paracol (28oct11)

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+% \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 {\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.
+% 
+% The {\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! or
+% \!\clearpage!.  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 $\SS$ 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! and
+% \!\clearpage!.  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 will grow further.
+% 
+% 
+% 
+% \subsection{Current Column-Pages and Their Contexts}
+% \label{sec:imp-ovv-ccol}
+% 
+% 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 become virtualy boundless when we take variables
+% defined in various styles and by users themselves into account.
+% Therefore, we have 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 $\Uidx\ft=\!\pcol@currfoot!$
+% is the \!\insert! containing the footnotes added in the \ccolpage.  Its
+% constituent \!\box!, \!\count!, \!\dimen! and \!\skip! are denoted as
+% $\ft^b$, $\ft^c$, $\ft^d$, $\ft^s$ respectively.
+% 
+% \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 in-column floats deferred to the next \colpage.
+% 
+% \item $\Uidx\tf=\!\pcol@textfloatsep!$
+% is the vertical skip replaced with \!\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 $\Uidx\mb=\!\@mparbottom!$
+% is the bottom position of the last \!\marginpar! staff 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}
+% 

+% 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{token} 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}
+% 
+% 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)
+% \end{eqnarray*}
+% 

+% where $\pp(p)$ is a {\em\Uidx\pctext} of $p$ being an integer whose
+% meaning is defined as follows.
+% 

+% \begin{itemize}
+% \item $\pp(p)<0$\\
+% $\pp(p)$ is equal to the (negative) value of the counter \counter{page}
+% (i.e. \!\c@page!) for the page $p$, which we refer to as $\Uidx\page(p)$
+% hereafter.
+% 
+% \item $0\leq\pp(p)<256$\\
+% The page $p$ has multi-column floats or the single-column
+% {\em\Uidx\preenv} preceeding \beginparacol{} in the {\em\Uidx\spage}
+% where it resides and spannig all columns.  $\pp(p)=i$ represents
+% $\!\insert!{\cdot}i$ for those {\em\Uidx\spanning} whose registers have
+% the followings.
+% 

+% \begin{itemize}
+% \item
+% $\pp^b(p)=\!\box!{\cdot}i$ contains the \spanning.
+% 
+% \item
+% $\pp^p(p)=\!\count!{\cdot}i=\page(p)$.
+% 
+% \item
+% $\pp^h(p)=\!\dimen!{\cdot}i=\!\@colht!$ if positive for the height of
+% columns shrunken 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 $\pp(p)\notin\LBRP0{256}$ 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
+% 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 $\pp(p)\notin\LBRP0{256}$ to
+% mean \!\pcol@topskip!.
+% \end{itemize}
+% 
+% \item $\pp(p)\geq256$\\
+% $\pp(p)=\page(p)+256$ to represent non-negative value $\page(p)$.
+% \end{itemize}
+% 

+% 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 \cs{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
+% $\page(q)$ represented by $\pp(q)$ for all $q\in[p,\ptop]$ are let be
+% $\page(p)+(q-p)$.  This update also takes place on \cswitch{} from the
+% leftmost column building a \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 $\PP$ to represent $\page(\ptop)+1$ which
+% \counter{page} is let have, 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 $q\leq p$.  However, it is expected that the progress
+% of the leftmost column usually preceeds other columns to give consistent
+% \counter{page} reference even with jumps.  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} at shipping-out of a whole page.
+% 
+% Also note that we also keep $\pp(\ptop)$ in \Midx{\!\pcol@currpage!}
+% which is initialized by \!\pcol@output@start! to represent the \!\insert!
+% for the \spanning{} preceding \beginparacol.  Then the macro is redefined
+% to have the value representing the new page in \!\pcol@startpage!, by
+% itself or \!\pcol@setordpage! invoked from the macro, to start the
+% page\footnote{

+% 

+% Other \!\def!initions of \!\pcol@currpage! in \!\pcol@setpnoelt!,
+% \!\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}
+% $\Uidx\CL$ is defined as follows.

+% 

+% \SpecialMainIndex{\pcol@counters}
+% $$
+% \CL=\CC-\CG=\!\pcol@counters!=\{\Uidx\cl_1,\ldots\}=\!\@elt!|{|\cl_1|}|\cdots
+% $$
+% 
+% 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 $\cl_i\in\CL$.
+% 
+% 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 $\cl_k\in\CL$ 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}

+% 
+% 
+% 
+% \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!}]
+% has footnotes \!\insert!ed in a page by \!\footnote! and \!\footnotetext!.
+% The register is referred to by \!\pcol@makenormalcol! to combine footnotes
+% to other \preenv{} to make a \spanning, and by \!\pcol@output@switch!
+% to save it in $\cc_c(\ft)$ when we leave from the column $c$.  The macro
+% \!\pcol@restartcolumn! restores $\cc_d(\ft)$ to the register by
+% \!\pcol@getcurrfoot! 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[\rm\Uidx{\!\bx@A!}, \ldots, \Uidx{\!\bx@R!}]
+% have floats created by \!\@xfloat! in the ordinary usage of \LaTeX.  In
+% addtion to it, we use these registers to save \preenv{}
+% (\!\pcol@output@start!), completed \colpage{}s (\!\pcol@opcol!),
+% \ccolpage{}s and thier footnotes (\!\pcol@output@switch!), \spanning{}
+% and thier \fpage{}s (\!\pcol@startpage!), \fcolumn{}s
+% (\!\pcol@flushcolumn!), single-column floats having $\cc_c(\vb^b)$ for
+% \sync{}ation (\!\pcol@synccolumn!), and \spanning{} carried over at
+% \Endparacol{} (\!\pcol@output@end!). 
+% \end{description}
+% 
+% 
+% 
+% \subsubsection{Integer Registers}
+% 
+% \begin{description}
+% \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 then
+% $-10004$ 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 by \!\pcol@restartcolumn!
+% to insert the \!\penalty! in the register to resume a \colpage{}
+% unless it is suspended after a sectioning command,
+% i.e. $\CSIndex{if@nobreak}=\true$.
+% 
+% \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@setpnoelt!, \!\pcol@nextpage!, \!\pcol@nextpelt!,
+% \!\pcol@checkshipped!, \!\pcol@outputelt!, \!\pcol@specialoutput!,
+% \!\pcol@output@switch!, \!\pcol@setcurrcol!, \!\pcol@flushcolumn!,
+% \!\pcol@measurecolumn!, \!\pcol@synccolumn!, \!\pcol@makeflushedpage!,
+% \!\pcol@flushfloats!, \!\pcol@output@end!, \!\paracol!,
+% \!\pcol@synccounter!, \!\pcol@com@syncallcounters!, \!\pcol@stepcounter!,
+% \!\pcol@com@switchcolumn!, \!\pcol@mctext!.
+% \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
+% $\CSIndex{if@afterindent}=\false$.
+% 
+% \item[\Uidx{\!\m@ne!}]
+% is a \!\count! register to have $-1$.  It is used in \!\pcol@setpnoelt!,
+% \!\pcol@nextpelt! and \!\pcol@getpelt! to decrement \!\@tempcnta! which
+% initially has $p-\pbase$ for a page $p$.
+% 
+% \item[\Uidx{\!\@cclv!}]
+% is a \!\chardef! register to have 255.  It is used in
+% \!\pcol@setpnoelt! and \!\pcol@getpinfo! to examine if
+% $\page(p)\in[0,255]$ for a page $p$.  See the description of \!\box!-type
+% registers for its another usage of \!\box!\!\@cclv!.
+% 
+% \item[\Uidx{\!\@cclvi!}]
+% is a \!\mathchardef! register to have 256.  It is used in
+% \!\pcol@setordpage! to let $\pp(p)={\page(p)}+256$ and \!\pcol@getpinfo! to
+% let $\page(p)=\pp(p)-256$ for a page $p$ such that $\page(p)\in[0,255]$.
+% 
+% \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.
+% 
+% \item[\Uidx{\!\@M!}]
+% is a \!\mathchardef! register to have 10000.  It is used in
+% \!\pcol@output! to examine if $\!\outputpenalty!<-10000$ to mean a special
+% \!\output! request, in \!\pcol@synccolumn! to put $\!\penalty!=-10000$
+% to force page break for flushing columns, and in \!\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[\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.
+% 
+% \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 \!\paracol! and \!\pcol@mctext! 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 \counter{page} being a \!\count! register to have the
+% page number.  It is referred to by \!\pcol@setpnoelt!,
+% \!\pcol@setordpage!, and \!\pcol@output@start! to let
+% $\pp(p)$ represent $\page(p)$.  The macro \!\pcol@startpage! also does
+% that for multi-column \fpage{}s incrementing the register.  Then
+% $\page(p)$ is reloaded to the register from $\pp(p)$ by \!\pcol@getpelt!,
+% \!\pcol@outputelt!, \!\pcol@sync! and \!\pcol@makeflushedpage!.  The other
+% user is \!\pcol@remctrelt! which lets
+% $|\cl@|{\cdot}\theta=\!\pcol@stepcounter!\Arg{\theta}$
+% 

+% \SpecialArrayIndex{\theta}{\cl@}
+% 

+% unless $\theta\neq\counter{page}$.
+% 
+% \item[$\cs{c@}{\cdot}\theta$]
+% \Uidx{\SpecialArrayIndex{\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! 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@getpinfo! to have $\pp(p)$ for a page $p$.
+% 
+% \item[\Uidx{\!\@tempcnta!}]
+% is a \!\count! register for temporary use.  The usages of this register
+% are as follows.
+% 

+% \begin{itemize}
+% \item\begingroup\hbadness3700
+% In \!\pcol@setpageno!, \!\pcol@setpnoelt!, \!\pcol@nextpage!,
+% \!\pcol@nextpelt!,\break\!\pcol@getcurrpage! and \!\pcol@getpelt!, it
+% has $p-q$ when we scan $\pp(q)$ for all $q\in[\pbase,\ptop]$ and the
+% \ccolpage{} is at $p$.
+% \par\endgroup
+% 
+% \item
+% In \!\pcol@setordpage!, it has $\pp(p)=\page(p)$ or $\pp(p)=\page(p)+256$
+% for a page $p$.
+% 
+% \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@outputelt!, it has $c$ when we scan $\s_c(q)$ for all
+% $c\In0\C$ to build the shipping out image of a page $q$.
+% 
+% \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@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@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@mctext!, it temporarily has $d$ being the target of \cswitch{}
+% during we let $\!\pcol@nextcol!=0$ to visit the first column for putting
+% a \mctext{}.
+% \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 \!\columnwidth! by \!\paracol!, while
+% \!\pcol@mctext!  and \!\endparacol! let it be \!\textwidth!.
+% 
+% \item[\Uidx{\!\maxdepth!}]
+% is \TeX's primitive register to have the maximum depth of the page being
+% built.  It is referred to by \!\pcol@cflt! to let \!\boxmaxdepth! of
+% \!\@outputbox!, in which top floats and the main vertical list are
+% combined, be \!\maxdepth!.
+% 
+% \item[\Uidx{\!\boxmaxdepth!}]
+% is \TeX's primitive register to have the maximum depth of \!\vbox!es.
+% The macro \!\pcol@cflt! let it be \!\maxdepth! for \!\@outputbox! in which
+% top floats and the main vertical list are combined, while the macro
+% \!\pcol@makenormalcol! let it be \!\@maxdepth! for \!\@outputbox! in which
+% \preenv{} is hold.
+% 
+% \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 \!\paracol!
+% also refers to it to save it in \!\pcol@firstprevdepth! for the \preenv.
+% 
+% \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
+% 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 \!\paracol!
+% 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.  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 it when it finds a empty list.
+% 
+% \item
+% The \cctext{} $\cc_c(\tr)$ may have \!\maxdimen! if the column $c$ has a
+% \fcolumn{} in the \lpage{} of \env{paracol} environment and the floats in
+% it can be put as top floats.  The macro \!\pcol@makefcolumn! makes this
+% special assignment and \!\pcol@makeflushedpage! examines it.
+% 
+% \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 $\VB$,
+% and that of four items $\VP$.  We also let $\DT$ and $\DP$ be the minimum
+% depth of the \colpage{}s which gives $\VT$ and $\VP$ respectively.  For
+% the measurement, the macro \!\pcol@sync! lets $\VT=\VB=\VP=-\!\maxdimen!$
+% 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 $\VP=-\!\maxdimen!$ to mean the last page is
+% empty.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\textheight!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the
+% height of 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), and by \!\pcol@outputelt!,
+% \!\pcol@output@flush!, \!\pcol@output@clear! and \!\pcol@output@end! to
+% build a page to be shipped out.
+% 
+% \item[\Uidx{\!\textwidth!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of a page.  The register is referred to by \!\pcol@outputelt!,
+% \!\pcol@makeflushedpage! and \!\pcol@flushfloats! to build a \!\hbox! of
+% \!\textwidth! wide to have all columns.  It also referred to by
+% \!\paracol! for the calculation of \!\columnwidth!, and by \!\pcol@mctext!
+% and \!\endparacol! to set it in \!\hsize! etc.
+% 
+% \item[\Uidx{\!\columnwidth!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of a column.  After the register is initialized by \!\paracol! according
+% to the number of columns $\C$ and other parameters, it is referred to by
+% \!\pcol@outputelt!, \!\pcol@makeflushedpage! and \!\pcol@flushfloats! to
+% put each \colpage{} into a \!\hbox! of \!\columnwidth! wide for shipping a
+% page out.  The register is also let have \!\textwidth! by \!\endparacol!
+% for \postenv.
+% 
+% \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 \!\columnwidth! by \!\paracol! and
+% \!\textwidth! by \!\endparacol! for outermost paragraphs inside\slash
+% outside \env{paracol} environment respectively.
+% 
+% \item[\Uidx{\!\columnsep!}]
+% is a \!\dimen! register for an API parameter of \LaTeX{} to have the width
+% of inter-column spaces.  It is referred to by \!\paracol! to calculate
+% \!\columnwidth!.
+% 
+% \item[\Uidx{\!\z@!}]
+% is a \!\dimen! register to have 0\,|pt| and is used in the following macros.
+% 

+% \begin{quote}\raggedright
+% \!\pcol@makecol!,
+% \!\pcol@combinefloats!,
+% \!\pcol@outputelt!,
+% \!\pcol@output@start!,
+% \!\pcol@floatplacement!,
+% \!\pcol@sync!,
+% \!\pcol@measurecolumn!,
+% \!\pcol@synccolumn!,
+% \!\pcol@output@end!.
+% \end{quote}
+% 

+% It is also used to give the number 0 in the following macros.
+% 

+% \begin{quote}\raggedright
+% \!\pcol@opcol!,
+% \!\pcol@setpnoelt!,
+% \!\pcol@setordpage!,
+% \!\pcol@nextpelt!,
+% \!\pcol@checkshipped!,
+% \!\pcol@getpelt!,
+% \!\pcol@getpinfo!,
+% \!\pcol@outputelt!,
+% \!\pcol@output@start!,
+% \!\pcol@output@switch!,
+% \!\pcol@setcurrcol!,
+% \!\pcol@sync!,
+% \!\pcol@synccolumn!,
+% \!\pcol@makeflushedpage!,
+% \!\pcol@flushfloats!,
+% \!\pcol@freshpage!,
+% \!\pcol@output@end!,
+% \!\paracol!,
+% \!\pcol@synccounter!,
+% \!\pcol@com@syncallcounters!,
+% \!\pcol@stepcounter!,
+% \!\pcol@stpclelt!,
+% \!\pcol@com@switchcolumn!,
+% \!\pcol@switchcolumn!,
+% \!\pcol@mctext!,
+% \!\pcol@switchcol!,
+% \!\endparacol!.
+% \end{quote}
+% 
+% \item[\Uidx{\!\p@!}]
+% is a \!\dimen! register to have 1\,|pt|.  It is used in
+% \!\pcol@cflt!, \!\pcol@addflhd!, \!\pcol@synccolumn! and
+% \!\pcol@output@end! as the shorthand of |pt|.
+% 
+% \item[\Uidx{\!\@maxdepth!}]
+% is a \!\dimen! register to have \!\maxdepth! in case that it is
+% temporarily modified.  It is used in \!\pcol@makenormalcol! to let
+% \!\boxmaxdepth! have it.
+% 
+% \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 \begingroup\hbadness1750
+% In macros \!\pcol@startpage!, \!\pcol@output@start!, \!\pcol@flushfloats!
+% and\break\!\pcol@output@end!, it is initialized to \!\textheight!.  In first
+% two, the value of the register is reduced to reflect \spanning{} and then
+% set into $\pp^h(p)$, if \spanning{} exists.
+% \par\endgroup
+% 
+% \item \begingroup\tolerance1500 \hbadness1500
+% In macros \!\pcol@getpelt!, \!\pcol@sync!, \!\pcol@flushcolumn!,
+% \!\pcol@measure~column!  and \!\pcol@makeflushedpage!, it is let have
+% $\pp^h(p)$.  In addition \!\pcol@sync! examines if $\!\@colht!<\VT+\VB$, and
+% \!\pcol@makefcolumn! uses it to initialize the room of a \fpage.
+% \par\endgroup
+% 
+% \item
+% In macros \!\pcol@startcolumn!, \!\pcol@flushcolumn! and
+% \!\pcol@freshpage!, it is used to let \!\@colroom! have it.
+% 
+% \item
+% In macros \!\pcol@output@flush! and \!\pcol@output@clear!, it is given to
+% \!\pcol@makeflushedpage! 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}
+% 
+% \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!.  The macro \!\pcol@output! also refers to this
+% register to let \!\vsize! have it.   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{\!\@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@makeflushedpage!.
+% 
+% \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.  It is initialize to be 0 by \!\pcol@floatplacement!,
+% saved in $\cc_c(\mb)$ by \!\pcol@setcurrcol!, and restored from it by
+% \!\pcol@iigetcurrcol!.
+% 
+% \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 
+% \!\pcol@addflhd! and \!\pcol@hdflelt! to measure the height of top and
+% bottom floats, and in \!\pcol@measurecolumn! for them and $\VT$, $\VB$ and
+% $\VP$.  The other user \!\pcol@synccolumn! lets it have
+% $\!\textfloatsep!-\!\floatsep!$ or 0 for the adjustment of the position
+% of $\cc_c(\vb^b)$ in the last top float and \!\pcol@textfloatsep!
+% following it for a \sync{}ation whose point determined by a column having
+% empty main vertical list.
+% 
+% \item[\Uidx{\!\dimen@ii!}]
+% is a \!\dimen! register for temporary use.  It is used in 
+% \!\pcol@measurecolumn! for $\VT$, $\VP$ and $\DP$.
+% 
+% \item[\Uidx{\!\@tempdima!}]
+% is a \!\dimen! register for temporary use.  The usages of this register
+% are as follows.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@combinefloats!, it has the natural component of
+% \!\textfloatsep! to be used for the shrink of the vertical skip following
+% it, when we put them below the bottom floats in the last page of
+% \env{paracol} environment.
+% 
+% \item
+% In \!\pcol@startpage!, 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@outputelt!, it has $\pp^h(p)$ to examine if $p$ is a \fpage.
+% 
+% \item
+% In \!\pcol@makefcolumn! and \!\pcol@makefcolelt!, it has the room for
+% floats to be put in a \fcolumn{} in the \lpage{}.
+% 
+% \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.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\@tempdimb!}]
+% is a \!\dimen! register for temporary use.  It has $\VB$ in \!\pcol@sync!
+% and \!\pcol@measurecolumn!, has the size of a float in
+% \!\pcol@makefcolelt!, and has $\cc_c(\tf)=\!\pcol@textfloatsep!$ in
+% \!\pcol@synccolumn!.
+% 
+% \item[\Uidx{\!\@tempdimc!}]
+% is a \!\dimen! register for temporary use.  It has $\DT$ in
+% \!\pcol@sync!, \!\pcol@measurecolumn! and \!\pcol@synccolumn!, and has
+% \!\floatsep! or \!\@fpsep! in \!\pcol@makefcolumn! and
+% \!\pcol@makefcolelt!.
+% 
+% \item[\Uidx{\!\@pageht!}]
+% is a \!\dimen! register to be used in \LaTeX's \!\@specialoutput! to have
+% the height of \!\@holdpg!.  However, we use it as a scratchpad to save
+% $\pp^h(\ptop)$ in \!\pcol@makeflushedpage!.
+% 
+% \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 to have
+% $\DP$ in \!\pcol@sync!, \!\pcol@measurecolumn! and \!\pcol@output@end!.
+% \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.
+% 
+% \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
+% \!\paracol! 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@output@end! temporarily lets the register has 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{\!\floatsep!}]
+% is a \!\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! and \!\pcol@makefcolelt! to examine the
+% capacity of a \fcolumn{} in the \lpage, and by \!\pcol@addflhd! and
+% \!\pcol@hdflelt!  to measure the total height of top and bottom floats.
+% 
+% \item[\Uidx{\!\textfloatsep!}]
+% is a \!\skip! register to have the vertical skip between the main vertical
+% list and top\slash bottom floats.  It is referred to by
+% \!\pcol@combinefloats! to insert a skip below the bottom floats in the
+% \lpage{} of \env{paracol} environment, by \!\pcol@measurecolumn! to take
+% this skip into account in the calculation of $\VP$, 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 a \!\skip! register to have the vertical skip between adjacent
+% multi-column floats, and is used in \!\pcol@startpage! to cancel the skip
+% below the last float.
+% 
+% \item[\Uidx{\!\dbltextfloatsep!}]
+% is a \!\skip! register to have the vertical skip between the last
+% multi-column float and the top of columns, and is used in
+% \!\pcol@startpage! to put the skip.
+% 
+% \item[\Uidx{\!\@fptop!}]
+% is a \!\skip! register to have the vertical skip inserted at the top of
+% a \fcolumn, and is used in \!\pcol@makefcolumn! and
+% \!\pcol@makeflushedpage!.
+% 
+% \item[\Uidx{\!\@fpsep!}]
+% is a \!\skip! register to have the vertical skip between adjacent floats
+% in a \fcolumn, and is used in \!\pcol@makefcolumn! and
+% \!\pcol@makeflushedpage!.
+% 
+% \item[\Uidx{\!\@fpbot!}]
+% is a \!\skip! register to have the vertical skip inserted at the bottom of
+% a \fcolumn, and is used in \!\pcol@makefcolumn! and
+% \!\pcol@makeflushedpage!.
+% 
+% \item[\Uidx{\!\@tempskipa!}]
+% is a \!\skip! register for temporary use.  It is used to throw $\pp^t(p)$
+% away in \!\pcol@startpage!, \!\pcol@outputelt!, \!\pcol@flushcolumn!
+% and \!\pcol@makeflushedpage! because we don't need it.  The macro
+% \!\pcol@output@start! uses it to determine \!\topskip! for the \spage.
+% \end{description}
+% 
+% 
+% 
+% \subsubsection{Box Registers}
+% 
+% \begin{description}
+% \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@specialoutput! to discard the dummy \!\vbox! inserted by
+% \!\pcol@invokeoutput!, and is let have the main vertical list of a column
+% to be passed to \!\@makecol! by \!\pcol@flushcolumn! and
+% \!\pcol@makeflushedpage!.
+% 
+% \item[\Uidx{\!\voidb@x!}]
+% is a \!\box! register to be void always.  It is referred to
+% by \!\pcol@outputelt! to initialize \!\@outputbox! and to examine if
+% $\S_c$ is empty, by \!\pcol@output@switch! and \!\pcol@setcurrcolnf! to
+% let $\cc_c(\ft^b)$ be void if a column does not have footnotes, and by
+% \!\pcol@getcurrfoot! to let \!\footins! be void if so.
+% 
+% \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@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 shipping-out image
+% of a column or a page.  The usages of the register are as follows.
+% 

+% \begin{itemize}
+% \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 page to be shipped out by
+% \!\@outputpage!.
+% 
+% \item \begingroup\tolerance1700\hbadness1700
+% In \!\pcol@output@start!, it has the \preenv{} built by
+% \!\pcol@makenormalcol!.
+% \par\endgroup
+% 
+% \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! in which it has each of flushed
+% \colpage{} built by \!\@makecol!.
+% 
+% \item
+% In \!\pcol@flushfloats!, it has the complete page for flushed \fcolumn{}s
+% each of which \!\@makefcolumn! builds also in it.
+% 
+% \item
+% In \!\pcol@output@end!, it has the shipping-out image of the \lpage{} of
+% \env{paracol} environment built by \!\pcol@makeflushedpage!.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\@tempboxa!}]
+% is a \!\box! register for temporary use.  The usages of the register are
+% as follows.
+% 

+% \begin{itemize}
+% \item \begingroup\tolerance2100\hbadness2100
+% In \!\pcol@cflt! and \!\pcol@startpage!, it has top single-\slash
+% multi-column floats combined by the application of
+% \!\@comflelt!\slash\!\@comdblflelt! to \!\@toplist!\slash\!\@dbltoplist!
+% respectively.
+% \par\endgroup
+% 
+% \item
+% In \!\pcol@specialoutput!, it is used to discard the dummy \!\vbox! put by
+% \!\pcol@invokeoutput!.
+% 
+% \item
+% In \!\pcol@measurecolumn!, it is used to examine if the main vertical list
+% is empty.
+% % \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 \!\paracol!.
+% 
+% \item[\Uidx{\!\everypar!}]
+% is \TeX's primitive to have tokens inserted at the beginning of each
+% paragarph.  In \!\pcol@mctext! 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{\!\@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 \!\paracol!, and then turned $\false$ by \!\endparacol!.
+% 
+% \item[\Uidx{\CSIndex{if@firstcolumn}}]
+% is a switch to be $\true$ iff the first column is being typeset.  It is
+% turned $\true$ by \!\paracol!, and so by \!\pcol@switchcol! iff it is to
+% switch to the column 0.
+% 
+% \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 the value set by a \mctext{} to $\cc_c(\sw)$ for all
+% $c\In0\C$.  The \!\pcol@restartcolumn! inserts $\!\penalty!=10000$ by
+% \!\nobreak! if the switch is $\true$.
+% 
+% \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!.
+% 
+% \item[\Uidx{\CSIndex{if@fcolmade}}]\begingroup\hfuzz0.45pt
+% is a switch to be $\true$ iff a \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!, \!\pcol@freshpage!
+% and \!\pcol@output@end!, 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 macro
+% \!\pcol@makeflushedpage! and \!\pcol@flushfloats! also turns the switch
+% $\true$ iff \fcolumn{}s are to be built so that the latter itself
+% and \!\pcol@output@end! know that.
+% \par\endgroup
+% 
+% \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@outputpage! 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@outputpage! 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 \!\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 $\CSIndex{ifpcol@clear}$
+% for flushing, so as to invoke \!\pcol@sync!.
+% 
+% \item
+% In \!\pcol@sync!, it is turned $\true$ iff the page with the \sync{}ation
+% point being set is not to be flushed, so that it is examined by
+% \!\pcol@synccolumn!.
+% 
+% \item
+% In \!\pcol@makefcolumn!, it is turned $\true$ 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 \!\@fpmim!, to mean it is possible that the floats
+% 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@measureupdate! examines it for the update of $\VP$
+% and $\DP$.
+% 
+% \item
+% In \!\pcol@flushfloats!, 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@makeflushedpage!, it is turned $\true$ iff $\cc_c(\tr)=\infty$
+% and $\VP=\pp^h(\ptop)$ to mean the floats in $\cc_c(\tl)$ should be put in
+% a \fcolumn{} in the \lpage{} as usual.
+% 
+% \item
+% In \!\pcol@output@end!, at first it is turned $\true$ iff the last page is
+% not empty when we have \fcolumn{}s to be built, so that the last page is
+% shipped out prior to the pages of \fcolumn{}s.  Then 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 $\!\pcol@cmpctrelt!\arg{\theta}$, 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 $\!\pcol@ac@caption@def!\arg{s}\arg{t}$, \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@lof! are initialized to be \!\let!-equal to
+% \!\@tempswatrue! as the default.
+% \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 \!\@@par! in which the \TeX's
+% orinigal definition is kept, while \!\paracol! 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! for
+% a warning message.
+% 
+% \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 the \lrep{}
+% for $c$ being $|\pcol@thectr@|{\cdot}\theta{\cdot}c$
+% 

