
% Furthermore, we have to take care of the fact that a few our own settings
% related to \!\output!  routine has already been made in \!\pcol@zparacol!,
% namely $\CSIndex{if@twocolumn}=\true$ and
% $\!\@combinefloats!=\!\pcol@combinefloats!$, which should make the macros
% in the original sequnce confused especially by the former.  Therefore, we
% turns $\CSIndex{if@twocolumn}=\false$ and let \!\@combinefloats! have the
% original definition kept in \!\pcol@@combinefloats!\footnote{
% 
% Though we know \cs{pcol@combinefloats} acts exactly as \cs{@combinefloats}
% because \cs{pcol@zparacol} initializes $\cs{pcol@textfloatsep}=\infty$ and
% $\cs{ifpcol@lastpage}=\false$.  On the other hand, we don't cancel the
% re\cs{def}itnition of \cs{footnoterule} because it should be
% $\cs{textwidth}=\cs{columnwidth}$ outside of \env{paracol} environments.}
% 
% temporarily, i.e., only in the group automatically surrounding the
% invocation of \!\output!.
% 
% Another addition is to assign \!\@maxdepth! to \!\maxdepth! in order to
% nullify the temporary setting to 0 done in \!\@addtobot!.  By this
% assignment, in \env{paracol} environments \TeX's page builder always
% refers to the value in \!\@maxdepth!.  Yet another addition is to add
% $\CSIndex{ifpcol@sptextstart}=\false$ to the condition for the warning of
% too short \!\vsize!, because a \mctext{} can start near the bottom of a
% page with a small \!\@colroom! less than $1.5\times\!\baselineskip!$ and
% thus the warning is unnecessary and inappropriate when
% $\CSIndex{ifpcol@sptextstart}=\true$.
% 
%    \begin{macrocode}
\def\pcol@output{\let\par\@@par \let\set@color\pcol@set@color
  \global\pcol@mcid\z@
  \pcol@Logstart{\pcol@output\number\outputpenalty
    (\number\c@page:\number\pcol@currcol)}%
  \ifnum\outputpenalty<-\@M
    \pcol@specialoutput
  \else\ifpcol@output
    \pcol@makecol
    \pcol@opcol
    \pcol@startcolumn\@ne
    \@whilesw\if@fcolmade\fi{\pcol@opcol \pcol@startcolumn\@ne}%
  \else
    \@twocolumnfalse \let\@combinefloats\pcol@@combinefloats
    \@makecol
    \@opcol
    \@startcolumn
    \@whilesw\if@fcolmade\fi{\@opcol \@startcolumn}%
  \fi\fi
  \global\maxdepth\@maxdepth
  \ifnum\outputpenalty>-\@Miv
    \ifdim\@colroom<1.5\baselineskip
      \ifdim\@colroom<\textheight
        \ifpcol@sptextstart
          \global\vsize\@colroom
        \else
          \@latex@warning@no@line{Text page \thepage\space
                                  contains only floats}%
          \@emptycol
        \fi
      \else
        \global\vsize\@colroom
      \fi
    \else
      \global\vsize\@colroom
    \fi
  \else
    \global\vsize\maxdimen
  \fi
  \pcol@Logend\pcol@output}

%    \end{macrocode}
% \end{macro}
% 
% 
% 
% \section{Completing Column-Page}
% \label{sec:imp-opcol}
% 
% \begin{macro}{\pcol@@makecol}
% \changes{v1.2-7}{2013/05/11}
%	{Introduced to cope with the careless implementaion of \cs{@makecol}
%	 in p\string\LaTeX.}
% \changes{v1.3-6}{2013/09/17}
%	{Add an argument $d$ to be assigned to \cs{boxmaxdepth} to let it
%	 have 0 rather than \cs{@maxdepth} for last page.}
% 
% The macro $\!\pcol@@makecol!\<d\>$ is used in \!\pcol@flushcolumn! and
% \!\pcol@imakeflushedpage! which simply require \LaTeX's original
% \!\@makecol! to build the ship-out image of a \colpage.  The reason why we
% need our own version is that a variation of \LaTeX, namely p\LaTeX{} for
% Japanese, carelessly implements its own \!\@makecol! to make the resulting
% \!\@outputbox! has a depth larger than \!\@maxdepth! if the \colpage{} has
% \Mcfnote{}s whose last line is unusually deep.  To cope with the problem,
% this macro at first invokes \!\@makecol!, and then reshape \!\@outputbox!
% assigning $d=\!\@maxdepth!$ to \!\boxmaxdepth! to cap its depth, unless
% this macro is used for the \lpage{} with $d=0$ because depth of the last
% component of the \!\@outputbox! is incorporated in \!\@colht!.
% 
%    \begin{macrocode}
%% Completing Column-Page

\def\pcol@@makecol#1{\@makecol
  \setbox\@outputbox\vbox to\@colht{\boxmaxdepth#1\unvbox\@outputbox}}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@makecol}
% \changes{v1.0}{2011/10/10}
%	{Introduced for special float handling in a column-page with
%	 synchronization points.}
% \changes{v1.2-2}{2013/05/11}
%	{Add save/discard of page-wise footnotes.}
% \changes{v1.2-7}{2013/05/11}
%	{Remove unnecessary check of \cs{ifpcol@lastpage} on the
%	 redefinition of \cs{@textbottom}.}
% \changes{v1.3-1}{2013/09/17}
%	{Add a function to capture a broken spanning text, to combine it
%	 with pre-spanning-text stuff, and to shift it left on
%	 column-swapping.}
% \changes{v1.3-3}{2013/09/17}
%	{Add the addition of the element to $\pi^s(p)$ for a broken
%	 spanning text.}
% \changes{v1.3-4}{2013/09/17}
%	{Add $\pi^m(p)\EQ\cs{pcol@mparbottom}$ to the argument of
%	 \cs{pcol@defcurrpage}.}
% \changes{v1.3-3}{2013/09/17}
%	{Add \cs{@colht} and \cs{relax} as the first and third argument of
%	 \cs{pcol@shrinkcolbyfn}.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% \changes{v1.33-2}{2016/11/19}
% 	{Move down the \cs{def}inition of \cs{pcol@currfoot} with $\bot$ to
%	 place it just before the \cs{ifpcol@scfnote}/\cs{fi} construct to
%	 make it clear how \cs{pcol@currfoot} is \cs{def}ined.}
% 
% The macro \!\pcol@makecol! is invoked solely from \!\pcol@output! to build
% the shipping image of the \ccolpage{} which just has completed in
% \!\@outputbox!.  This macro has two additional functions to its original
% version \!\@makecol!\footnote{
% 
% Not \cs{pcol@@makecol} because the depth capping of \cs{@outputbox} is
% done by \cs{pcol@opcol} when it saves the box into $\cc_c(\vb^b)$.}
% 
% invoked in this macro.
% 
% First, if $\cc_c(\tf)\neq\infty$ to mean the \colpage{} has \sync{}ation
% points, \!\@makecol! is invoked with a special \!\def!inition of
% \!\@textbottom! to put a vertical skip having $1/10000\,|fil|$ as its
% stretch and shrink.  This modification is to nullify not only finite
% stretches (as \!\raggedbottom! does) but also finite shrinks possibly
% inserted just below the last \sync{}ation point to move up the first
% visible item upward a little bit if active.  Therefore, \!\flushbottom!
% setting is nullified for \colpage{}s having \sync{}ation points and a
% small exceess from the bottom of a \colpage{} cannot be absorbed by
% shrinks but visible at the bottom\footnote{
% 
% That is, the author gives higher priority to the perfect alignment of the
% items following a \sync{}ation point.}.
% 
% Note that the original definition of \!\@textbottom! is saved in
% \Midx{\!\pcol@textbottom!} before the invocation of \!\@makecol! and is
% restored after that\footnote{
% 
% This save/restore cannot be done by a grouping because \!\@makecol! builds
% \!\@outputbox! by local assignments.}.
% 
% Second, if $\CSIndex{pcol@sptext}=\true$ and $c=0$ to mean a \mctext{}
% encounters a page break, we have the first half (or second or succeeding
% part if the text lays across three or more pages) of the text in
% \!\box!|255|.  Therefore, we add an element $\spt(H_n,h_n)$ to the tail of
% the list of \mctext{}s $\pp^s(\ptop)=\!\pcol@sptextlist!$, where $H_n$ is
% the height of \prespan{} in \!\pcol@prespan!\footnote{
% 
% Since we have a \sync{}ation point before a \mctext{} always, \prespan{}
% or its sole contents \cs{vbox} has a vertical skip at its tail to make the
% its depth 0 as discussed in \secref{sec:imp-sout-sync}.}
% 
% plus the total height of top floats calculated by \!\pcol@addflhd! with
% $\cc_c(\tl)=\!\@toplist!$, and $h_n$ is the height-plus-depth of
% \!\box!|255|.  Note that $H_n$ and $h_n$ are represented in the form of
% integer and thus we produce them by expansions with \!\number!.
% 
% The addition, however, is not made if $h_n=0$ because painting its
% \bground{} is harmful if an extension is specified to make the region
% visible, while not painting or drawing a segment of \cseprule{} is very
% natural.  Note that this $h_n=0$ case includes that in which \!\box!|255|
% has nothing but its height-plus-depth is non-zero because of discarding
% leading skips of the \mctext{} as pre-break skips.  This special case is
% detected by decapsulating \!\box!|255| by \!\unvcopy!  and examining the
% height-plus-depth of the result\footnote{
% 
% We cannot do
% \cs{setbox}\cs{@cclv}\cs{vbox}\texttt{\Arg{\cs{unvbox}\cs{@cclv}}}
% because it erases the effect of pre-break skip following some visible
% material.}.
% 
% Also note that the list to be added is always for the \tpage{}, i.e.,
% $\pp^s(\ptop)$ and thus we get and update it by \!\pcol@getcurrpinfo! and
% \!\pcol@defcurrpage!, because the \mctext{} immediately follows a
% \sync{}ation point in $\ptop$.  Then we let \!\box!|255| have the
% \prespan{} followed by the \mctext{} being the original contents of
% \!\box!|255|, which may be shifted left by
% $\WT-w_c=\!\textwidth!-\!\columnwidth!$ by the macro
% \!\pcol@shiftspanning! if \cswap{} is in effect so that its left edge is
% aligned to that of the leftmost column, i.e., of the text area.
% 
% The third addition is for \Scfnote{}s.  If they are presented in
% \!\footins!, we shrink \!\@colht! by its height plus depth
% by \!\pcol@shrinkcolbyfn! and put the stretch and shrink factor of
% \!\skip!\!\footins! at the bottom of \!\box!|255| by \!\pcol@unvbox@cclv!
% to {\em remove} footnotes from the \colpage{} but keeping the
% stretch\slash shrink contribution to the page breaking by their existence.
% Then we save \!\footins! into a new \!\insert! to be referred to as
% \!\pcol@currfoot!\footnote{
% 
% Not in \cs{pcol@footins} because it is destroyed in \cs{pcol@startpage}
% just before saving operation into $\pp^f(p)$.}
% 
% by \!\pcol@savefootins! if $p=\ptop$ so that it is saved in $\pp^f(p)$ by
% \!\pcol@startpage! afterward, or simply discard the contents of
% \!\footins! otherwise because $\pp^f(p)$ has already been fixed.  Note
% that these saving\slash discarding make \!\footins! void and thus
% \!\@makecol! will not put footnotes.
% 
% On the other hand, if footnote typesetting is \mcfnote{}, \!\footins! is
% kept unchanged so that its contents will be put by \!\@makecol! if it has
% something.  As for \!\pcol@currfoot!, it should have its default value
% $\!\voidb@x!=\bot$ assigned to it beforehand, so that, if $p=\ptop$,
% \!\pcol@startpage! will make $\pp^f(p)=\bot$ unless \Scfnote{s} are given
% in \!\footins!.
% 
%    \begin{macrocode}
\def\pcol@makecol{\let\pcol@textbottom\@textbottom
  \ifdim\pcol@textfloatsep=\maxdimen\else
    \def\@textbottom{\vskip\z@\@plus.0001fil\@minus.0001fil}\fi
  \ifpcol@sptext \ifnum\pcol@currcol=\z@
    \pcol@getcurrpinfo\@tempcnta\@tempdima\@tempskipa
    \setbox\@tempboxa\vbox{\unvcopy\@cclv}%
    \@tempdimb\ht\@tempboxa \advance\@tempdimb\dp\@tempboxa
    \ifdim\@tempdimb>\z@
      \@tempdimb\ht\@cclv \advance\@tempdimb\dp\@cclv
      \dimen@\ht\pcol@prespan \pcol@addflhd\@toplist\pcol@textfloatsep
      \@cons\pcol@sptextlist{{\number\dimen@}{\number\@tempdimb}}%
    \fi
    \pcol@defcurrpage{\number\@tempcnta}\pcol@spanning\pcol@footins
                     {\pcol@sptextlist}{\pcol@mparbottom}%
    \setbox\@cclv\vbox{\unvbox\pcol@prespan \pcol@shiftspanning\@cclv
                       \unvbox\@cclv}%
  \fi\fi
  \def\pcol@currfoot{\voidb@x}%
  \ifpcol@scfnote \ifvoid\footins\else
    \pcol@shrinkcolbyfn\@colht\footins\relax
    \setbox\@cclv\vbox{\pcol@unvbox@cclv\footins}%
    \ifnum\pcol@page=\pcol@toppage
      \pcol@Log\pcol@makecol{save}\footins
      \pcol@Fb
      \pcol@savefootins\pcol@currfoot
      \pcol@Fe{makecol(pagefn)}%
    \else
      \pcol@Log\pcol@makecol{discard}\footins
      \setbox\@tempboxa\box\footins
    \fi
  \fi\fi
  \pcol@Logstart\pcol@makecol
  \ifvoid\footins\else \pcol@Log\@makecol{put}\footins \fi
  \@makecol
  \pcol@Logend\pcol@makecol
  \let\@textbottom\pcol@textbottom}
%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\@combinefloats}
% \begin{macro}{\pcol@combinefloats}
% \changes{v1.0}{2011/10/10}
%	{Introduced for special float handling in a column-page with
%	 synchronization points.}
% \changes{v1.2-2}{2013/05/11}
%	{Remove the shrink of \cs{textfloatsep} because each column in the last
%	 page is now made not taller than \cs{@colht} definitely by the
%	 introduction of the pre-flushing column height check.}
% \changes{v1.2-7}{2013/05/11}
%	{Add the assignment of \cs{@maxdepth} to \cs{maxdepth} to nullify
%	 the temproary setting done by \cs{@addtobot}.}
% \changes{v1.3-6}{2013/09/17}
%	{Add special operations for columns having synchronization point to
%	 move the infinite stretch and shrink to let it follow bottom floats
%	 ratehr than preceding them.}
% \begin{macro}{\pcol@@combinefloats}
% \changes{v1.2-7}{2013/05/11}
%	{Introduced to solve the \cs{output} request sneaking.}
% 
% The macro \!\pcol@combinefloats! being our own version of \!\@combinefloats!
% is used in \LaTeX's \!\@makecol! because the original and our
% own are made \!\let!-equal by \!\pcol@zparacol!, and also used in
% \!\pcol@makenormalcol!  explicitly.  The customization is twofold for both
% of top and bottom floats.
% 
% For the top floats, we invoke the original \!\@cflt! if
% $\cc_c(\tf)=\infty$ to mean the \colpage{} to be shipped out does not have
% \sync{}ation points, or otherwise our own \!\pcol@cflt! which we will
% discuss shortly.  Prior to the invocation of \!\@cflt!, in addition, we
% let $\!\maxdepth!=\!\@maxdepth!$ so that the macro refers to the value used
% throughout a \env{paracol} environment instead of that modified by
% \!\@addtobot! possibly affect the work in \!\@cflt! by the following
% sequence.
% 
% \begin{eqnarray*}
% \!\pcol@flushcolumn!(c)&\to&\!\pcol@trynextcolumn!\to\cdots\to\!\@addtobot!\\
% &\to&\!\pcol@flushcolumn!(c{+}k)\to\!\pcol@@makecol!\to\!\@makecol!\\
% &\to&\!\pcol@combinefloats!\to\!\@cflt!
% \end{eqnarray*}
%
% For the bottom floats, we invoke the original \!\@cflb! always but, if
% the \colpage{} has \sync{}ation points, we insert vertical skips of
% $s=0\,|pt|\ |plus|\ 0.0001\,|fil|\ |minus|\ 0.0001\,|fil|$ and $-s$ before
% and after the invocation respectively.  Since \!\@textbottom! is let have
% the skip of $s$ by \!\pcol@makecol! for a \colpage{} having \sync{}ation
% points and is inserted below bottom floats by \!\@makecol!\footnote{
% 
% The insertion point is common to \LaTeX{} and p\LaTeX{}.},
% 
% the effect of \!\@textbottom! is canceled by the skip of $-s$ but looks
% moved above bottom floats.  Therefore, if the natural height of the
% \colpage{} is smaller than \!\@colht!, bottom floats are flushed to the
% page bottom as if \colpage{} itself is flushed by \!\newpage! etc.  On the
% other hand, if the natural height is larger, more importantly, all shrinks
% below the last \sync{}ation point is canceled by the infinite shrink in
% $s$ above the bottom float but we should have sufficient space for shrinks
% there thanks to \!\textfloatsep! to avoid the interference between the
% bottom text and bottom floats.
% 
% In addition, if $\CSIndex{ifpcol@lastpage}=\true$ to mean the \colpage{} is
% in the \lpage{}, we insert \!\textfloatsep! in \!\@outputbox! below the
% bottom floats so that they are well separated from \postenv.  The switch
% is also $\true$ in the invocation from \!\pcol@makenormalcol! for
% \preenv{}, so that the bottom floats in it are well separated from the top
% of multi-column stuff in the \spage.
% 
% On the other hand, the original \!\@combinefloats! saved in
% \!\pcol@@combinefloats! by \!\pcol@zparacol! is used in \!\pcol@output! to
% restore the original when it finds \!\output! request sneaking.
% 
%    \begin{macrocode}
\def\pcol@combinefloats{%
  \global\maxdepth\@maxdepth
  \ifx\@toplist\@empty\else
    \ifdim\pcol@textfloatsep=\maxdimen \@cflt \else \pcol@cflt \fi
  \fi
  \ifx\@botlist\@empty\else
    \ifdim\pcol@textfloatsep=\maxdimen \@cflb
    \else
      \setbox\@outputbox\vbox{\unvbox\@outputbox
        \vskip\z@\@plus.0001fil\@minus.0001fil}%
      \@cflb
      \setbox\@outputbox\vbox{\unvbox\@outputbox
        \vskip\z@\@plus-.0001fil\@minus-.0001fil}%
    \fi
    \ifpcol@lastpage
      \setbox\@outputbox\vbox{\box\@outputbox \vskip\textfloatsep}%
    \fi
  \fi}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@cflt}
% \changes{v1.0}{2011/10/10}
%	{Introduced for special float handling in a column-page with
%	 synchronization points.}
% \changes{v1.2-7}{2013/05/11}
%	{Replace \cs{maxdepth} with \cs{@maxdepth}.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% \changes{v1.33-2}{2016/11/19}
% 	{Add {\tt\%} to the end of the line to open \cs{vbox} for
%	 \cs{@outputbox} to obey the coding convention.}
% 
% The macro \!\pcol@cflt! is invoked solely from \!\pcol@combinefloats! if
% the \colpage{} for which the macro combines the top floats has
% \sync{}ation points.  The macro has the same structure as \LaTeX's version
% \!\@cflt! but has three modifications.  The first one is that the floats
% are packed in a \!\vbox! rather than listed in \!\@outputbox! to nullify
% the stretch and shrink of \!\floatsep! to keep the \sync{}ation point from
% moving by them\footnote{
% 
% Maybe unnecessary because of \!\@textbottom! inserted by \!\pcol@makecol!
% but \ldots}.
% 
% The second is that we use \!\@maxdepth! instead of \!\maxdepth! to make it
% clear we always use the value common throughout a \env{paracol}
% environment.  The third is that the \!\textfloatsep! is replaced with
% $\!\pcol@textfloatsep!=\cc_c(\tf)$ (definitely finite) which can have a
% value different from \!\textfloatsep! when the float space is enlarged for
% \sync{}ation.  If this enlargement is required, $\cc_c(\tf)$ is biased by
% 10000\,|pt| and thus is assuredly\footnote{
% 
% Though not definitely in theoretical sense.}
% 
% larger than 5000\,|pt|.  If so, the insertion of \!\topfigrule! should be
% inhibited because it has already been inserted by \!\pcol@synccolumn! or
% there are no real floats but we only have the float for main vertical list
% prior to the \sync{}ation point, or {\em\Uidx\mvlfloat} in short.
% 
%    \begin{macrocode}
\def\pcol@cflt{%
  \let\@elt\@comflelt
  \setbox\@tempboxa\vbox{}%
  \@toplist
  \setbox\@outputbox\vbox{%
    \boxmaxdepth\@maxdepth
    \box\@tempboxa
    \vskip-\floatsep
    \ifdim\pcol@textfloatsep>5000\p@
      \advance\pcol@textfloatsep-\@M\p@
    \else
      \topfigrule
    \fi
    \vskip\pcol@textfloatsep
    \unvbox\@outputbox}%
  \let\@elt\relax
  \pcol@Fb
  \xdef\@freelist{\@freelist\@toplist}%
  \pcol@Fe{cflt}%
  \global\let\@toplist\@empty}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@opcol}
% \changes{v1.0}{2011/10/10}
%	{Remove unnecessary assignment of \cs{@colht}.}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{pcol@maxpage} as \cs{pcol@toppage}.}
% \changes{v1.2-1}{2013/05/11}
%	{Add \cs{pcol@clearcst@unvbox} to add coloring \cs{special}s at the
%	 top and bottom of the column-page to be shipped out, together with
%	 the setting $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping.}
% \changes{v1.3-2}{2013/09/17}
%	{Rename \cs{pcol@outputpage} as \cs{pcol@outputcolumns}.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% \changes{v1.33-2}{2016/11/19}
% 	{Add {\tt\%} to the end of the line to open \cs{vbox} for
%	 \cs{@currbox} to obey the coding convention.}
% 
% The macro \!\pcol@opcol! is invoked from \!\pcol@output! for the ordinary
% completed \colpage{} built by \!\pcol@makecol!, or from the loop creating
% \fcolumn{}s in \!\pcol@output! or \!\pcol@freshpage!.  At first it
% saves the \colpage{} of column $c$ in \!\@outputbox!, which
% \!\pcol@makecol! or \!\@tryfcolumn! just has built for an ordinary or
% \fcolumn{} respectively, in an \!\insert! acquired from \!\@freelist! by
% \!\@next!, and then adds it to the tail of $\S_c=|\pcol@shipped|{\cdot}c$
% 
% \SpecialArrayIndex{c}{\pcol@shipped}
% 
% by \!\@cons!.  In this saving operation, we add the sequence of uncoloring
% \!\special!s at the bottom to clear \colorstack{} by
% \!\pcol@clearcst@unvbox! giving it \!\@outputbox! to be \!\unvbox!ed and
% possibly coloring \!\special!s for the \colpage{}'s \colorctext{} saved in
% $\csts$ at the top, so that the succeeding \colpage{} in printing order
% starts with its own \colorctext.  For this addition, furthermore, we let
% $\!\boxmaxdepth!=\!\@maxdepth!$ to keep the depth capping made in the box
% builder from nullified\footnote{
% 
% Or to apply the capping dropped from p\LaTeX's \cs{@makecol}, or to do
% nothing for the box made by \cs{@tryfcolumn} and thus being 0 deep.}.
% 
% Then if $c=0$, we fix the page number of the page $p$ having the
% \colpage{} and let $\pp^p(q)$ have $\page(p)+(q-p)$ usually but possibly
% $\page(p)+2(q-p)$ with \npaired{} \parapag{}ing, for all
% $q\in[p{+1},\ptop]$ by \!\pcol@setpageno!.  After that, we invoke
% \!\pcol@nextpage! to let $p=p'$ for the next \colpage{} of $c$, where
% $p'=p+1$ usually but can be $p+k+1$ if we have consecutive $k$ \fpage{}s
% from $p+1$.
% 
% Next, we check if the oldest page $\pbase$ is made ready to be shipped out
% by the participation of the completed \colpage{} by \!\pcol@checkshipped!.
% If so, we invoke \!\pcol@outputcolumns! giving argument 0 to ship out
% $\pbase$ and its successor \fpage{}s.
% 
% Finally we set up the next page $p$ by \!\pcol@startpage! if $p>\ptop$
% meaning it is new one, or by \!\pcol@getcurrpage! otherwise, and
% reinitialize parameters for floats by \!\pcol@floatplacement! before
% returning to the invoker.
% 
%    \begin{macrocode}
\def\pcol@opcol{%
  \pcol@Fb
  \@next\@currbox\@freelist{\global\setbox\@currbox\vbox to\@colht{%
      \boxmaxdepth\@maxdepth
      \pcol@clearcst@unvbox\@outputbox}}\pcol@ovf
  \pcol@Fe{opcol}%
  \expandafter\@cons\csname pcol@shipped\number\pcol@currcol\endcsname\@currbox
  \ifnum\pcol@currcol=\z@ \pcol@setpageno \fi
  \pcol@nextpage
  \pcol@checkshipped
  \if@tempswa \pcol@outputcolumns\z@ \fi
  \ifnum\pcol@page>\pcol@toppage \pcol@startpage
  \else                          \pcol@getcurrpage
  \fi
  \pcol@floatplacement}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@setpageno}
% \changes{v1.33-2}{2016/11/19}
% 	{Add \cs{let}\cs{@elt}\cs{relax} before \cs{edef} of \cs{reserved@a}
%	 for the sake of clarity.}
% \begin{macro}{\pcol@setpnoelt}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{ifpcol@textonly} as \cs{ifpcol@nospan}.}
% \changes{v1.2-2}{2013/05/11}
%	{Completely recode reflecting the redesign of page context.}
% \changes{v1.3-2}{2013/09/17}
%	{Add an operation to increment $\string\mathit{page}(p)$ by two for
%	 non-paired parallel-paging.}
% \changes{v1.3-3}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^s(p)$, and add a
%	 invoker \cs{pcol@makecol}.}
% \changes{v1.3-4}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^m(p)$.}
% 
% The macro \!\pcol@setpageno! is invoked from \!\pcol@opcol! when it
% proceeses the \colpage{} of the first column $c=0$ to fix the page number
% $\page(p)\gets\counter{page}=\!\c@page!$ of the page $p=\!\pcol@page!$
% having the \colpage{}.  It is also invoked from \!\pcol@output@switch!
% when it leaves from the first column to reflect a jump of \counter{page}
% made in the column building.  In both cases, the macro lets $\pp^p(q)$
% have $\page'(q)=\page(p)+(q-p)$, except for the case of \npaired{}
% \parapag{}ing in which $\page'(q)=\page(p)+2(q-p)$ instead, for all
% $q\in[p,\ptop]$.
% 
% Since we possibly have to update $\pp(q)$ such that $q\geq p$, at first we
% temporarily let
% $\Uidx\PPP=(\PP,\pp(\ptop))=\!\pcol@pages!\!\pcol@currpage!$ empty
% after copying its original value into $\mathit{\Pi}'=\!\reserved@a!$.
% Then we scan $\pi'(q)\in\mathit{\Pi}'$ for all $q\in[\pbase,\ptop]$ by
% applying \!\pcol@setpnoelt! to each $\pi'(q)$ giving its five components
% to the macro, so that the macro updates $\pp(q)$ by \!\pcol@defcurrpage!
% letting $\pp^p(q)=\page'(q)$ if $q\geq p$, or equivalently $p-q\leq0$.
% Note that we let \!\c@page!  have $\page'(q)$, but this assignment is
% temporary and \!\c@page! will regain the value $\page(p)$ after
% \!\pcol@setpageno! finishes.
% 
%    \begin{macrocode}
\def\pcol@setpageno{\begingroup
  \@tempcnta\pcol@page \advance\@tempcnta-\pcol@basepage
  \let\@elt\relax \edef\reserved@a{\pcol@pages\pcol@currpage}%
  \global\let\pcol@pages\@empty \global\let\pcol@currpage\@empty
  \let\@elt\pcol@setpnoelt \reserved@a
  \endgroup}
\def\pcol@setpnoelt#1#2#3#4#5{%
  {\let\@elt\relax \xdef\pcol@pages{\pcol@pages\pcol@currpage}}%
  \ifnum\@tempcnta>\z@ \gdef\pcol@currpage{\@elt{#1}#2#3{#4}{#5}}%
  \else \pcol@defcurrpage{\number\c@page}{#2}{#3}{#4}{#5}%
    \advance\c@page\@ne
    \ifpcol@paired\else \advance\c@page\@ne \fi
  \fi
  \advance\@tempcnta\m@ne}
%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@defcurrpage}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced by the redesign of page context, partly replacing
%	 \cs{pcol@setordpage} which once we call \cs{pcol@settextpage}.}
% \changes{v1.3-3}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^s(p)$, and add a
%	 invoker \cs{pcol@makecol}.}
% \changes{v1.3-4}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^m(p)$.}
% 
% The macro
% $\!\pcol@defcurrpage!
% \Arg{\pp^p(p)}\arg{\pp^i(p)}\arg{\pp^f(p)}\Arg{\pp^s(p)}\Arg{\pp^m(p)}$ 
% is invoked from \!\pcol@makecol! to update $\pp^s(\ptop)$,
% \!\pcol@setpnoelt! to update $\pp^p(p)$, \!\pcol@startpage! to initialize
% a newly created page, \!\pcol@output@start! to initialize a \spage{},
% \!\pcol@output@switch! to update $\pp^s(\ptop)$ and/or $\pp^f(\ptop)$, and
% \!\pcol@setmpbelt! to update $\pp^m(p)$.  The macro \!\xdef!ines
% \!\pcol@currpage! letting it have the \pctext{} $\pp(p)$ given by the
% arguments.
% 
%    \begin{macrocode}
\def\pcol@defcurrpage#1#2#3#4#5{{%
  \let\@elt\relax \xdef\pcol@currpage{\@elt{#1}#2#3{#4}{#5}}}}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@nextpage}
% \changes{v1.2-7}{2013/05/11}
%	{Remove unnecessary scan of $\pi(p_t)$.}
% \begin{macro}{\pcol@nextpelt}
% \changes{v1.2-2}{2013/05/11}
%	{Revise reflecting the redesign of page context.}
% \changes{v1.3-3}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^s(p)$, and add a
%	 invoker \cs{pcol@makecol}.}
% \changes{v1.3-4}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^m(p)$.}
% \changes{v1.3-6}{2013/09/17}
%	{Fix the bug that $\pi^h(q)$ is not referred correctly.}
% 
% The macro \!\pcol@nextpage! is invoked solely in \!\pcol@opcol! to let
% $p$ be $p+k+1$ where $k$ is the number of \fpage{}s directly following
% $p$, i.e., $k=\Abs{\Set{q>p}{p<\forall q'\leq q:\pp(q')^h<0}}$.  For
% this update, the macro scans $\pp(q)\in\PP$ for all $q\In\pbase\ptop$
% applying \!\pcol@nextpelt! to $\pp(q)$, to perform the following where
% $p_0$ is $p$ before update and $f=\CSIndex{if@tempswa}$ being $\true$ at
% initial, to let $p\gets p+k$, and then increments $p$ to have $p+k+1$.
% $$
% \<p,f\>\gets\cases{
% 	\<p,f\>&	$q\leq p_0$\cr
% 	\<p{+}1,f\>&	$q>p_0\;\land\;f\;\land\;\pp^i(q)\neq\bot\;\land\;
%			\pp^h(q)<0$\cr
%	\<p,\false\>&	otherwise}
% $$
% 
%    \begin{macrocode}
\def\pcol@nextpage{\begingroup
  \@tempcnta\pcol@page \advance\@tempcnta-\pcol@basepage
  \@tempswatrue
  \let\@elt\pcol@nextpelt \pcol@pages
  \global\advance\pcol@page\@ne
  \endgroup}
\def\pcol@nextpelt#1#2#3#4#5{%
  \ifnum\@tempcnta<\z@
    \ifvoid#2\@tempswafalse
    \else\ifdim\dimen#2<\z@
      \if@tempswa \global\advance\pcol@page\@ne \fi
    \else \@tempswafalse
    \fi\fi
  \fi
  \advance\@tempcnta\m@ne}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@checkshipped}
% The macro \!\pcol@checkshipped! is invoked solely in \!\pcol@opcol! to let
% \CSIndex{if@tempswa} be $\true$ iff
% $S_c=|\pcol@shipped|{\cdot}c\neq\emptyset$
% 
% \SpecialArrayIndex{c}{\pcol@shipped}
% 
% for all $c\In0\C$ to mean the oldest page $\pbase$ is ready to be shipped
% out.
% 
%    \begin{macrocode}
\def\pcol@checkshipped{\@tempswatrue
  \@tempcnta\z@ \@whilenum\@tempcnta<\pcol@ncol\do{%
    \expandafter\ifx\csname pcol@shipped\number\@tempcnta\endcsname\@empty
      \@tempswafalse \fi
   \advance\@tempcnta\@ne}}

%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{2}
% \begin{macro}{\pcol@getcurrpage}
% \changes{v1.3-4}{2013/09/17}
%	{Add a user \cs{pcol@addmarginpar}.}
% \begin{macro}{\pcol@getpelt}
% \changes{v1.2-2}{2013/05/11}
%	{Revise reflecting the redesign of page context.}
% \begin{macro}{\pcol@getpinfo}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{ifpcol@textonly} as \cs{ifpcol@nospan}.}
% \changes{v1.2-2}{2013/05/11}
%	{Revise reflecting the redesign of page context.}
% \begin{macro}{\pcol@getcurrpinfo}
% \changes{v1.2-2}{2013/05/11}
%	{Revise reflecting the redesign of page context.}
% \changes{v1.3-3}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^s(p)$, and add a
%	 invoker \cs{pcol@makecol}.}
% \changes{v1.3-4}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^m(p)$.}
% 
% The macro \!\pcol@getcurrpage! is invoked in \!\pcol@opcol!,
% \!\pcol@restartcolumn!, \!\pcol@addmarginpar!, \!\pcol@flushcolumn! and
% \!\pcol@freshpage! to let;
% 
% \begin{eqnarray*}
% &&\!\c@page!=\pp^p(p)\quad
%   \!\@colht!=\pp^h(p)\quad
%   \!\topskip!=\pp^t(p)\quad
%   \CSIndex{ifpcol@nospan}=(\pp^i(p)=\bot)\\
% &&\Midx{\!\pcol@spanning!}=\pp^i(p)\quad
%   \Midx{\!\pcol@footins!}=\pp^f(p)\quad
%   \Midx{\!\pcol@sptextlist!}=\pp^s(p)\\
% &&\Midx{\!\pcol@mparbottom!}=\pp^m(p)
% \end{eqnarray*}
% 
% for $p=\!\pcol@page!\in[p_b,p_t]$.  To do that, the macro scans all
% $\pp(q)\in\PPP=(\PP,\pp(\ptop))$ applying \!\pcol@getpelt! to
% $\pp(q)=
% \Arg{\pp^p(q)}\arg{\pp^i(q)}\arg{\pp^f(q)}\Arg{\pp^s(q)}\Arg{\pp^m(q)}$
% to invoke
% $$
% \!\pcol@getpinfo!
% \Arg{\pp^p(q)}\arg{\pp^i(q)}\arg{\pp^f(q)}\Arg{\pp^s(q)}\Arg{\pp^m(q)}
% \arg{pg}\arg{ch}\arg{ts}
% $$
% with the following arguments for \!\global! assignments, if $q=p$.
% $$
% \arg{pg}=\!\global!\!\c@page!\quad
% \arg{ch}=\!\global!\!\@colht!\quad\arg{ts}=\!\global!\!\topskip!
% $$
% Then the macro \!\pcol@getpinfo! do the obvious assighments to
% \!\pcol@spanning!, \!\pcol@footins!, \!\pcol@sptextlist!,
% \!\pcol@mparbottom! and $\arg{pg}$, and the following
% condintional assignments.
% 
% \begin{eqnarray*}
% &&\<\arg{ch},\arg{ts},\CSIndex{ifpcol@nospan}\>=
% \left\{\begin{array}{llll}
%	\<\!\textheight!,&\!\pcol@topskip!,&\true\>&\quad\pp^i(q)=\bot\\
%	\<\pp^h(q),&\pp^t(q),&\false\>&\quad\pp^i(q)\neq\bot\end{array}\right.
% \end{eqnarray*}
% 
% \begin{Sloppy}{2800}\noindent
% The other macro $\!\pcol@getcurrpinfo!\arg{pg}\arg{ch}\arg{ts}$ is invoked
% in \!\pcol@makecol!, \!\pcol@startpage!, \!\pcol@output@switch!,
% \!\pcol@sync!, \!\pcol@flushcolumn! and \!\pcol@make~flushedpage! do the
% similar assignments using \!\pcol@getpinfo!, but it is not for $\pp(p)$
% but for $\pp(\ptop)={}$\!\pcol@currpage!.  The macro \!\pcol@getpinfo!
% also has a direct invoker \!\pcol@outputelt!.
% \end{Sloppy}
% 
%    \begin{macrocode}
\def\pcol@getcurrpage{\begingroup
  \@tempcnta\pcol@page \advance\@tempcnta-\pcol@basepage
  \let\@elt\pcol@getpelt \pcol@pages\pcol@currpage
  \endgroup}
\def\pcol@getpelt#1#2#3#4#5{%
  \ifnum\@tempcnta=\z@
    \pcol@getpinfo{#1}#2#3{#4}{#5}%
                  {\global\c@page}{\global\@colht}{\global\topskip}%
  \fi
  \advance\@tempcnta\m@ne}
\def\pcol@getpinfo#1#2#3#4#5#6#7#8{\pcol@nospantrue
  \gdef\pcol@spanning{#2}\gdef\pcol@footins{#3}\gdef\pcol@sptextlist{#4}%
  \gdef\pcol@mparbottom{#5}%
  #6#1\relax
  \ifvoid#2\relax #7\textheight #8\pcol@topskip
  \else #7\dimen#2\relax #8\skip#2\relax \pcol@nospanfalse
  \fi}
\def\pcol@getcurrpinfo{%
  \edef\reserved@a{\expandafter\@cdr\pcol@currpage\@nil}%
  \expandafter\pcol@getpinfo\reserved@a}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@floatplacement}
% \changes{v1.0}{2011/10/10}
%	{Add initialization of \cs{pcol@textfloatsep}.}
% \changes{v1.3-4}{2013/09/17}
%	{Remove clearing operation on \cs{@mparbottom} because it is no
%	 longer in column-context.}
% 
% The macro \!\pcol@floatplacement! is invoked from \!\pcol@opcol!,
% \!\pcol@output@start!, \!\pcol@flushcolumn!, \!\pcol@freshpage! and
% \!\pcol@output@end! to reinitialize the parameters of \cwise{} float
% placement at the beginning of a \colpage{} or that of \postenv.  The macro
% lets \!\@textfloatsheight! be 0 and then invokes \!\@floatplacement!, as
% \!\@opcol! does its tail\footnote{
% 
% But $\!\@mparbottom!=0$ is not done because it is meaningless now.}.
% 
% In addition, the macro lets \!\pcol@textfloatsep! be \!\maxdimen! to mean
% the new \colpage{} does not have \sync{}ation point at initial.
% 
%    \begin{macrocode}
\def\pcol@floatplacement{%
  \global\@textfloatsheight\z@ \global\pcol@textfloatsep\maxdimen
  \@floatplacement}

%    \end{macrocode}
% \end{macro}
% 
% 
% 
% \section{Starting New Page}
% \label{sec:imp-startpage}
% 
% \begin{macro}{\pcol@startpage}
% \changes{v1.0}{2011/10/10}
%	{Add assignment of \cs{pcol@firstprevdepth} to be \cs{relax}.}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{pcol@maxpage} as \cs{pcol@toppage}.}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{pcol@settextpage} as \cs{pcol@setordpage}.}
% \changes{v1.2-2}{2013/05/11}
%	{Revise reflecting the redesign of page context.}
% \changes{v1.3-2}{2013/09/17}
%	{Duplicate \cs{stepcounter} of \cs{c@page} if non-paired
%	 parallel-paging is in effect.} 
% \changes{v1.3-3}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^s(p)$.}
% \changes{v1.3-4}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^m(p)$.}
% \changes{v1.32-3}{2015/10/10}
% 	{Add $\hbox{\cs{f@depth}}\EQ0$ to override
%	 $\hbox{\cs{f@depth}}\EQ\hbox{\texttt{1sp}}$ done by
%	 \cs{@dblfloatplacement}.}
% \changes{v1.32-3}{2015/10/10}
% 	{Modify the code to apply \cs{@sdblcolelt} to \cs{@dbldeferlist} so
%	 as to work with both 2015 (or newer) and 2014 (or older) versions
%	 of \LaTeX.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
% The macro \!\pcol@startpage! is invoked from \!\pcol@opcol! with
% $\!\pcol@currpage!=\pp(p{-}1)$ to start a new page $p=\!\pcol@page!$, or
% from \!\pcol@output@start! with a too large \preenv{} or
% \!\pcol@freshpage! with $\!\pcol@currpage!=|{}|$ and $\!\c@page!=\page(p)$
% to start a new page $p=0$.
% 
% First, we let $\!\pcol@firstprevdepth!=\!\relax!$ to mean we have (had)
% left from the \spage{} so that \!\pcol@output@end! will be informed of
% that.  Next we let $\ptop=p$ and then, if invoked from \!\pcol@opcol!,
% obtain $\pp^p(p{-}1)$ by \!\pcol@getcurrpinfo! to have $\page(p{-}1)$ in
% \!\c@page!, and let $\PP\gets\PPP=(\PP,\pp(p{-}1))$ with
% $\pp^f(p{-}1)=\!\pcol@currfoot!$ into which \!\pcol@makecol! saved
% \Scfnote{}s if any.  Next we lets $\!\c@page!=\page(p{-}1)+1$ unless
% \npaired{} \parapag{}ing is in effect or in other words if
% $\CSIndex{ifpcol@paired}=\true$, or $\!\c@page!=\page(p{-}1)+2$ otherwise,
% by \!\stepcounter!.  Then we let $\!\@colht!=\!\textheight!$ as the base
% value without \spanning, and $\!\topskip!=\!\pcol@topskip!$ because the
% new page is the second or succeeding one built in \env{paracol}
% environment.
% 
%    \begin{macrocode}
%% Starting New Page

\def\pcol@startpage{%
  \global\let\pcol@firstprevdepth\relax
  \global\pcol@toppage\pcol@page
  \ifx\pcol@currpage\@empty\else
    \pcol@getcurrpinfo{\global\c@page}\@tempdima\@tempskipa
    \@cons\pcol@pages
      {{\number\c@page}\pcol@spanning\pcol@currfoot
       {\pcol@sptextlist}{\pcol@mparbottom}}%
    \stepcounter{page}\ifpcol@paired\else \stepcounter{page}\fi
  \fi
  \global\@colht\textheight
  \global\topskip\pcol@topskip
%    \end{macrocode}
% 
% Then, we build \fpage{}s if any as follows.  First we invoke
% \!\@dblfloatplacement! to reinitialize the parameters for \pwise{} float
% placement.  In addition, we let $\!\f@depth!=0$ to nullify the
% setting $\!\f@depth!=|1sp|$ possiblly done by \!\@dblfloatplacement! as
% discussed in the item-(\ref{item:ovv-float-@dblfloatplacement}) of
% \secref{sec:imp-ovv-float}.  Then we repeat \!\@tryfcolumn!  giving it
% \!\@dbldeferlist!  having \pwise{} floats not contributed to previous
% pages yet, while $\CSIndex{if@fcolmade}=\true$ meaning it builds \fpage{}s
% in \!\@outputbox!.  For each \fpage{}, we acquire an \!\insert!  from
% \!\@freelist! by \!\@next! for $\pp^i(\ptop)$ to let it have the
% followings to represent the \fpage{}.
% 
% \begin{eqnarray*}
% \pp^p(\ptop)&=&\!\c@page!\quad
% \pp^b(\ptop)=\!\@outputbox!\quad
% \pp^h(\ptop)=-\!\maxdimen!\quad
% \pp^t(\ptop)=\!\pcol@topskip!\\
% \pp^f(\ptop)&=&\bot\quad
% \pp^s(\ptop)=\emptyset\quad
% \pp^m(\ptop)=\emptyset
% \end{eqnarray*}
% 
% We also increment $p$ and $\ptop$, and also \!\c@page! by one or two
% according to \CSIndex{ifpcol@paired} by \!\stepcounter!, to let them have
% the values for the page following the \fpage{}s.
% 
%    \begin{macrocode}
  \@dblfloatplacement \let\f@depth\z@
  \@tryfcolumn\@dbldeferlist
  \@whilesw\if@fcolmade\fi{%
    \pcol@Fb
    \@next\@currbox\@freelist{%
      \global\setbox\@currbox\box\@outputbox}\pcol@ovf
    \pcol@Fe{startpage(fcol)}%
    \global\dimen\@currbox-\maxdimen
    \global\skip\@currbox\pcol@topskip
    \@cons\pcol@pages{{\number\c@page}\@currbox\voidb@x{}{}}%
    \stepcounter{page}\ifpcol@paired\else \stepcounter{page}\fi
    \global\advance\pcol@page\@ne \global\pcol@toppage\pcol@page
    \@tryfcolumn\@dbldeferlist}%
%    \end{macrocode}
% 
% Next, we copy \!\@dbldeferlist! containing \pwise{} floats which
% could not be included in \fpage{}s to \!\reserved@b!, clear the list, and
% then scan the copied list by applying \!\@sdblcolelt! to each list
% element to invoke \!\@addtodblcol! for adding the element to \!\@dbltoplist!
% or keeping it in \!\@dbldeferlist! or \!\@deferlist! depending on \LaTeX's
% version, as \LaTeX's \!\@startdblcolumn!  does.  In addition, as discussed
% in item-(\ref{item:ovv-float-@addtodblcol}) of
% \secref{sec:imp-ovv-float}, we also clear \!\@deferlist! after saving it in
% \!\reserved@c! prior to the scan, and then after the scan we concatenate
% \!\@dbldeferlist! and \!\@deferlist! to let the former have the result and
% restore \!\@deferlist! from \!\reserved@c!.
% 
% Then If this scan results in empty \!\@dbltoplist! to mean the new page
% does not have any \spanning, we invoke \!\pcol@defcurrpage! with
% $\pp^i(\ptop)=\pp^f(\ptop)=\bot$ and $\pp^s(\ptop)=\pp^m(\ptop)=\emptyset$
% so that $\pp(\ptop)$ reprsents a page perfectly empty.
% 
%    \begin{macrocode}
  \begingroup
    \let\reserved@b\@dbldeferlist \let\reserved@c\@deferlist
    \global\let\@dbldeferlist\@empty \global\let\@deferlist\@empty
    \let\@elt\@sdblcolelt
    \reserved@b
    \let\@elt\relax \xdef\@dbldeferlist{\@dbldeferlist\@deferlist}%
    \global\let\@deferlist\reserved@c
  \endgroup
  \ifx\@dbltoplist\@empty
    \pcol@defcurrpage{\number\c@page}\voidb@x\voidb@x{}{}%
%    \end{macrocode}
% 
% Otherwise, i.e., \!\@dbltoplist! is not empty, we scan all elements in it
% by letting $\!\@elt!=\!\@comdblflelt!$ to have all \pwise{} floats in
% \!\@tempboxa!.  Then, after returning all elements to \!\@freelist!, we
% acquire an \!\insert! from \!\@freelist! to be $\pp^i(\ptop)$ by \!\@next!
% and store the contents of \!\@tempboxa! in $\pp^b(\ptop)$ after removing
% the last vertical skip \!\dblfloatsep! and then adding \!\dblfigrule! and
% the vertical skip \!\dbltextfloatsep!.  The other elements of $\pp(\ptop)$
% are set as follows to represent the page with \spanning{} which makes the
% height of each column \!\@colht! shrunk from its initial value
% \!\textheight!  by the series of \!\@addtodblcol!.
% 
% \begin{eqnarray*}
% \pp^p(\ptop)&=&\!\c@page!=\page(\ptop)\quad
% \pp^h(\ptop)=\!\@colht!\quad
% \pp^t(\ptop)=\!\pcol@topskip!\quad
% \pp^f(\ptop)=\bot\\
% \pp^s(\ptop)&=&\emptyset\quad
% \pp^m(\ptop)=\emptyset\quad
% \end{eqnarray*}
% 
% Finally, regardless of the existence of the \pwise{} floats, we let
% $\!\pcol@footins!=\bot$ to mean the \tpage{} does not have any \Scfnote{}s,
% so far if footnote typesetting is \scfnote, or never otherwise.
% 
%    \begin{macrocode}
  \else
    \setbox\@tempboxa\vbox{}%
    \begingroup
      \let\@elt\@comdblflelt
      \@dbltoplist
      \let\@elt\relax
      \pcol@Fb
      \xdef\@freelist{\@freelist\@dbltoplist}%
      \pcol@Fe{startpage(dbltop)}%
      \global\let\@dbltoplist\@empty
      \pcol@Fb
      \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{%
        \unvbox\@tempboxa \vskip-\dblfloatsep \dblfigrule
        \vskip\dbltextfloatsep}}\pcol@ovf
      \pcol@Fe{startpage(spanning)}%
      \global\dimen\@currbox\@colht
      \global\skip\@currbox\pcol@topskip
      \pcol@defcurrpage{\number\c@page}\@currbox\voidb@x{}{}%
    \endgroup
  \fi
  \gdef\pcol@footins{\voidb@x}}

%    \end{macrocode}
% \end{macro}
% 
% 
% 
% \section{Shipping Page Out}
% \label{sec:imp-outputpage}
% 
% \begin{macro}{\pcol@outputcolumns}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{ifpcol@stopoutput} as \cs{ifpcol@outputflt}.}
% \changes{v1.3-2}{2013/09/17}
%	{Rename \cs{pcol@outputpage} as \cs{pcol@outputcolumns}.}
% 
% The macro \!\pcol@outputcolumns!$\arg{all}$ is invoked from \!\pcol@opcol!
% with $\arg{all}=0$ to ship out the page $\pbase$ and \fpage{}s following
% it if any, or \!\pcol@sync! with $\arg{all}=1$ to ship out all pages in
% $\PP$.  It copies $\PP=\!\pcol@pages!$ into $\mathit{\Pi}'=\!\reserved@b!$
% and clear $\PP$ once to remove pages shipped out from it.  Then, after
% initializing $f_o=\CSIndex{if@tempswa}=\true$ to ship out (the first)
% ordinary page and $f_f=\CSIndex{ifpcol@outputflt}=\true$ to ship out
% \fpage{}s (following the first page), it scans all
% $\pp(q)\in\mathit{\Pi}'$ applying $\!\pcol@outputelt!\arg{all}$ to
% $\pp(q)$ to ship it out or keep it in $\PP$.
% 
%    \begin{macrocode}
%% Shipping Page Out

\def\pcol@outputcolumns#1{\begingroup
  \def\@elt{\pcol@outputelt#1}\@tempswatrue \pcol@outputflttrue
  \let\reserved@b\pcol@pages \gdef\pcol@pages{}%
  \reserved@b
  \endgroup}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@outputelt}
% \changes{v1.2-2}{2013/05/11}
%	{Revise reflecting the redesign of page context.}
% \changes{v1.3-3}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^s(p)$.}
% \changes{v1.3-4}{2013/09/17}
%	{Revise reflecting the new page context element $\pi^m(p)$.}
% 
% The macro $\!\pcol@outputelt!
% \arg{all}\Arg{\pp^p(q)}\arg{\pp^i(q)}\arg{\pp^f(q)}
% \Arg{\pp^s(q)}\Arg{\pp^m(q)}$ ships out the ordinary or \fpage{} $q$ if
% $f_o=\true$ or $f_f=\true$ respectively.  After initializing
% \!\@outputbox! to be $\bot$, we retrive the page $q$'s information by
% \!\pcol@getpinfo! to have $\page(q)$ in \!\c@page! locally, \!\textheight!
% or $\pp^h(q)$ in $h=\!\@tempdima!$,
% $f_{\it{}ns}=\CSIndex{ifpcol@nospan}=(\pp^i(q)=\bot)$, and
% $\!\pcol@footins!={\pp^f(q)}$.
% 
%    \begin{macrocode}
\def\pcol@outputelt#1#2#3#4#5#6{%
  \setbox\@outputbox\box\voidb@x
  \pcol@getpinfo{#2}#3#4{#5}{#6}\c@page\@tempdima\@tempskipa
%    \end{macrocode}
% 
% Then, we do one of the followings according to $h$ and $f_o$.
% 
% \begin{itemize}
% \item $h<0$\\
% It means $q$ is a \fpage{}.  If $f_f=\true$, we let \!\@outputbox! have
% $\pp^b(q)$ to be shipped out, paint its \bground{} with $\bgc_{\{F,f\}}$
% by \!\pcol@bg@paintbox! letting the basic height \!\pcol@bg@floatheight!
% of the paining region 
% $\bgr_{\{F,f\}}$ be
% $\HT=\!\pcol@bg@textheight!=\!\textheight!+\!\maxdepth!$, and return
% $\!\insert!{\cdot}\pp^i(q)$ to \!\@freelist! by \!\@cons! because it is no
% longer necessary.  Then if $\CL<\C$ to mean \parapag{}ing is in effect, we
% let \!\pcol@rightpage! be an empty box but paint its \bground{} too, because
% the right counterpart of left parallel float page should be always blank.
% Note that we temporarily increment $\page(q)$ by one for \npaired{} right
% \parapag{}ee so that the paiting macro performs page-parity dependent
% operations correctly.
% 
% \Index{parallel-paging}
% \Index{float page}
% 
% On the other hand if $f_f=\false$, we simply return $\pp(q)$ back to $\PP$.
% \end{itemize}
% 
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{ifpcol@stopoutput} as \cs{ifpcol@outputflt}.}
% \changes{v1.3-3}{2013/09/17}
%	{Add painting of page-wise float page.}
% \changes{v1.3-2}{2013/09/17}
%	{Add building a empty right parallel float page.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
  \ifdim\@tempdima<\z@
    \ifpcol@outputflt
      \def\pcol@bg@floatheight{\pcol@bg@textheight}%
      \setbox\@outputbox\vbox to\textheight{%
        \pcol@bg@paintbox{Ff}\unvbox\pcol@spanning}%
      \pcol@Fb
      \@cons\@freelist\pcol@spanning
      \pcol@Fe{outputelt(spanning)}%
      \ifnum\pcol@ncolleft<\pcol@ncol
        \setbox\pcol@rightpage\vbox to\textheight{%
          \ifpcol@paired\else \advance\c@page\@ne \fi
          \pcol@bg@paintbox{Ff}\vfil}%
      \fi
    \else
      \@cons\pcol@pages{{#2}#3#4{#5}{#6}}%
    \fi
%    \end{macrocode}
% 
% \begin{itemize}
% \item $h\geq0\;\land\;f_o=\true$\\
% It means $q$ is a non-\fpage{} to be shipped out.  If $\arg{all}=0$, we
% let $f_o=\false$ to keep succeeding non-\fpage{}s from being shipped out.
% Then we build the ship-out image of the right \parapag{}e $q$ in
% \!\pcol@rightpage! by \!\pcol@ioutputelt! giving it the box and the column
% range $\LBRP\CL\C$ if $\CL<\C$ to mean \parapag{}ing, and then that of the
% left \parapag{}e in \!\@outputbox! by \!\pcol@ioutputelt! again but giving
% it $\LBRP0\CL$ and \!\@outputbox!.  Note that the right-first left-second
% order is essential, because in the process to build right \parapag{}e we
% have to examine the existence of $\pp^i(q)$ and $\pp^f(q)$ and then refer
% to their height and depth to make the region corresponding to them blank,
% while the boxes of these \!\insert!s are made void in the building process
% of the left \parapag{}e obviously.
% 
% Then after the ship-out image building, we \!\global!ly let
% $\CSIndex{ifpcol@firstpage}=\false$ to tell \!\pcol@ioutputelt! and
% \!\pcol@makeflushedpage! that the pages they build are no longer first of
% a \env{paracol} environment and thus $\pp^i(q)$ should have \pwise{}
% floats rather than \preenv{} hereafter.
% \end{itemize}
% 
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{ifpcol@textonly} as \cs{ifpcol@nospan}.}
% \changes{v1.1}{2012/05/11}
% 	{Use $\cs{pcol@columnwidth}{\cdot}c$ instead of \cs{columnwidth} as
%	 the width of $c$'s \cs{hbox}.}
% \changes{v1.2-4}{2013/05/11}
%	{Add column-swapping for even pages if specified.}
% \changes{v1.2-2}{2013/05/11}
%	{Add ship-out of page-wise footnote.}
% \changes{v1.2-7}{2013/05/11}
%	{Add $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping.}
% \changes{v1.3-2}{2013/09/17}
%	{Move the core of ship-out image building to \cs{pcol@ioutputelt} for
% 	 parallel pageing.}
% 
%    \begin{macrocode}
  \else\if@tempswa
    \ifnum#1=\z@ \@tempswafalse \fi
    \ifnum\pcol@ncolleft<\pcol@ncol
      \pcol@Logstart{\pcol@outputelt{right}}%
      \pcol@ioutputelt\pcol@ncolleft\pcol@ncol\pcol@rightpage
      \pcol@Logend{\pcol@outputelt{right}}%
    \fi
    \pcol@Logstart{\pcol@outputelt{left}}%
    \pcol@ioutputelt\z@\pcol@ncolleft\@outputbox
    \pcol@Logend{\pcol@outputelt{left}}%
    \global\pcol@firstpagefalse
%    \end{macrocode}
% 
% \begin{itemize}
% \item $h\geq0\;\land\;f_o=\false$\\
% It means $q$ is a non-\fpage{} to be kept.  Therefore, we let
% $f_f=\false$ to keep \fpage{}s following it from being shipped out.  Then
% we return $\pp(q)$ to $\PP$ by \!\@cons!.
% \end{itemize}
% 
%    \begin{macrocode}
  \else
    \pcol@outputfltfalse
    \@cons\pcol@pages{{#2}#3#4{#5}{#6}}%
  \fi\fi
%    \end{macrocode}
% 
% Finally, if $\!\@outputbox!\neq\bot$ to mean $\pp(q)$ is to be
% shipped out, we invoke \!\@outputpage! to do it and increment $\pbase$ to
% let it has $q+1$.  Note that since we have let $\!\c@page!=\page(q)$, the
% direct and indirect references to it in \!\@outputpage! are correctly done.
% Also note that the \!\global! increment of it by \!\stepcounter! in
% \!\@outputpage! will be overriden by the \!\global! assignment to it done
% by \!\pcol@startpage! or \!\pcol@getcurrpage! invoked from \!\pcol@opcol!
% if $\arg{all}=0$, or by \!\pcol@getcurrpinfo! invoked from \!\pcol@sync!
% otherwise.
% 
%    \begin{macrocode}
  \ifvoid\@outputbox\else
    \global\advance\pcol@basepage\@ne \@outputpage
  \fi}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@ioutputelt}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced for parallel-paging.}
% \changes{v1.3-3}{2013/09/17}
%	{Add column-separating rule drawing and background painting.}
% \changes{v1.3-4}{2013/09/17}
%	{Add a logic to cope with non-uniform column-separating gaps.}
% 
% The macro $\!\pcol@ioutputelt!\<\Cfrom\>\<\Cto\>\arg{b}$ is invoked solely
% in \!\pcol@outputelt! but can be done twice with
% $(\Cfrom,\Cto,b)=(\CL,\C,\!\pcol@rightpage!)$ if \parapag{}ing is in
% effect and with $(\Cfrom,\Cto,b)=(0,\CL,\!\@outputbox!)$ always, to build
% the ship-out image of the right or left \parapag{}e $q$ in the box $b$
% respectively.
% 
% After opening a \!\vbox! of \!\textheight! tall for $b$, at first we
% increment $\page(q)$ by one for right \parapag{}e if it is \npaired, so
% that painting macros perform page-parity dependent operations correctly.
% 
% Next, we put materials to be shipped out in the box $b$ as follows.
% First, if $\pp^f(q)\neq\bot$ to mean the page $q$ has \Scfnote{}, we paint
% their \bground{} with $\bgc_{\{N,n\}}$ by \!\pcol@bg@paintbox! letting the
% basic height \!\pcol@bg@footnoteheight! of the paining region
% $\bgr_{\{N,n\}}$ be the height-plus-depth of $\pp^f(q)$.
% We do the painting at this earliest stage of the image building in order
% to use the left-top corner of the text area where we are now at as the
% origin for painting, and to let the region may be overlaid by those of
% columns and \csepgap{}s.  We also let $h=\pp^h(q)=\!\@tempdima!$ shrunk by
% the height-plus-depth by \!\pcol@shrinkcolbyfn!.
% 
%    \begin{macrocode}
\def\pcol@ioutputelt#1#2#3{\setbox#3\vbox to\textheight{%
  \ifpcol@paired\else\ifnum#1=\z@\else \advance\c@page\@ne \fi\fi
  \ifvoid\pcol@footins\else
    \def\pcol@bg@footnoteheight{\@elt{\ht\pcol@footins}\@elt{\dp\pcol@footins}}%
    \pcol@bg@paintbox{Nn}%
    \pcol@shrinkcolbyfn\@tempdima\pcol@footins\relax
  \fi
%    \end{macrocode}
%
% Second, if $f_{\it ns}=\false$ to mean $\pp(q)$ has \spanning{} in
% $\pp^b(q)$, we do one of the followings.
% 
% \begin{itemize}
% \item
% If $\Cfrom=0$ to mean the target is the left \parapag{}e, $\pp^b(q)$ is
% put by \!\unvbox!, painting its \bground{} with $\bgc_{\{F,f\}}$ by
% \!\pcol@bg@paintbox! letting the basic height \!\pcol@bg@floatheight!  of
% the paining region $\bgr_{\{F,f\}}$ be the height-plus-depth of $\pp^b(q)$
% if $q$ is not the first page and thus $\pp^b(q)$ has \pwise{} floats.  We
% also return the \!\insert!  $\pp^i(q)$ to \!\@freelist! by \!\@cons!.
% 
% \item
% If $\Cfrom\neq0$ to mean right \parapag{}e and $q$ is the first page,
% \!\pcol@rightpage! has \preenv{} in the right \parapag{}e.  Therefore, we
% simply put the box but making its height and depth equal to those of
% $\pp^b(q)$, without painting because the box has already been painted, and
% with \!\nointerlineskip! to prevent baseline-skip insertion below the box.
% 
% \item
% Otherwise, i.e., $\Cfrom\neq0$ and $q$ is not the first page, we put an
% empty box whose height and depth equal to those of $\pp^b(q)$ by
% \!\pcol@phantom!, with painting as done for floats in the left \parapag{}e
% and with \!\nointerlineskip!.
% \end{itemize}
% 
% Note that after putting \spanning{} and/or painting the \bground{}, we
% temporarily increment \!\topmargin! by the height-plus-depth of
% $\pp^b(q)$, so that painting macros for columns, \csepgap{}s and
% \mctext{}s assume the top edge of column area as that of text area when
% they extend the top edges of their regions upward to the page top.
% 
% \Index{extension of background painting region}
% 
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
  \ifpcol@nospan\else
    \def\pcol@bg@floatheight{%
      \@elt{\ht\pcol@spanning}\@elt{\dp\pcol@spanning}}%
    \@tempdimb\ht\pcol@spanning \advance\@tempdimb\dp\pcol@spanning
    \ifnum#1=\z@
      \ifpcol@firstpage\else \pcol@bg@paintbox{Ff}\fi
      \pcol@Fb
      \@cons\@freelist\pcol@spanning \unvbox\pcol@spanning
      \pcol@Fe{ioutputelt(spanning)}%
    \else\ifpcol@firstpage
      \ht\pcol@rightpage\ht\pcol@spanning
      \dp\pcol@rightpage\dp\pcol@spanning
      \box\pcol@rightpage \nointerlineskip
    \else
      \pcol@bg@paintbox{Ff}\pcol@phantom\pcol@spanning \nointerlineskip
    \fi\fi
    \advance\topmargin\@tempdimb
  \fi
%    \end{macrocode}
%
% Third, we invoke \!\pcol@buildcolseprule! giving it $h$ being $\pp^h(q)$
% but possibly shrunk by \Scfnote{}s, the column range $\LBRP\Cfrom\Cto$,
% and \!\@maxdepth! to mean $q$ is non-\lpage, to draw a \cseprule{}
% possibly broken by the speces for \mctext{}s in the box \!\pcol@tempboxa!
% and to paint the \bground{}s of columns, \csepgap{}s and \mctext{} in the
% box \!\@tempboxa! which we put into $b$ immediately.
% 
% Fourth, we put a \!\hbox! of \!\textwidth! wide having \!\hbox!es
% of $\w_c=|\pcol@columnwidth|{\cdot}c$
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% 
% wide containing $\sigma_c$ followed by \!\hss! for all $c\In\Cfrom\Cto$,
% where $\sigma_c=\!\box!{\cdot}s_c(q)$ being the first element removed from
% $\S_c$ by \!\@next! and then returned to \!\@freelist! by \!\@cons! if it
% is not $\bot$, or \!\voidb@x!  otherwise.  We sepearate \!\hbox!es of
% $\sigma_c$ by making each \!\hbox! preceded by \Midx{\!\pcol@@hfil!} being
% \!\relax! for the first one and the macro \!\pcol@hfil! for others giving
% it an argument $c^g=\!\pcol@colsepid!\in\{c,c{-}1\}$ which we discuss
% shortly to put a gap of $\gap_{c^g}=|\pcol@columnsep|{\cdot}c^g$
% 
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
% wide optionally having a \cseprule{} and being painted.
% 
% Note that the scanning order of $c\In\Cfrom\Cto$ is usually ascending of
% course, but is descending if \cswap{} is specified and $\page(q)\bmod2=0$.
% For this ordering, we invoke
% $\!\pcol@swapcolumn!\arg{c'}\arg{c}\<\Cfrom\>\<\Cto\>$ to have $c$ for
% the $(c'-\Cfrom)$-th iteration of the scanning where $c'=\!\@tempcnta!$
% and $c=\!\@tempcntb!$.  Another operation done by the macro is to let
% $c^g=c-1$ if swapped or $c^g=c$ otherwise, because if swapped the
% column-$c$ is followed by the gap which follows $c-1$ if not swapped.
% 
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
  \pcol@buildcolseprule\@tempdima#1#2\@maxdepth \unvbox\@tempboxa
  \hb@xt@\textwidth{%
    \let\pcol@@hfil\relax
    \@tempcnta#1\relax \@whilenum\@tempcnta<#2\do{%
      \pcol@swapcolumn\@tempcnta\@tempcntb#1#2\relax
      \expandafter\@next\expandafter\@currbox
        \csname pcol@shipped\number\@tempcntb\endcsname
        \relax{\let\@currbox\voidb@x}%
      \ifvoid\@currbox\else
        \pcol@Fb
        \@cons\@freelist\@currbox
        \pcol@Fe{ioutputelt(page)}%
      \fi
      \expandafter\@tempdima
        \csname pcol@columnwidth\number\@tempcntb \endcsname
      \pcol@@hfil \hb@xt@\@tempdima{\box\@currbox\hss}%
      \edef\pcol@@hfil{\noexpand\pcol@hfil{\pcol@colsepid}}%
     \advance\@tempcnta\@ne}}%
%    \end{macrocode}
%
% Fifth, if $\pp^f(q)\neq\bot$ to mean the page $q$ has \Scfnote{}s, we put
% them at the bottom of \!\@outputbox! by \!\pcol@putfootins!, and return
% $\pp^f(q)$ to \!\@freelist!, if $\Cfrom=0$ meaning left \parapag{}e.
% Otherwise for the right \parapag{}e, we simply put an empty box whose
% height and depth equal to those of $\pp^f(q)$ by \!\pcol@phantom!,
% preceded by a vertical skip of $\!\skip!{\cdot}\pp^f(q)$ and then
% \!\nointerlineskip! to inhibit baseline skip insertion above the box, and
% followed by null \!\vskip! as done in \!\pcol@putfootins!.
% 
% Sixth and finally\footnote{
% 
% Not necessary to be finally, but we placed this assignment at the end of
% the box to make it clear the depth capping is only for the box.},
% 
% we let $\!\boxmaxdepth!=\!\@maxdepth!$ to cap the depth of $b$ which we
% are now closing, as done for each \colpage{} and as expected to be applied
% to \Scfnote{}s.
% 
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
  \ifvoid\pcol@footins\else
    \ifnum#1=\z@
      \pcol@Log\pcol@outputelt{output}\pcol@footins
      \pcol@putfootins\pcol@footins
      \pcol@Fb
      \@cons\@freelist\pcol@footins
      \pcol@Fe{ioutputelt(footins)}%
    \else
      \vskip\skip\pcol@footins \nointerlineskip
      \pcol@phantom\pcol@footins \vskip\z@
    \fi
  \fi
  \boxmaxdepth\@maxdepth}}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@phantom}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced for parallel-paging.}
% 
% The macro \!\pcol@phantom!$\<b\>$ is used in \!\pcol@ioutputelt!,
% \!\pcol@makeflushedpage! and \!\pcol@output@end! to put an empty box, whose
% height and depth are equal to that of the argument box $b$ being a kind of
% \pwstuff, into \!\pcol@rightpage! for the right \parapag{}e whose left
% counterpart has $b$ in it.  That is, the macro is used to make a region
% corresponding to $b$ blank.  To put the empty box, we locally let
% \!\@tempboxa! have it setting its height and depth to those of $b$ and
% then put it.
% 
%    \begin{macrocode}
\def\pcol@phantom#1{{%
  \setbox\@tempboxa\vbox{}\ht\@tempboxa\ht#1\dp\@tempboxa\dp#1\box\@tempboxa}}

%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\pcol@buildcolseprule}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for column-separating rule drawing and background
%	 painting for columns, column-separating gaps and spanning texts.}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced for non-uniform column-separating gaps.}
% \changes{v1.34}{2018/05/07}
% 	{Rename \cs{pcol@tempbox} as \cs{pcol@tempboxa}.}
% \begin{macro}{\pcol@buildcselt@S}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background under-painting for spanning texts.}
% \begin{macro}{\pcol@buildcselt}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for column-separating rule drawing and background
%	 painting for columns, column-separating gaps and spanning texts.}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced for non-uniform column-separating gaps.}
% \changes{v1.34}{2018/05/07}
% 	{Rename \cs{pcol@tempbox} as \cs{pcol@tempboxa}.}
% 
% The macro $\!\pcol@buildcolseprule!\<H_{n+1}\>\<\Cfrom\>\<\Cto\>\<d\>$ is
% used in \!\pcol@ioutputelt!, \!\pcol@imakeflushedpage! and
% \!\pcol@iflushfloats!  to build a box containing \cseprule{} possibly
% broken by \mctext{}s and to paint \bground{}s of columns and \csepgap{}s
% for $c\In\Cfrom\Cto$ and \mctext{}s in the \lpage{} ($d=0$) or non-last
% page ($d=\!\@maxdepth!$) $p$ having \colpage{}s of $H_{n+1}$ tall where
% $n=\Abs{\pp^s(p)}$.
% 
% For initializing the drawing and painting process, we let
% $\!\@tempdimb!=H_0+h_0=0$,
% $(\!\pcol@bg@from!,\!\pcol@bg@to!)=(\CBfrom,\CBto)=(\Cfrom,\Cto)$, and
% make boxes $b_r=\!\pcol@tempboxa!$ for the rule and $b_b=\!\@tempboxa!$ for
% the \bground{} empty.  Then we apply
% \!\pcol@buildcselt@S!$\<H_i\>\<h_i\>$ to each element $\spt(H_i,h_i)$ of
% $\pp^s(p)$ to under-paint the \bground{} of each \mctext{} by
% \!\pcol@bg@paintbox! defining its region $\bgr_S(i)$ by letting their top
% edge positions $y_0=\!\pcol@bg@spanningtop!=H_i$, and height
% $y_1-y_0=\!\pcol@bg@spanningheight!=h_i$ if $H_i+h_i<H_{n+1}$ to mean the
% \mctext{} is non-last, or $(H_{n+1}-H_i)+d$ if last to fill the narrow
% strip of $d=\!\@maxdepth!$ tall below the text for non-\lpage{}s.
% 
% Then we scan $\pp^s(p)$ again but applying
% $\!\pcol@buildcselt!\~\<H_i\>\<h_i\>$ to each element $\spt(H_i,h_i)$ to
% do the followings.
% 
% \begin{enumerate}
% \item
% To $b_r$, add a vertical rule whose height is $H'_i=H_i-(H_{i-1}+h_{i-1})$
% and width is \!\columnseprule! if $H'_i>0$, and then a vertical skip of
% $h_i$, as the rule segment between $(i{-}1)$-th and $i$-th \mctext{}s.
% Note that $H_i$ and $h_i$ are represented in the form of integers and thus
% we need |sp| to use them as dimensions.
% 
% \item
% To $b_b$, add painted \bground{}s for all columns $c\In\Cfrom\Cto$ and
% \csepgap{}s $c\In\Cfrom{\Cto{-}1}$ by \!\pcol@bg@paintcolumns! defining
% their regions $\bgr_{\{c,g\}}^c(i)$ by letting common top edge position
% $y_0=\!\pcol@bg@columntop!=H_{i-1}+h_{i-1}$ and common height
% $y_1-y_0=\!\pcol@bg@columnheight!=H'_i$, if $H'_i>0$.  Also add painted
% \bground{} for the $i$-th \mctext{} by \!\pcol@bg@paintbox! as we did for
% under-painting but this time the region is $\bgr_s(i)$.
% 
% \item
% Let $\!\@tempdimb!=H_i+h_i$ for the next element $\spt(H_{i+1},h_{i+1})$.
% \end{enumerate}
% 
% Then if $H'_{n+1}>0$, we add the last rule segment of $H'_{n+1}$ tall to
% $b_r$, and add painted \bground{}s for columns and \csepgap{}s as done in
% the step\Tie2 above but letting $y_1-y_0=H'_{n+1}+d$ to let the common
% bottom edge of the their regions reach the bottom of text area for
% non-\lpage{}s.
% 
%    \begin{macrocode}
\def\pcol@buildcolseprule#1#2#3#4{%
  \@tempdima#1\relax \dimen@#4\relax
  \let\pcol@bg@from#2\relax \let\pcol@bg@to#3\relax
  \setbox\pcol@tempboxa\vbox{}\setbox\@tempboxa\vbox{}%
  \let\@elt\pcol@buildcselt@S \pcol@sptextlist
  \@tempdimb\z@ \let\@elt\pcol@buildcselt \pcol@sptextlist
  \let\@elt\relax \advance\@tempdima-\@tempdimb
  \ifdim\@tempdima>\z@
    \setbox\pcol@tempboxa\vbox{\unvbox\pcol@tempboxa
      \hrule\@height\@tempdima\@width\columnseprule}%
    \setbox\@tempboxa\vbox{\unvbox\@tempboxa
      \let\@elt\relax
      \edef\pcol@bg@columntop{\number\@tempdimb sp}%
      \edef\pcol@bg@columnheight{%
        \@elt{\number\@tempdima sp}\@elt{\number\dimen@ sp}}%
      \pcol@bg@paintcolumns}%
  \fi}
\def\pcol@buildcselt@S#1#2{%
  \setbox\@tempboxa\vbox{\unvbox\@tempboxa
    \let\@elt\relax
    \def\pcol@bg@spanningtop{\@elt{#1sp}}%
    \advance\@tempdima-#1sp\relax \advance\@tempdima-#2sp\relax
    \advance\dimen@\@tempdima
    \edef\pcol@bg@spanningheight{\@elt{#2sp}%
      \ifdim\@tempdima>\z@\else \@elt{\number\dimen@ sp}\fi}%
    \pcol@bg@paintbox{S}}}
\def\pcol@buildcselt#1#2{%
  \@tempdimc#1sp \advance\@tempdimc-\@tempdimb
  \setbox\pcol@tempboxa\vbox{\unvbox\pcol@tempboxa
    \ifdim\@tempdimc>\z@ \hrule\@height\@tempdimc\@width\columnseprule \fi
    \vskip#2sp}%
  \setbox\@tempboxa\vbox{\unvbox\@tempboxa
    \let\@elt\relax
    \edef\pcol@bg@columntop{\number\@tempdimb sp}%
    \edef\pcol@bg@columnheight{\@elt{\number\@tempdimc sp}}%
    \ifdim\@tempdimc>\z@ \pcol@bg@paintcolumns \fi
    \def\pcol@bg@spanningtop{\@elt{#1sp}}%
    \advance\@tempdima-#1sp\relax \advance\@tempdima-#2sp\relax
    \advance\dimen@\@tempdima
    \edef\pcol@bg@spanningheight{\@elt{#2sp}%
      \ifdim\@tempdima>\z@\else \@elt{\number\dimen@ sp}\fi}%
    \pcol@bg@paintbox{s}}%
  \@tempdimb#1sp \advance\@tempdimb#2sp\relax}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@hfil}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for column-separating rule drawing.}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced for non-uniform column-separating gaps.}
% \changes{v1.34}{2018/05/07}
% 	{Rename \cs{pcol@tempbox} as \cs{pcol@tempboxa}.}
% 
% The macro $\!\pcol@hfil!\<c\>$ is used in \!\pcol@ioutputelt!,
% \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats! to separate column
% $c{+}1$ and $c$ or $c$ and $c{+}1$ according as the columns are
% swapped or not in the page the caller macros are building.
% 
% \Index{column-swapping}
% 
% If $\!\columnseprule!=r>0$, the macro puts the followings; a horizontal
% space of $\gap_{c}/2=|\pcol@columnsep|{\cdot}c/2$
% 
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
% followed by a skip $-r/2$ to nullify the width of the rule; the rule in
% \!\pcol@tempboxa! which \!\pcol@buildcolseprule! built, with color
% $|\pcol@colseprulecolor|{\cdot}c$
% 
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
% or \!\pcol@colseprulecolor! according as the former is defined or not,
% i.e., \!\colseprulecolor!\oarg{mode}\ARg{color}$|[|c|]|$ is declared or
% not; and $\gap_c/2$ again but preceded by $-r/2$.  On the other hand if
% $r=0$, we simply put a space of $\gap_c$.  Note that the skips of
% $\gap_c/2$ and $\gap_c$ are accompanied by 1\,|fil| inifinit stretch to
% avoid underfull when $\sum_{c=\Cfrom}^{\Cto-2}(\w_c+\gap_c)+\w_{\Cto-1}<\WT$
% where $(\Cfrom,\Cto)=\{(0,\CL),(\CL,C)\}$, due to arithmetic errors in
% calculations of $\w_c$ and $\gap_c$\footnote{
% 
% It is assured the sum of $w_c$ and $\gap_c$ cannot exceed $\WT$ even with
% arithmetic errors and thus overfull never occurs.}. 
% 
%    \begin{macrocode}
\def\pcol@hfil#1{{%
  \@tempdima\csname pcol@columnsep#1\endcsname\relax
  \ifdim\columnseprule>\z@
    \hskip.5\@tempdima\@plus1fil\relax
    \hskip-.5\columnseprule
    \@ifundefined{pcol@colseprulecolor#1}%
      {\pcol@colseprulecolor}{\@nameuse{pcol@colseprulecolor#1}}%
    \copy\pcol@tempboxa \hskip-.5\columnseprule
    \hskip.5\@tempdima\@plus1fil\relax
  \else \hskip\@tempdima\@plus1fil\relax
  \fi}}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@@outputpage}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced keep the original definition of \cs{@outputpage}.}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced keep the original definition of \cs{@outputpage}.}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced keep the original definition of \cs{@outputpage}.}
% \begin{macro}{\@outputpage}
% \changes{v1.3-2}{2013/09/17}
%	{Redefined for parallel-paging.}
% \changes{v1.3-3}{2013/09/17}
%	{Redefined for background painting.}
% \changes{v1.3-4}{2013/09/17}
%	{Redefined for marginal note placement.}
% \changes{v1.34}{2018/05/07}
% 	{Rename \cs{pcol@tempbox} as \cs{pcol@tempboxa}.}
% 
% The macro \!\@outputpage!, being our own version of \LaTeX's one kept in
% \!\pcol@@outputpage!, ships out a page $p$ or \parapag{}e pair in $p$.
% The reason why we redefine this macro is that we need a few special
% operations for \parapag{}ing and \bgpaint{} {\em outside} of \env{paracol}
% environments.  Therefore, the macro is not only used in our own macros
% \!\pcol@outputelt!, \!\pcol@output@start!, \!\pcol@output@flush!,
% \!\pcol@output@clear!, \!\pcol@flushfloats! and \!\pcol@output@end!, but
% also in \LaTeX's \!\@opcol! and \!\@doclearpage!\footnote{
% 
% And possibly in \CSIndex{@outputdblcol} if double-column typesetting is
% done outside \env{paracol}.}
% 
% invoked from our own or \LaTeX's \!\output! routine.
% 
% First we calculate $H'_M=\!\topmargin!+\!\headheight!+\!\headsep!$ to place
% the origin of \bgpaint{} at the top edge of text area in what \LaTeX{}
% assumes as a page, i.e., shifted 1\,inch down from the real page.  Then if
% $\CSIndex{ifpcol@output}=\true$ to mean this macro is used in a
% \env{paracol} environment, we build the painted \bground{}s of left and
% right \parapag{}es in $\!\pcol@tempboxa!=b_l$ and $\!\@tempboxa!=b_r$ by
% putting a vertical skip of $H'_M$, and invoking \!\pcol@bg@paintpage!
% with the setting $(\!\pcol@bg@from!,\!\pcol@bg@to!)=(\CBfrom,\CBto)$ be
% $(0,\CL)$ and $(\CL,\C)$ respectively.  Note that \!\pcol@bg@paintpage!
% paints \bground{}s of regions $\bgr_a^{[c]}$ for all
% $a\in\{T,B,L,R,C,S,t,b,l,r\}$ and $c\In\CBfrom\CBto$, and for $b_r$ we
% temporarily increment $\page(p)$ by one if \npaired{} \parapag{}ing is in
% effect.
% 
% Otherwise, i.e., if $\CSIndex{ifpcol@output}=\false$ indicating outside
% use, we build the painted \bground{}s in $b_l$ and $b_r$ similarly but
% with the following differences;  \bgpaint{} is done if
% $\CSIndex{ifpcol@havelastpage}=\true$ to mean the page to be shipped has
% the \lpage{} of closed \env{paracol} as its part and
% $\!\set@color!\neq\!\relax!$ to mean some coloring package is loaded;
% page \bground{} painting is done by \!\pcol@bg@@paintpage! because
% \!\pcol@bg@paintpage! is not available outside \env{paracol} environments;
% the \bground{} of \postenv{} is painted by \!\pcol@bg@@paintbox! for the
% region $\bgr_{\{P,p\}}=[(0,\WT)(\HB,\HT)]$ where
% $\HB=\!\pcol@bg@preposttop!
% \in\{\!\pcol@bg@preposttop@left!,\!\pcol@bg@preposttop@right!\}$
% having the bottom edge of the last 
% \env{paracol} environment (having right \parapag{}e for $b_r$).  In
% addition, we examine if $\!\pcol@rightpage!\neq\bot$ to mean the right
% \parapag{}e was built by \!\pcol@output@end! when the last \env{paracol}
% environment was closed and, if so, make the box \!\textheight! tall adding
% \!\vfil! to its bottom.
% 
% Then regardless of \CSIndex{ifpcol@output}, we do the followings; let the
% height and depth of $b_l$ and $b_r$ be 0 because they cannot occupy any
% real spaces in the ship-out image; temporarily let
% $\CSIndex{ifpcol@swapcolumn}=\false$ if $\page(p)$ is odd, $\CL=\C$ to
% mean \parapag{}ing is not in effect\footnote{
% 
% Since the assignments of $\CL$ and $\C$ in \CSIndex{pcol@zparacol} are
% \CSIndex{global} and they are not nodified anywhere else, examining their
% equality outside \env{paracol} environments is safe and meaningful.},
% 
% \parapag{}ing is done in \npaired{} mode\footnote{
% 
% We need this examination because $\CSIndex{ifpcol@swapcolumn}=\false$ for
% \npaired{} \parapag{}ing is made locally by \!\pcol@zparacol!.},
% 
% or we are outside \env{paracol} environments and the page does not have
% anything produced in environments.  That is, we let
% $\CSIndex{ifpcol@swapcolumn}=\true$ if the page has something produced by
% a \env{paracol} environment, \cswap{} and \parapag{}ing are specified for
% the (last) environment\footnote{
% 
% Column-swapping may be enabled {\em after} the last \env{paracol}
% environment was closed but we consider the enablement is effective for the
% page having the environment.},
% 
% and the page number is even.  Note that a page may have two or more
% (\lpage{}s of) \env{paracol} environements whose \parapag{}ing style can
% be inconsistent including the case some of them are not \parapag{}ed.  If
% this inconsistency happens the page is shipped out following the style of
% the last environment.  Also note that even if the last environment is not
% \parapag{}ed, the right \parapag{}e kept in \!\pcol@rightpage! is assuredly
% shipped out.
% 
% Then if \cswap{} is in effect, we ship out the right \parapag{}e at first
% by \!\pcol@outputpage@r! and then the left one by \!\pcol@outputpage@l! to
% swap the left and right.  Otherwise, the ship-out order is normal and thus
% the invocation order is \!\pcol@outputpage@l!  then \!\pcol@outputpage@r!.
% Note that if \npaired{} \parapag{}ing is in effect, the page number to
% given to \!\pcol@outputpage@r! as its argument is $\page(p)+1$ if it is
% the second one, i.e., not swapped, while the argument in other cases and
% of \!\pcol@outputpage@l! are always $\page(p)$.  Then finally, we
% \!\global!ly let $\CSIndex{ifpcol@havelastpage}=\false$ because so far the
% next page does not have \env{paracol}'s \lpage{} especially when we are
% outside it, let \!\pcol@bg@preposttop@left! and
% \!\pcol@bg@preposttop@right! have 0 because, if we are outside, the next
% \preenv{} should start from the top of a page, and let
% $\mpbout=\!\pcol@mparbottom@out!$ be $\mpboutz=\!\pcol@mparbottom@zero!$
% because so far we have no marginal notes given in \env{paracol}
% environments\footnote{
% 
% This assignment in a \env{paracol} environment is meaningless because
% $\mpbout$ is meaningless too, but not harmful.}.
% 
%    \begin{macrocode}
\let\pcol@@outputpage\@outputpage
\def\@outputpage{\begingroup
  \@tempdima\topmargin \advance\@tempdima\headheight \advance\@tempdima\headsep
  \ifpcol@output
    \setbox\pcol@tempboxa\vtop{\vskip\@tempdima \global\pcol@bg@paintedfalse
     \let\pcol@bg@from\z@ \let\pcol@bg@to\pcol@ncolleft
     \pcol@bg@paintpage}%
    \ifpcol@bg@painted \@tempswatrue \else \@tempswafalse \fi
    \setbox\@tempboxa\vtop{\vskip\@tempdima \global\pcol@bg@paintedfalse
      \ifpcol@paired\else \advance\c@page\@ne \fi
      \let\pcol@bg@from\pcol@ncolleft \let\pcol@bg@to\pcol@ncol
      \pcol@bg@paintpage}%
  \else
    \def\reserved@a{\vskip\@tempdima \global\pcol@bg@paintedfalse
      \ifpcol@havelastpage \ifx\set@color\relax\else
        \pcol@bg@@paintpage \pcol@bg@@paintbox{Pp}%
      \fi\fi}%
    \setbox\pcol@tempboxa\vbox{%
      \let\pcol@bg@preposttop\pcol@bg@preposttop@left
      \let\pcol@bg@from\z@ \let\pcol@bg@to\pcol@ncolleft \reserved@a}%
    \ifpcol@bg@painted \@tempswatrue \else \@tempswafalse \fi
    \setbox\@tempboxa\vbox{\ifpcol@paired\else \advance\c@page\@ne \fi
      \let\pcol@bg@preposttop\pcol@bg@preposttop@right
      \let\pcol@bg@from\pcol@ncolleft \let\pcol@bg@to\pcol@ncol
      \reserved@a}%
    \ifvoid\pcol@rightpage\else
      \pcol@Logstart{\@outputpage{rightset}}%
      \setbox\pcol@rightpage\vbox to\textheight{\unvbox\pcol@rightpage \vfil}%
      \pcol@Logend{\@outputpage{rightset}}%
    \fi
  \fi
  \ht\pcol@tempboxa\z@ \dp\pcol@tempboxa\z@
  \ht\@tempboxa\z@ \dp\@tempboxa\z@
  \ifodd\c@page                                 \pcol@swapcolumnfalse \fi
  \ifnum\pcol@ncolleft<\pcol@ncol\else          \pcol@swapcolumnfalse \fi
  \ifpcol@output\else \ifpcol@havelastpage\else \pcol@swapcolumnfalse \fi\fi
  \@tempcnta\c@page
  \ifpcol@paired\else \advance\@tempcnta\@ne    \pcol@swapcolumnfalse \fi
  \ifpcol@swapcolumn \pcol@outputpage@r\c@page \pcol@outputpage@l\@tempcnta
  \else              \pcol@outputpage@l\c@page \pcol@outputpage@r\@tempcnta
  \fi
  \global\pcol@havelastpagefalse \gdef\pcol@bg@preposttop@left{0pt}%
  \global\let\pcol@bg@preposttop@right\pcol@bg@preposttop@left
  \global\let\pcol@mparbottom@out\pcol@mparbottom@zero
  \endgroup}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\pcol@outputpage@l}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced for shipping out left parallel-pages.}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for column-separating rule drawing and background
%	 painting in left parallel-pages.}
% \changes{v1.34}{2018/05/07}
% 	{Rename \cs{pcol@tempbox} as \cs{pcol@tempboxa}.}
% \begin{macro}{\pcol@outputpage@r}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced for shipping out right parallel-pages.}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for column-separating rule drawing and background
%	 painting in right parallel-pages.}
% \begin{macro}{\pcol@outputpage@ev}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% The macro $\!\pcol@outputpage@l!\arg{page}$, used solely in our own
% version of \!\@outputpage!, at first lets \!\c@page! have $\arg{page}$
% which definitely has the value that \!\c@page! had when we start
% \!\@outputpage!.  That is, even when this macro is invoked after
% \!\pcol@outputpage@r! due to swapped \parapag{}ing,
% 
% \Index{column-swapping}
% 
% this assignment cancels the increment of \!\c@page! done in \LaTeX's
% \!\@outputpage! or in other word \!\pcol@@outputpage! because in this case
% \parapag{}es are \paired{}.  Then we make \!\@themargin! \!\let!-equal to
% \!\evensidemargin! if two-side typesetting is in effect and \!\c@page! is
% even, or to \!\oddsidemargin! otherwise for the reference in
% \!\pcol@outputpage@ev! as shown shortly.
% 
% Next, if \bgpaint{} took place in \!\@outputpage!, we let \!\everyvbox!
% have the macro invocation $\!\pcol@outputpage@ev!\<b_l\>$ to be expanded
% to the following sequence so that they are the leading materials in the
% \!\vbox! to be \!\shipout!; examination if the document is processed by a
% Japanese \LaTeX{} named p\LaTeX{} and then, if so, a control sequence
% \!\yoko! to put materials naturally; the painted \bground{} $b_l$ shifted
% right by \!\@themargin!; \!\nointerlineskip!  to inhibit \!\baselineskip!
% insertion after $b_l$; emptying \!\everyvbox! to ensure nothing will be
% inserted into internal \!\vbox!es; and the assignment of \!\yoko! to
% \!\let! it be \!\relax! if necessary.  This trick with \!\everyvbox! is
% necessary\footnote{
% 
% Unless we rewrite \CSIndex{@outputpage}.}
% 
% because $b_l$ should be put {\em before} \!\pcol@@outputpage! puts the
% page header, or the header would be overlaid by regions, e.g.,
% $\bgr_{\{t,T\}}$ in natural cases.
% 
% The tricky elements to handle \!\yoko! in the sequence is necessary for
% p\LaTeX{} whose \!\@outputpage! has \!\yoko! as the first element of the
% \!\vbox! to be \!\shipout!, because \!\yoko! must be the first element of
% a box but our \!\everyvbox! to put \bground{} would make it non-first.
% That is by the tricky elements, the \!\vbox! should have \!\yoko! as the
% first element from \!\everyvbox! and then that put by p\LaTeX's
% \!\@outputpage! is nullified by \!\let!\!\yoko!\!\relax! in the
% \!\everyvbox! just for the \!\vbox! to be shipped out.  On the other hand
% in ordinary \LaTeX, \!\yoko! does not appear in the \!\vbox! or is
% modified.  The examination of the use of p\LaTeX{} is also trickily done
% by comparing the expansion results of \!\meaning!\!\yoko! and
% \!\string!\!\yoko!.  Since the former results in the tokens ``\!\yoko!''
% which \!\string!\!\yoko!  gives us iff \!\yoko! is a primitive of
% underlying \TeX{} being p\TeX{} if so, the comparison should give us
% equality iff p\LaTeX{} is in use\footnote{
% 
% Unless some other \TeX{} has a primitive named \CSIndex{yoko}.  This
% examination is more strict than that with \CSIndex{pfmtname} for
% \CSIndex{ifpcol@bfbottom}.}.
% 
% Then we invoke \!\pcol@@outputpage! being (p)\LaTeX's original version of
% \!\@outputpage! to ship out \!\@outputbox! finally.
% 
% The macro \!\pcol@outputpage@r!$\arg{page}$ performs similar operations but
% it does them only when $\!\pcol@rightpage!\neq\bot$ to mean we are in an
% \env{paracol} environment with \parapag{}ing or outside it but in the page
% in which it resides.  Other differences are as follows; $\arg{page}$ can
% be $\page(p)+1$ for \npaired{} right \parapag{}es; \!\@outputbox! is
% locally made \!\let!-equal to \!\pcol@rightpage! prior to the invocation
% of \!\pcol@@outputpage!; and $b_r$ is given to \!\pcol@outputpage@ev! as
% its argument.
% 
%    \begin{macrocode}
\def\pcol@outputpage@l#1{%
  \pcol@Logstart{\@outputpage{left}}%
  \global\c@page#1\relax
  \let\@themargin\oddsidemargin
  \if@twoside\ifodd\c@page\else \let\@themargin\evensidemargin \fi\fi
  \if@tempswa \everyvbox{\pcol@outputpage@ev\pcol@tempboxa}\fi
  \pcol@@outputpage
  \pcol@Logend{\@outputpage{left}}}
\def\pcol@outputpage@r#1{%
  \begingroup
  \ifvoid\pcol@rightpage\else
    \global\c@page#1\relax
    \let\@outputbox\pcol@rightpage
    \pcol@Logstart{\@outputpage{right}}%
    \let\@themargin\oddsidemargin
    \if@twoside\ifodd\c@page\else \let\@themargin\evensidemargin \fi\fi
    \ifpcol@bg@painted \everyvbox{\pcol@outputpage@ev\@tempboxa}\fi
    \pcol@@outputpage
    \pcol@Logend{\@outputpage{right}}%
  \fi
  \endgroup}
\def\pcol@outputpage@ev#1{%
  \edef\reserved@a{\meaning\yoko}\edef\reserved@b{\string\yoko}%
  \ifx\reserved@a\reserved@b \yoko\fi
  \moveright\@themargin\box#1\nointerlineskip \everyvbox{}%
  \ifx\reserved@a\reserved@b \let\yoko\relax \fi}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% 
% 
% 
% \section{Starting New Column-Page}
% \label{sec:imp-startcolumn}
% 
% \begin{macro}{\pcol@startcolumn}
% \changes{v1.3-3}{2013/09/17}
%	{Add \cs{@colht} and \cs{@tempdimb} as the first and third argument of
%	 \cs{pcol@shrinkcolbyfn}.}
% \changes{v1.32-2}{2015/10/10}
% 	{Fix the memory leak caused by mistakingly preserving $\pi^f(p)$
%	 when $p\EQ p_t$.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
% The macro $\!\pcol@startcolumn!\arg{f}$ is invoked from \!\pcol@output!
% with $f=1$ and \!\pcol@freshpage! with $f=0$ to start a new \colpage.
% This macro has two additional functions to \LaTeX's \!\@startcolumn!, one
% for \Scfnote{}s and the other for coloring.
% 
% First, if the page $p$ in which the new \colpage{} resides has \Scfnote{}s
% in $\pp^f(p)=\!\pcol@footins!$ because the column is not the leading one,
% 
% \Index{leading column}
% 
% we temporarily shrink \!\@colht! and \!\@colroom! by the space required to
% put $\pp^f(p)$ by \!\pcol@shrinkcolbyfn! during the trial of deferred
% float placement, remembering the existence of the footnotes by letting
% $\!\@tempdimb!=-\!\skip!\!\pcol@footins!$ which should be 0 otherwise.
% This shrinkage is essentially required when $p<\ptop$ because $\pp^f(p)$
% has been fixed to be a part of $p$ and thus deferred floats cannot push
% footnotes down to succeeding pages.  In the case of $p=\ptop$, the
% shrinkage is also desirable to avoid unnecessary pushing down of footnotes
% which \TeX{} has decided to be in $p$.
% 
% Then after trying put deferred floats in the \colpage{} by \!\@tryfcolumn!
% and \!\pcol@trynextcolumn! as done in \LaTeX's \!\@startcolumn!, we
% \!\insert! $\pp^f(p)$, if it is has some footnoes, by letting \!\footins!
% have it by \!\pcol@getcurrfoot! so that \TeX{} will be aware of the
% footnotes when it examines the page break of the \colpage{}.  That is, if
% $p<\ptop$ the \!\insert!ion is to keep the vertical space for $\pp^f(p)$ in
% the building process of the \colpage{} in $p$ because any \Scfnote{s}
% cannot be added to $p$ any more, and thus $\pp^f(p)$ is preserved until
% the page $p$ is shipped out.  On the other hand if $p=\ptop$, \Scfnote{s}
% in $p$ can grow further and thus \!\insert!ed footnotes will be captured
% again by \!\pcol@output@switch! or \!\pcol@startpage!.  Therefore, if
% $p=\ptop$, we release $\pp^f(p)$ to \!\@freelist!.
% 
% Then if $p=\ptop$, we also \!\insert! deferred footnotes in $\df$ until
% their total height reaches \!\@colht! by \!\pcol@deferredfootins! if $f=1$
% to mean this macro is invoked from \!\pcol@output!\footnote{
% 
% The \cs{insert}ion of $\pp^f(p)$ also requiers $f=1$ but this examination
% is redundant because $\pp^f(p)=\bot$ definately if $f=0$.}.
% 
% Note that the deferred footnote \!\insert!ion in the case of $f=0$ will
% be done afterward when \!\pcol@freshpage! does \!\pcol@restartcolumn! at
% its tail.  Also note that \!\pcol@deferredfootins! examines if
% $\!\@tempdimb!=0$ to mean $\pp^f(p)=\bot$ and thus \!\skip!\!\footins!
% should be taken into account in its extraction of the footnotes from $\df$.
% 
% Then after restoring \!\@colht! and canceling the temporary shrinkage of
% \!\@colroom!, we invoke \!\pcol@savecolorstack! to save \colpage{}'s
% \colorctext{} into $\csts$ so that coloring \!\special!s to reestablish
% $\csts$ will be put at its top if it has something when we leave it.
% 
%    \begin{macrocode}
%% Starting New Column Page

\def\pcol@startcolumn#1{%
  \@tempdima\@colht \@tempdimb\z@
  \ifvoid\pcol@footins\else
    \pcol@shrinkcolbyfn\@colht\pcol@footins\@tempdimb
  \fi
  \global\@colroom\@colht
  \@tryfcolumn\@deferlist
  \if@fcolmade\else
    \pcol@trynextcolumn
    \ifpcol@scfnote \ifnum#1>\z@
      \ifvoid\pcol@footins\else
        \edef\pcol@currfoot{\pcol@footins}%
        \pcol@getcurrfoot\copy
        \pcol@Log\pcol@startcolumn{insert}\footins
        \insert\footins{\unvbox\footins}%
        \ifnum\pcol@page=\pcol@toppage
          \pcol@Fb
          \@cons\@freelist\pcol@footins
          \pcol@Fe{startcolumn(pagefn)}%
        \fi
      \fi
      \ifnum\pcol@page=\pcol@toppage
        \pcol@deferredfootins\pcol@startcolumn \fi
    \fi\fi
  \fi
  \advance\@tempdima-\@colht
  \global\advance\@colroom\@tempdima
  \global\advance\@colht\@tempdima
  \pcol@savecolorstack}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@trynextcolumn}
% \changes{v1.2-2}{2013/05/11}
%	{No change in the code itself but its explanation is modified
%	 according to the drastic redesign of \cs{pcol@startcolumn}.}
% 
% The macro \!\pcol@trynextcolumn! is invoked from \!\pcol@startcolumn! and
% \!\pcol@flush~column! to try to move deferred floats in \!\@deferlist!
% into \!\@toplist! or \!\@botlist!.  The body of this macro is perfectly
% equivalent to the \cs{else} part of \CSIndex{if@fcolmade} in \LaTeX's
% \!\@startcolumn!.
% 
%    \begin{macrocode}
\def\pcol@trynextcolumn{\begingroup
  \let\reserved@b\@deferlist
  \global\let\@deferlist\@empty
  \let\@elt\@scolelt
  \reserved@b
  \endgroup}

%    \end{macrocode}
% \end{macro}
% 
% 
% 
% \section{Background Painting}
% \label{sec:imp-bgpaint}
% 
% \begin{macro}{\pcol@bg@from}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@to}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% The control sequence pair
% $(\!\pcol@bg@from!,\!\pcol@bg@to!)=(\Uidx\CBfrom,\Uidx\CBto)$ are made
% \!\let!-equal to $(0,\CL)$ or $(\CL,\C)$ by \!\pcol@buildcolseprule! and
% \!\@outputpage!  for \bgpaint{} of columns and \csepgap{}s, and referred
% to by column scanning loops in \!\pcol@bg@paint@ii! and
% \!\pcol@bg@columnleft!.  The control sequence \!\pcol@bg@to! is also
% referred to by \!\pcol@bg@paint@i! to decrement it by one temporarily so
% that the loop in \!\pcol@bg@paint@ii! scans $c\In\CBfrom{\CBto{-}1}$
% rather than $\LBRP\CBfrom\CBto$.  Since this decrement is done whenever a
% painting macro is used regardless some setting of $\CBto$, \!\pcol@bg@to!
% has default setting with $\C$ to avoid unbound reference at the
% decrement.  Note that since this decrement is done in a \!\vbox! and an
% appropriate setting must have been done if $\CBto$ is referred in
% \!\pcol@bg@paint@ii!, this decrement and default setting are safe.
% 
%    \begin{macrocode}
%% Background Painting

\let\pcol@bg@to\pcol@ncol
%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \KeepSpace{4}
% \begin{macro}{\pcol@bg@paintpage}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@paintpage}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@paintcolumns}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@paintcolumns}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@paintbox}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@paintbox}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% The macros \!\pcol@bg@@paintpage!, \!\pcol@bg@@paintcolumns! and
% $\!\pcol@bg@@paintbox!\Arg{A}$ are made \!\let!-equal to their interface
% counterparts \!\pcol@bg@paintpage!, \!\pcol@bg@paint~columns! and
% \!\pcol@bg@paintbox! by \!\pcol@zparacol! if some coloring package has
% been loaded.  Otherwise, these interface macros are \!\let!-equal to
% \!\relax! for first two and \!\@gobble! for the last, so that macros in
% \!\output! routine freely use them unaware of coloring capability.  One
% exception is in \!\@outputpage! which uses \!\pcol@bg@@paintpage! and
% \!\pcol@bg@@paintbox! explicitly when it is outside \env{paracol}
% environments, examining the availability of coloring.
% 
% The macro \!\pcol@bg@paintpage! and \!\pcol@bg@@paintpage! are used in
% \!\@outputpage! to paint \bground{}s of regions $\bgr_a^{[c]}$ for all
% $a\in\{T,B,L,R,G,C,t,b,l,r\}$ and $c\In\CBfrom\CBto$ for $a=C$ while
% $c\In\CBfrom{\CBto{-}1}$ for $a=G$.  Therefore, the macro invokes
% \!\pcol@bg@paint@i! with two
% $\!\pcol@bg@paint@ii!\Arg{A_b}\Arg{A_g}\Arg{A_c}$, letting
% $A_b=|TBLR|$, $A_g=|G|$ and $A_c=|C|$ in the first invocation and then
% $A_b=|tblr|$ and $A_g=A_c=\emptyset$ in the second.
% 
% The macro \!\pcol@bg@paintcolumns! is used in \!\pcol@buildcolseprule! and
% \!\pcol@buildcselt! to paint \bground{}s of regions $\bgr_g^c(i)$ for
% $c\In\CBfrom{\CBto{-}1}$ and $\bgr_c^c(i)$ for $c\In\CBfrom\CBto$.
% Therefore, the macro invokes \!\pcol@bg@paint@i! with \!\pcol@bg@paint@ii!
% giving it $A_b=\emptyset$, $A_g=|g|$ and $A_c=|c|$.
% 
% The macro $\!\pcol@bg@paintbox!\Arg{A}$ is used in the following macros
% with $A$ shown in the parantheses to paint the \bground{}s of regions
% $\bgr_{\{a_1,a_2\}}$ where $(a_1,a_2)\in\{(S,s),(F,f),(N,n),\~(P,p)\}$.
% 
% \begin{quote}\raggedright
% \!\pcol@outputelt!\Tie(|Ff|),
% \!\pcol@ioutputelt!\Tie(|Nn|, |Ff|),
% \!\pcol@buildcselt!\Tie(|Ss|),
% \!\pcol@output@start!\Tie(|Pp|),
% \!\pcol@output@clear!\Tie(|Ff|),
% \!\pcol@makeflushedpage!\Tie(|Ff|),
% \!\pcol@imakeflushedpage!\Tie(|Nn|),
% \!\pcol@output@end!\Tie(|Nn|).
% \end{quote}
% 
% The macro \!\@outputpage! also uses the function but \!\pcol@bg@@paintbox!
% explicitly with $A=|Pp|$.  Therefore \!\pcol@bg@@paintbox! invokes
% \!\pcol@bg@paint@i! with \!\pcol@bg@paint@ii!  giving it $A_b=A$ and
% $A_g=A_c=\emptyset$.
% 
%    \begin{macrocode}
\def\pcol@bg@@paintpage{%
  \pcol@bg@paint@i{%
    \pcol@bg@paint@ii{TBLR}{G}{C}\pcol@bg@paint@ii{tblr}{}{}}}
\def\pcol@bg@@paintcolumns{\pcol@bg@paint@i{\pcol@bg@paint@ii{}{g}{c}}}
\def\pcol@bg@@paintbox#1{\pcol@bg@paint@i{\pcol@bg@paint@ii{#1}{}{}}}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@bg@paint@i}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% The macro $\!\pcol@bg@paint@i!\Arg{body}$ is used in
% \!\pcol@bg@@paintpage!, \!\pcol@bg@@paint~columns! and
% \!\pcol@bg@@paintbox! to paint \bground{}s by a sequence of
% \!\pcol@bg@paint@ii! specified in $\arg{body}$.  The painted \bground{} is
% built in \!\@tempboxa! being a \!\vtop! having a null \!\vskip! as its
% first element so that everything put in the box is below its reference
% point at its top.  Then, before invoking \!\pcol@bg@paint@ii! in
% $\arg{body}$, we do the followings;  \!\global!ly let
% $\CSIndex{ifpcol@bg@painted}=\false$ to indicate so far any painted
% \bground{} are produced;  make \!\pcol@bg@leftmargin! \!\let!-equal
% to \!\pcol@lrmargin! to use this \!\dimen! register locally with the
% more appropriate alias;  negate \!\pagerim! locally to calculate $\HT$
% easily;  decrement $\CBto$ by one locally for the column scanning loop for
% $c\In\CBfrom{\CBto{-}1}$ in \!\pcol@bg@paint@ii!;  and \!\offinterlineskip!
% to inhbit inter-line \!\baselineskip! insertion in the box.  Then after
% the invocation of the sequence of \!\pcol@bg@paint@ii! in $\arg{body}$ and
% closing the box, we let the height, depth and width of the box be 0 so
% that it does not occupy any real space in the outer box in which the box
% is put.  Finally, if $\CSIndex{ifpcol@bg@painted}=\true$ meaning that some
% painted \bground{}s are built in the box, we put the box into the outer
% box surrounding it by \!\nointerlineskip! to inhibit inter-line
% \!\baselineskip! insertion before and after it.
% 
%    \begin{macrocode}
\def\pcol@bg@paint@i#1{%
  \setbox\@tempboxa\vtop{\vskip\z@
    \global\pcol@bg@paintedfalse
    \let\pcol@bg@leftmargin\pcol@lrmargin
    \pagerim-\pagerim \advance\pcol@bg@to\m@ne
    \offinterlineskip #1}%
  \ht\@tempboxa\z@ \dp\@tempboxa\z@ \wd\@tempboxa\z@
  \ifpcol@bg@painted \nointerlineskip \box\@tempboxa \nointerlineskip \fi}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@bg@paint@ii}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% The macro $\!\pcol@bg@paint@ii!\Arg{A_b}\Arg{A_g}\Arg{A_c}$ appears only
% in the argument of \!\pcol@bg@paint@i! used in
% \!\pcol@bg@@paintpage!, \!\pcol@bg@@paintcolumns! and
% \!\pcol@bg@@paintbox! to paint \bground{}s of regions $\bgr_a$ for
% $a\in{}A_b\subseteq\{T,B,L,R,S,F,N,P,t,b,l,r,s,f,n,p\}$, $\bgr_a^c$ for
% $a\in{}A_g\subseteq\{G,g\}$ and $c\In\CBfrom{\Cto{-}1}$, and $\bgr_a^c$ for
% $a\in A_c\subseteq\{C,c\}$ and $c\In\CBfrom\CBto$.
% 
% First we invoke \!\pcol@bg@swappage! with \CSIndex{ifpcol@bg@swap} to
% let \!\pcol@bg@left~margin! and \CSIndex{ifpcol@bg@@swap} have values
% accorging to \CSIndex{ifpcol@bg@swap}, \CSIndex{if@twoside} and the parity
% of $\page(p)$.  Then we invoke $\!\pcol@bg@paintregion!\arg{a}\arg{c}$ for
% all $a\in A_b$ and $c=-1$ to paint the \bground{} of $\bgr_a$.  Second, we
% invoke \!\pcol@bg@swappage! again but with \CSIndex{ifpcol@swapcolumn}
% instead of \CSIndex{ifpcol@bg@swap}, and \!\pcol@bg@paintregion! as well
% but for $a\in\{A_g,A_c\}$ and $c\In\CBfrom{\CBto{-}1}$.  Third and
% finally, we make yet another invocation of \!\pcol@bg@paintregion! for
% $a\in A_c$ and $c=\CBto-1$.
% 
%    \begin{macrocode}
\def\pcol@bg@paint@ii#1#2#3{%
  \pcol@bg@swappage\ifpcol@bg@swap\fi
  \@tfor\reserved@b:=#1\do{\pcol@bg@paintregion\reserved@b\m@ne}%
  \pcol@bg@swappage\ifpcol@swapcolumn\fi
  \@tfor\reserved@b:=#2#3\do{%
    \pcol@currcol\pcol@bg@from \@whilenum\pcol@currcol<\pcol@bg@to\do{%
      \pcol@bg@paintregion\reserved@b\pcol@currcol
     \advance\pcol@currcol\@ne}}%
  \@tfor\reserved@b:=#3\do{\pcol@bg@paintregion\reserved@b\pcol@currcol}}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@bg@swappage}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% The macro $\!\pcol@bg@swappage!\arg{if}\cs{fi}$ is used solely in
% \!\pcol@bg@paint@ii! but twice with $\arg{if}=\CSIndex{ifpcol@bg@swap}$
% and then with $\arg{if}=\CSIndex{ifpcol@swapcolumn}$, to let
% \!\pcol@bg@leftmargin! and \CSIndex{ifpcol@bg@@swap} have values for
% \mirror{}ing according to the truth values of $\arg{if}$ and
% \CSIndex{if@twoside} and the parity of $\page(p)$ of the page $p$ for
% which \bgpaint{} is taking place.  That is, they are let have the values
% as follows.
% 
% \begin{eqnarray*}
% W&=&\cases{\CSIndex{oddsidemargin}&
%              $\page(p)\bmod2=1\;\lor\CSIndex{if@twoside}=\false$\cr
%            \CSIndex{evensidemargin}&
%              $\page(p)\bmod2=0\;\land\CSIndex{if@twoside}=\true$}\\
% \rlap{$\displaystyle(\!\pcol@bg@leftmargin!,\CSIndex{ifpcol@bg@@swap})$}
%   \phantom{W}\\
% &=&\cases{(W,\;\false)&$\page(p)\bmod2=1\lor\;\arg{if}=\false$\cr
%           (\WP-(W+\WT+2\,|in|),\;\true)&
%             $\page(p)\bmod2=\land\;\arg{if}=\true$}
% \end{eqnarray*}
% 
% Note that $\WP-(W+\WT+2\,|in|)$ means the right margin width minus 1\,|in|
% with given left margin width $W$, and thus
% $\WM=\!\pcol@bg@leftmargin!+1\,|in|$ gives us the right margin width we
% need in \mirror{}ed \bgpaint.
% 
%    \begin{macrocode}
\def\pcol@bg@swappage#1#2{%
  \pcol@bg@leftmargin\oddsidemargin \pcol@bg@@swapfalse
  \ifodd\c@page\else
    \if@twoside \pcol@bg@leftmargin\evensidemargin \fi
    #1% \ifpcol@{bg@swap,swapcolumn}
    \pcol@bg@@swaptrue
    \advance\pcol@bg@leftmargin\textwidth \advance\pcol@bg@leftmargin2in
    \advance\pcol@bg@leftmargin-\paperwidth
    \pcol@bg@leftmargin-\pcol@bg@leftmargin
    #2% \fi
  \fi}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@bg@paintregion}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@paintregion@i}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% The macro $\!\pcol@bg@paintregion!\arg{a}\arg{c}$ is used only in
% $\!\pcol@bg@paint@ii!\Arg{A_b}\Arg{A_g}\Arg{A_c}$ but as many times as
% $\Abs{A_b}+\Abs{A_g}(\CBto-\CBfrom-1)+\Abs{A_c}(\CBto-\CBfrom)$ to paint
% \bground{} region $\bgr_a^{[c]}$ specified by $|\pcol@bg@@|{\cdot}a$
% 
% \SpecialArrayIndex{a}{\pcol@bg@@}
% 
% with color $\bgc_a^c=|\pcol@bg@color@|{\cdot}a{\cdot}|@|{\cdot}c$
% 
% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}
% 
% or, if it is undefined, $\bgc_a=|\pcol@bg@color@|{\cdot}a$.
% 
% \SpecialArrayIndex{a}{\pcol@bg@color@}
%
% If $\bgr_a^c$ or $\bgr_a$ is defined, the painted \bground{} is built in
% \!\@tempboxa! with \!\vtop! having null vertical skip at its top and by
% $\!\pcol@bg@paintregion@i!\Arg{F_x}\Arg{F_y}\Arg{F_w}\Arg{F_h}$ where
% the arguments are defined in the body of the macro $|\pcol@bg@@|{\cdot}a$
% 
% \SpecialArrayIndex{a}{\pcol@bg@@}
% 
% and thus we need triple \!\expandafter! to give them to the macro.  Prior
% to the invocatoin of the macro, we let $\!\reserved@a!=a'$ have
% $a{\cdot}|@|{\cdot}c$ if $\bgc_a^c$ is defined for $a\in\{G,C,g,c\}$, or
% $a$ otherwise definitely for $a\notin\{G,C,g,c\}$.
% 
% Then \!\pcol@bg@paintregion@i! calculates $x_0=\!\@tempdima!$,
% $y_0=\!\@tempdimb!$, $x_1=\!\@tempdimc!$ and $y_1=\!\dimen@!$ of the
% region $\bgr_a^{[c]}$ by $\!\pcol@bg@calculate!\arg{z}\arg{z_0}\Arg{F}$
% giving it
% $(z,z_0,F)\in\{(x_0,0,F_x),(y_0,0,F_y),(x_1,x_0,F_w),(y_1,y_0,F_h)\}$,
% where $(x_0,y_0)$ and $(x_1,y_1)$ is the left-top and right-bottom corner
% of the painting region in the text-area coordinate, i.e., left-right and
% top-down coordinate whose origin is at the left-top corner of the leftmost
% column.  Next we modify $\{x,y\}_{\{0,1\}}$ for \bgext{} by
% $\!\pcol@bg@addext!\arg{z}\Arg{s}\Arg{d}$ with $(z,s,d)\in
% \{(x_0,\hbox{`|-|'},|l|),(y_0,\hbox{`|-|'},|t|),
% (x_1,\emptyset,|r|),\~(y_1,\emptyset,|b|)\}$.
% 
% Now we have $[(x_0,y_0)(x_1,y_1)]$ and thus, if not \mirror{}ed, we place
% $\bgr_a^{[c]}$ at $(x_0,y_0)$ by a vertical skip of $y_0$ and shifting a
% \!\hbox! for the region right by $x_0$ by \!\moveright!, and paint the box
% putting a \!\vrule! of $(x_1-x_0)$ wide and $(y_1-y_0)$ tall, letting
% \!\current@color! have $\bgc_r^{[c]}=|\pcol@bg@colr|{\cdot}a'$ and then
% invoking \!\pcol@set@color! being the orinigal definition of
% \!\set@color!.
% 
% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}
% \SpecialArrayIndex{a}{\pcol@bg@color@}
% 
% On the other hand if \mirror{}ing is to be done, the region should be
% $[(\WT{-}x_1,y_0)(\WT{-}x_0,y_1)]$ and thus the shift amount for
% \!\moveright! of the \!\hbox! is $(\WT-x_1)$.
% 
% Then after \!\pcol@bg@paintregion@i! finshes its work,
% \!\pcol@bg@paintregion! lets the switch
% \CSIndex{ifpcol@bg@painted}${}=\true$ because we painted $\bgr_a^{[c]}$,
% lets the height, depth and width of \!\@tempboxa!  be 0 to make it a
% phantom, and then put it into the outside box opened by
% \!\pcol@bg@paint@i!.  On the other hand, if neither $\bgc_r^c$ nor
% $\bgc_r$ defined to mean the \bgpaint{} of the region is not specified, we
% do nothing.
% 
%    \begin{macrocode}
\def\pcol@bg@paintregion#1#2{%
  \@ifundefined{pcol@bg@color@#1@\number#2}%
    {\def\reserved@a{#1}}{\edef\reserved@a{#1@\number#2}}%
  \@ifundefined{pcol@bg@color@\reserved@a}\relax
    {\setbox\@tempboxa\vtop{\vskip\z@
       \expandafter\expandafter\expandafter
         \pcol@bg@paintregion@i\csname pcol@bg@@#1\endcsname}%
     \global\pcol@bg@paintedtrue
     \ht\@tempboxa\z@ \dp\@tempboxa\z@ \wd\@tempboxa\z@ \box\@tempboxa}}
\def\pcol@bg@paintregion@i#1#2#3#4{%
  \pcol@bg@calculate\@tempdima\z@{#1}%
  \pcol@bg@calculate\@tempdimb\z@{#2}%
  \pcol@bg@calculate\@tempdimc\@tempdima{#3}%
  \pcol@bg@calculate\dimen@\@tempdimb{#4}%
  \pcol@bg@addext\@tempdima{-}{l}\pcol@bg@addext\@tempdimc{}{r}%
  \pcol@bg@addext\@tempdimb{-}{t}\pcol@bg@addext\dimen@{}{b}%
  \vskip\@tempdimb
  \ifpcol@bg@@swap
    \advance\@tempdima-\@tempdimc \@tempdima-\@tempdima
    \advance\@tempdimc-\textwidth \@tempdimc-\@tempdimc
    \moveright\@tempdimc\hbox{%
      \advance\dimen@-\@tempdimb
      \edef\current@color{\@nameuse{pcol@bg@color@\reserved@a}}\pcol@set@color
      \vrule\@width\@tempdima\@height\dimen@}%
  \else
    \moveright\@tempdima\hbox{%
      \advance\@tempdimc-\@tempdima \advance\dimen@-\@tempdimb
      \edef\current@color{\@nameuse{pcol@bg@color@\reserved@a}}\pcol@set@color
      \vrule\@width\@tempdimc\@height\dimen@}%
  \fi}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \KeepSpace{3}
% \begin{macro}{\pcol@bg@calculate}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@advance}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@negative}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@nadvance}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@dimen}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% The macro $\!\pcol@bg@calculate!\arg{z}\arg{z_0}\arg{F}$ is used in
% \!\pcol@bg@paintregion@i! and \!\pcol@bg@addext! to accumulate dimensional
% values specified in $F$ into a \!\dimen! register $z$ with initial value
% $z_0$.  The specificatoin $F$ is a sequence of $\!\@elt!\Arg{f}$ to add $f$
% to $z$, $\!\pcol@bg@negative!\Arg{F^-}$ to subtract the amount specified
% by $F^-$ from $z$, or macros expanded to either of them.
% 
% The macro makes \!\pcol@bg@dimen! \!\let!-equal to $z$ and \!\@elt! to
% \!\pcol@bg@advance!, lets $z=z_0$, and then does what is specified in $F$\@.
% Therefore, $\!\@elt!\arg{f}$ appearing directly or indirectly in $F$ does
% $\!\advance!\arg{z}\arg{f}$ for the accumulation.  On the other hand,
% \!\pcol@bg@negative! makes \!\@elt! \!\let!-equal to \!\pcol@bg@nadvance!
% to let $\!\@elt!\arg{f}$ do $\!\advance!\arg{z}{-}\arg{f}$ for
% subtraction, does $F^-$, and then remake $\!\@elt!=\!\pcol@bg@advance!$.
% Note that $f$ may be expanded to a negative amount having `|-|' its
% beginning to results in $\!\@elt!\arg{f}$ expanded to
% $\!\advance!\arg{z}{-}{-}\arg{f'}$ with some positive amount $f'$, but
% this double negation is legitimate in \TeX{} and is equivalent to
% $\!\advance!\arg{z}\arg{f'}$.  The macro \!\pcol@bg@negative! is used in
% the following macros.
% 
% \begin{quote}\raggedright
% \!\pcol@bg@ext@inf@l!,
% \!\pcol@bg@ext@inf@r!,
% \!\pcol@bg@ext@inf@t!,
% \!\pcol@bg@@t!,
% \!\pcol@bg@@b!,
% \!\pcol@bg@@l!,
% \!\pcol@bg@@r!,
% \!\pcol@bg@@n!,
% \!\pcol@bg@@p!.
% \end{quote}
% 
%    \begin{macrocode}
\def\pcol@bg@calculate#1#2#3{\let\pcol@bg@dimen#1\relax
  \let\@elt\pcol@bg@advance \pcol@bg@dimen#2\relax #3}
\def\pcol@bg@negative#1{\let\@elt\pcol@bg@nadvance #1\relax
  \let\@elt\pcol@bg@advance}
\def\pcol@bg@advance#1{\advance\pcol@bg@dimen#1\relax}
\def\pcol@bg@nadvance#1{\advance\pcol@bg@dimen-#1\relax}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{3}
% \begin{macro}{\pcol@bg@addext}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@ext@inf@l}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@ext@inf@r}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@ext@inf@t}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@ext@inf@b}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% The macro $\!\pcol@bg@addext!\arg{z}\Arg{s}\Arg{d}$ is used only in
% \!\pcol@bg@paintregion@i! but four times with $(z,s,d)\in
% \{(x_0,\hbox{`|-|'},|l|),(y_0,\hbox{`|-|'},|t|),
% (x_1,\emptyset,|r|),\~(y_1,\emptyset,|b|)\}$, to perform \bgext{} on a
% \!\dimen! register $z$.
% 
% First the macro gets $e=|\pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}a'
% \in e_a^{[c]}(\{x,y\}^{\{{+},{-}\}})$
% 
% \SpecialArrayIndex{d{\cdot}\string\texttt{@}
%     {\cdot}a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@ext@}
% \SpecialArrayIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}
% 
% where $a'=\!\reserved@a!\~\in\{a{\cdot}|@|{\cdot}c,a\}$.  Then if
% $e<9000\PT$ being a finite \bgext, we let $z\gets z\pm e$
% according to $s$, i.e. $+$ if $s=\emptyset$ while $-$ if $s={}$`|-|'.
% Otherwise, i.e., $e\geq9000\PT$ for a infinite \bgext, let $e'$
% be the value shown below by invoking $|\pcol@bg@ext@inf@|{\cdot}d$
% 
% \SpecialArrayMainIndex{d}{\pcol@bg@ext@inf@}
% $$
% e'=\cases{-(\WM-\WR)&$d=|l|$\cr
%           \WP-(\WM-\WR)&$d=|r|$\cr
% 	    -(\HM-\HR)&$d=|t|$\cr
% 	    \HP-(\HM-\HR)&$d=|b|$\cr}
% $$
% where $\WM-\WR$ is specified by \!\pcol@bg@pageleft! and $\HM-\HR$ by
% \!\pcol@bg@pagetop!.  Then we let $z=e'\pm(e-10000\PT)$ according to $s$
% again, i.e., move $z$ {\em inside\/} by $(10000\PT-e)$ from $e'$.
% 
%    \begin{macrocode}
\def\pcol@bg@addext#1#2#3{%
  \dimen@ii\@nameuse{pcol@bg@ext@#3@\reserved@a}\relax
  \ifdim\dimen@ii<9000\p@\relax \advance#1#2\dimen@ii
  \else
    \pcol@bg@calculate#1\z@{\@nameuse{pcol@bg@ext@inf@#3}}%
    \advance\dimen@ii-\@M\p@ \advance#1#2\dimen@ii
  \fi}
\def\pcol@bg@ext@inf@l{\pcol@bg@negative\pcol@bg@pageleft}
\def\pcol@bg@ext@inf@r{\pcol@bg@negative\pcol@bg@pageleft
  \pcol@bg@paperwidth}
\def\pcol@bg@ext@inf@t{\pcol@bg@negative\pcol@bg@pagetop}
\def\pcol@bg@ext@inf@b{\pcol@bg@negative\pcol@bg@pagetop
  \pcol@bg@paperheight}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{7}
% \begin{macro}{\pcol@bg@paperwidth}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@paperheight}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@pageleft}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@pagetop}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@textheight}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@columnleft}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@columnright}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@columnwidth}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@columnsep}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% The following macros specify the whole or a part of
% $F\in\{F_x,F_y,F_w,F_h\}$ being the body of $|\pcol@bg@@|{\cdot}a$ for
% \bgpaint{} regions $\bgr_a^{[c]}$.
% 
% \begin{eqnarray*}
% \!\pcol@bg@paperwidth!&=&	\WP-2\WR=\!\paperwidth!-2\!\pagerim!
% 	\quad(t,T,b,B,r,R)\\
% \!\pcol@bg@paperheight!&=&	\HP-2\HR=\!\paperheight!-2\!\pagerim!
% 	\quad(b,B)\\
% \!\pcol@bg@pageleft!&=&	\WM-\WR=
% 				(\!\pcol@bg@leftmargin!+1\,|in|)-\!\pagerim!\\
% &	\rlap{$(t,T,b,B,l,L,r,R)$}\\
% \!\pcol@bg@pagetop!&=&	\HM-\WR\\
% 	&=&(\!\topmargin!+\!\headheight!+\!\headsep!+1\,|in|)-\!\pagerim!\\
% &	\rlap{$(t,T,b,B)$}\\
% \!\pcol@bg@textheight!&=&	\HT=\!\textheight!+\!\@maxdepth!\\
% &	\rlap{$(b,B,l,L,r,R,C,G,n,N,p,P)$}\\
% \!\pcol@bg@columnleft!&=&	\W_c=\sum_{d=\CBfrom}^{c-1}(w_c+g_c)
% 	\quad(c,C)\\
% \!\pcol@bg@columnright!&=&	\W_c+w_c=
% 				\!\pcol@bg@columnleft!+\!\pcol@bg@columnwidth!\\
% &	\rlap{$(g,G)$}\\
% \!\pcol@bg@columnwidth!&=&	w_c=|\pcol@columnwidth|{\cdot}c
% 	\quad(c,C)\\
% \!\pcol@bg@columnsep!&=&	g_c=|\pcol@columnsep|{\cdot}c
% 	\quad(g,G)
% \end{eqnarray*}
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
% Note that \!\pagerim! in $F$ means $-\!\pagerim!$ because its sign is
% reversed by \!\pcol@bg@paint@i!.  The macros are used in
% $|\pcol@bg@@|{\cdot}a$
% 
% \SpecialArrayIndex{a}{\pcol@bg@@}
% 
% whose region identifier $a$ is shown in paretheses above, but besides them
% \!\pcol@bg@paperwidth! is also used in \!\pcol@bg@ext@inf@r!,
% \!\pcol@bg@paperheight! in \!\pcol@bg@ext@inf@b!, \!\pcol@bg@pageleft! in
% \!\pcol@bg@ext@inf@l! and \!\pcol@bg@ext@inf@r!, and \!\pcol@bg@pagetop!
% in \!\pcol@bg@ext@inf@t!  and \!\pcol@bg@ext@inf@b!.  Also note that
% \!\pcol@bg@textheight! is used in \!\pcol@output@clear! while it is
% temporarily redefined in \!\pcol@output@start! and \!\pcol@output@end!.
% 
%    \begin{macrocode}
\def\pcol@bg@paperwidth{\@elt\paperwidth \@elt{2\pagerim}}
\def\pcol@bg@paperheight{\@elt\paperheight \@elt{2\pagerim}}
\def\pcol@bg@pageleft{\@elt{1in}\@elt\pcol@bg@leftmargin \@elt\pagerim}
\def\pcol@bg@pagetop{\@elt{1in}\@elt\topmargin \@elt\headheight \@elt\headsep
  \@elt\pagerim}
\def\pcol@bg@textheight{\@elt\textheight \@elt\@maxdepth}
\def\pcol@bg@columnleft{%
  \@tempcnta\pcol@bg@from \@whilenum\@tempcnta<\pcol@currcol\do{%
    \@elt{\@nameuse{pcol@columnwidth\number\@tempcnta}}%
    \@elt{\@nameuse{pcol@columnsep\number\@tempcnta}}%
   \advance\@tempcnta\@ne}}
\def\pcol@bg@columnright{\pcol@bg@columnleft \pcol@bg@columnwidth}
\def\pcol@bg@columnwidth{\@elt{\@nameuse{pcol@columnwidth\number\pcol@currcol}}}
\def\pcol@bg@columnsep{\@elt{\@nameuse{pcol@columnsep\number\pcol@currcol}}}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{7}
% \begin{macro}{\pcol@bg@preposttop}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@preposttop@left}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@preposttop@right}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@columntop}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@columnheight}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@floatheight}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@footnoteheight}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@spanningtop}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% \begin{macro}{\pcol@bg@spanningheight}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for background painting.}
% 
% Besides the macros shown above, $|\pcol@bg@@|{\cdot}a$ uses the following
% macros defined by macros using \!\pcol@bg@paintpage!,
% \!\pcol@bg@paintcolumns! or \!\pcol@bg@paintbox!.
% 
% \begin{itemize}
% \item
% \!\pcol@bg@preposttop! being \!\pcol@bg@preposttop@left! or
% \!\pcol@bg@preposttop@right! for $a\in\{p,P\}$ by \!\@outputpage! and
% \!\pcol@output@end!, the latter of which may define only the left one if
% the closing environment is not \parapag{}ed.  That is, both of left and
% right macros are usually equivalent, but the right one can be smaller than
% the left if we have two or more (\lpage{}s of) \env{paracol} environments
% in a page and the closing environment is not \parapag{}ed while some
% others are.  In such case, \!\@outputpage! or \!\pcol@output@start!,
% another macro referring to them, must paint the region below
% \!\pcol@bg@preposttop@right! in the right page as a part of \preenv{} or
% \postenv{} by \!\let!ting \!\pcol@bg@preposttop! be
% \!\pcol@bg@preposttop@left! and \!\pcol@bg@preposttop@right! for the left
% and right \parapag{}es respectively.  Both macros have common initial
% value 0.
% 
% \item
% \!\pcol@bg@columntop! and \!\pcol@bg@columnheight! for $a\in\{c,g\}$ by
% \!\pcol@build~colseprule! and \!\pcol@buildcselt!.
% 
% \item
% \!\pcol@bg@spanningtop! and \!\pcol@bg@spanningheight! for $a\in\{s,S\}$ by
% \!\pcol@buildcselt!.
% 
% \item
% \!\pcol@bg@floatheight! for $a\in\{f,F\}$ by \!\pcol@outputelt!,
% \!\pcol@ioutputelt!, \!\pcol@output@clear! and \!\pcol@makeflushedpage!
% 
% \item
% \!\pcol@bg@footnoteheight! for $a\in\{n,N\}$ by \!\pcol@ioutputelt!,
% \!\pcol@imakeflushed~page! and \!\pcol@output@end!.
% \end{itemize}
% 
%    \begin{macrocode}
\def\pcol@bg@preposttop@left{0pt}
\let\pcol@bg@preposttop@right\pcol@bg@preposttop@left

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{18}
% \begin{macro}{\pcol@bg@@c}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@C}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@g}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@G}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@s}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@S}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@t}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@T}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@b}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@B}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@l}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@L}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@r}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@R}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@f}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@F}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@n}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@N}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@p}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% \begin{macro}{\pcol@bg@@P}
% \changes{v1.3-3}{2013/09/17}{Introduced for background painting.}
% 
% The macros $|\pcol@bg@@|{\cdot}a$
% 
% \SpecialArrayMainIndex{a}{\pcol@bg@@}
% 
% define arguments $F_x$, $F_y$, $F_w$ and $F_h$ to be passed to
% \!\pcol@bg@paintregion@i! in their bodies to calculate $(x_0,y_0)$ and
% $(x_1{-}x_0,y_1{-}y_0)$ for regions $\bgr_a^{[c]}$ as shown below in the
% form of $(x_0,y_0)+(x_1{-}x_0,y_1{-}y_0)$ (to have $(x_1,y_1)$), where
% $H^c=\!\pcol@bg@columntop!$, $h^c=\!\pcol@bg@columnheight!$,
% $H^s=\!\pcol@bg@spanningtop!$, $h^s=\!\pcol@bg@spanningheight!$,
% $h^f=\!\pcol@bg@floatheight!$, $h^n=\!\pcol@bg@footnoteheight!$ and
% $H^p=\!\pcol@bg@preposttop!$ calculated by macros which invoke \bgpaint{}
% macros, while $s^n=\!\skip!\!\footins!$.
% 
% \begin{eqnarray*}
% \bgr_c^c&\;:\;&(\W_c\;,\;H^c)\ +\ (w_c\;,\;h^c)\\
% \bgr_C^c&:&(\W_c\;,\;0)\ +\ (w_c\;,\;\HT)\\
% \bgr_g^c&:&((\W_c+w_c)\;,\;H^c)\ +\ (g_c\;,\;h^c)\\
% \bgr_G^c&:&((\W_c+w_c)\;,\;0)\ +\ (g_c\;,\;\HT)\\
% \bgr_{\{s,S\}}&:&(0\;,\;H^s)\ +\ (\WT\;,\;h^s)\\
% \bgr_{\{t,T\}}&:&(-(\WM-\WR)\;,\;-(\HM-\HR))\ +\ ((\WP-2\WR)\;,\;\HM-\HR)\\
% \bgr_{\{b,B\}}&:&(-(\WM-\WR)\;,\;\HT)\ +\ 
%                  ((\WP-2\WR)\;,\;(\HP-2\HR)-((\HM-\HR)+\HT))\\
% \bgr_{\{l,L\}}&:&(-(\WM-\WR)\;,\;0)\ +\ ((\WM-\WR)\;,\;\HT)\\
% \bgr_{\{r,R\}}&:&(\WT\;,\;0)\ +\ ((\WP-2\WR)-((\WM-\WR)+\WT)\;,\;\HT)\\
% \bgr_{\{f,F\}}&:&(0\;,\;0)\ +\ (\WT\;,\;h^f)\\
% \bgr_{\{n,N\}}&:&(0\;,\;\HT-(h^n+s^n))\ +\ (\WT\;,\;h^n+s^n)\\
% \bgr_{\{p,P\}}&:&(0\;,\;H^p)\ +\ (\WT\;,\;\HT-H^p)
% \end{eqnarray*}
% 
%    \begin{macrocode}
\def\pcol@bg@@c{%
  {\pcol@bg@columnleft}%
  {\@elt\pcol@bg@columntop}%
  {\pcol@bg@columnwidth}%
  {\pcol@bg@columnheight}}
\def\pcol@bg@@C{%
  {\pcol@bg@columnleft}%
  {}%
  {\pcol@bg@columnwidth}%
  {\pcol@bg@textheight}}
\def\pcol@bg@@g{%
  {\pcol@bg@columnright}%
  {\@elt\pcol@bg@columntop}%
  {\pcol@bg@columnsep}%
  {\pcol@bg@columnheight}}
\def\pcol@bg@@G{%
  {\pcol@bg@columnright}%
  {}%
  {\pcol@bg@columnsep}%
  {\pcol@bg@textheight}}
\def\pcol@bg@@s{%
  {}%
  {\pcol@bg@spanningtop}%
  {\@elt\textwidth}%
  {\pcol@bg@spanningheight}}
\def\pcol@bg@@t{%
  {\pcol@bg@negative\pcol@bg@pageleft}%
  {\pcol@bg@negative\pcol@bg@pagetop}%
  {\pcol@bg@paperwidth}%
  {\pcol@bg@pagetop}}
\def\pcol@bg@@b{%
  {\pcol@bg@negative\pcol@bg@pageleft}%
  {\pcol@bg@textheight}%
  {\pcol@bg@paperwidth}%
  {\pcol@bg@paperheight
    \pcol@bg@negative{\pcol@bg@pagetop \pcol@bg@textheight}}}
\def\pcol@bg@@l{%
  {\pcol@bg@negative\pcol@bg@pageleft}%
  {}%
  {\pcol@bg@pageleft}%
  {\pcol@bg@textheight}}
\def\pcol@bg@@r{%
  {\@elt\textwidth}%
  {}%
  {\pcol@bg@paperwidth
    \pcol@bg@negative{\pcol@bg@pageleft \@elt\textwidth}}%
  {\pcol@bg@textheight}}
\def\pcol@bg@@f{%
  {}%
  {}%
  {\@elt\textwidth}%
  {\pcol@bg@floatheight}}
\def\pcol@bg@@n{%
  {}%
  {\pcol@bg@textheight
    \pcol@bg@negative{\pcol@bg@footnoteheight \@elt{\skip\footins}}}%
  {\@elt\textwidth}%
  {\pcol@bg@footnoteheight \@elt{\skip\footins}}}
\def\pcol@bg@@p{%
  {}%
  {\@elt\pcol@bg@preposttop}%
  {\@elt\textwidth}%
  {\pcol@bg@textheight \pcol@bg@negative{\@elt\pcol@bg@preposttop}}}
\let\pcol@bg@@S\pcol@bg@@s
\let\pcol@bg@@T\pcol@bg@@t
\let\pcol@bg@@B\pcol@bg@@b
\let\pcol@bg@@L\pcol@bg@@l
\let\pcol@bg@@R\pcol@bg@@r
\let\pcol@bg@@F\pcol@bg@@f
\let\pcol@bg@@N\pcol@bg@@n
\let\pcol@bg@@P\pcol@bg@@p

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% 
% 
% \KeepSpace{10}
% \section{Special Output Routines}
% \label{sec:imp-sout}
% 
% \subsection{Dispatcher}
% \label{sec:imp-sout-disp}
% 
% \changes{v1.22}{2013/06/30}
%	{\cs{pcol@op@cpush} was introduced for output request to push color
%	 stack but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@op@cpush} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.22}{2013/06/30}
%	{\cs{pcol@op@cpop} was introduced for output request to pop color
%	 stack but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@op@cpop} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.22}{2013/06/30}
%	{\cs{pcol@op@cset} was introduced for output request to set
%	 $\gamma_0^c$ but removed in v1.34}
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@op@cpop} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% 
% \begin{macro}{\pcol@op@start}
% \begin{macro}{\pcol@op@switch}
% \begin{macro}{\pcol@op@flush}
% \begin{macro}{\pcol@op@clear}
% \begin{macro}{\pcol@op@end}
% 
% The macro $|\pcol@op@|{\cdot}f$ where $f\in
% F=\{|start|,|switch|,|flush|,|clear|,|end|\}$ has
% our own \!\outputpenalty! code less than $-10000$ to invoke the
% corresponding macro $|\pcol@output@|{\cdot}f$.  The code macros are given
% to \!\pcol@invokeoutput! as its argument by \!\pcol@zparacol! ($f=|start|$),
% \!\pcol@switchcol! ($f=|switch|$), \!\pcol@visitallcols! ($f=|switch|$),
% \!\pcol@com@flushpage! ($f=|flush|$), \!\pcol@com@clearpage!
% ($f=|clear|$), \!\pcol@flushclear! ($f=|switch|$), and \!\endparacol!
% ($f=|end|$) to set one of them into \!\outputpenalty!, so that the other
% user \!\pcol@specialoutput! examines which special function is invoked.
% 
% \SpecialIndex{\pcol@output@start}
% \SpecialIndex{\pcol@output@switch}
% \SpecialIndex{\pcol@output@flush}
% \SpecialIndex{\pcol@output@clear}
% \SpecialIndex{\pcol@output@end}
% 
%    \begin{macrocode}
%% Special Output Routines: Dispatcher

\def\pcol@op@start{-10010}
\def\pcol@op@switch{-10011}
\def\pcol@op@flush{-10012}
\def\pcol@op@clear{-10013}
\def\pcol@op@end{-10014}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \changes{v1.24}{2013/07/27}
%	{\cs{pcol@op@mcpush} was introduced for coloring specified in math
%	 mode but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@op@mcpush} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.24}{2013/07/27}
%	{\cs{pcol@op@mcpush@pone} was introduced for coloring specified in
%	 math mode but removed in v1.34.}
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@op@mcpush@pone} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.24}{2013/07/27}
%	{\cs{pcol@op@mcpop} was introduced for coloring specified in math
%	 mode but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@op@mcpop} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.24}{2013/07/27}
%	{\cs{pcol@op@mcpop@pone} was introduced for coloring specified in
%	 math mode but removed in v1.34.}
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@op@mcpop@pone} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% 
% \begin{macro}{\pcol@specialoutput}
% \changes{v1.0}{2011/10/10}
%	{Remove unnecessary \cs{pcol@latex@specialoutput}.}
% \changes{v1.2-2}{2013/05/11}
%	{Add footnote logging if $\cs{outputpenalty}\EQ-10004$.}
% \changes{v1.22}{2013/06/30}
%	{Add the invocation of \cs{pcol@output@}${\cdot}f$ for
%	 $f\in\{\string\texttt{cpush},\string\texttt{cpop},
% 	 \string\texttt{cset}\}$}
% \changes{v1.24}{2013/07/27}
%	{Add examination with $P_{\string\rm{push}}$ and $P_{\string\rm{pop}}$
%	 and invocation of \cs{pcol@output@mcpush} and
%	 \cs{pcol@output@mcpop}.} 
% \changes{v1.34}{2018/05/07}
%	{Remove examinations related to $f\in\{{\tt cpush},{\tt cpop},{\tt
%	 mcpush},{\tt mcpop}\}$.}
% 
% The macro \!\pcol@specialoutput! is invoked solely in \!\pcol@output! to
% invoke our own or \LaTeX's special output routine.  It examines if
% $P=\!\outputpenalty!\in\Set{\cs{pcol@op@}{\cdot}f}{f\in F}$ and then, if
% so, before invoking $|\pcol@output@|{\cdot}f$, we rebuild \!\@holdpg!
% removing \!\lastbox! and the last vertical skip as done in \LaTeX's
% \!\@specialoutput!.  We also let $\!\outputpenalty!=-10000$\footnote{
% 
% It can be any value larger than -10004.}
% 
% so that \!\vsize! is correctly set to \!\@colroom! in the second half of
% \!\pcol@output! after this macro finishes.
% 
% \hfuzz9pt
% Otherwise, i.e., if $P\notin\Set{\cs{pcol@op@}{\cdot}f}{f\in{}F}$,
% we simply invokes \LaTeX's \!\@specialoutput!\footnote{
% 
% With footnote logging if $\cs{outputpenalty}=-10004$.}.
% 
%    \begin{macrocode}
\def\pcol@specialoutput{%
  \ifnum\outputpenalty=\pcol@op@start\relax
    \let\reserved@a\pcol@output@start
  \else\ifnum\outputpenalty=\pcol@op@switch\relax
    \let\reserved@a\pcol@output@switch
  \else\ifnum\outputpenalty=\pcol@op@flush\relax
    \let\reserved@a\pcol@output@flush
  \else\ifnum\outputpenalty=\pcol@op@clear\relax
    \let\reserved@a\pcol@output@clear
  \else\ifnum\outputpenalty=\pcol@op@end\relax
    \let\reserved@a\pcol@output@end
  \else \let\reserved@a\@specialoutput
  \fi\fi\fi\fi\fi
  \ifnum\outputpenalty=-\@Miv\relax
    \ifvoid\footins\else \pcol@Log\dummy{dummy}\footins \fi
  \fi
  \ifx\reserved@a\@specialoutput\else
    \global\setbox\@holdpg\vbox{\unvbox\@holdpg \unvbox\@cclv
      \setbox\@tempboxa\lastbox \unskip}%
    \outputpenalty-\@M
  \fi
  \reserved@a}

%    \end{macrocode}
% \end{macro}
% 
% 
% 
% \subsection{Building Starting Page} \label{sec:imp-sout-start}
% 
% \begin{macro}{\pcol@output@start}
% \changes{v1.0}{2011/10/10}
% 	{Change the order of operations.}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{pcol@maxpage} as \cs{pcol@toppage}.}
% \changes{v1.0}{2011/10/10}
%	{Add special operation in case of too small room for column-pages.}
% \changes{v1.2-2}{2013/05/11}
%	{Add initialization of $\string\mathit{\string\Phi}$ and
%	 page-wise footnote output operations, and revise reflecting
%	 the redesign of page context.} 
% \changes{v1.2-7}{2013/05/11}
%	{Add \cs{pcol@outputtrue} to solve the \cs{output} request sneaking.}
% \changes{v1.2-7}{2013/05/11}
%	{Include the effect of the separation of pre-environment bottom
%	 floats and columns in the starting page into the check of too large
%	 pre-envronment stuff.}
% \changes{v1.3-6}{2013/09/17}
%	{Change the page builder for too tall pre-environment stuff from
%	 \cs{pcol@makenormalcol} to \cs{@makecol} because the page should be
%	 built by the ordinary mechanism.}
% \changes{v1.3-3}{2013/09/17}
%	{Let $\cs{ifpcol@output}\EQ\string\mathit{false}$ temporarily before
%	 the invocation of \cs{@outputpage} for too tall pre-environment
%	 stuff because the page is considered as outside
%	 \string\texttt{paracol} envrionments.}
% \changes{v1.32-3}{2015/10/10}
% 	{Add depth clearing of imported deferred floats in case that some of
%	 them has \texttt{1sp}.}
% \changes{v1.35-4}{2018/12/31}
% 	{Add \cs{belowfootnoteskip} to $H_f$ being the space for the
%	 non-merged pre-environment footnotes.}
% 
% The macro \!\pcol@output@start! is invoked solely from
% \!\pcol@specialoutput! to process the special \!\output! request made in
% \!\pcol@zparacol! and to build the {\em\Uidx\spage} from which parallel
% columns start possibly with the stuff preceding \beginparacol{}, or
% {\em\Uidx\preenv} in short.  First, we turn
% $\CSIndex{ifpcol@output}=\true$ so that \!\output!  requests for page
% breaks are processed by our own macros such as \!\pcol@makecol! hereafter.
% Then we let $p=\pbase={\ptop}=0$ and $\PP=\emptyset$ because we have
% nothing for $q<\ptop=0$.  We also move \!\@deferlist! to \!\@dbldeferlist!
% and then let \!\@deferlist! be empty because all \cwise{} dererred floats
% become \pwise{}.  In this float importation, as discussed in
% item-(\ref{item:ovv-float-@output@start}) of
% \secref{sec:imp-ovv-float}, we force all floats in the list have
% depth 0 to ensure no one has |1sp| to conform our own and old-fashioned
% \pwise{} float placement mechanism\footnote{
% 
% Though having \texttt{1sp} is almost imposiible.}.
% 
% We then and let $\df=\bot$ because we don't have any deferred footnotes.
% 
% Next we caculate $H=H_r-(H_m+H_f+H_b)$ where $H_r=\!\@colroom!$; $H_m$ is
% the height-plus-depth of the main vertical list in \!\@holdpg!; $H_f$ is
% the sum of \!\skip!\!\footins!, the height-plus-depth of \!\footins! and
% \!\belowfootnoteskip!, if \!\footins! is not $\bot$ or 0 otherwise; and
% $H_b=\!\textfloatsep!$ if the \preenv{} has bottom floats or 0 otherwise.
% That is, $H$ is the room for each of \colpage{} in the \spage.  Then we
% examine if $H<1.5\times\!\baselineskip!$ to mean \!\pcol@output!  would
% force a page break with warning.  If so, we assume we have a page break
% before \beginparacol{} to ship out \preenv{} to avoid the warning.
% Therefore, we invoke \LaTeX's \!\@makecol!\footnote{
% 
% \Sloppy{2500}%
% We can be unaware of our customization for \sync{}ation in
% \CSIndex{pcol@combinefloats} because \CSIndex{pcol@textfloatsep} is
% made $\infty$ by \CSIndex{pcol@zparacol}.}
% 
% giving it \!\@holdpg!  through \!\@cclv! to build the ship-out image in
% \!\@outputbox!.  Then the box is passed to \!\@outputbox! for which we
% temporarily let $\CSIndex{ifpcol@output}=\false$ because the page is
% assumed to be outside the \env{paracol} environment having just started.
% 
% After that we invoke \!\pcol@startpage! to let it produce $\pp(\ptop)$ for
% the \spage{} $\ptop=0$ letting $\!\pcol@currpage!$ be empty so that the
% macro will not refer to it.  The page $\pp(0)$ is usually empty but can
% have non-empty $\pp^i(0)$ with imported deferred floats which are now
% \pwise.  Moreover, we can have two or more pages if deferred \pwise{}
% floats produce \fpage{s}.  However, we can be unaware of these effects of
% floats because the resulting $\PP^+$ with them is correct of course.
% 
% Then let $\!\topskip!=\!\pcol@topskip!$ being the value at \beginparacol,
% and $\cs{ifpcol@}\~|firstpage|={\false}$, because we have the \spage{}
% without \preenv{} and thus the first item of each column will be at its
% top.
% 
% \CSINDEX{ifpcol@firstpage}
% 
%    \begin{macrocode}
%% Special Output Routines: Building First Page