+% \SpecialArrayIndex{\theta{\cdot}c}{\pcol@thectr@}

+% 

+% 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}.
+% 
+% \item[\Uidx{\!\nobreak!}]
+% is an API macro to insert $\!\penalty!=10000$ to inhibit line or page
+% breaks.  It is used in \!\pcol@restartcolumn! to meet the page-break
+% inhibition request made by $\CSIndex{if@nobreak}=\true$.
+% 
+% \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@restartcolumn! to insert \!\interlinepenalty! if
+% $\CSIndex{if@nobreak}=\false$.
+% 
+% \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
+% disabling it by making it \!\let!-equal to \!\pcol@gobblethree!.
+% 
+% \item[\Uidx{\!\footnoterule!}]
+% is an API macro to draw a horizontal line above footnotes, or to insert
+% whatever it has before them.  The macro is used in \!\pcol@makenormalcol!
+% to combine the main vertical list and footnotes if provided to build the
+% \preenv{} in \!\@outputbox!.
+% 
+% \item[\Uidx{\!\dblfigrule!}]
+% is an API macro to draw a horizontal line between the last multi-column
+% 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 single-column
+% 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@makeflushedpage! 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@makenormalcol! to specify the color of
+% footnotes if provided to include them as a part of \preenv{} in
+% \!\@outputbox!.
+% 
+% \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 \!\pcol@ovf! in case of
+% \!\@freelist! shortage, in \!\paracol! for illegal nesting, in
+% \!\pcol@switchenv! for illegal \cswitch{} commands\slash
+% environments in a \csenv, in \!\pcol@switchcolumn! for invalid target
+% column, and in \!\addcontentsonly! for unknown contents type.
+% 
+% \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.
+% 
+% \item[\Uidx{\!\@height!}]
+% is an internal macro having the keyword |height|.  It is used in
+% \!\pcol@output@start! to draw an invisible \!\hrule!.
+% 
+% \item[\Uidx{\!\@width!}]
+% is an internal macro having the keyword |width|.  It is used in
+% \!\pcol@output@start! to draw an invisible \!\hrule!.
+% 
+% \item[\Uidx{\!\@plus!}]
+% is an internal macro having the keyword |plus|.  It is used in
+% \!\pcol@makecol! to \!\def!ine \!\@textbottom! with the body of a vertical
+% skip with infinite stretch and shrink, and in \!\pcol@synccolumn! to put a
+% vertical skip with infinite stretch to push up the main vertical list
+% above a \sync{}ation point.
+% 
+% \item[\Uidx{\!\@minus!}]
+% is an internal macro having the keyword |minus|.  It is used in
+% \!\pcol@makecol! to \!\def!ine \!\@textbottom! with the body of a vertical
+% skip with infinite stretch and shrink, and in \!\pcol@combinefloats! to
+% put a vertical skip with a shrink of \!\textfloatsep! so that the skip of
+% \!\textfloatsep! above it can be canceled if necessary.
+% 
+% \item[\Uidx{\!\hb@xt@!}]
+% is an internal macro having the sequence ``\!\hbox!| to|''.  It is used in 
+% \!\pcol@outputelt!, \!\pcol@makeflushedpage! and \!\pcol@flushfloats! 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
+% \!\paracol! 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@}
+% \end{itemize}
+% 
+% \item[\Uidx{$\!\@nameuse!\arg{cs}$}]
+% is an internal macro to do $|\|\arg{cs}$.  It is used in the following
+% macros.
+% 

+% \begin{itemize}
+% \item
+% \!\column*! for \!\pcol@com@column*!.
+% 
+% \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
+% $\!\pcol@aconlyelt!\<t\>\<c\>$ 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}

+% \end{itemize}
+% 
+% \item[\Uidx{$\!\@ifundefined!\arg{cs}\arg{then}\arg{else}$}]
+% is an internal macro to do $\arg{then}$ or $\arg{else}$ if $\arg{cs}$ is
+% undefined or defined respectively.  It is used in
+% $\!\addcontentsonly!\<t\>\<c\>$ to stop the execution if
+% $|\pcol@ac@def@|{\cdot}t$ is not defined.
+% 

+% \SpecialArrayIndex{t}{\pcol@ac@def@}
+% 
+% \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
+% \!\paracol!, the initial definition of \!\pcol@com@column*!,
+% \!\pcol@com@switchcolumn! and \!\pcol@iswitchcolumn! to examine if they
+% are followed by a `|[|'.
+% 
+% \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@switchcolumn! 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 of \fcolumn{}s or \fpage{}s while
+% $\CSIndex{if@fcolmade}=\true$.
+% 
+% \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@outputelt!,
+% \!\pcol@output@start!,
+% \!\pcol@output@switch!,
+% \!\pcol@sync!,
+% \!\pcol@makeflushedpage!,
+% \!\pcol@flushfloats!,
+% \!\pcol@freshpage!,
+% \!\pcol@output@end!,
+% \!\pcol@synccounter!,
+% \!\pcol@com@syncallcounters!,
+% \!\pcol@stepcounter!
+% \end{quote}
+% 

+% The macro is also used in \!\pcol@flushcolumn! to iterate building
+% \fcolumn{}s of a column $c$ in pages $q$ such that
+% $q\in(\cc_c(\vb^p),\ptop)$.
+% 
+% \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 multi-column top
+% floats.
+% 
+% \item
+% \!\pcol@output@start! for the \preenv{} and \colpage{}s of all columns.
+% 
+% \item
+% \!\pcol@output@switch! for the \colpage{} from which we are leaving, and
+% for footnotes in it if exist.
+% 
+% \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 multi-column floats in the \lpage{} if the
+% main vertical list of the page is empty.
+% \end{itemize}
+% 

+% The macro is also used in \!\pcol@outputelt! to obtain completed
+% \colpage{}s from $\S_c$.
+% 
+% \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@opcol! to add the completed \ccolpage{} of $c$ to $\S_c$.
+% 
+% \item
+% \!\pcol@startpage! to add \fpage{}s to $\PP$.
+% 
+% \item
+% \!\pcol@outputelt! to return shipped-out pages, \spanning{} and
+% \colpage{}s to \!\@freelist!, or to add $\pp(q)$ to $\PP$ if the page $q$
+% is kept.
+% 
+% \item
+% \!\pcol@output@start! to return the \ccolpage{} of 0 to \!\@freelist!.
+% 
+% \item
+% \!\pcol@restartcolumn! to return the \ccolpage{} 
+% to be resumed, and its footnotes if any, to \!\@freelist!.
+% 
+% \item
+% \!\pcol@flushcolumn! to return footnotes 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{} to \!\@freelist!, and to
+% return footnotes in the \colpage{} to be flushed to \!\@freelist! if any.
+% 
+% \item
+% \!\pcol@output@end! to return all \ccolpage{}s to \!\@freelist!.
+% 
+% \item
+% $\!\globalcounter!\<\theta\>$ to add a \gcounter{} $\theta$ to $\CG$.
+% 
+% \item
+% $\!\pcol@iremctrelt!\<\theta\>$ to add \lcounter{} $\theta$ to $\CL$.
+% 
+% \item
+% $\!\pcol@storectrelt!\<\theta\>$ to add $\<\theta,\val_c(\theta)\>$ to
+% $\Cc_c$ for a column $c$.
+% 
+% \item
+% $\!\pcol@savectrelt!\<\theta\>$ to add $\<\theta,\val(\theta)\>$ to
+% $\Cc_c$ for a column $c$.
+% 
+% \item
+% $\!\pcol@cmpctrelt!\<\theta\>$ to add $\theta$ to the list of \lcounter{}s
+% to be synchronized.
+% 
+% \item
+% $\!\addcontentsonly!\<t\>\<c\>$ to add $\<t,c\>$ to $\T$.
+% \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{\!\@eha!}]
+% is an internal macro having a help message saying the command causing an
+% error is ignored.  It is used in \!\paracol!, \!\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! as the argument of
+% \!\PackageError!.
+% 
+% \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 \!\pcol@output! in case
+% that a page with floats and very short main vertical list is built.
+% 
+% \item[\Uidx{\!\color@begingroup!}]
+% is an internal macro to open a group in which a color is specified.  It is
+% used in \!\pcol@makenormalcol! to enclose footnotes with \!\normalcolor!
+% for \preenv{}.
+% 
+% \item[\Uidx{\!\color@endgroup!}]
+% is an internal macro to close a group in which a color is specified.  It is
+% used in \!\pcol@makenormalcol! to enclose footnotes with \!\normalcolor!
+% for \preenv{}.
+% 
+% \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{\!\@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
+% kept in \!\pcol@ac@enable@toc! after disabling \!\addcontentsline!.
+% 
+% \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 kept in \!\pcol@ac@enable@toc! after
+% disabling \!\addcontentsline! if necessary.
+% 
+% \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{\!\@specialoutput!}]
+% is an internal macro for \!\output! routine to process an \!\output!
+% request made by \LaTeX's original \!\clearpage! and $\!\end!\Arg{float}$.
+% It is used in \!\pcol@specialoutput! to process the request for floats.
+% 
+% \item[\Uidx{\!\@makecol!}]
+% is an internal macro for \!\output! routine to build the shipping-out
+% image of a column in \!\@outputbox! consisting of top floats, main
+% vertical list in \!\box!|255|, footnotes in \!\footins!, and bottom
+% floats.  It is used in \!\pcol@makecol! for an ordinary \colpage{},
+% in \!\pcol@flushcolumn! for a \ccolpage{} to be flushed, and in
+% \!\pcol@makeflushedpage! for \colpage{}s in $\ptop$ to be flushed.
+% 
+% \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 have been put by
+% \!\@makecol!, and to have the result in \!\@outputbox! again.  It is used
+% in \!\pcol@makenormalcol! for \preenv{}, while \!\paracol! makes it
+% \!\let!-equal to our own \!\pcol@combinefloats! so that \!\@makecol! uses
+% it.
+% 
+% \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.  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.  It is used in
+% \!\pcol@combinefloats!.
+% 
+% \item[\Uidx{$\!\@comflelt!\arg{flt}$}]
+% is an internal macro for \!\output! routine to put $\arg{flt}$ being a
+% single-column 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 to each element of \!\@toplist!.
+% 
+% \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 staff 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.
+% 
+% \item[\Uidx{\!\@outputpage!}]
+% is an internal macro for \!\output! routine to output a page kept in
+% \!\@outputbox! together with the headder and footer.  It is used in
+% \!\pcol@outputelt! for ordinary completed pages, in \!\pcol@output@start!
+% for (almost) full page \preenv{}, in \!\pcol@output@flush! for the
+% flushed \tpage, in \!\pcol@output@clear! for the flushed \tpage{} and
+% following \fpage{}s, in \!\pcol@flushfloats! for pages having flushed
+% \fcolumn{}s, and in \!\pcol@output@end! for the non-empty \lpage{}
+% followed by pages having \fcolumn{}s.
+% 
+% \item[\Uidx{\!\@dblfloatplacement!}]
+% is an internal macro for \!\output! routine to reinitialize multi-column
+% float placement paramenters.  It is used in \!\pcol@startpage! and
+% \!\pcol@output@clear! prior to processing multi-column floats in
+% \!\@dbldeferlist!.
+% 
+% \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 multi-column floats in
+% \!\@dbldeferlist!, and in \!\pcol@startcolumn! for single-column floats in
+% $\cc_c(\dl)$.
+% 
+% \item[\Uidx{$\!\@sdblcolelt!\arg{flt}$}]
+% is an internal macro for \!\output! routine which examines if a
+% multi-column 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!
+% otherwise.  It is used in \!\pcol@startpage! to apply to each element of
+% (the copy of) \!\@dbldeferlist!.
+% 
+% \item[\Uidx{$\!\@comdblflelt!\arg{flt}$}]
+% is an internal macro for \!\output! routine to put $\arg{flt}$ being a
+% multi-column float to the tail of \!\@tempboxa! which finally has the
+% \spanning{} for multi-column floats.  It is used in \!\pcol@startpage! to
+% apply to each element of \!\@dbltoplist! to have the \spanning.
+% 
+% \item[\Uidx{\!\@floatplacement!}]
+% is an internal macro for \!\output! routine to reinitialize single-column
+% float placement parameters.  It is used in our own version of it,
+% \!\pcol@floatplacement!.
+% 
+% \item[\Uidx{$\!\@scolelt!\arg{flt}$}]
+% is an internal macro for \!\output! routine which examines if a
+% single-column 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{$\!\@makefcolumn!\arg{lst}$}]
+% 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@flushfloats! for $\cc_c(\dl)$ of single-column floats, and in
+% \!\pcol@output@clear! for \!\@dbldeferlist! of multi-column floats which
+% become single-column ones.
+% 
+% \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
+% only in \!\pcol@output@end! for the case multi-column floats are left at
+% \Endparacol{} and they are put in \fpage{}s.
+% 
+% \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 only in \!\pcol@output@end! for the case multi-column floats
+% are left at \Endparacol{} after which they become single-column ones.
+% 
+% \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! in case that a page
+% with floats and very short main vertical list is built.
+% \end{description}
+%
+% 
+% 
+% \subsubsection{Structural Macros}
+% 
+% \begin{description}
+% \item[\Uidx{\!\topfraction!}]
+% is an API macro to have the maximum fraction of the space for top floats
+% in a column.  It is used by \!\pcol@makeflushedpage! to recalculate
+% $\!\@toproom!=\cc_c(\tr)=\!\topfraction!\times\pp^h(\ptop)$.
+% 
+% \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@cflt! does $\!\@elt!=\!\@comflelt!$ for $\cc_c(\tl)$, and then
+% $\!\@elt!=\!\relax!$ to concatenate \!\@freelist! and $\cc_c(\tl)$.
+% 
+% \item
+% \!\pcol@setpageno! does $\!\@elt!=\!\pcol@setpnoelt!$ for $\PP$.
+% 
+% \item
+% \!\pcol@setpnoelt! does $\!\@elt!=\!\relax!$ to add $\pp(q)$ to $\PP$.  It
+% also uses \!\@elt! to \!\def!ine \!\pcol@currpage! with
+% $\!\@elt!\<\pp(q)\>$ or $\!\@elt!|{|\pp(q)|}|$.
+% 
+% \item
+% \!\pcol@setordpage! does $\!\@elt!=\!\relax!$ to \!\xdef!ine
+% \!\pcol@currpage! with $\!\@elt!|{|\pp(q)|}|$.
+% 
+% \item
+% \!\pcol@nextpage! does $\!\@elt!=\!\pcol@nextpelt!$ for $\PPP$.
+% 
+% \item
+% \!\pcol@getcurrpage! does $\!\@elt!=\!\pcol@getpelt!$ for $\PPP$.
+% 
+% \item
+% \!\pcol@startpage! does $\!\@elt!=\!\@sdblcolelt!$ for (the copy of)
+% \!\@dbldeferlist!, $\!\@elt!=\!\@comdblflelt!$ for \!\@dbltoplist!,
+% and then $\!\@elt!=\!\relax!$ to concatenate \!\@freelist! and
+% \!\@dbltoplist!.  It also uses \!\@elt! to \!\xdef!ine \!\pcol@currpage!
+% with $\!\@elt!\<\pp(\ptop)\>$.
+% 
+% \item
+% \!\pcol@outputpage! does $\!\@elt!=\!\pcol@outputelt!$ with two arguments
+% for (the copy of) $\PP$.
+% 
+% \item
+% \!\pcol@trynextcolumn! does $\!\@elt!=\!\@scolelt!$ for (the copy of)
+% $\cc_c(\dl)$.
+% 
+% \item
+% \!\pcol@output@start! uses \!\@elt! to \!\xdef!fine \!\pcol@currpage! with
+% $\!\@elt!\<\pp(0)\>$.
+% 
+% \item
+% \!\pcol@makenormalcol! does $\!\@elt!=\!\relax!$ to concatenate
+% \!\@freelist! and \!\@midlist!.
+% 
+% \item
+% \!\pcol@setcurrcol! does $\!\@elt!=\!\relax!$ 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@makefcolumn! does $\!\@elt!=\!\pcol@makefcolelt!$ 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! does $\!\@elt!=\!\pcol@hdflelt!$ for its argument
+% $\cc_c(\tl)$ or $\cc_c(\bl)$, and then $\!\@elt!=\!\relax!$ to give the
+% default.
+% 
+% \item
+% \!\pcol@output@end! does $\!\@elt!=\!\relax!$ to add the \spanning{} of
+% the last page to the head of \!\@dbldeferlist!.
+% 
+% \item
+% \!\paracol! does $\!\@elt!=\!\pcol@remctrelt!$ for $\CG$,
+% $\!\@elt!=\!\pcol@thectrelt!$ for $\CL$, $\!\@elt!=\!\pcol@loadctrelt!$
+% for $\Cc_0$, $\!\@elt!=\!\pcol@cmpctrelt!$ for $\CL$,
+% $\!\@elt!=\!\pcol@defcomelt!$ for \!\pcol@localcommands!, and then
+% $\!\@elt!=\!\relax!$ to give the default.
+% 
+% \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@remctrelt! does $\!\@elt!=\!\pcol@iremctrelt!$ for (the copy of)
+% $\CL$.
+% 
+% \item
+% $\!\pcol@sscounters!\arg{elt}$ does $\!\@elt!=\arg{elt}$, where
+% $\arg{elt}=\!\pcol@storectrelt!$ or $\arg{elt}=\!\pcol@savectrelt!$, for
+% $\CL$, 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\hfuzz0.37pt
+% $\!\pcol@synccounter!\arg{lst}$ does $\!\@elt!=\!\relax!$ 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
+% $\!\pcol@stepcounter!\<\theta\>$ does $\!\@elt!=\!\pcol@stpldelt!$ for
+% $\CL$, $\!\@elt!=|\pcol@|\~|stpclelt|$
+% 

+% \SpecialIndex{\pcol@stpclelt}

+% 

+% for $\clist(\theta)$, and then $\!\@elt!=\!\@stpelt!$ for
+% $\clist(\theta)$.
+% 
+% \item
+% \!\pcol@switchcol! does $\!\@elt!=\!\pcol@setctrelt!$ for $\CC_c$,
+% $\!\@elt!=|\pcol@|\~|aconlyelt|$
+% 

+% \SpecialIndex{\pcol@aconlyelt}

+% 

+% for $\T$, and then $\!\@elt!=\!\relax!$ to give the default.
+% \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@flushcolumn! ($\cc_c(\dl)$)\\
+% \!\pcol@makefcolumn! ($\cc_c(\dl)$, $\cc_c(\tl)$)\\
+% \!\pcol@measurecolumn! ($\cc_c(\bl),\cc_c(\dl)$)\\
+% \!\pcol@addflhd! ($\cc_c(\tl)$, $\cc_c(\tl)$)\\
+% \!\pcol@synccolumn! ($\cc_c(\tl)$)\\
+% \!\pcol@makeflushedpage! ($\cc_c(\dl)$)\\
+% \!\pcol@flushfloats! ($\cc_c(\dl)$)
+% \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! ($\cc_c(\dl)$, \!\@dbltoplist!)\\
+% \!\pcol@trynextcolumn! ($\cc_c(\dl)$)\\
+% \!\pcol@output@start! ($\PP$, $\pp(\ptop)$, $\cc_c(\dl)$)\\
+% \!\pcol@makenormalcol! (\!\@midlist!)\\
+% \!\pcol@flushcolumn! ($\cc_c(\dl)$)\\
+% \!\pcol@makefcolumn! ($\cc_c(\dl)$, $\cc_c(\tl)$)\\
+% \!\pcol@makeflushedpage! ($\cc_c(\tl)$)\\
+% \!\pcol@freshpage! ($\PP$, $\pp(\ptop)$)\\
+% \!\paracol! (\!\@gtempa!)\\
+% \!\pcol@remctrelt! ($\CL$)\\
+% \!\pcol@sscounters! ($\Cc_c$)
+% \end{quote}
+% 
+% \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! ($\pp(\ptop)$)\\
+% \!\pcol@outputelt! ($\pp(q)$, $\s_c(q)$)\\
+% \!\pcol@output@start! ($\pp(0)$, $\cc_c(\vb)$)\\
+% \!\pcol@output@switch! ($\cc_c(\vb)$)\\
+% \!\pcol@restartcolumn! ($\cc_c(\vb)$)\\
+% \!\pcol@igetcurrcol! ($\cc_c(\vb)$)\\
+% \!\pcol@setcurrcol! ($\cc_c(\vb)$)\\
+% \!\pcol@sync! ($\pp(\ptop)$)\\
+% \!\pcol@flushcolumn! ($\cc_c(\vb), \s_c(q)$)\\
+% \!\pcol@measurecolumn! ($\cc_c(\vb)$)\\
+% \!\pcol@synccolumn! ($\cc_c(\vb)$)\\
+% \!\pcol@makeflushedpage! ($\pp(\ptop)$, $\cc_c(\vb)$)\\
+% \!\pcol@freshpage! ($\cc_c(\vb)$)\\
+% \!\pcol@output@end! (top float, $\cc_c(\vb)$)
+% \end{quote}
+% 
+% \item[\Uidx{\!\@freelist!}]
+% is an internal macro having available \!\insert!s for floats originially,
+% but also \colpage{}s, pages and footonotes 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! ($\pp(q)$, $\s_c(q)$)\\
+% \!\pcol@output@start! ($\cc_0(\vb)$)\\
+% \!\pcol@makenormalcol! (\!\@midlist!)\\
+% \!\pcol@restartcolumn! ($\cc_c(\vb)$, $\cc_c(\ft)$)\\
+% \!\pcol@flushcolumn! ($\cc_c(\ft)$)\\
+% \!\pcol@makefcolumn! ($\cc_c(\tl)$)\\
+% \!\pcol@makeflushedpage! ($\pp(\ptop)$, $\cc_c(\ft)$, $\cc_c(\tl)$)\\
+% \!\pcol@output@end! ($\cc_c(\vb)$)
+% \end{quote}
+% 
+% \item[\Uidx{\!\@nil!}]
+% is an internal control sequence which is conventionally used to terminate
+% a variable length argument.  It is used in \!\pcol@getcurrpinfo! for the
+% invocation of \!\@cdr!.
+% 
+% \item[\Uidx{\!\@dbldeferlist!}]
+% is an internal macro having the list of multi-column 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 multi-column floats to be put in the empty
+% \lpage{} to it and then move the whole of the list to \!\@deferlist!.
+% 
+% \item[\Uidx{\!\@dbltoplist!}]
+% is an internal macro having the list of multi-column floats which
+% \!\@sdblcolelt! decided to be put in the new page.  The macro
+% \!\pcol@startpage! scans it to put all floats in the page $\ptop$, and then
+% empties it after returning all floats to \!\@freelist!.
+% 
+% \item[\Uidx{\!\@deferlist!}]
+% is an internal macro having the list of single-column 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@flushfloats!, 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@setcurrcol! and \!\pcol@igetcurrcol! saves\slash restores it
+% in/from $\cc_c(\dl)$, respectively.
+% 
+% \item
+% \!\pcol@measurecolumn! examines its emptiness to make $\VP=\pp^h(\ptop)$
+% if not empty.
+% 
+% \item
+% \!\pcol@makeflushedpage! examines its emptiness to remember whether any
+% floats are deferred for \!\pcol@output@end!.
+% 
+% \item
+% \!\pcol@output@end! lets it have \!\@dbldeferlist! so that it processed as
+% sigle-float floats after \Endparacol.
+% \end{itemize}
+% 
+% \item[\Uidx{\!\@toplist!}]
+% is an internal macro having the list of single-column 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@measurecolumn! for the measurement of the combined
+% size of top floats, while \!\pcol@setcurrcol! and \!\pcol@igetcurrcol!
+% saves\slash restores the list in/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@makefcolumn! itself or by
+% \!\pcol@makeflushedpage!.
+% 
+% \item[\Uidx{\!\@botlist!}]
+% is an internal macro having the list of single-column 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 invokes the scanner \!\@cflb! unless empty.  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 in/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 in/from
+% $\cc_c(\ml)$ respectively.
+% 
+% \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 \!\paracol!.
+% 
+% \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@setpageno!, it has $\PPP$ so that we update $\PP$ and
+% $\pp(\ptop)$ scanning their original contents.
+% 
+% \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@flushcolumn!, it is used to throw $\pp^b(\ptop)$ away because
+% we don't need it.
+% 
+% \item
+% In $\!\pcol@defcomelt!\arg{com}$, it is used to implement
+% $\!\let!|\|\arg{com}=|\pcol@com@|{\cdot}\~\arg{com}$.
+% 
+% \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@}

+% 

+% and then it has $\theta$ 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@}

+% \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@outputpage! ($\PP$)\\
+% \!\pcol@trynextcolumn! ($\cc_c(\dl)$)\\
+% \!\pcol@makefcolumn! ($\cc_c(\dl)$)\\
+% \!\pcol@remctrelt! ($\CC$)
+% \end{quote}
+% 

+% In addition, $\!\pcol@iremctrelt!\<\theta\>$ uses it to have $\theta$ in
+% it for \CSIndex{ifx}-comparison.
+% 
+% \item[\Uidx{\!\@gtempa!}]
+% is an internal macro used as a \!\global!ly modifiable scratchpad.  Its
+% usages are as follows.
+% 

+% \begin{itemize}
+% \item
+% In \!\pcol@measurecolumn!, it has \!\lastpenalty! in a \!\vbox! whose
+% value is examined outside the \!\vbox! for the empty check of
+% $\cc_c(\vb^b)$.
+% 
+% \item
+% In \!\paracol! and \!\pcol@cmpctrelt!, it has the list of counters to be
+% synchronized.
+% 
+% \item
+% \!\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}
+% 
+% \subsubsection{\cs{count} Registers}
+% 
+% Here we declare registers and switches.  The first group is for \!\count!
+% registers.
+% 

+% \begin{macro}{\pcol@currcol}
+% 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@opcol!,
+% \!\pcol@output@switch!,
+% \!\pcol@getcurrcol!,
+% \!\pcol@setcurrcol!,
+% \!\pcol@sscounters!,
+% \!\pcol@setctrelt!,
+% \!\pcol@com@switchcolumn!,
+% \!\pcol@switchcol!,
+% \!\pcol@aconlyelt!,
+% \!\pcol@com@flushpage!,
+% \!\pcol@com@clearpage!.
+% \end{quote}
+% 

+% 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}
+% 

+% \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.  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!; 0 in \!\paracol!, \!\pcol@mctext!,
+% \!\endparacol!; and $c=\!\pcol@currcol!$ in \!\pcol@com@flushpage! and
+% \!\pcol@com@clearpage! to stay in the current column $c$.
+% \end{macro}
+% 

+% \begin{macro}{\pcol@ncol}
+% The register \!\pcol@ncol! has the number of columns $\C$ given as the
+% argument of \!\paracol! being the sole modifier of the register.  The
+% following macros refer to the register to scan all columns $c\In0C$.
+% 

+% \begin{quote}\raggedright
+% \!\pcol@checkshipped!,
+% \!\pcol@outputelt!,
+% \!\pcol@output@start!,
+% \!\pcol@output@switch!,
+% \!\pcol@sync!,
+% \!\pcol@makeflushedpage!,
+% \!\pcol@flushfloats!,
+% \!\pcol@freshpage!,
+% \!\pcol@output@end!,
+% \!\pcol@synccounter!,
+% \!\pcol@com@syncallcounters!,
+% \!\pcol@stepcounter!,
+% \end{quote}
+% 

+% The other references are made by \!\pcol@com@switchcolumn! and
+% \!\pcol@switchcolumn! to examine $c<\C$.
+% \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 intialized 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, by \!\pcol@startpage! to start a new page, and by
+% \!\pcol@output@clear! for pages of \fcolumn{}s and \fpage{}s.  The other
+% type of updates of the register is done by \!\pcol@restartcolumn! which
+% let $p$ 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@opcol!, \!\pcol@setpageno!, \!\pcol@getcurrpage! and
+% \!\pcol@output@switch! 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!
+% and \!\pcol@getcurrpage! 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
+% macro \!\pcol@opcol! refers to the register to examine if the \ccolpage{}
+% explores a new page, while \!\pcol@flushcolumn! examines if the
+% \ccolpage{} is behind the top page.
+% \end{macro}
+% 

+%    \begin{macrocode}
+
+%% Register Declaration
+
+\newcount\pcol@currcol
+\newcount\pcol@nextcol
+\newcount\pcol@ncol
+\newcount\pcol@page
+\newcount\pcol@basepage
+\newcount\pcol@toppage
+%    \end{macrocode}
+% 
+% 
+% 
+% \subsubsection{Switches}
+% 
+% The second declaration group is for switches.
+% 

+% \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., $\pp(p)<0$ or $\pp(p)\geq256$.  It is set by
+% \!\pcol@setpnoelt! for its local use, and by \!\pcol@getpinfo! for the
+% examination in \!\pcol@outputelt!, \!\pcol@makeflushedpage! and
+% \!\pcol@output@end!.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@sync}
+% \changes{v1.0}{2011/10/10}
+%	{Add initialization to be $\mathit{false}$.}

+% 

+% The switch |\ifpcol@sync| is true iff \!\pcol@output@switch! is invoked
+% from \!\pcol@mctext! or \!\pcol@iswitchcolumn! via \!\output! for
+% \sync{}ing column switching.  Besides being turned true by these macros,
+% the switch is turned false by \!\pcol@sync! after the \sync{}ation to give
+% the default state.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@mctext}
+% \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
+%	 multi-column text.}

+% 

+% The switch |\ifpcol@mctext| is true iff \!\pcol@output@switch! is invoked
+% from \!\pcol@mctext! to put \mctext.  The switch is turned false by
+% \!\pcol@output@switch! to give the default state after it examines the
+% switch to {\em broadcast} \CSIndex{if@nobreak} and \!\everypar! to all
+% columns if true.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@clear}
+% \changes{v1.0}{2011/10/10}
+%	{Add initialization to be $\mathit{false}$.}

+% 

+% The switch |\ifpcol@clear| is true iff \!\pcol@output@switch! is invoked
+% from \!\pcol@make~flushedpage! to flush pages.  The macro
+% \!\pcol@makeflushedpage! also turns the switch false after the invocation
+% of \!\pcol@output@switch! to give the default state.  The macros
+% \!\pcol@sync! and \!\pcol@flushcolumn! being descendats of
+% \!\pcol@output@switch! also examine the switch.
+% \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@outputpage! which invokes
+% \!\pcol@outputelt! for all $\pp(p)\in\PP$.  Then if \!\pcol@outputpage! 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@outputpage! is invoked from
+% \!\pcol@sync! to ship out all pages including \fpage{}s in $\PP$, the
+% switch is kept $\true$ throughout all invocations \!\pcol@outputelt!.
+% \end{macro}
+% 

+% \begin{macro}{\ifpcol@lastpage}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for special operations in the last page.}

+% 

+% The switch |\ifpcol@lastpage| is used to know whether they works on the
+% {\em\Uidx\lpage} of \env{paracol} environment in the following macros
+% to do special operations if so.
+% 

+% \begin{itemize}
+% \item
+% \!\pcol@makecol! does not make \!\@textbottom! have inifinite stretch and
+% shrink even if the \lpage{} has \sync{}ation point.
+% 
+% \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@makefcolumn! trys to make deferred floats as top floats.
+% \end{itemize}
+% 

+% The switch is initialized to be $\false$ by \!\paracol! and then turned
+% $\true$ by \!\pcol@output@end! which may also turned it $\false$ again for
+% \fpage{}s following the \lpage{} if any.
+% \end{macro}
+% 

+%    \begin{macrocode}
+\newif\ifpcol@nospan
+\newif\ifpcol@sync \pcol@syncfalse
+\newif\ifpcol@mctext \pcol@mctextfalse
+\newif\ifpcol@clear \pcol@clearfalse
+\newif\ifpcol@outputflt
+\newif\ifpcol@lastpage
+%    \end{macrocode}
+% 
+% 
+% 
+% \subsubsection{\cs{dimen} and \cs{skip} Registers}
+% 
+% The last declaration group is for three \!\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@measurecolumn!.  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 the height of the tallest column
+% in the \tpage{} $\ptop$ in which an \exsync{} takes place.  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@makeflushedpage! when it is invokded from \!\pcol@output@end! to
+% know the height of the last multi-column stuff of the \env{paracol}
+% environment.  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.\ $c'<c$ mades 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 defined 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 \!\paracol! 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@measurecolumn!,
+% \!\pcol@addflhd! and \!\pcol@synccolumn!.
+% \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
+% \!\paracol!, it is referred to by \!\pcol@getpinfo!, \!\pcol@startpage!,
+% \!\pcol@output@start! and \!\endparacol!.
+% \end{macro}
+% 

+%    \begin{macrocode}
+\newdimen\pcol@prevdepth
+\newdimen\pcol@colht
+\newdimen\pcol@textfloatsep
+\newskip\pcol@topskip
+
+%    \end{macrocode}
+% 
+% 
+% 
+% \section{\cs{output} Routine}
+% \label{sec:imp-output}
+% 
+% \begin{macro}{\pcol@ovf}
+% Before giving the definitions of macros in \!\output! rontine, 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@flushcolumn!, \!\pcol@synccolumn! and
+% \!\pcol@output@end!.
+% \end{macro}
+% 

+%    \begin{macrocode}
+%% \output Routine
+
+\def\pcol@ovf{%
+  \PackageError{paracol}{Too many unprocessed columns/floats}\@ehb}
+
+%    \end{macrocode}
+% 
+% \begin{macro}{\pcol@output}
+% The macro \!\pcol@output! is the \Paracol's version of \!\output! which
+% is let have this macro as its sole token by \!\paracol!.  The structure of
+% this macro is same as that of \LaTeX's \!\output! but the following
+% replacements are made.
+% 

+% \begin{itemize}
+% \item
+% $\!\@specialoutput!\to\!\pcol@specialoutput!$ to process \Paracol's own
+% special output functions, starting first page, \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.
+% 
+% \item
+% $\!\@opcol!\to\!\pcol@opcol!$ to hold the \ccolpage{} which just has
+% completed.
+% 
+% \item
+% $\!\@startcolumn!\to\!\pcol@startcolumn!$ to creat a new \colpage{}.
+% \end{itemize}
+% 

+%    \begin{macrocode}
+\def\pcol@output{\let\par\@@par
+  \ifnum\outputpenalty<-\@M
+    \pcol@specialoutput
+  \else
+    \pcol@makecol
+    \pcol@opcol
+    \pcol@startcolumn
+    \@whilesw\if@fcolmade\fi{\pcol@opcol \pcol@startcolumn}%
+  \fi
+  \ifnum\outputpenalty>-\@Miv
+    \ifdim\@colroom<1.5\baselineskip
+      \ifdim\@colroom<\textheight
+        \@latex@warning@no@line{Text page \thepage\space
+                                contains only floats}%
+        \@emptycol
+      \else
+        \global\vsize\@colroom
+      \fi
+    \else
+      \global\vsize\@colroom
+    \fi
+  \else
+    \global\vsize\maxdimen
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \section{Completing Column-Page}
+% \label{sec:imp-opcol}
+% 
+% \begin{macro}{\pcol@makecol}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for special float handling in a column-page with
+%	 synchronization point.}

+% 

+% 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 just invokes its original version \!\@makecol!
+% if $\cc_c(\tf)=\infty$ to mean the \colpage{} does not have \sync{}ation
+% points.  Otherwise, \!\@makecol! is invoked too but with a special
+% \!\def!inition of \!\@textbottom! to put a vertical skip having
+% $1/1000\,|fil|$ 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.}.
+% 

+%    \begin{macrocode}
+%% Completing Column-Page
+
+\def\pcol@makecol{\let\pcol@textbottom\@textbottom
+  \ifdim\pcol@textfloatsep=\maxdimen\else \ifpcol@lastpage\else
+    \def\@textbottom{\vskip\z@\@plus.0001fil\@minus.0001fil}\fi\fi
+  \@makecol \let\@textbottom\pcol@textbottom}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@combinefloats}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for special float handling in a column-page with
+%	 synchronization point.}

+% 

+% The macro \!\pcol@combinefloats! is our own version of \!\@combinefloats!
+% which is used in \!\@makecol! and \!\pcol@makenormalcol!.  Since the
+% original and our own are made \!\let!-equal by \!\paracol!, our own is
+% active throughout the environment.  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 our own \!\pcol@cflt! which we will discuss
+% shortly.  For the bottom floats, we invoke the original \!\@cflb! always
+% but, 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.  We also insert a vertical skip whose natural height is 0
+% but shrink is the natural height of \!\textfloatsep! because the
+% \colpage{} can be taller than the height specified by \!\@colht! by up to
+% this amount.
+% 
+% Note that the macro acts exactly same as the original when it is invoked
+% from \!\pcol@makenormalcol! because \!\pcol@textfloatsep! and
+% \CSIndex{ifpcol@lastpage} has their initial values $\infty$ and $\false$
+% given by \!\paracol!.
+% 

+%    \begin{macrocode}
+\def\pcol@combinefloats{%
+  \ifx\@toplist\@empty\else
+    \ifdim\pcol@textfloatsep=\maxdimen \@cflt \else \pcol@cflt \fi
+  \fi
+  \ifx\@botlist\@empty\else \@cflb
+    \ifpcol@lastpage
+      \setbox\@outputbox\vbox{\unvbox\@outputbox \vskip\textfloatsep
+        \@tempdima\textfloatsep \vskip\z@\@minus\@tempdima}%
+    \fi
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@cflt}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced for special float handling in a column-page with
+%	 synchronization point.}

+% 

+% 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 two modification.  The first one is 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 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
+  \xdef\@freelist{\@freelist\@toplist}%
+  \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}.}

+% 

+% 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!.  Then if $c=0$, we fix the page number of the page $p$
+% having the \colpage{} and let $\pp(q)$ represent $\page(p)+(q-p)$ 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 consectutive $k$ \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@outputpage! 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{%
+  \@next\@currbox\@freelist{\global\setbox\@currbox\box\@outputbox}\pcol@ovf
+  \expandafter\@cons\csname pcol@shipped\number\pcol@currcol\endcsname\@currbox
+  \ifnum\pcol@currcol=\z@ \pcol@setpageno \fi
+  \pcol@nextpage
+  \pcol@checkshipped
+  \if@tempswa \pcol@outputpage\z@ \fi
+  \ifnum\pcol@page>\pcol@toppage \pcol@startpage
+  \else                          \pcol@getcurrpage
+  \fi
+  \pcol@floatplacement}
+
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@setpageno}
+% \begin{macro}{\pcol@setpnoelt}
+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{ifpcol@textonly} as \cs{ifpcol@nospan}.}

+% 

+% 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 $\pp(q)$
+% represent $\page'(q)=\page(p)+(q-p)$ 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 $\pi'(q)$ to update $\pp(q)$ as
+% follows.
+% 

+% $$
+% \pp(q)=\cases{
+%   \pi'(q)&		$q<p$\cr
+%   \page'(q)&
+% 	$q\geq p\;\land\;\pi'(q)\notin[0,255]\;\land\page'(q)<0$\cr
+%   \pi'(q)&
+% 	$q\geq p\;\land\;\pi'(q)\in[0,255]$\quad
+%	(also let $\pp^p(q)=\page'(q)$)\cr
+%   \page'(q)+256&
+% 	$q\geq p\;\land\;\pi'(q)\notin[0,255]\;\land\page'(q)\geq0$}
+% $$
+% For the update shown above, the macro \!\pcol@setpnoelt! for $\pi'(q)$ at
+% first add $\pp(q-1)$ to the tail of $\PPP$ where $\pp(\pbase-1)$
+% is defined as empty.  Then for $q$ such that $q\geq p$, it invokes
+% $\!\pcol@setordpage!$ to let $\pp(q)=\page'(q)<0$ or
+% $\pp(q)=\page'(q)+256\geq256$ if $\pi'(q)\notin[0,256]$ for an orginary
+% page without \spanning, or lets $\pp^p(q)=\page'(q)$
+% otherwise.  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
+  \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{%
+  {\let\@elt\relax \xdef\pcol@pages{\pcol@pages\pcol@currpage}}%
+  \pcol@nospantrue
+  \ifnum#1<\z@         \gdef\pcol@currpage{\@elt{#1}}%
+  \else\ifnum#1>\@cclv \gdef\pcol@currpage{\@elt{#1}}%
+  \else                \gdef\pcol@currpage{\@elt#1}\pcol@nospanfalse
+  \fi\fi
+  \ifnum\@tempcnta>\z@\else
+    \ifpcol@nospan \pcol@setordpage
+    \else          \global\count#1\c@page
+    \fi
+    \advance\c@page\@ne
+  \fi
+  \advance\@tempcnta\m@ne}
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@setordpage}
+% \changes{v1.0}{2011/10/10}
+%	{Renamed from \cs{pcol@settextpage}.}

+% 

+% The macro \!\pcol@setordpage! is invoked from \!\pcol@setpnoelt! and
+% \!\pcol@startpage! to let $\pp(q)$ for the ordinary page $q$ without
+% \spanning{} as follows.
+% $$
+% \pp(q)=\cases{\!\c@page!&	$\!\c@page!<0$\cr
+% 		\!\c@page!+256&	$\!\c@page!\geq0$}
+% $$
+% In the invocatoin from \!\pcol@setpnoelt!, $q\in[p,\ptop]$ and
+% $\!\c@page!=\page(p)+(q-p)$, while $q=p=\ptop$ and $\!\c@page!=\page(p)$
+% in the invocation from \!\pcol@startpage!.
+% 

+%    \begin{macrocode}
+\def\pcol@setordpage{\begingroup
+  \@tempcnta\c@page
+  \ifnum\@tempcnta<\z@\else \advance\@tempcnta\@cclvi \fi
+  \let\@elt\relax \xdef\pcol@currpage{\@elt{\number\@tempcnta}}
+  \endgroup}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@nextpage}
+% \begin{macro}{\pcol@nextpelt}
+% 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
+% $p$.  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 $f=\CSIndex{if@tempswa}$ being $\true$ at initial, to
+% let $p\gets p+k$, and then increments $p$ to have $p+k+1$.
+% $$
+% \<p,f\>\gets\cases{
+% 	\<p,f\>&	$q\leq p$\cr
+% 	\<p{+}1,f\>&	$q>p\;\land\;f\;\land\;\pp(q)\in[0,255]\;\land\;
+%			\pp^h(q)<0$\cr
+%	\<p,\false\>&	otherwise}
+% $$
+% 

+%    \begin{macrocode}
+\def\pcol@nextpage{\begingroup
+  \@tempcnta\pcol@page \advance\@tempcnta-\pcol@basepage
+  \@tempswatrue
+  \let\@elt\pcol@nextpelt \pcol@pages\pcol@currpage
+  \global\advance\pcol@page\@ne
+  \endgroup}
+\def\pcol@nextpelt#1{%
+  \ifnum\@tempcnta<\z@
+    \ifnum#1<\z@ \@tempswafalse
+    \else\ifnum#1>\@cclv \@tempswafalse
+    \else\ifdim\dimen#1<\z@
+      \if@tempswa \global\advance\pcol@page\@ne \fi
+    \else \@tempswafalse
+    \fi\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 $S_c=|\pcol@shipped|{\cdot}c\neq()$
+% 

+% \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}
+% 
+% \begin{macro}{\pcol@getcurrpage}
+% \begin{macro}{\pcol@getpelt}
+% \begin{macro}{\pcol@getpinfo}
+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{ifpcol@textonly} as \cs{ifpcol@nospan}.}

+% 

+% \begin{macro}{\pcol@getcurrpinfo}
+% The macro \!\pcol@getcurrpage! is ivoked in \!\pcol@opcol!,
+% \!\pcol@restartcolumn!, \!\pcol@flushcolumn! and \!\pcol@freshpage! to let
+% \!\c@page!, \!\@colht!, \!\topskip! and \CSIndex{ifpcol@nospan} be those
+% represented in $\pp(p)\in\PPP=(\PP,\pp(\ptop))$ where
+% $\pp(\ptop)=\!\pcol@currpage!$.  To do that, the macro scans all
+% $\pp(q)\in\PPP$ applying \!\pcol@getpelt!  to $\pp(q)$ to invoke
+% $\!\pcol@getpinfo!\arg{\pi}\arg{pg}\arg{ch}\arg{ts}$ with the following
+% arguments for \!\global! assignments, if $q=p$.
+% $$
+% \arg{\pi}=\pp(q)\quad\arg{pg}=\!\global!\!\c@page!\quad
+% \arg{ch}=\!\global!\!\@colht!\quad\arg{ts}=\!\global!\!\topskip!
+% $$
+% Then the macro \!\pcol@getpinfo! do the following assighments.
+% 

+% \begin{eqnarray*}
+% &&\<\arg{pg},\arg{ch},\arg{ts},\CSIndex{ifpcol@nospan}\>=\\
+% &&\qquad\qquad\left\{\begin{array}{lllll}
+%	\<\pp(q),&\!\textheight!,&\!\pcol@topskip!,&\true\>&\quad\pp(q)<0\\
+%	\<\pp^p(q),&\pp^h(q),&\pp^t(q),&\false\>&\quad0\leq\pp(q)<256\\
+%	\<\pp(q){-}256,&\!\textheight!,&\!\pcol@topskip!,&\true\>&
+% 		\quad\pp(q)\geq256\end{array}\right.
+% \end{eqnarray*}
+% 

+% The other macro $\!\pcol@getcurrpinfo!\arg{cs}\arg{pg}\arg{ch}\arg{ts}$ is
+% invoked in \!\pcol@startpage!, \!\pcol@sync! and \!\pcol@makeflushedpage!
+% do the similar assignments using \!\pcol@getpinfo!, but it is not for
+% $\pp(p)$ but for $\pp(\ptop)$ which is assigned to $\arg{cs}$.  The macro
+% \!\pcol@getpinfo! also has a direct invoker \!\pcol@outputelt!.
+% 

+%    \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{%
+  \ifnum\@tempcnta=\z@
+    \pcol@getpinfo{#1}{\global\c@page}{\global\@colht}{\global\topskip}\fi
+  \advance\@tempcnta\m@ne}
+\def\pcol@getpinfo#1#2#3#4{\count@#1\relax \pcol@nospantrue
+  \ifnum\count@>\@cclv
+    \advance\count@-\@cclvi #2\count@ #3\textheight #4\pcol@topskip
+  \else\ifnum\count@<\z@
+    #2\count@ #3\textheight #4\pcol@topskip
+  \else #2\count\count@  #3\dimen\count@ #4\skip\count@ \pcol@nospanfalse
+  \fi\fi}
+\def\pcol@getcurrpinfo#1{%
+  \edef#1{\expandafter\@cdr\pcol@currpage\@nil}%
+  \pcol@getpinfo#1}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\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}.}

+% 

+% 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! 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 first page of \env{paracol} environment so that
+% \!\pcol@output@end! will be informed of that.  Next we let $\ptop=p$ and
+% then, if invoked from \!\pcol@opcol!, lets $\!\c@page!=\page(p{-}1)+1$
+% invoking \!\pcol@getcurrpinfo! to have $\page(p{-}1)$ in \!\c@page! from
+% $\pp(p{-}1)$ and \!\stepcounter! to increment it, and
+% $\PP\gets\PPP=(\PP,\pp(p{-}1))$.  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\@currbox{\global\c@page}\@tempdima\@tempskipa
+    \stepcounter{page}%
+    \xdef\pcol@pages{\pcol@pages\pcol@currpage}%
+  \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 double-column
+% (multiple-column) float placement.  Then we repeat \!\@tryfcolumn! giving
+% it \!\@dbldeferlist! having double-column 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! to let $\pp(p)=\pp(\ptop)$ have the
+% followings to represent the \fpage{}.
+% $$
+% \pp^b(p)=\!\@outputbox!\quad
+% \pp^p(p)=\!\c@page!\quad
+% \pp^h(p)=-\!\maxdimen!\quad
+% \pp^t(p)=\!\pcol@topskip!
+% $$
+% We also increment $p$ and $\ptop$, and also \!\c@page! by \!\stepcounter!,
+% to let them have the values for the page following the \fpage{}s.
+% 

+%    \begin{macrocode}
+  \@dblfloatplacement
+  \@tryfcolumn\@dbldeferlist
+  \@whilesw\if@fcolmade\fi{%
+    \@next\@currbox\@freelist{%
+      \global\setbox\@currbox\box\@outputbox}\pcol@ovf
+    \global\count\@currbox\c@page
+    \global\dimen\@currbox-\maxdimen
+    \global\skip\@currbox\pcol@topskip
+    \@cons\pcol@pages\@currbox
+    \stepcounter{page}%
+    \global\advance\pcol@page\@ne \global\pcol@toppage\pcol@page
+    \@tryfcolumn\@dbldeferlist}%
+%    \end{macrocode}
+% 

+% Next, we copy \!\@dbldeferlist! containing double-column 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!, as \LaTeX's \!\@startdblcolumn!
+% does.  If this scan results in empty \!\@dbltoplist! to mean the new page
+% does not have any \spanning, we invoke \!\pcol@setordpage! so that
+% $\pp(\ptop)$ reprsents a page without \spanning.
+% 

+%    \begin{macrocode}
+  \begingroup
+    \let\reserved@b\@dbldeferlist
+    \global\let\@dbldeferlist\@empty
+    \let\@elt\@sdblcolelt
+    \reserved@b
+  \endgroup
+  \ifx\@dbltoplist\@empty
+    \pcol@setordpage
+%    \end{macrocode}
+% 

+% Otherwise, i.e., \!\@dbltoplist! is not empty, we scan all elements in it
+% by letting \!\@comdblflelt! to have all double-floats in \!\@tempboxa!.
+% Then, after returning all elements to \!\@freelist!, we acquire a
+% \!\insert! from \!\@freelist! to be $\pp(\ptop)$ 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 element of $\pp(\ptop)$ is
+% set as follows to represent the page with \spanning{} which make the height
+% of each column \!\@colht! shrunk from its initial value \!\textheight!
+% by the series of \!\@addtodblcol!.
+% $$
+% \pp^p(\ptop)=\!\c@page!=\page(\ptop)\quad
+% \pp^h(\ptop)=\!\@colht!\quad
+% \pp^t(\ptop)=\!\pcol@topskip!
+% $$
+% 

+%    \begin{macrocode}
+  \else
+    \setbox\@tempboxa\vbox{}%
+    \begingroup
+      \let\@elt\@comdblflelt
+      \@dbltoplist
+      \let\@elt\relax
+      \xdef\@freelist{\@freelist\@dbltoplist}%
+      \global\let\@dbltoplist\@empty
+      \@next\@currbox\@freelist{%
+        \global\setbox\@currbox\vbox{%
+          \unvbox\@tempboxa \vskip-\dblfloatsep \dblfigrule
+          \vskip\dbltextfloatsep}}%
+        \pcol@ovf
+      \global\count\@currbox\c@page
+      \global\dimen\@currbox\@colht
+      \global\skip\@currbox\pcol@topskip
+      \xdef\pcol@currpage{\@elt\@currbox}%
+    \endgroup
+  \fi
+}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \section{Shipping Page Out}
+% \label{sec:imp-outputpage}
+% 
+% \begin{macro}{\pcol@outputpage}
+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{ifpcol@stopoutput} as \cs{ifpcol@outputflt}.}

+% 

+% The macro \!\pcol@outputpage! is invoked from \!\pcol@opcol! with argument
+% $\arg{all}=0$ 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{} (following the first page), scan 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@outputpage#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}
+% The macro $\!\pcol@outputelt!\arg{all}\<\pp(q)\>$ ships out the ordinary
+% or \fpage{} $q$ if $f_o=\true$ or $f_f=\true$ respectively.  After
+% initializing \!\@outputbox! to be \!\voidb@x!, we retrive the page $q$'s
+% information by \!\pcol@getpinfo! to have $\page(q)$ in \!\c@page! locally,
+% \!\textheight! or $\pp^h(q)$ in $h=\!\@tempdima!$, and
+% $f_{\it ns}=\CSIndex{ifpcol@nospan}=(\pp(q)\notin[0,255])$.
+% 

+%    \begin{macrocode}
+\def\pcol@outputelt#1#2{%
+  \setbox\@outputbox\box\voidb@x
+  \def\@currbox{#2}%
+  \pcol@getpinfo\@currbox\c@page\@tempdima\@tempskipa
+%    \end{macrocode}
+% 

+% Then, we do one of the follolwings 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 ship it out and return $\!\insert!{\cdot}\pp(q)$ to
+% \!\@freelist! by \!\@cons! because it is no longer necessary.  Otherwise,
+% we return $\pp(q)$ back to $\PP$.
+% \end{itemize}
+% 

+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{ifpcol@stopoutput} as \cs{ifpcol@outputflt}.}

+% 

+%    \begin{macrocode}
+  \ifdim\@tempdima<\z@
+    \ifpcol@outputflt
+      \setbox\@outputbox\box\@currbox
+      \@cons\@freelist\@currbox
+    \else
+      \@cons\pcol@pages\@currbox
+    \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 put materials to be shipped out in \!\@outputbox! whose height is
+% \!\textheight! as follows.  First, if $f_{\it ns}=\false$ to mean
+% $\pp(q)$ has \spanning{} in $\pp^b(q)$, they are put in the box by
+% \!\unvbox! and $\!\insert!{\cdot}\pp(q)$ is returned to \!\@freelist! by
+% \!\@cons!.  Then we put a \!\hbox! of \!\textwidth! wide having \!\hbox!es
+% of \!\columnwidth! wide containing $\sigma_c$ followed by \!\hss! for all
+% $c\In0\C$, 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 empty, or \!\voidb@x!  otherwise.  We sepearate
+% \!\hbox!es of $\sigma_c$ by \!\hfil!  by making each \!\hbox!  preceded by
+% \!\pcol@hfil!