\def\pcol@output@start{%
  \global\pcol@outputtrue
  \global\pcol@page\z@ \global\pcol@toppage\z@ \global\pcol@basepage\z@
  \global\let\pcol@pages\@empty
  \global\let\@dbldeferlist\@deferlist \global\let\@deferlist\@empty
  {\def\@elt##1{\global\dp##1\z@}\@dbldeferlist}%
  \setbox\z@\box\pcol@topfnotes
  \@tempdima\@colroom
  \advance\@tempdima-\ht\@holdpg \advance\@tempdima-\dp\@holdpg
  \ifvoid\footins\else
    \advance\@tempdima-\skip\footins
    \advance\@tempdima-\ht\footins \advance\@tempdima-\dp\footins
    \advance\@tempdima-\belowfootnoteskip
  \fi
  \ifx\@botlist\@empty\else \advance\@tempdima-\textfloatsep \fi
  \ifdim\@tempdima<1.5\baselineskip
    \setbox\@cclv\box\@holdpg \@makecol
    \pcol@outputfalse \@outputpage \pcol@outputtrue
    \global\let\pcol@currpage\@empty \pcol@startpage
    \global\topskip\pcol@topskip \global\pcol@firstpagefalse
%    \end{macrocode}
% 
% Otherwise, i.e., if $H\geq1.5\times\!\baselineskip!$, we invoke
% \!\pcol@makenormalcol! to make the \preenv{} as the \spanning{} of the
% \spage.  The macro is different from \!\@makecol! as follows;  the height
% of resulting \!\@outputbox! is natural rather than \!\textheight!;
% \Mgfnote{}s is excluded if any; and the skip of \!\textfloatsep! is added
% below the bottom floats also if any,
% 
% Then we let $h$ be the height-plus-depth of \!\@outputbox! being the
% \spanning{} and shrink \!\@colht! by $h$.  Next if
% $h>\HB=\!\pcol@bg@preposttop!
% \in\{\!\pcol@bg@preposttop@left!,\~\!\pcol@bg@preposttop@right!\}$, being
% the bottom of the previous \env{paracol} environment (having right
% \parapag{}e) or 0 if the curret page does not have it, to mean we have
% ordinary single-columned stuff in \preenv{}, we paint its \bground{} by
% \!\pcol@bg@paintbox! temporarily letting $\!\pcol@bg@textheight!=h$ so
% that $y_0=\HB$ and $y_1=h$ for $\bgr_{\{p,P\}}$.  This \bgpaint{} is not
% only for $\pp^b(0)$ which we acquire from from \!\@freelist! by \!\@next!
% and let have the \spanning, but also for \!\pcol@rightpage! if $\CL<\C$ to
% mean \parapag{}ing for which we temporarily increment \!\c@page! by one if
% \npaired.
% 
% We also let $\pp^h(0)$ be the shrunk \!\@colht!, and $\pp^t(0)$ be
% \!\topskip! if $h=0$ assuming that the page does
% not have any \spanning{}\footnote{
% 
% Checking the emptiness by \cs{pcol@ifempty} does not work well for the
% very first page of a document because it has a \cs{write} as the very
% first item.}
% 
% to typeset \colpage{}s from the top of the page, or otherwise be 0
% together with \!\topskip! to inhibit the ordinary \!\topskip! insertion.
% 
% As for $\pp^m(0)$, we define it as follows, referring to
% $\mpbout=\!\pcol@mparbottom@out!=\{\mpb_L^l,\mpb_L^r,\mpb_R^l,\mpb_R^r\}$,
% where $\mpb_X^x$ has exactly one element $\mpar(h,t)$ which may be the
% position of last marginal notes in the last \env{paracol} environment in
% the page we are working on, or $\mpb_X^x=\{\mpar(0,0)\}$ if such marginal
% note or the environment itself does not exist in the page.  On the other
% hand, $B=\!\@mparbottom!$ may have non-zero for the bottom edge of the
% last marginal note in \preenv{} including the last \env{paracol}
% environment if any.  Therefore, what we need to do is to let
% $\mpb_L^x=\{\mpar(0,B)\}$ to reflect the marginal node whose bottom is at
% $B$ and which can be different from what $\mpb_L^x$ had, where $x$ is the
% target margin in the \preenv{} determined by \CSIndex{if@mparswitch}, the
% parity of $\page(0)$ and \CSIndex{if@reversemargin}.
% 
% The replacement is done by \!\pcol@do@mpbout! which invokes
% $\!\pcol@do@mpbout@whole!\arg{m_L^l}\~\arg{m_L^r}\arg{\mpb_R^l}\arg{\mpb_R^r}$
% where $m_L^x\in\{M_L^x,\,\!\pcol@do@mpbout@elem!\arg{M_L^x}\}$ whose choice
% is made according that $x\in\{l,r\}$ is the target margin (latter) or not
% (former).  Therefore, prior to the invocation of \!\pcol@do@mpbout!, we
% \!\def!fine \!\pcol@do@mpbout@whole! so that it \!\xdef!ines
% $\mpbout=\!\pcol@mparbottom@out!$ with its four arguments, and
% \!\pcol@do@mpbout@elem! to let it be expanded to
% $\!\@elt!\Arg{0}\Arg{B}=\mpar(0,B)$.  After that, we also invoke
% \!\pcol@bias@mpbout! giving it $-h$ to replace $\mpar(t,b)$ being the sole
% element of each $\mpb_{\{L,R\}}^{\{l,r\}}$ in the resulting $\mpbout$ with
% $\mpar(t-h,b-h)$ to have what we give to $\pp^m(0)$.  This replacement
% transforms the coordinates for text area to that for columns, and makes it
% possible for the first marginal note in each margin in the \env{paracol}
% environment we now start to exploit the space for \preenv{} even if it is
% tall extraordinarily.
% 
% Then we let $\pp(0)$ have $\pp^i(0)$ and $\pp^m(0)$ shown above, and
% $\pp^p(0)=\!\c@page!$, $\pp^f(0)=\bot$ and $\pp^s(0)=\emptyset$ by
% \!\pcol@defcurrpage!, and let $\CSIndex{ifpcol@firstpage}=\true$ because
% $\pp^b(0)$ has \preenv.
% 
% \changes{v1.3-6}{2013/09/17}
%	{Delete the argument of \cs{pcol@makenormalcol} because now it is
%	 not used too tall pre-environment stuff.}
% \changes{v1.3-3}{2013/09/17}
%	{Add background painting of pre-environment stuff.}
% \changes{v1.3-4}{2013/09/17}
%	{Add initialization of $\pi^m(0)$.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
  \else
    \pcol@makenormalcol
    \@tempdima\ht\@outputbox \advance\@tempdima\dp\@outputbox
    \global\advance\@colht-\@tempdima
    \def\reserved@a{%
      \ifdim\pcol@bg@preposttop=\@tempdima\else
        \edef\pcol@bg@textheight{\@elt{\number\@tempdima sp}}%
        \pcol@bg@paintbox{Pp}%
      \fi}
    \ifnum\pcol@ncolleft<\pcol@ncol
      \global\setbox\pcol@rightpage\vbox{%
        \ifpcol@paired\else \advance\c@page\@ne \fi
        \let\pcol@bg@preposttop\pcol@bg@preposttop@right
        \reserved@a \unvbox\pcol@rightpage}%
    \fi
    \pcol@Fb
    \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{%
      \let\pcol@bg@preposttop\pcol@bg@preposttop@left
      \reserved@a \unvbox\@outputbox}}\pcol@ovf
    \pcol@Fe{output@start(preenv)}%
    \global\dimen\@currbox\@colht
    \ifdim\@tempdima=\z@ \@tempskipa\topskip \else \@tempskipa\z@ \fi
    \global\skip\@currbox\@tempskipa \global\topskip\@tempskipa
    \def\pcol@do@mpbout@whole##1##2##3##4{%
      \xdef\pcol@mparbottom@out{{##1}{##2}{##3}{##4}}}%
    \def\pcol@do@mpbout@elem\@elt##1##2{\@elt{0}{\number\@mparbottom}}%
    \pcol@do@mpbout
    \pcol@bias@mpbout{-\@tempdima}%
    \pcol@defcurrpage{\number\c@page}\@currbox\voidb@x{}{\pcol@mparbottom@out}%
    \global\pcol@firstpagetrue
  \fi
%    \end{macrocode}
% 
% Then regardless of $H$, we do the followings for all columns $c\In0\C$ to
% build $\cc_c$, after initializing \!\@colroom! to be \!\@colht!, and
% invoking \!\pcol@floatplacement! to reinitialize the parameters of
% \cwise{} float placement.
% 
% First, if we have let $\!\topskip!=0$ with the \preenv,
% we let $\cc_c(\vb^b)$ have an invisible \!\hrule! whose
% height and depth are 0 as the very first vertical item of the \colpage.
% When we visit the column $c$ for the first time afterward, we will
% \!\unvbox! the box to let \TeX's page builder have $\!\topskip!=0$ and the
% invisible rule.  Then the first vertical item of the \colpage{} is added
% but it is recognized as non-first by \TeX's page builder and thus it
% inserts \!\baselineskip! referring to \!\prevdepth! as the depth of the
% last item.  The important issue is that the \!\prevdepth! to be referred
% is assured having its value at \beginparacol, which is usually the depth
% of the last item of \spanning, by the following mechanism: (1)
% \!\pcol@invokeoutput! invoked in \!\pcol@zparacol! saves \!\prevdepth! in
% \!\pcol@prevdepth! before the \!\output! request for
% \!\pcol@output@start!; (2) \!\pcol@prevdepth! is saved in $\cc_c(\pd)$ by
% \!\pcol@setcurrcolnf!  invoked from \!\pcol@output@start! as discussed
% afterward; (3) when the column $c$ is visited for the first time, the
% special output routine \!\pcol@output@start! itself ($c=0$) or
% \!\pcol@output@switch! ($c>0$) restores \!\pcol@prevdepth! from
% $\cc_c(\pd)$ by \!\pcol@getcurrcol!; (4) \!\pcol@invokeoutput!  which made
% the \!\output! request for (3) lets \!\prevdepth! have the value of
% \!\pcol@prevdepth! after the request.  Therefore, the baseline progress
% from the last line of the \spanning{} to the first line of each
% \colpage{} should be very natural as we see in the third and fourth lines
% of \secref{sec:man-close} of Part \ref{part:man}.
% 
% Then we invoke \!\pcol@setcurrcolnf! to save the following values for
% $\cc_c(e)$ ($e\neq\vb$); $\cc_c(\ft)=\!\voidb@x!$ because $c$ does not
% have \Mcfnote{}s so far;  $\cc_c(\pd)=\!\prevdepth!$ as discussed above;
% $\cc_c(\tl)=\cc_c(\ml)=\cc_c(\bl)=\emptyset$ because
% \!\pcol@makenormalcol! and \!\@combinefloats! invoked from it emptied
% them; $\cc_c(\dl)=\emptyset$ as discussed above;
% $\cc_c(\tn)=\!\c@topnumber!$, $\cc_c(\bn)=\!\c@botnumber!$ and
% $\cc_c(\tn)=\!\c@totalnumber!$ as initialized by \!\@floatplacement!
% invoked from \!\pcol@floatplacement!;
% $\cc_c(\tr)=\!\topfraction!\times\!\@colht!$ and
% $\cc_c(\br)=\!\bottomfraction!\times\!\@colht!$ as initialized by
% \!\@floatplacement!; $\cc_c(\sw)$ is defined by \CSIndex{if@nobreak} and
% \cs{if@after}\~|indent|
% 
% \expandafter\SpecialIndex\csname if@afterindent\endcsname
% 
% at the time of \beginparacol; and
% $\cc_c(\ep)=\!\everypar!$ at the time of \beginparacol.  We also let
% $\cc_c(\vb^p)=0$ because $p=0$ and $\cc_c(\vb^r)=\!\@colroom!$ defined
% above.  In addition, we let $\S_c=\emptyset$ because we don't have any
% \colpage{} having been completed.
% 
% \SpecialArrayIndex{c}{\pcol@columncolor}
% \SpecialArrayIndex{c}{\pcol@columncolor@box}
% We also examine if $\Celtshadow^c=\cs{pcol@columncolor}\cdot c$ is defined
% and, if so, acquire an \!\insert! from \!\@freelist! to let
% $\Celt^c=\cs{pcol@columncolor@box}\cdot c$ have the coloring \!\special!
% for the color defined in $\Celtshadow^c$ by invoking \!\pcol@set@color!
% being the origina \!\set@color! with nullification of \!\aftergroup!.
% Otherwise, we let $\Celt^c=\bot$ .
% 
% \changes{v1.0}{2011/10/10}
%	{Add clearing of $S_c$.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% \changes{v1.34}{2018/05/07}
%	{Add initialization of
%	 $\gamma_0^c\EQ\cs{pcol@columncolor@box}\cdot c$.} 
% 
%    \begin{macrocode}
  \global\@colroom\@colht \pcol@floatplacement
  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
    \pcol@Fb
    \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{%
      \ifdim\topskip=\z@ \hrule\@height\z@\@width\z@ \fi}}\pcol@ovf
    \pcol@Fe{output@start(col)}%
    \pcol@setcurrcolnf
    \global\count\@currbox\z@
    \global\dimen\@currbox\@colroom
    \expandafter\gdef\csname pcol@shipped\number\pcol@currcol\endcsname{}%
    \pcol@ifccdefined
      {\@next\@currbox\@freelist{\global\setbox\@currbox\vbox{%
        \def\current@color{\pcol@ccuse{}}\let\aftergroup\@gobble
        \pcol@set@color}}\pcol@ovf}%
      {\def\@currbox{\voidb@x}}%
    \pcol@ccxdef{\@currbox}%
   \advance\pcol@currcol\@ne}%
%    \end{macrocode}
%
% \changes{v1.2-1}{2013/05/11}
%	{Add emptying \cs{pcol@colorstack} and the invocation of
%	 \cs{pcol@savecolorstack} at the beginnig of the first
%	 column-page to be built.}
% \changes{v1.2-2}{2013/05/11}
%	{Add insertion of \cs{footins} having footnotes to be merged if it
%	 is not void.}
% \changes{v1.22}{2013/06/30}
%	{Move emptying \cs{pcol@colorstack} to \cs{pcol@zparacol}.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% \changes{v1.35-1}{2018/12/31}
% 	{Add \cs{interlinepenalty} insertion for the first column to avoid
%	 vertical overfull due to the first item taller than the column
%	 room.} 
% 
% Finally, we let $c=\!\pcol@currcol!=0$ for the first column, and regain the
% parameters in $\cc_0$ by \!\pcol@getcurrcol!.  Then before putting
% $\cc_0(\vb^b)$ to the main vertical list by \!\unvbox! returning
% $\cc_0(\vb)$ to \!\@freelist! by \!\@cons! because it has become useless
% so far, we save the \colorctext{} just with $\Celt^c$ into $\csts$ by
% \!\pcol@savecolorstack! because $\CST$ is emptied by \!\pcol@zparacol!.
% Then we \!\insert! \!\footins! through itself to the main vertical list if
% it is not $\bot$ and thus has footnotes to be \mgfnote{}.  This
% \!\insert!ion is different from other footnote \!\insert!ion because
% \!\footins! is not \!\unvbox!ed but is put as a whole and is followed by
% \!\penalty!\!\interlinepenalty!, so that footnotes will not be broken by
% \TeX's page builder to prevent the reconnection of a broken footnote with
% innapropriate glue discarding, which we will discuss in
% \secref{sec:imp-fnote}.  We also add a penalty 10000 or
% \!\interlinepenalty! according to $\CSIndex{if@nobreak}=\true$ or not to
% allow the first column to start from a new page when its first item is
% taller than the room in the \spage{}.
% 
%    \begin{macrocode}
  \global\pcol@currcol\z@
  \pcol@getcurrcol
  \pcol@savecolorstack
  \pcol@Fb
  \@cons\@freelist\@currbox \unvbox\@currbox
  \pcol@Fe{output@start(col)}%
  \ifvoid\footins\else
    \pcol@Log\pcol@output@start{insert}\footins
    \insert\footins{\box\footins\penalty\interlinepenalty}%
  \fi
  \if@nobreak \nobreak \else \addpenalty\interlinepenalty \fi}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@makenormalcol}
% \changes{v1.2-2}{2013/05/11}
%	{Replace the building operation of \cs{@outputbox} with footnotes
%	 with the invocation of \cs{pcol@combinefootins} and add the
%	 examination of \cs{ifpcol@mgfnote}.}
% \changes{v1.2-7}{2013/05/11}
%	{Turn \cs{ifpcol@lastpage} be $\string\true$ temporarily for
%	 \cs{pcol@combinefloats} to separate bottom floats in 
%	 pre-environment stuff and the multi-column stuff in
%	 \string\texttt{paracol} environment by \cs{textfloatsep}.}
% \changes{v1.3-6}{2013/09/17}
%	{Completely redesigined to use \cs{@makecol} if pre-environment
%	 stuff has bottom floats.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
% The macro \!\pcol@makenormalcol! is invoked solely from
% \!\pcol@output@start! to let \!\@output~box! have the \preenv{} as
% \spanning{} of the \spage.  The operations this macro performs are very
% similar to those of \!\@makecol!, which in fact is used in this macro
% itself, but has the following differences.
% 
% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
% \item
% If $\CSIndex{ifpcol@mgfnote}=\true$, we exclude footnotes in \!\footins!
% from \!\@outputbox!, because they are \mgfnote{} with \Scfnote{}s given in
% columns, by saving it into \!\@tempboxa! during the building process and
% restoring it from the box register.
% 
% \item
% If \preenv{} does not have bottom floats, we build \!\@outputbox! by
% ourselves without relying on \!\@makecol! because the skips put into the
% bottom (or near it) by the macro is harmful to making \preenv{} and
% parallel columns naturally connected.  Therfore, we move
% \!\@holdpg! to \!\@outputbox! adding \!\footins! to its tail if any by
% \!\pcol@combinefootins!, and then combine top floats if any by
% \!\pcol@combinefloats!\footnote{
% 
% Since we do not have bottom floats, the order of materials in the
% resulting \!\@outputbox! being top floats, main text and footnotes should
% be consistent with other pages with any \LaTeX{} including p\LaTeX.}.
% 
% In addition, we clear \!\@midlist! and retuns its contents to
% \!\@freelist! as \!\@makecol! does.
% 
% \item
% If \preenv{} has bottom floats, on the other hand, we use \!\@makecol! to
% build \preenv{} in \!\@outputbox! moving \!\@holdpg! into \!\box!|255|
% prior to the invocation\footnote{
% 
% Therefore the order of footnotes and bottom floats is consistent with
% other pages and columns, i.e., footnote-first in the native \LaTeX{} while
% float-first in p\LaTeX{}, for example.}.
% 
% Also before invocation in addition, we temporarily let
% $\CSIndex{ifpcol@lastpage}=\true$ to let
% $\!\@combinefloats!=\!\pcol@combinefloats!$ used in \!\@makecol!  put a
% vertical skip of \!\textfloatsep! below the bottom floats so that the
% floats are well seperated from the top of multi-column stuff in the
% \spage.  We also nullify \!\@textbottom! by making it \!\let!-equal to
% \!\relax! because it is unncessary to put an infinitely stretchable skip
% at the bottom\footnote{
% 
% Even if unharmful.},
% 
% and let $\!\vbadness!=10000$ to avoid an inevitable underfull message
% because \!\@makecol! lets \!\@outputbox! as tall as \!\textheight!.
% 
% \item
% In both cases but especially that with bottom floats, resulting
% \!\@outputbox! is decapsulated by \!\unvbox! to make its height {\em
% natural}.
% \end{enumerate}
% 
% Note that the special function for \sync{}ed \colpage{} in
% \!\pcol@combinefloats! used directly or indirectly in this macro, on the
% other hand, is not active in the invocation because \!\pcol@zparacol!
% initialized $\!\pcol@textfloatsep!=\infty$ to mean we have no \sync{}ation
% points.  Also
% note that bottom floats and non-\mgfnote{} footnotes are put in
% \!\@outputbox! and thus they will not appear at the bottom of the page
% but above the \colpage{}s in the page\footnote{
% 
% We could put them at the bottom by keeping them somewhere and insert them
% in \!\pcol@outputcolumns!, but it will cause another problem that the
% numbers of the figures and footnotes are smaller than those in \colpage{}s
% which are above them.}.
% 
%    \begin{macrocode}
\def\pcol@makenormalcol{%
  \ifpcol@mgfnote \setbox\@tempboxa\box\footins \fi
  \begingroup
  \ifx\@botlist\@empty
    \ifvoid\footins \setbox\@outputbox\box\@holdpg
    \else           \pcol@combinefootins\@holdpg\footins
    \fi
    \pcol@Fb
    \let\@elt\relax \xdef\@freelist{\@freelist\@midlist}%
    \pcol@Fe{makenormalcol}%
    \global\let\@midlist\@empty
    \pcol@combinefloats
  \else
    \pcol@lastpagetrue
    \setbox\@cclv\box\@holdpg \let\@textbottom\relax \vbadness\@M
    \@makecol
  \fi
  \global\setbox\@outputbox\vbox{\unvbox\@outputbox}%
  \endgroup
  \ifpcol@mgfnote \setbox\footins\box\@tempboxa \fi}

%    \end{macrocode}
% \end{macro}
% 
% 
% 
% \subsection{Column-Switching}
% \label{sec:imp-sout-switch}
% 
% \begin{macro}{\pcol@output@switch}
% \changes{v1.2-1}{2013/05/11}
%	{Add \cs{pcol@clearcst@unvbox} to add coloring \cs{special}s at the
%	 top and bottom of the column-page to be saved.}
% \changes{v1.3-1}{2013/09/17}
%	{Add the capture of a spanning text when it is closed.}
% \changes{v1.3-3}{2013/09/17}
%	{Add $\pi^s(p)\EQ\cs{pcol@sptextlist}$ to the argument of
%	 \cs{pcol@defcurrpage}.}
% \changes{v1.3-4}{2013/09/17}
%	{Add $\pi^m(p)\EQ\cs{pcol@mparbottom}$ to the argument of
%	 \cs{pcol@defcurrpage}.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% \changes{v1.33-2}{2016/11/19}
% 	{Let \cs{dimen@} have the height of \cs{pcol@prespan} if it is not
%	 $\bot$, or 0 if $\bot$ for the sake of clarity.}
% 
% The macro \!\pcol@output@switch! is invoked from
% \!\pcol@specialoutput! to process the special \!\output! request made in
% \!\pcol@switchcol!, \!\pcol@visitallcols! and \!\pcol@flushclear!, for a
% \cswitch{} from $c=\!\pcol@currcol!$ to $d=\!\pcol@nextcol!$ which can be
% $c$.  The macro is also invoked from \!\pcol@makeflushedpage!  to \sync{}e
% and to flush all \ccolpage{}s but staying in $c$.
% 
% First, we examine if the \cswitch{} is to close a \mctext, i.e.,
% $\CSIndex{ifpcol@sptext}={\true}$ and $c=0$, and if so we do the
% following; let $h_p$ be the height of \!\pcol@prespan! having \prespan{}
% if it is not $\bot$, or 0 if $\bot$ to mean we have had a page break in
% the \mctext; add $h_p$ to \!\@colroom! which we temporarily shrank when
% the \mctext{} starts; add an elemnent $\spt(H,h)$ to the tail of
% $\pp^s(\ptop)=\!\pcol@sptextlist!$ by \!\pcol@getcurrpage! and
% \!\pcol@defcurrpage!, where $H$ is $h_p$ plus the total height of top
% floats measured by \!\pcol@addflhd!, and $h$ is the height-plus-depth of
% \!\@holdpg! having (a part of) \mctext, represented in the form of
% integers and thus expanded with \!\number!; shift \!\@holdpg! left by
% \!\pcol@shiftspanning! if the column-0 is not the leftmost due to \cswap;
% and then put \prespan{} and (maybe shifted) \!\@holdpg! into \!\@holdpg!
% itself so as to let \!\@holdpg! have everything in the \colpage{} 0 as
% usual.
% 
% Note that it can be $\!\pcol@prespan!=\bot$ if \mctext{} had a page break
% (or multiple ones) in it as shown above.  This empty \prespan{}, however,
% does not always means that we have no top floats because the page break in
% the \mctext{} can produce a \colpage{} with top floats which are deferred
% from the previous page(s), or though unlikely the \mctext{} itself has
% float environments.  Therefore, the measurement of the total height of top
% floats are always necessary.  Also note that we perform these operations
% at the first \cswitch{} for \cscan{}ing from $c=0$ with
% $\CSIndex{ifpcol@sptext}=\true$, i.e., prior to the \sync{}ation itself
% which takes place afterword, as explained shortly.
% 
% Then regardless of the operations above, we acquire an \!\insert! from
% \!\@freelist! by \!\@next! for $\cc_c(\vb)$ to store the \ccolpage{} in
% (maybe modified) \!\@holdpg! by \!\pcol@clearcst@unvbox! to add uncoloring
% \!\special!s to rewind the \colorstack{} $\CST^c$ at the bottom and
% possibly coloring ones to establish that saved in $\csts$ at the top as
% the \colorctext{} for the \colpage{} when it has the first item.
% 
% Then if $\!\footins!\neq\bot$, we perform one of the followings.
% 
% \begin{itemize}
% \item
% If \Scfnote{} typesetting is in effect and $p=\ptop$, we save \!\footins!
% into $\pp^f(p)$ by the sequence of \!\pcol@getcurrpinfo! to get $\pp(p)$,
% \!\pcol@savefootins! to move it in $\pp^f(p)$, and \!\pcol@defcurrpage! to
% update $\pp(p)$ with $\pp^f(p)$.
% 
% \item
% If \Scfnote{} typesetting is in effect but $p<\ptop$, we simply discard
% the contents of \!\footins!  by making it $\bot$, because \!\footins!
% should have $\pp^f(p)$ which has been already fixed.
% 
% \item
% If \Mcfnote{} typesettinng is in effect, by \!\pcol@savefootins! we save
% \!\footins! into \!\pcol@currfoot!, which should be $\bot$ in other cases,
% so that it will be saved into $\cc_c(\ft)$ by \!\pcol@setcurrcol!
% afterward.
% \end{itemize}
% %
% Then if $c=0$, we invoke \!\pcol@setpageno! to reflect the jump of
% \!\c@page! made in the building process of the \colpage{} to $\pp(q)$ for
% all $q\in[p,\ptop]$.  After that, we save $c$'s \cctext{} into $\cc_c$ by
% \!\pcol@setcurrcol! and let $\cc_c(\vb^p)=p$ and
% $\cc_c(\vb^r)=\!\@colroom!$.
% 
%    \begin{macrocode}
%% Special Output Routines: Column-Switching

\def\pcol@output@switch{%
  \ifpcol@sptext\ifnum\pcol@currcol=\z@
    \ifvoid\pcol@prespan \dimen@\z@ \else \dimen@\ht\pcol@prespan \fi
    \global\advance\@colroom\dimen@
    \pcol@addflhd\@toplist\pcol@textfloatsep
    \pcol@getcurrpinfo\@tempcnta\@tempdima\@tempskipa
    \@tempdimb\ht\@holdpg \advance\@tempdimb\dp\@holdpg
    \@cons\pcol@sptextlist{{\number\dimen@}{\number\@tempdimb}}%
    \pcol@defcurrpage{\number\@tempcnta}\pcol@spanning\pcol@footins
                     {\pcol@sptextlist}{\pcol@mparbottom}%
    \pcol@shiftspanning\@holdpg
    \setbox\@holdpg\vbox{\unvbox\pcol@prespan \unvbox\@holdpg}%
  \fi\fi
  \pcol@Fb
  \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{
    \pcol@clearcst@unvbox\@holdpg}}\pcol@ovf
  \pcol@Fe{output@switch}%
  \def\pcol@currfoot{\voidb@x}%
  \ifvoid\footins\else
    \ifpcol@scfnote
      \ifnum\pcol@page=\pcol@toppage
        \pcol@getcurrpinfo\@tempcnta\@tempdima\@tempskipa
        \pcol@Log\pcol@output@switch{save}\footins
        \pcol@Fb
        \pcol@savefootins\pcol@footins
        \pcol@Fe{output@switch(pagefn)}%
        \pcol@defcurrpage{\number\@tempcnta}\pcol@spanning\pcol@footins
                         {\pcol@sptextlist}{\pcol@mparbottom}%
      \else
        \pcol@Log\pcol@output@switch{discard}\footins
        \setbox\@tempboxa\box\footins
      \fi
    \else
      \pcol@Log\pcol@output@switch{save}\footins
      \pcol@Fb
      \pcol@savefootins\pcol@currfoot
      \pcol@Fe{output@switch(colfn)}%
    \fi
  \fi
  \ifnum\pcol@currcol=\z@ \pcol@setpageno \fi
  \pcol@setcurrcol
  \global\count\@currbox\pcol@page
  \global\dimen\@currbox\@colroom
%    \end{macrocode}
% 
% Next, we examine if $\CSIndex{ifpcol@sptext}=\true$ and $c=0$ again, and
% if so we {\em broadcast} \CSIndex{if@nobreak} and
% \CSIndex{if@afterindent}, or in other words $\cc_c(\sw)$, and tokens in
% $\!\everypar!=\cc_c(\ep)$, to pretend all columns follow the \mctext.
% That is, for each column $e$, we restore its \cctext{} from $\cc_e$ by
% \!\pcol@getcurrcol!, let \CSIndex{if@nobreak} and \CSIndex{if@afterindent}
% have the values for $c$ ($\in\{0,\C{-}1\}$) and $\!\everypar!=\cc_c(\ep)$,
% and then save the context to $\cc_e$ by \!\pcol@setcurrcol! so that
% $\cc_e(\sw)=\cc_c(\sw)$ and $\cc_e(\ep)=\cc_c(\ep)$.  After that, we
% \!\global!ly turn $\CSIndex{ifpcol@sptext}=\false$ to give it the default
% state.
% 
% Note that this broadcast is essential when the \mctext{} has sectioning
% commands to have consistent settings of the page break inhibition, the
% skip above the another sectioning command following them, and the
% indentation of the first paragraph, for all columns.  On the other hand,
% broadcasting of \!\everypar! is natural even when it does not have
% sectioning commands because all columns may be considered following the
% \mctext.  Also note that, as mentioned in the explanation of the first
% examination at the beginning of this macro, we perform these operations at
% the first \cswitch{} for \cscan{}ning from $c=0$ with
% $\CSIndex{ifpcol@sptext}=\true$ prior to the \sync{ation} following the
% \mctext.  This means, if $\CSIndex{if@nobreak}={\true}$,
% $\!\penalty!=10000$ is inserted at the top and bottom end of the space for
% \mctext{} in the columns such that $c\neq0$, the former by this \cscan{}
% and the latter by the \cswitch{} to $c$ made after the synchronization.
% Therefore, if our \sync{ation} mechanism and \TeX's page builder once
% agreed both end can be in a page, both end will not chosen as page
% break points\footnote{
% 
% As for $c=0$, its top end of \mctext{} is a feasible break point to make
% the penalty insertion asymmetric.  Therefore, we need to reinvestigate if
% the condition of the broadcast is really appropriate, and, if
% inappropriate, have to go back to the old implementation in which
% \cs{ifpcol@sync} is included in the condition.  Otherwise, if proved
% appropriate, we will have to consider to make the penalty insertion
% symmetric by adding \cs{nobreak} at the top of \mctext{} in $c=0$.}.
% 
% \changes{v1.0}{2011/10/10}
%	{Restrict the broadcast of \cs{if@nobreak} and \cs{everypar} only
%	 when a column-switching is accompanied with spanning text.}
% \changes{v1.2-7}{2013/05/11}
%	{Modify broadcasting of $\kappa_c(\sigma)$ so that \cs{@afterindent}
%	 is broadcasted with \cs{@nobreak}.}
% \changes{v1.3-1}{2013/09/17}
%	{Rename \cs{ifpcol@mctext} as \cs{ifpcol@sptext}.}
% \changes{v1.3-6}{2013/09/17}
%	{Modify the condition of broadcasting $\kappa_0(\sigma)$ and
%	 $\kappa_0(\varepsilon)$ accompanied with \cs{ifpcol@sptext} from
%	 \cs{ifpcol@sync} to $c\EQ0$ so that the broadcast is made in the
%	 first column-switching in column-scanning.}
% 
%    \begin{macrocode}
  \let\reserved@a\@nobreakfalse \let\reserved@b\@afterindentfalse
  \ifpcol@sptext\ifnum\pcol@currcol=\z@
    \if@nobreak \let\reserved@a\@nobreaktrue \fi
    \if@afterindent \let\reserved@b\@afterindenttrue \fi
    \@temptokena\everypar
    \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
      \pcol@getcurrcol \reserved@a \reserved@b \everypar\@temptokena
      \pcol@setcurrcol
     \advance\pcol@currcol\@ne}%
    \global\pcol@sptextfalse
  \fi\fi
%    \end{macrocode}
% 
% \changes{v1.2-2}{2013/05/11}
%	{Add the case
%	 $\cs{ifpcol@clear}\EQ\cs{ifpcol@sync}\EQ\string\mathit{true}$ for
%	 the invocation of \cs{pcol@restartcolumn} for pre-flushing column
%	 height check.}
% \changes{v1.3-6}{2013/09/17}
%	{Modify the code structure to let
%	 $\cs{if@tempswa}\EQ\string\mathit{true}$ according to the
%	 modification of the broadcast of $\kappa_0(\sigma)$ and
%	 $\kappa_0(\varepsilon)$.}
% 
% Finally we invoke \!\pcol@sync! for the \sync{}ation if
% \CSIndex{ifpcol@sync} or \CSIndex{ifpcol@clear} is $\true$, and then
% \!\pcol@restartcolumn! to restart the \ccolpage{} $d$ if
% $\CSIndex{ifpcol@clear}={}\false$ to mean ordinary (but possibly
% \sync{}ed) \cswitch{} or $\CSIndex{ifpcol@clear}={}\true$ but
% $\CSIndex{ifpcol@sync}={}\true$ too to mean pre-flushing column height
% check, before finishing \!\output!  routine letting
% $\CSIndex{ifpcol@sync}=\false$ for next \cswitch.
% 
%    \begin{macrocode}
  \@tempswafalse \ifpcol@sync \@tempswatrue \fi \ifpcol@clear \@tempswatrue \fi
  \if@tempswa \pcol@sync \fi
  \@tempswatrue
  \ifpcol@clear \ifpcol@sync\else \@tempswafalse \fi\fi
  \if@tempswa \pcol@restartcolumn \fi
  \global\pcol@syncfalse}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@shiftspanning}
% \changes{v1.3-1}{2013/09/17}
%	{Introduced to shift a spanning text to left if the column-0 is not
%	 leftmost due to column-swapping.}
% 
% The macro $\!\pcol@shiftspanning!\arg{b}$ is used in \!\pcol@makecol! and
% \!\pcol@output@switch! to let box register $b$ have itself but shifted
% left by $\WT-w_0=\!\textwidth!-\!\columnwidth!$ so that the left edge of
% its contents \mctext{} is aligned to the left edge of the leftmost column
% being different from column-0 due to \cswap, i.e., if
% $\CSIndex{ifpcol@swapcolumn}=\true$ and $\!\c@page!\bmod2=0$.  Note that
% \!\c@page! is {\em not} obtained from $\pp^p(p)$ by the invokers but have
% the value when the \!\output! request is made to let invokers work, and
% thus have the correct value even when a jump occurs prior to the request.
% 
%    \begin{macrocode}
\def\pcol@shiftspanning#1{%
  \ifpcol@swapcolumn\ifodd\c@page\else
    \setbox#1\vbox{\@tempdima\textwidth \advance\@tempdima-\columnwidth
      \moveleft\@tempdima\box#1}
  \fi\fi}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@restartcolumn}
% \changes{v1.0}{2011/10/10}
%	{Add \cs{pcol@getcurrfoot} to restore parameters of $\kappa_c(\tau)$
%	 into \cs{footins}.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
% The macro \!\pcol@restartcolumn! is invoked from \!\pcol@output@switch! or
% \!\pcol@freshpage! to restart the \ccolpage{} $d=\!\pcol@nextcol!$ which
% becomes $c=\!\pcol@currcol!$ by the very first assignment in this macro.
% Then we restore the \cctext{} in $\cc_c$ by \!\pcol@getcurrcol! and let
% $p=\cc_c(\vb^p)$ and $\!\@colroom!=\cc_c(\vb^r)$ before returning
% $\cc_c(\vb)$ to \!\@freelist! by \!\@cons! because it has become useless
% so far.  We also restore the \pctext{} of $p$ by \!\pcol@getcurrpage!.
% 
%    \begin{macrocode}
\def\pcol@restartcolumn{%
  \global\pcol@currcol\pcol@nextcol
  \pcol@getcurrcol
  \global\pcol@page\count\@currbox
  \global\@colroom\dimen\@currbox
  \pcol@Fb
  \@cons\@freelist\@currbox
  \pcol@Fe{restartcolumn(col)}%
  \pcol@getcurrpage
%    \end{macrocode}
% 
% \changes{v1.2-2}{2013/05/11}
%	{Redesign the footnote insertion mechanism to cope with
%	 page-wise footnotes.}
% \changes{v1.2-1}{2013/05/11}
%	{Add \cs{pcol@restorecst@restart} to return main vertical list
% 	 with coloring operations.}
% \changes{v1.3-1}{2013/09/17}
%	{Rename \cs{pcol@restorecst@restart} as \cs{pcol@putbackmvl}.}
% \changes{v1.3-6}{2013/09/17}
%	{Change the code structure to move the insertion of page break
%	 penalty for ordinary column-wise footnotes from below the main
%	 text to below the footnotes.}
% \changes{v1.3-3}{2013/09/17}
%	{Add \cs{@colht} and \cs{@tempdimb} as the first and third argument
%	 of \cs{pcol@shrinkcolbyfn}.}
% 
% Then we perform footnote \!\insert!ion as follows.
% 
% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
% \item\label{item:scftop}
% If footnote typesetting is \scfnote{} and $p=\ptop$, we do the followings.
% 
% \begin{enumerate}\def\labelenumii{(\alph{enumii})}
% \item\label{item:scftop-main}
% Put the contents of $\cc_c(\vb^b)$ by \!\pcol@putbackmvl! to make
% the \colorctext{} in |.dvi| consistent with the current |.tex|'s one, and
% to save \prespan{} into \!\pcol@prespan! if we are opening a \mctext{}.
% 
% \item\label{item:scftop-pen}
% Put $\!\penalty!=10000$ by \!\nobreak! if $\CSIndex{if@nobreak}=\true$ or
% \!\interlinepenalty! by \!\addpenalty!\footnote{
% 
% As done in \!\@specialoutput! but \!\penalty!\!\interlinepenalty! should
% be sufficient.}
% 
% otherwise, as the page break penalty at the returning point.  Note that
% adding the \!\penalty! will be nullified by \TeX{} if $\cc_c(\vb^b)$ has
% nothing and thus, if the \colpage{} is still empty when we leave from it,
% its emptiness without any items is assured.  Also note that the penalty
% insertion here {\em looks} essential to keep \TeX's page builder from
% confusing with \scfnote{} footnotes which it has not seen in a
% \colpage\footnote{
% 
% At least a test with tall \scfnote{} footnotes gave us a confusing
% result.}.
% 
% \item\label{item:scftop-fnote}
% If $\pp^f(p)\neq\bot$, let \!\pcol@currfoot! and then \!\footins! have
% the footnotes in it by an \!\edef! and \!\pcol@getcurrfoot!, return the
% \!\insert! for them to \!\@freelist!, invoke \!\pcol@shrinkcolbyfn! to
% shrink \!\@colht! temporarily by their total height and to remember the
% exsistence of them with $\!\@tempdimb!=-\!\skip!\!\footins!$, and then
% \!\insert!  the footnotes so that it contributes to the building process
% of the \colpage{} to be restarted.  Otherwise, i.e. if $\pp^f(p)=\bot$,
% \!\@colht! is unchanged and $\!\@tempdimb!=0$.
% 
% \item\label{item:scftop-defer}
% Invoke \!\pcol@deferredfootins! to \!\insert! deferred footnotes in $\df$
% until their total height reaches (possibly shrunk) \!\@colht!.  This
% height capping is to keep \TeX's page builder from holding too large
% number of footnotes unprocessed causing confused ordering on presenting
% them to \!\output! routine.
% \end{enumerate}
% 
% \item
% If footnote typesetting is \scfnote{} but $p<\ptop$, we do the followings.
% 
% \begin{enumerate}\def\labelenumii{(\alph{enumii})}
% \item
% If $\pp^f(p)\neq\bot$, get it into \!\footins! as done in
% (\ref{item:scftop-fnote}) but giving \!\copy! to \!\pcol@getcurrfoot!
% because $\pp^f(p)$ has been fixed and thus will be kept until it is
% shipped out, and then \!\insert! it.
% 
% \item
% Put $\cc_c(\vb^b)$ and the penalty as done in (\ref{item:scftop-main}) and
% (\ref{item:scftop-pen}).
% \end{enumerate}
% 
% Thes order of footnotes, main vertical list and then penalty is essential
% to ensure that the \colpage{} in $p<\ptop$ has room for footnotes whose
% residence in $p$ has already been fixed.
% 
% \item
% If footnote typesetting is \mcfnote{}, we do the followings.
% 
% \begin{enumerate}\def\labelenumii{(\alph{enumii})}
% \item
% Put $\cc_c(\vb^b)$ as done in (\ref{item:scftop-main}).
% 
% \item
% If $\cc_c(ft)\neq\bot$, get it by \!\pcol@getcurrfoot! returning the
% \!\insert! to \!\@freelist!, and then \!\insert! it.
% 
% \item
% Put a penalty as done in (\ref{item:scftop-pen}).
% \end{enumerate}
% 
% The order of main vertical list, footnotes and then penalty is appropriate
% for \Mcfnote{}s because they definitely have space in the \colpage{} and
% \TeX{} will break the page below the insertion, possibly just below thanks
% to the penalty, to keep the footnotes and references to them in a page.
% \end{enumerate}
% 
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
  \ifpcol@scfnote
    \edef\pcol@currfoot{\pcol@footins}%
    \ifnum\pcol@page=\pcol@toppage
      \@tempdima\@colht \@tempdimb\z@
      \pcol@putbackmvl
      \if@nobreak \nobreak \else \addpenalty\interlinepenalty \fi
      \ifvoid\pcol@footins\else
        \pcol@Fb
        \pcol@getcurrfoot\box \@cons\@freelist\pcol@currfoot
        \pcol@Fe{restartcolumn(pagefn)}%
        \pcol@Log\pcol@restartcolumn{insert}\footins
        \pcol@shrinkcolbyfn\@colht\footins\@tempdimb
        \insert\footins{\unvbox\footins}%
      \fi
      \pcol@deferredfootins\pcol@restartcolumn
      \@colht\@tempdima
    \else
      \ifvoid\pcol@footins\else
        \pcol@getcurrfoot\copy
        \pcol@Log\pcol@restartcolumn{insdmy}\footins
        \insert\footins{\unvbox\footins}%
      \fi
      \pcol@putbackmvl
      \if@nobreak \nobreak \else \addpenalty\interlinepenalty \fi
    \fi
  \else
    \pcol@putbackmvl
    \ifvoid\pcol@currfoot\else
      \pcol@Fb
      \pcol@getcurrfoot\box \@cons\@freelist\pcol@currfoot
      \pcol@Fe{restartcolumn(colfn)}%
      \pcol@Log\pcol@restartcolumn{insert}\footins
      \insert\footins{\unvbox\footins}%
    \fi
    \if@nobreak \nobreak \else \addpenalty\interlinepenalty \fi
  \fi}

%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\pcol@getcurrcol}
% \changes{v1.1}{2012/05/11}
% 	{Add assignment $w_c$ to \cs{columnwidth}, \cs{hsize} and
%	 \cs{linewidth}.} 
% \changes{v1.2-5}{2013/05/11}
% 	{Move assignment $w_c$ to \cs{hsize} and \cs{linewidth} to
%	 \cs{pcol@invokeoutput}.}
% \begin{macro}{\pcol@igetcurrcol}
% \begin{macro}{\pcol@iigetcurrcol}
% \changes{v1.0}{2011/10/10}
%	{Add restoration of \cs{pcol@textfloatsep}.}
% \changes{v1.3-4}{2013/09/17}
%	{Remove the argument for $\kappa_c(\mu)\EQ\cs{@mparbottom}$ because it
%	 is no longer in the column context.}
% 
% The macro \!\pcol@getcurrcol! is invoked from the following macros to
% restore the typesetting parameters of the column $c=\!\pcol@currcol!$ from
% $\cc_c$, and to let \!\columnwidth! have
% $\w_c=|\pcol@columnwidth|{\cdot}c$\footnote{
% 
% \cs{hsize} and \cs{linewidth} are let have $\w_c$ and $\w_c-\lrm$
% respectively in \cs{pcol@invokeoutput}.}.
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% 
% \begin{itemize}\item[]\begin{tabular}{lll}
% \!\pcol@output@start!&\!\pcol@output@switch!&\!\pcol@restartcolumn!\\
% \!\pcol@flushcolumn!&\!\pcol@measurecolumn!&\!\pcol@synccolumn!\\
% \!\pcol@makeflushedpage!&\!\pcol@imakeflushedpage!&\!\pcol@iflushfloats!\\
% \!\pcol@freshpage!&\!\pcol@output@end!
% \end{tabular}
% \end{itemize}
% 
% Since we represent $\cc_c$ as;
% 
% \begin{eqnarray*}
% &&\Arg{\cc_c(\vb)}\Arg{\cc_c(\ft)}\Arg{\cc_c(\pd)}\Arg{\cc_c(\tl)}
% \Arg{\cc_c(\ml)}\Arg{\cc_c(\bl)}\Arg{\cc_c(\dl)}\Arg{\cc_c(\tf)}|%|\\
% &&\Arg{\Arg{\cc_c(\fh)}\Arg{\cc_c(\tn)}\Arg{\cc_c(\tr)}
%        \Arg{\cc_c(\bn)}\Arg{\cc_c(\br)}\Arg{\cc_c(\cn)}\Arg{\cc_c(\sw)}
%        \Arg{\cc_c(\ep)}}
% \end{eqnarray*}
% 
% in the body of $|\pcol@col|{\cdot}c$,
% 
% \SpecialArrayIndex{c}{\pcol@col}
% 
% we restore first eight by \!\pcol@igetcurrcol! giving everything above as
% its arguments by the expansion of
% $$
% \!\csname!| pcol@col|\!\number!\!\pcol@currcol!\!\endcsname!
% $$
% and then of the resulting control sequence.  Then this macro gives its
% nineth argument to \!\pcol@iigetcurrcol! which restores the last eight.  We
% also do
% $$
% \!\global!\!\columnwidth!|\pcol@columnwidth|{\cdot}c
% $$
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% 
% by a pair of \!\expandafter! for the first two control sequences.
% 
% Note that the restore operations are \!\global!, except for $\cc_c(\vb)$
% and $\cc_d(\ft)$ because they are referred to only in \!\output!,
% including \CSIndex{if@nobreak} for which \!\@nobreaktrue!  and
% \!\@nobreakfalse! are defined \!\global! by \LaTeX.  Also note that
% \!\dimen!-type parameters are saved in the form of integers and thus
% restoring them needs to specify the unit |sp|.
% 
%    \begin{macrocode}
\def\pcol@getcurrcol{%
  \expandafter\expandafter\expandafter\pcol@igetcurrcol
    \csname pcol@col\number\pcol@currcol\endcsname
  \expandafter\global\expandafter\columnwidth
    \csname pcol@columnwidth\number\pcol@currcol\endcsname}
\def\pcol@igetcurrcol#1#2#3#4#5#6#7#8#9{%
  \def\@currbox{#1}\def\pcol@currfoot{#2}\global\pcol@prevdepth#3sp\relax
  \gdef\@toplist{#4}\gdef\@midlist{#5}\gdef\@botlist{#6}\gdef\@deferlist{#7}%
  \global\pcol@textfloatsep#8sp\pcol@iigetcurrcol#9}
\def\pcol@iigetcurrcol#1#2#3#4#5#6#7#8{%
  \global\@textfloatsheight#1sp\relax
  \global\@topnum#2\relax \global\@toproom#3sp\relax
  \global\@botnum#4\relax \global\@botroom#5sp\relax
  \global\@colnum#6\relax
  \global\@afterindentfalse \@nobreaktrue
  \ifcase#7
    \@nobreakfalse \or
    \global\@afterindenttrue \else
    \relax
  \fi
  \global\everypar{#8}}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@getcurrfoot}
% \changes{v1.2-2}{2013/05/11}
%	{Add an argument being \cs{box} or \cs{copy}}
% 
% The macro $\!\pcol@getcurrfoot!\arg{com}$ is invoked from
% \!\pcol@startcolumn! (\!\copy!, $\pp^f(p)$), 
% \!\pcol@restartcolumn! (\!\copy!\slash\!\box!, $\pp^f(p)$\slash$\cc_c(\ft)$),
% \!\pcol@flushcolumn! (\!\box!, $\cc_c(\ft)$) and  \!\pcol@imakeflushedpage!
% (\!\box!, $\cc_c(\ft)$) to put everything in $\!\pcol@currfoot!$, having
% the second element in the parens following macro names, into \!\footins!
% using $\arg{com}$ shown as the first element in parens for the \!\box!
% component.  That is, if the source $\pp^f(p)$ or $\cc_c(\ft^b)$ is void,
% we let $\!\box!{\cdot}\!\footins!$ be so.  Otherwise, we move \!\box!,
% \!\count!, \!\dimen! and \!\skip! of the source into those of
% \!\footins!\footnote{
% 
% Moving \!\count!, \!\dimen! and \!\skip! is redundant almost always
% because it is very unlikely that these footnote parameters are modified
% dynamically.  Moreover, dynamic modification of them is hardly consistent
% with repetitive self-\!\insert!ion of \!\footins! in
% \!\pcol@restartcolumn! and \!\@reinserts! of \LaTeX.  However, we dare to
% move them in order to, for example, allow each column has its own footnote
% parameters.}.
% 
% 
%    \begin{macrocode}
\def\pcol@getcurrfoot#1{%
  \ifvoid\pcol@currfoot \global\setbox\footins\box\voidb@x
  \else
    \global\setbox\footins#1\pcol@currfoot
    \global\count\footins\count\pcol@currfoot
    \global\dimen\footins\dimen\pcol@currfoot
    \global\skip\footins\skip\pcol@currfoot
  \fi}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@setcurrcol}
% \changes{v1.0}{2011/10/10}
%	{Add save of \cs{pcol@textfloatsep}.}
% \changes{v1.3-4}{2013/09/17}
%	{Remove $\kappa_c(\mu)\EQ\cs{@mparbottom}$ from the body of
%	 $\cs{pcol@col}{\cdot}c$ because it is no longer in the column
%	 context.}
% 
% \begin{macro}{\pcol@setcurrcolnf}
% The macro \!\pcol@setcurrcol! is invoked from \!\pcol@output@switch!,
% \!\pcol@measurecolumn! and \!\pcol@synccolumn! to save \cctext{} of
% $c=\!\pcol@currcol!$ in $\cc_c$.  It is also used in \!\pcol@setcurrcolnf!
% invoked from \!\pcol@output@start!, \!\pcol@flushcolumn!,
% \!\pcol@imakeflushedpage!, \!\pcol@iflushfloats! and \!\pcol@freshpage! for
% the saving when the \colpage{} is known to have no footnotes.
% 
% The macro \!\pcol@setcurrcol! at first calculates the combined code for
% \CSIndex{if@nobreak} and \CSIndex{if@afterindent}, and then saves
% parameters into $\cc_c$ by \!\xdef! to have the sequence shown in the
% description of \!\pcol@getcurrcol!.  Note that \!\dimen!-type parameters
% are saved by expansions with \!\number! and thus as decimal integers.
% 
% The macro \!\pcol@setcurrcolnf! \!\def!ines $\cc_c(\ft)=\!\pcol@currfoot!$
% as \!\voidb@x!, and then invoke \!\pcol@setcurrcol! for saving.
% 
%    \begin{macrocode}
\def\pcol@setcurrcol{{\let\@elt\relax
  \@tempcnta\if@nobreak\if@afterindent\@ne\else\tw@\fi\else\z@\fi
  \expandafter\xdef\csname pcol@col\number\pcol@currcol\endcsname{%
    {\@currbox}{\pcol@currfoot}{\number\pcol@prevdepth}%
    {\@toplist}{\@midlist}{\@botlist}{\@deferlist}{\number\pcol@textfloatsep}%
    {{\number\@textfloatsheight}%
     {\number\@topnum}{\number\@toproom}{\number\@botnum}{\number\@botroom}%
     {\number\@colnum}{\number\@tempcnta}{\the\everypar}}}}}
\def\pcol@setcurrcolnf{\def\pcol@currfoot{\voidb@x}\pcol@setcurrcol}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@putbackmvl}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to restart a column with coloring.}
% \changes{v1.3-1}{2013/09/17}
%	{Renamed from \cs{pcol@restorecst@restart} and the operations to
%	 save pre-spanning-text stuff is added.}
% \changes{v1.33-2}{2016/11/19}
% 	{Add {\tt\%} to the end of the line to open \cs{vbox} for
%	 \cs{pcol@prespan} to obey the coding convention.}
% \changes{v1.34}{2018/05/07}
%	{Change nullification of
%	 $\mathit{\Gamma}_s\EQ\cs{pcol@colorstack@saved}$ from \cs{gdef} to
%	 \cs{box}-assignment of $\bot$ because it is now a \cs{vbox}.}
% 
% The macro \!\pcol@putbackmvl!, solely used in
% \!\pcol@restartcolumn!, has two functions;  \colorstack{} restoration and
% \prespan{} preservation.  It examines the emptiness of the \colpage{} of the
% column $c$ to be restarted in $\cc_c(\vb)=\!\@currbox!$.  If so, the
% \colorstack{} $\CST^c$ is saved into $\csts=\!\pcol@colorstack@saved!$ by
% \!\pcol@savecolorstack! as the opening \colorctext{} of the \colpage{},
% and \!\pcol@prespan! for \prespan{} is made $\bot$.
% 
% Otherwise, $\csts$ is let $\bot$ because the opening \colorctext{} has
% already been put when we left from the \colpage{}.  Then if
% $\CSIndex{ifpcol@sptextstart}=\true$ to mean a \mctext{} is to start, we
% save $\cc_c(\vb)$ into \!\pcol@prespan! adding the colorling \!\special!s
% to restore \colorctext{} from $\CST^c$ by
% \!\pcol@restorecolorstack!\footnote{
% 
% If \cs{pcol@prespan} is connected to (the first part of) the \mctext,
% the reestablishment of the \colorstack{} here correctly places coloring
% \cs{special}s in \texttt{.dvi}.  On the other hand, if the \mctext{} is
% slown away to the next page as a whole, the reestablishment here is
% essential for the correct paring of the pushes and pops, the latter of
% which are at the bottom of the \colpage{} whose tail is \cs{pcol@prespan}.}.
% 
% We also shrink $\cc_c(\vb^r)=\!\@colroom!$ by the height of the \prespan{}
% so that \mctext{} will be captured by \!\pcol@makecol! if it is broken
% into two (or more) pages, and put a invisible \!\hrule! to the main
% vertical list letting $\!\topskip!=0$ to supress \!\topskip! insertion
% prior to the \mctext{} but instead to make the text led by
% \!\baselineskip! (or \!\lineskip!) according to the \!\prevdepth!  being
% the depth of the tallest column and the height of the first \!\hbox! in
% the \mctext.  Otherwise, i.e., if $\CSIndex{ifpcol@sptextstart}=\false$,
% we simply put back $\cc_c(\vb)$ into the main vertical list and then the
% coloring \!\special!s by \!\pcol@restorecolorstack!.
% 
% Note that $\CSIndex{ifpcol@sptextstart}$ is temporarily made $\false$ by
% this macro if the \!\pcol@output@switch! invoking \!\pcol@restartcolumn!
% did not make \sync{}ed \cswitch{}, i.e., if $\CSIndex{ifpcol@flush}=\true$
% to mean the page is flushed before the \sync{}ation, or
% $\CSIndex{ifpcol@sync}=\false$ for \cscan{}ning prior to the \sync{}ation.
% 
%    \begin{macrocode}
\def\pcol@putbackmvl{%
  \ifpcol@flush \pcol@sptextstartfalse \fi
  \ifpcol@sync\else \pcol@sptextstartfalse \fi
  \pcol@ifempty\@currbox
   {\pcol@savecolorstack
    \ifpcol@sptextstart \global\setbox\pcol@prespan\box\voidb@x \fi}%
   {\global\setbox\pcol@colorstack@saved\box\voidb@x
    \ifpcol@sptextstart
      \global\setbox\pcol@prespan\vbox{%
        \unvbox\@currbox \pcol@restorecolorstack}%
      \global\advance\@colroom-\ht\pcol@prespan
      \global\topskip\z@ \hrule\@height\z@\@width\z@
    \else
      \unvbox\@currbox \pcol@restorecolorstack
    \fi}}

%    \end{macrocode}
% \end{macro}
% 
% 
% 
% \KeepSpace{3}
% \subsection{Color Management}
% \label{sec:imp-sout-color}
% 
% \changes{v1.2-1}{2013/05/11}
%	{Add the subsection ``Color Management'' to describe newly
%	 introduced macros for coloring.}
% \changes{v1.3-6}{2013/09/17}
%	{Move commands outside \cs{output} routine to the newly introduced
%	 section ``Commands for Text Coloring'' to distinguish
%	 macros inside and outside \cs{output} routine.}
% \changes{v1.22}{2013/06/30}
% 	{\cs{pcol@output@cpush} was introduced for color stack pushing but
%	 removed in v1.34.}
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@output@cpush} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.22}{2013/06/30}
% 	{\cs{pcol@output@icpush} was introduced to implement
%	 \cs{pcol@output@cpush} but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@output@icpush} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.24}{2013/07/27}
%	{\cs{pcol@output@mcpush} was introduced for coloring specified in
%	 math mode but removed in v1.34.}
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@output@mcpush} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.24}{2013/07/27}
%	{\cs{pcol@output@imcpush} was introduced for coloring specified in
%	 math mode but removed in v1.34.}
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@output@imcpush} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.22}{2013/06/30}
% 	{\cs{pcol@output@cpop} was introduced for color stack popping but
%	 removed in v1.34.}
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@output@cpop} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.2-1}{2013/05/11}
% 	{\cs{pcol@reset@color@elt} was introduced to implement
%	 \cs{pcol@reset@color@pop} but removed in v1.34.} 
% \changes{v1.22}{2013/06/30}
% 	{\cs{pcol@reset@color@elt} was moved from the position where
%	 \cs{pcol@reset@color@pop} was defined 
%	 because it became to be used only by \cs{pcol@output@cpop}, but
%	 removed in v1.34.}
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@reset@color@elt} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.24}{2013/07/27}
%	{\cs{pcol@output@mcpop} was introduced for coloring specified in
%	 math mode but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@output@mcpop} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.24}{2013/07/27}
%	{\cs{pcol@output@mcpop@elt} was introduced for coloring specified in
%	 math mode but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@output@mcpop@elt} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.22}{2013/06/30}
% 	{\cs{pcol@output@cset} was introduced to set $\gamma_0^c$ but
%	 removed in v1.34.}
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@output@cset} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.22}{2013/06/30}
% 	{\cs{pcol@output@icset} was introduced to implement
%	 \cs{pcol@output@cset} but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@output@icset} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \changes{v1.22}{2013/06/30}
% 	{\cs{pcol@return@from@color} was introduced to implement
%	 \cs{pcol@output@cpush}, \cs{pcol@output@cpop} and
%	 \cs{pcol@output@cset} but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@return@from@color} is removed according to the change of
%	 text coloring from \cs{output} to \cs{insert}.}
% 
% \begin{macro}{\pcol@magicpenalty}
% \begin{macro}{\pcol@ifempty}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to examine the emptiness of the box, extracting the code
% 	 from \cs{pcol@measurecolumn} so as to be used for coloring as
%	 well.}
% 
% The macro $\!\pcol@ifempty!\arg{box}\arg{then}\arg{else}$ is used in
% \!\pcol@putbackmvl!, \!\pcol@clearcst@unvbox! and
% \!\pcol@measurecolumn! to examine if $\arg{box}$ is empty, and to perform
% $\arg{then}$ if so or $\arg{else}$ otherwise.  Since \TeX{} does not
% provide any convenient way for the examination unfortunately, we perform a
% series of tricky operations to put the followings into \!\@tempboxa!; a
% penalty of $\!\pcol@magicpenalty!=12345$ whose existence in the
% $\arg{box}$ is (almost) impossible; contents of $\arg{box}$ put by
% \!\unvcopy!; and then a \!\global! \!\def!inition of \!\@gtempa! to let it
% have the decimal representation of \!\lastpenalty!.  Since \!\lastpenalty!
% has $\arg{pen}$ if the last item is $\!\penalty!\arg{pen}$, or 0
% otherwise, $\!\@gtempa!=\!\pcol@magicpenalty!$ iff $\arg{box}$ is empty.
% 
%    \begin{macrocode}
%% Special Output Routines: Color Management

\def\pcol@magicpenalty{12345}
\def\pcol@ifempty#1#2#3{%
  \setbox\@tempboxa\vbox{\penalty\pcol@magicpenalty
    \unvcopy#1\xdef\@gtempa{\number\lastpenalty}}%
  \ifnum\@gtempa=\pcol@magicpenalty\relax \def\reserved@a{#2}%
  \else                                   \def\reserved@a{#3}%
  \fi
  \reserved@a}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@clearcst@unvbox}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to put coloring \cs{special}s above and below of a
%	 column-page.}
% \begin{macro}{\pcol@clearcolorstack}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to clear color context.}
% \changes{v1.34}{2018/05/07}
%	{Completely change its definition according to the new text coloring
%	 with \cs{insert}.}
% 
% The macro \!\pcol@clearcst@unvbox!$\arg{box}$, invoked from \!\pcol@opcol!
% and \!\pcol@output@switch!, puts the following above and below
% $\arg{box}$ containing the main vertical list of a \colpage{} from which
% we are now leaving, if \!\pcol@ifempty! judges that $\arg{box}$ is not
% empty.  Above the $\arg{box}$, we put coloring \!\special!s to establish
% the \colorstack{} of |.dvi| saved in $\csts=\!\pcol@colorstack@saved!$ by
% \!\pcol@restorecst! as the opening \colorctext{} of the \colpage{}.  The
% stack $\csts$, however, can be $\bot$ if $\arg{box}$ already has the
% \!\special!s, i.e., when we visit the \colpage{} it had already had
% some items.  Below $\arg{box}$, on the other hand, we put uncoloring
% \!\special!s by \!\pcol@clearcolorstack! to rewind $\CSTraw^c$ to clear the
% \colorctext{} of the \colpage{} in |.dvi| temporarily so that afterward it
% is made consistent with that in |.tex|.
% 
% The macro \!\pcol@clearcolorstack!, solely invoked from
% \!\pcol@clearcst@unvbox! shown above\footnote{
% 
% But we have this macro to avoid the complication in \cs{def}ining
% \cs{reserved@a} and \cs{reserved@b} with an argument if we did it in the
% argument of \cs{pcol@ifempty} in \cs{pcol@clearcst@unvbox}.},
% 
% scans $\CSTraw^c=(\Celt^c,\cstraw)$ by \!\pcol@scancst! giving
% $\cstraw=\!\pcol@colorins!$ to it as its argument.  Since we gives
% $\cstraw$ to the macro, this scan includes removals of all $\celtpop_i$
% and $\mceltpop_{i,m}$, all $\celt_i$ having matching $\celtpop_i$, all
% $\mcelt_{i,m}$ having matching $\mceltpop_{i,m}$, and all elements to
% update $\Celt^c$, from $\cstraw$ to let \!\pcol@colorins! have $\cst$.
% Prior to this invocation, we \!\def!ine $\!\reserved@a!\<\celt_i\>$ and
% $\!\reserved@b!\<\Celt^c\>$ to let them have \!\reset@color! so that
% uncoloring \!\special! will be put into the main vertical list for each
% $\celt_i\in\cst$ and $\Celt^c$ before update if any, regardless of
% coloring \!\special! they have.  That is, we invoke \!\reset@color! as
% many times as the appearance of $\celt_i\in\cst$ and once if
% $\Celt^c\neq\bot$ before the invocation, ignoring the color information in
% each element and the order of elements, expecting \!\reset@color! just
% pops printer's \colorstack{} to rewind it as we intend.
% 
% Note that in some printer |.def|inition could \!\def!ine \!\reset@color! to
% let printer's text color be \!\current@color! to make the stack rewinding
% resulting in the sequence of coloring operations with \!\current@color! at
% the invocation of \!\output!.  This meaningless operations might cause a
% problem when a colored \colpage{} of $c_1$ is physically followed by another
% \colpage{} of the succeeding column $c_2$ without any coloring, because the
% \colpage{} of $c_2$ will be colored with \!\current@color! at the page break
% in $c_1$.  If this problem is serious, we could initialize $\Celt^c$ with
% \!\current@color! at \beginparacol{} for all $c$ such that $\Celtshadow^c$
% is undefined, in order to make sure that any \colpage{} has at least one
% coloring \!\special! with $\Celt^c$ at its beginning so that, for example,
% coloring operations at the tail of the \colpage{} of $c_1$ is overridden
% by that of the default color of $c_2$ placed at the head of its \colpage{}.
% 
%    \begin{macrocode}
\def\pcol@clearcst@unvbox#1{%
  \pcol@ifempty#1\relax
   {\pcol@restorecst\pcol@colorstack@saved \unvbox#1\pcol@clearcolorstack}}
\def\pcol@clearcolorstack{%
  \def\reserved@a##1{\reset@color}\def\reserved@b##1{\reset@color}%
  \pcol@scancst\pcol@colorins}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \changes{v1.2-1}{2013/05/11}
% 	{\cs{pcol@set@color@elt} was introduced to implement color context
%	 reestablishment but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@set@color@elt} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% 
% \begin{macro}{\pcol@restorecolorstack}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to reestablish color context.}
% \changes{v1.34}{2018/05/07}
%	{Completely change its definition according to the new text coloring
%	 with \cs{insert}.}
% \begin{macro}{\pcol@restorecst}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to reestablish color context.}
% \changes{v1.34}{2018/05/07}
%	{Completely change its definition according to the new text coloring
%	 with \cs{insert}.}
% 
% The macro \!\pcol@restorecolorstack!, used in \!\pcol@putbackmvl!
% and \!\pcol@output@end!, makes \colorctext{} in
% |.dvi| consistent with that in |.tex| by giving $\cst=\!\pcol@colorins!$
% to \!\pcol@restorecst! to let it scan $\CST^c=(\Celt^c,\cst)$.
% The callee macro $\!\pcol@restorecst!\arg{box}$, also used in
% \!\pcol@clearcst@unvbox! with $\arg{box}=\csts=\!\pcol@colorstack@saved!$,
% invokes \!\pcol@scancst! after \!\def!ining $\!\reserved@a!\<\celt_i\>$ to
% apply \!\unvbox! to $\celt_i$ in $\cst$ or $\csts$ and
% $\!\reserved@b!\<\Celt^c\>$ to apply \!\unvcopy! to $\Celt^c$ so that
% coloring \!\special!s they have will be put into the main vertical list.
% 
%    \begin{macrocode}
\def\pcol@restorecolorstack{\pcol@restorecst\pcol@colorins}
\def\pcol@restorecst{%
  \def\reserved@a##1{\unvbox##1}\def\reserved@b##1{\unvcopy##1}%
  \pcol@scancst}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@scancst}
% \changes{v1.34}{2018/05/07}
%	{Introduced to implement new text coloring with \cs{insert}.}
% \begin{macro}{\pcol@iscancst}
% \changes{v1.34}{2018/05/07}
%	{Introduced to implement new text coloring with \cs{insert}.}
% 
% \begin{Sloppy}{1500}
% The macro $\!\pcol@scancst!\arg{box}$ is invoked from
% \!\pcol@clearcolorstack! and \!\pcol@restorecst!.  In the former
% invocation, we have $\arg{box}=\cstraw=\!\pcol@colorins!$ to rewind
% $\CSTraw=(\Celt^c,\cstraw)$ with $\!\reserved@a!\arg{\celt_i}$ and
% $\!\reserved@b!\arg{\Celt^c}$ having \!\reset@color!.  In the latter one,
% we have
% $\arg{box}\in\{\cst{=}\!\pcol@colorins!,\,\csts{=}\!\pcol@colorstack@saved!\}$
% to reestablish $\CST^c=(\Celt^c,\cst)$ or $\csts$ with
% $\!\reserved@a!\arg{\celt_i}$ to apply \!\unvbox! to $\celt_i$ and 
% $\!\reserved@b!\arg{\Celt^c}$ to apply \!\unvcopy! to $\Celt^c$.
% Therefore, if $\arg{box}=\!\pcol@colorins!$, we at first put (un)coloring
% \!\special! for $\Celt^c$, unless it is $\bot$, to the main vertical
% list applying \!\reserved@b! to it.  This means the \!\special! for
% $\Celt^c$ is put first prior to those for elements in $\cstraw$ or $\cst$
% consistently in reestablishing but not in rewinding.  However as we
% discussed in the description of \!\pcol@clearcolorstack!, the order of
% rewinding does not affect the result for almost all printers because only
% the number of pop operations is siginficant for them\footnote{
% 
% And even for the minority because multiple updates of printer's color with
% one particular color are independent of the order of them.}.
% 
% Then if $\arg{box}\neq\bot$ we invoke \!\pcol@iscancst! to examine the
% contents of $\arg{box}$ from its bottom to top.  Prior to the invocation,
% we do the following;  let \!\@tempboxa! have an empty \!\vbox! as its initial
% value of reformed $\arg{box}$;  let \!\pcol@tempboxa! have an empty
% \!\vbox! as its initial value of the sequence of \!\special!s to be put
% into the main vertical list; let $\npop=\!\@tempcntb!=0$; let
% $M=\!\reserved@b!=()$ as its initial value of the list of identifiers of
% math-mode pops; $\CSIndex{if@tempswa}=\true$ to mean the first \!\vbox! to
% update $\Celt^c$ found in the scan (i.e., the bottommost one) is
% effective.
% \end{Sloppy}
% 
% In the macro \!\pcol@iscancst!, we repeatedly examine the last \!\vbox! in
% $\arg{box}$ taken by \!\lastbox! into $\celt=\!\pcol@tempboxb!$ until
% $\celt$ becomes $\bot$, and perform one of the following for $\celt$.
% 
% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
% \def\HT{\mathit{height}}\def\DP{\mathit{depth}}\def\WD{\mathit{width}}
% \item
% If $\HT(\celt)=0$ and $\WD(\celt)=0$ to mean $\celt=\celtpop_i$, increment
% $\npop$.
% 
% \item
% If $\HT(\celt)=0$ and $\WD(\celt)=m>0$ to mean $\celt=\mceltpop_{i,m}$, let
% $M=(m,M)$.
% 
% \item
% If $\HT(\celt)\neq0$, $\DP(\celt)=0$ and $\WD(\celt)=0$ to mean
% $\celt=\celt_i$, decrement $\npop$ if $\npop>0$, or otherwise add $\celt$
% to the head of \!\@tempboxa! and apply $\!\reserved@a!\arg{\celt}$ to add
% its result to the head of \!\pcol@tempboxa!.
% 
% \item
% If $\HT(\celt)\neq0$, $\DP(\celt)=0$ and $\WD(\celt)=m>0$ to mean
% $\celt=\mcelt_{i,m}$, do nothing if $m\in M$, or otherwise add $\celt$
% to the head of \!\@tempboxa! and apply $\!\reserved@a!\arg{\celt}$ to add
% its result to the head of \!\pcol@tempboxa!.
% 
% \item
% If $\HT(\celt)\neq0$, $\DP(\celt)\neq0$ to mean $\celt$ has a \!\special!
% with which $\Celt^c$ is updated.  If $\CSIndex{if@tempswa}=\true$ to mean
% $\celt$ is the first (bottommost) occurence, $\Celt^c$ is updated
% acquiring an \!\insert! from \!\@freelist! if it was $\bot$.  In this
% case of $\bot$, we have to put an uncoloring \!\special! by
% \!\reset@color!, because \!\pcol@scancst! did not do it but
% \!\columncolor! or \!\normalcolumncolor! pushed the corresponding color
% \!\special!.  Then we let $\CSIndex{if@tempswa}=\false$.
% 
% Otherwise, i.e., if $\CSIndex{if@tempswa}=\false$ for second or succeeding
% occurences, we do nothing because updates by them are overridden by the
% first one.
% \end{enumerate}
% 
% Note that the cases other than (3) and (4) happen only in rewinding, and
% thus in reestablishing we only have (3) and (4) with $\npop=0$ and $M=()$
% always so that every $\celt$ is kept into new $\arg{box}$ and a coloring
% \!\special! for it will be put into the main vertical list.
% 
% Then we go back to \!\pcol@scancst! to let $\arg{box}=\!\@tempboxa!$,
% meaningless in reestablishing but not harmful, and put the contents of
% \!\pcol@tempboxa! to the main vertical list.
% 
% 
%    \begin{macrocode}
\def\pcol@scancst#1{%
  \@tempcnta#1\relax
  \ifnum\@tempcnta=\pcol@colorins
    \ifvoid\pcol@ccuse{@box}\else
      \reserved@b{\pcol@ccuse{@box}}\fi
  \fi
  \ifvoid\@tempcnta\else
    \setbox\@tempboxa\vbox{}\setbox\pcol@tempboxa\vbox{}\@tempcntb\z@
    \def\reserved@b{}\let\@elt\relax \@tempswatrue \pcol@iscancst
    \global\setbox\@tempcnta\box\@tempboxa \unvbox\pcol@tempboxa
  \fi}
\def\pcol@iscancst{%
  \setbox\@tempcnta\vbox{%
    \unvbox\@tempcnta \global\setbox\pcol@tempboxb\lastbox}%
  \ifvoid\pcol@tempboxb \let\reserved@c\relax
  \else
    \let\reserved@c\pcol@iscancst
    \ifdim\ht\pcol@tempboxb=\z@
      \ifdim\wd\pcol@tempboxb=\z@ \advance\@tempcntb\@ne
      \else \edef\reserved@b{\@elt{\number\wd\pcol@tempboxb}\reserved@b}%
      \fi
    \else\ifdim\dp\pcol@tempboxb=\z@
      \ifdim\wd\pcol@tempboxb=\z@
        \ifnum\@tempcntb>\z@ \advance\@tempcntb\m@ne
        \else
          \setbox\@tempboxa\vbox{\copy\pcol@tempboxb \unvbox\@tempboxa}%
          \setbox\pcol@tempboxa\vbox{%
            \reserved@a\pcol@tempboxb \unvbox\pcol@tempboxa}%
        \fi
      \else
        \count@\wd\pcol@tempboxb \chardef\reserved@d\z@
        \def\@elt##1{\ifnum##1=\count@ \chardef\reserved@d\@ne \fi}%
        \reserved@b \let\@elt\relax
        \ifnum\reserved@d=\z@
          \setbox\@tempboxa\vbox{\copy\pcol@tempboxb \unvbox\@tempboxa}%
          \setbox\pcol@tempboxa\vbox{%
            \reserved@a\pcol@tempboxb \unvbox\pcol@tempboxa}%
        \fi
      \fi
    \else\if@tempswa
      \ifvoid\pcol@ccuse{@box}%
        \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{}}\pcol@ovf
        \pcol@ccxdef{\@currbox}\reset@color
      \fi
      \global\setbox\pcol@ccuse{@box}\vbox{\unvbox\pcol@tempboxb}%
      \@tempswafalse
    \fi\fi\fi
  \fi
  \reserved@c}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@savecolorstack}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to save the opening color context of a column-page.}
% \changes{v1.34}{2018/05/07}
%	{Completely change its definition according to the new text coloring
%	 with \cs{insert}.}
% 
% The macro \!\pcol@savecolorstack! is used in \!\pcol@startcolumn!,
% \!\pcol@output@start! and \!\pcol@putbackmvl! to save the opening
% \colorctext{} in $\CST^c$ of a \ccolpage{} $c$ known to be or found empty
% into $\csts=\!\pcol@colorstack@saved!$.  If both of
% $\Celt^c=|\pcol@columncolor@box|\cdot c$ and $\cst=\!\pcol@colorins!$ are
% $\bot$, $\csts$ is let be $\bot$.  Otherwise, $\csts$ is let be a \!\vbox!
% having a \!\vbox! for $\Celt^c$ at the top if it is not $\bot$ and then the
% contents of $\cst$ if it is not $\bot$.
% 
% \SpecialArrayIndex{c}{\pcol@columncolor@box}
% 
%    \begin{macrocode}
\def\pcol@savecolorstack{%
  \ifvoid\pcol@colorins \@tempswafalse \else \@tempswatrue \fi
  \ifvoid\pcol@ccuse{@box}%
    \setbox\@tempboxa\box\voidb@x
  \else
    \setbox\@tempboxa\vbox{\unvcopy\pcol@ccuse{@box}}%
    \ht\@tempboxa1sp \dp\@tempboxa\z@ \wd\@tempboxa\z@
    \@tempswatrue
  \fi
  \if@tempswa
    \global\setbox\pcol@colorstack@saved\vbox{%
      \ifvoid\@tempboxa\else \box\@tempboxa \fi
      \ifvoid\pcol@colorins\else \unvcopy\pcol@colorins \fi}
  \else \global\setbox\pcol@colorstack@saved\box\voidb@x
  \fi}

%    \end{macrocode}
% \end{macro}
% 
% \changes{v1.2-1}{2013/05/11}
% 	{\cs{pcol@colorstack@full} was introduced to represent
%	 $\string\mathit{\Gamma}^c$ but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@colorstack@full} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% 
% \KeepSpace{3}
% \begin{macro}{\pcol@ccuse}
% \changes{v1.34}{2018/05/07}
%	{Introduced to implement new text coloring with \cs{insert}.}
% \begin{macro}{\pcol@ifccdefined}
% \changes{v1.34}{2018/05/07}
%	{Introduced to implement new text coloring with \cs{insert}.}
% \begin{macro}{\pcol@ccxdef}
% \changes{v1.34}{2018/05/07}
%	{Introduced to implement new text coloring with \cs{insert}.}
% 
% The macro $\!\pcol@ccuse!\arg{pfx}$ is to expand a macro
% $|\pcol@columncolor|\cdot\arg{pfx}\cdot c$ for the current column $c$.  It
% is used in \!\pcol@output@start! and \!\pcol@scancst@shadow! with
% $\arg{pfx}=\hbox{`'}$ to have $\Celtshadow^c$, and in \!\pcol@scancst!,
% \!\pcol@iscancst!, \!\pcol@savecolorstack!, \!\pcol@output@end! and
% \!\pcol@icolumncolor! with $\arg{pfx}=|@box|$ to have $\Celt^c$.
% 
% \SpecialArrayIndex{c}{\pcol@columncolor}
% \SpecialArrayIndex{c}{\pcol@columncolor@box}
% 
% The macro $\!\pcol@ifccdefined!\arg{then}\arg{else}$ is used in
% \!\pcol@output@start! and \!\pcol@scancst@shadow! to examine whether
% $\Celtshadow^c=|\pcol@columncolor|\cdot c$ is defined and to do
% $\arg{then}$ if so or $\arg{else}$ otherwise.
% 
% \SpecialArrayIndex{c}{\pcol@columncolor}
% 
% The macro $\!\pcol@ccxdef!\arg{body}$ \!\xdef!ines a macro
% $\Celt^c=|\pcol@columncolor@box|\cdot c$ as $\arg{body}$ for the current
% column $c$.  It is used in \!\pcol@output@start!, \!\pcol@iscancst! and
% \!\pcol@icolumncolor!  with $\arg{body}=\!\@currbox!$ when an \!\insert!
% for $\Celt^c$ is acquired, and in \!\pcol@output@end! with
% $\arg{body}=\!\voidb@x!$ after releasing $\Celt^c$ to \!\@freelist!.
% 
% \SpecialArrayIndex{c}{\pcol@columncolor@box}
% 
%    \begin{macrocode}
\def\pcol@ccuse#1{\@nameuse{pcol@columncolor#1\number\pcol@currcol}}
\def\pcol@ifccdefined#1#2{%
  \expandafter\ifx\csname pcol@columncolor\number\pcol@currcol\endcsname\relax
  #2\else#1\fi}
\def\pcol@ccxdef#1{%
  \expandafter\xdef
    \csname pcol@columncolor@box\number\pcol@currcol\endcsname{#1}}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% 
% 
% \subsection{Footnote Handling}
% \label{sec:imp-sout-scfnote}
% \changes{v1.2-2}{2013/05/11}
%	{Add the subsection ``Footnote Handling'' to describe newly
%	 introduced macros for page-wise footnotes.}
% 
% \begin{macro}{\pcol@savefootins}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to save footnotes in multiple occasions.}
% 
% The macro $\!\pcol@savefootins!\arg{cs}$, invoked from \!\pcol@makecol!
% for \Scfnote{}s and from \!\pcol@output@switch! for both \mcfnote{} and
% \Scfnote{}s, saves \!\footins! to an \!\insert! register obtained by
% \!\@next! from \!\@freelist!, and \!\def!ines $\arg{cs}$ being
% \!\pcol@currfoot! or \!\pcol@footins! so that it has the register as its
% body and the register is then saved into $\pp^f(p)$ or $\cc_c(\ft)$.  We
% save not only \!\box! component of \!\footins! but also \!\count!,
% \!\dimen! and \!\skip!\footnote{
% 
% Knowing these three components are virtually constants.}.
% 
%    \begin{macrocode}
%% Special Output Routines: Footnote Handling

\def\pcol@savefootins#1{%
  \@next#1\@freelist{%
    \global\setbox#1\box\footins
    \global\count#1\count\footins
    \global\dimen#1\dimen\footins
    \global\skip#1\skip\footins}{\def#1{\voidb@x}\pcol@ovf}}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@shrinkcolbyfn}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to shrink \cs{@colht} temporarily by the
%	 height-plus-depth of page-wise footnotes and the natural size
% 	 of the skip above them.}
% \changes{v1.3-3}{2013/09/17}
%	{Add the first argument $\langle\string\mathit{height}\rangle$ for
%	 the user \cs{pcol@ioutputelt}.}
% \changes{v1.3-6}{2013/09/17}
%	{Add the third argument $\langle\string\mathit{skip}\rangle$ to
%	 avoid accidental destruction of \cs{@tempdimb} which was modified
%	 unconditionally.}
% 
% The macro $\!\pcol@shrinkcolbyfn!\arg{height}\arg{ins}\arg{skip}$, invoked
% from \!\pcol@makecol!, \!\pcol@ioutputelt!, \!\pcol@startcolumn!,
% \!\pcol@restartcolumn!, \!\pcol@flushcolumn! and \!\pcol@makeflushedpage!,
% shrinks $\arg{height}\in\{\!\@colht!,\!\@tempdima!\}$ temporarily so that a
% column or the set of all columns resides in a page with \Scfnote{}s in the
% \!\insert! $\arg{ins}$.  The shrinkage is calculated by adding the sum of
% the height plus depth of all footnotes, i.e., that of $\arg{ins}$, and the
% natural component of $\!\skip!\arg{ins}$, i.e., the vertical space
% inserted between the columns and the footnotes.  Note that the stretch and
% shrink components of $\!\skip!\arg{ins}$ cannot be incorporated into the
% calculation but their contribution to each \colpage{} is taken care of by
% the following macro \!\pcol@unvbox@cclv! if required.  Also note that the
% inverse of $\!\skip!\arg{ins}$ is kept in $\arg{skip}$ if it is not
% \!\relax! so that \!\pcol@deferredfootins! knows $\arg{ins}\neq\bot$ when
% this macro is invoked from \!\pcol@startcolumn! and
% \!\pcol@restartcolumn! with $\arg{skip}=\!\@tempdimb!$.
% 
%    \begin{macrocode}
\def\pcol@shrinkcolbyfn#1#2#3{%
  \ifx#3\relax\else #3-\skip#2\relax \fi
  \advance#1-\ht#2\advance#1-\dp#2\advance#1-\skip#2\relax}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@unvbox@cclv}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to add stretch/shrink components of
%	 \cs{skip}\cs{footins} at the bottom of a column-page if the page has
%	 page-wise footnotes.}
% 
% The macro $\!\pcol@unvbox@cclv!\arg{ins}$, invoked from \!\pcol@makecol! and
% \!\pcol@flushcolumn! when they work on a column-page with \Scfnote{}s,
% adds the stretch and shrink components of $\!\skip!\arg{ins}$ at the end
% of \!\box!|255|, where $\arg{ins}$ is non-void $\pp^f(p)$ having
% \Scfnote{}s.  Before the addition, the macro goes back to the baseline of
% \!\box!|255|\footnote{
% 
% The comparison of the depth of \cs{box}\texttt{255} and \cs{@maxdepth} and
% taking the latter if it is smaller is really just-in-case.}
% 
% to nullify the baseline progress mechanism so as to make it sure the exact
% amount of the vertical skip is added.  Then it adds the stretch and shrink
% by at first adding the skip itself and then the negative amount of its
% natural component.
% 
%    \begin{macrocode}
\def\pcol@unvbox@cclv#1{%
  \@tempdima\dp\@cclv \unvbox\@cclv
  \vskip \ifdim\@tempdima>\@maxdepth -\@maxdepth \else -\@tempdima \fi
  \vskip\skip#1\@tempdima\skip#1\vskip-\@tempdima}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@deferredfootins}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to insert deferred footnotes.}
% \changes{v1.3-6}{2013/09/17}
%	{Fix the bug that the height cap was underestimated by the duplicated
%	 subtraction of \cs{skip}\cs{footins} if the page has already have
%	 non-deferred footnotes.}
% 
% The macro $\!\pcol@deferredfootins!\arg{macro}$, invoked from
% \!\pcol@startcolumn! and \!\pcol@restartcolumn!, tries to \!\insert! some
% of leading deferred footnotes in $\df$ through \!\footins!\footnote{
% 
% The argument $\arg{macro}$ has the invoker itself shown in debug
% messages.}.
% 
% In order to avoid that \!\footins! has footnotes across three or more
% pages to make confusion in the order of footnotes kept inside of \TeX, we
% cap the total height of footnotes by $h=\!\@colht!$ if it has already
% shrunk by non-deferred footnotes in the page we are working on indicated
% by $\!\@tempdimb!<0$, or $h=\!\@colht!-\!\skip!\!\footins!$ if the page
% does not have non-deferred footnotes indicated by $\!\@tempdimb!=0$.  That
% is, we extract leading elements of $\df$ by \!\vsplit! until their total
% height reaches $h$ and, if some elements are obtained in \!\@tempboxa!,
% \!\insert!  them through \!\footins!.  As for the remaining elements if
% any, we add a leading \!\penalty!\!\interlinepenalty! which should have
% been removed by \!\vsplit!.
% 
% Note that we temporarily let $\!\splitmaxdepth!=\!\@maxdepth!$,
% $\!\splittopskip!=0$ and $\!\vbadness!=\infty$ at the \!\vsplit! so that
% the depth of the split first half is \!\@maxdepth! at deepest, the second
% half does not have any skip at its top, and \TeX{} will not complain of
% (almost) inevitable underfull.  Also note that the successful extraction
% of the leading elements is examined by checking \!\ht!\!\@tempboxa! and
% thus we need to \!\unvbox!  it in itself because \!\vsplit! makes the
% height $h$ regardless of its contents.
% 
%    \begin{macrocode}
\def\pcol@deferredfootins#1{%
  \ifdim\@tempdimb=\z@ \@tempdimb\@colht \advance\@tempdimb-\skip\footins
  \else \@tempdimb\@colht
  \fi
  \ifvoid\pcol@topfnotes\else \ifdim\@tempdimb>\z@
    \begingroup
      \splitmaxdepth\@maxdepth \splittopskip\z@ \vbadness\@M
      \setbox\@tempboxa\vsplit\pcol@topfnotes to\@tempdimb
      \ifvoid\pcol@topfnotes\else
        \global\setbox\pcol@topfnotes\vbox{\penalty\interlinepenalty
          \unvbox\pcol@topfnotes}%
      \fi
      \setbox\@tempboxa\vbox{\unvbox\@tempboxa}%
      \ifdim\ht\@tempboxa>\z@
        \pcol@Log#1{add}\@tempboxa
        \insert\footins{\unvbox\@tempboxa}%
      \fi
    \endgroup
  \fi\fi}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@combinefootins}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to put footnotes into pre-environment stuff.}
% \changes{v1.35-4}{2018/12/31}
% 	{Add the insertion of vertical skip \cs{belowfootnoteskip}.}
% \begin{macro}{\pcol@putfootins}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to put page-wise footnotes to a page.}
% \changes{v1.3-2}{2013/09/17}
%	{Change users \cs{pcol@outputelt} to \cs{pcol@ioutputelt}.}
% \changes{v1.3-6}{2013/09/17}
%	{Remove \cs{pcol@output@end} from users.}
% 
% The macro $\!\pcol@combinefootins!\arg{b}\arg{f}$, invoked solely from
% \!\pcol@makenormalcol!\footnote{
% 
% And thus having the arguments $\arg{b}$ and $\arg{f}$ is unnecessary, but
% we keep this implementation to avoid unnecessary recoding from a
% development version.},
% 
% constructs the \preenv{} in \!\@outputbox!, combining the stuff in the box
% $b$ and pre-environment footnotes in the \!\insert! $f$.  It is almost
% equivalent to the \cs{else} part of \!\@makecol! in which the main
% vertical list and \Mcfnote{}s are combined.  The operation to put
% footnotes is almost equivalent to the second half of the \cs{else} part
% except that \!\insert!  is not always \!\footins! but $f$ and is done by
% \!\pcol@putfootins! in which a null vertical skip is added after $f$ but
% this skip is removed by \!\unskip! after the invocation.  The other
% difference is that the vertical space of \!\belowfootnoteskip! is added if
% it is not 0\footnote{
% 
% We avoid null space insertion to minimize the difference from older
% versions in traced output.}
% 
% to have some space between non-merged \Preenv{} footnotes and the first
% lines in a \env{paracol} environment.
% 
% The null vertical skip is put for \Scfnote{}s, for which the macro
% \!\pcol@putfootins! is invoked from \!\pcol@ioutputelt! and
% \!\pcol@makeflushedpage!.  Since we shrink the height of \colpage{}s by
% the height-plus-depth of \Scfnote{}s, the natural height of the box in
% which \colpage{}s and \Scfnote{}s are combined would be less than
% \!\textheight! due to the depth of the last footnote line if we simply
% made the footnotes the last items of the box.  Though this shortage at
% most \!\maxdepth! is expected to be covered by the stretch factor of
% \!\skip!\!\footins! without too large badness causing an underfull
% message\footnote{
% 
% With default settings of $\cs{maxdimen}=5\,|pt|$ and the stretch factor
% 4\,|pt| of \cs{skip}\cs{footins}, the badness $100\times(5/4)^3\approx195$
% is significantly less than the default $\cs{vbadness}=1000$.},
% 
% someday we could face an underfull with some unusual settings of
% \!\maxdimen!, \!\skip!\!\footins! and/or \!\vbadness!.  Therefore, we put a
% null vertical skip so that the real bottom of the footnotes, instead of
% the last baseline, is placed at the baseline of the box, to make the
% natural height of the box is \!\textheight! exactly.  Note that this
% shifting \Scfnote{}s up will not make last baselines of footnotes among
% pages unaligned, because the last line have a strut.
% 
%    \begin{macrocode}
\def\pcol@combinefootins#1#2{%
  \setbox\@outputbox\vbox{%
    \boxmaxdepth\@maxdepth
    \unvbox#1\relax
    \pcol@putfootins#2\unskip
    \ifdim\belowfootnoteskip=\z@\else \vskip\belowfootnoteskip \fi}}
\def\pcol@putfootins#1{%
  \vskip\skip#1\relax
  \color@begingroup
    \normalcolor
    \footnoterule
    \unvbox#1\relax
  \color@endgroup \vskip\z@}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% 
% 
% \KeepSpace{3}
% \subsection{Marginal Notes}
% \label{sec:imp-sout-mpar}
% \changes{v1.3-4}{2013/09/17}
%	{Add this section ``Marginal Notes''.}
% 
% \begin{macro}{\@addmarginpar}
% \changes{v1.3-4}{2013/09/17}
%	{Made \cs{let}-equal to \cs{pcol@addmarginpar} in
%	 \string\texttt{paracol} environments.}
% \begin{macro}{\pcol@addmarginpar}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to make a margin sharable by marginal notes from
%	 different columns.}
% \changes{v1.35-3}{2018/12/31}
% 	{Fix the bug referring to \cs{@marbox} inappropriately.}
% \changes{v1.35-3}{2018/12/31}
% 	{Add vertical shifting of marginal note to emulate of
%	 \cs{marginnote}.}
% \begin{macro}{\pcol@@addmarginpar}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to keep the original definition of \cs{@addmarginpar}.}
% \def\swap{\mathit{swap}}
% 
% The macro \!\pcol@addmarginpar! is our own version of \!\@addmarginpar!,
% which \!\pcol@zparacol! makes \!\let!-equal to \!\pcol@addmarginpar!
% keeping its original definition in \!\pcol@@addmarginpar!.  Therefore, in
% an \env{paracol} environment, the \!\output! request made by \LaTeX's
% \!\marginpar! in the column $c$ and page $p$ is processed by
% \!\pcol@addmarginpar! through our own \!\output! routine being
% \!\pcol@output!, \!\pcol@specialoutput! and \LaTeX's \!\@specialoutput!.
% What we do in this macro are as follows;  determine the margin which a
% marginal note goes to; temporarily modify the parameter
% $m_w=\!\marginparwidth!$ or $m_s=\!\marginparsep!$ according to the margin
% and the column; determine the position to place the marginal note
% consulting $\pp^m(p)=\!\pcol@mparbottom!$ obtained by
% \!\pcol@getcurrpage!: and update $\pp^m(p)$ according to the postion.
% 
% First, there are the following parameters to determine the margin, and thus
% the value of $\CSIndex{if@firstcolumn}$ referred to in \LaTeX's
% \!\@addmarginpar! and meaning left if $\true$ or right if $\false$.
% 
% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
% \item
% The macros \!\pcol@mpthreshold@l! and \!\pcol@mpthreshold@r! defined by
% \!\marginpar~threshold!\ give us the threshold of the column number to let
% columns less than it go to the left margin while those equal to or greater
% than it to the right, according to the \parapag{}e the column belongs to.
% Therefore, we let $\CSIndex{if@firstcolumn}=\true$ iff
% $c<\!\pcol@mpthreshold@l!\land c<\CL$ or $c<\!\pcol@mpthreshold@r!\land
% c\geq\CL$, as the fundamental setting.
% 
% \item
% If $\CSIndex{ifpcol@swapmarginpar}=\true$ because the specifier `|m|' is
% given to \!\twosided! explicitly or implicitly, the decision in (1) is
% reversed if $\page(p)\bmod2=0$, and then this decision is reversed again
% if $c\geq\CL$ and $\CSIndex{ifpcol@paired}=\false$ to mean $c$ is in a
% \npaired{} right \parapag{}e.  The second reversal is done because
% $\page(p)$ is \emph{common} to both left and right \parapag{}es and is for
% the left page in usual cases without page number jumps.  Therefore,
% $(\page(p)\bmod2)$ is for left \parapag{}es and thus for right counterparts
% the decision should be made by $((\page(p)+1)\bmod2)$ and thus the result
% should be reversed.
% 
% \item
% If \CSIndex{if@reversemargin} is made $\true$ by \LaTeX's
% \!\reversemarginpar!, the decision made by (1) and then possibly reversed
% by (2) is finally reversed.
% \end{enumerate}
% 
% Second, we calculate
% $$
% D=\!\@tempdima!=\sum_{d=\Cfrom}^{\swap(c)-1}(w_{\swap(d)}+g_{\swap'(d)})
% $$
% where $x'=swap(x)$ is given by
% $\!\pcol@swapcolumn!\<x\>\<x'\>\<\Cfrom\>\<\Cto\>$ to let
% $x'=\Cto-(x-\Cfrom)-1$ if $\CSIndex{ifpcol@swapcolumn}=\true$ and
% $\page(p)\bmod2=0$ or $x'=x$ otherwise,
% $\swap'(x)=\!\pcol@colsepid!\in\{\swap(x)-1,x\}$ according to swapped or
% not, $(\Cfrom,\Cto)\in\{(0,\CL),(\CL,\C)\}$ according to $c<\CL$ or not,
% and $\w_x$ and $\gap_x$ are the width of $x$-th column and gap given by
% $|\pcol@columnwidth|{\cdot}x$ and $|\pcol@columnsep|{\cdot}x$
% respectively.
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
% That is, $D$ is the distance from the left edge of the column $c$ to that
% of leftmost column in the (paralell-)
% 
% \Index{parallel-paging}
% 
% page in which $c$ resides.  Then if $\CSIndex{if@firstcolumn}=\true$ to
% let the margial note go to the left margin, we add $D$ to
% $m_w=\!\marginparwidth!$ so that \LaTeX's \!\@addmarginpar! being
% \!\pcol@@addmarginpar! aligns the left edge of the marginal note at the
% point apart from the column's left edge by $(D+m_w)+m_s$ rather than
% $m_w+m_s$, or in other words $m_w+m_s$ apart from the left edge of the
% leftmost column.  On the other hand if $\CSIndex{if@firstcolumn}=\false$,
% we add $\WT-(D+w_c)$ where $\WT$ is \!\textwidth!, being the distance from
% the right edge of the column $c$ to that of the rightmost column, to
% $m_s=\!\marginparsep!$ so that \!\pcol@@addmarginpar!  aligns the left
% edge of the marginal note at the point apart from the column's right edge
% by $\WT-(D+w_c)+m_s$ rather than $m_s$, or in other words $m_s$ apart from
% the right edge of the rightmost column.
% 
% Third, we let \Midx{\!\pcol@marbox!} be the first element of \!\@currlist!
% obtained by \!\@xnext! for the right marginal note if
% $\CSIndex{if@firstcolumn}=\false$, or \!\@currbox! for the left marginal
% note otherwise.  Then we let $t=\!\@tempdima!$ be the distance from the
% top edge of the column to that of the marginal note, namely \!\@pageht!
% minus the height of \!\pcol@marbox! plus |\dimen|\!\@currbox! being
% downward shift amount optionally given by \!\marginnote!.  We also let
% $h=\!\@tempdimb!$ be the height-plus-depth of the box \!\pcol@marbox!
% plus \!\marginparpush!, or in other words the vertical space the marginal
% note requires.  Then we give $t$ and $h$ to \!\pcol@getmparbottom! to let
% \!\@mparbottom! have the bottom of the exisiting marginal text below which
% we put the margial text in \!\pcol@marbox!, and to let \!\pcol@mpblist!
% have the new list to be replaced with $\mpb_{\{L,R\}}^{\{l,r\}}$ in
% $\pp^m(p)$.
% 
% Forth, we update $\pp^m(p)$ with the new list in \!\pcol@mpblist! by a
% process similar to \!\pcol@setpageno! but with \!\pcol@setmpbelt! to scan
% the list of pages $\PPP$.
% 
% Fifth, we shift down \!\pcol@marbox! by |\dimen|\!\@currbox! and, if the
% shift amount is greater than the height of the box and thus the height of
% shifting result is zero, decrement \!\@mparbottom! by the amount to
% deceive \LaTeX's \!\@addmarginpar! into believing \!\@mparbottom! is above
% the real one by the amount.  In other words, by the decrement we let
% \!\@addmarginpar! see the top edge of the shifted marginal note in the
% box, rather than that of the box itself, for the placement with
% \!\@mparbottom!.
% 
% Finally, we invoke \LaTeX's original \!\@addmarginpar! being
% \!\pcol@@addmarginpar! to put the marginal note according to
% \CSIndex{if@firstcolumn}, temporarily modified \!\marginparsep! and
% \!\marginparwidth!, and \!\@mparbottom!.  Note that since
% \!\pcol@zparacol! lets $\CSIndex{if@twocolumn}\~=\true$,
% \!\pcol@@addmarginpar! determine the margin only by
% \CSIndex{if@firstcolumn}.  Also note that it can be $\!\@mparbottom!>t$
% (before decrement with the positive shift amount) to mean the marginal
% note should be shifted down from its natural position, and if so
% \!\pcol@@addmarginpar!  will give us a warning as the correct consequence
% of the placement.
% 
%    \begin{macrocode}
%% Special Output Routines: Marginal Notes

\def\pcol@addmarginpar{%
  \pcol@getcurrpage \@firstcolumntrue
  \ifnum\pcol@currcol<\pcol@ncolleft
    \let\reserved@a\z@ \let\reserved@b\pcol@ncolleft
    \ifnum\pcol@mpthreshold@l>\pcol@currcol\else \@firstcolumnfalse \fi
  \else
    \let\reserved@a\pcol@ncolleft \let\reserved@b\pcol@ncol
    \ifnum\pcol@mpthreshold@r>\pcol@currcol\else \@firstcolumnfalse \fi
  \fi
  \ifpcol@swapmarginpar
    \ifodd\c@page\else
      \if@firstcolumn \@firstcolumnfalse \else \@firstcolumntrue \fi
    \fi
    \ifpcol@paired\else \ifnum\pcol@currcol<\pcol@ncolleft\else
      \if@firstcolumn \@firstcolumnfalse \else \@firstcolumntrue \fi
    \fi\fi
  \fi
  \if@reversemargin
    \if@firstcolumn \@firstcolumnfalse \else \@firstcolumntrue \fi
  \fi
  \pcol@swapcolumn\pcol@currcol\count@\reserved@a\reserved@b
  \@tempdima\z@
  \@tempcnta\reserved@a \@whilenum\@tempcnta<\count@\do{%
    \pcol@swapcolumn\@tempcnta\@tempcntb\reserved@a\reserved@b
    \advance\@tempdima\csname pcol@columnwidth\number\@tempcntb\endcsname\relax
    \advance\@tempdima\csname pcol@columnsep\pcol@colsepid\endcsname\relax
   \advance\@tempcnta\@ne}%
  \if@firstcolumn \advance\marginparwidth\@tempdima
  \else
    \advance\marginparsep\textwidth \advance\marginparsep-\@tempdima
    \advance\marginparsep-\columnwidth
  \fi
  \expandafter\@xnext\@currlist\@@\pcol@marbox\@gtempa
  \if@firstcolumn\let\pcol@marbox\@currbox \fi
  \@tempdima\@pageht \advance\@tempdima-\ht\pcol@marbox
  \advance\@tempdima\dimen\@currbox
  \@tempdimb\ht\pcol@marbox \advance\@tempdimb\dp\pcol@marbox
  \advance\@tempdimb\marginparpush
  \pcol@getmparbottom\@tempdima\@tempdimb
  \begingroup
    \@tempcnta\pcol@page \advance\@tempcnta-\pcol@basepage
    \edef\reserved@a{\pcol@pages\pcol@currpage}%
    \global\let\pcol@pages\@empty \global\let\pcol@currpage\@empty
    \let\@elt\pcol@setmpbelt \reserved@a
  \endgroup
  \ifdim\dimen\@currbox=\z@\else
    \ifdim\dimen\@currbox>\ht\pcol@marbox
       \advance\@mparbottom-\dimen\pcol@marbox
    \fi
    \setbox\pcol@marbox\hbox{\lower\dimen\@currbox\box\pcol@marbox}%
  \fi
  \pcol@@addmarginpar}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{3}
% \begin{macro}{\pcol@getmparbottom}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to find the space where a marginal note is placed.}
% \begin{macro}{\pcol@getmparbottom@i}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to find the space where a marginal note is placed.}
% \begin{macro}{\pcol@getmpbelt}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to find the space where a marginal note is placed.}
% \changes{v1.33-1}{2016/11/19}
% 	{Fix the bug by which $t_k$ such that $t_k\geq t$ and $t_k-t\geq h$
%	 but $t_k-b_{k-1}<h$ is found.}
% 
% The macro $\!\pcol@getmparbottom!\<t\>\<h\>$ is solely used in
% \!\pcol@addmarginpar!\footnote{
% 
% Thus giving $t$ and $h$ as arguments is not necessary but we dare to do
% it.}
% 
% to let $B=\!\@mparbottom!$ point the bottom of the marginal note below
% which a new marginal note $m$, whose natural top is at $t$ and occupancy
% height is $h$, in the current column $c$ and the page $p$ is placed, or 0
% if the side margin has had no marginal notes yet.  It is also \!\def!ines
% $M'=\Midx{\!\pcol@mpblist!}$ having $\mpar(t',t'{+}h)$ for the new marginal
% note $m$ placed at $t'$ in it and being replaced with one of
% $\mpb_{\{L,R\}}^{\{l,r\}}$ in $\pp^m(p)$ by \!\pcol@setmpbelt!.
% 
% First we examine if $\pp^m(p)=\!\pcol@mparbottom!$ is empty and if so we
% simply let $B=0$ and $M'=(\mpar(t,t+h))$ because there are no marginal
% notes in the page $p$ at all.  Otherwise we obtain
% $M\in\Set{\mpb_X^x}{X\in\{L,R\},\;x\in\{l,r\}}$ in \!\reserved@a! according
% to the side margin to which the new marginal note $m$ goes to, i.e.,
% according to $\CSIndex{if@firstcolumn}$ and $c<\CL$ or not, by
% \!\pcol@getmparbottom@i! giving it the body of $\pp^m(p)$ by
% \!\expandafter!.  Then we apply $\!\pcol@getmpbelt!$ to each
% $\mpar(t_i,b_i)\in M$ to have
% $t_k=\min\Set{t_i}{t_i\geq{t},\;t_i-\max(t,b_{i-1})\geq{h}}$ and let
% $B=b_{k-1}$ and
% 
% \begin{eqnarray*}
% M'&=&(\mpar(t_1,b_1),\;\ldots,\;\mpar(t_{k-1},b_{k-1}),\;
%       \mpar(\max(t,B),\,\max(t,B)+h),\\
% &&\phantom{\LP}
%       \mpar(t_k,b_k),\;\ldots,\;\mpar(t_n,b_n))
% \end{eqnarray*}
% 
% where $n=\Abs{M}$, assuming $b_0=0$.  That is, we try to find the first
% avilable gap between marginal notes below $t$ to accommodate the
% marginal note $m$ of $h$ tall.  Then if such $t_k$ is not found because
% $t>t_n$ to mean $m$ appears below the last marginal note as in natural
% cases, or $t_i-\max(t,b_{i-1})<h$ for all $t_i$ s.t.\ $t_i>t$ to mean
% there are no available gaps, we let $B=t_n$ and
% $M'=(M,\mpar(\max(t,B),\,\max(t,B)+h))$ to place $m$ at the bottom.
% 
%    \begin{macrocode}
\def\pcol@getmparbottom#1#2{%
  \global\@mparbottom\z@
  \ifx\pcol@mparbottom\@empty
    \begingroup
      \@tempdimc#2\relax \advance\@tempdimc#1\relax \let\@elt\relax
      \xdef\pcol@mpblist{\@elt{\number#1}{\number\@tempdimc}}%
    \endgroup
  \else
    \expandafter\pcol@getmparbottom@i\pcol@mparbottom
    \begingroup
      \@tempdima#1\relax \@tempdimb#2\relax \@tempswafalse
      \let\@elt\pcol@getmpbelt \global\let\pcol@mpblist\@empty \reserved@a
      \if@tempswa\else
        \ifdim\@tempdima<\@mparbottom \@tempdima\@mparbottom \fi
        \advance\@tempdimb\@tempdima
        \@cons\pcol@mpblist{{\number\@tempdima}{\number\@tempdimb}}%
      \fi
    \endgroup
  \fi}
\def\pcol@getmparbottom@i#1#2#3#4{%
  \ifnum\pcol@currcol<\pcol@ncolleft
    \if@firstcolumn \def\reserved@a{#1}\else\def\reserved@a{#2}\fi
  \else
    \if@firstcolumn \def\reserved@a{#3}\else\def\reserved@a{#4}\fi
  \fi}
\def\pcol@getmpbelt#1#2{%
  \ifdim#1sp<\@tempdima
    \global\@mparbottom#2sp\relax \@cons\pcol@mpblist{{#1}{#2}}%
    \ifdim\@tempdima<#2sp\relax \@tempdima#2sp\relax \fi
  \else
    \@tempdimc\@tempdima \advance\@tempdimc\@tempdimb
    \ifdim#1sp<\@tempdimc
      \@tempdima#2sp\relax \global\@mparbottom#2sp\relax
      \@cons\pcol@mpblist{{#1}{#2}}%
    \else
      \@cons\pcol@mpblist{{\number\@tempdima}{\number\@tempdimc}\@elt{#1}{#2}}%
      \@tempswatrue
      \def\pcol@getmpbelt##1##2{\@cons\pcol@mpblist{{##1}{##2}}}
    \fi
  \fi}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@setmpbelt}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to update $\pi^m(p)$.}
% \begin{macro}{\pcol@setmpbelt@i}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to update $\pi^m(p)$.}
% 
% The macro $\!\pcol@setmpbelt!
% \Arg{\pp^p(q)}\<\pp^i(q)\>\<\pp^f(q)\>\Arg{\pp^s(q)}\Arg{\pp^m(q)}$ is
% used solely in \!\pcol@addmarginpar! and is applied to $\PPP$ to update an
% element $M\in\Set{\mpb_X^x}{X\in\{L,R\},x\in{l,r}}$ in $\pp^m(p)$ with
% $M'=\!\pcol@mpblist!$ given by \!\pcol@getmparbottom!.  The structure of
% the macro is similar to \!\pcol@setpnoelt! to upadate $\pp^p(q)$ s.t.\
% $q\geq p$, but in this macro the target of the update is only $p$.  Then
% for $q=p$, we invoke \!\pcol@setmpbelt@i! giving it the body of $\pp^m(p)$
% being
% $\Arg{\mpb_L^l}\Arg{\mpb_L^r}\Arg{\mpb_R^l}\Arg{\mpb_R^r}$, or
% $\<\emptyset\>\<\emptyset\>\<\emptyset\>\<\emptyset\>$ if
% $\pp^m(p)=\emptyset$, to obtain what $\pp^m(p)$ should have in
% $\pp_{\mathit{new}}^m(p)=\!\reserved@a!$ in which $\mpb_X^x$ is replaced
% with $M'$, where $X=L$ or $X=R$ if $c<\CL$ or not respectively, and $x=l$
% or $x=r$ if $\CSIndex{if@firstcolumn}=\true$ or not respectively, and then
% update $\pp^m(p)$ by $\!\pcol@defcurrpage!
% \Arg{\pp^p(p)}\<\pp^i(p)\>\<\pp^f(p)\>\Arg{\pp^s(p)}
% \Arg{\pp_{\mathit{new}}^m(q)}$.
% 
%    \begin{macrocode}
\def\pcol@setmpbelt#1#2#3#4#5{%
  {\let\@elt\relax \xdef\pcol@pages{\pcol@pages\pcol@currpage}}%
  \ifnum\@tempcnta=\z@
    \def\reserved@a{#5}%
    \ifx\reserved@a\@empty \pcol@setmpbelt@i{}{}{}{}\else \pcol@setmpbelt@i#5\fi
    \pcol@defcurrpage{#1}{#2}{#3}{#4}{\reserved@a}%
  \else \gdef\pcol@currpage{\@elt{#1}#2#3{#4}{#5}}%
  \fi
  \advance\@tempcnta\m@ne}
\def\pcol@setmpbelt@i#1#2#3#4{%
  \ifnum\pcol@currcol<\pcol@ncolleft
    \if@firstcolumn \def\reserved@a{{\pcol@mpblist}{#2}{#3}{#4}}%
    \else           \def\reserved@a{{#1}{\pcol@mpblist}{#3}{#4}}%
    \fi
  \else
    \if@firstcolumn \def\reserved@a{{#1}{#2}{\pcol@mpblist}{#4}}%
    \else           \def\reserved@a{{#1}{#2}{#3}{\pcol@mpblist}}%
    \fi
  \fi}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@mparbottom@zero}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to give the default of \cs{pcol@mparbottom@out}.}
% \begin{macro}{\pcol@mparbottom@out}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to keep the last elements of $\pi^m(p_t)$ at
%	 \cs{end}\string\texttt{\char`\{paracol\char`\}.}}
% 
% The macro $\Uidx\mpboutz=\!\pcol@mparbottom@zero!$ is used in
% \!\@outputpage!, \!\pcol@getmparbottom@last! and \!\pcol@output@end! to
% give the default value of $\Uidx\mpbout=\!\pcol@mparbottom@out!$ with
% $\mpar(0,0)$ for all elements $M\in\Set{\mpb_X^x}{X\in\{L,R\},x=\{l,r\}}$
% to mean a page has no marginal notes carrying over from the preceding
% \env{paracol} environments.
% 
% As for $\mpbout$, besides the top level initialization to make it
% $\mpboutz$, it is updated in \!\pcol@output@end! through macros
% \!\pcol@getmparbottom@last! and \!\pcol@bias@mpbout! to have the last
% element of each $M\in\Set{\mpb_X^x}{X\in\{L,R\},x=\{l,r\}}$ in
% $\pp^m(\ptop)$ with transformation from coordinates of columns to that of
% text area, or directly with $\mpboutz$ if the \lpage{} will not have
% \postenv.  The resulting $\mpbout$ is at first used in \!\pcol@output@end!
% itself through \!\pcol@do@mpbout! to let \!\@mparbottom! have the value
% $b$ of $\mpar(t,b)$ in $\mpb_L^l$ or $\mpb_L^r$ according to the side
% margin which marginal notes in \postenv{} goes to.
% 
% Then $\mpbout$ is passed to the next \env{paracol} environment if it
% resides in the page where the previous environment also resides, to be
% referred to by \!\pcol@output@start! which also performs
% \!\pcol@do@mpbout! and \!\pcol@bias@mpbout! to let $\pp^m(0)$ have the
% lists according to $\mpbout$ and $\!\@mparbottom!$ which can be modified
% in \postenv{} of the previous environment or in other word
% in \preenv{} of starting envionment.  By this setting of $\pp^m(0)$,
% marginal note placement in the \spage{} is aware of the marginal notes
% having been placed in previous environments and in \preenv{} and thus can
% correctly examines if a marginal note to be added in a margin collide 
% the last one in the margin.  On the other hand, if the \postenv{}
% encounters a page break before a new environment starts, our own
% \!\@outputpage! should be invoked at the page break to let
% $\mpbout=\mpboutz$ because the marginal notes in previous environments do
% not afffect those in the new environment.
% 
% Note that $\mpbout$ is also referred to and updated by
% \!\pcol@do@mpb@all@i! and \!\pcol@do@mpb@all@ii! because they are used in
% \!\pcol@bias@mpbout! and \!\pcol@getmparbottom@last! through
% \!\pcol@do@mpb@all!.
% 
%    \begin{macrocode}
\gdef\pcol@mparbottom@zero{{\@elt{0}{0}}{\@elt{0}{0}}{\@elt{0}{0}}{\@elt{0}{0}}}
\global\let\pcol@mparbottom@out\pcol@mparbottom@zero

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \KeepSpace{2}
% \begin{macro}{\pcol@do@mpbout}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to do specified operations on $\string\cal{M}$ and its
%	 element $M_L^x$ acccording to the side margin for marginal notes
%	 outside \texttt{paracol} environments.}
% \begin{macro}{\pcol@do@mpbout@i}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to do specified operations on $\string\cal{M}$ and its
%	 element $M_L^x$ acccording to the side margin for marginal notes
%	 outside \texttt{paracol} environments.}
% \begin{macro}{\pcol@do@mpbout@whole}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to do a specified operation on $\string\cal{M}$.}
% \begin{macro}{\pcol@do@mpbout@elem}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to do a specified operation on an element $M_L^x$ in
%	 $\string\cal{M}$.}
% 
% The macro \!\pcol@do@mpbout! is used in \!\pcol@output@start! and
% \!\pcol@output@end! to perform operations specified by
% \!\pcol@do@mpbout@whole!  and \!\pcol@do@mpbout@elem!.  The macro just
% invokes \!\pcol@do@mpbout@i! giving it all
% $M\in\Set{\mpb_X^x}{X\in\{L,R\},x\in\{l,r\}}$ by \!\expandafter!.
% 
% Then \!\pcol@do@mpbout@i! determines the side margin $x\in\{l,r\}$ letting
% $x=l$ iff $\CSIndex{if@mparswitch}=\true$, $\page(p)\bmod2=0$ and
% $\CSIndex{if@reversemargin}=\false$, to invoke \!\pcol@do@mpbout@whole!
% giving it all $M$ but $\mpb_L^x$ whose sole element $\mpar(t,b)$
% may be modified by $\!\pcol@do@mpbout@elem!\!\@elt!\Arg{t}\Arg{b}$.
% 
% In \!\pcol@output@start!, \!\pcol@do@mpbout@whole! is to \!\xdef!ine
% $\mpbout$ with all $M$ and \!\pcol@do@mpbout@elem! is expanded to
% $\mpar(0,B)$, where $B=\!\@mparbottom!$, regardless of $\mpb_L^x$ so that
% it is replaced with $(\mpar(0,B))$ in the modified $\mpbout$ keeping other
% elements unchanged.  In \!\pcol@output@end!, \!\pcol@do@mpbout@whole! is
% to throw all $M$ away into a \!\hbox! while \!\pcol@do@mpbout@elem! lets
% $B=b$ so that the bottom of the last marginal note in the side margin
% specified by $x$ is passed to \postenv{} through \!\@mparbottom!.
% 
%    \begin{macrocode}
\def\pcol@do@mpbout{\expandafter\pcol@do@mpbout@i\pcol@mparbottom@out}
\def\pcol@do@mpbout@i#1#2#3#4{\@tempcnta\@ne
  \if@mparswitch \ifodd\c@page\else \@tempcnta\m@ne \fi\fi
  \if@reversemargin \@tempcnta-\@tempcnta \fi
  \ifnum\@tempcnta<\z@
    \pcol@do@mpbout@whole{\pcol@do@mpbout@elem#1}{#2}{#3}{#4}%
  \else
    \pcol@do@mpbout@whole{#1}{\pcol@do@mpbout@elem#2}{#3}{#4}%
  \fi}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@bias@mpbout}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to perform coordinate transformation of the elements in
% 	 $\string\cal{M}$.}
% \begin{macro}{\pcol@bias@mpbout@i}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to perform coordinate transformation of the elements in
% 	 $\string\cal{M}$.}
% 
% The macro $\!\pcol@bias@mpbout!\Arg{y}$ is used in \!\pcol@output@start!
% with $-y$ being the heigh-plus-depth of \preenv{}, in
% \!\pcol@output@end! with $y$ being that of \spanning{} in the \lpage, and
% in $\!\pcol@getmparbottom@last!\Arg{y}$ with its argument $y$.  The macro
% modifies $\mpar(t,b)$ in all $M\in\Set{\mpb_X^x}{X\in\{L,R\},x\in\{l,r\}}$
% of $\mpbout$ so that they have $\mpar(t{+}y,b{+}y)$ for the transformation
% from text area coordinates to columns in the first and third, while for
% the reverse transformation in the second, by invoking \!\pcol@do@mpb@all!
% giving it $\mpbout$ and letting \!\reserved@a! have
% $\!\pcol@bias@mpbout@i!\Arg{y}$.  That is,
% $\!\pcol@bias@mpbout@i!\Arg{y}\!\@elt!\Arg{t}\Arg{b}\!\@nil!$ is then
% invoked in \!\pcol@do@mpb@all@ii! with $t$ and $b$ from $\mpar(t,b)$ in
% each $M$, and then it \!\def!ines \!\reserved@b! with $\mpar(t{+}y,b{+}y)$
% so that updated $M$ has it.
% 
%    \begin{macrocode}
\def\pcol@bias@mpbout#1{\def\reserved@a{\pcol@bias@mpbout@i{#1}}%
  \pcol@do@mpb@all\pcol@mparbottom@out}
\def\pcol@bias@mpbout@i#1\@elt#2#3\@nil{%
  \dimen@#2sp\relax \advance\dimen@#1\relax
  \dimen@ii#3sp\relax \advance\dimen@ii#1\relax
  \def\reserved@b{\@elt{\number\dimen@}{\number\dimen@ii}}}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@getmparbottom@last}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to let $\string\cal{M}$ have the occupancy information of
%	 the bottom marginal note in each margin.}
% \begingroup\let\small\footnotesize
% \begin{macro}{\pcol@getmparbottom@last@i}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to let $\string\cal{M}$ have the occupancy information of
%	 the bottom marginal note in each margin.}
% 
% The macro $\!\pcol@getmparbottom@last!\Arg{y}$ is used solely in
% \!\pcol@output@end! to let
% $\mpbout=\Arg{m_L^l}\Arg{m_L^r}\Arg{m_R^l}\Arg{m_R^r}$, where
% $m_X^x=\mpar(t_n,b_n)\in\mpb_X^x$, $n=\Abs{\mpb_X^x}$ asuming
% $\mpar(t_0,b_0)={\mpar}(y,y)$, and $y$ is the negative counterpart of the
% height-plus-depth of the \spanning{} in the \lpage.  Therefore, $\mpbout$
% is let have the occupancy information of the last marginal note if any, or
% the top edge of text area otherwise, in each margin.
% 
% The macro at first examines if $\pp^m(\ptop)=\emptyset$ and, if so, lets
% all elements in $\mpbout$ have $(\mpar(y,y))$ by letting it $\mpboutz$ and
% then adding $y$ to each $t=b=0$ by \!\pcol@bias@mpbout! giving it $y$.
% Otherwise, i.e., if $\pp^m(\ptop)\neq\emptyset$, it invokes
% \!\pcol@do@mpb@all! giving it $\pp^m(\ptop)$ and letting \!\reserved@a!
% have $\!\pcol@getmparbottom@last@i!\Arg{y}$.  That is,
% $\!\pcol@getmparbottom@last@i!\Arg{y}\~\mpar(t_1,b_1)\cdots
% \mpar(t_n,b_n)\!\@nil!$ is then invoked in \!\pcol@do@mpb@all@ii! for each
% $\mpb_X^x$ to let \!\reserved@b! have $\mpar(y,y)$ at first and then to
% let it have $\mpar(t_i,b_i)$ for all $i\in[1,n]$.  Therefore,
% \!\reserved@b! should finally have $\mpar(t_n,b_n)$ assuming $t_0=b_0=y$,
% and then becomes $m_X^x$.
% \end{macro}\endgroup
% 
%    \begin{macrocode}
\def\pcol@getmparbottom@last#1{%
  \ifx\pcol@mparbottom\@empty
    \global\let\pcol@mparbottom@out\pcol@mparbottom@zero
    \pcol@bias@mpbout{#1}%
  \else
    \def\reserved@a{\pcol@getmparbottom@last@i{#1}}%
    \pcol@do@mpb@all\pcol@mparbottom
  \fi}
\def\pcol@getmparbottom@last@i#1#2\@nil{%
  \edef\reserved@b{\@elt{\number#1}{\number#1}}%
  \def\@elt##1##2{\def\reserved@b{\@elt{##1}{##2}}}%
  #2\let\@elt\relax}

%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\pcol@do@mpb@all}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to implement \cs{pcol@bias@mpbout} and
%	 \cs{pcol@getmparbottom@last}.}
% \begin{macro}{\pcol@do@mpb@all@i}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to implement \cs{pcol@bias@mpbout} and
%	 \cs{pcol@getmparbottom@last}.}
% \begin{macro}{\pcol@do@mpb@all@ii}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to implement \cs{pcol@bias@mpbout} and
%	 \cs{pcol@getmparbottom@last}.}
% 
% The macro $\!\pcol@do@mpb@all!\<L\>$ is used in \!\pcol@bias@mpbout! with
% $L=\mpbout$ and in \!\pcol@getmparbottom@last! with $L=\pp^m(\ptop)$, to
% process all four elements $\mpb_X^x$ in $L$ applying \!\reserved@a! to
% each of them and to let $\mpbout$ have the result through \!\reserved@b!.
% The macro simply invokes \!\pcol@do@mpb@all@i! giving it the body of $L$
% by \!\expandafter!.  Then $\!\pcol@do@mpb@all@i!
% \Arg{\mpb_L^l}\Arg{\mpb_L^r}\Arg{\mpb_R^l}\Arg{\mpb_R^r}$ initialize
% $\mpbout=\emptyset$ and then invokes \!\pcol@do@mpb@all@ii! four times
% giving it each $\mpb_X^x$.  Then
% $\!\pcol@do@mpb@all@ii!\,\mpar(t_1,b_1)\cdots\~{\mpar}(t_n,b_n)\!\@nil!$
% invokes \!\reserved@a! giving it all of $\mpar(t_i,b_1)$ at once to
% process them and to have the result in \!\reserved@b! being added to
% $\mpbout$.
% 
%    \begin{macrocode}
\def\pcol@do@mpb@all#1{\expandafter\pcol@do@mpb@all@i#1}
\def\pcol@do@mpb@all@i#1#2#3#4{\begingroup \let\@elt\relax
  \gdef\pcol@mparbottom@out{}%
  \pcol@do@mpb@all@ii#1\@nil\pcol@do@mpb@all@ii#2\@nil
  \pcol@do@mpb@all@ii#3\@nil\pcol@do@mpb@all@ii#4\@nil
  \endgroup}
\def\pcol@do@mpb@all@ii#1\@nil{%
  \reserved@a#1\@nil
  \xdef\pcol@mparbottom@out{\pcol@mparbottom@out{\reserved@b}}}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% 
% 
% \subsection{Synchronization}
% \label{sec:imp-sout-sync}
% 
% \begin{macro}{\pcol@sync}
% \changes{v1.0}{2011/10/10}
%	{Add measurement of $D_T$.}
% \changes{v1.2-3}{2013/05/11}
%	{Modify the action on the page overflow to return from \cs{output}
%	 without flushing so that the page is broken outside \cs{output} to
%	 place top floats above the synchronization point set in the next
%	 page.}
% \changes{v1.2-2}{2013/05/11}
%	{Revise reflecting the redesign of page context.}
% \changes{v1.2-2}{2013/05/11}
% 	{Add pre-flushing column height check taking page-wise
%	 footnotes into account.}
% \changes{v1.3-6}{2013/09/17}
%	{Add the initialization of
%	 $\cs{ifpcol@dfloats}\EQ\string\mathit{false}$ before invoking
%	 \cs{pcol@measurecolumn}.}
% 
% The macro \!\pcol@sync! is invoked solely from \!\pcol@output@switch! for
% \exsync{} in the following three cases in which
% $\CSIndex{ifpcol@sync}\lor\CSIndex{ifpcol@clear}=\true$ commonly.
% 
% \begin{itemize}
% \item
% $\CSIndex{ifpcol@sync}\land\lnot\CSIndex{ifpcol@clear}$ to mean ordinary
% \sync{}ed \cswitch.
% 
% \item
% $\CSIndex{ifpcol@sync}\land\CSIndex{ifpcol@clear}$ to mean \pfcheck.
% 
% \item
% $\lnot\CSIndex{ifpcol@sync}\land\CSIndex{ifpcol@clear}$ to mean page
% flushing.
% \end{itemize}
% 
% In any cases\footnote{
% 
% In the last case of page flushing, invoking \!\pcol@flushcolumn! is
% redundant because it is made $p=\ptop$ by \pfcheck{} always preceding the
% flushing, but the invocation is harmless.},
% 
% first we invoke \!\pcol@flushcolumn! for all $c\In0\C$ to flush the
% \ccolpage{} of $c$ into $\S_c$ if the \colpage{} is not in $\ptop$, i.e.,
% $\cc_c(\vb^p)<\ptop$ and then, if we have deferred floats, to ship out
% following \fpage{}s up to $\ptop-1$ into $\S_c$ and to place them in
% $\ptop$.  This float placement in $\ptop$ is only for top and bottom
% floats in \sync{}ed \cswitch{}, while a \fcolumn{} may be made in other
% cases.  Then we ship out all pages $p$ such that $p<\ptop$ by
% \!\pcol@outputcolumns! giving argument 1.  After that, we obtain the
% \pctext{} of $\ptop$ by \!\pcol@getcurrpinfo!.
% 
% Next, we measure the vertical sizes of the contents in the \ccolpage{} of
% $c$ which is now in $\ptop$ for all $c\In0\C$ by \!\pcol@measurecolumn! as
% follows, where $h(x)$ and $d(x)$ are the height and depth of an object $x$
% respectively.
% 
% \begin{eqnarray*}
% \sigma&=&\rlap{\!\floatsep!}\hskip8em
% \sigma_t=\cases{\cc_c(\tf)&     $\cc_c(\tf)<\infty$\cr
% 		    \!\textfloatsep!&$\cc_c(\tf)=\infty$}\qquad
% \sigma_b=\!\textfloatsep!\\
% \Uidx\fc(t)&=&\rlap{$\displaystyle(\cc_c(\tl)\neq())$}\hskip8em
%     \fc(m)=(\cc_c(\vb)\neq\!\vbox!|{}|)\\
% \fc(f)&=&\rlap{$\displaystyle(\cc_c(\ft)\neq\bot)$}\hskip8em
%     \fc(b)=\fc(b')=(\cc_c(\bl)\neq())\\
% \Uidx\Fc(X)&=&\rlap{$\displaystyle\exists x\in X:\fc(x)$}\hskip8em
%     f_b=\CSIndex{ifpcol@bfbottom}\\
% \Uidx\vc(t)&=&\!\skip!{\cdot}\cc_c(\vb)=
% 	\sum_{\Sub{\phi\in\cc_c(\tl)}}(h(\phi)+d(\phi))+
% 	(\Abs{\cc_c(\tl)}-1)\cdot\sigma+\sigma_t\\
% \vc(m)&=&h(\cc_c(\vb))+d(\cc_c(\vb))\\
% \vc(f)&=&h(\cc_c(\ft))+d(\cc_c(\ft))\\
% \vc(b)&=&\sum_{\Sub{\phi\in\cc_c(\bl)}}(h(\phi)+d(\phi))+
% 	(\Abs{\cc_c(\bl)}-1)\cdot\sigma+\sigma_b\\
% \vc(b')&=&\vc(b)+\sigma_b\\
% \pd_c&=&\cases{\cc_c(\pd)&$\fc(m)$\cr
%                \infty   &$\lnot \fc(m)$}\\
% \Uidx\size_c(x)&=&\cases{\vc(x)&$\fc(x)$\cr
%                     0     &$\lnot \fc(x)$}\\
% \Uidx\Size_c(X)&=&\cases{\displaystyle\sum_{x\in X}\size_c(x)&$\Fc(X)$\cr
%                          -\infty&                         $\lnot \Fc(X)$}\\
% \Uidx\VT&=&\!\@tempdima!=\max_{0\leq c<\C}\{\Size_c(\{t,m\})\}\\
% \Uidx\VB&=&\!\@tempdimb!=\max_{0\leq c<\C}\{\size_c(f)+\size_c(b)\}\\
% \Uidx\VP&=&\!\@pageht!=\max_{0\leq c<\C}\{\Size_c(\{t,m,f,b\})\}\\
% \Uidx\VPP&=&\!\pcol@colht!=\max_{0\leq c<\C}\{\Size_c(\{t,m,f,b'\})\}\\
% \Uidx\DT&=&\!\@tempdimc!=\min\Set{\pd_c}{\Size_c{\{t,m\}=\VT}}\\
% \Uidx\dc&=&\cases{
%   0&			$\fc(b)\land(\lnot \fc(f)\lor f_b)$\cr
%   d(\cc_c(\ft))&	$\fc(f)\land(\lnot \fc(b)\lor\lnot f_b)$\cr
%   d(\cc_c(\pd))&	$\lnot \fc(b)\land\lnot \fc(f)$}\\
% \Uidx\DP&=&\!\@pagedp!=\min\Set{\dc}{\Size_c(\{t,m,f,b'\})=\VPP}\\
% \Uidx\cmax&=&\!\@tempcntb!=\ARG\max_{0\leq c<\C}\{\Size_c(\{t,m,f,b\})\}
% \end{eqnarray*}
% 
% That is, $\VT$ is the maximum of combined vertical size (height plus
% depth) of the top floats and the main vertical list, $\VB$ is that of
% the footnotes and bottom floats, and $\VP$ is that of all items.
% $\VPP$ is similar to $\VP$ but we add \!\textfloatsep! to the size of
% bottom floats.  Note that $\VT$, $\VP$ and $\VPP$ are $-\infty$ if any
% \colpage{}s don't have corresponding items, while $\VB=0$ if so.
% Also note that $\cmax$ is the ordinal of the column whose size is $\VP$.
% 
% $\DT$ and $\DP$ are the minimum $\pd_c$ and $\dc$ respectively among those
% gives $\VT$ and $\VPP$ respectively, where $\pd_c$ is $\cc_c(\pd)$ if
% $f_m=\true$ or $\infty$ otherwise, and $\dc$ is 0 if $c$ has bottom float,
% or the depth of the last footnote if any and without any bottom float, or
% $\cc_c(\pd)$ otherwise.  The reason why $\DT$ and $\DP$ have minimums is
% that they are set into \!\prevdepth! for the items just following the
% \sync{}ation point, and thus a smaller value results in a larger interline
% skip and the special value $-1000\,|pt|$ to inhibit the skip by, e.g.,
% \!\nointerlineskip!, is given the highest priority.
% 
% Note that $\VPP$ and $\DP$ are only for the \lpage{} and thus referred to
% by \!\pcol@output@end! to close the environment, and the former is done by
% \!\pcol@makeflushedpage! if it works on the page.  The reason why we add
% \!\textfloatsep! to $\VPP$ is to make the last page well separated from
% the \postenv{} if the tallest column, taking the addition into account,
% has bottom floats.  Also note that we let
% $\CSIndex{ifpcol@dfloats}=\false$ before scanning columns with
% \!\pcol@measurecolumn! so that the switch becomes $\true$ after the scan
% iff a column has deferred floats (in the \lpage{}).
% 
%    \begin{macrocode}
%% Special Output Routines: Synchronization

\def\pcol@sync{%
  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do\pcol@flushcolumn
  \pcol@outputcolumns\@ne
  \pcol@getcurrpinfo{\global\c@page}{\global\@colht}{\global\topskip}%
  \@tempdima-\maxdimen \@tempdimb-\maxdimen \pcol@colht-\maxdimen
  \@pageht-\maxdimen \@tempdimc\maxdimen \@pagedp\maxdimen \@tempcntb\z@
  \pcol@dfloatsfalse
  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do\pcol@measurecolumn
%    \end{macrocode}
% 
% As described above, any items can be empty, naturally for top floats,
% footnotes and bottom floats, but also including main vertical lists if the
% \ccolpage{}s were not in $\ptop$ before the invocation of
% \!\pcol@flushcolumn!.  Moreover, all main vertical lists can be empty if
% all \lcolpage{}s just have started (by \!\newpage!, for example).  More
% weirdly, the case of all-empty main vertical lists can be accompanied with
% other non-empty items when columns have floats or footnotes which cannot
% be in $\ptop-1$ but are found their places in $\ptop$.
%
% Taking it into account that any items can be empty and the other item
% of \Scfnote{}s, we have to determine whether the following two operations
% are taken;  invocation of \!\pcol@synccolumn! for each \colpage{} to set a
% \sync{}ation point or to add an infinite stretch (and shrink) to its
% bottom;  and the examination of the height of each \colpage{}, taking the
% \sync{}ation point to be set into account, to tell the necessity of
% explicit page break with $\CSIndex{ifpcol@flush}=\true$.  For the latter
% we calculate the examination target $V=\!\@tempdimb!$ to be compared with
% $\pp^h(\ptop)$, while for the former we determine the value of a switch
% $f=\CSIndex{if@tempswa}$ so that we invoke \!\pcol@synccolumn! iff
% $f=\true$ and $V\geq0$.
% 
% For \sync{}ed \cswitch{} with $\CSIndex{ifpcol@clear}=\false$, we let
% $f=(\VT\geq0)$ to mean at least one \colpage{} has a top float or
% non-empty main vertical list, i.e., $\Fc(\{t,m\})={\true}$ for some
% $c\In0\C$.  That is if $\VT<0$, since the next items added to all
% \colpage{}s are placed at the top of the page\footnote{
% 
% In usual cases, but it can mean some of them have negative vertical
% sizes.  Even though we can detect such a very unlikely special case, it is
% very tough to define the reasonable \sync{}ation point above the top of
% $\ptop$.  Therefore, we assume the point is at the top of $\ptop$ and thus
% do nothing.},
% 
% we don't need to set \sync{}ation points in them.  As for $V$, we let
% $V=\max(\VT,0)+\max(\VB,0)+v^f$ where $v^f$ is the sum of
% height-plus-depth of $\pp^f(\ptop)$ and $\!\skip!{\cdot}\pp^f(\ptop)$ if
% $\ptop$ has \Scfnote{}s, or 0 otherwise\footnote{
% 
% In the real implementation, $V=-\infty$ if $\VT=\VB=-\infty$ and no
% \Scfnote{}s are presented, but this difference does not affect the
% decisoins because $f\land(V\geq0)=(\VT<0)\land(V\geq0)=\false$ and
% $V\leq\pp^f(\ptop)$ with either $V=0$ or $V=-\infty$.}.
% 
% Note that it can be $\VP+v^f\leq\pp^h(\ptop)<\VT+\VB+v^f=V$ to mean
% setting the \sync{}ation point at $\VT$ below $\ptop$'s top edge would
% push bottom stuff beyond its bottom edge and thus we need an explicit page
% break to place the point at the top of $\ptop+1$ (in usual cases).
% 
% For \pfcheck{} or page flushing with $\CSIndex{ifpcol@clear}=\true$ on
% the other hand, we let $f=\lnot\!\pcol@sync!$ to invoke \!\pcol@synccolumn!
% only for page flushing and thus not for \pfcheck{}.  As for $V$, we let
% $V'=\VPP$ or $V'=\VP$ according as we working on \lpage{} or not, and
% then let $V=\max(V',0)+v^f$ or $V=V'$ according as $\ptop$ has \Scfnote{}s
% or not.  That is, we have to invoke \!\pcol@synccolumn! unless $\ptop$ is
% perfectly empty.
% 
% Then if $\CSIndex{ifpcol@clear}=\false$ and
% $\max(V,\;V-D'_T+\VE)>\pp^h(\ptop)$ where $D'_T=\DT$ if $0\leq\DT<\infty$ or
% 0 otherwise, or $\CSIndex{ifpcol@clear}=\true$ and
% $V>\pp^h(\ptop)$\footnote{
% 
% The examination is redundant in page flushing with
% $\CSIndex{ifpcol@sync}=\false$ because it is assured that no overflow
% happens in any \colpage{} by \pfcheck{} and explicit page breaking, but is
% not harmful.},
% 
% we flush the page.  That is, if the condition above holds,
% we let $\CSIndex{ifpcol@flush}=\true$ and $d=\!\pcol@nextcol!={\cmax}$ to
% tell \!\pcol@switchcol! or \!\pcol@flushclear! to make an explicit page
% break in the column $\cmax$ from which we restart, and $f=\false$ to skip
% \!\pcol@synccolumn! to postpone the \exsync{}.  Note that the bias
% $\VE=\!\pcol@@ensurevspace!$ in \sync{}ed \cswitch{} is to avoid breaking a
% \colpage{} just below the \sync{}ation point due to too small space below
% the point, less than \!\baselineskip! in default but can be other
% threshold explicitly defined by \!\ensurevspace!.  That is,
% since $V-\DT+k\!\baselineskip!$ usually means the vertical position at
% which $k$-th baseline below the \sync{}ation point is placed, the flushing
% condition with $\VE=k\!\baselineskip!$ ensures that the page is flushed
% iff the space below the point cannot accommodate $k$ lines.  Also note that
% necessary flushing with $V>\pp^h(p)$ assuredly takes place even when
% $\DT$ is unusually large and/or $\VE$ is negative to make $-\DT+\VE<0$.
% 
% Finally if $V\geq0$ and $f=\true$, we invoke \!\pcol@synccolumn! for each
% column $c\In0\C$ to set a \sync{}ation point in it or to add an infinite
% stretch (and shrink) at its bottom for flushing.
% 
% \changes{v1.3-6}{2013/09/17}
%	{Modify the flushing condition of synchronized column switching from
%	 $V\GT\pi^h(p)$ to $\max(V,V-D_T+V_E)\GT\pi^h(p)$ to avoid page
%	 break just below the synchronization point as much as possible.}
% 
%    \begin{macrocode}
  \@tempswatrue \global\pcol@flushfalse
  \ifpcol@clear
    \ifpcol@lastpage \@tempdimb\pcol@colht \else \@tempdimb\@pageht \fi
    \ifpcol@sync \@tempswafalse \fi
  \else
    \ifdim\@tempdima<\z@      \@tempswafalse
    \else\ifdim\@tempdimb<\z@ \@tempdimb\@tempdima
    \else                     \advance\@tempdimb\@tempdima
    \fi\fi
  \fi
  \ifpcol@scfnote\ifvoid\pcol@footins\else
    \ifdim\@tempdimb<\z@ \@tempdimb\z@ \fi
    \advance\@tempdimb\ht\pcol@footins \advance\@tempdimb\dp\pcol@footins
    \advance\@tempdimb\skip\pcol@footins
  \fi\fi
  \dimen@\@tempdimb
  \ifpcol@clear\else \ifdim\dimen@<\z@\else
    \ifdim\@tempdimc=\maxdimen\else \ifdim\@tempdimc<\z@\else
      \advance\dimen@-\@tempdimc
    \fi\fi
    \advance\dimen@\pcol@@ensurevspace
    \ifdim\dimen@<\@tempdimb \dimen@\@tempdimb \fi
  \fi\fi
  \ifdim\dimen@>\@colht
    \global\pcol@flushtrue \@tempswafalse \pcol@nextcol\@tempcntb
  \fi
  \ifdim\@tempdimb<\z@\else \if@tempswa
    \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do\pcol@synccolumn
  \fi\fi}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@flushcolumn}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{pcol@maxpage} as \cs{pcol@toppage}.}
% \changes{v1.0}{2011/10/10}
%	{Add \cs{vfil} at the bottom of flushed column-page.}
% \changes{v1.0}{2011/10/10}
%	{Change order of the garbage collection of \cs{pcol@currfoot} and
%	 \cs{pcol@getcurrfoot}.} 
% \changes{v1.2-2}{2013/05/11}
% 	{Revise reflecting the redesign of \cs{pcol@getcurrfoot}.}
% \changes{v1.2-2}{2013/05/11}
% 	{Add operations for page-wise footnotes.}
% \changes{v1.2-2}{2013/05/11}
% 	{Add the examination of $\kappa_c(\rho)\EQ\infty$ to cope with a
%	 rare-case interaction of pre-flushing column height check and float
%	 columns in last pages.}
% \changes{v1.2-7}{2013/05/11}
% 	{Save \cs{ifpcol@lastpage} into \cs{ifpcol@lastpagesave} and turn
% 	 \cs{ifpcol@lastpage} $\string\mathit{false}$ temporarily during
% 	 the macro works on non-top and thus non-last pages to fix the bug
%	 that \cs{@makecol} and \cs{pcol@makefcolumn} misunderstand the page
%	 they work on is last.}
% \changes{v1.2-7}{2013/05/11}
% 	{Replace \cs{@makecol} with \cs{pcol@@makecol} to cap the depth of
%	 \cs{@outputbox} by \cs{@maxdepth} even with p\string\LaTeX.}
% \changes{v1.21}{2013/06/06}
%	{Add page and column numbers to logging.}
% \changes{v1.3-6}{2013/09/17}
%	{Fix the problem that a flushed column in a non-top page causes
% 	 overfull due to its hight-plus-depth greater than $\pi^h(p)$.}
% \changes{v1.3-3}{2013/09/17}
%	{Add \cs{@colht} and \cs{relax} as the first and third argument
%	 of \cs{pcol@shrinkcolbyfn} for all of three invocations of it.}
% \changes{v1.3-6}{2013/09/17}
%	{Add \cs{@maxdepth} as the first argument of \cs{pcol@@makecol}.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
% The macro \!\pcol@flushcolumn! is invoked for each column $c\In0\C$ from
% \!\pcol@sync! to ship out the \ccolpage{} of $c$ into $\S_c$ if it is not
% leading one\Index{leading column-page}, i.e., $p=\cc_c(\vb^p)<\ptop$.  The
% macro also ships out \fpage{}s from $p+1$ up to $\ptop-1$ if we have
% deferred floats to fill them and, if this float flushing still leaves
% deferred floats, puts some of them to the \lcolpage{} being
% current\Index{current column-page}{} now as its top and/or bottom floats.
% 
% First we obtain the \cctext{} in $\cc_c$ by \!\pcol@getcurrcol! and
% examines if $p=\cc_c(\vb^p)<\ptop$.  If it does not hold to mean $c$ has
% \lcolpage{}, we do nothing.
% 
% Otherwise, we save \CSIndex{ifpcol@lastpage} into
% \CSIndex{ifpcol@lastpagesave} turning the former switch $\false$ because we
% are working on a non-\lcolpage{} definitely in a non-\lpage.  Then we put
% the contents of the \ccolpage{} $\cc_c(\vb^b)$ adding \!\vfil! at its tail
% into \!\box!|255| being the \TeX's standard interface to carry the main
% vertical list for \!\output!  routine.  We also move everything in
% $\cc_c(\ft)$ obtained by \!\pcol@getcurrfoot! into \!\footins! and return
% $\cc_c(\ft)$ to \!\@freelist! if $\cc_c(\ft^b)$ is not void.
% 
% Then we obtain $p$'s \pctext{} by \!\pcol@getcurrpage! and, if it has
% \Scfnote{}s in $\pp^f(p)$, we shrink \!\@colht! by the space required for
% the footnotes using \!\pcol@shrinkcolbyfn! and add the stretch\slash
% shrink compontents of $\!\skip!\cdot\pp^f(p)$ at the bottom of
% \!\box!|255| by \!\pcol@unvbox@cclv!, as we did in \!\pcol@makecol!.
% Otherwise we take a special care of the case that the height-plus-depth of
% $\cc_c(\vb^b)$ is greater than $\pp^h(p)$ due to that its height is almost
% equal to $\pi^h(p)$ and thus its depth makes the hight-plus-depth
% exceeding $\pi^h(p)$.  This excess is revealed by the \!\vfil! we just
% have added making the height-plus-depth the height of \!\box!|255|, and
% would cause overfull in \!\@makecol! and \!\pcol@@makecol! because they
% need the height, i.e., not height-plus-depth, of \!\box!|255| not
% exceeding $\pp^h(p)$.  Therefore if it happens, we we remove the \!\vfil!
% and cap the height of \!\box!|255| by \!\@maxdepth!  to pretend as if the
% box is directly passed from \TeX's page builder.
% 
% Next we examine if $\cc_c(\tr)$ was made $\infty$ by \!\pcol@makefcolumn!
% invoked from this macro itself when it processed the \colpage{} in the
% previous \pfcheck{} for environment closing, which found a page break
% should be done.  That is, $\cc_c(\tr)=\infty$ means the \ccolpage{} was
% once judged to be in the \lpage{} but \pfcheck{} forced a page break to
% make it non-last, it should have all deferred floats now listed in
% $\cc_c(\tl)$ at \Endparacol{}, but their total size is less than the
% threshold to make a usual \fcolumn{} for the \lpage.  If so, since the page
% is not last now, we put all floats in $\cc_c(\tl)$ by \!\pcol@makefcolpage!
% as the ship-out image in \!\@outputbox!, ignoring the contents added to
% \!\box!|255| in the operations above because $\cc_c(\vb^b)$ should be
% empty, and letting $\cc_c(\tr)=0$ to mean the floats have been
% processed\footnote{
% 
% $\cc_c(\tl)$ can have any values other than $\infty$ because definitely it
% will not be referred to in its inherent sense in the situation with no
% further float additions and no deferred floats.}.
% 
% Otherwise, since the \colpage{} can be put as usual, we invoke
% \!\pcol@@makecol!\footnote{
% 
% Neither \cs{pcol@makecol} because \!\box!\texttt{255} has \!\vfil! at its
% tail and the \colpage{} should be short enough, nor \cs{@makecol} because
% we need to ensure the depth of resulting \cs{@outputbox} is capped.}
% 
% giving \!\@maxdepth! to it to build the complete \colpage{} in
% \!\@outputbox! with depth capping and with the following setting\footnote{
% 
% \LaTeX's has another \!\insert! named \!\@kludgeins! for \!\enlargepage!
% but \Paracol{} does not cares about it.}.
% $$
% \begin{array}{lll}
% \!\box!|255|=\cc_c(\vb^b)&
% \!\footins!=\cc_c(\ft)&
% \!\@colht!=\pp^h(\cc_c(\vb^p))\\
% \!\@midlist!=\cc_c(\ml)&
% \!\@toplist!=\cc_c(\tl)&
% \!\@botlist!=\cc_c(\bl)
% \end{array}
% $$
% Finally, regardless of $\cc_c(\tr)=\infty$ or not, the resulting
% \!\@outputbox! becomes $\s_c(p)$ and is added to the tail of $\S_c$
% by \!\@cons!.
% 
%    \begin{macrocode}
\def\pcol@flushcolumn{%
  \pcol@getcurrcol
  \ifnum\count\@currbox<\pcol@toppage
    \ifpcol@lastpage \pcol@lastpagesavetrue \else \pcol@lastpagesavefalse \fi
    \pcol@lastpagefalse
    \pcol@page\count\@currbox
    \setbox\@cclv\vbox{\unvbox\@currbox \vfil}%
    \ifvoid\pcol@currfoot\else
      \pcol@Fb
      \@cons\@freelist\pcol@currfoot
      \pcol@Fe{flushcolumn(colfn)}%
    \fi
    \pcol@getcurrfoot\box
    \pcol@getcurrpage
    \ifvoid\pcol@footins
      \ifdim\ht\@cclv>\@colht
        \setbox\@cclv\vbox{\boxmaxdepth\@maxdepth \unvbox\@cclv \unskip}%
      \fi
    \else
      \pcol@shrinkcolbyfn\@colht\pcol@footins\relax
      \setbox\@cclv\vbox{\pcol@unvbox@cclv\pcol@footins}%
    \fi
    \pcol@Logstart{\pcol@flushcolumn(\number\c@page:\number\pcol@currcol)}
    \ifdim\@toproom=\maxdimen
      \setbox\@outputbox\pcol@makefcolpage \global\@toproom\z@
    \else
      \pcol@@makecol\@maxdepth
    \fi
    \pcol@Logend\pcol@flushcolumn
    \global\setbox\@currbox\box\@outputbox
    \expandafter\@cons\csname pcol@shipped\number\pcol@currcol\endcsname
      \@currbox
%    \end{macrocode}
% 
% Then for each $q\in[p{+}1,\ptop{-}1]$, we repeat the followings; get $q$'s
% \pctext{} by \!\pcol@getcurrpage!; shrink \!\@colht! by
% \!\pcol@shrinkcolbyfn! if $q$ has \Scfnote{}s; try to make a \fcolumn{} in
% \!\@outputbox! by \!\@makefcolumn! giving it \!\@deferlist! being
% $\cc_c(\dl)$ at initial but will be shrunk; if the \fcolumn{} is made,
% acquire an \!\insert! by \!\@next! to keep the contents of \!\@outputbox!
% and to be added to the tail of $\S_c$ by \!\@cons!.
% 
% \changes{v1.2-2}{2013/05/11}
%	{Add \cs{@colht} shrinking by page-wise footnotes.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
    \advance\pcol@page\@ne
    \ifx\@deferlist\@empty\else
      \@whilenum\pcol@page<\pcol@toppage\do{%
        \pcol@getcurrpage
        \ifvoid\pcol@footins\else
          \pcol@shrinkcolbyfn\@colht\pcol@footins\relax
        \fi
        \@makefcolumn\@deferlist
        \if@fcolmade
          \pcol@Fb
          \@next\@currbox\@freelist{\global\setbox\@currbox\box\@outputbox}%
            \pcol@ovf
          \pcol@Fe{flushcolumn(fcol)}%
          \expandafter\@cons
            \csname pcol@shipped\number\pcol@currcol\endcsname\@currbox
        \fi
       \advance\pcol@page\@ne}%
    \fi
%    \end{macrocode}
% 
% Next, since we reach $\ptop$ and thus restore \CSIndex{ifpcol@lastpage}
% from \CSIndex{ifpcol@lastpagesave} because the \tpage{} can be last.
% Then we acquire the \ccolpage{} of $c$ which is now in $\ptop$ and thus
% empty, by \!\@next!.  Then we let $\!\@colht!=\!\@colroom!=\pp^h(\ptop)$
% by \!\pcol@getcurrpinfo! but shrinking them by \!\pcol@shrinkcolbyfn! if
% $\ptop$ has \Scfnote{}s, and reinitialize the float placement parameters by
% \!\pcol@floatplacement!.  Then, if $\cc_c(\dl)$ still has some floats,
% we make a \fcolumn{} for some of them in the \tpage{} by
% \!\pcol@makefcolumn! if $\CSIndex{ifpcol@clear}={}\true$ meaning flushing,
% or try to move some of them to $\cc_c(\tl)=\!\@toplist!$ and/or
% $\cc_c(\bl)=\!\@botlist!$ by \!\pcol@trynextcolumn! otherwise.  Note that
% since \!\@colroom! is used in \!\pcol@makefcolumn! as a working register,
% we let $\!\@colroom!=\pp^h(\ptop)$ again after its invocation.  After that
% we save \cctext{} including those given by \!\pcol@floatplacement! and
% modified by \!\pcol@makefcolumn! or \!\pcol@trynextcolumn! into $\cc_c$ by
% \!\pcol@setcurrcolnf!  because all footnotes are shipped out, and let
% $\cc_c(\vb^p)=\ptop$.  We also let $\cc_c(\vb^r)=\!\@colroom!$ possibly
% modified by \!\pcol@trynextcolumn! but after canceling the shrinkage of
% \!\@colht! due to \Scfnote{}s, i.e.,
% $\cc_c(\vb^r)\gets\cc_c(\vb^r)+(H-H')$ where $H$ and $H'$ are \!\@colht!
% before and after the shrinkage respectively.
% 
% \changes{v1.0}{2011/10/10}
%	{Add $\cs{@colht}\EQ\pi^h(p)$.}
% \changes{v1.0}{2011/10/10}
%	{Replace \cs{pcol@trynextcolumn} with \cs{pcol@makefcolumn} for the
%	 case of $\cs{ifpcol@clear}\EQ\mathit{true}$.}
% \changes{v1.2-2}{2013/05/11}
%	{Revise reflecting the redesign of page context.}
% \changes{v1.2-2}{2013/05/11}
%	{Add \cs{@colht} shrinking by page-wise footnotes.}
% \changes{v1.2-7}{2013/05/11}
% 	{Add the restore of \cs{ifpcol@lastpage} from
%	 \cs{ifpcol@lastpagesave}.}
% \changes{v1.21}{2013/06/06}
%	{Fix the bug that $\kappa_c(\beta^p)$ is let have \cs{pcol@page},
%        which can be less than $p_t\EQ\cs{pcol@toppage}$, to cause the column
%	 $c$ is lost or moved to a wrong page.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
    \ifpcol@lastpagesave \pcol@lastpagetrue \fi
    \pcol@Fb
    \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{}}\pcol@ovf
    \pcol@Fe{flushcolumn(col)}%
    \pcol@getcurrpinfo\@tempcnta{\global\@colht}\@tempskipa
    \@pageht\@colht
    \ifvoid\pcol@footins\else \pcol@shrinkcolbyfn\@colht\pcol@footins\relax \fi
    \global\@colroom\@colht \pcol@floatplacement
    \ifx\@deferlist\@empty\else
      \ifpcol@clear
        \pcol@makefcolumn \global\@colroom\@colht
      \else
        \pcol@trynextcolumn
    \fi\fi
    \pcol@setcurrcolnf
    \global\count\@currbox\pcol@toppage
    \advance\@pageht-\@colht \advance\@pageht\@colroom
    \global\dimen\@currbox\@pageht
  \fi %\ifnum\count\@currbox<\pcol@toppage
  \advance\pcol@currcol\@ne}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@makefcolumn}
% \changes{v1.0}{2011/10/10}
%	{Introduced to take special care of the float-column in the last
%	 page. }
% \changes{v1.2-2}{2013/05/11}
%	{Encapsulate the float column in a \cs{vbox} of \cs{@colht} so that
% 	 vertical skips at the top and bottom are not lost when the column
%	 is put back to the main vertical list, and makes the assignment to
%	 \cs{@currbox} global because the box is now referred to after
%	 \cs{output} is completed.}
% \changes{v1.2-7}{2013/05/11}
% 	{Replace the sequence of operations to make a usual float column
%	 with \cs{@toplist} with the newly introduced
%	 \cs{pcol@makefcolpage}.}
% \changes{v1.33-2}{2016/11/19}
% 	{Remove a space after the \cs{vbox} to be assigned to \cs{@currbox}
%	 to obey the coding convention.}
% 
% The macro \!\pcol@makefcolumn! is invoked solely from \!\pcol@flushcolumn!
% to put deferred floats in the currently empty \colpage{} of $c$ in the
% \tpage{} $\ptop$ which is being flushed.  Since we have to take special care
% of the case of environment closing, we cannot do this operation by
% \!\@makefcolumn!, while in other cases for \!\flushpage! and \!\clearpage!
% we also have to pay a small attention.
% 
% First, we scan the copy of $\cc_c(\dl)$ applying \!\pcol@makefcolelt! to
% each element to have the floats to be put in \!\@toplist!, which is
% assuredly empty because the \ccolpage{} of $c$ has already been shipped
% out to empty it, and those still deferred in $\cc_c(\dl)$.  Prior to scan,
% we let $H_r=\pp^h(\ptop)\footnotemark+\alpha$\footnotetext{
% 
% $\pp^h(\ptop)$ referred in this macro may have been shrunk by \Scfnote{}s
% in \cs{pcol@flushcolumn}.},
% 
% as the space initially available for
% floats each of which being $\phi$ is assumed to consume
% $v(\phi)=h(\phi)+d(\phi)+\alpha$, and $H_t=\!\@colroom!=-\alpha$ as the
% initial value of the accumulated size of $v(\phi)$ for all $\phi$ to be
% put, where $\alpha=\!\floatsep!$ if $\CSIndex{ifpcol@lastpage}=\true$
% 
% \SpecialIndex{\ifpcol@lastpage}
% 
% as discussed afterward, or $\alpha=\!\@fpsep!$ otherwise.
% 
% Then if the resulting \!\@toplist! is not empty\footnote{
% 
% It can happen if the first float is larger than $\pp^h(\ptop)$.},
% 
% we examine if $\ptop$ is the \lpage{} ($|\ifpcol@|\~|lastpage|=\true$)
% 
% \SpecialIndex{\ifpcol@lastpage}
% 
% and $\cc_c(\dl)$ is empty to mean the last \colpage{} have all deferred
% floats.  This case is subtle because if we make the \colpage{} a \fcolumn{}
% it can be sparse and unnecessarily throw the \postenv{} to the next
% page.  Therefore, we intend to pack floats to the page top as top floats
% and thus have let $\alpha=\!\floatsep!$ in the building process of
% \!\@toplist! above\footnote{
% 
% We dare to do it knowing the natural component of \!\floatsep! is a little
% bit (4pt) larger than that \!\@fpsep! and the possibility of having
% fewer floats than those given by \!\@makefcolumn!.},
% 
% but it may make a too tall \colpage{} only having floats shrinking
% the \postenv{} in the page.  In addition, if other columns have
% \fpage{}s in the \lpage, packing the floats as top floats should give
% inconsistent appearance but we don't know whether the columns following
% $c$ has \fpage{}s.  Therefore, we performs this float packing if making
% the \fpage{} gives too sparse, more specifically if
% $H_t<\!\floatpagefraction!\times\pp^h(\ptop)=\!\@fpmin!$, but postpone the
% final decision until the \colpage{} is eventually shipped out by
% \!\pcol@flushcolumn! or \!\pcol@makeflushedpage!.  That is, if the all
% conditions above hold, we keep \!\@toplist! so that it is saved in
% $\cc_c(\tl)$ and let $\cc_c(\tr)=\infty$ to indicate that the column has
% pending floats.  Note that the floats are shipped out by
% \!\pcol@flushcolumn! if the \pfcheck{} currently being performed finds a 
% too tall column in $\ptop$ to force a page break making $\ptop$ non-last.
% Also note that, in any cases, letting $\cc_c(\tr)=\infty$ is safe because
% no longer we will have any float additions to the \colpage.
% 
% Otherwise, i.e., if we are working on a non-\lpage{} to be flushed or a
% \fcolumn{} is to be made for the \lpage, we put all floats in \!\@toplist!
% in a \!\vbox! of $\pp^h(\ptop)$ tall by \!\pcol@makefcolpage! and then 
% let $\cc_c(\vb^b)$ be another \!\vbox! having it.  This encapsulation of
% the \fcolumn{} is necessary because $\cc_c(\vb^b)$ can be put back to the
% main vertical list after the \pfcheck{} to remove skips above and below
% the floats, namely \!\@fptop! and \!\@fpbot!, if the contents were not
% encapsulated.
% 
%    \begin{macrocode}
\def\pcol@makefcolumn{%
  \ifpcol@lastpage \@tempdimc\floatsep \else \@tempdimc\@fpsep \fi
  \@tempdima\@colht \advance\@tempdima\@tempdimc \global\@colroom-\@tempdimc
  \begingroup
    \let\@elt\pcol@makefcolelt
    \let\reserved@b\@deferlist
    \global\let\@deferlist\@empty
    \reserved@b
  \endgroup
  \ifx\@toplist\@empty\else
    \@tempswatrue
    \ifpcol@lastpage \ifx\@deferlist\@empty \ifdim\@colroom<\@fpmin
      \@tempswafalse \global\@toproom\maxdimen
    \fi\fi\fi
    \if@tempswa \global\setbox\@currbox\vbox{\pcol@makefcolpage}\fi
  \fi}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@makefcolelt}
% \changes{v1.0}{2011/10/10}
%	{Introduced to take special care of the float-column in the last
%	 page. }
% 
% The macro $\!\pcol@makefcolelt!\<\phi\>$ is invoked solely from
% \!\pcol@makefcolumn! to be applied to each float element $\phi$ in (the
% copy of) $\cc_c(\dl)$.  We examine if $v(\phi)=h(\phi)+d(\phi)+\alpha\leq
% H_r$ to mean the \fcolumn{} being built has room large enough for the float
% $\phi$.  If so, we add $\phi$ to \!\@toplist! by \!\@cons!, and let
% $H_r\gets H_r-v(\phi)$ and $H_t\gets H_t+v(\phi)$.  Otherwise, we add
% $\phi$ to $\cc_c(\dl)$ by \!\@cons! to make it deferred again, and
% let $H_r=-\infty$ so that the examinations for any succeeding elements
% fail.
% 
%    \begin{macrocode}
\def\pcol@makefcolelt#1{%
  \@tempdimb\ht#1{}\advance\@tempdimb\dp#1{}\advance\@tempdimb\@tempdimc
  \ifdim\@tempdimb>\@tempdima \@cons\@deferlist#1\relax
    \@tempdima-\maxdimen
  \else \@cons\@toplist#1\relax
    \advance\@tempdima-\@tempdimb \global\advance\@colroom\@tempdimb
  \fi}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@makefcolpage}
% \changes{v1.2-7}{2013/05/11}
% 	{Introduced to implement the operations to make a float column
%	 performed in three macros.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% \changes{v1.33-2}{2016/11/19}
% 	{Add {\tt\%} to the end of the line to open \cs{vbox} to obey the
%	 coding convention.} 
% 
% The macro \!\pcol@makefcolpage! is invoked from \!\pcol@flushcolumn!,
% \!\pcol@makefcolumn! and \!\pcol@imakeflushedpage! to build a \fcolumn{}
% having floats in \!\@toplist!, which is then returned to \!\@freelist! and
% then emptied.  The floats are put in a \!\vbox! of \!\@colht! tall with
% vertical skips of \!\@fptop!, \!\@fpsep! and \!\@fpbot! above, between and
% below them respectively.  The box is then let be $\s_c(p)$ or
% $\cc_c(\vb^b)$ explictly or implicitly by the invokers, with an
% encapsulation in the case of \!\pcol@makefcolumn!.
% 
%    \begin{macrocode}
\def\pcol@makefcolpage{\vbox to\@colht{%
    \vskip\@fptop \vskip-\@fpsep
    \def\@elt##1{\vskip\@fpsep\box##1}\@toplist \vskip\@fpbot}%
  \pcol@Fb
  \xdef\@freelist{\@freelist\@toplist}\global\let\@toplist\@empty
  \pcol@Fe{makefcolpage}%
}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@measurecolumn}
% \changes{v1.0}{2011/10/10}
%	{Drastically changed to measure $D_T$, to deal with empty
%	 main vertical list, and to omit \cs{topfigrule} and \cs{botfigrule}
%	 from float size measurement.} 
% 
% The macro \!\pcol@measurecolumn! is invoked for each column $c\In0\C$ from
% \!\pcol@sync! to measure the sizes of the top floats $\size_c(t)$, main
% vertical list $\size_c(m)$, footnotes $\size_c(f)$ and bottom floats
% $\size_c(b)$ in the \ccolpage{} in the page $\ptop$.  After obtaining the
% \cctext{} in $\cc_c$ by \!\pcol@getcurrcol!, we calculate
% $\size_c(t)=\!\skip!{\cdot}\cc_c(\vb)$ by \!\pcol@addflhd! giving it
% $\cc_c(\tl)$ and $\cc_c(\tf)=\!\pcol@textfloatsep!$ as its arguments also
% to have $\CSIndex{if@tempswa}={\fc(t)}$.  Note that $\cc_c(\tf)=\infty$ means
% the \colpage{} does not have any \sync{}ation points yet and thus
% \!\textfloatsep! is used in the calculation as the skip between the top
% floats and main vertical list, while the value itself possibly for a
% \mvlfloat{} discussed later is used if $\cc_c(\tf)<\infty$.  We also
% calculate $\size_c(m)=h(\cc_c(\vb))+d(\cc_c(\vb))$, and then the sum of it
% and $\size_c(t)$.
% 
%    \begin{macrocode}
\def\pcol@measurecolumn{%
  \pcol@getcurrcol
  \@tempswafalse
  \dimen@\z@ \pcol@addflhd\@toplist\pcol@textfloatsep
  \global\skip\@currbox\dimen@
  \advance\dimen@\ht\@currbox \advance\dimen@\dp\@currbox \dimen@ii\dimen@
%    \end{macrocode}
% 
% Next we examine if the main vertical list $\cc_c(\vb^b)$ is empty by
% \!\pcol@ifempty! and, if so, we let $\pd_c=\cc_c(\pd)=\infty$ and save it
% (together with others) by \!\pcol@setcurrcol! so that, if the column
% defines the $\VT$ finally by its top floats, $\DT$ is let $\infty$ and the
% fact that the column has empty list is remembered.  Otherwise, we let
% $\pd_c=\cc_c(\pd)$ and $\CSIndex{if@tempswa}=\true$ to represent
% $\Fc(\{t,m\})=f_t\lor f_m$ because $f_m=\true$.  Then we invoke
% \!\pcol@measureupdate! to let $\VT=\size_c(t)+\size_c(m)=\Size_c(\{t,m\})$
% and $\DT=\pd_c$ if $\Fc(\{t,m\})=\true$ and $\VT<\Size_c(\{t,m\})$.
% 
%    \begin{macrocode}
  \pcol@ifempty\@currbox
   {\global\pcol@prevdepth\maxdimen \pcol@setcurrcol}%
   {\@tempswatrue}%
  \pcol@measureupdate\@tempdima\dimen@ii\@tempdimc\pcol@prevdepth
%    \end{macrocode}
% 
% \changes{v1.2-2}{2013/05/11}
%	{Add calculation of $V_P$ and $c_{\string\max}$.}
% 
% Next we let $\size_c(f)=0$ if $\cc_c(\ft^b)$ is void, or otherwise let
% $\size_c(f)=h(\cc_c(\ft^b))+d(\cc_c(\ft^b))+{}\cc_c(\ft^s)$\footnote{
% 
% We ignore the height and depth of \!\footnoterule! because they are
% expected to be 0 and are so in the default setting.}
% 
% and $\CSIndex{if@tempswa}=\true$ because $\fc(f)=\true$ and thus
% $\Fc(\{t,m,f\})=\true$.  After that, we calculate $\size_c(f)+\size_c(b)$
% by \!\pcol@addflhd! giving it $\cc_c(\bl)$ and $\infty$ to mean
% \!\textfloatsep! should be used for the calculation as its argument also
% to have $\CSIndex{if@tempswa}={\Fc}(\{t,m,f,b\})$.  Then we let
% $\VB=\size_c(f)+\size_c(b)$ if $\VB<\size_c(f)+\size_c(b)$, and let
% $\VP=\size_c(t)+\size_c(m)+\size_c(f)+\size_c(b)=\Size_c(\{t,m,f,b\})$ and
% $c_{\max}=c$ if $\Fc(\{t,m,f,b\})=\true$ and $\VP<\Size_c(\{t,m,f,b\})$.
% 
%    \begin{macrocode}
  \ifvoid\pcol@currfoot \dimen@\z@
  \else
    \dimen@\ht\pcol@currfoot \advance\dimen@\dp\pcol@currfoot
    \advance\dimen@\skip\pcol@currfoot
    \@tempswatrue
  \fi
  \pcol@addflhd\@botlist\maxdimen
  \ifdim\dimen@>\@tempdimb \@tempdimb\dimen@ \fi
  \advance\dimen@\dimen@ii
  \if@tempswa \ifdim\dimen@>\@pageht
    \@pageht\dimen@ \@tempcntb\pcol@currcol
  \fi\fi
%    \end{macrocode}
% 
% Next, we let $\dc$ be the depth of the lowest non-empty items among the
% main vertical list, footnotes and bottom floats.  That is, we let
% $\dc\gets\cc_c(\pd)$ at first, and then, if
% $\CSIndex{ifpcol@bfbottom}={\true}$, override it by $\dc\gets
% d(\cc_c(\ft^b))$ if there are footnotes, and finally override it by
% $\dc\gets0$ for the bottom floats if exist adding \!\textfloatsep! to
% $\Size_c(\{t,m,f,b\})$ to have $\Size_c(\{t,m,f,b'\})$.  This overriding
% order of $d(\cc_c(\ft^b))$ and then 0 by bottom floats is reversed when
% $\CSIndex{ifpcol@bfbottom}=\false$ according to the implementation of
% \!\@makecol!.  Then, we invoke \!\pcol@measureupdate! again to let
% $\VPP=\Size_c(\{t,m,f,b'\})$ and $\DP=\dc$ if $\Fc(\{t,m,f,b\})=\true$ and
% $\VPP<\Size_c(\{t,m,f,b'\})$.  It also lets $\DP=\dc$ if
% $\Fc(\{t,m,f,b\})=\true$, $\VPP=\Size_c(\{t,m,f,b'\})$ and $\DP>\dc$.
% 
% Finally, we let $\CSIndex{ifpcol@dfloats}=\true$ if
% $\cc_c(\dl)\neq\emptyset$ to tell \!\pcol@makeflushedpage! that the
% \lpage{} must be {\em full size} and \!\pcol@output@end! to flush the
% deferred \cwise{} floats.
% 
% \changes{v1.3-6}{2013/09/17}
%	{Revise the mechanism to tell \cs{pcol@makeflushedpage} and
%	 \cs{pcol@output@end} that a column in a last page has deferred
%	 column-wise floats with newly introduced \cs{ifpcol@dfloats}.}
% 
%    \begin{macrocode}
  \dimen@ii\pcol@prevdepth
  \ifpcol@bfbottom
    \ifvoid\pcol@currfoot\else \dimen@ii\dp\pcol@currfoot \fi
    \ifx\@botlist\@empty\else \dimen@ii\z@ \advance\dimen@\textfloatsep \fi
  \else
    \ifx\@botlist\@empty\else \dimen@ii\z@ \advance\dimen@\textfloatsep \fi
    \ifvoid\pcol@currfoot\else \dimen@ii\dp\pcol@currfoot \fi
  \fi
  \pcol@measureupdate\pcol@colht\dimen@\@pagedp\dimen@ii
  \ifx\@deferlist\@empty\else \pcol@dfloatstrue \fi
  \advance\pcol@currcol\@ne}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@addflhd}
% \changes{v1.0}{2011/10/10}
%	{Drastically changed to omit \cs{topfigrule} and \cs{botfigrule}
%	 from float size measurement, to take care of top float enlargement,
%	 to add the measurement of $D_T$, and to revise the definition of
%	 $D_P$.}
% 
% \begin{macro}{\pcol@hdflelt}
% \def\xl{\lambda_x}
% \changes{v1.3-3}{2013/09/17}
%	{Add a user \cs{pcol@makecol}.}
% 
% The macro $\!\pcol@addflhd!\arg{list}\arg{tfs}$ is invoked twice from
% \!\pcol@measurecolumn! for a column $c$ to measure $\size_c(x)$
% ($x\in\{t,b\}$) of top ($x=t$) or bottom ($x=b$) floats.
% The arguments and registers referred to in the macro have the folloiwngs
% according to $x=t$ or $x=b$.
% $$
% \nosv\begin{array}{l|ll}
% &		x=t&			x=b\\\hline
% \arg{list}&	\cc_c(\tl)&		\cc_c(\bl)\\
% \arg{tfs}&	\!\pcol@textfloatsep!&	\!\maxdimen!\\
% \CSIndex{if@tempswa}&
%		\false&			\Fc(\{t,m,f\})\\
% \!\dimen@!&	0&			\size(f)
% \end{array}
% $$
% The macro is also used in \!\pcol@makecol! and \!\pcol@output@switch! for
% $x=t$ but with \!\dimen@! having the height of \!\pcol@prespan! for the
% measurement of the total height of \prespan{} including top
% floats\footnote{
% 
% In these invocations, \CSIndex{if@tempswa} is meaningless and not examined
% by the invokers.}.
% 
% The macro at first examines if $\cc_c(\xl)=\arg{list}$ is empty and does
% nothing if so.  Otherwise, \CSIndex{if@tempswa} is turned $\true$ to have
% $\fc(t)=\true$ for $x=t$ or $\Fc(\{t,m,f,b\})=\true$ for $x=b$.  Then we
% scan all floats in $\arg{list}$ applying \!\pcol@hdflelt! to each float
% $\phi$ to add $h(\phi)+d(\phi)+\!\floatsep!$ to \!\dimen@!, from/to which
% we then subtract \!\floatsep! and add $\sigma_x$ because the last\slash
% first float is followed\slash preceded by the vertical skip of $\sigma_x$
% instead of \!\floatsep!, to have $\size_c(t)$ for $x=t$ or
% $\size_c(f)+\size_c(b)$ for $x=b$ being {\em returned} to
% \!\pcol@measurecolumn!.
% 
% Note that $\sigma_t$ is $\arg{tfs}=\!\pcol@textfloatsep!$ if it is less
% than $\infty$ or \!\textfloatsep! otherwise, while
% $\sigma_b=\!\textfloatsep!$ always because $\arg{tfs}=\!\maxdimen!$.  Also
% note that $\sigma_t$ can be biased by 10000\,|pt| and thus larger than
% 5000\,|pt|, if we have a \mvlfloat{} in top floats as discussed later.
% Another caution is that we ignore the contribution by \!\topfigrule! nor
% \!\botfigrule! because they should insert vertical items whose total
% height and depth are 0.
% 
%    \begin{macrocode}
\def\pcol@addflhd#1#2{%
  \ifx#1\@empty\else
    \@tempswatrue
    \let\@elt\pcol@hdflelt
    #1\advance\dimen@-\floatsep
    \ifdim#2=\maxdimen \advance\dimen@\textfloatsep
    \else
      \advance\dimen@\pcol@textfloatsep
      \ifdim\pcol@textfloatsep>5000\p@ \advance\dimen@-\@M\p@ \fi
    \fi
    \let\@elt\relax
  \fi}
\def\pcol@hdflelt#1{\advance\dimen@\ht#1\advance\dimen@\dp#1%
  \advance\dimen@\floatsep}
%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@measureupdate}
% \changes{v1.0}{2011/10/10}
%	{Introduced to let $D_T$ and $D_P$ have the minimum depth of items
%	 among those which give $V_T$ and $V_P$.}
% 
% The macro $\!\pcol@measureupdate!\<V\>\<v\>\<D\>\<d\>$ is invoked
% twice in \!\pcol@measurecolumn! for $c$ to update $V\in\{\VT,\VPP\}$
% and $D=\{\DT,\DP\}$ as follows if \CSIndex{if@tempswa}, being
% $\Fc(\{t,m\})$ for $V=\VT$ or $\Fc(\{t,m,f,b\})$ for $V=\VPP$, is $\true$.
% $$
% V\gets\max(V,v)\qquad
% D\gets\cases{\min(D,d)&$V=v$\cr
%              D&        $V\neq v$}
% $$
% The arguments $v$ and $d$ have the followings according to $V$.
% $$
% \arraycolsep0pt
% \begin{array}{rll}
% V=\VT \;{:}\;&v=\Size_c(\{t,m\})&\quad d=\delta_c\\
% V=\VPP\;{:}\;&v=\Size_c(\{t,m,f,b'))&\quad d=\dc
% \end{array}
% $$
% 
%    \begin{macrocode}
\def\pcol@measureupdate#1#2#3#4{\if@tempswa
  \ifdim#1<#2\relax#1#2\relax#3#4\relax
  \else\ifdim#1=#2\ifdim#3>#4\relax#3#4\fi\fi\fi\fi}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@synccolumn}
% \changes{v1.0}{2011/10/10}
%	{Drastically changed to correctly implement the top float
%	 enlargement and MVL-float.}
% \changes{v1.2-2}{2013/05/11}
%	{Change code structure removing the case for overflown synchronized
%	 pages.}
% \changes{v1.2-2}{2013/05/11}
%	{Remove \cs{penalty}\string\texttt{-10000} made unnecessary by the
%	 redesign of overflow synchronized pages.}
% \changes{v1.2-7}{2013/05/11}
%	{Add an shrink of $1/10000\,\string\texttt{fil}$ to the bottom of
%	 flushed column pages to cancel finite shrinks just below
%	 synchronization points.}
% 
% The macro \!\pcol@synccolumn! is invoked for each column $c\In0\C$ from
% \!\pcol@sync! to set a \sync{}ation point at $\VT$ from the top of the
% \ccolpage{} of $c$ if $\CSIndex{ifpcol@clear}={\false}$, or flush it
% otherwise.  After obtaining $c$'s \cctext{} $\cc_c$ by
% \!\pcol@getcurrcol!, we process one of the following three cases.
% 
% The first case is for flushing with $\CSIndex{ifpcol@clear}=\true$.  In
% this case we simply add \!\vfil! at the tail of the main vertical list in
% $\cc_c(\vb^b)$ to make the whole \colpage{} possibly with other items fit
% in a box of \!\@colht! tall and, if $\cc_c(\tf)\neq\infty$ to mean the
% column to be flushed has a \sync{}ation point, we also add an infitite
% shrink of $1/10000\,|fil|$ so as to cancel a finite shrink just below the
% point, as done in \!\pcol@makecol!\footnote{
% 
% Just in case, because it looks impossible that the natural height of the
% \colpage{} exceeds $\pp^h(\ptop)$ with \pfcheck.}.
% 
% We also let $\cc_c(\pd)=1000\,|pt|$ to mimic \TeX's mechanism of
% \!\prevdepth! with the empty main vertical list in the next
% \colpage{}\footnote{
% 
% The author is not sure if this setting is really necessary but, at least,
% it looks working well (though other setting looks all right too).}.
% 
%    \begin{macrocode}
\def\pcol@synccolumn{%
  \pcol@getcurrcol
  \ifpcol@clear
    \global\pcol@prevdepth\@m\p@
    \global\setbox\@currbox\vbox{\unvbox\@currbox
      \ifdim\pcol@textfloatsep=\maxdimen \vfil
      \else \vskip\z@\@plus1fil\@minus.0001fil
      \fi}%
%    \end{macrocode}
% 
% The second and third cases are for \sync{}ed \cswitch{}.  The second case
% is for $\DT=\infty$ to mean the \sync{}ation point is set just below the
% top floats of a column whose main vertical list is empty because it is
% definitely $\VT\geq0>-\infty$.  In this case, we should not put anything
% back to the main vertical list, because the column having defined the
% point will restart from the top of its \colpage{} with \!\topskip! and
% thus other columns should do so for the stuff following the point.
% Therefore, we put $\cc_c(\vb^b)$ as the last top float, namely
% {\em\Uidx\mvlfloat} because it is for the main vertical list, acquiring an
% \!\insert! from \!\@freelist! by \!\@next! and assigning it to
% \Midx{\!\pcol@float!} so that we pretend main vertical lists of all
% columns are empty.
% 
% The float has zero height and depth, and contains the
% followings if we have some real floats; a vertical skip of $-\!\floatsep!$
% to go back to the bottom of the last real float; \!\topfigrule! and a skip
% of \!\textfloatsep! to separate $\cc_c(\vb^b)$ from the last real float;
% and $\cc_c(\vb^b)$ followed by \!\vss! to avoid overfull and underfull.
% Otherwise, i.e., we don't have any real floats, neither of the skips nor
% \!\topfigrule! are put in the \mvlfloat{} because we let
% $\!\floatsep!=\!\textfloatsep!=0$ and $\!\topfigrule!=\!\relax!$
% temporarily in a group.  Then we set the \sync{}ation point by enlarging
% the space below the \mvlfloat{} so that the total size of all floats
% including \!\floatsep! and \!\textfloatsep!, which may be 0 as set in the
% process above, is equal to $\VT$.  This enlarging is done by letting
% $\cc_c(\tf)=\VT-(\vc(t)-\!\textfloatsep!+\!\floatsep!)$, the second term
% of which is the vertical size of the top float sequence up to the
% \mvlfloat, and by replacing \!\textfloatsep! with $\cc_c(\tf)$ in the top
% float insertion process in \!\pcol@cflt! so that the top floats including
% the \mvlfloat{} consumes $\VT$ as a whole\footnote{
% 
% This enlarging cannot be done by making the float's height
% $\VT-\vc(t)-\!\floatsep!$ (or \!\textfloatsep!) because the height can be
% negative.}.
% 
% Note that the process above involves \!\floatsep! and \!\textfloatsep!
% with some finite stretch and shrink, but these factors will not contribute
% the final result because they are canceled by \!\vss! in the \mvlfloat{}
% and by the small inifinite stretch and shrink put by \!\pcol@makecol! and
% this macro for flushing.  Also note that $\cc_c(\tf)$ is then biased by
% 10000\,|pt| so that \!\pcol@cflt!  will not put \!\topfigrule! because it
% has been already put as a part of the \mvlfloat{} or we don't have any
% real floats.  We also let $\cc_c(\pd)=1000$ to mean the \colpage{}'s main
% vertical list is empty, so as to mimic \TeX's mechanism of \!\prevdepth!
% with an empty list again.
% 
% Another attention we have to pay is that \colpage{}s with
% $\cc_c(\tf)=\infty$ does not have any \sync{}ation points, and thus
% $\cc_c(\tf)<\infty$ means a \sync{}ation has already taken place in them.
% If this $\cc_c(\tf)<\infty$ happens with $\DT=\infty$\footnote{
% 
% This can happen when a \sync{}ation with $\DT=\infty$ is immediately
% followed by another \sync{}ation or, more unlikely, by additions of
% items whose total amount is negative and then a \sync{}ation.},
% 
% we cannot update $\cc_c(\tf)$ because \!\pcol@measurecolumn! took care of
% its value on measuring $\vc(t)$.  Therefore, we do nothing if
% $\cc_c(\tf)<\infty$ but just let succeeding stuff be added to the main
% vertical list as in \cswitch{} without \sync{}ation.
% 
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% \changes{v1.33-2}{2016/11/19}
% 	{Add {\tt\%} to the end of the line to open \cs{vbox} for
%	 \cs{pcol@float} to obey the coding convention.} 
% 
%    \begin{macrocode}
  \else
    \@tempdimb\@tempdima
    \advance\@tempdimb-\skip\@currbox
    \ifdim\@tempdimc=\maxdimen
      \ifdim\pcol@textfloatsep=\maxdimen \begingroup
        \ifx\@toplist\@empty
          \textfloatsep\z@ \floatsep\z@ \let\topfigrule\relax
        \fi
        \pcol@Fb
        \@next\pcol@float\@freelist{\global\setbox\pcol@float\vbox to\z@{%
          \vskip-\floatsep \topfigrule \vskip\textfloatsep
          \unvbox\@currbox \vss}}\pcol@ovf
        \pcol@Fe{synccolumn(topfloat)}%
        \@cons\@toplist\pcol@float
        \advance\@tempdimb\textfloatsep \advance\@tempdimb-\floatsep
        \advance\@tempdimb\@M\p@
        \global\pcol@prevdepth\@m\p@
        \global\pcol@textfloatsep\@tempdimb
      \endgroup \fi
%    \end{macrocode}
% 
% The third and last case is for $\DT<\infty$ and thus most usual.  In this
% case, we enclose everything in $\cc_c(\vb^b)$ in a \!\vbox!  whose height
% is $h_c^v=\VT-\vc(t)$ and let $\cc_c(\vb^b)$ have it so that the item
% following the \sync{}ation point start at $\VT$.  An attention we have to
% pay is that it can be $h_c^v<\!\topskip!$ to let \TeX{} insert a vertical
% skip of the difference between them when the box is returned to the main
% vertical list pushing down the \sync{}ation point a little bit\footnote{
% 
% This can happen not very unlikely especially with $\vc(t)$ a little bit
% less than $\VT$ and $\cc_c(\vb^b)$ being empty.}.
% 
% Therefore, if so, we let $\cc_c(\vb^b)$ have the followings; a \!\vbox! of
% \!\topskip! tall having its old contents at its top above which no
% vertical skip will be inserted; a vertical skip $-\!\topskip!$ going back
% to the page top; and a vertical skip $h_c^v$ going down to the
% \sync{}ation point.
% 
% The encapsulation of the old contents $\cc_c(\vb^b)$ in the box of $h_c^v$
% tall gives us the following two features desirable for \sync{}ation.
% First, all vertical glues in the box are {\em frozen}, nullifying finite
% stretches in them because we insert an infinite stretch of
% $1/10000\,|fil|$ at the bottom of $\cc_c(\vb^b)$ to push up its old
% contents respecting other infinite stretches if any, as done by
% \!\raggedbottom!, and also nullifying finite and infinite shrinks because
% $h_c^v\geq\vc(m)$ definitely.  This freezing and nullification keeps
% \sync{}ation points already in $\cc_c(\vb^b)$ from being observed moving a
% little bit vertically.  That is, if we have a glue just below a
% \sync{}ation point and it were {\em visible} to \TeX's page builder, the
% item below the glue could move up/down when the builder found a break
% point with some shrink\slash stretch.  Though this moving up/down is
% inhibited by the small infinite stretch\slash shrink which the \colpage{}
% will at its bottom finally, it is undesirable to make \TeX{}
% misunderstanding that the glues are strethable\slash shrinkable though
% they are not in reality.
% 
% Second, since the boxes in all \colpage{} are zero deep due to the
% infinite stretch at their bottoms and these bottoms are aligned at the
% \sync{}ation point, we have a clear view of the baseline progress after
% the \sync{}ation regardless of their contents.  That is, we let
% $\cc_c(\pd)=\DT$ to {\em broadcast} $\DT$ to all columns, so that 
% the baselines of first items following the \sync{}ation
% point are aligned \!\baselineskip! below the bottom baseline of the column
% which defines $\DT$\footnote{
% 
% Since $\DT$ is given by one of the tallest columns whose depth is smallest
% among them, it is very likely that the bottom baseline of the column is
% lowest among all columns.  However, another column can have the lowest one
% when its vertical size is a little bit shorter than $\VT$ and its depth is
% small (e.g., 0).  Though of course we can define $\DT$ being $\VT$ minus
% the height of the column having the largest height to make the first
% baseline below the \sync{}ation point apart from the lowest one by
% \cs{baselineskip}, we dare to choose the definition of $\DT$ because such
% lowest baseline often means that the column have some skip at its bottom
% to give us the impressoin that the space between the baselines of the
% tallest column and its first item is a little bit too large.},
% 
% if $\DT$ plus the hight of each item is less than \!\baselineskip!.
% 
% In addition, we let $\cc_c(\tf)=\!\textfloatsep!$ to
% indicate the \colpage{} has the \sync{}ation point we just have set, if it
% was $\infty$ to mean the point is the first one.  By this setting,
% \!\pcol@makecol! and this macro itself will know that the \colpage{} needs
% to have a small infinite shrink at its bottom to cancel finite ones below
% the \sync{}ation point, while \!\pcol@cflt! acts as \LaTeX's \!\@cflt!
% because it should be $\cc_c(\tf)\leq5000\,|pt|$ to mean the \colpage{}
% does not have a \mvlfloat.
% 
% \changes{v1.33-2}{2016/11/19}
% 	{Add {\tt\%} to the end of the line to open \cs{vbox} for
%	 \cs{@currbox} and two lines for \cs{vbox}es in it to obey the
%	 coding convention.} 
% 
%    \begin{macrocode}
    \else
      \global\pcol@prevdepth\@tempdimc
      \ifdim\pcol@textfloatsep=\maxdimen
        \global\pcol@textfloatsep\textfloatsep \fi
      \global\setbox\@currbox\vbox{%
        \ifdim\@tempdimb<\topskip
          \vbox to\topskip{\unvbox\@currbox \vskip\z@\@plus.0001fil}%
          \vskip-\topskip \vskip\@tempdimb
        \else
          \vbox to\@tempdimb{\unvbox\@currbox \vskip\z@\@plus.0001fil}%
        \fi}%
    \fi
  \fi
%    \end{macrocode}
% 
% Finally, we let $\cc_c(\tn)=0$ to inhibit futher addition of top floats
% because we have fixed the space for them\footnote{
% 
% Allowing the addition is tremendously tough even when the \colpage{} has
% sufficiently large space above the \sync{}ation point.},
% 
% and save it and other \cctext{} members into $\cc_c$ by \!\pcol@setcurrcol!.
% 
%    \begin{macrocode}
  \global\@topnum\z@ \pcol@setcurrcol
  \advance\pcol@currcol\@ne}