+% 

+% \SpecialMainIndex{\pcol@hfil}
+% 

+% being \!\relax! for the first one and \!\hfil! for others.
+% \end{itemize}
+% 

+% \changes{v1.0}{2011/10/10}
+%	{Rename \cs{ifpcol@textonly} as \cs{ifpcol@nospan}.}

+% 

+%    \begin{macrocode}
+  \else\if@tempswa
+    \ifnum#1=\z@ \@tempswafalse \fi
+    \setbox\@outputbox\vbox to\textheight{%
+      \ifpcol@nospan\else
+        \@cons\@freelist\@currbox
+        \unvbox\@currbox
+      \fi
+      \hb@xt@\textwidth{%
+        \let\pcol@hfil\relax
+        \@tempcnta\z@ \@whilenum\@tempcnta<\pcol@ncol\do{%
+          \expandafter\@next\expandafter\@currbox
+            \csname pcol@shipped\number\@tempcnta\endcsname
+            \relax{\let\@currbox\voidb@x}%
+          \ifvoid\@currbox\else \@cons\@freelist\@currbox \fi
+          \pcol@hfil \hb@xt@\columnwidth{\box\@currbox\hss}%
+          \let\pcol@hfil\hfil
+         \advance\@tempcnta\@ne}}}%
+%    \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!.  Note that if $f_{\it ns}=\true$
+% to mean $\pp(q)\notin[0,255]$ for a page without \spanning, we have to
+% surround $\pp(q)$ giving to \!\@cons! by |{| and |}| because it is a
+% decimal number rather than a \!\chardef! token for an \!\insert! with
+% \spanning.
+% \end{itemize}
+% 

+%    \begin{macrocode}
+  \else
+    \pcol@outputfltfalse
+    \ifpcol@nospan
+      \@cons\pcol@pages{{\@currbox}}
+    \else
+      \@cons\pcol@pages\@currbox
+    \fi
+  \fi\fi
+%    \end{macrocode}
+% 

+% Finally, if $\!\@outputbox!\neq\!\voidb@x!$ 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
+    \@outputpage \global\advance\pcol@basepage\@ne
+  \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \section{Starting New Column-Page}
+% \label{sec:imp-startcolumn}
+% 
+% \begin{macro}{\pcol@startcolumn}
+% \begin{macro}{\pcol@trynextcolumn}
+% The macro \!\pcol@startcolumn! is invoked from \!\pcol@output! and
+% \!\pcol@freshpage! to start a new \colpage.  This macro has the exactly
+% same functionality as \LaTeX's \!\@startcolumn!, but \CSIndex{else} part of
+% \CSIndex{if@fcolmade} construct is enclosed in the macro
+% \!\pcol@trynextcolumn!  which is also invoked in \!\pcol@flushcolumn!.
+% That is, the only reason why we have our own version of \!\@startcolumn!
+% is this additional use of the \CSIndex{else} part.
+% 

+%    \begin{macrocode}
+%% Starting New Column Page
+
+\def\pcol@startcolumn{%
+  \global\@colroom\@colht
+  \@tryfcolumn\@deferlist
+  \if@fcolmade\else \pcol@trynextcolumn \fi}
+\def\pcol@trynextcolumn{\begingroup
+  \let\reserved@b\@deferlist
+  \global\let\@deferlist\@empty
+  \let\@elt\@scolelt
+  \reserved@b
+  \endgroup}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 
+% 
+% 
+% \section{Special Output Routines}
+% \label{sec:imp-sout}
+% 
+% \subsection{Dispatcher}
+% \label{sec:imp-sout-disp}
+% 
+% \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 macros $|\pcol@op@|{\cdot}f$ where $f\in
+% F=\{|start|,|switch|,|flush|,|clear|,|end|\}$ has our own
+% \!\outputpenalty! code less than $-10000$ to invoke the corresponding
+% macros $|\pcol@output@|{\cdot}f$.  The code macros are given to
+% \!\pcol@invokeoutput! as its argument by \!\paracol! ($f=|start|$),
+% \!\pcol@switchcol! ($f=|switch|$), \!\pcol@com@flushpage! ($f=|flush|$),
+% \!\pcol@com@clearpage! ($f=|clear|$) 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}
+% 

+% \begin{macro}{\pcol@specialoutput}
+% \changes{v1.0}{2011/10/10}
+%	{Remove unnecessary \cs{pcol@latex@specialoutput}.}

+% 

+% The macro \!\pcol@specialoutput! is invoked solely in \!\pcol@output! to
+% invoke our own or \LaTeX's special output routine.  It examines if
+% $\!\outputpenalty!\in\{|pcol@op@|{\cdot}f\vert f\in F\}$.  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.
+% 
+% Otherwise, i.e., if $\!\outputpenalty!\notin\{|pcol@op@|{\cdot}f\vert f\in
+% F\}$, we simply invokes \LaTeX's \!\@specialoutput!.
+% 

+%    \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
+  \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.}

+% 

+% The macro \!\pcol@output@start! is invoked solely from
+% \!\pcol@specialoutput! to process the special \!\output! request made in
+% \!\paracol! and to build the {\em\Uidx\spage} from which parallel columns
+% start.  First we invoke \!\pcol@makenormalcol! to let \!\@outputbox! have
+% the stuff preceding \beginparacol{}, or {\em\Uidx\preenv} in short, in the
+% \spage{} as its \spanning.  Then we shrink \!\@colht! by the sum of the
+% height $h$ and depth $d$ of the \spanning.  Next we let $p=\pbase=\ptop=0$
+% and $\PP=()$ because we have nothing for $q<\ptop=0$.  We also move
+% \!\@deferlist! to \!\@dbldeferlist! and then let \!\@deferlist! be empty
+% because all single-column dererred floats become multi-column.
+% 
+% Then we examine if $\!\@colht!<1.5\times\!\baselineskip!$ to mean
+% \!\pcol@output! would force a page break with warning.  If so, we ship out
+% the \preenv{} by \!\@outputpage! to avoid the break and warning, and
+% invoke \!\pcol@startpage! for the \spage{} $\ptop=0$ letting $\pp(0)$ be
+% empty so that the macro will not refer to it.  We also let \!\topskip! be
+% the value at \beginparacol, i.e., \!\pcol@topskip! because the first item
+% of each column will start from the top of the \spage.
+% 
+% Otherwise, the \spanning{} are moved in $\pp^b(0)$ which is acquired from
+% \!\@freelist! by \!\@next!, and $\pp^p(0)$ and $\pp^h(0)$ are let be
+% \!\c@page! and \!\@colht! respectively for \spage.  As for $\pp^t(0)$, we
+% let it be \!\topskip! if $h=d=0$ assuming that the page does not have any
+% \spanning{} to typeset \colpage{}s from the top of the page.  Otherwise,
+% i.e., either $h\neq0$ or $d\neq0$, $\pp^t(0)$ and \!\topskip! are let be 0
+% to inhibit the ordinary \!\topskip! insertion.
+% 
+% Then for the both cases, we initialize \!\@colroom! to be \!\@colht!, and
+% invoke \!\pcol@floatplacement! to reinitialize the parameters of
+% single-column float placement.
+% 

+%    \begin{macrocode}
+%% Special Output Routines: Building First Page
+
+\def\pcol@output@start{%
+  \pcol@makenormalcol
+  \global\advance\@colht-\ht\@outputbox
+  \global\advance\@colht-\dp\@outputbox
+  \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
+  \ifdim\@colht<1.5\baselineskip
+    \@outputpage
+    \global\let\pcol@currpage\@empty \pcol@startpage
+    \global\topskip\pcol@topskip 
+  \else
+    \@next\@currbox\@freelist{\global\setbox\@currbox\box\@outputbox}\pcol@ovf
+    \global\count\@currbox\c@page \global\dimen\@currbox\@colht
+    \@tempskipa\z@
+    \ifdim\ht\@currbox=\z@ \ifdim\dp\@currbox=\z@
+      \@tempskipa\topskip
+    \fi\fi
+    \global\skip\@currbox\@tempskipa \global\topskip\@tempskipa
+    \xdef\pcol@currpage{\@elt\@currbox}%
+  \fi
+  \global\@colroom\@colht
+  \pcol@floatplacement
+%    \end{macrocode}
+% 

+% Then for all columns $c\In0\C$ we do the followings to build $\cc_c$.
+% 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 \!\paracol! 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}.
+% 
+% 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 footnotes;  $\cc_c(\pd)=\!\prevdepth!$ as discussed above;
+% $\cc_c(\tl)=\cc_c(\ml)=\cc_c(\bl)=()$ because \!\pcol@makenormalcol! and
+% \!\@combinefloats! invoked from it emptied them;  $\cc_c(\dl)=()$ as
+% discussed above;  $\cc_c(\fh)=\cc_c(\mb)=0$ as initialized by
+% \!\pcol@floatplacement!;  $\cc_c(\tn)=\!\c@topnumber!$,
+% $\cc_c(\bn)=\!\c@botnumber!$ 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
+% \CSIndex{if@afterindent} 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 $\S_c=\phi$ because we don't have any
+% \colpage{} having been completed.
+% 

+% \changes{v1.0}{2011/10/10}
+%	{Add clearing of $S_c$.}

+% 

+%    \begin{macrocode}
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+    \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{%
+      \ifdim\topskip=\z@ \hrule\@height\z@\@width\z@
+      \fi}}
+      \pcol@ovf
+    \pcol@setcurrcolnf
+    \global\count\@currbox\z@
+    \global\dimen\@currbox\@colroom
+    \expandafter\gdef\csname pcol@shipped\number\pcol@currcol\endcsname{}%
+   \advance\pcol@currcol\@ne}%
+%    \end{macrocode}
+%

+% Finally, we let $c=\!\pcol@currcol!=0$ for the first column, regain the
+% parameters in $\cc_0$, and put $\cc_0(\vb^b)$ to the main
+% vertical list by \!\unvbox! returning $\cc_0(\vb)$ to \!\@freelist! by
+% \!\@cons! because it has become useless so far.
+% 

+%    \begin{macrocode}
+  \global\pcol@currcol\z@
+  \pcol@getcurrcol
+  \@cons\@freelist\@currbox
+  \unvbox\@currbox}
+
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@makenormalcol}
+% The macro \!\pcol@makenormalcol! is invoked solely from
+% \!\pcol@output@start! to let \!\@output~box! have the \preenv{} as the
+% \spanning{} of the \spage.  The macro is very similar to the first half of
+% \!\@makecol! but \!\@cclv! in it is replaced with \!\@holdpg! because the
+% stuff have been stored in \!\@holdpg! by \!\pcol@specialoutput!.  Note
+% that bottom floats and 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@outputpage!, 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{%
+  \ifvoid\footins \setbox\@outputbox\box\@holdpg
+  \else
+    \setbox\@outputbox\vbox{
+      \boxmaxdepth\@maxdepth
+      \unvbox\@holdpg
+      \vskip\skip\footins
+      \color@begingroup
+        \normalcolor
+        \footnoterule
+        \unvbox\footins
+      \color@endgroup}%
+   \fi
+  \let\@elt\relax
+  \xdef\@freelist{\@freelist\@midlist}%
+  \global\let\@midlist\@empty
+  \@combinefloats}
+
+%    \end{macrocode}
+% \end{macro}
+% 

+% \begin{macro}{\pcol@floatplacement}
+% \changes{v1.0}{2011/10/10}
+%	{Add initialization of \cs{pcol@textfloatsep}.}

+% 

+% 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 single-column float
+% placement at the beginning of a \colpage{} or that of \postenv.  The macro
+% lets \!\@mparbottom! and \!\@textfloatsheight! be 0 and then invokes
+% \!\@floatplacement!, as \!\@opcol! does its tail.  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\@mparbottom\z@ \global\@textfloatsheight\z@
+  \global\pcol@textfloatsep\maxdimen
+  \@floatplacement}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% 
+% 
+% \subsection{Column-Switching}
+% \label{sec:imp-sout-switch}
+% 
+% \begin{macro}{\pcol@output@switch}
+% The macro \!\pcol@output@switch! is invoked from
+% \!\pcol@specialoutput! to process the special \!\output! request made in
+% \!\pcol@switchcol! and to switch from a column $c=\!\pcol@currcol!$ to
+% $d=\!\pcol@nextcol!$ which can be $c$.  The macro also is invoked from
+% \!\pcol@makeflushedpage! to \sync{}e and to flush all \ccolpage{}s
+% but staying in $c$.
+% 
+% First, we acquire an \!\insert! to be $\cc_c(\vb)$ and to store the
+% \ccolpage{} built in \!\@holdpg!, from \!\@freelist! by
+% \!\@next!.  Then, if the \colpage{} has footnotes, we acquire another
+% \!\insert! to be $\cc_c(\ft)$ to which all items \!\box!,
+% \!\count!, \!\dimen! and \!\skip! of \!\footins! are moved.  Otherwise,
+% i.e., no footnotes in the \colpage{}, $\cc_c(\ft)$ is let be \!\voidb@x!.
+% 
+% 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{%
+  \@next\@currbox\@freelist{\global\setbox\@currbox\box\@holdpg}\pcol@ovf
+  \ifvoid\footins
+    \def\pcol@currfoot{\voidb@x}%
+  \else
+    \@next\pcol@currfoot\@freelist{%
+      \global\setbox\pcol@currfoot\box\footins
+      \global\count\pcol@currfoot\count\footins
+      \global\dimen\pcol@currfoot\dimen\footins
+      \global\skip\pcol@currfoot\skip\footins}\pcol@ovf
+  \fi
+  \ifnum\pcol@currcol=\z@ \pcol@setpageno \fi
+  \pcol@setcurrcol
+  \global\count\@currbox\pcol@page
+  \global\dimen\@currbox\@colroom
+%    \end{macrocode}
+% 

+% Next, $\CSIndex{ifpcol@sync}=\true$ for \sync{}ation and
+% $\CSIndex{ifpcol@mctext}=\true$ to mean the \colpage{} suspends after a
+% \mctext, we {\em broadcast} the \CSIndex{if@nobreak} if true and tokens in
+% $\!\everypar!=\cc_c(\ep)$ for the page break inhibition to all columns
+% $e\In0\C$ so as to inhibit page break at the \sync{}ation point and after
+% the first line following it in any columns.  That is, for each column $e$,
+% we restore its \cctext{} from $\cc_e$ by \!\pcol@getcurrcol!, let
+% $\CSIndex{if@nobreak}=\true$ if it is true in $c$ ($=0$) and
+% $\!\everypar!=\cc_c(\ep)$, and then save the context to $\cc_e$ by
+% \!\pcol@setcurrcol! so that $\cc_e(\sw)=1$ or 2 according to the saved
+% state of \CSIndex{if@afterindent} and $\cc_e(\ep)=\cc_c(\ep)$.  Note
+% that this broadcast is essential when the \mctext{} has sectioning
+% commands, and broadcasting of \!\everypar! is natural even when it does
+% not have sectioning because all columns may be considered following the
+% \mctext.
+% 

+% \changes{v1.0}{2011/10/10}
+%	{Restrict the broadcast of \cs{if@nobreak} and \cs{everypar} only
+%	 when a column-switching is accompanied with multi-column text.}

+% 

+%    \begin{macrocode}
+  \@tempswafalse
+  \ifpcol@sync
+    \ifpcol@mctext
+      \if@nobreak \@tempswatrue \fi
+      \@temptokena\everypar
+      \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+        \pcol@getcurrcol \if@tempswa \@nobreaktrue \fi
+        \everypar\@temptokena
+        \pcol@setcurrcol
+       \advance\pcol@currcol\@ne}%
+    \fi
+    \@tempswatrue
+    \global\pcol@mctextfalse
+  \fi
+%    \end{macrocode}
+% 

+% 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
+% $\CSIndex{ifpcol@clear}={}\false$.
+% 

+%    \begin{macrocode}
+  \ifpcol@clear \@tempswatrue \fi
+  \if@tempswa \pcol@sync \fi
+  \ifpcol@clear\else \pcol@restartcolumn \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}.}

+% 

+% 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!.
+% 
+% Then we move everything in $\cc_c(\ft)$ into \!\footins! by
+% \!\pcol@getcurrfoot!, and, if $\cc_c(\ft^b)$ was not void,
+% \!\insert! its contents into \!\footins! itself by \!\unvbox!, returning
+% $\cc_c(\ft)$ to \!\@freelist!.  Note that for the safe garbage collection
+% of $\cc_c(\ft)$ we return it to \!\@freelist! if not void and then 
+% invoke \!\pcol@getcurrfoot! because the latter makes $\cc_c(\ft^b)$
+% void.  After that, we put the contents of $\cc_c(\vb^b)$ being the
+% \ccolpage{} to the main vertical list by \!\unvbox!.  We also 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 to the list as the page break penalty at the returning point.
+% 

+%    \begin{macrocode}
+\def\pcol@restartcolumn{%
+  \global\pcol@currcol\pcol@nextcol
+  \pcol@getcurrcol
+  \global\pcol@page\count\@currbox
+  \global\@colroom\dimen\@currbox
+  \@cons\@freelist\@currbox
+  \pcol@getcurrpage
+  \ifvoid\pcol@currfoot\else \@cons\@freelist\pcol@currfoot \fi
+  \pcol@getcurrfoot
+  \ifvoid\footins\else \insert\footins{\unvbox\footins}\fi
+  \unvbox\@currbox
+  \if@nobreak \nobreak \else \addpenalty\interlinepenalty \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@getcurrcol}
+% \begin{macro}{\pcol@igetcurrcol}
+% \begin{macro}{\pcol@iigetcurrcol}
+% \changes{v1.0}{2011/10/10}
+%	{Add restoration of \cs{pcol@textfloatsep}.}

+% 

+% The macro \!\pcol@getcurrcol! is invoked from the following macros to
+% restore the typesetting parameters of the column $c=\!\pcol@currcol!$ from
+% $\cc_c$.
+% 

+% \begin{itemize}\item[]\begin{tabular}{lll}
+% \!\pcol@output@start!&\!\pcol@output@switch!&\!\pcol@restartcolumn!\\
+% \!\pcol@flushcolumn!&\!\pcol@measurecolumn!&\!\pcol@synccolumn!\\
+% \!\pcol@makeflushedpage!&\!\pcol@flushfloats!&\!\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(\mb)}\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 double 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 nine.
+% 
+% Note that the restore operation is \!\global!, except for $\cc_c(\vb)$ and
+% $\cc_d(\ft)$, 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}
+\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#9{%
+  \global\@textfloatsheight#1sp\relax \global\@mparbottom#2sp\relax
+  \global\@topnum#3\relax \global\@toproom#4sp\relax
+  \global\@botnum#5\relax \global\@botroom#6sp\relax
+  \global\@colnum#7\relax
+  \global\@afterindentfalse \@nobreaktrue
+  \ifcase#8
+    \@nobreakfalse \or
+    \global\@afterindenttrue \else
+    \relax
+  \fi
+  \global\everypar{#9}}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@getcurrfoot}
+% The macro \!\pcol@getcurrfoot! is invoked from \!\pcol@restartcolumn!,
+% \!\pcol@flushcolumn! and \!\pcol@makeflushedpage! to put everything in
+% $\cc_c(\ft)=\!\pcol@currfoot!$ into \!\footins!.  That is, if
+% $\cc_c(\ft^b)$ is void, we let $\!\box!{\cdot}\!\footins!$ be so.
+% Otherwise, we move \!\box!, \!\count!, \!\dimen! and \!\skip! of
+% $\cc_c(\ft)$ into those of \!\footins!\footnote{

+% 

+% Moving \!\count!, \!\dimen! and \!\skip! is redundant almost always
+% because it is very unlikely that these footonote 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{%
+  \ifvoid\pcol@currfoot \global\setbox\footins\box\voidb@x
+  \else
+    \global\setbox\footins\box\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}
+% \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@makeflushedpage!, \!\pcol@flushfloats! 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 numbers.
+% 
+% The macro \!\pcol@setcurrcolnf! \!\def!ines $\cc_c(\ft)=\!\pcol@currfoot!$
+% as \!\voidb@x!, and then invoke \!\pcol@setcurrcol! for saving.
+% 

+% \changes{v1.0}{2011/10/10}
+%	{Add save of \cs{pcol@textfloatsep}.}

+% 

+%    \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\@mparbottom}%
+     {\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}
+% 
+% 
+% 
+% \subsection{Syncronization}
+% \label{sec:imp-sout-sync}
+% 
+% \begin{macro}{\pcol@sync}
+% \changes{v1.0}{2011/10/10}
+%	{Add measurement of $D_T$.}

+% 

+% The macro \!\pcol@sync! is invoked solely from \!\pcol@output@switch! for
+% \exsync{} with page flushing ($\CSIndex{ifpcol@clear}=\true$) or without
+% it.  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 top
+% and/or bottom floats in $\ptop$.  Then we ship out all pages $p$ such that
+% $p<\ptop$ by \!\pcol@outputpage! 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{$\displaystyle(\cc_c(\ft)\neq\mathit{void})$}\hskip8em
+%     \fc(b)=(\cc_c(\bl)\neq())\\
+% \Uidx\Fc(X)&=&\exists x\in X:\fc(x)\\
+% \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&=&\!\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&			$\fc(b)$\cr
+%   d(\cc_c(\ft))&	$\lnot \fc(b)\land \fc(f)$\cr
+%   d(\cc_c(\pd))&	$\lnot \fc(b)\land\lnot \fc(f)$}\\
+% \Uidx\DP&=&\!\@pagedp!=\min\Set{\dc}{\Size_c(\{t,m,f,b'\})=\VP}\\
+% \end{eqnarray*}
+% 

+% That is, $\VT$ is the maximum of combined vertical size (height plus
+% depth) of the top floats and the main vertical list, and $\VB$ is that of
+% the footnotes and bottom floats.  $\VP$ is the maximum of the sum of all
+% four sizes but we add \!\textfloatsep! if the tallest column has bottom
+% floats.  Note that $\VT$ and $\VP$ are $-\infty$ if any \colpage{}s don't
+% have corresponding items, while $\VB=0$ if so.
+% 
+% $\DT$ and $\DP$ are the minimum $\pd_c$ and $\dc$ respectively among those
+% gives $\VT$ and $\VP$ 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 is given the
+% highest priority.
+% 
+% Note that $\VP$ and $\DP$ are only for the \lpage{} and thus referred to
+% only by \!\pcol@output@end! to close the environment.  The reason why we
+% add \!\textfloatsep! to $\VP$ is to make the last page is well separated
+% from the \postenv{} if the tallest column, taking the addition into
+% account, has bottom floats.
+% 
+% 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
+% non-empty top floats when columns have floats which cannot be put in
+% $\ptop-1$ but are found to be placed in $\ptop$.
+%
+% Therefore, we have to take care of the case $\VT<0$ to mean that all top
+% floats and main vertical lists are empty\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.},
+% 

+% i.e., $\Fc(\{t,m\})=\false$ for all $c\In0\C$, to let succeeding stuff in
+% all \ccolpage{}s are put as if they are preceded by a \!\flushpage!.  In
+% other words, we do nothing if $\VT<0$.
+% 
+% Then if $\VT\geq0$, we set the \sync{}ation point $\VT$ below the top of
+% $\ptop$.  However, since the \sync{}ation {\em pushes down} everything
+% below the main vertical list, footnotes and bottom floats in a \colpage{}
+% $c$ such that $\Size_c(\{t,m\})<\VT$ may be overflown from the bottom of
+% the page.  Therefore, we examine $\VT+\VB\geq\!\@colht!$ (it can be
+% $\VT+\VB>\VP$) and if so flush all \ccolpage{}s in $\ptop$ to set the
+% \sync{}ation point at the top of the next page $\ptop+1$.  This flush is
+% also done when it is requested explicitly by
+% $\CSIndex{ifpcol@clear}=\true$.  That is, we let
+% $\CSIndex{if@tempswa}=\true$ iff one of them holds to flush the
+% \colpage{}s in \!\pcol@synccolumn! invoked for each $c\In0\C$, which sets
+% the \sync{}ation point otherwise.  This macro also takes care of the case
+% of $\VT\geq0$ but empty main vertical lists as the special case that $\VT$
+% is given by a column whose main vertical list is empty, i.e., its top
+% float defines the \sync{}ation point.  In such a case in which we have
+% $\DT=\infty$, the macro sets the \sync{}ation point at the top of the
+% page for the main vertical list and enlarges the space for top floats if
+% necessary.
+% 
+% Finally, we let $\CSIndex{ifpcol@sync}=\false$ to give the default for the
+% next invocation of \!\pcol@output@switch!.
+% 

+%    \begin{macrocode}
+%% Special Output Routines: Synchronization
+
+\def\pcol@sync{%
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do\pcol@flushcolumn
+  \pcol@outputpage\@ne
+  \pcol@getcurrpinfo\@currbox{\global\c@page}{\global\@colht}{\global\topskip}%
+  \@tempdima-\maxdimen \@tempdimb-\maxdimen \pcol@colht-\maxdimen
+  \@tempdimc\maxdimen \@pagedp\maxdimen
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do\pcol@measurecolumn
+  \ifdim\@tempdima<\z@\else
+    \advance\@tempdimb\@tempdima
+    \@tempswafalse
+    \ifdim\@tempdimb<\@colht \ifpcol@clear\else
+      \@tempswatrue
+    \fi\fi
+    \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do\pcol@synccolumn
+  \fi
+  \global\pcol@syncfalse}
+
+%    \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}.}
 
+% 

+% 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 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 after obtaining $p$'s \pctext{} by \!\pcol@getcurrpage!,
+% we invoke \!\@makecol!\footnote{

+% 

+% Not \!\pcol@makecol! because \!\box!\texttt{255} has \!\vfil! at its
+% tail and the \colpage{} should be short enough.}
+% 

+% to build the complete \colpage{} in \!\@outputbox! to be
+% added to the tail of $\S_c$ by \!\@cons!, with the following
+% setting\footnote{

+% 

+% \LaTeX's has another \!\insert! named \!\@kludgeins! for \!\enlargepage!
+% but \Paracol{} does not cares about it.}.
+% $$
+% \begin{array}{lll}
+% \!\box!|255|=\cc_c(\vb^b)&
+% \!\footins!=\cc_c(\ft)&
+% \!\@colht!=\pp^h(\cc_c(\vb^p))\\
+% \!\@midlist!=\cc_c(\ml)&
+% \!\@toplist!=\cc_c(\tl)&
+% \!\@botlist!=\cc_c(\bl)
+% \end{array}
+% $$
+% 

+%    \begin{macrocode}
+\def\pcol@flushcolumn{%
+  \pcol@getcurrcol
+  \ifnum\count\@currbox<\pcol@toppage
+    \pcol@page\count\@currbox
+    \setbox\@cclv\vbox{\unvbox\@currbox \vfil}%
+    \ifvoid\pcol@currfoot\else \@cons\@freelist\pcol@currfoot \fi
+    \pcol@getcurrfoot
+    \pcol@getcurrpage
+    \@makecol
+    \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!; 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!.
+% 

+%    \begin{macrocode}
+    \advance\pcol@page\@ne
+    \ifx\@deferlist\@empty\else
+      \@whilenum\pcol@page<\pcol@toppage\do{%
+        \pcol@getcurrpage
+        \@makefcolumn\@deferlist
+        \if@fcolmade
+          \@next\@currbox\@freelist{\global\setbox\@currbox\box\@outputbox}%
+            \pcol@ovf
+          \expandafter\@cons
+            \csname pcol@shipped\number\pcol@currcol\endcsname\@currbox
+        \fi
+       \advance\pcol@page\@ne}%
+    \fi
+%    \end{macrocode}
+% 

+% Next, we acquire the \ccolpage{} of $c$ which is now in $\ptop$ and thus
+% is empty by \!\@next!.  Then we let $\!\@colht!=\!\@colroom!=\pp^h(\ptop)$
+% by \!\pcol@getcurrpinfo!, 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 $\cc_c(\tl)=\!\@toplist!$ 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@trynextcolumn!  into $\cc_c$ by \!\pcol@setcurrcolnf!
+% because all footnotes are shipped out, and let $\cc_c(\vb^p)=\ptop$ and
+% $\cc_c(\vb^r)=\!\@colroom!$ possibly modified by \!\pcol@trynextcolumn!
+% too.
+% 

+% \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 $\cs{ifpcol@clear}\EQ\mathit{true}$.}

+% 

+%    \begin{macrocode}
+    \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{}}\pcol@ovf
+    \pcol@getcurrpinfo\reserved@a\@tempcnta{\global\@colht}\@tempskipa
+    \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@page
+    \global\dimen\@currbox\@colroom
+  \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. }

+% 

+% 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!\footnote{

+% 

+% We can do it for other cases of \!\flushpage! and \!\clearpage! but
+% \!\pcol@makefcolumn! covers it easily.}.
+% 
+% 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 $H_r=\pp^h(\ptop)+\alpha$ 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{} ($|\ifpcol@|\~|lastpage|=\true$)
+% 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 all columns are processed by \!\pcol@flushcolumn!.
+% 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.
+% 
+% Otherwise, i.e., if we make a \fcolumn{} in the \lpage, we put all floats in
+% \!\@toplist! in $\cc_c(\vb^b)$ of $\pp^h(\ptop)$ tall, together with
+% \!\vskip!  of \!\@fptop! and \!\@fpbot! at the top and bottom and that of
+% \!\@fpsep!  between floats as \!\@makefcolumn! does.  Note that the last
+% \!\vfilneg! is to cancel \!\vfil! which will be inserted at the bottom by
+% \!\pcol@synccolumn!.  Then we return all floats in \!\@toplist! to
+% \!\@freelist! and empty the list.
+% 

+%    \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
+      \setbox\@currbox\vbox to\@colht{\vskip\@fptop \vskip-\@fpsep
+        \def\@elt##1{\vskip\@fpsep\box##1}\@toplist \vskip\@fpbot \vfilneg}%
+      \xdef\@freelist{\@freelist\@toplist}%
+      \global\let\@toplist\@empty
+    \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@magicpenalty}
+% \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 \!\pcol@textfloatsep! as its arguments also to have
+% $\CSIndex{if@tempswa}=\fc(t)$.  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@magicpenalty{12345}
+\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.
+% Unfortunately, \TeX{} does not provide any convenient way for examination,
+% we perform a series of tricky operations to put the followings into
+% \!\@tempboxa!; a penalty of $\!\pcol@magicpenalty!=12345$ whose existence
+% in $\cc_c(\vb^b)$ is (almost) impossible; contents of $\cc_c(\vb^b)$ 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 $\cc_c(\vb^b)$ is empty.
+% Therefore 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 $\VT<\Size_c(\{t,m\})$.  It
+% also lets $\DT=\pd_c$ if $\Fc(\{t,m\})=\true$, $\VT=\Size_c(\{t,m\})$ and
+% $\DT>\pd_c$.
+% 

+%    \begin{macrocode}
+  \setbox\@tempboxa\vbox{\penalty\pcol@magicpenalty
+    \unvcopy\@currbox \xdef\@gtempa{\number\lastpenalty}}%
+  \ifnum\@gtempa=\pcol@magicpenalty\relax \global\pcol@prevdepth\maxdimen
+    \pcol@setcurrcol
+  \else \@tempswatrue
+  \fi
+  \pcol@measureupdate\@tempdima\dimen@ii\@tempdimc\pcol@prevdepth
+%    \end{macrocode}
+% 

+% 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 \!\maxdimen! as its
+% argument also to have $\CSIndex{if@tempswa}=\Fc(\{t,m,f,b\})$.  Then we
+% let $V_b=\size_c(f)+\size_c(b)$ if $V_b<\size_c(f)+\size_c(b)$, and
+% calculate $\size_c(t)+\size_c(m)+\size_c(f)+\size_c(b)$ being
+% $\Size_c(\{t,m,f,b\})$ for a non-empty \colpage{}.
+% 

+%    \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
+%    \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 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 $\Size_c(\{t,m,f,b'\})$.  After that, we
+% throw away the calculation of $\Size_c(\{t,m,f,b'\})$ and $\dc$ above and
+% let them be $\pp^h(\ptop)$ and 0 if $\cc_c(\dl)\neq\emptyset$, because the
+% \lpage{} should be {\em full size} for the following pages having
+% \fcolumn{}s.  Finally, we invoke \!\pcol@measureupdate! again to let
+% $\VP=\Size_c(\{t,m,f,b'\})$ and $\DP=\dc$ if $\Fc(\{t,m,f,b\})=\true$ and
+% $\VP<\Size_c(\{t,m,f,b'\})$.  It also lets $\DP=\dc$ if
+% $\Fc(\{t,m,f,b\})=\true$, $\VP=\Size_c(\{t,m,f,b'\})$ and $\DP>\dc$.
+% 

+%    \begin{macrocode}
+  \dimen@ii\pcol@prevdepth
+  \ifvoid\pcol@currfoot\else \dimen@ii\dp\pcol@currfoot \fi
+  \ifx\@botlist\@empty\else \dimen@ii\z@ \advance\dimen@\textfloatsep \fi
+  \ifx\@deferlist\@empty\else \dimen@\@colht \dimen@ii\z@ \fi
+  \pcol@measureupdate\pcol@colht\dimen@\@pagedp\dimen@ii
+  \advance\pcol@currcol\@ne}
+%    \end{macrocode}
+% \end{macro}\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}
+% 

+% 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 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 float is
+% followed 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.  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 $\<V\>=V_X$ and
+% $\<D\>=D_X$ where $X\in\{T,P\}$ as follows if \CSIndex{if@tempswa}, being
+% $\Fc(\{t,m\})$ for $X=T$ or $\Fc(\{t,m,f,b\})$ for $X=P$, 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 $X$.
+% $$
+% \arraycolsep0pt
+% \begin{array}{rll}
+% X=T\;{:}\;&\<v\>=\Size_c(\{t,m\})&\quad \<d\>=\delta_c\\
+% X=B\;{:}\;&\<v\>=\Size_c(\{t,m,f,b'))&\quad \<d\>=\dc
+% \end{array}
+% $$
+% 

+%    \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.}

+% 

+% 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 $\CSIndex{if@tempswa}=\true$, or flush it otherwise.
+% After obtaining $c$'s \cctext{} $\cc_c$ by \!\pcol@getcurrcol!, we process
+% one of the following three cases.
+% 
+% The first non-flushing 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.  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 $\cc_c(\vb^b)$ is put in it following a
+% vertical skip of $-\!\floatsep!$ to go back to the bottom of the last real
+% float, and \!\topfigrule! and a skip of \!\textfloatsep! to separate it
+% from the last real float, if we have some floats.  Otherwise, neither of
+% the skips nor \!\topfigrule! are put 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
+% $\cc_c(\tf)=\VT-\vc(t)+\!\textfloatsep!-\!\floatsep!$ so as to enlarge the
+% space by $h_c^v=\VT-\vc(t)$ replacing \!\textfloatsep! with $\cc_c(\tf)$
+% in the top float insertion process\footnote{

+% 

+% This enlarging cannot be done by making the float's height 
+% $h_c^v-\!\floatsep!$ (or \!\textfloatsep!) because the height can be
+% negative.}.
+% 

+% 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\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).}.
+% 
+% Note 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.
+% 

+%    \begin{macrocode}
+\def\pcol@synccolumn{%
+  \pcol@getcurrcol
+  \if@tempswa
+    \@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
+        \@next\pcol@float\@freelist{\global\setbox\pcol@float\vbox to\z@{
+          \vskip-\floatsep \topfigrule \vskip\textfloatsep
+          \unvbox\@currbox \vss}}\pcol@ovf
+        \@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 second case is also non-flushing but $\DT<\infty$ and thus most
+% usual.  In this case, we enclose everything in $\cc_c(\vb^b)$ in a \!\vbox!
+% whose height is $h_c^v$ 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 when the box is returned to the main
+% vertical list pushing down the \sync{}ation point a little bit.
+% 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.
+% 
+% Note that, in both cases of $h_c^v<\!\topskip!$ or not, we insert an
+% infinite stretch of $1/1000\,|fil|$ at the bottom of $\cc_c(\vb^b)$ to push
+% up its old contents respecting other infinite stretches if any, as done by
+% \!\raggedbottom!\footnote{

+% 

+% This means finite stretches are nullified.  We could respect them by
+% obtaining the total amount of them in \!\pagestretch! together with
+% infinite ones to let stretches act as much as possible especially with
+% \!\flushbottom! setting.  However, this improvement (if so) is too small
+% to pay a tough coding effort.}.
+% 

+% In addition, we let $\cc_c(\pd)=\DT$ to {\em broadcast} $\DT$ to all
+% columns by which the baselines of first items following the \sync{}ation
+% point are aligned, if $\DT$ plus the hight of each item is less than
+% \!\baselineskip!.  Further, 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.
+% 

+%    \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
+%    \end{macrocode}
+% 

+% The third and last case is for flushing.  In this case we simply add
+% \!\vfil! and \!\penalty! of $-10000$ to make the \colpage{} is immediately
+% flushed when it is revisited.  We also let $\cc_c(\pd)=1000$ to mimic
+% \TeX's \!\prevdepth! with empty main vertical list again.
+% 

+%    \begin{macrocode}
+  \else
+    \global\pcol@prevdepth\@m\p@
+    \global\setbox\@currbox\vbox{\unvbox\@currbox \vfil \penalty-\@M}%
+  \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}.}

+% 

+% 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 shipping-out image of the
+% \tpage{} in \!\@outputbox! whose height is then set to be \!\textheight!.
+% 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
+  \setbox\@outputbox\vbox to\textheight{\unvbox\@outputbox}%
+  \@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}.}
+% 

+% The macro \!\pcol@output@clear! is invoked solely from
+% \!\pcol@specialoutput! to process the \!\output! request made by
+% \!\clearpage!.  The first three and the last lines 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 single-column floats in all columns if any, and then do it for
+% multi-column floats by the following invocations enclosed in a group;
+% \!\@dblfloatplacement! to set up placement parameters; \!\@makefcolumn!
+% with \!\@dbldeferlist! to have a \fpage{} in \!\@outputbox!  if any; and a
+% loop of \!\@outputpage! and \!\@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
+  \setbox\@outputbox\vbox to\textheight{\unvbox\@outputbox}%
+  \@outputpage
+  \pcol@flushfloats
+  \begingroup
+    \@dblfloatplacement
+    \@makefcolumn\@dbldeferlist
+    \@whilesw\if@fcolmade\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 $V_P<0$.}

+% 

+% 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
+% shipping-out image of the main vertical list of each \colpage{} $c$ in
+% $\ptop$.  Then after obtaining $p$'s \pctext{} to have
+% $\page(\ptop)=\pp^p(\ptop)$, $\!\@colht!=\pp^h(\ptop)$ and
+% \CSIndex{ifpcol@nospan} by \!\pcol@getcurrpage!, we build the shipping-out
+% image of $\ptop$ in \!\@outputbox! as follows.
+% 
+% First, if $\CSIndex{ifpcol@nospan}=\false$ to mean the page $\ptop$ has
+% \spanning{} in $\pp(\ptop)$, it is put in \!\@outputbox! and is returned
+% to \!\@freelist! by \!\@cons!.  Then we examine if $\arg{ht}=-\infty$ to
+% mean the macro is invoked from \!\pcol@output@end! (i.e.,
+% $\arg{ht}=\!\pcol@colht!$) and all columns are empty.  If so, we do
+% nothing but scans $\cc_c(\dl)$ for all $c\In0\C$ by \!\pcol@getcurrcol! to
+% let $\CSIndex{if@fcolmade}=\exists c\In0\C:(\cc_c(\dl)\neq())$ to tell it
+% to \!\pcol@output@end!.
+% 

+%    \begin{macrocode}
+\def\pcol@makeflushedpage#1{%
+  \pcol@cleartrue \pcol@output@switch \pcol@clearfalse
+  \pcol@getcurrpinfo\@currbox{\global\c@page}{\global\@colht}\@tempskipa
+  \global\@fcolmadefalse
+  \setbox\@outputbox\vbox{%
+    \ifpcol@nospan\else
+      \unvbox\@currbox
+      \@cons\@freelist\@currbox
+    \fi
+    \ifdim#1=-\maxdimen
+      \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+        \pcol@getcurrcol
+        \ifx\@deferlist\@empty\else \global\@fcolmadetrue \fi
+       \advance\pcol@currcol\@ne}%
+%    \end{macrocode}
+% 

+% Otherwise, i.e., the macro is invoked from \!\pcol@output@flush! or
+% \!\pcol@output@clear!, or from \!\pcol@output@end! with
+% $\!\pcol@colht!\geq0$ being the size of the tallest column, we put
+% $\cc_c(\vb^b)$ for all $c\In0\C$ in a \!\hbox! of \!\textwidth! wide
+% separating them by \!\hfil! as follows.  First, if
+% $\arg{ht}<\!\@colht!=\pp^h(\ptop)$ to mean the invoker is
+% \!\pcol@output@end! and the tallest column is shorter than \!\@colht!, we
+% let $\!\@colht!=\arg{ht}$ to let \!\@makecol! build a short \colpage{},
+% saving the original value in \!\@pageht! temporarily.  Note that it can
+% be $\arg{ht}>\!\@colht!$ due to the additional \!\textfloatsep! below the
+% bottom floats but this excess is recovered by the shrink following it.
+% Then for each $c$ we obtain $c$'s \cctext{} $\cc_c$ by
+% \!\pcol@getcurrcol!, let $\CSIndex{if@fcolmade}=\true$ if
+% $\cc_t(\dl)\neq()$, move $\cc_c(\vb^b)$ into \!\box!|255|, and let
+% $\footins=\cc_c(\ft)$ by \!\pcol@getcurrfoot! returning it to
+% \!\@freelist! if $c$ has footnotes.
+% 
+% 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 $\cc_c(\tr)$ have its original value
+% $\!\floatpagefraction!\times\pp^h(\ptop)$ and $\!\topfigrule!=\!\relax!$
+% temporarily because the floats are not top ones in reality, if so.  Then
+% we also check $\arg{ht}=\pp^h(\ptop)$ 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 \fpage{} as usual and thus we put them in \!\@outputbox! of
+% $\pp^h(\ptop)$ tall, together with \!\vskip! of \!\@fptop! and \!\@fpbot!
+% at the top and bottom and that of \!\@fpsep! between floats as
+% \!\@makefcolumn! does.  Otherwise we invoke \!\@makecol!\footnote{

+% 

+% Not \!\pcol@makecol! because the main vertical list has \!\vfil! at its
+% tail and the shrink below bottom floats should not be nullified.}
+% 

+% to have the shipping-out image of the \colpage{} in \!\@outputbox!,
+% possibily with the deferred floats in $\cc_c(\tl)$ but without
+% \!\topfigrule!.
+% 
+% Then we put the \!\@outputbox! above in a \!\hbox! of \!\columnwidth! wide
+% preceded by \!\pcol@hfil! being \!\relax! for the first column while
+% \!\hfil! for others.  Finally, we save \cctext{} especially those for
+% float parameters into $\cc_c$ by \!\pcol@setcurrcolnf! because all
+% footnotes have been shipped out.
+% 

+% \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.}

+% 

+%    \begin{macrocode}
+    \else
+      \hb@xt@\textwidth{%
+        \let\pcol@hfil\relax \@pageht\@colht \ifdim#1<\@colht \@colht#1\fi
+        \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+          \pcol@getcurrcol
+          \ifx\@deferlist\@empty\else \global\@fcolmadetrue \fi
+          \setbox\@cclv\box\@currbox
+          \ifvoid\pcol@currfoot\else \@cons\@freelist\pcol@currfoot \fi
+          \pcol@getcurrfoot
+          \@tempswafalse
+          \ifdim\@toproom=\maxdimen
+            \global\@toproom\topfraction\@pageht \let\topfigrule\relax
+            \ifdim\@colht=\@pageht \@tempswatrue \fi
+          \fi
+          \if@tempswa
+            \setbox\@outputbox\vbox to\@colht{\vskip\@fptop \vskip-\@fpsep
+              \def\@elt##1{\vskip\@fpsep\box##1}\@toplist \vskip\@fpbot}%
+            \xdef\@freelist{\@freelist\@toplist}\global\@toplist\@empty
+          \else \@makecol
+          \fi
+          \pcol@hfil \hb@xt@\columnwidth{\box\@outputbox\hss}%
+          \let\pcol@hfil\hfil
+          \pcol@setcurrcolnf
+         \advance\pcol@currcol\@ne}}%
+    \fi}}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@flushfloats}
+% \changes{v1.0}{2011/10/10}
+%	{Add reinitialization of \cs{@colht}.}

+% 

+% The macro \!\pcol@flushfloats! is invoked from \!\pcol@output@clear! and
+% \!\pcol@output@end! to flush all deferred single-column floats in each
+% column if any.  After letting $\!\@colht!=\!\textheight!$ for
+% \fcolumn{}s, we iterate shipping out a page having the \fcolumn{}s while
+% $\CSIndex{if@fcolmade}=\exists c\In0\C:(\cc_c(\dl)\neq())$.
+% 
+% In the loop, we open a \!\vbox! containing a \!\hbox! of \!\textwidth! wide
+% to be set into \!\@outputbox!.  For the \!\hbox!, we put an inner \!\hbox!
+% of \!\columnwidth! wide preceded by \!\pcol@hfil! being \!\relax! at
+% initial or \!\hfil! otherwise, for each $c\In0\C$ by the following
+% operations after initializing $\CSIndex{if@tempswa}=f=\false$.  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 $f\gets
+% f\lor(\cc_d(\dl)\neq())$ with $\cc_d(\dl)$ shrunk by \!\@makefcolumn! to
+% let $f$ have $\exists{}c\In0\C:(\cc_c(\dl)\neq())$ at the end of the inner
+% loop for $c$, and then save the \cctext{} into $\cc_c$ by
+% \!\pcol@setcurrcolnf! because we have no footntoes in $c$.
+% 
+% After the end of the inner loop, we move $f$ to \CSIndex{if@fcolmade} for
+% the termination check of the outer loop, and invoke \!\@outputpage! to ship
+% out the \fpage.
+% 

+%    \begin{macrocode}
+\def\pcol@flushfloats{%
+  \global\@colht\textheight
+  \@whilesw\if@fcolmade\fi{%
+    \setbox\@outputbox\vbox{\hb@xt@\textwidth{%
+      \let\pcol@hfil\relax
+      \@tempswafalse
+      \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+        \pcol@getcurrcol
+        \@makefcolumn\@deferlist
+        \pcol@hfil \hb@xt@\columnwidth{\if@fcolmade \box\@outputbox \fi \hss}%
+        \ifx\@deferlist\@empty\else \@tempswatrue \fi
+        \let\pcol@hfil\hfil
+        \pcol@setcurrcolnf
+       \advance\pcol@currcol\@ne}%
+      \global\@fcolmadefalse
+      \if@tempswa \global\@fcolmadetrue \fi}}%
+    \@outputpage}}
+
+%    \end{macrocode}
+% \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}.}

+% 

+% 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 interate
+% \!\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!.}.
+% 

+% 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
+    \@whilesw\if@fcolmade\fi{\pcol@opcol \pcol@startcolumn}%
+    \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.}
 
+% 

+% The macro \!\pcol@output@end! is invoked solely from
+% \!\pcol@specialoutput! to process the \!\output! request made by
+% \!\endparacol!.  We invoke \!\pcol@makeflushedpage!, after letting
+% $\CSIndex{ifpcol@lastpage}=\true$ to notify it of the \lpage{}
+% production, giving it $h=\!\pcol@colht!$ in which \!\pcol@sync! sets the
+% height of the tallest \colpage{} to have the shipping-out image of the
+% \tpage{} in \!\@outputbox!.  Then we process on of the following cases.
+% 
+% The first case is for $\CSIndex{if@fcolmade}=\true$ to mean
+% \!\pcol@makeflushedpage! found columns with deferred floats.  Therefore,
+% since we need to have one or more multi-column pages, we ship out the page
+% in \!\@outputpage! setting its height to \!\textheight! adding \!\vfil! at
+% its tail by \!\@outputpage!, unless the \lpage{} is perfectly empty,
+% i.e., $h=-\infty$ and $\CSIndex{ifpcol@nospan}=f_{\it ns}=\true$.  Then we
+% invoke \!\pcol@flushfloats! to produce and ship out \fpage{}s.  Finally 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.
+% 

+%    \begin{macrocode}
+%% Special Output Routines: Last Page
+
+\def\pcol@output@end{%
+  \pcol@lastpagetrue \pcol@makeflushedpage\pcol@colht
+  \@tempswafalse
+  \if@fcolmade
+    \ifdim\pcol@colht>-\maxdimen \@tempswatrue \fi
+    \ifpcol@nospan\else \@tempswatrue \fi
+    \if@tempswa
+      \setbox\@outputbox\vbox to\textheight{\unvbox\@outputbox \vfil}%
+      \@outputpage
+    \fi
+    \pcol@flushfloats
+    \@tempswatrue \@pagedp\@m\p@
+%    \end{macrocode}
+% 

+% The second case is for $h=-\infty$ without deferred single-column floats
+% to mean all columns in the \lpage{} are empty.  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 $f_{\it sp}=\true$ and
+% $\pd=1000$ 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! except for the last vertical skip being
+% \!\dbltextfloatsep!.  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 multi-column floats but
+% they have not yet put into any pages but are kept in \!\@dbldeferlist!.
+% 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! and let $\pd=\pd'$\footnote{

+% 

+% The author of course know this situation is very unlikely but he is
+% monomaniac.}.
+% 

+%    \begin{macrocode}
+  \else\ifdim\pcol@colht=-\maxdimen
+    \ifx\pcol@firstprevdepth\relax
+      \@tempswatrue \@pagedp\@m\p@
+      \ifpcol@nospan\else
+        \@next\@currbox\@freelist{\global\setbox\@currbox\vbox{
+          \unvbox\@outputbox \unskip}}\pcol@ovf
+        \count\@currbox10\relax
+        {\let\@elt\relax \xdef\@dbldeferlist{\@elt\@currbox\@dbldeferlist}}%
+      \fi
+    \else \unvbox\@outputbox \@pagedp\pcol@firstprevdepth sp\relax
+    \fi
+%    \end{macrocode}
+% 

+% The last case without deferred floats and with some non-empty columns is
+% most usual.  In this case, we simply put \!\@outputbox! letting
+% $\!\topskip!=0$ because \!\topskip! has already been inserted in
+% \colpage{}s or \preenv{} in the box.
+% 

+%    \begin{macrocode}
+  \else
+    \topskip\z@ \box\@outputbox
+  \fi\fi
+%    \end{macrocode}
+% 

+% The followings are for clean-up and set-up for the \postenv; return all
+% $\cc_c(\vb)$ obtained by \!\pcol@getcurrcol! to \!\@freelist!; 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 multi-column 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
+% single-column 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!.}.
+% 

+%    \begin{macrocode}
+  \pcol@currcol\z@ \@whilenum\pcol@currcol<\pcol@ncol\do{%
+    \pcol@getcurrcol \@cons\@freelist\@currbox
+   \advance\pcol@currcol\@ne}%
+  \global\pcol@prevdepth\@pagedp
+  \global\@colht\textheight
+  \global\@colroom\textheight
+  \global\let\@deferlist\@dbldeferlist \gdef\@dbldeferlist{}%
+  \pcol@floatplacement
+  \if@tempswa
+    \pcol@lastpagefalse
+    \@startcolumn \@whilesw\if@fcolmade\fi{\@opcol\@startcolumn}%
+  \fi}
+
+%    \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}.}

+% 

+% 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 top of a page; and finally
+% restore \!\prevdepth!.
+% 
+% The 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.
+% 
+% The macro is invoked from \!\paracol! ($f=|start|$), \!\pcol@switchcol!
+% for \!\switchcolumn! and \csenv{}s ($f=|switch|$), \!\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{%
+  \penalty-\@Miv \global\pcol@prevdepth\prevdepth \vbox{}%
+  \penalty#1\relax \prevdepth\pcol@prevdepth}
+
+%    \end{macrocode}
+% 
+% \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}.}
 
+% 

+% The API macro $\!\paracol!\<\C\>$ is invoked by \beginparacol{} to start
+% \Midx{\env{paracol}} environment.  After making it sure to be in vertical
+% mode by \CSIndex{par} and letting $\!\pcol@ncol!=\C$, we 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 $\CL=\!\pcol@counters!$ 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 $\CL$ applying \!\pcol@thectrelt! to each element $\cl\in\CL$
+% 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 not invoke \!\pcol@switchcol! nor thus scanning
+% $\CL$ with \!\pcol@setctrelt! which defines \lrep{}s, unless a \mctext{}
+% is specified with \beginparacol.
+% 
+% Next we give the intial value of $\val_c(\cl)$ for each column $c$ and
+% \lcounter{} $\cl\in\CL$ 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 $\CL$ 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 $\CL$ 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}
+\def\paracol#1{\par
+  \global\pcol@ncol#1\relax
+  \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}
+% \end{macro}
+% 

+% Next, we set up a few \LaTeX's typesetting parameters which should have
+% appropriate values in the environment.  First we let
+% $$
+% \!\columnwidth!={\!\textwidth!-(\C-1)\!\columnsep!\over\C}
+% $$
+% for $\C$-column typesetting and let \!\hsize! and \!\linewidth! have it as
+% their initial values.  We then let $\CSIndex{if@twocolumn}=\true$ and
+% $\CSIndex{if@firstcolumn}=\true$ so that \textit{float}|*| environments
+% work for multi-column floats and \!\marginpar! produces marginal notes
+% appropriately.  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 initialize our own variables;  $\!\pcol@topskip!=\!\topskip!$ 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
+% \Midx{\!\@combinefloats!} \!\let!-equal to our own \!\pcol@combinefloats!
+% throughout the environment so that our customization is in effect for any
+% invocations including those from \LaTeX's own macros.
+% 

+%    \begin{macrocode}
+  \global\columnwidth\textwidth
+  \@tempdima\columnsep \multiply\@tempdima\pcol@ncol
+  \advance\@tempdima-\columnsep
+  \global\advance\columnwidth-\@tempdima \global\divide\columnwidth\pcol@ncol
+  \global\hsize\columnwidth \global\linewidth\columnwidth
+  \global\@twocolumntrue \global\@firstcolumntrue \col@number\@ne
+  \global\pcol@topskip\topskip
+  \global\pcol@textfloatsep\maxdimen
+  \pcol@lastpagefalse \xdef\pcol@firstprevdepth{\number\prevdepth}%
+  \let\@combinefloats\pcol@combinefloats
+%    \end{macrocode}
+% 

+% Next, we scans 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@mctext!, 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@mctext\relax}%
+  \def\paracol##1{\PackageError{paracol}{%
+    Environment paracol cannot be nested.}\@eha}%
+%    \end{macrocode}
+% 

+% Then 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}
+% 

+% Finally, we let $\!\pcol@nextcol!=0$ in case \beginparacol{} has the
+% optional argument for \mctext{}, and invoke \!\pcol@mctext! if it has.
+% 

+%    \begin{macrocode}
+  \pcol@nextcol\z@
+  \@ifnextchar[%]
+    \pcol@mctext\relax}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\pcol@localcommands}
+% \changes{v1.0}{2011/10/10}
+%	{Introduced to make API commands environment-local.}

+% 

+% 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 \!\paracol!.
+% 

+% \begin{center}\begin{tabular}{llll}
+% \!\switchcolumn!&
+% \!\endcolumn!(|*|)&
+% \!\nthcolumn!(|*|)&\!\endnthcolumn!(|*|)\\
+% \!\leftcolumn!(|*|)&\!\endleftcolumn!(|*|)&
+% \!\rightcolumn!(|*|)&\!\endrightcolumn!(|*|)\\
+% \!\flushpage!&
+% \!\clearpage!&
+% \!\synccounter!&
+% \!\syncallcounters!
+% \end{tabular}\end{center}
+% 

+% Note that we omit \!\column!(|*|) from the list as discussed in the
+% description of \!\paracol!.
+% 

+%    \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{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 \!\paracol! 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}
+% 
+% 
+% 
+% \section{Counter Operations}
+% \label{sec:imp-counter}
+% 
+% \begin{macro}{\globalcounter}
+% \begin{macro}{\pcol@gcounters}
+% The API macro $\!\globalcounter!\arg{ctr}$ defines that $\arg{ctr}$ is a
+% \gcounter, and thus add it to $\CG=\Midx{\!\pcol@gcounters!}$, which has
+% \counter{page} at initial.  Note that initial definition of
+% \!\pcol@gcounters! is done by \!\gdef! just for cosistent \!\global!
+% assignments to it.
+% 

+%    \begin{macrocode}
+%% Counter Opearations
+
+\def\globalcounter#1{\@cons\pcol@gcounters{{#1}}}
+\gdef\pcol@gcounters{\@elt{page}}
+%    \end{macrocode}
+% \end{macro}\end{macro}
+% 

+% \begin{macro}{\pcol@remctrelt}
+% \begin{macro}{\pcol@iremctrelt}
+% The macro $\!\pcol@remctrelt!\<\cg\>$ is invoked solely from \!\paracol!
+% and is applied to each \gcounter{} $\cg\in\CG$ to remove it from
+% $\CC=\!\pcol@counters!$ in which we have $\CL$ finally.  The macro is also
+% move $|\cl@|{\cdot}\cg=\clist(\cg)$
+% 

+% \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!ine $|\cl@|{\cdot}\cg=\!\pcol@stepcounter!\Arg{\cg}$
+% 

+% \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 occurences
+% 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 do $\CC'\gets\CC$,
+% $\CC\gets\emptyset$, and then apply \!\pcol@iremctrelt! to each
+% $\theta\in\CC'$ to let $\CC\gets\CC\cup\{\theta\}$ by \!\@cons! if
+% $\theta\neq\cg$.
+% 

+%    \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
+  \def\reserved@a{#1}\let\reserved@b\pcol@counters
+  \global\let\pcol@counters\@empty
+  {\let\@elt\pcol@iremctrelt \reserved@b}}
+\def\pcol@iremctrelt#1{%
+  \def\reserved@b{#1}%
+  \ifx\reserved@a\reserved@b\else \@cons\pcol@counters{{#1}}\fi}
+
+%    \end{macrocode}
+% \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 \!\paracol!
+% and is applied to each $\cl\in\CL$ to define its \lrep{} of
+% default and that of the leftmost column 0.  It performs a lengthy sequence
+% with many occurences 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}
+% 
+% \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
+% \!\paracol! 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 $\cl\in\CL$ 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
+% $\cl\in\CL=\!\pcol@counters!$ 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
+% \!\paracol!  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 $\!\pcol@com@synccounter!\<\theta\>$, 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 \!\paracol! 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!, 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 $\cl\in\CL$.
+% 

+%    \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 occurences
+% 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}
+% 
+% \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 $\cl\in\CL$ 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@mctext!, \!\pcol@com@endcolumn!, \!\pcol@com@flushpage!,
+% \!\pcol@com@clearpage! and \!\endparacol!.
+% 

+%    \begin{macrocode}
+%% Column-Switching Commands and Environments
+
+\def\pcol@par{\ifvmode\else \par \fi}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \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 $d\geq0$.}