%    \end{macrocode}
% \end{macro}
% 
% 
% 
% \subsection{Page Flushing}
% \label{sec:imp-sout-flush}
% 
% \begin{macro}{\pcol@output@flush}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{pcol@makelastpage} as \cs{pcol@makeflushedpage}.}
% \changes{v1.0}{2011/10/10}
%	{Remove unnecessary assignment of \cs{@colht}.}
% \changes{v1.2-2}{2013/05/11}
%	{Add \cs{pcol@Logstart} and \cs{pcol@Logend}.}
% \changes{v1.2-7}{2013/05/11}
%	{Add $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping.}
% \changes{v1.2-7}{2013/05/11}
%	{Add $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping.}
% \changes{v1.3-2}{2013/09/17}
%	{Add depth capping of \cs{pcol@rightpage}.}
% 
% The macro \!\pcol@output@flush! is invoked solely from
% \!\pcol@specialoutput! to process the \!\output! request made by
% \!\flushpage!.  We invoke \!\pcol@makeflushedpage! giving it \!\@colht! as
% the height of each \colpage{} to have the ship-out image of the
% \tpage{} including its \spanning{} and \Scfnote{}s in \!\@outputbox! whose
% height is then set to be \!\textheight!\footnote{
% 
% Just in case because the height of source \cs{@outputbox} should be exactly
% \cs{textheight} though not specified so on its construction in
% \cs{pcol@makeflushedpage}.},
% 
% ensureing that its depth is capped by $\!\boxmaxdepth!=\!\@maxdepth!$.  We
% also perform these height setting and depth capping on \!\pcol@rightpage!
% if $\CL<\C$ to mean \parapag{}ing.  Then we invoke \!\@outputpage! for
% shipping out, and then finally \!\pcol@freshpage! to have a new page to
% start new \colpage{}s in it.
% 
%    \begin{macrocode}
%% Special Output Routines: Page Flushing

\def\pcol@output@flush{%
  \pcol@makeflushedpage\@colht
  \pcol@Logstart\pcol@output@flush
  \setbox\@outputbox\vbox to\textheight{\boxmaxdepth\@maxdepth
    \unvbox\@outputbox}%
  \ifnum\pcol@ncolleft<\pcol@ncol
    \setbox\pcol@rightpage\vbox to\textheight{\boxmaxdepth\@maxdepth
      \unvbox\pcol@rightpage}%
  \fi
  \pcol@Logend\pcol@output@flush
  \@outputpage
  \pcol@freshpage}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@output@clear}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{pcol@makelastpage} as \cs{pcol@makeflushedpage}.}
% \changes{v1.0}{2011/10/10}
%	{Remove unnecessary increment of \cs{pcol@page} and assignment of
%	 \cs{@colht}.}
% \changes{v1.2-2}{2013/05/11}
%	{Add \cs{pcol@Logstart} and \cs{pcol@Logend}.}
% \changes{v1.2-7}{2013/05/11}
%	{Add $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping.}
% \changes{v1.3-2}{2013/09/17}
%	{Add depth capping of \cs{pcol@rightpage} and building an empty
%	 right parallel-page for each page-wise float page.}
% \changes{v1.3-3}{2013/09/17}
%	{Add background painting of float pages.}
% \changes{v1.32-3}{2015/10/10}
% 	{Add $\hbox{\cs{f@depth}}\EQ0$ to override
%	 $\hbox{\cs{f@depth}}\EQ\hbox{\texttt{1sp}}$ done by
%	 \cs{@dblfloatplacement}.}
% 
% The macro \!\pcol@output@clear! is invoked solely from
% \!\pcol@specialoutput! to process the \!\output! request made by
% \!\clearpage!.  The first part up to \!\@outputpage! and the last line of
% this macro are same as \!\pcol@output@flush! to flush the \tpage{} and to
% have a newpage.  In the remaining mid part, we invoke \!\pcol@flushfloats!
% to ship out all deferred \cwise{} floats in all columns if any, and
% then do it for \pwise{} floats by the following invocations enclosed in a
% group; letting $\!\pcol@rightpage!=\bot$ for ordinary paging;
% \!\@dblfloatplacement! to set up placement parameters followed by
% $\!\f@depth!=0$ to nullify the setting $\!\f@depth!=|1sp|$ possiblly done
% by it as discussed in the item-(\ref{item:ovv-float-@dblfloatplacement})
% of \secref{sec:imp-ovv-float}; \!\@makefcolumn!  with
% \!\@dbldeferlist! to have a \fpage{} in \!\@outputbox! if any; and a loop
% of \bgpaint{} of \!\@outputbox! and, if $\CL<\C$, of empty
% \!\pcol@rightpage!, and \!\@outputpage! followed by \!\@makefcolumn!
% repeated while we have a \fpage{}, i.e., $\CSIndex{if@fcolmade}=\true$.
% 
% Note that the mid part is same as that found in \!\@doclearpage! but we
% omit various adjuncts surrouding it as follows;  examination of
% \CSIndex{if@twocolumn} because we should have multiple columns;
% examination of \CSIndex{if@firstcolumn} because we have to clear the page
% immediately even when we are not in the first column;  concatenating
% \!\@dbltoplist! with \!\@dbldeferlist! and clearing it because the author
% believes \!\@dbltoplist! must be empty on the invocation of this macro;
% and letting $\!\@colht!=\!\textheight!$ because \!\pcol@flushfloats! did
% it.
% 
%    \begin{macrocode}
\def\pcol@output@clear{%
  \pcol@makeflushedpage\@colht
  \pcol@Logstart\pcol@output@clear
  \setbox\@outputbox\vbox to\textheight{\boxmaxdepth\@maxdepth
    \unvbox\@outputbox}%
  \ifnum\pcol@ncolleft<\pcol@ncol
    \setbox\pcol@rightpage\vbox to\textheight{\boxmaxdepth\@maxdepth
      \unvbox\pcol@rightpage}%
  \fi
  \pcol@Logend\pcol@output@clear
  \@outputpage
  \pcol@flushfloats
  \begingroup
    \setbox\pcol@rightpage\box\voidb@x
    \@dblfloatplacement \let\f@depth\z@
    \@makefcolumn\@dbldeferlist
    \@whilesw\if@fcolmade\fi{%
      \def\pcol@bg@floatheight{\pcol@bg@textheight}%
      \setbox\@outputbox\vbox to\textheight{%
        \pcol@bg@paintbox{Ff}\unvbox\@outputbox}%
      \ifnum\pcol@ncolleft<\pcol@ncol
        \setbox\pcol@rightpage\vbox to\textheight{\pcol@bg@paintbox{Ff}\vfil}%
      \fi
      \@outputpage
      \@makefcolumn\@dbldeferlist}%
  \endgroup
  \pcol@freshpage}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@makeflushedpage}
% \changes{v1.0}{2011/10/10}
%	{Renamed from \cs{pcol@makelastpage}.}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{ifpcol@textonly} as \cs{ifpcol@nospan}.}
% \changes{v1.0}{2011/10/10}
%	{Judge the last page is empty if $V_P\EQ-\infty$ instead of $V_P<0$.}
% \changes{v1.2-2}{2013/05/11}
%	{Revise reflecting the redesign of page context.}
% \changes{v1.3-2}{2013/09/17}
%	{Completely redesigned with new macro \cs{pcol@imakeflushedpage}.}
% \changes{v1.3-3}{2013/09/17}
%	{Add background painting of page-wise floats, and a part of
%	 opreations for column-separation rule drawing and background
%	 painting of page-wise footnotes.} 
% \changes{v1.3-6}{2013/09/17}
%	{Revise the mechanism of special care about last page introducing
%	 \cs{ifpcol@dfloats}.}
% 
% The macro $\!\pcol@makeflushedpage!\arg{ht}$ is invoked from
% \!\pcol@output@flush! or \!\pcol@output@clear! with $\arg{ht}=\!\@colht!$
% and from \!\pcol@output@end! with $\arg{ht}=\!\pcol@colht!$.  At first, we
% invoke \!\pcol@output@switch! with setting $\CSIndex{ifpcol@clear}=\true$
% to flush all pages up to $\ptop-1$ and to let $\cc_c(\vb^b)$ have the
% ship-out image of the main vertical list of each \colpage{} $c$ in
% $\ptop$.  This invocatoin also lets $\!\pcol@colht!=\VPP$ so that hereafter
% we will refer $\VPP$ throuth $\arg{ht}$ if it is $\!\pcol@colht!$ for
% \lpage.  Then after obtaining $\ptop$'s \pctext{} to have
% $\page(\ptop)=\pp^p(\ptop)$, $\!\@colht!=\pp^h(\ptop)$ and
% \CSIndex{ifpcol@nospan} by \!\pcol@getcurrpinfo!, we build the ship-out
% image of $\ptop$ in \!\@outputbox!, and \!\pcol@rightpage! if
% \parapag{}ing, taking special care of the \lpage{} case as follows.
% 
% \begin{enumerate}\def\labelenumi{(\arabic{enumi})}
% \item\label{item:mfp-nonlast}
% If $\CSIndex{ifpcol@lastpage}=\false$, each of $\cc_c(\vb^b)$ has ship-out
% image even if some or all of them are empty.  It is unecessary to be aware
% of the perfectly empty case because it should mean the page $\ptop$ is
% made blank intentionally.
% 
% \item\label{item:mfp-last-dfloats}
% If $\CSIndex{ifpcol@lastpage}=\true$ but $\CSIndex{ifpcol@dfloats}=\true$
% too, the last page must have {\em full size} because we will have parallel
% columned pages having \fcolumn{}s for deferred floats.  However, if the
% page has nothing, i.e., $\pp^i(\ptop)=\pp^f(\ptop)=\bot$ and
% $\VPP=-\infty$, we must let $\!\@outputbox!=\bot$ (and
% $\!\pcol@rightpage!=\bot$ as well) to avoid an unnecessary blank page is
% shipped out.  On the other hand, if $\pp^i(\ptop)\neq\bot$ or
% $\pp^f(\ptop)\neq\bot$ while $\VPP=-\infty$, we build a full size page as
% usual but letting $\!\@textbottom!=\!\vfil!$ temporarily to avoid underfull
% in the process of building columns.  Note that if $\pp^f(\ptop)\neq\bot$,
% the \Scfnote{}s are always put into \!\@outputbox! regardless
% \CSIndex{ifpcol@mgfnote} because the \lpage{} is not combined with
% \postenv.
% 
% \item\label{item:mfp-last-empty}
% If $\CSIndex{ifpcol@lastpage}=\true$, $\CSIndex{ifpcol@dfloats}=\false$
% and $\VPP=-\infty$, we have to let $\!\@outputbox!=\bot$ unless
% $\pp^i(\ptop)\neq\bot$ or $\pp^f(\ptop)\neq\bot$ having non-\Mgfnote{}s.
% If $\pp^f(\ptop)$ has non-\Mgfnote{}s, \!\@outputbox! and
% \!\pcol@rightpage!  must have $\pp^f(\ptop)$ possibly with $\pp^i(\ptop)$
% but without any columns, and must be put into the main vertical list as
% the leading part of \postenv{} by modifying $\VPP=0$.  On the other hand
% $\pp^f(\ptop)=\bot$ or it has \Mgfnote{}s, \!\@outputbox! must have only
% $\pp^i(\ptop)$\footnote{
% 
% \!\pcol@rightpage! must have the couterpart in right \parapag{}e if the
% \spanning{} is \preenv, while it is made $\bot$ by \!\pcol@output@end! if
% the \spanning{} are \pwise{} floats.}.
% 
% Since \pwise{} floats become ordinary floats in \postenv, we cannot paint
% its \bground{} and must remove \!\dbltextfloatsep! at the bottom of
% $\pp^i(\ptop)$.
% 
% \item\label{item:mfp-last-nonempty}
% If $\CSIndex{ifpcol@lastpage}=\true$, $\CSIndex{ifpcol@dfloats}=\false$
% and $\VPP>-\infty$, \!\@outputpage! and \!\pcol@rightpage! must have short
% columns of $\VPP$ tall, together with $\pp^i(\ptop)$ as in non-\lpage{}s
% but without $\pp^f(\ptop)$ if it has \Mgfnote{}s.
% \end{enumerate}
% 
% To implement a part of special cares above, we at first let
% $\CSIndex{if@tempswa}=\true$ iff $\cs{ifpcol@}\~|lastpage|=\false$,
% 
% \CSINDEX{ifpcol@lastpage}
% 
% $\VPP>-\infty$ or $\pp^f(\ptop)\neq\bot$.
% 
%    \begin{macrocode}
\def\pcol@makeflushedpage#1{%
  \pcol@cleartrue \pcol@output@switch \pcol@clearfalse
  \pcol@getcurrpinfo{\global\c@page}{\global\@colht}\@tempskipa
  \ifpcol@lastpage \@tempswafalse \else \@tempswatrue \fi
  \ifdim\pcol@colht=-\maxdimen\else \@tempswatrue \fi
  \ifvoid\pcol@footins\else \@tempswatrue \fi
%    \end{macrocode}
% 
% Next, if $\CSIndex{ifpcol@nospan}=\true$ to mean the page $\ptop$ does not
% have \spanning{} in $\pp^i(\ptop)$, we initialize both \!\@outputbox!  and
% \!\pcol@rightpage! to be $\bot$.  Otherwise, after letting
% $\CSIndex{if@tempswa}=\true$ if $\CSIndex{ifpcol@dfloats}=\true$ to make the
% \lpage{} full size if we are working on it as discussed in\Tie
% (\ref{item:mfp-last-dfloats}), we put $\pp^i(\ptop)$ in \!\@outputbox!,
% and paint its \bground{} by \!\pcol@bg@paintbox!  \!\edef!ining the height
% paramenter \!\pcol@bg@floatheight! with $h$ being the height-plus-depth of
% $\pp^i(\ptop)$ with the following two exceptions; one is the case of
% $\CSIndex{ifpcol@firstpage}={\true}$ to mean we are in \spage{} and thus
% the \spanning{} is \preenv{} having already been painted by
% \!\pcol@output@start!; and the other is the case of
% $\CSIndex{if@tempswa}=\false$ to mean we are working on a truly \lpage{}
% being empty except for the \spanning{} itself and thus the \pwise{}
% floats become a part of deferred floats in \postenv{} as discussed in\Tie
% (\ref{item:mfp-last-empty}).  In the latter exceptional case, excluding
% the case that the \lpage{} is also the \spage\footnote{
% 
% Extremely exceptional because the closing environment does not have
% anything.},
% 
% we also remove the last skip being \!\dbltextfloatsep! so that those
% floats are naturally connected with other floats given in
% \postenv{} also as discussed in\Tie(\ref{item:mfp-last-empty}).  Then we
% {\em pack} the \!\@outputbox! in itself by \!\vbox! so that any
% stretch\slash shrink factors in it cannot affect the ship-out image
% especially when we paint its \bground{}\footnote{
% 
% Though that hardly happens.}.
% 
% Then we do the similar procedure for \!\pcol@rightpage! and make its height
% and depth equal to those of \!\@outputbox!\footnote{
% 
% If \pwise{} floats become a part of \postenv's floats, \!\pcol@rightpage!
% will be made $\bot$ by \!\pcol@output@end! afterward.}.
% 
% Finally we temporarily add $h$ to \!\topmargin! as done in
% \!\pcol@ioutputelt! so that \bgpaint{} of columns and so on with
% \bginfext{} can reach the paper top edge.
% 
% \changes{v1.3-6}{2013/09/17}
%	{Revise the condition of leaving page-wise floats as ordinary
%	 post-environment floats using \cs{if@tempswa} with
%	 \cs{ifpcol@dfloats}.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
  \begingroup
    \ifpcol@nospan
      \global\setbox\@outputbox\box\voidb@x
      \global\setbox\pcol@rightpage\box\voidb@x
    \else
      \ifpcol@dfloats \@tempswatrue \fi
      \let\@elt\relax
      \edef\pcol@bg@floatheight{%
        \@elt{\number\ht\pcol@spanning sp}\@elt{\number\dp\pcol@spanning sp}}%
      \def\reserved@a{%
        \ifpcol@firstpage\else \if@tempswa \pcol@bg@paintbox{Ff}\fi\fi}%
      \@tempdima\ht\pcol@spanning \advance\@tempdima\dp\pcol@spanning
      \global\setbox\@outputbox\vbox{%
        \reserved@a \unvbox\pcol@spanning
        \ifpcol@firstpage\else \if@tempswa\else \unskip \fi\fi}%
      \global\setbox\@outputbox\vbox{\box\@outputbox}%
      \pcol@Fb
      \@cons\@freelist\pcol@spanning
      \pcol@Fe{makeflushedpage(spanning)}%
      \ifnum\pcol@ncolleft<\pcol@ncol
        \global\setbox\pcol@rightpage\vbox{%
          \ifpcol@paired\else \advance\c@page\@ne \fi
          \reserved@a \unvbox\pcol@rightpage}%
        \global\ht\pcol@rightpage\ht\@outputbox
        \global\dp\pcol@rightpage\dp\@outputbox
        \global\setbox\pcol@rightpage\vbox{\box\pcol@rightpage}%
      \fi
      \advance\topmargin\@tempdima
    \fi
%    \end{macrocode}
% 
% Next, after \!\global!ly letting $\CSIndex{ifpcol@firstpage}=\false$ because
% we will ship a page which may be the \spage{} shortly, we build the
% ship-out image of columns if required fundamentally by
% $\CSIndex{if@tempswa}=\true$.  First,
% if the page $\ptop$ has \Scfnote{}s, we shrink
% $\!\@colht!={\pp^h}(\ptop)$ by \!\pcol@shrinkcolbyfn! to keep the room for
% the footnotes, to have $H=\!\@pageht!$ being the possibly shrunk
% $\pp^h(\ptop)$ for the reference
% in \!\pcol@imakeflushedpage! after the further possible modification of
% \!\@colht! we will make shortly.  Second, if
% $\CSIndex{ifpcol@lastpage}=\true$ but $\CSIndex{ifpcol@dfloats}=\true$
% too, we turn $\CSIndex{ifpcol@lastpage}=\false$ because we need a
% full-sized \lpage{}, temporarily letting $\!\@textbottom!=\!\vfil!$ if
% $\VPP=-\infty$ to avoid underfull due to perfectly empty \colpage{}s as
% discussed in\Tie(\ref{item:mfp-last-dfloats})\footnote{
% 
% Each \colpage{} $cc_c(\vb^b)$ itself exists because the empty \colpage{}
% has been visited by \cscan{} prior to \!\output! request for environment
% closing.}.
% 
% Third, if we are working on a truly \lpage{} and $\arg{ht}<H$ to mean the
% tallest column is shorter than $H$, we let $\!\@colht!=\arg{ht}$ to let
% \!\@makecol! build short \colpage{}s.  Note that it is definitely
% $\arg{ht}\leq H$ because the \pfcheck{} on the \lpage{} makes that sure.
% Fourth and finally, unless all columns in truly \lpage{} are empty as
% discussed in (\ref{item:mfp-last-empty}), we invoke
% $\!\pcol@imakeflushedpage!\<\Cfrom\>\<\Cto\>\<b\>$ once or twice, to put
% columns in right \parapag{}e to $b=\!\pcol@rightpage!$ with
% $\LBRP\Cfrom\Cto=\LBRP\CL\C$ if $\CL<\C$, and then to put left ones in
% $b=\!\@outputbox!$ with $\LBRP\Cfrom\Cto=\LBRP0\CL$ always\footnote{
% 
% The order of right to left is not essential in this macro but we follow
% the convention in \!\pcol@outputelt!.}.
% 
% \changes{v1.0}{2011/10/10}
%	{Let \cs{@colht} be $\langle\mathit{ht}\rangle$ if the former is
%	 less than the latter.}
% \changes{v1.0}{2011/10/10}
%	{Add special care of the float column in the last page.}
% \changes{v1.2-2}{2013/05/11}
%	{Add \cs{@colht} shrinking by page-wise footnotes.}
% \changes{v1.3-3}{2013/09/17}
%	{Add \cs{@colht} and \cs{relax} as the first and third argument
%	 of \cs{pcol@shrinkcolbyfn} for all of three invocations of it.}
% \changes{v1.3-6}{2013/09/17}
%	{Remove empty column scan for \cs{if@fcolmade} because it is now
%	 unnecessary thanks to \cs{ifpcol@dfloats}.}
% \changes{v1.3-6}{2013/09/17}
%	{Revise the condition of column-page building and setting of
%	 \cs{@colht}.}
% 
%    \begin{macrocode}
    \global\pcol@firstpagefalse
    \if@tempswa
      \ifvoid\pcol@footins\else
        \pcol@shrinkcolbyfn\@colht\pcol@footins\relax
      \fi
      \let\pcol@@hfil\relax \@pageht\@colht
      \ifpcol@lastpage \ifpcol@dfloats
        \ifdim\pcol@colht<\z@ \def\@textbottom{\vfil}\fi
        \pcol@lastpagefalse
      \fi\fi
      \ifpcol@lastpage \ifdim#1<\@colht \@colht#1\fi\fi
      \ifdim\@colht<\z@ \else
        \ifnum\pcol@ncolleft<\pcol@ncol
          \pcol@imakeflushedpage\pcol@ncolleft\pcol@ncol\pcol@rightpage
        \fi
        \pcol@imakeflushedpage\z@\pcol@ncolleft\@outputbox
      \fi
    \fi
%    \end{macrocode}
%
% After putting all \colpage{}s, we examine if the page $\ptop$ has
% \Scfnote{}s in $\pp^f(\ptop)$.  If so, and unless $\ptop$ is a truly
% \lpage{} and \Mgfnote{} typesetting is in effect to mean the \Scfnote{}s
% will be merged with \postenv{}, we put the footnotes in $\pp^f(\ptop)$
% below the \colpage{}s.  Prior to this however, we let
% \Midx{\!\pcol@fnheight@lpage!} have the height-plus-depth of the footnote,
% so that \!\pcol@output@end! know the size for the \bgpaint{} of the
% footnotes, which \!\pcol@imakeflushedpage!  performed for non-\lpage{}s.
% We also put an empty box of the size into \!\pcol@rightpage! by
% \!\pcol@phantom! together with the \!\skip! component of $\pp^f(\ptop)$ to
% keep the space necessary especially when $\ptop$ is the \lpage.  Then we
% put the footnotes in $\pp^f(\ptop)$ into \!\@outputpage!  by
% \!\pcol@putfootins!, reclaiming the contents of $\pp^f(\ptop)$ and letting
% $\pp^f(\ptop)=\bot$ so that \!\pcol@output@end!  will be unaware of the
% footnotes.  We also let $\VPP=\!\pcol@colht!=0$ if $\ptop$ is a truly
% \lpage{} and it had $-\infty$ to indicate that the \lpage{} is not empty
% but has footnotes as discussed in\Tie(\ref{item:mfp-last-empty}).
% 
% \changes{v1.2-2}{2013/05/11}
%	{Add incorporation of page-wise footnotes.}
% \changes{v1.3-6}{2013/09/17}
%	{page-wise footnotes for the last page followed by pages for
%	 deferred column-wise floats are now put by this macro.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
    \gdef\pcol@fnheight@lpage{0pt}%
    \ifvoid\pcol@footins\else
      \@tempswatrue \ifpcol@lastpage \ifpcol@mgfnote \@tempswafalse \fi\fi
      \if@tempswa
        \pcol@Log\pcol@makeflushedpage{output}\pcol@footins
        \@tempdima\ht\pcol@footins \advance\@tempdima\dp\pcol@footins
        \xdef\pcol@fnheight@lpage{\number\@tempdima sp}%
        \ifnum\pcol@ncolleft<\pcol@ncol
          \global\setbox\pcol@rightpage\vbox{\unvbox\pcol@rightpage
            \vskip\skip\pcol@footins \nointerlineskip
            \pcol@phantom\pcol@footins \vskip\z@}%
        \fi
        \global\setbox\@outputbox\vbox{%
          \unvbox\@outputbox \pcol@putfootins\pcol@footins}%
        \pcol@Fb
        \@cons\@freelist\pcol@footins \gdef\pcol@footins{\voidb@x}%
        \pcol@Fe{makeflushedpage(pagefn)}%
        \ifdim\pcol@colht=-\maxdimen \global\pcol@colht\z@ \fi
      \fi
    \fi
  \endgroup}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@imakeflushedpage}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced for parallel-paging.}
% \changes{v1.3-3}{2013/09/17}
%	{Implement column-separating rule and background paiting of
%	 columns, column-separating gaps, spanning texts and page-wise
%	 footnotes.}
% \changes{v1.3-4}{2013/09/17}
%	{Implement variable-width column-separating gaps.}
% 
% The macro $\!\pcol@imakeflushedpage!\<\Cfrom\>\<\Cto\>\arg{b}$ is invoked
% solely in \!\pcol@makeflushedpage! but can be twice with
% $(\Cfrom,\Cto,b)=(\CL,\C,\!\pcol@rightpage!)$ if \parapag{}ing is in effect
% and with $(\Cfrom,\Cto,b)=(0,\CL,\!\@outputbox!)$ always, to build the
% ship-out image of the right or left \parapag{}e $\ptop$ in the box $b$
% already having \spanning{} or its blank counterpart if any, respectively.
% 
% After opening the \!\vbox! of the ship-out image for $b$, at first we
% examine if $\CSIndex{ifpcol@paired}={\false}$ and $\Cfrom>0$, and if so we
% temporarily increment $\page(\ptop)$ by one so that we check its parity
% for \mirror{}ed \bgpaint{} correctly.  Then if the page $\ptop$ has
% \Scfnote{}s in $\pp^f(\ptop)$, we paint its \bground, or that of its blank
% counterpart, by \!\pcol@bg@paintbox! \!\def!ining the parameter
% \!\pcol@bg@footnoteheight!  with the height-plus-depth of $\pp^f(\ptop)$,
% as the very first element of the ship-out image as done in
% \!\pcol@ioutputelt!, unless $\ptop$ is the truely \lpage{} for which the
% \bgpaint{} is done in \!\pcol@output@end!.  Then we put \spanning{} in $b$
% itself if any.
% 
% Next, we invoke \!\pcol@buildcolseprule! for \cseprule{} drawing and
% \bgpaint{} giving it $H$ in \!\@colht! possibly shurnk from $\pp^h(\ptop)$
% by \Scfnote{}s, $\LBRP\Cfrom\Cto$ for the set of columns to be put, and
% \!\@maxdepth! for non-\lpage{}s to paint the \bground{}s of columns and
% \csepgap{}s so that those of the last segment reach the page bottom, while
% for \lpage{} we give 0 to let the bottom be the real bottom of the
% columns.  Then we put the painted \bground{}s in \!\@tempboxa!
% immediately.
% 
%    \begin{macrocode}
\def\pcol@imakeflushedpage#1#2#3{\global\setbox#3\vbox{%
  \ifpcol@paired\else\ifnum#1=\z@\else \advance\c@page\@ne \fi\fi
  \ifvoid\pcol@footins\else \ifpcol@lastpage\else
    \def\pcol@bg@footnoteheight{%
      \@elt{\ht\pcol@footins}\@elt{\dp\pcol@footins}}%
    \pcol@bg@paintbox{Nn}%
  \fi\fi
  \unvbox#3\nointerlineskip
  \ifpcol@lastpage \pcol@buildcolseprule\@colht#1#2\z@
  \else            \pcol@buildcolseprule\@colht#1#2\@maxdepth
  \fi
  \unvbox\@tempboxa
%    \end{macrocode}
% 
% Now we put columns in a \!\hbox! of $\WT=\!\textwidth!$ wide.  That is,
% for each $c$, being $c'$ or $\C-1-c'$ for the $c'$-th iteration determined
% by \!\pcol@swapcolumn! according to the effectiveness of \cswap{} and the
% parity of $\page(\ptop)$, we obtain $c$'s \cctext{} $\cc_c$ by
% \!\pcol@getcurrcol!, move $\cc_c(\vb^b)$ into \!\box!|255|, and let
% $\!\footins!=\cc_c(\ft)$ by \!\pcol@getcurrfoot! returning it to
% \!\@freelist! if $c$ has \Mcfnote{}s.
% 
% After that we examine if $\cc_c(\tr)=\infty$ to mean we are working on the
% \lpage{} and the \colpage{} is for a \fcolumn{} whose floats can be put as
% top floats, and let $\!\topfigrule!=\!\relax!$ temporarily because the
% floats are not top ones in reality, if so.  Note that the abnormal setting
% $\cc_c(\tr)=\infty$ is not recovered because it will never be referred to
% and the register \!\@toproom! it represents will be updated with correct
% value before it is referred to in \postenv.  Then we also check
% $\arg{ht}=H$ to mean the \lpage{} is full size.  If both of them hold,
% the floats in $\cc_c(\tl)$ should be (or may be) put in the \fcolumn{} as
% usual and thus we put them in \!\@outputbox! of $H$ tall by
% \!\pcol@makefcolpage!.  Otherwise we invoke \!\pcol@@makecol!\footnote{
% 
% Not \cs{pcol@makecol} because the main vertical list has \!\vfil! and, if
% it has a \sync{}ation point, a infinite shrink by \cs{pcol@synccolumn} at
% its tail already, and we should not do any special operations for
% \Scfnote{}s.  Also it is not \cs{@makecol} because we need to ensure the
% depth of resulting \cs{@outputbox} is capped.},
% 
% to have the ship-out image of the \colpage{} in \!\@outputbox!, possibily
% only for the deferred floats in $\cc_c(\tl)$ but without \!\topfigrule! in
% this case.  Note that we don't take care of the stretch\slash shrink of
% \!\skip!\!\footins!  for \Scfnote{}s because \pfcheck{} on the \colpage{}
% makes it sure that the natural height of the \colpage{} cannot be greater
% than \!\@colht!.  Also note that we give \!\@maxdepth! to
% \!\pcol@@makecol! for non-\lpage{}s for depth capping, but for the
% \lpage{} we pass 0 to the macro because $H=\!\@colht!$ should be large
% enough to accommodate everything in the column including its last box even
% if the box is unusually deep.
% 
% Then we put the \!\@outputbox! above in a \!\hbox! of \!\columnwidth! wide
% preceded by \!\pcol@@hfil! being \!\relax! for the first column, while
% it is $\!\pcol@hfil!\<c^g\>$, where $c^g=\!\pcol@colsepid!$ being $c$ or
% $c-1$ without or with \cswap{} respectively, to put a \csepgap{} possibly
% with \cseprule{} segments in \!\pcol@tempboxa! built by
% \!\pcol@buildcolseprule!.  Finally, we save \cctext{} especially those
% for float parameters into $\cc_c$ by \!\pcol@setcurrcolnf! because all
% \Mcfnote{}s have been shipped out.
% 
% \changes{v1.2-4}{2013/05/11}
%	{Add column-swapping for even pages if specified.}
% \changes{v1.2-2}{2013/05/11}
% 	{Revise reflecting the redesign of \cs{pcol@getcurrfoot}.}
% \changes{v1.2-2}{2013/05/11}
%	{Add \cs{pcol@Logstart} and \cs{pcol@Logend}.}
% \changes{v1.2-7}{2013/05/11}
% 	{Enclose the column-page building process in a group to fix the bug
%	 which lets $\cs{topfigrule}\EQ\cs{relax}$ affecting to another
%	 column.}
% \changes{v1.2-7}{2013/05/11}
% 	{Replace the sequence of operations to make a usual float column
%	 with \cs{@toplist} with the newly introduced
%	 \cs{pcol@makefcolpage}.}
% \changes{v1.2-7}{2013/05/11}
% 	{Replace \cs{@makecol} with \cs{pcol@@makecol} to cap the depth of
%	 \cs{@outputbox} by \cs{@maxdepth} even with p\string\LaTeX.}
% \changes{v1.3-6}{2013/09/17}
%	{Add \cs{@maxdepth} or 0 as the argument of \cs{pcol@@makecol} to
%	 fix the problem that the last page is too large due to
%	 \cs{@maxdepth}, by the latter.}
% \changes{v1.3-6}{2013/09/17}
%	{Remove the examination of $\kappa_c(\lambda_d)$ for
%	 \cs{if@fcolmade} because it is made unnecesary now by
%	 \cs{ifpcol@dfloats}.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
  \hb@xt@\textwidth{%
    \@tempcntb#1\@whilenum\@tempcntb<#2\do{%
      \pcol@swapcolumn\@tempcntb\pcol@currcol#1#2\relax
      \pcol@getcurrcol
      \setbox\@cclv\box\@currbox
      \ifvoid\pcol@currfoot\else
        \pcol@Fb
        \@cons\@freelist\pcol@currfoot
        \pcol@Fe{imakeflushedpage(colfn)}%
      \fi
      \pcol@getcurrfoot\box
      \@tempswafalse
      \begingroup
        \ifdim\@toproom=\maxdimen
          \let\topfigrule\relax \ifdim\@colht=\@pageht \@tempswatrue \fi
        \fi
        \if@tempswa
          \pcol@Logstart{\pcol@makeflushedpage(1)}%
          \setbox\@outputbox\pcol@makefcolpage
          \pcol@Logend{\pcol@makeflushedpage(1)}%
        \else
          \pcol@Logstart{\pcol@makeflushedpage(2)}%
          \ifpcol@lastpage \pcol@@makecol\z@ \else \pcol@@makecol\@maxdepth \fi
          \pcol@Logend{\pcol@makeflushedpage(2)}%
        \fi
        \pcol@@hfil \hb@xt@\columnwidth{\box\@outputbox\hss}%
      \endgroup
      \edef\pcol@@hfil{\noexpand\pcol@hfil{\pcol@colsepid}}%
      \pcol@setcurrcolnf
     \advance\@tempcntb\@ne}}}}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@flushfloats}
% \changes{v1.0}{2011/10/10}
%	{Add reinitialization of \cs{@colht}.}
% \changes{v1.2-4}{2013/05/11}
%	{Add column-swapping for even pages if specified.}
% \changes{v1.3-2}{2013/09/17}
%	{Completely redesigned with new macro \cs{pcol@iflushfloats}.}
% \begin{macro}{\pcol@iflushfloats}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced for parallel-paging.}
% \changes{v1.3-3}{2013/09/17}
%	{Implement column-separating rule and background paiting of
%	 columns and column-separating gaps}
% \changes{v1.3-4}{2013/09/17}
%	{Implement variable-width column-separating gaps.}
% 
% The macro \!\pcol@flushfloats! is invoked from \!\pcol@output@clear! and
% \!\pcol@output@end! to flush all deferred \cwise{} floats in each
% column if any.  After letting $\!\@colht!=\!\textheight!$ for
% \fcolumn{}s, we iterate shipping out a page having \fcolumn{}s while
% $\CSIndex{if@fcolmade}=\exists c\In0\C:(\cc_c(\dl)\neq())$.
% 
% In the loop, we initialize $\CSIndex{if@fcolmade}=\false$, and then
% invoke \!\pcol@iflushfloats! twice or once according to $\CL<\C$ or not to
% mean \parapag{}ing is in effect or not, respectively.  That is, if
% $\CL<\C$ we invoke the macro with $\LBRP\CL\C$ and \!\pcol@rightpage! for
% the right \parapag{}e, and do it with $\LBRP0\CL$ and \!\@outputbox!
% always.  Note that if $\CL=\C$, we let $\!\pcol@rightpage!=\bot$ to tell
% \!\@outputpage!, which we invoke at the end of the loop to ship out a page
% or a \parapag{}e pair, that the \parapag{}ing is not in effect.
% 
% The macro $\!\pcol@iflushfloats!\<\Cfrom\>\<\Cto\>\<b\>$ opens
% a \!\vbox! to be set into $b$.  Then if $\CSIndex{ifpcol@paired}={\false}$
% and $\Cfrom>0$ to mean we are working on a right \npaired{} \parapag{}e,
% we temporarily add \!\c@page! by one for page parity examination for
% \mirror{}ed \bgpaint.  Then, the macro \!\pcol@buildcolseprule! is invoked
% with $\!\@colht!=\!\textheight!$ and $\LBRP\Cfrom\Cto$ for \cseprule{}
% drawing in \!\pcol@tempboxa! and \bgpaint{} for columns and \csepgap{}s in
% \!\@tempboxa! put into $b$ immediately.
% 
% Then we open a \!\hbox! of \!\textwidth! wide and initialize
% $f=\CSIndex{if@tempswa}$ to be \CSIndex{if@fcolmade}.  Then for each
% $c\In\Cfrom\Cto$, being $c'$ or $\C-1-c'$ for the $c'$-th iteration
% determined by \!\pcol@swapcolumn! according to the effectiveness of
% \cswap{} and the parity of \!\c@page!, we put an inner \!\hbox! of
% $\!\columnwidth!=\w_c$ wide preceded by \!\pcol@@hfil! being \!\relax! at
% initial or $\!\pcol@hfil!\<c_g\>$ otherwise for a \csepgap{} and
% \cseprule{}, where $c_g\in\{c,c{-}1\}$ without or with \cswap{}
% respectively.  That is, at first we obtain $c$'s \cctext{} including
% $\cc_c(\dl)$ by \!\pcol@getcurrcol!  and pass $\cc_c(\dl)$ to
% \!\@makefcolumn! to produce a \fcolumn{} in \!\@outputbox!  to be put into
% the inner \!\hbox!.  Then we do $f\gets f\lor(\cc_d(\dl)\neq\emptyset)$
% with $\cc_d(\dl)$ shrunk by \!\@makefcolumn! to let $f$ have
% $\exists{}c\In0\Cto:(\cc_c(\dl)\neq\emptyset)$ at the end of the loop for
% $c$, and then save the \cctext{} into $\cc_c$ by \!\pcol@setcurrcolnf!
% because we have no footnotes in $c$.
% 
% After the end of the loop, we move $f$ to \CSIndex{if@fcolmade} for
% the termination check of the loop in \!\pcol@flushfloats!.
% 
%    \begin{macrocode}
\def\pcol@flushfloats{%
  \global\@colht\textheight
  \@whilesw\if@fcolmade\fi{%
    \global\@fcolmadefalse
    \ifnum\pcol@ncolleft<\pcol@ncol
      \pcol@iflushfloats\pcol@ncolleft\pcol@ncol\pcol@rightpage
    \else
      \setbox\pcol@rightpage\box\voidb@x
    \fi
    \pcol@iflushfloats\z@\pcol@ncolleft\@outputbox
    \@outputpage}}
\def\pcol@iflushfloats#1#2#3{\setbox#3\vbox{%
  \ifpcol@paired\else\ifnum#1=\z@\else \advance\c@page\@ne \fi\fi
  \pcol@buildcolseprule\@colht#1#2\@maxdepth \unvbox\@tempboxa
  \hb@xt@\textwidth{%
    \let\pcol@@hfil\relax
    \if@fcolmade \@tempswatrue \else \@tempswafalse \fi
    \@tempcntb#1\@whilenum\@tempcntb<#2\do{%
      \pcol@swapcolumn\@tempcntb\pcol@currcol#1#2\relax
      \pcol@getcurrcol
      \@makefcolumn\@deferlist
      \pcol@@hfil \hb@xt@\columnwidth{%
        \if@fcolmade \box\@outputbox \else \vbox to\@colht{}\fi \hss}%
      \ifx\@deferlist\@empty\else \@tempswatrue \fi
      \edef\pcol@@hfil{\noexpand\pcol@hfil{\pcol@colsepid}}%
      \pcol@setcurrcolnf
     \advance\@tempcntb\@ne}%
    \if@tempswa \global\@fcolmadetrue \else \global\@fcolmadefalse \fi}}}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@freshpage}
% \changes{v1.0}{2011/10/10}
%	{Rename \cs{pcol@maxpage} as \cs{pcol@toppage}.}
% \changes{v1.0}{2011/10/10}
%	{Add save and restore of \cs{@currbox}.}
% \changes{v1.0}{2011/10/10}
%	{Remove unnecessary assignment of \cs{pcol@currcol}.}
% \changes{v1.2-2}{2013/05/11}
%	{Add argument 0 for the invocations of \cs{pcol@startcolumn} to
%	 inhibit inserting deferred page-wise footnotes.}
% 
% The macro \!\pcol@freshpage! is invoked from \!\pcol@output@flush! and
% \!\pcol@output@clear! to start a new page after column flushing.  At
% first, we let $p=\pbase=\ptop=0$ and $\PP=\emptyset$ because we know no
% pages are kept.  Then we invoke \!\pcol@startpage! to start a new page
% with a \!\def!inition of $\!\pcol@currpage!=|{}|$ to indicate the invoker
% is this macro (i.e., not \!\pcol@opcol!).  Then after keeping \!\@colht!
% in $h=\!\pcol@colht!$, we do the followings for each column $c\In0\C$.
% 
% First we obtain $c$'s \cctext{} in $\cc_c$ by \!\pcol@getcurrcol! but let
% $p=0$ and $\!\@colroom!=h$, which can be modified by $c'<c$, without
% referring to $\cc_c(\vb^p)$ nor $\cc_c(\vb^r)$ because they are obsolete.
% We also save \!\@currbox! to \Midx{\!\pcol@currboxsave!} because it may be
% modified by \!\pcol@opcol! if we make \fcolumn{}s afterward.  Then we invoke
% \!\pcol@getcurrpage! to have the \pctext{} of $p=0$, because it might be
% modified by a column $c'<c$ by producing \fcolumn{}s.  After that and the
% invocation of \!\pcol@floatplacement! for setting float parametners, we
% invoke \!\pcol@startcolumn! for $c$'s \colpage{} at $p=0$, and iterate
% \!\pcol@opcol! and \!\pcol@startcolumn! while a \fcolumn{} is made by the
% latter\footnote{
% 
% Each column can have deferred floats on the invocation from
% \!\pcol@output@flush!.}.
% 
% Note that we give the argument 0 to each invocation of
% \!\pcol@startcolumn! to keep it from inserting deferred \Scfnote{}s, which
% will be taken care of by \!\pcol@restartcolumn! if any.  At last in the
% loop, we restore \!\@currbox! from \!\pcol@currboxsave!, let
% $\cc_c(\vb^b)$ be an empty \!\vbox! because the main vertical list is
% empty, and save the \cctext{} into $\cc_c$ by \!\pcol@setcurrcolnf!
% because of no footnotes obviously, after saving $p$ and \!\@colroom!,
% which might be modified by the \fcolumn{} production, into $\cc_c(\vb^p)$
% and $\cc_c(\vb^r)$.
% 
% After the loop above, finally we invoke \!\pcol@restartcolumn! to return
% to the column in which \!\flushpage! or \!\clearpage! was issued.
% 
%    \begin{macrocode}
\def\pcol@freshpage{%
  \global\pcol@page\z@ \global\pcol@toppage\z@ \global\pcol@basepage\z@
  \global\let\pcol@pages\@empty \global\let\pcol@currpage\@empty
  \pcol@startpage \pcol@colht\@colht
  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
    \pcol@getcurrcol \pcol@page\z@ \@colroom\pcol@colht
    \let\pcol@currboxsave\@currbox
    \pcol@getcurrpage
    \pcol@floatplacement
    \pcol@startcolumn\z@
    \@whilesw\if@fcolmade\fi{\pcol@opcol \pcol@startcolumn\z@}%
    \let\@currbox\pcol@currboxsave
    \global\setbox\@currbox\vbox{}%
    \global\count\@currbox\pcol@page \global\dimen\@currbox\@colroom
    \pcol@setcurrcolnf
   \advance\pcol@currcol\@ne}%
  \pcol@restartcolumn}

%    \end{macrocode}
% \end{macro}
% 
% 
% 
% \subsection{Last Page}
% \label{sec:imp-sout-end}
% 
% \begin{macro}{\pcol@output@end}
% \changes{v1.0}{2011/10/10}
%	{Drastically changed to take special care of float columns in the
%	 last page, to deal with the empty last page with and without
%	 deferred floats, and to try to make post-environment float pages.} 
% \changes{v1.2-2}{2013/05/11}
%	{Add incorporation of page-wise footnotes in the last ordinary
%	 pages followed by float-pages.}
% \changes{v1.2-7}{2013/05/11}
%	{Add \cs{pcol@outputfalse} to solve the \cs{output} request sneaking.}
% \changes{v1.2-7}{2013/05/11}
%	{Add $\cs{boxmaxdepth}\EQ\cs{@maxdepth}$ for depth capping knowing
%	 it is redundant.}
% \changes{v1.3-2}{2013/09/17}
%	{Add parallel-paging operations.}
% \changes{v1.3-3}{2013/09/17}
%	{Add background painting of page-wise footnotes and setting
%	 of \cs{pcol@preposttop}.}
% \changes{v1.3-4}{2013/09/17}
%	{Add opeartios to pass $\string\cal{M}$ to the next
%	 \string\texttt{paracol} environment and \cs{@mparbottom} to post
%	 environment typesetting.}
% 
% The macro \!\pcol@output@end! is invoked solely from
% \!\pcol@specialoutput! to process the \!\output! request made by
% \!\endparacol!.  We invoke \!\pcol@makeflushedpage! for the \lpage{}
% production as the setting $\CSIndex{ifpcol@lastpage}=\true$ done by
% \!\endparacol! indicates, giving it $h=\!\pcol@colht!$ in which
% \!\pcol@sync! sets the height of the tallest \colpage{} to have the
% ship-out image of the \tpage{} in \!\@outputbox!.
% 
% Next, we define $\mpbout=\!\pcol@mparbottom@out!$ as follows.  First, we
% invoke \!\pcol@getmparbottom@last! giving it $y=\VPP-\!\ht!\!\@outputbox!$
% being the negative counterpart of
% the height of \spanning{} in the \lpage, to let $\mpbout$ have the occupancy
% information of the bottom marginal note in each margin if any, or
% $\mpar(y,y)$ otherwise.  Then we transform $y$-coordinates in $\mpbout$
% from those for columns to those for text area by
% $\!\pcol@bias@mpbout!\Arg{-y}$ to have the final result.  Then to pass
% \!\@mparbottom! for post-environment typesetting,
% 
% \Index{post-environment stuff}
% 
% we invoke \!\pcol@do@mpbout! \!\def!ining \!\pcol@do@mpbout@whole! to do
% nothing and \!\pcol@do@mpbout@elem! to let $\!\@mparbottom!=b$ where
% $\mpb_L^x=(\mpar(t,b))$ and $x\in\{l,r\}$ according to the margin which
% post-environment marginal notes go to.
% 
% \Index{post-environment stuff}
% 
%    \begin{macrocode}
%% Special Output Routines: Last Page

\def\pcol@output@end{%
  \pcol@Logstart\pcol@output@end
  \pcol@makeflushedpage\pcol@colht
  \@tempdima\pcol@colht \ifdim\pcol@colht<\z@ \@tempdima\z@ \fi
  \advance\@tempdima-\ht\@outputbox
  \pcol@getmparbottom@last\@tempdima
  \pcol@bias@mpbout{-\@tempdima}
  \def\pcol@do@mpbout@whole##1##2##3##4{\setbox\@tempboxa\hbox{##1##2##3##4}}%
  \def\pcol@do@mpbout@elem\@elt##1##2{\global\@mparbottom##2sp}%
  \pcol@do@mpbout
%    \end{macrocode}
% 
% Next we process one of the following cases.
% 
% The first case is for $\CSIndex{ifpcol@dfloats}=\true$ to mean the
% \lpage{} is followed by one or more pages having deferred \cwise{}
% floats and thus \!\pcol@makeflushedpage! builds the ship-out image of the
% \lpage{} in {\em full size} in \!\@outputbox! unless the page has nothing
% perfectly.  Therefore, we ship the image out by \!\@outputbox! unless it
% is $\bot$ for perfectly empty case.  Then we invoke \!\pcol@flushfloats!
% to produce and ship out \fpage{}s, lettinng $\CSIndex{if@fcolmade}={\true}$
% to tell the macro that at least we will have one \fpage{}.  Now we have
% shipped out everyting in the closing environment and thus we let
% $\CSIndex{ifpcol@output}=\false$ to tell \!\output! routine to work
% ordinarily.  Then we let $\CSIndex{if@tempswa}=f_{\it sp}=\true$ to
% remember we will start a new page and thus $\!\@pagedp!=\pd=\DP=1000$ to
% mimic \TeX's \!\prevdepth! mechanism.  Finally we let
% $\CSIndex{@mparbottom}=0$ and $\mpbout=\mpboutz$ because no marginal notes
% are carried over to post-environment typesetting.
% 
% \Index{post-environment stuff}
% 
% \changes{v1.3-6}{2013/09/17}
%	{Simplify the case with deferred floats thanks to
%	 \cs{ifpcol@dfloats} and redesign of \cs{pcol@makeflushedpage}.}
% 
%    \begin{macrocode}
  \@tempswafalse
  \ifpcol@dfloats
    \ifvoid\@outputbox\else \@outputpage \fi
    \global\@fcolmadetrue \pcol@flushfloats
    \global\pcol@outputfalse
    \@tempswatrue \@pagedp\@m\p@ \global\@mparbottom\z@
    \global\let\pcol@mparbottom@out\pcol@mparbottom@zero
%    \end{macrocode}
% 
% Before proceeding to the second and third cases, we let
% $\CSIndex{ifpcol@output}=\false$ because we have nothing to ship out.
% 
% Then the second case is for $h=-\infty$ without deferred \cwise{}
% floats to mean all columns in the \lpage{} are empty and the page does not
% have non-merged \Scfnote{}s.  In this case, we examine if
% $\Midx{\!\pcol@firstprevdepth!}=\!\relax!$ to mean we have had at least
% one new page in \env{paracol} environment, i.e., \!\pcol@startpage! have
% been invoked at least once.  If so, we let $f_{\it sp}=\true$, $\pd=1000$,
% $\!\@mparbottom!=0$ and $\mpbout=\mpboutz$ again and put nothing to the
% main vertical list so that the \postenv{} starts from the top of the page.
% However, we have to take care of the case that $f_{\it ns}=\false$ and
% thus \!\@outputbox!  has \spanning.  If so, we acquire an \!\insert! from
% \!\@freelist! by \!\@next! to let it have the \spanning, i.e., the
% contents of \!\@outputbox!\footnote{
% 
% It does not have \!\dbltextfloatsep! at its tail because the skip has been
% removed by \!\pcol@makeflushedpage!.}.
% 
% Then the \!\insert! is added to the head of \!\@dbldeferlist! with the
% float placement code 10 to force \LaTeX's float placement mechanism to put
% it to the page to be started shortly.
% 
% On the other hand, $\!\pcol@firstprevdepth!\neq\!\relax!$ means that it
% has $\!\prevdepth!=\pd'$ just before \beginparacol{} in decimal integer
% representation.  Since we have not started any pages in the environment,
% and all columns in the \lpage{} is empty, we have almost nothing in the
% environment.  Note that the environment can have \pwise{} floats but they
% have not yet put into any pages but are kept in \!\@dbldeferlist!, or
% \Mgfnote{}s but they are merged to those in \postenv.  Therefore, the
% \preenv{} and \postenv{} must be {\em connected} naturally and thus we put
% the \preenv{} kept in \!\@outputbox! to the main vertical list by
% \!\unvbox!, letting $\pd=\pd'$ and keeping $f_{\it sp}=\false$\footnote{
% 
% The author of course know this situation is very unlikely but he is
% monomaniac.}.
% 
% In this case, the setting of \!\@mparbottom! and $\mpbout$ done at the
% beginning of this macro is correct because they describe the marginal
% notes in \preenv{} including \env{paracol} enviroments preceeding it even
% if any.
% 
% \changes{v1.3-3}{2013/09/17}
%	{Add settings for background painting of post-environment stuff.}
% \changes{v1.3-4}{2013/09/17}
%	{Add letting $\cs{@mparbottom}\EQ0$ and
%	 ${\string\cal{M}}\EQ{\string\cal{M}}_0$ for the simple empty page
%	 case.}
% \changes{v1.3-6}{2013/09/17}
%	{Remove \cs{unskip} from the operation to let page-wise floats be 
%	 ordinary ones because \cs{pcol@makeflushedpage} does it.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
  \else
    \global\pcol@outputfalse
    \ifdim\pcol@colht=-\maxdimen
      \ifx\pcol@firstprevdepth\relax
        \@tempswatrue \@pagedp\@m\p@ \global\@mparbottom\z@
        \global\let\pcol@mparbottom@out\pcol@mparbottom@zero
        \ifpcol@nospan\else
          \pcol@Fb
          \@next\@currbox\@freelist{\global\setbox\@currbox\box\@outputbox}%
            \pcol@ovf
          \pcol@Fe{output@end(spanning)}%
          \count\@currbox10\relax
          {\let\@elt\relax \xdef\@dbldeferlist{\@elt\@currbox\@dbldeferlist}}%
          \global\setbox\pcol@rightpage\box\voidb@x
        \fi
      \else \unvbox\@outputbox \@pagedp\pcol@firstprevdepth sp\relax
      \fi
%    \end{macrocode}
% 
% The last case without deferred floats and with some non-empty columns or
% non-merged \Scfnote{}s is
% most usual.  In this case, we may simply put \!\@outputbox! letting
% $\!\topskip!=0$ because \!\topskip! has already been inserted in
% \colpage{}s or \preenv{} in the box\footnote{
% 
% If the \lpage{} has non-merged \Scfnote{}s without any other items,
% \cs{topskip} has not been inserted, but this inconsistency without
% \cs{topskip} is acceptable.}.
% 
% However before putting the box back to the main vertical list, we have to
% take care of the \bgpaint{} as follows.  First we let
% $\CSIndex{ifpcol@havelastpage}=\true$ to let \!\@outputpage! paint the
% \bground{} of the \postenv{} when the page having the \lpage{} completes.
% Second, we let \!\pcol@bg@preposttop@left! have the height-plus-depth of
% the \!\@outputbox! having the short \lpage{} because the \bground{} of
% \postenv{}, or of \preenv{} if we have another \env{paracol} environment
% in the same page, to be painted is just below the box.  We also
% \!\pcol@bg@preposttop@right! have the same value but only if $\CL<\C$,
% because otherwise we have to keep this macro unchanged so that the
% non-existent right \parapag{}e of the closing environment can be the
% \postenv{} of a preceding environment and/or the \preenv{} of a succeeding
% one with \parapag{}ing.  Note that in the aforementioned {\em fresh page}
% cases and the perfectly empty case, we may be unaware of these macros
% because it should have been made 0 by the last invocation of
% \!\@outputpage! in the fresh page case or the \preenv{} and \postenv{} are
% contiguous in the empty case.
% 
% Third and finally, we have to paint the \bground{} of non-merged
% \Scfnote{}s because the painting is left by \!\pcol@makeflushedpage! for
% this macro.  Therefore, if $\!\pcol@fnheight@lpage!>0$ to mean we have
% footnotes whose total height-plus-depth is in the macro, we paint their
% \bground{} by \!\pcol@bg@paintbox! \!\def!ining \!\pcol@bg@footnoteheight!
% with the size and temporarily re\!\def!ining \!\pcol@bg@textheight! to be
% the height-plus-depth of \!\@outputbox!  because the foontnotes are at the
% bottom of the box instead of the page.  Note that the order of painting is
% right first and then left second if we have \parapag{}es because we refer
% the height-plus-depth of \!\@outputbox! being put into the main vertical
% list making the box $\bot$.  Also note that if the right \parapag{}e is
% \npaired, we temporarily increment \!\c@page! in \!\pcol@rightpage! to let
% \!\pcol@bg@paintbox! handle \bginfext{} to side margins correctly.
% Another remark is that we don't modify $\pd=\!\@pagedp!$ and thus it keeps
% $\DP$ in this case, and $f_{sp}$ is kept $\false$.
% 
% \changes{v1.3-3}{2013/09/17}
%	{Add background painting of page-wise footnotes.}
% 
%    \begin{macrocode}
    \else
      \global\pcol@havelastpagetrue
      \@tempdima\ht\@outputbox \advance\@tempdima\dp\@outputbox
      \xdef\pcol@bg@preposttop@left{\number\@tempdima sp}%
      \ifnum\pcol@ncolleft<\pcol@ncol
        \global\let\pcol@bg@preposttop@right\pcol@bg@preposttop@left
      \fi
      \def\pcol@bg@textheight{\@elt{\ht\@outputbox}\@elt{\dp\@outputbox}}%
      \def\reserved@a{%
        \ifdim\pcol@fnheight@lpage>\z@
          \def\pcol@bg@footnoteheight{\@elt\pcol@fnheight@lpage}%
          \pcol@bg@paintbox{Nn}%
        \fi}%
      \ifnum\pcol@ncolleft<\pcol@ncol
        \global\setbox\pcol@rightpage\vbox{%
          \ifpcol@paired\else \advance\c@page\@ne \fi
          \reserved@a \unvbox\pcol@rightpage}%
      \fi
      \topskip\z@ \vbox{\reserved@a \unvbox\@outputbox}%
    \fi
  \fi
%    \end{macrocode}
% 
% Now we have put almost everything in the \lpage{} but we may still have
% \Scfnote{}s in $\pp^f(\ptop)$ to be merged with those in \postenv.
% Therefore, we \!\insert! them through \!\footins! as a part of \postenv,
% and then do that for deferred footnotes in $\df=\!\pcol@topfnotes!$
% without using \!\pcol@deferredfootins! because we don't need the height
% capping.
% 
% \changes{v1.2-2}{2013/05/11}
%	{Add insertion of page-wise footnotes to be merged.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% 
%    \begin{macrocode}
  \ifvoid\pcol@footins\else
    \pcol@Log\pcol@output@end{insert}\pcol@footins
    \pcol@Fb
    \insert\footins{\unvbox\pcol@footins}\@cons\@freelist\pcol@footins
    \pcol@Fe{output@end(pagefn)}%
  \fi
  \ifvoid\pcol@topfnotes\else \insert\footins{\unvbox\pcol@topfnotes}\fi
%    \end{macrocode}
% 
% The following operationss are for clean-up and set-up for the \postenv;
% for all c, return $\cc_c(\vb)$ obtained by \!\pcol@getcurrcol! and
% $\Celt^c\neq\bot$ letting it $\bot$ to \!\@freelist!; reestablish the
% \colorstack{} by \!\pcol@restorecolorstack! for column-0\footnote{
% 
% It can be any other column.}
% 
% so that the \colorstack{} is just $\cst$ and is rewinded at \Endparacol,
% and let $\cst=\bot$; reload $\cc_d$ for $d=\!\pcol@lastcol!$ being the
% column in which \Endparacol{} occurs to let $\!\everypar!=\cc_d(\ep)$ and
% to let \CSIndex{if@nobreak} and \CSIndex{if@afterindent} have the value
% represented by $\cc_d(\sw)$, so that the first paragraph of the \postenv{}
% is typeset following them\footnote{
% 
% For rare cases that the last item of the closing environment is a
% sectioning command, but a user has such very unusual usage.};
% 
% let $\!\pcol@prevdepth!=\pd$ so that it is set to \!\prevdepth! by
% \!\pcol@invokeoutput!; let $\!\@colht!=\!\@colroom!=\!\textheight!$ to
% mean the single-column page does not have any floats so far because those
% produced in or before the environment have already been shipped out, are
% put to the main vertical list packed in \!\@outputbox!, or are in
% \!\@dbldeferlist!.
% 
% As for deferred \pwise{} floats produced in the environment, including
% those once put in the \lpage{} but returned to the list by the operation
% described above, we move them to \!\@deferlist! because they are now
% \cwise{} floats.  Then we invoke \!\pcol@floatplacement! to
% reinitialize float placement parameters.  Finally, if $f_{\it sp}=\true$,
% we invoke \!\@startcolumn! and then repeat invocations of \!\@opcol! and
% \!\@startcolumn! while \fpage{}s are produced, after letting
% $\CSIndex{ifpcol@lastpage}=\false$ to make \!\@combinefloats! work as
% \LaTeX's original\footnote{
% 
% Letting $\!\pcol@textfloatsep!=\infty$ is done by \!\pcol@floatplacement!.}.
% 
% \changes{v1.2-1}{2013/05/11}
% 	{Add color resetting.}
% \changes{v1.31}{2013/10/10}
%	{Add \cs{pcol@getcurrcol} for the column specified by
%	 \cs{pcol@lastcol} to pass \cs{if@nobreak}, \cs{if@afterindent} and
%	 \cs{everypar} of the column to post-environment stuff.}
% \changes{v1.32-2}{2015/10/10}
% 	{Add \cs{pcol@Fb}/\cs{pcol@Fe} pair(s).}
% \changes{v1.34}{2018/05/07}
%	{Remove nullification of $\gamma_0^0$ because it is not meaningless
%	 now, add release of $\gamma_0^c\NEQ\bot$ and then nullification of
%	 it for all $c$, move color stack reestablishment down to the loop
%	 with $c$ to ensure $\gamma_0^0\EQ\bot$, and add nullification of
%	 $\mathit{\Gamma}$.}
% 
%    \begin{macrocode}
  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
    \pcol@Fb
    \pcol@getcurrcol \@cons\@freelist\@currbox
    \ifvoid\pcol@ccuse{@box}\else
      \@cons\@freelist{\pcol@ccuse{@box}}%
      \pcol@ccxdef{\voidb@x}%
    \fi
    \pcol@Fe{output@end(col)}%
   \advance\pcol@currcol\@ne}%
  \pcol@currcol\z@ \pcol@restorecolorstack
  \global\setbox\pcol@colorins\box\voidb@x
  \pcol@currcol\pcol@lastcol\relax \pcol@getcurrcol
  \global\pcol@prevdepth\@pagedp
  \global\@colht\textheight
  \global\@colroom\textheight
  \global\let\@deferlist\@dbldeferlist \gdef\@dbldeferlist{}%
  \pcol@floatplacement
  \pcol@lastpagefalse
  \if@tempswa
    \@startcolumn \@whilesw\if@fcolmade\fi{\@opcol\@startcolumn}%
  \fi
  \pcol@Logend\pcol@output@end
}

%    \end{macrocode}
% \end{macro}
% 
% 
% 
% \section{Starting Environment}
% \label{sec:imp-startenv}
% 
% \begin{macro}{\pcol@invokeoutput}
% \changes{v1.0}{2011/10/10}
%	{Let \cs{pcol@prevdepth} have \cs{prevdepth} directly instead of via
%	 \cs{tempdima}.}
% \changes{v1.2-2}{2013/05/11}
%	{Add logging.}
% \changes{v1.2-5}{2013/05/11}
%	{Move the setting of \cs{linewidth} and \cs{hsize} from
%	 \cs{pcol@getcurrcol} to this macro and add \cs{parshape}.}
% \changes{v1.21}{2013/06/06}
%	{Add zero-clearing of \cs{deadcycles}.}
% 
% Before giving the definition of \env{paracol} environment and commands
% used in it, we define the macro $\!\pcol@invokeoutput!\arg{pen}$ invoked
% from them to make an \!\output!-request with \!\penalty! of
% $\arg{pen}=|\pcol@op@|{\cdot}f$.  The macro's structure is similar to that
% for the request sequence in \!\end@float! as follows; insert a \!\penalty!
% of $-10004$ to save the main vertical list in \!\@holdpg!; save
% \!\prevdepth!; insert a \!\vbox! to make it sure the following \!\penalty!
% of $\arg{pen}$ is kept even when we are at the top of a page; and finally
% restore \!\prevdepth!.
% 
% A difference is that we zero-clear \!\deadcycles! because it can be reach
% $\!\maxdeadcycles!=100$ easily if a page has many \sync{}ations and many
% columns.  Another and more important difference is in the save\slash
% restore of \!\prevdepth!.  First, the value of the register is saved in
% our own \!\pcol@prevdepth! instead of \!\@tempdima! by a \!\global!
% assignment so that \!\output!-routine refers to it\footnote{
% 
% The assignment is not necessary to be done \!\global!ly but we dare to do
% it to make all assignments to \!\pcol@prevdepth! being \!\global!
% consistently.}.
% 
% Second, the value restored to \!\prevdepth! may be different from that we
% just have saved because \!\output!-routine may update \!\pcol@prevdepth!
% to have, for example, the value saved in $\cc_c(\pd)$ when we left from
% $c$ which we are now restarting.
% 
% In addition to above, after the invocatoin of \!\output!-routine, we let
% $\!\linewidth!=\w_c-\lrm$ so that the register is shrunk from $\w_c$ by the
% total width of left and right margins of the \env{list}-like environment
% surrounding \env{paracol} if $\lrm=\!\pcol@lrmargin!>0$ to mean that.
% Then if so, we set \!\parshape! to let every line of paragraphs in the
% column $c$ is indented by \!\@totalleftmargin! and has width of
% \!\linewidth!, as \LaTeX's \!\list!  does.  We also let $\!\hsize!=\w_c$
% because it should have the width of the column even in a \env{list}-like
% environment.
% 
% The macro is invoked from \!\pcol@zparacol! ($f=|start|$),
% \!\pcol@switchcol! for \!\switch~column! and \csenv{}s ($f=|switch|$),
% \!\pcol@visitallcols! for \cscan{} prior to \sync{}ed \cswitch{} and page
% flushing ($f=|switch|$), \!\pcol@flushclear! for \pfcheck{}
% ($f=|switch|$), \!\pcol@com@flushpage!  for \!\flushpage! ($f=|flush|$),
% \!\pcol@com@clearpage! for \!\clearpage!  ($f=|clear|$), and
% \!\endparacol!  ($f=|end|$).
% \SpecialIndex{\pcol@op@start}
% \SpecialIndex{\pcol@op@switch}
% \SpecialIndex{\pcol@op@flush}
% \SpecialIndex{\pcol@op@clear}
% \SpecialIndex{\pcol@op@end}
% 
%    \begin{macrocode}
%% Starting Environment

\def\pcol@invokeoutput#1{\deadcycles\z@
  \pcol@Logstart{\pcol@invokeoutput
    {#1:\the\pcol@currcol/\the\pcol@nextcol%
     \ifnum#1=-10011:\ifpcol@sync s\fi \ifpcol@clear c\fi\fi}}%
  \penalty-\@Miv \global\pcol@prevdepth\prevdepth \vbox{}%
  \penalty#1\relax \prevdepth\pcol@prevdepth
  \linewidth\columnwidth \advance\linewidth-\pcol@lrmargin
  \ifdim\pcol@lrmargin>\z@ \parshape\@ne\@totalleftmargin\linewidth \fi
  \hsize\columnwidth
  \pcol@Logend{\pcol@invokeoutput{#1}}}

%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{2}
% \begin{macro}{\paracol}
% \changes{v1.0}{2011/10/10}
%	{Change the order of operations for sake of clarity.}
% \changes{v1.0}{2011/10/10}
%	{Add the mechanism of inter-environment local counter conservation.}
% \changes{v1.0}{2011/10/10}
%	{Let $\cs{col@number}\EQ1$ instead of $C$ to keep \cs{maketitle} from
%	 producing title with \cs{twocolumn}.}
% \changes{v1.0}{2011/10/10}
%	{Add initialization of \cs{pcol@textfloatsep}, \cs{ifpcol@lastpage},
%	 \cs{pcol@firstprevdepth} and \cs{@combinefloats}.}
% \changes{v1.0}{2011/10/10}
%	{Make API commands environment-local and inhibit nesting of
%	 \texttt{paracol}.} 
% \changes{v1.3-2}{2013/09/17}
%	{Modify to add the optinal argument $C_L$ and optional
%	 `\string\texttt{*}' for parallel-paging.}
% \begin{macro}{\pcol@xparacol}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced to let $C_L\EQ C$ if the optional argument $C_L$ is not
%	 given to \cs{paracol}.}
% \begin{macro}{\pcol@yparacol}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced to process the optional `\string\texttt{*}' given with
%	 the optioal argument $C_L$ of \cs{paracol}.}
% \begin{macro}{\pcol@zparacol}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced to add the optinal argument $C_L$ and optional
%	 `\string\texttt{*}' to \cs{paracol} for parallel-paging and to do
%	 what had done by \cs{paracol}.}
% 
% The API macro $\!\paracol!|[|\CL|][*]|\Arg{\C}$\oarg{text} is invoked by
% \beginparacol{} to start a \Midx{\env{paracol}} environment.  The macro
% sipmly examines the existence of the optional argument $\CL$, whose
% default value $\C$ is given by \!\pcol@xparacol!, to decide the
% number of columns in left \parapag{}es.  Then if the optional argument is
% given, \!\pcol@yparacol! examines the existence of `|*|' following it for
% \npaired{} \parapag{}ing to let $\CSIndex{ifpcol@paired}=\false$, while
% \!\paracol! gave the default $\true$ for \paired{} one to the switch.
% Then the all other operations to start the environment is doen by
% \!\pcol@zparacol!.
% 
%    \begin{macrocode}
\def\paracol{\global\pcol@pairedtrue \@ifnextchar[%]
  \pcol@yparacol\pcol@xparacol}
\def\pcol@xparacol#1{\pcol@zparacol[#1]{#1}}
\def\pcol@yparacol[#1]{%
  \@ifstar{\global\pcol@pairedfalse \pcol@zparacol[#1]}%
          {\pcol@zparacol[#1]}}
%    \end{macrocode}
% 
% In \!\pcol@zparacol!, after making it sure to be in vertical mode by
% \CSIndex{par}, at first we examine if we are neither in a box by
% \CSIndex{ifinner} nor with ordinary two-column typesetting by
% \CSIndex{if@twocolumn}, and complain about inappropriateness unless our
% expectation is satisfied.  Then we let $\CL$ and $\C$ have the value given
% through the corresponding arguments, unless $\CL>\C$ to let us make
% $\CL=\C$ silently.  Next we examine $\CL<\C$, and if not we let
% $\CSIndex{ifpcol@paired}=\true$ regardless the setting in
% \!\pcol@yparacol! because \npaired{} typesetting is meaningless without
% \parapag{}ing.  On the other hand, if \npaired{} typesetting is specified,
% we let $\CSIndex{ifpcol@swapcolumn}={\false}$ but {\em not} \!\global!ly
% because \cswap{} is meaningless in \npaired{} mode in the environment now
% starting.
% 
% Second, we perform the operations done by \!\item! if
% $\CSIndex{if@newlist}=\true$ and $\CSIndex{if@inlabel}\~=\false$ to mean
% the first one in a \env{list}-like environment will appear at the very
% first line of the leftmost column.  That is, we invoke \!\@nbitem! if
% $\CSIndex{if@nobreak}=\true$, or add a penalty \!\@beginparpenalty! and a
% vertical skip $\!\@topsep!-\!\parskip!-\!\itemsep!$ so that the first
% \!\item! is \!\@topsep! apart from the last line above the environment,
% and then let $\CSIndex{if@newlist}=\false$.  The reason why we do these
% operations here is that, if the \env{paracol} environment is enclosed in a
% \env{list}-like environment without anything between two \!\begin! for
% environments, we have to align all first \!\item!s in all columns.  That
% is, if we did not do that, the {\em literally first} \!\item! would do
% that resulting in the column having the \!\item! led by the vertical skip
% of \!\@topsep! while others should have ordinary inter-\!\item! skips.
% Therefore, we perform the operations on behalf of all first \!\item!s in
% all columns to have the skip of \!\@topsep! {\em above} the \env{paracol}
% environment we are opening.  Note that if \beginparacol{} immediately
% follows a \!\begin! for a \env{trivlist}-like environment,
% $\CSIndex{if@inlabel}=\true$ because the first \!\item! was given in the
% opening macro and thus the operations shown above has already been
% performed.
% 
% \changes{v1.3-6}{2013/09/17}
%	{Add operations for the vertical skips at the beginning of a
%	 \texttt{list}-like environment.}
% \changes{v1.35-6}{2018/12/31}
% 	{Add error check with \cs{ifinner} and \cs{if@twocolumn}.}
% \changes{v1.35-2}{2018/12/31}
% 	{Add $\lnot$\cs{if@inlabel} to the condition to perform operations
%	 for first \cs{item}.}
% 
%    \begin{macrocode}
\def\pcol@zparacol[#1]#2{\par
  \ifinner \@parmoderr \fi
  \if@twocolumn \PackageError{paracol}{%
    Environment paracol cannot work with ordinary two-column
    typesetting.}\@ehb\fi
  \global\pcol@ncolleft#1\relax \global\pcol@ncol#2\relax
  \ifnum\pcol@ncolleft>\pcol@ncol \global\pcol@ncolleft\pcol@ncol \fi
  \ifnum\pcol@ncolleft<\pcol@ncol\else \global\pcol@pairedtrue \fi
  \ifpcol@paired\else \pcol@swapcolumnfalse \fi
  \if@newlist \if@inlabel\else
    \if@nobreak \@nbitem
    \else
      \addpenalty\@beginparpenalty
      \addvspace\@topsep
      \addvspace{-\parskip}\addvspace{-\itemsep}%
    \fi
    \global\@newlistfalse
  \fi\fi
%    \end{macrocode}
% 
% The third operation group is to set up lists for counters as follows.
% First we obtain $\CC=\!\cl@@ckpt!$ to have all counters defined by
% \!\newcounter! and \counter{page}.  Then we scan $\CG=\!\pcol@gcounters!$
% applying \!\pcol@remctrelt! to each element to have
% $\CTL=\!\pcol@counters!$ for all \lcounter{}s by removing all $\cg\in\CG$
% from $\CC$, and to move $\clist(\cg)=|\cl@|{\cdot}\cg$ to
% $|\pcol@cl@|{\cdot}\cg$ redefining
% $|\cl@|{\cdot}\cg=\!\pcol@stepcounter!\Arg{\cg}$
% 
% \SpecialArrayIndex{\theta}{\cl@}
% 
% to clear descendant \lcounter{}s of $\cg$, i.e., those in $\clist(\cg)$.
% 
% Next we scan $\CTL$ applying \!\pcol@thectrelt! to each element $\cl\in\CTL$
% to let $|\pcol@thectr@|{\cdot}\~\cl=|\the|{\cdot}\cl$
% 
% \SpecialArrayIndex{\theta}{\pcol@thectr@}
% \SpecialArrayIndex{\theta}{\the}
% 
% so that the former has the {\em default} \lrep{} of $\cl$.  The macro
% \!\pcol@thectrelt! also lets
% $|\the|{\cdot}\cl=|\pcol@thectr@|{\cdot}\cl{\cdot}0$
% 
% \SpecialArrayIndex{\theta{\cdot}c}{\pcol@thectr@}
% \SpecialArrayIndex{\theta}{\the}
% 
% if the \lrep{} for $\cl$ and $c=0$ has been defined by
% \!\definethecounter!.  This is necessary because in the first visit to the
% leftmost column 0 we will neither invoke \!\pcol@switchcol! nor thus scan
% $\CTL$ with \!\pcol@setctrelt! which defines \lrep{}s, unless a \mctext{}
% is specified with \beginparacol.
% 
% Next we give the initial value of $\val_c(\cl)$ for each column $c$ and
% \lcounter{} $\cl\in\CTL$ by the followings enclosed in a group.  First we
% scan $\Cc_0$ applying \!\pcol@loadctrelt! to each
% $\cl\in\Cc'_0=\Set{\theta}{\<\theta,\val_0(\theta)\>\in\Cc_0}$ to have
% the value $\val_0(\cl)$ in $|\pcol@ctr@|{\cdot}\cl$
% 
% \SpecialArrayIndex{\theta}{\pcol@ctr@}
% 
% temporarily.  Next we scan $\CTL$ to pick \lcounter{}s $\theta$ such that
% $\Uidx\Val(\theta)\neq\val_0(\theta)$ where $\Val(\theta)$ is the value of
% $\theta$ outside \env{paracol} environment, or $\theta\notin\Cc'_0$, to
% let them be listed in \!\@gtempa!.  That is, we pick \lcounter{}s which
% have been updated or defined after the closing of the previous
% \env{paracol}, or everything in $\CTL$ at the first \beginparacol{} because
% $\Cc_0=\emptyset$\footnote{
% 
% Undefined in fact.}.
% 
% Finally, we invoke \!\pcol@synccounter! giving it \!\@gtempa! as its
% argument to let $\val_c(\theta)=\Val(\theta)$ for all $c$ and for each
% $\theta$ in \!\@gtempa!.  That is, when \env{paracol} environment appears
% two or more times, the value of a \lcounter{} at the beginning of the
% second or succeeding environment is kept unchanged from that at the end of
% the previous environment, unless it has been updated between them.  Note
% that these scans above are enclosed in a group in order to make
% $|\pcol@ctr@|{\cdot}\cl$
% 
% \SpecialArrayIndex{\theta}{\pcol@ctr@}
% 
% local and thus collected as a garbage at \!\endgroup!.
% 
%    \begin{macrocode}
  \global\let\pcol@counters\cl@@ckpt
  \let\@elt\pcol@remctrelt \pcol@gcounters
  \let\@elt\pcol@thectrelt \pcol@counters
  \begingroup
    \let\@elt\pcol@loadctrelt \csname pcol@counters0\endcsname
    \let\@elt\pcol@cmpctrelt \global\let\@gtempa\@empty \pcol@counters
    \pcol@synccounter\@gtempa
  \endgroup
%    \end{macrocode}
% 
% Fourth, we set up a few \LaTeX's typesetting parameters which should have
% appropriate values in the environment.  We let
% $\CSIndex{if@twocolumn}=\true$ so that \textit{float}|*| environments work
% for \pwise{} floats and LaTeX's \!\@addmarginpar! determine the margin
% for marginal notes by \CSIndex{if@firstcolumn} whose truth value is
% determined by our own \!\@addmarginpar!.  We also let $\!\col@number!=1$
% instead of $\C$ so that its (almost surely) sole user \!\maketitle! will
% not produce the title with \!\twocolumn! which cannot be in the
% environment.
% 
% Then we invoke $\!\pcol@setcolumnwidth!\<\Cfrom\>\<\Cto\>\<r\>\<s\>$ once
% or twice with
% $(\Cfrom,\Cto,r,s)=(0,\CL,\!\pcol@columnratioleft!,\!\pcol@colwidthspecleft!)$
% always for left \parapag{}e, and with
% $(\CL,\C,\!\pcol@columnratioright!,\!\pcol@colwidthspecright!)$ for right
% one if $\CL<\C$ to define column widths $\w_c=|\pcol@columnwidth|{\cdot}c$
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% 
% and that of \csepgap{}s $\gap_c=|\pcol@columnsep|{\cdot}c$
% 
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
% for all $c\In0\C=\LBRP0\CL\cup\LBRP\CL\C$.
% 
% Then we initialize other variables as follows;
% $\lrm=\!\pcol@lrmargin!=\!\textwidth!-\!\linewidth!$ so that, if $\lrm>0$,
% \!\linewidth! for $c$ has $\w_c-\lrm$ reflecting the paragraph shape of the
% \env{list}-like environment surrounding \env{paracol} environment;
% $\!\pcol@topskip!=\!\topskip!$ for the second and succeeding pages;
% $\!\pcol@textfloatsep!=\infty$ to mean we don't have any \sync{}ation
% points so far; $\CSIndex{ifpcol@lastpage}=\false$ because the \spage{} is
% not the last so far; and $\!\pcol@firstprevdepth!=\!\prevdepth!$ in
% decimal integer form for the extreme empty case.
% 
% We also make the macro \!\@combinefloats! \!\let!-equal to our own
% \!\pcol@combinefloats!  throughout the environment, after saving its
% original definition into \Midx{\!\pcol@@combinefloats!} for processing
% \!\output! request sneaked from outsied of environment, so that our
% customization is in effect for any invocations including those from
% \LaTeX's own macros.  Similarly, \!\@addmarginpar! is made \!\let!-equal
% to our own \!\pcol@addmarginpar!  while its orginal definition is saved
% into \!\pcol@@addmarginpar! but in this case we need the original for the
% implementaion of our own.  On the other hand, \!\end@dblfloat! is simply
% replaced with our own \!\pcol@end@dblfloat! being what \LaTeX{} had had until
% 2014 as discussed in item-(\ref{item:ovv-float-end@dblfloat}) of
% \secref{sec:imp-ovv-float}.
% 
% \changes{v1.1}{2012/05/11}
% 	{Replace the calculation of \cs{columnwidth} with the call of
%	 \cs{pcol@setcolumnwidth} and the assignment of $w_0$ to it.}
% \changes{v1.2-4}{2013/05/11}
%	{Modify the setting of \cs{if@firstcolumn} according to
%	 column-swapping.}
% \changes{v1.2-5}{2013/05/11}
%	{Remove the setting \cs{columnwidth}, \cs{hsize} and \cs{linewidth}
%	 because they are properly set in and after \cs{pcol@output@start}.}
% \changes{v1.2-5}{2013/05/11}
%	{Add the setting of \cs{pcol@lrmargin}.}
% \changes{v1.2-7}{2013/05/11}
%	{Add the saving of \cs{@combinefloats}.}
% \changes{v1.3-4}{2013/09/17}
%	{Revise the mechanism to define the width of columns and
%	 column-separating gaps, and add local overriding definition of
%	 \cs{@addmarginpar}.}
% \changes{v1.3-2}{2013/09/17}
%	{Add operations to define the width of columns and column-separating
%	 gaps in right parallel-pages.}
% \changes{v1.32-3}{2015/10/10}
% 	{Add replacement of \cs{end@dblfloat} with \cs{pcol@end@dblfloat}.}
% 
%    \begin{macrocode}
  \global\@twocolumntrue \col@number\@ne
  \pcol@setcolumnwidth\z@\pcol@ncolleft
    \pcol@columnratioleft\pcol@colwidthspecleft
  \ifnum\pcol@ncolleft<\pcol@ncol
    \pcol@setcolumnwidth\pcol@ncolleft\pcol@ncol
      \pcol@columnratioright\pcol@colwidthspecright
  \fi
  \pcol@lrmargin\textwidth \advance\pcol@lrmargin-\linewidth
  \global\pcol@topskip\topskip
  \global\pcol@textfloatsep\maxdimen
  \pcol@lastpagefalse \xdef\pcol@firstprevdepth{\number\prevdepth}%
  \let\pcol@@combinefloats\@combinefloats \let\@combinefloats\pcol@combinefloats
  \let\pcol@@addmarginpar\@addmarginpar \let\@addmarginpar\pcol@addmarginpar
  \let\end@dblfloat\pcol@end@dblfloat
%    \end{macrocode}
%
% Fifth, we save the original definition of \!\set@color! into
% \!\pcol@set@color!, and then examine if $\!\set@color!\neq\!\relax!$
% meaning some coloring package is loaded.  If any coloring packages are not
% loaded, we make macros for \bgpaint{}, namely \!\pcol@bg@paintpage!,
% \!\pcol@bg@paintcolumns! and \!\pcol@bg@paintbox!, \!\let!-equal to
% \!\relax! for the first two and to \!\@gobble! for the last so that they do
% nothing without coloring package.
% 
% If the coloring is enabled, on the other hand, we redefine \LaTeX's
% \!\set@color!  so that it works as \!\pcol@set@color@push!  with
% \colorstack.  We also prepare the text colring mechanism to let
% $\CSIndex{ifpcol@inner}=\true$ in every \!\vbox! in the \env{paracol}
% environment as follows.  First, we let $\CSIndex{ifpcol@inner}=\false$
% because we are not in any \!\vbox!es obviously.  Then, to use
% \!\everyvbox! for our own pupose, we do the followings; (1) \!\global!ly
% assign a token \Midx{\!\pcol@dummytoken!}, which should never occurs, to
% \!\pcol@everyvbox!; (2) save \!\everyvbox!  into \!\pcol@everyvbox!
% locally; (3) let \!\everyvbox! have a \!\the!-reference to
% \!\pcol@everyvbox! and |\pcol@innerture| to let
% $\CSIndex{ifpcol@inner}={\true}$; and then (4) make \!\everyvbox!
% \!\let!-equal to \!\pcol@everyvbox!.  By the last operation (4), any
% \!\everyvbox! appearing in the \env{paracol} environment is replaced with
% \!\pcol@everyvbox! to keep the real \!\everyvbox! from modified nullifying
% our own operation |\pcol@innertrue|.  On the other hand, since both
% \!\everyvbox!  and \!\pcol@everyvbox! are registers to hold tokens and
% thus any operations applicable to \!\everyvbox! are also applicable to
% \!\pcol@everyvbox!, any updates on \!\everyvbox! and explicit references
% to it are simulated by \!\pcol@everyvbox!.  Then the initial tokens given
% to \!\pcol@everyvbox!  by the saving operation (2) or tokens given inside
% the environment are correctly processed whenever a \!\vbox! is opened,
% toghether with |\pcol@innertrue| to fulfill our own purpose, because the
% real \!\everyvbox! is let have a \!\the!-reference to \!\pcol@everyvbox!
% by (3).  We also reserve the invocation of \!\pcol@restoreeveryvbox! by
% \!\aftergroup! so that the macro is invoked just after \Endparacol{} to
% examine if any \!\global! assignments to \!\everyvbox! has been made in
% the environment.  The funny \!\global!  assignment (1) is done for this
% examination so that we detect global assignments done in the environment
% having been closed because they should have changed the global value of
% \!\pcol@everyvbox! to something different from \!\pcol@dummytoken!.
% 
% Then we continue the case having some coloring package to make \bgpaint{}
% macros \!\pcol@bg@paintpage!, \!\pcol@bg@paintbox! and
% \!\pcol@bg@paintcolumns! activated by making them \!\let!-equal to thier
% |@@| counterparts namely \!\pcol@bg@@paintpage!, \!\pcol@bg@@paintbox! and
% \!\pcol@bg@@paintcolumns! which implement \bgpaint{}.
% 
% Finally we empty the shadow \colorstack{}
% $\cstshadow={}$\!\pcol@colorstack@shadow!  to give it initial value
% regardless of the availability of coloring package.
% 
% \changes{v1.2-1}{2013/05/11}
% 	{Add redefinitions of \cs{set@color} and \cs{reset@color}.}
% \changes{v1.22}{2013/06/30}
% 	{Add a trick with \cs{everyvbox} to turn on \cs{ifpcol@inner} in
%	 every \cs{vbox}.}
% \changes{v1.22}{2013/06/30}
% 	{Move initial emptying of $\string\mathit{\Gamma}$ from
%	 \cs{pcol@output@start} to \cs{pcol@zparacol}.}
% \changes{v1.22}{2013/06/30}
% 	{Add initial emptying of $\string\hat{\mathit{\Gamma}}$ and $\chi$.}
% \changes{v1.3-3}{2013/09/17}
%	{Add definition of painting macros dependent to the availability of
%	 a coloring package.}
% \changes{v1.34}{2018/05/07}
%	{Remove the initializations of \cs{pcol@colorstack} and
%	 \cs{pcol@colorstack@buf} because they no longer exist.}
% 
%    \begin{macrocode}
  \global\let\pcol@set@color\set@color
  \ifx\set@color\relax
    \let\pcol@bg@paintpage\relax \let\pcol@bg@paintbox\@gobble
    \let\pcol@bg@paintcolumns\relax
  \else
    \let\set@color\pcol@set@color@push
    \pcol@innerfalse
    \global\pcol@everyvbox{\pcol@dummytoken}%
    \pcol@everyvbox\everyvbox
    \everyvbox{\the\pcol@everyvbox \pcol@innertrue}
    \let\everyvbox\pcol@everyvbox
    \aftergroup\pcol@restoreeveryvbox
    \let\pcol@bg@paintpage\pcol@bg@@paintpage
    \let\pcol@bg@paintbox\pcol@bg@@paintbox
    \let\pcol@bg@paintcolumns\pcol@bg@@paintcolumns
  \fi
  \gdef\pcol@colorstack@shadow{}%
%    \end{macrocode}
% 
% \changes{v1.2-2}{2013/05/11}
% 	{Add initialization of \cs{pcol@footnotebase} and
%	 \cs{pcol@nfootnotes}, and redefinitions of \cs{footnote},
%	 \cs{footnotemark}, \cs{footnotetext} and \cs{@footnotetext}.}
% 
% The sixth settings are for (mainly \mcfnote) footnotes.  We initialize two
% footnote-related count registers letting $\bf=\!\pcol@footnotebase!$ have
% \!\c@footnote! and zero-clearing $\nf=\!\pcol@nfootnotes!$.  Then we
% redefine \LaTeX's API macros \!\footnote!, \!\footnotemark! and
% \!\footnotetext! to let them be our own \!\pcol@footnote!,
% \!\pcol@footnotemark! and \!\pcol@footnotetext! so that they have
% starred-versions.  The other API macro to be redefined, if \Scfnote{}
% typesetting is in effect, is \!\footnoterule!  which lets
% $\!\columnwidth!=\!\textwidth!$ before invoking its original version saved
% in \!\pcol@footnoterule! so that it acts as in single-columned typesetting
% rateher than multi-columned.  Then we redefine \LaTeX's internal macro
% \!\@footnotetext! letting it be our own \!\pcol@fntext! for encapsulating
% a footnote in a \!\vbox! and for deferred \!\insert!ion with \Scfnote{}
% typesetting.
% 
%    \begin{macrocode}
  \pcol@footnotebase\c@footnote \global\pcol@nfootnotes\z@
  \let\footnote\pcol@footnote
  \let\footnotemark\pcol@footnotemark
  \let\footnotetext\pcol@footnotetext
  \ifpcol@scfnote
    \def\footnoterule{{\columnwidth\textwidth \pcol@footnoterule}}%
  \fi
  \let\@footnotetext\pcol@fntext
%    \end{macrocode}
% 
% Seventh, we let \!\marginpar!, \!\@mn@@marginnote! and \!\@xympar! be our
% own versions \!\pcol@marginpar!, \!\pcol@marginnote! and \!\pcol@xympar!
% respectively for the emulation of \!\marginnote!, saving the original
% version of the first and third into \!\pcol@@marginpar! and
% \!\pcol@@xympar!.  Then we inactivate API macros \!\twosided! and
% \!\footnotelayout!  together with their backward-compatible macros
% \!\swapcolumninevenpages!, \!\noswapcolumnineven~pages!,
% \!\multi~columnfootnotes!, \!\singlecolumnfootnotes! and
% \!\mergedfootnotes!, so that they commonly invoke \!\pcol@ignore! because
% their inherent operations turning corresponding switches are harmful in
% \env{paracol} environment.  Note that the inactivation of \!\twosided! is
% done by redefinition of \!\pcol@twosided! because we need optional
% argument processing by \!\twosided! even when it is inactivated.
% 
% \changes{v1.2-4}{2013/05/11}
%	{Add nullificaion of \cs{[no]swapcolumninevenpages}.}
% \changes{v1.2-2}{2013/05/11}
%	{Add nullificaton of API macros of footnote typesetting definition.}
% \changes{v1.3-3}{2013/09/17}
%	{Add new API inactivation for \cs{pcol@twosided}.}
% \changes{v1.3-4}{2013/09/17}
%	{Add new API inactivation for \cs{pcol@twosided}.}
% \changes{v1.3-5}{2013/09/17}
%	{Add new API inactivation for \cs{footnotelayout}.}
% \changes{v1.35-3}{2018/12/31}
% 	{Add local modifications of \cs{marginpar}, \cs{@mn@@marginnote} and
%	 \cs{@xympar} for the emulation of \cs{marginnote}.}
% 
%    \begin{macrocode}
  \let\pcol@@marginpar\marginpar \let\marginpar\pcol@marginpar
  \let\@mn@@marginnote\pcol@marginnote
  \let\pcol@@xympar\@xympar \let\@xympar\pcol@xympar
  \def\pcol@twosided[#1]{\pcol@ignore\twosided}%
  \def\swapcolumninevenpages{\pcol@ignore\swapcolumninevenpages}%
  \def\noswapcolumninevenpages{\pcol@ignore\noswapcolumninevenpages}%
  \def\footnotelayout#1{\pcol@ignore\footnotelayout}%
  \def\multicolumnfootnotes{\pcol@ignore\multicolumnfootnotes}%
  \def\singlecolumnfootnotes{\pcol@ignore\singlecolumnfootnotes}%
  \def\mergedfootnotes{\pcol@ignore\mergedfootnotes}%
%    \end{macrocode}
% 
% Eigth, we scan the list \!\pcol@localcommands! of $\arg{com}$ being the
% name of commands, e.g., |switchcolumn|, available only in the environment
% or customized for the environment, applying \!\pcol@defcomelt! to each
% $\arg{com}$ to let $|\|\arg{com}=|\pcol@com@|{\cdot}\arg{com}$
% 
% \SpecialArrayMainIndex{\<\string\mathit{com}\>}{\pcol@com@}
% 
% the latter of which is the real implementation of the former.  Note that
% the list does not have all \elocal{} API commands but we omit
% \!\column!(|*|) for \env{column}(|*|) environments because their
% implementations \!\pcol@com@column!(|*|) are modified after the first
% invocation.  Therefore, we \!\def!ine \!\column!(|*|) to have
% \!\pcol@com@column!(|*|) in their bodies\footnote{
% 
% We can do this for other commands instead of adhearing to \cs{let} to
% eliminate the execption, but the author loves to use \cs{let} as much as
% possible.}.
% 
% We also give the first \!\def!initions of
% \!\pcol@com@column!(|*|) to let them do nothing but re\!\def!ine
% themselves by \!\pcol@defcolumn! unless
% \!\pcol@com@column*! is given an optional \mctext{} argument which is
% directly processed by \!\pcol@sptext!, if they appear as the first
% \cswitch{} command\slash environment after \beginparacol.  Then we
% re\!\def!ine \!\paracol! itself so that it will complain of illegal
% nesting by \!\PackageError!.
% 
%    \begin{macrocode}
  \let\@elt\pcol@defcomelt \pcol@localcommands
  \def\column{\pcol@com@column}%
  \@namedef{column*}{\@nameuse{pcol@com@column*}}%
  \global\let\pcol@com@column\pcol@defcolumn
  \global\@namedef{pcol@com@column*}{\pcol@defcolumn
    \@ifnextchar[%]
     \pcol@sptext\relax}%
  \def\paracol##1{\PackageError{paracol}{%
    Environment paracol cannot be nested.}\@eha}%
%    \end{macrocode}
% 
% Ninth, we let \!\output! have our output routine \!\pcol@output! as its sole
% token, and then make \!\output! request with
% $\!\penalty!=\!\pcol@op@start!$ by \!\pcol@invokeoutput! to invoke
% \!\pcol@output@start! for initialization, after letting
% $\!\@elt!=\!\relax!$ to make it sure that any lists can be manipulated
% without unexpected application of a macro to their elements.
% 
%    \begin{macrocode}
  \output{\pcol@output}%
  \let\@elt\relax
  \pcol@invokeoutput\pcol@op@start
%    \end{macrocode}
% 
% Tenth and finally, we let $\!\pcol@nextcol!=0$ in case \beginparacol{} has
% the optional argument for \mctext{}, and invoke \!\pcol@sptext! if it has.
% Otherwise, we invoke $|\pcol@colpream|{\cdot}0$ being the \colpream{} of
% the first column 0, which will be invoked by \!\pcol@switchcol! if
% \mctext{} is given.
% 
% \SpecialArrayIndex{c}{\pcol@colpream}
% 
% \changes{v1.35-5}{2018/12/31}
% 	{Add the invocation of $\cs{pcol@colpream}{\cdot}0$.}
% 
%    \begin{macrocode}
  \pcol@nextcol\z@
  \@ifnextchar[%]
    \pcol@sptext{\@nameuse{pcol@colpream0}}}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@paracol}
% The macro \!\pcol@paracol! has the definition of \!\paracol!, which is
% redefined in the macro itself, so that the only referrer
% \!\pcol@icolumncolor! examines if it appears in \env{paracol}, i.e.,
% $\!\pcol@paracol!\neq\!\paracol!$.
% 
%    \begin{macrocode}
\let\pcol@paracol\paracol

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\thecolumn}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced to let users know which column they are working in.}
% 
% The API macro \!\thecolumn! gives the value of \!\pcol@currcol! to users
% to let them know which column they are working in so that, for example,
% they do some column-dependent opreations.
% 
%    \begin{macrocode}
\def\thecolumn{\number\pcol@currcol}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@ignore}
% \changes{v1.2-4}{2013/05/11}
%	{Introduced for nullificaion of \cs{[no]swapcolumninevenpages}.}
% \changes{v1.2-2}{2013/05/11}
%	{Introduced for nullificaton of API macros of footnote typesetting
%	 definition.}
% 
% The macro \!\pcol@ignore!$\arg{macro}$ is to complain that the
% $\arg{macro}$ being one of the followings appears in \env{paracol}
% environment.
% 
% \begin{itemize}\raggedright\item[]
% \!\twosided!,
% \!\swapcolumninevenpages!,
% \!\noswapcolumninevenpages!,
% \!\footnotelayout!,
% \!\multicolumnfootnotes!,
% \!\singlecolumnfootnotes!,
% \!\mergedfootnotes!
% \end{itemize}
% 
% That is, these macros, except for \!\twosided!, are re\!\def!ined in
% \!\pcol@zparacol! to invoke this macro with the argument identifying
% themselves, which is shown in the warning message given by
% \!\PackageWarning!.  As for \!\twosided!, the target of the
% re\!\def!inition is \!\pcol@twosided! so that its optional argument is
% captured before the complaint.
% 
%    \begin{macrocode}
\def\pcol@ignore#1{\PackageWarning{paracol}{The command \string#1 is not
  effective in paracol environment and thus ignored}}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@localcommands}
% \changes{v1.0}{2011/10/10}
%	{Introduced to make API commands environment-local.}
% \changes{v1.3-5}{2013/09/17}
%	{Add \cs{@elt}\string\texttt{\char`\{cleardoublepage\char`\}} for
%	 \cs{cleardoublepage}.} 
% 
% The macro \!\pcol@localcommands! is the list of the names of the following
% {\em\Uidx\elocal} API commands (or {\em\Uidx\lcommand{}s} in short) and is
% solely referred to by \!\pcol@zparacol!.
% 
% \begin{center}\begin{tabular}{llll}
% \!\switchcolumn!&
% \!\endcolumn!(|*|)&
% \!\nthcolumn!(|*|)&\!\endnthcolumn!(|*|)\\
% \!\leftcolumn!(|*|)&\!\endleftcolumn!(|*|)&
% \!\rightcolumn!(|*|)&\!\endrightcolumn!(|*|)\\
% \!\flushpage!&
% \!\clearpage!&
% \!\cleardoublepage!\\
% \!\synccounter!&
% \!\syncallcounters!
% \end{tabular}\end{center}
% 
% Note that we omit \!\column!(|*|) from the list as discussed in the
% description of \!\pcol@zparacol!.
% 
%    \begin{macrocode}
\def\pcol@localcommands{%
  \@elt{switchcolumn}%
  \@elt{endcolumn}\@elt{endcolumn*}%
  \@elt{nthcolumn}\@elt{endnthcolumn}\@elt{nthcolumn*}\@elt{endnthcolumn*}%
  \@elt{leftcolumn}\@elt{endleftcolumn}\@elt{leftcolumn*}\@elt{endleftcolumn*}%
  \@elt{rightcolumn}\@elt{endrightcolumn}%
    \@elt{rightcolumn*}\@elt{endrightcolumn*}%
  \@elt{flushpage}\@elt{clearpage}\@elt{cleardoublepage}%
  \@elt{synccounter}\@elt{syncallcounters}}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@defcomelt}
% \changes{v1.0}{2011/10/10}
%	{Introduced to make API commands environment-local.}
% 
% The macro \!\pcol@defcomelt! is invoked solely from \!\pcol@zparacol! to be
% applied to each element $\arg{com}$ in \!\pcol@localcommands!.  Two
% lengthy \!\let!s with \!\expandafter!s are for doing
% $\!\let!|\|\arg{com}|=\pcol@com@|{\cdot}\arg{com}$ to bind the \elocal{}
% API command $|\|\arg{com}$ and its implementation
% $|\pcol@com@|{\cdot}\arg{com}$.
% 
% \SpecialArrayIndex{\<\string\mathit{com}\>}{\pcol@com@}
% 
%    \begin{macrocode}
\def\pcol@defcomelt#1{%
  \expandafter\let\expandafter\reserved@a\csname pcol@com@#1\endcsname
  \expandafter\let\csname #1\endcsname\reserved@a}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\@dbldeferlist}
% \changes{v1.32-3}{2015/10/10}
% 	{Add top-level definition in case that future \LaTeX{} removes it at
%	 all.}
% \begin{macro}{\pcol@end@dblfloat}
% \changes{v1.32-3}{2015/10/10}
% 	{Added to go back to old mechanism.}
% As discussed in \secref{sec:imp-ovv-float}, 2015 version of \LaTeX{}
% no longer uses \!\@dbldeferlist! but the macro itself is still kept in
% \LaTeX{}.  However it will be removed in future to make the first
% \!\@cons! with it resulting in an error.  Therefore, here we have its top
% level definition with empty duplicatedly in case of its future
% elimination.  The macro \!\end@dblfloat!, on the other hand, is replaced
% with a new definition in the new \LaTeX{} of course, and thus we define
% \!\pcol@end@dblfloat! here to keep its old definition and to replace the
% new one in \env{paracol} environment as discussed in
% item-(\ref{item:ovv-float-end@dblfloat}) of \secref{sec:imp-ovv-float}.
% 
%    \begin{macrocode}
\gdef\@dbldeferlist{}
\def\pcol@end@dblfloat{%
  \if@twocolumn
    \@endfloatbox
    \ifnum\@floatpenalty <\z@
      \@largefloatcheck
      \@cons\@dbldeferlist\@currbox
    \fi
    \ifnum \@floatpenalty =-\@Mii \@Esphack\fi
  \else
    \end@float
  \fi
}
%    \end{macrocode}
% \end{macro}\end{macro}
% 
% 
% 
% \KeepSpace{6}
% \section{Column Width Setting}
% \label{sec:imp-cwidth}
% \changes{v1.3-4}{2013/09/17}
%	{Add the secion ``Column Width Setting'' mainly to discuss the new
%	 API \cs{setcolumnwidth}.}
% 
% \begin{macro}{\columnratio}
% \changes{v1.1}{2012/05/11}
% 	{Introduced to specify column width fractions.}
% \changes{v1.3-2}{2013/09/17}
%	{Add optional second argument for fractions in right
%	 parallel-pages.} 
% \begin{macro}{\pcol@icolumnratio}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced to process the optional second argument of
%	 \cs{columnratio}.}
% \begin{macro}{\pcol@columnratioleft}
% \changes{v1.1}{2012/05/11}
% 	{Introduced to keep column width fractions.}
% \changes{v1.3-2}{2013/09/17}
%	{Renamed from \cs{pcol@columnratio} to clarify it has fractions for
%	 left parallel-pages.}
% \begin{macro}{\pcol@columnratioright}
% \changes{v1.3-2}{2013/09/17}
%	{Introduced to keep column width fractions for right
%	 parallel-pages.}
% 
% The API macro $\!\columnratio!
% \Arg{r^l_0,r^l_1,\cdots,r^l_{k^l-1}}|[|r^r_0,r^r_1,\cdots,r^r_{k^r-1}|]|$
% defines the column width fraction $r^l_c$ for column $c$ in left
% \parapag{}es and optionally $r^r_c$ for those in right \parapag{}es.  This
% macro and its callee \!\pcol@icolumnratio! just \!\global!y \!\def!ine
% macros \!\pcol@columnratioleft! and \!\pcol@columnratioright!  whose
% bodies have the first and second arguments respectively, or commonly have
% the first if the second optional one is not given, so that they are given
% to \!\pcol@setcolwidth@r! as its third argument through
% \!\pcol@setcolumnwidth! invoked in \!\pcol@zparacol!.  Both of
% \!\pcol@columnratioleft! and \!\pcol@columnratioright! are initialized to
% be empty so that all columns have same width and are separated by
% \!\columnsep! as default.  Note that \!\pcol@columnratioleft! can be made
% \!\let!-equial to \!\relax! by the related API macro \!\setcolumnwidth! so
% that \!\pcol@setcolumnwidth! knows which of specifications given by two
% API macros is effective and chooses \!\pcol@setcolwidth@r! or
% \!\pcol@setcolwidth@s!.
% 
%    \begin{macrocode}
%% Column Width Setting

\def\columnratio#1{\global\let\pcol@colwidthspecleft\relax
  \gdef\pcol@columnratioleft{#1}%
  \@ifnextchar[%]
    \pcol@icolumnratio{\gdef\pcol@columnratioright{#1}}}
\def\pcol@icolumnratio[#1]{\gdef\pcol@columnratioright{#1}}
\columnratio{}\relax

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{2}
% \begin{macro}{\setcolumnwidth}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to specify column widths and column-separating gaps more
%	 detailedly.}
% \begin{macro}{\pcol@isetcolumnwidth}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to process the optional second argument of
%	 \cs{setcolumnwidth}.}
% \begin{macro}{\pcol@colwidthspecleft}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to keep column width specifications for left
%	 parallel-pages.}
% \begin{macro}{\pcol@colwidthspecright}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to keep column width specifications for right
%	 parallel-pages.}
% 
% The API macro $\!\setcolumnwidth!
% \Arg{s^l_0,s^l_1,\cdots,s^l_{k^l-1}}|[|s^r_0,s^r_1,\cdots,s^r_{k^r-1}|]|$
% defines the column width specification $s^l_c$ for column $c$ in left
% \parapag{}es and optionally $s^r_c$ for those in right \parapag{}es, where
% each specification $s^x_c$ has the form of $|[|w_c|][/[|g_c|]]|$ for width
% and gap specifier $\w_c$ and $\gap_c$.  After \!\let!ting
% $\!\pcol@columnratioleft!=\!\relax!$ to disable the setting by
% \!\columnratio! and to enable that done by this macro, the macro and its
% callee \!\pcol@isetcolumnwidth! just \!\global!y \!\def!ine macros
% \!\pcol@colwidthspecleft! and \!\pcol@colwidthspecright!  whose bodies have
% the first and second arguments respectively, or commonly have the first if
% the second optional one is not given, so that they are given to
% \!\pcol@setcolwidth@s! as its fourth argument through
% \!\pcol@setcolumnwidth! invoked in \!\pcol@zparacol!.  Both of
% \!\pcol@colwidthspecleft! and \!\pcol@colwidthspecright! are initially
% undefined because the default specification is given by
% \!\columnratio!|{}|.
% 
%    \begin{macrocode}
\def\setcolumnwidth#1{\global\let\pcol@columnratioleft\relax
  \gdef\pcol@colwidthspecleft{#1}%
  \@ifnextchar[%]
    \pcol@isetcolumnwidth{\gdef\pcol@colwidthspecright{#1}}}
\def\pcol@isetcolumnwidth[#1]{\gdef\pcol@colwidthspecright{#1}}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@setcolumnwidth}
% \changes{v1.3-4}{2013/09/17}
%	{Move original functions to \cs{pcol@setcolumnwidth@r} and redefine
%	 this macro to switch \cs{pcol@setcolumnwidth@r} and
%	 \cs{pcol@setcolumnwidth@s}.}
% 
% \begin{Sloppy}{1500}
% The macro $\!\pcol@setcolumnwidth!\<\Cfrom\>\<\Cto\>\arg{ratio}\arg{spec}$
% is invoked solely from \!\pcol@zparacol! but can be twice, with;
% $$
% (\Cfrom,\Cto,\arg{ratio},\arg{spec})=
%   (0,\CL,\!\pcol@columnratioleft!,\!\pcol@colwidthspecleft!)
% $$
% always and with;
% $$
% (\Cfrom,\Cto,\arg{ratio},\arg{spec})=
%   (\CL,\C,\!\pcol@columnratioright!,\!\pcol@colwidthspecright!)
% $$
% if $\CL<\C$ for \parapag{}ing.  The macro simply invokes
% \!\pcol@setcolwidth@s! if $\!\pcol@columnratioleft!=\!\relax!$ because
% \!\setcolumnwidth! did so, or \!\pcol@setcolwidth@r! otherwise, with all
% arguments given by \!\pcol@zparacol!.
% \end{Sloppy}
% 
%    \begin{macrocode}
\def\pcol@setcolumnwidth{%
  \ifx\pcol@columnratioleft\relax \let\reserved@a\pcol@setcolwidth@s
  \else                           \let\reserved@a\pcol@setcolwidth@r
  \fi
  \reserved@a}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@setcolwidth@r}
% \changes{v1.1}{2012/05/11}
% 	{Introduced to calculate $w_c$.}
% \changes{v1.3-4}{2013/09/17}
%	{Renamed from \cs{pcol@setcolumnwidth} to make it clear what the
%	 marco works for.}
% \changes{v1.3-2}{2013/09/17}
%	{Add arguments $C^0$, $C^1$, $\langle\string\mathit{ratio}\rangle$
%	 and $\langle\string\mathit{spec}\rangle$ for columns in right
%	 parallel-pages.}
% \changes{v1.3-3}{2013/09/17}
%	{Add setting of $g_c\EQ\cs{pcol@columnsep}{\cdot}c=\cs{columnsep}.}
% 
% \begin{Hfuzz}{0.3pt}%
% The macro $\!\pcol@setcolwidth@r!\<\Cfrom\>\<\Cto\>\arg{ratio}\arg{spec}$
% is invoked solely from \!\pcol@zparacol! through \!\pcol@setcolumnwidth!
% once or twice with the arguments described in the explanation of the
% latter macro.  The macro calculates $\w_c=|\pcol@columnwidth|{\cdot}c$
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% 
% for all $c\In\Cfrom\Cto$, from the fractions $r_0$, $r_1$, \ldots,
% $r_{k-1}$ given through the third argument $\arg{ratio}$, which was given
% to \!\columnratio! and then kept in \!\pcol@columnratioleft! or
% \!\pcol@columnratioright!.  The macro also lets
% $\gap_c=|\pcol@columnsep|{\cdot}c=\!\columnsep!$
% 
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
% for all $c\In\Cfrom\Cto$.
% \end{Hfuzz}
% 
% First, we calculate $W=\!\textwidth!-(\Cto-\Cfrom-1)\times\!\columnsep!$
% being the sum of $\w_c$ for all $c\In\Cfrom\Cto$.  Then we let
% $\w_c=r_d{}W$ and $\gap_c=\!\columnsep!$ for all $c\In\Cfrom{k'}$ where
% $k'=\min(k,\Cto-1)$, in the \!\@for! loop scanning $r_d$ for all
% $d=c-\Cfrom\In0k$.  Finally, we let
% $\w_c=(W-\sum_{d=\Cfrom}^{k'-1}w_d)/(\Cto-\Cfrom-k')$ and
% $\gap_c=\!\columnsep!$ for all $c\In{k'}\Cto$.  Note that
% $|\pcol@columnwidth|{\cdot}c$ and $|\pcol@columnsep|{\cdot}c$ are macros
% having the integer representations of $\w_c$ and $\gap_c$ with the unit
% |sp|.
% 
%    \begin{macrocode}
\def\pcol@setcolwidth@r#1#2#3#4{%
  \@tempcntb#2\advance\@tempcntb-#1\advance\@tempcntb\m@ne
  \@tempdima-\columnsep \multiply\@tempdima\@tempcntb
  \advance\@tempdima\textwidth \@tempdimb\@tempdima
  \@tempcnta#1\relax\@tempcntb#2\advance\@tempcntb\m@ne
  \@for\reserved@a:=#3\do{%
    \ifnum\@tempcnta<\@tempcntb
      \@tempdimc\reserved@a\@tempdima
      \expandafter\xdef\csname pcol@columnwidth\number\@tempcnta\endcsname{%
        \number\@tempdimc sp}%
      \global\@namedef{pcol@columnsep\number\@tempcnta}{\columnsep}%
      \advance\@tempdimb-\@tempdimc
      \advance\@tempcnta\@ne
    \fi}%
  \@tempcntb#2\advance\@tempcntb-\@tempcnta
  \divide\@tempdimb\@tempcntb
  \@whilenum\@tempcnta<#2\do{%
    \expandafter\xdef\csname pcol@columnwidth\number\@tempcnta\endcsname{%
      \number\@tempdimb sp}%
    \global\@namedef{pcol@columnsep\number\@tempcnta}{\columnsep}%
    \advance\@tempcnta\@ne}%
}

%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{3}
% \begin{macro}{\pcol@setcolwidth@s}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to calculate $w_c$ and $g_c$.}
% \begin{macro}{\pcol@setcw@c}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to process column width components in the argument
%	 $\langle\string\mathit{spec}\rangle$ of \cs{pcol@setcolwidth@s}.}
% \begin{macro}{\pcol@setcw@s}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to process column-separating gap components in the
%	 argument $\langle\string\mathit{spec}\rangle$ of
%	 \cs{pcol@setcolwidth@s}.}
% \begin{macro}{\pcol@setcw@filunit}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to define the unit of infinite stretch factors in the
%	 argument $\langle\string\mathit{spec}\rangle$ of
%	 \cs{pcol@setcolwidth@s}.}
% 
% \begin{Hfuzz}{0.3pt}%
% The macro $\!\pcol@setcolwidth@s!\<\Cfrom\>\<\Cto\>\arg{ratio}\arg{spec}$
% is invoked solely from \!\pcol@zparacol! through \!\pcol@setcolumnwidth!
% once or twice with the arguments described in the explanation of the
% latter macro.  The macro calculates $\w_c=|\pcol@columnwidth|{\cdot}c$
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% 
% for all $c\In\Cfrom\Cto$ and $\gap_c=|\pcol@columnsep|{\cdot}c$
% 
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
% for all $c\In\Cfrom{\Cto{-}1}$, from the column\slash gap specifications
% $s_0$, $s_1$, \ldots, $s_{k-1}$ given through the fourth argument
% $\arg{spec}$, which was given to \!\setcolumnwidth! and then kept in
% \!\pcol@colwidthspecleft! or \!\pcol@colwidthspecright!.
% \end{Hfuzz}
% 
% Each specification $s_d$ for $\w_c$ and $\gap_c$ where $c=\Cfrom+d$ has
% the form $|[|w'_d|][/[|g'_d|]]|$ to specify the natural width $w^n_d$ and
% $g^n_d$ and inifite stretch factor $w^f_d$ and $g^f_d$ of column\slash gap
% sepcfication as follows;
% 
% \begin{eqnarray*}
% w^n_d&=&\cases{0&$w'_d=\emptyset$\cr
%                0&$w'_d=f\!\fill!$\cr
%                \mathit{natural}(w'_d)&otherwise}\qquad
% w^f_d = \cases{1&$w'_d=\emptyset$\cr
%                f&$w'_d=f\!\fill!$\cr
%                \mathit{stretch}(w'_d)&otherwise}\\[1ex]
% g^n_d&=&\cases{\!\columnsep!&$g'_d=\emptyset$\cr
%                0&$g'_d=f\!\fill!$\cr
%                \mathit{natural}(g'_d)&otherwise}\qquad
% g^f_d = \cases{0&$g'_d=\emptyset$\cr
%                f&$g'_d=f\!\fill!$\cr
%                \mathit{stretch}(g'_d)&otherwise}
% \end{eqnarray*}
% 
% where $\mathit{natural}(x)$ is the natural width of the skip $x$ and
% $\mathit{stretch}(x)$ is the infinite stretch factor of $x$.  Note that
% any finite stretch factors or any shirnk factors do not affect them, and
% infinite strech units |fil|, |fill| and |filll| are not distinguished.
% From factors above, we determine $w_c$ and $\gap_c$ as follows;
% 
% \begin{eqnarray*}
% W&=&\sum_{d=0}^{m-2}(w^n_d+g^n_d)+w^n_{m-1}\\
% F&=&\sum_{d=0}^{m-2}(w^f_d+g^f_d)+w^f_{m-1}\\
% x_c&=&\cases{(\WT/W)x^n_{c-\Cfrom}&$W\geq\WT\;\lor\;F\leq0$\cr
%              x^n_{c-\Cfrom}+(x^f_{c-\Cfrom}/F)(\WT-W)&$W<\WT\;\land\;F>0$}
%     \qquad(x\in{\w,\gap})
% \end{eqnarray*}
% where $\WT=\!\textwidth!$ and $m=\Cto-\Cfrom$.
% 
% To perform the assignments above, the macro at first invoke
% $\!\pcol@setcw@scan!\<\Cfrom\>\<\Cto\>\~\ARg{spec}$ letting
% $\!\pcol@setcw@c!=\!\pcol@setcw@s!=\!\pcol@setcw@accumwd!$ and
% \!\pcol@setcw@filunit!${}=1$\,pt to scan $s_d$ for all $d\In0{m}$ and to
% accumulate $W+g^n_{m-1}$ and $F+g^f_{m-1}$ in \!\dimen@! and \!\dimen@ii!
% and then subtract $g^n_{m-1}$ and $g^f_{m-1}$ from them to have $W$ and
% $F$.  Note that $F$ is represented by a dimension with the unit of pt by
% the definition of \!\pcol@setcw@filunit!.  Then we invoke
% \!\pcol@setcw@calcfactors! to calculate $(\WT/W)=\!\pcol@setcw@scale!$ and
% $(\WT-W)/F=\!\@tempdimb!$.  Finally we scan $s_d$ again but in this case
% we let $\!\pcol@setcw@c!=\!\pcol@setcw@set!|{width}|$,
% $\!\pcol@setcw@s!=\!\pcol@setcw@set!|{sep}|$ and
% $\!\pcol@setcw@filunit!=\!\@tempdimb!=(\WT-W)/F$ to let $w_c$ and $\gap_c$
% have the values shown above.
% 
%    \begin{macrocode}
\def\pcol@setcolwidth@s#1#2#3#4{\begingroup
  \dimen@\z@ \dimen@ii\z@ \def\pcol@setcw@filunit{\@ne\p@}%
  \let\pcol@setcw@c\pcol@setcw@accumwd \let\pcol@setcw@s\pcol@setcw@accumwd
  \pcol@setcw@scan#1#2{#4}%
  \advance\dimen@-\@tempdima \advance\dimen@ii-\@tempdimb
  \pcol@setcw@calcfactors
  \def\pcol@setcw@c{\pcol@setcw@set{width}}%
  \def\pcol@setcw@s{\pcol@setcw@set{sep}}%
  \let\pcol@setcw@filunit\dimen@ii
  \pcol@setcw@scan#1#2{#4}%
  \endgroup}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@setcw@scan}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to scan the argument
%	 $\langle\string\mathit{spec}\rangle$ of \cs{pcol@setcolwidth@s}.}
% 
% The macro $\!\pcol@setcw@scan!\<\Cfrom\>\<\Cto\>\~\ARg{spec}$ is to scan
% first $m=\Cto-\Cfrom$ elements in $\arg{spec}=s_0,s_1,\ldots$ being the
% column\slash gap specifications given to \!\setcolumnwidth!.  At first we
% add `,' as many as $m$ to the tail of $\arg{spec}$ to make it sure the
% resulting $\arg{spec}$ has $m$ or more elements.  Then we scan all
% elements in the extended $\arg{spec}$ by a \!\@for! loop having many
% \!\expandafter! but equivalent to;
% 
% \begin{quote}
% |\@for\reserved@a:=|$s_0,s_1,\ldots$|\do{|\textit{body}|}|
% \end{quote}
% 
% In the \textit{body} above, we invoke
% $\!\pcol@setcw@getspec!\;s_i|//|\!\@nil!$ to parse $s_i$ to have $w^n_i$,
% $w^f_i$ to be processed by \!\pcol@setcw@c! and $g^n_i$ and $g^f_i$ by
% \!\pcol@setcw@s!, for all $i\In0m$.
% 
%    \begin{macrocode}
\def\pcol@setcw@scan#1#2#3{\def\reserved@a{#3}%
  \@tempcnta#1\relax \@whilenum\@tempcnta<#2\do{
    \edef\reserved@a{\reserved@a,}\advance\@tempcnta\@ne}%
  \@tempcnta#1\relax
  \expandafter\@for\expandafter\reserved@a\expandafter:\expandafter=\reserved@a
    \do{%
      \ifnum\@tempcnta<#2\relax
        \expandafter\pcol@setcw@getspec\reserved@a//\@nil
      \fi
      \advance\@tempcnta\@ne}}
%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\pcol@setcw@getspec}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to parse an element in the argument
%	 $\langle\string\mathit{spec}\rangle$ of \cs{pcol@setcolwidth@s}.}
% \begin{macro}{\pcol@setcw@getspec@i}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to parse an element in the argument
%	 $\langle\string\mathit{spec}\rangle$ of \cs{pcol@setcolwidth@s}.}
% \begin{macro}{\pcol@setcw@fill}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to extract \cs{fill} factor from an element in the
%	 argument  $\langle\string\mathit{spec}\rangle$ of
%	 \cs{pcol@setcolwidth@s}.}
% 
% The macro
% $\!\pcol@setcw@getspec!\<w'_d\>|/|\<g'_d\>|/|\arg{garbage}\!\@nil!$ is
% used solely in \!\pcol@setcw@scan! to parse a column\slash gap
% specification $s_d=|[|w'_d|][/[|g'_d|]]|$, to extract factors $w_d^n$,
% $w_d^f$, $g_d^n$ and $g_d^f$, and to process width factors by
% \!\pcol@setcw@c! and gap factors by \!\pcol@setcw@s!.  Since the macro is
% invoked with arguments in the form of $s_d|//|\!\@nil!$, if $s_d$ has
% `|/|' in it $w'_d$ and $g'_d$ should have everything preceeding and
% following the `|/|' respectively while $\arg{garbage}$ should have the
% redundant `|/|'.   Otherwise, i.e., if $s_d$ does not have `|/|',
% $w'_d=s_d$ and $g'_d=\emptyset$ while $\arg{garbage}=\emptyset$\footnote{
% 
% If $s_d$ have two or more `|/|', everything following the second one is
% thrown away into $\arg{garbage}$ together with `|//|'.  Therefore we could
% check if $s_d$ has at most one `|/|' by examining $\arg{garbage}$ but we
% abandon it simply ingoring $\arg{garbage}$.}.
% 
% Therefore, we invoke $\!\pcol@setcw@getspec@i!\arg{default}\Arg{x'_d}$ twice
% with $(\arg{default},x'_d)=(\!\fill!,w'_d)$ for a column and
% $(\arg{default},x'_d)=(\!\columnsep!,g'_d)$ for a gap, and \!\pcol@setcw@c!
% and \!\pcol@setcw@s! after each invocation respectively.
% 
% In this macro, at first we scan all tokens in $x'_d$ by \!\@tfor! to
% remove all space tokens in it\footnote{
% 
% A proper skip specification and ``$f\!\fill!$'' is always proper without
% space tokens in them.}.
% 
% Then if $x'_d$ after the space removal has nothing, we let
% $x'_d=\arg{default}$.  Next we examine if $x'_d=f\!\fill!$ in a trickey
% way by temporarily \!\let!ting $\!\@gtempa!=\!\relax!$, defining \!\fill!
% as ``|1pt|\!\gdef!\!\@gtempa!|{}|'' and making an assignment
% ``\!\@tempskipa!  $x'_d$''.  That is, if $x'_d=f\!\fill!$, \!\@tempskipa!
% will have $f{\cdot}|1pt|$ being a proper dimension and \!\@gtempa! is made
% empty.  Otherwise, \!\@tempskipa! should have $x'_d$ which must be a
% proper skip and \!\@gtempa! remains unchanged from \!\relax!.  Therefore,
% if $\!\@gtempa!=\!\relax!$ we let $\!\@tempskipa!=x'_d$ again\footnote{
% 
% Because the first assignment is done in a group.}.
% 
% Otherwise, we invoke $\!\pcol@setcw@fill!\;x'_d$ to let
% \!\@tempskipa! have $0\,|pt|\ |plus|\ f\,|fil|$ where $f$ is replaced by 1
% if $f=\emptyset$.
% 
% Now \!\@tempskipa! has $x_d^n$ as its natural component and may have some
% infinite strectch component $x_d^f$ specified explicitly or with \!\fill!.
% Therefore, we assign \!\@tempskipa! to \!\@tempdima! so that it has
% $x_d^n$, and then, after adding 0\,|pt| |plus| 1000\,|pt| |minus|
% 1000\,|pt| to \!\@tempskipa! to make it sure it has both strech and shrink
% components\footnote{
% 
% Almost sure becaues they could be $-1000$\,pt, but we ignore the
% possibility.}
% 
% keeping infinite stretch factor if any, invoke \!\pcol@extract@fil! giving
% it \!\the!-expansion of \!\@tempskipa! as the argument to let
% $\!\@tempdimb!=x_d^f\times\!\pcol@setcw@filunit!$.
% 
%    \begin{macrocode}
\def\pcol@setcw@getspec#1/#2/#3\@nil{%
  \pcol@setcw@getspec@i\fill{#1}\pcol@setcw@c
  \pcol@setcw@getspec@i\columnsep{#2}\pcol@setcw@s}
\def\pcol@setcw@getspec@i#1#2{%
  \def\reserved@a{}%
  \@tfor\reserved@b:=#2\do{\edef\reserved@a{\reserved@a\reserved@b}}
  \ifx\reserved@a\@empty \let\reserved@a#1\fi
  \let\@gtempa\relax
  {\def\fill{1\p@\gdef\@gtempa{}}\@tempskipa\reserved@a}%
  \ifx\@gtempa\relax \@tempskipa\reserved@a\relax
  \else \expandafter\pcol@setcw@fill\reserved@a
  \fi
  \@tempdima\@tempskipa
  \advance\@tempskipa0\p@\@plus\@m\p@\@minus\@m\p@\relax
  \expandafter\pcol@extract@fil\the\@tempskipa\@nil}
\def\pcol@setcw@fill#1\fill{\def\reserved@b{#1}%
  \ifx\reserved@b\@empty \let\reserved@b\@ne \fi
  \@tempskipa0\p@\@plus\reserved@b fil\relax}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@setcw@accumwd}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to accumulate natural and fill factors of the element in
%	 the argument $\langle\string\mathit{spec}\rangle$ of
%	 \cs{pcol@setcolwidth@s}.} 
% 
% The macro \!\pcol@setcw@accumwd! is made \!\let!-equal to \!\pcol@setcw@c!
% and \!\pcol@setcw@s! commonly and thus invoked from \!\pcol@setcw@getspec!
% with setting $\!\@tempdima!=x_d^n$ and $\!\@tempdimb!=x_d^f\times1\,|pt|$,
% where $x\in\{w,g\}$.  The macro simply add them to \!\dimen@! and
% \!\dimen@ii! repsectively to accumurate $x_d^n$ and $x_d^f$ in them.
% 
%    \begin{macrocode}
\def\pcol@setcw@accumwd{\advance\dimen@\@tempdima \advance\dimen@ii\@tempdimb}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@setcw@set}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to define $w_c$ and $g_c$ according to the element in
%	 the argument $\langle\string\mathit{spec}\rangle$ of
%	 \cs{pcol@setcolwidth@s}.} 
% 
% The macro $\!\pcol@setcw@set!\ARg{wors}$ is made the body of
% \!\pcol@setcw@c! with $\arg{wors}=|width|$ and of
% \!\pcol@setcw@s! with $\arg{wors}=|sep|$ and thus invoked from
% \!\pcol@setcw@getspec!  with setting $\!\@tempdima!=x_d^n$ and
% $$
% (\!\pcol@setcw@scale!,\!\@tempdimb!)
% \in\{(\emptyset,\,(x_d^f/F)(\WT-W)),\;(\WT/W,\,0)\}
% $$
% Therefore, we calculate
% $x_c=\!\pcol@setcw@scale!\times\!\@tempdima!+\!\@tempdimb!$ and
% \!\xdef!ine $|\pcol@column|{\cdot}\<wors\>{\cdot}c$ to let it have the
% integer representation of $x_c$ with the unit |sp|.
% 
% \SpecialArrayIndex{c}{\pcol@columnwidth}
% \SpecialArrayIndex{c}{\pcol@columnsep}
% 
%    \begin{macrocode}
\def\pcol@setcw@set#1{%
  \@tempdima\pcol@setcw@scale\@tempdima \advance\@tempdima\@tempdimb
  \expandafter\xdef\csname pcol@column#1\number\@tempcnta\endcsname{%
    \number\@tempdima sp}}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@setcw@calcfactors}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to caclulate scaling and stretch factors from
%	 the argument $\langle\string\mathit{spec}\rangle$ of
%	 \cs{pcol@setcolwidth@s}.} 
% \begin{macro}{\pcol@setcw@calcf}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to caclulate scaling or stretch factor from
%	 the argument $\langle\string\mathit{spec}\rangle$ of
%	 \cs{pcol@setcolwidth@s}.} 
% \changes{v1.31}{2013/10/10}
%	{Capitalize the first word of the error message for consistency.}
% \begin{macro}{\pcol@setcw@scale}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to have the scaling factor of $w_c$ and $g_c$.}
% 
% The macro \!\pcol@setcw@calcfactors! is used solely in
% \!\pcol@setcolwidth@s! to calculate $\phi_s=\!\pcol@setcw@scale!$ and
% $\phi_f=\!\dimen@ii!$ as follows
% $$
% (\phi_s,\phi_f)=\cases{(\WT/\W,\;0)& $W\geq\WT\;\lor\;F\leq0$\cr
%                        (1,\;(\WT-W)/F)&$W<\WT\;\land\;F>0$}
% $$
% where $W=\!\dimen@!$, $F\times1\,|pt|=\!\dimen@ii!$ and $\WT=\!\textwidth!$,
% and $\phi_s=1$ is represented by empty body of \!\pcol@setcw@scale!.
% First we deal with the special and trivial case of $W=\WT$ to let
% $\phi_s=1$ and $\phi_f=0$ so as to avoid arithmetic error in the
% calculation of $\WT/W$.  If $W\neq\WT$ on the other hand, we calculate
% $\WT/W$ by $\!\pcol@setcw@calcf!\<\WT\>\<W\>\<\phi_s\>$ to have a
% provisional result.  Then if $W<\WT$ and $F>0$, we let $\phi_s=1$ and
% invoke \!\pcol@setcw@calcf! again giving it $(\WT-W)$ and $F\times1\,|pt|$
% but throw away the result $(\WT-W)/(F\times1\,|pt|)$ because \!\@tempdimb!
% should have $(\WT-W)/F$ which is then set into $\phi_f=\!\dimen@ii!$.
% Otherwise, we keep the provisional result of $\phi_s$ as the final one and
% let $\phi_f=\!\dimen@ii!=0$.
% 
% The macro $\!\pcol@setcw@calcf!\<x\>\<y\>\<z\>$ caclulates $z\approx x/y$
% and let $\!\@tempdimb!=Z=z\times1\,|pt|$ as follows.  First we find the
% following three parameters.
% 
% \begin{eqnarray*}
% k_1&=&\min\Set{k}{k\geq0,\;x\cdot2^k\geq2^{13}\,|pt|}\\
% k_2&=&\max\Set{k}{y\bmod2^k=0}\\
% k_3&=&\min\Set{k}{k\geq0,\;\lceil y/2^{k_2+k}\rceil\leq2^{15}}
% \end{eqnarray*}
% 
% With these parameters, we calculate $z'=\lfloor(x\cdot2^{k_1})/\lceil
% y/2^{k_2+k_3}\rceil\rfloor$ to have a good approximation of
% $(x/y)\cdot2^{k}$ where $k=k_1+k_2+k_3$ without arithmetic overflow.  Then
% if $z'/2^k\geq2^{14}$ or in other words $Z$ is larger than \!\maxdimen!,
% we complain that by \!\PackageError! and, in case a user dare to
% continue the typesetting process, we let $Z=10000\,|pt|$.  Otherwise, we
% calculate $Z=(z'/2^k)\cdot2^{16}=z'\cdot2^{16-k}$ to have it in
% \!\@tempdimb! by $Z=z'\times2^{16-k}$ if $k<16$, or by $Z=z'/2^{k-16}$
% otherwise.  Finally we invoke \!\pcol@extract@pt! giving it
% \!\the!-representaion of $Z$ to have $z$.
% 
% Note that it is assured $z\leq x/y$ regardless of successfulness of the
% calculation and thus the scaling $\phi_s x_d^n$ and strething
% $x_d^n+\phi_f x_d^f$ cannot exceed their exact value to make it also sure
% that $\sum_{c=\Cfrom}^{\Cto-2}(\w_c+\gap_c)+\w_{\Cto-1}\leq\WT$ and thus
% the series of columns and \csepgap{}s should not cause overfull when a
% page is shipped out with \!\hfil! added to each \csepgap{} for underfull
% avoidance.
% 
%    \begin{macrocode}
\def\pcol@setcw@calcfactors{%
  \ifdim\dimen@=\textwidth \def\pcol@setcw@scale{}\dimen@ii\z@
  \else
    \pcol@setcw@calcf\textwidth\dimen@\pcol@setcw@scale
    \ifdim\dimen@<\textwidth \ifdim\dimen@ii>\z@
      \def\pcol@setcw@scale{}%
      \@tempdimc\textwidth \advance\@tempdimc-\dimen@
      \pcol@setcw@calcf\@tempdimc\dimen@ii\reserved@a \dimen@ii\@tempdimb
    \else \dimen@ii\z@ \fi
    \else \dimen@ii\z@ \fi
  \fi}
\def\pcol@setcw@calcf#1#2#3{%
  \@tempdimb#1\@tempdima#2\@tempcnta\z@
  \ifdim\@tempdima=\z@ \@tempdima1sp\relax\fi
  \@whiledim\@tempdimb<8192\p@\do{%
    \multiply\@tempdimb\tw@ \advance\@tempcnta\@ne}%
  \@tempdimc\@tempdima
  \@whiledim\@tempdima=\@tempdimc\do{%
    \divide\@tempdimc\tw@ \multiply\@tempdimc\tw@
    \ifdim\@tempdima=\@tempdimc
      \divide\@tempdima\tw@ \divide\@tempdimc\tw@ \advance\@tempcnta\@ne
    \fi}
  \advance\@tempdima-1sp\relax
  \@whilenum\@tempdima>32768\do{\divide\@tempdima\tw@ \advance\@tempcnta\@ne}%
  \advance\@tempdima1sp\relax
  \divide\@tempdimb\@tempdima \@tempdimc\@tempdimb \@tempcntb\@tempcnta
  \@whilenum\@tempcntb>\z@\do{\divide\@tempdimc\tw@ \advance\@tempcntb\m@ne}
  \ifnum\@tempdimc>16383\relax
    \PackageError{%
      Scaling/filling factor for column/gap width is too large.}\@eha
    \@tempdimb\@M\p@
  \else
    \@tempcntb\sixt@@n \advance\@tempcntb-\@tempcnta
    \ifnum\@tempcntb<\z@
      \@whilenum\@tempcntb<\z@\do{\divide\@tempdimb\tw@ \advance\@tempcntb\@ne}%
    \else
      \@whilenum\@tempcntb>\z@\do{%
        \multiply\@tempdimb\tw@ \advance\@tempcntb\m@ne}%
    \fi
  \fi
  \expandafter\pcol@extract@pt\the\@tempdimb#3}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{3}
% \begin{macro}{\pcol@defkw}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to define $\cs{pcol@kw@}{\cdot}k$ where
%	 $k\in\{\string\texttt{pt},\string\texttt{plus},\string\texttt{minus},
% 	 \string\texttt{fil}\}$.}
% \begin{macro}{\pcol@kw@pt}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to have the keyword \string\texttt{pt}.}
% \begin{macro}{\pcol@kw@plus}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to have the keyword \string\texttt{plus}.}
% \begin{macro}{\pcol@kw@minus}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to have the keyword \string\texttt{minus}.}
% \begin{macro}{\pcol@kw@fil}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to have the keyword \string\texttt{fil}.}
% 
% The macro
% $\!\pcol@defkw!|1.0|\arg{pt}\verb*| |\arg{plus}\verb*| 1.0|\arg{fil}
% \verb*| |\arg{minus}\verb*| 1.0|\arg{garbage}\!\@nil!$ is used just once at
% the top level to \!\def!ine \!\pcol@kw@pt!, \!\pcol@kw@plus!,
% \!\pcol@kw@minus! and \!\pcol@kw@fil! letting them have $\arg{pt}=|pt|$,
% $\arg{plus}=|plus|$, $\arg{minus}=|minus|$ and $\arg{fil}=|fil|$ in their
% body respectively but with $\!\catcode!=12$ (other) which is used in
% \!\the!-representation of glues.  For the definition, we invoke
% \!\pcol@defkw! giving it \!\the!-representation of \!\@tempskipa! letting
% it have $1\,|pt|\ |plus|\ 1\,|fil|\ |minus|\ 1\,|fil|$ having all keywards
% we need to have\footnote{
% 
% We can do what \!\pcol@defkw! does by temporarily giving $\!\catcode!=12$
% to the characters for the keywords of course, but this method is much
% easier.}.
% 
% The macro \!\pcol@kw@pt! is used in
% $\!\pcol@extract@fil@ii!\arg{unit}\!\@nil!$ to examine if
% $\arg{unit}=|pt|$, and in \!\pcol@def@extract@pt! to \!\def!ine
% \!\pcol@extract@pt! having |pt| in its argument specification.  The macros
% \!\pcol@kw@plus! and \!\pcol@kw@minus! are used only in
% \!\pcol@def@extract@fil!, and
% \!\pcol@kw@fil! only in \!\pcol@def@extract@fil@iii!, to \!\def!ine
% \!\pcol@extract@fil! having |plus| and |minus|, and
% \!\pcol@extract@fil@iii! having |fil|, in their argument specifications
% respectively.
% 
%    \begin{macrocode}
\@tempskipa 1\p@\@plus1fil\@minus1fil\relax
\def\pcol@defkw1.0#1 #2 1.0#3 #4 1.0#5\@nil{%
  \def\pcol@kw@pt{#1}\def\pcol@kw@plus{#2}\def\pcol@kw@fil{#3}%
  \def\pcol@kw@minus{#4}}
\expandafter\pcol@defkw\the\@tempskipa\@nil