+% 

+% \begin{macro}{\pcol@iswitchcolumn}
+% The macro $\!\pcol@com@switchcolumn!|[|d|]|$, 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 occurences not as the very first \cswitch{} command
+% nor environment of \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 $\!\pcol@switchcol!|[|d|]|$ 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 $\!\pcol@iswitchcolumn!|[|\arg{txt}|]|$ invokes
+% $\!\pcol@mctext!|[|\arg{txt}|]|$ 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@mctext\pcol@switchcol}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% 
+% \begin{macro}{\pcol@mctext}
+% \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 $\cs{ifpcol@mctexttrue}\EQ\mathit{true}$ for restriction of the
+%	 broadcast of \cs{if@nobreak} and \cs{everypar}.}

+% 

+% The macro $\!\pcol@mctext!|[|\arg{txt}|]|$ is invoked from \!\paracol! and
+% \!\pcol@iswitchcolumn! to put a \Uidx\mctext{} $\arg{txt}$ given as the
+% optional argument of the former and \!\switchcolumn!|*|.  The macro has
+% \!\long!  attribute because the \mctext{} may have \CSIndex{par}.  Since
+% the text is put in the column 0 always, we switch to the column by
+% \!\pcol@switchcol! turning $\CSIndex{ifpcol@sync}=\true$ to set a
+% \sync{}ation point above the text, afetr saving the target column
+% $d=\!\pcol@nextcol!$ in \!\@tempcnta!.  Then the text is put in a group in
+% which we let $\!\hsize!=\!\textwidth!$ to let \mctext{} span across all
+% columns, and $\!\col@number!=1$ 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 let
+% $\CSIndex{pcol@mctext}=\true$ so that \!\pcol@output@switch!  broadcasts
+% $\CSIndex{if@nobreak}$ if true and \!\everypar! which is \!\global!ized by
+% a sequence with three \!\expandafter!.  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 then invoke \!\pcol@switchcol!
+% to switch the coloumn $d$.
+% 

+%    \begin{macrocode}
+\long\def\pcol@mctext[#1]{%
+  \@tempcnta\pcol@nextcol
+  \global\pcol@synctrue \pcol@nextcol\z@
+  \pcol@switchcol
+  \begingroup
+    \hsize\textwidth \col@number\@ne #1\pcol@par
+    \global\pcol@mctexttrue
+    \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}.}

+% 

+% The macro \!\pcol@switchcol! is invoked from \!\pcol@switchcolumn!,
+% \!\pcol@iswitchcolumn!, \!\pcol@mctext! 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, we make an
+% \!\output! request with $\!\penalty!=\!\pcol@op@switch!$ to invoke
+% \!\pcol@output@switch! by \!\pcol@invokeoutput! to switch to the column
+% $d$.
+% 
+% Then we let $\CSIndex{if@firstcolumn}$ be $\true$ or $\false$ according to
+% $d=0$ or not respectively, so that \!\marginpar! produces marginal notes
+% appropriately.  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 $\!\addcontentsonly!\arg{t_d}\arg{d}$.
+% Finally, we let $\!\@elt!=\!\relax!$ to make it sure that any lists can be
+% manipulated without unexpected application of a macro to their elements.
+% 

+%    \begin{macrocode}
+\def\pcol@switchcol{%
+  \pcol@savecounters
+  \pcol@invokeoutput\pcol@op@switch
+  \ifnum\pcol@currcol=\z@ \global\@firstcolumntrue
+  \else                   \global\@firstcolumnfalse
+  \fi
+  \let\@elt\pcol@setctrelt
+  \csname pcol@counters\number\pcol@currcol\endcsname
+  \let\@elt\pcol@aconlyelt \pcol@aconly
+  \let\@elt\relax}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \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 \Midx{\env{column}}.
+% Basically, the macros do \!\switchcolumn!\~(|*|), 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 \!\paracol! 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 tell 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}
+% 
+% \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
+%	 inhibitation 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
+%	 inhibitation 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
+%	 inhibitation 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
+%	 inhibitation 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
+%	 inhibitation 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
+%	 inhibitation 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 \Midx{\env{nthcolumn}}, \Midx{\env{leftcolumn}}
+% and \Midx{\env{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.}

+% 

+% 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 swicthing commands and environments cannot be used in #1}\@eha}
+  \reserved@a}
+
+%    \end{macrocode}
+% \end{macro}
+% 
+% \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}
+% 
+% 
+% 
+% \section{Disabing \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 $t$ if $d=c$ by
+% the invocation of $|\pcol@ac@def@|{\cdot}t$ 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}
+% 
+% \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}
+% 
+% \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
+% $\!\pcol@aconlyelt!\<t_c\>\<c\>$ when $t_c$ 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 disabing 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}
+% 
+% 
+% 
+% \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}.}

+% 

+% The macros \!\pcol@com@flushpage! and \!\pcol@com@clearpage! are the
+% implementations of \elocal{} API macro \!\flushpage! and \!\clearpage!
+% respectively.  They have a common structure in which we at first invoke
+% \!\pcol@par! to make it sure to be in vertical mode, let
+% $\!\pcol@nextcol!=\!\pcol@currcol!$ to stay in the current column, and then
+% make an \!\output! request by \!\pcol@invokeoutput! with \!\penalty! being
+% \!\pcol@op@flush! or \!\pcol@op@clear! according to the commands.
+% 

+%    \begin{macrocode}
+%% Page Flushing Commands
+
+\def\pcol@com@flushpage{\pcol@par
+  \pcol@nextcol\pcol@currcol
+  \pcol@invokeoutput\pcol@op@flush}
+\def\pcol@com@clearpage{\pcol@par
+  \pcol@nextcol\pcol@currcol
+  \pcol@invokeoutput\pcol@op@clear}
+
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\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}.}

+% 

+% 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.  Then we make an \!\output! request by
+% \!\pcol@invokeoutput! with $\!\penalty!=\!\pcol@op@end!$.  Next, we let
+% \!\columnwidth!, \!\hsize! and \!\linewidth! commonly be \!\textwidth!
+% for single-column typesetting and also let
+% $\CSIndex{if@twocolumn}=\false$.  Finally, we let
+% $\!\topskip!=\!\pcol@topskip!$ to make it sure that the parameter has the
+% value used outside in \env{paracol} environment.
+% 

+%    \begin{macrocode}
+%% Closing Environment
+
+\def\endparacol{\pcol@par
+  \pcol@nextcol\z@ \pcol@switchcol
+  \pcol@invokeoutput\pcol@op@end
+  \global\columnwidth\textwidth
+  \global\hsize\columnwidth
+  \global\linewidth\columnwidth
+  \global\@twocolumnfalse
+  \global\topskip\pcol@topskip}
+%    \end{macrocode}
+% \end{macro}
+%\iffalse
+%</paracol>
+%\fi
+\endinput
diff --git a/Master/texmf-dist/source/latex/paracol/man.dtx b/Master/texmf-dist/source/latex/paracol/man.dtx
new file mode 100644
index 00000000000..0714752826d
--- /dev/null
+++ b/Master/texmf-dist/source/latex/paracol/man.dtx
@@ -0,0 +1,824 @@
+% \begingroup
+% \hbadness9000 \hfuzz6pt
+% 
+% \begin{paracol}{2}[\section{Introduction}]
+% This document describes the usage of yet another multi-column package named
+% \textsf{paracol}.  The unique feature of the package is that columns are
+% typeset {\em in parallel.}
+% 
+% Suppose you are writing a bilingual document whose left column is written in
+% a language, say English, and right column has the translation of the left
+% column in another language, e.g. Japanese.  With the \textsf{paracol}
+% package you may write an English part of arbitrary length and then {\em
+% switch} to its Japanese counterpart to place both parts side by side.  Of
+% course you may return to the English writing similarly.
+% 
+% The {\em\Uidx\cswitch} is always allowed when you complete an outermost
+% level paragraph.  You may be unaware whether a column is broken into
+% multiple pages before switching because the package automatically goes
+% back and forward to the correct page and vertical position when you switch
+% the column.  Moreover, you may {\em\Uidx\sync{}e} columns so that the tops
+% of the first paragraphs after switching in all columns are vertically
+% aligned.  At a \sync{}ation point, you may give a single-column text,
+% for example a common section header, optionally.  You may also switch
+% single-column and multi-column in a page arbitrary.
+% 
+% This manual itself is an example of two-column documents typeset by
+% \textsf{paracol}.  Since the author is not familiar with languages other
+% than English and Japanese and the latter should be hardly understood by
+% most of readers, the right column is the translation of the left English
+% column into a computational language.  That is, the right column is the
+% \LaTeX{} source code of the left column\footnote{Not really but its essence
+% is shown.}\label{firstfootnote}.
+% 
+% \switchcolumn
+%\begin{Verbatim}
+%\begin{paracol}{2}[\section{Introduction}]
+%\hbadness5000
+%This document describes the usage of yet
+%another multi-column package named
+%\textsf{paracol}.  The unique feature of
+%the package is that columns are typeset
+%{\em in parallel.}
+% 
+%Suppose you are writing a bilingual
+%document whose left column is written in a
+%language, say English, and right column has
+%the translation of the left column in
+%another language, e.g. Japanese.  With the
+%\textsf{paracol} package you may write an
+%English part of arbitrary length and then
+%{\em switch} to its Japanese counterpart to
+%place both parts side by side.  Of course
+%you may return to the English writing
+%similarly.
+%
+%The column switching is always allowed when
+%you complete an outermost level paragraph.
+%You may be unaware whether a column is
+%broken into multiple pages before switching
+%because the package automatically goes back
+%and forward to the correct page and
+%vertical position when you switch the
+%column.  Moreover, you may {\em
+%synchronize} columns so that the tops of
+%the first paragraphs after switching in all
+%columns are vertically aligned.  At a
+%synchronization point, you may give a
+%single-column text, for example a common
+%section header, optionally.  You may also
+%switch single-column and multi-column in a
+%page arbitrary.
+%
+%This manual itself is an example of
+%two-column documents typeset by
+%\textsf{paracol}.  Since the author is not
+%familiar with languages other than English
+%and Japanese and the latter should be
+%hardly understood by most of readers, the
+%right column is the translation of the left
+%English column into a computational
+%language.  That is, the right column is the
+%\LaTeX{} source code of the left column%
+%\footnote{Not really but its essence is
+%shown.}.
+%
+%\switchcolumn
+% \end{Verbatim}
+% |\begin{verbatim}|\\
+% {\it Here is the source of above.}\\
+% |\end{verbatim}|\footnote{

+% This \texttt{verbatim} construct is simply referred as to
+% ``\textit{source}'' hereafter.}
+% 
+% 
+% 
+% \switchcolumn*[\section{Basic Usage}]
+% Loading the package is very simple.  What you have to do is
+% \!\usepackage!|{|\Uidx{\env{paracol}}|}| in the preamble.  Note that
+% \textsf{paracol} can be used with \LaTeXe{} and does not work with
+% \LaTeX{} 2.09.
+% 
+% \switchcolumn
+% 
+%\begin{Verbatim}
+%\switchcolumn*[\section{Basic Usage}]
+%Loading the package is very simple.  What
+%you have to do is |\usepackage{paracol}|
+%\end{Verbatim}
+% |in the preamble.  ...|\footnote{

+% Hereafter, a part of the source code may be omitted like this.}\\
+% |\switchcolumn|\\
+% \textit{source}
+% 
+% \switchcolumn*
+% The fundamental means of parallel-column typesetting are the environment
+% \env{paracol} and the command \Uidx{\!\switchcolumn!}.  The \env{paracol}
+% environment needs an argument to specify the number of columns.  Thus the
+% following is the basic construct for two-parallel-column documents.
+% \begin{quote}
+% \!\begin!|{|\env{paracol}|}{2}|\\
+% \textit{left column text}\\
+% \!\switchcolumn!\\
+% \textit{right column text}\\
+% \!\switchcolumn!\\
+% \textit{left column text}\\
+% \!\switchcolumn!\\
+% \textit{right column text}\\
+% \!\switchcolumn!\\
+% \mbox{\hspace{4em}}$\vdots$\\
+% \!\end!|{|\env{paracol}|}|
+% \end{quote}
+% 
+% \switchcolumn
+%\begin{Verbatim}
+%\switchcolumn*
+%The fundamental means of parallel-column
+%typesetting are the environment |paracol|
+%and the command |\switchcolumn|.  ...
+%\switchcolumn
+%\end{Verbatim}
+% \textit{source}
+% 
+% \switchcolumn[1]*
+%\begin{Verbatim}
+%\switchcolumn[1]*
+%\end{Verbatim}
+% \textit{source}
+%\begin{Verbatim}
+%\switchcolumn[0]
+%The |\switchcolumn| command may have an
+%optional argument to specify the column
+%number (zero origin) to start.  ...
+%\end{Verbatim}
+% 
+% \switchcolumn[0]
+% The \!\switchcolumn! command may have an optional argument to specify the
+% column number (zero origin) to start.  That is, \!\switchcolumn!|[0]|
+% means to switch to the leftmost column, |\switchcolumn[1]| is to start the
+% second column and so on.  Thus the |\switchcolumn| without the optional
+% argument may be considered as \!\switchcolumn!|[|$i+1\bmod{n}$|]| where
+% $i$ is the last column number and $n$ is the number of columns given to
+% \env{paracol} environment.
+% 
+% 
+% 
+% \switchcolumn[0]*[\section{Column Synchronization}\label{sec:sync}]
+% The \!\switchcolumn! command may also be followed by a `|*|' to
+% {\em\Uidx\sync{}e} columns.  After you switch from a column to another by
+% \!\switchcolumn!|*| (or \!\switchcolumn!|[|$i$|]*|), all the columns are
+% vertically aligned at the bottom of the {\em deepest} one preceding the
+% command.  For example, the previous section has three \!\switchcolumn!|*|
+% commands at which left and right columns are vertically aligned.
+% 
+% The {\em starred} version of \!\switchcolumn! may have an optional argument
+% to specify a {\em\Uidx\mctext} whose bottom is the vertical alignment
+% points of the columns.  For example, \!\section! commands in this manual are
+% given as optional arguments of\break\!\switchcolumn!|*| like;
+%\begin{Verbatim}
+%  \switchcolumn*[\section{Basic Usage}]
+%\end{Verbatim}
+% The \env{paracol} environment may also start with a \mctext{} by
+% specifying it as the optional argument of \!\begin!|{|\env{paracol}|}|.
+% For example, at the beginning of this document, the author put;
+%\begin{Verbatim}
+%  \begin{paracol}{2}[\section{Introduction}]
+%\end{Verbatim}
+% 
+% \switchcolumn
+%\begin{Verbatim}
+%\switchcolumn[0]*[%
+%  \section{Column Synchronization}
+%  \label{sec:sync}]
+%The |\switchcolumn| command may also be
+%followed by a `|*|' to {\em synchronize}
+%columns. ...
+% 
+%The {\em starred} version of
+%|\switchcolumn| may have an optional
+%argument to specify a multi-column text
+%whose bottom is the vertical alignment
+%points of the columns.  ...
+%\switchcolumn
+%\end{Verbatim}
+% \textit{source}
+% 
+% 
+% 
+% \begin{column*}[\section{Environments for Columns}\label{sec:env}]
+% \subsection{Environment \texttt{column}}
+% The \!\switchcolumn! is simple but you may prefer to pack the contents of a
+% column in an environment.  The \Uidx{\env{column}} environment is
+% available for this well-structurization of \LaTeX{} sources for parallel
+% columned documents. A construct;
+% \begin{quote}
+% \!\begin!|{|\env{column}|}|\\
+% \textit{text for a column}\\
+% \!\end!|{|\env{column}|}|
+% \end{quote}
+% is (almost) equivalent to;
+% \begin{quote}
+% \!\switchcolumn!\\
+% \textit{text for a column}
+% \end{quote}
+% The \Uidx{\env{column*}} environment is also available for the column
+% \sync{}ation and may have an optional argument for \mctext.
+% \end{column*}
+% 
+% \begin{column}
+% \subsection{\ttfamily Environment column}
+%\begin{Verbatim}
+%\begin{column*}[%
+%  \section{Environments for Columns}
+%  \label{sec:env}]
+%\subsection{Environment \texttt{column}}
+%The |\switchcolumn| is simple but you may
+%prefer to pack the contents of a column in
+%an environment.  ...
+%\end{column*}
+%\begin{column}
+%\end{Verbatim}
+% \textit{source}\\
+% |\end{column}|
+% \end{column}
+% 
+% \begin{nthcolumn*}{1}
+% \subsection{\ttfamily Environment nthcolumn}
+%\begin{Verbatim}
+%\begin{nthcolumn*}{1}
+%\end{Verbatim}
+% \textit{source}
+%\begin{Verbatim}
+%\end{nthcolumn*}
+% 
+%\begin{nthcolumn}{0}
+%\subsection{Environment \texttt{nthcolumn}}
+%The |\switchcolumn| can start an
+%arbitrarily specified column with the
+%column number given through its optional
+%argument, but the |column| environment
+%cannot do it. ...
+%\end{nthcolumn}
+%\end{Verbatim}
+% \end{nthcolumn*}
+% \begin{nthcolumn}{0}
+% \subsection{Environment \texttt{nthcolumn}}
+% The \!\switchcolumn! can start an arbitrarily specified column with the
+% column number given through its optional argument, but the \env{column}
+% environment cannot do it.  If you want to start $i$-th column, you have to
+% do \!\begin!|{|\Uidx{\env{nthcolumn}}|}{|$i$|}| (or
+% \Uidx{\env{nthcolumn*}} with an optional argument to \sync{}e).
+% \end{nthcolumn}
+% 
+% 
+% 
+% \begin{leftcolumn*}
+% \subsection[Environment \texttt{leftcolumn} and \texttt{rightcolumn}]

+%     {Environment \texttt{leftcolumn} and\\\texttt{rightcolumn}}
+% The environment \Uidx{\env{leftcolumn}} and \Uidx{\env{rightcolumn}} (and
+% their starred versions with an optional argument) are available as more
+% convenient means than saying \!\begin!|{|\env{nthcolumn}|}{0}| and
+% \!\begin!|{|\env{nthcolumn}|}{1}|.
+% 

+% \Uidx{\EnvIndex{leftcolumn*}}\Uidx{\EnvIndex{rightcolumn*}}

+% 
+% \begin{figure*}\nosv
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\textwidth{}\\
+%     double-column figure \#1\\
+%     \\\hline
+%     \end{tabular}}
+% \caption{A Double-Column Figure}
+% \end{figure*}
+% \begin{figure}[t]\nosv
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\columnwidth{}\\\\
+%     single-column figure \#1\\
+%     \\\\\hline
+%     \end{tabular}}
+% \caption{A Single-Column Figure}
+% \end{figure}
+% \end{leftcolumn*}
+% 
+% \begin{rightcolumn}
+% \subsection{\ttfamily Environment leftcolumn and\\rightcolumn}
+%\begin{Verbatim}
+%\begin{leftcolumn*}
+%\subsection{%
+%  Environment \texttt{leftcolumn} and\\
+%  \texttt{rightcolumn}}
+%The environment |leftcolumn| and
+%|rightcolumn| (and their starred versions
+%with an optional argument) are available as
+%more convenient means than saying
+%|\begin{nthcolumn}{0}| and
+%|\begin{nthcolumn}{1}|.
+%\begin{figure*}...\end{figure*}
+%\begin{figure}[t]...\end{figure}
+%\end{leftcolumn*}
+%\begin{rightcolumn}
+%\end{Verbatim}
+% \textit{source and a \texttt{figure} env}\\
+% |\end{rightcolumn}|
+% \begin{figure}[t]\nosv
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\columnwidth{}\\
+%     \ttfamily single-column figure \#2\\
+%     \\\hline
+%     \end{tabular}}
+% \caption{\ttfamily Another Single-Column Figure}
+% \end{figure}
+% \end{rightcolumn}
+% 
+% 
+% 
+% \begin{leftcolumn*}[\section{Floats, Footnotes and Counters}
+%     \label{sec:float}]
+% \begin{table}[b]\nosv
+% \caption{A Single-Column Table}
+% \centerline{\begin{tabular}[t]{|l|c|r|}\hline
+%   An&example&of\\\hline
+%   single&column&table\\\hline
+%   \end{tabular}}
+% \end{table}
+% \subsection{Figures and Tables}
+% As shown in this page, double-column figures\slash tables (or those
+% spanned multiple columns if you have three or more) may be placed by
+% \env{figure*} and \env{table*} environments as usual.  A single-column
+% figure\slash table will be placed in the column in which you put
+% \env{figure} and \env{table}.  For example, the contents of \env{figure}
+% environment in a \env{leftcolumn} environment is \emph{always} placed in a
+% left column.  That is, even if the column of the \emph{current} page does
+% not have enough room to place the figure, it will not thrown to the right
+% column but will be placed in the left column of the next page\footnote{

+% 

+% Or some farther page if \LaTeX{} cannot solve the placement problem wisely.}.
+% 
+% Another caution about float placement is that you have to be careful when
+% you try to put a top-float explicitly with |t|-option or implicitly without
+% placement option (i.e., |tbp| in most classes) and to \sync{}e columns.
+% The rule is as follows; after you \sync{}e columns in a page, the page
+% cannot have top-floats any more.  When you \sync{}e columns,
+% \textsf{paracol} fixes a virtual horizontal line in the page as the
+% \sync{}ation barrier.  Thus no top-floats cannot be added above the
+% line\footnote{

+% 

+% Even if you have enough space above, sorry.}.
+% 

+% Therefore, the author put two \env{figure} environments for the figures
+% shown in the previous page into the \env{leftcolumn*} and \env{rightcolumn}
+% environment for the previous section.
+% 
+% \subsection{Footnotes and Marginal Notes}
+% Footnotes are also put at the bottom of the column in which \!\footnote!
+% commands and their references (like this\footnote{

+% 

+% An example of footnote.})
+% 

+% reside, as shown in page~\pageref{firstfootnote} and this page.  Marginal
+% notes behave similarly like what you are seeing in the left margin of this
+% sentence\marginpar{

+% 

+% \raggedright An example of marginal note.}
+% 

+% and the right marginal note in this page\footnote{

+% 

+% If you have three or more columns, marginal notes of the second or
+% succeeding columns are placed just right of the column.  Thus marginal notes
+% of non-leftmost and non-rightmost columns will appear in the space
+% separating columns rather than the margin of a page.}.
+% 
+% \subsection{Local and Global Counters}
+% \UsageIndex{local counter}
+% \UsageIndex{global counter}
+% 

+% You probably found that the numbering of figures and tables is \emph{global}
+% while that of footnotes are \emph{local}.  That is, the figure in the right
+% column of the previous page has number~3 following its left-column
+% counterpart Figure~2.  The tables in the page are also numbered as 1 and 2
+% crossing the column boundary.  However, the footnotes in each column have
+% their own numbering sequence.  Moreover, the footnote numbers in left
+% columns are typeset in Roman font while those in right columns have italic
+% shapes.  Similarly, sub-section numbering is local and the headings in right
+% columns have typewriter-face numbers.
+% 
+% This happens because the author declared the counters \counter{figure} and
+% \counter{table} are \emph{global} in the preamble of this document by
+% saying;
+% \begin{itemize}\item[]
+% \Uidx{\!\globalcounter!}|{figure}|\\
+% \!\globalcounter!|{table}|
+% \end{itemize}
+% and do nothing about \counter{footnote} and \counter{subsection} counters.
+% By default, all the counters except for |page| are local to columns.  The
+% value of a \lcounter of a column is saved somewhere when you leave the
+% column, and it is restored when you revisit the column.  The initial value
+% of the \lcounter{}s are the value they have at
+% \!\begin!|{|\env{paracol}|}|.  After you close the \env{paracol}
+% environment, the values of the left-most column are used for the rest of
+% your document until you start new \env{paracol} environment.  On a
+% restart, \lcounter{}s in a column have the values they had at the last
+% \Endparacol, except for those which have been modified outside the
+% environment because the modifications are \emph{broadcasted} to
+% \lcounter{}s in all columns.  You will see the effect of this
+% inter-environment counter value conservation in the footnote numbers in
+% the right column in page~\pageref{rightfootnote3} and
+% \pageref{rightfootnote4}.
+% 
+% This broadcasting of a \lcounter{} value can be done explicity in
+% \env{paracol} environment by a command $\Uidx{\!\synccounter!}\Arg{ctr}$.
+% This command makes $\mathit{ctr}$ in all columns have the value of that in
+% the column in which the command appears.  In addition, another command
+% \Uidx{\!\syncallcounters!} peforms this broadcasting for all \lcounter{}s.
+% 
+% If you make a counter global by the command \!\globalcounter!, the
+% save/restore operations are not performed to the counter and thus it is
+% globally incremented by |\[ref]|\AB|stepcounter|
+% 

+% \SpecialIndex{\refstepcounter}\SpecialIndex{\stepcounter}

+% 

+% or commands such as \!\caption! and \!\section!.  Note that the value of a
+% \gcounter depends on the place where it is incremented (or set) in
+% the \emph{source code} rather than where it appears in the output.  Thus
+% if the author put a \env{table} environment here to increment \env{table}
+% counter, the right-column table at the bottom of page~\pageref{tab:right}
+% would be Table~3 because its \env{table} environment does not appear yet
+% in the source code.  Note that, however, though the counter \counter{page}
+% is global as expected, its numbering is consistent among all columns as
+% far as you refer to the value by $\!\pageref!\Arg{label}$ and/or see the
+% values in table of contents, etc.
+% 
+% Another counter which the author made global in this documnet is
+% \counter{section}.  As explained in Section~\ref{sec:sync}, an optional
+% \mctext{} of \cswitch{} is considered as in the left-most
+% column.  Since \!\section! commands in this document are always \mctext{}s,
+% so far, it seems unnecessary to make \counter{section} global because it is
+% incremented correctly in the left-most column.  However, the stepping
+% \counter{section} has a side effect to reset its decendent counter
+% \counter{subsection} and referred from \!\thesubsection! command.  Thus if
+% \counter{section} were local, the right-column sub-sections in
+% Section~\ref{sec:env} would be numbered as ``0.1'', ``0.2'' and ``0.3''
+% because the local value of \counter{section} would be zero.  Moreover, the
+% right-column sub-sections of this section would be ``0.4'', ``0.5'' and
+% ``0.6'' because stepping \counter{section} local to left-columns would not
+% reset \counter{subsection} local to right-columns.
+% 
+% You may give a local appearance to a counter \textit{ctr} for the $i$-th
+% column (zero origin) by a command;
+% \begin{itemize}\item[]
+% \Uidx{\!\definethecounter!}|{|\textit{ctr}|}{|$i$|}{|\textit{def}|}|
+% \end{itemize}
+% where \textit{def} is to be the body of the local definition of
+% |\the|\textit{ctr}.  For example, the preamble of this document has the
+% following to give non-default defitions to \!\thefootnote! and
+% \!\thesubsection! for right columns.
+% 

+%\begin{Verbatim}
+%  \definethecounter{footnote}{1}{%
+%    \textit{\arabic{footnote}}}
+%  \definethecounter{subsection}{1}{%
+%    \texttt{%
+%      \arabic{section}.\arabic{subsection}}}
+%\end{Verbatim}
+%\end{leftcolumn*}
+% 
+% \begin{rightcolumn}
+% \begin{table}[b]\nosv
+% \caption{\ttfamily Another Single-Column Table}
+% \label{tab:right}
+% \centerline{\ttfamily \begin{tabular}[t]{|l|r|}\hline
+%   Another&example\\\hline
+%   of&single\\\hline
+%   column&table\\\hline
+%   \end{tabular}}
+% \end{table}
+% \subsection{\ttfamily Figures and Tables}
+%\begin{Verbatim}
+%\begin{leftcolumn*}[\section{%
+%   Floats, Footnotes and Counters}]
+%\begin{table}[b]\nosv
+%\caption{A Single-Column Table}
+%\centerline{\begin{tabular}[t]{|l|c|r|}
+%  \hline
+%  An&example&of\\\hline
+%  single&column&table\\\hline
+%  \end{tabular}}
+%\end{table}
+%\subsection{Figures and Tables}
+%As shown in this page, double-column
+%figures\slash tables (or those spanned
+%multiple columns if you have three or more
+%columns) may be placed by |figure*| and
+%\end{Verbatim}
+% {\ttfamily |table*| environments as usual\footnote{Another example
+% of footnote.}\label{rightfootnote3}. ...}
+% 
+% \subsection{\ttfamily Footnotes and Marginal Notes}
+%\begin{Verbatim}
+%Footnotes are also put at the bottom of the
+%column in which |\footnote| commands and
+%their references (like this\footnote{%
+%An example of footnote.}) reside, as shown
+%in page~2 and this page.  Marginal notes
+%behave similarly like what you are seeing
+%in the left margin of this
+%sentense\marginpar{\raggedright An example
+%of marginal note.} and the right marginal
+%\end{Verbatim}
+% |note in this page\footnote{...}. ...|