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{4}
% \begin{macro}{\pcol@def@extract@fil}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to define \cs{pcol@extract@fil}.}
% \begin{macro}{\pcol@extract@fil}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to extract infinite stretch factor from a skip if any.}
% \begin{macro}{\pcol@extract@fil@i}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to extract the factor of \string\texttt{fil} from the
% 	 stretch factor in a skip if any.} 
% \begin{macro}{\pcol@extract@fil@ii}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to extract the factor of \string\texttt{fil} from the
% 	 stretch factor in a skip if any.} 
% \begin{macro}{\pcol@def@extract@fil@iii}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to define \cs{pcol@extract@fil@iii}.}
% \begin{macro}{\pcol@extract@fil@iii}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to extract the factor of \string\texttt{fil} from the
% 	 stretch factor in a skip.} 
% 
% The macro
% $\!\pcol@extract@fil!\<\mathit{garbge}_1\>\verb*| plus |\<s\>\verb*| minus|
% \<\mathit{garbage}_2\>\!\@nil!$ is used solely in \!\pcol@setcw@getspec@i!
% to extract the infinite stretch factor $f$ in the stretch component $s$ of
% a column\slash gap specification $x'_d$ and to let
% $\!\@tempdimb!=f\cdot{}u$ where
% $u=\!\pcol@setcw@filunit!\in\{1\,|pt|,\;\phi_f=\!\dimen@ii!\}$ if $f$
% exist or $\!\@tempdimb!=0$ otherwise.  First of all, since the macro has
% keywords |plus| and |minus| in $\!\catcode!=12$ in its argument
% specification, we \!\def!ine it using \!\pcol@def@extract@fil!, whose body
% is equivalent to
% 
% \begin{itemize}\item[]
% \let\@sverb\latex@sverb
% \verb*|\def\pcol@extract@fil#1 plus #2 minus#3\@nil|
% |{\pcol@extract@fil@i#2\@nil}|
% \end{itemize}
% 
% just once at the top level.  Then since $s$ should have the form
% $\<n\>|.|\<m\>\arg{unit}$ where $n$ and $m$ are decimal digit sequences and
% $\arg{unit}\in\{|pt|,|fil|,|fill|,|filll|\}$, we examine if
% $\arg{unit}=|pt|$ or not by a trickey way in
% $\!\pcol@extract@fil@i!\<n\>|.|\<m{\cdot}\mathit{unit}\>\!\@nil!$.  That
% is, we do $\!\count@!\<m{\cdot}\mathit{unit}\>\!\@nil!$ with
% \!\afterassignment! to invoke $\!\pcol@extract@fil@ii!\arg{unit}\!\@nil!$
% after $m$ is assigned to \!\count@! to capture $\arg{unit}$.  Then if it
% is |pt| we let $\!\@tempdimb!=0$, or otherwise invoke
% $\!\pcol@extract@fil@iii!\<f\>|fil|\arg{garbage}\!\@nil!$ giving it $s$
% because it should have a postfix being |fil|, |fill| or |filll|, to have
% $\!\@tempdimb!=f\cdot u$ finally.  Note that since
% \!\pcol@extract@fil@iii!  also has the keyword |fil| in its argument
% specification, we \!\def!ine it using \!\pcol@def@extract@fil@iii!, whose
% body is equivalent to
% 
% \begin{quote}
% \let\@sverb\latex@sverb
% \verb*|\def\pcol@extract@fil@iii#1fil#2\@nil{%|\\
% |    \@tempdimb\pcol@setcw@filunit\relax \@tempdimb#1\@tempdimb}|
% \end{quote}
% 
% just once at the top level too.
% 
%    \begin{macrocode}
\edef\pcol@def@extract@fil{%
  \def\noexpand\pcol@extract@fil
  ##1\space\pcol@kw@plus\space##2\space\pcol@kw@minus##3\noexpand\@nil{%
    \noexpand\pcol@extract@fil@i##2\noexpand\@nil}}
\pcol@def@extract@fil
\def\pcol@extract@fil@i#1.#2\@nil{\def\reserved@a{#1.#2}%
  \afterassignment\pcol@extract@fil@ii\count@#2\@nil}
\def\pcol@extract@fil@ii#1\@nil{\def\reserved@b{#1}%
  \ifx\reserved@b\pcol@kw@pt \@tempdimb\z@
  \else \expandafter\pcol@extract@fil@iii\reserved@a\@nil
  \fi}
\edef\pcol@def@extract@fil@iii{%
  \def\noexpand\pcol@extract@fil@iii##1\pcol@kw@fil##2\noexpand\@nil{%
    \@tempdimb\noexpand\pcol@setcw@filunit\relax \@tempdimb##1\@tempdimb}}
\pcol@def@extract@fil@iii

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@def@extract@pt}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to define \cs{pcol@extract@pt}.}
% \begin{macro}{\pcol@extract@pt}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to extract the factor of \string\texttt{pt} from the
%	 \cs{the} representaion of a dimension.}
% 
% The macro $\!\pcol@extract@pt!\<f\>|pt|\<scale\>$ is solely used in
% \!\pcol@setcw@calcf! to extract $f$ from a dimension in the form of
% $f|pt|$ and to let the macro $\<scale\>$ have $f$.  Since this macro has
% the keyword |pt| in its argument specification, we \!\def!ine it using
% \!\pcol@def@extract@pt!, whose body is equivalent to
% 
% \begin{quote}
% \let\@sverb\latex@sverb
% |\def\pcol@extract@pt#1pt#2{\def#2{#1}}|
% \end{quote}
% just once at the top level again.
% 
%    \begin{macrocode}
\edef\pcol@def@extract@pt{%
  \def\noexpand\pcol@extract@pt##1\pcol@kw@pt##2{\def##2{##1}}}
\pcol@def@extract@pt

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% 
% 
% \section{Counter Operations}
% \label{sec:imp-counter}
% 
% \begin{macro}{\globalcounter}
% \changes{v1.2-7}{2013/05/11}
% 	{Examine if the argument counter is already in
%	 $\string\mathit{\Theta}^g$ to avoid the duplicatoin in the list
%	 which caused a bug.}
% \changes{v1.32-1}{2015/10/10}
% 	{Modified according to the introduction of \cs{globalcounter*}.}
% \begin{macro}{\pcol@globalcounter@s}
% \changes{v1.32-1}{2015/10/10}
% 	{Added for \cs{globalcounter*}.}
% \begin{macro}{\pcol@globalcounter}
% \changes{v1.32-1}{2015/10/10}
% 	{Renamed from \cs{globalcounter} according to the introduction of
%	 \cs{globalcounter*}.}
% \begin{macro}{\pcol@gcounters}
% The API macro $\!\globalcounter!\ARg{ctr}$, implemented by
% \!\pcol@globalcounter! and also used in \!\pcol@fnlayout@p! to globalize the
% counter \counter{footnote}, defines that $\arg{ctr}$ is a \gcounter, and
% thus adds it to $\CG=\Midx{\!\pcol@gcounters!}$, which has \counter{page}
% at initial.  Note that we examines if $\arg{ctr}\in\CG$ prior to the
% addition to avoid the duplication in $\CG$.  Also note that initial
% definition of \!\pcol@gcounters! is done by \!\gdef! just for consistent
% \!\global!  assignments to it.  On the other hand \!\globalcounter!|*|,
% implemented by \!\pcol@globalcounter@s!, makes all counters kept in
% \!\cl@@ckpt! global by letting \!\pcol@gcounters! have the list.
% Switching these two functionality is done by \!\globalcounter! examining
% if it is followed by a |*| by \!\@ifstar!.
% 
%    \begin{macrocode}
%% Counter Operations

\def\globalcounter{\@ifstar\pcol@globalcounter@s\pcol@globalcounter}
\def\pcol@globalcounter@s{\global\let\pcol@gcounters\cl@@ckpt}
\def\pcol@globalcounter#1{{%
  \@tempswafalse \def\reserved@a{#1}%
  \def\@elt##1{\def\reserved@b{##1}%
    \ifx\reserved@a\reserved@b \@tempswatrue \fi}%
  \pcol@gcounters
  \if@tempswa\else \@cons\pcol@gcounters{{#1}}\fi}}
\gdef\pcol@gcounters{\@elt{page}}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\localcounter}
% \changes{v1.2-6}{2013/05/11}
%	{Introduced to remove the argument counter from
%	 $\string\mathit{\Theta}^g$.}
% 
% The API macro \!\localcounter!\marg{ctr}, also used in
% \!\pcol@fnlayout@c! to localize the counter \counter{footnote},
% declares that $\arg{ctr}$ is a \lcounter, and thus removes it from $\CG$
% by \!\pcol@removecounter! if $\arg{ctr}\neq\counter{page}$.
% 
%    \begin{macrocode}
\def\localcounter#1{%
  \expandafter\ifx\csname c@#1\endcsname\c@page\else
    \pcol@removecounter\pcol@gcounters{#1}%
  \fi}
%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\pcol@remctrelt}
% \changes{v1.2-6}{2013/05/11}
%	{Recode to use newly introduced \cs{pcol@removecounter}.}
% \begin{macro}{\pcol@removecounter}
% \changes{v1.2-6}{2013/05/11}
%	{Introduced for the counter removal operation in
%	 \cs{localcounter} and \cs{pcol@remctrelt}.}
% \begin{macro}{\pcol@iremctrelt}
% \changes{v1.2-6}{2013/05/11}
%	{Add the first argument $\string\mathit{\Theta}'$ as the counter
%	 list from which the second argument $\theta$ is removed.}
% 
% The macro $\!\pcol@remctrelt!\Arg\cg$ is invoked solely from
% \!\pcol@zparacol!  and is applied to each \gcounter{} $\cg\in\CG$ to
% remove it from $\CC=\!\pcol@counters!$ in which we have $\CTL$ finally.
% The macro also moves $|\cl@|{\cdot}\cg=\clist(\cg)$
% 
% \SpecialArrayIndex{\theta}{\cl@}
% 
% to $|\pcol@cl@|{\cdot}\cg$
% 
% \SpecialArrayMainIndex{\theta}{\pcol@cl@}
% 
% to keep the list of the descendant \lcounter{}s of $\cg$ in it, and then
% re\!\def!ines $|\cl@|{\cdot}\cg=\!\pcol@stepcounter!\Arg\cg$
% 
% \SpecialArrayMainIndex{\theta}{\cl@}
% 
% so that it is invoked on $\!\stepcounter!\Arg\cg$ to let $\val_c(\cl)=0$
% for all $c\In0\C$ and $\cl\in\clist(\cg)$, if $\cg\neq\counter{page}$.
% These operations are performed by a lengthy sequence with many occurrences
% of \!\expandafter!, \!\csname! and \!\endcsname! but the sequence is
% equivalent to the following.
% 
% \begin{quote}
% $\!\let!|\pcol@cl@|{\cdot}\cg|=\cl@|{\cdot}\cg$\\
% $\CSIndex{ifx}|\c@|{\cdot}\cg\!\c@page!|\else |
%     |\def\cl@|{\cdot}\cg|{|\!\pcol@stepcounter!|{|\cg|}}\fi|$
% \end{quote}
% 
% As for the removal of $\cg$ from $\CC$, we invoke
% $\!\pcol@removecounter!\<\mathit{\Theta}'\>\Arg{\theta}$ giving it
% $\mathit{\Theta}'=\CC$ and $\theta=\cg$.  This macro, also invoked from
% $\!\localcounter!\Arg\cl$ with $\mathit{\Theta}'=\CG$ and $\theta=\cl$,
% does $\mathit{\Theta}''\gets\mathit{\Theta}'$,
% $\mathit{\Theta}'=\emptyset$, and then apply
% $\!\pcol@iremctrelt!\arg{\mathit{\Theta}'}$ to each
% $\theta'\in\mathit{\Theta}''$ to let
% $\mathit{\Theta}'\gets\mathit{\Theta}'\cup\{\theta'\}$ by \!\@cons! if
% $\theta'\neq\theta$.
% 
%    \begin{macrocode}
\def\pcol@remctrelt#1{%
  \expandafter\let\expandafter\reserved@a\csname cl@#1\endcsname
  \expandafter\let\csname pcol@cl@#1\endcsname\reserved@a
  \expandafter\ifx\csname c@#1\endcsname\c@page\else
    \@namedef{cl@#1}{\pcol@stepcounter{#1}}%
  \fi
  \pcol@removecounter\pcol@counters{#1}}
\def\pcol@removecounter#1#2{%
  \def\reserved@a{#2}\let\reserved@b#1\relax \global\let#1\@empty
  {\def\@elt{\pcol@iremctrelt#1}\reserved@b}}
\def\pcol@iremctrelt#1#2{%
  \def\reserved@b{#2}%
  \ifx\reserved@a\reserved@b\else \@cons#1{{#2}}\fi}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\definethecounter}
% The API macro $\!\definethecounter!\<\cl\>\<c\>\arg{rep}$ define the
% \lrep{} $\arg{rep}$ for a \lcounter{} $\cl$ in a column $c$.  It
% \!\def!ines $|\pcol@thectr@|{\cdot}\cl{\cdot}c$
% 
% \SpecialArrayMainIndex{\theta{\cdot}c}{\pcol@thectr@}
% 
% to have $\arg{rep}$ in its  body.
% 
%    \begin{macrocode}
\def\definethecounter#1#2#3{\@namedef{pcol@thectr@#1#2}{#3}}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@thectrelt}
% The macro $\!\pcol@thectrelt!\<\cl\>$ is invoked solely in \!\pcol@zparacol!
% and is applied to each $\cl\in\CTL$ to define its \lrep{} of
% default and that of the leftmost column 0.  It performs a lengthy sequence
% with many occurrences of \!\expandafter!, \!\csname! and \!\endcsname! but
% the sequence is equivalent to the followings.
% 
% \begin{quote}
% $\!\let!|\pcol@thectr@|{\cdot}\cl|=\the|{\cdot}\cl$\\
% $\CSIndex{ifx}|\pcol@thectr@|{\cdot}\cl{\cdot}0\!\relax!|\else |
%     \!\let!|\the|{\cdot}\cl|=\pcol@thectr@|{\cdot}\cl{\cdot}0| \fi|$
% \end{quote}
% 
% \SpecialArrayMainIndex{\theta}{\pcol@thectr@}
% \SpecialArrayIndex{\theta{\cdot}c}{\pcol@thectr@}
% \SpecialArrayMainIndex{\theta}{\the}
% 
%    \begin{macrocode}
\def\pcol@thectrelt#1{%
  \expandafter\let\expandafter\reserved@a\csname the#1\endcsname
  \expandafter\let\csname pcol@thectr@#1\endcsname\reserved@a
  \expandafter\let\expandafter\reserved@a\csname pcol@thectr@#10\endcsname
  \ifx\reserved@a\relax\else
    \expandafter\let\csname the#1\endcsname\reserved@a
  \fi}

%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\pcol@loadctrelt}
% \changes{v1.0}{2011/10/10}
%	{Introduced for inter-environment local counter conservation.}
% \begin{macro}{\pcol@storecounters}
% \changes{v1.0}{2011/10/10}
%	{Introduced for inter-environment local counter conservation.}
% \begin{macro}{\pcol@storectrelt}
% \changes{v1.0}{2011/10/10}
%	{Introduced for inter-environment local counter conservation.}
% 
% The macro $\!\pcol@loadctrelt!\<\cl\>\<\val_c(\cl)\>$ is invoked from
% \!\pcol@zparacol! and \!\pcol@synccounter! and is applied to each element
% $\<\cl,\val_c(\cl)\>\in\Cc_c$ for a column $c$ to define a macro
% $|\pcol@ctr@|{\cdot}\cl=v(\cl)$
% 
% \SpecialArrayMainIndex{\theta}{\pcol@ctr@}
% 
% having $\val_c(\cl)$ in its body for a temporary use.  This macro or its
% redefined version is then referred to by $\!\pcol@cmpctrelt!\<\cl\>$ or
% $\!\pcol@storectrelt!\<\cl\>$.  The latter is invoked from
% \!\pcol@storecounters! via \!\pcol@sscounters! to add $\<\cl,v(\cl)\>$ to
% \!\@gtempa! by \!\@cons! to rebuild $\CC_c$ for a column $c$ in
% \!\@gtempa!.
% 
% The macro \!\pcol@storecounters! is invoked solely from
% $\!\pcol@synccounter!\<\theta\>$ to update a \lcounter{} $\theta$ with
% $\Val(\theta)$ for \csync.  That is, \!\pcol@storecounters! is used to add
% $\<\cl,v(\cl)\>$ to \!\@gtempa! for all $\cl\in\CTL$ by \!\pcol@sscounters!
% giving it \!\pcol@storectrelt! as its argument, where $v(\cl)$ is modified
% if $\cl=\theta$ or unmodifed otherwise after it is defined by
% \!\pcol@loadctrelt!.
% 
%    \begin{macrocode}
\def\pcol@loadctrelt#1#2{\@namedef{pcol@ctr@#1}{#2}}
\def\pcol@storecounters{\pcol@sscounters\pcol@storectrelt}
\def\pcol@storectrelt#1{\@cons\@gtempa{{#1}{\@nameuse{pcol@ctr@#1}}}}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@savecounters}
% \changes{v1.0}{2011/10/10}
%	{Move the body to \cs{pcol@sscounters}.}
% 
% \begin{macro}{\pcol@savectrelt}
% The macro \!\pcol@savecounters! is invoked from
% \!\pcol@com@syncallcounters!, \!\pcol@stepcounter! and \!\pcol@switchcol!
% to let $\CC_c$ for a column $c$ have the list of $\<\cl,\val_c(\cl)\>$
% where $\val_c(\cl)$ is the value of $|\c@|{\cdot}\cl$ to be saved in
% the list.
% 
% \SpecialArrayIndex{\theta}{\c@}
% 
% It does this operation invoking \!\pcol@sscounters! giving it
% \!\pcol@savectrelt! as its argument.
% 
% The macro $\!\pcol@savectrelt!\<\cl\>$ adds $\<\cl,\val_c(\cl)\>$ to
% \!\@gtempa! by \!\@cons! to rebuild $\CC_c$ for a column $c$ in
% \!\@gtempa!.
% 
%    \begin{macrocode}
\def\pcol@savecounters{\pcol@sscounters\pcol@savectrelt}
\def\pcol@savectrelt#1{\@cons\@gtempa{{#1}{\number\csname c@#1\endcsname}}}
%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@sscounters}
% \changes{v1.0}{2011/10/10}
%	{Introduced to implement the common operations of
%	 \cs{pcol@storecounters} and \cs{pcol@savecounters}.}
% 
% The macro $\!\pcol@sscounters!\arg{elt}$ is invoked from
% \!\pcol@storecounters! with $\arg{elt}=\!\pcol@storectrelt!$ or
% \!\pcol@savecounters! with $\arg{elt}=\!\pcol@savectrelt!$ to build
% $\CC_c=|\pcol@counters|{\cdot}c$ for a column $c$.
% 
% \SpecialArrayMainIndex{c}{\pcol@counters}
% 
% To do that, it lets $\!\@gtempa!=()$ and then apply $\arg{elt}$ to all
% $\cl\in\CTL=\!\pcol@counters!$ to have updated $\CC_c$ in \!\@gtempa!.
% Then finally, \!\@gtempa! is moved into $\CC_c$ by \!\xdef!\footnote{
% 
% It can be done by \cs{global}\cs{let} more efficiently but it is lengthy
% due to two \cs{expandafter}.}.
% 
%    \begin{macrocode}
\def\pcol@sscounters#1{\begingroup
  \global\let\@gtempa\@empty
  \let\@elt#1\relax \pcol@counters
  \let\@elt\relax
  \expandafter\xdef\csname pcol@counters\number\pcol@currcol\endcsname{%
    \@gtempa}%
  \endgroup}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@cmpctrelt}
% \changes{v1.0}{2011/10/10}
%	{Introduced for inter-environment local counter conservation.}
% 
% The macro $\!\pcol@cmpctrelt!\<\theta\>$ is invoked solely from
% \!\pcol@zparacol!  and is applied to each $\theta\in\CC$ to examine if
% $\val_0(\theta)=\Val(\theta)$ where $\val_0(\theta)$ is in
% $|\pcol@ctr@|{\cdot}\theta$.
% 
% \SpecialArrayIndex{\theta}{\pcol@ctr@}
% 
% If the examination fails including due to that $|\pcol@ctr@|{\cdot}\theta$
% 
% \SpecialArrayIndex{\theta}{\pcol@ctr@}
% 
% is undefined, we add $\theta$ to the list \!\@gtempa! by \!\@cons!.
% 
%    \begin{macrocode}
\def\pcol@cmpctrelt#1{\@tempswafalse \@tempcnta\@nameuse{c@#1}%
  \expandafter\ifx\csname pcol@ctr@#1\endcsname\relax \@tempswatrue
  \else\ifnum\@nameuse{pcol@ctr@#1}=\@tempcnta\else \@tempswatrue
  \fi\fi
  \if@tempswa \@cons\@gtempa{{#1}}\fi}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\synccounter}
% \changes{v1.0}{2011/10/10}
%	{Introduced as an environment-local API command.}
% \begin{macro}{\pcol@com@synccounter}
% \changes{v1.0}{2011/10/10}
%	{Introduced for the implementation of the new API command
%	 \cs{synccounter}.} 
% 
% The macro $\!\pcol@com@synccounter!\<\theta\>$, being the implementation
% of the \elocal{} API macro \!\synccounter!, lets
% $\val_c(\theta)=\Val(\theta)$ for all $c\In0\C$.  That is, the value of
% the counter $\theta$ is {\em broadcasted} to all columns for the
% {\em\Uidx\csync} of $\theta$.  This broadcast is done by
% \!\pcol@synccounter! with an argument $\!\@elt!|{|\theta|}|$ so that it
% works only on $\theta$.
% 
%    \begin{macrocode}
\def\pcol@com@synccounter#1{\pcol@synccounter{\@elt{#1}}}
%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@synccounter}
% \changes{v1.0}{2011/10/10}
%	{Introduced for \cs{synccounter} and inter-environment local counter
%	 conservation.}
% \begin{macro}{\pcol@syncctrelt}
% \changes{v1.0}{2011/10/10}
%	{Introduced for \cs{synccounter} and inter-environment local counter
%	 conservation.}
% 
% The macro $\!\pcol@synccounter!\arg{lst}$ is invoked from
% \!\pcol@zparacol! with $\arg{lst}=\!\@gtempa!$ and from
% $\!\pcol@com@synccounter!\arg{ctr}$ with $\arg{lst}=\!\@elt!\Arg{ctr}$, to
% let $\val_c(\theta)=\Val(\theta)$ for all $c\In0\C$ and all $\theta$ in
% $\arg{lst}$.  To do that, at first we move $\arg{lst}$ into \!\reserved@a!
% in order to make \!\@gtempa! free so that it can be used in
% \!\pcol@storecounters!.  Next, for each $c\In0\C$, we let
% $v(\cl)=\val_c(\cl)$ by applying \!\pcol@loadctrelt! to all
% $\<\cl,\val_c(\cl)\>\in\Cc_c$, then scan $\arg{lst}$ applying
% $\!\pcol@syncctrelt!\<\theta\>$ for each $\theta$ in $\arg{lst}$ to let
% $v(\theta)=\Val(\theta)$, and finally store all $v(\cl)$ back to $\Cc_c$
% by \!\pcol@storecounters!, where $v(\theta)$ is
% $|\pcol@ctr@|{\cdot}\theta$.
% 
% \SpecialArrayIndex{\theta}{\pcol@ctr@}
% 
%    \begin{macrocode}
\def\pcol@synccounter#1{{%
  \let\@elt\relax \edef\reserved@a{#1}%
  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
    \let\@elt\pcol@loadctrelt \@nameuse{pcol@counters\number\pcol@currcol}%
    \let\@elt\pcol@syncctrelt \reserved@a
    \pcol@storecounters
    \advance\pcol@currcol\@ne}}}
\def\pcol@syncctrelt#1{%
    \expandafter\edef\csname pcol@ctr@#1\endcsname{\number\@nameuse{c@#1}}}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\syncallcounters}
% \changes{v1.0}{2011/10/10}
%	{Introduced as an environment-local API command.}
% \begin{macro}{\pcol@com@syncallcounters}
% \changes{v1.0}{2011/10/10}
%	{Introduced for the implementation of the new API command
%	 \cs{syncallcounters}.} 
% 
% The macro \!\pcol@com@syncallcounters!, being the implementation of the
% \elocal{} API macro \!\syncallcounters!, makes all \lcounter{}s in all
% columns have the value in the current column.  That is, for each
% $c\In0\C$, we invoke \!\pcol@savecounters! to let $\val_c(\cl)={\Val}(\cl)$
% for all $\cl\in\CTL$.
% 
%    \begin{macrocode}
\def\pcol@com@syncallcounters{{%
  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
    \pcol@savecounters \advance\pcol@currcol\@ne}}}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@setctrelt}
% \changes{v1.0}{2011/10/10}
%	{Replace \cs{setcounter} with direct assignment with \cs{csname} and
%	 \cs{endcsname}}
% 
% The macro $\!\pcol@setctrelt!\<\cl\>\<\val_c(\cl)\>$ is solely inovked
% from \!\pcol@switchcol! to swich to a column $c$ and is applied to each
% $\<\cl,\val_c(\cl)\>\in\Cc_c$ to let $\Val(\cl)=\val_c(\cl)$ \!\global!ly.
% It also define the \lrep{} of $\cl$, being $|\the|{\cdot}\cl$,
% 
% \SpecialArrayIndex{\theta}{\the}
% 
% to be $|\pcol@thectr@|{\cdot}\cl{\cdot}c$
% 
% \SpecialArrayIndex{\theta{\cdot}c}{\pcol@thectr@}
% 
% if it is defined, or otherwise to be $|\pcol@thectr@|{\cdot}\cl$ which keeps
% the original $|\the|{\cdot}\cl$.
% 
% \SpecialArrayIndex{\theta}{\the}
% 
% This \lrep{} definition is done by a lengthy sequence with many occurrences
% of \!\expandafter!, \!\csname! and \!\endcsname!, but it is equivalent to
% the followings.
% 
% \begin{quote}
% $\CSIndex{ifx}|\pcol@thectr@|{\cdot}\cl{\cdot}c\!\relax!| |
%     \!\let!|\the|{\cdot}\cl|=\pcol@thectr@|{\cdot}\cl$\\
% $|\else |\!\let!|\the|{\cdot}\cl|=\pcol@thectr@|{\cdot}\cl{\cdot}c$\\
% |\fi|
% \end{quote}
% % 
%    \begin{macrocode}
\def\pcol@setctrelt#1#2{%
  \global\csname c@#1\endcsname#2\relax
  \expandafter\ifx\csname pcol@thectr@#1\number\pcol@currcol\endcsname\relax
    \expandafter\let\expandafter\reserved@a\csname pcol@thectr@#1\endcsname
  \else
    \expandafter\let\expandafter\reserved@a
      \csname pcol@thectr@#1\number\pcol@currcol\endcsname
  \fi
  \expandafter\let\csname the#1\endcsname\reserved@a}

%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\pcol@stepcounter}
% \changes{v1.0}{2011/10/10}
%	{Change the order of operations.}
% \changes{v1.0}{2011/10/10}
%	{Replace \cs{csname}/\cs{endcsname} with \cs{@nameuse}.}
% \begin{macro}{\pcol@stpldelt}
% \begin{macro}{\pcol@stpclelt}
% 
% The macro $\!\pcol@stepcounter!\<\cg\>$ is invoked from
% $\!\stepcounter!\<\cg\>$ for a \gcounter{} $\cg$ because
% $|\cl@|{\cdot}\cg$
% 
% \SpecialArrayIndex{\theta}{\cl@}
% 
% is modified by \!\pcol@remctrelt! so as to invoke this macro to zero-clear
% \lcounter{}s $\theta\in\clist(\cg)$.  To do that, we do the followings in
% a group for each $c\In0\C$.  First we apply
% $\!\pcol@stpldelt!\<\cl\>\<\val_c(\cl)\>$ to each
% $\<\cl,\val_c(\cl)\>\in\Cc_c$ to let $\Val(\cl)=\val_c(\cl)$ locally.
% Then we apply $\!\pcol@stpclelt!\<\theta\>$ to each $\theta\in\clist(\cg)$
% to let $\Val(\theta)=0$.  Finally, we invoke \!\pcol@savecounters! to let
% $\val_c(\cl)=\Val(\cl)$ for all $\cl\in\CTL$ to reflect the zero-clear of
% $\theta\in\clist(\cg)$.
% 
% After the operations above, we apply $\!\@stpelt!\<\theta\>$ to each
% $\theta\in\clist(\cg)$ for \!\global! zero-clearing.
% 
%    \begin{macrocode}
\def\pcol@stepcounter#1{\begingroup
  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
    \let\@elt\pcol@stpldelt \@nameuse{pcol@counters\number\pcol@currcol}%
    \let\@elt\pcol@stpclelt \@nameuse{pcol@cl@#1}%
    \pcol@savecounters
   \advance\pcol@currcol\@ne}%
  \endgroup
  \let\@elt\@stpelt \@nameuse{pcol@cl@#1}}
\def\pcol@stpldelt#1#2{\csname c@#1\endcsname#2\relax}
\def\pcol@stpclelt#1{\csname c@#1\endcsname\z@}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% 
% 
% \section{Column-Switching Commands and Environments}
% \label{sec:imp-switch}
% 
% \begin{macro}{\pcol@par}
% \changes{v1.0}{2011/10/10}
%	{Introduced for \cs{par}-if-necessary operation.}
% 
% Before giving the definition of \cswitch{} commands and environments, we
% define a commonly used macro \!\pcol@par!, which do \CSIndex{par} if
% necessary, i.e., we are not in vertical mode.  The reason why we don't
% simply do \CSIndex{par} is that it may have some definition different from
% \!\@@par! and thus an incautious repetition of \CSIndex{par} may cause
% undesirable results.  This macro is used in \!\pcol@com@switchcolumn!,
% \!\pcol@sptext!, \!\pcol@com@endcolumn!, \!\pcol@flushclear!,
% and \!\endparacol!.
% 
%    \begin{macrocode}
%% Column-Switching Commands and Environments

\def\pcol@par{\ifvmode\else \par \fi}

%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{2}
% \begin{macro}{\switchcolumn}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@switchcolumn} for localization.}
% \begin{macro}{\pcol@com@switchcolumn}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implementation of \cs{switchcolumn}.}
% \changes{v1.0}{2011/10/10}
%	{Add \cs{pcol@defcolumn} to clarify the behavior of \texttt{column}.}
% \begin{macro}{\pcol@switchcolumn}
% \changes{v1.0}{2011/10/10}
%	{Add the check of $d\geq0$.}
% \changes{v1.31}{2013/10/10}
%	{Add a space before the number of columns in the error message.}
% 
% \begin{macro}{\pcol@iswitchcolumn}
% The macro $\!\pcol@com@switchcolumn!|[|d|]|$, being the implementation of the
% \elocal{} API macro \!\switchcolumn!, switches to the column $d$ if provided
% through its optional argument, or to $d=(c+1)\bmod\C$ otherwise where $c$
% is the ordinal of the current column.  After making it sure to be in
% vertical mode by \!\pcol@par!, it invokes \!\pcol@defcolumn! to give
% \!\pcol@com@column!(|*|) their
% \!\def!initions for occurrences not as the very first \cswitch{} command
% or environment of the current \env{paracol} environment.  Then, after
% calculating $d=(c+1)\bmod\C$, this macro simply invokes
% $\!\pcol@switchcol!|[|d|]|$ with or without the calculated $d$ depending
% on the existance of the optional argument delimitor `|[|'.
% 
% The macro $\!\pcol@switchcolumn!|[|d|]|$ lets $\!\pcol@nextcol!=d$ and
% confirms $0\leq d<\C$ or abort the execution by \!\PackageError! if it
% does not hold.  Then it invokes \!\pcol@iswitchcolumn! if
% $\!\switchcolumn!|[|d|]|$ is followed by a `|*|', or \!\pcol@switchcol!
% othewise.
% 
% The macro $\!\pcol@iswitchcolumn!|[|\arg{text}|]|$ invokes
% $\!\pcol@sptext!|[|\arg{text}|]|$ if the optional argument is provided, or
% \!\pcol@switchcol! otherwise, after letting $\CSIndex{ifpcol@sync}=\true$
% for \exsync{}.
% 
%    \begin{macrocode}
\def\pcol@com@switchcolumn{\pcol@par
  \pcol@defcolumn
  \@tempcnta\pcol@currcol \advance\@tempcnta\@ne
  \ifnum\@tempcnta<\pcol@ncol\else \@tempcnta\z@ \fi
  \@ifnextchar[%]
    \pcol@switchcolumn{\pcol@switchcolumn[\@tempcnta]}}
\def\pcol@switchcolumn[#1]{%
  \pcol@nextcol#1\relax
  \@tempswafalse
  \ifnum#1<\z@ \@tempswatrue \fi
  \ifnum#1<\pcol@ncol\else \@tempswatrue \fi
  \if@tempswa
    \PackageError{paracol}{%
      Column number \number#1 must be less than \number\pcol@ncol}\@eha
    \pcol@nextcol\z@
  \fi
  \@ifstar\pcol@iswitchcolumn\pcol@switchcol}
\def\pcol@iswitchcolumn{%
  \global\pcol@synctrue
  \@ifnextchar[%]
    \pcol@sptext\pcol@switchcol}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@sptext}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{long} to allow \cs{par} in its argument.}
% \changes{v1.0}{2011/10/10}
%	{Replace \cs{par} with \cs{pcol@par}.}
% \changes{v1.0}{2011/10/10}
%	{Add $\cs{ifpcol@mctext}\EQ\mathit{true}$ for restriction of the
%	 broadcast of \cs{if@nobreak} and \cs{everypar}.}
% \changes{v1.2-4}{2013/05/11}
%	{Add \cs{pcol@swapcolumn} for column-swapping.}
% \changes{v1.2-5}{2013/05/11}
% 	{Add setting of \cs{columnwidth}, \cs{linewidth} and \cs{parshape}
%	 to have indented spanning text with surrounding
%	 \string\texttt{list}-like environments.}
% \changes{v1.3-1}{2013/09/17}
%	{Add $\cs{ifpcol@sptextstart}\EQ\string\mathit{true}$ before first
% 	 synchronized column-switching to let \cs{pcol@output@switch} save
%	 pre-spanning-text stuff, move the timing of
%	 $\cs{ifpcol@sptext}\EQ\string\mathit{true}$ from the end of
%	 spanning text to the beginning so that \cs{output} routine for a
%	 page break in the text capture the pre-break portion, and remove
%	 the invocation of \cs{pcol@swapcolumn} because spanning texts are
%	 now always put into the column-0.}
% \changes{v1.3-6}{2013/09/17}
%	{Add globalization of \cs{@svsechd} and \cs{@svsec}.}
% 
% The macro $\!\pcol@sptext!|[|\arg{text}|]|$ is invoked from
% \!\pcol@zparacol! and \!\pcol@iswitchcolumn! to put a \Uidx\mctext{}
% $\arg{text}$ given as the optional argument of the former or that of
% \!\switchcolumn!|*| and its relative envrironment openers for the latter.
% The macro has \!\long!  attribute because the \mctext{} may have
% \CSIndex{par}.  Since the text is put in the column-0 regardless of its
% physical position, we let \!\pcol@nextcol!  have 0 after saving the target
% column $d=\!\pcol@nextcol!$ in \!\@tempcnta!.  Then we switch to the
% column by \!\pcol@switchcol!, after turning $\CSIndex{ifpcol@sync}=\true$
% to set a \sync{}ation point above the text and
% $\CSIndex{ifpcol@sptextstart}=\true$ to tell \!\pcol@output@switch! to
% prepare the capture of \mctext{} saveing the \prespan{}.
% 
% Next, we let $\CSIndex{ifpcol@sptextstart}=\false$ and
% $\CSIndex{ifpcol@sptext}=\true$ to indicate the main vertical list
% contains only the \mctext{} and it is to be captured by \!\output!
% routine.  Then the $\arg{text}$ is put in a group in which we let
% $\!\columnwidth!=\!\hsize!=\!\textwidth!$ and
% $\!\linewidth!=\!\textwidth!-\lrm$ with \!\parshape! to indent lines by
% \!\@totalleftmargin! if $\lrm>0$, to let \mctext{} span across all columns
% reflecting the indentation in the \env{list}-like environments surrounding
% \env{paracol} if any.  We also let $\!\col@number!=1$ to ensure again that
% \!\maketitle!  produces a title without \!\twocolumn! if it is in the
% \mctext.
% 
% Then, after invoking \!\pcol@par! to ensure to be in vertical
% mode, we \!\global!ize \!\@svsechd! and \!\@svsec! which may be defined in
% a lower-level sectioning command such as \!\paragraph! in the \mctext{} so
% that they are properly expanded in \!\everypar! inserted at the beginning
% of the first paragraph of the column to which we switch shortly, even when
% the sectioning command is used inappropriately in the \mctext.
% We also \!\global!ize \!\everypar! by a sequence with three
% \!\expandafter! so that \!\pcol@output@switch! for the \sync{}ed
% \cswitch{} we make shortly broadcasts it to other columns.  Finally after
% closing the group, we let $\!\pcol@nextcol!=d$ and
% $\CSIndex{pcol@sync}=\true$ to set another \sync{}ation point below the
% \mctext{} and to make the captured text combined with \prespan, and then
% invoke \!\pcol@switchcol!  to switch the coloumn $d$.
% 
%    \begin{macrocode}
\long\def\pcol@sptext[#1]{%
  \@tempcnta\pcol@nextcol
  \global\pcol@synctrue \pcol@nextcol\z@
  \global\pcol@sptextstarttrue
  \pcol@switchcol
  \global\pcol@sptextstartfalse \global\pcol@sptexttrue
  \begingroup
    \columnwidth\textwidth \hsize\columnwidth
    \linewidth\columnwidth \advance\linewidth-\pcol@lrmargin
    \ifdim\pcol@lrmargin>\z@ \parshape\@ne\@totalleftmargin\linewidth \fi
    \col@number\@ne #1\pcol@par
    \global\let\@svsechd\@svsechd \global\let\@svsec\@svsec
    \expandafter\global\expandafter\everypar\expandafter{\the\everypar}%
  \endgroup
  \pcol@nextcol\@tempcnta \global\pcol@synctrue \pcol@switchcol}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@switchcol}
% \changes{v1.0}{2011/10/10}
%	{Add \cs{pcol@aconly} for disabling \cs{addcontentsline}.}
% \changes{v1.2-2}{2013/05/11}
% 	{Add column-scanning and page-overflow check for synchronized
%	 column-switching.}
% \changes{v1.2-4}{2013/05/11}
%	{Add \cs{pcol@swapcolumn} for column-swapping to turn
%	 \cs{if@firstcolumn}.}
% \changes{v1.3-4}{2013/09/17}
%	{Remove settig \cs{if@firstcolumn} and the invocation of
%	 \cs{pcol@swapcolumn} for it because the position of marginal notes
%	 are now controlled by \cs{pcol@addmarginpar}.}
% \changes{v1.3-5}{2013/09/17}
%	{Add setting $V_E\EQ\cs{pcol@@ensurevspace}$ and reinitialization of
%	 \cs{pcol@ensurevspace} for avoidance of post-synchronization
%	 inconsistent page break.}
% \changes{v1.35-5}{2018/12/31}
% 	{Add the invocation of $\cs{pcol@colpream}\cdot c$.}
% 
% The macro \!\pcol@switchcol! is invoked from \!\pcol@switchcolumn!,
% \!\pcol@iswitchcolumn!, \!\pcol@sptext! and \!\endparacol! to switch the
% column $d=\!\pcol@nextcol!$.  First, we save \lcounter{}s in the current
% column $c$ into $\Cc_c$ by \!\pcol@savecounters!.
%
% Next, if $\CSIndex{ifpcol@sync}=\true$, we do the followings.  At first we
% let $\VE={}$\!\pcol@@ensure~vspace! have the natrual component of
% \!\pcol@ensurevspace! which can have a glue specified by \!\ensurevspace!,
% so that it is referred to by \!\pcol@sync! as the minimum space required
% below the \sync{}ation point we are now setting.  Second, we invoke
% \!\pcol@visitallcols! temporarily turning $\CSIndex{ifpcol@sync}=\false$
% for \cscan{}ning to visit all columns but current one to give \TeX's page
% builder the chance to break \colpage{}s in the \tpage{} with \Scfnote{}s
% which could have not been presented in the last visit of the columns.
% Third, we make an \!\output! request with $\!\penalty!=\!\pcol@op@switch!$
% to invoke \!\pcol@output@switch! by \!\pcol@invokeoutput! with
% $\CSIndex{ifpcol@sync}=\true$ to make \sync{}ed switch to the column $d$.
% This invocation may result in $\CSIndex{ifpcol@flush}=\true$ to mean the
% \tpage{} should be broken before setting the \sync{}ation point.
% Therefore if so, since \!\pcol@output@switch! switched to the tallest
% column rather than $d$, we put \!\vfil! and \!\penalty!|-10000| to force
% page break, make \cscan{} with \!\newpage! put into each column to have
% some floats in the column in the new \tpage{}, and then invoke
% \!\pcol@output@switch!  again until it returns
% $\CSIndex{ifpcol@flush}=\false$ telling us it successfully sets the
% \sync{}ation point switching to the column $d$.  Then as the last operation
% specific to \sync{}ed \cswitch{}, we invoke \!\ensurevspace! with
% \!\baselineskip! to give the default of $\VE$ for the next \sync{}ation.
% 
% Otherwise, i.e., if $\CSIndex{ifpcol@sync}=\false$, we simply make the
% \!\output! request for \!\pcol@output@switch! to switch to the column $d$.
% 
% Then we scan $\Cc_d$ applying \!\pcol@setctrelt! to each
% $\<\cl,\val_d(\cl)\>\in\Cc_d$ to let $\Val(\cl)={\val_d(\cl)}$.  We also
% scan $\T=\!\pcol@aconly!$ applying \!\pcol@aconlyelt! to each
% $\<t_c,c\>\in T$ to inhibit \!\addcontentsline! to the contents file of
% type $t_d$ as specified so by $\!\addcontentsonly!\arg{t_d}\~\arg{d}$.
% After that, we let $\!\@elt!=\!\relax!$ to make it sure that any lists can
% be manipulated without unexpected application of a macro to their
% elements.
% 
% Finally, we invoke $|\pcol@colpream|{\cdot}c$, where $c=-1$ if
% $\CSIndex{ifpcol@sptextstart}=\true$ to mean the \cswitch{} is for a
% \sptext{}, or $c=d$ otherwise.
% 
% \SpecialArrayIndex{c}{\pcol@colpream}
% 
%    \begin{macrocode}
\def\pcol@switchcol{%
  \pcol@savecounters
  \ifpcol@sync
    \@tempdima\pcol@ensurevspace\relax
    \edef\pcol@@ensurevspace{\number\@tempdima sp\relax}%
    \global\pcol@syncfalse \pcol@visitallcols\@@par \global\pcol@synctrue
    \pcol@invokeoutput\pcol@op@switch
    \@whilesw\ifpcol@flush\fi{%
      \vfil \penalty-\@M
      \global\pcol@syncfalse \pcol@visitallcols\newpage \global\pcol@synctrue
      \pcol@invokeoutput\pcol@op@switch}%
    \ensurevspace{\baselineskip}%
  \else
    \pcol@invokeoutput\pcol@op@switch
  \fi
  \let\@elt\pcol@setctrelt
  \csname pcol@counters\number\pcol@currcol\endcsname
  \let\@elt\pcol@aconlyelt \pcol@aconly \let\@elt\relax
  \@nameuse{pcol@colpream\ifpcol@sptextstart-1\else\number\pcol@currcol\fi}}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@visitallcols}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for column-scanning in synchronized column-switching and
%	 page flushing.}
% 
% The macro $\!\pcol@visitallcols!\arg{cs}$, invoked from \!\pcol@switchcol!
% and \!\pcol@flushclear!, performs \cscan{}ning putting $\arg{cs}$ into the
% visited columns.  That is, we repeat the invocation of
% \!\pcol@output@switch! to visit $d$ through \!\pcol@invokeoutput! with
% $\!\penalty!=\!\pcol@op@switch!$ for all $d\In0\C-\{c\}$.  In each visit,
% we put $\arg{cs}\in\{\!\@@par!,\!\newpage!\}$ to have a chance of or to
% force page break in each visited \colpage{}.  Finally we go back to $c$ to
% restore its \cctext{} especially when we are leaving the column 0 for
% \mctext.  That is, $\cc_c(\sw)$ and $\cc_c(\ep)$ should be presented to
% \!\pcol@output@switch! to broadcast them to other columns.
% 
%    \begin{macrocode}
\def\pcol@visitallcols#1{\begingroup
  \@tempcnta\z@ \@tempcntb\pcol@currcol
  \@whilenum\@tempcnta<\pcol@ncol\do{%
    \ifnum\@tempcnta=\@tempcntb\else
      \pcol@nextcol\@tempcnta \pcol@invokeoutput\pcol@op@switch #1%
    \fi
    \advance\@tempcnta\@ne}%
  \pcol@nextcol\@tempcntb \pcol@invokeoutput\pcol@op@switch
  \endgroup}

%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{3}
% \begin{macro}{\column}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@column} for localization.}
% \begin{macro}{\column*}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@column*} for localization.}
% \begin{macro}{\pcol@com@column}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{column}.}
% \begin{macro}{\pcol@com@column*}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{column*}.}
% \begin{macro}{\pcol@defcolumn}
% \changes{v1.0}{2011/10/10}
%	{Replace \cs{column} with \cs{pcol@com@column} and \cs{switchcolumn}
%	 with \cs{pcol@switchenv}.}
% 
% The macros \!\pcol@com@column!(|*|), the implementations of the \elocal{}
% API commands \!\column!(*), starts the environment |column(*)|.
% 
% \Midx{\EnvIndex{column}}\Midx{\EnvIndex{column*}}
% 
% Basically, the macros do \!\switch~column!\~(|*|), but if the environment
% starts just after \beginparacol{} the macro have to switch to the column
% 0.  Therefore, the definitions for this very-beginning appearance are
% given in \!\pcol@zparacol! to do (almost) nothing, and then those for
% other ones are given by \!\pcol@defcolumn! invoked in
% \!\pcol@com@switchcolumn!  to invoke
% \!\pcol@switchenv!|{column|(|*|)|}|(|*|) which then invokes
% \!\switchcolumn!.  Note that the definition of non-starred
% \!\pcol@com@column! has \!\relax!  after the invocatoin of
% \!\pcol@switchenv!  so that \!\@ifnextchar! and \!\@ifstar! to examine the
% existence of `|[|' and `|*|' definitely tells us no even if the body of the
% environment starts with a `|[|' or `|*|'.
% 
%    \begin{macrocode}
\def\pcol@defcolumn{%
  \gdef\pcol@com@column{\pcol@switchenv{column}\relax}%
  \global\@namedef{pcol@com@column*}{\pcol@switchenv{column*}*}}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{10}
% \begin{macro}{\nthcolumn}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@nthcolumn} for localization.}
% \begin{macro}{\nthcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@nthcolumn*} for localization.}
% \begin{macro}{\pcol@com@nthcolumn}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{nthcolumn} with the
%	 inhibition of column-switching in the environment.}
% \begin{macro}{\pcol@com@nthcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{nthcolumn*} with the
%	 inhibition of column-switching in the environment.}
% \begin{macro}{\leftcolumn}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@leftcolumn} for localization.}
% \begin{macro}{\leftcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@leftcolumn*} for localization.}
% \begin{macro}{\pcol@com@leftcolumn}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{leftcolumn} with the
%	 inhibition of column-switching in the environment.}
% \begin{macro}{\pcol@com@leftcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{leftcolumn*} with the
%	 inhibition of column-switching in the environment.}
% \begin{macro}{\rightcolumn}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@rightcolumn} for localization.}
% \begin{macro}{\rightcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@rightcolumn*} for localization.}
% \begin{macro}{\pcol@com@rightcolumn}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{rightcolumn} with the
%	 inhibition of column-switching in the environment.}
% \begin{macro}{\pcol@com@rightcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{rightcolumn*} with the
%	 inhibition of column-switching in the environment.}
% 
% The macros $\!\pcol@com@nthcolumn!(|*|)\arg{d}$,
% \!\pcol@com@leftcolumn!(|*|) and |\pcol@com@right|\~|column|(|*|) are the
% implementations of \elocal{} API macros \!\nthcolumn!(|*|)$\arg{d}$,
% \!\leftcolumn!(|*|) and \!\rightcolumn!(|*|) respectively.  They start
% corresponding environments |nthcolumn|(|*|), |leftcolumn|(|*|), and
% |rightcolumn|(|*|)
% 
% \Midx{\EnvIndex{nthcolumn}}\Midx{\EnvIndex{nthcolumn*}}
% \Midx{\EnvIndex{leftcolumn}}\Midx{\EnvIndex{leftcolumn*}}
% \Midx{\EnvIndex{rightcolumn}}\Midx{\EnvIndex{rightcolumn*}}
% 
% simply invoking \!\pcol@switchenv!$\Arg{env}$\~(|*|), where $\arg{env}$ is
% the name of each environment, giving it $d$, 0 and 1 repectively as its
% optional argument for the target column.
% 
%    \begin{macrocode}
\def\pcol@com@nthcolumn#1{\pcol@switchenv{nthcolumn}[#1]\relax}
\@namedef{pcol@com@nthcolumn*}#1{\pcol@switchenv{nthcolumn*}[#1]*}
\def\pcol@com@leftcolumn{\pcol@switchenv{leftcolumn}[0]\relax}
\@namedef{pcol@com@leftcolumn*}{\pcol@switchenv{leftcolumn*}[0]*}
\def\pcol@com@rightcolumn{\pcol@switchenv{rightcolumn}[1]\relax}
\@namedef{pcol@com@rightcolumn*}{\pcol@switchenv{rightcolumn*}[1]*}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@switchenv}
% \changes{v1.0}{2011/10/10}
%	{Introduced to inhibit column-switching in the environment.}
% \changes{v1.31}{2013/10/10}
%	{Fix the misspell ``swicthing'' in the error message.}
% 
% The macro $\!\pcol@switchenv!\arg{env}$ is invoked from
% $|\pcol@com@|{\cdot}\arg{env}$ where $\arg{env}\in
% \{\env{column}\~(|*|),\env{nthcolumn}(|*|),\env{leftcolumn}(|*|),
% \env{rightcolumn}(|*|)\}$ to invoke \!\switchcolumn! with the arguments
% following $\arg{env}$ given by the invoker macros.  Before invoking
% \!\switchcolumn!, we save it in \!\reserved@a! for the invocation and
% re\!\def!ine it so that it will complain the illegal usage of \cswitch{}
% commands\slash environments in the environment $\arg{env}$ by
% \!\PackageError!.
% 
%    \begin{macrocode}
\def\pcol@switchenv#1{\let\reserved@a\switchcolumn
  \def\switchcolumn{\PackageError{paracol}{%
    Column switching commands and environments cannot be used in #1}\@eha}
  \reserved@a}

%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{14}
% \begin{macro}{\endcolumn}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@endcolumn} for localization.}
% \begin{macro}{\endcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@endcolumn*} for localization.}
% \begin{macro}{\pcol@com@endcolumn}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{endcolumn} with the
%	 globalizatoin of \cs{everypar}.}
% \begin{macro}{\pcol@com@endcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{endcolumn*} with the
%	 globalizatoin of \cs{everypar}.}
% \begin{macro}{\endnthcolumn}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@endnthcolumn} for localization.}
% \begin{macro}{\endnthcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@endnthcolumn*} for
%	 localization.}
% \begin{macro}{\pcol@com@endnthcolumn}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{endnthcolumn} with the
%	 globalizatoin of \cs{everypar}.}
% \begin{macro}{\pcol@com@endnthcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{endnthcolumn*} with the
%	 globalizatoin of \cs{everypar}.}
% \begin{macro}{\endleftcolumn}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@endleftcolumn} for
%	 localization.} 
% \begin{macro}{\endleftcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@endleftcolumn*} for
%	 localization.}
% \begin{macro}{\pcol@com@endleftcolumn}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{endleftcolumn} with the
%	 globalizatoin of \cs{everypar}.}
% \begin{macro}{\pcol@com@endleftcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{endleftcolumn*} with the
%	 globalizatoin of \cs{everypar}.}
% \begin{macro}{\endrightcolumn}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@endrightcolumn} for
%	 localization.}
% \begin{macro}{\endrightcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@endrightcolumn*} for
%	 localization.}
% \begin{macro}{\pcol@com@endrightcolumn}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{endrightcolumn} with the
%	 globalizatoin of \cs{everypar}.}
% \begin{macro}{\pcol@com@endrightcolumn*}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{endrightcolumn*} with the
%	 globalizatoin of \cs{everypar}.}
% 
% The macro \!\pcol@com@endcolumn! is the implementation of the \elocal{}
% API macro \!\endcolumn! to close \env{column} environment.  The macro
% makes it sure we are in vertical mode by \!\pcol@par! and \!\global!ize
% \!\everypar! so that it is saved in $\cc_c(\ep)$ of the current column
% $c$ on the switch to another column.  The macro also gives the commmon
% definition of \!\pcol@com@endcolumn*!  for \!\endcolumn*!,
% \!\pcol@com@endnthcolumn!(|*|) for \!\endnthcolumn!(|*|),
% \!\pcol@com@endleftcolumn!(|*|) for \!\endleftcolumn!(|*|), and
% \!\pcol@com@endrightcolumn!(|*|) for \!\endrightcolumn!(|*|).
% 
%    \begin{macrocode}
\def\pcol@com@endcolumn{\pcol@par
  \expandafter\global\expandafter\everypar\expandafter{\the\everypar}}
\expandafter\let\csname pcol@com@endcolumn*\endcsname\pcol@com@endcolumn
\let\pcol@com@endnthcolumn\pcol@com@endcolumn
\expandafter\let\csname pcol@com@endnthcolumn*\endcsname\pcol@com@endcolumn
\let\pcol@com@endleftcolumn\pcol@com@endcolumn
\expandafter\let\csname pcol@com@endleftcolumn*\endcsname\pcol@com@endcolumn
\let\pcol@com@endrightcolumn\pcol@com@endcolumn
\expandafter\let\csname pcol@com@endrightcolumn*\endcsname\pcol@com@endcolumn

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\definecolumnpreamble}
% \changes{v1.35-5}{2018/12/31}
% 	{Introduced to define a column preamble.}
% 
% The API macro \!\definecolumnpreamble!\marg{c}\marg{pream} is to define
% the \colpream{} $\arg{pream}$ for the column $c$ or that for \sptext{}s if
% $c=-1$.  After assiging $c$ to \!\@tempcnta! to ensure $c$ is a number,
% the macro $|\pcol@colpream|{\cdot}c$ is |\def|ined to have $\arg{pream}$.
% 
% \SpecialArrayMainIndex{c}{\pcol@colpream}
% 
%    \begin{macrocode}
\def\definecolumnpreamble#1#2{\@tempcnta#1\relax
  \expandafter\gdef\csname pcol@colpream\number\@tempcnta\endcsname{#2}}

%    \end{macrocode}
% \end{macro}
% 
% 
% \begin{macro}{\ensurevspace}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced to declare the minimum space $V_E$ below a
%	 synchronization point to let it stay in a page.}
% \begin{macro}{\pcol@ensurevspace}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced to keep $V_E$ declared by \cs{ensurevspace}.}
% \begin{macro}{\pcol@@ensurevspace}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced to pass $V_E$ declared by \cs{ensurevspace} to
%	 \cs{output} routine.}
% 
% The API macro $\!\ensurevspace!\ARg{space}$ is to declare that the
% \sync{}ation point following it must be thrown to the next page unless the
% page has the vertical $\arg{space}$ below the \sync{}ation point.  The
% macro makes a dummy assignment of $\arg{space}$ to \!\@tempdima! to ensure
% the argument is a dimension including forced one, or in other words to
% raise an error if not in this macro rather than at the time $\arg{space}$
% is {\em evaluated} in \!\pcol@switchcol!.  Then $\arg{space}$ is kept in
% \!\pcol@ensurevspace! so that $\arg{space}$ is evaluated in
% \!\pcol@switchcol! for the \sync{}ation in question to pass the value to
% \!\pcol@sync!  through the macro $\!\pcol@@ensurevspace!=\Uidx\VE$,
% especially when it has register references, for example to
% \!\baselineskip!.  To give the default of \!\pcol@ensurevspace!, we invoke
% \!\ensurevspace! at the top level with \!\baselineskip!.
% 
%    \begin{macrocode}
\def\ensurevspace#1{{\@tempdima#1\relax \gdef\pcol@ensurevspace{#1}}}
\ensurevspace{\baselineskip}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% 
% 
% \section{Disabling \cs{addcontentsline}}
% \label{sec:imp-aconly}
% 
% \begin{macro}{\addcontentsonly}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% \begin{macro}{\pcol@aconly}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% 
% The API macro $\!\addcontentsonly!\arg{t}\arg{c}$ makes the type $t$
% contents file written by commands appearing only in the column $c$.  The
% macro simply add the pair $\<t,c\>$ to the list $\Uidx\T=\!\pcol@aconly!$
% being empty at initial, after confirming we know the type $t$, one of
% |toc|, |lof| and |lot| so far, by the fact $|\pcol@ac@def|{\cdot}t$ is
% defined, or abort execution by \!\PackageError!.
% 
%    \begin{macrocode}
%% Disabling \addcontentsline

\def\addcontentsonly#1#2{%
  \@ifundefined{pcol@ac@def@#1}
    {\PackageError{paracol}{Unknown contents type #1}\@eha}\relax
  \@cons\pcol@aconly{{#1}{#2}}}
\gdef\pcol@aconly{}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@aconlyelt}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% 
% The macro $\!\pcol@aconlyelt!\arg{t_d}\arg{d}$ is invoked solely in
% \!\pcol@switchcol!  for the \cswitch{} to column $c$, and is applied to
% each $\<t_d,d\>\in\T$ to enable \!\addcontentsline! for $t_d$ if $d=c$ by
% the invocation of $|\pcol@ac@def@|{\cdot}t_d$
% 
% \SpecialArrayMainIndex{t}{\pcol@ac@def@}
% 
% with an argument |enable|, or to disable if $d\neq c$ with |disable|.
% 
%    \begin{macrocode}
\def\pcol@aconlyelt#1#2{%
  \ifnum#2=\pcol@currcol \@nameuse{pcol@ac@def@#1}{enable}%
  \else \@nameuse{pcol@ac@def@#1}{disable}%
  \fi}
%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\pcol@gobblethree}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% \begin{macro}{\pcol@addcontentsline}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% 
% \hfuzz0.39pt
% The macro $\!\pcol@gobblethree!\arg{file}\arg{sec}\arg{entry}$ is used in
% \!\pcol@ac@disable@toc! and \!\pcol@ac@caption! to make
% \!\addcontentsline! \!\let!-equal to this macro, which does nothing but
% discarding three arguments, for disabling.  The macro
% \!\pcol@addcontentsline! is the \LaTeX's original \!\addcontentsline! and
% is used in the macros mentioned above to let \!\addcontentsline! act as
% original.
% 
%    \begin{macrocode}
\def\pcol@gobblethree#1#2#3{}
\let\pcol@addcontentsline\addcontentsline

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\pcol@ac@def@toc}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% \begin{macro}{\pcol@ac@enable@toc}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% \begin{macro}{\pcol@ac@disable@toc}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% 
% The macro $\!\pcol@ac@def@toc!\arg{eord}$ is invoked solely in
% $\!\pcol@aconlyelt!|{toc}|\arg{c}$ to enable or disable
% \!\addcontentsline! according to $\arg{eord}$ by making \!\@sect!
% \!\let!-equal to \!\pcol@ac@enable@toc! which is the \LaTeX's original
% \!\@sect!, or to \!\pcol@ac@disable@toc! respectively.  The macro
% $\!\pcol@ac@disable@toc!
% \<a_1\>\<a_2\>\<a_3\>\<a_4\>\<a_5\>\<a_6\>|[|\<a_7\>|]|\<a_8\>$ at first
% disables \!\addcontentsline! by making it \!\let!-equal to
% \!\pcol@gobblethree!, then invokes the original \!\@sect! saved in
% \!\pcol@ac@enable@toc! ginving it all arguments $a_1$ to $a_8$, and
% finally enables it by making it \!\let!-equal to \!\pcol@addcontentsline!.
% Note that the argument $a_7$ is surrounded by |{| and |}| on the
% invocation of \!\@sect! to conceal `|]|' in $a_7$.
% 
%    \begin{macrocode}
\def\pcol@ac@def@toc#1{%
  \expandafter\let\expandafter\@sect\csname pcol@ac@#1@toc\endcsname}
\let\pcol@ac@enable@toc\@sect
\def\pcol@ac@disable@toc#1#2#3#4#5#6[#7]#8{%
  \let\addcontentsline\pcol@gobblethree
  \pcol@ac@enable@toc{#1}{#2}{#3}{#4}{#5}{#6}[{#7}]{#8}%
  \let\addcontentsline\pcol@addcontentsline}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{5}
% \begin{macro}{\pcol@ac@def@lof}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% \begin{macro}{\pcol@ac@def@lot}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% \begin{macro}{\pcol@ac@caption@enable}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% \begin{macro}{\pcol@ac@caption@disable}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% \begin{macro}{\pcol@ac@caption@def}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% \begin{macro}{\pcol@ac@caption@if@lof}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% \begin{macro}{\pcol@ac@caption@if@lot}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% 
% The macro $\!\pcol@ac@def@lof!\arg{eord}$ and
% $\!\pcol@ac@def@lot!\arg{eord}$ are invoked solely in
% $\!\pcol@aconlyelt!\<t\>\<c\>$ when $t$ is |lof| or |lot|
% respectively.  They invoke \!\pcol@ac@caption@enable!$\<t\>$ or
% $\!\pcol@ac@caption@disable!\<t\>$ according to $\arg{eord}$, and then
% these macros invoke $\!\pcol@ac@caption@def!\<s\>\<t\>$ where
% $s=\!\@tempswatrue!$ or $s=\!\@tempswafalse!$ respectievely to let
% $\!\@caption!=\!\pcol@ac@caption!$ and $|\pcol@ac@caption@if@|{\cdot}t=s$
% which are \!\let!-equal to \!\@tempswatrue! in default.  That is,
% $|\pcol@ac@catption@if@|{\cdot}t$ lets $\CSIndex{if@tempswa}={}\true$ iff
% \!\addcontentsline! for $t$ is to be enable.
% 
%    \begin{macrocode}
\def\pcol@ac@def@lof#1{\@nameuse{pcol@ac@caption@#1}{lof}}
\def\pcol@ac@def@lot#1{\@nameuse{pcol@ac@caption@#1}{lot}}
\def\pcol@ac@caption@enable{\pcol@ac@caption@def\@tempswatrue}
\def\pcol@ac@caption@disable{\pcol@ac@caption@def\@tempswafalse}
\def\pcol@ac@caption@def#1#2{\let\@caption\pcol@ac@caption
 \expandafter\let\csname pcol@ac@caption@if@#2\endcsname#1}
\let\pcol@ac@caption@if@lof\@tempswatrue
\let\pcol@ac@caption@if@lot\@tempswatrue
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@ac@caption}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% \begin{macro}{\pcol@ac@caption@latex}
% \changes{v1.0}{2011/10/10}
%	{Introduced for disabling \cs{addcontentsline}.}
% 
% The macro $\!\pcol@ac@caption!\arg{type}|[|\arg{lcap}|]|\<cap\>$ is made
% \!\let!-equal to \!\@caption! by \!\pcol@ac@caption@def! to do what
% \!\@caption! do but with enabling\slash disabling \!\addcontentsline!.  At
% first, it invokes $|\pcol@ac@cation@if@|{\cdot}t$ where
% $t=|\ext@|{\cdot}\arg{type}$
% 
% \SpecialIndex{\ext@figure}\SpecialIndex{\ext@table}
% 
% to let \CSIndex{if@tempswa} be $\true$ or $\false$ according to the
% enable\slash disable status of $t$.  Then, after letting
% $\!\addcontentsline!=\!\pcol@gobblethree!$ for disabling if $\false$, we
% invoke \!\pcol@ac@caption@latex!, being the \LaTeX's orignial \!\@caption!,
% giving all three arguments of \!\pcol@ac@caption! itself surrounding
% $\arg{lcap}$ with |{| and |}| for the concealment of `|]|'.  Finally, we
% let $\!\addcontentsline!=\!\pcol@addcontentsline!$ so that other macros
% uses it with its original definition.
% 
%    \begin{macrocode}
\long\def\pcol@ac@caption#1[#2]#3{%
  \@nameuse{pcol@ac@caption@if@\@nameuse{ext@#1}}%
  \if@tempswa\else \let\addcontentsline\pcol@gobblethree \fi
  \pcol@ac@caption@latex{#1}[{#2}]{#3}%
  \let\addcontentsline\pcol@addcontentsline}
\let\pcol@ac@caption@latex\@caption

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% 
% 
% \KeepSpace{7}
% \section{Page Flushing Commands}
% \label{sec:imp-flush}
% 
% \begin{macro}{\flushpage}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@flushpage} for
%	 localization.}
% \begin{macro}{\pcol@com@flushpage}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{flushpage} with the
%	 replacement of \cs{par} with \cs{pcol@par}.}
% \begin{macro}{\clearpage}
% \changes{v1.0}{2011/10/10}
%	{Made \cs{let}-equal to \cs{pcol@com@clearpage} for
%	 localization.}
% \begin{macro}{\pcol@com@clearpage}
% \changes{v1.0}{2011/10/10}
%	{Introduced as the implemenatation of \cs{clearpage} with the
%	 replacement of \cs{par} with \cs{pcol@par}.}
% \begin{macro}{\cleardoublepage}
% \changes{v1.3-5}{2013/09/17}
%	{Added as a member of local commands and made \cs{let}-equal to
%	 \cs{pcol@com@cleardoublepage}.}
% \begin{macro}{\pcol@com@cleardoublepage}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced as the implemenatation of \cs{cleardoulbepage}.}
% 
% The macros \!\pcol@com@flushpage!, \!\pcol@com@clearpage! and
% \!\pcol@com@cleardoublepage! are the implementations of \elocal{} API
% macro \!\flushpage!, \!\clearpage! and \!\cleardoublepage!  respectively.
% The first two have a common structure in which we at first invoke
% \!\pcol@flushclear! for \cscan{} and \pfcheck, and then make an \!\output!
% request by \!\pcol@invokeoutput! with \!\penalty! being \!\pcol@op@flush!
% or \!\pcol@op@clear! according to the commands.  On the other hand the
% last one simply invokes \!\pcol@com@clearpage! unconditionally, and then
% \!\pcol@com@flushpage!\footnote{
% 
% Unlike \LaTeX's \!\cleardoublepage!, it is unnecessary to put an empty
% \!\hbox! before \!\flushpage! because it is active even at the top of a
% page.}
% 
% if two-sided paging is enabled by $\CSIndex{if@twoside}=\true$, we are
% in an even-numbered page, and $\CSIndex{ifpcol@paired}=\false$ to mean we
% are not doing \npaired{} \parapag{}ing.
% 
%    \begin{macrocode}
%% Page Flushing Commands

\def\pcol@com@flushpage{\pcol@flushclear\voidb@x
  \pcol@invokeoutput\pcol@op@flush}
\def\pcol@com@clearpage{\pcol@flushclear\voidb@x
  \pcol@invokeoutput\pcol@op@clear}
\def\pcol@com@cleardoublepage{\pcol@com@clearpage
  \if@twoside \ifodd\c@page\else \ifpcol@paired\else \pcol@com@flushpage
  \fi\fi\fi}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@flushclear}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for column-scanning in synchronized column-switching and
%	 page flushing.}
% 
% The macro $\!\pcol@flushclear!\arg{box}$, invoked from
% \!\pcol@com@flushpage!, \!\pcol@com@clear~page! and \!\endparacol!,
% performs \cscan{} and \pfcheck{} prior to page flushing or environment
% closing.  After confirming we are in vertical mode by \!\pcol@par! and
% letting $d=\!\pcol@nextcol!$ be $c=\!\pcol@currcol!$ to stay in $c$, we
% invoke \!\pcol@visitallcols! for \cscan{} to give \TeX's page builder the
% chance to break the \tpage{} prior to flushing it.
% 
% Then we repeat \pfcheck{} invoking \!\pcol@output@switch! through
% \!\pcol@invokeoutput! with $\!\penalty!=\!\pcol@op@switch!$ and
% $\CSIndex{ifpcol@clear}=|\ifpcol@|\~|sync|=\true$
% 
% \SpecialIndex{\ifpcol@sync}
% 
% until the special \!\output! routine finishes with
% $\CSIndex{ifpcol@flush}=\false$ and $\arg{box}=\bot$, where
% $\arg{box}=\df=\!\pcol@topfnotes!$ if this macro is invoked from
% \!\endparacol! with non-merged \Scfnote{} typesetting.  In the repetition,
% we put \!\vfil! and \!\penalty!|-10000| to force page break into the
% tallest column, temporarily turning $\CSIndex{ifpcol@lastpage}=\false$
% using \!\ifpcol@lastpagesave!  because the broken page is not last one,
% each time the \pfcheck{} tells us to do it.  That is, we repeat the check
% while we have too tall columns due to \Scfnote{}s or, when closing
% \env{paracol} environment, deferred non-merged \Scfnote{}s.
% 
% Finally we let $\CSIndex{ifpcol@clear}$ have its default setting, i.e.,
% $\false$.
% 
%    \begin{macrocode}
\def\pcol@flushclear#1{\pcol@par
  \pcol@nextcol\pcol@currcol
  \pcol@visitallcols\@@par
  \pcol@cleartrue \global\pcol@synctrue
  \ifpcol@lastpage \pcol@lastpagesavetrue \else \pcol@lastpagesavefalse \fi
  \pcol@invokeoutput\pcol@op@switch \ifvoid#1\else \global\pcol@flushtrue \fi
  \@whilesw\ifpcol@flush\fi{%
    \pcol@lastpagefalse
    \vfil \penalty-\@M \pcol@cleartrue \global\pcol@synctrue
    \ifpcol@lastpagesave \pcol@lastpagetrue \fi
    \pcol@invokeoutput\pcol@op@switch
    \ifvoid#1\else \global\pcol@flushtrue \fi}%
  \pcol@clearfalse}

%    \end{macrocode}
% \end{macro}
% 
% 
% 
% 
% \KeepSpace{8}
% \section{Commands for Footnotes}
% \label{sec:imp-fnote}
% \changes{v1.2-2}{2013/05/11}
%	{Add the subsection ``Commands for Footnotes'' to describe newly
%	 introduced macros for page-wise footnotes.}
% 
% \begin{macro}{\footnotelayout}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced for easier declaration of footnote layout.}
% \begin{macro}{\pcol@fnlayout@c}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced for easier declaration of column-wise footnotes.}
% \begin{macro}{\pcol@fnlayout@p}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced for easier declaration of page-wise footnotes.}
% \begin{macro}{\pcol@fnlayout@m}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced for easier declaration of merged footnotes.}
% \begin{macro}{\multicolumnfootnotes}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to delclare the defalut column-wise footnote
%	 typesetting explicitly.}
% \begin{macro}{\singlecolumnfootnotes}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to delclare the page-wise but non-merged footnote
%	 typesetting.}
% \begin{macro}{\mergedfootnotes}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to delclare the page-wise and merged footnote
%	 typesetting.}
% 
% The API macros $\!\footnotelayout!\Arg{l}$ is to determine that footnotes
% are \mcfnote{} ($l=|c|$), \scfnote{} without merging ($l=|p|$), or
% \mgfnote{} and \scfnote{} ($l=m$).  The macro examines if
% $l\in\{|c|,|p|,|m|\}$ by the existence of the corresponding macro
% $|\pcol@fnlayout@|{\cdot}l$
% 
% \SpecialArrayIndex{l}{\pcol@fnlayout@}
% 
% and invokes it, or complains if not by \!\PackageError!.
% 
% The macros \!\pcol@fnlayout@c!, \!\pcol@fnlayout@p! and
% \!\pcol@fnlayout@m! turn switches $f_s=\CSIndex{ifpcol@scfnote}$,
% $f_m=\CSIndex{ifpcol@mgfnote}$ and
% $f_a=\CSIndex{ifpcol@fncounteradjustment}$ and make the counter
% \counter{footnote} global or local as follows.
% $$
% \nosv\begin{array}{l|llll}
% l&f_s&f_m&f_a&\counter{footnote}\\\hline
% \verb|c|&\false&\false&\false&\hbox{local}\\
% \verb|p|&\true&\false&\true&\hbox{global}\\
% \verb|m|&\true&\true&\true&\hbox{global}
% \end{array}
% $$
% Note that turning \CSIndex{ifpcol@fncounteradjustment} is done by
% \!\fncounteradjustment! ($\true$) or \!\nofncounteradjustment! ($\false$).
% Also note that the setting of |\ifpcol@fncounter|\~|adjustment|
% 
% \SpecialIndex{\ifpcol@fncounteradjustment}
% 
% and the globalization\slash localization of \counter{footnote} are just to
% give defaults and thus can be overridden by API macros giving non-default
% settings.  Another remark is that backward-compatible macros
% \!\multicolumnfootnotes!, \!\singlecolumnfootnotes! and
% \!\mergedfootnotes! are \!\let!-equal to \!\pcol@fnlayout@c!,
% \!\pcol@fnlayout@p! and \!\pcol@fnlayout@m! respectively.
% 
%    \begin{macrocode}
%% Commands for Footnotes

\def\footnotelayout#1{\@ifundefined{pcol@fnlayout@#1}%
  {\PackageError{paracol}{Unknown footnote layout specifier #1}}%
  {\@nameuse{pcol@fnlayout@#1}}}
\def\pcol@fnlayout@c{\global\pcol@scfnotefalse \global\pcol@mgfnotefalse
  \localcounter{footnote}\nofncounteradjustment}
\def\pcol@fnlayout@p{\global\pcol@scfnotetrue \global\pcol@mgfnotefalse
  \globalcounter{footnote}\fncounteradjustment}
\def\pcol@fnlayout@m{\pcol@fnlayout@p\global\pcol@mgfnotetrue}

\let\multicolumnfootnotes\pcol@fnlayout@c
\let\singlecolumnfootnotes\pcol@fnlayout@p
\let\mergedfootnotes\pcol@fnlayout@m

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{2}
% \begin{macro}{\@footnotetext}
% \begin{macro}{\pcol@fntext}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for footnote encapsulation and deferring.}
% \begin{macro}{\pcol@fntexttop}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for footnote encapsulation.}
% \begin{macro}{\pcol@fntextother}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for footnote encapsulation and deferring.}
% 
% The macro \!\pcol@fntext!\marg{text} is our own version of \LaTeX's
% \!\@footnotetext! used in \!\footnote! and \!\footnotetext! to \!\insert!
% the footnote $\arg{text}$ through \!\footins!.  Since the original and our
% own are made \!\let!-equal by \!\pcol@zparacol!, our own is active
% throughout the environment.  The customization is done to examine if the
% footnote should be deferred and to encapsulate the footnote in a \!\vbox!.
% 
% The deferred footnote insertion is in effect if the footnote typesetting
% is \scfnote{} and \!\footnote! or \!\footnotetext!  appears in a page
% $p<\ptop$.  If so, we put the footnote $\arg{text}$ encapsulated in a
% \!\vbox! by \!\pcol@fntextbody! to the tail of $\df=\!\pcol@topfnotes!$
% with \!\penalty!\!\interlinepenalty! preceding it for the split in
% \!\pcol@deferredfootins!, using \!\pcol@fntextother!\marg{text} whose sole
% user is this macro.  Note that the decision of deferring is done based on
% $p=\!\pcol@page!$ which could be less than that of the page in which the
% footnoted text appears because the paragraph having the text will have a
% page break before the text.  Therefore, $p$ for the footnote can be
% $\ptop$, but this misjudment will not cause problems because the footnote
% will eventually be put in $\ptop$ through $\df$ when the page break
% occurs.
% 
% Otherwise the footnote $\arg{text}$ is processed by
% \!\pcol@fntexttop!\marg{text}, also used solely in this macro, to
% \!\insert! it through \!\footins! as usual but after the encapsulation by
% \!\pcol@fntextbody! and with \!\penalty!\!\interlinepenalty! following it
% to allow \TeX's page builder to split footnotes.
% 
% Note that \!\pcol@fntexttop! and \!\pcol@fntextother! have \!\long!
% property because $\arg{text}$ may have two or more paragraphs.
% 
%    \begin{macrocode}
\def\pcol@fntext{%
  \let\reserved@a\pcol@fntexttop
  \ifpcol@scfnote \ifnum\pcol@page<\pcol@toppage
    \let\reserved@a\pcol@fntextother
  \fi\fi
  \reserved@a}
\long\def\pcol@fntexttop#1{%
  \pcol@Logfn{\pcol@fntexttop{\@thefnmark}}%
  \insert\footins{\pcol@fntextbody{#1}\penalty\interlinepenalty}}
\long\def\pcol@fntextother#1{%
  \global\setbox\pcol@topfnotes\vbox{\unvbox\pcol@topfnotes
    \penalty\interlinepenalty\pcol@fntextbody{#1}}}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@fntextbody}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for footnote encapsulation and height capping.}
% 
% The macro \!\pcol@fntextbody!\marg{text}, invoked from \!\pcol@fntexttop!
% and \!\pcol@fntext~other!, encapsulates the footnote $\arg{text}$ in a
% \!\vbox! whose height is $h_{\max}=\!\textheight!-\!\skip!\~\!\footins!$ at
% tallest.  The encapsulation is to inhibit page breaks in a footnote
% because the split by the break will make some skips and other items
% eliminated causing a weird result when split portions are {\em joined}.
% The height capping is thus required to find a page in which the footnote
% resides.
% 
% The macro at first does operations done in \LaTeX's 
% \!\@footnotetext! to put $\arg{text}$ in \!\@tempboxa! but with one
% exception that $\!\hsize!=\!\textwidth!$ rather than \!\columnwidth! when
% \Scfnote{} typesetting is in effect.  Note that this part is blindly copied
% from the original though it should be meaningless to set
% \!\interlinepenalty!, \!\splittopskip!, \!\splitmaxdepth! and
% \!\floatingpenalty! because $\arg{text}$ is encapsulated.
% 
% Then the height-plus-depth of the box is compared with $h_{\max}$ and, if
% it exceeds the limit, the height of the box is set $h_{\max}$, the
% footnote is made followed by a \!\vss! to avoid overfull, and a warning
% message of too tall is put by \!\PackageWarning!.  Finally, the box is put
% into \!\footins! or $\df$ by the invoker of this macro.
% 
%    \begin{macrocode}
\long\def\pcol@fntextbody#1{\setbox\@tempboxa\vbox{%
    \reset@font\footnotesize
    \interlinepenalty\interfootnotelinepenalty
    \splittopskip\footnotesep
    \splitmaxdepth\dp\strutbox \floatingpenalty\@MM
    \hsize \ifpcol@scfnote \textwidth \else \columnwidth \fi
    \@parboxrestore
    \protected@edef\@currentlabel{\p@footnote\@thefnmark}%
    \color@begingroup
    \@makefntext{%
      \rule\z@\footnotesep\ignorespaces#1\@finalstrut\strutbox}%
    \color@endgroup}%
  \@tempdima\ht\@tempboxa \advance\@tempdima\dp\@tempboxa
  \@tempdimb\textheight \advance\@tempdimb-\skip\footins
  \ifdim\@tempdima>\@tempdimb
    \setbox\@tempboxa\vbox to\@tempdimb{\unvbox\@tempboxa\vss}%
    \PackageWarning{paracol}{Too tall footnote}%
  \fi
  \box\@tempboxa}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\fncounteradjustment}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to make \string\texttt{footnote} counter is consistent
%	 with its origin at the beginning of \string\texttt{paracol} and the
%	 number of footnotes given in the environment at its end.}
% \begin{macro}{\nofncounteradjustment}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to disable the footnote counter adjustment.}
% 
% The API macros \!\fncounteradjustment! and \!\nofncounteradjustment! turns
% |\ifpcol@|\~|fncounteradjustment|
% 
% \SpecialIndex{\ifpcol@fncounteradjustment} 
% 
% $\true$ or $\false$, to enable or disable the \counter{footnote} counter
% adjustment letting $\!\c@footnote!=\bf+\nf$ in \Endparacol, respectively.
% After the definition we disable the adjustment to give the default setting.
% 
%    \begin{macrocode}
\def\fncounteradjustment{\global\pcol@fncounteradjustmenttrue}
\def\nofncounteradjustment{\global\pcol@fncounteradjustmentfalse}
\nofncounteradjustment

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \KeepSpace{2}
% \begin{macro}{\pcol@footnoterule}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to keep the original definition of \cs{footnoterule}.}
% \begin{macro}{\pcol@@footnote}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to keep the original definition of \cs{footnote}.}
% \begin{macro}{\pcol@@footnotemark}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to keep the original definition of \cs{footnotemark}.}
% \begin{macro}{\pcol@@footnotetext}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced to keep the original definition of \cs{footnotetext}.}
% 
% The macros \!\pcol@footnoterule!, \!\pcol@@footnote!,
% \!\pcol@@footnotemark! and \!\pcol@@footnotetext! are to keep the original
% defitions of \!\footnoterule!, \!\footnote!, \!\footnotemark! and
% \!\footnotetext! in them, respectively, so that we define our own versions
% with references to the originals.
% 
%    \begin{macrocode}
\let\pcol@footnoterule\footnoterule
\let\pcol@@footnote\footnote
\let\pcol@@footnotemark\footnotemark
\let\pcol@@footnotetext\footnotetext
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{4}
% \begin{macro}{\footnote}
% \begin{macro}{\pcol@footnote}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for \cs{footnote*} and footnote counter adjustment.}
% \begin{macro}{\pcol@ifootnote}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for \cs{footnote*} and footnote counter adjustment.}
% \begin{macro}{\footnotemark}
% \begin{macro}{\pcol@footnotemark}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for \cs{footnotemark*} and footnote counter adjustment.}
% \begin{macro}{\pcol@ifootnotemark}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for \cs{footnotemark*} and footnote counter adjustment.}
% 
% The macros \!\pcol@footnote! and \!\pcol@footnotemark! are the
% implementations of our own versions of \!\footnote! and \!\footnotemark!
% which are made \!\let!-equal to them by \!\pcol@zparacol!, respectively.
% The reasons why we need to have our own are two-fold; to have starred
% version of them; and to maintain $\nf=\!\pcol@nfootnotes!$ for the
% \counter{footnote} counter adjustment.
% 
% The implementations of the starred versions
% \!\footnote!|*|\oarg{num}\marg{text} and 
% \!\footnotemark!|*|\~\oarg{num} have common structure in which we invoke
% \!\pcol@adjustfnctr!$\arg{macro}$\oarg{num} if `|*|' is given, to let
% \!\c@footnote! have the number relative to $\bf=\!\pcol@footnotebase!$ or
% to itself.  Then the macros \!\pcol@ifootnote! or \!\pcol@ifootnotemark!
% are invoked from \!\pcol@adjustfnctr! or the else-part of \!\@ifstar! to
% perform the operations common to both cases with and without `|*|', i.e.,
% invoking the original version \!\pcol@@footnote! or \!\pcol@@footnotemark!
% after incrementing $\nf$.  One caution is that
% $\arg{macro}=\!\pcol@ifootnote!$ for \!\footnote!, but
% $\arg{macro}=|{|\!\pcol@ifootnotemark!\!\relax!|}|$ for \!\footnotemark!
% so that \!\@ifnextchar! in \!\pcol@@footnotemark!  invoked from
% \!\pcol@ifootnotemark! eats \!\relax! to terminate space skipping and thus
% spaces following \oarg{num} are kept.
% 
%    \begin{macrocode}
\def\pcol@footnote{\@ifstar{\pcol@adjustfnctr\pcol@ifootnote}\pcol@ifootnote}
\def\pcol@ifootnote{\global\advance\pcol@nfootnotes\@ne \pcol@@footnote}
\def\pcol@footnotemark{\@ifstar
  {\pcol@adjustfnctr{\pcol@ifootnotemark\relax}}%
  \pcol@ifootnotemark}
\def\pcol@ifootnotemark{\global\advance\pcol@nfootnotes\@ne
  \pcol@@footnotemark}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\pcol@adjustfnctr}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for \cs{footnote*} and \cs{footnotemark*}.}
% \begin{macro}{\pcol@iadjustfnctr}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for \cs{footnote*} and \cs{footnotemark*}.}
% \begin{macro}{\pcol@calcfnctr}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for \cs{footnote*}, \cs{footnotemark*} and
%	 \cs{footnotetext*}.}
% 
% The macro \!\pcol@adjustfnctr!$\arg{macro}$\oarg{num}, invoked from the
% then-part of \!\@ifstar! in \!\pcol@footnote! and \!\pcol@footnotemark!,
% calculates the number to be set into \!\c@footnote! by
% \!\pcol@calcfnctr!$\arg{num}$\!\@nil! after processing the optional
% argument $\arg{num}$ by \!\pcol@iadjustfnctr! with default `|+1|', and
% then invoke $\arg{macro}$ being \!\pcol@ifootnote! or
% \!\pcol@ifootnotemark!\!\relax!.  Since \!\pcol@calcfnctr! returns the
% number \!\c@footnote! should have and the counter is incremented by
% \!\stepcounter! in \!\pcol@@footnote! or \!\pcol@@footnotemark!, we
% decrement the counter prior to invoke $\arg{macro}$.
% 
% The macro \!\pcol@calcfnctr!$\arg{num}$\!\@nil!, also invoked from
% \!\pcol@iifootnotetext!, calculate $m$ specified by $\arg{num}$ as follows,
% where $f=\!\c@footnote!$, to return it through \!\@tempcnta!.
% $$
% m=\cases{f+k&$\arg{num}=|+|k$\cr
%           f-k&$\arg{num}=|-|k$\cr
%           \bf+k&$\arg{num}=k$}
% $$
% 
%    \begin{macrocode}
\def\pcol@adjustfnctr#1{\@ifnextchar[%]
  {\pcol@iadjustfnctr{#1}}{\pcol@iadjustfnctr{#1}[+1]}}
\def\pcol@iadjustfnctr#1[#2]{\pcol@calcfnctr#2\@nil
  \global\c@footnote\@tempcnta \global\advance\c@footnote\m@ne#1}
\def\pcol@calcfnctr#1#2\@nil{\@tempcnta\c@footnote
  \def\reserved@a{#1}\def\reserved@b{+}%
  \ifx\reserved@a\reserved@b \advance\@tempcnta#2\relax
  \else \def\reserved@b{-}%
  \ifx\reserved@a\reserved@b \advance\@tempcnta-#2\relax
  \else \@tempcnta\pcol@footnotebase \advance\@tempcnta#1#2\relax
  \fi\fi}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{2}
% \begin{macro}{\footnotetext}
% \begin{macro}{\pcol@footnotetext}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for \cs{footnotetext*}.}
% \begin{macro}{\pcol@ifootnotetext}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for \cs{footnotetext*}.}
% \begin{macro}{\pcol@iifootnotetext}
% \changes{v1.2-2}{2013/05/11}
% 	{Introduced for \cs{footnotetext*}.}
% 
% The macros \!\pcol@footnotetext! is the implementation of our own versions
% of \!\footnotetext!  which is made \!\let!-equal to it by
% \!\pcol@zparacol!.  The reasons why we need to have our own is to have the
% starred version.  That is, if `|*|' is not given, we simply invoke the
% original version \!\pcol@@footnotetext!.  Otherwise we invoke
% \!\pcol@ifootnotetext! which then examines if the optional argument
% \oarg{num} is presented.  If so, we invoke \!\pcol@iifootnotetext! in
% which \!\pcol@calcfnctr!$\arg{num}$\!\@nil! is invoked to have the value
% $m$ being the footnote ordinal with which we invoke
% \!\pcol@@footnotetext!\oarg{\mbox{$m$}} with two \!\expandafter!s to
% extract $m$ from \!\@tempcnta!.  Otherwise, i.e., \oarg{num} is not given,
% we increment \!\c@footnote! by \!\stepcounter! before invoking
% \!\pcol@@footnotetext!.
% 
%    \begin{macrocode}
\def\pcol@footnotetext{\@ifstar\pcol@ifootnotetext\pcol@@footnotetext}
\def\pcol@ifootnotetext{\@ifnextchar[%]
  \pcol@iifootnotetext{\stepcounter{footnote}\pcol@@footnotetext}}
\def\pcol@iifootnotetext[#1]{\pcol@calcfnctr#1\@nil
  \expandafter\pcol@@footnotetext\expandafter[\number\@tempcnta]}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% 
% 
% \KeepSpace{13}
% \section{Commands for Marginal Notes}
% \label{sec:imp-mpar}
% \changes{v1.35-3}{2018/12/31}
% 	{Add the section ``Commands for Marginal Notes'' to describe newly
%	 introduced macros for the emulation of \cs{marginnote}.}
% 
% \begin{macro}{\marginpar}
% \changes{v1.35-3}{2018/12/31}
% 	{Locally modified in \cs{pcol@zparacol} for the emulation of
%	 \cs{marginnote}.}
% \begin{macro}{\pcol@marginpar}
% \changes{v1.35-3}{2018/12/31}
% 	{Introduced as the in-\texttt{paracol} version of \cs{marginpar} for
%	 the emulation of \cs{marginnote}.}
% \begin{macro}{\pcol@@marginpar}
% \changes{v1.35-3}{2018/12/31}
% 	{Introduced to keep the orginal version of \cs{marginpar} for
%	 the emulation of \cs{marginnote}.}
% \begin{macro}{\@mn@@marginnote}
% \changes{v1.35-3}{2018/12/31}
% 	{Locally modified in \cs{pcol@zparacol} for the emulation of
%	 \cs{marginnote}.}
% \begin{macro}{\pcol@marginnote}
% \changes{v1.35-3}{2018/12/31}
% 	{Introduced as the in-\texttt{paracol} version of
%	 \cs{@mn@@marginnote} for the emulation of \cs{marginnote}.}
% \begin{macro}{\pcol@mn@warning}
% \changes{v1.35-3}{2018/12/31}
% 	{Introduced to put a warning message to show \cs{marginnote} is
%	 emulated.}
% \begin{macro}{\@xympar}
% \changes{v1.35-3}{2018/12/31}
% 	{Locally modified in \cs{pcol@zparacol} for the emulation of
%	 \cs{marginnote}.}
% \begin{macro}{\pcol@xympar}
% \changes{v1.35-3}{2018/12/31}
% 	{Introduced as the in-\texttt{paracol} version of
%	 \cs{@xympar} for the emulation of \cs{marginnote}.}
% \begin{macro}{\pcol@@xympar}
% \changes{v1.35-3}{2018/12/31}
% 	{Introduced to keep the orginal version of \cs{@xympar} for the
%	 emulation of \cs{marginnote}.} 
% \begin{macro}{\pcol@mparoffset}
% \changes{v1.35-3}{2018/12/31}
% 	{Introduced to have the vertical offset for the emulation of
%	 \cs{marginnote}.}
% The API macro \!\marginnote!\oarg{left}\marg{right}\oarg{voffset} given by
% the package \textsf{marginnote} is emulated using
% \!\marginpar!\oarg{left}\marg{right} and \!\pcol@addmarginpar! in
% \!\output! routine.  The basic mechanism is to pass the vertical offset
% $\arg{voffset}$ to \!\pcol@addmarginpar! through $|\dimen|\arg{b}$ where
% $b$ is the \!\insert! to carry $\arg{left}$.  The offset passing is
% implemented as follows.
% 
% \begin{itemize}
% \item
% \!\marginpar! is made \!\let!-equal to our own version \!\pcol@marginpar!
% in \!\pcol@zparacol! so that it \!\let! the macro \!\pcol@mparoffset! be
% \!\z@! and then invoke \LaTeX's origincal version kept in
% \!\pcol@@marginpar!, because the marginal note given by \!\marginpar! will
% not be shifted.
% 
% \item
% The internal macro
% \!\@mn@@marginnote!\oarg{left}\marg{right}\oarg{voffset} defined in
% \textsf{marginnote} is made \!\let!-equal to our own version
% \!\pcol@marginnote! in \!\pcol@zparacol! so that it |\def|ines
% \!\pcol@mparoffset! to have $\arg{voffset}$ and then invoke
% \!\pcol@@marginpar!\oarg{left}\~\marg{right} for the emulation.  In the
% invokation, \textsf{marginnote}'s typesetting macros \!\margin~font!,
% \!\raggedleftmarginnote! and \!\raggedrightmarginnote! are attached to
% $\arg{left}$ and $\arg{right}$.
% 
% \item
% \LaTeX's internal macro \!\@xympar! for the last operations of
% \!\marginpar! is made \!\let!-equal to our own version in
% \!\pcol@zparacol! so that it assigns the offset in \!\pcol@mparoffset! to
% |\dimen|\!\@marbox! for $\arg{left}$, if $\!\@floatpenalty!<0$ to mean
% other macros for \!\marginpar! have not detected any errors.
% \end{itemize}
% 
% In addition, we raise a warning that \!\marginnote! is emulated by
% \!\pcol@mn@warning!, which is made \!\let!-equal to \!\relax! in the caller
% \!\pcol@marginnote! after the invokation so that the warning message is
% put just once.
% 
%    \begin{macrocode}
%% Commands for Marginal Notes

\def\pcol@marginpar{\let\pcol@mparoffset\z@ \pcol@@marginpar}
\long\def\pcol@marginnote[#1]#2[#3]{\endgroup
  \pcol@mn@warning \global\let\pcol@mn@warning\relax
  \def\pcol@mparoffset{#3}%
  \pcol@@marginpar[\marginfont\raggedleftmarginnote#1]%
                  {\marginfont\raggedrightmarginnote#2}}
\def\pcol@mn@warning{%
  \PackageWarning{paracol}{\string\margninnote\space is emulated by
    \string\marginpar.}}
\def\pcol@xympar{%
  \ifnum\@floatpenalty<\z@ \global\dimen\@marbox\pcol@mparoffset\relax \fi
  \pcol@@xympar}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% 
% \KeepSpace{9}
% \section{Two-Sided Typesetting}
% \label{sec:imp-swap}
% \changes{v1.2-4}{2013/05/11}
%	{Add the section ``Column-Swapping'' to describe newly
%	 introduced macros for column-swapping.}
% \changes{v1.3-5}{2013/09/17}
%	{Rename the section title from ``Column-Swapping'' to ``Two-Sided
%	 Typesetting''.}
% 
% \begin{macro}{\twosided}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced as an easier API for various two-sided typesetting.}
% \changes{v1.3-3}{2013/09/17}
%	{Add two-sided background painting.}
% \changes{v1.3-4}{2013/09/17}
%	{Add two-sided marginal note placement.}
% \begin{macro}{\pcol@twosided}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced to implement \cs{twosided}.}
% \changes{v1.31}{2013/10/10}
%	{Fix spelling ``twosiding'' replacing it with ``two-siding'' in the
%	 error message.}
% \begin{macro}{\pcol@twosided@p}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced to implement \cs{twosided} with \string\texttt{[p]}.}
% \begin{macro}{\pcol@twosided@c}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced to implement \cs{twosided} with \string\texttt{[c]}.}
% \begin{macro}{\pcol@twosided@m}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced to implement \cs{twosided} with \string\texttt{[m]}.}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced for two-sided marginal note placement.}
% \begin{macro}{\pcol@twosided@b}
% \changes{v1.3-5}{2013/09/17}
%	{Introduced to implement \cs{twosided} with \string\texttt{[b]}.}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced for two-sided background painting.}
% \begin{macro}{\swapcolumninevenpages}
% \changes{v1.2-4}{2013/05/11}
%	{Introduced to enable column-swapping.}
% \begin{macro}{\noswapcolumninevenpages}
% \changes{v1.2-4}{2013/05/11}
%	{Introduced to disable column-swapping.}
% 
% \def\inornot{\mathrel{{\in}/{\notin}}}
% 
% The API macro $\!\twosided!|[|T|]|$ where $T=t_1t_2\cdots$ is to
% enable\slash disable two-sided paging with
% $\CSIndex{if@twoside}=\true/\false$ ($|p|\inornot T$), two-sided \cswap{}
% with $\CSIndex{ifpcol@swapcolumn}\~={\true/\false}$ ($|c|\inornot T$),
% two-sided % marginal note placement with
% $\CSIndex{ifpcol@swapmarginpar}={\true/\false}$ ($|m|\inornot T$), and/or
% two-sided \bgpaint{} with $\CSIndex{ifpcol@bg@swap}={\true/\false}$
% ($|b|\inornot{}T$) individually, or to enable all of them as a whole
% when the optional argument is not given.
% 
% The macro invokes \!\pcol@twosided! with the optional argument $T$ if
% provided, or with $T=|pcmb|$ otherwise to enable all features.  Then
% \!\pcol@twosided! at first turns all the switches $\false$ an then scans
% all non-space tokens $t\in T$ invoking $|\pcol@twosided@|{\cdot}t$ if it
% is defined and thus $t\in\{|p|,|c|,|m|,|b|\}$ to turn the corresponding
% switch $\true$, or complains that the feature $t$ is unknown.
% 
% Note that backward-compatible API macros 
% \!\swapcolumninevenpages! and \!\noswapcolumn~inevenpages! are still
% availabel to turn $\CSIndex{ifpcol@swapcolumn}$ $\true$ an $\false$
% respectivey.
% 
%    \begin{macrocode}
%% Column Swapping

\def\twosided{\@ifnextchar[%]
  {\pcol@twosided}{\pcol@twosided[pcmb]}}
\def\pcol@twosided[#1]{%
  \global\@twosidefalse \global\pcol@swapcolumnfalse
  \global\pcol@swapmarginparfalse \global\pcol@bg@swapfalse
  \@tfor\reserved@a:=#1\do{%
    \@ifundefined{pcol@twosided@\reserved@a}%
      {\PackageError{paracol}{Unknown two-siding feature \reserved@a}}%
      {\@nameuse{pcol@twosided@\reserved@a}}}}
\def\pcol@twosided@p{\global\@twosidetrue}
\def\pcol@twosided@c{\global\pcol@swapcolumntrue}
\def\pcol@twosided@m{\global\pcol@swapmarginpartrue}
\def\pcol@twosided@b{\global\pcol@bg@swaptrue}

\def\swapcolumninevenpages{\global\pcol@swapcolumntrue}
\def\noswapcolumninevenpages{\global\pcol@swapcolumnfalse}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@swapcolumn}
% \changes{v1.2-4}{2013/05/11}
%	{Introduced to convert column ordinal and its position.}
% \changes{v1.3-2}{2013/09/17}
%	{Add two arguments $C^0$ and $C^1$ as the third and fourth ones to
%	 modifiy the calculation of $c_2$ with them for column-swapping with
%	 parallel-paging.}
% \changes{v1.3-3}{2013/09/17}
%	{Add the assignment of \cs{pcol@colsepid} to let it have $c_2-1$ if
%	 swapped or $c_2$ otherwise.}
% \changes{v1.3-4}{2013/09/17}
%	{Add a user \cs{pcol@addmarginpar} and remove \cs{paracol},
%	 \cs{pcol@sptxt} and \cs{pcol@switchcol}.} 
% \begin{macro}{\pcol@colsepid}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to be let have $c_2-1$ if swapped or $c_2$ otherwise by
%	 \cs{pcol@swapcolumn}.}
% 
% The macro \!\pcol@swapcolumn!$\<c_1\>\<c_2\>\<\Cfrom\>\<\Cto\>$ converts
% the column ordinal $c$ or position $c'$ in the \!\count!
% register\footnote{
% 
% Or the \!\dimen! register \!\z@!.}
% 
% $c_1$ to the position or ordinal to set it in the \!\count! register
% $c_2$, for a \parapag{}e having columns $c\In\Cfrom\Cto$.  That is, we let
% $c_2=(\Cto-1)-(c_1-\Cfrom)$ if $\CSIndex{ifpcol@swapcolumn}=\true$ to mean
% the \cswap{} is in effect and \!\c@page! is even, while $c_2=c_1$
% otherwise.  We also let $c^g=\!\pcol@colsepid!=c_2-1$ if swapped, or
% $c^g=c_2$ otherwise, so that it has the ordinal of the \csepgap{}
% {\em physically} following the column $c_2$.
% 
% The macro is used in \!\pcol@ioutputelt!, \!\pcol@addmarginpar!,
% \!\pcol@imakeflushedpage! and \!\pcol@iflushfloats! with
% $(c_1,c_2)=(c',c)$, and in \!\pcol@addmarginpar! (another use) with
% $(c_1,c_2)=(c,c')$.  Note that in the uses in the macros above except for
% \!\pcol@addmarginpar!, \!\c@page!  definitely has the page number for the
% page to be shipped out.  As for \!\pcol@addmarginpar! on the other hand,
% \!\c@page! can be different from the ship-out page number to produce a
% weird result if their parities are different, due to page jump.  However
% this problem is not so severe because it just affects the position of
% marginal notes which \LaTeX{} itself may misplace.
% 
%    \begin{macrocode}
\def\pcol@swapcolumn#1#2#3#4{%
  \edef\pcol@colsepid{\number#1}%
  \ifpcol@swapcolumn
    \ifodd\c@page\relax #2#1\relax
    \else
      #2#4\relax \advance#2-#1\relax \advance#2#3\relax \advance#2-\tw@
      \edef\pcol@colsepid{\number#2}%
      \advance#2\@ne
    \fi
  \else #2#1\relax
  \fi}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \KeepSpace{2}
% \begin{macro}{\marginparthreshold}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to spacify the smallest ordinal of columns whose marginal
%	 notes go to the right margin if not swapped.}
% \begin{macro}{\pcol@marginparthreshold}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to implement \cs{marginparthreshold}.}
% \begin{macro}{\pcol@mpthreshold@l}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to keep the value specified by \cs{marginparthreshold}
%	 for columns in left parallel-pages.}
% \begin{macro}{\pcol@mpthreshold@r}
% \changes{v1.3-4}{2013/09/17}
%	{Introduced to keep the value specified by \cs{marginparthreshold}
%	 for columns in right parallel-pages.}
% 
% The API macro $\!\marginparthreshold!\Arg{t_l}|[|t_r|]|$ determines the
% smallest ordinal $t_l$ of columns in left \parapag{}es whose marginal
% notes go to the right margin in fundamental setting of marginal note
% positioning, while the threshold in right \parapag{}es is given by $t_r$
% if provided or by $t_l$ otherwise.  That is, marginal notes given in a
% column $c$ in a page $p$ s.t.\ $c\In0\CL$ (resp.\ $\LBRP\CL\C$) go left if
% $c<t_l$ (resp.\ $c<t_r$) while they go right if $c\geq t_l$ (resp.\ $c\geq
% t_r$), providing
% $$
% (\CSIndex{ifpcol@swapmarginpar}\;\land\;\page(p)\bmod2=0)
% \not\equiv\CSIndex{if@reversemargin}=\false
% $$
% or the margins are swapped otherwise.
% 
% The macro \!\def!ines \!\pcol@mpthreshold@l! to let it have $t_l$ after a
% assigning $t_l$ to \!\@tempcnta! to ensure $t_l$ gives some number, and
% then do the same for \!\pcol@mpthreshold@r! with $t_r$ by
% \!\pcol@marginparthreshold! if $t_r$ is provided, or let the marco have
% $t_l$ otherwise.  Note that at the top level we do
% \!\marginparthreshold!|{1}| to give defaults.  Also note that
% \!\pcol@mpthreshold@l! and \!\pcol@mpthreshold@r! are referred to solely
% in \!\pcol@addmarginpar!.
% 
%    \begin{macrocode}
\def\marginparthreshold#1{\@tempcnta#1\relax
  \xdef\pcol@mpthreshold@l{\number\@tempcnta}%
  \@ifnextchar[%]
    \pcol@marginparthreshold{\xdef\pcol@mpthreshold@r{\number\@tempcnta}}}
\def\pcol@marginparthreshold[#1]{\@tempcnta#1\relax
  \xdef\pcol@mpthreshold@r{\number\@tempcnta}}
\marginparthreshold{1}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% 
% \KeepSpace{5}
% \section{Commands for Text Coloring}
% \label{sec:imp-commcolor}
% \changes{v1.3-6}{2013/09/17}
%	{Add the section ``Commands for Text Coloring'' to distinguish
%	 macros inside and outside \cs{output} routine and describe latters
%	 in this section.}
% 
% \begin{macro}{\columncolor}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to define the default color of a column.}
% \changes{v1.22}{2013/06/30}
%	{Add the definition of \cs{pcol@colorcommand} for warning in
% 	 \cs{pcol@icolumncolor}.}
% \begin{macro}{\pcol@xcolumncolor}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to implement \cs{columncolor}.}
% \begin{macro}{\pcol@ycolumncolor}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to implement \cs{columncolor}.}
% \begin{macro}{\pcol@columncolor}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to implement \cs{columncolor}.}
% 
% The API macro \!\columncolor!\oarg{mode}\marg{color}\oarg{c} defines the
% default color specified by $\arg{color}$ optionally with color
% $\arg{mode}$ of the column $c$ being the current column or that specified
% by the optional argument.  After \!\def!ining \Midx{\!\pcol@colorcommand!}
% being the \!\string! of this macro itself, and processing two optional
% arguments $\arg{mode}$ and $c$ through macros \!\pcol@xcolumncolor!,
% \!\pcol@ycolumncolor! and \!\pcol@columncolor!, the macro
% \!\pcol@icolumncolor!\marg{cmd}\oarg{c} is invoked to perform real
% operations with the coloring command
% $\arg{cmd}=\!\color!$\oarg{mode}\marg{color}.
% 
%    \begin{macrocode}
%% Commands for Text Coloring

\def\columncolor{\def\pcol@colorcommand{\string\columncolor}%
  \@ifnextchar[%]
    \pcol@xcolumncolor\pcol@ycolumncolor}
\def\pcol@xcolumncolor[#1]#2{\pcol@columncolor{\color[#1]{#2}}}
\def\pcol@ycolumncolor#1{\pcol@columncolor{\color{#1}}}
\def\pcol@columncolor#1{\@ifnextchar[%]
  {\pcol@icolumncolor{#1}}{\pcol@icolumncolor{#1}[\number\pcol@currcol]}}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\normalcolumncolor}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to define the default color of a column is
%	 \cs{normalcolor}.} 
% \changes{v1.22}{2013/06/30}
%	{Add the definition of \cs{pcol@colorcommand} for warning in
% 	 \cs{pcol@icolumncolor}.}
% 
% The API macro \!\normalcolumncolor!\oarg{c} defines the default color of
% the column $c$, being the current column or that specified by the optional
% argument, is \!\normalcolor!.  That is, after \!\def!ining
% \Midx{\!\pcol@colorcommand!}  being the \!\string! of this macro itself,
% this macro simply invokes \!\pcol@icolumncolor!\marg{cmd}\oarg{c} to
% perform real operations with the coloring command
% $\arg{cmd}=\!\normalcolor!$.
% 
%    \begin{macrocode}
\def\normalcolumncolor{\def\pcol@colorcommand{\string\normalcolumncolor}%
  \@ifnextchar[%]
    {\pcol@icolumncolor\normalcolor}%
    {\pcol@icolumncolor\normalcolor[\number\pcol@currcol]}}
%    \end{macrocode}
% \end{macro}
% 
% \KeepSpace{1}
% \changes{v1.22}{2013/06/30}
%	{\cs{pcol@getshadowcc} was introduced for setting $\hat\gamma_0^c$
%	 into $\gamma_0^c$ locally, but removed in v1.34.} 
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@getshadowcc} is removed according to the change of text
%	 coloring from \cs{output} to \cs{insert}.}
% \begin{macro}{\pcol@icolumncolor}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to implement \cs{columncolor} and
%	 \cs{normalcolumncolor}.} 
% \changes{v1.22}{2013/06/30}
%	{Add warning of ineffective uses of \cs{columncolor} and
%	 \cs{normalcolumncolor}, and modify the mechanism to update
%	 $\gamma_0^c$ and to rewind\slash reestablish color stack.}
% \changes{v1.23}{2013/07/08}
%	{Add an argument of \cs{relax} to \cs{pcol@color@invokeoutput}
%	 because any insertion after \cs{vadjust} is not required or
%	 justified.}
% \changes{v1.24}{2013/07/27}
%	{Add math mode to the cases of ineffective use.}
% \changes{v1.34}{2018/05/07}
%	{Remove the invocations of \cs{pcol@iicolumncolor} for
%	 $\cs{pcol@columncolor@shadow}\cdot c$ because it no longer exists,
%	 completly change the opearations in the case the target column $c$
%	 is the current one according to the new method with \cs{insert},
%	 and add immediate setting of $\gamma_0^c$ in the case $c$ is not
%	 current.}
% \begin{macro}{\pcol@iicolumncolor}
% \changes{v1.22}{2013/06/30}
%	{Introduced for setting $\gamma_0^c$ and $\hat\gamma_0^c$, and
%	 pushing $\chi$.}
% \changes{v1.34}{2018/05/07}
%	{Remove the third argument, change the second argument from a
%	 control sequence name to the target column, add a grouping to
%	 surround the entire body of the macro, and change the body of
%	 $\gamma_0^c$ so that it only has the color information.}
% \begin{macro}{\pcol@scancst@shadow}
% \changes{v1.34}{2018/05/07}
%	{Introduced to rewind or establish the color stack $\hat\Gamma^c$.}
% 
% The macro \!\pcol@icolumncolor!\marg{cmd}\oarg{c}, invoked from
% \!\pcol@columncolor! and \!\normal~columncolor!, performs the operations to
% define the default color of the column $c$ with the coloring command
% $\arg{cmd}\in\{\!\color!\hbox{\oarg{mode}}\ARg{color},\,\!\normalcolor!\}$
% as follows.  First we examine if \!\set@color! is not \!\relax! and we are
% in non-internal vertical or non-restricted horizontal mode and, if not, we
% complain the command whose name is in \!\pcol@colorcommand! is ineffective
% by \!\PackageWarning! and do nothing.
% 
% Otherwise and if we are not in a \env{paracol} environment, i.e.,
% \!\paracol! is not \!\let!-equal to \!\pcol@paracol!, we simply invoke
% \!\pcol@iicolumncolor! to let $\Celtshadow^c=|\pcol@columncolor|\cdot c$
% have the color $\chi$ specified by $\arg{cmd}$ so that the next
% \beginparacol{} will let $\Celt^c$ have the coloring \!\special!  for
% $\chi$.  If we are in a \env{paracol} environment but in a column $c'\neq
% c$, on the other hand, we also let $\Celtshadow=\chi$ but in addition let
% $\Celt^c=|\pcol@columncolor@box|\cdot c$ have the coloring \!\special! for
% $\chi$ immediately so that it is effective in the next \cswitch{} to $c$.
% This immediate setting of $\Celt^c$ is done by invoking $\arg{cmd}$ with
% the original \!\set@color!  saved in \!\pcol@set@color! and the
% nullification of \!\aftergroup!, after acquiring an \!\insert! for it if
% necessary,
% 
% \SpecialArrayIndex{c}{\pcol@columncolor}
% \SpecialArrayIndex{c}{\pcol@columncolor@box}
% 
% Otherwise, i.e., if we are in a \env{paracol} environment and in the
% column $c$, at first we invoke \!\pcol@scancst@shadow! to rewind
% $\CSTshadow^c$ applying $\!\@elt!=\!\reset@color!$ to
% $\celtshadow_i\in\CSTshadow^c$.  Then, after letting $\Celtshadow^c=\chi$,
% we invoke \!\pcol@scancst@shadow! again to reestablish $\CSTshadow^c$ with
% the new $\Celtshadow^c$ so that $\Celtshadow^c$ is at the bottom of the
% \colorstack{} in |.tex|.  In this scan $\!\@elt!\arg{\celtshadow_i}$
% \!\def!ines \!\current@color! to let it have $\celtshadow_i$ and then
% invokes \!\pcol@set@color! to put the coloring \!\special! for
% $\celtshadow_i$ nullifying \!\aftergroup!.  Then we \!\insert! a \!\vbox!,
% whose height and depth are 1\,|pt| and width is 0, having the coloring
% \!\special! for $\chi$ so that \!\output! will let $\Celt^c$ have the
% \!\special! in a synchronous manner.  After that we put a
% $\!\penalty!=10000$ if $\CSIndex{if@nobreak}=\true$ to keep the
% \!\insert!ion from being followed by a page break.
% 
% The macro $\!\pcol@iicolumncolor!\arg{cmd}\arg{c}$ at first
% invokes $\arg{cmd}$ to let \!\current@color! have the printer-specific color
% information $\chi$ of $\arg{color}$ or what \!\normalcolor! specifies,
% temporarily letting \!\set@color! be \!\relax! to let \!\color! or
% \!\normalcolor! just do the \!\def!inition of \!\current@color! without
% putting coloring \!\special!s nor preparing \colorstack{} popping.  Then
% we \!\xdef!ine $\Celtshadow^c=|\pcol@columncolor|{\cdot}c$ to have $\chi$.
% 
% \SpecialArrayIndex{c}{\pcol@columncolor}
% 
% \begingroup\hfuzz3.1pt
% The macro \!\pcol@scancst@shadow! applies \!\@elt! to $\Celtshadow^c$ to
% put a coloring or uncoloring \!\special! for it if it is defined, and then
% do the same for all
% $\celtshadow_i\in\cstshadow=\!\pcol@colorstack@shadow!$.
% \par\endgroup
% 
%    \begin{macrocode}
\def\pcol@icolumncolor#1[#2]{%
  \@tempswafalse
  \ifpcol@inner \@tempswatrue \fi
  \ifinner      \@tempswatrue \fi
  \ifmmode      \@tempswatrue \fi
  \ifx\set@color\relax
    \PackageWarning{paracol}{\pcol@colorcommand\space is not effective
      without some coloring package}%
  \else\if@tempswa
    \PackageWarning{paracol}{\pcol@colorcommand\space is not effective
      when not in outer par mode}%
  \else
    \begingroup
    \let\@elt\relax
    \ifx\pcol@paracol\paracol
      \pcol@iicolumncolor{#1}{#2}%
    \else\ifnum#2=\pcol@currcol
      \def\@elt##1{\reset@color}\pcol@scancst@shadow
      \pcol@iicolumncolor{#1}{#2}%
      \def\@elt##1{\def\current@color{##1}\let\aftergroup\@gobble
        \pcol@set@color}%
      \pcol@scancst@shadow
      \setbox\@tempboxa\vbox{\let\set@color\pcol@set@color
        \let\aftergroup\@gobble #1}%
      \ht\@tempboxa1sp \dp\@tempboxa1sp \wd\@tempboxa\z@\relax
      \insert\pcol@colorins{\box\@tempboxa}%
      \ifvmode\if@nobreak \nobreak \fi\fi
    \else
      \pcol@iicolumncolor{#1}{#2}%
      \pcol@currcol#2\relax
      \ifvoid\pcol@ccuse{@box}%
        \@next\@currbox\@freelist{}\pcol@ovf
        \pcol@ccxdef{\@currbox}%
      \fi
      \global\setbox\pcol@ccuse{@box}\vbox{\let\set@color\pcol@set@color
        \let\aftergroup\@gobble #1}%
    \fi\fi
    \endgroup
  \fi\fi
  \ignorespaces}
\def\pcol@iicolumncolor#1#2{{\let\set@color\relax #1%
  \expandafter\xdef\csname pcol@columncolor#2\endcsname{\current@color}}}
\def\pcol@scancst@shadow{%
  \pcol@ifccdefined{\@elt{\pcol@ccuse{}}}\relax
  \pcol@colorstack@shadow}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{1}
% \begin{macro}{\pcol@mcpushlimit}
% \changes{v1.24}{2013/07/27}
%	{Introduced for coloring specified in math mode.}
% \changes{v1.34}{2018/05/07}
%	{Move down to place it just before the \cs{def}inition of
%	 \cs{pcol@set@color@push} being the sole referrer, and change its
%	 body from 100 to 1000.}
% \begin{macro}{\set@color}
% \begin{macro}{\pcol@set@color}
% \begin{macro}{\pcol@set@color@push}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to work as \cs{set@color}.}
% \changes{v1.22}{2013/06/30}
%	{Modified to push color stack by \cs{output} always.}
% \changes{v1.23}{2013/07/08}
%	{Add an argument of null \cs{hskip} to \cs{pcol@color@invokeoutput}
%	 so that the first word of a colored text is hyphenated.}
% \changes{v1.24}{2013/07/27}
%	{Add the mechanism special for math mode.}
% \changes{v1.3-6}{2013/09/17}
%	{Change the second argument of \cs{pcol@color@invokeoutput} from
%	 \cs{hskip}\cs{z@} to \cs{pcol@fcwhyphenate} to make null skip
%	 insertion conditional.}
% \changes{v1.34}{2018/05/07}
%	{Completely change its definition according to the new text coloring
%	 with \cs{insert}.}
% 
% The macro \!\pcol@set@color@push! is invoked whenever \LaTeX's
% counterpart \!\set@color!  appears in a \env{paracol} environment through
% coloring commands such as \!\color!, because \!\pcol@zparacol! replaces
% \LaTeX's macro with it saving the original version in \!\pcol@set@color!,
% if the original \!\set@color! is not \!\relax! to mean some coloring
% package is in use.  This original version is used through
% \!\pcol@set@color! by \!\pcol@bg@paintregion@i!, \!\pcol@output@start! and
% \!\pcol@icolumncolor!  besides this macro \!\pcol@set@color@push!,
% while \!\output! lets $\!\set@color!=\!\pcol@set@color!$ for the references
% outside of our control.
% 
% The macro at first invokes its original version being \!\pcol@set@color!
% to put an appropriate coloring \!\special! to |.dvi| and reserve the
% invocation of \!\reset@color! by \!\aftergroup!.  Then, it performs one of
% two different operations depending on TeX's mode, i.e., math mode or not.
% If we are in math mode and not in a \!\vbox!, at first we increment
% $m=\!\pcol@mcid!$ and examine if $m>\!\pcol@mcpushlimit!=1000$, and if so
% we stop the execution with \!\PackageError!\footnote{
% 
% And let $m=1$ to allow a user to continue the execution bravely.}
% 
% in order to avoid too many macros $|\pcol@reset@color@mpop@|\cdot m$ are
% defined\footnote{
% 
% \SpecialArrayIndex{m}{\pcol@reset@color@mpop@}
% 
% We could make the number of math-mode coloring operations virtually
% unlimited by putting all digits of the decimal representation of $m$
% followed by a terminator by multiple
% \cs{aftergroup}s so that \cs{pcol@reset@color@mpop} is put by
% \cs{aftergroup} prior to them to capture them as its argument, but 
% limiting with $2^{31}-1$ is still necessary and that with 1000 is
% reasonable.}. 
% 
% Otherwise, i.e., if $m\leq\!\pcol@mcpushlimit!$, we
% reserve the invocation of the macro $|\pcol@reset@color@mpop@|{\cdot}i$
% 
% \SpecialArrayMainIndex{m}{\pcol@reset@color@mpop@}
% 
% for our own pop by \!\aftergroup! defining the macro as
% $\!\pcol@reset@color@mpop!\Arg{m}$.  If we are not in math mode, on the
% other hand, and neither in a \!\vbox!  nor in restricted horizontal mode,
% we simply reserve the invocation of the macro $\pcol@reset@color@pop$.
% 
% Then, regardless that we are in math mode or not, we push the contents of
% \!\current@color!, which \!\set@color! should refer to as the color
% information to be set, into the shadow \colorstack{}
% $\cstshadow=\!\pcol@colorstack@shadow!$ for the stack rewinding\slash
% reestablishing in \!\columncolor! and \!\normalcolumncolor!.  Since this
% push is done non-\!\global!ly with \!\edef!, we save\slash restore the
% definition of \!\@elt! to\slash from \Midx{\!\pcol@elt@save!} before\slash
% after the push, resepctively\footnote{
% 
% Just in case.}.
% 
% Then we \!\insert! a \!\vbox! through \!\pcol@colorins! for the push of
% $\celt_i$ or $\mcelt_{i,m}$ to $\cstraw$ synchronous with a page break or
% \cswitch{}.  The height of the \!\vbox! is 1\,|pt|, depth is 0 and
% width is $m$\,|sp| if we are in math mode or 0 otherwise, and its
% contents is the coloring \!\special! given by \!\pcol@set@color! so that
% the \!\special! is what the macro put at the beginning of this macro but
% without the reservation of \!\reset@color!.  After the insertion, we put
% \!\pcol@fcwhyphenate!, being \!\hskip!\!\z@! when
% \!\coloredwordhyphenated!  is effective, to split the coloring \!\special!
% from the first colored word so that the word may be hyphenated if we are
% in horizontal mode.  If we are in vertical mode, on the other hand, we do
% \!\nobreak! if $\CSIndex{if@nobreak}=\true$ to keep the \!\insert!ion from
% being followed by a page break.
% 
%    \begin{macrocode}
\def\pcol@mcpushlimit{1000}
\def\pcol@set@color@push{\pcol@set@color
  \ifmmode\else\ifinner \pcol@innertrue \fi\fi
  \ifpcol@inner\else
    \ifmmode
      \global\advance\pcol@mcid\@ne
      \ifnum \pcol@mcid>\pcol@mcpushlimit\relax
        \PackageError{paracol}{Too many coloring commands in math mode}\@ehb
        \global\pcol@mdid\@ne
      \fi
      \@tempdima\pcol@mcid sp\relax
      \expandafter\aftergroup
        \csname pcol@reset@color@mpop@\number\pcol@mcid\endcsname
      \expandafter\xdef
        \csname pcol@reset@color@mpop@\number\pcol@mcid\endcsname
          {\noexpand\pcol@reset@color@mpop{\number\pcol@mcid}}%
    \else
      \aftergroup\pcol@reset@color@pop \@tempdima\z@
    \fi
    \let\pcol@elt@save\@elt \let\@elt\relax
    \edef\pcol@colorstack@shadow{\pcol@colorstack@shadow\@elt{\current@color}}%
    \let\@elt\pcol@elt@save
    \setbox\@tempboxa\vbox{\let\aftergroup\@gobble \pcol@set@color}%
    \ht\@tempboxa1sp \dp\@tempboxa\z@ \wd\@tempboxa\@tempdima
    \insert\pcol@colorins{\box\@tempboxa}\ifhmode \pcol@fcwhyphenate \fi
    \ifvmode\if@nobreak \nobreak \fi\fi
  \fi}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@reset@color@pop}
% \changes{v1.2-1}{2013/05/11}
% 	{Introduced to work as \cs{reset@color}.}
% \changes{v1.22}{2013/06/30}
%	{Modified to pop color stack by \cs{output} and to examine if
%	 $\cs{ifpcol@output}\EQ\mathit{true}$.}
% \changes{v1.23}{2013/07/08}
%	{Add an argument of \cs{relax} to \cs{pcol@color@invokeoutput}
%	 so that the last word of a colored text is not followed by a line
%	 break candidate.}
% \changes{v1.34}{2018/05/07}
%	{Completely change its definition according to the new text coloring
%	 with \cs{insert}.}
% \begin{macro}{\pcol@reset@color@mpop}
% \changes{v1.24}{2013/07/27}
%	{Introduced for coloring specified in math mode.}
% \changes{v1.34}{2018/05/07}
%	{Completely change its definition according to the new text coloring
%	 with \cs{insert}.}
% 
% The macro \!\pcol@reset@color@pop! and its math-mode relative
% $\!\pcol@reset@color@mpop!\~\Arg{m}$ are invoked by
% \!\aftergroup! mechanism in \!\pcol@set@color@push!, directly for the
% former and through the macro $|\pcol@reset@color@mpop@|{\cdot}m$
% 
% \SpecialArrayIndex{m}{\pcol@reset@color@mpop@}
% 
% for the latter.  They \!\insert! a \!\vbox! for $\celtpop_i$ or
% $\mceltpop_{i,m}$ to add it to $\cstraw$ synchronously with a page break
% or \cswitch{}.  Therefore, the height and depth of the \!\vbox! are 0 and
% width is 0 for $\celtpop_i$ or $m$\,|sp| for $\mceltpop_{i,m}$.  The
% contents of the \!\vbox! is an uncoloring \!\special! given by
% \!\reset@color! but this is done just for debugging to show what
% \!\pcol@colorins! has by, for example, \!\pcol@ShowBox!.  Then if we are
% in vertical mode and $\CSIndex{if@nobreak}=\true$, we do \!\nobreak! to
% keep the \!\insert!ion from being followed by a page break even in
% \!\pcol@reset@color@mpop! because its corresponding
% \!\pcol@set@color@push! may have been in a displayed math construct after
% which we are in vertical mode.
% 
% One caution is that \!\pcol@reset@color@pop! can be invoked outside the
% \env{paracol} environment in which the corresponding
% \!\pcol@set@color@push! appears.  In this case with
% $\CSIndex{ifpcol@output}=\false$, we don't need to do the pop operation
% and cannot make the \!\insert!ion for it because \!\output! is not for
% \env{paracol}.
% 
%    \begin{macrocode}
\def\pcol@reset@color@pop{%
  \ifpcol@output
    \setbox\@tempboxa\vbox{\reset@color}%
    \ht\@tempboxa\z@ \dp\@tempboxa\z@ \wd\@tempboxa\z@
    \insert\pcol@colorins{\box\@tempboxa}%
    \ifvmode\if@nobreak \nobreak \fi\fi
  \fi}
\def\pcol@reset@color@mpop#1{%
  \setbox\@tempboxa\vbox{\reset@color}%
  \ht\@tempboxa\z@ \dp\@tempboxa\z@ \wd\@tempboxa#1sp\relax
  \insert\pcol@colorins{\box\@tempboxa}%
  \ifvmode\if@nobreak \nobreak \fi\fi
}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \changes{v1.22}{2013/06/30}
% 	{\cs{pcol@color@invokeoutput} was introduced for \cs{output}
%	 request for coloring but removed in v1.34.}
% \changes{v1.23}{2013/07/08}
%	{\cs{pcol@color@invokeoutput} was modified to add second argument
%	 $s$ to insert a null skip after \cs{vadjust} only when the macro is
%	 invoked from \cs{pcol@set@color@push} in horizontal mode.}
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@color@invokeoutput} is removed according to the change of
%	 text coloring from \cs{output} to \cs{insert}.}
% \changes{v1.22}{2013/06/30}
% 	{\cs{pcol@color@invokeoutput@v} was introduced for \cs{output}
%	 request for coloring but removed in v1.34.}
% \changes{v1.34}{2018/05/07}
%	{\cs{pcol@color@invokeoutput@v} is removed according to the change of
%	 text coloring from \cs{output} to \cs{insert}.}
% 
% \KeepSpace{1}
% \begin{macro}{\coloredwordhyphenated}
% \changes{v1.3-6}{2013/09/17}
%	{Introduced to enable null skip insertion before the first word
%	 after a coloring command not always but conditionally.}
% \begin{macro}{\nocoloredwordhyphenated}
% \changes{v1.3-6}{2013/09/17}
%	{Introduced to disable null skip insertion before the first word
%	 after a coloring command.}
% \begin{macro}{\pcol@fcwhyphenate}
% \changes{v1.3-6}{2013/09/17}
%	{Introduced to enable null skip insertion before the first word
%	 after a coloring command not always but conditionally.}
% 
% The API macro \!\coloredwordhyphenated! \!\def!ines the macro
% \!\pcol@fcwhyphenate! being \!\hskip!\!\z@! so that the null space is
% inserted after the coloring \!\special! and \!\insert! put by
% \!\pcol@set@color@push! if we are in horizontal mode, so that the word
% following them can be hyphenated.  The other API macro
% \!\nocoloredwordhyphenated! makes $\!\pcol@fcwhyphenate!=\!\relax!$ to
% inhibit the insertion.  Since the null skip is a line break candidate, the
% skip might cause an unexpected and undesirable line break.  However, this
% demerit is less important than the merit of making it possible to
% hyphenate the first word in multi-column documents with narrow lines, and
% thus we make \!\coloredwordhyphenated! effective in default while giving
% users a means to disable the insertion (occasionally) by
% \!\nocoloredwordhyphenated!.
% 
%    \begin{macrocode}
\def\coloredwordhyphenated{\def\pcol@fcwhyphenate{\hskip\z@}}
\def\nocoloredwordhyphenated{\let\pcol@fcwhyphenate\relax}
\coloredwordhyphenated

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}
% 
% 
% 
% \KeepSpace{8}
% \section{Commands for Column-Separating Rule Color and Background Painting}
% \label{sec:imp-commbg}
% \changes{v1.3-3}{2013/09/17}
%	{Add the subsection ``Commands for Column-Separating Rule Color and
%	 Background Painting'' to describe newly
%	 introduced API macros to specify colors of column-separating rules
%	 and background painting.}
% 
% \begin{macro}{\colseprulecolor}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to spcify the colors of column-separating rules.}
% \begin{macro}{\pcol@defcseprulecolor@x}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{colseprulecolor}.}
% \begin{macro}{\pcol@defcseprulecolor@y}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{colseprulecolor}.}
% \begin{macro}{\pcol@defcseprulecolor}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{colseprulecolor}.}
% \begin{macro}{\normalcolseprulecolor}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to spcify that color of column-separating rules is normal.}
% \begin{macro}{\pcol@defcseprulecolor@i}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{colseprulecolor} and
%	 \cs{normalcolseprulecolor}.}
% \begin{macro}{\pcol@colseprulecolor}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to keep the color for all column-separating rules.}
% 
% The macro \!\colseprulecolor!\oarg{mode}\marg{color}$|[|c|]|$ \!\def!ines
% \!\pcol@colseprulecolor! to have the $\arg{color}$ optionally with
% coloring $\arg{mode}$ of all \cseprule{}s if the optional argument $c$ is
% not provided, or $|\pcol@colseprulecolor|{\cdot}c$
% 
% \SpecialArrayMainIndex{c}{\pcol@colseprulecolor}
% 
% that of the rule drawn between a particular column pair $c$ and $c+1$.
% After \!\def!ining \Midx{\!\pcol@colorcommand!} to be \!\colseprulecolor!
% in case we have to give a warning, the macro invokes
% \!\pcol@defcseprulecolor@x!\oarg{mode}\marg{color} or
% \!\pcol@defcseprulecolor@y!\marg{color} according to the provision of the
% optional argument $\arg{mode}$ to invoke \!\pcol@defcseprulecolor!  with
% argument \marg{cmd}${}={}$\!\color!\oarg{mode}\marg{color} so that this
% macro invokes $\!\pcol@defcseprulecolor@i!\ARg{cmd}|[|c|]|$ where
% $c=\emptyset$ if the optional arguemnt $c$ is not provided.
% 
% The macro $\!\normalcolseprulecolor!|[|c|]|$, on the other hand, defines
% $|\pcol@colseprule|\~|color|[{\cdot}c]$
% 
% \SpecialArrayIndex{c}{\pcol@colseprulecolor}
% \SpecialIndex{\pcol@colseprulecolor}
% 
% with whatever \!\normalcolor! gives, and thus it invokes
% \!\pcol@defcseprulecolor@i! letting $\arg{cmd}=\!\normalcolor!$, after
% \!\def!ining \!\pcol@colorcommand! to be \!\normalcolsep~rule~color!.
% 
% The macro $\!\pcol@defcseprulecolor@i!\ARg{cmd}|[|c|]|$ examines if
% $\!\set@color!=\!\relax!$ to mean no coloring packages have been loaded
% and, if so, do nothing giving a warning the command in
% \!\pcol@colorcommand! is not effective.  Otherwise, we examine if
% $\arg{cmd}$ has proper arguments by invoking it but temporally nullifying
% \!\set@color! and then \!\def!ine $|\pcol@colseprulecolor|[{\cdot}c]$
% 
% \SpecialArrayIndex{c}{\pcol@colseprulecolor}
% \SpecialIndex{\pcol@colseprulecolor}
% 
% to be $\arg{cmd}$.
% 
% Note that at the top level we \!\def!ine \!\pcol@colseprulecolor! to be
% \!\normalcolor! to give the default for all \cseprule{}s.  Also note that
% macros $|\pcol@colseprulecolor|{\cdot}c$
% 
% \SpecialArrayIndex{c}{\pcol@colseprulecolor}
% 
% are referred to solely in \!\pcol@hfil!
% which also uses \!\pcol@colseprulecolor! for columns for which
% $|\pcol@colseprulecolor|{\cdot}c$
% 
% \SpecialArrayIndex{c}{\pcol@colseprulecolor}
% 
% is not defined.
% 
%    \begin{macrocode}
%% Commands for Column-Separating Rule Color and Background Painting

\def\colseprulecolor{\def\pcol@colorcommand{\string\colseprulecolor}%
  \@ifnextchar[%]
    \pcol@defcseprulecolor@x\pcol@defcseprulecolor@y}
\def\pcol@defcseprulecolor@x[#1]#2{\pcol@defcseprulecolor{\color[#1]{#2}}}
\def\pcol@defcseprulecolor@y#1{\pcol@defcseprulecolor{\color{#1}}}
\def\pcol@defcseprulecolor#1{\@ifnextchar[%]
  {\pcol@defcseprulecolor@i{#1}}{\pcol@defcseprulecolor@i{#1}[]}}
\def\normalcolseprulecolor{%
  \def\pcol@colorcommand{\string\normalcolseprulecolor}%
  \@ifnextchar[%]
    {\pcol@defcseprulecolor@i\normalcolor}%
    {\pcol@defcseprulecolor@i\normalcolor[]}}
\def\pcol@defcseprulecolor@i#1[#2]{%
  \ifx\set@color\relax
    \PackageWarning{paracol}{\pcol@colorcommand\space is not effective
      without some coloring package}%
  \else
    {\let\set@color\relax #1}%
    \global\@namedef{pcol@colseprulecolor#2}{#1}%
  \fi}
\gdef\pcol@colseprulecolor{\normalcolor}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{8}
% \begin{macro}{\backgroundcolor}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to define colors for background painting.}
% \begin{macro}{\nobackgroundcolor}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to undefine colors for background painting.}
% \begin{macro}{\pcol@backgroundcolor@e}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor} and
%	 \cs{nobackgroundcolor}.}
% \begin{macro}{\pcol@backgroundcolor}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor} and
%	 \cs{nobackgroundcolor}.}
% \changes{v1.31}{2013/10/10}
%	{Fix the mispell ``colorling'' in the error message.}
% \begin{macro}{\pcol@backgroundcolor@i}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor} and
%	 \cs{nobackgroundcolor}.}
% \begin{macro}{\pcol@bg@region}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor} and
%	 \cs{nobackgroundcolor}.}
% \begin{macro}{\pcol@backgroundcolor@ii}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor} and
%	 \cs{nobackgroundcolor}.}
% \begin{macro}{\pcol@backgroundcolor@iii}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor}.}
% \begin{macro}{\pcol@backgroundcolor@iv}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor}.}
% \begin{macro}{\pcol@backgroundcolor@v}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor}.}
% 
% {\nosv\gdef\|{\;|\;}}
% \def\fdef{f_{\mathit{def}}}
% 
% The macro
% \!\backgroundcolor!\marg{region}\oarg{mode}\marg{color}
% defines the $\arg{color}$ optionally with $\arg{mode}$ of the
% $\arg{region}$ whose syntax is specified as follows.
% 
% % \begin{eqnarray*}
% \arg{region}&{:}{:}{=}&\arg{regionid}\arg{extension}\\
% \arg{regionid}&{:}{:}{=}&\<a\>\|\arg{corg}|[|c|]|\\
% \arg{a}&{:}{:}{=}&\arg{corg}\||s|\||S|\||t|\||T|\||l|\||L|\||r|\||R|\|
%                               |f|\||F|\||n|\||N|\||p|\||P|\\
% \arg{corg}&{:}{:}{=}&|c|\||C|\||g|\||G|\\
% \arg{extension}&{:}{:}{=}&\emptyset\||(|x_0|,|y_0|)|\|
%                                      |(|x_0|,|y_0|)(|x_1|,|y_1|)|
% \end{eqnarray*}
% % 
% On the other hand, the counteraprt macro
% \!\nobackgroundcolor!\marg{region} undefines the color of $\arg{region}$.
% Both macros invoke \!\pcol@backgroundcolor! giving all arguments to it to
% parse the argument $\arg{region}$, after letting
% $\fdef=\CSIndex{if@tempswa}=\true$ and
% $\!\pcol@backgroundcolor@e!=\!\pcol@backgroundcolor@w!$ in
% \!\backgroundcolor!, or $\fdef=\CSIndex{if@tempswa}=\true$ and
% $\!\pcol@backgroundcolor@e!=\!\pcol@backgroundcolor@z!$ in
% \!\nobackgroundcolor!.  Note that the \!\let!-assignment to
% \!\pcol@backgroundcolor@e! is effective when we found an error in the
% parse of the argument $\arg{region}$ to throw away what remains in the
% argument unprocessed and, for \!\backgroundcolor!, the other arguments
% \oarg{mode}\marg{color}.
% 
% Then the macro \!\pcol@backgroundcolor! examines if $|\pcol@bg@@|{\cdot}a$
% 
% \SpecialArrayIndex{a}{\pcol@bg@@}
% 
% is defined, and if not, raises an error that $a$ is invalid and then, in case
% the user dare to continue the execution, invokes
% \!\pcol@backgroundcolor@e! to throw all arguments away after letting
% $a'=\!\pcol@bg@region!=|xx|$ so that the undefining
% $|\pcol@bg@color|{\cdot}a'$ does not cause any troubles.
% 
% \SpecialArrayIndex{a}{\pcol@bg@color@}
% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}
% 
% Otherwise, i.e., if $|\pcol@bg@@|{\cdot}a$ is defined, it 
% invokes $\!\pcol@backgroundcolor@i!|[|c|]|$ or \!\pcol@backgroundcolor@ii!
% according to the provision of the optional argument $|[|c|]|$, after
% \!\def!ining $a'=\Midx{\!\pcol@bg@region!}$ to be $a$.  Then
% \!\pcol@backgroundcolor@i! examines if $|\pcol@bg@|\~|mayhavecol@|{\cdot}a$
% 
% \SpecialIndex{\pcol@bg@mayhavecol@c}\SpecialIndex{\pcol@bg@mayhavecol@C}
% \SpecialIndex{\pcol@bg@mayhavecol@g}\SpecialIndex{\pcol@bg@mayhavecol@G}
% 
% is defined, and if not, raises an error again in a similar way, or
% otherwise invokes \!\pcol@backgroundcolor@ii! after re\!\def!ining
% $a'=a{\cdot}|@|{\cdot}c$.
% 
% Then if $\fdef=\true$, the macro \!\pcol@backgroundcolor@ii! examines if
% $\!\set@color!=\!\relax!$, and if so it complains that any coloring
% packages have not been loaded and invokes \!\pcol@backgroundcolor@w! just
% for throwing away optional arguments for \bgext{} and
% \oarg{mode}\marg{color}.  Otherwise, i.e., if $\!\set@color!\neq\!\relax!$,
% it invokes \!\pcol@backgroundcolor@iii!  after adding $a'$ to the tail of
% \!\pcol@bg@defined!.  On the other hand if $\fdef=\false$, it invokes
% \!\pcol@backgroundcolor@z! without checking the availability of coloring
% macros.
% 
% The macro \!\pcol@backgroundcolor@iii! at first invokes
% $\!\pcol@bg@defext!\Arg{d}\Arg{e}$ with $e=0$ for all
% $d\in\{|l|,|r|,|t|,|b|\}$ to have default (no) \bgext{}s.  Then if
% $|(|x_0|,|y_0|)|$ is provided, \!\pcol@bg@defext! is invoked again by
% \!\pcol@backgroundcolor@iv! for all
% $d\in\{|l|,|r|,|t|,|b|\}$ but with $e=x_0$ for
% $d\in\{|l|,|r|\}$ and with $e=y_0$ for $d\in\{|t|,|b|\}$.
% Further, if % $|(|x_1|,|y_1|)|$ is also provided, \!\pcol@bg@defext! is
% invoked once again by \!\pcol@backgroundcolor@v! for all
% $(d,e)\in\{(|r|,x_1),(|b|,y_1)\}$.  Finally \!\pcol@backgroundcolor@v!
% invokes \!\pcol@backgroundcolor@x!, which is also invoked from
% \!\pcol@backgroundcolor@iii! and \!\pcol@backgroundcolor@iv! if they find no
% (further) \bgext{}s.
% 
%    \begin{macrocode}
\def\backgroundcolor#1{\@tempswatrue
  \let\pcol@backgroundcolor@e\pcol@backgroundcolor@w
  \pcol@backgroundcolor#1\@nil}
\def\nobackgroundcolor#1{\@tempswafalse
  \let\pcol@backgroundcolor@e\pcol@backgroundcolor@z
  \pcol@backgroundcolor#1\@nil}
\def\pcol@backgroundcolor#1{%
  \@ifundefined{pcol@bg@@#1}%
    {\PackageError{paracol}%
       {Invalid background coloring region identifier #1}%
     \def\pcol@bg@region{xx}\pcol@backgroundcolor@e}%
    {\def\pcol@bg@region{#1}%
     \@ifnextchar[%]
       \pcol@backgroundcolor@i \pcol@backgroundcolor@ii}}
\def\pcol@backgroundcolor@i[#1]{%
  \@ifundefined{pcol@bg@mayhavecol@\pcol@bg@region}%
    {\PackageError{paracol}%
       {Column number \number#1 is not effective for background coloring region
        \pcol@bg@region}%
     \def\pcol@bg@region{xx}\pcol@backgroundcolor@e}%
    {\edef\pcol@bg@region{\pcol@bg@region @#1}%
     \pcol@backgroundcolor@ii}}
\def\pcol@backgroundcolor@ii{%
  \if@tempswa
    \ifx\set@color\relax
      \PackageWarning{paracol}{\string\backgroundcolor\space is not effective
        without some coloring package}%
      \let\reserved@b\pcol@backgroundcolor@w
    \else
      \let\reserved@b\pcol@backgroundcolor@iii
      \@cons\pcol@bg@defined{{\pcol@bg@region}}%
    \fi
  \else
    \let\reserved@b\pcol@backgroundcolor@z
  \fi
  \reserved@b}
\def\pcol@backgroundcolor@iii{%
  \pcol@bg@defext{l}\z@ \pcol@bg@defext{r}\z@
  \pcol@bg@defext{t}\z@ \pcol@bg@defext{b}\z@
  \@ifnextchar(%)
    \pcol@backgroundcolor@iv \pcol@backgroundcolor@x}
\def\pcol@backgroundcolor@iv(#1,#2){%
  \pcol@bg@defext{l}{#1}\pcol@bg@defext{r}{#1}%
  \pcol@bg@defext{t}{#2}\pcol@bg@defext{b}{#2}%
  \@ifnextchar(%)
    \pcol@backgroundcolor@v \pcol@backgroundcolor@x}
\def\pcol@backgroundcolor@v(#1,#2){%
  \pcol@bg@defext{r}{#1}\pcol@bg@defext{b}{#2}%
  \pcol@backgroundcolor@x}
%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@backgroundcolor@x}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor}.}
% \begin{macro}{\pcol@backgroundcolor@y}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor}.}
% 
% The macro \!\pcol@backgroundcolor@x! is used in
% \!\pcol@backgroundcolor@iii!, \!\pcol@backgroundcolor@iv! and
% \!\pcol@backgroundcolor@v! to define the color for \bgpaint{} of the
% region $a'=\!\pcol@bg@region!$.  Since the macro is followed by the
% arguments \oarg{mode}\marg{color} of \!\backgroundcolor!, the macro
% invokes \!\color! to let it \!\def!ine \!\current@color! but without real
% coloring operations by letting
% \!\set@color!${}={}$\!\pcol@backgroundcolor@y!.  Therefore
% \!\pcol@backgroundcolor@y! is invoked in \!\color! and it \!\xdef!ines
% $|\pcol@bg@colpr|{\cdot}a'$ to let it have whatever \!\current@color! has.
% 
% \SpecialArrayIndex{a}{\pcol@bg@color@}
% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}
% 
%    \begin{macrocode}
\def\pcol@backgroundcolor@x#1\@nil{\begingroup
  \let\set@color\pcol@backgroundcolor@y \color}
\def\pcol@backgroundcolor@y{%
  \expandafter\xdef\csname pcol@bg@color@\pcol@bg@region\endcsname
   {\current@color}%
  \endgroup}
%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \KeepSpace{2}
% \begin{macro}{\pcol@backgroundcolor@z}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{nobackgroundcolor}.}
% \begin{macro}{\pcol@backgroundcolor@w}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor}.}
% \begin{macro}{\pcol@backgroundcolor@wi}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor} and
%	 \cs{nobackgroundcolor}.}
% \begin{macro}{\pcol@bg@color@xx}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor} and
%	 \cs{nobackgroundcolor}.}
% 
% The macro \!\pcol@backgroundcolor@z! is invoked from
% \!\pcol@backgroundcolor@ii! directly to work for \!\nobackgroundcolor! to
% disable the \bgpaint{} for a region $a'=\!\pcol@bg@region!$, or from
% \!\pcol@backgroundcolor! and \!\pcol@backgroundcolor@i! through
% \!\pcol@backgroundcolor@e! when they find an error in the argument
% $\arg{region}$ of \!\nobackground~color!.  Similarly the macro
% \!\pcol@backgroundcolor@w! is invoked from \!\pcol@background~color@ii!
% directly when it finds no coloring packages have not been loaded, or
% \!\pcol@backgroundcolor! and \!\pcol@backgroundcolor@i! through
% \!\pcol@backgroundcolor@e! on error too but in the argument of
% \!\backgroundcolor!.  Both macros throw away whatever remains in
% $\arg{region}$ unprocessed and then invoke \!\pcol@backgroundcolor@wi!,
% but \!\pcol@backgroundcolor@z! gives it a dummy argument pair, while
% \!\pcol@backgroundcolor@w! passes \oarg{mode}\marg{color} to it.
% 
% Then \!\pcol@backgroundcolor@wi! throw all arguments away and lets
% $|\pcol@bg@color@|{\cdot}a'\~=\!\relax!$ so that the region $a'$ is
% untouched in \bgpaint{} macros.  Note that since
% $a'=|xx|$ being an absolutely non-exsistent region when this macro is used
% for error recovery, undefining \pcol@bg@color@xx is not harmful.
% 
%    \begin{macrocode}
\def\pcol@backgroundcolor@z#1\@nil{\pcol@backgroundcolor@wi[]{}}
\def\pcol@backgroundcolor@w#1\@nil{\@ifnextchar[%]
  \pcol@backgroundcolor@wi{\pcol@backgroundcolor@wi[]}}
\def\pcol@backgroundcolor@wi[#1]#2{%
  \expandafter\global\expandafter\let
    \csname pcol@bg@color@\pcol@bg@region\endcsname\relax}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \KeepSpace{2}
% \begin{macro}{\pcol@bg@mayhavecol@c}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor} and
%	 \cs{nobackgroundcolor}.}
% \begin{macro}{\pcol@bg@mayhavecol@C}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor} and
%	 \cs{nobackgroundcolor}.}
% \begin{macro}{\pcol@bg@mayhavecol@g}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor} and
%	 \cs{nobackgroundcolor}.}
% \begin{macro}{\pcol@bg@mayhavecol@G}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor} and
%	 \cs{nobackgroundcolor}.}
% 
% The macros $|\pcol@bg@mayhavecol@|{\cdot}a$ where $a\in\{|c|,|C|,|g|,|G|\}$
% are used in \!\pcol@background~color@i! when the region specifier $a$ in
% $\arg{region}$ argument of \!\backgroundcolor! or \!\noback~groundcolor! is
% followed by optional $|[|c|]|$, so that the invoker macro examines if $a$
% can have the optional column oridinal.
% 
% \SpecialArrayMainIndex{a}{\pcol@bg@mayhavecol@}
% 
% Therefore, the macros just need not to be \!\relax! and thus commonly have
% empty bodies.
% 
%    \begin{macrocode}
\def\pcol@bg@mayhavecol@c{}
\def\pcol@bg@mayhavecol@C{}
\def\pcol@bg@mayhavecol@g{}
\def\pcol@bg@mayhavecol@G{}

%    \end{macrocode}
% \end{macro}\end{macro}\end{macro}\end{macro}
% 
% \begin{macro}{\pcol@bg@defext}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{backgroundcolor}.}
% The macro $\!\pcol@bg@defext!\Arg{d}\Arg{e}$ is used by
% \!\pcol@backgroundcolor@iii!,
% \!\pcol@back~groundcolor@iv! and \!\pcol@backgroundcolor@v! to \!\def!ine 
% $|\pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}a'$ be $e=0$ for all
% $d\in\{|l|,|r|,|t|,|b|\}$ in the first, be $e=x_0$ for $d\in\{|l|,|r|\}$
% and $e=y_0$ for $d\in\{|t|,|b|\}$ in the second, and be $e=x_0$, $x_1$,
% $y_0$ and $y_1$ for $d$ being |l|, |r|, |t|, |b| respectively in the last.
% 
% \SpecialArrayMainIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}
% \SpecialArrayMainIndex
%   {d{\cdot}\string\texttt{@}{\cdot}a{\cdot}\string\texttt{@}{\cdot}c}
%   {\pcol@bg@ext@}
% 
% The macro at first lets \!\@tempdima! have $e$ to confirm $e$ is a proper
% dimension and then \!\xdef!ines
% $|\pcol@bg@ext@|{\cdot}d{\cdot}|@|{\cdot}a'$ to let it have the integer
% representaion of $e$ followed by |sp|.
% 
% \SpecialArrayMainIndex{d{\cdot}\string\texttt{@}{\cdot}a}{\pcol@bg@ext@}
% \SpecialArrayMainIndex
%   {d{\cdot}\string\texttt{@}{\cdot}a{\cdot}\string\texttt{@}{\cdot}c}
%   {\pcol@bg@ext@}
% 
% 
%    \begin{macrocode}
\def\pcol@bg@defext#1#2{%
  \@tempdima#2\relax
  \expandafter\xdef\csname pcol@bg@ext@#1@\pcol@bg@region\endcsname{%
    \number\@tempdima sp}}

%    \end{macrocode}
% \end{macro}
% 
% \begin{macro}{\resetbackgroundcolor}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to disable background-paiting for all regions.}
% \begingroup \let\SMALL\small \let\small\footnotesize
% \begin{macro}{\pcol@resetbackgroundcolor}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{resetbackgroundcolor}.}
% \let\small\SMALL
% \begin{macro}{\pcol@bg@defined}
% \changes{v1.3-3}{2013/09/17}
%	{Introduced to implement \cs{resetbackgroundcolor}.}
% 
% The API macro \!\resetbackgroundcolor! disables \bgpaint{} of all regions
% whose colors have been specified by \!\backgroundcolor!.  Since the region
% specifiers $a'_1$, $a'_2$, \ldots, $a'_n$ for which \bgpaint{} is specified
% are recorded in $\!\pcol@bg@defined!=
% \!\@elt!\Arg{a'_1}\!\@elt!\Arg{a'_2}\cdots\!\@elt!\Arg{a'_n}$ by
% \!\pcol@backgroundcolor!, the macro invokes \!\pcol@bg@defined!
% temporarily letting $\!\@elt!=\!\pcol@resetbackgroundcolor!$ to let
% $|\pcol@bg@|\~|color@|{\cdot}a'_i$ be \!\relax! for all $i\in[1,n]$, and
% clears \!\pcol@bg@defined!, whose initial state is also empty.
% 
% \SpecialArrayIndex{a}{\pcol@bg@color@}
% \SpecialArrayIndex{a{\cdot}\string\texttt{@}{\cdot}c}{\pcol@bg@color@}
% 
%    \begin{macrocode}
\def\resetbackgroundcolor{{%
  \let\@elt\pcol@resetbackgroundcolor \pcol@bg@defined
  \gdef\pcol@bgdefined{}}}
\def\pcol@resetbackgroundcolor#1{%
  \expandafter\global\expandafter\let\csname pcol@bg@color@#1\endcsname\relax}
\gdef\pcol@bg@defined{}

%    \end{macrocode}
% \end{macro}\end{macro}\endgroup\end{macro}
% 
% 
% 
% \section{Closing Environment}
% \label{sec:imp-end}
% 
% \begin{macro}{\endparacol}
% \changes{v1.0}{2011/10/10}
%	{Replace \cs{par} with \cs{pcol@par}.}
% \changes{v1.2-2}{2013/05/11}
%	{Add pre-flushing column height check and footnote counter
%	 adjustment.}
% \changes{v1.2-5}{2013/05/11}
%	{Remove \cs{global} assignment of \cs{hsize} and \cs{linewidth}
%	 because assigments of them in \string\texttt{paracol} are now
%	 perfectly local.}
% \changes{v1.31}{2013/10/10}
%	{Add saving $c$ into \cs{pcol@lastcol} to let \cs{pcol@output@end}
%	 know the column visited last.}
% \begin{macro}{\pcol@lastcol}
% \changes{v1.31}{2013/10/10}
%	{Introduced to keep the column visited last to pass its typesetting
%	 parameters to post-environment.}
% 
% The macro \!\endparacol! is invoked from \Endparacol{} to close
% \env{paracol} environment.  After making it sure to be in vertical mode by
% \!\pcol@par!, we switch to the column 0 by \!\pcol@switchcol! to let
% \lcounter{} have the values for the column 0 so that they are referred to
% outside the environment, after saving the current column $c$ in
% \!\pcol@lastcol! to be referred to in \!\pcol@output@end! so that
% $\cc_c(\sw)$ and $\cc_c(\ep)$ are passed to \postenv.
% 
% \begin{Sloppy}{1800}
% Then we invoke \!\pcol@flushclear! for \pfcheck{}, turning
% $\CSIndex{ifpcol@lastpage}=\true$ to tell \!\pcol@output@switch! for the
% check that it works on the \lpage, and giving $\bot$ to \!\pcol@flushclear! 
% as its argument, unless footnote typesetting is \scfnote{} but not
% \mgfnote{} for which we give $\df$ to ensure all deferred footnotes are
% put in the checking process.  Note that the argument for \Mcfnote{}
% typesetting is $\df$ but it is definitely $\bot$ in this mode.  After that
% we make an \!\output! request by \!\pcol@invokeoutput! with
% $\!\penalty!=\!\pcol@op@end!$ and still with
% $\CSIndex{ifpcol@lastpage}=\true$ to build the \lpage.
% \end{Sloppy}
% 
% Next, we let $\!\columnwidth!=\!\textwidth!$ and
% $\CSIndex{if@twocolumn}=\false$ for single-column typesetting, and also
% let $\!\topskip!=\!\pcol@topskip!$ to make it sure that the parameter has
% the value used outside in \env{paracol} environment.  Finally, if the
% \counter{footnote} counter adjustment is required by
% $\CSIndex{ifpcol@fncounteradjustment}=\true$, we let
% $\!\c@footnote!=\bf+\nf$.
% 
%    \begin{macrocode}
%% Closing Environment

\def\endparacol{\pcol@par
  \edef\pcol@lastcol{\number\pcol@currcol}%
  \pcol@nextcol\z@ \pcol@switchcol
  \pcol@lastpagetrue
  \ifpcol@mgfnote \pcol@flushclear\voidb@x
  \else \pcol@flushclear\pcol@topfnotes
  \fi
  \pcol@invokeoutput\pcol@op@end
  \global\columnwidth\textwidth
  \global\@twocolumnfalse
  \global\topskip\pcol@topskip
  \ifpcol@fncounteradjustment
    \global\c@footnote\pcol@footnotebase
    \global\advance\c@footnote\pcol@nfootnotes
  \fi}

%    \end{macrocode}
% \end{macro}\end{macro}
% 
% \begin{macro}{\pcol@restoreeveryvbox}
% \changes{v1.22}{2013/06/30}
% 	{Introduced to reflect \cs{global} updates on \cs{everyvbox} in
%	 \string\texttt{paracol} environments.}
% 
% The macro \!\pcol@restoreeveryvbox! is invoked just after \Endparacol{} by
% \!\aftergroup! mechanism activated by \!\pcol@zparacol!.  It examines if
% \!\pcol@everyvbox! has tokens different from \!\pcol@dummytoken! which
% \!\pcol@zparacol! \!\global!ly assigned to the register.  Since the dummy
% token cannot be assigned to \!\everyvbox!\footnote{
% 
% Unless a very surprising coincidence happens or a user intentionally
% violates the coherence of the implementation.},
% 
% the difference means the \!\everyvbox! has been \!\global!ly updated with
% the value that \!\pcol@everyvbox! has now.  Therefore if so, we
% globally update \!\everyvbox! with \!\pcol@everyvbox! to refrect the
% global update in the environment.
% 
%    \begin{macrocode}
\def\pcol@restoreeveryvbox{%
  \expandafter\def\expandafter\reserved@a\expandafter{\the\pcol@everyvbox}%
  \def\reserved@b{\pcol@dummytoken}%
  \ifx\reserved@a\reserved@b\else \global\everyvbox\pcol@everyvbox \fi}
%    \end{macrocode}
% \end{macro}
%\iffalse
%</paracol>
%\fi
\endinput