+% \marginpar{\raggedright\ttfamily
+% Another example of marginal note.}
+% 
+% \begin{figure}[t]\nosv
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\columnwidth{}\\\\\\\\
+%     \ttfamily another figure with [t] option\\
+%     \ttfamily to fill space
+%     \\\\\\\\\hline
+%     \end{tabular}}
+% \caption{\ttfamily
+% Another Figure with [t] Option}
+% \end{figure}
+%
+% \begin{figure}[b]\nosv
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\columnwidth{}\\
+%     \ttfamily a figure with [b] option\\
+%     \ttfamily to fill space\\
+%     \\\hline
+%     \end{tabular}}
+% \caption{\ttfamily
+% A Figure with [b] Option}
+% \end{figure}
+% 
+% \subsection{\ttfamily Local and Global Counters}
+%\begin{Verbatim}
+%You probably found that the numbering of
+%figures and tables is \emph{global} while
+%that of footnotes are \emph{local}. ...
+%\end{leftcolumn*}
+%\end{Verbatim}
+% \textit{source}.
+%
+% \begin{figure}[p]\nosv
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\columnwidth{}\\\\\\\\
+%     \ttfamily a figure with [p] option\\
+%     \ttfamily to fill space
+%     \\\\\\\\\hline
+%     \end{tabular}}
+% \caption{\ttfamily
+% A Figure with [p] Option}
+% \end{figure}
+% 
+% \begin{figure}[p]\nosv
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\columnwidth{}\\\\\\\\
+%     \ttfamily another figure with [p] option\\
+%     \ttfamily to fill space
+%     \\\\\\\\\hline
+%     \end{tabular}}
+% \caption{\ttfamily
+% Another Figure with [p] Option}
+% \end{figure}
+% 
+% \begin{figure}[p]\nosv
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\columnwidth{}\\\\\\\\
+%     \ttfamily yet another figure with [p]\\
+%     \ttfamily option to fill space
+%     \\\\\\\\\hline
+%     \end{tabular}}
+% \caption{\ttfamily
+% Yet Another Figure with [p] Option}
+% \end{figure}
+% 
+% \begin{figure}[p]\nosv
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\columnwidth{}\\\\\\\\
+%     \ttfamily fourth figure with [p]\\
+%     \ttfamily option to fill space
+%     \\\\\\\\\hline
+%     \end{tabular}}
+% \caption{\ttfamily
+% Forth Figure with [p] Option}
+% \end{figure}
+% 
+% \begin{figure}[t]\nosv
+% \centerline{\begin{tabular}[b]{|c|}\hline
+%     \hbox to.9\columnwidth{}\\\\\\\\
+%     \ttfamily yet another figure with [t]\\
+%     \ttfamily option to fill space
+%     \\\\\\\\\hline
+%     \end{tabular}}
+% \caption{\ttfamily
+% Yet Another Figure with [t] Option}
+% \end{figure}
+% \end{rightcolumn}  
+% 
\switchcolumn*
+% 
\flushpage
+% \end{paracol}
+% 
+% 
+% 
+% \section{Closing \texttt{paracol} Environment and Page Flushing}
+% \label{sec:man-close}
+% The final example shown here is this single-column text which the author put
+% after \env{paracol} environment is closed.  As you are seeing, \env{paracol}
+% environment can be finished at any vertical position in a page and can be
+% followed by ordinary single column texts.
+% 
+% \begin{paracol}{2}
+% \begin{leftcolumn}
+% The environment may also be restarted anywhere you like as shown here.
+% 
+% The last issue is to flush a page.  The ordinary \!\newpage! command works
+% as you expect.  If you say \!\newpage! in the left column in a page, the
+% contents following it will appear in the left column in the next page.  Note
+% that this does not affect the layout of the right column.
+% 
+% To flush all columns in a page, a command \Uidx{\!\flushpage!} is
+% available.  This command in $i$-th column is almost equivalent to;
+% \begin{itemize}\item[]
+% \!\switchcolumn!|[|$i$|]*[|\!\newpage!|]|
+% \end{itemize}
+% but more robust\footnotemark.
+% The ordinary page breaking command \Uidx{\!\clearpage!} may also be used
+% to flush all columns and to start a fresh page, but it has a side effect
+% to put all figures and tables which are not yet output.
+% \end{leftcolumn}
+% 
+% \begin{rightcolumn}
+%\begin{Verbatim}
+%\begin{leftcolumn}
+%The environment may also be restarted
+%anywhere you like as shown here. ...
+%\end{leftcolumn}
+%\end{Verbatim}
+% \textit{source}\\
+% |\end{paracol}|\\
+% |Now the aurthor will do ...|
+% \end{rightcolumn}
+% \end{paracol}
+% 
+% Now the aurthor will do |\flushpage| shortly to start a real binlingual
+% example from the next page, after showing another example of closing 
+% \env{paracol} environment in this sentence and of restarting in the next
+% one.
+% \begin{paracol}{2}
+% \begin{leftcolumn}
+% O.K., we have restarted \env{paracol} environment and we will see the
+% effect of \!\flushpage! now!!\footnotetext{

+% 

+% For example \texttt{\string\switchcolumn*} may flush a page for the
+% \sync{}ation and thus \texttt{\string\newpage} may leave an empty page.}
+% 

+% \end{leftcolumn}
+% \begin{rightcolumn}
+%\begin{Verbatim}
+%\begin{paracol}{2}
+%\begin{leftcolumn}
+%O.K., we have restarted |paracol|
+%environment and we will see the effect of
+%|\flushpage| now!!
+%\end{leftcolumn}
+%\end{Verbatim}
+% \textit{source}
+% \flushpage
+% \end{rightcolumn}
+% 
+% 
+% 
+% \newenvironment{Gverse}{\begin{leftcolumn*}

+% 	\begin{myverse}}

+%   {\end{myverse}\end{leftcolumn*}}
+% \newenvironment{Everse}{\begin{rightcolumn}\begin{myverse}}

+%   {\end{myverse}\end{rightcolumn}}
+% \makeatletter
+% \newenvironment{myverse}{\leftmargini0pt\partopsep0pt\verse}{\endverse}
+% 
+% \begin{leftcolumn*}[

+% \centerline{\Large An Die Freude/To Joy}\smallskip
+% \centerline{\large Friedrich Schiller}\smallskip
+% The following is the libretto of the fourth movement of Beethoven's Ninth
+% Symphony, his adaptation of Schiller's ode ``An Die Freude'' (or ``To Joy'' in
+% English). Beethoven's additions and revisions are indicated in italics.]
+% \end{leftcolumn*}
+% \begin{Gverse}
+% \itshape O Freunde, nicht diese T\"one! \\
+% Sondern la{\ss}t uns angenehmere anstimmen und freu\-denvollere

+% \footnote{If I had been a good student in my German class, this footnote
+% would say ``This part was added by Beethoven.'' in German.}.
+% \end{Gverse}
+% \begin{Everse}
+% \itshape Oh friends, no more of these sad tones!\\
+% Let us rather raise our voices together\\
+% In more pleasant and joyful tones

+% \footnote{This part was added by Beethoven.}\label{rightfootnote4}.
+% \end{Everse}
+% \begin{Gverse}
+% Freude!\\
+% Freude, sch\"oner G\"otterfunken
+% Tochter aus Elysium,\\
+% Wir betreten feuertrunken,
+% Himmlische, dein Heiligtum!\\
+% Deine Zauber binden wieder,
+% {\itshape Was die Mode streng geteilt;\\
+% Alle Menschen werden Br\"uder\footnote{

+% Original: Was der Mode Schwert geteilt;\\
+% Bettler werden F\"urstenbr\"uder,},}
+% Wo dein sanfter Fl\"u\-gel weilt
+% \end{Gverse}
+% \begin{Everse}
+% Joy! \\
+% Joy, thou shining spark of God,\\
+% Daughter of Elysium,\\
+% With fiery rapture, goddess,\\
+% We approach thy shrine.\\
+% Your magic reunites\\
+% {\itshape That which stern custom has parted;\\
+% All humans will become brothere\footnote{

+% Original: 
+% What custom's sword has parted;\\
+% Beggars become princes' brothers}}\\
+% Under your protective wing.
+% \end{Everse}
+% \begin{Gverse}
+% Wem der gro{\ss}e Wurf gelungen,
+% eines Freundes Freund zu sein;\\
+% Wer ein holdes Weib errungen,
+% mische seinen Jubel ein!\\
+% Ja, wer auch nur eine Seele 
+% sein nennt auf dem Erdenrund!\\
+% Und wer's nie gekonnt, der stehle 
+% weinend sich aus diesem Bund! 
+% \end{Gverse}
+% \begin{Everse}
+% Let the man who has had the fortune\\
+% To be a helper to his friend,\\
+% And the man who has won a noble woman,\\
+% Join in our chorus of jubilation!\\
+% Yes, even if he holds but one soul\\
+% As his own in all the world!\\
+% But let the man who knows nothing of this\\
+% Steal away alone and in sorrow.
+% \end{Everse}
+% \begin{Gverse}
+% Freude trinken alle Wesen
+% an den Br\"usten der Natur;\\
+% Alle Guten, all B\"osen
+% folgen ihrer Rosenspur.\\
+% K\"usse gab sie uns und Reben,
+% einen Freund, gepr\"uft im Tod;\\
+% Wollust ward dem Wurm gegeben,
+% und der Cherub steht vor Gott. 
+% \end{Gverse}
+% \begin{Everse}
+% All the world's creatures drink\\
+% From the breasts of nature;\\
+% Both the good and the evil\\
+% Follow her trail of roses.\\
+% She gave us kisses and wine\\
+% And a friend loyal unto death;\\
+% She gave the joy of life to the lowliest,\\
+% And to the angels who dwell with God. 
+% \end{Everse}
+% \begin{Gverse}
+% Froh, wie seine Sonnen fliegen 
+% durch des Himmels pr\"acht'gen Plan,\\
+% Laufet, Br\"uder, eure Bahn,
+% freudig, wie ein Held zum Siegen. 
+% \end{Gverse}
+% \begin{Everse}
+% Joyous, as his suns speed\\
+% Through the glorious order of Heaven,\\
+% Hasten, brothers, on your way,\\
+% Joyful as a hero to victory.
+% \end{Everse}
+% \begin{Gverse}
+% Seid umschlungen, Millionen! 
+% Diesen Ku{\ss} der ganzen Welt!\\
+% Br\"uder, \"uber'm Sternenzelt
+% mu{\ss} ein lieber Vater woh\-nen. 
+% \end{Gverse}
+% \begin{Everse}
+% Be embraced, all ye millions!\\
+% With a kiss for all the world!\\
+% Brothers, beyond the stars\\
+% Surely dwells a loving Father. 
+% \end{Everse}
+% \begin{Gverse}
+% Ihr st\"urzt nieder, Millionen?
+% Ahnest du den Sch\"opfer, Welt?\\
+% Such'ihn \"uberm Sternenzelt! 
+% \"Uber Sternen mu{\ss} er wohnen.
+% \end{Gverse}
+% \begin{Everse}
+% Do you kneel before him, oh millions?\\
+% Do you sense the Creator's presence?\\
+% Seek him beyond the stars!\\
+% He must dwell beyond the stars.
+% \end{Everse}
+% \end{paracol}
+% \endgroup
+\endinput
diff --git a/Master/texmf-dist/source/latex/paracol/paracol.dtx b/Master/texmf-dist/source/latex/paracol/paracol.dtx
new file mode 100644
index 00000000000..6f0a4a248e6
--- /dev/null
+++ b/Master/texmf-dist/source/latex/paracol/paracol.dtx
@@ -0,0 +1,558 @@
+%\iffalse
+%<paracol>%% Style file `paracol'.
+%<man>%% LaTeX file 'paracol-man'.
+%<*paracol|man>
+%% Copyright (C) 2005-2011
+%%   Hiroshi Nakashima <h.nakashima@DOMAIN;  DOMAIN=media.kyoto-u.ac.jp>
+%%   (Kyoto University)
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License distributed from CTAN
+%% archives in directory macros/latex/base/lppl.txt; either
+%% version 1 of the License, or any later version.
+
+%</paracol|man>
+%<*dtx>
+\ProvidesFile{paracol.dtx}
+%</dtx>
+%<paracol>\NeedsTeXFormat{LaTeX2e}[1994/12/01]
+%<paracol>\ProvidesPackage{paracol}
+%<man>\ProvidesFile{paracol-man.tex}
+% \fi
+% \ProvidesFile{paracol.dtx}
+[2011/10/10 v1.0 ]
+% \iffalse
+%<*man>
+\documentclass{ltxdoc}
+\usepackage{paracol}
+\usepackage{newvbtm}
+\DisableCrossrefs
+\PageIndex
+\CodelineNumbered
+\RecordChanges
+%</man>
+%<man>\OnlyDescription
+%<man>\def\ONLYDESCRIPTION{}
+%<*man>
+\textwidth210mm
+\advance\textwidth-40mm \oddsidemargin20mm \advance\oddsidemargin-1in
+\columnsep10mm
+\marginparwidth20mm \advance\marginparwidth-\marginparsep
+\marginparsep.5\marginparsep
+\raggedbottom
+\begin{document}
+\DocInput{paracol.dtx}
+\end{document}
+%</man>
+% \fi
+% 
+% 
+% 
+% \makeatletter
+% 
+% \newcount\ChangeCount \ChangeCount10000
+% \def\changes@#1#2#3{%
+%   \global\advance\ChangeCount\@ne
+%   \protected@edef\@tempa{\noexpand\glossary{#1\levelchar
+%                                  \number\ChangeCount
+%                                  \actualchar
+%                                  \ifx\saved@macroname\@empty
+%                                    \generalname
+%                                  \else
+%                                    \string\verb\quotechar*

+%                                    \verbatimchar\saved@macroname
+%                                    \verbatimchar
+%                                  \fi
+%                                  :\levelchar #3}}%
+%   \@tempa\endgroup\@esphack}
+% 
+% \def\theglossary{\onecolumn \glossary@prologue
+%	\GlossaryParms \let\item\@idxitem
+%       \rightskip 1em plus 1fil
+%       \parfillskip-1em
+%       \ignorespaces}
+% \def\endtheglossary{\relax}
+% 
+% 
+% 
+% \errorcontextlines10000
+% \GetFileInfo{paracol.dtx}
+% \setcounter{IndexColumns}{2}
+% 
+% \def\bottomfraction{.9}
+% \def\cs#1{\hbox{\tt\char\escapechar#1}}
+% \def\Item{\vskip-\itemsep\vskip-\parsep\vskip0pt\nobreak\item}
+%
+% \def\nosv{\catcode`\|12\relax}
+% \begingroup
+% \nosv
+% \gdef\Set#1#2{\{#1\,|\,#2\}}
+% \gdef\Abs#1{|#1|}
+% \endgroup
+% 
+% \def\eqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
+% \global\@eqnswtrue
+% \global\@eqcnt\z@\tabskip\@centering\let\\=\@eqncr
+% $$\halign to \displaywidth\bgroup\hskip\@centering
+%   $\displaystyle\tabskip\z@{##}$\@eqnsel&\global\@eqcnt\@ne
+%   \hfil$\;{##}\;$\hfil
+%   &\global\@eqcnt\tw@ $\displaystyle\tabskip\z@{##}$\hfil
+%    \tabskip\@centering&\llap{##}\tabskip\z@\cr}
+%
+% \def\Meta#1{\penalty\@highpenalty
+%	\hbox{{\tt\char`\{}{\it\meta{#1}}{\tt\char`\}}}}
+% \def\opt#1{{\tt[}{\it\meta{#1}}{\tt]}}
+% \def\optn#1{{\tt[#1]}}
+%
+% \let\latex@addmarginpar\@addmarginpar
+% \let\latex@latex@warning@no@line\@latex@warning@no@line
+% \def\@addmarginpar{\let\@latex@warning@no@line\@gobble
+%	\latex@addmarginpar
+%	\let\@latex@warning@no@line\latex@latex@warning@no@line}
+% \let\@font@warning\@gobble
+%
+% \long\def\m@cro@#1#2{\endgroup \topsep\MacroTopsep \trivlist
+%    \edef\saved@macroname{\string#2}

+%   \def\makelabel##1{\llap{##1\hskip\@totalleftmargin}}

+%   \if@inlabel
+%     \let\@tempa\@empty \count@\macro@cnt
+%     \loop \ifnum\count@>\z@
+%       \edef\@tempa{\@tempa\hbox{\strut}}\advance\count@\m@ne \repeat
+%     \edef\makelabel##1{\llap{\vtop to\baselineskip
+%                                {\@tempa\hbox{##1}\vss}

+%			       \hskip\@totalleftmargin}}

+%     \advance \macro@cnt \@ne
+%   \else  \macro@cnt\@ne  \fi
+%   \edef\@tempa{\noexpand\item[

+%      #1

+%        \noexpand\PrintMacroName
+%      \else
+%        \noexpand\PrintEnvName
+%      \fi
+%      {\string#2}]}

+%   \@tempa
+%   \global\advance\c@CodelineNo\@ne
+%    #1

+%       \SpecialMainIndex{#2}\nobreak
+%       \DoNotIndex{#2}

+%    \else
+%       \SpecialMainEnvIndex{#2}\nobreak
+%    \fi
+%   \global\advance\c@CodelineNo\m@ne
+%   \ignorespaces}
+% 
+% \def\dummymacro{\topsep\MacroTopsep \trivlist \item[]}
+% \let\enddummymacro\endtrivlist
+% 
+% \def\DescribeOpt{\leavevmode\@bsphack\begingroup\MakePrivateLetters
+%   \Describe@Opt}
+% \def\Describe@Opt#1{\endgroup \Describe@pt{#1}}
+% \def\Describe@pt#1#2{

+%               \marginpar{\raggedleft\PrintDescribeMacro{#1}}

+% 		\SpecialOptUsageIndex{#1}{#2}}
+% 
+% \def\Midx{\begingroup
+% 	\let\Index\MainIndex
+%	\let\CodeIndex\CodeMainIndex
+%	\let\ArgedCodeIndex\ArgedCodeMainIndex
+%	\let\MathIndex\MathMainIndex
+%	\let\SpecialIndex\SpecialMainIndex
+% 	\MIDX}
+% \def\MIDX#1{#1\endgroup}
+% \def\Uidx{\begingroup
+% 	\let\Index\UsageIndex
+%	\let\CodeIndex\CodeUsageIndex
+%	\let\ArgedCodeIndex\ArgedCodeUsageIndex
+%	\let\MathIndex\MathUsageIndex
+%	\let\SpecialIndex\SpecialUsageIndex
+% 	\UIDX}
+% \def\UIDX#1{#1\endgroup}
+% 
+% \def\Index{\@Index{}}
+% \def\MainIndex{\@Index{\encapchar main}}
+% \def\UsageIndex{\@Index{\encapchar usage}}
+% \def\@Index#1{\@ifnextchar[
]
+%	{\@IndexWithActualChar{#1}}{\@IndexPlain{#1}}}
+% \def\@IndexPlain#1#2{\special@index{#2#1}\ignorespaces}
+% \def\@IndexWithActualChar#1[#2]#3{\special@index{#3\actualchar#2#1}

+%	\ignorespaces}
+% \let\LaTeX@theindex\theindex
+% \def\theindex{\LaTeX@theindex \hbadness\@M}
+% 
+% \def\CodeMainIndex{\Code@Index{\encapchar main}}
+% \def\CodeUsageIndex{\Code@Index{\encapchar usage}}
+% \def\CodeIndex{\Code@Index{}}
+% \def\Code@Index{\S@nitizedIndex\IndexVerb@timed}
+% 
+% \def\ArgedCodeMainIndex{\Arged@Code@Index{\encapchar main}}
+% \def\ArgedCodeUsageIndex{\Arged@Code@Index{\encapchar usage}}
+% \def\ArgedCodeIndex{\Arged@Code@Index{}}
+% \def\Arged@Code@Index{\S@nitizedArgedIndex\IndexVerb@timed}
+% 
+% \def\MathMainIndex{\Math@Index{\encapchar main}}
+% \def\MathUsageIndex{\Math@Index{\encapchar usage}}
+% \def\MathIndex{\Math@Index{}}
+% \def\Math@Index{\S@nitizedIndex\IndexM@thed}
+% 
+% \def\S@nitizedIndex#1#2{\@bsphack
+%	\begingroup \@sanitize \S@nitized@Index{#1}{#2}}
+% \def\S@nitized@Index#1#2#3{\endgroup
+% 	\special@index{#1{#3}#2}\@esphack\ignorespaces}
+% \def\S@nitizedArgedIndex#1#2{\@bsphack
+%	\begingroup \@sanitize \S@nitized@rgedIndex{#1}{#2}}
+% \def\S@nitizedNonArgedIndex#1#2{\@bsphack
+%	\begingroup \@sanitize \S@nitizedNon@rgedIndex{#1}{#2}}
+% \def\S@nitized@rgedIndex#1#2#3{\endgroup
+%	\ArgedIndexMainAndSub{#1}{#2}{#3}}
+% \def\S@nitizedNon@rgedIndex#1#2#3{\endgroup
+% 	\special@index{#1{#3}#2}

+%	\ArgedIndexSub{#1}{#2}{#3}}
+% \def\S@nitized@rgedIndex#1#2#3{\endgroup
+%	\ArgedIndexMainAndSub{#1}{#2}{#3}}
+% \def\S@nitizedNon@rgedIndex#1#2#3{\endgroup
+% 	\special@index{#1{#3}#2}

+%	\ArgedIndexSub{#1}{#2}{#3}}
+% \def\ArgedIndexMainAndSub#1#2#3#4{\ArgedIndexMain{#1}{#2}{#3}{#4}

+%	\ArgedIndexSub{#1}{#2}{#3}{#4}}
+% \def\ArgedIndexMain#1#2#3#4{\begingroup
+%	\def\@tempa{\@rgedIndexMain{#1}{#2}{#3}}

+%	\def\e{}\edef\@tempb{{#4}}

+%	\expandafter\@tempa\@tempb

+%	\endgroup}
+% \def\@rgedIndexMain#1#2#3#4{\special@index{#1{#3} (#4)#2}}
+% \def\ArgedIndexSub#1#2#3#4{\begingroup
+%	\def\@tempa{\@rgedIndexSub{#1}{#2}{#3}}

+%	\def\e{e}\edef\@tempb{{#4}}

+%	\expandafter\@tempa\@tempb

+%	\endgroup}
+% \def\@rgedIndexSub#1#2#3#4{\special@index{#4s:\levelchar#1{#3}#2}}
+% 
+% \def\IndexBr@cedWith#1#2{#2\actualchar#1{#2}}
+% \def\IndexVerb@timed#1{#1\actualchar\string\verb\quotechar*\verbatimchar
+% 	#1\verbatimchar}
+% \def\IndexM@thed#1{#1\actualchar\doll@rm@rk#1\doll@rm@rk}
+% 
+% \def\env#1{\texttt{#1}\EnvIndex{#1}}
+% \def\EnvIndex#1{\ArgedCodeIndex{#1}{environment}}
+% \def\counter#1{\texttt{#1}\CounterIndex{#1}}
+% \def\CounterIndex#1{\ArgedCodeIndex{#1}{counter}}
+% 
+% \begingroup
+% \catcode`\_12 \catcode`\$12
+% \gdef\TheUnderScore{_}
+% \gdef\doll@rm@rk{$}
+% \endgroup
+% 
+% \def\SpecialIndex#1{\@bsphack
+%	\RemoveAtFromCS{#1}

+% 	\protected@edef\@tempa{\noexpand\special@index{\RAFCtempa
+%		\actualchar \string\verb
+% 		\quotechar*\verbatimchar\string#1\verbatimchar}}\@tempa
+%	\@esphack}
+% \def\SpecialMainIndex#1{\@bsphack
+%	\RemoveAtFromCS{#1}

+% 	\protected@edef\@tempa{\noexpand\special@index{\RAFCtempa
+%		\actualchar \string\verb
+% 		\quotechar*\verbatimchar\string#1\verbatimchar
+%		\encapchar main}}\@tempa
+%	\@esphack}
+% \def\SpecialUsageIndex#1{\@bsphack
+%	\RemoveAtFromCS{#1}

+% 	\protected@edef\@tempa{\noexpand\special@index{\RAFCtempa
+%		\actualchar \string\verb
+% 		\quotechar*\verbatimchar\string#1\verbatimchar
+%		\encapchar usage}}\@tempa
+%	\@esphack}
+% \long\def\Special@Index#1#2{\@bsphack
+%	\RemoveAtFromCS{#2}

+% 	\protected@edef\@tempa{\noexpand\special@index{\RAFCtempa
+%		\actualchar \string\verb
+% 		\quotechar*\verbatimchar\string#2\verbatimchar #1}}\@tempa
+%	\@esphack}
+% \def\SpecialIndex{\Special@Index{}}
+% \def\SpecialMainIndex{\Special@Index{\encapchar main}}
+% \def\SpecialUsageIndex{\Special@Index{\encapchar usage}}
+% \def\SpecialArrayIndex#1{\Special@Index{${\cdot}#1$}}
+% \def\SpecialArrayMainIndex#1{\Special@Index{${\cdot}#1$\encapchar main}}
+% \def\SpecialArrayUsageIndex#1{\Special@Index{${\cdot}#1$\encapchar usage}}
+% 
+% \def\Macro{\begingroup \@sanitize \iMacro}
+% \def\iMacro#1{\endgroup
+%	\def\SpecialMainIndex##1{\SWiIndex{##1}{\encapchar main}}

+%	\macro{#1}}
+% \let\endMacro\endmacro
+% 
+% \def\SpecialWeirdIndex{\@bsphack \begingroup \@sanitize \SWIndex{}}
+% \def\SWIndex#1#2{\endgroup \SWiIndex{#2}{#1}}
+% \def\SWiIndex#1#2{%
+%	\protected@edef\@tempa{\noexpand\special@index{

+%		#1\actualchar \string\verb
+%		\quotechar*\verbatimchar#1\verbatimchar#2}}\@tempa
+% 	\@esphack}
+% 
+% \let\RAFCempty\@empty
+% \let\RAFCgobble\@gobble
+% \makeatother
+% \long\def\RemoveAtFromCS#1{

+% 	\edef\RAFCtempa{\expandafter\RAFCgobble\string#1}

+% 	\edef\RAFCtempa{\expandafter\string\csname\RAFCtempa\endcsname}

+%	\expandafter\iRemoveAtFromCS\RAFCtempa@\NIL}
+% \def\iRemoveAtFromCS#1#2@#3\NIL{\def\RAFCtempb{#3}

+% 	\ifx\RAFCtempb\RAFCempty \def\RAFCtempa{#2}\let\next\relax
+%	\else \def\RAFCtempa{#2@}\def\next{\iiRemoveAtFromCS#3\NIL}

+% 	\def\RAFCtempb{#2}

+%	\ifx\RAFCtempb\RAFCempty
+%	\else\ifx\RAFCtempb\CommonCSPrefix
+%	\else\ifx\RAFCtempb\CommonIfPrefix
+%	\else \def\RAFCtempa{}\def\next{\xRemoveAtFromCS#2@#3\NIL}\fi\fi\fi\fi
+%	\next}
+% \def\iiRemoveAtFromCS#1{\ifx#1@\edef\RAFCtempa{\RAFCtempa@}

+%	\let\next\iiRemoveAtFromCS
+%	\else \def\next{\xRemoveAtFromCS#1}\fi
+% 	\next}
+% \def\xRemoveAtFromCS#1@\NIL{\edef\RAFCtempa{#1\RAFCtempa}}
+% \makeatletter
+% 
+% \begingroup
+% \makeatother
+% \gdef\TheAtMark{@}
+% \catcode`\@\active
+% \gdef\!{\begingroup \catcode`\@\active \IndexedVerb}
+% \gdef\IndexedVerb#1!{\def@{\TheAtMark \penalty\exhyphenpenalty}

+% 	\def~{\penalty\exhyphenpenalty}

+% 	\texttt{\string#1}\let@\TheAtMark \def~{}

+% 	\edef\RAFCTempa{\expandafter\RAFCgobble\string#1}

+%	\expandafter\SpecialIndex\csname\RAFCTempa\endcsname \endgroup}
+% \endgroup
+% \let\~\allowbreak
+% 
+% \def\CSIndex#1{\expandafter\def\expandafter\@tempa\expandafter{\csname
+% 	#1\endcsname}

+% 	\edef\@tempb{\expandafter\string\@tempa}

+%	\texttt{\@tempb}

+% 	\expandafter\SpecialIndex\@tempa}
+% 
+% \begingroup
+% \gdef\@sverbcat{\catcode`\@\active\catcode`\#\active}
+% \catcode`\@\active \gdef@{\char`\@\penalty\exhyphenpenalty}
+% \catcode`\#\active \gdef#{\penalty\exhyphenpenalty}
+% \endgroup
+% \let\latex@sverb\@sverb
+% \def\@sverb{\@sverbcat\latex@sverb}
+% 
+% \def\Paracol{\textsf{paracol}}
+% \let\LB[\let\RB]\let\LP(\let\RP)
+% \def\LBRP#1#2{\LB#1,#2\RP}
+% \def\In{\in\LBRP}
+% \let\Sec\S
+% \def\secref{\Sec\ref}
+% \let\<\langle \let\>\rangle
+% \let\ARG\arg
+% \def\arg#1{\<\mathit{#1}\>}
+% \def\Arg#1{\texttt{\char`\{}#1\texttt{\char`\}}}
+% \def\ARg#1{\texttt{\char`\{}\textit{#1}\texttt{\char`\}}}
+% \def\Sub#1{{\hbox to0pt{\hss$\scriptstyle #1$\hss}}}
+% 
+% 
+% 
+% \edef\CommonCSPrefix{\expandafter\RAFCgobble\string\pcol}
+% \edef\CommonIfPrefix{\expandafter\RAFCgobble\string\ifpcol}
+% 
+% \def\bpage{base page\Index{base page}}
+% \def\beginparacol{\CSIndex{begin}\allowbreak
+% 	\texttt{\char`\{paracol\char`\}}\EnvIndex{paracol}}
+% \def\cctext{column-context\Index{column-context}}
+% \def\colpage{column-page\Index{column-page}}
+% \def\cswitch{column-switching\Index{column-switching}}
+% \def\csenv{column-switching environment\Index{column-switching environment}}
+% \def\csync{counter synchronization\Index{counter synchronization}}
+% \def\ccolpage{current column-page\Index{current column-page}}
+% \def\Endparacol{\CSIndex{end}\allowbreak
+% 	\texttt{\char`\{paracol\char`\}}\EnvIndex{paracol}}
+% \def\elocal{environment-local\Index{environment-local}}
+% \def\exsync{explicit synchronization\Index{explicit synchronization}}
+% \def\fcolumn{float column\Index{float column}}
+% \def\fpage{float page\Index{float page}}
+% \def\gcounter{global counter\Index{global counter}}
+% \def\imsync{implicit synchronization\Index{implicit synchronization}}
+% \def\lpage{last page\Index{last page}}
+% \def\lcommand{local command\Index{local command}}
+% \def\lcolumn{leading column\Index{leading column}}
+% \def\lcolpage{leading column-page\Index{leading column-page}}
+% \def\lcounter{local counter\Index{local counter}}
+% \def\lrep{local representation\Index{local representation}}
+% \def\mctext{multi-column text\Index{multi-column text}}
+% \def\mvlfloat{MVL-float\Index{MVL-float}}
+% \def\pctext{page context\Index{page context}}
+% \def\postenv{post-environment stuff\Index{post-environment stuff}}
+% \def\preenv{pre-environment stuff\Index{pre-environment stuff}}
+% \def\spanning{spanning stuff\Index{spanning stuff}}
+% \def\spage{starting page\Index{starting page}}
+% \def\sync{synchroniz\Index{synchronize}}
+% \def\tpage{top page\Index{top page}}
+% 
+% \def\vb{\Index[$\beta$]{-b}\beta}
+% \def\pd{\Index[$\delta$]{-d}\delta}
+% \def\ep{\Index[$\varepsilon$]{-e}\varepsilon}
+% \def\clist{\Index[$\zeta(\theta)$]{-f(-j)}\zeta}
+% \def\fh{\Index[$\eta$]{-h}\eta}
+% \def\CC{\Index[$\string\mathit{\Theta}$]{-J}\mathit{\Theta}}
+% \def\Cc{\Index[$\string\mathit{\Theta}_c$]{-J_c}\mathit{\Theta}}
+% \def\CG{\Index[$\string\mathit{\Theta}^g$]{-J^g}\mathit{\Theta}^g}
+% \def\cg{\Index[$\theta^g$]{-j^g}\theta^g}
+% \def\CL{\Index[$\string\mathit{\Theta}^l$]{-J^l}\mathit{\Theta}^l}
+% \def\cl{\Index[$\theta^l$]{-j^l}\theta^l}
+% \def\cc{\Index[$\kappa_c$]{-k_c}\kappa}
+% \def\bl{\Index[$\lambda_b$]{-l_b}\lambda_b}
+% \def\dl{\Index[$\lambda_d$]{-l_d}\lambda_d}
+% \def\ml{\Index[$\lambda_m$]{-l_m}\lambda_m}
+% \def\tl{\Index[$\lambda_t$]{-l_t}\lambda_t}
+% \def\mb{\Index[$\mu$]{-m}\mu}
+% \def\bn{\Index[$\nu_b$]{-n_b}\nu_b}
+% \def\cn{\Index[$\nu_c$]{-n_c}\nu_c}
+% \def\tn{\Index[$\nu_t$]{-n_t}\nu_t}
+% \def\tf{\Index[$\xi$]{-o}\xi}
+% \def\PP{\Index[$\string\mathit{\Pi}$]{-P}\mathit{\Pi}}
+% \def\PPP{\Index[$\string\mathit{\Pi}^+$]{-P+}\mathit{\Pi}^+}
+% \def\pp{\Index[$\pi(p)$]{-p(p)}\pi}
+% \def\br{\Index[$\rho_b$]{-r_b}\rho_b}
+% \def\tr{\Index[$\rho_t$]{-r_t}\rho_t}
+% \def\sw{\Index[$\sigma$]{-s}\sigma}
+% \def\ft{\Index[$\tau$]{-t}\tau}
+% 
+% \def\C{\Index[$C$]{C}C}
+% \def\dc{\Index[$d_c$]{d_c}d_c}
+% \def\DP{\Index[$D_P$]{D_P}D_P}
+% \def\DT{\Index[$D_T$]{D_T}D_T}
+% \def\false{\Index[$\string\mathit{false}$]{false}\mathit{false}}
+% \def\Fc{\Index[$F_c(X)$]{F_c}F_c}
+% \def\fc{\Index[$f_c(x)$]{f_c}f_c}
+% \def\pbase{\Index[$p_b$]{p_b}p_b}
+% \def\ptop{\Index[$p_t$]{p_t}p_t}
+% \def\page{\Index[$\string\mathit{page}(p)$]{page(p)}\mathit{page}}
+% \def\true{\Index[$\string\mathit{true}$]{true}\mathit{true}}
+% \def\S{\Index[$S_c$]{S_c}S}
+% \def\SS{\Index[$S$]{S}S}
+% \def\s{\Index[$s_c(p)$]{s_c(p)}s}
+% \def\size{\Index[$\string\mathit{size}(x)$]{size}\mathit{size}}
+% \def\Size{\Index[$\string\mathit{SIZE}(x)$]{SIZE}\mathit{SIZE}}
+% \def\T{\Index[$T$]{T}T}
+% \def\val{\Index[$\string\mathit{val}_c(\theta)$]{val_c(j)}

+% 	\mathit{val}}
+% \def\Val{\Index[$\string\mathit{val}(\theta)$]{val(j)}

+% 	\mathit{val}}
+% \def\vc{\Index[$v_c(x)$]{v_c}v_c}
+% \def\VB{\Index[$V_B$]{V_B}V_B}
+% \def\VP{\Index[$V_P$]{V_P}V_P}
+% \def\VT{\Index[$V_T$]{V_T}V_T}
+% 
+% 
+%
+% \def\bracepair{`{\tt\char`\{\char`\}'}}
+% \@addtoreset{section}{part}
+% \def\part#1{\refstepcounter{part}

+%   \addcontentsline{toc}{part}{\thepart\hspace{1em}#1}

+%   \vbox to\unitlength{\vfil\centerline{\Large\bfseries PART\ \thepart}\vfil
+%     \centerline{\huge\bfseries#1}\vfil\vfil}}
+% \def\Env#1#2{\!\begin!{\tt\char`\{\env{#1}\char`\}}#2\quad
+%   $\mathit{body}$\quad\!\end!{\tt\char`\{\env{#1}\char`\}}}
+% \def\ENV#1#2{\!\begin!{\tt\char`\{\Midx{\env{#1}}\char`\}}#2\quad
+%   $\mathit{body}$\quad\!\end!{\tt\char`\{\env{#1}\char`\}}}
+% \def\meta#1{\mbox{$\mathit{#1}$}}
+% 
+% \let\l@part\l@section
+% \def\l@section{\@dottedtocline{1}{0pt}{1.5em}}
+% 
+% \newverbatim{Verbatim}{\topsep0pt\partopsep0pt\parsep0pt\parskip0pt\tt}{}{}{}
+% \globalcounter{section}
+% \globalcounter{figure}
+% \globalcounter{table}
+% \definethecounter{footnote}{1}{\textit{\arabic{footnote}}}
+% \definethecounter{subsection}{1}{%
+%   \texttt{\arabic{section}.\arabic{subsection}}}
+% \addcontentsonly{toc}{0}
+%
+% \let\AB\allowbreak
+% 
+% \hyphenation{col-umn col-umns}
+%
+% \let\EQ\relax \let\GT\relax \let\BAR\relax \let\NEQ\relax
+% 
+% 
+% 
+% \changes{v0.9}{2005/01/28}
+%	{The style paracol is born.}
+% \changes{v0.91}{2011/09/16}
+%	{The style is included in CTAN with a very small modification.}
+% \changes{v1.0}{2011/10/10}
+%	{Add this document and fix the following problems on the author's
+%	 30th wedding anniversary.}
+%
+% 
+% 
+% \title{Package \textsf{paracol}:\\
+% 	Yet Another Multi-Column Package to Typeset Columns in
+% 	\textit{Parallel}}
+% 
+% \author{Hiroshi Nakashima\\(Kyoto University)}
+% \date{version \expandafter\@gobble\fileversion: \filedate}
+% \setbox0\vbox{\vskip\topskip\maketitle\vskip0pt}\unitlength\ht0\copy0
+% 
+% \ifx\ONLYDESCRIPTION\undefined
+% \tableofcontents
+% \newpage
+% 
\vbox to\unitlength{\unvbox0\vfil}
+% \part{User's Manual}
+% \let\MidxSave\Midx \let\Midx\Uidx
+% \fi
+% 
+% \begin{abstract}
+% This package provides a \LaTeX{} environment named |paracol| in which you
+% may {\em switch} and {\em synchronize} columns by a command
+% |\switchcolumn| and by internal environments |column|, |nthcolumn|,
+% |leftcolumn| and |rightcolumn|.
+% \end{abstract}
+% 
+% \input{man.dtx}
+% \newpage
+% \input{ref.dtx}
+% 
+% \IndexPrologue{\newpage\section*{Index}
+% Underlined number refers to the page where the specification of
+% corresponding entry is described, while italicized number is for the page
+% in which the usage of the entry is explained.}
+% \StopEventually{\ifx\ONLYDESCRIPTION\undefined\newpage\fi
+% \section*{Acknowledgments}
+%
+% The author thanks to Yacine Daddi Addoun who gave the author the motivation
+% to write the style for his bilingual document.  He also thanks to Robin
+% Fairbairns who kindly invited the style to CTAN after the author's lazy six
+% years failing to upload the style.
+% 
+% For the implementation of the style file, the author referred to the base
+% implementations of \texttt{\char`\\output}, \texttt{\char`\\newcounter}
+% and related macros of \LaTeXe{} written by Leslie Lamport, Johannes Braams
+% and other authors.
+%
+% \PrintIndex}
+% 
+% \newpage
+% \let\Midx\MidxSave
+% \advance\oddsidemargin1in\evensidemargin\oddsidemargin
+% \advance\textwidth-1in\columnwidth\textwidth
+% \hsize\textwidth \linewidth\textwidth
+% \part{Implementation}
+% \input{impl.dtx}
+% 
+% \IndexPrologue{\newpage\section*{Index}
+% Underlined number refers to the page where the implementation or the
+% definition of the correspoinding entry is described, while italicized
+% number is for the page in which the specificatoin or usage of the entry is
+% explained.
+% 

+% To find a control sequence, remove prefixes \cs{@}, \cs{pcol@} and 
+% \cs{ifpcol@} from its name if it has one of them.}
+% \Finale
+% \GlossaryPrologue{\newpage\section*{Revision History}}
+% \def\EQ{=} \def\GT{>} \def\BAR{|} \def\NEQ{\neq}
+% \PrintChanges
+\endinput
diff --git a/Master/texmf-dist/source/latex/paracol/paracol.ins b/Master/texmf-dist/source/latex/paracol/paracol.ins
new file mode 100644
index 00000000000..28955d06e4a
--- /dev/null
+++ b/Master/texmf-dist/source/latex/paracol/paracol.ins
@@ -0,0 +1,8 @@
+\input docstrip.tex
+\keepsilent
+\askforoverwritefalse
+\generate{\nopreamble \nopostamble
+	  \file{paracol.sty}%
+		{\from{paracol.dtx}{paracol}\from{impl.dtx}{paracol}}
+	  \file{paracol-man.tex}{\from{paracol.dtx}{man}}}
+\endbatchfile
diff --git a/Master/texmf-dist/source/latex/paracol/ref.dtx b/Master/texmf-dist/source/latex/paracol/ref.dtx
new file mode 100644
index 00000000000..5383aa5e3fb
--- /dev/null
+++ b/Master/texmf-dist/source/latex/paracol/ref.dtx
@@ -0,0 +1,321 @@
+% \section{Reference Manual}
+% \subsection{Environment \texttt{paracol}}
+% 
+% \begin{description}
+% \item[\ENV{paracol}{\marg{num}\oarg{text}}]\mbox{}\par
+% The environment \env{paracol} contains \meta{body} typeset in \meta{num}
+% columns in parallel.  The optional \meta{text} is put spanning all columns
+% prior to the multi-columned \meta{body}.
+% 

+% \begin{itemize}
+% \item
+% The environment may start from \emph{any} vertical position in a page,
+% i.e., not necessary at the top of a page.  The single-column contents of
+% the {\em\Uidx\spage} in which \beginparacol{} lies are naturally connected
+% to the beginning part of \meta{body} in each column, unless the page has
+% footnotes or bottom floats.  If these kind of bottom stuff exist, they are
+% put above the multi-columned \meta{body}, or the multi-column \meta{text}
+% 

+% \UsageIndex{multi-column text}

+% 

+% if provided.  The \emph{deferred} floats which have not yet appeared in
+% the starting page and thus will appear in the next or succeeding pages are
+% considered as multi-column floats given in the environment.
+% 
+% \item
+% All \Uidx\lcounter{}s in all columns are initialized to have the values at
+% \beginparacol{} on its first occurence.  On the second and succeeding
+% occurences of \beginparacol, the \lcounter{}s in each column have the
+% value at the last \Endparacol, unless they are modified after the
+% \Endparacol.  If a counter is modified (or declared by \!\newcounter!)
+% after the \Endparacol, the local versions of the counter in all column
+% commonly have the value at \beginparacol.
+% 
+% \item
+% The environment may end at \emph{any} vertical position in a page, i.e.,
+% the {\em\Uidx\postenv} being the single-column texts and others
+% following \Endparacol{} may not start from the top of a page.  If any
+% columns don't have deferred single-column floats and the most advanced
+% {\em\Uidx\lcolumn} at \Endparacol{} has neither of footnotes nor bottom
+% floats, its bottom is naturally connected to the \postenv{}.  If the
+% \lcolumn{} has these kinds of bottom stuff, they are put above the
+% \postenv{}, with a vertical skip of \!\textfloatsep! separating them if
+% bottom floats exist.  All deferred single-column floats given in the
+% environment are flushed before the \postenv{} appears, possibly creating
+% {\em\Uidx\fcolumn{}s} only with floats.  On the other hand, deferred
+% multi-column floats given in the environment are considered as deferred
+% single-column floats given just after \Endparacol.
+% 
+% \item
+% The values of all \lcounter{}s in the leftmost column are used as the
+% initial values of them in the \postenv.
+% 
+% \item
+% The \env{paracol} environment cannot be nested, or you will have an error
+% message of illegal nesting.
+% 
+% \item
+% The commands \!\switchcolumn!, \!\synccounter!, \!\syncallcounters! and
+% \!\flushpage!, and environments \env{column}(|*|), \env{nthcolumn}(|*|),
+% \env{leftcolumn}(|*|) and \env{rightcolumn}(|*|) are {\em local} to
+% \env{paracol} environment and thus undefined outside the
+% environment\footnote{

+% 

+% Unless you dare to define them.}.
+% 

+% The command \!\clearpage! is of course usable outside and inside the
+% environment but its function inside is a little bit different from outside.
+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+% \subsection{Column-Switching Command and Environments}
+% 
+% \begin{description}
+% \item[\Midx{\!\switchcolumn!}\oarg{col}]\mbox{}
+% \Item[\Midx{\!\switchcolumn!}\oarg{col}\texttt{*}\oarg{text}]\mbox{}\par
+% The command switches columns from $i$ to $j$ where $i$ and $j$ is the
+% zero-origin ordinals of the columns from/to which we are leaving\slash
+% visiting respectively.  Without the optional \meta{col}, $j=i+1\bmod n$
+% where $n$ is the number of columns given to \beginparacol, while
+% $j=\meta{col}$ with the optional argument.  If the command (or
+% \oarg{col} if specified) is followed by a |*|, the \cswitch{} takes
+% place after \sync{}ation and, if specified, the optional multi-column
+% \meta{text} is put.
+% 

+% \Index{multi-column text}

+% 

+% \begin{itemize}
+% \item
+% Using \!\switchcolumn! in a \env{list} and other relative environments
+% such as \env{itemize} causes an ugly result without any error\slash
+% warning messages.  This caution is effectual for all \csenv{}s
+% too.
+% 
+% \item
+% If $\meta{col}\notin\LBRP0n$, an error is reported and, if you dare to
+% continue, you will switch to the leftmost column 0.
+% 
+% \item
+% The \sync{}ation point is set just below the last line of the \lcolumn{}
+% in a page $p$, partly taking deferred floats into account.  That is, all
+% deferred floats are put in the pages up to $p-1$ and at the top of $p$ if
+% possible.  Then, if a non-\lcolumn{} has footnotes and/or bottom floats
+% and they cannot be pushed down below the \sync{}ation point, the point is
+% moved to the next page top.
+% 
+% \item
+% In a page having one or more \sync{}ation points, stretch and shrink
+% factors of all vertical spaces, such as those surrounding sectionning
+% commands, are ingonred.  Therefore, even if you specify \!\flushbottom!,
+% the page is typeset as if \!\raggedbottom! were specified.
+% 
+% \item
+% After a sync{}ation point is set, top floats will not be put in the page
+% having the point any more and thus will be deferred to the next or
+% succeeding page.
+% \end{itemize}
+% 
+% 
+% 
+% \item[\ENV{column}{}]\mbox{}
+% \Item[\ENV{column*}{\oarg{text}}]\mbox{}\par
+% The environment \env{column} contains \meta{body} for the column next to
+% what we are in just before \!\begin!|{|\env{column}|}|.  The starred
+% version \env{column*} does the same after \sync{}ation and, if specified,
+% the optional multi-column \meta{text} is put.
+% 

+% \Index{multi-column text}

+% 

+% \begin{itemize}
+% \item
+% The environments are almost equivalent to;
+% \begin{quote}
+% |{|\!\switchcolumn!\quad\meta{body}\quad\CSIndex{par}|}|\\
+% |{|\!\switchcolumn!|*|\oarg{text}\quad\meta{body}\quad\CSIndex{par}|}|
+% \end{quote}
+% except for their first occurences which don't switch to the column 1
+% (i.e., right column if two-columned) but stay in the leftmost column 0.
+% More precicesly, \!\begin!|{|\env{column}(|*|)|}| does not make \cswitch{}
+% if it is not preceded by \!\switchcolumn! nor other \csenv{}s.
+% 
+% \item
+% The \meta{body} of the environments cannot have \!\switchcolumn! nor other
+% \csenv{}s including \env{column}(|*|) themselves, or you will have an
+% error message of illegal use of command\slash environment.
+% 
+% \item
+% Column-switching\index{column-switching} does not take place at
+% \!\end!|{|\env{column}(|*|)|}|.  Therefore, texts following the
+% environments are put in the column in which \meta{body} resides until a
+% \cswitch{} commnad\slash environment is given.
+% \end{itemize}
+% 
+% 
+% 
+% \item[\ENV{nthcolumn}{\marg{col}}]\mbox{}
+% \Item[\ENV{nthcolumn*}{\marg{col}\oarg{text}}]\mbox{}\par
+% The environment \env{nthcolumn} contains \meta{body} for the column
+% \meta{col}.  The starred version \env{nthcolumn*} does the same after
+% \sync{}ation and, if specified, the optional multi-column \meta{text} is
+% put.
+% 

+% \Index{multi-column text}

+% 

+% \begin{itemize}
+% \item
+% The environments are equivalent to;
+% 

+% \begin{quote}
+% |{|\!\switchcolumn!\oarg{col}\quad\meta{body}\quad\CSIndex{par}|}|\\
+% |{|\!\switchcolumn!\oarg{col}|*|\oarg{text}\quad
+%     \meta{body}\quad\CSIndex{par}|}|
+% \end{quote}
+% 
+% \item
+% The \meta{body} of the environments cannot have \!\switchcolumn! nor other
+% \csenv{}s including \env{nthcolumn}(|*|) themselves, or you will have an
+% error message of illegal use of command\slash environment.
+% 
+% \item
+% Column-switching\index{column-switching} does not take place at
+% \!\end!|{|\env{nthcolumn}(|*|)|}|.  Therefore, texts following the
+% environments are put in the column in which \meta{body} resides until a
+% \cswitch{} commnad\slash environment is given.
+% \end{itemize}
+% 
+% 
+% 
+% \newpage
+% \item[\ENV{leftcolumn}{}]\mbox{}
+% \Item[\ENV{leftcolumn*}{\oarg{text}}]\mbox{}
+% \Item[\ENV{rightcolumn}{}]\mbox{}
+% \Item[\ENV{rightcolumn*}{\oarg{text}}]\mbox{}\par\nobreak
+% The environment \env{leftcolumn} contains \meta{body} for the leftmost
+% column 0, while \env{rightcolumn} for the column 1 being the right column
+% in two-column typesetting.  The starred versions \env{leftcolumn*} and
+% \env{rightcolumn*} do the same after \sync{}ation and, if specified, the
+% optional multi-column \meta{text} is put.
+% 

+% \Index{multi-column text}

+% 

+% \begin{itemize}
+% \item
+% The environments \env{leftcolumn}(|*|) are equivalent to;
+% 

+% \begin{quote}
+% \Env{nthcolumn}{\Arg{\texttt{0}}}\\
+% \Env{nthcolumn*}{\Arg{\texttt{0}}\oarg{text}}
+% \end{quote}
+% 

+% while \env{rightcolumn}(|*|) are equivalent to;
+% 

+% \begin{quote}
+% \Env{nthcolumn}{\Arg{\texttt{1}}}\\
+% \Env{nthcolumn*}{\Arg{\texttt{1}}\oarg{text}}
+% \end{quote}
+% 

+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+% \subsection{Commands for Counters}
+% 
+% \begin{description}
+% \item[\Midx{\!\globalcounter!}\marg{ctr}]\mbox{}\par
+% The command declares that the counter \meta{ctr} is global to all columns.
+% An update of a \Uidx\gcounter{} in a column is seen by any other columns.
+% 

+% \begin{itemize}
+% \item
+% All column-local values of a descendant \lcounter{} of a \gcounter{} are
+% zero-cleared when the \gcounter{} is explicitly stepped by \!\stepcounter!
+% or \!\refstepcounter!, or implicitly by a sectioning command and so on.
+% 
+% \item
+% The counter \counter{page} is always global but an explicit update of it
+% by e.g., \!\setcounter! in a non-leftmost column is not seen by other
+% columns and is canceled even for the column itself after a \cswitch{} or a
+% page break in the column.  Therefore, if you want to make a \emph{jump} of
+% \counter{page}, it must be done in the leftmost column 0.  Note that a
+% jump from a page $p$ to $q$ can be seen in other columns even if they have
+% gone beyond $p$ \emph{before} the column 0 makes the jump, as far as
+% \counter{page} having $q$ (or its successor) is referred to by \!\pageref!
+% or through \emph{contents} files such as |.toc|\footnote{

+% 

+% Direct reference to \counter{page} may give an inconsisent result, as you
+% might have in ordinary \LaTeX{} documents.}.
+% \end{itemize}
+% 
+% 
+% 
+% \item[\Midx{\!\definethecounter!}\marg{ctr}\marg{col}\marg{rep}]\mbox{}\par
+% The command defines |\the|\meta{ctr} being \marg{rep} for the local use in
+% the column \meta{col}.  That is, |\the|\meta{ctr} in the column \meta{col}
+% acts as if it is defined by
+% \!\renewcommand!\Arg{\cs{the}\meta{ctr}}\Arg{\meta{rep}}.
+% 
+% 
+% 
+% \item[\Midx{\!\synccounter!}\marg{ctr}]\mbox{}\par
+% The command \emph{broadcasts} the value of the \lcounter{} \meta{ctr} in
+% the column in which the command appears to the values in all other columns.
+% 
+% \item[\Midx{\!\syncallcounters!}]\mbox{}\par
+% The command broadcasts the values of all \lcounter{}s in the column in
+% which the command appears to the values in all other columns.
+% \end{description}
+% 
+% 
+% 
+% \subsection{Control of Contents Output}
+% 
+% \begin{description}
+% \item[\Midx{\!\addcontentsonly!}\marg{file}\marg{col}]\mbox{}\par
+% The command inhibits the output of contents information to
+% $\meta{file}\in\{|toc|,|lof|,|lot|\}$ from columns other than \meta{col}.
+% 

+% \begin{itemize}
+% \ifx\ONLYDESCRIPTION\undefined
+% \item
+% For example, this manual has \!\addcontentsonly!|{toc}{0}| to inhibit the
+% contents information output from \!\subsection! commands in
+% Section~\ref{sec:env} and~\ref{sec:float}, or the table should have
+% duplicated entries of sub-sections. 
+% 
+% \else
+% \item
+% For example, if this manual had the table of contents,
+% \!\addcontentsonly!|{toc}{0}| should be specified to inhibit the contents
+% information output from \!\subsection! commands in Section~\ref{sec:env}
+% and~\ref{sec:float}, or the table should have duplicated entries of
+% sub-sections.
+% \fi
+% 
+% \item
+% It must be $\meta{file}\in\{|toc|,|lof|,|lot|\}$, or you will have an
+% error message of illegal type of contents file.
+% \end{itemize}
+% \end{description}
+% 
+% 
+% 
+% \subsection{Page Flushing Commands}
+% 
+% \begin{description}
+% \item[\Midx{\!\flushpage!}]\mbox{}\par
+% The command flushes pages up to the {\em\Uidx\tpage} in which the \lcolumn{}
+% resides.  Deferred floats which can be put in the pages up to the \tpage{}
+% are also flushed.
+% 
+% \item[\Midx{\!\clearpage!}]\mbox{}\par
+% The command does what \!\flushpage! does and then flushes all floats still
+% deferred if any.  The deferred float flushing beyond the \tpage{} takes
+% place at first for single-column ones creating \fcolumn{}s for them, and
+% then for multi-column ones creating {\em\Uidx\fpage{}s} only with
+% multi-column floats, as \LaTeX's \!\clearpage! does outside \env{paracol}
+% environment.
+% \end{description}
+\endinput